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+The Project Gutenberg EBook of Encyclopaedia Britannica, 11th Edition,
+Volume 11, Slice 3, by Various
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 3
+       "Frost" to "Fyzabad"
+
+Author: Various
+
+Release Date: August 13, 2011 [EBook #37064]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK ENCYC. BRITANNICA, VOL 11, SL 3 ***
+
+
+
+
+Produced by Marius Masi, Don Kretz and the Online
+Distributed Proofreading Team at https://www.pgdp.net
+
+
+
+
+
+
+
+
+Transcriber's notes:
+
+(1) Numbers following letters (without space) like C2 were originally
+      printed in subscript. Letter subscripts are preceded by an
+      underscore, like C_n.
+
+(2) Characters following a carat (^) were printed in superscript.
+
+(3) Side-notes were relocated to function as titles of their respective
+      paragraphs.
+
+(4) Macrons and breves above letters and dots below letters were not
+      inserted.
+
+(5) [root] stands for the root symbol; [alpha], [beta], etc. for greek
+      letters.
+
+(6) RN stands for Real Number symbol and (Pd) for Partial derivative
+      symbol
+
+(7) The following typographical errors have been corrected:
+
+    ARTICLE FRUIT: "The covering of the seed is marked i. n is the
+      nucellus or perisperm, enclosing the embryo-sac es, in which the
+      endosperm is formed." 'in' amended from 'is'.
+
+    ARTICLE FRUIT: "It occupies the whole cavity of the embryo-sac, or
+      is formed only at certain portions of it, at the apex, as in
+      Rhinanthus, ..." 'occupies' amended from 'occupied'.
+
+    ARTICLE FUEL: "Owing to the siliceous nature of the ash of straw,
+      it is desirable to have a means of clearing the grate bars from
+      slags and clinkers at short intervals, and to use a steam jet to
+      clear the tubes from similar deposits." 'straw' amended from
+      'sraw'.
+
+    ARTICLE FUEL: "In a research upon the heating power and other
+      properties of coal for naval use, carried out by the German
+      admiralty, the results tabulated below were obtained with coals
+      from different localities." 'from' amended from 'form'.
+
+    ARTICLE FUEL: "C + 2H2O = CO2 + 2H2" '+' amended from '='.
+
+    ARTICLE FULHAM: "The principal thoroughfares are Fulham Palace Road
+      running S. from Hammersmith, Fulham Road and King's Road, W. from
+      Chelsea, converging and leading to Putney Bridge over the Thames;
+      ..." 'converging' amended from 'coverging'.
+
+    ARTICLE FULLER, THOMAS: "Their eldest child, John, baptized at
+      Broadwindsor by his father, 6th June 1641, was afterwards rector of
+      Sidney Sussex College, edited the Worthies of England, 1662, and
+      became rector of Great Wakering, Essex, where he died in 1687."
+      added 'rector'.
+
+    ARTICLE FUNCTION: "When Taylor's theorem leads to a representation
+      of the function by means of an infinite series, the function is
+      said to be "analytic" (cf. § 21)." 'Taylor's' amended from
+      'Talyor's'.
+
+    ARTICLE FUNCTION: "or a series which converges uniformly may be
+      integrated term by term." 'uniformly' amended from 'unformly'.
+
+    ARTICLE FUNGI: "Parasitism.--Some fungi, though able to live as
+      saprophytes, occasionally enter the body of living plants, and are
+      thus termed facultative parasites." 'Parasitism' amended from
+      'Parasatism'.
+
+    ARTICLE FUNGI: "Recent experiments have shown that the difficulties
+      of getting orchid seeds to germinate are due to the absence of the
+      necessary fungus, which must be in readiness to infect the young
+      seedling immediately after it emerges from the seed." added
+      'after'.
+
+
+
+
+          ENCYCLOPAEDIA BRITANNICA
+
+  A DICTIONARY OF ARTS, SCIENCES, LITERATURE
+           AND GENERAL INFORMATION
+
+              ELEVENTH EDITION
+
+
+           VOLUME XI, SLICE III
+
+             FROST to FYZABAD
+
+
+
+
+ARTICLES IN THIS SLICE:
+
+
+  FROST                             FULMAR
+  FROSTBITE                         FULMINIC ACID
+  FROSTBURG                         FULTON, ROBERT
+  FROTHINGHAM, OCTAVIUS BROOKS      FULTON (Missouri, U.S.A.)
+  FROUDE, JAMES ANTHONY             FULTON (New York, U.S.A.)
+  FRUCTOSE                          FUM
+  FRUGONI, CARLO INNOCENZIO MARIA   FUMARIC AND MALEIC ACIDS
+  FRUIT                             FUMAROLE
+  FRUIT AND FLOWER FARMING          FUMIGATION
+  FRUMENTIUS                        FUMITORY
+  FRUNDSBERG, GEORG VON             FUNCHAL
+  FRUSTUM                           FUNCTION
+  FRUYTIERS, PHILIP                 FUNDY, BAY OF
+  FRY                               FUNERAL RITES
+  FRY, SIR EDWARD                   FUNGI
+  FRY, ELIZABETH                    FUNJ
+  FRYXELL, ANDERS                   FUNKIA
+  FUAD PASHA                        FUNNEL
+  FUCHOW                            FUR
+  FUCHS, JOHANN NEPOMUK VON         FURAZANES
+  FUCHS, LEONHARD                   FURETIÈRE, ANTOINE
+  FUCHSIA                           FURFOOZ
+  FUCHSINE                          FURFURANE
+  FUCINO, LAGO DI                   FURIES
+  FUEL                              FURLONG
+  FUENTE OVEJUNA                    FURNACE
+  FUENTERRABIA                      FURNEAUX, TOBIAS
+  FUERO                             FURNES
+  FUERTEVENTURA                     FURNESS, HORACE HOWARD
+  FUGGER                            FURNESS
+  FUGITIVE SLAVE LAWS               FURNISS, HARRY
+  FUGLEMAN                          FURNITURE
+  FUGUE                             FURNIVALL, FREDERICK JAMES
+  FÜHRICH, JOSEPH VON               FURSE, CHARLES WELLINGTON
+  FUJI                              FÜRST, JULIUS
+  FU-KIEN                           FÜRSTENBERG
+  FUKUI                             FÜRSTENWALDE
+  FUKUOKA                           FÜRTH
+  FULA                              FURTWÄNGLER, ADOLF
+  FULCHER OF CHARTRES               FURZE
+  FULDA                             FUSARO, LAGO
+  FULGENTIUS, FABIUS PLANCIADES     FUSELI, HENRY
+  FULGINIAE                         FUSEL OIL
+  FULGURITE                         FUSIBLE METAL
+  FULHAM                            FUSILIER
+  FULK (king of Jerusalem)          FUSION
+  FULK (archbishop of Reims)        FÜSSEN
+  FULKE, WILLIAM                    FUST, JOHANN
+  FULK NERRA                        FUSTEL DE COULANGES, NUMA DENIS
+  FÜLLEBORN, GEORG GUSTAV           FUSTIAN
+  FULLER, ANDREW                    FUSTIC
+  FULLER, GEORGE                    FUTURES
+  FULLER, MARGARET                  FUX, JOHANN JOSEPH
+  FULLER, MELVILLE WESTON           FUZE
+  FULLER, THOMAS                    FYNE, LOCH
+  FULLER, WILLIAM                   FYRD
+  FULLER'S EARTH                    FYT, JOHANNES
+  FULLERTON, LADY GEORGIANA         FYZABAD
+
+
+
+
+FROST (a common Teutonic word, cf. Dutch, _vorst_, Ger. _Frost_, from
+the common Teutonic verb meaning "to freeze," Dutch, _vriezen_, Ger.
+_frieren_; the Indo-European root is seen in Lat. _pruina_, hoar-frost,
+cf. _prurire_, to itch, burn, _pruna_, burning coal, Sansk. _plush_, to
+burn), in meteorology, the act, or agent of the process, of freezing;
+hence the terms "hoar-frost" and "white-frost" applied to visible frozen
+vapour formed on exposed surfaces. A frost can only occur when the
+surface temperature falls below 32° F., the freezing-point of water; if
+the temperature be between 28° and 32° it is a "light frost," if below
+28° it is a "heavy," "killing" or "black frost"; the term "black frost"
+is also used when no hoar-frost is present. The number of degrees below
+freezing-point is termed "degrees of frost." As soon as a mass of air is
+cooled to its dew-point, water begins to be precipitated in the form of
+rain, dew, snow or hail. Hoarfrost is only formed at the immediate
+surface of the land if the latter be at a temperature below 32°, and
+this may occur even when the temperature of the air a few feet above the
+ground is 12°-16° above the freezing-point. The heaviest hoar-frosts are
+formed under weather conditions similar to those under which the
+heaviest summer dews occur, namely, clear and calm nights, when there is
+no cloud to impede the radiation of heat from the surface of the land,
+which thereby becomes rapidly and completely cooled. The danger of frost
+is minimized when the soil is very moist, as for example after 10-12 mm.
+of rain; and it is a practice in America to flood fields on the receipt
+of a frost warning, radiation being checked by the light fog sheets
+which develop over moist soils, just as a cloud-layer in the upper
+atmosphere impedes radiation on a grand scale. A layer of smoke will
+also impede radiation locally, and to this end smoky fires are sometimes
+lit in such positions that the smoke may drift over planted ground which
+it is desirable to preserve from frost. Similarly, frost may occur in
+open country when a town, protected by its smoke-cloud above, is free of
+it. In a valley with fairly high and steep flanks frost sometimes occurs
+locally at the bottom, because the layer of air cooled by contact with
+the cold surface of the higher ground is heavier than that not so
+cooled, and therefore tends to flow or settle downwards along the slope
+of the land. When meteorological considerations point to a frost, an
+estimate of the night temperature may be obtained by multiplying the
+difference between the readings of the wet and dry bulb thermometer by
+2.5 and subtracting the result from the dry bulb temperature. This rule
+applies when the evening air is at about 50° and 30.1 in. pressure, the
+sky being clear. An instrument has been devised in France for the
+prediction of frost. It consists of a wet bulb and a dry bulb
+thermometer, mounted on a board on which is also a scale of lines
+corresponding to degrees of the dry bulb, and a pointer traversing a
+scale graduated according to degrees of the wet bulb. Observations for
+the night are taken about half an hour before sunset. By means of the
+pointer and scale, the point may be found at which the line of the
+dry-bulb reading meets the pointer set to the reading of the wet bulb.
+The scale is further divided by colours so that the observed point may
+fall within one of three zones, indicating certain frost, probable frost
+or no probability of frost.
+
+
+
+
+FROSTBITE, a form of mortification (q.v.), due to the action of extreme
+cold in cutting off the blood-supply from the fingers, toes, nose, ears,
+&c. In comparatively trifling forms it occurs as "chaps" and
+"chilblains," but the term frostbite is usually applied only to more
+severe cases, where the part affected becomes in danger of gangrene. An
+immediate application of snow, or ice-water, will restore the
+circulation; the application of heat would cause inflammation. But if
+the mortification has gone too far for the circulation to be restored,
+the part will be lost, and surgical treatment may be necessary.
+
+
+
+
+FROSTBURG, a town of Allegany county, Maryland, U.S.A., 11 m. W. of
+Cumberland. Pop. (1890) 3804; (1900) 5274 (578 foreign-born and 236
+negroes); (1910) 6028. It is served by the Cumberland & Pennsylvania
+railway and the Cumberland & Westernport electric railway. The town is
+about 2000 ft. above sea-level on a plateau between the Great Savage and
+Dans mountains, and its delightful scenery and air have made it
+attractive as a summer resort. It is the seat of the second state normal
+school, opened in 1904. Frostburg is in the midst of the coal region of
+the state, and is itself almost completely undermined; it has planing
+mills and manufactures large quantities of fire-brick. The municipality
+owns and operates its waterworks. Natural gas is piped to Frostburg from
+the West Virginia fields, 120 m. away. Frostburg was first settled in
+1812; was called Mount Pleasant until about 1830, when the present name
+was substituted in honour of Meshech Frost, one of the town's founders;
+and was incorporated in 1870.
+
+
+
+
+FROTHINGHAM, OCTAVIUS BROOKS (1822-1895), American clergyman and author,
+was born in Boston on the 26th of November 1822, son of Nathaniel
+Langdon Frothingham (1793-1870), a prominent Unitarian preacher of
+Boston, and through his mother's family related to Phillips Brooks. He
+graduated from Harvard College in 1843 and from the Divinity School in
+1846. He was pastor of the North Unitarian church of Salem,
+Massachusetts, in 1847-1855. From 1855 to 1860 he was pastor of a new
+Unitarian society in Jersey City, where he gave up the Lord's Supper,
+thinking that it ministered to self-satisfaction; and it was as a
+radical Unitarian that he became pastor of another young church in New
+York City in 1860. Indeed in 1864 he was recognized as leader of the
+radicals after his reply to Dr Hedge's address to the graduating
+students of the Divinity School on _Anti-Supernaturalism in the Pulpit_.
+In 1865, when he had practically given up "transcendentalism," his
+church building was sold and his congregation began to worship in Lyric
+Hall under the name of the Independent Liberal Church; in 1875 they
+removed to the Masonic Temple, but four years later ill-health compelled
+Frothingham's resignation, and the church dissolved. Paralysis
+threatened him and he never fully recovered his health; in 1881 he
+returned to Boston, where he died on the 27th of November 1895. To this
+later period of his life belongs his best literary work. While he was in
+New York he was for a time art critic of the _Tribune_. Always himself
+on the unpopular side and an able but thoroughly fair critic of the
+majority, he habitually under-estimated his own worth; he was not only
+an anti-slavery leader when abolition was not popular even in New
+England, and a radical and rationalist when it was impossible for him to
+stay conveniently in the Unitarian Church, but he was the first
+president of the National Free Religious Association (1867) and an early
+and ardent disciple of Darwin and Spencer. To his radical views he was
+always faithful. It is a mistake to say that he grew more conservative
+in later years; but his judgment grew more generous and catholic. He was
+a greater orator than man of letters, and his sermons in New York were
+delivered to large audiences, averaging one thousand at the Masonic
+Temple, and were printed each week; in eloquence and in the charm of his
+spoken word he was probably surpassed in his day by none save George
+William Curtis. Personally he seemed cold and distant, partly because of
+his impressive appearance, and partly because of his own modesty, which
+made him backward in seeking friendships.
+
+  His principal published works are: _Stories from the Life of the
+  Teacher_ (1863), _A Child's Book of Religion_ (1866), and other works
+  of religious teaching for children; several volumes of sermons;
+  _Beliefs of Unbelievers_ (1876), _The Cradle of the Christ: a Study in
+  Primitive Christianity_ (1877), _The Spirit of New Faith_ (1877), _The
+  Rising and the Setting Faith_ (1878), and other expositions of the
+  "new faith" he preached; _Life of Theodore Parker_ (1874),
+  _Transcendentalism in New England_ (1876), which is largely
+  biographical, _Gerrit Smith, a Biography_ (1878), _George Ripley_
+  (1882), in the "American Men of Letters" series, _Memoir of William
+  Henry Channing_ (1886), _Boston Unitarianism, 1820-1850_ (1890),
+  really a biography of his father; and _Recollections and Impressions,
+  1822-1890_ (1891).
+
+
+
+
+FROUDE, JAMES ANTHONY (1818-1894), English historian, son of R.H.
+Froude, archdeacon of Totnes, was born at Dartington, Devon, on the 23rd
+of April 1818. He was educated at Westminster and Oriel College, Oxford,
+then the centre of the ecclesiastical revival. He obtained a second
+class and the chancellor's English essay prize, and was elected a fellow
+of Exeter College (1842). His elder brother, Richard Hurrell Froude
+(1803-1836), had been one of the leaders of the High Church movement at
+Oxford. Froude joined that party and helped J.H. Newman, afterwards
+cardinal, in his _Lives of the English Saints_. He was ordained deacon
+in 1845. By that time his religious opinions had begun to change, he
+grew dissatisfied with the views of the High Church party, and came
+under the influence of Carlyle's teaching. Signs of this change first
+appeared publicly in his _Shadows of the Clouds_, a volume containing
+two stories of a religious sort, which he published in 1847 under the
+pseudonym of "Zeta," and his complete desertion of his party was
+declared a year later in his _Nemesis of Faith_, an heretical and
+unpleasant book, of which the earlier part seems to be autobiographical.
+
+On the demand of the college he resigned his fellowship at Oxford, and
+mainly at least supported himself by writing, contributing largely to
+_Fraser's Magazine_ and the _Westminster Review_. The excellence of his
+style was soon generally recognized. The first two volumes of his
+_History of England from the Fall of Wolsey to the Defeat of the Spanish
+Armada_ appeared in 1856, and the work was completed in 1870. As an
+historian he is chiefly remarkable for literary excellence, for the art
+with which he represents his conception of the past. He condemns a
+scientific treatment of history and disregards its philosophy. He held
+that its office was simply to record human actions and that it should be
+written as a drama. Accordingly he gives prominence to the personal
+element in history. His presentations of character and motives, whether
+truthful or not, are undeniably fine; but his doctrine that there should
+be "no theorizing" about history tended to narrow his survey, and
+consequently he sometimes, as in his remarks on the foreign policy of
+Elizabeth, seems to misapprehend the tendencies of a period on which he
+is writing.
+
+Froude's work is often marred by prejudice and incorrect statements. He
+wrote with a purpose. The keynote of his _History_ is contained in his
+assertion that the Reformation was "the root and source of the expansive
+force which has spread the Anglo-Saxon race over the globe." Hence he
+overpraises Henry VIII. and others who forwarded the movement, and
+speaks too harshly of some of its opponents. So too, in his _English in
+Ireland_ (1872-1874), which was written to show the futility of attempts
+to conciliate the Irish, he aggravates all that can be said against the
+Irish, touches too lightly on English atrocities, and writes unjustly of
+the influence of Roman Catholicism. A strong anti-clerical prejudice is
+manifest in his historical work generally, and is doubtless the result
+of the change in his views on Church matters and his abandonment of the
+clerical profession. Carlyle's influence on him may be traced both in
+his admiration for strong rulers and strong government, which led him to
+write as though tyranny and brutality were excusable, and in his
+independent treatment of character. His rehabilitation of Henry VIII.
+was a useful protest against the idea that the king was a mere
+sanguinary profligate, but his representation of him as the self-denying
+minister of his people's will is erroneous, and is founded on the false
+theory that the preambles of the acts of Henry's parliaments represented
+the opinions of the educated laymen of England. As an advocate he
+occasionally forgets that sobriety of judgment and expression become an
+historian. He was not a judge of evidence, and seems to have been
+unwilling to admit the force of any argument or the authority of any
+statement which militated against his case. In his _Divorce of Catherine
+of Aragon_ (1891) he made an unfortunate attempt to show that certain
+fresh evidence on the subject, brought forward by Dr Gairdner, Dr
+Friedmann and others, was not inconsistent with the views which he has
+expressed in his _History_ nearly forty years before. He worked
+diligently at original manuscript authorities at Simancas, the Record
+Office and Hatfield House; but he used his materials carelessly, and
+evidently brought to his investigation of them a mind already made up as
+to their significance. His _Life of Caesar_ (1879), a glorification of
+imperialism, betrays an imperfect acquaintance with Roman politics and
+the life of Cicero; and of his two pleasant books of travel, _The
+English in the West Indies_ (1888) shows that he made little effort to
+master his subject, and _Oceana_ (1886), the record of a tour in
+Australia and New Zealand, among a multitude of other blunders, notes
+the prosperity of the working-classes in Adelaide at the date of his
+visit, when, in fact, owing to a failure in the wheat-crop, hundreds
+were then living on charity. He was constitutionally inaccurate, and
+seems to have been unable to represent the exact sense of a document
+which lay before him, or even to copy from it correctly. Historical
+scholars ridiculed his mistakes, and Freeman, the most violent of his
+critics, never let slip a chance of hitting at him in the _Saturday
+Review_. Froude's temperament was sensitive, and he suffered from these
+attacks, which were often unjust and always too savage in tone. The
+literary quarrel between him and Freeman excited general interest when
+it blazed out in a series of articles which Freeman wrote in the
+_Contemporary Review_ (1878-1879) on Froude's _Short Study_ of Thomas
+Becket.
+
+Notwithstanding its defects, Froude's _History_ is a great achievement;
+it presents an important and powerful account of the Reformation period
+in England, and lays before us a picture of the past magnificently
+conceived, and painted in colours which will never lose their freshness
+and beauty. As with Froude's work generally, its literary merit is
+remarkable; it is a well-balanced and orderly narrative, coherent in
+design and symmetrical in execution. Though it is perhaps needlessly
+long, the thread of the story is never lost amid a crowd of details;
+every incident is made subordinate to the general idea, appears in its
+appropriate place, and contributes its share to the perfection of the
+whole. The excellence of its form is matched by the beauty of its style,
+for Froude was a master of English prose. The most notable
+characteristic of his style is its graceful simplicity; it is never
+affected or laboured; his sentences are short and easy, and follow one
+another naturally. He is always lucid. He was never in doubt as to his
+own meaning, and never at a loss for the most appropriate words in which
+to express it. Simple as his language is, it is dignified and worthy of
+its subject. Nowhere perhaps does his style appear to more advantage
+than in his four series of essays entitled _Short Studies on Great
+Subjects_ (1867-1882), for it is seen there unfettered by the
+obligations of narrative. Yet his narrative is admirably told. For the
+most part flowing easily along, it rises on fit occasions to splendour,
+picturesque beauty or pathos. Few more brilliant pieces of historical
+writing exist than his description of the coronation procession of Anne
+Boleyn through the streets of London, few more full of picturesque power
+than that in which he relates how the spire of St Paul's was struck by
+lightning; and to have once read is to remember for ever the touching
+and stately words in which he compares the monks of the London
+Charterhouse preparing for death with the Spartans at Thermopylae.
+Proofs of his power in the sustained narration of stirring events are
+abundant; his treatment of the Pilgrimage of Grace, of the sea fight at
+St Helens and the repulse of the French invasion, and of the murder of
+Rizzio, are among the most conspicuous examples of it. Nor is he less
+successful when recording pathetic events, for his stories of certain
+martyrdoms, and of the execution of Mary queen of Scots, are told with
+exquisite feeling and in language of well-restrained emotion. And his
+characters are alive. We may not always agree with his portraiture, but
+the men and women whom he saw exist for us instinct with the life with
+which he endows them and animated by the motives which he attributes to
+them. His successes must be set against his failures. At the least he
+wrote a great history, one which can never be disregarded by future
+writers on his period, be their opinions what they may; which attracts
+and delights a multitude of readers, and is a splendid example of
+literary form and grace in historical composition.
+
+The merits of his work met with full recognition. Each instalment of his
+_History_, in common with almost everything which he wrote, was widely
+read, and in spite of some adverse criticisms was received with eager
+applause. In 1868 he was elected rector of St Andrews University,
+defeating Disraeli by a majority of fourteen. He was warmly welcomed in
+the United States, which he visited in 1872, but the lectures on Ireland
+which he delivered there caused much dissatisfaction. On the death of
+his adversary Freeman in 1892, he was appointed, on the recommendation
+of Lord Salisbury, to succeed him as regius professor of modern history
+at Oxford. Except to a few Oxford men, who considered that historical
+scholarship should have been held to be a necessary qualification for
+the office, his appointment gave general satisfaction. His lectures on
+Erasmus and other 16th-century subjects were largely attended. With some
+allowance for the purpose for which they were originally written, they
+present much the same characteristics as his earlier historical books.
+His health gave way in the summer of 1894, and he died on the 20th of
+October.
+
+His long life was full of literary work. Besides his labours as an
+author, he was for fourteen years editor of _Fraser's Magazine_. He was
+one of Carlyle's literary executors, and brought some sharp criticism
+upon himself by publishing Carlyle's _Reminiscences_ and the _Memorials
+of Jane Welsh Carlyle_, for they exhibited the domestic life and
+character of his old friend in an unpleasant light. Carlyle had given
+the manuscripts to him, telling him that he might publish them if he
+thought it well to do so, and at the close of his life agreed to their
+publication. Froude therefore declared that in giving them to the world
+he was carrying out his friend's wish by enabling him to make a
+posthumous confession of his faults. Besides publishing these
+manuscripts he wrote a _Life of Carlyle_. His earlier study of Irish
+history afforded him suggestions for a historical novel entitled _The
+Two Chiefs of Dunboy_ (1889). In spite of one or two stirring scenes it
+is a tedious book, and its personages are little more than machines for
+the enunciation of the author's opinions and sentiments. Though Froude
+had some intimate friends he was generally reserved. When he cared to
+please, his manners and conversation were charming. Those who knew him
+well formed a high estimate of his ability in practical affairs. In 1874
+Lord Carnarvon, then colonial secretary, sent Froude to South Africa to
+report on the best means of promoting a confederation of its colonies
+and states, and in 1875 he was again sent to the Cape as a member of a
+proposed conference to further confederation. Froude's speeches in South
+Africa were rather injudicious, and his mission was a failure (see SOUTH
+AFRICA: _History_). He was twice married. His first wife, a daughter of
+Pascoe Grenfell and sister of Mrs Charles Kingsley, died in 1860; his
+second, a daughter of John Warre, M.P. for Taunton, died in 1874.
+
+  Froude's _Life_, by Herbert Paul, was published in 1905.     (W. Hu.)
+
+
+
+
+FRUCTOSE, LAEVULOSE, or FRUIT-SUGAR, a carbohydrate of the formula
+C6H12O6. It is closely related to ordinary d-glucose, with which it
+occurs in many fruits, starches and also in honey. It is a hydrolytic
+product of inulin, from which it may be prepared; but it is more usual
+to obtain it from "invert sugar," the mixture obtained by hydrolysing
+cane sugar with sulphuric acid. Cane sugar then yields a syrupy mixture
+of glucose and fructose, which, having been freed from the acid and
+concentrated, is mixed with water, cooled in ice and calcium hydroxide
+added. The fructose is precipitated as a saccharate, which is filtered,
+suspended in water and decomposed by carbon dioxide. The liquid is
+filtered, the filtrate concentrated, and the syrup so obtained washed
+with cold alcohol. On cooling the fructose separates. It may be obtained
+as a syrup, as fine, silky needles, a white crystalline powder, or as a
+granular crystalline, somewhat hygroscopic mass. When anhydrous it melts
+at about 95° C. It is readily soluble in water and in dilute alcohol,
+but insoluble in absolute alcohol. It is sweeter than cane sugar and is
+more easily assimilated. It has been employed under the name diabetin as
+a sweetening agent for diabetics, since it does not increase the
+sugar-content of the urine; other medicinal applications are in phthisis
+(mixed with quassia or other bitter), and for children suffering from
+tuberculosis or scrofula in place of cane sugar or milk-sugar.
+
+Chemically, fructose is an oxyketone or ketose, its structural formula
+being CH2OH·(CH·OH)3·CO·CH2OH; this result followed from its conversion
+by H. Kiliani into methylbutylacetic acid. The form described above is
+_laevo_-rotatory, but it is termed d-fructose, since it is related to
+d-glucose. Solutions exhibit mutarotation, fresh solutions having a
+specific rotation of -104.0°, which gradually diminishes to -92°. It was
+synthesized by Emil Fischer, who found the synthetic sugar which he
+named [alpha]-acrose to be (d + l)-fructose, and by splitting this
+mixture he obtained both the d and l forms. Fructose resembles d-glucose
+in being fermentable by yeast (it is the one ketose which exhibits this
+property), and also in its power of reducing alkaline copper and silver
+solutions; this latter property is assigned to the readiness with which
+hydroxyl and ketone groups in close proximity suffer oxidation. For the
+structural (stereochemical) relations of fructose see SUGAR.
+
+
+
+
+FRUGONI, CARLO INNOCENZIO MARIA (1692-1768), Italian poet, was born at
+Genoa on the 21st of November 1692. He was originally destined for the
+church and at the age of fifteen, in opposition to his strong wishes,
+was shut up in a convent; but although in the following year he was
+induced to pronounce monastic vows, he had no liking for this life. He
+acquired considerable reputation as an elegant writer both of Latin and
+Italian prose and verse; and from 1716 to 1724 he filled the chairs of
+rhetoric at Brescia, Rome, Genoa, Bologna and Modena successively,
+attracting by his brilliant fluency a large number of students at each
+university. Through Cardinal Bentivoglio he was recommended to Antonio
+Farnese, duke of Parma, who appointed him his poet laureate; and he
+remained at the court of Parma until the death of Antonio, after which
+he returned to Genoa. Shortly afterwards, through the intercession of
+Bentivoglio, he obtained from the pope the remission of his monastic
+vows, and ultimately succeeded in recovering a portion of his paternal
+inheritance. After the peace of Aix-la-Chapelle he returned to the court
+of Parma, and there devoted the later years of his life chiefly to
+poetical composition. He died on the 20th of December 1768. As a poet
+Frugoni was one of the best of the school of the Arcadian Academy, and
+his lyrics and pastorals had great facility and elegance.
+
+  His collected works were published at Parma in 10 vols. in 1799, and a
+  more complete edition appeared at Lucca in the same year in 15 vols. A
+  selection from his works was published at Brescia in 1782, in 4 vols.
+
+
+
+
+FRUIT (through the French from the Lat. _fructus_; _frui_, to enjoy), in
+its widest sense, any product of the soil that can be enjoyed by man or
+animals; the word is so used constantly in the Bible, and extended, as a
+Hebraism, to offspring or progeny of man and of animals, in such
+expressions as "the fruit of the body," "of the womb," "fruit of thy
+cattle" (Deut. xxviii. 4), &c., and generally to the product of any
+action or effort. Between this wide and frequently figurative use of the
+word and its application in the strict botanical sense treated below,
+there is a popular meaning, regarding the objects denoted by the word
+entirely from the standpoint of edibility, and differentiating them
+roughly from those other products of the soil, which, regarded
+similarly, are known as vegetables. In this sense "fruit" is applied to
+such seed-envelopes of plants as are edible, either raw or cooked, and
+are usually sweet, juicy or of a refreshing flavour. But applications of
+the word in this sense are apt to be loose and shifting according to the
+fashion of the time.
+
+Fruit, in the botanical sense, is developed from the flower as the
+result of fertilization of the ovule. After fertilization various
+changes take place in the parts of the flower. Those more immediately
+concerned in the process, the anther and stigma, rapidly wither and
+decay, while the filaments and style often remain for some time; the
+floral envelopes become dry, the petals fall, and the sepals are either
+deciduous, or remain persistent in an altered form; the ovary becomes
+enlarged, forming the _pericarp_; and the ovules are developed as the
+seeds, containing the embryo-plant. The term fruit is strictly applied
+to the mature pistil or ovary, with the seeds in its interior; but it
+often includes other parts of the flower, such as the bracts and floral
+envelopes. Thus the fruit of the hazel and oak consists of the ovary
+enveloped by the bracts; that of the apple and pear, of the ovary and
+floral receptacle; and that of the pine-apple, of the whole
+inflorescence. Such fruits are sometimes distinguished as _pseudocarps_.
+In popular language, the fruit includes all those parts which exhibit a
+striking change as the result of fertilization. In general, the fruit is
+not ripened unless fertilization has been effected; but cases occur as
+the result of cultivation in which the fruit swells and becomes to all
+appearance perfect, while no seeds are produced. Thus, there are
+seedless oranges, grapes and pineapples. When the ovules are
+unfertilized, it is common to find that the ovary withers and does not
+come to maturity; but in the case of bananas, plantains and bread-fruit,
+the non-development of seeds seems to lead to a larger growth and a
+greater succulence of fruit.
+
+  The fruit, like the ovary, may be formed of a single carpel or of
+  several. It may have one cell or cavity, being _unilocular_; or many,
+  _multilocular_, &c. The number and nature of the divisions depend on
+  the number of carpels and the extent to which their edges are folded
+  inwards. The appearances presented by the ovary do not always remain
+  permanent in the fruit. Great changes are observed to take place, not
+  merely as regards the increased size of the ovary, its softening or
+  hardening, but also in its internal structure, owing to the
+  suppression, additional formation or enlargement of parts. Thus, in
+  the ash (fig. 1) an ovary with two cells, each containing an ovule
+  attached to a central placenta, is changed into a unilocular fruit
+  with one seed; one ovule becomes abortive, while the other, g,
+  gradually enlarging until the septum is pushed to one side, unites
+  with the walls of the cell, and the placenta appears to be parietal.
+  In the oak and hazel, an ovary with three and two cells respectively,
+  and two ovules in each, produces a one-celled fruit with one seed. In
+  the coco-nut, a trilocular and triovular ovary produces a one-celled,
+  one-seeded fruit. This abortion may depend on the pressure caused by
+  the development of certain ovules, or it may proceed from
+  non-fertilization of all the ovules and consequent non-enlargement of
+  the carpels. Again, by the growth of the placenta, or the folding
+  inwards of parts of the carpels, divisions occur in the fruit which
+  did not exist in the ovary. In _Cathartocarpus Fistula_ a one-celled
+  ovary is changed into a fruit having each of its seeds in a separate
+  cell, in consequence of spurious dissepiments being produced
+  horizontal from the inner wall of the ovary. In flax (_Linum_) by the
+  folding inwards of the back of the carpels a five-celled ovary becomes
+  a ten-celled fruit. In _Astragalus_ the folding inwards of the dorsal
+  suture converts a one-celled ovary into a two-celled fruit; and in
+  _Oxytropis_ the folding of the ventral suture gives rise to a similar
+  change. The development of cellular or pulpy matter, and the
+  enlargement of parts not forming whorls of the flower, frequently
+  alter the appearance of the fruit, and render it difficult to discover
+  its formation. In the gooseberry (fig. 29), grape, guava, tomato and
+  pomegranate, the seeds nestle in pulp formed by the placentas. In the
+  orange the pulpy matter surrounding the seeds is formed by succulent
+  cells, which are produced from the inner partitioned lining of the
+  pericarp. In the strawberry the receptacle becomes succulent, and
+  bears the mature carpels on its convex surface (fig. 2); in the rose
+  there is a fleshy hollow receptacle which bears the carpels on its
+  concave surface (fig. 3). In the juniper the scaly bracts grow up
+  round the seeds and become succulent, and in the fig (fig. 4) the
+  receptacle becomes succulent and encloses an inflorescence.
+
+  [Illustration:
+
+    Fig. 1.--Samara or winged fruit of Ash (_Fraxinus_). 1, Entire, with
+    its wing a; 2, lower portion cut transversely, to show that it
+    consists of two cells; one of which, l, is abortive, and is reduced
+    to a very small cavity, while the other is much enlarged and filled
+    with a seed g.
+
+    Fig. 2.--Fruit of the Strawberry (_Fragaria vesca_), consisting of
+    an enlarged succulent receptacle, bearing on its surface the small
+    dry seed-like fruits (achenes). (After Duchartre.)
+
+    From Strasburger's _Lehrbuch der Botanik_, by permission of Gustav
+    Fischer.
+
+    Fig. 3.--Fruit of the Rose cut vertically. s', Fleshy hollowed
+    receptacle; s, persistent sepals; _fr_, ripe carpels; e, stamens,
+    withered.
+
+    Fig. 4.--Peduncle of Fig (_Ficus Carica_), ending in a hollow
+    receptacle enclosing numerous male and female flowers.
+
+    Fig. 5.--Fruit of Cherry (_Prunus Cerasus_) in longitudinal section.
+    ep, Epicarp; m, mesocarp; en, endocarp.
+
+    From Strasburger's _Lehrbuch der Botanik_, by permission of Gustav
+    Fischer.]
+
+  The pericarp consists usually of three layers, the external, or
+  _epicarp_ (fig. 5, ep); the middle, or _mesocarp_, m; and the
+  internal, or _endocarp_, _en_. These layers are well seen in such a
+  fruit as the peach, plum or cherry, where they are separable one from
+  the other; in them the epicarp forms what is commonly called the skin;
+  the mesocarp, much developed, forms the flesh or pulp, and hence has
+  sometimes been called _sarcocarp_; while the endocarp, hardened by the
+  production of woody cells, forms the _stone_ or _putamen_ immediately
+  covering the kernel or seed. The pulpy matter found in the interior of
+  fruits, such as the gooseberry, grape and others, is formed from the
+  placentas, and must not be confounded with the sarcocarp. In some
+  fruits, as in the nut, the three layers become blended together and
+  are indistinguishable. In bladder senna (_Colutea arborescens_) the
+  pericarp retains its leaf-like appearance, but in most cases it
+  becomes altered both in consistence and in colour. Thus in the date
+  the epicarp is the outer brownish skin, the pulpy matter is the
+  mesocarp or sarcocarp, and the thin papery-like lining is the endocarp
+  covering the hard seed. In the medlar the endocarp becomes of a stony
+  hardness. In the melon the epicarp and endocarp are very thin, while
+  the mesocarp forms the bulk of the fruit, differing in texture and
+  taste in its external and internal parts. The rind of the orange
+  consists of epicarp and mesocarp, while the endocarp forms partitions
+  in the interior, filled with pulpy cells. The part of the pericarp
+  attached to the peduncle is the base, and the point where the style or
+  stigma existed is the apex. This latter is not always the apparent
+  apex, as in the case of the ovary; it may be lateral or even basilar.
+  The style sometimes remains in a hardened form, rendering the fruit
+  _apiculate_; at other times it falls off, leaving only traces of its
+  existence. The presence of the style or stigma serves to distinguish
+  certain single-seeded pericarps from seeds.
+
+  [Illustration:
+
+    FIG. 6.--Seed-vessel or capsule of Campion, opening by ten teeth at
+    the apex. The calyx c is seen surrounding the seed-vessel.
+
+    FIG. 7.--Capsule of Poppy, opening by pores p, under the radiating
+    peltate stigma s.]
+
+
+    Dehiscence of fruits.
+
+  When the fruit is mature and the seeds are ripe, the carpels usually
+  give way either at the ventral or dorsal suture or at both, and so
+  allow the seeds to escape. The fruit in this case is _dehiscent_. But
+  some fruits are _indehiscent_, falling to the ground entire, and the
+  seeds eventually reaching the soil by their decay. By dehiscence the
+  pericarp becomes divided into different pieces, or _valves_, the fruit
+  being univalvular, bivalvular or multivalvular, &c., according as
+  there are one, two or many valves. The splitting extends the whole
+  length of the fruit, or is partial, the valves forming teeth at the
+  apex, as in the order Caryophyllaceae (fig. 6). Sometimes the valves
+  are detached only at certain points, and thus dehiscence takes place
+  by pores at the apex, as in poppy (fig. 7), or at the base, as in
+  _Campanula_. Indehiscent fruits are either dry, as the nut, or fleshy,
+  as the cherry and apple. They are formed of one or several carpels. In
+  the former case they usually contain only a single seed, which may
+  become so incorporated with the pericarp as to appear to be naked, as
+  in the grain of wheat and generally in grasses. In such cases the
+  presence of the remains of style or stigma determines their true
+  nature.
+
+  [Illustration:
+
+    FIG. 8.--Dry dehiscent fruit. The pod (legume) of the Pea; r, the
+    dorsal suture; b, the ventral; c, calyx; s, seeds.
+
+    From Vines' _Students' Text-Book of Botany_, by permission of Swan
+    Sonnenschein & Co.
+
+    FIG. 9.--(1) Fruit or capsule of Meadow Saffron (_Colchicum
+    autumnale_), dehiscing along the septa (septicidally); (2) same cut
+    across, showing the three chambers with the seeds attached along the
+    middle line (axile placentation).
+
+    FIG. 10.--Diagram to illustrate the septicidal dehiscence in a
+    pentalocular capsule. The loculaments l correspond to the number of
+    the carpels, which separate by splitting through the septa, s.
+
+    FIG. 11.--The seed vessel (capsule) of the Flower-de-Luce (_Iris_),
+    opening in a loculicidal manner. The three valves bear the septa in
+    the centre, and the opening takes place through the back of the
+    loculaments. Each valve is formed by the halves of contiguous
+    carpels.
+
+    FIG. 12.--Diagram to illustrate loculicidal dehiscence. The
+    loculaments l, split at the back, and the valves separate, bearing
+    the septa s on their centres.
+
+    FIG. 13.--Diagram to illustrate septifragal dehiscence, in which the
+    dehiscence takes place through the back of the loculaments l, and
+    the valves separate from the septa s, which are left attached to the
+    placentas in the centre.]
+
+  Dehiscent fruits, when composed of single carpels, may open by the
+  ventral suture only, as in the paeony, hellebore, _Aquilegia_ (fig.
+  28) and _Caltha_; by the dorsal suture only, as in magnolias and some
+  _Proteaceae_, or by both together, as in the pea (fig. 8) and bean; in
+  these cases the dehiscence is _sutural_. When composed of several
+  united carpels, two types of dehiscence occur--a longitudinal and a
+  transverse. In the longitudinal the separation may take place by the
+  dissepiments throughout their length, so that the fruit is resolved
+  into its original carpels, and each valve represents a carpel, as in
+  rhododendron, _Colchicum_, &c.; this dehiscence, in consequence of
+  taking place through the septum, is called _septicidal_ (figs. 9, 10).
+  The valves separate from their commissure, or central line of union,
+  carrying the placentas with them, or they leave the latter in the
+  centre, so as to form with the axis a column of a cylindrical, conical
+  or prismatic shape. Dehiscence is _loculicidal_ when the union between
+  the edges of the carpels is persistent, and they dehisce by the dorsal
+  suture, or through the back of the loculaments, as in the lily and
+  iris (figs. 11, 12). In these cases each valve consists of a half of
+  each of two contiguous carpels. The placentas either remain united to
+  the axis, or they separate from it, being attached to the septa on the
+  valves. When the outer walls of the carpels break off from the septa,
+  leaving them attached to the central column, the dehiscence is said to
+  be _septifragal_ (fig. 13), and where, as in _Linum catharticum_ and
+  _Calluna_, the splitting takes place first of all in a septicidal
+  manner, the fruit is described as _septicidally septifragal_; while in
+  other cases, as in thorn apple (_Datura Stramonium_), where the
+  splitting is at first loculicidal, the dehiscence is _loculicidally
+  septifragal_. In all those forms the separation of the valves takes
+  place either from above downwards or from below upwards. In
+  _Saxifraga_ a splitting for a short distance of the ventral sutures of
+  the carpels takes place, so that a large apical pore is formed. In the
+  fruit of Cruciferae, as wallflower (fig. 14), the valves separate from
+  the base of the fruit, leaving a central _replum_, or frame, which
+  supports the false septum formed by a prolongation from the parietal
+  placentas on opposite sides of the fruit, extending between the
+  ventral sutures of the carpels. In Orchidaceae (fig. 15) the pericarp,
+  when ripe, separates into three valves in a loculicidal manner, but
+  the midribs of the carpels, to which the placentas are attached, often
+  remain adherent to the axis both at the apex and base after the valves
+  bearing the seeds have fallen. The other type of dehiscence is
+  transverse, or _circumscissile_, when the upper part of the united
+  carpels falls off in the form of a lid or operculum, as in _Anagallis_
+  and in henbane (_Hyoscyamus_) (fig. 16).
+
+  [Illustration:
+
+    FIG. 14.--Siliqua or seed-vessel of Wallflower (_Cheiranthus
+    Cheiri_), opening by two valves, which separate from the base
+    upwards, leaving the seeds attached to the dissepiment which is
+    supported by the replum.
+
+    From Strasburger's _Lehrbuch der Botanik_, by permission of Gustav
+    Fischer.
+
+    FIG. 15.--Capsule of an Orchid (_Xylobium_). v, valve.
+
+    FIG. 16.--Seed-vessel of _Anagallisarvensis_, opening by
+    circumscissile dehiscence.
+
+    From Strasburger's _Lehrbuch der Botanik_, by permission of Gustav
+    Fischer.
+
+    FIG. 17.--Lomentum of _Hedysarum_ which, when ripe, separates
+    transversely into single-seeded portions or mericarps.
+
+    FIG. 18.--Fruit of _Geranium pratense_, after splitting.]
+
+  Sometimes the axis is prolonged beyond the base of the carpels, as in
+  the mallow and castor-oil plant, the carpels being united to it
+  throughout their length by their faces, and separating from it without
+  opening. In the Umbelliferae the two carpels separate from the lower
+  part of the axis, and remain attached by their apices to a
+  prolongation of it, called a _carpophore_ or _podocarp_, which splits
+  into two (fig. 25) and suspends them; hence the fruit is termed a
+  _cremocarp_, which divides into two _mericarps_. The general term
+  _schizocarp_ is applied to all dry fruits, which break up into two or
+  more one-seeded indehiscent mericarps, as in _Hedysarum_ (fig. 17). In
+  the order Geraniaceae the styles remain attached to a central column,
+  and the mericarps separate from below upwards, before dehiscing by
+  their ventral suture (fig. 18). Carpels which separate one from
+  another in this manner are called _cocci_. They are well seen in the
+  order Euphorbiaceae, where there are usually three such carpels, and
+  the fruit is termed tricoccus. In many of them, as _Hura crepitans_,
+  the cocci separate with great force and elasticity. In many leguminous
+  plants, such as _Ornithopus_, _Hedysarum_ (fig. 17), _Entada_,
+  _Coronilla_ and the gum-arabic plant (_Acacia arabica_), the fruit
+  becomes a schizocarp by the formation of transverse partitions from
+  the folding in of the sides of the pericarp, and distinct separations
+  taking place at these partitions.
+
+  Fruits are formed by one flower, or are the product of several flowers
+  combined. In the former case they are either _apocarpous_, of one
+  mature carpel or of several separate free carpels; or _syncarpous_, of
+  several carpels, more or less completely united. When the fruit is
+  composed of the ovaries of several flowers united, it is usual to find
+  the bracts and floral envelopes also joined with them, so as to form
+  one mass; hence such fruits are known as multiple, confluent or
+  _anthocarpous_. The term simple is applied to fruits which are formed
+  by the ovary of a single flower, whether they are composed of one or
+  several carpels, and whether these carpels are separate or combined.
+
+  [Illustration: From Vines' _Students' Text-Book of Botany_, by
+  permission of Swan Sonnenschein & Co.
+
+    FIG. 19.--Dry one-seeded fruit of dock (_Rumex_) cut vertically. ov,
+    Pericarp formed from ovary wall; s, seed; e, endosperm; pl, embryo
+    with radicle pointing upwards and cotyledons downwards--enlarged.
+
+    FIG. 20.--Achene of _Ranunculus arvensis_ in longitudinal section;
+    e, endosperm; pl, embryo. (After Baillon, enlarged.)
+
+    From Strasburger's _Lehrbuch der Botanik_, by permission of Gustav
+    Fischer.
+
+    FIG. 21.--Fruit of Common Sycamore (_Acer Pseudoplatanus_), dividing
+    into two mericarps m; s, pedicel; fl, wings (nat. size).]
+
+
+    Dispersal of fruit or seed.
+
+  The object of the fruit in the economy of the plant is the protection
+  and nursing of the developing seed and the dispersion of the ripe
+  seeds. Hence, generally, one-seeded fruits are indehiscent, while
+  fruits containing more than one seed open to allow of the dispersal of
+  the seeds over as wide an area as possible. The form, colour,
+  structure and method of dehiscence of fruits and the form of the
+  contained seeds are intimately associated with the means of dispersal,
+  which fall into several categories. (1) By a mechanism residing in the
+  fruit. Thus many fruits open suddenly when they are dry, and the seeds
+  are ejected by the twisting or curving of the valves, or in some other
+  way; e.g. in gorse, by the spiral curving of the valves; in
+  _Impatiens_, by the twisting of the cocci; in squirting cucumber, by
+  the pressure exerted on the pulpy contents by the walls of the
+  pericarp. (2) By aid of various external agencies such as water.
+  Fruits or seeds are sometimes sufficiently buoyant to float for a long
+  time on sea- or fresh-water; e.g. coco-nut, by means of its thick,
+  fibrous coat (mesocarp), is carried hundreds of miles in the sea, the
+  tough, leathery outer coat (epicarp) preventing it from becoming
+  water-soaked. Fruits and seeds of West Indian plants are thrown up on
+  the coasts of north-west Europe, having been carried by the Gulf
+  Stream, and will often germinate; many are rendered buoyant by
+  air-containing cavities, and the embryo is protected from the seawater
+  by the tough coat of fruit or seed. Water-lily seeds are surrounded
+  with a spongy tissue when set free from the fruit, and float for some
+  distance before dropping to the bottom. (3) The most general agent in
+  the dispersal of seeds is the wind or currents of air--the fruit or
+  seed being rendered buoyant by wing-developments as in fruits of ash
+  (fig. 1) or maple (fig. 21), seeds of pines and firs, or many members
+  of the order Bignoniaceae; or hair-developments as in fruits of
+  clematis, where the style forms a feathery appendage, fruits of many
+  Compositae (dandelion, thistle, &c.), which are crowned by a plumose
+  pappus, or seeds of willow and poplar, or _Asclepias_ (fig. 36), which
+  bear tufts of silky hairs; to this category belong bladder-like
+  fruits, such as bladder-senna, which are easily rolled by the wind, or
+  cases like the so-called rose of Jericho, a small cruciferous plant
+  (_Anastatica hierocuntica_), where the plant dries up after developing
+  its fruits and becomes detached from the ground; the branches curl
+  inwards, and the whole plant is rolled over the dry ground by the
+  wind. The wind also aids the dispersal of the seeds in the case of
+  fruits which open by small teeth (many Caryophyllaceae [fig. 6]) or
+  pores (poppy [fig. 7], _Campanula_, &c.); the seeds are in these cases
+  small and numerous, and are jerked through the pores when the
+  capsules, which are generally borne on long, dry stems or stalks, are
+  shaken by the wind. (4) In other cases members of the animal world aid
+  in seed-dispersal. Fruits often bear stiff hairs or small hooks, which
+  cling to the coat of an animal or the feathers of a bird; such are
+  fruits of cleavers (_Galium Aparine_), a common hedge-row plant,
+  _Ranunculus arvensis_ (fig. 20), carrot, _Geum_, &c.; or the fruit or
+  seed has an often bright-coloured, fleshy covering, which is sought by
+  birds as food, as in stone-fruits such as plum, cherry (fig. 5), &c.,
+  where the seed is protected from injury in the mouth or stomach of the
+  animal by the hard endocarp; or the hips of the rose (fig. 3), where
+  the succulent scarlet "fruit" (the swollen receptacle) envelops a
+  number of small dry true fruits (achenes), which cling by means of
+  stiff hairs to the beak of the bird.
+
+  [Illustration:
+
+    FIG. 22.--Vertical section of a grain of wheat, showing embryo below
+    at the base of the endosperm e; s, scutellum separating embryo from
+    endosperm; f.l, foliage leaf; p.s, sheath of plumule; p.r, primary
+    root; s.p.r, sheath of primary root.
+
+    FIG. 23.--Fruit of Comfrey (_Symphytum_) surrounded by persistent
+    calyx, c. The style s appears to arise from the base of the carpels,
+    enlarged.
+
+    FIG. 24.--Ovary of _Foeniculum officinale_ with pendulous ovules, in
+    longitudinal section. (After Berg and Schmidt, magnified.)
+
+    From Strasburger's _Lehrbuch der Botanik_, by permission of Gustav
+    Fischer.
+
+    FIG. 25.--Fruit of _Carum Carui_. A, Ovary of the flower; B, ripe
+    fruit. The two carpels have separated so as to form two mericarps
+    (m). Part of the septum constitutes the carpophore (a). p, Top of
+    flower-stalk; d, disk on top of ovary; n, stigma.
+
+    From Vines' _Students' Text-Book of Botany_, by permission of Swan
+    Sonnenschein & Co.]
+
+
+    Forms of fruit.
+
+  Simple fruits have either a _dry_ or _succulent_ pericarp. The
+  _achene_ is a dry, one-seeded, indehiscent fruit, the pericarp of
+  which is closely applied to the seed, but separable from it. It is
+  solitary, forming a single fruit, as in the dock (fig. 19) and in the
+  cashew, where it is supported on a fleshy peduncle; or _aggregate_, as
+  in _Ranunculus_ (fig. 20), where several achenes are placed on a
+  common elevated receptacle. In the strawberry the achenes (fig. 2) are
+  aggregated on a convex succulent receptacle. In the rose they are
+  supported on a concave receptacle (fig. 3), and in the fig the
+  succulent receptacle completely encloses the achenes (fig. 4). In
+  _Dorstenia_ the achenes are situated on a flat or slightly concave
+  receptacle. Hence what in common language are called the seeds of the
+  strawberry, rose and fig, are in reality ripe carpels. The styles
+  occasionally remain attached to the achenes in the form of feathery
+  appendages, as in _Clematis_. In Compositae, the fruit is an inferior
+  achene (_cypsela_), to which the pappus (modified calyx) remains
+  adherent. Such is also the nature of the fruit in Dipsacaceae (e.g.
+  scabious). When the pericarp is thin, and appears like a bladder
+  surrounding the seed, the achene is termed a _utricle_, as in
+  Amarantaceae. When the pericarp is extended in the form of a winged
+  appendage, a _samara_ or _samaroid achene_ is produced, as in the ash
+  (fig. 1) and common sycamore (fig. 21). In these cases there are
+  usually two achenes united, one of which, however, as in _Fraxinus_
+  (fig. 1), may be abortive. The wing surrounds the fruit longitudinally
+  in the elm. When the pericarp becomes so incorporated with the seed as
+  to be inseparable from it, as in grains of wheat (fig. 22), maize,
+  oats and other grasses, then the name _caryopsis_ is given. The
+  one-seeded portions (mericarps) of schizocarps often take the form of
+  achenes, e.g. the mericarps of the mallows or of umbellifers (figs.
+  24, 25). In Labiatae and Boraginaceae (e.g. comfrey, fig. 23), where
+  the bicarpellary ovary becomes our one-seeded portions in the fruit,
+  the partial fruits are of the nature of achenes or nutlets according
+  to the texture (leathery or hard) of the pericarp.
+
+  [Illustration: From Strasburger's _Lehrbuch der Botanik_, by
+  permission of Gustav Fischer.
+
+    FIG. 26.--Cupule of _Quercus Aegilops_. cp, cupule; gl, fruit.
+    (After Duchartre.)]
+
+  The _nut_ or _glans_ is a dry one-celled indehiscent fruit with a
+  hardened pericarp, often surrounded by bracts at the base, and, when
+  mature, containing only one seed. In the young state the ovary often
+  contains two or more ovules, but only one comes to maturity. It is
+  illustrated by the fruits of the hazel and chestnut, which are covered
+  by leafy bracts, in the form of a _husk_, and by the acorn, in which
+  the bracts and receptacle form a _cupula_ or _cup_ (fig. 26). The
+  parts of the pericarp of the nut are united so as to appear one. In
+  common language the term nut is very vaguely applied both to fruit and
+  seeds.
+
+  The _drupe_ is a succulent usually one-seeded indehiscent fruit, with
+  a pericarp easily distinguishable into epicarp, mesocarp and endocarp.
+  This term is applied to such fruits as the cherry (fig. 5), peach,
+  plum, apricot or mango. The endocarp is usually hard, forming the
+  stone (putamen) of the fruit, which encloses the kernel or seed. The
+  mesocarp is generally pulpy and succulent, so as to be truly a
+  sarcocarp, as in the peach, but it is sometimes of a tough texture, as
+  in the almond, and at other times is more or less fibrous, as in the
+  coco-nut. In the almond there are often two ovules formed, only one of
+  which comes to perfection. In the raspberry and bramble several small
+  drupes or _drupels_ are aggregated so as to constitute an _etaerio_.
+
+  The _follicle_ is a dry unilocular many-seeded fruit, formed from one
+  carpel and dehiscing by the ventral suture. It is rare to meet with a
+  solitary follicle forming the fruit. There are usually several
+  aggregated together, either in a whorl on a shortened receptacle, as
+  in hellebore, aconite, larkspur, columbine (figs. 27, 28) or the order
+  Crassulaceae, or in a spiral manner on an elongated receptacle, as in
+  _Magnolia_ and _Banksia_. Occasionally, follicles dehisce by the
+  dorsal suture, as in _Magnolia grandiflora_ and _Banksia_.
+
+  [Illustration:
+
+    FIG. 27.--Fruit of Columbine (_Aquilegia_), formed of five
+    follicles.
+
+    FIG. 28.--Single follicle, showing dehiscence by the ventral suture.
+
+    FIG. 29.--Transverse section of berry of Gooseberry, showing the
+    seeds attached to the parietal placentas and immersed in pulp, which
+    is formed partly from the endocarp, partly from the seed-coat.
+
+    FIG. 30.--Section of the fruit of the Apple (_Pyrus Malus_), or
+    pome, consisting of a fleshy covering formed by the floral
+    receptacle and the true fruit or core with five cavities with
+    seeds.]
+
+  The _legume_ or _pod_ is a dry monocarpellary unilocular many-seeded
+  fruit, formed from one carpel, dehiscing both by the ventral and the
+  dorsal suture. It characterizes leguminous plants, as the bean and pea
+  (fig. 8). In the bladder-senna it forms an inflated legume. In some
+  Leguminosae, as _Arachis_, _Cathartocarpus Fistula_ and the tamarind,
+  the fruit must be considered a legume, although it does not dehisce.
+  The first of these plants produces its fruit underground, and is
+  called earth-nut; the second has a partitioned legume and is
+  schizocarpic; and both the second and third have pulpy matter
+  surrounding the seeds. Some legumes are schizocarpic by the formation
+  of constrictions externally. Such a form is the _lomentum_ or
+  _lomentaceous legume_ of _Hedysarum_ (fig. 17), _Coronilla_,
+  _Ornithopus_, _Entada_ and of some Acacias. In _Medicago_ the legume
+  ~~ is twisted like a snail, and in _Caesalpinia coriaria_, or
+  Divi-divi, it is vermiform or curved like a worm. Sometimes the number
+  of seeds is reduced, as in _Erythrina monosperma_ and _Geoffroya
+  superba_, which are one-seeded, and in _Pterocarpus_ and _Dalbergia_,
+  which are two-seeded.
+
+  [Illustration: FIG. 31.--Transverse section of the fruit of the Melon
+  (_Cucumis Melo_), showing the placentas with the seeds attached to
+  them. The three carpels forming the pepo are separated by partitions.
+  From the centre processes pass outwards, ending in the curved
+  placenta.
+
+  The _berry_ (_bacca_) is a term applied generally to all fruits with
+  seeds immersed in pulp, and includes fruits of very various origin. In
+  _Actaea_ (baneberry) or _Berberis_ (barberry) it is derived from a
+  single free carpel; generally, however, it is the product of a
+  syncarpous ovary, which is superior, as in grape or potato, or
+  inferior, as in gooseberry (fig. 29) or currant. In the pomegranate
+  there is a peculiar baccate many-celled inferior fruit, having a tough
+  rind, enclosing two rows of carpels placed one above the other. The
+  seeds are immersed in pulp, and are attached irregularly to the wall,
+  base and centre of the loculi. In the baobab there is a multilocular
+  syncarpous fruit, in which the seeds are immersed in pulp.
+
+  The _pepo_, another indehiscent syncarpous fruit, is illustrated by
+  the fruit of the gourd, melon (fig. 31) and other Cucurbitaceae. It is
+  formed of three carpels, surmounted by the calyx; the rind is thick
+  and fleshy, and there are three or more seed-bearing parietal
+  placentas, either surrounding a central cavity or prolonged inwards
+  into it. The fruit of the papaw resembles the pepo, but the calyx is
+  not superior.
+
+  The _hesperidium_ is the name given to such indehiscent fleshy
+  syncarpous fruits as the orange, lemon and shaddock, in which the
+  epicarp and mesocarp form a separable rind, and the endocarp sends
+  prolongations inwards, forming triangular divisions, to the inner
+  angle of which the seeds are attached, pulpy cells being developed
+  around them from the wall. Both pepo and hesperidium may be considered
+  as modifications of the berry.
+
+  The _pome_ (fig. 30), seen in the apple, pear, quince, medlar and
+  hawthorn, is a fleshy indehiscent syncarpous fruit, in the formation
+  of which the receptacle takes part. The outer succulent part is the
+  swollen receptacle, the horny core being the true fruit developed from
+  the usually five carpels and enclosing the seeds. In the medlar the
+  core (or true pericarp) is of a stony hardness, while the outer
+  succulent covering is open at the summit. The pome somewhat resembles
+  the fruit of the rose (fig. 3), where the succulent receptacle
+  surrounds a number of separate achenes.
+
+  The name _capsule_ is applied generally to all dry syncarpous fruits,
+  which dehisce by valves. It may thus be unilocular or multilocular,
+  one- or many-seeded. The true valvular capsule is observed in
+  _Colchicum_ (fig. 9), lily and iris (fig. 11). The _porose capsule_ is
+  seen in the poppy (fig. 7), _Antirrhinum_ and _Campanula_. In
+  _Campanula_ the pores occur at the base of the capsule, which becomes
+  inverted when ripe. When the capsule opens by a lid, or by
+  circumscissile dehiscence, it is called a _pyxidium_, as in pimpernel
+  (_Anagallis arvensis_) (fig. 16), henbane and monkey-pot (_Lecythis_).
+  The capsule assumes a screw-like form in _Helicteres_, and a star-like
+  form in star-anise (_Illicium anisatum_). In certain instances the
+  cells of the capsule separate from each other, and open with
+  elasticity to scatter the seeds. This kind of capsule is met with in
+  the sandbox tree (_Hura crepitans_) and other Euphorbiaceae, where the
+  cocci, containing each a single seed, burst asunder with force; and in
+  Geraniaceae, where the cocci, each containing, when mature, usually
+  one seed, separate from the carpophore, become curved upwards by their
+  adherent styles, and open by the ventral suture (fig. 18).
+
+  The _siliqua_ is a dry syncarpous bilocular many-seeded fruit, formed
+  from two carpels, with a false septum, dehiscing by two valves from
+  below upwards, the valves separating from the placentas and leaving
+  them united by the septum (fig. 32). The seeds are attached on both
+  sides of the septum, either in one row or in two. When the fruit is
+  long and narrow it is a _siliqua_ (fig. 14); when broad and short,
+  _silicula_ (fig. 33). It occurs in cruciferous plants, as wallflower,
+  cabbage and cress. In _Glaucium_ and _Eschscholtzia_ (Papaveraceae)
+  the dissepiment is of a spongy nature. It may become transversely
+  constricted (_lomentaceous_), as in radish (_Raphanus_) and sea-kale,
+  and it may be reduced, as in woad (_Isatis_), to a one-seeded
+  condition.
+
+  It sometimes happens that the ovaries of two flowers unite so as to
+  form a double fruit (_syncarp_). This may be seen in many species of
+  honeysuckle. But the fruits which are now to be considered consist
+  usually of the floral envelopes, as well as the ovaries of several
+  flowers united into one, and are called _multiple_ or _confluent_. The
+  term _anthocarpous_ has also been applied as indicating that the
+  floral envelopes as well as the carpels are concerned in the formation
+  of the fruit.
+
+  The _sorosis_ is a succulent multiple fruit formed by the confluence
+  of a spike of flowers, as in the fruit of the pine-apple (fig. 34),
+  the bread-fruit and jack-fruit. Similarly the fruit of the mulberry
+  represents a catkin-like inflorescence.
+
+  The _syconus_ is an anthocarpous fruit, in which the receptacle
+  completely encloses numerous flowers and becomes succulent. The fig
+  (fig. 4) is of this nature, and what are called its seeds are the
+  achenes of the numerous flowers scattered over the succulent hollowed
+  receptacle. In _Dorstenia_ the axis is less deeply hollowed, and of a
+  harder texture, the fruit exhibiting often very anomalous forms.
+
+  The _strobilus_, or _cone_, is a seed-bearing spike, more or less
+  elongated, covered with scales, each of which may be regarded as
+  representing a separate flower, and has often two seeds at its base;
+  the seeds are naked, no ovary being present. This fruit is seen in the
+  cones of firs, spruces, larches and cedars, which have received the
+  name of Coniferae, or cone-bearers, on this account. Cone-like fruit
+  is also seen in most Cycadaceae. The scales of the strobilus are
+  sometimes thick and closely united, so as to form a more or less
+  angular and rounded mass, as in the cypress; while in the juniper they
+  become fleshy, and are so incorporated as to form a globular fruit
+  like a berry. The dry fruit of the cypress and the succulent fruit of
+  the juniper have received the name of _galbulus_. In the hop the fruit
+  is called also a strobilus, but in it the scales are thin and
+  membranous, and the seeds are not naked but are contained in
+  pericarps.
+
+  [Illustration:
+
+    FIG. 32.--Honesty (_Lunaria biennis_), showing the septum after the
+    carpels have fallen away.
+
+    From Strasburger's _Lehrbuch der Botanik_, by permission of Gustav
+    Fischer.
+
+    FIG. 33.--Silicula or pouch of shepherd's purse (_Capsella_),
+    opening by two folded valves, which separate from above downwards.
+    The partition is narrow, hence the silicula is angustiseptal.
+
+    From Strasburger's _Lehrbuch der Botanik_, by permission of Gustav
+    Fischer.
+
+    FIG. 34.--Fruit of the pine-apple (_Ananassa sativa_), developed
+    from a spike of numerous flowers with bracts, united so as to form a
+    collective or anthocarpous fruit. The crown of the pine-apple, c,
+    consists of a series of empty bracts prolonged beyond the fruit.]
+
+  The same causes which produce alterations in the other parts of the
+  flower give rise to anomalous appearances in the fruit. The carpels,
+  in place of bearing seeds, are sometimes changed into leaves, with
+  lobes at their margins. Leaves are sometimes produced from the upper
+  part of the fruit. In the genus _Citrus_, to which the orange and
+  lemon belong, it is very common to meet with a separation of the
+  carpels, so as to produce what are called horned oranges and fingered
+  citrons. In this case a syncarpous fruit has a tendency to become
+  apocarpous. In the orange we occasionally find a supernumerary row of
+  carpels produced, giving rise to the appearance of small and imperfect
+  oranges enclosed within the original one; the navel orange is of this
+  nature. It sometimes happens that, by the union of flowers, double
+  fruits are produced. Occasionally a double fruit is produced, not by
+  the incorporation of two flowers, but by the abnormal development of a
+  second carpel in the flower.
+
+    _Arrangement of Fruits._
+
+    A. True fruits--developed from the ovary alone.
+        1. Pericarp not fleshy or fibrous.
+            i. Indehiscent--not opening to allow the escape of the
+                seeds--generally one-seeded. Achene; caryopsis; cypsela;
+                nut; schizocarp.
+            ii. Dehiscent--the pericarp splits to allow the escape of the
+                seeds--generally many-seeded. Follicle; legume; siliqua;
+                capsule.
+        2. Pericarp generally differentiated into distinct layers, one
+            of which is succulent or fibrous. Drupe; berry.
+    B. Pseudocarps--the development extends beyond the ovary. Pome;
+    syconus; sorosis.
+
+  _The Seed._--The _seed_ is formed from the ovule as the result of
+  fertilization. It is contained in a seed-vessel formed from the ovary
+  in the plants called _angiospermous_; while in _gymnospermous_
+  plants, such as Coniferae and Cycadaceae, it is naked, or, in other
+  words, has no true pericarp. It sometimes happens in Angiosperms, that
+  the seed-vessel is ruptured at an early period of growth, so that the
+  seeds become more or less exposed during their development; this
+  occurs in mignonette, where the capsule opens at the apex, and in
+  _Cuphea_, where the placenta bursts through the ovary and floral
+  envelopes, and appears as an erect process bearing the young seeds.
+  After fertilization the ovule is greatly changed, in connexion with
+  the formation of the embryo. In the embryo-sac of most Angiosperms
+  (q.v.) there is a development of cellular tissue, the endosperm, more
+  or less filling the embryo-sac. In Gymnosperms (q.v.) the endosperm is
+  formed preparatory to fertilization. The fertilized egg enlarges and
+  becomes multicellular, forming the embryo. The embryo-sac enlarges
+  greatly, displacing gradually the surrounding nucellus, which
+  eventually forms merely a thin layer around the sac, or completely
+  disappears. The remainder of the nucellus and the integuments of the
+  ovules form the seed-coats. In some cases (fig. 35) a delicate inner
+  coat or _tegmen_ can be distinguished from a tougher outer coat or
+  _testa_; often, however, the layers are not thus separable. The
+  consistency of the seed-coat, its thickness, the character of its
+  surface, &c., vary widely, the variations being often closely
+  associated with the environment or with the means of seed-dispersal.
+  An account of the development of the seed from the ovule will be found
+  in the article ANGIOSPERMS. When the pericarp is dehiscent the
+  seed-covering is of a strong and often rough character; but when the
+  pericarp is indehiscent and encloses the seed for a long period, the
+  outer seed-coat is thin and soft. The cells of the testa are often
+  coloured, and have projections and appendages of various kinds. Thus
+  in _Abrus precatorius_ and _Adenanthera pavonina_ it is of a bright
+  red colour; in French beans it is beautifully mottled; in the almond
+  it is veined; in the tulip and primrose it is rough; in the snapdragon
+  it is marked with depressions; in cotton and _Asclepias_ (fig. 36) it
+  has hairs attached to it; and in mahogany, _Bignonia_, and the pines
+  and firs it is expanded in the form of wing-like appendages (fig. 37).
+  In _Collomia_, _Acanthodium_, _Cobaea scandens_ and other seeds, it
+  contains spiral cells, from which, when moistened with water, the
+  fibres uncoil in a beautiful manner; and in flax (_Linum_) and others
+  the cells are converted into mucilage. These structural peculiarities
+  of the testa in different plants have relation to the scattering of
+  the seed and its germination upon a suitable nidus. But in some plants
+  the pericarps assume structures which subserve the same purpose; this
+  especially occurs in small pericarps enclosing single seeds, as
+  achenes, caryopsides, &c. Thus in Compositae and valerian, the pappose
+  limb of the calyx forms a parachute to the pericarp; in Labiatae and
+  some Compositae spiral cells are formed in the epicarp; and the
+  epicarp is prolonged as a wing in _Fraxinus_ (fig. 1) and _Acer_ (fig.
+  21).
+
+  [Illustration:
+
+    FIG. 35.--Seed of Pea (_Pisum_) with one cotyledon removed. c,
+    Remaining cotyledon; ch, chalaza-point at which the nourishing
+    vessels enter; e, tegmen or inner coat; f, funicle or stalk; g,
+    plumule of embryo; m, micropyle; pl, placenta; r, radicle of embryo;
+    t, tigellum or stalk between root and plumule; te, testa.
+
+    FIG. 36.--Seed of _Asclepias_, with a cluster of hairs arising from
+    the edges of the micropyle.]
+
+  Sometimes there is an additional covering to the seed, formed after
+  fertilization, to which the name _arillus_ has been given (fig. 38).
+  This is seen in the passion-flower, where the covering arises from the
+  placenta or extremity of the funicle at the base of the ovule and
+  passes upwards towards the apex, leaving the micropyle uncovered. In
+  the nutmeg and spindle tree this additional coat is formed from above
+  downwards, constituting in the former case a laciniated scarlet
+  covering called _mace_. In such instances it has been called an
+  _arillode_ (fig. 39). This arillode, after growing downwards, may be
+  reflected upwards so as to cover the micropyle. The fleshy scarlet
+  covering formed around the naked seed in the yew is by some considered
+  of the nature of an aril. On the testa, at various points, there are
+  produced at times other cellular bodies, to which the name of
+  _strophioles_, or _caruncles_, has been given, the seeds being
+  strophiolate or carunculate. These tumours may occur near the base of
+  the seed, as in _Polygala_, or at the apex, as in Castor-oil plant
+  (_Ricinus_); or they may occur in the course of the raphe, as in
+  blood-root (_Sanguinaria_) and _Asarabacca_. The funicles of the
+  ovules frequently attain a great length in the seed, and in some
+  magnolias, when the fruit dehisces, they appear as long scarlet cords
+  suspending the seeds outside. The hilum or umbilicus of the seed is
+  usually well marked, as a scar of varying size; in the calabar bean
+  and in some species of Mucuna and Dolichos it extends along a large
+  portion of the edge of the seed; it frequently exhibits marked
+  colours, being black in the bean, white in many species of Phaseolus,
+  &c. The micropyle (fig. 35, m) of the seed may be recognizable by the
+  naked eye, as in the pea and bean tribe, _Iris_, &c., or it may be
+  very minute or microscopic. It indicates the true apex of the seed,
+  and is important as marking the point to which the root of the embryo
+  is directed. At the micropyle in the bean is observed a small process
+  of integument, which, when the young plant sprouts, is pushed up like
+  a lid; it is called the _embryotega_. The chalaza (fig. 38, ch) is
+  often of a different colour from the rest of the seed. In the orange
+  (fig. 40) it is of a reddish-brown colour, and is easily recognized at
+  one end of the seed when the integuments are carefully removed. In
+  anatropal seeds the raphe forms a distinct ridge along one side of the
+  seed (fig. 41).
+
+  The position of the seed as regards the pericarp resembles that of the
+  ovule in the ovary, and the same terms are applied--erect, ascending,
+  pendulous, suspended, curved, &c. These terms have no reference to the
+  mode in which the fruit is attached to the axis. Thus the seed may be
+  erect while the fruit itself is pendent, in the ordinary meaning of
+  that term. The part of the seed next the axis or the ventral suture is
+  its face, the opposite side being the back. Seeds exhibit great
+  varieties of form. They may be flattened laterally (_compressed_), or
+  from above downwards (_depressed_). They may be round, oval,
+  triangular, polygonal, rolled up like a snail, as in _Physostemon_, or
+  coiled up like a snake, as in _Ophiocaryon paradoxum_.
+
+  [Illustration:
+
+    FIG. 37.--Seed of Pine (_Pinus_), with a membranous appendage w to
+    the testa, called a wing.
+
+    FIG. 38.--Young anatropal seed of the white Water-lily (_Nymphaea
+    alba_), cut vertically. It is attached to the placenta by the
+    funicle f, cellular prolongations from which form an aril a a. The
+    vessels of the cord are prolonged to the base of the nucellus n by
+    means of the raphe r. The base of the nucellus is indicated by the
+    chalaza ch, while the apex is at the micropyle m. The covering of
+    the seed is marked i. n is the nucellus or perisperm, enclosing the
+    embryo-sac es, in which the endosperm is formed. The embryo e, with
+    its suspensor, is contained in the sac, the radicle pointing to the
+    micropyle m.
+
+    FIG. 39.--Arillode a, or false aril, of the Spindle-tree
+    (_Euonymus_), arising from the micropyle f.
+
+    FIG. 40.--Anatropal seed of the Orange (_Citrus Aurantium_) opened
+    to show the chalaza c, which forms a brown spot at one end.
+
+    FIG. 41.--Entire anatropal seed of the Orange (_Citrus Aurantium_),
+    with its rugose or wrinkled testa, and the raphe r ramifying in the
+    thickness of the testa on one side.]
+
+  The endosperm formed in the embryo-sac of angiosperms after
+  fertilization, and found previous to it in gymnosperms, consists of
+  cells containing nitrogenous and starchy or fatty matter, destined for
+  the nutriment of the embryo. It occupies the whole cavity of the
+  embryo-sac, or is formed only at certain portions of it, at the apex,
+  as in _Rhinanthus_, at the base, as in _Vaccinium_, or in the middle,
+  as in _Veronica_. As the endosperm increases in size along with the
+  embryo-sac and the embryo, the substance of the original nucellus of
+  the ovule is gradually absorbed. Sometimes, however, as in Musaceae,
+  Cannaceae, Zingiberaceae, no endosperm is formed; the cells of the
+  original nucellus, becoming filled with food-materials for the embryo,
+  are not absorbed, but remain surrounding the embryo-sac with the
+  embryo, and constitute the _perisperm_. Again, in other plants, as
+  Nymphaeaceae (fig. 38) and Piperaceae, both endosperm and perisperm
+  are present. It was from observations on cases such as these that old
+  authors, imagining a resemblance betwixt the plant-ovule and the
+  animal ovum, applied the name _albumen_ to the outer nutrient mass or
+  perisperm, and designated the endosperm as _vitellus_. The term
+  albumen is very generally used as including all the nutrient matter
+  stored up in the seed, but it would be advisable to discard the name
+  as implying a definite chemical substance. There is a large class of
+  plants in which although at first after fertilization a mass of
+  endosperm is formed, yet, as the embryo increases in size, the
+  nutrient matter from the endospermic cells passes out from them, and
+  is absorbed by the cells of the embryo plant. In the mature seed, in
+  such cases, there is no separate mass of tissue containing nutrient
+  food-material apart from the embryo itself. Such a seed is said to be
+  _exalbuminous_, as in Compositae, Cruciferae and most Leguminosae
+  (e.g. pea, fig. 35). When either endosperm or perisperm or both are
+  present the seed is said to be _albuminous_.
+
+  [Illustration: FIG. 42.--The dicotyledonous embryo of the Pea laid
+  open. c, c, The two fleshy cotyledons, or seed-lobes, which remain
+  under ground when the plant sprouts; r, the radicular extremity of the
+  axis whence the root arises; t, the axis (hypocotyl) bearing the young
+  stalk and leaves g (plumule), which lie in a depression of the
+  cotyledons f.]
+
+  The albumen varies much in its nature and consistence, and furnishes
+  important characters. It may be farinaceous or mealy, consisting
+  chiefly of cells filled with starch, as in cereal grains, where it is
+  abundant; fleshy or cartilaginous, consisting of thicker cells which
+  are still soft, as in the coco-nut, and which sometimes contain oil,
+  as in the oily albumen of _Croton_, _Ricinus_ and poppy; horny, when
+  the cell-walls are slightly thickened and capable of distension, as in
+  date and coffee; the cell-walls sometimes become greatly thickened,
+  filling up the testa as a hard mass, as in vegetable ivory
+  (_Phytelephas_). The albumen may be uniform throughout, or it may
+  present a mottled appearance, as in the nutmeg, the seeds of Anonaceae
+  and some Palms, where it is called _ruminated_. This mottled
+  appearance is due to a protrusion of a dark lamella of the integument
+  between folded protuberances of albumen. A cavity is sometimes left in
+  the centre which is usually filled with fluid, as in the coco-nut. The
+  relative size of the embryo and of the endosperm varies much. In
+  Monocotyledons the embryo is usually small, and the endosperm large,
+  and the same is true in the case of coffee and many other plants
+  amongst Dicotyledons. The opposite is the case in other plants, as in
+  the Labiatae, Plumbaginaceae, &c.
+
+  The embryo consists of an axis bearing the _cotyledons_ (fig. 42, c),
+  or the first leaves of the plant. To that part of this axis
+  immediately beneath the cotyledons the terms _hypocotyl_, _caulicle_
+  or _tigellum_ (t) have been applied, and continuous backwards with it
+  is the young root or _radicle_ (r), the descending axis, their point
+  of union being the collar or neck. The terminal growing bud of the
+  axis is called the _plumule_ or _gemmule_ (g), and represents the
+  ascending axis. The radicular extremity points towards the micropyle,
+  while the cotyledonary extremity is pointed towards the base of the
+  ovule or the chalaza. Hence, by ascertaining the position of the
+  micropyle and chalaza, the two extremities of the embryo can in
+  general be discovered. It is in many cases difficult to recognize the
+  parts in an embryo; thus in _Cuscuta_, the embryo appears as an
+  elongated axis without divisions; and in _Caryocar_ the mass of the
+  embryo is made up by the radicular extremity and hypocotyl, in a
+  groove of which the cotyledonary extremity lies embedded (fig. 52). In
+  some monocotyledonous embryos, as in Orchidaceae, the embryo is a
+  cellular mass showing no parts. In parasitic plants also which form no
+  chlorophyll, as _Orobanche_, _Monotropa_, &c., the embryo remains
+  without differentiation, consisting merely of a mass of cells until
+  the ripening of the seed. When the embryo is surrounded by the
+  endosperm on all sides except its radicular extremity it is internal
+  (see figs. 19, 20); when lying outside the endosperm, and only coming
+  into contact with it at certain points, it is external, as in grasses
+  (e.g. wheat, fig. 22). When the embryo follows the direction of the
+  axis of the seed, it is axile or axial (fig. 43); when it is not in
+  the direction of the axis, it becomes abaxile or abaxial. In
+  campylotropal seeds the embryo is curved, and in place of being
+  embedded in endosperm, is frequently external to it, following the
+  concavity of the seed (fig. 44), and becoming peripherical, with the
+  chalaza situated in the curvature of the embryo, as in
+  Caryophyllaceae.
+
+  It has been already stated that the radicle of the embryo is directed
+  to the micropyle, and the cotyledons to the chalaza. In some cases, by
+  the growth of the integuments, the former is turned round so as not to
+  correspond with the apex of the nucellus, and then the embryo has the
+  radicle directed to one side, and is called excentric, as is seen in
+  Primulaceae, Plantaginaceae and many palms, especially the date. The
+  position of the embryo in different kinds of seeds varies. In an
+  orthotropal seed the embryo is inverted or _antitropal_, the radicle
+  pointing to the apex of the seed, or to the part opposite the hilum.
+  Again, in an anatropal seed the embryo is erect or _homotropal_ (fig.
+  43), the radicle being directed to the base of the seed. In curved or
+  campylotropal seeds the embryo is folded so that its radicular and
+  cotyledonary extremities are approximated, and it becomes
+  _amphitropal_ (fig. 44). In this instance the seed may be
+  exalbuminous, and the embryo may be folded on itself; or albuminous,
+  the embryo surrounding more or less completely the endosperm and being
+  peripherical. According to the mode in which the seed is attached to
+  the pericarp, the radicle may be directed upwards or downwards, or
+  laterally, as regards the ovary. In an orthotropal seed attached to
+  the base of the pericarp it is superior, as also in a suspended
+  anatropal seed. In other anatropal seeds the radicle is inferior. When
+  the seed is horizontal as regards the pericarp, the radicle is either
+  centrifugal, when it points to the outer wall of the ovary; or
+  centripetal, when it points to the axis or inner wall of the ovary.
+  These characters are of value for purposes of classification, as they
+  are often constant in large groups of genera.
+
+  Plants in which there are two cotyledons produced in the embryo are
+  _dicotyledonous_. The two cotyledons thus formed are opposite to each
+  other (figs. 42 and 45), but are not always of the same size. Thus, in
+  Abronia and other members of the order Nyctaginaceae, one of them is
+  smaller than the other (often very small), and in _Carapa guianensis_
+  there appears to be only one, in consequence of the intimate union
+  which takes place between the two. The union between the cotyledonary
+  leaves may continue after the young plant begins to germinate. Such
+  embryos have been called _pseudomonocotyledonous_. The texture of the
+  cotyledons varies. They may be thick, as in the pea (fig. 42),
+  exhibiting no traces of venation, with their flat internal surfaces in
+  contact, and their backs more or less convex; or they may be in the
+  form of thin and delicate laminae, flattened on both sides, and having
+  distinct venation, as in _Ricinus_, _Jatropha_, _Euonymus_, &c. The
+  cotyledons usually form the greater part of the mature embryo, and
+  this is remarkably well seen in such exalbuminous seeds as the bean
+  and pea.
+
+  [Illustration:
+
+    FIG. 43.--Seed of Pansy (_Viola tricolor_) cut vertically. The
+    embryo pl is axial, in the midst of fleshy endosperm al. The seed is
+    anatropal, and the embryo is homotropal; the cotyledons co point to
+    the base of the nucellus or chalaza ch, while the radicle, or the
+    other extremity of the embryo, points to the micropyle, close to the
+    hilum h. The hilum or base of the seed, and the chalaza or base of
+    the nucellus are united by means of the raphe r.
+
+    FIG. 44.--Seed of the Red Campion (_Lychnis_), cut vertically,
+    showing the peripheral embryo, with its two cotyledons and its
+    radicle. The embryo is curved round the albumen, so that its
+    cotyledons and radicle both come near the hilum (_amphitropal_).
+
+    FIG. 45.--Mature dicotyledonous embryo of the Almond, with one of
+    the cotyledons removed. r, Radicle; t, young stem or caulicle; c,
+    one of the cotyledons left; i, line of insertion of the cotyledon
+    which has been removed; g, plumule.
+
+    FIG. 46.--Exalbuminous seed of Wallflower (Cheiranthus) cut
+    vertically. The radicle r is folded on the edges of the cotyledons c
+    which are accumbent.
+
+    FIG. 47.--Transverse section of the seed of the Wallflower
+    (_Cheiranthus_), showing the radicle r folded on the edges of the
+    accumbent cotyledons c.
+
+    FIG. 48.--Transverse section of the seed of the Dame's Violet
+    (_Hesperis_). The radicle r is folded on the back of the cotyledons
+    c, which are said to be incumbent.]
+
+  Cotyledons are usually entire and sessile. But they occasionally
+  become lobed, as in the walnut and the lime; or petiolate, as in
+  _Geranium molle_; or auriculate, as in the ash. Like leaves in the
+  bud, cotyledons may be either applied directly to each other, or may
+  be folded in various ways. In geranium the cotyledons are twisted and
+  doubled; in convolvulus they are corrugated; and in the potato and in
+  _Bunias_, they are spiral,--the same terms being applied as to the
+  foliage leaves. The radicle and cotyledons are either straight or
+  variously curved. Thus, in some cruciferous plants, as the wallflower,
+  the cotyledons are applied by their faces, and the radicle (figs. 46,
+  47) is folded on their edges, so as to be lateral; the cotyledons are
+  here _accumbent_. In others, as _Hesperis_, the cotyledons (fig. 48)
+  are applied to each other by their faces, and the radicle, r, is
+  folded on their back, so as to be dorsal, and the cotyledons are
+  _incumbent_. Again, the cotyledons are _conduplicate_ when the radicle
+  is dorsal, and enclosed between their folds. In other divisions the
+  radicle is folded in a spiral manner, and the cotyledons follow the
+  same course.
+
+  In many gymnosperms more than two cotyledons are present, and they are
+  arranged in a whorl. This occurs in Coniferae, especially in the pine,
+  fir (fig. 49), spruce and larch, in which six, nine, twelve and even
+  fifteen have been observed. They are linear, and resemble in their
+  form and mode of development the clustered or fasciculated leaves of
+  the larch. Plants having numerous cotyledons are termed
+  _polycotyledonous_. In species of _Streptocarpus_ the cotyledons are
+  permanent, and act the part of leaves. One of them is frequently
+  largely developed, while the other is small or abortive.
+
+  [Illustration:
+
+    FIG. 49.--Polycotylodonous embryo of the Pine (_Pinus_) beginning to
+    sprout. t, Hypocotyl; r, radicle. The cotyledons c are numerous.
+    Within the cotyledons the primordial leaves are seen, constituting
+    the plumule or first bud of the plant.
+
+    FIG. 50.--Embryo of a species of Arrow-grass (_Triglochin_), showing
+    a uniform conical mass, with a slit s near the lower part. The
+    cotyledon c envelops the young bud, which protrudes at the slit
+    during germination. The radicle is developed from the lower part of
+    the axis r.
+
+    FIG. 51.--Grain of wheat (_Triticum_) germinating, showing (b) the
+    cotyledon and (c) the rootlets surrounded by their sheaths
+    (_coleorrhizae_).
+
+    FIG. 52.--Embryo of _Caryocar_. t, Thick hypocotyl, forming nearly
+    the whole mass, becoming narrowed and curved at its extremity, and
+    applied to the groove s. In the figure this narrowed portion is
+    slightly separated from the groove; c, two rudimentary cotyledons.]
+
+  In those plants in which there is only a single cotyledon in the
+  embryo, hence called _monocotyledonous_, the embryo usually has a
+  cylindrical form more or less rounded at the extremities, or elongated
+  and fusiform, often oblique. The axis is usually very short compared
+  with the cotyledon, which in general encloses the plumule by its lower
+  portion, and exhibits on one side a small slit which indicates the
+  union of the edges of the vaginal or sheathing portion of the leaf
+  (fig. 50). In grasses, by the enlargement of the embryo in a
+  particular direction, the endosperm is pushed on one side, and thus
+  the embryo comes to lie outside at the base of the endosperm (figs.
+  22, 51). The lamina of the cotyledon is not developed. Upon the side
+  of the embryo next the endosperm and enveloping it is a large
+  shield-shaped body, termed the _scutellum_. This is an outgrowth from
+  the base of the cotyledon, enveloping more or less the cotyledon and
+  plumule, in some cases, as in maize, completely investing it; in other
+  cases, as in rice, merely sending small prolongations over its
+  anterior face at the apex. By others this scutellum is considered as
+  the true cotyledon, and the sheathing structure covering the plumule
+  is regarded as a ligule or axillary stipule (see GRASSES). In many
+  aquatic monocotyledons (e.g. _Potamogeton_, _Ruppia_ and others) there
+  is a much-developed hypocotyl, which forms the greater part of the
+  embryo and acts as a store of nutriment in germination; these are
+  known as _macropodous_ embryos. A similar case is that of _Caryocar_
+  among Dicotyledons, where the swollen hypocotyl occupies most of the
+  embryo (fig. 52). In some grasses, as oats and rice, a projection of
+  cellular tissue is seen upon the side of the embryo opposite to the
+  scutellum, that is, on the anterior side. This has been termed the
+  _epiblast_. It is very large in rice. This by some was considered the
+  rudimentary second cotyledon; but is now generally regarded as an
+  outgrowth of the sheath of the true cotyledon.     (A. B. R.)
+
+
+
+
+FRUIT AND FLOWER FARMING. The different sorts of fruits and flowers are
+dealt with in articles under their own headings, to which reference may
+be made; and these give the substantial facts as to their cultivation.
+See also the article HORTICULTURE.
+
+
+TABLE I.--_Extent of Orchards in Great Britain in each Year, 1887 to
+1901._
+
+  +------+---------++------+---------++------+---------+
+  | Year.|  Acres. || Year.|  Acres. || Year.|  Acres. |
+  +------+---------++------+---------++------+---------+
+  | 1887 | 202,234 || 1892 | 208,950 || 1897 | 224,116 |
+  | 1888 | 199,178 || 1893 | 211,664 || 1898 | 226,059 |
+  | 1889 | 199,897 || 1894 | 214,187 || 1899 | 228,603 |
+  | 1890 | 202,305 || 1895 | 218,428 || 1900 | 232,129 |
+  | 1891 | 209,996 || 1896 | 221,254 || 1901 | 234,660 |
+  +------+---------++------+---------++------+---------+
+
+
+TABLE II.--_Areas under Orchards in England, Wales and Scotland--Acres._
+
+  +------+----------+--------+---------+--------------+
+  | Year.| England. | Wales. |Scotland.|Great Britain.|
+  +------+----------+--------+---------+--------------+
+  | 1896 | 215,642  |  3677  |  1935   |   221,254    |
+  | 1897 | 218,261  |  3707  |  2148   |   224,116    |
+  | 1898 | 220,220  |  3690  |  2149   |   226,059    |
+  | 1899 | 222,712  |  3666  |  2225   |   228,603    |
+  | 1900 | 226,164  |  3695  |  2270   |   232,129    |
+  | 1901 | 228,580  |  3767  |  2313   |   234,660    |
+  | 1908 | 244,430  |  3577  |  2290   |   250,297    |
+  +------+----------+--------+---------+--------------+
+
+
+GREAT BRITAIN
+
+The extent of the fruit industry may be gathered from the figures for
+the acreage of land under cultivation in orchards and small fruit
+plantations. The Board of Agriculture returns concerning the orchard
+areas of Great Britain showed a continuous expansion year by year from
+199,178 acres in 1888 to 234,660 acres in 1901, as will be learnt from
+Table I. There was, it is true, an exception in 1892, but the decline in
+that year is explained by the circumstance that since 1891 the
+agricultural returns have been collected only from holdings of more than
+one acre, whereas they were previously obtained from all holdings of a
+quarter of an acre or more. As there are many holdings of less than an
+acre in extent upon which fruit is grown, and as fruit is largely raised
+also in suburban and other gardens which do not come into the returns,
+it may be taken for granted that the actual extent of land devoted to
+fruit culture exceeds that which is indicated by the official figures.
+In the Board of Agriculture returns up to June 1908, 308,000 acres are
+stated to be devoted to fruit cultivation of all kinds in Great Britain.
+Table II. shows that the expansion of the orchard area of Great Britain
+is mainly confined to England, for it has slightly decreased in Wales
+and Scotland. The acreage officially returned as under orchards is that
+of arable or grass land which is also used for fruit trees of any kind.
+Conditions of soil and climate determine the irregular distribution of
+orchards in Great Britain. The dozen counties which possess the largest
+extent of orchard land all lie in the south or west of the island.
+According to the returns for 1908 (excluding small fruit areas) they
+were the following:--
+
+  +----------+--------++-----------+--------++----------+------+
+  |  County. | Acres. ||  County.  | Acres. ||  County. |Acres.|
+  +----------+--------++-----------+--------++----------+------+
+  | Kent     | 32,751 || Worcester | 23,653 || Salop    | 4685 |
+  | Devon    | 27,200 || Gloucester| 20,424 || Dorset   | 4464 |
+  | Hereford | 28,316 || Cornwall  |  5,415 || Monmouth | 3914 |
+  | Somerset | 25,279 || Middlesex |  5,300 || Wilts    | 3630 |
+  +----------+--------++-----------+--------++----------+------+
+
+Leaving out of consideration the county of Kent, which grows a greater
+variety of fruit than any of the others, the counties of Devon,
+Hereford, Somerset, Worcester and Gloucester have an aggregate orchard
+area of 124,872 acres. These five counties of the west and south-west of
+England--constituting in one continuous area what is essentially the
+cider country of Great Britain--embrace therefore rather less than half
+of the entire orchard area of the island, while Salop, Monmouth and
+Wilts have about 300 less than they had a few years ago. Five English
+counties have less than 1000 acres each of orchards, namely, the county
+of London, and the northern counties of Cumberland, Westmorland,
+Northumberland and Durham. Rutland has just over 100 acres. The largest
+orchard areas in Wales are in the two counties adjoining
+Hereford--Brecon with 1136 acres and Radnor with 727 acres; at the other
+extreme is Anglesey, with a decreasing orchard area of only 22 acres. Of
+the Scottish counties, Lanark takes the lead with 1285 acres, Perth,
+Stirling and Haddington following with 684 and 129 acres respectively.
+Ayr and Midlothian are the only other counties possessing 100 acres or
+more of orchards, whilst Kincardine, Orkney and Shetland return no
+orchard area, and Banff, Bute, Kinross, Nairn, Peebles, Sutherland and
+Wigtown return less than 10 acres each. It may be added that in 1908
+Jersey returned 1090 acres of orchards, Guernsey, &c., 144 acres, and
+the Isle of Man, 121 acres; the two last-named places showing a decline
+as compared with eight years previously.
+
+Outside the cider counties proper of England, the counties in which
+orchards for commercial fruit-growing have increased considerably in
+recent years include Berks, Buckingham, Cambridge, Essex, Lincoln,
+Middlesex, Monmouth, Norfolk, Oxford, Salop, Sussex, Warwick and Wilts.
+Apples are the principal fruit grown in the western and south-western
+counties, pears also being fairly common. In parts of Gloucestershire,
+however, and in the Evesham and Pershore districts of Worcestershire,
+plum orchards exist. Plums are almost as largely grown as apples in
+Cambridgeshire. Large quantities of apples, plums, damsons, cherries,
+and a fair quantity of pears are grown for the market in Kent, whilst
+apples, plums and pears predominate in Middlesex. In many counties
+damsons are cultivated around fruit plantations to shelter the latter
+from the wind.
+
+Of small fruit (currants, gooseberries, strawberries, raspberries, &c.)
+no return was made of the acreage previous to 1888, in which year it was
+given as 36,724 acres for Great Britain. In 1889 it rose to 41,933
+acres.
+
+Later figures are shown in Table III. It will be observed that, owing to
+corrections made in the enumeration in 1897, a considerable reduction in
+the area is recorded for that year, and presumably the error then
+discovered existed in all the preceding returns. The returns for 1907
+gave the acreage of small fruit as 82,175 acres, and in 1908 at 84,880
+acres--an area more than double that of 1889.
+
+
+TABLE III.--_Areas of Small Fruit in Great Britain._
+
+  +-------+--------+-------+--------+-------+--------+
+  | Year. | Acres. | Year. | Acres. | Year. | Acres. |
+  +-------+--------+-------+--------+-------+--------+
+  | 1890  | 46,234 | 1894  | 68,415 | 1898  | 69,753 |
+  | 1891  | 58,704 | 1895  | 74,547 | 1899  | 71,526 |
+  | 1892  | 62,148 | 1896  | 76,245 | 1900  | 73,780 |
+  | 1893  | 65,487 | 1897  | 69,792 | 1901  | 74,999 |
+  +-------+--------+-------+--------+-------+--------+
+
+
+TABLE IV.--_Areas under Small Fruit in England, Wales and
+Scotland--Acres._
+
+  +-------+----------+--------+-----------+----------------+
+  | Year. | England. | Wales. | Scotland. | Great Britain. |
+  +-------+----------+--------+-----------+----------------+
+  | 1898  |  63,438  |  1044  |   5271    |     69,753     |
+  | 1899  |  64,867  |  1106  |   5553    |     71,526     |
+  | 1900  |  66,749  |  1109  |   5922    |     73,780     |
+  | 1901  |  67,828  |  1092  |   6079    |     74,999     |
+  | 1908  |  75,750  |  1200  |   7930    |     84,880     |
+  +-------+----------+--------+-----------+----------------+
+
+There has undoubtedly been a considerable expansion, rather than a
+contraction, of small fruit plantations since 1896. The acreage of small
+fruit in Great Britain is about one-third that of the orchards. As may
+be seen in Table IV., it is mainly confined to England, though Scotland
+has over 4000 more acres of small fruit than of orchards. About
+one-third of the area of small fruit in England belongs to Kent alone,
+that county having returned 24,137 acres in 1908. Cambridge now ranks
+next with 6878 acres, followed by Norfolk with 5876 acres,
+Worcestershire with 4852 acres, Middlesex with 4163 acres, Hants with
+3320 acres and Essex with 2150 acres. It should be remarked that between
+1900 and 1908 Cambridgeshire had almost doubled its area of small
+fruits, from 3740 to 6878 acres; whilst both Norfolk and Worcestershire
+in 1908 had larger areas devoted to small fruits than Middlesex--in
+which county there had been a decrease of about 400 acres during the
+same period. The largest county area of small fruit in Wales is 806
+acres in Denbighshire, and in Scotland 2791 acres in Perthshire, 2259
+acres in Lanarkshire, followed by 412 acres in Forfarshire. The only
+counties in Great Britain which make no return under the head of small
+fruit are Orkney and Shetland; and Sutherland only gives 2½ acres. It is
+hardly necessary to say that considerable areas of small fruit, in
+kitchen gardens and elsewhere, find no place in the official returns,
+which, however, include small fruit grown between and under orchard
+trees.
+
+Gooseberries are largely grown in most small fruit districts. Currants
+are less widely cultivated, but the red currant is more extensively
+grown than the black, the latter having suffered seriously from the
+ravages of the black currant mite. Kent is the great centre for
+raspberries and for strawberries, though, in addition, the latter fruit
+is largely grown in Cambridgeshire (2411 acres), Hampshire (2327 acres),
+Norfolk (2067 acres) and Worcestershire (1273 acres). Essex,
+Lincolnshire, Cheshire, Cornwall and Middlesex each has more than 500
+acres devoted to strawberry cultivation.
+
+The following statement from returns for 1908 shows the area under
+different kinds of fruit in 1907 and 1908 in Great Britain, and also
+whether there had been an increase or decrease:
+
+  +-----------------+---------+---------+-------------+
+  |                 |  1907.  |  1908.  | Increase or |
+  |                 |         |         |  Decrease.  |
+  +-----------------+---------+---------+-------------+
+  |                 |  Acres. |  Acres. |    Acres.   |
+  | Small Fruit--   |         |         |             |
+  |   Strawberries  |  27,827 |  28,815 |   + 988     |
+  |   Raspberries   |   8,878 |   9,323 |   + 445     |
+  |   Currants and  |         |         |             |
+  |    Gooseberries |  25,590 |  26,241 |   + 651     |
+  |   Other kinds   |  19,880 |  20,501 |   + 621     |
+  |                 +---------+---------+-------------+
+  |                 |  82,175 |  84,880 |   +2705     |
+  |                 +---------+---------+-------------+
+  | Orchards--      |         |         |             |
+  |   Apples        | 172,643 | 172,751 |   + 108     |
+  |   Pears         |   8,911 |   9,604 |   + 693     |
+  |   Cherries      |  12,027 |  11,868 |   - 159     |
+  |   Plums         |  14,901 |  15,683 |   + 782     |
+  |   Other kinds   |  41,694 |  40,391 |   -1303     |
+  |                 +---------+---------+-------------+
+  |                 | 250,176 | 250,297 |   + 121     |
+  +-----------------+---------+---------+-------------+
+
+It appears from the Board of Agriculture returns that 27,433 acres of
+small fruit was grown in orchards, so that the total extent of land
+under fruit cultivation in Great Britain at the end of 1908 was about
+308,000 acres.
+
+There are no official returns as to the acreage devoted to orchard
+cultivation in Ireland. The figures relating to small fruit, moreover,
+extend back only to 1899, when the area under this head was returned as
+4809 acres, which became 4359 acres in 1900 and 4877 acres in 1901. In
+most parts of the country there are districts favourable to the culture
+of small fruits, such as strawberries, raspberries, gooseberries and
+currants, and of top fruits, such as apples, pears, plums and damsons.
+The only localities largely identified with fruit culture as an industry
+are the Drogheda district and the Armagh district. In the former all the
+kinds named are grown except strawberries, the speciality being
+raspberries, which are marketed in Dublin, Belfast and Liverpool. In the
+Armagh district, again, all the kinds named are grown, but in this case
+strawberries are the speciality, the markets utilized being Richhill,
+Belfast, and those in Scotland. In the Drogheda district the grower
+bears the cost of picking, packing and shipping, but he cannot estimate
+his net returns until his fruit is on the market. Around Armagh the
+Scottish system prevails--that is, the fruit is sold while growing, the
+buyer being responsible for the picking and marketing.
+
+The amount of fruit imported into the United Kingdom has such an
+important bearing on the possibilities of the industry that the
+following figures also may be useful:
+
+  The quantities of apples, pears, plums, cherries and grapes imported
+  in the raw condition into the United Kingdom in each year, 1892 to
+  1901, are shown in Table V. Previous to 1892 apples only were
+  separately enumerated. Up to 1899 inclusive the quantities were given
+  in bushels, but in 1900 a change was made to hundred-weights. This
+  renders the quantities in that and subsequent years not directly
+  comparable with those in earlier years, but the comparison of the
+  values, which are also given in the table, continues to hold good. The
+  figures for 1908 have been added to show the increase that had taken
+  place. In some years the value of imported apples exceeds the
+  aggregate value of the pears, plums, cherries and grapes imported. The
+  extreme values for apples shown in the table are £844,000 in 1893 and
+  £2,079,000 in 1908. Grapes rank next to apples in point of value, and
+  over the seventeen years the amount ranged between £394,000 in 1892
+  and £728,000 in 1908. On the average, the annual outlay on imported
+  pears is slightly in excess of that on plums. The extremes shown are
+  £167,000 in 1895 and £515,000 in 1908. In the case of plums, the
+  smallest outlay tabulated is £166,000 in 1895, whilst the largest is
+  £498,000 in 1897. The amounts expended upon imported cherries varied
+  between £96,000 in 1895 and £308,000 in 1900. In 1900 apricots and
+  peaches, imported raw, previously included with raw plums, were for
+  the first time separately enumerated, the import into the United
+  Kingdom for that year amounting to 13,689 cwt., valued at £25,846; in
+  1901 the quantity was 13,463 cwt. and the value £32,350. The latter
+  rose in 1908 to £60,000. In 1900, also, currants, gooseberries and
+  strawberries, hitherto included in unenumerated raw fruit, were
+  likewise for the first time separately returned. Of raw currants the
+  import was 64,462 cwt., valued at £87,170 (1908, £121,850); of raw
+  gooseberries 26,045 cwt., valued at £14,626 (1908, £25,520); and of
+  raw strawberries, 52,225 cwt., valued at £85,949. In 1907 only 44,000
+  cwt. of strawberries were imported. In 1901 the quantities and values
+  were respectively--currants, 70,402 cwt., £75,308; gooseberries,
+  21,735 cwt., £11,420; strawberries, 38,604 cwt., £51,290. Up to 1899
+  the imports of tomatoes were included amongst unenumerated raw
+  vegetables, so that the quantity was not separately ascertainable. For
+  1900 the import of tomatoes was 833,032 cwt., valued at £792,339,
+  which is equivalent to a fraction under 2½d. per lb. For 1901 the
+  quantity was 793,991 cwt., and the value £734,051; for 1906, there
+  were 1,124,700 cwt., valued at £953,475; for 1907, 1,135,499 cwt.,
+  valued at £1,020,805; and for 1908, 1,160,283 cwt., valued at
+  £955,983.
+
+
+  TABLE V.--_Imports of Raw Apples, Pears, Plums, Cherries and Grapes
+  into the United Kingdom, 1892 to 1901. Quantities in Thousands of
+  Bushels (thousands of cwt. in 1900 and 1901). Values in Thousands of
+  Pounds Sterling._
+
+    +------+-------------------------------------------------+
+    |      |                  Quantities.                    |
+    | Year.+---------+--------+--------+-----------+---------+
+    |      | Apples. | Pears. | Plums. | Cherries. | Grapes. |
+    +------+---------+--------+--------+-----------+---------+
+    | 1892 |  4515   |   637  |   413  |    217    |   762   |
+    | 1893 |  3460   |   915  |   777  |    346    |   979   |
+    | 1894 |  4969   |  1310  |   777  |    311    |   833   |
+    | 1895 |  3292   |   407  |   401  |    196    |   865   |
+    | 1896 |  6177   |   483  |   560  |    219    |   883   |
+    | 1897 |  4200   |  1052  |  1044  |    312    |   994   |
+    | 1898 |  3459   |   492  |   922  |    402    |  1136   |
+    | 1899 |  3861   |   572  |   558  |    281    |  1158   |
+    | 1900 |  2129*  |   477* |   423* |    243*   |   593*  |
+    | 1901 |  1830*  |   349* |   264* |    213*   |   680*  |
+    +------+---------+--------+--------+-----------+---------+
+    |                         Values.                        |
+    +------+---------+--------+--------+-----------+---------+
+    | 1892 |  1354   |   297  |   200  |    135    |   394   |
+    | 1893 |   844   |   347  |   332  |    195    |   530   |
+    | 1894 |  1389   |   411  |   302  |    167    |   470   |
+    | 1895 |   960   |   167  |   166  |     96    |   487   |
+    | 1896 |  1582   |   207  |   242  |    106    |   443   |
+    | 1897 |  1187   |   378  |   498  |    178    |   495   |
+    | 1898 |  1108   |   222  |   435  |    231    |   550   |
+    | 1899 |  1186   |   266  |   294  |    154    |   588   |
+    | 1900 |  1225   |   367  |   393  |    308    |   595   |
+    | 1901 |  1183   |   296  |   244  |    214    |   695   |
+    | 1908 |  2079   |   515  |   428  |    235    |   728   |
+    +------+---------+--------+--------+-----------+---------+
+      * Thousands of cwts.
+
+  In 1908 the outlay of the United Kingdom upon imported raw fruits,
+  such as can easily be produced at home, was £4,195,654, made up as
+  follows:
+
+    Apples      £2,079,703  |  Plums                £428,966
+    Grapes         728,026  |  Currants              121,852
+    Pears          515,914  |  Apricots and peaches   60,141
+    Cherries       235,523  |  Gooseberries           25,529
+
+  In addition about £280,000 was spent upon "unenumerated" raw fruit,
+  and £560,000 on nuts other than almonds "used as fruit," which would
+  include walnuts and filberts, both produced at home. It is certain,
+  therefore, that the expenditure on imported fruits, such as are grown
+  within the limits of the United Kingdom, exceeds four millions
+  sterling per annum. The remainder of the outlay on imported fruit in
+  1908, amounting to over £5,000,000, was made up of £2,269,651 for
+  oranges, £471,713 for lemons, £1,769,249 for bananas, and £560,301 for
+  almond-nuts; these cannot be grown on an industrial scale in the
+  British Isles.
+
+  It may be interesting to note the source of some of these imported
+  fruits. The United States and Canada send most of the apples, the
+  quantity for 1907 being 1,413,000 cwt. and 1,588,000 cwt.
+  respectively, while Australia contributes 280,000 cwt. Plums come
+  chiefly from France (200,000 cwt.), followed with 38,000 cwt. from
+  Germany and 28,000 cwt. from the Netherlands. Pears are imported
+  chiefly from France (204,000 cwt.) and Belgium (176,000); but the
+  Netherlands send 52,000 cwt., and the United States 24,000 cwt. The
+  great bulk of imported tomatoes comes from the Canary Islands, the
+  quantity in 1907 being 604,692 cwt. The Channel Islands also sent
+  223,800 cwt., France 115,500 cwt., Spain 169,000 cwt., and Portugal a
+  long way behind with 11,700 cwt. Most of the strawberries imported
+  come from France (33,800 cwt.) and the Netherlands (10,300 cwt.).
+
+_Fruit-growing in Kent._--Kent is by far the largest fruit-growing
+county in England. For centuries that county has been famous for its
+fruit, and appears to have been the centre for the distribution of trees
+and grafts throughout the country. The cultivation of fruit land upon
+farms in many parts of Kent has always been an important feature in its
+agriculture. An excellent description of this noteworthy characteristic
+of Kentish farming is contained in a comprehensive paper on the
+agriculture of Kent by Mr Charles Whitehead,[1] whose remarks, with
+various additions and modifications, are here reproduced.
+
+  Where the conditions are favourable, especially in East and Mid Kent,
+  there is a considerable acreage of fruit land attached to each farm,
+  planted with cherry, apple, pear, plum and damson trees, and with bush
+  fruits, or soft fruits as they are sometimes called, including
+  gooseberries, currants, raspberries, either with or without standard
+  trees, and strawberries, and filberts and cob-nuts in Mid Kent. This
+  acreage has largely increased, and will no doubt continue to increase,
+  as, on the whole, fruit-growing has been profitable and has materially
+  benefited those fortunate enough to have fruit land on their farms.
+  There are also cultivators who grow nothing but fruit. These are
+  principally in the district of East Kent, between Rochester and
+  Canterbury, and in the district of Mid Kent near London, and they
+  manage their fruit land, as a rule, better than farmers, as they give
+  their undivided attention to it and have more technical knowledge. But
+  there has been great improvement of late in the management of fruit
+  land, especially of cherry and apple orchards, the grass of which is
+  fed off by animals having corn or cake, or the land is well manured.
+  Apple trees are grease-banded and sprayed systematically by advanced
+  fruit-growers to prevent or check the attacks of destructive insects.
+  Far more attention is being paid to the selection of varieties of
+  apples and pears having colour, size, flavour, keeping qualities, and
+  other attributes to meet the tastes of the public, and to compete with
+  the beautiful fruit that comes from the United States and Canada.
+
+  Of the various kinds of apples at present grown in Kent mention should
+  be made of Mr Gladstone, Beauty of Bath, Devonshire Quarrenden, Lady
+  Sudely, Yellow Ingestre and Worcester Pearmain. These are dessert
+  apples ready to pick in August and September, and are not stored. For
+  storing, King of the Pippins, Cox's Orange Pippin (the best dessert
+  apple in existence), Cox's Pomona, Duchess, Favourite, Gascoyne's
+  Scarlet Seedling, Court Pendu Plat, Baumann's Red Reinette, Allington
+  Pippin, Duke of Devonshire and Blenheim Orange. Among kitchen apples
+  for selling straight from the trees the most usually planted are Lord
+  Grosvenor, Lord Suffield, Keswick Codlin, Early Julian, Eclinville
+  Seedling, Pott's Seedling, Early Rivers, Grenadier, Golden Spire,
+  Stirling Castle and Domino. For storing, the cooking sorts favoured
+  now are Stone's or Loddington, Warner's King, Wellington, Lord Derby,
+  Queen Caroline, Tower of Glamis, Winter Queening, Lucombe's Seedling,
+  Bismarck, Bramley's Seedling, Golden Noble and Lane's Prince Albert.
+  Almost all these will flourish equally as standards, pyramids and
+  bushes. Among pears are Hessle, Clapp's Favourite, William's Bon
+  Chrétien, Beurré de Capiaumont, Fertility, Beurré Riche, Chissel,
+  Beurré Clairgeau, Louise Bonne of Jersey, Doyenne du Comice and Vicar
+  of Winkfield. Among plums, Rivers's Early Prolific, Tsar, Belgian
+  Purple, Black Diamond, Kentish Bush Plum, Pond's Seedling, Magnum
+  Bonum and Victoria are mainly cultivated. The damson known as Farleigh
+  Prolific, or Crittenden's, is most extensively grown throughout the
+  county, and usually yields large crops, which make good prices. As a
+  case in point, purchasers were offering to contract for quantities of
+  this damson at £20 per ton in May of 1899, as the prospects of the
+  yield were unsatisfactory. On the other hand, in one year recently
+  when the crop was abnormally abundant, some of the fruit barely paid
+  the expenses of sending to market. The varieties of cherries most
+  frequently grown are Governor Wood, Knight's Early Black, Frogmore
+  Blackheart, Black Eagle, Waterloo, Amberheart, Bigarreau, Napoleon
+  Bigarreau and Turk. A variety of cherry known as the Kentish cherry,
+  of a light red colour and fine subacid flavour, is much grown in Kent
+  for drying and cooking purposes. Another cherry, similar in colour and
+  quality, which comes rather late, known as the Flemish, is also
+  extensively cultivated, as well as the very dark red large Morello,
+  used for making cherry brandy. These three varieties are grown
+  extensively as pyramids, and the last-named also on walls and sides of
+  buildings. Sometimes the cherry crop is sold by auction to dealers,
+  who pick, pack and consign the fruit to market. Large prices are often
+  made, as much as £80 per acre being not uncommon. The crop on a large
+  cherry orchard in Mid Kent has been sold for more than £100 per acre.
+
+  Where old standard trees have been long neglected and have become
+  overgrown by mosses and lichens, the attempts made to improve them
+  seldom succeed. The introduction of bush fruit trees dwarfed by
+  grafting on the Paradise stock has been of much advantage to fruit
+  cultivators, as they come into bearing in two or three years, and are
+  more easily cultivated, pruned, sprayed and picked than standards.
+  Many plantations of these bush trees have been formed in Kent of
+  apples, pears and plums. Half standards and pyramids have also been
+  planted of these fruits, as well as of cherries. Bushes of
+  gooseberries and currants, and clumps or stools of raspberry canes,
+  have been planted to a great extent in many parts of the East and Mid
+  divisions of Kent, but not much in the Weald, where apples are
+  principally grown. Sometimes fruit bushes are put in alternate rows
+  with bush of standard trees of apple, pear, plum or damson, or they
+  are planted by themselves. The distances apart for planting are
+  generally for cherry and apple trees on grass 30 ft. by 30 ft.; for
+  standard apples and pear trees from 20 ft. to 24 ft. upon arable land,
+  with bush fruit, as gooseberries and currants, under them. These are
+  set 6 ft. by 6 ft. apart, and 5 ft. by 2 ft. for raspberries, and
+  strawberries 2 ft. 6 in. to 3 ft. by 1 ft. 6 in. to 1 ft. 3 in. apart.
+  On some fruit farms bush or dwarf trees--apples, pears, plums--are
+  planted alone, at distances varying from 8 ft. to 10 ft. apart, giving
+  from 485 to 680 bush trees per acre, nothing being grown between them
+  except perhaps strawberries or vegetables during the first two or
+  three years. It is believed that this is the best way of ensuring
+  fruit of high quality and colour. Another arrangement consists in
+  putting standard apple or pear trees 30 ft. apart (48 trees per acre),
+  and setting bush trees of apples or pears 15 ft. apart between them;
+  these latter come quickly into bearing, and are removed when the
+  standards are fully grown. Occasionally gooseberry or currant bushes,
+  or raspberry canes or strawberry plants, are set between the bush
+  trees, and taken away directly they interfere with the growth of
+  these. Half standard apple or plum trees are set triangularly 15 ft.
+  apart, and strawberry plants at a distance of 1½ ft. from plant to
+  plant and 2½ ft. from row to row. Or currant or gooseberry bushes are
+  set between the half standards, and strawberry plants between these.
+
+  These systems involve high farming. The manures used are London
+  manure, where hops are not grown, and bone meal, super-phosphate,
+  rags, shoddy, wool-waste, fish refuse, nitrate of soda, kainit and
+  sulphate of ammonia. Where hops are grown the London manure is wanted
+  for them. Fruit plantations are always dug by hand with the Kent spud.
+  Fruit land is never ploughed, as in the United States and Canada. The
+  soil is levelled down with the "Canterbury" hoe, and then the
+  plantations are kept free from weeds with the ordinary draw or "plate"
+  hoe. The best fruit farmers spray fruit trees regularly in the early
+  spring, and continue until the blossoms come out, with quassia and
+  soft soap and paraffin emulsions, and a very few with Paris green
+  only, where there is no under fruit, in order to prevent and check the
+  constant attacks of the various caterpillars and other insect pests.
+  This is a costly and laborious process, but it pays well, as a rule.
+  The fallacy that fruit trees on grass land require no manure, and that
+  the grass may be allowed to grow up to their trunks without any harm,
+  is exploding, and many fruit farmers are well manuring their grass
+  orchards and removing the grass for some distance round the stems,
+  particularly where the trees are young.
+
+  Strawberries are produced in enormous quantities in the northern part
+  of the Mid Kent district round the Crays, and from thence to
+  Orpington; also near Sandwich, and to some extent near Maidstone.
+  Raspberry canes have been extensively put in during the last few
+  years, and in some seasons yield good profits. There is a very great
+  and growing demand for all soft fruits for jam-making, and prices are
+  fairly good, taking an average of years, notwithstanding the heavy
+  importations from France, Belgium, Holland, Spain and Italy. The
+  extraordinary increase in the national demand for jam and other fruit
+  preserves has been of great benefit to Kent fruit producers. The
+  cheapness of duty-free sugar, as compared with sugar paying duty in
+  the United States and other large fruit-producing countries, afforded
+  one of the very few advantages possessed by British cultivators, but
+  the reimposition of the sugar duty in the United Kingdom in 1901 has
+  modified the position in this respect. Jam factories were established
+  in several parts of Kent about 1889 or 1890, but most of them
+  collapsed either from want of capital or from bad management. There
+  are still a few remaining, principally in connexion with large fruit
+  farms. One of these is at Swanley, whose energetic owners farm nearly
+  2000 acres of fruit land in Kent. The fruit grown by them that will
+  not make satisfactory prices in a fresh raw state is made into jam, or
+  if time presses it is first made into pulp, and kept until the
+  opportunity comes for making it into jam. In this factory there are
+  fifteen steam-jacketed vats in one row, and six others for candied
+  peel. A season's output on a recent occasion comprised about 3500 tons
+  of jam, 850 tons of candied peel and 750 gross (108,000 bottles) of
+  bottled fruit. A great deal of the fruit preserved is purchased,
+  whilst much of that grown on the farms is sold. A strigging machine is
+  employed, which does as much work as fifty women in taking currants
+  off their strigs or stalks. Black currant pulp is stored in casks till
+  winter, when there is time to convert it into jam. Strawberries cannot
+  be pulped to advantage, but it is otherwise with raspberries, the pulp
+  of which is largely made. Apricots for jam are obtained chiefly from
+  France and Spain. There is another flourishing factory near
+  Sittingbourne worked on the same lines. It is very advantageous to
+  fruit farmers to have jam factories in connexion with their farms or
+  to have them near, as they can thoroughly grade their fruit, and send
+  only the best to market, thus ensuring a high reputation for its
+  quality. Carriage is saved, which is a serious charge, though railway
+  rates from Kent to the great manufacturing towns and to Scotland are
+  very much less proportionally than those to London, and consequently
+  Kent growers send increasing quantities to these distant markets,
+  where prices are better, not being so directly interfered with by
+  imported fruit, which generally finds its way to London.
+
+  Kentish fruit-growers are becoming more particular in picking,
+  grading, packing and storing fruit, as well as in marketing it. A
+  larger quantity of fruit is now carefully stored, and sent to selected
+  markets as it ripens, or when there is an ascertained demand, as it is
+  found that if it is consigned to market direct from the trees there
+  must frequently be forced sales and competition with foreign fruit
+  that is fully matured and in good order. It was customary formerly for
+  Kentish growers to consign all their fruit to the London markets; now
+  a good deal of it is sent to Manchester, Birmingham, Liverpool,
+  Sheffield, Newcastle and other large cities. Some is sent even to
+  Edinburgh and Glasgow. Many large growers send no fruit to London now.
+  It is by no means uncommon for growers to sell their fruit crops on
+  the trees or bushes by auction or private treaty, or to contract to
+  supply a stipulated quantity of specified fruit, say of currants,
+  raspberries or strawberries, to jam manufacturers. There is a
+  considerable quantity of fruit, such as grapes, peaches, nectarines,
+  grown under glass, and this kind of culture tends to increase.
+
+  Filberts and cob-nuts are a special product of Kent, in the
+  neighbourhood of Maidstone principally, and upon the Ragstone soils,
+  certain conditions of soil and situation being essential for their
+  profitable production. A part of the filbert and cob-nut crop is
+  picked green in September, as they do well for dessert, though their
+  kernels are not large or firm, and it pays to sell them green, as they
+  weigh more heavily. One grower in Mid Kent has 100 acres of nuts, and
+  has grown 100 tons in a good year. The average price of late years has
+  been about 5d. per lb., which would make the gross return of the 100
+  acres amount to £4660. Kentish filberts have long been proverbial for
+  their excellence. Cobs are larger and look better for dessert, though
+  their flavour is not so fine. They are better croppers, and are now
+  usually planted. This cultivation is not much extending, as it is very
+  long before the trees come into full bearing. The London market is
+  supplied entirely with these nuts from Kent, and there is some demand
+  in America for them. Filbert and cob trees are most closely pruned.
+  All the year's growth is cut away except the very finest young wood,
+  which the trained eye of the tree-cutter sees at a glance is
+  blossom-bearing. The trees are kept from 5½ to 7 ft. high upon stems
+  from 1½ to 2 ft. high, and are trained so as to form a cup of from 7
+  to 8 ft. in diameter.
+
+  There seems no reason to expect any decrease in the acreage of fruit
+  land in Kent, and if the improvement in the selection of varieties and
+  in the general management continues it will yet pay. A hundred years
+  ago every one was grubbing fruit land in order that hops might be
+  planted, and for this many acres of splendid cherry orchards were
+  sacrificed. Now the disposition is to grub hop plants and substitute
+  apples, plums, or small fruit or cherry trees.
+
+  _Fruit-growing in other Districts._--The large fruit plantations in
+  the vicinity of London are to be found mostly in the valley of the
+  Thames, around such centres as Brentford, Isleworth, Twickenham,
+  Heston, Hounslow, Cranford and Southall. All varieties of orchard
+  trees, but mostly apples, pears, and plums and small fruit, are grown
+  in these districts, the nearness of which to the metropolitan fruit
+  market at Covent Garden is of course an advantage. Some of the
+  orchards are old, and are not managed on modern principles. They
+  contain, moreover, varieties of fruit many of which are out of date
+  and would not be employed in establishing new plantations. In the
+  better-managed grounds the antiquated varieties have been removed, and
+  their places taken by newer and more approved types. In addition to
+  apples, pears, plums, damsons, cherries and quinces as top fruit,
+  currants, gooseberries and raspberries are grown as bottom fruit.
+  Strawberries are extensively grown in some of the localities, and in
+  favourable seasons outdoor tomatoes are ripened and marketed.
+
+  Fruit is extensively grown in Cambridgeshire and adjacent counties in
+  the east of England. A leading centre is Cottenham, where the Lower
+  Greensand crops out and furnishes one of the best of soils for
+  fruit-culture. In Cottenham about a thousand acres are devoted to
+  fruit, and nearly the same acreage to asparagus, which is, however,
+  giving place to fruit. Currants, gooseberries and strawberries are the
+  most largely grown, apples, plums and raspberries following. Of
+  varieties of plums the Victoria is first in favour, and then Rivers's
+  Early Prolific, Tsar and Gisborne. London is the chief market, as it
+  receives about half the fruit sent away, whilst a considerable
+  quantity goes to Manchester, and some is sent to a neighbouring jam
+  factory at Histon, where also a moderate acreage of fruit is grown.
+  Another fruit-growing centre in Cambridgeshire is at Willingham,
+  where--besides plums, gooseberries and raspberries--outdoor tomatoes
+  are a feature. Greengages are largely grown near Cambridge. Wisbech is
+  the centre of an extensive fruit district, situated partly in
+  Cambridgeshire and partly in Norfolk. Gooseberries, strawberries and
+  raspberries are largely grown, and as many as 80 tons of the
+  first-named fruit have been sent away from Wisbech station in a single
+  day. In the fruit-growing localities of Huntingdonshire apples, plums
+  and gooseberries are the most extensively grown, but pears,
+  greengages, cherries, currants, strawberries and raspberries are also
+  cultivated. As illustrating variations in price, it may be mentioned
+  that about the year 1880 the lowest price for gooseberries was £10 per
+  ton, whereas it has since been down to £4. Huntingdonshire fruit is
+  sent chiefly to Yorkshire, Scotland and South Wales, but railway
+  freights are high.
+
+  Essex affords a good example of successful fruit-farming at Tiptree
+  Heath, near Kelvedon, where under one management about 260 acres out
+  of a total of 360 are under fruit. The soil, a stiff loam, grows
+  strawberries to perfection, and 165 acres are allotted to this fruit.
+  The other principal crops are 43 acres of raspberries and 30 acres of
+  black currants, besides which there are small areas of red currants,
+  gooseberries, plums, damsons, greengages, cherries, apples, quinces
+  and blackberries. The variety of strawberry known as the Small Scarlet
+  is a speciality here, and it occupies 55 acres, as it makes the best
+  of jam. The Paxton, Royal Sovereign and Noble varieties are also
+  grown. Strawberries stand for six or seven years on this farm, and
+  begin to yield well when two years old. A jam factory is worked in
+  conjunction with the fruit farm. Pulp is not made except when there is
+  a glut of fruit. Perishable fruit intended for whole-fruit preserves
+  is never held over after it is gathered. The picking of strawberries
+  begins at 4 A.M., and the first lot is made into jam by 6 A.M.
+
+  Hampshire, like Cambridgeshire and Norfolk, are the only counties in
+  which the area of small fruit exceeds that of orchards. The returns
+  for 1908 show that Hampshire had 3320 acres of small fruit to 2236
+  acres of orchards; Cambridge had 6878 acres of small fruit to 5221 of
+  orchards; and Norfolk had 5876 acres of small fruit against 5188 acres
+  of orchards. Compared with twenty years previously, the acreage of
+  small fruit had trebled. This is largely due in Hampshire to the
+  extension of strawberry culture in the Southampton district, where the
+  industry is in the hands of many small growers, few of whom cultivate
+  more than 20 acres each. Sarisbury and Botley are the leading parishes
+  in which the business is carried on. Most of the strawberry holdings
+  are from half an acre to 5 acres in extent, a few are from 5 to 10
+  acres, fewer still from 10 to 20 acres and only half-a-dozen over that
+  limit. Runners from one-year plants are used for planting, being found
+  more fruitful than those from older plants. Peat-moss manure from
+  London stables is much used, but artificial manures are also employed
+  with good results. Shortly after flowering the plants are bedded down
+  with straw at the rate of about 25 cwt. per acre. Picking begins some
+  ten days earlier than in Kent, at a date between 1st June and 15th
+  June. The first week's gathering is sent mostly to London, but
+  subsequently the greater part of the fruit goes to the Midlands and to
+  Scotland and Ireland.
+
+  In recent years fruit-growing has much increased in South
+  Worcestershire, in the vicinity of Evesham and Pershore. Hand-lights
+  are freely used in the market gardens of this district for the
+  protection of cucumbers and vegetable marrows, besides which tomatoes
+  are extensively grown out of doors. At one time the egg plum and the
+  Worcester damson were the chief fruit crops, apples and cherries
+  ranking next, pears being grown to only a moderate extent. According
+  to the 1908 returns, however, apples come first, plums second, pears
+  third and cherries fourth. In a prolific season a single tree of the
+  Damascene or Worcester damson will yield from 400 to 500 lb. of
+  fruit. There is a tendency to grow plum trees in the bush shape, as
+  they are less liable than standards to injury from wind. The manures
+  used include soot, fish guano, blood manure and phosphates--basic slag
+  amongst the last-named. In the Pershore district, where there is a jam
+  factory, plums are the chief tree fruit, whilst most of the orchard
+  apples and pears are grown for cider and perry. Gooseberries are a
+  feature, as are also strawberries, red and black currants and a few
+  white, but raspberries are little grown. The soil, a strong or medium
+  loam of fair depth, resting on clay, is so well adapted to plums that
+  trees live for fifty years. In order to check the ravages of the
+  winter moth, plum and apple trees are grease-banded at the beginning
+  of October and again at the end of March. The trees are also sprayed
+  when necessary with insecticidal solutions. Pruning is done in the
+  autumn. An approved distance apart at which to grow plum trees is 12
+  ft. by 12 ft. In the Earl of Coventry's fruit plantation, 40 acres in
+  extent, at Croome Court, plums and apples are planted alternately, the
+  bottom fruit being black currants, which are less liable to injury
+  from birds than are red currants or gooseberries. Details concerning
+  the methods of cultivation of fruit and flowers in various parts of
+  England, the varieties commonly grown, the expenditure involved, and
+  allied matters, will be found in Mr W.E. Bear's papers in the _Journal
+  of the Royal Agricultural Society_ in 1898 and 1899.
+
+  Apart altogether from market gardening and commercial fruit-growing,
+  it must be borne in mind that an enormous business is done in the
+  raising of young fruit-trees every year. Hundreds of thousands of
+  apples, pears, plums, cherries, peaches, nectarines and apricots are
+  budded or grafted each year on suitable stocks. They are trained in
+  various ways, and are usually fit for sale the third year. These young
+  trees replace old ones in private and commercial gardens, and are also
+  used to establish new plantations in different parts of the kingdom.
+
+  _The Woburn Experimental Fruit Farm._--The establishment in 1894 of
+  the experimental fruit farm at Ridgmont, near Woburn, Beds, has
+  exercised a healthy influence upon the progress and development of
+  fruit-farming in England. The farm was founded and carried on by the
+  public-spirited enterprise of the Duke of Bedford and Mr Spencer U.
+  Pickering, the latter acting as director. The main object of the
+  experimental station was "to ascertain facts relative to the culture
+  of fruit, and to increase our knowledge of, and to improve our
+  practice in, this industry." The farm is 20 acres in extent, and
+  occupies a field which up to June 1894 had been used as arable land
+  for the ordinary rotation of farm crops. The soil is a sandy loam 9 or
+  10 in. deep, resting on a bed of Oxford Clay. Although it contains a
+  large proportion of sand, the land would generally be termed very
+  heavy, and the water often used to stand on it in places for weeks
+  together in a wet season. The tillage to which the ground was
+  subjected for the purposes of the fruit farm much improved its
+  character, and in dry weather it presents as good a tilth as could be
+  desired. Chemical analyses of the soil from different parts of the
+  field show such wide differences that it is admitted to be by no means
+  an ideal one for experimental purposes. Without entering upon further
+  details, it may be useful to give a summary of the chief results
+  obtained.
+
+  Apples have been grown and treated in a variety of ways, but of the
+  different methods of treatment careless planting, coupled with
+  subsequent neglect, has given the most adverse results, the crop of
+  fruit being not 5% of that from trees grown normally. Of the separate
+  deleterious items constituting total neglect, by far the most
+  effective was the growth of weeds on the surface; careless planting,
+  absence of manure, and the omission of trenching all had comparatively
+  little influence on the results. A set of trees that had been
+  carelessly planted and neglected, but subsequently tended in the early
+  part of 1896, were in the autumn of that year only 10% behind their
+  normally-treated neighbours, thus demonstrating that the response to
+  proper attention is prompt. The growth of grass around young apple
+  trees produced a very striking effect, the injury being much greater
+  than that due to weeds. It is possible, however, that in wet years the
+  ill-effects of both grass and weeds would be less than in dry seasons.
+  Nevertheless, the grass-grown trees, after five years, were scarcely
+  bigger than when planted, and the actual increase in weight which they
+  showed during that time was about eighteen times smaller than in the
+  case of similar trees in tilled ground. It is believed that one of the
+  main causes of the ill-effects is the large increase in the
+  evaporation of water from the soil which is known to be produced by
+  grass, the trees being thereby made to suffer from drought, with
+  constant deprivation of other nourishment as well. That grass growing
+  round young apple trees is deleterious was a circumstance known to
+  many horticulturists, but the extent to which it interferes with the
+  development of the trees had never before been realized. Thousands of
+  pounds are annually thrown away in England through want of knowledge
+  of this fact. Yet trees will flourish in grass under certain
+  conditions. Whether the dominant factor is the age (or size) of the
+  tree has been investigated by grassing over trees which have hitherto
+  been in the open ground, and the results appear to indicate that the
+  grass is as deleterious to the older trees as it was to the younger
+  ones. Again, it appears to have been demonstrated that young apple
+  trees, at all events in certain soils, require but little or no manure
+  in the early stages of their existence, so that in this case also
+  large sums must be annually wasted upon manurial dressings which
+  produce no effects. The experiments have dealt with dwarf trees of
+  Bramley, Cox and Potts, six trees of each variety constituting one
+  investigation. Some of the experiments were repeated with Stirling
+  Castle, and others with standard trees of Bramley, Cox and Lane's
+  Prince Albert. All were planted in 1894-1895, the dwarfs being then
+  three years old and the standards four. In each experiment the
+  "normal" treatment is altered in some one particular, this normal
+  treatment consisting of planting the trees carefully in trenched
+  ground, and subsequently keeping the surface clean; cutting back after
+  planting, pruning moderately in autumn, and shortening the growths
+  when it appeared necessary in summer; giving in autumn a dressing of
+  mixed mineral manures, and in February one of nitrate of soda, this
+  dressing being probably equivalent to one of 12 tons of dung per acre.
+  In the experiments on branch treatment, the bad effects of omitting to
+  cut the trees back on planting, or to prune them subsequently, is
+  evident chiefly in the straggling and bad shape of the resulting
+  trees, but such trees also are not so vigorous as they should be. The
+  quantity of fruit borne, however, is in excess of the average. The
+  check on the vigour and growth of a tree by cutting or injuring its
+  roots is in marked contrast with the effects of a similar interference
+  with the branches. Trees which had been root-pruned each year were in
+  1898 little more than half as big as the normal trees, whilst those
+  root-pruned every second year were about two-thirds as big as the
+  normal. The crops borne by these trees were nevertheless heavy in
+  proportion to the size of the trees. Such frequent root-pruning is
+  not, of course, a practice which should be adopted. It was found that
+  trees which had been carefully lifted every other year and replanted
+  at once experienced no ill-effects from the operation; but in a case
+  where the trees after being lifted had been left in a shed for three
+  days before replanting--which would reproduce to a certain extent the
+  conditions experienced when trees are sent out from a
+  nursery--material injury was suffered, these trees after four years
+  being 28% smaller than similar ones which had not been replanted. Sets
+  of trees planted respectively in November, January and March have, on
+  the whole, shown nothing in favour of any of these different times for
+  planting purposes. Some doubt is thrown on the accepted view that
+  there is a tendency, at any rate with young apple and pear trees, to
+  fruit in alternate seasons.
+
+  Strawberries of eighty-five different varieties have been experimented
+  with, each variety being represented in 1900 by plants of five
+  different ages, from one to five years. In 1896 and 1898 the crops of
+  fruit were about twice as heavy as in 1897 and 1899, but it has not
+  been found possible to correlate these variations with the
+  meteorological records of the several seasons. Taking the average of
+  all the varieties, the relative weights of crop per plant, when these
+  are compared with the two-year-old plants in the same season, are, for
+  the five ages of one to five years, 31, 100, 122, 121 and 134,
+  apparently showing that the bearing power increases rapidly up to two
+  years, less rapidly up to three years, after which age it remains
+  practically constant. The relative average size of the berries shows a
+  deterioration with the age of the plant. The comparative sizes from
+  plants of one to five years old were 115, 100, 96, 91 and 82
+  respectively. If the money value of the crop is taken to be directly
+  dependent on its total weight, and also on the size of the fruits, the
+  relative values of the crop for the different ages would be 34, 100,
+  117, 111 and 110, so that, on the Ridgmont ground, strawberry plants
+  could be profitably retained up to five years and probably longer. As
+  regards what may be termed the order of merit of different varieties
+  of strawberries, it appears that even small differences in position
+  and treatment cause large variations, not only in the features of the
+  crop generally, but also in the relative behaviour of the different
+  varieties. The relative cropping power of the varieties under
+  apparently similar conditions may often be expressed by a number five
+  or tenfold as great in one case as in the other. A comparison of the
+  relative behaviour of the same varieties in different seasons is
+  attended by similar variations. The varying sensitiveness of different
+  varieties of strawberry plants to small and undefinable differences in
+  circumstances is indeed one of the most important facts brought to
+  light in the experiments.
+
+  _Fruit Culture in Ireland._--The following figures have been kindly
+  supplied by the Irish Board of Agriculture, and deal with the acreage
+  under fruit culture in Ireland up to the end of the year 1907.
+
+    1. _Orchard Fruit_--       Statute Acres.
+        Apples                     5829
+        Pears                       224
+        Plums                       223
+        Damsons                     138
+        Other kinds                 129
+                                   ----
+                      Total        6543
+
+    2. _Small Fruit_--
+        Currants, black             234
+        Currants, red and white     159
+        Gooseberries                675
+        Raspberries                 374
+        Strawberries                994
+        Mixed fruit                2470
+                                   ----
+                      Total        4906
+
+  It therefore appears that while Ireland grows only about
+  one-thirty-third the quantity of apples that England does, it is
+  nevertheless nearly 5000 acres ahead of Scotland and about 2000 acres
+  ahead of Wales. It grows 41 times fewer pears than England, but still
+  is ahead of Scotland and a long way ahead of Wales in this fruit.
+  There are 70 times fewer plums grown in Ireland than in England, and
+  about the same in Scotland, while Wales does very little indeed. In
+  small fruit Ireland is a long way behind Scotland in the culture of
+  strawberries and raspberries, although with currants and gooseberries
+  it is very close. Considering the climate, and the fact that there
+  are, according to the latest available returns, over 62,000 holdings
+  above 1 acre but not exceeding 5 acres (having a total of 224,000
+  acres), it is possible fruit culture may become more prevalent than it
+  has been in the past.
+
+_The Flower-growing Industry._--During the last two or three decades of
+the 19th century a very marked increase in flower production occurred in
+England. Notably was this the case in the neighbourhood of London,
+where, within a radius of 15 or 20 m., the fruit crops, which had
+largely taken the place of garden vegetables, were themselves ousted in
+turn to satisfy the increasing demand for land for flower cultivation.
+No flower has entered more largely into the development of the industry
+than the narcissus or daffodil, of which there are now some 600
+varieties. Comparatively few of these, however, are grown for market
+purposes, although all are charming from the amateur point of view. On
+some flower farms a dozen or more acres are devoted to narcissi alone,
+the production of bulbs for sale as well as of flowers for market being
+the object of the growers.
+
+In the London district the country in the Thames valley west of the
+metropolis is as largely occupied by flower farms as it is by fruit
+farms--in fact, the cultivation of flowers is commonly associated with
+that of fruit. In the vicinity of Richmond narcissi are extensively
+grown, as they also are more to the west in the Long Ditton district,
+and likewise around Twickenham, Isleworth, Hounslow, Feltham and
+Hampton. Roses come more into evidence in the neighbourhood of Hounslow,
+Cranford, Hillingdon and Uxbridge, and in some gardens daffodils and
+roses occupy alternate rows. In this district also such flowers as
+herbaceous paeonies, Spanish irises, German irises, Christmas roses,
+lilies of the valley, chrysanthemums, foxgloves, hollyhocks,
+wallflowers, carnations, &c., are extensively grown in many market
+gardens. South of London is the Mitcham country, long noted for its
+production of lavender. The incessant growth of the lavender plant upon
+the same land, however, has led to the decline of this industry, which
+has been largely transferred to districts in the counties of Bedford,
+Essex and Hertford. At Mitcham, nevertheless, mixed flowers are very
+largely grown for the supply of the metropolis, and one farm alone has
+nearly 100 acres under flowers and glass-houses. Chrysanthemums, asters,
+Iceland poppies, gaillardias, pansies, bedding calceolarias, zonal
+pelargoniums and other plants are cultivated in immense quantities. At
+Swanley and Eynsford, in Kent, flowers are extensively cultivated in
+association with fruit and vegetables. Narcissi, chrysanthemums,
+violets, carnations, campanulas, roses, pansies, irises, sweet peas, and
+many other flowers are here raised, and disposed of in the form both of
+cut flowers and of plants.
+
+The Scilly Isles are important as providing the main source of supply of
+narcissi to the English markets in the early months of the year. This
+trade arose almost by accident, for it was about the year 1865 that a
+box of narcissi sent to Covent Garden Market, London, realized £1; and
+the knowledge of this fact getting abroad, the farmers of the isles
+began collecting wild bulbs from the fields in order to cultivate them
+and increase their stocks. Some ten years, however, elapsed before the
+industry promised to become remunerative. In 1885 a Bulb and Flower
+Association was established to promote the industrial growth of flowers.
+The exports of flowers in that year reached 65 tons, and they steadily
+increased until 1893, when they amounted to 450 tons. A slight decline
+followed, but in 1896 the quantity exported was no less than 514 tons.
+This would represent upwards of 3½ million bunches of flowers, chiefly
+narcissi and anemones. Rather more than 500 acres are devoted to
+flower-growing in the isles, by far the greater part of this area being
+assigned to narcissi, whilst anemones, gladioli, marguerites, arum
+lilies, Spanish irises, pinks and wallflowers are cultivated on a much
+smaller scale. The great advantage enjoyed by the Scilly flower-growers
+is earliness of production, due to climatic causes; the soil, moreover,
+is well suited to flower culture and there is an abundance of sunshine.
+The long journey to London is somewhat of a drawback, in regard to both
+time and freight, but the earliness of the flowers more than compensates
+for this. Open-air narcissi are usually ready at the beginning of
+January, and the supply is maintained in different varieties up to the
+middle or end of May. The narcissus bulbs are usually planted in
+October, 4 in. by 3 in. apart for the smaller sorts and 6 in. by 4 to 6
+in. for the larger. A compost of farmyard manure, seaweed, earth and
+road scrapings is the usual dressing, but nitrate of soda, guano and
+bones are also occasionally employed. A better plan, perhaps, is to
+manure heavily the previous crop, frequently potatoes, no direct
+manuring then being needed for the bulbs, these not being left in the
+ground more than two or three years. The expenses of cultivation are
+heavy, the cost of bulbs alone--of which it requires nearly a quarter of
+a million of the smaller varieties, or half as many of the largest, to
+plant an acre--being considerable. The polyanthus varieties of narcissus
+are likely to continue the most remunerative to the flower-growers of
+Scilly, as they flourish better in these isles than on the mainland.
+
+In the district around the Wash, in the vicinity of such towns as
+Wisbech, Spalding and Boston, the industrial culture of bulbs and
+flowers underwent great expansion in the period between 1880 and 1909.
+At Wisbech one concern alone has a farm of some 900 acres, devoted
+chiefly to flowers and fruit, the soil being a deep fine alluvium. Roses
+are grown here, one field containing upwards of 100,000 trees. Nearly 20
+acres are devoted to narcissi, which are grown for the bulbs and also,
+together with tulips, for cut flowers. Carnations are cultivated both
+in the field and in pots. Cut flowers are sent out in large quantities,
+neatly and effectively packed, the parcel post being mainly employed as
+a means of distribution. In the neighbourhood of Spalding crocuses and
+snowdrops are less extensively grown than used to be the case. On one
+farm, however, upwards of 20 acres are devoted to narcissi alone, whilst
+gladioli, lilies and irises are grown on a smaller scale. Around Boston
+narcissi are also extensively grown for the market, both bulbs and cut
+blooms being sold. The bulbs are planted 3 in. apart in rows, the latter
+being 9 in. apart, and are allowed to stand from two to four years.
+
+  The imports of fresh flowers into the United Kingdom were not
+  separately shown prior to 1900. In that year, however, their value
+  amounted to £200,585, in 1901 to £225,011, in 1906 to £233,884, in
+  1907 to £233,641, and in 1908 to £229,802, so that the trade showed a
+  fairly steady condition. From the monthly totals quoted in Table VI.
+  it would appear that the trade sinks to its minimum dimensions in the
+  four months July to October inclusive, and that after September the
+  business continually expands up to April, subsequent to which
+  contraction again sets in. About one-half of the trade belongs
+  practically to the three months of February, March and April.
+
+
+  TABLE VI.--_Values of Fresh Flowers imported into the United Kingdom._
+
+    +-----------+----------+----------+----------+
+    |   Month.  |   1906.  |   1907.  |   1908.  |
+    +-----------+----------+----------+----------+
+    | January   |  £31,035 |  £18,545 |  £29,180 |
+    | February  |   34,647 |   25,541 |   30,541 |
+    | March     |   50,232 |   42,611 |   35,185 |
+    | April     |   30,809 |   50,418 |   42,681 |
+    | May       |   22,980 |   21,767 |   23,129 |
+    | June      |   17,641 |   18,358 |   16,904 |
+    | July      |    3,386 |    4,509 |    3,467 |
+    | August    |    1,646 |    1,539 |    1,081 |
+    | September |      852 |      736 |      953 |
+    | October   |    4,481 |    3,180 |    4,504 |
+    | November  |   17,506 |   15,763 |   15,097 |
+    | December  |   18,669 |   30,674 |   27,080 |
+    |           +----------+----------+----------+
+    |    Total  | £233,884 | £233,641 | £229,802 |
+    +-----------+----------+----------+----------+
+
+_Hothouse Culture of Fruit and Flowers._--The cultivation of fruit and
+flowers under glass has increased enormously since about the year 1880,
+especially in the neighbourhood of London, where large sums of money
+have been sunk in the erection and equipment of hothouses. In the parish
+of Cheshunt, Herts, alone there are upwards of 130 acres covered with
+glass, and between that place on the north and London on the south
+extensive areas of land are similarly utilized. In Middlesex, in the
+north, in the districts of Edmonton, Enfield, Ponders End and Finchley,
+and in the west from Isleworth to Hampton, Feltham, Hillingdon, Sipson
+and Uxbridge, many crops are now cultivated under glass. At Erith,
+Swanley, and other places in Kent, as also at Worthing, in Sussex,
+glass-house culture has much extended. A careful estimate puts the area
+of industrial hothouses in England at about 1200 acres, but it is
+probably much more than this. Most of the greenhouses are fixtures, but
+in some parts of the kingdom structures that move on rails and wheels
+are used, to enable the ground to be prepared in the open for one crop
+while another is maturing under glass. The leading products are grapes,
+tomatoes and cucumbers, the last-named two being true fruits from the
+botanist's point of view, though commercially included with vegetables.
+To these may be added on the same ground dwarf or French beans, and
+runner or climbing beans. Peaches, nectarines and strawberries are
+largely grown under glass, and, in private hothouses--from which the
+produce is used mainly for household consumption, and which are not
+taken into consideration here--pineapples, figs and other fruit.
+Conservative estimates indicate the average annual yield of hothouse
+grapes to be about 12 tons per acre and of tomatoes 20 tons. The greater
+part of the space in the hothouses is assigned to fruit, but whilst some
+houses are devoted exclusively to flowers, in others, where fruit is the
+main object, flowers are forced in considerable quantities in winter and
+early spring. The flowers grown under glass include tulips, hyacinths,
+primulas, cyclamens, spiraeas, mignonettes, fuchsias, calceolarias,
+roses, chrysanthemums, daffodils, arum lilies or callas, liliums,
+azaleas, eucharises, camellias, stephanotis, tuberoses, bouvardias,
+gardenias, heaths or ericas, poinsettias, lilies of the valley, zonal
+pelargoniums, tuberous and fibrous rooted begonias, and many others.
+There is an increasing demand for foliage hothouse plants, such as
+ferns, palms, crotons, aspidistras, araucarias, dracaenas, India-rubber
+plants, aralias, grevilleas, &c. Berried plants like solanums and
+aucubas also find a ready sale, while the ornamental kinds of asparagus
+such as _sprengeri_ and _plumosus_ nanus, are ever in demand for
+trailing decorations, as well as myrsiphyilum. Special mention must be
+made of the winter or perpetual flowering carnations which are now grown
+by hundreds of thousands in all parts of the kingdom for decorative work
+during the winter season. The converse of forcing plants into early
+blossom is adopted with such an important crop as lily of the valley.
+During the summer season the crowns are placed in refrigerators with
+about 2 degrees of frost, and quantities are taken out as required every
+week and transferred to the greenhouse to develop. Tomatoes are grown
+largely in houses exclusively occupied by them, in which case two and
+sometimes three crops can be gathered in the year. In the Channel
+Islands, where potatoes grown under glass are lifted in April and May,
+in order to secure the high prices of the early markets, tomato
+seedlings are planted out from boxes into the ground as quickly as the
+potatoes are removed, the tomato planter working only a few rows behind
+the potato digger. The trade in imported tomatoes is so considerable
+that home growers are well justified in their endeavours to meet the
+demand more fully with native produce, whether raised under glass or in
+the open. Tomatoes were not separately enumerated in the imports
+previous to 1900. It has already been stated that in 1900 the raw
+tomatoes imported amounted to 833,032 cwt., valued at £792,339, and in
+1901 to 793,991 cwt., valued at £734,051. From the monthly quantities
+given in Table VII., it would appear that the imports are largest in
+June, July and August, about one-half of the year's total arriving
+during those three months. It is too early in June and July for
+home-grown outdoor tomatoes to enter into competition with the imported
+product, but home-grown hothouse tomatoes should be qualified to
+challenge this trade.
+
+
+TABLE VII.--_Quantities of Tomatoes imported into the United Kingdom._
+
+  +-----------+-----------+------------+------------+
+  | Month.    |   1906.   |    1907.   |    1908.   |
+  +-----------+-----------+------------+------------+
+  | January   |    61,940 |     56,022 |     73,409 |
+  | February  |    58,187 |     58,289 |     69,350 |
+  | March     |   106,458 |     98,028 |     86,928 |
+  | April     |   103,273 |    109,057 |     74,917 |
+  | May       |    67,933 |    114,041 |     88,901 |
+  | June      |    62,906 |    144,379 |    127,793 |
+  | July      |   238,362 |    150,907 |    171,978 |
+  | August    |   180,046 |    102,600 |    124,757 |
+  | September |   114,860 |    101,198 |    119,224 |
+  | October   |    52,678 |     67,860 |     75,722 |
+  | November  |    41,513 |     66,522 |     74,292 |
+  | December  |    36,316 |     66,591 |     73,012 |
+  |           +-----------+------------+------------+
+  |   Total   | 1,124,472 |  1,135,494 |  1,160,283 |
+  |           +-----------+------------+------------+
+  |   Value   |  £953,475 | £1,135,499 | £1,160,283 |
+  +-----------+-----------+------------+------------+
+
+An important feature of modern flower growing is the production and
+cultivation of what are known as "hardy herbaceous perennials." Some
+2000 or 3000 different species and varieties of these are now raised in
+special nurseries; and during the spring, summer and autumn seasons
+magnificent displays are to be seen not only in the markets but at the
+exhibitions in London and at the great provincial shows held throughout
+the kingdom. The production of many of these perennials is so easy that
+amateurs in several instances have taken it up as a business hobby; and
+in some cases, chiefly through advertising in the horticultural press,
+very lucrative concerns have been established.
+
+Ornamental flowering trees and shrubs constitute another feature of
+modern gardening. These are grown and imported by thousands chiefly for
+their sprays of blossom or foliage, and for planting in large or small
+gardens, public parks, &c., for landscape effect. Indeed there is
+scarcely an easily grown plant from the northern or southern temperate
+zones that does not now find a place in the nursery or garden, provided
+it is sufficiently attractive to sell for its flowers, foliage or
+appearance.
+
+_Conditions of the Fruit and Flower growing Industries._--As regards
+open-air fruit-growing, the outlook for new ventures is perhaps brighter
+than in the hothouse industry, not--as Mr Bear has pointed out--because
+the area of fruit land in England is too small, but because the level of
+efficiency, from the selection of varieties to the packing and marketing
+of the produce, is very much lower in the former than in the latter
+branch of enterprise. In other words, whereas the practice of the
+majority of hothouse nurserymen is so skilled, so up-to-date, and so
+entirely under high pressure that a new competitor, however well
+trained, will find it difficult to rise above mediocrity, the converse
+is true of open-air fruit-growers. Many, and an increasing proportion,
+of the latter are thoroughly efficient in all branches of their
+business, and are in possession of plantations of the best market
+varieties of fruit, well cultivated, pruned and otherwise managed. But
+the extent of fruit plantations completely up to the mark in relation to
+varieties and treatment of trees and bushes, and in connexion with which
+the packing and marketing of the produce are equally satisfactory, is
+small in proportion to the total fruit area of the country. Information
+concerning the best treatment of fruit trees has spread widely in recent
+years, and old plantations, as a rule, suffer from the neglect or errors
+of the past, however skilful their present holders may be. Although the
+majority of professional market fruit-growers may be well up to the
+standard in skill, there are numerous contributors to the fruit supply
+who are either ignorant of the best methods of cultivation and marketing
+or careless in their application. The bad condition of the great
+majority of farm orchards is notorious, and many landowners, farmers and
+amateur gardeners who have planted fruit on a more or less extensive
+scale have mismanaged their undertakings. For these reasons new growers
+of open-air fruit for market have opportunities of succeeding by means
+of superiority to the majority of those with whom they will compete,
+provided that they possess the requisite knowledge, energy and capital.
+It has been asserted on sound authority that there is no chance of
+success for fruit-growers except in districts favourable as regards
+soil, climate and nearness to a railway or a good market; and, even
+under these conditions, only for men who have had experience in the
+industry and are prepared to devote their unremitting attention to it.
+Most important is it to a beginner that he should ascertain the
+varieties of fruit that flourish best in his particular district.
+Certain kinds seem to do well or fairly well in all parts of the
+country; others, whilst heavy croppers in some localities, are often
+unsatisfactory in others.
+
+As has been intimated, there is probably in England less room for
+expansion of fruit culture under glass than in the open. The large
+increase of glass-houses in modern times appears to have brought the
+supply of hothouse produce, even at greatly reduced prices, at least up
+to the level of the demand; and as most nurserymen continue to extend
+their expanse of glass, the prospect for new competitors is not a bright
+one. Moreover, the vast scale upon which some of the growers conduct the
+hothouse industry puts small producers at a great disadvantage, not only
+because the extensive producers can grow grapes and other fruit more
+economically than small growers--with the possible exception of those
+who do all or nearly all their own work--but also, and still more,
+because the former have greater advantages in transporting and marketing
+their fruit. There has, in recent years, been a much greater fall in the
+prices of hothouse than of open-air fruit, especially under the existing
+system of distribution, which involves the payment by consumers of 50 to
+100% more in prices than growers receive. The best openings for new
+nurseries are probably not where they are now to be found in large
+groups, and especially not in the neighbourhood of London, but in
+suitable spots near the great centres of population in the Midlands and
+the North, or big towns elsewhere not already well supplied with
+nurseries. By such a selection of a locality the beginner may build up a
+retail trade in hothouse fruit, or at least a trade with local
+fruiterers and grocers, thus avoiding railway charges and salesmen's
+commissions to a great extent, though it may often be advantageous to
+send certain kinds of produce to a distant market. Above all, a man who
+has no knowledge of the hothouse industry should avoid embarking his
+capital in it, trusting himself in the hands of a foreman, as experience
+shows that such a venture usually leads to disaster. Some years of
+training in different nurseries are desirable for any young man who is
+desirous of becoming a grower of hothouse fruits or flowers.
+
+There can be no doubt that flower-growing is greatly extending in
+England, and that competition among home growers is becoming more
+severe. Foreign supplies of flowers have increased, but not nearly as
+greatly in proportion as home supplies, and it seems clear that home
+growers have gained ground in relation to their foreign rivals, except
+with respect to flowers for the growth of which foreigners have
+extraordinary natural advantages. There seems some danger of the home
+culture of the narcissus being over-done, and the florists'
+chrysanthemum appears to be produced in excess of the demand. Again, in
+the production of violets the warm and sunny South of France has an
+advantage not possessed by England, whilst Holland, likewise for
+climatic reasons, maintains her hold upon the hyacinth and tulip trade.
+Whether the production of flowers as a whole is gaining ground upon the
+demand or not is a difficult question to answer. It is true that the
+prices of flowers have fallen generally; but production, at any rate
+under glass, has been cheapened, and if a fair profit can be obtained,
+the fall in prices, without which the existing consumption of flowers
+would be impossible, does not necessarily imply over-production. There
+is some difference of opinion among growers upon this point; but nearly
+all agree that profits are now so small that production on a large scale
+is necessary to provide a fair income. Industrial flower-growing affords
+such a wide scope for the exercise of superior skill, industry and
+alertness, that it is not surprising to find some who are engaged in it
+doing remarkably well to all appearance, while others are struggling on
+and hardly paying their way. That a man with only a little capital,
+starting in a small way, has many disadvantages is certain; also, that
+his chance of saving money and extending his business quickly is much
+smaller than it was. To the casual looker-on, who knows nothing of the
+drudgery of the industry, flower-growing seems a delightful method of
+getting a living. That it is an entrancing pursuit there is no doubt;
+but it is equally true that it is a very arduous one, requiring careful
+forethought, ceaseless attention and abundant energy. Fortunately for
+those who might be tempted, without any knowledge of the industry, to
+embark capital in it, flower-growing, if at all comprehensive in scope,
+so obviously requires a varied and extensive technical knowledge,
+combined with good commercial ability, that any one can see that a
+thorough training is necessary to a man who intends to adopt it as a
+business, especially if hothouse flowers are to be produced.
+
+  The market for fruit, and more especially for flowers, is a fickle
+  one, and there is nearly always some uncertainty as to the course of
+  prices. The perishable nature of soft fruit and cut flowers renders
+  the markets very sensitive to anything in the nature of a glut, the
+  occurrence of which is usually attended with disastrous results to
+  producers. Foreign competition, moreover, has constantly to be faced,
+  and it is likely to increase rather than diminish. French growers have
+  a great advantage over the open-air cultivators of England, for the
+  climate enables them to get their produce into the markets early in
+  the season, when the highest prices are obtainable. The geographical
+  advantage which France enjoys in being so near to England is, however,
+  considerably discounted by the increasing facilities for cold storage
+  in transit, both by rail and sea. The development of such facilities
+  permits of the retail sale in England of luscious fruit as fresh and
+  attractive as when it was gathered beneath the sunny skies of
+  California. In the case of flowers, fashion is an element not to be
+  ignored. Flowers much in request in one season may meet with very
+  little demand in another, and it is difficult for the producer to
+  anticipate the changes which caprice may dictate. Even for the same
+  kind of flower the requirements are very uncertain, and the white
+  blossom which is all the rage in one season may be discarded in favour
+  of one of another colour in the next. The sale of fresh flowers for
+  church decoration at Christmas and Easter has reached enormous
+  dimensions. The irregularity in the date of the festival, however,
+  causes some inconvenience to growers. If it falls very early the great
+  bulk of suitable flowers may not be sufficiently forward for sale,
+  whilst a late Easter may find the season too far advanced. The trade
+  in cut flowers, therefore, is generally attended by uncertainty, and
+  often by anxiety.     (W. FR.; J. WS.)
+
+
+UNITED STATES
+
+In the United States horticulture and market gardening have now assumed
+immense proportions. In a country of over 3,000,000 sq. m., stretching
+from the Atlantic to the Pacific on the one hand, and from the Gulf of
+Mexico to the great northern lakes and the Dominion of Canada on the
+other, a great variation of climatic conditions is not unnatural. From a
+horticultural point of view there are practically two well-defined
+regions: (1) that to the east of the Rocky Mountains across to the
+Atlantic, where the climate is more like that of eastern Asia than of
+western Europe so far as rainfall, temperature and seasonable conditions
+are concerned; (2) that to the west of the Rockies, known as the Pacific
+coast region, where the climate is somewhat similar to that of western
+Europe. It may be added that in the northern states--in Washington,
+Montana, North Dakota, Minnesota, Wisconsin, &c.--the winters are often
+very severe, while the southern states practically enjoy a temperature
+somewhat similar to that of the Riviera. Indeed the range of temperature
+between the extreme northern states and the extreme southern may vary as
+much as 120° F. The great aim of American gardeners, therefore, has been
+to find out or to produce the kinds of fruits, flowers and vegetables
+that are likely to flourish in different parts of this immense country.
+
+_Fruit Culture._--There is probably no country in the world where so
+many different kinds of fruit can be grown with advantage to the nation
+as in the United States. In the temperate regions apples, pears and
+plums are largely grown, and orchards of these are chiefly to be found
+in the states of New York, Massachusetts, Pennsylvania, Michigan,
+Missouri, Colorado, and also in northern Texas, Arkansas and N.
+California. To these may be added cranberries and quinces, which are
+chiefly grown in the New England states. The quinces are not a crop of
+first-rate importance, but as much as 800,000 bushels of cranberries are
+grown each year. The peach orchards are assuming great proportions, and
+are chiefly to be found in Georgia and Texas, while grapes are grown
+throughout the Republic from east to west in all favourable localities.
+Oranges, lemons and citrons are more or less extensively grown in
+Florida and California, and in these regions what are known as Japanese
+or "Kelsey" plums (forms of _Prunus triflora_) are also grown as
+marketable crops. Pomegranates are not yet largely grown, but it is
+possible their culture will develop in southern Texas and Louisiana,
+where the climate is tempered by the waters of the Gulf of Mexico.
+Tomatoes are grown in most parts of the country so easily that there is
+frequently a glut; while the strawberry region extends from Florida to
+Virginia, Pennsylvania and other states--thus securing a natural
+succession from south to north for the various great market centres.
+
+Of the fruits mentioned apples are undoubtedly the most important. Not
+only are the American people themselves supplied with fresh fruit, but
+immense quantities are exported to Europe--Great Britain alone absorbing
+as much as 1,430,000 cwt. in 1908. The varieties originally grown were
+of course those taken or introduced from Europe by the early settlers.
+Since the middle of the 19th century great changes have been brought
+about, and the varieties mostly cultivated now are distinctly American.
+They have been raised by crossing and intercrossing the most suitable
+European forms with others since imported from Russia. In the extreme
+northern states indeed, where it is essential to have apple trees that
+will stand the severest winters, the Russian varieties crossed with the
+berry crab of eastern Europe (_Pyrus baccata_) have produced a race
+eminently suited to that particular region. The individual fruits are
+not very large, but the trees are remarkably hardy. Farther south larger
+fruited varieties are grown, and among these may be noted Baldwins,
+Newton pippins, Spitzenbergs and Rhode Island greening. Apple orchards
+are numerous in the State of New York, where it is estimated that over
+100,000 acres are devoted to them. In the hilly regions of Missouri,
+Arkansas and Colorado there are also great plantations of apples. The
+trees, however, are grown on different principles from those in New York
+State. In the latter state apple trees with ordinary care live to more
+than 100 years of age and produce great crops; in the other states,
+however, an apple tree is said to be middle-aged at 20, decrepit at 30
+and practically useless at 40 years of age. They possess the advantage,
+however, of bearing early and heavily.
+
+Until the introduction of the cold-storage system, about the year 1880,
+America could hardly be regarded as a commercial fruit-growing country.
+Since then, however, owing to the great improvements made in railway
+refrigerating vans and storage houses, immense quantities of fruit can
+be despatched in good condition to any part of the world; or they can be
+kept at home in safety until such time as the markets of Chicago, New
+York, Boston, Baltimore, Philadelphia, &c., are considered favourable
+for their reception.
+
+Apple trees are planted at distances varying from 25 ft. to 30 ft. apart
+in the middle western states, to 40 ft. to 50 ft. apart in New York
+State. Here and there, however, in some of the very best orchards the
+trees are planted 60 ft. apart every way. Each tree thus has a chance to
+develop to its utmost limits, and as air and light reach it better, a
+far larger fruit-bearing surface is secured. Actual experience has shown
+that trees planted at 60 ft. apart--about 28 to the acre--produce more
+fruit by 43 bushels than trees at 30 ft. apart--i.e. about 48 to the
+acre.
+
+Until recent years pruning as known to English and French gardeners was
+practically unknown. There was indeed no great necessity for it, as the
+trees, not being cramped for space, threw their branches outwards and
+upwards, and thus rarely become overcrowded. When practised, however,
+the operation could scarcely be called pruning; lopping or trimming
+would be more accurate descriptions.
+
+Apple orchards are not immune from insect pests and fungoid diseases,
+and an enormous business is now done in spraying machines and various
+insecticides. It pays to spray the trees, and figures have been given to
+show that orchards that have been sprayed four times have produced an
+average income of £211 per acre against £103 per acre from unsprayed
+orchards.
+
+The spring frosts are also troublesome, and in the Colorado and other
+orchards the process known as "smudging" is now adopted to save the
+crops. This consists in placing 20 or 30, or even more, iron or tin pots
+to an acre, each pot containing wooden chips soaked in tar (or pitch)
+mixed with kerosene. Whenever the thermometer shows 3 or 4 degrees of
+frost the smudge-pots are lighted. A dense white smoke then arises and
+is diffused throughout the orchards, enveloping the blossoming heads of
+the trees in a dense cloud. This prevents the frost from killing the
+tender pistils in the blossoms, and when several smudge-pots are alight
+at the same time the temperature of the orchard is raised two or three
+degrees. This work has generally to be done between 3 and 5 A.M., and
+the growers naturally have an anxious time until all danger is over. The
+failure to attend to smudging, even on one occasion, may result in the
+loss of the entire crop of plums, apples or pears.
+
+Next to apples perhaps peaches are the most important fruit crop. The
+industry is chiefly carried on in Georgia, Texas and S. Carolina, and on
+a smaller scale in some of the adjoining states. Peaches thus flourish
+in regions that are quite unsuitable for apples or pears. In many
+orchards in Georgia, where over 3,000,000 acres have been planted, there
+are as many as 100,000 peach trees; while some of the large fruit
+companies grow as many as 365,000. In one place in West Virginia there
+is, however, a peach orchard containing 175,000 trees, and in Missouri
+another company has 3 sq. m. devoted to peach culture. As a rule the
+crops do well. Sometimes, however, a disease known as the "yellows"
+makes sad havoc amongst them, and scarcely a fruit is picked in an
+orchard which early in the season gave promise of a magnificent crop.
+
+Plums are an important crop in many states. Besides the European
+varieties and those that have been raised by crossing with American
+forms, there is now a growing trade done in Japanese plums. The largest
+of these is popularly known as "Kelseys," named after John Kelsey, who
+raised the first fruit in 1876 from trees brought to California in 1870.
+Sometimes the fruits are 3 in. in diameter, and like most of the
+Japanese varieties are more heart-shaped and pointed than plums of
+European origin. One apparent drawback to the Kelsey plum is its
+irregularity in ripening. It has been known in some years to be quite
+ripe in June, while in others the fruits are still green in October.
+
+Pears are much grown in such states as Massachusetts, New York,
+Pennsylvania, Missouri and California; while bush fruits like currants,
+gooseberries and raspberries find large spaces devoted in most of the
+middle and northern states. Naturally a good deal of crossing and
+intercrossing has taken place amongst the European and American forms of
+these fruits, but so far as gooseberries are concerned no great advance
+seems to have been made in securing varieties capable of resisting the
+devastating gooseberry mildew.
+
+Other fruits of more or less commercial value are oranges, lemons and
+citrons, chiefly in Florida. Lemons are practically a necessity to the
+American people, owing to the heat of the summers, when cool and
+refreshing drinks with an agreeable acidulous taste are in great demand.
+The pomelo (grape-fruit) is a kind of lemon with a thicker rind and a
+more acid flavour. At one time its culture was confined to Florida, but
+of recent years it has found its way into Californian orchards.
+Notwithstanding the prevailing mildness of the climate in both
+California and Florida, the crops of oranges, lemons, citrons, &c., are
+sometimes severely injured by frosts when in blossom.
+
+Other fruits likely to be heard of in the future are the kaki or
+persimmon, the loquat, which is already grown in Louisiana, as well as
+the pomegranate.
+
+Great aid and encouragement are given by the government to the progress
+of American fruit-growing, and by the experiments that are being
+constantly carried out and tabulated at Cornell University and by the
+U.S.A. department of agriculture.
+
+_Flower Culture._--So far as flowers are concerned there appears to be
+little difference between the kinds of plants grown in the United States
+and in England, France, Belgium, Germany, Holland, &c. Indeed there is a
+great interchange of new varieties of plants between Europe and America,
+and modifications in systems of culture are being gradually introduced
+from one side of the Atlantic to the other. The building of greenhouses
+for commercial purposes is perhaps on a somewhat different scale from
+that in England, but there are probably no extensive areas of glass such
+as are to be seen north of London from Enfield Highway to Broxburne. Hot
+water apparatus differs merely in detail, although most of the boilers
+used resemble those on the continent of Europe rather than in England.
+Great business is done in bulbs--mostly imported from Holland--stove and
+greenhouse plants, hardy perennials, orchids, ferns of the "fancy" and
+"dagger" types of Nephrolepis, and in carnations and roses. Amongst the
+latter thousands of such varieties as Beauty, Liberty, Killarney,
+Richmond and Bride are grown, and realize good prices as a rule in the
+markets. Carnations of the winter-flowering or "perpetual" type have
+long been grown in America, and enormous prices have been given for
+individual plants on certain occasions, rivalling the fancy prices paid
+in England for certain orchids. The American system of carnation-growing
+has quite captivated English cultivators, and new varieties are being
+constantly raised in both countries. Chrysanthemums are another great
+feature of American florists, and sometimes during the winter season a
+speculative grower will send a living specimen to one of the London
+exhibitions in the hope of booking large orders for cuttings of it later
+on. Sweet peas, dahlias, lilies of the valley, arum lilies and indeed
+every flower that is popular in England is equally popular in America,
+and consequently is largely grown.
+
+  _Vegetables._--So far as these are concerned, potatoes, cabbages,
+  cauliflowers, beans of all kinds, cucumbers, tomatoes (already
+  referred to under fruits), musk-melons, lettuces, radishes, endives,
+  carrots, &c.; are naturally grown in great quantities, not only in the
+  open air, but also under glass. The French system of intensive
+  cultivation as practised on hot beds of manure round Paris is
+  practically unknown at present. In the southern states there would be
+  no necessity to practise it, but in the northern ones it is likely to
+  attract attention.     (J. Ws.)
+
+
+FOOTNOTE:
+
+  [1] _Jour. Roy. Agric. Soc._, 1899.
+
+
+
+
+FRUMENTIUS (c. 300-c. 360), the founder of the Abyssinian church,
+traditionally identified in Abyssinian literature with Abba Salama or
+Father of Peace (but see ETHIOPIA), was a native of Phoenicia. According
+to the 4th-century historian Rufinus (x. 9), who gives Aedesius himself
+as his authority, a certain Tyrian, Meropius, accompanied by his kinsmen
+Frumentius and Aedesius, set out on an expedition to "India," but fell
+into the hands of Ethiopians on the shore of the Red Sea and, with his
+ship's crew, was put to death. The two young men were taken to the king
+at Axum, where they were well treated and in time obtained great
+influence. With the help of Christian merchants who visited the country
+Frumentius gave Christianity a firm footing, which was strengthened when
+in 326 he was consecrated bishop by Athanasius of Alexandria, who in his
+_Epistola ad Constantinum_ mentions the consecration, and gives some
+details of the history of Frumentius's mission. Later witnesses speak of
+his fidelity to the homoousian during the Arian controversies. Aedesius
+returned to Tyre, where he was ordained presbyter.
+
+
+
+
+FRUNDSBERG, GEORG VON (1473-1528), German soldier, was born at
+Mindelheim on the 24th of September 1473. He fought for the German king
+Maximilian I. against the Swiss in 1499, and in the same year was among
+the imperial troops sent to assist Ludovico Sforza, duke of Milan,
+against the French. Still serving Maximilian, he took part in 1504 in
+the war over the succession to the duchy of Bavaria-Landshut, and
+afterwards fought in the Netherlands. Convinced of the necessity of a
+native body of trained infantry Frundsberg assisted Maximilian to
+organize the _Landsknechte_ (q.v.), and subsequently at the head of
+bands of these formidable troops he was of great service to the Empire
+and the Habsburgs. In 1509 he shared in the war against Venice, winning
+fame for himself and his men; and after a short visit to Germany
+returned to Italy, where in 1513 and 1514 he gained fresh laurels by his
+enterprises against the Venetians and the French. Peace being made, he
+returned to Germany, and at the head of the infantry of the Swabian
+league assisted to drive Ulrich of Württemberg from his duchy in 1519.
+At the diet of Worms in 1521 he spoke words of encouragement to Luther,
+and when the struggle between France and the Empire was renewed he took
+part in the invasion of Picardy, and then proceeding to Italy brought
+the greater part of Lombardy under the influence of Charles V. through
+his victory at Bicocca in April 1522. He was partly responsible for the
+great victory over the French at Pavia in February 1525, and, returning
+to Germany, he assisted to suppress the Peasant revolt, using on this
+occasion, however, diplomacy as well as force. When the war in Italy was
+renewed Frundsberg raised an army at his own expense, and skilfully
+surmounting many difficulties, joined the constable de Bourbon near
+Piacenza and marched towards Rome. Before he reached the city, however,
+his unpaid troops showed signs of mutiny, and their leader, stricken
+with illness and unable to pacify them, gave up his command. Returning
+to Germany, he died at Mindelheim on the 20th of August 1528. He was a
+capable and chivalrous soldier, and a devoted servant of the Habsburgs.
+His son Caspar (1500-1536) and his grandson Georg (d. 1586) were both
+soldiers of some distinction. With the latter's death the family became
+extinct.
+
+  See Adam Reissner, _Historia Herrn Georgs und Herrn Kaspars von
+  Frundsberg_ (Frankfort, 1568). A German translation of this work was
+  published at Frankfort in 1572. F.W. Barthold, _Georg von Frundsberg_
+  (Hamburg, 1833); J. Heilmann, _Kriegsgeschichte von Bayern, Franken,
+  Pfalz und Schwaben_ (Munich, 1868).
+
+
+
+
+
+FRUSTUM (Latin for a "piece broken off"), a term in geometry for the
+part of a solid figure, such as a cone or pyramid, cut off by a plane
+parallel to the base, or lying between two parallel planes; and hence in
+architecture a name given to the drum of a column.
+
+
+
+
+FRUYTIERS, PHILIP (1627-1666), Flemish painter and engraver, was a pupil
+of the Jesuits' college at Antwerp in 1627, and entered the Antwerp gild
+of painters without a fee in 1631. He is described in the register of
+that institution as "illuminator, painter and engraver." The current
+account of his life is "that he worked exclusively in water colours, yet
+was so remarkable in this branch of his art for arrangement, drawing,
+and especially for force and clearness of colour, as to excite the
+admiration of Rubens, whom he portrayed with all his family." The truth
+is that he was an artist of the most versatile talents, as may be judged
+from the fact that in 1646 he executed an Assumption with figures of
+life size, and four smaller pictures in oil, for the church of St
+Jacques at Antwerp, for which he received the considerable sum of 1150
+florins. Unhappily no undoubted production of his hand has been
+preserved. All that we can point to with certainty is a series of etched
+plates, chiefly portraits, which are acknowledged to have been
+powerfully and skilfully handled. If, however, we search the portfolios
+of art collections on the European continent, we sometimes stumble upon
+miniatures on vellum, drawn with great talent and coloured with
+extraordinary brilliancy. In form they quite recall the works of Rubens,
+and these, it may be, are the work of Philip Fruytiers.
+
+
+
+
+FRY, the name of a well-known English Quaker family, originally living
+in Wiltshire. About the middle of the 18th century JOSEPH FRY
+(1728-1787), a doctor, settled in Bristol, where he acquired a large
+practice, but eventually abandoned medicine for commerce. He became
+interested in china-making, soap-boiling and type-founding businesses in
+Bristol, and in a chemical works at Battersea, all of which ventures
+proved very profitable. The type-founding business was subsequently
+removed to London and conducted by his son Edmund. Joseph Fry, however,
+is best remembered as the founder of the great Bristol firm of J.S. Fry
+& Sons, chocolate manufacturers. He purchased the chocolate-making
+patent of William Churchman and on it laid the foundations of the
+present large business. After his death the Bristol chocolate factory
+was carried on with increasing success by his widow and by his son,
+JOSEPH STORRS FRY (1767-1835).
+
+In 1795 a new and larger factory was built in Union Street, Bristol,
+which still forms the centre of the firm's premises, and in 1798 a
+Watt's steam-engine was purchased and the cocoa-beans ground by steam.
+On the death of Joseph Storrs Fry his three sons, Joseph (1795-1879),
+Francis, and Richard (1807-1878) became partners in the firm, the
+control being mainly in the hands of FRANCIS FRY (1803-1886). Francis
+Fry was in every way a remarkable character. The development of the
+business to its modern enormous proportion was chiefly his work, but
+this did not exhaust his activities. He took a principal part in the
+introduction of railways to the west of England, and in 1852 drew up a
+scheme for a general English railway parcel service. He was an ardent
+bibliographer, taking a special interest in early English Bibles, of
+which he made in the course of a long life a large and striking
+collection, and of the most celebrated of which he published facsimiles
+with bibliographical notes. Francis Fry died in 1886, and his son
+Francis J. Fry and nephew Joseph Storrs Fry carried on the business,
+which in 1896 was for family reasons converted into a private limited
+company, Joseph Storrs Fry being chairman and all the directors members
+of the Fry family.
+
+
+
+
+FRY, SIR EDWARD (1827-   ), English judge, second son of Joseph Fry
+(1795-1879), was born at Bristol on the 4th of November 1827, and
+educated at University College, London, and London University. He was
+called to the bar in 1854 and was made a Q.C. in 1869, practising in the
+rolls court and becoming recognized as a leading equity lawyer. In 1877
+he was raised to the bench and knighted. As chancery judge he will be
+remembered for his careful interpretations and elucidations of the
+Judicature Acts, then first coming into operation. In 1883 he was made a
+lord justice of appeal, but resigned in 1892; and subsequently his
+knowledge of equity and talents for arbitration were utilized by the
+British government from time to time in various special directions,
+particularly as chairman of many commissions. He was also one of the
+British representatives at the Paris North Sea Inquiry Commission
+(1905), and was appointed a member of the Hague Permanent Arbitration
+Court. He wrote _A Treatise on the Specific Performance of Public
+Contracts_ (London, 1858, and many subsequent editions).
+
+
+
+
+FRY, ELIZABETH (1780-1845), English philanthropist, and, after Howard,
+the chief promoter of prison reform in Europe, was born in Norwich on
+the 21st of May 1780. Her father, John Gurney, afterwards of Earlham
+Hall, a wealthy merchant and banker, represented an old family which for
+some generations had belonged to the Society of Friends. While still a
+girl she gave many indications of the benevolence of disposition,
+clearness and independence of judgment, and strength of purpose, for
+which she was afterwards so distinguished; but it was not until after
+she had entered her eighteenth year that her religion assumed a decided
+character, and that she was induced, under the preaching of the American
+Quaker, William Savery, to become an earnest and enthusiastic though
+never fanatical "Friend." In August 1800 she became the wife of Joseph
+Fry, a London merchant.
+
+Amid increasing family cares she was unwearied in her attention to the
+poor and the neglected of her neighbourhood; and in 1811 she was
+acknowledged by her co-religionists as a "minister," an honour and
+responsibility for which she was undoubtedly qualified, not only by
+vigour of intelligence and warmth of heart, but also by an altogether
+unusual faculty of clear, fluent and persuasive speech. Although she had
+made several visits to Newgate prison as early as February 1813, it was
+not until nearly four years afterwards that the great public work of her
+life may be said to have begun. The association for the Improvement of
+the Female Prisoners in Newgate was formed in April 1817. Its aim was
+the much-needed establishment of some of what are now regarded as the
+first principles of prison discipline, such as entire separation of the
+sexes, classification of criminals, female supervision for the women,
+and adequate provision for their religious and secular instruction, as
+also for their useful employment. The ameliorations effected by this
+association, and largely by the personal exertions of Mrs Fry, soon
+became obvious, and led to a rapid extension of similar methods to other
+places. In 1818 she, along with her brother, visited the prisons of
+Scotland and the north of England; and the publication (1819) of the
+notes of this tour, as also the cordial recognition of the value of her
+work by the House of Commons committee on the prisons of the metropolis,
+led to a great increase of her correspondence, which now extended to
+Italy, Denmark and Russia, as well as to all parts of the United
+Kingdom. Through a visit to Ireland, which she made in 1827, she was led
+to direct her attention to other houses of detention besides prisons;
+and her observations resulted in many important improvements in the
+British hospital system, and in the treatment of the insane. In 1838 she
+visited France, and besides conferring with many of the leading prison
+officials, she personally visited most of the houses of detention in
+Paris, as well as in Rouen, Caen and some other places. In the following
+year she obtained an official permission to visit all the prisons in
+that country; and her tour, which extended from Boulogne and Abbeville
+to Toulouse and Marseilles, resulted in a report which was presented to
+the minister of the interior and the prefect of police. Before returning
+to England she had included Geneva, Zürich, Stuttgart and
+Frankfort-on-Main in her inspection. The summer of 1840 found her
+travelling through Belgium, Holland and Prussia on the same mission; and
+in 1841 she also visited Copenhagen. In 1842, through failing health,
+Mrs Fry was compelled to forgo her plans for a still more widely
+extended activity, but had the satisfaction of hearing from almost every
+quarter of Europe that the authorities were giving increased practical
+effect to her suggestions. In 1844 she was seized with a lingering
+illness, of which she died on the 12th of October 1845. She was
+survived by a numerous family, the youngest of whom was born in 1822.
+
+Two interesting volumes of _Memoirs, with Extracts from her Journals and
+Letters_, edited by two of her daughters, were published in 1847. See
+also _Elizabeth Fry_, by G. King Lewis (1910).
+
+
+
+
+FRYXELL, ANDERS (1795-1881), Swedish historian, was born at Hesselskog,
+Dalsland, Sweden, on the 7th of February 1795. He was educated at
+Upsala, took holy orders in 1820, was made a doctor of philosophy in
+1821, and in 1823 began to publish the great work of his life, the
+_Stories from Swedish History_. He did not bring this labour to a close
+until, fifty-six years later, he published the forty-sixth and crowning
+volume of his vast enterprise. Fryxell, as a historian, appealed to
+every class by the picturesqueness of his style and the breadth of his
+research; he had the gift of awakening to an extraordinary degree the
+national sense in his readers. In 1824 he published his _Swedish
+Grammar_, which was long without a rival. In 1833 he received the title
+of professor, and in 1835 he was appointed to the incumbency of Sunne,
+in the diocese of Karlstad, where he resided for the remainder of his
+life. In 1840 he was elected to the Swedish Academy in succession to the
+poet Wallin (1779-1839). In 1847 Fryxell received from his bishop
+permission to withdraw from all the services of the Church, that he
+might devote himself without interruption to historical investigation.
+Among his numerous minor writings are prominent his _Characteristics of
+Sweden between 1592 and 1600_ (1830), his _Origins of the Inaccuracy
+with which the History of Sweden in Catholic Times has been Treated_
+(1847), and his _Contributions to the Literary History of Sweden_. It is
+now beginning to be seen that the abundant labours of Fryxell were
+rather of a popular than of a scientific order, and although their
+influence during his lifetime was unbounded, it is only fair to later
+and exacter historians to admit that they threaten to become obsolete in
+more than one direction. On the 21st of March 1881 Anders Fryxell died
+at Stockholm, and in 1884 his daughter Eva Fryxell (born 1829) published
+from his MS. an interesting _History of My History_, which was really a
+literary autobiography and displays the persistency and tirelessness of
+his industry.     (E. G.)
+
+
+
+
+FUAD PASHA (1815-1869), Turkish statesman, was the son of the
+distinguished poet Kechéji-zadé Izzet Molla. He was educated at the
+medical school and was at first an army surgeon. About 1836 he entered
+the civil service as an official of the foreign ministry. He became
+secretary of the embassy in London; was employed on special missions in
+the principalities and at St Petersburg (1848), and was sent to Egypt as
+special commissioner in 1851. In that year he became minister for
+foreign affairs, a post to which he was appointed also on four
+subsequent occasions and which he held at the time of his death. During
+the Crimean War he commanded the troops on the Greek frontier and
+distinguished himself by his bravery. He was Turkish delegate at the
+Paris conference of 1856; was charged with a mission to Syria in 1860;
+grand vizier in 1860 and 1861, and also minister of war. He accompanied
+the sultan Abd-ul-Aziz on his journey to Egypt and Europe, when the
+freedom of the city of London was conferred on him. He died at Nice
+(whither he had been ordered for his health) in 1869. Fuad was renowned
+for his boldness and promptness of decision, as well as for his ready
+wit and his many bons mots. Generally regarded as the partisan of a
+pro-English policy, he rendered most valuable service to his country by
+his able management of the foreign relations of Turkey, and not least by
+his efficacious settlement of affairs in Syria after the massacres of
+1860.
+
+
+
+
+FUCHOW, FU-CHAU, FOOCHOW, a city of China, capital of the province of
+Fu-kien, and one of the principal ports open to foreign commerce. In the
+local dialect it is called Hokchiu. It is situated on the river Min,
+about 35 m. from the sea, in 26° 5' N. and 119º 20' E., 140 m. N. of
+Amoy and 280 S. of Hang-chow. The city proper, lying nearly 3 m. from
+the north bank of the river, is surrounded by a wall about 30 ft. high
+and 12 ft. thick, which makes a circuit of upwards of 5 m. and is
+pierced by seven gateways surrounded by tall fantastic watch-towers.
+The whole district between the city and the river, the island of
+Nantai, and the southern banks of the Min are occupied by extensive
+suburbs; and the river itself bears a large floating population.
+Communication from bank to bank is afforded by a long stone bridge
+supported by forty solid stone piers in its northern section and by nine
+in its southern. The most remarkable establishment of Fuchow is the
+arsenal situated about 3 m. down the stream at Pagoda Island, where the
+sea-going vessels usually anchor. It was founded in 1867, and is
+conducted under the direction of French engineers according to European
+methods. In 1870 it employed about 1000 workmen besides fifty European
+superintendents, and between that date and 1880 it turned out about 20
+or 30 small gunboats. In 1884 it was partially destroyed by the French
+fleet, and for a number of years the workshops and machinery were
+allowed to stand idle and go to decay. On the 1st of August 1895 an
+attack was made on the English mission near the city of Ku-chang, 120 m.
+west of Fuchow, on which occasion nine missionaries, of whom eight were
+ladies, were massacred. The port was opened to European commerce in
+1842; and in 1853 the firm of Russell and Co. shipped the first cargoes
+of tea from Fuchow to Europe and America. The total trade in foreign
+vessels in 1876 was imports to the value of £1,531,617, and exports to
+the value of £3,330,489. In 1904 the imports amounted to £1,440,351, and
+the exports to £1,034,436. The number of vessels that entered in 1876
+was 275, and of these 211 were British, 27 German, 11 Danish and 9
+American. While in 1904, 480 vessels entered the port, 216 of which were
+British. A large trade is carried on by the native merchants in timber,
+paper, woollen and cotton goods, oranges and olives; but the foreign
+houses mainly confine themselves to opium and tea. Commercial
+intercourse with Australia and New Zealand is on the increase. The
+principal imports, besides opium, are shirtings, T-cloths, lead and tin,
+medicines, rice, tobacco, and beans and peas. Two steamboat lines afford
+regular communication with Hong-Kong twice a month. The town is the seat
+of several important missions, of which the first was founded in 1846.
+That supported by the American board had in 1876 issued 1,3000,000
+copies of Chinese books and tracts.
+
+
+
+
+FUCHS, JOHANN NEPOMUK VON (1774-1856), German chemist and mineralogist,
+was born at Mattenzell, near Brennberg in the Bavarian Forest, on the
+15th of May 1774. In 1807 he became professor of chemistry and
+mineralogy at the university of Landshut, and in 1823 conservator of the
+mineralogical collections at Munich, where he was appointed professor of
+mineralogy three years later, on the removal thither of the university
+of Landshut. He retired in 1852, was ennobled by the king of Bavaria in
+1854, and died at Munich on the 5th of March 1856. His name is chiefly
+known for his mineralogical observations and for his work on soluble
+glass.
+
+  His collected works, including _Über den Einfluss der Chemie und
+  Mineralogie_ (1824), _Die Naturgeschichte des Mineralreichs_ (1842),
+  _Über die Theorien der Erde_ (1844), were published at Munich in 1856.
+
+
+
+
+FUCHS, LEONHARD (1501-1566), German physician and botanist, was born at
+Wembdingen in Bavaria on the 17th of January 1501. He attended school at
+Heilbronn and Erfurt, and in 1521 graduated at the university of
+Ingolstadt. About the same time he espoused the doctrines of the
+Reformation. Having in 1524 received his diploma as doctor of medicine,
+he practised for two years in Munich. He became in 1526 professor of
+medicine at Ingolstadt, and in 1528 physician to the margrave of
+Anspach. In Anspach he was the means of saving the lives of many during
+the epidemic locally known as the "English sweating-sickness." By the
+duke of Württemberg he was, in 1535, appointed to the professorship of
+medicine at the university of Tübingen, a post held by him till his
+death on the 10th of May 1566. Fuchs was an advocate of the Galenic
+school of medicine, and published several Latin translations of
+treatises by its founder and by Hippocrates. But his most important
+publication was _De historia stirpium commentarii insignes_ (Basel,
+1542), a work illustrated with more than five hundred excellent outline
+illustrations, including figures of the common foxglove and of another
+species of the genus _Digitalis_, which was so named by him.
+
+
+
+
+FUCHSIA, so named by Plumier in honour of the botanist Leonhard Fuchs, a
+genus of plants of the natural order Onagraceae, characterized by
+entire, usually opposite leaves, pendent flowers, a funnel-shaped,
+brightly coloured, quadripartite, deciduous calyx, 4 petals, alternating
+with the calycine segments, 8, rarely 10, exserted stamens, a long
+filiform style, an inferior ovary, and fruit, a fleshy ovoid many-seeded
+berry. All the members of the genus, with the exception of the New
+Zealand species, _F. excorticata, F. Colensoi_ and _F. procumbens_, are
+natives of Central and South America--occurring in the interior of
+forests or in damp and shady mountainous situations. The various species
+differ not a little in size as well as in other characters; some, as _F.
+verrucosa_, being dwarf shrubs; others, as _F. arborescens_ and _F.
+apetala_, attaining a height of 12 to 16 ft., and having stems several
+inches in diameter. Plumier, in his _Nova plantarum Americanarum genera_
+(p. 14, tab. 14, Paris, 1703), gave a description of a species of
+fuchsia, the first known, under the name of _Fuchsia triphylla, flore
+coccineo_, and a somewhat conventional outline figure of the same plant
+was published at Amsterdam in 1757 by Burmann. In the _Histoire des
+plantes médicinales_ of the South American traveller Feuillée (p. 64,
+pl. XLVII.), written in 1709-1711, and published by him with his
+_Journal_, Paris, 1725, the name _Thilco_ is applied to a species of
+fuchsia from Chile, which is described, though not evidently so figured,
+as having a pentamerous calyx. The _F. coccinea_ of Alton (fig.) (see
+J.D. Hooker, in _Journal Linnean Soc_., Botany, vol. x. p. 458, 1867),
+the first species of fuchsia cultivated in England, where it was long
+confined to the greenhouse, was brought from South America by Captain
+Firth in 1788 and placed in Kew Gardens. Of this species Mr Lee, a
+nurseryman at Hammersmith, soon afterwards obtained an example, and
+procured from it by means of cuttings several hundred plants, which he
+sold at a guinea each. In 1823 _F. macrostemma_ and _F. gracilis_, and
+during the next two or three years several other species, were
+introduced into England; but it was not until about 1837, or soon after
+florists had acquired _F. fulgens_, that varieties of interest began to
+make their appearance. The numerous hybrid forms now existing are the
+result chiefly of the intercrossing of that or other long-flowered with
+globose-flowered plants. _F. Venus-victrix_, raised by Mr Gulliver,
+gardener to the Rev. S. Marriott of Horsemonden, Kent, and sold in 1822
+to Messrs Cripps, was the earliest white-sepalled fuchsia. The first
+fuchsia with a white corolla was produced about 1853 by Mr Storey. In
+some varieties the blossoms are variegated, and in others they are
+double. There appears to be very little limit to the number of forms to
+be obtained by careful cultivation and selection. To hybridize, the
+flower as soon as it opens is emasculated, and it is then fertilized
+with pollen from some different flower.
+
+[Illustration: _Fuchsia coccinea_. 1, Flower cut open after removal of
+sepals; 2, fruit; 3, floral diagram.]
+
+Ripe seed is sown either in autumn or about February or March in light,
+rich, well-drained mould, and is thinly covered with sandy soil and
+watered. A temperature of 70° to 75° Fahr. has been found suitable for
+raising. The seedlings are pricked off into shallow pots or pans, and
+when 3 in. in height are transferred to 3-in. pots, and are then treated
+the same as plants from cuttings. Fuchsias may be grafted as readily as
+camellias, preferably by the splice or whip method, the apex of a young
+shoot being employed as a scion; but the easiest and most usual method
+of propagation is by cuttings. The most expeditious way to procure these
+is to put plants in heat in January, and to take their shoots when 3 in.
+in length. For summer flowering in England they are best made about the
+end of August, and should be selected from the shortest-jointed young
+wood. They root readily in a compost of loam and silver-sand if kept
+close and sprinkled for a short time. In from two to three weeks they
+may be put into 3-in. pots containing a compost of equal parts of rich
+loam, silver-sand and leaf-mould. They are subsequently moved from the
+frame or bed, first to a warm and shady, and then to a more airy part of
+the greenhouse. In January a little artificial heat may be given, to be
+gradually increased as the days lengthen. The side-shoots are generally
+pruned when they have made three or four joints, and for bushy plants
+the leader is stopped soon after the first potting. Care is taken to
+keep the plants as near the glass as possible, and shaded from bright
+sunshine, also to provide them plentifully with water, except at the
+time of shifting, when the roots should be tolerably dry. For the second
+potting a suitable soil is a mixture of well-rotted cow-dung or old
+hotbed mould with leaf-mould and sandy peat, and to promote drainage a
+little peat-moss may be placed immediately over the crocks in the lower
+part of the pot. Weak liquid manure greatly promotes the advance of the
+plants, and should be regularly supplied twice or thrice a week during
+the flowering season. After this, water is gradually withheld from them,
+and they may be placed in the open air to ripen their wood.
+
+Among the more hardy or half-hardy plants for inside borders are
+varieties of the Chilean species, _F. macrostemma_ (or _F.
+magellanica_), a shrub 6 to 12 ft. high with a scarlet calyx, such as
+_F. m. globosa, F. m. gracilis_; one of the most graceful and hardy of
+these, a hybrid _F. riccartoni_, was raised at Riccarton, near
+Edinburgh, in 1830. For inside culture may be mentioned _F. boliviana_
+(Bolivia), 2 to 4 ft. high, with rich crimson flowers with a
+trumpet-shaped tube; _F. corymbiflora_ (Peru), 4 to 6 ft. high, with
+scarlet flowers nearly 2 in. long in long terminal clusters; F. fulgens
+(Mexico), 4 to 6 ft., with drooping apical clusters of scarlet flowers;
+_F. microphylla_ (Central America), with small leaves and small scarlet
+funnel-shaped flowers, the petals deep red; _F. procumbens_ (New
+Zealand), a pretty little creeper, the small flowers of which are
+succeeded by oval magenta-crimson berries which remain on for months;
+and _F. splendens_ (Mexico), 6 ft. high, with very showy scarlet and
+green flowers. But these cannot compare in beauty or freedom of blossom
+with the numerous varieties raised by gardeners. The nectar of fuchsia
+flowers has been shown to contain nearly 78% of cane sugar, the
+remainder being fruit sugar. The berries of some fuchsias are subacid or
+sweet and edible. From certain species a dye is obtainable. The
+so-called "native fuchsias" of southern and eastern Australia are plants
+of the genus _Correa_, natural order Rutaceae.
+
+
+
+
+FUCHSINE, or MAGENTA, a red dye-stuff consisting of a mixture of the
+hydrochlorides or acetates of pararosaniline and rosaniline. It was
+obtained in 1856 by J. Natanson (_Ann_., 1856, 98, p. 297) by the action
+of ethylene chloride on aniline, and by A.W. Hofmann in 1858 from
+aniline and carbon tetrachloride. It is prepared by oxidizing "aniline
+for red" (a mixture of aniline and ortho- and para-toluidine) with
+arsenic acid (H. Medlock, _Dingler's Poly. Jour_., 1860, 158, p. 146);
+by heating aniline for red with nitrobenzene, concentrated hydrochloric
+acid and iron (Coupier, _Ber_., 1873, 6, p. 423); or by condensing
+formaldehyde with aniline and ortho-toluidine and oxidizing the mixture.
+It forms small crystals, showing a brilliant green reflex, and is
+soluble in water and alcohol with formation of a deep red solution. It
+dyes silk, wool and leather direct, and cotton after mordanting with
+tannin and tartar emetic (see DYEING). An aqueous solution of fuchsine
+is decolorized on the addition of sulphurous acid, the easily soluble
+fuchsine sulphurous acid being formed. This solution is frequently used
+as a test reagent for the detection of aldehydes, giving, in most cases,
+a red coloration on the addition of a small quantity of the aldehyde.
+
+  The constitution of the fuchsine bases (pararosaniline and rosaniline)
+  was determined by E. and O. Fischer in 1878 (_Ann_., 1878, 194, p.
+  242); A.W. Hofmann having previously shown that oxidation of pure
+  aniline alone or of pure toluidine yielded no fuchsine, whilst
+  oxidation of a mixture of aniline and para-toluidine gave rise to the
+  fine red dye-stuff para-fuchsine (pararosaniline hydrochloride)
+
+    CH3·C6H4NH2 + 2C6H5NH2 + 3O = HO·C(C6H4NH2)3 + 2H2O.
+                                  Colour base (pararosaniline).
+
+    HO·C(C6H4NH2)3·HCl = H2O + (H2N·C6H4)2C : C6H4 : NH2Cl.
+                                  Pararosaniline hydrochloride.
+
+  A. Rosenstiehl (_Jahres_., 1869, p. 693) found also that different
+  rosanilines were obtained according to whether ortho- or
+  para-toluidine was oxidized with aniline; and he gave the name
+  rosaniline to the one obtained from aniline and ortho-toluidine,
+  reserving the term pararosaniline for the other. E. and O. Fischer
+  showed that these compounds were derivatives of triphenylmethane and
+  tolyldiphenylmethane respectively. Pararosaniline was reduced to the
+  corresponding leuco compound (paraleucaniline), from which by
+  diazotization and boiling with alcohol, the parent hydrocarbon was
+  obtained
+
+    (H2N·C5H4)2C : C6H4:NH2Cl --> HC(C6H4NH2·HCl)3 --> HC(C6H4N2Cl3)
+    Pararosaniline hydrochloride.  Paraleucaniline.
+
+                                                      --> HC(C6H5)3.
+                                                   Triphenylmethane.
+
+  The reverse series of operations was also carried out by the Fischers,
+  triphenylmethane being nitrated, and the nitro compound then reduced
+  to triaminotriphenylmethane or paraleucaniline, which on careful
+  oxidation is converted into the dye-stuff. A similar series of
+  reactions was carried out with rosaniline, which was shown to be the
+  corresponding derivative of tolyldiphenylmethane.
+
+  The free pararosaniline, C19H19N3O, and rosaniline, C20H21N3O, may be
+  obtained by precipitating solutions of their salts with a caustic
+  alkali, colourless precipitates being obtained, which crystallize from
+  hot water in the form of needles or plates. The position of the amino
+  groups in pararosaniline was determined by the work of H. Caro and C.
+  Graebe (_Ber_., 1878, II, p. 1348) and of E. and O. Fischer (_Ber._,
+  1880, 13, p. 2204) as follows: Nitrous acid converts pararosaniline
+  into aurin, which when superheated with water yields
+  para-dioxybenzophenone. As the hydroxyl groups in aurin correspond to
+  the amino groups in pararosaniline, two of these in the latter
+  compound must be in the para position. The third is also in the para
+  position; for if benzaldehyde be condensed with aniline, condensation
+  occurs in the para position, for the compound formed may be converted
+  into para-dioxybenzophenone,
+
+    C6H5CHO --> C6H5CH(C6H4NH2)2 --> C6H5CH(C6H4OH)2 --> CO(C6H4OH)2;
+
+  but if para-nitrobenzaldehyde be used in the above reaction and the
+  resulting nitro compound NO2.C6H4.CH(C6H4NH2)2 be reduced, then
+  pararosaniline is the final product, and consequently the third amino
+  group occupies the para position. Many derivatives of pararosaniline
+  and rosaniline are known, in which the hydrogen atoms of the amino
+  groups are replaced by alkyl groups; this has the effect of producing
+  a blue or violet shade, which becomes deeper as the number of groups
+  increases (see DYEING).
+
+
+
+
+FUCINO, LAGO DI [Lat. _Lacus Fucinus_], a lake bed of the Abruzzi,
+Italy, in the province of Aquila, 2 m. E. of the town of Avezzano. The
+lake was 37 m. in circumference and 65 ft. deep. From the lack of an
+outlet, the level of the lake was subject to great variations, often
+fraught with disastrous consequences. As early as A.D. 52 the emperor
+Claudius, realizing a project of Julius Caesar, constructed a tunnel 3½
+m. long, with 40 shafts at intervals, by which the surplus waters found
+an outlet to the Liris (or Garigliano). No less than 30,000 workmen were
+employed for eleven years in driving this tunnel. In the following reign
+the tunnel was allowed to fall into disrepair, but was repaired by
+Trajan. When, however, it finally went out of use is uncertain. The
+various attempts made to reopen it from 1240 onwards were unsuccessful.
+By 1852 the lake had gradually risen until it was 30 ft. above its
+original level, and had become a source of danger to the surrounding
+countryside. A company undertook to drain it on condition of becoming
+proprietors of the site when dry; in 1854, however, the rights and
+privileges were purchased by Prince Giulio Torlonia (d. 1886), the great
+Roman banker, who carried on the work at his own expense until, in 1876,
+the lake was finally drained at the cost of some £1,700,000. The
+reclaimed area is 12½ m. long, 7 m. broad, and is cultivated by
+families from the Torlonia estates. The outlet by which it was drained
+is 4 m. long and 24 sq. yds. in section.
+
+  See A. Brisse and L. de Rotron, _Le Desséchement du lac Fucin, exécuté
+  par S.E. le Prince A. Torlonia_ (Rome, 1876).     (T. As.)
+
+
+
+
+FUEL (O. Fr. _feuaile_, popular Lat. _focalia_, from _focus_, hearth,
+fire), a term applicable to all substances that can be usefully employed
+for the production of heat by combustion. Any element or combination of
+elements susceptible of oxidation may under appropriate conditions be
+made to burn; but only those that ignite at a moderate initial
+temperature and burn with comparative rapidity, and, what is practically
+of more importance, are obtainable in quantity at moderate prices, can
+fairly be regarded as fuels. The elementary substances that can be so
+classed are primarily hydrogen, carbon and sulphur, while others finding
+more special applications are silicon, phosphorus, and the more readily
+oxidizable metals, such as iron, manganese, aluminium and magnesium.
+More important, however, than the elements are the carbohydrates or
+compounds of carbon, oxygen and hydrogen, which form the bulk of the
+natural fuels, wood, peat and coal, as well as of their liquid and
+gaseous derivatives--coal-gas, coal-tar, pitch, oil, &c., which have
+high values as fuel. Carbon in the elementary form has its nearest
+representative in the carbonized fuels, charcoal from wood and coke from
+coal.
+
+
+_Solid Fuels._
+
+  Wood.
+
+Wood may be considered as having the following average composition when
+in the air-dried state: Carbon, 39.6; hydrogen, 4.8; oxygen, 34.8; ash,
+1.0; water, 20%. When it is freshly felled, the water may be from 18 to
+50%. Air-dried or even green wood ignites readily when a considerable
+surface is exposed to the kindling flame, but in large masses with
+regular or smooth surfaces it is often difficult to get it to burn. When
+previously torrefied or scorched by heating to a temperature of about
+200°, at which incipient charring is set up, it is exceedingly
+inflammable. The ends of imperfectly charred boughs from the charcoal
+heaps in this condition are used in Paris and other large towns in
+France for kindling purposes, under the name of _fumerons_. The
+inflammability, however, varies with the density,--the so-called hard
+woods, oak, beech and maple, taking fire less readily than the softer,
+and, more especially, the coniferous varieties rich in resin. The
+calorific power of absolutely dry woods may as an average be taken at
+about 4000 units, and when air-dried, i.e. containing 25% of water, at
+2800 to 3000 units. Their evaporative values, i.e. the quantities of
+water evaporated by unit weight, are 3.68 and 4.44.
+
+Wood being essentially a flaming fuel is admirably adapted for use with
+heat-receiving surfaces of large extent, such as locomotive and marine
+boilers, and is also very clean in use. The absence of all cohesion in
+the cinders or unburnt carbonized residue causes a large amount of
+ignited particles to be projected from the chimney, when a rapid draught
+is used, unless special spark-catchers of wire gauze or some analogous
+contrivance are used. When burnt in open fireplaces the volatile
+products given off in the apartment on the first heating have an acrid
+penetrating odour, which is, however, very generally considered to be
+agreeable. Owing to the large amount of water present, no very high
+temperatures can be obtained by the direct combustion of wood, and to
+produce these for metallurgical purposes it is necessary to convert it
+previously either into charcoal or into inflammable gas.
+
+
+  Peat.
+
+Peat includes a great number of substances of very unequal fuel value,
+the most recently formed spongy light brown kind approximating in
+composition to wood, while the dense pitchy brown compact substance,
+obtained from the bottom of bogs of ancient formation, may be compared
+with lignite or even in some instances with coal. Unlike wood, however,
+it contains incombustible matter in variable but large quantity, from 5
+to 15% or even more. Much of this, when the amount is large, is often
+due to sand mechanically intermixed; when air-dried the proportion of
+water is from 8 to 20%. When these constituents are deducted the average
+composition may be stated to be--carbon, 52 to 66; hydrogen, 4.7 to
+7.4; oxygen, 28 to 39; and nitrogen, 1.5 to 3%. Average air-dried peat
+may be taken as having a calorific value of 3000 to 3500 units, and when
+dried at 100° C., and with a minimum of ash (4 to 5%), at about 5200
+units, or from a quarter to one-third more than that of an equal weight
+of wood. The lighter and more spongy varieties of peat when air-dried
+are exceedingly inflammable, firing at a temperature of 200° C.; the
+denser pulpy kinds ignite less readily when in the natural state, and
+often require a still higher temperature when prepared by pulping and
+compression or partial carbonization. Most kinds burn with a red smoky
+flame, developing a very strong odour, which, however, has its admirers
+in the same way that wood smoke has. This arises from the destructive
+distillation of imperfectly carbonized organic matter. The ash, like
+that of wood, is light and powdery, except when much sand is present,
+when it is of a denser character.
+
+Peat is principally found in high latitudes, on exposed high tablelands
+and treeless areas in more temperate climates, and in the valleys of
+slow-flowing rivers,--as in Ireland, the west of Scotland, the tableland
+of Bavaria, the North German plain, and parts of the valleys of the
+Somme, Oise and a few other rivers in northern France. A principal
+objection to its use is its extreme bulk, which for equal evaporative
+effect is from 8 to 18 times that of coal. Various methods have been
+proposed, and adopted more or less successfully, for the purpose of
+increasing the density of raw peat by compression, either with or
+without pulping; the latter process gives the heaviest products, but the
+improvement is scarcely sufficient to compensate for the cost.
+
+
+  Lignite.
+
+Lignite or brown coal is of intermediate character between peat and coal
+proper. The best kinds are undistinguishable in quality from
+free-burning coals, and the lowest earthy kinds are not equal to average
+peat. When freshly raised, the proportion of water may be from 45 to 50%
+and even more, which is reduced from 28 to 20% by exposure to dry air.
+Most varieties, however, when fully dried, break up into powder, which
+considerably diminishes their utility as fuel, as they cannot be
+consolidated by coking. Lignite dust may, however, be compacted into
+serviceable blocks for burning, by pressure in machines similar to those
+used for brickmaking, either in the wet state as raised from the mines
+or when kiln-dried at 200° C. This method was adopted to a very large
+extent in Prussian Saxony. The calorific value varies between 3500 and
+5000 units, and the evaporative factor from 2.16 when freshly raised to
+5.84 for the best kinds of lignite when perfectly dried.
+
+
+  Other natural fuels.
+
+Of the other natural fuels, apart from coal (q.v.), the most important
+is so-called vegetable refuse, such as cotton stalks, brushwood, straw,
+and the woody residue of sugar-cane after the extraction of the
+saccharine juice known as megasse or cane trash. These are extensively
+used in countries where wood and coal are scarce, usually for providing
+steam in the manufactures where they arise, e.g. straw for thrashing,
+cotton stalks for ploughing, irrigating, or working presses, and cane
+trash for boiling down sugar or driving the cane mill. According to J.
+Head (_Proc. Inst. of Civil Engineers_, vol. xlviii. p. 75), the
+evaporative values of 1 lb. of these different articles when burnt in a
+tubular boiler are--coal, 8 lb.; dry peat, 4 lb.; dry wood, 3.58-3.52
+lb.; cotton stalks or megasse, 3.2-2.7 lb.; straw, 2.46-2.30 lb.
+Owing to the siliceous nature of the ash of straw, it is desirable to
+have a means of clearing the grate bars from slags and clinkers at short
+intervals, and to use a steam jet to clear the tubes from similar
+deposits.
+
+The common fuel of India and Egypt is derived from the dung of camels
+and oxen, moulded into thin cakes, and dried in the sun. It has a very
+low heating power, and in burning gives off acrid ammoniacal smoke and
+vapour.
+
+Somewhat similar are the tan cakes made from spent tanners' bark, which
+are used to some extent in eastern France and in Germany. They are made
+by moulding the spent bark into cakes, which are then slowly dried by
+exposure to the air. Their effect is about equivalent to 80 and 30% of
+equal weights of wood and coal respectively.
+
+Sulphur, phosphorus and silicon, the other principal combustible
+elements, are only of limited application as fuels. The first is used in
+the liquidation of sulphur-bearing rocks. The ore is piled into large
+heaps, which are ignited at the bottom, a certain proportion, from
+one-fourth to one-third, of the sulphur content being sacrificed, in
+order to raise the mass to a sufficient temperature to allow the
+remainder to melt and run down to the collecting basin. Another
+application is in the so-called "pyritic smelting," where ores of copper
+(q.v.) containing iron pyrites, FeS2, are smelted with appropriate
+fluxes in a hot blast, without preliminary roasting, the sulphur and
+iron of the pyrites giving sufficient heat by oxidation to liquefy both
+slag and metal. Phosphorus, which is of value from its low igniting
+point, receives its only application in the manufacture of lucifer
+matches. The high temperature produced by burning phosphorus is in part
+due to the product of combustion (phosphoric acid) being solid, and
+therefore there is less heat absorbed than would be the case with a
+gaseous product. The same effect is observed in a still more striking
+manner with silicon, which in the only special case of its application
+to the production of heat, namely, in the Bessemer process of
+steel-making, gives rise to an enormous increase of temperature in the
+metal, sufficient indeed to keep the iron melted. The absolute calorific
+value of silicon is lower than that of carbon, but the product of
+combustion (silica) being non-volatile at all furnace temperatures, the
+whole of the heat developed is available for heating the molten iron,
+instead of a considerable part being consumed in the work of
+volatilization, as is the case with carbonic oxide, which burns to waste
+in the air.
+
+
+    Calorific power.
+
+  _Assay and Valuation of Carbonaceous Fuels._--The utility or value of
+  a fuel depends upon two principal factors, namely, its calorific power
+  and its calorific intensity or pyrometric effect, that is, the
+  sensible temperature of the products of combustion. The first of these
+  is constant for any particular product of combustion independently of
+  the method by which the burning is effected, whether by oxygen, air or
+  a reducible metallic oxide. It is most conveniently determined in the
+  laboratory by measuring the heat evolved during the combustion of a
+  given weight of the fuel. The method of Lewis Thompson is one of the
+  most useful. The calorimeter consists of a copper cylinder in which a
+  weighed quantity of coal intimately mixed with 10-12 parts of a
+  mixture of 3 parts of potassium chlorate and 1 of potassium nitrate is
+  deflagrated under a copper case like a diving-bell, placed at the
+  bottom of a deep glass jar filled with a known weight of water. The
+  mixture is fired by a fuse of lamp-cotton previously soaked in a nitre
+  solution and dried. The gases produced by the combustion rising
+  through the water are cooled, with a corresponding increase of
+  temperature in the latter, so that the difference between the
+  temperature observed before and after the experiment measures the heat
+  evolved. The instrument is so constructed that 30 grains (2 grammes)
+  of coal are burnt in 29,010 grains of water, or in the proportion of 1
+  to 937, these numbers being selected that the observed rise of
+  temperature in Fahrenheit degrees corresponds to the required
+  evaporative value in pounds, subject only to a correction for the
+  amount of heat absorbed by the mass of the instrument, for which a
+  special coefficient is required and must be experimentally determined.
+  The ordinary bomb calorimeter is also used. An approximate method is
+  based upon the reduction of lead oxide by the carbon and hydrogen of
+  the coal, the amount of lead reduced affording a measure of the oxygen
+  expended, whence the heating power may be calculated, 1 part of pure
+  carbon being capable of producing 34½ times its weight of lead. The
+  operation is performed by mixing the weighed sample with a large
+  excess of litharge in a crucible, and exposing it to a bright red heat
+  for a short time. After cooling, the crucible is broken and the
+  reduced button of lead is cleaned and weighed. The results obtained by
+  this method are less accurate with coals containing much disposable
+  hydrogen and iron pyrites than with those approximating to anthracite,
+  as the heat equivalent of the hydrogen in excess of that required to
+  form water with the oxygen of the coal is calculated as carbon, while
+  it is really about four times as great. Sulphur in iron pyrites also
+  acts as a reducing agent upon litharge, and increases the apparent
+  effect in a similar manner.
+
+  The evaporative power of a coal found by the above methods, and also
+  by calculating the separate calorific factors of the components as
+  determined by the chemical analysis, is always considerably above that
+  obtained by actual combustion under a steam boiler, as in the latter
+  case numerous sources of loss, such as imperfect combustion of gases,
+  loss of unburnt coal in cinders, &c., come into play, which cannot be
+  allowed for in laboratory experiments. It is usual, therefore, to
+  determine the value of a coal by the combustion of a weighed quantity
+  in the furnace of a boiler, and measuring the amount of water
+  evaporated by the heat developed.
+
+  In a research upon the heating power and other properties of coal for
+  naval use, carried out by the German admiralty, the results tabulated
+  below were obtained with coals from different localities.
+
+    +-----------------------+-----------+------------+-----------+------------------+
+    |                       | Slag left |  Ashes in  |  Soot in  | Water evaporated |
+    |                       | in Grate. |   Ashpit.  |   Flues.  | by 1 lb. of Coal.|
+    +-----------------------+-----------+------------+-----------+------------------+
+    | Westphalian gas coals | 0.33-6.42 | 2.83- 6.53 | 0.32-0.46 |   6.60-7.45 lb.  |
+    |  Do. bituminous coals | 0.98-9.10 | 1.97- 9.63 | 0.24-0.88 |   7.30-8.66      |
+    |  Do. dry coals        | 1.93-5.70 | 4.37-10.63 | 0.24-0.48 |   7.03-8.51      |
+    | Silesian coals        | 0.92-1.30 | 3.15- 3.50 | 0.24-0.30 |   6.73-7.10      |
+    | Welsh steam coals     | 1.20-4.07 | 4.07       | 0.32      |   8.41           |
+    | Newcastle coals       | 1.92      | 2.57       | 0.35      |   7.28           |
+    +-----------------------+-----------+------------+-----------+------------------+
+
+  The heats of combustion of elements and compounds will be found in
+  most of the larger works on physical and chemical constants; a
+  convenient series is given in the _Annuaire du Bureau des Longitudes_,
+  appearing in alternate years. The following figures for the principal
+  fuel elements are taken from the issue for 1908; they are expressed in
+  gramme "calories" or heat units, signifying the weight of water in
+  grammes that can be raised 1° C. in temperature by the combustion of 1
+  gramme of the substance, when it is oxidized to the condition shown in
+  the second column:
+
+    +----------------+---------------------------------+-----------+
+    |    Element.    |      Product of Combustion.     | Calories. |
+    +----------------+---------------------------------+-----------+
+    | Hydrogen     \ | Water, H2O, condensed to liquid |  34,500   |
+    |              / |      "      as vapour           |  29,650   |
+    | Carbon--       |                                 |           |
+    |   Diamond      | Carbon Dioxide, CO2             |   7,868   |
+    |   Graphite     |    "      "                     |   7,900   |
+    |   Amorphous    |    "      "                     |   8,133   |
+    | Silicon--      |                                 |           |
+    |   Amorphous    | Silicon Dioxide, SiO2           |   6,414   |
+    |   Crystallized |    "      "                     |   6,570   |
+    | Phosphorus     | Phosphoric pentoxide, P2O5      |   5,958   |
+    | Sulphur        | Sulphur dioxide, SO2, gaseous   |   2,165   |
+    +----------------+---------------------------------+-----------+
+
+  The results may also be expressed in terms of the atomic equivalent of
+  the combustible by multiplying the above values by the atomic weight
+  of the substance, 12 for carbon, 28 for silicon, &c.
+
+  In all fuels containing hydrogen the calorific value as found by the
+  calorimeter is higher than that obtainable under working conditions by
+  an amount equal to the latent heat of volatilization of water which
+  reappears as heat when the vapour is condensed, though under ordinary
+  conditions of use the vapour passes away uncondensed. This gives rise
+  to the distinction of higher and lower calorific values for such
+  substances, the latter being those generally used in practice. The
+  differences for the more important compound gaseous fuels are as
+  follows:--
+
+                             Calorific Value.
+                            Higher.      Lower.
+    Acetylene, C2H2         11,920      11,500
+    Ethylene, C2H4          11,880      11,120
+    Methane, CH4            13,240      11,910
+    Carbon monoxide, CO      2,440       2,440
+
+
+    Caloric intensity.
+
+  The calorific intensity or pyrometric effect of any particular fuel
+  depends upon so many variable elements that it cannot be determined
+  except by actual experiment. The older method was to multiply the
+  weight of the products of combustion by their specific heats, but this
+  gave untrustworthy results as a rule, on account of two
+  circumstances--the great increase in specific heat at high
+  temperatures in compound gases such as water and carbon dioxide, and
+  their instability when heated to 1800° or 2000°. At such temperatures
+  dissociation to a notable extent takes place, especially with the
+  latter substance, which is also readily reduced to carbon monoxide
+  when brought in contact with carbon at a red heat--a change which is
+  attended with a large heat absorption. This effect is higher with soft
+  kinds of carbon, such as charcoal or soft coke, than with dense coke,
+  gas retort carbon or graphite. These latter substances, therefore, are
+  used when an intense local heat is required, as for example, in the
+  Deville furnace, to which air is supplied under pressure. Such a
+  method is, however, only of very special application, the ordinary
+  method being to supply air to the fire in excess of that required to
+  burn the fuel to prevent the reduction of the carbon dioxide. The
+  volume of flame, however, is increased by inert gas, and there is a
+  proportionate diminution of the heating effect. Under the most
+  favourable conditions, when the air employed has been previously
+  raised to a high temperature and pressure, the highest attainable
+  flame temperature from carbonaceous fuel seems to be about 2100°-2300°
+  C.; this is realized in the bright spots or "eyes" of the tuyeres of
+  blast furnaces.
+
+  Very much higher temperatures may be reached when the products of
+  combustion are not volatile, and the operation can be effected by
+  using the fuel and oxidizing agent in the proportions exactly
+  required for perfect combustion and intimately mixed. These
+  conditions are met in the "Thermit" process of Goldschmidt, where
+  finely divided aluminium is oxidized by the oxide of some similar
+  metal, such as iron, manganese or chromium, the reaction being started
+  by a primer of magnesium and barium peroxide. The reaction is so
+  rapidly effected that there is an enormous rise in temperature,
+  estimated to be 5400° F. (3000° C.), which is sufficient to melt the
+  most refractory metals, such as chromium. The slag consists of alumina
+  which crystallizes in the forms of corundum and ruby, and is utilized
+  as an abrasive under the name of corubin.
+
+  The chemical examination includes the determination of (1) moisture,
+  (2) ash, (3) coke, (4) volatile matter, (5) fixed carbon in coke, (6)
+  sulphur, (7) chlorine, (8) phosphorus. Moisture is determined by
+  noting the loss in weight when a sample is heated at 100° for about
+  one hour. The ash is determined by heating a sample in a muffle
+  furnace until all the combustible matter has been burnt off. The ash,
+  which generally contains silica, oxides of the alkaline earths, ferric
+  oxide (which gives the ash a red colour), sulphur, &c., is analysed by
+  the ordinary gravimetric methods. The determination of coke is very
+  important on account of the conclusions concerning the nature of the
+  coal which it permits to be drawn. A sample is finely powdered and
+  placed in a covered porcelain crucible, which is surrounded by an
+  outer one, the space between them being packed with small coke. The
+  crucibles are heated in a wind furnace for 1 to 1½ hours, then allowed
+  to cool, the inner crucible removed, and the coke weighed. The coke
+  may be (1) pulverulent, (2) slightly fritted, (3) spongy and swelled,
+  (4) compact. Pulverulent cokes indicate a non-caking bituminous coal,
+  rich in oxygen if the amount be below 60%, but if the amount be very
+  much less it generally indicates a lignite; if the amount be above 80%
+  it indicates an anthracite containing little oxygen or hydrogen. A
+  fritted coke indicates a slightly coking coal, while the spongy
+  appearance points to a highly coking coal which has been partly fused
+  in the furnace. A compact coke is yielded by good coking coals, and is
+  usually large in amount. The volatile matters are determined as the
+  loss of weight on coking less the amount of moisture. The "fixed
+  carbon" is the carbon retained in the coke, which contains in addition
+  the ash already determined. The fixed carbon is therefore the
+  difference between the coke and the ash, and may be determined from
+  these figures; or it may be determined directly by burning off the
+  coke in a muffle and noting the loss in weight. Sulphur may be present
+  as (1) organic sulphur, (2) as iron pyrites or other sulphides, (3) as
+  the sulphates of calcium, aluminium and other metals; but the amount
+  is generally so small that only the total sulphur is determined. This
+  is effected by heating a mixture of the fuel with lime and sodium
+  carbonate in a porcelain dish to redness in a muffle until all the
+  carbonaceous matter has been burnt off. The residue, which contains
+  the sulphur as calcium sulphate, is transferred to a beaker containing
+  water to which a little bromine has been added. Hydrochloric acid is
+  carefully added, the liquid filtered and the residue washed. To the
+  filtrate ammonia is added, and then barium chloride, which
+  precipitates the sulphur as barium sulphate. Sulphur existing in the
+  form of sulphates may be removed by washing a sample with boiling
+  water and determining the sulphuric acid in the solution. The washed
+  sample is then fused in the usual way to determine the proportion of
+  sulphur existing as iron pyrites. The distinction between sulphur
+  present as sulphate and sulphide is of importance in the examination
+  of coals intended for iron smelting, as the sulphates of the earthy
+  metals are reduced by the gases of the furnace to sulphides, which
+  pass into the slag without affecting the quality of the iron produced,
+  while the sulphur of the metallic sulphides in the ash acts
+  prejudicially upon the metal. Coals for gas-making should contain
+  little sulphur, as the gases produced in the combustion are noxious
+  and have very corrosive properties. Chlorine is rarely determined, but
+  when present in quantity it corrodes copper and brass boiler tubes,
+  with which consequently chlorine-bearing coals cannot be used. The
+  element is determined by fusing with soda lime in a muffle, dissolving
+  the residue in water and precipitating with silver nitrate. Phosphorus
+  is determined in the ash by fusing it with a mixture of sodium and
+  potassium carbonates, extracting the residue with hydrochloric acid,
+  and twice evaporating to dryness with the same acid. The residue is
+  dissolved in hydrochloric acid, a few drops of ferric chloride added,
+  and then ammonia in excess. The precipitate of ferric phosphate is
+  then treated as in the ordinary estimation of phosphates. If it be
+  necessary to determine the absolute amount of carbon and hydrogen in a
+  fuel, the dried sample is treated with copper oxide as in the ordinary
+  estimation of these elements in organic compounds.     (H. B.)
+
+
+_Liquid Fuel._
+
+Vegetable oil is not used for fuel except for laboratory purposes,
+partly because its constituent parts are less adaptable for combustion
+under the conditions necessary for steam-raising, but chiefly because of
+the commercial difficulty of producing it with sufficient economy to
+compete with mineral fuel either solid or liquid.
+
+The use of petroleum as fuel had long been recognized as a scientific
+possibility, and some attempts had been made to adopt it in practice
+upon a commercial scale, but the insufficiency, and still more the
+irregularity, of the supplies prevented it from coming into practical
+use to any important extent until about 1898, when discoveries of oil
+specially adapted by chemical composition for fuel purposes changed the
+aspect of the situation. These discoveries of special oil were made
+first in Borneo and later in Texas, and experience in treating the oils
+from both localities has shown that while not less adapted to produce
+kerosene or illuminating oil, they are better adapted to produce fuel
+oil than either the Russian or the Pennsylvanian products. Texas oil did
+not hold its place in the market for long, because the influx of water
+into the wells lowered their yield, but discoveries of fuel oil in
+Mexico have come later and will help to maintain the balance of the
+world's supply, although this is still a mere fraction of the assured
+supply of coal.
+
+With regard to the chemical properties of petroleum, it is not necessary
+to say more in the present place than that the lighter and more volatile
+constituents, known commercially as naphtha and benzene, must be removed
+by distillation in order to leave a residue composed principally of
+hydrocarbons which, while containing the necessary carbon for
+combustion, shall be sufficiently free from volatile qualities to avoid
+premature ignition and consequent danger of explosion. Attempts have
+been made to use crude oil for fuel purposes, and these have had some
+success in the neighbourhood of the oil wells and under boilers of
+unusually good ventilation both as regards their chimneys and the
+surroundings of their stokeholds; but for reasons both of commerce and
+of safety it is not desirable to use crude oil where some distillation
+is possible. The more complete the process of distillation, and the
+consequent removal of the volatile constituents, the higher the
+flash-point, and the more turgid and viscous is the fuel resulting; and
+if the process is carried to an extreme, the residue or fuel becomes
+difficult to ignite by the ordinary process of spraying or atomizing
+mechanically at the moment immediately preceding combustion. The
+proportions which have been found to work efficiently in practice are as
+follows:--
+
+  Carbon             88.00 %
+  Hydrogen           10.75 %
+  Oxygen              1.25 %
+                   ---------
+        Total       100
+
+The standards of safety for liquid fuel as determined by flash-point are
+not yet finally settled, and are changing from time to time. The British
+admiralty require a flash-point of 270° F., and to this high standard,
+and the consequent viscosity of the fuel used by vessels in the British
+fleet, may partly be attributed the low rate of combustion that was at
+first found possible in them. The German admiralty have fixed a
+flash-point of 187° F., and have used oil of this standard with perfect
+safety, and at the same time with much higher measure of evaporative
+duty than has been attained in British war-vessels. In the British
+mercantile marine Lloyd's Register has permitted fuel with a flash-point
+as low as 150° F. as a minimum, and no harm has resulted. The British
+Board of Trade, the department of the government which controls the
+safety of passenger vessels, has fixed a higher standard upon the basis
+of a minimum of 185°. In the case of locomotives the flash-point as a
+standard of safety is of less importance than in the case of stationary
+or marine boilers, because the storage is more open, and the
+ventilation, both of the storage tanks and the boilers during
+combustion, much more perfect than in any other class of steam-boilers.
+
+The process of refining by distillation is also necessary to reduce two
+impurities which greatly retard storage and combustion, i.e. water and
+sulphur. Water is found in all crude petroleum as it issues from the
+wells, and sulphur exists in important quantities in oil from the Texas
+wells. Its removal was at first found very expensive, but there no
+longer exists difficulty in this respect, and large quantities of
+petroleum fuel practically free from sulphur are now regularly exported
+from Texas to New York and to Europe.
+
+Water mixed with fuel is in intimate mechanical relation, and frequently
+so remains in considerable quantities even after the process of
+distillation. It is in fact so thoroughly mixed as to form an emulsion.
+The effect of feeding such a mixture into a furnace is extremely
+injurious, because the water must be decomposed chemically into its
+constituents, hydrogen and oxygen, thus absorbing a large quantity of
+heat which would otherwise be utilized for evaporation. Water also
+directly delays combustion by producing from the jet a long, dull, red
+flame instead of a short bright, white flame, and the process of
+combustion, which should take place by vaporization of the oil near the
+furnace mouth, is postponed and transferred to the upper part of the
+combustion-box, the tubes, and even the base of the chimney, producing
+loss of heat and injury to the boiler structure. The most effective
+means of ridding the fuel of this dangerous impurity is by heat and
+settlement. The coefficients of expansion of water and oil by heat are
+substantially different, and a moderate rise of temperature therefore
+separates the particles and precipitates the water, which is easily
+drawn off--leaving the oil available for use. The heating and
+precipitation are usually performed upon a patented system of settling
+tanks and heating apparatus known as the Flannery-Boyd system, which has
+proved itself indispensable for the successful use at sea of petroleum
+fuel containing any large proportion of water.
+
+
+  Progress of liquid fuel.
+
+The laboratory and mechanical use of petroleum for fuel has already been
+referred to, but it was not until the year 1870 that petroleum was
+applied upon a wider and commercial scale. In the course of distillation
+of Russian crude petroleum for the production of kerosene or lamp oil,
+large quantities of refuse were produced--known by the Russian name of
+_astatki_--and these were found an incumbrance and useless for any
+commercial purpose. To a Russian oil-refiner gifted with mechanical
+instinct and the genius for invention occurred the idea of utilizing the
+waste product as fuel by spraying or atomizing it with steam, so that,
+the thick and sluggish fluid being broken up into particles, the air
+necessary for combustion could have free access to it. The earliest
+apparatus for this purpose was a simple piece of gas-tube, into which
+the thick oil was fed; by another connexion steam at high pressure was
+admitted to an inner and smaller tube, and, the end of the tube nearest
+to the furnace being open, the pressure of the steam blew the oil into
+the furnace, and by its velocity broke it up into spray. The apparatus
+worked with success from the first. Experience pointed out the proper
+proportionate sizes for the inlets of steam and oil, the proper pressure
+for the steam, and the proportionate sizes for the orifices of admission
+to the furnaces, as well as the sizes of air-openings and best
+arrangements of fire-bricks in the furnaces themselves; and what had
+been a waste product now became a by-product of great value. Practically
+all the steam power in South Russia, both for factories and navigation
+of the inland seas and rivers, is now raised from _astatki_ fuel.
+
+In the Far East, including Burma and parts of China and Japan, the use
+of liquid fuel spread rapidly during the years 1899, 1900 and 1901,
+owing entirely to the development of the Borneo oil-fields by the
+enterprise of Sir Marcus Samuel and the large British corporation known
+as the Shell Transport and Trading Company, of which he is the head.
+This corporation has since amalgamated with the Royal Dutch Petroleum
+Company controlling the extensive wells in Dutch Borneo, and together
+they supply large quantities of liquid fuel for use in the Far East. In
+the United States of America liquid fuel is not only used for
+practically the whole of the manufacturing and locomotive purposes of
+the state of Texas, but factories in New York, and a still larger number
+in California, are now discarding the use of coal and adopting
+petroleum, because it is more economical in its consumption and also
+more easily handled in transit, and saves nearly all the labour of
+stoking. So far the supplies for China and Japan have been exported from
+Borneo, but the discoveries of new oil-fields in California, of a
+character specially adapted for fuel, have encouraged the belief that it
+may be possible to supply Chile and Peru and other South American
+countries, where coal is extremely expensive, with Californian fuel; and
+it has also found its way across the Pacific to Japan. There are
+believed to be large deposits in West Africa, but in the meantime the
+only sources of supply to those parts of Africa where manufacture is
+progressing, i.e. South Africa and Egypt, are the oil-fields of Borneo
+and Texas, from which the import has well begun, from Texas to
+Alexandria via the Mediterranean, and from Borneo to Cape Town via
+Singapore.
+
+In England, notwithstanding the fact that there exist the finest
+coal-fields in the world, there has been a surprising development of the
+use of petroleum as fuel. The Great Eastern railway adapted 120
+locomotive engines to its use, and these ran with regularity and success
+both on express passenger and goods trains until the increase in price
+due to short supply compelled a return to coal fuel. The London,
+Brighton & South Coast railway also began the adaptation of some of
+their locomotive engines, but discontinued the use of liquid fuel from
+the same cause. Several large firms of contractors and cement
+manufacturers, chiefly on the banks of the Thames, made the same
+adaptations which proved mechanically successful, but were not continued
+when the price of liquid fuel increased with the increased demand.
+
+[Illustration: FIG. 1.--Holden Burner.]
+
+
+  Economy of liquid fuel.
+
+The chief factors of economy are the greater calorific value of oil than
+coal (about 16 lb. of water per lb. of oil fuel evaporated from a
+temperature of 212° F.), not only in laboratory practice, but in actual
+use on a large scale, and the saving of labour both in transit from the
+source of supply to the place of use and in the act of stoking the
+furnaces. The use of cranes, hand labour with shovels, wagons and
+locomotives, horses and carts, is unavoidable for the transit of coal;
+and labour to trim the coal, to stoke it when under combustion, and to
+handle the residual ashes, are all indispensable to steam-raising by
+coal. On the other hand, a system of pipes and pumps, and a limited
+quantity of skilled labour to manage them, is all that is necessary for
+the transit and combustion of petroleum fuel; and it is certain that
+even in England will be found places which, from topographical and other
+circumstances, will use petroleum more economically than coal as fuel
+for manufacturing purposes under reasonable conditions of price for the
+fuel.
+
+[Illustration: FIG. 2.--Rusden and Eeles Burner.]
+
+The theoretical calorific value of oil fuel is more nearly realized in
+practice than the theoretical calorific value of coal, because the
+facilities for complete combustion, due to the artificial admixture of
+the air by the atomizing process, are greater in the case of oil than
+coal, and for this reason, among others, the practical evaporative
+results are proportionately higher with liquid fuel. In some cases the
+work done in a steam-engine by 2 tons of coal has been performed by 1
+ton of oil fuel, but in others the proportions have been as 3 to 2, and
+these latter can be safely relied on in practice as a minimum. This
+saving, combined with the savings of labour and transit already
+explained, will in the near future make the use of liquid fuel
+compulsory, except in places so near to coal-fields that the cost of
+coal becomes sufficiently low to counterbalance the savings in weight of
+fuel consumed and in labour in handling it. In some locomotives on the
+Great Eastern railway the consumption of oil and coal for the same
+development of horse-power was as 17 lb. oil is to 35 lb. coal; all,
+however, did not realize so high a result.
+
+
+  Liquid fuel in locomotives.
+
+The mechanical apparatus for applying petroleum to steam-raising in
+locomotives is very simple. The space in the tender usually occupied by
+coal is closed up by steel-plating closely riveted and tested, so as to
+form a storage tank. From this tank a feed-pipe is led to a burner of
+the combined steam-and-oil type already indicated, and this burner is so
+arranged as to enter a short distance inside the furnace mouth. The
+ordinary fire-bars are covered with a thin layer of coal, which starts
+the ignition in the first place, and the whole apparatus is ready for
+work. The burner best adapted for locomotive practice is the Holden
+Burner (fig. 1), which was used on the Great Eastern railway. The
+steam-pipe is connected at A, the oil-pipe at B, and the hand-wheels C
+and D are for the adjustment of the internal orifices according to the
+rate of combustion required. The nozzle E is directed towards the
+furnace, and the external ring FF, supplied by the small pipe G and the
+by-pass valve H, projects a series of steam jets into the furnace,
+independent of the injections of atomized fuel, and so induces an
+artificial inrush of air for the promotion of combustion. This type of
+burner has also been tried on stationary boilers and on board ship. It
+works well, although the great consumption of steam by the supplementary
+ring is a difficulty at sea, where the water lost by the consumption of
+steam cannot easily be made up.
+
+
+  Liquid fuel at sea.
+
+Although the application of the new fuel for land and locomotive boilers
+has already been large, the practice at sea has been far more extensive.
+The reason is chiefly to be found in the fact that although the sources
+of supply are at a distance from Great Britain, yet they are in
+countries to whose neighbourhood British steamships regularly trade, and
+in which British naval squadrons are regularly stationed, so that the
+advantages of adopting liquid fuel have been more immediate and the
+economy more direct. The certainty of continuous supply of the fuel and
+the wide distribution of storage stations have so altered the conditions
+that the general adoption of the new fuel for marine purposes becomes a
+matter of urgency for the statesman, the merchant and the engineer. None
+of these can afford to neglect the new conditions, lest they be noted
+and acted upon by their competitors. Storage for supply now exists at a
+number of sea ports: London, Barrow, Southampton, Amsterdam, Copenhagen,
+New Orleans, Savannah, New York, Philadelphia, Singapore, Hong Kong,
+Madras, Colombo, Suez, Hamburg, Port Arthur, Rangoon, Calcutta, Bombay,
+Alexandria, Bangkok, Saigon, Penang, Batavia, Surabaya, Amoy, Swatow,
+Fuchow, Shanghai, Hankow, Sydney, Melbourne, Adelaide, Zanzibar,
+Mombasa, Yokohama, Kobe and Nagasaki; also in South African and South
+American ports.
+
+[Illustration: FIG. 3.--Storage of Liquid Fuel on Oil-carrying Steamers
+(Flannery-Boyd System).]
+
+The British admiralty have undertaken experiments with liquid fuel at
+sea, and at the same time investigations of the possibility of supply
+from sources within the regions of the British empire. There is an
+enormous supply of shale under the north-eastern counties of England,
+but no oil that can be pumped--still less oil with a pressure above it
+so as to "gush" like the wells in America--and the only sources of
+liquid supply under the British flag appear to be in Burma and Trinidad.
+The Borneo fields are not under British control, although developed
+entirely by British capital. The Italian admiralty have fitted several
+large warships with boiler apparatus to burn petroleum. The German
+admiralty are regularly using liquid fuel on the China station. The
+Dutch navy have fitted coal fuel and liquid fuel furnaces in
+combination, so that the smaller powers required may be developed by
+coal alone, and the larger powers by supplementing coal fuel with oil
+fuel. The speeds of some vessels of the destroyer type have by this
+means been accelerated nearly two knots.
+
+[Illustration: FIG. 4.--Installation on ss. "Trochas."]
+
+[Illustration: FIG. 5.--Details of Furnace, Meyer System.]
+
+[Illustration: FIG. 6.--Details of Exterior Elongation of Furnace, Meyer
+System.]
+
+
+  Advantages in warships.
+
+The questions which govern the use of fuel in warships are more largely
+those of strategy and fighting efficiency than economy of evaporation.
+Indeed, the cost of constructing and maintaining in fighting efficiency
+a modern warship is so great that the utmost use strategically must be
+obtained from the vessel, and in this comparison the cost of fuel is
+relatively so small an item that its increase or decrease may be
+considered almost a negligible quantity. The desideratum in a warship is
+to obtain the greatest fighting efficiency based on the thickest
+armour, the heaviest and most numerous guns, the highest maximum speed,
+and, last and not least, the greatest range of effective action based
+upon the maximum supplies of fuel, provisions and other consumable
+stores that the ship can carry. Now, if by changing the type of fuel it
+be possible to reduce its weight by 30%, and to abolish the stokers, who
+are usually more than half the ship's company, the weight saved will be
+represented not merely by the fuel, but by the consumable stores
+otherwise necessary for the stokers. Conversely, the radius of effective
+action of the ship will be doubled as regards consumable stores if the
+crew be halved, and will be increased by 50% if the same weight of fuel
+be carried in the form of liquid instead of coal. In space the gain by
+using oil fuel is still greater, and 36 cubic feet of oil as stored are
+equal in practical calorific value to 67 cubic feet of coal according to
+the allowance usual for ship's bunkering. On the other hand, coal has
+been relied upon, when placed in the side bunkers of unarmoured ships,
+as a protection against shot and shell, and this advantage, if it really
+exists, could not be claimed in regard to liquid fuel.
+
+Recent experiments in coaling warships at sea have not been very
+successful, as the least bad weather has prevented the safe transmission
+of coal bags from the collier to the ship. The same difficulty does not
+exist for oil fuel, which has been pumped through flexible tubing from
+one ship to the other even in comparatively rough weather.
+Smokelessness, so important a feature of sea strategy, has not always
+been attained by liquid fuel, but where the combustion is complete, by
+reason of suitable furnace arrangements and careful management, there is
+no smoke. The great drawback, however, to the use of liquid fuel in fast
+small vessels is the confined space allotted to the boilers, such
+confinement being unavoidable in view of the high power concentrated in
+a small hull. The British admiralty's experiments, however, have gone
+far to solve the problem, and the quantity of oil which can be consumed
+by forced draught in confined boilers now more nearly equals the
+quantity of coal consumed under similar conditions. All recent vessels
+built for the British navy are so constructed that the spaces between
+their double bottoms are oil-tight and capable of storing liquid fuel in
+the tanks so formed. Most recent battleships and cruisers have also
+liquid fuel furnace fittings, and in 1910 it already appeared probable
+that the use of oil fuel in warships would rapidly develop.
+
+In view of recent accusations of insufficiency of coal storage in
+foreign naval depots, by reason of the allegation that coal so stored
+quickly perishes, it is interesting to note that liquid fuel may be
+stored in tanks for an indefinite time without any deterioration
+whatever.
+
+
+  Advantages in merchant ships.
+
+In the case of merchant steamers large progress has also been made. The
+Shell Transport and Trading Company have twenty-one vessels successfully
+navigating in all parts of the world and using liquid fuel. The
+Hamburg-American Steamship Company have four large vessels similarly
+fitted for oil fuel, which, however, differ in furnace arrangements, as
+will be hereafter described, although using coal when the fluctuation of
+the market renders that the more economical fuel. One of the large
+American transatlantic lines is adopting liquid fuel, and French,
+German, Danish and American mercantile vessels are also beginning to use
+it in considerable amounts.
+
+In the case of very large passenger steamers, such as those of 20 knots
+and upwards in the Atlantic trade, the saving in cost of fuel is
+trifling compared with the advantage arising from the greater weight and
+space available for freight. Adopting a basis of 3 to 2 as between coal
+consumption and oil consumption, there is an increase of 1000 tons of
+dead weight cargo in even a medium-sized Atlantic steamer, and a
+collateral gain of about 100,000 cub. ft. of measurement cargo, by
+reason of the ordinary bunkers being left quite free, and the oil being
+stored in the double bottom spaces hitherto unutilized except for the
+purpose of water ballast. The cleanliness and saving of time from
+bunkering by the use of oil fuel is also an important factor in
+passenger ships, whilst considerable additional speed is obtainable. The
+cost of the installation, however, is very considerable, as it includes
+not only burners and pipes for the furnaces, but also the construction
+of oil-tight tanks, with pumps and numerous valves and pipe connexions.
+
+[Illustration: FIG. 7.--Furnace on ss. "Ferdinand Laeisz." A, it is
+proposed to do away with this ring of brickwork as being useless; B, it
+is proposed to fill this space up, thus continuing lining of furnace to
+combustion chamber, and also to fit protection bricks in way of saddle
+plate.]
+
+[Illustration: FIG. 8.--Fuel Tanks, &c., of ss. "Murex."]
+
+[Illustration: FIG. 9.--Furnace Gear of ss. "Murex."]
+
+  Fig. 2 shows a burner of Rusden and Eeles' patent as generally used on
+  board ships for the purpose of injecting the oil. A is a movable cap
+  holding the packing B, which renders the annular spindle M oil and
+  steam tight. E is the outer casing containing the steam jacket from
+  which the steam, after being fed through the steam-supply pipe G,
+  passes into the annular space surrounding the spindle P. It will be
+  seen that if the spindle P be travelled inwards by turning the handle
+  N, the orifice at the nozzle RR will be opened so as to allow the
+  steam to flow out radially. If at the same time the annular spindle M
+  be drawn inwards by revolving the handle L, the oil which passes
+  through the supply pipe F will also have emission at RR, and, coming
+  in contact with the outflowing steam, will be pulverized and sprayed
+  into the furnace. Fig. 3 is a profile and plan of a steamer adapted
+  for carrying oil in bulk, and showing all the storage arrangements for
+  handling liquid fuel. Fig. 4 shows the interior arrangement of the
+  boiler furnace of the steamship "Trocas." A is broken fire-brick
+  resting on the ordinary fire-bars, B is a brick bridge, C a casing of
+  fire-brick intended to protect the riveted seam immediately above it
+  from the direct impact of the flame, and D is a lining of fire-brick
+  at the back of the combustion-box, also intended to protect the
+  plating from the direct impact of the petroleum flame. The arrangement
+  of the furnace on the Meyer system is shown in fig. 5, where E is an
+  annular projection built at the mouth of the furnace, and BB are
+  spiral passages for heating the air before it passes into the furnace.
+  Fig. 6 shows the rings CC and details of the casting which forms the
+  projection or exterior elongation of the furnace. The brickwork
+  arrangement adopted for the double-ended boilers on the
+  Hamburg-American Steamship Company's "Ferdinand Laeisz" is represented
+  in fig. 7. The whole furnace is lined with fire-brick, and the burner
+  is mounted upon a circular disk plate which covers the mouth of the
+  furnace. The oil is injected not by steam pulverization, but by
+  pressure due to a steam-pump. The oil is heated to about 60°C. before
+  entering the pump, and further heated to 90°C. after leaving the pump.
+  It is then filtered, and passes to the furnace injector C at about
+  30-lb. pressure; and its passage through this injector and the spiral
+  passages of which it consists pulverizes the oil into spray, in which
+  form it readily ignites on reaching the interior of the furnace. The
+  injector is on the Körting principle, that is, it atomizes by fracture
+  of the liquid oil arising from its own momentum under pressure. The
+  advantage of this system as compared with the steam-jet system is the
+  saving of fresh water, the abstraction of which is so injurious to the
+  boiler by the formation of scale.
+
+  [Illustration: FIG. 10.--Section through Furnace of ss. "Murex."]
+
+  The general arrangement of the fuel tanks and filling pipes on the ss.
+  "Murex" is shown in fig. 8; and fig. 9 represents the furnace gear of
+  the same vessel, A being the steam-pipe, B the oil-pipe, C the
+  injector, D the swivel upon which the injector is hung so that it may
+  be swung clear of the furnace, E the fire-door, and F the handle for
+  adjusting the injector. In fig. 10, which represents a section of the
+  furnace, H is a fire-brick pier and K a fire-brick baffling bridge.
+
+  It is found in practice that to leave out the fire-bars ordinarily
+  used for coal produces a better result with liquid fuel than the
+  alternative system of keeping them in place and protecting them by a
+  layer of broken fire-brick.
+
+  Boilers fitted upon all the above systems have been run for thousands
+  of miles without trouble. In new construction it is desirable to give
+  larger combustion chambers and longer and narrower boiler tubes than
+  in the case of boilers intended for the combustion of coal alone.
+       (F. F.*)
+
+
+_Gaseous Fuel._
+
+Strictly speaking, much, and sometimes even most, of the heating
+effected by solid or liquid fuel is actually performed by the gases
+given off during the combustion. We speak, however, of gaseous fuel only
+in those cases where we supply a combustible gas from the outset, or
+where we produce from ordinary solid (or liquid) fuel in one place a
+stream of combustible gas which is burned in another place, more or less
+distant from that where it has been generated.
+
+  The various descriptions of gaseous fuel employed in practice may be
+  classified under the following heads:
+
+  I. Natural Gas.
+
+  II. Combustible Gases obtained as by-products in various technical
+        operations.
+
+  III. Coal Gas (Illuminating Gas).
+
+  IV. Combustible Gases obtained by the partial combustion of coal, &c.
+
+I. _Natural Gas._--From time immemorial it has been known that in some
+parts of the Caucasus and of China large quantities of gases issue from
+the soil, sometimes under water, which can be lighted and burn with a
+luminous flame. The "eternal fires" of Baku belong to this class. In
+coal-mines frequently similar streams of gas issue from the coal; these
+are called "blowers," and when they are of somewhat regular occurrence
+are sometimes conducted away in pipes and used for underground lighting.
+As a regular source of heating power, however, natural gas is employed
+only in some parts of the United States, especially in Pennsylvania,
+Kansas, Ohio and West Virginia, where it always occurs in the
+neighbourhood of coal and petroleum fields. The first public mention of
+it was made in 1775, but it was not till 1821 that it was turned to use
+at Fredonia, N.Y. In Pennsylvania natural gas was discovered in 1859,
+but at first very little use was made of it. Its industrial employment
+dates only from 1874, and became of great importance about ten years
+later. Nobody ever doubted that the gas found in these localities was an
+accumulation of many ages and that, being tapped by thousands of
+bore-holes, it must rapidly come to an end. This assumption was
+strengthened by the fact that the "gas-wells," which at first gave out
+the gas at a pressure of 700 or 800, sometimes even of 1400 lb. per sq.
+in., gradually showed a more and more diminishing pressure and many of
+them ceased to work altogether. About the year 1890 the belief was
+fairly general that the stock of natural gas would soon be entirely
+exhausted. Indeed, the value of the annual production of natural gas in
+the United States, computed as its equivalent of coal, was then
+estimated at twenty-one million dollars, in 1895 at twelve millions, in
+1899 at eleven and a half millions. But the output rose again to a value
+of twenty-seven millions in 1901, and to fifty million dollars in 1907.
+Mostly the gas, derived from upwards of 10,000 gas-wells, is now
+artificially compressed to a pressure of 300 or 400 lb. per sq. in. by
+means of steam-power or gas motors, fed by the gas itself, and is
+conveyed over great distances in iron pipes, from 9 or 10 to 36 in. in
+diameter. In 1904 nearly 30,000 m. of pipe lines were in operation. In
+1907 the quantity of natural gas consumed in the United States (nearly
+half of which was in Pennsylvania) was 400,000 million cub. ft., or
+nearly 3 cub. m. Canada (Ontario) also produces some natural gas,
+reaching a maximum of about $746,000 in 1907.
+
+The principal constituent of natural gas is always methane, CH4, of
+which it contains from 68.4 to 94.0% by volume. Those gases which
+contain less methane contain all the more hydrogen, viz. 2.9 to 29.8%.
+There is also some ethylene, ethane and carbon monoxide, rarely
+exceeding 2 or 3%. The quantity of incombustible gases--oxygen, carbon
+dioxide, nitrogen--ranges from mere traces to about 5%. The density is
+from 0.45 to 0.55. The heating power of 1000 cub. ft. of natural gas is
+equal to from 80 to 120 lb., on the average 100 lb., of good coal, but
+it is really worth much more than this proportion would indicate, as it
+burns completely, without smoke or ashes, and without requiring any
+manual labour. It is employed for all domestic and for most industrial
+purposes.
+
+The origin of natural gas is not properly understood, even now. The most
+natural assumption is, of course, that its formation is connected with
+that of the petroleum always found in the same neighbourhood, the latter
+principally consisting of the higher-boiling aliphatic hydrocarbons of
+the methane series. But whence do they both come? Some bring them into
+connexion with the formation of coal, others with the decomposition of
+animal remains, others with that of _diatomaceae_, &c., and even an
+inorganic origin of both petroleum and natural gas has been assumed by
+chemists of the rank of D.I. Mendeléeff and H. Moissan.
+
+II. _Gases obtained as By-products._--There are two important cases in
+which gaseous by-products are utilized as fuel; both are intimately
+connected with the manufacture of iron, but in a very different way, and
+the gases are of very different composition.
+
+(a) _Blast-furnace Gases._--The gases issuing from the mouths of
+blast-furnaces (see IRON AND STEEL) were first utilized in 1837 by Faber
+du Faur, at Wasseralfingen. Their use became more extensive after 1860,
+and practically universal after 1870. The volume of gas given off per
+ton of iron made is about 158,000 cub. ft. Its percentage composition by
+volume is:
+
+  Carbon monoxide    21.6  to  29.0,  mostly about  26%
+  Hydrogen            1.8   "   6.3,    "      "     3%
+  Methane             0.1   "   0.8,    "      "   0.5%
+  Carbon dioxide      6     "  12,      "      "   9.5%
+  Nitrogen           51     "  60,      "      "  56  %
+  Steam               5     "  12,      "      "   5  %
+                                                  -----
+                                                 100  %
+
+There is always a large amount of mechanically suspended flue-dust in
+this gas. It is practically equal to a poor producer-gas (see below),
+and is everywhere used, first for heating the blast in Cowper stoves or
+similar apparatus, and secondly for raising all the steam required for
+the operation of the blast-furnace, that is, for driving the
+blowing-engines, hoisting the materials, &c. Where the iron ore is
+roasted previously to being fed into the furnace, this can also be done
+by this gas, but in some cases the waste in using it is so great that
+there is not enough left for the last purpose. The calorific power of
+this gas per cubic foot is from 80 to 120 B.Th.U.
+
+Since about 1900 a great advance has been made in this field. Instead of
+burning the blast-furnace gas under steam boilers and employing the
+steam for producing mechanical energy, the gas is directly burned in
+gas-motors on the explosion principle. Thus upwards of three times the
+mechanical energy is obtained in comparison with the indirect way
+through the steam boiler. After all the power required for the
+operations of the blast-furnace has been supplied, there is a surplus of
+from 10 to 20 h.p. for each ton of pig-iron made, which may be applied
+to any other purpose.
+
+(b) _Coke-oven Gases._--Where the coking of coal is performed in the old
+beehive ovens or similar apparatus the gas issuing at the mouth of the
+ovens is lost. The attempts at utilizing the gases in such cases have
+not been very successful. It is quite different where coke is
+manufactured in the same way as illuminating gas, viz. by the
+destructive distillation of coal in closed apparatus (retorts), heated
+from the outside. This industry, which is described in detail in G.
+Lunge's _Coal-Tar and Ammonia_ (4th ed., 1909), originated in France,
+but has spread far more in Germany, where more than half of the coke
+produced is made by it; in the United Kingdom and the United States its
+progress has been much slower, but there also it has long been
+recognized as the only proper method. The output of coke is increased by
+about 15% in comparison with the beehive ovens, as the heat required for
+the process of distillation is not produced by burning part of the coal
+itself (as in the beehive ovens), but by burning part of the gas. The
+quality of the coke for iron-making is quite as good as that of beehive
+coke, although it differs from it in appearance. Moreover, the gases can
+be made to yield their ammonia, their tar, and even their benzene
+vapours, the value of which products sometimes exceeds that of the coke
+itself. And after all this there is still an excess of gas available for
+any other purpose.
+
+As the principle of distilling the coal is just the same, whether the
+object is the manufacture of coal gas proper or of coke as the main
+product, although there is much difference in the details of the
+manufacture, it follows that the quality of the gas is very similar in
+both cases, so far as its heating value is concerned. Of course this
+heating value is less where the benzene has been extracted from
+coke-oven gas, since this compound is the richest heat-producer in the
+gas. This is, however, of minor importance in the present case, as there
+is only about 1% benzene in these gases.
+
+The composition of coke-oven gases, after the extraction of the ammonia
+and tar, is about 53% hydrogen, 36% methane, 6% carbon monoxide, 2%
+ethylene and benzene, 0.5% sulphuretted hydrogen, 1.5% carbon dioxide,
+1% nitrogen.
+
+III. _Coal Gas (Illuminating Gas)._--Although ordinary coal gas is
+primarily manufactured for illuminating purposes, it is also extensively
+used for cooking, frequently also for heating domestic rooms, baths,
+&c., and to some extent also for industrial operations on a small scale,
+where cleanliness and exact regulation of the work are of particular
+importance. In chemical laboratories it is preferred to every other kind
+of fuel wherever it is available. The manufacture of coal gas being
+described elsewhere in this work (see GAS, § _Manufacture_), we need
+here only point out that it is obtained by heating bituminous coal in
+fireclay retorts and purifying the products of this destructive
+distillation by cooling, washing and other operations. The residual gas,
+the ordinary composition of which is given in the table below, amounts
+to about 10,000 cub. ft. for a ton of coal, and represents about 21% of
+its original heating value, 56.5% being left in the coke, 5.5% in the
+tar and 17% being lost. As we must deduct from the coke that quantity
+which is required for the heating of the retorts, and which, even when
+good gas producers are employed, amounts to 12% of the weight of the
+coal, or 10% of its heat value, the total loss of heat rises to 27%.
+Taking, further, into account the cost of labour, the wear and tear, and
+the capital interest on the plant, coal gas must always be an expensive
+fuel in comparison with coal itself, and cannot be thought of as a
+general substitute for the latter. But in many cases the greater expense
+of the coal gas is more than compensated by its easy distribution, the
+facility and cleanliness of its application, the general freedom from
+the mechanical loss, unavoidable in the case of coal fires, the
+prevention of black smoke and so forth. The following table shows the
+average composition of coal gas by volume and weight, together with the
+heat developed by its single constituents, the latter being expressed in
+kilogram-calories per cub. metre (0.252 kilogram-calories = 1 British
+heat unit; 1 cub. metre = 35.3 cub. ft.; therefore 0.1123 calories per
+cub. metre = 1 British heat unit per cub. foot).
+
+  +----------------------+----------+----------+------------+--------------+------------+
+  |                      |          |          | Heat-value |  Heat-value  | Heat-value |
+  |    Constituents.     |  Volume  |  Weight  | per Cubic  | per Quantity |  per cent. |
+  |                      | per cent.| per cent.|   Metre    | contained in |  of Total. |
+  |                      |          |          |  Calories. |  1 Cub. Met. |            |
+  +----------------------+----------+----------+-----------+---------------+------------+
+  | Hydrogen, H2         |   47     |    7.4   |   2,582    |     1213     |    22.8    |
+  | Methane, CH4         |   34     |   42.8   |   8,524    |     2898     |    54.5    |
+  | Carbon monoxide, CO  |    9     |   19.9   |   3,043    |      273     |     5.1    |
+  | Benzene vapour, C6H6 |    1.2   |    7.4   |  33,815    |      405     |     7.7    |
+  | Ethylene, C2H4       |    3.8   |    8.4   |  13,960    |      530     |     9.9    |
+  | Carbon dioxide, CO2  |    2.5   |    8.6   |     ..     |       ..     |      ..    |
+  | Nitrogen, N2         |    2.5   |    5.5   |     ..     |       ..     |      ..    |
+  |                      +----------+----------+------------+--------------+------------+
+  |        Total         |  100.0   |  100.0   |     ..     |     5319     |   100.0    |
+  +----------------------+----------+----------+------------+--------------+------------+
+
+One cubic metre of such gas weighs 568 grammes. _Rich gas_, or gas made
+by the destructive distillation of certain bituminous schists, of oil,
+&c., contains much more of the heavy hydrocarbons, and its heat-value is
+therefore much higher than the above. The carburetted water gas, very
+generally made in America, and sometimes employed in England for mixing
+with coal gas, is of varying composition; its heat-value is generally
+rather less than that of coal gas (see below).
+
+IV. _Combustible Gases produced by the Partial Combustion of Coal,
+&c._--These form by far the most important kind of gaseous fuel. When
+coal is submitted to destructive distillation to produce the
+illuminating gas described in the preceding paragraph, only a
+comparatively small proportion of the heating value of the coal (say, a
+sixth or at most a fifth part) is obtained in the shape of gaseous fuel,
+by far the greater proportion remaining behind in the shape of coke.
+
+An entirely different class of gaseous fuels comprises those produced by
+the incomplete combustion of the total carbon contained in the raw
+material, where the result is a mixture of gases which, being capable of
+combining with more oxygen, can be burnt and employed for heating
+purposes. Apart from some descriptions of waste gases belonging to this
+class (of which the most notable are those from blast-furnaces), we must
+distinguish two ways of producing such gaseous fuels entirely different
+in principle, though sometimes combined in one operation. The incomplete
+combustion of carbon may be brought about by means of atmospheric
+oxygen, by means of water, or by a simultaneous combination of these two
+actions. In the first case the chemical reaction is
+
+  C + O= CO       (a);
+
+the nitrogen accompanying the oxygen in the atmospheric air necessarily
+remains mixed with carbon monoxide, and the resulting gases, which
+always contain some carbon dioxide, some products of the destructive
+distillation of the coal, &c., are known as _producer gas_ or _Siemens
+gas_. In the second case the chemical reaction is mainly
+
+  C + H2O = CO + H2   (b);
+
+that is to say, the carbon is converted into monoxide and the hydrogen
+is set free. As both of these substances can combine with oxygen, and as
+there is no atmospheric nitrogen to deal with, the resulting gas (_water
+gas_) is, apart from a few impurities, entirely combustible. Another
+kind of water gas is formed by the reaction
+
+  C + 2H2O = CO2 + 2H2   (c),
+
+but this reaction, which converts all the carbon into the incombustible
+form of CO2, is considered as an unwelcome, although never entirely
+avoidable, concomitant of (b).
+
+The reaction by which water gas is produced being endothermic (as we
+shall see), this gas cannot be obtained except by introducing the
+balance of energy in another manner. This might be done by heating the
+apparatus from without, but as this method would be uneconomical, the
+process is carried out by alternating the endothermic production of
+water gas with the exothermic combustion of carbon by atmospheric air.
+Pure water gas is not, therefore, made by a continuous process, but
+alternates with the production of other gases, combustible or not. But
+instead of constantly interrupting the process in this way, a continuous
+operation may be secured by simultaneously carrying on both the
+reactions (a) and (b) in such proportions that the heat generated by (a)
+at least equals the heat absorbed by (b). For this purpose the apparatus
+is fed at the same time with atmospheric air and with a certain quantity
+of steam, preferably in a superheated state. Gaseous mixtures of this
+kind have been made, more or less intentionally, for a long time past.
+One of the best known of them, intended less for the purpose of serving
+as ordinary fuel than for that of driving machinery, is the Dowson gas.
+
+An advantage common to all kinds of gaseous fuel, which indeed forms the
+principal reason why it is intentionally produced from solid fuel, in
+spite of inevitable losses in the course of the operation, is the
+following. The combustion of solid fuel (coal, &c.) cannot be carried on
+with the theoretically necessary quantity of atmospheric air, but
+requires a considerable excess of the latter, at least 50%, sometimes
+100% and more. This is best seen from the analyses of smoke gases. If
+all the oxygen of the air were converted into CO2 and H2O, the amount of
+CO2 in the smoke gases should be in the case of pure carbon nearly 21
+volumes %, as carbon dioxide occupies the same volume as oxygen; while
+ordinary coal, where the hydrogen takes up a certain quantity of oxygen
+as well, should show about 18.5% CO2. But the best smoke gases of steam
+boilers show only 12 or 13%, much more frequently only 10% CO2, and
+gases from reverberatory furnaces often show less than 5%. This means
+that the volume of the smoke gases escaping into the air is from 1½ to 2
+times (in the case of high-temperature operations often 4 times) greater
+than the theoretical minimum; and as these gases always carry off a
+considerable quantity of heat, the loss of heat is all the greater the
+less complete is the utilization of the oxygen and the higher the
+temperature of the operation. This explains why, in the case of the
+best-constructed steam-boiler fires provided with heat economizers,
+where the smoke gases are deprived of most of their heat, the proportion
+of the heat value of the fuel actually utilized may rise to 70 or even
+75%, while in some metallurgical operations, in glass-making and similar
+cases, it may be below 5%.
+
+One way of overcoming this difficulty to a certain extent is to reduce
+the solid fuel to a very fine powder, which can be intimately mixed with
+the air so that the consumption of the latter is only very slightly in
+excess of the theoretical quantity; but this process, which has been
+only recently introduced on a somewhat extended scale, involves much
+additional expense and trouble, and cannot as yet be considered a real
+success. Generally, too, it is far less easily applied than gaseous
+fuel. The latter can be readily and intimately mixed with the exact
+quantity of air that is required and distributed in any suitable way,
+and much of the waste heat can be utilized for a preliminary heating of
+the air and the gas to be burned by means of "recuperators."
+
+We shall now describe the principal classes of gaseous fuel, produced by
+the partial combustion of coal.
+
+A. _Producer Gas, Siemens Gas._--As we have seen above, this gas is made
+by the incomplete combustion of fuel. The materials generally employed
+for its production are anthracite, coke or other fuels which are not
+liable to cake during the operation, and thus stop the draught or
+otherwise disturb the process, but by special measures also bituminous
+coal, lignite, peat and other fuel may be utilized for gas producers.
+The fuel is arranged in a deep layer, generally from 4 ft. up to 10 ft.,
+and the air is introduced from below, either by natural draught or by
+means of a blast, and either by a grate or only by a slit in the wall of
+the "gas producer." Even if the primary action taking place at the
+entrance of the air consisted in the complete combustion of the carbon
+to dioxide, CO2, the latter, in rising through the high column of
+incandescent fuel, must be reduced to monoxide: CO2 + C = 2CO. But as
+the temperature in the producer rises rather high, and as in ordinary
+circumstances the action of oxygen on carbon above 1000° C. consists
+almost entirely in the direct formation of CO, we may regard this
+compound as primarily formed in the hotter parts of the gas-producer. It
+is true that ordinary producer gas always contains more or less CO2, but
+this may be formed higher up by air entering through leakages in the
+apparatus. If we ignore the hydrogen contained in the fuel, the
+theoretical composition of producer gas would be 33.3% CO and 66.7% N,
+both by volume and weight. Its weight per cubic metre is 1.251 grammes,
+and its heat value 1013 calories per cubic metre, or less than one-fifth
+of the heat-value of coal gas. Practically, however, producer gas
+contains a small percentage of gases, increasing its heat-value, like
+hydrogen, methane, &c., but on the other hand it is never free from
+carbon dioxide to the extent of from 2 to 8%. Its heat-value may
+therefore range between 800 and 1100 calories per cubic metre. Even when
+taking as the basis of our calculation a theoretical gas of 33.3% CO, we
+find that there is a great loss of heat-value in the manufacture of this
+gas. Thermochemistry teaches us that the reaction C + O develops 29.5%
+of the heat produced by the complete oxidation of C to CO2, thus leaving
+only 70.5% for the stage CO + O = CO2. If, therefore, the gas given off
+in the producer is allowed to cool down to ordinary temperature, nearly
+30% of the heat-value of the coal is lost by radiation. If, however, the
+gas producer is built in close proximity to the place where the
+combustion takes place, so that the gas does not lose very much of its
+heat, the loss is correspondingly less. Even then there is no reason why
+this mode of burning the fuel, i.e. first with "primary air" in the
+producer (C + O = CO), then with "secondary air" in the furnace (CO + O
+= CO2), should be preferred to the direct complete burning of the fuel
+on a grate, unless the above-mentioned advantage is secured, viz.
+reduction of the smoke gases to a minimum by confining the supply of air
+as nearly as possible to that required for the formation of CO2, which
+is only possible by producing an intimate mixture of the producer gas
+with the secondary air. The advantage in question is not very great
+where the heat of the smoke gases can be very fully utilized, e.g. in
+well-constructed steam boilers, salt-pans and the like, and as a matter
+of fact gas producers have not found much use in such cases. But a very
+great advantage is attained in high-temperature operations, where the
+smoke gases escape very hot, and where it is on that account
+all-important to confine their quantity to a minimum.
+
+It is precisely in these cases that another requirement frequently comes
+in, viz. the production at a given point of a higher temperature than is
+easily attained by ordinary fires. Gas-firing lends itself very well to
+this end, as it is easily combined with a preliminary heating up of the
+air, and even of the gas itself, by means of "recuperators." The
+original and best-known form of these, due to Siemens Brothers, consists
+of two brick chambers filled with loosely stacked fire-bricks in such
+manner that any gases passed through the chambers must seek their way
+through the interstices left between the bricks, by which means a
+thorough interchange of temperature takes place. The smoke gases,
+instead of escaping directly into the atmosphere, are made to pass
+through one of these chambers, giving up part of their heat to the
+brickwork. After a certain time the draught is changed by means of
+valves, the smoke gases are passed through another chamber, and the cold
+air intended to feed the combustion is made to pass through the first
+chamber, where it takes up heat from the white-hot bricks, and is thus
+heated up to a bright red heat until the chamber is cooled down too far,
+when the draughts are again reversed. Sometimes the producer gas itself
+is heated up in this manner (especially when it has been cooled down by
+travelling a long distance); in that case four recuperator chambers must
+be provided instead of two. Another class of recuperators is not founded
+on the alternating system, but acts continuously; the smoke gases travel
+always in the same direction in flues contiguous to other flues or pipes
+in which the air flows in the opposite direction, an interchange of heat
+taking place through the walls of the flues or pipes. Here the surface
+of contact must be made very large if a good effect is to be produced.
+In both cases not merely is a saving effected of all the calories which
+are abstracted by the cold air from the recuperator, but as less fuel
+has to be burned to get a given effect, the quantity of smoke gas is
+reduced. For details and other producer gases, see GAS, II. _For Fuel
+and Power._
+
+Gas-firing in the manner just described can be brought about by very
+simple means, viz. by lowering the fire-grate of an ordinary fire-place
+to at least 4 ft. below the fire-bridge, and by introducing the air
+partly below the grate and partly behind the fire-place, at or near the
+point where the greatest heat is required. Usually, however, more
+elaborate apparatus is employed, some of which we shall describe below.
+Gas-firing has now become universal in some of the most important
+industries and nearly so in others. The present extension of
+steel-making and other branches of metallurgy is intimately connected
+with this system, as is the modern method of glass-making, of heating
+coal gas retorts and so forth.
+
+The composition of producer gas differs considerably, principally
+according to the material from which it is made. Analyses of ordinary
+producer gas (not such as falls under the heading of "semi-water gas,"
+see _sub_ C) by volume show 22 to 33% CO, 1 to 7% CO2, 0.5 to 2% H2, 0.5
+to 3% hydrocarbons, and 64 to 68% N2.
+
+B. _Water Gas._--The reaction of steam on highly heated carbonaceous
+matter was first observed by Felice Fontana in 1780. This was four years
+before Henry Cavendish isolated hydrogen from water, and thirteen years
+before William Murdoch made illuminating gas by the distillation of
+coal, so that it was no wonder that Fontana's laboratory work was soon
+forgotten. Nor had the use of carburetted water gas, as introduced by
+Donovan in 1830 for illuminating purposes, more than a very short life.
+More important is the fact that during nine years the illumination of
+the town of Narbonne was carried on by incandescent platinum wire,
+heated by water gas, where also internally heated generators were for
+the first time regularly employed. The Narbonne process was abandoned in
+1865, and for some time no real progress was made in this field in
+Europe. But in America, T.S.C. Lowe, Strong, Tessié du Motay and others
+took up the matter, the first permanent success being obtained by the
+introduction (1873) of Lowe's system at Phoenixville, Pa. In the United
+States the abundance of anthracite, as well as of petroleum naphtha,
+adapted for carburetting the gas, secures a great commercial advantage
+to this kind of illuminant over coal gas, so that now three-fourths of
+all American gas-works employ carburetted water gas. In Europe the
+progress of this industry was naturally much less rapid, but here also
+since 1882, when the apparatus of Lowe and Dwight was introduced in the
+town of Essen, great improvements have been worked out, principally by
+E. Blass, and by these improvements water gas obtained a firm footing
+also for certain heating purposes. The American process for making
+carburetted water gas, as an auxiliary to ordinary coal gas, was first
+introduced by the London Gas Light and Coke Company on a large scale in
+1890.
+
+Water gas in its original state is called "blue gas," because it burns
+with a blue, non-luminous flame, which produces a very high temperature.
+According to the equation C + H2O = CO + H2, this gas consists
+theoretically of equal volumes of carbon monoxide and hydrogen. We shall
+presently see why it is impossible to avoid the presence of a little
+carbon dioxide and other gases, but we shall for the moment treat of
+water gas as if it were composed according to the above equation. The
+reaction C + H2O = CO + H2 is endothermic, that is, its thermal value is
+negative. One gram-molecule of carbon produces 97 great calories (1
+great calorie or kilogram-calorie = 1000 gram-calories) when burning to
+CO2, and this is of course the maximum effect obtainable from this
+source. If the same gram-molecule of carbon is used for making water
+gas, that is, CO + H2, the heat produced by the combustion of the
+product is 68.4 + 57.6 = 126 great calories, an apparent surplus of 29
+calories, which cannot be got out of nothing. This is made evident by
+another consideration. In the above reaction C is not burned to CO2, but
+to CO, a reaction which produces 28.6 calories per gram-molecule. But as
+the oxygen is furnished from water, which must first be decomposed by
+the expenditure of energy, we must introduce this amount, 68.5 calories
+in the case of liquid water, or 57.6 calories in the case of steam, as a
+negative quantity, and the difference, viz. + 28.6 - 57.6 = 29 great
+calories, represents the amount of heat to be expended from another
+source in order to bring about the reaction of one gram-molecule of
+carbon on one gram-molecule of H2O in the shape of steam. This explains
+why steam directed upon incandescent coal will produce water gas only
+for a very short time: even a large mass of coal will quickly be cooled
+down so much that at first a gas of different composition is formed and
+soon the process will cease altogether. We can avoid this result by
+carrying on the process in a retort heated from without by an ordinary
+coal fire, and all the early water gas apparatus was constructed in this
+way; but such a method is very uneconomical, and was long ago replaced
+by a process first patented by J. and T.N. Kirkham in 1854, and very
+much improved by successive inventors. This process consists in
+conducting the operation in an upright brick shaft, charged with
+anthracite, coke or other suitable fuel. This shaft resembles an
+ordinary gas producer, but it differs in being worked, not in a
+continuous manner, which, as shown above, would be impossible, but by
+alternately blowing air and steam through the coal for periods of a few
+minutes each. During the first phase, when carbon is burned by
+atmospheric oxygen, and thereby heat is produced, this heat, or rather
+that part of it which is not carried away by radiation and by the
+products of combustion on leaving the apparatus, is employed in raising
+the temperature of the remaining mass of fuel, and is thus available for
+the second phase, in which the reaction (b) C + H2O = CO + H2 goes on
+with the abstraction of a corresponding amount of heat from the
+incandescent fuel, so that the latter rapidly cools down, and the
+process must be reversed by blowing in air and so forth. The formation
+of exactly equal volumes of carbon monoxide and hydrogen goes on only at
+temperatures over 1200° C., that is, for a very few minutes. Even at
+1100° C. a little CO2 can be proved to exist in the gas, and at 900° its
+proportion becomes too high to allow the process to go on. About 650° C.
+the CO has fallen to a minimum, and the reaction is now essentially (c)
+C + 2H2O = CO2 + 2H2; soon after the temperature of the mass will have
+fallen to such a low point that the steam passes through it without any
+perceptible action. The gas produced by reaction (c) contains only
+two-thirds of combustible matter, and is on that account less valuable
+than proper water gas formed by reaction (b); moreover, it requires the
+generation of twice the amount of steam, and its presence is all the
+less desirable since it must soon lead to a total cessation of the
+process. In ordinary circumstances it is evident that the more steam is
+blown in during a unit of time, the sooner reaction (c) will set in; on
+the other hand, the more heat has been accumulated in the producer the
+longer can the blowing-in of steam be continued.
+
+The process of making water gas consequently comprises two alternating
+operations, viz. first "blowing-up" by means of a current of air, by
+which the heat of the mass of fuel is raised to about 1200° C.; and,
+secondly "steaming," by injecting a current of (preferably superheated)
+steam until the temperature of the fuel had fallen to about 900° C., and
+too much carbon dioxide appears in the product. During the steaming the
+gas is carried off by a special conduit into a scrubber, where the dust
+mechanically carried away in the current is washed out, and the gas is
+at the same time cooled down nearly to the ordinary temperature. It is
+generally stored in a gas-holder, from which it is conducted away as
+required. It is never quite free from nitrogen, as the producer at the
+beginning of steaming contains much of this gas, together with CO or
+CO2. The proportion of hydrogen may exceed 50%, in consequence of
+reaction (c) setting in at the close of the steaming. Ordinary "blue"
+water gas, if, as usual, made from coke or anthracite, contains 48-52%
+H2, 40-41% CO, 1-5% CO2, 4-5% N2, and traces of hydrocarbons, especially
+methane. If made from bituminous coal, it contains more of the latter.
+If "carburetted" (a process which increases its volume 50% and more) by
+the vapours from superheated petroleum naphtha, the proportion of CO
+ranges about 25%, with about as much methane, and from 10 to 15% of
+"illuminants" (heavy hydrocarbons). The latter, of course, greatly
+enhance the fuel-value of the gas. Pure water gas would possess the
+following fuel-value per cubic metre:
+
+  0.5 cub. met. H2 = 1291 calories
+  0.5  "    "   CO = 1522    "
+                     ----
+                     2813    "
+
+Ordinary "blue" water gas has a fuel-value of at least 2500 calories.
+Carburetted water gas, which varies very much in its percentage of
+hydrocarbons, sometimes reaches nearly the heat-value of coal gas, but
+such gas is only in exceptional cases used for heating purposes.
+
+We must now turn to the "blowing-up" stage of the process. Until
+recently it was assumed that during this stage the combustion of carbon
+cannot be carried on beyond the formation of carbon monoxide, for as the
+gas-producer must necessarily contain a deep layer of fuel (generally
+about 6 to 10 ft.), any CO2 formed at first would be reduced to CO; and
+it was further assumed that hardly any CO2 would be formed from the
+outset, as the temperature of the apparatus is too high for this
+reaction to take place. But as the combustion of C to CO produces only
+about 30% of the heat produced when C is burned into CO2, the quantity
+of fuel consumed for "blowing-up" is very large, and in fact
+considerably exceeds that consumed in "steaming." There is, of course, a
+further loss by radiation and minor sources, and the result is that 1
+kilogram of carbon yields only about 1.2 cub. met. of water gas. Each
+period of blowing-up generally occupies from 8 to 12 minutes, that of
+steaming only 4 or 5 minutes. This low yield of water gas until quite
+recently appeared to be unavoidable, and the only question seemed to be
+whether and to what extent the gas formed during blowing-up, which is in
+fact identical with ordinary producer gas (Siemens gas), could be
+utilized. In America, where the water gas is mostly employed for
+illuminating purposes, at least part of the blowing-up gas is utilized
+for heating the apparatus in which the naphtha is volatilized and the
+vapours are "fixed" by superheating. This process, however, never
+utilizes anything like the whole of the blowing-up gas, nor can this be
+effected by raising and superheating the steam necessary for the second
+operation; indeed, the employment of this gas for raising steam is not
+very easy, owing to the irregularities of and constant interruptions in
+the supply. In some systems the gas made during the blowing-up stage is
+passed through chambers, loosely filled with bricks, like Siemens
+recuperators, where it is burned by "secondary" air: the heat thus
+imparted to the brickwork is utilized by passing through the
+recuperator, and thus superheating, the steam required for the next
+steaming operation. In many cases, principally where no carburetting is
+practised, the blowing-up gas is simply burned at the mouth of the
+producer, and is thus altogether lost; and in no case can it be utilized
+without great waste. A very important improvement in this respect was
+effected by C. Dellwik and E. Fleischer. They found that the view that
+it is unavoidable to burn the carbon to monoxide during the blowing-up
+holds good only for the pressure of blast formerly applied. This did not
+much exceed that which is required for overcoming the frictional
+resistance within the producer. If, however, the pressure is
+considerably increased, and the height of the column of fuel reduced,
+both of these conditions being strictly regulated in accordance with the
+result desired, it is easy to attain a combustion of the carbon to
+dioxide, with only traces of monoxide, in spite of the high temperature.
+Evidently the excess of oxygen coming into contact with each particle of
+carbon in a given unit of time produces other conditions of chemical
+equilibrium than those existing at lower pressures. At any rate,
+experience has shown that by this process, in which the full heat-value
+of carbon is utilized during the blowing-up stage, the time of
+heating-up can be reduced from 10 to 1½ or 2 minutes, and the steaming
+can be prolonged from 4 or 5 to 8 or 10 minutes, with the result that
+twice the quantity of water gas is obtained, viz. upwards of 2 cub.
+metres from 1 kilogram of carbon.
+
+The application of water gas as a fuel mainly depends upon the high
+temperatures which it is possible to attain by its aid, and these are
+principally due to the circumstance that it forms a much smaller flame
+than coal gas, not to speak of Siemens gas, which contains at most 33%
+of combustible matter against 90% or more in water gas. The latter
+circumstance also allows the gas to be conducted and distributed in
+pipes of moderate dimensions. Its application, apart from its use as an
+illuminant (with which we are not concerned here), was formerly retarded
+by its high cost in comparison with Siemens gas and other sources of
+heat, but as this state of affairs has been changed by the modern
+improvements, its use is rapidly extending, especially for metallurgical
+purposes.
+
+C. _Mixed Gas (Semi-Water Gas)._--This class is sometimes called Dowson
+gas, irrespective of its method of production, although it was made and
+extensively used a long time before J.E. Dowson constructed his
+apparatus for generating such a gas principally for driving gas-engines.
+By a combination of the processes for generating Siemens gas and water
+gas, it is produced by injecting into a gas-producer at the same time a
+certain quantity of air and a corresponding quantity of steam, the
+latter never exceeding the amount which can be decomposed by the
+heat-absorbing reaction, C + H2O = CO + H2, at the expense of the heat
+generated by the action of the air in the reaction C + O = CO. Such gas
+used to be frequently obtained in an accidental way by introducing
+liquid water or steam into an ordinary gas-producer for the purpose of
+facilitating its working by avoiding an excessive temperature, such as
+might cause the rapid destruction of the brickwork and the fusion of the
+ashes of the fuel into troublesome cakes. It was soon found that by
+proceeding in this way a certain advantage could be gained in regard to
+the consumption of fuel, as the heat abstracted by the steam from the
+brickwork and the fuel itself was usefully employed for decomposing
+water, its energy thus reappearing in the shape of a combustible gas. It
+is hardly necessary to mention explicitly that the total heat obtained
+by any such process from a given quantity of carbon (or hydrogen) can in
+no case exceed that which is generated by direct combustion; some
+inventors, however, whether inadvertently or intentionally, have
+actually represented this to be possible, in manifest violation of the
+law of the conservation of energy.
+
+Roughly speaking, this gas may be said to be produced by the combination
+of the reactions, described _sub_ A and B, to the joint reaction: 2C + O
++ H2O = 2CO + H2. The decomposition of H2O (applied in the shape of
+steam) absorbs 57.6 gram calories, the formation of 2CO produces 59 gram
+calories; hence there is a small positive excess of 1.4 calories at
+disposal. This in reality would not be sufficient to cover the loss by
+radiation, &c.; hence rather more free oxygen (i.e. atmospheric air)
+must be employed than is represented by the above equation. All this
+free oxygen is, of course, accompanied by nearly four times its volume
+of nitrogen.
+
+The mixed gas thus obtained differs very much in composition, but is
+always much richer in hydrogen (of which it contains sometimes as much
+as 20%) and poorer in carbon monoxide (sometimes down to 20%) than
+Siemens gas; generally it contains more of CO2 than the latter. The
+proportion of nitrogen is always less, about 50%. It is therefore a more
+concentrated fuel than Siemens gas, and better adapted to the driving of
+gas-engines. It scarcely costs more to make than ordinary Siemens gas,
+except where the steam is generated and superheated in special
+apparatus, as is done in the Dowson producer, which, on the other hand,
+yields a correspondingly better gas. As is natural, its properties are
+some way between those of Siemens gas and of water gas; but they
+approach more nearly the former, both as to costs and as to fuel-value,
+and also as to the temperatures reached in combustion. This is easily
+understood if we consider that gas of just the same description can be
+obtained by mixing one volume of real water gas with the four volumes of
+Siemens gas made during the blowing-up stage--an operation which is
+certainly too expensive for practical use.
+
+A modification of this gas is the _Mond gas_, which is made, according
+to Mond's patent, by means of such an excess of steam that most of the
+nitrogen of the coke is converted into ammonia (Grouven's reaction). Of
+course much of this steam passes on undecomposed, and the quantity of
+the gas is greatly increased by the reaction C + 2H2O = CO2 + 2H2; hence
+the fuel-value of this gas is less than that of semi-water gas made in
+other ways. Against this loss must be set the gain of ammonia which is
+recovered by means of an arrangement of coolers and scrubbers, and,
+except at very low prices of ammonia, the profit thus made is probably
+more than sufficient to cover the extra cost. But as the process
+requires very large and expensive plant, and its profits would vanish in
+the case of the value of ammonia becoming much lower (a result which
+would very probably follow if it were somewhat generally introduced), it
+cannot be expected to supplant the other descriptions of gaseous fuel to
+more than a limited extent.
+
+Semi-water gas is especially adapted for the purpose of driving
+gas-engines on the explosive principle (gas-motors). Ordinary
+producer-gas is too poor for this purpose in respect of heating power;
+moreover, owing to the prevalence of carbon monoxide, it does not light
+quickly enough. These defects are sufficiently overcome in semi-water
+gas by the larger proportion of hydrogen contained in it. For the
+purpose in question the gas should be purified from tar and ashes, and
+should also be cooled down before entering the gas-engine. The Dowson
+apparatus and others are constructed on this principle.
+
+_Air Gas._--By forcing air over or through volatile inflammable liquids
+a gaseous mixture can be obtained which burns with a bright flame and
+which can be used for illumination. Its employment for heating purposes
+is quite exceptional, e.g. in chemical laboratories, and we abstain,
+therefore, from describing any of the numerous appliances, some of them
+bearing very fanciful names, which have been devised for its
+manufacture.     (G. L.)
+
+
+
+
+FUENTE OVEJUNA [_Fuenteovejuna_], a town of Spain, in the province of
+Cordova; near the sources of the river Guadiato, and on the Fuente del
+Arco-Belmez-Cordova railway. Pop. (1900) 11,777. Fuente Ovejuna is built
+on a hill, in a well-irrigated district, which, besides producing an
+abundance of wheat, wine, fruit and honey, also contains argentiferous
+lead mines and stone quarries. Cattle-breeding is an important local
+industry, and leather, preserved meat, soap and flour are manufactured.
+The parish church formerly belonged to the knights of Calatrava (c.
+1163-1486).
+
+
+
+
+FUENTERRABIA (formerly sometimes written _Fontarabia_; Lat. _Fons
+Rapidus_), a town of northern Spain, in the province of Guipúzcoa; on
+the San Sebastian-Bayonne railway; near the Bay of Biscay and on the
+French frontier. Pop. (1870) about 750; (1900) 4345. Fuenterrabia stands
+on the slope of a hill on the left bank of the river Bidassoa, and near
+the point where its estuary begins. Towards the close of the 19th
+century the town became popular as a summer resort for visitors from the
+interior of Spain, and, in consequence, its appearance underwent many
+changes and much of its early prosperity returned. Hotels and villas
+were built in the new part of the town that sprang up outside the
+picturesque walled fortress, and there is quite a contrast between the
+part inside the heavy, half-ruined ramparts, with its narrow, steep
+streets and curious gable-roofed houses, its fine old church and castle
+and its massive town hall, and the new suburbs and fishermen's quarter
+facing the estuary of the Bidassoa. Many industries flourish on the
+outskirts of the town, including rope and net manufactures, flour mills,
+saw mills, mining railways, paper mills.
+
+Fuenterrabia formerly possessed considerable strategic importance, and
+it has frequently been taken and retaken in wars between France and
+Spain. The rout of Charlemagne in 778, which has been associated with
+Fontarabia, by Milton (_Paradise Lost_, i. 587), is generally understood
+to have taken place not here but at Roncesvalles (q.v.), which is nearly
+40 m. E.S.E. Unsuccessful attempts to seize Fuenterrabia were made by
+the French troops in 1476 and again in 1503. In a subsequent campaign
+(1521) these were more successful, but the fortress was retaken in 1524.
+The prince of Condé sustained a severe repulse under its walls in 1638,
+and it was on this occasion that the town received from Philip IV. the
+rank of city (_muy noble, muy leal, y muy valerosa ciudad_, "most noble,
+most loyal, and most valiant city"), a privilege which involved some
+measure of autonomy. After a severe siege, Fuenterrabia surrendered to
+the duke of Berwick and his French troops in 1719; and in 1794 it again
+fell into the hands of the French, who so dismantled it that it has
+never since been reckoned by the Spaniards among their fortified places.
+It was by the ford opposite Fuenterrabia that the duke of Wellington, on
+the 8th of October 1813, successfully forced a passage into France in
+the face of an opposing army commanded by Marshal Soult. Severe fighting
+also took place here during the Carlist War in 1837.
+
+
+
+
+FUERO, a Spanish term, derived from the Latin _forum_. The Castillan use
+of the word in the sense of a right, privilege or charter is most
+probably to be traced to the Roman _conventus juridici_, otherwise known
+as _jurisdictiones_ or _fora_, which in Pliny's time were already
+numerous in the Iberian peninsula. In each of these provincial _fora_
+the Roman magistrate, as is well known, was accustomed to pay all
+possible deference to the previously established common law of the
+district; and it was the privilege of every free subject to demand that
+he should be judged in accordance with the customs and usages of his
+proper forum. This was especially true in the case of the inhabitants of
+those towns which were in possession of the _jus italicum_. It is not,
+indeed, demonstrable, but there are many presumptions, besides some
+fragments of direct evidence, which make it more than probable that the
+old administrative arrangements both of the provinces and of the towns,
+but especially of the latter, remained practically undisturbed at the
+period of the Gothic occupation of Spain.[1] The Theodosian Code and the
+Breviary of Alaric alike seem to imply a continuance of the municipal
+system which had been established by the Romans; nor does the later Lex
+Visigothorum, though avowedly designed in some points to supersede the
+Roman law, appear to have contemplated any marked interference with the
+former _fora_, which were still to a large extent left to be regulated
+in the administration of justice by unwritten, immemorial, local custom.
+Little is known of the condition of the subject populations of the
+peninsula during the Arab occupation; but we are informed that the
+Christians were, sometimes at least, judged according to their own laws
+in separate tribunals presided over by Christian judges;[2] and the mere
+fact of the preservation of the name _alcalde_, an official whose
+functions corresponded so closely to those of the _judex_ or _defensor
+civitatis_, is fitted to suggest that the old municipal _fora_, if much
+impaired, were not even then in all cases wholly destroyed. At all
+events when the word _forum_[3] begins to appear for the first time in
+documents of the 10th century in the sense of a liberty or privilege,
+it is generally implied that the thing so named is nothing new. The
+earliest extant written fuero is probably that which was granted to the
+province and town of Leon by Alphonso V. in 1020. It emanated from the
+king in a general council of the kingdom of Leon and Castile, and
+consisted of two separate parts; in the first 19 chapters were contained
+a series of statutes which were to be valid for the kingdom at large,
+while the rest of the document was simply a municipal charter.[4] But in
+neither portion does it in any sense mark a new legislative departure,
+unless in so far as it marks the beginning of the era of written
+charters for towns. The "fuero general" does not profess to supersede
+the _consuetudines antiquorum jurium_ or Chindaswint's codification of
+these in the Lex Visigothorum; the "fuero municipal" is really for the
+most part but a resuscitation of usages formerly established, a
+recognition and definition of liberties and privileges that had long
+before been conceded or taken for granted. The right of the burgesses to
+self-government and self-taxation is acknowledged and confirmed, they,
+on the other hand, being held bound to a constitutional obedience and
+subjection to the sovereign, particularly to the payment of definite
+imperial taxes, and the rendering of a certain amount of military
+service (as the ancient municipia had been). Almost contemporaneous with
+this fuero of Leon was that granted to Najera (Naxera) by Sancho el
+Mayor of Navarre (_ob._ 1035), and confirmed, in 1076, by Alphonso
+VI.[5] Traces of others of perhaps even an earlier date are occasionally
+to be met with. In the fuero of Cardeña, for example, granted by
+Ferdinand I. in 1039, reference is made to a previous forum Burgense
+(Burgos), which, however, has not been preserved, if, indeed, it ever
+had been reduced to writing at all. The phraseology of that of Sepulveda
+(1076) in like manner points back to an indefinitely remote
+antiquity.[6] Among the later fueros of the 11th century, the most
+important are those of Jaca (1064) and of Logroño (1095). The former of
+these, which was distinguished by the unusual largeness of its
+concessions, and by the careful minuteness of its details, rapidly
+extended to many places in the neighbourhood, while the latter charter
+was given also to Miranda by Alphonso VI., and was further extended in
+1181 by Sancho el Sabio of Navarre to Vitoria, thus constituting one of
+the earliest written _fora_ of the "Provincias Vascongadas." In the
+course of the 12th and 13th centuries the number of such documents
+increased very rapidly; that of Toledo especially, granted to the
+Mozarabic population in 1101, but greatly enlarged and extended by
+Alphonso VII. (1118) and succeeding sovereigns, was used as a basis for
+many other Castilian fueros. Latterly the word fuero came to be used in
+Castile in a wider sense than before, as meaning a general code of laws;
+thus about the time of Saint Ferdinand the old Lex Visigothorum, then
+translated for the first time into the vernacular, was called the Fuero
+Juzgo, a name which was soon retranslated into the barbarous Latin of
+the period as Forum Judicum;[7] and among the compilations of Alphonso
+the Learned in like manner were an _Espejo de Fueros_ and also the
+_Fuero de las leyes_, better known perhaps as the _Fuero Real_. The
+famous code known as the _Ordenamiento Real de Alcalá_, or _Fuero Viejo
+de Castilla_, dates from a still later period. As the power of the
+Spanish crown was gradually concentrated and consolidated, royal
+pragmaticas began to take the place of constitutional laws; the local
+fueros of the various districts slowly yielded before the superior force
+of imperialism; and only those of Navarre and the Basque provinces (see
+BASQUES) have had sufficient vitality to enable them to survive to
+comparatively modern times. While actually owning the lordship of the
+Castilian crown since about the middle of the 14th century, these
+provinces rigidly insisted upon compliance with their consuetudinary
+law, and especially with that which provided that the _señor_, before
+assuming the government, should personally appear before the assembly
+and swear to maintain the ancient constitutions. Each of the provinces
+mentioned had distinct sets of fueros, codified at different periods,
+and varying considerably as to details; the main features, however, were
+the same in all. Their rights, after having been recognized by
+successive Spanish sovereigns from Ferdinand the Catholic to Ferdinand
+VII., were, at the death of the latter in 1833, set aside by the
+government of Castaños. The result was a civil war, which terminated in
+a renewed acknowledgment of the fueros by Isabel II. (1839). The
+provisional government of 1868 also promised to respect them, and
+similar pledges were given by the governments which succeeded. In
+consequence, however, of the Carlist rising of 1873-1876, the Basque
+fueros were finally extinguished in 1876. The history of the _Foraes_ of
+the Portuguese towns, and of the _Fors du Béarn_, is precisely analogous
+to that of the fueros of Castile.
+
+  Among the numerous works that more or less expressly deal with this
+  subject, that of Marina (_Ensayo historico-critico sobre la antigua
+  legislacion y principales cuerpos legales de los reynos de Leon y
+  Castilla_) still continues to hold a high place. Reference may also be
+  made to Colmeiro's _Curso de derecho político según la historia de
+  Leon y de Castilla_ (Madrid, 1873); to Schäfer's _Geschichte von
+  Spanien_, ii. 418-428, iii. 293 seq.; and to Hallam's _Middle Ages_,
+  c. iv.
+
+
+FOOTNOTES:
+
+  [1] The nature of the evidence may be gathered from Savigny, _Gesch.
+    d. röm. Rechts_. See especially i. pp. 154, 259 seq.
+
+  [2] Compare Lembke u. Schäfer, _Geschichte von Spanien_, i. 314; ii.
+    117.
+
+  [3] Or rather _forus_. See Ducange, s.v.
+
+  [4] Cap. xx. begins: "Constituimus etiam ut Legionensis civitas, quae
+    depopulata fuit a Sarracenis in diebus patris mei Veremundi regis,
+    repopulatur _per hos foros subscriptos_."
+
+  [5] "Mando et concedo et confirmo ut ista civitas cum sua plebe et
+    cum omnibus suis pertinentiis sub tali lege et sub tali foro maneat
+    per saecula cuncta. Amen. Isti sunt fueros quae habuerunt in Naxera
+    in diebus Sanctii regis et Gartiani regis."
+
+  [6] "Ego Aldefonsus rex et uxor mea Agnes confirmamus ad
+    Septempublica suo foro quod habuit in tempore antiquo de avolo meo et
+    in tempore comitum Ferrando Gonzalez et comite Garcia Ferdinandez et
+    comite Domno Santio."
+
+  [7] This Latin is later even than that of Ferdinand, whose words are:
+    "Statuo et mando quod Liber Judicum, quo ego misi Cordubam,
+    translatetur in vulgarem et vocetur forum de Corduba ... et quod per
+    saecula cuncta sit pro foro et nullus sit ausus istud forum aliter
+    appellare nisi forum de Corduba, et jubeo et mando quod omnis morator
+    et populator ... veniet ad judicium et ad forum de Corduba."
+
+
+
+
+FUERTEVENTURA, an island in the Atlantic Ocean, forming part of the
+Spanish archipelago of the Canary Islands (q.v.). Pop. (1900) 11,669;
+area 665 sq. m. Fuerteventura lies between Lanzarote and Grand Canary.
+It has a length of 52 m., and an average width of 12 m. Though less
+mountainous than the other islands, its aspect is barren. There are only
+two springs of fresh water, and these are confined to one valley. Lava
+streams and other signs of volcanic action abound, but there has been no
+igneous activity since the Spaniards took possession. At each extremity
+of the island are high mountains, which send off branches along the
+coast so as to enclose a large arid plain. The highest peak reaches 2500
+ft. In external appearance, climate and productions, Fuerteventura
+greatly resembles Lanzarote. An interval of three years without rain has
+been known. Oliva (pop. 1900, 2464) is the largest town. A smaller place
+in the centre of the island named Betancuria (586) is the administrative
+capital. Cabras (1000) on the eastern coast is the chief port.
+Dromedaries are bred here.
+
+
+
+
+FUGGER, the name of a famous German family of merchants and bankers. The
+founder of the family was Johann Fugger, a weaver at Graben, near
+Augsburg, whose son, Johann, settled in Augsburg probably in 1367. The
+younger Johann added the business of a merchant to that of a weaver, and
+through his marriage with Clara Widolph became a citizen of Augsburg.
+After a successful career he died in 1408, leaving two sons, Andreas and
+Jakob, who greatly extended the business which they inherited from their
+father. Andreas, called the "rich Fugger," had several sons, among them
+being Lukas, who was very prominent in the municipal politics of
+Augsburg and who was very wealthy until he was ruined by the repudiation
+by the town of Louvain of a great debt owing to him, and Jakob, who was
+granted the right to bear arms in 1452, and who founded the family of
+Fugger vom Reh--so called from the first arms of the Fuggers, a roe
+(_Reh_) or on a field azure--which became extinct on the death of his
+great-grandson, Ulrich, in 1583. Johann Fugger's son, Jakob, died in
+1469, and three of his seven sons, Ulrich (1441-1510), Georg (1453-1506)
+and Jakob (1459-1525), men of great resource and industry, inherited the
+family business and added enormously to the family wealth. In 1473
+Ulrich obtained from the emperor Frederick III. the right to bear arms
+for himself and his brothers, and about the same time he began to act
+as the banker of the Habsburgs, a connexion destined to bring fame and
+fortune to his house. Under the lead of Jakob, who had been trained for
+business in Venice, the Fuggers were interested in silver mines in Tirol
+and copper mines in Hungary, while their trade in spices, wool and silk
+extended to almost all parts of Europe. Their wealth enabled them to
+make large loans to the German king, Maximilian I., who pledged to them
+the county of Kirchberg, the lordship of Weissenhorn and other lands,
+and bestowed various privileges upon them. Jakob built the castle of
+Fuggerau in Tirol, and erected the Fuggerei at Augsburg, a collection of
+106 dwellings, which were let at low rents to poor people and which
+still exist. Jakob Fugger and his two nephews, Ulrich (d. 1525) and
+Hieronymus (d. 1536), the sons of Ulrich, died without direct heirs, and
+the family was continued by Georg's sons, Raimund (1489-1535) and Anton
+(1493-1560), under whom the Fuggers attained the summit of their wealth
+and influence.
+
+Jakob Fugger's florins had contributed largely to the election of
+Charles V. to the imperial throne in 1519, and his nephews and heirs
+maintained close and friendly relations with the great emperor. In
+addition to lending him large sums of money, they farmed his valuable
+quicksilver mines at Almaden, his silver mines at Guadalcanal, the great
+estates of the military orders which had passed into his hands, and
+other parts of his revenue as king of Spain; receiving in return several
+tokens of the emperor's favour. In 1530 Raimund and Anton were granted
+the imperial dignity of counts of Kirchberg and Weissenhorn, and
+obtained full possession of these mortgaged properties; in 1534 they
+were given the right of coining money; and in 1541 received rights of
+jurisdiction over their lands. During the diet of Augsburg in 1530
+Charles V. was the guest of Anton Fugger at his house in the Weinmarkt,
+and the story relates how the merchant astonished the emperor by
+lighting a fire of cinnamon with an imperial bond for money due to him.
+This incident forms the subject of a picture by Carl Becker which is in
+the National Gallery at Berlin. Continuing their mercantile career, the
+Fuggers brought the new world within the sphere of their operations, and
+also carried on an extensive and lucrative business in farming
+indulgences. Moreover, both brothers found time to acquire landed
+property, and were munificent patrons of literature and art. When Anton
+died he is said to have been worth 6,000,000 florins, besides a vast
+amount of property in Europe, Asia and America; and before this time the
+total wealth of the family had been estimated at 63,000,000 florins. The
+Fuggers were devotedly attached to the Roman Catholic Church, which
+benefited from their liberality. Jakob had been made a count palatine
+(_Pfalzgraf_) and had received other marks of favour from Pope Leo X.,
+and several members of the family had entered the church; one, Raimund's
+son, Sigmund, becoming bishop of Regensburg.
+
+In addition to the bishop, three of Raimund Fugger's sons attained some
+degree of celebrity. Johann Jakob (1516-1575), was the author of
+_Wahrhaftigen Beschreibung des österreichischen und habsburgischen
+Nahmens_, which was largely used by S. von Bircken in his _Spiegel der
+Ehren des Erzhauses Österreich_ (Nuremberg, 1668), and of a _Geheim
+Ernbuch des Fuggerischen Geschlechtes_. He was also a patron of art, and
+a distinguished counsellor of Duke Albert IV. of Bavaria. After the
+death of his son Konstantin, in 1627, this branch of the family was
+divided into three lines, which became extinct in 1738, 1795 and 1846
+respectively. Another of Raimund's sons was Ulrich (1526-1584), who,
+after serving Pope Paul III. at Rome, became a Protestant. Hated on this
+account by the other members of his family, he took refuge in the
+Rhenish Palatinate; greatly interested in the Greek classics, he
+occupied himself in collecting valuable manuscripts, which he bequeathed
+to the university of Heidelberg. Raimund's other son was Georg (d.
+1579), who inherited the countships of Kirchberg and Weissenhorn, and
+founded a branch of the family which still exists, its present head
+being Georg, Count Fugger of Kirchberg and Weissenhorn (b. 1850).
+
+Anton Fugger left three sons, Marcus (1529-1597), Johann (d. 1598) and
+Jakob (d. 1598), all of whom left male issue. Marcus was the author of
+a book on horse-breeding, _Wie und wo man ein Gestüt von guten edeln
+Kriegsrossen aufrichten soll_ (1578), and of a German translation of the
+_Historia ecclesiastica_ of Nicephorus Callistus. He founded the
+Nordendorf branch of the family, which became extinct on the death of
+his grandson, Nicolaus, in 1676. Another grandson of Marcus was Franz
+Fugger (1612-1664), who served under Wallenstein during the Thirty
+Years' War, and was afterwards governor of Ingolstadt. He was killed at
+the battle of St Gotthard on the 1st of August 1664.
+
+Johann Fugger had three sons, Christoph (d. 1615) and Marcus (d. 1614),
+who founded the families of Fugger-Glött and Fugger-Kirchheim
+respectively, and Jakob, bishop of Constance from 1604 until his death
+in 1626. Christoph's son, Otto Heinrich (1592-1644), was a soldier of
+some distinction and a knight of the order of the Golden Fleece. He was
+one of the most active of the Bavarian generals during the Thirty Years'
+War, and acted as governor of Augsburg, where his rule aroused much
+discontent. The family of Kirchheim died out in 1672. That of Glött was
+divided into several branches by the sons of Otto Heinrich and of his
+brother Johann Ernst (d. 1628). These lines, however, have gradually
+become extinct except the eldest line, represented in 1909 by Karl
+Ernst, Count Fugger of Glött (b. 1859). Anton Fugger's third son Jakob,
+the founder of the family of Wellenburg, had two sons who left issue,
+but in 1777 the possessions of this branch of the family were again
+united by Anselm Joseph (d. 1793), Count Fugger of Babenhausen. In 1803
+Anselm's son, Anselm Maria (d. 1821), was made a prince of the Holy
+Roman Empire, the title of Prince Fugger of Babenhausen being borne by
+his direct descendant Karl (b. 1861). On the fall of the empire in 1806
+the lands of the Fuggers, which were held directly of the empire, were
+mediatized under Bavaria and Württemberg. The heads of the three
+existing branches of the Fuggers are all hereditary members of the
+Bavarian Upper House.
+
+Augsburg has many interesting mementoes of the Fuggers, including the
+family burial-chapel in the church of St Anna; the Fugger chapel in the
+church of St Ulrich and St Afra; the Fuggerhaus, still in the possession
+of one branch of the family; and a statue of Johann Jakob Fugger.
+
+  In 1593 a collection of portraits of the Fuggers, engraved by
+  Dominique Custos of Antwerp, was issued at Augsburg. Editions with 127
+  portraits appeared in 1618 and 1620, the former accompanied by a
+  genealogy in Latin, the latter by one in German. Another edition of
+  this _Pinacotheca Fuggerorum_, published at Vienna in 1754, includes
+  139 portraits. See _Chronik der Familie Fugger vom Jahre 1599_, edited
+  by C. Meyer (Munich, 1902); A. Geiger, _Jakob Fugger, 1459-1525_
+  (Regensburg, 1895); A. Schulte, _Die Fugger in Rom, 1495-1523_
+  (Leipzig, 1904); R. Ehrenberg, _Das Zeitalter der Fugger_ (Jena,
+  1896); K. Häbler, _Die Geschichte der Fuggerschen Handlung in Spanien_
+  (Weimar, 1897); A. Stauber, _Das Haus Fugger_ (Augsburg, 1900); and M.
+  Jansen, _Die Anfänge der Fugger_ (Leipzig, 1907).
+
+
+
+
+FUGITIVE SLAVE LAWS, a term applied in the United States to the Statutes
+passed by Congress in 1793 and 1850 to provide for the return of negro
+slaves who escaped from one state into another or into a public
+territory. A fugitive slave clause was inserted in the Articles of
+Confederation of the New England Confederation of 1643, providing for
+the return of the fugitive upon the certificate of one magistrate in the
+jurisdiction out of which the said servant fled--no trial by jury being
+provided for. This seems to have been the only instance of an
+inter-colonial provision for the return of fugitive slaves; there were,
+indeed, not infrequent escapes by slaves from one colony to another, but
+it was not until after the growth of anti-slavery sentiment and the
+acquisition of western territory, that it became necessary to adopt a
+uniform method for the return of fugitive slaves. Such provision was
+made in the Ordinance of 1787 (for the Northwest Territory), which in
+Article VI. provided that in the case of "any person escaping into the
+same [the Northwest Territory] from whom labor or service is lawfully
+claimed in any one of the original states, such fugitive may be lawfully
+reclaimed and conveyed to the person claiming his or her labor or
+service as aforesaid." An agreement of the sort was necessary to
+persuade the slave-holding states to union, and in the Federal
+Constitution, Article IV., Section II., it is provided that "no person
+held to service or labor in one state, under the laws thereof, escaping
+into another, shall, in consequence of any law or regulation therein, be
+discharged from such service or labor, but shall be delivered up on
+claim of the party to whom such service or labour may be due."
+
+The first specific legislation on the subject was enacted on the 12th of
+February 1793, and like the Ordinance for the Northwest Territory and
+the section of the Constitution quoted above, did not contain the word
+"slave"; by its provisions any Federal district or circuit judge or any
+state magistrate was authorized to decide finally and without a jury
+trial the status of an alleged fugitive. The measure soon met with
+strong opposition in the northern states, and Personal Liberty Laws were
+passed to hamper officials in the execution of the law; Indiana in 1824
+and Connecticut in 1828 providing jury trial for fugitives who appealed
+from an original decision against them. In 1840 New York and Vermont
+extended the right of trial by jury to fugitives and provided them with
+attorneys. As early as the first decade of the 19th century individual
+dissatisfaction with the law of 1793 had taken the form of systematic
+assistance rendered to negroes escaping from the South to Canada or New
+England--the so-called "Underground Railroad."[1] The decision of the
+Supreme Court of the United States in the case of _Prigg_ v.
+_Pennsylvania_ in 1842 (16 Peters 539), that state authorities could not
+be forced to act in fugitive slave cases, but that national authorities
+must carry out the national law, was followed by legislation in
+Massachusetts (1843), Vermont (1843), Pennsylvania (1847) and Rhode
+Island (1848), forbidding state officials to help enforce the law and
+refusing the use of state gaols for fugitive slaves. The demand from the
+South for more effective Federal legislation was voiced in the second
+fugitive slave law, drafted by Senator J.M. Mason of Virginia, and
+enacted on the 18th of September 1850 as a part of the Compromise
+Measures of that year. Special commissioners were to have concurrent
+jurisdiction with the U.S. circuit and district courts and the inferior
+courts of Territories in enforcing the law; fugitives could not testify
+in their own behalf; no trial by jury was provided; penalties were
+imposed upon marshals who refused to enforce the law or from whom a
+fugitive should escape, and upon individuals who aided negroes to
+escape; the marshal might raise a _posse comitatus_; a fee of $10 was
+paid to the commissioner when his decision favoured the claimant and
+only $5 when it favoured the fugitive; and both the fact of the escape
+and the identity of the fugitive were to be determined on purely _ex
+parte_ testimony. The severity of this measure led to gross abuses and
+defeated its purpose; the number of abolitionists increased, the
+operations of the Underground Railroad became more efficient, and new
+Personal Liberty Laws were enacted in Vermont (1850), Connecticut
+(1854), Rhode Island (1854), Massachusetts (1855), Michigan (1855),
+Maine (1855 and 1857), Kansas (1858) and Wisconsin (1858). These
+Personal Liberty Laws forbade justices and judges to take cognizance of
+claims, extended the _habeas corpus_ act and the privilege of jury trial
+to fugitives, and punished false testimony severely. The supreme court
+of Wisconsin went so far (1859) as to declare the Fugitive Slave Law
+unconstitutional. These state laws were one of the grievances officially
+referred to by South Carolina (in Dec. 1860) as justifying her secession
+from the Union. Attempts to carry into effect the law of 1850 aroused
+much bitterness. The arrests of Sims and of Shadrach in Boston in 1851;
+of "Jerry" M'Henry, in Syracuse, New York, in the same year; of Anthony
+Burns in 1854, in Boston; and of the two Garner families in 1856, in
+Cincinnati, with other cases arising under the Fugitive Slave Law of
+1850, probably had as much to do with bringing on the Civil War as did
+the controversy over slavery in the Territories.
+
+With the beginning of the Civil War the legal status of the slave was
+changed by his master's being in arms. General B.F. Butler, in May 1861,
+declared negro slaves contraband of war. A confiscation bill was passed
+in August 1861 discharging from his service or labour any slave employed
+in aiding or promoting any insurrection against the government of the
+United States. By an act of the 17th of July 1862 any slave of a
+disloyal master who was in territory occupied by northern troops was
+declared _ipso facto_ free. But for some time the Fugitive Slave Law was
+considered still to hold in the case of fugitives from masters in the
+border states who were loyal to the Union government, and it was not
+until the 28th of June 1864 that the Act of 1850 was repealed.
+
+  See J.F. Rhodes, _History of the United States from the Compromise of
+  1850_, vols. i. and ii. (New York, 1893); and M.G. M'Dougall,
+  _Fugitive Slaves, 1619-1865_ (Boston, 1891).
+
+
+FOOTNOTE:
+
+  [1] The precise amount of organization in the Underground Railroad
+    cannot be definitely ascertained because of the exaggerated use of
+    the figure of railroading in the documents of the "presidents" of the
+    road, Robert Purvis and Levi Coffin, and of its many "conductors,"
+    and their discussion of the "packages" and "freight" shipped by them.
+    The system reached from Kentucky and Virginia across Ohio, and from
+    Maryland across Pennsylvania and New York, to New England and Canada,
+    and as early as 1817 a group of anti-slavery men in southern Ohio had
+    helped to Canada as many as 1000 slaves. The Quakers of Pennsylvania
+    possibly began the work of the mysterious Underground Railroad; the
+    best known of them was Thomas Garrett (1789-1871), a native of
+    Pennsylvania, who, in 1822, removed to Wilmington, Delaware, where he
+    was convicted in 1848 on four counts under the Fugitive Slave Law and
+    was fined $8000; he is said to have helped 2700 slaves to freedom.
+    The most picturesque figure of the Underground Railroad was Harriet
+    Tubman (c. 1820), called by her friend, John Brown, "General" Tubman,
+    and by her fellow negroes "Moses." She made about a score of trips
+    into the South, bringing out with her 300 negroes altogether. At one
+    time a reward of $40,000 was offered for her capture. She was a
+    mystic, with remarkable clairvoyant powers, and did great service as
+    a nurse, a spy and a scout in the Civil War. Levi Coffin (1798-1877),
+    a native of North Carolina (whose cousin, Vestal Coffin, had
+    established before 1819 a "station" of the Underground near what is
+    now Guilford College, North Carolina), in 1826 settled in Wayne
+    County, Ohio; his home at New Garden (now Fountain City) was the
+    meeting point of three "lines" from Kentucky; and in 1847 he removed
+    to Cincinnati, where his labours in bringing slaves out of the South
+    were even more successful. It has been argued that the Underground
+    Railroad delayed the final decision of the slavery question, inasmuch
+    as it was a "safety valve"; for, without it, the more intelligent and
+    capable of the negro slaves would, it is asserted, have become the
+    leaders of insurrections in the South, and would not have been
+    removed from the places where they could have done most damage.
+    Consult William Still, _The Underground Railroad_ (Philadelphia,
+    1872), a collection of anecdotes by a negro agent of the Pennsylvania
+    Anti-Slavery Society, and of the Philadelphia branch of the Railroad;
+    and the important and scholarly work of Wilbur H. Siebert, _The
+    Underground Railroad from Slavery to Freedom_ (New York, 1898).
+
+
+
+
+FUGLEMAN (from the Ger. _Flügelmann_, the man on the _Flügel_ or wing),
+properly a military term for a soldier who is selected to act as
+"guide," and posted generally on the flanks with the duty of directing
+the march in the required line, or of giving the time, &c., to the
+remainder of the unit, which conforms to his movements, in any military
+exercise. The word is then applied to a ringleader or one who takes the
+lead in any movement or concerted movement.
+
+
+
+
+FUGUE (Lat. _fuga_, flight), in music, the mutual "pursuit" of voices or
+parts. It was, up to the end of the 16th century, if not later, the name
+applied to two art-forms. (A) _Fuga ligata_ was the exact reproduction
+by one or more voices of the statement of a leading part. The
+reproducing voice (_comes_) was seldom if ever written out, for all
+differences between it and the _dux_ were rigidly systematic; e.g. it
+was an exact inversion, or exactly twice as slow, or to be sung
+backwards, &c. &c. Hence, a rule or _canon_ was given, often in
+enigmatic form, by which the _comes_ was deduced from the _dux_: and so
+the term _canon_ became the appropriate name for the form itself, and is
+still retained. (B) A composition in which the canonic style was
+cultivated without canonic restriction was, in the 16th century, called
+_fuga ricercata_ or simply a _ricercare_, a term which is still used by
+Bach as a title for the fugues in _Das musikalische Opfer_.
+
+The whole conception of fugue, rightly understood, is one of the most
+important in music, and the reasons why some contrapuntal compositions
+are called fugues, while others are not, are so trivial, technically as
+well as aesthetically, that we have preferred to treat the subject
+separately under the general heading of CONTRAPUNTAL FORMS, reserving
+only technical terms for definition here.
+
+(i.) If in the beginning or "exposition" the material with which the
+opening voice accompanies the answer is faithfully reproduced as the
+accompaniment to subsequent entries of the subject, it is called a
+_countersubject_ (see COUNTERPOINT, under sub-heading _Double
+Counterpoint_). Obviously the process may be carried further, the first
+countersubject going on to a second when the subject enters in the third
+part and so on. The term is also applied to new subjects appearing later
+in the fugue in combination (immediate or destined) with the original
+subject. Cherubini, holding the doctrine that a fugue cannot have more
+than one subject, insists on applying the term to the less prominent of
+the subjects of what are commonly called double fugues, i.e. fugues
+which begin with two parts and two subjects simultaneously, and so also
+with _triple_ and _quadruple fugues_.
+
+(ii.) _Episodes_ are passages separating the entries of the subject.[1]
+Episodes are usually developed from the material of the subject and
+countersubjects; they are very rarely independent, but then
+conspicuously so.
+
+(iii.) _Stretto_, the overlapping of subject and answer, is a resource
+the possibilities of which may be exemplified by the setting of the
+words _omnes generationes_ in Bach's _Magnificat_ (see BACH).
+
+(iv.) The distinction between _real_ and _tonal_ fugue, which is still
+sometimes treated as a thing of great historical and technical
+importance, is really a mere detail resulting from the fact that a
+violent oscillation between the keys of tonic and dominant is no part of
+the function of a fugal exposition, so that the answer is (especially in
+its first notes and in points that tend to shift the key) not so much a
+transposition of the subject to the key of the dominant as an adaptation
+of it from the tonic part to the dominant part of the scale, or vice
+versa; in short, the answer is as far as possible _on_ the dominant, not
+_in_ the dominant. The modifications this principle produces in the
+answer (which have been happily described as resembling
+"fore-shortening") are the only distinctive marks of tonal fugue; and
+the text-books are half filled with the attempt to reduce them from
+matters of ear to rules of thumb, which rules, however, have the merit
+(unusual in those of the academic fugue) of being founded on observation
+of the practice of great masters. But the same principle as often as not
+produces answers that are exact transpositions of the subject; and so
+the only kind of real fugue (i.e. fugue with an exact answer) that could
+rightly be contrasted with tonal fugue would be that in which the answer
+ought to be tonal but is not. It must be admitted that tonal answers are
+rare in the modal music of the 16th century, though their melodic
+principles are of yet earlier date; still, though tonal fugue does not
+become usual until well on in the 17th century, the idea that it is a
+separate species is manifestly absurd, unless the term simply means
+"fugue in modern tonality or key," whatever the answer may be.
+
+The term "answer" is usually reserved for those entries of the subject
+that are placed in what may be called the "complementary" position of
+the scale, whether they are "tonally" modified or not. Thus the order of
+entries in the exposition of the first fugue of the _Wohltemp_. _Klav_.
+is subject, answer, answer, subject; a departure from the usual rule
+according to which subject and answer are strictly alternate in the
+exposition.
+
+In conclusion we may remind the reader of the most accurate as well as
+the most vivid description ever given of the essentials of a fugue, in
+the famous lines in _Paradise Lost_, book xi.
+
+              "His volant touch,
+  Instinct through all proportions, low and high,
+  Fled and pursued transverse the resonant fugue."
+
+It is hard to realize that this description of organ-music was written
+in no classical period of instrumental polyphony, but just half-way
+between the death of Frescobaldi and the birth of Bach. Every word is a
+definition, both retrospective and prophetic; and in "transverse" we see
+all that Sir Frederick Gore Ouseley expresses in his popular distinction
+between the "perpendicular" or homophonic style in which harmony is
+built up in chords, and the "horizontal" or polyphonic style in which it
+is woven in threads of independent melody.   (D. F. T.)
+
+
+FOOTNOTE:
+
+  [1] An episode occurring during the exposition is sometimes called
+    _codetta_, a distinction the uselessness of which at once appears on
+    an analysis of Bach's 2nd fugue in the _Wohltemp_. _Klav_. (the term
+    codetta is more correctly applied to notes filling in a gap between
+    subject and its first answer, but such a gap is rare in good
+    examples).
+
+
+
+
+FÜHRICH, JOSEPH VON (1800-1876), Austrian painter, was born at Kratzau
+in Bohemia on the 9th of February 1800. Deeply impressed as a boy by
+rude pictures adorning the wayside chapels of his native country, his
+first attempt at composition was a sketch of the Nativity for the
+festival of Christmas in his father's house. He lived to see the day
+when, becoming celebrated as a composer of scriptural episodes, his
+sacred subjects were transferred in numberless repetitions to the
+roadside churches of the Austrian state, where humble peasants thus
+learnt to admire modern art reviving the models of earlier ages. Führich
+has been fairly described as a "Nazarene," a romantic religious artist
+whose pencil did more than any other to restore the old spirit of Dürer
+and give new shape to countless incidents of the gospel and scriptural
+legends. Without the power of Cornelius or the grace of Overbeck, he
+composed with great skill, especially in outline. His mastery of
+distribution, form, movement and expression was considerable. In its
+peculiar way his drapery was perfectly cast. Essentially creative as a
+landscape draughtsman, he had still no feeling for colour; and when he
+produced monumental pictures he was not nearly so successful as when
+designing subjects for woodcuts. Führich's fame extended far beyond the
+walls of the Austrian capital, and his illustrations to Tieck's
+_Genofeva_, the Lord's Prayer, the Triumph of Christ, the Road to
+Bethlehem, the Succession of Christ according to Thomas à Kempis, the
+Prodigal Son, and the verses of the Psalter, became well known. His
+Prodigal Son, especially, is remarkable for the fancy with which the
+spirit of evil is embodied in a figure constantly recurring, and like
+that of Mephistopheles exhibiting temptation in a human yet demoniacal
+shape. Führich became a pupil at the Academy of Prague in 1816. His
+first inspiration was derived from the prints of Dürer and the Faust of
+Cornelius, and the first fruit of this turn of study was the Genofeva
+series. In 1826 he went to Rome, where he added three frescoes to those
+executed by Cornelius and Overbeck in the Palazzo Massimi. His subjects
+were taken from the life of Tasso, and are almost solitary examples of
+his talent in this class of composition. In 1831 he finished the Triumph
+of Christ now in the Raczynski palace at Berlin. In 1834 he was made
+custos and in 1841 professor of composition in the Academy of Vienna.
+After this he completed the monumental pictures of the church of St
+Nepomuk, and in 1854-1861 the vast series of wall paintings which cover
+the inside of the Lerchenfeld church at Vienna. In 1872 he was pensioned
+and made a knight of the order of Franz Joseph; 1875 is the date of his
+illustrations to the Psalms. He died on the 13th of March 1876.
+
+  His autobiography was published in 1875, and a memoir by his son Lucas
+  in 1886.
+
+
+
+
+FUJI (Fuji-san, Fujiyama, Fusiyama), a celebrated mountain of Japan,
+standing W.S.W. of Tokyo, its base being about 70 m. by rail from that
+city. It rises to a height of 12,395 ft. and its southern slopes reach
+the shore of Suruga Bay. It is a cone of beautifully simple form, the
+more striking to view because it stands isolated; but its summit is not
+conical, being broken by a crater some 2000 ft. in diameter, for Fuji is
+a quiescent volcano. Small outbursts of steam are still to be observed
+at some points. An eruption is recorded so lately as the first decade of
+the 18th century. The mountain is the resort of great numbers of
+pilgrims (see also JAPAN).
+
+
+
+
+FU-KIEN (formerly MIN), a south-eastern province of China, bounded N. by
+the province of Cheh-kiang, S. by that of Kwang-tung, W. by that of
+Kiang-si and E. by the sea. It occupies an area of 53,480 sq. m. and its
+population is estimated at 20,000,000. The provincial capital is Fuchow
+Fu, and it is divided into eleven prefectures, besides that ruled over
+by the prefect of the capital city. Fu-kien is generally mountainous,
+being overspread by the Nan-shan ranges, which run a general course of
+N.E. and S.W. The principal river is the Min, which is formed by the
+junction, in the neighbourhood of the city of Yen-p'ing Fu, of three
+rivers, namely, the Nui-si, which takes its rise in the mountains on the
+western frontier in the prefecture of Kien-ning Fu, the Fuh-tun Ki, the
+source of which is found in the district of Kwang-tsih in the north-west
+of the province, and the Ta-shi-ki (Shao Ki), which rises in the
+mountains in the western district of Ning-hwa. From Yen-p'ing Fu the
+river takes a south-easterly course, and after passing along the south
+face of the city of Fuchow Fu, empties itself into the sea about 30 m.
+below that town. Its upper course is narrow and rocky and abounds in
+rapids, but as it approaches Fuchow Fu the channel widens and the
+current becomes slow and even. Its depth is very irregular, and it is
+navigable only by native boats of a small class. Two other rivers flow
+into the sea near Amoy, neither of which, however, is navigable for any
+distance from its mouth owing to the shallows and rapids with which they
+abound. Thirty-five miles inland from Amoy stands the city of Chang
+Chow, famous for the bridge which there spans the Kin-lung river. This
+bridge is 800 ft. long, and consists of granite monoliths stretching
+from one abutment to another. The soil of the province is, as its name,
+"Happy Establishment," indicates, very productive, and the scenery is of
+a rich and varied character. Most of the hills are covered with verdure,
+and the less rugged are laid out in terraces. The principal products of
+the province are tea, of which the best kind is that known as Bohea,
+which takes its name, by a mispronunciation, from the Wu-e Mountains, in
+the prefecture of Kien-ning Fu, where it is grown; grains of various
+kinds, oranges, plantins, lichis, bamboo, ginger, gold, silver, lead,
+tin, iron, salt (both marine and rock), deers' horns, beeswax, sugar,
+fish, birds' nests, medicine, paper, cloth, timber, &c. Fu-kien has
+three open ports, Fuchow Fu opened in 1842, Amoy opened to trade in the
+same year and Funing. The latter port was only opened to foreign trade
+in 1898, but in 1904 it imported and exported goods to the value of
+£7668 and £278,160 respectively.
+
+
+
+
+FUKUI, a town of Japan in the province of Echizen, Nippon, near the west
+coast, 20 m. N. by E. of Wakasa Bay. It lies in a volcanic district much
+exposed to earthquakes, and suffered severely during the disturbances of
+1891-1892, when a chasm over 40 m. long was opened across the Neo valley
+from Fukui to Katabira. But Fukui subsequently revived, and is now in a
+flourishing condition, with several local industries, especially the
+manufacture of paper, and an increasing population exceeding 50,000.
+Fukui has railway communication. There are ruins of a castle of the
+Daimios of Echizen.
+
+
+
+
+FUKUOKA, a town on the north-west coast of the island of Kiushiu, Japan,
+in the province of Chikuzen, 90 m. N.N.E. of Nagasaki by rail. Pop.
+about 72,000. With Hakata, on the opposite side of a small coast stream,
+it forms a large centre of population, with an increasing export trade
+and several local industries. Of these the most important is
+silk-weaving, and Hakata especially is noted for its durable silk
+fabrics. Fukuoka was formerly the residence of the powerful daimio of
+Chikuzen, and played a conspicuous part in the medieval history of
+Japan; the renowned temple of Yeiyas in the district was destroyed by
+fire during the revolution of 1868. There are several other places of
+this name in Japan, the most important being Fukuoka in the province of
+Mutsu, North Nippon, a railway station on the main line from Tokyo to
+Aimori Ura Bay. Pop. about 5000.
+
+
+
+
+FULA (FULBE, FELLATAH or PEULS), a numerous and powerful African people,
+spread over an immense region from Senegal nearly to Darfur. Strictly
+they have no country of their own, and nowhere form the whole of the
+population, though nearly always the dominant native race. They are most
+numerous in Upper Senegal and in the countries under French sway
+immediately south of Senegambia, notably Futa Jallon. Farther east they
+rule, subject to the control of the French, Segu and Massena, countries
+on both banks of the upper Niger, to the south-west of Timbuktu. The
+districts within the great bend of the Niger have a large Fula
+population. East of that river Sokoto and its tributary emirates are
+ruled by Fula princes, subject to the control of the British Nigerian
+administration. Fula are settled in Bornu, Bagirmi, Wadai and the upper
+Nile Valley,[1] but have no political power in those countries. Their
+most southerly emirate is Adamawa, the country on both sides of the
+upper Benue. In this vast region of distribution the Fula populations
+are most dense towards the west and north, most scattered towards the
+east and south. Originally herdsmen in the western and central Sudan,
+they extended their sway east of the Niger, under the leadership of
+Othman Dan Fodio, during the early years of the 19th century, and having
+subdued the Hausa states, founded the empire of Sokoto with the vassal
+emirates of Kano, Gando, Nupe, Adamawa, &c.
+
+The question of the ethnic affinities of the Fula has given rise to an
+enormous amount of speculation, but the most reasonable theory is that
+they are a mixture of Berber and Negro. This is now the most generally
+accepted theory. Certainly there is no reason to connect them with the
+ancient Egyptians. In the district of Senegal known as Fuladugu or "Fula
+Land," where the purest types of the race are found, the people are of a
+reddish brown or light chestnut colour, with oval faces, ringlety or
+even smooth hair, never woolly, straight and even aquiline noses,
+delicately shaped lips and regular features quite differentiating them
+from the Negro type. Like most conquering races the Fula are, however,
+not of uniform physique, in many districts approximating to the local
+type. They nevertheless maintain throughout their widespread territory a
+certain national solidarity, thanks to common speech, traditions and
+usages. The ruling caste of the Fula differs widely in character from
+the herdsmen of the western Sudan. The latter are peaceable, inoffensive
+and abstemious. They are mainly monogamous, and by rigidly abstaining
+from foreign marriages have preserved racial purity. The ruling caste in
+Nigeria, on the other hand, despise their pastoral brethren, and through
+generations of polygamy with the conquered tribes have become more
+Negroid in type, black, burly and coarse featured. Love of luxury, pomp
+and finery is their chief characteristic. Taken as a whole, the Fula
+race is distinguished by great intelligence, frankness of disposition
+and strength of character. As soldiers they are renowned almost
+exclusively as cavalry; and the race has produced several leaders
+possessed of much strategical skill. Besides the ordinary Negro weapons,
+they use iron spears with leatherbound handles and swords. They are
+generally excellent rulers, stern but patient and just. The Nigerian
+emirs acquired, however, an evil reputation during the 19th century as
+slave raiders. They have long been devout Mahommedans, and mosques and
+schools exist in almost all their towns. Tradition says that of old
+every Fula boy and girl was a scholar; but during the decadence of their
+power towards the close of the 19th century education was not highly
+valued. Power seems to have somewhat spoilt this virile race, but such
+authorities as Sir Frederick Lugard believe them still capable of a
+great future.
+
+The Fula language has as yet found no place in any African linguistic
+family. In its rudiments it is akin to the Hamito-Semitic group. It
+possesses two grammatical genders, not masculine and feminine, but the
+human and the non-human; the adjective agrees in assonance with its
+noun, and euphony plays a great part in verbal and nominal inflections.
+In some ways resembling the Negro dialects, it betrays non-Negroid
+influences in the use of suffixes. The name of the people has many
+variations. Fulbe or Fula (sing. Pullo, Peul) is the Mandingan name,
+Follani the Hausa, Fellatah the Kanuri, Fullan the Arab, and Fulde on
+the Benue. Like the name Abate, "white," given them in Kororofa, all
+these seem to refer to their light reddish hue.
+
+  See F. Ratzel, _History of Mankind_ (English ed., London, 1896-1898);
+  Sir F. Lugard, "Northern Nigeria," in _Geographical Journal_ (July
+  1904); Grimai de Guirodon, _Les Puls_ (1887); E.A. Brackenbury, _A
+  Short Vocabulary of the Fulani Language_ (Zungeru, 1907); the articles
+  NIGERIA and SOKOTO and authorities there cited.
+
+
+FOOTNOTE:
+
+  [1] Sir Wm. Wallace in a report on Northern Nigeria ("Colonial
+    Office" series, No. 551, 1907) calls attention to the exodus "of
+    thousands of Fulani of all sorts, but mostly Mellawa, from the French
+    Middle Niger," and states that the majority of the emigrants are
+    settling in the Nile valley.
+
+
+
+
+FULCHER (or FOUCHER) OF CHARTRES (1058-c. 1130), French chronicler, was
+a priest who was present at the council of Clermont in 1095, and
+accompanied Robert II., duke of Normandy, on the first crusade in 1096.
+Having spent some time in Italy and taken part in the fighting on the
+way to the Holy Land, he became chaplain to Baldwin, who was chosen king
+of Jerusalem in 1100, and lived with Baldwin at Edessa and then at
+Jerusalem. He accompanied this king on several warlike expeditions, but
+won more lasting fame by writing his _Historia Hierosolymitana_ or
+_Gesta Francorum Jerusalem expugnantium_, one of the most trustworthy
+sources for the history of the first crusade. In its final form it is
+divided into three books, and covers the period between the council of
+Clermont and 1127, and the author only gives details of events which he
+himself had witnessed. It was used by William of Tyre. Fulcher died
+after 1127, probably at Jerusalem. He has been confused with Foucher of
+Mongervillier (d. 1171), abbot of St-Père-en-Vallée at Chartres, and
+also with another person of the same name who distinguished himself at
+the siege of Antioch in 1098.
+
+  The _Historia_, but in an incomplete form, was first published by J.
+  Bongars in the _Gesta Dei per Francos_ (Hanover, 1611). The best
+  edition is in tome iii. of the _Recueil des historiens des croisades,
+  Historiens occidentaux_ (Paris, 1866); and there is a French
+  translation in tome xxiv. of Guizot's _Collection des mémoires
+  relatifs à l'histoire de France_ (Paris, 1823-1835).
+
+  See H. von Sybel, _Geschichte des ersten Kreuzzuges_ (Leipzig, 1881);
+  and A. Molinier, _Les Sources de l'histoire de France_, tome ii.
+  (Paris, 1902).
+
+
+
+
+FULDA, a town and episcopal see of Germany, in the Prussian province of
+Hesse-Nassau, between the Rhön and the Vogel-Gebirge, 69 m. N.E. from
+Frankfort-on-Main on the railway to Bebra. Although irregularly built
+the town is pleasantly situated, and contains two fine squares, on one
+of which stands a fine statue of St Boniface. The present cathedral was
+built at the beginning of the 18th century on the model of St Peter's at
+Rome, but it has an ancient crypt, which contains the bones of St
+Boniface and was restored in 1892. Opposite the cathedral is the former
+monastery of St Michael, now the episcopal palace. The Michaelskirche,
+attached to it, is a small round church built, in imitation of the Holy
+Sepulchre, in 822 and restored in 1853. Of other buildings may be
+mentioned the Library, with upwards of 80,000 printed books and many
+valuable MSS., the stately palace with its gardens and orangery, the
+former Benedictine nunnery (founded 1625, and now used as a seminary),
+and the Minorite friary (1238) now used as a furniture warehouse. Among
+the secular buildings are the fine _Schloss_, the _Bibliothek_, the town
+hall and the post office. There are several schools, a hospital founded
+in the 13th century, and some new artillery barracks. Many industries
+are carried on in Fulda. These include weaving and dyeing, the
+manufacture of linen, plush and other textiles and brewing. There are
+also railway works in the town. A large trade is done in cattle and
+grain, many markets being held here. Fine views are obtained from
+several hills in the neighbourhood, among these being the Frauenberg,
+the Petersberg and the Kalvarienberg.
+
+Fulda owes its existence to its famous abbey. It became a town in 1208,
+and during the middle ages there were many struggles between the abbots
+and the townsfolk. During the Peasants' War it was captured by the
+rebels and during the Seven Years' War by the Hanoverians. It came
+finally into the possession of Prussia in 1866. From 1734 to 1804 Fulda
+was the seat of a university, and latterly many assemblies of German
+bishops have been held in the town.
+
+The great Benedictine abbey of Fulda occupies the place in the
+ecclesiastical history of Germany which Monte Cassino holds in Italy, St
+Gall in South Germany, Corvey in Saxony, Tours in France and Iona in
+Scotland. Founded in 744 at the instigation of St Boniface by his pupil
+Sturm, who was the first abbot, it became the centre of a great
+missionary work. It was liberally endowed with land by the princes of
+the Carolingian house and others, and soon became one of the most famous
+and wealthy establishments of its kind. About 968 the pope declared that
+its abbot was primate of all the abbots in Germany and Gaul, and later
+he became a prince of the Empire. Fulda was specially famous for its
+school, which was the centre of the theological learning of the early
+middle ages. Among the teachers here were Alcuin, Hrabanus Maurus, who
+was abbot from 822 to 842, and Walafrid Strabo. Early in the 10th
+century the monastery was reformed by introducing monks from Scotland,
+who were responsible for restoring in its old strictness the Benedictine
+rule. Later the abbey lost some of its lands and also its high position,
+and some time before the Reformation the days of its glory were over.
+Johann von Henneberg, who was abbot from 1529 to 1541, showed some
+sympathy with the teaching of the reformers, but the Counter-Reformation
+made great progress here under Abbot Balthasar von Dernbach. Gustavus
+Adolphus gave the abbey as a principality to William, landgrave of
+Hesse, but William's rule only lasted for ten years. In 1752 the abbot
+was raised to the rank of a bishop, and Fulda ranked as a
+prince-bishopric. This was secularized in 1802, and in quick succession
+it belonged to the prince of Orange, the king of France and the
+grand-duchy of Frankfort. In 1816 the greater part of the principality
+was ceded by Prussia to Hesse-Cassel, a smaller portion being united
+with Bavaria. Sharing the fate of Hesse-Cassel, this larger portion was
+annexed by Prussia in 1866. In 1829 a new bishopric was founded at
+Fulda.
+
+  For the town see A. Hartmann, _Zeitgeschichte von Fulda_ (Fulda,
+  1895); J. Schneider, _Führer durch die Stadt Fulda_ (Fulda, 1899); and
+  _Chronik von Fulda und dessen Umgebungen_ (1839). For the history of
+  the abbey see Gegenbaur, _Das Kloster Fulda im Karolinger Zeitalter_
+  (Fulda, 1871-1874); Arndt, _Geschichte des Hochstifts Fulda_ (Fulda,
+  1860); and the _Fuldaer Geschichtsblätter_ (1902 fol.).
+
+
+
+
+FULGENTIUS, FABIUS PLANCIADES, Latin grammarian, a native of Africa,
+flourished in the first half of the 6th (or the last part of the 5th)
+century A.D. He is to be distinguished from Fulgentius, bishop of Ruspe
+(468-533), to whom he was probably related, and also from the bishop's
+pupil and biographer, Fulgentius Ferrandus. Four extant works are
+attributed to him. (1) _Mythologiarum libri iii._, dedicated to a
+certain Catus, a presbyter of Carthage, containing 75 myths briefly
+told, and then explained in the mystical and allegorical manner of the
+Stoics and Neoplatonists. For this purpose the author generally invokes
+the aid of etymologies which, borrowed from the philosophers, are highly
+absurd. As a Christian, Fulgentius sometimes (but less frequently than
+might have been expected) quotes the Bible by the side of the
+philosophers, to give a Christian colouring to the moral lesson. (2)
+_Expositio Vergilianae continentiae (continentia_ = contents), a sort of
+appendix to (1), dedicated to Catus. The poet himself appears to the
+author and explains the twelve books of the _Aeneid_ as a picture of
+human life. The three words _arma_ (= virtus), _vir_ (= sapientia),
+_primus_ (= princeps) in the first line represent respectively
+_substantia corporalis, sensualis, ornans_. Book i. symbolizes the birth
+and early childhood of man (the shipwreck of Aeneas denotes the peril of
+birth), book vi. the plunge into the depths of wisdom. (3) _Expositio
+sermonum antiquorum_, explanations of 63 rare and obsolete words,
+supported by quotations (sometimes from authors and works that never
+existed). It is much inferior to the similar work of Nonius, with which
+it is often edited. (4) _Liber absque litteris de aetatibus mundi et
+hominis_. In the MS. heading of this work, the name of the author is
+given as Fabius Claudius Gordianus Fulgentius (Claudius is the name of
+the father, and Gordianus that of the grandfather of the bishop, to whom
+some attribute the work). The title _Absque litteris_ indicates that one
+letter of the alphabet is wholly omitted in each successive book (A in
+bk. i., B in bk. ii.). Only 14 books are preserved. The matter is
+chiefly taken from sacred history. In addition to these, Fulgentius
+speaks of early poetical attempts after the manner of Anacreon, and of a
+work called _Physiologus_, dealing with medical questions, and including
+a discussion of the mystical signification of the numbers 7 and 9.
+Fulgentius is a representative of the so-called late African style,
+taking for his models Apuleius, Tertullian and Martianus Capella. His
+language is bombastic, affected and incorrect, while the lengthy and
+elaborate periods make it difficult to understand his meaning.
+
+  See the edition of the four works by R. Helm (1898, Teubner series);
+  also M. Zink, _Der Mytholog Fulgentius_ (1867); E. Jungmann, "De
+  Fulgentii aetate et scriptis," in _Acta Societatis Philologae
+  Lipsiensis_, i. (1871); A. Ebert, _Allgemeine Geschichte der Litt. des
+  Mittelalters_, i.; article "Fulgentius" by C.F. Böhr in Ersch and
+  Gruber's _Allgemeine Encyklopädie_; Teuffel-Schwabe, _History of Roman
+  Literature_ (Eng. trans.).
+
+
+
+
+FULGINIAE (mod. _Foligno_), an ancient town of Umbria, Italy, on the
+later line of the Via Flaminia, 15 m. S. of Nuceria. It appears to have
+been of comparatively late origin, inasmuch as it had no city walls,
+but, in imperial times especially, owing to its position on the new line
+of the Via Flaminia, it must have increased in importance as being the
+point of departure of roads to Perusia and to Picenum over the pass of
+Plestia. It appears to have had an amphitheatre, and three bridges over
+the Topino are attributed to the Roman period. Three miles to the N.
+lies the independent community of Forum Flaminii, the site of which is
+marked by the church of S. Giovanni Profiamma, at or near which the
+newer line of the Via Flaminia rejoined the older. It was no doubt
+founded by the builder of the road, C. Flaminius, consul in 220 B.C.
+(See FOLIGNO and FLAMINIA, VIA.)     (T. As.)
+
+
+
+
+FULGURITE (from Lat. _fulgur_, lightning), in petrology, the name given
+to rocks which have been fused on the surface by lightning, and to the
+characteristic holes in rocks formed by the same agency. When lightning
+strikes the naked surfaces of rocks, the sudden rise of temperature may
+produce a certain amount of fusion, especially when the rocks are dry
+and the electricity is not readily conducted away. Instances of this
+have been observed on Ararat and on several mountains in the Alps,
+Pyrenees, &c. A thin glassy crust, resembling a coat of varnish, is
+formed; its thickness is usually not more than one-eighth of an inch,
+and it may be colourless, white or yellow. When examined under the
+microscope, it usually shows no crystallization, and contains minute
+bubbles due to the expansion of air or other gases in the fused
+pellicle. Occasionally small microliths may appear, but this is uncommon
+because so thin a film would cool with extreme rapidity. The minerals of
+the rock beneath are in some cases partly fused, but the more refractory
+often appear quite unaffected. The glass has arisen from the melting of
+the most fusible ingredients alone.
+
+Another type of fulgurite is commonest in dry sands and takes the shape
+of vertical tubes which may be nearly half an inch in diameter.
+Generally they are elliptical in cross section, or flattened by the
+pressure exerted by the surrounding sand on the fulgurite at a time when
+it was still very hot and plastic. These tubes are often vertical and
+may run downwards for several feet through the sand, branching and
+lessening as they descend. Tubular perforations in hard rocks have been
+noted also, but these are short and probably follow original cracks. The
+glassy material contains grains of sand and many small round or
+elliptical cavities, the long axes of which are radial. Minerals like
+felspar and mica are fused more readily than quartz, but analysis shows
+that some fulgurite glasses are very rich in silica, which perhaps was
+dissolved in the glass rather than simply fused. The central cavity of
+the tube and the bubbles in its walls point to the expansion of the
+gases (air, water, &c.) in the sand by sudden and extreme heating. Very
+fine threads of glass project from the surface of the tube as if fused
+droplets had been projected outwards with considerable force. Where the
+quartz grains have been greatly heated but not melted they become white
+and semi-opaque, but where they are in contact with the glass they
+usually show partial solution. Occasionally crystallization has begun
+before the glass solidified, and small microliths, the nature of which
+is undeterminable, occur in streams and wisps in the clear hyaline
+matrix.     (J. S. F.)
+
+
+
+
+FULHAM, a western metropolitan borough of London, England, bounded N.W.
+by Hammersmith, N.E. by Kensington, E. by Chelsea, and S.E., S. and S.W.
+by the river Thames. Pop. (1901) 137,289. The principal thoroughfares
+are Fulham Palace Road running S. from Hammersmith, Fulham Road and
+King's Road, W. from Chelsea, converging and leading to Putney Bridge
+over the Thames; North End Road between Hammersmith and Fulham Roads;
+Lillie Road between South Kensington and Fulham Palace Road; and
+Wandsworth Bridge Road leading S. from New King's Road to Wandsworth
+Bridge. In the north Fulham includes the residential district known as
+West Kensington, and farther south that of Walham Green. The manor house
+or palace of the bishops of London stands in grounds, beautifully
+planted and surrounded by a moat, believed to be a Danish work, near the
+river west of Putney Bridge. Its oldest portion is the picturesque
+western quadrangle, built by Bishop Fitzjames (1506-1522). The parish
+church of All Saints, between the bridge and the grounds, was erected in
+1881 from designs by Sir Arthur Blomfield. The fine old monuments from
+the former building, dating from the 16th to the 18th centuries, are
+mostly preserved, and in the churchyard are the memorials of several
+bishops of London and of Theodore Hook (1841). The public recreation
+grounds include the embankment and gardens between the river and the
+palace grounds, and there are also two well-known enclosures used for
+sports within the borough. Of these Hurlingham Park is the headquarters
+of the Hurlingham Polo Club and a fashionable resort; and Queen's Club,
+West Kensington, has tennis and other courts for the use of members, and
+is also the scene of important football matches, and of the athletic
+meetings between Oxford and Cambridge Universities, and those between
+the English and American Universities held in England. In Seagrave Road
+is the Western fever hospital. The parliamentary borough of Fulham
+returns one member. The borough council consists of a mayor, 6 aldermen
+and 36 councillors. Area, 1703.5 acres.
+
+Fulham, or in its earliest form _Fullanham_, is uncertainly stated to
+signify "the place" either "of fowls" or "of dirt." The manor is said to
+have been given to Bishop Erkenwald about the year 691 for himself and
+his successors in the see of London, and Holinshed relates that the
+Bishop of London was lodging in his manor place in 1141 when Geoffrey de
+Mandeville, riding out from the Tower of London, took him prisoner. At
+the Commonwealth the manor was temporarily out of the bishops' hands,
+being sold to Colonel Edmund Harvey. There is no record of the first
+erection of a parish church, but the first known rector was appointed in
+1242, and a church probably existed a century before this. The earliest
+part of the church demolished in 1881, however, did not date farther
+back than the 15th century. In 879 Danish invaders, sailing up the
+Thames, wintered at Fulham and Hammersmith. Near the former wooden
+Putney Bridge, built in 1729 and replaced in 1886, the earl of Essex
+threw a bridge of boats across the river in 1642 in order to march his
+army in pursuit of Charles I., who thereupon fell back on Oxford.
+Margravine Road recalls the existence of Bradenburg House, a riverside
+mansion built by Sir Nicholas Crispe in the time of Charles I., used as
+the headquarters of General Fairfax in 1647 during the civil wars, and
+occupied in 1792 by the margrave of Bradenburg-Anspach and Bayreuth and
+his wife, and in 1820 by Caroline, consort of George IV.
+
+
+
+
+FULK, king of Jerusalem (b. 1092), was the son of Fulk IV., count of
+Anjou, and his wife Bertrada (who ultimately deserted her husband and
+became the mistress of Philip I. of France). He became count of Anjou in
+1109, and considerably added to the prestige of his house. In particular
+he showed himself a doughty opponent to Henry I. of England, against
+whom he continually supported Louis VI. of France, until in 1127 Henry
+won him over by betrothing his daughter Matilda to Fulk's son Geoffrey
+Plantagenet. Already in 1120 Fulk had visited the Holy Land, and become
+a close friend of the Templars. On his return he assigned to the order
+of the Templars an annual subsidy, while he also maintained two knights
+in the Holy Land for a year. In 1128 he was preparing to return to the
+East, when he received an embassy from Baldwin II., king of Jerusalem,
+who had no male heir to succeed him, offering his daughter Melisinda in
+marriage, with the right of eventual succession to the kingdom. Fulk
+readily accepted the offer; and in 1129 he came and was married to
+Melisinda, receiving the towns of Acre and Tyre as her dower. In 1131,
+at the age of thirty-nine, he became king of Jerusalem. His reign is not
+marked by any considerable events: the kingdom which had reached its
+zenith under Baldwin II., and did not begin to decline till the capture
+of Edessa in the reign of Baldwin III., was quietly prosperous under his
+rule. In the beginning of his reign he had to act as regent of Antioch,
+and to provide a husband, Raymund of Poitou, for the infant heiress
+Constance. But the great problem with which he had to deal was the
+progress of the atabeg Zengi of Mosul. In 1137 he was beaten near Barin,
+and escaping into the fort was surrounded and forced to capitulate. A
+little later, however, he greatly improved his position by strengthening
+his alliance with the vizier of Damascus, who also had to fear the
+progress of Zengi (1140); and in this way he was able to capture the
+fort of Banias, to the N. of Lake Tiberias. Fulk also strengthened the
+kingdom on the south; while his butler, Paganus, planted the fortress of
+Krak to the south of the Dead Sea, and helped to give the kingdom an
+access towards the Red Sea, he himself constructed Blanche Garde and
+other forts on the S.W. to overawe the garrison of Ascalon, which was
+still held by the Mahommedans, and to clear the road towards Egypt.
+Twice in Fulk's reign the eastern emperor, John Comnenus, appeared in
+northern Syria (1137 and 1142); but his coming did not affect the king,
+who was able to decline politely a visit which the emperor proposed to
+make to Jerusalem. In 1143 he died, leaving two sons, who both became
+kings, as Baldwin III. and Amalric I.
+
+Fulk continued the tradition of good statesmanship and sound
+churchmanship which Baldwin I. and Baldwin II. had begun. William of
+Tyre speaks of him as a fine soldier, an able politician, and a good son
+of the church, and only blames him for partiality to his friends, and a
+forgetfulness of names and faces, which placed him at a disadvantage and
+made him too dependent on his immediate intimates. Little, perhaps, need
+be made of these censures: the real fault of Fulk was his neglect to
+envisage the needs of the northern principalities, and to head a
+combined resistance to the rising power of Zengi of Mosul.
+
+  His reign in Jerusalem is narrated by R. Röhricht (_Geschichte des
+  Königreichs Jerusalem_, Innsbruck, 1898), and has been made the
+  subject of a monograph by G. Dodu (_De Fulconis Hierosolymitani
+  regno_, Paris, 1894).     (E. Br.)
+
+
+
+
+FULK (d. 900), archbishop of Reims, and partisan of Charles the Simple
+in his struggle with Odo, count of Paris, was elected to the see as
+archbishop in 883 upon the death of Hincmar. In 887 he was engaged in a
+struggle with the Normans who invaded his territories. Upon the
+deposition of Charles the Fat he sided with Charles the Simple in his
+contest for the West Frankish dominions against Count Odo of Paris, and
+crowned him king in his own metropolitan church at Reims after most of
+the nobles had gone over to Odo (893). Upon the death of Odo he
+succeeded in having Charles recognized as king by a majority of the West
+Frankish nobility. In 892 he obtained special privileges for his
+province from Pope Formosus, who promised that thereafter, when the
+archbishopric became vacant, the revenues should not be enjoyed by
+anyone while the vacancy existed, but should be reserved for the new
+incumbent, provided the election took place within the canonical limit
+of three months. From 898 until his death he held the office of
+chancellor, which for some time afterwards was regularly filled by the
+archbishop of Reims. In his efforts to keep the wealthy abbeys and
+benefices of the church out of the hands of the nobles, he incurred the
+hatred of Baldwin, count of Flanders, who secured his assassination on
+the 17th of June 900, a crime which the weak Carolingian monarch left
+unpunished.
+
+  Fulk left some letters, which are collected in Migne, _Patrologia
+  Latina_, vol. cxxxi. 11-14.
+
+
+
+
+FULKE, WILLIAM (1538-1589), Puritan divine, was born in London and
+educated at Cambridge. After studying law for six years, he became a
+fellow at St John's College, Cambridge, in 1564. He took a leading part
+in the "vestiarian" controversy, and persuaded the college to discard
+the surplice. In consequence he was expelled from St. John's for a
+time, but in 1567 he became Hebrew lecturer and preacher there. After
+standing unsuccessfully for the headship of the college in 1569, he
+became chaplain to the earl of Leicester, and received from him the
+livings of Warley, in Essex, and Dennington in Suffolk. In 1578 he was
+elected master of Pembroke Hall, Cambridge. As a Puritan
+controversialist he was remarkably active; in 1580 the bishop of Ely
+appointed him to defend puritanism against the Roman Catholics, Thomas
+Watson, ex-bishop of Lincoln (1513-1584), and John Feckenham, formerly
+abbot of Westminster, and in 1581 he was one of the disputants with the
+Jesuit, Edmund Campion, while in 1582 he was among the clergy selected
+by the privy council to argue against any papist. His numerous polemical
+writings include _A Defense of the sincere true Translations of the
+holie Scriptures into the English tong_ (London, 1583), and confutations
+of Thomas Stapleton (1535-1598), Cardinal Allen and other Roman Catholic
+controversialists.
+
+
+
+
+FULK NERRA (c. 970-1040), count of Anjou, eldest son of Count Geoffrey
+I., "Grisegonelle" (Grey Tunic) and Adela of Vermandois, was born about
+970 and succeeded his father in the countship of Anjou on the 21st of
+July 987. He was successful in repelling the attacks of the count of
+Rennes and laying the foundations of the conquest of Touraine (see
+ANJOU). In this connexion he built a great number of strong castles,
+which has led in modern times to his being called "the great builder."
+He also founded several religious houses, among them the abbeys of
+Beaulieu, near Loches (c. 1007), of Saint-Nicholas at Angers (1020) and
+of Ronceray at Angers (1028), and, in order to expiate his crimes of
+violence, made three pilgrimages to the Holy Land (in 1002-1003, c. 1008
+and in 1039). On his return from the third of these journeys he died at
+Metz in Lorraine on the 21st of June 1040. By his first marriage, with
+Elizabeth, daughter of Bouchard le Vénérable, count of Vendôme, he had a
+daughter, Adela, who married Boon of Nevers and transmitted to her
+children the countship of Vendôme. Elizabeth having died in 1000, Fulk
+married Hildegarde of Lorraine, by whom he had a son, Geoffrey Martel
+(q.v.), and a daughter Ermengarde, who married Geoffrey, count of
+Gâtinais, and was the mother of Geoffrey "le Barbu" (the Bearded) and of
+Fulk "le Réchin" (see ANJOU).
+
+  See Louis Halphen, _Le Comté d'Anjou au XI^e siècle_ (Paris, 1906).
+  The biography of Fulk Nerra by Alexandre de Salies, _Histoire de
+  Foulques Nerra_ (Angers, 1874) is confused and uncritical. A very
+  summary biography is given by Célestin Port, _Dictionnaire historique,
+  géographique et biographique de Maine-et-Loire_ (3 vols.,
+  Paris-Angers, 1874-1878), vol. ii. pp. 189-192, and there is also a
+  sketch in Kate Norgate, _England under the Angevin Kings_ (2 vols.,
+  London, 1887), vol. i. ch. iii.     (L. H.*)
+
+
+
+
+FÜLLEBORN, GEORG GUSTAV (1769-1803), German philosopher, philologist and
+miscellaneous writer, was born at Glogau, Silesia, on the 2nd of March
+1769, and died at Breslau on the 6th of February 1803. He was educated
+at the University of Halle, and was made doctor of philosophy in
+recognition of his thesis _De Xenophane, Zenone et Gorgia_. He took
+diaconal orders in 1791, but almost immediately became professor of
+classics at Breslau. His philosophical works include annotations to
+Garve's translation of the _Politics_ of Aristotle (1799-1800), and a
+large share in the _Beiträge zur Geschichte der Philosophie_ (published
+in twelve parts between 1791 and 1799), in which he collaborated with
+Forberg, Reinhold and Niethammer. In philology he wrote _Encyclopaedia
+philologica sive primae lineae Isagoges in antiquorum studia_ (1798; 2nd
+ed., 1805); _Kurze Theorie des lateinischen Stils_ (1793); _Leitfaden
+der Rhetorik_ (1802); and an annotated edition of the _Satires_ of
+Persius. Under the pseudonym "Edelwald Justus" he published several
+collections of popular tales--_Bunte Blätter_ (1795); _Kleine Schriften
+zur Unterhaltung_ (1798); _Nebenstunden_ (1799). After his death were
+published _Taschenbuch für Brunnengäste_ (1806) and _Kanzelreden_
+(1807). He was a frequent contributor to the press, where his writings
+were very popular.
+
+  See Schummel, _Gedächtnisrede_ (1803) and _Garve und Fülleborn_;
+  Meusel, _Gelehrtes Teutschland_, vol. ii.
+
+
+
+
+FULLER, ANDREW (1754-1815), English Baptist divine, was born on the 6th
+of February 1754, at Wicken in Cambridgeshire. In his boyhood and youth
+he worked on his father's farm. In his seventeenth year he became a
+member of the Baptist church at Soham, and his gifts as an exhorter met
+with so much approval that, in the spring of 1775, he was called and
+ordained as pastor of that congregation. In 1782 he removed to Kettering
+in Northamptonshire, where he became friendly with some of the most
+eminent ministers of the denomination. Before leaving Soham he had
+written the substance of a treatise in which he had sought to counteract
+the prevailing Baptist hyper-Calvinism which, "admitting nothing
+spiritually good to be the duty of the unregenerate, and nothing to be
+addressed to them in a way of exhortation excepting what related to
+external obedience," had long perplexed his own mind. This work he
+published, under the title _The Gospel worthy of all Acceptation_, soon
+after his settlement in Kettering; and although it immediately involved
+him in a somewhat bitter controversy which lasted for nearly twenty
+years, it was ultimately successful in considerably modifying the views
+prevalent among English dissenters. In 1793 he published a treatise,
+_The Calvinistic and Socinian systems examined and compared as to their
+moral tendency_, in which he rebutted the accusation of antinomianism
+levelled by the Socinians against those who over-emphasized the
+doctrines of free grace. This work, along with another against Deism,
+entitled _The Gospel its own Witness_, is regarded as the production on
+which his reputation as a theologian mainly rests. Fuller also published
+an admirable _Memoir of the Rev. Samuel Pearce_, of Birmingham, and a
+volume of _Expository Lectures in Genesis_, besides a considerable
+number of smaller pieces, chiefly sermons and pamphlets, which were
+issued in a collected form after his death. He was a man of forceful
+character, more prominent on the practical side of religion than on the
+devotional, and accordingly not pre-eminently successful in his local
+ministry. His great work was done in connexion with the Baptist
+Missionary Society, formed at Kettering in 1792, of which he was
+secretary until his death on the 7th of May 1815. Both Princeton and
+Yale, U.S.A., conferred on him the degree of D. D., but he never used
+it.
+
+  Several editions of his collected works have appeared, and a _Memoir_,
+  principally compiled from his own papers, was published about a year
+  after his decease by Dr Ryland, his most intimate friend and coadjutor
+  in the affairs of the Baptist mission. There is also a biography by
+  the Rev. J.W. Morris (1816); and his son prefixed a memoir to an
+  edition of his chief works in Bohn's Standard Library (1852).
+
+
+
+
+FULLER, GEORGE (1822-1884), American figure and portrait painter, was
+born at Deerfield, Massachusetts, in 1822. At the age of twenty he
+entered the studio of the sculptor H.K. Brown, at Albany, New York,
+where he drew from the cast and modelled heads. Having attained some
+proficiency he went about the country painting portraits, settling at
+length in Boston, where he studied the works of the earlier Americans,
+Stuart, Copley and Allston. After three years in that city, and twelve
+in New York, where in 1857 he was elected a member of the National
+Academy of Design, he went to Europe for a brief visit and for study.
+During all this time his work had received little recognition and
+practically no financial encouragement, and on his return he settled on
+the family farm at Deerfield, where he continued to work in his own way
+with no thought of the outside world. In 1876, however, he was forced by
+pressing needs to dispose of his work, and he sent some pictures to a
+dealer in Boston, where he met with immediate success, financial and
+artistic, and for the remaining eight years of his life he never lacked
+patrons. He died in Boston on the 21st of March 1884. He was a poetic
+painter, and a dreamer of delicate fancies and quaint, intangible phases
+of nature, his canvases being usually enveloped in a brown mist that
+renders the outlines vague. Among his noteworthy canvases are: "The
+Turkey Pasture," "Romany Girl," "And she was a Witch," "Nydia,"
+"Winifred Dysart" and "The Quadroon."
+
+
+
+
+FULLER, MARGARET, Marchioness Ossoli (1810-1850), American authoress,
+eldest child of Timothy Fuller (1778-1835), a lawyer and politician of
+some eminence, was born at Cambridgeport, Massachusetts, on the 23rd of
+May 1810. Her education was conducted by her father, who, she states,
+made the mistake of thinking to "gain time by bringing forward the
+intellect as early as possible," the consequence being "a premature
+development of brain that made her a youthful prodigy by day, and by
+night a victim of spectral illusions, nightmare and somnambulism." At
+six years she began to read Latin, and at a very early age she had
+selected as her favourite authors Shakespeare, Cervantes and Molière.
+Soon the great amount of study exacted of her ceased to be a burden, and
+reading became a habit and a passion. Having made herself familiar with
+the masterpieces of French, Italian and Spanish literature, she in 1833
+began the study of German, and within the year had read some of the
+masterpieces of Goethe, Körner, Novalis and Schiller.
+
+After her father's death in 1835 she went to Boston to teach languages,
+and in 1837 she was chosen principal teacher in the Green Street school,
+Providence, Rhode Island, where she remained till 1839. From this year
+until 1844 she stayed at different places in the immediate neighbourhood
+of Boston, forming an intimate acquaintance with the colonists of Brook
+Farm, and numbering among her closest friends R.W. Emerson, Nathaniel
+Hawthorne and W.H. Channing. In 1839 she published a translation of
+Eckermann's _Conversations with Goethe_, which was followed in 1842 by a
+translation of the correspondence between Karoline von Günderode and
+Bettina von Arnim, entitled _Günderode_. Aided by R.W. Emerson and
+George Ripley, she in 1840 started _The Dial_, a poetical and
+philosophical magazine representing the opinions and aims of the New
+England Transcendentalists. This journal she continued to edit for two
+years, and while in Boston she also conducted conversation classes for
+ladies in which philosophical and social subjects were discussed with a
+somewhat over-accentuated earnestness. These meetings may be regarded as
+perhaps the beginning of the modern movement in behalf of women's
+rights. R.W. Emerson, who had met her as early as 1836, thus describes
+her appearance: "She was then twenty-six years old. She had a face and
+frame that would indicate fulness and tenacity of life. She was rather
+under the middle height; her complexion was fair, with strong fair hair.
+She was then, as always, carefully and becomingly dressed, and of
+ladylike self-possession. For the rest her appearance had nothing
+prepossessing. Her extreme plainness, a trick of incessantly opening and
+shutting her eyelids, the nasal tone of her voice, all repelled; and I
+said to myself we shall never get far." On better acquaintance this
+unprepossessing exterior seemed, however, to melt away, and her
+inordinate self-esteem to be lost in the depth and universality of her
+sympathy. She possessed an almost irresistible power of winning the
+intellectual and moral confidence of those with whom she came in
+contact, and "applied herself to her companion as the sponge applies
+itself to water." She obtained from each the best they had to give. It
+was indeed more as a conversationalist than as a writer that she earned
+the title of the Priestess of Transcendentalism. It was her intimate
+friends who admired her most. Smart and pungent though she is as a
+writer, the apparent originality of her views depends more on
+eccentricity than either intellectual depth or imaginative vigour. In
+1844 she removed to New York at the desire of Horace Greeley to write
+literary criticism for _The Tribune_, and in 1846 she published a
+selection from her articles on contemporary authors in Europe and
+America, under the title _Papers on Literature and Art_. The same year
+she paid a visit to Europe, passing some time in England and France, and
+finally taking up her residence in Italy. There she was married in
+December 1847 to the marquis Giovanni Angelo Ossoli, a friend of
+Mazzini. During 1848-1849 she was present with her husband in Rome, and
+when the city was besieged she, at the request of Mazzini, took charge
+of one of the two hospitals while her husband fought on the walls. In
+May 1850, along with her husband and infant son, she embarked at Leghorn
+for America, but when they had all but reached their destination the
+vessel was wrecked on Fire Island beach on the 16th of June, and the
+Ossolis were among the passengers who perished.
+
+  _Life Without and Life Within_ (Boston, 1860) is a collection of
+  essays, poems, &c., supplementary to her _Collected Works_, printed in
+  1855. See the _Autobiography of Margaret Fuller Ossoli_, with
+  additional memoirs by J.F. Clarke, R.W. Emerson and W.H. Channing (2
+  vols., Boston, 1852); also _Margaret Fuller (Marchesa Ossoli)_, by
+  Julia Ward Howe (1883), in the "Eminent Women" series; _Margaret
+  Fuller Ossoli_ (Boston, 1884), by Thomas Wentworth Higginson in the
+  "American Men of Letters" series, which is based largely on unedited
+  material; and _The Love Letters of Margaret Fuller, 1845-1846_ (London
+  and New York, 1903), with an introduction by Julia Ward Howe.
+
+
+
+
+FULLER, MELVILLE WESTON (1833-1910), American jurist, chief justice of
+the Supreme Court of the United States, was born at Augusta, Maine, on
+the 11th of February 1833. After graduating at Bowdoin College in 1853
+he spent a year at the Harvard Law School, and in 1855 began the
+practice of law at Augusta, where he was an associate-editor of a
+Democratic paper, _The Age_, and served in the city council and as city
+attorney. In 1856 he removed to Chicago, Illinois, where he continued to
+practise until 1888, rising to a high position at the bar of the
+Northwest. For some years he was active in Democratic politics, being a
+member of the Illinois Constitutional Convention in 1862 and of the
+State House of Representatives from 1863 to 1865. He was a delegate to
+various National conventions of his party, and in that of 1876 placed
+Thomas A. Hendricks in nomination for the presidency. In 1888, by
+President Cleveland's appointment, he succeeded Morrison R. Waite as
+chief-justice of the Supreme Court of the United States. In 1899 he was
+appointed by President McKinley a member of the arbitration commission
+at Paris to settle the Venezuela-British Guiana boundary dispute.
+
+
+
+
+FULLER, THOMAS (1608-1661), English divine and historian, eldest son of
+Thomas Fuller, rector of Aldwincle St Peter's, Northamptonshire, was
+born at his father's rectory and was baptized on the 19th of June 1608.
+Dr John Davenant, bishop of Salisbury, was his uncle and godfather.
+According to Aubrey, Fuller was "a boy of pregnant wit." At thirteen he
+was admitted to Queens' College, Cambridge, then presided over by Dr
+John Davenant. His cousin, Edward Davenant, was a tutor in the same
+college. He was apt and quick in study; and in Lent 1624-1625 he became
+B.A. and in July 1628 M.A. Being overlooked in an election of fellows of
+his college, he was removed by Bishop Davenant to Sidney Sussex College,
+November 1628. In 1630 he received from Corpus Christi College the
+curacy of St Benet's, Cambridge.
+
+Fuller's quaint and humorous oratory soon attracted attention. He
+published in 1631 a poem on the subject of David and Bathsheba, entitled
+_David's Hainous Sinne, Heartie Repentance, Heavie Punishment_. In June
+of the same year his uncle gave him a prebend in Salisbury, where his
+father, who died in the following year, held a canonry. The rectory of
+Broadwindsor, Dorsetshire, then in the diocese of Bristol, was his next
+preferment (1634); and on the 11th of June 1635 he proceeded B.D. At
+Broadwindsor he compiled _The Historie of the Holy Warre_ (1639), a
+history of the crusades, and _The Holy State and the Prophane State_
+(1642). This work describes the holy state as existing in the family and
+in public life, gives rules of conduct, model "characters" for the
+various professions and profane biographies. It was perhaps the most
+popular of all his writings. He was in 1640 elected proctor for Bristol
+in the memorable convocation of Canterbury, which assembled with the
+Short Parliament. On the sudden dissolution of the latter he joined
+those who urged that convocation should likewise dissolve as usual. That
+opinion was overruled; and the assembly continued to sit by virtue of a
+royal writ. Fuller has left in his _Church History_ a valuable account
+of the proceedings of this synod, for sitting in which he was fined
+£200, which, however, was never exacted. His first published volume of
+sermons appeared in 1640 under the title of _Joseph's party-coloured
+Coat_, which contains many of his quaint utterances and odd conceits.
+His grosser mannerisms of style, derived from the divines of the former
+generation, disappeared for the most part in his subsequent discourses.
+
+About 1640 he had married Eleanor, daughter of Hugh Grove of Chisenbury,
+Wiltshire. She died in 1641. Their eldest child, John, baptized at
+Broadwindsor by his father, 6th June 1641, was afterwards rector of
+Sidney Sussex College, edited the _Worthies of England_, 1662, and
+became rector of Great Wakering, Essex, where he died in 1687.
+
+At Broadwindsor, early in the year 1641, Thomas Fuller, his curate Henry
+Sanders, the church wardens, and others, nine persons altogether,
+certified that their parish, represented by 242 grown-up male persons,
+had taken the Protestation ordered by the speaker of the Long
+Parliament. Fuller was not formally dispossessed of his living and
+prebend on the triumph of the Presbyterian party, but he relinquished
+both preferments about this time. For a short time he preached with
+success at the Inns of Court, and thence removed, at the invitation of
+the master of the Savoy (Dr Balcanqual) and the brotherhood of that
+foundation, to be lecturer at their chapel of St Mary Savoy. Some of the
+best discourses of the witty preacher were delivered at the Savoy to
+audiences which extended into the chapel-yard. In one he set forth with
+searching and truthful minuteness the hindrances to peace, and urged the
+signing of petitions to the king at Oxford, and to the parliament, to
+continue their care in advancing an accommodation. In his _Appeal of
+Injured Innocence_ Fuller says that he was once deputed to carry a
+petition to the king at Oxford. This has been identified with a petition
+entrusted to Sir Edward Wardour, clerk of the pells, Dr Dukeson, "Dr
+Fuller," and four or five others from the city of Westminster and the
+parishes contiguous to the Savoy. A pass was granted by the House of
+Lords, on the 2nd of January 1643, for an equipage of two coaches, four
+or six horses and eight or ten attendants. On the arrival of the
+deputation at Uxbridge, on the 4th of January, officers of the
+Parliamentary army stopped the coaches and searched the gentlemen; and
+they found upon the latter "two scandalous books arraigning the
+proceedings of the House," and letters with ciphers to Lord Viscount
+Falkland and the Lord Spencer. Ultimately a joint order of both Houses
+remanded the party; and Fuller and his friends suffered a brief
+imprisonment. The Westminster Petition, notwithstanding, reached the
+king's hands; and it was published with the royal reply (see J.E.
+Bailey, _Life of Thomas Fuller_, pp. 245 _et seq._). When it was
+expected, three months later, that a favourable result would attend the
+negotiations at Oxford, Fuller preached a sermon at Westminster Abbey,
+on the 27th of March 1643, on the anniversary of Charles I.'s accession,
+on the text, "Yea, let him take all, so my Lord the King return in
+peace." On Wednesday, the 26th of July, he preached on church
+reformation, satirizing the religious reformers, and maintaining that
+only the Supreme Power could initiate reforms.
+
+He was now obliged to leave London, and in August 1643 he joined the
+king at Oxford. He lived in a hired chamber at Lincoln College for 17
+weeks. Thence he put forth a witty and effective reply to John
+Saltmarsh, who had attacked his views on ecclesiastical reform. Fuller
+subsequently published by royal request a sermon preached on the 10th of
+May 1644, at St Mary's, Oxford, before the king and Prince Charles,
+called _Jacob's Vow_.
+
+The spirit of Fuller's preaching, always characterized by calmness and
+moderation, gave offence to the high royalists, who charged him with
+lukewarmness in their cause. To silence unjust censures he became
+chaplain to the regiment of Sir Ralph Hopton. For the first five years
+of the war, as he said, when excusing the non-appearance of his _Church
+History_, "I had little list or leisure to write, fearing to be made a
+history, and shifting daily for my safety. All that time I could not
+live to study, who did only study to live." After the defeat of Hopton
+at Cheriton Down, Fuller retreated to Basing House. He took an active
+part in its defence, and his life with the troops caused him to be
+afterwards regarded as one of "the great cavalier parsons." In his
+marches with his regiment round about Oxford and in the west, he devoted
+much time to the collection of details, from churches, old buildings,
+and the conversation of ancient gossips, for his _Church-History_ and
+_Worthies of England_. He compiled in 1645 a small volume of prayers and
+meditations,--the _Good Thoughts in Bad Times_,--which, set up and
+printed in the besieged city of Exeter, whither he had retired, was
+called by himself "the first fruits of Exeter press." It was inscribed
+to Lady Dalkeith, governess to the infant princess, Henrietta Anne (b.
+1644), to whose household he was attached as chaplain. The corporation
+gave him the Bodleian lectureship on the 21st of March 1645/6, and he
+held it until the 17th of June following, soon after the surrender of
+the city to the parliament. _The Fear of losing the Old Light_ (1646)
+was his farewell discourse to his Exeter friends. Under the Articles of
+Surrender Fuller made his composition with the government at London, his
+"delinquency" being that he had been present in the king's garrisons. In
+_Andronicus, or the Unfortunate Politician_ (1646), partly authentic and
+partly fictitious, he satirized the leaders of the Revolution; and for
+the comfort of sufferers by the war he issued (1647) a second devotional
+manual, entitled _Good Thoughts in Worse Times_, abounding in fervent
+aspirations, and drawing moral lessons in beautiful language out of the
+events of his life or the circumstances of the time. In grief over his
+losses, which included his library and manuscripts (his "upper and
+nether millstone"), and over the calamities of the country, he wrote his
+work on the _Cause and Cure of a Wounded Conscience_ (1647). It was
+prepared at Boughton House in his native county, where he and his son
+were entertained by Edward Lord Montagu, who had been one of his
+contemporaries at the university and had taken the side of the
+parliament.
+
+For the next few years of his life Fuller was mainly dependent upon his
+dealings with booksellers, of whom he asserted that none had ever lost
+by him. He made considerable progress in an English translation from the
+MS. of the _Annales_ of his friend Archbishop Ussher. Amongst his
+benefactors it is curious to find Sir John Danvers of Chelsea, the
+regicide. Fuller in 1647 began to preach at St Clement's, Eastcheap, and
+elsewhere in the capacity of lecturer. While at St Clement's he was
+suspended; but speedily recovering his freedom, he preached wherever he
+was invited. At Chelsea, where also he occasionally officiated, he
+covertly preached a sermon on the death of Charles I., but he did not
+break with his Roundhead patrons. James Hay, 2nd earl of Carlisle, made
+him his chaplain, and presented him in 1648 or 1649 to the curacy of
+Waltham Abbey. His possession of the living was in jeopardy on the
+appointment of Cromwell's "Tryers"; but he evaded their inquisitorial
+questions by his ready wit. He was not disturbed at Waltham in 1655,
+when the Protector's edict prohibited the adherents of the late king
+from preaching. Lionel, 3rd earl of Middlesex, who lived at Copt Hall,
+near Waltham, gave him what remained of the books of the lord treasurer
+his father; and through the good offices of the marchioness of Hertford,
+part of his own pillaged library was restored to him. Fuller was thus
+able to prosecute his literary labours, producing successively his
+descriptive geography of the Holy Land, called _A Pisgah-Sight of
+Palestine_ (1650), and his _Church-History of Britain_ (1655), from the
+birth of Jesus Christ until the year 1648. With the _Church-History_ was
+printed _The History of the University of Cambridge since the Conquest_
+and _The History of Waltham Abbey_. These works were furthered in no
+slight degree by his connexion with Sion College, London, where he had a
+chamber, as well for the convenience of the press as of his city
+lectureships. The _Church-History_ was angrily attacked by Dr P. Heylyn,
+who, in the spirit of High-Churchmanship, wished, as he said, to
+vindicate the truth, the church and the injured clergy. About 1652
+Fuller married his second wife, Mary Roper, youngest sister of Thomas,
+Viscount Baltinglass, by whom he had several children. At the Oxford Act
+of 1657, Robert South, who was _Terrae filius_, lampooned Fuller, whom
+he described in this _Oratio_ as living in London, ever scribbling and
+each year bringing forth new _folia_ like a tree. At length, continues
+South, the _Church-History_ came forth with its 166 dedications to
+wealthy and noble friends; and with this huge volume under one arm, and
+his wife (said to be little of stature) on the other, he ran up and
+down the streets of London, seeking at the houses of his patrons
+invitations to dinner, to be repaid by his dull jests at table.
+
+His last and best patron was George Berkeley, 1st Earl Berkeley
+(1628-1698), of Cranford House, Middlesex, whose chaplain he was, and
+who gave him Cranford rectory (1658). To this nobleman Fuller's reply to
+Heylyn's _Examen Historicum_, called _The Appeal of Injured Innocence_
+(1659), was inscribed. At the end of the _Appeal_ is an epistle "to my
+loving friend Dr Peter Heylyn," conceived in the admirable Christian
+spirit which characterized all Fuller's dealings with controversialists.
+"Why should _Peter_," he asked, "fall out with _Thomas_, both being
+disciples to the same Lord and Master? I assure you, sir, whatever you
+conceive to the contrary, I am cordial to the cause of the English
+Church, and my hoary hairs will go down to the grave in sorrow for her
+sufferings."
+
+In _An Alarum to the Counties of England and Wales_ (1660) Fuller argued
+for a free and full parliament--free from force, as he expressed it, as
+well as from abjurations or previous engagements. _Mixt Contemplations
+in Better Times_ (1660), dedicated to Lady Monk, tendered advice in the
+spirit of its motto, "Let your moderation be known to all men: the Lord
+is at hand." There is good reason to suppose that Fuller was at the
+Hague immediately before the Restoration, in the retinue of Lord
+Berkeley, one of the commissioners of the House of Lords, whose last
+service to his friend was to interest himself in obtaining him a
+bishopric. _A Panegyrick to His Majesty on his Happy Return_ was the
+last of Fuller's verse-efforts. On the 2nd of August, by royal letters,
+he was admitted D.D. at Cambridge. He resumed his lectures at the Savoy,
+where Samuel Pepys heard him preach; but he preferred his conversation
+or his books to his sermons. Fuller's last promotion was that of
+chaplain in extraordinary to Charles II. In the summer of 1661 he
+visited the west in connexion with the business of his prebend, which
+had been restored to him. On Sunday, the 12th of August, while preaching
+at the Savoy, he was seized with typhus fever, and died at his new
+lodgings in Covent Garden on the 16th of August. He was buried in
+Cranford church, where a mural tablet was afterwards set up on the north
+side of the chancel, with an epitaph which contains a conceit worthy of
+his own pen, to the effect that while he was endeavouring (viz. in _The
+Worthies_) to give immortality to others, he himself attained it.
+
+Fuller's wit and vivacious good-humour made him a favourite with men of
+both sides, and his sense of humour kept him from extremes. Probably
+Heylyn and South had some excuse for their attitude towards his very
+moderate politics. "By his particular temper and management," said
+Echard (_Hist. of England_, iii. 71), "he weathered the late great storm
+with more success than many other great men." He was known as "a perfect
+walking library." The strength of his memory was proverbial, and some
+amusing anecdotes are connected with it.
+
+His writings were the product of a highly original mind. He had a
+fertile imagination and a happy faculty of illustration. Antithetic and
+axiomatic sentences abound in his pages, embodying literally the wisdom
+of the many in the wit of one. He was "quaint," and something more.
+"Wit," said Coleridge, in a well-known eulogy, "was the stuff and
+substance of Fuller's intellect. It was the element, the earthen base,
+the material which he worked in; and this very circumstance has
+defrauded him of his due praise for the practical wisdom of the
+thoughts, for the beauty and variety of the truths, into which he shaped
+the stuff. Fuller was incomparably the most sensible, the least
+prejudiced, great man of an age that boasted a galaxy of great men"
+(_Literary Remains_, vol. ii. (1836), pp. 389-390). This opinion was
+formed after the perusal of the _Church-History_. That work and _The
+History of the Worthies of England_ are unquestionably Fuller's greatest
+efforts. They embody the collections of an entire life; and since his
+day they have been the delight of many readers. The _Holy State_ has
+taken rank amongst the best books of "characters." Charles Lamb made
+some selections from Fuller, and had a profound admiration for the
+"golden works" of the "dear, fine, silly old angel." Since Lamb's time,
+mainly through the appreciative criticisms of S.T. Coleridge, Robert
+Southey and others, Fuller's works have received much attention.
+
+  There is an elaborate account of the life and writings of Fuller by
+  William Oldys in the _Biographia Britannica_, vol. iii. (1750), based
+  on Fuller's own works and the anonymous _Life of ... Dr Thomas Fuller_
+  (1661; reprinted in a volume of selections by A.L.J. Gosset, 1893).
+  The completest account of him is _The Life of Thomas Fuller, with
+  Notices of his Books, his Kinsmen and his Friends_ (1874), by J.E.
+  Bailey, who gives a detailed bibliography (pp. 713-762) of his works.
+  _The Worthies of England_ was reprinted by John Nichols (1811) and by
+  P.A. Nuttall (1840). His _Collected Sermons_ were edited by J.E.
+  Bailey and W.E.A. Axon in 1891. Fuller's quaint wit lends itself to
+  selection, and there are several modern volumes of extracts from his
+  works.
+
+
+
+
+FULLER, WILLIAM (1670-c. 1717), English impostor, was born at Milton in
+Kent on the 20th of September 1670. His paternity is doubtful, but he
+was related to the family of Herbert. After 1688 he served James II.'s
+queen, Mary of Modena, and the Jacobites, seeking at the same time to
+gain favour with William III.; and after associating with Titus Oates,
+being imprisoned for debt and pretending to reveal Jacobite plots, the
+House of Commons in 1692 declared he was an "imposter, cheat and false
+accuser." Having stood in the pillory he was again imprisoned until
+1695, when he was released; and at this time he took the opportunity to
+revive the old and familiar story that Mary of Modena was not the mother
+of the prince of Wales. In 1701 he published his autobiographical _Life
+of William Fuller_ and some _Original Letters of the late King James_.
+Unable to prove the assertions made in his writings he was put in the
+pillory, whipped and fined. He died, probably in prison, about 1717.
+Fuller's other writings are _Mr William Fuller's trip to Bridewell, with
+a full account of his barbarous usage in the pillory; The sincere and
+hearty confession of Mr William Fuller_ (1704); and _An humble appeal to
+the impartial judgment of all parties in Great Britain_ (1716).
+
+  He must be distinguished from WILLIAM FULLER (1608-1675), dean of St
+  Patrick's (1660), bishop of Limerick (1663), and bishop of Lincoln
+  (1667), the friend of Samuel Pepys; and also from William Fuller (c.
+  1580-1659), dean of Ely and later dean of Durham.
+
+
+
+
+FULLER'S EARTH (Ger. _Walkererde_, Fr. _terre à foulon_, _argile
+smectique_)--so named from its use by fullers as an absorbent of the
+grease and oil of cloth,--a clay-like substance, which from its
+variability is somewhat difficult to define. In colour it is most often
+greenish, olive-green or greenish-grey; on weathering it changes to a
+brown tint or it may bleach. As a rule it falls to pieces when placed in
+water and is not markedly plastic; when dry it adheres strongly to the
+tongue; since, however, these properties are possessed by many clays
+that do not exhibit detergent qualities, the only test of value lies in
+the capacity to absorb grease or clarify oil. Fuller's earth has a
+specific gravity of 1.7-2.4, and a shining streak; it is usually
+unctuous to the touch. Microscopically, it consists of minute
+irregular-shaped particles of a mineral that appears to be the result of
+a chloritic or talcose alteration of a felspar. The small size of most
+of the grains, less than .07 mm., makes their determination almost
+impossible. Chemical analysis shows that the peculiar properties of this
+earth are due to its physical rather than its chemical nature.
+
+  The following analyses of the weathered and unweathered condition of
+  the earth from Nutfield, Surrey, represent the composition of one of
+  the best known varieties:--
+
+    Blue Earth (dried at 100° C.).
+
+    Insoluble residue  69.96  | Insoluble residue--
+    Fe2O3               2.48  |   SiO2            62.81
+    Al2O3               3.46  |   Al2O3            3.46
+    CaO                 5.87  |   Fe2O3            1.30
+    MgO                 1.41  |   CaO              1.53
+    P2O5                0.27  |   MgO              0.86
+    SO3                 0.05  |                   -----
+    NaCl                0.05  |                   69.96
+    K2O                 0.74  |                   =====
+    H2O (combined)     15.57  |
+                       -----  |
+                       99.86  |
+                       =====  |
+
+
+    Yellow Earth (dried at 100° C.).
+
+    Insoluble residue  76.13  | Insoluble residue--
+    Fe2O3               2.41  |   SiO2            59.37
+    Al2O3               1.77  |   Al2O3           10.05
+    CaO                 4.31  |   Fe2O3            3.86
+    MgO                 1.05  |   CaO              1.86
+    P2O5                0.14  |   MgO              1.04
+    SO3                 0.07  |                   -----
+    NaCl                0.14  |                   76.18
+    K2O                 0.84  |                   =====
+    H2O (combined)     13.19  |
+                      ------  |
+                      100.05  |
+                      ======  |
+
+  (Analysis by P.G. Sanford, _Geol. Mag._, 1889, 6, pp. 456, 526.)
+
+  Of other published analyses, not a few show a lower silica content
+  (44%, 50%), along with a higher proportion of alumina (11%, 23%).
+
+Fuller's earth may occur on any geological horizon; at Nutfield in
+Surrey, England, it is in the Cretaceous formations; at Midford near
+Bath it is of Jurassic age; at Bala, North Wales, it occurs in
+Ordovician strata; in Saxony it appears to be the decomposition product
+of a diabasic rock. In America it is found in California in rocks
+ranging from Cretaceous to Pleistocene age; in S. Dakota, Custer county
+and elsewhere a yellow, gritty earth of Jurassic age is worked; in
+Florida and Georgia occurs a brittle, whitish earth of Oligocene age.
+Other deposits are worked in Arkansas, Texas, Colorado, Massachusetts
+and South Carolina.
+
+Fuller's earth is either mined or dug in the open according to local
+circumstances. It is then dried in the sun or by artificial heat and
+transported in small lumps in sacks. In other cases it is ground to a
+fine powder after being dried; or it is first roughly ground and made
+into a slurry with water, which is allowed to carry off the finer from
+the coarser particles and deposit them in a creamy state in suitable
+tanks. After consolidation this fine material is dried artificially on
+drying floors, broken into lumps, and packed for transport. The use of
+fuller's earth for cleansing wool and cloth has greatly decreased, but
+the demand for the material is as great or greater than it ever was. It
+is now used very largely in the filtration of mineral oils, and also for
+decolourizing certain vegetable oils. It is employed in the formation of
+certain soaps and cleansing preparations.
+
+The term "Fuller's Earth" has a special significance in geology, for it
+was applied by W. Smith in 1799 to certain clays in the neighbourhood of
+Bath, and the use of the expression is still retained by English
+geologists, either in this form or in the generalized "Fullonian." The
+Fullonian lies at the base of the Great Oolite or Bathonian series, but
+its palaeontological characters place it between that series and the
+underlying Inferior Oolite. The zonal fossils are _Perisphinctes
+arbustigerus_ and _Macrocephalus subcontractus_ with _Ostrea acuminata_,
+_Rhynchonella concinna_ and _Goniomya angulifera_. The formation is in
+part the equivalent of the "Vesulien" of J. Marcou (Vesoul in
+Haute-Saône). In Dorsetshire and Somersetshire, where it is best
+developed, it is represented by an Upper Fuller's Earth Clay, the
+Fuller's Earth Rock (an impersistent earthy limestone, usually
+fossiliferous), and the Lower Fuller's Earth Clay. Commercial fuller's
+earth has been obtained only from the Upper Clay. In eastern
+Gloucestershire and northern Oxfordshire the Fuller's Earth passes
+downwards without break into the Inferior Oolite; northward it dies out
+about Chipping Norton in Oxfordshire and passes laterally into the
+Stonesfield Slates series; in the midland counties it may perhaps be
+represented by the "Upper Estuarine Series." In parts of Dorsetshire the
+clays have been used for brickmaking and the limestone (rock) for local
+buildings.
+
+  See H.B. Woodward, "Jurassic Rocks of Great Britain," vol. iv. (1894),
+  _Mem. Geol. Survey_ (London).     [J. A. H.]
+
+
+
+
+FULLERTON, LADY GEORGIANA CHARLOTTE (1812-1885), English novelist and
+philanthropist, youngest daughter of the 1st Earl Granville, was born at
+Tixall Hall in Staffordshire on the 23rd of September 1812. In 1833 she
+married Alexander George Fullerton, then an Irish officer in the guards.
+After living in Paris for some eight years she and her husband
+accompanied Lord Granville to Cannes and thence to Rome. In 1843 her
+husband entered the Roman Catholic church, and in the following year
+Lady Georgiana Fullerton published her first novel, _Ellen Middleton_,
+which attracted W.E. Gladstone's attention in the _English Review_. In
+1846 she entered the Roman Catholic church. The death of her only son in
+1854 plunged her in grief, and she continued to wear mourning until the
+end of her life. In 1856 she became one of the third order of St
+Francis, and thenceforward devoted herself to charitable work. In
+conjunction with Miss Taylor she founded the religious community known
+as "The Poor Servants of the Mother of God Incarnate," and she also took
+an active part in bringing to England the sisters of St Vincent of Paul.
+Her philanthropic work is described in Mrs Augustus Craven's work _Lady
+Georgiana Fullerton, sa vie et ses [oe]uvres_ (Paris, 1888), which was
+translated into English by Henry James Coleridge. She died at
+Bournemouth on the 19th of January 1885. Among her other novels were
+_Grantley Manor_ (1847), _Lady Bird_ (1852), and _Too Strange not to be
+True_ (1864).
+
+
+
+
+FULMAR, from the Gaelic _Fulmaire_, the _Fulmarus glacialis_ of modern
+ornithologists, one of the largest of the petrels (_Procellariidae_) of
+the northern hemisphere, being about the size of the common gull (_Larus
+canus_) and not unlike it in general coloration, except that its
+primaries are grey instead of black. This bird, which ranges over the
+North Atlantic, is seldom seen on the European side below lat. 53° N.,
+but on the American side comes habitually to lat. 45° or even lower. In
+the Pacific it is represented by a scarcely separable form, _F.
+glupischa_. It has been commonly believed to have two breeding-places in
+the British Islands, namely, St Kilda and South Barra; but, according to
+Robert Gray (_Birds of the West of Scotland_, p. 499), it has abandoned
+the latter since 1844, though still breeding in Skye. Northward it
+established itself about 1838 on Myggenaes Holm, one of the Faeroes,
+while it has several stations off the coast of Iceland and Spitsbergen,
+as well as at Bear Island. Its range towards the pole seems to be only
+bounded by open water, and it is the constant attendant upon all who are
+employed in the whale and seal fisheries, showing the greatest boldness
+in approaching boats and ships, and feeding on the offal obtained from
+them. By British seamen it is commonly called the "molly mawk"[1]
+(corrupted from _Mallemuck_), and is extremely well known to them, its
+flight, as it skims over the waves, first with a few beats of the wings
+and then gliding for a long way, being very peculiar. It only visits the
+land to deposit its single white egg, which is laid on a rocky ledge,
+where a shallow nest is made in the turf and lined with a little dried
+grass. Many of its breeding-places are a most valuable property to those
+who live near them and take the eggs and young, which, from the nature
+of the locality, are only to be had at a hazardous risk of life. In St
+Kilda a large number of the young are killed in one week of August, the
+only time when, by the custom of the community, they are allowed to be
+taken. These, after the oil is extracted from them, serve the islanders
+with food for the winter. The oil has been chemically analysed and found
+to be a fish-oil, and to possess nearly all the qualities of that
+obtained from the liver of the cod, with a lighter specific gravity. It,
+however, has an extremely strong scent, which is said by those who have
+visited St Kilda to pervade every thing and person on the island, and is
+certainly retained by an egg or skin of the bird for many years.
+Whenever a live example is seized in the hand it ejects a considerable
+quantity of this oil from its mouth.
+
+
+FOOTNOTE:
+
+  [1] A name misapplied in the southern hemisphere to _Diomedea
+    melanophrys_, one of the albatrosses.
+
+
+
+
+FULMINIC ACID, HCNO or H2C2N2O2, an organic acid isomeric with cyanic
+and cyanuric acids; its salts, termed fulminates, are very explosive and
+are much employed as detonators. The free acid, which is obtained by
+treating the salts with acids, is an oily liquid smelling like prussic
+acid; it is very explosive, and the vapour is poisonous to about the
+same degree as that of prussic acid. The first fulminate prepared was
+the "fulminating silver" of L.G. Brugnatelli, who found in 1798 that if
+silver be dissolved in nitric acid and the solution added to spirits of
+wine, a white, highly explosive powder was obtained. This substance is
+to be distinguished from the black "fulminating silver" obtained by
+C.L. Berthollet in 1788 by acting with ammonia on precipitated silver
+oxide. The next salt to be obtained was the mercuric salt, which was
+prepared in 1799 by Edward Charles Howard, who substituted mercury for
+silver in Brugnatelli's process. A similar method is that of J. von
+Liebig (1823), who heated a mixture of alcohol, nitric acid and mercuric
+nitrate; the salt is largely manufactured by processes closely
+resembling the last. A laboratory method is to mix solutions of sodium
+nitromethane, CH2:NO(ONa), and mercuric chloride, a yellow basic salt
+being formed at the same time. Mercuric fulminate is less explosive than
+the silver salt, and forms white needles (with ½H2O) which are tolerably
+soluble in water. The use of mercuric fulminate as a detonator dates
+from about 1814, when the explosive cap was invented. It is still the
+commonest detonator, but it is now usually mixed with other substances;
+the British service uses for percussion caps 6 parts of fulminate, 6 of
+potassium chlorate and 4 of antimony sulphide, and for time fuses 4
+parts of fulminate, 6 of potassium chlorate and 4 of antimony sulphide,
+the mixture being damped with a shellac varnish; for use in blasting, a
+home office order of 1897 prescribes a mixture of 4 parts of fulminate
+and 1 of potassium chlorate. In 1900 Bielefeldt found that a fulminate
+placed on top of an aromatic nitro compound, such as trinitrotoluene,
+formed a useful detonator; this discovery has been especially taken
+advantage of in Germany, in which country detonators of this nature are
+being largely employed. Tetranitromethylaniline (tetryl) has also been
+employed (Brit. Pat. 13340 of 1905). It has been proposed to replace
+fulminate by silver azoimide (Wöhler & Matter, Brit. Pat. 4468 of 1908),
+and by lead azoimide (Hyronimus, Brit. Pat. 1819 of 1908).
+
+  The constitution of fulminic acid has been investigated by many
+  experimenters, but apparently without definitive results. The
+  researches of Liebig (1823), Liebig and Gay-Lussac (1824), and of
+  Liebig again in 1838 showed the acid to be isomeric with cyanic acid,
+  and probably (HCNO)2, since it gave mixed and acid salts. Kekulé, in
+  1858, concluded that it was nitroacetonitrile, NO2·CH2·CN, a view
+  opposed by Steiner (1883), E. Divers and M. Kawakita (1884), R. Scholl
+  (1890), and by J.U. Nef (1894), who proposed the formulae:
+
+    C : N·OH        / N : CH      CH : N·O
+    ··           O /      ·       ·           C : N·OH.
+    C : N·OH,       \ N : C·OH,   CH : N·0,
+
+     Steiner,        Divers,       Scholl,      Nef.
+
+  The formulae of Kekulé, Divers and Armstrong have been discarded, and
+  it remains to be shown whether Nef's carbonyloxime formula (or the
+  bimolecular formula of Steiner) or Scholl's glyoxime peroxide formula
+  is correct. There is some doubt as to the molecular formula of
+  fulminic acid. The existence of double salts, and the observations of
+  L. Wöhler and K. Theodorovits (_Ber._, 1905, 38, p. 345), that only
+  compounds containing two carbon atoms yielded fulminates, points to
+  (HCNO)2; on the other hand, Wöhler (_loc. cit._ p. 1351) found that
+  cryoscopic and electric conductivity measurements showed sodium
+  fulminate to be NaCNO. Nef based his formula, which involves bivalent
+  carbon, on many reactions; in particular, that silver fulminate with
+  hydrochloric acid gave salts of formylchloridoxime, which with water
+  gave hydroxylamine and formic acid, thus
+
+                      // NOAg         // N·OH
+    C : NO OAg -> HC //       --> HC //       --> H·CO2H + H2N·OH,
+                     \   Cl          \   OH
+
+  and also on the production from sodium nitromethane and mercuric
+  chloride, thus CH2 : NO·Ohg --> H2O + C : NOhg(hg = ½Hg). H. Wieland
+  and F.C. Palazzo (1907) support this formula, finding that methyl
+  nitrolic acid, NO2·CH : N·OH, yielded under certain conditions
+  fulminic acid, and vice versa (Palazzo, 1907). M.Z. Jowitschitsch
+  (_Ann._, 1906, 347, p. 233) inclines to Scholl's formula; he found
+  that the synthetic silver salt of glyoxime peroxide resembled silver
+  fulminate in yielding hydroxylamine with hydrochloric acid, but
+  differed in being less explosive, and in being soluble in nitric acid.
+  H. Wieland and his collaborators regard "glyoxime peroxide" as an
+  oxide of furazane (q.v.), and have shown that a close relationship
+  exists between the nitrile oxides, furoxane, and fulminic acid (see
+  Ann. Rep., London Chem. Soc., 1909, p. 84). _Fulminuric acid_,
+  (HCNO)3, obtained by Liebig by boiling mercuric fulminate with water,
+  was synthesized in 1905 by C. Ulpiani and L. Bernardini (_Gazetta_,
+  iii. 35, p. 7), who regard it as NO2·CH(CN)·CO·NH2. It deflagrates at
+  145°, and forms a characteristic cuprammonium salt.
+
+  The early history of mercuric fulminate and a critical account of its
+  application as a detonator is given in _The Rise and Progress of the
+  British Explosives Industry_ (International Congress of Applied
+  Chemistry, 1909). The manufacture and modern aspects are treated in
+  Oscar Guttmann, _The Manufacture of Explosives_, and _Manufacture of
+  Explosives, Twenty Years' Progress_ (1909).
+
+
+
+
+FULTON, ROBERT (1765-1815), American engineer, was born in 1765 in
+Little Britain (now Fulton, Lancaster county), Pa. His parents were
+Irish, and so poor that they could afford him only a very scanty
+education. At an early age he was bound apprentice to a jeweller in
+Philadelphia, but subsequently adopted portrait and landscape painting
+as his profession. In his twenty-second year, with the object of
+studying with his countryman, Benjamin West, he went to England, and
+there became acquainted with the duke of Bridgewater, Earl Stanhope and
+James Watt. Partly by their influence he was led to devote his attention
+to engineering, especially in connexion with canal construction; he
+obtained an English patent in 1794 for superseding canal locks by
+inclined planes, and in 1796 he published a _Treatise on the Improvement
+of Canal Navigation_. He then took up his residence in Paris, where he
+projected the first panorama ever exhibited in that city, and
+constructed a submarine boat, the "Nautilus," which was tried in Brest
+harbour in 1801 before a commission appointed by Napoleon I., and by the
+aid of which he was enabled to blow up a small vessel with a torpedo. It
+was at Paris also in 1803 that he first succeeded in propelling a boat
+by steam-power, thus realizing a design which he had conceived ten years
+previously. Returning to America he continued his experiments with
+submarine explosives, but failed to convince either the English, French
+or United States governments of the adequacy of his methods. With steam
+navigation he had more success. In association with Robert R. Livingston
+(q.v.), who in 1798 had been granted the exclusive right to navigate the
+waters of New York state with steam-vessels, he constructed the
+"Clermont," which, engined by Boulton & Watt of Birmingham, began to ply
+on the Hudson between New York and Albany in 1807. The privilege
+obtained by Livingston in 1798 was granted jointly to Fulton and
+Livingston in 1803, and by an act passed in 1808 the monopoly was
+secured to them and their associates for a period depending on the
+number of steamers constructed, but limited to a maximum of thirty
+years. In 1814-1815, on behalf of the United States government, he
+constructed the "Fulton," a vessel of 38 tons with central
+paddle-wheels, which was the first steam warship. He died at New York on
+the 24th of February 1815. Among Fulton's inventions were machines for
+spinning flax, for making ropes, and for sawing and polishing marble.
+
+  See C.D. Colden, _Life of Robert Fulton_ (New York, 1817); Robert H.
+  Thurston, _History of the Growth of the Steam-Engine_ (New York,
+  1878); George H. Preble, _Chronological History of Steam Navigation_
+  (Philadelphia, 1883); and Mrs A.C. Sutcliffe, _Robert Fulton and the
+  Clermont_ (New York, 1909).
+
+
+
+
+FULTON, a city and the county-seat of Callaway county, Missouri, U.S.A.,
+25 m. N.E. of Jefferson City. Pop. (1890) 4314; (1900) 4883 (1167
+negroes); (1910) 5228. It is served by the Chicago & Alton railway. The
+city has an important stock market and manufactures fire-brick and
+pottery. At Fulton are the Westminster College (Presbyterian, founded in
+1853), the Synodical College for Young Women (Pres., founded in 1871),
+the William Woods College for Girls (Christian Church, 1890), and the
+Missouri school for the deaf (1851). Here, too, is a state hospital for
+the insane (1847), the first institution of the kind in Missouri. The
+place was laid out as a town in 1825 and named Volney, but in honour of
+Robert Fulton the present name was adopted a little later. Fulton was
+incorporated in 1859.
+
+
+
+
+FULTON, a city of Oswego county, New York, U.S.A., on the right bank of
+the Oswego river, about 10 m. S. by E. of Oswego. Pop. (1900) 5281;
+(1905, state census) 8847; (1910) 10,480. Fulton is served by the
+Delaware, Lackawanna & Western, the New York Central & Hudson River, and
+the New York, Ontario & Western railways, by electric railway to Oswego
+and Syracuse and by the Oswego Canal. The city has a Carnegie library.
+Ample water-power is furnished by the Oswego river, which here flows in
+a series of rapids, and the manufactures are many in kind. On the 3rd of
+July 1756, on an island (afterward called Battle Island) 4 m. N. of the
+present city of Fulton, a British force of about 300 under Captain John
+Bradstreet (1711-1774) defeated an attacking force of French and Indians
+(numbering about 700) under De Villiers. Soon after this, Bradstreet
+built a fort within the present limits of Fulton. The first civilian
+settler came in 1793, and the first survey (which included only a part
+of the subsequent village) was made in 1815. Fulton was incorporated as
+a village in 1835, and in April 1902 was combined with the village of
+Oswego Falls (pop. in 1900, 2925) and was chartered as a city.
+
+
+
+
+FUM, or FUNJ HWANG, one of the four symbolical creatures which in
+Chinese mythology are believed to keep watch and ward over the Celestial
+Empire. It was begotten by fire, was born in the Hill of the Sun's Halo,
+and its body bears inscribed on it the five cardinal virtues. It has the
+breast of a goose, the hindquarters of a stag, a snake's neck, a fish's
+tail, a fowl's forehead, a duck's down, the marks of a dragon, the back
+of a tortoise, the face of a swallow, the beak of a cock, is about six
+cubits high, and perches only on the woo-tung tree. The appearance of
+Fum heralds an age of universal virtue. Its figure is that which is
+embroidered on the dresses of some mandarins.
+
+
+
+
+FUMARIC AND MALEIC ACIDS, two isomeric unsaturated acids of composition
+C4H4O4. _Fumaric acid_ is found in fumitory (_Fumaria officinalis_), in
+various fungi (_Agaricus piperatus_, &c.), and in Iceland moss. It is
+obtained by heating malic acid alone to 150° C., or by heating it with
+hydrochloric acid (V. Dessaignes, _Jahresb_., 1856, p. 463) or with a
+large quantity of hydrobromic acids (A. Kekulé, _Ann._, 1864, 130, p.
+21). It may also be obtained by boiling monobromsuccinic acid with
+water; by the action of dichloracetic acid and water on silver malonate
+(T. Komnenos, _Ann._, 1883, 218, p. 169); by the cyanide synthesis from
+acetylene di-iodide; and by heating maleic acid to 210° C. (Z. Skraup,
+_Monats. f. Chemie_, 1891, 12, p. 112). It crystallizes in small prisms
+or needles, and is practically insoluble in cold water. It sublimes to
+some extent at about 200° C., being partially converted into maleic
+anhydride and water, the reaction becoming practically quantitative if
+dehydrating agents be used. Reducing agents (zinc and caustic alkali,
+hydriodic acid, sodium amalgam, &c.) convert it into succinic acid.
+Bromine converts it into dibromsuccinic acid. Potassium permanganate
+oxidizes it to racemic acid (A. Kekulé and R. Anschutz, _Ber._, 1881,
+14, p. 713). By long-continued heating with caustic soda at 100° C. it
+is converted into inactive malic acid.
+
+_Maleic acid_ is obtained by distilling malic or fumaric acids; by
+heating fumaric acid with acetyl chloride to 100° C; or by the
+hydrolysis of trichlorphenomalic acid (ß-trichloraceto-acrylic acid) [A.
+Kekulé, _Ann._, 1884, 223, p. 185]. It crystallizes in monoclinic
+prisms, which are easily soluble in water, melt at 130° C., and boil at
+160° C., decomposing into water and maleic anhydride. When heated with
+concentrated hydrobromic or hydriodic acids, it is converted into
+fumaric acid. It yields an anilide; oxidation converts it into
+mesotartaric acid. Maleic anhydride is obtained by distilling fumaric
+acid with phosphorus pentoxide. It forms triclinic crystals which melt
+at 60° C. and boil at 196° C.
+
+  Both acids are readily esterified by the action of alkyl halides on
+  their silver salts, and the maleic ester is readily transformed into
+  the fumaric ester by warming with iodine, the same result being
+  obtained by esterification of maleic acid in alcoholic solution by
+  means of hydrochloric acid. Both acids yield acetylene by the
+  electrolysis of aqueous solutions of their alkali salts, and on
+  reduction both yield succinic acid, whilst by the addition of
+  hydrobromic acid they both yield monobromsuccinic acid (R. Fittig,
+  _Ann._, 1877, 188, p. 98). From these results it follows that the two
+  acids are structurally identical, and the isomerism has consequently
+  to be explained on other grounds. This was accomplished by W.
+  Wislicenus ["Über die räumliche Anordnung der Atome," &c., _Trans, of
+  the Saxon Acad. of Sciences_ (Math. Phys. Section), 1887, p. 14] by an
+  extension of the van't Hoff hypothesis (see STEREO-ISOMERISM). The
+  formulae of the acids are written thus:
+
+    HC·CO2H                    HC·CO2H
+    ··        Maleic acid.       ··      Fumaric acid.
+    HC·CO2H                 HO2C·C·H
+
+  These account for maleic acid readily yielding an anhydride, whereas
+  fumaric acid does not, and for the behaviour of the acids towards
+  bromine, fumaric acid yielding ordinary dibromsuccinic acid, and
+  maleic acid the isomeric isodibromsuccinic acid.
+
+
+
+
+FUMAROLE, a vent from which volcanic vapours issue, named indirectly
+from the Lat. _fumariolum_, a smoke-hole. The vapours from fumaroles
+were studied first by R.W. Bunsen, on his visit to Iceland, and
+afterwards by H. Sainte-Claire Deville and other chemists and geologists
+in France, who examined the vapours from Santorin, Etna, &c. The hottest
+vapours issue from dry fumaroles, at temperatures of at least 500° C.,
+and consist chiefly of anhydrous chlorides, notably sodium chloride. The
+acid fumaroles yield vapours of lower temperature (300° to 400°)
+containing much water vapour, with hydrogen chloride and sulphur
+dioxide. The alkaline fumaroles are still cooler, though above 100°, and
+evolve ammonium chloride with other vapours. Cold fumaroles, below 100°,
+discharge principally aqueous vapour, with carbon dioxide, and perhaps
+hydrogen sulphide. The fumaroles of Mont Pelé in Martinique during the
+eruption of 1902 were examined by A. Lacroix, and the vapours analysed
+by H. Moissan, who found that they consisted chiefly of water vapour,
+with hydrogen chloride, sulphur, carbon dioxide, carbon monoxide,
+methane, hydrogen, nitrogen, oxygen and argon. These vapours issued at a
+temperature of about 400°. Armand Gautier has pointed out that these
+gases are practically of the same composition as those which he obtained
+on heating granite and certain other rocks. (See VOLCANO).
+
+
+
+
+FUMIGATION (from Lat. _fumigare_, to smoke), the process of producing
+smoke or fumes, as by burning sulphur, frankincense, tobacco, &c.,
+whether as a ceremony of incantation, or for perfuming a room, or for
+purposes of disinfection or destruction of vermin. In medicine the term
+has been used of the exposure of the body, or a portion of it, to fumes
+such as those of nitre, sal-ammoniac, mercury, &c.; fumigation, by the
+injection of tobacco smoke into the great bowel, was a recognized
+procedure in the 18th century for the resuscitation of the apparently
+drowned. "Fumigated" or "fumed" oak is oak which has been darkened by
+exposure to ammonia vapour.
+
+
+
+
+FUMITORY, in botany, the popular name for the British species of
+_Fumaria_, a genus of small, branched, often climbing annual herbs with
+much-divided leaves and racemes of small flowers. The flowers are
+tubular with a spurred base, and in the British species are pink to
+purplish in colour. They are weeds of cultivation growing in fields and
+waste places. _F. capreolata_ climbs by means of twisting petioles. In
+past times fumitory was in esteem for its reputed cholagogue and other
+medicinal properties; and in England, boiled in water, milk or whey, it
+was used as a cosmetic. The root of the allied species (_Corydalis cava_
+or _tuberosa_) is known as _radix aristolochia_, and has been used
+medicinally for various cutaneous and other disorders, in doses of 10 to
+30 grains. Some eleven alkaloids have been isolated from it. The herbage
+of _Fumaria officinalis_ and _F. racemosa_ is used in China under the
+name of _Tsze-hwa-ti-ting_ as an application for glandular swellings,
+carbuncles and abscesses, and was formerly valued in jaundice, and in
+cases of accidental swallowing of the beard of grain (see F. Porter
+Smith, _Contrib. towards the Mat. Medica ... of China_, p. 99, 1871).
+The name fumitory, Latin _fumus terrae_, has been supposed to be derived
+from the fact that its juice irritates the eyes like smoke (see Fuchs,
+_De historia stirpium_, p. 338, 1542); but _The Grete Herball_, cap.
+clxix., 1529, fol., following the _De simplici medicina_ of Platearius,
+fo. xciii. (see in _Nicolai Praepositi dispensatorium ad aromatarios_,
+1536), says: "It is called Fumus terre fume or smoke of the erthe
+bycause it is engendred of a cours fumosyte rysynge frome the erthe in
+grete quantyte lyke smoke: this grosse or cours fumosyte of the erthe
+wyndeth and wryeth out: and by workynge of the ayre and sonne it turneth
+into this herbe."
+
+
+
+
+FUNCHAL, the capital of the Portuguese archipelago of the Madeiras; on
+the south coast of Madeira, in 32° 37' N. and 16° 54' W. Pop. (1900)
+20,850. Funchal is the see of a bishop, in the archiepiscopal province
+of Lisbon; it is also the administrative centre of the archipelago, and
+the residence of the governor and foreign consuls. The city has an
+attractive appearance from the sea. Its whitewashed houses, in their
+gardens full of tropical plants, are built along the curving shore of
+Funchal Bay, and on the lower slopes of an amphitheatre of mountains,
+which form a background 4000 ft. high. Numerous country houses
+(_quintas_), with terraced gardens, vineyards and sugar-cane
+plantations occupy the surrounding heights. Three mountain streams
+traverse the city through deep channels, which in summer are dry, owing
+to the diversion of the water for irrigation. A small fort, on an
+isolated rock off shore, guards the entrance to the bay, and a larger
+and more powerfully armed fort crowns an eminence inland. The chief
+buildings include the cathedral, Anglican and Presbyterian churches,
+hospitals, opera-house, museum and casino. There are small public
+gardens and a meteorological observatory. In the steep and narrow
+streets, which are lighted by electricity, wheeled traffic is
+impossible; sledges drawn by oxen, and other primitive conveyances are
+used instead (see MADEIRA). In winter the fine climate and scenery
+attract numerous invalids and other visitors, for whose accommodation
+there are good hotels; many foreigners engaged in the coal and wine
+trades also reside here permanently. The majority of these belong to the
+British community, which was first established here in the 18th century.
+Funchal is the headquarters of Madeiran industry and commerce (see
+MADEIRA). It has no docks and no facilities for landing passengers or
+goods; vessels are obliged to anchor in the roadstead, which, however,
+is sheltered from every wind except the south. Funchal is connected by
+cable with Carcavellos (for Lisbon), Porthcurnow (for Falmouth, England)
+and St Vincent in the Cape Verde Islands (for Pernambuco, Brazil).
+
+
+
+
+FUNCTION,[1] in mathematics, a variable number the value of which
+depends upon the values of one or more other variable numbers. The
+theory of functions is conveniently divided into (I.) Functions of Real
+Variables, wherein real, and only real, numbers are involved, and (II.)
+Functions of Complex Variables, wherein complex or imaginary numbers are
+involved.
+
+
+I. FUNCTIONS OF REAL VARIABLES
+
+1. _Historical._--The word function, defined in the above sense, was
+introduced by Leibnitz in a short note of date 1694 concerning the
+construction of what we now call an "envelope" (_Leibnizens
+mathematische Schriften_, edited by C.I. Gerhardt, Bd. v. p. 306), and
+was there used to denote a variable length related in a defined way to a
+variable point of a curve. In 1698 James Bernoulli used the word in a
+special sense in connexion with some isoperimetric problems (Joh.
+Bernoulli, _Opera_, t. i. p. 255). He said that when it is a question of
+selecting from an infinite set of like curves that one which best
+fulfils some function, then of two curves whose intersection determines
+the thing sought one is always the "line of the function" (_Linea
+functionis_). In 1718 John Bernoulli (_Opera_, t. ii. p. 241) defined a
+"function of a variable magnitude" as a quantity made up in any way of
+this variable magnitude and constants; and in 1730 (Opera, t. iii. p.
+174) he noted a distinction between "algebraic" and "transcendental"
+functions. By the latter he meant integrals of algebraic functions. The
+notation [f](x) for a function of a variable x was introduced by
+Leonhard Euler in 1734 (_Comm. Acad. Petropol._ t. vii. p. 186), in
+connexion with the theorem of the interchange of the order of
+differentiations. The notion of functionality or functional relation of
+two magnitudes was thus of geometrical origin; but a function soon came
+to be regarded as an analytical expression, not necessarily an algebraic
+expression, containing the variable or variables. Thus we may have
+rational integral algebraic functions such as _ax_² + _bx_ + c, or
+rational algebraic functions which are not integral, such as
+
+  a1x^n + a2x^(n - 1) + ... + a_n
+  -------------------------------,
+  b1x^m + b2x^(m - 1) + ... + b_m
+
+or irrational algebraic functions, such as [root]x, or, more generally
+the algebraic functions that are determined implicitly by an algebraic
+equation, as, for instance,
+
+  [f]_n(x, y) + [f]_(n - 1) (x, y) + ... + [f]0 = 0
+
+where [f]_n(x, y), ... mean homogeneous expressions in x and y having
+constant coefficients, and having the degrees indicated by the suffixes,
+and [f]0 is a constant. Or again we may have trigonometrical functions,
+such as sin x and tan x, or inverse trigonometrical functions, such as
+sin^(-1)x, or exponential functions, such as e^x and a^x, or logarithmic
+functions, such as log x and log (1 + x). We may have these functional
+symbols combined in various ways, and thus there arises a great number
+of functions. Further we may have functions of more than one variable,
+as, for instance, the expression xy/(x² + y²), in which both x and y are
+regarded as variable. Such functions were introduced into analysis
+somewhat unsystematically as the need for them arose, and the later
+developments of analysis led to the introduction of other classes of
+functions.
+
+2. _Graphic Representation._--In the case of a function of one variable
+x, any value of x and the corresponding value y of the function can be
+the co-ordinates of a point in a plane. To any value of x there
+corresponds a point N on the axis of x, in accordance with the rule that
+x is the abscissa of N. The corresponding value of y determines a point
+P in accordance with the rule that x is the abscissa and y the ordinate
+of P. The ordinate y gives the value of the function which corresponds
+to that value of the variable x which is specified by N; and it may be
+described as "the value of the function at N." Since there is a
+one-to-one correspondence of the points N and the numbers x, we may also
+describe the ordinate as "the value of the function at x." In simple
+cases the aggregate of the points P which are determined by any
+particular function (of one variable) is a curve, called the "graph of
+the function" (see § 14). In like manner a function of two variables
+defines a surface.
+
+3. _The Variable._--Graphic methods of representation, such as those
+just described, enabled mathematicians to deal with irrational values of
+functions and variables at the time when there was no theory of
+irrational numbers other than Euclid's theory of incommensurables. In
+that theory an irrational number was the ratio of two incommensurable
+geometric magnitudes. In the modern theory of number irrational numbers
+are defined in a purely arithmetical manner, independent of the
+measurement of any quantities or magnitudes, whether geometric or of any
+other kind. The definition is effected by means of the system of
+_ordinal_ numbers (see NUMBER). When this formal system is established,
+the theory of measurement may be founded upon it; and, in particular,
+the co-ordinates of a point are defined as numbers (not lengths), which
+are assigned in accordance with a rule. This rule involves the
+measurement of lengths. The theory of functions can be developed without
+any reference to graphs, or co-ordinates or lengths. The process by
+which analysis has been freed from any consideration of measurable
+quantities has been called the "arithmetization of analysis." In the
+theory so developed, the variable upon which a function depends is
+always to be regarded as a number, and the corresponding value of the
+function is also a number. Any reference to points or co-ordinates is to
+be regarded as a picturesque mode of expression, pointing to a possible
+application of the theory to geometry. The development of "arithmetized
+analysis" in the 19th century is associated with the name of Karl
+Weierstrass.
+
+All possible values of a variable are numbers. In what follows we shall
+confine our attention to the case where the numbers are real. When
+complex numbers are introduced, instead of real ones, the theory of
+functions receives a wide extension, which is accompanied by appropriate
+limitations (see below, II. Functions of Complex Variables). The set of
+all real numbers forms a _continuum_. In fact the notion of a
+one-dimensional continuum first becomes precise in virtue of the
+establishment of the system of real numbers.
+
+4. _Domain of a Variable.--Theory of Aggregates._--The notion of a
+"variable" is that of a number to which we may assign at pleasure any
+one of the values that belong to some chosen set, or _aggregate_, of
+numbers; and this set, or aggregate, is called the "domain of the
+variable." This domain may be an "interval," that is to say it may
+consist of two terminal numbers, all the numbers between them and no
+others. When this is the case the number is said to be "continuously
+variable." When the domain consists of all real numbers, the variable is
+said to be "unrestricted." A domain which consists of all the real
+numbers which exceed some fixed number may be described as an "interval
+unlimited towards the right"; similarly we may have an interval
+"unlimited towards the left."
+
+  In more complicated cases we must have some rule or process for
+  assigning the aggregate of numbers which constitute the domain of a
+  variable. The methods of definition of particular types of aggregates,
+  and the theorems relating to them, form a branch of analysis called
+  the "theory of aggregates" (_Mengenlehre, Théorie des ensembles,
+  Theory of sets of points_). The notion of an "aggregate" in general
+  underlies the system of ordinal numbers. An aggregate is said to be
+  "infinite" when it is possible to effect a one-to-one correspondence
+  of all its elements to some of its elements. For example, we may make
+  all the integers correspond to the even integers, by making 1
+  correspond to 2, 2 to 4, and generally n to 2n. The aggregate of
+  positive integers is an infinite aggregate. The aggregates of all
+  rational numbers and of all real numbers and of points on a line are
+  other examples of infinite aggregates. An aggregate whose elements are
+  real numbers is said to "extend to infinite values" if, after any
+  number N, however great, is specified, it is possible to find in the
+  aggregate numbers which exceed N in absolute value. Such an aggregate
+  is always infinite. The "neighbourhood of a number (or point) a for a
+  positive number h" is the aggregate of all numbers (or points) x for
+  which the absolute value of x - a denoted by |x - a|, does not exceed
+  h.
+
+5. _General Notion of Functionality._--A function of one variable was
+for a long time commonly regarded as the ordinate of a curve; and the
+two notions (1) that which is determined by a curve supposed drawn, and
+(2) that which is determined by an analytical expression supposed
+written down, were not for a long time clearly distinguished. It was for
+this reason that Fourier's discovery that a single analytical expression
+is capable of representing (in different parts of an interval) what
+would in his time have been called different functions so profoundly
+struck mathematicians (§ 23). The analysts who, in the middle of the
+19th century, occupied themselves with the theory of the convergence of
+Fourier's series were led to impose a restriction on the character of a
+function in order that it should admit of such representation, and thus
+the door was opened for the introduction of the general notion of
+functional dependence. This notion may be expressed as follows: We have
+a variable number, y, and another variable number, x, a domain of the
+variable x, and a rule for assigning one or more definite values to y
+when x is any point in the domain; then y is said to be a "function" of
+the variable x, and x is called the "argument" of the function.
+According to this notion a function is, as it were, an indefinitely
+extended table, like a table of logarithms; to each point in the domain
+of the argument there correspond values for the function, but it remains
+arbitrary what values the function is to have at any such point.
+
+  For the specification of any particular function two things are
+  requisite: (1) a statement of the values of the variable, or of the
+  aggregate of points, to which values of the function are to be made to
+  correspond, i.e. of the "domain of the argument"; (2) a rule for
+  assigning the value or values of the function that correspond to any
+  point in this domain. We may refer to the second of these two
+  essentials as "the rule of calculation." The relation of functions to
+  analytical expressions may then be stated in the form that the rule of
+  calculation is: "Give the function the value of the expression at any
+  point at which the expression has a determinate value," or again more
+  generally, "Give the function the value of the expression at all
+  points of a definite aggregate included in the domain of the
+  argument." The former of these is the rule of those among the earlier
+  analysts who regarded an analytical expression and a function as the
+  same thing, and their usage may be retained without causing confusion
+  and with the advantage of brevity, the analytical expression serving
+  to specify the domain of the argument as well as the rule of
+  calculation, e.g. we may speak of "the function 1/x." This function is
+  defined by the analytical expression 1/x at all points except the
+  point x = 0. But in complicated cases separate statements of the
+  domain of the argument and the rule of calculation cannot be dispensed
+  with. In general, when the rule of calculation is determined as above
+  by an analytical expression at any aggregate of points, the function
+  is said to be "represented" by the expression at those points.
+
+  When the rule of calculation assigns a single definite value for a
+  function at each point in the domain of the argument the function is
+  "uniform" or "one-valued." In what follows it is to be understood that
+  all the functions considered are one-valued, and the values assigned
+  by the rule of calculation real. In the most important cases the
+  domain of the argument of a function of one variable is an interval,
+  with the possible exception of isolated points.
+
+6. _Limits._--Let [f](x) be a function of a variable number x; and let a
+be a point such that there are points of the domain of the argument x in
+the neighbourhood of a for any number h, however small. If there is a
+number L which has the property that, after any positive number
+[epsilon], however small, has been specified, it is possible to find a
+positive number h, so that |L - [f](x)| < [epsilon] for all points x of
+the domain (other than a) for which |x-a| < h, then L is the "limit of
+[f](x) at the point a." The condition for the existence of L is that,
+after the positive number [epsilon] has been specified, it must be
+possible to find a positive number h, so that |[f](x') - [f](x)| <
+[epsilon] for all points x and x' of the domain (other than a) for which
+|x - a| < h and |x' - a| < h.
+
+It is a fundamental theorem that, when this condition is satisfied,
+there exists a perfectly definite number L which is the limit of [f](x)
+at the point a as defined above. The limit of [f](x) at the point a is
+denoted by Lt_(x = a)[f](x), or by lim_(x = a)[f](x).
+
+  If [f](x) is a function of one variable x in a domain which extends to
+  infinite values, and if, after [epsilon] has been specified, it is
+  possible to find a number N, so that |[f](x') - [f](x)| <[epsilon] for
+  all values of x and x' which are in the domain and exceed N, then
+  there is a number L which has the property that |[f](x) - L| <
+  [epsilon] for all such values of x. In this case [f](x) has a limit L
+  at x = [oo]. In like manner [f](x) may have a limit at x = -[oo]. This
+  statement includes the case where the domain of the argument consists
+  exclusively of positive integers. The values of the function then form
+  a "sequence," u1, u2, ... u_n, ..., and this sequence can have a limit
+  at n = [oo].
+
+  The principle common to the above definitions and theorems is called,
+  after P. du Bois Reymond, "the general principle of convergence to a
+  limit."
+
+  It must be understood that the phrase "x = [oo]" does not mean that x
+  takes some particular value which is infinite. There is no such value.
+  The phrase always refers to a limiting process in which, as the
+  process is carried out, the variable number x increases without limit:
+  it may, as in the above example of a sequence, increase by taking
+  successively the values of all the integral numbers; in other cases it
+  may increase by taking the values that belong to any domain which
+  "extends to infinite values."
+
+  A very important type of limits is furnished by _infinite series_.
+  When a sequence of numbers u1, u2, ... u_n, ... is given, we may form
+  a new sequence s1, s2, ... s_n, ... from it by the rules s1 = u1, s2 =
+  u1 + u2, ... s_n = u1 + u2 + ... + u_n or by the equivalent rules s1 =
+  u, s_n - s_(n - 1) = u_n(n = 2, 3, ...). If the new sequence has a
+  limit at n = [oo], this limit is called the "sum of the infinite
+  series" u1 + u2 + ..., and the series is said to be "convergent" (see
+  SERIES).
+
+  A function which has not a limit at a point a may be such that, if a
+  certain aggregate of points is chosen out of the domain of the
+  argument, and the points x in the neighbourhood of a are restricted to
+  belong to this aggregate, then the function has a limit at a. For
+  example, sin(1/x) has limit zero at 0 if x is restricted to the
+  aggregate 1/[pi], ½[pi], ... 1/n[pi], ... or to the aggregate ½[pi],
+  2/5[pi], ... n/(n² + 1)[pi], ..., but if x takes all values in the
+  neighbourhood of 0, sin (1/x) has not a limit at 0. Again, there may
+  be a limit at a if the points x in the neighbourhood of a are
+  restricted by the condition that x - a is positive; then we have a
+  "limit on the right" at a; similarly we may have a "limit on the left"
+  at a point. Any such limit is described as a "limit for a restricted
+  domain." The limits on the left and on the right are denoted by [f](a
+  - 0) and [f](a + 0).
+
+  The limit L of [f](x) at a stands in no necessary relation to the
+  value of [f](x) at a. If the point a is in the domain of the argument,
+  the value of [f](x) at a is assigned by the rule of calculation, and
+  may be different from L. In case [f](a) = L the limit is said to be
+  "attained." If the point a is not in the domain of the argument, there
+  is no value for [f](x) at a. In the case where [f](x) is defined for
+  all points in an interval containing a, except the point a, and has a
+  limit L at a, we may arbitrarily annex the point a to the domain of
+  the argument and assign to [f](a) the value L; the function may then
+  be said to be "extrinsically defined." The so-called "indeterminate
+  forms" (see INFINITESIMAL CALCULUS) are examples.
+
+7. _Superior and Inferior Limits; Infinities._--The value of a function
+at every point in the domain of its argument is finite, since, by
+definition, the value can be assigned, but this does not necessarily
+imply that there is a number N which exceeds all the values (or is less
+than all the values). It may happen that, however great a number N we
+take, there are among the values of the function numbers which exceed N
+(or are less than -N).
+
+If a number can be found which is greater than every value of the
+function, then either ([alpha]) there is one value of the function which
+exceeds all the others, or (ß) there is a number S which exceeds every
+value of the function but is such that, however small a positive number
+[epsilon] we take, there are values of the function which exceed S -
+[epsilon]. In the case ([alpha]) the function has a greatest value; in
+case (ß) the function has a "superior limit" S, and then there must be a
+point a which has the property that there are points of the domain of
+the argument, in the neighbourhood of a for any h, at which the values
+of the function differ from S by less than [epsilon]. Thus S is the
+limit of the function at a, either for the domain of the argument or for
+some more restricted domain. If a is in the domain of the argument, and
+if, after omission of a, there is a superior limit S which is in this
+way the limit of the function at a, if further [f](a) = S, then S is the
+greatest value of the function: in this case the greatest value is a
+limit (at any rate for a restricted domain) which is attained; it may be
+called a "superior limit which is attained." In like manner we may have
+a "smallest value" or an "inferior limit," and a smallest value may be
+an "inferior limit which is attained."
+
+  All that has been said here may be adapted to the description of
+  greatest values, superior limits, &c., of a function in a restricted
+  domain contained in the domain of the argument. In particular, the
+  domain of the argument may contain an interval; and therein the
+  function may have a superior limit, or an inferior limit, which is
+  attained. Such a limit is a _maximum_ value or a _minimum_ value of
+  the function.
+
+  Again, if, after any number N, however great, has been specified, it
+  is possible to find points of the domain of the argument at which the
+  value of the function exceeds N, the values of the function are said
+  to have an "infinite superior limit," and then there must be a point a
+  which has the property that there are points of the domain, in the
+  neighbourhood of a for any h, at which the value of the function
+  exceeds N. If the point a is in the domain of the argument the
+  function is said to "tend to become infinite" at a; it has of course a
+  finite value at a. If the point a is not in the domain of the argument
+  the function is said to "become infinite" at a; it has of course no
+  value at a. In like manner we may have a (negatively) infinite
+  inferior limit. Again, after any number N, however great, has been
+  specified and a number h found, so that all the values of the
+  function, at points in the neighbourhood of a for h, exceed N in
+  absolute value, all these values may have the same sign; the function
+  is then said to become, or to tend to become, "determinately
+  (positively or negatively) infinite"; otherwise it is said to become
+  or to tend to become, "indeterminately infinite."
+
+  All the infinities that occur in the theory of functions are of the
+  nature of variable finite numbers, with the single exception of the
+  infinity of an infinite aggregate. The latter is described as an
+  "actual infinity," the former as "improper infinities." There is no
+  "actual infinitely small" corresponding to the actual infinity. The
+  only "infinitely small" is zero. All "infinite values" are of the
+  nature of superior and inferior limits which are not attained.
+
+8. _Increasing and Decreasing Functions._--A function [f](x) of one
+variable x, defined in the interval between a and b, is "increasing
+throughout the interval" if, whenever x and x' are two numbers in the
+interval and x' > x, then [f](x') > [f](x); the function "never
+decreases throughout the interval" if, x' and x being as before, [f](x')
+> [f](x). Similarly for decreasing functions, and for functions which
+never increase throughout an interval. A function which either never
+increases or never diminishes throughout an interval is said to be
+"monotonous throughout" the interval. If we take in the above definition
+b > a, the definition may apply to a function under the restriction that
+x' is not b and x is not a; such a function is "monotonous within" the
+interval. In this case we have the theorem that the function (if it
+never decreases) has a limit on the left at b and a limit on the right
+at a, and these are the superior and inferior limits of its values at
+all points within the interval (the ends excluded); the like holds
+_mutatis mutandis_ if the function never increases. If the function is
+monotonous throughout the interval, [f](b) is the greatest (or least)
+value of [f](x) in the interval; and if [f](b) is the limit of [f](x) on
+the left at b, such a greatest (or least) value is an example of a
+superior (or inferior) limit which is attained. In these cases the
+function tends continually to its limit.
+
+  These theorems and definitions can be extended, with obvious
+  modifications, to the cases of a domain which is not an interval, or
+  extends to infinite values. By means of them we arrive at sufficient,
+  but not necessary, criteria for the existence of a limit; and these
+  are frequently easier to apply than the general principle of
+  convergence to a limit (§ 6), of which principle they are particular
+  cases. For example, the function represented by x log (1/x)
+  continually diminishes when 1/e > x > 0 and x diminishes towards
+  zero, and it never becomes negative. It therefore has a limit on the
+  right at x = 0. This limit is zero. The function represented by x sin
+  (1/x) does not continually diminish towards zero as x diminishes
+  towards zero, but is sometimes greater than zero and sometimes less
+  than zero in any neighbourhood of x = 0, however small. Nevertheless,
+  the function has the limit zero at x = 0.
+
+9. _Continuity of Functions._--A function [f](x) of one variable x is
+said to be continuous at a point a if (1) [f](x) is defined in an
+interval containing a; (2) [f](x) has a limit at a; (3) [f](a) is equal
+to this limit. The limit in question must be a limit for continuous
+variation, not for a restricted domain. If [f](x) has a limit on the
+left at a and [f](a) is equal to this limit, the function may be said to
+be "continuous to the left" at a; similarly the function may be
+"continuous to the right" at a.
+
+A function is said to be "continuous throughout an interval" when it is
+continuous at every point of the interval. This implies continuity to
+the right at the smaller end-value and continuity to the left at the
+greater end-value. When these conditions at the ends are not satisfied
+the function is said to be continuous "within" the interval. By a
+"continuous function" of one variable we always mean a function which is
+continuous throughout an interval.
+
+  The principal properties of a continuous function are:
+
+  1. The function is practically constant throughout sufficiently small
+  intervals. This means that, after any point a of the interval has been
+  chosen, and any positive number [epsilon], however small, has been
+  specified, it is possible to find a number h, so that the difference
+  between any two values of the function in the interval between a-h and
+  a + h is less than [epsilon]. There is an obvious modification if a is
+  an end-point of the interval.
+
+  2. The continuity of the function is "uniform." This means that the
+  number h which corresponds to any [epsilon] as in (1) may be the same
+  at all points of the interval, or, in other words, that the numbers h
+  which correspond to [epsilon] for different values of a have a
+  positive inferior limit.
+
+  3. The function has a greatest value and a least value in the
+  interval, and these are superior and inferior limits which are
+  attained.
+
+  4. There is at least one point of the interval at which the function
+  takes any value between its greatest and least values in the interval.
+
+  5. If the interval is unlimited towards the right (or towards the
+  left), the function has a limit at [oo] (or at -[oo]).
+
+10. _Discontinuity of Functions._--The discontinuities of a function of
+one variable, defined in an interval with the possible exception of
+isolated points, may be classified as follows:
+
+(1) The function may become infinite, or tend to become infinite, at a
+point.
+
+(2) The function may be undefined at a point.
+
+(3) The function may have a limit on the left and a limit on the right
+at the same point; these may be different from each other, and at least
+one of them must be different from the value of the function at the
+point.
+
+(4) The function may have no limit at a point, or no limit on the left,
+or no limit on the right, at a point.
+
+  In case a function [f](x), defined as above, has no limit at a point
+  a, there are four limiting values which come into consideration.
+  Whatever positive number h we take, the values of the function at
+  points between a and a + h (a excluded) have a superior limit (or a
+  greatest value), and an inferior limit (or a least value); further, as
+  h decreases, the former never increases and the latter never
+  decreases; accordingly each of them tends to a limit. We have in this
+  way two limits on the right--the inferior limit of the superior limits
+  in diminishing neighbourhoods, and the superior limit of the inferior
+  limits in diminishing neighbourhoods. These are denoted by /{[f](a +
+  o)} and {[f](a + 0)}/, and they are called the "limits of
+  indefiniteness" on the right. Similar limits on the left are denoted
+  by /{[f](a - 0)} and {[f](a - 0)}/. Unless [f](x) becomes, or tends to
+  become, infinite at a, all these must exist, any two of them may be
+  equal, and at least one of them must be different from [f](a), if
+  [f](a) exists. If the first two are equal there is a limit on the
+  right denoted by [f](a + 0); if the second two are equal, there is a
+  limit on the left denoted by [f](a - 0). In case the function becomes,
+  or tends to become, infinite at a, one or more of these limits is
+  infinite in the sense explained in § 7; and now it is to be noted
+  that, e.g. the superior limit of the inferior limits in diminishing
+  neighbourhoods on the right of a may be negatively infinite; this
+  happens if, after any number N, however great, has been specified, it
+  is possible to find a positive number h, so that all the values of the
+  function in the interval between a and a + h (a excluded) are less
+  than -N; in such a case [f](x) tends to become negatively infinite
+  when x decreases towards a; other modes of tending to infinite limits
+  may be described in similar terms.
+
+11. _Oscillation of Functions._--The difference between the greatest and
+least of the numbers [f](a), /{[f](a + 0)}, {[f](a + 0)}/, /{[f](a -
+0)}, {[f](a - 0)}/, when they are all finite, is called the
+"oscillation" or "fluctuation" of the function [f](x) at the point a.
+This difference is the limit for h = 0 of the difference between the
+superior and inferior limits of the values of the function at points in
+the interval between a - h and a + h. The corresponding difference for
+points in a finite interval is called the "oscillation of the function
+in the interval." When any of the four limits of indefiniteness is
+infinite the oscillation is infinite in the sense explained in § 7.
+
+  For the further classification of functions we divide the domain of
+  the argument into partial intervals by means of points between the
+  end-points. Suppose that the domain is the interval between a and b.
+  Let intermediate points x1, x2 ... x{n - 1}_, be taken so that b >
+  X_(n - 1) > x_(n - 2) ... > X1 > a_. We may devise a rule by which, as
+  n increases indefinitely, all the differences b - x_(n - 1), x_(n - 1)
+  - x_(n - 2), ... x1 - a tend to zero as a limit. The interval is then
+  said to be divided into "indefinitely small partial intervals."
+
+  A function defined in an interval with the possible exception of
+  isolated points may be such that the interval can be divided into a
+  set of finite partial intervals within each of which the function is
+  monotonous (§ 8). When this is the case the sum of the oscillations of
+  the function in those partial intervals is finite, provided the
+  function does not tend to become infinite. Further, in such a case the
+  sum of the oscillations will remain below a fixed number for any mode
+  of dividing the interval into indefinitely small partial intervals. A
+  class of functions may be defined by the condition that the sum of the
+  oscillations has this property, and such functions are said to have
+  "restricted oscillation." Sometimes the phrase "limited fluctuation"
+  is used. It can be proved that any function with restricted
+  oscillation is capable of being expressed as the sum of two monotonous
+  functions, of which one never increases and the other never diminishes
+  throughout the interval. Such a function has a limit on the right and
+  a limit on the left at every point of the interval. This class of
+  functions includes all those which have a finite number of maxima and
+  minima in a finite-interval, and some which have an infinite number.
+  It is to be noted that the class does not include all continuous
+  functions.
+
+12. _Differentiable Function._--The idea of the differentiation of a
+continuous function is that of a process for measuring the rate of
+growth; the increment of the function is compared with the increment of
+the variable. If _[f](x)_ is defined in an interval containing the point
+a, and _a - k_ and _a + k_ are points of the interval, the expression
+
+  [f](a + h) - [f](a)
+  -------------------         (1)
+           h
+
+represents a function of h, which we may call [phi](h), defined at all
+points of an interval for h between -k and k except the point 0. Thus
+the four limits /[phi](+0), [phi](+0)/, /[phi](-0), [phi](-0)/ exist,
+and two or more of them may be equal. When the first two are equal
+either of them is the "progressive differential coefficient" of [f](x)
+at the point a; when the last two are equal either of them is the
+"regressive differential coefficient" of [f](x) at a; when all four are
+equal the function is said to be "differentiable" at a, and either of
+them is the "differential coefficient" of [f](x) at a, or the "first
+derived function" of [f](x) at a. It is denoted by d[f](x) / dx or by
+[f]'(x). In this case [phi](h) has a definite limit at h = 0, or is
+determinately infinite at h = 0 (§ 7). The four limits here in question
+are called, after Dini, the "four derivates" of [f](x) at a. In
+accordance with the notation for derived functions they may be denoted
+by
+
+  ----------              ----------
+  [f]' + (a), [f]' + (a), [f]' - (a), f' - (a).
+              ---------               --------
+
+  A function which has a finite differential coefficient at all points
+  of an interval is continuous throughout the interval, but if the
+  differential coefficient becomes infinite at a point of the interval
+  the function may or may not be continuous throughout the interval; on
+  the other hand a function may be continuous without being
+  differentiable. This result, comparable in importance, from the point
+  of view of the general theory of functions, with the discovery of
+  Fourier's theorem, is due to G.F.B. Riemann; but the failure of an
+  attempt made by Ampère to prove that every continuous function must be
+  differentiable may be regarded as the first step in the theory.
+  Examples of analytical expressions which represent continuous
+  functions that are not differentiable have been given by Riemann,
+  Weierstrass, Darboux and Dini (see § 24). The most important theorem
+  in regard to differentiable functions is the "theorem of intermediate
+  value." (See INFINITESIMAL CALCULUS.)
+
+13. _Analytic Function._--If [f](x) and its first n differential
+coefficients, denoted by[f]'(x), [f]''(x), ... [f](^n)(x), are
+continuous in the interval between a and a + h, then
+
+                                   h²
+  [f](a + h) = [f](a) + h[f]'(a) + -- f''(a) + ...
+                                   2!
+
+      h^(n - 1)
+    + --------- [f]^(n - 1)(a) + R_n,
+       (n - 1)!
+
+where R_n may have various forms, some of which are given in the article
+INFINITESIMAL CALCULUS. This result is known as "Taylor's theorem."
+
+When Taylor's theorem leads to a representation of the function by means
+of an infinite series, the function is said to be "analytic" (cf. § 21).
+
+14. _Ordinary Function._--The idea of a curve representing a continuous
+function in an interval is that of a line which has the following
+properties: (1) the co-ordinates of a point of the curve are a value x
+of the argument and the corresponding value y of the function; (2) at
+every point the curve has a definite tangent; (3) the interval can be
+divided into a finite number of partial intervals within each of which
+the function is monotonous; (4) the property of monotony within partial
+intervals is retained after interchange of the axes of co-ordinates x
+and y. According to condition (2) y is a continuous and differentiable
+function of x, but this condition does not include conditions (3) and
+(4): there are continuous partially monotonous functions which are not
+differentiable, there are continuous differentiable functions which are
+not monotonous in any interval however small; and there are continuous,
+differentiable and monotonous functions which do not satisfy condition
+(4) (cf. § 24). A function which can be represented by a curve, in the
+sense explained above, is said to be "ordinary," and the curve is the
+graph of the function (§2). All analytic functions are ordinary, but not
+all ordinary functions are analytic.
+
+15. _Integrable Function._--The idea of integration is twofold. We may
+seek the function which has a given function as its differential
+coefficient, or we may generalize the question of finding the area of a
+curve. The first inquiry leads directly to the indefinite integral, the
+second directly to the definite integral. Following the second method we
+define "the definite integral of the function [f](x) through the
+interval between a and b" to be the limit of the sum
+
+   _n
+  \   [f](x'_r)(x_r - x_(r - 1))
+  /_
+    1
+
+when the interval is divided into ultimately indefinitely small partial
+intervals by points x1, x2, ... x_(n - 1). Here x'_r denotes any point
+in the rth partial interval, x0 is put for a, and x_n for b. It can be
+shown that the limit in question is finite and independent of the mode
+of division into partial intervals, and of the choice of the points such
+as x'_r, provided (1) the function is defined for all points of the
+interval, and does not tend to become infinite at any of them; (2) for
+any one mode of division of the interval into ultimately indefinitely
+small partial intervals, the sum of the products of the oscillation of
+the function in each partial interval and the difference of the
+end-values of that partial interval has limit zero when n is increased
+indefinitely. When these conditions are satisfied the function is said
+to be "integrable" in the interval. The numbers a and b which limit the
+interval are usually called the "lower and upper limits." We shall call
+them the "nearer and further end-values." The above definition of
+integration was introduced by Riemann in his memoir on trigonometric
+series (1854). A still more general definition has been given by
+Lebesgue. As the more general definition cannot be made intelligible
+without the introduction of some rather recondite notions belonging to
+the theory of aggregates, we shall, in what follows, adhere to Riemann's
+definition.
+
+  We have the following theorems:--
+
+  1. Any continuous function is integrable.
+
+  2. Any function with restricted oscillation is integrable.
+
+  3. A discontinuous function is integrable if it does not tend to
+  become infinite, and if the points at which the oscillation of the
+  function exceeds a given number [sigma], however small, can be
+  enclosed in partial intervals the sum of whose breadths can be
+  diminished indefinitely.
+
+  These partial intervals must be a set chosen out of some complete set
+  obtained by the process used in the definition of integration.
+
+  4. The sum or product of two integrable functions is integrable.
+
+  As regards integrable functions we have the following theorems:
+
+  1. If S and I are the superior and inferior limits (or greatest and
+  least values) of [f](x) in the interval between a and b, [int] [a to
+  b] [f](x)dx is intermediate between S(b - a) and I(b - a).
+
+  2. The integral is a continuous function of each of the end-values.
+
+  3. If the further end-value b is variable, and if [int] [a to x]
+  [f](x)_dx_ = F(x), then if [f](x) is continuous at b, F(x) is
+  differentiable at b, and F'(b) = [f](b).
+
+  4. In case [f](x) is continuous throughout the interval F(x) is
+  continuous and differentiable throughout the interval, and F'(x) =
+  [f](x) throughout the interval.
+
+  5. In case [f]'(x) is continuous throughout the interval between a and
+  b,
+      _
+     / b
+     |   [f]'(x)dx = [f](b) - [f](a).
+    _/a
+
+  6. In case [f](x) is discontinuous at one or more points of the
+  interval between a and b, in which it is integrable,
+      _
+     / x
+     |   [f](x)dx
+    _/a
+
+  is a function of x, of which the four derivates at any point of the
+  interval are equal to the limits of indefiniteness of [f](x) at the
+  point.
+
+  7. It may be that there exist functions which are differentiable
+  throughout an interval in which their differential coefficients are
+  not integrable; if, however, F(x) is a function whose differential
+  coefficient, F'(x), is integrable in an interval, then
+             _
+            / x
+    F(x) =  |   F'(x)dx + const.,
+           _/a
+
+  where a is a fixed point, and x a variable point, of the interval.
+  Similarly, if any one of the four derivates of a function is
+  integrable in an interval, all are integrable, and the integral of
+  either differs from the original function by a constant only.
+
+  The theorems (4), (6), (7) show that there is some discrepancy between
+  the indefinite integral considered as the function which has a given
+  function as its differential coefficient, and as a definite integral
+  with a variable end-value.
+
+  We have also two theorems concerning the integral of the product of
+  two integrable functions [f](x) and [phi](x); these are known as "the
+  first and second theorems of the mean." The first theorem of the mean
+  is that, if [phi](x) is one-signed throughout the interval between a
+  and b, there is a number M intermediate between the superior and
+  inferior limits, or greatest and least values, of [f](x) in the
+  interval, which has the property expressed by the equation
+       _                _
+      / b              / b
+    M |   [phi](x)dx = |   [f](x)[phi](x)dx.
+     _/a              _/a
+
+  The second theorem of the mean is that, if [f](x) is monotonous
+  throughout the interval, there is a number [xi] between a and b which
+  has the property expressed by the equation
+      _                             _                       _
+     / b                           /[xi]                   / b
+     |   [f](x)[phi](x)dx = [f](a) |   [phi](x)dx + [f](b) |    [phi](x)dx.
+    _/a                           _/a                     _/[xi]
+
+  (_See_ FOURIER'S SERIES.)
+
+16. _Improper Definite Integrals._--We may extend the idea of
+integration to cases of functions which are not defined at some point,
+or which tend to become infinite in the neighbourhood of some point, and
+to cases where the domain of the argument extends to infinite values. If
+c is a point in the interval between a and b at which [f](x) is not
+defined, we impose a restriction on the points x'_r of the definition:
+none of them is to be the point c. This comes to the same thing as
+defining [int] [a to b] [f](x)dx to be
+                 _                        _
+                / c-[epsilon]            / b
+             Lt |        [f](x)dx +   Lt |     [f](x)dx,      (1)
+               _/a                      _/c+[epsilon]'
+    [epsilon]=0             [epsilon]'=0
+
+where, to fix ideas, b is taken > a, and [epsilon] and [epsilon]' are
+positive. The same definition applies to the case where [f](x) becomes
+infinite, or tends to become infinite, at c, provided both the limits
+exist. This definition may be otherwise expressed by saying that a
+partial interval containing the point c is omitted from the interval of
+integration, and a limit taken by diminishing the breadth of this
+partial interval indefinitely; in this form it applies to the cases
+where c is a or b.
+
+Again, when the interval of integration is unlimited to the right, or
+extends to positively infinite values, we have as a definition
+    _                  _
+   / [oo]             / h
+   |   [f](x)dx =  Lt |  [f](x)dx,
+  _/a                _/a
+               h=[oo]
+
+provided this limit exists. Similar definitions apply to
+    _                   _
+   /-[oo]              / [oo]
+   |   [f](x)dx and to |      [f](x)dx.
+  _/a                 _/-[oo]
+
+All such definite integrals as the above are said to be "improper." For
+example, [int] {0 to [oo]} (sin x / x)dx is improper in two ways. It
+means
+                        _
+                       / h        sin x
+   Lt             Lt   |          ----- dx,
+  h=[oo]  [epsilon]=0 _/[epsilon]   x
+
+in which the positive number [epsilon] is first diminished indefinitely,
+and the positive number h is afterwards increased indefinitely.
+
+The "theorems of the mean" (§ 15) require modification when the
+integrals are improper (see FOURIER'S SERIES).
+
+When the improper definite integral of a function which becomes, or
+tends to become, infinite, exists, the integral is said to be
+"convergent." If [f](x) tends to become infinite at a point c in the
+interval between a and b, and the expression (1) does not exist, then
+the expression [int] [a to b][f](x)_dx_, which has no value, is called a
+"divergent integral, "and it may happen that there is a definite value
+for
+      _    _                       _                    _
+     |    / c-[epsilon]           / b                    |
+  Lt |    |           [f](x) dx + |            [f](x) dx |
+     |_  _/a                     _/c+[epsilon]'         _|
+
+provided that [epsilon] and [epsilon]' are connected by some definite
+relation, and both, remaining positive, tend to limit zero. The value of
+the above limit is then called a "principal value" of the divergent
+integral. Cauchy's principal value is obtained by making [epsilon]' =
+[epsilon], i.e. by taking the omitted interval so that the infinity is
+at its middle point. A divergent integral which has one or more
+principal values is sometimes described as "semi-convergent."
+
+17. _Domain of a Set of Variables._--The numerical continuum of n
+dimensions (C_n) is the aggregate that is arrived at by attributing
+simultaneous values to each of n variables x1, x2, ... x_n, these values
+being any real numbers. The elements of such an aggregate are called
+"points," and the numbers x1, x2 ... x_n the "co-ordinates" of a point.
+Denoting in general the points (x1, x2, ... x_n) and (x'1, x'2 ... x'_n)
+by x and x', the sum of the differences |x1 - x'1| + |x2 - x'2| + ... +
+|x_n - x'_n| may be denoted by |x - x'| and called the "difference of
+the two points." We can in various ways choose out of the continuum an
+aggregate of points, which may be an infinite aggregate, and any such
+aggregate can be the "domain" of a "variable point." The domain is said
+to "extend to an infinite distance" if, after any number N, however
+great, has been specified, it is possible to find in the domain points
+of which one or more co-ordinates exceed N in absolute value. The
+"neighbourhood" of a point a for a (positive) number h is the aggregate
+constituted of all the points x, which are such that the "difference"
+denoted by |x - a| < h. If an infinite aggregate of points does not
+extend to an infinite distance, there must be at least one point a,
+which has the property that the points of the aggregate which are in the
+neighbourhood of a for any number h, however small, themselves
+constitute an infinite aggregate, and then the point a is called a
+"limiting point" of the aggregate; it may or may not be a point of the
+aggregate. An aggregate of points is "perfect" when all its points are
+limiting points of it, and all its limiting points are points of it; it
+is "connected" when, after taking any two points a, b of it, and
+choosing any positive number [epsilon], however small, a number m and
+points x', x", ... x^(m) of the aggregate can be found so that all the
+differences denoted by |x' - a|, |x" - x'|, ... |b - x^(m)| are less
+than [epsilon]. A perfect connected aggregate is a _continuum_. This is
+G. Cantor's definition.
+
+  The definition of a continuum in C_n leaves open the question of the
+  number of dimensions of the continuum, and a further explanation is
+  necessary in order to define arithmetically what is meant by a
+  "homogeneous part" H_n of C_n. Such a part would correspond to an
+  interval in C1, or to an area bounded by a simple closed contour in
+  C2; and, besides being perfect and connected, it would have the
+  following properties: (1) There are points of C_n, which are not
+  points of H_n; these form a complementary aggregate H'_n. (2) There
+  are points "within" H_n; this means that for any such point there is a
+  neighbourhood consisting exclusively of points of H_n. (3) The points
+  of H_n which do not lie "within" H_n are limiting points of H'_n; they
+  are not points of H'_n, but the neighbourhood of any such point for
+  any number h, however small, contains points within H_n and points of
+  H'_n: the aggregate of these points is called the "boundary" of H_n.
+  (4) When any two points a, b within H_n are taken, it is possible to
+  find a number [epsilon] and a corresponding number m, and to choose
+  points x', x", ... x^m, so that the neighbourhood of a for [epsilon]
+  contains x', and consists exclusively of points within H_n, and
+  similarly for x' and x", x" and x"', ... x^m and b. Condition (3)
+  would exclude such an aggregate as that of the points within and upon
+  two circles external to each other and a line joining a point on one
+  to a point on the other, and condition (4) would exclude such an
+  aggregate as that of the points within and upon two circles which
+  touch externally.
+
+18. Functions of Several Variables.--A function of several variables
+differs from a function of one variable in that the argument of the
+function consists of a set of variables, or is a variable point in a C_n
+when there are n variables. The function is definable by means of the
+domain of the argument and the rule of calculation. In the most
+important cases the domain of the argument is a homogeneous part H_n of
+C_n with the possible exception of isolated points, and the rule of
+calculation is that the value of the function in any assigned part of
+the domain of the argument is that value which is assumed at the point
+by an assigned analytical expression. The limit of a function at a point
+a is defined in the same way as in the case of a function of one
+variable.
+
+  We take a positive fraction [epsilon] and consider the neighbourhood
+  of a for h, and from this neighbourhood we exclude the point a, and we
+  also exclude any point which is not in the domain of the argument.
+  Then we take x and x' to be any two of the retained points in the
+  neighbourhood. The function [f] has a limit at a if for any positive
+  [epsilon], however small, there is a corresponding h which has the
+  property that |[f](x') - [f](x)| < [epsilon], whatever points x, x' in
+  the neighbourhood of a for h we take (a excluded). For example, when
+  there are two variables x1, x2, and both are unrestricted, the domain
+  of the argument is represented by a plane, and the values of the
+  function are correlated with the points of the plane. The function has
+  a limit at a point a, if we can mark out on the plane a region
+  containing the point a within it, and such that the difference of the
+  values of the function which correspond to any two points of the
+  region (neither of the points being a) can be made as small as we
+  please in absolute value by contracting all the linear dimensions of
+  the region sufficiently. When the domain of the argument of a function
+  of n variables extends to an infinite distance, there is a "limit at
+  an infinite distance" if, after any number [epsilon], however small,
+  has been specified, a number N can be found which is such that
+  |[f](x') - [f](x)| < [epsilon], for all points x and x' (of the
+  domain) of which one or more co-ordinates exceed N in absolute value.
+  In the case of functions of several variables great importance
+  attaches to limits for a restricted domain. The definition of such a
+  limit is verbally the same as the corresponding definition in the case
+  of functions of one variable (§ 6). For example, a function of x1 and
+  x2 may have a limit at (x1 = 0, x2 = 0) if we first diminish x1
+  without limit, keeping x2 constant, and afterwards diminish x2 without
+  limit. Expressed in geometrical language, this process amounts to
+  approaching the origin along the axis of x2. The definitions of
+  superior and inferior limits, and of maxima and minima, and the
+  explanations of what is meant by saying that a function of several
+  variables becomes infinite, or tends to become infinite, at a point,
+  are almost identical verbally with the corresponding definitions and
+  explanations in the case of a function of one variable (§ 7). The
+  definition of a continuous function (§ 9) admits of immediate
+  extension; but it is very important to observe that a function of two
+  or more variables may be a continuous function of each of the
+  variables, when the rest are kept constant, without being a continuous
+  function of its argument. For example, a function of x and y may be
+  defined by the conditions that when x = 0 it is zero whatever value y
+  may have, and when x [/=] 0 it has the value of sin {4tan^(-1)(y/x)}.
+  When y has any particular value this function is a continuous function
+  of x, and, when x has any particular value this function is a
+  continuous function of y; but the function of x and y is discontinuous
+  at (x = 0, y = 0).
+
+19. _Differentiation and Integration._--The definition of partial
+differentiation of a function of several variables presents no
+difficulty. The most important theorems concerning differentiable
+functions are the "theorem of the total differential," the theorem of
+the interchangeability of the order of partial differentiations, and the
+extension of Taylor's theorem (see INFINITESIMAL CALCULUS).
+
+With a view to the establishment of the notion of integration through a
+domain, we must define the "extent" of the domain. Take first a domain
+consisting of the point a and all the points x for which |x - a| < ½h,
+where h is a chosen positive number; the extent of this domain is h^n, n
+being the number of variables; such a domain may be described as
+"square," and the number h may be called its "breadth"; it is a
+homogeneous part of the numerical continuum of n dimensions, and its
+boundary consists of all the points for which |x - a| = ½h. Now the
+points of any domain, which does not extend to an infinite distance, may
+be assigned to a finite number m of square domains of finite breadths,
+so that every point of the domain is either within one of these square
+domains or on its boundary, and so that no point is within two of the
+square domains; also we may devise a rule by which, as the number m
+increases indefinitely, the breadths of all the square domains are
+diminished indefinitely. When this process is applied to a homogeneous
+part, H, of the numerical continuum C_n, then, at any stage of the
+process, there will be some square domains of which all the points
+belong to H, and there will generally be others of which some, but not
+all, of the points belong to H. As the number m is increased
+indefinitely the sums of the extents of both these categories of square
+domains will tend to definite limits, which cannot be negative; when the
+second of these limits is zero the domain H is said to be "measurable,"
+and the first of these limits is its "extent"; it is independent of the
+rule adopted for constructing the square domains and contracting their
+breadths. The notion thus introduced may be adapted by suitable
+modifications to continua of lower dimensions in C_n.
+
+  The integral of a function f(x) through a measurable domain H, which
+  is a homogeneous part of the numerical continuum of n dimensions, is
+  defined in just the same way as the integral through an interval, the
+  extent of a square domain taking the place of the difference of the
+  end-values of a partial interval; and the condition of integrability
+  takes the same form as in the simple case. In particular, the
+  condition is satisfied when the function is continuous throughout the
+  domain. The definition of an integral through a domain may be adapted
+  to any domain of measurable extent. The extensions to "improper"
+  definite integrals may be made in the same way as for a function of
+  one variable; in the particular case of a function which tends to
+  become infinite at a point in the domain of integration, the point is
+  enclosed in a partial domain which is omitted from the integration,
+  and a limit is taken when the extent of the omitted partial domain is
+  diminished indefinitely; a divergent integral may have different
+  (principal) values for different modes of contracting the extent of
+  the omitted partial domain. In applications to mathematical physics
+  great importance attaches to convergent integrals and to principal
+  values of divergent integrals. For example, any component of magnetic
+  force at a point within a magnet, and the corresponding component of
+  magnetic induction at the same point are expressed by different
+  principal values of the same divergent integral. Delicate questions
+  arise as to the possibility of representing the integral of a function
+  of n variables through a domain H_n, as a repeated integral, of
+  evaluating it by successive integrations with respect to the variables
+  one at a time and of interchanging the order of such integrations.
+  These questions have been discussed very completely by C. Jordan, and
+  we may quote the result that all the transformations in question are
+  valid when the function is continuous throughout the domain.
+
+20. _Representation of Functions in General._--We have seen that the
+notion of a function is wider than the notion of an analytical
+expression, and that the same function may be "represented" by one
+expression in one part of the domain of the argument and by some other
+expression in another part of the domain (§ 5). Thus there arises the
+general problem of the representation of functions. The function may be
+given by specifying the domain of the argument and the rule of
+calculation, or else the function may have to be determined in
+accordance with certain conditions; for example, it may have to satisfy
+in a prescribed domain an assigned differential equation. In either case
+the problem is to determine, when possible, a single analytical
+expression which shall have the same value as the function at all points
+in the domain of the argument. For the representation of most functions
+for which the problem can be solved recourse must be had to limiting
+processes. Thus we may utilize infinite series, or infinite products, or
+definite integrals; or again we may represent a function of one variable
+as the limit of an expression containing two variables in a domain in
+which one variable remains constant and another varies. An example of
+this process is afforded by the expression Lt_y = [oo]xy/(x²y + 1),
+which represents a function of x vanishing at x = 0 and at all other
+values of x having the value of 1/x. The method of series falls under
+this more general process (cf. § 6). When the terms u1, u2, ... of a
+series are functions of a variable x, the sum s_n of the first n terms
+of the series is a function of x and n; and, when the series is
+convergent, its sum, which is Lt_n = [oo]s_n, can represent a function
+of x. In most cases the series converges for some values of x and not
+for others, and the values for which it converges form the "domain of
+convergence." The sum of the series represents a function in this
+domain.
+
+  The apparently more general method of representation of a function of
+  one variable as the limit of a function of two variables has been
+  shown by R. Baire to be identical in scope with the method of series,
+  and it has been developed by him so as to give a very complete account
+  of the possibility of representing functions by analytical
+  expressions. For example, he has shown that Riemann's totally
+  discontinuous function, which is equal to 1 when x is rational and to
+  0 when x is irrational, can be represented by an analytical
+  expression. An infinite process of a different kind has been adapted
+  to the problem of the representation of a continuous function by T.
+  Brodén. He begins with a function having a graph in the form of a
+  regular polygon, and interpolates additional angular points in an
+  ordered sequence without limit. The representation of a function by
+  means of an infinite product falls clearly under Baire's method, while
+  the representation by means of a definite integral is analogous to
+  Brodén's method. As an example of these two latter processes we may
+  cite the Gamma function [[Gamma](x)] defined for positive values of x
+  by the definite integral
+      _
+     / [oo]
+     |     e^(-t)t^(x - 1)dt,
+    _/0
+
+  or by the infinite product
+
+                                              /      x   \
+    L t_(n = [oo]) n^x/x (1 + x)(1 + ½x) ... ( 1 + -----  ).
+                                              \    n - 1 /
+
+  The second of these expressions avails for the representation of the
+  function at all points at which x is not a negative integer.
+
+21. _Power Series._--Taylor's theorem leads in certain cases to a
+representation of a function by an infinite series. We have under
+certain conditions (§ 13)
+
+                     _n-1
+                    \    (x - a)^r
+  [f](x) = [f](a) + /_   --------- [f]^(r) (a) + R_n;
+                      r=1    r!
+
+and this becomes
+
+                     _[oo]
+                    \     (x - a)^r
+  [f](x) = [f](a) + /_    --------- [f]^(r) (a),
+                      r=1     r!
+
+provided that ([alpha]) a positive number k can be found so that at all
+points in the interval between a and a + k (except these points) [f](x)
+has continuous differential coefficients of all finite orders, and at a
+has progressive differential coefficients of all finite orders; (ß)
+Cauchy's form of the remainder R_n, viz. [(x - a)^n / (n - 1)!] (1 -
+[theta])^(n - 1)[f]^n {a + [theta](x - a)}, has the limit zero when n
+increases indefinitely, for all values of [theta] between 0 and 1, and
+for all values of x in the interval between a and a + k, except possibly
+a + k. When these conditions are satisfied, the series (1) represents
+the function at all points of the interval between a and a + k, except
+possibly a + k, and the function is "analytic" (§ 13) in this domain.
+Obvious modifications admit of extension to an interval between a and a
+- k, or between a - k and a + k. When a series of the form (1)
+represents a function it is called "the Taylor's series for the
+function."
+
+Taylor's series is a power series, i.e. a series of the form
+
+   _[oo]
+  \     a_n (x - a)^n.
+  /_
+    n=0
+
+  As regards power series we have the following theorems:
+
+  1. If the power series converges at any point except a there is a
+  number k which has the property that the series converges absolutely
+  in the interval between a - k and a + k, with the possible exception
+  of one or both end-points.
+
+  2. The power series represents a continuous function in its domain of
+  convergence (the end-points may have to be excluded).
+
+  3. This function is analytic in the domain, and the power series
+  representing it is the Taylor's series for the function.
+
+  The theory of power series has been developed chiefly from the point
+  of view of the theory of functions of complex variables.
+
+22. _Uniform Convergence._--We shall suppose that the domain of
+convergence of an infinite series of functions is an interval with the
+possible exception of isolated points. Let [f](x) be the sum of the
+series at any point x of the domain, and [f]_n(x) the sum of the first n
++ 1 terms. The condition of convergence at a point a is that, after any
+positive number [epsilon], however small, has been specified, it must be
+possible to find a number n so that |[f]_m(a) - [f]_p(a)| < [epsilon]
+for all values of m and p which exceed n. The sum, [f](a), is the limit
+of the sequence of numbers [f]_n(a) at n = [oo]. The convergence is
+said to be "uniform" in an interval if, after specification of
+[epsilon], the same number n suffices at all points of the interval to
+make |[f](x) - [f]_m(x)| < [epsilon] for all values of m which exceed n.
+The numbers n corresponding to any [epsilon], however small, are all
+finite, but, when [epsilon] is less than some fixed finite number, they
+may have an infinite superior limit (§ 7); when this is the case there
+must be at least one point, a, of the interval which has the property
+that, whatever number N we take, [epsilon] can be taken so small that,
+at some point in the neighbourhood of a, n must be taken > N to make
+|[f](x) - f_m(x)| < [epsilon] when m > n; then the series does not
+converge uniformly in the neighbourhood of a. The distinction may be
+otherwise expressed thus: Choose a first and [epsilon] afterwards, then
+the number n is finite; choose [epsilon] first and allow a to vary, then
+the number n becomes a function of a, which may tend to become infinite,
+or may remain below a fixed number; if such a fixed number exists, ho
+wever small [epsilon] may be, the convergence is uniform.
+
+  For example, the series sin x - ½ sin 2x + {1/3} sin 3x - ... is
+  convergent for all real values of x, and, when [pi] > x > -[pi] its
+  sum is ½x; but, when x is but a little less than [pi], the number of
+  terms which must be taken in order to bring the sum at all near to the
+  value of ½x is very large, and this number tends to increase
+  indefinitely as x approaches [pi]. This series does not converge
+  uniformly in the neighbourhood of x = [pi]. Another example is
+  afforded by the series
+
+     _[oo]   nx        (n + 1)x
+    \     -------- - -------------- ,
+    /_    n²x² + 1   (n + 1)²x² + 1
+      n=0
+
+  of which the remainder after n terms is nx/(n²x² + 1). If we put x =
+  1/n, for any value of n, however great, the remainder is ½; and the
+  number of terms required to be taken to make the remainder tend to
+  zero depends upon the value of x when x is near to zero--it must, in
+  fact, be large compared with 1/x. The series does not converge
+  uniformly in the neighbourhood of x = 0.
+
+As regards series whose terms represent continuous functions we have the
+following theorems:
+
+(1) If the series converges uniformly in an interval it represents a
+function which is continuous throughout the interval.
+
+(2) If the series represents a function which is discontinuous in an
+interval it cannot converge uniformly in the interval.
+
+(3) A series which does not converge uniformly in an interval may
+nevertheless represent a function which is continuous throughout the
+interval.
+
+(4) A power series converges uniformly in any interval contained within
+its domain of convergence, the end-points being excluded.
+
+(5) If [Sigma] (r=0 to [oo]) [f]_r(x) = [f](x) converges uniformly in
+the interval between a and b
+
+    _              _[oo]  _
+   / b            \      / b
+   |  [f](x)dx =  /_     |   [f]_r(x)dx,
+  _/ a              r=0 _/a
+
+or a series which converges uniformly may be integrated term by term.
+
+(6) If [Signa] (r=0 to [oo]) [f]'_r(x) converges uniformly in an
+interval, then [Signa] (r=o to [oo]) [f]_r(x) converges in the interval,
+and represents a continuous differentiable function, [phi](x); in fact
+we have
+
+               _[oo]
+  [phi]'(x) = \    [f]'_r(x),
+              /_
+                r=0
+
+or a series can be differentiated term by term if the series of derived
+functions converges uniformly.
+
+A series whose terms represent functions which are not continuous
+throughout an interval may converge uniformly in the interval. If
+[Signa] (r=0 to [oo]) [f]_r(x) = [f](x), is such a series, and if all
+the functions [f]_r(x) have limits at a, then [f](x) has a limit at a,
+which is [Signa] (r=0 a=0 to [oo]) Lt [f]_r(x). A similar theorem holds
+for limits on the left or on the right.
+
+23. _Fourier's Series._--An extensive class of functions admit of being
+represented by series of the form
+
+        _[oo]  /        n[pi]x           n[pi]x \
+  a0 + \      ( a_n cos ------ + b_n sin ------  ),  (i.)
+       /_      \          c                c    /
+         n=1
+
+and the rule for determining the coefficients a_n, b_n of such a series,
+in order that it may represent a given function [f](x) in the interval
+between -c and c, was given by Fourier, viz. we have
+            _                      _
+        1  / c                 1  / c           n[pi]x
+  a0 = --- |  [f](x)dx,  a_n = -- |   [f](x)cos ------ dx,
+       2c _/-c                 c _/-c             c
+           _
+          / c  1            n[pi]x
+    b_n = |    -- [f](x)sin ------ dx.
+         _/-c  c              c
+
+The interval between -c and c may be called the "periodic interval," and
+we may replace it by any other interval, e.g. that between 0 and 1,
+without any restriction of generality. When this is done the sum of the
+series takes the form
+
+           _     _r=n
+          / 1   \    [f](z)cos {2r[pi](z - x)} dz,
+   Lt     |     /_
+  n=[oo] _/0     r=-n
+
+
+and this is
+           _
+          / 1       sin {(2n + 1)(z - x)[pi]}
+    Lt    |  [f](z) ------------------------ dz.     (ii.)
+  n=[oo] _/0            sin {(z - x)[pi]}
+
+Fourier's theorem is that, if the periodic interval can be divided into
+a finite number of partial intervals within each of which the function
+is ordinary (§ 14), the series represents the function within each of
+those partial intervals. In Fourier's time a function of this character
+was regarded as completely arbitrary.
+
+  By a discussion of the integral (ii.) based on the Second Theorem of
+  the Mean (§ 15) it can be shown that, if [f](x) has restricted
+  oscillation in the interval (§ 11), the sum of the series is equal to
+  ½{[f](x + 0) + [f](x - 0)} at any point x within the interval, and
+  that it is equal to ½{[f]( + 0) + [f](1 - 0} at each end of the
+  interval. (See the article FOURIER'S SERIES.) It therefore represents
+  the function at any point of the periodic interval at which the
+  function is continuous (except possibly the end-points), and has a
+  definite value at each point of discontinuity. The condition of
+  restricted oscillation includes all the functions contemplated in the
+  statement of the theorem and some others. Further, it can be shown
+  that, in any partial interval throughout which [f](x) is continuous,
+  the series converges uniformly, and that no series of the form (i),
+  with coefficients other than those determined by Fourier's rule, can
+  represent the function at all points, except points of discontinuity,
+  in the same periodic interval. The result can be extended to a
+  function [f](x) which tends to become infinite at a finite number of
+  points a of the interval, provided (1) [f](x) tends to become
+  determinately infinite at each of the points a, (2) the improper
+  definite integral of [f](x) through the interval is convergent, (3)
+  [f](x) has not an infinite number of discontinuities or of maxima or
+  minima in the interval.
+
+24. _Representation of Continuous Functions by Series._--If the series
+for [f](x) formed by Fourier's rule converges at the point a of the
+periodic interval, and if [f](x) is continuous at a, the sum of the
+series is [f](a); but it has been proved by P. du Bois Reymond that the
+function may be continuous at a, and yet the series formed by Fourier's
+rule may be divergent at a. Thus some continuous functions do not admit
+of representation by Fourier's series. All continuous functions,
+however, admit of being represented with arbitrarily close approximation
+in either of two forms, which may be described as "terminated Fourier's
+series" and "terminated power series," according to the two following
+theorems:
+
+(1) If [f](x) is continuous throughout the interval between 0 and 2[pi],
+and if any positive number [epsilon] however small is specified, it is
+possible to find an integer n, so that the difference between the value
+of [f](x) and the sum of the first n terms of the series for [f](x),
+formed by Fourier's rule with periodic interval from 0 to 2[pi], shall
+be less than [epsilon] at all points of the interval. This result can be
+extended to a function which is continuous in any given interval.
+
+(2) If [f](x) is continuous throughout an interval, and any positive
+number [epsilon] however small is specified, it is possible to find an
+integer n and a polynomial in x of the nth degree, so that the
+difference between the value of [f](x) and the value of the polynomial
+shall be less than [epsilon] at all points of the interval.
+
+Again it can be proved that, if [f](x) is continuous throughout a given
+interval, polynomials in x of finite degrees can be found, so as to form
+an infinite series of polynomials whose sum is equal to [f](x) at all
+points of the interval. Methods of representation of continuous
+functions by infinite series of rational fractional functions have also
+been devised.
+
+  Particular interest attaches to continuous functions which are not
+  differentiable. Weierstrass gave as an example the function
+  represented by the series [Sigma] (n=0 to [oo]) a^n cos(b^[n] x[pi]),
+  where a is positive and less than unity, and b is an odd integer
+  exceeding (1 + (3/2)[pi]) / a. It can be shown that this series is
+  uniformly convergent in every interval, and that the continuous
+  function [f](x) represented by it has the property that there is, in
+  the neighbourhood of any point x0, an infinite aggregate of points x',
+  having x0 as a limiting point, for which {[f](x') - [f](x0)} / (x' -
+  x0) tends to become infinite with one sign when x' - x0 approaches
+  zero through positive values, and infinite with the opposite sign when
+  x' - x0 approaches zero through negative values. Accordingly the
+  function is not differentiable at any point. The definite integral of
+  such a function [f](x) through the interval between a fixed point and
+  a variable point x, is a continuous differentiable function F(x), for
+  which F'(x) = [f](x); and, if [f](x) is one-signed throughout any
+  interval F(x) is monotonous throughout that interval, but yet F(x)
+  cannot be represented by a curve. In any interval, however small, the
+  tangent would have to take the same direction for infinitely many
+  points, and yet there is no interval in which the tangent has
+  everywhere the same direction. Further, it can be shown that all
+  functions which are everywhere continuous and nowhere differentiable
+  are capable of representation by series of the form [Sigma][a]_n
+  [phi]_n (x), where [Sigma][a]_n is an absolutely convergent series of
+  numbers, and [phi]_n(x) is an analytic function whose absolute value
+  never exceeds unity.
+
+25. _Calculations with Divergent Series._--When the series described in
+(1) and (2) of § 24 diverge, they may, nevertheless, be used for the
+approximate numerical calculation of the values of the function,
+provided the calculation is not carried beyond a certain number of
+terms. Expansions in series which have the property of representing a
+function approximately when the expansion is not carried too far are
+called "asymptotic expansions." Sometimes they are called
+"semi-convergent series"; but this term is avoided in the best modern
+usage, because it is often used to describe series whose convergence
+depends upon the order of the terms, such as the series 1 - ½ + 1/3 - ...
+
+  In general, let [f]0(x) + [f]1(x) + ... be a series of functions which
+  does not converge in a certain domain. It may happen that, if any
+  number [epsilon], however small, is first specified, a number n can
+  afterwards be found so that, at a point a of the domain, the value
+  [f](a) of a certain function [f](x) is connected with the sum of the
+  first n + 1 terms of the series by the relation |[f](a) - [Sigma] (r=0
+  to n) [f]_r(a) | < [epsilon]. It must also happen that, if any number
+  N, however great, is specified, a number n'(>n) can be found so that,
+  for all values of m which exceed n', | [Sigma](r=0 to m) [f]_r(a) | >
+  N. The divergent series [f]0(x) + [f]1(x) + ... is then an asymptotic
+  expansion for the function f(x) in the domain.
+
+  The best known example of an asymptotic expansion is Stirling's
+  formula for n! when n is large, viz.
+             _____
+            /
+    n! =  \/(2[pi]) ½n^(n + ½) e^(-n + [theta] / 12n),
+
+  where [theta] is some number lying between 0 and 1. This formula is
+  included in the asymptotic expansion for the Gamma function. We have
+  in fact
+
+    log {[Gamma](x)} = (x - ½) log x - x + ½ log 2[pi] + [~omega](x),
+
+  where [~omega](x) is the function defined by the definite integral
+                   _
+                  / [oo]
+    ~[omega](x) = |     {[1 - e^(-t)]^(-1) - t^(-1) - ½} t^(-1) e^(-tx)dt.
+                 _/0
+
+  The multiplier of e^(-tx) under the sign of integration can be
+  expanded in the power series
+
+     B1      B2        B3
+    ---- -  ---- t² + ---- t^4 - ...,
+     2!      4!        6!
+
+  where B1, B2, ... are "Bernoulli's numbers" given by the formula
+
+                               _[oo]
+                              \
+    B_m = 2.2m! (2[pi])^(-2m) /_   [r^(-2m)].
+                                r=1
+
+  When the series is integrated term by term, the right-hand member of
+  the equation for [~omega](x) takes the form
+
+     B1   1     B2   1     B3   1
+    ---- --- - ---- --- + ---- --- - ...,
+    1.2   x    3.4  x³    5.6  x^5
+
+  This series is divergent; but, if it is stopped at any term, the
+  difference between the sum of the series so terminated and the value
+  of [~omega](x) is less than the last of the retained terms. Stirling's
+  formula is obtained by retaining the first term only. Other well-known
+  examples of asymptotic expansions are afforded by the descending
+  series for Bessel's functions. Methods of obtaining such expansions
+  for the solutions of linear differential equations of the second order
+  were investigated by G.G. Stokes (_Math. and Phys. Papers_, vol. ii.
+  p. 329), and a general theory of asymptotic expansions has been
+  developed by H. Poincaré. A still more general theory of divergent
+  series, and of the conditions in which they can be used, as above, for
+  the purposes of approximate calculation has been worked out by É.
+  Borel. The great merit of asymptotic expansions is that they admit of
+  addition, subtraction, multiplication and division, term by term, in
+  the same way as absolutely convergent series, and they admit also of
+  integration term by term; that is to say, the results of such
+  operations are asymptotic expansions for the sum, difference,
+  product, quotient, or integral, as the case may be.
+
+26. _Interchange of the Order of Limiting Operations._--When we require
+to perform any limiting operation upon a function which is itself
+represented by the result of a limiting process, the question of the
+possibility of interchanging the order of the two processes always
+arises. In the more elementary problems of analysis it generally happens
+that such an interchange is possible; but in general it is not possible.
+In other words, the performance of the two processes in different orders
+may lead to two different results; or the performance of them in one of
+the two orders may lead to no result. The fact that the interchange is
+possible under suitable restrictions for a particular class of
+operations is a theorem to be proved.
+
+  Among examples of such interchanges we have the differentiation and
+  integration of an infinite series term by term (§ 22), and the
+  differentiation and integration of a definite integral with respect to
+  a parameter by performing the like processes upon the subject of
+  integration (§ 19). As a last example we may take the limit of the sum
+  of an infinite series of functions at a point in the domain of
+  convergence. Suppose that the series [Sigma] (r=0 to [oo]) [f]_r(x)
+  represents a function ([f]x) in an interval containing a point a, and
+  that each of the functions [f]_r(x) has a limit at a. If we first put
+  x = a, and then sum the series, we have the value [f](a); if we first
+  sum the series for any x, and afterwards take the limit of the sum at
+  x = a, we have the limit of [f](x) at a; if we first replace each
+  function [f]_r(x) by its limit at a, and then sum the series, we may
+  arrive at a value different from either of the foregoing. If the
+  function [f](x) is continuous at a, the first and second results are
+  equal; if the functions [f]_r(x) are all continuous at a, the first
+  and third results are equal; if the series is uniformly convergent,
+  the second and third results are equal. This last case is an example
+  of the interchange of the order of two limiting operations, and a
+  sufficient, though not always a necessary, condition, for the validity
+  of such an interchange will usually be found in some suitable
+  extension of the notion of uniform convergence.
+
+  AUTHORITIES.--Among the more important treatises and memoirs connected
+  with the subject are: R. Baire, _Fonctions discontinues_ (Paris,
+  1905); O. Biermann, _Analytische Functionen_ (Leipzig, 1887); É.
+  Borel, _Théorie des fonctions_ (Paris, 1898) (containing an
+  introductory account of the Theory of Aggregates), and _Séries
+  divergentes_ (Paris, 1901), also _Fonctions de variables réelles_
+  (Paris, 1905); T.J. I'A. Bromwich, _Introduction to the Theory of
+  Infinite Series_ (London, 1908); H.S. Carslaw, _Introduction to the
+  Theory of Fourier's Series and Integrals_ (London, 1906); U. Dini,
+  _Functionen e. reellen Grösse_ (Leipzig, 1892), and _Serie di Fourier_
+  (Pisa, 1880); A. Genocchi u. G. Peano, _Diff.- u. Int.-Rechnung_
+  (Leipzig, 1899); J. Harkness and F. Morley, _Introduction to the
+  Theory of Analytic Functions_ (London, 1898); A. Harnack, _Diff. and
+  Int. Calculus_ (London, 1891); E.W. Hobson, _The Theory of Functions
+  of a real Variable and the Theory of Fourier's Series_ (Cambridge,
+  1907); C. Jordan, _Cours d'analyse_ (Paris, 1893-1896); L. Kronecker,
+  _Theorie d. einfachen u. vielfachen Integrale_ (Leipzig, 1894); H.
+  Lebesgue, _Leçons sur l'intégration_ (Paris, 1904); M. Pasch, _Diff.-
+  u. Int.-Rechnung_ (Leipzig, 1882); E. Picard, _Traité d'analyse_
+  (Paris, 1891); O. Stolz, _Allgemeine Arithmetik_ (Leipzig, 1885), and
+  _Diff.- u. Int.-Rechnung_ (Leipzig, 1893-1899); J. Tannery, _Théorie
+  des fonctions_ (Paris, 1886); W.H. and G.C. Young, _The Theory of Sets
+  of Points_ (Cambridge, 1906); Brodén, "Stetige Functionen e. reellen
+  Veränderlichen," _Crelle_, Bd. cxviii.; G. Cantor, A series of memoirs
+  on the "Theory of Aggregates" and on "Trigonometric series" in _Acta
+  Math_. tt. ii., vii., and _Math. Ann_. Bde. iv.-xxiii.; Darboux,
+  "Fonctions discontinues," _Ann. Sci. École normale sup_. (2), t. iv.;
+  Dedekind, _Was sind u. was sollen d. Zahlen_? (Brunswick, 1887), and
+  _Stetigkeit u. irrationale Zahlen_ (Brunswick, 1872); Dirichlet,
+  "Convergence des séries trigonométriques," _Crelle_, Bd. iv.; P. Du
+  Bois Reymond, _Allgemeine Functionentheorie_ (Tübingen, 1882), and
+  many memoirs in _Crelle_ and in _Math. Ann_.; Heine,
+  "Functionenlehre," _Crelle_, Bd. lxxiv.; J. Pierpont, _The Theory of
+  Functions of a real Variable_ (Boston, 1905); F. Klein, "Allgemeine
+  Functionsbegriff," _Math. Ann_. Bd. xxii.; W.F. Osgood, "On Uniform
+  Convergence," _Amer. J. of Math_. vol. xix.; Pincherle, "Funzioni
+  analitiche secondo Weierstrass," _Giorn. di mat_. t. xviii.;
+  Pringsheim, "Bedingungen d. Taylorschen Lehrsatzes," _Math. Ann_. Bd.
+  xliv.; Riemann, "Trigonometrische Reihe," _Ges. Werke_ (Leipzig,
+  1876); Schoenflies, "Entwickelung d. Lehre v. d.
+  Punktmannigfaltigkeiten," _Jahresber. d. deutschen Math.-Vereinigung_,
+  Bd. viii.; Study, Memoir on "Functions with Restricted Oscillation,"
+  _Math. Ann_. Bd. xlvii.; Weierstrass, Memoir on "Continuous Functions
+  that are not Differentiable," _Ges. math. Werke_, Bd. ii. p. 71
+  (Berlin, 1895), and on the "Representation of Arbitrary Functions,"
+  ibid. Bd. iii. p. 1; W.H. Young, "On Uniform and Non-uniform
+  Convergence," _Proc. London Math. Soc._ (Ser. 2) t. 6. Further
+  information and very full references will be found in the articles by
+  Pringsheim, Schoenflies and Voss in the _Encyclopädie der math.
+  Wissenschaften_, Bde. i., ii. (Leipzig, 1898, 1899).     (A. E. H. L.)
+
+
+II.--FUNCTIONS OF COMPLEX VARIABLES
+
+In the preceding section the doctrine of functionality is discussed with
+respect to real quantities; in this section the theory when complex or
+imaginary quantities are involved receives treatment. The following
+abstract explains the arrangement of the subject matter: (§ 1), _Complex
+numbers_, states what a complex number is; (§ 2), _Plotting of simple
+expressions involving complex numbers_, illustrates the meaning in some
+simple cases, introducing the notion of conformal representation and
+proving that an algebraic equation has complex, if not real, roots; (§
+3), _Limiting operations_, defines certain simple functions of a complex
+variable which are obtained by passing to a limit, in particular the
+exponential function, and the generalized logarithm, here denoted by
+[lambda](z); (§ 4), _Functions of a complex variable in general_, after
+explaining briefly what is to be understood by a region of the complex
+plane and by a path, and expounding a logical principle of some
+importance, gives the accepted definition of a function of a complex
+variable, establishes the existence of a complex integral, and proves
+Cauchy's theorem relating thereto; (§ 5), _Applications_, considers the
+differentiation and integration of series of functions of a complex
+variable, proves Laurent's theorem, and establishes the expansion of a
+function of a complex variable as a power series, leading, in (§ 6),
+_Singular points_, to a definition of the region of existence and
+singular points of a function of a complex variable, and thence, in (§
+7), _Monogenic Functions_, to what the writer believes to be the
+simplest definition of a function of a complex variable, that of
+Weierstrass; (§ 8), _Some elementary properties of single valued
+functions_, first discusses the meaning of a pole, proves that a single
+valued function with only poles is rational, gives Mittag-Leffler's
+theorem, and Weierstrass's theorem for the primary factors of an
+integral function, stating generalized forms for these, leading to the
+theorem of (§ 9), _The construction of a monogenic function with a given
+region of existence_, with which is connected (§10), _Expression of a
+monogenic function by rational functions in a given region_, of which
+the method is applied in (§ 11), _Expression of_ (1 - z)^(-1) _by
+polynomials_, to a definite example, used here to obtain (§ 12), _An
+expansion of an arbitrary function by means of a series of polynomials,
+over a star region_, also obtained in the original manner of
+Mittag-Leffler; (§ 13), _Application of Cauchy's theorem to the
+determination of definite integrals_, gives two examples of this method;
+(§ 14), _Doubly Periodic Functions_, is introduced at this stage as
+furnishing an excellent example of the preceding principles. The reader
+who wishes to approach the matter from the point of view of Integral
+Calculus should first consult the section (§ 20) below, dealing with
+_Elliptic Integrals_; (§ 15), _Potential Functions, Conformal
+representation in general_, gives a sketch of the connexion of the
+theory of potential functions with the theory of conformal
+representation, enunciating the Schwarz-Christoffel theorem for the
+representation of a polygon, with the application to the case of an
+equilateral triangle; (§ 16), _Multiple-valued Functions, Algebraic
+Functions_, deals for the most part with algebraic functions, proving
+the residue theorem, and establishing that an algebraic function has a
+definite Order; (§ 17), _Integrals of Algebraic Functions_, enunciating
+Abel's theorem; (§ 18), _Indeterminateness of Algebraic Integrals_,
+deals with the periods associated with an algebraic integral,
+establishing that for an elliptic integral the number of these is two;
+(§ 19), _Reversion of an algebraic integral_, mentions a problem
+considered below in detail for an elliptic integral; (§ 20), _Elliptic
+Integrals_, considers the algebraic reduction of any elliptic integral
+to one of three standard forms, and proves that the function obtained by
+reversion is single-valued; (§ 21), _Modular Functions_, gives a
+statement of some of the more elementary properties of some functions of
+great importance, with a definition of Automorphic Functions, and a hint
+of the connexion with the theory of linear differential equations; (§
+22), _A property of integral functions, deduced from the theory of
+modular functions_, proves that there cannot be more than one value not
+assumed by an integral function, and gives the basis of the well-known
+expression of the modulus of the elliptic functions in terms of the
+ratio of the periods; (§ 23), _Geometrical applications of Elliptic
+Functions_, shows that any plane curve of deficiency unity can be
+expressed by elliptic functions, and gives a geometrical proof of the
+addition theorem for the function RN(u); (§ 24), _Integrals of Algebraic
+Functions in connexion with the theory of plane curves_, discusses the
+generalization to curves of any deficiency; (§ 25), _Monogenic Functions
+of several independent variables_, describes briefly the beginnings of
+this theory, with a mention of some fundamental theorems: (§ 26),
+_Multiply-Periodic Functions and the Theory of Surfaces_, attempts to
+show the nature of some problems now being actively pursued.
+
+Beside the brevity necessarily attaching to the account here given of
+advanced parts of the subject, some of the more elementary results are
+stated only, without proof, as, for instance: the monogeneity of an
+algebraic function, no reference being made, moreover, to the cases of
+differential equations whose integrals are monogenic; that a function
+possessing an algebraic addition theorem is necessarily an elliptic
+function (or a particular case of such); that any area can be
+conformally represented on a half plane, a theorem requiring further
+much more detailed consideration of the meaning of _area_ than we have
+given; while the character and properties, including the connectivity,
+of a Riemann surface have not been referred to. The theta functions are
+referred to only once, and the principles of the theory of Abelian
+Functions have been illustrated only by the developments given for
+elliptic functions.
+
+§ 1. _Complex Numbers._--Complex numbers are numbers of the form x + iy,
+where x, y are ordinary real numbers, and i is a symbol imagined capable
+of combination with itself and the ordinary real numbers, by way of
+addition, subtraction, multiplication and division, according to the
+ordinary commutative, associative and distributive laws; the symbol i is
+further such that i² = -1.
+
+  Taking in a plane two rectangular axes Ox, Oy, we assume that every
+  point of the plane is definitely associated with two real numbers x, y
+  (its co-ordinates) and conversely; thus any point of the plane is
+  associated with a single complex number; in particular, for every
+  point of the axis Ox, for which y = O, the associated number is an
+  ordinary real number; the complex numbers thus include the real
+  numbers. The axis Ox is often called the real axis, and the axis Oy
+  the imaginary axis. If P be the point associated with the complex
+  variable z = x + iy, the distance OP be called r, and the positive
+  angle less than 2[pi] between Ox and OP be called [theta], we may
+  write z = r(cos[theta] + i sin[theta]); then r is called the modulus
+  or absolute value of z and often denoted by |z| and [theta] is called
+  the phase or amplitude of z, and often denoted by ph (z); strictly the
+  phase is ambiguous by additive multiples of 2[pi]. If z' = x' + iy' be
+  represented by P', the complex argument z' + z is represented by a
+  point P" obtained by drawing from P' a line equal to and parallel to
+  OP; the geometrical representation involves for its validity certain
+  properties of the plane; as, for instance, the equation z' + z = z +
+  z' involves the possibility of constructing a parallelogram (with OP"
+  as diagonal). It is important constantly to bear in mind, what is
+  capable of easy algebraic proof (and geometrically is Euclid's
+  proposition III. 7), that the modulus of a sum or difference of two
+  complex numbers is generally less than (and is never greater than) the
+  sum of their moduli, and is greater than (or equal to) the difference
+  of their moduli; the former statement thus holds for the sum of any
+  number of complex numbers. We shall write E(i[theta]) for cos[theta] +
+  i sin [theta]; it is at once verified that E(i[alpha]). E(iß) =
+  E[i([alpha] + ß)], so that the phase of a product of complex
+  quantities is obtained by addition of their respective phases.
+
+§ 2. _Plotting and Properties of Simple Expressions involving a Complex
+Number._--If we put [zeta] = (z-i)/(z + i), and, putting [zeta] = [xi] +
+i[eta], take a new plane upon which [xi], [eta] are rectangular
+co-ordinates, the equations [xi] = (x² + y²-1)/[x² + (y + 1)²], [eta] =
+-2xy/[x² + (y + i)²] will determine, corresponding to any point of the
+first plane, a point of the second plane. There is the one exception of
+z = -i, that is, x = 0, y = -1, of which the corresponding point is at
+infinity. It can now be easily proved that as z describes the real axis
+in its plane the point [zeta] describes once a circle of radius unity,
+with centre at [zeta] = 0, and that there is a definite correspondence
+of point to point between points in the z-plane which are above the real
+axis and points of the [zeta]-plane which are interior to this circle;
+in particular z = i corresponds to [zeta] = 0.
+
+  Moreover, [zeta] being a rational function of z, both [xi] and [eta]
+  are continuous differentiable functions of x and y, save when [zeta]
+  is infinite; writing [zeta] = [f](x, y) = [f](z - iy, y), the fact
+  that this is really independent of y leads at once to (Pd)f/(Pd)x +
+  i(Pd)[f]/(Pd)y = 0, and hence to
+
+    (Pd)[xi]   (Pd)[eta]  (Pd)[xi]     (Pd)[eta]  (Pd)²[xi]   (Pd)²[xi]
+    -------- = ---------, -------- = - ---------, --------- + --------- = 0;
+     (Pd)x       (Pd)y'    (Pd)y         (Pd)x'     (Pd)x²      (Pd)y²
+
+  so that [xi] is not any arbitrary function of x, y, and when [xi] is
+  known [eta] is determinate save for an additive constant. Also, in
+  virtue of these equations, if [zeta], [zeta]' be the values of [zeta]
+  corresponding to two near values of z, say z and z', the ratio
+  ([zeta]'-[zeta])/(z'- z) has a definite limit when z' = z, independent
+  of the ultimate phase of z'- z, this limit being therefore equal to
+  (Pd)[zeta]/(Pd)x, that is, (Pd)[xi]/(Pd)x + i(Pd)[eta])/(Pd)x.
+  Geometrically this fact is interpreted by saying that if two curves in
+  the z-plane intersect at a point P, at which both the differential
+  coefficients (Pd)[xi]/(Pd)x, (Pd)[eta]/(Pd)x are not zero, and P', P"
+  be two points near to P on these curves respectively, and the
+  corresponding points of the [zeta]-plane be Q, Q', Q", then (1) the
+  ratios PP"/PP', QQ"/QQ' are ultimately equal, (2) the angle P'PP" is
+  equal to Q'QQ", (3) the rotation from PP' to PP" is in the same sense
+  as from QQ' to QQ", it being understood that the axes of [xi], [eta]
+  in the one plane are related as are the axes of x, y. Thus any diagram
+  of the z-plane becomes a diagram of the [zeta]-plane with the same
+  angles; the magnification, however, which is equal to
+     _                           _
+    |  /(Pd)[xi]\²    /(Pd)[xi]\² | ½
+    | ( -------- ) + ( -------- ) |
+    |_ \ (Pd)x  /     \  (Pd)y / _|
+
+  varies from point to point. Conversely, it appears subsequently that
+  the expression of any copy of a diagram (say, a map) which preserves
+  angles requires the intervention of the complex variable.
+
+  As another illustration consider the case when [zeta] is a polynomial
+  in z,
+
+    [zeta] = p0 z^n + p1 z^(n - 1) + ... + p_n;
+
+  H being an arbitrary real positive number, it can be shown that a
+  radius R can be found such for every |z| > R we have |[zeta]| > H;
+  consider the lower limit of |[zeta]| for |z| < R; as [xi]² + [eta]² is
+  a real continuous function of x, y for |z| < R, there is a point (x,
+  y), say (x0, y0), at which |[zeta]| is least, say equal to [rho], and
+  therefore within a circle in the [zeta]-plane whose centre is the
+  origin, of radius [rho], there are no points [zeta] representing
+  values corresponding to |z| < R. But if [zeta]0 be the value of [zeta]
+  corresponding to (x0, y0), and the expression of [zeta] - [zeta]0 near
+  z0 = x0 + iy0, in terms of z - z0, be A(z - z0)^m + B(z - z0)^(m + 1)
+  + ..., where A is not zero, to two points near to (x0, y0), say (x1,
+  y1) or z1 and z2 = z0 + (z1 - z0)(cos [pi]/m + i sin [pi]/m), will
+  correspond two points near to [zeta]0, say [zeta]1, and 2[zeta]0
+  -[zeta]'1, situated so that [zeta]0 is between them. One of these must
+  be within the circle ([rho]). We infer then that [rho] = 0, and have
+  proved that every polynomial in z vanishes for some value of z, and
+  can therefore be written as a product of factors of the form z -
+  [alpha], where [alpha] denotes a complex number. This proposition
+  alone suffices to suggest the importance of complex numbers.
+
+§ 3. _Limiting Operations._--In order that a complex number [zeta] =
+[xi] + i[eta] may have a limit it is necessary and sufficient that each
+of [xi] and [eta] has a limit. Thus an infinite series w0 + w1 + w2 +
+..., whose terms are complex numbers, is convergent if the real series
+formed by taking the real parts of its terms and that formed by the
+imaginary terms are both convergent. The series is also convergent if
+the real series formed by the moduli of its terms is convergent; in that
+case the series is said to be absolutely convergent, and it can be shown
+that its sum is unaltered by taking the terms in any other order.
+Generally the necessary and sufficient condition of convergence is that,
+for a given real positive [epsilon], a number m exists such that for
+every n > m, and every positive p, the batch of terms w_n + w_(n + 1) +
+... + w_(n + p) is less than [epsilon] in absolute value. If the terms
+depend upon a complex variable z, the convergence is called _uniform_
+for a range of values of z, when the inequality holds, for the same
+[epsilon] and m, for all the points z of this range.
+
+  The infinite series of most importance are those of which the general
+  term is a_nz^n, wherein a_n is a constant, and z is regarded as
+  variable, n = 0, 1, 2, 3, ... Such a series is called a power series,
+  if a real and positive number M exists such that for z = z0 and every
+  n, |a_n z0^n| < M, a condition which is satisfied, for instance, if
+  the series converges for z = z0, then it is at once proved that the
+  series converges absolutely for every z for which |z| < |z0|, and
+  converges uniformly over every range |z| < r' for which r' < |z0|. To
+  every power series there belongs then a circle of convergence within
+  which it converges absolutely and uniformly; the function of z
+  represented by it is thus continuous within the circle (this being the
+  result of a general property of uniformly convergent series of
+  continuous functions); the sum for an interior point z is, however,
+  continuous with the sum for a point z0 on the circumference, as z
+  approaches to z0 provided the series converges for z = z0, as can be
+  shown without much difficulty. Within a common circle of convergence
+  two power series [Sigma] a_n z^n, [Sigma] b_n z^n can be multiplied
+  together according to the ordinary rule, this being a consequence of a
+  theorem for absolutely convergent series. If r1 be less than the
+  radius of convergence of a series [Sigma] a_nz^n and for |z| = r1, the
+  sum of the series be in absolute value less than a real positive
+  quantity M, it can be shown that for |z| = r1 every term is also less
+  than M in absolute value, namely, |a_n| < Mr1^(-n). If in every
+  arbitrarily small neighbourhood of z = 0 there be a point for which
+  two converging power series [Sigma]a_nz^n, [Sigma]b_n z^n agree in
+  value, then the series are identical, or a_n = b_n; thus also if
+  [Sigma]a_nz^n vanish at z = 0 there is a circle of finite radius about
+  z = 0 as centre within which no other points are found for which the
+  sum of the series is zero. Considering a power series [f](z) =
+  [Sigma]a_nz^n of radius of convergence R, if |z0| < R and we put z =
+  z0 + t with |t| < R-|z0|, the resulting series [Sigma]a_n (z0 + t)^n
+  may be regarded as a double series in z0 and t, which, since |z0| + t
+  < R, is absolutely convergent; it may then be arranged according to
+  powers of t. Thus we may write [f](z) = [Sigma]A_n t^n; hence A0 =
+  [f](z0), and we have [[f](z0 + t) - [f](z0)]/t = [Sigma](n=1) A_n
+  t^(n-l), wherein the continuous series on the right reduces to A1 for
+  t = 0; thus the ratio on the left has a definite limit when t = 0,
+  equal namely to A1 or [Sigma]na_nz0^(n - 1). In other words, the
+  original series may legitimately be differentiated at any interior
+  point z0 of its circle of convergence. Repeating this process we find
+  [f](z0 + t) = [Sigma]t^n [f]^(n) (z0)/n!, where [f]^(n) (z0) is the
+  nth differential coefficient. Repeating for this power series, in t,
+  the argument applied about z = 0 for [Sigma]a_n z^n, we infer that for
+  the series [f](z) every point which reduces it to zero is an isolated
+  point, and of such points only a finite number lie within a circle
+  which is within the circle of convergence of [f](z).
+
+  Perhaps the simplest possible power series is e^z = exp(z) = 1 + z²/2!
+  + z³/3! + ... of which the radius of convergence is infinite. By
+  multiplication we have exp(z)·exp(z^1) = exp(z + z^1). In particular
+  when x, y are real, and z = x + iy, exp(z) = exp(x)exp(iy). Now the
+  functions
+
+    U0 = sin y, V0 = 1 - cos y, U1 = y - sin y,
+    V1 = ½y² - 1 + cos y, U2 = (1/6)y³ - y + sin y,
+      V2 = (1/24)y^4 - ½y² + 1 - cos y, ...
+
+  all vanish for y = 0, and the differential coefficient of any one
+  after the first is the preceding one; as a function (of a real
+  variable) is increasing when its differential coefficient is positive,
+  we infer, for y positive, that each of these functions is positive;
+  proceeding to a limit we hence infer that
+
+    cos y = 1 - ½y² + (1/24)y^4 - ..., sin y = y - (1/6)y³ +
+      (1/120)y^5 - ...,
+
+  for positive, and hence, for all values of y. We thus have exp(iy) =
+  cos y + i sin y, and exp (z) = exp (x)·(cos y + i sin y). In other
+  words, the modulus of exp (z) is exp (x) and the phase is y. Hence
+  also
+
+    exp(z + 2[pi]i) = exp(x) [cos (y + 2[pi]) + i sin(y + 2[pi])],
+
+  which we express by saying that exp (z) has the period 2[pi]i, and
+  hence also the period 2k[pi]i, where k is an arbitrary integer. From
+  the fact that the constantly increasing function exp (x) can vanish
+  only for x = 0, we at once prove that exp (z) has no other periods.
+
+  Taking in the plane of z an infinite strip lying between the lines y =
+  0, y = 2[pi] and plotting the function [zeta] = exp (z) upon a new
+  plane, it follows at once from what has been said that every complex
+  value of [zeta] arises when z takes in turn all positions in this
+  strip, and that no value arises twice over. The equation [zeta] =
+  exp(z) thus defines z, regarded as depending upon [zeta], with only an
+  additive ambiguity 2k[pi]i, where k is an integer. We write z =
+  [lambda]([zeta]); when [zeta] is real this becomes the logarithm of
+  [zeta]; in general [lambda]([zeta]) = log |[zeta]| + i ph ([zeta]) +
+  2k[pi]i, where k is an integer; and when [zeta] describes a closed
+  circuit surrounding the origin the phase of [zeta] increases by 2[pi],
+  or k increases by unity. Differentiating the series for [zeta] we have
+  d[zeta]/dz = [zeta], so that z, regarded as depending upon [zeta], is
+  also differentiable, with dz/d[zeta] = [zeta]^(-1). On the other hand,
+  consider the series [zeta] - 1 - ½([zeta] - 1)² + 1/3([zeta] - 1)³ -
+  ...; it converges when [zeta] = 2 and hence converges for |[zeta] - 1|
+  < 1; its differential coefficient is, however, 1 - ([zeta] - 1) +
+  ([zeta] - 1)² - ..., that is, (1 + [zeta] - 1)^(-1). Wherefore if
+  [phi]([zeta]) denote this series, for |[zeta] - 1| < 1, the difference
+  [lambda]([zeta]) - [phi]([zeta]), regarded as a function of [xi] and
+  [eta], has vanishing differential coefficients; if we take the value
+  of [lambda]([zeta]) which vanishes when [zeta] = 1 we infer thence
+  that for |[zeta] - 1| < 1, [lambda]([zeta]) = [Sigma][n = 1] [(-1)^(n
+  - 1)]/n ([zeta] - 1)^n. It is to be remarked that it is impossible for
+  [zeta] while subject to |[zeta] - 1| < 1 to make a circuit about the
+  origin. For values of [zeta] for which |[zeta] - 1| [not less than] 1,
+  we can also calculate [lambda]([zeta]) with the help of infinite
+  series, utilizing the fact that [lambda]([zeta][zeta]') =
+  [lambda]([zeta]) + [lambda]([zeta]').
+
+  The function [lambda]([zeta]) is required to define [zeta]^a when
+  [zeta] and a are complex numbers; this is defined as exp
+  [a[lambda]([zeta])], that is as [Sigma] (n=0) a^n[[lambda]
+  ([zeta])]^n/n!. When a is a real integer the ambiguity of
+  [lambda]([zeta]) is immaterial here, since exp [a[lambda]([zeta]) +
+  2ka[pi]i] = exp[a[lambda]([zeta])]; when a is of the form 1/q, where q
+  is a positive integer, there are q values possible for [zeta]^(1/q),
+  of the form exp [1/q [lambda]([zeta])] exp(2k[pi]i/q), with k = 0, 1,
+  ... q - 1, all other values of k leading to one of these; the qth
+  power of any one of these values is [zeta]; when a = p/q, where p, q
+  are integers without common factor, q being positive, we have
+  [zeta]^(p/q) = ([zeta]^(1/q))^p. The definition of the symbol [zeta]^a
+  is thus a generalization of the ordinary definition of a power, when
+  the numbers are real. As an example, let it be required to find the
+  meaning of i^i; the number i is of modulus unity and phase ½[pi]; thus
+  [lambda](i) = i(½[pi] + 2k[pi]); thus
+
+    i^i = exp(-½[pi] - 2k[pi]) = exp(-½[pi]) exp(-2k[pi]),
+
+  is always real, but has an infinite number of values.
+
+  The function exp (z) is used also to define a generalized form of the
+  cosine and sine functions when z is complex; we write, namely, cos z =
+  ½[exp(iz) + exp(-iz)] and sin z = -½i[exp(iz) - exp(-iz)]. It will be
+  found that these obey the ordinary relations holding when z is real,
+  except that their moduli are not inferior to unity. For example, cos i
+  = 1 + ½! + ¼! + ... is obviously greater than unity.
+
+§4. _Of Functions of a Complex Variable in General._--We have in what
+precedes shown how to generalize the ordinary rational, algebraic and
+logarithmic functions, and considered more general cases, of functions
+expressible by power series in z. With the suggestions furnished by
+these cases we can frame a general definition. So far our use of the
+plane upon which z is represented has been only illustrative, the
+results being capable of analytical statement. In what follows this
+representation is vital to the mode of expression we adopt; as then the
+properties of numbers cannot be ultimately based upon spatial
+intuitions, it is necessary to indicate what are the geometrical ideas
+requiring elucidation.
+
+  Consider a square of side a, to whose perimeter is attached a definite
+  direction of description, which we take to be counter-clockwise;
+  another square, also of side a, may be added to this, so that there is
+  a side common; this common side being erased we have a composite
+  region with a definite direction of perimeter; to this a third square
+  of the same size may be attached, so that there is a side common to it
+  and one of the former squares, and this common side may be erased. If
+  this process be continued any number of times we obtain a region of
+  the plane bounded by one or more polygonal closed lines, no two of
+  which intersect; and at each portion of the perimeter there is a
+  definite direction of description, which is such that the region is on
+  the left of the describing point. Similarly we may construct a region
+  by piecing together triangles, so that every consecutive two have a
+  side in common, it being understood that there is assigned an upper
+  limit for the greatest side of a triangle, and a lower limit for the
+  smallest angle. In the former method, each square may be divided into
+  four others by lines through its centre parallel to its sides; in the
+  latter method each triangle may be divided into four others by lines
+  joining the middle points of its sides; this halves the sides and
+  preserves the angles. When we speak of a _region_ of the plane in
+  general, unless the contrary is stated, we shall suppose it capable of
+  being generated in this latter way by means of a finite number of
+  triangles, there being an upper limit to the length of a side of the
+  triangle and a lower limit to the size of an angle of the triangle. We
+  shall also require to speak of a _path_ in the plane; this is to be
+  understood as capable of arising as a limit of a polygonal path of
+  finite length, there being a definite direction or sense of
+  description at every point of the path, which therefore never meets
+  itself. From this the meaning of a closed path is clear. The boundary
+  points of a region form one or more closed paths, but, in general, it
+  is only in a limiting sense that the interior points of a closed path
+  are a region.
+
+  There is a logical principle also which must be referred to. We
+  frequently have cases where, about every interior or boundary, point
+  z0 of a certain region a circle can be put, say of radius r0, such
+  that for all points z of the region which are interior to this circle,
+  for which, that is, |z - z0| < r0, a certain property holds. Assuming
+  that to r0 is given the value which is the upper limit for z0, of the
+  possible values, we may call the points |z - z0| < r0, the
+  neighbourhood belonging to or _proper_ to z0, and may speak of the
+  property as the property (z, z0). The value of r0 will in general vary
+  with z0; what is in most cases of importance is the question whether
+  the lower limit of r0 for all positions is zero or greater than zero.
+  (A) This lower limit is certainly greater than zero provided the
+  property (z, z0) is of a kind which we may call extensive; such,
+  namely, that if it holds, for some position of z0 and all positions of
+  z, within a certain region, then the property (z, z1) holds within a
+  circle of radius R about any interior point z1 of this region for all
+  points z for which the circle |z - z1| = R is within the region. Also
+  in this case r0 varies continuously with z0. (B) Whether the property
+  is of this extensive character or not we can prove that the region can
+  be divided into a finite number of sub-regions such that, for every
+  one of these, the property holds, (1) for _some_ point z0 within or
+  upon the boundary of the sub-region, (2) for _every_ point z within or
+  upon the boundary of the sub-region.
+
+  We prove these statements (A), (B) in reverse order. To prove (B) let
+  a region for which the property (z, z0) holds for all points z and
+  some point z0 of the region, be called _suitable_: if each of the
+  triangles of which the region is built up be suitable, what is desired
+  is proved; if not let an unsuitable triangle be subdivided into four,
+  as before explained; if one of these subdivisions is unsuitable let it
+  be again subdivided; and so on. Either the process terminates and then
+  what is required is proved; or else we obtain an indefinitely
+  continued sequence of unsuitable triangles, each contained in the
+  preceding, which converge to a point, say [zeta]; after a certain
+  stage all these will be interior to the proper region of [zeta]; this,
+  however, is contrary to the supposition that they are all unsuitable.
+
+  We now make some applications of this result (B). Suppose a definite
+  finite real value attached to every interior or boundary point of the
+  region, say [f](x, y). It may have a finite upper limit H for the
+  region, so that no point (x, y) exists for which [f](x, y) > H, but
+  points (x, y) exist for which [f](x, y) > H - [epsilon], however small
+  [epsilon] may be; if not we say that its upper limit is infinite.
+  There is then at least one point of the region such that, for points
+  of the region within a circle about this point, the upper limit of
+  [f](x, y) is H, however small the radius of the circle be taken; for
+  if not we can put about every point of the region a circle within
+  which the upper limit of [f](x, y) is less than H; then by the result
+  (B) above the region consists of a finite number of sub-regions within
+  each of which the upper limit is less than H; this is inconsistent
+  with the hypothesis that the upper limit for the whole region is H. A
+  similar statement holds for the lower limit. A case of such a function
+  [f](x, y) is the radius r0 of the neighbourhood proper to any point
+  z0, spoken of above. We can hence prove the statement (A) above.
+
+  Suppose the property (z, z0) extensive, and, if possible, that the
+  lower limit of r0 is zero. Let then [zeta] be a point such that the
+  lower limit of r0 is zero for points z0 within a circle about [zeta]
+  however small; let r be the radius of the neighbourhood proper to
+  [zeta]; take z0 so that |z0 - [zeta]| < ½r; the property (z, z0),
+  being extensive, holds within a circle, centre z0, of radius r - |z0 -
+  [zeta]|, which is greater than |z0 - [zeta]|, and increases to r as
+  |z0 - [zeta]| diminishes; this being true for all points z0 near
+  [zeta], the lower limit of r0 is not zero for the neighbourhood of
+  [zeta], contrary to what was supposed. This proves (A). Also, as is
+  here shown that r0 [ = >] r - |z0-[zeta]|, may similarly be shown that
+  r [=>] r0 - |z0 - [zeta]|. Thus r0 differs arbitrarily little from r
+  when |z0-[zeta]| is sufficiently small; that is, r0 varies
+  continuously with z0. Next suppose the function [f](x, y), which has a
+  definite finite value at every point of the region considered, to be
+  continuous but not necessarily real, so that about every point z0,
+  within or upon the boundary of the region, [eta] being an arbitrary
+  real positive quantity assigned beforehand, a circle is possible, so
+  that for all points z of the region interior to this circle, we have
+  |[f](x, y) - [f](x0, y0)| < ½[eta], and therefore (x', y') being any
+  other point interior to this circle, |[f](x', y') - [f](x, y)| <
+  [eta]. We can then apply the result (A) obtained above, taking for the
+  neighbourhood proper to any point z0 the circular area within which,
+  for any two points (x, y), (x', y'), we have |[f](x', y') - [f](x, y)|
+  < [eta]. This is clearly an extensive property. Thus, a number r is
+  assignable, greater than zero, such that, for any two points (x, y),
+  (x', y') within a circle |z - z0| = r about any point z0, we have
+  |[f](x', y') - [f](x, y)| < [eta], and, in particular, |[f](x, y) -
+  [f](x0, y0)| < [eta], where [eta] is an arbitrary real positive
+  quantity agreed upon beforehand.
+
+  Take now any path in the region, whose extreme points are z0, z, and
+  let z1, ... z_(n - 1) be intermediate points of the path, in order;
+  denote the continuous function [f](x, y) by [f](z), and let [f]_r
+  denote any quantity such that |[f]_r - [f](z_r)| [=<] |[f](z_(r + 1))
+  - [f](z_r)|; consider the sum
+
+    (z1 - z0)[f]0 + (z2 - z1)[f]1 + ... + (z - z_(n - 1))[f](n - 1).
+
+  By the definition of a path we can suppose, n being large enough, that
+  the intermediate points z1, ... z_(n - 1) are so taken that if z_i,
+  z_(i + 1) be any two points intermediate, in order, to z_r and z_(r +
+  1), we have |z_(i + i) - z_i| < |z_(r + 1) - z_r|; we can thus suppose
+  |z1 - z0|, |z2 - z1|, ... |z - z_(n - 1)|all to converge constantly
+  to zero. This being so, we can show that the sum above has a definite
+  limit. For this it is sufficient, as in the case of an integral of a
+  function of one real variable, to prove this to be so when the
+  convergence is obtained by taking new points of division intermediate
+  to the former ones. If, however, z_(r, 1), z_(r, 2), ... z_(r, m - 1)
+  be intermediate in order to z_r and z_(r + 1), and |[f]_(r, i) -
+  [f](z_(r, i))| < |[f](z_(r, i + 1)) - [f](z_(r, i))|, the difference
+  between [Sigma](z_(r + 1) - z_r)[f]_r and
+
+    [Sigma]{(z_(r, 1) - z_r)[f]_(r, 0) + (z_(r, 2) - z{r, 1})[f]_(r, 1)
+      + ... + (z_(r + 1) - z_(r, m - 1))[f]_(r, m - 1)},
+
+  which is equal to
+
+    [Sigma]_r [Sigma]_i (z_(r, i + 1) - z_(r, i))([f]_(r, i) - [f]_r),
+
+  is, when |z_(r + 1) - z_r| is small enough, to ensure |[f](z_(r +
+  1)) - [f](z_r)| < [eta], less in absolute value than
+
+    [Sigma]2[eta] [Sigma] |z_(r, i + 1) - z{r, i}|,
+
+  which, if S be the upper limit of the perimeter of the polygon from
+  which the path is generated, is < 2[eta]S, and is therefore
+  arbitrarily small.
+
+  The limit in question is called [int](z_0 to z) [f](z)dz. In
+  particular when [f](z) = 1, it is obvious from the definition that its
+  value is z - z0; when [f](z) = z, by taking [f]_r = ½(z_(r + 1) -
+  z_r), it is equally clear that its value is ½(z² - z0²); these results
+  will be applied immediately.
+
+  Suppose now that to every interior and boundary point z0 of a certain
+  region there belong two definite finite numbers [f](z0), F(z0), such
+  that, whatever real positive quantity [eta] may be, a real positive
+  number [epsilon] exists for which the condition
+
+    | [f](z) - [f](z0)         |
+    | ---------------- - F(z0) | < [eta],
+    |      z-z0                |
+
+  which we describe as the condition (z, z0), is satisfied for every
+  point z, within or upon the boundary of the region, satisfying the
+  limitation |z - z0| < [epsilon]. Then [f](z0) is called a
+  differentiable function of the complex variable z0 over this region,
+  its differential coefficient being F(z0). The function [f](z0) is thus
+  a continuous function of the real variables x0, y0, where z0 = x0 +
+  iy0, over the region; it will appear that F(z0) is also continuous and
+  in fact also a differentiable function of z0.
+
+  Supposing [eta] to be retained the same for all points z0 of the
+  region, and [sigma]0 to be the upper limit of the possible values of
+  [epsilon] for the point z0, it is to be presumed that [sigma]0 will
+  vary with z0, and it is not obvious as yet that the lower limit of the
+  values of [sigma]0 as z0 varies over the region may not be zero. We
+  can, however, show that the region can be divided into a finite number
+  of sub-regions for each of which the condition (z, z0), above, is
+  satisfied for all points z, within or upon the boundary of this
+  sub-region, for an appropriate position of z0, within or upon the
+  boundary of this sub-region. This is proved above as result (B).
+
+  Hence it can be proved that, for a differentiable function [f](z), the
+  integral [int](z_1 to z) [f](z)dz has the same value by whatever path
+  within the region we pass from z1 to z. This we prove by showing that
+  when taken round a closed path in the region the integral
+  [int][f](z)dz vanishes. Consider first a triangle over which the
+  condition (z, z0) holds, for some position of z0 and every position of
+  z, within or upon the boundary of the triangle. Then as
+
+    [f](z) = [f](z0) + (z - z0)F(z0) + [eta][theta](z - z0), where |[theta]| < 1,
+
+  we have
+      _                               _           _            _
+     /                               /           /            /
+     |[f](z)dz = [[f](z0) - z0F(z0)] |dz + F(z0) |zdz + [eta] |[theta](z - z0)dz,
+    _/                              _/          _/           _/
+
+  which, as the path is closed, is [eta] [int][theta](z-z0)dz. Now, from
+  the theorem that the absolute value of a sum is less than the sum of
+  the absolute values of the terms, this last is less, in absolute
+  value, than [eta]ap, where a is the greatest side of the triangle and
+  p is its perimeter; if [Delta] be the area of the triangle, we have
+  [Delta] = ½ab sin C > ([alpha]/[pi])ba, where [alpha] is the least
+  angle of the triangle, and hence a(a + b + c) < 2a(b + c) <
+  4[pi][Delta]/[alpha]; the integral [int][f](z)dz round the perimeter
+  of the triangle is thus < 4[pi][eta][Delta]/[alpha]. Now consider any
+  region made up of triangles, as before explained, in each of which the
+  condition (z, z0) holds, as in the triangle just taken. The integral
+  [int][f](z)dz round the boundary of the region is equal to the sum of
+  the values of the integral round the component triangles, and thus
+  less in absolute value than 4[pi][eta]K/[alpha], where K is the whole
+  area of the region, and [alpha] is the smallest angle of the component
+  triangles. However small [eta] be taken, such a division of the region
+  into a finite number of component triangles has been shown possible;
+  the integral round the perimeter of the region is thus arbitrarily
+  small. Thus it is actually zero, which it was desired to prove. Two
+  remarks should be added: (1) The theorem is proved only on condition
+  that the closed path of integration belongs to the region at every
+  point of which the conditions are satisfied. (2) The theorem, though
+  proved only when the region consists of triangles, holds also when the
+  boundary points of the region consist of one or more closed paths, no
+  two of which meet.
+
+  Hence we can deduce the remarkable result that the value of [f](z) at
+  any interior point of a region is expressible in terms of the value of
+  [f](z) at the boundary points. For consider in the original region the
+  function [f](z)/(z - z0), where z0 is an interior point: this
+  satisfies the same conditions as [f](z) except in the immediate
+  neighbourhood of z0. Taking out then from the original region a small
+  regular polygonal region with z0 as centre, the theorem holds for the
+  remaining portion. Proceeding to the limit when the polygon becomes a
+  circle, it appears that the integral [int] dz[f](z)/(z - z0) round the
+  boundary of the original region is equal to the same integral taken
+  counter-clockwise round a small circle having z0 as centre; on this
+  circle, however, if z - z0 = rE(i[theta]), dz/(z - z0) = id[theta],
+  and [f](z) differs arbitrarily little from f(z0) if r is sufficiently
+  small; the value of the integral round this circle is therefore,
+  ultimately, when r vanishes, equal to 2[pi]i[f](z0). Hence [f](z0) = 1
+  / 2[pi]i [int] [dt[f](t)/(t - z0)], where this integral is round the
+  boundary of the original region. From this it appears that
+                                             _
+                 [f](z) - [f](z0)     1     / dt[f](t)
+    F(z0) = lim. ---------------- = ------  | --------
+                      z - z0        2[pi]i _/  (t-z0)²
+
+  also round the boundary of the original region. This form shows,
+  however, that F(z0) is a continuous, finite, differentiable function
+  of z0 over the whole interior of the original region.
+
+§ 5. _Applications._--The previous results have manifold applications.
+
+  (1) If an infinite series of differentiable functions of z be
+  uniformly convergent along a certain path lying with the region of
+  definition of the functions, so that S(2) = u0(z) + u1(z) + ... + u_(n
+  - 1)(z) + R_n(z), where |R_n(z)| < [epsilon] for all points of the
+  path, we have
+      _           _            _                  _                   _
+     /z          /z           /z                 /z                  /z
+     |  S(z)dz = |  u0(z)dz + |  u1(z)dz + ... + |  u_(n - 1)(z)dz + |  R_n(z)dz,
+    _/z0        _/z0         _/z0               _/z0                _/z0
+
+  wherein, in absolute value, [int](z_0 to z) R_n(z)dz < [epsilon]L, if
+  L be the length of the path. Thus the series may be integrated, and
+  the resulting series is also uniformly convergent.
+
+  (2) If [f](x, y) be definite, finite and continuous at every point of
+  a region, and over any closed path in the region [int][f](x, y)dz = 0,
+  then [psi](z) = [int](z_0 to z) [f](x, y)dz, for interior points z0,
+  z, is a differentiable function of z, having for its differential
+  coefficient the function [f](x, y), which is therefore also a
+  differentiable function of z at interior points.
+
+  (3) Hence if the series u0(z) + u1(z) + ... to [oo] be uniformly
+  convergent over a region, its terms being differentiable functions of
+  z, then its sum S(z) is a differentiable function of z, whose
+  differential coefficient, given by (1 / 2[pi]i) [int] (2[pi]i /
+  (t - z)²), is obtainable by differentiating the series. This theorem,
+  unlike (1), does not hold for functions of a real variable.
+
+  (4) If the region of definition of a differentiable function [f](z)
+  include the region bounded by two concentric circles of radii r, R,
+  with centre at the origin, and z0 be an interior point of this region,
+                       _                     _
+                 1    /  [f](t)dt     1     / [f](t)dt
+    [f](z0) = ------  |  -------- - ------  | --------,
+              2[pi]i _/R  t - z0    2[pi]i _/r t - z0
+
+  where the integrals are both counter-clockwise round the two
+  circumferences respectively; putting in the first (t - z0)^(-1) =
+  [Sigma]_(n=0) z0^n/t^(n + 1), and in the second (t - z0)^(-1) =
+  [Sigma]_(n=0) t^n/z0^(n + 1), we find [f](z0) = [Sigma] (-[oo] to
+  [oo]) A_nz0^n, wherein A_n = (1 / 2[pi]i) [int] [f(t) / t^(n + 1)] dt,
+  taken round any circle, centre the origin, of radius intermediate
+  between r and R. Particular cases are: ([alpha]) when the region of
+  definition of the function includes the whole interior of the outer
+  circle; then we may take r = 0, the coefficients A_n for which n < 0
+  all vanish, and the function [f](z0) is expressed for the whole
+  interior |z0| < R by a power series [Sigma] (0 to [oo]) A_n z0^n. In
+  other words, _about every interior point c of the region of definition
+  a differentiable function of z is expressible by a power series in z -
+  c; a very important result.
+
+  (ß) If the region of definition, though not including the origin,
+  extends to within arbitrary nearness of this on all sides, and at the
+  same time the product z^m [f](z) has a finite limit when |z|
+  diminishes to zero, all the coefficients A_n for which n < -m vanish,
+  and we have
+
+    f(z0) = A_(-m) z0^(-m) + A_(-m + 1) z0^(-m + 1)
+      + ... + A_(-1) z0^(-1) + A0 + A1z0 ... to [oo].
+
+  Such a case occurs, for instance, when [f](z) = cosec z, the number m
+  being unity.
+
+§ 6. _Singular Points._--The _region of existence_ of a differentiable
+function of z is an unclosed aggregate of points, each of which is an
+interior point of a neighbourhood consisting wholly of points of the
+aggregate, at every point of which the function is definite and finite
+and possesses a unique finite differential coefficient. Every point of
+the plane, not belonging to the aggregate, which is a limiting point of
+points of the aggregate, such, that is, that points of the aggregate lie
+in every neighbourhood of this, is called a _singular point_ of the
+function.
+
+  About every interior point z0 of the region of existence the function
+  may be represented by a power series in z-z0, and the series converges
+  and represents the function over any circle centre at z0 which
+  contains no singular point in its interior. This has been proved
+  above. And it can be similarly proved, putting z = 1/[zeta], that if
+  the region of existence of the function contains all points of the
+  plane for which |z| > R, then the function is representable for all
+  such points by a power series in z^(-1) or [zeta]; in such case we say
+  that the region of existence of the function contains the point z =
+  [oo]. A series in z^(-1) has a finite limit when |z| = [oo]; a series
+  in z cannot remain finite for all points z for which |z| > R; for if,
+  for |z| = R, the sum of a power series [Sigma]a_n z^n in z is in
+  absolute value less than M, we have |a_n| < Mr(-n), and therefore, if
+  M remains finite for all values of r however great, a_n = 0. Thus the
+  region of existence of a function if it contains all finite points of
+  the plane cannot contain the point z = [oo]; such is, for instance,
+  the case of the function exp (z) = [Sigma]z^n/n!. This may be regarded
+  as a particular case of a well-known result (§ 7), that the
+  circumference of convergence of any power series representing the
+  function contains at least one singular point. As an extreme case
+  functions exist whose region of existence is circular, there being a
+  singular point in every arc of the circumference, however small; for
+  instance, this is the case for the functions represented for |z| < 1
+  by the series [Sigma]_(n=0) z^m, where m = n², the series
+  [Sigma]_(n=0) z^m where m = n!, and the series [Sigma](n=1 to 0)
+  z^m/(m + 1)(m + 2) where m = a^n, a being a positive integer, although
+  in the last case the series actually converges for every point of the
+  circle of convergence |z| = 1. If z be a point interior to the circle
+  of convergence of a series representing the function, the series may
+  be rearranged in powers of z - z0; as z0 approaches to a singular
+  point of the function, lying on the circle of convergence, the radii
+  of convergence of these derived series in z - z0 diminish to zero;
+  when, however, a circle can be put about z0, not containing any
+  singular point of the function, but containing points outside the
+  circle of convergence of the original series, then the series in z -
+  z0 gives the value of the function for these external points. If the
+  function be supposed to be given only for the interior of the original
+  circle, by the original power series, the series in z - z0 converging
+  beyond the original circle gives what is known as an _analytical
+  continuation_ of the function. It appears from what has been proved
+  that the value of the function at all points of its region of
+  existence can be obtained from its value, supposed given by a series
+  in one original circle, by a succession of such processes of
+  analytical continuation.
+
+§ 7. _Monogenic Functions._--This suggests an entirely different way of
+formulating the fundamental parts of the theory of functions of a
+complex variable, which appears to be preferable to that so far followed
+here.
+
+  Starting with a convergent power series, say in powers of z, this
+  series can be arranged in powers of z - z0, about any point z0
+  interior to its circle of convergence, and the new series converges
+  certainly for |z - z0| < r - |z0|, if r be the original radius of
+  convergence. If for every position of z0 this is the greatest radius
+  of convergence of the derived series, then the original series
+  represents a function existing only within its circle of convergence.
+  If for some position of z0 the derived series converges for |z - z0| <
+  r - |z0| + D, then it can be shown that for points z, interior to the
+  original circle, lying in the annulus r - |z0| < |z - z0| < r - |z0| +
+  D, the value represented by the derived series agrees with that
+  represented by the original series. If for another point z1 interior
+  to the original circle the derived series converges for |z - z1| < r -
+  |z1| + E, and the two circles |z - z0| = r - |z0| + D, |z - z1| = r -
+  |z1| + E have interior points common, lying beyond |z| = r, then it
+  can be shown that the values represented by these series at these
+  common points agree. Either series then can be used to furnish an
+  analytical continuation of the function as originally defined.
+  Continuing this process of continuation as far as possible, we arrive
+  at the conception of the function as defined by an aggregate of power
+  series of which every one has points of convergence common with some
+  one or more others; the whole aggregate of points of the plane which
+  can be so reached constitutes the region of existence of the function;
+  the limiting points of this region are the points in whose
+  neighbourhood the derived series have radii of convergence diminishing
+  indefinitely to zero; these are the singular points. The circle of
+  convergence of any of the series has at least one such singular point
+  upon its circumference. So regarded the function is called a
+  _monogenic_ function, the epithet having reference to the single
+  origin, by one power series, of the expressions representing the
+  function; it is also sometimes called a _monogenic analytical_
+  function, or simply an _analytical_ function; all that is necessary to
+  define it is the value of the function and of all its differential
+  coefficients, at some one point of the plane; in the method previously
+  followed here it was necessary to suppose the function differentiable
+  at every point of its region of existence. The theory of the
+  integration of a monogenic function, and Cauchy's theorem, that
+  [int][f](z)dz = 0 over a closed path, are at once deducible from the
+  corresponding results applied to a single power series for the
+  interior of its circle of convergence. There is another advantage
+  belonging to the theory of monogenic functions: the theory as
+  originally given here applies in the first instance only to single
+  valued functions; a monogenic function is by no means necessarily
+  single valued--it may quite well happen that starting from a
+  particular power series, converging over a certain circle, and
+  applying the process of analytical continuation over a closed path
+  back to an interior point of this circle, the value obtained does not
+  agree with the initial value. The notion of basing the theory of
+  functions on the theory of power series is, after Newton, largely due
+  to Lagrange, who has some interesting remarks in this regard at the
+  beginning of his _Théorie des fonctions analytiques_. He applies the
+  idea, however, primarily to functions of a real variable for which the
+  expression by power series is only of very limited validity; for
+  functions of a complex variable probably the systematization of the
+  theory owes most to Weierstrass, whose use of the word monogenic is
+  that adopted above. In what follows we generally suppose this point of
+  view to be regarded as fundamental.
+
+§ 8. _Some Elementary Properties of Single Valued Functions._--A _pole_
+is a singular point of the function [f](z) which is not a singularity of
+the function 1/[f](z); this latter function is therefore, by the
+definition, capable of representation about this point, z0, by a series
+[[f](z)]^(-1 ) = [Sigma]a_n (z - z0)^n. If herein a0 is not zero we can
+hence derive a representation for [f](z) as a power series about z0,
+contrary to the hypothesis that z0 is a singular point for this
+function. Hence a0 = 0; suppose also a1 = 0, a2 = 0, ... a_(m - 1) = 0,
+but a_m ± 0. Then [[f](z)]^(-1) = (z - z0)^m [a_m + a_(m + 1)(z - z0) +
+...], and hence (z - z0)^m [f](z) = a_m^(-1) + [Sigma]b_n (z - z0)^n,
+namely, the expression of [f](z) about z = z0 contains a finite number
+of negative powers of z - z0 and a (finite or) infinite number of
+positive powers. Thus a pole is always an isolated singularity.
+
+  The integral [int][f](z)dz taken by a closed circuit about the pole
+  not containing any other singularity is at once seen to be 2[pi]iA1,
+  where A1 is the coefficient of (z - z0)^(-1) in the expansion of
+  [f](z) at the pole; this coefficient has therefore a certain
+  uniqueness, and it is called the _residue of [f](z) at the pole_.
+  Considering a region in which there are no other singularities than
+  poles, all these being interior points, _the integral (1 / 2[pi]i)
+  [int][f](z)dz round the boundary of this region is equal to the sum
+  of the residues at the included poles_, a very important result. Any
+  singular point of a function which is not a pole is called an
+  _essential singularity_; if it be isolated the function is capable, in
+  the neighbourhood of this point, of approaching arbitrarily near to
+  any assigned value. For, the point being isolated, the function can be
+  represented, in its neighbourhood, as we have proved, by a series
+  [Sigma] (-[oo] to [oo]) a_n(z - z0)^n; it thus cannot remain finite in
+  the immediate neighbourhood of the point. The point is necessarily an
+  isolated essential singularity also of the function {[f](z) - A}^(-1)
+  for if this were expressible by a power series about the point, so
+  would also the function [f](z) be; as {[f](z) - A}^(-1) approaches
+  infinity, so does [f](z) approach the arbitrary value A. Similar
+  remarks apply to the point z = [oo], the function being regarded as a
+  function of [zeta] = z^(-1). In the neighbourhood of an essential
+  singularity, which is a limiting point also of poles, the function
+  clearly becomes infinite. For an essential singularity which is not
+  isolated the same result does not necessarily hold.
+
+A single valued function is said to be an _integral_ function when it
+has no singular points except z = [oo]. Such is, for instance, an
+integral polynomial, which has z = [oo] for a pole, and the functions
+exp (z) which has z = [oo] as an essential singularity. A function which
+has no singular points for finite values of z other than poles is called
+a _meromorphic_ function. If it also have a pole at z = [oo] it is a
+_rational_ function; for then, if a1, ... a_s be its finite poles, of
+orders m1; m2, ... m_s, the product (z - a1)^m1 ... (z - a_s)^m_s[f](z)
+is an integral function with a pole at infinity, capable therefore, for
+large values of z, of an expression (z^ - 1)^(-m) [Sigma]_(r=0) a_r(z^ -
+1)^r; thus (z - a1)^m1 ... (z - a_s)^m_s[f](z) is capable of a form
+[Sigma]_(r=0) b_r z^r, but z^(-m) [Sigma]_(r=0) b_r z^r remains finite
+for z = [oo]. Therefore b_(r + 1) = b_(r + 2) = ... = 0, and[f](z) is a
+rational function.
+
+  If for a single valued function F(z) every singular point in the
+  finite part of the plane is isolated there can only be a finite number
+  of these in any finite part of the plane, and they can be taken to be
+  a1, a2, a3, ... with |a1| [=<] |a2| [=<] |a3| ... and limit |a_n| =
+  [oo]. About a_s the function is expressible as [Sigma] (-[oo] to [oo])
+  A_n(z - a_s)^n; let [f]_s(z) = [Sigma] (-[oo] to 1) A^n(z - a_s)^n be
+  the sum of the negative powers in this expansion. Assuming z = 0 not
+  to be a singular point, let [f]_s(z) be expanded in powers of z, in
+  the form [Sigma]_(n=0) C_n z^n, and µ_s be chosen so that F_s(z) =
+  [f]_s(z) - [Sigma] (1 to µ_s-1) C_nz^n = [Sigma] (µ_s to [oo]) C_n z^n
+  is, for |z| < r_s < |a_s|, less in absolute value than the general
+  term [epsilon]_s of a fore-agreed convergent series of real positive
+  terms. Then the series [phi](z) = [Sigma] (s=1 to [oo]) F_s(z)
+  converges uniformly in any finite region of the plane, other than at
+  the points a_s, and is expressible about any point by a power series,
+  and near a_s, [phi](z) - f_s(z) is expressible by a power series in
+  z-a_s. Thus F(z) - [phi](z) is an integral function. In particular
+  when all the finite singularities of F(z) are poles, F(z) is hereby
+  expressed as the sum of an integral function and a series of rational
+  functions. The condition |F_s(z)| < [epsilon]_s is imposed only to
+  render the series [Sigma]F_s(z) uniformly convergent; this condition
+  may in particular cases be satisfied by a series [Sigma] G_s(z) where
+  G_s(z) = [f]_s(z) - [Sigma] (1 to [nu]_s-1) C_nz^n and [nu]_s < µ_s.
+  An example of the theorem is the function [pi] cot [pi]z - z^(-1) for
+  which, taking at first only half the poles, [f]_s(z) = 1/(z-s); in
+  this case the series [Sigma]F_s(z) where F_s(z) = (z - s)^-1 + s^-1 is
+  uniformly convergent; thus [pi]cot[pi]z - z^-1 - [Sigma] (-[oo] to
+  [oo]) [(z - s)^-1 + s^-1], where s = 0 is excluded from the summation,
+  is an integral function. It can be proved that this integral function
+  vanishes.
+
+  Considering an integral function [f](z), if there be no finite
+  positions of z for which this function vanishes, the function
+  [lambda][[f](z)] is at once seen to be an integral function, [phi](z),
+  or [f](z) = exp[[phi](z)]; if however great R may be there be only a
+  finite number of values of z for which [f](z) vanishes, say z = a1,
+  ... a_m, then it is at once seen that [f](z) = exp [[phi](z)].(z -
+  a1)^h1...(z - a_m)^h_m, where [phi](z) is an integral function, and
+  h1, ... h_m are positive integers. If, however, [f](z) vanish for z =
+  a1, a2 ... where |a1| [=<] |a2| [=<] ... and limit |a_n| = [oo], and
+  if for simplicity we assume that z - 0 is not a zero and all the zeros
+  a1, a2, ... are of the first order, we find, by applying the preceding
+  theorem to the function (1 / [f](z)) (d[f](z) / dz), that [f](z) =
+  exp[[phi](z)] [Pi] (n=1 to [oo]) {(1 - z/a_n) exp[phi]_n(z)}, where
+  [phi](z) is an integral function, and [phi]_n(z) is an integral
+  polynomial of the form
+
+                  z      z²            z^s
+    [phi]_n(z) = --- + ----- + ... + ------.
+                 a_n   2a²_n         sa_n^s
+
+  The number s may be the same for all values of n, or it may increase
+  indefinitely with n; it is sufficient in any case to take s = n. In
+  particular for the function sin[pi]x / [pi]x, we have
+                         _                      _
+    sin[pi]x      [oo]  |  /    x \       / x \  |
+    -------- = [Pi]     | ( 1 - -- ) exp (  -- ) |,
+     [pi]x       -[oo]  |_ \    n /       \ n / _|
+
+  where n = 0 is excluded from the product. Or again we have
+                                 _                       _
+        1                  [oo] |  /    x \       /  x \  |
+    ---------- = xe^C_x [Pi]    | ( 1 - -- ) exp ( - -- ) |,
+    [Gamma](x)             n=1  |_ \    n /       \  n / _|
+
+  where C is a constant, and [Gamma](x) is a function expressible when x
+  is real and positive by the integral [int] (0 to [oo])
+  e^(-t) t^(x - 1)dt.
+
+  There exist interesting investigations as to the connexion of the
+  value of s above, the law of increase of the modulus of the integral
+  function [f](z), and the law of increase of the coefficients in the
+  series [f](z) = [Sigma] a_n z^n as n increases (see the bibliography
+  below under _Integral Functions_). It can be shown, moreover, that an
+  integral function actually assumes every finite complex value, save,
+  in exceptional cases, one value at most. For instance, the function
+  exp (z) assumes every finite value except zero (see below under § 21,
+  _Modular Functions_).
+
+The two theorems given above, the one, known as Mittag-Leffler's
+theorem, relating to the expression as a sum of simpler functions of a
+function whose singular points have the point z = [oo] as their only
+limiting point, the other, Weierstrass's factor theorem, giving the
+expression of an integral function as a product of factors each with
+only one zero in the finite part of the plane, may be respectively
+generalized as follows:--
+
+  I. If a1, a2, a3, ... be an infinite series of isolated points having
+  the points of the aggregate (c) as their limiting points, so that in
+  any neighbourhood of a point of (c) there exists an infinite number of
+  the points a1, a2, ..., and with every point a_i there be associated a
+  polynomial in (z - a_i)^-1, say g_i; then there exists a single valued
+  function whose region of existence excludes only the points (a) and
+  the points (c), having in a point a_i a pole whereat the expansion
+  consists of the terms g_i, together with a power series in z - a_i;
+  the function is expressible as an infinite series of terms g_i -
+  [gamma]_i, where [gamma]_i is also a rational function.
+
+  II. With a similar aggregate (a), with limiting points (c), suppose
+  with every point a_i there is associated a positive integer r_i. Then
+  there exists a single valued function whose region of existence
+  excludes only the points (c), vanishing to order r_i at the point a_i,
+  but not elsewhere, expressible in the form
+
+       [oo] /    a_n - c_n \^r_n
+    [Pi]   ( 1 - ---------  )    exp(g_n),
+       n=1  \     z - c_n  /
+
+  where with every point a_n is associated a proper point c_n of (c),
+  and
+
+                _ µ_n
+               \       1  / a_n - c_n \^s
+    g_n = r_n  /_     -- (  ---------  ),
+                  s=1  s  \  z - c_n  /
+
+  µ_n being a properly chosen positive integer.
+
+  If it should happen that the points (c) determine a path dividing the
+  plane into separated regions, as, for instance, if a_n = R(1 - n^-1)
+  exp(i[pi] [root]2·n), when (c) consists of the points of the circle
+  |z| = R, the product expression above denotes different monogenic
+  functions in the different regions, not continuable into one another.
+
+§ 9. _Construction of a Monogenic Function with a given Region of
+Existence._--A series of isolated points interior to a given region can
+be constructed in infinitely many ways whose limiting points are the
+boundary points of the region, or are boundary points of the region of
+such denseness that one of them is found in the neighbourhood of every
+point of the boundary, however small. Then the application of the last
+enunciated theorem gives rise to a function having no singularities in
+the interior of the region, but having a singularity in a boundary point
+in every small neighbourhood of every boundary point; this function has
+the given region as region of existence.
+
+§ 10. _Expression of a Monogenic Function by means of Rational Functions
+in a given Region._--Suppose that we have a region R0 of the plane, as
+previously explained, for all the interior or boundary points of which z
+is finite, and let its boundary points, consisting of one or more closed
+polygonal paths, no two of which have a point in common, be called C0.
+Further suppose that all the points of this region, including the
+boundary points, are interior points of another region R, whose boundary
+is denoted by C. Let z be restricted to be within or upon the boundary
+of C0; let a, b, ... be finite points upon C or outside R. Then when b
+is near enough to a, the fraction (a - b)/(z - b) is arbitrarily small
+for all positions of z; say
+
+  | a - b |
+  | ----- | < [epsilon], for |a - b| < [eta];
+  | z - b |
+
+the rational function of the complex variable t,
+         _                _
+    1   |     / a - b \^n  |
+  ----- |1 - (  -----  )   |,
+  t - a |_    \ t - b /   _|
+
+in which n is a positive integer, is not infinite at t = a, but has a
+pole at t = b. By taking n large enough, the value of this function, for
+all positions z of t belonging to R0, differs as little as may be
+desired from (t - a)^-1. By taking a sum of terms such as
+
+       _              _               _
+      \      {   1   |     / a - b \^n | }^p
+  F = /_ A_p { ----- |1 - (  -----  )  | },
+             { t - a |_    \ t - b /  _| }
+
+we can thus build a rational function differing, in value, in R0, as
+little as may be desired from a given rational function
+         _
+        \
+  [f] = /_ A_p (t - a)^(-p),
+
+and differing, outside R or upon the boundary of R, from [f], in the
+fact that while [f] is infinite at t = a, F is infinite only at t = b.
+By a succession of steps of this kind we thus have the theorem that,
+given a rational function of t whose poles are outside R or upon the
+boundary of R, and an arbitrary point c outside R or upon the boundary
+of R, which can be reached by a finite continuous path outside R from
+all the poles of the rational function, we can build another rational
+function differing in R0 arbitrarily little from the former, whose poles
+are all at the point c.
+
+  Now any monogenic function [f](t) whose region of definition includes
+  C and the interior of R can be represented at all points z in R[0] by
+                      _
+               1     /  [f](t)dt
+    [f](z) = ------  |  --------,
+             2[pi]i _/   t - z
+
+  where the path of integration is C. This integral is the limit of a
+  sum
+                _
+          1    \  [f](t_i) (t_(i + 1) - t_i)
+    S = ------ /_ --------------------------,
+        2[pi]i             t_i - z
+
+  where the points t_i are upon C; and the proof we have given of the
+  existence of the limit shows that the sum S converges to [f](z)
+  uniformly in regard to z, when z is in R0, so that we can suppose,
+  when the subdivision of C into intervals t_(i + 1) - t_i, has been
+  carried sufficiently far, that
+
+    | S - [f](z) | < [epsilon],
+
+  for all points z of R0, where [epsilon] is arbitrary and agreed upon
+  beforehand. The function S is, however, a rational function of z with
+  poles upon C, that is external to R0. We can thus find a rational
+  function differing arbitrarily little from S, and therefore
+  arbitrarily little from [f](z), for all points z of R0, with poles at
+  arbitrary positions outside R0 which can be reached by finite
+  continuous curves lying outside R from the points of C.
+
+  In particular, to take the simplest case, if C0, C be simple closed
+  polygons, and [GAMMA] be a path to which C approximates by taking the
+  number of sides of C continually greater, we can find a rational
+  function differing arbitrarily little from [f](z) for all points of R0
+  whose poles are at one finite point c external to [GAMMA]. By a
+  transformation of the form t - c = r^-1, with the appropriate change
+  in the rational function, we can suppose this point c to be at
+  infinity, in which case the rational function becomes a polynomial.
+  Suppose [epsilon]1, [epsilon]2, ... to be an indefinitely continued
+  sequence of real positive numbers, converging to zero, and P_r to be
+  the polynomial such that, within C0, |P_r - [f](z)| < [epsilon]_r;
+  then the infinite series of polynomials
+
+    P1(z) + {P2(z) - P1(z)} + {P3(z) - P2(z)} + ...,
+
+  whose sum to n terms is P_n(z), converges for all finite values of z
+  and represents [f](z) within C0.
+
+  When C consists of a series of disconnected polygons, some of which
+  may include others, and, by increasing indefinitely the number of
+  sides of the polygons C, the points C become the boundary points
+  [Gamma] of a region, we can suppose the poles of the rational
+  function, constructed to approximate to [f](z) within R0, to be at
+  points of [Gamma]. A series of rational functions of the form
+
+    H1(z) + {H2(z) - H1(z)} + {H3(z) - H2(z)} + ...
+
+  then, as before, represents [f](z) within R0. And R0 may be taken to
+  coincide as nearly as desired with the interior of the region bounded
+  by [Gamma].
+
+§ 11. _Expression of (1 - z)^(-1) by means of Polynomials.
+Applications._--We pursue the ideas just cursorily explained in some
+further detail.
+
+  Let c be an arbitrary real positive quantity; putting the complex
+  variable [zeta] = [xi] + i[eta], enclose the points [zeta] = l, [zeta]
+  = 1 + c by means of (i.) the straight lines [eta] = ±a, from [xi] = l
+  to [xi] = 1 + c, (ii.) a semicircle convex to [zeta] = 0 of equation
+  ([xi] - 1)² + [eta]² = a², (iii.) a semicircle concave to [zeta] =
+  0 of equation ([xi] - 1 - c)² + [eta]² = a². The quantities c and a
+  are to remain fixed. Take a positive integer r so that 1/r (c/a) is
+  less than unity, and put [sigma] = 1/r (c/a). Now take
+
+    c1 = 1 + c/r, c2 = 1 + 2c/r, ... c_r = 1 + c;
+
+  if n1, n2, ... n_r, be positive integers, the rational function
+                _                      _
+        1      |     /    c1 - 1   \^n1 |
+    ---------- |1 - (  -----------  )   |
+    1 - [zeta] |_    \ c1 - [zeta] /   _|
+
+  is finite at [zeta] = 1, and has a pole of order n1 at [zeta] = c1;
+  the rational function
+                _                      _   _                     _
+         1     |     /    c1 - 1   \^n1 | |     /   c2 - c1  \^n2 |^n1
+    ---------- |1 - (  ------------ )   | |1 - (  ----------- )   |
+    1 - [zeta] |_    \ c1 - [zeta] /   _| |_    \ c2 - [zeta]/   _|
+
+  is thus finite except for [zeta] = c2, where it has a pole of order
+  n1n2; finally, writing
+
+           / c_s - c_(s-1) \^n_s
+    x_s = (  -------------  ),
+           \ c_s - [zeta]  /
+
+  the rational function
+
+    U = (1 - [zeta])^(-1) (1 - x1)(1 - x2)^n1 (1 - x3)^n1n2 ...
+      (1 - x_r)^(n1n2 ... n_(r - 1))
+
+  has a pole only at [zeta] = 1 + c, of order n1n2 ... n_r.
+
+  The difference (1 - [zeta])^(-1) - U is of the form (1 -
+  [zeta])^(-1)P, where P, of the form
+
+    1 - (1 - [rho]1)(1 - [rho]2)...(1 - [rho]_k),
+
+  in which there are equalities among [rho]1, [rho]2, ... [rho]_k, is of
+  the form
+
+    [Sigma][rho]1 - [Sigma][rho]1[rho]2 + [Sigma][rho]1[rho]2[rho]3 - ...;
+
+  therefore, if |r_i| = |[rho]_i|, we have
+
+    |P| < [Sigma]r1 + [Sigma]r1r2 + [Sigma]r1r2r3 + ... <
+      (1 + r1)(1 + r2)...(1 + r_k) - 1;
+
+  now, so long as [zeta] is without the closed curve above described
+  round [zeta] = 1, [zeta] = 1 + c, we have
+
+    |     1    |    1    |c_m - c_(m-1)|   c/r
+    |----------| < ---,  |-------------| < --- < [sigma],
+    |1 - [zeta]|    a    |c_m - [zeta] |    a
+
+  and hence
+
+    |(1 - [zeta])^(-1) - U| < a^(-1) {(1 + [sigma]^n1) (1 + [sigma]^n2)^n1
+      (1 + [sigma]^n3)^n1n2 ... (1 + [sigma]^n_r)^(n1n2 ... n_(r-1)) - 1}.
+
+  Take an arbitrary real positive [epsilon], and µ, a positive number,
+  so that [epsilon]^µ - 1 < [epsilon]a, then a value of n1 such that
+  [sigma]^n1 < µ/(1 + µ) and therefore [sigma]^n1 / (1 - [sigma]^n1 < µ,
+  and values for n2, n3 ... such that[sigma]^n2 < 1/n1 [sigma]²n1,
+  [sigma]^n3 < 1/n1n2 [sigma]^{3n1, ... [sigma]^n_r} < 1/(n1...n_(r -
+  1)} [sigma]^n_rn1; then, as 1 + x < e^x, we have |(-[zeta])^(-1) - U|
+  < a^-1 {exp([sigma]^n1 + n1[sigma]^n2 + n1n2[sigma]^n3 + ... +
+  n1n2...n_(r - 1)[sigma]^n_r) - 1}, and therefore less than
+
+    a^(-1) {exp([sigma]^n1 + [sigma]²n1 + ... + [sigma]^n_rn1) - 1},
+
+  which is less than
+        _                         _
+    1  |     /  [sigma]^n1  \      |
+    -- |exp ( -------------- ) - 1 |
+    a  |_    \1 - [sigma]^n1/     _|
+
+  and therefore less than [epsilon].
+
+  The rational function U, with a pole at [zeta] = 1 + c, differs
+  therefore from (1 - [zeta])^(-1), for all points outside the closed
+  region put about [zeta] = 1, [zeta] = l + c, by a quantity numerically
+  less than [epsilon]. So long as a remains the same, r and [sigma] will
+  remain the same, and a less value of [epsilon] will require at most an
+  increase of the numbers n1, n2, ... n_r; but if a be taken smaller it
+  may be necessary to increase r, and with this the complexity of the
+  function U.
+
+  Now put
+
+            c[zeta]               (c + 1)z
+    z = --------------,  [zeta] = --------;
+        c + 1 - [zeta]              c + z
+
+  thereby the points [zeta] = 0, 1, 1 + c become the points z = 0, 1,
+  [oo], the function (1 - z)^(-1) being given by (1-z)^(-1) = c(c +
+  1)^(-1)(1 - [zeta])^(-1) + (c + 1)^(-1); the function U becomes a
+  rational function of z with a pole only at z = [oo], that is, it
+  becomes a polynomial in z, say [(c + 1)/c]H - 1/c, where H is also a
+  polynomial in z, and
+                       _              _
+      1           c   |      1         |
+    ----- - H = ----- | ---------- - U |;
+    1 - z       c + 1 |_1 + [zeta]    _|
+
+  the lines [eta] = ±a become the two circles expressed, if z = x + iy,
+  by
+
+                      c(c + 1)
+    (x + c)² + y² = ± -------- y,
+                         a
+
+  the points ([eta] = 0, [xi] = 1 - a), ([eta] = 0, [xi] = 1 + c + a)
+  become respectively the points (y = 0, x = c(1 - a)/(c + a), (y = 0, x
+  = -c(l + c + a)/a), whose limiting positions for a = 0 are
+  respectively (y = 0, x = 1), (y = 0, x = -[oo]). The circle (x + c)² +
+  y² = c(c + 1)y/a can be written
+
+        (x + c)²  (x + c)^4
+    y = ------- + --------- {µ + [root][µ² - (x + c)²]}^(-2),
+          2µ         2µ
+
+  where µ = ½c(c + 1)/a; its ordinate y, for a given value of x, can
+  therefore be supposed arbitrarily small by taking a sufficiently
+  small.
+
+  We have thus proved the following result; taking in the plane of z any
+  finite region of which every interior and boundary point is at a
+  finite distance, however short, from the points of the real axis for
+  which 1 =< x =< [oo], we can take a quantity a, and hence, with an
+  arbitrary c, determine a number r; then corresponding to an arbitrary
+  [epsilon]_s, we can determine a polynomial P_s, such that, for all
+  points interior to the region, we have
+
+    |(1 - z^(-1)) - P_s| < [epsilon]_s;
+
+  thus the series of polynomials
+
+    P1 + (P2 - P1) + (P3 - P2) + ...,
+
+  constructed with an arbitrary aggregate of real positive numbers
+  [epsilon]1, [epsilon]2, [epsilon]3, ... with zero as their limit,
+  converges uniformly and represents (1-z)^(-1) for the whole region
+  considered.
+
+  § 12. _Expansion of a Monogenic Function in Polynomials, over a Star
+  Region._--Now consider any monogenic function [f](z) of which the
+  origin is not a singular point; joining the origin to any singular
+  point by a straight line, let the part of this straight line, produced
+  beyond the singular point, lying between the singular point and z =
+  [oo], be regarded as a barrier in the plane, the portion of this
+  straight line from the origin to the singular point being erased.
+  Consider next any finite region of the plane, whose boundary points
+  constitute a path of integration, in a sense previously explained, of
+  which every point is at a finite distance greater than zero from each
+  of the barriers before explained; we suppose this region to be such
+  that any line joining the origin to a boundary point, when produced,
+  does not meet the boundary again. For every point x in this region R
+  we can then write
+                    _
+                   /  dt     [f](t)
+    2[pi]i[f](x) = |  --  -----------,
+                  _/   t  1 - xt^(-1)
+
+  where [f](x) represents a monogenic branch of the function, in case it
+  be not everywhere single valued, and t is on the boundary of the
+  region. Describe now another region R0 lying entirely within R, and
+  let x be restricted to be within R0 or upon its boundary; then for any
+  point t on the boundary of R, the points z of the plane for which
+  zt^(-1) is real and positive and equal to or greater than 1, being
+  points for which |z| = |t| or |z| > |t|, are without the region R0,
+  and not infinitely near to its boundary points. Taking then an
+  arbitrary real positive [epsilon] we can determine a polynomial in
+  xt^(-1), say P(xt^(-1)), such that for all points x in R0 we have
+
+    |[1 - xt^(-1)]^(-1) - P[xt^(-1)]| < [epsilon];
+
+  the form of this polynomial may be taken the same for all points t on
+  the boundary of R, and hence, if E be a proper variable quantity of
+  modulus not greater than [epsilon],
+                     _                          _
+    |               / dt                |   |  / dt       |
+    |2[pi]i[f](x) - | --[f](t)P(xt^(-1))| = |  | --[f](t)E| <= [epsilon]LM,
+    |              _/  t                |   | _/  t       |
+
+  where L is the length of the path of integration, the boundary of R,
+  and M is a real positive quantity such that upon this boundary
+  |t^(-1)[f](t)| < M. If now
+
+    P(xt^(-1)) = c0 + c1xt^(-1) + ... + c_mx^mt^(-m),
+
+  and
+             _
+      1     /
+    ------  | t^(-r-1)[f](t)dt = µ_r,
+    2[pi]i _/
+
+  this gives
+
+    |[f](x) - {c0µ0 + c1µ1x + ... + c_mµ_mx^m}| =< [epsilon]LM/2[pi],
+
+  where the quantities µ0, µ1, µ2, ... are the coefficients in the
+  expansion of [f](x) about the origin.
+
+  If then an arbitrary finite region be constructed of the kind
+  explained, excluding the barriers joining the singular points of
+  [f](x) to x = [oo], it is possible, corresponding to an arbitrary real
+  positive number [sigma], to determine a number m, and a polynomial
+  Q(x), of order m, such that for all interior points of this region
+
+    |[f](x) - Q(x)| < [sigma].
+
+  Hence as before, within this region [f](x) can be represented by a
+  series of polynomials, converging uniformly; when [f](x) is not a
+  single valued function the series represents one branch of the
+  function.
+
+  The same result can be obtained without the use of Cauchy's integral.
+  We explain briefly the character of the proof. If a monogenic function
+  of t, [phi](t) be capable of expression as a power series in t-x about
+  a point x, for |t - x| =< [rho], and for all points of this circle
+  |[phi](t)| < g, we know that |[phi]^(n)(x)| < g[rho]^(-n)(n!). Hence,
+  taking |z| < 1/3[rho], and, for any assigned positive integer µ,
+  taking m so that for n > m we have (µ + n)^µ < (3/2)^n, we have
+
+    |[phi]^((µ + n))(x)z^n|   [phi]^(µ + n)(x)
+    |---------------------| < ----------------(µ + n)^(µ)|z|^n
+    |          n!         |       (µ + n)!
+
+              g        /3 \     /[rho]\           g
+      < ------------- ( -- )^n ( ----- )^n < -----------,
+        [rho]^(µ + n)  \2 /     \  3  /      [rho]^µ 2^n
+
+  and therefore
+
+                        _m
+                       \   [phi]^(µ + n)(x)
+    [phi]^(µ)(x + z) = /_  ---------------- z^n + [epsilon]_µ,
+                      n = 0       n!
+
+  where
+
+                         g       _[oo]  1         g
+    |[epsilon]_(µ)| < --------  \      --- < -----------
+                       [rho]^µ  /_     2^n   [rho]^µ 2^m
+                             n = m + 1
+
+  Now draw barriers as before, directed from the origin, joining the
+  singular point of [phi](z) to z = [oo], take a finite region excluding
+  all these barriers, let [rho] be a quantity less than the radii of
+  convergence of all the power series developments of [phi](z) about
+  interior points of this region, so chosen moreover that no circle of
+  radius [rho] with centre at an interior point of the region includes
+  any singular point of [phi](z), let g be such that |[phi](z)| < g for
+  all circles of radius [rho] whose centres are interior points of the
+  region, and, x being any interior point of the region, choose the
+  positive integer n so that 1/n |x| 1/3 - [rho]; then take the points
+  a1 = x/n, a2 = 2x/n, a3 = 3x/n, ... a_n = x; it is supposed that the
+  region is so taken that, whatever x may be, all these are interior
+  points of the region. Then by what has been said, replacing x, z
+  respectively by 0 and x/n, we have
+
+                         _m1   [phi]^(µ + [lambda]1)(0)  /x \^[lambda]1
+    [phi]^(µ)  (a{1}) = \      ------------------------ ( -- ) + [alpha]_µ
+                        /_            [lambda]{1}!       \n /
+                   [lambda]1 = 0
+
+  with
+
+    |[alpha]{µ}| < g/[rho]^µ 2^m1,
+
+  provided (µ + m1 + 1)^µ < (3/2)^(m1+1); in fact for µ =< 2n^(2n-2) it
+  is sufficient to take m1 = n^2n; by another application of the same
+  inequality, replacing x, z respectively by a1 and x/n, we have
+
+                      _ m2   [phi]^(µ+[lambda]2)(a1)  /x \^[lambda]2
+    [phi]^(µ)(a2) =  \       ----------------------- ( -- )   + ß'_µ,
+                     /_            [lambda]{2}!       \n /
+                [lambda]2 = 0
+
+  where
+
+    |ß'µ| < g/[rho]^µ 2^m2
+
+  provided (µ + m2 + 1)^µ < {3/2}^(m2 + 1); we take m2 = n^(2n - 2),
+  supposing µ < 2^(2n - 4). So long as [lambda]2 =< = m} =< n^(2n - 2)
+  and µ < 2n^(2n - 4) we have µ + [lambda]{2} < 2n^(2n - 2), and we can
+  use the previous inequality to substitute here for [phi]^(µ +
+  [lambda]2) (a1). When this is done we find
+
+                      _ m2         _ m1 [phi]^(µ + [lambda]1 + [lambda]2)(0)
+    [phi]^(µ)(a2) =  \            \     ------------------------------------
+                     /_           /_            [lambda]1! [lambda]2!
+                [lambda]2=0  [lambda]1=0
+
+       /x \ ^[lambda]1 + [lambda]2
+      ( -- )                       + ß_µ,
+       \n /
+
+  where |ß_µ| < 2g/[rho]^µ 2^(m2), the numbers m1, m2 being respectively
+  n^2n and n^(2n - 2).
+
+  Applying then the original inequality to [phi]^(µ) (a3) = [phi]^(µ)
+  (a2 + x/n), and then using the series just obtained, we find a series
+  for [phi]^(µ) (a3). This process being continued, we finally obtain
+
+                _ m1        _ m2           _ m_n
+    [phi](x) = \            \       ...   \         [phi]^(h)(0) /x \^h
+               /_           /_            /_        ----------- ( -- ) + [epsilon],
+         [lambda]1=0  [lambda]2=0   [lambda]_n=0         K       \n /
+
+  where h = [lambda]1 + [lambda]2 + ... + [lambda]_n , K = [lambda]1!
+  [lambda]2! ... [lambda]_n!, m1 = n^(2n), m1 = n^(2n - 2), ... , m1 =
+  n², |[epsilon]| < 2g/2^(m_n).
+
+  By this formula [phi](x) is represented, with any required degree of
+  accuracy, by a polynomial, within the region in question; and thence
+  can be expressed as before by a series of polynomials converging
+  uniformly (and absolutely) within this region.
+
+§ 13. _Application of Cauchy's Theorem to the Determination of Definite
+Integrals._--Some reference must be made to a method whereby real
+definite integrals may frequently be evaluated by use of the theorem of
+the vanishing of the integral of a function of a complex variable round
+a contour within which the function is single valued and non singular.
+
+  We are to evaluate an integral [int][a to b] [f](x)dx; we form a
+  closed contour of which the portion of the real axis from x = a to x =
+  b forms a part, and consider the integral [int][f](z)dz round this
+  contour, supposing that the value of this integral can be determined
+  along the curve forming the completion of the contour. The contour
+  being supposed such that, within it, [f](z) is a single valued and
+  finite function of the complex variable z save at a finite number of
+  isolated interior points, the contour integral is equal to the sum of
+  the values of [int][f](z)dz taken round these points. Two instances
+  will suffice to explain the method. (1) The integral [int][0 to [oo]]
+  (tan x)/x dx is convergent if it be understood to mean the limit when
+  [epsilon], [zeta], [sigma], ... all vanish of the sum of the integrals
+
+      _½[pi]-[epsilon]           _(3/2)[pi]-[zeta]            _(5/2)[pi]-[sigma]
+     /                tan x     /                  tan x     /                  tan x
+     |                ----- dx, |                  ----- dx, |                  ----- dx, ...
+    _/ 0                x      _/½[pi]+[epsilon]     x      _/(3/2)[pi]+[zeta]    x
+
+  Now draw a contour consisting in part of the whole of the positive and
+  negative real axis from x = -n[pi] to x = + n[pi], where n is a
+  positive integer, broken by semicircles of small radius whose centres
+  are the points x = ±½[pi], x = ±¾[pi], ... , the contour containing
+  also the lines x = n[pi] and x = -n[pi] for values of y between 0 and
+  n[pi] tan [alpha], where [alpha] is a small fixed angle, the contour
+  being completed by the portion of a semicircle of radius n[pi] sec
+  [alpha] which lies in the upper half of the plane and is terminated at
+  the points x = ±n[pi], y = n[pi] tan [alpha]. Round this contour the
+  integral [int](tan z /z) dz has the value zero. The contributions to
+  this contour integral arising from the semicircles of centres -½(2s -
+  1)[pi], + ½(2s - 1)[pi], supposed of the same radius, are at once seen
+  to have a sum which ultimately vanishes when the radius of the
+  semicircles diminishes to zero. The part of the contour lying on the
+  real axis gives what is meant by 2 [int][0 to n[pi]](tan x / x) dx.
+  The contribution to the contour integral from the two straight
+  portions at x = ±n[pi] is
+
+      _n[pi] tan [alpha]
+     /                   /  tan iy        tan iy   \
+     |              idy ( ---------- - -----------  )
+    _/ 0                 \n[pi] + iy   -n[pi] + iy /
+
+  where i tan iy, = -[exp(y) - exp(-y)]/[exp(y) + exp(-y)], is a real
+  quantity which is numerically less than unity, so that the
+  contribution in question is numerically less than
+
+      _n[pi] tan [alpha]
+     /                    2n[pi]
+     |              dy ------------, that is than 2[alpha].
+    _/ 0               n²[pi]² + y²
+
+  Finally, for the remaining part of the contour, for which, with R =
+  n[pi] sec [alpha], we have z = R(cos [theta] + i sin [theta]) =
+  RE(i[theta]), we have
+
+    dz
+    -- = id[theta], i tan z =
+    z
+
+      exp(-R sin [theta]) E(iR cos [theta]) - exp(R sin [theta]) E(-iR cos [theta])
+      -----------------------------------------------------------------------------;
+      exp(-R sin [theta]) E(iR cos [theta]) + exp(R sin [theta]) E(-iR cos [theta])
+
+  when n and therefore R is very large, the limit of this contribution
+  to the contour integral is thus
+       _
+      / [pi]-[alpha]
+    - |             d[theta] = -([pi] - 2[alpha]).
+     _/ [alpha]
+
+  Making n very large the result obtained for the whole contour is
+       _
+      / [oo] tan x
+    2 |      ----- dx - ([pi] - 2[alpha]) - 2[alpha][epsilon] = 0;
+     _/ 0      x
+
+  where [epsilon] is numerically less than unity. Now supposing [alpha]
+  to diminish to zero we finally obtain
+      _
+     / [oo] tan x      [pi]
+     |      ----- dx = ----
+    _/  0     x         2
+
+  (2) For another case, to illustrate a different point, we may take the
+  integral
+      _
+     /  z^(a-1)
+     |  ------- dz,
+    _/   1 + z
+
+  wherein a is real quantity such that 0 < a < 1, and the contour
+  consists of a small circle, z = rE(i[theta]), terminated at the points
+  x = r cos [alpha], y = ± r sin [alpha], where [alpha] is small, of the
+  two lines y = ± r sin [alpha] for r cos [alpha] =< x =< R cos ß, where
+  R sin ß = r sin [alpha], and finally of a large circle z = RE(i[phi]),
+  terminated at the points x = R cos ß, y = ± R sin ß. We suppose
+  [alpha] and ß both zero, and that the phase of z is zero for r cos a
+  =< x =< R cos ß, y = r sin [alpha] = R sin ß. Then on r cos [alpha] =<
+  x =< R cos ß, y = -r sin [alpha], the phase of z will be 2[pi], and
+  z^([alpha] - 1) will be equal to x^([alpha] - 1) exp (2[pi]i(a - 1)),
+  where x is real and positive. The two straight portions of the contour
+  will thus together give a contribution
+                               _
+                              / R cos ß       x^(a - 1)
+    [1 - exp (2[pi]i[alpha])] |               --------- dx.
+                             _/ r cos [alpha]   1 + x
+
+  It can easily be shown that if the limit of z[f](z) for z = 0 is zero,
+  the integral [int] [f](z)dz taken round an arc, of given angle, of a
+  small circle enclosing the origin is ultimately zero when the radius
+  of the circle diminishes to zero, and if the limit of z[f](z) for z =
+  [oo] is zero, the same integral taken round an arc, of given angle, of
+  a large circle whose centre is the origin is ultimately zero when the
+  radius of the circle increases indefinitely; in our case with [f](z) =
+  z^([alpha] - 1)/(1 + z), we have z[f](z) = z^a/(1 + z), which, for 0 <
+  a < 1, diminishes to zero both for z = 0 and for z = [oo]. Thus,
+  finally the limit of the contour integral when r = 0, R = [oo] is
+                               _
+                              / [oo]  x^([alpha] - 1)
+    [1 - exp (2[pi]i[alpha])] |       --------------- dx.
+                             _/ 0          1 + x
+
+  Within the contour [f](z) is single valued, and has a pole at z = 1;
+  at this point the phase of z is [pi] and z^(a - 1) is exp [i[pi](a -
+  1)] or - exp (i[pi]a); this is then the residue of [f](z) at z = -1;
+  we thus have
+                         _
+                        / [oo]  x^(a - 1)
+    [1 - exp (2[pi]ia)] |       --------- dx = -2[pi]i exp (i[pi]a),
+                       _/ 0       1 + x
+
+  that is
+      _
+     / [oo]  x^(a - 1)
+     |       --------- dx = [pi] cosec (a[pi]).
+    _/ 0       1 + x
+
+§ 14. _Doubly Periodic Functions._--An excellent illustration of the
+preceding principles is furnished by the theory of single valued
+functions having in the finite part of the plane no singularities but
+poles, which have two periods.
+
+  Before passing to this it may be convenient to make here a few remarks
+  as to the periodicity of (single valued) monogenic functions. To say
+  that [f](z) is periodic is to say that there exists a constant [omega]
+  such that for every point z of the interior of the region of existence
+  of [f](z) we have [f](z + [omega]) = [f](z). This involves,
+  considering all existing periods [omega] = [rho] + i[sigma], that
+  there exists a lower limit of [rho]² + [sigma]² other than zero; for
+  otherwise all the differential coefficients of [f](z) would be zero,
+  and [f](z) a constant; we can then suppose that not both [rho] and
+  [sigma] are numerically less than [epsilon], where [epsilon] >
+  [sigma]. Hence, if g be any real quantity, since the range (-g, ... g)
+  contains only a finite number of intervals of length [epsilon], and
+  there cannot be two periods [omega] = [rho] + i[sigma] such that
+  µ[epsilon] =< [rho] < (µ + 1)[epsilon], [nu][epsilon] =< [sigma] <
+  ([nu] + 1)[epsilon], where µ, [nu] are integers, it follows that there
+  is only a finite number of periods for which both [rho] and [sigma]
+  are in the interval (-g ... g). Considering then all the periods of
+  the function which are real multiples of one period [omega], and in
+  particular those periods [lambda][omega] wherein 0 < [lambda] =< 1,
+  there is a lower limit for [lambda], greater than zero, and therefore,
+  since there is only a finite number of such periods for which the real
+  and imaginary parts both lie between -g and g, a least value of
+  [lambda], say [lambda]0. If [Omega] = [lambda]0[omega] and [lambda] =
+  M[lambda]0 + [lambda]', where M is an integer and 0 [< = ] [lambda]' <
+  [lambda]0, any period [lambda][omega] is of the form M[Omega] +
+  [lambda]'[omega]; since, however, [Omega], M[Omega] and
+  [lambda][omega] are periods, so also is [lambda]'[omega], and hence,
+  by the construction of [lambda]0, we have [lambda]' = 0; thus all
+  periods which are real multiples of [omega] are expressible in the
+  form M[Omega] where M is an integer, and [Omega] a period.
+
+  If beside [omega] the functions have a period [omega]' which is not a
+  real multiple of [omega], consider all existing periods of the form
+  µ[omega] + [nu][omega]' wherein µ, [nu] are real, and of these those
+  for which 0 [< = ] µ =< 1, 0 < [nu] =< 1; as before there is a least
+  value for [nu], actually occurring in one or more periods, say in the
+  period [Omega]' = µ0[omega] + [nu]0[omega]'; now take, if µ[omega] +
+  [nu][omega]' be a period, [nu] = N'[nu]0 + [nu]', where N' is an
+  integer, and 0 =< [nu]' < [nu]0; thence µ[omega] + [nu][omega]' =
+  µ[omega] + N'([Omega]' - µ0[omega]) + [nu]'[omega]'; take then µ - Nµ0
+  = N[lambda]0 + [lambda]', where N is an integer and [lambda]0 is as
+  above, and 0 =< [lambda]' < [lambda]0; we thus have a period N[Omega]
+  + N'[Omega]' + [lambda]'[omega] + [nu]'[omega]', and hence a period
+  [lambda]'[omega] + [nu]'[omega]', wherein [lambda]' < [lambda]0, [nu]'
+  < [nu]0; hence [nu]' = 0 and [lambda]' = 0. All periods of the form
+  µ[omega] + [nu][omega]' are thus expressible in the form N[Omega] +
+  N'[Omega]', where [Omega], [Omega]' are periods and N, N' are
+  integers. But in fact any complex quantity, P + iQ, and in particular
+  any other possible period of the function, is expressible, with µ,
+  [nu] real, in the form µ[omega] + [nu][omega]'; for if [omega] = [rho]
+  + i[sigma], [omega]' = [rho]' + i[sigma]', this requires only P =
+  µ[rho] + [nu][rho]', Q = µ[sigma] + [nu][sigma]', equations which,
+  since [omega]'/[omega] is not real, always give finite values for µ
+  and [nu].
+
+  It thus appears that if a single valued monogenic function of z be
+  periodic, either all its periods are real multiples of one of them,
+  and then all are of the form M[Omega], where [Omega] is a period and M
+  is an integer, or else, if the function have two periods whose ratio
+  is not real, then all its periods are expressible in the form N[Omega]
+  + N'[Omega]', where [Omega], [Omega]' are periods, and N, N' are
+  integers. In the former case, putting [zeta] = 2[pi]iz/[Omega], and
+  the function [f](z) = [phi]([zeta]), the function [phi]([zeta]) has,
+  like exp ([zeta]), the period 2[pi]i, and if we take t = exp([zeta])
+  or [zeta] = [lambda](t) the function is a single valued function of t.
+  If then in particular [f](z) is an integral function, regarded as a
+  function of t, it has singularities only for t = 0 and t = [oo], and
+  may be expanded in the form [Sigma](-[oo] to [oo]) a_nt^n.
+
+  Taking the case when the single valued monogenic function has two
+  periods [omega], [omega]' whose ratio is not real, we can form a
+  network of parallelograms covering the plane of z whose angular points
+  are the points c + m[omega] + m'[omega]', wherein c is some constant
+  and m, m' are all possible positive and negative integers; choosing
+  arbitrarily one of these parallelograms, and calling it the primary
+  parallelogram, all the values of which the function is at all capable
+  occur for points of this primary parallelogram, any point, z', of the
+  plane being, as it is called, _congruent_ to a definite point, z, of
+  the primary parallelogram, z' - z being of the form m[omega] +
+  m'[omega]', where m, m' are integers. Such a function cannot be an
+  integral function, since then, if, in the primary parallelogram
+  |[f](z)| < M, it would also be the case, on a circle of centre the
+  origin and radius R, that |[f](z)| < M, and therefore, if
+  [Sigma]a_nz^n be the expansion of the function, which is valid for an
+  integral function for all finite values of z, we should have |a_n| <
+  MR^(-n), which can be made arbitrarily small by taking R large enough.
+  The function must then have singularities for finite values of z.
+
+  We consider only functions for which these are poles. Of these there
+  cannot be an infinite number in the primary parallelogram, since then
+  those of these poles which are sufficiently near to one of the
+  necessarily existing limiting points of the poles would be arbitrarily
+  near to one another, contrary to the character of a pole. Supposing
+  the constant c used in naming the corners of the parallelograms so
+  chosen that no pole falls on the perimeter of a parallelogram, it is
+  clear that the integral 1/(2[pi]i) [int][f](z)dz round the perimeter
+  of the primary parallelogram vanishes; for the elements of the
+  integral corresponding to two such opposite perimeter points as z, z +
+  [omega] (or as z, z + [omega]') are mutually destructive. This
+  integral is, however, equal to the sum of the residues of [f](z) at
+  the poles interior to the parallelogram. Which sum is therefore zero.
+  There cannot therefore be such a function having only one pole of the
+  first order in any parallelogram; we shall see that there can be such
+  a function with two poles only in any parallelogram, each of the first
+  order, with residues whose sum is zero, and that there can be such a
+  function with one pole of the second order, having an expansion near
+  this pole of the form (z - a)^(-2) + (power series in z - a).
+
+  Considering next the function [phi](z) = [[f](z)]^(-1) d[f](z)/dz, it
+  is easily seen that an ordinary point of [f](z) is an ordinary point
+  of [phi](z), that a zero of order m for [f](z) in the neighbourhood of
+  which [f](z) has a form, (z - a)^m multiplied by a power series, is a
+  pole of [phi](z) of residue m, and that a pole of [f](z) of order n is
+  a pole of [phi](z) of residue -n; manifestly [phi](z) has the two
+  periods of [f](z). We thus infer, since the sum of the residues of
+  [phi](z) is zero, that for the function [f](z), the sum of the orders
+  of its vanishing at points belonging to one parallelogram, [Sigma]m,
+  is equal to the sum of the orders of its poles, [Sigma]n; which is
+  briefly expressed by saying that the number of its zeros is equal to
+  the number of its poles. Applying this theorem to the function
+  [f](z) - A, where A is an arbitrary constant, we have the result, that
+  the function [f](z) assumes the value A in one of the parallelograms
+  as many times as it becomes infinite. Thus, by what is proved above,
+  every conceivable complex value does arise as a value for the doubly
+  periodic function [f](z) in any one of its parallelograms, and in fact
+  at least twice. The number of times it arises is called the _order_ of
+  the function; the result suggests a property of rational functions.
+
+  Consider further the integral [int] z [f]'(z)/[f](z) dz, where [f]'(z)
+  = d[f](z)/dz taken round the perimeter of the primary parallelogram;
+  the contribution to this arising from two opposite perimeter points
+  such as z and z + [omega] is of the form -[omega] [int] z
+  [f]'(z)/[f](z) dz, which, as z increases from z0 to z0 + [omega]',
+  gives, if [lambda] denote the generalized logarithm, -
+  [omega]{[lambda][[f](z0 + [omega]')] - [lambda][[f](z0)]}, that is,
+  since [f](z0 + [omega]') = [f](z0), gives 2[pi]iN[omega], where N is
+  an integer; similarly the result of the integration along the other
+  two opposite sides is of the form 2[pi]iN'[omega]', where N' is an
+  integer. The integral, however, is equal to 2[pi]i times the sum of
+  the residues of z[f]'(z)/[f](z) at the poles interior to the
+  parallelogram. For a zero, of order m, of [f](z) at z = a, the
+  contribution to this sum is 2[pi]ima, for a pole of order n at z = b
+  the contribution is -2[pi]inb; we thus infer that [Sigma]ma -
+  [Sigma]nb = N[omega] + N'[omega]'; this we express in words by saying
+  that the sum of the values of z where [f](z) = 0 within any
+  parallelogram is equal to the sum of the values of z where [f](z) =
+  [oo] save for integral multiples of the periods. By considering
+  similarly the function [f](z) - A where A is an arbitrary constant, we
+  prove that each of these sums is equal to the sum of the values of z
+  where the function takes the value A in the parallelogram.
+
+We pass now to the construction of a function having two arbitrary
+periods [omega], [omega]' of unreal ratio, which has a single pole of
+the second order in any one of its parallelograms.
+
+  For this consider first the network of parallelograms whose corners
+  are the points [Omega] = m[omega] + m'[omega]', where m, m' take all
+  positive and negative integer values; putting a small circle about
+  each corner of this network, let P be a point outside all these
+  circles; this will be interior to a parallelogram whose corners in
+  order may be denoted by z0, z0 + [omega], z0 + [omega] + [omega]', z0
+  + [omega]'; we shall denote z0, z0 + [omega] by A0, B0; this
+  parallelogram [Pi]0 is surrounded by eight other parallelograms,
+  forming with [Pi]0 a larger parallelogram [Pi]1, of which one side,
+  for instance, contains the points z0 - [omega] - [omega]', z0 -
+  [omega]', z0 - [omega]' + [omega], z0 - [omega]' + 2[omega], which we
+  shall denote by A1, B1, C1, D1. This parallelogram [Pi]1 is surrounded
+  by sixteen of the original parallelograms, forming with [Pi]1 a still
+  larger parallelogram [Pi]2 of which one side, for instance, contains
+  the points z0 - 2[omega] - 2[omega]', z0 - [omega] - 2[omega]', z0 -
+  2[omega]', z0 + [omega] - 2[omega]', z0 + 2[omega] - 2[omega]', z0 +
+  3[omega] - 2[omega]', which we shall denote by A2, B2, C2, D2, E2, F2.
+  And so on. Now consider the sum of the inverse cubes of the distances
+  of the point P from the corners of all the original parallelograms.
+  The sum will contain the terms
+
+           1      / 1      1      1  \     / 1      1             1  \
+    S0 = ----- + ( ---- + ---- + ---- ) + ( ---- + ---- + ... +  ---- ) +  ...
+         PA0³     \PA1³   PB1³   PC1³/     \PA2³   PB2³          PE2³/
+
+  and three other sets of terms, each infinite in number, formed in a
+  similar way. If the perpendiculars from P to the sides A0B0, A1B1C1,
+  A2B2C2D2E2, and so on, be p, p + q, p + 2q and so on, the sum S0 is at
+  most equal to
+
+    1       3           5              2n + 1
+    -- + -------- + --------- + ... + --------- + ...
+    p³   (p + q)³   (p + 2q)³         (p + nq)³
+
+  of which the general term is ultimately, when n is large, in a ratio
+  of equality with 2q^(-3)n^(-2), so that the series S0 is convergent,
+  as we know the sum [Sigma]n^(-2) to be; this assumes that p[/ = ]0; if
+  P be on A0B0 the proof for the convergence of S0 - 1/PA0³, is the
+  same. Taking the three other sums analogous to S0 we thus reach the
+  result that the series
+
+    [phi](z) = -2[Sigma](z - [Omega])^(-3),
+
+  where [Omega] is m[omega] + m'[omega]', and m, m' are to take all
+  positive and negative integer values, and z is any point outside small
+  circles described with the points [Omega] as centres, is _absolutely
+  convergent_. Its sum is therefore independent of the order of its
+  terms. By the nature of the proof, which holds for all positions of z
+  outside the small circles spoken of, the series is also clearly
+  _uniformly convergent_ outside these circles. Each term of the series
+  being a monogenic function of z, the series may therefore be
+  differentiated and integrated outside these circles, and represents a
+  monogenic function. It is clearly periodic with the periods [omega],
+  [omega]'; for [phi](z + [omega]) is the same sum as [phi](z) with the
+  terms in a slightly different order. Thus [phi](z + [omega]) =
+  [phi](z) and [phi](z + [omega]') = [phi](z).
+
+  Consider now the function
+                      _   _              _
+              1      / z |            2   |
+    [f](z) =  -- +   |   | [phi](z) + --  | dz,
+              z²    _/ 0 |_           z³ _|
+
+  where, for the subject of integration, the area of uniform convergence
+  clearly includes the point z = 0; this gives
+
+    d[f](z)
+    ------- = [phi](z)
+      dz
+
+  and
+                            _                           _
+             1             |        1             1      |
+    [f](z) = -- + [Sigma]' |  -------------- - --------  |,
+             z²            |_ (z - [Omega])²   [Omega]² _|
+
+  wherein [Sigma]' is a sum excluding the term for which m = 0 and m' =
+  0. Hence [f](z + [omega]) - [f](z) and [f](z + [omega]') - [f](z) are
+  both independent of z. Noticing, however, that, by its form, [f](z) is
+  an even function of z, and putting z = -½[omega], z = -½[omega]'
+  respectively, we infer that also [f](z) has the two periods [omega]
+  and [omega]'. In the primary parallelogram [Pi]0, however, [f](z) is
+  only infinite at z = 0 in the neighbourhood of which its expansion is
+  of the form z^(-2) + (power series in z). Thus [f](z) is such a doubly
+  periodic function as was to be constructed, having in any
+  parallelogram of periods only one pole, of the second order.
+
+It can be shown that any single valued meromorphic function of z with
+[omega] and [omega]' as periods can be expressed rationally in terms of
+[f](z) and [phi](z), and that [[phi](z)]² is of the form 4[[f](z)]³ +
+A[f](z) + B, where A, B are constants.
+
+  To prove the last of these results, we write, for |z| < |[Omega]|,
+
+           1            1          2z         3z²
+    -------------- - -------- = -------- + --------- + ...,
+    (z - [Omega])²   [Omega]²   [Omega]³   [Omega]^4
+
+  and hence, if [Sigma]'[Omega]^(-2n) = [sigma]_n, since
+  [Sigma]'[Omega]^(-(2n - 1)) = 0, we have, for sufficiently small z
+  greater than zero,
+
+    [f](z) = z^(-2) + 3[sigma]2·z² + 5[sigma]3·z^4 + ...
+
+  and
+
+    [phi](z) = -2z^(-3) + 6[sigma]2·z + 20[sigma]3·z³ + ...;
+
+  using these series we find that the function
+
+    F(z) = [[phi](z)]² - 4[[f](z)]³ + 60[sigma]2[f](z) + 140[sigma]3
+
+  contains no negative powers of z, being equal to a power series in z²
+  beginning with a term in z². The function F(z) is, however, doubly
+  periodic, with periods [omega], [omega]', and can only be infinite
+  when either [f](z) or [phi](z) is infinite; this follows from its form
+  in [f](z) and [phi](z); thus in one parallelogram of periods it can be
+  infinite only when z = 0; we have proved, however, that it is not
+  infinite, but, on the contrary, vanishes, when z = 0. Being,
+  therefore, never infinite for finite values of z it is a constant, and
+  therefore necessarily always zero. Putting therefore [f](z) = [zeta]
+  and [phi](z) = d[zeta]/dz we see that
+
+      dz
+    ------- = (4[zeta]³ - 60[sigma]2[zeta] - 140[sigma]3)^(-½)
+    d[zeta]
+
+  Historically it was in the discussion of integrals such as
+      _
+     /
+     | d[zeta](4[zeta]³ - 60[sigma]2·[zeta] - 140[sigma]3)^(-½),
+    _/
+
+  regarded as a branch of Integral Calculus, that the doubly periodic
+  functions arose. As in the familiar case
+         _
+        / [zeta]
+    z = |       (1 - [zeta]²)^(-½) d[zeta],
+       _/ 0
+
+  where [zeta] = sin z, it has proved finally to be simpler to regard
+  [zeta] as a function of z. We shall come to the other point of view
+  below, under § 20, _Elliptic Integrals_.
+
+To prove that any doubly periodic function F(z) with periods [omega],
+[omega]', having poles at the points z = a1, ... z = a_m of a
+parallelogram, these being, for simplicity of explanation, supposed to
+be all of the first order, is rationally expressible in terms of
+[phi](z) and [f](z), and we proceed as follows:--
+
+  Consider the expression
+
+                 ([zeta], 1)_m + [eta]([zeta], 1)_(m - 2)
+    [Phi](z) =  ------------------------------------------
+                ([zeta]- A1)([zeta] - A2)...([zeta] - A_m)
+
+  where A_s = [f](a_s), [zeta] is an abbreviation for [f](z) and [eta]
+  for [phi](z), and ([zeta], 1)_m, ([zeta], 1)_(m - 2), denote integral
+  polynomials in [zeta], of respective orders m and m - 2, so that there
+  are 2m unspecified, homogeneously entering, constants in the
+  numerator. It is supposed that no one of the points a1, ... a_m is one
+  of the points m[omega] + m'[omega]' where f(z) = [oo]. The function
+  [Phi](z) is a monogenic function of z with the periods [omega],
+  [omega]', becoming infinite (and having singularities) only when (1)
+  [zeta] = [oo] or (2) one of the factors [zeta] - A_s is zero. In a
+  period parallelogram including z = 0 the first arises only for z = 0;
+  since for [zeta] = [oo], [eta] is in a finite ratio to [zeta]^(3/2);
+  the function [Phi](z) for [zeta] = [oo] is not infinite provided the
+  coefficient of [zeta]^m in ([zeta], 1)_m is not zero; thus [Phi](z) is
+  regular about z = 0. When [zeta] - A_s = 0, that is [f](z) = f(a_s),
+  we have z = ±a_s + m[omega] + m'[omega]', and no other values of z, m
+  and m' being integers; suppose the unspecified coefficients in the
+  numerator so taken that the numerator vanished to the first order in
+  each of the m points -a1, -a2, ... -a_m; that is, if [phi](a_s) = B_s,
+  and therefore [phi](-a_s) = -B_s, so that we have the m relations
+
+    (A_s, 1)_m - B_s(A_s, 1)_(m - 2) = 0;
+
+  then the function [Phi](z) will only have the m poles a1, ... a_m.
+  Denoting further the m zeros of F(z) by a1', ... a_m', putting
+  [f](a_s') = A_s', [phi](a_s') = B_s', suppose the coefficients of the
+  numerator of [Phi](z) to satisfy the further m-1 conditions
+
+    (A_s', 1)_m + B_s'(A_s',1)_(m - 2) = 0
+
+  for s = 1, 2, ... (m - 1). The ratios of the 2m coefficients in the
+  numerator of [Phi](z) can always be chosen so that the m + (m - 1)
+  linear conditions are all satisfied. Consider then the ratio
+
+    F(z)/[Phi](z);
+
+  it is a doubly periodic function with no singularity other than the
+  one pole a_m'. It is therefore a constant, the numerator of [Phi](z)
+  vanishing spontaneously in a_m'. We have
+
+    F(z) = A[Phi](z),
+
+  where A is a constant; by which F(z) is expressed rationally in terms
+  of [f](z) and [phi](z), as was desired.
+
+  When z = 0 is a pole of F(z), say of order r, the other poles, each of
+  the first order, being a1, ... a_m, similar reasoning can be applied
+  to a function
+
+    ([zeta], 1)_h + [eta]([zeta], 1)_k
+    ----------------------------------,
+      ([zeta] - A1)...([zeta] - A_m)
+
+  where h, k are such that the greater of 2h - 2m, 2k + 3 - 2m is equal
+  to r; the case where some of the poles a1, ... a_m are multiple is to
+  be met by introducing corresponding multiple factors in the
+  denominator and taking a corresponding numerator. We give a solution
+  of the general problem below, of a different form.
+
+  One important application of the result is the theorem that the
+  functions [f](z + t), [phi](z + t), which are such doubly periodic
+  function of z as have been discussed, can each be expressed, so far as
+  they depend on z, rationally in terms of [f](z) and [phi](z), and
+  therefore, so far as they depend on z and t, rationally in terms of
+  [f](z), [f](t), [phi](z) and [phi](t). It can in fact be shown, by
+  reasoning analogous to that given above, that
+                                      _                    _
+                                     |  [phi](z) - [phi](t) |²
+    [f](z + t) + [f](z) + [f](t) = ¼ |  ------------------- |.
+                                     |_   [f](z) - [f](t)  _|
+
+  This shows that if F(z) be any single valued monogenic function which
+  is doubly periodic and of meromorphic character, then F(z + t) is an
+  algebraic function of F(z) and F(t). Conversely any single valued
+  monogenic function of meromorphic character, F(z), which is such that
+  F(z + t) is an algebraic function of F(z) and F(t), can be shown to be
+  a doubly periodic function, or a function obtained from such by
+  degeneration (in virtue of special relations connecting the
+  fundamental constants).
+
+  The functions [f](z), [phi](z) above are usually denoted by RN(z),
+  RN'(z); further the fundamental differential equation is usually
+  written
+
+    (RN'z)² = 4(RNz)³ - g2RNz - g3,
+
+  and the roots of the cubic on the right are denoted by e1, e2, e3; for
+  the odd function, RN'z, we have, for the congruent arguments
+  -½[omega]and ½[omega], RN'(½[omega]) = -RN'(-½[omega]) =
+  -RN'(½[omega]), and hence RN'(½[omega]) = 0; hence we can take e1 =
+  RN(½[omega]), e2 = RN(½[omega] + ½[omega]'), e3 = RN(½[omega]). It can
+  then be proved that [RN(z) - e1][RN(z + ½[omega]) - e1] = (e1 - e2)(e1
+  - e3), with similar equations for the other half periods. Consider
+  more particularly the function RN(z) - e1; like RN(z) it has a pole of
+  the second order at z = 0, its expansion in its neighbourhood being of
+  the form z^(-2)(1 - e1z² + Az^4 + ...); having no other pole, it has
+  therefore either two zeros, or a double zero in a period parallelogram
+  ([omega], [omega]'). In fact near its zero ½[omega] its expansion is
+  (x - ½[omega]) RN'(½[omega]) + ½(z - ½[omega])² RN"(½[omega]) + ...;
+  we have seen that RN'(½[omega]) = 0; thus it has a zero of the second
+  order wherever it vanishes. Thus it appears that the square root
+  [RN(z) - e1]^½, if we attach a definite sign to it for some particular
+  value of z, is a single valued function of z; for it can at most have
+  two values, and the only small circuits in the plane which could lead
+  to an interchange of these values are those about either a pole or a
+  zero, neither of which, as we have seen, has this effect; the function
+  is therefore single valued for any circuit. Denoting the function, for
+  a moment, by [f]1(z), we have [f]1(z + [omega]) = ±[f]1(z), [f]1(z +
+  [omega]') = ±[f]1(z); it can be seen by considerations of continuity
+  that the right sign in either of these equations does not vary with z;
+  not both these signs can be positive, since the function has only one
+  pole, of the first order, in a parallelogram ([omega], [omega]'); from
+  the expansion of [f]1(z) about z = 0, namely z^(-1) (1 - ½e1z² + ...),
+  it follows that [f]1(z) is an odd function, and hence [f]1(-½[omega]')
+  = -[f]1(½[omega]'), which is not zero since [[f]1(½[omega]')]² = e3 -
+  e1, so that we have [f]1(z + [omega]') = -[f]1(z); an equation f1(z +
+  [omega]) = -[f]1(z) would then give [f]1(z + [omega] + [omega]') =
+  [f]1(z), and hence [f]1(½[omega] + ½[omega]') = [f]1(-½[omega] -
+  ½[omega]'), of which the latter is -[f]1(½[omega] + ½[omega]'); this
+  would give [f]1(½[omega] + ½[omega]') = 0, while [[f]1 (½[omega] +
+  ½[omega]')]² = e2 - e1. We thus infer that [f]1(z + [omega]) =
+  [f]1(z), [f]1(z + [omega]') = -[f]1(z), [f]1(z + [omega] + [omega]') =
+  -[f]1(z). The function [f]1(z) is thus doubly periodic with the
+  periods [omega] and 2[omega]'; in a parallelogram of which two sides
+  are [omega] and 2[omega]' it has poles at z = 0, z = [omega]' each of
+  the first order, and zeros of the first order at z = ½[omega], z =
+  ½[omega] + [omega]'; it is thus a doubly periodic function of the
+  second order with two different poles of the first order in its
+  parallelogram ([omega], 2[omega]'). We may similarly consider the
+  functions [f]2(z) = [RN(z) - e2]^½, [f]3(z) = [RN(z) - e3]^½; they
+  give
+
+    [f]2(z + [omega] + [omega]') = [f]2(z), [f]2(z + [omega]) = -[f]2(z), [f]2(z + [omega]') = -[f]2(z),
+
+    [f]3(z + [omega]') = [f]3z, [f]3(z + [omega]) = -[f]3(z), [f]3(z + [omega] + [omega]') = -[f]3(z).
+
+  Taking u = z(e1 - e3)^½, with a definite determination of the constant
+  (e1 - e3)^½, it is usual, taking the preliminary signs so that for z =
+  0 each of z[f]1(z), z[f]2(z), z[f]3(z) is equal to + 1, to put
+
+            (e1 - e3)^½          [f]1(z)          f2(z)
+    sn(u) = -----------, cn(u) = -------, dn(u) = -----,
+              [f]3(z)            [f]3(z)          f3(z)
+
+    k² = (e2 - e3)/(e1 - e3), K = ½[omega](e1 - e3)^½, iK' = ½[omega]'(e1 - e3)^½;
+
+  thus sn(u) is an odd doubly periodic function of the second order with
+  the periods 4K, 2iK, having poles of the first order at u = iK', u =
+  2K + iK', and zeros of the first order at u = 0, u = 2K; similarly
+  cn(u), dn(u) are even doubly periodic functions whose periods can be
+  written down, and sn²(u) + cn²(u) = 1, k²sn²(u) + dn²(u) = 1; if x =
+  sn(u) we at once find, from the relations given here, that
+
+    du
+    -- = [(1 - x²) (1 - k²x²)]^(-½);
+    dx
+
+  if we put x = sin[phi] we have
+
+      du
+    ------ = [1 - k²sin² [phi]]^(-½),
+    d[phi]
+
+  and if we call [phi] the amplitude of u, we may write [phi] = am(u), x
+  = sin·am(u), which explains the origin of the notation sn(u).
+  Similarly cn(u) is an abbreviation of cos·am(u), and dn(u) of
+  [Delta]am(u), where [Delta]([phi]) meant (1 - k²sin² [phi])^½. The
+  addition equation for each of the functions [f]1(z), [f]2(z), [f]3(z)
+  is very simple, being
+
+                   /(Pd)    (Pd) \      [f](z) + [f](t)   [f](z)[f]'(t) - [f](t)[f]'(z)
+    [f](z + t) = ½( ----- + ----- ) log --------------- = -----------------------------,
+                   \(Pd)z   (Pd)i/      [f](z) - [f](t)         [f]²(z) - [f]²(t)
+
+  where f1'(z) means d[f]1(z)/dz, which is equal to -[f]2(z)·[f]3(z),
+  and [f]²(z) means [[f](z)]². This may be verified directly by
+  showing, if R denote the right side of the equation, that (Pd)R/(Pd)z
+  = (Pd)R/(Pd)t; this will require the use of the differential equation
+
+    [[f]1'^(z)]² = [[f]1²(z) + e1 - e2] [[f]1²(z) + e1 - e3],
+
+  and in fact we find
+
+     / (Pd)²   (Pd)²\
+    ( ------ - ----- ) log [[f](z) + [f](t)] = [f]²(z) - [f]²(t) =
+     \(Pd)z²    dt² /
+
+       / (Pd)²   (Pd)²\
+      ( ------ - ----- ) log [[f](z) - [f](t)];
+       \(Pd)z²    dt² /
+
+  hence it will follow that R is a function of z + t, and R is at once
+  seen to reduce to [f](z) when t = 0. From this the addition equation
+  for each of the functions sn(u), cn(u), dn(u) can be deduced at once;
+  if s1, c1, d1, s2, c2, d2 denote respectively sn(u1), cn(u1), dn(u1),
+  sn(u2), cn(u2), dn(u2), they can be put into the forms
+
+    sn(u1 + u2) = (s1c2d2 + s2c1d1)/D,
+
+    cn(u1 + u2) = (c1c2 - s1s2d1d2)/D,
+
+    dn(u1 + u2) = (d1d2 - k²s1s2c1c2)/D,
+
+  where
+
+    D = 1 - k²s1²s2².
+
+  The introduction of the function [f]1(z) is equivalent to the
+  introduction of the function RN(z; [omega], 2[omega]') constructed
+  from the periods [omega], 2[omega]' as was RN(z) from [omega] and
+  [omega]'; denoting this function by RN1(z) and its differential
+  coefficient by RN'1(z), we have in fact
+
+                       RN'1(z)
+    [f]1(z) = ½ ----------------------
+                RN1([omega]') - RN1(z)
+
+  as we see at once by considering the zeros and poles and the limit of
+  z[f]1(z) when z = 0. In terms of the function RN1(z) the original
+  function RN(z) is expressed by
+
+    RN(z) = RN1(z) + RN1(z + [omega]') - RN1([omega]'),
+
+  as a consideration of the poles and expansion near z = 0 will show.
+
+  A function having [omega], [omega]' for periods, with poles at two
+  arbitrary points a, b and zeros at a', b', where a' + b' = a + b save
+  for an expression m[omega] + m'[omega]', in which m, m' are integers,
+  is a constant multiple of
+
+    {RN[z - ½(a' + b')] - RN[a' - ½(a' + b')]} / {RN[z - ½(a + b)] - RN[a - ½(a + b)]};
+
+  if the expansion of this function near z = a be
+                                _
+    [lambda](z - a)^(-1) + µ + \  µ_n(z - a)^n,
+                               /_
+                               n = 1
+
+  the expansion near z = b is
+                                 _
+    -[lambda](z - b)^(-1) + µ + \  (-1)^n µ_n (z - b)^n,
+                                /_
+                                n = 1
+
+  as we see by remarking that if z'- b = -(z - a) the function has the
+  same value at z and z'; hence the differential equation satisfied by
+  the function is easily calculated in terms of the coefficients in the
+  expansions.
+
+  From the function RN(z) we can obtain another function, termed the
+  Zeta-function; it is usually denoted by [zeta](z), and defined by
+                    _      _           _
+              1    / [pi] |  1          |      _   /     1           1         z   \
+    [zeta](z) -- = |      |  -- - RN(z) |dz = \ ' ( ----------- + ------- + ------- ),
+              z   _/ 0    |_ z²        _|     /_   \z - [Omega]   [Omega]  [Omega]²/
+
+  for which as before we have equations
+
+    [zeta](z + [omega]) = [zeta](z) + 2[pi]i[eta],
+    [zeta](z + [omega]') = [zeta](z) + 2[pi]i[eta]',
+
+  where 2[eta], 2[eta]' are certain constants, which in this case do not
+  both vanish, since else [zeta](z) would be a doubly periodic function
+  with only one pole of the first order. By considering the integral
+      _
+     /
+     | [zeta](z)dz
+    _/
+
+  round the perimeter of a parallelogram of sides [omega], [omega]'
+  containing z = 0 in its interior, we find [eta][omega]' -
+  [eta]'[omega] = 1, so that neither of [eta], [eta]' is zero. We have
+  [zeta]'(z) = -RN(z). From [zeta](z) by means of the equation
+                         _   _              _
+    [sigma](z)       {  / z |             1  |   }
+    ---------- = exp {  |   | [zeta](x) - -- |dz } =
+        z            { _/ 0 |_            z _|   }
+             _                                           _
+            |  /       2   \       /   z          z²   \  |
+      [Pi]' | ( 1 - ------- ) exp ( ------- + --------- ) |,
+            |_ \    [Omega]/       \[Omega]   2[Omega]²/ _|
+
+  we determine an integral function [sigma](z), termed the
+  Sigma-function, having a zero of the first order at each of the points
+  z = [Omega]; it can be seen to satisfy the equations
+
+    [sigma](z + [omega])
+    -------------------- = -exp [2[pi] i[eta](z + ½[omega])],
+         [sigma](z)
+
+    [sigma](z + [omega]')
+    --------------------- = -exp [2[pi] i[eta]'(z + ½[omega]')].
+         [sigma](z)
+
+  By means of these equations, if a1 + a2 + ... + a_m = a'1 + a'2 + ...
+  + a'_m, it is readily shown that
+
+    [sigma](z - a'1)[sigma](z - a'2) ... [sigma](z - a'_m)
+    ------------------------------------------------------
+      [sigma](z - a1[sigma](z - a2) ... [sigma](z - a_m)
+
+  is a doubly periodic function having a1, ... a_m as its simple poles,
+  and a'1, ... a'_m as its simple zeros. Thus the function [sigma](z)
+  has the important property of enabling us to write any meromorphic
+  doubly periodic function as a product of factors each having one zero
+  in the parallelogram of periods; these form a generalization of the
+  simple factors, z - a, which have the same utility for rational
+  functions of z. We have [zeta](z) = [sigma]'(z)/[sigma](z).
+
+  The functions [zeta](z), RN(z) may be used to write any meromorphic
+  doubly periodic function F(z) as a sum of terms having each only one
+  pole; for if in the expansion of F(z) near a pole z = a the terms with
+  negative powers of z-a be
+
+    A1(z - a)^(-1) + A2(z - a){-2} + ... + A_(m + 1)(z - a)^(-(m + 1)),
+
+  then the difference
+
+                                                       A_(m + 1)
+    F(z) - A1[zeta](z - a) - A2[Fraktur](z - a)- ... + ---------(-1)^m RN^(m - 1)(z - a)
+                                                           m!
+
+  will not be infinite at z = a. Adding to this a sum of further terms
+  of the same form, one for each of the poles in a parallelogram of
+  periods, we obtain, since the sum of the residues A is zero, a doubly
+  periodic function without poles, that is, a constant; this gives the
+  expression of F(z) referred to. The indefinite integral [int]F(z)dz
+  can then be expressed in terms of z, functions RN(z - a) and their
+  differential coefficients, functions [zeta](z - a) and functions
+  log[sigma](z - a).
+
+§ 15. _Potential Functions. Conformal Representation in
+General._--Consider a circle of radius a lying within the region of
+existence of a single valued monogenic function, u + iv, of the complex
+variable z, = x + iy, the origin z = 0 being the centre of this circle.
+If z = rE(i[phi]) = r(cos [phi] + i sin [phi]) be an internal point of
+this circle we have
+                    _
+             1     / (U + iV)
+  u + iv = ------  | -------- dt,
+           2[pi]i _/  t - z
+
+where U + iV is the value of the function at a point of the
+circumference and t = aE(i[theta]); this is the same as
+                   _
+             1    /  (U + iV) [1 - (r/a)E(i[theta] - i[phi])]
+  u + iv = -----  | ----------------------------------------- d[theta].
+           2[pi] _/ 1 + (r/a)² - 2(r/a) cos ([theta] - [phi])
+
+If in the above formula we replace z by the external point
+(a²/r)E(i[phi]) the corresponding contour integral will vanish, so that
+also
+              _
+        1    /  (U + iV) [(r/a)² - (r/a)E(i[theta] - i[phi])]
+  0 = -----  |  --------------------------------------------- d[theta];
+      2[pi] _/    1 + (r/a)² - 2(r/a) cos ([theta] - [phi])
+
+hence by subtraction we have
+              _
+        1    /             U(a² - r²)
+  u = -----  | ---------------------------------- d[theta],
+      2[pi] _/ a² + r² - 2ar cos ([theta] - [phi])
+
+and a corresponding formula for v in terms of V. If O be the centre of
+the circle, Q be the interior point z, P the point aE(i[theta]) of the
+circumference, and [omega] the angle which QP makes with OQ produced,
+this integral is at once found to be the same as
+             _                    _
+       1    /               1    /
+  u = ----  | Ud[omega] - -----  | Ud[theta]
+      [pi] _/             2[pi] _/
+
+of which the second part does not depend upon the position of z, and the
+equivalence of the integrals holds for every arc of integration.
+
+  Conversely, let U be any continuous real function on the
+  circumference, U0 being the value of it at a point P0 of the
+  circumference, and describe a small circle with centre at P0 cutting
+  the given circle in A and B, so that for all points P of the arc AP0B
+  we have |U - U0| < [epsilon], where [epsilon] is a given small real
+  quantity. Describe a further circle, centre P0 within the former,
+  cutting the given circle in A' and B', and let Q be restricted to lie
+  in the small space bounded by the arc A'P0B' and this second circle;
+  then for all positions of P upon the greater arc AB of the original
+  circle QP² is greater than a definite finite quantity which is not
+  zero, say QP² > D². Consider now the integral
+                 _
+           1    /               (a² - r²)
+    u' = -----  | U ---------------------------------- d[theta], =
+         2[pi] _/   a² + r² - 2ar cos ([theta] - [phi]
+
+             _                    _
+       1    /               1    /
+      ----  | Ud[omega] - -----  | Ud[theta],
+      [pi] _/             2[pi] _/
+
+  which we evaluate as the sum of two, respectively along the small arc
+  AP0B and the greater arc AB. It is easy to verify that, for the whole
+  circumference,
+                 _
+           1    /               (a² - r²)
+    U0 = -----  | U0 ---------------------------------- d[theta] =
+         2[pi] _/    a² + r² - 2ar cos ([theta] - [phi]
+
+             _                     _
+       1    /                1    /
+      ----  | U0d[omega] - -----  | U0d[theta].
+      [pi] _/              2[pi] _/
+
+  Hence we can write
+                      _                                _
+                1    /                           1    /
+    u' - U0 = -----  |     (U - U0) d[omega] - -----  |    (U - U0) d[theta] +
+              2[pi] _/AP0B                     2[pi] _/AP0B
+
+              _
+        1    /           (a² - r²)
+      -----  |  (U - U0) --------- d[theta].
+      2[pi] _/AB            QP²
+
+  If the finite angle between QA and QB be called [Phi] and the finite
+  angle AOB be called [Theta], the sum of the first two components is
+  numerically less than
+
+    [epsilon]
+    --------- ([Phi] + [Theta]).
+      2[pi]
+
+  If the greatest value of |(U - U0)| on the greater arc AB be called H,
+  the last component is numerically less than
+
+    H
+    -- (a² - r²),
+    D²
+
+  of which, when the circle, of centre P0, passing through A'B' is
+  sufficiently small, the factor a² - r² is arbitrarily small. Thus it
+  appears that u' is a function of the position of Q whose limit, when
+  Q, interior to the original circle, approaches indefinitely near to
+  P0, is U0. From the form
+                _                    _
+          1    /               1    /
+    u' = ----  | Ud[omega] - -----  | Ud[theta],
+         [pi] _/             2[pi] _/
+
+  since the inclination of QP to a fixed direction is, when Q varies, P
+  remaining fixed, a solution of the differential equation
+
+    (Pd)²[psi]    (Pd)²
+    ---------- + ------ = 0,
+      (Pd)x²     (Pd)y²
+
+  where z, = x + iy, is the point Q, we infer that u' is a
+  differentiable function satisfying this equation; indeed, when r < a,
+  we can write
+            _
+      1    /                (a² - r²)
+    -----  | U ----------------------------------- d[theta]
+    2[pi] _/   a² + r² - 2ar cos ([theta] - [phi])
+                _   _                                                                 _
+          1    /   |       r                            r²                             |
+      = -----  | U | 1 + 2 -- cos ([theta] - [phi]) + 2 -- cos 2([theta] - [phi]) + ...| d[theta]
+        2[pi] _/   |_      a                            a²                            _|
+
+      = a0 + a1x + b1y + a2(x² - y²) + 2b2xy + ...,
+
+  where
+
+                 _                       _                                   _
+           1    /                  1    / U cos[theta]                 1    / U sin[theta]
+    a0 = -----  | Ud[theta], a1 = ----  | ------------ d[theta], b1 = ----  | ------------ d[theta],
+         2[pi] _/                 [pi] _/      a                      [pi] _/       a
+
+                _                                     _
+          1    / U cos 2[theta]                 1    / U sin 2[theta]
+    a2 = ----  | -------------- d[theta], b2 = ----  | -------------- d[theta].
+         [pi] _/       a²                      [pi] _/       a²
+
+  In this series the terms of order n are sums, with real coefficients,
+  of the various integral polynomials of dimension n which satisfy the
+  equation (Pd)²[psi]/(Pd)x² + (Pd)²[psi]/(Pd)y²; the series is thus the
+  real part of a power series in z, and is capable of differentiation
+  and integration within its region of convergence.
+
+  Conversely we may suppose a function, P, defined for the interior of a
+  finite region R of the plane of the real variables x, y, capable of
+  expression about any interior point x0, y0 of this region by a power
+  series in x - x0, y - y0, with real coefficients, these various series
+  being obtainable from one of them by continuation. For any region R0
+  interior to the region specified, the radii of convergence of these
+  power series will then have a lower limit greater than zero, and hence
+  a finite number of these power series suffice to specify the function
+  for all points interior to R0. Each of these series, and therefore the
+  function, will be differentiable; suppose that at all points of R0 the
+  function satisfies the equation
+
+    (Pd)²P   (Pd)P²
+    ------ + ------ = 0,
+    (Pd)x²   (Pd)y²
+
+  we then call it a monogenic potential function. From this, save for an
+  additive constant, there is defined another potential function by
+  means of the equation
+         _
+        /(x, y) /(Pd)P      (Pd)P   \
+    Q = |      ( ----- dy - ----- dx ).
+       _/       \(Pd)x      (Pd)y   /
+
+  The functions P, Q, being given by a finite number of power series,
+  will be single valued in R0, and P + iQ will be a monogenic function
+  of z within R0· In drawing this inference it is supposed that the
+  region R0 is such that every closed path drawn in it is capable of
+  being deformed continuously to a point lying within R0, that is, is
+  _simply connected_.
+
+  Suppose in particular, c being any point interior to R0, that P
+  approaches continuously, as z approaches to the boundary of R, to the
+  value log r, where r is the distance of c to the points of the
+  perimeter of R. Then the function of z expressed by
+
+    [zeta] = (z - c) exp (-P - iQ)
+
+  will be developable by a power series in (z - z0) about every point z0
+  interior to R0, and will vanish at z = c; while on the boundary of R
+  it will be of constant modulus unity. Thus if it be plotted upon a
+  plane of [zeta] the boundary of R will become a circle of radius unity
+  with centre at [zeta] = 0, this latter point corresponding to z = c. A
+  closed path within R0, passing once round z = c, will lead to a closed
+  path passing once about [zeta] = 0. Thus every point of the interior
+  of R will give rise to one point of the interior of the circle. The
+  converse is also true, but is more difficult to prove; in fact, the
+  differential coefficient d[zeta]/dz does not vanish for any point
+  interior to R. This being assumed, we obtain a conformal
+  representation of the interior of the region R upon the interior of a
+  circle, in which the arbitrary interior point c of R corresponds to
+  the centre of the circle, and, by utilizing the arbitrary constant
+  arising in determining the function Q, an arbitrary point of the
+  boundary of R corresponds to an arbitrary point of the circumference
+  of the circle.
+
+  There thus arises the problem of the determination of a real monogenic
+  potential function, single valued and finite within a given arbitrary
+  region, with an assigned continuous value at all points of the
+  boundary of the region. When the region is circular this problem is
+  solved by the integral 1/[pi] [int] Ud[omega] - 1/[pi] [int] Ud[theta]
+  previously given. When the region is bounded by the outermost portions
+  of the circumferences of two overlapping circles, it can hence be
+  proved that the problem also has a solution; more generally, consider
+  a finite simply connected region, whose boundary we suppose to consist
+  of a single closed path in the sense previously explained, ABCD;
+  joining A to C by two non-intersecting paths AEC, AFC lying within the
+  region, so that the original region may be supposed to be generated by
+  the overlapping regions AECD, CFAB, of which the common part is AECF;
+  suppose now the problem of determining a single valued finite
+  monogenic potential function for the region AECD with a given
+  continuous boundary value can be solved, and also the same problem for
+  the region CFAB; then it can be shown that the same problem can be
+  solved for the original area. Taking indeed the values assigned for
+  the original perimeter ABCD, assume arbitrarily values for the path
+  AEC, continuous with one another and with the values at A and C; then
+  determine the potential function for the interior of AECD; this will
+  prescribe values for the path CFA which will be continuous at A and C
+  with the values originally proposed for ABC; we can then determine a
+  function for the interior of CFAB with the boundary values so
+  prescribed. This in its turn will give values for the path AEC, so
+  that we can determine a new function for the interior of AECD. With
+  the values which this assumes along CFA we can then again determine a
+  new function for the interior of CFAB. And so on. It can be shown that
+  these functions, so alternately determined, have a limit representing
+  such a potential function as is desired for the interior of the
+  original region ABCD. There cannot be two functions with the given
+  perimeter values, since their difference would be a monogenic
+  potential function with boundary value zero, which can easily be shown
+  to be everywhere zero. At least two other methods have been proposed
+  for the solution of the same problem.
+
+  A particular case of the problem is that of the conformal
+  representation of the interior of a closed polygon upon the upper half
+  of the plane of a complex variable t. It can be shown without much
+  difficulty that if a, b, c, ... be real values of t, and [alpha], ß,
+  [gamma], ... be n real numbers, whose sum is n - 2, the integral
+         _
+        /
+    z = | (t - a)^([alpha] - 1) (t - b)^(ß - 1)  ... dt,
+       _/
+
+  as t describes the real axis, describes in the plane of z a polygon of
+  n sides with internal angles equal to [alpha][pi], ß[pi], ..., and, a
+  proper sign being given to the integral, points of the upper half of
+  the plane of t give rise to interior points of the polygon. Herein the
+  points a, b, ... of the real axis give rise to the corners of the
+  polygon; the condition [Sigma][alpha] = n - 2 ensures merely that the
+  point t = [oo] does not correspond to a corner; if this condition be
+  not regarded, an additional corner and side is introduced in the
+  polygon. Conversely it can be shown that the conformal representation
+  of a polygon upon the half plane can be effected in this way; for a
+  polygon of given position of more than three sides it is necessary for
+  this to determine the positions of all but three of a, b, c, ...;
+  three of them may always be supposed to be at arbitrary positions,
+  such as t = 0, t = 1, t = [oo].
+
+  As an illustration consider in the plane of z = x + iy, the portion of
+  the imaginary axis from the origin to z = ih, where h is positive and
+  less than unity; let C be this point z = ih; let BA be of length unity
+  along the positive real axis, B being the origin and A the point z =
+  1; let DE be of length unity along the negative real axis, D being
+  also the origin and E the point z = -1; let EFA be a semicircle of
+  radius unity, F being the point z = i. If we put [zeta] = [(z² +
+  h²)/(1 + h²z²)]^½, with [zeta] = 1 when z = 1, the function is single
+  valued within the semicircle, in the plane of z, which is slit along
+  the imaginary axis from the origin to z = ih; if we plot the value of
+  [zeta] upon another plane, as z describes the continuous curve ABCDE,
+  [zeta] will describe the real axis from [zeta] = 1 to [zeta] = -1, the
+  point C giving [zeta] = 0, and the points B, D giving the points
+  [zeta] = ±h. Near z = 0 the expansion of [zeta] is [zeta] - h = z² 1 -
+  h^4 / 2h + ..., or [zeta] + h = -z² (1 - h^4)/2h + ...; in either case
+  an increase of ½[pi] in the phase of z gives an increase of [pi] in
+  the phase of [zeta] - h or [zeta] + h. Near z = ih the expansion of
+  [zeta] is [zeta] = (z - ih)^½ [2ih/(1 - h^4)]^½ + ..., and an increase
+  of 2[pi] in the phase of z - ih also leads to an increase of [pi] in
+  the phase of [zeta]. Then as z describes the semicircle EFA, [zeta]
+  also describes a semicircle of radius unity, the point z = i becoming
+  [zeta] = i. There is thus a conformal representation of the interior
+  of the slit semicircle in the z-plane, upon the interior of the whole
+  semicircle in the [zeta]-plane, the function
+
+    z = [([zeta]² - h²) / (1 - h²[zeta]²)]^½
+
+  being single valued in the latter semicircle. By means of a
+  transformation t = ([zeta] + 1)²/([zeta] - 1)², the semicircle in the
+  plane of [zeta] can further be conformably represented upon the upper
+  half of the whole plane of t.
+
+  As another illustration we may take the conformal representation of an
+  equilateral triangle upon a half plane. Taking the elliptic function
+  RN(u) for which RN'²(u) = 4RN³(u) - 4, so that, with [epsilon] = exp
+  (2/3[pi]i), we have e1 = 1, e2 = [epsilon]², e3 = [epsilon], the half
+  periods may be taken to be
+                _                              _
+               / [oo]     dt                  / [oo]     dt
+    ½[omega] = |     -----------, ½[omega]' = |     ----------- = ½[epsilon][omega];
+              _/ 1   2(t³ - 1)^½             _/ e3  2(t³ - 1)^½
+
+  drawing the equilateral triangle whose vertices are O, of argument O,
+  A of argument [omega], and B of argument [omega] + [omega]' =
+  -[epsilon]²[omega], and the equilateral triangle whose angular points
+  are O, B and C, of argument [omega]', let E, of argument
+  {1/3}(2[omega] + [omega]'), and D, of argument 1/3([omega] +
+  2[omega]'), be the centroids of these triangles respectively, and let
+  BE, OE, AE cut OA, AB, BO in K, L, H respectively, and BD, OD, CD cut
+  OC, BC, OB in F, G, H respectively; then if u = [xi] + i[eta] be any
+  point of the interior of the triangle OEH and v = [epsilon]u0 =
+  [epsilon]([xi] - i[eta]) be any point of the interior of the triangle
+  OHD, the points respectively of the ten triangles OEK, EKA, EAL, ELB,
+  EBH, DHB, DBG, DGC, DCF, DFO are at once seen to be given by
+  -[epsilon]v, [omega] + [epsilon]u, [omega] - [eta]²v, [omega] +
+  [omega]' + [epsilon]²u, [omega] + [omega]' - v, [omega] + [omega]' -
+  u, [omega] + [omega]' + [epsilon]v, [omega]' - [epsilon]u, [omega]' +
+  [epsilon]²v, -[epsilon]²u. Further, when u is real, since the term
+  -2(u + m[omega] + m'[epsilon]²[omega])^(-3), which is the conjugate
+  complex of -2(u + m[omega] + m'[epsilon]²[omega])³, arises in the
+  infinite sum which expresses RN'(u), namely as -2(u + µ[omega] +
+  µ'[epsilon][omega])^(-3), where µ = m - m', µ' = -m', it follows that
+  RN'(u) is real; in a similar way we prove that RN'(u) is pure
+  imaginary when u is pure imaginary, and that RN'(u) = RN'([epsilon]u)
+  = RN'([epsilon]²u), as also that for v = [epsilon]u0, RN'(v) is the
+  conjugate complex of RN'(u). Hence it follows that the variable
+
+    t = ½iRN'(u)
+
+  takes each real value once as u passes along the perimeter of the
+  triangle ODE, being as can be shown respectively [oo], 1, 0, -1 at O,
+  D, H, E, and takes every complex value of imaginary part positive once
+  in the interior of this triangle. This leads to
+              _
+             / [oo]
+    u = 1/3i |     (t² - 1)^(-2/3) dt
+            _/ t
+
+  in accordance with the general theory.
+
+  It can be deduced that [tau] = t² represents the triangle ODH on the
+  upper half plane of [tau], and [zeta] = {i-[tau]^(-1)}^(½) represents
+  similarly the triangle OBD.
+
+§ 16. _Multiple valued Functions. Algebraic Functions._--The
+explanations and definitions of a monogenic function hitherto given have
+been framed for the most part with a view to single valued functions.
+But starting from a power series, say in z - c, which represents a
+single value at all points of its circle of convergence, suppose that,
+by means of a derived series in z - c', where c' is interior to the
+circle of convergence, we can continue the function beyond this, and
+then by means of a series derived from the first derived series we can
+make a further continuation, and so on; it may well be that when, after
+a closed circuit, we again consider points in the first circle of
+convergence, the value represented may not agree with the original
+value. One example is the case z^(½), for which two values exist for
+any value of z; another is the generalized logarithm [Lambda] (z), for
+which there is an infinite number of values. In such cases, as before,
+the region of existence of the function consists of all points which can
+be reached by such continuations with power series, and the singular
+points, which are the limiting points of the point-aggregate
+constituting the region of existence, are those points in whose
+neighbourhood the radii of convergence of derived series have zero for
+limit. In this description the point z = [oo] does not occupy an
+exceptional position, a power series in z - c being transformed to a
+series in 1/z when z is near enough to c by means of z - c = c(1 -
+cz^(-1)) [1 - (1 - cz^(-1))]^(-1), and a series in 1/z to a series in z
+- c, when z is near enough to c, by means of
+
+  1    1   /    z - c \^(-1)
+  -- = -- ( 1 + -----  ).
+  z    c   \      c   /
+
+  The commonest case of the occurrence of multiple valued functions is
+  that in which the function s satisfies an algebraic equation [f](s, z)
+  = p_0s^n + p1s^(n - 1) + ... + p_n = 0, wherein p0, p1, ... p_n are
+  integral polynomials in z. Assuming [f](s, z) incapable of being
+  written as a product of polynomials rational in s and z, and excepting
+  values of z for which the polynomial coefficient of s^n vanishes, as
+  also the values of z for which beside [f](s, z) = 0 we have also
+  (Pd)f(s, z)/(Pd)s = 0, and also in general the point z = [oo], the
+  roots of this equation about any point z = c are given by n power
+  series in z-c. About a finite point z = c for which the equation
+  (Pd)f(s, z)/(Pd)s = 0 is satisfied by one or more of the roots s of
+  [f](s, z) = 0, the n roots break up into a certain number of cycles,
+  the r roots of a cycle being given by a set of power series in a
+  radical (z - c)^(1/r), these series of the cycle being obtainable from
+  one another by replacing (z - c)^(1/r) by [omega](z - r)^(1/r), where
+  [omega], equal to exp (2[pi]ih/r), is one of the rth roots of unity.
+  Putting then z - c = t^r we may say that the r roots of a cycle are
+  given by a single power series in t, an increase of 2[pi] in the phase
+  of t giving an increase of 2[pi]r in the phase of z - c. This single
+  series in t, giving the values of s belonging to one cycle in the
+  neighbourhood of z = c when the phase of z-c varies through 2[pi]r, is
+  to be looked upon as defining a single _place_ among the aggregate of
+  values of z and s which satisfy [f](s, z) = 0; two such places may be
+  at the same _point_ (z = c, s = d) without coinciding, the
+  corresponding power series for the neighbouring points being
+  different. Thus for an ordinary value of z, z = c, there are n places
+  for which the neighbouring values of s are given by n power series in
+  z-c; for a value of z for which (Pd)f(s, z)/(Pd)s = 0 there are less
+  than n places. Similar remarks hold for the neighbourhood of z = [oo];
+  there may be n places whose neighbourhood is given by n power series
+  in z^(-1) or fewer, one of these being associated with a series in t,
+  where t = (z^(-1))^(1/r); the sum of the values of r which thus arise
+  is always n. In general, then, we may say, with t of one of the forms
+  (z-c), (z-c)^(1/r), z^(-1), (z^(-1))^(1/r). that the neighbourhood of
+  any place (c, d) for which [f](c, d) = 0 is given by a pair of
+  expressions z = c + P(t), s = d + Q(t), where P(t) is a (particular
+  case of a) power series vanishing for t = 0, and Q(t) is a power
+  series vanishing for t = 0, and t vanishes at (c, d), the expression
+  z-c being replaced by z^(-1) when c is infinite, and similarly the
+  expression s-d by s^(-1) when d is infinite. The last case arises when
+  we consider the finite values of z for which the polynomial
+  coefficient of s^n vanishes. Of such a pair of expressions we may
+  obtain a continuation by writing t = t0 + [lambda]1[tau] +
+  [lambda]2[tau]² + ·· , where [tau] is a new variable and [lambda]1 is
+  not zero; in particular for an ordinary finite place this equation
+  simply becomes t = t0 + [tau]. It can be shown that all the pairs of
+  power series z = c + P(t), s = d + Q(t) which are necessary to
+  represent all pairs of values of z, s satisfying the equation [f](s,
+  z) = 0 can be obtained from one of them by this process of
+  continuation, a fact which we express by saying that the equation
+  [f](s, z) = 0 defines a _monogenic algebraic construct_. With less
+  accuracy we may say that an irreducible algebraic equation [f](s, z) =
+  0 determines a single monogenic function s of z.
+
+  Any rational function of z and s, where [f](s, z) = 0, may be
+  considered in the neighbourhood of any place (c, d) by substituting
+  therein z = c + P(t), s = d + Q(t); the result is necessarily of the
+  form t^m H(t), where H(t) is a power series in t not vanishing for t =
+  0 and m is an integer. If this integer is positive, the function is
+  said to vanish to order m at the place; if this integer is negative, =
+  -µ, the function is infinite to order µ at the place. More generally,
+  if A be an arbitrary constant, and, near (c, d), R(s, z)-A is of the
+  form t^mH(t), where m is positive, we say that R(s, z) becomes m times
+  equal to A at the place; if R(s, z) is infinite of order µ at the
+  place, so also is R(s, z) - A. It can be shown that the sum of the
+  values of m at all the places, including the places z = [oo], where
+  R(s, z) vanishes, which we call the number of zeros of R(s, z) on the
+  algebraic construct, is finite, and equal to the sum of the values of
+  µ where R (s, z) is infinite, and more generally equal to the sum of
+  the values of m where R(s, z) = A; this we express by saying that a
+  rational function R(s, z) takes any value (including [oo]) the same
+  number of times on the algebraic construct; this number is called the
+  _order_ of the rational function.
+
+  That the total number of zeros of R (s, z) is finite is at once
+  obvious, these values being obtainable by rational elimination of s
+  between [f](s, z) = 0, R(s, z) = 0. That the number is equal to the
+  total number of infinities is best deduced by means of a theorem which
+  is also of more general utility. Let R(s, z) be any rational function
+  of s, z, which are connected by [f](s, z) = 0; about any place (c, d)
+  for which z = c + P(t), s = d + Q(t), expand the product
+
+            dz
+    R(s, z) --
+            dt
+
+  in powers of t and pick out the coefficient of t^(-1). There is only a
+  finite number of places of this kind. The theorem is that the sum of
+  these coefficients of t^(-1) is zero. This we express by
+     _          _
+    |        dz  |
+    |R(s, z) --  |      = 0.
+    |_       dt _|t^(-1)
+
+  The theorem holds for the case n = 1, that is, for rational functions
+  of one variable z; in that case, about any finite point we have z - c
+  = t, and about z = [oo] we have z^(-1) = t, and therefore dz/dt =
+  -t^(-2); in that case, then, the theorem is that in any rational
+  function of z,
+
+     _  / A1        A2               A_m    \
+    \  ( ----- + -------- + ... + ---------  ) + Pz^h + Qz^(h - 1) + ... + R,
+    /_  \z - a   (z - a)²         (z - a)^m /
+
+  the sum [Sigma]A1 of the sum of the residues at the finite poles is
+  equal to the coefficient of 1/z in the expansion, in ascending powers
+  of 1/z, about z = [oo]; an obvious result. In general, if for a finite
+  place of the algebraic construct associated with [f](s, z) = 0, whose
+  neighbourhood is given by z = c + t^r, s = d + Q(t), there be a
+  coefficient of t^(-1) in R(s, z)dz/dt, this will be r times the
+  coefficient of t^(-r) in R(s, z) or R[d + Q(t), c + t^r], namely will
+  be the coefficient of t^(-r) in the sum of the r series obtainable
+  from R[d + Q(t), c + t^r] by replacing t by [omega]t, where [omega] is
+  an rth root of unity; thus the sum of the coefficients of t^(-1) in
+  R(s, z)dz/dt for all the places which arise for z = c, and the
+  corresponding values of s, is equal to the coefficient of (z - c)^(-1)
+  in R(s1, z) + R(s2z) + ... + R(s_n, z), where s1, ... s_n are the n
+  values of s for a value of z near to z = c; this latter sum [Sigma]
+  R(s_i, z) is, however, a rational function of z only. Similarly, near
+  z = [oo], for a place given by z^(-1) = t^r, s = d + Q(t), or s^(-1) =
+  Q(t), the coefficient of t^(-1) in R(s, z)dz/dt is equal to -r times
+  the coefficient of t^r in R[d + Q(t), t^(-r)], that is equal to the
+  negative coefficient of z^(-l) in the sum of the r series R[d +
+  Q([omega]t), t^(-r)], so that, as before, the sum of the coefficients
+  of t^(-1) in R(s, z)dz/dt at the various places which arise for z =
+  [oo] is equal to the negative coefficient of z^(-1) in the same
+  rational function of z, [Sigma] R(s_i, z). Thus, from the
+  corresponding theorem for rational functions of one variable, the
+  general theorem now being proved is seen to follow.
+
+  Apply this theorem now to the rational function of s and z,
+
+       1    dR(s, z)
+    ------- -------;
+    R(s, z)   dz
+
+  at a zero of R(s, z) near which R(s, z) = t^mH(t), we have
+
+       1    dR(s, z) dz    d
+    ------- -------  -- = -- {[lambda] [R(s, z)]}
+    R(s, z)    dz    dt   dt
+
+  where [lambda] denotes the generalized logarithmic function, that is
+  equal to
+
+    mt^(-1) + power series in t;
+
+  similarly at a place for which R(s, z) = t^(-µ) K(t); the theorem
+     _                     _
+    |     1    dR(s, z) dz  |
+    |  ------- -------- --  | t^(-1) = 0
+    |_ R(s, z)    dz    dt _|
+
+  thus gives [Sigma]m = [Sigma]µ, or, in words, the total number of
+  zeros of R(s, z) on the algebraic construct is equal to the total
+  number of its poles. The same is therefore true of the function R(s,
+  z) - A, where A is an arbitrary constant; thus the number in question,
+  being equal to the number of poles of R(s, z) - A, is equal also to
+  the number of times that R(s, z) = A on the algebraic construct.
+
+  We have seen above that all single valued doubly periodic meromorphic
+  functions, with the same periods, are rational functions of two
+  variables s, z connected by an equation of the form s² = 4z³ + Az + B.
+  Taking account of the relation connecting these variables s, z with
+  the argument of the doubly periodic functions (which was above denoted
+  by z), it can then easily be seen that the theorem now proved is a
+  generalization of the theorem proved previously establishing for a
+  doubly periodic function a definite _order_. There exists a
+  generalization of another theorem also proved above for doubly
+  periodic functions, namely, that the sum of the values of the argument
+  in one parallelogram of periods for which a doubly periodic function
+  takes a given value is independent of that value; this generalization,
+  known as Abel's Theorem, is given § 17 below.
+
+§ 17. _Integrals of Algebraic Functions._--In treatises on Integral
+Calculus it is proved that if R(z) denote any rational function, an
+indefinite integral [int]R(z)dz can be evaluated in terms of rational
+and logarithmic functions, including the inverse trigonometrical
+functions. In generalization of this it was long ago discovered that if
+s² = az² + bz + c and R(s, z) be any rational function of s, z any
+integral [int]R(s, z)dz can be evaluated in terms of rational functions
+of s, z and logarithms of such functions; the simplest case is
+[int]s^(-1)dz or [int](az² + bz + c)^(-½)dz. More generally if f(s, z) =
+0 be such a relation connecting s, z that when [theta] is an appropriate
+rational function of s and z both s and z are rationally expressible, in
+virtue of [f](s, z) = 0 in terms of [theta], the integral [int]R(s, z)dz
+is reducible to a form [int]H ([theta])d[theta], where H([theta]) is
+rational in [theta], and can therefore also be evaluated by rational
+functions and logarithms of rational functions of s and z. It was
+natural to inquire whether a similar theorem holds for integrals
+[int]R(s, z)dz wherein s² is a cubic polynomial in z. The answer is in
+the negative. For instance, no one of the three integrals
+    _     _      _
+   / dz  / zdz  /    dz
+   | --, | ---, | --------
+  _/ s  _/  s  _/ (z - c)s
+
+can be expressed by rational and logarithms of rational functions of s
+and z; but it can be shown that every integral [int]R(s, z)dz can be
+expressed by means of integrals of these three types together with
+rational and logarithms of rational functions of s and z (see below
+under § 20, Elliptic Integrals). A similar theorem is true when s² =
+quartic polynomial in z; in fact when s² = A(z - a)(z - b)(z - c)(z -
+d), putting y = s(z - a)^(-2), x = (z - a)^(-1), we obtain y2 = cubic
+polynomial in x. Much less is the theorem true when the fundamental
+relation [f](s, z) = 0 is of more general type. There exists then,
+however, a very general theorem, known as _Abel's Theorem_, which may be
+enunciated as follows: Beside the rational function R(s, z) occurring in
+the integral [int]R(s, z)dz, consider another rational function H(s, z);
+let (a1), ... (a_m) denote the places of the construct associated with
+the fundamental equation [f](s, z) = 0, for which H(s, z) is equal to
+one value A, each taken with its proper multiplicity, and let (b1), ...
+(b_m) denote the places for which H(s, z) = B, where B is another value;
+then the sum of the m integrals [int] [(b_i) to (a_i)] R(s, z)dz is
+equal to the sum of the coefficients of t^(-1) in the expansions of the
+function
+
+          dz           / H(s, z) - B \
+  R(s, z) -- [lambda] (  -----------  ),
+          dt           \ H(s, z) - A /
+
+where [lambda] denotes the generalized logarithmic function, at the
+various places where the expansion of R(s, z)dz/dt contains negative
+powers of t. This fact may be obtained at once from the equation
+   _                        _
+  |       1              dz  |
+  |  ----------- R(s, z) --  |      = 0,
+  |_ H(s, z) - µ         dt _|t^(-1)
+
+wherein µ is a constant. (For illustrations see below, under § 20,
+Elliptic Integrals.)
+
+§ 18. _Indeterminateness of Algebraic Integrals._--The theorem that the
+integral [int][a to x] [f](z)dz is independent of the path from a to z,
+holds only on the hypothesis that any two such paths are equivalent,
+that is, taken together from the complete boundary of a region of the
+plane within which [f](z) is finite and single valued, besides being
+differentiable. Suppose that these conditions fail only at a finite
+number of isolated points in the finite part of the plane. Then any path
+from a to z is equivalent, in the sense explained, to any other path
+together with closed ~~ paths beginning and ending at the arbitrary
+point a each enclosing one or more of the exceptional points, these
+closed paths being chosen, when [f](z) is not a single valued function,
+so that the final value of [f](z) at a is equal to its initial value. It
+is necessary for the statement that this condition may be capable of
+being satisfied.
+
+  For instance, the integral [int][1 to z] z^(-1)dz is liable to an
+  additive indeterminateness equal to the value obtained by a closed
+  path about z = 0, which is equal to 2[pi]i; if we put u = [int][1 to
+  z] z^(-1)dz and consider z as a function of u, then we must regard
+  this function as unaffected by the addition of 2[pi]i to its argument
+  u; we know in fact that z = exp (u) and is a single valued function of
+  u, with the period 2[pi]i. Or again the integral [int][0 to z] (1 +
+  z²)^(-1)dz is liable to an additive indeterminateness equal to the
+  value obtained by a closed path about either of the points z = ±i;
+  thus if we put u = [int][0 to z] (1 + z²)^(-1)dz, the function z of u
+  is periodic with period [pi], this being the function tan (u). Next we
+  take the integral u = [int][(0) to (z)] (1 - z²)^(-½)dz, agreeing that
+  the upper and lower limits refer not only to definite values of z, but
+  to definite values of z each associated with a definite determination
+  of the sign of the associated radical (1 - z²)^(-½). We suppose 1 + z,
+  1 - z each to have phase zero for z = 0; then a single closed circuit
+  of z = -1 will lead back to z = 0 with (l - z²)^½ = -1; the additive
+  indeterminateness of the integral, obtained by a closed path which
+  restores the initial value of the subject of integration, may be
+  obtained by a closed circuit containing both the points ±1 in its
+  interior; this gives, since the integral taken about a vanishing
+  circle whose centre is either of the points z = ± 1 has ultimately the
+  value zero, the sum
+      _              _                  _                  _
+     / -1   dz      / 0       dz       / 1       dz       / 0     dz
+     |   -------- + |    ----------- + |    ----------- + |   ----------,
+    _/ 0 (1-z²)^½  _/-1  -(1 - z²)^½  _/ 0  -(1 - z²)^½  _/ 1 (1 - z²)^½
+
+  where, in each case, (1 - z²)^½ is real and positive; that is, it gives
+        _
+       / 1     dz
+    -4 |   ----------
+      _/ 0 (1 - z²)^½
+
+  or 2[pi]. Thus the additive indeterminateness of the integral is of
+  the form 2k[pi], where k is an integer, and the function z of u, which
+  is sin (u), has 2[pi] for period. Take now the case
+         _
+        / (z)                   dz
+    u = |      ------------------------------------,
+       _/ (z0) [root]{(z - a)(z - b)(z - c)(z - d)}
+
+  adopting a definite determination for the phase of each of the factors
+  z - a, z - b, z - c, z - d at the arbitrary point z0, and supposing
+  the upper limit to refer, not only to a definite value of z, but also
+  to a definite determination of the radical under the sign of
+  integration. From z0 describe a closed loop about the point z = a,
+  consisting, suppose, of a straight path from z0 to a, followed by a
+  vanishing circle whose centre is at a, completed by the straight path
+  from a to z0. Let similar loops be imagined for each of the points b,
+  c, d, no two of these having a point in common. Let A denote the value
+  obtained by the positive circuit of the first loop; this will be in
+  fact equal to twice the integral taken from z0 along the straight path
+  to a; for the contribution due to the vanishing circle is ultimately
+  zero, and the effect of the circuit of this circle is to change the
+  sign of the subject of integration. After the circuit about a, we
+  arrive back at z0 with the subject of integration changed in sign; let
+  B, C, D denote the values of the integral taken by the loops enclosing
+  respectively b, c and d when in each case the initial determination of
+  the subject of integration is that adopted in calculating A. If then
+  we take a circuit from z0 enclosing both a and b but not either c or
+  d, the value obtained will be A - B, and on returning to z0 the
+  subject of integration will have its initial value. It appears thus
+  that the integral is subject to an additive indeterminateness equal to
+  any one of the six differences such as A - B. Of these there are only
+  two linearly independent; for clearly only A - B, A - C, A - D are
+  linearly independent, and in fact, as we see by taking a closed
+  circuit enclosing all of a, b, c, d, we have A - B + C - D = 0; for
+  there is no other point in the plane beside a, b, c, d about which the
+  subject of integration suffers a change of sign, and a circuit
+  enclosing all of a, b, c, d may by putting z = 1/[zeta] be reduced to
+  a circuit about [zeta] = 0 about which the value of the integral is
+  zero. The general value of the integral for any position of z and the
+  associated sign of the radical, when we start with a definite
+  determination of the subject of integration, is thus seen to be of the
+  form u0 + m(A - B) + n(A - C), where m and n are integers. The value
+  of A - B is independent of the position of z0, being obtainable by a
+  single closed positive circuit about a and b only; it is thus equal to
+  twice the integral taken once from a to b, with a proper initial
+  determination of the radical under the sign of integration. Similar
+  remarks to the above apply to any integral [int]H(z)dz, in which H(z)
+  is an algebraic function of z; in any such case H(z) is a rational
+  function of z and a quantity s connected therewith by an irreducible
+  rational algebraic equation [f](s, z) = 0. Such an integral [f]K(z,
+  s)dz is called an Abelian Integral.
+
+§ 19. _Reversion of an Algebraic Integral._--In a limited number of
+cases the equation u = [int] [z0 to z] H(z)dz, in which H(z) is an
+algebraic function of z, defines z as a single valued function of u.
+Several cases of this have been mentioned in the previous section; from
+what was previously proved under § 14, _Doubly Periodic Functions_, it
+appears that it is necessary for this that the integral should have at
+most two linearly independent additive constants of indeterminateness;
+for instance, for an integral
+       _
+      / z
+  u = |   [(z - a)(z - b)(z - c)(z - d)(z - e)(z - f)]^(-½) dz,
+     _/ z0
+
+there are three such constants, of the form A - B, A - C, A - D, which
+are not connected by any linear equation with integral coefficients, and
+z is not a single valued function of u.
+
+§ 20. _Elliptic Integrals._--An integral of the form [int] R(z, s)dz,
+where s denotes the square root of a quartic polynomial in z, which may
+reduce to a cubic polynomial, and R denotes a rational function of z and
+s, is called an _elliptic integral_.
+
+  To each value of z belong two values of s, of opposite sign; starting,
+  for some particular value of z, with a definite one of these two
+  values, the sign to be attached to s for any other value of z will be
+  determined by the path of integration for z. When z is in the
+  neighbourhood of any finite value z0 for which the radical s is not
+  zero, if we put z - z0 = t, we can find s - s0 = a power series in t,
+  say s = s0 + Q(t); when z is in the neighbourhood of a value, a, for
+  which s vanishes, if we put z = a + t², we shall obtain s = tQ(t),
+  where Q(t) is a power series in t; when z is very large and s² is a
+  quartic polynomial in z, if we put z^(-1) = t, we shall find s^(-1) =
+  t²Q(t); when z is very large and s² is a cubic polynomial in z, if we
+  put z^(-1) = t², we shall find s^(-l) = t³Q(t). By means of
+  substitutions of these forms the character of the integral [int] R(z,
+  s)dz may be investigated for any position of z; in any case it takes a
+  form [int] [Ht^(-m) + Kt^(-m + 1) + ... + Pt^(-1) + R + St + ...]dt
+  involving only a finite number of negative powers of t in the subject
+  of integration. Consider first the particular case [int] s^(-1)dz; it
+  is easily seen that neither for any finite nor for infinite values of
+  z can negative powers of t enter; the integral is _everywhere finite_,
+  and is said to be of _the first kind_; it can, moreover, be shown
+  without difficulty that no integral [int] R(z, s)dz, save a constant
+  multiple of [int] s^(-1)dz, has this property. Consider next, s² being
+  of the form a0z^4 + 4a1z³ + ..., wherein a0 may be zero, the integral
+  [int] {a0z² + 2a1z) s^(-1)dz; for any finite value of z this integral
+  is easily proved to be everywhere finite; but for infinite values of z
+  its value is of the form At^(-1) + Q(t), where Q(t) is a power series;
+  denoting by [root]a0 a particular square root of a0 when a0 is not
+  zero, the integral becomes infinite for z = [oo] for both signs of s,
+  the value of A being + [root]a0 or - [root]a0 according as s is
+  [root]a0·z² (1 + [2a1/a0] z^(-1) + ...) or is the negative of this;
+  hence the integral J1 = [int] ([a0z² + 2a1z / s] + [root]a0)dz becomes
+  infinite when z is infinite, for the former sign of s, its infinite
+  term being 2[root]a0 t^(-1) or 2a0·z, but does not become infinite for
+  z infinite for the other sign of s. When a0 = 0 the signs of s for z =
+  [oo] are not separated, being obtained one from the other by a circuit
+  of z about an infinitely large circle, and the form obtained
+  represents an integral becoming infinite as before for z = [oo], its
+  infinite part being 2[root]a1·t^(-1) or 2[root]a1·[root]z. Similarly
+  if z0 be any finite value of z which is not a root of the polynomial
+  [f](z) to which s² is equal, and s0 denotes a particular one of the
+  determinations of s for z = z0, the integral
+          _
+         /  / s0² + ½(z - z0) [f]'(z0)      s0     \
+    J2 = | (  ------------------------ + ---------  ) dz,
+        _/  \       (z - z0)²s           (z - z0)² /
+
+  wherein [f]'(z) = d[f](z)/dz, becomes infinite for z = z0, s = s0, but
+  not for z = z0, s = -s0. its infinite term in the former case being
+  the negative of 2s0(z - z0). For no other finite or infinite value of
+  z is the integral infinite. If z = [theta] be a root of [f](z), in
+  which case the corresponding value of s is zero, the integral
+                         _
+                        /       dz
+    J3 = ½[f]'([theta]) | --------------
+                       _/ (z - [theta])s
+
+  becomes infinite for z = 0, its infinite part being, if z - [theta] =
+  t², equal to -[[f]'([theta])] ½t^(-1): and this integral is not
+  elsewhere infinite. In each of these cases, of the integrals J1, J2,
+  J3, the subject of integration has been chosen so that when the
+  integral is written near its point of infinity in the form
+  [int][At^(-2) + Bt^(-1) + Q(t)]dt, the coefficient B is zero, so that
+  the infinity is of algebraic kind, and so that, when there are two
+  signs distinguishable for the critical value of z, the integral
+  becomes infinite for only one of these. An integral having only
+  algebraic infinities, for finite or infinite values of z, is called an
+  integral of the _second kind_, and it appears that such an integral
+  can be formed with only one such infinity, that is, for an infinity
+  arising only for one particular, and arbitrary, pair of values (s, z)
+  satisfying the equation s² = [f](z), this infinity being of the first
+  order. A function having an algebraic infinity of the mth order (m >
+  1), only for one sign of s when these signs are separable, at (1) z =
+  [oo], (2) z = z0, (3) z = a, is given respectively by (s d/dz)^(m -
+  1)J1, (s d/dz)^(m - 1) J2, (s d/dz )^(m - 1) J3, as we easily see. If
+  then we have any elliptic integral having algebraic infinities we can,
+  by subtraction from it of an appropriate sum of constant multiples of
+  J1, J2, J3 and their differential coefficients just written down,
+  obtain, as the result, an integral without algebraic infinities. But,
+  in fact, if J, J^1 denote any two of the three integrals J1, J2, J3,
+  there exists an equation AJ + BJ' + C[f]s^(-1)dz = rational function
+  of s, z, where A, B, C are properly chosen constants. For the rational
+  function
+
+    s + s0
+    ------ + z [root]a0
+    z - z0
+
+  is at once found to become infinite for (z0, s0), not for (z0, -s0),
+  its infinite part for the first point being 2s/(z - z0), and to become
+  infinite for z infinitely large, and one sign of s only when these are
+  separable, its infinite part there being 2z [root] a0 or 2 [root] a1
+  [root] z when a0 = 0. It does not become infinite for any other pair
+  (z, s) satisfying the relation s² = [f](z); this is in accordance
+  with the easily verified equation
+                                                      _
+    s + s0                                           / dz
+    ------- + z [root]a0 - J1 + J2 + (a0z0² + 2a1z0) | -- = 0;
+    z - z^0                                         _/ s
+
+  and there exists the analogous equation
+                                                                    _
+         s                                                         / dz
+    ----------- + z [root]a0 - J1 + J3 + (a0[theta]² + 2a1[theta]) | -- = 0.
+    z - [theta]                                                   _/ s
+
+  Consider now the integral
+          _
+         /  /s + s0                \  dz
+    P =  | ( --------- + z [root]a0 ) --;
+        _/  \z - z0                /  2s
+
+  this is at once found to be infinite, for finite values of z, only for
+  (z0, s0), its infinite part being log (z - z0), and for z = [oo], for
+  one sign of s only when these are separable, its infinite part being
+  -log t, that is -log z when a0 /= 0, and -log (z^½) when a0 = 0. And,
+  if [f]([theta]) = 0, the integral
+          _
+         /   /    s                   \  dz
+    P1 = |  ( ----------- + z [root]a0 ) --
+        _/   \z - [theta]             /  2s
+
+  is infinite at z = [theta], s = 0 with an infinite part log t, that is
+  log (z - [theta])^½, is not infinite for any other finite value of z,
+  and is infinite like P for z = [oo]. An integral possessing such
+  logarithmic infinities is said to be of the third kind.
+
+  Hence it appears that any elliptic integral, by subtraction from it of
+  an appropriate sum formed with constant multiples of the integral J3
+  and the rational functions of the form (s d/dz)^(m - 1) J1 with
+  constant multiples of integrals such as P or P1, with constant
+  multiples of the integral u = [int]s^(-1)dz, and with rational
+  functions, can be reduced to an integral H becoming infinite only for
+  z = [oo], for one sign of s only when these are separable, its
+  infinite part being of the form A log t, that is, A log z or A log
+  (z^½). Such an integral H = [int]R(z, s)dz does not exist, however, as
+  we at once find by writing R(z, s) = P(z) + sQ(z), where P(z), Q(z)
+  are rational functions of z, and examining the forms possible for
+  these in order that the integral may have only the specified infinity.
+  An analogous theorem holds for rational functions of z and s; there
+  exists no rational function which is finite for finite values of z and
+  is infinite only for z = [oo] for one sign of s and to the first order
+  only; but there exists a rational function infinite in all to the
+  first order for each of two or more pairs (z, s), however they may be
+  situated, or infinite to the second order for an arbitrary pair (z,
+  s); and any rational function may be formed by a sum of constant
+  multiples of functions such as
+
+    s + s0                      s
+    ------ + z [root]a0 or ----------- + z [root]a0
+    z - z0                 z - [theta]
+
+  and their differential coefficients.
+
+  The consideration of elliptic integrals is therefore reducible to that
+  of the three
+         _          _                                      _
+        /  dz      /  /a0z² + 2a1z             \          /  /s + s0             \ dz
+    u = |  --, J = | ( ----------- + z [root]a0 ) dz, P = | ( ------ + z [root]a0 )--
+       _/  s      _/  \     s                  /         _/  \z - z0             / 2s
+
+  respectively of the first, second and third kind. Now the equation s²
+  = a0z^4 + ... = a0(z - [theta]) (z - [phi]) (z - [psi]) (z - [chi]),
+  by putting
+
+    y = 2s(z - [theta])^(-2) [a0([theta] - [phi]) ([theta] - [psi]) ([theta] - [chi])]^(-½)
+
+             1        1   /       1                 1                 1       \
+    x = ----------- + -- ( --------------- + -------------- + ---------------  )
+        z - [theta]   3   \[theta] - [phi]   [theta] - [psi]   [theta] - [chi]/
+
+  is at once reduced to the form y² = 4x³- g2x - g3 = 4(x - e1)(x - e2(x
+  - e3), say; and these equations enable us to express s and z
+  rationally in terms of x and y. It is therefore sufficient to consider
+  three elliptic integrals
+         _          _           _
+        /  dx      /  xdx      /  y + y0  dx
+    u = |  --, J = |  ---, P = |  ------  --.
+       _/  y      _/   y      _/  x - x0  2y
+
+  Of these consider the first, putting
+         _
+        / ([oo]) dx
+    u = |        --,
+       _/ (x)    y
+
+  where the limits involve not only a value for x, but a definite sign
+  for the radical y. When x is very large, if we put x^(-1) = t², y^(-1)
+  = 2t³(1 - ¼ g2t^4 - ¼ g3t^6)^(-½), we have
+          _
+         / t  /    1             \          1
+    u =  |   ( 1 + -- g2t^4 + ... )dt = t + -- g2t^5 + ...,
+        _/ 0  \    8             /          40
+
+  whereby a definite power series in u, valid for sufficiently small
+  value of u, is found for t, and hence a definite power series for x,
+  of the form
+
+    x = u^(-2) + (1/20)g2u² + ...
+
+  Let this expression be valid for 0 < |u| < R, and the function defined
+  thereby, which has a pole of the second order for u = 0, be denoted by
+  [phi](u). In the range in question it is single valued and satisfies
+  the differential equation
+
+    [[phi]'(u)]² = 4[[phi](u)]³ - g2[phi](u) - g3;
+
+  in terms of it we can write x = [phi](u), y = -[phi]'(u), and,
+  [phi]'(u) being an odd function, the sign attached to y in the
+  original integral for x = [oo] is immaterial. Now for any two values
+  u, v in the range in question consider the function
+                 _                     _
+                | [phi]'(u) - [phi]'(v) |²
+    F(u, v) = ¼ | --------------------- | - [phi](u) - [phi](v);
+                |_ [phi](u) - [phi](v) _|
+
+  it is at once seen, from the differential equation, to be such that
+  (Pd)F/(Pd)u = (Pd)F/(Pd)v; it is therefore a function of u + v;
+  supposing |u + v| < R we infer therefore, by putting v = 0, that
+                      _                      _
+                     | [phi]'(u) - [phi]'(v)] |²
+    [phi](u + v) = ¼ | ---------------------  | - [phi](u) - [phi](v).
+                     |_ [phi](u) - [phi](v)  _|
+
+  By repetition of this equation we infer that if u1, ... u_n be any
+  arguments each of which is in absolute value less than R, whose sum is
+  also in absolute value less than R, then [phi](u1 + ... + u_n) is a
+  rational function of the 2n functions [phi](u_s), [phi]'(u_s); and
+  hence, if |u| < R, that
+
+    [phi](u) = H [[phi](u/n), [phi]'(u/n)],
+
+  where H is some rational function of the arguments [phi](u/n),
+  [phi]'(u/n). In fact, however, so long as |u/n| < R, each of the
+  functions [phi](u/n), [phi]'(u/n) is single valued and without
+  singularity save for the pole at u = 0; and a rational function of
+  single valued functions, each of which has no singularities other than
+  poles in a certain region, is also a single valued function without
+  singularities other than poles in this region. We infer, therefore,
+  that the function of u expressed by H[[phi](u/n), [phi]'(u/n)] is
+  single valued and without singularities other than poles so long as
+  |u| < nR; it agrees with [phi](u) when |u| < R, and hence furnishes a
+  continuation of this function over the extended range |u| < nR.
+  Moreover, from the method of its derivation, it satisfies the
+  differential equation [[phi]'(u)]² = 4[[phi](u)]³ - g2[phi](u) - g3.
+  This equation has therefore one solution which is a single valued
+  monogenic function with no singularities other than poles for any
+  finite part of the plane, having in particular for u = 0, a pole of
+  the second order; and the method adopted for obtaining this near u = 0
+  shows that the differential equation has no other such solution. This,
+  however, is not the only solution which is a single valued meromorphic
+  function, a the functions [phi](u + [alpha]), wherein [alpha] is
+  arbitrary, being such. Taking now any range of values of u, from u =
+  0, and putting for any value of u, x = [phi](u), y = -[phi]'(u), so
+  that y² = 4x³ - g2x - g3, we clearly have
+         _
+        / ([oo]) dx
+    u = |        --;
+       _/ (x, y) y
+
+  conversely if x0 = [phi](u0), y0 = -[phi]'(u0) and [xi], [eta] be any
+  values satisfying [eta]2 = 4[xi]² - g2[xi] - g3, which are
+  sufficiently near respectively to x0, y0, while v is defined by
+               _
+              / ([xi], [eta])  d[xi]
+    v - u0 = -|                -----,
+             _/ (x0, y0)       [eta]
+
+  then [xi], [eta] are respectively [phi](v) and -[phi]'(v); for this
+  equation leads to an expansion for [xi]-x0 in terms of v = u0 and only
+  one such expansion, and this is obtained by the same work as would be
+  necessary to expand [phi](v) when v is near to u0; the function
+  [phi](u) can therefore be continued by the help of this equation, from
+  v = u0, provided the lower limit of |[xi] - x0| necessary for the
+  expansions is not zero in the neighbourhood of any value (x0, y0). In
+  fact the function [phi](u) can have only a finite number of poles in
+  any finite part of the plane of u; each of these can be surrounded by
+  a small circle, and in the portion of the finite part of the plane of
+  u which is outside these circles, the lower limit of the radii of
+  convergence of the expansions of [phi](u) is greater than zero; the
+  same will therefore be the case for the lower limit of the radii |[xi]
+  - x0| necessary for the continuations spoken of above provided that
+  the values of ([xi], [eta]) considered do not lead to infinitely
+  increasing values of v; there does not exist, however, any definite
+  point ([xi]0, [eta]0) in the neighbourhood of which the integral [int]
+  [([xi], [eta]) to (x0, y0)] d[xi]/[eta] increases indefinitely, it is
+  only by a path of infinite length that the integral can so increase.
+  We infer therefore that if ([xi],[eta]) be any point, where [eta]2 =
+  4[xi]³ - g2[xi] - g3, and v be defined by
+         _
+        / ([oo])         dx
+    v = |                -- ,
+       _/ ([xi], [eta])  y
+
+  then [xi] = [phi](v) and [eta] = -[phi]'(v). Thus this equation
+  determines ([xi], [eta]) without ambiguity. In particular the additive
+  indeterminatenesses of the integral obtained by closed circuits of the
+  point of integration are periods of the function [phi](u); by
+  considerations advanced above it appears that these periods are sums
+  of integral multiples of two which may be taken to be
+                _                        _
+               / [oo]  dx               / [oo]  dx
+    [omega] = 2|       --, [omega]' = 2 |       --;
+              _/ e1    y               _/ e3    y
+
+  these quantities cannot therefore have a real ratio, for else, being
+  periods of a monogenic function, they would, as we have previously
+  seen, be each integral multiples of another period; there would then
+  be a closed path for (x, y), starting from an arbitrary point (x0,
+  y0), other than one enclosing two of the points (e1, 0), (e2, 0), (e3,
+  0), ([oo], [oo]), which leads back to the initial point (x0, y0),
+  which is impossible. On the whole, therefore, it appears that the
+  function [phi](u) agrees with the function RN(u) previously discussed,
+  and the discussion of the elliptic integrals can be continued in the
+  manner given under § 14, _Doubly Periodic Functions_.
+
+§ 21. _Modular Functions._--One result of the previous theory is the
+remarkable fact that if
+              _                        _
+             / [oo]  dx               / [oo]  dx
+  [omega] = 2|       --, [omega]' = 2 |       --,
+            _/ e1    y               _/ e3    y
+
+where y² = 4(x - e1) (x - e2) (x - e3), then we have
+
+  e1 = (½[omega])^(-2) + [Sigma]' {[(m + ½)[omega] + m'[omega]']^(-2) -
+    [m[omega] + m'[omega]']^(-2)},
+
+and a similar equation for e3, where the summation refers to all integer
+values of m and m' other than the one pair m = 0, m' = 0. This, with
+similar results, has led to the consideration of functions of the
+complex ratio [omega]'/[omega].
+
+  It is easy to see that the series for RN(u), u^(-2) + [Sigma] [(u +
+  m[omega] + m'[omega]')²-(m[omega] + m'[omega]')²], is unaffected by
+  replacing [omega], [omega]' by two quantities [Omega], [Omega]' equal
+  respectively to p[omega] + q[omega]', p'[omega]' + q'[omega]', where
+  p, q, p', q' are any integers for which pq' - p'q = ±1; further it can
+  be proved that all substitutions with integer coefficients [Omega] =
+  p[omega] + q[omega]', [Omega]' = p'[omega] + q'[omega]', wherein pq' -
+  p'q = 1, can be built up by repetitions of the two particular
+  substitutions ([Omega] = -[omega]', [Omega]' = [omega]), ([Omega] =
+  [omega], [Omega]' = [omega] + [omega]'). Consider the function of the
+  ratio [omega]'/[omega] expressed by
+
+    h = -RN (½[omega]') / RN(½[omega]);
+
+  it is at once seen from the properties of the function RN(u) that by
+  the two particular substitutions referred to we obtain the
+  corresponding substitutions for h expressed by
+
+    h' = 1/h, h' = 1 - h;
+
+  thus, by all the integer substitutions [Omega] = p[omega] + q[omega]',
+  [Omega]' = p'[omega] + q'[omega]', in which pq' - p'q = 1, the
+  function h can only take one of the six values h, 1/h, 1 - h, 1/(1 -
+  h), h/(h - 1), (h - 1)/h, which are the roots of an equation in
+  [theta],
+
+    (1 - [theta] + [theta]²)³   (1 - h + h²)³
+    ------------------------- = -------------;
+     [theta]²(1 - [theta])²      h²(1 - h)²
+
+  the function of [tau], = [omega]'/[omega], expressed by the right
+  side, is thus unaltered by every one of the substitutions [tau]' = (p'
+  + q'[tau] / p + q[tau]), wherein p, q, p', q' are integers having pq'
+  - p'q = 1. If the imaginary part [sigma], of [tau], which we may write
+  [tau] = [rho] + i[sigma], is positive, the imaginary part of [tau]',
+  which is equal to [sigma](pq' - p'q)/[(p + q[rho])² + q²[sigma]²], is
+  also positive; suppose [sigma] to be positive; it can be shown that
+  the upper half of the infinite plane of the complex variable [tau] can
+  be divided into regions, all bounded by arcs of circles (or straight
+  lines), no two of these regions overlapping, such that any
+  substitution of the kind under consideration, [tau]' = (p' +
+  q'[tau])/(p + q[tau]) leads from an arbitrary point [tau], of one of
+  these regions, to a point [tau]' of another; taking [tau] = [rho] +
+  i[sigma], one of these regions may be taken to be that for which -½ <
+  [rho] < ½, [rho]² + [sigma]² > 1, together with the points for which
+  [rho] is negative on the curves limiting this region; then every other
+  region is obtained from this so-called fundamental region by one and
+  only one of the substitutions [tau] = (p' + q'[tau])/(p + q[tau]), and
+  hence by a definite combination of the substitutions [tau]' =
+  -1/[tau], [tau]' = 1 + [tau]. Upon the infinite half plane of [tau],
+  the function considered above,
+
+               4  [RN²(½[omega]) + RN(z(½[omega]) RN(½[omega]') + RN² (½[omega]')]³
+    z([tau]) = -- -----------------------------------------------------------------
+               27    RN²(½[omega]) RN²(½[omega]') [RN(½[omega]) + RN(½[omega]')]²
+
+  is a single valued monogenic function, whose only essential
+  singularities are the points [tau]' = (p' + q'[tau])/(p + q[tau]) for
+  which [tau] = [oo], namely those for which [tau]' is any real rational
+  value; the real axis is thus a line over which the function z([tau])
+  cannot be continued, having an essential singularity in every arc of
+  it, however short; in the fundamental region, z([tau]) has thus only
+  the single essential singularity, r = [rho] + i[sigma], where [sigma]
+  = [oo]; in this fundamental region z([tau]) takes any assigned complex
+  value just once, the relation z([tau]') = z([tau]) requiring, as can
+  be shown, that [tau]' is of the form (p' + q'[tau])/(p + q[tau]), in
+  which p, q, p', q' are integers with pq' - p'q = 1; the function
+  z([tau]) has thus a similar behaviour in every other of the regions.
+  The division of the plane into regions is analogous to the division of
+  the plane, in the case of doubly periodic functions, into
+  parallelograms; in that case we considered only functions without
+  essential singularities, and in each of the regions the function
+  assumed every complex value twice, at least. Putting, as another
+  function of [tau], J([tau]) = z([tau])[z([tau]) - 1], it can be shown
+  that J([tau]) = 0 for [tau] = exp (2/3[pi]i), that J([tau]) = 1 for
+  [tau] = i, these being values of [tau] on the boundary of the
+  fundamental region; like z([tau]) it has an essential singularity for
+  [tau] = [rho] + i[sigma], [sigma] = + [oo]. In the theory of linear
+  differential equations it is important to consider the inverse
+  function [tau](J); this is infinitely many valued, having a cycle of
+  three values for circulation of J about J = 0 (the circuit of this
+  point leading to a linear substitution for [tau] of period 3, such as
+  [tau]' = -(1 + [tau])^(-1)), having a cycle of two values about J = 1
+  (the circuit leading to a linear substitution for [tau] of period 2,
+  such as [tau]' = -[tau]^(-1)), and having a cycle of infinitely many
+  values about J = [oo] (the circuit leading to a linear substitution
+  for [tau] which is not periodic, such as [tau]' = 1 + [tau]). These
+  are the only singularities for the function [tau](J). Each of the
+  functions
+                                       _                                _
+                                      |   RN(½[omega]) + 2RN(½[omega]')  |^(1/8)
+    [J([tau])]^(1/3), [J([tau])-1]^½, | - -----------------------------  |     ,
+                                      |_  RN(½[omega]) - RN(½)[omega]') _|
+
+  beside many others (see below), is a single valued function of [tau],
+  and is expressible without ambiguity in terms of the single valued
+  function of [tau],
+
+                       /i[pi][tau]\    [oo]
+    [eta]([tau]) = exp( ---------- ) [Pi]   [1-exp (2i[pi]n[tau])],
+                       \    12    /     n=1
+
+                    /i[pi][tau]\   _[oo]
+              = exp(----------- ) \    (-1)^m exp [(3m² + m) i[pi][tau]].
+                    \    12    /  /_
+                                m = -[oo]
+
+  It should be remarked, however, that [eta]([tau]) is not unaltered by
+  all the substitutions we have considered; in fact
+
+    [eta](-[tau]^(-1)) = (-i[tau])½[eta]([tau]), [eta](1 + [tau]) =
+      exp (1/12 i[pi]) [eta]([tau]).
+
+  The aggregate of the substitutions [tau]' = (p' + q'[tau])/(p +
+  q[tau]), wherein p, q, p', q' are integers with pq' - p'q = 1,
+  represents a _Group_; the function J([tau]), unaltered by all these
+  substitutions, is called a _Modular Function_. More generally any
+  function unaltered by all the substitutions of a group of linear
+  substitutions of its variable is called an _Automorphic Function_. A
+  rational function, of its variable h, of this character, is the
+  function (1 - h + h²)³ h^(-2)(1 - h)^(-2) presenting itself
+  incidentally above; and there are other rational functions with a
+  similar property, the group of substitutions belonging to any one of
+  these being, what is a very curious fact, associable with that of the
+  rotations of one of the regular solids, about an axis through its
+  centre, which bring the solid into coincidence with itself. Other
+  automorphic functions are the double periodic functions already
+  discussed; these, as we have seen, enable us to solve the algebraic
+  equation y² = 4x³ - g2x - g3 (and in fact many other algebraic
+  equations, see below, under § 23, _Geometrical Applications of
+  Elliptic Functions_) in terms of single valued functions x = RN(u), y
+  = -RN'(u). A similar utility, of a more extended kind, belongs to
+  automorphic functions in general; but it can be shown that such
+  functions necessarily have an infinite number of essential
+  singularities except for the simplest cases.
+
+  The modular function J([tau]) considered above, unaltered by the group
+  of linear substitutions [tau]' = (p' + q'[tau]) / (p + q[tau]), where
+  p, q, p', q' are integers with pq' - p'q = 1, may be taken as the
+  independent variable x of a differential equation of the third order,
+  of the form
+
+    s'''   3   /s''\²    1 - a²     1 - ß²   [alpha]² + ß² - [gamma]² - 1
+    ---- - -- ( --- ) = --------- + ------ + ----------------------------,
+     s'    2   \ s'/    2(x - 1)²     2x²              2x(x - 1)
+
+  where s' = ds/dx, &c., of which the dependent variable s is equal to
+  [tau]. A differential equation of this form is satisfied by the
+  quotient of two independent integrals of the linear differential
+  equation of the second order satisfied by the hypergeometric
+  functions. If the solution of the differential equation for s be
+  written s([alpha], ß, [gamma], x), we have in fact [tau] = s(½, 1/3,
+  0, J). If we introduce also the function of [tau] given by
+
+               2RN (½[omega]') + f V(½[omega])
+    [lambda] = -------------------------------,
+                RN(½[omega]') - RN(½[omega])
+
+  we similarly have [tau] = s(0, 0, 0, [lambda]); this function [lambda]
+  is a single valued function of [tau], which is also a modular
+  function, being unaltered by a group of integral substitutions also of
+  the form [tau]' = (p' + q'[tau])/(p + q[tau]), with pq' - p'q = 1, but
+  with the restriction that p' and q are even integers, and therefore p
+  and q' are odd integers. This group is thus a subgroup of the general
+  modular group, and is in fact of the kind called a self-conjugate
+  subgroup. As in the general case this subgroup is associated with a
+  subdivision of the plane into regions of which any one is obtained
+  from a particular region, called the fundamental region, by a
+  particular one of the substitutions of the subgroup. This fundamental
+  region, putting [tau] = [rho] + i[sigma], may be taken to be that
+  given by -1 < [rho] < 1, ([rho] + ½)² + [sigma]² > ¼, ([rho]-½)² +
+  [sigma]² > ¼, and is built up of six of the regions which arose for
+  the general modular group associated with J([tau]). Within this
+  fundamental region, [lambda] takes every complex value just once,
+  except the values [lambda] = 0, 1, [oo], which arise only at the
+  angular points [tau] = 0, [tau] = [oo], [tau] = -1 and the equivalent
+  point [tau] = 1; these angular points are essential singularities for
+  the function [lambda]([tau]). For [lambda]([tau]) as for J([tau]), the
+  region of existence is the upper half plane of [tau], there being an
+  essential singularity in every length of the real axis, however short.
+
+  If, beside the plane of [tau], we take a plane to represent the values
+  of [lambda], the function [tau] = s(0, 0, 0, [lambda]) being
+  considered thereon, the values of [tau] belonging to the interior of
+  the fundamental region of the [tau]-plane considered above, will
+  require the consideration of the whole of the [lambda]-plane taken
+  once with the exception of the portions of the real axis lying between
+  -[oo] and 0 and between 1 and + [oo], the two sides of the first
+  portion corresponding to the circumferences of the [tau]-plane
+  expressed by ([rho] + ½)² + [sigma]² = ¼, ([rho] - ½)² + [sigma]² = ¼,
+  while the two sides of the latter portion, for which [lambda] is real
+  and > 1, correspond to the lines of the [tau]-plane expressed by [rho]
+  = ±1. The line for which [lambda] is real, positive and less than
+  unity corresponds to the imaginary axis of the [tau]-plane, lying in
+  the interior of the fundamental region. All the values of [tau] = s(0,
+  0, 0, [lambda]) may then be derived from those belonging to the
+  fundamental region of the [tau]-plane by making [lambda] describe a
+  proper succession of circuits about the points [lambda] = 0, [lambda]
+  = 1; any such circuit subjects [tau] to a linear substitution of the
+  subgroup of [tau] considered, and corresponds to a change of [tau]
+  from a point of the fundamental region to a corresponding point of one
+  of the other regions.
+
+§ 22. _A Property of Integral Functions deduced from the Theory of
+Modular Functions._--Consider now the function exp(z), for finite values
+of z; for such values of z, exp(z) never vanishes, and it is impossible
+to assign a closed circuit for z in the finite part of the plane of z
+which will make the function [lambda] = exp(z) pass through a closed
+succession of values in the plane of [lambda] having [lambda] = 0 in its
+interior; the function s[0, 0, 0, exp(z)], however z vary in the finite
+part of the plane, will therefore never be subjected to those linear
+substitutions imposed upon s(0, 0, 0, [lambda]) by a circuit of [lambda]
+about [lambda] = 0; more generally, if [phi](z) be an integral function
+of z, never becoming either zero or unity for finite values of z, the
+function [lambda] = [phi](z), however z vary in the finite part of the
+plane, will never make, in the plane of [lambda], a circuit about either
+[lambda] = 0 or [lambda] = 1, and s(0, 0, 0, [lambda]), that is s[0, 0,
+0, [phi](z)], will be single valued for all finite values of z; it will
+moreover remain finite, and be monogenic. In other words, s[0, 0, 0,
+[phi](z)] is also an integral function--whose imaginary part, moreover,
+by the property of s(0, 0, 0, [lambda]), remains positive for all finite
+values of z. In that case, however, exp{is[0, 0, 0, [phi](z)]} would
+also be an integral function of z with modulus less than unity for all
+finite values of z. If, however, we describe a circle of radius R in the
+z plane, and consider the greatest value of the modulus of an integral
+function upon this circle, this certainly increases indefinitely as R
+increases. We can infer therefore that _an integral function [phi](z)
+which does not vanish for any finite value of z, takes the value unity
+and hence_ (by considering the function A^(-1)[phi](z)) _takes every
+other value for some definite value of z_; or, an integral function for
+which both the equations [phi](z) = A, [phi](z) = B are unsatisfied by
+definite values of z, does not exist, A and B being arbitrary constants.
+
+  A similar theorem can be proved in regard to the values assumed by the
+  function [phi](z) for points z of modulus greater than R, however
+  great R may be, also with the help of modular functions. In general
+  terms it may be stated that it is a very exceptional thing for an
+  integral function not to assume every complex value an infinite number
+  of times.
+
+  Another application of modular functions is to prove that the function
+  s([alpha], ß, [gamma], [lambda]) is a single valued function of [tau]
+  = s(0, 0, 0, [lambda]); for, putting [tau]' = ([tau] - i)/([tau] + i),
+  the values of [tau]' which correspond to the singular points [lambda]
+  = 0, 1, [oo] of s([alpha], ß, [gamma], [lambda]), though infinite in
+  number, all lie on the circumference of the circle |[tau]'| = 1,
+  within which therefore s([alpha], ß, [gamma], x) is expressible in a
+  form [Sigma] [n = 0 to [oo]] a_n[tau]'^n. More generally any monogenic
+  function of [lambda] which is single valued save for circuits of the
+  points [lambda] = 0, 1, [oo], is a single valued function of [tau] =
+  s(0, 0, 0, [lambda]). Identifying [lambda] with the square of the
+  modulus in Legendre's form of the elliptical integral, we have [tau] =
+  iK'/K, where
+         _                                         _
+        /1                dt                      /1                  dt
+    K = |  --------------------------------, K' = |  -------------------------------------;
+       _/0  [root][1 - t²] [1 - [lambda]t²]      _/0 [root][1 - t²] [1 - (1 - [lambda])t²]
+
+  functions such as [lambda]^¼, (1 - [lambda])^¼, [[lambda](1 -
+  [lambda])]^¼, which have only [lambda] = 0, 1, [oo] as singular
+  points, were expressed by Jacobi as power series in q =
+  e^(i[pi][tau]), and therefore, at least for a limited range of values
+  of [tau], as single valued functions of [tau]; it follows by the
+  theorem given that any product of a root of [lambda] and a root of 1 -
+  [lambda] is a single valued function of [tau]. More generally the
+  differential equation
+
+             d²y                                  dy
+    x(1 - x) --- + [[gamma] - ([alpha] + ß + 1)x] -- -[alpha]ß[gamma] = 0
+             dx²                                  dx
+
+  may be solved by expressing both the independent and dependent
+  variables as single valued functions of a single variable [tau], the
+  expression for the independent variable being x = [lambda]([tau]).
+
+§ 23. _Geometrical Applications of Elliptic Functions._--Consider any
+irreducible algebraic equation rational in x, y, f(x, y) = 0, of such a
+form that the equation represents a plane curve of order n with ½n(n -
+3) double points; taking upon this curve n-3 arbitrary fixed points,
+draw through these and the double points the most general curve of order
+n -2; this will intersect [f] in n(n - 2) - n(n - 3) - (n - 3) = 3
+other points, and will contain homogeneously at least ½(n - 1)n - ½n(n -
+3) - (n - 3) = 3 arbitrary constants, and so will be of the form
+[lambda][phi] + [lambda]1[phi]1 + [lambda]2[phi]2 + ... = 0, wherein
+[lambda]3, [lambda]4, ... are in general zero. Put now [xi] =
+[phi]1/[phi], [eta] = [phi]2/[phi] and eliminate x, y between these
+equations and [f](x, y) = 0, so obtaining a rational irreducible
+equation F([xi], [eta]) = 0, representing a further plane curve. To any
+point (x, y) of [f] will then correspond a definite point ([xi], [eta])
+of F.
+
+  For a general position of (x, y) upon [f] the equations [phi]1(x',
+  y')/[phi](x', y') = [phi]1(x, y)/[phi](x, y), [phi]2(x', y')/[phi](x',
+  y') = [phi]2(x, y)/[phi](x, y), subject to [f](x', y') = 0, will have
+  the same number of solutions (x', y'); if their only solution is x' =
+  x, y' = y, then to any position ([xi],[eta]) of F will conversely
+  correspond only one position (x, y) of [f]. If these equations have
+  another solution beside (x, y), then any curve [lambda][phi] +
+  [lambda]1[phi]1 + [lambda]2[phi]2 = 0 which passes (through the double
+  points of [f] and) through the n - 2 points of [f] constituted by the
+  fixed n-3 points and a point (x0, y0), will necessarily pass through a
+  further point, say (x0', y0'), and will have only one further
+  intersection with [f]; such a curve, with the n - 2 assigned points,
+  beside the double points, of [f], will be of the form µ[psi] +
+  µ1[psi]1 + ... = 0, where µ2, µ3, ... are generally zero; considering
+  the curves [psi] + t[psi]1 = 0, for variable t, one of these passes
+  through a further arbitrary point of [f], by choosing t properly, and
+  conversely an arbitrary value of t determines a single further point
+  of [f]; the co-ordinates of the points of [f] are thus rational
+  functions of a parameter t, which is itself expressible rationally by
+  the co-ordinates of the point; it can be shown algebraically that such
+  a curve has not ½(n - 3)n but ½(n - 3)n + 1 double points. We may
+  therefore assume that to every point of F corresponds only one point
+  of [f], and there is a birational transformation between these curves;
+  the coefficients in this transformation will involve rationally the
+  co-ordinates of the n-3 fixed points taken upon [f], that is, at the
+  least, by taking these to be consecutive points, will involve the
+  co-ordinates of one point of [f], and will not be rational in the
+  coefficients of [f] unless we can specify a point of [f] whose
+  co-ordinates are rational in these. The curve F is intersected by a
+  straight line a[xi] + b[eta] + c = 0 in as many points as the number
+  of unspecified intersections of [f] with a[phi] + b[phi]1 + c[phi]2 =
+  0, that is, 3; or F will be a cubic curve, without double points.
+
+  Such a cubic curve has at least one point of inflection Y, and if a
+  variable line YPQ be drawn through Y to cut the curve again in P and
+  Q, the locus of a point R such that YR is the harmonic mean of YP and
+  YQ, is easily proved to be a straight line. Take now a triangle of
+  reference for homogeneous co-ordinates XYZ, of which this straight
+  line is Y = 0, and the inflexional tangent at Y is Z = 0; the equation
+  of the cubic curve will then be of the form
+
+    ZY² = aX³ + bX²Z + cXZ² + dZ³;
+
+  by putting X equal to [lambda]X + µZ, that is, choosing a suitable
+  line through Y to be X = 0, and choosing [lambda] properly, this is
+  reduced to the form
+
+    ZY² = 4X³ - g2XZ²  -g3Z³,
+
+  of which a representation is given, valid for every point, in terms of
+  the elliptic functions RN(u), RN'(u), by taking X = ZRN(u), Y =
+  ZRN'(u). The value of u belonging to any point is definite save for
+  sums of integral multiples of the periods of the elliptic functions,
+  being given by
+         _
+        /  (x)  ZdX - XdZ
+    u = |       ---------,
+       _/ ([oo])   ZY
+
+  where ([oo]) denotes the point of inflection.
+
+  It thus appears that the co-ordinates of any point of a plane curve,
+  [f], of order n with ½(n - 3)n double points are expressible as
+  elliptic functions, there being, save for periods, a definite value of
+  the argument u belonging to every point of the curve. It can then be
+  shown that if a variable curve, [phi], of order m be drawn, passing
+  through the double points of the curve, the values of the argument u
+  at the remaining intersections of [phi] with [f], have a sum which is
+  unaffected by variation of the coefficients of [phi], save for
+  additive aggregates of the periods. In virtue of the birational
+  transformation this theorem can be deduced from the theorem that if
+  any straight line cut the cubic y² = 4x³ - g2x - g3, in points (u1),
+  (u2), (u3), the sum u1 + u2 + u3 is zero, or a period; or the general
+  theorem is a corollary from Abel's theorem proved under § 17,
+  _Integrals of Algebraic Functions_. To prove the result directly for
+  the cubic we remark that the variation of one of the intersections (x,
+  y) of the cubic with the straight line y = mx + n, due to a variation
+  [delta]m, [delta]n in m and n, is obtained by differentiation of the
+  equation for the three abscissae, namely the equation
+
+    F(x) = 4x³ - g2x - g3 - (mx + n)² = 0,
+
+  and is thus given by
+
+    dx     x[delta]m + [delta]n
+    -- = 2 --------------------,
+    y             F'(x)
+
+  and the sum of three such fractions as that on the right for the three
+  roots of F(x) = 0 is zero; hence u1 + u2 + u3 is independent of the
+  straight line considered; if in particular this become the inflexional
+  tangent each of u1, u2, u3 vanishes. It may be remarked in passing
+  that x1 + x2 + x3 = 1/4m², and hence is 1/4{(y1 - y2)/(x1 - x2)}²; so
+  that we have another proof of the addition equation for the function
+  RN(u). From this theorem for the cubic curve many of its geometrical
+  properties, as for example those of its inflections, the properties of
+  inscribed polygons, of the three kinds of corresponding points, and
+  the theory of residuation, are at once obvious. And similar results
+  hold for the curve of order n with ½(n - 3)n double points.
+
+§ 24. _Integrals of Algebraic Functions in Connexion with the Theory of
+Plane Curves._--The developments which have been explained in connexion
+with elliptic functions may enable the reader to appreciate the vastly
+more extensive theory similarly arising for any algebraical
+irrationality, [f](x, y) = o.
+
+  The algebraical integrals [int] R(x, y)dx associated with this may as
+  before be divided into those of the _first kind_, which have no
+  infinities, those of the _second kind_, possessing only algebraical
+  infinities, and those of the _third kind_, for which logarithmic
+  infinities enter. Here there is a certain number, p, greater than
+  unity, of linearly independent integrals of the first kind; and this
+  number p is unaltered by any birational transformation of the
+  fundamental equation [f](x, y) = 0; a rational function can be
+  constructed with poles of the first order at p + 1 arbitrary positions
+  (x, y), satisfying [f](x, y) = 0, but not with a fewer number unless
+  their positions are chosen properly, a property we found for the case
+  p = 1; and p is the number of linearly independent curves of order n-3
+  passing through the double points of the curve of order n expressed by
+  [f](x, y) = 0. Again any integral of the second kind can be expressed
+  as a sum of p integrals of this kind, with poles of the first order at
+  arbitrary positions, together with rational functions and integrals of
+  the first kind; and an integral of the second kind can be found with
+  one pole of the first order of arbitrary position, and an integral of
+  the third kind with two logarithmic infinities, also of arbitrary
+  position; the corresponding properties for p = 1 are proved above.
+
+  There is, however, a difference of essential kind in regard to the
+  inversion of integrals of the first kind; if u = [int] R(x, y)dx be
+  such an integral, it can be shown, in common with all algebraic
+  integrals associated with [f](x, y) = 0, to have 2p linearly
+  independent additive constants of indeterminateness; the upper limit
+  of the integral cannot therefore, as we have shown, be a single valued
+  function of the value of the integral. The corresponding theorem, if
+  [int] R_i(x, y)dx denote one of the integrals of the first kind, is
+  that the p equations
+      _                         _
+     /                         /
+     | R_i (x1, y1)dx1 + ... + | Ri (x_p, y_p) dx_p = u_i,
+    _/                        _/
+
+  determine the rational symmetric functions of the p positions (x1,
+  y1), ... (x_p, y_p) as single valued functions of the p variables, u1,
+  ... u_p. It is thus necessary to enter into the theory of functions of
+  several independent variables; and the equation [f](x, y) = 0 is thus
+  not, in this way, capable of solution by single valued functions of
+  one variable. That solution in fact is to be sought with the help of
+  automorphic functions, which, however, as has been remarked, have, for
+  p > 1, an infinite number of essential singularities.
+
+§ 25. _Monogenic Functions of Several Independent Variables._--A
+monogenic function of several independent complex variables u_i, ... u_p
+is to be regarded as given by an aggregate of power series all
+obtainable by continuation from any one of them in a manner analogous to
+that before explained in the case of one independent variable. The
+singular points, defined as the limiting points of the range over which
+such continuation is possible, may either be _poles_, or _polar points
+of indetermination_, or _essential singularities_.
+
+  A pole is a point (u1^(0), ... u_p^(0)) in the neighbourhood of which
+  the function is expressible as a quotient of converging power series
+  in u1 - u1^(0) ... u_p - u_p^(0); of these the denominator series D
+  must vanish at (u1^(0), ... u_p^(0)), since else the fraction is
+  expressible as a power series and the point is not a singular point,
+  but the numerator series N must not also vanish at (u1^(0), ...
+  u_p^(0)), or if it does, it must be possible to write D = M0, N = MN0,
+  where M is a converging power series vanishing at (u1^(0), ...
+  u_p^(0)), and N0 is a converging power series, in (u1 - u1^(0) ... u_p
+  - u_p^(0)), not so vanishing. A polar point of indetermination is a
+  point about which the function can be expressed as a quotient of two
+  converging power series, both of which vanish at the point. As in such
+  a simple case as (Ax + By) / (ax + by), about x = 0, y = 0, it can be
+  proved that then the function can be made to approach to any
+  arbitrarily assigned value by making the variables u1, ... u_p
+  approach to u1^(0), ... u_p^(0) by a proper path. It is the necessary
+  existence of such polar points of indetermination, which in case p > 2
+  are not merely isolated points, which renders the theory essentially
+  more difficult than that of functions of one variable. An essential
+  singularity is any which does not come under one of the two former
+  descriptions and includes very various possibilities. A point at
+  infinity in this theory is one for which any one of the variables u1,
+  ... u_p is indefinitely great; such points are brought under the
+  preceding definitions by means of the convention that for u_i^(0) =
+  [oo], the difference u_i - u_i^(0) is to be understood to stand for
+  u_i^(-1) . This being so, a single valued function of u1, ... u_p
+  without essential singularities for infinite or finite values of the
+  variables can be shown, by induction, to be, as in the case of p = 1,
+  necessarily a rational function of the variables. A function having no
+  singularities for finite values of all the variables is as before
+  called an integral function; it is expressible by a power series
+  converging for all finite values of the variables; a single valued
+  function having for finite values of the variables no singularities
+  other than poles or polar points of indetermination is called a
+  meromorphic function; as for p = 1 such a function can be expressed as
+  a quotient of two integral functions having no common zero point other
+  than the points of indetermination of the function; but the proof of
+  this theorem is difficult.
+
+  The single valued functions which occur, as explained above, in the
+  inversion of algebraic integrals of the first kind, for p > 1, are
+  meromorphic. They must also be periodic, unaffected that is when the
+  variables u1, ... u_p are _simultaneously_ increased each by a proper
+  constant, these being the additive constants of indeterminateness for
+  the p integrals [int] R_i(x, y)dx arising when (x, y) makes a closed
+  circuit, the same for each integral. The theory of such single valued
+  meromorphic periodic functions is simpler than that of meromorphic
+  functions of several variables in general, as it is sufficient to
+  consider only finite values of the variables; it is the natural
+  extension of the theory of doubly periodic functions previously
+  discussed. It can be shown to reduce, though the proof of this
+  requires considerable developments of which we cannot speak, to the
+  theory of a single integral function of u1, ... u_p, called the _Theta
+  Function_. This is expressible as a series of positive and negative
+  integral powers of quantities exp (c1u1), exp (c2u2), ... exp (c_p
+  u_p), wherein c1, ... c_p are proper constants; for p = 1 this theta
+  function is essentially the same as that above given under a different
+  form (see § 14, _Doubly Periodic Functions_), the function [sigma](u).
+  In the case of p = 1, all meromorphic functions periodic with the same
+  two periods have been shown to be rational functions of two of them
+  connected by a single algebraic equation; in the same way all
+  meromorphic functions of p variables, periodic with the same sets of
+  simultaneous periods, 2p sets in all, can be shown to be expressible
+  rationally in terms of p + 1 such periodic functions connected by a
+  single algebraic equation. Let x1, ... x_p, y denote p + 1 such
+  functions; then each of the partial derivatives dx_i/(Pd)u_i will
+  equally be a meromorphic function of the same periods, and so
+  expressible rationally in terms of x1, ... x_p, y; thus there will
+  exist p equations of the form
+
+    dx_i = R1 du1 + ... + R_p du_p,
+
+  and hence p equations of the form
+
+    du_i = H_(i, 1)dx1 + ... + H_(i, p)dx_p,
+
+  wherein H_(i, j) are rational functions of x1, ... x_p, y, these being
+  connected by a fundamental algebraic (rational) equation, say [f](x1,
+  ... x_p, y) = 0. This then is the generalized form of the
+  corresponding equation for p = 1.
+
+§ 26. _Multiply-Periodic Functions and the Theory of Surfaces._--The
+theory of algebraic integrals [int] R(x, y)dx, wherein x, y are
+connected by a rational equation [f](x, y) = 0, has developed
+concurrently with the theory of algebraic curves; in particular the
+existence of the number p invariant by all birational transformations is
+one result of an extensive theory in which curves capable of birational
+correspondence are regarded as equivalent; this point of view has made
+possible a general theory of what might otherwise have remained a
+collection of isolated theorems.
+
+  In recent years developments have been made which point to a similar
+  unity of conception as possible for surfaces, or indeed for algebraic
+  constructs of any number of dimensions. These developments have been
+  in two directions, at first followed independently, but now happily
+  brought into the most intimate connexion. On the analytical side, E.
+  Picard has considered the possibility of classifying integrals of the
+  form [int](Rds + Sdy), belonging to a surface [f](x, y, z) = 0,
+  wherein R and S are rational functions of x, y, z, according as they
+  are (1) everywhere finite, (2) have poles, which then lie along curves
+  upon the surface, or (3) have logarithmic infinities, also then lying
+  along curves, and has brought the theory to a high degree of
+  perfection. On the geometrical side A. Clebsch and M. Noether, and
+  more recently the Italian school, have considered the geometrical
+  characteristics of a surface which are unaltered by birational
+  transformation. It was first remarked that for surfaces of order n
+  there are associated surfaces of order n-4, having properties in
+  relation thereto analogous to those of curves of order n-3 for a plane
+  curve of order n; if such a surface [f](x, y, z) = 0 have a double
+  curve with triple points triple also for the surface, and [phi](x, y,
+  z) = 0 be a surface of order n - 4 passing through the double curve,
+  the double integral
+      _  _
+     /  /  [phi] dx dy
+     |  |  -----------
+    _/ _/  (Pd)f/(Pd)z
+
+  is everywhere finite; and, the most general everywhere finite integral
+  of this form remains invariant in a birational transformation of the
+  surface [f], the theorem being capable of generalization to algebraic
+  constructs of any number of dimensions. The number of linearly
+  independent surfaces of order n - 4, possessing the requisite
+  particularity in regard to the singular lines and points of the
+  surface, is thus a number invariant by birational transformation, and
+  the equality of these numbers for two surfaces is a necessary
+  condition of their being capable of such transformation. The number of
+  surfaces of order m having the assigned particularity in regard to the
+  singular points and lines of the fundamental surface can be given by a
+  formula for a surface of given singularity; but the value of this
+  formula for m = n - 4 is not in all cases equal to the actual number
+  of surfaces of order n - 4 with the assigned particularity, and for a
+  cone (or ruled surface) is in fact negative, being the negative of the
+  deficiency of the plane section of the cone. Nevertheless this number
+  for m = n - 4 is also found to be invariant for birational
+  transformation. This number, now denoted by p_a, is then a second
+  invariant of birational transformation. The former number, of actual
+  surfaces of order n - 4 with the assigned particularity in regard to
+  the singularities of the surface, is now denoted by p_g. The
+  difference p_g - p_a, which is never negative, is a most important
+  characteristic of a surface. When it is zero, as in the case of the
+  general surface of order n, and in a vast number of other ordinary
+  cases, the surface is called regular.
+
+  On a plane algebraical curve we may consider linear series of sets of
+  points, obtained by the intersection with it of curves [lambda][phi] +
+  [lambda]1[phi]1 + ... = 0, wherein [lambda], [lambda]1, ... are
+  variable coefficients; such a series consists of the sets of points
+  where a rational function of given poles, belonging to the construct
+  [f](x, y) = 0, has constant values. And we may consider series of sets
+  of points determined by variable curves whose coefficients are
+  algebraical functions, not necessarily rational functions, of
+  parameters. Similarly on a surface we may consider linear systems of
+  curves, obtained by the intersection with the given surface of
+  variable surfaces [lambda][phi] + [lambda]1[phi]1 + ... = 0, and may
+  consider algebraic systems, of which the individual curve is given by
+  variable surfaces whose coefficients are algebraical, not necessarily
+  rational, functions of parameters. Of a linear series upon a plane
+  curve there are two numbers manifestly invariant in birational
+  transformation, the _order_, which is the number of points forming a
+  set of the series, and the _dimension_, which is the number of
+  parameters [lambda]1/[lambda], [lambda]2/[lambda], ... entering
+  linearly in the equation of the series. The series is _complete_ when
+  it is not contained in a series of the same order but of higher
+  dimension. So for a linear system of curves upon a surface, we have
+  three invariants for birational transformation; the _order_, being in
+  the number of variable intersections of two curves of the system, the
+  _dimension_, being the number of linear parameters [lambda]1/[lambda],
+  [lambda]2/[lambda], ... in the equation for the system, and the
+  _deficiency_ of the individual curves of the system. Upon any curve of
+  the linear system the other curves of the system define a linear
+  series, called the _characteristic_ series; but even when the linear
+  system is complete, that is, not contained in another linear system of
+  the same order and higher dimension, it does not follow that the
+  characteristic series is complete; it may be contained in a series
+  whose dimension is greater by p_g - p_a than its own dimension. When
+  this is so it can be shown that the linear system of curves is
+  contained in an algebraic system whose dimension is greater by p_g -
+  p_a than the dimension of the linear system. The extra p = p_g - p_a
+  variable parameters so entering may be regarded as the independent
+  co-ordinates of an algebraic construct [f](y, x1, ... x_p) = 0; this
+  construct has the property that its co-ordinates are single valued
+  meromorphic functions of p variables, which are periodic, possessing
+  2p systems of periods; the p variables are expressible in the forms
+           _
+          /
+    u_i = | R1(x, y) dx1 + ... + R_p(x, y) dx_p,
+         _/
+
+  wherein R_i(x, y) denotes a rational function of x1, ... x_p and y.
+  The original surface has correspondingly p integrals of the form
+  [int](R dx + S dy), wherein R, S are rational in x, y, z, which are
+  everywhere finite; and it can be shown that it has no other such
+  integrals. From this point of view, then, the number p, = p_g - p_a
+  is, for a surface, analogous to the deficiency of a plane curve;
+  another analogy arises in the comparison of the theorems: for a plane
+  curve of zero deficiency there exists no algebraic series of sets of
+  points which does not consist of sets belonging to a linear series;
+  for a surface for which p_g - p_a = 0 there exists no algebraic system
+  of curves not contained in a linear system.
+
+  But whereas for a plane curve of deficiency zero, the co-ordinates of
+  the points of the curve are rational functions of a single parameter,
+  it is not necessarily the case that for a surface having p_g - p_a = 0
+  the co-ordinates of the points are rational functions of two
+  parameters; it is necessary that p_g - p_a = 0, but this is not
+  sufficient. For surfaces, beside the p_g linearly independent surfaces
+  of order n - 4 having a definite particularity at the singularities of
+  the surface, it is useful to consider surfaces of order k(n - 4), also
+  having each a definite particularity at the singularities, the number
+  of these, not containing the original surface as component, which are
+  linearly independent, is denoted by P_k. It can then be stated that a
+  sufficient condition for a surface to be rational consists of the two
+  conditions p_a = 0, P2 = 0. More generally it becomes a problem to
+  classify surfaces according to the values of the various numbers which
+  are invariant under birational transformation, and to determine for
+  each the simplest form of surface to which it is birationally
+  equivalent. Thus, for example, the hyperelliptic surface discussed by
+  Humbert, of which the co-ordinates are meromorphic functions of two
+  variables of the simplest kind, with four sets of periods, is
+  characterized by p_g = 1, p_a = -1; or again, any surface possessing a
+  linear system of curves of which the order exceeds twice the
+  deficiency of the individual curves diminished by two, is reducible by
+  birational transformation to a ruled surface or is a rational surface.
+  But beyond the general statement that much progress has already been
+  made in this direction, of great interest to the student of the theory
+  of functions, nothing further can be added here.
+
+  BIBLIOGRAPHY.--The learner will find a lucid introduction to the
+  theory in E. Goursat, _Cours d'analyse mathématique_, t. ii. (Paris,
+  1905), or, with much greater detail, in A.R. Forsyth, _Theory of
+  Functions of a Complex Variable_ (2nd ed., Cambridge, 1900); for
+  logical rigour in the more difficult theorems, he should consult W.F.
+  Osgood, _Lehrbuch der Functionentheorie_, Bd. i. (Leipzig, 1906-1907);
+  for greater precision in regard to the necessary quasi-geometrical
+  axioms, beside the indications attempted here, he should consult W.H.
+  Young, _The Theory of Sets of Points_ (Cambridge, 1906), chs.
+  viii.-xiii., and C. Jordan, _Cours d'analyse_, t. i. (Paris, 1893),
+  chs. i., ii.; a comprehensive account of the _Theory of Functions of
+  Real Variables_ is by E.W. Hobson (Cambridge, 1907). Of the theory
+  regarded as based after Weierstrass upon the theory of power series,
+  there is J. Harkness and F. Morley, _Introduction to the Theory of
+  Analytic Functions_ (London, 1898), an elementary treatise; for the
+  theory of the convergence of series there is also T.J. I'A. Bromwich,
+  _An Introduction to the Theory of Infinite Series_ (London, 1908); but
+  the student should consult the collected works of Weierstrass (Berlin,
+  1894 ff.), and the writings of Mittag-Leffler in the early volumes of
+  the _Acta mathematica_; earlier expositions of the theory of functions
+  on the basis of power series are in C. Méray, _Leçons nouvelles sur
+  l'analyse infinitésimale_ (Paris, 1894), and in Lagrange's books on
+  the Theory of Functions. An account of the theory of potential in its
+  applications to the present theory is found in most treatises; in
+  particular consult E. Picard, _Traité d'analyse_, t. ii. (Paris,
+  1893). For elliptic functions there is an introductory book, P. Appell
+  and E. Lacour, _Principes de la théorie des fonctions elliptiques et
+  applications_ (Paris, 1897), beside the treatises of G.H. Halphen,
+  _Traité des fonctions elliptiques et de leurs applications_ (three
+  parts, Paris, 1886 ff.), and J. Tannery et J. Molk, _Éléments de la
+  théorie des fonctions elliptiques_ (Paris, 1893 ff.); a book, A.G.
+  Greenhill, _The Applications of Elliptic Functions_ (London, 1892),
+  shows how the functions enter in problems of many kinds. For modular
+  functions there is an extensive treatise, F. Klein and R. Fricke,
+  _Theorie der elliptischen Modulfunctionen_ (Leipzig, 1890); see also
+  the most interesting smaller volume, F. Klein, _Über das Ikosaeder_
+  (Leipzig, 1884) (also obtainable in English). For the theory of
+  Riemann's surface, and algebraic integrals, an interesting
+  introduction is P. Appeil and E. Goursat, _Théorie des fonctions
+  algébriques et de leurs intégrales_; for Abelian functions see also H.
+  Stahl, _Theorie der Abel'schen Functionen_ (Leipzig, 1896), and H.F.
+  Baker, _An Introduction to the Theory of Multiply Periodic Functions_
+  (Cambridge, 1907), and H.F. Baker, _Abel's Theorem and the Allied
+  Theory, including the Theory of the Theta Functions_ (Cambridge,
+  1897); for theta functions of one variable a standard work is C.G.
+  Jacobi, _Fundamenta nova, &c._ (Königsberg, 1828); for the general
+  theory of theta functions, consult W. Wirtinger, _Untersuchungen über
+  Theta-Functionen_ (Leipzig, 1895). For a history of the theory of
+  algebraic functions consult A. Brill and M. Noether, _Die Entwicklung
+  der Theorie der algebraischen Functionen in älterer und neuerer Zeit,
+  Bericht der deutschen Mathematiker-Vereinigung_ (1894); and for a
+  special theory of algebraic functions, K. Hensel and G. Landsberg,
+  _Theorie der algebraischen Function u.s.w._ (Leipzig, 1902). The
+  student will, of course, consult also Riemann's and Weierstrass's
+  _Ges. Werke_. For the applications to geometry in general an important
+  contribution, of permanent value, is E. Picard and G. Simart, _Théorie
+  des fonctions algébriques de deux variables indépendantes_ (Paris,
+  1897-1906). This work contains, as Note v. t. ii. p. 485, a valuable
+  summary by MM. Castelnuovo and Enriques, _Sur quelques résultats
+  nouveaux dans la théorie des surfaces algébriques_, containing many
+  references to the numerous memoirs to be found, for the most part, in
+  the transactions of scientific societies and the mathematical journals
+  of Italy.
+
+  Beside the books above enumerated there exists an unlimited number of
+  individual memoirs, often of permanent importance and only
+  imperfectly, or too elaborately, reproduced in the pages of the
+  volumes in which the student will find references to them. The German
+  _Encyclopaedia of Mathematics_, and the Royal Society's _Reference
+  Catalogue of Current Scientific Literature, Pure Mathematics_,
+  published yearly, should also be consulted.     (H. F. Ba.)
+
+
+FOOTNOTE:
+
+  [1] The word "function" (from Lat. _fungi_, to perform) has many
+    uses, with the fundamental sense of an activity special or proper to
+    an office, business or profession, or to an organ of an animal or
+    plant, the definite work for which the organ is an apparatus. From
+    the use of the word, as in the Italian _funzione_, for a ceremony of
+    the Roman Church, "function" is often employed for a public ceremony
+    of any kind, and loosely of a social entertainment or gathering.
+
+
+
+
+FUNDY, BAY OF, an inlet of the North Atlantic, separating New Brunswick
+from Nova Scotia. It is 145 m. long and 48 m. wide at the mouth, but
+gradually narrows towards the head, where it divides into Chignecto Bay
+to the north, which subdivides into Shepody Bay and Cumberland Basin
+(the French Beaubassin), and Minas Channel, leading into Minas Basin, to
+the east and south. Off its western shore opens Passamaquoddy Bay, a
+magnificent sheet of deep water with good anchorage, receiving the
+waters of the St Croix river and forming part of the boundary between
+New Brunswick and the state of Maine, The Bay of Fundy is remarkable for
+the great rise and fall of the tide, which at the head of the bay has
+been known to reach 62 ft. In Passamaquoddy Bay the rise and fall is
+about 25 ft., which gradually increases toward the narrow upper reaches.
+At spring tides the water in the Bay of Fundy is 19 ft. higher than it
+is in Bay Verte, in Northumberland Strait, only 15 m. distant. Though
+the bay is deep, navigation is rendered dangerous by the violence and
+rapidity of the tide, and in summer by frequent fogs. At low tide, at
+such points as Moncton or Amherst, only an expanse of red mud can be
+seen, and the tide rushes in a bore or crest from 3 to 6 ft. in height.
+Large areas of fertile marshes are situated at the head of the bay, and
+the remains of a submerged forest show that the land has subsided in the
+latest geological period at least 40 ft. The bay receives the waters of
+the St Croix and St John rivers, and has numerous harbours, of which the
+chief are St Andrews (on Passamaquoddy Bay) and St John in New
+Brunswick, and Digby and Annapolis (on an inlet known as Annapolis
+Basin) in Nova Scotia. It was first explored by the Sieur de Monts (d.
+c. 1628) in 1604 and named by him La Baye Française.
+
+
+
+
+FUNERAL RITES, the ceremonies associated with different methods of
+disposing of the dead. (See also BURIAL AND BURIAL ACTS; CEMETERY; and
+CREMATION.) In general we have little record, except in their tombs, of
+races which, in a past measured not merely by hundreds but by thousands
+of years, occupied the earth; and exploration of these often furnishes
+our only clue to the religions, opinions, customs, institutions and arts
+of long vanished societies. In the case of the great culture folks of
+antiquity, the Babylonians, Egyptians, Hindus, Persians, Greeks and
+Romans, we have, besides their monuments, the evidence of their
+literatures, and so can know nearly as much of their rites as we do of
+our own. The rites of modern savages not only help us to interpret
+prehistoric monuments, but explain peculiarities in our own rituals and
+in those of the culture folks of the past of which the significance was
+lost or buried under etiological myths. We must not then confine
+ourselves to the rites of a few leading races, neglecting their less
+fortunate brethren who have never achieved civilization. It is better to
+try to classify the rites of all races alike according as they embody
+certain leading conceptions of death, certain fears, hopes, beliefs
+entertained about the dead, about their future, and their relations with
+the living.
+
+  The main ideas, then, underlying funeral rites may roughly be
+  enumerated as follows:
+
+  1. The pollution or taboo attaching to a corpse.
+
+  2. Mourning.
+
+  3. The continued life of the dead as evinced in the housing and
+  equipment of the dead, in the furnishing of food for them, and in the
+  orientation and posture assigned to the body.
+
+  4. Communion with the dead in a funeral feast and otherwise.
+
+  5. Sacrifice for the dead and expiation of their sins.
+
+  6. Death witchery.
+
+  7. Protection of the dead from ghouls.
+
+  8. Fear of ghosts.
+
+1. A dead body is unclean, and the uncleanness extends to things and
+persons which touch it. Hence the Jewish law (Num. v. 2) enacted that
+"whoever is unclean by the dead shall be put outside the camp, that they
+defile not the camp in the midst whereof the Lord dwells." Such persons
+were unclean until the even, and might not eat of the holy things unless
+they bathed their flesh in water. A high priest might on no account "go
+in to any dead body" (Lev. xxi. 11). Why a corpse is so widely tabooed
+is not certain; but it is natural to see one reason in the corruption
+which in warm climates soon sets in. The common experience that where
+one has died another is likely to do so may also have contributed,
+though, of course, there was no scientific idea of infection. The old
+Persian scriptures are full of this taboo. He who has touched a corpse
+is "powerless in mind, tongue and hand" (_Zend Avesta_ in _Sacred Books
+of the East_, pt. i. p. 120), and the paralysis is inflicted by the
+innumerable _drugs_ or evil spirits which invest a corpse. Fire and
+earth, being alike creations of the good and pure god Ahuramazda, a
+body must not be burned or buried; and so the ancient Persians and their
+descendants the Parsees build Dakmas or "towers of silence" on hill-tops
+far from human habitations. Inside these the corpses are laid on a
+flagged terrace which drains into a central pit. Twice a year the bones,
+picked clean by dogs and birds of prey, are collected in the pit, and
+when it is full another tower is built. In ancient times perhaps the
+bodies of the magi or priests alone were exposed at such expense; the
+common folk were covered with wax and laid in the earth, the wax saving
+the earth from pollution. In Rome and Greece the corpse was buried by
+night, lest it should pollute the sunlight; and a trough of water was
+set at the door of the house of death that men might purify themselves
+when they came out, before mixing in general society. Priests and
+magistrates in Rome might not meet or look on a corpse, for they were
+thereby rendered unclean and incapable of fulfilling their official
+duties without undergoing troublesome rites of purification. At a Roman
+funeral, when the remains had been laid in the tomb, all present were
+sprinkled with lustral water from a branch of olive or laurel called
+_aspergillum_; and when they had gone home they were asperged afresh and
+stepped over a fire. The house was also swept out with a broom, probably
+lest the ghost of the dead should be lying about the floor. Many races,
+to avoid pollution, destroy the house and property of the deceased. Thus
+the Navahos pull down the hut in which he died, leaving its ruins on the
+ground; but if it be an expensive hut, a shanty is extemporized
+alongside, into which the dying man is transferred before death. No one
+will use the timbers of a hut so ruined. A burial custom of the Solomon
+Islands, noted by R.H. Codrington (_The Melanesians_, p. 255), may be
+dictated by the same scruple. There "the mourners having hung up a dead
+man's arms on his house make great lamentations; all remains afterwards
+untouched, the house goes to ruin, mantled, as time goes on, with the
+vines of the growing yams, a picturesque and indeed, perhaps, a touching
+sight; for these things are not set up that they may in a ghostly manner
+accompany their former owner." H. Oldenberg (_Religion des Veda_, p.
+426) describes how Hindus shave themselves and cut off their nails after
+a death, at the same time that they wash, renew the hearth fire, and
+furnish themselves with new vessels. For the hair and nails may harbour
+pollution, just as the medieval Greeks believed that evil spirits could
+lurk in a man's beard (Leo Allatius, _De opinionibus quorundam
+Graecorum_). The dead man's body is shorn and the nails cut for a
+kindred reason; for it must be purified as much as can be before it is
+burned as an offering on the pyre and before he enters on a new sphere
+of existence.
+
+2. We are accustomed to regard mourning costume as primarily an outward
+sign of our grief. Originally, however, the special garb seems to have
+been intended to warn the general public that persons so attired were
+unclean. In ancient Rome mourners stayed at home and avoided all feasts
+and amusements; laying aside gold, purple and jewels, they wore black
+dresses called _lugubria_ or even skins. They cut neither hair nor
+beard, nor lighted fire. Under the emperors women began to wear white.
+On the west coast of Africa negroes wear white, on the Gold Coast red.
+The Chinese wear hemp, which is cheap, for mourning dress must as a rule
+be destroyed when the season of grief is past to get rid of the taboo.
+Among the Aruntas of Australia the wives of a dead man smear themselves
+with white pipe-clay until the last ceremonies are finished, sometimes
+adding ashes--this not to conceal themselves from the ghost (which may
+partly be the aim of some mourning costumes), but to show the ghost that
+they are duly sorrowing for their loss. These widows must not talk
+except on their hands for a whole year. "Among the Maoris," says Frazer
+(_Golden Bough_, i. 323), "anyone who had handled a corpse, helped to
+convey it to the grave, or touched a dead man's bones; was cut off from
+all intercourse and almost all communication with mankind. He could not
+enter any house, or come into contact with any person or thing, without
+utterly bedevilling them. He might not even touch food with his hands,
+which had become so frightfully tabooed or unclean as to be quite
+useless. Food would be set for him on the ground, and he would then sit
+or kneel down, and, with his hands carefully held behind his back, would
+gnaw at it as best he could." Often a degraded outcast was kept in a
+village to feed mourners. Such a taboo is strictly similar to those
+which surround a sacred chief or his property, a menstruous woman or a
+homicide, rendering them dangerous to themselves and to all who approach
+them.
+
+3. Primitive folk cannot conceive of a man's soul surviving apart from
+his body, nor of another life as differing from this, and the dead must
+continue to enjoy what they had here. Accordingly the Patagonians kill
+horses at the grave that the dead may ride to _Alhuemapu_, or country of
+the dead. After a year they collect a chief's bones, arrange them, tie
+them together and dress them in his best garments with beads and
+feathers. Then they lay him with his weapons in a square pit, round
+which dead horses are placed set upright on their feet by stakes. As
+late as 1781 in Poland F. Casimir's horse was slain and buried with him.
+In the Caucasus a Christian lady's jewels are buried with her. The
+Hindus used to burn a man's widow on his pyre, because he could not do
+without her; and St Boniface commends the self-sacrifice of the Wend
+widows who in his day burned themselves alive on their husbands' pyres.
+
+The tumuli met with all over the north of Europe (in the Orkneys alone
+2000 remain) are regular houses of the dead, models of those they
+occupied in life. The greater the dignity of the deceased, the loftier
+was his barrow. Silbury hill is 170 ft. high; the tomb of Alyattes,
+father of Croesus, was a fourth of a league round; the Pyramids are
+still the largest buildings in existence; at Oberea in Tahiti is a
+barrow 267 ft. long, 87 wide and 44 high. Some Eskimo just leave a dead
+man's body in his house, and shut it up, often leaving by his side a
+dog's head to guide him on his last journey, along with his tools and
+kayak. The Sea Dyaks set a chief adrift in his war canoe with his
+weapons. So in Norse story Hake "was laid wounded on a ship with the
+dead men and arms; the ship was taken out to sea and set on fire." The
+Viking was regularly buried in his ship or boat under a great mound. He
+sailed after death to Valhalla. In the ship was laid a stone as anchor
+and the tools, clothes, weapons and treasures of the dead. The
+Egyptians, whose land was the gift of the river Nile, equally believed
+that the dead crossed over water, and fashioned the hearse in the form
+of a boat. Hence perhaps was derived the Greek myth of Charon and the
+Styx, and the custom, which still survives in parts of Europe, of
+placing a coin in the mouth of the dead with which to pay the ferryman.
+The Egyptians placed in the tomb books of a kind to guide the dead to
+the next world. The Copts in a later age did the same, and to this
+custom we owe the recovery in Egypt of much ancient literature. The
+Armenians till lately buried with a priest his missal or gospel.
+
+In Egyptian entombments of the XIIth to the XIVth dynasties were added
+above the sepulchres what Professor Petrie terms soul-houses, viz. small
+models of houses furnished with couch and table, &c., for the use of the
+_ka_ or double whenever it might wish to come above ground and partake
+of meats and drinks. They recall, in point of size, the hut-urns of the
+Etruscans, but the latter had another use, for they contain incinerated
+remains. Etruscan tombs, like those of Egypt and Asia Minor, were made
+to resemble the dwelling-houses of the living, and furnished with
+coffered ceilings, panelled walls, couches, stools, easy chairs with
+footstools attached, all hewn out of the living rock (Dennis, _Cities
+and Cemeteries of Etruria_, vol i. p. lxx.).
+
+Of the old Peruvian mummies in the Kircherian Museum at Rome, several
+are of women with babies in their arms, whence it is evident that a
+mother had her suckling buried with her; it would console her in the
+next world and could hardly survive her in this. The practice of burying
+ornaments, tools and weapons with the dead characterizes the inhumations
+of the Quaternary epoch, as if in that dim and remote age death was
+already regarded as the portal of another life closely resembling this.
+The cups, tools, weapons, ornaments and other articles deposited with
+the dead are often carefully broken or turned upside down and inside
+out; for the soul or _manes_ of objects is liberated by such fracture or
+inversion and so passes into the dead man's use and possession. For the
+same reason where the dead are burned, their properties are committed to
+the flames. The ghost of the warrior has a ghostly sword and buckler to
+fight with and a ghostly cup to drink from, and he is also nourished by
+the impalpable odour and reek of the animal victims sacrificed over his
+grave. Instead of valuable objects cheap images and models are often
+substituted; and why not, if the mere ghosts of the things are all that
+the wraith can enjoy? Thus Marco Polo (ii. 76) describes how in the land
+of Kinsay (Hang-chau) "the friends and relations make a great mourning
+for the deceased, and clothe themselves in hempen garments, and follow
+the corpse, playing on a variety of instruments and singing hymns to
+their idols. And when they come to the burning place they take
+representations of things cut out of parchment, such as caparisoned
+horses, male and female slaves, camels, armour, suits of cloth of gold
+(and money), in great quantities, and these things they put on the fire
+along with the corpse so that they are all burned with it. And they tell
+you that the dead man shall have all these slaves and animals of which
+the effigies are burned, alive in flesh and blood, and the money in
+gold, at his disposal in the next world; and that the instruments which
+they have caused to be played at his funeral, and the idol hymns that
+have been chaunted shall also be produced again to welcome him in the
+next world." The manufacture of such paper _simulacra_ for consumption
+at funerals is still an important industry in Chinese cities. The
+ancient Egyptians, assured that a man's _ka_ or double shall revivify
+his body, took pains to guard the flesh from corruption, steeping the
+corpse in natron and stuffing it with spices. A body so prepared is
+called a mummy (q.v.), and the custom was already of a hoary antiquity
+in 3200 B.C., when the oldest dated mummy we have was made. The bowels,
+removed in the process, were placed in jars over the corpse in the tomb,
+together with writing tablets, books, musical instruments, &c., of the
+dead. Cemeteries also remain full of mummies of crocodiles, cats, fish,
+cows and other sacred animals. The Greeks settled in Egypt learned to
+mummify their dead, but the custom was abhorrent to the Jews, although
+the Christian belief in the resurrection of the flesh must have been
+formed to a large extent under Egyptian influence. Half the superiority
+of the Jewish to other ancient religions lay in this, that it prescribed
+no funeral rites other than the simplest inhumation.
+
+The dead all over the world and from remote antiquity have been laid not
+anyhow in the earth, but with the feet and face towards the region in
+which their future will be spent; the Samoans and Fijians towards the
+far west whither their souls have preceded them; the Guarayos with head
+turned eastwards because their god Tamoi has in that quarter "his happy
+hunting grounds where the dead will meet again" (Tylor, _Prim. Cult._
+ii. 422). The legend is that Christ was buried with His head to the
+west, and the church follows the custom, more ancient than itself, of
+laying the dead looking to the East, because that is the attitude of
+prayer, and because at the last trump they will hurry eastwards. So in
+Eusebius (_Hist. Eccl._ 430.19) a martyr explains to his pagan judge
+that the heavenly Jerusalem, the fatherland of the pious, lay exactly in
+the east at the rising place of the sun. Where the body is laid out
+straight it is difficult to discern the presence of any other idea than
+that it is at rest. In Scandinavian barrows, e.g. in the one opened at
+Goldhavn in 1830, the skeletons have been found seated on a low stone
+bench round the wall of the grave chamber facing its opening, which
+always looks south or east, never north. Here the dead were continuing
+the drinking bouts they enjoyed on earth.
+
+The Peruvians mummified their dead and placed them jointed and huddled
+up with knees to chin, looking toward the sunset, with the hands held
+before the face. In the oldest prehistoric tombs along the Nile the
+bodies are doubled up in the same position. It would seem as if in these
+and numerous other similar cases the dead were deliberately given in
+their graves the attitude of a foetus in the womb, and, as Dr Budge
+remarks (_Egyptian Ideas of the Future Life_, London, 1899, p. 162), "we
+may perhaps be justified in seeing in this custom the symbol of a hope
+that, as the child is born from this position into the world, so might
+the deceased be born into the life beyond the grave." The late
+Quaternary skeletons of the Mentone cave were laid in a layer of
+ferrugineous earth specially laid down for them, and have contracted a
+red colour therefrom. Many other prehistoric skeletons found in Italy
+have a reddish colour, perhaps for the same reason, or because, as often
+to-day, the bones were stripped of flesh and painted. Ambrose relates
+that the skeletons of the martyrs Gervasius and Protasius, which he
+found and deposited A.D. 386 under the altar of his new basilica in
+Milan, were _mirae magnitudinis ut prisca aetas ferebat_, and were also
+coloured red. He imagined the red to be the remains of the martyrs'
+blood! _Hic sanguis clamat coloris indicio._ Salomon Reinach has rightly
+divined that what Ambrose really hit upon was a prehistoric tomb. Red
+earth was probably chosen as a medium in which to lay a corpse because
+demons flee from red. Sacred trees and stones are painted red, and for
+the most solemn of their rites savages bedaub themselves with red clay.
+It is a favourite taboo colour.
+
+4. A feast is an essential feature of every primitive funeral, and in
+the Irish "wake" it still survives. A dead man's soul or double has to
+be fed at the tomb itself, perhaps to keep it from prowling about the
+homes of the survivors in search of victuals; and such food must also be
+supplied to the dead at stated intervals for months or years. Many races
+leave a narrow passage or tube open down to the cavity in which the
+corpse lies, and through it pour down drinks for the dead. Traces of
+such tubes are visible in the prehistoric tombs of the British Isles.
+However, such provision of food is not properly a funeral feast unless
+the survivors participate. In the Eastern churches and in Russia the
+departed are thus fed on the ninth, twelfth and fortieth days from
+death. "Ye appease the shades of the dead with wine and meals," was the
+charge levelled at the Catholics by the 4th-century Manichaeans, and it
+has hardly ceased to be true even now after the lapse of sixteen
+centuries. The funeral feast proper, however, is either a meal of
+communion with or in the dead, which accompanies interment, or a banquet
+off the flesh of victims slain in atonement of the dead man's sins. Some
+anthropologists see in the common meal held at the grave "the pledge and
+witness of the unity of the kin, the chief means, if not of making, at
+least of repairing and renewing it."[1] The flesh provided at these
+banquets is occasionally that of the dead man himself; Herodotus and
+Strabo in antiquity relate this of several half-civilized races in the
+East and West, and a similar story is told by Marco Polo of certain
+Tatars. Nor among modern savages are funeral feasts off the flesh of the
+dead unknown, and they seem to be intended to effect and renew a
+sacramental union or kinship of the living with the dead. The Uaupes in
+the Amazons incinerate a corpse a month after death, pound up the ashes,
+and mix them with their fermented drink. They believe that the virtues
+of the dead will thus be passed on to his survivors. The life of the
+tribe is kept inside the tribe and not lost. Such cannibal sacraments,
+however, are rare, and, except in a very few cases, the evidence for
+them weak. The slaying and eating of animal victims, however, at the
+tomb is universal and bears several meanings, separately or all at once.
+The animals may be slain in order that their ghosts may accompany the
+deceased in his new life. This significance we have already dwelt upon.
+Or it is believed that the shade feeds upon them, as the shades came up
+from Hades and lapped up out of a trench the blood of the animals slain
+by Ulysses. The survivors by eating the flesh of a victim, whose blood
+and soul the dead thus consume, sacramentally confirm the mystic tie of
+blood kinship with the dead. Or lastly, the victim may be offered for
+the sins of the dead. His sins are even supposed to be transferred into
+it and eaten by the priest. Such expiatory sacrifices of animals for the
+dead survive in the Christian churches of Armenia, Syria and of the East
+generally. Their vicarious character is emphasized in the prayers which
+accompany them, but the popular understanding of them probably combines
+all the meanings above enumerated. It has been suggested by Robertson
+Smith (_Religion of the Semites_, 336) that the world-wide customs of
+tearing the hair, rending the garments, and cutting and wounding the
+body were originally intended to establish a life-bond between the dead
+and the living. The survivors, he argues, in leaving portions of their
+hair and garments, and yet more by causing their own blood to stream
+over the corpse from self-inflicted wounds, by cutting off a finger and
+throwing it into the grave, leave what is eminently their own with the
+dead, so drawing closer their tie with him. Conversely, many savages
+daub themselves with the blood and other effluences of their dead
+kinsmen, and explain their custom by saying that in this way a portion
+of the dead is incorporated in themselves. Often the survivors,
+especially the widows, attach the bones or part of them to their persons
+and wear them, or at least keep them in their houses. The retention of
+the locks of the deceased and of parts of his dress is equally common.
+There is also another side to such customs. Having in their possession
+bits of the dead, and being so far in communion with him, the survivors
+are surer of his friendship. They have ensured themselves against ghosts
+who are apt to be by nature envious and mischievous. But whatever their
+original significance, the tearing of cheeks and hair and garments and
+cutting with knives are mostly expressions of real sorrow, and, as
+Robertson Smith remarks, of deprecation and supplication to an angry god
+or spirit. It must not be supposed that the savage or ancient man feels
+less than ourselves the poignancy of loss.
+
+6. Death-witchery has close parallels in the witch and heretic hunts of
+the Christians, but, happily for us, only flourishes to-day among
+savages. Sixty % of the deaths which occur in West Africa are, according
+to Miss Mary Kingsley--a credible witness--believed to be due to
+witchcraft and sorcery. The blacks regard old age or effusion of blood
+as the sole legitimate causes of death. All ordinary diseases are in
+their opinion due to private magic on the part of neighbours, just as a
+widespread epidemic marks the active hatred "of some great outraged
+nature spirit, not of a mere human dabbler in devils."[2] Similarly in
+Christian countries an epidemic is set down to the wrath of a God
+offended by the presence of Jews, Arians and other heretics. The duty of
+an African witch-doctor is to find out who bewitched the deceased, just
+as it was of an inquisitor to discover the heretic. Every African
+post-mortem accordingly involves the murder of the person or persons who
+bewitched the dead man and caused him to die. The death-rate by these
+means is nearly doubled; but, since the use of poison against an
+obnoxious neighbour is common, the right person is occasionally
+executed. It is also well for neighbours not to quarrel, for, if they do
+and one of them dies of smallpox, the other is likely to be slain as a
+witch, and his lungs, liver and spleen impaled on a pole at the entrance
+of the village. It is the same case with the Australian blacks: "no such
+thing as natural death is realized by the native; a man who dies has of
+necessity been killed by some other man, or perhaps even by a woman, and
+sooner or later that man or woman will be attacked. In the normal
+condition of the tribe every death meant the killing of another
+individual."[3]
+
+7. Lastly, a primitive interment guards against the double risk of the
+ghost haunting the living and of ghouls or vampires taking possession of
+the corpse. The latter end is likely to be achieved if the body is
+cremated, for then there is no nidus to harbour the demon; but whether,
+in the remote antiquity to which belong many barrows containing
+incinerated remains, this motive worked, cannot be ascertained. The
+Indo-European race seems to have cremated at an early epoch, perhaps
+before the several races of East and West separated. In Christian
+funeral rites many prayers are for the protection of the body from
+violation by vampires, and it would seem as if such a motive dictated
+the architectural solidity of some ancient tombs. Christian graves were
+for protection regularly sealed with the cross; and the following is a
+characteristic prayer from the old Armenian rite for the burial of a
+layman:
+
+  "Preserve, Almighty Lord, this man's spirit with all saints and with
+  all lovers of Thy holy name. And do Thou seal and guard the sepulchre
+  of Thy servant, Thou who shuttest up the depths and sealest them with
+  Thy almighty right hand ... so let the seal of Thy Lordship abide
+  unmoved upon this man's dwelling-place and upon the shrine which
+  guards Thy servant. And _let not any filthy and unclean devil dare to
+  approach him, such as assail the body and souls of the heathen_, who
+  possess not the birth of the holy font, and have not the dread seal
+  laid upon their graves."
+
+A terrible and revolting picture of the superstitious belief in ghouls
+which violate Christian tombs is given by Leo Allatius (who held it) in
+his tract _De opinionibus quorundam Graecorum_ (Paris, 1646). It was
+probably the fear of such demonic assaults on the dead that inspired the
+insanitary custom of burying the dead under the floors of churches, and
+as near as possible to the altar. In the Greek Church this practice was
+happily forbidden by the code of Justinian as well as by the older law
+in the case of churches consecrated with _Encaenia_ and deposition of
+relics. In the Armenian Church the same rule holds, and Ephrem Syrus in
+his testament particularly forbade his body to be laid within a church.
+Such prohibitions, however, are a witness to the tendency in question.
+
+The custom of lighting candles round a dead body and watching at its
+side all night was originally due to the belief that a corpse, like a
+person asleep, is specially liable to the assaults of demons. The
+practice of tolling a bell at death must have had a similar origin, for
+it was a common medieval belief that the sound of a consecrated bell
+drives off the demons which when a man dies gather near in the air to
+waylay his fleeting soul. For a like reason the consecrated bread of the
+Eucharist was often buried with believers, and St Basil is said to have
+specially consecrated a Host to be placed in his coffin.
+
+8. Some of the rites described under the previous heads may be really
+inspired by the fear of the dead haunting the living, but it must be
+kept in mind that the taboo attaching to a dead body is one thing and
+fear of a ghost another. A corpse is buried or burned, or scaffolded on
+a tree, a tower or a house-top, in order to get it out of the way and
+shield society from the dangerous infection of its taboo; but ghosts
+_quâ_ ghosts need not be feared and a kinsman's ghost usually is not. On
+the contrary, it is fed and consoled with everything it needs, is asked
+not to go away but to stay, is in a thousand ways assured of the sorrow
+and sympathy of the survivors. Even if the body be eaten, it is merely
+to keep the soul of the deceased inside the circle of kinsmen, and
+Strabo asserts that the ancient Irish and Massagetae regarded it as a
+high honour to be so consumed by relatives. In Santa Cruz in Melanesia
+they keep the bones for arrow heads and store a skull in a box and set
+food before it "saying that this is the man himself" (R.H. Codrington,
+_The Melanesians_, p. 264), or the skull and jaw bone are kept and "are
+called _mangite_, which are _saka_, hot with spiritual power, and by
+means of which the help of the _lio'a_, the powerful ghost of the man
+whose relics these are, can be obtained" (ibid. p. 262). Here we have
+the savage analogue to Christian relics. So the Australian natives make
+pointing sticks out of the small bones of the arm, with which to bewitch
+enemies.
+
+We may conclude then that in the most primitive societies, where
+blood-kinship is the only social tie and root of social custom it is the
+shades, not of kinsmen, but of strangers, who as such are enemies, that
+are dangerous and uncanny. In more developed societies, however, all
+ghosts alike are held to be so; and if a ghost walks it is because its
+body has not been properly interred or because its owner was a
+malefactor. Still, even allowing for this, it remains true that for a
+friendly ghost the proper place is the grave and not the homes of the
+living, and accordingly the Aruntas with cries of _Wah! Wah!_ with
+wearing of fantastic head-dresses, wild dancing and beating of the air
+with hands and weapons "drive the spirit away from the old camp which it
+is supposed to haunt," and which has been set fire to, and hunt it at a
+run into the grave prepared, and there stamp it down into the earth.
+"The loud shouting of the men and women shows him that they do not wish
+to be frightened by him in his present state, and that they will be
+angry with him if he does not rest." (Spencer and Gillen, _Native
+Tribes of Central Australia_, p. 508). In Mesopotamia cemeteries have
+been discovered where the sepulchral jars were set upside down, clearly
+by way of hindering the ghosts from escaping into the upper world. In
+the Dublin museum we see specimens of ancient Celtic tombs showing the
+same peculiarity. For a like reason perhaps the name of the dead must
+among the Aruntas not be uttered, nor the grave approached, by certain
+classes of kinsmen. The same repugnance to naming the dead exists all
+over the world, and leads survivors who share the dead man's name to
+adopt another, at least for a time. If the dead man's name was that of a
+plant, tree, animal or stream, that too is changed. Here is a potent
+cause of linguistic change, that also renders any historical tradition
+impossible. The survivors seem to fear that the ghost will come when he
+hears his name called; but it also hangs together with the taboo which
+hedges round the dead as it does kings, chieftains and priests.
+
+  AUTHORITIES.--B. Spencer and F.J. Gillen, _The Native Tribes of
+  Central Australia_ (London, 1899); F.B. Jevons, _Introduction to
+  History of Religion_ (London, 1896); E.S. Hartland, _The Legend of
+  Perseus_, vol. ii.; J.G. Frazer, _The Golden Bough_ (London, 1900);
+  L.W. Faraday, "Custom and Belief in the Icelandic Sagas," in
+  _Folk-lore_, vol. xvii. No. 4; E.B. Tylor, _Primitive Culture_
+  (London, 1903); E.A. W. Budge, _The Mummy_ (Cambridge, 1893); C.
+  Royer, "Les Rites funéraires aux époques préhistoriques," _Revue
+  d'anthropologie_ (1876); Forrer, _Über die Totenbestattung bei den
+  Pfahlbauern_ (Ausland, 1885); J. Lubbock, _Origin of Civilization_
+  (London, 1875) and _Prehistoric Times_ (London, 1865); L.A. Muratori,
+  "De antiquis Christianorum sepulchris," _Anecd. Graeca_ (Padua, 1709);
+  Onaphr. Panvinius, _De ritu sepeliendi mortuos apua veteres
+  Christianos_, reprinted in Volbeding's _Thesaurus_ (Leipzig, 1841).
+       (F. C. C.)
+
+
+FOOTNOTES:
+
+  [1] E.S. Hartland, _Legend of Perseus_ (1895), ii. 278.
+
+  [2] Mary Kingsley, _West African Studies_ (1901), p. 178.
+
+  [3] B. Spencer and F.J. Gillen, _The Native Tribes of Central
+    Australia_ (1899), p. 48.
+
+
+
+
+FUNGI (pl. of Lat. _fungus_, a mushroom), the botanical name covering in
+the broad sense all the lower cellular Cryptogams devoid of chlorophyll,
+which arise from spores, and the thallus of which is either unicellular
+or composed of branched or unbranched tubes or cell-filaments (hyphae)
+with apical growth, or of more or less complex wefted sheets or
+tissue-like masses of such (mycelium). The latter may in certain cases
+attain large dimensions, and even undergo cell-divisions in their
+interior, resulting in the development of true tissues. The spores,
+which may be uni- or multicellular, are either abstricted free from the
+ends of hyphae (acrogenous), or formed from segments in their course
+(_chlamydospores_) or from protoplasm in their interior (endogenous).
+The want of chlorophyll restricts their mode of life--which is rarely
+aquatic--since they are therefore unable to decompose the carbon dioxide
+of the atmosphere, and renders them dependent on other plants or
+(rarely) animals for their carbonaceous food-materials. These they
+obtain usually in the form of carbohydrates from the dead remains of
+other organisms, or in this or other forms from the living cells of
+their hosts; in the former case they are termed saprophytes, in the
+latter parasites. While some moulds (_Penicillium_, _Aspergillus_) can
+utilize almost any organic food-materials, other fungi are more
+restricted in their choice--e.g. insect-parasites, horn- and
+feather-destroying fungi and parasites generally. It was formerly the
+custom to include with the Fungi the Schizomycetes or Bacteria, and the
+Myxomycetes or Mycetozoa; but the peculiar mode of growth and division,
+the cilia, spores and other peculiarities of the former, and the
+emission of naked amoeboid masses of protoplasm, which creep and fuse to
+streaming plasmodia, with special modes of nutrition and spore-formation
+of the latter, have led to their separation as groups of organisms
+independent of the true Fungi. On the other hand, lichens, previously
+regarded as autonomous plants, are now known to be dual organisms--fungi
+symbiotic with algae.
+
+The number of species in 1889 was estimated by Saccardo at about 32,000,
+but of these 8500 were so-called _Fungi imperfecti_--i.e. forms of which
+we only know certain stages, such as conidia, pycnidia, &c., and which
+there are reasons for regarding as merely the corresponding stages of
+higher forms. Saccardo also included about 400 species of Myxomycetes
+and 650 of Schizomycetes. Allowing for these and for the cases,
+undoubtedly not few, where one and the same fungus has been described
+under different names, we obtain Schroeter's estimate (in 1892) of
+20,000 species. In illustration of the very different estimates that
+have been made, however, may be mentioned that of De Bary in 1872 of
+150,000 species, and that of Cooke in 1895 of 40,000, and Massee in 1899
+of over 50,000 species, the fact being that no sufficient data are as
+yet to hand for any accurate census. As regards their geographical
+distribution, fungi, like flowering plants, have no doubt their centres
+of origin and of dispersal; but we must not forget that every exchange
+of wood, wheat, fruits, plants, animals, or other commodities involves
+transmission of fungi from one country to another; while the migrations
+of birds and other animals, currents of air and water, and so forth, are
+particularly efficacious in transmitting these minute organisms. Against
+this, of course, it may be argued that parasitic forms can only go where
+their hosts grow, as is proved to be the case by records concerning the
+introduction of _Puccinia malvacearum_, _Peronospora viticola_,
+_Hemileia vastatrix_, &c. Some fungi--e.g. moulds and yeasts--appear to
+be distributed all over the earth. That the north temperate regions
+appear richest in fungi may be due only to the fact that North America
+and Europe have been much more thoroughly investigated than other
+countries; it is certain that the tropics are the home of very numerous
+species. Again, the accuracy of the statement that the fleshy Agaricini,
+Polyporei, _Pezizae_, &c., are relatively rarer in the tropics may
+depend on the fact that they are more difficult to collect and remit for
+identification than the abundantly recorded woody and coriaceous forms
+of these regions. When we remember that many parts of the world are
+practically unexplored as regards fungi, and that new species are
+constantly being discovered in the United States, Australia and northern
+Europe--the best explored of all--it is clear that no very accurate
+census of fungi can as yet be made, and no generalizations of value as
+to their geographical distribution are possible.
+
+The existence of fossil fungi is undoubted, though very few of the
+identifications can be relied on as regards species or genera. They
+extend back beyond the Carboniferous, where they occur as hyphae, &c.,
+preserved in the fossil woods, but the best specimens are probably those
+in amber and in siliceous petrifactions of more recent origin.
+
+[Illustration: FIG. 1.--1, _Peronospora parasitica_ (De Bary). Mycelium
+with haustoria (h); 2, _Erysiphe_; A and B, mycelium (m), with haustoria
+(h). (After De Bary.)]
+
+  _Organs._--Individual hyphae or their branches often exhibit
+  specializations of form. In many Basidiomycetes minute branches arise
+  below the septa; their tips curve over the outside of the latter, and
+  fuse with the cell above just beyond it, forming a _clamp-connexion_.
+  Many parasitic hyphae put out minute lateral branches, which pierce
+  the cell-wall of the host and form a peg-like (_Trichosphaeria_),
+  sessile (_Cystopus_), or stalked (_Hemileia_), knot-like, or a more or
+  less branched (_Peronospora_) or coiled (_Protomyces_) haustorium. In
+  _Rhizopus_ certain hyphae creep horizontally on the surface of the
+  substratum, and then anchor their tips to it by means of a tuft of
+  short branches (_appressorium_), the walls of which soften and gum
+  themselves to it, then another branch shoots out from the tuft and
+  repeats the process, like a strawberry-runner. Appressoria are also
+  formed by some parasitic fungi, as a minute flattening of the tip of a
+  very short branch (_Erysiphe_), or the swollen end of any hypha which
+  comes in contact with the surface of the host (_Piptocephalis_,
+  _Syncephalis_), haustoria piercing in each case the cell-wall below.
+  In _Botrytis_ the appressoria assume the form of dense tassels of
+  short branches. In _Arthrobotrys_ side-branches of the mycelium sling
+  themselves around the host (_Tylenchus_) much as tendrils round a
+  support.
+
+  Many fungi (_Phallus_, _Agaricus_, _Fumago_, &c.) when strongly
+  growing put out ribbon-like or cylindrical cords, or sheet-like
+  mycelial plates of numerous parallel hyphae, all growing together
+  equally, and fusing by anastomoses, and in this way extend long
+  distances in the soil, or over the surfaces of leaves, branches, &c.
+  These mycelial strands may be white and tender, or the outer hyphae
+  may be hard and black, and very often the resemblance of the
+  subterranean forms to a root is so marked that they are termed
+  rhizomorphs. The outermost hyphae may even put forth thinner hyphae,
+  radiating into the soil like root-hairs, and the convergent tips may
+  be closely appressed and so divided by septa as to resemble the
+  root-apex of a higher plant (_Armillaria mellea_).
+
+  _Sclerotia._--Fungi, like other plants, are often found to store up
+  large quantities of reserve materials (oil, glycogen, carbohydrates,
+  &c.) in special parts of their vegetative tissues, where they lie
+  accumulated between a period of active assimilation and one of renewed
+  activity, forming reserves to be consumed particularly during the
+  formation of large fructifications. These reserve stores may be packed
+  away in single hyphae or in swollen cells, but the hyphae containing
+  them are often gathered into thick cords or mycelial strands
+  (_Phallus_, mushroom, &c.), or flattened and anastomosing ribbons and
+  plates, often containing several kinds of hyphae (_Merulius
+  lacrymans_). In other cases the strands undergo differentiation into
+  an outer layer with blackened, hardened cell-walls and a core of
+  ordinary hyphae, and are then termed rhizomorphs (_Armillaria
+  mellea_), capable not only of extending the fungus in the soil, like
+  roots, but also of lying dormant, protected by the outer casing. Such
+  aggregations of hyphae frequently become knotted up into dense masses
+  of interwoven and closely packed hyphae, varying in size from that of
+  a pin's head or a pea (_Peziza_, _Coprinus_) to that of a man's fist
+  or head, and weighing 10 to 25 lb. or more (_Polyporus Mylittae_, _P.
+  tumulosus_, _Lentinus Woermanni_, _P. Sapurema_, &c.). The interwoven
+  hyphae fuse and branch copiously, filling up all interstices. They
+  also undergo cutting up by numerous septa into short cells, and these
+  often divide again in all planes, so that a pseudoparenchyma results,
+  the walls of which may be thickened and swollen internally, or
+  hardened and black on the exterior. In many cases the swollen
+  cell-walls serve as reserves, and sometimes the substance is so
+  thickly deposited in strata as to obliterate the lumen, and the hyphae
+  become nodular (_Polyporus sacer_, _P. rhinoceros_, _Lentinus
+  Woermanni_). The various sclerotia, if kept moist, give rise to the
+  fructifications of the fungi concerned, much as a potato tuber does to
+  a potato plant, and in the same way the reserve materials are
+  consumed. They are principally Polyporei, Agaricini, Pezizae; none are
+  known among the Phycomycetes, Uredineae or Ustilagineae. The functions
+  of mycelial strands, rhizomorphs and sclerotia are not only to collect
+  and store materials, but also to extend the fungus, and in many cases
+  similar strands act as organs of attack. The same functions of storage
+  in advance of fructification are also exercised by the stromata so
+  common in Ascomycetes.
+
+  _Tissue Differentiations._--The simpler mycelia consist of hyphae all
+  alike and thin-walled, or merely differing in the diameter of the
+  branches of various orders, or in their relations to the environment,
+  some plunging into the substratum like roots, others remaining on its
+  surface, and others (aerial hyphae) rising into the air. Such hyphae
+  may be multicellular, or they may consist of simple tubes with
+  numerous nuclei and no septa (_Phycomycetes_), and are then
+  non-cellular. In the more complex tissue-bodies of higher fungi,
+  however, we find considerable differences in the various layers or
+  strands of hyphae.
+
+  An epidermis-like or cortical protective outer layer is very common,
+  and is usually characterized by the close septation of the densely
+  interwoven hyphae and the thickening and dark colour of their outer
+  walls (sclerotia, _Xylaria_, &c.). Fibre-like hyphae with the lumen
+  almost obliterated by the thick walls occur in mycelial cords
+  (_Merulius_). Latex-tubes abound in the tissues of _Lactarius_,
+  _Stereum_, _Mycena_, _Fistulina_, filled with white or coloured milky
+  fluids, and Istvanffvi has shown that similar tubes with fluid or oily
+  contents are widely spread in other Hymenomycetes. Sometimes fatty oil
+  or watery sap is found in swollen hyphal ends, or such tubes contain
+  coloured sap. Cystidia and paraphyses may be also classed here. In
+  _Merulius lacrymans_ Hartig has observed thin-walled hyphae with large
+  lumina, the septa of which are perforated like those of sieve-tubes.
+
+  As regards its composition, the cell-wall of fungi exhibits variations
+  of the same kind as those met with in higher plants. While the
+  fundamental constituent is a cellulose in many Mucorini and other
+  Phycomycetes, in others bodies like pectose, callose, &c., commonly
+  occur, and Wisselingh's researches show that chitin, a gluco-proteid
+  common in animals, forms the main constituent in many cases, and is
+  probably deposited directly as such, though, like the other
+  substances, it may be mixed with cellulose. As in other cell-walls, so
+  here the older membranes may be altered by deposits of various
+  substances, such as resin, calcium oxalate, colouring matters; or more
+  profoundly altered throughout, or in definite layers, by
+  lignification, suberization (_Trametes_, _Daedalea_), or swelling to a
+  gelatinous mucilage (_Tremella_, _Gymnosporangium_), while
+  cutinization of the outer layers is common. One of the most striking
+  alterations of cell-walls is that termed _carbonization_, in which the
+  substance gradually turns black, hard and brittle, as if charred--e.g.
+  _Xylaria_, _Ustulina_, some sclerotia. At the other extreme the
+  cell-walls of many lichen-fungi are soft and colourless, but turn blue
+  in iodine, as does starch. The young cell-wall is always tenuous and
+  flexible, and may remain so throughout, but in many cases thickenings
+  and structural differentiations, as well as the changes referred to
+  above, alter the primary wall considerably. Such thickening may be
+  localized, and _pits_ (e.g. _Uredospores_, septa of Basidiomycetes),
+  _spirals_, _reticulations_, _rings_, &c. (capillitium fibres of
+  _Podaxon_, _Calostoma_, _Battarrea_), occur as in the vessels of
+  higher plants, while sculptured networks, pittings and so forth are as
+  common on fungus-spores as they are on pollen grains.
+
+  _Cell-Contents._--The cells of fungi, in addition to protoplasm,
+  nuclei and sap-vacuoles, like other vegetable cells, contain formed
+  and amorphous bodies of various kinds. Among those directly visible to
+  the microscope are oil drops, often coloured (_Uredineae_) crystals of
+  calcium oxalate (_Phallus_, _Russula_), proteid crystals (_Mucor_,
+  _Pilobolus_, &c.) and resin (Polyporei). The oidia of Erysipheae
+  contain fibrosin bodies and the hyphae of Saprolegnieae cellulin
+  bodies, but starch apparently never occurs. Invisible to the
+  microscope, but rendered visible by reagents, are glycogen, _Mucor_,
+  Ascomycetes, yeast, &c. In addition to these cell-contents we have
+  good indirect evidence of the existence of large series of other
+  bodies, such as proteids, carbohydrates, organic acids, alkaloids,
+  enzymes, &c. These must not be confounded with the numerous substances
+  obtained by chemical analysis of masses of the fungus, as there is
+  often no proof of the manner of occurrence of such bodies, though we
+  may conclude with a good show of probability that some of them also
+  exist preformed in the living cell. Such are sugars (glucose, mannite,
+  &c.), acids (acetic, citric and a whole series of lichen-acids),
+  ethereal oils and resinous bodies, often combined with the intense
+  colours of fungi and lichens, and a number of powerful alkaloid
+  poisons, such as muscarin (_Amanita_), ergotin (_Claviceps_), &c.
+
+  Among the enzymes already extracted from fungi are _invertases_
+  (yeasts, moulds, &c.), which split cane-sugar and other complex sugars
+  with hydrolysis into simpler sugars such as dextrose and levulose;
+  _diastases_, which convert starches into sugars (_Aspergillus_, &c.);
+  _cytases_, which dissolve cellulose similarly (_Botrytis_, &c.);
+  _peptases_, using the term as a general one for all enzymes which
+  convert proteids into peptones and other bodies (_Penicillium_, &c.);
+  lipases, which break up fatty oils (_Empusa_, _Phycomyces_, &c.);
+  oxydases, which bring about the oxidations and changes of colour
+  observed in _Boletus_, and _zymase_, extracted by Buchner from yeast,
+  which brings about the conversion of sugar into alcohol and
+  carbon-dioxide. That such enzymes are formed in the protoplasm is
+  evident from the behaviour of hyphae, which have been observed to
+  pierce cell-membranes, the chitinous coats of insects, artificial
+  collodion films and layers of wax, &c. That a fungus can secrete more
+  than one enzyme, according to the materials its hyphae have to attack,
+  has been shown by the extraction of diastase, inulase, trehalase,
+  invertase, maltase, raffinase, malizitase, emulsin, trypsin and lipase
+  from _Aspergillus_ by Bourquelot, and similar events occur in other
+  fungi. The same fact is indicated by the wide range of organic
+  substances which can be utilized by _Penicillium_ and other moulds,
+  and by the behaviour of parasitic fungi which destroy various
+  cell-contents and tissues. Many of the coloured pigments of fungi are
+  fixed in the cell-walls or excreted to the outside (_Peziza
+  aeruginosa_). Matruchot has used them for staining the living
+  protoplasm of other fungi by growing the two together. Striking
+  instances of coloured mycella are afforded by _Corticium sanguineum_,
+  blood-red; _Elaphomyces Leveillei_, yellow-green; _Chlorosplenium
+  aeruginosum_, verdigris green; and the _Dematei_, brown or black.
+
+  _Nuclei._--Although many fungi have been regarded as devoid of nuclei,
+  and all have not as yet been proved to contain them, the numerous
+  investigations of recent years have revealed them in the cells of all
+  forms thoroughly examined, and we are justified in concluding that the
+  nucleus is as essential to the cell of a fungus as to that of other
+  organisms. The hyphae of many contain numerous, even hundreds of
+  nuclei (Phycomycetes); those of others have several (_Aspergillus_) in
+  each segment, or only two (_Exoascus_) or one (_Erysiphe_) in each
+  cell. Even the isolated cells of the yeast plant have each one
+  nucleus. As a rule the nuclei of the mycelium are very minute (1.5-2 µ
+  in _Phycomyces_), but those of many asci and spores are large and
+  easily rendered visible. As with other plants, so in fungi the
+  essential process of fertilization consists in the fusion of two
+  nuclei, but owing to the absence of well-marked sexual organs from
+  many fungi, a peculiar interest attaches to certain nuclear fusions in
+  the vegetative cells or in young spores of many forms. Thus in
+  Ustilagineae the chlamydospores, and in Uredineae the teleutospores,
+  each contain two nuclei when young, which fuse as the spores mature.
+  In young asci a similar fusion of two nuclei occurs, and also in
+  basidia, in each case the nucleus of the ascus or of the basidium
+  resulting from the fusion subsequently giving rise by division to the
+  nuclei of the ascospores and basidiospores respectively. The
+  significance of these fusions will be discussed under the various
+  groups. Nuclear division is usually accompanied by all the essential
+  features of karyokinesis.
+
+  _Spores._--No agreement has ever been arrived at regarding the
+  consistent use of the term spore. This is apparently owing to the
+  facts that too much has been attempted in the definition, and that
+  differences arise according as we aim at a morphological or a
+  physiological definition. Physiologically, any cell or group of cells
+  separated off from a hypha or unicellular fungus, and capable of
+  itself growing out--germinating--to reproduce the fungus, is a spore;
+  but it is evident that so wide a definition does not exclude the
+  ordinary vegetative cells of sprouting fungi, such as yeasts, or small
+  sclerotium like cell-aggregates of forms like _Coniothecium_.
+  Morphologically considered, spores are marked by peculiarities of
+  form, size, colour, place of origin, definiteness in number, mode of
+  preparation, and so forth, such that they can be distinguished more or
+  less sharply from the hyphae which produce them. The only
+  physiological peculiarity exhibited in common by all spores is that
+  they germinate and initiate the production of a new fungus-plant.
+  Whether a spore results from the sexual union of two similar gametes
+  (zygospore) or from the fertilization of an egg-cell by the protoplasm
+  of a male organ (oospore); or is developed asexually as a motile
+  (zoospore) or a quiescent body cut off from a hypha (conidium) or
+  developed along its course (oidium or chlamydospore), or in its
+  protoplasm (endospore), are matters of importance which have their
+  uses in the classification and terminology of spores, though in many
+  respects they are largely of academic interest.
+
+  [Illustration: FIG. 2.--_Peronospora parasitica_ (De Bary).
+  Conidiophore with conidia.]
+
+  Klebs has attempted to divide spores into three categories as follows:
+  (1) kinospores, arising by relatively simple cell-divisions and
+  subserving rapid dissemination and propagation, e.g. zoospores,
+  conidia, endogonidia, stylospores, &c.; (2) paulospores, due to simple
+  rearrangement of cell-contents, and subserving the persistence of the
+  fungus through periods of exigency, e.g. gemmae, chlamydospores,
+  resting-cells, cysts, &c.; (3) carpospores, produced by a more or less
+  complex formative process, often in special fructifications, and
+  subserving either or both multiplication and persistence, e.g.
+  zygospores, oospores, brand-spores, aecidiospores, ascospores,
+  basidiospores, &c. Little or nothing is gained by these definitions,
+  however, which are especially physiological. In practice these various
+  kinds of spores of fungi receive further special names in the separate
+  groups, and names, moreover, which will appear, to those unacquainted
+  with the history, to have been given without any consistency or regard
+  to general principles; nevertheless, for ordinary purposes these names
+  are far more useful in most cases, owing to their descriptive
+  character, than the proposed new names, which have been only partially
+  accepted.
+
+  _Sporophores._--In some of the simpler fungi the spores are not borne
+  on or in hyphae which can be distinguished from the vegetative parts
+  or mycelium, but in the vast majority of cases the sporogenous hyphae
+  either ascend free into the air or radiate into the surrounding water
+  as distinct branches, or are grouped into special columns, cushions,
+  layers or complex masses obviously different in colour, consistency,
+  shape and other characters from the parts which gather up and
+  assimilate the food-materials. The term "receptacle" sometimes applied
+  to these spore-bearing hyphae is better replaced by sporophore. The
+  sporophore is obsolete when the spore-bearing hyphae are not sharply
+  distinct from the mycelium, simple when the constituent hyphae are
+  isolated, and compound when the latter are conjoined. The chief
+  distinctive characters of the sporogenous hyphae are their
+  orientation, usually vertical; their limited apical growth; their
+  peculiar branching, form, colour, contents, consistency; and their
+  spore-production. According to the characters of the last, we might
+  theoretically divide them into conidiophores, sporangiophores,
+  gametophores, oidiophores, &c.; but since the two latter rarely occur,
+  and more than one kind of spore or spore-case may occur on a
+  sporophore, it is impossible to carry such a scheme fully into
+  practice.
+
+  A simple sporophore may be merely a single short hypha, the end of
+  which stops growing and becomes cut off as a conidium by the formation
+  of a septum, which then splits and allows the conidium to fall. More
+  generally the hypha below the septum grows forwards again, and repeats
+  this process several times before the terminal conidium falls, and so
+  a chain of conidia results, the oldest of which terminates the series
+  (_Erysiphe_); when the primary branch has thus formed a basipetal
+  series, branches may arise from below and again repeat this process,
+  thus forming a tuft (_Penicillium_). Or the primary hypha may first
+  swell at its apex, and put forth a series of short peg-like branches
+  (_sterigmata_) from the increased surface thus provided, each of which
+  develops a similar basipetal chain of conidia (_Aspergillus_), and
+  various combinations of these processes result in the development of
+  numerous varieties of exquisitely branched sporophores of this type
+  (_Botrytis_, _Botryosporium_, _Verticillium_, &c.).
+
+  [Illustration: FIG. 3.--_Cystopus candidus_.
+
+    A. a, Conidia.
+       b, Conidiophores.
+       c, Conidium emitting zoospores.
+       d, Free zoospore.
+    B.og, Oogonium.
+      os, Oosphere.
+      an, Antheridium.
+    C. Formation of zoospores by oospores.
+       z, Free zoospores. (After De Bary.)]
+
+  A second type is developed as follows: the primary hypha forms a
+  septum below its apex as before, and the terminal conidium, thus
+  abstricted, puts out a branch at its apex, which starts as a mere
+  point and rapidly swells to a second conidium; this repeats the
+  process, and so on, so that we now have a chain of conidia developed
+  in acropetal succession, the oldest being below, and, as in
+  _Penicillium_, &c., branches put forth lower down may repeat the
+  process (_Hormodendron_). In all these cases we may speak of simple
+  conidiophores. The simple sporophore does not necessarily terminate in
+  conidia, however. In _Mucor_, for example, the end of the primary
+  hypha swells into a spheroidal head (sporangium), the protoplasm of
+  which undergoes segmentation into more or less numerous globular
+  masses, each of which secretes an enveloping cell-wall and becomes a
+  spore (endospore), and branched systems of sporangia may arise as
+  before (_Thamnidium_). Such may be termed sporangiophores. In
+  _Sporodinia_ the branches give rise also to short branches, which meet
+  and fuse their contents to form zygospores. In Peronospora,
+  Saprolegnia, &c., the ends of the branches swell up into sporangia,
+  which develop zoospores in their interior (zoosporangia), or their
+  contents become oospheres, which may be fertilized by the contents of
+  other branches (antheridia) and so form egg-cases (oogonia). Since in
+  such cases the sporophore bears sexual cells, they may be conveniently
+  termed gametophores.
+
+  Compound sporophores arise when any of the branched or unbranched
+  types of spore-bearing hyphae described above ascend into the air in
+  consort, and are more or less crowded into definite layers, cushions,
+  columns or other complex masses. The same laws apply to the individual
+  hyphae and their branches as to simple sporophores, and as long as the
+  conidia, sporangia, gametes, &c., are borne on their external
+  surfaces, it is quite consistent to speak of these as compound
+  sporophores, &c., in the sense described, however complex they may
+  become. Among the simplest cases are the sheet-like aggregates of
+  sporogenous hyphae in _Puccinia_, _Uromyces_, &c., or of basidia in
+  _Exobasidium_, _Corticium_, &c., or of asci in _Exoascus_,
+  _Ascocorticium_, &c. In the former, where the layer is small, it is
+  often termed a sorus, but where, as in the latter, the sporogenous
+  layer is extensive, and spread out more or less sheet-like on the
+  supporting tissues, it is more frequently termed a hymenium. Another
+  simple case is that of the columnar aggregates of sporogenous hyphae
+  in forms like _Stilbum_, _Coremium_, &c. These lead us to cases where
+  the main mass of the sporophore forms a supporting tissue of closely
+  crowded or interwoven hyphae, the sporogenous terminal parts of the
+  hyphae being found at the periphery or apical regions only. Here we
+  have the cushion-like type (stroma) of _Nectria_ and many
+  Pyrenomycetes, the clavate "receptacle" of _Clavaria_, &c., passing
+  into the complex forms met with in _Sparassis_, _Xylaria_,
+  _Polyporei_, and _Agaricini_, &c. In these cases the compound
+  sporophore is often termed the hymenophore, and its various parts
+  demand special names (pileus, stipes, gills, pores, &c.) to denote
+  peculiarities of distribution of the hymenium over the surface.
+
+  Other series of modifications arise in which the tissues corresponding
+  to the stroma invest the sporogenous hyphal ends, and thus enclose the
+  spores, asci, basidia, &c., in a cavity. In the simplest case the
+  stroma, after bearing its crop of conidia or oidia, develops
+  ascogenous branches in the loosened meshes of its interior (e.g.
+  _Onygena_). Another simple case is where the plane or slightly convex
+  surface of the stroma rises at its margins and overgrows the
+  sporogenous hyphal ends, so that the spores, asci, &c., come to lie in
+  the depression of a cavity--e.g. _Solenia_, _Cyphella_--and even
+  simpler cases are met with in _Mortierella_, where the zygospore is
+  invested by the overgrowth of a dense mat of closely branching hyphae,
+  and in _Gymnoascus_, where a loose mat of similarly barren hyphae
+  covers in the tufts of asci as they develop.
+
+  In such examples as the above we may regard the hymenium (_Solenia_,
+  _Cyphella_), zygospores, or asci as truly invested by later growth,
+  but in the vast majority of cases the processes which result in the
+  enclosure of the spores, asci, &c., in a "fructification" are much
+  more involved, inasmuch as the latter is developed in the interior of
+  hyphal tissues, which are by no means obviously homologous with a
+  stroma. Thus in _Penicillium_, _Eurotium_, _Erysiphe_, &c., hyphal
+  ends which are the initials of ascogenous branches, are invested by
+  closely packed branches at an early stage of development, and the asci
+  develop inside what has by that time become a complete investment.
+  Whether a true sexual process precedes these processes or not does not
+  affect the present question, the point being that the resulting
+  spheroidal "fructification" (cleistocarp, perithecium) has a definite
+  wall of its own not directly comparable with a stroma. In other cases
+  (_Hypomyces_, _Nectria_) the perithecia arise on an already mature
+  stroma, while yet more numerous examples can be given (_Poronia_,
+  _Hypoxylon_, _Claviceps_, &c.) where the perithecia originate below
+  the surface of a stroma formed long before. Similarly with the various
+  types of conidial or oidial "fructifications," termed pycnidia,
+  spermogonia, aecidia, &c. In the simplest of these cases--e.g.
+  _Fumago_--a single mycelial cell divides by septa in all three planes
+  until a more or less solid clump results. Then a hollow appears in the
+  centre owing to the more rapid extension of the outer parts, and into
+  this hollow the cells lining it put forth short sporogenous branches,
+  from the tips of which the spores (stylospores, conidia, spermatia)
+  are abstricted. In a similar way are developed the pycnidia of
+  _Cicinnobolus_, _Pleospora_, _Cucurbitaria_, _Leptosphaeria_ and
+  others. In other cases (_Diplodia_, _Aecidium_, &c.) conidial or
+  oidial "fructifications" arise by a number of hyphae interweaving
+  themselves into a knot, as if they were forming a Sclerotium. The
+  outer parts of the mass then differentiate as a wall or investment,
+  and the interior becomes a hollow, into which hyphal ends grow and
+  abstrict the spores. Much more complicated are the processes in a
+  large series of "fructifications," where the mycelium first develops a
+  densely packed mass of hyphae, all alike, in which labyrinths of
+  cavities subsequently form by separation of hyphae in the previously
+  homogeneous mass, and the hymenium covers the walls of these cavities
+  and passages as with a lining layer. Meanwhile differences in
+  consistency appear in various strata, and a dense outer protective
+  layer (peridium), soft gelatinous layers, and so on are formed, the
+  whole eventually attaining great complexity--e.g. puff-balls,
+  earth-stars and various _Phalloideae_.
+
+  _Spore-Distribution._--Ordinary conidia and similarly abstricted dry
+  spores are so minute, light and numerous that their dispersal is
+  ensured by any current of air or water, and we also know that rats and
+  other burrowing animals often carry them on their fur; similarly with
+  birds, insects, slugs, worms, &c., on claws, feathers, proboscides,
+  &c., or merely adherent to the slimy body. In addition to these
+  accidental modes of dispersal, however, there is a series of
+  interesting adaptations on the part of the fungus itself. Passing over
+  the locomotor activity of zoospores (_Pythium_, _Peronospora_,
+  _Saprolegnia_) we often find spores held under tension in sporangia
+  (_Pilobolus_) or in asci (_Peziza_) until ripe, and then forcibly shot
+  out by the sudden rupture of the sporangial wall under the pressure of
+  liquid behind--mechanism comparable to that of a pop-gun, if we
+  suppose air replaced by watery sap. Even a single conidium, held tense
+  to the last moment by the elastic cell-wall, may be thus shot forward
+  by a spurt of liquid under pressure in the hypha abstricting it (e.g.
+  _Empusa_), and similarly with _basidiospores_ (_Coprinus_, _Agaricus_,
+  &c.). A more complicated case is illustrated by _Sphaerobolus_, where
+  the entire mass of spores, enclosed in its own peridium, is suddenly
+  shot up into the air like a bomb from a mortar by the elastic
+  retroversion of a peculiar layer which, up to the last moment,
+  surrounded the bomb, and then suddenly splits above, turns inside out,
+  and drives the former as a projectile from a gun. Gelatinous or
+  mucilaginous degenerations of cell-walls are frequently employed in
+  the interests of spore dispersal. The mucilage surrounding endospores
+  of _Mucor_, conidia of _Empusa_, &c., serves to gum the spore to
+  animals. Such gums are formed abundantly in pycnidia, and, absorbing
+  water, swell and carry out the spores in long tendrils, which emerge
+  for days and dry as they reach the air, the glued spores gradually
+  being set free by rain, wind, &c. In oidial chains (_Sclerotinia_) a
+  minute double wedge of wall-substance arises in the middle lamella
+  between each pair of contiguous oidia, and by its enlargement splits
+  the separating lamella. These disjunctors serve as points of
+  application for the elastic push of the swelling spore-ends, and as
+  the connecting outer lamella of cell-wall suddenly gives way, the
+  spores are jerked asunder. In many cases the slimy masses of spermatia
+  (_Uredineae_), conidia (_Claviceps_), basidiospores (_Phallus_,
+  _Coprinus_), &c., emit more or less powerful odours, which attract
+  flies or other insects, and it has been shown that bees carry the
+  fragrant oidia of _Sclerotinia_ to the stigma of _Vaccinium_ and
+  infect it, and that flies carry away the foetid spores of _Phallus_,
+  just as pollen is dispersed by such insects. Whether the strong odour
+  of trimethylamine evolved by the spores of _Tilletia_ attracts insects
+  is not known.
+
+  The recent observations and exceedingly ingenious experiments of Falck
+  have shown that the sporophores of the Basidiomycetes--especially the
+  large sporophores of such forms as _Boletus_, _Polyporus_--contain
+  quantities of reserve combustible material which are burnt up by the
+  active metabolism occurring when the fruit-body is ripe. By this means
+  the temperature of the sporophore is raised and the difference between
+  it and the surrounding air may be one of several degrees. As a result
+  convection currents are produced in the air which are sufficient to
+  catch the basidiospores in their fall and carry them, away from the
+  regions of comparative atmospheric stillness near the ground, to the
+  upper air where more powerful air-currents can bring about their wide
+  distribution.
+
+_Classification._--It has been accepted for some time now that the
+majority of the fungi proper fall into three main groups, the
+Phycomycetes, Ascomycetes and Basidiomycetes, the Schizomycetes and
+Myxomycetes (Mycetozoa) being considered as independent groups not
+coming under the true fungi.
+
+The chief schemes of classification put forward in detail have been
+those of P.A. Saccardo (1882-1892), of Oskar Brefeld and Von Tavel
+(1892), of P.E.L. Van Tieghem (1893) and of J. Schroeter (1892). The
+scheme of Brefeld, which was based on the view that the Ascomycetes and
+Basidiomycetes were completely asexual and that these two groups had
+been derived from one division (Zygomycetes) of the Phycomycetes, has
+been very widely accepted. The recent work of the last twelve years has
+shown, however, that the two higher groups of fungi exhibit distinct
+sexuality, of either a normal or reduced type, and has also rendered
+very doubtful the view of the origin of these two groups from the
+Phycomycetes. The real difficulty of classification of the fungi lies in
+the polyphyletic nature of the group. There is very little doubt that
+the primitive fungi have been derived by degradation from the lower
+algae. It appears, however, that such a degradation has occurred not
+only once in evolution but on several occasions, so that we have in the
+Phycomycetes not a series of naturally related forms, but groups which
+have arisen perfectly independently of one another from various groups
+of the algae. It is also possible in the absence of satisfactory
+intermediate forms that the Ascomycetes and Basidiomycetes have also
+been derived from the algae independently of the Phycomycetes, and
+perhaps of one another.
+
+A natural classification on these lines would obviously be very
+complicated, so that in the present state of our knowledge it will be
+best to retain the three main groups mentioned above, bearing in mind
+that the Phycomycetes especially are far from being a natural group. The
+following gives a tabular survey of the scheme adopted in the present
+article:
+
+  A. PHYCOMYCETES. Alga-like fungi with unicellular thallus and
+  well-marked sexual organs.
+
+  CLASS I.--Oomycetes. Mycelium usually well developed, but sometimes
+  poor or absent. Sexual reproduction by oogonia and antheridia; asexual
+  reproduction by zoospores or conidia.
+
+    1. Monoblepharidineae. Mycelium present, antheridia with
+    antherozoids, oogonium with single oosphere: Monoblepharidaceae.
+
+    2. Peronosporineae. Mycelium present; antheridia but no
+    antherozoids; oogonia with one or more oospheres: Peronosporaceae,
+    Saprolegniaceae.
+
+    3. Chytridineae. Mycelium poorly developed or absent; oogonia and
+    antheridia (without antherozoids) known in some cases; zoospores
+    common: Chytridiaceae. Ancylistaceae.
+
+  CLASS II.--Zygomycetes. Mycelium well developed; sexual reproduction
+  by zygospores; asexual reproduction by sporangia and conidia.
+
+    1. Mucorineae. Sexual reproduction as above, asexual by sporangia or
+    conidia or both: Mucoraceae. Mortierellaceae, Chaetocladiaceae,
+    Piptocephalidaceae.
+
+    2. Entomophthorineae. Sexual reproduction typical but with sometimes
+    inequality of the fusing gametes (gametangia ?): Entomophthoraceae.
+
+  B. HIGHER FUNGI. Fungi with segmental thallus; sexual reproduction
+  sometimes with typical antheridia and oogonia (ascogonia) but usually
+  much reduced.
+
+  CLASS I.--Ustilaginales. Forms with septate thallus, and reproduction
+  by chlamydospores which on germination produce sporidia; sexuality
+  doubtful.
+
+  CLASS II.--Ascomycetes. Thallus septate; spores developed in special
+  type of sporangium, the ascus, the number of spores being usually
+  eight. Sexual reproduction sometimes typical, usually reduced.
+
+  Exoascineae, Saccharomycetineae, Perisporinea, Discomycetes,
+  Pyrenomycetes, Tuberineae, Laboulbeniineae.
+
+  CLASS III.--Basidiales. Thallus septate. Conidia (basidiospores) borne
+  in fours on a special conidiophore, the basidium. Sexual reproduction
+  always much reduced.
+
+    1. Uredineae. Life-history in some cases very complex and with
+    well-marked sexual process and alternation of generations, in others
+    much reduced; basidium (promycelium) derived usually from a
+    thick-walled spore (teleutospore).
+
+    2. Basidiomycetes. Life-history always very simple, no well-marked
+    alternation of generations; basidium borne directly on the mycelium.
+
+      (A) Protobasidiomycetes. Basidia septate. Auriculariaceae,
+      Pilacreaceae, Tremellinaceae.
+
+      (B) Autobasidiomycetes. Basidia non-septate. Hymenomycetes,
+      Gasteromycetes.
+
+A. PHYCOMYCETES.--Most of the recent work of importance in this group
+deals with the cytology of sexual reproduction and of spore-formation,
+and the effect of external conditions on the production of reproductive
+organs.
+
+  _Monoblepharidaceae_ consists of a very small group of aquatic forms
+  living on fallen twigs in ponds and ditches. Only one genus,
+  _Monoblepharis_, can certainly be placed here, though a somewhat
+  similar genus, _Myrioblepharis_, with a peculiar multiciliate zoospore
+  like that of Vaucheria, is provisionally placed in the same group.
+  _Monoblepharis_ was first described by Cornu in 1871, but from that
+  time until 1895 when Roland Thaxter described several species from
+  America the genus was completely lost sight of. _Monoblepharis_ has
+  oogonia with single oospheres and antheridia developing a few amoeboid
+  uniciliate antherozoids; these creep to the opening of the oogonium
+  and then swim in. The resemblance between this genus and _Oedogonium_
+  among the algae is very striking, as is also that of _Myrioblepharis_
+  and _Vaucheria_.
+
+  _Peronosporaceae_ are a group of endophytic parasites--about 100
+  species--of great importance as comprising the agents of "damping off"
+  disease (_Pythium_), vine-mildew (_Plasmopara_), potato disease
+  (Phytophthora), onion-mildew (_Peronospora_). _Pythium_ is a
+  semi-aquatic form attacking seedlings which are too plentifully
+  supplied with water; its hyphae penetrate the cell-walls and rapidly
+  destroy the watery tissues of the living plant; then the fungus lives
+  in the dead remains. When the free ends of the hyphae emerge again
+  into the air they swell up into spherical bodies which may either fall
+  off and behave as conidia, each putting out a germ-tube and infecting
+  the host; or the germ-tube itself swells up into a zoosporangium which
+  develops a number of zoospores. In the rotting tissues branches of the
+  older mycelium similarly swell up and form antheridia and oogonia
+  (fig. 4). The contents of the antheridium are not set free, but that
+  organ penetrates the oogonium by means of a narrow outgrowth, the
+  fertilizing tube, and a male nucleus then passes over into the single
+  oosphere, which at first multinucleate becomes uninucleate before
+  fertilization. _Pythium_ is of interest as illustrating the dependence
+  of zoospore-formation on conditions and the indeterminate nature of
+  conidia. The other genera are more purely parasitic; the mycelium
+  usually sends haustoria into the cells of the host and puts out
+  branched, aerial conidiophores through the stomata, the branches of
+  which abstrict numerous "conidia"; these either germinate directly or
+  their contents break up into zoospores (fig. 5). The development of
+  the "conidia" as true conidial spores or as zoosporangia may occur in
+  one and the same species (_Cystopus candidus_, _Phytophthora
+  infestans_) as in _Pythium_ described above; in other cases the direct
+  conidial germination is characteristic of genera--e.g. _Peronospora_;
+  while others emit zoospores--e.g. _Plasmopara_, &c. In _Cystopus_
+  (_Albugo_) the "conidia" are abstricted in basipetal chain-like series
+  from the ends of hyphae which come to the surface in tufts and break
+  through the epidermis as white pustules. Each "conidium" contains
+  numerous nuclei and is really a zoosporangium, as after dispersal it
+  breaks up into a number of zoospores. The Peronosporaceae reproduce
+  themselves sexually by means of antheridia and oogonia as described in
+  _Pythium_. In _Cystopus Bliti_ the oosphere contains numerous nuclei,
+  and all the male nuclei from the antheridium pass into it, the male
+  and female nuclei then fusing in pairs. We thus have a process of
+  "multiple fertilization"; the oosphere really represents a large
+  number of undifferentiated gametes and has been termed a coenogamete.
+  Between _Cystopus Bliti_ on the one hand and _Pythium de Baryanum_ on
+  the other a number of cytologically intermediate forms are known. The
+  oospore on germination usually gives origin to a zoosporangium, but
+  may form directly a germ tube which infects the host.
+
+  [Illustration: From Strasburger's _Lehrbuch der Botanik_, by
+  permission of Gustav Fischer.
+
+  FIG. 4.--Fertilization of the Peronosporeae. After Wager.
+
+    1, _Peronospora parasitica_. Young multinucleate oogonium (og) and
+    antheridium (an).
+
+    2, _Albugo candida_. Oogonium with the central uninucleate oosphere
+    and the fertilizing tube (a) of the antheridium which introduces the
+    male nucleus.
+
+    3, The same. Fertilized egg-cell (o) surrounded by the periplasm
+    (p).]
+
+  [Illustration: FIG. 5.--_Phytophthora infestans_. Fungus of Potato
+  Disease.
+
+    A, B, Section of Leaf of Potato with sporangiophores of
+    _Phytophthora infestans_ passing through the stomata D, on the under
+    surface of the leaf.
+
+    E, Sporangia.
+
+    F, G, H, J, Further development of the sporangia.
+
+    K, Germination of the zoospores formed in the sporangia.
+
+    L, M, N, Fertilization of the oogonium and development of the
+    oospore in _Peronospora_.]
+
+  _Saprolegniaceae_ are aquatic forms found growing usually on dead
+  insects lying in water but occasionally on living fish (e.g. the
+  salmon disease associated with _Saprolegnia ferax_). The chief genera
+  are _Saprolegnia, Achlya, Pythiopsis, Dictyuchus, Aplanes._ Motile
+  zoospores which escape from the zoosporangium are present except in
+  Aplanes. The sexual reproduction shows all transitions between forms
+  which are normally sexual, like the Peronosporaceae, to forms in which
+  no antheridium is developed and the oospheres develop
+  parthenogenetically. The oogonia, unlike the Peronosporaceae, contain
+  more than one oosphere. Klebs has shown that the development of
+  zoosporangia or of oogonia and pollinodia respectively in
+  _Saprolegnia_ is dependent on the external conditions; so long as a
+  continued stream of suitable food-material is ensured the mycelium
+  grows on without forming reproductive organs, but directly the
+  supplies of nitrogenous and carbonaceous food fall below a certain
+  degree of concentration sporangia are developed. Further reduction of
+  the supplies of food effects the formation of oogonia. This explains
+  the sequence of events in the case of a _Saprolegnia_-mycelium
+  radiating from a dead fly in water. Those parts nearest the fly and
+  best supplied develop barren hyphae only; in a zone at the periphery,
+  where the products of putrefaction dissolved in the water form a
+  dilute but easily accessible supply, the zoosporangia are developed in
+  abundance; oogonia, however, are only formed in the depths of this
+  radiating mycelium, where the supplies of available food materials are
+  least abundant.
+
+  _Chytridineae._--These parasitic and minute, chiefly aquatic, forms
+  may be looked upon as degenerate Oomycetes, since a sexual process and
+  feeble unicellular mycelium occur in some; or they may be regarded as
+  series of primitive forms leading up to higher members. There is no
+  means of deciding the question. They are usually included in
+  Oomycetes, but their simple structure, minute size, usually uniciliate
+  zoospores, and their negative characters would justify their retention
+  as a separate group. It contains less than 200 species, chiefly
+  parasitic on or in algae and other water-plants or animals, of various
+  kinds, or in other fungi, seedlings, pollen and higher plants. They
+  are often devoid of hyphae, or put forth fine protoplasmic filaments
+  into the cells of their hosts. After absorbing the cell-contents of
+  the latter, which it does in a few hours or days, the fungus puts out
+  a sporangium, the contents of which break up into numerous minute
+  swarm-spores, usually one-ciliate, rarely two-ciliate. Any one of
+  these soon comes to rest on a host-cell, and either pierces it and
+  empties its contents into its cavity, where the further development
+  occurs (_Olpidium_), or merely sends in delicate protoplasmic
+  filaments (_Rhizophydium_) or a short hyphal tube of, at most, two or
+  three cells, which acts as a haustorium, the further development
+  taking place outside the cell-wall of the host (_Chytridium_). In some
+  cases resting spores are formed inside the host (_Chytridium_), and
+  give rise to zoosporangia on germination. In a few species a sexual
+  process is described, consisting in the conjugation of similar cells
+  (_Zygochytrium_) or the union of two dissimilar ones (_Polyphagus_).
+  In the development of distinct antheridial and oogonial cells the
+  allied Ancylistineae show close alliances to _Pythium_ and the
+  Oomycetes. On the other hand, the uniciliate zoospores of _Polyphagus_
+  have slightly amoeboid movements, and in this and the
+  pseudopodium-like nature of the protoplasmic processes, such forms
+  suggest resemblances to the Myxomycetes. Opinions differ as to whether
+  the Chytridineae are degraded or primitive forms, and the group still
+  needs critical revision. Many new forms will doubtless be discovered,
+  as they are rarely collected on account of their minuteness. Some
+  forms cause damping off of seedlings--e.g. _Olpidium Brassicae_;
+  others discoloured spots and even tumour-like swellings--e.g.
+  _Synchytium Scabiosae_, _S. Succisae_, _Urophlyctis_, &c., on higher
+  plants. Analogies have been pointed out between Chytridiaceae and
+  unicellular algae, such as Chlorosphaeraceae, Protococcaceae,
+  "Palmellaceae," &c., some of which are parasitic, and suggestions may
+  be entertained as to possible origin from such algae.
+
+  The _Zygomycetes_, of which about 200 species are described, are
+  especially important from a theoretical standpoint, since they
+  furnished the series whence Brefeld derived the vast majority of the
+  fungi. They are characterized especially by the zygospores, but the
+  asexual organs (sporangia) exhibit interesting series of changes,
+  beginning with the typical sporangium of _Mucor_ containing numerous
+  endospores, passing to cases where, as in _Thamnidium_, these are
+  accompanied with more numerous small sporangia (sporangioles)
+  containing few spores, and thence to _Chaetocladium_ and
+  _Piptocephalis_, where the sporangioles form but one spore and fall
+  and germinate as a whole; that is to say, the monosporous sporangium
+  has become a conidium, and Brefeld regarded these and similar series
+  of changes as explaining the relation of ascus to conidium in higher
+  fungi. According to his view, the ascus is in effect the sporangium
+  with several spores, the conidium the sporangiole with but one spore,
+  and that not loose but fused with the sporangiole wall. On this basis,
+  with other interesting morphological comparisons, Brefeld erected his
+  hypothesis, now untenable, that the Ascomycetes and Basidiomycetes
+  diverge from the Zygomycetes, the former having particularly
+  specialized the ascus (sporangial) mode of reproduction, the latter
+  having specialized the conidial (indehiscent one-spored sporangiole)
+  mode. In addition to sporangia and the conidial spores referred to,
+  some Mucorini show a peculiar mode of vegetative reproduction by means
+  of gemmae or chlamydospores--i.e. short segments of the hyphae become
+  stored with fatty reserves and act as spores. The gemmae formed on
+  submerged Mucors may bud like a yeast, and even bring about alcoholic
+  fermentation in a saccharine solution.
+
+  [Illustration: From Strasburger's _Lehrbuch der Botanik_, by
+  permission of Gustav Fischer.
+
+  FIG. 6.--_Mucor Mucedo._ Different stages in the formation and
+  germination of the zygospore. (After Brefeld, 1-4. 5 from v. Tavel,
+  _Pilze_.)
+
+    1, Two conjugating branches in contact.
+
+    2, Septation of the conjugating cells (a) from the suspensors (b).
+
+    3, More advanced stage, the conjugating cells (a) are still distinct
+    from one another; the warty thickenings of their walls have
+    commenced to form.
+
+    4, Ripe zygospore (b) between the suspensors (a).
+
+    5, Germinating zygospore with a germ-tube bearing a sporangium.]
+
+  The segments of the hyphae in this group usually contain several
+  nuclei. At the time of sporangial formation the protoplasm with
+  numerous nuclei streams into the swollen end of the sporangiophore and
+  there becomes cut off by a cell-wall to form the sporangium. The
+  protoplasm then becomes cut up by a series of clefts into a number of
+  smaller and smaller pieces which are unicellular in _Pilobolus_,
+  multicellular in _Sporodinia_. These then become surrounded by a
+  cell-wall and form the spores. This mode of spore-formation is totally
+  different from that in the ascus; hence one of the difficulties of the
+  acceptance of Brefeld's view of the homology of ascus and sporangium.
+  The cytology of zygospore-formation is not known in detail; the
+  so-called gametes which fuse are multinucleate and are no doubt of the
+  nature of gametangia. The fate of these nuclei is doubtful, probably
+  they fuse in pairs (fig. 6).
+
+  Blakeslee has lately made some very important observations of the
+  Zygomycetes. It is well known that while in some forms, e.g.
+  _Spordinia_, zygospores are easily obtained, in others, e.g. most
+  species of _Mucor_, they are very erratic in their appearance. This
+  has now been explained by Blakeslee, who finds that the Mucorinae can
+  be divided into two groups, termed homothallic and heterothallic
+  respectively. In the first group zygospores can arise by the union of
+  branches from the _same_ mycelium and so can be produced by the growth
+  from a single spore; this group includes _Spordinia grandis_,
+  _Spinellus fusiger_, some species of _Mucor_, &c. The majority of
+  forms, however, fall into the heterothallic group, in which the
+  association of branches from two mycelia _different in nature_ is
+  necessary for the formation of zygospores. These structures cannot
+  then be produced from the product of a single spore nor even from the
+  thalli derived from _any_ two spores. The two kinds of thalli
+  Blakeslee considers to have a differentiation of the nature of sex and
+  he distinguishes them as ( + ) and (-) forms; the former being usually
+  distinguished by a somewhat greater luxuriance of growth.
+
+  The classification of the Mucorini depends on the prevalence and
+  characters of the conidia, and of the sporangia and zygospores--e.g.
+  the presence or absence of a columella in the former, the formation of
+  an investment round the latter. Most genera are saprophytes, but
+  some--_Chaetocladium_, _Piptocephalis_--are parasites on other
+  Mucorini, and one or two are associated casually with the rotting of
+  tomatoes and other fruits, bulbs, &c., the fleshy parts of which are
+  rapidly destroyed if once the hyphae gain entrance. Even more
+  important is the question of mycosis in man and other animals,
+  referred to species of _Mucor_, and investigated by Lucet and
+  Costantin. Klebs has concluded that transpiration is the important
+  factor in determining the formation of sporangia, while
+  zygote-development depends on totally different conditions; these
+  results have been called in question by Falck.
+
+  The _Entomophthoraceae_ contain three genera, _Empusa_,
+  _Entomophthora_ and _Basidiobolus_. The two first genera consist of
+  forms which are parasitic on insects. _Empusa Muscae_ causes the
+  well-known epidemic in house-flies during the autumn; the dead,
+  affected flies are often found attached to the window surrounded by a
+  white halo of conidia. _B. ranarum_ is found in the alimentary canal
+  of the frog and growing on its excrement. In these three genera the
+  conidia are cast off with a jerk somewhat in the same way as the
+  sporangium of _Pilobolus_.
+
+B. HIGHER FUNGI.--Now that Brefeld's view of the origin of these forms
+from the Zygomycetes has been overthrown, the relationship of the higher
+and lower forms of fungi is left in obscurity. The term _Eumycetes_ is
+sometimes applied to this group to distinguish them from the
+Phycomycetes, but as the same name is also applied to the fungi as a
+whole to differentiate them from the Mycetozoa and Bacteria, the term
+had best be dropped. The Higher Fungi fall into three groups: the
+_Ustilaginales_, of doubtful position, and the two very sharply marked
+groups _Basidiales_ and _Ascomycetes_.
+
+[Illustration: From Vine's _Students' Text Book of Botany_, by
+permission of Swan Sonnenschein & Co.
+
+FIG. 7.--Germinating resting-gonidia. A, of _Ustilago receptaculorum_;
+B, of _Tilletia Caries_.
+
+  sp, The gonidium.
+
+  pm, The promycelium.
+
+  d,  The sporidia: in B the sporidia have coalesced in pairs at v.]
+
+  I. _Ustilaginales._--This includes two families Ustilaginaceae (smuts)
+  and Tilletiaceae (bunts). The bunts and smuts which damage our grain
+  and fodder plants comprise about 400 species of internal parasites,
+  found in all countries on herbaceous plants, and especially on
+  Monocotyledons. They are remarkable for their dark spores developed in
+  gall-like excrescences on the leaves, stems, &c., or in the fruits of
+  the host. The discovery of the yeast-conidia of these fungi, and their
+  thorough investigation by Brefeld, have thrown new lights on the
+  group, as also have the results elucidating the nature of the ordinary
+  dark spores--smuts, bunt, &c.--which by their mode of origin and
+  development are chlamydospores. When the latter germinate a slender
+  "promycelium" is put out; in _Ustilago_ and its allies this is
+  transversely septate, and bears lateral conidia (sporidia); in
+  _Tilletia_ and its allies non-septate, and bears a terminal tuft of
+  conidia (sporidia) (fig. 7). Brefeld regarded the promycelium as a
+  kind of _basidium_, bearing lateral or terminal conidia (comparable to
+  _basidiospores_), but since the number of basidiospores is not fixed,
+  and the basidium has not yet assumed very definite morphological
+  characters, Brefeld termed the group _Hemibasidii_, and regarded them
+  as a half-way stage in the evolution of the true Basidiomycetes from
+  Phycomycetes, the _Tilletia_ type leading to the true basidium
+  (Autobasidium), the _Ustilago_ type to the protobasidium, with lateral
+  spores; but this view is based on very poor evidence, so that it is
+  best to place these forms as a separate group, the _Ustilaginales_.
+  The yeast-conidia, which bud off from the conidia or their resulting
+  mycelium when sown in nutrient solutions, are developed in successive
+  crops by budding exactly as in the yeast plant, but they cannot
+  ferment sugar solutions. It is the rapid spread of these yeast-conidia
+  in manure and soil waters which makes it so difficult to get rid of
+  smuts, &c., in the fields, and they, like the ordinary conidia,
+  readily infect the seedling wheat, oats, barley or other cereals.
+  Infection in these cases occurs in the seedling at the place where
+  root and shoot meet, and the infecting hypha having entered the plant
+  goes on living in it and growing up with it as if it had no parasitic
+  action at all. When the flowers form, however, the mycelium sends
+  hyphae into the young ovaries and rapidly replaces the stores of sugar
+  and starch, &c., which would have gone to make the grain, by the
+  soot-like mass of spores so well known as smut, &c. These spores
+  adhere to the grain, and unless destroyed, by "steeping" or other
+  treatment, are sown with it, and again produce sporidia and
+  yeast-conidia which infect the seedlings. In other species the
+  infection occurs through the style of the flower, but the fungus after
+  reaching the ovule develops no further during that year but remains
+  dormant in the embryo of the seed. On germination, however, the fungus
+  behaves in the same way as one which has entered in the seedling
+  stage. The cytology of these forms is very little known; Dangeard
+  states that there is a fusion of two nuclei in the chlamydospore, but
+  this requires confirmation. Apart from this observation there is no
+  other trace of sexuality in the group.
+
+  II. _Ascomycetes._--This, except in the case of a few of the simpler
+  forms, is a very sharply marked group characterized by a special type
+  of sporangium, the ascus. In the development of the ascus we find two
+  nuclei at the base which fuse together to form the single nucleus of
+  the young _ascus_. The single nucleus divides by three successive
+  divisions to form eight nuclei lying free in the protoplasm of the
+  ascus. Then by a special method, described first by Harper, a mass of
+  protoplasm is cut out round each nucleus; thus eight uninucleate
+  ascospores are formed by free-cell formation. The protoplasm remaining
+  over is termed _epiplasm_ and often contains glycogen (fig. 8). In
+  some cases nuclear division is carried further before spore-formation
+  occurs, and the number of spores is then 16, 32 and 64, &c.; in a few
+  cases the number of spores is less than eight by abortion of some of
+  the eight nuclei. The ascus is thus one of the most sharply
+  characterized structures among the fungi.
+
+  In some forms we find definite male and female sexual organs
+  (_Sphaerotheca_, _Pyronema_, &c.), in others the antheridium is
+  abortive or absent, but the ascogonium (oogonium) is still present and
+  the female nuclei fuse in pairs (_Lachnea stercorea_, _Humaria
+  granulata_, _Ascobolus furfuraceus_); while in other forms ascogonium
+  and antheridium are both absent and fusion occurs between vegetative
+  nuclei (_Humaria rutilans_, and probably the majority of other forms).
+  In other cases the sexual fusion is apparently absent altogether, as
+  in _Exoascus_. In the first case (fig. 9) we have a true sexual
+  process, while in the second and third cases we have a _reduced_
+  sexual process in which the fusion of other nuclei has replaced the
+  fusion of the normal male and female nuclei. It is to be noted that
+  all the forms exhibit the fusion of nuclei in the ascus, so that those
+  with the normal or reduced sexual process described above have two
+  nuclear fusions in their life-history. The advantage or significance
+  of the second (ascus) fusion is not clearly understood.
+
+  [Illustration: From Strasburger's _Lehrbuch der Botanik_, by
+  permission of Gustav Fischer.
+
+  FIG. 8.--Development of the Ascus.
+
+    A-C, _Pyronema confluens_. (After Harper.)
+
+    D, Young ascus of _Boudiera_ with eight spores. (After Claussen.)]
+
+  The group of the Hemiasci was founded by Brefeld to include forms
+  which were supposed to be a connecting link between Phycomycetes and
+  Ascomycetes. As mentioned before, the connexion between these two
+  groups is very doubtful, and the derivation of the ascus from an
+  ordinary sporangium of the Zygomycetes cannot be accepted. The
+  majority of the forms which were formerly included in this group have
+  been shown to be either true Phycomycetes (like _Ascoidea_) or true
+  Ascomycetes (like _Thelebolus_). _Eremascus_ and _Dipodascus_, which
+  are often placed among the Hemiasci, possibly do not belong to the
+  Ascomycetes series at all.
+
+  [Illustration: From Strasburger's _Lehrbuch der Botanik_, by
+  permission of Gustav Fischer.
+
+  Fig. 9.--_Sphaerotheca Castagnei_. Fertilization and Development of
+  the Perithecium. (After Harper.)
+
+    1, Oogonium (og) with the antheridial branch (az) applied to its
+    surface
+
+    2, Separation of antheridium (an).
+
+    3, Passage of the antheridial nucleus towards that of the oogonium.
+
+    4, Union of the nuclei.
+
+    5, Fertilized oogonium surrounded by two layers of hyphae derived
+    from the stalk-cell (st).
+
+    6, The multicellular ascogonium derived by division from the
+    oogonium; the terminal cell with the two nuclei (as) gives rise to
+    the ascus.]
+
+  _Exoascaceae_ are a small group of doubtful extent here used to
+  include _Exoascus_, _Taphrina_, _Ascorticium_ and _Endomyces_. The
+  mycelium is very much reduced in extent. The asci are borne directly
+  on the mycelium and are therefore fully exposed, being devoid from the
+  beginning of any investment. The _Taphrineae_, which include
+  _Exoascus_ and _Taphrina_, are important parasites--e.g. pocket-plums
+  and witches' brooms on birches, &c., are due to their action (fig.
+  10). _Exoascus_ and _Ascorticium_ present interesting parallels to
+  _Exobasidium_ and _Corticium_ among the Basidiomycetes.
+
+  _Saccharomycetaceae_ include the well-known yeasts which belong mainly
+  to the genus _Saccharomyces_. They are characterized by their
+  unicellular nature, their power of rapid budding, their capacity for
+  fermenting various sugars, and their power of forming endogenous
+  spores. The sporangium with its endogenous spores has been compared
+  with an ascus, and on these grounds the group is placed among the
+  Ascomycetes--a very doubtful association. The group has attained an
+  importance of late even beyond that to which it was brought by
+  Pasteur's researches on alcoholic fermentation, chiefly owing to the
+  exact results of the investigations of Hansen, who first applied the
+  methods of pure cultures to the study of these organisms, and showed
+  that many of the inconsistencies hitherto existing in the literature
+  were due to the coexistence in the cultures of several species or
+  races of yeasts morphologically almost indistinguishable, but
+  physiologically very different. About fifty species of _Saccharomyces_
+  are described more or less completely, but since many of these cannot
+  be distinguished by the microscope, and some have been found to
+  develop physiological races or varieties under special conditions of
+  growth, the limits are still far too ill-defined for complete
+  botanical treatment of the genus. A typical yeast is able to develop
+  new cells by budding when submerged in a saccharine solution, and to
+  ferment the sugar--i.e. so to break up its molecules that, apart from
+  small quantities used for its own substance, masses of it out of all
+  proportion to the mass of yeast used become resolved into other
+  bodies, such as carbon dioxide and alcohol, the process requiring
+  little or no oxygen. Brefeld regards the budding process as the
+  formation of conidia. Under other conditions, of which the temperature
+  is an important one, the nucleus in the yeast-cell divides, and each
+  daughter-nucleus again, and four spores are formed in the mother cell,
+  a process obviously comparable to the typical development of
+  ascospores in an ascus. Under yet other conditions the quiescent
+  yeast-cells floating on the surface of the fermented liquor grow out
+  into elongated sausage-shaped or cylindrical cells and branching
+  cell-series, which mat together into mycelium-like veils. At the
+  bottom of the fermented liquor the cells often obtain fatty contents
+  and thick walls, and behave as resting cells (chlamydospores). The
+  characters employed by experts for determining a species of yeast are
+  the sum of its peculiarities as regards form and size: the shapes,
+  colours, consistency, &c., of the colonies grown on certain definite
+  media; the optimum temperature for spore-formation, and for the
+  development of the "veils"; and the behaviour as regards the various
+  sugars.
+
+  [Illustration: From Strasburger's _Lehrbuch der Botanik_, by
+  permission of Gustav Fischer.
+
+  FIG. 10.--_Taphrina Pruni._ Transverse section through the epidermis
+  of an infected plum. Four ripe asci, a1, a2, with eight spores, a3,
+  a4, with yeast-like conidia abstricted from the spores. After
+  Sadebeck.
+
+    st, Stalk-cells of the asci.
+
+    m, Filaments of the mycelium cut transversely.
+
+    cut, Cuticle.
+
+    sp, Epidermis.]
+
+  The following summary of some of the principal characteristics of
+  half-a-dozen species will serve to show how such peculiarities can be
+  utilized for systematic purposes:
+
+    +---------------------+------------------+----------------------------------+----------------------------------------+
+    |                     |     Optimum      |          Characters of           |                                        |
+    |      Species.       | Temperature for  +----------+-----------+-----------+         Sugars Fermented and           |
+    |                     +---------+--------+ Fermenta-|   Cells.  |  Spores.  |              Products, &c.             |
+    |                     | Spores. | Veils. |   tion   |           |           |                                        |
+    +---------------------+---------+--------+----------+-----------+-----------+----------------------------------------+
+    |_S. cereviseae I_.   |   30°   | 20°-28°|   High   | Rounded   | Globoid   | / Inverts maltose and saccharose and   |
+    |_S. Pastorianus I_   | 27°-5°  | 26°-28°|   Low    | Rounded   | Globoid   |<    form alcohol 4-6 vol. %.           |
+    |_S. ellipsoideus_    |   25°   | 33°-34°|   Low    | Rounded   | Globoid   | \                                      |
+    |                     |         |        |          |           |           |                                        |
+    |_S. anomalus_        | 28°-31° |   ?    |   High   | Elliptical| Hat-shaped| Ditto, and evolves a fragrant ether.   |
+    |                     |         |        |          |                       |                                        |
+    |_S. Ludwigii_        | 30°-31° |   ?    |    ?     | Elongated | Globoid   | Will not invert maltose.               |
+    |                     |         |        |          |                       |                                        |
+    |_S. membranaefaciens_|   30°   |   ?    |   High   | Elongated | Globoid   | Inverts neither maltose nor saccharose.|
+    +---------------------+---------+--------+----------+-----------+-----------+----------------------------------------+
+
+  Two questions of great theoretical importance have been raised over
+  and over again in connexion with yeasts, namely, (1) the morphological
+  one as to whether yeasts are merely degraded forms of higher fungi, as
+  would seem implied by their tendency to form elongated, hypha-like
+  cells in the veils, and their development of "ascospores" as well as
+  by the wide occurrence of yeast-like "sprouting forms" in other fungi
+  (e.g. _Mucor_, Exoasci, Ustilagineae, higher Ascomycetes and
+  Basidiomycetes); and (2) the question as to the physiological nature
+  and meaning of fermentation. With regard to the first question no
+  satisfactory proof has as yet been given that Saccharomycetes are
+  derivable by culture from any higher form, the recent statements to
+  that effect not having been confirmed. At the same time there are
+  strong grounds for insisting on the resemblances between _Endomyces_,
+  a hyphal fungus bearing yeast-like asci, and such a form as
+  _Saccharomyces anomalus_. Concerning the second question, the recent
+  investigations of Buchner and others have shown that a ferment
+  (zymase) can be extracted from yeast-cells which causes sugar to break
+  up into carbon dioxide and alcohol. It has since been shown by Buchner
+  and Albert that yeast-cells which have been killed by alcohol and
+  ether, or with acetone, still retain the enzyme. Such material is far
+  more active than the zymase obtained originally by Buchner from the
+  expressed juice of yeast-cells. Thus alcoholic fermentation is brought
+  into line with the other fermentations.
+
+  _Schizosaccharomyces_ includes a few species in which the cells do not
+  "bud" but become elongated and then divide transversely. In the
+  formation of sporangia two cells fuse together by means of outgrowths,
+  in a manner very similar to that of _Spirogyra_; sometimes, however,
+  the wall between two cells merely breaks down. The fused cell becomes
+  a sporangium, and in it eight spores are developed. In certain cases
+  single cells develop parthenogenetically, without fusion, each cell
+  producing, however, only four spores. In _Zygosaccharomyces_ described
+  by Barker (1901) we have a form of the usual sprouting type, but here
+  again there is a fusion of two cells to form a sporangium.
+
+  _Cytology._--The study of the nucleus of yeast-cells is rendered
+  difficult by the presence of other deeply staining granules termed by
+  Guillermond _metachromatic granules_. These have often been mistaken
+  for nuclei and have to be carefully distinguished by differential
+  stains. In the process of budding the nucleus divides apparently by a
+  process of direct division. In the formation of spores the nucleus of
+  the cell divides, the protoplasm collects round the nuclei to form the
+  spores by free-cell formation; the protoplasm (epiplasm) not used in
+  this process becomes disorganized. A fusion of nuclei was originally
+  described by Jansens and Leblanc, but it was observed neither by Wager
+  nor Guillermond and is probably absent. In _Schizosaccharomyces_ and
+  _Zygosaccharomyces_, however, we have a fusion of nuclei in connexion
+  with the conjugation of cells which precedes sporangium-formation. The
+  theory may be put forward that the ordinary forms have been derived
+  from sexual forms like _Schizosaccharomyces_ and _Zygosaccharomyces_
+  by a loss of sexuality, the sporangium being formed
+  parthenogenetically without any nuclear fusion. This suggests a
+  possible relationship to _Eremascus_, which can only doubtfully be
+  placed in the Ascomycetes (_vide supra_).
+
+  _Carpoascomycetes._--The other divisions of the Ascomycetes may be
+  distinguished as Carpoascomycetes because they do not bear the asci
+  free on the mycelium but enclosed in definite fruit bodies or
+  ascocarps. The ascocarps can be distinguished into two portions, a
+  mass of sterile or vegetative hyphae forming the main mass of the
+  fruit body, and surrounding the fertile ascogenous hyphae which bear
+  at their ends the asci. When the ascogonium (female organ) is present
+  the ascogenous hyphae arise from it, with or without its previous
+  fusion with an antheridium. In other cases the ascogenous hyphae arise
+  directly from the vegetative hyphae. In connexion with this condition
+  of reduction a fusion of nuclei has been observed in _Humaria
+  rutilans_ and is probably of frequent occurrence. The asci may be
+  derived from the terminal cell of the branches of the ascogenous
+  hyphae, but usually they are derived from the penultimate cell, the
+  tip curving over to form the so-called crozier. By this means the
+  ascus cell is brought uppermost, and after the fusion of the two
+  nuclei it develops enormously and produces the ascospores. The
+  ascospores escape from the asci in various ways, sometimes by a
+  special ejaculation-mechanism. The Ascomycetes, at least the
+  Carpoascomycetes, exhibit a well-marked alternation of sexual and
+  asexual generations. The ordinary mycelium is the gametophyte since it
+  bears the ascogonia and antheridia when present; the ascogenous hyphae
+  with their asci represent the sporophyte since they are derived from
+  the fertilized ascogonium. The matter is complicated by the apogamous
+  transition from gametophyte to sporophyte in the absence of the
+  ascogonium; also by the fact that there are normally two fusions in
+  the life-history as mentioned earlier. If there are two fusions one
+  would expect two reductions, and Harper has suggested that the
+  division of the nuclei into eight in the ascus, instead of into four
+  spores as in most reduction processes, is associated with a _double_
+  reduction process in the ascus. Miss Fraser in _Humaria rutilans_
+  finds two reductions: a normal synaptic reduction in the first nuclear
+  division of the ascus, and a peculiar reduction division termed
+  _brachymeiosis_ in the third ascus division.
+
+  Various types of ascocarp are characteristic of the different
+  divisions of the Carpoascomycetes: the cleistothecium, apothecium and
+  perithecium.
+
+  _Perisporineae._--This includes two chief families, Erysiphaceae and
+  Perisporiaceae. They are characterized by an ascocarp without any
+  opening to the exterior, the ascospores being set free by the decay or
+  rupture of the ascocarp wall; such a fruit-body is termed a
+  _cleistothecium_ (cleistocarp). The Erysiphaceae are a sharply marked
+  group of forms which live as parasites. They form a superficial
+  mycelium on the surface of the plant, the hyphae not usually
+  penetrating the tissues but merely sending haustoria into the
+  epidermal cells. Only in rare cases is the mycelium intercellular.
+  Owing to their appearance they go by the popular name of mildews.
+  _Sphaerotheca Humuli_ is the well known hop-mildew, _Sphaerotheca
+  Mors-Uvae_ is the gooseberry mildew, the recent advent of which has
+  led to special legislation in Great Britain to prevent its spreading,
+  as when rampant it makes the culture of gooseberries impossible.
+  _Erysiphe_, _Uncinula_ and _Phyllactinia_ are other well-known genera.
+  The form of the fruit body, the difference and the nature of special
+  outgrowths upon it--the appendages--are characteristic of the various
+  genera. Besides peritheca the members of the Erysiphaceae possess
+  conidia borne in simple chains. De Bary brought forward very strong
+  evidence for the origin of the ascocarp in _Sphaerotheca_ and
+  _Erysiphe_ by a sexual process, but Harper in 1895 was the first to
+  prove conclusively, by the observation of the nuclear fusion, that
+  there was a definite fertilization in _Sphaerotheca Humuli_ by the
+  fusion of a male (antheridial) nucleus with a female, ascogonial
+  (oogonial) nucleus. Since then Harper has shown that the same process
+  occurs in _Erysiphe_ and _Phyllactinia_.
+
+  [Illustration: FIG. 11.--Development of _Eurotium repens_. (After De
+  Bary.)
+
+    A, Small portion of mycelium with conidiophore (c), and archicarp
+    (as).
+
+    B, The spiral archicarp (as), with the antheridium (p).
+
+    D, The same, beginning to be surrounded by the hyphae forming the
+    perithecium wall.
+
+    D, The perithecium.
+
+    E, F, Sections of young perithecia.
+
+    w, Parietal cells.
+
+    f, Pseudo-parenchyma.
+
+    as, Ascogonium.
+
+    G, An ascus.
+
+    H, An ascospore.]
+
+  The Perisporiaceae are saprophytic forms, the two chief genera being
+  _Aspergillus_ and _Penicillium_. The blue-green mould _P. crustaceum_
+  and the green mould _A. herbariorium_ ( = _Eurotium herbariorum_) are
+  extraordinarily widely distributed, moulds being found on almost any
+  food-material which is exposed to the air. They have characteristic
+  conidiophores bearing numerous conidia, and also cleistothecia which
+  are spherical in form and yellowish in colour. The latter arise from
+  the crown of a spirally coiled archicarp (bearing an ascogonium at its
+  end) and a straight antheridium. Vegetative hyphae then grow up and
+  surround these and enclose them in a continuous sheath of plectenchyma
+  (fig. 11). It has lately been shown by Fraser and Chambers that in
+  _Eurotium_ both ascogonium and antheridium contain a number of nuclei
+  (i.e. are coenogametes), but that the antheridium disorganizes without
+  passing its contents into the ascogonium. There is apparently a
+  reduced sexual process by the fusion of the ascogonial (female) nuclei
+  in pairs. _Aspergillus Oryzae_ plays an important part in
+  saccharifying the starch of rice, maize, &c., by means of the abundant
+  diastase it secretes, and, in symbiosis with a yeast which ferments
+  the sugar formed, has long been used by the Japanese for the
+  preparation of the alcoholic liquor saké. The process has now been
+  successfully introduced into European commerce.
+
+  [Illustration: From Strasburger's _Lehrbuch der Botanik_, by
+  permission of Gustav Fischer.
+
+  FIG. 12.--_Peziza aurantiaca._ (After Krombholz, nat. size.)]
+
+  [Illustration: FIG. 13.--_Ascobolus furfuraceus._ Diagrammatic section
+  of the fructification. (After Janczewski.)
+
+    m, Mycelium.
+
+    c, Archicarp.
+
+    l, Pollinodium.
+
+    s, Ascogenous filaments.
+
+    a, Asri.
+
+    r, p, The sterile tissue from which the paraphyses h spring.]
+
+  _Discomycetes._--Used in its widest sense this includes the
+  Hysteriaceae, Phacidiaceae, Helvellaceae, &c. The group is
+  characterized in general by the possession of an ascocarp which,
+  though usually a completely closed structure during the earlier stages
+  of development, at maturity opens out to form a bowl or saucer-shaped
+  organ, thus completely exposing the layer of asci which forms the
+  hymenium. Such an ascocarp goes by the name of _apothecium_. Owing to
+  the shape of the fruit-body many of these forms are known as
+  cup-fungi, the cup or apothecium often attaining a large size,
+  sometimes several inches across (fig. 12). Functional male and female
+  organs have been shown to exist in _Pyronema_ and _Boudiera_; in
+  _Lachnea stercorea_ both ascogonia and antheridia are present, but the
+  antheridium is non-functional, the ascogonial (female) nuclei fusing
+  in pairs; this is also the case in _Humaria granulata_ and _Ascobolus
+  furfuraceus_, where the antheridium is entirely absent. In _H.
+  rutilans_, however, both sexual organs are absent and the ascogenous
+  hyphae arise apogamously from the ordinary hyphae of the mycelim. In
+  all these cases the ascogonium and antheridium contain numerous
+  nuclei; they are to be looked upon as gametangia in which there is no
+  differentiation of gametes, and since they act as single gametes they
+  are termed coenogametes. In some forms as in _Ascobolus_ the
+  ascogonium is multicellular, the various cells communicating by pores
+  in the transverse walls (fig. 13).
+
+  In the Helvellaceae there is no apothecium but a large irregular fruit
+  body which at maturity bears the asci on its surface. The development
+  is only slightly known, but there is some evidence for believing that
+  the fruit-body is closed in its very early stages.
+
+  [Illustration: From Strasburger's _Lehrbuch der Botanik_, by
+  permission of Gustav Fischer.
+
+  FIG. 14.--Perithecium of Podospora fimiseda in longitudinal section
+  After v. Tavel.
+
+    s, Asci.
+
+    a, Paraphyses.
+
+    e, Periphyses.
+
+    m, Mycelial hyphae.]
+
+  The genus _Peziza_ (in its widest sense) may be taken as the type of
+  the group. Most of them grow on living plants or on dead vegetable
+  remains, very often on fallen wood; a number, however, are found
+  growing on earth which is rich in humus. The genus _Sclerotinia_ may
+  be mentioned here; a number of forms have been investigated by
+  Woronin. The conidia are fragrant and are carried by bees to the
+  stigma of the bilberry; here they germinate with the pollen and the
+  hyphae pass with the pollen tubes down the style; the former infect
+  the ovules and produce sclerotia, therein reducing the fruits to a
+  mummified condition. From the sclerotia later the apothecium develops.
+  One species, _S. heteroica_, is _heteroecious_; the ascospores
+  infecting the leaves of _Vaccinium uliginosum_, while the conidia
+  which then arise infect only _Ledum palustre_. This is the only case
+  of heteroecism known in the vegetable kingdom outside the Uredineae.
+
+  _Pyrenomycetes._--This is an extraordinarily large and varied group of
+  forms which mostly live parasitically or saprophytically on vegetable
+  tissue, but a few are parasitic on insect-larvae. The group is
+  characterized by a special type of ascocarp, the _perithecium_. This
+  is typically of a flask-shaped form opening with a small pore at the
+  top. The asci live at the bottom often mixed with paraphyses, while
+  the upper "neck" of the flask is lined with special hyphae, the
+  periphyses, which aid in the ejection of the spores (fig. 14). The
+  simpler forms bear the perithecia directly on the mycelium, but the
+  more highly developed forms often bear them on a special mycelial
+  development--the stroma, which is often of large size and special
+  shape and colour, and of dense consistence. The cytological details of
+  development of the perithecia are not well known; most of them appear
+  to develop their ascogenous hyphae in an apogamous way without any
+  connexion with an ascogonium. Besides the special ascocarps, accessory
+  reproductive organs are known in the majority of cases in the form of
+  conidia.
+
+  _Tuberineae._--These are a small group of fungi including the
+  well-known truffles. They are found living saprophytically (in part
+  parasitically) underground in forests. The asci are developed in the
+  large dense fruit bodies (cleistothecia) and the spores escape by the
+  decay of the wall. The fruit-body is of complicated structure, but its
+  early stages of development are not known. Many of the fruit-bodies
+  have a pleasant flavour and are eaten under the name of truffles
+  (_Tuber brumale_ and other species). The exact life-history of the
+  truffle is not known.
+
+  _Laboulbeniineae_ are a group of about 150 species of fungi found on
+  insects, especially beetles, and principally known from the researches
+  of Thaxter in America. The plant is a small, dark brown, erect
+  structure (receptacle) of a few cells, and 1-10 mm. high, attached to
+  the insect by the lowermost end (foot), and easily mistaken for a hair
+  or similar appendage of the insect. The receptacle ends above in
+  appendages, each consisting of one or a few cells, some of which are
+  the male organs, others the female organs, and others again may be
+  barren hairs. The male organ (antheridium) consists of a few cells,
+  the terminal one of which either abstricts from its end, or emits from
+  its interior the non-motile spermatia, reminding us of those of the
+  Florideae. The female organ is essentially a flask-shaped structure;
+  the neck of the flask growing out as the trichogyne, and the belly
+  composed of an axial carpogenic cell surrounded by investing cells,
+  and with one cell (trichophoric) between it and the trichogyne. These
+  three elements--trichogyne, trichophoric cell, and carpogenic
+  cell--are regarded as the procarp. The spermatia have been shown by
+  Thaxter to fuse with the trichogyne, after which the axial cell below
+  (carpogenic cell) undergoes divisions, and ultimately forms asci
+  containing ascospores, while cells investing this form a perithecium,
+  the whole structure reminding us essentially of the fructification of
+  a Pyrenomycete. Many modifications in details occur, and the plants
+  may be dioecious. No injury is done to the infested insects. It has
+  lately been shown that there is a fusion of nuclei in connexion with
+  ascus formation, so that there can be no doubt of the position of this
+  extraordinary group of plants among the Ascomycetes. The various cells
+  of these organisms are connected by large pits which are traversed by
+  thick protoplasmic threads connecting one cell with the next. In this
+  point and in their method of fertilization the Laboulbeniineae suggest
+  a possible relationship of Ascomycetes and the Red Algae.
+
+  [Illustration: From Strasburger's _Lehrbuch der Botanik_, by
+  permission of Gustav Fischer.
+
+  FIG. 15.--_Armillaria mellea._ (After Ruhland.)
+
+    A, Young basidium with the two primary nuclei.
+
+    B, After fusion of the two nuclei. _Hypholoma appendiculatum_.
+
+    C, A basidium before the four nuclei derived from the secondary
+    nucleus of the basidium have passed into the four basidiospores.
+
+    D, Passage of a nucleus through the sterigma into the basidiospore.]
+
+  _Basidiales._--This very large group of plants is characterized by the
+  possession of a special type of conidiophore--the basidium, which
+  gives its name to the group. The basidium is a unicellular or
+  multicellular structure from which four basidiospores arise as
+  outgrowths; it starts as a binucleate structure, but soon, like the
+  ascus, becomes uninucleate by the fusion of the two nuclei. Then two
+  successive nuclear divisions occur resulting in the formation of four
+  nuclei which later migrate respectively into the four basidiospores
+  (fig. 15). The Basidiales are further characterized by the complete
+  loss of normal sexuality, but at some time or other in the
+  life-history there takes place an association of two nuclei in a cell;
+  the two nuclei are derived from separate cells or possibly in some
+  cases are sister nuclei of the same cell. The two nuclei when once
+  associated are termed "conjugate" nuclei, and they always divide at
+  the same time, a half of each passing into each cell. This conjugate
+  condition is finally brought to a close by the nuclear fusion in the
+  basidium. Between the nuclear association and the nuclear fusion in
+  the basidium many thousands of cell generations may be intercalated.
+  This nuclear association of equivalent nuclei apparently represents a
+  reduced sexual process (like the fusion of female nuclei in _Humaria
+  granulata_ and of vegetative nuclei in _H. rutilans_, among the
+  Ascomycetes) in which, however, the actual fusion (normally, in a
+  sexual process, occurring immediately after association) is delayed
+  until the formation of the basidium. During the tetrad division in the
+  basidium nuclear reduction occurs. There is thus in all the Basidiales
+  an alternation of generations, obscured, however, by the apogamous
+  transition from the gametophyte to sporophyte. The sporophyte may be
+  considered to begin at the stage of nuclear association and end with
+  the nuclear reduction in the basidium.
+
+  [Illustration: FIG. 16.--_Puccinia graminis._
+
+    A, Mass of teleutospores (t) on a leaf of couch-grass.
+
+    e, Epidermis ruptured.
+
+    b, Sub-epidermal fibres. (After De Bary.)
+
+    B, Part of vertical section through leaf of Berberis vulgaris, with
+    a, aecidium fruits, p, peridium, and sp, spermogonia. (After Sachs.)
+
+    C, Mass of uredospores (ur), with one teleutospore (t).
+
+    sh, Sub-hymenial hyphae. (After De Bary.)]
+
+  _Uredineae._--This is a large group of about 2000 forms. They are all
+  intercellular parasites living mostly on the leaves of higher plants.
+  Owing to the presence of oily globules of an orange-yellow or
+  rusty-red colour in their hyphae and spores they are termed
+  Rust-Fungi. They are distinguished from the other fungi and the rest
+  of the Basidiales by the great variety of the spores and the great
+  elaboration of the life-history to be found in many cases. Five
+  different kinds of spores may be present--teleutospores, sporidia ( =
+  basidiospores), aecidiospores, spermatia and uredospores (fig. 16).
+  The teleutospore, with the sporidia which arise from it, is always
+  present, and the division into genera is based chiefly on its
+  characters. The teleutospore puts forth on germination a four-celled
+  structure, the promycelium or basidium, and this bears later four
+  sporidia or basidiospores, one on each cell. When the sporidia infect
+  a plant the mycelium so produced gives origin to aecidiospores and
+  spermatia; the aecidiospores on infection produce a mycelium which
+  bears uredospores and later teleutospores. This is the life-history of
+  the most complicated forms, of the so-called _eu_ forms. In the
+  _opsis_ forms the uredospores are absent, the mycelium from the
+  aecidiospores producing directly the teleutospores. In _brachy_ and
+  _hemi_ the aecidiospores are absent, the mycelium from the sporidia
+  giving origin directly to the uredospores; the former possess
+  spermatia, in the latter they are absent. In _lepto_ and _micro_ forms
+  both aecidiospores and uredospores are absent, the sporidia producing
+  a mycelium which gives rise directly to teleutospores; in the _lepto_
+  forms the teleutospores can germinate directly, in the _micro_ forms
+  only after a period of rest. We have thus a series showing a
+  progressive reduction in the complexity of the life-history, the
+  _lepto_ and _micro_ forms having a life-history like that of the
+  Basidiomycetes. The _eu_ and _opsis_ forms may exhibit the remarkable
+  phenomenon of heteroecism, i.e. the dependence of the fungus on two
+  distinct host-plants for the completion of the life-history.
+  Heteroecism is very common in this group and is now known in over one
+  hundred and fifty species. In all cases of heteroecism the sporidia
+  infect one host leading to the production of aecidiospores and
+  spermatia (if present), while the aecidiospores are only able to
+  infect another host on which the uredospores (if present) and the
+  teleutospores are developed. A few examples are appended:
+
+    +-----------------------------+------------------+------------------+
+    |           Species.          | Teleutospores on | Aecidiospores on |
+    +-----------------------------+------------------+------------------+
+    | _Coleosporium Senecionis_   | _Pinus_          |   _Senecio_      |
+    | _Melampsora Rostrupi_       | _Populus_        |   _Mecurialis_   |
+    | _Pucciniastrum Goeppertiana_| _Vaccinium_      |   _Abies_        |
+    | _Gymnosporangium Sabinae_   | _Juniperus_      |   _Pyrus_        |
+    | _Uromyces Pisi_             | _Pisum, &c._     |   _Euphorbia_    |
+    | _Puccinia graminis_         | _Triticum, &c._  |   _Berberis_     |
+    | _P. dispersa_               | _Secale, &c._    |   _Anchusa_      |
+    | _P. coronata_               | _Agrostis_       |   _Rhamnus_      |
+    | _P. Ari-Phalaridis_         | _Phalaris_       |   _Arum_         |
+    | _P. Caricis_                | _Carex_          |   _Urtica_       |
+    | _Cronartium Ribicola_       | _Ribes_          |   _Pinus_        |
+    | _Chrysomyxa Rhododendri_    | _Rhododendron_   |   _Picea_        |
+    +-----------------------------+------------------+------------------+
+
+  Some of the Uredineae also exhibit the peculiarity of the development
+  of biologic forms within a single morphological species, sometimes
+  termed specialization of parasitism; this will be dealt with later
+  under the section Physiology.
+
+  [Illustration: From Strasburger's _Lehrbuch der Botanik_, by
+  permission of Gustav Fischer.
+
+  FIG. 17.--_Phragmidium Violaceum._ (After Blackman.)
+
+    A, Portion of a young aecidium.
+
+    st, Sterile cell.
+
+    a, Fertile cells; at a2 the passage of a nucleus from the adjoining
+    cell is seen.
+
+    B, Formation of the first spore-mother-cell (sm), from the basal
+    cell (a) of one of the rows of spores.
+
+    C, A further stage in which from sm1 the first aecidiospore (a) and
+    the intercalary cell (z) have arisen.
+
+    sm2, The second spore-mother-cell.
+
+    D, Ripe aecidiospore.]
+
+  _Cytology of Uredineae._--The study of the nuclear behaviour of the
+  cells of the Uredineae has thrown great light on the question of
+  sexuality. This group like the rest of the Basidiales exhibits an
+  association of nuclei at some point in its life-history, but unlike
+  the case of the Basidiomycetes the point of association in the
+  Uredineae is very well defined in all those forms which possess
+  aecidiospores. We find thus that in the _eu_ and _opsis_ forms the
+  association of nuclei takes place at the base of the aecidium which
+  produces the aecidiospores. There we find an association of nuclei
+  either by the fusion of two similar cells as described by Christmann
+  or by the migration of the nucleus of a vegetative cell into a special
+  cell of the aecidium. After this association the nuclei continue in
+  the conjugate condition so that the aecidiospores, the
+  uredospore-bearing mycelium, the uredospores and the young
+  teleutospores all contain two paired nuclei in their cells (fig. 17).
+  Before the teleutospore reaches maturity the nuclei fuse, and the
+  uninucleate condition then continues again until aecidium formation.
+  In the _hemi_, _brachy_, _micro_ and _lepto_ forms, which possess no
+  aecidium, we find that the association takes place at various points
+  in the ordinary mycelium but always before the formation of the
+  uredospores in the _hemi_ and _brachy_ forms, and before the formation
+  of teleutospores in _micro_ and _lepto_ form. Whether the association
+  of nuclei in the ordinary mycelium takes place by the migration of a
+  nucleus from one cell to another or whether two daughter nuclei become
+  conjugate in one cell, is not yet clear. The most reasonable
+  interpretation of the spermatia is that they are abortive male cells.
+  They have never been found to cause infection, and they have not the
+  characters of conidia; the large size of their nuclei, the reduction
+  of their cytoplasm and the absence of reserve material and their thin
+  cell wall all point to their being male gametes. Although in the forms
+  without aecidia the two generations are not sharply marked off from
+  one another, we may look up the generation with single nuclei in the
+  cells as the gametophyte and that with conjugate nuclei as the
+  sporophyte. The subjoined diagram will indicate the relationship of
+  the forms.
+
+  _Basidiomycetes._--This group is characterized by its greatly reduced
+  life-history as compared with that of the _eu_ forms among the
+  Uredineae. All the forms have the same life-history as the _lepto_
+  forms of that group, so that there is no longer any trace of sexual
+  organs. There is also a further reduction in that the basidium is not
+  derived from a teleutospore but is borne directly on the mycelium.
+  Formerly, before the relationship of promycelium and basidium were
+  understood, the Uredineae were considered as quite independent of the
+  Basidiomycetes. Later, however, these Uredineae were placed as a mere
+  subdivision of the Basidiomycetes. Although the Uredineae clearly lead
+  on to the Basidiomycetes, yet owing to their retaining in many cases
+  definite traces of sexual organs they are clearly a more primitive
+  group. Their marked parasitic habit also separates them off, so that
+  they are best included with the Basidiomycetes in a larger cohort
+  which may be called Basidiales. Most of Basidiomycetes are
+  characterized by the large sporophore on which the basidia with its
+  basidiospores are borne.
+
+  [Illustration: From _Annals of Botany_, by permission of the Clarendon
+  Press.
+
+  FIG. 18.]
+
+  It must be clearly borne in mind that though the Basidiomycetes show
+  no traces of differentiated sexual organs yet, like the _micro_ and
+  _lepto_ forms of the Uredineae, they still show (in the association of
+  nuclei and later fusion of nuclei in the basidium), a reduced
+  fertilization which denotes their derivation, through the Uredineae,
+  from more typically sexual forms. No one has yet made out in any form
+  the exact way in which the association of nuclei takes place in the
+  group. The mycelium is always found to contain conjugate nuclei before
+  the formation of basidia, but the point at which the conjugate
+  condition arises seems very variable. Miss Nichols finds that it
+  occurs very soon after the germination of the spore in _Coprinus_, but
+  no fusion of cells or migration of nuclei was to be observed.
+
+  _Protobasidiomycetes._--This, by far the smaller division of
+  Basidiomycetes, includes those forms which have a septate basidium.
+  There are three families--Auriculariaceae, Pilacreaceae and
+  Tremellinaceae. The first named contains a small number of forms with
+  the basidium divided like the promycelium of the Uredineae. They are
+  characterized by their gelatinous consistence and large size of their
+  sporophore. _Hirneola_ (_Auricularia_) _Auricula-Judae_ is the
+  well-known Jew's Ear, so named from the resemblance of the sporophore
+  to a human ear.
+
+  [Illustration: FIG. 19.--_Amanita muscaria_.
+
+    A, The young plant.
+
+    B, The mature plant.
+
+    C, Longitudinal section of mature plant.
+
+    p, The _pileus_.
+
+    g, The gills.
+
+    a, The _annulus_, or remnant of _velum partiale_,
+
+    v, Remains of _volva_ or _velum universale_.
+
+    s, The stalk.]
+
+  The Pilacreaceae are a family found by Brefeld to contain the genus
+  _Pilacre_. _P. Petersii_ has a transversely divided basidium as in
+  _Auriculariaceae_, but the basidia are surrounded with a peridium-like
+  sheath. The _Tremellinaceae_ are characterized by the possession of
+  basidia which are divided by two _vertical_ walls at right angles to
+  one another. From each of the four segments in the case of _Tremella_
+  a long outgrowth arises which reaches to the surface of the hymenium
+  and bears the basidiospores. In _Dacryomyces_ only two outgrowths and
+  two spores are produced.
+
+  _Autobasidiomycetes._--In this by far the larger division of the
+  Basidiomycetes the basidia are undivided and the four basidiospores
+  are borne on short sterigmata nearly always at the apex of the
+  basidium. The group may be divided into two main divisions,
+  _Hymenomycetes_ and _Gasteromycetes_.
+
+  _Hymenomycetes_ are a very large group containing over 11,000 species,
+  most of which live in soil rich in humus or on fallen wood or stems, a
+  few only being parasites. In the simplest forms (e.g. _Exobasidium_)
+  the basidia are borne directly on the ordinary mycelium, but in the
+  majority of cases the basidia are found developed in layers (hymenium)
+  on special sporophores of characteristic form in the various groups.
+  In these sporophores (such as the well-known toadstools and mushrooms
+  where the ordinary vegetative mycelium is underground) we have
+  structures specially developed for bearing the basidiospores and
+  protecting them from rain, &c., and for the distribution of the
+  spores--see earlier part of article on distribution of spores (figs.
+  19 and 20). The underground mycelium in many cases spreads wider and
+  wider each year, often in a circular manner, and the sporophores
+  springing from it appear in the form of a ring--the so-called fairy
+  rings. _Armillaria melleus_ and _Polyporus annosus_ are examples of
+  parasitic forms which attack and destroy living trees, while _Merulius
+  lacrymans_ is the well-known "dry rot" fungus.
+
+  [Illustration: FIG. 20.--_Agaricus mucidus_. Portion of hymenium. s,
+  Sporidia; st, sterigmata; g, sterile cells; c, cystidium, with
+  operculum o.]
+
+  _Gasteromycetes_ are characterized by having closed sporophores or
+  fruit-bodies which only open after the spores are ripe and then often
+  merely by a small pore. The fruit-bodies are of very various shapes,
+  showing a differentiation into an outer _peridium_ and an inner
+  spore-bearing mass, the _gleba_. The gleba is usually differentiated
+  into a number of chambers which are lined directly by the hymenium
+  (basidial layer), or else the chambers contain an interwoven mass of
+  hyphae, the branches of which bear the basidia. By the breaking down
+  of the inner tissues the spores often come to lie as a loose powdery
+  mass in the interior of the hollow fruit-body, mixed sometimes with a
+  capillitium. The best-known genera are _Bovista, Lycoperdon_
+  (puff-ball) _Scleroderma, Geaster_ (earth-star, q.v.). In the
+  last-named genus the peridium is double and the outer layer becomes
+  ruptured and spreads out in the form of star-shaped pieces; the inner
+  layer, however, merely opens at the apex by a small pore.
+
+  The most complex members of the Gasteromycetes belong to the
+  _Phalloideae_, which is sometimes placed as a distinct division of the
+  Autobasidiomycetes. _Phallus impudicus_, the stink-horn, is
+  occasionally found growing in woods in Britain. The fruit-body before
+  it ruptures may reach the size of a hen's egg and is white in colour;
+  from this there grows out a hollow cylindrical structure which can be
+  distinguished at the distance of several yards by its disgusting
+  odour. It is highly poisonous.
+
+_Physiology._--The physiology of the fungi comes under the head of that
+of plants generally, and the works of Pfeffer, Sachs, Vines, Darwin and
+Klebs may be consulted for details. But we may refer generally here to
+certain phenomena peculiar to these plants, the life-actions of which
+are restricted and specialized by their peculiar dependence on organic
+supplies of carbon and nitrogen, so that most fungi resemble the
+colourless cells of higher plants in their nutrition. Like these they
+require water, small but indispensable quantities of salts of potassium,
+magnesium, sulphur and phosphorus, and supplies of carbonaceous and
+nitrogenous materials in different stages of complexity in the different
+cases. Like these, also, they respire oxygen, and are independent of
+light; and their various powers of growth, secretion, and general
+metabolism, irritability, and response to external factors show similar
+specific variations in both cases. It is quite a mistake to suppose
+that, apart from the chlorophyll function, the physiology of the
+fungus-cell is fundamentally different from that of ordinary
+plant-cells. Nevertheless, certain biological phenomena in fungi are
+especially pronounced, and of these the following require particular
+notice.
+
+  _Parasitism._--Some fungi, though able to live as saprophytes,
+  occasionally enter the body of living plants, and are thus termed
+  facultative parasites. The occasion may be a wound (e.g. _Nectria_,
+  _Dasyscypha_, &c.), or the enfeeblement of the tissues of the host, or
+  invigoration of the fungus, the mycelium of which then becomes strong
+  enough to overcome the host's resistance (_Botrytis_). Many fungi,
+  however, cannot complete their life-history apart from the host-plant.
+  Such _obligate_ parasites may be epiphytic (_Erysipheae_), the
+  mycelium remaining on the outside and at most merely sending haustoria
+  into the epidermal cells, or endophytic (_Uredineae_, _Ustilagineae_,
+  &c.), when the mycelium is entirely inside the organs of the host. An
+  epiphytic fungus is not necessarily a parasite, however, as many
+  saprophytes (moulds, &c.) germinate and develop a loose mycelium on
+  living leaves, but only enter and destroy the tissues after the leaf
+  has fallen; in some cases, however, these saprophytic epiphytes can do
+  harm by intercepting light and air from the leaf (_Fumago_, &c.), and
+  such cases make it difficult to draw the line between saprophytism and
+  parasitism. Endophytic parasites may be intracellular, when the fungus
+  or its mycelium plunges into the cells and destroys their contents
+  directly (_Olpidium_, _Lagenidium_, _Sclerotinia_, &c.), but they are
+  far more frequently intercellular, at any rate while young, the
+  mycelium growing in the lacunae between the cells (_Peronospora_,
+  _Uredineae_) into which it may send short (_Cystopus_), or long and
+  branched (_Peronospora Calotheca_) haustoria, or it extends in the
+  middle lamella (_Ustilago_), or even in the solid substance of the
+  cell-wall (_Botrytis_). No sharp lines can be drawn, however, since
+  many mycelia are intercellular at first and subsequently become
+  intracellular (_Ustilagineae_), and the various stages doubtless
+  depend on the degrees of resistance which the host tissues are able to
+  offer. Similar gradations are observed in the direct effect of the
+  parasite on the host, which may be local (_Hemileia_) when the
+  mycelium never extends far from the point of infection, or general
+  (_Phytophthora_) when it runs throughout the plant. Destructive
+  parasites rapidly ruin the whole plant-body (_Pythium_), whereas
+  restrained parasites only tax the host slightly, and ill effects may
+  not be visible for a long time, or only when the fungus is epidemic
+  (_Rhytisma_). A parasite may be restricted during a long
+  incubation-period, however, and rampant and destructive later
+  (_Ustilago_). The latter fact, as well as the extraordinary
+  fastidiousness, so to speak, of parasites in their choice of hosts or
+  of organs for attack, point to reactions on the part of the
+  host-plant, as well as capacities on that of the parasite, which may
+  be partly explained in the light of what we now know regarding enzymes
+  and chemotropism. Some parasites attack many hosts and almost any
+  tissue or organ (_Botrytis cinerea_), others are restricted to one
+  family (_Cystopus Candidus_) or genus (_Phytophthora infestans_) or
+  even species (_Pucciniastrum Padi_), and it is customary to speak of
+  root-parasites, leaf-parasites, &c., in expression of the fact that a
+  given parasite occurs only on such organs--e.g. _Dematophora necatrix_
+  on roots, _Calyptospora Goeppertiana_ on stems, _Ustilago Scabiosae_
+  in anthers, _Claviceps purpurea_ in ovaries, &c. Associated with these
+  relations are the specializations which parasites show in regard to
+  the age of the host. Many parasites can enter a seedling, but are
+  unable to attack the same host when older--e.g. _Pythium_,
+  _Phytophthora omnivora_.
+
+  _Chemotropism._--Taken in conjunction with Pfeffer's beautiful
+  discovery that certain chemicals exert a distinct attractive influence
+  on fungus hyphae (_chemotropism_), and the results of Miyoshi's
+  experimental application of it, the phenomena of enzyme-secretion
+  throw considerable light on the processes of infection and parasitism
+  of fungi. Pfeffer showed that certain substances in definite
+  concentrations cause the tips of hyphae to turn towards them; other
+  substances, though not innutritious, repel them, as also do nutritious
+  bodies if too highly concentrated. Marshall Ward showed that the
+  hyphae of _Botrytis_ pierce the cell-walls of a lily by secreting a
+  cytase and dissolving a hole through the membrane. Miyoshi then
+  demonstrated that if _Botrytis_ is sown in a lamella of gelatine, and
+  this lamella is superposed on another similar one to which a
+  chemotropic substance is added, the tips of the hyphae at once turn
+  from the former and enter the latter. If a thin cellulose membrane is
+  interposed between the lamellae, the hyphae nevertheless turn
+  chemotropically from the one lamella to the other and pierce the
+  cellulose membrane in the process. The hyphae will also dissolve their
+  way through a lamella of collodion, paraffin, parchment paper,
+  elder-pith, or even cork or the wing of a fly, to do which it must
+  excrete very different enzymes. If the membrane is of some impermeable
+  substance, like gold leaf, the hyphae cannot dissolve its way through,
+  but the tip finds the most minute pore and traverses the barrier by
+  means of it, as it does a stoma on a leaf We may hence conclude that a
+  parasitic hyphae pierces some plants or their stomata and refuses to
+  enter others, because in the former case there are chemotropically
+  attractive substances present which are absent from the latter, or are
+  there replaced by repellent poisonous or protective substances such as
+  enzymes or antitoxins.
+
+  _Specialization of Parasitism._--The careful investigations of recent
+  years have shown that in several groups of fungi we cannot be content
+  to distinguish as units morphologically different species, but we are
+  compelled to go deeper and analyse further the species. It has been
+  shown especially in the _Uredineae_ and _Erysiphaceae_ that many forms
+  which can hardly be distinguished morphologically, or which cannot be
+  differentiated at all by structural characters, are not really
+  homogeneous but consist of a number of forms which are sharply
+  distinguishable by their infecting power. Eriksson found, for example,
+  that the well-known species _Puccinia graminis_ could be split up into
+  a number of forms which though morphologically similar were
+  physiologically distinct. He found that the species really consisted
+  of six distinct races, each having a more or less narrow range of
+  grasses on which it can live. The six races he named _P. graminis
+  Secalis_, _Tritici_, _Avenae_, _Airae_, _Agrostis_, _Poae_. The first
+  named will grow on rye and barley but not on wheat or oat. The form
+  _Tritici_ is the least sharply marked and will grow on wheat, barley,
+  rye and oat but not on the other grasses. The form _Avenae_ will grow
+  on oat and many grasses but not on the other three cereals mentioned.
+  The last three forms grow only on the genera _Aira_, _Agrostis_ and
+  _Poa_ respectively. All these forms have of course their
+  aecidium-stage on the barberry. The terms biologic forms, biological
+  species, physiological species, physiological races, specialized forms
+  have all been applied to these; perhaps the term biologic forms is the
+  most satisfactory. A similar specialization has been observed by
+  Marshall Ward in the _Puccinia_ parasitic on species of _Bromus_, and
+  by Neger, Marchal and especially Salmon in the Erysiphaceae. In the
+  last-named family the single morphological species _Erysiphe graminis_
+  is found growing on the cereals, barley, oat, wheat, rye and a number
+  of wild grasses (such as _Poa_, _Bromus_, _Dactylis_). On each of
+  these host-plants the fungus has become specialized so that the form
+  on barley cannot infect the other three cereals or the wild grasses
+  and so on. Just as the uredospores and aecidiospores both show these
+  specialized characters in the case of _Puccinia graminis_ so we find
+  that both the conidia and ascospores of _E. graminis_ show this
+  phenomenon. Salmon has further shown in investigating the relation of
+  _E. graminis_ to various species of the genus, _Bromus_, that certain
+  species may act as "bridging species," enabling the transfer of a
+  biologic form to a host-plant which it cannot normally infect. Thus
+  the biologic form on _B. racemosus_ cannot infect _B. commutatus_. If,
+  however, conidia from _B. racemosus_ are sown on _B. hordaceus_, the
+  conidia which develop on that plant are now able to infect _B.
+  commutatus_; thus _B. hordaceus_ acts as a bridging species. Salmon
+  also found that injury of a leaf by mechanical means, by heat, by
+  anaesthetics, &c., would affect the immunity of the plant and allow
+  infection by conidia which was not able to enter a normal leaf. The
+  effect of the abnormal conditions is probably to stop the production
+  of, or weaken or destroy the protective enzymes or antitoxins, the
+  presence of which normally confers immunity on the leaf.
+
+  _Symbiosis._--The remarkable case of life in common first observed in
+  lichens, where a fungus and an alga unite to form a compound
+  organism--the lichen--totally different from either, has now been
+  proved to be universal in these plants, and lichens are in all cases
+  merely algae enmeshed in the interwoven hyphae of fungi (see LICHENS).
+  This dualism, where the one constituent (alga) furnishes
+  carbohydrates, and the other (fungus) ensures a supply of mineral
+  matters, shade and moisture, has been termed _symbiosis_. Since then
+  numerous other cases of symbiosis have been demonstrated. Many trees
+  are found to have their smaller roots invaded by fungi and deformed by
+  their action, but so far from these being injurious, experiments go to
+  show that this mycorhiza (fungus-root) is necessary for the well-being
+  of the tree. This is also the case with numerous other plants of moors
+  and woodlands--e.g. Ericaceae, Pyrolaceae, Gentianaceae, Orchidaceae,
+  ferns, &c. Recent experiments have shown that the difficulties of
+  getting orchid seeds to germinate are due to the absence of the
+  necessary fungus, which must be in readiness to infect the young
+  seedling immediately after it emerges from the seed. The well-known
+  failures with rhododendrons, heaths, &c., in ordinary garden soils are
+  also explained by the need of the fungus-infected peat for their
+  roots. The rôle of the fungus appears to be to supply materials from
+  the leaf-mould around, in forms which ordinary root-hairs are
+  incapable of providing for the plant; in return the latter supports
+  the fungus at slight expense from its abundant stores of reserve
+  materials. Numerous other cases of symbiosis have been discovered
+  among the fungi of fermentation, of which those between _Aspergillus_
+  and yeast in saké manufacture, and between yeasts and bacteria in
+  kephir and in the ginger-beer plant are best worked out. For cases of
+  symbiosis see BACTERIOLOGY.
+
+  AUTHORITIES.--_General_: Engler and Prantl, _Die natürlichen
+  Pflanzenfamilien_, i. Teil (1892 onwards); Zopf, _Die Pilze_ (Breslau,
+  1890); De Bary, _Comparative Morphology of Fungi_, &c. (Oxford, 1887);
+  von Tafel, _Vergleichende Morphologie der Pilze_ (Jena, 1892);
+  Brefeld, _Unters. aus dem Gesamtgebiete der Mykologie_, Heft i. 13
+  (1872-1905); Lotsy, _Vorträge über botanische Stammesgeschichte_
+  (Jena, 1907). _Distribution_, &c.: Cooke, _Introduction to the Study
+  of Fungi_ (London, 1895); Felix in _Zeitschr. d. deutsch. geologisch.
+  Gesellsch._ (1894-1896); Staub, _Sitzungsber. d. bot. Sec. d. Kgl.
+  ungarischen naturwiss. Gesellsch. zu Budapest_ (1897). _Anatomy_, &c.:
+  Bommer, "Sclerotes et cordons mycéliens," _Mém. de l'Acad. Roy. de
+  Belg._ (1894); Mangin, "Observ. sur la membrane des mucorinées,"
+  _Journ. de Bot._ (1899); Zimmermann, _Die Morph. und Physiologie des
+  Pflanzenzellkernes_ (Jena, 1896); Wisselingh, "Microchem. Unters. über
+  die Zellwände d. Fungi," _Pringsh. Jahrb._ B. 31, p. 619 (1898);
+  Istvanffvi, "Unters. über die phys. Anat. der Pilze," _Prings. Jahrb._
+  (1896). _Spore Distribution_: Fulton, "Dispersal of the Spores of
+  Fungi by Insects," _Ann. Bot._ (1889); Falck, "Die Sporenverbreitung
+  bei den Basidiomyceten," _Beitr. zur Biol. d. Pflanzen_, ix. (1904).
+  _Spores and Sporophores_: Zopf, _Die Pilze_; also the works of von
+  Tafel and Brefeld. _Classification_: van Tieghem, _Journ. de bot._ p.
+  77 (1893), and the works of Brefeld, Engler and Prantl, von Tafel,
+  Saccardo and Lotsy already cited, _Oomycetes_: Wager, "On the
+  Fertilization of _Peronospora parasitica_," _Ann. Bot._ vol. xiv.
+  (1900); Stevens, "The Compound Oosphere of _Albugo Bliti_," _Bot.
+  Gaz._ vol. 28 (1899); "Gametogenesis and Fertilization in _Albugo_,"
+  ibid. vol. 32 (1901); Miyake, "The Fertilization of _Pythium de
+  Baryanum_," _Ann. of Bot._ vol. xv. (1901); Trow, "On Fertilization in
+  the Saprolegnieae," _Ann. of Bot._ vol. xviii. (1904); Thaxter, "New
+  and Peculiar Aquatic Fungi," _Bot. Gaz._ vol. 20 (1895); Lagerheim,
+  "Unters. über die Monoblepharideae," _Bih. Svenska Vet. Acad.
+  Handlingar_, 25. Afd. iii. (1900); Woronin, "Beitrag zur Kenntnis der
+  Monoblepharideen," _Mém. de l'Acad. Imp. d. Sc. de St-Pétersbourg_, 8
+  sér. vol. 16 (1902). _Zygomycetes_: Harper, "Cell-division in
+  Sporangia and Asci," _Ann. Bot._ vol. xiii. (1899); Klebs, _Die
+  Bedingungen der Fortpflanzung_, &c. (Jena, 1896), and "Zur Physiologie
+  der Fortpflanzung" _Prings. Jahr._ (1898 and 1899), "Über _Sporodinia
+  grandis_," _Bot. Zeit._ (1902); Falck, "Die Bedingungen der
+  Zygotenbildung bei Sporodinia grandis," Cohn's Beitr. z. Biol. d.
+  Pflanzen, Bd. 8 (1902); Gruber "Verhalten der Zellkerne in den
+  Zygosporen von _Sporodinia grandis_," _Ber. d. deutschen bot. Ges._
+  Bd. 19 (1901); Blakeslee, "Sexual Reproduction in the Mucorineae,"
+  _Proc. Am. Acad._ (1904); "Zygospore germination in the Mucorineae,"
+  _Annales mycologici_ (1906). _Ustilagineae_: Plowright, _British
+  Uredineae and Ustilagineae_ (London, 1889); Massee, _British Fungi_
+  (Phycomycetes and Ustilagineae) (London, 1891); Brefeld, _Unters. aus
+  dem Gesamtgeb. der Mykol._ Hefte xi. and xii.; and Falck, "Die
+  Bluteninfektion bei den Brandpilzen," ibid. Heft xiii. 1905; Dangeard,
+  "La Reproduction sexuelle des Ustilaginées," C.R., Oct. 9, 1893;
+  Maire, "Recherches cytologiques et taxonomiques sur les
+  Basidiomyceten," _Annexé au Bull. de la Soc. Mycol. de France_ (1902).
+  _Saccharomycetaceae_: Jorgensen, _The Micro-organisms of Fermentation_
+  (1899); Barker, _Ann. of Bot._ vol. xiv. (1901); "On Spore-formation
+  among the Saccharomycetes," _Journ. of the Fed. Institute of Brewing_,
+  vol. 8 (1902); Guillermond, _Recherches cytologiques sur lés levures_
+  (Paris, 1902); Hansen, _Centralbl. f. Bakt. u. Parasitenp._ Abt. ii.
+  Bd. 12 (1904). _Exoascaceae_: Giesenhagen, "_Taphrina, Exoascus,
+  Magnusiella_" (complete literature given), _Bot. Zeit._ Bd. 7 (1901).
+  _Erysiphaceae_: Harper, "Die Entwicklung des Perithecium bei
+  _Sphaerotheca castagnei_," _Ber. d. deut bot Ges._ (1896); "Sexual
+  Reproduction and the Organization of the Nucleus in certain Mildews,"
+  _Publ. Carnegie Institution_ (Washington, 1906); Blackman & Fraser,
+  "Fertilization in _Sphaerotheca_," _Ann. of Bot._ (1905).
+  _Perisporiaceae_: Brefeld, _Untersuchungen aus dem Gesamtgeb. der
+  Mykol._ Heft 10 (1891); Fraser and Chamber, _Annales mycologici_
+  (1907). _Discomycetes_: Harper, "Über das Verhalten der Kerne bei
+  Ascomyceten," _Jahr. f. wiss. Bot._ Bd. 29 (1890); "Sexual
+  Reproduction in _Pyronema confluens_," _Ann. of Bot._ 14 (1900);
+  Claussen, "Zur Entw. der Ascomyceten," Boudiera, Bot. Zeit. Bd. 63
+  (1905); Dangeard, "Sur le _Pyronema confluens_," _Le Botaniste_, 9
+  série (1903) (and numerous papers in same journal earlier and later);
+  Ramlow, "Zur Entwick. von _Thelebolus stercoren_," _Bot. Zeit._
+  (1906); Woronin, "Über die Sclerotienkrankheit der Vaccineen Beeren,"
+  _Mem. de l'Acad. Imp. des Sciences de St-Pétersbourg_, 7 série, 36
+  (1888); Dittrich, "Zur Entwickelungsgeschichte der Helvellineen,"
+  Cohn's _Beitr. z. Biol. d. Pflanzen_ (1892). _Pyrenomycetes_: Fisch,
+  "Beitr. z. Entwickelungsgeschichte einiger Ascomyceten," _Bot. Zeit._
+  (1882); Frank, "Über einige neue u. weniger bekannte Pflanzkrankh.,"
+  _Landw. Jahrb._ Bd. 12 (1883); Ward, "_Onygena equina_, a
+  horn-destroying fungus," _Phil. Trans._, vol. 191 (1899); Dawson, "On
+  the Biology of Poroniapunctata," Ann. of Bot. 14 (1900). _Tuberineae_:
+  Buchholtz, "Zur Morphologie u. Systematik der Fungi hypogaei," _Ann.
+  Mycol._ Bd. 1 (1903); Fischer in Engler and Prantl, _Die natürlichen
+  Pflanzenfamilien_ (1896). _Laboulbeniineae_: Thaxter, "Monograph of
+  the Laboulbeniaceae," _Mem. Amer. Acad. of Arts and Sciences_, vol. 12
+  (1895). _Uredineae_: Eriksson and Henning, _Die Getreideroste_
+  (Stockholm, 1896); Eriksson, _Botan. Gaz._ vol. 25 (1896); "On the
+  Vegetative Life of some Uredineae," Ann. of Bot. (1905); Klebahn, _Die
+  wirtwechselnden Rostpilze_ (Berlin, 1904); Sapin-Trouffy, "Recherches
+  histologiques sur la famille des Urédinées," _Le Botaniste_
+  (1896-1897); Blackman, "On the Fertilization, Alternation of
+  Generations and General Cytology of the Uredineae," _Ann. of Bot._
+  vol. 18 (1904); Blackman and Fraser, "Further Studies on the Sexuality
+  of Uredineae," _Ann. of Bot._ vol. 20 (1906); Christman, "Sexual
+  Reproduction of Rusts," _Ann. of Bot._ vol. 20 (1906); Ward, "The
+  Brooms and their Rust Fungus," _Ann. of Bot._ vol. 15 (1901).
+  _Basidiomycetes_: Dangeard, "La Reprod. sexuelle des Basidiomycètes,"
+  _Le Botaniste_ (1894 and 1900); Maire, "Recherches cytologiques et
+  taxonomiques sur les Basidiomycètes," _Annexe du Bull. de la Soc.
+  Mycol. de France_ (1902); Möller, "Protobasidiomyceten," _Schimper's
+  Mitt. aus den Tropen_, Heft 8 (Jena, 1895); Nichols, "The Nature and
+  Origin of the Binucleated Cells in certain Basidiomycetes," _Trans.
+  Wisconsin Acad. of Sciences_, vol. 15 (1905); Wager, "The Sexuality of
+  the Fungi," _Ann. of Bot._ 13 (1899); Woronin, "_Exobasidium
+  Vaccinii_," _Verh. Naturf. Ges. zu Freiburg_, Bd. 4 (1867).
+  _Fermentation_: Buchner, "Gährung ohne Hefezellen," _Bot. Zeit._ Bd.
+  18 (1898); Albert, _Cent. f. Bakt._ Bd. 17 (1901); Green, _The
+  Soluble Ferments and Fermentation_ (Cambridge, 1899). _Parasitism_:
+  "On some Relations between Host and Parasite," _Proc. Roy. Soc_. vol.
+  47 (1890); "A Lily Disease," _Ann. of Botany_, vol. 2 (1888); Eriksson
+  & Hennings, _Die Getreideroste (vide supra_); Ward, "On the Question
+  of Predisposition and Immunity in Plants," _Proc. Cambridge Phil.
+  Soc_. vol. 11 (1902); also _Annals of Bot_. vol. 16 (1902) and vol. 19
+  (1905); Neger, "Beitr. z. Biol. d. Erysipheen" _Flora_, Bde. 88 and 90
+  (1901-1902); Salmon, "Cultural Experiments with 'Biologic Forms' of
+  the Erysiphaceae," _Phil. Trans_. (1904); "On Erysiphe graminis and
+  its adaptative parasitism within the genus, _Bromus_," _Ann. Mycol_.
+  vol. 11 (1904), also _Ann. of Bot_. vol. 19 (1905). _Symbiosis_: Ward,
+  "The Ginger-Beer Plant," _Phil. Trans. Roy. Soc_. (1892); "Symbiosis,"
+  _Ann. of Bot_. 13 (1899); Shalk, "Der Sinn der Mykorrhizenbildung,"
+  _Jahrb. f. wiss. Bot_. Bd. 34 (1900); Bernard, "On some Different
+  Cases of Germination," _Gardener's Chronicle_ (1900); Pierce, _Publ.
+  Univ. California_ (1900).     (H. M. W.; V. H. B.)
+
+
+
+
+FUNJ (FUNNIYEH, FUNG, FUNGHA), a very mixed negroid race, occupying
+parts of Sennar and the hilly country to the south between the White and
+Blue Niles. They traditionally come from west of the White Nile and are
+affiliated by some to the Kordofan Nubas, by others, more justifiably,
+to the negro Shilluks. These Funj, who became the dominant race in
+Sennar in the 15th century, almost everywhere assimilated the speech,
+religion and habits of the Arabs settled in that region. Until the 19th
+century they were one of the most powerful of African peoples in the
+eastern Sudan. About the end of the 15th century they overthrew the
+kingdom of Aloa, between the two Niles, and conquered the neighbouring
+peoples of the Sudan, Nubia and even Kordofan. The Funj had mixed much
+with the Arabs before their conquests, and had been converted to Islam.
+But they were still in many ways savages, for James Bruce (who traversed
+the district in 1772) says that their most famous king, Malek-el-Gahman,
+preferred human liver to any other food, and the Belgian traveller E.
+Pruyssenaere (1826-1864) found them still performing pagan rites on
+their sacred Mount Gula. Ernst Marno declared that as late as 1870 the
+most southern branch of the race, the Boruns, a non-Arabic speaking
+tribe, were cannibals. The Funj kings were content with levying tribute
+on their neighbours, and in this loose way Shendi, Berber and Dongola
+were once tributary. The Arab viziers gradually absorbed all power, the
+Funj sovereignty becoming nominal; and in 1821 the Egyptians easily
+destroyed the Funj domination. To-day the Funj are few, and represent no
+real type. They are a bright, hospitable folk. Many of them are skilful
+surgeons and go far afield in their work. The fellahin, indeed, call
+surgeons "Senaari" (men of Sennar). See further SENNAR AND SUDAN
+(Anglo-Egyptian).
+
+
+
+
+FUNKIA, in botany, a genus of rather handsome, hardy, herbaceous plants
+belonging to the natural order Liliaceae, and natives of China and
+Japan. They are tuberous, with broadly ovate or heart-shaped leaves and
+racemes of white or pale lilac, drooping, funnel-shaped flowers. They
+are useful for the borders of a shrubbery, the lawn or rock-work, or may
+be grown in pots for the greenhouse. The plants are propagated by
+dividing the crowns in autumn or when growth begins in spring.
+
+
+
+
+FUNNEL (through an O. Fr. _founil_, found in Breton, from Lat.
+_infundibulum_, that through which anything is poured, from _fundere_,
+to pour), a vessel shaped like a cone having a small tube at the apex
+through which powder, liquid, &c., may be easily passed into another
+vessel with a small opening. The term is used in metal-casting of the
+hole through which the metal is poured into a mould, and in anatomy and
+zoology of an _infundibulum_ or funnel-shaped organ. The word is thus
+used generally of any shaft or passage to convey light, air or smoke, as
+of the chimney of an engine or a steam-boat, or the flue of an ordinary
+chimney. It is also used of a shaft or channel in rocks, and in the
+decoying of wild-fowl is applied to the cone-shaped passage leading from
+a pond and covered with a net, a "funnel-net," into which the birds are
+decoyed.
+
+
+
+
+FUR (connected with O. Fr. _forre_, a sheath or case; so "an outer
+covering"), the name specially given to the covering of the skin in
+certain animals which are natives of the colder climates, lying
+alongside of another and longer covering, called the overhair. The fur
+differs from the overhair, in that it is soft, silky, curly, downy and
+barbed lengthwise, while the overhair is straight, smooth and
+comparatively rigid. These properties of fur constitute its essential
+value for felting purposes, and mark its difference from wool and silk;
+the first, after some slight preparation by the aid of hot water,
+readily unites its fibres into a strong and compact mass; the others can
+best be managed by spinning and weaving.
+
+On the living animal the overhair keeps the fur filaments apart,
+prevents their tendency to felt, and protects them from injury--thus
+securing to the animal an immunity from cold and storm; while, as a
+matter of fact, this very overhair, though of an humbler name, is most
+generally the beauty and pride of the pelt, and marks its chief value
+with the furrier. We arrive thus at two distinct and opposite uses and
+values of fur. Regarded as useful for felt it is denominated staple fur,
+while with respect to its use with and on the pelt it is called fancy
+fur.
+
+_History._--The manufacture of fur into a felt is of comparatively
+modern origin, while the use of fur pelts as a covering for the body,
+for the couch, or for the tent is coeval with the earliest history of
+all northern tribes and nations. Their use was not simply a barbarous
+expedient to defend man from the rigours of an arctic winter; woven wool
+alone cannot, in its most perfect form, accomplish this. The pelt or
+skin is requisite to keep out the piercing wind and driving storm, while
+the fur and overhair ward off the cold; and "furs" are as much a
+necessity to-day among more northern peoples as they ever were in the
+days of barbarism. With them the providing of this necessary covering
+became the first purpose of their toil; subsequently it grew into an
+object of barter and traffic, at first among themselves, and afterwards
+with their neighbours of more temperate climes; and with the latter it
+naturally became an article of fashion, of ornament and of luxury. This,
+in brief, has been the history of its use in China, Tatary, Russia,
+Siberia and North America, and at present the employment of fancy furs
+among civilized nations has grown to be more extensive than at any
+former period.
+
+The supply of this demand in earlier times led to such severe
+competition as to terminate in tribal pillages and even national wars;
+and in modern times it has led to commercial ventures on the part of
+individuals and companies, the account of which, told in its plainest
+form, reads like the pages of romance. Furs have constituted the price
+of redemption for royal captives, the gifts of emperors and kings, and
+the peculiar badge of state functionaries. At the present day they vie
+with precious gems and gold as ornaments and garniture for wealth and
+fashion; but by their abundance, and the cheapness of some varieties,
+they have recently come within the reach of men of moderate incomes. The
+history of furs can be read in Marco Polo, as he grows eloquent with the
+description of the rich skins of the khan of Tatary; in the early
+fathers of the church, who lament their introduction into Rome and
+Byzantium as an evidence of barbaric and debasing luxury; in the
+political history of Russia, stretching out a powerful arm over Siberia
+to secure her rich treasures; in the story of the French occupation of
+Canada, and the ascent of the St Lawrence to Lake Superior, and the
+subsequent contest to retain possession against England; in the history
+of early settlements of New England, New York and Virginia; in Irving's
+_Astoria_; in the records of the Hudson's Bay Company; and in the annals
+of the fairs held at Nizhniy Novgorod and Leipzig. Here it may suffice
+to give some account of the present condition of the trade in fancy
+furs. The collection of skins is now chiefly a matter of private
+enterprise. Few, if any, monopolies exist.
+
+_Natural Supplies._--We are dependent upon the Carnivora, Rodentia,
+Ungulata and Marsupialia for our supplies of furs, the first two classes
+being by far of the greatest importance. The Carnivora include bears,
+wolverines, wolves, raccoons, foxes, sables, martens, skunks, kolinskis,
+fitch, fishers, ermines, cats, sea otters, fur seals, hair seals, lions,
+tigers, leopards, lynxes, jackals, &c. The Rodentia include beavers,
+nutrias, musk-rats or musquash, marmots, hamsters, chinchillas, hares,
+rabbits, squirrels, &c. The Ungulata include Persian, Astrachan,
+Crimean, Chinese and Tibet lambs, mouflon, guanaco, goats, ponies, &c.
+The Marsupialia include opossums, wallabies and kangaroos. These, of
+course, could be subdivided, but for general purposes of the fur trade
+the above is deemed sufficient.
+
+The question frequently arises, not only for those interested in the
+production of fur apparel, but for those who derive so much comfort and
+pleasure from its use, whether the supply of fur-bearing animals is
+likely to be exhausted. Although it is a fact that the demand is ever
+increasing, and that some of the rarer animals are decreasing in
+numbers, yet on the other hand some kinds of furs are occasionally
+neglected through vagaries of fashion, which give nature an opportunity
+to replenish their source. These respites are, however, becoming fewer
+every day, and what were formerly the most neglected kinds of furs are
+becoming more and more sought after. The supply of some of the most
+valuable, such as sable, silver and natural black fox, sea otter and
+ermine, which are all taken from animals of a more or less shy nature,
+does very gradually decrease with persistent hunting and the
+encroachment of man upon the districts where they live, but the climate
+of these vast regions is so cold and inhospitable that the probabilities
+of man ever permanently inhabiting them in numbers sufficient to scare
+away or exterminate the fur-bearing wild animals is unlikely. Besides
+these there are many useful, though commonplace, fur-bearing animals
+like mink, musquash, skunk, raccoon, opossum, hamster, rabbit, hares and
+moles, that thrive by depredations upon cultivated land. Some of these
+are reared upon extensive wild farms. In addition there are domestic
+fur-bearing animals, such as Persian, Astrachan and Chinese lambs, and
+goats, easily bred and available.
+
+With regard to the rearing of the Persian lamb, there is a prevalent
+idea that the skins of the unborn lamb are frequently used; this,
+however, is a mistake. A few such skins have been taken, but they are
+too delicate to be of any service. The youngest, known as "broadtails,"
+are killed when a few days old, but for the well-developed curly fur,
+the lambs must be six or seven weeks old. During these weeks their
+bodies are covered with leather so that the fur may develop in close,
+light and clean curls. The experiment has been tried of rearing rare,
+wild, fur-bearing animals in captivity, and although climatic conditions
+and food have been precisely as in their natural environment, the fur
+has been poor in quality and bad in colour, totally unlike that taken
+from animals in the wild state. The sensation of fear or the restriction
+of movement and the obtaining of food without exertion evidently prevent
+the normal development of the creature.
+
+In mountainous districts in the more temperate zones some good supplies
+are found. Chinchillas and nutrias are obtained from South America,
+whence come also civet cats, jaguars, ocelots and pumas. Opossums and
+wallabies, good useful furs, come from Australia and New Zealand. The
+martens, foxes and otters imported from southern Europe and southern
+Asia, are very mixed in quality, and the majority are poor compared with
+those of Canada and the north.
+
+Certain characteristics In the skin reveal to the expert from what
+section of territory they come, but in classifying them it is considered
+sufficient to mention territories only.
+
+Some of the poorer sorts of furs, such as hamster, marmot, Chinese goats
+and lambs, Tatar ponies, weasels, kaluga, various monkeys, antelopes,
+foxes, otters, jackals and others from the warmer zones, which until
+recently were neglected on account of their inferior quality of colour,
+by the better class of the trade, are now being deftly dressed or dyed
+in Europe and America, and good effects are produced, although the lack
+of quality when compared with the better furs from colder climates which
+possess full top hair, close underwool and supple leathers, is readily
+manifest. It is only the pressure of increasing demand that makes
+marketable hard pelts with harsh brittle hair of nondescript hue, and
+these would, naturally, be the last to attract the notice of dealers.
+
+As it is impossible that we shall ever discover any new fur-bearing
+animals other than those we know, it behoves responsible authorities to
+enforce close seasons and restrictions, as to the sex and age, in the
+killing for the purpose of equalizing the numbers of the catches. As
+evidence of indiscriminate slaughter the case of the American buffaloes
+may be cited. At one time thousands of buffalo skins were obtainable and
+provided material for most useful coats and rugs for rough wear in cold
+regions, but to-day only a herd or so of the animals remain, and in
+captivity.
+
+The majority of animals taken for their fur are trapped or snared, the
+gun being avoided as much as possible in order that the coat may be
+quite undamaged. Many weary hours are spent in setting baits, traps and
+wires, and, frequently, when the hunter retraces his steps to collect
+the quarry it is only to find it gone, devoured by some large animal
+that has visited his traps before him. After the skins have been
+carefully removed--the sooner after death the better for the subsequent
+condition of the fur--they are lightly tacked out, pelt outwards, and,
+without being exposed to the sun or close contact with a fire, allowed
+to dry in a hut or shady place where there is some warmth or movement of
+air. With the exception of sealskins, which are pickled in brine, all
+raw skins come to the various trade markets simply dried like this.
+
+_Quality and Colour._--The best fur is obtained by killing animals when
+the winter is at its height and the colder the season the better its
+quality and colour. Fur skins taken out of season are indifferent, and
+the hair is liable to shed itself freely; a good furrier will, however,
+reject such faulty specimens in the manufacturing. The finest furs are
+obtained from the Arctic and northern regions, and the lower the
+latitude the less full and silky the fur, till, at the torrid zone, fur
+gives place to harsh hair without any underwool. The finest and closest
+wools are possessed by the amphibious Carnivora and Rodentia, viz.
+seals, otters, beavers, nutrias and musquash, the beauty of which is not
+seen until after the stiff water or top hairs are pulled out or
+otherwise removed. In this class of animal the underneath wool of the
+belly is thicker than that of the back, while the opposite is true of
+those found on the land. The sea otter, one of the richest and rarest of
+furs, especially for men's wear, is an exception to this unhairing
+process, which it does not require, the hair being of the same length as
+the wool, silky and bright, quite the reverse of the case of other
+aquatic animals.
+
+Of sealskins there are two distinct classes, the fur seals and the hair
+seals. The latter have no growth of fur under the stiff top hair and are
+killed, with few exceptions (generally of the marbled seals), on account
+of the oil and leather they yield. The best fur seals are found off the
+Alaska coast and down as far south as San Francisco.
+
+It is found that in densely wooded districts furs are darker in colour
+than in exposed regions, and that the quality of wool and hair is softer
+and more silky than those from bare tracts of country, where nature
+exacts from its creatures greater efforts to secure food, thereby
+developing stronger limbs and a consequently coarser body covering.
+
+As regards density of colour the skunk or black marten has the blackest
+fur, and some cats of the domestic kind, specially reared for their fur,
+are nearly black. Black bears have occasionally very black coats, but
+the majority have a brownish underwool. The natural black fox is a
+member of the silver fox family and is very rare, the skins bringing a
+high price. Most silver foxes have dark necks and in some the dark shade
+runs a quarter, half-way, or three-quarters, or even the whole length of
+the skin, but it is rather of a brownish hue. Some Russian sables are of
+a very dense bluish brown almost a black, which is the origin
+undoubtedly of the term "sables," while some, from one district in
+particular, have a quantity of silver hairs, evenly interspersed in the
+fur, a peculiarity which has nothing to do with age. The best sea otters
+have very dark coats which are highly esteemed, a few with silver hairs
+in parts; where these are equally and evenly spread the skins are very
+valuable. Otters and beavers that run dark in the hair or wool are more
+valuable than the paler ones, the wools of which are frequently touched
+with a chemical to produce a golden shade. This is also done with
+nutrias after unhairing. The darker sorts of mink, musquash, raccoon
+and wolverine are more valuable than the paler skins.
+
+_Collective Supplies and Sales._--There are ten large American and
+Canadian companies with extensive systems for gathering the annual hauls
+of skins from the far-scattered trappers. These are the Hudson's Bay
+Co., Russian Fur Co., Alaska Commercial Co., North American Commercial
+Co., Russian Sealskin Co., Harmony Fur Co., Royal Greenland Fur Co.,
+American Fur Co., Missouri Co. and Pacific Co. Most of the raw skins are
+forwarded to about half-a-dozen brokers in London, who roughly sort them
+in convenient lots, issuing catalogues to the traders of the world, and
+after due time for examination of the goods by intending purchasers, the
+lots are sold by public auction. The principal sales of general furs are
+held in London in January and March, smaller offerings being made in
+June and October; while the bulk of fur sealskins is sold separately in
+December. The Hudson's Bay Co.'s sales take place before the others,
+and, as no reserves are placed on any lot, the results are taken as
+exactly indicating current values. While many buyers from America and
+Russia are personally in attendance at the sales, many more are
+represented by London and Leipzig agents who buy for them upon
+commission. In addition to the fur skins coming from North America vast
+numbers from Russia, Siberia, China, Japan, Australia and South America
+are offered during the same periods at public auction. Fairs are also
+held in Siberia, Russia and Germany for the distribution of fur skins as
+follows:--
+
+  January:   Frankfort-on-the-  Small collection of provincial produce,
+               Oder               such as otter, fox, fitch and marten.
+
+  February:  Irbit, Siberia     General Russian furs.
+
+  Easter:    Leipzig, Germany   General furs.
+
+  August:    Nizhniy Novgorod,  Persian lamb and general furs.
+               Russia
+
+  August:    Kiakhta, Siberia   Chinese furs and ermine.
+
+  December:  Ishim, Siberia     Chiefly squirrels.
+
+Of course there are many transactions, generally in the cheaper and
+coarser kinds of furs, used only in central Europe, Russia and Asia
+which in no way interest the London market, and there are many direct
+consignments of skins from collectors in America and Russia to London,
+New York and Leipzig merchants. But the bulk of the fine furs of the
+world is sold at the large public trade auction sales in London. The
+chief exceptions are the Persian and Astrachan lambs, which are bought
+at the Russian fairs, and are dressed and dyed in Leipzig, and the
+ermine and Russian squirrels, which are dressed and manufactured into
+linings either in Russia or Germany before offered for sale to the
+wholesale merchants or manufacturers.
+
+The annual collection of fur skins varies considerably in quantity
+according to the demand and to the good or bad climatic conditions of
+the season; and it is impossible to give a complete record, as many
+skins are used in the country of their origin or exported direct to
+merchants. But a fairly exact statement of the numbers sold in the great
+public trade auction sales in London during the year 1905-1906 is
+herewith set out.
+
+       _Year ending 31st of March 1906._      Total Number
+                                                of Skins.
+
+  Badger                                         28,634
+  Badger, Japanese                                6,026
+  Bear                                           18,576
+  Beaver                                         80,514
+  Cat, Civet                                    157,915
+  Cat, House                                    126,703
+   "   Wild                                      32,253
+  Chinchilla (La Plata), known also as Bastard   43,578
+      "      Peruvian finest                      5,603
+  Deer, Chinese                                 124,355
+  Ermine                                         40,641
+  Fisher                                          5,949
+  Fitch                                          77,578
+  Fox, Blue                                       1,893
+   "   Cross                                     10,276
+   "   Grey                                      59,561
+   "   Japanese                                  81,429
+   "   Kit                                        4,023
+   "   Red                                      158,961
+   "   Silver                                     2,510
+   "   White                                     27,463
+  Goats, Chinese                                261,190
+  Hares                                          41,256
+  Kangaroo                                        7,115
+  Kid, Chinese linings and skins equal to     5,080,047
+  Kolinsky                                      114,251
+  Lamb, Mongolian linings and skins equal to    214,072
+    "   Slink        "        "       "         167,372
+    "   Tibet        "        "       "         794,130
+  Leopard                                         3,574
+  Lynx                                           88,822
+  Marmot, linings and skins equal to          1,600,600
+  Marten, Baum                                    4,573
+    "     Japanese                               16,461
+    "     Stone                                  12,939
+  Mink, Canadian and American                   299,254
+    "   Japanese                                360,373
+  Mouflon                                        23,594
+  Musk-rat or Musquash, Brown                 5,126,339
+    "           "       Black                    41,788
+  Nutria                                         82,474
+  Opossum, American                             902,065
+    "      Australian                         4,161,685
+  Otter, River                                   21,235
+    "    Sea                                        522
+  Raccoon                                       310,712
+  Sable, Canadian and American                   97,282
+    "    Japanese                                   556
+    "    Russian                                 26,399
+  Seals, Fur                                     77,000
+    "    Hair                                    31,943
+  Skunk                                       1,068,408
+  Squirrel                                      194,596
+    "     Linings each averaging 126 skins    1,982,736
+  Tiger                                             392
+  Wallaby                                        60,956
+  Wolf                                           56,642
+  Wolverine                                       1,726
+  Wombat                                        193,625
+
+A brief account of the different qualities of the pelts, with some
+general remarks as to their customary uses, follows. The prices quoted
+are subject to constant fluctuation and represent purely trade prices
+for bulk, and it should be explained that the very great variations are
+due to different sizes, qualities and colours, and moreover are only
+_first cost_, before skins are dressed and prepared. These preparations
+are in some cases expensive, and there is generally a considerable
+percentage of waste. The prices cannot be taken as a guide to the
+wholesale price of a single and finished skin, but simply as _relative_
+value.
+
+The fullest and darkest skins of each kind are the most valuable, and,
+in cases of bluish grey or white, the fuller, clearer and brighter are
+the more expensive. A few albinos are found in every species, but
+whatever their value to a museum, they are of little commercial
+importance. Some odd lots of skins arrive designated simply as
+"sundries," so no classification is possible, and this will account for
+the absence of a few names of skins of which the imports are
+insignificant in quantity, or are received direct by the wholesale
+merchants.
+
+
+  _Names, Qualities and Uses of Pelts._[1]
+
+  ASTRACHAN.--See _Lambs_, below.
+
+  BADGER.--Size 2 × 1 ft. American sorts have coarse thick underwool of
+  a pale fawn or stone colour with a growth of longer black and white
+  hairs, 3 or 4 in. long; a very durable but clumsy fur. The best skins
+  are exported to France, Spain and Italy, and used for carriage rugs
+  and military purposes. Asiatic, including Japanese, skins are more
+  woolly. Russian and Prussian kinds are coarser and darker, and used
+  mostly for brush trade. Value 6d. to 19s.
+
+  BEAR, AUSTRALIAN.--See _Wombat_, below.
+
+  BEAR, BLACK.--Size 6 × 3 ft. Fine dark brown underwool with bright
+  black and flowing top hair 4 in. long. Cubs are nearly as long in the
+  hair although only about half the size and not only softer and better,
+  but have the advantage of being very much lighter in pelt. Widely
+  distributed in North America, the best come from Canada, are costly
+  and are used for military caps, boas, muffs, trimmings, carriage rugs
+  and coachmen's capes, and the fur wears exceedingly well. Value 17s.
+  6d. to 86s. Those from East India and warm climates are harsh, poor
+  and only fit for floor rugs.
+
+  BEAR, BROWN.--Size 6 × 3 ft. Similar in quality to the black, but far
+  more limited in number; the colours range from light yellow to a rich
+  dark brown. The best come from Hudson Bay territory and are valuable.
+  Used for muffs, trimmings, boas, and carriage rugs. Inferior sorts,
+  almost grizzly in effect and some very pale, are found in Europe and
+  Asia and are mostly used locally. In India there is a species called
+  Isabelline bear, which was formerly imported to Great Britain, but
+  does not now arrive in any quantity worth mentioning. Value 10s. 6d.
+  to 60s., Isabelline sort 10s. 6d. to 78s.
+
+  BEAR, GRIZZLY.--Size 8 × 4 ft. Coarse hair, heavy pelt, mostly dark
+  yellowish and brown colours, only found in western parts of United
+  States, Russia and Siberia. Used as carriage rugs and floor rugs, most
+  durable for latter purpose and of fine effect. They are about half the
+  value of brown bear. Value 15s. to 54s.
+
+  BEAR, ISABELLINE.--See _Bear_, _Brown_, above.
+
+  BEAR, WHITE.--Size 10 × 5 ft. The largest of all bears. Short close
+  hair except on flanks, colour white to yellow. An inhabitant of the
+  Arctic circle, best from Greenland. Used for floor rugs, very durable;
+  and very white specimens are valuable. Value 20s. to 520s.
+
+  BEAVER. Size 3 × 2 ft. The largest of rodents, it possesses a close
+  underwool of bluish-brown hue, nearly an inch in depth, with coarse,
+  bright, black or reddish-brown top hair, 3 in. long. Found widely in
+  North America. After being unhaired the darkest wools are the most
+  valuable, although many people prefer the bright, lighter brown tones.
+  Used for collars, cuffs, boas, muffs, trimmings, coat linings and
+  carriage aprons, and is of a most durable nature, in addition to
+  having a rich and good appearance. Value 10s. to 39s. 6d.
+
+  BROADTAIL.--See _Lambs_, below.
+
+  CARACAL.--A small lynx from India, the fur very poor, seldom imported.
+
+  CARACUL.--See _Goats_ and _Lambs_, below.
+
+  CAT, CIVET.--Size 9 × 4½ in., short, thick and dark underwool with
+  silky black top hair with irregular and unique white markings. It is
+  similar to skunk, but is much lighter in weight, softer and less full,
+  without any disagreeable odour. Used for coat linings it is very warm
+  and durable. A few come from China, but the fur is yellowish-grey,
+  slightly spotted and worth little. Value 1s. 1d. to 1s. 11d.
+
+  CAT, HOUSE, &C.--18 × 9 in., mostly black and dark brown, imported
+  from Holland, Bavaria, America and Russia, where they are reared for
+  their coats. The best, from Holland, are used for coat linings.
+  Although in colour, weight and warmth they are excellent, the fur is
+  apt to become loose and to fall off with friction of wear. The black
+  are known as genet, although the true genet is a spotted wild cat.
+  Wild sorts of the tabby order are coarser, and not so good and silky
+  in effect as when domestically reared. Value of the black sorts 2d. to
+  3s. Wild 9d. to 14s. Some small wild cats, very poor flat fur of a
+  pale fawn colour with yellow spots, are imported from Australia and
+  used for linings. Value 5½d. to 1s. 1d.
+
+  CHEETAH.--Size of a small leopard and similar in colour, but has black
+  spots in lieu of rings. Only a few are now imported, which are used
+  for mats. Value 2s. 6d. to 18s.
+
+  CHINCHILLA, PERUVIAN and BOLIVIAN.--Size 12 × 7 in., fur 1 to 1¼ in.
+  deep. Delicate blue-grey with black shadings, one of nature's most
+  beautiful productions, though not a durable one. Used for ladies'
+  coats, stoles, muffs, hats and trimmings. Yearly becoming scarcer and
+  most costly. Value 8s. 6d. to 56s. 8d.
+
+  CHINCHILLA, LA PLATA, incorrectly named and known in the trade as
+  "bastard chinchilla," size 9 × 4 in., in a similar species, but owing
+  to lower altitudes and warmer climatic conditions of habitation is
+  smaller, with shorter and less beautiful fur, the underwool colour
+  being darker and the top colour less pure. Used exactly as the better
+  kind, and the picked skins are most effective. As with the best sort
+  it is not serviceable for constant wear. Value 4s. 2d. to 27s. 6d.
+
+  CHINCHILLONE.--Size 13 × 8 in., obtained also from South America. Fur
+  is longer and weaker and poorer and yellower than chinchilla. Probably
+  a crossbred animal, very limited importation. Value 3s. 6d. to 16s.
+  8d.
+
+  DEER, CHINESE and EAST INDIAN.--Small, light, pelted skins, the
+  majority of which are used for mats. Reindeer and other varieties are
+  of little interest for use other than trophy mats. Thousands are taken
+  for the leather trade. Value of Chinese 1s. 2d. to 1s. 6d. each.
+
+  DOG.--The only dogs that are used in the fur trade in civilized
+  countries are those imported from China, which are heavy and coarse,
+  and only used in the cheaper trade, chiefly for rugs. Value 6d. to 1s.
+
+  DOG WOLF.--See _Wolf_, below.
+
+  ERMINE.--Size 12 × 2½ in. Underwool short and even, with a shade
+  longer top hair. Pelt light and close in texture, and durable. In the
+  height of winter the colour is pure white with exception of the tip of
+  tail, which is quite black. Supplies are obtained from Siberia and
+  America. Best are from Ishim in Siberia. Used for cloak linings,
+  stoles, muffs and trimmings, also for embellishment of British state,
+  parliamentary and legal robes. When this fur is symmetrically spotted
+  with black lamb pieces it is styled miniver, in which form it is used
+  at the grand coronation functions of British sovereigns. Value 1s. 3d.
+  to 8s. 6d.
+
+  FISHER.--Size 30 × 12 in., tail 12 to 18 in. long, the largest of the
+  martens; has a dark shaded deep underwool with fine, glossy, dark and
+  strong top hair 2 in. or more long. Best obtained from British
+  America. The tails are almost black and make up most handsomely into
+  trimmings, muffs, &c. Tails worked separately in these forms are as
+  rich and fine and more durable than any other fur suitable for a like
+  purpose. The fur of the skin itself is something like a dark silky
+  raccoon, but is not as attractive as the tails. Value 12s. to 46s.
+
+  FITCH.--Size 12 × 3 in., of the marten species, also known as the pole
+  cat. Yellow underwool 1/3 in. deep, black top hair, 1½ to 1¾ in. long,
+  very fine and open in growth, and not close as in martens. Largest
+  skins come from Denmark, Holland and Germany. The Russian are smaller,
+  but more silky and, as now dyed, make a cheap and fair substitute for
+  sable. They are excellent for linings of ladies' coats, being of light
+  weight and fairly strong in the pelt. English mayors' and civic
+  officials' robes are frequently trimmed with this fur in lieu of
+  sable. Value of the German variety 2s. to 5s. 6d. and of the Russian
+  7d. to 1s. 4d.
+
+  FOX, BLUE.--Size 24 × 8 in. Underwool thick and long. Top hair fine
+  and not so plentiful as in other foxes. Found in Alaska, Hudson Bay
+  territory, Archangel and Greenland. Although called blue, the colour
+  is a slaty or drab tone. Those from Archangel are more silky and of a
+  smoky bluish colour and are the most valuable. These are scarce and
+  consequently dear. The white foxes that are dyed smoke and celestial
+  blue are brilliant and totally unlike the browner shades of this fox.
+  Value 34s. to 195s.
+
+  FOX, COMMON.--The variation of size and quality is considerable, and
+  the colour is anything from grey to red. In Great Britain the animal
+  is now only regarded for the sport it provides. On the European
+  continent, however, some hundreds of thousands of skins, principally
+  German, Russian and Norwegian, are sold annually, for home use, and
+  for dyeing and exportation, chiefly to the United States. The
+  qualities do not compare with those species found in North America and
+  the Arctic circle. The Asiatic, African and South American varieties
+  are, with the exception of those taken in the mountains, poorly furred
+  and usually brittle and therefore of no great service. No commercial
+  value can be quoted.
+
+  FOX, CROSS.--Size 20 × 7 in., are about as large as the silver and
+  generally have a pale yellowish or orange tone with some silvery
+  points and a darkish cross marking on the shoulders. Some are very
+  similar to the pale red fox from the North-West of America and a few
+  are exceptionally large. The darkest and best come from Labrador and
+  Hudson Bay, and the ordinary sorts from the north-west of the United
+  States and, as with silver and other kinds, the quality is inferior
+  when taken from warmer latitudes. Value 10s. 6d. to 60s.
+
+  FOX, GREY.--Size 27 × 10 in. Has a close dark drab underwool with
+  yellowish grizzly, grey, regular and coarse top hair. The majority
+  used for the trade come from Virginia and the southern and western
+  parts of the United States. Those from the west are larger than the
+  average, with more fur of a brighter tone. The fur is fairly
+  serviceable for carriage rugs, the leather being stout, but its
+  harshness of quality and nondescript colour does not contribute to
+  make it a favourite. Value 9d. to 4s. 9d.
+
+  FOX, JAPANESE.--See _Fox, Red_, and _Raccoon_, below.
+
+  FOX, KIT.--Size 20 × 6 in. The underwool is short and soft, as is also
+  the top hair, which is of very pale grey mixed with some
+  yellowish-white hair. It is the smallest of foxes, and is found in
+  Canada and the northern section of the United States. It is similar in
+  colour and quality to the prairie fox and to many kinds from the
+  warmer zones, such as from Turkey, eastern Asia and elsewhere. Value
+  1s. 3d. to 5s. 6d.
+
+  FOX, RED.--Size 24 × 8 in., though a few kinds are much larger. The
+  underwool is long and soft and the hair plentiful and strong. It is
+  found widely in the northern parts of America and in smaller numbers
+  south of the United States, also in China, Japan and Australia. The
+  colours vary from pale yellowish to a dark red, some being very
+  brilliant. Those of Kamschatka are rich and fine in quality. Farther
+  north, especially near the sea, the fur is coarse. Where the best
+  coloured skins are not used for carriage rugs they are extensively
+  dyed, and badger and other white hairs are inserted to resemble silver
+  fox. They are also dyed a sable colour. The skins, being the strongest
+  of foxes', both in the fur and pelt, are serviceable. The preparations
+  in imitation of the natural black and silver sorts are very good and
+  attractive. Value 1s. to 41s.
+
+  FOX, SILVER. Size 30 × 10 in. Underwool close and fine. Top hair black
+  to silvery, 3 in. long. The fur upon the necks usually runs dark,
+  almost black, and in some cases the fur is black half-way down the
+  length of the skin, in rarer cases three-quarters of the length and,
+  in the most exceptional instances, the whole length, and when this is
+  the case they are known as "Natural Black Foxes" and fetch enormous
+  prices. The even silvery sorts are highly esteemed, and the fur is one
+  of the most effective and precious. The finest are taken in Labrador.
+  The farther south they are found, the poorer and coarser the fur. The
+  brush has invariably a white tip. Value £1 to £320.
+
+  FOX, WHITE.--Size 20 × 7 in. Animals of this species are generally
+  small in size and inhabit the extreme northern sections of Hudson Bay,
+  Newfoundland, Greenland, Labrador and Siberia. The Canadian are silky
+  in nature and inclined to a creamy colour, while the Siberian are more
+  woolly and rather whiter. Those taken in central Asia near or in
+  Chinese territory are poorer and yellowish. The underwool in all sorts
+  is generally of a bluish-grey tone, but the top hair in the depth of
+  winter is usually full enough in quantity to hide any such variation.
+  Those skins in which the underwool is quite white are rare and much
+  more expensive. In summer specimens of this species, as with other
+  white furred animals, have slightly discoloured coats. The skins that
+  are not perfectly white are dyed jet black, dark or light smoke,
+  violet-blue, blue-grey, and also in imitation of the drab shades of
+  the natural blue. Value 18s. to 66s.
+
+  GENET.--Size 10 × 4 in. The genet proper is a small white spotted cat
+  found in Europe, but the quantity is too small to be of commercial
+  interest. The name has been adopted for the black cats used so much in
+  the trade. (See CATS, above.) Value 1s. to 6s. 6d.
+
+  GOATS.--Size varies greatly. The European, Arabian and East Indian
+  kinds are seldom used for rugs, the skins are chiefly dressed as
+  leather for books and furniture, and the kids for boots and gloves,
+  and the finer wool and hair are woven into various materials. Many
+  from Russia are dyed black for floor and carriage rugs; the hair is
+  brittle, with poor underwool and not very durable; the cost, however,
+  is small. The Chinese export thousands of similar skins in black, grey
+  and white, usually ready dressed and made into rugs of two skins each.
+  A great many are dyed black and brown, in imitation of bear, and are
+  used largely in the western parts of the United States and Canada for
+  sleigh and carriage rugs. Many are used for their leather. Thousands
+  of the kids are also dyed black and worked into cross-shaped pieces,
+  in which shape they are largely exported to Germany, France, Great
+  Britain and America, and sold by the retail as caracal, kid or
+  caracul. The grey ones are in good demand for motor coats. The word
+  caracul has been adopted from the Turkish and signifies black-eared.
+  See also LAMBS, CARACUL. Value of Chinese white 3s. 6d. to 6s. 6d.:
+  grey, 4s. to 6s. 9d.
+
+  The Angora from the heights of central Asia Minor has curly, fleecy,
+  silky, white wool, 4 to 7 in. long. The fur is not used in Great
+  Britain, as formerly, and the greater quantity, known as mohair, is
+  now imported for purposes of weaving. This species of goat was some
+  years since introduced into Cape Colony, but its wool is not so good
+  as the Asiatic breed. Good business, however, is done with the
+  product, but chiefly for leather. Value 4s. to 12s. 6d.
+
+  The Mongolian goat has a very soft silk underwool, and after the long
+  top hair is removed it is dressed and imported and erroneously named
+  mouflon. The colour is a light fawn, but it is so pale that it lends
+  itself to be dyed any colour. It was popular some years since in the
+  cheaper trade, but it is not now much seen in England. Value 2s. to
+  6s.
+
+  The Tibet goat is similar to the Angora in the fineness of its wool,
+  and many are used in the making of cashmere shawls. The Tibet lamb so
+  largely imported and used for children's wear is often miscalled Tibet
+  goat. Value 3s. to 7s. 6d.
+
+  GUANACO.--Size 30 × 15 in. Is a species of goat found in Patagonia and
+  other parts of South America. It has a very long neck and exceedingly
+  soft woolly fur of a light reddish-fawn colour with very white flanks.
+  It is usually imported in small quantities, native dressed, and ready
+  made into rugs. The dressing is hard and brittle. If the skins are
+  dressed in Europe they afford a very comfortable rug, though a very
+  marked one in effect. They have a similar wool to the vicuna, but
+  coarser and redder; both are largely used in South America. Value 1s.
+  to 4s. 6d.
+
+  HAMSTER.--Size 8 × 3½ in. A destructive rodent, is found in great
+  numbers in Russia and Germany. The fur is very flat and poor, of a
+  yellowish pale brown with a little marking of black. Being of a light
+  weight it is used for linings. Value 3d. to 1s.
+
+  HARE.--Size 24 × 9 in. The common hare of Europe does not much
+  interest the furrier, the fur being chiefly used by makers of hatters'
+  felt. The white hares, however, of Russia, Siberia and other regions
+  in the Arctic circle are very largely used in the cheaper trade of
+  Europe, America and the British colonies. The fur is of the whitest
+  when killed in winter, and that upon the flanks of the animal is very
+  much longer than that upon its back. The flanks are usually cut off
+  and made into muffs and stoles. The hair is, however, brittle and is
+  not at all durable. This fur is dyed jet black and various shades of
+  brown and grey, and manufactured into articles for the small drapers
+  and for exportation. The North American hares are also dyed black and
+  brown and used in the same way. Value of white 2d. to 5d.
+
+  JACKAL.--Size 2 to 3 ft. long. Is found in India and north and south
+  Africa. Indian are light brown and reddish, those from the Cape are
+  dark grey and rather silvery. Few are imported. Fur generally poor and
+  harsh, only suitable for carriage rugs. Value 1s. to 3s. 6d.
+
+  JAGUAR.--Size 7 to 10 ft. long. Is found in Mexico and British
+  Honduras. The markings are an irregular ring formation with a spot in
+  the centre. Leopards have rings only and cheetahs solid spots.
+  Suitable only for hearth-rugs. Supply very limited. Value 5s. to 45s.
+
+  KALUGA.--See _Souslik_, below.
+
+  KANGAROO.--The sizes vary considerably, some being huge, others quite
+  small. The larger varieties, viz. the red and the great, do not
+  usually interest furriers, the fur being harsh and poor without
+  underwool. They are tanned for the leather trade. The sorts used for
+  carriage aprons, coat linings and the outside of motor coats include:
+  blue kangaroo, bush kangaroo, bridled kangaroo, wallaroo, yellow
+  kangaroo, rock wallaby, swamp wallaby and short-tailed wallaby. Many
+  of the swamp sort are dyed to imitate skunk and look well. Generally
+  the colours are yellowish or brown. Some are dark brown as in the
+  swamp, which being strong are suitable for motor coats. The rock
+  wallabies are soft and woolly and often of a pretty bluish tone, and
+  make moderately useful carriage rugs and perambulator aprons. The
+  redder and browner sorts are also good for rugs as they are thick in
+  the pelt. On the European continent many of these are dyed. The best
+  of the lighter weights are frequently insufficiently strong in the
+  hair to stand the friction of wear in a coat lining. Value, kangaroo
+  9d. to 3s., wallaby 1½ d. to 5s. 3d., wallaroo 1s. to 5s. 6d.
+
+  KIDS.--See _Goats_, above.
+
+  KOLINSKY.--Size 12 × 2½ in. Is one of the marten tribe. The underwool
+  is short and rather weak, but regular, as is also the top hair; the
+  colour is usually yellow. They have been successfully dyed and used as
+  a substitute for sable. They are found in Siberia, Amoor, China and
+  Japan, but the best are from Siberia. They are light in weight and
+  therefore suitable for linings of coats. The tails are used for
+  artists' "sable" brushes. The fur has often been designated as red or
+  Tatar sable. Value 1s. 6d. to 4s. 6d.
+
+  LAMBS.--The sorts that primarily interest the fur trade in Europe and
+  America are those from south Russia, Persia and Afghanistan, which are
+  included under the following wholesale or retail commercial terms:
+  Persian lamb, broadtail, astrachan, Shiraz, Bokharan and caracul lamb.
+  With the public the general term astrachan is an old one, embracing
+  all the above curly sorts; the flatter kinds, as broadtail and caracul
+  lamb, have always been named separately. The Persian lambs, size 18 ×
+  9 in., are the finest and the best of them. When dressed and dyed they
+  should have regular, close and bright curl, varying from a small to a
+  very large one, and if of equal size, regularity, tightness and
+  brightness, the value is comparatively a matter of fancy. Those that
+  are dull and loose, or very coarse and flat in the curl, are of far
+  less market value.
+
+  All the above enumerated lambs are naturally a rusty black or brown,
+  and with very few exceptions are dyed a jet black. Lustre, however,
+  cannot be imparted unless the wool was originally of a silky nature.
+  Broadtails, size 10 × 5 in., are the very young of the Persian sheep,
+  and are killed before the wool has time to develop beyond the flat
+  wavy state which can be best compared to a piece of moiré silk. They
+  are naturally exceedingly light in weight, and those that are of an
+  even pattern, possessing a lustrous sheen, are costly. There is,
+  notwithstanding, a great demand for these from the fashionable world,
+  as not only are they very effective, but being so flat in the wool the
+  figure of the wearer can be shown as perfectly as in a garment made of
+  silk. It cannot be regarded as an economical fur, as the pelt is too
+  delicate to resist hard wear.
+
+    Persian Lamb price 12s. 6d. to 25s.
+    Broadtail      "   10s.     "  35s.
+
+  Astrachan, Shiraz and Bokharan lambs, size 22 by 9 in., are of a
+  coarser, looser curl, and chiefly used for coat linings, while the
+  Persians are used for outside of garments, collars, cuffs, stoles,
+  muffs, hats and trimmings and gloves. The so-called caracul lambs,
+  size 12 × 6 in., are the very young of the astrachan sheep, and the
+  pick of them are almost as effective as broadtails, although less fine
+  in the texture. See also remarks as to caracul kid under Goats, above.
+
+    Astrachan  price 1s.    to 5s. 6d.
+    Caracul Lamb "   2s. 6d " 10s. 6d.
+    Shiraz       "   4s. 6d " 10s.
+    Bokharan     "   1s. 6d "  3s. 6d.
+
+  Grey lambs, size 24 × 10 in., are obtained from the Crimea and known
+  in the trade as "crimmers." They are of a similar nature to the
+  caracul lambs, but looser in curl, ranging from a very light to a dark
+  grey. The best are the pale bluish greys, and are chiefly used for
+  ladies' coats, stoles, muffs and hats. Price 2s. to 6s. Mongolian
+  lambs, size 24 × 15 in., are of a short wavy loose curl, creamy white
+  colour, and are usually exported from China dressed, the majority
+  being ready-made into cross-shaped coats or linings. They are used
+  principally for linings of good evening wraps for ladies. Price 1s. to
+  2s. 6d. Slink lambs come from South America and China. The former are
+  very small and generally those that are stillborn. They have a
+  particularly thin pelt with very close wool of minute curl. The China
+  sorts are much larger. The smallest are used for glove linings and the
+  others for opera cloak linings. Price 1s. to 6s. 6d.
+
+  LEOPARD.--Size 3 to 6 ft. long. There are several kinds, the chief
+  being the snow or ounce, Chinese, Bengal, Persian, East Indian and
+  African. The first variety inhabit the Himalayas and are beautifully
+  covered with a deep soft fur quite long compared to the flat harsh
+  hair of the Bengal sort. The colours are pale orange and white with
+  very dark markings, a strong contrast making a fine effect. Most
+  artists prize these skins above all others. The Chinese are of a
+  medium orange brown colour, but full in fur. The East Indian are less
+  full and not so dark. The Bengal are dark and medium in colour, short
+  and hard hair, but useful for floor rugs, as they do not hold the dust
+  like the fuller and softer hair of the kinds previously named. They
+  are also used for drummers' aprons and saddle cloths in the Indian
+  army. The African are small with pale lemon colour grounds very
+  closely marked with black spots on the skin, the strong contrast
+  making a pleasing effect. Occasionally, where something very marked is
+  wanted, skating jackets and carriage aprons are made from the softest
+  and flattest of skins, but usually they are made into settee covers,
+  floor rugs and foot muffs. Value 2s. to 40s.
+
+  LION.--Size 5 to 6 ft. long. These skins are found in Africa, Arabia
+  and part of India, and are every year becoming scarcer. They are only
+  used for floor rugs, and the males are more highly esteemed on account
+  of the set-off of the mane. Value, lions' £10 to £100; lionesses' £5
+  to £25.
+
+  LYNX.--Size 45 × 20 in. The underwool is thinner than fox, but the top
+  hair is fine, silky and flowing, 4 in. long, of a pale grey, slightly
+  mottled with fine streaks and dark spots. The fur upon the flanks is
+  longer and white with very pronounced markings of dark spots, and this
+  part of the skin is generally worked separately from the rest and is
+  very effective for gown trimmings. Where the colour is of a sandy and
+  reddish hue the value is far less than where it is of a bluish tone.
+  They inhabit North America as far south as California, also Norway and
+  Sweden. Those from the Hudson Bay district and Sweden are the best and
+  are very similar. Those taken in Central Asia are mostly used locally.
+  For attire the skins manufactured in Europe are generally dyed black
+  or brown, in which state it has a similar appearance to dyed fox, but
+  having less thick underwool and finer hair flows freely. The finest
+  skins when dyed black are used very largely in America in place of the
+  dyed black fox so fashionable for mourning wear in Great Britain and
+  France. The British Hussar busbies are made of the dark brown lynx,
+  and it is the free silky easy movement of the fur with the least
+  disturbance in the atmosphere that gives it such a pleasing effect. It
+  is used for rugs in its natural state and also in Turkey as trimmings
+  for garments. Value 13s. 6d. to 56s.
+
+  LYNX CAT or BAY LYNX.--Is about half the size and depth of fur of a
+  lynx proper, and inhabits the central United States. It is a flat and
+  reddish fur compared to the lynx and is suitable for cheap carriage
+  aprons. A few come from Canada and are of better quality. Value 5s. to
+  15s.
+
+  MARMOT.--Size 18 × 12 in. Is a rodent and is found in considerable
+  numbers in the south of Prussia. The fur is a yellowish brown and
+  rather harsh and brittle and has no underwool. Since, however, the
+  value of all good furs has advanced, dyers and manufacturers have made
+  very successful efforts with this fur. The Viennese have been
+  particularly successful, and their method has been to dye the skins a
+  good brown and then not put in the dark stripes, which exist in sable
+  and mink, until the garment or article is finished, thus obtaining as
+  perfectly symmetrical effects as if the articles were made of small
+  skins instead of large ones. Marmots are also found in North America,
+  Canada and China; the best, however, come from Russia. It should
+  always be a cheap fur, having so few good qualities to recommend it.
+  Value 9d. to 2s. 6d.
+
+  MARTEN, AMERICAN.--See _Sable_, below.
+
+  MARTEN, BAUM.--Size 16 × 5 in. Is sometimes called the pine marten,
+  and is found in quantity in the wooded and mountainous districts of
+  Russia, Norway, Germany and Switzerland. It possesses a thick
+  underwool with strong top hair, and ranges from a pale to a dark
+  bluish brown. The best, from Norway, are very durable and of good
+  appearance and an excellent substitute for American sable. The tails
+  when split into two or three, with small strips of narrow tape so as
+  to separate the otherwise dense fur, formerly made very handsome sets
+  of trimmings, ties and muffs, and the probabilities are, as with other
+  fashions, such use will have its period of revival. Value 6s. to 85s.
+
+  MARTEN, BLACK.--See _Skunk_, below.
+
+  MARTEN, JAPANESE.--Size 16 × 5 in. Is of a woolly nature with rather
+  coarse top hair and quite yellow in colour. It is dyed for the cheap
+  trade for boas and muffs, but it is not an attractive fur at the best
+  of times. It lacks a silky, bright and fresh appearance, and therefore
+  is unlikely to be in great demand, except where economy is an object.
+  Value 6s. 6d. to 18s. 6d.
+
+  MARTEN, STONE.--Size and quality similar to the baum; the colour,
+  however, of the underwool is a stony white and the top hair is very
+  dark, almost black. They live in rocky and stony districts. Skins of a
+  pale bluish tone are generally used in their natural state for stoles,
+  boas and muffs, but the less clear coloured skins are dyed in
+  beautiful shades similar in density to the dark and valuable sables
+  from Russia, and are the most effective skins that can be purchased at
+  a reasonable price. The tails have also been worked, in the manner
+  explained with regard to the baum marten, as sets of trimmings and in
+  other forms. Stone martens are found in Russia, Bosnia, Turkey,
+  Greece, Germany, the Alps and France. The Bosnian and the French are
+  the best in colour. The Asiatic sorts are less woolly, but being silky
+  are useful when dyed. There are many from Afghanistan and India which
+  are too poor to interest the European markets. Value 7s. 6d. to 26s.
+
+  MINK.--Size 16 × 5 in. Is of the amphibious class and is found
+  throughout North America and in Russia, China and Japan. The underwool
+  is short, close and even, as is also the top hair, which is very
+  strong. The best skins are very dark and are obtained from Nova
+  Scotia. In the central states of America the colour is a good brown,
+  but in the north-west and south-west the fur is coarse and generally
+  pale. It is very durable for linings, and is an economical substitute
+  for sable for coats, capes, boas and trimmings. Values have greatly
+  increased, and the fur possessing good qualities as to colour and
+  durability will doubtless always be in good request. The Russian
+  species is dark but flat and poor in quality, and the Chinese and
+  Japanese are so pale that they are invariably dyed. These, however,
+  are of very inferior nature. Value of American 3s. 3d. to 40s.,
+  Japanese 3d. to 2s. 3d.
+
+  MOLE.--Size 3½ × 2½ in. Moles are plentiful in the British Isles and
+  Europe, and owing to their lovely velvety coats of exquisite blue
+  shade and to the dearness of other furs are much in demand. Though the
+  fur is cheap in itself, the expense of dressing and working up these
+  little skins is considerable, and they possess the unique charm of an
+  exceptional colour with little weight of pelt; the quality of
+  resistance to friction is, however, so slight as to make them
+  expensive in wear. The best are the dark blue from the Fen district of
+  Cambridgeshire in England. Value ½d. to 2d.
+
+  MONGOLIAN LAMBS.--See _Lambs_, above.
+
+  MONKEY, BLACK.--Size 18 × 10 in. Among the species of monkeys only one
+  interests to any extent the fur trade, and that is the black monkey
+  taken on the west coast of Africa (_Colobus satanas_). The hair is
+  very long, very black and bright with no underwool, and the white pelt
+  of the base of the hair, by reason of the great contrast of colour, is
+  very noticeable. The skins were in 1850 very fashionable in England
+  for stoles, muffs and trimmings, and in America also as recently as
+  1890. They are now mostly bought for Germany and the continent. Value
+  6d. to 1s. 6d.
+
+  MOUFLON.--Size 30 × 15 in. Is a sheep found in Russia and Corsica and
+  now very little in demand, and but few are imported into Great
+  Britain. Many Mongolian goats with the long hairs pulled out are sold
+  as mouflon. Value 4s. to 10s. 6d.
+
+  MUSK-OX.--Size 6 × 3 ft. These animals have a dense coat of fine, long
+  brown wool, with very long dark brown hair on the head, flanks and
+  tail, and, in the centre, a peculiar pale oval marking. There is no
+  other fur that is so thick, and it is eminently suitable for sleighing
+  rugs, for which purpose it is highly prized in Canada. The musk-ox
+  inhabits the north part of Greenland and part of Canada, but in very
+  limited numbers. Value 10s. to 130s.
+
+  MUSQUASH or MUSK-RAT, BROWN and BLACK RUSSIAN.--Size 12 × 8 in. A very
+  prolific rodent of the amphibious class obtained from Canada and the
+  United States, similar in habit to the English vole, with a fairly
+  thick and even brown underwool and rather strong top dark hair of
+  medium density. It is a very useful fur for men's coat linings and
+  ladies' driving or motoring coats, being warm, durable and not too
+  heavy. If the colour were less motley and the joins between the skins
+  could be made less noticeable, it would be largely in demand for
+  stoles, ties and muffs. As it is, this fur is only used for these
+  smaller articles for the cheaper trade. It has, however, of later
+  years been "unhaired," the underwool clipped very even and then dyed
+  seal colour, in which way very useful and attractive garments are
+  supplied at less than half the cost of the cheaper sealskins. They do
+  not wear as well, however, as the pelt and the wool are not of a
+  strength comparable to those of sealskin. With care, however, such a
+  garment lasts sufficiently long to warrant the present outlay. Value
+  5½d. to 1s. 9d.
+
+  There is a so-called black variety found in Delaware and New Jersey,
+  but the number is very small compared to the brown species. They are
+  excellent for men's coat linings and the outside of ladies' coats, for
+  stoles, muffs, collars and cuffs. Value 10d. to 3s. 7d.
+
+  The Russian musquash is very small, 7 × 4 in., and is limited in
+  numbers compared to the brown. Only a few thousands are imported to
+  London. It is of a very pretty silvery-blue shade of even wool with
+  very little silky top hair, having silvery-white sides and altogether
+  a very marked effect. The odour, however, even after dressing is
+  rather pungent of musk, which is generally an objection. Value 4s. to
+  6s. 6d.
+
+  NUTRIA.--Size 20 × 12 in. Is a rodent known in natural history as the
+  coypu, about half the size of a beaver, and when unhaired has not more
+  than half, generally less, the depth of fur, which is also not so
+  close. Formerly the fur was only used for hatters' felt, but with the
+  rise in prices of furs these skins have been more carefully removed
+  and--with improved dressing, unhairing and silvering processes--the
+  best provides a very effective and suitable fur for ladies' coats,
+  capes, stoles, muffs, hats and gloves, while the lower qualities make
+  very useful, light-weighted and inexpensive linings for men's or
+  women's driving coats. It is also dyed sealskin colour, but its woolly
+  nature renders it less effective than the more silky musquash. They
+  are obtained from the northern part of South America. Value is. 6d. to
+  6s. 6d.
+
+  OCELOT.--Size 36 × 13 in. Is of the nature of a leopard and prettily
+  marked with stripes and oblong spots. Only a few are now imported from
+  South America for carriage aprons or mats. The numbers are very
+  limited. Value 1s. to 2s. 6d.
+
+  OPOSSUM, AMERICAN.--Size 18 × 10 in. Is a marsupial, a class with this
+  exception not met with out of Australia. The underwool is of a very
+  close frizzy nature, and nearly white, with long bluish grey mixed
+  with some black top hair. It is only found in the central sections of
+  the United States. About 1870 in England it was dyed dark brown or
+  black and used for boas, muffs and trimmings, but until recently has
+  been neglected on the continent. With, however, recent experiments in
+  brown and skunk coloured dyes, it bids fair to become a popular fur.
+  Value 2½d. to 5s. 6d.
+
+  OPOSSUM, AUSTRALIAN.--Size 16 × 8 in. Is a totally different nature of
+  fur to the American. Although it has wool and top hair, the latter is
+  so sparse and fine that the coat may be considered as one of close
+  even wool. The colour varies according to the district of origin, from
+  a blue grey to yellow with reddish tones. Those from the neighbourhood
+  of Sydney are light clear blue, while those from Victoria are dark
+  iron grey and stronger in the wool. These animals are most prolific
+  and evidently increasing in numbers. Their fur is pretty, warm and as
+  yet inexpensive, and is useful for rugs, coat linings, stoles, muffs,
+  trimmings and perambulator aprons. The worst coloured ones are
+  frequently dyed black and brown. The most pleasing natural grey come
+  from Adelaide. The reddest are the cheapest. Value 3¾d. to 3s. 6d.
+
+  OPOSSUM, RINGTAILED.--Size 7 × 4 in. Has a very short close and dark
+  grey wool, some being almost black. There are but a few thousands
+  imported, and being so flat they are only of use for coat linings, but
+  they are very warm and light in weight. Value 6d. to 10d.
+
+  OPOSSUM, TASMANIAN (grey and black).--Size 20 × 10 in. Is of a similar
+  description, but darker and stronger in the wool and larger. Besides
+  these there are some very rich brown skins which were formerly in such
+  request in Europe, especially Russia, that undue killing occurred
+  until 1899, when the government stopped for a time the taking of any
+  of this class. They are excellent for carriage aprons, being not only
+  very light in weight and warm, but handsome. Value 2s. 6d. to 8s. 6d.
+
+  OTTER, RIVER.--The size varies considerably, as does the underwool and
+  the top hair, according to the country of origin. There are few rivers
+  in the world where they do not live. But it is in the colder northern
+  regions that they are found in the greatest numbers and with the best
+  fur or underwool, the top hair, which, with the exception of the
+  scarce and very rich dark brown specimens they have in common with
+  most aquatic animals, is pulled out before the skins are manufactured.
+  Most of the best river otter comes from Canada and the United States
+  and averages 36 × 18 in. in size. Skins from Germany and China are
+  smaller, and shorter in the wool. The colours of the under wools of
+  river otters vary, some being very dark, others almost yellow. Both as
+  a fur and as a pelt it is extremely strong, but owing to its short and
+  close wool it is usually made up for the linings, collars and cuffs of
+  men's coats. A large number of skins, after unhairing, is dyed seal
+  colour and used in America. Those from hot climates are very poor in
+  quality. Value 28s. to 118s.
+
+  OTTER, SEA.--Size 50 × 25 in. Possesses one of the most beautiful of
+  coats. Unlike other aquatic animals the skin undergoes no process of
+  unhairing, the fur being of a rich dense silky wool with the softest
+  and shortest of water hairs. The colours vary from pale grey brown to
+  a rich black, and many have even or uneven sprinkling of white or
+  silvery-white hairs. The blacker the wool and the more regular the
+  silver points, the more valuable the skin. Sea otters are,
+  unfortunately, decreasing in numbers, while the demand is increasing.
+  The fur is most highly esteemed in Russia and China; in the latter
+  country it is used to trim mandarins' state robes. In Europe and
+  America it is much used for collar, long facings and cuffs of a
+  gentleman's coat; such a set may cost from £200 to £600, and in all
+  probability will soon cost more. Taking into consideration the size,
+  it is not so costly as the natural black fox, or the darkest Russian
+  sable, which is now the most expensive of all. The smaller and young
+  sea otters of a grey or brown colour are of small value compared to
+  the large dark and silvery ones. Value £10 to £220. A single skin has
+  been known to fetch £400.
+
+  OUNCE.--See _Leopard_, above.
+
+  PERSIAN LAMBS.--See _Lambs_, above.
+
+  PLATYPUS.--Size 12 × 8 in. One of the most singular of fur-bearing
+  animals, being the link between bird and beast. It has fur similar to
+  otter, is of aquatic habits, being web-footed with spurs of a cock and
+  the bill of a duck. The skins are not obtained in any numbers, but
+  being brought over by travellers as curiosities and used for muffs,
+  collars and cuffs, &c., they are included here for reference. Value
+  2s. to 3s. 6d.
+
+  _Pony_ or _Tatar Foal._--Size 36 × 20 in. These skins are of
+  comparatively recent importation to the civilized world. They are
+  obtained from the young of the numerous herds of wild horses that roam
+  over the plains of Turkestan. The coat is usually a shade of brown,
+  sometimes greyish, fairly bright and with a suggestion of waviness.
+  Useful for motor coats. Value 3s. to 10s. 6d.
+
+  PUMA.--Size 4½ × 3 ft. Is a native of South America, similar to a lion
+  in habits and colour of coat. The hair and pelt is, however, of less
+  strength, and only a few are now used for floor rugs. Value 5s. to
+  10s.
+
+  RACCOON.--Size 20 × 12 in. Is an animal varying considerably in size
+  and in quality and colour of fur, according to the part of North
+  America in which it is found. In common parlance, it may be described
+  as a species of wild dog with close affinity to the bear. The
+  underwool is 1 to 1½ in. deep, pale brown, with long top hairs of a
+  dark and silvery-grey mixture of a grizzly type, the best having a
+  bluish tone and the cheapest a yellowish or reddish-brown. A limited
+  number of very dark and black sorts exist and are highly valued for
+  trimmings. The very finest skins are chiefly used for stoles and
+  muffs, and the general run for coachmen's capes and carriage rugs,
+  which are very handsome when the tails, which are marked with rings of
+  dark and light fur alternately, are left on. Raccoons are used in
+  enormous quantities in Canada for men's coats, the fur outside. The
+  poorer qualities are extensively bought and made up in a similar way
+  for Austria-Hungary and Germany. These make excellent linings for
+  coats or footsacks for open driving in very cold climates. The worst
+  coloured skins are dyed black or brown and are used for British
+  military busbies, or caps, stoles, boas, muffs and coachmen's capes.
+  The best skins come from the northern parts of the United States. A
+  smaller and poorer species inhabits South America, and a very few are
+  found in the north of India, but these do not interest the European
+  trade. From Japan a similar animal is obtained in smaller quantities
+  with very good but longer fur, of yellowish motley light-brown shades.
+  It is more often imported and sold as Japanese fox, but its
+  resemblance to the fur of the American raccoon is so marked as to
+  surely identify it. When dyed dark blue or skunk colour it is
+  good-looking and is sold widely in Europe. Raccoon skins are also
+  frequently unhaired, and if the underwool is of good quality the
+  effect is similar to beaver. It is the most useful fur for use in
+  America or Russia, having a full quantity of fur which will retain
+  heat. Value 10d. to 26s.
+
+  SABLE, AMERICAN and CANADIAN.--Size 17 × 5 in. The skins are sold in
+  the trade sale as martens, but as there are many that are of a very
+  dark colour and the majority are almost as silky as the Russian sable,
+  the retail trade has for generations back applied the term of sable to
+  this fur. The prevailing colour is a medium brown, and many are quite
+  yellow. The dyeing of these very pale skins has been for so long well
+  executed that it has been possible to make very good useful and
+  effective articles of them at a moderate price compared to Russian
+  sable. The finest skins are found in the East Main and the Esquimaux
+  Bay, in the Hudson's Bay Company's districts, and the poorest in
+  Alaska. They are not found very far south of the northern boundary of
+  the United States. The best skins are excellent in quality, colour and
+  effect, and wear well. Value 27s. 3d. to 290s.
+
+  SABLE, CHINESE and JAPANESE.--Size 14 × 4½ in. These are similar to
+  the Amur skins previously referred to, but of much poorer quality and
+  generally only suitable for linings. The very palest skins are dyed
+  and made by the Chinese into mandarins' coats, in which form they are
+  found in the London trade sales, but being overdressed they are
+  inclined to be loose in the hair and the colour of the dye is not
+  good. The Japanese kind are imported raw, but are few in numbers, very
+  pale and require dyeing. Value 15s. to 150s.
+
+  SABLE, RUSSIAN.--Size 15 × 5 in. These skins belong to a species of
+  marten, very similar to the European and American, but much more silky
+  in the nature of their fur. They have long been known as "sables,"
+  doubtless owing to the density of colour to which many of them attain,
+  and they have always been held in the highest esteem by connoisseurs
+  as possessing a combination of rare qualities. The underwool is close,
+  fine and very soft, the top hair is regular, fine, silky and flowing,
+  varying from 1½ to 2½ in. in depth. In colour they range from a pale
+  stony or yellowish shade to a rich dark brown, almost black with a
+  bluish tone. The pelts are exceedingly fine and close in texture and,
+  although of little weight, are very durable, and articles made of them
+  produce a sensation of warmth immediately they are put upon the body.
+
+  The Yakutsk, Okhotsk and Kamschatka sorts are good, the last being the
+  largest and fullest furred, but of less density of colour than the
+  others. Many from other districts are pale or yellowish brown, and
+  those from Saghalien are poor in quality. The most valuable are the
+  darkest from Yakutsk in Siberia, particularly those that have silvery
+  hairs evenly distributed over the skin. These however are exceedingly
+  scarce, and when a number are required to match for a large garment,
+  considerable time may be necessary to collect them. This class of skin
+  is the most expensive fur in the world, reckoning values by a square
+  foot unit.
+
+  The Amur skins are paler, but often of a pretty bluish stony tone with
+  many frequently interspersed silvery hairs. The quality too is lower,
+  that is, the fur is not so close or deep, but they are very effective,
+  particularly for close-fitting garments, as they possess the least
+  appearance of bulk. The paler skins from all districts in Siberia are
+  now cleverly coloured or "topped," that is, just the tips of the hair
+  are stained dark, and it is only an expert who can detect them from
+  perfectly natural shades. If this colouring process is properly
+  executed it remains fairly fast. Notwithstanding the reported rights
+  of the Russian imperial authorities over some regions with respect to
+  these and other valuable fur-bearing animals, there are in addition to
+  the numbers regularly sent to the trade auction sales in London many
+  good parcels of raw skins to be easily bought direct, provided price
+  is not the first consideration. Value 25s. to 980s.
+
+  SEAL, FUR.--Sizes range from 24 × 15 in. to 55 × 25 in., the width
+  being taken at the widest part of the skin after preparation. The
+  centre of the skin between the fins is very narrow and the skins taper
+  at each end, particularly at the tail. The very small pups are of a
+  beautiful quality, but too tiny to make into garments, and, as the aim
+  of a good furrier is to avoid all lateral or cross seams, skins are
+  selected that are the length of the garment that is to be made. The
+  most useful skins for coats are the large pups 42 in. long, and the
+  quality is very good and uniform. The largest skins, known in the
+  trade as "wigs," which range up to 8 ft. in length, are uneven and
+  weak in the fur, and hunters do not seek to obtain them. The supply of
+  the best sort is chiefly from the North Pacific, viz. Pribilof
+  Islands, Alaska, north-west coast of America, Copper Island of the
+  Aleutian group near to Kamschatka, Robben Island and Japan. Other
+  kinds are taken from the South Pacific and South Atlantic Oceans,
+  around Cape Horn, the Falkland Islands up to Lobos Islands at the
+  entrance of the La Plata river, off the Cape of Good Hope and Crozet
+  Isles. With, however, the exception of the pick of the Lobos Island
+  seals the fur of the southern sea seals is very poor and only suitable
+  for the cheapest market. Formerly many skins were obtained from New
+  Zealand and Australia, but the importation is now small and the
+  quality not good. The preparation of seal skin occupies a longer time
+  than any other fur skin, but its fine rich effect when finished and
+  its many properties of warmth and durability well repay it. Value 10s.
+  to 232s.
+
+  SEAL, HAIR.--There are several varieties of these seals in the seas
+  stretching north from Scotland, around Newfoundland, Greenland and the
+  north-west coast of America, and they are far more numerous than fur
+  seals. Generally they have coarse rigid hair and none possess any
+  underwool. They are taken principally for the oil and leather they
+  yield. Some of the better haired sorts are dyed black and brown and
+  used for men's motor coats when quite a waterproof garment is wanted,
+  and they are used also for this quality in China. The young of the
+  Greenland seals are called whitecoats on account of the early growth
+  being of a yellowish white colour; the hair is ¾ to 1 in. long, and at
+  this early stage of their life is soft compared to that of the older
+  seals. These fur skins are dyed black or dark brown and are used for
+  military caps and hearth-rugs. Value 2s. to 15s. There are fewer hair
+  seals in the southern than in the northern seas.
+
+  SHEEP.--Vary much in size and in quality of wool. Many of the domestic
+  kind in central and northern Europe and Canada are used for drivers'
+  and peasants' coat linings, &c. In Great Britain many coats of the
+  home-reared sheep, having wools two and a half to five inches long,
+  are dyed various colours and used as floor rugs. Skins with very short
+  wool are dyed black and used for military saddle-cloths. The bulk,
+  however, is used in the wool trade. The Hungarian peasants are very
+  fond of their natural brown sheep coats, the leather side of which is
+  not lined, but embellished by a very close fancy embroidery, worked
+  upon the leather itself; these garments are reversible, the fur being
+  worn inside when the weather is cold. Chinese sheep are largely used
+  for cheap rugs. Value of English sheep from 3s. to 10s.
+
+  SKUNK or BLACK MARTEN.--Size 15 × 8 in. The underwool is full and
+  fairly close with glossy, flowing top hair about 2½ in. long. The
+  majority have two stripes of white hair, extending the whole length of
+  the skin, but these are cut out by the manufacturing furrier and sold
+  to the dealers in pieces for exportation. The animals are found widely
+  spread throughout North and South America. The skins which are of the
+  greatest interest to the European trade are those from North America,
+  the South American species being small, coarse and generally brown.
+  The best skins come from Ohio and New York. If it were not for its
+  disagreeable odour, skunk would be worth much more than the usual
+  market value, as it is naturally the blackest fur, silky in appearance
+  and most durable. The improved dressing processes have to a large
+  extent removed the naturally pungent scent. The fur is excellent for
+  stoles, boas, collars, cuffs, muffs and trimmings. Value 1s. 6d. to
+  11s.
+
+  SOUSLIK.--Size 7 in. × 2¼. Is a small rodent found in the south of
+  Russia and also in parts of America. It has very short hair and is a
+  poor fur even for the cheapest linings, which is the only use to which
+  the skin could be put. It is known as kaluga when imported in
+  ready-made linings from Russia where the skins are dressed and worked
+  in an inferior way. Value 1d. to 3d.
+
+  SQUIRREL.--Size 10 × 5 in. This measurement refers to the Russian and
+  Siberian sorts, which are the only kind imported for the fur. The
+  numerous other species are too poor in their coats to attract notice
+  from fur dealers. The back of the Russian squirrel has an even close
+  fur varying from a clear bluish-grey to a reddish-brown, the bellies
+  in the former being of a flat quality and white, in the latter
+  yellowish. The backs are worked into linings separately, as are the
+  bellies or "locks." The pelts, although very light, are tough and
+  durable, hence their good reputation for linings for ladies' walking
+  or driving coats. The best skins also provide excellent material for
+  coats, capes, stoles, ties, collars, cuffs, gloves, muffs, hoods and
+  light-weight carriage aprons. The tails are dark and very small, and
+  when required for ends of boas three or four are made as one. Value
+  per skin from 2½d. to 1s. 1d.
+
+  TIBET LAMB.--Size 27 × 13 in. These pretty animals have a long, very
+  fine, silky and curly fleece of a creamy white. The majority are
+  consigned to the trade auction sales in London ready dressed and
+  worked into cross-shaped coats, and the remainder, a fourth of the
+  total, come as dressed skins. They are excellent for trimmings of
+  evening mantles and for children's ties, muffs and perambulator
+  aprons. The fur is too long and bulky for linings. Value per skin from
+  4s. 6d. to 8s. 6d.
+
+  TIGER.--Size varies considerably, largest about 10 ft. from nose to
+  root of tail. Tigers are found throughout India, Turkestan, China,
+  Mongolia and the East Indies. The coats of the Bengal kind are short
+  and of a dark orange brown with black stripes, those from east or
+  further India are similar in colour, but longer in the hair, while
+  those from north of the Himalayas and the mountains of China are not
+  only huge in size, but have a very long soft hair of delicate orange
+  brown with very white flanks, and marked generally with the blackest
+  of stripes. The last are of a noble appearance and exceedingly scarce.
+  They all make handsome floor rugs.
+
+    Value of the Indian       from  £3 to £15.
+      "     "    Chinese        "  £10 to £65.
+
+  VICUNA is a species of long-necked sheep native to South America,
+  bearing some resemblance to the guanaco, but the fur is shorter,
+  closer and much finer. The colour is a pale golden-brown and the fur
+  is held in great repute in South America for carriage rugs. The supply
+  is evidently small as the prices are high. There is scarcely a
+  commercial quotation in London, few coming in except from private
+  sources. 2s. 6d. to 5s. 6d. may be considered as the average value.
+
+  WALLABY.--See _Kangaroo_, above.
+
+  WALLAROO.--See _Kangaroo_, above.
+
+  WOLF.--Size 50 × 25 in. Is closely allied to the dog tribe and, like
+  the jackals, is found through a wide range of the world,--North and
+  South America, Europe and Asia. Good supplies are available from North
+  America and Siberia and a very few from China. The best are the full
+  furred ones of a very pale bluish-grey with fine flowing black top
+  hair, which are obtained from the Hudson Bay district. Those from the
+  United States and Asia are harsher in quality and browner. A few black
+  American specimens come into the market, but usually the quality is
+  poor compared to the lighter furred animal. The Siberian is smaller
+  than the North American and the Russian still smaller. Besides the
+  wolf proper a large number of prairie or dog wolves from America and
+  Asia are used for cheaper rugs. In size they are less than half that
+  of a large wolf and are of a motley sandy colour. Numbers of the
+  Russian are retained for home use. The finest wolves are very light
+  weighted and most suitable for carriage aprons, in fact, ideal for the
+  purpose, though lacking the strength of some other furs.
+
+    Wolves       value  2s. 6d. to 64s.
+    Dog wolves     "    1s.     to  2s. 6d.
+
+  WOLVERINE.--Size 16 × 18 in. Is native to America, Siberia, Russia and
+  Scandinavia and generally partakes of the nature of a bear. The
+  underwool is full and thick with strong and bright top hair about 2½
+  in. long. The colour is of two or three shades of brown in one skin,
+  the centre being an oval dark saddle, edged as it were with quite a
+  pale tone and merging to a darker one towards the flanks. This
+  peculiar character alone stamps it as a distinguished fur, in addition
+  to which it has the excellent advantage of being the most durable fur
+  for carriage aprons, as well as the richest in colour. It is not
+  prolific, added to which it is very difficult to match a number of
+  skins in quality as well as colour. Hence it is an expensive fur, but
+  its excellent qualities make it valuable. The darkest of the least
+  coarse skins are worth the most. Prices from 6s. to 37s.
+
+  WOMBAT, KOALA or Australian Bear.--Size 20 × 12 in. Has light grey or
+  brown close thick wool half an inch deep without any top hair, with a
+  rather thick spongy pelt. It is quite inexpensive and only suitable
+  for cheap rough coats, carriage rugs, perambulator aprons and linings
+  for footbags. The coats are largely used in western America and
+  Canada. Value 3d. to 1s. 8½d.
+
+_Preparing and Dressing._--A furrier or skin merchant must possess a
+good eye for colour to be successful, the difference in value on this
+subtle matter solely (in the rarer precious sorts, especially sables,
+natural black, silver and blue fox, sea otters, chinchillas, fine mink,
+&c.) being so considerable that not only a practised but an intuitive
+sense of colour is necessary to accurately determine the exact merits of
+every skin. In addition to this a knowledge is required of what the
+condition of a pelt should be; a good judge knows by experience whether
+a skin will turn out soft and strong, after dressing, and whether the
+hair is in the best condition of strength and beauty. The dressing of
+the pelt or skin that is to be preserved for fur is totally different to
+the making of leather; in the latter tannic acid is used, but never
+should be with a fur skin, as is so often done by natives of districts
+where a regular fur trade is not carried on. The results of applying
+tannic acid are to harden the pelt and discolour and weaken the fur. The
+best methods for dressing fur skins are those of a tawer or currier, the
+aim being to retain all the natural oil in the pelt, in order to
+preserve the natural colour of the fur, and to render the pelt as supple
+as possible. Generally the skins are placed in an alkali bath, then by
+hand with a blunt wooden instrument the moisture of the pelt is worked
+out and it is drawn carefully to and fro over a straight, dull-edged
+knife to remove any superfluous flesh and unevenness. Special grease is
+then rubbed in and the skin placed in a machine which softly and
+continuously beats in the softening mixture, after which it is put into
+a slowly revolving drum, fitted with wooden paddles, partly filled with
+various kinds of fine hard sawdust according to the nature of the furs
+dealt with. This process with a moderate degree of heat thoroughly
+cleans it of external greasy matter, and all that is necessary before
+manufacturing is to gently tap the fur upon a leather cushion stuffed
+with horsehair with smooth canes of a flexibility suited to the strength
+of the fur. After dressing most skins alter in shape and decrease in
+size.
+
+With regard to the merits of European dressing, it may be fairly taken
+that English, German and French dressers have specialities of
+excellence. In England, for instance, the dressing of sables, martens,
+foxes, otters, seals, bears, lions, tigers and leopards is first rate;
+while with skunk, mink, musquash, chinchillas, beavers, lambs and
+squirrels, the Germans show better results, particularly in the last.
+The pelt after the German dressing is dry, soft and white, which is due
+to a finishing process where meal is used, thus they compare favourably
+with the moister and consequently heavier English finish. In France they
+do well with cheaper skins, such as musquash, rabbit and hare, which
+they dye in addition to dressing. Russian dressing is seldom reliable;
+not only is there an unpleasant odour, but in damp weather the pelts
+often become clammy, which is due to the saline matter in the dressing
+mixture. Chinese dressing is white and supple, but contains much powder,
+which is disagreeable and difficult to get rid of, and in many instances
+the skin is rendered so thin that the roots of the fur are weakened,
+which means that it is liable to shed itself freely, when subject to
+ordinary friction in handling or wearing. American and Canadian dressing
+is gradually improving, but hitherto their results have been inferior to
+the older European methods.
+
+In the case of seal and beaver skins the process is a much more
+difficult one, as the water or hard top hairs have to be removed by hand
+after the pelt has been carefully rendered moist and warm. With seal
+skins the process is longer than with any other fur preparation and the
+series of processes engage many specialists, each man being constantly
+kept upon one section of the work. The skins arrive simply salted. After
+being purchased at the auction sales they are washed, then stretched
+upon a hoop, when all blubber and unnecessary flesh is removed, and the
+pelt is reduced to an equal thickness, but not so thin as it is finally
+rendered. Subsequently the hard top hairs are taken out as in the case
+of otters and beavers and the whole thoroughly cleaned in the revolving
+drums. The close underwool, which is of a slightly wavy nature and
+mostly of a pale drab colour, is then dyed by repeated applications of a
+rich dark brown colour, one coat after another, each being allowed to
+thoroughly dry before the next is put on, till the effect is almost a
+lustrous black on the top. The whole is again put through the cleaning
+process and evenly reduced in thickness by revolving emery wheels, and
+eventually finished off in the palest buff colour.
+
+The English dye for seals is to-day undoubtedly the best; its
+constituents are more or less of a trade secret, but the principal
+ingredients comprise gall nuts, copper dust, camphor and antimony, and
+it would appear after years of careful watching that the atmosphere and
+particularly the water of London are partly responsible for good and
+lasting results. The Paris dyers do excellent work in this direction,
+but the colour is not so durable, probably owing to a less pure water.
+In America of late, strides have been made in seal dyeing, but
+preference is still given to London work. In Paris, too, they obtain
+beautiful results in the "topping" or colouring Russian sables and the
+Germans are particularly successful in dyeing Persian lambs black and
+foxes in all blue, grey, black and smoke colours and in the insertion of
+white hairs in imitation of the real silver fox. Small quantities of
+good beaver are dyed in Russia occasionally, and white hairs put in so
+well that an effect similar to sea otter is obtained.
+
+The process of inserting white hairs is called in the trade "pointing,
+"and is either done by stitching them in with a needle or by adhesive
+caoutchouc.
+
+The Viennese are successful in dyeing marmot well, and their cleverness
+in colouring it with a series of stripes to represent the natural
+markings of sable which has been done after the garments have been made,
+so as to obtain symmetry of lines, has secured for them a large trade
+among the dealers of cheap furs in England and the continent.
+
+_Manufacturing Methods and Specialities._--In the olden times the
+Skinners' Company of the city of London was an association of furriers
+and skin dressers established under royal charter granted by Edward III.
+At that period the chief concern of the body was to prevent buyers from
+being imposed upon by sellers who were much given to offering old furs
+as new; a century later the Skinners' Company received other charters
+empowering them to inspect not only warehouses and open markets, but
+workrooms. In 1667 they were given power to scrutinize the preparing of
+rabbit or cony wool for the wool trade and the registration of the then
+customary seven years' apprenticeship. To-day all these privileges and
+powers are in abeyance, and the interest that they took in the fur trade
+has been gradually transferred to the leather-dressing craft.
+
+The work done by English furriers was generally good, but since about
+1865 has considerably improved on account of the influx of German
+workmen, who have long been celebrated for excellent fur work, being In
+their own country obliged to satisfy officially appointed experts and to
+obtain a certificate of capacity before they can be there employed. The
+French influence upon the trade has been, and still is, primarily one of
+style and combination of colour, bad judgment in which will mar the
+beauty of the most valuable furs. It is a recognized law among
+high-class furriers that furs should be simply arranged, that is, that
+an article should consist of one fur or of two furs of a suitable
+contrast, to which lace may be in some cases added with advantage. As
+illustrative of this, it may be explained that any brown tone of fur
+such as sable, marten, mink, black marten, beaver, nutria, &c., will go
+well upon black or very dark-brown furs, while those of a white or grey
+nature, such as ermine, white lamb, chinchilla, blue fox, silver fox,
+opossum, grey squirrel, grey lamb, will set well upon seal or black
+furs, as Persian lamb, broadtail, astrachan, caracul lamb, &c. White is
+also permissible upon some light browns and greys, but brown motley
+colours and greys should never be in contrast. One neutralizes the other
+and the effect is bad. The qualities, too have to be considered--the
+fulness of one, the flatness of the other, or the coarseness or fineness
+of the furs. The introduction of a third fur in the same garment or
+indiscriminate selection of colours of silk linings, braids, buttons,
+&c., often spoils an otherwise good article.
+
+With regard to the natural colours of furs, the browns that command the
+highest prices are those that are of a bluish rather than a reddish
+tendency. With greys it is those that are bluish, not yellow, and with
+white those that are purest, and with black the most dense, that are
+most esteemed and that are the rarest.
+
+Perhaps for ingenuity and the latest methods of manipulating skins in
+the manufacturing of furs the Americans lead the way, but as fur cutters
+are more or less of a roving and cosmopolitan character the larger fur
+businesses in London, Berlin, Vienna, St Petersburg, Paris and New York
+are guided by the same thorough and comparatively advanced principles.
+
+During the period just mentioned the tailors' methods of scientific
+pattern cutting have been adopted by the leading furriers in place of
+the old chance methods of fur cutters, so that to-day a fur garment may
+be as accurately and gracefully fitted as plush or velvet, and with all
+good houses a material pattern is fitted and approved before the skins
+are cut.
+
+Through the advent of German and American fur sewing-machines since
+about 1890 fur work has been done better and cheaper. There are,
+however, certain parts of a garment, such as the putting in of sleeves
+and placing on of collars, &c., that can only be sewn by hand. For
+straight seams the machines are excellent, making as neat a seam as is
+found in glove work, unless, of course, the pelts are especially heavy,
+such as bears and sheep rugs.
+
+A very great feature of German and Russian work is the fur linings
+called rotondes, sacques or plates, which are made for their home use
+and exportation chiefly to Great Britain, America and France.
+
+In Weissenfels, near Leipzig, the dressing of Russian grey squirrel and
+the making it into linings is a gigantic industry, and is the principal
+support of the place. After the dressing process the backs of the
+squirrels are made up separately from the under and thinner white and
+grey parts, the first being known as squirrel-back and the other as
+squirrel-lock linings. A few linings are made from entire skins and
+others are made from the quite white pieces, which in some instances are
+spotted with the black ear tips of the animals to resemble ermine. The
+smaller and uneven pieces of heads and legs are made up into linings, so
+there is absolutely no waste. Similar work is done in Russia on almost
+as extensive a scale, but neither the dressing nor the work is so good
+as the German.
+
+The majority of heads, gills or throats, sides or flanks, paws and
+pieces of skins cut up in the fur workshops of Great Britain, America
+and France, weighing many tons, are chiefly exported to Leipzig, and
+made up in neighbouring countries and Greece, where labour can be
+obtained at an alarmingly low rate. Although the sewing, which is
+necessarily done by hand, the sections being of so unequal and tortuous
+a character, is rather roughly executed, the matching of colours and
+qualities is excellent. The enormous quantities of pieces admit of good
+selection and where odd colours prevail in a lining it is dyed. Many
+squirrel-lock linings are dyed blue and brown and used for the outside
+of cheap garments. They are of little weight, warm and effective, but
+not of great durability.
+
+The principal linings are as follows: Sable sides, sable heads and paws,
+sable gills, mink sides, heads and gills, marten sides, heads and gills,
+Persian lamb pieces and paws, caracul lamb pieces or paws, musquash
+sides and heads, nutria sides, genet pieces, raccoon sides or flanks,
+fox sides, kolinski whole skins, and small rodents as kaluga and
+hamster. The white stripes cut out of skunks are made into rugs.
+
+Another great source of inexpensive furs is China, and for many years
+past enormous quantities of dressed furs, many of which are made up in
+the form of linings and Chinese loose-shaped garments, have been
+imported by England, Germany and France for the lower class of business;
+the garments are only regarded as so much fur and are reworked. With,
+however, the exception of the best white Tibet lambs, the majority of
+Chinese furs can only be regarded as inferior material. While the work
+is often cleverly done as to matching and manipulation of the pelt which
+is very soft, there are great objections in the odour and the
+brittleness or weakness of the fur. One of the most remarkable results
+of the European intervention in the Boxer rising in China (1900) was the
+absurd price paid for so-called "loot" of furs, particularly in
+mandarins' coats of dyed and natural fox skins and pieces, and natural
+ermine, poor in quality and yellowish in colour; from three to ten times
+their value was paid for them when at the same time huge parcels of
+similar quality were warehoused in the London docks, because purchasers
+could not be found for them.
+
+With regard to Japanese furs, there is little to commend them. The best
+are a species of raccoon usually sold as fox, and, being of close long
+quality of fur, they are serviceable for boas, collars, muffs and
+carriage aprons. The sables, martens, minks and otters are poor in
+quality, and all of a very yellow colour and they are generally dyed for
+the cheap trade. A small number of very pretty guanaco and vicuna
+carriage rugs are imported into Europe, and many come through travellers
+and private sources, but generally they are so badly dressed that they
+are quite brittle upon the leather side. Similar remarks are applicable
+to opossum rugs made in Australia. From South Africa a quantity of
+jackal, hyena, fox, leopard and sheep karosses, i.e. a peculiarly shaped
+rug or covering used by native chiefs, is privately brought over. The
+skins are invariably tanned and beautifully sewn, the furs are generally
+flat in quality and not very strong in the hair, and are retained' more
+as curiosities than for use as a warm covering.
+
+_Hatters' Furs and Cloths and Shawls._--The hat trade is largely
+interested in the fur piece trade, the best felt hats being made from
+beaver and musquash wool and the cheaper sorts from nutria, hare and
+rabbit wools. For weaving, the most valuable pieces are mohair taken
+from the angora and vicuna. They are limited in quantity and costly, and
+the trade depends upon various sorts of other sheep and goat wools for
+the bulk of its productions.
+
+_Frauds and Imitations._--The opportunities for cheating in the fur
+trade are very considerable, and most serious frauds have been
+perpetrated in the selling of sables that have been coloured or
+"topped"; that is, just the tips of the hairs stained dark to represent
+more expensive skins. It is only by years of experience that some of
+these colourings can be detected. Where the skins are heavily dyed it is
+comparatively easy to see the difference between a natural and a dyed
+colour, as the underwool and top hair become almost alike and the
+leather is also dark, whereas in natural skins the base of the underwool
+is much paler than the top, or of a different colour, and the leather Is
+white unless finished in a pale reddish tone as is sometimes the case
+when mahogany sawdust is used in the final cleaning. As has been
+explained, sable is a term applied for centuries past to the darker
+sorts of the Russian Siberian martens, and for years past the same term
+has been bestowed by the retail trade upon the American and Canadian
+martens. The baum and stone martens caught in France, the north of
+Turkey and Norway are of the same family, but coarser in underwool and
+the top hair is less in quantity and not so silky. The kolinski, or as
+it is sometimes styled Tatar sable, is the animal, the tail of which
+supplies hair for artists' brushes. This is also of the marten species
+and has been frequently offered, when dyed dark, as have baum and stone
+martens, as Russian sables. Hares, too, are dyed a sable colour and
+advertised as sable. The fur, apart from a clumsy appearance, is so
+brittle, however, as to be of scarcely any service whatever.
+
+Among the principal imitations of other furs is musquash, out of which
+the top hair has been pulled and the undergrowth of wool clipped and
+dyed exactly the same colour as is used for seal, which is then offered
+as seal or red river seal. Its durability, however, is far less than
+that of seal. Rabbit is prepared and dyed and frequently offered as
+"electric sealskin." Nutria also is prepared to represent sealskin, and
+in its natural colour, after the long hairs are plucked out, it is sold
+as otter or beaver. The wool is, however, poor compared to the otter and
+beaver, and the pelt thin and in no way comparable to them in strength.
+White hares are frequently sold as white fox, but the fur is weak,
+brittle and exceedingly poor compared to fox and possesses no thick
+underwool. Foxes, too, and badger are dyed a brownish black, and white
+hairs inserted to imitate silver fox, but the white hairs are too coarse
+and the colour too dense to mislead any one who knows the real article.
+But if sold upon its own merits, pointed fox is a durable fur.
+
+Garments made of sealskin pieces and Persian lamb pieces are frequently
+sold as if they were made of solid skins, the term "pieces" being simply
+suppressed. The London Chamber of Commerce have issued to the British
+trade a notice that any misleading term in advertising and all attempts
+at deception are illegal, and offenders are liable under the Merchandise
+Marks Act 1887.
+
+  The most usual misnaming of manufactured furs is as follow:--
+
+  Musquash, pulled and dyed      Sold as seal.
+  Nutria, pulled and dyed        Sold as seal.
+  Nutria, pulled and natural     Sold as beaver.
+  Rabbit, sheared and dyed       Sold as seal or electric seal.
+  Otter, pulled and dyed         Sold as seal.
+  Marmot, dyed                   Sold as mink or sable.
+  Fitch, dyed                    Sold as sable.
+  Rabbit, dyed                   Sold as sable or French sable.
+  Hare, dyed                     Sold as sable, or fox, or lynx.
+  Musquash, dyed                 Sold as mink or sable.
+  Wallaby, dyed                  Sold as skunk.
+  White Rabbit                   Sold as ermine.
+  White Rabbit, dyed             Sold as chinchilla.
+  White Hare, dyed or natural    Sold as fox, foxaline, and
+                                   other similar names.
+  Goat, dyed                     Sold as bear, leopard, &c.
+  Dyed manufactured articles of
+    all kinds                    Sold as "natural."
+  White hairs inserted in foxes
+    and sables                   Sold as real or natural furs.
+  Kids                           Sold as lamb or broadtails.
+  American sable                 Sold as real Russian sable.
+  Mink                           Sold as sable.
+
+_The Preservation of Furs._--For many years raw sealskins have been
+preserved in cold storage, but it is only within a recent period, owing
+to the difficulty there was in obtaining the necessary perfectly dry
+atmosphere, that dressed and made-up furs have been preserved by
+freezing. Furs kept in such a condition are not only immune from the
+ravages of the larvae of moth, but all the natural oils in the pelt and
+fur are conserved, so that its colour and life are prolonged, and the
+natural deterioration is arrested. Sunlight has a tendency to bleach
+furs and to encourage the development of moth eggs, therefore continued
+exposure is to be avoided. When furs are wetted by rain they should be
+well shaken and allowed to dry in a current of air without exposure to
+sun or open fire.
+
+Where a freezing store for furs is not accessible, furs should be well
+shaken and afterwards packed in linen and kept in a perfectly cool dry
+place, and examined in the summer at periods of not less than five
+weeks. Naphthalene and the usual malodorous powders are not only very
+disagreeable, but quite useless. Any chemical that is strong enough to
+destroy the life in a moth egg would also be sufficiently potent to
+injure the fur itself. In England moth life is practically continuous
+all the year round, that is, as regards those moths that attack furs,
+though the destructive element exists to a far greater extent during
+spring and summer.
+
+  _Comparative Durability of Various Furs and Weight of Unlined Skins
+  per Square Foot._
+
+  The following estimates of durability refer to the use of fur when
+  made up "hair outside" in garments or stoles, not as a lining. The
+  durability of fur used as linings, which is affected by other
+  conditions, is set forth separately. Otter, with its water hairs
+  removed, the strongest of furs for external use, is, in this table,
+  taken as the standard at 100 and other furs marked accordingly:--
+
+
+  _The Precious Furs._
+
+    +---------------------------------------+-------------+------------+
+    |                                       |  Points of  | [2]Weight  |
+    |                                       | Durability. | in oz. per |
+    |                                       |             |   sq. ft.  |
+    +---------------------------------------+-------------+------------+
+    | Sable                                 |      60     |     2½     |
+    | Sea                                   |      75     |     3      |
+    | Fox, Silver or Black                  |      40     |     3      |
+    |  "   White                            |      20     |     3      |
+    | Ermine                                |      25     |     1¼     |
+    | Chinchilla                            |      15     |     1½     |
+    | Sea-otter (for stoles or collars)     |     100     |     4¼     |
+    +---------------------------------------+-------------+------------+
+
+
+  _The Less Valuable Furs._
+
+    +----------------------------------------+-------------+------------+
+    |                                        |  Points of  |   Weight   |
+    |                                        | Durability. | in oz. per |
+    |                                        |             |   sq. ft.  |
+    +----------------------------------------+-------------+------------+
+    | Sable "topped," i.e. top hairs coloured|      55     |    2½      |
+    |   "  tinted, i.e. fur all coloured.    |      50     |    2½      |
+    | Baum Marten, natural                   |      65     |    2¾      |
+    |  "     "     tinted                    |      45     |    2¾      |
+    | Stone Marten                           |      40     |    2¾      |
+    | Nutria                                 |      27     |    3¼      |
+    | Musquash, natural                      |      37     |    3¼      |
+    |    "   water hairs removed, sheared    |             |            |
+    |         and seal finished.             |      33     |    3¼      |
+    | Skunk                                  |      70     |    2¾      |
+    | Mink                                   |      70     |    3¼      |
+    | Lynx, natural                          |      25     |    2¾      |
+    |  "  tinted black                       |      20     |    2¾      |
+    | Marmot, tinted                         |      10     |    3       |
+    | Fox, tinted black                      |      25     |    3       |
+    |  "     "    blue                       |      20     |    3       |
+    | Opossum                                |      37     |    3       |
+    | Otter (with water hairs)               |     100     |    4       |
+    |   "  (water hairs removed)             |      95     |    3(15/16)|
+    | Beaver (water hairs cut level with fur)|      90     |    4       |
+    |   "  (water hairs removed).            |      85     |    3(15/16)|
+    | Moleskin                               |       7     |    1¾      |
+    | Persian Lamb                           |      65     |    3¼      |
+    | Grey     "                             |      30     |    3¼      |
+    | Broadtail                              |      15     |    2¼      |
+    | Caracul Kid                            |      10     |    3¼      |
+    |    "   Lamb                            |      15     |    3¼      |
+    | Squirrel                               |      25     |    1¾      |
+    | Hare                                   |       5     |    1¾      |
+    | Rabbit                                 |       5     |    2¼      |
+    +----------------------------------------+-------------+------------+
+
+
+  _Quantities of Fur needed, in Square Feet._
+
+  The "Paris Model" figure is the basis of these estimates for ladies'
+  garments, the standard measurements being height 5 ft. 6 in., waist 23
+  in., bust 38 in.
+
+                                                             Sq. Ft.
+                                                         (approximate).
+
+    Straight stole ½ length (just below the waist line)        2¾
+    Straight stole ¾ length (just below the knee)              3¾
+    Stole, broad enough at the neck to cover the top of
+      arm ¾ length                                             5
+    The same, full length (to hem of skirt)                    6
+    Eton jacket, without collar                               13
+    Plain cape, 15 in. long                                    6½
+    Deep cape, 30 in. long                                    15
+    Full cape with broad stole front, ¾ length                15
+    Inverness cape (to knee)                                  25
+    Double-breasted, straight, semi-fitting coat, covering
+      hips                                                    16
+    Double-breasted sacque jacket, 36 in. long, full sleeves  20
+    Same, 30 in. long                                         18
+    Same, 22 in. long                                         15
+    Long, full, shawl cape with points at back and front,
+      well below knee                                         15
+    Shorter shawl cape                                        16
+    Motoring or driving coat, ¾ length                        22
+    Motoring or driving coat, full length                     27
+
+
+  _Weight and Durability of Furs for Men's Coat Linings._
+
+  Otter with the water hairs removed, the strongest fur suited for
+  linings, is here taken as the standard.
+
+    +---------------------------------+-----------+-------------+
+    |                                 | Points of |    Weight   |
+    |                                 |Durability.| in oz. per  |
+    |                                 |           |   sq. ft.   |
+    +---------------------------------+-----------+-------------+
+    | Otter (the water hairs removed) |    100    |    3(15/16) |
+    | Beaver     "      "             |     90    |    3(15/16) |
+    | Mink                            |     90    |    3¼       |
+    | Sealskin                        |     75    |    3        |
+    | Raccoon                         |     75    |    4½       |
+    | Persian lamb or astrachan       |     70    |    3¼       |
+    | Sable                           |     65    |    2½       |
+    | Musquash                        |     55    |    3½       |
+    | Nutria                          |     40    |    3¼       |
+    | Grey Opossum                    |     40    |    3        |
+    | Wallaby                         |     30    |    3¾       |
+    | Squirrel                        |     30    |    1¾       |
+    | Hamster                         |     15    |    1¼       |
+    | Rabbit                          |     10    |    2¼       |
+    +---------------------------------+-----------+-------------+
+
+
+  _Durability and Weight of Linings for Ladies' Coats or Wraps._
+
+  Sable gills, the strongest fur suited for ladies' linings, is taken as
+  the standard.
+
+    +---------------------------------+-----------+-------------+
+    |                                 | Points of |    Weight   |
+    |                                 |Durability.| in oz. per  |
+    |                                 |           |   sq. ft.   |
+    +---------------------------------+-----------+-------------+
+    | Sable gills                     |    100    |    2(7/8)   |
+    | Sable                           |     85    |    2½       |
+    | Sable paws                      |     64    |    1(5/8)   |
+    | Ermine                          |     57    |    1¼       |
+    | Squirrel back                   |     50    |    1¾       |
+    | Squirrel heads                  |     36    |    2½       |
+    | Squirrel lock                   |     21    |    1(3/16)  |
+    | Hamster                         |     10    |    1¼       |
+    | Rabbit                          |      7    |    2¼       |
+    +---------------------------------+-----------+-------------+
+
+
+  _Durability and Weight of Motoring Furs made up with Fur outside._
+
+  Otter with the water hairs, the strongest fur suited for motoring
+  garments, is taken as the standard.
+
+    +-------------------------------------+-----------+-------------+
+    |                                     | Points of |    Weight   |
+    |                                     |Durability.| in oz. per  |
+    |                                     |           |   sq. ft.   |
+    +-------------------------------------+-----------+-------------+
+    | Otter (with water hairs)            |    100    |     4       |
+    | Sealskin, marble                    |     80    |     3       |
+    | "Hair Sealskin" (tinted) with water |           |             |
+    |   hairs (a special variety of seal) |     75    |     3¼      |
+    | Raccoon                             |     65    |     4½      |
+    | Russian Pony                        |     35    |     2(5/8)  |
+    +-------------------------------------+-----------+-------------+
+
+
+  _Durability and Weight of Furs for Rugs and Foot-sacks._
+
+    +-------------------------------------+-----------+-------------+
+    |                                     | Points of |    Weight   |
+    |                                     |Durability.| in oz. per  |
+    |                                     |           |   sq. ft.   |
+    +-------------------------------------+-----------+-------------+
+    | Wolverine                           |    100    |     6       |
+    | Bear (black or brown natural)       |     94    |     7       |
+    | Bear (tinted black)                 |     88    |     7½      |
+    | Beaver                              |     88    |     4       |
+    | Raccoon                             |     77    |     4½      |
+    | Opossum                             |     61    |     3       |
+    | Wolf                                |     50    |     6½      |
+    | Jackal                              |     27    |     4½      |
+    | Australian Bear                     |     16    |     6       |
+    | Goat                                |     11    |     4(1/6)  |
+    +-------------------------------------+-----------+-------------+
+
+  Wolverine, the strongest fur suited for rugs and foot-sacks, is taken
+  as the standard.
+
+  For a rug about 20 to 25 sq. ft. of fur are needed, for a foot-sack
+  14½.     (W. S. P.)
+
+
+FOOTNOTES:
+
+  [1] The measurements given are from nose to root of tail of average
+    large sizes after the dressing process, which has a shrinking
+    tendency. The depths of fur quoted are the greatest, but there are
+    plenty of good useful skins possessing a lesser depth.
+
+  [2] Stout, old-fashioned boxcloth is almost the only cloth that
+    (after a soft, heavy lining has been added to it) affords even
+    two-thirds as much protection against cold as does fur. It weighs
+    4.273 oz. per sq. ft. more than the heaviest of coat-furs, and is so
+    rigid as to be uncomfortable, while the subtileness of fur makes it
+    "kind" to the body.
+
+
+
+
+FURAZANES (_furo_--a.a'--_diazoles_), organic compounds obtained by
+heating the glyoximes (dioximes of ortho-diketones) with alkalis or
+ammonia. Dimethylfurazane is prepared by heating dimethylglyoxime with
+excess of ammonia for six hours at 165° C. (L. Wolff, _Ber._, 1895, 28,
+p. 70). It is a liquid (at ordinary temperature) which boils at 156° C.
+(744 mm.). Potassium permanganate oxidizes it first to
+methylfurazane-carboxylic acid and then to furazanedicarboxylic acid.
+Methyl-ethylfurazane and diphenylfurazane are also known. By warming
+oxyfurazane acetic acid with excess of potassium permanganate to 100° C.
+oxyfurazanecarboxylic acid is obtained (A. Hantzsch and J. Urbahn,
+_Ber._, 1895, 28, p. 764). It crystallizes in prisms, which melt at 175°
+C. Furazanecarboxylic acid is prepared by the action of a large excess
+of potassium permanganate on a hot solution of furazanepropionic acid.
+It melts at 107º C, and dissolves in caustic soda, with a deep yellow
+colour and formation of nitrosocyanacetic acid (L. Wolff and P.F. Ganz,
+_Ber._, 1891, 24, p. 1167). Furoxane is an oxide of furazane, considered
+by H. Wieland to be identical with glyoxime peroxide; Kekulés
+dibromnitroacetonitrile is dibromfuroxane.
+
+The formulae of the compounds above mentioned are:
+
+  HC:N\        CH3·C:N\             HC:N\         HC--CH \
+   ·   O           ·   O             ·   O        ··  ·   O
+  HC:N/        CH3·C:N/         HO2C·C:N/         N·O·N  /
+
+  Furazane.   Dimethyl-     Furazanecarboxylic   Furoxane.
+              furazane.            acid.
+
+
+
+
+FURETIÈRE, ANTOINE (1619-1688), French scholar and miscellaneous writer,
+was born in Paris on the 28th of December 1619. He first studied law,
+and practised for a time as an advocate, but eventually took orders and
+after various preferments became abbé of Chalivoy in the diocese of
+Bourges in 1662. In his leisure moments he devoted himself to letters,
+and in virtue of his satires--_Nouvelle Allégorique, ou histoire des
+derniers troubles arrivés au royaume d'éloquence_ (1658); _Voyage de
+Mercure_ (1653)--he was admitted a member of the French Academy in 1662.
+That learned body had long promised a complete dictionary of the French
+tongue; and when they heard that Furetière was on the point of issuing a
+work of a similar nature, they interfered, alleging that he had
+purloined from their stores, and that they possessed the exclusive
+privilege of publishing such a book. After much bitter recrimination on
+both sides the offender was expelled in 1685; but for this act of
+injustice he took a severe revenge in his satire, _Couches de
+l'académie_ (Amsterdam, 1687). His _Dictionnaire universel_ was
+posthumously published in 1690 (Rotterdam, 2 vols.). It was afterwards
+revised and improved by the Protestant jurist, Henri Basnage de Beauval
+(1656-1710), who published his edition (3 vols.) in 1701; and it was
+only superseded by the compilation known as the _Dictionnaire de
+Trévoux_ (Paris, 3 vols., 1704; 7th ed., 8 vols., 1771), which was in
+fact little more than a reimpression of Basnage's edition. Furetière is
+perhaps even better known as the author of _Le Roman bourgeois_ (1666).
+It cast ridicule on the fashionable romances of Mlle de Scudéry and of
+La Calprenède, and is of interest as descriptive of the ~~ everyday
+life of his times. There is no element of burlesque, as in Scarron's
+_Roman comique_, but the author contents himself with stringing together
+a number of episodes and portraits, obviously drawn from life, without
+much attempt at sequence. The book was edited in 1854 by Edward Fournier
+and Charles Asselineau and by P. Jannet.
+
+  The _Fureteriana_, which appeared in Paris eight years after
+  Furetière's death, which took place on the 14th of May 1688, is a
+  collection of but little value.
+
+
+
+
+FURFOOZ, a village some 10 m. from Dinant in the Ardennes, Belgium.
+Three caves containing prehistoric remains were here excavated in 1872.
+Of these the _Trou de Frontal_ is the most famous. In it were found
+human skeletons with brachycephalic skulls, associated with animal
+bones, those of the reindeer being particularly plentiful. Among the
+skeletons was discovered an oval vase of pottery. The Furfooz type of
+mankind is believed to date from the close of the Quaternary age. G. de
+Mortillet dates the type in the Robenhausen epoch of the Neolithic
+period. His theory is that the bones are those of men of that period
+buried in what had been a cave-dwelling of the Madelenian epoch.
+
+
+
+
+FURFURANE, or FURANE, C4H4O, a colourless liquid boiling at 32° C.,
+found in the distillation products of pine wood. It was first
+synthetically prepared by H. Limpricht (_Ann._, 1873, 165, p. 281) by
+distilling barium mucate with soda lime, pyromucic acid C4H3O·CO2H being
+formed, which, on further loss of carbon dioxide, yielded furfurane. A.
+Henniger (_Ann. chim. phys._, 1886 [2], 7, p. 220), by distilling
+erthyrite with formic acid, obtained a dihydrofurfurane
+
+  C4H6(OH)4 + 2H2CO2 = C4H6O + CO+CO2 + 4H2O,
+
+which, on treatment with phosphorus pentachloride, yielded furfurane.
+Furfurane is insoluble in water and possesses a characteristic smell. It
+does not react with sodium or with phenylhydrazine, but yields
+dye-stuffs with isatin and phenanthrenequinone. It reacts violently with
+hydrochloric acid, producing a brown amorphous substance. Methyl and
+phenyl derivatives have been prepared by C. Paal (_Ber._, 1884, 17, p.
+915). Paal prepared acetonyl acetophenone by condensing sodium
+acetoacetate with phenacylbromide, and this substance on dehydration
+yields [alpha][alpha]'-phenylmethylfurfurane, the acetonyl acetophenone
+probably reacting in the tautomeric "enolic" form,
+
+  CH3·CO·CHNa·COOR + C6H5·CO·CH2Br = CH3·CO·CH(CH2COC6H5)·COOR.
+
+This ester readily hydrolyses, and the acid formed yields acetonyl
+acetophenone (by loss of carbon dioxide), which then on dehydration
+yields the furfurane derivative, thus
+
+          CH--CH                         CH--CH
+        //      \\                     //     \\
+  CH3·C           C·C6H5 = H2O + CH3·C          C·C6H5.
+        \       /                      \___ ___/
+          OH  OH                           O
+
+L. Knorr (_Ber._, 1889, 22, p. 158) obtained diacetosuccinic ester by
+condensing sodium acetoacetate with iodine, and by dehydrating the ester
+he prepared [alpha][alpha]'-dimethylfurfurane ßß'-dicarboxylic acid
+(carbopyrotritaric acid), which on distillation yields
+[alpha][alpha]'-dimethylfurfurane as a liquid boiling at 94° C. Paal
+also obtained this compound by using monochloracetone in the place of
+phenacylbromide. By the distillation of mucic acid or isosaccharic acid,
+furfurane-[alpha]-carboxylic acid (pyromucic acid), C4H3O·CO2H, is
+obtained; it crystallizes in needles or leaflets, and melts at 134° C.
+
+_Furfurol_ (furol), C4H3O·CHO, is the aldehyde of pyromucic acid, and is
+formed on distilling bran, sugar, wood and most carbohydrates with
+dilute sulphuric acid, or by distilling the pentoses with hydrochloric
+acid. It is a colourless liquid which boils at 162° C., and is
+moderately soluble in water; it turns brown on exposure to air and has a
+characteristic aromatic smell. It shows all the usual properties of an
+aldehyde, forming a bisulphite compound, an oxime and a hydrazone;
+whilst it can be reduced to the corresponding furfuryl alcohol by means
+of sodium amalgam, and oxidized to pyromucic acid by means of silver
+oxide. It also shows all the condensation reactions of benzaldehyde
+(q.v.); condensing with aldehydes and ketones in the presence of caustic
+soda to form more complex aldehydes and ketones with unsaturated side
+chains, such as furfuracrolein, C4H3O·CH:CH·CHO, and furfuracetone,
+C4H3O·CH:CH·CO·CH3. With alcoholic potassium cyanide It changes to
+furoin, C4H3O·CHOH·CO·C4H3O, which can be oxidized to furil,
+C4H3O·CO·CO·C4H3O, whilst alcoholic potash converts it into furfuryl
+alcohol. With fatty acids and acid anhydrides it gives the "Perkin"
+reaction (see CINNAMIC ACID). Furfurol is shown to have its aldehydic
+group in the a position, by conversion into furfurpropionic acid,
+C4H3O·CH2·CH2·CO2H, which on oxidation by bromine water and subsequent
+reduction of the oxidized product is converted into n-pimelic acid,
+HO2C(CH2)5CO2H. Furfurol in minute quantities can be detected by the red
+colour it forms with a solution of aniline acetate.
+
+  Furfurane--[alpha][alpha]'-dicarboxylic acid or dehydromucic acid,
+  C4H2O(CO2H)2, is formed when mucic acid is heated with hydrochloric
+  acid at 100° C. On being heated, it loses carbon dioxide and gives
+  pyromucic acid. By digesting acetoacetic ester with sodium succinate
+  and acetic anhydride, methronic acid, C8H8O5, is obtained; for the
+  constitution of this acid, see L. Knorr, _Ber._, 1889, 22, p. 152, and
+  R. Fittig, Ann., 1889, 259, p. 166.
+
+  Di- and tetrahydrofurfurane compounds are also known (see A. Lipp,
+  Ber., 1889, 22, p. 1196; W.H. Perkin, junr. _Journ. Chem. Soc._, 1899,
+  57, p. 944; and S. Ruhemann, ibid., 1896, 69, p. 1383).
+
+
+
+
+FURIES (Lat. _Furiae_, also called DIRAE), in Roman mythology an
+adaptation of the Greek Erinyes (q.v.), with whom they are generally
+identical. A special aspect of them in Virgil is that of agents employed
+by the higher gods to stir up mischief, strife and hatred upon earth.
+Mention may here be made of an old Italian deity Furina (or Furrina),
+whose worship fell early into disuse, and who was almost forgotten in
+the time of Varro. By the mythologists of Cicero's time the name was
+connected with the verb _furere_ and the noun _furia_, which in the
+plural (not being used in the singular in this sense) was accepted as
+the equivalent of the Greek Erinyes. But it is more probably related to
+_furvus_, _fuscus_, and signifies one of the spirits of darkness, who
+watched over men's lives and haunted their abodes. This goddess had her
+own special priest, a grove across the Tiber where Gaius Gracchus was
+slain, and a festival on the 25th of July. Authorities differ as to the
+existence of more than one goddess called Furina, and their identity
+with the Forinae mentioned in two inscriptions found at Rome (_C.I.L._
+vi. 422 and 10,200).
+
+
+
+
+FURLONG (from the O. Eng. _furlang_, i.e. "furrow-long"), a measure of
+length, originally the length of a furrow in the "common field" system.
+As the field in this system was generally taken to be a square, 10 acres
+in extent, and as the acre varied in different districts and at
+different times, the "furlong" also varied. The side of a square
+containing 10 statute acres is 220 yds. or 40 poles, which was the
+usually accepted length of the furlong. This is also the length of
+{1/8}th of the statute mile. "Furlong" was as early as the 9th century
+used to translate the Latin _stadium_, 1/8th of the Roman mile.
+
+
+
+
+FURNACE, a contrivance for the production and utilization of heat by the
+combustion of fuel. The word is common to all the Romance tongues,
+appearing in more or less modified forms of the Latin _fornax_. But in
+all those languages the word has a more extended meaning than in
+English, as it covers every variety of heating apparatus; while here, in
+addition to furnaces proper, we distinguish other varieties as _ovens_,
+_stoves_ and _kilns_. The first of these, in the form _Ofen_, is used in
+German as a general term like the French _four_; but in English it has
+been restricted to those apparatus in which only a moderate temperature,
+usually below a red heat, is produced in a close chamber. Our bakers'
+ovens, hot-air ovens or stoves, annealing ovens for glass or metal, &c.,
+would all be called _fours_ in French and _Öfen_ in German, in common
+with furnaces of all kinds. Stove, an equivalent of oven, is from the
+German _Stube_, i.e. a heated room, and is commonly so understood; but
+is also applied to open fire-places, which appears to be somewhat of a
+departure from the original signification.
+
+Furnaces are constructed according to many different patterns with
+varying degrees of complexity in arrangement; but all may be considered
+as combining three essential parts, namely, the fire-place in which the
+fuel is consumed, the heated chamber, laboratory, hearth or working bed,
+as it is variously called, where the heat is applied to the special work
+for which the furnace is designed, and the apparatus for producing rapid
+combustion by the supply of air under pressure to the fire. In the
+simplest cases the functions of two or more of these parts may be
+combined into one, as in the smith's forge, where the fire-place and
+heating chamber are united, the iron being placed among the coals, only
+the air for burning being supplied under pressure from a blowing engine
+by a second special contrivance, the tuyere, tuiron, twyer or
+blast-pipe; but in the more refined modern furnaces, where great economy
+of fuel is an object, the different functions are distributed over
+separate and distinct apparatus, the fuel being converted into gas in
+one, dried in another, and heated in a third, before arriving at the
+point of combustion in the working chamber of the furnace proper.
+
+  Furnaces may be classified according as the products of combustion are
+  employed (1) only for heating purposes, or (2) both for heating and
+  bringing about some chemical change. The furnaces employed for
+  steam-raising or for heating buildings are invariably of the first
+  type (see BOILER and HEATING), while those employed in metallurgy are
+  generally of the second. The essential difference in construction is
+  that in the first class the substances heated do not come into contact
+  with either the fuel or the furnace gases, whereas in the second they
+  do. Metallurgical furnaces of the first class are termed crucible,
+  muffle or retort furnaces, and of the second shaft and reverberatory
+  furnaces. The following is a detailed subdivision:--
+
+  (1) Fuel and substance in contact.
+     (a) Height of furnace greater than diameter = shaft furnaces.
+         ([alpha]) No blast = kilns.
+         (ß) With blast = blast furnaces.
+     (b) Height not much greater than diameter = hearth furnaces.
+
+  (2) Substance heated by products of combustion = reverberatory
+        furnaces.
+     (a) Charge not melted = roasting or calcining furnaces.
+     (b) Charge melted = melting furnaces.
+
+  (3) Substance is not directly heated by the fuel or by the products
+        of combustion.
+     (a) Heating chamber fixed and forming part of furnace = muffle
+           furnaces.
+     (b) Crucible furnaces.
+     (c) Retort furnaces.
+
+Another classification may be based upon the nature of the heating
+agent, according as it is coal (or some similar combustible) oil, gas or
+electricity. In this article the general principles of metallurgical
+furnaces will be treated; the subject of gas- and oil-heated furnaces is
+treated in the article Fuel, and of the electric furnace in the article
+Electrometallurgy. For special furnaces reference should be made to the
+articles on the industry concerned, e.g. GLASS, GAS, § MANUFACTURE, &c.
+
+_Shaft, Blast and Hearth Furnaces._--The blast furnace in its simplest
+form is among the oldest, if not the oldest, of metallurgical
+contrivances. In the old copper-smelting district of Arabia Petraea,
+clay blast-pipes dating back to the earlier dynasties of ancient Egypt
+have been found buried in slag heaps; and in India the native smiths and
+iron-workers continue to use furnaces of similar types. These, when
+reduced to their most simple expression, are mere basin-shaped hollows
+in the ground, containing ignited charcoal and the substances to be
+heated, the fire being urged by a blast of air blown in through one or
+more nozzles from a bellows at or near the top. They are essentially the
+same as the smith's forge. This class of furnace is usually known as an
+open fire or hearth, and is represented in a more advanced stage of
+development by the Catalan, German and Walloon forges formerly used in
+the production of malleable iron.
+
+[Illustration: FIG. 1.--Elevation of Catalan Forge.]
+
+  Fig. 1 represents a Catalan forge. The cavity in the ground is
+  represented by a pit of square or rectangular section lined with brick
+  or stone of a kind not readily acted on by heat, about 1½ or 2 ft.
+  deep, usually somewhat larger above than below, with a tuyere or
+  blast-pipe of copper penetrating one of the walls near the top, with a
+  considerable downward inclination, so that the air meets the fuel some
+  way down. In iron-smelting the ore is laid in a heap upon the fuel
+  (charcoal) filling up the hearth, and is gradually brought to the
+  metallic state by the reducing action of the carbon monoxide formed at
+  the tuyere. The metal sinks through the ignited fuel, forming, in the
+  hearth, a spongy mass or ball, which is lifted out by the smelters at
+  the end of each operation, and carried to the forge hammer. The earthy
+  matters form a fusible glass or slag melt, and collect at the lowest
+  point of the hearth, whence they are removed by opening a hole pierced
+  through the front wall at the bottom. The active portion of such a
+  furnace is essentially that above the blast-pipe, the function of the
+  lower part being merely the collection of the reduced metal; the fire
+  may therefore be regarded as burning in an unconfined space, with the
+  waste of a large amount of its heating power. By continuing the walls
+  of the hearth above the tuyere, into a shaft or stack either of the
+  same or some other section, we obtain a furnace of increased capacity,
+  but with no greater power of consuming fuel, in which the material to
+  be treated can be heated up gradually by loading it into the stack,
+  alternately with layers of fuel, the charge descending regularly to
+  the point of combustion, and absorbing a proportion of the heat of the
+  flame that went to waste in the open fire. This principle is capable
+  of very wide extension, the blast furnace being mainly limited in
+  height by the strength the column of materials or "burden" has to
+  resist crushing, under the weight due to the head adopted, and the
+  power of the blowing engine to supply blast of sufficient density to
+  overcome the resistance of the closely packed materials to the free
+  passage of the spent gases. The consuming power of the furnace or the
+  rate at which it can burn the fuel supplied is measured by the number
+  of tuyeres and their section.
+
+The development of blast furnaces is practically the development of
+iron-smelting. The profile has been very much varied at different times.
+The earliest examples were square or rectangular in horizontal section,
+but the general tendency of modern practice is to substitute round
+sections, their construction being facilitated by the use of specially
+moulded bricks which have entirely superseded the sandstone blocks
+formerly used. The vertical section, on the other hand, is subject to
+considerable variation according to the work to which the furnace is
+applied. Where the operation is simply one of fusion, as in the
+iron-founder's cupola, in which there is no very great change in volume
+in the materials on their descent to the tuyeres, the stack is nearly or
+quite straight-sided; but when, as is the case with the smelting of iron
+ores with limestone flux, a large proportion of volatile matter has to
+be removed in the process, a wall of varying inclination is used, so
+that the body of the furnace is formed of two dissimilar truncated
+cones, joined by their bases, the lower one passing downwards into a
+short, nearly cylindrical, position. For further consideration of this
+subject see IRON AND STEEL.
+
+_Hearth furnaces_ are employed in certain metallurgical operations, e.g.
+in the air-reduction process for smelting lead ores. The principle is
+essentially that of the Catalan forge. Such furnaces are very wasteful,
+and have little to recommend them (see Schnabel, Metallurgy, 1905, vol.
+1. p. 409).
+
+_Reverberatory Furnaces._--Blast furnaces are, from the intimate contact
+between the burden to be smelted and the fuel, the least wasteful of
+heat; but their use supposes the possibility of obtaining fuel of good
+quality and free from sulphur or other substances likely to deteriorate
+the metal produced. In all cases, therefore, where it is desired to do
+the work out of contact with the solid fuel, the operation of burning or
+heat-producing must be performed in a special fire-place or combustion
+chamber, the body of flame and heated gas being afterwards made to act
+upon the surface of the material exposed in a broad thin layer in the
+working bed or laboratory of the furnace by reverberation from the low
+vaulted roof covering the bed. Such furnaces are known by the general
+name of reverberatory or reverbatory furnaces, also as air or wind
+furnaces, to distinguish them from those worked with compressed air or
+blast.
+
+Originally the term cupola was used for the reverberatory furnace, but
+in the course of time it has changed its meaning, and is now given to a
+small blast furnace such as that used by iron-founders--reverberatory
+smelting furnaces in the same trade being called air furnaces.
+
+[Illustration: FIG. 2.--Longitudinal section of Reverberatory Furnace.]
+
+[Illustration: FIG. 3.--Reverberatory Furnace (horizontal section).]
+
+[Illustration: FIG. 4.--Reverberatory Furnace (elevation at flue end).]
+
+  Figs. 2, 3 and 4 represent a reverberatory furnace such as is used for
+  the fusion of copper ores for regulus, and may be taken as generally
+  representing its class. The fire-place A is divided from the working
+  bed B by a low wall C known as the fire bridge, and at the opposite
+  end there is sometimes, though not invariably, a second bridge of less
+  height called the flue bridge D. A short diagonal flue or up-take E
+  conveys the current of spent flame to the chimney F, which is of
+  square section, diminishing by steps at two or three different
+  heights, and provided at the top with a covering plate or damper G,
+  which may be raised or lowered by a chain reaching to the ground, and
+  serves for regulating the speed of the exhaust gases, and thereby the
+  draught of air through the fire. Where several furnaces are connected
+  with the same chimney stack, the damper takes the form of a sliding
+  plate in the mouth of the connecting flue, so that the draught in one
+  may be modified without affecting the others. The fire bridge is
+  partially protected against the intense heat of the body of flame
+  issuing through the fire arch by a passage to which the air has free
+  access. The material to be melted is introduced into the furnace from
+  the hoppers HH through the charging holes in the roof. When melted the
+  products separate on the bed (which is made of closely packed sand or
+  other infusible substances), according to their density; the lighter
+  earthy matters forming an upper layer of slag are drawn out by the
+  slag hole K at the flue end into an iron wagon or bogie, while the
+  metal subsides to the bottom of the bed, and at the termination of the
+  operation is run out by the tap hole L into moulds or granulated into
+  water. The opposite opening M is the working door, through which the
+  tool for stirring the charge is introduced. It is covered by a plate
+  suspended to a lever, similar to that seen in the end elevation (fig.
+  4) in front of the slag hole.
+
+According to the purposes to which they are applied, reverberatory
+furnaces may be classed into two groups, namely, fusion or melting
+furnaces, and calcining or wasting furnaces, also called calciners. The
+former have a very extended application in many branches of industry,
+being used by both founders and smelters in the fusion of metals; in the
+concentration of poor metallic compounds by fusion into regulus; in the
+reduction of lead and tin ores; for refining copper and silver; and for
+making malleable iron by the puddling processes and welding. Calcining
+furnaces have a less extended application, being chiefly employed in the
+conversion of metallic sulphides into oxides by continued exposure to
+the action of air at a temperature far below that of fusion, or into
+chlorides by roasting with common salt. As some of these substances (for
+example, lead sulphide and copper pyrites) are readily fusible when
+first heated, but become more refractory as part of the sulphur is
+dissipated and oxygen takes its place, it is important that the heat
+should be very carefully regulated at first, otherwise the mass may
+become clotted or fritted together, and the oxidizing effect of the air
+soon ceases unless the fritted masses be broken small again. This is
+generally done by making the bed of the furnace very long in proportion
+to its breadth and to the fire-grate area, which may be the more easily
+done as a not inconsiderable amount of heat is given out during the
+oxidation of the ore--such increased length being often obtained by
+placing two or even three working beds one above the other, and allowing
+the flame to pass over them in order from below upwards. Such calciners
+are used especially in roasting zinc blende into zinc oxide, and in the
+conversion of copper sulphides into chlorides in the wet extraction
+process. In some processes of lead-smelting, where the minerals treated
+contain sand, the long calciner is provided with a melting bottom close
+to the fire-place, so that the desulphurized ore leaves the furnace as a
+glassy slag or silicate, which is subsequently reduced to the metallic
+state by fusion with fluxes in blast furnaces. Reverberatory furnaces
+play an important part in the manufacture of sodium carbonate;
+descriptions and illustrations are given in the article ALKALI
+MANUFACTURE.
+
+_Muffle, Crucible and Retort Furnaces._--A third class of furnaces is so
+arranged that the work is done by indirect heating; that is, the
+material under treatment, whether subjected to calcination, fusion or
+any other process, is not brought in contact either with fuel or flame,
+but is raised to the proper temperature by exposure in a chamber heated
+externally by the products of combustion. These are known as muffle or
+chamber furnaces; and by supposing the crucibles or retorts to represent
+similar chambers of only temporary duration, the ordinary pot melting
+air furnaces, and those for the reduction of zinc ores or the
+manufacture of coal gas, may be included in the same category. These are
+almost invariably air furnaces, though sometimes air under pressure is
+used, as, for example, in the combustion of small anthracitic coal,
+where a current of air from a fan-blower is sometimes blown under the
+grate to promote combustion. Types of muffle furnaces are figured in the
+article ANNEALING, HARDENING AND TEMPERING.
+
+_Furnace Materials._--The materials used in the construction of furnaces
+are divisible into two classes, namely, ordinary and refractory or
+fire-resisting. The former are used principally as casing, walls,
+pillars or other supporting parts of the structure, and includes
+ordinary red or yellow bricks, clay-slate, granite and most building
+stones; the latter are reserved for the parts immediately in contact
+with the fuel and flame, such as the lining of the fire-place, the
+arches, roof and flues, the lower part if not the whole of the chimney
+lining in reverberatory furnaces, and the whole of the internal walls of
+blast furnaces. Among such substances are fireclay and firebricks,
+certain sandstones, silica in the form of ganister, and Dinas stone and
+bricks, ferric oxide and alumina, carbon (as coke and graphite),
+magnesia, lime and chromium oxide--their relative importance being
+indicated by their order, the last two or three indeed being only of
+limited use.
+
+The most essential point in good fireclays, or in the bricks or other
+objects made from them, is the power of resisting fusion at the highest
+heat to which they may be exposed. This supposes them to be free from
+metallic oxides forming easily fusible compounds with silica, such as
+lime or iron, the presence of the former even in comparatively small
+proportion being very detrimental. As clays they must be sufficiently
+plastic to be readily moulded, but at the same time possess sufficient
+stiffness not to contract too strongly in drying, whereby the objects
+produced would be liable to be warped or cracked before firing. In most
+cases, however, the latter tendency is guarded against, in making up the
+paste for moulding, by adding to the fresh clay a certain proportion of
+burnt material of the same kind, such as old bricks or potsherds, ground
+to a coarse powder. Coke dust or graphite is used for the same purpose
+in crucible making (see FIREBRICK).
+
+  The most highly valued fireclays are derived from the Coal Measures.
+  Among the chief localities are the neighbourhood of Stourbridge in
+  Worcestershire and Stannington near Sheffield, which supply most of
+  the materials for crucibles used in steel and brass melting, and the
+  pots for glass houses; Newcastle-on-Tyne and Glenboig near Glasgow,
+  where heavy blast furnace and other firebricks, gas retorts, &c., are
+  made in large quantities. Coarse-grained but very strong firebricks
+  are also made of the waste of china clay works.
+
+  In Belgium the clay raised at Andenne is very largely used for making
+  retorts for zinc furnaces. The principal French fireclays are derived
+  from the Tertiary strata in the south, and more nearly resemble
+  porcelain clays than those of the Coal Measures. They give wares of
+  remarkably fine texture and surface, combined with high refractory
+  character.
+
+  In Germany, Ips and Passau on the Danube, and Gross Almerode in Hesse,
+  are the best known localities producing fireclay goods, the crucibles
+  from the last-mentioned place, known as Hessian crucibles, going all
+  over the world. These, though not showing a great resistance to
+  extreme heat, are very slightly affected by sudden alternations in
+  heating, as they may be plunged cold into a strongly heated furnace
+  without cracking, a treatment to which French and Stourbridge pots
+  cannot be subjected with safety.
+
+Plumbago or graphite is largely used in the production of crucibles, not
+in the pure state but in admixture with fireclay; the proportion of the
+former varies with the quality from 25 to nearly 50%. These are the most
+enduring of all crucibles, the best lasting out 70 or 80 meltings in
+brass foundries, about 50 with bronze, and 8 to 10 in steel-melting.
+
+Silica is used in furnace-building in the forms of sand, ganister, a
+finely ground sandstone from the Coal Measures of Yorkshire, and the
+analogous substance known as Dinas clay, which is really nearly pure
+silica, containing at most about 2½% of bases. Dinas clay is found at
+various places in the Vale of Neath in South Wales, in the form of a
+loose disintegrated sandstone, which is crushed between rollers, mixed
+with about 1% of lime, and moulded into bricks that are fired in kilns
+at a very high temperature. These bricks are specially used for the
+roof, fire arches, and other parts subjected to intense heat in
+reverberatory steel-melting furnaces, and, although infusible under
+ordinary conditions, are often fairly melted by the heat without fluxing
+or corrosion after a certain amount of exposure. Ganister, a slightly
+plastic siliceous sand, is similarly used for the lining of Bessemer
+steel converters; it is found in the neighbourhood of Sheffield.
+
+Alumina as a refractory material is chiefly used in the form of bauxite,
+but its applications are somewhat special. It has been found to stand
+well for the linings of rotatory puddling furnaces, where, under
+long-continued heating, it changes into a substance as hard and
+infusible as natural emery. In the Paris Exhibition of 1878 bricks very
+hard and dense in character, said to be of pure alumina, were exhibited
+by Muller & Co. of Paris, as well as bricks of magnesia, the latter
+being specially remarkable for their great weight. They are intended for
+use at the extreme temperatures obtainable in steel furnaces, or for the
+melting of platinum before the oxy-hydrogen blowpipe. For the latter
+purpose, however, lime is generally used; but as this substance has only
+small stability, it is usually bedded in a casing of firebrick. Oxide of
+chromium and chrome iron ore have been proposed as refractory crucible
+materials. The former may be used as a bed for melting platinum in the
+same way as lime or magnesia, without affecting the quality of the
+metal.
+
+Ferric oxide, though not strictly infusible, is largely used as a
+protecting lining for furnaces in which malleable iron is made, a
+portion of the ore being reduced and recovered in the process. In an
+oxidizing atmosphere it is indifferent to silica, and therefore
+siliceous bricks containing a considerable proportion of ferric oxide,
+when used in flues of boilers, brewers' coppers, &c. and similar
+situations, are perfectly fire-resisting so long as the heated gas
+contains a large proportion of unconsumed air. The red firebricks known
+as Windsor bricks, which are practically similar in composition to soft
+red sandstone, are of this character.
+
+The electric furnace has led to the discovery of several important
+materials, which have been employed as furnace linings. Carborundum
+(q.v.) was applied by Engels in 1899, firebricks being washed with
+carborundum paste and then baked. Siloxicon, a compound of carbon,
+silicon and oxygen, formed from carbon and silica in the electric
+furnace, was patented by E.G. Acheson in 1903. It is very refractory,
+and is applied by mixing with water and some bond, such as sodium
+silicate or gas-tar. An amorphous, soft silicon carbide, also formed in
+the electric furnace, was patented by B. Talbot in 1899. For basic
+linings, magnesia crystallized in the electric furnace is being
+extensively used, replacing dolomite to some extent (see E. Kilburn
+Scott, "Refractory Materials for Furnace Linings," _Faraday Soc._, 1906,
+p. 289).
+
+  _Furnace Construction._--In the construction of furnaces provision has
+  to be made for the unequal expansion of the different parts under the
+  effect of heat. This is especially necessary in the case of
+  reverberatory furnaces, which are essentially weak structures, and
+  therefore require to be bound together by complicated systems of tie
+  rods and uprights or buck staves. The latter are very commonly made of
+  old flat bottom rails, laid with the flat of the flange against the
+  wall. Puddling furnaces are usually entirely cased with iron plates,
+  and blast furnaces with hoops round each course of the stack, or in
+  those of thinner constructions the firebrick work is entirely enclosed
+  in a wrought iron casing or jacket. Such parts as may be subjected to
+  extreme heat and the fretting action of molten material, as the tuyere
+  and slag breasts of blast furnaces, and the fire bridges and bed
+  plates of reverberatory furnaces, are often made in cast iron with
+  double walls, a current of water or air being kept circulating through
+  the intermediate space. In this way the metal, owing to its high
+  conductivity and low specific heat as compared to that of water, is
+  kept at a temperature far below its melting point if the water is
+  renewed quickly enough. It is of course necessary in such cases that
+  the circulation shall be perfectly free, in order to prevent the
+  accumulation of steam under pressure in the interior of the casting.
+  This method has received considerable extension, notably in
+  furnace-smelting of iron ores containing manganese, where the entire
+  hearth is often completely water-cased, and in some lead furnaces
+  where no firebrick lining is used, the lower part of the furnace stack
+  being a mere double iron box cooled by water sufficiently to keep a
+  coating of slag adhering to the inner shell which prevents the metal
+  from being acted upon.
+
+  _Mechanical Furnaces._--The introduction and withdrawal of the charges
+  in fusion furnaces is effected by gravitation, the solid masses of raw
+  ore, fuel and flux being thrown in at the top, and flowing out of the
+  furnace at the taphole or slag run at the bottom. Vertical kilns, such
+  as those used for burning limestone, are worked in a similar
+  manner--the raw stone going in at the top, and the burnt product
+  falling through holes in the bottom when allowed to do so. With
+  reverberatory calciners, however, where the work is done upon a
+  horizontal bed, a considerable amount of hand labour is expended in
+  raking out the charge when finished, and in drawing slags from fusion
+  furnaces; and more particularly in the puddling process of refining
+  iron the amount of manual exertion required is very much greater. To
+  diminish the item of expenditure on this head, various kinds of
+  mechanical furnaces have been adopted, all of which can be classified
+  under three heads of gravitating furnaces, mechanical stirrers and
+  revolving furnaces.
+
+  1. In _gravitating furnaces_ the bed is laid at a slope just within
+  the angle of repose of the charge, which is introduced at the upper
+  end, and is pushed down the slope by fresh material, when necessary,
+  in the contrary direction to the flame which enters at the lower end.
+  Gerstenhofer's pyrites burner is a furnace of this class. It has a
+  tall vertical chamber heated from below, and traversed by numerous
+  narrow horizontal cross bars at different heights. The ore in fine
+  powder is fed in at the top, through a hopper, in a regular thin
+  stream, by a pair of rollers, and in falling lodges on the flats of
+  the bars, forming a talus upon each of the height corresponding to the
+  angle of rest of the material, which is, however, at short intervals
+  removed to lower levels by the arrival of fresh ore from above. In
+  this way a very large surface is exposed to the heat, and the ore, if
+  containing sufficient sulphur to maintain the combustion, is perfectly
+  burned when it arrives at the bottom; if, however, it is imperfectly
+  sized or damp, or if it contains much earthy matter, the result is not
+  very satisfactory. There are many other furnaces in which the same
+  principle is utilized.
+
+  2. _Mechanical stirrers_ constitute a second division of mechanical
+  furnaces, in which the labour of rabbling or stirring the charges is
+  performed by combinations of levers and wheel-work taking motion from
+  a rotating shaft, and more or less perfectly imitating the action of
+  hand labour. They are almost entirely confined to puddling furnaces.
+
+  3. _Revolving furnaces_, the third and most important division of
+  mechanical furnaces, are of two kinds. The first of these resemble an
+  ordinary reverberatory furnace by having a flat bed which, however,
+  has the form of a circular disk mounted on a central shaft, and
+  receives a slow movement of rotation from a water-wheel or other
+  motor, so that every part of the surface is brought successively under
+  the action of the fire, the charge being stirred and ultimately
+  removed by passing under a series of fixed scraper arms placed above
+  the surface at various points. Brunton's calciner, used in the
+  "burning" of the pyritic minerals associated with tin ore, is a
+  familiar example of this type. The hearth may either rotate on an
+  inclined axis, so that the path of its surface is oblique to that of
+  the flame, or the working part may be a hollow cylinder, between the
+  fireplace and flue, with its axis horizontal or nearly so, whose inner
+  surface represents the working bed, mounted upon friction rollers, and
+  receiving motion from a special steam-engine by means of a central
+  belt of spur gearing. Furnaces of the second kind were first used in
+  alkali works for the conversion of sulphate into carbonate of sodium
+  in the process known as black ash fusion, but have since been applied
+  to other processes. As calciners they are used in tin mines and for
+  the chlorination of silver ores. Mechanical furnaces are figured in
+  the article ALKALI MANUFACTURE.
+
+  _Use of Heated Air._--The calorific intensity of fuel is found to be
+  very considerably enhanced, if the combustion be effected with air
+  previously heated to any temperature between that of boiling water and
+  a dull red heat, the same effect being observed both with solid and
+  gaseous fuel. The latter, especially when brought to the burning point
+  at a high temperature, produces a heat that can be resisted by the
+  most refractory substances only, such as silica, alumina and magnesia.
+  This is attained in the regenerative furnace of Siemens, detailed
+  consideration of which belongs more properly to the subject of iron.
+
+  _Economy of Waste Heat._--In every system of artificial heating, the
+  amount of heat usefully applied is but a small proportion of that
+  developed by combustion. Even under the most advantageous application,
+  that of evaporation of water in a steam boiler where the gases of the
+  fire have to travel through a great length of flues bounded by thin
+  iron surfaces of great heat-absorbing capacity, the temperature of the
+  current at the chimney is generally much above that required to
+  maintain an active draught in the fireplace; and other tubes
+  containing water, often in considerable numbers, forming the so-called
+  fuel economizers, may often be interposed between the boiler and the
+  chimney with marked advantage as regards saving of fuel. In
+  reverberatory and air furnaces used in the different operations of
+  iron manufacture, where an extremely high temperature has to be
+  maintained in spaces of comparatively small extent, such as the beds
+  of puddling, welding and steel-melting furnaces, the temperature of
+  the exhaust gases is exceedingly high, and if allowed to pass directly
+  into the chimney they appear as a great body of flame at the top. It
+  is now general to save a portion of this heat by passing the flame
+  through flues of steam boilers, air-heating apparatus, or both--so
+  that the steam required for the necessary operations of the forge and
+  heated blast for the furnace itself may be obtained without further
+  expenditure of fuel. The most perfect method of utilizing the waste
+  heat hitherto applied is that of the Siemens regenerator, in which the
+  spent gases are made to travel through chambers, known as regenerators
+  or recuperators of heat, containing a quantity of thin firebricks
+  piled into a cellular mass so as to offer a very large heat-absorbing
+  surface, whereby their temperature is very considerably reduced, and
+  they arrive at the chimney at a heat not exceeding 300 or 400 degrees.
+  As soon as the bricks have become red hot, the current is diverted to
+  an adjacent chamber or pair of chambers, and the acquired heat is
+  removed by a current of cool gas or air passing towards the furnace,
+  where it arrives at a temperature sufficiently high to ensure the
+  greatest possible heating effect in combustion.
+
+  In iron-smelting blast furnaces the waste gases are of considerable
+  fuel value, and may render important services if properly applied.
+  Owing to the conditions of the work, which require the maintenance of
+  a sensibly reducing atmosphere, they contain a very notable proportion
+  of carbonic oxide, and are drawn off by large wrought iron tubes near
+  the top of the furnace and conveyed by branch pipes to the different
+  boilers and air-heating apparatus, which are now entirely heated by
+  the combustion of such gases, or mixed with air and exploded in gas
+  engines. Formerly they were allowed to burn to waste at the mouth of a
+  short chimney place above the furnace top, forming a huge body of
+  flame, which was one of the most striking features of the Black
+  Country landscape at night.
+
+  _Laboratory and Portable Furnaces._--Small air-furnaces with hot
+  plates or sand bath flues were formerly much employed in chemical
+  laboratories, as well as small blast furnaces for crucibles heated
+  with charcoal or coke. The use of such furnaces has very considerably
+  diminished, owing to the general introduction of coal-gas for heating
+  purposes in laboratories, which has been rendered possible by the
+  invention of the Bunsen burner, in which the mixture of air and gas
+  giving the least luminous but most powerfully heating flame is
+  effected automatically by the effluent gas. These burners, or
+  modifications of them, have also been applied to muffle furnaces,
+  which are convenient when only a few assays have to be made--the
+  furnace being a mere clay shell and soon brought to a working
+  temperature; but the fuel is too expensive to allow of their being
+  used habitually or on a large scale. Petroleum, or rather the heavy
+  oils obtained in tar refineries, having an equal or superior heating
+  power to coal-gas, may also be used in laboratories for producing high
+  temperatures. The oil is introduced in a thin stream upon a series of
+  inclined and channelled bars, where it is almost immediately
+  volatilized and burnt by air flowing in through parallel orifices.
+  Furnaces of this kind may be used for melting cast iron or bronze in
+  small quantities, and were employed by H. Sainte Claire Deville in
+  experiments in the metallurgy of the platinum group of metals.
+
+  Sefstrom's blast furnace, used in Sweden for the assay of iron ores,
+  is a convenient form of portable furnace applied to melting in
+  crucibles. It consists of a sheet-iron cylinder about 8 or 9 in. in
+  diameter, within which is fixed one of smaller size lined with
+  fireclay. The space between the two cylinders serves as a heater and
+  distributor for the blast, which is introduced through the nozzle at
+  the bottom, and enters the furnace through a series of several small
+  tuyeres arranged round the inner lining. Charcoal is the fuel used,
+  and the crucibles stand upon the bottom of the clay lining. When a
+  large body of fuel is required, the cylinder can be lengthened by an
+  iron hoop which fits over the top ring. Deville's portable blast
+  furnace is very similar in principle to the above, but the body of the
+  furnace is formed of a single cast iron cylinder lined with fireclay,
+  closed below by a cast iron plate perforated by a ring of small
+  holes--a hemispherical basin below forming the air-heating chamber.
+
+
+
+
+FURNEAUX, TOBIAS (1735-1781), English navigator, was born at Swilly near
+Plymouth on the 21st of August 1735. He entered the royal navy, and was
+employed on the French and African coasts and in the West Indies during
+the latter part of the Seven Years' War (1760-1763). He served as second
+lieutenant of the "Dolphin" under Captain Samuel Wallis on the latter's
+voyage round the globe (August 1766-May 1768); was made a commander in
+November 1771; and commanded the "Adventure" which accompanied Captain
+Cook (in the "Resolution") in Cook's second voyage. On this expedition
+Furneaux was twice separated from his leader (February 8-May 19, 1773;
+October 22, 1773-July 14, 1774, the date of his return to England). On
+the former occasion he explored a great part of the south and east
+coasts of Tasmania, and made the earliest British chart of the same.
+Most of his names here survive; Cook, visiting this shore-line on his
+third voyage, confirmed Furneaux's account and delineation of it (with
+certain minor criticisms and emendations), and named after him the
+islands in Banks Straits, opening into Bass's Straits, and the group now
+known as the Low Archipelago. After the "Adventure" was finally
+separated from the "Resolution" off New Zealand in October 1773,
+Furneaux returned home alone, bringing with him Omai of Ulaietea. This
+first South Sea Islander seen in the British Isles returned to his home
+with Cook in 1776-1777. Furneaux was made a captain in 1775, and
+commanded the "Syren" in the British attack of the 28th of June 1776
+upon Charleston, South Carolina. His successful efforts to introduce
+domestic animals and potatoes into the South Sea Islands are worthy of
+note. He died at Swilly on the 19th of September 1781.
+
+  See Hawkesworth's _Narrative of Wallis' Voyage_; Captain Cook's
+  _Narrative of his Second Voyage_; also T. Furneaux's life by Rev.
+  Henry Furneaux in the _Dictionary of National Biography_.
+
+
+
+
+
+FURNES (Flem. _Veurne_), an old-fashioned little town amid the dunes
+near the coast in West Flanders, Belgium, about 26 m. S.W. of Bruges.
+Pop. (1904) 6099. It is the centre of a considerable area extending to
+the French frontier, and its market is an important one for the disposal
+of corn, stock, hops and dairy produce. During the Norman raids Furnes
+was destroyed, and the present town was built by Baldwin Bras de Fer,
+first count of Flanders, about the year 870. At the height of the
+prosperity of the Flemish communes in the 14th century there were
+dependent on the barony of Furnes not fewer than fifty-two rich
+villages, but these have all disappeared, partly no doubt as the
+consequence of repeated French invasions down to the end of the 18th
+century, but chiefly through the encroachment of the sea followed by the
+accumulation of sand along the whole of this portion of the coast.
+Furnes contains many curious old houses and the church of St Walburga,
+which is a fine survival of the 13th century with some older portions.
+The old church and buildings, grouped round the Grand Place, which is
+the scene of the weekly market, present a quaint picture which is
+perhaps not to be equalled in the country. Near Furnes on the seashore
+is the fashionable bathing place called La Panne.
+
+Furnes one day a year becomes a centre of attraction to all the people
+of Flanders. This is the last Sunday in July, when the fête of Calvary
+and the Crucifixion is celebrated. Of all popular festivities in Belgium
+this is the nearest approach to the old Passion Play. The whole story of
+Christ is told with great precision by means of succeeding groups which
+typify the different phases of the subject. The people of Furnes pose as
+Roman soldiers or Jewish priests, as the apostles or mere spectators,
+while the women put on long black veils so that they may figure in the
+procession as the just women.
+
+
+
+
+FURNESS, HORACE HOWARD (1833-   ), American Shakespearian scholar, was
+born in Philadelphia on the 2nd of November 1833, being the son of
+William Henry Furness (1802-1896) minister of the First Unitarian church
+in that city, a powerful preacher and writer. He graduated at Harvard in
+1854, and was admitted to the bar in 1859, but soon devoted himself to
+the study of Shakespeare. He accumulated a collection of illustrative
+material of great richness and extent, and brought out in 1871 the first
+volume of a new Variorum edition, designed to represent and summarize
+the conclusions of the best authorities in all languages--textual,
+critical and annotative. The volumes appeared as follows: _Romeo and
+Juliet_ (1871); _Macbeth_ (1873) (revised edition, 1903); _Hamlet_ (2
+vols., 1877); _King Lear_ (1880); _Othello_ (1886); _The Merchant of
+Venice_ (1888); _As You Like It_ (1890); _The Tempest_ (1892); _A
+Midsummer Night's Dream_ (1895); _The Winter's Tale_ (1898); _Much Ado
+about Nothing_ (1899); _Twelfth Night_ (1901); _Love's Labour's Lost_
+(1904). The edition has been generally accepted as a thorough and
+scholarly piece of work; its chief fault is that, beginning with
+_Othello_ (1858), the editor used the First Folio text as his basis,
+while in others he makes the text of the Cambridge (Globe) editors his
+foundation. His wife, Helen Kate Furness (1837-1883), compiled _A
+Concordance to the Poems of Shakespeare_ (1872).
+
+
+
+
+FURNESS, a district of Lancashire, England, separated from the major
+portion of the county by Morecambe Bay. It is bounded S.E. by this inlet
+of the Irish Sea, S.W. by the sea, W. by the Duddon estuary and
+Cumberland, and N. and E. by Westmorland. Its area is about 250 sq. m.
+It forms the greater part of the North Lonsdale parliamentary division
+of Lancashire, and contains the parliamentary borough of
+Barrow-in-Furness. The surface is almost entirely hilly. The northern
+half is included in the celebrated Lake District, and contains such
+eminences as the Old Man of Coniston and Wetherlam. Apart from the
+Duddon, which forms part of the western boundary, the principal rivers
+are the Leven and Crake, flowing southward into a common estuary in
+Morecambe Bay. The Leven drains Windermere and the Crake Coniston Lake.
+The usage of the term "Lake District," however, tends to limit the name
+of Furness in common thought to the district south of the Lakes, where
+several of the place-names are suffixed with that of the district, as
+Barrow-in-Farness, Dalton-in-Furness, Broughton-in-Furness. Between the
+Duddon and Morecambe Bay lies Walney Island, 8 m. in length, and in the
+shallow strait between it and the mainland are several smaller islands.
+That part of Furness which forms a peninsula between the Leven estuary
+and Morecambe Bay, and the Duddon estuary, is rich in hematite iron ore,
+which has been worked from very early times. It was known and smelted by
+British and Romans, and by the monks of Furness Abbey and Conishead
+Priory, both in the district. It was owing to the existence of this ore
+that the town of Barrow grew up in the 19th century; at first as a port
+from which the ore was exported to South Wales, while later furnaces
+were established on the spot, and acquired additional importance on the
+introduction of the Bessemer process, which requires a non-phosphoric
+ore such as is found here. The hematite is also worked at Ulverston,
+Askam, Dalton and elsewhere, but the furnaces now depend in part upon
+ore imported from Spain. The supposed extension of the ore under the
+sands of the Duddon estuary led to the construction of a sea wall to
+facilitate the working. The district is served by the main line of the
+Furness railway, from Carnforth (junction with the London &
+North-Western railway), passing the pleasant watering-place of Grange,
+and approximately following the coast by Ulverston, Dalton and Barrow,
+with branches to Lake Side, Windermere, and to Coniston.
+
+
+  Furness Abbey.
+
+Apart from its industrial importance and scenic attractions, Furness has
+an especial interest on account of its famous abbey. The ruins of this,
+beautifully situated in a wooded valley, are extensive, and mainly of
+fine transitional Norman and Early English date, acquiring additional
+picturesqueness from the warm colour of the red sandstone of which they
+are built. The abbey of Furness, otherwise Furdenesia or the further
+_nese_ (promontory), which was dedicated to St Mary, was founded in 1127
+by a small body of monks belonging to the Benedictine order of Savigny.
+In 1124 they had settled at Tulketh, near Preston, but migrated in 1127
+to Furness under the auspices of Stephen, count of Boulogne, afterwards
+king, at that time lord of the liberty of Furness. In 1148 the
+brotherhood joined the Cistercian order. Stephen granted to the monks
+the lordship of Furness, and his charter was confirmed by Henry I.,
+Henry II. and subsequent kings. The abbot's power throughout the
+lordship was almost absolute; he had a market and fair at Dalton, was
+free from service to the county and wapentake, and held a sheriff's
+tourn. By a succession of gifts the abbey became one of the richest in
+England and was the largest Cistercian foundation in the kingdom. At the
+Dissolution its revenues amounted to between £750 and £800 a year,
+exclusive of meadows, pastures, fisheries, mines, mills and salt works,
+and the wealth of the monks enabled them to practise a regal
+hospitality. The abbot was one of the twenty Cistercian abbots summoned
+to the parliament of 1264, but was not cited after 1330, as he did not
+hold of the king _in capite per baroniam_. The abbey founded several
+offshoot houses, one of the most important being Rushen Abbey in the
+Isle of Man. In 1535 the royal commissioners visited the abbey and
+reported four of its inmates, including the abbot, for incontinence. In
+1536 the abbot was charged with complicity in the Pilgrimage of Grace,
+and on the 7th of April 1537, under compulsion, surrendered the abbey to
+the king. A few monks were granted pensions, and the abbot was endowed
+with the profits of the rectory of Dalton, valued at £33, 6s. 8d. per
+annum. In 1540 the estates and revenues were annexed by act of
+parliament to the Duchy of Lancaster. About James I.'s reign the site
+and territories were alienated to the Prestons of Preston-Patrick, from
+whom they descended to the dukes of Devonshire.
+
+Conishead Priory, near Ulverston, an Augustinian foundation of the reign
+of Henry II., has left no remains, but of the priory of Cartmel (1188)
+the fine church is still in use. It is a cruciform structure of
+transitional Norman and later dates, its central tower having the upper
+storey set diagonally upon the lower. The chancel contains some superb
+Jacobean carved oak screens, with stalls of earlier date.
+
+
+
+
+FURNISS, HARRY (1854-   ), British caricaturist and illustrator, was
+born at Wexford, Ireland, of English and Scottish parents. He was
+educated in Dublin, and in his schooldays edited a _Schoolboy's Punch_
+in close imitation of the original. He came to London when he was
+nineteen, and began to draw for the illustrated papers, being for some
+years a regular contributor to the _Illustrated London News_. His first
+drawing in _Punch_ appeared in 1880, and he joined its staff in 1884. He
+illustrated Lucy's "Diary of Toby, M.P.," in _Punch_, where his
+political caricatures became a popular feature. Among his other
+successes were a series of "Puzzle Heads," and his annual "Royal Academy
+guy'd." In _Royal Academy Antics_ (1890) he published a volume of
+caricatures of the work of leading artists. He resigned from the staff
+of _Punch_ in 1894, produced for a short time a weekly comic paper _Lika
+Joko_, and in 1898 began a humorous monthly, _Fair Game_; but these were
+short-lived. Among the numerous books he illustrated were James Payn's
+_Talk of the Town_, Lewis Carroll's _Sylvie and Bruno_, Gilbert à
+Beckett's _Comic Blackstone_, G.E. Farrow's _Wallypug Book_, and his own
+novel, _Poverty Bay_ (1905). _Our Joe, his great Fight_ (1903), was a
+collection of original cartoons. His volume of reminiscences,
+_Confessions of a Caricaturist_ (1901), was followed by _Harry Furniss
+at Home_ (1904). In 1905 he published _How to draw in Pen and Ink_, and
+produced the first number of _Harry Furniss's Christmas Annual_.
+
+
+
+
+FURNITURE (from "furnish," Fr. _fournir_), a general term of obscure
+origin, used to describe the chattels and fittings required to adapt
+houses and other buildings for use. Wood, ivory, precious stones,
+bronze, silver and gold have been used from the most ancient times in
+the construction or for the decoration of furniture. The kinds of
+objects required for furniture have varied according to the changes of
+manners and customs, as well as with reference to the materials at the
+command of the workman, in different climates and countries. Of really
+ancient furniture there are very few surviving examples, partly by
+reason of the perishable materials of which it was usually constructed;
+and partly because, however great may have been the splendour of Egypt,
+however consummate the taste of Greece, however luxurious the life of
+Rome, the number of household appliances was very limited. The chair,
+the couch, the table, the bed, were virtually the entire furniture of
+early peoples, whatever the degree of their civilization, and so they
+remained until the close of what are known in European history as the
+middle ages. During the long empire-strewn centuries which intervened
+between the lapse of Egypt and the obliteration of Babylon, the
+extinction of Greece and the dismemberment of Rome and the great
+awakening of the Renaissance, household comfort developed but little.
+The Ptolemies were as well lodged as the Plantagenets, and peoples who
+spent their lives in the open air, going to bed in the early hours of
+darkness, and rising as soon as it was light, needed but little
+household furniture.
+
+Indoor life and the growth of sedentary habits exercised a powerful
+influence upon the development of furniture. From being splendid, or at
+least massive, and exceedingly sparse and costly, it gradually became
+light, plentiful and cheap. In the ancient civilizations, as in the
+periods when our own was slowly growing, household plenishings, save in
+the rudest and most elementary forms, were the privilege of the
+great--no person of mean degree could have obtained, or would have dared
+to use if he could, what is now the commonest object in every house, the
+chair (q.v.). Sparse examples of the furniture of Egypt, Nineveh, Greece
+and Rome are to be found in museums; but our chief sources of
+information are mural and sepulchral paintings and sculptures. The
+Egyptians used wooden furniture carved and gilded, covered with splendid
+textiles, and supported upon the legs of wild animals; they employed
+chests and coffers as receptacles for clothes, valuables and small
+objects generally. Wild animals and beasts of the chase were carved upon
+the furniture of Nineveh also; the lion, the bull and the ram were
+especially characteristic. The Assyrians were magnificent in their
+household appointments; their tables and couches were inlaid with ivory
+and precious metals. Cedar and ebony were much used by these great
+Eastern peoples, and it is probable that they were familiar with
+rosewood, walnut and teak. Solomon's bed was of cedar of Lebanon. Greek
+furniture was essentially Oriental in form; the more sumptuous varieties
+were of bronze, damascened with gold and silver. The Romans employed
+Greek artists and workmen and absorbed or adapted many of their
+mobiliary fashions, especially in chairs and couches. The Roman tables
+were of splendid marbles or rare woods. In the later ages of the empire,
+in Rome and afterwards in Constantinople, gold and silver were
+plentifully used in furniture; such indeed was the abundance of these
+precious metals that even cooking utensils and common domestic vessels
+were made of them.
+
+The architectural features so prominent in much of the medieval
+furniture begin in these Byzantine and late Roman thrones and other
+seats. These features became paramount as Pointed architecture became
+general in Europe, and scarcely less so during the Renaissance. Most of
+the medieval furniture, chests, seats, trays, &c., of Italian make were
+richly gilt and painted. In northern Europe carved oak was more
+generally used. State seats in feudal halls were benches with ends
+carved in tracery, backs panelled or hung with cloths (called cloths of
+estate), and canopies projecting above. Bedsteads were square frames,
+the testers of panelled wood, resting on carved posts. Chests of oak
+carved with panels of tracery, or of Italian cypress (when they could be
+imported), were used to hold and to carry clothes, tapestries, &c., to
+distant castles and manor houses; for house furniture, owing to its
+scarcity and cost, had to be moved from place to place. Copes and other
+ecclesiastical vestments were kept in chests with ornamental lock plates
+and iron hinges. The splendour of most feudal houses depended on
+pictorial tapestries which could be packed and carried from place to
+place. Wardrobes were rooms fitted for the reception of dresses, as well
+as for spices and other valuable stores. Excellent carving in relief was
+executed on caskets, which were of wood or of ivory, with painting and
+gilding, and decorated with delicate hinge and lock metal-work. The
+general subjects of sculpture were taken from legends of the saints or
+from metrical romances. Renaissance art made a great change in
+architecture, and this change was exemplified in furniture. Cabinets
+(q.v.) and panelling took the outlines of palaces and temples. In
+Florence, Rome, Venice, Milan and other capitals of Italy, sumptuous
+cabinets, tables, chairs, chests, &c., were made to the orders of the
+native princes. Vasari (_Lives of Painters_) speaks of scientific
+diagrams and mathematical problems illustrated in costly materials, by
+the best artists of the day, on furniture made for the Medici family.
+The great extent of the rule of Charles V. helped to give a uniform
+training to artists from various countries resorting to Italy, so that
+cabinets, &c., which were made in vast numbers in Spain, Flanders and
+Germany, can hardly be distinguished from those executed in Italy.
+Francis I. and Henry VIII. encouraged the revived arts in their
+respective dominions. _Pietra dura_, or inlay of hard pebbles, agate,
+lapis lazuli, and other stones, ivory carved and inlaid, carved and gilt
+wood, marquetry or veneering with thin woods, tortoise-shell, brass,
+&c., were used in making sumptuous furniture during the first period of
+the Renaissance. Subjects of carving or relief were generally drawn from
+the theological and cardinal virtues, from classical mythology, from the
+seasons, months, &c. Carved altarpieces and woodwork in churches partook
+of the change in style.
+
+The great period of furniture in almost every country was, however,
+unquestionably the 18th century. That century saw many extravagances in
+this, as in other forms of art, but on the whole it saw the richest
+_floraison_ of taste, and the widest sense of invention. This is the
+more remarkable since the furniture of the 17th century has often been
+criticized as heavy and coarse. The criticism is only partly justified.
+Throughout the first three-quarters of the period between the accession
+of James I. and that of Queen Anne, massiveness and solidity were the
+distinguishing characteristics of all work. Towards the reign of James
+II., however, there came in one of the most pleasing and elegant styles
+ever known in England. Nearly a generation before then Boulle was
+developing in France the splendid and palatial method of inlay which,
+although he did not invent it, is inseparably associated with his name.
+We owe it perhaps to the fact that France, as the neighbour of Italy,
+was touched more immediately by the Renaissance than England that the
+reign of heaviness came earlier to an end in that country than on the
+other side of the Channel. But there is a heaviness which is pleasing as
+well as one which is forbidding, and much of the furniture made in
+England any time after the middle of the 17th century was highly
+attractive. If English furniture of the Stuart period be not sought
+after to the same extent as that of a hundred years later, it is yet
+highly prized and exceedingly decorative. Angularity it often still
+possessed, but generally speaking its elegance of form and richness of
+upholstering lent it an attraction which not long before had been
+entirely lacking. Alike in France and in England, the most attractive
+achievements of the cabinetmaker belong to the 18th century--English
+Queen Anne and early Georgian work is universally charming; the regency
+and the reigns of Louis XV. and XVI. formed a period of the greatest
+artistic splendour. The inspiration of much of the work of the great
+English school was derived from France, although the gropings after the
+Chinese taste and the earlier Gothic manner were mainly indigenous. The
+French styles of the century, which began with excessive flamboyance,
+closed before the Revolution with a chaste perfection of detail which is
+perhaps more delightful than anything that has ever been done in
+furniture. In the achievements of Riesener, David Röntgen, Gouthière,
+Oeben and Rousseau de la Rottière we have the high-water mark of
+craftsmanship. The marquetry of the period, although not always
+beautiful in itself, was executed with extraordinary smoothness and
+finish; the mounts of gilded bronze, which were the leading
+characteristic of most of the work of the century, were finished with a
+minute delicacy of touch which was until then unknown, and has never
+been rivalled since. If the periods of Francis I. and Henry II., of
+Louis XIV. and the regency produced much that was sumptuous and even
+elegant, that of Louis XVI., while men's minds were as yet undisturbed
+by violent political convulsions, stands out as, on the whole, the one
+consummate era in the annals of furniture. Times of great achievement
+are almost invariably followed directly by those in which no tall
+thistles grow and in which every little shrub is magnified to the
+dimensions of a forest tree; and the so-called "empire style" which had
+begun even while the last monarch of the _ancien régime_ still reigned,
+lacked alike the graceful conception and the superb execution of the
+preceding style. Heavy and usually uninspired, it was nurtured in
+tragedy and perished amid disaster. Yet it is a profoundly interesting
+style, both by reason of the classical roots from which it sprang and
+the attempt, which it finally reflected, to establish new ideas in every
+department of life. Founded upon the wreck of a lingering feudalism it
+reached back to Rome and Greece, and even to Egypt. If it is rarely
+charming, it is often impressive by its severity. Mahogany, satinwood
+and other rich timbers were characteristic of the style of the end of
+the 18th century; rosewood was most commonly employed for the choicer
+work of the beginning of the 19th. Bronze mounts were in high favour,
+although their artistic character varied materially.
+
+Previously to the middle of the 18th century the only cabinetmaker who
+gained sufficient personal distinction to have had his name preserved
+was André Charles Boulle; beginning with that period France and England
+produced many men whose renown is hardly less than that of artists in
+other media. With Chippendale there arose a marvellously brilliant
+school of English cabinetmakers, in which the most outstanding names are
+those of Sheraton, Heppelwhite, Shearer and the Adams. But if the school
+was splendid it was lamentably short-lived, and the 19th century
+produced no single name in the least worthy to be placed beside these
+giants. Whether, in an age of machinery, much room is left for fine
+individual execution may be doubted, and the manufacture of furniture
+now, to a great extent, takes place in large factories both in England
+and on the continent. Owing to the necessary subdivision of labour in
+these establishments, each piece of furniture passes through numerous
+distinct workshops. The master and a few artificers formerly
+superintended each piece of work, which, therefore, was never far
+removed from the designer's eye. Though accomplished artists are
+retained by the manufacturers of London, Paris and other capitals, there
+can no longer be the same relation between the designer and his work.
+Many operations in these modern factories are carried on by machinery.
+This, though an economy of labour, entails loss of artistic effect. The
+chisel and the knife are no longer in such cases guided and controlled
+by the sensitive touch of the human hand.
+
+[Illustration: PLATE I.
+
+  FIG. 1.--Venetian Folding Chair of carved and gilt walnut, leather
+  back and seat; about 1530.
+
+  FIG. 2.--Oak Arm-chair. English, 17th century.
+
+  FIG. 3.--Arm-chair, solid seat, cane back; about 1660.
+
+  FIG. 4.--Arm-chair, stuffed back and seat; about 1650.
+
+  FIG. 5.--Painted and carved High-Back Chair; about 1660.
+
+  FIG. 6.--Carved Walnut Chairs. English, early 18th century. The
+  arm-chair is inlaid.
+
+  FIG. 7.--Walnut Chair; about 1710.
+
+  FIG. 8.--Carved Mahogany Chair in the style of Chippendale; 2nd half
+  of 18th century.
+
+  FIG. 9.--Carved Mahogany Arm-chair, in the style of Chippendale, with
+  ribbon pattern.
+
+  FIG. 10.--Carved and Inlaid Mahogany Chair, in the style of
+  Hepplewhite; late 18th century.
+
+  FIG. 11.--Mahogany Chair in the style of Sheraton; about 1780.
+
+  Fig. 12.--Painted and gilt Arm-chair with cane seat, in the style of
+  Adam; about 1790.
+
+  FIG. 13.--Arm-chair of carved and gilt wood with stuffed back, seat
+  and arms. French, Louis XV. style.
+
+  FIG. 14.--Mahogany Arm-chair. Empire style, early 19th century, said
+  to have belonged to the Bonaparte family.
+
+  FIG. 15.--Painted and gilt Beech Chair. English, about 1800.]
+
+[Illustration: PLATE II.
+
+  FIG. 1.--Front of Oak Coffer with wrought iron bands. French, 2nd half
+  of 13th century.
+
+  FIG. 2.--English Oak Chest, dated 1637.
+
+  FIG. 3.--Italian (Florentine) Coffer of Wood with gilt arabesque
+  stucco ornament, about 1480.
+
+  FIG. 4.--Italian "Cassone" or Marriage Coffer, 13th century. Carved
+  and gilt wood with painted front and ends.
+
+  FIG. 5.--Walnut Table with expanding leaves. Swiss, 17th century.
+
+  FIG. 6.--Oak Gate-Legged Table. English, 17th century.
+
+  FIG. 7.--Writing Table. French, end of Louis XV. period. Riesener
+  marquetry, ormolu mounts and Sèvres plaques.
+
+  FIG. 8.--Painted Satin-Wood Tables, in the style of Sheraton, about
+  1790.
+
+  (The above are in the Victoria and Albert Museum, except Fig. 8, which
+  were in the Bethnal Green Exhibition, 1892.)]
+
+[Illustration: PLATE III.
+
+  1. CARVED OAK SIDEBOARD. English, 17th century. Victoria and Albert
+  Museum.
+
+  2. CARVED OAK COURT CUPBOARD. English, early 17th century. Victoria
+  and Albert Museum.
+
+  3. EBONY CARVED CABINET. The interior decorated with inlaid ivory and
+  coloured woods; French or Dutch, middle of 17th century. Victoria and
+  Albert Museum.
+
+  4. VENEERED CHEST OF DRAWERS. About 1690. Lent to Bethnal Green
+  Exhibition by Sir Spencer Ponsonby-Fane, G.C.B.
+
+  5. EBONY ARMOIRE. With tortoise-shell panels inlaid with brass and
+  other metals, and ormolu mountings. Designed by Bérain, and executed
+  by André Boulle. French, Louis XIV. period. Victoria and Albert
+  Museum.
+
+  6. GLASS-FRONTED BOOKCASE AND CABINET. Of mahogany. In the style of
+  Sheraton, about 1790. Lent to the Bethnal Green Exhibition by the late
+  Vincent J. Robinson, C.I.E.]
+
+[Illustration: PLATE IV.
+
+  1. COMMODE OF PINE. With marquetry of brass, ebony, tortoise-shell,
+  mother-of-pearl, ivory, and green-stained bone. "Boulle" work with
+  designs in the style of Bérain. French, late period of Louis XIV.
+
+  2. COMMODE. With panels of Japanese lacquer and ormolu mountings, in
+  the style of Caffieri. French, Louis XV. period.
+
+  3. TABLE OF KING AND TULIP WOODS. With ormolu mountings. Louis XV.
+  period.
+
+  4. ESCRITOIRE À TOILETTE. Formerly belonging to Marie Antoinette. Of
+  tulip and sycamore woods inlaid with other coloured woods, ormolu
+  mounts. Louis XV. period.
+
+  5. FOUR-POST BEDSTEAD. Of oak inlaid with bog-oak and holly, from the
+  "Inlaid Room" at Sizergh Castle, Westmorland. Latter half of sixteenth
+  century.
+
+  6. CARVED AND GILT BEDSTEAD. With blue silk damask coverings and
+  hangings. French, late 18th century. Louis XVI. period.
+
+  From the Victoria and Albert Museum, S. Kensington.]
+
+[Illustration: PLATE V.
+
+  _Photo, Mansell & Co._
+
+  THE "BUREAU DU ROI," MADE FOR LOUIS XV., NOW IN THE LOUVRE. For
+  description, see DESK.]
+
+A decided, if not always intelligent, effort to devise a new style in
+furniture began during the last few years of the 19th century, which
+gained the name of "_l'art nouveau_." Its pioneers professed to be free
+from all old traditions and to seek inspiration from nature alone.
+Happily nature is less forbidding than many of these interpretations of
+it, and much of the "new art" is a remarkable exemplification of the
+impossibility of altogether ignoring traditional forms. The style was
+not long in degenerating into extreme extravagance. Perhaps the most
+striking consequence of this effort has been, especially in England, the
+revival of the use of oak. Lightly polished, or waxed, the cheap foreign
+oaks often produce very agreeable results, especially when there is
+applied to them a simple inlay of boxwood and stained holly, or a modern
+form of pewter. The simplicity of these English forms is in remarkable
+contrast to the tortured and ungainly outlines of continental seekers
+after a conscious and unpleasing "originality."
+
+Until a very recent period the most famous collections of historic
+furniture were to be found in such French museums as the Louvre, Cluny
+and the Garde Meuble. Now, however, they are rivalled, if not surpassed,
+by the magnificent collections of the Victoria and Albert Museum at
+South Kensington, and the Wallace collection at Hertford House, London.
+The latter, in conjunction with the Jones bequest at South Kensington,
+forms the finest of all gatherings of French furniture of the great
+periods, notwithstanding that in the Bureau du Roi the Louvre possesses
+the most magnificent individual example in existence. In America there
+are a number of admirable collections representative of the graceful and
+homely "colonial furniture" made in England and the United States during
+the Queen Anne and Georgian periods.
+
+  See also the separate articles in this work on particular forms of
+  furniture. The literature of the subject has become very extensive,
+  and it is needless to multiply here the references to books. Perrot
+  and Chipiez, in their great _Histoire de l'art dans l'antiquité_ (1882
+  et seq.) deal with ancient times, and A. de Champeaux, in _Le Meuble_
+  (1885), with the middle ages and later period; English furniture is
+  admirably treated by Percy Macquoid in his _History of English
+  Furniture_ (1905); and Lady Dilke's _French Furniture in the 18th
+  Century_ (1901), and Luke Vincent Lockwood's _Colonial Furniture in
+  America_ (1901), should also be consulted.     (J. P. B.)
+
+
+
+
+FURNIVALL, FREDERICK JAMES (1825-1910), English philologist and editor,
+was born at Egham, Surrey, on the 4th of February 1825, the son of a
+surgeon. He was called to the bar in 1849, but his attention was soon
+diverted to philological studies and social problems. He gave Frederick
+Denison Maurice valuable assistance in the Christian Socialist movement,
+and was one of the founders of the Working Men's College. For half a
+century he indefatigably promoted the study of early English literature,
+partly by his own work as editor, and still more efficaciously by the
+agency of the numerous learned societies of which he was both founder
+and director, especially the Early English Text Society (1864), which
+has been of inestimable service in promoting the study of early and
+middle English. He also established and conducted the Chaucer, Ballad,
+New Shakespeare and Wyclif Societies, and at a later period societies
+for the special study of Browning and Shelley. He edited texts for the
+Early English Text Society, for the Roxburghe Club and the Rolls Series;
+but his most important labours were devoted to Chaucer, whose study he
+as an editor greatly assisted by his "Six-Text" edition of the
+_Canterbury Tales_, and other publications of the Chaucer Society. He
+was the honorary secretary of the Philological Society, and was one of
+the original promoters of the Oxford _New English Dictionary_. He
+co-operated with its first editor, Herbert Coleridge, and after his
+death was for some time principal editor during the preliminary period
+of the collection of material. The completion of his half-century of
+labour was acknowledged in 1900 by a handsome testimonial, including the
+preparation by his friends of a volume of philological essays specially
+dedicated to him, _An English Miscellany_ (Oxford, 1901), and a
+considerable donation to the Early English Text Society. Dr Furnivall
+was always an enthusiastic oarsman, and till the end kept up his
+interest in rowing; with John Beesley in 1845 he introduced the new type
+of narrow sculling boat, and in 1886 started races on the Thames for
+sculling fours and sculling eights. He died on the 2nd of July 1910.
+
+
+
+
+FURSE, CHARLES WELLINGTON (1868-1904), English painter, born at Staines,
+the son of the Rev. C.W. Furse, archdeacon of Westminster, was descended
+collaterally from Sir Joshua Reynolds, and in his short span of life
+achieved such rare excellence as a portrait and figure painter that he
+forms an important link in the chain of British portraiture which
+extends from the time when Van Dyck was called to the court of Charles
+I. to our own day. His talent was precocious; at the age of seven he
+gave indications of it in a number of drawings illustrating Scott's
+novels. He entered the Slade school in 1884, winning the Slade
+scholarship in the following year, and completed his education at
+Julian's _atelier_ in Paris. Hard worker as he was, his activity was
+frequently interrupted by spells of illness, for he had developed signs
+of consumption when he was still attending the Slade school. An
+important canvas called "Cain" was his first contribution (1888) to the
+Royal Academy, to the associateship of which he was elected in the year
+of his death. For some years before he had been a staunch supporter of
+the New English Art Club, to the exhibitions of which he was a regular
+contributor. He was married in October 1900 to Katherine, daughter of
+John Addington Symonds. His fondness for sport and of an open-air life
+found expression in his art and introduced a new, fresh and vigorous
+note into portraiture. There is never a suggestion of the studio or of
+the fatiguing pose in his portraits. The sitters appear unconscious of
+being painted, and are generally seen in the pursuit of their favourite
+outdoor sport or pastime, in the full enjoyment of life. Such are the
+"Diana of the Uplands," the "Lord Roberts" and "The Return from the
+Ride" at the Tate Gallery; the four children in the "Cubbing with the
+York and Ainsty," "The Lilac Gown," "Mr and Mrs Oliver Fishing" and the
+portrait of Lord Charles Beresford. Most of these pictures, and indeed
+nearly all the work completed in the few years of Furse's activity, show
+a pronounced decorative tendency. His sense of space, composition and
+decorative design can best be judged by his admirable mural decorations
+for Liverpool town hall, executed between 1899 and 1902. A memorial
+exhibition of Furse's paintings and sketches was held at the Burlington
+Fine Arts Club in 1906.
+
+
+
+
+FÜRST, JULIUS (1805-1873), German Orientalist, was born of Jewish
+parents at Zerkowo in Posen, on the 12th of May 1805. He studied
+philosophy and philology at Berlin, and oriental literature at Posen,
+Breslau and Halle. In 1857 he was appointed to a lectureship at the
+university of Leipzig, and he was promoted to a professorship in 1864,
+which he held until his death at Leipzig on the 9th of February 1873.
+Among his writings may be mentioned _Lehrgebäude der aramäischen Idiome_
+(Leipzig, 1835); _Librorum sacrorum Veteris Testamenti concordantiae
+Hebraicae atque Chaldaicae_ (Leipzig, 1837-1840); _Hebräisches und
+chaldäisches Wörterbuch_ (1851, English translation by S. Davidson
+1867); _Kultur und Literaturgeschichte der Juden in Asien_ (1849). Fürst
+also edited a valuable _Bibliotheca Judaica_ (Leipzig, 1849-1863), and
+was the author of some other works of minor importance. From 1840 to
+1851 he was editor of _Der Orient_, a journal devoted to the language,
+literature, history and antiquities of the Jews.
+
+
+
+
+FÜRSTENBERG, the name of two noble houses of Germany.
+
+1. The more important is in possession of a mediatized principality in
+the district of the Black Forest and the Upper Danube, which comprises
+the countship of Heiligenberg, about 7 m. to the N. of the Lake of
+Constance, the landgraviates of Stühlingen and Baar, and the lordships
+of Jungnau, Trochtelfingen, Hausen and Möskirch or Messkirch. The
+territory is discontinuous; and as it lies partly in Baden, partly in
+Württemberg, and partly in the Prussian province of Sigmaringen, the
+head of the family is an hereditary member of the first chamber of Baden
+and of the chamber of peers in Württemberg and in Prussia. The relations
+of the principality with Baden are defined by the treaty of May 1825,
+and its relations with Württemberg by the royal declaration of 1839. The
+_Stammort_ or ancestral seat of the family is Fürstenberg in the Black
+Forest, about 13 m. N. of Schaffhausen, but the principal residence of
+the present representatives of the main line is at Donaueschingen.
+
+The family of Fürstenberg claims descent from a certain Count Unruoch, a
+contemporary of Charlemagne, but their authentic pedigree is only
+traceable to Egino II., count of Urach, who died before 1136. In 1218
+his successors inherited the possessions of the house of Zähringen in
+the Baar district of the Black Forest, where they built the town and
+castle of Fürstenberg. Of the two sons of Egino V. of Urach, Conrad, the
+elder, inherited the Breisgau and founded the line of the counts of
+Freiburg, while the younger, Heinrich (1215-1284), received the
+territories lying in the Kinzigthal and Baar, and from 1250 onward
+styled himself first lord, then count, of Fürstenberg. His territories
+were subsequently divided among several branches of his descendants,
+though temporarily reunited under Count Friedrich III., whose wife,
+Anna, heiress of the last count of Wardenberg, brought him the countship
+of Heiligenberg and lordships of Jungnau and Trochtelfingen in 1534. On
+Friedrich's death (1559) his territories were divided between his two
+sons, Joachim and Christof I. Of these the former founded the line of
+Heiligenberg, the latter that of Kinzigthal. The Kinzigthal branch was
+again subdivided in the 17th century between the two sons of Christof
+II. (d. 1614), the elder, Wratislaw II. (d. 1642), founding the line of
+Mösskirch, the younger, Friedrich Rudolf (d. 1655), that of Stühlingen.
+The Heiligenberg branch received an accession of dignity by the
+elevation of Count Hermann Egon (d. 1674) to the rank of prince of the
+Empire in 1664, but his line became extinct with the death of his son
+Prince Anton Egon, favourite of King Augustus the Strong and regent of
+Saxony, in 1716. The heads of both the Mösskirch and Stühlingen lines
+were now raised to the dignity of princes of the Empire (1716). The
+Mösskirch branch died out with Prince Karl Friedrich (d. 1744); the
+territories of the Stühlingen branch had been divided on the death of
+Count Prosper Ferdinand (1662-1704) between his two sons, Joseph Wilhelm
+Ernst (1699-1762) and Ludwig August Egon (1705-1759). The first of these
+was created prince of the Empire on the 10th of December 1716, and
+founded the princely line of the Swabian Fürstenbergs; in 1772 he
+obtained from the emperor Francis I. for all his legitimate sons and
+their descendants the right to bear, instead of the style of landgrave,
+that of prince, which had so far been confined to the reigning head of
+the family. Ludwig, on the other hand, founded the family of the
+landgraves of Fürstenberg, who, since their territories lay in Austria
+and Moravia, were known as the "cadet line in Austria." The princely
+line became extinct with the death of Karl Joachim in 1804, and the
+inheritance passed to the Bohemian branch of the Austrian cadet line in
+the person of Karl Egon II. (see below). Two years later the
+principality was mediatized.
+
+In 1909 there were two branches of the princely house of Fürstenberg:
+(1) the main branch, that of Fürstenberg-Donaueschingen, the head of
+which was Prince Maximilian Egon (b. 1863), who succeeded his cousin
+Karl Egon III. in 1896; (2) that of Fürstenberg-Königshof, in Bohemia,
+the head of which was Prince Emil Egon (b. 1876), chamberlain and
+secretary of legation to the Austro-Hungarian embassy in London (1907).
+The cadet line of the landgraves of Fürstenberg is now extinct, its last
+representative having been the landgrave Joseph Friedrich Ernst of
+Fürstenberg-Weitra (1860-1896), son of the landgrave Ernst (1816-1889)
+by a morganatic marriage. He was not recognized as _ebenbürtig_ by the
+family. The landgraves of Fürstenberg were in 1909 represented only by
+the landgravines Theresa (b. 1839) and Gabrielle (b. 1844), daughters
+of the landgrave Johann Egon (1802-1879).
+
+From the days of Heinrich of Urach, a relative and notable supporter of
+Rudolph of Habsburg, the Fürstenbergs have played a stirring part in
+German history as statesmen, ecclesiastics and notably soldiers. There
+was a popular saying that "the emperor fights no great battle but a
+Fürstenberg falls." In the Heiligenberg line the following may be more
+particularly noticed.
+
+FRANZ EGON (1625-1682), bishop of Strassburg, was the elder son of Egon
+VII., count of Fürstenberg (1588-1635), who served with distinction as a
+Bavarian general in the Thirty Years' War. He began life as a soldier in
+the imperial service, but on the elevation of his friend Maximilian
+Henry of Bavaria to the electorate of Cologne in 1650, he went to his
+court and embraced the ecclesiastical career. He soon gained a complete
+ascendancy over the weak-minded elector, and, with his brother William
+Egon (see below), was mainly instrumental in making him the tool of the
+aggressive policy of Louis XIV. of France. Ecclesiastical preferments
+were heaped upon him. As a child he had been appointed to a canonry of
+Cologne; to these he added others at Strassburg, Liége, Hildesheim and
+Spires; he became also suffragan bishop and dean of Cologne and provost
+of Hildesheim, and in 1663 bishop of Strassburg. Later he was also
+prince-abbot of Lüders and Murbach and abbot of Stablo and Malmedy. On
+the conclusion of a treaty between the emperor and the elector of
+Cologne, on the 11th of May 1674, Franz was deprived of all his
+preferments in Germany, and was compelled to take refuge in France. He
+was, however, amnestied with his brother William by a special article of
+the treaty of Nijmwegen (1679), whereupon he returned to Cologne. After
+the French occupation of Strassburg (1681) he took up his residence
+there and died on the 1st of April 1682.
+
+His brother WILLIAM EGON (1629-1704), bishop of Strassburg, began his
+career as a soldier in the French service. He went to the court of the
+elector of Cologne at the same time as Franz Egon, whose zeal for the
+cause of Louis XIV. of France he shared. In 1672 the intrigues of the
+two Fürstenbergs had resulted in a treaty of offensive alliance between
+the French monarchy and the electorate of Cologne, and, the brothers
+being regarded by the Imperialists as the main cause of this disaster,
+William was seized by imperial soldiers in the monastery of St Pantaleon
+at Cologne, hurried off to Vienna and there tried for his life. He was
+saved by the intervention of the papal nuncio, but was kept in prison
+till the signature of the treaty of Nijmwegen (1679). As a reward for
+his services Louis XIV. appointed him bishop of Strassburg in succession
+to his brother in 1682, in 1686 obtained for him from Pope Innocent XI.
+the cardinal's hat, and in 1688 succeeded in obtaining his election as
+coadjutor-archbishop of Cologne and successor to the elector Maximilian
+Henry. At the instance of the emperor, however, the pope interposed his
+veto; the canons followed the papal lead, and, the progress of the
+Allies against Louis XIV. depriving him of all prospect of success,
+William Egon retired to France. Here he took up his abode at his abbey
+of St Germain des Près near Paris, where he died on the 10th of April
+1704.
+
+In the Stühlingen line the most notable was KARL EGON (1796-1854),
+prince of Fürstenberg, the son of Prince Karl Alois of Fürstenberg, a
+general in the Austrian service, who was killed at the battle of
+Loptingen on the 25th of March 1799. In 1804 he inherited the Swabian
+principality of Fürstenberg and all the possessions of the family except
+the Moravian estates. He studied at Freiburg and Würzburg, and in 1815
+accompanied Prince Schwarzenberg to Paris as staff-officer. In 1817 he
+came of age, and in the following year married the princess Amalie of
+Baden. By the mediatization of his principality in 1806 the greater part
+of his vast estates had fallen under the sovereignty of the grand-duke
+of Baden, and Prince Fürstenberg took a conspicuous part in the upper
+house of the grand-duchy. In politics he distinguished himself by a
+liberalism rare in a great German noble, carrying through by his
+personal influence with his peers the abolition of tithes and feudal
+dues and stanchly advocating the freedom of the press. He was not less
+distinguished by his large charities: among other foundations he
+established a hospital at Donaueschingen. For the industrial development
+of the country, too, he did much, and proved himself also a notable
+patron of the arts. His palace of Donaueschingen, with its collections
+of paintings, engravings and coins, was a centre of culture, where
+poets, painters and musicians met with princely entertainment. He died
+on the 14th of September 1869, and was succeeded by his son Karl Egon
+II. (1820-1892), with the death of whose son, Karl Egon III., in 1896,
+the title and estates passed to Prince Maximilian Egon, head of the
+cadet line of Fürstenberg-Pürglitz.
+
+  See Münch, _Gesch. des Hauses und des Landes Fürstenberg_, 4 vols.
+  (Aix-la-Chapelle, 1829-1847); S. Riezler, _Gesch. des fürstlichen
+  Hauses Fürstenberg bis 1507_ (Tübingen, 1883); _Fürstenbergisches
+  Urkundenbuch_, edited by S. Riezler and F.L. Baumann, vols. i.-vii.
+  (Tübingen, 1877-1891), continued _s. tit. Mitteilungen aus dem
+  fürstlich. Fürstenbergischem Archiv_ by Baumann and G. Tumbült, 2
+  vols. (ib. 1899-1902); Stokvis, _Manuel d'histoire_ (Leiden,
+  1890-1893); _Almanach de Gotha; Allgemeine deutsche Biographie_.
+
+2. The second Fürstenberg family has its possessions in Westphalia and
+the country of the Rhine, and takes its name from the castle of
+Fürstenberg on the Ruhr. The two most remarkable men whom it has
+produced are Franz Friedrich Wilhelm, freiherr von Fürstenberg, and
+Franz Egon, count von Fürstenberg-Stammheim. The former (1728-1810)
+became ultimately vicar-general of the prince-bishop of Münster, and
+effected a great number of important reforms in the administration of
+the country, besides doing much for its educational and industrial
+development. The latter (1797-1859) was an enthusiastic patron of art,
+who zealously advocated the completion of the Cologne cathedral, and
+erected the beautiful church of St Apollinaris near Remagen on the
+Rhine. He was a member of the Prussian Upper House in 1849, collaborated
+in founding the _Preussisches Wochenblatt_, and was an ardent defender
+of Catholic interests. His son, Count Gisbert von Fürstenberg-Stammheim
+(b. 1836), was in 1909 head of the Rhenish line of the house of
+Fürstenberg.
+
+
+
+
+FÜRSTENWALDE, a town of Germany, in the Prussian province of
+Brandenburg, on the right bank of the Spree, and on the railway from
+Berlin to Frankfort-on-Oder, 28 m. E. of the former city. Pop. (1905)
+20,498. Its beautiful cathedral church contains several old monuments.
+The industries are important, including, besides brewing and malting,
+manufactures of starch, vinegar, electric lamps and gas-fittings,
+stoves, &c., iron-founding and wool-weaving. Fürstenwalde is one of the
+oldest towns of Brandenburg. From 1385 it was the seat of the bishop of
+Lebus, whose bishopric was incorporated with the electorate of Brunswick
+in 1595.
+
+
+
+
+FÜRTH, a manufacturing town of Germany, in the kingdom of Bavaria, at
+the confluence of the Pegnitz with the Regnitz, 5 m. N.W. from Nuremberg
+by rail, at the junction of lines to Hof and Würzburg. Pop. (1885)
+35,455; (1905) 60,638. It is a modern town in appearance, with broad
+streets and palatial business houses. Of its four Evangelical churches,
+the old St Michaeliskirche is a handsome structure; but its chief
+edifices are the new town hall, with a tower 175 ft. high and the
+magnificent synagogue. The Jews have also a high school, which enjoys a
+great reputation. There are besides a classical, a wood-carving and an
+agricultural school and a library. Fürth is the seat of several
+important industries; particularly, the production of chromolithographs
+and picture-books, the manufacture of mirrors and mirror-frames, bronze
+and gold-leaf wares, pencils, toys, haberdashery, optical instruments,
+silver work, turnery, chicory, machinery, fancy boxes and cases, and an
+extensive trade is carried on in these goods as also in hops, metals,
+wool, groceries and coal. A large annual fair is held at Michaelmas and
+lasts for eleven days. The earliest railway in Germany was that between
+Nuremberg and Fürth (opened on the 7th of December 1835).
+
+Fürth was founded, according to tradition, by Charlemagne, who erected a
+chapel there. It was for a time a _Vogtei_ (advocateship) under the
+burgraves of Nuremberg, but about 1314 it was bequeathed to the see of
+Bamberg, and in 1806 it came into the possession of Bavaria. In 1632
+Gustavus Adolphus besieged it in vain, and in 1634 it was pillaged and
+burnt by the Croats. It owes its rise to prosperity to the tolerance it
+meted out to the Jews, who found here an asylum from the oppression
+under which they suffered in Nuremberg.
+
+  See Fronmüller, _Chronik der Stadt Fürth_ (1887).
+
+
+
+
+FURTWÄNGLER, ADOLF (1853-1907), German archaeologist, was born at
+Freiburg im Breisgau, and was educated there, at Leipzig and at Munich,
+where he was a pupil of H. Brunn, whose comparative method in
+art-criticism he much developed. He took part in the excavations at
+Olympia in 1878, became an assistant in the Berlin Museum in 1880, and
+professor at Berlin (1884) and later at Munich. His latest excavation
+work was at Aegina. He was a prolific writer, with a prodigious
+knowledge and memory, and a most ingenious and confident critic; and his
+work not only dominated the field of archaeological criticism but also
+raised its standing both at home and abroad. Among his numerous
+publications the most important were a volume on the bronzes found at
+Olympia, vast works on ancient gems and Greek vases, and the invaluable
+_Masterpieces of Greek Sculpture_ (English translation by Eugénie
+Strong). He died at Athens on the 10th of October 1907.
+
+
+
+
+FURZE, GORSE or WHIN; botanical name _Ulex_ (Ger. _Stechginster_, Fr.
+_ajonc_), a genus of thorny papilionaceous shrubs, of few species,
+confined to west and central Europe and north-west Africa. Common furze,
+_U. europaeus_, is found on heaths and commons in western Europe from
+Denmark to Italy and Greece, and in the Canaries and Azores, and is
+abundant in nearly all parts of the British Isles. It grows to a height
+of 2-6 ft.; it has hairy stems, and the smaller branches end each in a
+spine; the leaves, sometimes lanceolate on the lowermost branches, are
+mostly represented by spines from 2 to 6 lines long, and branching at
+their base; and the flowers, about three-quarters of an inch in length,
+have a shaggy, yellowish-olive calyx, with two small ovate bracts at its
+base, and appear in early spring and late autumn. They are yellow and
+sweet-scented and visited by bees. The pods are few-seeded; their
+crackling as they burst may often be heard in hot weather. This species
+comprises the varieties _vulgaris_, or _U. europaeus_ proper, which has
+spreading branches, and strong, many-ridged spines, and _strictus_
+(Irish furze), with erect branches, and slender 4-edged spines. The
+other British species of furze is _U. nanus_, dwarf furze, a native of
+Belgium, Spain and the west of France; it is a procumbent plant, less
+hairy than _U. europaeus_, with smaller and more orange-coloured
+flowers, which spring from the primary spines, and have a nearly smooth
+calyx, with minute basal bracts. Furze, or gorse, is sometimes employed
+for fences.
+
+Notwithstanding its formidable spines, the young shoots yield a
+palatable and nutritious winter forage for horses and cattle. To fit it
+for this purpose it must be chopped and bruised to destroy the spines.
+This is sometimes done in a primitive and laborious way by laying the
+gorse upon a block of wood and beating it with a mallet, flat at one end
+and armed with crossed knife-edges at the other, by the alternate use of
+which it is bruised and chopped. There are now a variety of machines by
+which this is done rapidly and efficiently, and which are in use where
+this kind of forage is used to any extent. The agricultural value of
+this plant has often been over-rated by theoretical writers. In the case
+of very poor, dry soils it does, however, yield much valuable food at a
+season when green forage is not otherwise to be had. It is on this
+account of importance to dairymen; and to them it has this further
+recommendation, that cows fed upon it give much rich milk, which is free
+from any unpleasant flavour. To turn it to good account, it must be sown
+in drills, kept clean by hoeing, and treated as a regular green crop. If
+sown in March, on land fitly prepared and afterwards duly cared for, it
+is ready for use in the autumn of the following year. A succession of
+cuttings of proper age is obtained for several years from the same
+field. It is cut by a short stout scythe, and must be brought from the
+field daily; for when put in a heap after being chopped and bruised it
+heats rapidly. It is given to horses and cows in combination with
+chopped hay or straw. An acre will produce about 2000 faggots of green
+two-year-old gorse, weighing 20 lb. each.
+
+This plant is invaluable in mountain sheep-walks. The rounded form of
+the furze bushes that are met with in such situations shows how
+diligently the annual growth, as far as it is accessible, is nibbled by
+the sheep. The food and shelter afforded to them in snowstorms by
+clusters of such bushes is of such importance that the wonder is our
+sheep farmers do not bestow more pains to have it in adequate quantity.
+Young plants of whin are so kept down by the sheep that they can seldom
+attain to a profitable size unless protected by a fence for a few years.
+In various parts of England it is cut for fuel. The ashes contain a
+large proportion of alkali, and are a good manure, especially for peaty
+land.
+
+
+
+
+FUSARO, LAGO, a lake of Campania, Italy, ½ m. W. of Baia, and 1 m. S. of
+the acropolis of Cumae. It is the ancient _Acherusia palus_, separated
+from the sea on the W. by a line of sandhills. It may have been the
+harbour of Cumae in early antiquity. In the 1st century A.D. an
+artificial outlet was dug for it at its S. end, with a tunnel, lined
+with _opus reticulatum_ and brick, under the hill of Torregaveta. This
+hill is covered with the remains of a large villa, which is almost
+certainly that of Servilius Vatia, described by Seneca (_Epist._ 55).
+There are remains of other villas on the shores of the lake. Oyster
+cultivation is carried on there.
+
+  See J. Beloch, _Campanien_ (2nd ed., Breslau, 1890), 188.     (T. As.)
+
+
+
+
+FUSELI, HENRY (1741-1825), English painter and writer on art, of
+German-Swiss family, was born at Zürich in Switzerland on the 7th of
+February 1741; he himself asserted in 1745, but this appears to have
+been a mere whim. He was the second child in a family of eighteen. His
+father was John Caspar Füssli, of some note as a painter of portraits
+and landscapes, and author of Lives of the _Helvetic Painters_. This
+parent destined his son for the church, and with this view sent him to
+the Caroline college of his native town, where he received an excellent
+classical education. One of his schoolmates there was Lavater, with whom
+he formed an intimate friendship.
+
+After taking orders in 1761 Fuseli was obliged to leave his country for
+a while in consequence of having aided Lavater to expose an unjust
+magistrate, whose family was still powerful enough to make its vengeance
+felt. He first travelled through Germany, and then, in 1765, visited
+England, where he supported himself for some time by miscellaneous
+writing: there was a sort of project of promoting through his means a
+regular literary communication between England and Germany. He became in
+course of time acquainted with Sir Joshua Reynolds, to whom he showed
+his drawings. By Sir Joshua's advice he then devoted himself wholly to
+art. In 1770 he made an art-pilgrimage to Italy, where he remained till
+1778, changing his name from Füssli to Fuseli, as more Italian-sounding.
+Early in 1779 he returned to England, taking Zürich on his way. He found
+a commission awaiting him from Alderman Boydell, who was then organizing
+his celebrated Shakespeare gallery. Fuseli painted a number of pieces
+for this patron, and about this time published an English edition of
+Lavater's work on physiognomy. He likewise gave Cowper some valuable
+assistance in preparing the translation of Homer. In 1788 Fuseli married
+Miss Sophia Rawlins (who it appears was originally one of his models,
+and who proved an affectionate wife), and he soon after became an
+associate of the Royal Academy. Two years later he was promoted to the
+grade of Academician. In 1799 he exhibited a series of paintings from
+subjects furnished by the works of Milton, with a view to forming a
+Milton gallery corresponding to Boydell's Shakespeare gallery. The
+number of the Milton paintings was forty-seven, many of them very large;
+they were executed at intervals within nine years. This exhibition,
+which closed in 1800, proved a failure as regards profit. In 1799 also
+he was appointed professor of painting to the Academy. Four years
+afterwards he was chosen keeper, and resigned his professorship; but he
+resumed it in 1810, and continued to hold both offices till his death.
+In 1805 he brought out an edition of Pilkington's _Lives of the
+Painters_, which, however, did not add much to his reputation. Canova,
+when on his visit to England, was much taken with Fuseli's works, and on
+returning to Rome in 1817 caused him to be elected a member of the first
+class in the Academy of St Luke. Fuseli, after a life of uninterrupted
+good health, died at Putney Hill on the 16th of April 1825, at the
+advanced age of eighty-four, and was buried in the crypt of St Paul's
+cathedral. He was comparatively rich at his death, though his
+professional gains had always appeared to be meagre.
+
+As a painter, Fuseli had a daring invention, was original, fertile in
+resource, and ever aspiring after the highest forms of excellence. His
+mind was capable of grasping and realizing the loftiest conceptions,
+which, however, he often spoiled on the canvas by exaggerating the due
+proportions of the parts, and throwing his figures into attitudes of
+fantastic and over-strained contortion. He delighted to select from the
+region of the supernatural, and pitched everything upon an ideal scale,
+believing a certain amount of exaggeration necessary in the higher
+branches of historical painting. "Damn Nature! she always puts me out,"
+was his characteristic exclamation. In this theory he was confirmed by
+the study of Michelangelo's works and the marble statues of the Monte
+Cavallo, which, when at Rome, he used often to contemplate in the
+evening, relieved against a murky sky or illuminated by lightning. But
+this idea was by him carried out to an excess, not only in the forms,
+but also in the attitudes of his figures; and the violent and
+intemperate action which he often displays destroys the grand effect
+which many of his pieces would otherwise produce. A striking
+illustration of this occurs in his famous picture of "Hamlet breaking
+from his Attendants to follow the Ghost": Hamlet, it has been said,
+looks as though he would burst his clothes with convulsive cramps in all
+his muscles. This intemperance is the grand defect of nearly all
+Fuseli's compositions. On the other hand, his paintings are never either
+languid or cold. His figures are full of life and earnestness, and seem
+to have an object in view which they follow with rigid intensity. Like
+Rubens he excelled in the art of setting his figures in motion. Though
+the lofty and terrible was his proper sphere, Fuseli had a fine
+perception of the ludicrous. The grotesque humour of his fairy scenes,
+especially those taken from _A Midsummer-Night's Dream_, is in its way
+not less remarkable than the poetic power of his more ambitious works.
+As a colourist Fuseli has but small claims to distinction. He scorned to
+set a palette as most artists do; he merely dashed his tints recklessly
+over it. Not unfrequently he used his paints in the form of a dry
+powder, which he rubbed up with his pencil with oil, or turpentine, or
+gold size, regardless of the quantity, and depending for accident on the
+general effect. This recklessness may perhaps be explained by the fact
+that he did not paint in oil till he was twenty-five years of age.
+Despite these drawbacks he possessed the elements of a great painter.
+
+Fuseli painted more than 200 pictures, but he exhibited only a minority
+of them. His earliest painting represented "Joseph interpreting the
+Dreams of the Baker and Butler"; the first to excite particular
+attention was the "Nightmare," exhibited in 1782. He produced only two
+portraits. His sketches or designs numbered about 800; they have
+admirable qualities of invention and design, and are frequently superior
+to his paintings.
+
+His general powers of mind were large. He was a thorough master of
+French, Italian, English and German, and could write in all these
+tongues with equal facility and vigour, though he preferred German as
+the vehicle of his thoughts. His writings contain passages of the best
+art-criticism that English literature can show. The principal work is
+his series of _Lectures_ in the Royal Academy, twelve in number,
+commenced in 1801.
+
+  Many interesting anecdotes of Fuseli, and his relations to
+  contemporary artists, are given in his _Life_ by John Knowles, who
+  also edited his works in 3 vols. 8vo, London, 1831.     (W. M. R.)
+
+
+
+
+FUSEL OIL (from the Ger. _Fusel_, bad spirits), the name applied to the
+volatile oily liquids, of a nauseous fiery taste and smell, which are
+obtained in the rectification of spirituous liquors made by the
+fermentation of grain, potatoes, the marc of grapes, and other
+material, and which, as they are of higher boiling point than ethyl
+alcohol, occur in largest quantity in the last portions of the
+distillate. Besides ethyl or ordinary alcohol, and amyl alcohol, which
+are present in them all, there have been found in fusel oil several
+other bodies of the C_n H_(2n + 1)·OH series, also certain ethers, and
+members of the C_n H_(2n + 1)·CO2H series of fatty acids. Normal propyl
+alcohol is contained in the fusel oil of the marc brandy of the south of
+France, and isoprimary butyl alcohol in that of beet-root molasses. The
+chief constituent of the fusel oil procured in the manufacture of
+alcohol from potatoes and grain, usually known as fusel oil and
+potato-spirit, is isoprimary amyl alcohol, or isobutylcarbinol. Ordinary
+fusel oil yields also an isomeric amyl alcohol (active amyl alcohol)
+boiling at about 128°. Variable quantities of fusel oil, less or greater
+according to the stage of ripening, exist in commercial spirits (see
+SPIRITS).
+
+Fusel oil and its chief constituent, amyl alcohol, are direct nerve
+poisons. In small doses it causes only thirst and headache, with furred
+tongue and some excitement. In large doses it is a convulsent poison.
+Impure beverages induce all the graver neurotic and visceral disorders
+in alcoholism; and, like fusel oil, furfurol and the essence of
+absinthe, are convulsent poisons. Pure ethyl alcohol intoxication,
+indeed, is rarely seen, being modified in the case of spirits by the
+higher alcohols contained in fusel oil. According to Rabuteau the toxic
+properties of the higher alcohols increase with their molecular weight
+and boiling point. Richet considers that the fusel oil contained in
+spirits constitutes the chief danger in the consumption of alcoholic
+beverages. The expert can immediately detect the peculiarly virulent
+characters of the mixed intoxication due to the consumption of spirits
+containing a large percentage of fusel oil.
+
+
+
+
+FUSIBLE METAL, a term applied to certain alloys, generally composed of
+bismuth, lead and tin, which possess the property of melting at
+comparatively low temperatures. Newton's fusible metal (named after Sir
+Isaac Newton) contains 50 parts of bismuth, 31.25 of lead and 18.75 of
+tin; that of Jean Darcet (1725-1801), 50 parts of bismuth with 25 each
+of lead and tin; and that of Valentin Rose the elder, 50 of bismuth with
+28.1 of lead and 24.1 of tin. These melt between 91° and 95° C. The
+addition of cadmium gives still greater fusibility; in Wood's metal, for
+instance, which is Darcet's metal with half the tin replaced by cadmium,
+the melting point is lowered to 66°-71° C.; while another described by
+Lipowitz and containing 15 parts of bismuth, 8 of lead, 4 of tin and 3
+of cadmium, softens at about 55° and is completely liquid a little above
+60°. By the addition of mercury to Darcet's metal the melting point may
+be reduced so low as 45°. These fusible metals have the peculiarity of
+expanding as they cool; Rose's metal, for instance, remains pasty for a
+considerable range of temperature below its fusing point, contracts
+somewhat rapidly from 80° to 55°, expands from 55° to 35°, and contracts
+again from 35° to 0°. For this reason they may be used for taking casts
+of anatomical specimens or making _clichés_ from wood-blocks, the
+expansion on cooling securing sharp impressions. By suitable
+modification in the proportions of the components, a series of alloys
+can be made which melt at various temperatures above the boiling point
+of water; for example, with 8 parts of bismuth, 8 of lead and 3 of tin
+the melting point is 123°, and with 8 of bismuth, 30 of lead and 24 of
+tin it is 172°. With tin and lead only in equal proportions it is 241°.
+Such alloys are used for making the fusible plugs inserted in the
+furnace-crowns of steam boilers, as a safeguard in the event of the
+water-level being allowed to fall too low. When this happens the plug
+being no longer covered with water is heated to such a temperature that
+it melts and allows the contents of the boiler to escape into the
+furnace. In automatic fire-sprinklers the orifices of the pipes are
+closed with fusible metal, which melts and liberates the water when,
+owing to an outbreak of fire in the room, the temperature rises above a
+predetermined limit.
+
+
+
+
+FUSILIER, originally (in French about 1670, in English about 1680) the
+name of a soldier armed with a light flintlock musket called the fusil;
+now a regimental designation. Various forms of flintlock small arms had
+been used in warfare since the middle of the 16th century. At the time
+of the English civil war (1642-1652) the term "firelock" was usually
+employed to distinguish these weapons from the more common matchlock
+musket. The special value of the firelock in armies of the 17th century
+lay in the fact that the artillery of the time used open powder barrels
+for the service of the guns, making it unsafe to allow lighted matches
+in the muskets of the escort. Further, a military escort was required,
+not only for the protection, but also for the surveillance of the
+artillerymen of those days. Companies of "firelocks" were therefore
+organized for these duties, and out of these companies grew the
+"fusiliers" who were employed in the same way in the wars of Louis XIV.
+In the latter part of the Thirty Years' War (1643) fusiliers were simply
+mounted troops armed with the fusil, as carabiniers were with the
+carbine. But the escort companies of artillery came to be known by the
+name shortly afterwards, and the regiment of French Royal Fusiliers,
+organized in 1671 by Vauban, was considered the model for Europe. The
+general adoption of the flintlock musket and the suppression of the pike
+in the armies of Europe put an end to the original special duties of
+fusiliers, and they were subsequently employed to a large extent in
+light infantry work, perhaps on account of the greater individual
+aptitude for detached duties naturally shown by soldiers who had never
+been restricted to a fixed and unchangeable place in the line of battle.
+The senior fusilier regiment in the British service, the (7th) Royal
+Fusiliers (City of London Regiment), was formed on the French model in
+1685; the 5th foot (now Northumberland Fusiliers), senior to the 7th in
+the army, was not at that time a fusilier regiment. The distinctive
+head-dress of fusiliers in the British service is a fur cap, generally
+resembling, but smaller than and different in details from, that of the
+Foot Guards.
+
+In Germany the name "fusilier" is borne by certain infantry regiments
+and by one battalion in each grenadier regiment.
+
+
+
+
+FUSION, the term generally applied to the melting of a solid substance,
+or the change of state of aggregation from the solid to the liquid. The
+term "liquefaction" is frequently employed in the same sense, but is
+often restricted to the condensation of a gas or vapour. The converse
+process of freezing or solidification, the change from the liquid to the
+solid state, is subject to the same laws, and must be considered
+together with fusion. The solution of a solid in a foreign liquid, and
+the deposition or crystallization of a solid from a solution, are so
+closely related to the fusion of a pure substance, that it will also be
+necessary to consider some of the analogies which they present.
+
+1. _General Phenomena._--There are two chief varieties of the process of
+fusion, namely, crystalline and amorphous, which are in many ways
+distinct, although it is possible to find intermediate cases which
+partake of the characteristics of both. The melting of ice may be taken
+as a typical case of crystalline fusion. The passage from rigid solid to
+mobile liquid occurs at a definite surface without any intermediate
+stage or plastic condition. The change takes place at a definite
+temperature, the fusing or freezing point (abbreviated F.P.), and
+requires the addition of a definite quantity of heat to the solid, which
+is called the latent heat of fusion. There is also in general a
+considerable change of volume during fusion, which amounts in the case
+of ice to a contraction of 9%. Typical cases of amorphous solidification
+are those of silica, glass, plastic sulphur, pitch, alcohol and many
+organic liquids. In this type the liquid gradually becomes more and more
+viscous as the temperature falls, and ultimately attains the rigidity
+characteristic of a solid, without any definite freezing point or latent
+heat. The condition of the substance remains uniform throughout, if its
+temperature is uniform; there is no separation into the two distinct
+phases of solid and liquid, and there is no sudden change of volume at
+any temperature.
+
+A change or transition from one crystalline form to another may occur in
+the solid state with evolution or absorption of heat at a definite
+temperature, and is analogous to the change from solid to liquid, but
+usually takes place more slowly owing to the small molecular mobility of
+the solid state. Thus rhombic sulphur when heated passes slowly at 95.6°
+C. into the monosymmetric form which melts at 120°, but if heated
+rapidly the rhombic form melts at 114.5. The two forms, rhombic and
+monosymmetric, can exist in equilibrium at 95.6°, the transition point
+at which they have the same vapour pressure. Similarly a solid solution
+of carbon in iron, when cooled slowly, passes at about 700° C., with
+considerable evolution of heat, into the form of "pearlite," which is
+soft when cold, but if rapidly chilled the carbon remains in solution
+and the steel is very hard (see also ALLOYS).
+
+In the case of crystalline fusion it is necessary to distinguish two
+cases, the homogeneous and the heterogeneous. In the first case the
+composition of the solid and liquid phases are the same, and the
+temperature remains constant during the whole process of fusion. In the
+second case the solid and liquid phases differ in composition; that of
+the liquid phase changes continuously, and the temperature does not
+remain constant during the fusion. The first case comprises the fusion
+of pure substances, and that of eutectics, or cryohydrates; the second
+is the general case of an alloy or a solution. These have been very
+fully studied and their phenomena greatly elucidated in recent years.
+
+There is also a sub-variety of amorphous fusion, which may be styled
+colloid or gelatinous, and may be illustrated by the behaviour of
+solutions of water in gelatin. Many of these jellies melt at a fairly
+definite temperature on heating, and coagulate or set at a definite
+temperature on cooling. But in some cases the process is not reversible,
+and there is generally marked hysteresis, the temperature of setting and
+other phenomena depending on the rate of cooling. This case has not yet
+been fully worked out; but it appears probable that in many cases the
+jelly possesses a spongy framework of solid, holding liquid in its
+meshes or interstices. It might be regarded as a case of "heterogeneous"
+amorphous fusion, in which the liquid separates into two phases of
+different composition, one of which solidifies before the other. The two
+phases cannot, as a rule, be distinguished optically, but it is
+generally possible to squeeze out some of the liquid phase when the
+jelly has set, which proves that the substance is not really
+homogeneous. In very complicated mixtures, such as acid lavas or slags
+containing a large proportion of silica, amorphous and crystalline
+solidification may occur together. In this case the crystals separate
+first during the process of cooling, the mother liquor increases
+gradually in viscosity, and finally sets as an amorphous ground-mass or
+matrix, in which crystals of different kinds and sizes, formed at
+different stages of the cooling, remain embedded. The formation of
+crystals in an amorphous solid after it has set is also of frequent
+occurrence. It is termed devitrification, but is a very slow process
+unless the solid is in a plastic state.
+
+2. _Homogeneous Crystalline Fusion._--The fusion of a solid of this type
+is characterized most clearly by the perfect constancy of temperature
+during the process. In fact, the law of constant temperature, which is
+generally stated as the first of the so-called "laws of fusion," does
+not strictly apply except to this case. The constancy of the F.P. of a
+pure substance is so characteristic that change of the F.P. is often one
+of the most convenient tests of the presence of foreign material. In the
+case of substances like ice, which melt at a low temperature and are
+easily obtained in large quantities in a state of purity, the point of
+fusion may be very accurately determined by observing the temperature of
+an intimate mixture of the solid and liquid while slowly melting as it
+absorbs heat from surrounding bodies. But in the majority of cases it is
+more convenient to observe the freezing point as the liquid is cooled.
+By this method it is possible to ensure perfect uniformity of
+temperature throughout the mass by stirring the liquid continuously
+during the process of freezing, whereas it is difficult to ensure
+uniformity of temperature in melting a solid, however gradually the heat
+is supplied, unless the solid can be mixed with the liquid. It is also
+possible to observe the F.P. in other ways, as by noting the temperature
+at the moment of the breaking of a wire, of the stoppage of a stirrer,
+or of the maximum rate of change of volume, but these methods are
+generally less certain in their indications than the point of greatest
+constancy of temperature in the case of homogeneous crystalline solids.
+
+  _Fusing Points of Common Metals_
+
+  Mercury     -38.8°     Antimony     630°
+  Potassium    62.5°     Aluminium    655°
+  Sodium       95.6°     Silver       962°
+  Tin         231.9°     Gold        1064°
+  Bismuth     269.2°     Copper      1082°
+  Cadmium     320.7°     Nickel      1427°
+  Lead        327.7°     Palladium   1535°
+  Zinc        419.0°     Platinum    1710°
+
+The above table contains some of the most recent values of fusing points
+of metals determined (except the first three and the last three) with
+platinum thermometers. The last three values are those obtained by
+extrapolation with platinum-rhodium and platinum-iridium couples. (See
+Harker, _Proc. Roy. Soc._ A 76, p. 235, 1905.) Some doubt has recently
+been raised with regard to the value for platinum, which is much lower
+than that previously accepted, namely 1775°.
+
+3. _Superfusion, Supersaturation._--It is generally possible to cool a
+liquid several degrees below its normal freezing point without a
+separation of crystals, especially if it is protected from agitation,
+which would assist the molecules to rearrange themselves. A liquid in
+this state is said to be "undercooled" or "superfused." The phenomenon
+is even more familiar in the case of solutions (e.g. sodium sulphate or
+acetate) which may remain in the "metastable" condition for an
+indefinite time if protected from dust, &c. The introduction into the
+liquid under this condition of the smallest fragment of the crystal,
+with respect to which the solution is supersaturated, will produce
+immediate crystallization, which will continue until the temperature is
+raised to the saturation point by the liberation of the latent heat of
+fusion. The constancy of temperature at the normal freezing point is due
+to the equilibrium of exchange existing between the liquid and solid.
+Unless both solid and liquid are present, there is no condition of
+equilibrium, and the temperature is indeterminate.
+
+It has been shown by H.A. Miers (_Jour. Chem. Soc._, 1906, 89, p. 413)
+that for a supersaturated solution in metastable equilibrium there is an
+inferior limit of temperature, at which it passes into the "labile"
+state, i.e. spontaneous crystallization occurs throughout the mass in a
+fine shower. This seems to be analogous to the fine misty condensation
+which occurs in a supersaturated vapour in the absence of nuclei (see
+VAPORIZATION) when the supersaturation exceeds a certain limit.
+
+  4. _Effect of Pressure on the F.P._--The effect of pressure on the
+  fusing-point depends on the change of volume during fusion. Substances
+  which expand on _freezing_, like ice, have their freezing points
+  lowered by increase of pressure; substances which expand on _fusing_,
+  like wax, have their melting points raised by pressure. In each case
+  the effect of pressure is to retard increase of volume. This effect
+  was first predicted by James Thomson on the analogy of the effect of
+  pressure on the boiling point, and was numerically verified by Lord
+  Kelvin in the case of ice, and later by Bunsen in the case of paraffin
+  and spermaceti. The equation by which the change of the F.P. is
+  calculated may be proved by a simple application of the Carnot cycle,
+  exactly as in the case of vapour and liquid. (See THERMODYNAMICS.) If
+  L be the latent heat of fusion in mechanical units, v' the volume of
+  unit mass of the solid, and v" that of the liquid, the work done in
+  an elementary Carnot cycle of range d[theta] will be dp(v"- v'), if
+  dp is the increase of pressure required to produce a change d[theta]
+  in the F.P. Since the ratio of the work-difference or cycle-area to
+  the heat-transferred L must be equal to d[theta]/[theta], we have the
+  relation
+
+    d[theta]/dp = [theta](v" - v')/L.   (1)
+
+  The sign of d[theta], the change of the F.P., is the same as that of
+  the change of volume (v" - v'). Since the change of volume seldom
+  exceeds 0.1 c.c. per gramme, the change of the F.P. per atmosphere is
+  so small that it is not as a rule necessary to take account of
+  variations of atmospheric pressure in observing a freezing point. A
+  variation of 1 cm. in the height of the barometer would correspond to
+  a change of .0001° C. only in the F.P. of ice. This is far beyond the
+  limits of accuracy of most observations. Although the effect of
+  pressure is so small, it produces, as is well known, remarkable
+  results in the motion of glaciers, the moulding and regelation of ice,
+  and many other phenomena. It has also been employed to explain the
+  apparent inversion of the order of crystallization in rocks like
+  granite, in which the arrangement of the crystals indicates that the
+  quartz matrix solidified subsequently to the crystals of felspar,
+  mica or hornblende embedded in it, although the quartz has a higher
+  melting point. It is contended that under enormous pressure the
+  freezing points of the more fusible constituents might be raised above
+  that of the quartz, if the latter is less affected by pressure. Thus
+  Bunsen found the F.P. of paraffin wax 1.4° C. below that of spermaceti
+  at atmospheric pressure. At 100 atmospheres the two melted at the same
+  temperature. At higher pressures the paraffin would solidify first.
+  The effect of pressure on the silicates, however, is much smaller, and
+  it is not so easy to explain a change of several hundred degrees in
+  the F.P. It seems more likely in this particular case that the order
+  of crystallization depends on the action of superheated water or steam
+  at high temperatures and pressures, which is well known to exert a
+  highly solvent and metamorphic action on silicates.
+
+  5. _Variation of Latent Heat._--C.C. Person in 1847 endeavoured to
+  show by the application of the first law of thermodynamics that the
+  increase of the latent heat per degree should be equal to the
+  difference (s"- s') between the specific heats of the liquid and
+  solid. If, for instance, water at 0° C. were first frozen and then
+  cooled to -t° C., the heat abstracted per gramme would be (L'+ s't)
+  calories. But if the water were first cooled to -t° C., and then
+  frozen at -t°C., by abstracting heat L", the heat abstracted would be
+  L" + s"t. Assuming that the heat abstracted should be the same in
+  the two cases, we evidently obtain L'- L" = (s"- s')t. This theory
+  has been approximately verified by Petterson, by observing the
+  freezing of a liquid cooled below its normal F.P. (_Jour. Chem. Soc._
+  24, p. 151). But his method does not represent the true variation of
+  the latent heat with temperature, since the freezing, in the case of a
+  superfused liquid, really takes place at the normal freezing point. A
+  quantity of heat s"t is abstracted in cooling to -t, (L"- s"t) in
+  raising to 0° and freezing at 0°, and s't in cooling the ice to -t.
+  The latent heat L" at -t does not really enter into the experiment.
+  In order to make the liquid freeze at a different temperature, it is
+  necessary to subject it to pressure, and the effect of the pressure on
+  the latent heat cannot be neglected. The entropy of a liquid [phi]"
+  at its F.P. reckoned from any convenient zero [phi]0 in the solid
+  state may be represented by the expression
+                       _
+                      /
+   [phi]" - [phi]0 =  | s'd[theta] / [theta] + L / [theta].  (2)
+                     _/
+
+  Since [theta]d[phi]"/d[theta] = s", we obtain by differentiation the
+  relation
+
+    dL / d[theta] = s"- s' + L / [theta],   (3)
+
+  which is exactly similar to the equation for the specific heat of a
+  vapour maintained in the saturated condition. If we suppose that the
+  specific heats s' and s'' of the solid and liquid at equilibrium
+  pressure are nearly the same as those ordinarily observed at constant
+  pressure, the relation (3) differs from that of Person only by the
+  addition of the term L/[theta]. Since s" is greater than s' in all
+  cases hitherto investigated, and L/[theta] is necessarily positive, it
+  is clear that the latent heat of fusion must increase with rise of
+  temperature, or diminish with fall of temperature. It is possible to
+  imagine the F.P. so lowered by pressure (positive or negative) that
+  the latent heat should vanish, in which case we should probably obtain
+  a continuous passage from the liquid to the solid state similar to
+  that which occurs in the case of amorphous substances. According to
+  equation (3), the rate of change of the latent heat of water is
+  approximately 0.80 calorie per degree at 0° C. (as compared with 0.50,
+  Person), if we assume s" = 1, and s' = 0.5. Putting (s" - s') = 0.5
+  in equation (2), we find L = 0 at -160° C. approximately, but no
+  stress can be laid on this estimate, as the variation of (s" - s') is
+  so uncertain.
+
+6. _Freezing of Solutions and Alloys._--The phenomena of freezing of
+heterogeneous crystalline mixtures may be illustrated by the case of
+aqueous solutions and of metallic solutions or alloys, which have been
+most widely studied. The usual effect of an impurity, such as salt or
+sugar in solution in water, is to lower the freezing point, so that no
+crystallization occurs until the temperature has fallen below the normal
+F.P. of the pure solvent, the depression of F.P. being nearly
+proportional to the concentration of the solution. When freezing begins,
+the solvent generally separates out from the solution in the pure state.
+This separation of the solvent involves an increase in the strength of
+the remaining solution, so that the temperature does not remain constant
+during the freezing, but continues to fall as more of the solvent is
+separated. There is a perfectly definite relation between temperature
+and concentration at each stage of the process, which may be represented
+in the form of a curve as AC in fig. 1, called the freezing point curve.
+The equilibrium temperature, at the surface of contact between the solid
+and liquid, depends only on the composition of the liquid phase and not
+at all on the quantity of solid present. The abscissa of the F.P. curve
+represents the composition of that portion of the original solution
+which remains liquid at any temperature. If instead of starting with a
+dilute solution we start with a strong solution represented by a point
+N, and cool it as shown by the vertical line ND, a point D is generally
+reached at which the solution becomes "saturated." The dissolved
+substance or "solute" then separates out as the solution is further
+cooled, and the concentration diminishes with fall of temperature in a
+definite relation, as indicated by the curve CB, which is called the
+solubility curve. Though often called by different names, the two curves
+AC and CB are essentially of a similar nature. To take the case of an
+aqueous solution of salt as an example, along CB the solution is
+saturated with respect to salt, along AC the solution is saturated with
+respect to ice. When the point C is reached along either curve, the
+solution is saturated with respect to both salt and ice. The
+concentration cannot vary further, and the temperature remains constant,
+while the salt and ice crystallize out together, maintaining the exact
+proportions in which they exist in the solution. The resulting solid was
+termed a cryohydrate by F. Guthrie, but it is really an intimate mixture
+of two kinds of crystals, and not a chemical compound or hydrate
+containing the constituents in chemically equivalent proportions. The
+lowest temperature attainable by means of a freezing mixture is the
+temperature of the F.P. of the corresponding cryohydrate. In a mixture
+of salt and ice with the least trace of water a saturated brine is
+quickly formed, which dissolves the ice and falls rapidly in
+temperature, owing to the absorption of the latent heat of fusion. So
+long as both ice and salt are present, if the mixture is well stirred,
+the solution must necessarily become saturated with respect to both ice
+and salt, and this can only occur at the cryohydric temperature, at
+which the two curves of solubility intersect.
+
+[Illustration: FIG. 1.--F.P. or Solubility Curve: simple case.]
+
+The curves in fig. 1 also illustrate the simplest type of freezing point
+curve in the case of alloys of two metals A and B which do not form
+mixed crystals or chemical compounds. The alloy corresponding to the
+cryohydrate, possessing the lowest melting point, is called the eutectic
+alloy, as it is most easily cast and worked. It generally possesses a
+very fine-grained structure, and is not a chemical compound. (See
+ALLOYS.)
+
+[Illustration: FIG. 2.--Cooling Curves of Alloys: typical case.]
+
+To obtain a complete F.P. curve even for a binary alloy is a laborious
+and complicated process, but the information contained in such a curve
+is often very valuable. It is necessary to operate with a number of
+different alloys of suitably chosen composition, and to observe the
+freezing points of each separately. Each alloy should also be analysed
+after the process if there is any risk of its composition having been
+altered by oxidation or otherwise. The freezing points are generally
+best determined by observing the gradual cooling of a considerable mass,
+which is well stirred so long as it remains liquid. The curve of cooling
+may most conveniently be recorded, either photographically, using a
+thermocouple and galvanometer, as in the method of Sir W.
+Roberts-Austen, or with pen and ink, if a platinum thermometer is
+available, according to the method put in practice by C.T. Heycock and
+F.H. Neville. A typical set of curves obtained in this manner is shown
+in fig. 2. When the pure metal A in cooling reaches its F.P. the
+temperature suddenly becomes stationary, and remains accurately constant
+for a considerable period. Often it falls slightly below the F.P. owing
+to super-fusion, but rises to the F.P. and remains constant as soon as
+freezing begins. The second curve shows the cooling of A with 10% of
+another metal B added. The freezing begins at a lower temperature with
+the separation of pure A. The temperature no longer remains constant
+during freezing, but falls more and more rapidly as the proportion of B
+in the liquid increases. When the eutectic temperature is reached there
+is a second F.P. or arrest at which the whole of the remaining liquid
+solidifies. With 20% of B the first F.P. is further lowered, and the
+temperature falls faster. The eutectic F.P. is of longer duration, but
+still at the same temperature. For an alloy of the composition of the
+eutectic itself there is no arrest until the eutectic temperature is
+reached, at which the whole solidifies without change of temperature.
+There is a great advantage in recording these curves automatically, as
+the primary arrest is often very slight, and difficult to observe in any
+other way.
+
+  7. _Change of Solubility with Temperature._--The lowering of the F.P.
+  of a solution with increase of concentration, as shown by the F.P. or
+  solubility curves, may be explained and calculated by equation (1) in
+  terms of the osmotic pressure of the dissolved substance by analogy
+  with the effect of mechanical pressure. It is possible in salt
+  solutions to strain out the salt mechanically by a suitable filter or
+  "semi-permeable membrane," which permits the water to pass, but
+  retains the salt. To separate 1 gramme of salt requires the
+  performance of work PV against the osmotic pressure P, where V is the
+  corresponding diminution in the volume of the solution. In dilute
+  solutions, to which alone the following calculation can be applied,
+  the volume V is the reciprocal of the concentration C of the solution
+  in grammes per unit volume, and the osmotic pressure P is equal to
+  that of an equal number of molecules of gas in the same space, and may
+  be deduced from the usual equation of a gas,
+
+    P = R[theta] / VM = R[theta]C / M,   (4)
+
+  where M is the molecular weight of the salt in solution, [theta] the
+  absolute temperature, and R a constant which has the value 8.32
+  joules, or nearly 2 calories, per degree C. It is necessary to
+  consider two cases, corresponding to the curves CB and AB in fig. 1,
+  in which the solution is saturated with respect to salt and water
+  respectively. To facilitate description we take the case of a salt
+  dissolved in water, but similar results apply to solutions in other
+  liquids and alloys of metals.
+
+  (a) If unit mass of salt is separated in the solid state from a
+  saturated solution of salt (curve CB) by forcing out through a
+  semi-permeable membrane against the osmotic pressure P the
+  corresponding volume of water V in which it is dissolved, the heat
+  evolved is the latent heat of saturated solution of the salt Q
+  together with the work done PV. Writing (Q + PV) for L, and V for (v"
+  - v') in equation (1), and substituting P for p, we obtain
+
+    Q + PV = V[theta]dP / d[theta],   (5)
+
+  which is equivalent to equation (1), and may be established by similar
+  reasoning. Substituting for P and V in terms of C from equation (4),
+  if Q is measured in calories, R = 2, and we obtain
+
+    QC = 2[theta]²dC / d[theta],   (6)
+
+  which may be integrated, assuming Q constant, with the result
+
+    2log_eC" / C' = Q / [theta]' - Q / [theta]",   (7)
+
+  where C', C" are the concentrations of the saturated solution
+  corresponding to the temperatures [theta]' and [theta]". This
+  equation may be employed to calculate the latent heat of solution Q
+  from two observations of the solubility. It follows from these
+  equations that Q is of the same sign as dC/d[theta], that is to say,
+  the solubility increases with rise of temperature if heat is absorbed
+  in the formation of the saturated solution, which is the usual case.
+  If, on the other hand, heat is liberated on solution, as in the case
+  of caustic potash or sulphate of calcium, the solubility diminishes
+  with rise of temperature.
+
+  (b) In the case of a solution saturated with respect to ice (curve
+  AC), if one gramme of water having a volume v is separated by
+  freezing, we obtain a precisely similar equation to (5), but with L
+  the latent heat of fusion of water instead of Q, and v instead of V.
+  If the solution is dilute, we may neglect the external work Pv in
+  comparison with L, and also the heat of dilution, and may write P/t
+  for dP/d[theta], where t is the depression of the F.P. below that of
+  the pure solvent. Substituting for P in terms of V from equation (4),
+  we obtain
+
+    t = 2[theta]²v / LVM = 2[theta]²w / LWM,   (8)
+
+  where W is the weight of water and w that of salt in a given volume of
+  solution. If M grammes of salt are dissolved in 100 of water, w = M
+  and W = 100. The depression of the F.P. in this case is called by van
+  't Hoff the "Molecular Depression of the F.P." and is given by the
+  simple formula
+
+    t = .02[theta]² / L.   (9)
+
+  Equation (8) may be used to calculate L or M, if either is known, from
+  observations of t, [theta] and w/W. The results obtained are
+  sufficiently approximate to be of use in many cases in spite of the
+  rather liberal assumptions and approximations effected in the course
+  of the reasoning. In any case the equations give a simple theoretical
+  basis with which to compare experimental data in order to estimate the
+  order of error involved in the assumptions. We may thus estimate the
+  variation of the osmotic pressure from the value given by the gaseous
+  equation, as the concentration of the solution or the molecular
+  dissociation changes. The most uncertain factor in the formula is the
+  molecular weight M, since the molecule in solution may be quite
+  different from that denoted by the chemical formula of the solid. In
+  many cases the molecule of a metal in dilute solution in another metal
+  is either monatomic, or forms a compound molecule with the solvent
+  containing one atom of the dissolved metal, in which case the
+  molecular depression is given by putting the atomic weight for M. In
+  other cases, as Cu, Hg, Zn, in solution in cadmium, the depression of
+  the F.P. per atom, according to Heycock and Neville, is only half as
+  great, which would imply a diatomic molecule. Similarly As and Au in
+  Cd appear to be triatomic, and Sn in Pb tetratomic. Intermediate cases
+  may occur in which different molecules exist together in equilibrium
+  in proportions which vary according to the temperature and
+  concentration. The most familiar case is that of an electrolyte, in
+  which the molecule of the dissolved substance is partly dissociated
+  into ions. In such cases the degree of dissociation may be estimated
+  by observing the depression of the F.P., but the results obtained
+  cannot always be reconciled with those deduced by other methods, such
+  as measurement of electrical conductivity, and there are many
+  difficulties which await satisfactory interpretation.
+
+  Exactly similar relations to (8) and (9) apply to changes of boiling
+  point or vapour pressure produced by substances in solution (see
+  VAPORIZATION), the laws of which are very closely connected with the
+  corresponding phenomena of fusion; but the consideration of the vapour
+  phase may generally be omitted in dealing with the fusion of mixtures
+  where the vapour pressure of either constituent is small.
+
+[Illustration: FIG. 3.--Solubility Curves of Hydrates.]
+
+8. _Hydrates._--The simple case of a freezing point curve, illustrated
+in fig. 1, is generally modified by the occurrence of compounds of a
+character analogous to hydrates of soluble salts, in which the dissolved
+substance combines with one or more molecules of the solvent. These
+hydrates may exist as compound molecules in the solution, but their
+composition cannot be demonstrated unless they can be separated in the
+solid state. Corresponding to each crystalline hydrate there is
+generally a separate branch of the solubility curve along which the
+crystals of the hydrate are in equilibrium with the saturated solution.
+At any given temperature the hydrate possessing the least solubility is
+the most stable. If two are present in contact with the same solution,
+the more soluble will dissolve, and the less soluble will be formed at
+its expense until the conversion is complete. The two hydrates cannot be
+in equilibrium with the same solution except at the temperature at which
+their solubilities are equal, i.e. at the point where the corresponding
+curves of solubility intersect. This temperature is called the
+"Transition Point." In the case of ZnSO4, as shown in fig. 3, the
+heptahydrate, with seven molecules of water, is the least soluble
+hydrate at ordinary temperatures, and is generally deposited from
+saturated solutions. Above 39° C., however, the hexahydrate, with six
+molecules, is less soluble, and a rapid conversion of the hepta- into
+the hexahydrate occurs if the former is heated above the transition
+point. The solubility of the hexahydrate is greater than that of the
+heptahydrate below 39°, but increases more slowly with rise of
+temperature. At about 80° C. the hexahydrate gives place to the
+monohydrate, which dissolves in water with evolution of heat, and
+diminishes in solubility with rise of temperature. Intermediate hydrates
+exist, but they are more soluble, and cannot be readily isolated. Both
+the mono- and hexahydrates are capable of existing in equilibrium with
+saturated solutions at temperatures far below their transition points,
+provided that the less soluble hydrate is not present in the crystalline
+form. The solubility curves can therefore be traced, as in fig. 3, over
+an extended range of temperature. The equilibrium of each hydrate with
+the solvent, considered separately, would present a diagram of two
+branches similar to fig. 1, but as a rule only a small portion of each
+curve can be realized, and the complete solubility curve, as
+experimentally determined, is composed of a number of separate pieces
+corresponding to the ranges of minimum solubility of different hydrates.
+Failure to recognize this, coupled with the fact that in strong and
+viscous solutions the state of equilibrium is but slowly attained, is
+the probable explanation of the remarkable discrepancies existing in
+many recorded data of solubility.
+
+  _Transition Points of Hydrates._
+
+  Na2CrO4·10H2O   19.9°     NaBr·2H20      50.7°
+  Na2SO4·10H2O    32.4°     MnCl2·4H2O     57.8°
+  Na2CO3·10H2O    35.1°     Na3PO4·12H2O   73.4°
+  Na2S2O3·5H2O    48.0°     Ba(OH)2·8H2O   77.9°
+
+The transition points of the hydrates given in the above list (Richards,
+_Proc. Amer. Acad._, 1899, 34, p. 277) afford well-marked constant
+temperatures which can be utilized as fixed points for experimental
+purposes.
+
+9. _Formation of Mixed Crystals._--An important exception to the general
+type already described, in which the addition of a dissolved substance
+lowers the F.P. of the solvent, is presented by the formation of mixed
+crystals, or "solid solutions," in which the solvent and solute occur
+mixed in varying proportions. This isomorphous replacement of one
+substance by another, in the same crystal with little or no change of
+form, has long been known and studied in the case of minerals and salts,
+but the relations between composition and melting-point have seldom been
+investigated, and much still remains obscure. In this case the process
+of freezing does not necessitate the performance of work of separation
+of the constituents of the solution, the F.P. is not necessarily
+depressed, and the effect cannot be calculated by the usual formula for
+dilute solutions. One of the simplest types of F.P. curve which may
+result from the occurrence of mixed crystals is illustrated by the case
+of alloys of gold and silver, or gold and platinum, in which the F.P.
+curve is nearly a straight line joining the freezing-points of the
+constituents. The equilibrium between the solid and liquid, in both of
+which the two metals are capable of mixing in all proportions, bears in
+this case an obvious and close analogy to the equilibrium between a
+mixed liquid (e.g. alcohol and water) and its vapour. In the latter
+case, as is well known, the vapour will contain a larger proportion of
+the more volatile constituent. Similarly in the case of the formation of
+mixed crystals, the liquid should contain a larger proportion of the
+more fusible constituent than the solid with which it is in equilibrium.
+The composition of the crystals which are being deposited at any moment
+will, therefore, necessarily change as solidification proceeds,
+following the change in the composition of the liquid, and the
+temperature will fall until the last portions of the liquid to solidify
+will consist chiefly of the more fusible constituent, at the F.P. of
+which the solidification will be complete. If, however, as seems to be
+frequently the case, the composition of the solid and liquid phases do
+not greatly differ from each other, the greater part of the
+solidification will occur within a comparatively small range of
+temperature, and the initial F.P. of the alloy will be well marked. It
+is possible in this case to draw a second curve representing the
+composition of the _solid_ phase which is in equilibrium with the liquid
+at any temperature. This curve will not represent the average
+composition of the crystals, but that of the outer coating only which is
+in equilibrium with the liquid at the moment. H.W.B. Roozeboom (_Zeit.
+Phys. Chem._ xxx. p. 385) has attempted to classify some of the possible
+cases which may occur in the formation of mixed crystals on the basis of
+J.W. Gibbs's thermodynamic potential, the general properties of which
+may be qualitatively deduced from a consideration of observed phenomena.
+But although this method may enable us to classify different types, and
+even to predict results in a qualitative manner, it does not admit of
+numerical calculation similar to equation (8), as the Gibbs's function
+itself is of a purely abstract nature and its form is unknown. There is
+no doubt that the formation of mixed crystals may explain many apparent
+anomalies in the study of F.P. curves. The whole subject has been most
+fruitful of results in recent years, and appears full of promise for the
+future.
+
+  For further details in this particular branch the reader may consult a
+  report by Neville (_Brit. Assoc. Rep._, 1900), which contains numerous
+  references to original papers by Roberts-Austen, Le Chatelier,
+  Roozeboom and others. For the properties of solutions see SOLUTION.
+       (H. L. C.)
+
+
+
+
+
+FÜSSEN, a town of Germany, in the kingdom of Bavaria, at the foot of the
+Alps (Tirol), on the Lech, 2500 ft. above the sea, with a branch line to
+Oberdorf on the railway to Augsburg. Pop. 4000. It has six Roman
+Catholic churches, a Franciscan monastery and a castle. Rope-making is
+an important industry. The castle, lying on a rocky eminence, is
+remarkable for the peace signed here on the 22nd of April 1745 between
+the elector Maximilian III., Joseph of Bavaria and Maria Theresa. Two
+miles to the S.E., immediately on the Austrian frontier, romantically
+situated on a rock overlooking the Schwanensee, is the magnificent
+castle of Hohenschwangau, and a little to the north, on the site of an
+old castle, that of Neuschwanstein, built by Louis II. of Bavaria.
+
+  See H. Feistle, _Füssen und Umgebung_ (1898).
+
+
+
+
+FUST, JOHANN (   ?-1466), early German printer, belonged to a rich and
+respectable burgher family of Mainz, which is known to have flourished
+from 1423, and to have held many civil and religious offices. The name
+was always written Fust, but in 1506 Johann Schöffer, in dedicating the
+German translation of Livy to the emperor Maximilian, called his
+grandfather Faust, and thenceforward the family assumed this name, and
+the Fausts of Aschaffenburg, an old and quite distinct family, placed
+Johann Fust in their pedigree. Johann's brother Jacob, a goldsmith, was
+one of the burgomasters in 1462, when Mainz was stormed and sacked by
+the troops of Count Adolf of Nassau, on which occasion he seems to have
+perished (see a document, dated May 8, 1463, published by Wyss in
+_Quartalbl. des hist. Vereins für Hessen_, 1879, p. 24). There is no
+evidence that, as is commonly asserted, Johann Fust was a goldsmith, but
+he appears to have been a money-lender or banker. On account of his
+connexion with Gutenberg (q.v.), he has been represented by some as the
+inventor of printing, and the instructor as well as the partner of
+Gutenberg, by others as his patron and benefactor, who saw the value of
+his discovery and supplied him with means to carry it out, whereas
+others paint him as a greedy and crafty speculator, who took advantage
+of Gutenberg's necessity and robbed him of the fruits of his invention.
+However this may be, the Helmasperger document of November 6, 1455,
+shows that Fust advanced money to Gutenberg (apparently 800 guilders in
+1450, and another 800 in 1452) for carrying on his work, and that Fust,
+in 1455, brought a suit against Gutenberg to recover the money he had
+lent, claiming 2020 (more correctly 2026) guilders for principal and
+interest. It appears that he had not paid in the 300 guilders a year
+which he had undertaken to furnish for expenses, wages, &c., and,
+according to Gutenberg, had said that he had no intention of claiming
+interest. The suit was apparently decided in Fust's favour, November 6,
+1455, in the refectory of the Barefooted Friars of Mainz, when Fust made
+oath that he himself had borrowed 1550 guilders and given them to
+Gutenberg. There is no evidence that Fust, as is usually supposed,
+removed the portion of the printing materials covered by his mortgage to
+his own house, and carried on printing there with the aid of Peter
+Schöffer, of Gernsheim (who is known to have been a scriptor at Paris in
+1449), to whom, probably about 1455,[1] he gave his only daughter Dyna
+or Christina in marriage. Their first publication was the Psalter,
+August 14, 1457, a folio of 350 pages, the first printed book with a
+complete date, and remarkable for the beauty of the large initials
+printed each in two colours, red and blue, from types made in two
+pieces.[2] The Psalter was reprinted with the same types, 1459 (August
+29), 1490, 1502 (Schöffer's last publication) and 1516. Fust and
+Schöffer's other works are given below.[3] In 1464 Adolf of Nassau
+appointed for the parish of St Quintin three _Baumeisters_
+(master-builders) who were to choose twelve chief parishioners as
+assistants for life. One of the first of these "Vervaren," who were
+named on May-day 1464, was Johannes Fust, and in 1467 Adam von Hochheim
+was chosen instead of "the late" (_selig_) Johannes Fust. Fust is said
+to have gone to Paris in 1466 and to have died of the plague, which
+raged there in August and September. He certainly was in Paris on the
+4th of July, when he gave Louis de Lavernade of the province of Forez,
+then chancellor of the duke of Bourbon and first president of the
+parliament of Toulouse, a copy of his second edition of Cicero, as
+appears from a note in Lavernade's own hand at the end of the book,
+which is now in the library of Geneva. But nothing further is known than
+that on the 30th of October, probably in 1471, an annual mass was
+instituted for him by Peter Schöffer, Conrad Henlif (for Henekes, or
+Henckis, Schöffer's partner? who married Fust's widow about 1468[4]) and
+Johann Fust (the son), in the abbey-church of St Victor of Paris, where
+he was buried; and that Peter Schöffer founded a similar memorial
+service for Fust in 1473 in the church of the Dominicans at Mainz
+(Bockenheimer, _Gesch. der Stadt Mainz_, iv. 15).
+
+Fust was formerly often confused with the famous magician Dr Johann
+Faust, who, though an historical figure, had nothing to do with him (see
+FAUST).
+
+  See further the articles GUTENBERG and TYPOGRAPHY.     (J. H. H.)
+
+
+FOOTNOTES:
+
+  [1] This date is uncertain; some place the marriage in 1453 or soon
+    after, others about 1464. It is probable that Fust alluded to this
+    relationship when he spoke of Schöffer as _pueri mei_ in the
+    colophons of Cicero's _De officiis_ of 1465 and 1466.
+
+  [2] This method was patented in England by Solomon Henry in 1780, and
+    by Sir William Congreve in 1819.
+
+  [3] (3) Durandus, _Rationale divinorum officiorum_ (1459), folio, 160
+    leaves; (4) the _Clementine Constitutions_, with the gloss of
+    Johannes Andreae (1460), 51 leaves; (5) _Biblia Sacra Latina_ (1462),
+    folio, 2 vols., 242 and 239 leaves, 48 lines to a full page; (6) the
+    Sixth Book of Decretals, with Andreae's gloss, 17th December 1465,
+    folio, 141 leaves; (7) Cicero, _De officiis_ (1465). 4to, 88 leaves,
+    the first edition of a Latin classic and the first book containing
+    Greek characters, while in the colophon Fust for the first time calls
+    Schöffer "puerum suum"; (8) the same, 4th February 1466; (9)
+    _Grammatica rhytmica_ (1466), folio, 11 leaves. They also printed in
+    1461-1462 several papal bulls, proclamations of Adolf of Nassau, &c.
+    Nothing is known to have appeared for three years after the storming
+    and capture of Mainz in 1462.
+
+  [4] Some confusion in the history of the Fust family has arisen since
+    the publication of Bernard's _Orig. de l'imprimerie_ (1853). On p.
+    262, vol. i. he gave an extract from the correspondence between
+    Oberlin and Bodmann (now preserved in the Paris Nat. Library), from
+    which it would appear that Peter Schöffer was the son-in-law, not of
+    Johann Fust, but of a brother of his, Conrad Fust. Of the latter,
+    however, no other trace has been found, and he is no doubt a fiction
+    of F.J. Bodmann, who, partly basing himself on the "Conrad" (Henlif,
+    or Henckis) mentioned above, added the rest to gratify Oberlin (see
+    Wyss in _Quartalblätter des hist. Vereins für Hessen_, 1879, p. 17).
+
+
+
+
+FUSTEL DE COULANGES, NUMA DENIS (1830-1889), French historian, was born
+in Paris on the 18th of March 1830, of Breton descent. After studying at
+the École Normale Supérieure he was sent to the French school at Athens
+in 1853, directed some excavations in Chios, and wrote an historical
+account of the island. After his return he filled various educational
+offices, and took his doctor's degree with two theses, _Quid Vestae
+cultus in institutis veterum privatis publicisque valuerit_ and _Polybe,
+ou la Grèce conquise par les Romains_ (1858). In these works his
+distinctive qualities were already revealed. His minute knowledge of the
+language of the Greek and Roman institutions, coupled with his low
+estimate of the conclusions of contemporary scholars, led him to go
+direct to the original texts, which he read without political or
+religious bias. When, however, he had succeeded in extracting from the
+sources a general idea that seemed to him clear and simple, he attached
+himself to it as if to the truth itself, employing dialectic of the most
+penetrating, subtle and even paradoxical character in his deduction of
+the logical consequences. From 1860 to 1870 he was professor of history
+at the faculty of letters at Strassburg, where he had a brilliant career
+as a teacher, but never yielded to the influence exercised by the German
+universities in the field of classical and Germanic antiquities.
+
+It was at Strassburg that he published his remarkable volume _La Cité
+antique_ (1864), in which he showed forcibly the part played by religion
+in the political and social evolution of Greece and Rome. Although his
+making religion the sole factor of this evolution was a perversion of
+the historical facts, the book was so consistent throughout, so full of
+ingenious ideas, and written in so striking a style, that it ranks as
+one of the masterpieces of the French language in the 19th century. By
+this literary merit Fustel set little store, but he clung tenaciously to
+his theories. When he revised the book in 1875, his modifications were
+very slight, and it is conceivable that, had he recast it, as he often
+expressed the desire to do in the last years of his life, he would not
+have abandoned any part of his fundamental thesis. The work is now
+largely superseded.
+
+Fustel de Coulanges was the most conscientious of men, the most
+systematic and uncompromising of historians. Appointed to a lectureship
+at the École Normale Supérieure in February 1870, to a professorship at
+the Paris faculty of letters in 1875, and to the chair of medieval
+history created for him at the Sorbonne in 1878, he applied himself to
+the study of the political institutions of ancient France. The invasion
+of France by the German armies during the war of 1870-71 attracted his
+attention to the Germanic invasions under the Roman Empire. Pursuing the
+theory of J.B. Dubos, but singularly transforming it, he maintained that
+those invasions were not marked by the violent and destructive character
+usually attributed to them; that the penetration of the German
+barbarians into Gaul was a slow process; that the Germans submitted to
+the imperial administration; that the political institutions of the
+Merovingians had their origins in the Roman laws at least as much as, if
+not more than, in German usages; and, consequently, that there was no
+conquest of Gaul by the Germans. This thesis he sustained brilliantly in
+his _Histoire des institutions politiques de l'ancienne France_, the
+first volume of which appeared in 1874. It was the author's original
+intention to complete this work in four volumes, but as the first volume
+was keenly attacked in Germany as well as in France, Fustel was forced
+in self-defence to recast the book entirely. With admirable
+conscientiousness he re-examined all the texts and wrote a number of
+dissertations, of which, though several (e.g. those on the Germanic mark
+and on the _allodium_ and _beneficium_) were models of learning and
+sagacity, all were dominated by his general idea and characterized by a
+total disregard for the results of such historical disciplines as
+diplomatic. From this crucible issued an entirely new work, less well
+arranged than the original, but richer in facts and critical comments.
+The first volume was expanded into three volumes, _La Gaule romaine_
+(1891), _L'Invasion germanique et la fin de l'empire_ (1891) and _La
+Monarchie franque_ (1888), followed by three other volumes, _L'Alleu et
+le domaine rural pendant l'époque mérovingienne_ (1889), _Les Origines
+du système féodal: le bénéfice et le patronat ..._ (1890) and _Les
+Transformations de la royauté pendant l'époque carolingienne_ (1892).
+Thus, in six volumes, he had carried the work no farther than the
+Carolingian period. The result of this enormous labour, albeit worthy of
+a great historian, clearly showed that the author lacked all sense of
+historical proportion. He was a diligent seeker after the truth, and was
+perfectly sincere when he informed a critic of the exact number of
+"truths" he had discovered, and when he remarked to one of his pupils a
+few days before his death, "Rest assured that what I have written in my
+book is the truth." Such superb self-confidence can accomplish much, and
+it undoubtedly helped to form Fustel's talent and to give to his style
+that admirable concision which subjugates even when it fails to
+convince; but a student instinctively distrusts an historian who settles
+the most controverted problems with such impassioned assurance. The
+dissertations not embodied in his great work were collected by himself
+and (after his death) by his pupil, Camille Jullian, and published as
+volumes of miscellanies: _Recherches sur quelques problèmes d'histoire_
+(1885), dealing with the Roman colonate, the land system in Normandy,
+the Germanic mark, and the judiciary organization in the kingdom of the
+Franks; _Nouvelles recherches sur quelques problèmes d'histoire_ (1891);
+and _Questions historiques_ (1893), which contains his paper on Chios
+and his thesis on Polybius.
+
+His life was devoted almost entirely to his teaching and his books. In
+1875 he was elected member of the Académie des Sciences Morales, and in
+1880 reluctantly accepted the post of director of the École Normale.
+Without intervening personally in French politics, he took a keen
+interest in the questions of administration and social reorganization
+arising from the fall of the imperialist régime and the disasters of the
+war. He wished the institutions of the present to approximate more
+closely to those of the past, and devised for the new French
+constitution a body of reforms which reflected the opinions he had
+formed upon the democracy at Rome and in ancient France. But these were
+dreams which did not hold him long, and he would have been scandalized
+had he known that his name was subsequently used as the emblem of a
+political and religious party. He died at Massy (Seine-et-Oise) on the
+12th of September 1889. Throughout his historical career--at the École
+Normale and the Sorbonne and in his lectures delivered to the empress
+Eugénie--his sole aim was to ascertain the truth, and in the defence of
+truth his polemics against what he imagined to be the blindness and
+insincerity of his critics sometimes assumed a character of harshness
+and injustice. But, in France at least, these critics were the first to
+render justice to his learning, his talents and his disinterestedness.
+
+  See Paul Guiraud, _Fustel de Coulanges_ (1896); H. d'Arbois de
+  Jubainville, _Deux Manières d'écrire l'histoire: critique de Bossuet,
+  d'Augustin Thierry et de Fustel de Coulanges_ (1896); and Gabriel
+  Monod, _Portraits et souvenirs_ (1897).     (C. B.*)
+
+
+
+
+FUSTIAN, a term which includes a variety of heavy woven cotton fabrics,
+chiefly prepared for men's wear. It embraces plain twilled cloth called
+jean, and cut fabrics similar to velvet, known as velveteen, moleskin,
+corduroy, &c. The term was once applied to a coarse cloth made of cotton
+and flax; now, fustians are usually of cotton and dyed various colours.
+In the reign of Edward III. the name was given to a woollen fabric. The
+name is said to be derived from El-Fustat, a suburb of Cairo, where it
+was first made; and certainly a kind of cloth has long been known under
+that name. In a petition to parliament, _temp._ Philip and Mary,
+"fustian of Naples" is mentioned. In the 13th and 14th centuries
+priests' robes and women's dresses were made of fustian, but though
+dresses are still made from some kinds the chief use is for labourers'
+clothes.
+
+
+
+
+FUSTIC (Fr. _fustoc_, from Arab. _fustuq_, Gr. [Greek: pistakê],
+pistachio) YELLOW WOOD or OLD FUSTIC, a dye-stuff consisting of the wood
+of _Chlorophora tinctoria_, a large tree of the natural order Moraceae,
+growing in the West Indies and tropical America. Fustic occurs in
+commerce in blocks, which are brown without, and of a brownish-yellow
+within. It is sometimes employed for inlaid work. The dye-stuff termed
+young fustic or Zante fustic, and also Venetian sumach, is the wood of
+_Rhus cotinus_ (fustet, or smoke tree), a southern European and Asiatic
+shrub of the natural order Anacardiaceae, called by Gerarde "red
+sumach," and apparently the "coccygia" and "cotinus" of Pliny (_Nat.
+Hist._ xiii. 41, xvi. 30). Its colouring matter is fisetin, C15H10O6,
+which was synthesized by S. von Kostanecki (_Ber._, 1904, 37, p. 384).
+(See DYEING.)
+
+
+
+
+FUTURES, a term used in the produce markets for purchases or sales of
+commodities to be completed at a future date, as opposed to cash or
+"spot" transactions, which are settled immediately. See MARKET, and (for
+a detailed discussion of the question as affecting cotton) COTTON:
+_Marketing and Supply_.
+
+
+
+
+FUX, JOHANN JOSEPH (1660-1741), Austrian musician, was born at
+Hirtenfeld (Styria) in 1660. Of his youth and early training nothing is
+known. In 1696 he was organist at one of the principal churches of
+Vienna, and in 1698 was appointed by the emperor Leopold I. as his
+"imperial court-composer," with a salary of about £6 a month. At the
+court of Leopold and of his successors Joseph I. and Charles VI., Fux
+remained for the rest of his life. To his various court dignities that
+of organist at St Stephen's cathedral was added in 1704. He married the
+daughter of the government secretary Schnitzbaum. As a proof of the high
+favour in which he was held by the art-loving Charles VI., it is told
+that at the coronation of that emperor as king of Bohemia in 1723 an
+opera, _La Constanza e la Fortezza_, especially composed by Fux for the
+occasion, was given at Prague in an open-air theatre. Fux at the time
+was suffering from gout, but the emperor had him carried in a litter all
+the way from Vienna, and gave him a seat in the imperial box. Fux died
+at Vienna on the 13th of February 1741. His life, although passed in the
+great world, was eventless, and his only troubles arose from the
+intrigues of his Italian rivals at court. Of the numerous operas which
+Fux wrote it is unnecessary to speak. They do not essentially differ
+from the style of the Italian _opera seria_ of the time. Of greater
+importance are his sacred compositions, psalms, motets, oratorios and
+masses, the celebrated _Missa Canonica_ amongst the latter. It is an all
+but unparalleled _tour de force_ of learned musicianship, being written
+entirely in that most difficult of contrapuntal devices--the canon. As a
+contrapuntist and musical scholar generally, Fux was unsurpassed by any
+of his contemporaries, and his great theoretical work, the _Gradus ad
+Parnassum_, long remained by far the most thorough treatment of
+counterpoint and its various developments. The title of the original
+Latin edition is _Gradus ad Parnassum sive manuductio ad compositionem
+musicae regularem, methoda nova ac certa nondum ante tam exacta ordine
+in lucem edita, elaborata a Joanne Josepho Fux_ (Vienna, 1715). It was
+translated into most European languages during the 18th century, and is
+still studied by musicians interested in the history of their art. The
+expenses of the publication were defrayed by the emperor Charles VI.
+
+  Fux's biography was published by Ludwig von Köchel (Vienna, 1871). It
+  is based on minute original research and contains, amongst other
+  valuable materials, a complete catalogue of the composer's numerous
+  works.
+
+
+
+
+FUZE or FUSE, an appliance for firing explosives in blasting operations,
+military shells, &c. (see BLASTING and AMMUNITION, § SHELL). The
+spelling is not governed by authority, but modern convenience has
+dictated the adoption of the "z" by military engineers as a general
+rule, in order to distinguish this sense from that of melting by heat
+(see below). The word, according to the _New English Dictionary_, is one
+of the forms in which the Lat. _fusus_, spindle, has been adapted
+through Romanic into English, the ordinary fuze taking the shape of a
+spindle-like tube. Similarly the term "fusee" (Fr. _fusée_, spindle full
+of tow, Late Lat. _fusata_) is applied to a coned spindle sometimes used
+in the wheel train of watches and spring clocks to equalize the action
+of the mainspring (see WATCH); and the application of the same term to a
+special kind of match may also be due to its resemblance to a spindle.
+Again, in heraldry, another form, "fusil," derived through the French
+from a Late Lat. diminutive (_fusillus_ or _fusellus_) of this same
+_fusus_, is used of a bearing, an elongated lozenge. According to other
+etymological authorities, however (see Skeat, _Etym. Dict._, 1898),
+"fuze" or "fuse," and "fusee" in the sense of match, are all forms
+derived through the Fr. fusil, from Late Lat. _focile_, steel for
+striking fire from a flint, from Lat. _focus_, hearth. The Fr. _fusil_
+and English "fusil" were thus transferred to the "firelock," i.e. the
+light musket of the 17th century (see FUSILIER).
+
+In electrical engineering a "fuse" (always so spelled) is a safety
+device, commonly consisting of a strip or wire of easily fusible metal,
+which melts and thus interrupts the circuit of which it forms part,
+whenever that circuit, through some accident or derangement, is caused
+to carry a current larger than that for which it is intended. In this
+sense the word must be connected with _fusus_, the past participle of
+Lat. _fundere_, to pour, whence comes the verb "fuse," to melt by heat,
+often used figuratively in the sense of blend, mix.
+
+
+
+
+FYNE, LOCH, an inlet of the sea, Argyllshire, Scotland. From the head, 6
+m. above Inveraray, to the mouth on the Sound of Bute, it has a
+south-westerly and then southerly trend and is 44 m. long, its width
+varying from ¼ m. to 6 m. It receives the Fyne, Shira, Aray and many
+other streams, and, on the western side, gives off Lochs Shira, Gair,
+Gilp (with Ardrishaig, the Crinan Canal and Lochgilphead) and East
+Tarbert (with Tarbert village). The glens debouching on the lake are
+Fyne, Shira, Aray, Kinglas and Hell's Glen. The coast generally is
+picturesque and in many parts well wooded. All vessels using the Crinan
+Canal navigate the loch to and from Ardrishaig, and there are daily
+excursions during the season, as far up as Inveraray. There are ferries
+at St Catherine's and Otter, and piers at Tarbert, Ardrishaig, Kilmory,
+Crarae, Furnace, Inveraray, Strachur and elsewhere. The industries
+comprise granite quarrying at Furnace and Crarae, distilling at
+Ardrishaig, gunpowder-making at Furnace and Kilfinan, and, above all,
+fishing. Haddock, whiting and codling are taken, and the famous "Loch
+Fyne herrings" command the highest price in the market.
+
+
+
+
+FYRD, the name given to the English army, or militia, during the
+Anglo-Saxon period (see ARMY, 60). It is first mentioned in the
+_Anglo-Saxon Chronicle_ under the date 605. The ealdorman, or sheriff,
+of the shire was probably charged with the duty of calling out and
+leading the fyrd, which appears always to have retained a local
+character, as during the time of the Danish invasions we read of the
+fyrd of Kent, of Somerset and of Devon. As attendance at the fyrd was
+included in the _trinoda necessitas_ it was compulsory on all holders of
+land; but that it was not confined to them is shown by the following
+extract from the laws of Ine, king of the West Saxons, dated about 690,
+which prescribes the penalty for the serious offence of neglecting the
+fyrd: "If a _gesithcund_ man owning land neglect the fyrd, let him pay
+120 shillings, and forfeit his land; one not owning land 60 shillings; a
+ceorlish man 30 shillings as _fyrdwite_." The fyrd was gradually
+superseded by the gathering of the thegns and their retainers, but it
+was occasionally called out for defensive purposes even after the Norman
+Conquest.
+
+
+
+
+FYT, JOHANNES (1609-1661), Belgian animal painter, was born at Antwerp
+and christened on the 19th of August 1609. He was registered apprentice
+to Hans van den Berghe in 1621. Professionally van den Berghe was a
+restorer of old pictures rather than a painter of new ones. At twenty
+Johannes Fyt entered the gild of St Luke as a master, and from that time
+till his death in 1661 he produced a vast number of pictures in which
+the bold facility of Snyders is united to the powerful effects of
+Rembrandt, and harmonies of gorgeous tone are not less conspicuous than
+freedom of touch and a true semblance of nature. There never was such a
+master of technical processes as Fyt in the rendering of animal life in
+its most varied forms. He may have been less correct in outline, less
+bold in action than Snyders, but he was much more skilful and more true
+in the reproduction of the coat of deer, dogs, greyhounds, hares and
+monkeys, whilst in realizing the plumage of peacocks, woodcocks, ducks,
+hawks, and cocks and hens, he had not his equal, nor was any artist even
+of the Dutch school more effective in relieving his compositions with
+accessories of tinted cloth, porcelain ware, vases and fruit. He was not
+clever at figures, and he sometimes trusted for these to the
+co-operation of Cornelius Schut or Willeborts, whilst his architectural
+backgrounds were sometimes executed by Quellyn. "Silenus amongst Fruit
+and Flowers," in the Harrach collection at Vienna, "Diana and her Nymphs
+with the Produce of the Chase," in the Belvedere at Vienna, and "Dead
+Game and Fruit in front of a Triumphal Arch," belonging to Baron von
+Rothschild at Vienna, are specimens of the co-operation respectively of
+Schut, Willeborts and Quellyn. They are also Fyt's masterpieces. The
+earliest dated work of the master is a cat grabbing at a piece of dead
+poultry near a hare and birds, belonging to Baron Cetto at Munich, and
+executed in 1644. The latest is a "Dead Snipe with Ducks," of 1660,
+sold with the Jäger collection at Cologne in 1871. Great power is shown
+in the bear and boar hunts at Munich and Ravensworth castle. A "Hunted
+Roedeer with Dogs in the Water," in the Berlin Museum, has some of the
+life and more of the roughness of Snyders, but lacks variety of tint and
+finish. A splendid specimen is the Page and Parrot near a table covered
+with game, guarded by a dog staring at a monkey, in the Wallace
+collection. With the needle and the brush Fyt was equally clever. He
+etched 16 plates, and those representing dogs are of their kind unique.
+
+
+
+
+FYZABAD, or FAIZABAD, a city, district and division of British India in
+the United Provinces. The city stands on the left bank of the river
+Gogra, 78 m. by rail E. of Lucknow. Pop. (1901) 75,085. To the E. of
+Fyzabad, and now forming a suburb, is the ancient site of Ajodhya
+(q.v.). Fyzabad was founded about 1730 by Sa'adat Ali Khan, the first
+nawab wazir of Oudh, who built a hunting-lodge here. It received its
+present name in the reign of his successor; and Shuja-ud-daula, the
+third nawab, laid out a large town and fortified it, and here he was
+buried. It was afterwards the residence of the Begums of Oudh, famous in
+connexion with the impeachment of Warren Hastings. When the court of
+Oudh was removed to Lucknow in 1775 all the leading merchants and
+bankers abandoned the place. At the census of 1869 Fyzabad contained
+only 37,804 inhabitants; but it is now again advancing in prosperity and
+population. On the outbreak of the Mutiny in 1857, the cantonment
+contained two regiments of infantry, a squadron of cavalry, and a light
+field battery of artillery--all natives. Owing to their threatening
+demeanour after the Meerut massacre, many of the European women and
+children were sheltered by one of the great landholders of Oudh, and
+others were sent to less disturbed parts of the country. The troops
+rose, as was anticipated, and although they at first permitted their
+officers to take boats and proceed towards Dinapur, a message was
+afterwards sent to a rebel force lower down the river to intercept the
+fugitives. Of four boats, one, having passed the rebels unnoticed,
+succeeded in reaching Dinapur safely. Of those in the other three boats,
+one alone escaped. Fyzabad is now a station for European as well as for
+native troops. It is the headquarters of a brigade in the 8th division
+of the northern army. There is a government college. Sugar-refining and
+trade in agricultural produce are important.
+
+THE DISTRICT OF FYZABAD, lying between the two great rivers Gogra and
+Gumti, has an area of 1740 sq. m. It is entirely alluvial and well
+wooded, and has a good climate. Pop. (1901) 1,225,374, an increase of
+.7% in the decade. The district is traversed throughout its length by
+the Oudh and Rohilkhand railway from Lucknow to Benares, with a branch
+to Allahabad. Tanda, with a population in 1901 of 19,853, has the
+largest production of cotton goods in Oudh.
+
+The DIVISION OF FYZABAD has an area of 12,113 sq. m., and comprises the
+six districts of Fyzabad, Gonda, Bahraich, Sultanpur, Partabgarh and
+Bara Banki. Pop. (1901) 6,855,991, an increase of 2% in the decade.
+
+
+
+
+
+
+End of the Project Gutenberg EBook of Encyclopaedia Britannica, 11th
+Edition, Volume 11, Slice 3, by Various
+
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+
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+<body>
+
+
+<pre>
+
+The Project Gutenberg EBook of Encyclopaedia Britannica, 11th Edition,
+Volume 11, Slice 3, by Various
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 3
+       "Frost" to "Fyzabad"
+
+Author: Various
+
+Release Date: August 13, 2011 [EBook #37064]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK ENCYC. BRITANNICA, VOL 11, SL 3 ***
+
+
+
+
+Produced by Marius Masi, Don Kretz and the Online
+Distributed Proofreading Team at https://www.pgdp.net
+
+
+
+
+
+
+</pre>
+
+
+
+<table border="0" cellpadding="10" style="background-color: #dcdcdc; color: #696969; " summary="Transcriber's note">
+<tr>
+<td style="width:25%; vertical-align:top">
+Transcriber&rsquo;s note:
+</td>
+<td class="norm">
+A few typographical errors have been corrected. They
+appear in the text <span class="correction" title="explanation will pop up">like this</span>, and the
+explanation will appear when the mouse pointer is moved over the marked
+passage. Sections in Greek will yield a transliteration
+when the pointer is moved over them, and words using diacritic characters in the
+Latin Extended Additional block, which may not display in some fonts or browsers, will
+display an unaccented version. <br /><br />
+<a name="artlinks">Links to other EB articles:</a> Links to articles residing in other EB volumes will
+be made available when the respective volumes are introduced online.
+</td>
+</tr>
+</table>
+<div style="padding-top: 3em; ">&nbsp;</div>
+
+<h2>THE ENCYCLOP&AElig;DIA BRITANNICA</h2>
+
+<h2>A DICTIONARY OF ARTS, SCIENCES, LITERATURE AND GENERAL INFORMATION</h2>
+
+<h3>ELEVENTH EDITION</h3>
+<div style="padding-top: 3em; ">&nbsp;</div>
+
+<hr class="full" />
+<h3>VOLUME XI SLICE III<br /><br />
+Frost to Fyzabad</h3>
+<hr class="full" />
+<div style="padding-top: 3em; ">&nbsp;</div>
+
+<p class="center1" style="font-size: 150%; font-family: 'verdana';">Articles in This Slice</p>
+<table class="reg" style="width: 90%; font-size: 90%; border: gray 2px solid;" cellspacing="8" summary="Contents">
+
+<tr><td class="tcl"><a href="#ar1">FROST</a></td> <td class="tcl"><a href="#ar59">FULMAR</a></td></tr>
+<tr><td class="tcl"><a href="#ar2">FROSTBITE</a></td> <td class="tcl"><a href="#ar60">FULMINIC ACID</a></td></tr>
+<tr><td class="tcl"><a href="#ar3">FROSTBURG</a></td> <td class="tcl"><a href="#ar61">FULTON, ROBERT</a></td></tr>
+<tr><td class="tcl"><a href="#ar4">FROTHINGHAM, OCTAVIUS BROOKS</a></td> <td class="tcl"><a href="#ar62">FULTON</a> (Missouri, U.S.A.)</td></tr>
+<tr><td class="tcl"><a href="#ar5">FROUDE, JAMES ANTHONY</a></td> <td class="tcl"><a href="#ar63">FULTON</a> (New York, U.S.A.)</td></tr>
+<tr><td class="tcl"><a href="#ar6">FRUCTOSE</a></td> <td class="tcl"><a href="#ar64">FUM</a></td></tr>
+<tr><td class="tcl"><a href="#ar7">FRUGONI, CARLO INNOCENZIO MARIA</a></td> <td class="tcl"><a href="#ar65">FUMARIC AND MALEIC ACIDS</a></td></tr>
+<tr><td class="tcl"><a href="#ar8">FRUIT</a></td> <td class="tcl"><a href="#ar66">FUMAROLE</a></td></tr>
+<tr><td class="tcl"><a href="#ar9">FRUIT AND FLOWER FARMING</a></td> <td class="tcl"><a href="#ar67">FUMIGATION</a></td></tr>
+<tr><td class="tcl"><a href="#ar10">FRUMENTIUS</a></td> <td class="tcl"><a href="#ar68">FUMITORY</a></td></tr>
+<tr><td class="tcl"><a href="#ar11">FRUNDSBERG, GEORG VON</a></td> <td class="tcl"><a href="#ar69">FUNCHAL</a></td></tr>
+<tr><td class="tcl"><a href="#ar12">FRUSTUM</a></td> <td class="tcl"><a href="#ar70">FUNCTION</a></td></tr>
+<tr><td class="tcl"><a href="#ar13">FRUYTIERS, PHILIP</a></td> <td class="tcl"><a href="#ar71">FUNDY, BAY OF</a></td></tr>
+<tr><td class="tcl"><a href="#ar14">FRY</a></td> <td class="tcl"><a href="#ar72">FUNERAL RITES</a></td></tr>
+<tr><td class="tcl"><a href="#ar15">FRY, SIR EDWARD</a></td> <td class="tcl"><a href="#ar73">FUNGI</a></td></tr>
+<tr><td class="tcl"><a href="#ar16">FRY, ELIZABETH</a></td> <td class="tcl"><a href="#ar74">FUNJ</a></td></tr>
+<tr><td class="tcl"><a href="#ar17">FRYXELL, ANDERS</a></td> <td class="tcl"><a href="#ar75">FUNKIA</a></td></tr>
+<tr><td class="tcl"><a href="#ar18">FUAD PASHA</a></td> <td class="tcl"><a href="#ar76">FUNNEL</a></td></tr>
+<tr><td class="tcl"><a href="#ar19">FUCHOW</a></td> <td class="tcl"><a href="#ar77">FUR</a></td></tr>
+<tr><td class="tcl"><a href="#ar20">FUCHS, JOHANN NEPOMUK VON</a></td> <td class="tcl"><a href="#ar78">FURAZANES</a></td></tr>
+<tr><td class="tcl"><a href="#ar21">FUCHS, LEONHARD</a></td> <td class="tcl"><a href="#ar79">FURETIÈRE, ANTOINE</a></td></tr>
+<tr><td class="tcl"><a href="#ar22">FUCHSIA</a></td> <td class="tcl"><a href="#ar80">FURFOOZ</a></td></tr>
+<tr><td class="tcl"><a href="#ar23">FUCHSINE</a></td> <td class="tcl"><a href="#ar81">FURFURANE</a></td></tr>
+<tr><td class="tcl"><a href="#ar24">FUCINO, LAGO DI</a></td> <td class="tcl"><a href="#ar82">FURIES</a></td></tr>
+<tr><td class="tcl"><a href="#ar25">FUEL</a></td> <td class="tcl"><a href="#ar83"> FURLONG</a></td></tr>
+<tr><td class="tcl"><a href="#ar26">FUENTE OVEJUNA</a></td> <td class="tcl"><a href="#ar84">FURNACE</a></td></tr>
+<tr><td class="tcl"><a href="#ar27">FUENTERRABIA</a></td> <td class="tcl"><a href="#ar85"> FURNEAUX, TOBIAS</a></td></tr>
+<tr><td class="tcl"><a href="#ar28">FUERO</a></td> <td class="tcl"><a href="#ar86">FURNES</a></td></tr>
+<tr><td class="tcl"><a href="#ar29">FUERTEVENTURA</a></td> <td class="tcl"><a href="#ar87">FURNESS, HORACE HOWARD</a></td></tr>
+<tr><td class="tcl"><a href="#ar30">FUGGER</a></td> <td class="tcl"><a href="#ar88">FURNESS</a></td></tr>
+<tr><td class="tcl"><a href="#ar31">FUGITIVE SLAVE LAWS</a></td> <td class="tcl"><a href="#ar89">FURNISS, HARRY</a></td></tr>
+<tr><td class="tcl"><a href="#ar32">FUGLEMAN</a></td> <td class="tcl"><a href="#ar90"> FURNITURE</a></td></tr>
+<tr><td class="tcl"><a href="#ar33">FUGUE</a></td> <td class="tcl"><a href="#ar91"> FURNIVALL, FREDERICK JAMES</a></td></tr>
+<tr><td class="tcl"><a href="#ar34">FÜHRICH, JOSEPH VON</a></td> <td class="tcl"><a href="#ar92">FURSE, CHARLES WELLINGTON</a></td></tr>
+<tr><td class="tcl"><a href="#ar35">FUJI</a></td> <td class="tcl"><a href="#ar93"> FÜRST, JULIUS</a></td></tr>
+<tr><td class="tcl"><a href="#ar36">FU-KIEN</a></td> <td class="tcl"><a href="#ar94">FÜRSTENBERG</a></td></tr>
+<tr><td class="tcl"><a href="#ar37">FUKUI</a></td> <td class="tcl"><a href="#ar95">FÜRSTENWALDE</a></td></tr>
+<tr><td class="tcl"><a href="#ar38">FUKUOKA</a></td> <td class="tcl"><a href="#ar96">FÜRTH</a></td></tr>
+<tr><td class="tcl"><a href="#ar39">FULA</a></td> <td class="tcl"><a href="#ar97"> FURTWÄNGLER, ADOLF</a></td></tr>
+<tr><td class="tcl"><a href="#ar40">FULCHER OF CHARTRES</a></td> <td class="tcl"><a href="#ar98">FURZE</a></td></tr>
+<tr><td class="tcl"><a href="#ar41">FULDA</a></td> <td class="tcl"><a href="#ar99">FUSARO, LAGO</a></td></tr>
+<tr><td class="tcl"><a href="#ar42">FULGENTIUS, FABIUS PLANCIADES</a></td> <td class="tcl"><a href="#ar100">FUSELI, HENRY</a></td></tr>
+<tr><td class="tcl"><a href="#ar43">FULGINIAE</a></td> <td class="tcl"><a href="#ar101">FUSEL OIL</a></td></tr>
+<tr><td class="tcl"><a href="#ar44">FULGURITE</a></td> <td class="tcl"><a href="#ar102">FUSIBLE METAL</a></td></tr>
+<tr><td class="tcl"><a href="#ar45">FULHAM</a></td> <td class="tcl"><a href="#ar103">FUSILIER</a></td></tr>
+<tr><td class="tcl"><a href="#ar46">FULK</a> (king of Jerusalem)</td> <td class="tcl"><a href="#ar104">FUSION</a></td></tr>
+<tr><td class="tcl"><a href="#ar47">FULK</a> (archbishop of Reims)</td> <td class="tcl"><a href="#ar105">FÜSSEN</a></td></tr>
+<tr><td class="tcl"><a href="#ar48">FULKE, WILLIAM</a></td> <td class="tcl"><a href="#ar106">FUST, JOHANN</a></td></tr>
+<tr><td class="tcl"><a href="#ar49">FULK NERRA</a></td> <td class="tcl"><a href="#ar107">FUSTEL DE COULANGES, NUMA DENIS</a></td></tr>
+<tr><td class="tcl"><a href="#ar50">FÜLLEBORN, GEORG GUSTAV</a></td> <td class="tcl"><a href="#ar108">FUSTIAN</a></td></tr>
+<tr><td class="tcl"><a href="#ar51">FULLER, ANDREW</a></td> <td class="tcl"><a href="#ar109">FUSTIC</a></td></tr>
+<tr><td class="tcl"><a href="#ar52">FULLER, GEORGE</a></td> <td class="tcl"><a href="#ar110">FUTURES</a></td></tr>
+<tr><td class="tcl"><a href="#ar53">FULLER, MARGARET</a></td> <td class="tcl"><a href="#ar111">FUX, JOHANN JOSEPH</a></td></tr>
+<tr><td class="tcl"><a href="#ar54">FULLER, MELVILLE WESTON</a></td> <td class="tcl"><a href="#ar112">FUZE</a></td></tr>
+<tr><td class="tcl"><a href="#ar55">FULLER, THOMAS</a></td> <td class="tcl"><a href="#ar113">FYNE, LOCH</a></td></tr>
+<tr><td class="tcl"><a href="#ar56">FULLER, WILLIAM</a></td> <td class="tcl"><a href="#ar114">FYRD</a></td></tr>
+<tr><td class="tcl"><a href="#ar57">FULLER'S EARTH</a></td> <td class="tcl"><a href="#ar115">FYT, JOHANNES</a></td></tr>
+<tr><td class="tcl"><a href="#ar58">FULLERTON, LADY GEORGIANA CHARLOTTE</a></td> <td class="tcl"><a href="#ar116">FYZABAD</a></td></tr>
+</table>
+
+<hr class="art" />
+<p><span class="pagenum"><a name="page251" id="page251"></a>251</span></p>
+<p><span class="bold">FROST<a name="ar1" id="ar1"></a></span> (a common Teutonic word, cf. Dutch, <i>vorst</i>, Ger. <i>Frost</i>,
+from the common Teutonic verb meaning &ldquo;to freeze,&rdquo; Dutch,
+<i>vriezen</i>, Ger. <i>frieren</i>; the Indo-European root is seen in Lat.
+<i>pruina</i>, hoar-frost, cf. <i>prurire</i>, to itch, burn, <i>pruna</i>, burning coal,
+Sansk. <i>plush</i>, to burn), in meteorology, the act, or agent of the
+process, of freezing; hence the terms &ldquo;hoar-frost&rdquo; and &ldquo;white-frost&rdquo;
+applied to visible frozen vapour formed on exposed surfaces.
+A frost can only occur when the surface temperature falls below
+32° F., the freezing-point of water; if the temperature be
+between 28° and 32° it is a &ldquo;light frost,&rdquo; if below 28° it is a
+&ldquo;heavy,&rdquo; &ldquo;killing&rdquo; or &ldquo;black frost&rdquo;; the term &ldquo;black frost&rdquo;
+is also used when no hoar-frost is present. The number of
+degrees below freezing-point is termed &ldquo;degrees of frost.&rdquo; As
+soon as a mass of air is cooled to its dew-point, water begins to
+be precipitated in the form of rain, dew, snow or hail. Hoarfrost
+is only formed at the immediate surface of the land if the
+latter be at a temperature below 32°, and this may occur even
+when the temperature of the air a few feet above the ground is
+12°-16° above the freezing-point. The heaviest hoar-frosts are
+formed under weather conditions similar to those under which
+the heaviest summer dews occur, namely, clear and calm nights,
+when there is no cloud to impede the radiation of heat from the
+surface of the land, which thereby becomes rapidly and completely
+cooled. The danger of frost is minimized when the soil
+is very moist, as for example after 10-12 mm. of rain; and it
+is a practice in America to flood fields on the receipt of a frost
+warning, radiation being checked by the light fog sheets which
+develop over moist soils, just as a cloud-layer in the upper
+atmosphere impedes radiation on a grand scale. A layer of
+smoke will also impede radiation locally, and to this end smoky
+fires are sometimes lit in such positions that the smoke may
+drift over planted ground which it is desirable to preserve from
+frost. Similarly, frost may occur in open country when a town,
+protected by its smoke-cloud above, is free of it. In a valley
+with fairly high and steep flanks frost sometimes occurs locally
+at the bottom, because the layer of air cooled by contact with
+the cold surface of the higher ground is heavier than that not so
+cooled, and therefore tends to flow or settle downwards along the
+slope of the land. When meteorological considerations point
+to a frost, an estimate of the night temperature may be obtained
+by multiplying the difference between the readings of the wet
+and dry bulb thermometer by 2.5 and subtracting the result
+from the dry bulb temperature. This rule applies when the
+evening air is at about 50° and 30.1 in. pressure, the sky being
+clear. An instrument has been devised in France for the prediction
+of frost. It consists of a wet bulb and a dry bulb thermometer,
+mounted on a board on which is also a scale of lines
+corresponding to degrees of the dry bulb, and a pointer traversing
+a scale graduated according to degrees of the wet bulb. Observations
+for the night are taken about half an hour before sunset.
+By means of the pointer and scale, the point may be found at
+which the line of the dry-bulb reading meets the pointer set to
+the reading of the wet bulb. The scale is further divided by
+colours so that the observed point may fall within one of three
+zones, indicating certain frost, probable frost or no probability
+of frost.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FROSTBITE,<a name="ar2" id="ar2"></a></span> a form of <span class="sc">mortification</span> (<i>q.v.</i>), due to the action
+of extreme cold in cutting off the blood-supply from the fingers,
+toes, nose, ears, &amp;c. In comparatively trifling forms it occurs
+as &ldquo;chaps&rdquo; and &ldquo;chilblains,&rdquo; but the term frostbite is usually
+applied only to more severe cases, where the part affected
+becomes in danger of gangrene. An immediate application of
+snow, or ice-water, will restore the circulation; the application
+of heat would cause inflammation. But if the mortification has
+gone too far for the circulation to be restored, the part will be
+lost, and surgical treatment may be necessary.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FROSTBURG,<a name="ar3" id="ar3"></a></span> a town of Allegany county, Maryland, U.S.A.,
+11 m. W. of Cumberland. Pop. (1890) 3804; (1900) 5274
+(578 foreign-born and 236 negroes); (1910) 6028. It is served
+by the Cumberland &amp; Pennsylvania railway and the Cumberland
+&amp; Westernport electric railway. The town is about 2000 ft.
+above sea-level on a plateau between the Great Savage and Dans
+mountains, and its delightful scenery and air have made it
+attractive as a summer resort. It is the seat of the second state
+normal school, opened in 1904. Frostburg is in the midst of the
+coal region of the state, and is itself almost completely undermined;
+it has planing mills and manufactures large quantities
+of fire-brick. The municipality owns and operates its waterworks.
+Natural gas is piped to Frostburg from the West Virginia
+fields, 120 m. away. Frostburg was first settled in 1812; was
+called Mount Pleasant until about 1830, when the present name
+was substituted in honour of Meshech Frost, one of the town&rsquo;s
+founders; and was incorporated in 1870.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FROTHINGHAM, OCTAVIUS BROOKS<a name="ar4" id="ar4"></a></span> (1822-1895), American
+clergyman and author, was born in Boston on the 26th of
+November 1822, son of Nathaniel Langdon Frothingham (1793-1870),
+a prominent Unitarian preacher of Boston, and through
+his mother&rsquo;s family related to Phillips Brooks. He graduated
+from Harvard College in 1843 and from the Divinity School in
+1846. He was pastor of the North Unitarian church of Salem,
+Massachusetts, in 1847-1855. From 1855 to 1860 he was pastor
+of a new Unitarian society in Jersey City, where he gave up the
+Lord&rsquo;s Supper, thinking that it ministered to self-satisfaction;
+and it was as a radical Unitarian that he became pastor of another
+young church in New York City in 1860. Indeed in 1864 he was
+recognized as leader of the radicals after his reply to Dr Hedge&rsquo;s
+address to the graduating students of the Divinity School on
+<i>Anti-Supernaturalism in the Pulpit</i>. In 1865, when he had
+practically given up &ldquo;transcendentalism,&rdquo; his church building
+was sold and his congregation began to worship in Lyric Hall
+under the name of the Independent Liberal Church; in 1875
+they removed to the Masonic Temple, but four years later ill-health
+compelled Frothingham&rsquo;s resignation, and the church
+dissolved. Paralysis threatened him and he never fully recovered
+his health; in 1881 he returned to Boston, where he died on the
+27th of November 1895. To this later period of his life belongs
+his best literary work. While he was in New York he was for a
+time art critic of the <i>Tribune</i>. Always himself on the unpopular
+side and an able but thoroughly fair critic of the majority, he
+habitually under-estimated his own worth; he was not only an
+anti-slavery leader when abolition was not popular even in New
+England, and a radical and rationalist when it was impossible
+for him to stay conveniently in the Unitarian Church, but he
+<span class="pagenum"><a name="page252" id="page252"></a>252</span>
+was the first president of the National Free Religious Association
+(1867) and an early and ardent disciple of Darwin and Spencer.
+To his radical views he was always faithful. It is a mistake to
+say that he grew more conservative in later years; but his
+judgment grew more generous and catholic. He was a greater
+orator than man of letters, and his sermons in New York were
+delivered to large audiences, averaging one thousand at the
+Masonic Temple, and were printed each week; in eloquence and
+in the charm of his spoken word he was probably surpassed in
+his day by none save George William Curtis. Personally he
+seemed cold and distant, partly because of his impressive appearance,
+and partly because of his own modesty, which made him
+backward in seeking friendships.</p>
+
+<div class="condensed">
+<p>His principal published works are: <i>Stories from the Life of the
+Teacher</i> (1863), <i>A Child&rsquo;s Book of Religion</i> (1866), and other works
+of religious teaching for children; several volumes of sermons;
+<i>Beliefs of Unbelievers</i> (1876), <i>The Cradle of the Christ: a Study in
+Primitive Christianity</i> (1877), <i>The Spirit of New Faith</i> (1877),
+<i>The Rising and the Setting Faith</i> (1878), and other expositions of
+the &ldquo;new faith&rdquo; he preached; <i>Life of Theodore Parker</i> (1874),
+<i>Transcendentalism in New England</i> (1876), which is largely biographical,
+<i>Gerrit Smith, a Biography</i> (1878), <i>George Ripley</i> (1882),
+in the &ldquo;American Men of Letters&rdquo; series, <i>Memoir of William
+Henry Channing</i> (1886), <i>Boston Unitarianism, 1820-1850</i> (1890),
+really a biography of his father; and <i>Recollections and Impressions,
+1822-1890</i> (1891).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FROUDE, JAMES ANTHONY<a name="ar5" id="ar5"></a></span> (1818-1894), English historian,
+son of R.H. Froude, archdeacon of Totnes, was born at
+Dartington, Devon, on the 23rd of April 1818. He was educated
+at Westminster and Oriel College, Oxford, then the centre of the
+ecclesiastical revival. He obtained a second class and the
+chancellor&rsquo;s English essay prize, and was elected a fellow of
+Exeter College (1842). His elder brother, Richard Hurrell
+Froude (1803-1836), had been one of the leaders of the High
+Church movement at Oxford. Froude joined that party and
+helped J.H. Newman, afterwards cardinal, in his <i>Lives of the
+English Saints</i>. He was ordained deacon in 1845. By that time
+his religious opinions had begun to change, he grew dissatisfied
+with the views of the High Church party, and came under the
+influence of Carlyle&rsquo;s teaching. Signs of this change first appeared
+publicly in his <i>Shadows of the Clouds</i>, a volume containing two
+stories of a religious sort, which he published in 1847 under the
+pseudonym of &ldquo;Zeta,&rdquo; and his complete desertion of his party
+was declared a year later in his <i>Nemesis of Faith</i>, an heretical
+and unpleasant book, of which the earlier part seems to be
+autobiographical.</p>
+
+<p>On the demand of the college he resigned his fellowship at
+Oxford, and mainly at least supported himself by writing,
+contributing largely to <i>Fraser&rsquo;s Magazine</i> and the <i>Westminster
+Review</i>. The excellence of his style was soon generally recognized.
+The first two volumes of his <i>History of England
+from the Fall of Wolsey to the Defeat of the Spanish Armada</i>
+appeared in 1856, and the work was completed in 1870. As an
+historian he is chiefly remarkable for literary excellence, for the
+art with which he represents his conception of the past. He
+condemns a scientific treatment of history and disregards its
+philosophy. He held that its office was simply to record human
+actions and that it should be written as a drama. Accordingly
+he gives prominence to the personal element in history. His
+presentations of character and motives, whether truthful or not,
+are undeniably fine; but his doctrine that there should be &ldquo;no
+theorizing&rdquo; about history tended to narrow his survey, and
+consequently he sometimes, as in his remarks on the foreign
+policy of Elizabeth, seems to misapprehend the tendencies of a
+period on which he is writing.</p>
+
+<p>Froude&rsquo;s work is often marred by prejudice and incorrect
+statements. He wrote with a purpose. The keynote of his
+<i>History</i> is contained in his assertion that the Reformation was
+&ldquo;the root and source of the expansive force which has spread
+the Anglo-Saxon race over the globe.&rdquo; Hence he overpraises
+Henry VIII. and others who forwarded the movement, and
+speaks too harshly of some of its opponents. So too, in his
+<i>English in Ireland</i> (1872-1874), which was written to show the
+futility of attempts to conciliate the Irish, he aggravates all
+that can be said against the Irish, touches too lightly on English
+atrocities, and writes unjustly of the influence of Roman Catholicism.
+A strong anti-clerical prejudice is manifest in his historical
+work generally, and is doubtless the result of the change in his
+views on Church matters and his abandonment of the clerical
+profession. Carlyle&rsquo;s influence on him may be traced both in
+his admiration for strong rulers and strong government, which
+led him to write as though tyranny and brutality were excusable,
+and in his independent treatment of character. His rehabilitation
+of Henry VIII. was a useful protest against the idea that
+the king was a mere sanguinary profligate, but his representation
+of him as the self-denying minister of his people&rsquo;s will is erroneous,
+and is founded on the false theory that the preambles of the acts
+of Henry&rsquo;s parliaments represented the opinions of the educated
+laymen of England. As an advocate he occasionally forgets
+that sobriety of judgment and expression become an historian.
+He was not a judge of evidence, and seems to have been unwilling
+to admit the force of any argument or the authority of any
+statement which militated against his case. In his <i>Divorce of
+Catherine of Aragon</i> (1891) he made an unfortunate attempt to
+show that certain fresh evidence on the subject, brought forward
+by Dr Gairdner, Dr Friedmann and others, was not inconsistent
+with the views which he has expressed in his <i>History</i> nearly
+forty years before. He worked diligently at original manuscript
+authorities at Simancas, the Record Office and Hatfield House;
+but he used his materials carelessly, and evidently brought to his
+investigation of them a mind already made up as to their significance.
+His <i>Life of Caesar</i> (1879), a glorification of imperialism,
+betrays an imperfect acquaintance with Roman politics and the
+life of Cicero; and of his two pleasant books of travel, <i>The
+English in the West Indies</i> (1888) shows that he made little effort
+to master his subject, and <i>Oceana</i> (1886), the record of a tour in
+Australia and New Zealand, among a multitude of other blunders,
+notes the prosperity of the working-classes in Adelaide at the
+date of his visit, when, in fact, owing to a failure in the wheat-crop,
+hundreds were then living on charity. He was constitutionally
+inaccurate, and seems to have been unable to represent the
+exact sense of a document which lay before him, or even to
+copy from it correctly. Historical scholars ridiculed his mistakes,
+and Freeman, the most violent of his critics, never let slip a
+chance of hitting at him in the <i>Saturday Review</i>. Froude&rsquo;s
+temperament was sensitive, and he suffered from these attacks,
+which were often unjust and always too savage in tone. The
+literary quarrel between him and Freeman excited general
+interest when it blazed out in a series of articles which Freeman
+wrote in the <i>Contemporary Review</i> (1878-1879) on Froude&rsquo;s
+<i>Short Study</i> of Thomas Becket.</p>
+
+<p>Notwithstanding its defects, Froude&rsquo;s <i>History</i> is a great
+achievement; it presents an important and powerful account
+of the Reformation period in England, and lays before us a
+picture of the past magnificently conceived, and painted in
+colours which will never lose their freshness and beauty. As
+with Froude&rsquo;s work generally, its literary merit is remarkable;
+it is a well-balanced and orderly narrative, coherent in design
+and symmetrical in execution. Though it is perhaps needlessly
+long, the thread of the story is never lost amid a crowd of details;
+every incident is made subordinate to the general idea, appears
+in its appropriate place, and contributes its share to the perfection
+of the whole. The excellence of its form is matched by the beauty
+of its style, for Froude was a master of English prose. The most
+notable characteristic of his style is its graceful simplicity; it is
+never affected or laboured; his sentences are short and easy,
+and follow one another naturally. He is always lucid. He was
+never in doubt as to his own meaning, and never at a loss for the
+most appropriate words in which to express it. Simple as his
+language is, it is dignified and worthy of its subject. Nowhere
+perhaps does his style appear to more advantage than in his four
+series of essays entitled <i>Short Studies on Great Subjects</i> (1867-1882),
+for it is seen there unfettered by the obligations of narrative.
+Yet his narrative is admirably told. For the most part flowing
+easily along, it rises on fit occasions to splendour, picturesque
+beauty or pathos. Few more brilliant pieces of historical
+<span class="pagenum"><a name="page253" id="page253"></a>253</span>
+writing exist than his description of the coronation procession
+of Anne Boleyn through the streets of London, few more full of
+picturesque power than that in which he relates how the spire
+of St Paul&rsquo;s was struck by lightning; and to have once read is
+to remember for ever the touching and stately words in which
+he compares the monks of the London Charterhouse preparing
+for death with the Spartans at Thermopylae. Proofs of his
+power in the sustained narration of stirring events are abundant;
+his treatment of the Pilgrimage of Grace, of the sea fight at
+St Helens and the repulse of the French invasion, and of the
+murder of Rizzio, are among the most conspicuous examples of
+it. Nor is he less successful when recording pathetic events,
+for his stories of certain martyrdoms, and of the execution of
+Mary queen of Scots, are told with exquisite feeling and in
+language of well-restrained emotion. And his characters are
+alive. We may not always agree with his portraiture, but the
+men and women whom he saw exist for us instinct with the life
+with which he endows them and animated by the motives which
+he attributes to them. His successes must be set against his
+failures. At the least he wrote a great history, one which can
+never be disregarded by future writers on his period, be their
+opinions what they may; which attracts and delights a multitude
+of readers, and is a splendid example of literary form and grace
+in historical composition.</p>
+
+<p>The merits of his work met with full recognition. Each
+instalment of his <i>History</i>, in common with almost everything
+which he wrote, was widely read, and in spite of some adverse
+criticisms was received with eager applause. In 1868 he was
+elected rector of St Andrews University, defeating Disraeli
+by a majority of fourteen. He was warmly welcomed in the
+United States, which he visited in 1872, but the lectures on
+Ireland which he delivered there caused much dissatisfaction.
+On the death of his adversary Freeman in 1892, he was appointed,
+on the recommendation of Lord Salisbury, to succeed him as
+regius professor of modern history at Oxford. Except to a
+few Oxford men, who considered that historical scholarship
+should have been held to be a necessary qualification for the
+office, his appointment gave general satisfaction. His lectures
+on Erasmus and other 16th-century subjects were largely
+attended. With some allowance for the purpose for which
+they were originally written, they present much the same
+characteristics as his earlier historical books. His health gave
+way in the summer of 1894, and he died on the 20th of
+October.</p>
+
+<p>His long life was full of literary work. Besides his labours as
+an author, he was for fourteen years editor of <i>Fraser&rsquo;s Magazine</i>.
+He was one of Carlyle&rsquo;s literary executors, and brought some
+sharp criticism upon himself by publishing Carlyle&rsquo;s <i>Reminiscences</i>
+and the <i>Memorials of Jane Welsh Carlyle</i>, for they
+exhibited the domestic life and character of his old friend in an
+unpleasant light. Carlyle had given the manuscripts to him,
+telling him that he might publish them if he thought it well
+to do so, and at the close of his life agreed to their publication.
+Froude therefore declared that in giving them to the world he
+was carrying out his friend&rsquo;s wish by enabling him to make a
+posthumous confession of his faults. Besides publishing these
+manuscripts he wrote a <i>Life of Carlyle</i>. His earlier study of
+Irish history afforded him suggestions for a historical novel
+entitled <i>The Two Chiefs of Dunboy</i> (1889). In spite of one or
+two stirring scenes it is a tedious book, and its personages are
+little more than machines for the enunciation of the author&rsquo;s
+opinions and sentiments. Though Froude had some intimate
+friends he was generally reserved. When he cared to please,
+his manners and conversation were charming. Those who
+knew him well formed a high estimate of his ability in practical
+affairs. In 1874 Lord Carnarvon, then colonial secretary, sent
+Froude to South Africa to report on the best means of promoting
+a confederation of its colonies and states, and in 1875 he was
+again sent to the Cape as a member of a proposed conference to
+further confederation. Froude&rsquo;s speeches in South Africa were
+rather injudicious, and his mission was a failure (see <span class="sc"><a href="#artlinks">South
+Africa</a></span>: <i>History</i>). He was twice married. His first wife, a
+daughter of Pascoe Grenfell and sister of Mrs Charles Kingsley,
+died in 1860; his second, a daughter of John Warre, M.P. for
+Taunton, died in 1874.</p>
+
+<div class="condensed">
+<p>Froude&rsquo;s <i>Life</i>, by Herbert Paul, was published in 1905.</p>
+</div>
+<div class="author">(W. Hu.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">FRUCTOSE<a name="ar6" id="ar6"></a></span>, <span class="sc">Laevulose</span>, or <span class="sc">Fruit-Sugar</span>, a carbohydrate
+of the formula C<span class="su">6</span>H<span class="su">12</span>O<span class="su">6</span>. It is closely related to ordinary <i>d</i>-glucose,
+with which it occurs in many fruits, starches and also
+in honey. It is a hydrolytic product of inulin, from which it
+may be prepared; but it is more usual to obtain it from &ldquo;invert
+sugar,&rdquo; the mixture obtained by hydrolysing cane sugar with
+sulphuric acid. Cane sugar then yields a syrupy mixture of
+glucose and fructose, which, having been freed from the acid
+and concentrated, is mixed with water, cooled in ice and calcium
+hydroxide added. The fructose is precipitated as a saccharate,
+which is filtered, suspended in water and decomposed by carbon
+dioxide. The liquid is filtered, the filtrate concentrated, and
+the syrup so obtained washed with cold alcohol. On cooling the
+fructose separates. It may be obtained as a syrup, as fine,
+silky needles, a white crystalline powder, or as a granular
+crystalline, somewhat hygroscopic mass. When anhydrous it
+melts at about 95° C. It is readily soluble in water and in dilute
+alcohol, but insoluble in absolute alcohol. It is sweeter than
+cane sugar and is more easily assimilated. It has been employed
+under the name diabetin as a sweetening agent for diabetics,
+since it does not increase the sugar-content of the urine; other
+medicinal applications are in phthisis (mixed with quassia or
+other bitter), and for children suffering from tuberculosis or
+scrofula in place of cane sugar or milk-sugar.</p>
+
+<p>Chemically, fructose is an oxyketone or ketose, its structural
+formula being CH<span class="su">2</span>OH·(CH·OH)<span class="su">3</span>·CO·CH<span class="su">2</span>OH; this result followed
+from its conversion by H. Kiliani into methylbutylacetic
+acid. The form described above is <i>laevo</i>-rotatory, but it is
+termed <i>d</i>-fructose, since it is related to <i>d</i>-glucose. Solutions
+exhibit mutarotation, fresh solutions having a specific rotation
+of &minus;104.0°, which gradually diminishes to &minus;92°. It was
+synthesized by Emil Fischer, who found the synthetic sugar
+which he named &alpha;-acrose to be (<i>d</i> + <i>l</i>)-fructose, and by splitting
+this mixture he obtained both the d and <i>l</i> forms. Fructose
+resembles d-glucose in being fermentable by yeast (it is the one
+ketose which exhibits this property), and also in its power of
+reducing alkaline copper and silver solutions; this latter
+property is assigned to the readiness with which hydroxyl and
+ketone groups in close proximity suffer oxidation. For the
+structural (stereochemical) relations of fructose see <span class="sc"><a href="#artlinks">Sugar</a></span>.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FRUGONI, CARLO INNOCENZIO MARIA<a name="ar7" id="ar7"></a></span> (1692-1768),
+Italian poet, was born at Genoa on the 21st of November 1692.
+He was originally destined for the church and at the age of
+fifteen, in opposition to his strong wishes, was shut up in a
+convent; but although in the following year he was induced to
+pronounce monastic vows, he had no liking for this life. He
+acquired considerable reputation as an elegant writer both of
+Latin and Italian prose and verse; and from 1716 to 1724 he
+filled the chairs of rhetoric at Brescia, Rome, Genoa, Bologna
+and Modena successively, attracting by his brilliant fluency a
+large number of students at each university. Through Cardinal
+Bentivoglio he was recommended to Antonio Farnese, duke of
+Parma, who appointed him his poet laureate; and he remained
+at the court of Parma until the death of Antonio, after which
+he returned to Genoa. Shortly afterwards, through the intercession
+of Bentivoglio, he obtained from the pope the remission
+of his monastic vows, and ultimately succeeded in recovering
+a portion of his paternal inheritance. After the peace of Aix-la-Chapelle
+he returned to the court of Parma, and there devoted
+the later years of his life chiefly to poetical composition. He
+died on the 20th of December 1768. As a poet Frugoni was
+one of the best of the school of the Arcadian Academy, and
+his lyrics and pastorals had great facility and elegance.</p>
+
+<div class="condensed">
+<p>His collected works were published at Parma in 10 vols. in 1799,
+and a more complete edition appeared at Lucca in the same year in
+15 vols. A selection from his works was published at Brescia in
+1782, in 4 vols.</p>
+</div>
+
+<p><span class="pagenum"><a name="page254" id="page254"></a>254</span></p>
+
+
+<hr class="art" />
+<p><span class="bold">FRUIT<a name="ar8" id="ar8"></a></span> (through the French from the Lat. <i>fructus</i>; <i>frui</i>, to
+enjoy), in its widest sense, any product of the soil that can be
+enjoyed by man or animals; the word is so used constantly
+in the Bible, and extended, as a Hebraism, to offspring or
+progeny of man and of animals, in such expressions as &ldquo;the
+fruit of the body,&rdquo; &ldquo;of the womb,&rdquo; &ldquo;fruit of thy cattle&rdquo; (Deut.
+xxviii. 4), &amp;c., and generally to the product of any action or
+effort. Between this wide and frequently figurative use of the
+word and its application in the strict botanical sense treated
+below, there is a popular meaning, regarding the objects denoted
+by the word entirely from the standpoint of edibility, and
+differentiating them roughly from those other products of the
+soil, which, regarded similarly, are known as vegetables. In
+this sense &ldquo;fruit&rdquo; is applied to such seed-envelopes of plants
+as are edible, either raw or cooked, and are usually sweet, juicy
+or of a refreshing flavour. But applications of the word in this
+sense are apt to be loose and shifting according to the fashion
+of the time.</p>
+
+<p>Fruit, in the botanical sense, is developed from the flower
+as the result of fertilization of the ovule. After fertilization
+various changes take place in the parts of the flower. Those
+more immediately concerned in the process, the anther and
+stigma, rapidly wither and decay, while the filaments and style
+often remain for some time; the floral envelopes become dry,
+the petals fall, and the sepals are either deciduous, or remain
+persistent in an altered form; the ovary becomes enlarged,
+forming the <i>pericarp</i>; and the ovules are developed as the
+seeds, containing the embryo-plant. The term fruit is strictly
+applied to the mature pistil or ovary, with the seeds in its interior;
+but it often includes other parts of the flower, such as the bracts
+and floral envelopes. Thus the fruit of the hazel and oak consists
+of the ovary enveloped by the bracts; that of the apple and pear,
+of the ovary and floral receptacle; and that of the pine-apple,
+of the whole inflorescence. Such fruits are sometimes distinguished
+as <i>pseudocarps</i>. In popular language, the fruit includes
+all those parts which exhibit a striking change as the result of
+fertilization. In general, the fruit is not ripened unless fertilization
+has been effected; but cases occur as the result of cultivation
+in which the fruit swells and becomes to all appearance perfect,
+while no seeds are produced. Thus, there are seedless oranges,
+grapes and pineapples. When the ovules are unfertilized, it is
+common to find that the ovary withers and does not come to
+maturity; but in the case of bananas, plantains and bread-fruit,
+the non-development of seeds seems to lead to a larger growth
+and a greater succulence of fruit.</p>
+
+<div class="condensed">
+<p>The fruit, like the ovary, may be formed of a single carpel or of
+several. It may have one cell or cavity, being <i>unilocular</i>; or many,
+<i>multilocular</i>, &amp;c. The number and nature of the divisions depend
+on the number of carpels and the extent to which their edges are
+folded inwards. The appearances presented by the ovary do not
+always remain permanent in the fruit. Great changes are observed
+to take place, not merely as regards the increased size of the ovary,
+its softening or hardening, but also in its internal structure, owing
+to the suppression, additional formation or enlargement of parts.
+Thus, in the ash (fig. 1) an ovary with two cells, each containing an
+ovule attached to a central placenta, is changed into a unilocular
+fruit with one seed; one ovule becomes abortive, while the other, <i>g</i>,
+gradually enlarging until the septum is pushed to one side, unites
+with the walls of the cell, and the placenta appears to be parietal.
+In the oak and hazel, an ovary with three and two cells respectively,
+and two ovules in each, produces a one-celled fruit with one seed.
+In the coco-nut, a trilocular and triovular ovary produces a one-celled,
+one-seeded fruit. This abortion may depend on the pressure
+caused by the development of certain ovules, or it may proceed from
+non-fertilization of all the ovules and consequent non-enlargement
+of the carpels. Again, by the growth of the placenta, or the folding
+inwards of parts of the carpels, divisions occur in the fruit which
+did not exist in the ovary. In <i>Cathartocarpus Fistula</i> a one-celled
+ovary is changed into a fruit having each of its seeds in a separate
+cell, in consequence of spurious dissepiments being produced horizontal
+from the inner wall of the ovary. In flax (<i>Linum</i>) by the
+folding inwards of the back of the carpels a five-celled ovary becomes
+a ten-celled fruit. In <i>Astragalus</i> the folding inwards of the dorsal
+suture converts a one-celled ovary into a two-celled fruit; and in
+<i>Oxytropis</i> the folding of the ventral suture gives rise to a similar
+change. The development of cellular or pulpy matter, and the
+enlargement of parts not forming whorls of the flower, frequently
+alter the appearance of the fruit, and render it difficult to discover
+its formation. In the gooseberry (fig. 29), grape, guava, tomato
+and pomegranate, the seeds nestle in pulp formed by the placentas.
+In the orange the pulpy matter surrounding the seeds is formed
+by succulent cells, which are produced from the inner partitioned
+lining of the pericarp. In the strawberry the receptacle becomes
+succulent, and bears the mature carpels on its convex surface (fig. 2);
+in the rose there is a fleshy hollow receptacle which bears the carpels
+on its concave surface (fig. 3). In the juniper the scaly bracts grow
+up round the seeds and become succulent, and in the fig (fig. 4) the
+receptacle becomes succulent and encloses an inflorescence.</p>
+
+<div class="center pt2"><img style="width:473px; height:497px; vertical-align: middle;" src="images/img254.jpg" alt="" /></div>
+
+<p><span class="sc">Fig.</span> 1.&mdash;Samara or winged fruit of Ash (<i>Fraxinus</i>). 1, Entire,
+with its wing <i>a</i>; 2, lower portion cut transversely, to show that it
+consists of two cells; one of which, <i>l</i>, is abortive, and is reduced to
+a very small cavity, while the other is much enlarged and filled
+with a seed <i>g</i>.</p>
+
+<p><span class="sc">Fig.</span> 2.&mdash;Fruit of the Strawberry (<i>Fragaria vesca</i>), consisting of
+an enlarged succulent receptacle, bearing on its surface the small
+dry seed-like fruits (achenes). (After Duchartre.)</p>
+
+<p class="f80">From Strasburger&rsquo;s <i>Lehrbuch der Botanik</i>, by permission of Gustav Fischer.</p>
+
+<p><span class="sc">Fig.</span> 3.&mdash;Fruit of the Rose cut vertically. <i>s&rsquo;</i>, Fleshy hollowed
+receptacle; <i>s</i>, persistent sepals; <i>fr</i>, ripe carpels; <i>e</i>, stamens,
+withered.</p>
+
+<p><span class="sc">Fig.</span> 4.&mdash;Peduncle of Fig (<i>Ficus Carica</i>), ending in a hollow
+receptacle enclosing numerous male and female flowers.</p>
+
+<p><span class="sc">Fig.</span> 5.&mdash;Fruit of Cherry (<i>Prunus Cerasus</i>) in longitudinal section.
+<i>ep</i>, Epicarp; <i>m</i>, mesocarp; <i>en</i>, endocarp.</p>
+
+<p class="f80">From Strasburger&rsquo;s <i>Lehrbuch der Botanik</i>, by permission of Gustav Fischer.</p>
+
+<p class="pt2">The pericarp consists usually of three layers, the external, or
+<i>epicarp</i> (fig. 5, <i>ep</i>); the middle, or <i>mesocarp</i>, <i>m</i>; and the internal,
+or <i>endocarp</i>, <i>en</i>. These layers are well seen in such a fruit as the
+peach, plum or cherry, where they are separable one from the
+other; in them the epicarp forms what is commonly called the
+skin; the mesocarp, much developed, forms the flesh or pulp,
+and hence has sometimes been called <i>sarcocarp</i>; while the endocarp,
+hardened by the production of woody cells, forms the <i>stone</i> or
+<i>putamen</i> immediately covering the kernel or seed. The pulpy
+matter found in the interior of fruits, such as the gooseberry, grape
+and others, is formed from the placentas, and must not be confounded
+with the sarcocarp. In some fruits, as in the nut, the
+three layers become blended together and are indistinguishable.
+In bladder senna (<i>Colutea arborescens</i>) the pericarp retains its leaf-like
+appearance, but in most cases it becomes altered both in consistence
+and in colour. Thus in the date the epicarp is the outer
+brownish skin, the pulpy matter is the mesocarp or sarcocarp, and
+the thin papery-like lining is the endocarp covering the hard seed.
+In the medlar the endocarp becomes of a stony hardness. In the
+melon the epicarp and endocarp are very thin, while the mesocarp
+forms the bulk of the fruit, differing in texture and taste in its external
+and internal parts. The rind of the orange consists of epicarp
+and mesocarp, while the endocarp forms partitions in the interior,
+filled with pulpy cells. The part of the pericarp attached to the
+peduncle is the base, and the point where the style or stigma existed
+is the apex. This latter is not always the apparent apex, as in the
+case of the ovary; it may be lateral or even basilar. The style
+sometimes remains in a hardened form, rendering the fruit <i>apiculate</i>;
+at other times it falls off, leaving only traces of its existence. The
+presence of the style or stigma serves to distinguish certain single-seeded
+pericarps from seeds.</p>
+
+<p><span class="pagenum"><a name="page255" id="page255"></a>255</span></p>
+
+<table class="flt" style="float: right; width: 250px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:199px; height:177px" src="images/img255a.jpg" alt="" /></td></tr>
+<tr><td class="caption1"><span class="sc">Fig.</span> 6.&mdash;Seed-vessel or capsule
+of Campion, opening by ten
+teeth at the apex. The calyx <i>c</i>
+is seen surrounding the seed-vessel.</td></tr>
+
+<tr><td class="caption1"><span class="sc">Fig.</span> 7.&mdash;Capsule of Poppy,
+opening by pores <i>p</i>, under the
+radiating peltate stigma <i>s</i>.</td></tr></table>
+
+<p>When the fruit is mature and the seeds are ripe, the carpels
+usually give way either at the ventral or dorsal suture or at both,
+and so allow the seeds to escape. The fruit in this case
+is <i>dehiscent</i>. But some fruits are <i>indehiscent</i>, falling to
+<span class="sidenote">Dehiscence of fruits.</span>
+the ground entire, and the seeds eventually reaching the
+soil by their decay. By dehiscence the pericarp becomes divided
+into different pieces, or <i>valves</i>, the fruit being univalvular, bivalvular
+or multivalvular, &amp;c., according as there are one, two or many
+valves. The splitting extends the whole length of the fruit, or is
+partial, the valves forming teeth
+at the apex, as in the order Caryophyllaceae
+(fig. 6). Sometimes
+the valves are detached only at
+certain points, and thus dehiscence
+takes place by pores at the apex,
+as in poppy (fig. 7), or at the base,
+as in <i>Campanula</i>. Indehiscent
+fruits are either dry, as the nut,
+or fleshy, as the cherry and apple.
+They are formed of one or several
+carpels. In the former case they
+usually contain only a single seed,
+which may become so incorporated
+with the pericarp as to appear to
+be naked, as in the grain of wheat
+and generally in grasses. In such
+cases the presence of the remains
+of style or stigma determines
+their true nature.</p>
+
+<div class="center pt2" style="clear: both;"><img style="width:515px; height:417px; vertical-align: middle;" src="images/img255b.jpg" alt="" /></div>
+
+<table class="flt" style="float: left; width: 200px;" summary="Illustration">
+<tr><td class="figleft1"><img style="width:149px; height:252px" src="images/img255c.jpg" alt="" /></td></tr></table>
+
+<p><span class="sc">Fig.</span> 8.&mdash;Dry dehiscent fruit. The pod
+(legume) of the Pea; <i>r</i>, the dorsal suture;
+<i>b</i>, the ventral; <i>c</i>, calyx; <i>s</i>, seeds.</p>
+
+<p class="f80">From Vines&rsquo; <i>Students&rsquo; Text-Book of Botany</i>, by permission
+of Swan Sonnenschein &amp; Co.</p>
+
+<p><span class="sc">Fig.</span> 9.&mdash;(1) Fruit or capsule of Meadow
+Saffron (<i>Colchicum autumnale</i>), dehiscing along
+the septa (septicidally); (2) same cut across,
+showing the three chambers with the seeds
+attached along the middle line (axile placentation).</p>
+
+<p><span class="sc">Fig.</span> 10.&mdash;Diagram to illustrate the septicidal
+dehiscence in a pentalocular capsule.
+The loculaments <i>l</i> correspond to the number of the carpels, which
+separate by splitting through the septa, <i>s</i>.</p>
+
+<p><span class="sc">Fig.</span> 11.&mdash;The seed vessel (capsule) of the Flower-de-Luce (<i>Iris</i>),
+opening in a loculicidal manner. The three valves bear the septa
+in the centre, and the opening takes place through the back of the
+loculaments. Each valve is formed by the halves of contiguous
+carpels.</p>
+
+<p><span class="sc">Fig.</span> 12.&mdash;Diagram to illustrate loculicidal dehiscence. The loculaments
+<i>l</i>, split at the back, and the valves separate, bearing the
+septa <i>s</i> on their centres.</p>
+
+<p><span class="sc">Fig.</span> 13.&mdash;Diagram to illustrate septifragal dehiscence, in which
+the dehiscence takes place through the back of the loculaments <i>l</i>,
+and the valves separate from the septa <i>s</i>, which are left attached to
+the placentas in the centre.</p>
+
+<p class="pt2">Dehiscent fruits, when composed
+of single carpels, may open
+by the ventral suture only, as in the paeony, hellebore, <i>Aquilegia</i> (fig.
+28) and <i>Caltha</i>; by the dorsal suture only, as in magnolias and some
+<i>Proteaceae</i>, or by both together, as in the pea (fig. 8) and bean;
+in these cases the dehiscence is <i>sutural</i>. When composed of several
+united carpels, two types of dehiscence occur&mdash;a longitudinal and a
+transverse. In the longitudinal the separation may take place by
+the dissepiments throughout their length, so that the fruit is resolved
+into its original carpels, and each valve represents a carpel, as in
+rhododendron, <i>Colchicum</i>, &amp;c.; this dehiscence, in consequence of
+taking place through the septum, is called <i>septicidal</i> (figs. 9, 10).
+The valves separate from their commissure, or central line of union,
+carrying the placentas with them, or they leave the latter in the
+centre, so as to form with the axis a column of a cylindrical, conical
+or prismatic shape. Dehiscence is <i>loculicidal</i> when the union
+between the edges of the carpels is persistent, and they dehisce by
+the dorsal suture, or through the back of the loculaments, as in the
+lily and iris (figs. 11, 12). In these cases each valve consists of a
+half of each of two contiguous carpels. The placentas either remain
+united to the axis, or they separate from it, being attached to the
+septa on the valves. When the outer walls of the carpels break off
+from the septa, leaving them attached to the central column, the
+dehiscence is said to be <i>septifragal</i> (fig. 13), and where, as in <i>Linum
+catharticum</i> and <i>Calluna</i>, the splitting takes place first of all in a
+septicidal manner, the fruit is described as <i>septicidally septifragal</i>;
+while in other cases, as in thorn apple (<i>Datura Stramonium</i>), where
+the splitting is at first loculicidal, the dehiscence is <i>loculicidally
+septifragal</i>. In all those forms the separation of the valves takes
+place either from above downwards or from below upwards. In
+<i>Saxifraga</i> a splitting for a short distance of the ventral sutures of
+the carpels takes place, so that a large apical pore is formed. In
+the fruit of Cruciferae, as wallflower (fig. 14), the valves separate
+from the base of the fruit, leaving a central <i>replum</i>, or frame, which
+supports the false septum formed by a prolongation from the parietal
+placentas on opposite sides of the fruit, extending between the
+ventral sutures of the carpels. In Orchidaceae (fig. 15) the pericarp,
+when ripe, separates into three valves in a loculicidal manner,
+but the midribs of the carpels, to which the placentas are attached,
+often remain adherent to the axis both at the apex and base after
+the valves bearing the seeds have fallen. The other type of dehiscence
+is transverse, or <i>circumscissile</i>, when the upper part of the
+united carpels falls off in the form of a lid or operculum, as in <i>Anagallis</i>
+and in henbane (<i>Hyoscyamus</i>) (fig. 16).</p>
+
+<div class="center pt2"><img style="width:513px; height:383px; vertical-align: middle;" src="images/img255d.jpg" alt="" /></div>
+
+<p><span class="sc">Fig. 14.</span>&mdash;Siliqua or seed-vessel of Wallflower (<i>Cheiranthus Cheiri</i>),
+opening by two valves, which separate from the base upwards,
+leaving the seeds attached to the dissepiment which is supported by
+the replum.</p>
+
+<p class="f80">From Strasburger&rsquo;s <i>Lehrbuch der Botanik</i>, by permission of Gustav Fischer.</p>
+
+<p><span class="sc">Fig. 15.</span>&mdash;Capsule of an Orchid (<i>Xylobium</i>). <i>v</i>, valve.</p>
+
+<p><span class="sc">Fig. 16.</span>&mdash;Seed-vessel of <i>Anagallisarvensis</i>, opening by circumscissile
+dehiscence.</p>
+
+<p class="f80">From Strasburger&rsquo;s <i>Lehrbuch der Botanik</i>, by permission of Gustav Fischer.</p>
+
+<p><span class="sc">Fig. 17.</span>&mdash;Lomentum of <i>Hedysarum</i> which, when ripe, separates
+transversely into single-seeded portions or mericarps.</p>
+
+<p><span class="sc">Fig. 18.</span>&mdash;Fruit of <i>Geranium pratense</i>, after splitting.</p>
+
+<p class="pt2">Sometimes the axis is prolonged beyond the base of the carpels,
+as in the mallow and castor-oil plant, the carpels being united to it
+throughout their length by their faces, and separating from it without
+opening. In the Umbelliferae the two carpels separate from the
+lower part of the axis, and remain attached by their apices to a
+prolongation of it, called a <i>carpophore</i> or <i>podocarp</i>, which splits
+into two (fig. 25) and suspends them; hence the fruit is termed a
+<i>cremocarp</i>, which divides into two <i>mericarps</i>. The general term
+<i>schizocarp</i> is applied to all dry fruits, which break up into two or
+more one-seeded indehiscent mericarps, as in <i>Hedysarum</i> (fig. 17).
+In the order Geraniaceae the styles remain attached to a central
+column, and the mericarps separate from below upwards, before
+dehiscing by their ventral suture (fig. 18). Carpels which separate
+one from another in this manner are called <i>cocci</i>. They are well
+<span class="pagenum"><a name="page256" id="page256"></a>256</span>
+seen in the order Euphorbiaceae, where there are usually three such
+carpels, and the fruit is termed tricoccus. In many of them, as
+<i>Hura crepitans</i>, the cocci separate with great force and elasticity.
+In many leguminous plants, such as <i>Ornithopus</i>, <i>Hedysarum</i> (fig. 17),
+<i>Entada</i>, <i>Coronilla</i> and the gum-arabic plant (<i>Acacia arabica</i>), the
+fruit becomes a schizocarp by the formation of transverse partitions
+from the folding in of the sides of the pericarp, and distinct separations
+taking place at these partitions.</p>
+
+<p>Fruits are formed by one flower, or are the product of several
+flowers combined. In the former case they are either <i>apocarpous</i>,
+of one mature carpel or of several separate free carpels; or <i>syncarpous</i>,
+of several carpels, more or less completely united. When
+the fruit is composed of the ovaries of several flowers united, it is
+usual to find the bracts and floral envelopes also joined with them,
+so as to form one mass; hence such fruits are known as multiple,
+confluent or <i>anthocarpous</i>. The term simple is applied to fruits
+which are formed by the ovary of a single flower, whether they are
+composed of one or several carpels, and whether these carpels are
+separate or combined.</p>
+
+<div class="center pt2"><img style="width:464px; height:366px; vertical-align: middle;" src="images/img256.jpg" alt="" /></div>
+
+<p class="f80">From Vines&rsquo; <i>Students&rsquo; Text-Book of Botany</i>, by
+permission of Swan Sonnenschein &amp; Co.</p>
+
+<p><span class="sc">Fig. 19.</span>&mdash;Dry one-seeded fruit of dock (<i>Rumex</i>) cut vertically.
+ov, Pericarp formed from ovary wall; <i>s</i>, seed; <i>e</i>, endosperm; <i>pl</i>,
+embryo with radicle pointing upwards and cotyledons downwards&mdash;enlarged.</p>
+
+<p><span class="sc">Fig. 20.</span>&mdash;Achene of <i>Ranunculus arvensis</i> in longitudinal section;
+<i>e</i>, endosperm; <i>pl</i>, embryo. (After Baillon, enlarged.)</p>
+
+<p class="f80">From Strasburger&rsquo;s <i>Lehrbuch der Botanik</i>, by permission of Gustav Fischer.</p>
+
+<p><span class="sc">Fig. 21.</span>&mdash;Fruit of Common Sycamore (<i>Acer Pseudoplatanus</i>),
+dividing into two mericarps <i>m</i>; <i>s</i>, pedicel; <i>fl</i>, wings (nat. size).</p>
+
+<p class="pt2">The object of the fruit in the economy of the plant is the protection
+and nursing of the developing seed and the dispersion of the ripe
+seeds. Hence, generally, one-seeded fruits are indehiscent,
+while fruits containing more than one seed open to allow
+<span class="sidenote">Dispersal of fruit or seed.</span>
+of the dispersal of the seeds over as wide an area as
+possible. The form, colour, structure and method of
+dehiscence of fruits and the form of the contained seeds are intimately
+associated with the means of dispersal, which fall into several
+categories. (1) By a mechanism residing in the fruit. Thus many
+fruits open suddenly when they are dry, and the seeds are ejected
+by the twisting or curving of the valves, or in some other way;
+<i>e.g.</i> in gorse, by the spiral curving of the valves; in <i>Impatiens</i>, by
+the twisting of the cocci; in squirting cucumber, by the pressure
+exerted on the pulpy contents by the walls of the pericarp. (2)
+By aid of various external agencies such as water. Fruits or seeds
+are sometimes sufficiently buoyant to float for a long time on sea- or
+fresh-water; <i>e.g.</i> coco-nut, by means of its thick, fibrous coat
+(mesocarp), is carried hundreds of miles in the sea, the tough,
+leathery outer coat (epicarp) preventing it from becoming water-soaked.
+Fruits and seeds of West Indian plants are thrown up on
+the coasts of north-west Europe, having been carried by the Gulf
+Stream, and will often germinate; many are rendered buoyant by
+air-containing cavities, and the embryo is protected from the seawater
+by the tough coat of fruit or seed. Water-lily seeds are
+surrounded with a spongy tissue when set free from the fruit, and
+float for some distance before dropping to the bottom. (3) The
+most general agent in the dispersal of seeds is the wind or currents
+of air&mdash;the fruit or seed being rendered buoyant by wing-developments
+as in fruits of ash (fig. 1) or maple (fig. 21), seeds of pines
+and firs, or many members of the order Bignoniaceae; or hair-developments
+as in fruits of clematis, where the style forms a feathery
+appendage, fruits of many Compositae (dandelion, thistle, &amp;c.),
+which are crowned by a plumose pappus, or seeds of willow and
+poplar, or <i>Asclepias</i> (fig. 36), which bear tufts of silky hairs; to
+this category belong bladder-like fruits, such as bladder-senna,
+which are easily rolled by the wind, or cases like the so-called rose
+of Jericho, a small cruciferous plant (<i>Anastatica hierocuntica</i>), where
+the plant dries up after developing its fruits and becomes detached
+from the ground; the branches curl inwards, and the whole plant is
+rolled over the dry ground by the wind. The wind also aids the
+dispersal of the seeds in the case of fruits which open by small teeth
+(many Caryophyllaceae [fig. 6]) or pores (poppy [fig. 7], <i>Campanula</i>,
+&amp;c.); the seeds are in these cases small and numerous, and are jerked
+through the pores when the capsules, which are generally borne on
+long, dry stems or stalks, are shaken by the wind. (4) In other cases
+members of the animal world aid in seed-dispersal. Fruits often
+bear stiff hairs or small hooks, which cling to the coat of an animal
+or the feathers of a bird; such are fruits of cleavers (<i>Galium Aparine</i>),
+a common hedge-row plant, <i>Ranunculus arvensis</i> (fig. 20), carrot,
+<i>Geum</i>, &amp;c.; or the fruit or seed has an often bright-coloured, fleshy
+covering, which is sought by birds as food, as in stone-fruits such as
+plum, cherry (fig. 5), &amp;c., where the seed is protected from injury
+in the mouth or stomach of the animal by the hard endocarp; or
+the hips of the rose (fig. 3), where the succulent scarlet &ldquo;fruit&rdquo;
+(the swollen receptacle) envelops a number of small dry true fruits
+(achenes), which cling by means of stiff hairs to the beak of the bird.</p>
+
+<div class="center pt2"><img style="width:469px; height:373px; vertical-align: middle;" src="images/img256a.jpg" alt="" /></div>
+
+<p><span class="sc">Fig. 22.</span>&mdash;Vertical section of a grain of wheat, showing embryo
+below at the base of the endosperm <i>e</i>; <i>s</i>, scutellum separating
+embryo from endosperm; <i>f.l</i>, foliage leaf; <i>p.s</i>, sheath of plumule;
+<i>p.r</i>, primary root; <i>s.p.r</i>, sheath of primary root.</p>
+
+<p><span class="sc">Fig. 23.</span>&mdash;Fruit of Comfrey (<i>Symphytum</i>) surrounded by persistent
+calyx, <i>c</i>. The style s appears to arise from the base of the carpels,
+enlarged.</p>
+
+<p><span class="sc">Fig. 24.</span>&mdash;Ovary of <i>Foeniculum officinale</i> with pendulous ovules, in
+longitudinal section. (After Berg and Schmidt, magnified.)</p>
+
+<p class="f80">From Strasburger&rsquo;s <i>Lehrbuch der Botanik</i>, by permission of Gustav Fischer.</p>
+
+<p><span class="sc">Fig. 25.</span>&mdash;Fruit of <i>Carum Carui</i>. A, Ovary of the flower; B, ripe
+fruit. The two carpels have separated so as to form two mericarps
+(<i>m</i>). Part of the septum constitutes the carpophore (<i>a</i>). <i>p</i>, Top of
+flower-stalk; <i>d</i>, disk on top of ovary; <i>n</i>, stigma.</p>
+
+<p class="f80">From Vines&rsquo; <i>Students&rsquo; Text-Book of Botany</i>, by permission of Swan Sonnenschein
+&amp; Co.</p>
+
+<p class="pt2">Simple fruits have either a <i>dry</i> or <i>succulent</i> pericarp. The <i>achene</i>
+is a dry, one-seeded, indehiscent fruit, the pericarp of which is closely
+applied to the seed, but separable from it. It is solitary,
+forming a single fruit, as in the dock (fig. 19) and in the
+<span class="sidenote">Forms of fruit.</span>
+cashew, where it is supported on a fleshy peduncle; or
+<i>aggregate</i>, as in <i>Ranunculus</i> (fig. 20), where several achenes are
+placed on a common elevated receptacle. In the strawberry the
+achenes (fig. 2) are aggregated on a convex succulent receptacle.
+In the rose they are supported on a concave receptacle (fig. 3), and
+in the fig the succulent receptacle completely encloses the achenes
+(fig. 4). In <i>Dorstenia</i> the achenes are situated on a flat or slightly
+concave receptacle. Hence what in common language are called the
+seeds of the strawberry, rose and fig, are in reality ripe carpels.
+The styles occasionally remain attached to the achenes in the form
+of feathery appendages, as in <i>Clematis</i>. In Compositae, the fruit
+is an inferior achene (<i>cypsela</i>), to which the pappus (modified calyx)
+remains adherent. Such is also the nature of the fruit in
+Dipsacaceae (<i>e.g.</i> scabious). When the pericarp is thin, and
+appears like a bladder surrounding the seed, the achene is termed
+a <i>utricle</i>, as in Amarantaceae. When the pericarp is extended in
+the form of a winged appendage, a <i>samara</i> or <i>samaroid achene</i> is
+produced, as in the ash (fig. 1) and common sycamore (fig. 21).
+In these cases there are usually two achenes united, one of which,
+however, as in <i>Fraxinus</i> (fig. 1), may be abortive. The wing surrounds
+the fruit longitudinally in the elm. When the pericarp becomes
+so incorporated with the seed as to be inseparable from it,
+as in grains of wheat (fig. 22), maize, oats and other grasses, then the
+name <i>caryopsis</i> is given. The one-seeded portions (mericarps) of
+schizocarps often take the form of achenes, <i>e.g.</i> the mericarps of the
+<span class="pagenum"><a name="page257" id="page257"></a>257</span>
+mallows or of umbellifers (figs. 24, 25). In Labiatae and Boraginaceae
+(<i>e.g.</i> comfrey, fig. 23), where the bicarpellary ovary becomes
+our one-seeded portions in the fruit, the partial fruits are of the
+nature of achenes or nutlets according to the texture (leathery or
+hard) of the pericarp.</p>
+
+<table class="flt" style="float: right; width: 330px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:274px; height:301px" src="images/img257a.jpg" alt="" /></td></tr>
+<tr><td class="caption80">From Strasburger&rsquo;s <i>Lehrbuch der Botanik</i>,
+by permission of Gustav Fischer.</td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 26.</span>&mdash;Cupule of <i>Quercus
+Aegilops</i>. <i>cp</i>, cupule; <i>gl</i>, fruit.
+(After Duchartre.)</td></tr></table>
+
+<p>The <i>nut</i> or <i>glans</i> is a dry one-celled indehiscent fruit with a
+hardened pericarp, often surrounded by bracts at the base, and,
+when mature, containing only
+one seed. In the young state
+the ovary often contains two
+or more ovules, but only one
+comes to maturity. It is illustrated
+by the fruits of the hazel
+and chestnut, which are covered
+by leafy bracts, in the form of
+a <i>husk</i>, and by the acorn, in
+which the bracts and receptacle
+form a <i>cupula</i> or <i>cup</i> (fig. 26).
+The parts of the pericarp of the
+nut are united so as to appear
+one. In common language the
+term nut is very vaguely
+applied both to fruit and seeds.</p>
+
+<p>The <i>drupe</i> is a succulent
+usually one-seeded indehiscent
+fruit, with a pericarp easily
+distinguishable into epicarp,
+mesocarp and endocarp. This
+term is applied to such fruits
+as the cherry (fig. 5), peach,
+plum, apricot or mango. The
+endocarp is usually hard, forming
+the stone (putamen) of the fruit, which encloses the kernel
+or seed. The mesocarp is generally pulpy and succulent, so as to be
+truly a sarcocarp, as in the peach, but it is sometimes of a tough
+texture, as in the almond, and at other times is more or less fibrous,
+as in the coco-nut. In the almond there are often two ovules
+formed, only one of which comes to perfection. In the raspberry
+and bramble several small drupes or <i>drupels</i> are aggregated so as to
+constitute an <i>etaerio</i>.</p>
+
+<p>The <i>follicle</i> is a dry unilocular many-seeded fruit, formed from
+one carpel and dehiscing by the ventral suture. It is rare to meet
+with a solitary follicle forming the fruit. There are usually several
+aggregated together, either in a whorl on a shortened receptacle,
+as in hellebore, aconite, larkspur, columbine (figs. 27, 28) or the order
+Crassulaceae, or in a spiral manner on an elongated receptacle, as
+in <i>Magnolia</i> and <i>Banksia</i>. Occasionally, follicles dehisce by the
+dorsal suture, as in <i>Magnolia grandiflora</i> and <i>Banksia</i>.</p>
+
+<div class="center pt2" style="clear: both;"><img style="width:431px; height:302px; vertical-align: middle;" src="images/img257b.jpg" alt="" /></div>
+
+<p><span class="sc">Fig. 27.</span>&mdash;Fruit of Columbine (<i>Aquilegia</i>), formed of five follicles.</p>
+
+<p><span class="sc">Fig. 28.</span>&mdash;Single follicle, showing dehiscence by the ventral suture.</p>
+
+<p><span class="sc">Fig. 29.</span>&mdash;Transverse section of berry of Gooseberry, showing the
+seeds attached to the parietal placentas and immersed in pulp,
+which is formed partly from the endocarp, partly from the seed-coat.</p>
+
+<p><span class="sc">Fig. 30.</span>&mdash;Section of the fruit of the Apple (<i>Pyrus Malus</i>), or pome,
+consisting of a fleshy covering formed by the floral receptacle and
+the true fruit or core with five cavities with seeds.</p>
+
+<p class="pt2">The <i>legume</i> or <i>pod</i> is a dry monocarpellary unilocular many-seeded
+fruit, formed from one carpel, dehiscing both by the ventral and the
+dorsal suture. It characterizes leguminous plants, as the bean and
+pea (fig. 8). In the bladder-senna it forms an inflated legume. In
+some Leguminosae, as <i>Arachis</i>, <i>Cathartocarpus Fistula</i> and the
+tamarind, the fruit must be considered a legume, although it does
+not dehisce. The first of these plants produces its fruit underground,
+and is called earth-nut; the second has a partitioned
+legume and is schizocarpic; and both the second and third have
+pulpy matter surrounding the seeds. Some legumes are schizocarpic
+by the formation of constrictions externally. Such a form is the
+<i>lomentum</i> or <i>lomentaceous legume</i> of <i>Hedysarum</i> (fig. 17), <i>Coronilla</i>,
+<i>Ornithopus</i>, <i>Entada</i> and of some Acacias. In <i>Medicago</i> the legume
+is twisted like a snail, and in <i>Caesalpinia coriaria</i>, or Divi-divi, it is
+vermiform or curved like a worm. Sometimes the number of seeds
+is reduced, as in <i>Erythrina monosperma</i> and <i>Geoffroya superba</i>,
+which are one-seeded, and in <i>Pterocarpus</i> and <i>Dalbergia</i>, which are
+two-seeded.</p>
+
+<table class="flt" style="float: right; width: 270px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:223px; height:229px" src="images/img257c.jpg" alt="" /></td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 31.</span>&mdash;Transverse section
+of the fruit of the Melon
+(<i>Cucumis Melo</i>), showing the
+placentas with the seeds attached
+to them. The three carpels
+forming the pepo are separated
+by partitions. From the centre
+processes pass outwards, ending
+in the curved placenta.</td></tr></table>
+
+<p>The <i>berry</i> (<i>bacca</i>) is a term applied generally to all fruits with
+seeds immersed in pulp, and includes fruits of very various origin.
+In <i>Actaea</i> (baneberry) or <i>Berberis</i>
+(barberry) it is derived from a
+single free carpel; generally, however,
+it is the product of a syncarpous
+ovary, which is superior,
+as in grape or potato, or inferior,
+as in gooseberry (fig. 29) or currant.
+In the pomegranate there is a
+peculiar baccate many-celled
+inferior fruit, having a tough rind,
+enclosing two rows of carpels
+placed one above the other. The
+seeds are immersed in pulp, and
+are attached irregularly to the
+wall, base and centre of the loculi.
+In the baobab there is a multilocular
+syncarpous fruit, in which
+the seeds are immersed in pulp.</p>
+
+<p>The <i>pepo</i>, another indehiscent
+syncarpous fruit, is illustrated by
+the fruit of the gourd, melon (fig.
+31) and other Cucurbitaceae. It
+is formed of three carpels, surmounted
+by the calyx; the rind
+is thick and fleshy, and there are
+three or more seed-bearing parietal placentas, either surrounding a
+central cavity or prolonged inwards into it. The fruit of the papaw
+resembles the pepo, but the calyx is not superior.</p>
+
+<p>The <i>hesperidium</i> is the name given to such indehiscent fleshy
+syncarpous fruits as the orange, lemon and shaddock, in which the
+epicarp and mesocarp form a separable rind, and the endocarp
+sends prolongations inwards, forming triangular divisions, to the
+inner angle of which the seeds are attached, pulpy cells being developed
+around them from the wall. Both pepo and hesperidium may
+be considered as modifications of the berry.</p>
+
+<p>The <i>pome</i> (fig. 30), seen in the apple, pear, quince, medlar and
+hawthorn, is a fleshy indehiscent syncarpous fruit, in the formation
+of which the receptacle takes part. The outer succulent part is the
+swollen receptacle, the horny core being the true fruit developed
+from the usually five carpels and enclosing the seeds. In the medlar
+the core (or true pericarp) is of a stony hardness, while the outer
+succulent covering is open at the summit. The pome somewhat
+resembles the fruit of the rose (fig. 3), where the succulent receptacle
+surrounds a number of separate achenes.</p>
+
+<p>The name <i>capsule</i> is applied generally to all dry syncarpous fruits,
+which dehisce by valves. It may thus be unilocular or multilocular,
+one- or many-seeded. The true valvular capsule is observed in
+<i>Colchicum</i> (fig. 9), lily and iris (fig. 11). The <i>porose capsule</i> is seen
+in the poppy (fig. 7), <i>Antirrhinum</i> and <i>Campanula</i>. In <i>Campanula</i>
+the pores occur at the base of the capsule, which becomes inverted
+when ripe. When the capsule opens by a lid, or by circumscissile
+dehiscence, it is called a <i>pyxidium</i>, as in pimpernel (<i>Anagallis
+arvensis</i>) (fig. 16), henbane and monkey-pot (<i>Lecythis</i>). The capsule
+assumes a screw-like form in <i>Helicteres</i>, and a star-like form in star-anise
+(<i>Illicium anisatum</i>). In certain instances the cells of the
+capsule separate from each other, and open with elasticity to scatter
+the seeds. This kind of capsule is met with in the sandbox tree
+(<i>Hura crepitans</i>) and other Euphorbiaceae, where the cocci, containing
+each a single seed, burst asunder with force; and in Geraniaceae,
+where the cocci, each containing, when mature, usually one
+seed, separate from the carpophore, become curved upwards by their
+adherent styles, and open by the ventral suture (fig. 18).</p>
+
+<p>The <i>siliqua</i> is a dry syncarpous bilocular many-seeded fruit, formed
+from two carpels, with a false septum, dehiscing by two valves
+from below upwards, the valves separating from the placentas and
+leaving them united by the septum (fig. 32). The seeds are attached
+on both sides of the septum, either in one row or in two. When
+the fruit is long and narrow it is a <i>siliqua</i> (fig. 14); when broad
+and short, <i>silicula</i> (fig. 33). It occurs in cruciferous plants, as wallflower,
+cabbage and cress. In <i>Glaucium</i> and <i>Eschscholtzia</i> (Papaveraceae)
+the dissepiment is of a spongy nature. It may become
+transversely constricted (<i>lomentaceous</i>), as in radish (<i>Raphanus</i>)
+and sea-kale, and it may be reduced, as in woad (<i>Isatis</i>), to a
+one-seeded
+condition.</p>
+
+<p>It sometimes happens that the ovaries of two flowers unite so as
+to form a double fruit (<i>syncarp</i>). This may be seen in many species
+of honeysuckle. But the fruits which are now to be considered
+consist usually of the floral envelopes, as well as the ovaries of
+several flowers united into one, and are called <i>multiple</i> or <i>confluent</i>.
+The term <i>anthocarpous</i> has also been applied as indicating that the
+floral envelopes as well as the carpels are concerned in the formation
+of the fruit.</p>
+
+<p>The <i>sorosis</i> is a succulent multiple fruit formed by the confluence
+<span class="pagenum"><a name="page258" id="page258"></a>258</span>
+of a spike of flowers, as in the fruit of the pine-apple (fig. 34), the
+bread-fruit and jack-fruit. Similarly the fruit of the mulberry
+represents a catkin-like inflorescence.</p>
+
+<p>The <i>syconus</i> is an anthocarpous fruit, in which the receptacle
+completely encloses numerous flowers and becomes succulent. The
+fig (fig. 4) is of this nature, and what are called its seeds are the
+achenes of the numerous flowers scattered over the succulent hollowed
+receptacle. In <i>Dorstenia</i> the axis is less deeply hollowed, and of a
+harder texture, the fruit exhibiting often very anomalous forms.</p>
+
+<p>The <i>strobilus</i>, or <i>cone</i>, is a seed-bearing spike, more or less elongated,
+covered with scales, each of which may be regarded as representing
+a separate flower, and has often two seeds at its base; the
+seeds are naked, no ovary being present. This fruit is seen in the
+cones of firs, spruces, larches and cedars, which have received the
+name of Coniferae, or cone-bearers, on this account. Cone-like
+fruit is also seen in most Cycadaceae. The scales of the strobilus
+are sometimes thick and closely united, so as to form a more or less
+angular and rounded mass, as in the cypress; while in the juniper
+they become fleshy, and are so incorporated as to form a globular
+fruit like a berry. The dry fruit of the cypress and the succulent
+fruit of the juniper have received the name of <i>galbulus</i>. In the hop
+the fruit is called also a strobilus, but in it the scales are thin and
+membranous, and the seeds are not naked but are contained in
+pericarps.</p>
+
+<div class="center pt2"><img style="width:522px; height:349px; vertical-align: middle;" src="images/img258a.jpg" alt="" /></div>
+
+<p><span class="sc">Fig. 32.</span>&mdash;Honesty (<i>Lunaria biennis</i>), showing the septum after
+the carpels have fallen away.</p>
+
+<p class="f80">From Strasburger&rsquo;s <i>Lehrbuch der Botanik</i>, by permission of Gustav Fischer.</p>
+
+<p><span class="sc">Fig. 33.</span>&mdash;Silicula or pouch of shepherd&rsquo;s purse (<i>Capsella</i>), opening
+by two folded valves, which separate from above downwards. The
+partition is narrow, hence the silicula is angustiseptal.</p>
+
+<p>From Strasburger&rsquo;s <i>Lehrbuch der Botanik</i>, by permission of Gustav Fischer.</p>
+
+<p><span class="sc">Fig. 34.</span>&mdash;Fruit of the pine-apple (<i>Ananassa sativa</i>), developed
+from a spike of numerous flowers with bracts, united so as to
+form a collective or anthocarpous fruit. The crown of the pine-apple,
+c, consists of a series of empty bracts prolonged beyond the fruit.</p>
+
+<p class="pt2">The same causes which produce alterations in the other parts of
+the flower give rise to anomalous appearances in the fruit. The
+carpels, in place of bearing seeds, are sometimes changed into leaves,
+with lobes at their margins. Leaves are sometimes produced from
+the upper part of the fruit. In the genus <i>Citrus</i>, to which the orange
+and lemon belong, it is very common to meet with a separation of
+the carpels, so as to produce what are called horned oranges and
+fingered citrons. In this case a syncarpous fruit has a tendency to
+become apocarpous. In the orange we occasionally find a supernumerary
+row of carpels produced, giving rise to the appearance of
+small and imperfect oranges enclosed within the original one; the
+navel orange is of this nature. It sometimes happens that, by the
+union of flowers, double fruits are produced. Occasionally a double
+fruit is produced, not by the incorporation of two flowers, but by
+the abnormal development of a second carpel in the flower.</p>
+
+
+<p class="pt2 center"><i>Arrangement of Fruits.</i></p>
+
+<p>A. True fruits&mdash;developed from the ovary alone.</p>
+<div class="list">
+    <p>1. Pericarp not fleshy or fibrous.</p>
+</div>
+<div class="list1">
+        <p>i. Indehiscent&mdash;not opening to allow the escape of the
+            seeds&mdash;generally one-seeded. Achene; caryopsis;
+            cypsela; nut; schizocarp.</p>
+        <p>ii. Dehiscent&mdash;the pericarp splits to allow the escape
+            of the seeds&mdash;generally many-seeded. Follicle;
+            legume; siliqua; capsule.</p>
+</div>
+<div class="list">
+    <p>2. Pericarp generally differentiated into distinct layers, one
+        of which is succulent or fibrous. Drupe; berry.</p>
+</div>
+<p>B. Pseudocarps&mdash;the development extends beyond the ovary.
+Pome; syconus; sorosis.</p>
+
+<p class="pt1"><i>The Seed.</i>&mdash;The <i>seed</i> is formed from the ovule as the result of
+fertilization. It is contained in a seed-vessel formed from the ovary
+in the plants called <i>angiospermous</i>; while in <i>gymnospermous</i> plants,
+such as Coniferae and Cycadaceae, it is naked, or, in other words,
+has no true pericarp. It sometimes happens in Angiosperms, that
+the seed-vessel is ruptured at an early period of growth, so that
+the seeds become more or less exposed during their development;
+this occurs in mignonette, where the capsule opens at the apex,
+and in <i>Cuphea</i>, where the placenta bursts through the ovary and
+floral envelopes, and appears as an erect process bearing the young
+seeds. After fertilization the ovule is greatly changed, in connexion
+with the formation of the embryo. In the embryo-sac of most
+Angiosperms (<i>q.v.</i>) there is a development of cellular tissue, the
+endosperm, more or less filling the embryo-sac. In Gymnosperms
+(<i>q.v.</i>) the endosperm is formed preparatory to fertilization. The
+fertilized egg enlarges and becomes multicellular, forming the
+embryo. The embryo-sac enlarges greatly, displacing gradually
+the surrounding nucellus, which eventually forms merely a thin layer
+around the sac, or completely disappears. The remainder of the
+nucellus and the integuments of the ovules form the seed-coats.
+In some cases (fig. 35) a delicate inner coat or <i>tegmen</i> can be distinguished
+from a tougher outer coat or <i>testa</i>; often, however, the
+layers are not thus separable. The consistency of the seed-coat,
+its thickness, the character of its surface, &amp;c., vary widely, the
+variations being often closely associated with the environment or
+with the means of seed-dispersal. An account of the development
+of the seed from the ovule will be found in the article <span class="sc"><a href="#artlinks">Angiosperms</a></span>.
+When the pericarp is dehiscent the seed-covering is of a strong and
+often rough character; but when the pericarp is indehiscent and
+encloses the seed for a long period, the outer seed-coat is thin and
+soft. The cells of the testa are often coloured, and have projections
+and appendages of various kinds. Thus in <i>Abrus precatorius</i> and
+<i>Adenanthera pavonina</i> it is of a bright red colour; in French beans
+it is beautifully mottled; in the almond it is veined; in the tulip
+and primrose it is rough; in the snapdragon it is marked with
+depressions; in cotton and <i>Asclepias</i> (fig. 36) it has hairs attached to
+it; and in mahogany, <i>Bignonia</i>, and the pines and firs it is expanded
+in the form of wing-like appendages (fig. 37). In <i>Collomia</i>, <i>Acanthodium</i>,
+<i>Cobaea scandens</i> and other seeds, it contains spiral cells, from
+which, when moistened with water, the fibres uncoil in a beautiful
+manner; and in flax (<i>Linum</i>) and others the cells are converted into
+mucilage. These structural peculiarities of the testa in different
+plants have relation to the scattering of the seed and its germination
+upon a suitable nidus. But in some plants the pericarps assume
+structures which subserve the same purpose; this especially occurs
+in small pericarps enclosing single seeds, as achenes, caryopsides, &amp;c.
+Thus in Compositae and valerian, the pappose limb of the calyx
+forms a parachute to the pericarp; in Labiatae and some Compositae
+spiral cells are formed in the epicarp; and the epicarp is prolonged
+as a wing in <i>Fraxinus</i> (fig. 1) and <i>Acer</i> (fig. 21).</p>
+
+<div class="center pt2"><img style="width:408px; height:199px; vertical-align: middle;" src="images/img258b.jpg" alt="" /></div>
+
+<p><span class="sc">Fig. 35.</span>&mdash;Seed of Pea (<i>Pisum</i>) with one cotyledon removed. <i>c</i>,
+Remaining cotyledon; <i>ch</i>, chalaza-point at which the nourishing
+vessels enter; <i>e</i>, tegmen or inner coat; <i>f</i>, funicle or stalk; <i>g</i>,
+plumule of embryo; <i>m</i>, micropyle; <i>pl</i>, placenta; <i>r</i>, radicle of
+embryo; <i>t</i>, tigellum or stalk between root and plumule; <i>te</i>, testa.</p>
+
+<p><span class="sc">Fig. 36.</span>&mdash;Seed of <i>Asclepias</i>, with a cluster of hairs arising from
+the edges of the micropyle.</p>
+
+<p class="pt2">Sometimes there is an additional covering to the seed, formed
+after fertilization, to which the name <i>arillus</i> has been given (fig. 38).
+This is seen in the passion-flower, where the covering arises from the
+placenta or extremity of the funicle at the base of the ovule and
+passes upwards towards the apex, leaving the micropyle uncovered.
+In the nutmeg and spindle tree this additional coat is formed from
+above downwards, constituting in the former case a laciniated
+scarlet covering called <i>mace</i>. In such instances it has been called
+an <i>arillode</i> (fig. 39). This arillode, after growing downwards, may
+be reflected upwards so as to cover the micropyle. The fleshy
+scarlet covering formed around the naked seed in the yew is by
+some considered of the nature of an aril. On the testa, at various
+points, there are produced at times other cellular bodies, to which
+the name of <i>strophioles</i>, or <i>caruncles</i>, has been given, the seeds being
+strophiolate or carunculate. These tumours may occur near the
+base of the seed, as in <i>Polygala</i>, or at the apex, as in Castor-oil
+plant (<i>Ricinus</i>); or they may occur in the course of the raphe, as in
+blood-root (<i>Sanguinaria</i>) and <i>Asarabacca</i>. The funicles of the ovules
+frequently attain a great length in the seed, and in some magnolias,
+when the fruit dehisces, they appear as long scarlet cords suspending
+the seeds outside. The hilum or umbilicus of the seed is usually
+<span class="pagenum"><a name="page259" id="page259"></a>259</span>
+well marked, as a scar of varying size; in the calabar bean and in
+some species of Mucuna and Dolichos it extends along a large
+portion of the edge of the seed; it frequently exhibits marked
+colours, being black in the bean, white in many species of Phaseolus,
+&amp;c. The micropyle (fig. 35, <i>m</i>) of the seed may be recognizable by
+the naked eye, as in the pea and bean tribe, <i>Iris</i>, &amp;c., or it may be
+very minute or microscopic. It indicates the true apex of the seed,
+and is important as marking the point to which the root of the embryo
+is directed. At the micropyle in the bean is observed a small
+process of integument, which, when the young plant sprouts, is
+pushed up like a lid; it is called the <i>embryotega</i>. The chalaza (fig.
+38, <i>ch</i>) is often of a different colour from the rest of the seed. In the
+orange (fig. 40) it is of a reddish-brown colour, and is easily recognized
+at one end of the seed when the integuments are carefully removed.
+In anatropal seeds the raphe forms a distinct ridge along one side
+of the seed (fig. 41).</p>
+
+<p>The position of the seed as regards the pericarp resembles that of
+the ovule in the ovary, and the same terms are applied&mdash;erect,
+ascending, pendulous, suspended, curved, &amp;c. These terms have
+no reference to the mode in which the fruit is attached to the axis.
+Thus the seed may be erect while the fruit itself is pendent, in the
+ordinary meaning of that term. The part of the seed next the axis
+or the ventral suture is its face, the opposite side being the back.
+Seeds exhibit great varieties of form. They may be flattened
+laterally (<i>compressed</i>), or from above downwards (<i>depressed</i>). They
+may be round, oval, triangular, polygonal, rolled up like a snail, as in
+<i>Physostemon</i>, or coiled up like a snake, as in <i>Ophiocaryon paradoxum</i>.</p>
+
+<div class="center pt2"><img style="width:507px; height:206px; vertical-align: middle;" src="images/img259a.jpg" alt="" /></div>
+
+<p><span class="sc">Fig. 37.</span>&mdash;Seed of Pine (<i>Pinus</i>), with a membranous appendage
+<i>w</i> to the testa, called a wing.</p>
+
+<p><span class="sc">Fig. 38.</span>&mdash;Young anatropal seed of the white Water-lily (<i>Nymphaea
+alba</i>), cut vertically. It is attached to the placenta by the funicle f,
+cellular prolongations from which form an aril <i>a a</i>. The vessels of
+the cord are prolonged to the base of the nucellus n by means of
+the raphe <i>r</i>. The base of the nucellus is indicated by the chalaza ch,
+while the apex is at the micropyle <i>m</i>. The covering of the seed is
+marked <i>i. n</i> is the nucellus or perisperm, enclosing the embryo-sac es,
+<span class="correction" title="amended from is">in</span> which the endosperm is formed. The embryo <i>e</i>, with its suspensor,
+is contained in the sac, the radicle pointing to the micropyle <i>m</i>.</p>
+
+<p><span class="sc">Fig. 39.</span>&mdash;Arillode <i>a</i>, or false aril, of the Spindle-tree (<i>Euonymus</i>),
+arising from the micropyle <i>f</i>.</p>
+
+<p><span class="sc">Fig. 40.</span>&mdash;Anatropal seed of the Orange (<i>Citrus Aurantium</i>)
+opened to show the chalaza <i>c</i>, which forms a brown spot at one end.</p>
+
+<p><span class="sc">Fig. 41.</span>&mdash;Entire anatropal seed of the Orange (<i>Citrus Aurantium</i>),
+with its rugose or wrinkled testa, and the raphe <i>r</i> ramifying in the
+thickness of the testa on one side.</p>
+
+<p class="pt2">The endosperm formed in the embryo-sac of angiosperms after
+fertilization, and found previous to it in gymnosperms, consists of
+cells containing nitrogenous and starchy or fatty matter, destined
+for the nutriment of the embryo. It <span class="correction" title="amended from occupied">occupies</span> the whole cavity of
+the embryo-sac, or is formed only at certain portions of it, at the
+apex, as in <i>Rhinanthus</i>, at the base, as in <i>Vaccinium</i>, or in the middle,
+as in <i>Veronica</i>. As the endosperm increases in size along with the
+embryo-sac and the embryo, the substance of the original nucellus
+of the ovule is gradually absorbed. Sometimes, however, as in
+Musaceae, Cannaceae, Zingiberaceae, no endosperm is formed;
+the cells of the original nucellus, becoming filled with food-materials
+for the embryo, are not absorbed, but remain surrounding the
+embryo-sac with the embryo, and constitute the <i>perisperm</i>. Again,
+in other plants, as Nymphaeaceae (fig. 38) and Piperaceae, both
+endosperm and perisperm are present. It was from observations
+on cases such as these that old authors, imagining a resemblance
+betwixt the plant-ovule and the animal ovum, applied the name
+<i>albumen</i> to the outer nutrient mass or perisperm, and designated
+the endosperm as <i>vitellus</i>. The term albumen is very generally
+used as including all the nutrient matter stored up in the seed, but
+it would be advisable to discard the name as implying a definite
+chemical substance. There is a large class of plants in which
+although at first after fertilization a mass of endosperm is formed,
+yet, as the embryo increases in size, the nutrient matter from the
+endospermic cells passes out from them, and is absorbed by the
+cells of the embryo plant. In the mature seed, in such cases, there
+is no separate mass of tissue containing nutrient food-material
+apart from the embryo itself. Such a seed is said to be <i>exalbuminous</i>,
+as in Compositae, Cruciferae and most Leguminosae (<i>e.g.</i> pea, fig. 35).
+When either endosperm or perisperm or both are present the seed
+is said to be <i>albuminous</i>.</p>
+
+<table class="flt" style="float: right; width: 275px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:223px; height:132px" src="images/img259b.jpg" alt="" /></td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 42.</span>&mdash;The dicotyledonous
+embryo of the Pea laid open.
+<i>c</i>, <i>c</i>, The two fleshy cotyledons,
+or seed-lobes, which remain under
+ground when the plant sprouts;
+<i>r</i>, the radicular extremity of the
+axis whence the root arises; <i>t</i>,
+the axis (hypocotyl) bearing the
+young stalk and leaves <i>g</i> (plumule),
+which lie in a depression of
+the cotyledons <i>f</i>.</td></tr></table>
+
+<p>The albumen varies much in its nature and consistence, and
+furnishes important characters. It may be farinaceous or mealy,
+consisting chiefly of cells filled with starch, as in cereal grains,
+where it is abundant; fleshy or cartilaginous, consisting of thicker
+cells which are still soft, as in the coco-nut, and which sometimes
+contain oil, as in the oily albumen of <i>Croton</i>, <i>Ricinus</i> and poppy;
+horny, when the cell-walls are slightly thickened and capable of
+distension, as in date and coffee; the cell-walls sometimes become
+greatly thickened, filling up the testa as a hard mass, as in vegetable
+ivory (<i>Phytelephas</i>). The albumen may be uniform throughout, or
+it may present a mottled appearance,
+as in the nutmeg, the seeds of
+Anonaceae and some Palms, where
+it is called <i>ruminated</i>.  This
+mottled appearance is due to a
+protrusion of a dark lamella of
+the integument between folded
+protuberances of albumen. A
+cavity is sometimes left in the
+centre which is usually filled with
+fluid, as in the coco-nut. The
+relative size of the embryo and of
+the endosperm varies much. In
+Monocotyledons the embryo is
+usually small, and the endosperm
+large, and the same is true in the
+case of coffee and many other
+plants amongst Dicotyledons.
+The opposite is the case in other
+plants, as in the Labiatae, Plumbaginaceae,
+&amp;c.</p>
+
+<p>The embryo consists of an axis bearing the <i>cotyledons</i> (fig. 42, <i>c</i>),
+or the first leaves of the plant. To that part of this axis immediately
+beneath the cotyledons the terms <i>hypocotyl</i>, <i>caulicle</i> or <i>tigellum</i> (<i>t</i>)
+have been applied, and continuous backwards with it is the young
+root or <i>radicle</i> (<i>r</i>), the descending axis, their point of union being
+the collar or neck. The terminal growing bud of the axis is called
+the <i>plumule</i> or <i>gemmule</i> (<i>g</i>), and represents the ascending axis. The
+radicular extremity points towards the micropyle, while the cotyledonary
+extremity is pointed towards the base of the ovule or the
+chalaza. Hence, by ascertaining the position of the micropyle and
+chalaza, the two extremities of the embryo can in general be discovered.
+It is in many cases difficult to recognize the parts in an
+embryo; thus in <i>Cuscuta</i>, the embryo appears as an elongated
+axis without divisions; and in <i>Caryocar</i> the mass of the embryo is
+made up by the radicular extremity and hypocotyl, in a groove of
+which the cotyledonary extremity lies embedded (fig. 52). In some
+monocotyledonous embryos, as in Orchidaceae, the embryo is a
+cellular mass showing no parts. In parasitic plants also which form
+no chlorophyll, as <i>Orobanche</i>, <i>Monotropa</i>, &amp;c., the embryo remains
+without differentiation, consisting merely of a mass of cells until the
+ripening of the seed. When the embryo is surrounded by the endosperm
+on all sides except its radicular extremity it is internal (see
+figs. 19, 20); when lying outside the endosperm, and only coming
+into contact with it at certain points, it is external, as in grasses (<i>e.g.</i>
+wheat, fig. 22). When the embryo follows the direction of the axis
+of the seed, it is axile or axial (fig. 43); when it is not in the direction
+of the axis, it becomes abaxile or abaxial. In campylotropal seeds
+the embryo is curved, and in place of being embedded in endosperm,
+is frequently external to it, following the concavity of the seed (fig.
+44), and becoming peripherical, with the chalaza situated in the
+curvature of the embryo, as in Caryophyllaceae.</p>
+
+<p>It has been already stated that the radicle of the embryo is
+directed to the micropyle, and the cotyledons to the chalaza. In
+some cases, by the growth of the integuments, the former is turned
+round so as not to correspond with the apex of the nucellus, and then
+the embryo has the radicle directed to one side, and is called excentric,
+as is seen in Primulaceae, Plantaginaceae and many palms, especially
+the date. The position of the embryo in different kinds of seeds
+varies. In an orthotropal seed the embryo is inverted or <i>antitropal</i>,
+the radicle pointing to the apex of the seed, or to the part opposite
+the hilum. Again, in an anatropal seed the embryo is erect or
+<i>homotropal</i> (fig. 43), the radicle being directed to the base of the
+seed. In curved or campylotropal seeds the embryo is folded so
+that its radicular and cotyledonary extremities are approximated,
+and it becomes <i>amphitropal</i> (fig. 44). In this instance the seed
+may be exalbuminous, and the embryo may be folded on itself;
+or albuminous, the embryo surrounding more or less completely the
+endosperm and being peripherical. According to the mode in
+which the seed is attached to the pericarp, the radicle may be
+directed upwards or downwards, or laterally, as regards the ovary.
+In an orthotropal seed attached to the base of the pericarp it is
+superior, as also in a suspended anatropal seed. In other anatropal
+seeds the radicle is inferior. When the seed is horizontal as regards
+the pericarp, the radicle is either centrifugal, when it points to the
+outer wall of the ovary; or centripetal, when it points to the axis
+or inner wall of the ovary. These characters are of value for purposes
+of classification, as they are often constant in large groups of genera.</p>
+
+<p><span class="pagenum"><a name="page260" id="page260"></a>260</span></p>
+
+<p>Plants in which there are two cotyledons produced in the embryo
+are <i>dicotyledonous</i>. The two cotyledons thus formed are opposite
+to each other (figs. 42 and 45), but are not always of the same size.
+Thus, in Abronia and other members of the order Nyctaginaceae, one
+of them is smaller than the other (often very small), and in <i>Carapa
+guianensis</i> there appears to be only one, in consequence of the
+intimate union which takes place between the two. The union
+between the cotyledonary leaves may continue after the young plant
+begins to germinate. Such embryos have been called <i>pseudomonocotyledonous</i>.
+The texture of the cotyledons varies. They may be
+thick, as in the pea (fig. 42), exhibiting no traces of venation, with
+their flat internal surfaces in contact, and their backs more or less
+convex; or they may be in the form of thin and delicate laminae,
+flattened on both sides, and having distinct venation, as in <i>Ricinus</i>,
+<i>Jatropha</i>, <i>Euonymus</i>, &amp;c. The cotyledons usually form the greater
+part of the mature embryo, and this is remarkably well seen in such
+exalbuminous seeds as the bean and pea.</p>
+
+<div class="center pt2"><img style="width:420px; height:297px; vertical-align: middle;" src="images/img260a.jpg" alt="" /></div>
+
+<p><span class="sc">Fig. 43.</span>&mdash;Seed of Pansy (<i>Viola tricolor</i>) cut vertically. The embryo
+<i>pl</i> is axial, in the midst of fleshy endosperm al. The seed is
+anatropal, and the embryo is homotropal; the cotyledons co point
+to the base of the nucellus or chalaza <i>ch</i>, while the radicle, or the
+other extremity of the embryo, points to the micropyle, close to the
+hilum <i>h</i>. The hilum or base of the seed, and the chalaza or base of
+the nucellus are united by means of the raphe <i>r</i>.</p>
+
+<p><span class="sc">Fig. 44.</span>&mdash;Seed of the Red Campion (<i>Lychnis</i>), cut vertically,
+showing the peripheral embryo, with its two cotyledons and its
+radicle. The embryo is curved round the albumen, so that its
+cotyledons and radicle both come near the hilum (<i>amphitropal</i>).</p>
+
+<p><span class="sc">Fig. 45.</span>&mdash;Mature dicotyledonous embryo of the Almond, with
+one of the cotyledons removed. <i>r</i>, Radicle; <i>t</i>, young stem or
+caulicle; <i>c</i>, one of the cotyledons left; <i>i</i>, line of insertion of the
+cotyledon which has been removed; <i>g</i>, plumule.</p>
+
+<p><span class="sc">Fig. 46.</span>&mdash;Exalbuminous seed of Wallflower (Cheiranthus) cut
+vertically. The radicle <i>r</i> is folded on the edges of the cotyledons <i>c</i>
+which are accumbent.</p>
+
+<p><span class="sc">Fig. 47.</span>&mdash;Transverse section of the seed of the Wallflower (<i>Cheiranthus</i>),
+showing the radicle <i>r</i> folded on the edges of the accumbent
+cotyledons <i>c</i>.</p>
+
+<p><span class="sc">Fig. 48.</span>&mdash;Transverse section of the seed of the Dame&rsquo;s Violet
+(<i>Hesperis</i>). The radicle <i>r</i> is folded on the back of the cotyledons <i>c</i>,
+which are said to be incumbent.</p>
+
+<p class="pt2">Cotyledons are usually entire and sessile. But they occasionally
+become lobed, as in the walnut and the lime; or petiolate, as in
+<i>Geranium molle</i>; or auriculate, as in the ash. Like leaves in the
+bud, cotyledons may be either applied directly to each other, or
+may be folded in various ways. In geranium the cotyledons are
+twisted and doubled; in convolvulus they are corrugated; and in
+the potato and in <i>Bunias</i>, they are spiral,&mdash;the same terms being
+applied as to the foliage leaves. The radicle and cotyledons are
+either straight or variously curved. Thus, in some cruciferous
+plants, as the wallflower, the cotyledons are applied by their faces,
+and the radicle (figs. 46, 47) is folded on their edges, so as to be
+lateral; the cotyledons are here <i>accumbent</i>. In others, as <i>Hesperis</i>,
+the cotyledons (fig. 48) are applied to each other by their faces,
+and the radicle, <i>r</i>, is folded on their back, so as to be dorsal, and
+the cotyledons are <i>incumbent</i>. Again, the cotyledons are <i>conduplicate</i>
+when the radicle is dorsal, and enclosed between their folds.
+In other divisions the radicle is folded in a spiral manner, and the
+cotyledons follow the same course.</p>
+
+<p>In many gymnosperms more than two cotyledons are present,
+and they are arranged in a whorl. This occurs in Coniferae, especially
+in the pine, fir (fig. 49), spruce and larch, in which six, nine,
+twelve and even fifteen have been observed. They are linear, and
+resemble in their form and mode of development the clustered or
+fasciculated leaves of the larch. Plants having numerous cotyledons
+are termed <i>polycotyledonous</i>. In species of <i>Streptocarpus</i> the
+cotyledons are permanent, and act the part of leaves. One of them
+is frequently largely developed, while the other is small or abortive.</p>
+
+<div class="center pt2"><img style="width:484px; height:242px; vertical-align: middle;" src="images/img260b.jpg" alt="" /></div>
+
+<p><span class="sc">Fig. 49.</span>&mdash;Polycotylodonous embryo of the Pine (<i>Pinus</i>) beginning
+to sprout. <i>t</i>, Hypocotyl; <i>r</i>, radicle. The cotyledons <i>c</i> are numerous.
+Within the cotyledons the primordial leaves are seen, constituting
+the plumule or first bud of the plant.</p>
+
+<p><span class="sc">Fig. 50.</span>&mdash;Embryo of a species of Arrow-grass (<i>Triglochin</i>), showing
+a uniform conical mass, with a slit <i>s</i> near the lower part. The
+cotyledon <i>c</i> envelops the young bud, which protrudes at the slit
+during germination. The radicle is developed from the lower part
+of the axis <i>r</i>.</p>
+
+<p><span class="sc">Fig. 51.</span>&mdash;Grain of wheat (<i>Triticum</i>) germinating, showing (<i>b</i>)
+the cotyledon and (<i>c</i>) the rootlets surrounded by their sheaths
+(<i>coleorrhizae</i>).</p>
+
+<p><span class="sc">Fig. 52.</span>&mdash;Embryo of <i>Caryocar</i>. <i>t</i>, Thick hypocotyl, forming nearly
+the whole mass, becoming narrowed and curved at its extremity,
+and applied to the groove <i>s</i>. In the figure this narrowed portion is
+slightly separated from the groove; <i>c</i>, two rudimentary cotyledons.</p>
+
+<p class="pt2">In those plants in which there is only a single cotyledon in the
+embryo, hence called <i>monocotyledonous</i>, the embryo usually has a
+cylindrical form more or less rounded at the extremities, or elongated
+and fusiform, often oblique. The axis is usually very short compared
+with the cotyledon, which in general encloses the plumule
+by its lower portion, and exhibits on one side a small slit which indicates
+the union of the edges of the vaginal or sheathing portion of
+the leaf (fig. 50). In grasses, by the enlargement of the embryo in a
+particular direction, the endosperm is pushed on one side, and thus
+the embryo comes to lie outside at the base of the endosperm (figs. 22,
+51). The lamina of the cotyledon is not developed. Upon the side
+of the embryo next the endosperm and enveloping it is a large
+shield-shaped body, termed the <i>scutellum</i>. This is an outgrowth
+from the base of the cotyledon, enveloping more or less the cotyledon
+and plumule, in some cases, as in maize, completely investing it;
+in other cases, as in rice, merely sending small prolongations over its
+anterior face at the apex. By others this scutellum is considered
+as the true cotyledon, and the sheathing structure covering the
+plumule is regarded as a ligule or axillary stipule (see <span class="sc"><a href="#artlinks">Grasses</a></span>).
+In many aquatic monocotyledons (<i>e.g.</i> <i>Potamogeton</i>, <i>Ruppia</i> and
+others) there is a much-developed hypocotyl, which forms the
+greater part of the embryo and acts as a store of nutriment in
+germination; these are known as <i>macropodous</i> embryos. A similar
+case is that of <i>Caryocar</i> among Dicotyledons, where the swollen
+hypocotyl occupies most of the embryo (fig. 52). In some grasses,
+as oats and rice, a projection of cellular tissue is seen upon the side
+of the embryo opposite to the scutellum, that is, on the anterior
+side. This has been termed the <i>epiblast</i>. It is very large in rice.
+This by some was considered the rudimentary second cotyledon;
+but is now generally regarded as an outgrowth of the sheath of the
+true cotyledon.</p>
+</div>
+<div class="author">(A. B. R.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">FRUIT AND FLOWER FARMING.<a name="ar9" id="ar9"></a></span> The different sorts of
+fruits and flowers are dealt with in articles under their own
+headings, to which reference may be made; and these give
+the substantial facts as to their cultivation. See also the article
+<span class="sc"><a href="#artlinks">Horticulture</a></span>.</p>
+
+<p class="pt2 center sc">Great Britain</p>
+
+<p class="pt2 center"><span class="sc">Table</span> I.&mdash;<i>Extent of Orchards in Great Britain in each Year,
+1887 to 1901.</i></p>
+
+<table class="ws" summary="Contents">
+
+<tr><td class="tcc rb lb tb bb">Year.</td> <td class="tcc rb2 lb tb bb">Acres.</td> <td class="tcc rb lb tb bb">Year.</td> <td class="tcc rb2 lb tb bb">Acres.</td> <td class="tcc rb lb tb bb">Year.</td> <td class="tcc rb lb tb bb">Acres.</td></tr>
+
+<tr><td class="tcc rb lb">1887</td> <td class="tcc rb2">202,234</td> <td class="tcc rb">1892</td> <td class="tcc rb2">208,950</td> <td class="tcc rb">1897</td> <td class="tcc rb">224,116</td></tr>
+<tr><td class="tcc rb lb">1888</td> <td class="tcc rb2">199,178</td> <td class="tcc rb">1893</td> <td class="tcc rb2">211,664</td> <td class="tcc rb">1898</td> <td class="tcc rb">226,059</td></tr>
+<tr><td class="tcc rb lb">1889</td> <td class="tcc rb2">199,897</td> <td class="tcc rb">1894</td> <td class="tcc rb2">214,187</td> <td class="tcc rb">1899</td> <td class="tcc rb">228,603</td></tr>
+<tr><td class="tcc rb lb">1890</td> <td class="tcc rb2">202,305</td> <td class="tcc rb">1895</td> <td class="tcc rb2">218,428</td> <td class="tcc rb">1900</td> <td class="tcc rb">232,129</td></tr>
+<tr><td class="tcc rb lb bb">1891</td> <td class="tcc rb2 bb">209,996</td> <td class="tcc rb bb">1896</td> <td class="tcc rb2 bb">221,254</td> <td class="tcc rb bb">1901</td> <td class="tcc rb bb">234,660</td></tr>
+
+</table>
+
+<p class="pt2 center"><span class="sc">Table</span> II.&mdash;<i>Areas under Orchards in England, Wales and
+Scotland&mdash;Acres.</i></p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcc allb">Year.</td> <td class="tcc allb">England.</td> <td class="tcc allb">Wales.</td> <td class="tcc allb">Scotland.</td> <td class="tcc allb">Great Britain.</td></tr>
+
+<tr><td class="tcc lb rb">1896</td> <td class="tcc rb">215,642</td> <td class="tcc rb">3677</td> <td class="tcc rb">1935</td> <td class="tcc rb">221,254</td></tr>
+<tr><td class="tcc lb rb">1897</td> <td class="tcc rb">218,261</td> <td class="tcc rb">3707</td> <td class="tcc rb">2148</td> <td class="tcc rb">224,116</td></tr>
+<tr><td class="tcc lb rb">1898</td> <td class="tcc rb">220,220</td> <td class="tcc rb">3690</td> <td class="tcc rb">2149</td> <td class="tcc rb">226,059</td></tr>
+<tr><td class="tcc lb rb">1899</td> <td class="tcc rb">222,712</td> <td class="tcc rb">3666</td> <td class="tcc rb">2225</td> <td class="tcc rb">228,603</td></tr>
+<tr><td class="tcc lb rb">1900</td> <td class="tcc rb">226,164</td> <td class="tcc rb">3695</td> <td class="tcc rb">2270</td> <td class="tcc rb">232,129</td></tr>
+<tr><td class="tcc lb rb">1901</td> <td class="tcc rb">228,580</td> <td class="tcc rb">3767</td> <td class="tcc rb">2313</td> <td class="tcc rb">234,660</td></tr>
+<tr><td class="tcc lb rb bb">1908</td> <td class="tcc rb bb">244,430</td> <td class="tcc rb bb">3577</td> <td class="tcc rb bb">2290</td> <td class="tcc rb bb">250,297</td></tr>
+</table>
+
+<p>The extent of the fruit industry may be gathered from the
+figures for the acreage of land under cultivation in orchards
+and small fruit plantations. The Board of Agriculture returns
+concerning the orchard areas of Great Britain showed a continuous
+expansion year by year from 199,178 acres in 1888 to 234,660
+acres in 1901, as will be learnt from Table I. There was, it is
+true, an exception in 1892, but the decline in that year is explained
+by the circumstance that since 1891 the agricultural
+returns have been collected only from holdings of more than
+one acre, whereas they were previously obtained from all holdings
+of a quarter of an acre or more. As there are many holdings
+of less than an acre in extent upon which fruit is grown, and as
+fruit is largely raised also in suburban and other gardens which
+<span class="pagenum"><a name="page261" id="page261"></a>261</span>
+do not come into the returns, it may be taken for granted that
+the actual extent of land devoted to fruit culture exceeds that
+which is indicated by the official figures. In the Board of
+Agriculture returns up to June 1908, 308,000 acres are stated
+to be devoted to fruit cultivation of all kinds in Great Britain.
+Table II. shows that the expansion of the orchard area of Great
+Britain is mainly confined to England, for it has slightly decreased
+in Wales and Scotland. The acreage officially returned
+as under orchards is that of arable or grass land which is also
+used for fruit trees of any kind. Conditions of soil and climate
+determine the irregular distribution of orchards in Great Britain.
+The dozen counties which possess the largest extent of orchard
+land all lie in the south or west of the island. According to the
+returns for 1908 (excluding small fruit areas) they were the
+following:&mdash;</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcc rb lb tb bb">County.</td> <td class="tcc rb2 lb tb bb">Acres.</td> <td class="tcc rb lb tb bb">County.</td> <td class="tcc rb2 lb tb bb">Acres.</td> <td class="tcc rb lb tb bb">County.</td> <td class="tcc rb lb tb bb">Acres.</td></tr>
+
+<tr><td class="tcl lb rb">Kent</td> <td class="tcc rb2">32,751</td> <td class="tcl rb">Worcester</td> <td class="tcc rb2">23,653</td> <td class="tcl rb">Salop</td> <td class="tcc rb">4685</td></tr>
+<tr><td class="tcl lb rb">Devon</td> <td class="tcc rb2">27,200</td> <td class="tcl rb">Gloucester</td> <td class="tcc rb2">20,424</td> <td class="tcl rb">Dorset</td> <td class="tcc rb">4464</td></tr>
+<tr><td class="tcl lb rb">Hereford</td> <td class="tcc rb2">28,316</td> <td class="tcl rb">Cornwall</td> <td class="tcc rb2">5,415</td> <td class="tcl rb">Monmouth</td> <td class="tcc rb">3914</td></tr>
+<tr><td class="tcl lb rb bb">Somerset</td> <td class="tcc rb2 bb">25,279</td> <td class="tcl rb bb">Middlesex</td> <td class="tcc rb2 bb">5,300</td> <td class="tcl rb bb">Wilts</td> <td class="tcc rb bb">3630</td></tr>
+</table>
+
+<p class="noind">Leaving out of consideration the county of Kent, which grows
+a greater variety of fruit than any of the others, the counties
+of Devon, Hereford, Somerset, Worcester and Gloucester have
+an aggregate orchard area of 124,872 acres. These five counties
+of the west and south-west of England&mdash;constituting in one
+continuous area what is essentially the cider country of Great
+Britain&mdash;embrace therefore rather less than half of the entire
+orchard area of the island, while Salop, Monmouth and Wilts
+have about 300 less than they had a few years ago. Five English
+counties have less than 1000 acres each of orchards, namely,
+the county of London, and the northern counties of Cumberland,
+Westmorland, Northumberland and Durham. Rutland has
+just over 100 acres. The largest orchard areas in Wales are in
+the two counties adjoining Hereford&mdash;Brecon with 1136 acres
+and Radnor with 727 acres; at the other extreme is Anglesey,
+with a decreasing orchard area of only 22 acres. Of the Scottish
+counties, Lanark takes the lead with 1285 acres, Perth, Stirling
+and Haddington following with 684 and 129 acres respectively.
+Ayr and Midlothian are the only other counties possessing 100
+acres or more of orchards, whilst Kincardine, Orkney and
+Shetland return no orchard area, and Banff, Bute, Kinross,
+Nairn, Peebles, Sutherland and Wigtown return less than 10
+acres each. It may be added that in 1908 Jersey returned 1090
+acres of orchards, Guernsey, &amp;c., 144 acres, and the Isle of Man,
+121 acres; the two last-named places showing a decline as
+compared with eight years previously.</p>
+
+<p>Outside the cider counties proper of England, the counties in
+which orchards for commercial fruit-growing have increased
+considerably in recent years include Berks, Buckingham,
+Cambridge, Essex, Lincoln, Middlesex, Monmouth, Norfolk,
+Oxford, Salop, Sussex, Warwick and Wilts. Apples are the
+principal fruit grown in the western and south-western counties,
+pears also being fairly common. In parts of Gloucestershire,
+however, and in the Evesham and Pershore districts of Worcestershire,
+plum orchards exist. Plums are almost as largely grown
+as apples in Cambridgeshire. Large quantities of apples, plums,
+damsons, cherries, and a fair quantity of pears are grown for the
+market in Kent, whilst apples, plums and pears predominate in
+Middlesex. In many counties damsons are cultivated around
+fruit plantations to shelter the latter from the wind.</p>
+
+<p>Of small fruit (currants, gooseberries, strawberries, raspberries,
+&amp;c.) no return was made of the acreage previous to 1888, in
+which year it was given as 36,724 acres for Great Britain. In
+1889 it rose to 41,933 acres.</p>
+
+<p>Later figures are shown in Table III. It will be observed that,
+owing to corrections made in the enumeration in 1897, a considerable
+reduction in the area is recorded for that year, and presumably
+the error then discovered existed in all the preceding
+returns. The returns for 1907 gave the acreage of small fruit
+as 82,175 acres, and in 1908 at 84,880 acres&mdash;an area more than
+double that of 1889.</p>
+
+<p class="pt2 center"><span class="sc">Table</span> III.&mdash;<i>Areas of Small Fruit in Great Britain</i>.</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcc rb lb tb bb">Year.</td> <td class="tcc rb2 lb tb bb">Acres.</td> <td class="tcc rb lb tb bb">Year.</td> <td class="tcc rb2 lb tb bb">Acres.</td> <td class="tcc rb lb tb bb">Year.</td> <td class="tcc rb lb tb bb">Acres.</td></tr>
+
+<tr><td class="tcc lb rb">1890</td> <td class="tcc rb2">46,234</td> <td class="tcc rb">1894</td> <td class="tcc rb2">68,415</td> <td class="tcc rb">1898</td> <td class="tcc rb">69,753</td></tr>
+<tr><td class="tcc lb rb">1891</td> <td class="tcc rb2">58,704</td> <td class="tcc rb">1895</td> <td class="tcc rb2">74,547</td> <td class="tcc rb">1899</td> <td class="tcc rb">71,526</td></tr>
+<tr><td class="tcc lb rb">1892</td> <td class="tcc rb2">62,148</td> <td class="tcc rb">1896</td> <td class="tcc rb2">76,245</td> <td class="tcc rb">1900</td> <td class="tcc rb">73,780</td></tr>
+<tr><td class="tcc lb rb bb">1893</td> <td class="tcc rb2 bb">65,487</td> <td class="tcc rb bb">1897</td> <td class="tcc rb2 bb">69,792</td> <td class="tcc rb bb">1901</td> <td class="tcc rb bb">74,999</td></tr>
+</table>
+
+<p class="pt2 center"><span class="sc">Table</span> IV.&mdash;<i>Areas under Small Fruit in England, Wales and
+Scotland&mdash;Acres</i>.</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcc allb">Year.</td> <td class="tcc allb">England.</td> <td class="tcc allb">Wales.</td> <td class="tcc allb">Scotland.</td> <td class="tcc allb">Great Britain.</td></tr>
+
+<tr><td class="tcc lb rb">1898</td> <td class="tcc rb">63,438</td> <td class="tcc rb">1044</td> <td class="tcc rb">5271</td> <td class="tcc rb">69,753</td></tr>
+<tr><td class="tcc lb rb">1899</td> <td class="tcc rb">64,867</td> <td class="tcc rb">1106</td> <td class="tcc rb">5553</td> <td class="tcc rb">71,526</td></tr>
+<tr><td class="tcc lb rb">1900</td> <td class="tcc rb">66,749</td> <td class="tcc rb">1109</td> <td class="tcc rb">5922</td> <td class="tcc rb">73,780</td></tr>
+<tr><td class="tcc lb rb">1901</td> <td class="tcc rb">67,828</td> <td class="tcc rb">1092</td> <td class="tcc rb">6079</td> <td class="tcc rb">74,999</td></tr>
+<tr><td class="tcc lb rb bb">1908</td> <td class="tcc rb bb">75,750</td> <td class="tcc rb bb">1200</td> <td class="tcc rb bb">7930</td> <td class="tcc rb bb">84,880</td></tr>
+</table>
+
+<p>There has undoubtedly been a considerable expansion, rather
+than a contraction, of small fruit plantations since 1896. The
+acreage of small fruit in Great Britain is about one-third that of
+the orchards. As may be seen in Table IV., it is mainly confined
+to England, though Scotland has over 4000 more acres of small
+fruit than of orchards. About one-third of the area of small
+fruit in England belongs to Kent alone, that county having
+returned 24,137 acres in 1908. Cambridge now ranks next with
+6878 acres, followed by Norfolk with 5876 acres, Worcestershire
+with 4852 acres, Middlesex with 4163 acres, Hants with 3320
+acres and Essex with 2150 acres. It should be remarked that
+between 1900 and 1908 Cambridgeshire had almost doubled
+its area of small fruits, from 3740 to 6878 acres; whilst both
+Norfolk and Worcestershire in 1908 had larger areas devoted
+to small fruits than Middlesex&mdash;in which county there had
+been a decrease of about 400 acres during the same period.
+The largest county area of small fruit in Wales is 806 acres
+in Denbighshire, and in Scotland 2791 acres in Perthshire,
+2259 acres in Lanarkshire, followed by 412 acres in Forfarshire.
+The only counties in Great Britain which make no return under
+the head of small fruit are Orkney and Shetland; and Sutherland
+only gives 2½ acres. It is hardly necessary to say that considerable
+areas of small fruit, in kitchen gardens and elsewhere, find
+no place in the official returns, which, however, include small
+fruit grown between and under orchard trees.</p>
+
+<p>Gooseberries are largely grown in most small fruit districts.
+Currants are less widely cultivated, but the red currant is more
+extensively grown than the black, the latter having suffered
+seriously from the ravages of the black currant mite. Kent is
+the great centre for raspberries and for strawberries, though,
+in addition, the latter fruit is largely grown in Cambridgeshire
+(2411 acres), Hampshire (2327 acres), Norfolk (2067 acres)
+and Worcestershire (1273 acres). Essex, Lincolnshire, Cheshire,
+<span class="pagenum"><a name="page262" id="page262"></a>262</span>
+Cornwall and Middlesex each has more than 500 acres devoted
+to strawberry cultivation.</p>
+
+<p>The following statement from returns for 1908 shows the
+area under different kinds of fruit in 1907 and 1908 in Great
+Britain, and also whether there had been an increase or decrease:</p>
+
+<table class="ws" summary="Contents">
+
+<tr><td class="tccm allb">&nbsp;</td> <td class="tccm allb">1907.</td> <td class="tccm allb">1908.</td> <td class="tccm allb">Increase or<br />Decrease.</td></tr>
+<tr><td class="tcc lb rb">&nbsp;</td> <td class="tcc rb">Acres.</td> <td class="tcc rb">Acres.</td> <td class="tcc rb">Acres.</td></tr>
+<tr><td class="tcl lb rb">Small Fruit&mdash;</td> <td class="tcr rb">&nbsp;</td> <td class="tcr rb">&nbsp;</td> <td class="tcr rb">&nbsp;</td></tr>
+<tr><td class="tcl lb rb"> &emsp; Strawberries</td> <td class="tcr rb">27,827</td> <td class="tcr rb">28,815</td> <td class="tcr rb">+ 988</td></tr>
+<tr><td class="tcl lb rb"> &emsp; Raspberries</td> <td class="tcr rb">8,878</td> <td class="tcr rb">9,323</td> <td class="tcr rb">+ 445</td></tr>
+<tr><td class="tcl lb rb"> &emsp; Currants and Gooseberries</td> <td class="tcr rb">25,590</td> <td class="tcr rb">26,241</td> <td class="tcr rb">+ 651</td></tr>
+<tr><td class="tcl lb rb"> &emsp; Other kinds</td> <td class="tcr rb">19,880</td> <td class="tcr rb">20,501</td> <td class="tcr rb">+ 621</td></tr>
+<tr><td class="tcl lb rb"> &nbsp;</td> <td class="tcr allb">82,175</td> <td class="tcr allb">84,880</td> <td class="tcr allb">+2705</td></tr>
+<tr><td class="tcl lb rb">Orchards&mdash;</td> <td class="tcr rb">&nbsp;</td> <td class="tcr rb">&nbsp;</td> <td class="tcr rb">&nbsp;</td></tr>
+<tr><td class="tcl lb rb"> &emsp; Apples</td> <td class="tcr rb">172,643</td> <td class="tcr rb">172,751</td> <td class="tcr rb">+ 108</td></tr>
+<tr><td class="tcl lb rb"> &emsp; Pears</td> <td class="tcr rb">8,911</td> <td class="tcr rb">9,604</td> <td class="tcr rb">+ 693</td></tr>
+<tr><td class="tcl lb rb"> &emsp; Cherries</td> <td class="tcr rb">12,027</td> <td class="tcr rb">11,868</td> <td class="tcr rb">&minus; 159</td></tr>
+<tr><td class="tcl lb rb"> &emsp; Plums</td> <td class="tcr rb">14,901</td> <td class="tcr rb">15,683</td> <td class="tcr rb">+ 782</td></tr>
+<tr><td class="tcl lb rb"> &emsp; Other kinds</td> <td class="tcr rb">41,694</td> <td class="tcr rb">40,391</td> <td class="tcr rb">&minus;1303</td></tr>
+<tr><td class="tcl lb rb bb">&nbsp;</td> <td class="tcr allb">250,176</td> <td class="tcr allb">250,297</td> <td class="tcr allb">+ 121</td></tr>
+
+</table>
+
+<p>It appears from the Board of Agriculture returns that 27,433
+acres of small fruit was grown in orchards, so that the total
+extent of land under fruit cultivation in Great Britain at the end
+of 1908 was about 308,000 acres.</p>
+
+<p>There are no official returns as to the acreage devoted to
+orchard cultivation in Ireland. The figures relating to small fruit,
+moreover, extend back only to 1899, when the area under this
+head was returned as 4809 acres, which became 4359 acres in
+1900 and 4877 acres in 1901. In most parts of the country
+there are districts favourable to the culture of small fruits,
+such as strawberries, raspberries, gooseberries and currants,
+and of top fruits, such as apples, pears, plums and damsons.
+The only localities largely identified with fruit culture as an
+industry are the Drogheda district and the Armagh district.
+In the former all the kinds named are grown except strawberries,
+the speciality being raspberries, which are marketed in Dublin,
+Belfast and Liverpool. In the Armagh district, again, all the
+kinds named are grown, but in this case strawberries are the
+speciality, the markets utilized being Richhill, Belfast, and those
+in Scotland. In the Drogheda district the grower bears the
+cost of picking, packing and shipping, but he cannot estimate
+his net returns until his fruit is on the market. Around Armagh
+the Scottish system prevails&mdash;that is, the fruit is sold while
+growing, the buyer being responsible for the picking and
+marketing.</p>
+
+<p>The amount of fruit imported into the United Kingdom has
+such an important bearing on the possibilities of the industry
+that the following figures also may be useful:</p>
+
+<div class="condensed">
+<p>The quantities of apples, pears, plums, cherries and grapes
+imported in the raw condition into the United Kingdom in each
+year, 1892 to 1901, are shown in Table V. Previous to 1892 apples
+only were separately enumerated. Up to 1899 inclusive the quantities
+were given in bushels, but in 1900 a change was made to hundred-weights.
+This renders the quantities in that and subsequent years
+not directly comparable with those in earlier years, but the comparison
+of the values, which are also given in the table, continues
+to hold good. The figures for 1908 have been added to show the
+increase that had taken place. In some years the value of imported
+apples exceeds the aggregate value of the pears, plums, cherries
+and grapes imported. The extreme values for apples shown in the
+table are £844,000 in 1893 and £2,079,000 in 1908. Grapes rank next
+to apples in point of value, and over the seventeen years the amount
+ranged between £394,000 in 1892 and £728,000 in 1908. On the
+average, the annual outlay on imported pears is slightly in excess
+of that on plums. The extremes shown are £167,000 in 1895 and
+£515,000 in 1908. In the case of plums, the smallest outlay tabulated
+is £166,000 in 1895, whilst the largest is £498,000 in 1897. The
+amounts expended upon imported cherries varied between £96,000
+in 1895 and £308,000 in 1900. In 1900 apricots and peaches, imported
+raw, previously included with raw plums, were for the first
+time separately enumerated, the import into the United Kingdom
+for that year amounting to 13,689 cwt., valued at £25,846; in 1901
+the quantity was 13,463 cwt. and the value £32,350. The latter
+rose in 1908 to £60,000. In 1900, also, currants, gooseberries and
+strawberries, hitherto included in unenumerated raw fruit, were
+likewise for the first time separately returned. Of raw currants
+the import was 64,462 cwt., valued at £87,170 (1908, £121,850);
+of raw gooseberries 26,045 cwt., valued at £14,626 (1908, £25,520);
+and of raw strawberries, 52,225 cwt., valued at £85,949. In 1907
+only 44,000 cwt. of strawberries were imported. In 1901 the
+quantities and values were respectively&mdash;currants, 70,402 cwt.,
+£75,308; gooseberries, 21,735 cwt., £11,420; strawberries, 38,604
+cwt., £51,290. Up to 1899 the imports of tomatoes were included
+amongst unenumerated raw vegetables, so that the quantity was
+not separately ascertainable. For 1900 the import of tomatoes
+was 833,032 cwt., valued at £792,339, which is equivalent to a
+fraction under 2½d. per &#8468;. For 1901 the quantity was 793,991 cwt.,
+and the value £734,051; for 1906, there were 1,124,700 cwt., valued
+at £953,475; for 1907, 1,135,499 cwt., valued at £1,020,805; and
+for 1908, 1,160,283 cwt., valued at £955,983.</p>
+
+<div class="list">
+<p class="pt2"><span class="sc">Table V</span>.&mdash;<i>Imports of Raw Apples, Pears, Plums, Cherries and
+Grapes into the United Kingdom, 1892 to 1901. Quantities in
+Thousands of Bushels (thousands of cwt. in 1900 and 1901).
+Values in Thousands of Pounds Sterling.</i></p>
+</div>
+
+<table class="ws" summary="Contents">
+<tr><td class="tccm allb" rowspan="2">Year.</td> <td class="tccm allb" colspan="5">Quantities.</td></tr>
+<tr><td class="tcc allb">Apples.</td> <td class="tcc allb">Pears.</td> <td class="tcc allb">Plums.</td> <td class="tcc allb">Cherries.</td> <td class="tcc allb">Grapes.</td></tr>
+
+<tr><td class="tcc lb rb">1892</td> <td class="tcc rb">4515</td> <td class="tcr rb">637</td> <td class="tcr rb">413</td> <td class="tcc rb">217</td> <td class="tcr rb">762</td></tr>
+<tr><td class="tcc lb rb">1893</td> <td class="tcc rb">3460</td> <td class="tcr rb">915</td> <td class="tcr rb">777</td> <td class="tcc rb">346</td> <td class="tcr rb">979</td></tr>
+<tr><td class="tcc lb rb">1894</td> <td class="tcc rb">4969</td> <td class="tcr rb">1310</td> <td class="tcr rb">777</td> <td class="tcc rb">311</td> <td class="tcr rb">833</td></tr>
+<tr><td class="tcc lb rb">1895</td> <td class="tcc rb">3292</td> <td class="tcr rb">407</td> <td class="tcr rb">401</td> <td class="tcc rb">196</td> <td class="tcr rb">865</td></tr>
+<tr><td class="tcc lb rb">1896</td> <td class="tcc rb">6177</td> <td class="tcr rb">483</td> <td class="tcr rb">560</td> <td class="tcc rb">219</td> <td class="tcr rb">883</td></tr>
+<tr><td class="tcc lb rb">1897</td> <td class="tcc rb">4200</td> <td class="tcr rb">1052</td> <td class="tcr rb">1044</td> <td class="tcc rb">312</td> <td class="tcr rb">994</td></tr>
+<tr><td class="tcc lb rb">1898</td> <td class="tcc rb">3459</td> <td class="tcr rb">492</td> <td class="tcr rb">922</td> <td class="tcc rb">402</td> <td class="tcr rb">1136</td></tr>
+<tr><td class="tcc lb rb">1899</td> <td class="tcc rb">3861</td> <td class="tcr rb">572</td> <td class="tcr rb">558</td> <td class="tcc rb">281</td> <td class="tcr rb">1158</td></tr>
+<tr><td class="tcc lb rb">1900</td> <td class="tcc rb">2129*</td> <td class="tcr rb">477*</td> <td class="tcr rb">423*</td> <td class="tcc rb">243*</td> <td class="tcr rb">593*</td></tr>
+<tr><td class="tcc lb rb">1901</td> <td class="tcc rb">1830*</td> <td class="tcr rb">349*</td> <td class="tcr rb">264*</td> <td class="tcc rb">213*</td> <td class="tcr rb">680*</td></tr>
+
+<tr><td class="tcc allb" colspan="6">Values.</td></tr>
+
+<tr><td class="tcc lb rb">1892</td> <td class="tcc rb">1354</td> <td class="tcr rb">297</td> <td class="tcr rb">200</td> <td class="tcc rb">135</td> <td class="tcr rb">394</td></tr>
+<tr><td class="tcc lb rb">1893</td> <td class="tcc rb">&ensp;844</td> <td class="tcr rb">347</td> <td class="tcr rb">332</td> <td class="tcc rb">195</td> <td class="tcr rb">530</td></tr>
+<tr><td class="tcc lb rb">1894</td> <td class="tcc rb">1389</td> <td class="tcr rb">411</td> <td class="tcr rb">302</td> <td class="tcc rb">167</td> <td class="tcr rb">470</td></tr>
+<tr><td class="tcc lb rb">1895</td> <td class="tcc rb">&ensp;960</td> <td class="tcr rb">167</td> <td class="tcr rb">166</td> <td class="tcc rb">&ensp;96</td> <td class="tcr rb">487</td></tr>
+<tr><td class="tcc lb rb">1896</td> <td class="tcc rb">1582</td> <td class="tcr rb">207</td> <td class="tcr rb">242</td> <td class="tcc rb">106</td> <td class="tcr rb">443</td></tr>
+<tr><td class="tcc lb rb">1897</td> <td class="tcc rb">1187</td> <td class="tcr rb">378</td> <td class="tcr rb">498</td> <td class="tcc rb">178</td> <td class="tcr rb">495</td></tr>
+<tr><td class="tcc lb rb">1898</td> <td class="tcc rb">1108</td> <td class="tcr rb">222</td> <td class="tcr rb">435</td> <td class="tcc rb">231</td> <td class="tcr rb">550</td></tr>
+<tr><td class="tcc lb rb">1899</td> <td class="tcc rb">1186</td> <td class="tcr rb">266</td> <td class="tcr rb">294</td> <td class="tcc rb">154</td> <td class="tcr rb">588</td></tr>
+<tr><td class="tcc lb rb">1900</td> <td class="tcc rb">1225</td> <td class="tcr rb">367</td> <td class="tcr rb">393</td> <td class="tcc rb">308</td> <td class="tcr rb">595</td></tr>
+<tr><td class="tcc lb rb">1901</td> <td class="tcc rb">1183</td> <td class="tcr rb">296</td> <td class="tcr rb">244</td> <td class="tcc rb">214</td> <td class="tcr rb">695</td></tr>
+<tr><td class="tcc lb rb bb">1908</td> <td class="tcc rb bb">2079</td> <td class="tcr rb bb">515</td> <td class="tcr rb bb">428</td> <td class="tcc rb bb">235</td> <td class="tcr rb bb">728</td></tr>
+
+<tr><td class="tcc" colspan="6">* Thousands of cwts.</td></tr>
+</table>
+
+<p>In 1908 the outlay of the United Kingdom upon imported raw
+fruits, such as can easily be produced at home, was £4,195,654,
+made up as follows:</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcl">Apples</td> <td class="tcr rb">£2,079,703</td> <td class="tcl">Plums</td> <td class="tcr">£428,966</td></tr>
+<tr><td class="tcl">Grapes</td> <td class="tcr rb">728,026</td> <td class="tcl">Currants</td> <td class="tcr">121,852</td></tr>
+<tr><td class="tcl">Pears</td> <td class="tcr rb">515,914</td> <td class="tcl">Apricots and peaches</td> <td class="tcr">60,141</td></tr>
+<tr><td class="tcl">Cherries</td> <td class="tcr rb">235,523</td> <td class="tcl">Gooseberries</td> <td class="tcr">25,529</td></tr>
+</table>
+
+<p>In addition about £280,000 was spent upon &ldquo;unenumerated&rdquo; raw
+fruit, and £560,000 on nuts other than almonds &ldquo;used as fruit,&rdquo;
+which would include walnuts and filberts, both produced at home.
+It is certain, therefore, that the expenditure on imported fruits,
+such as are grown within the limits of the United Kingdom, exceeds
+four millions sterling per annum. The remainder of the outlay on
+imported fruit in 1908, amounting to over £5,000,000, was made
+up of £2,269,651 for oranges, £471,713 for lemons, £1,769,249 for
+bananas, and £560,301 for almond-nuts; these cannot be grown on
+an industrial scale in the British Isles.</p>
+
+<p>It may be interesting to note the source of some of these imported
+fruits. The United States and Canada send most of the apples,
+the quantity for 1907 being 1,413,000 cwt. and 1,588,000 cwt.
+respectively, while Australia contributes 280,000 cwt. Plums
+come chiefly from France (200,000 cwt.), followed with 38,000 cwt.
+from Germany and 28,000 cwt. from the Netherlands. Pears are
+imported chiefly from France (204,000 cwt.) and Belgium (176,000);
+but the Netherlands send 52,000 cwt., and the United States 24,000
+cwt. The great bulk of imported tomatoes comes from the Canary
+Islands, the quantity in 1907 being 604,692 cwt. The Channel
+Islands also sent 223,800 cwt., France 115,500 cwt., Spain 169,000
+cwt., and Portugal a long way behind with 11,700 cwt. Most of
+the strawberries imported come from France (33,800 cwt.) and the
+Netherlands (10,300 cwt.).</p>
+</div>
+
+<p><i>Fruit-growing in Kent</i>.&mdash;Kent is by far the largest fruit-growing
+county in England. For centuries that county has been famous
+for its fruit, and appears to have been the centre for the distribution
+of trees and grafts throughout the country. The cultivation
+<span class="pagenum"><a name="page263" id="page263"></a>263</span>
+of fruit land upon farms in many parts of Kent has always been
+an important feature in its agriculture. An excellent description
+of this noteworthy characteristic of Kentish farming is contained
+in a comprehensive paper on the agriculture of Kent by Mr
+Charles Whitehead,<a name="fa1a" id="fa1a" href="#ft1a"><span class="sp">1</span></a> whose remarks, with various additions and
+modifications, are here reproduced.</p>
+
+<div class="condensed">
+<p>Where the conditions are favourable, especially in East and Mid
+Kent, there is a considerable acreage of fruit land attached to each
+farm, planted with cherry, apple, pear, plum and damson trees,
+and with bush fruits, or soft fruits as they are sometimes called,
+including gooseberries, currants, raspberries, either with or without
+standard trees, and strawberries, and filberts and cob-nuts in Mid
+Kent. This acreage has largely increased, and will no doubt continue
+to increase, as, on the whole, fruit-growing has been profitable
+and has materially benefited those fortunate enough to have fruit
+land on their farms. There are also cultivators who grow nothing
+but fruit. These are principally in the district of East Kent, between
+Rochester and Canterbury, and in the district of Mid Kent near
+London, and they manage their fruit land, as a rule, better than
+farmers, as they give their undivided attention to it and have more
+technical knowledge. But there has been great improvement of
+late in the management of fruit land, especially of cherry and apple
+orchards, the grass of which is fed off by animals having corn or
+cake, or the land is well manured. Apple trees are grease-banded
+and sprayed systematically by advanced fruit-growers to prevent
+or check the attacks of destructive insects. Far more attention is
+being paid to the selection of varieties of apples and pears having
+colour, size, flavour, keeping qualities, and other attributes to meet
+the tastes of the public, and to compete with the beautiful fruit that
+comes from the United States and Canada.</p>
+
+<p>Of the various kinds of apples at present grown in Kent mention
+should be made of Mr Gladstone, Beauty of Bath, Devonshire
+Quarrenden, Lady Sudely, Yellow Ingestre and Worcester Pearmain.
+These are dessert apples ready to pick in August and September,
+and are not stored. For storing, King of the Pippins, Cox&rsquo;s Orange
+Pippin (the best dessert apple in existence), Cox&rsquo;s Pomona, Duchess,
+Favourite, Gascoyne&rsquo;s Scarlet Seedling, Court Pendu Plat, Baumann&rsquo;s
+Red Reinette, Allington Pippin, Duke of Devonshire and Blenheim
+Orange. Among kitchen apples for selling straight from the trees
+the most usually planted are Lord Grosvenor, Lord Suffield, Keswick
+Codlin, Early Julian, Eclinville Seedling, Pott&rsquo;s Seedling, Early
+Rivers, Grenadier, Golden Spire, Stirling Castle and Domino. For
+storing, the cooking sorts favoured now are Stone&rsquo;s or Loddington,
+Warner&rsquo;s King, Wellington, Lord Derby, Queen Caroline, Tower of
+Glamis, Winter Queening, Lucombe&rsquo;s Seedling, Bismarck, Bramley&rsquo;s
+Seedling, Golden Noble and Lane&rsquo;s Prince Albert. Almost all these
+will flourish equally as standards, pyramids and bushes. Among
+pears are Hessle, Clapp&rsquo;s Favourite, William&rsquo;s Bon Chrétien, Beurré
+de Capiaumont, Fertility, Beurré Riche, Chissel, Beurré Clairgeau,
+Louise Bonne of Jersey, Doyenne du Comice and Vicar of Winkfield.
+Among plums, Rivers&rsquo;s Early Prolific, Tsar, Belgian Purple, Black
+Diamond, Kentish Bush Plum, Pond&rsquo;s Seedling, Magnum Bonum
+and Victoria are mainly cultivated. The damson known as Farleigh
+Prolific, or Crittenden&rsquo;s, is most extensively grown throughout the
+county, and usually yields large crops, which make good prices.
+As a case in point, purchasers were offering to contract for quantities
+of this damson at £20 per ton in May of 1899, as the prospects of the
+yield were unsatisfactory. On the other hand, in one year recently
+when the crop was abnormally abundant, some of the fruit barely
+paid the expenses of sending to market. The varieties of cherries
+most frequently grown are Governor Wood, Knight&rsquo;s Early Black,
+Frogmore Blackheart, Black Eagle, Waterloo, Amberheart, Bigarreau,
+Napoleon Bigarreau and Turk. A variety of cherry known as the
+Kentish cherry, of a light red colour and fine subacid flavour, is
+much grown in Kent for drying and cooking purposes. Another
+cherry, similar in colour and quality, which comes rather late, known
+as the Flemish, is also extensively cultivated, as well as the very
+dark red large Morello, used for making cherry brandy. These three
+varieties are grown extensively as pyramids, and the last-named
+also on walls and sides of buildings. Sometimes the cherry crop is
+sold by auction to dealers, who pick, pack and consign the fruit to
+market. Large prices are often made, as much as £80 per acre being
+not uncommon. The crop on a large cherry orchard in Mid Kent
+has been sold for more than £100 per acre.</p>
+
+<p>Where old standard trees have been long neglected and have
+become overgrown by mosses and lichens, the attempts made to
+improve them seldom succeed. The introduction of bush fruit trees
+dwarfed by grafting on the Paradise stock has been of much advantage
+to fruit cultivators, as they come into bearing in two or three years,
+and are more easily cultivated, pruned, sprayed and picked than
+standards. Many plantations of these bush trees have been formed in
+Kent of apples, pears and plums. Half standards and pyramids have
+also been planted of these fruits, as well as of cherries. Bushes of
+gooseberries and currants, and clumps or stools of raspberry canes,
+have been planted to a great extent in many parts of the East and
+Mid divisions of Kent, but not much in the Weald, where apples are
+principally grown. Sometimes fruit bushes are put in alternate rows
+with bush of standard trees of apple, pear, plum or damson, or they
+are planted by themselves. The distances apart for planting are generally
+for cherry and apple trees on grass 30 ft. by 30 ft.; for standard
+apples and pear trees from 20 ft. to 24 ft. upon arable land, with bush
+fruit, as gooseberries and currants, under them. These are set 6 ft. by
+6 ft. apart, and 5 ft. by 2 ft. for raspberries, and strawberries 2 ft. 6 in.
+to 3 ft. by 1 ft. 6 in. to 1 ft. 3 in. apart. On some fruit farms bush
+or dwarf trees&mdash;apples, pears, plums&mdash;are planted alone, at distances
+varying from 8 ft. to 10 ft. apart, giving from 485 to 680 bush trees
+per acre, nothing being grown between them except perhaps strawberries
+or vegetables during the first two or three years. It is believed
+that this is the best way of ensuring fruit of high quality and colour.
+Another arrangement consists in putting standard apple or pear
+trees 30 ft. apart (48 trees per acre), and setting bush trees of apples
+or pears 15 ft. apart between them; these latter come quickly into
+bearing, and are removed when the standards are fully grown.
+Occasionally gooseberry or currant bushes, or raspberry canes or
+strawberry plants, are set between the bush trees, and taken away
+directly they interfere with the growth of these. Half standard
+apple or plum trees are set triangularly 15 ft. apart, and strawberry
+plants at a distance of 1½ ft. from plant to plant and 2½ ft. from row
+to row. Or currant or gooseberry bushes are set between the half
+standards, and strawberry plants between these.</p>
+
+<p>These systems involve high farming. The manures used are
+London manure, where hops are not grown, and bone meal, super-phosphate,
+rags, shoddy, wool-waste, fish refuse, nitrate of soda,
+kainit and sulphate of ammonia. Where hops are grown the London
+manure is wanted for them. Fruit plantations are always dug by
+hand with the Kent spud. Fruit land is never ploughed, as in the
+United States and Canada. The soil is levelled down with the
+&ldquo;Canterbury&rdquo; hoe, and then the plantations are kept free from
+weeds with the ordinary draw or &ldquo;plate&rdquo; hoe. The best fruit
+farmers spray fruit trees regularly in the early spring, and continue
+until the blossoms come out, with quassia and soft soap and paraffin
+emulsions, and a very few with Paris green only, where there is no
+under fruit, in order to prevent and check the constant attacks of
+the various caterpillars and other insect pests. This is a costly and
+laborious process, but it pays well, as a rule. The fallacy that fruit
+trees on grass land require no manure, and that the grass may be
+allowed to grow up to their trunks without any harm, is exploding,
+and many fruit farmers are well manuring their grass orchards and
+removing the grass for some distance round the stems, particularly
+where the trees are young.</p>
+
+<p>Strawberries are produced in enormous quantities in the northern
+part of the Mid Kent district round the Crays, and from thence to
+Orpington; also near Sandwich, and to some extent near Maidstone.
+Raspberry canes have been extensively put in during the last few
+years, and in some seasons yield good profits. There is a very great
+and growing demand for all soft fruits for jam-making, and prices
+are fairly good, taking an average of years, notwithstanding the
+heavy importations from France, Belgium, Holland, Spain and Italy.
+The extraordinary increase in the national demand for jam and other
+fruit preserves has been of great benefit to Kent fruit producers.
+The cheapness of duty-free sugar, as compared with sugar paying
+duty in the United States and other large fruit-producing countries,
+afforded one of the very few advantages possessed by British
+cultivators, but the reimposition of the sugar duty in the United
+Kingdom in 1901 has modified the position in this respect. Jam
+factories were established in several parts of Kent about 1889 or
+1890, but most of them collapsed either from want of capital or from
+bad management. There are still a few remaining, principally in
+connexion with large fruit farms. One of these is at Swanley, whose
+energetic owners farm nearly 2000 acres of fruit land in Kent. The
+fruit grown by them that will not make satisfactory prices in a fresh
+raw state is made into jam, or if time presses it is first made into
+pulp, and kept until the opportunity comes for making it into jam.
+In this factory there are fifteen steam-jacketed vats in one row, and
+six others for candied peel. A season&rsquo;s output on a recent occasion
+comprised about 3500 tons of jam, 850 tons of candied peel and
+750 gross (108,000 bottles) of bottled fruit. A great deal of the fruit
+preserved is purchased, whilst much of that grown on the farms is
+sold. A strigging machine is employed, which does as much work
+as fifty women in taking currants off their strigs or stalks. Black
+currant pulp is stored in casks till winter, when there is time to
+convert it into jam. Strawberries cannot be pulped to advantage,
+but it is otherwise with raspberries, the pulp of which is largely made.
+Apricots for jam are obtained chiefly from France and Spain. There
+is another flourishing factory near Sittingbourne worked on the
+same lines. It is very advantageous to fruit farmers to have jam
+factories in connexion with their farms or to have them near, as
+they can thoroughly grade their fruit, and send only the best to market,
+thus ensuring a high reputation for its quality. Carriage is saved,
+which is a serious charge, though railway rates from Kent to the great
+manufacturing towns and to Scotland are very much less proportionally
+than those to London, and consequently Kent growers send
+increasing quantities to these distant markets, where prices are
+better, not being so directly interfered with by imported fruit,
+which generally finds its way to London.</p>
+
+<p>Kentish fruit-growers are becoming more particular in picking,
+<span class="pagenum"><a name="page264" id="page264"></a>264</span>
+grading, packing and storing fruit, as well as in marketing it. A
+larger quantity of fruit is now carefully stored, and sent to selected
+markets as it ripens, or when there is an ascertained demand, as it
+is found that if it is consigned to market direct from the trees there
+must frequently be forced sales and competition with foreign fruit
+that is fully matured and in good order. It was customary formerly
+for Kentish growers to consign all their fruit to the London markets;
+now a good deal of it is sent to Manchester, Birmingham, Liverpool,
+Sheffield, Newcastle and other large cities. Some is sent even to
+Edinburgh and Glasgow. Many large growers send no fruit to
+London now. It is by no means uncommon for growers to sell
+their fruit crops on the trees or bushes by auction or private treaty,
+or to contract to supply a stipulated quantity of specified fruit, say
+of currants, raspberries or strawberries, to jam manufacturers. There
+is a considerable quantity of fruit, such as grapes, peaches, nectarines,
+grown under glass, and this kind of culture tends to increase.</p>
+
+<p>Filberts and cob-nuts are a special product of Kent, in the neighbourhood
+of Maidstone principally, and upon the Ragstone soils, certain
+conditions of soil and situation being essential for their profitable
+production. A part of the filbert and cob-nut crop is picked green
+in September, as they do well for dessert, though their kernels are
+not large or firm, and it pays to sell them green, as they weigh more
+heavily. One grower in Mid Kent has 100 acres of nuts, and has
+grown 100 tons in a good year. The average price of late years has
+been about 5d. per &#8468;, which would make the gross return of the
+100 acres amount to £4660. Kentish filberts have long been proverbial
+for their excellence. Cobs are larger and look better for
+dessert, though their flavour is not so fine. They are better croppers,
+and are now usually planted. This cultivation is not much extending,
+as it is very long before the trees come into full bearing. The London
+market is supplied entirely with these nuts from Kent, and there is
+some demand in America for them. Filbert and cob trees are most
+closely pruned. All the year&rsquo;s growth is cut away except the very
+finest young wood, which the trained eye of the tree-cutter sees at
+a glance is blossom-bearing. The trees are kept from 5½ to 7 ft.
+high upon stems from 1½ to 2 ft. high, and are trained so as to form
+a cup of from 7 to 8 ft. in diameter.</p>
+
+<p>There seems no reason to expect any decrease in the acreage of
+fruit land in Kent, and if the improvement in the selection of varieties
+and in the general management continues it will yet pay. A hundred
+years ago every one was grubbing fruit land in order that hops might
+be planted, and for this many acres of splendid cherry orchards were
+sacrificed. Now the disposition is to grub hop plants and substitute
+apples, plums, or small fruit or cherry trees.</p>
+
+<p><i>Fruit-growing in other Districts.</i>&mdash;The large fruit plantations in
+the vicinity of London are to be found mostly in the valley of the
+Thames, around such centres as Brentford, Isleworth, Twickenham,
+Heston, Hounslow, Cranford and Southall. All varieties of orchard
+trees, but mostly apples, pears, and plums and small fruit, are grown
+in these districts, the nearness of which to the metropolitan fruit
+market at Covent Garden is of course an advantage. Some of the
+orchards are old, and are not managed on modern principles. They
+contain, moreover, varieties of fruit many of which are out of date
+and would not be employed in establishing new plantations. In
+the better-managed grounds the antiquated varieties have been
+removed, and their places taken by newer and more approved types.
+In addition to apples, pears, plums, damsons, cherries and quinces
+as top fruit, currants, gooseberries and raspberries are grown as
+bottom fruit. Strawberries are extensively grown in some of the
+localities, and in favourable seasons outdoor tomatoes are ripened and
+marketed.</p>
+
+<p>Fruit is extensively grown in Cambridgeshire and adjacent counties
+in the east of England. A leading centre is Cottenham, where the
+Lower Greensand crops out and furnishes one of the best of soils for
+fruit-culture. In Cottenham about a thousand acres are devoted
+to fruit, and nearly the same acreage to asparagus, which is, however,
+giving place to fruit. Currants, gooseberries and strawberries are the
+most largely grown, apples, plums and raspberries following. Of
+varieties of plums the Victoria is first in favour, and then Rivers&rsquo;s
+Early Prolific, Tsar and Gisborne. London is the chief market,
+as it receives about half the fruit sent away, whilst a considerable
+quantity goes to Manchester, and some is sent to a neighbouring jam
+factory at Histon, where also a moderate acreage of fruit is grown.
+Another fruit-growing centre in Cambridgeshire is at Willingham,
+where&mdash;besides plums, gooseberries and raspberries&mdash;outdoor
+tomatoes are a feature. Greengages are largely grown near Cambridge.
+Wisbech is the centre of an extensive fruit district,
+situated partly in Cambridgeshire and partly in Norfolk. Gooseberries,
+strawberries and raspberries are largely grown, and as many
+as 80 tons of the first-named fruit have been sent away from Wisbech
+station in a single day. In the fruit-growing localities of Huntingdonshire
+apples, plums and gooseberries are the most extensively grown,
+but pears, greengages, cherries, currants, strawberries and raspberries
+are also cultivated. As illustrating variations in price, it may be
+mentioned that about the year 1880 the lowest price for gooseberries
+was £10 per ton, whereas it has since been down to £4. Huntingdonshire
+fruit is sent chiefly to Yorkshire, Scotland and South Wales,
+but railway freights are high.</p>
+
+<p>Essex affords a good example of successful fruit-farming at Tiptree
+Heath, near Kelvedon, where under one management about 260
+acres out of a total of 360 are under fruit. The soil, a stiff loam,
+grows strawberries to perfection, and 165 acres are allotted to this
+fruit. The other principal crops are 43 acres of raspberries and 30
+acres of black currants, besides which there are small areas of red
+currants, gooseberries, plums, damsons, greengages, cherries, apples,
+quinces and blackberries. The variety of strawberry known as the
+Small Scarlet is a speciality here, and it occupies 55 acres, as it
+makes the best of jam. The Paxton, Royal Sovereign and Noble
+varieties are also grown. Strawberries stand for six or seven years
+on this farm, and begin to yield well when two years old. A jam
+factory is worked in conjunction with the fruit farm. Pulp is not
+made except when there is a glut of fruit. Perishable fruit intended
+for whole-fruit preserves is never held over after it is gathered.
+The picking of strawberries begins at 4 <span class="scs">A.M.</span>, and the first lot is made
+into jam by 6 <span class="scs">A.M.</span></p>
+
+<p>Hampshire, like Cambridgeshire and Norfolk, are the only counties
+in which the area of small fruit exceeds that of orchards. The returns
+for 1908 show that Hampshire had 3320 acres of small fruit to 2236
+acres of orchards; Cambridge had 6878 acres of small fruit to 5221
+of orchards; and Norfolk had 5876 acres of small fruit against
+5188 acres of orchards. Compared with twenty years previously,
+the acreage of small fruit had trebled. This is largely due in Hampshire
+to the extension of strawberry culture in the Southampton
+district, where the industry is in the hands of many small growers,
+few of whom cultivate more than 20 acres each. Sarisbury and
+Botley are the leading parishes in which the business is carried on.
+Most of the strawberry holdings are from half an acre to 5 acres in
+extent, a few are from 5 to 10 acres, fewer still from 10 to 20 acres
+and only half-a-dozen over that limit. Runners from one-year plants
+are used for planting, being found more fruitful than those from
+older plants. Peat-moss manure from London stables is much
+used, but artificial manures are also employed with good results.
+Shortly after flowering the plants are bedded down with straw at
+the rate of about 25 cwt. per acre. Picking begins some ten days
+earlier than in Kent, at a date between 1st June and 15th June.
+The first week&rsquo;s gathering is sent mostly to London, but subsequently
+the greater part of the fruit goes to the Midlands and to Scotland and
+Ireland.</p>
+
+<p>In recent years fruit-growing has much increased in South
+Worcestershire, in the vicinity of Evesham and Pershore. Hand-lights
+are freely used in the market gardens of this district for the
+protection of cucumbers and vegetable marrows, besides which
+tomatoes are extensively grown out of doors. At one time the egg
+plum and the Worcester damson were the chief fruit crops, apples and
+cherries ranking next, pears being grown to only a moderate extent.
+According to the 1908 returns, however, apples come first, plums
+second, pears third and cherries fourth. In a prolific season a single
+tree of the Damascene or Worcester damson will yield from 400 to
+500 &#8468; of fruit. There is a tendency to grow plum trees in the bush
+shape, as they are less liable than standards to injury from wind.
+The manures used include soot, fish guano, blood manure and
+phosphates&mdash;basic slag amongst the last-named. In the Pershore
+district, where there is a jam factory, plums are the chief tree fruit,
+whilst most of the orchard apples and pears are grown for cider and
+perry. Gooseberries are a feature, as are also strawberries, red and
+black currants and a few white, but raspberries are little grown.
+The soil, a strong or medium loam of fair depth, resting on clay, is so
+well adapted to plums that trees live for fifty years. In order to check
+the ravages of the winter moth, plum and apple trees are grease-banded
+at the beginning of October and again at the end of March.
+The trees are also sprayed when necessary with insecticidal solutions.
+Pruning is done in the autumn. An approved distance apart at
+which to grow plum trees is 12 ft. by 12 ft. In the Earl of Coventry&rsquo;s
+fruit plantation, 40 acres in extent, at Croome Court, plums and
+apples are planted alternately, the bottom fruit being black currants,
+which are less liable to injury from birds than are red currants or
+gooseberries. Details concerning the methods of cultivation of
+fruit and flowers in various parts of England, the varieties commonly
+grown, the expenditure involved, and allied matters, will be found in
+Mr W.E. Bear&rsquo;s papers in the <i>Journal of the Royal Agricultural
+Society</i> in 1898 and 1899.</p>
+
+<p>Apart altogether from market gardening and commercial fruit-growing,
+it must be borne in mind that an enormous business is
+done in the raising of young fruit-trees every year. Hundreds of
+thousands of apples, pears, plums, cherries, peaches, nectarines and
+apricots are budded or grafted each year on suitable stocks. They
+are trained in various ways, and are usually fit for sale the third
+year. These young trees replace old ones in private and commercial
+gardens, and are also used to establish new plantations in different
+parts of the kingdom.</p>
+
+<p><i>The Woburn Experimental Fruit Farm.</i>&mdash;The establishment in
+1894 of the experimental fruit farm at Ridgmont, near Woburn,
+Beds, has exercised a healthy influence upon the progress and
+development of fruit-farming in England. The farm was founded
+and carried on by the public-spirited enterprise of the Duke of
+Bedford and Mr Spencer U. Pickering, the latter acting as director.
+The main object of the experimental station was &ldquo;to ascertain facts
+relative to the culture of fruit, and to increase our knowledge of, and
+to improve our practice in, this industry.&rdquo; The farm is 20 acres in
+extent, and occupies a field which up to June 1894 had been used as
+<span class="pagenum"><a name="page265" id="page265"></a>265</span>
+arable land for the ordinary rotation of farm crops. The soil is a
+sandy loam 9 or 10 in. deep, resting on a bed of Oxford Clay. Although
+it contains a large proportion of sand, the land would generally be
+termed very heavy, and the water often used to stand on it in places
+for weeks together in a wet season. The tillage to which the ground
+was subjected for the purposes of the fruit farm much improved its
+character, and in dry weather it presents as good a tilth as could be
+desired. Chemical analyses of the soil from different parts of the field
+show such wide differences that it is admitted to be by no means an
+ideal one for experimental purposes. Without entering upon further
+details, it may be useful to give a summary of the chief results
+obtained.</p>
+
+<p>Apples have been grown and treated in a variety of ways, but of
+the different methods of treatment careless planting, coupled with
+subsequent neglect, has given the most adverse results, the crop
+of fruit being not 5% of that from trees grown normally. Of the
+separate deleterious items constituting total neglect, by far the most
+effective was the growth of weeds on the surface; careless planting,
+absence of manure, and the omission of trenching all had comparatively
+little influence on the results. A set of trees that had been
+carelessly planted and neglected, but subsequently tended in the
+early part of 1896, were in the autumn of that year only 10%
+behind their normally-treated neighbours, thus demonstrating that
+the response to proper attention is prompt. The growth of grass
+around young apple trees produced a very striking effect, the injury
+being much greater than that due to weeds. It is possible, however,
+that in wet years the ill-effects of both grass and weeds would be
+less than in dry seasons. Nevertheless, the grass-grown trees, after
+five years, were scarcely bigger than when planted, and the actual
+increase in weight which they showed during that time was about
+eighteen times smaller than in the case of similar trees in tilled
+ground. It is believed that one of the main causes of the ill-effects
+is the large increase in the evaporation of water from the soil which
+is known to be produced by grass, the trees being thereby made to
+suffer from drought, with constant deprivation of other nourishment
+as well. That grass growing round young apple trees is deleterious
+was a circumstance known to many horticulturists, but the extent to
+which it interferes with the development of the trees had never before
+been realized. Thousands of pounds are annually thrown away in England
+through want of knowledge of this fact. Yet trees will flourish
+in grass under certain conditions. Whether the dominant factor is
+the age (or size) of the tree has been investigated by grassing over
+trees which have hitherto been in the open ground, and the results
+appear to indicate that the grass is as deleterious to the older trees as
+it was to the younger ones. Again, it appears to have been demonstrated
+that young apple trees, at all events in certain soils, require
+but little or no manure in the early stages of their existence, so
+that in this case also large sums must be annually wasted upon
+manurial dressings which produce no effects. The experiments
+have dealt with dwarf trees of Bramley, Cox and Potts, six trees
+of each variety constituting one investigation. Some of the experiments
+were repeated with Stirling Castle, and others with standard
+trees of Bramley, Cox and Lane&rsquo;s Prince Albert. All were planted
+in 1894-1895, the dwarfs being then three years old and the standards
+four. In each experiment the &ldquo;normal&rdquo; treatment is altered in
+some one particular, this normal treatment consisting of planting
+the trees carefully in trenched ground, and subsequently keeping
+the surface clean; cutting back after planting, pruning moderately
+in autumn, and shortening the growths when it appeared necessary
+in summer; giving in autumn a dressing of mixed mineral manures,
+and in February one of nitrate of soda, this dressing being probably
+equivalent to one of 12 tons of dung per acre. In the experiments
+on branch treatment, the bad effects of omitting to cut the trees back
+on planting, or to prune them subsequently, is evident chiefly in
+the straggling and bad shape of the resulting trees, but such trees also
+are not so vigorous as they should be. The quantity of fruit borne,
+however, is in excess of the average. The check on the vigour and
+growth of a tree by cutting or injuring its roots is in marked contrast
+with the effects of a similar interference with the branches. Trees
+which had been root-pruned each year were in 1898 little more than
+half as big as the normal trees, whilst those root-pruned every second
+year were about two-thirds as big as the normal. The crops borne
+by these trees were nevertheless heavy in proportion to the size of
+the trees. Such frequent root-pruning is not, of course, a practice
+which should be adopted. It was found that trees which had been
+carefully lifted every other year and replanted at once experienced
+no ill-effects from the operation; but in a case where the trees after
+being lifted had been left in a shed for three days before replanting&mdash;which
+would reproduce to a certain extent the conditions experienced
+when trees are sent out from a nursery&mdash;material injury was suffered,
+these trees after four years being 28% smaller than similar ones
+which had not been replanted. Sets of trees planted respectively
+in November, January and March have, on the whole, shown
+nothing in favour of any of these different times for planting
+purposes. Some doubt is thrown on the accepted view that there
+is a tendency, at any rate with young apple and pear trees, to fruit
+in alternate seasons.</p>
+
+<p>Strawberries of eighty-five different varieties have been experimented
+with, each variety being represented in 1900 by plants of
+five different ages, from one to five years. In 1896 and 1898 the
+crops of fruit were about twice as heavy as in 1897 and 1899, but
+it has not been found possible to correlate these variations with the
+meteorological records of the several seasons. Taking the average of all
+the varieties, the relative weights of crop per plant, when these are
+compared with the two-year-old plants in the same season, are, for
+the five ages of one to five years, 31, 100, 122, 121 and 134, apparently
+showing that the bearing power increases rapidly up to two years,
+less rapidly up to three years, after which age it remains practically
+constant. The relative average size of the berries shows a deterioration
+with the age of the plant. The comparative sizes from plants of
+one to five years old were 115, 100, 96, 91 and 82 respectively. If
+the money value of the crop is taken to be directly dependent on its
+total weight, and also on the size of the fruits, the relative values
+of the crop for the different ages would be 34, 100, 117, 111 and 110,
+so that, on the Ridgmont ground, strawberry plants could be profitably
+retained up to five years and probably longer. As regards
+what may be termed the order of merit of different varieties of
+strawberries, it appears that even small differences in position and
+treatment cause large variations, not only in the features of the
+crop generally, but also in the relative behaviour of the different
+varieties. The relative cropping power of the varieties under
+apparently similar conditions may often be expressed by a number
+five or tenfold as great in one case as in the other. A comparison
+of the relative behaviour of the same varieties in different seasons
+is attended by similar variations. The varying sensitiveness of
+different varieties of strawberry plants to small and undefinable
+differences in circumstances is indeed one of the most important
+facts brought to light in the experiments.</p>
+
+<p><i>Fruit Culture in Ireland.</i>&mdash;The following figures have been kindly
+supplied by the Irish Board of Agriculture, and deal with the acreage
+under fruit culture in Ireland up to the end of the year 1907.</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcl">1. <i>Orchard Fruit</i>&mdash;</td> <td class="tcr">Statute Acres.</td></tr>
+<tr><td class="tcl"> &emsp;&emsp; Apples</td> <td class="tcr">5829</td></tr>
+<tr><td class="tcl"> &emsp;&emsp; Pears</td> <td class="tcr">224</td></tr>
+<tr><td class="tcl"> &emsp;&emsp; Plums</td> <td class="tcr">223</td></tr>
+<tr><td class="tcl"> &emsp;&emsp; Damsons</td> <td class="tcr">138</td></tr>
+<tr><td class="tcl"> &emsp;&emsp; Other kinds</td> <td class="tcr">129</td></tr>
+<tr><td class="tcl"> &nbsp;</td> <td class="tcr">&mdash;&mdash;</td></tr>
+<tr><td class="tcl"> &nbsp;</td> <td class="tcr">Total &emsp;&emsp;&emsp;&emsp; 6543</td></tr>
+
+<tr><td class="tcl">2. <i>Small Fruit</i>&mdash;</td> <td class="tcr">&nbsp;</td></tr>
+<tr><td class="tcl"> &emsp;&emsp; Currants, black</td> <td class="tcr">234</td></tr>
+<tr><td class="tcl"> &emsp;&emsp; Currants, red and white</td> <td class="tcr">159</td></tr>
+<tr><td class="tcl"> &emsp;&emsp; Gooseberries</td> <td class="tcr">675</td></tr>
+<tr><td class="tcl"> &emsp;&emsp; Raspberries</td> <td class="tcr">374</td></tr>
+<tr><td class="tcl"> &emsp;&emsp; Strawberries</td> <td class="tcr">994</td></tr>
+<tr><td class="tcl"> &emsp;&emsp; Mixed fruit</td> <td class="tcr">2470</td></tr>
+<tr><td class="tcl"> &nbsp;</td> <td class="tcr">&mdash;&mdash;</td></tr>
+<tr><td class="tcl"> &nbsp;</td> <td class="tcr">Total &emsp;&emsp;&emsp;&emsp; 4906</td></tr>
+</table>
+
+<p>It therefore appears that while Ireland grows only about one-thirty-third
+the quantity of apples that England does, it is nevertheless
+nearly 5000 acres ahead of Scotland and about 2000 acres ahead of
+Wales. It grows 41 times fewer pears than England, but still is
+ahead of Scotland and a long way ahead of Wales in this fruit.
+There are 70 times fewer plums grown in Ireland than in England,
+and about the same in Scotland, while Wales does very little indeed.
+In small fruit Ireland is a long way behind Scotland in the culture
+of strawberries and raspberries, although with currants and gooseberries
+it is very close. Considering the climate, and the fact that
+there are, according to the latest available returns, over 62,000
+holdings above 1 acre but not exceeding 5 acres (having a total of
+224,000 acres), it is possible fruit culture may become more prevalent
+than it has been in the past.</p>
+</div>
+
+<p><i>The Flower-growing Industry.</i>&mdash;During the last two or three
+decades of the 19th century a very marked increase in flower
+production occurred in England. Notably was this the case in
+the neighbourhood of London, where, within a radius of 15 or
+20 m., the fruit crops, which had largely taken the place of garden
+vegetables, were themselves ousted in turn to satisfy the increasing
+demand for land for flower cultivation. No flower has entered
+more largely into the development of the industry than the
+narcissus or daffodil, of which there are now some 600 varieties.
+Comparatively few of these, however, are grown for market
+purposes, although all are charming from the amateur point of
+view. On some flower farms a dozen or more acres are devoted
+to narcissi alone, the production of bulbs for sale as well as of
+flowers for market being the object of the growers.</p>
+
+<p>In the London district the country in the Thames valley west
+of the metropolis is as largely occupied by flower farms as it is
+by fruit farms&mdash;in fact, the cultivation of flowers is commonly
+associated with that of fruit. In the vicinity of Richmond
+narcissi are extensively grown, as they also are more to the west
+in the Long Ditton district, and likewise around Twickenham,
+Isleworth, Hounslow, Feltham and Hampton. Roses come more
+into evidence in the neighbourhood of Hounslow, Cranford,
+<span class="pagenum"><a name="page266" id="page266"></a>266</span>
+Hillingdon and Uxbridge, and in some gardens daffodils and
+roses occupy alternate rows. In this district also such flowers
+as herbaceous paeonies, Spanish irises, German irises, Christmas
+roses, lilies of the valley, chrysanthemums, foxgloves, hollyhocks,
+wallflowers, carnations, &amp;c., are extensively grown in
+many market gardens. South of London is the Mitcham country,
+long noted for its production of lavender. The incessant growth
+of the lavender plant upon the same land, however, has led to
+the decline of this industry, which has been largely transferred
+to districts in the counties of Bedford, Essex and Hertford. At
+Mitcham, nevertheless, mixed flowers are very largely grown
+for the supply of the metropolis, and one farm alone has nearly
+100 acres under flowers and glass-houses. Chrysanthemums,
+asters, Iceland poppies, gaillardias, pansies, bedding calceolarias,
+zonal pelargoniums and other plants are cultivated in immense
+quantities. At Swanley and Eynsford, in Kent, flowers are
+extensively cultivated in association with fruit and vegetables.
+Narcissi, chrysanthemums, violets, carnations, campanulas,
+roses, pansies, irises, sweet peas, and many other flowers are here
+raised, and disposed of in the form both of cut flowers and of
+plants.</p>
+
+<p>The Scilly Isles are important as providing the main source
+of supply of narcissi to the English markets in the early months
+of the year. This trade arose almost by accident, for it was
+about the year 1865 that a box of narcissi sent to Covent Garden
+Market, London, realized £1; and the knowledge of this fact
+getting abroad, the farmers of the isles began collecting wild
+bulbs from the fields in order to cultivate them and increase their
+stocks. Some ten years, however, elapsed before the industry
+promised to become remunerative. In 1885 a Bulb and Flower
+Association was established to promote the industrial growth
+of flowers. The exports of flowers in that year reached 65 tons,
+and they steadily increased until 1893, when they amounted
+to 450 tons. A slight decline followed, but in 1896 the quantity
+exported was no less than 514 tons. This would represent
+upwards of 3½ million bunches of flowers, chiefly narcissi and
+anemones. Rather more than 500 acres are devoted to flower-growing
+in the isles, by far the greater part of this area being
+assigned to narcissi, whilst anemones, gladioli, marguerites,
+arum lilies, Spanish irises, pinks and wallflowers are cultivated
+on a much smaller scale. The great advantage enjoyed by the
+Scilly flower-growers is earliness of production, due to climatic
+causes; the soil, moreover, is well suited to flower culture and
+there is an abundance of sunshine. The long journey to London
+is somewhat of a drawback, in regard to both time and freight,
+but the earliness of the flowers more than compensates for this.
+Open-air narcissi are usually ready at the beginning of January,
+and the supply is maintained in different varieties up to the
+middle or end of May. The narcissus bulbs are usually planted
+in October, 4 in. by 3 in. apart for the smaller sorts and 6 in.
+by 4 to 6 in. for the larger. A compost of farmyard manure,
+seaweed, earth and road scrapings is the usual dressing, but
+nitrate of soda, guano and bones are also occasionally employed.
+A better plan, perhaps, is to manure heavily the previous crop,
+frequently potatoes, no direct manuring then being needed for
+the bulbs, these not being left in the ground more than two or
+three years. The expenses of cultivation are heavy, the cost
+of bulbs alone&mdash;of which it requires nearly a quarter of a million
+of the smaller varieties, or half as many of the largest, to plant
+an acre&mdash;being considerable. The polyanthus varieties of
+narcissus are likely to continue the most remunerative to the
+flower-growers of Scilly, as they flourish better in these isles
+than on the mainland.</p>
+
+<p>In the district around the Wash, in the vicinity of such towns
+as Wisbech, Spalding and Boston, the industrial culture of bulbs
+and flowers underwent great expansion in the period between
+1880 and 1909. At Wisbech one concern alone has a farm of
+some 900 acres, devoted chiefly to flowers and fruit, the soil
+being a deep fine alluvium. Roses are grown here, one field
+containing upwards of 100,000 trees. Nearly 20 acres are
+devoted to narcissi, which are grown for the bulbs and also,
+together with tulips, for cut flowers. Carnations are cultivated
+both in the field and in pots. Cut flowers are sent out in large
+quantities, neatly and effectively packed, the parcel post being
+mainly employed as a means of distribution. In the neighbourhood
+of Spalding crocuses and snowdrops are less extensively
+grown than used to be the case. On one farm, however, upwards
+of 20 acres are devoted to narcissi alone, whilst gladioli, lilies
+and irises are grown on a smaller scale. Around Boston narcissi
+are also extensively grown for the market, both bulbs and cut
+blooms being sold. The bulbs are planted 3 in. apart in rows, the
+latter being 9 in. apart, and are allowed to stand from two to
+four years.</p>
+
+<div class="condensed">
+<p>The imports of fresh flowers into the United Kingdom were not
+separately shown prior to 1900. In that year, however, their value
+amounted to £200,585, in 1901 to £225,011, in 1906 to £233,884, in
+1907 to £233,641, and in 1908 to £229,802, so that the trade showed
+a fairly steady condition. From the monthly totals quoted in
+Table VI. it would appear that the trade sinks to its minimum
+dimensions in the four months July to October inclusive, and that
+after September the business continually expands up to April,
+subsequent to which contraction again sets in. About one-half of
+the trade belongs practically to the three months of February,
+March and April.</p>
+
+<p class="pt2 center"><span class="sc">Table VI.</span>&mdash;<i>Values of Fresh Flowers imported into the United
+Kingdom.</i></p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcc allb">Month.</td> <td class="tcc allb">1906.</td> <td class="tcc allb">1907.</td> <td class="tcc allb">1908.</td></tr>
+
+<tr><td class="tcl lb rb">January</td> <td class="tcr rb">£31,035</td> <td class="tcr rb">£18,545</td> <td class="tcr rb">£29,180</td></tr>
+<tr><td class="tcl lb rb">February</td> <td class="tcr rb">34,647</td> <td class="tcr rb">25,541</td> <td class="tcr rb">30,541</td></tr>
+<tr><td class="tcl lb rb">March</td> <td class="tcr rb">50,232</td> <td class="tcr rb">42,611</td> <td class="tcr rb">35,185</td></tr>
+<tr><td class="tcl lb rb">April</td> <td class="tcr rb">30,809</td> <td class="tcr rb">50,418</td> <td class="tcr rb">42,681</td></tr>
+<tr><td class="tcl lb rb">May</td> <td class="tcr rb">22,980</td> <td class="tcr rb">21,767</td> <td class="tcr rb">23,129</td></tr>
+<tr><td class="tcl lb rb">June</td> <td class="tcr rb">17,641</td> <td class="tcr rb">18,358</td> <td class="tcr rb">16,904</td></tr>
+<tr><td class="tcl lb rb">July</td> <td class="tcr rb">3,386</td> <td class="tcr rb">4,509</td> <td class="tcr rb">3,467</td></tr>
+<tr><td class="tcl lb rb">August</td> <td class="tcr rb">1,646</td> <td class="tcr rb">1,539</td> <td class="tcr rb">1,081</td></tr>
+<tr><td class="tcl lb rb">September</td> <td class="tcr rb">852</td> <td class="tcr rb">736</td> <td class="tcr rb">953</td></tr>
+<tr><td class="tcl lb rb">October</td> <td class="tcr rb">4,481</td> <td class="tcr rb">3,180</td> <td class="tcr rb">4,504</td></tr>
+<tr><td class="tcl lb rb">November</td> <td class="tcr rb">17,506</td> <td class="tcr rb">15,763</td> <td class="tcr rb">15,097</td></tr>
+<tr><td class="tcl lb rb">December</td> <td class="tcr rb">18,669</td> <td class="tcr rb">30,674</td> <td class="tcr rb">27,080</td></tr>
+
+<tr><td class="tcl lb rb bb"> &emsp;&emsp; Total</td> <td class="tcr allb">£233,884</td> <td class="tcr allb">£233,641</td> <td class="tcr allb">£229,802</td></tr>
+</table>
+
+</div>
+
+<p><i>Hothouse Culture of Fruit and Flowers.</i>&mdash;The cultivation
+of fruit and flowers under glass has increased enormously
+since about the year 1880, especially in the neighbourhood
+of London, where large sums of money have been sunk in the
+erection and equipment of hothouses. In the parish of Cheshunt,
+Herts, alone there are upwards of 130 acres covered with glass,
+and between that place on the north and London on the south
+extensive areas of land are similarly utilized. In Middlesex,
+in the north, in the districts of Edmonton, Enfield, Ponders End
+and Finchley, and in the west from Isleworth to Hampton,
+Feltham, Hillingdon, Sipson and Uxbridge, many crops are now
+cultivated under glass. At Erith, Swanley, and other places in
+Kent, as also at Worthing, in Sussex, glass-house culture has
+much extended. A careful estimate puts the area of industrial
+hothouses in England at about 1200 acres, but it is probably
+much more than this. Most of the greenhouses are fixtures,
+but in some parts of the kingdom structures that move on rails
+and wheels are used, to enable the ground to be prepared in the
+open for one crop while another is maturing under glass. The
+leading products are grapes, tomatoes and cucumbers, the last-named
+two being true fruits from the botanist&rsquo;s point of view,
+though commercially included with vegetables. To these may
+be added on the same ground dwarf or French beans, and runner
+or climbing beans. Peaches, nectarines and strawberries are
+largely grown under glass, and, in private hothouses&mdash;from
+which the produce is used mainly for household consumption,
+and which are not taken into consideration here&mdash;pineapples,
+figs and other fruit. Conservative estimates indicate the average
+annual yield of hothouse grapes to be about 12 tons per acre and
+of tomatoes 20 tons. The greater part of the space in the hothouses
+is assigned to fruit, but whilst some houses are devoted
+exclusively to flowers, in others, where fruit is the main
+object, flowers are forced in considerable quantities in winter
+and early spring. The flowers grown under glass include tulips,
+hyacinths, primulas, cyclamens, spiraeas, mignonettes, fuchsias,
+<span class="pagenum"><a name="page267" id="page267"></a>267</span>
+calceolarias, roses, chrysanthemums, daffodils, arum lilies or
+callas, liliums, azaleas, eucharises, camellias, stephanotis,
+tuberoses, bouvardias, gardenias, heaths or ericas, poinsettias,
+lilies of the valley, zonal pelargoniums, tuberous and fibrous rooted
+begonias, and many others. There is an increasing demand for
+foliage hothouse plants, such as ferns, palms, crotons, aspidistras,
+araucarias, dracaenas, India-rubber plants, aralias, grevilleas,
+&amp;c. Berried plants like solanums and aucubas also find a ready
+sale, while the ornamental kinds of asparagus such as <i>sprengeri</i>
+and <i>plumosus</i> nanus, are ever in demand for trailing decorations,
+as well as myrsiphyilum. Special mention must be made of the
+winter or perpetual flowering carnations which are now grown
+by hundreds of thousands in all parts of the kingdom for
+decorative work during the winter season. The converse of
+forcing plants into early blossom is adopted with such an important
+crop as lily of the valley. During the summer season the
+crowns are placed in refrigerators with about 2 degrees of frost,
+and quantities are taken out as required every week and transferred
+to the greenhouse to develop. Tomatoes are grown
+largely in houses exclusively occupied by them, in which case two
+and sometimes three crops can be gathered in the year. In the
+Channel Islands, where potatoes grown under glass are lifted
+in April and May, in order to secure the high prices of the early
+markets, tomato seedlings are planted out from boxes into the
+ground as quickly as the potatoes are removed, the tomato
+planter working only a few rows behind the potato digger.
+The trade in imported tomatoes is so considerable that home
+growers are well justified in their endeavours to meet the demand
+more fully with native produce, whether raised under glass or
+in the open. Tomatoes were not separately enumerated in the
+imports previous to 1900. It has already been stated that in
+1900 the raw tomatoes imported amounted to 833,032 cwt.,
+valued at £792,339, and in 1901 to 793,991 cwt., valued at
+£734,051. From the monthly quantities given in Table VII.,
+it would appear that the imports are largest in June, July and
+August, about one-half of the year&rsquo;s total arriving during those
+three months. It is too early in June and July for home-grown
+outdoor tomatoes to enter into competition with the imported
+product, but home-grown hothouse tomatoes should be qualified
+to challenge this trade.</p>
+
+<p class="pt2 center"><span class="sc">Table</span> VII.&mdash;<i>Quantities of Tomatoes imported into the United
+Kingdom.</i></p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcc allb">Month.</td> <td class="tcc allb">1906.</td> <td class="tcc allb">1907.</td> <td class="tcc allb">1908.</td></tr>
+<tr><td class="tcl lb rb">January</td> <td class="tcr rb">61,940</td> <td class="tcr rb">56,022</td> <td class="tcr rb">73,409</td></tr>
+<tr><td class="tcl lb rb">February</td> <td class="tcr rb">58,187</td> <td class="tcr rb">58,289</td> <td class="tcr rb">69,350</td></tr>
+<tr><td class="tcl lb rb">March</td> <td class="tcr rb">106,458</td> <td class="tcr rb">98,028</td> <td class="tcr rb">86,928</td></tr>
+<tr><td class="tcl lb rb">April</td> <td class="tcr rb">103,273</td> <td class="tcr rb">109,057</td> <td class="tcr rb">74,917</td></tr>
+<tr><td class="tcl lb rb">May</td> <td class="tcr rb">67,933</td> <td class="tcr rb">114,041</td> <td class="tcr rb">88,901</td></tr>
+<tr><td class="tcl lb rb">June</td> <td class="tcr rb">62,906</td> <td class="tcr rb">144,379</td> <td class="tcr rb">127,793</td></tr>
+<tr><td class="tcl lb rb">July</td> <td class="tcr rb">238,362</td> <td class="tcr rb">150,907</td> <td class="tcr rb">171,978</td></tr>
+<tr><td class="tcl lb rb">August</td> <td class="tcr rb">180,046</td> <td class="tcr rb">102,600</td> <td class="tcr rb">124,757</td></tr>
+<tr><td class="tcl lb rb">September</td> <td class="tcr rb">114,860</td> <td class="tcr rb">101,198</td> <td class="tcr rb">119,224</td></tr>
+<tr><td class="tcl lb rb">October</td> <td class="tcr rb">52,678</td> <td class="tcr rb">67,860</td> <td class="tcr rb">75,722</td></tr>
+<tr><td class="tcl lb rb">November</td> <td class="tcr rb">41,513</td> <td class="tcr rb">66,522</td> <td class="tcr rb">74,292</td></tr>
+<tr><td class="tcl lb rb">December</td> <td class="tcr rb">36,316</td> <td class="tcr rb">66,591</td> <td class="tcr rb">73,012</td></tr>
+
+<tr><td class="tcl lb"> &emsp; Total</td> <td class="tcr allb">1,124,472</td> <td class="tcr allb">1,135,494</td> <td class="tcr allb">1,160,283</td></tr>
+
+<tr><td class="tcl lb bb"> &emsp; Value</td> <td class="tcr allb">£953,475</td> <td class="tcr allb">£1,135,499</td> <td class="tcr allb">£1,160,283</td></tr>
+</table>
+
+<p>An important feature of modern flower growing is the production
+and cultivation of what are known as &ldquo;hardy herbaceous
+perennials.&rdquo; Some 2000 or 3000 different species and varieties
+of these are now raised in special nurseries; and during the
+spring, summer and autumn seasons magnificent displays are
+to be seen not only in the markets but at the exhibitions in
+London and at the great provincial shows held throughout the
+kingdom. The production of many of these perennials is so
+easy that amateurs in several instances have taken it up as a
+business hobby; and in some cases, chiefly through advertising
+in the horticultural press, very lucrative concerns have been
+established.</p>
+
+<p>Ornamental flowering trees and shrubs constitute another
+feature of modern gardening. These are grown and imported
+by thousands chiefly for their sprays of blossom or foliage, and
+for planting in large or small gardens, public parks, &amp;c., for
+landscape effect. Indeed there is scarcely an easily grown plant
+from the northern or southern temperate zones that does not now
+find a place in the nursery or garden, provided it is sufficiently
+attractive to sell for its flowers, foliage or appearance.</p>
+
+<p><i>Conditions of the Fruit and Flower growing Industries.</i>&mdash;As
+regards open-air fruit-growing, the outlook for new ventures is
+perhaps brighter than in the hothouse industry, not&mdash;as Mr
+Bear has pointed out&mdash;because the area of fruit land in England
+is too small, but because the level of efficiency, from the selection
+of varieties to the packing and marketing of the produce, is very
+much lower in the former than in the latter branch of enterprise.
+In other words, whereas the practice of the majority of hothouse
+nurserymen is so skilled, so up-to-date, and so entirely under high
+pressure that a new competitor, however well trained, will find
+it difficult to rise above mediocrity, the converse is true of open-air
+fruit-growers. Many, and an increasing proportion, of the
+latter are thoroughly efficient in all branches of their business,
+and are in possession of plantations of the best market varieties
+of fruit, well cultivated, pruned and otherwise managed. But
+the extent of fruit plantations completely up to the mark in
+relation to varieties and treatment of trees and bushes, and in
+connexion with which the packing and marketing of the produce
+are equally satisfactory, is small in proportion to the total fruit
+area of the country. Information concerning the best treatment
+of fruit trees has spread widely in recent years, and old plantations,
+as a rule, suffer from the neglect or errors of the past,
+however skilful their present holders may be. Although the
+majority of professional market fruit-growers may be well up
+to the standard in skill, there are numerous contributors to
+the fruit supply who are either ignorant of the best methods
+of cultivation and marketing or careless in their application.
+The bad condition of the great majority of farm orchards is
+notorious, and many landowners, farmers and amateur gardeners
+who have planted fruit on a more or less extensive scale have
+mismanaged their undertakings. For these reasons new growers
+of open-air fruit for market have opportunities of succeeding by
+means of superiority to the majority of those with whom they
+will compete, provided that they possess the requisite knowledge,
+energy and capital. It has been asserted on sound authority
+that there is no chance of success for fruit-growers except in
+districts favourable as regards soil, climate and nearness to a
+railway or a good market; and, even under these conditions,
+only for men who have had experience in the industry and are
+prepared to devote their unremitting attention to it. Most
+important is it to a beginner that he should ascertain the varieties
+of fruit that flourish best in his particular district. Certain kinds
+seem to do well or fairly well in all parts of the country; others,
+whilst heavy croppers in some localities, are often unsatisfactory
+in others.</p>
+
+<p>As has been intimated, there is probably in England less room
+for expansion of fruit culture under glass than in the open.
+The large increase of glass-houses in modern times appears to
+have brought the supply of hothouse produce, even at greatly
+reduced prices, at least up to the level of the demand; and as
+most nurserymen continue to extend their expanse of glass,
+the prospect for new competitors is not a bright one. Moreover,
+the vast scale upon which some of the growers conduct the
+hothouse industry puts small producers at a great disadvantage,
+not only because the extensive producers can grow grapes and
+other fruit more economically than small growers&mdash;with the
+possible exception of those who do all or nearly all their own
+work&mdash;but also, and still more, because the former have greater
+advantages in transporting and marketing their fruit. There has,
+in recent years, been a much greater fall in the prices of hothouse
+than of open-air fruit, especially under the existing system of
+distribution, which involves the payment by consumers of 50
+to 100% more in prices than growers receive. The best openings
+for new nurseries are probably not where they are now to be
+found in large groups, and especially not in the neighbourhood
+<span class="pagenum"><a name="page268" id="page268"></a>268</span>
+of London, but in suitable spots near the great centres of population
+in the Midlands and the North, or big towns elsewhere not
+already well supplied with nurseries. By such a selection of a
+locality the beginner may build up a retail trade in hothouse
+fruit, or at least a trade with local fruiterers and grocers, thus
+avoiding railway charges and salesmen&rsquo;s commissions to a great
+extent, though it may often be advantageous to send certain
+kinds of produce to a distant market. Above all, a man who has
+no knowledge of the hothouse industry should avoid embarking
+his capital in it, trusting himself in the hands of a foreman, as
+experience shows that such a venture usually leads to disaster.
+Some years of training in different nurseries are desirable for
+any young man who is desirous of becoming a grower of hothouse
+fruits or flowers.</p>
+
+<p>There can be no doubt that flower-growing is greatly extending
+in England, and that competition among home growers is becoming
+more severe. Foreign supplies of flowers have increased,
+but not nearly as greatly in proportion as home supplies, and it
+seems clear that home growers have gained ground in relation
+to their foreign rivals, except with respect to flowers for the
+growth of which foreigners have extraordinary natural advantages.
+There seems some danger of the home culture of the narcissus
+being over-done, and the florists&rsquo; chrysanthemum appears to
+be produced in excess of the demand. Again, in the production
+of violets the warm and sunny South of France has an advantage
+not possessed by England, whilst Holland, likewise for climatic
+reasons, maintains her hold upon the hyacinth and tulip trade.
+Whether the production of flowers as a whole is gaining ground
+upon the demand or not is a difficult question to answer. It is
+true that the prices of flowers have fallen generally; but production,
+at any rate under glass, has been cheapened, and if a fair
+profit can be obtained, the fall in prices, without which the
+existing consumption of flowers would be impossible, does not
+necessarily imply over-production. There is some difference of
+opinion among growers upon this point; but nearly all agree
+that profits are now so small that production on a large scale is
+necessary to provide a fair income. Industrial flower-growing
+affords such a wide scope for the exercise of superior skill,
+industry and alertness, that it is not surprising to find some
+who are engaged in it doing remarkably well to all appearance,
+while others are struggling on and hardly paying their way.
+That a man with only a little capital, starting in a small way,
+has many disadvantages is certain; also, that his chance of
+saving money and extending his business quickly is much
+smaller than it was. To the casual looker-on, who knows
+nothing of the drudgery of the industry, flower-growing seems a
+delightful method of getting a living. That it is an entrancing
+pursuit there is no doubt; but it is equally true that it is a very
+arduous one, requiring careful forethought, ceaseless attention
+and abundant energy. Fortunately for those who might be
+tempted, without any knowledge of the industry, to embark
+capital in it, flower-growing, if at all comprehensive in scope, so
+obviously requires a varied and extensive technical knowledge,
+combined with good commercial ability, that any one can see
+that a thorough training is necessary to a man who intends to
+adopt it as a business, especially if hothouse flowers are to be
+produced.</p>
+
+<div class="condensed">
+<p>The market for fruit, and more especially for flowers, is a fickle
+one, and there is nearly always some uncertainty as to the course
+of prices. The perishable nature of soft fruit and cut flowers renders
+the markets very sensitive to anything in the nature of a glut, the
+occurrence of which is usually attended with disastrous results to
+producers. Foreign competition, moreover, has constantly to be
+faced, and it is likely to increase rather than diminish. French
+growers have a great advantage over the open-air cultivators of
+England, for the climate enables them to get their produce into the
+markets early in the season, when the highest prices are obtainable.
+The geographical advantage which France enjoys in being so near
+to England is, however, considerably discounted by the increasing
+facilities for cold storage in transit, both by rail and sea. The development
+of such facilities permits of the retail sale in England of luscious
+fruit as fresh and attractive as when it was gathered beneath the
+sunny skies of California. In the case of flowers, fashion is an
+element not to be ignored. Flowers much in request in one season
+may meet with very little demand in another, and it is difficult
+for the producer to anticipate the changes which caprice may dictate.
+Even for the same kind of flower the requirements are very uncertain,
+and the white blossom which is all the rage in one season may be
+discarded in favour of one of another colour in the next. The sale
+of fresh flowers for church decoration at Christmas and Easter has
+reached enormous dimensions. The irregularity in the date of the
+festival, however, causes some inconvenience to growers. If it falls
+very early the great bulk of suitable flowers may not be sufficiently
+forward for sale, whilst a late Easter may find the season too far
+advanced. The trade in cut flowers, therefore, is generally attended
+by uncertainty, and often by anxiety.</p>
+</div>
+<div class="author">(W. Fr.; J. Ws.)</div>
+
+<p class="pt2 center sc">United States</p>
+
+<p>In the United States horticulture and market gardening have
+now assumed immense proportions. In a country of over
+3,000,000 sq. m., stretching from the Atlantic to the Pacific
+on the one hand, and from the Gulf of Mexico to the great
+northern lakes and the Dominion of Canada on the other, a
+great variation of climatic conditions is not unnatural. From a
+horticultural point of view there are practically two well-defined
+regions: (1) that to the east of the Rocky Mountains across
+to the Atlantic, where the climate is more like that of eastern
+Asia than of western Europe so far as rainfall, temperature and
+seasonable conditions are concerned; (2) that to the west of the
+Rockies, known as the Pacific coast region, where the climate
+is somewhat similar to that of western Europe. It may be added
+that in the northern states&mdash;in Washington, Montana, North
+Dakota, Minnesota, Wisconsin, &amp;c.&mdash;the winters are often very
+severe, while the southern states practically enjoy a temperature
+somewhat similar to that of the Riviera. Indeed the range of
+temperature between the extreme northern states and the
+extreme southern may vary as much as 120° F. The great aim
+of American gardeners, therefore, has been to find out or to
+produce the kinds of fruits, flowers and vegetables that are
+likely to flourish in different parts of this immense country.</p>
+
+<p><i>Fruit Culture.</i>&mdash;There is probably no country in the world
+where so many different kinds of fruit can be grown with advantage
+to the nation as in the United States. In the temperate
+regions apples, pears and plums are largely grown, and orchards
+of these are chiefly to be found in the states of New York,
+Massachusetts, Pennsylvania, Michigan, Missouri, Colorado,
+and also in northern Texas, Arkansas and N. California. To
+these may be added cranberries and quinces, which are chiefly
+grown in the New England states. The quinces are not a crop
+of first-rate importance, but as much as 800,000 bushels of
+cranberries are grown each year. The peach orchards are
+assuming great proportions, and are chiefly to be found in
+Georgia and Texas, while grapes are grown throughout the
+Republic from east to west in all favourable localities. Oranges,
+lemons and citrons are more or less extensively grown in Florida
+and California, and in these regions what are known as Japanese
+or &ldquo;Kelsey&rdquo; plums (forms of <i>Prunus triflora</i>) are also grown
+as marketable crops. Pomegranates are not yet largely grown,
+but it is possible their culture will develop in southern Texas
+and Louisiana, where the climate is tempered by the waters of
+the Gulf of Mexico. Tomatoes are grown in most parts of the
+country so easily that there is frequently a glut; while the
+strawberry region extends from Florida to Virginia, Pennsylvania
+and other states&mdash;thus securing a natural succession from south
+to north for the various great market centres.</p>
+
+<p>Of the fruits mentioned apples are undoubtedly the most
+important. Not only are the American people themselves
+supplied with fresh fruit, but immense quantities are exported
+to Europe&mdash;Great Britain alone absorbing as much as 1,430,000
+cwt. in 1908. The varieties originally grown were of course
+those taken or introduced from Europe by the early settlers.
+Since the middle of the 19th century great changes have been
+brought about, and the varieties mostly cultivated now are
+distinctly American. They have been raised by crossing and
+intercrossing the most suitable European forms with others
+since imported from Russia. In the extreme northern states
+indeed, where it is essential to have apple trees that will stand
+the severest winters, the Russian varieties crossed with the
+berry crab of eastern Europe (<i>Pyrus baccata</i>) have produced
+<span class="pagenum"><a name="page269" id="page269"></a>269</span>
+a race eminently suited to that particular region. The individual
+fruits are not very large, but the trees are remarkably hardy.
+Farther south larger fruited varieties are grown, and among
+these may be noted Baldwins, Newton pippins, Spitzenbergs
+and Rhode Island greening. Apple orchards are numerous
+in the State of New York, where it is estimated that over 100,000
+acres are devoted to them. In the hilly regions of Missouri,
+Arkansas and Colorado there are also great plantations of apples.
+The trees, however, are grown on different principles from those
+in New York State. In the latter state apple trees with ordinary
+care live to more than 100 years of age and produce great crops;
+in the other states, however, an apple tree is said to be middle-aged
+at 20, decrepit at 30 and practically useless at 40 years of
+age. They possess the advantage, however, of bearing early and
+heavily.</p>
+
+<p>Until the introduction of the cold-storage system, about the
+year 1880, America could hardly be regarded as a commercial
+fruit-growing country. Since then, however, owing to the
+great improvements made in railway refrigerating vans and
+storage houses, immense quantities of fruit can be despatched
+in good condition to any part of the world; or they can be kept
+at home in safety until such time as the markets of Chicago,
+New York, Boston, Baltimore, Philadelphia, &amp;c., are considered
+favourable for their reception.</p>
+
+<p>Apple trees are planted at distances varying from 25 ft. to
+30 ft. apart in the middle western states, to 40 ft. to 50 ft. apart
+in New York State. Here and there, however, in some of the
+very best orchards the trees are planted 60 ft. apart every way.
+Each tree thus has a chance to develop to its utmost limits, and
+as air and light reach it better, a far larger fruit-bearing surface
+is secured. Actual experience has shown that trees planted at
+60 ft. apart&mdash;about 28 to the acre&mdash;produce more fruit by 43
+bushels than trees at 30 ft. apart&mdash;<i>i.e.</i> about 48 to the acre.</p>
+
+<p>Until recent years pruning as known to English and French
+gardeners was practically unknown. There was indeed no great
+necessity for it, as the trees, not being cramped for space, threw
+their branches outwards and upwards, and thus rarely become
+overcrowded. When practised, however, the operation could
+scarcely be called pruning; lopping or trimming would be more
+accurate descriptions.</p>
+
+<p>Apple orchards are not immune from insect pests and fungoid
+diseases, and an enormous business is now done in spraying
+machines and various insecticides. It pays to spray the trees,
+and figures have been given to show that orchards that have
+been sprayed four times have produced an average income of
+£211 per acre against £103 per acre from unsprayed orchards.</p>
+
+<p>The spring frosts are also troublesome, and in the Colorado
+and other orchards the process known as &ldquo;smudging&rdquo; is now
+adopted to save the crops. This consists in placing 20 or 30,
+or even more, iron or tin pots to an acre, each pot containing
+wooden chips soaked in tar (or pitch) mixed with kerosene.
+Whenever the thermometer shows 3 or 4 degrees of frost the
+smudge-pots are lighted. A dense white smoke then arises and
+is diffused throughout the orchards, enveloping the blossoming
+heads of the trees in a dense cloud. This prevents the frost
+from killing the tender pistils in the blossoms, and when several
+smudge-pots are alight at the same time the temperature of the
+orchard is raised two or three degrees. This work has generally
+to be done between 3 and 5 <span class="scs">A.M.</span>, and the growers naturally
+have an anxious time until all danger is over. The failure to
+attend to smudging, even on one occasion, may result in the
+loss of the entire crop of plums, apples or pears.</p>
+
+<p>Next to apples perhaps peaches are the most important fruit
+crop. The industry is chiefly carried on in Georgia, Texas
+and S. Carolina, and on a smaller scale in some of the adjoining
+states. Peaches thus flourish in regions that are quite unsuitable
+for apples or pears. In many orchards in Georgia,
+where over 3,000,000 acres have been planted, there are as
+many as 100,000 peach trees; while some of the large fruit
+companies grow as many as 365,000. In one place in West
+Virginia there is, however, a peach orchard containing 175,000
+trees, and in Missouri another company has 3 sq. m. devoted
+to peach culture. As a rule the crops do well. Sometimes,
+however, a disease known as the &ldquo;yellows&rdquo; makes sad havoc
+amongst them, and scarcely a fruit is picked in an orchard which
+early in the season gave promise of a magnificent crop.</p>
+
+<p>Plums are an important crop in many states. Besides the
+European varieties and those that have been raised by crossing
+with American forms, there is now a growing trade done in
+Japanese plums. The largest of these is popularly known as
+&ldquo;Kelseys,&rdquo; named after John Kelsey, who raised the first fruit
+in 1876 from trees brought to California in 1870. Sometimes the
+fruits are 3 in. in diameter, and like most of the Japanese
+varieties are more heart-shaped and pointed than plums of
+European origin. One apparent drawback to the Kelsey plum
+is its irregularity in ripening. It has been known in some years
+to be quite ripe in June, while in others the fruits are still green
+in October.</p>
+
+<p>Pears are much grown in such states as Massachusetts, New
+York, Pennsylvania, Missouri and California; while bush fruits
+like currants, gooseberries and raspberries find large spaces
+devoted in most of the middle and northern states. Naturally a
+good deal of crossing and intercrossing has taken place amongst
+the European and American forms of these fruits, but so far as
+gooseberries are concerned no great advance seems to have been
+made in securing varieties capable of resisting the devastating
+gooseberry mildew.</p>
+
+<p>Other fruits of more or less commercial value are oranges,
+lemons and citrons, chiefly in Florida. Lemons are practically a
+necessity to the American people, owing to the heat of the
+summers, when cool and refreshing drinks with an agreeable
+acidulous taste are in great demand. The pomelo (grape-fruit)
+is a kind of lemon with a thicker rind and a more acid flavour.
+At one time its culture was confined to Florida, but of recent
+years it has found its way into Californian orchards. Notwithstanding
+the prevailing mildness of the climate in both California
+and Florida, the crops of oranges, lemons, citrons, &amp;c., are
+sometimes severely injured by frosts when in blossom.</p>
+
+<p>Other fruits likely to be heard of in the future are the kaki
+or persimmon, the loquat, which is already grown in Louisiana,
+as well as the pomegranate.</p>
+
+<p>Great aid and encouragement are given by the government to
+the progress of American fruit-growing, and by the experiments
+that are being constantly carried out and tabulated at Cornell
+University and by the U.S.A. department of agriculture.</p>
+
+<p><i>Flower Culture.</i>&mdash;So far as flowers are concerned there appears
+to be little difference between the kinds of plants grown in the
+United States and in England, France, Belgium, Germany,
+Holland, &amp;c. Indeed there is a great interchange of new varieties
+of plants between Europe and America, and modifications in
+systems of culture are being gradually introduced from one side
+of the Atlantic to the other. The building of greenhouses for
+commercial purposes is perhaps on a somewhat different scale
+from that in England, but there are probably no extensive
+areas of glass such as are to be seen north of London from
+Enfield Highway to Broxburne. Hot water apparatus differs
+merely in detail, although most of the boilers used resemble
+those on the continent of Europe rather than in England. Great
+business is done in bulbs&mdash;mostly imported from Holland&mdash;stove
+and greenhouse plants, hardy perennials, orchids, ferns of the
+&ldquo;fancy&rdquo; and &ldquo;dagger&rdquo; types of Nephrolepis, and in carnations
+and roses. Amongst the latter thousands of such varieties as
+Beauty, Liberty, Killarney, Richmond and Bride are grown,
+and realize good prices as a rule in the markets. Carnations
+of the winter-flowering or &ldquo;perpetual&rdquo; type have long been
+grown in America, and enormous prices have been given for
+individual plants on certain occasions, rivalling the fancy prices
+paid in England for certain orchids. The American system of
+carnation-growing has quite captivated English cultivators,
+and new varieties are being constantly raised in both countries.
+Chrysanthemums are another great feature of American florists,
+and sometimes during the winter season a speculative grower
+will send a living specimen to one of the London exhibitions in
+the hope of booking large orders for cuttings of it later on. Sweet
+<span class="pagenum"><a name="page270" id="page270"></a>270</span>
+peas, dahlias, lilies of the valley, arum lilies and indeed every
+flower that is popular in England is equally popular in America,
+and consequently is largely grown.</p>
+
+<div class="condensed">
+<p><i>Vegetables.</i>&mdash;So far as these are concerned, potatoes, cabbages,
+cauliflowers, beans of all kinds, cucumbers, tomatoes (already
+referred to under fruits), musk-melons, lettuces, radishes, endives,
+carrots, &amp;c.; are naturally grown in great quantities, not only in the
+open air, but also under glass. The French system of intensive
+cultivation as practised on hot beds of manure round Paris is practically
+unknown at present. In the southern states there would be
+no necessity to practise it, but in the northern ones it is likely to
+attract attention.</p>
+</div>
+<div class="author">(J. Ws.)</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1a" id="ft1a" href="#fa1a"><span class="fn">1</span></a> <i>Jour. Roy. Agric. Soc.</i>, 1899.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FRUMENTIUS<a name="ar10" id="ar10"></a></span> (<i>c.</i> 300-<i>c.</i> 360), the founder of the Abyssinian
+church, traditionally identified in Abyssinian literature with
+Abba Salama or Father of Peace (but see <span class="sc"><a href="#artlinks">Ethiopia</a></span>), was a
+native of Phoenicia. According to the 4th-century historian
+Rufinus (x. 9), who gives Aedesius himself as his authority, a
+certain Tyrian, Meropius, accompanied by his kinsmen Frumentius
+and Aedesius, set out on an expedition to &ldquo;India,&rdquo;
+but fell into the hands of Ethiopians on the shore of the Red Sea
+and, with his ship&rsquo;s crew, was put to death. The two young men
+were taken to the king at Axum, where they were well treated
+and in time obtained great influence. With the help of Christian
+merchants who visited the country Frumentius gave Christianity
+a firm footing, which was strengthened when in 326 he was
+consecrated bishop by Athanasius of Alexandria, who in his
+<i>Epistola ad Constantinum</i> mentions the consecration, and gives
+some details of the history of Frumentius&rsquo;s mission. Later
+witnesses speak of his fidelity to the homoousian during the
+Arian controversies. Aedesius returned to Tyre, where he was
+ordained presbyter.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FRUNDSBERG, GEORG VON<a name="ar11" id="ar11"></a></span> (1473-1528), German soldier,
+was born at Mindelheim on the 24th of September 1473. He
+fought for the German king Maximilian I. against the Swiss
+in 1499, and in the same year was among the imperial troops
+sent to assist Ludovico Sforza, duke of Milan, against the French.
+Still serving Maximilian, he took part in 1504 in the war over
+the succession to the duchy of Bavaria-Landshut, and afterwards
+fought in the Netherlands. Convinced of the necessity
+of a native body of trained infantry Frundsberg assisted Maximilian
+to organize the <i>Landsknechte</i> (<i>q.v.</i>), and subsequently at
+the head of bands of these formidable troops he was of great
+service to the Empire and the Habsburgs. In 1509 he shared in
+the war against Venice, winning fame for himself and his men;
+and after a short visit to Germany returned to Italy, where
+in 1513 and 1514 he gained fresh laurels by his enterprises
+against the Venetians and the French. Peace being made, he
+returned to Germany, and at the head of the infantry of the
+Swabian league assisted to drive Ulrich of Württemberg from
+his duchy in 1519. At the diet of Worms in 1521 he spoke words
+of encouragement to Luther, and when the struggle between
+France and the Empire was renewed he took part in the invasion
+of Picardy, and then proceeding to Italy brought the greater
+part of Lombardy under the influence of Charles V. through his
+victory at Bicocca in April 1522. He was partly responsible for
+the great victory over the French at Pavia in February 1525, and,
+returning to Germany, he assisted to suppress the Peasant revolt,
+using on this occasion, however, diplomacy as well as force.
+When the war in Italy was renewed Frundsberg raised an army
+at his own expense, and skilfully surmounting many difficulties,
+joined the constable de Bourbon near Piacenza and marched
+towards Rome. Before he reached the city, however, his unpaid
+troops showed signs of mutiny, and their leader, stricken with
+illness and unable to pacify them, gave up his command.
+Returning to Germany, he died at Mindelheim on the 20th of
+August 1528. He was a capable and chivalrous soldier, and a
+devoted servant of the Habsburgs. His son Caspar (1500-1536)
+and his grandson Georg (d. 1586) were both soldiers of some
+distinction. With the latter&rsquo;s death the family became extinct.</p>
+
+<div class="condensed">
+<p>See Adam Reissner, <i>Historia Herrn Georgs und Herrn Kaspars
+von Frundsberg</i> (Frankfort, 1568). A German translation of this
+work was published at Frankfort in 1572. F.W. Barthold, <i>Georg
+von Frundsberg</i> (Hamburg, 1833); J. Heilmann, <i>Kriegsgeschichte
+von Bayern, Franken, Pfalz und Schwaben</i> (Munich, 1868).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FRUSTUM<a name="ar12" id="ar12"></a></span> (Latin for a &ldquo;piece broken off&rdquo;), a term in geometry
+for the part of a solid figure, such as a cone or pyramid,
+cut off by a plane parallel to the base, or lying between two
+parallel planes; and hence in architecture a name given to the
+drum of a column.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FRUYTIERS, PHILIP<a name="ar13" id="ar13"></a></span> (1627-1666), Flemish painter and
+engraver, was a pupil of the Jesuits&rsquo; college at Antwerp in 1627,
+and entered the Antwerp gild of painters without a fee in 1631.
+He is described in the register of that institution as &ldquo;illuminator,
+painter and engraver.&rdquo; The current account of his life is &ldquo;that
+he worked exclusively in water colours, yet was so remarkable
+in this branch of his art for arrangement, drawing, and especially
+for force and clearness of colour, as to excite the admiration of
+Rubens, whom he portrayed with all his family.&rdquo; The truth
+is that he was an artist of the most versatile talents, as may be
+judged from the fact that in 1646 he executed an Assumption
+with figures of life size, and four smaller pictures in oil, for the
+church of St Jacques at Antwerp, for which he received the
+considerable sum of 1150 florins. Unhappily no undoubted
+production of his hand has been preserved. All that we can
+point to with certainty is a series of etched plates, chiefly portraits,
+which are acknowledged to have been powerfully and
+skilfully handled. If, however, we search the portfolios of art
+collections on the European continent, we sometimes stumble
+upon miniatures on vellum, drawn with great talent and
+coloured with extraordinary brilliancy. In form they quite
+recall the works of Rubens, and these, it may be, are the work
+of Philip Fruytiers.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FRY,<a name="ar14" id="ar14"></a></span> the name of a well-known English Quaker family,
+originally living in Wiltshire. About the middle of the 18th
+century <span class="sc">Joseph Fry</span> (1728-1787), a doctor, settled in Bristol,
+where he acquired a large practice, but eventually abandoned
+medicine for commerce. He became interested in china-making,
+soap-boiling and type-founding businesses in Bristol, and in a
+chemical works at Battersea, all of which ventures proved very
+profitable. The type-founding business was subsequently removed
+to London and conducted by his son Edmund. Joseph
+Fry, however, is best remembered as the founder of the great
+Bristol firm of J.S. Fry &amp; Sons, chocolate manufacturers.
+He purchased the chocolate-making patent of William Churchman
+and on it laid the foundations of the present large business.
+After his death the Bristol chocolate factory was carried on with
+increasing success by his widow and by his son, <span class="sc">Joseph Storrs
+Fry</span> (1767-1835).</p>
+
+<p>In 1795 a new and larger factory was built in Union Street,
+Bristol, which still forms the centre of the firm&rsquo;s premises, and
+in 1798 a Watt&rsquo;s steam-engine was purchased and the cocoa-beans
+ground by steam. On the death of Joseph Storrs Fry his
+three sons, Joseph (1795-1879), Francis, and Richard (1807-1878)
+became partners in the firm, the control being mainly in the
+hands of <span class="sc">Francis Fry</span> (1803-1886). Francis Fry was in every
+way a remarkable character. The development of the business
+to its modern enormous proportion was chiefly his work, but
+this did not exhaust his activities. He took a principal part in
+the introduction of railways to the west of England, and in 1852
+drew up a scheme for a general English railway parcel service.
+He was an ardent bibliographer, taking a special interest in
+early English Bibles, of which he made in the course of a long
+life a large and striking collection, and of the most celebrated
+of which he published facsimiles with bibliographical notes.
+Francis Fry died in 1886, and his son Francis J. Fry and nephew
+Joseph Storrs Fry carried on the business, which in 1896 was
+for family reasons converted into a private limited company,
+Joseph Storrs Fry being chairman and all the directors members
+of the Fry family.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FRY, SIR EDWARD<a name="ar15" id="ar15"></a></span> (1827-&emsp;&emsp;), English judge, second son
+of Joseph Fry (1795-1879), was born at Bristol on the 4th of
+November 1827, and educated at University College, London,
+and London University. He was called to the bar in 1854 and
+was made a Q.C. in 1869, practising in the rolls court and becoming
+recognized as a leading equity lawyer. In 1877 he was raised
+to the bench and knighted. As chancery judge he will be
+<span class="pagenum"><a name="page271" id="page271"></a>271</span>
+remembered for his careful interpretations and elucidations of
+the Judicature Acts, then first coming into operation. In 1883
+he was made a lord justice of appeal, but resigned in 1892; and
+subsequently his knowledge of equity and talents for arbitration
+were utilized by the British government from time to time in
+various special directions, particularly as chairman of many
+commissions. He was also one of the British representatives
+at the Paris North Sea Inquiry Commission (1905), and was
+appointed a member of the Hague Permanent Arbitration Court.
+He wrote <i>A Treatise on the Specific Performance of Public Contracts</i>
+(London, 1858, and many subsequent editions).</p>
+
+
+<hr class="art" />
+<p><span class="bold">FRY, ELIZABETH<a name="ar16" id="ar16"></a></span> (1780-1845), English philanthropist, and,
+after Howard, the chief promoter of prison reform in Europe,
+was born in Norwich on the 21st of May 1780. Her father,
+John Gurney, afterwards of Earlham Hall, a wealthy merchant
+and banker, represented an old family which for some generations
+had belonged to the Society of Friends. While still a girl she
+gave many indications of the benevolence of disposition, clearness
+and independence of judgment, and strength of purpose, for which
+she was afterwards so distinguished; but it was not until after
+she had entered her eighteenth year that her religion assumed
+a decided character, and that she was induced, under the preaching
+of the American Quaker, William Savery, to become an earnest
+and enthusiastic though never fanatical &ldquo;Friend.&rdquo; In August
+1800 she became the wife of Joseph Fry, a London merchant.</p>
+
+<p>Amid increasing family cares she was unwearied in her attention
+to the poor and the neglected of her neighbourhood; and in
+1811 she was acknowledged by her co-religionists as a &ldquo;minister,&rdquo;
+an honour and responsibility for which she was undoubtedly
+qualified, not only by vigour of intelligence and warmth of heart,
+but also by an altogether unusual faculty of clear, fluent and
+persuasive speech. Although she had made several visits to
+Newgate prison as early as February 1813, it was not until
+nearly four years afterwards that the great public work of her
+life may be said to have begun. The association for the Improvement
+of the Female Prisoners in Newgate was formed in April
+1817. Its aim was the much-needed establishment of some of
+what are now regarded as the first principles of prison discipline,
+such as entire separation of the sexes, classification of criminals,
+female supervision for the women, and adequate provision for
+their religious and secular instruction, as also for their useful
+employment. The ameliorations effected by this association,
+and largely by the personal exertions of Mrs Fry, soon became
+obvious, and led to a rapid extension of similar methods to other
+places. In 1818 she, along with her brother, visited the prisons
+of Scotland and the north of England; and the publication
+(1819) of the notes of this tour, as also the cordial recognition
+of the value of her work by the House of Commons committee
+on the prisons of the metropolis, led to a great increase of her
+correspondence, which now extended to Italy, Denmark and
+Russia, as well as to all parts of the United Kingdom. Through
+a visit to Ireland, which she made in 1827, she was led to direct
+her attention to other houses of detention besides prisons; and
+her observations resulted in many important improvements
+in the British hospital system, and in the treatment of the insane.
+In 1838 she visited France, and besides conferring with many
+of the leading prison officials, she personally visited most of the
+houses of detention in Paris, as well as in Rouen, Caen and some
+other places. In the following year she obtained an official
+permission to visit all the prisons in that country; and her tour,
+which extended from Boulogne and Abbeville to Toulouse and
+Marseilles, resulted in a report which was presented to the
+minister of the interior and the prefect of police. Before returning
+to England she had included Geneva, Zürich, Stuttgart and
+Frankfort-on-Main in her inspection. The summer of 1840
+found her travelling through Belgium, Holland and Prussia
+on the same mission; and in 1841 she also visited Copenhagen.
+In 1842, through failing health, Mrs Fry was compelled to forgo
+her plans for a still more widely extended activity, but had the
+satisfaction of hearing from almost every quarter of Europe
+that the authorities were giving increased practical effect to her
+suggestions. In 1844 she was seized with a lingering illness, of
+which she died on the 12th of October 1845. She was survived
+by a numerous family, the youngest of whom was born in 1822.</p>
+
+<p>Two interesting volumes of <i>Memoirs, with Extracts from her
+Journals and Letters</i>, edited by two of her daughters, were published
+in 1847. See also <i>Elizabeth Fry</i>, by G. King Lewis (1910).</p>
+
+
+<hr class="art" />
+<p><span class="bold">FRYXELL, ANDERS<a name="ar17" id="ar17"></a></span> (1795-1881), Swedish historian, was
+born at Hesselskog, Dalsland, Sweden, on the 7th of February
+1795. He was educated at Upsala, took holy orders in 1820,
+was made a doctor of philosophy in 1821, and in 1823 began to
+publish the great work of his life, the <i>Stories from Swedish
+History</i>. He did not bring this labour to a close until, fifty-six
+years later, he published the forty-sixth and crowning volume
+of his vast enterprise. Fryxell, as a historian, appealed to every
+class by the picturesqueness of his style and the breadth of his
+research; he had the gift of awakening to an extraordinary
+degree the national sense in his readers. In 1824 he published
+his <i>Swedish Grammar</i>, which was long without a rival. In 1833
+he received the title of professor, and in 1835 he was appointed
+to the incumbency of Sunne, in the diocese of Karlstad, where
+he resided for the remainder of his life. In 1840 he was elected
+to the Swedish Academy in succession to the poet Wallin (1779-1839).
+In 1847 Fryxell received from his bishop permission to
+withdraw from all the services of the Church, that he might devote
+himself without interruption to historical investigation. Among
+his numerous minor writings are prominent his <i>Characteristics
+of Sweden between 1592 and 1600</i> (1830), his <i>Origins of the Inaccuracy
+with which the History of Sweden in Catholic Times has
+been Treated</i> (1847), and his <i>Contributions to the Literary History
+of Sweden</i>. It is now beginning to be seen that the abundant
+labours of Fryxell were rather of a popular than of a scientific
+order, and although their influence during his lifetime was
+unbounded, it is only fair to later and exacter historians to
+admit that they threaten to become obsolete in more than one
+direction. On the 21st of March 1881 Anders Fryxell died at
+Stockholm, and in 1884 his daughter Eva Fryxell (born 1829)
+published from his MS. an interesting <i>History of My History</i>,
+which was really a literary autobiography and displays the
+persistency and tirelessness of his industry.</p>
+<div class="author">(E. G.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">FUAD PASHA<a name="ar18" id="ar18"></a></span> (1815-1869), Turkish statesman, was the son
+of the distinguished poet Kechéji-zadé Izzet Molla. He was
+educated at the medical school and was at first an army surgeon.
+About 1836 he entered the civil service as an official of the
+foreign ministry. He became secretary of the embassy in
+London; was employed on special missions in the principalities
+and at St Petersburg (1848), and was sent to Egypt as special
+commissioner in 1851. In that year he became minister for
+foreign affairs, a post to which he was appointed also on four
+subsequent occasions and which he held at the time of his death.
+During the Crimean War he commanded the troops on the
+Greek frontier and distinguished himself by his bravery. He
+was Turkish delegate at the Paris conference of 1856; was
+charged with a mission to Syria in 1860; grand vizier in 1860
+and 1861, and also minister of war. He accompanied the
+sultan Abd-ul-Aziz on his journey to Egypt and Europe, when
+the freedom of the city of London was conferred on him. He
+died at Nice (whither he had been ordered for his health) in
+1869. Fuad was renowned for his boldness and promptness
+of decision, as well as for his ready wit and his many bons mots.
+Generally regarded as the partisan of a pro-English policy,
+he rendered most valuable service to his country by his
+able management of the foreign relations of Turkey, and not
+least by his efficacious settlement of affairs in Syria after the
+massacres of 1860.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUCHOW,<a name="ar19" id="ar19"></a></span> <span class="sc">Fu-Chau, Foochow</span>, a city of China, capital of
+the province of Fu-kien, and one of the principal ports open to
+foreign commerce. In the local dialect it is called Hokchiu.
+It is situated on the river Min, about 35 m. from the sea, in
+26° 5&prime; N. and 119º 20&prime; E., 140 m. N. of Amoy and 280 S. of
+Hang-chow. The city proper, lying nearly 3 m. from the north
+bank of the river, is surrounded by a wall about 30 ft. high and
+12 ft. thick, which makes a circuit of upwards of 5 m. and is pierced
+by seven gateways surrounded by tall fantastic watch-towers.
+<span class="pagenum"><a name="page272" id="page272"></a>272</span>
+The whole district between the city and the river, the island of
+Nantai, and the southern banks of the Min are occupied by
+extensive suburbs; and the river itself bears a large floating
+population. Communication from bank to bank is afforded
+by a long stone bridge supported by forty solid stone piers in its
+northern section and by nine in its southern. The most remarkable
+establishment of Fuchow is the arsenal situated about
+3 m. down the stream at Pagoda Island, where the sea-going
+vessels usually anchor. It was founded in 1867, and is conducted
+under the direction of French engineers according to European
+methods. In 1870 it employed about 1000 workmen besides
+fifty European superintendents, and between that date and
+1880 it turned out about 20 or 30 small gunboats. In 1884 it
+was partially destroyed by the French fleet, and for a number of
+years the workshops and machinery were allowed to stand idle
+and go to decay. On the 1st of August 1895 an attack was
+made on the English mission near the city of Ku-chang, 120 m.
+west of Fuchow, on which occasion nine missionaries, of whom
+eight were ladies, were massacred. The port was opened to
+European commerce in 1842; and in 1853 the firm of Russell
+and Co. shipped the first cargoes of tea from Fuchow to Europe
+and America. The total trade in foreign vessels in 1876 was
+imports to the value of £1,531,617, and exports to the value
+of £3,330,489. In 1904 the imports amounted to £1,440,351,
+and the exports to £1,034,436. The number of vessels that
+entered in 1876 was 275, and of these 211 were British, 27
+German, 11 Danish and 9 American. While in 1904, 480
+vessels entered the port, 216 of which were British. A large
+trade is carried on by the native merchants in timber, paper,
+woollen and cotton goods, oranges and olives; but the foreign
+houses mainly confine themselves to opium and tea. Commercial
+intercourse with Australia and New Zealand is on the increase.
+The principal imports, besides opium, are shirtings, T-cloths,
+lead and tin, medicines, rice, tobacco, and beans and peas.
+Two steamboat lines afford regular communication with Hong-Kong
+twice a month. The town is the seat of several important
+missions, of which the first was founded in 1846. That supported
+by the American board had in 1876 issued 1,3000,000 copies of
+Chinese books and tracts.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUCHS, JOHANN NEPOMUK VON<a name="ar20" id="ar20"></a></span> (1774-1856), German
+chemist and mineralogist, was born at Mattenzell, near Brennberg
+in the Bavarian Forest, on the 15th of May 1774. In 1807 he
+became professor of chemistry and mineralogy at the university
+of Landshut, and in 1823 conservator of the mineralogical
+collections at Munich, where he was appointed professor of
+mineralogy three years later, on the removal thither of the
+university of Landshut. He retired in 1852, was ennobled by
+the king of Bavaria in 1854, and died at Munich on the 5th of
+March 1856. His name is chiefly known for his mineralogical
+observations and for his work on soluble glass.</p>
+
+<div class="condensed">
+<p>His collected works, including <i>Über den Einfluss der Chemie und
+Mineralogie</i> (1824), <i>Die Naturgeschichte des Mineralreichs</i> (1842),
+<i>Über die Theorien der Erde</i> (1844), were published at Munich in 1856.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FUCHS, LEONHARD<a name="ar21" id="ar21"></a></span> (1501-1566), German physician and
+botanist, was born at Wembdingen in Bavaria on the 17th
+of January 1501. He attended school at Heilbronn and Erfurt,
+and in 1521 graduated at the university of Ingolstadt. About
+the same time he espoused the doctrines of the Reformation.
+Having in 1524 received his diploma as doctor of medicine, he
+practised for two years in Munich. He became in 1526 professor
+of medicine at Ingolstadt, and in 1528 physician to the margrave
+of Anspach. In Anspach he was the means of saving the lives
+of many during the epidemic locally known as the &ldquo;English
+sweating-sickness.&rdquo; By the duke of Württemberg he was, in
+1535, appointed to the professorship of medicine at the university
+of Tübingen, a post held by him till his death on the 10th of May
+1566. Fuchs was an advocate of the Galenic school of medicine,
+and published several Latin translations of treatises by its
+founder and by Hippocrates. But his most important publication
+was <i>De historia stirpium commentarii insignes</i> (Basel, 1542),
+a work illustrated with more than five hundred excellent outline
+illustrations, including figures of the common foxglove and of
+another species of the genus <i>Digitalis</i>, which was so named by
+him.</p>
+
+
+<hr class="art" />
+
+<table class="flt" style="float: right; width: 370px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:315px; height:496px" src="images/img272.jpg" alt="" /></td></tr>
+<tr><td class="caption"><i>Fuchsia coccinea</i>.</td></tr>
+<tr><td class="caption1">1, Flower cut open after removal of
+sepals; 2, fruit; 3, floral diagram.</td></tr></table>
+
+<p><span class="bold">FUCHSIA,<a name="ar22" id="ar22"></a></span> so named by Plumier in honour of the botanist
+Leonhard Fuchs, a genus of plants of the natural order Onagraceae,
+characterized by entire, usually opposite leaves, pendent flowers,
+a funnel-shaped, brightly coloured, quadripartite, deciduous
+calyx, 4 petals, alternating with the calycine segments, 8, rarely
+10, exserted stamens, a long filiform style, an inferior ovary,
+and fruit, a fleshy ovoid many-seeded berry. All the members
+of the genus, with the exception of the New Zealand species,
+<i>F. excorticata, F. Colensoi</i> and <i>F. procumbens</i>, are natives of
+Central and South America&mdash;occurring in the interior of forests
+or in damp and shady mountainous situations. The various
+species differ not a little in size as well as in other characters;
+some, as <i>F. verrucosa</i>, being dwarf shrubs; others, as <i>F. arborescens</i>
+and <i>F. apetala</i>, attaining a height of 12 to 16 ft., and having
+stems several inches in diameter. Plumier, in his <i>Nova plantarum
+Americanarum genera</i> (p. 14, tab. 14, Paris, 1703), gave
+a description of a species of fuchsia, the first known, under the
+name of <i>Fuchsia triphylla, flore coccineo</i>, and a somewhat conventional
+outline figure
+of the same plant was
+published at Amsterdam
+in 1757 by Burmann.
+In the <i>Histoire
+des plantes médicinales</i>
+of the South American
+traveller Feuillée (p. 64,
+pl. XLVII.), written in
+1709-1711, and published
+by him with his
+<i>Journal</i>, Paris, 1725,
+the name <i>Thilco</i> is
+applied to a species of
+fuchsia from Chile,
+which is described,
+though not evidently
+so figured, as having
+a pentamerous calyx.
+The <i>F. coccinea</i> of Alton
+(fig.) (see J.D. Hooker,
+in <i>Journal Linnean Soc</i>.,
+Botany, vol. x. p. 458,
+1867), the first species
+of fuchsia cultivated in
+England, where it was
+long confined to the
+greenhouse, was brought
+from South America by
+Captain Firth in 1788 and placed in Kew Gardens. Of this
+species Mr Lee, a nurseryman at Hammersmith, soon afterwards
+obtained an example, and procured from it by means
+of cuttings several hundred plants, which he sold at a guinea
+each. In 1823 <i>F. macrostemma</i> and <i>F. gracilis</i>, and during
+the next two or three years several other species, were introduced
+into England; but it was not until about 1837, or
+soon after florists had acquired <i>F. fulgens</i>, that varieties of
+interest began to make their appearance. The numerous
+hybrid forms now existing are the result chiefly of the
+intercrossing of that or other long-flowered with globose-flowered
+plants. <i>F. Venus-victrix</i>, raised by Mr Gulliver,
+gardener to the Rev. S. Marriott of Horsemonden, Kent, and sold
+in 1822 to Messrs Cripps, was the earliest white-sepalled fuchsia.
+The first fuchsia with a white corolla was produced about 1853
+by Mr Storey. In some varieties the blossoms are variegated,
+and in others they are double. There appears to be very little
+limit to the number of forms to be obtained by careful cultivation
+and selection. To hybridize, the flower as soon as it opens is
+emasculated, and it is then fertilized with pollen from some
+different flower.</p>
+
+<p>Ripe seed is sown either in autumn or about February or March
+in light, rich, well-drained mould, and is thinly covered with
+<span class="pagenum"><a name="page273" id="page273"></a>273</span>
+sandy soil and watered. A temperature of 70° to 75° Fahr. has
+been found suitable for raising. The seedlings are pricked off
+into shallow pots or pans, and when 3 in. in height are transferred
+to 3-in. pots, and are then treated the same as plants from
+cuttings. Fuchsias may be grafted as readily as camellias,
+preferably by the splice or whip method, the apex of a young
+shoot being employed as a scion; but the easiest and most usual
+method of propagation is by cuttings. The most expeditious
+way to procure these is to put plants in heat in January, and to
+take their shoots when 3 in. in length. For summer flowering
+in England they are best made about the end of August, and
+should be selected from the shortest-jointed young wood. They
+root readily in a compost of loam and silver-sand if kept close
+and sprinkled for a short time. In from two to three weeks they
+may be put into 3-in. pots containing a compost of equal parts of
+rich loam, silver-sand and leaf-mould. They are subsequently
+moved from the frame or bed, first to a warm and shady, and
+then to a more airy part of the greenhouse. In January a little
+artificial heat may be given, to be gradually increased as the
+days lengthen. The side-shoots are generally pruned when they
+have made three or four joints, and for bushy plants the leader is
+stopped soon after the first potting. Care is taken to keep the
+plants as near the glass as possible, and shaded from bright
+sunshine, also to provide them plentifully with water, except
+at the time of shifting, when the roots should be tolerably dry.
+For the second potting a suitable soil is a mixture of well-rotted
+cow-dung or old hotbed mould with leaf-mould and sandy peat,
+and to promote drainage a little peat-moss may be placed
+immediately over the crocks in the lower part of the pot. Weak
+liquid manure greatly promotes the advance of the plants, and
+should be regularly supplied twice or thrice a week during the
+flowering season. After this, water is gradually withheld from
+them, and they may be placed in the open air to ripen their wood.</p>
+
+<p>Among the more hardy or half-hardy plants for inside borders
+are varieties of the Chilean species, <i>F. macrostemma</i> (or <i>F.
+magellanica</i>), a shrub 6 to 12 ft. high with a scarlet calyx, such
+as <i>F. m. globosa, F. m. gracilis</i>; one of the most graceful and
+hardy of these, a hybrid <i>F. riccartoni</i>, was raised at Riccarton,
+near Edinburgh, in 1830. For inside culture may be mentioned
+<i>F. boliviana</i> (Bolivia), 2 to 4 ft. high, with rich crimson flowers
+with a trumpet-shaped tube; <i>F. corymbiflora</i> (Peru), 4 to 6 ft.
+high, with scarlet flowers nearly 2 in. long in long terminal
+clusters; F. fulgens (Mexico), 4 to 6 ft., with drooping apical
+clusters of scarlet flowers; <i>F. microphylla</i> (Central America),
+with small leaves and small scarlet funnel-shaped flowers, the
+petals deep red; <i>F. procumbens</i> (New Zealand), a pretty little
+creeper, the small flowers of which are succeeded by oval magenta-crimson
+berries which remain on for months; and <i>F. splendens</i>
+(Mexico), 6 ft. high, with very showy scarlet and green flowers.
+But these cannot compare in beauty or freedom of blossom with
+the numerous varieties raised by gardeners. The nectar of
+fuchsia flowers has been shown to contain nearly 78% of cane
+sugar, the remainder being fruit sugar. The berries of some
+fuchsias are subacid or sweet and edible. From certain species
+a dye is obtainable. The so-called &ldquo;native fuchsias&rdquo; of southern
+and eastern Australia are plants of the genus <i>Correa</i>, natural
+order Rutaceae.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUCHSINE,<a name="ar23" id="ar23"></a></span> or <span class="sc">Magenta</span>, a red dye-stuff consisting of a mixture
+of the hydrochlorides or acetates of pararosaniline and rosaniline.
+It was obtained in 1856 by J. Natanson (<i>Ann</i>., 1856, 98, p. 297)
+by the action of ethylene chloride on aniline, and by A.W.
+Hofmann in 1858 from aniline and carbon tetrachloride. It
+is prepared by oxidizing &ldquo;aniline for red&rdquo; (a mixture of aniline
+and ortho- and para-toluidine) with arsenic acid (H. Medlock,
+<i>Dingler&rsquo;s Poly. Jour</i>., 1860, 158, p. 146); by heating aniline
+for red with nitrobenzene, concentrated hydrochloric acid and
+iron (Coupier, <i>Ber</i>., 1873, 6, p. 423); or by condensing formaldehyde
+with aniline and ortho-toluidine and oxidizing the mixture.
+It forms small crystals, showing a brilliant green reflex, and is
+soluble in water and alcohol with formation of a deep red solution.
+It dyes silk, wool and leather direct, and cotton after mordanting
+with tannin and tartar emetic (see <span class="sc"><a href="#artlinks">Dyeing</a></span>). An aqueous solution
+of fuchsine is decolorized on the addition of sulphurous
+acid, the easily soluble fuchsine sulphurous acid being formed.
+This solution is frequently used as a test reagent for the detection
+of aldehydes, giving, in most cases, a red coloration on the
+addition of a small quantity of the aldehyde.</p>
+
+<div class="condensed">
+<p>The constitution of the fuchsine bases (pararosaniline and rosaniline)
+was determined by E. and O. Fischer in 1878 (<i>Ann</i>., 1878,
+194, p. 242); A.W. Hofmann having previously shown that oxidation
+of pure aniline alone or of pure toluidine yielded no fuchsine,
+whilst oxidation of a mixture of aniline and para-toluidine gave
+rise to the fine red dye-stuff para-fuchsine (pararosaniline hydrochloride)</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcr">CH<span class="su">3</span>·C<span class="su">6</span>H<span class="su">4</span>NH<span class="su">2</span> + 2C<span class="su">6</span>H<span class="su">5</span>NH<span class="su">2</span> + 3O = HO·C(C<span class="su">6</span>H<span class="su">4</span>NH<span class="su">2</span>)<span class="su">3</span> + 2H<span class="su">2</span>O.</td></tr>
+
+<tr><td class="tcr">Colour base (pararosaniline).</td></tr>
+
+<tr><td class="tcr">HO·C(C<span class="su">6</span>H<span class="su">4</span>NH<span class="su">2</span>)<span class="su">3</span>·HCl = H<span class="su">2</span>O + (H<span class="su">2</span>N·C<span class="su">6</span>H<span class="su">4</span>)<span class="su">2</span>C : C<span class="su">6</span>H<span class="su">4</span> : NH<span class="su">2</span>Cl.</td></tr>
+
+<tr><td class="tcr">Pararosaniline hydrochloride.</td></tr>
+</table>
+
+<p class="noind">A. Rosenstiehl (<i>Jahres</i>., 1869, p. 693) found also that different rosanilines
+were obtained according to whether ortho- or para-toluidine
+was oxidized with aniline; and he gave the name rosaniline to the
+one obtained from aniline and ortho-toluidine, reserving the term
+pararosaniline for the other. E. and O. Fischer showed that these
+compounds were derivatives of triphenylmethane and tolyldiphenylmethane
+respectively. Pararosaniline was reduced to the
+corresponding leuco compound (paraleucaniline), from which by
+diazotization and boiling with alcohol, the parent hydrocarbon was
+obtained</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcl">(H<span class="su">2</span>N·C<span class="su">5</span>H<span class="su">4</span>)<span class="su">2</span>C : C<span class="su">6</span>H<span class="su">4</span>:NH<span class="su">2</span>Cl &rarr; </td> <td class="tcc">HC(C<span class="su">6</span>H<span class="su">4</span>NH<span class="su">2</span>·HCl)<span class="su">3</span> &rarr;</td> <td class="tcc">HC(C<span class="su">6</span>H<span class="su">4</span>N<span class="su">2</span>Cl<span class="su">3</span>)
+
+ &rarr; </td> <td class="tcc">HC(C<span class="su">6</span>H<span class="su">5</span>)<span class="su">3</span>.</td></tr>
+
+<tr><td class="tcl">Pararosaniline hydrochloride.</td> <td class="tcc">Paraleucaniline.</td> <td class="tcc">&nbsp;</td> <td class="tcc">Triphenylmethane.</td></tr>
+</table>
+
+<p class="noind">The reverse series of operations was also carried out by the Fischers,
+triphenylmethane being nitrated, and the nitro compound then
+reduced to triaminotriphenylmethane or paraleucaniline, which on
+careful oxidation is converted into the dye-stuff. A similar series of
+reactions was carried out with rosaniline, which was shown to be
+the corresponding derivative of tolyldiphenylmethane.</p>
+
+<p>The free pararosaniline, C<span class="su">19</span>H<span class="su">19</span>N<span class="su">3</span>O, and rosaniline,
+C<span class="su">20</span>H<span class="su">21</span>N<span class="su">3</span>O,
+may be obtained by precipitating solutions of their salts with a
+caustic alkali, colourless precipitates being obtained, which crystallize
+from hot water in the form of needles or plates. The position
+of the amino groups in pararosaniline was determined by the work
+of H. Caro and C. Graebe (<i>Ber</i>., 1878, II, p. 1348) and of E. and O.
+Fischer (<i>Ber.</i>, 1880, 13, p. 2204) as follows: Nitrous acid converts
+pararosaniline into aurin, which when superheated with water yields
+para-dioxybenzophenone. As the hydroxyl groups in aurin correspond
+to the amino groups in pararosaniline, two of these in the latter
+compound must be in the para position. The third is also in the
+para position; for if benzaldehyde be condensed with aniline,
+condensation occurs in the para position, for the compound formed
+may be converted into para-dioxybenzophenone,</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcc">C<span class="su">6</span>H<span class="su">5</span>CHO &rarr; C<span class="su">6</span>H<span class="su">5</span>CH(C<span class="su">6</span>H<span class="su">4</span>NH<span class="su">2</span>)<span class="su">2</span> &rarr; C<span class="su">6</span>H<span class="su">5</span>CH(C<span class="su">6</span>H<span class="su">4</span>OH)<span class="su">2</span>
+
+ &rarr; CO(C<span class="su">6</span>H<span class="su">4</span>OH)<span class="su">2</span>;</td></tr>
+</table>
+
+<p class="noind">but if para-nitrobenzaldehyde be used in the above reaction and the
+resulting nitro compound NO<span class="su">2</span>.C<span class="su">6</span>H<span class="su">4</span>.CH(C<span class="su">6</span>H<span class="su">4</span>NH<span class="su">2</span>)<span class="su">2</span> be reduced,
+then pararosaniline is the final product, and consequently the third
+amino group occupies the para position. Many derivatives of pararosaniline
+and rosaniline are known, in which the hydrogen atoms of
+the amino groups are replaced by alkyl groups; this has the effect
+of producing a blue or violet shade, which becomes deeper as the
+number of groups increases (see <span class="sc"><a href="#artlinks">Dyeing</a></span>).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FUCINO, LAGO DI<a name="ar24" id="ar24"></a></span> [Lat. <i>Lacus Fucinus</i>], a lake bed of the
+Abruzzi, Italy, in the province of Aquila, 2 m. E. of the town of
+Avezzano. The lake was 37 m. in circumference and 65 ft. deep.
+From the lack of an outlet, the level of the lake was subject to
+great variations, often fraught with disastrous consequences.
+As early as <span class="scs">A.D.</span> 52 the emperor Claudius, realizing a project of
+Julius Caesar, constructed a tunnel 3½ m. long, with 40 shafts at
+intervals, by which the surplus waters found an outlet to the
+Liris (or Garigliano). No less than 30,000 workmen were employed
+for eleven years in driving this tunnel. In the following
+reign the tunnel was allowed to fall into disrepair, but was
+repaired by Trajan. When, however, it finally went out of use is
+uncertain. The various attempts made to reopen it from 1240
+onwards were unsuccessful. By 1852 the lake had gradually
+risen until it was 30 ft. above its original level, and had become a
+source of danger to the surrounding countryside. A company
+undertook to drain it on condition of becoming proprietors of the
+site when dry; in 1854, however, the rights and privileges were
+purchased by Prince Giulio Torlonia (d. 1886), the great Roman
+banker, who carried on the work at his own expense until, in 1876,
+the lake was finally drained at the cost of some £1,700,000. The
+<span class="pagenum"><a name="page274" id="page274"></a>274</span>
+reclaimed area is 12½ m. long, 7 m. broad, and is cultivated by
+families from the Torlonia estates. The outlet by which it was
+drained is 4 m. long and 24 sq. yds. in section.</p>
+
+<div class="condensed">
+<p>See A. Brisse and L. de Rotron, <i>Le Desséchement du lac Fucin,
+exécuté par S.E. le Prince A. Torlonia</i> (Rome, 1876).</p>
+</div>
+<div class="author">(T. As.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">FUEL<a name="ar25" id="ar25"></a></span> (O. Fr. <i>feuaile</i>, popular Lat. <i>focalia</i>, from <i>focus</i>, hearth,
+fire), a term applicable to all substances that can be usefully
+employed for the production of heat by combustion. Any
+element or combination of elements susceptible of oxidation may
+under appropriate conditions be made to burn; but only those
+that ignite at a moderate initial temperature and burn with comparative
+rapidity, and, what is practically of more importance,
+are obtainable in quantity at moderate prices, can fairly be
+regarded as fuels. The elementary substances that can be so
+classed are primarily hydrogen, carbon and sulphur, while others
+finding more special applications are silicon, phosphorus, and the
+more readily oxidizable metals, such as iron, manganese, aluminium
+and magnesium. More important, however, than the
+elements are the carbohydrates or compounds of carbon, oxygen
+and hydrogen, which form the bulk of the natural fuels, wood,
+peat and coal, as well as of their liquid and gaseous derivatives&mdash;coal-gas,
+coal-tar, pitch, oil, &amp;c., which have high values as fuel.
+Carbon in the elementary form has its nearest representative in
+the carbonized fuels, charcoal from wood and coke from coal.</p>
+
+<p class="pt2 center"><i>Solid Fuels</i>.</p>
+
+<p>Wood may be considered as having the following average
+composition when in the air-dried state: Carbon, 39.6; hydrogen,
+4.8; oxygen, 34.8; ash, 1.0; water, 20%.
+When it is freshly felled, the water may be from 18 to
+<span class="sidenote">Wood.</span>
+50%. Air-dried or even green wood ignites readily when a considerable
+surface is exposed to the kindling flame, but in large
+masses with regular or smooth surfaces it is often difficult to get
+it to burn. When previously torrefied or scorched by heating to
+a temperature of about 200°, at which incipient charring is set up,
+it is exceedingly inflammable. The ends of imperfectly charred
+boughs from the charcoal heaps in this condition are used in Paris
+and other large towns in France for kindling purposes, under the
+name of <i>fumerons</i>. The inflammability, however, varies with
+the density,&mdash;the so-called hard woods, oak, beech and maple,
+taking fire less readily than the softer, and, more especially,
+the coniferous varieties rich in resin. The calorific power of
+absolutely dry woods may as an average be taken at about 4000
+units, and when air-dried, <i>i.e</i>. containing 25% of water, at 2800
+to 3000 units. Their evaporative values, <i>i.e</i>. the quantities of
+water evaporated by unit weight, are 3.68 and 4.44.</p>
+
+<p>Wood being essentially a flaming fuel is admirably adapted for
+use with heat-receiving surfaces of large extent, such as locomotive
+and marine boilers, and is also very clean in use. The
+absence of all cohesion in the cinders or unburnt carbonized
+residue causes a large amount of ignited particles to be projected
+from the chimney, when a rapid draught is used, unless special
+spark-catchers of wire gauze or some analogous contrivance are
+used. When burnt in open fireplaces the volatile products given
+off in the apartment on the first heating have an acrid penetrating
+odour, which is, however, very generally considered to be
+agreeable. Owing to the large amount of water present, no very
+high temperatures can be obtained by the direct combustion of
+wood, and to produce these for metallurgical purposes it is
+necessary to convert it previously either into charcoal or into
+inflammable gas.</p>
+
+<p>Peat includes a great number of substances of very unequal
+fuel value, the most recently formed spongy light brown kind
+approximating in composition to wood, while the
+dense pitchy brown compact substance, obtained from
+<span class="sidenote">Peat.</span>
+the bottom of bogs of ancient formation, may be compared with
+lignite or even in some instances with coal. Unlike wood, however,
+it contains incombustible matter in variable but large
+quantity, from 5 to 15% or even more. Much of this, when the
+amount is large, is often due to sand mechanically intermixed;
+when air-dried the proportion of water is from 8 to 20%. When
+these constituents are deducted the average composition may
+be stated to be&mdash;carbon, 52 to 66; hydrogen, 4.7 to 7.4; oxygen,
+28 to 39; and nitrogen, 1.5 to 3%. Average air-dried peat may
+be taken as having a calorific value of 3000 to 3500 units, and when
+dried at 100° C., and with a minimum of ash (4 to 5%), at about
+5200 units, or from a quarter to one-third more than that of an
+equal weight of wood. The lighter and more spongy varieties of
+peat when air-dried are exceedingly inflammable, firing at a
+temperature of 200° C.; the denser pulpy kinds ignite less readily
+when in the natural state, and often require a still higher temperature
+when prepared by pulping and compression or partial
+carbonization. Most kinds burn with a red smoky flame, developing
+a very strong odour, which, however, has its admirers in the
+same way that wood smoke has. This arises from the destructive
+distillation of imperfectly carbonized organic matter. The ash,
+like that of wood, is light and powdery, except when much sand
+is present, when it is of a denser character.</p>
+
+<p>Peat is principally found in high latitudes, on exposed high
+tablelands and treeless areas in more temperate climates, and
+in the valleys of slow-flowing rivers,&mdash;as in Ireland, the west of
+Scotland, the tableland of Bavaria, the North German plain,
+and parts of the valleys of the Somme, Oise and a few other
+rivers in northern France. A principal objection to its use is its
+extreme bulk, which for equal evaporative effect is from 8 to 18
+times that of coal. Various methods have been proposed, and
+adopted more or less successfully, for the purpose of increasing
+the density of raw peat by compression, either with or without
+pulping; the latter process gives the heaviest products, but the
+improvement is scarcely sufficient to compensate for the cost.</p>
+
+<p>Lignite or brown coal is of intermediate character between
+peat and coal proper. The best kinds are undistinguishable in
+quality from free-burning coals, and the lowest earthy
+kinds are not equal to average peat. When freshly
+<span class="sidenote">Lignite.</span>
+raised, the proportion of water may be from 45 to 50% and
+even more, which is reduced from 28 to 20% by exposure to
+dry air. Most varieties, however, when fully dried, break up
+into powder, which considerably diminishes their utility as fuel,
+as they cannot be consolidated by coking. Lignite dust may,
+however, be compacted into serviceable blocks for burning, by
+pressure in machines similar to those used for brickmaking,
+either in the wet state as raised from the mines or when kiln-dried
+at 200° C. This method was adopted to a very large extent
+in Prussian Saxony. The calorific value varies between 3500
+and 5000 units, and the evaporative factor from 2.16 when freshly
+raised to 5.84 for the best kinds of lignite when perfectly dried.</p>
+
+<p>Of the other natural fuels, apart from coal (<i>q.v.</i>), the most
+important is so-called vegetable refuse, such as cotton stalks,
+brushwood, straw, and the woody residue of sugar-cane
+after the extraction of the saccharine juice known as
+<span class="sidenote">Other natural fuels.</span>
+megasse or cane trash. These are extensively used in
+countries where wood and coal are scarce, usually for
+providing steam in the manufactures where they arise, <i>e.g.</i>
+straw for thrashing, cotton stalks for ploughing, irrigating, or
+working presses, and cane trash for boiling down sugar or driving
+the cane mill. According to J. Head (<i>Proc. Inst. of Civil Engineers</i>,
+vol. xlviii. p. 75), the evaporative values of 1 &#8468; of these
+different articles when burnt in a tubular boiler are&mdash;coal, 8 &#8468;;
+dry peat, 4 &#8468;; dry wood, 3.58-3.52 &#8468;; cotton stalks or
+megasse, 3.2-2.7 &#8468;; straw, 2.46-2.30 &#8468;. Owing to the
+siliceous nature of the ash of <span class="correction" title="amended from sraw">straw</span>, it is desirable to have a
+means of clearing the grate bars from slags and clinkers at short
+intervals, and to use a steam jet to clear the tubes from similar
+deposits.</p>
+
+<p>The common fuel of India and Egypt is derived from the
+dung of camels and oxen, moulded into thin cakes, and dried
+in the sun. It has a very low heating power, and in burning
+gives off acrid ammoniacal smoke and vapour.</p>
+
+<p>Somewhat similar are the tan cakes made from spent tanners&rsquo;
+bark, which are used to some extent in eastern France and in
+Germany. They are made by moulding the spent bark into cakes,
+which are then slowly dried by exposure to the air. Their effect
+is about equivalent to 80 and 30% of equal weights of wood and
+coal respectively.</p>
+
+<p><span class="pagenum"><a name="page275" id="page275"></a>275</span></p>
+
+<p>Sulphur, phosphorus and silicon, the other principal combustible
+elements, are only of limited application as fuels. The
+first is used in the liquidation of sulphur-bearing rocks. The ore
+is piled into large heaps, which are ignited at the bottom, a
+certain proportion, from one-fourth to one-third, of the sulphur
+content being sacrificed, in order to raise the mass to a sufficient
+temperature to allow the remainder to melt and
+run down to the collecting basin. Another application
+is in the so-called &ldquo;pyritic smelting,&rdquo; where
+ores of copper (<i>q.v.</i>) containing iron pyrites, FeS<span class="su">2</span>,
+are smelted with appropriate fluxes in a hot blast,
+without preliminary roasting, the sulphur and iron
+of the pyrites giving sufficient heat by oxidation to
+liquefy both slag and metal. Phosphorus, which is
+of value from its low igniting point, receives its only
+application in the manufacture of lucifer matches.
+The high temperature produced by burning phosphorus is in
+part due to the product of combustion (phosphoric acid) being
+solid, and therefore there is less heat absorbed than would be the
+case with a gaseous product. The same effect is observed in a
+still more striking manner with silicon, which in the only special
+case of its application to the production of heat, namely, in the
+Bessemer process of steel-making, gives rise to an enormous
+increase of temperature in the metal, sufficient indeed to keep
+the iron melted. The absolute calorific value of silicon is lower
+than that of carbon, but the product of combustion (silica)
+being non-volatile at all furnace temperatures, the whole of
+the heat developed is available for heating the molten iron,
+instead of a considerable part being consumed in the work of
+volatilization, as is the case with carbonic oxide, which burns
+to waste in the air.</p>
+
+<div class="condensed">
+<p><i>Assay and Valuation of Carbonaceous Fuels</i>.&mdash;The utility or value
+of a fuel depends upon two principal factors, namely, its calorific
+power and its calorific intensity or pyrometric effect, that
+is, the sensible temperature of the products of combustion.
+<span class="sidenote">Calorific power.</span>
+The first of these is constant for any particular product of
+combustion independently of the method by which the burning is
+effected, whether by oxygen, air or a reducible metallic oxide. It
+is most conveniently determined in the laboratory by measuring
+the heat evolved during the combustion of a given weight of the fuel.
+The method of Lewis Thompson is one of the most useful. The
+calorimeter consists of a copper cylinder in which a weighed quantity
+of coal intimately mixed with 10-12 parts of a mixture of 3 parts
+of potassium chlorate and 1 of potassium nitrate is deflagrated
+under a copper case like a diving-bell, placed at the bottom of a deep
+glass jar filled with a known weight of water. The mixture is fired
+by a fuse of lamp-cotton previously soaked in a nitre solution and
+dried. The gases produced by the combustion rising through the
+water are cooled, with a corresponding increase of temperature in
+the latter, so that the difference between the temperature observed
+before and after the experiment measures the heat evolved. The
+instrument is so constructed that 30 grains (2 grammes) of coal are
+burnt in 29,010 grains of water, or in the proportion of 1 to 937,
+these numbers being selected that the observed rise of temperature
+in Fahrenheit degrees corresponds to the required evaporative value
+in pounds, subject only to a correction for the amount of heat
+absorbed by the mass of the instrument, for which a special coefficient
+is required and must be experimentally determined. The ordinary
+bomb calorimeter is also used. An approximate method is based
+upon the reduction of lead oxide by the carbon and hydrogen of the
+coal, the amount of lead reduced affording a measure of the oxygen
+expended, whence the heating power may be calculated, 1 part of
+pure carbon being capable of producing 34½ times its weight of lead.
+The operation is performed by mixing the weighed sample with a
+large excess of litharge in a crucible, and exposing it to a bright
+red heat for a short time. After cooling, the crucible is broken and
+the reduced button of lead is cleaned and weighed. The results
+obtained by this method are less accurate with coals containing
+much disposable hydrogen and iron pyrites than with those approximating
+to anthracite, as the heat equivalent of the hydrogen in
+excess of that required to form water with the oxygen of the coal
+is calculated as carbon, while it is really about four times as great.
+Sulphur in iron pyrites also acts as a reducing agent upon litharge,
+and increases the apparent effect in a similar manner.</p>
+
+<p>The evaporative power of a coal found by the above methods,
+and also by calculating the separate calorific factors of the components
+as determined by the chemical analysis, is always considerably
+above that obtained by actual combustion under a steam boiler,
+as in the latter case numerous sources of loss, such as imperfect
+combustion of gases, loss of unburnt coal in cinders, &amp;c., come into
+play, which cannot be allowed for in laboratory experiments. It is
+usual, therefore, to determine the value of a coal by the combustion
+of a weighed quantity in the furnace of a boiler, and measuring the
+amount of water evaporated by the heat developed.</p>
+
+<p>In a research upon the heating power and other properties of coal
+for naval use, carried out by the German admiralty, the results
+tabulated below were obtained with coals <span class="correction" title="amended from form">from</span> different localities.</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tccm allb">&nbsp;</td> <td class="tccm allb">Slag left<br />in Grate.</td> <td class="tccm allb">Ashes in<br />Ashpit.</td> <td class="tccm allb">Soot in<br />Flues.</td> <td class="tccm allb">Water<br />evaporated by<br />1 &#8468; of Coal</td></tr>
+
+<tr><td class="tcl lb rb">Westphalian gas coals</td> <td class="tcl rb">0.33-6.42</td> <td class="tcl rb">2.83-6.53</td> <td class="tcl rb">0.32-0.46</td> <td class="tcl rb">6.60-7.45 &#8468;</td></tr>
+<tr><td class="tcl lb rb"> &emsp; Do. bituminous coals</td> <td class="tcl rb">0.98-9.10</td> <td class="tcl rb">1.97-9.63</td> <td class="tcl rb">0.24-0.88</td> <td class="tcl rb">7.30-8.66</td></tr>
+<tr><td class="tcl lb rb"> &emsp; Do. dry coals</td> <td class="tcl rb">1.93-5.70</td> <td class="tcl rb">4.37-10.63</td> <td class="tcl rb">0.24-0.48</td> <td class="tcl rb">7.03-8.51</td></tr>
+<tr><td class="tcl lb rb">Silesian coals</td> <td class="tcl rb">0.92-1.30</td> <td class="tcl rb">3.15-3.50</td> <td class="tcl rb">0.24-0.30</td> <td class="tcl rb">6.73-7.10</td></tr>
+<tr><td class="tcl lb rb">Welsh steam coals</td> <td class="tcl rb">1.20-4.07</td> <td class="tcl rb">4.07</td> <td class="tcl rb">0.32</td> <td class="tcl rb">8.41</td></tr>
+<tr><td class="tcl lb rb bb">Newcastle coals</td> <td class="tcl rb bb">1.92</td> <td class="tcl rb bb">2.57</td> <td class="tcl rb bb">0.35</td> <td class="tcl rb bb">7.28</td></tr>
+
+</table>
+
+<p>The heats of combustion of elements and compounds will be
+found in most of the larger works on physical and chemical constants;
+a convenient series is given in the <i>Annuaire du Bureau des Longitudes</i>,
+appearing in alternate years. The following figures for the principal
+fuel elements are taken from the issue for 1908; they are expressed
+in gramme &ldquo;calories&rdquo; or heat units, signifying the weight of water
+in grammes that can be raised 1° C. in temperature by the combustion
+of 1 gramme of the substance, when it is oxidized to the condition
+shown in the second column:</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcc allb">Element.</td> <td class="tcc allb">Product of Combustion.</td> <td class="tcc allb">Calories.</td></tr>
+
+<tr><td class="tclm lb rb cl" rowspan="2">Hydrogen</td> <td class="tcl rb">Water, H<span class="su">2</span>O, condensed to liquid</td> <td class="tcr rb">34,500</td></tr>
+<tr><td class="tcl rb">&emsp;&emsp; &rdquo; &emsp;&emsp; as vapour</td> <td class="tcr rb">29,650</td></tr>
+<tr><td class="tcl lb rb">Carbon&mdash;</td> <td class="tcl rb">&nbsp;</td> <td class="tcr rb">&nbsp;</td></tr>
+<tr><td class="tcl lb rb"> &emsp; Diamond</td> <td class="tcl rb">Carbon Dioxide, CO<span class="su">2</span></td> <td class="tcr rb">7,868</td></tr>
+<tr><td class="tcl lb rb"> &emsp; Graphite</td> <td class="tcl rb">&emsp; &rdquo; &emsp;&emsp;&emsp; &rdquo;</td> <td class="tcr rb">7,900</td></tr>
+<tr><td class="tcl lb rb"> &emsp; Amorphous</td> <td class="tcl rb">&emsp; &rdquo; &emsp;&emsp;&emsp; &rdquo;</td> <td class="tcr rb">8,133</td></tr>
+<tr><td class="tcl lb rb">Silicon&mdash;</td> <td class="tcl rb">&nbsp;</td> <td class="tcr rb">&nbsp;</td></tr>
+<tr><td class="tcl lb rb"> &emsp; Amorphous</td> <td class="tcl rb">Silicon Dioxide, SiO<span class="su">2</span></td> <td class="tcr rb">6,414</td></tr>
+<tr><td class="tcl lb rb"> &emsp; Crystallized</td> <td class="tcl rb">&emsp; &rdquo; &emsp;&emsp;&emsp; &rdquo;</td> <td class="tcr rb">6,570</td></tr>
+<tr><td class="tcl lb rb"> Phosphorus</td> <td class="tcl rb">Phosphoric pentoxide, P<span class="su">2</span>O<span class="su">5</span></td> <td class="tcr rb">5,958</td></tr>
+<tr><td class="tcl lb rb bb"> Sulphur</td> <td class="tcl rb bb">Sulphur dioxide, SO<span class="su">2</span>, gaseous</td> <td class="tcr rb bb">2,165</td></tr>
+
+</table>
+
+<p class="noind">The results may also be expressed in terms of the atomic equivalent
+of the combustible by multiplying the above values by the atomic
+weight of the substance, 12 for carbon, 28 for silicon, &amp;c.</p>
+
+<p>In all fuels containing hydrogen the calorific value as found by
+the calorimeter is higher than that obtainable under working conditions
+by an amount equal to the latent heat of volatilization of
+water which reappears as heat when the vapour is condensed,
+though under ordinary conditions of use the vapour passes away uncondensed.
+This gives rise to the distinction of higher and lower
+calorific values for such substances, the latter being those generally
+used in practice. The differences for the more important compound
+gaseous fuels are as follows:&mdash;</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcl">&nbsp;</td> <td class="tcc" colspan="2">Calorific Value.</td></tr>
+<tr><td class="tcl">&nbsp;</td> <td class="tcr">Higher.</td> <td class="tcr">Lower.</td></tr>
+<tr><td class="tcl">Acetylene, C<span class="su">2</span>H<span class="su">2</span></td> <td class="tcr">11,920</td> <td class="tcr">11,500</td></tr>
+<tr><td class="tcl">Ethylene, C<span class="su">2</span>H<span class="su">4</span></td> <td class="tcr">11,880</td> <td class="tcr">11,120</td></tr>
+<tr><td class="tcl">Methane, CH<span class="su">4</span></td> <td class="tcr">13,240</td> <td class="tcr">11,910</td></tr>
+<tr><td class="tcl">Carbon monoxide, CO</td> <td class="tcr">2,440</td> <td class="tcr">2,440</td></tr>
+</table>
+
+<p>The calorific intensity or pyrometric effect of any particular fuel
+depends upon so many variable elements that it cannot be determined
+except by actual experiment. The older method
+was to multiply the weight of the products of combustion
+<span class="sidenote">Caloric intensity.</span>
+by their specific heats, but this gave untrustworthy
+results as a rule, on account of two circumstances&mdash;the great increase
+in specific heat at high temperatures in compound gases such as
+water and carbon dioxide, and their instability when heated to
+1800° or 2000°. At such temperatures dissociation to a notable
+extent takes place, especially with the latter substance, which is also
+readily reduced to carbon monoxide when brought in contact with
+carbon at a red heat&mdash;a change which is attended with a large
+heat absorption. This effect is higher with soft kinds of carbon,
+such as charcoal or soft coke, than with dense coke, gas retort
+carbon or graphite. These latter substances, therefore, are used
+when an intense local heat is required, as for example, in the Deville
+furnace, to which air is supplied under pressure. Such a method is,
+however, only of very special application, the ordinary method being
+to supply air to the fire in excess of that required to burn the fuel
+to prevent the reduction of the carbon dioxide. The volume of
+flame, however, is increased by inert gas, and there is a proportionate
+diminution of the heating effect. Under the most favourable conditions,
+when the air employed has been previously raised to a high
+temperature and pressure, the highest attainable flame temperature
+from carbonaceous fuel seems to be about 2100°-2300° C.; this is
+realized in the bright spots or &ldquo;eyes&rdquo; of the tuyeres of blast furnaces.</p>
+
+<p>Very much higher temperatures may be reached when the products
+of combustion are not volatile, and the operation can be effected
+by using the fuel and oxidizing agent in the proportions exactly
+<span class="pagenum"><a name="page276" id="page276"></a>276</span>
+required for perfect combustion and intimately mixed. These
+conditions are met in the &ldquo;Thermit&rdquo; process of Goldschmidt,
+where finely divided aluminium is oxidized by the oxide of some
+similar metal, such as iron, manganese or chromium, the reaction
+being started by a primer of magnesium and barium peroxide.
+The reaction is so rapidly effected that there is an enormous rise in
+temperature, estimated to be 5400° F. (3000° C.), which is sufficient
+to melt the most refractory metals, such as chromium. The slag
+consists of alumina which crystallizes in the forms of corundum and
+ruby, and is utilized as an abrasive under the name of corubin.</p>
+
+<p>The chemical examination includes the determination of (1)
+moisture, (2) ash, (3) coke, (4) volatile matter, (5) fixed carbon in
+coke, (6) sulphur, (7) chlorine, (8) phosphorus. Moisture is determined
+by noting the loss in weight when a sample is heated at 100°
+for about one hour. The ash is determined by heating a sample
+in a muffle furnace until all the combustible matter has been burnt
+off. The ash, which generally contains silica, oxides of the alkaline
+earths, ferric oxide (which gives the ash a red colour), sulphur, &amp;c.,
+is analysed by the ordinary gravimetric methods. The determination
+of coke is very important on account of the conclusions concerning
+the nature of the coal which it permits to be drawn. A sample is
+finely powdered and placed in a covered porcelain crucible, which
+is surrounded by an outer one, the space between them being packed
+with small coke. The crucibles are heated in a wind furnace for
+1 to 1½ hours, then allowed to cool, the inner crucible removed,
+and the coke weighed. The coke may be (1) pulverulent, (2)
+slightly fritted, (3) spongy and swelled, (4) compact. Pulverulent
+cokes indicate a non-caking bituminous coal, rich in oxygen if the
+amount be below 60%, but if the amount be very much less it
+generally indicates a lignite; if the amount be above 80% it indicates
+an anthracite containing little oxygen or hydrogen. A fritted
+coke indicates a slightly coking coal, while the spongy appearance
+points to a highly coking coal which has been partly fused in the
+furnace. A compact coke is yielded by good coking coals, and is
+usually large in amount. The volatile matters are determined as the
+loss of weight on coking less the amount of moisture. The &ldquo;fixed
+carbon&rdquo; is the carbon retained in the coke, which contains in addition
+the ash already determined. The fixed carbon is therefore the difference
+between the coke and the ash, and may be determined from
+these figures; or it may be determined directly by burning off the
+coke in a muffle and noting the loss in weight. Sulphur may be
+present as (1) organic sulphur, (2) as iron pyrites or other sulphides,
+(3) as the sulphates of calcium, aluminium and other metals; but
+the amount is generally so small that only the total sulphur is
+determined. This is effected by heating a mixture of the fuel
+with lime and sodium carbonate in a porcelain dish to redness in a
+muffle until all the carbonaceous matter has been burnt off. The
+residue, which contains the sulphur as calcium sulphate, is transferred
+to a beaker containing water to which a little bromine has
+been added. Hydrochloric acid is carefully added, the liquid
+filtered and the residue washed. To the filtrate ammonia is added,
+and then barium chloride, which precipitates the sulphur as barium
+sulphate. Sulphur existing in the form of sulphates may be removed
+by washing a sample with boiling water and determining the sulphuric
+acid in the solution. The washed sample is then fused in the usual
+way to determine the proportion of sulphur existing as iron pyrites.
+The distinction between sulphur present as sulphate and sulphide
+is of importance in the examination of coals intended for iron
+smelting, as the sulphates of the earthy metals are reduced by the
+gases of the furnace to sulphides, which pass into the slag without
+affecting the quality of the iron produced, while the sulphur of the
+metallic sulphides in the ash acts prejudicially upon the metal.
+Coals for gas-making should contain little sulphur, as the gases
+produced in the combustion are noxious and have very corrosive
+properties. Chlorine is rarely determined, but when present in
+quantity it corrodes copper and brass boiler tubes, with which consequently
+chlorine-bearing coals cannot be used. The element is
+determined by fusing with soda lime in a muffle, dissolving the residue
+in water and precipitating with silver nitrate. Phosphorus is
+determined in the ash by fusing it with a mixture of sodium and
+potassium carbonates, extracting the residue with hydrochloric acid,
+and twice evaporating to dryness with the same acid. The residue
+is dissolved in hydrochloric acid, a few drops of ferric chloride added,
+and then ammonia in excess. The precipitate of ferric phosphate
+is then treated as in the ordinary estimation of phosphates. If it be
+necessary to determine the absolute amount of carbon and hydrogen in
+a fuel, the dried sample is treated with copper oxide as in the ordinary
+estimation of these elements in organic compounds.</p>
+</div>
+<div class="author">(H. B.)</div>
+
+<p class="pt2 center"><i>Liquid Fuel.</i></p>
+
+<p>Vegetable oil is not used for fuel except for laboratory purposes,
+partly because its constituent parts are less adaptable
+for combustion under the conditions necessary for steam-raising,
+but chiefly because of the commercial difficulty of producing it
+with sufficient economy to compete with mineral fuel either solid
+or liquid.</p>
+
+<p>The use of petroleum as fuel had long been recognized as a
+scientific possibility, and some attempts had been made to adopt
+it in practice upon a commercial scale, but the insufficiency,
+and still more the irregularity, of the supplies prevented it from
+coming into practical use to any important extent until about
+1898, when discoveries of oil specially adapted by chemical
+composition for fuel purposes changed the aspect of the situation.
+These discoveries of special oil were made first in Borneo and
+later in Texas, and experience in treating the oils from both
+localities has shown that while not less adapted to produce
+kerosene or illuminating oil, they are better adapted to produce
+fuel oil than either the Russian or the Pennsylvanian products.
+Texas oil did not hold its place in the market for long, because
+the influx of water into the wells lowered their yield, but discoveries
+of fuel oil in Mexico have come later and will help to
+maintain the balance of the world&rsquo;s supply, although this is still
+a mere fraction of the assured supply of coal.</p>
+
+<p>With regard to the chemical properties of petroleum, it is not
+necessary to say more in the present place than that the lighter
+and more volatile constituents, known commercially as naphtha
+and benzene, must be removed by distillation in order to leave
+a residue composed principally of hydrocarbons which, while
+containing the necessary carbon for combustion, shall be sufficiently
+free from volatile qualities to avoid premature ignition
+and consequent danger of explosion. Attempts have been made
+to use crude oil for fuel purposes, and these have had some
+success in the neighbourhood of the oil wells and under boilers
+of unusually good ventilation both as regards their chimneys
+and the surroundings of their stokeholds; but for reasons both
+of commerce and of safety it is not desirable to use crude oil
+where some distillation is possible. The more complete the
+process of distillation, and the consequent removal of the volatile
+constituents, the higher the flash-point, and the more turgid
+and viscous is the fuel resulting; and if the process is carried to
+an extreme, the residue or fuel becomes difficult to ignite by the
+ordinary process of spraying or atomizing mechanically at the
+moment immediately preceding combustion. The proportions
+which have been found to work efficiently in practice are as
+follows:&mdash;</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcl">Carbon</td> <td class="tcr">88.00 %</td></tr>
+<tr><td class="tcl">Hydrogen</td> <td class="tcr">10.75 %</td></tr>
+<tr><td class="tcl">Oxygen</td> <td class="tcr">1.25 %</td></tr>
+<tr><td class="tcl"> &nbsp;</td> <td class="tcr">&mdash;&mdash;&mdash; &emsp;</td></tr>
+<tr><td class="tcl"> &emsp;&emsp;&emsp;&emsp; Total</td> <td class="tcr">100 &emsp;</td></tr>
+</table>
+
+<p>The standards of safety for liquid fuel as determined by
+flash-point are not yet finally settled, and are changing from time
+to time. The British admiralty require a flash-point of 270° F.,
+and to this high standard, and the consequent viscosity of the
+fuel used by vessels in the British fleet, may partly be attributed
+the low rate of combustion that was at first found possible in
+them. The German admiralty have fixed a flash-point of 187° F.,
+and have used oil of this standard with perfect safety, and at the
+same time with much higher measure of evaporative duty than
+has been attained in British war-vessels. In the British mercantile
+marine Lloyd&rsquo;s Register has permitted fuel with a flash-point
+as low as 150° F. as a minimum, and no harm has resulted.
+The British Board of Trade, the department of the government
+which controls the safety of passenger vessels, has fixed a higher
+standard upon the basis of a minimum of 185°. In the case of
+locomotives the flash-point as a standard of safety is of less
+importance than in the case of stationary or marine boilers,
+because the storage is more open, and the ventilation, both of the
+storage tanks and the boilers during combustion, much more
+perfect than in any other class of steam-boilers.</p>
+
+<p>The process of refining by distillation is also necessary to
+reduce two impurities which greatly retard storage and combustion,
+<i>i.e.</i> water and sulphur. Water is found in all crude
+petroleum as it issues from the wells, and sulphur exists in
+important quantities in oil from the Texas wells. Its removal
+was at first found very expensive, but there no longer exists
+difficulty in this respect, and large quantities of petroleum fuel
+practically free from sulphur are now regularly exported from
+Texas to New York and to Europe.</p>
+
+<p><span class="pagenum"><a name="page277" id="page277"></a>277</span></p>
+
+<p>Water mixed with fuel is in intimate mechanical relation, and
+frequently so remains in considerable quantities even after the
+process of distillation. It is in fact so thoroughly mixed as to
+form an emulsion. The effect of feeding such a mixture into a
+furnace is extremely injurious, because the water must be decomposed
+chemically into its constituents, hydrogen and oxygen,
+thus absorbing a large quantity of heat which would otherwise
+be utilized for evaporation. Water also directly delays combustion
+by producing from the jet a long, dull, red flame instead
+of a short bright, white flame, and the process of combustion,
+which should take place by vaporization of the oil near the
+furnace mouth, is postponed and transferred to the upper part of
+the combustion-box, the tubes, and even the base of the chimney,
+producing loss of heat and injury to the boiler structure. The
+most effective means of ridding the fuel of this dangerous
+impurity is by heat and settlement. The coefficients of expansion
+of water and oil by heat are substantially different, and a
+moderate rise of temperature therefore separates the particles
+and precipitates the water, which is easily drawn off&mdash;leaving
+the oil available for use. The heating and precipitation are
+usually performed upon a patented system of settling tanks
+and heating apparatus known as the Flannery-Boyd system,
+which has proved itself indispensable for the successful use at
+sea of petroleum fuel containing any large proportion of water.</p>
+
+<p>The laboratory and mechanical use of petroleum for fuel has
+already been referred to, but it was not until the year 1870 that
+petroleum was applied upon a wider and commercial
+scale. In the course of distillation of Russian crude
+<span class="sidenote">Progress of liquid fuel.</span>
+petroleum for the production of kerosene or lamp oil,
+large quantities of refuse were produced&mdash;known by
+the Russian name of <i>astatki</i>&mdash;and these were found an incumbrance
+and useless for any commercial purpose. To a Russian
+oil-refiner gifted with mechanical instinct and the genius for
+invention occurred the idea of utilizing the waste product as
+fuel by spraying or atomizing it with steam, so that, the thick
+and sluggish fluid being broken up into particles, the air
+necessary for combustion could have free access to it. The
+earliest apparatus for this
+purpose was a simple piece
+of gas-tube, into which the
+thick oil was fed; by
+another connexion steam
+at high pressure was admitted
+to an inner and
+smaller tube, and, the end
+of the tube nearest to the
+furnace being open, the
+pressure of the steam blew
+the oil into the furnace,
+and by its velocity broke
+it up into spray. The apparatus
+worked with
+success from the first. Experience
+pointed out the
+proper proportionate sizes
+for the inlets of steam and
+oil, the proper pressure for
+the steam, and the proportionate
+sizes for the orifices
+of admission to the furnaces,
+as well as the sizes of
+air-openings and best arrangements of fire-bricks in the furnaces
+themselves; and what had been a waste product now became
+a by-product of great value. Practically all the steam power
+in South Russia, both for factories and navigation of the inland
+seas and rivers, is now raised from <i>astatki</i> fuel.</p>
+
+<p>In the Far East, including Burma and parts of China and
+Japan, the use of liquid fuel spread rapidly during the years
+1899, 1900 and 1901, owing entirely to the development of the
+Borneo oil-fields by the enterprise of Sir Marcus Samuel and the
+large British corporation known as the Shell Transport and
+Trading Company, of which he is the head. This corporation
+has since amalgamated with the Royal Dutch Petroleum Company
+controlling the extensive wells in Dutch Borneo, and
+together they supply large quantities of liquid fuel for use in the
+Far East. In the United States of America liquid fuel is not
+only used for practically the whole of the manufacturing and
+locomotive purposes of the state of Texas, but factories in New
+York, and a still larger number in California, are now discarding
+the use of coal and adopting petroleum, because it is more
+economical in its consumption and also more easily handled in
+transit, and saves nearly all the labour of stoking. So far the
+supplies for China and Japan have been exported from Borneo,
+but the discoveries of new oil-fields in California, of a character
+specially adapted for fuel, have encouraged the belief that it may
+be possible to supply Chile and Peru and other South American
+countries, where coal is extremely expensive, with Californian
+fuel; and it has also found its way across the Pacific to Japan.
+There are believed to be large deposits in West Africa, but in the
+meantime the only sources of supply to those parts of Africa
+where manufacture is progressing, <i>i.e.</i> South Africa and Egypt,
+are the oil-fields of Borneo and Texas, from which the import
+has well begun, from Texas to Alexandria via the Mediterranean,
+and from Borneo to Cape Town via Singapore.</p>
+
+<p>In England, notwithstanding the fact that there exist the
+finest coal-fields in the world, there has been a surprising development
+of the use of petroleum as fuel. The Great Eastern railway
+adapted 120 locomotive engines to its use, and these ran with
+regularity and success both on express passenger and goods
+trains until the increase in price due to short supply compelled
+a return to coal fuel. The London, Brighton &amp; South Coast
+railway also began the adaptation of some of their locomotive
+engines, but discontinued the use of liquid fuel from the same
+cause. Several large firms of contractors and cement manufacturers,
+chiefly on the banks of the Thames, made the same
+adaptations which proved mechanically successful, but were
+not continued when the price of liquid fuel increased with the
+increased demand.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:826px; height:410px" src="images/img277.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 1.</span>&mdash;Holden Burner.</td></tr></table>
+
+<p>The chief factors of economy are the greater calorific value
+of oil than coal (about 16 &#8468; of water per &#8468; of oil fuel evaporated
+from a temperature of 212° F.), not only in laboratory practice,
+but in actual use on a large scale, and the saving of labour both
+<span class="sidenote">Economy of liquid fuel.</span>
+in transit from the source of supply to the place of use and in
+the act of stoking the furnaces. The use of cranes,
+hand labour with shovels, wagons and locomotives,
+horses and carts, is unavoidable for the transit of
+coal; and labour to trim the coal, to stoke it when
+under combustion, and to handle the residual ashes, are all
+indispensable to steam-raising by coal. On the other hand, a
+system of pipes and pumps, and a limited quantity of skilled
+<span class="pagenum"><a name="page278" id="page278"></a>278</span>
+labour to manage them, is all that is necessary for the transit
+and combustion of petroleum fuel; and it is certain that even
+in England will be found places which, from topographical
+and other circumstances, will use petroleum more economically
+than coal as fuel for manufacturing purposes under reasonable
+conditions of price for the fuel.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:700px; height:540px" src="images/img278a.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 2.</span>&mdash;Rusden and Eeles Burner.</td></tr></table>
+
+<p>The theoretical calorific value of oil fuel is more nearly realized
+in practice than the theoretical calorific value of coal, because
+the facilities for complete combustion, due to the artificial
+admixture of the air by the atomizing process, are greater in
+the case of oil than coal, and for this reason, among others, the
+practical evaporative results are proportionately higher with
+liquid fuel. In some cases the work done in a steam-engine by
+2 tons of coal has been performed by 1 ton of oil fuel, but in
+others the proportions have been as 3 to 2, and these latter can be
+safely relied on in practice as a minimum. This saving, combined
+with the savings of labour and transit already explained, will
+in the near future make the use of liquid fuel compulsory, except
+in places so near to coal-fields that the cost of coal becomes
+sufficiently low to counterbalance the savings in weight of fuel
+consumed and in labour in handling it. In some locomotives
+on the Great Eastern railway the consumption of oil and coal
+for the same development of horse-power was as 17 &#8468; oil is
+to 35 &#8468; coal; all, however, did not realize so high a result.</p>
+
+<p>The mechanical apparatus for applying petroleum to steam-raising
+in locomotives is very simple. The space in the tender
+usually occupied by coal is closed up by steel-plating closely
+riveted and tested, so as to form a storage tank. From this tank
+<span class="sidenote"><b>Liquid fuel in locomotives.</b></span>
+a feed-pipe is led to a burner of the combined steam-and-oil
+type already indicated, and this burner is so arranged
+as to enter a short distance inside the furnace
+mouth. The ordinary fire-bars are covered with a thin
+layer of coal, which starts the ignition in the first
+place, and the whole apparatus is ready for work. The burner
+best adapted for locomotive practice is the Holden Burner
+(fig. 1), which was used on the Great Eastern railway. The
+steam-pipe is connected at A, the oil-pipe at B, and the hand-wheels
+C and D are for the adjustment of the
+internal orifices according to the rate of combustion
+required. The nozzle E is directed
+towards the furnace, and the external ring
+FF, supplied by the small pipe G and the
+by-pass valve H, projects a series of steam
+jets into the furnace, independent of the
+injections of atomized fuel, and so induces an
+artificial inrush of air for the promotion of
+combustion. This type of burner has also
+been tried on stationary boilers and on board
+ship. It works well, although the great consumption
+of steam by the supplementary ring
+is a difficulty at sea, where the water lost by
+the consumption of steam cannot easily be
+made up.</p>
+
+<p>Although the application of the new fuel
+for land and locomotive boilers has already
+been large, the practice at sea has
+been far more extensive. The reason
+is chiefly to be found in the fact that
+although the sources of supply are at a distance
+<span class="sidenote"><b>Liquid fuel at sea.</b></span>
+from Great Britain, yet they are in
+countries to whose neighbourhood British
+steamships regularly trade, and in which
+British naval squadrons are regularly stationed,
+so that the advantages of adopting liquid fuel
+have been more immediate and the economy
+more direct. The certainty of continuous supply of the fuel and
+the wide distribution of storage stations have so altered the
+conditions that the general adoption of the new fuel for marine
+purposes becomes a matter of urgency for the statesman, the
+merchant and the engineer. None of these can afford to neglect
+the new conditions, lest they be noted and acted upon by their
+competitors. Storage for supply now exists at a number of sea
+ports: London, Barrow, Southampton, Amsterdam, Copenhagen,
+New Orleans, Savannah, New York, Philadelphia,
+Singapore, Hong Kong, Madras, Colombo, Suez, Hamburg,
+Port Arthur, Rangoon, Calcutta, Bombay, Alexandria,
+Bangkok, Saigon, Penang, Batavia, Surabaya, Amoy, Swatow,
+Fuchow, Shanghai, Hankow, Sydney, Melbourne, Adelaide,
+Zanzibar, Mombasa, Yokohama, Kobe and Nagasaki; also
+in South African and South American ports.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:900px; height:280px" src="images/img278b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 3.</span>&mdash;Storage of Liquid Fuel on Oil-carrying Steamers
+(Flannery-Boyd System).</td></tr></table>
+
+<p>The British admiralty have undertaken experiments with
+liquid fuel at sea, and at the same time investigations of the
+<span class="pagenum"><a name="page279" id="page279"></a>279</span>
+possibility of supply from sources within the regions of the
+British empire. There is an enormous supply of shale under the
+north-eastern counties of England, but no oil that can be pumped&mdash;still
+less oil with a pressure above it so as to &ldquo;gush&rdquo; like the
+wells in America&mdash;and the only sources of liquid supply under the
+British flag appear to be in Burma and Trinidad. The Borneo
+fields are not under British control, although developed
+entirely by British capital. The Italian admiralty have fitted
+several large warships with boiler apparatus to burn petroleum.
+The German admiralty are regularly using liquid fuel on the
+China station. The Dutch navy have fitted coal fuel and liquid
+fuel furnaces in combination, so that the smaller powers required
+may be developed by coal alone, and the larger powers by
+supplementing coal fuel with oil fuel. The speeds of some
+vessels of the destroyer type have by this means been accelerated
+nearly two knots.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:571px; height:319px" src="images/img279a.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 4.</span>&mdash;Installation on ss. &ldquo;Trochas.&rdquo;</td></tr></table>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:657px; height:250px" src="images/img279b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 5.</span>&mdash;Details of Furnace, Meyer System.</td></tr></table>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:458px; height:246px" src="images/img279c.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 6.</span>&mdash;Details of Exterior Elongation of Furnace, Meyer System.</td></tr></table>
+
+<p>The questions which govern the use of fuel in warships are
+more largely those of strategy and fighting efficiency than
+economy of evaporation. Indeed, the cost of constructing
+and maintaining in fighting efficiency a modern
+<span class="sidenote">Advantages in warships.</span>
+warship is so great that the utmost use strategically
+must be obtained from the vessel, and in this comparison
+the cost of fuel is relatively so small an item that its increase
+or decrease may be considered almost a negligible quantity.
+The desideratum in a warship is to obtain the greatest fighting
+efficiency based on the thickest armour, the heaviest and most
+numerous guns, the highest maximum speed, and, last and not
+least, the greatest range of effective action based upon the
+maximum supplies of fuel, provisions and other consumable
+stores that the ship can carry. Now, if by changing the type
+of fuel it be possible to reduce its weight by 30%, and to abolish
+the stokers, who are usually more than half the ship&rsquo;s
+company, the weight saved will be represented not
+merely by the fuel, but by the consumable stores
+otherwise necessary for the stokers. Conversely, the
+radius of effective action of the ship will be doubled
+as regards consumable stores if the crew be halved, and
+will be increased by 50% if the same weight of fuel be
+carried in the form of liquid instead of coal. In space
+the gain by using oil fuel is still greater, and 36 cubic
+feet of oil as stored are equal in practical calorific value
+to 67 cubic feet of coal according to the allowance usual
+for ship&rsquo;s bunkering. On the other hand, coal has
+been relied upon, when placed in the side bunkers of
+unarmoured ships, as a protection against shot and
+shell, and this advantage, if it really exists, could not
+be claimed in regard to liquid fuel.</p>
+
+<p>Recent experiments in coaling warships at sea have
+not been very successful, as the least bad weather has
+prevented the safe transmission of coal bags from the collier to
+the ship. The same difficulty does not exist for oil fuel, which
+has been pumped through flexible tubing from one ship to the
+other even in comparatively rough weather. Smokelessness,
+so important a feature of sea strategy, has not always been
+attained by liquid fuel, but where the combustion is complete,
+by reason of suitable furnace arrangements and
+careful management, there is no smoke. The
+great drawback, however, to the use of liquid
+fuel in fast small vessels is the confined space
+allotted to the boilers, such confinement being
+unavoidable in view of the high power concentrated
+in a small hull. The British admiralty&rsquo;s
+experiments, however, have gone far
+to solve the problem, and the quantity of oil
+which can be consumed by forced draught in
+confined boilers now more nearly equals the
+quantity of coal consumed under similar conditions.
+All recent vessels built for the British
+navy are so constructed that the spaces between
+their double bottoms are oil-tight and capable
+of storing liquid fuel in the tanks so formed. Most recent battleships
+and cruisers have also liquid fuel furnace fittings, and in
+1910 it already appeared probable that the use of oil fuel in warships
+would rapidly develop.</p>
+
+<p>In view of recent accusations of insufficiency of coal storage in
+foreign naval depots, by reason of the allegation that coal so
+stored quickly perishes, it is interesting to note that liquid fuel
+may be stored in tanks for an indefinite time without any
+deterioration whatever.</p>
+
+<p>In the case of merchant steamers large progress has also been
+made. The Shell Transport and Trading Company have twenty-one
+vessels successfully navigating in all parts of the
+world and using liquid fuel. The Hamburg-American
+<span class="sidenote">Advantages in merchant ships.</span>
+Steamship Company have four large vessels similarly
+fitted for oil fuel, which, however, differ in furnace
+arrangements, as will be hereafter described, although using
+coal when the fluctuation of the market renders that the more
+economical fuel. One of the large American transatlantic
+lines is adopting liquid fuel, and French, German, Danish and
+American mercantile vessels are also beginning to use it in
+considerable amounts.</p>
+
+<p>In the case of very large passenger steamers, such as those
+of 20 knots and upwards in the Atlantic trade, the saving in cost
+of fuel is trifling compared with the advantage arising from the
+greater weight and space available for freight. Adopting a basis
+of 3 to 2 as between coal consumption and oil consumption,
+there is an increase of 1000 tons of dead weight cargo in even a
+<span class="pagenum"><a name="page280" id="page280"></a>280</span>
+medium-sized Atlantic steamer, and a collateral gain of about
+100,000 cub. ft. of measurement cargo, by reason of the ordinary
+bunkers being left quite free, and the oil being stored in the double
+bottom spaces hitherto unutilized except for the purpose of
+water ballast. The cleanliness and saving of time from bunkering
+by the use of oil fuel is also an important factor in passenger
+ships, whilst considerable additional speed
+is obtainable. The cost of the installation,
+however, is very considerable, as
+it includes not only burners and pipes for
+the furnaces, but also the construction of
+oil-tight tanks, with pumps and numerous
+valves and pipe connexions.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:706px; height:389px" src="images/img280a.jpg" alt="" /></td></tr>
+<tr><td class="tcl f90"><span class="sc">Fig. 7.</span>&mdash;Furnace on ss. &ldquo;Ferdinand Laeisz.&rdquo; A, it is proposed to do away with this ring
+of brickwork as being useless; B, it is proposed to fill this space up, thus continuing lining
+of furnace to combustion chamber, and also to fit protection bricks in way of saddle plate.</td></tr></table>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:897px; height:162px" src="images/img280b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 8.</span>&mdash;Fuel Tanks, &amp;c., of ss. &ldquo;Murex.&rdquo;</td></tr></table>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:850px; height:540px" src="images/img280c.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 9.</span>&mdash;Furnace Gear of ss. &ldquo;Murex.&rdquo;</td></tr></table>
+
+<table class="flt" style="float: right; width: 330px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:278px; height:251px" src="images/img281.jpg" alt="" /></td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 10.</span>&mdash;Section through Furnace
+of ss. &ldquo;Murex.&rdquo;</td></tr></table>
+
+<div class="condensed">
+<p>Fig. 2 shows a burner of Rusden and
+Eeles&rsquo; patent as generally used on board
+ships for the purpose of injecting the oil.
+A is a movable cap holding the packing B,
+which renders the annular spindle M oil and
+steam tight. E is the outer casing containing
+the steam jacket from which the steam,
+after being fed through the steam-supply
+pipe G, passes into the annular space surrounding
+the spindle P. It will be seen that
+if the spindle P be travelled inwards by
+turning the handle N, the orifice at the
+nozzle RR will be opened so as to allow
+the steam to flow out radially. If at the
+same time the annular spindle M be drawn
+inwards by revolving the handle L, the oil
+which passes through the supply pipe F will
+also have emission at RR, and, coming in
+contact with the outflowing steam, will be
+pulverized and sprayed into the furnace. Fig. 3 is a profile and
+plan of a steamer adapted for carrying oil in bulk, and showing
+all the storage arrangements for handling liquid fuel. Fig. 4 shows
+the interior arrangement of the boiler furnace of the steamship
+&ldquo;Trocas.&rdquo; A is broken fire-brick resting on the ordinary
+fire-bars, B is a brick bridge, C a casing of fire-brick intended
+to protect the riveted seam immediately above it from the direct
+<span class="pagenum"><a name="page281" id="page281"></a>281</span>
+impact of the flame, and D is a lining of fire-brick at the back of the
+combustion-box, also intended to protect the plating from the direct
+impact of the petroleum flame. The arrangement of the furnace on
+the Meyer system is shown in fig. 5, where E is an annular projection
+built at the mouth of the furnace, and BB are spiral passages
+for heating the air before it passes into the furnace. Fig. 6 shows
+the rings CC and details of the casting which forms the projection
+or exterior elongation of the furnace. The brickwork arrangement
+adopted for the double-ended boilers on the Hamburg-American
+Steamship Company&rsquo;s &ldquo;Ferdinand Laeisz&rdquo; is represented in fig. 7.
+The whole furnace is lined with fire-brick, and the burner is mounted
+upon a circular disk plate which covers the mouth of the furnace.
+The oil is injected not by steam pulverization, but by pressure due
+to a steam-pump. The oil is heated to about 60°C. before entering
+the pump, and further heated to 90°C. after leaving the pump. It
+is then filtered, and passes
+to the furnace injector C at
+about 30-&#8468; pressure; and
+its passage through this injector
+and the spiral passages
+of which it consists
+pulverizes the oil into spray,
+in which form it readily
+ignites on reaching the
+interior of the furnace. The
+injector is on the Körting
+principle, that is, it atomizes
+by fracture of the liquid oil
+arising from its own momentum
+under pressure.
+The advantage of this
+system as compared with
+the steam-jet system is the
+saving of fresh water, the
+abstraction of which is so
+injurious to the boiler by the formation of scale.</p>
+
+<p>The general arrangement of the fuel tanks and filling pipes on the
+ss. &ldquo;Murex&rdquo; is shown in fig. 8; and fig. 9 represents the furnace
+gear of the same vessel, A being the steam-pipe, B the oil-pipe,
+C the injector, D the swivel upon which the injector is hung so that
+it may be swung clear of the furnace, E the fire-door, and F the
+handle for adjusting the injector. In fig. 10, which represents a
+section of the furnace, H is a fire-brick pier and K a fire-brick
+baffling bridge.</p>
+
+<p>It is found in practice that to leave out the fire-bars ordinarily
+used for coal produces a better result with liquid fuel than the
+alternative system of keeping them in place and protecting them
+by a layer of broken fire-brick.</p>
+
+<p>Boilers fitted upon all the above systems have been run for
+thousands of miles without trouble. In new construction it is
+desirable to give larger combustion chambers and longer and narrower
+boiler tubes than in the case of boilers intended for the combustion
+of coal alone.</p>
+</div>
+<div class="author">(F. F.*)</div>
+
+<p class="pt2 center"><i>Gaseous Fuel.</i></p>
+
+<p>Strictly speaking, much, and sometimes even most, of the
+heating effected by solid or liquid fuel is actually performed by
+the gases given off during the combustion. We speak, however,
+of gaseous fuel only in those cases where we supply a combustible
+gas from the outset, or where we produce from ordinary solid
+(or liquid) fuel in one place a stream of combustible gas which
+is burned in another place, more or less distant from that where
+it has been generated.</p>
+
+<div class="condensed">
+<p>The various descriptions of gaseous fuel employed in practice
+may be classified under the following heads:</p>
+
+<div class="list">
+<p>I. Natural Gas.</p>
+
+<p>II. Combustible Gases obtained as by-products in various
+technical operations.</p>
+
+<p>III. Coal Gas (Illuminating Gas).</p>
+
+<p>IV. Combustible Gases obtained by the partial combustion of
+coal, &amp;c.</p>
+</div></div>
+
+<p>I. <i>Natural Gas.</i>&mdash;From time immemorial it has been known
+that in some parts of the Caucasus and of China large quantities
+of gases issue from the soil, sometimes under water, which can
+be lighted and burn with a luminous flame. The &ldquo;eternal
+fires&rdquo; of Baku belong to this class. In coal-mines frequently
+similar streams of gas issue from the coal; these are called
+&ldquo;blowers,&rdquo; and when they are of somewhat regular occurrence
+are sometimes conducted away in pipes and used for underground
+lighting. As a regular source of heating power, however, natural
+gas is employed only in some parts of the United States, especially
+in Pennsylvania, Kansas, Ohio and West Virginia, where it
+always occurs in the neighbourhood of coal and petroleum
+fields. The first public mention of it was made in 1775, but it was
+not till 1821 that it was turned to use at Fredonia, N.Y. In
+Pennsylvania natural gas was discovered in 1859, but at first
+very little use was made of it. Its industrial employment dates
+only from 1874, and became of great importance about ten
+years later. Nobody ever doubted that the gas found in these
+localities was an accumulation of many ages and that, being
+tapped by thousands of bore-holes, it must rapidly come to an
+end. This assumption was strengthened by the fact that the
+&ldquo;gas-wells,&rdquo; which at first gave out the gas at a pressure of 700
+or 800, sometimes even of 1400 &#8468; per sq. in., gradually showed
+a more and more diminishing pressure and many of them ceased
+to work altogether. About the year 1890 the belief was fairly
+general that the stock of natural gas would soon be entirely
+exhausted. Indeed, the value of the annual production of natural
+gas in the United States, computed as its equivalent of coal,
+was then estimated at twenty-one million dollars, in 1895 at
+twelve millions, in 1899 at eleven and a half millions. But the
+output rose again to a value of twenty-seven millions in 1901,
+and to fifty million dollars in 1907. Mostly the gas, derived
+from upwards of 10,000 gas-wells, is now artificially compressed
+to a pressure of 300 or 400 &#8468; per sq. in. by means of steam-power
+or gas motors, fed by the gas itself, and is conveyed over
+great distances in iron pipes, from 9 or 10 to 36 in. in diameter.
+In 1904 nearly 30,000 m. of pipe lines were in operation. In
+1907 the quantity of natural gas consumed in the United States
+(nearly half of which was in Pennsylvania) was 400,000 million
+cub. ft., or nearly 3 cub. m. Canada (Ontario) also produces
+some natural gas, reaching a maximum of about $746,000 in
+1907.</p>
+
+<p>The principal constituent of natural gas is always methane,
+CH<span class="su">4</span>, of which it contains from 68.4 to 94.0% by volume. Those
+gases which contain less methane contain all the more hydrogen,
+viz. 2.9 to 29.8%. There is also some ethylene, ethane and
+carbon monoxide, rarely exceeding 2 or 3%. The quantity
+of incombustible gases&mdash;oxygen, carbon dioxide, nitrogen&mdash;ranges
+from mere traces to about 5%. The density is from
+0.45 to 0.55. The heating power of 1000 cub. ft. of natural gas
+is equal to from 80 to 120 &#8468;, on the average 100 &#8468;, of good
+coal, but it is really worth much more than this proportion
+would indicate, as it burns completely, without smoke or ashes,
+and without requiring any manual labour. It is employed for
+all domestic and for most industrial purposes.</p>
+
+<p>The origin of natural gas is not properly understood, even
+now. The most natural assumption is, of course, that its formation
+is connected with that of the petroleum always found in
+the same neighbourhood, the latter principally consisting of the
+higher-boiling aliphatic hydrocarbons of the methane series.
+But whence do they both come? Some bring them into connexion
+with the formation of coal, others with the decomposition
+of animal remains, others with that of <i>diatomaceae</i>, &amp;c., and
+even an inorganic origin of both petroleum and natural gas has
+been assumed by chemists of the rank of D.I. Mendeléeff and
+H. Moissan.</p>
+
+<p>II. <i>Gases obtained as By-products.</i>&mdash;There are two important
+cases in which gaseous by-products are utilized as fuel; both
+are intimately connected with the manufacture of iron, but in
+a very different way, and the gases are of very different
+composition.</p>
+
+<p>(<i>a</i>) <i>Blast-furnace Gases.</i>&mdash;The gases issuing from the mouths
+of blast-furnaces (see <span class="sc"><a href="#artlinks">Iron and Steel</a></span>) were first utilized in
+1837 by Faber du Faur, at Wasseralfingen. Their use became
+more extensive after 1860, and practically universal after 1870.
+The volume of gas given off per ton of iron made is about 158,000
+cub. ft. Its percentage composition by volume is:</p>
+
+<table class="ws f90" summary="Contents">
+<tr><td class="tcl">Carbon monoxide</td> <td class="tcl">21.6</td> <td class="tcc">to</td> <td class="tcl">29.0,</td> <td class="tcc">mostly</td> <td class="tcc">about</td> <td class="tcl">26</td> <td class="tcr">%</td></tr>
+<tr><td class="tcl">Hydrogen</td> <td class="tcl">&ensp;1.8</td> <td class="tcc">&rdquo;</td> <td class="tcl">&ensp;6.3,</td> <td class="tcc">&rdquo;</td> <td class="tcc">&rdquo;</td> <td class="tcl">&ensp;3</td> <td class="tcr">%</td></tr>
+<tr><td class="tcl">Methane</td> <td class="tcl">&ensp;0.1</td> <td class="tcc">&rdquo;</td> <td class="tcl">&ensp;0.8,</td> <td class="tcc">&rdquo;</td> <td class="tcc">&rdquo;</td> <td class="tcl">&ensp;0.5</td> <td class="tcr">%</td></tr>
+<tr><td class="tcl">Carbon dioxide</td> <td class="tcl">&ensp;6</td> <td class="tcc">&rdquo;</td> <td class="tcl">12,</td> <td class="tcc">&rdquo;</td> <td class="tcc">&rdquo;</td> <td class="tcl">&ensp;9.5</td> <td class="tcr">%</td></tr>
+<tr><td class="tcl">Nitrogen</td> <td class="tcl">51</td> <td class="tcc">&rdquo;</td> <td class="tcl">60,</td> <td class="tcc">&rdquo;</td> <td class="tcc">&rdquo;</td> <td class="tcl">56</td> <td class="tcr">%</td></tr>
+<tr><td class="tcl">Steam</td> <td class="tcl">&ensp;5</td> <td class="tcc">&rdquo;</td> <td class="tcl">12,</td> <td class="tcc">&rdquo;</td> <td class="tcc">&rdquo;</td> <td class="tcl">&ensp;5</td> <td class="tcr">%</td></tr>
+<tr><td class="tcl" colspan="6">&nbsp;</td> <td class="tcl" colspan="2">&mdash;&mdash;&mdash;</td></tr>
+<tr><td class="tcl" colspan="6">&nbsp;</td> <td class="tcl">100</td> <td class="tcr">%</td></tr>
+</table>
+
+<p class="noind">There is always a large amount of mechanically suspended
+<span class="pagenum"><a name="page282" id="page282"></a>282</span>
+flue-dust in this gas. It is practically equal to a poor producer-gas
+(see below), and is everywhere used, first for heating the blast
+in Cowper stoves or similar apparatus, and secondly for raising
+all the steam required for the operation of the blast-furnace,
+that is, for driving the blowing-engines, hoisting the materials,
+&amp;c. Where the iron ore is roasted previously to being fed into
+the furnace, this can also be done by this gas, but in some cases
+the waste in using it is so great that there is not enough left for
+the last purpose. The calorific power of this gas per cubic foot
+is from 80 to 120 B.Th.U.</p>
+
+<p>Since about 1900 a great advance has been made in this field.
+Instead of burning the blast-furnace gas under steam boilers
+and employing the steam for producing mechanical energy, the
+gas is directly burned in gas-motors on the explosion principle.
+Thus upwards of three times the mechanical energy is obtained
+in comparison with the indirect way through the steam boiler.
+After all the power required for the operations of the blast-furnace
+has been supplied, there is a surplus of from 10 to
+20 h.p. for each ton of pig-iron made, which may be applied
+to any other purpose.</p>
+
+<p>(<i>b</i>) <i>Coke-oven Gases.</i>&mdash;Where the coking of coal is performed
+in the old beehive ovens or similar apparatus the gas issuing
+at the mouth of the ovens is lost. The attempts at utilizing the
+gases in such cases have not been very successful. It is quite
+different where coke is manufactured in the same way as illuminating
+gas, viz. by the destructive distillation
+of coal in closed apparatus
+(retorts), heated from the outside.
+This industry, which is described in
+detail in G. Lunge&rsquo;s <i>Coal-Tar and
+Ammonia</i> (4th ed., 1909), originated
+in France, but has spread far
+more in Germany, where more than
+half of the coke produced is made
+by it; in the United Kingdom and the
+United States its progress has been
+much slower, but there also it has long
+been recognized as the only proper
+method. The output of coke is
+increased by about 15% in comparison with the beehive ovens,
+as the heat required for the process of distillation is not produced
+by burning part of the coal itself (as in the beehive ovens), but
+by burning part of the gas. The quality of the coke for iron-making
+is quite as good as that of beehive coke, although it
+differs from it in appearance. Moreover, the gases can be made
+to yield their ammonia, their tar, and even their benzene vapours,
+the value of which products sometimes exceeds that of the coke
+itself. And after all this there is still an excess of gas available
+for any other purpose.</p>
+
+<p>As the principle of distilling the coal is just the same, whether
+the object is the manufacture of coal gas proper or of coke as the
+main product, although there is much difference in the details
+of the manufacture, it follows that the quality of the gas is very
+similar in both cases, so far as its heating value is concerned.
+Of course this heating value is less where the benzene has been
+extracted from coke-oven gas, since this compound is the richest
+heat-producer in the gas. This is, however, of minor importance
+in the present case, as there is only about 1% benzene in these
+gases.</p>
+
+<p>The composition of coke-oven gases, after the extraction of
+the ammonia and tar, is about 53% hydrogen, 36% methane,
+6% carbon monoxide, 2% ethylene and benzene, 0.5% sulphuretted
+hydrogen, 1.5% carbon dioxide, 1% nitrogen.</p>
+
+<p>III. <i>Coal Gas</i> (<i>Illuminating Gas</i>).&mdash;Although ordinary coal gas
+is primarily manufactured for illuminating purposes, it is also
+extensively used for cooking, frequently also for heating domestic
+rooms, baths, &amp;c., and to some extent also for industrial operations
+on a small scale, where cleanliness and exact regulation of
+the work are of particular importance. In chemical laboratories
+it is preferred to every other kind of fuel wherever it is available.
+The manufacture of coal gas being described elsewhere in this
+work (see <span class="sc"><a href="#artlinks">Gas</a></span>, § <i>Manufacture</i>), we need here only point out that
+it is obtained by heating bituminous coal in fireclay retorts and
+purifying the products of this destructive distillation by cooling,
+washing and other operations. The residual gas, the ordinary
+composition of which is given in the table below, amounts to
+about 10,000 cub. ft. for a ton of coal, and represents about
+21% of its original heating value, 56.5% being left in the coke,
+5.5% in the tar and 17% being lost. As we must deduct from
+the coke that quantity which is required for the heating of the
+retorts, and which, even when good gas producers are employed,
+amounts to 12% of the weight of the coal, or 10% of its heat
+value, the total loss of heat rises to 27%. Taking, further, into
+account the cost of labour, the wear and tear, and the capital
+interest on the plant, coal gas must always be an expensive fuel
+in comparison with coal itself, and cannot be thought of as a
+general substitute for the latter. But in many cases the greater
+expense of the coal gas is more than compensated by its easy
+distribution, the facility and cleanliness of its application, the
+general freedom from the mechanical loss, unavoidable in the
+case of coal fires, the prevention of black smoke and so forth.
+The following table shows the average composition of coal gas
+by volume and weight, together with the heat developed by
+its single constituents, the latter being expressed in kilogram-calories
+per cub. metre (0.252 kilogram-calories = 1 British heat
+unit; 1 cub. metre = 35.3 cub. ft.; therefore 0.1123 calories per
+cub. metre = 1 British heat unit per cub. foot).</p>
+
+<table class="ws f90" summary="Contents">
+<tr><td class="tccm allb">Constituents.</td> <td class="tccm allb">Volume<br />per cent.</td> <td class="tccm allb">Weight<br />per cent.</td> <td class="tccm allb">Heat-value<br />per Cubic<br />Metre<br />Calories.
+ </td> <td class="tccm allb">Heat-value<br />per Quantity<br />contained in<br />1 Cub. Met.</td> <td class="tccm allb">Heat-value<br />per cent.<br />of Total.</td></tr>
+
+<tr><td class="tcl lb rb">Hydrogen, H<span class="su">2</span></td> <td class="tcr rb">47&ensp;</td> <td class="tcr rb">7.4</td> <td class="tcr rb">2,582</td> <td class="tcr rb">1213</td> <td class="tcr rb">22.8</td></tr>
+<tr><td class="tcl lb rb">Methane, CH<span class="su">4</span></td> <td class="tcr rb">34&ensp;</td> <td class="tcr rb">42.8</td> <td class="tcr rb">8,524</td> <td class="tcr rb">2898</td> <td class="tcr rb">54.5</td></tr>
+<tr><td class="tcl lb rb">Carbon monoxide, CO</td> <td class="tcr rb">9&ensp;</td> <td class="tcr rb">19.9</td> <td class="tcr rb">3,043</td> <td class="tcr rb">273</td> <td class="tcr rb">5.1</td></tr>
+<tr><td class="tcl lb rb">Benzene vapour, C<span class="su">6</span>H<span class="su">6</span></td> <td class="tcr rb">1.2</td> <td class="tcr rb">7.4</td> <td class="tcr rb">33,815</td> <td class="tcr rb">405</td> <td class="tcr rb">7.7</td></tr>
+<tr><td class="tcl lb rb">Ethylene, C<span class="su">2</span>H<span class="su">4</span></td> <td class="tcr rb">3.8</td> <td class="tcr rb">8.4</td> <td class="tcr rb">13,960</td> <td class="tcr rb">530</td> <td class="tcr rb">9.9</td></tr>
+<tr><td class="tcl lb rb">Carbon dioxide, CO<span class="su">2</span></td> <td class="tcr rb">2.5</td> <td class="tcr rb">8.6</td> <td class="tcc rb">..</td> <td class="tcc rb">..</td> <td class="tcc rb">..</td></tr>
+<tr><td class="tcl lb rb">Nitrogen, N<span class="su">2</span></td> <td class="tcr rb">2.5</td> <td class="tcr rb">5.5</td> <td class="tcc rb">..</td> <td class="tcc rb">..</td> <td class="tcc rb">..</td></tr>
+
+<tr><td class="tcc lb rb bb">Total</td> <td class="tcr allb">100.0</td> <td class="tcr allb">100.0</td> <td class="tcc allb">..</td> <td class="tcr allb">5319</td> <td class="tcr allb">100.0</td></tr>
+
+</table>
+
+<p>One cubic metre of such gas weighs 568 grammes. <i>Rich gas</i>,
+or gas made by the destructive distillation of certain bituminous
+schists, of oil, &amp;c., contains much more of the heavy hydrocarbons,
+and its heat-value is therefore much higher than the above.
+The carburetted water gas, very generally made in America, and
+sometimes employed in England for mixing with coal gas, is
+of varying composition; its heat-value is generally rather less
+than that of coal gas (see below).</p>
+
+<p>IV. <i>Combustible Gases produced by the Partial Combustion of
+Coal, &amp;c.</i>&mdash;These form by far the most important kind of gaseous
+fuel. When coal is submitted to destructive distillation to
+produce the illuminating gas described in the preceding paragraph,
+only a comparatively small proportion of the heating
+value of the coal (say, a sixth or at most a fifth part) is obtained
+in the shape of gaseous fuel, by far the greater proportion remaining
+behind in the shape of coke.</p>
+
+<p>An entirely different class of gaseous fuels comprises those
+produced by the incomplete combustion of the total carbon
+contained in the raw material, where the result is a mixture of
+gases which, being capable of combining with more oxygen, can
+be burnt and employed for heating purposes. Apart from some
+descriptions of waste gases belonging to this class (of which the
+most notable are those from blast-furnaces), we must distinguish
+two ways of producing such gaseous fuels entirely different in
+principle, though sometimes combined in one operation. The
+incomplete combustion of carbon may be brought about by
+means of atmospheric oxygen, by means of water, or by a
+simultaneous combination of these two actions. In the first
+case the chemical reaction is</p>
+
+<p class="center">C + O = CO &emsp;&emsp;&emsp;</p>
+<div class="author1">(<i>a</i>);</div>
+
+<p class="noind">the nitrogen accompanying the oxygen in the atmospheric air
+necessarily remains mixed with carbon monoxide, and the resulting
+gases, which always contain some carbon dioxide, some
+<span class="pagenum"><a name="page283" id="page283"></a>283</span>
+products of the destructive distillation of the coal, &amp;c., are known
+as <i>producer gas</i> or <i>Siemens gas</i>. In the second case the chemical
+reaction is mainly</p>
+
+<p class="center">C + H<span class="su">2</span>O = CO + H<span class="su">2</span></p>
+<div class="author1">(<i>b</i>);</div>
+
+<p class="noind">that is to say, the carbon is converted into monoxide and the
+hydrogen is set free. As both of these substances can combine
+with oxygen, and as there is no atmospheric nitrogen to deal
+with, the resulting gas (<i>water gas</i>) is, apart from a few impurities,
+entirely combustible. Another kind of water gas is formed by
+the reaction</p>
+
+<p class="center">C + 2H<span class="su">2</span>O = CO<span class="su">2</span> <span class="correction" title="amended from =">+</span> 2H<span class="su">2</span></p>
+<div class="author1">(<i>c</i>),</div>
+
+<p class="noind">but this reaction, which converts all the carbon into the incombustible
+form of CO<span class="su">2</span>, is considered as an unwelcome, although
+never entirely avoidable, concomitant of (<i>b</i>).</p>
+
+<p>The reaction by which water gas is produced being endothermic
+(as we shall see), this gas cannot be obtained except by introducing
+the balance of energy in another manner. This might be done
+by heating the apparatus from without, but as this method would
+be uneconomical, the process is carried out by alternating the
+endothermic production of water gas with the exothermic
+combustion of carbon by atmospheric air. Pure water gas is
+not, therefore, made by a continuous process, but alternates
+with the production of other gases, combustible or not. But
+instead of constantly interrupting the process in this way, a
+continuous operation may be secured by simultaneously carrying
+on both the reactions (<i>a</i>) and (<i>b</i>) in such proportions that the heat
+generated by (<i>a</i>) at least equals the heat absorbed by (<i>b</i>). For
+this purpose the apparatus is fed at the same time with atmospheric
+air and with a certain quantity of steam, preferably
+in a superheated state. Gaseous mixtures of this kind have been
+made, more or less intentionally, for a long time past. One of
+the best known of them, intended less for the purpose of serving
+as ordinary fuel than for that of driving machinery, is the
+Dowson gas.</p>
+
+<p>An advantage common to all kinds of gaseous fuel, which
+indeed forms the principal reason why it is intentionally produced
+from solid fuel, in spite of inevitable losses in the course
+of the operation, is the following. The combustion of solid fuel
+(coal, &amp;c.) cannot be carried on with the theoretically necessary
+quantity of atmospheric air, but requires a considerable excess
+of the latter, at least 50%, sometimes 100% and more. This is
+best seen from the analyses of smoke gases. If all the oxygen
+of the air were converted into CO<span class="su">2</span> and H<span class="su">2</span>O, the amount of CO<span class="su">2</span>
+in the smoke gases should be in the case of pure carbon nearly
+21 volumes %, as carbon dioxide occupies the same volume as
+oxygen; while ordinary coal, where the hydrogen takes up a
+certain quantity of oxygen as well, should show about 18.5%
+CO<span class="su">2</span>. But the best smoke gases of steam boilers show only 12
+or 13%, much more frequently only 10% CO<span class="su">2</span>, and gases from
+reverberatory furnaces often show less than 5%. This means
+that the volume of the smoke gases escaping into the air is
+from 1½ to 2 times (in the case of high-temperature operations
+often 4 times) greater than the theoretical minimum; and as
+these gases always carry off a considerable quantity of heat,
+the loss of heat is all the greater the less complete is the utilization
+of the oxygen and the higher the temperature of the operation.
+This explains why, in the case of the best-constructed steam-boiler
+fires provided with heat economizers, where the smoke
+gases are deprived of most of their heat, the proportion of the
+heat value of the fuel actually utilized may rise to 70 or even 75%,
+while in some metallurgical operations, in glass-making and
+similar cases, it may be below 5%.</p>
+
+<p>One way of overcoming this difficulty to a certain extent is
+to reduce the solid fuel to a very fine powder, which can be
+intimately mixed with the air so that the consumption of the
+latter is only very slightly in excess of the theoretical quantity;
+but this process, which has been only recently introduced on a
+somewhat extended scale, involves much additional expense and
+trouble, and cannot as yet be considered a real success. Generally,
+too, it is far less easily applied than gaseous fuel. The latter
+can be readily and intimately mixed with the exact quantity of
+air that is required and distributed in any suitable way, and
+much of the waste heat can be utilized for a preliminary heating
+of the air and the gas to be burned by means of &ldquo;recuperators.&rdquo;</p>
+
+<p>We shall now describe the principal classes of gaseous fuel,
+produced by the partial combustion of coal.</p>
+
+<p>A. <i>Producer Gas, Siemens Gas.</i>&mdash;As we have seen above, this
+gas is made by the incomplete combustion of fuel. The materials
+generally employed for its production are anthracite, coke or
+other fuels which are not liable to cake during the operation,
+and thus stop the draught or otherwise disturb the process, but
+by special measures also bituminous coal, lignite, peat and other
+fuel may be utilized for gas producers. The fuel is arranged in
+a deep layer, generally from 4 ft. up to 10 ft., and the air is
+introduced from below, either by natural draught or by means of
+a blast, and either by a grate or only by a slit in the wall of the
+&ldquo;gas producer.&rdquo; Even if the primary action taking place at
+the entrance of the air consisted in the complete combustion of
+the carbon to dioxide, CO<span class="su">2</span>, the latter, in rising through the high
+column of incandescent fuel, must be reduced to monoxide:
+CO<span class="su">2</span> + C = 2CO. But as the temperature in the producer rises
+rather high, and as in ordinary circumstances the action of
+oxygen on carbon above 1000° C. consists almost entirely in
+the direct formation of CO, we may regard this compound as
+primarily formed in the hotter parts of the gas-producer. It is
+true that ordinary producer gas always contains more or less
+CO<span class="su">2</span>, but this may be formed higher up by air entering through
+leakages in the apparatus. If we ignore the hydrogen contained
+in the fuel, the theoretical composition of producer gas would
+be 33.3% CO and 66.7% N, both by volume and weight. Its
+weight per cubic metre is 1.251 grammes, and its heat value 1013
+calories per cubic metre, or less than one-fifth of the heat-value
+of coal gas. Practically, however, producer gas contains a small
+percentage of gases, increasing its heat-value, like hydrogen,
+methane, &amp;c., but on the other hand it is never free from carbon
+dioxide to the extent of from 2 to 8%. Its heat-value may
+therefore range between 800 and 1100 calories per cubic metre.
+Even when taking as the basis of our calculation a theoretical gas
+of 33.3% CO, we find that there is a great loss of heat-value in
+the manufacture of this gas. Thermochemistry teaches us that
+the reaction C + O develops 29.5% of the heat produced by the
+complete oxidation of C to CO<span class="su">2</span>, thus leaving only 70.5% for
+the stage CO + O = CO<span class="su">2</span>. If, therefore, the gas given off in the
+producer is allowed to cool down to ordinary temperature,
+nearly 30% of the heat-value of the coal is lost by radiation.
+If, however, the gas producer is built in close proximity to the
+place where the combustion takes place, so that the gas does not
+lose very much of its heat, the loss is correspondingly less. Even
+then there is no reason why this mode of burning the fuel, <i>i.e.</i>
+first with &ldquo;primary air&rdquo; in the producer (C + O = CO), then with
+&ldquo;secondary air&rdquo; in the furnace (CO + O =CO<span class="su">2</span>), should be
+preferred to the direct complete burning of the fuel on a grate,
+unless the above-mentioned advantage is secured, viz. reduction
+of the smoke gases to a minimum by confining the supply of air
+as nearly as possible to that required for the formation of CO<span class="su">2</span>,
+which is only possible by producing an intimate mixture of the
+producer gas with the secondary air. The advantage in question
+is not very great where the heat of the smoke gases can be very
+fully utilized, <i>e.g.</i> in well-constructed steam boilers, salt-pans
+and the like, and as a matter of fact gas producers have not
+found much use in such cases. But a very great advantage is
+attained in high-temperature operations, where the smoke
+gases escape very hot, and where it is on that account all-important
+to confine their quantity to a minimum.</p>
+
+<p>It is precisely in these cases that another requirement frequently
+comes in, viz. the production at a given point of a higher temperature
+than is easily attained by ordinary fires. Gas-firing lends
+itself very well to this end, as it is easily combined with a preliminary
+heating up of the air, and even of the gas itself, by
+means of &ldquo;recuperators.&rdquo; The original and best-known form
+of these, due to Siemens Brothers, consists of two brick chambers
+filled with loosely stacked fire-bricks in such manner that any
+gases passed through the chambers must seek their way through
+the interstices left between the bricks, by which means a thorough
+<span class="pagenum"><a name="page284" id="page284"></a>284</span>
+interchange of temperature takes place. The smoke gases,
+instead of escaping directly into the atmosphere, are made to
+pass through one of these chambers, giving up part of their
+heat to the brickwork. After a certain time the draught is
+changed by means of valves, the smoke gases are passed through
+another chamber, and the cold air intended to feed the combustion
+is made to pass through the first chamber, where it
+takes up heat from the white-hot bricks, and is thus heated up
+to a bright red heat until the chamber is cooled down too far,
+when the draughts are again reversed. Sometimes the producer
+gas itself is heated up in this manner (especially when it has
+been cooled down by travelling a long distance); in that case
+four recuperator chambers must be provided instead of two.
+Another class of recuperators is not founded on the alternating
+system, but acts continuously; the smoke gases travel always
+in the same direction in flues contiguous to other flues or pipes
+in which the air flows in the opposite direction, an interchange
+of heat taking place through the walls of the flues or pipes. Here
+the surface of contact must be made very large if a good effect
+is to be produced. In both cases not merely is a saving effected
+of all the calories which are abstracted by the cold air from the
+recuperator, but as less fuel has to be burned to get a given
+effect, the quantity of smoke gas is reduced. For details and
+other producer gases, see <span class="sc"><a href="#artlinks">Gas</a></span>, II. <i>For Fuel and Power.</i></p>
+
+<p>Gas-firing in the manner just described can be brought about
+by very simple means, viz. by lowering the fire-grate of an
+ordinary fire-place to at least 4 ft. below the fire-bridge, and by
+introducing the air partly below the grate and partly behind
+the fire-place, at or near the point where the greatest heat
+is required. Usually, however, more elaborate apparatus is
+employed, some of which we shall describe below. Gas-firing
+has now become universal in some of the most important industries
+and nearly so in others. The present extension of
+steel-making and other branches of metallurgy is intimately
+connected with this system, as is the modern method of glass-making,
+of heating coal gas retorts and so forth.</p>
+
+<p>The composition of producer gas differs considerably, principally
+according to the material from which it is made. Analyses
+of ordinary producer gas (not such as falls under the heading of
+&ldquo;semi-water gas,&rdquo; see <i>sub</i> C) by volume show 22 to 33% CO,
+1 to 7% CO<span class="su">2</span>, 0.5 to 2% H<span class="su">2</span>, 0.5 to 3% hydrocarbons, and
+64 to 68% N<span class="su">2</span>.</p>
+
+<p>B. <i>Water Gas.</i>&mdash;The reaction of steam on highly heated
+carbonaceous matter was first observed by Felice Fontana in
+1780. This was four years before Henry Cavendish isolated
+hydrogen from water, and thirteen years before William Murdoch
+made illuminating gas by the distillation of coal, so that it was
+no wonder that Fontana&rsquo;s laboratory work was soon forgotten.
+Nor had the use of carburetted water gas, as introduced by
+Donovan in 1830 for illuminating purposes, more than a very
+short life. More important is the fact that during nine years
+the illumination of the town of Narbonne was carried on by
+incandescent platinum wire, heated by water gas, where also
+internally heated generators were for the first time regularly
+employed. The Narbonne process was abandoned in 1865, and
+for some time no real progress was made in this field in Europe.
+But in America, T.S.C. Lowe, Strong, Tessié du Motay and others
+took up the matter, the first permanent success being obtained
+by the introduction (1873) of Lowe&rsquo;s system at Phoenixville, Pa.
+In the United States the abundance of anthracite, as well as of
+petroleum naphtha, adapted for carburetting the gas, secures a
+great commercial advantage to this kind of illuminant over coal
+gas, so that now three-fourths of all American gas-works employ
+carburetted water gas. In Europe the progress of this industry
+was naturally much less rapid, but here also since 1882, when
+the apparatus of Lowe and Dwight was introduced in the town
+of Essen, great improvements have been worked out, principally
+by E. Blass, and by these improvements water gas obtained a
+firm footing also for certain heating purposes. The American
+process for making carburetted water gas, as an auxiliary to
+ordinary coal gas, was first introduced by the London Gas Light
+and Coke Company on a large scale in 1890.</p>
+
+<p>Water gas in its original state is called &ldquo;blue gas,&rdquo; because it
+burns with a blue, non-luminous flame, which produces a very
+high temperature. According to the equation C + H<span class="su">2</span>O = CO + H<span class="su">2</span>,
+this gas consists theoretically of equal volumes of carbon
+monoxide and hydrogen. We shall presently see why it is
+impossible to avoid the presence of a little carbon dioxide and
+other gases, but we shall for the moment treat of water gas as
+if it were composed according to the above equation. The
+reaction C + H<span class="su">2</span>O = CO + H<span class="su">2</span> is endothermic, that is, its thermal
+value is negative. One gram-molecule of carbon produces 97
+great calories (1 great calorie or kilogram-calorie = 1000 gram-calories)
+when burning to CO<span class="su">2</span>, and this is of course the maximum
+effect obtainable from this source. If the same gram-molecule
+of carbon is used for making water gas, that is, CO + H<span class="su">2</span>, the
+heat produced by the combustion of the product is 68.4 +
+57.6 = 126 great calories, an apparent surplus of 29 calories,
+which cannot be got out of nothing. This is made evident by
+another consideration. In the above reaction C is not burned
+to CO<span class="su">2</span>, but to CO, a reaction which produces 28.6 calories per
+gram-molecule. But as the oxygen is furnished from water,
+which must first be decomposed by the expenditure of energy,
+we must introduce this amount, 68.5 calories in the case of
+liquid water, or 57.6 calories in the case of steam, as a negative
+quantity, and the difference, viz. + 28.6 &minus; 57.6 = 29 great calories,
+represents the amount of heat to be expended from another
+source in order to bring about the reaction of one gram-molecule
+of carbon on one gram-molecule of H<span class="su">2</span>O in the shape of steam.
+This explains why steam directed upon incandescent coal will
+produce water gas only for a very short time: even a large
+mass of coal will quickly be cooled down so much that at first a
+gas of different composition is formed and soon the process will
+cease altogether. We can avoid this result by carrying on the
+process in a retort heated from without by an ordinary coal fire,
+and all the early water gas apparatus was constructed in this
+way; but such a method is very uneconomical, and was long ago
+replaced by a process first patented by J. and T.N. Kirkham
+in 1854, and very much improved by successive inventors. This
+process consists in conducting the operation in an upright brick
+shaft, charged with anthracite, coke or other suitable fuel. This
+shaft resembles an ordinary gas producer, but it differs in being
+worked, not in a continuous manner, which, as shown above,
+would be impossible, but by alternately blowing air and steam
+through the coal for periods of a few minutes each. During the
+first phase, when carbon is burned by atmospheric oxygen, and
+thereby heat is produced, this heat, or rather that part of it
+which is not carried away by radiation and by the products
+of combustion on leaving the apparatus, is employed in raising
+the temperature of the remaining mass of fuel, and is thus
+available for the second phase, in which the reaction (<i>b</i>)
+C + H<span class="su">2</span>O = CO + H<span class="su">2</span> goes on with the abstraction of a corresponding
+amount of heat from the incandescent fuel, so that the latter
+rapidly cools down, and the process must be reversed by blowing
+in air and so forth. The formation of exactly equal volumes
+of carbon monoxide and hydrogen goes on only at temperatures
+over 1200° C., that is, for a very few minutes. Even at 1100° C.
+a little CO<span class="su">2</span> can be proved to exist in the gas, and at 900° its
+proportion becomes too high to allow the process to go on.
+About 650° C. the CO has fallen to a minimum, and the reaction
+is now essentially (<i>c</i>) C + 2H<span class="su">2</span>O = CO<span class="su">2</span> + 2H<span class="su">2</span>; soon after the
+temperature of the mass will have fallen to such a low point
+that the steam passes through it without any perceptible action.
+The gas produced by reaction (<i>c</i>) contains only two-thirds of
+combustible matter, and is on that account less valuable than
+proper water gas formed by reaction (<i>b</i>); moreover, it requires
+the generation of twice the amount of steam, and its presence is
+all the less desirable since it must soon lead to a total cessation
+of the process. In ordinary circumstances it is evident that the
+more steam is blown in during a unit of time, the sooner reaction
+(<i>c</i>) will set in; on the other hand, the more heat has been
+accumulated in the producer the longer can the blowing-in of
+steam be continued.</p>
+
+<p>The process of making water gas consequently comprises
+<span class="pagenum"><a name="page285" id="page285"></a>285</span>
+two alternating operations, viz. first &ldquo;blowing-up&rdquo; by means
+of a current of air, by which the heat of the mass of fuel is raised
+to about 1200° C.; and, secondly &ldquo;steaming,&rdquo; by injecting a
+current of (preferably superheated) steam until the temperature
+of the fuel had fallen to about 900° C., and too much carbon
+dioxide appears in the product. During the steaming the gas
+is carried off by a special conduit into a scrubber, where the dust
+mechanically carried away in the current is washed out, and the
+gas is at the same time cooled down nearly to the ordinary
+temperature. It is generally stored in a gas-holder, from which
+it is conducted away as required. It is never quite free from
+nitrogen, as the producer at the beginning of steaming contains
+much of this gas, together with CO or CO<span class="su">2</span>. The proportion of
+hydrogen may exceed 50%, in consequence of reaction (<i>c</i>)
+setting in at the close of the steaming. Ordinary &ldquo;blue&rdquo; water
+gas, if, as usual, made from coke or anthracite, contains 48-52%
+H<span class="su">2</span>, 40-41% CO, 1-5% CO<span class="su">2</span>, 4-5% N<span class="su">2</span>, and traces of hydrocarbons,
+especially methane. If made from bituminous coal,
+it contains more of the latter. If &ldquo;carburetted&rdquo; (a process
+which increases its volume 50% and more) by the vapours from
+superheated petroleum naphtha, the proportion of CO ranges
+about 25%, with about as much methane, and from 10 to 15%
+of &ldquo;illuminants&rdquo; (heavy hydrocarbons). The latter, of course,
+greatly enhance the fuel-value of the gas. Pure water gas would
+possess the following fuel-value per cubic metre:</p>
+
+<table class="ws f90" summary="Contents">
+<tr><td class="tcc">0.5</td> <td class="tcc">cub. met.</td> <td class="tcl">H<span class="su">2</span></td> <td class="tcr">= 1291</td> <td class="tcc">calories</td></tr>
+<tr><td class="tcc">0.5</td> <td class="tcc">&ensp; &rdquo; &emsp; &rdquo; &ensp;</td> <td class="tcl">CO</td> <td class="tcr">= 1522</td> <td class="tcc">&rdquo;</td></tr>
+<tr><td class="tcc" colspan="3">&nbsp;</td> <td class="tcr"><span class="ov">2813</span></td> <td class="tcc">&rdquo;</td></tr>
+</table>
+
+<p class="noind">Ordinary &ldquo;blue&rdquo; water gas has a fuel-value of at least 2500
+calories. Carburetted water gas, which varies very much in
+its percentage of hydrocarbons, sometimes reaches nearly the
+heat-value of coal gas, but such gas is only in exceptional cases
+used for heating purposes.</p>
+
+<p>We must now turn to the &ldquo;blowing-up&rdquo; stage of the process.
+Until recently it was assumed that during this stage the combustion
+of carbon cannot be carried on beyond the formation of
+carbon monoxide, for as the gas-producer must necessarily
+contain a deep layer of fuel (generally about 6 to 10 ft.), any CO<span class="su">2</span>
+formed at first would be reduced to CO; and it was further
+assumed that hardly any CO<span class="su">2</span> would be formed from the outset,
+as the temperature of the apparatus is too high for this reaction
+to take place. But as the combustion of C to CO produces only
+about 30% of the heat produced when C is burned into CO<span class="su">2</span>,
+the quantity of fuel consumed for &ldquo;blowing-up&rdquo; is very large,
+and in fact considerably exceeds that consumed in &ldquo;steaming.&rdquo;
+There is, of course, a further loss by radiation and minor sources,
+and the result is that 1 kilogram of carbon yields only about
+1.2 cub. met. of water gas. Each period of blowing-up generally
+occupies from 8 to 12 minutes, that of steaming only 4 or 5
+minutes. This low yield of water gas until quite recently appeared
+to be unavoidable, and the only question seemed to be whether
+and to what extent the gas formed during blowing-up, which
+is in fact identical with ordinary producer gas (Siemens gas),
+could be utilized. In America, where the water gas is mostly
+employed for illuminating purposes, at least part of the blowing-up
+gas is utilized for heating the apparatus in which the naphtha
+is volatilized and the vapours are &ldquo;fixed&rdquo; by superheating.
+This process, however, never utilizes anything like the whole
+of the blowing-up gas, nor can this be effected by raising and
+superheating the steam necessary for the second operation;
+indeed, the employment of this gas for raising steam is not very
+easy, owing to the irregularities of and constant interruptions
+in the supply. In some systems the gas made during the blowing-up
+stage is passed through chambers, loosely filled with bricks,
+like Siemens recuperators, where it is burned by &ldquo;secondary&rdquo;
+air: the heat thus imparted to the brickwork is utilized by passing
+through the recuperator, and thus superheating, the steam
+required for the next steaming operation. In many cases,
+principally where no carburetting is practised, the blowing-up
+gas is simply burned at the mouth of the producer, and is thus
+altogether lost; and in no case can it be utilized without great
+waste. A very important improvement in this respect was
+effected by C. Dellwik and E. Fleischer. They found that the
+view that it is unavoidable to burn the carbon to monoxide
+during the blowing-up holds good only for the pressure of blast
+formerly applied. This did not much exceed that which is
+required for overcoming the frictional resistance within the
+producer. If, however, the pressure is considerably increased,
+and the height of the column of fuel reduced, both of these
+conditions being strictly regulated in accordance with the result
+desired, it is easy to attain a combustion of the carbon to dioxide,
+with only traces of monoxide, in spite of the high temperature.
+Evidently the excess of oxygen coming into contact with each
+particle of carbon in a given unit of time produces other conditions
+of chemical equilibrium than those existing at lower pressures. At
+any rate, experience has shown that by this process, in which the
+full heat-value of carbon is utilized during the blowing-up stage,
+the time of heating-up can be reduced from 10 to 1½ or 2 minutes,
+and the steaming can be prolonged from 4 or 5 to 8 or 10 minutes,
+with the result that twice the quantity of water gas is obtained,
+viz. upwards of 2 cub. metres from 1 kilogram of carbon.</p>
+
+<p>The application of water gas as a fuel mainly depends upon
+the high temperatures which it is possible to attain by its aid,
+and these are principally due to the circumstance that it forms
+a much smaller flame than coal gas, not to speak of Siemens gas,
+which contains at most 33% of combustible matter against
+90% or more in water gas. The latter circumstance also allows
+the gas to be conducted and distributed in pipes of moderate
+dimensions. Its application, apart from its use as an illuminant
+(with which we are not concerned here), was formerly retarded
+by its high cost in comparison with Siemens gas and other
+sources of heat, but as this state of affairs has been changed by
+the modern improvements, its use is rapidly extending, especially
+for metallurgical purposes.</p>
+
+<p>C. <i>Mixed Gas</i> (<i>Semi-Water Gas</i>).&mdash;This class is sometimes
+called Dowson gas, irrespective of its method of production,
+although it was made and extensively used a long time before
+J.E. Dowson constructed his apparatus for generating such a
+gas principally for driving gas-engines. By a combination of
+the processes for generating Siemens gas and water gas, it is
+produced by injecting into a gas-producer at the same time a
+certain quantity of air and a corresponding quantity of steam,
+the latter never exceeding the amount which can be decomposed
+by the heat-absorbing reaction, C + H<span class="su">2</span>O = CO + H<span class="su">2</span>, at the expense
+of the heat generated by the action of the air in the
+reaction C + O = CO. Such gas used to be frequently obtained in
+an accidental way by introducing liquid water or steam into
+an ordinary gas-producer for the purpose of facilitating its
+working by avoiding an excessive temperature, such as might
+cause the rapid destruction of the brickwork and the fusion of
+the ashes of the fuel into troublesome cakes. It was soon found
+that by proceeding in this way a certain advantage could be
+gained in regard to the consumption of fuel, as the heat abstracted
+by the steam from the brickwork and the fuel itself was usefully
+employed for decomposing water, its energy thus reappearing
+in the shape of a combustible gas. It is hardly necessary to
+mention explicitly that the total heat obtained by any such
+process from a given quantity of carbon (or hydrogen) can in
+no case exceed that which is generated by direct combustion;
+some inventors, however, whether inadvertently or intentionally,
+have actually represented this to be possible, in manifest violation
+of the law of the conservation of energy.</p>
+
+<p>Roughly speaking, this gas may be said to be produced by
+the combination of the reactions, described <i>sub</i> A and B, to the
+joint reaction: 2C + O + H<span class="su">2</span>O = 2CO + H<span class="su">2</span>. The decomposition
+of H<span class="su">2</span>O (applied in the shape of steam) absorbs 57.6 gram calories,
+the formation of 2CO produces 59 gram calories; hence there is
+a small positive excess of 1.4 calories at disposal. This in reality
+would not be sufficient to cover the loss by radiation, &amp;c.;
+hence rather more free oxygen (<i>i.e.</i> atmospheric air) must be
+employed than is represented by the above equation. All this
+free oxygen is, of course, accompanied by nearly four times
+its volume of nitrogen.</p>
+
+<p><span class="pagenum"><a name="page286" id="page286"></a>286</span></p>
+
+<p>The mixed gas thus obtained differs very much in composition,
+but is always much richer in hydrogen (of which it contains
+sometimes as much as 20%) and poorer in carbon monoxide
+(sometimes down to 20%) than Siemens gas; generally it
+contains more of CO<span class="su">2</span> than the latter. The proportion of nitrogen
+is always less, about 50%. It is therefore a more concentrated
+fuel than Siemens gas, and better adapted to the driving of gas-engines.
+It scarcely costs more to make than ordinary Siemens
+gas, except where the steam is generated and superheated in
+special apparatus, as is done in the Dowson producer, which,
+on the other hand, yields a correspondingly better gas. As is
+natural, its properties are some way between those of Siemens
+gas and of water gas; but they approach more nearly the
+former, both as to costs and as to fuel-value, and also as to the
+temperatures reached in combustion. This is easily understood
+if we consider that gas of just the same description can be
+obtained by mixing one volume of real water gas with the four
+volumes of Siemens gas made during the blowing-up stage&mdash;an
+operation which is certainly too expensive for practical use.</p>
+
+<p>A modification of this gas is the <i>Mond gas</i>, which is made,
+according to Mond&rsquo;s patent, by means of such an excess of steam
+that most of the nitrogen of the coke is converted into ammonia
+(Grouven&rsquo;s reaction). Of course much of this steam passes on
+undecomposed, and the quantity of the gas is greatly increased
+by the reaction C + 2H<span class="su">2</span>O = CO<span class="su">2</span> + 2H<span class="su">2</span>; hence the fuel-value
+of this gas is less than that of semi-water gas made in other ways.
+Against this loss must be set the gain of ammonia which is
+recovered by means of an arrangement of coolers and scrubbers,
+and, except at very low prices of ammonia, the profit thus made
+is probably more than sufficient to cover the extra cost. But
+as the process requires very large and expensive plant, and its
+profits would vanish in the case of the value of ammonia becoming
+much lower (a result which would very probably follow if it were
+somewhat generally introduced), it cannot be expected to supplant
+the other descriptions of gaseous fuel to more than a
+limited extent.</p>
+
+<p>Semi-water gas is especially adapted for the purpose of driving
+gas-engines on the explosive principle (gas-motors). Ordinary
+producer-gas is too poor for this purpose in respect of heating
+power; moreover, owing to the prevalence of carbon monoxide,
+it does not light quickly enough. These defects are sufficiently
+overcome in semi-water gas by the larger proportion of hydrogen
+contained in it. For the purpose in question the gas should be
+purified from tar and ashes, and should also be cooled down before
+entering the gas-engine. The Dowson apparatus and others
+are constructed on this principle.</p>
+
+<p><i>Air Gas.</i>&mdash;By forcing air over or through volatile inflammable
+liquids a gaseous mixture can be obtained which burns with a
+bright flame and which can be used for illumination. Its employment
+for heating purposes is quite exceptional, <i>e.g.</i> in chemical
+laboratories, and we abstain, therefore, from describing any of the
+numerous appliances, some of them bearing very fanciful names,
+which have been devised for its manufacture.</p>
+<div class="author">(G. L.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">FUENTE OVEJUNA<a name="ar26" id="ar26"></a></span> [<i>Fuenteovejuna</i>], a town of Spain, in the
+province of Cordova; near the sources of the river Guadiato,
+and on the Fuente del Arco-Belmez-Cordova railway. Pop.
+(1900) 11,777. Fuente Ovejuna is built on a hill, in a well-irrigated
+district, which, besides producing an abundance of
+wheat, wine, fruit and honey, also contains argentiferous lead
+mines and stone quarries. Cattle-breeding is an important
+local industry, and leather, preserved meat, soap and flour
+are manufactured. The parish church formerly belonged to
+the knights of Calatrava (<i>c.</i> 1163-1486).</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUENTERRABIA<a name="ar27" id="ar27"></a></span> (formerly sometimes written <i>Fontarabia</i>;
+Lat. <i>Fons Rapidus</i>), a town of northern Spain, in the province
+of Guipúzcoa; on the San Sebastian-Bayonne railway; near
+the Bay of Biscay and on the French frontier. Pop. (1870)
+about 750; (1900) 4345. Fuenterrabia stands on the slope of a
+hill on the left bank of the river Bidassoa, and near the point
+where its estuary begins. Towards the close of the 19th century
+the town became popular as a summer resort for visitors from
+the interior of Spain, and, in consequence, its appearance underwent
+many changes and much of its early prosperity returned.
+Hotels and villas were built in the new part of the town that
+sprang up outside the picturesque walled fortress, and there is
+quite a contrast between the part inside the heavy, half-ruined
+ramparts, with its narrow, steep streets and curious gable-roofed
+houses, its fine old church and castle and its massive town hall,
+and the new suburbs and fishermen&rsquo;s quarter facing the estuary
+of the Bidassoa. Many industries flourish on the outskirts of
+the town, including rope and net manufactures, flour mills, saw
+mills, mining railways, paper mills.</p>
+
+<p>Fuenterrabia formerly possessed considerable strategic importance,
+and it has frequently been taken and retaken in
+wars between France and Spain. The rout of Charlemagne in
+778, which has been associated with Fontarabia, by Milton
+(<i>Paradise Lost</i>, i. 587), is generally understood to have taken
+place not here but at Roncesvalles (<i>q.v.</i>), which is nearly 40 m.
+E.S.E. Unsuccessful attempts to seize Fuenterrabia were
+made by the French troops in 1476 and again in 1503. In a
+subsequent campaign (1521) these were more successful, but the
+fortress was retaken in 1524. The prince of Condé sustained a
+severe repulse under its walls in 1638, and it was on this occasion
+that the town received from Philip IV. the rank of city (<i>muy
+noble, muy leal, y muy valerosa ciudad</i>, &ldquo;most noble, most loyal,
+and most valiant city&rdquo;), a privilege which involved some
+measure of autonomy. After a severe siege, Fuenterrabia
+surrendered to the duke of Berwick and his French troops in
+1719; and in 1794 it again fell into the hands of the French,
+who so dismantled it that it has never since been reckoned by
+the Spaniards among their fortified places. It was by the ford
+opposite Fuenterrabia that the duke of Wellington, on the 8th of
+October 1813, successfully forced a passage into France in the
+face of an opposing army commanded by Marshal Soult. Severe
+fighting also took place here during the Carlist War in 1837.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUERO,<a name="ar28" id="ar28"></a></span> a Spanish term, derived from the Latin <i>forum</i>. The
+Castillan use of the word in the sense of a right, privilege or
+charter is most probably to be traced to the Roman <i>conventus
+juridici</i>, otherwise known as <i>jurisdictiones</i> or <i>fora</i>, which in
+Pliny&rsquo;s time were already numerous in the Iberian peninsula. In
+each of these provincial <i>fora</i> the Roman magistrate, as is well
+known, was accustomed to pay all possible deference to the
+previously established common law of the district; and it was
+the privilege of every free subject to demand that he should be
+judged in accordance with the customs and usages of his proper
+forum. This was especially true in the case of the inhabitants of
+those towns which were in possession of the <i>jus italicum</i>. It is
+not, indeed, demonstrable, but there are many presumptions,
+besides some fragments of direct evidence, which make it more
+than probable that the old administrative arrangements both of
+the provinces and of the towns, but especially of the latter,
+remained practically undisturbed at the period of the Gothic
+occupation of Spain.<a name="fa1b" id="fa1b" href="#ft1b"><span class="sp">1</span></a> The Theodosian Code and the Breviary
+of Alaric alike seem to imply a continuance of the municipal
+system which had been established by the Romans; nor does the
+later Lex Visigothorum, though avowedly designed in some
+points to supersede the Roman law, appear to have contemplated
+any marked interference with the former <i>fora</i>, which were still to
+a large extent left to be regulated in the administration of justice
+by unwritten, immemorial, local custom. Little is known of the
+condition of the subject populations of the peninsula during the
+Arab occupation; but we are informed that the Christians were,
+sometimes at least, judged according to their own laws in
+separate tribunals presided over by Christian judges;<a name="fa2b" id="fa2b" href="#ft2b"><span class="sp">2</span></a> and the
+mere fact of the preservation of the name <i>alcalde</i>, an official
+whose functions corresponded so closely to those of the <i>judex</i> or
+<i>defensor civitatis</i>, is fitted to suggest that the old municipal <i>fora</i>,
+if much impaired, were not even then in all cases wholly destroyed.
+At all events when the word <i>forum</i><a name="fa3b" id="fa3b" href="#ft3b"><span class="sp">3</span></a> begins to appear for the first
+time in documents of the 10th century in the sense of a liberty or
+<span class="pagenum"><a name="page287" id="page287"></a>287</span>
+privilege, it is generally implied that the thing so named is
+nothing new. The earliest extant written fuero is probably that
+which was granted to the province and town of Leon by Alphonso
+V. in 1020. It emanated from the king in a general council of the
+kingdom of Leon and Castile, and consisted of two separate
+parts; in the first 19 chapters were contained a series of statutes
+which were to be valid for the kingdom at large, while the rest of
+the document was simply a municipal charter.<a name="fa4b" id="fa4b" href="#ft4b"><span class="sp">4</span></a> But in neither
+portion does it in any sense mark a new legislative departure,
+unless in so far as it marks the beginning of the era of written
+charters for towns. The &ldquo;fuero general&rdquo; does not profess to
+supersede the <i>consuetudines antiquorum jurium</i> or Chindaswint&rsquo;s
+codification of these in the Lex Visigothorum; the &ldquo;fuero
+municipal&rdquo; is really for the most part but a resuscitation of
+usages formerly established, a recognition and definition of
+liberties and privileges that had long before been conceded or
+taken for granted. The right of the burgesses to self-government
+and self-taxation is acknowledged and confirmed, they, on the
+other hand, being held bound to a constitutional obedience and
+subjection to the sovereign, particularly to the payment of
+definite imperial taxes, and the rendering of a certain amount of
+military service (as the ancient municipia had been). Almost
+contemporaneous with this fuero of Leon was that granted to
+Najera (Naxera) by Sancho el Mayor of Navarre (<i>ob.</i> 1035), and
+confirmed, in 1076, by Alphonso VI.<a name="fa5b" id="fa5b" href="#ft5b"><span class="sp">5</span></a> Traces of others of perhaps
+even an earlier date are occasionally to be met with. In the fuero
+of Cardeña, for example, granted by Ferdinand I. in 1039,
+reference is made to a previous forum Burgense (Burgos), which,
+however, has not been preserved, if, indeed, it ever had been
+reduced to writing at all. The phraseology of that of Sepulveda
+(1076) in like manner points back to an indefinitely remote
+antiquity.<a name="fa6b" id="fa6b" href="#ft6b"><span class="sp">6</span></a> Among the later fueros of the 11th century, the
+most important are those of Jaca (1064) and of Logroño (1095).
+The former of these, which was distinguished by the unusual
+largeness of its concessions, and by the careful minuteness of its
+details, rapidly extended to many places in the neighbourhood,
+while the latter charter was given also to Miranda by Alphonso
+VI., and was further extended in 1181 by Sancho el Sabio of
+Navarre to Vitoria, thus constituting one of the earliest written
+<i>fora</i> of the &ldquo;Provincias Vascongadas.&rdquo; In the course of the 12th
+and 13th centuries the number of such documents increased very
+rapidly; that of Toledo especially, granted to the Mozarabic
+population in 1101, but greatly enlarged and extended by
+Alphonso VII. (1118) and succeeding sovereigns, was used as a
+basis for many other Castilian fueros. Latterly the word fuero
+came to be used in Castile in a wider sense than before, as meaning
+a general code of laws; thus about the time of Saint Ferdinand
+the old Lex Visigothorum, then translated for the first
+time into the vernacular, was called the Fuero Juzgo, a name
+which was soon retranslated into the barbarous Latin of the period
+as Forum Judicum;<a name="fa7b" id="fa7b" href="#ft7b"><span class="sp">7</span></a> and among the compilations of Alphonso
+the Learned in like manner were an <i>Espejo de Fueros</i> and also the
+<i>Fuero de las leyes</i>, better known perhaps as the <i>Fuero Real</i>. The
+famous code known as the <i>Ordenamiento Real de Alcalá</i>, or <i>Fuero
+Viejo de Castilla</i>, dates from a still later period. As the power of
+the Spanish crown was gradually concentrated and consolidated,
+royal pragmaticas began to take the place of constitutional laws;
+the local fueros of the various districts slowly yielded before the
+superior force of imperialism; and only those of Navarre and the
+Basque provinces (see <span class="sc"><a href="#artlinks">Basques</a></span>) have had sufficient vitality to
+enable them to survive to comparatively modern times. While
+actually owning the lordship of the Castilian crown since about the
+middle of the 14th century, these provinces rigidly insisted upon
+compliance with their consuetudinary law, and especially with
+that which provided that the <i>señor</i>, before assuming the government,
+should personally appear before the assembly and swear
+to maintain the ancient constitutions. Each of the provinces
+mentioned had distinct sets of fueros, codified at different periods,
+and varying considerably as to details; the main features, however,
+were the same in all. Their rights, after having been recognized
+by successive Spanish sovereigns from Ferdinand the
+Catholic to Ferdinand VII., were, at the death of the latter in
+1833, set aside by the government of Castaños. The result was a
+civil war, which terminated in a renewed acknowledgment of the
+fueros by Isabel II. (1839). The provisional government of 1868
+also promised to respect them, and similar pledges were given
+by the governments which succeeded. In consequence, however,
+of the Carlist rising of 1873-1876, the Basque fueros were finally
+extinguished in 1876. The history of the <i>Foraes</i> of the Portuguese
+towns, and of the <i>Fors du Béarn</i>, is precisely analogous to
+that of the fueros of Castile.</p>
+
+<div class="condensed">
+<p>Among the numerous works that more or less expressly deal with
+this subject, that of Marina (<i>Ensayo historico-critico sobre la antigua
+legislacion y principales cuerpos legales de los reynos de Leon y
+Castilla</i>) still continues to hold a high place. Reference may also
+be made to Colmeiro&rsquo;s <i>Curso de derecho político según la historia de
+Leon y de Castilla</i> (Madrid, 1873); to Schäfer&rsquo;s <i>Geschichte von
+Spanien</i>, ii. 418-428, iii. 293 seq.; and to Hallam&rsquo;s <i>Middle Ages</i>,
+c. iv.</p>
+</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1b" id="ft1b" href="#fa1b"><span class="fn">1</span></a> The nature of the evidence may be gathered from Savigny, <i>Gesch.
+d. röm. Rechts</i>. See especially i. pp. 154, 259 seq.</p>
+
+<p><a name="ft2b" id="ft2b" href="#fa2b"><span class="fn">2</span></a> Compare Lembke u. Schäfer, <i>Geschichte von Spanien</i>, i. 314; ii. 117.</p>
+
+<p><a name="ft3b" id="ft3b" href="#fa3b"><span class="fn">3</span></a> Or rather <i>forus</i>. See Ducange, <i>s.v.</i></p>
+
+<p><a name="ft4b" id="ft4b" href="#fa4b"><span class="fn">4</span></a> Cap. xx. begins: &ldquo;Constituimus etiam ut Legionensis civitas,
+quae depopulata fuit a Sarracenis in diebus patris mei Veremundi
+regis, repopulatur <i>per hos foros subscriptos</i>.&rdquo;</p>
+
+<p><a name="ft5b" id="ft5b" href="#fa5b"><span class="fn">5</span></a> &ldquo;Mando et concedo et confirmo ut ista civitas cum sua plebe et
+cum omnibus suis pertinentiis sub tali lege et sub tali foro maneat
+per saecula cuncta. Amen. Isti sunt fueros quae habuerunt in
+Naxera in diebus Sanctii regis et Gartiani regis.&rdquo;</p>
+
+<p><a name="ft6b" id="ft6b" href="#fa6b"><span class="fn">6</span></a> &ldquo;Ego Aldefonsus rex et uxor mea Agnes confirmamus ad Septempublica
+suo foro quod habuit in tempore antiquo de avolo meo et in
+tempore comitum Ferrando Gonzalez et comite Garcia Ferdinandez
+et comite Domno Santio.&rdquo;</p>
+
+<p><a name="ft7b" id="ft7b" href="#fa7b"><span class="fn">7</span></a> This Latin is later even than that of Ferdinand, whose words are:
+&ldquo;Statuo et mando quod Liber Judicum, quo ego misi Cordubam,
+translatetur in vulgarem et vocetur forum de Corduba ... et quod
+per saecula cuncta sit pro foro et nullus sit ausus istud forum aliter
+appellare nisi forum de Corduba, et jubeo et mando quod omnis
+morator et populator ... veniet ad judicium et ad forum de
+Corduba.&rdquo;</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FUERTEVENTURA,<a name="ar29" id="ar29"></a></span> an island in the Atlantic Ocean, forming
+part of the Spanish archipelago of the Canary Islands (<i>q.v.</i>).
+Pop. (1900) 11,669; area 665 sq. m. Fuerteventura lies between
+Lanzarote and Grand Canary. It has a length of 52 m., and an
+average width of 12 m. Though less mountainous than the other
+islands, its aspect is barren. There are only two springs of fresh
+water, and these are confined to one valley. Lava streams and
+other signs of volcanic action abound, but there has been no
+igneous activity since the Spaniards took possession. At each
+extremity of the island are high mountains, which send off
+branches along the coast so as to enclose a large arid plain.
+The highest peak reaches 2500 ft. In external appearance,
+climate and productions, Fuerteventura greatly resembles
+Lanzarote. An interval of three years without rain has been
+known. Oliva (pop. 1900, 2464) is the largest town. A smaller
+place in the centre of the island named Betancuria (586) is the
+administrative capital. Cabras (1000) on the eastern coast is
+the chief port. Dromedaries are bred here.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUGGER,<a name="ar30" id="ar30"></a></span> the name of a famous German family of merchants
+and bankers. The founder of the family was Johann Fugger,
+a weaver at Graben, near Augsburg, whose son, Johann, settled
+in Augsburg probably in 1367. The younger Johann added the
+business of a merchant to that of a weaver, and through his
+marriage with Clara Widolph became a citizen of Augsburg.
+After a successful career he died in 1408, leaving two sons,
+Andreas and Jakob, who greatly extended the business which
+they inherited from their father. Andreas, called the &ldquo;rich
+Fugger,&rdquo; had several sons, among them being Lukas, who was
+very prominent in the municipal politics of Augsburg and who
+was very wealthy until he was ruined by the repudiation by the
+town of Louvain of a great debt owing to him, and Jakob, who
+was granted the right to bear arms in 1452, and who founded the
+family of Fugger vom Reh&mdash;so called from the first arms of the
+Fuggers, a roe (<i>Reh</i>) or on a field azure&mdash;which became extinct
+on the death of his great-grandson, Ulrich, in 1583. Johann
+Fugger&rsquo;s son, Jakob, died in 1469, and three of his seven sons,
+Ulrich (1441-1510), Georg (1453-1506) and Jakob (1459-1525),
+men of great resource and industry, inherited the family business
+and added enormously to the family wealth. In 1473 Ulrich
+obtained from the emperor Frederick III. the right to bear arms
+for himself and his brothers, and about the same time he began
+<span class="pagenum"><a name="page288" id="page288"></a>288</span>
+to act as the banker of the Habsburgs, a connexion destined to
+bring fame and fortune to his house. Under the lead of Jakob,
+who had been trained for business in Venice, the Fuggers were
+interested in silver mines in Tirol and copper mines in Hungary,
+while their trade in spices, wool and silk extended to almost
+all parts of Europe. Their wealth enabled them to make large
+loans to the German king, Maximilian I., who pledged to them
+the county of Kirchberg, the lordship of Weissenhorn and other
+lands, and bestowed various privileges upon them. Jakob
+built the castle of Fuggerau in Tirol, and erected the Fuggerei
+at Augsburg, a collection of 106 dwellings, which were let at low
+rents to poor people and which still exist. Jakob Fugger and
+his two nephews, Ulrich (d. 1525) and Hieronymus (d. 1536),
+the sons of Ulrich, died without direct heirs, and the family was
+continued by Georg&rsquo;s sons, Raimund (1489-1535) and Anton
+(1493-1560), under whom the Fuggers attained the summit of
+their wealth and influence.</p>
+
+<p>Jakob Fugger&rsquo;s florins had contributed largely to the election
+of Charles V. to the imperial throne in 1519, and his nephews
+and heirs maintained close and friendly relations with the great
+emperor. In addition to lending him large sums of money, they
+farmed his valuable quicksilver mines at Almaden, his silver
+mines at Guadalcanal, the great estates of the military orders
+which had passed into his hands, and other parts of his revenue
+as king of Spain; receiving in return several tokens of the
+emperor&rsquo;s favour. In 1530 Raimund and Anton were granted
+the imperial dignity of counts of Kirchberg and Weissenhorn,
+and obtained full possession of these mortgaged properties;
+in 1534 they were given the right of coining money; and in 1541
+received rights of jurisdiction over their lands. During the diet
+of Augsburg in 1530 Charles V. was the guest of Anton Fugger
+at his house in the Weinmarkt, and the story relates how the
+merchant astonished the emperor by lighting a fire of cinnamon
+with an imperial bond for money due to him. This incident
+forms the subject of a picture by Carl Becker which is in the
+National Gallery at Berlin. Continuing their mercantile career,
+the Fuggers brought the new world within the sphere of their
+operations, and also carried on an extensive and lucrative
+business in farming indulgences. Moreover, both brothers
+found time to acquire landed property, and were munificent
+patrons of literature and art. When Anton died he is said to
+have been worth 6,000,000 florins, besides a vast amount of
+property in Europe, Asia and America; and before this time
+the total wealth of the family had been estimated at 63,000,000
+florins. The Fuggers were devotedly attached to the Roman
+Catholic Church, which benefited from their liberality. Jakob
+had been made a count palatine (<i>Pfalzgraf</i>) and had received
+other marks of favour from Pope Leo X., and several members
+of the family had entered the church; one, Raimund&rsquo;s son,
+Sigmund, becoming bishop of Regensburg.</p>
+
+<p>In addition to the bishop, three of Raimund Fugger&rsquo;s sons
+attained some degree of celebrity. Johann Jakob (1516-1575),
+was the author of <i>Wahrhaftigen Beschreibung des österreichischen
+und habsburgischen Nahmens</i>, which was largely used by S. von
+Bircken in his <i>Spiegel der Ehren des Erzhauses Österreich</i> (Nuremberg,
+1668), and of a <i>Geheim Ernbuch des Fuggerischen Geschlechtes</i>.
+He was also a patron of art, and a distinguished counsellor of
+Duke Albert IV. of Bavaria. After the death of his son Konstantin,
+in 1627, this branch of the family was divided into three
+lines, which became extinct in 1738, 1795 and 1846 respectively.
+Another of Raimund&rsquo;s sons was Ulrich (1526-1584), who, after
+serving Pope Paul III. at Rome, became a Protestant. Hated
+on this account by the other members of his family, he took
+refuge in the Rhenish Palatinate; greatly interested in the
+Greek classics, he occupied himself in collecting valuable manuscripts,
+which he bequeathed to the university of Heidelberg.
+Raimund&rsquo;s other son was Georg (d. 1579), who inherited the
+countships of Kirchberg and Weissenhorn, and founded a branch
+of the family which still exists, its present head being Georg,
+Count Fugger of Kirchberg and Weissenhorn (b. 1850).</p>
+
+<p>Anton Fugger left three sons, Marcus (1529-1597), Johann
+(d. 1598) and Jakob (d. 1598), all of whom left male issue.
+Marcus was the author of a book on horse-breeding, <i>Wie und
+wo man ein Gestüt von guten edeln Kriegsrossen aufrichten soll</i>
+(1578), and of a German translation of the <i>Historia ecclesiastica</i>
+of Nicephorus Callistus. He founded the Nordendorf branch
+of the family, which became extinct on the death of his grandson,
+Nicolaus, in 1676. Another grandson of Marcus was Franz
+Fugger (1612-1664), who served under Wallenstein during the
+Thirty Years&rsquo; War, and was afterwards governor of Ingolstadt.
+He was killed at the battle of St Gotthard on the 1st of August
+1664.</p>
+
+<p>Johann Fugger had three sons, Christoph (d. 1615) and
+Marcus (d. 1614), who founded the families of Fugger-Glött and
+Fugger-Kirchheim respectively, and Jakob, bishop of Constance
+from 1604 until his death in 1626. Christoph&rsquo;s son, Otto Heinrich
+(1592-1644), was a soldier of some distinction and a knight
+of the order of the Golden Fleece. He was one of the most
+active of the Bavarian generals during the Thirty Years&rsquo; War,
+and acted as governor of Augsburg, where his rule aroused
+much discontent. The family of Kirchheim died out in 1672.
+That of Glött was divided into several branches by the sons
+of Otto Heinrich and of his brother Johann Ernst (d. 1628).
+These lines, however, have gradually become extinct except the
+eldest line, represented in 1909 by Karl Ernst, Count Fugger of
+Glött (b. 1859). Anton Fugger&rsquo;s third son Jakob, the founder of
+the family of Wellenburg, had two sons who left issue, but in 1777
+the possessions of this branch of the family were again united by
+Anselm Joseph (d. 1793), Count Fugger of Babenhausen. In
+1803 Anselm&rsquo;s son, Anselm Maria (d. 1821), was made a prince of
+the Holy Roman Empire, the title of Prince Fugger of Babenhausen
+being borne by his direct descendant Karl (b. 1861). On
+the fall of the empire in 1806 the lands of the Fuggers, which
+were held directly of the empire, were mediatized under Bavaria
+and Württemberg. The heads of the three existing branches
+of the Fuggers are all hereditary members of the Bavarian
+Upper House.</p>
+
+<p>Augsburg has many interesting mementoes of the Fuggers,
+including the family burial-chapel in the church of St Anna;
+the Fugger chapel in the church of St Ulrich and St Afra; the
+Fuggerhaus, still in the possession of one branch of the family;
+and a statue of Johann Jakob Fugger.</p>
+
+<div class="condensed">
+<p>In 1593 a collection of portraits of the Fuggers, engraved by
+Dominique Custos of Antwerp, was issued at Augsburg. Editions
+with 127 portraits appeared in 1618 and 1620, the former accompanied
+by a genealogy in Latin, the latter by one in German. Another
+edition of this <i>Pinacotheca Fuggerorum</i>, published at Vienna in 1754,
+includes 139 portraits. See <i>Chronik der Familie Fugger vom Jahre
+1599</i>, edited by C. Meyer (Munich, 1902); A. Geiger, <i>Jakob Fugger,
+1459-1525</i> (Regensburg, 1895); A. Schulte, <i>Die Fugger in Rom,
+1495-1523</i> (Leipzig, 1904); R. Ehrenberg, <i>Das Zeitalter der Fugger</i>
+(Jena, 1896); K. Häbler, <i>Die Geschichte der Fuggerschen Handlung
+in Spanien</i> (Weimar, 1897); A. Stauber, <i>Das Haus Fugger</i> (Augsburg,
+1900); and M. Jansen, <i>Die Anfänge der Fugger</i> (Leipzig,
+1907).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FUGITIVE SLAVE LAWS<a name="ar31" id="ar31"></a></span>, a term applied in the United
+States to the Statutes passed by Congress in 1793 and 1850 to
+provide for the return of negro slaves who escaped from one
+state into another or into a public territory. A fugitive slave
+clause was inserted in the Articles of Confederation of the New
+England Confederation of 1643, providing for the return of the
+fugitive upon the certificate of one magistrate in the jurisdiction
+out of which the said servant fled&mdash;no trial by jury being provided
+for. This seems to have been the only instance of an inter-colonial
+provision for the return of fugitive slaves; there were,
+indeed, not infrequent escapes by slaves from one colony to
+another, but it was not until after the growth of anti-slavery
+sentiment and the acquisition of western territory, that it
+became necessary to adopt a uniform method for the return of
+fugitive slaves. Such provision was made in the Ordinance of
+1787 (for the Northwest Territory), which in Article VI. provided
+that in the case of &ldquo;any person escaping into the same [the
+Northwest Territory] from whom labor or service is lawfully
+claimed in any one of the original states, such fugitive may be
+lawfully reclaimed and conveyed to the person claiming his or
+her labor or service as aforesaid.&rdquo; An agreement of the sort was
+<span class="pagenum"><a name="page289" id="page289"></a>289</span>
+necessary to persuade the slave-holding states to union, and in
+the Federal Constitution, Article IV., Section II., it is provided
+that &ldquo;no person held to service or labor in one state, under the
+laws thereof, escaping into another, shall, in consequence of any
+law or regulation therein, be discharged from such service or
+labor, but shall be delivered up on claim of the party to whom
+such service or labour may be due.&rdquo;</p>
+
+<p>The first specific legislation on the subject was enacted on the
+12th of February 1793, and like the Ordinance for the Northwest
+Territory and the section of the Constitution quoted above, did
+not contain the word &ldquo;slave&rdquo;; by its provisions any Federal
+district or circuit judge or any state magistrate was authorized
+to decide finally and without a jury trial the status of an alleged
+fugitive. The measure soon met with strong opposition in the
+northern states, and Personal Liberty Laws were passed to hamper
+officials in the execution of the law; Indiana in 1824 and Connecticut
+in 1828 providing jury trial for fugitives who appealed
+from an original decision against them. In 1840 New York and
+Vermont extended the right of trial by jury to fugitives and
+provided them with attorneys. As early as the first decade of
+the 19th century individual dissatisfaction with the law of 1793
+had taken the form of systematic assistance rendered to negroes
+escaping from the South to Canada or New England&mdash;the
+so-called &ldquo;Underground Railroad.&rdquo;<a name="fa1c" id="fa1c" href="#ft1c"><span class="sp">1</span></a> The decision of the
+Supreme Court of the United States in the case of <i>Prigg</i> v.
+<i>Pennsylvania</i> in 1842 (16 Peters 539), that state authorities
+could not be forced to act in fugitive slave cases, but that
+national authorities must carry out the national law, was
+followed by legislation in Massachusetts (1843), Vermont (1843),
+Pennsylvania (1847) and Rhode Island (1848), forbidding state
+officials to help enforce the law and refusing the use of state
+gaols for fugitive slaves. The demand from the South for more
+effective Federal legislation was voiced in the second fugitive slave
+law, drafted by Senator J.M. Mason of Virginia, and enacted on
+the 18th of September 1850 as a part of the Compromise Measures
+of that year. Special commissioners were to have concurrent
+jurisdiction with the U.S. circuit and district courts and the
+inferior courts of Territories in enforcing the law; fugitives could
+not testify in their own behalf; no trial by jury was provided;
+penalties were imposed upon marshals who refused to enforce the
+law or from whom a fugitive should escape, and upon individuals
+who aided negroes to escape; the marshal might raise a <i>posse
+comitatus</i>; a fee of $10 was paid to the commissioner when his
+decision favoured the claimant and only $5 when it favoured the
+fugitive; and both the fact of the escape and the identity of the
+fugitive were to be determined on purely <i>ex parte</i> testimony.
+The severity of this measure led to gross abuses and defeated its
+purpose; the number of abolitionists increased, the operations
+of the Underground Railroad became more efficient, and new
+Personal Liberty Laws were enacted in Vermont (1850), Connecticut
+(1854), Rhode Island (1854), Massachusetts (1855),
+Michigan (1855), Maine (1855 and 1857), Kansas (1858) and
+Wisconsin (1858). These Personal Liberty Laws forbade justices
+and judges to take cognizance of claims, extended the <i>habeas
+corpus</i> act and the privilege of jury trial to fugitives, and
+punished false testimony severely. The supreme court of
+Wisconsin went so far (1859) as to declare the Fugitive Slave Law
+unconstitutional. These state laws were one of the grievances
+officially referred to by South Carolina (in Dec. 1860) as justifying
+her secession from the Union. Attempts to carry into effect the
+law of 1850 aroused much bitterness. The arrests of Sims and
+of Shadrach in Boston in 1851; of &ldquo;Jerry&rdquo; M&rsquo;Henry, in
+Syracuse, New York, in the same year; of Anthony Burns in
+1854, in Boston; and of the two Garner families in 1856, in
+Cincinnati, with other cases arising under the Fugitive Slave
+Law of 1850, probably had as much to do with bringing on the
+Civil War as did the controversy over slavery in the Territories.</p>
+
+<p>With the beginning of the Civil War the legal status of the
+slave was changed by his master&rsquo;s being in arms. General B.F.
+Butler, in May 1861, declared negro slaves contraband of war.
+A confiscation bill was passed in August 1861 discharging from
+his service or labour any slave employed in aiding or promoting
+any insurrection against the government of the United States.
+By an act of the 17th of July 1862 any slave of a disloyal master
+who was in territory occupied by northern troops was declared
+<i>ipso facto</i> free. But for some time the Fugitive Slave Law was
+considered still to hold in the case of fugitives from masters in
+the border states who were loyal to the Union government, and
+it was not until the 28th of June 1864 that the Act of 1850 was
+repealed.</p>
+
+<div class="condensed">
+<p>See J.F. Rhodes, <i>History of the United States from the Compromise
+of 1850</i>, vols. i. and ii. (New York, 1893); and M.G. M&rsquo;Dougall,
+<i>Fugitive Slaves, 1619-1865</i> (Boston, 1891).</p>
+</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1c" id="ft1c" href="#fa1c"><span class="fn">1</span></a> The precise amount of organization in the Underground Railroad
+cannot be definitely ascertained because of the exaggerated use of
+the figure of railroading in the documents of the &ldquo;presidents&rdquo; of
+the road, Robert Purvis and Levi Coffin, and of its many &ldquo;conductors,&rdquo;
+and their discussion of the &ldquo;packages&rdquo; and &ldquo;freight&rdquo;
+shipped by them. The system reached from Kentucky and Virginia
+across Ohio, and from Maryland across Pennsylvania and New
+York, to New England and Canada, and as early as 1817 a group of
+anti-slavery men in southern Ohio had helped to Canada as many as
+1000 slaves. The Quakers of Pennsylvania possibly began the
+work of the mysterious Underground Railroad; the best known of
+them was Thomas Garrett (1789-1871), a native of Pennsylvania,
+who, in 1822, removed to Wilmington, Delaware, where he was
+convicted in 1848 on four counts under the Fugitive Slave Law and
+was fined $8000; he is said to have helped 2700 slaves to freedom.
+The most picturesque figure of the Underground Railroad was
+Harriet Tubman (c. 1820), called by her friend, John Brown,
+&ldquo;General&rdquo; Tubman, and by her fellow negroes &ldquo;Moses.&rdquo; She
+made about a score of trips into the South, bringing out with her
+300 negroes altogether. At one time a reward of $40,000 was offered
+for her capture. She was a mystic, with remarkable clairvoyant
+powers, and did great service as a nurse, a spy and a scout in the
+Civil War. Levi Coffin (1798-1877), a native of North Carolina
+(whose cousin, Vestal Coffin, had established before 1819 a &ldquo;station&rdquo;
+of the Underground near what is now Guilford College, North Carolina),
+in 1826 settled in Wayne County, Ohio; his home at New
+Garden (now Fountain City) was the meeting point of three &ldquo;lines&rdquo;
+from Kentucky; and in 1847 he removed to Cincinnati, where his
+labours in bringing slaves out of the South were even more successful.
+It has been argued that the Underground Railroad delayed the final
+decision of the slavery question, inasmuch as it was a &ldquo;safety
+valve&rdquo;; for, without it, the more intelligent and capable of the
+negro slaves would, it is asserted, have become the leaders of insurrections
+in the South, and would not have been removed from
+the places where they could have done most damage. Consult
+William Still, <i>The Underground Railroad</i> (Philadelphia, 1872), a collection
+of anecdotes by a negro agent of the Pennsylvania Anti-Slavery
+Society, and of the Philadelphia branch of the Railroad; and the
+important and scholarly work of Wilbur H. Siebert, <i>The Underground
+Railroad from Slavery to Freedom</i> (New York, 1898).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FUGLEMAN<a name="ar32" id="ar32"></a></span> (from the Ger. <i>Flügelmann</i>, the man on the
+<i>Flügel</i> or wing), properly a military term for a soldier who is
+selected to act as &ldquo;guide,&rdquo; and posted generally on the flanks
+with the duty of directing the march in the required line, or of
+giving the time, &amp;c., to the remainder of the unit, which conforms
+to his movements, in any military exercise. The word is then
+applied to a ringleader or one who takes the lead in any movement
+or concerted movement.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUGUE<a name="ar33" id="ar33"></a></span> (Lat. <i>fuga</i>, flight), in music, the mutual &ldquo;pursuit&rdquo;
+of voices or parts. It was, up to the end of the 16th century,
+if not later, the name applied to two art-forms. (A) <i>Fuga
+ligata</i> was the exact reproduction by one or more voices of the
+statement of a leading part. The reproducing voice (<i>comes</i>)
+was seldom if ever written out, for all differences between it
+and the <i>dux</i> were rigidly systematic; <i>e.g.</i> it was an exact inversion,
+or exactly twice as slow, or to be sung backwards, &amp;c. &amp;c.
+Hence, a rule or <i>canon</i> was given, often in enigmatic form, by
+which the <i>comes</i> was deduced from the <i>dux</i>: and so the term
+<i>canon</i> became the appropriate name for the form itself, and is
+still retained. (B) A composition in which the canonic style
+was cultivated without canonic restriction was, in the 16th
+century, called <i>fuga ricercata</i> or simply a <i>ricercare</i>, a term which
+is still used by Bach as a title for the fugues in <i>Das musikalische
+Opfer</i>.</p>
+
+<p>The whole conception of fugue, rightly understood, is one of
+the most important in music, and the reasons why some contrapuntal
+compositions are called fugues, while others are not,
+are so trivial, technically as well as aesthetically, that we have
+<span class="pagenum"><a name="page290" id="page290"></a>290</span>
+preferred to treat the subject separately under the general
+heading of <span class="sc"><a href="#artlinks">Contrapuntal Forms</a></span>, reserving only technical
+terms for definition here.</p>
+
+<p>(i.) If in the beginning or &ldquo;exposition&rdquo; the material with which
+the opening voice accompanies the answer is faithfully reproduced
+as the accompaniment to subsequent entries of the subject, it
+is called a <i>countersubject</i> (see <span class="sc"><a href="#artlinks">Counterpoint</a></span>, under sub-heading
+<i>Double Counterpoint</i>). Obviously the process may be carried
+further, the first countersubject going on to a second when the
+subject enters in the third part and so on. The term is also
+applied to new subjects appearing later in the fugue in combination
+(immediate or destined) with the original subject. Cherubini,
+holding the doctrine that a fugue cannot have more than one
+subject, insists on applying the term to the less prominent of
+the subjects of what are commonly called double fugues, <i>i.e.</i>
+fugues which begin with two parts and two subjects simultaneously,
+and so also with <i>triple</i> and <i>quadruple fugues</i>.</p>
+
+<p>(ii.) <i>Episodes</i> are passages separating the entries of the subject.<a name="fa1d" id="fa1d" href="#ft1d"><span class="sp">1</span></a>
+Episodes are usually developed from the material of the subject
+and countersubjects; they are very rarely independent, but
+then conspicuously so.</p>
+
+<p>(iii.) <i>Stretto</i>, the overlapping of subject and answer, is a resource
+the possibilities of which may be exemplified by the setting of
+the words <i>omnes generationes</i> in Bach&rsquo;s <i>Magnificat</i> (see <span class="sc"><a href="#artlinks">Bach</a></span>).</p>
+
+<p>(iv.) The distinction between <i>real</i> and <i>tonal</i> fugue, which is
+still sometimes treated as a thing of great historical and technical
+importance, is really a mere detail resulting from the fact that
+a violent oscillation between the keys of tonic and dominant
+is no part of the function of a fugal exposition, so that the answer
+is (especially in its first notes and in points that tend to shift the
+key) not so much a transposition of the subject to the key of
+the dominant as an adaptation of it from the tonic part to the
+dominant part of the scale, or vice versa; in short, the answer
+is as far as possible <i>on</i> the dominant, not <i>in</i> the dominant. The
+modifications this principle produces in the answer (which have
+been happily described as resembling &ldquo;fore-shortening&rdquo;) are
+the only distinctive marks of tonal fugue; and the text-books
+are half filled with the attempt to reduce them from matters
+of ear to rules of thumb, which rules, however, have the merit
+(unusual in those of the academic fugue) of being founded on
+observation of the practice of great masters. But the same
+principle as often as not produces answers that are exact transpositions
+of the subject; and so the only kind of real fugue
+(<i>i.e.</i> fugue with an exact answer) that could rightly be contrasted
+with tonal fugue would be that in which the answer ought to
+be tonal but is not. It must be admitted that tonal answers are
+rare in the modal music of the 16th century, though their melodic
+principles are of yet earlier date; still, though tonal fugue does
+not become usual until well on in the 17th century, the idea
+that it is a separate species is manifestly absurd, unless the term
+simply means &ldquo;fugue in modern tonality or key,&rdquo; whatever the
+answer may be.</p>
+
+<p>The term &ldquo;answer&rdquo; is usually reserved for those entries of
+the subject that are placed in what may be called the &ldquo;complementary&rdquo;
+position of the scale, whether they are &ldquo;tonally&rdquo;
+modified or not. Thus the order of entries in the exposition of
+the first fugue of the <i>Wohltemp</i>. <i>Klav</i>. is subject, answer, answer,
+subject; a departure from the usual rule according to which
+subject and answer are strictly alternate in the exposition.</p>
+
+<p>In conclusion we may remind the reader of the most accurate
+as well as the most vivid description ever given of the essentials
+of a fugue, in the famous lines in <i>Paradise Lost</i>, book xi.</p>
+
+<table class="reg f90" summary="poem"><tr><td> <div class="poemr">
+   <p class="i6">&ldquo;His volant touch,</p>
+<p>Instinct through all proportions, low and high,</p>
+<p>Fled and pursued transverse the resonant fugue.&rdquo;</p>
+</div> </td></tr></table>
+
+<p class="noind">It is hard to realize that this description of organ-music was
+written in no classical period of instrumental polyphony, but
+just half-way between the death of Frescobaldi and the birth
+of Bach. Every word is a definition, both retrospective and
+prophetic; and in &ldquo;transverse&rdquo; we see all that Sir Frederick
+Gore Ouseley expresses in his popular distinction between the
+&ldquo;perpendicular&rdquo; or homophonic style in which harmony is
+built up in chords, and the &ldquo;horizontal&rdquo; or polyphonic style in
+which it is woven in threads of independent melody.</p>
+<div class="author">(D. F. T.)</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1d" id="ft1d" href="#fa1d"><span class="fn">1</span></a> An episode occurring during the exposition is sometimes called
+<i>codetta</i>, a distinction the uselessness of which at once appears on
+an analysis of Bach&rsquo;s 2nd fugue in the <i>Wohltemp</i>. <i>Klav</i>. (the term
+codetta is more correctly applied to notes filling in a gap between
+subject and its first answer, but such a gap is rare in good examples).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FÜHRICH, JOSEPH VON<a name="ar34" id="ar34"></a></span> (1800-1876), Austrian painter, was
+born at Kratzau in Bohemia on the 9th of February 1800. Deeply
+impressed as a boy by rude pictures adorning the wayside chapels
+of his native country, his first attempt at composition was a
+sketch of the Nativity for the festival of Christmas in his father&rsquo;s
+house. He lived to see the day when, becoming celebrated as
+a composer of scriptural episodes, his sacred subjects were
+transferred in numberless repetitions to the roadside churches of
+the Austrian state, where humble peasants thus learnt to admire
+modern art reviving the models of earlier ages. Führich has
+been fairly described as a &ldquo;Nazarene,&rdquo; a romantic religious artist
+whose pencil did more than any other to restore the old spirit
+of Dürer and give new shape to countless incidents of the gospel
+and scriptural legends. Without the power of Cornelius or the
+grace of Overbeck, he composed with great skill, especially in
+outline. His mastery of distribution, form, movement and
+expression was considerable. In its peculiar way his drapery
+was perfectly cast. Essentially creative as a landscape
+draughtsman, he had still no feeling for colour; and when
+he produced monumental pictures he was not nearly so
+successful as when designing subjects for woodcuts. Führich&rsquo;s
+fame extended far beyond the walls of the Austrian capital,
+and his illustrations to Tieck&rsquo;s <i>Genofeva</i>, the Lord&rsquo;s Prayer,
+the Triumph of Christ, the Road to Bethlehem, the Succession
+of Christ according to Thomas à Kempis, the Prodigal
+Son, and the verses of the Psalter, became well known. His
+Prodigal Son, especially, is remarkable for the fancy with which
+the spirit of evil is embodied in a figure constantly recurring,
+and like that of Mephistopheles exhibiting temptation in a human
+yet demoniacal shape. Führich became a pupil at the Academy
+of Prague in 1816. His first inspiration was derived from the
+prints of Dürer and the Faust of Cornelius, and the first fruit of
+this turn of study was the Genofeva series. In 1826 he went to
+Rome, where he added three frescoes to those executed by
+Cornelius and Overbeck in the Palazzo Massimi. His subjects
+were taken from the life of Tasso, and are almost solitary examples
+of his talent in this class of composition. In 1831 he finished
+the Triumph of Christ now in the Raczynski palace at Berlin.
+In 1834 he was made custos and in 1841 professor of composition
+in the Academy of Vienna. After this he completed the monumental
+pictures of the church of St Nepomuk, and in 1854-1861
+the vast series of wall paintings which cover the inside of the
+Lerchenfeld church at Vienna. In 1872 he was pensioned and
+made a knight of the order of Franz Joseph; 1875 is the date of his
+illustrations to the Psalms. He died on the 13th of March 1876.</p>
+
+<div class="condensed">
+<p>His autobiography was published in 1875, and a memoir by his
+son Lucas in 1886.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FUJI<a name="ar35" id="ar35"></a></span> (Fuji-san, Fujiyama, Fusiyama), a celebrated mountain
+of Japan, standing W.S.W. of Tokyo, its base being about 70 m.
+by rail from that city. It rises to a height of 12,395 ft. and its
+southern slopes reach the shore of Suruga Bay. It is a cone of
+beautifully simple form, the more striking to view because it
+stands isolated; but its summit is not conical, being broken by
+a crater some 2000 ft. in diameter, for Fuji is a quiescent volcano.
+Small outbursts of steam are still to be observed at some points.
+An eruption is recorded so lately as the first decade of the 18th
+century. The mountain is the resort of great numbers of pilgrims
+(see also <span class="sc"><a href="#artlinks">Japan</a></span>).</p>
+
+
+<hr class="art" />
+<p><span class="bold">FU-KIEN<a name="ar36" id="ar36"></a></span> (formerly <span class="sc">Min</span>), a south-eastern province of China,
+bounded N. by the province of Cheh-kiang, S. by that of Kwang-tung,
+W. by that of Kiang-si and E. by the sea. It occupies an
+area of 53,480 sq. m. and its population is estimated at 20,000,000.
+The provincial capital is Fuchow Fu, and it is divided into eleven
+prefectures, besides that ruled over by the prefect of the capital
+city. Fu-kien is generally mountainous, being overspread by the
+Nan-shan ranges, which run a general course of N.E. and S.W.
+<span class="pagenum"><a name="page291" id="page291"></a>291</span>
+The principal river is the Min, which is formed by the junction,
+in the neighbourhood of the city of Yen-p&rsquo;ing Fu, of three rivers,
+namely, the Nui-si, which takes its rise in the mountains on the
+western frontier in the prefecture of Kien-ning Fu, the Fuh-tun
+Ki, the source of which is found in the district of Kwang-tsih in
+the north-west of the province, and the Ta-shi-ki (Shao Ki), which
+rises in the mountains in the western district of Ning-hwa. From
+Yen-p&rsquo;ing Fu the river takes a south-easterly course, and after
+passing along the south face of the city of Fuchow Fu, empties
+itself into the sea about 30 m. below that town. Its upper course
+is narrow and rocky and abounds in rapids, but as it approaches
+Fuchow Fu the channel widens and the current becomes slow
+and even. Its depth is very irregular, and it is navigable only by
+native boats of a small class. Two other rivers flow into the sea
+near Amoy, neither of which, however, is navigable for any
+distance from its mouth owing to the shallows and rapids with
+which they abound. Thirty-five miles inland from Amoy stands
+the city of Chang Chow, famous for the bridge which there spans
+the Kin-lung river. This bridge is 800 ft. long, and consists of
+granite monoliths stretching from one abutment to another. The
+soil of the province is, as its name, &ldquo;Happy Establishment,&rdquo;
+indicates, very productive, and the scenery is of a rich and varied
+character. Most of the hills are covered with verdure, and the
+less rugged are laid out in terraces. The principal products of
+the province are tea, of which the best kind is that known as
+Bohea, which takes its name, by a mispronunciation, from the
+Wu-e Mountains, in the prefecture of Kien-ning Fu, where it is
+grown; grains of various kinds, oranges, plantins, lichis, bamboo,
+ginger, gold, silver, lead, tin, iron, salt (both marine and rock),
+deers&rsquo; horns, beeswax, sugar, fish, birds&rsquo; nests, medicine, paper,
+cloth, timber, &amp;c. Fu-kien has three open ports, Fuchow Fu
+opened in 1842, Amoy opened to trade in the same year and
+Funing. The latter port was only opened to foreign trade in
+1898, but in 1904 it imported and exported goods to the value of
+£7668 and £278,160 respectively.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUKUI<a name="ar37" id="ar37"></a></span>, a town of Japan in the province of Echizen, Nippon,
+near the west coast, 20 m. N. by E. of Wakasa Bay. It lies in
+a volcanic district much exposed to earthquakes, and suffered
+severely during the disturbances of 1891-1892, when a chasm over
+40 m. long was opened across the Neo valley from Fukui to
+Katabira. But Fukui subsequently revived, and is now in a
+flourishing condition, with several local industries, especially the
+manufacture of paper, and an increasing population exceeding
+50,000. Fukui has railway communication. There are ruins of
+a castle of the Daimios of Echizen.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUKUOKA<a name="ar38" id="ar38"></a></span>, a town on the north-west coast of the island of
+Kiushiu, Japan, in the province of Chikuzen, 90 m. N.N.E. of
+Nagasaki by rail. Pop. about 72,000. With Hakata, on the
+opposite side of a small coast stream, it forms a large centre of
+population, with an increasing export trade and several local
+industries. Of these the most important is silk-weaving, and
+Hakata especially is noted for its durable silk fabrics. Fukuoka
+was formerly the residence of the powerful daimio of Chikuzen,
+and played a conspicuous part in the medieval history of Japan;
+the renowned temple of Yeiyas in the district was destroyed by
+fire during the revolution of 1868. There are several other places
+of this name in Japan, the most important being Fukuoka in the
+province of Mutsu, North Nippon, a railway station on the main
+line from Tokyo to Aimori Ura Bay. Pop. about 5000.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FULA<a name="ar39" id="ar39"></a></span> (<span class="sc">Fulbe</span>, <span class="sc">Fellatah</span> or <span class="sc">Peuls</span>), a numerous and powerful
+African people, spread over an immense region from Senegal
+nearly to Darfur. Strictly they have no country of their own, and
+nowhere form the whole of the population, though nearly always
+the dominant native race. They are most numerous in Upper
+Senegal and in the countries under French sway immediately
+south of Senegambia, notably Futa Jallon. Farther east they
+rule, subject to the control of the French, Segu and Massena,
+countries on both banks of the upper Niger, to the south-west of
+Timbuktu. The districts within the great bend of the Niger
+have a large Fula population. East of that river Sokoto and its
+tributary emirates are ruled by Fula princes, subject to the
+control of the British Nigerian administration. Fula are settled
+in Bornu, Bagirmi, Wadai and the upper Nile Valley,<a name="fa1e" id="fa1e" href="#ft1e"><span class="sp">1</span></a> but have
+no political power in those countries. Their most southerly
+emirate is Adamawa, the country on both sides of the upper
+Benue. In this vast region of distribution the Fula populations
+are most dense towards the west and north, most scattered
+towards the east and south. Originally herdsmen in the western
+and central Sudan, they extended their sway east of the Niger,
+under the leadership of Othman Dan Fodio, during the early
+years of the 19th century, and having subdued the Hausa states,
+founded the empire of Sokoto with the vassal emirates of Kano,
+Gando, Nupe, Adamawa, &amp;c.</p>
+
+<p>The question of the ethnic affinities of the Fula has given rise
+to an enormous amount of speculation, but the most reasonable
+theory is that they are a mixture of Berber and Negro. This is
+now the most generally accepted theory. Certainly there is no
+reason to connect them with the ancient Egyptians. In the
+district of Senegal known as Fuladugu or &ldquo;Fula Land,&rdquo; where
+the purest types of the race are found, the people are of a reddish
+brown or light chestnut colour, with oval faces, ringlety or even
+smooth hair, never woolly, straight and even aquiline noses,
+delicately shaped lips and regular features quite differentiating
+them from the Negro type. Like most conquering races the
+Fula are, however, not of uniform physique, in many districts
+approximating to the local type. They nevertheless maintain
+throughout their widespread territory a certain national solidarity,
+thanks to common speech, traditions and usages. The
+ruling caste of the Fula differs widely in character from the
+herdsmen of the western Sudan. The latter are peaceable,
+inoffensive and abstemious. They are mainly monogamous,
+and by rigidly abstaining from foreign marriages have preserved
+racial purity. The ruling caste in Nigeria, on the other hand,
+despise their pastoral brethren, and through generations of
+polygamy with the conquered tribes have become more Negroid
+in type, black, burly and coarse featured. Love of luxury,
+pomp and finery is their chief characteristic. Taken as a whole,
+the Fula race is distinguished by great intelligence, frankness of
+disposition and strength of character. As soldiers they are
+renowned almost exclusively as cavalry; and the race has
+produced several leaders possessed of much strategical skill.
+Besides the ordinary Negro weapons, they use iron spears with
+leatherbound handles and swords. They are generally excellent
+rulers, stern but patient and just. The Nigerian emirs acquired,
+however, an evil reputation during the 19th century as slave
+raiders. They have long been devout Mahommedans, and
+mosques and schools exist in almost all their towns. Tradition
+says that of old every Fula boy and girl was a scholar; but
+during the decadence of their power towards the close of the 19th
+century education was not highly valued. Power seems to have
+somewhat spoilt this virile race, but such authorities as Sir
+Frederick Lugard believe them still capable of a great future.</p>
+
+<p>The Fula language has as yet found no place in any African
+linguistic family. In its rudiments it is akin to the Hamito-Semitic
+group. It possesses two grammatical genders, not
+masculine and feminine, but the human and the non-human;
+the adjective agrees in assonance with its noun, and euphony
+plays a great part in verbal and nominal inflections. In some
+ways resembling the Negro dialects, it betrays non-Negroid
+influences in the use of suffixes. The name of the people has many
+variations. Fulbe or Fula (sing. Pullo, Peul) is the Mandingan
+name, Follani the Hausa, Fellatah the Kanuri, Fullan the
+Arab, and Fulde on the Benue. Like the name Abate, &ldquo;white,&rdquo;
+given them in Kororofa, all these seem to refer to their light
+reddish hue.</p>
+
+<div class="condensed">
+<p>See F. Ratzel, <i>History of Mankind</i> (English ed., London, 1896-1898);
+Sir F. Lugard, &ldquo;Northern Nigeria,&rdquo; in <i>Geographical Journal</i>
+(July 1904); Grimai de Guirodon, <i>Les Puls</i> (1887); E.A. Brackenbury,
+<i>A Short Vocabulary of the Fulani Language</i> (Zungeru, 1907);
+the articles <span class="sc"><a href="#artlinks">Nigeria</a></span> and <span class="sc"><a href="#artlinks">Sokoto</a></span> and authorities there cited.</p>
+</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1e" id="ft1e" href="#fa1e"><span class="fn">1</span></a> Sir Wm. Wallace in a report on Northern Nigeria (&ldquo;Colonial
+Office&rdquo; series, No. 551, 1907) calls attention to the exodus &ldquo;of
+thousands of Fulani of all sorts, but mostly Mellawa, from the
+French Middle Niger,&rdquo; and states that the majority of the emigrants
+are settling in the Nile valley.</p>
+</div>
+
+<p><span class="pagenum"><a name="page292" id="page292"></a>292</span></p>
+
+
+<hr class="art" />
+<p><span class="bold">FULCHER<a name="ar40" id="ar40"></a></span> (or <span class="sc">Foucher</span>) <b>OF CHARTRES</b> (1058-<i>c.</i> 1130),
+French chronicler, was a priest who was present at the council
+of Clermont in 1095, and accompanied Robert II., duke of
+Normandy, on the first crusade in 1096. Having spent some
+time in Italy and taken part in the fighting on the way to the
+Holy Land, he became chaplain to Baldwin, who was chosen
+king of Jerusalem in 1100, and lived with Baldwin at Edessa
+and then at Jerusalem. He accompanied this king on several
+warlike expeditions, but won more lasting fame by writing his
+<i>Historia Hierosolymitana</i> or <i>Gesta Francorum Jerusalem expugnantium</i>,
+one of the most trustworthy sources for the history
+of the first crusade. In its final form it is divided into three
+books, and covers the period between the council of Clermont
+and 1127, and the author only gives details of events which he
+himself had witnessed. It was used by William of Tyre. Fulcher
+died after 1127, probably at Jerusalem. He has been confused
+with Foucher of Mongervillier (d. 1171), abbot of St-Père-en-Vallée
+at Chartres, and also with another person of the same
+name who distinguished himself at the siege of Antioch in
+1098.</p>
+
+<div class="condensed">
+<p>The <i>Historia</i>, but in an incomplete form, was first published by
+J. Bongars in the <i>Gesta Dei per Francos</i> (Hanover, 1611). The best
+edition is in tome iii. of the <i>Recueil des historiens des croisades,
+Historiens occidentaux</i> (Paris, 1866); and there is a French translation
+in tome xxiv. of Guizot&rsquo;s <i>Collection des mémoires relatifs à
+l&rsquo;histoire de France</i> (Paris, 1823-1835).</p>
+
+<p>See H. von Sybel, <i>Geschichte des ersten Kreuzzuges</i> (Leipzig, 1881);
+and A. Molinier, <i>Les Sources de l&rsquo;histoire de France</i>, tome ii. (Paris,
+1902).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FULDA<a name="ar41" id="ar41"></a></span>, a town and episcopal see of Germany, in the Prussian
+province of Hesse-Nassau, between the Rhön and the Vogel-Gebirge,
+69 m. N.E. from Frankfort-on-Main on the railway
+to Bebra. Although irregularly built the town is pleasantly
+situated, and contains two fine squares, on one of which stands a
+fine statue of St Boniface. The present cathedral was built
+at the beginning of the 18th century on the model of St Peter&rsquo;s
+at Rome, but it has an ancient crypt, which contains the bones
+of St Boniface and was restored in 1892. Opposite the cathedral
+is the former monastery of St Michael, now the episcopal palace.
+The Michaelskirche, attached to it, is a small round church built,
+in imitation of the Holy Sepulchre, in 822 and restored in 1853.
+Of other buildings may be mentioned the Library, with upwards
+of 80,000 printed books and many valuable MSS., the stately
+palace with its gardens and orangery, the former Benedictine
+nunnery (founded 1625, and now used as a seminary), and the
+Minorite friary (1238) now used as a furniture warehouse. Among
+the secular buildings are the fine <i>Schloss</i>, the <i>Bibliothek</i>, the
+town hall and the post office. There are several schools, a hospital
+founded in the 13th century, and some new artillery barracks.
+Many industries are carried on in Fulda. These include weaving
+and dyeing, the manufacture of linen, plush and other textiles
+and brewing. There are also railway works in the town. A
+large trade is done in cattle and grain, many markets being held
+here. Fine views are obtained from several hills in the neighbourhood,
+among these being the Frauenberg, the Petersberg and
+the Kalvarienberg.</p>
+
+<p>Fulda owes its existence to its famous abbey. It became a
+town in 1208, and during the middle ages there were many
+struggles between the abbots and the townsfolk. During the
+Peasants&rsquo; War it was captured by the rebels and during the
+Seven Years&rsquo; War by the Hanoverians. It came finally into the
+possession of Prussia in 1866. From 1734 to 1804 Fulda was
+the seat of a university, and latterly many assemblies of German
+bishops have been held in the town.</p>
+
+<p>The great Benedictine abbey of Fulda occupies the place in
+the ecclesiastical history of Germany which Monte Cassino holds
+in Italy, St Gall in South Germany, Corvey in Saxony, Tours
+in France and Iona in Scotland. Founded in 744 at the instigation
+of St Boniface by his pupil Sturm, who was the first abbot,
+it became the centre of a great missionary work. It was liberally
+endowed with land by the princes of the Carolingian house and
+others, and soon became one of the most famous and wealthy
+establishments of its kind. About 968 the pope declared that
+its abbot was primate of all the abbots in Germany and Gaul,
+and later he became a prince of the Empire. Fulda was specially
+famous for its school, which was the centre of the theological
+learning of the early middle ages. Among the teachers here
+were Alcuin, Hrabanus Maurus, who was abbot from 822 to 842,
+and Walafrid Strabo. Early in the 10th century the monastery
+was reformed by introducing monks from Scotland, who were
+responsible for restoring in its old strictness the Benedictine rule.
+Later the abbey lost some of its lands and also its high position,
+and some time before the Reformation the days of its glory
+were over. Johann von Henneberg, who was abbot from 1529
+to 1541, showed some sympathy with the teaching of the reformers,
+but the Counter-Reformation made great progress here
+under Abbot Balthasar von Dernbach. Gustavus Adolphus
+gave the abbey as a principality to William, landgrave of Hesse,
+but William&rsquo;s rule only lasted for ten years. In 1752 the abbot
+was raised to the rank of a bishop, and Fulda ranked as a
+prince-bishopric.  This was secularized in 1802, and in quick succession
+it belonged to the prince of Orange, the king of France and the
+grand-duchy of Frankfort. In 1816 the greater part of the
+principality was ceded by Prussia to Hesse-Cassel, a smaller
+portion being united with Bavaria. Sharing the fate of Hesse-Cassel,
+this larger portion was annexed by Prussia in 1866. In
+1829 a new bishopric was founded at Fulda.</p>
+
+<div class="condensed">
+<p>For the town see A. Hartmann, <i>Zeitgeschichte von Fulda</i> (Fulda,
+1895); J. Schneider, <i>Führer durch die Stadt Fulda</i> (Fulda, 1899);
+and <i>Chronik von Fulda und dessen Umgebungen</i> (1839). For the
+history of the abbey see Gegenbaur, <i>Das Kloster Fulda im Karolinger
+Zeitalter</i> (Fulda, 1871-1874); Arndt, <i>Geschichte des Hochstifts Fulda</i>
+(Fulda, 1860); and the <i>Fuldaer Geschichtsblätter</i> (1902 fol.).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FULGENTIUS, FABIUS PLANCIADES<a name="ar42" id="ar42"></a></span>, Latin grammarian,
+a native of Africa, flourished in the first half of the 6th (or the
+last part of the 5th) century <span class="scs">A.D.</span> He is to be distinguished
+from Fulgentius, bishop of Ruspe (468-533), to whom he was
+probably related, and also from the bishop&rsquo;s pupil and biographer,
+Fulgentius Ferrandus. Four extant works are attributed to
+him. (1) <i>Mythologiarum libri iii.</i>, dedicated to a certain
+Catus, a presbyter of Carthage, containing 75 myths briefly told,
+and then explained in the mystical and allegorical manner of
+the Stoics and Neoplatonists. For this purpose the author
+generally invokes the aid of etymologies which, borrowed from
+the philosophers, are highly absurd. As a Christian, Fulgentius
+sometimes (but less frequently than might have been expected)
+quotes the Bible by the side of the philosophers, to give a
+Christian colouring to the moral lesson. (2) <i>Expositio Vergilianae
+continentiae</i> (<i>continentia</i> = contents), a sort of appendix to (1),
+dedicated to Catus. The poet himself appears to the author and
+explains the twelve books of the <i>Aeneid</i> as a picture of human
+life. The three words <i>arma</i> (= virtus), <i>vir</i> (= sapientia), <i>primus</i>
+(= princeps) in the first line represent respectively <i>substantia
+corporalis, sensualis, ornans</i>. Book i. symbolizes the birth and
+early childhood of man (the shipwreck of Aeneas denotes the
+peril of birth), book vi. the plunge into the depths of wisdom.
+(3) <i>Expositio sermonum antiquorum</i>, explanations of 63 rare and
+obsolete words, supported by quotations (sometimes from authors
+and works that never existed). It is much inferior to the similar
+work of Nonius, with which it is often edited. (4) <i>Liber absque
+litteris de aetatibus mundi et hominis</i>. In the MS. heading of this
+work, the name of the author is given as Fabius Claudius
+Gordianus Fulgentius (Claudius is the name of the father, and
+Gordianus that of the grandfather of the bishop, to whom some
+attribute the work). The title <i>Absque litteris</i> indicates that one
+letter of the alphabet is wholly omitted in each successive book
+(A in bk. i., B in bk. ii.). Only 14 books are preserved. The
+matter is chiefly taken from sacred history. In addition to these,
+Fulgentius speaks of early poetical attempts after the manner of
+Anacreon, and of a work called <i>Physiologus</i>, dealing with medical
+questions, and including a discussion of the mystical signification
+of the numbers 7 and 9. Fulgentius is a representative of the
+so-called late African style, taking for his models Apuleius,
+Tertullian and Martianus Capella. His language is bombastic,
+affected and incorrect, while the lengthy and elaborate periods
+make it difficult to understand his meaning.</p>
+
+<p><span class="pagenum"><a name="page293" id="page293"></a>293</span></p>
+
+<div class="condensed">
+<p>See the edition of the four works by R. Helm (1898, Teubner
+series); also M. Zink, <i>Der Mytholog Fulgentius</i> (1867); E. Jungmann,
+&ldquo;De Fulgentii aetate et scriptis,&rdquo; in <i>Acta Societatis Philologae
+Lipsiensis</i>, i. (1871); A. Ebert, <i>Allgemeine Geschichte der Litt. des
+Mittelalters</i>, i.; article &ldquo;Fulgentius&rdquo; by C.F. Böhr in Ersch and
+Gruber&rsquo;s <i>Allgemeine Encyklopädie</i>; Teuffel-Schwabe, <i>History of
+Roman Literature</i> (Eng. trans.).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FULGINIAE<a name="ar43" id="ar43"></a></span> (mod. <i>Foligno</i>), an ancient town of Umbria,
+Italy, on the later line of the Via Flaminia, 15 m. S. of Nuceria.
+It appears to have been of comparatively late origin, inasmuch
+as it had no city walls, but, in imperial times especially, owing
+to its position on the new line of the Via Flaminia, it must have
+increased in importance as being the point of departure of roads
+to Perusia and to Picenum over the pass of Plestia. It appears
+to have had an amphitheatre, and three bridges over the Topino
+are attributed to the Roman period. Three miles to the N. lies
+the independent community of Forum Flaminii, the site of
+which is marked by the church of S. Giovanni Profiamma, at
+or near which the newer line of the Via Flaminia rejoined the
+older. It was no doubt founded by the builder of the road,
+C. Flaminius, consul in 220 <span class="scs">B.C.</span> (See <span class="sc"><a href="#artlinks">Foligno</a></span> and <span class="sc"><a href="#artlinks">Flaminia</a></span>,
+<span class="sc">Via</span>.)</p>
+<div class="author">(T. As.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">FULGURITE<a name="ar44" id="ar44"></a></span> (from Lat. <i>fulgur</i>, lightning), in petrology, the
+name given to rocks which have been fused on the surface by
+lightning, and to the characteristic holes in rocks formed by the
+same agency. When lightning strikes the naked surfaces of
+rocks, the sudden rise of temperature may produce a certain
+amount of fusion, especially when the rocks are dry and the
+electricity is not readily conducted away. Instances of this
+have been observed on Ararat and on several mountains in the
+Alps, Pyrenees, &amp;c. A thin glassy crust, resembling a coat of
+varnish, is formed; its thickness is usually not more than one-eighth
+of an inch, and it may be colourless, white or yellow. When
+examined under the microscope, it usually shows no crystallization,
+and contains minute bubbles due to the expansion of air
+or other gases in the fused pellicle. Occasionally small microliths
+may appear, but this is uncommon because so thin a film would
+cool with extreme rapidity. The minerals of the rock beneath
+are in some cases partly fused, but the more refractory often
+appear quite unaffected. The glass has arisen from the melting
+of the most fusible ingredients alone.</p>
+
+<p>Another type of fulgurite is commonest in dry sands and
+takes the shape of vertical tubes which may be nearly half an
+inch in diameter. Generally they are elliptical in cross section,
+or flattened by the pressure exerted by the surrounding sand on
+the fulgurite at a time when it was still very hot and plastic.
+These tubes are often vertical and may run downwards for
+several feet through the sand, branching and lessening as they
+descend. Tubular perforations in hard rocks have been noted
+also, but these are short and probably follow original cracks.
+The glassy material contains grains of sand and many small
+round or elliptical cavities, the long axes of which are radial.
+Minerals like felspar and mica are fused more readily than
+quartz, but analysis shows that some fulgurite glasses are very
+rich in silica, which perhaps was dissolved in the glass rather
+than simply fused. The central cavity of the tube and the
+bubbles in its walls point to the expansion of the gases
+(air, water, &amp;c.) in the sand by sudden and extreme heating.
+Very fine threads of glass project from the surface of the tube
+as if fused droplets had been projected outwards with considerable
+force. Where the quartz grains have been greatly
+heated but not melted they become white and semi-opaque,
+but where they are in contact with the glass they usually show
+partial solution. Occasionally crystallization has begun before
+the glass solidified, and small microliths, the nature of which is
+undeterminable, occur in streams and wisps in the clear hyaline
+matrix.</p>
+<div class="author">(J. S. F.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">FULHAM<a name="ar45" id="ar45"></a></span>, a western metropolitan borough of London,
+England, bounded N.W. by Hammersmith, N.E. by Kensington,
+E. by Chelsea, and S.E., S. and S.W. by the river Thames.
+Pop. (1901) 137,289. The principal thoroughfares are Fulham
+Palace Road running S. from Hammersmith, Fulham Road
+and King&rsquo;s Road, W. from Chelsea, <span class="correction" title="amended from coverging">converging</span> and leading to
+Putney Bridge over the Thames; North End Road between
+Hammersmith and Fulham Roads; Lillie Road between South
+Kensington and Fulham Palace Road; and Wandsworth Bridge
+Road leading S. from New King&rsquo;s Road to Wandsworth Bridge.
+In the north Fulham includes the residential district known as
+West Kensington, and farther south that of Walham Green.
+The manor house or palace of the bishops of London stands in
+grounds, beautifully planted and surrounded by a moat, believed
+to be a Danish work, near the river west of Putney Bridge. Its
+oldest portion is the picturesque western quadrangle, built by
+Bishop Fitzjames (1506-1522). The parish church of All
+Saints, between the bridge and the grounds, was erected in
+1881 from designs by Sir Arthur Blomfield. The fine old monuments
+from the former building, dating from the 16th to the
+18th centuries, are mostly preserved, and in the churchyard are
+the memorials of several bishops of London and of Theodore Hook
+(1841). The public recreation grounds include the embankment
+and gardens between the river and the palace grounds, and
+there are also two well-known enclosures used for sports within
+the borough. Of these Hurlingham Park is the headquarters
+of the Hurlingham Polo Club and a fashionable resort; and
+Queen&rsquo;s Club, West Kensington, has tennis and other courts
+for the use of members, and is also the scene of important
+football matches, and of the athletic meetings between Oxford
+and Cambridge Universities, and those between the English
+and American Universities held in England. In Seagrave Road
+is the Western fever hospital. The parliamentary borough of
+Fulham returns one member. The borough council consists of
+a mayor, 6 aldermen and 36 councillors. Area, 1703.5 acres.</p>
+
+<p>Fulham, or in its earliest form <i>Fullanham</i>, is uncertainly
+stated to signify &ldquo;the place&rdquo; either &ldquo;of fowls&rdquo; or &ldquo;of dirt.&rdquo;
+The manor is said to have been given to Bishop Erkenwald
+about the year 691 for himself and his successors in the see of
+London, and Holinshed relates that the Bishop of London was
+lodging in his manor place in 1141 when Geoffrey de Mandeville,
+riding out from the Tower of London, took him prisoner. At
+the Commonwealth the manor was temporarily out of the
+bishops&rsquo; hands, being sold to Colonel Edmund Harvey. There
+is no record of the first erection of a parish church, but the first
+known rector was appointed in 1242, and a church probably
+existed a century before this. The earliest part of the church
+demolished in 1881, however, did not date farther back than
+the 15th century. In 879 Danish invaders, sailing up the
+Thames, wintered at Fulham and Hammersmith. Near the
+former wooden Putney Bridge, built in 1729 and replaced in
+1886, the earl of Essex threw a bridge of boats across the river
+in 1642 in order to march his army in pursuit of Charles I., who
+thereupon fell back on Oxford. Margravine Road recalls the
+existence of Bradenburg House, a riverside mansion built by
+Sir Nicholas Crispe in the time of Charles I., used as the headquarters
+of General Fairfax in 1647 during the civil wars, and
+occupied in 1792 by the margrave of Bradenburg-Anspach
+and Bayreuth and his wife, and in 1820 by Caroline, consort of
+George IV.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FULK<a name="ar46" id="ar46"></a></span>, king of Jerusalem (b. 1092), was the son of Fulk IV.,
+count of Anjou, and his wife Bertrada (who ultimately deserted
+her husband and became the mistress of Philip I. of France).
+He became count of Anjou in 1109, and considerably added to
+the prestige of his house. In particular he showed himself a
+doughty opponent to Henry I. of England, against whom he
+continually supported Louis VI. of France, until in 1127 Henry
+won him over by betrothing his daughter Matilda to Fulk&rsquo;s son
+Geoffrey Plantagenet. Already in 1120 Fulk had visited the
+Holy Land, and become a close friend of the Templars. On his
+return he assigned to the order of the Templars an annual subsidy,
+while he also maintained two knights in the Holy Land
+for a year. In 1128 he was preparing to return to the East,
+when he received an embassy from Baldwin II., king of Jerusalem,
+who had no male heir to succeed him, offering his daughter
+Melisinda in marriage, with the right of eventual succession to
+the kingdom. Fulk readily accepted the offer; and in 1129
+he came and was married to Melisinda, receiving the towns of
+<span class="pagenum"><a name="page294" id="page294"></a>294</span>
+Acre and Tyre as her dower. In 1131, at the age of thirty-nine,
+he became king of Jerusalem. His reign is not marked by any
+considerable events: the kingdom which had reached its zenith
+under Baldwin II., and did not begin to decline till the capture
+of Edessa in the reign of Baldwin III., was quietly prosperous
+under his rule. In the beginning of his reign he had to act as
+regent of Antioch, and to provide a husband, Raymund of
+Poitou, for the infant heiress Constance. But the great problem
+with which he had to deal was the progress of the atabeg Zengi
+of Mosul. In 1137 he was beaten near Barin, and escaping into
+the fort was surrounded and forced to capitulate. A little
+later, however, he greatly improved his position by strengthening
+his alliance with the vizier of Damascus, who also had to fear
+the progress of Zengi (1140); and in this way he was able to
+capture the fort of Banias, to the N. of Lake Tiberias. Fulk
+also strengthened the kingdom on the south; while his butler,
+Paganus, planted the fortress of Krak to the south of the Dead
+Sea, and helped to give the kingdom an access towards the
+Red Sea, he himself constructed Blanche Garde and other forts
+on the S.W. to overawe the garrison of Ascalon, which was still
+held by the Mahommedans, and to clear the road towards Egypt.
+Twice in Fulk&rsquo;s reign the eastern emperor, John Comnenus,
+appeared in northern Syria (1137 and 1142); but his coming
+did not affect the king, who was able to decline politely a visit
+which the emperor proposed to make to Jerusalem. In 1143 he
+died, leaving two sons, who both became kings, as Baldwin III.
+and Amalric I.</p>
+
+<p>Fulk continued the tradition of good statesmanship and
+sound churchmanship which Baldwin I. and Baldwin II. had
+begun. William of Tyre speaks of him as a fine soldier, an able
+politician, and a good son of the church, and only blames him
+for partiality to his friends, and a forgetfulness of names and
+faces, which placed him at a disadvantage and made him too
+dependent on his immediate intimates. Little, perhaps, need
+be made of these censures: the real fault of Fulk was his neglect
+to envisage the needs of the northern principalities, and to
+head a combined resistance to the rising power of Zengi of
+Mosul.</p>
+
+<div class="condensed">
+<p>His reign in Jerusalem is narrated by R. Röhricht (<i>Geschichte des
+Königreichs Jerusalem</i>, Innsbruck, 1898), and has been made the
+subject of a monograph by G. Dodu (<i>De Fulconis Hierosolymitani
+regno</i>, Paris, 1894).</p>
+</div>
+<div class="author">(E. Br.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">FULK<a name="ar47" id="ar47"></a></span> (d. 900), archbishop of Reims, and partisan of Charles
+the Simple in his struggle with Odo, count of Paris, was elected
+to the see as archbishop in 883 upon the death of Hincmar.
+In 887 he was engaged in a struggle with the Normans who
+invaded his territories. Upon the deposition of Charles the Fat
+he sided with Charles the Simple in his contest for the West
+Frankish dominions against Count Odo of Paris, and crowned
+him king in his own metropolitan church at Reims after most
+of the nobles had gone over to Odo (893). Upon the death of
+Odo he succeeded in having Charles recognized as king by a
+majority of the West Frankish nobility. In 892 he obtained
+special privileges for his province from Pope Formosus, who
+promised that thereafter, when the archbishopric became
+vacant, the revenues should not be enjoyed by anyone while
+the vacancy existed, but should be reserved for the new incumbent,
+provided the election took place within the canonical
+limit of three months. From 898 until his death he held the
+office of chancellor, which for some time afterwards was regularly
+filled by the archbishop of Reims. In his efforts to keep the
+wealthy abbeys and benefices of the church out of the hands
+of the nobles, he incurred the hatred of Baldwin, count
+of Flanders, who secured his assassination on the 17th of
+June 900, a crime which the weak Carolingian monarch left
+unpunished.</p>
+
+<div class="condensed">
+<p>Fulk left some letters, which are collected in Migne, <i>Patrologia
+Latina</i>, vol. cxxxi. 11-14.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FULKE, WILLIAM<a name="ar48" id="ar48"></a></span> (1538-1589), Puritan divine, was born
+in London and educated at Cambridge. After studying law for
+six years, he became a fellow at St John&rsquo;s College, Cambridge,
+in 1564. He took a leading part in the &ldquo;vestiarian&rdquo; controversy,
+and persuaded the college to discard the surplice. In consequence
+he was expelled from St. John&rsquo;s for a time, but in 1567 he became
+Hebrew lecturer and preacher there. After standing unsuccessfully
+for the headship of the college in 1569, he became chaplain
+to the earl of Leicester, and received from him the livings of
+Warley, in Essex, and Dennington in Suffolk. In 1578 he was
+elected master of Pembroke Hall, Cambridge. As a Puritan
+controversialist he was remarkably active; in 1580 the bishop
+of Ely appointed him to defend puritanism against the Roman
+Catholics, Thomas Watson, ex-bishop of Lincoln (1513-1584),
+and John Feckenham, formerly abbot of Westminster, and in
+1581 he was one of the disputants with the Jesuit, Edmund
+Campion, while in 1582 he was among the clergy selected
+by the privy council to argue against any papist. His
+numerous polemical writings include <i>A Defense of the sincere
+true Translations of the holie Scriptures into the English
+tong</i> (London, 1583), and confutations of Thomas Stapleton
+(1535-1598), Cardinal Allen and other Roman Catholic
+controversialists.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FULK NERRA<a name="ar49" id="ar49"></a></span> (<i>c.</i> 970-1040), count of Anjou, eldest son of
+Count Geoffrey I., &ldquo;Grisegonelle&rdquo; (Grey Tunic) and Adela of
+Vermandois, was born about 970 and succeeded his father in
+the countship of Anjou on the 21st of July 987. He was successful
+in repelling the attacks of the count of Rennes and laying the
+foundations of the conquest of Touraine (see <span class="sc"><a href="#artlinks">Anjou</a></span>). In this
+connexion he built a great number of strong castles, which has
+led in modern times to his being called &ldquo;the great builder.&rdquo;
+He also founded several religious houses, among them the abbeys
+of Beaulieu, near Loches (<i>c.</i> 1007), of Saint-Nicholas at Angers
+(1020) and of Ronceray at Angers (1028), and, in order to expiate
+his crimes of violence, made three pilgrimages to the Holy Land
+(in 1002-1003, <i>c.</i> 1008 and in 1039). On his return from the
+third of these journeys he died at Metz in Lorraine on the 21st of
+June 1040. By his first marriage, with Elizabeth, daughter of
+Bouchard le Vénérable, count of Vendôme, he had a daughter,
+Adela, who married Boon of Nevers and transmitted to her
+children the countship of Vendôme. Elizabeth having died in
+1000, Fulk married Hildegarde of Lorraine, by whom he had a
+son, Geoffrey Martel (<i>q.v.</i>), and a daughter Ermengarde, who
+married Geoffrey, count of Gâtinais, and was the mother of
+Geoffrey &ldquo;le Barbu&rdquo; (the Bearded) and of Fulk &ldquo;le Réchin&rdquo;
+(see <span class="sc"><a href="#artlinks">Anjou</a></span>).</p>
+
+<div class="condensed">
+<p>See Louis Halphen, <i>Le Comté d&rsquo;Anjou au XI<span class="sp">e</span> siècle</i> (Paris, 1906).
+The biography of Fulk Nerra by Alexandre de Salies, <i>Histoire de
+Foulques Nerra</i> (Angers, 1874) is confused and uncritical. A very
+summary biography is given by Célestin Port, <i>Dictionnaire historique,
+géographique et biographique de Maine-et-Loire</i> (3 vols., Paris-Angers,
+1874-1878), vol. ii. pp. 189-192, and there is also a sketch in Kate
+Norgate, <i>England under the Angevin Kings</i> (2 vols., London, 1887),
+vol. i. ch. iii.</p>
+</div>
+<div class="author">(L. H.*)</div>
+
+
+<hr class="art" />
+<p><span class="bold">FÜLLEBORN, GEORG GUSTAV<a name="ar50" id="ar50"></a></span> (1769-1803), German philosopher,
+philologist and miscellaneous writer, was born at Glogau,
+Silesia, on the 2nd of March 1769, and died at Breslau on the
+6th of February 1803. He was educated at the University of
+Halle, and was made doctor of philosophy in recognition of his
+thesis <i>De Xenophane, Zenone et Gorgia</i>. He took diaconal orders
+in 1791, but almost immediately became professor of classics at
+Breslau. His philosophical works include annotations to Garve&rsquo;s
+translation of the <i>Politics</i> of Aristotle (1799-1800), and a large
+share in the <i>Beiträge zur Geschichte der Philosophie</i> (published in
+twelve parts between 1791 and 1799), in which he collaborated
+with Forberg, Reinhold and Niethammer. In philology he
+wrote <i>Encyclopaedia philologica sive primae lineae Isagoges in
+antiquorum studia</i> (1798; 2nd ed., 1805); <i>Kurze Theorie des
+lateinischen Stils</i> (1793); <i>Leitfaden der Rhetorik</i> (1802); and an
+annotated edition of the <i>Satires</i> of Persius. Under the pseudonym
+&ldquo;Edelwald Justus&rdquo; he published several collections of popular
+tales&mdash;<i>Bunte Blätter</i> (1795); <i>Kleine Schriften zur Unterhaltung</i>
+(1798); <i>Nebenstunden</i> (1799). After his death were published
+<i>Taschenbuch für Brunnengäste</i> (1806) and <i>Kanzelreden</i> (1807).
+He was a frequent contributor to the press, where his writings
+were very popular.</p>
+
+<div class="condensed">
+<p>See Schummel, <i>Gedächtnisrede</i> (1803) and <i>Garve und Fülleborn</i>;
+Meusel, <i>Gelehrtes Teutschland</i>, vol. ii.</p>
+</div>
+
+<p><span class="pagenum"><a name="page295" id="page295"></a>295</span></p>
+
+
+<hr class="art" />
+<p><span class="bold">FULLER, ANDREW<a name="ar51" id="ar51"></a></span> (1754-1815), English Baptist divine, was
+born on the 6th of February 1754, at Wicken in Cambridgeshire.
+In his boyhood and youth he worked on his father&rsquo;s farm. In his
+seventeenth year he became a member of the Baptist church at
+Soham, and his gifts as an exhorter met with so much approval
+that, in the spring of 1775, he was called and ordained as pastor
+of that congregation. In 1782 he removed to Kettering in
+Northamptonshire, where he became friendly with some of the
+most eminent ministers of the denomination. Before leaving
+Soham he had written the substance of a treatise in which he had
+sought to counteract the prevailing Baptist hyper-Calvinism
+which, &ldquo;admitting nothing spiritually good to be the duty
+of the unregenerate, and nothing to be addressed to them
+in a way of exhortation excepting what related to external
+obedience,&rdquo; had long perplexed his own mind. This work he
+published, under the title <i>The Gospel worthy of all Acceptation</i>,
+soon after his settlement in Kettering; and although it immediately
+involved him in a somewhat bitter controversy which lasted
+for nearly twenty years, it was ultimately successful in considerably
+modifying the views prevalent among English dissenters.
+In 1793 he published a treatise, <i>The Calvinistic and Socinian
+systems examined and compared as to their moral tendency</i>, in which
+he rebutted the accusation of antinomianism levelled by the
+Socinians against those who over-emphasized the doctrines of
+free grace. This work, along with another against Deism,
+entitled <i>The Gospel its own Witness</i>, is regarded as the production
+on which his reputation as a theologian mainly rests. Fuller
+also published an admirable <i>Memoir of the Rev. Samuel Pearce</i>,
+of Birmingham, and a volume of <i>Expository Lectures in Genesis</i>,
+besides a considerable number of smaller pieces, chiefly sermons
+and pamphlets, which were issued in a collected form after his
+death. He was a man of forceful character, more prominent on
+the practical side of religion than on the devotional, and accordingly
+not pre-eminently successful in his local ministry. His
+great work was done in connexion with the Baptist Missionary
+Society, formed at Kettering in 1792, of which he was secretary
+until his death on the 7th of May 1815. Both Princeton and
+Yale, U.S.A., conferred on him the degree of D. D., but he never
+used it.</p>
+
+<div class="condensed">
+<p>Several editions of his collected works have appeared, and a
+<i>Memoir</i>, principally compiled from his own papers, was published
+about a year after his decease by Dr Ryland, his most intimate
+friend and coadjutor in the affairs of the Baptist mission. There
+is also a biography by the Rev. J.W. Morris (1816); and his son
+prefixed a memoir to an edition of his chief works in Bohn&rsquo;s Standard
+Library (1852).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FULLER, GEORGE<a name="ar52" id="ar52"></a></span> (1822-1884), American figure and portrait
+painter, was born at Deerfield, Massachusetts, in 1822. At the
+age of twenty he entered the studio of the sculptor H.K. Brown,
+at Albany, New York, where he drew from the cast and modelled
+heads. Having attained some proficiency he went about the
+country painting portraits, settling at length in Boston, where he
+studied the works of the earlier Americans, Stuart, Copley and
+Allston. After three years in that city, and twelve in New York,
+where in 1857 he was elected a member of the National Academy
+of Design, he went to Europe for a brief visit and for study.
+During all this time his work had received little recognition and
+practically no financial encouragement, and on his return he
+settled on the family farm at Deerfield, where he continued to
+work in his own way with no thought of the outside world. In
+1876, however, he was forced by pressing needs to dispose of
+his work, and he sent some pictures to a dealer in Boston, where
+he met with immediate success, financial and artistic, and for the
+remaining eight years of his life he never lacked patrons. He
+died in Boston on the 21st of March 1884. He was a poetic
+painter, and a dreamer of delicate fancies and quaint, intangible
+phases of nature, his canvases being usually enveloped in a brown
+mist that renders the outlines vague. Among his noteworthy
+canvases are: &ldquo;The Turkey Pasture,&rdquo; &ldquo;Romany Girl,&rdquo; &ldquo;And
+she was a Witch,&rdquo; &ldquo;Nydia,&rdquo; &ldquo;Winifred Dysart&rdquo; and &ldquo;The
+Quadroon.&rdquo;</p>
+
+
+<hr class="art" />
+<p><span class="bold">FULLER, MARGARET<a name="ar53" id="ar53"></a></span>, Marchioness Ossoli (1810-1850),
+American authoress, eldest child of Timothy Fuller (1778-1835),
+a lawyer and politician of some eminence, was born at Cambridgeport,
+Massachusetts, on the 23rd of May 1810. Her education
+was conducted by her father, who, she states, made the mistake
+of thinking to &ldquo;gain time by bringing forward the intellect as
+early as possible,&rdquo; the consequence being &ldquo;a premature development
+of brain that made her a youthful prodigy by day, and by
+night a victim of spectral illusions, nightmare and somnambulism.&rdquo;
+At six years she began to read Latin, and at a very early
+age she had selected as her favourite authors Shakespeare,
+Cervantes and Molière. Soon the great amount of study
+exacted of her ceased to be a burden, and reading became
+a habit and a passion. Having made herself familiar with the
+masterpieces of French, Italian and Spanish literature, she in
+1833 began the study of German, and within the year had
+read some of the masterpieces of Goethe, Körner, Novalis
+and Schiller.</p>
+
+<p>After her father&rsquo;s death in 1835 she went to Boston to teach
+languages, and in 1837 she was chosen principal teacher in the
+Green Street school, Providence, Rhode Island, where she
+remained till 1839. From this year until 1844 she stayed at
+different places in the immediate neighbourhood of Boston,
+forming an intimate acquaintance with the colonists of Brook
+Farm, and numbering among her closest friends R.W. Emerson,
+Nathaniel Hawthorne and W.H. Channing. In 1839 she
+published a translation of Eckermann&rsquo;s <i>Conversations with
+Goethe</i>, which was followed in 1842 by a translation of the correspondence
+between Karoline von Günderode and Bettina von
+Arnim, entitled <i>Günderode</i>. Aided by R.W. Emerson and
+George Ripley, she in 1840 started <i>The Dial</i>, a poetical and
+philosophical magazine representing the opinions and aims of
+the New England Transcendentalists. This journal she continued
+to edit for two years, and while in Boston she also conducted
+conversation classes for ladies in which philosophical and
+social subjects were discussed with a somewhat over-accentuated
+earnestness. These meetings may be regarded as perhaps the
+beginning of the modern movement in behalf of women&rsquo;s rights.
+R.W. Emerson, who had met her as early as 1836, thus describes
+her appearance: &ldquo;She was then twenty-six years old. She had
+a face and frame that would indicate fulness and tenacity of life.
+She was rather under the middle height; her complexion was
+fair, with strong fair hair. She was then, as always, carefully and
+becomingly dressed, and of ladylike self-possession. For the
+rest her appearance had nothing prepossessing. Her extreme
+plainness, a trick of incessantly opening and shutting her eyelids,
+the nasal tone of her voice, all repelled; and I said to myself we
+shall never get far.&rdquo; On better acquaintance this unprepossessing
+exterior seemed, however, to melt away, and her inordinate self-esteem
+to be lost in the depth and universality of her sympathy.
+She possessed an almost irresistible power of winning the intellectual
+and moral confidence of those with whom she came in
+contact, and &ldquo;applied herself to her companion as the sponge
+applies itself to water.&rdquo; She obtained from each the best they
+had to give. It was indeed more as a conversationalist than as a
+writer that she earned the title of the Priestess of Transcendentalism.
+It was her intimate friends who admired her most.
+Smart and pungent though she is as a writer, the apparent
+originality of her views depends more on eccentricity than either
+intellectual depth or imaginative vigour. In 1844 she removed
+to New York at the desire of Horace Greeley to write literary
+criticism for <i>The Tribune</i>, and in 1846 she published a selection
+from her articles on contemporary authors in Europe and
+America, under the title <i>Papers on Literature and Art</i>. The same
+year she paid a visit to Europe, passing some time in England
+and France, and finally taking up her residence in Italy. There
+she was married in December 1847 to the marquis Giovanni
+Angelo Ossoli, a friend of Mazzini. During 1848-1849 she was
+present with her husband in Rome, and when the city was
+besieged she, at the request of Mazzini, took charge of one
+of the two hospitals while her husband fought on the walls.
+In May 1850, along with her husband and infant son, she
+embarked at Leghorn for America, but when they had all
+but reached their destination the vessel was wrecked on Fire
+<span class="pagenum"><a name="page296" id="page296"></a>296</span>
+Island beach on the 16th of June, and the Ossolis were among
+the passengers who perished.</p>
+
+<div class="condensed">
+<p><i>Life Without and Life Within</i> (Boston, 1860) is a collection of
+essays, poems, &amp;c., supplementary to her <i>Collected Works</i>, printed
+in 1855. See the <i>Autobiography of Margaret Fuller Ossoli</i>, with
+additional memoirs by J.F. Clarke, R.W. Emerson and W.H.
+Channing (2 vols., Boston, 1852); also <i>Margaret Fuller (Marchesa
+Ossoli)</i>, by Julia Ward Howe (1883), in the &ldquo;Eminent Women&rdquo;
+series; <i>Margaret Fuller Ossoli</i> (Boston, 1884), by Thomas Wentworth
+Higginson in the &ldquo;American Men of Letters&rdquo; series, which is
+based largely on unedited material; and <i>The Love Letters of Margaret
+Fuller, 1845-1846</i> (London and New York, 1903), with an introduction
+by Julia Ward Howe.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FULLER, MELVILLE WESTON<a name="ar54" id="ar54"></a></span> (1833-1910), American jurist,
+chief justice of the Supreme Court of the United States, was born
+at Augusta, Maine, on the 11th of February 1833. After graduating
+at Bowdoin College in 1853 he spent a year at the Harvard
+Law School, and in 1855 began the practice of law at Augusta,
+where he was an associate-editor of a Democratic paper, <i>The
+Age</i>, and served in the city council and as city attorney. In
+1856 he removed to Chicago, Illinois, where he continued to
+practise until 1888, rising to a high position at the bar of the
+Northwest. For some years he was active in Democratic politics,
+being a member of the Illinois Constitutional Convention in
+1862 and of the State House of Representatives from 1863 to
+1865. He was a delegate to various National conventions of
+his party, and in that of 1876 placed Thomas A. Hendricks in
+nomination for the presidency. In 1888, by President Cleveland&rsquo;s
+appointment, he succeeded Morrison R. Waite as chief-justice
+of the Supreme Court of the United States. In 1899 he was
+appointed by President McKinley a member of the arbitration
+commission at Paris to settle the Venezuela-British Guiana
+boundary dispute.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FULLER, THOMAS<a name="ar55" id="ar55"></a></span> (1608-1661), English divine and historian,
+eldest son of Thomas Fuller, rector of Aldwincle St Peter&rsquo;s,
+Northamptonshire, was born at his father&rsquo;s rectory and was
+baptized on the 19th of June 1608. Dr John Davenant, bishop
+of Salisbury, was his uncle and godfather. According to Aubrey,
+Fuller was &ldquo;a boy of pregnant wit.&rdquo; At thirteen he was admitted
+to Queens&rsquo; College, Cambridge, then presided over by Dr John
+Davenant. His cousin, Edward Davenant, was a tutor in the
+same college. He was apt and quick in study; and in Lent
+1624-1625 he became B.A. and in July 1628 M.A. Being overlooked
+in an election of fellows of his college, he was removed
+by Bishop Davenant to Sidney Sussex College, November 1628.
+In 1630 he received from Corpus Christi College the curacy of
+St Benet&rsquo;s, Cambridge.</p>
+
+<p>Fuller&rsquo;s quaint and humorous oratory soon attracted attention.
+He published in 1631 a poem on the subject of David and
+Bathsheba, entitled <i>David&rsquo;s Hainous Sinne, Heartie Repentance,
+Heavie Punishment</i>. In June of the same year his uncle gave him
+a prebend in Salisbury, where his father, who died in the following
+year, held a canonry. The rectory of Broadwindsor, Dorsetshire,
+then in the diocese of Bristol, was his next preferment
+(1634); and on the 11th of June 1635 he proceeded B.D. At
+Broadwindsor he compiled <i>The Historie of the Holy Warre</i> (1639),
+a history of the crusades, and <i>The Holy State and the Prophane
+State</i> (1642). This work describes the holy state as existing in
+the family and in public life, gives rules of conduct, model
+&ldquo;characters&rdquo; for the various professions and profane biographies.
+It was perhaps the most popular of all his writings.
+He was in 1640 elected proctor for Bristol in the memorable
+convocation of Canterbury, which assembled with the Short
+Parliament. On the sudden dissolution of the latter he joined
+those who urged that convocation should likewise dissolve as
+usual. That opinion was overruled; and the assembly continued
+to sit by virtue of a royal writ. Fuller has left in his <i>Church
+History</i> a valuable account of the proceedings of this synod,
+for sitting in which he was fined £200, which, however, was never
+exacted. His first published volume of sermons appeared in
+1640 under the title of <i>Joseph&rsquo;s party-coloured Coat</i>, which contains
+many of his quaint utterances and odd conceits. His grosser
+mannerisms of style, derived from the divines of the former
+generation, disappeared for the most part in his subsequent
+discourses.</p>
+
+<p>About 1640 he had married Eleanor, daughter of Hugh
+Grove of Chisenbury, Wiltshire. She died in 1641. Their eldest
+child, John, baptized at Broadwindsor by his father, 6th
+June 1641, was afterwards <span class="correction" title="added rector">rector</span> of Sidney Sussex College, edited
+the <i>Worthies of England</i>, 1662, and became rector of Great
+Wakering, Essex, where he died in 1687.</p>
+
+<p>At Broadwindsor, early in the year 1641, Thomas Fuller, his
+curate Henry Sanders, the church wardens, and others, nine
+persons altogether, certified that their parish, represented by
+242 grown-up male persons, had taken the Protestation ordered
+by the speaker of the Long Parliament. Fuller was not formally
+dispossessed of his living and prebend on the triumph of the
+Presbyterian party, but he relinquished both preferments about
+this time. For a short time he preached with success at the Inns
+of Court, and thence removed, at the invitation of the master
+of the Savoy (Dr Balcanqual) and the brotherhood of that
+foundation, to be lecturer at their chapel of St Mary Savoy.
+Some of the best discourses of the witty preacher were delivered
+at the Savoy to audiences which extended into the chapel-yard.
+In one he set forth with searching and truthful minuteness the
+hindrances to peace, and urged the signing of petitions to the
+king at Oxford, and to the parliament, to continue their care in
+advancing an accommodation. In his <i>Appeal of Injured Innocence</i>
+Fuller says that he was once deputed to carry a petition to the
+king at Oxford. This has been identified with a petition entrusted
+to Sir Edward Wardour, clerk of the pells, Dr Dukeson, &ldquo;Dr
+Fuller,&rdquo; and four or five others from the city of Westminster
+and the parishes contiguous to the Savoy. A pass was granted
+by the House of Lords, on the 2nd of January 1643, for an
+equipage of two coaches, four or six horses and eight or ten
+attendants. On the arrival of the deputation at Uxbridge, on
+the 4th of January, officers of the Parliamentary army stopped
+the coaches and searched the gentlemen; and they found upon
+the latter &ldquo;two scandalous books arraigning the proceedings
+of the House,&rdquo; and letters with ciphers to Lord Viscount Falkland
+and the Lord Spencer. Ultimately a joint order of both Houses
+remanded the party; and Fuller and his friends suffered a
+brief imprisonment. The Westminster Petition, notwithstanding,
+reached the king&rsquo;s hands; and it was published with the royal
+reply (see J.E. Bailey, <i>Life of Thomas Fuller</i>, pp. 245 <i>et seq.</i>).
+When it was expected, three months later, that a favourable
+result would attend the negotiations at Oxford, Fuller preached
+a sermon at Westminster Abbey, on the 27th of March 1643, on
+the anniversary of Charles I.&rsquo;s accession, on the text, &ldquo;Yea, let
+him take all, so my Lord the King return in peace.&rdquo; On
+Wednesday, the 26th of July, he preached on church reformation,
+satirizing the religious reformers, and maintaining that only the
+Supreme Power could initiate reforms.</p>
+
+<p>He was now obliged to leave London, and in August 1643 he
+joined the king at Oxford. He lived in a hired chamber at
+Lincoln College for 17 weeks. Thence he put forth a witty and
+effective reply to John Saltmarsh, who had attacked his views
+on ecclesiastical reform. Fuller subsequently published by
+royal request a sermon preached on the 10th of May 1644, at
+St Mary&rsquo;s, Oxford, before the king and Prince Charles, called
+<i>Jacob&rsquo;s Vow</i>.</p>
+
+<p>The spirit of Fuller&rsquo;s preaching, always characterized by calmness
+and moderation, gave offence to the high royalists, who
+charged him with lukewarmness in their cause. To silence
+unjust censures he became chaplain to the regiment of Sir
+Ralph Hopton. For the first five years of the war, as he said,
+when excusing the non-appearance of his <i>Church History</i>, &ldquo;I
+had little list or leisure to write, fearing to be made a history, and
+shifting daily for my safety. All that time I could not live to
+study, who did only study to live.&rdquo; After the defeat of Hopton
+at Cheriton Down, Fuller retreated to Basing House. He took
+an active part in its defence, and his life with the troops caused
+him to be afterwards regarded as one of &ldquo;the great cavalier
+parsons.&rdquo; In his marches with his regiment round about Oxford
+and in the west, he devoted much time to the collection of details,
+<span class="pagenum"><a name="page297" id="page297"></a>297</span>
+from churches, old buildings, and the conversation of ancient
+gossips, for his <i>Church-History</i> and <i>Worthies of England</i>. He
+compiled in 1645 a small volume of prayers and meditations,&mdash;the
+<i>Good Thoughts in Bad Times</i>,&mdash;which, set up and printed in
+the besieged city of Exeter, whither he had retired, was called
+by himself &ldquo;the first fruits of Exeter press.&rdquo; It was inscribed to
+Lady Dalkeith, governess to the infant princess, Henrietta Anne
+(b. 1644), to whose household he was attached as chaplain. The
+corporation gave him the Bodleian lectureship on the 21st of
+March 1645/6, and he held it until the 17th of June following,
+soon after the surrender of the city to the parliament. <i>The Fear
+of losing the Old Light</i> (1646) was his farewell discourse to his
+Exeter friends. Under the Articles of Surrender Fuller made his
+composition with the government at London, his &ldquo;delinquency&rdquo;
+being that he had been present in the king&rsquo;s garrisons. In
+<i>Andronicus, or the Unfortunate Politician</i> (1646), partly authentic
+and partly fictitious, he satirized the leaders of the Revolution;
+and for the comfort of sufferers by the war he issued (1647) a
+second devotional manual, entitled <i>Good Thoughts in Worse
+Times</i>, abounding in fervent aspirations, and drawing moral
+lessons in beautiful language out of the events of his life or the
+circumstances of the time. In grief over his losses, which included
+his library and manuscripts (his &ldquo;upper and nether millstone&rdquo;),
+and over the calamities of the country, he wrote his work on
+the <i>Cause and Cure of a Wounded Conscience</i> (1647). It was
+prepared at Boughton House in his native county, where he and
+his son were entertained by Edward Lord Montagu, who had
+been one of his contemporaries at the university and had taken
+the side of the parliament.</p>
+
+<p>For the next few years of his life Fuller was mainly dependent
+upon his dealings with booksellers, of whom he asserted that
+none had ever lost by him. He made considerable progress in
+an English translation from the MS. of the <i>Annales</i> of his friend
+Archbishop Ussher. Amongst his benefactors it is curious to
+find Sir John Danvers of Chelsea, the regicide. Fuller in 1647
+began to preach at St Clement&rsquo;s, Eastcheap, and elsewhere
+in the capacity of lecturer. While at St Clement&rsquo;s he was
+suspended; but speedily recovering his freedom, he preached
+wherever he was invited. At Chelsea, where also he occasionally
+officiated, he covertly preached a sermon on the death of Charles
+I., but he did not break with his Roundhead patrons. James
+Hay, 2nd earl of Carlisle, made him his chaplain, and presented
+him in 1648 or 1649 to the curacy of Waltham Abbey. His
+possession of the living was in jeopardy on the appointment of
+Cromwell&rsquo;s &ldquo;Tryers&rdquo;; but he evaded their inquisitorial questions
+by his ready wit. He was not disturbed at Waltham in
+1655, when the Protector&rsquo;s edict prohibited the adherents of
+the late king from preaching. Lionel, 3rd earl of Middlesex,
+who lived at Copt Hall, near Waltham, gave him what remained
+of the books of the lord treasurer his father; and through the
+good offices of the marchioness of Hertford, part of his own
+pillaged library was restored to him. Fuller was thus able to
+prosecute his literary labours, producing successively his descriptive
+geography of the Holy Land, called <i>A Pisgah-Sight of
+Palestine</i> (1650), and his <i>Church-History of Britain</i> (1655), from
+the birth of Jesus Christ until the year 1648. With the <i>Church-History</i>
+was printed <i>The History of the University of Cambridge
+since the Conquest</i> and <i>The History of Waltham Abbey</i>. These
+works were furthered in no slight degree by his connexion with
+Sion College, London, where he had a chamber, as well for
+the convenience of the press as of his city lectureships. The
+<i>Church-History</i> was angrily attacked by Dr P. Heylyn, who, in
+the spirit of High-Churchmanship, wished, as he said, to vindicate
+the truth, the church and the injured clergy. About 1652
+Fuller married his second wife, Mary Roper, youngest sister of
+Thomas, Viscount Baltinglass, by whom he had several children.
+At the Oxford Act of 1657, Robert South, who was <i>Terrae filius</i>,
+lampooned Fuller, whom he described in this <i>Oratio</i> as living
+in London, ever scribbling and each year bringing forth new
+<i>folia</i> like a tree. At length, continues South, the <i>Church-History</i>
+came forth with its 166 dedications to wealthy and noble friends;
+and with this huge volume under one arm, and his wife (said to
+be little of stature) on the other, he ran up and down the streets
+of London, seeking at the houses of his patrons invitations to
+dinner, to be repaid by his dull jests at table.</p>
+
+<p>His last and best patron was George Berkeley, 1st Earl Berkeley
+(1628-1698), of Cranford House, Middlesex, whose chaplain he
+was, and who gave him Cranford rectory (1658). To this nobleman
+Fuller&rsquo;s reply to Heylyn&rsquo;s <i>Examen Historicum</i>, called <i>The
+Appeal of Injured Innocence</i> (1659), was inscribed. At the end
+of the <i>Appeal</i> is an epistle &ldquo;to my loving friend Dr Peter Heylyn,&rdquo;
+conceived in the admirable Christian spirit which characterized
+all Fuller&rsquo;s dealings with controversialists. &ldquo;Why should
+<i>Peter</i>,&rdquo; he asked, &ldquo;fall out with <i>Thomas</i>, both being disciples
+to the same Lord and Master? I assure you, sir, whatever you
+conceive to the contrary, I am cordial to the cause of the English
+Church, and my hoary hairs will go down to the grave in sorrow
+for her sufferings.&rdquo;</p>
+
+<p>In <i>An Alarum to the Counties of England and Wales</i> (1660)
+Fuller argued for a free and full parliament&mdash;free from force,
+as he expressed it, as well as from abjurations or previous
+engagements. <i>Mixt Contemplations in Better Times</i> (1660),
+dedicated to Lady Monk, tendered advice in the spirit of its
+motto, &ldquo;Let your moderation be known to all men: the Lord
+is at hand.&rdquo; There is good reason to suppose that Fuller was at
+the Hague immediately before the Restoration, in the retinue
+of Lord Berkeley, one of the commissioners of the House of
+Lords, whose last service to his friend was to interest himself in
+obtaining him a bishopric. <i>A Panegyrick to His Majesty on his
+Happy Return</i> was the last of Fuller&rsquo;s verse-efforts. On the
+2nd of August, by royal letters, he was admitted D.D. at Cambridge.
+He resumed his lectures at the Savoy, where Samuel
+Pepys heard him preach; but he preferred his conversation or
+his books to his sermons. Fuller&rsquo;s last promotion was that of
+chaplain in extraordinary to Charles II. In the summer of 1661
+he visited the west in connexion with the business of his prebend,
+which had been restored to him. On Sunday, the 12th of August,
+while preaching at the Savoy, he was seized with typhus fever,
+and died at his new lodgings in Covent Garden on the 16th of
+August. He was buried in Cranford church, where a mural
+tablet was afterwards set up on the north side of the chancel,
+with an epitaph which contains a conceit worthy of his own pen,
+to the effect that while he was endeavouring (viz. in <i>The Worthies</i>)
+to give immortality to others, he himself attained it.</p>
+
+<p>Fuller&rsquo;s wit and vivacious good-humour made him a favourite
+with men of both sides, and his sense of humour kept him from
+extremes. Probably Heylyn and South had some excuse for
+their attitude towards his very moderate politics. &ldquo;By his
+particular temper and management,&rdquo; said Echard (<i>Hist. of
+England</i>, iii. 71), &ldquo;he weathered the late great storm with more
+success than many other great men.&rdquo; He was known as &ldquo;a
+perfect walking library.&rdquo; The strength of his memory was
+proverbial, and some amusing anecdotes are connected with it.</p>
+
+<p>His writings were the product of a highly original mind. He
+had a fertile imagination and a happy faculty of illustration.
+Antithetic and axiomatic sentences abound in his pages, embodying
+literally the wisdom of the many in the wit of one. He was
+&ldquo;quaint,&rdquo; and something more. &ldquo;Wit,&rdquo; said Coleridge, in a
+well-known eulogy, &ldquo;was the stuff and substance of Fuller&rsquo;s
+intellect. It was the element, the earthen base, the material
+which he worked in; and this very circumstance has defrauded
+him of his due praise for the practical wisdom of the thoughts,
+for the beauty and variety of the truths, into which he shaped
+the stuff. Fuller was incomparably the most sensible, the least
+prejudiced, great man of an age that boasted a galaxy of great
+men&rdquo; (<i>Literary Remains</i>, vol. ii. (1836), pp. 389-390). This
+opinion was formed after the perusal of the <i>Church-History</i>.
+That work and <i>The History of the Worthies of England</i> are
+unquestionably Fuller&rsquo;s greatest efforts. They embody the
+collections of an entire life; and since his day they have been
+the delight of many readers. The <i>Holy State</i> has taken rank
+amongst the best books of &ldquo;characters.&rdquo; Charles Lamb made
+some selections from Fuller, and had a profound admiration for
+the &ldquo;golden works&rdquo; of the &ldquo;dear, fine, silly old angel.&rdquo; Since
+<span class="pagenum"><a name="page298" id="page298"></a>298</span>
+Lamb&rsquo;s time, mainly through the appreciative criticisms of
+S.T. Coleridge, Robert Southey and others, Fuller&rsquo;s works have
+received much attention.</p>
+
+<div class="condensed">
+<p>There is an elaborate account of the life and writings of Fuller
+by William Oldys in the <i>Biographia Britannica</i>, vol. iii. (1750), based
+on Fuller&rsquo;s own works and the anonymous <i>Life of ... Dr Thomas
+Fuller</i> (1661; reprinted in a volume of selections by A.L.J. Gosset,
+1893). The completest account of him is <i>The Life of Thomas Fuller,
+with Notices of his Books, his Kinsmen and his Friends</i> (1874), by
+J.E. Bailey, who gives a detailed bibliography (pp. 713-762) of his
+works. <i>The Worthies of England</i> was reprinted by John Nichols
+(1811) and by P.A. Nuttall (1840). His <i>Collected Sermons</i> were
+edited by J.E. Bailey and W.E.A. Axon in 1891. Fuller&rsquo;s quaint
+wit lends itself to selection, and there are several modern volumes of
+extracts from his works.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FULLER, WILLIAM<a name="ar56" id="ar56"></a></span> (1670-<i>c.</i> 1717), English impostor, was
+born at Milton in Kent on the 20th of September 1670. His
+paternity is doubtful, but he was related to the family of Herbert.
+After 1688 he served James II.&rsquo;s queen, Mary of Modena, and
+the Jacobites, seeking at the same time to gain favour with
+William III.; and after associating with Titus Oates, being
+imprisoned for debt and pretending to reveal Jacobite plots, the
+House of Commons in 1692 declared he was an &ldquo;imposter,
+cheat and false accuser.&rdquo; Having stood in the pillory he was
+again imprisoned until 1695, when he was released; and at this
+time he took the opportunity to revive the old and familiar
+story that Mary of Modena was not the mother of the prince of
+Wales. In 1701 he published his autobiographical <i>Life of
+William Fuller</i> and some <i>Original Letters of the late King James</i>.
+Unable to prove the assertions made in his writings he was put
+in the pillory, whipped and fined. He died, probably in prison,
+about 1717. Fuller&rsquo;s other writings are <i>Mr William Fuller&rsquo;s
+trip to Bridewell, with a full account of his barbarous usage in the
+pillory; The sincere and hearty confession of Mr William Fuller</i>
+(1704); and <i>An humble appeal to the impartial judgment of all
+parties in Great Britain</i> (1716).</p>
+
+<div class="condensed">
+<p>He must be distinguished from <span class="sc">William Fuller</span> (1608-1675),
+dean of St Patrick&rsquo;s (1660), bishop of Limerick (1663), and bishop of
+Lincoln (1667), the friend of Samuel Pepys; and also from William
+Fuller (<i>c.</i> 1580-1659), dean of Ely and later dean of Durham.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FULLER&rsquo;S EARTH<a name="ar57" id="ar57"></a></span> (Ger. <i>Walkererde</i>, Fr. <i>terre à foulon</i>, <i>argile
+smectique</i>)&mdash;so named from its use by fullers as an absorbent of
+the grease and oil of cloth,&mdash;a clay-like substance, which from
+its variability is somewhat difficult to define. In colour it is
+most often greenish, olive-green or greenish-grey; on weathering
+it changes to a brown tint or it may bleach. As a rule it falls
+to pieces when placed in water and is not markedly plastic;
+when dry it adheres strongly to the tongue; since, however,
+these properties are possessed by many clays that do not exhibit
+detergent qualities, the only test of value lies in the capacity
+to absorb grease or clarify oil. Fuller&rsquo;s earth has a specific gravity
+of 1.7-2.4, and a shining streak; it is usually unctuous to the
+touch. Microscopically, it consists of minute irregular-shaped
+particles of a mineral that appears to be the result of a chloritic
+or talcose alteration of a felspar. The small size of most of the
+grains, less than .07 mm., makes their determination almost
+impossible. Chemical analysis shows that the peculiar properties
+of this earth are due to its physical rather than its chemical
+nature.</p>
+
+<div class="condensed">
+<p>The following analyses of the weathered and unweathered condition
+of the earth from Nutfield, Surrey, represent the composition
+of one of the best known varieties:&mdash;</p>
+
+<p class="pt2 center">Blue Earth (dried at 100° C.).</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcl">Insoluble residue</td> <td class="tcr rb">69.96</td> <td class="tcl">Insoluble residue&mdash;</td> <td class="tcr">&nbsp;</td></tr>
+<tr><td class="tcl">Fe<span class="su">2</span>O<span class="su">3</span></td> <td class="tcr rb">2.48</td> <td class="tcl">SiO<span class="su">2</span></td> <td class="tcr">62.81</td></tr>
+<tr><td class="tcl">Al<span class="su">2</span>O<span class="su">3</span></td> <td class="tcr rb">3.46</td> <td class="tcl">Al<span class="su">2</span>O<span class="su">3</span></td> <td class="tcr">3.46</td></tr>
+<tr><td class="tcl">CaO</td> <td class="tcr rb">5.87</td> <td class="tcl">Fe<span class="su">2</span>O<span class="su">3</span></td> <td class="tcr">1.30</td></tr>
+<tr><td class="tcl">MgO</td> <td class="tcr rb">1.41</td> <td class="tcl">CaO</td> <td class="tcr">1.53</td></tr>
+<tr><td class="tcl">P<span class="su">2</span>O<span class="su">5</span></td> <td class="tcr rb">0.27</td> <td class="tcl">MgO</td> <td class="tcr">0.86</td></tr>
+<tr><td class="tcl">SO<span class="su">3</span></td> <td class="tcr rb">0.05</td> <td class="tcl">&nbsp;</td> <td class="tcr">&mdash;&mdash;&mdash;</td></tr>
+<tr><td class="tcl">NaCl</td> <td class="tcr rb">0.05</td> <td class="tcr">&nbsp;</td> <td class="tcr">69.96</td></tr>
+<tr><td class="tcl">K<span class="su">2</span>O</td> <td class="tcr rb">0.74</td> <td class="tcl">&nbsp;</td> <td class="tcr">&mdash;&mdash;&mdash;</td></tr>
+<tr><td class="tcl">H<span class="su">2</span>O (combined)</td> <td class="tcr rb">15.57</td> <td class="tcl">&nbsp;</td></tr>
+<tr><td class="tcl"> &nbsp;</td> <td class="tcr rb">&mdash;&mdash;&mdash;</td> <td colspan="2">&nbsp;</td></tr>
+<tr><td class="tcl"> &nbsp;</td> <td class="tcr rb">99.86</td> <td colspan="2">&nbsp;</td></tr>
+<tr><td class="tcl"> &nbsp;</td> <td class="tcr rb">&mdash;&mdash;&mdash;</td> <td colspan="2">&nbsp;</td></tr>
+</table>
+
+<p class="pt1 center">Yellow Earth (dried at 100° C.).</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcl">Insoluble residue</td> <td class="tcr rb">76.13</td> <td class="tcl">Insoluble residue&mdash;</td> <td class="tcr">&nbsp;</td></tr>
+<tr><td class="tcl">Fe<span class="su">2</span>O<span class="su">3</span></td> <td class="tcr rb">2.41</td> <td class="tcl">SiO<span class="su">2</span></td> <td class="tcr">59.37</td></tr>
+<tr><td class="tcl">Al<span class="su">2</span>O<span class="su">3</span></td> <td class="tcr rb">1.77</td> <td class="tcl">Al<span class="su">2</span>O<span class="su">3</span></td> <td class="tcr">10.05</td></tr>
+<tr><td class="tcl">CaO</td> <td class="tcr rb">4.31</td> <td class="tcl">Fe<span class="su">2</span>O<span class="su">3</span></td> <td class="tcr">3.86</td></tr>
+<tr><td class="tcl">MgO</td> <td class="tcr rb">1.05</td> <td class="tcl">CaO</td> <td class="tcr">1.86</td></tr>
+<tr><td class="tcl">P<span class="su">2</span>O<span class="su">5</span></td> <td class="tcr rb">0.14</td> <td class="tcl">MgO</td> <td class="tcr">1.04</td></tr>
+<tr><td class="tcl">SO<span class="su">3</span></td> <td class="tcr rb">0.07</td> <td class="tcl">&nbsp;</td> <td class="tcr">&mdash;&mdash;&mdash;</td></tr>
+<tr><td class="tcl">NaCl</td> <td class="tcr rb">0.14</td> <td class="tcl">&nbsp;</td> <td class="tcr">76.18</td></tr>
+<tr><td class="tcl">K<span class="su">2</span>O</td> <td class="tcr rb">0.84</td> <td class="tcl">&nbsp;</td> <td class="tcr">&mdash;&mdash;&mdash;</td></tr>
+<tr><td class="tcl">H<span class="su">2</span>O (combined)</td> <td class="tcr rb">13.19</td> <td colspan="2">&nbsp;</td></tr>
+<tr><td class="tcl"> &nbsp;</td> <td class="tcr rb">&mdash;&mdash;&mdash;</td> <td colspan="2">&nbsp;</td></tr>
+<tr><td class="tcl"> &nbsp;</td> <td class="tcr rb">100.05</td> <td colspan="2">&nbsp;</td></tr>
+<tr><td class="tcl"> &nbsp;</td> <td class="tcr rb">&mdash;&mdash;&mdash;</td> <td colspan="2">&nbsp;</td></tr>
+</table>
+
+<p class="noind">(Analysis by P.G. Sanford, <i>Geol. Mag.</i>, 1889, 6, pp. 456, 526.)</p>
+
+<p>Of other published analyses, not a few show a lower silica content
+(44%, 50%), along with a higher proportion of alumina (11%, 23%).</p>
+</div>
+
+<p>Fuller&rsquo;s earth may occur on any geological horizon; at Nutfield
+in Surrey, England, it is in the Cretaceous formations; at Midford
+near Bath it is of Jurassic age; at Bala, North Wales, it occurs in
+Ordovician strata; in Saxony it appears to be the decomposition
+product of a diabasic rock. In America it is found in California
+in rocks ranging from Cretaceous to Pleistocene age; in S.
+Dakota, Custer county and elsewhere a yellow, gritty earth of
+Jurassic age is worked; in Florida and Georgia occurs a brittle,
+whitish earth of Oligocene age. Other deposits are worked in
+Arkansas, Texas, Colorado, Massachusetts and South Carolina.</p>
+
+<p>Fuller&rsquo;s earth is either mined or dug in the open according to
+local circumstances. It is then dried in the sun or by artificial
+heat and transported in small lumps in sacks. In other cases it
+is ground to a fine powder after being dried; or it is first roughly
+ground and made into a slurry with water, which is allowed to
+carry off the finer from the coarser particles and deposit them in a
+creamy state in suitable tanks. After consolidation this fine
+material is dried artificially on drying floors, broken into lumps,
+and packed for transport. The use of fuller&rsquo;s earth for cleansing
+wool and cloth has greatly decreased, but the demand for the
+material is as great or greater than it ever was. It is now used
+very largely in the filtration of mineral oils, and also for decolourizing
+certain vegetable oils. It is employed in the formation of
+certain soaps and cleansing preparations.</p>
+
+<p>The term &ldquo;Fuller&rsquo;s Earth&rdquo; has a special significance in
+geology, for it was applied by W. Smith in 1799 to certain clays
+in the neighbourhood of Bath, and the use of the expression is
+still retained by English geologists, either in this form or in the
+generalized &ldquo;Fullonian.&rdquo; The Fullonian lies at the base of the
+Great Oolite or Bathonian series, but its palaeontological
+characters place it between that series and the underlying
+Inferior Oolite. The zonal fossils are <i>Perisphinctes arbustigerus</i>
+and <i>Macrocephalus subcontractus</i> with <i>Ostrea acuminata</i>,
+<i>Rhynchonella concinna</i> and <i>Goniomya angulifera</i>. The formation
+is in part the equivalent of the &ldquo;Vesulien&rdquo; of J. Marcou (Vesoul
+in Haute-Saône). In Dorsetshire and Somersetshire, where it
+is best developed, it is represented by an Upper Fuller&rsquo;s Earth
+Clay, the Fuller&rsquo;s Earth Rock (an impersistent earthy limestone,
+usually fossiliferous), and the Lower Fuller&rsquo;s Earth Clay. Commercial
+fuller&rsquo;s earth has been obtained only from the Upper
+Clay. In eastern Gloucestershire and northern Oxfordshire
+the Fuller&rsquo;s Earth passes downwards without break into the
+Inferior Oolite; northward it dies out about Chipping Norton
+in Oxfordshire and passes laterally into the Stonesfield Slates
+series; in the midland counties it may perhaps be represented
+by the &ldquo;Upper Estuarine Series.&rdquo; In parts of Dorsetshire the
+clays have been used for brickmaking and the limestone (rock)
+for local buildings.</p>
+
+<div class="condensed">
+<p>See H.B. Woodward, &ldquo;Jurassic Rocks of Great Britain,&rdquo; vol.
+iv. (1894), <i>Mem. Geol. Survey</i> (London).</p>
+</div>
+<div class="author">[J. A. H.]</div>
+
+
+<hr class="art" />
+<p><span class="bold">FULLERTON, LADY GEORGIANA CHARLOTTE<a name="ar58" id="ar58"></a></span> (1812-1885),
+English novelist and philanthropist, youngest daughter of the
+1st Earl Granville, was born at Tixall Hall in Staffordshire on
+the 23rd of September 1812. In 1833 she married Alexander
+George Fullerton, then an Irish officer in the guards. After
+living in Paris for some eight years she and her husband accompanied
+Lord Granville to Cannes and thence to Rome. In 1843
+<span class="pagenum"><a name="page299" id="page299"></a>299</span>
+her husband entered the Roman Catholic church, and in the
+following year Lady Georgiana Fullerton published her first novel,
+<i>Ellen Middleton</i>, which attracted W.E. Gladstone&rsquo;s attention
+in the <i>English Review</i>. In 1846 she entered the Roman Catholic
+church. The death of her only son in 1854 plunged her in grief,
+and she continued to wear mourning until the end of her life.
+In 1856 she became one of the third order of St Francis, and
+thenceforward devoted herself to charitable work. In conjunction
+with Miss Taylor she founded the religious community
+known as &ldquo;The Poor Servants of the Mother of God Incarnate,&rdquo;
+and she also took an active part in bringing to England the
+sisters of St Vincent of Paul. Her philanthropic work is described
+in Mrs Augustus Craven&rsquo;s work <i>Lady Georgiana Fullerton, sa
+vie et ses &oelig;uvres</i> (Paris, 1888), which was translated into English
+by Henry James Coleridge. She died at Bournemouth on the 19th
+of January 1885. Among her other novels were <i>Grantley Manor</i>
+(1847), <i>Lady Bird</i> (1852), and <i>Too Strange not to be True</i> (1864).</p>
+
+
+<hr class="art" />
+<p><span class="bold">FULMAR<a name="ar59" id="ar59"></a></span>, from the Gaelic <i>Fulmaire</i>, the <i>Fulmarus glacialis</i> of
+modern ornithologists, one of the largest of the petrels (<i>Procellariidae</i>)
+of the northern hemisphere, being about the size of the
+common gull (<i>Larus canus</i>) and not unlike it in general coloration,
+except that its primaries are grey instead of black. This bird,
+which ranges over the North Atlantic, is seldom seen on the
+European side below lat. 53° N., but on the American side comes
+habitually to lat. 45° or even lower. In the Pacific it is represented
+by a scarcely separable form, <i>F. glupischa</i>. It has been commonly
+believed to have two breeding-places in the British Islands,
+namely, St Kilda and South Barra; but, according to Robert
+Gray (<i>Birds of the West of Scotland</i>, p. 499), it has abandoned
+the latter since 1844, though still breeding in Skye. Northward
+it established itself about 1838 on Myggenaes Holm, one of the
+Faeroes, while it has several stations off the coast of Iceland and
+Spitsbergen, as well as at Bear Island. Its range towards the
+pole seems to be only bounded by open water, and it is the constant
+attendant upon all who are employed in the whale and
+seal fisheries, showing the greatest boldness in approaching boats
+and ships, and feeding on the offal obtained from them. By
+British seamen it is commonly called the &ldquo;molly mawk&rdquo;<a name="fa1f" id="fa1f" href="#ft1f"><span class="sp">1</span></a>
+(corrupted from <i>Mallemuck</i>), and is extremely well known to them,
+its flight, as it skims over the waves, first with a few beats of
+the wings and then gliding for a long way, being very peculiar.
+It only visits the land to deposit its single white egg, which is
+laid on a rocky ledge, where a shallow nest is made in the turf
+and lined with a little dried grass. Many of its breeding-places
+are a most valuable property to those who live near them and
+take the eggs and young, which, from the nature of the locality,
+are only to be had at a hazardous risk of life. In St Kilda a
+large number of the young are killed in one week of August, the
+only time when, by the custom of the community, they are
+allowed to be taken. These, after the oil is extracted from them,
+serve the islanders with food for the winter. The oil has been
+chemically analysed and found to be a fish-oil, and to possess
+nearly all the qualities of that obtained from the liver of the cod,
+with a lighter specific gravity. It, however, has an extremely
+strong scent, which is said by those who have visited St Kilda
+to pervade every thing and person on the island, and is certainly
+retained by an egg or skin of the bird for many years. Whenever
+a live example is seized in the hand it ejects a considerable
+quantity of this oil from its mouth.</p>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1f" id="ft1f" href="#fa1f"><span class="fn">1</span></a> A name misapplied in the southern hemisphere to <i>Diomedea
+melanophrys</i>, one of the albatrosses.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FULMINIC ACID<a name="ar60" id="ar60"></a></span>, HCNO or H<span class="su">2</span>C<span class="su">2</span>N<span class="su">2</span>O<span class="su">2</span>, an organic acid
+isomeric with cyanic and cyanuric acids; its salts, termed
+fulminates, are very explosive and are much employed as detonators.
+The free acid, which is obtained by treating the salts
+with acids, is an oily liquid smelling like prussic acid; it is very
+explosive, and the vapour is poisonous to about the same degree
+as that of prussic acid. The first fulminate prepared was the
+&ldquo;fulminating silver&rdquo; of L.G. Brugnatelli, who found in 1798
+that if silver be dissolved in nitric acid and the solution added
+to spirits of wine, a white, highly explosive powder was obtained.
+This substance is to be distinguished from the black &ldquo;fulminating
+silver&rdquo; obtained by C.L. Berthollet in 1788 by acting with
+ammonia on precipitated silver oxide. The next salt to be
+obtained was the mercuric salt, which was prepared in 1799 by
+Edward Charles Howard, who substituted mercury for silver in
+Brugnatelli&rsquo;s process. A similar method is that of J. von Liebig
+(1823), who heated a mixture of alcohol, nitric acid and mercuric
+nitrate; the salt is largely manufactured by processes closely
+resembling the last. A laboratory method is to mix solutions
+of sodium nitromethane, CH<span class="su">2</span> : NO(ONa), and mercuric chloride,
+a yellow basic salt being formed at the same time. Mercuric
+fulminate is less explosive than the silver salt, and forms white
+needles (with ½H<span class="su">2</span>O) which are tolerably soluble in water. The
+use of mercuric fulminate as a detonator dates from about 1814,
+when the explosive cap was invented. It is still the commonest
+detonator, but it is now usually mixed with other substances;
+the British service uses for percussion caps 6 parts of fulminate,
+6 of potassium chlorate and 4 of antimony sulphide, and for
+time fuses 4 parts of fulminate, 6 of potassium chlorate and 4
+of antimony sulphide, the mixture being damped with a shellac
+varnish; for use in blasting, a home office order of 1897 prescribes
+a mixture of 4 parts of fulminate and 1 of potassium chlorate.
+In 1900 Bielefeldt found that a fulminate placed on top of an
+aromatic nitro compound, such as trinitrotoluene, formed a
+useful detonator; this discovery has been especially taken
+advantage of in Germany, in which country detonators of this
+nature are being largely employed. Tetranitromethylaniline
+(tetryl) has also been employed (Brit. Pat. 13340 of 1905).
+It has been proposed to replace fulminate by silver azoimide
+(Wöhler &amp; Matter, Brit. Pat. 4468 of 1908), and by lead azoimide
+(Hyronimus, Brit. Pat. 1819 of 1908).</p>
+
+<div class="condensed">
+<p>The constitution of fulminic acid has been investigated by many
+experimenters, but apparently without definitive results. The
+researches of Liebig (1823), Liebig and Gay-Lussac (1824), and of
+Liebig again in 1838 showed the acid to be isomeric with cyanic acid,
+and probably (HCNO)<span class="su">2</span>, since it gave mixed and acid salts. Kekulé,
+in 1858, concluded that it was nitroacetonitrile, NO<span class="su">2</span>·CH<span class="su">2</span>·CN, a
+view opposed by Steiner (1883), E. Divers and M. Kawakita (1884),
+R. Scholl (1890), and by J.U. Nef (1894), who proposed the formulae:</p>
+
+<div class="center ptb2"><img style="width:500px; height:62px; vertical-align: middle;" src="images/img299a.jpg" alt="" /></div>
+
+<p class="noind">The formulae of Kekulé, Divers and Armstrong have been discarded,
+and it remains to be shown whether Nef&rsquo;s carbonyloxime formula
+(or the bimolecular formula of Steiner) or Scholl&rsquo;s glyoxime peroxide
+formula is correct. There is some doubt as to the molecular formula
+of fulminic acid. The existence of double salts, and the observations
+of L. Wöhler and K. Theodorovits (<i>Ber.</i>, 1905, 38, p. 345), that only
+compounds containing two carbon atoms yielded fulminates, points
+to (HCNO)<span class="su">2</span>; on the other hand, Wöhler (<i>loc. cit.</i> p. 1351) found
+that cryoscopic and electric conductivity measurements showed
+sodium fulminate to be NaCNO. Nef based his formula, which
+involves bivalent carbon, on many reactions; in particular, that
+silver fulminate with hydrochloric acid gave salts of formylchloridoxime,
+which with water gave hydroxylamine and formic acid, thus</p>
+
+<div class="center ptb2"><img style="width:600px; height:45px; vertical-align: middle;" src="images/img299b.jpg" alt="" /></div>
+
+<p class="noind">and also on the production from sodium nitromethane and mercuric
+chloride, thus CH<span class="su">2</span> : NO·Ohg &rarr; H<span class="su">2</span>O + C : NOhg(hg = ½Hg). H.
+Wieland and F.C. Palazzo (1907) support this formula, finding that
+methyl nitrolic acid, NO<span class="su">2</span>·CH : N·OH, yielded under certain conditions
+fulminic acid, and vice versa (Palazzo, 1907). M.Z. Jowitschitsch
+(<i>Ann.</i>, 1906, 347, p. 233) inclines to Scholl&rsquo;s formula; he
+found that the synthetic silver salt of glyoxime peroxide resembled
+silver fulminate in yielding hydroxylamine with hydrochloric acid,
+but differed in being less explosive, and in being soluble in nitric
+acid. H. Wieland and his collaborators regard &ldquo;glyoxime peroxide&rdquo;
+as an oxide of furazane (<i>q.v.</i>), and have shown that a close relationship
+exists between the nitrile oxides, furoxane, and fulminic acid (see
+<i>Ann. Rep.</i>, London Chem. Soc., 1909, p. 84). <i>Fulminuric acid</i>,
+(HCNO)<span class="su">3</span>, obtained by Liebig by boiling mercuric fulminate with
+water, was synthesized in 1905 by C. Ulpiani and L. Bernardini
+(<i>Gazetta</i>, iii. 35, p. 7), who regard it as NO<span class="su">2</span>·CH(CN)·CO·NH<span class="su">2</span>. It
+deflagrates at 145°, and forms a characteristic cuprammonium salt.</p>
+
+<p>The early history of mercuric fulminate and a critical account of its
+application as a detonator is given in <i>The Rise and Progress of the
+British Explosives Industry</i> (International Congress of Applied
+Chemistry, 1909). The manufacture and modern aspects are treated
+in Oscar Guttmann, <i>The Manufacture of Explosives</i>, and <i>Manufacture
+of Explosives, Twenty Years&rsquo; Progress</i> (1909).</p>
+</div>
+
+<p><span class="pagenum"><a name="page300" id="page300"></a>300</span></p>
+
+
+<hr class="art" />
+<p><span class="bold">FULTON, ROBERT<a name="ar61" id="ar61"></a></span> (1765-1815), American engineer, was born
+in 1765 in Little Britain (now Fulton, Lancaster county), Pa.
+His parents were Irish, and so poor that they could afford him
+only a very scanty education. At an early age he was bound
+apprentice to a jeweller in Philadelphia, but subsequently
+adopted portrait and landscape painting as his profession. In
+his twenty-second year, with the object of studying with his
+countryman, Benjamin West, he went to England, and there
+became acquainted with the duke of Bridgewater, Earl Stanhope
+and James Watt. Partly by their influence he was led to devote
+his attention to engineering, especially in connexion with canal
+construction; he obtained an English patent in 1794 for superseding
+canal locks by inclined planes, and in 1796 he published
+a <i>Treatise on the Improvement of Canal Navigation</i>. He then took
+up his residence in Paris, where he projected the first panorama
+ever exhibited in that city, and constructed a submarine boat,
+the &ldquo;Nautilus,&rdquo; which was tried in Brest harbour in 1801 before
+a commission appointed by Napoleon I., and by the aid of which
+he was enabled to blow up a small vessel with a torpedo. It
+was at Paris also in 1803 that he first succeeded in propelling a
+boat by steam-power, thus realizing a design which he had
+conceived ten years previously. Returning to America he
+continued his experiments with submarine explosives, but failed
+to convince either the English, French or United States governments
+of the adequacy of his methods. With steam navigation
+he had more success. In association with Robert R. Livingston
+(<i>q.v.</i>), who in 1798 had been granted the exclusive right to
+navigate the waters of New York state with steam-vessels, he
+constructed the &ldquo;Clermont,&rdquo; which, engined by Boulton &amp;
+Watt of Birmingham, began to ply on the Hudson between
+New York and Albany in 1807. The privilege obtained by
+Livingston in 1798 was granted jointly to Fulton and Livingston
+in 1803, and by an act passed in 1808 the monopoly was
+secured to them and their associates for a period depending on
+the number of steamers constructed, but limited to a maximum
+of thirty years. In 1814-1815, on behalf of the United States
+government, he constructed the &ldquo;Fulton,&rdquo; a vessel of 38 tons
+with central paddle-wheels, which was the first steam warship.
+He died at New York on the 24th of February 1815. Among
+Fulton&rsquo;s inventions were machines for spinning flax, for making
+ropes, and for sawing and polishing marble.</p>
+
+<div class="condensed">
+<p>See C.D. Colden, <i>Life of Robert Fulton</i> (New York, 1817); Robert
+H. Thurston, <i>History of the Growth of the Steam-Engine</i> (New York,
+1878); George H. Preble, <i>Chronological History of Steam Navigation</i>
+(Philadelphia, 1883); and Mrs A.C. Sutcliffe, <i>Robert Fulton and the
+Clermont</i> (New York, 1909).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FULTON<a name="ar62" id="ar62"></a></span>, a city and the county-seat of Callaway county,
+Missouri, U.S.A., 25 m. N.E. of Jefferson City. Pop. (1890)
+4314; (1900) 4883 (1167 negroes); (1910) 5228. It is served by
+the Chicago &amp; Alton railway. The city has an important stock
+market and manufactures fire-brick and pottery. At Fulton
+are the Westminster College (Presbyterian, founded in 1853),
+the Synodical College for Young Women (Pres., founded in
+1871), the William Woods College for Girls (Christian Church,
+1890), and the Missouri school for the deaf (1851). Here, too,
+is a state hospital for the insane (1847), the first institution
+of the kind in Missouri. The place was laid out as a town in
+1825 and named Volney, but in honour of Robert Fulton the
+present name was adopted a little later. Fulton was incorporated
+in 1859.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FULTON<a name="ar63" id="ar63"></a></span>, a city of Oswego county, New York, U.S.A., on the
+right bank of the Oswego river, about 10 m. S. by E. of Oswego.
+Pop. (1900) 5281; (1905, state census) 8847; (1910) 10,480.
+Fulton is served by the Delaware, Lackawanna &amp; Western, the
+New York Central &amp; Hudson River, and the New York, Ontario
+&amp; Western railways, by electric railway to Oswego and Syracuse
+and by the Oswego Canal. The city has a Carnegie library.
+Ample water-power is furnished by the Oswego river, which here
+flows in a series of rapids, and the manufactures are many in
+kind. On the 3rd of July 1756, on an island (afterward called
+Battle Island) 4 m. N. of the present city of Fulton, a British
+force of about 300 under Captain John Bradstreet (1711-1774)
+defeated an attacking force of French and Indians (numbering
+about 700) under De Villiers. Soon after this, Bradstreet built
+a fort within the present limits of Fulton. The first civilian
+settler came in 1793, and the first survey (which included only
+a part of the subsequent village) was made in 1815. Fulton
+was incorporated as a village in 1835, and in April 1902 was
+combined with the village of Oswego Falls (pop. in 1900, 2925)
+and was chartered as a city.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUM<a name="ar64" id="ar64"></a></span>, or <span class="sc">Funj Hwang</span>, one of the four symbolical creatures
+which in Chinese mythology are believed to keep watch and ward
+over the Celestial Empire. It was begotten by fire, was born in
+the Hill of the Sun&rsquo;s Halo, and its body bears inscribed on it
+the five cardinal virtues. It has the breast of a goose, the hindquarters
+of a stag, a snake&rsquo;s neck, a fish&rsquo;s tail, a fowl&rsquo;s forehead,
+a duck&rsquo;s down, the marks of a dragon, the back of a tortoise,
+the face of a swallow, the beak of a cock, is about six cubits high,
+and perches only on the woo-tung tree. The appearance of Fum
+heralds an age of universal virtue. Its figure is that which is
+embroidered on the dresses of some mandarins.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUMARIC AND MALEIC ACIDS<a name="ar65" id="ar65"></a></span>, two isomeric unsaturated
+acids of composition C<span class="su">4</span>H<span class="su">4</span>O<span class="su">4</span>. <i>Fumaric acid</i> is found in fumitory
+(<i>Fumaria officinalis</i>), in various fungi (<i>Agaricus piperatus</i>, &amp;c.),
+and in Iceland moss. It is obtained by heating malic acid alone
+to 150° C., or by heating it with hydrochloric acid (V. Dessaignes,
+<i>Jahresb</i>., 1856, p. 463) or with a large quantity of hydrobromic
+acids (A. Kekulé, <i>Ann.</i>, 1864, 130, p. 21). It may also be obtained
+by boiling monobromsuccinic acid with water; by the action of
+dichloracetic acid and water on silver malonate (T. Komnenos,
+<i>Ann.</i>, 1883, 218, p. 169); by the cyanide synthesis from acetylene
+di-iodide; and by heating maleic acid to 210° C. (Z. Skraup,
+<i>Monats. f. Chemie</i>, 1891, 12, p. 112). It crystallizes in small
+prisms or needles, and is practically insoluble in cold water. It
+sublimes to some extent at about 200° C., being partially converted
+into maleic anhydride and water, the reaction becoming
+practically quantitative if dehydrating agents be used. Reducing
+agents (zinc and caustic alkali, hydriodic acid, sodium amalgam,
+&amp;c.) convert it into succinic acid. Bromine converts it into
+dibromsuccinic acid. Potassium permanganate oxidizes it to
+racemic acid (A. Kekulé and R. Anschutz, <i>Ber.</i>, 1881, 14,
+p. 713). By long-continued heating with caustic soda at 100° C.
+it is converted into inactive malic acid.</p>
+
+<p><i>Maleic acid</i> is obtained by distilling malic or fumaric acids;
+by heating fumaric acid with acetyl chloride to 100° C; or by
+the hydrolysis of trichlorphenomalic acid (&beta;-trichloraceto-acrylic
+acid) [A. Kekulé, <i>Ann.</i>, 1884, 223, p. 185]. It crystallizes
+in monoclinic prisms, which are easily soluble in water, melt
+at 130° C., and boil at 160° C., decomposing into water and
+maleic anhydride. When heated with concentrated hydrobromic
+or hydriodic acids, it is converted into fumaric acid. It yields
+an anilide; oxidation converts it into mesotartaric acid. Maleic
+anhydride is obtained by distilling fumaric acid with phosphorus
+pentoxide. It forms triclinic crystals which melt at 60° C. and
+boil at 196° C.</p>
+
+<div class="condensed">
+<p>Both acids are readily esterified by the action of alkyl halides on
+their silver salts, and the maleic ester is readily transformed into the
+fumaric ester by warming with iodine, the same result being obtained
+by esterification of maleic acid in alcoholic solution by means of
+hydrochloric acid. Both acids yield acetylene by the electrolysis
+of aqueous solutions of their alkali salts, and on reduction both
+yield succinic acid, whilst by the addition of hydrobromic acid they
+both yield monobromsuccinic acid (R. Fittig, <i>Ann.</i>, 1877, 188, p. 98).
+From these results it follows that the two acids are structurally
+identical, and the isomerism has consequently to be explained on
+other grounds. This was accomplished by W. Wislicenus [&rdquo;Über
+die räumliche Anordnung der Atome,&rdquo; &amp;c., <i>Trans, of the Saxon Acad.
+of Sciences</i> (Math. Phys. Section), 1887, p. 14] by an extension of
+the van&rsquo;t Hoff hypothesis (see <span class="sc"><a href="#artlinks">Stereo-Isomerism</a></span>). The formulae
+of the acids are written thus:</p>
+
+<div class="center ptb2"><img style="width:500px; height:43px; vertical-align: middle;" src="images/img300.jpg" alt="" /></div>
+
+<p class="noind">These account for maleic acid readily yielding an anhydride, whereas
+fumaric acid does not, and for the behaviour of the acids towards
+bromine, fumaric acid yielding ordinary dibromsuccinic acid, and
+maleic acid the isomeric isodibromsuccinic acid.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FUMAROLE<a name="ar66" id="ar66"></a></span>, a vent from which volcanic vapours issue,
+named indirectly from the Lat. <i>fumariolum</i>, a smoke-hole.
+<span class="pagenum"><a name="page301" id="page301"></a>301</span>
+The vapours from fumaroles were studied first by R.W. Bunsen,
+on his visit to Iceland, and afterwards by H. Sainte-Claire Deville
+and other chemists and geologists in France, who examined the
+vapours from Santorin, Etna, &amp;c. The hottest vapours issue
+from dry fumaroles, at temperatures of at least 500° C., and
+consist chiefly of anhydrous chlorides, notably sodium chloride.
+The acid fumaroles yield vapours of lower temperature (300° to
+400°) containing much water vapour, with hydrogen chloride
+and sulphur dioxide. The alkaline fumaroles are still cooler,
+though above 100°, and evolve ammonium chloride with other
+vapours. Cold fumaroles, below 100°, discharge principally
+aqueous vapour, with carbon dioxide, and perhaps hydrogen
+sulphide. The fumaroles of Mont Pelé in Martinique during the
+eruption of 1902 were examined by A. Lacroix, and the vapours
+analysed by H. Moissan, who found that they consisted chiefly
+of water vapour, with hydrogen chloride, sulphur, carbon dioxide,
+carbon monoxide, methane, hydrogen, nitrogen, oxygen and
+argon. These vapours issued at a temperature of about 400°.
+Armand Gautier has pointed out that these gases are practically
+of the same composition as those which he obtained on heating
+granite and certain other rocks. (See <span class="sc"><a href="#artlinks">Volcano</a></span>).</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUMIGATION<a name="ar67" id="ar67"></a></span> (from Lat. <i>fumigare</i>, to smoke), the process
+of producing smoke or fumes, as by burning sulphur, frankincense,
+tobacco, &amp;c., whether as a ceremony of incantation, or
+for perfuming a room, or for purposes of disinfection or destruction
+of vermin. In medicine the term has been used of the exposure
+of the body, or a portion of it, to fumes such as those of
+nitre, sal-ammoniac, mercury, &amp;c.; fumigation, by the injection
+of tobacco smoke into the great bowel, was a recognized procedure
+in the 18th century for the resuscitation of the apparently
+drowned. &ldquo;Fumigated&rdquo; or &ldquo;fumed&rdquo; oak is oak which has
+been darkened by exposure to ammonia vapour.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUMITORY,<a name="ar68" id="ar68"></a></span> in botany, the popular name for the British
+species of <i>Fumaria</i>, a genus of small, branched, often climbing
+annual herbs with much-divided leaves and racemes of small
+flowers. The flowers are tubular with a spurred base, and in the
+British species are pink to purplish in colour. They are weeds of
+cultivation growing in fields and waste places. <i>F. capreolata</i>
+climbs by means of twisting petioles. In past times fumitory
+was in esteem for its reputed cholagogue and other medicinal
+properties; and in England, boiled in water, milk or whey, it
+was used as a cosmetic. The root of the allied species (<i>Corydalis
+cava</i> or <i>tuberosa</i>) is known as <i>radix aristolochia</i>, and has been used
+medicinally for various cutaneous and other disorders, in doses
+of 10 to 30 grains. Some eleven alkaloids have been isolated
+from it. The herbage of <i>Fumaria officinalis</i> and <i>F. racemosa</i> is
+used in China under the name of <i>Tsze-hwa-ti-ting</i> as an application
+for glandular swellings, carbuncles and abscesses, and was
+formerly valued in jaundice, and in cases of accidental swallowing
+of the beard of grain (see F. Porter Smith, <i>Contrib. towards the
+Mat. Medica ... of China</i>, p. 99, 1871). The name fumitory,
+Latin <i>fumus terrae</i>, has been supposed to be derived from the
+fact that its juice irritates the eyes like smoke (see Fuchs, <i>De
+historia stirpium</i>, p. 338, 1542); but <i>The Grete Herball</i>, cap.
+clxix., 1529, fol., following the <i>De simplici medicina</i> of Platearius,
+fo. xciii. (see in <i>Nicolai Praepositi dispensatorium ad aromatarios</i>,
+1536), says: &ldquo;It is called Fumus terre fume or smoke of the
+erthe bycause it is engendred of a cours fumosyte rysynge frome
+the erthe in grete quantyte lyke smoke: this grosse or cours
+fumosyte of the erthe wyndeth and wryeth out: and by workynge
+of the ayre and sonne it turneth into this herbe.&rdquo;</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUNCHAL<a name="ar69" id="ar69"></a></span>, the capital of the Portuguese archipelago of the
+Madeiras; on the south coast of Madeira, in 32° 37&prime; N. and
+16° 54&prime; W. Pop. (1900) 20,850. Funchal is the see of a bishop,
+in the archiepiscopal province of Lisbon; it is also the administrative
+centre of the archipelago, and the residence of the
+governor and foreign consuls. The city has an attractive
+appearance from the sea. Its whitewashed houses, in their
+gardens full of tropical plants, are built along the curving shore
+of Funchal Bay, and on the lower slopes of an amphitheatre of
+mountains, which form a background 4000 ft. high. Numerous
+country houses (<i>quintas</i>), with terraced gardens, vineyards and
+sugar-cane plantations occupy the surrounding heights. Three
+mountain streams traverse the city through deep channels,
+which in summer are dry, owing to the diversion of the water
+for irrigation. A small fort, on an isolated rock off shore,
+guards the entrance to the bay, and a larger and more powerfully
+armed fort crowns an eminence inland. The chief buildings
+include the cathedral, Anglican and Presbyterian churches,
+hospitals, opera-house, museum and casino. There are small
+public gardens and a meteorological observatory. In the steep
+and narrow streets, which are lighted by electricity, wheeled
+traffic is impossible; sledges drawn by oxen, and other primitive
+conveyances are used instead (see <span class="sc"><a href="#artlinks">Madeira</a></span>). In winter the fine
+climate and scenery attract numerous invalids and other visitors,
+for whose accommodation there are good hotels; many foreigners
+engaged in the coal and wine trades also reside here permanently.
+The majority of these belong to the British community, which
+was first established here in the 18th century. Funchal is the
+headquarters of Madeiran industry and commerce (see <span class="sc"><a href="#artlinks">Madeira</a></span>).
+It has no docks and no facilities for landing passengers or goods;
+vessels are obliged to anchor in the roadstead, which, however,
+is sheltered from every wind except the south. Funchal is
+connected by cable with Carcavellos (for Lisbon), Porthcurnow
+(for Falmouth, England) and St Vincent in the Cape Verde
+Islands (for Pernambuco, Brazil).</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUNCTION<a name="ar70" id="ar70"></a></span>,<a name="fa1ga" id="fa1ga" href="#ft1ga"><span class="sp">1</span></a> in mathematics, a variable number the value
+of which depends upon the values of one or more other variable
+numbers. The theory of functions is conveniently divided into
+(I.) Functions of Real Variables, wherein real, and only real,
+numbers are involved, and (II.) Functions of Complex Variables,
+wherein complex or imaginary numbers are involved.</p>
+
+<p class="pt2 center sc">I. Functions of Real Variables</p>
+
+<p>1. <i>Historical.</i>&mdash;The word function, defined in the above sense,
+was introduced by Leibnitz in a short note of date 1694 concerning
+the construction of what we now call an &ldquo;envelope&rdquo;
+(<i>Leibnizens mathematische Schriften</i>, edited by C.I. Gerhardt,
+Bd. v. p. 306), and was there used to denote a variable length
+related in a defined way to a variable point of a curve. In 1698
+James Bernoulli used the word in a special sense in connexion with
+some isoperimetric problems (Joh. Bernoulli, <i>Opera</i>, t. i. p. 255).
+He said that when it is a question of selecting from an infinite set
+of like curves that one which best fulfils some function, then of
+two curves whose intersection determines the thing sought one
+is always the &ldquo;line of the function&rdquo; (<i>Linea functionis</i>). In 1718
+John Bernoulli (<i>Opera</i>, t. ii. p. 241) defined a &ldquo;function of a
+variable magnitude&rdquo; as a quantity made up in any way of this
+variable magnitude and constants; and in 1730 (Opera, t. iii.
+p. 174) he noted a distinction between &ldquo;algebraic&rdquo; and &ldquo;transcendental&rdquo;
+functions. By the latter he meant integrals of
+algebraic functions. The notation &fnof;(x) for a function of a variable
+x was introduced by Leonhard Euler in 1734 (<i>Comm. Acad.
+Petropol.</i> t. vii. p. 186), in connexion with the theorem of the
+interchange of the order of differentiations. The notion of
+functionality or functional relation of two magnitudes was thus
+of geometrical origin; but a function soon came to be regarded
+as an analytical expression, not necessarily an algebraic expression,
+containing the variable or variables. Thus we may have
+rational integral algebraic functions such as ax² + bx + c, or
+rational algebraic functions which are not integral, such as</p>
+
+<table class="math0" summary="math">
+
+<tr><td>a<span class="su">1</span>x<span class="sp">n</span> + a<span class="su">2</span>x<span class="sp">n&minus;1</span> + ... + a<span class="su">n</span></td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">b<span class="su">1</span>x<span class="sp">m</span> + b<span class="su">2</span>x<span class="sp">m&minus;1</span> + ... + b<span class="su">m</span></td></tr></table>
+
+<p class="noind">or irrational algebraic functions, such as &radic;x, or, more generally
+the algebraic functions that are determined implicitly by an
+algebraic equation, as, for instance,</p>
+
+<p class="center">&fnof;<span class="su">n</span>(x, y) + &fnof;<span class="su">n&minus;1</span>(x, y) + ... + &fnof;<span class="su">0</span> = 0</p>
+
+<p><span class="pagenum"><a name="page302" id="page302"></a>302</span></p>
+
+<p class="noind">where &fnof;<span class="su">n</span>(x, y), ... mean homogeneous expressions in x and y
+having constant coefficients, and having the degrees indicated
+by the suffixes, and &fnof;<span class="su">0</span> is a constant. Or again we may have
+trigonometrical functions, such as sin x and tan x, or inverse
+trigonometrical functions, such as sin<span class="sp">&minus;1</span>x, or exponential functions,
+such as e<span class="sp">x</span> and a<span class="sp">x</span>, or logarithmic functions, such as log x and log
+(1 + x). We may have these functional symbols combined in
+various ways, and thus there arises a great number of functions.
+Further we may have functions of more than one variable, as, for
+instance, the expression xy/(x² + y²), in which both x and y are
+regarded as variable. Such functions were introduced into
+analysis somewhat unsystematically as the need for them arose,
+and the later developments of analysis led to the introduction
+of other classes of functions.</p>
+
+<p>2. <i>Graphic Representation.</i>&mdash;In the case of a function of one
+variable x, any value of x and the corresponding value y of the
+function can be the co-ordinates of a point in a plane. To any
+value of x there corresponds a point N on the axis of x, in accordance
+with the rule that x is the abscissa of N. The corresponding
+value of y determines a point P in accordance with the rule that
+x is the abscissa and y the ordinate of P. The ordinate y gives
+the value of the function which corresponds to that value of
+the variable x which is specified by N; and it may be described
+as &ldquo;the value of the function at N.&rdquo; Since there is a one-to-one
+correspondence of the points N and the numbers x, we may also
+describe the ordinate as &ldquo;the value of the function at x.&rdquo; In
+simple cases the aggregate of the points P which are determined
+by any particular function (of one variable) is a curve, called
+the &ldquo;graph of the function&rdquo; (see § 14). In like manner a function
+of two variables defines a surface.</p>
+
+<p>3. <i>The Variable.</i>&mdash;Graphic methods of representation, such
+as those just described, enabled mathematicians to deal with
+irrational values of functions and variables at the time when there
+was no theory of irrational numbers other than Euclid&rsquo;s theory
+of incommensurables. In that theory an irrational number was
+the ratio of two incommensurable geometric magnitudes. In
+the modern theory of number irrational numbers are defined in
+a purely arithmetical manner, independent of the measurement
+of any quantities or magnitudes, whether geometric or of any
+other kind. The definition is effected by means of the system
+of <i>ordinal</i> numbers (see <span class="sc"><a href="#artlinks">Number</a></span>). When this formal system is
+established, the theory of measurement may be founded upon it;
+and, in particular, the co-ordinates of a point are defined as
+numbers (not lengths), which are assigned in accordance with a
+rule. This rule involves the measurement of lengths. The theory
+of functions can be developed without any reference to graphs, or
+co-ordinates or lengths. The process by which analysis has been
+freed from any consideration of measurable quantities has been
+called the &ldquo;arithmetization of analysis.&rdquo; In the theory so
+developed, the variable upon which a function depends is always
+to be regarded as a number, and the corresponding value of the
+function is also a number. Any reference to points or co-ordinates
+is to be regarded as a picturesque mode of expression,
+pointing to a possible application of the theory to geometry.
+The development of &ldquo;arithmetized analysis&rdquo; in the 19th century
+is associated with the name of Karl Weierstrass.</p>
+
+<p>All possible values of a variable are numbers. In what
+follows we shall confine our attention to the case where the
+numbers are real. When complex numbers are introduced,
+instead of real ones, the theory of functions receives a wide
+extension, which is accompanied by appropriate limitations
+(see below, II. Functions of Complex Variables). The set of all
+real numbers forms a <i>continuum</i>. In fact the notion of a one-dimensional
+continuum first becomes precise in virtue of the
+establishment of the system of real numbers.</p>
+
+<p>4. <i>Domain of a Variable.</i>&mdash;<i>Theory of Aggregates.</i>&mdash;The notion
+of a &ldquo;variable&rdquo; is that of a number to which we may assign
+at pleasure any one of the values that belong to some chosen set,
+or <i>aggregate</i>, of numbers; and this set, or aggregate, is called
+the &ldquo;domain of the variable.&rdquo; This domain may be an
+&ldquo;interval,&rdquo; that is to say it may consist of two terminal numbers,
+all the numbers between them and no others. When this is
+the case the number is said to be &ldquo;continuously variable.&rdquo;
+When the domain consists of all real numbers, the variable is
+said to be &ldquo;unrestricted.&rdquo; A domain which consists of all the
+real numbers which exceed some fixed number may be described
+as an &ldquo;interval unlimited towards the right&rdquo;; similarly we
+may have an interval &ldquo;unlimited towards the left.&rdquo;</p>
+
+<div class="condensed">
+<p>In more complicated cases we must have some rule or process for
+assigning the aggregate of numbers which constitute the domain of
+a variable. The methods of definition of particular types of aggregates,
+and the theorems relating to them, form a branch of analysis
+called the &ldquo;theory of aggregates&rdquo; (<i>Mengenlehre, Théorie des ensembles,
+Theory of sets of points</i>). The notion of an &ldquo;aggregate&rdquo; in general
+underlies the system of ordinal numbers. An aggregate is said to
+be &ldquo;infinite&rdquo; when it is possible to effect a one-to-one correspondence
+of all its elements to some of its elements. For example, we
+may make all the integers correspond to the even integers, by making
+1 correspond to 2, 2 to 4, and generally n to 2n. The aggregate of
+positive integers is an infinite aggregate. The aggregates of all
+rational numbers and of all real numbers and of points on a line are
+other examples of infinite aggregates. An aggregate whose elements
+are real numbers is said to &ldquo;extend to infinite values&rdquo; if, after any
+number N, however great, is specified, it is possible to find in the
+aggregate numbers which exceed N in absolute value. Such an
+aggregate is always infinite. The &ldquo;neighbourhood of a number
+(or point) a for a positive number h&rdquo; is the aggregate of all numbers
+(or points) x for which the absolute value of x &minus; a denoted by
+|x &minus; a|, does not exceed h.</p>
+</div>
+
+<p>5. <i>General Notion of Functionality.</i>&mdash;A function of one variable
+was for a long time commonly regarded as the ordinate of a
+curve; and the two notions (1) that which is determined by a
+curve supposed drawn, and (2) that which is determined by an
+analytical expression supposed written down, were not for a
+long time clearly distinguished. It was for this reason that
+Fourier&rsquo;s discovery that a single analytical expression is capable
+of representing (in different parts of an interval) what would
+in his time have been called different functions so profoundly
+struck mathematicians (§ 23). The analysts who, in the middle
+of the 19th century, occupied themselves with the theory of the
+convergence of Fourier&rsquo;s series were led to impose a restriction
+on the character of a function in order that it should admit of
+such representation, and thus the door was opened for the
+introduction of the general notion of functional dependence.
+This notion may be expressed as follows: We have a variable
+number, y, and another variable number, x, a domain of the
+variable x, and a rule for assigning one or more definite values
+to y when x is any point in the domain; then y is said to be a
+&ldquo;function&rdquo; of the variable x, and x is called the &ldquo;argument&rdquo;
+of the function. According to this notion a function is, as it
+were, an indefinitely extended table, like a table of logarithms;
+to each point in the domain of the argument there correspond
+values for the function, but it remains arbitrary what values the
+function is to have at any such point.</p>
+
+<div class="condensed">
+<p>For the specification of any particular function two things are
+requisite: (1) a statement of the values of the variable, or of the
+aggregate of points, to which values of the function are to be made
+to correspond, <i>i.e.</i> of the &ldquo;domain of the argument&rdquo;; (2) a rule
+for assigning the value or values of the function that correspond to
+any point in this domain. We may refer to the second of these two
+essentials as &ldquo;the rule of calculation.&rdquo; The relation of functions
+to analytical expressions may then be stated in the form that the
+rule of calculation is: &ldquo;Give the function the value of the expression
+at any point at which the expression has a determinate value,&rdquo; or
+again more generally, &ldquo;Give the function the value of the expression
+at all points of a definite aggregate included in the domain of the
+argument.&rdquo; The former of these is the rule of those among the
+earlier analysts who regarded an analytical expression and a function
+as the same thing, and their usage may be retained without causing
+confusion and with the advantage of brevity, the analytical expression
+serving to specify the domain of the argument as well as the
+rule of calculation, <i>e.g.</i> we may speak of &ldquo;the function 1/x.&rdquo; This
+function is defined by the analytical expression 1/x at all points
+except the point x = 0. But in complicated cases separate statements
+of the domain of the argument and the rule of calculation
+cannot be dispensed with. In general, when the rule of calculation
+is determined as above by an analytical expression at any aggregate
+of points, the function is said to be &ldquo;represented&rdquo; by the expression
+at those points.</p>
+
+<p>When the rule of calculation assigns a single definite value for a
+function at each point in the domain of the argument the function
+is &ldquo;uniform&rdquo; or &ldquo;one-valued.&rdquo; In what follows it is to be understood
+that all the functions considered are one-valued, and the values
+<span class="pagenum"><a name="page303" id="page303"></a>303</span>
+assigned by the rule of calculation real. In the most important
+cases the domain of the argument of a function of one variable is an
+interval, with the possible exception of isolated points.</p>
+</div>
+
+<p>6. <i>Limits.</i>&mdash;Let &fnof;(x) be a function of a variable number x;
+and let a be a point such that there are points of the domain
+of the argument x in the neighbourhood of a for any number
+h, however small. If there is a number L which has the property
+that, after any positive number &epsilon;, however small, has been
+specified, it is possible to find a positive number h, so that
+|L &minus; &fnof;(x)| &lt; &epsilon; for all points x of the domain (other than a) for
+which |x &minus; a| &lt; h, then L is the &ldquo;limit of &fnof;(x) at the point a.&rdquo;
+The condition for the existence of L is that, after the positive
+number &epsilon; has been specified, it must be possible to find a positive
+number h, so that |&fnof;(x&prime;) &minus; &fnof;(x)| &lt; &epsilon; for all points x and x&prime; of
+the domain (other than a) for which |x &minus; a| &lt; h and |x&prime; &minus; a| &lt; h.</p>
+
+<p>It is a fundamental theorem that, when this condition is
+satisfied, there exists a perfectly definite number L which is the
+limit of &fnof;(x) at the point a as defined above. The limit of &fnof;(x)
+at the point a is denoted by Lt<span class="su">x=a</span>&fnof;(x), or by
+lim<span class="su">x=a</span>&fnof;(x).</p>
+
+<div class="condensed">
+<p>If &fnof;(x) is a function of one variable x in a domain which extends
+to infinite values, and if, after &epsilon; has been specified, it is possible to
+find a number N, so that |&fnof;(x&prime;) &minus; &fnof;(x)| &lt; &epsilon; for all values of x and x&prime;
+which are in the domain and exceed N, then there is a number L
+which has the property that |&fnof;(x) &minus; L| &lt; &epsilon; for all such values of x.
+In this case &fnof;(x) has a limit L at x = &infin;. In like manner &fnof;(x) may
+have a limit at x = &minus;&infin;. This statement includes the case where
+the domain of the argument consists exclusively of positive integers.
+The values of the function then form a &ldquo;sequence,&rdquo; u<span class="su">1</span>, u<span class="su">2</span>, ...
+u<span class="su">n</span>, ..., and this sequence can have a limit at n = &infin;.</p>
+
+<p>The principle common to the above definitions and theorems is
+called, after P. du Bois Reymond, &ldquo;the general principle of convergence
+to a limit.&rdquo;</p>
+
+<p>It must be understood that the phrase &ldquo;x = &infin;&rdquo; does not mean
+that x takes some particular value which is infinite. There is no
+such value. The phrase always refers to a limiting process in which,
+as the process is carried out, the variable number x increases without
+limit: it may, as in the above example of a sequence, increase by
+taking successively the values of all the integral numbers; in other
+cases it may increase by taking the values that belong to any domain
+which &ldquo;extends to infinite values.&rdquo;</p>
+
+<p>A very important type of limits is furnished by <i>infinite series</i>.
+When a sequence of numbers u<span class="su">1</span>, u<span class="su">2</span>, ... u<span class="su">n</span>, ... is given, we may
+form a new sequence s<span class="su">1</span>, s<span class="su">2</span>, ... s<span class="su">n</span>, ... from it by the rules s<span class="su">1</span> = u<span class="su">1</span>,
+s<span class="su">2</span> = u<span class="su">1</span> + u<span class="su">2</span>, ... s<span class="su">n</span> = u<span class="su">1</span> + u<span class="su">2</span> + ... + u<span class="su">n</span> or by the equivalent rules
+s<span class="su">1</span> = u, s<span class="su">n</span> &minus; s<span class="su">n&minus;1</span> = u<span class="su">n</span>(n = 2, 3, ...). If the new sequence has a limit
+at n = &infin;, this limit is called the &ldquo;sum of the infinite series&rdquo;
+u<span class="su">1</span> + u<span class="su">2</span> + ..., and the series is said to be &ldquo;convergent&rdquo; (see
+<span class="sc"><a href="#artlinks">Series</a></span>).</p>
+
+<p>A function which has not a limit at a point a may be such that,
+if a certain aggregate of points is chosen out of the domain of the
+argument, and the points x in the neighbourhood of a are restricted
+to belong to this aggregate, then the function has a limit at a. For
+example, sin(1/x) has limit zero at 0 if x is restricted to the
+aggregate 1/&pi;, 1/2&pi;, ... 1/n&pi;, ... or to the aggregate 1/2&pi;,
+2/5&pi;, ... n/(n<span class="sp">2</span> + 1)&pi;, ..., but if x takes all values in the neighbourhood
+of 0, sin (1/x) has not a limit at 0. Again, there may be a limit
+at a if the points x in the neighbourhood of a are restricted by the
+condition that x &minus; a is positive; then we have a &ldquo;limit on the
+right&rdquo; at a; similarly we may have a &ldquo;limit on the left&rdquo; at a
+point. Any such limit is described as a &ldquo;limit for a restricted
+domain.&rdquo; The limits on the left and on the right are denoted by
+&fnof;(a &minus; 0) and &fnof;(a + 0).</p>
+
+<p>The limit L of &fnof;(x) at a stands in no necessary relation to the value
+of &fnof;(x) at a. If the point a is in the domain of the argument, the
+value of &fnof;(x) at a is assigned by the rule of calculation, and may be
+different from L. In case &fnof;(a) = L the limit is said to be &ldquo;attained.&rdquo;
+If the point a is not in the domain of the argument, there is no value
+for &fnof;(x) at a. In the case where &fnof;(x) is defined for all points in an
+interval containing a, except the point a, and has a limit L at a,
+we may arbitrarily annex the point a to the domain of the argument
+and assign to &fnof;(a) the value L; the function may then be said to
+be &ldquo;extrinsically defined.&rdquo; The so-called &ldquo;indeterminate forms&rdquo;
+(see <span class="sc"><a href="#artlinks">Infinitesimal Calculus</a></span>) are examples.</p>
+</div>
+
+<p>7. <i>Superior and Inferior Limits; Infinities.</i>&mdash;The value of a
+function at every point in the domain of its argument is finite,
+since, by definition, the value can be assigned, but this does not
+necessarily imply that there is a number N which exceeds all
+the values (or is less than all the values). It may happen that,
+however great a number N we take, there are among the values
+of the function numbers which exceed N (or are less than &minus;N).</p>
+
+<p>If a number can be found which is greater than every value
+of the function, then either (&alpha;) there is one value of the function
+which exceeds all the others, or (&beta;) there is a number S which
+exceeds every value of the function but is such that, however
+small a positive number &epsilon; we take, there are values of the function
+which exceed S &minus; &epsilon;. In the case (&alpha;) the function has a greatest
+value; in case (&beta;) the function has a &ldquo;superior limit&rdquo; S, and
+then there must be a point a which has the property that there
+are points of the domain of the argument, in the neighbourhood
+of a for any h, at which the values of the function differ from
+S by less than &epsilon;. Thus S is the limit of the function at a, either
+for the domain of the argument or for some more restricted
+domain. If a is in the domain of the argument, and if, after
+omission of a, there is a superior limit S which is in this way the
+limit of the function at a, if further &fnof;(a) = S, then S is the greatest
+value of the function: in this case the greatest value is a limit
+(at any rate for a restricted domain) which is attained; it may
+be called a &ldquo;superior limit which is attained.&rdquo; In like manner
+we may have a &ldquo;smallest value&rdquo; or an &ldquo;inferior limit,&rdquo; and a
+smallest value may be an &ldquo;inferior limit which is attained.&rdquo;</p>
+
+<div class="condensed">
+<p>All that has been said here may be adapted to the description of
+greatest values, superior limits, &amp;c., of a function in a restricted
+domain contained in the domain of the argument. In particular,
+the domain of the argument may contain an interval; and therein
+the function may have a superior limit, or an inferior limit, which
+is attained. Such a limit is a <i>maximum</i> value or a <i>minimum</i> value
+of the function.</p>
+
+<p>Again, if, after any number N, however great, has been specified,
+it is possible to find points of the domain of the argument at which
+the value of the function exceeds N, the values of the function are
+said to have an &ldquo;infinite superior limit,&rdquo; and then there must be
+a point a which has the property that there are points of the domain,
+in the neighbourhood of a for any h, at which the value of the function
+exceeds N. If the point a is in the domain of the argument the
+function is said to &ldquo;tend to become infinite&rdquo; at a; it has of course
+a finite value at a. If the point a is not in the domain of the argument
+the function is said to &ldquo;become infinite&rdquo; at a; it has of
+course no value at a. In like manner we may have a (negatively)
+infinite inferior limit. Again, after any number N, however great,
+has been specified and a number h found, so that all the values of
+the function, at points in the neighbourhood of a for h, exceed N in
+absolute value, all these values may have the same sign; the function
+is then said to become, or to tend to become, &ldquo;determinately
+(positively or negatively) infinite&rdquo;; otherwise it is said to become
+or to tend to become, &ldquo;indeterminately infinite.&rdquo;</p>
+
+<p>All the infinities that occur in the theory of functions are of the
+nature of variable finite numbers, with the single exception of the
+infinity of an infinite aggregate. The latter is described as an
+&ldquo;actual infinity,&rdquo; the former as &ldquo;improper infinities.&rdquo; There is no
+&ldquo;actual infinitely small&rdquo; corresponding to the actual infinity.
+The only &ldquo;infinitely small&rdquo; is zero. All &ldquo;infinite values&rdquo; are of
+the nature of superior and inferior limits which are not attained.</p>
+</div>
+
+<p>8. <i>Increasing and Decreasing Functions</i>.&mdash;A function &fnof;(x) of one
+variable x, defined in the interval between a and b, is &ldquo;increasing
+throughout the interval&rdquo; if, whenever x and x&prime; are two numbers
+in the interval and x&prime; &gt; x, then &fnof;(x&prime;) &gt; &fnof;(x); the function &ldquo;never
+decreases throughout the interval&rdquo; if, x&prime; and x being as before,
+&fnof;(x&prime;) &gt; &fnof;(x). Similarly for decreasing functions, and for functions
+which never increase throughout an interval. A function which
+either never increases or never diminishes throughout an interval
+is said to be &ldquo;monotonous throughout&rdquo; the interval. If we take
+in the above definition b &gt; a, the definition may apply to a function
+under the restriction that x&prime; is not b and x is not a; such a
+function is &ldquo;monotonous within&rdquo; the interval. In this case we
+have the theorem that the function (if it never decreases) has
+a limit on the left at b and a limit on the right at a, and these are
+the superior and inferior limits of its values at all points within
+the interval (the ends excluded); the like holds <i>mutatis mutandis</i>
+if the function never increases. If the function is monotonous
+throughout the interval, &fnof;(b) is the greatest (or least) value
+of &fnof;(x) in the interval; and if &fnof;(b) is the limit of &fnof;(x) on the left
+at b, such a greatest (or least) value is an example of a superior
+(or inferior) limit which is attained. In these cases the function
+tends continually to its limit.</p>
+
+<div class="condensed">
+<p>These theorems and definitions can be extended, with obvious
+modifications, to the cases of a domain which is not an interval, or
+extends to infinite values. By means of them we arrive at sufficient,
+but not necessary, criteria for the existence of a limit; and these
+are frequently easier to apply than the general principle of convergence
+to a limit (§ 6), of which principle they are particular cases.
+For example, the function represented by x log (1/x) continually
+<span class="pagenum"><a name="page304" id="page304"></a>304</span>
+diminishes when 1/e &gt; x &gt; 0 and x diminishes towards zero, and it
+never becomes negative. It therefore has a limit on the right at
+x = 0. This limit is zero. The function represented by x sin (1/x)
+does not continually diminish towards zero as x diminishes towards
+zero, but is sometimes greater than zero and sometimes less than
+zero in any neighbourhood of x = 0, however small. Nevertheless,
+the function has the limit zero at x = 0.</p>
+</div>
+
+<p>9. <i>Continuity of Functions</i>.&mdash;A function &fnof;(x) of one variable x
+is said to be continuous at a point a if (1) &fnof;(x) is defined in an
+interval containing a; (2) &fnof;(x) has a limit at a; (3) &fnof;(a) is
+equal to this limit. The limit in question must be a limit for
+continuous variation, not for a restricted domain. If &fnof;(x) has
+a limit on the left at a and &fnof;(a) is equal to this limit, the function
+may be said to be &ldquo;continuous to the left&rdquo; at a; similarly the
+function may be &ldquo;continuous to the right&rdquo; at a.</p>
+
+<p>A function is said to be &ldquo;continuous throughout an interval&rdquo;
+when it is continuous at every point of the interval. This implies
+continuity to the right at the smaller end-value and continuity
+to the left at the greater end-value. When these conditions at the
+ends are not satisfied the function is said to be continuous
+&ldquo;within&rdquo; the interval. By a &ldquo;continuous function&rdquo; of one
+variable we always mean a function which is continuous throughout
+an interval.</p>
+
+<div class="condensed">
+<p>The principal properties of a continuous function are:</p>
+
+<p>1. The function is practically constant throughout sufficiently small
+intervals. This means that, after any point a of the interval has been
+chosen, and any positive number &epsilon;, however small, has been
+specified, it is possible to find a number h, so that the difference
+between any two values of the function in the interval between a &minus; h and
+a + h is less than &epsilon;. There is an obvious modification if a is an
+end-point of the interval.</p>
+
+<p>2. The continuity of the function is &ldquo;uniform.&rdquo; This means that the
+number h which corresponds to any &epsilon; as in (1) may be the same at
+all points of the interval, or, in other words, that the numbers h which
+correspond to &epsilon; for different values of a have a positive
+inferior limit.</p>
+
+<p>3. The function has a greatest value and a least value in the interval,
+and these are superior and inferior limits which are attained.</p>
+
+<p>4. There is at least one point of the interval at which the function
+takes any value between its greatest and least values in the interval.</p>
+
+<p>5. If the interval is unlimited towards the right (or towards the left),
+the function has a limit at &infin; (or at &minus;&infin;).</p>
+</div>
+
+<p>10. <i>Discontinuity of Functions</i>.&mdash;The discontinuities of a
+function of one variable, defined in an interval with the possible
+exception of isolated points, may be classified as follows:</p>
+
+<p>(1) The function may become infinite, or tend to become
+infinite, at a point.</p>
+
+<p>(2) The function may be undefined at a point.</p>
+
+<p>(3) The function may have a limit on the left and a limit on
+the right at the same point; these may be different from each
+other, and at least one of them must be different from the value
+of the function at the point.</p>
+
+<p>(4) The function may have no limit at a point, or no limit on
+the left, or no limit on the right, at a point.</p>
+
+<div class="condensed">
+<p>In case a function &fnof;(x), defined as above, has no limit at a point a,
+there are four limiting values which come into consideration. Whatever
+positive number h we take, the values of the function at points
+between a and a + h (a excluded) have a superior limit (or a greatest
+value), and an inferior limit (or a least value); further, as h decreases,
+the former never increases and the latter never decreases; accordingly
+each of them tends to a limit. We have in this way two limits on
+the right&mdash;the inferior limit of the superior limits in diminishing
+neighbourhoods, and the superior limit of the inferior limits in
+diminishing neighbourhoods. These are denoted by <span class="ov">&fnof;(a + 0)</span> and
+<span class="un">&fnof;(a + 0)</span>, and they are called the &ldquo;limits of indefiniteness&rdquo; on the
+right. Similar limits on the left are denoted by <span class="ov">&fnof;(a &minus; 0)</span> and <span class="un">&fnof;(a &minus; 0)</span>.
+Unless &fnof;(x) becomes, or tends to become, infinite at a, all these must
+exist, any two of them may be equal, and at least one of them must
+be different from &fnof;(a), if &fnof;(a) exists. If the first two are equal there
+is a limit on the right denoted by &fnof;(a + 0); if the second two are
+equal, there is a limit on the left denoted by &fnof;(a &minus; 0). In case the
+function becomes, or tends to become, infinite at a, one or more of
+these limits is infinite in the sense explained in § 7; and now it is
+to be noted that, <i>e.g.</i> the superior limit of the inferior limits in
+diminishing neighbourhoods on the right of a may be negatively
+infinite; this happens if, after any number N, however great, has
+been specified, it is possible to find a positive number h, so that all
+the values of the function in the interval between a and a + h (a
+excluded) are less than &minus;N; in such a case &fnof;(x) tends to become
+negatively infinite when x decreases towards a; other modes of
+tending to infinite limits may be described in similar terms.</p>
+</div>
+
+<p>11. <i>Oscillation of Functions</i>.&mdash;The difference between the
+greatest and least of the numbers &fnof;(a), <span class="ov">&fnof;(a + 0)</span>, <span class="un">&fnof;(a + 0)</span>, <span class="ov">&fnof;(a &minus; 0)</span>,
+<span class="un">&fnof;(a &minus; 0)</span>, when they are all finite, is called the &ldquo;oscillation&rdquo; or
+&ldquo;fluctuation&rdquo; of the function &fnof;(x) at the point a. This difference
+is the limit for h = 0 of the difference between the superior and
+inferior limits of the values of the function at points in the
+interval between a &minus; h and a + h. The corresponding difference
+for points in a finite interval is called the &ldquo;oscillation of the
+function in the interval.&rdquo; When any of the four limits of
+indefiniteness is infinite the oscillation is infinite in the sense
+explained in § 7.</p>
+
+<div class="condensed">
+<p>For the further classification of functions we divide the domain
+of the argument into partial intervals by means of points between
+the end-points. Suppose that the domain is the interval between a
+and b. Let intermediate points x<span class="su">1</span>, x<span class="su">2</span> ... x<span class="su">n&minus;1</span>, be taken so that
+b &gt; x<span class="su">n&minus;1</span> &gt; x<span class="su">n&minus;2</span> ... &gt; x<span class="su">1</span> &gt; a. We may devise a rule by which, as n
+increases indefinitely, all the differences
+b &minus; x<span class="su">n&minus;1</span>, x<span class="su">n&minus;1</span> &minus; x<span class="su">n&minus;2</span>, ... x<span class="su">1</span> &minus; a
+tend to zero as a limit. The interval is then said to be divided
+into &ldquo;indefinitely small partial intervals.&rdquo;</p>
+
+<p>A function defined in an interval with the possible exception of
+isolated points may be such that the interval can be divided into a
+set of finite partial intervals within each of which the function is
+monotonous (§ 8). When this is the case the sum of the oscillations
+of the function in those partial intervals is finite, provided the
+function does not tend to become infinite. Further, in such a case
+the sum of the oscillations will remain below a fixed number for any
+mode of dividing the interval into indefinitely small partial intervals.
+A class of functions may be defined by the condition that the sum
+of the oscillations has this property, and such functions are said
+to have &ldquo;restricted oscillation.&rdquo; Sometimes the phrase &ldquo;limited
+fluctuation&rdquo; is used. It can be proved that any function with
+restricted oscillation is capable of being expressed as the sum of
+two monotonous functions, of which one never increases and the other
+never diminishes throughout the interval. Such a function has a
+limit on the right and a limit on the left at every point of the interval.
+This class of functions includes all those which have a finite number
+of maxima and minima in a finite-interval, and some which have an
+infinite number. It is to be noted that the class does not include all
+continuous functions.</p>
+</div>
+
+<p>12. <i>Differentiable Function</i>.&mdash;The idea of the differentiation
+of a continuous function is that of a process for measuring the
+rate of growth; the increment of the function is compared with
+the increment of the variable. If &fnof;(x) is defined in an interval
+containing the point a, and a &minus; k and a + k are points of the
+interval, the expression</p>
+
+<table class="math0" summary="math">
+<tr><td>&fnof;(a + h) &minus; &fnof;(a)</td></tr>
+<tr><td class="denom">h</td></tr>
+</table>
+
+<div class="author">(1)</div>
+
+<p class="noind">represents a function of h, which we may call &phi;(h), defined at all
+points of an interval for h between &minus;k and k except the point 0.
+Thus the four limits <span class="ov">&phi;(+0)</span>, <span class="un">&phi;(+0)</span>, <span class="ov">&phi;(&minus;0)</span>, <span class="un">&phi;(&minus;0)</span> exist, and two
+or more of them may be equal. When the first two are equal
+either of them is the &ldquo;progressive differential coefficient&rdquo; of
+&fnof;(x) at the point a; when the last two are equal either of them
+is the &ldquo;regressive differential coefficient&rdquo; of &fnof;(x) at a; when all
+four are equal the function is said to be &ldquo;differentiable&rdquo; at a,
+and either of them is the &ldquo;differential coefficient&rdquo; of &fnof;(x) at a,
+or the &ldquo;first derived function&rdquo; of &fnof;(x) at a. It is denoted by
+d&fnof;(x) / dx or by &fnof;&prime;(x). In this case &phi;(h) has a definite limit at h = 0,
+or is determinately infinite at h = 0 (§ 7). The four limits here in
+question are called, after Dini, the &ldquo;four derivates&rdquo; of &fnof;(x) at a.
+In accordance with the notation for derived functions they may
+be denoted by</p>
+
+<p class="center"><span class="ov">&fnof;&prime; + (a)</span>, <span class="un">&fnof;&prime; + (a)</span>, <span class="ov">&fnof;&prime; &minus; (a)</span>, <span class="un">&fnof;&prime; &minus; (a)</span>.</p>
+
+<div class="condensed">
+<p>A function which has a finite differential coefficient at all points
+of an interval is continuous throughout the interval, but if the
+differential coefficient becomes infinite at a point of the interval
+the function may or may not be continuous throughout the interval;
+on the other hand a function may be continuous without being
+differentiable. This result, comparable in importance, from the
+point of view of the general theory of functions, with the discovery
+of Fourier&rsquo;s theorem, is due to G.F.B. Riemann; but the failure
+of an attempt made by Ampère to prove that every continuous
+function must be differentiable may be regarded as the first step in
+the theory. Examples of analytical expressions which represent
+continuous functions that are not differentiable have been given by
+Riemann, Weierstrass, Darboux and Dini (see § 24). The most
+important theorem in regard to differentiable functions is the
+&ldquo;theorem of intermediate value.&rdquo; (See <span class="sc"><a href="#artlinks">Infinitesimal Calculus</a></span>.)</p>
+</div>
+
+<p><span class="pagenum"><a name="page305" id="page305"></a>305</span></p>
+
+<p>13. <i>Analytic Function</i>.&mdash;If &fnof;(x) and its first n differential
+coefficients, denoted by&fnof;&prime;(x), &fnof;&Prime;(x), ... &fnof;(<span class="sp">n</span>) (x), are continuous
+in the interval between a and a + h, then</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&fnof;(a + h) = &fnof;(a) + h&fnof;&prime;(a) +</td> <td>h²</td>
+<td rowspan="2">&fnof;&Prime;(a) + ... +</td> <td>h<span class="sp">n&minus;1</span></td>
+<td rowspan="2">&fnof;<span class="sp">(n&minus;1)</span>(a) + R<span class="su">n</span>,</td></tr>
+<tr><td class="denom">2!</td> <td class="denom">(n &minus; 1)!</td></tr></table>
+
+<p class="noind">where R<span class="su">n</span> may have various forms, some of which are given in
+the article <span class="sc"><a href="#artlinks">Infinitesimal Calculus</a></span>. This result is known as
+&ldquo;Taylor&rsquo;s theorem.&rdquo;</p>
+
+<p>When <span class="correction" title="amended from Talyor&rsquo;s">Taylor's</span> theorem leads to a representation of the
+function by means of an infinite series, the function is said to be
+&ldquo;analytic&rdquo; (cf. § 21).</p>
+
+<p>14. <i>Ordinary Function</i>.&mdash;The idea of a curve representing a
+continuous function in an interval is that of a line which has the
+following properties: (1) the co-ordinates of a point of the curve
+are a value x of the argument and the corresponding value y of
+the function; (2) at every point the curve has a definite tangent;
+(3) the interval can be divided into a finite number of partial
+intervals within each of which the function is monotonous;
+(4) the property of monotony within partial intervals is retained
+after interchange of the axes of co-ordinates x and y. According
+to condition (2) y is a continuous and differentiable function
+of x, but this condition does not include conditions (3) and (4):
+there are continuous partially monotonous functions which are
+not differentiable, there are continuous differentiable functions
+which are not monotonous in any interval however small; and
+there are continuous, differentiable and monotonous functions
+which do not satisfy condition (4) (cf. § 24). A function which
+can be represented by a curve, in the sense explained above, is
+said to be &ldquo;ordinary,&rdquo; and the curve is the graph of the function
+(§2). All analytic functions are ordinary, but not all ordinary
+functions are analytic.</p>
+
+<p>15. <i>Integrable Function</i>.&mdash;The idea of integration is twofold.
+We may seek the function which has a given function as its
+differential coefficient, or we may generalize the question of
+finding the area of a curve. The first inquiry leads directly to the
+indefinite integral, the second directly to the definite integral.
+Following the second method we define &ldquo;the definite integral
+of the function &fnof;(x) through the interval between a and b&rdquo; to be
+the limit of the sum</p>
+
+<p class="center"><span class="f150">&Sigma;</span><span class="sp1">n</span><span class="su1">1</span> &fnof;(x&prime;<span class="su">r</span>) (x<span class="su">r</span> &minus; x<span class="su">r&minus;1</span>)</p>
+
+<p class="noind">when the interval is divided into ultimately indefinitely small
+partial intervals by points x<span class="su">1</span>, x<span class="su">2</span>, ... x<span class="su">n&minus;1</span>. Here x&prime;<span class="su">r</span> denotes
+any point in the rth partial interval, x<span class="su">0</span> is put for a, and x<span class="su">n</span> for b.
+It can be shown that the limit in question is finite and independent
+of the mode of division into partial intervals, and of the
+choice of the points such as x&prime;<span class="su">r</span>, provided (1) the function is
+defined for all points of the interval, and does not tend to become
+infinite at any of them; (2) for any one mode of division of the
+interval into ultimately indefinitely small partial intervals, the
+sum of the products of the oscillation of the function in each
+partial interval and the difference of the end-values of that
+partial interval has limit zero when n is increased indefinitely.
+When these conditions are satisfied the function is said to be
+&ldquo;integrable&rdquo; in the interval. The numbers a and b which limit
+the interval are usually called the &ldquo;lower and upper limits.&rdquo;
+We shall call them the &ldquo;nearer and further end-values.&rdquo; The
+above definition of integration was introduced by Riemann in
+his memoir on trigonometric series (1854). A still more general
+definition has been given by Lebesgue. As the more general
+definition cannot be made intelligible without the introduction
+of some rather recondite notions belonging to the theory of
+aggregates, we shall, in what follows, adhere to Riemann&rsquo;s
+definition.</p>
+
+<div class="condensed">
+<p>We have the following theorems:&mdash;</p>
+
+<p>1. Any continuous function is integrable.</p>
+
+<p>2. Any function with restricted oscillation is integrable.</p>
+
+<p>3. A discontinuous function is integrable if it does not tend to
+become infinite, and if the points at which the oscillation of the
+function exceeds a given number &sigma;, however small, can be enclosed
+in partial intervals the sum of whose breadths can be diminished
+indefinitely.</p>
+
+<p>These partial intervals must be a set chosen out of some complete
+set obtained by the process used in the definition of integration.</p>
+
+<p>4. The sum or product of two integrable functions is integrable.</p>
+
+<p>As regards integrable functions we have the following theorems:</p>
+
+<p>1. If S and I are the superior and inferior limits (or greatest and
+least values) of &fnof;(x) in the interval between a and b, <span class="f150">&int;</span> <span class="sp1">b</span><span class="su1">a</span> &fnof;(x)<i>dx</i> is
+intermediate between S(b &minus; a) and I(b &minus; a).</p>
+
+<p>2. The integral is a continuous function of each of the end-values.</p>
+
+<p>3. If the further end-value b is variable, and if <span class="f150">&int;</span> <span class="sp1">x</span><span class="su1">a</span> &fnof;(x)<i>dx</i> = F(x),
+then if &fnof;(x) is continuous at b, F(x) is differentiable at b, and
+F&prime;(b) = &fnof;(b).</p>
+
+<p>4. In case &fnof;(x) is continuous throughout the interval F(x) is continuous
+and differentiable throughout the interval, and F&prime;(x) = &fnof;(x)
+throughout the interval.</p>
+
+<p>5. In case &fnof;&prime;(x) is continuous throughout the interval between a
+and b,</p>
+
+<p class="center"><span class="f150">&int;</span> <span class="sp1">b</span><span class="su1">a</span> &fnof;&prime;(x)<i>dx</i> = &fnof;(b) &minus; &fnof;(a).</p>
+
+<p>6. In case &fnof;(x) is discontinuous at one or more points of the interval
+between a and b, in which it is integrable,</p>
+
+<p class="center"><span class="f150">&int;</span> <span class="sp1">x</span><span class="su1">a</span> &fnof;(x)dx</p>
+
+<p class="noind">is a function of x, of which the four derivates at any point of the
+interval are equal to the limits of indefiniteness of &fnof;(x) at the point.</p>
+
+<p>7. It may be that there exist functions which are differentiable
+throughout an interval in which their differential coefficients are
+not integrable; if, however, F(x) is a function whose differential
+coefficient, F&prime;(x), is integrable in an interval, then</p>
+
+<p class="center">F(x) = <span class="f150">&int;</span> <span class="sp1">x</span><span class="su1">a</span> F&prime;(x)<i>dx</i> + const.,</p>
+
+<p class="noind">where a is a fixed point, and x a variable point, of the interval.
+Similarly, if any one of the four derivates of a function is integrable
+in an interval, all are integrable, and the integral of either differs from
+the original function by a constant only.</p>
+
+<p>The theorems (4), (6), (7) show that there is some discrepancy
+between the indefinite integral considered as the function which has
+a given function as its differential coefficient, and as a definite
+integral with a variable end-value.</p>
+
+<p>We have also two theorems concerning the integral of the product
+of two integrable functions &fnof;(x) and &phi;(x); these are known as &ldquo;the
+first and second theorems of the mean.&rdquo; The first theorem of the
+mean is that, if &phi;(x) is one-signed throughout the interval between
+a and b, there is a number M intermediate between the superior
+and inferior limits, or greatest and least values, of &fnof;(x) in the interval,
+which has the property expressed by the equation</p>
+
+<p class="center">M <span class="f150">&int;</span> <span class="sp1">b</span><span class="su1">a</span> &phi;(x)dx = <span class="f150">&int;</span> <span class="sp1">b</span><span class="su1">a</span>  &fnof;(x)&phi;(x)dx</p>
+
+<p>The second theorem of the mean is that, if &fnof;(x) is monotonous
+throughout the interval, there is a number &xi; between a and b which
+has the property expressed by the equation</p>
+
+<p class="center"><span class="f150">&int;</span> <span class="sp1">b</span><span class="su1">a</span> &fnof;(x) &phi;(x)dx = &fnof;(a) <span class="f150">&int;</span> <span class="sp1">&xi;</span><span class="su1">a</span>  &phi;(x)<i>dx</i> + &fnof;(b) <span class="f150">&int;</span> <span class="sp1">b</span><span class="su1">&xi;</span> &phi;(x)dx.</p>
+
+<p>(<i>See</i> <span class="sc"><a href="#artlinks">Fourier&rsquo;s Series</a></span>.)</p>
+</div>
+
+<p>16. <i>Improper Definite Integrals</i>.&mdash;We may extend the idea of
+integration to cases of functions which are not defined at some
+point, or which tend to become infinite in the neighbourhood of
+some point, and to cases where the domain of the argument
+extends to infinite values. If c is a point in the interval between
+a and b at which &fnof;(x) is not defined, we impose a restriction on
+the points x&prime;<span class="su">r</span> of the definition: none of them is to be the point c.
+This comes to the same thing as defining <span class="f150">&int;</span> <span class="sp1">b</span><span class="su1">a</span> &fnof;(x)<i>dx</i> to be</p>
+
+<p class="center">Lt <span class="su">&epsilon;=0</span><span class="f150">&int;</span> <span class="sp1">c&minus;&epsilon;</span><span class="su1">a</span>    &fnof;(x)dx + Lt <span class="su">&epsilon;&prime;=0</span><span class="f150">&int;</span> <span class="sp1">b</span><span class="su1">c+&epsilon;&prime;</span> &fnof;(x)dx,</p>
+<div class="author">(1)</div>
+
+<p class="noind">where, to fix ideas, b is taken &gt; a, and &epsilon; and &epsilon;&prime; are positive. The
+same definition applies to the case where &fnof;(x) becomes infinite, or
+tends to become infinite, at c, provided both the limits exist.
+This definition may be otherwise expressed by saying that a
+partial interval containing the point c is omitted from the
+interval of integration, and a limit taken by diminishing the
+breadth of this partial interval indefinitely; in this form it
+applies to the cases where c is a or b.</p>
+
+<p>Again, when the interval of integration is unlimited to the
+right, or extends to positively infinite values, we have as a
+definition</p>
+
+<p class="center"><span class="f150">&int;</span> <span class="sp1">&infin;</span><span class="su1">a</span> &fnof;(x)dx =  Lt <span class="su">h=&infin;</span><span class="f150">&int;</span> <span class="sp1">h</span><span class="su1">a</span> &fnof;(x)dx,</p>
+
+<p><span class="pagenum"><a name="page306" id="page306"></a>306</span></p>
+
+<p class="noind">provided this limit exists. Similar definitions apply to</p>
+
+<p class="center"><span class="f150">&int;</span> <span class="sp1">&minus;&infin;</span><span class="su1">a</span> &fnof;(x)dx, and to <span class="f150">&int;</span> <span class="sp1">&infin;</span><span class="su1">&minus;&infin;</span> &fnof;(x)dx.</p>
+
+<p>All such definite integrals as the above are said to be &ldquo;improper.&rdquo;
+For example, <span class="f150">&int;</span> <span class="sp1">&infin;</span><span class="su1">0</span> sin x / x dx is improper in two ways. It means</p>
+
+<p class="center">Lt <span class="su">h=&infin;</span>  Lt <span class="su">&epsilon;=0</span> <span class="f150">&int;</span> <span class="sp1">h</span><span class="su1">&epsilon;</span> sinx/x dx,</p>
+
+<p class="noind">in which the positive number &epsilon; is first diminished indefinitely,
+and the positive number h is afterwards increased indefinitely.</p>
+
+<p>The &ldquo;theorems of the mean&rdquo; (§ 15) require modification when
+the integrals are improper (see <span class="sc"><a href="#artlinks">Fourier&rsquo;s Series</a></span>).</p>
+
+<p>When the improper definite integral of a function which
+becomes, or tends to become, infinite, exists, the integral is said
+to be &ldquo;convergent.&rdquo; If &fnof;(x) tends to become infinite at a point
+c in the interval between a and b, and the expression (1) does not
+exist, then the expression <span class="f150">&int;</span> <span class="sp1">b</span><span class="su1">a</span> &fnof;(x)dx, which has no value, is called
+a &ldquo;divergent integral, &ldquo;and it may happen that there is a definite
+value  for</p>
+
+<p class="center">Lt <span class="f150">{</span> <span class="f150">&int;</span> <span class="sp1">c&minus;&epsilon;</span><span class="su1">a</span> &fnof;(x) dx    + <span class="f150">&int;</span> <span class="sp1">b</span><span class="su1">c+&epsilon;&prime;</span> &fnof;(x) dx <span class="f150">}</span></p>
+
+<p class="noind">provided that &epsilon; and &epsilon;&prime; are connected by some definite relation,
+and both, remaining positive, tend to limit zero. The value of
+the above limit is then called a &ldquo;principal value&rdquo; of the divergent
+integral. Cauchy&rsquo;s principal value is obtained by making &epsilon;&prime; = &epsilon;,
+<i>i.e.</i> by taking the omitted interval so that the infinity is at
+its middle point. A divergent integral which has one or more
+principal values is sometimes described as &ldquo;semi-convergent.&rdquo;</p>
+
+<p>17. <i>Domain of a Set of Variables.</i>&mdash;The numerical continuum
+of n dimensions (C<span class="su">n</span>) is the aggregate that is arrived at by attributing
+simultaneous values to each of n variables x<span class="su">1</span>, x<span class="su">2</span>, ... x<span class="su">n</span>,
+these values being any real numbers. The elements of such an
+aggregate are called &ldquo;points,&rdquo; and the numbers x<span class="su">1</span>, x<span class="su">2</span> ... x<span class="su">n</span>
+the &ldquo;co-ordinates&rdquo; of a point. Denoting in general the points
+(x<span class="su">1</span>, x<span class="su">2</span>, ... x<span class="su">n</span>) and (x&prime;<span class="su">1</span>, x&prime;<span class="su">2</span> ... x&prime;<span class="su">n</span>) by x and x&prime;, the sum of
+the differences |x<span class="su">1</span> &minus; x&prime;<span class="su">1</span>| + |x<span class="su">2</span> &minus; x&prime;<span class="su">2</span>| + ... + |x<span class="su">n</span> &minus; x&prime;<span class="su">n</span>| may
+be denoted by |x &minus; x&prime;| and called the &ldquo;difference of the two
+points.&rdquo; We can in various ways choose out of the continuum
+an aggregate of points, which may be an infinite aggregate, and
+any such aggregate can be the &ldquo;domain&rdquo; of a &ldquo;variable point.&rdquo;
+The domain is said to &ldquo;extend to an infinite distance&rdquo; if, after
+any number N, however great, has been specified, it is possible
+to find in the domain points of which one or more co-ordinates
+exceed N in absolute value. The &ldquo;neighbourhood&rdquo; of a point
+a for a (positive) number h is the aggregate constituted of all the
+points x, which are such that the &ldquo;difference&rdquo; denoted by
+|x &minus; a| &lt; h. If an infinite aggregate of points does not extend
+to an infinite distance, there must be at least one point a, which
+has the property that the points of the aggregate which are in
+the neighbourhood of a for any number h, however small, themselves
+constitute an infinite aggregate, and then the point a is
+called a &ldquo;limiting point&rdquo; of the aggregate; it may or may not
+be a point of the aggregate. An aggregate of points is &ldquo;perfect&rdquo;
+when all its points are limiting points of it, and all its limiting
+points are points of it; it is &ldquo;connected&rdquo; when, after taking
+any two points a, b of it, and choosing any positive number &epsilon;,
+however small, a number m and points x&prime;, x&Prime;, ... x<span class="sp">(m)</span> of the
+aggregate can be found so that all the differences denoted by
+|x&prime; &minus; a|, |x&Prime; &minus; x&prime;|, ... |b &minus; x<span class="sp">(m)</span>| are less than &epsilon;. A perfect connected
+aggregate is a <i>continuum</i>. This is G. Cantor&rsquo;s definition.</p>
+
+<div class="condensed">
+<p>The definition of a continuum in C<span class="su">n</span> leaves open the question of
+the number of dimensions of the continuum, and a further explanation
+is necessary in order to define arithmetically what is meant by a
+&ldquo;homogeneous part&rdquo; H<span class="su">n</span> of C<span class="su">n</span>. Such a part would correspond to
+an interval in C<span class="su">1</span>, or to an area bounded by a simple closed contour
+in C<span class="su">2</span>; and, besides being perfect and connected, it would have the
+following properties: (1) There are points of C<span class="su">n</span>, which are not points
+of H<span class="su">n</span>; these form a complementary aggregate H&prime;<span class="su">n</span>. (2) There are
+points &ldquo;within&rdquo; H<span class="su">n</span>; this means that for any such point there is
+a neighbourhood consisting exclusively of points of H<span class="su">n</span>. (3) The
+points of H<span class="su">n</span> which do not lie &ldquo;within&rdquo; H<span class="su">n</span> are limiting points of
+H&prime;<span class="su">n</span>; they are not points of H&prime;<span class="su">n</span>, but the neighbourhood of any such
+point for any number h, however small, contains points within H<span class="su">n</span>
+and points of H&prime;<span class="su">n</span>: the aggregate of these points is called the
+&ldquo;boundary&rdquo; of H<span class="su">n</span>. (4) When any two points a, b within H<span class="su">n</span> are
+taken, it is possible to find a number &epsilon; and a corresponding number
+m, and to choose points x&prime;, x&Prime;, ... x<span class="sp">(m)</span>, so that the neighbourhood
+of a for &epsilon; contains x&prime;, and consists exclusively of points within H<span class="su">n</span>,
+and similarly for x&prime; and x&Prime;, x&Prime; and x&Prime;&prime;, ... x<span class="sp">(m)</span> and b. Condition
+(3) would exclude such an aggregate as that of the points within and
+upon two circles external to each other and a line joining a point on
+one to a point on the other, and condition (4) would exclude such
+an aggregate as that of the points within and upon two circles which
+touch externally.</p>
+</div>
+
+<p>18. Functions of Several Variables.&mdash;A function of several
+variables differs from a function of one variable in that the
+argument of the function consists of a set of variables, or is a
+variable point in a C<span class="su">n</span> when there are n variables. The function
+is definable by means of the domain of the argument and the
+rule of calculation. In the most important cases the domain of
+the argument is a homogeneous part H<span class="su">n</span> of C<span class="su">n</span> with the possible
+exception of isolated points, and the rule of calculation is that
+the value of the function in any assigned part of the domain
+of the argument is that value which is assumed at the point by
+an assigned analytical expression. The limit of a function at a
+point a is defined in the same way as in the case of a function of
+one variable.</p>
+
+<div class="condensed">
+<p>We take a positive fraction &epsilon; and consider the neighbourhood of a
+for h, and from this neighbourhood we exclude the point a, and we
+also exclude any point which is not in the domain of the argument.
+Then we take x and x&prime; to be any two of the retained points in the
+neighbourhood. The function &fnof; has a limit at a if for any positive &epsilon;,
+however small, there is a corresponding h which has the property
+that |&fnof;(x&prime;) &minus; &fnof;(x)| &lt; &epsilon;, whatever points x, x&prime; in the neighbourhood
+of a for h we take (a excluded). For example, when there are two
+variables x<span class="su">1</span>, x<span class="su">2</span>, and both are unrestricted, the domain of the argument
+is represented by a plane, and the values of the function are
+correlated with the points of the plane. The function has a limit
+at a point a, if we can mark out on the plane a region containing
+the point a within it, and such that the difference of the values of
+the function which correspond to any two points of the region
+(neither of the points being a) can be made as small as we please
+in absolute value by contracting all the linear dimensions of the
+region sufficiently. When the domain of the argument of a function
+of n variables extends to an infinite distance, there is a &ldquo;limit at
+an infinite distance&rdquo; if, after any number &epsilon;, however small, has been
+specified, a number N can be found which is such that |&fnof;(x&prime;) &minus; &fnof;(x)| &lt; &epsilon;,
+for all points x and x&prime; (of the domain) of which one or more co-ordinates
+exceed N in absolute value. In the case of functions of
+several variables great importance attaches to limits for a restricted
+domain. The definition of such a limit is verbally the same as the
+corresponding definition in the case of functions of one variable
+(§ 6). For example, a function of x<span class="su">1</span> and x<span class="su">2</span> may have a limit at
+(x<span class="su">1</span> = 0, x<span class="su">2</span> = 0) if we first diminish x<span class="su">1</span> without limit, keeping x<span class="su">2</span> constant,
+and afterwards diminish x<span class="su">2</span> without limit. Expressed in
+geometrical language, this process amounts to approaching the
+origin along the axis of x<span class="su">2</span>. The definitions of superior and inferior
+limits, and of maxima and minima, and the explanations of what
+is meant by saying that a function of several variables becomes
+infinite, or tends to become infinite, at a point, are almost identical
+verbally with the corresponding definitions and explanations in the
+case of a function of one variable (§ 7). The definition of a continuous
+function (§ 9) admits of immediate extension; but it is very important
+to observe that a function of two or more variables may be
+a continuous function of each of the variables, when the rest are kept
+constant, without being a continuous function of its argument.
+For example, a function of x and y may be defined by the conditions
+that when x = 0 it is zero whatever value y may have, and when
+x &ne; 0 it has the value of sin {4 tan<span class="sp">&minus;1</span> (y/x)}. When y has any particular
+value this function is a continuous function of x, and, when x has
+any particular value this function is a continuous function of y;
+but the function of x and y is discontinuous at (x = 0, y = 0).</p>
+</div>
+
+<p>19. <i>Differentiation and Integration.</i>&mdash;The definition of partial
+differentiation of a function of several variables presents no
+difficulty. The most important theorems concerning differentiable
+functions are the &ldquo;theorem of the total differential,&rdquo;
+the theorem of the interchangeability of the order of partial
+differentiations, and the extension of Taylor&rsquo;s theorem (see
+<span class="sc"><a href="#artlinks">Infinitesimal Calculus</a></span>).</p>
+
+<p>With a view to the establishment of the notion of integration
+through a domain, we must define the &ldquo;extent&rdquo; of the domain.
+Take first a domain consisting of the point a and all the points x
+for which |x &minus; a| &lt; ½h, where h is a chosen positive number;
+the extent of this domain is h<span class="sp">n</span>, n being the number of variables;
+such a domain may be described as &ldquo;square,&rdquo;  and the number h
+may be called its &ldquo;breadth&rdquo;; it is a homogeneous part of the
+<span class="pagenum"><a name="page307" id="page307"></a>307</span>
+numerical continuum of n dimensions, and its boundary consists
+of all the points for which |x &minus; a| = ½h. Now the points of
+any domain, which does not extend to an infinite distance, may
+be assigned to a finite number m of square domains of finite
+breadths, so that every point of the domain is either within one
+of these square domains or on its boundary, and so that no point
+is within two of the square domains; also we may devise a rule
+by which, as the number m increases indefinitely, the breadths
+of all the square domains are diminished indefinitely. When
+this process is applied to a homogeneous part, H, of the numerical
+continuum <i>C<span class="su">n</span></i>, then, at any stage of the process, there will be
+some square domains of which all the points belong to H, and
+there will generally be others of which some, but not all, of the
+points belong to H. As the number m is increased indefinitely
+the sums of the extents of both these categories of square
+domains will tend to definite limits, which cannot be negative;
+when the second of these limits is zero the domain H is said to
+be &ldquo;measurable,&rdquo; and the first of these limits is its &ldquo;extent&rdquo;;
+it is independent of the rule adopted for constructing the square
+domains and contracting their breadths. The notion thus introduced
+may be adapted by suitable modifications to continua of
+lower dimensions in <i>C<span class="su">n</span></i>.</p>
+
+<div class="condensed">
+<p>The integral of a function &fnof;(x) through a measurable domain H,
+which is a homogeneous part of the numerical continuum of n
+dimensions, is defined in just the same way as the integral through
+an interval, the extent of a square domain taking the place of the
+difference of the end-values of a partial interval; and the condition
+of integrability takes the same form as in the simple case. In particular,
+the condition is satisfied when the function is continuous
+throughout the domain. The definition of an integral through a
+domain may be adapted to any domain of measurable extent. The
+extensions to &ldquo;improper&rdquo; definite integrals may be made in the
+same way as for a function of one variable; in the particular case
+of a function which tends to become infinite at a point in the domain
+of integration, the point is enclosed in a partial domain which is
+omitted from the integration, and a limit is taken when the extent
+of the omitted partial domain is diminished indefinitely; a divergent
+integral may have different (principal) values for different modes
+of contracting the extent of the omitted partial domain. In applications
+to mathematical physics great importance attaches to convergent
+integrals and to principal values of divergent integrals.
+For example, any component of magnetic force at a point within a
+magnet, and the corresponding component of magnetic induction
+at the same point are expressed by different principal values of the
+same divergent integral. Delicate questions arise as to the possibility
+of representing the integral of a function of n variables through a
+domain H<span class="su">n</span>, as a repeated integral, of evaluating it by successive
+integrations with respect to the variables one at a time and of interchanging
+the order of such integrations. These questions have been
+discussed very completely by C. Jordan, and we may quote the
+result that all the transformations in question are valid when the
+function is continuous throughout the domain.</p>
+</div>
+
+<p>20. <i>Representation of Functions in General</i>.&mdash;We have seen
+that the notion of a function is wider than the notion of an
+analytical expression, and that the same function may be
+&ldquo;represented&rdquo; by one expression in one part of the domain of
+the argument and by some other expression in another part of
+the domain (§ 5). Thus there arises the general problem of the
+representation of functions. The function may be given by
+specifying the domain of the argument and the rule of calculation,
+or else the function may have to be determined in accordance
+with certain conditions; for example, it may have to
+satisfy in a prescribed domain an assigned differential equation.
+In either case the problem is to determine, when possible, a
+single analytical expression which shall have the same value as
+the function at all points in the domain of the argument. For
+the representation of most functions for which the problem can
+be solved recourse must be had to limiting processes. Thus we
+may utilize infinite series, or infinite products, or definite integrals;
+or again we may represent a function of one variable
+as the limit of an expression containing two variables in a domain
+in which one variable remains constant and another varies.
+An example of this process is afforded by the expression
+Lt<span class="su">y</span> = &infin;xy / (x²y + 1), which represents a function of x vanishing at
+x = 0 and at all other values of x having the value of 1/x. The
+method of series falls under this more general process (cf. § 6).
+When the terms u<span class="su">1</span>, u<span class="su">2</span>, ... of a series are functions of a variable
+x, the sum s<span class="su">n</span> of the first n terms of the series is a function of x
+and n; and, when the series is convergent, its sum, which is
+Lt<span class="su">n</span> = &infin; s<span class="su">n</span>, can represent a function of x. In most cases the series
+converges for some values of x and not for others, and the values
+for which it converges form the &ldquo;domain of convergence.&rdquo;
+The sum of the series represents a function in this domain.</p>
+
+<div class="condensed">
+<p>The apparently more general method of representation of a
+function of one variable as the limit of a function of two variables
+has been shown by R. Baire to be identical in scope with the method
+of series, and it has been developed by him so as to give a very
+complete account of the possibility of representing functions by
+analytical expressions. For example, he has shown that Riemann&rsquo;s
+totally discontinuous function, which is equal to 1 when x is rational
+and to 0 when x is irrational, can be represented by an analytical
+expression. An infinite process of a different kind has been adapted
+to the problem of the representation of a continuous function by
+T. Brodén. He begins with a function having a graph in the form
+of a regular polygon, and interpolates additional angular points in
+an ordered sequence without limit. The representation of a function
+by means of an infinite product falls clearly under Baire&rsquo;s method,
+while the representation by means of a definite integral is analogous
+to Brodén&rsquo;s method. As an example of these two latter processes
+we may cite the Gamma function [&Gamma;(x)] defined for positive values
+of x by the definite integral</p>
+
+<p class="center"><span class="f150">&int;</span> <span class="sp1">&infin;</span><span class="su1">0</span> e<span class="sp">&minus;t</span> t<span class="sp">x&minus;1</span> dt,</p>
+
+<p class="noind">or by the infinite product</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">Lt<span class="su">n=&infin;</span> n<span class="sp">x</span>/x(1 + x)(1 + ½x) ... <span class="f150">(</span> 1 +</td> <td>x</td>
+<td rowspan="2"><span class="f150">)</span>.</td></tr>
+<tr><td class="denom">n &minus; 1</td></tr></table>
+
+<p class="noind">The second of these expressions avails for the representation of the
+function at all points at which x is not a negative integer.</p>
+</div>
+
+<p>21. <i>Power Series</i>.&mdash;Taylor&rsquo;s theorem leads in certain cases
+to a representation of a function by an infinite series. We have
+under certain conditions (§ 13)</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&fnof;(x) = &fnof;(a) + <span class="f150">&Sigma;</span><span class="sp1">n&minus;1</span><span class="su1">r=1</span></td> <td>(x &minus; a)<span class="sp">r</span></td>
+<td rowspan="2">&fnof;<span class="sp">(r)</span>(a) + R<span class="su">n</span>;</td></tr>
+<tr><td class="denom">r!</td></tr></table>
+
+<p class="noind">and this becomes</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&fnof;(x) = &fnof;(a) + <span class="f150">&Sigma;</span><span class="sp1">&infin;</span><span class="su1">r=1</span></td> <td>(x &minus; a)<span class="sp">r</span></td>
+<td rowspan="2">&fnof;<span class="sp">(r)</span>(a),</td></tr>
+<tr><td class="denom">r!</td></tr></table>
+
+<p class="noind">provided that (&alpha;) a positive number k can be found so that at
+all points in the interval between a and a + k (except these points)
+&fnof;(x) has continuous differential coefficients of all finite orders,
+and at a has progressive differential coefficients of all finite
+orders; (&beta;) Cauchy&rsquo;s form of the remainder <i>R<span class="su">n</span></i>, viz.
+[(x &minus; a) / (n &minus; 1)!] (1 &minus; &theta;)<span class="sp">n&minus;1</span> &fnof;<span class="sp">n</span> {a + &theta;(x &minus; a)}, has the limit zero when n increases
+indefinitely, for all values of &theta; between 0 and 1, and for
+all values of x in the interval between a and a + k, except possibly
+a + k. When these conditions are satisfied, the series (1) represents
+the function at all points of the interval between a and a + k,
+except possibly a + k, and the function is &ldquo;analytic&rdquo; (§ 13) in
+this domain. Obvious modifications admit of extension to an
+interval between a and a &minus; k, or between a &minus; k and a + k. When
+a series of the form (1) represents a function it is called &ldquo;the
+Taylor&rsquo;s series for the function.&rdquo;</p>
+
+<p>Taylor&rsquo;s series is a power series, <i>i.e</i>. a series of the form</p>
+
+<p class="center"><span class="f150">&Sigma;</span><span class="sp1">&infin;</span><span class="su1">n=0</span> a<span class="su">n</span> (x &minus; a)<span class="sp">n</span>.</p>
+
+<div class="condensed">
+<p class="noind">As regards power series we have the following theorems:</p>
+
+<p>1. If the power series converges at any point except a there is a
+number k which has the property that the series converges absolutely
+in the interval between a &minus; k and a + k, with the possible exception
+of one or both end-points.</p>
+
+<p>2. The power series represents a continuous function in its domain
+of convergence (the end-points may have to be excluded).</p>
+
+<p>3. This function is analytic in the domain, and the power series
+representing it is the Taylor&rsquo;s series for the function.</p>
+
+<p>The theory of power series has been developed chiefly from the
+point of view of the theory of functions of complex variables.</p>
+</div>
+
+<p>22. <i>Uniform Convergence</i>.&mdash;We shall suppose that the domain
+of convergence of an infinite series of functions is an interval with
+the possible exception of isolated points. Let &fnof;(x) be the sum
+of the series at any point x of the domain, and &fnof;<span class="su">n</span>(x) the sum of
+the first n + 1 terms. The condition of convergence at a point
+a is that, after any positive number &epsilon;, however small, has been
+specified, it must be possible to find a number n so that
+|&fnof;<span class="su">m</span>(a) &minus; &fnof;<span class="su">p</span>(a)| &lt; &epsilon; for all values of m and p which exceed n.
+The sum, &fnof;(a), is the limit of the sequence of numbers &fnof;<span class="su">n</span>(a) at
+<span class="pagenum"><a name="page308" id="page308"></a>308</span>
+n = &infin;. The convergence is said to be &ldquo;uniform&rdquo; in an interval
+if, after specification of &epsilon;, the same number n suffices at all
+points of the interval to make |&fnof;(x) &minus; &fnof;<span class="su">m</span>(x)| &lt; &epsilon; for all values of
+m which exceed n. The numbers n corresponding to any &epsilon;,
+however small, are all finite, but, when &epsilon; is less than some fixed
+finite number, they may have an infinite superior limit (§ 7);
+when this is the case there must be at least one point, a, of the
+interval which has the property that, whatever number N we
+take, &epsilon; can be taken so small that, at some point in the neighbourhood
+of a, n must be taken &gt; N to make |&fnof;(x) &minus; f<span class="su">m</span>(x)| &lt; &epsilon;
+when m &gt; n; then the series does not converge uniformly in the
+neighbourhood of a. The distinction may be otherwise expressed
+thus: Choose a first and &epsilon; afterwards, then the number n is
+finite; choose &epsilon; first and allow a to vary, then the number n
+becomes a function of a, which may tend to become infinite, or
+may remain below a fixed number; if such a fixed number
+exists, however small &epsilon; may be, the convergence is uniform.</p>
+
+<div class="condensed">
+<p>For example, the series sin x &minus; ½ sin 2x + <span class="spp">1</span>&frasl;<span class="suu">3</span> sin 3x &minus; ... is convergent
+for all real values of x, and, when &pi; &gt; x &gt; &minus;&pi; its sum is ½x;
+but, when x is but a little less than &pi;, the number of terms which
+must be taken in order to bring the sum at all near to the value of
+½x is very large, and this number tends to increase indefinitely as
+x approaches &pi;. This series does not converge uniformly in the
+neighbourhood of x = &pi;. Another example is afforded by the series</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">&Sigma;</span><span class="sp1">&infin;</span><span class="su1">n=0</span></td> <td>nx</td>
+<td rowspan="2">&minus;</td> <td>(n + 1)x</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">n²x² + 1</td> <td class="denom">(n + 1)²x² + 1</td></tr></table>
+
+<p class="noind">of which the remainder after n terms
+is nx/(n²x² + 1). If we put x = 1/n, for any value of n, however
+great, the remainder is ½; and the number of terms required to be
+taken to make the remainder tend to zero depends upon the value of
+x when x is near to zero&mdash;it must, in fact, be large compared with
+1/x. The series does not converge uniformly in the neighbourhood
+of x = 0.</p>
+</div>
+
+<p>As regards series whose terms represent continuous functions
+we have the following theorems:</p>
+
+<p>(1) If the series converges uniformly in an interval it represents
+a function which is continuous throughout the interval.</p>
+
+<p>(2) If the series represents a function which is discontinuous
+in an interval it cannot converge uniformly in the interval.</p>
+
+<p>(3) A series which does not converge uniformly in an interval
+may nevertheless represent a function which is continuous
+throughout the interval.</p>
+
+<p>(4) A power series converges uniformly in any interval contained
+within its domain of convergence, the end-points being
+excluded.</p>
+
+<p>(5) If <span class="f150">&Sigma;</span><span class="sp1">&infin;</span><span class="su1">r=0</span> &fnof;<span class="su">r</span>(x) = &fnof;(x) converges uniformly in the interval
+between a and b</p>
+
+<p class="center"><span class="f150">&int;</span> <span class="sp1">b</span><span class="su1">a</span> &fnof;(x)dx = <span class="f150">&Sigma;</span><span class="sp1">b</span><span class="su1">r=0</span> <span class="f150">&int;</span> <span class="sp1">b</span><span class="su1">a</span> &fnof;<span class="su">r</span>(x)dx,</p>
+
+<p class="noind">or a series which converges <span class="correction" title="amended from unformly">uniformly</span> may be integrated term by
+term.</p>
+
+<p>(6) If <span class="f150">&Sigma;</span><span class="sp1">&infin;</span><span class="su1">r=0</span> &fnof;&prime;<span class="su">r</span>(x) converges uniformly in an interval, then
+<span class="f150">&Sigma;</span><span class="sp1">&infin;</span><span class="su1">r=0</span> &fnof;<span class="su">r</span>(x) converges in the interval, and represents a continuous
+differentiable function, &phi;(x); in fact we have</p>
+
+<p class="center">&phi;&prime;(x) = <span class="f150">&Sigma;</span><span class="sp1">&infin;</span><span class="su1">r=0</span> &fnof;&prime;<span class="su">r</span>(x),</p>
+
+<p class="noind">or a series can be differentiated term by term if the series of
+derived functions converges uniformly.</p>
+
+<p>A series whose terms represent functions which are not continuous
+throughout an interval may converge uniformly in the
+interval. If <span class="f150">&Sigma;</span><span class="sp1">&infin;</span><span class="su1">r=0</span> &fnof;<span class="su">r</span>(x) = &fnof;(x), is such a series, and if all the
+functions &fnof;<span class="su">r</span>(x) have limits at a, then &fnof;(x) has a limit at a, which
+is <span class="f150">&Sigma;</span><span class="sp1">&infin;</span><span class="su1">r=0</span> Lt <span class="su">x=a</span> &fnof;<span class="su">r</span>(x). A similar theorem holds for limits on the left
+or on the right.</p>
+
+<p>23. Fourier&rsquo;s Series.&mdash;An extensive class of functions admit
+of being represented by series of the form</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">a<span class="su">0</span> + <span class="f150">&Sigma;</span><span class="sp1">&infin;</span><span class="su1">n=1</span> <span class="f150">(</span> a<span class="su">n</span> cos</td> <td>n&pi;x</td>
+<td rowspan="2">+ b<span class="su">n</span> sin</td> <td>n&pi;x</td>
+<td rowspan="2"><span class="f150">)</span>,</td></tr>
+<tr><td class="denom">c</td> <td class="denom">c</td></tr></table>
+
+<p class="noind">and the rule for determining the coefficients a<span class="su">n</span>, b<span class="su">n</span> of such a
+series, in order that it may represent a given function &fnof;(x) in
+the interval between &minus;c and c, was given by Fourier, viz. we
+have</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">a<span class="su">0</span> =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span> <span class="sp1">c</span><span class="su1">&minus;c</span> &fnof;(x)dx, &emsp; a<span class="su">n</span>=</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span> <span class="sp1">c</span><span class="su1">&minus;c</span> &fnof;(x)cos</td> <td>n&pi;x</td>
+<td rowspan="2">dx, &emsp; b<span class="su">n</span>=</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span> <span class="sp1">c</span><span class="su1">&minus;c</span> sin</td> <td>n&pi;x</td>
+<td rowspan="2">dx.</td></tr>
+<tr><td class="denom">2c</td> <td class="denom">c</td>
+<td class="denom">c</td> <td class="denom">c</td> <td class="denom">c</td></tr></table>
+
+<p class="noind">The interval between &minus;c and c may be called the &ldquo;periodic
+interval,&rdquo; and we may replace it by any other interval, <i>e.g.</i> that
+between 0 and 1, without any restriction of generality. When
+this is done the sum of the series takes the form</p>
+
+<p class="center">Lt <span class="su">n=&infin;</span> <span class="f150">&int;</span> <span class="sp1">1</span><span class="su1">0</span> <span class="f150">&Sigma;</span><span class="sp1">r = n</span><span class="su1">r = &minus;n</span> &fnof;(z) cos {2r&pi;(z &minus; x)}dz,</p>
+
+<p class="noind">and this is</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">Lt <span class="su">n=&infin;</span> <span class="f150">&int;</span> <span class="sp1">1</span><span class="su1">0</span> &fnof;(z)</td> <td>sin {(2n + 1) (z &minus; x)&pi;}</td>
+<td rowspan="2">dz.</td></tr>
+<tr><td class="denom">sin {(z &minus; x)&pi;}</td></tr></table>
+<div class="author1">(ii.)</div>
+
+<p>Fourier&rsquo;s theorem is that, if the periodic interval can be divided
+into a finite number of partial intervals within each of which the
+function is ordinary (§ 14), the series represents the function
+within each of those partial intervals. In Fourier&rsquo;s time a
+function of this character was regarded as completely arbitrary.</p>
+
+<div class="condensed">
+<p>By a discussion of the integral (ii.) based on the Second Theorem
+of the Mean (§ 15) it can be shown that, if &fnof;(x) has restricted oscillation
+in the interval (§ 11), the sum of the series is equal to ½{&fnof;(x + 0) + &fnof;(x &minus; 0)}
+at any point x within the interval, and that it is equal to
+½ {&fnof;(+0) + &fnof;(1 &minus; 0} at each end of the interval. (See the article
+<span class="sc"><a href="#artlinks">Fourier&rsquo;s Series</a></span>.) It therefore represents the function at any
+point of the periodic interval at which the function is continuous
+(except possibly the end-points), and has a definite value at each
+point of discontinuity. The condition of restricted oscillation
+includes all the functions contemplated in the statement of the
+theorem and some others. Further, it can be shown that, in any
+partial interval throughout which &fnof;(x) is continuous, the series
+converges uniformly, and that no series of the form (i), with coefficients
+other than those determined by Fourier&rsquo;s rule, can represent
+the function at all points, except points of discontinuity, in the same
+periodic interval. The result can be extended to a function &fnof;(x)
+which tends to become infinite at a finite number of points a of the
+interval, provided (1) &fnof;(x) tends to become determinately infinite
+at each of the points a, (2) the improper definite integral of &fnof;(x)
+through the interval is convergent, (3) &fnof;(x) has not an infinite number
+of discontinuities or of maxima or minima in the interval.</p>
+</div>
+
+<p>24. <i>Representation of Continuous Functions by Series</i>.&mdash;If the
+series for &fnof;(x) formed by Fourier&rsquo;s rule converges at the point
+a of the periodic interval, and if &fnof;(x) is continuous at a, the
+sum of the series is &fnof;(a); but it has been proved by P. du Bois
+Reymond that the function may be continuous at a, and yet the
+series formed by Fourier&rsquo;s rule may be divergent at a. Thus
+some continuous functions do not admit of representation by
+Fourier&rsquo;s series. All continuous functions, however, admit of
+being represented with arbitrarily close approximation in either
+of two forms, which may be described as &ldquo;terminated Fourier&rsquo;s
+series&rdquo; and &ldquo;terminated power series,&rdquo; according to the two
+following theorems:</p>
+
+<p>(1) If &fnof;(x) is continuous throughout the interval between 0 and
+2&pi;, and if any positive number &epsilon; however small is specified,
+it is possible to find an integer n, so that the difference between
+the value of &fnof;(x) and the sum of the first n terms of the series
+for &fnof;(x), formed by Fourier&rsquo;s rule with periodic interval from
+0 to 2&pi;, shall be less than &epsilon; at all points of the interval. This
+result can be extended to a function which is continuous in any
+given interval.</p>
+
+<p>(2) If &fnof;(x) is continuous throughout an interval, and any
+positive number &epsilon; however small is specified, it is possible to
+find an integer n and a polynomial in x of the nth degree, so
+that the difference between the value of &fnof;(x) and the value of the
+polynomial shall be less than &epsilon; at all points of the interval.</p>
+
+<p>Again it can be proved that, if &fnof;(x) is continuous throughout
+a given interval, polynomials in x of finite degrees can be found,
+so as to form an infinite series of polynomials whose sum is equal
+to &fnof;(x) at all points of the interval. Methods of representation
+of continuous functions by infinite series of rational fractional
+functions have also been devised.</p>
+
+<div class="condensed">
+<p>Particular interest attaches to continuous functions which are
+not differentiable. Weierstrass gave as an example the function
+represented by the series <span class="f150">&Sigma;</span> <span class="sp1">&infin;</span><span class="su1">0</span> a<span class="sp">n</span> cos (b<span class="sp">n</span> x&pi;), where a is positive and less
+than unity, and b is an odd integer exceeding (1 + <span class="spp">3</span>&frasl;<span class="suu">2</span>&pi;)/a. It can be
+shown that this series is uniformly convergent in every interval,
+<span class="pagenum"><a name="page309" id="page309"></a>309</span>
+and that the continuous function &fnof;(x) represented by it has the
+property that there is, in the neighbourhood of any point x<span class="su">0</span>, an
+infinite aggregate of points x&prime;, having x<span class="su">0</span> as a limiting point, for
+which {&fnof;(x&prime;) &minus; &fnof;(x<span class="su">0</span>)} / (x&prime; &minus; x<span class="su">0</span>) tends to become infinite with one
+sign when x&prime; &minus; x<span class="su">0</span> approaches zero through positive values, and
+infinite with the opposite sign when x&prime; &minus; x<span class="su">0</span> approaches zero through
+negative values. Accordingly the function is not differentiable at
+any point. The definite integral of such a function &fnof;(x) through the
+interval between a fixed point and a variable point x, is a continuous
+differentiable function F(x), for which F&prime;(x) = &fnof;(x); and, if &fnof;(x) is
+one-signed throughout any interval F(x) is monotonous throughout
+that interval, but yet F(x) cannot be represented by a curve. In
+any interval, however small, the tangent would have to take the
+same direction for infinitely many points, and yet there is no interval
+in which the tangent has everywhere the same direction. Further,
+it can be shown that all functions which are everywhere continuous
+and nowhere differentiable are capable of representation by series of
+the form &Sigma;a<span class="su">n</span>&phi;<span class="su">n</span>(x), where &Sigma;a<span class="su">n</span> is an absolutely convergent series of
+numbers, and &phi;<span class="su">n</span>(x) is an analytic function whose absolute value
+never exceeds unity.</p>
+</div>
+
+<p>25. <i>Calculations with Divergent Series</i>.&mdash;When the series
+described in (1) and (2) of § 24 diverge, they may, nevertheless,
+be used for the approximate numerical calculation of the values
+of the function, provided the calculation is not carried beyond a
+certain number of terms. Expansions in series which have the
+property of representing a function approximately when the
+expansion is not carried too far are called &ldquo;asymptotic expansions.&rdquo;
+Sometimes they are called &ldquo;semi-convergent series&rdquo;;
+but this term is avoided in the best modern usage, because
+it is often used to describe series whose convergence depends
+upon the order of the terms, such as the series 1 &minus; ½ + <span class="spp">1</span>&frasl;<span class="suu">3</span> &minus; ...</p>
+
+<div class="condensed">
+<p>In general, let &fnof;<span class="su">0</span>(x) + &fnof;<span class="su">1</span>(x) + ... be a series of functions which
+does not converge in a certain domain. It may happen that, if any
+number &epsilon;, however small, is first specified, a number n can afterwards
+be found so that, at a point a of the domain, the value &fnof;(a) of
+a certain function &fnof;(x) is connected with the sum of the first n + 1
+terms of the series by the relation |&fnof;(a) &minus; <span class="f150">&Sigma;</span> <span class="sp1">n</span><span class="su1">r = 0</span> &fnof;<span class="su">r</span>(a)| &lt; &epsilon;. It must
+also happen that, if any number N, however great, is specified, a
+number n&prime;(&gt;n) can be found so that, for all values of m which exceed
+n&prime;, |<span class="f150">&Sigma;</span> <span class="sp1">m</span><span class="su1">r = 0</span> &fnof;<span class="su">r</span>(a)| &gt; N. The divergent series &fnof;<span class="su">0</span>(x) + &fnof;<span class="su">1</span>(x) + ... is then an
+asymptotic expansion for the function f(x) in the domain.</p>
+
+<p>The best known example of an asymptotic expansion is Stirling&rsquo;s
+formula for n! when n is large, viz.</p>
+
+<p class="center">n! =  &radic;<span class="ov">(2&pi;)</span> ½n<span class="sp">n + ½</span> e<span class="sp">&minus;n + &theta;/12n</span>,</p>
+
+<p class="noind">where &theta; is some number lying between 0 and 1. This formula is
+included in the asymptotic expansion for the Gamma function.
+We have in fact</p>
+
+<p class="center">log {&Gamma;(x)} = (x &minus; ½) log x &minus; x + ½ log 2&pi; + <span class="ov">&omega;</span>(x),</p>
+
+<p class="noind">where <span class="ov">&omega;</span>(x) is the function defined by the definite integral</p>
+
+<p class="center"><span class="ov">&omega;</span>(x) = <span class="f150">&int;</span> <span class="sp1">&infin;</span><span class="su1">0</span>  {(1 &minus; e<span class="sp">&minus;t</span>)<span class="sp">&minus;1</span> &minus; t<span class="sp">&minus;1</span> &minus; ½} t<span class="sp">&minus;1</span> e<span class="sp">&minus;tx</span> dt.</p>
+
+<p class="noind">The multiplier of e<span class="sp">&minus;tx</span> under the sign of integration can be expanded
+in the power series</p>
+
+<table class="math0" summary="math">
+<tr> <td>B<span class="su">1</span></td>
+<td rowspan="2">&minus;</td> <td>B<span class="su">2</span></td>
+<td rowspan="2">t<span class="sp">2</span> +</td> <td>B<span class="su">3</span></td>
+<td rowspan="2">t<span class="sp">4</span> &minus; ...,</td></tr>
+<tr><td class="denom">2!</td> <td class="denom">4!</td> <td class="denom">6!</td></tr></table>
+
+<p class="noind">where B<span class="su">1</span>, B<span class="su">2</span>, ... are &ldquo;Bernoulli&rsquo;s numbers&rdquo; given by the formula</p>
+
+<p class="center">B<span class="su">m</span> = 2.2m! (2&pi;)<span class="sp">&minus;2m</span> <span class="f150">&Sigma;</span> <span class="sp1">&infin;</span><span class="su1">r = 1</span> (r<span class="sp">&minus;2m</span>).</p>
+
+<p class="noind">When the series is integrated term by term, the right-hand member
+of the equation for <span class="ov">&omega;</span>(x) takes the form</p>
+
+<table class="math0" summary="math">
+<tr><td>B<span class="su">1</span></td>
+<td rowspan="2">&nbsp;</td> <td>1</td>
+<td rowspan="2">&minus;</td> <td>B<span class="su">2</span></td>
+<td rowspan="2">&nbsp;</td> <td>1</td>
+<td rowspan="2">+</td> <td>B<span class="su">3</span></td>
+<td rowspan="2">&nbsp;</td> <td>1</td>
+<td rowspan="2">&minus; ...,</td></tr>
+<tr><td class="denom">1·2</td> <td class="denom">x</td>
+<td class="denom">3·4</td> <td class="denom">x<span class="sp">3</span></td>
+<td class="denom">5·6</td> <td class="denom">x<span class="sp">5</span></td></tr></table>
+
+<p class="noind">This series is divergent; but, if it is stopped at any term, the difference
+between the sum of the series so terminated and the value of <span class="ov">&omega;</span>(x) is
+less than the last of the retained terms. Stirling&rsquo;s formula is obtained
+by retaining the first term only. Other well-known examples of asymptotic
+expansions are afforded by the descending series for Bessel&rsquo;s
+functions. Methods of obtaining such expansions for the solutions of
+linear differential equations of the second order were investigated by
+G.G. Stokes (<i>Math. and Phys. Papers</i>, vol. ii. p. 329), and a general
+theory of asymptotic expansions has been developed by H. Poincaré.
+A still more general theory of divergent series, and of the conditions
+in which they can be used, as above, for the purposes of approximate
+calculation has been worked out by É. Borel. The great merit of
+asymptotic expansions is that they admit of addition, subtraction,
+multiplication and division, term by term, in the same way as
+absolutely convergent series, and they admit also of integration
+term by term; that is to say, the results of such operations are
+asymptotic expansions for the sum, difference, product, quotient,
+or integral, as the case may be.</p>
+</div>
+
+<p>26. <i>Interchange of the Order of Limiting Operations</i>.&mdash;When
+we require to perform any limiting operation upon a function
+which is itself represented by the result of a limiting process,
+the question of the possibility of interchanging the order of the
+two processes always arises. In the more elementary problems
+of analysis it generally happens that such an interchange is
+possible; but in general it is not possible. In other words, the
+performance of the two processes in different orders may lead
+to two different results; or the performance of them in one of the
+two orders may lead to no result. The fact that the interchange
+is possible under suitable restrictions for a particular class of
+operations is a theorem to be proved.</p>
+
+<div class="condensed">
+<p>Among examples of such interchanges we have the differentiation
+and integration of an infinite series term by term (§ 22), and the
+differentiation and integration of a definite integral with respect to
+a parameter by performing the like processes upon the subject of
+integration (§ 19). As a last example we may take the limit of the
+sum of an infinite series of functions at a point in the domain of
+convergence. Suppose that the series <span class="f150">&Sigma;</span> <span class="sp1">&infin;</span><span class="su1">0</span> &fnof;<span class="su">r</span>(x) represents a function
+(&fnof;x) in an interval containing a point a, and that each of the functions
+&fnof;<span class="su">r</span>(x) has a limit at a. If we first put x=a, and then sum the series,
+we have the value &fnof;(a); if we first sum the series for any x, and
+afterwards take the limit of the sum at x = a, we have the limit of
+&fnof;(x) at a; if we first replace each function &fnof;<span class="su">r</span>(x) by its limit at a, and
+then sum the series, we may arrive at a value different from either
+of the foregoing. If the function &fnof;(x) is continuous at a, the first and
+second results are equal; if the functions &fnof;<span class="su">r</span>(x) are all continuous at
+a, the first and third results are equal; if the series is uniformly
+convergent, the second and third results are equal. This last case
+is an example of the interchange of the order of two limiting operations,
+and a sufficient, though not always a necessary, condition,
+for the validity of such an interchange will usually be found in some
+suitable extension of the notion of uniform convergence.</p>
+
+<p><span class="sc">Authorities.</span>&mdash;Among the more important treatises and memoirs
+connected with the subject are: R. Baire, <i>Fonctions discontinues</i>
+(Paris, 1905); O. Biermann, <i>Analytische Functionen</i> (Leipzig, 1887);
+É. Borel, <i>Théorie des fonctions</i> (Paris, 1898) (containing an introductory
+account of the Theory of Aggregates), and <i>Séries divergentes</i>
+(Paris, 1901), also <i>Fonctions de variables réelles</i> (Paris, 1905); T.J.
+I&rsquo;A. Bromwich, <i>Introduction to the Theory of Infinite Series</i> (London,
+1908); H.S. Carslaw, <i>Introduction to the Theory of Fourier&rsquo;s Series
+and Integrals</i> (London, 1906); U. Dini, <i>Functionen e. reellen Grösse</i>
+(Leipzig, 1892), and <i>Serie di Fourier</i> (Pisa, 1880); A. Genocchi
+u. G. Peano, <i>Diff.- u. Int.-Rechnung</i> (Leipzig, 1899); J. Harkness
+and F. Morley, <i>Introduction to the Theory of Analytic Functions</i>
+(London, 1898); A. Harnack, <i>Diff. and Int. Calculus</i> (London, 1891);
+E.W. Hobson, <i>The Theory of Functions of a real Variable and the
+Theory of Fourier&rsquo;s Series</i> (Cambridge, 1907); C. Jordan, <i>Cours
+d&rsquo;analyse</i> (Paris, 1893-1896); L. Kronecker, <i>Theorie d. einfachen
+u. vielfachen Integrale</i> (Leipzig, 1894); H. Lebesgue, <i>Leçons sur
+l&rsquo;intégration</i> (Paris, 1904); M. Pasch, <i>Diff.- u. Int.-Rechnung</i>
+(Leipzig, 1882); E. Picard, <i>Traité d&rsquo;analyse</i> (Paris, 1891); O.
+Stolz, <i>Allgemeine Arithmetik</i> (Leipzig, 1885), and <i>Diff.- u. Int.-Rechnung</i>
+(Leipzig, 1893-1899); J. Tannery, <i>Théorie des fonctions</i>
+(Paris, 1886); W.H. and G.C. Young, <i>The Theory of Sets of Points</i>
+(Cambridge, 1906); Brodén, &ldquo;Stetige Functionen e. reellen Veränderlichen,&rdquo;
+<i>Crelle</i>, Bd. cxviii.; G. Cantor, A series of memoirs on the
+&ldquo;Theory of Aggregates&rdquo; and on &ldquo;Trigonometric series&rdquo; in <i>Acta
+Math</i>. tt. ii., vii., and <i>Math. Ann</i>. Bde. iv.-xxiii.; Darboux, &ldquo;Fonctions
+discontinues,&rdquo; <i>Ann. Sci. École normale sup</i>. (2), t. iv.; Dedekind,
+<i>Was sind u. was sollen d. Zahlen</i>? (Brunswick, 1887), and <i>Stetigkeit
+u. irrationale Zahlen</i> (Brunswick, 1872); Dirichlet, &ldquo;Convergence
+des séries trigonométriques,&rdquo; <i>Crelle</i>, Bd. iv.; P. Du Bois Reymond,
+<i>Allgemeine Functionentheorie</i> (Tübingen, 1882), and many memoirs
+in <i>Crelle</i> and in <i>Math. Ann</i>.; Heine, &ldquo;Functionenlehre,&rdquo; <i>Crelle</i>,
+Bd. lxxiv.; J. Pierpont, <i>The Theory of Functions of a real Variable</i>
+(Boston, 1905); F. Klein, &ldquo;Allgemeine Functionsbegriff,&rdquo; <i>Math.
+Ann</i>. Bd. xxii.; W.F. Osgood, &ldquo;On Uniform Convergence,&rdquo; <i>Amer.
+J. of Math</i>. vol. xix.; Pincherle, &ldquo;Funzioni analitiche secondo
+Weierstrass,&rdquo; <i>Giorn. di mat</i>. t. xviii.; Pringsheim, &ldquo;Bedingungen
+d. Taylorschen Lehrsatzes,&rdquo; <i>Math. Ann</i>. Bd. xliv.; Riemann,
+&ldquo;Trigonometrische Reihe,&rdquo; <i>Ges. Werke</i> (Leipzig, 1876); Schoenflies,
+&ldquo;Entwickelung d. Lehre v. d. Punktmannigfaltigkeiten,&rdquo; <i>Jahresber.
+d. deutschen Math.-Vereinigung</i>, Bd. viii.; Study, Memoir on
+&ldquo;Functions with Restricted Oscillation,&rdquo; <i>Math. Ann</i>. Bd. xlvii.;
+Weierstrass, Memoir on &ldquo;Continuous Functions that are not Differentiable,&rdquo;
+<i>Ges. math. Werke</i>, Bd. ii. p. 71 (Berlin, 1895), and on the
+&ldquo;Representation of Arbitrary Functions,&rdquo; ibid. Bd. iii. p. 1; W.H.
+Young, &ldquo;On Uniform and Non-uniform Convergence,&rdquo; <i>Proc. London
+Math. Soc.</i> (Ser. 2) t. 6. Further information and very full references
+will be found in the articles by Pringsheim, Schoenflies and Voss in
+the <i>Encyclopädie der math. Wissenschaften</i>, Bde. i., ii. (Leipzig, 1898,
+1899).</p>
+</div>
+<div class="author">(A. E. H. L.)</div>
+
+<p><span class="pagenum"><a name="page310" id="page310"></a>310</span></p>
+
+<p class="pt2 center sc">II&mdash;Functions of Complex Variables</p>
+
+<p>In the preceding section the doctrine of functionality is discussed
+with respect to real quantities; in this section the theory
+when complex or imaginary quantities are involved receives
+treatment. The following abstract explains the arrangement
+of the subject matter: (§ 1), <i>Complex numbers</i>, states what a
+complex number is; (§ 2), <i>Plotting of simple expressions involving
+complex numbers</i>, illustrates the meaning in some simple cases,
+introducing the notion of conformal representation and proving
+that an algebraic equation has complex, if not real, roots; (§ 3),
+<i>Limiting operations</i>, defines certain simple functions of a complex
+variable which are obtained by passing to a limit, in particular
+the exponential function, and the generalized logarithm, here
+denoted by &lambda;(z); (§ 4), <i>Functions of a complex variable in general</i>,
+after explaining briefly what is to be understood by a region of
+the complex plane and by a path, and expounding a logical
+principle of some importance, gives the accepted definition of a
+function of a complex variable, establishes the existence of a
+complex integral, and proves Cauchy&rsquo;s theorem relating thereto;
+(§ 5), <i>Applications</i>, considers the differentiation and integration
+of series of functions of a complex variable, proves Laurent&rsquo;s
+theorem, and establishes the expansion of a function of a complex
+variable as a power series, leading, in (§ 6), <i>Singular points</i>, to
+a definition of the region of existence and singular points of a
+function of a complex variable, and thence, in (§ 7), <i>Monogenic
+Functions</i>, to what the writer believes to be the simplest definition
+of a function of a complex variable, that of Weierstrass; (§ 8),
+<i>Some elementary properties of single valued functions</i>, first discusses
+the meaning of a pole, proves that a single valued function with
+only poles is rational, gives Mittag-Leffler&rsquo;s theorem, and Weierstrass&rsquo;s
+theorem for the primary factors of an integral function,
+stating generalized forms for these, leading to the theorem of
+(§ 9), <i>The construction of a monogenic function with a given region of
+existence</i>, with which is connected (§10), <i>Expression of a monogenic
+function by rational functions in a given region</i>, of which the
+method is applied in (§ 11), <i>Expression of</i> (1 &minus; z)<span class="sp">&minus;1</span> <i>by polynomials</i>,
+to a definite example, used here to obtain (§ 12), <i>An expansion
+of an arbitrary function by means of a series of polynomials, over
+a star region</i>,  also obtained in the original manner of Mittag-Leffler;
+(§ 13), <i>Application of Cauchy&rsquo;s theorem to the determination
+of definite integrals</i>, gives two examples of this method; (§ 14),
+<i>Doubly Periodic Functions</i>, is introduced at this stage as furnishing
+an excellent example of the preceding principles. The
+reader who wishes to approach the matter from the point of view
+of Integral Calculus should first consult the section (§ 20) below,
+dealing with <i>Elliptic Integrals</i>; (§ 15), <i>Potential Functions,
+Conformal representation in general</i>, gives a sketch of the connexion
+of the theory of potential functions with the theory of
+conformal representation, enunciating the Schwarz-Christoffel
+theorem for the representation of a polygon, with the application
+to the case of an equilateral triangle; (§ 16), <i>Multiple-valued
+Functions, Algebraic Functions</i>, deals for the most part with
+algebraic functions, proving the residue theorem, and establishing
+that an algebraic function has a definite Order; (§ 17), <i>Integrals
+of Algebraic Functions</i>, enunciating Abel&rsquo;s theorem; (§ 18),
+<i>Indeterminateness of Algebraic Integrals</i>, deals with the periods
+associated with an algebraic integral, establishing that for an
+elliptic integral the number of these is two; (§ 19), <i>Reversion of
+an algebraic integral</i>, mentions a problem considered below in
+detail for an elliptic integral; (§ 20), <i>Elliptic Integrals</i>, considers
+the algebraic reduction of any elliptic integral to one of three
+standard forms, and proves that the function obtained by
+reversion is single-valued; (§ 21), <i>Modular Functions</i>, gives a
+statement of some of the more elementary properties of some
+functions of great importance, with a definition of Automorphic
+Functions, and a hint of the connexion with the theory of linear
+differential equations; (§ 22), <i>A property of integral functions,
+deduced from the theory of modular functions</i>, proves that there
+cannot be more than one value not assumed by an integral
+function, and gives the basis of the well-known expression of
+the modulus of the elliptic functions in terms of the ratio of the
+periods; (§ 23), <i>Geometrical applications of Elliptic Functions</i>,
+shows that any plane curve of deficiency unity can be expressed
+by elliptic functions, and gives a geometrical proof of the addition
+theorem for the function &real;(u); (§ 24), <i>Integrals of Algebraic
+Functions in connexion with the theory of plane curves</i>, discusses
+the generalization to curves of any deficiency; (§ 25), <i>Monogenic
+Functions of several independent variables</i>, describes briefly the
+beginnings of this theory, with a mention of some fundamental
+theorems: (§ 26), <i>Multiply-Periodic Functions and the Theory
+of Surfaces</i>, attempts to show the nature of some problems now
+being actively pursued.</p>
+
+<p>Beside the brevity necessarily attaching to the account here
+given of advanced parts of the subject, some of the more elementary
+results are stated only, without proof, as, for instance:
+the monogeneity of an algebraic function, no reference being
+made, moreover, to the cases of differential equations whose
+integrals are monogenic; that a function possessing an algebraic
+addition theorem is necessarily an elliptic function (or a particular
+case of such); that any area can be conformally represented on
+a half plane, a theorem requiring further much more detailed
+consideration of the meaning of <i>area</i> than we have given; while
+the character and properties, including the connectivity, of a
+Riemann surface have not been referred to. The theta functions
+are referred to only once, and the principles of the theory of
+Abelian Functions have been illustrated only by the developments
+given for elliptic functions.</p>
+
+<p>§ 1. <i>Complex Numbers</i>.&mdash;Complex numbers are numbers of
+the form x + iy, where x, y are ordinary real numbers, and i is a
+symbol imagined capable of combination with itself and the
+ordinary real numbers, by way of addition, subtraction, multiplication
+and division, according to the ordinary commutative,
+associative and distributive laws; the symbol i is further such
+that i² = &minus;1.</p>
+
+<div class="condensed">
+<p>Taking in a plane two rectangular axes Ox, Oy, we assume that
+every point of the plane is definitely associated with two real numbers
+x, y (its co-ordinates) and conversely; thus any point of the plane is
+associated with a single complex number; in particular, for every
+point of the axis Ox, for which y = O, the associated number is an
+ordinary real number; the complex numbers thus include the real
+numbers. The axis Ox is often called the real axis, and the axis Oy
+the imaginary axis. If P be the point associated with the complex
+variable z = x + iy, the distance OP be called r, and the positive
+angle less than 2&pi; between Ox and OP be called &theta;, we may write
+z = r (cos &theta; + i sin &theta;); then r is called the modulus or absolute value
+of z and often denoted by |z| and &theta; is called the phase or amplitude
+of z, and often denoted by ph (z); strictly the phase is ambiguous
+by additive multiples of 2&pi;. If z&prime; = x&prime; + iy&prime; be represented by P&prime;,
+the complex argument z&prime; + z is represented by a point P&Prime; obtained
+by drawing from P&prime; a line equal to and parallel to OP; the geometrical
+representation involves for its validity certain properties
+of the plane; as, for instance, the equation z&prime; + z = z + z&prime; involves
+the possibility of constructing a parallelogram (with OP&Prime; as diagonal).
+It is important constantly to bear in mind, what is capable of easy
+algebraic proof (and geometrically is Euclid&rsquo;s proposition III. 7),
+that the modulus of a sum or difference of two complex numbers is
+generally less than (and is never greater than) the sum of their
+moduli, and is greater than (or equal to) the difference of their
+moduli; the former statement thus holds for the sum of any number
+of complex numbers. We shall write E(i&theta;) for cos &theta; + i sin &theta;; it is
+at once verified that E(i&alpha;). E(i&beta;) = E[i(&alpha; + &beta;)], so that the phase of a
+product of complex quantities is obtained by addition of their
+respective phases.</p>
+</div>
+
+<p>§ 2. <i>Plotting and Properties of Simple Expressions involving
+a Complex Number</i>.&mdash;If we put &zeta; = (z-i)/(z + i), and, putting
+&zeta; = &xi; + i&eta;, take a new plane upon which &xi;, &eta; are rectangular
+co-ordinates, the equations &xi;= (x² + y²&minus; 1)/[x² + (y + 1)²],
+&eta; = &minus;2xy/[x² + (y + i)²] will determine, corresponding to any
+point of the first plane, a point of the second plane. There is
+the one exception of z = &minus;i, that is, x = 0, y = &minus;1, of which the
+corresponding point is at infinity. It can now be easily proved
+that as z describes the real axis in its plane the point &zeta; describes
+once a circle of radius unity, with centre at &zeta; = 0, and that there
+is a definite correspondence of point to point between points
+in the z-plane which are above the real axis and points of the
+&zeta;-plane which are interior to this circle; in particular z = i
+corresponds to &zeta; = 0.</p>
+
+<div class="condensed">
+<p>Moreover, &zeta; being a rational function of z, both &xi; and &eta; are continuous
+differentiable functions of x and y, save when &zeta; is infinite;
+<span class="pagenum"><a name="page311" id="page311"></a>311</span>
+writing &zeta; = &fnof;(x, y) = &fnof;(z &minus; iy, y), the fact that this is really independent
+of y leads at once to &part;f/&part;x + i&part;&fnof;/&part;y = 0, and hence to</p>
+
+<table class="math0" summary="math">
+<tr><td>&part;&xi;</td>
+<td rowspan="2">=</td> <td>&part;&eta;</td>
+<td rowspan="2">,</td> <td>&part;&xi;</td>
+<td rowspan="2">= &minus;</td> <td>&part;&eta;</td>
+<td rowspan="2">,</td> <td>&part;²&xi;</td>
+<td rowspan="2">+</td> <td>&part;²&xi;</td>
+<td rowspan="2">= 0;</td></tr>
+<tr><td class="denom">&part;x</td> <td class="denom">&part;x&prime;</td>
+<td class="denom">&part;y</td> <td class="denom">&part;x&prime;</td>
+<td class="denom">&part;x²</td> <td class="denom">&part;y²</td></tr></table>
+
+<p class="noind">so that &xi; is not any arbitrary function of x, y, and when &xi; is known
+&eta; is determinate save for an additive constant. Also, in virtue of
+these equations, if &zeta;, &zeta;&prime; be the values of &zeta; corresponding to two
+near values of z, say z and z&prime;, the ratio (&zeta;&prime; &minus; &zeta;)/(z&prime; &minus; z) has a definite
+limit when z&prime; = z, independent of the ultimate phase of z&prime; &minus; z, this
+limit being therefore equal to &part;&zeta;/&part;x, that is, &part;&xi;/&part;x + i&part;&eta;)/&part;x. Geometrically
+this fact is interpreted by saying that if two curves in the
+z-plane intersect at a point P, at which both the differential coefficients
+&part;&xi;/&part;x, &part;&eta;/&part;x are not zero, and P&prime;, P&Prime; be two points near
+to P on these curves respectively, and the corresponding points of the
+&zeta;-plane be Q, Q&prime;, Q&Prime;, then (1) the ratios PP&Prime;/PP&prime;, QQ&Prime;/QQ&prime; are
+ultimately equal, (2) the angle P&prime;PP&Prime; is equal to Q&prime;QQ&Prime;, (3) the
+rotation from PP&prime; to PP&Prime; is in the same sense as from QQ&prime; to QQ&Prime;,
+it being understood that the axes of &xi;, &eta; in the one plane are related
+as are the axes of x, y. Thus any diagram of the z-plane becomes a
+diagram of the &zeta;-plane with the same angles; the magnification,
+however, which is equal to [(&part;&xi;/&part;x)² + (&part;&xi;/&part;y)² ]<span class="sp">1/2</span> varies from point to
+point. Conversely, it appears subsequently that the expression
+of any copy of a diagram (say, a map) which preserves angles requires
+the intervention of the complex variable.</p>
+
+<p>As another illustration consider the case when &zeta; is a polynomial
+in z,</p>
+
+<p class="center">&zeta; = p<span class="su">0</span>z<span class="sp">n</span> + p<span class="su">1</span>z<span class="sp">n&minus;1</span> + ... + p<span class="su">n</span>;</p>
+
+<p class="noind">H being an arbitrary real positive number, it can be shown that a
+radius R can be found such for every |z| &gt; R we have |&zeta;| &gt; H;
+consider the lower limit of |&zeta;| for |z| &lt; R; as &xi;² + &eta;² is a real
+continuous function of x, y for |z| &lt; R, there is a point (x, y),
+say (x<span class="su">0</span>, y<span class="su">0</span>), at which |&zeta;| is least, say equal to &rho;, and therefore
+within a circle in the &zeta;-plane whose centre is the origin, of radius &rho;,
+there are no points &zeta; representing values corresponding to |z| &lt; R.
+But if &zeta;<span class="su">0</span> be the value of &zeta; corresponding to (x<span class="su">0</span>, y<span class="su">0</span>), and the expression
+of &zeta; &minus; &zeta;<span class="su">0</span> near z<span class="su">0</span> = x<span class="su">0</span> + iy<span class="su">0</span>, in terms of z &minus; z<span class="su">0</span>, be A(z &minus; z<span class="su">0</span>)<span class="sp">m</span> +
+B(z &minus; z<span class="su">0</span>)<span class="sp">m + 1</span> + ..., where A is not zero, to two points near to (x<span class="su">0</span>, y<span class="su">0</span>),
+say (x<span class="su">1</span>, y<span class="su">1</span>) or z<span class="su">1</span> and
+z<span class="su">2</span> = z<span class="su">0</span> + (z<span class="su">1</span> &minus; z<span class="su">0</span>) (cos &pi;/m + i sin &pi;/m), will correspond
+two points near to &zeta;<span class="su">0</span>, say &zeta;<span class="su">1</span>, and 2&zeta;<span class="su">0</span> &minus; &zeta;&prime;<span class="su">1</span>, situated so that &zeta;<span class="su">0</span>
+is between them. One of these must be within the circle (&rho;). We
+infer then that &rho; = 0, and have proved that every polynomial in
+z vanishes for some value of z, and can therefore be written as a
+product of factors of the form z &minus; &alpha;, where &alpha; denotes a complex
+number. This proposition alone suffices to suggest the importance
+of complex numbers.</p>
+</div>
+
+<p>§ 3. <i>Limiting Operations</i>.&mdash;In order that a complex number
+&zeta; = &xi; + i&eta; may have a limit it is necessary and sufficient that each
+of &xi; and &eta; has a limit. Thus an infinite series w<span class="su">0</span> + w<span class="su">1</span> + w<span class="su">2</span> + ...,
+whose terms are complex numbers, is convergent if the real
+series formed by taking the real parts of its terms and that
+formed by the imaginary terms are both convergent. The
+series is also convergent if the real series formed by the moduli
+of its terms is convergent; in that case the series is said to be
+absolutely convergent, and it can be shown that its sum is
+unaltered by taking the terms in any other order. Generally
+the necessary and sufficient condition of convergence is that,
+for a given real positive &epsilon;, a number m exists such that for every
+n &gt; m, and every positive p, the batch of terms w<span class="su">n</span> + w<span class="su">n+1</span> +
+ ... + w<span class="su">n+p</span> is less than &epsilon; in absolute value. If the terms depend
+upon a complex variable z, the convergence is called <i>uniform</i>
+for a range of values of z, when the inequality holds, for the
+same &epsilon; and m, for all the points z of this range.</p>
+
+<div class="condensed">
+<p>The infinite series of most importance are those of which the
+general term is a<span class="su">n</span>z<span class="sp">n</span>, wherein a<span class="su">n</span> is a constant, and z is regarded as
+variable, n = 0, 1, 2, 3, ... Such a series is called a power series,
+if a real and positive number M exists such that for z = z<span class="su">0</span> and every
+n, |a<span class="su">n</span>z<span class="su">0</span><span class="sp">n</span>| &lt; M, a condition which is satisfied, for instance, if the
+series converges for z = z<span class="su">0</span>, then it is at once proved that the series
+converges absolutely for every z for which |z| &lt; |z<span class="su">0</span>|, and converges
+uniformly over every range |z| &lt; r&prime; for which r&prime; &lt; |z<span class="su">0</span>|.
+To every power series there belongs then a circle of convergence
+within which it converges absolutely and uniformly; the function
+of z represented by it is thus continuous within the circle (this being
+the result of a general property of uniformly convergent series of
+continuous functions); the sum for an interior point z is, however,
+continuous with the sum for a point z<span class="su">0</span> on the circumference, as z
+approaches to z<span class="su">0</span> provided the series converges for z = z<span class="su">0</span>, as can be
+shown without much difficulty. Within a common circle of convergence
+two power series &Sigma; a<span class="su">n</span>z<span class="sp">n</span>, &Sigma; b<span class="su">n</span>z<span class="sp">n</span> can be multiplied together
+according to the ordinary rule, this being a consequence of a theorem
+for absolutely convergent series. If r<span class="su">1</span> be less than the radius of
+convergence of a series &Sigma; a<span class="su">n</span> z<span class="sp">n</span> and for |z| = r<span class="su">1</span>, the sum of the series
+be in absolute value less than a real positive quantity M, it can be
+shown that for |z| = r<span class="su">1</span> every term is also less than M in absolute value,
+namely, |a<span class="su">n</span>| &lt; Mr<span class="su">1</span><span class="sp">&minus;n</span>. If in every arbitrarily small neighbourhood of
+z=0 there be a point for which two converging power series &Sigma;a<span class="su">n</span> z<span class="sp">n</span>,
+&Sigma;b<span class="su">n</span>z<span class="sp">n</span> agree in value, then the series are identical, or a<span class="su">n</span> = b<span class="su">n</span>; thus also
+if &Sigma;a<span class="su">n</span>z<span class="sp">n</span> vanish at z = 0 there is a circle of finite radius about z = 0 as
+centre within which no other points are found for which the sum of
+the series is zero. Considering a power series &fnof;(z) = &Sigma;a<span class="su">n</span>z<span class="sp">n</span> of radius of
+convergence R, if |z<span class="su">0</span>| &lt; R and we put z = z<span class="su">0</span> + t with |t| &lt; R-|z<span class="su">0</span>|,
+the resulting series &Sigma;a<span class="su">n</span>(z<span class="su">0</span> + t)<span class="sp">n</span> may be regarded as a double series
+in z<span class="su">0</span> and t, which, since |z<span class="su">0</span>| + t &lt; R, is absolutely convergent;
+it may then be arranged according to powers of t. Thus we may
+write &fnof;(z) = &Sigma; A<span class="su">n</span>t<span class="sp">n</span>; hence A<span class="su">0</span> = &fnof;(z<span class="su">0</span>), and we have [&fnof;(z<span class="su">0</span> + t) &minus; &fnof;(z<span class="su">0</span>)]/t =
+&Sigma;<span class="su">n=1</span> A<span class="su">n</span>t<span class="sp">n&minus;l</span>, wherein the continuous series on the right reduces to A<span class="su">1</span>
+for t = 0; thus the ratio on the left has a definite limit when t = 0,
+equal namely to A<span class="su">1</span> or &Sigma;na<span class="su">n</span>z<span class="su">0</span><span class="sp">n &minus; 1</span>. In other words, the original series
+may legitimately be differentiated at any interior point z<span class="su">0</span> of its circle
+of convergence. Repeating this process we find &fnof;(z<span class="su">0</span> + t) = &Sigma;t<span class="sp">n</span>&fnof;<span class="sp">(n)</span>(z<span class="su">0</span>)/n!,
+where &fnof;<span class="sp">(n)</span>(z<span class="su">0</span>) is the nth differential coefficient. Repeating for this
+power series, in t, the argument applied about z = 0 for &Sigma;a<span class="su">n</span>z<span class="sp">n</span>, we
+infer that for the series &fnof;(z) every point which reduces it to zero is
+an isolated point, and of such points only a finite number lie within
+a circle which is within the circle of convergence of &fnof;(z).</p>
+
+<p>Perhaps the simplest possible power series is e<span class="sp">z</span> = exp(z) = 1 + z<span class="sp">2</span>/2! +
+z<span class="sp">3</span>/3! + ... of which the radius of convergence is infinite. By
+multiplication we have exp(z)·exp(z<span class="sp">1</span>) = exp(z + z<span class="sp">1</span>). In particular
+when x, y are real, and z = x + iy, exp(z) = exp(x)exp(iy). Now the
+functions</p>
+
+<p class="center">U<span class="su">0</span> = sin y, V<span class="su">0</span> = 1 &minus; cos y, U<span class="su">1</span> = y &minus; sin y,</p>
+
+<p class="center">V<span class="su">1</span> = <span class="spp">1</span>&frasl;<span class="suu">2</span>y² &minus; 1 + cos y, U<span class="su">2</span> = <span class="spp">1</span>&frasl;<span class="suu">6</span>y³ &minus; y + sin y, V<span class="su">2</span> = <span class="spp">1</span>&frasl;<span class="suu">24</span>y<span class="sp">4</span> &minus; <span class="spp">1</span>&frasl;<span class="suu">2</span>y<span class="sp">2</span> + 1 &minus; cos y, ...</p>
+
+<p class="noind">all vanish for y = 0, and the differential coefficient of any one after
+the first is the preceding one; as a function (of a real variable) is
+increasing when its differential coefficient is positive, we infer, for
+y positive, that each of these functions is positive; proceeding to a
+limit we hence infer that</p>
+
+<p class="center">cos y = 1 &minus; <span class="spp">1</span>&frasl;<span class="suu">2</span>y² + <span class="spp">1</span>&frasl;<span class="suu">24</span>y<span class="sp">4</span> &minus; ..., &emsp; sin y = y &minus; <span class="spp">1</span>&frasl;<span class="suu">6</span>y³ + <span class="spp">1</span>&frasl;<span class="suu">120</span>y<span class="sp">5</span> &minus; ...,</p>
+
+<p class="noind">for positive, and hence, for all values of y. We thus have exp(iy) =
+cos y + i sin y, and exp (z) = exp (x)·(cos y + i sin y). In other words,
+the modulus of exp (z) is exp (x) and the phase is y. Hence also</p>
+
+<p class="center">exp(z + 2&pi;i) = exp(x) [cos (y + 2&pi;) + i sin(y + 2&pi;)],</p>
+
+<p class="noind">which we express by saying that exp (z) has the period 2&pi;i,
+and hence also the period 2k&pi;i, where k is an arbitrary integer.
+From the fact that the constantly increasing function exp (x) can
+vanish only for x = 0, we at once prove that exp (z) has no other
+periods.</p>
+
+<p>Taking in the plane of z an infinite strip lying between the lines
+y = 0, y = 2&pi; and plotting the function &zeta; = exp (z) upon a new plane,
+it follows at once from what has been said that every complex value
+of &zeta; arises when z takes in turn all positions in this strip, and that
+no value arises twice over. The equation &zeta; = exp(z) thus defines z,
+regarded as depending upon &zeta;, with only an additive ambiguity
+2k&pi;i, where k is an integer. We write z = &lambda;(&zeta;); when &zeta; is real this
+becomes the logarithm of &zeta;; in general &lambda;(&zeta;) = log |&zeta;| + i ph (&zeta;) +
+2k&pi;i, where k is an integer; and when &zeta; describes a closed circuit
+surrounding the origin the phase of &zeta; increases by 2&pi;, or k increases
+by unity. Differentiating the series for &zeta; we have d&zeta;/dz = &zeta;, so
+that z, regarded as depending upon &zeta;, is also differentiable, with
+dz/d&zeta; = &zeta;<span class="sp">&minus; 1</span>. On the other hand, consider the series &zeta; &minus; 1 &minus; ½(&zeta;&minus; 1)<span class="sp">2</span> +
+<span class="spp">1</span>&frasl;<span class="suu">3</span>(&zeta; &minus; 1)<span class="sp">3</span> &minus; ...; it converges when &zeta; = 2 and hence converges for
+|&zeta; &minus; 1| &lt; 1; its differential coefficient is, however, 1 &minus; (&zeta; &minus; 1) +
+(&zeta; &minus; 1)<span class="sp">2</span> &minus; ..., that is, (1 + &zeta; &minus; 1)<span class="sp">&minus; 1</span>. Wherefore if &phi;(&zeta;) denote this
+series, for |&zeta; &minus; 1| &lt; 1, the difference &lambda;(&zeta;) &minus; &phi;(&zeta;), regarded as a
+function of &xi; and &eta;, has vanishing differential coefficients; if we
+take the value of &lambda;(&zeta;) which vanishes when &zeta; = 1 we infer thence
+that for |&zeta; &minus; 1| &lt; 1, &lambda;(&zeta;) = &Sigma;<span class="su">n=1</span> [(&minus;1)<span class="sp">(n&minus;1)</span>/n (&zeta; &minus; 1)<span class="sp">n</span>. It is to be remarked
+that it is impossible for &zeta; while subject to |&zeta; &minus; 1| &lt; 1 to make a
+circuit about the origin. For values of &zeta; for which |&zeta; &minus; 1| &#8814; 1, we
+can also calculate &lambda;(&zeta;) with the help of infinite series, utilizing the
+fact that &lambda;(&zeta;&zeta;&prime;) = &lambda;(&zeta;) + &lambda;(&zeta;&prime;).</p>
+
+<p>The function &lambda;(&zeta;) is required to define &zeta;<span class="sp">a</span> when &zeta; and a are complex
+numbers; this is defined as exp [a&lambda;(&zeta;)], that is as &Sigma;<span class="su">n=0</span> a<span class="sp">n</span> [&lambda;(&zeta;)]<span class="sp">n</span>/n!.
+When a is a real integer the ambiguity of &lambda;(&zeta;) is immaterial here,
+since exp [a&lambda;(&zeta;) + 2ka&pi;i] = exp [a&lambda;(&zeta;)]; when a is of the form 1/q,
+where q is a positive integer, there are q values possible for &zeta;<span class="sp">1/q</span>, of
+the form exp [1/q &lambda;(&zeta;)] exp (2k&pi;i/q), with k = 0, 1, ... q &minus; 1, all other
+values of k leading to one of these; the qth power of any one of
+these values is &zeta;; when a = p/q, where p, q are integers without
+common factor, q being positive, we have &zeta;<span class="sp">p/q</span> = (&zeta;<span class="sp">1/q</span>)<span class="sp">p</span>. The
+definition of the symbol &zeta;<span class="sp">a</span> is thus a generalization of the ordinary
+definition of a power, when the numbers are real. As an example,
+let it be required to find the meaning of i<span class="sp">i</span>; the number i is of
+modulus unity and phase ½&pi;; thus &lambda;(i) = i (½&pi; + 2k&pi;); thus</p>
+
+<p class="center">i<span class="sp">i</span> = exp (&minus;½&pi; &minus; 2k&pi;) = exp (&minus;½&pi;) exp (&minus;2k&pi;),</p>
+
+<p class="noind">is always real, but has an infinite number of values.</p>
+
+<p><span class="pagenum"><a name="page312" id="page312"></a>312</span></p>
+
+<p>The function exp (z) is used also to define a generalized form of
+the cosine and sine functions when z is complex; we write, namely,
+cos z = ½[exp (iz) + exp (&minus;iz)] and sin z = &minus;½i [exp (iz) &minus; exp(&minus;iz)].
+It will be found that these obey the ordinary relations holding when
+z is real, except that their moduli are not inferior to unity. For
+example, cos i = 1 + 1/2! + 1/4! + ... is obviously greater than unity.</p>
+</div>
+
+<p>§4. <i>Of Functions of a Complex Variable in General</i>.&mdash;We have
+in what precedes shown how to generalize the ordinary rational,
+algebraic and logarithmic functions, and considered more
+general cases, of functions expressible by power series in z.
+With the suggestions furnished by these cases we can frame a
+general definition. So far our use of the plane upon which z is
+represented has been only illustrative, the results being capable
+of analytical statement. In what follows this representation is
+vital to the mode of expression we adopt; as then the properties
+of numbers cannot be ultimately based upon spatial intuitions,
+it is necessary to indicate what are the geometrical ideas requiring
+elucidation.</p>
+
+<div class="condensed">
+<p>Consider a square of side a, to whose perimeter is attached a
+definite direction of description, which we take to be counter-clockwise;
+another square, also of side a, may be added to this, so
+that there is a side common; this common side being erased we
+have a composite region with a definite direction of perimeter;
+to this a third square of the same size may be attached, so
+that there is a side common to it and one of the former squares,
+and this common side may be erased. If this process be continued
+any number of times we obtain a region of the plane bounded by one
+or more polygonal closed lines, no two of which intersect; and at
+each portion of the perimeter there is a definite direction of description,
+which is such that the region is on the left of the describing
+point. Similarly we may construct a region by piecing together
+triangles, so that every consecutive two have a side in common,
+it being understood that there is assigned an upper limit for the
+greatest side of a triangle, and a lower limit for the smallest angle.
+In the former method, each square may be divided into four others
+by lines through its centre parallel to its sides; in the latter method
+each triangle may be divided into four others by lines joining the
+middle points of its sides; this halves the sides and preserves the
+angles. When we speak of a <i>region</i> of the plane in general, unless
+the contrary is stated, we shall suppose it capable of being generated
+in this latter way by means of a finite number of triangles, there
+being an upper limit to the length of a side of the triangle and a
+lower limit to the size of an angle of the triangle. We shall also
+require to speak of a <i>path</i> in the plane; this is to be understood as
+capable of arising as a limit of a polygonal path of finite length,
+there being a definite direction or sense of description at every point
+of the path, which therefore never meets itself. From this the
+meaning of a closed path is clear. The boundary points of a region
+form one or more closed paths, but, in general, it is only in a limiting
+sense that the interior points of a closed path are a region.</p>
+
+<p>There is a logical principle also which must be referred to. We
+frequently have cases where, about every interior or boundary,
+point z<span class="su">0</span> of a certain region a circle can be put, say of radius r<span class="su">0</span>, such
+that for all points z of the region which are interior to this circle,
+for which, that is, |z &minus; z<span class="su">0</span>| &lt; r<span class="su">0</span>, a certain property holds. Assuming
+that to r<span class="su">0</span> is given the value which is the upper limit for z<span class="su">0</span>, of the
+possible values, we may call the points |z &minus; z<span class="su">0</span>| &lt; r<span class="su">0</span>, the neighbourhood
+belonging to or <i>proper</i> to z<span class="su">0</span>, and may speak of the property
+as the property (z, z<span class="su">0</span>). The value of r<span class="su">0</span> will in general vary with z<span class="su">0</span>;
+what is in most cases of importance is the question whether the
+lower limit of r<span class="su">0</span> for all positions is zero or greater than zero. (A)
+This lower limit is certainly greater than zero provided the property
+(z, z<span class="su">0</span>) is of a kind which we may call extensive; such, namely, that
+if it holds, for some position of z<span class="su">0</span> and all positions of z, within a certain
+region, then the property (z, z<span class="su">1</span>) holds within a circle of radius R
+about any interior point z<span class="su">1</span> of this region for all points z for which
+the circle |z &minus; z<span class="su">1</span>| = R is within the region. Also in this case r<span class="su">0</span>
+varies continuously with z<span class="su">0</span>. (B) Whether the property is of this
+extensive character or not we can prove that the region can be divided
+into a finite number of sub-regions such that, for every one of these,
+the property holds, (1) for <i>some</i> point z<span class="su">0</span> within or upon the boundary
+of the sub-region, (2) for <i>every</i> point z within or upon the boundary
+of the sub-region.</p>
+
+<p>We prove these statements (A), (B) in reverse order. To prove
+(B) let a region for which the property (z, z<span class="su">0</span>) holds for all points z and
+some point z<span class="su">0</span> of the region, be called <i>suitable</i>: if each of the triangles
+of which the region is built up be suitable, what is desired is proved;
+if not let an unsuitable triangle be subdivided into four, as before
+explained; if one of these subdivisions is unsuitable let it be again
+subdivided; and so on. Either the process terminates and then
+what is required is proved; or else we obtain an indefinitely continued
+sequence of unsuitable triangles, each contained in the
+preceding, which converge to a point, say &zeta;; after a certain stage
+all these will be interior to the proper region of &zeta;; this, however, is
+contrary to the supposition that they are all unsuitable.</p>
+
+<p>We now make some applications of this result (B). Suppose a
+definite finite real value attached to every interior or boundary
+point of the region, say &fnof;(x, y). It may have a finite upper limit H
+for the region, so that no point (x, y) exists for which &fnof;(x, y) &gt; H,
+but points (x, y) exist for which &fnof;(x, y) &gt; H &minus; &epsilon;, however small &epsilon; may
+be; if not we say that its upper limit is infinite. There is then at
+least one point of the region such that, for points of the region within
+a circle about this point, the upper limit of &fnof;(x, y) is H, however
+small the radius of the circle be taken; for if not we can put about
+every point of the region a circle within which the upper limit of
+&fnof;(x, y) is less than H; then by the result (B) above the region
+consists of a finite number of sub-regions within each of which the
+upper limit is less than H; this is inconsistent with the hypothesis
+that the upper limit for the whole region is H. A similar statement
+holds for the lower limit. A case of such a function &fnof;(x, y) is the
+radius r<span class="su">0</span> of the neighbourhood proper to any point z<span class="su">0</span>, spoken of
+above. We can hence prove the statement (A) above.</p>
+
+<p>Suppose the property (z, z<span class="su">0</span>) extensive, and, if possible, that the
+lower limit of r<span class="su">0</span> is zero. Let then &zeta; be a point such that the lower
+limit of r<span class="su">0</span> is zero for points z<span class="su">0</span> within a circle about &zeta; however small;
+let r be the radius of the neighbourhood proper to &zeta;; take z<span class="su">0</span> so
+that |z<span class="su">0</span>-&zeta;| &lt; ½r; the property (z, z<span class="su">0</span>), being extensive, holds
+within a circle, centre z<span class="su">0</span>, of radius r &minus; |z<span class="su">0</span> &minus; &zeta;|, which is greater
+than |z<span class="su">0</span> &minus; &zeta;|, and increases to r as |z<span class="su">0</span> &minus; &zeta;| diminishes; this being
+true for all points z<span class="su">0</span> near &zeta;, the lower limit of r<span class="su">0</span> is not zero for the
+neighbourhood of &zeta;, contrary to what was supposed. This proves
+(A). Also, as is here shown that r<span class="su">0</span> &#8925; r &minus; |z<span class="su">0</span> &minus; &zeta;|, may similarly be
+shown that r &#8925; r<span class="su">0</span> &minus; |z<span class="su">0</span> &minus; &zeta;|. Thus r<span class="su">0</span> differs arbitrarily little from
+r when |z<span class="su">0</span> &minus; &zeta;| is sufficiently small; that is, r<span class="su">0</span> varies continuously
+with z<span class="su">0</span>. Next suppose the function &fnof;(x, y), which has a
+definite finite value at every point of the region considered, to be
+continuous but not necessarily real, so that about every point z<span class="su">0</span>,
+within or upon the boundary of the region, &eta; being an arbitrary real
+positive quantity assigned beforehand, a circle is possible, so that
+for all points z of the region interior to this circle, we have
+|&fnof;(x, y) &minus;&fnof;(x<span class="su">0</span>, y<span class="su">0</span>)| &lt; ½&eta;, and therefore (x&prime;, y&prime;) being any other point
+interior to this circle, |&fnof;(x&prime;, y&prime;) &minus; &fnof;(x, y)| &lt; &eta;. We can then apply
+the result (A) obtained above, taking for the neighbourhood proper
+to any point z<span class="su">0</span> the circular area within which, for any two points
+(x, y), (x&prime;, y&prime;), we have |&fnof;(x&prime;, x&prime;) &minus; &fnof;(x, y)| &lt; &eta;. This is clearly an
+extensive property. Thus, a number r is assignable, greater than
+zero, such that, for any two points (x, y), (x&prime;, y&prime;) within a circle
+|z &minus; z<span class="su">0</span>| = r about any point z<span class="su">0</span>, we have |&fnof;(x&prime;, y&prime;) &minus; &fnof;(x, y)| &lt; &eta;,
+and, in particular, |&fnof;(x, y) &minus;&fnof;(x<span class="su">0</span>, y<span class="su">0</span>)| &lt; &eta;, where &eta; is an arbitrary
+real positive quantity agreed upon beforehand.</p>
+
+<p>Take now any path in the region, whose extreme points are z<span class="su">0</span>, z,
+and let z<span class="su">1</span>, ... z<span class="su">n&minus;1</span> be intermediate points of the path, in order;
+denote the continuous function &fnof;(x, y) by &fnof;(z), and let &fnof;<span class="su">r</span> denote any
+quantity such that |&fnof;<span class="su">r</span> &minus; &fnof;(z<span class="su">r</span>)| &#8924; |&fnof;(z<span class="su">r+1</span>) &minus; &fnof;(z<span class="su">r</span>)|; consider the sum</p>
+
+<p class="center">(z<span class="su">1</span> &minus; z<span class="su">0</span>)&fnof;<span class="su">0</span> + (z<span class="su">2</span> &minus; z<span class="su">1</span>)&fnof;<span class="su">1</span> + ... + (z &minus; z<span class="su">n&minus;1</span>)&fnof;<span class="su">n&minus;1</span>.</p>
+
+<p class="noind">By the definition of a path we can suppose, n being large enough,
+that the intermediate points z<span class="su">1</span>, ... z<span class="su">n &minus; 1</span> are so taken that if z<span class="su">i</span>,
+z<span class="su">i + 1</span> be any two points intermediate, in order, to z<span class="su">r</span> and z<span class="su">r + 1</span>, we have
+|z<span class="su">i + i</span>-z<span class="su">i</span>| &lt; |z<span class="su">r+1</span> &minus; z<span class="su">r</span>|; we can thus suppose |z<span class="su">1</span> &minus; z<span class="su">0</span>|, |z<span class="su">2</span> &minus; z<span class="su">1</span>|, ...
+|z &minus; z<span class="su">n&minus;1</span>|all to converge constantly to zero. This being so, we can
+show that the sum above has a definite limit. For this it is sufficient,
+as in the case of an integral of a function of one real variable, to
+prove this to be so when the convergence is obtained by taking new
+points of division intermediate to the former ones. If, however,
+z<span class="su">r, 1</span>, z<span class="su">r, 2</span>, ... z<span class="su">r, m&minus;1</span> be intermediate in order to z<span class="su">r</span> and z<span class="su">r+1</span>, and
+|&fnof;<span class="su">r, i</span> &minus; &fnof;(z<span class="su">r, i</span>)| &lt; |&fnof;(z<span class="su">r, i+1</span>) &minus; &fnof;(z<span class="su">r, i</span>)|, the difference between &Sigma;(z<span class="su">r+1</span> &minus; z<span class="su">r</span>)&fnof;<span class="su">r</span>
+and</p>
+
+<p class="center"><span class="f150">&Sigma;</span> { (z<span class="su">r, 1</span>-z<span class="su">r</span>)&fnof;<span class="su">r, 0</span> + (z<span class="su">r, 2</span> &minus; z<span class="su">r, 1</span>)&fnof;<span class="su">r, 1</span> + ... + (z<span class="su">r+1</span> &minus; z<span class="su">r, m&minus;1</span>)&fnof;<span class="su">r, m&minus;1</span> },</p>
+
+<p class="noind">which is equal to</p>
+
+<p class="center"><span class="f150">&Sigma;</span><span class="su">r</span> <span class="f150">&Sigma;</span><span class="su">i</span> (z<span class="su">r, i+1</span> &minus; z<span class="su">r, i</span>) (&fnof;<span class="su">r, i</span> &minus; &fnof;<span class="su">r</span>),</p>
+
+<p class="noind">is, when |z<span class="su">r+1</span> &minus; z<span class="su">r</span>| is small enough, to ensure |&fnof;(z<span class="su">r+1</span>) &minus; &fnof;(z<span class="su">r</span>)| &lt; &eta;,
+less in absolute value than</p>
+
+<p class="center"><span class="f150">&Sigma;</span>2&eta; <span class="f150">&Sigma;</span> |z<span class="su">r, i+1</span> &minus; z<span class="su">r, i</span>|,</p>
+
+<p class="noind">which, if S be the upper limit of the perimeter of the polygon from
+which the path is generated, is &lt; 2&eta;S, and is therefore arbitrarily
+small.</p>
+
+<p>The limit in question is called <span class="f150">&int;</span> <span class="sp1">z</span><span class="su1">z0</span> &fnof;(z)dz. In particular when
+&fnof;(z) = 1, it is obvious from the definition that its value is z &minus; z<span class="su">0</span>;
+when &fnof;(z) = z, by taking &fnof;<span class="su">r</span> = ½(z<span class="su">r+1</span> &minus; z<span class="su">r</span>), it is equally clear that its
+value is ½(z² &minus; z<span class="su">0</span>²); these results will be applied immediately.</p>
+
+<p>Suppose now that to every interior and boundary point z<span class="su">0</span> of a
+certain region there belong two definite finite numbers &fnof;(z<span class="su">0</span>), F(z<span class="su">0</span>),
+such that, whatever real positive quantity &eta; may be, a real positive
+number &epsilon; exists for which the condition</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">|</span></td> <td>&fnof;(z) &minus; &fnof;(z<span class="su">0</span>)</td>
+<td rowspan="2">&minus; F(z<span class="su">0</span>) <span class="f150">|</span> &lt; &eta;,</td></tr>
+<tr><td class="denom">z &minus; z<span class="su">0</span></td></tr></table>
+
+<p class="noind">which we describe as the condition (z, z<span class="su">0</span>), is satisfied for every point z,
+within or upon the boundary of the region, satisfying the limitation
+|z &minus; z<span class="su">0</span>| &lt; &epsilon;. Then &fnof;(z<span class="su">0</span>) is called a differentiable function of the
+complex variable z<span class="su">0</span> over this region, its differential coefficient being
+F(z<span class="su">0</span>). The function &fnof;(z<span class="su">0</span>) is thus a continuous function of the real
+<span class="pagenum"><a name="page313" id="page313"></a>313</span>
+variables x<span class="su">0</span>, y<span class="su">0</span>, where z<span class="su">0</span> = x<span class="su">0</span> + iy<span class="su">0</span>, over the region; it will appear
+that F(z<span class="su">0</span>) is also continuous and in fact also a differentiable function
+of z<span class="su">0</span>.</p>
+
+<p>Supposing &eta; to be retained the same for all points z<span class="su">0</span> of the region,
+and &sigma;<span class="su">0</span> to be the upper limit of the possible values of &epsilon; for the point z<span class="su">0</span>,
+it is to be presumed that &sigma;<span class="su">0</span> will vary with z<span class="su">0</span>, and it is not obvious
+as yet that the lower limit of the values of &sigma;<span class="su">0</span> as z<span class="su">0</span> varies over the
+region may not be zero. We can, however, show that the region
+can be divided into a finite number of sub-regions for each of which
+the condition (z, z<span class="su">0</span>), above, is satisfied for all points z, within or upon
+the boundary of this sub-region, for an appropriate position of z<span class="su">0</span>,
+within or upon the boundary of this sub-region. This is proved
+above as result (B).</p>
+
+<p>Hence it can be proved that, for a differentiable function &fnof;(z),
+the integral <span class="f150">&int;</span> <span class="sp1">z</span><span class="su1">z1</span> &fnof;(z)dz has the same value by whatever path within
+the region we pass from z<span class="su">1</span> to z. This we prove by showing that when
+taken round a closed path in the region the integral &int;&fnof;(z)dz vanishes.
+Consider first a triangle over which the condition (z, z<span class="su">0</span>) holds, for
+some position of z<span class="su">0</span> and every position of z, within or upon the
+boundary of the triangle. Then as</p>
+
+<p class="center">&fnof;(z) = &fnof;(z<span class="su">0</span>) + (z &minus; z<span class="su">0</span>) F(z<span class="su">0</span>) + &eta;&theta;(z &minus; z<span class="su">0</span>), where |&theta;| &lt; 1,</p>
+
+<p class="noind">we have</p>
+
+<p class="center">&int;&fnof;(z)dz = [&fnof;(z<span class="su">0</span>) &minus; z<span class="su">0</span> F(z<span class="su">0</span>)] &int;dz + F(z<span class="su">0</span>) &int;zdz + &eta;&int;&theta;(z &minus; z<span class="su">0</span>)dz,</p>
+
+<p class="noind">which, as the path is closed, is &eta; &int;&theta;(z &minus; z<span class="su">0</span>)dz. Now, from the theorem
+that the absolute value of a sum is less than the sum of the absolute
+values of the terms, this last is less, in absolute value, than &eta;ap,
+where a is the greatest side of the triangle and p is its perimeter; if
+&Delta; be the area of the triangle, we have &Delta; = ½ab sin C &gt; (&alpha;/&pi;) ba, where
+&alpha; is the least angle of the triangle, and hence a(a + b + c) &lt; 2a(b + c)
+&lt; 4&pi;&Delta;/&alpha;; the integral &int;&fnof;(z)dz round the perimeter of the triangle
+is thus &lt; 4&pi;&eta;&Delta;/&alpha;. Now consider any region made up of triangles,
+as before explained, in each of which the condition (z, z<span class="su">0</span>) holds, as
+in the triangle just taken. The integral &int;&fnof;(z)dz round the boundary
+of the region is equal to the sum of the values of the integral round
+the component triangles, and thus less in absolute value than
+4&pi;&eta;K/&alpha;, where K is the whole area of the region, and &alpha; is the smallest
+angle of the component triangles. However small &eta; be taken,
+such a division of the region into a finite number of component
+triangles has been shown possible; the integral round the perimeter
+of the region is thus arbitrarily small. Thus it is actually zero,
+which it was desired to prove. Two remarks should be added:
+(1) The theorem is proved only on condition that the closed path of
+integration belongs to the region at every point of which the conditions
+are satisfied. (2) The theorem, though proved only when
+the region consists of triangles, holds also when the boundary points
+of the region consist of one or more closed paths, no two of which
+meet.</p>
+
+<p>Hence we can deduce the remarkable result that the value of &fnof;(z)
+at any interior point of a region is expressible in terms of the value
+of &fnof;(z) at the boundary points. For consider in the original region
+the function &fnof;(z)/(z &minus; z<span class="su">0</span>), where z<span class="su">0</span> is an interior point: this satisfies
+the same conditions as &fnof;(z) except in the immediate neighbourhood
+of z<span class="su">0</span>. Taking out then from the original region a small regular
+polygonal region with z<span class="su">0</span> as centre, the theorem holds for the remaining
+portion. Proceeding to the limit when the polygon becomes a
+circle, it appears that the integral <span class="f150">&int;</span> dz&fnof;(z)/(z &minus; z<span class="su">0</span>) round the boundary of
+the original region is equal to the same integral taken counter-clockwise
+round a small circle having z<span class="su">0</span> as centre; on this circle,
+however, if z &minus; z<span class="su">0</span> = rE(i&theta;), dz/(z &minus; z<span class="su">0</span>) = id&theta;, and &fnof;(z) differs arbitrarily
+little from f(z<span class="su">0</span>) if r is sufficiently small; the value of the integral
+round this circle is therefore, ultimately, when r vanishes, equal to
+2&pi;i&fnof;(z<span class="su">0</span>). Hence &fnof;(z<span class="su">0</span>) = 1/2&pi;i <span class="f150">&int;</span> (dt&fnof;(t)/(t &minus; z<span class="su">0</span>), where this integral is round the
+boundary of the original region. From this it appears that</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">F(z<span class="su">0</span>) = lim.</td> <td>&fnof;(z) &minus; &fnof;(z<span class="su">0</span>)</td>
+<td rowspan="2">=</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span></td> <td>dt&fnof;(t)</td></tr>
+<tr><td class="denom">z &minus; z<span class="su">0</span></td> <td class="denom">2&pi;i</td>
+<td class="denom">(t &minus; z<span class="su">0</span>)²</td></tr></table>
+
+<p class="noind">also round the boundary of the original region. This form shows,
+however, that F(z<span class="su">0</span>) is a continuous, finite, differentiable function of z<span class="su">0</span>
+over the whole interior of the original region.</p>
+</div>
+
+<p>§ 5. <i>Applications.</i>&mdash;The previous results have manifold applications.</p>
+
+<div class="condensed">
+<p>(1) If an infinite series of differentiable functions of z be
+uniformly convergent along a certain path lying with the region
+of definition of the functions, so that S(2) = u<span class="su">0</span>(z) + u<span class="su">1</span>(z) + ... +
+u<span class="su">n&minus;1</span>(z) + R<span class="su">n</span>(z), where |R<span class="su">n</span>(z)| &lt; &epsilon; for all points of the path, we have</p>
+
+<table class="math0" summary="math">
+<tr><td>
+<span class="f150">&int;</span> <span class="sp1">z</span><span class="su1">z0</span> S(z)dz = <span class="f150">&int;</span> <span class="sp1">z</span><span class="su1">z0</span> u<span class="su">0</span>(z)dz + <span class="f150">&int;</span> <span class="sp1">z</span><span class="su1">z0</span> u<span class="su">1</span>(z)dz + ... + <span class="f150">&int;</span> <span class="sp1">z</span><span class="su1">z0</span>  u<span class="su">n&minus;1</span>(z)dz + <span class="f150">&int;</span> <span class="sp1">z</span><span class="su1">z0</span> R<span class="su">n</span>(z)dz,
+</td></tr></table>
+
+<p class="noind">wherein, in absolute value, <span class="f150">&int;</span> <span class="sp1">z</span><span class="su1">z0</span> R<span class="su">n</span>(z)dz &lt; &epsilon;L, if L be the length of the
+path. Thus the series may be integrated, and the resulting series
+is also uniformly convergent.</p>
+
+<p>(2) If &fnof;(x, y) be definite, finite and continuous at every point of a
+region, and over any closed path in the region &int;&fnof;(x, y)dz = 0, then
+&psi;(z) = <span class="f150">&int;</span> <span class="sp1">z</span><span class="su1">z0</span> &fnof;(x, y)dz, for interior points z<span class="su">0</span>, z, is a differentiable function
+of z, having for its differential coefficient the function &fnof;(x, y), which
+is therefore also a differentiable function of z at interior points.</p>
+
+<p>(3) Hence if the series u<span class="su">0</span>(z) + u<span class="su">1</span>(z) + ... to &infin; be uniformly convergent
+over a region, its terms being differentiable functions of z,
+then its sum S(z) is a differentiable function of z, whose differential
+coefficient, given by (1/2&pi;i) &int; 2&pi;i/(t &minus; z)², is obtainable by differentiating the
+series. This theorem, unlike (1), does not hold for functions of a
+real variable.</p>
+
+<p>(4) If the region of definition of a differentiable function &fnof;(z)
+include the region bounded by two concentric circles of radii r, R,
+with centre at the origin, and z<span class="su">0</span> be an interior point of this region,</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&fnof;(z<span class="su">0</span>) =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span></td> <td>&fnof;(t)dt</td>
+<td rowspan="2">&minus;</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span></td> <td>&fnof;(t)dt</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">2&pi;i</td> <td class="denom">R<span class="sp">t</span> &minus; z<span class="su">0</span></td>
+<td class="denom">2&pi;i</td> <td class="denom">r<span class="sp">t</span> &minus; z<span class="su">0</span></td></tr></table>
+
+<p class="noind">where the integrals are both counter-clockwise
+round the two circumferences respectively; putting in the
+first (t &minus; z<span class="su">0</span>)<span class="sp">&minus;1</span> = <span class="f150">&Sigma;</span><span class="su">n=0</span> z<span class="su">0</span><span class="sp">n</span>/t<span class="sp">n+1</span>, and in the second (t &minus; z<span class="su">0</span>)<span class="sp">&minus;1</span> = &minus; <span class="f150">&Sigma;</span><span class="su">n=0</span> t<span class="sp">n</span>/z<span class="su">0</span><span class="sp">n+1</span>,
+we find &fnof;(z<span class="su">0</span>) = <span class="f150">&Sigma;</span> <span class="sp1">&infin;</span><span class="su1">&minus;&infin;</span> A<span class="su">n</span>z<span class="su">0</span><span class="sp">n</span>, wherein A<span class="su">n</span> = (1/2&pi;i) <span class="f150">&int;</span> [&fnof;(t)/t<span class="sp">n+1</span>] dt, taken round any
+circle, centre the origin, of radius intermediate between r and R.
+Particular cases are: (&alpha;) when the region of definition of the
+function includes the whole interior of the outer circle; then we
+may take r = 0, the coefficients A<span class="su">n</span> for which n &lt; 0 all vanish, and
+the function &fnof;(z<span class="su">0</span>) is expressed for the whole interior |z<span class="su">0</span>| &lt; R by a
+power series <span class="f150">&Sigma;</span> <span class="sp1">&infin;</span><span class="su1">0</span> A<span class="su">n</span>z<span class="su">0</span><span class="sp">n</span>. In other words, <i>about every interior point c of
+the region of definition a differentiable function of z is expressible by a
+power series in z &minus; c</i>; a very important result.</p>
+
+<p>(&beta;) If the region of definition, though not including the origin,
+extends to within arbitrary nearness of this on all sides, and at the
+same time the product z<span class="sp">m</span>&fnof;(z) has a finite limit when |z| diminishes
+to zero, all the coefficients A<span class="su">n</span> for which n &lt; &minus;m vanish, and we have</p>
+
+<p class="center">f(z<span class="su">0</span>) = A<span class="su">&minus;m</span>z<span class="su">0</span><span class="sp">&minus;m</span> + A<span class="su">&minus;m+1</span>z<span class="su">0</span><span class="sp">&minus;m+1</span> + ... + A<span class="su">&minus;1</span>z<span class="su">0</span><span class="sp">&minus;1</span> + A<span class="su">0</span> + A<span class="su">1</span>z<span class="su">0</span> ... to &infin;.</p>
+
+<p class="noind">Such a case occurs, for instance, when &fnof;(z) = cosec z, the number m
+being unity.</p>
+</div>
+
+<p>§ 6. <i>Singular Points.</i>&mdash;The <i>region of existence</i> of a differentiable
+function of z is an unclosed aggregate of points, each of which
+is an interior point of a neighbourhood consisting wholly of
+points of the aggregate, at every point of which the function is
+definite and finite and possesses a unique finite differential
+coefficient. Every point of the plane, not belonging to the
+aggregate, which is a limiting point of points of the aggregate,
+such, that is, that points of the aggregate lie in every neighbourhood
+of this, is called a <i>singular point</i> of the function.</p>
+
+<div class="condensed">
+<p>About every interior point z<span class="su">0</span> of the region of existence the function
+may be represented by a power series in z &minus; z<span class="su">0</span>, and the series converges
+and represents the function over any circle centre at z<span class="su">0</span>
+which contains no singular point in its interior. This has been
+proved above. And it can be similarly proved, putting z = 1/&zeta;,
+that if the region of existence of the function contains all points of
+the plane for which |z| &gt; R, then the function is representable for
+all such points by a power series in z<span class="sp">&minus; 1</span> or &zeta;; in such case we say
+that the region of existence of the function contains the point z = &infin;.
+A series in z<span class="sp">&minus; 1</span> has a finite limit when |z| = &infin;; a series in z cannot
+remain finite for all points z for which |z| &gt; R; for if, for |z| = R,
+the sum of a power series &Sigma;a<span class="su">n</span>z<span class="sp">n</span> in z is in absolute value less than M,
+we have |a<span class="su">n</span>| &lt; Mr<span class="sp">&minus;n</span>, and therefore, if M remains finite for all values
+of r however great, a<span class="su">n</span> = 0. Thus the region of existence of a function
+if it contains all finite points of the plane cannot contain the point
+z = &infin;; such is, for instance, the case of the function exp (z) = &Sigma;z<span class="sp">n</span>/n!.
+This may be regarded as a particular case of a well-known result
+(§ 7), that the circumference of convergence of any power series
+representing the function contains at least one singular point. As
+an extreme case functions exist whose region of existence is circular,
+there being a singular point in every arc of the circumference,
+however small; for instance, this is the case for the functions represented
+for |z| &lt; 1 by the series <span class="f150">&Sigma;</span> <span class="su">n=0</span> z<span class="sp">m</span>, where m = n², the series <span class="f150">&Sigma;</span> <span class="su">n=0</span>z<span class="sp">m</span>
+where m = n!, and the series <span class="f150">&Sigma;</span> <span class="su">n=1</span> z<span class="sp">m</span>/(m + 1)(m + 2) where m = a<span class="sp">n</span>,
+a being a positive integer, although in the last case the series actually
+converges for every point of the circle of convergence |z| = 1. If z
+be a point interior to the circle of convergence of a series representing
+the function, the series may be rearranged in powers of z &minus; z<span class="su">0</span>; as z<span class="su">0</span>
+approaches to a singular point of the function, lying on the circle
+of convergence, the radii of convergence of these derived series in
+z &minus; z<span class="su">0</span> diminish to zero; when, however, a circle can be put about z<span class="su">0</span>,
+not containing any singular point of the function, but containing
+points outside the circle of convergence of the original series, then
+the series in z &minus; z<span class="su">0</span> gives the value of the function for these external
+points. If the function be supposed to be given only for the interior
+of the original circle, by the original power series, the series in z &minus; z<span class="su">0</span>
+converging beyond the original circle gives what is known as an
+<i>analytical continuation</i> of the function. It appears from what has
+<span class="pagenum"><a name="page314" id="page314"></a>314</span>
+been proved that the value of the function at all points of its region
+of existence can be obtained from its value, supposed given by a
+series in one original circle, by a succession of such processes of
+analytical continuation.</p>
+</div>
+
+<p>§ 7. <i>Monogenic Functions</i>.&mdash;This suggests an entirely different
+way of formulating the fundamental parts of the theory of
+functions of a complex variable, which appears to be preferable
+to that so far followed here.</p>
+
+<div class="condensed">
+<p>Starting with a convergent power series, say in powers of z, this
+series can be arranged in powers of z &minus; z<span class="su">0</span>, about any point z<span class="su">0</span> interior
+to its circle of convergence, and the new series converges certainly for
+|z &minus; z<span class="su">0</span>| &lt; r &minus; |z<span class="su">0</span>|, if r be the original radius of convergence. If for
+every position of z<span class="su">0</span> this is the greatest radius of convergence of the
+derived series, then the original series represents a function existing
+only within its circle of convergence. If for some position of z<span class="su">0</span>
+the derived series converges for |z &minus; z<span class="su">0</span>| &lt; r &minus; |z<span class="su">0</span>| + D, then it can be
+shown that for points z, interior to the original circle, lying in the
+annulus r &minus; |z<span class="su">0</span>| &lt; |z &minus; z<span class="su">0</span>| &lt; r &minus; |z<span class="su">0</span>| + D, the value represented by the
+derived series agrees with that represented by the original series.
+If for another point z<span class="su">1</span> interior to the original circle the derived series
+converges for |z &minus; z<span class="su">1</span>| &lt; r &minus; |z<span class="su">1</span>| + E, and the two circles |z &minus; z<span class="su">0</span>| =
+r &minus; |z<span class="su">0</span>| + D, |z &minus; z<span class="su">1</span>| = r &minus; |z<span class="su">1</span>| + E have interior points common, lying
+beyond |z| = r, then it can be shown that the values represented by
+these series at these common points agree. Either series then can
+be used to furnish an analytical continuation of the function as
+originally defined. Continuing this process of continuation as far
+as possible, we arrive at the conception of the function as defined
+by an aggregate of power series of which every one has points of
+convergence common with some one or more others; the whole
+aggregate of points of the plane which can be so reached constitutes
+the region of existence of the function; the limiting points of this
+region are the points in whose neighbourhood the derived series have
+radii of convergence diminishing indefinitely to zero; these are the
+singular points. The circle of convergence of any of the series has
+at least one such singular point upon its circumference. So regarded
+the function is called a <i>monogenic</i> function, the epithet having reference
+to the single origin, by one power series, of the expressions
+representing the function; it is also sometimes called a <i>monogenic
+analytical</i> function, or simply an <i>analytical</i> function; all that is
+necessary to define it is the value of the function and of all its
+differential coefficients, at some one point of the plane; in the method
+previously followed here it was necessary to suppose the function
+differentiable at every point of its region of existence. The theory
+of the integration of a monogenic function, and Cauchy&rsquo;s theorem,
+that &int;&fnof;(z)dz = 0 over a closed path, are at once deducible from the
+corresponding results applied to a single power series for the interior
+of its circle of convergence. There is another advantage belonging
+to the theory of monogenic functions: the theory as originally given
+here applies in the first instance only to single valued functions; a
+monogenic function is by no means necessarily single valued&mdash;it may
+quite well happen that starting from a particular power series,
+converging over a certain circle, and applying the process of analytical
+continuation over a closed path back to an interior point of this circle,
+the value obtained does not agree with the initial value. The
+notion of basing the theory of functions on the theory of power
+series is, after Newton, largely due to Lagrange, who has some
+interesting remarks in this regard at the beginning of his <i>Théorie
+des fonctions analytiques</i>. He applies the idea, however, primarily
+to functions of a real variable for which the expression by power
+series is only of very limited validity; for functions of a complex
+variable probably the systematization of the theory owes most to
+Weierstrass, whose use of the word monogenic is that adopted above.
+In what follows we generally suppose this point of view to be regarded
+as fundamental.</p>
+</div>
+
+<p>§ 8. <i>Some Elementary Properties of Single Valued Functions</i>.&mdash;A
+<i>pole</i> is a singular point of the function &fnof;(z) which is not a
+singularity of the function 1/&fnof;(z); this latter function is therefore,
+by the definition, capable of representation about this point,
+z<span class="su">0</span>, by a series [&fnof;(z)]<span class="sp">&minus;1</span> = &Sigma;a<span class="su">n</span>(z &minus; z<span class="su">0</span>)<span class="sp">n</span>. If herein a<span class="su">0</span> is not zero we
+can hence derive a representation for &fnof;(z) as a power series about
+z<span class="su">0</span>, contrary to the hypothesis that z<span class="su">0</span> is a singular point for this
+function. Hence a<span class="su">0</span> = 0; suppose also a<span class="su">1</span> = 0, a<span class="su">2</span> = 0, ... a<span class="su">m&minus;1</span> = 0,
+but a<span class="su">m</span> ± 0. Then [&fnof;(z)]<span class="sp">&minus;1</span> = (z &minus; z<span class="su">0</span>)<span class="sp">m</span>[a<span class="su">m</span> + a<span class="su">m+1</span> (z &minus; z<span class="su">0</span>) + ...], and
+hence (z &minus; z<span class="su">0</span>)<span class="sp">m</span>&fnof;(z) = a<span class="su">m</span><span class="sp">&minus;1</span> + &Sigma;b<span class="su">n</span> (z &minus; z<span class="su">0</span>)<span class="sp">n</span>, namely, the expression of
+&fnof;(z) about z = z<span class="su">0</span> contains a finite number of negative powers
+of z &minus; z<span class="su">0</span> and a (finite or) infinite number of positive powers.
+Thus a pole is always an isolated singularity.</p>
+
+<div class="condensed">
+<p>The integral &int;&fnof;(z)dz taken by a closed circuit about the pole not
+containing any other singularity is at once seen to be 2&pi;iA<span class="su">1</span>, where
+A<span class="su">1</span> is the coefficient of (z &minus; z<span class="su">0</span>)<span class="sp">&minus;1</span> in the expansion of &fnof;(z) at the pole;
+this coefficient has therefore a certain uniqueness, and it is called
+the <i>residue of &fnof;(z) at the pole</i>. Considering a region in which there
+are no other singularities than poles, all these being interior points,
+<i>the integral (1/2&pi;i) <span class="f150">&int;</span> &fnof;(z)dz round the boundary of this region is equal to
+the sum of the residues at the included poles</i>, a very important result.
+Any singular point of a function which is not a pole is called an
+<i>essential singularity</i>; if it be isolated the function is capable, in the
+neighbourhood of this point, of approaching arbitrarily near to any
+assigned value. For, the point being isolated, the function can be
+represented, in its neighbourhood, as we have proved, by a series
+<span class="f150">&Sigma;</span> <span class="sp1">&infin;</span><span class="su1">&minus;&infin;</span> a<span class="su">n</span>(z &minus; z<span class="su">0</span>)<span class="sp">n</span>; it thus cannot remain finite in the immediate neighbourhood
+of the point. The point is necessarily an isolated essential
+singularity also of the function {&fnof;(z) &minus; A}<span class="sp">&minus;1</span> for if this were expressible
+by a power series about the point, so would also the function &fnof;(z)
+be; as {&fnof;(z) &minus; A}<span class="sp">&minus; 1</span> approaches infinity, so does &fnof;(z) approach the
+arbitrary value A. Similar remarks apply to the point z = &infin;, the
+function being regarded as a function of &zeta; = z<span class="sp">&minus;1</span>. In the neighbourhood
+of an essential singularity, which is a limiting point also of
+poles, the function clearly becomes infinite. For an essential singularity
+which is not isolated the same result does not necessarily
+hold.</p>
+</div>
+
+<p>A single valued function is said to be an <i>integral</i> function
+when it has no singular points except z = &infin;. Such is, for
+instance, an integral polynomial, which has z = &infin; for a pole, and
+the functions exp (z) which has z = &infin; as an essential singularity.
+A function which has no singular points for finite values of
+z other than poles is called a <i>meromorphic</i> function. If it also
+have a pole at z = &infin; it is a <i>rational</i> function; for then, if
+a<span class="su">1</span>, ... a<span class="su">s</span> be its finite poles, of orders m<span class="su">1</span>; m<span class="su">2</span>, ... m<span class="su">s</span>, the
+product (z &minus; a<span class="su">1</span>)<span class="sp">m<span class="su">1</span></span> ... (z &minus; a<span class="su">s</span>) <span class="sp">m<span class="su">s</span></span>&fnof;(z) is an integral function with
+a pole at infinity, capable therefore, for large values of z, of an
+expression (z<span class="sp">&minus;1</span>)<span class="sp">&minus;m</span> <span class="f150">&Sigma;</span> <span class="su">r=0</span> a<span class="su">r</span>(z<span class="sp">&minus;1</span>)<span class="sp">r</span>; thus (z &minus; a<span class="su">1</span>)<span class="sp">m1</span> ... (z &minus; a<span class="su">s</span>)<span class="sp">m<span class="su">s</span></span>&fnof;(z)
+is capable of a form <span class="f150">&Sigma;</span> <span class="su">r=0</span> b<span class="su">r</span>z<span class="sp">r</span>, but z<span class="sp">&minus;m</span> <span class="f150">&Sigma;</span> <span class="su">r=0</span> b<span class="su">r</span>z<span class="sp">r</span> remains finite for
+z = &infin;. Therefore b<span class="su">r+1</span> = b<span class="su">r+2</span> = ... = 0, and&fnof;(z) is a rational
+function.</p>
+
+<div class="condensed">
+<p>If for a single valued function F(z) every singular point in the
+finite part of the plane is isolated there can only be a finite
+number of these in any finite part of the plane, and they can be
+taken to be a<span class="su">1</span>, a<span class="su">2</span>, a<span class="su">3</span>, ... with |a<span class="su">1</span>| &#8924; |a<span class="su">2</span>| &#8924; |a<span class="su">3</span>| ... and limit
+|a<span class="su">n</span>| = &infin;. About a<span class="su">s</span> the function is expressible as <span class="f150">&Sigma;</span> <span class="sp1">&infin;</span><span class="su1">&minus;&infin;</span> A<span class="su">n</span>(z &minus; a<span class="su">s</span>)<span class="sp">n</span>;
+let &fnof;<span class="su">s</span>(z) = <span class="f150">&Sigma;</span> <span class="sp1">1</span><span class="su1">&minus;&infin;</span> A<span class="sp">n</span>(z &minus; a<span class="su">s</span>)<span class="sp">n</span> be the sum of the negative powers in this
+expansion. Assuming z = 0 not to be a singular point, let &fnof;<span class="su">s</span>(z) be
+expanded in powers of z, in the form <span class="f150">&Sigma;</span> <span class="su">n=0</span> C<span class="su">n</span>z<span class="sp">n</span>, and &mu;<span class="su">s</span> be chosen so
+that F<span class="su">s</span>(z) = &fnof;<span class="su">s</span>(z) &minus; <span class="f150">&Sigma;</span> <span class="sp1">&mu;<span class="su">s</span>&minus;1</span><span class="su1">1</span> C<span class="su">n</span>z<span class="sp">n</span> = <span class="f150">&Sigma;</span> <span class="sp1">&infin;</span><span class="su1">&mu;<span class="su">s</span></span> C<span class="su">n</span>z<span class="sp">n</span> is, for |z| &lt; r<span class="su">s</span> &lt; |a<span class="su">s</span>|, less in absolute
+value than the general term &epsilon;<span class="su">s</span> of a fore-agreed convergent series of
+real positive terms. Then the series &phi;(z) = <span class="f150">&Sigma;</span> <span class="sp1">&infin;</span><span class="su1">s=1</span> F<span class="su">s</span>(z) converges uniformly
+in any finite region of the plane, other than at the points a<span class="su">s</span>,
+and is expressible about any point by a power series, and near
+a<span class="su">s</span>, &phi;(z) &minus; f<span class="su">s</span>(z) is expressible by a power series in z &minus; a<span class="su">s</span>. Thus
+F(z) &minus; &phi;(z) is an integral function. In particular when all the finite
+singularities of F(z) are poles, F(z) is hereby expressed as the sum
+of an integral function and a series of rational functions. The
+condition |F<span class="su">s</span>(z)| &lt; &epsilon;<span class="su">s</span> is imposed only to render the series &Sigma;F<span class="su">s</span>(z)
+uniformly convergent; this condition may in particular cases be
+satisfied by a series <span class="f150">&Sigma;</span> G<span class="su">s</span>(z) where G<span class="su">s</span>(z) = &fnof;<span class="su">s</span>(z) &minus; <span class="f150">&Sigma;</span> <span class="sp1">&nu;<span class="su">s</span>&minus;1</span><span class="su1">1</span> C<span class="su">n</span>z<span class="sp">n</span> and &nu;<span class="su">s</span> &lt; &mu;<span class="su">s</span>.
+An example of the theorem is the function &pi; cot &pi;z &minus; z<span class="sp">&minus; 1</span> for which,
+taking at first only half the poles, &fnof;<span class="su">s</span>(z) = 1/(z &minus; s); in this case the
+series <span class="f150">&Sigma;</span> F<span class="su">s</span>(z) where F<span class="su">s</span>(z) = (z &minus; s)<span class="sp">&minus;1</span> + s<span class="sp">&minus;1</span> is uniformly convergent;
+thus &pi; cot &pi;z &minus; z<span class="sp">&minus;1</span> &minus; <span class="f150">&Sigma;</span> <span class="sp1">&infin;</span><span class="su1">&minus;&infin;</span> [(z &minus; s)<span class="sp">&minus;1</span> + s<span class="sp">&minus;1</span>], where s = 0 is excluded from
+the summation, is an integral function. It can be proved that this
+integral function vanishes.</p>
+
+<p>Considering an integral function &fnof;(z), if there be no finite positions
+of z for which this function vanishes, the function &lambda;[&fnof;(z)] is at once
+seen to be an integral function, &phi;(z), or &fnof;(z) = exp[&phi;(z)]; if however
+great R may be there be only a finite number of values of z for which
+&fnof;(z) vanishes, say z = a<span class="su">1</span>, ... a<span class="su">m</span>, then it is at once seen that &fnof;(z) =
+exp [&phi;(z)]. (z &minus; a<span class="su">1</span>)<span class="sp">h1</span>...(z &minus; a<span class="su">m</span>)<span class="sp">h<span class="su">m</span></span>, where &phi;(z) is an integral function,
+and h<span class="su">1</span>, ... h<span class="su">m</span> are positive integers. If, however, &fnof;(z) vanish for z = a<span class="su">1</span>,
+a<span class="su">2</span> ... where |a<span class="su">1</span>| &#8924; |a2| &#8924; ... and limit |a<span class="su">n</span>| = &infin;, and if for simplicity
+we assume that z &minus; 0 is not a zero and all the zeros a<span class="su">1</span>, a<span class="su">2</span>, ... are
+of the first order, we find, by applying the preceding theorem to
+the function [1 / &fnof;(z)] [d&fnof;(z) / dz], that &fnof;(z) = exp [&phi;(z)] <span class="f150">&Pi;</span> <span class="sp1">&infin;</span><span class="su1">n=1</span> {(1 &minus; z/a<span class="su">n</span>) exp &phi;<span class="su">n</span>(z)},
+where &phi;(z) is an integral function, and &phi;<span class="su">n</span>(z) is an integral polynomial
+of the form &phi;<span class="su">n</span>(z) = z/a<span class="su">n</span> + z<span class="sp">2</span>/2a<span class="su">n</span><span class="sp">2</span> + ... + z<span class="sp">s</span>/sa<span class="su">n</span><span class="sp">s</span>. The number s may be the
+same for all values of n, or it may increase indefinitely with n; it is
+sufficient in any case to take s = n. In particular for the function
+<span class="pagenum"><a name="page315" id="page315"></a>315</span>
+sin&pi;x/&pi;x, we have</p>
+
+<table class="math0" summary="math">
+<tr><td>sin &pi;x</td>
+<td rowspan="2">= <span class="f150">&Pi;</span> <span class="sp1">&infin;</span><span class="su1">&minus;&infin;</span> <span class="f150">{ (</span>1 &minus;</td> <td>x</td>
+<td rowspan="2"><span class="f150">)</span> exp <span class="f150">(</span></td> <td>x</td>
+<td rowspan="2"><span class="f150">) }</span>,</td></tr>
+<tr><td class="denom">&pi;x</td> <td class="denom">n</td>
+<td class="denom">n</td></tr></table>
+
+<p class="noind">where n = 0 is excluded from the product. Or again we have</p>
+
+<table class="math0" summary="math">
+<tr><td>1</td>
+<td rowspan="2">= xe<span class="sp">C<span class="su">x</span></span> <span class="f150">&Pi;</span> <span class="sp1">&infin;</span><span class="su1">n=1</span> <span class="f150">{ (</span>1 +</td> <td>x</td>
+<td rowspan="2"><span class="f150">)</span> exp <span class="f150">(</span> &minus;</td> <td>x</td>
+<td rowspan="2"><span class="f150">) }</span>,</td></tr>
+<tr><td class="denom">&Gamma;(x)</td> <td class="denom">n</td>
+<td class="denom">n</td></tr></table>
+
+<p class="noind">where C is a constant, and &Gamma;(x) is a function expressible when x is
+real and positive by the integral <span class="f150">&int;</span> <span class="sp1">&infin;</span><span class="su1">0</span> e<span class="sp">&minus;t</span> t<span class="sp">x&minus;1</span>dt.</p>
+
+<p>There exist interesting investigations as to the connexion of the
+value of s above, the law of increase of the modulus of the integral
+function &fnof;(z), and the law of increase of the coefficients in the series
+&fnof;(z) = <span class="f150">&Sigma;</span> a<span class="su">n</span>z<span class="sp">n</span> as n increases (see the bibliography below under <i>Integral
+Functions</i>). It can be shown, moreover, that an integral function
+actually assumes every finite complex value, save, in exceptional
+cases, one value at most. For instance, the function exp (z) assumes
+every finite value except zero (see below under § 21, <i>Modular
+Functions</i>).</p>
+</div>
+
+<p>The two theorems given above, the one, known as Mittag-Leffler&rsquo;s
+theorem, relating to the expression as a sum of simpler
+functions of a function whose singular points have the point
+z = &infin; as their only limiting point, the other, Weierstrass&rsquo;s
+factor theorem, giving the expression of an integral function as
+a product of factors each with only one zero in the finite part of
+the plane, may be respectively generalized as follows:&mdash;</p>
+
+<div class="condensed">
+<p>I. If a<span class="su">1</span>, a<span class="su">2</span>, a<span class="su">3</span>, ... be an infinite series of isolated points having
+the points of the aggregate (c) as their limiting points, so that in
+any neighbourhood of a point of (c) there exists an infinite number
+of the points a<span class="su">1</span>, a<span class="su">2</span>, ..., and with every point a<span class="su">i</span> there be associated
+a polynomial in (z &minus; a<span class="su">i</span>)<span class="sp">&minus;1</span>, say g<span class="su">i</span>; then there exists a single valued
+function whose region of existence excludes only the points (a) and
+the points (c), having in a point a<span class="su">i</span> a pole whereat the expansion
+consists of the terms g<span class="su">i</span>, together with a power series in z &minus; a<span class="su">i</span>;
+the function is expressible as an infinite series of terms g<span class="su">i</span> &minus; &gamma;<span class="su">i</span>,
+where &gamma;<span class="su">i</span> is also a rational function.</p>
+
+<p>II. With a similar aggregate (a), with limiting points (c), suppose
+with every point a<span class="su">i</span> there is associated a positive integer r<span class="su">i</span>. Then
+there exists a single valued function whose region of existence
+excludes only the points (c), vanishing to order r<span class="su">i</span> at the point a<span class="su">i</span>,
+but not elsewhere, expressible in the form</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">&Pi;</span> <span class="sp1">&infin;</span><span class="su1">n=1</span> <span class="f150">(</span> 1 &minus;</td> <td>a<span class="su">n</span> &minus; c<span class="su">n</span></td>
+<td rowspan="2"><span class="f150">)</span> <span class="sp1">r <span class="su">n</span></span> exp (g<span class="su">n</span>),</td></tr>
+<tr><td class="denom">z &minus; c<span class="su">n</span></td></tr></table>
+
+<p class="noind">where with every point a<span class="su">n</span> is associated a proper point c<span class="su">n</span> of (c), and</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">g<span class="su">n</span> = r<span class="su">n</span> <span class="f150">&Sigma;</span> <span class="sp1">&mu; <span class="su">n</span></span><span class="su1">s=1</span></td> <td>1</td>
+<td rowspan="2"><span class="f150">(</span></td> <td>a<span class="su">n</span> &minus; c<span class="su">n</span></td>
+<td rowspan="2"><span class="f150">)</span> <span class="sp1">s</span>,</td></tr>
+<tr><td class="denom">s</td> <td class="denom">z &minus; c<span class="su">n</span></td></tr></table>
+
+<p class="noind">&mu;<span class="su">n</span> being a properly chosen positive integer.</p>
+
+<p>If it should happen that the points (c) determine a path dividing
+the plane into separated regions, as, for instance, if a<span class="su">n</span> = R(1 &minus; n<span class="sp">&minus;1</span>) exp (i&pi; &radic;2·n),
+when (c) consists of the points of the circle |z| = R, the
+product expression above denotes different monogenic functions in
+the different regions, not continuable into one another.</p>
+</div>
+
+<p>§ 9. <i>Construction of a Monogenic Function with a given Region
+of Existence.</i>&mdash;A series of isolated points interior to a given
+region can be constructed in infinitely many ways whose limiting
+points are the boundary points of the region, or are boundary
+points of the region of such denseness that one of them is found
+in the neighbourhood of every point of the boundary, however
+small. Then the application of the last enunciated theorem
+gives rise to a function having no singularities in the interior of
+the region, but having a singularity in a boundary point in every
+small neighbourhood of every boundary point; this function
+has the given region as region of existence.</p>
+
+<p>§ 10. <i>Expression of a Monogenic Function by means of Rational
+Functions in a given Region.</i>&mdash;Suppose that we have a region R<span class="su">0</span>
+of the plane, as previously explained, for all the interior or
+boundary points of which z is finite, and let its boundary points,
+consisting of one or more closed polygonal paths, no two of
+which have a point in common, be called C<span class="su">0</span>. Further suppose
+that all the points of this region, including the boundary points,
+are interior points of another region R, whose boundary is
+denoted by C. Let z be restricted to be within or upon the
+boundary of C<span class="su">0</span>; let a, b, ... be finite points upon C or outside
+R. Then when b is near enough to a, the fraction (a &minus; b)/(z &minus; b)
+is arbitrarily small for all positions of z; say</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">|</span></td> <td>a &minus; b</td>
+<td rowspan="2"><span class="f150">|</span> &lt; &epsilon;, for |a &minus; b| &lt; &eta;;</td></tr>
+<tr><td class="denom">z &minus; b</td></tr></table>
+
+<p class="noind">the rational function of the complex variable t,</p>
+
+<table class="math0" summary="math">
+<tr><td>1</td>
+<td rowspan="2"><span class="f150">[</span> 1 &minus; <span class="f150">(</span></td> <td>a &minus; b</td>
+<td rowspan="2"><span class="f150">)</span><span class="sp1">n</span> <span class="f150">]</span>,</td></tr>
+<tr><td class="denom">t &minus; a</td> <td class="denom">t &minus; a</td></tr></table>
+
+<p class="noind">in which n is a positive integer, is not infinite at t = a, but has a
+pole at t = b. By taking n large enough, the value of this function,
+for all positions z of t belonging to R<span class="su">0</span>, differs as little as may be
+desired from (t &minus; a)<span class="sp">&minus;1</span>. By taking a sum of terms such as</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">F = <span class="f150">&Sigma;</span> A<span class="su">p</span> <span class="f150">{</span></td> <td>1</td>
+<td rowspan="2"><span class="f150">[</span> 1 &minus; <span class="f150">(</span></td> <td>a &minus; b</td>
+<td rowspan="2"><span class="f150">)</span> <span class="sp1">n</span> <span class="f150">] }</span> <span class="sp1">p</span>,</td></tr>
+<tr><td class="denom">t &minus; a</td> <td class="denom">t &minus; b</td></tr></table>
+
+<p class="noind">we can thus build a rational function differing, in value, in
+R<span class="su">0</span>, as little as may be desired from a given rational function</p>
+
+<p class="center">&fnof; = <span class="f150">&Sigma;</span> A<span class="su">p</span>(t &minus; a)<span class="sp">&minus;p</span>,</p>
+
+<p class="noind">and differing, outside R or upon the boundary of R, from &fnof;,
+in the fact that while &fnof; is infinite at t = a, F is infinite only at
+t = b. By a succession of steps of this kind we thus have the
+theorem that, given a rational function of t whose poles are
+outside R or upon the boundary of R, and an arbitrary point c
+outside R or upon the boundary of R, which can be reached by a
+finite continuous path outside R from all the poles of the rational
+function, we can build another rational function differing in R<span class="su">0</span>
+arbitrarily little from the former, whose poles are all at the
+point c.</p>
+
+<div class="condensed">
+<p>Now any monogenic function &fnof;(t) whose region of definition includes
+C and the interior of R can be represented at all points z in R<span class="su">0</span> by</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&fnof;(z) =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span></td> <td>&fnof;(t)dt</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">2&pi;i</td> <td class="denom">t &minus; z</td></tr></table>
+
+<p class="noind">where the path of integration is C. This integral is the limit of a
+sum</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">S =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&Sigma;</span></td> <td>&fnof;(t<span class="su">i</span>) (t<span class="su">i+1</span> &minus; t<span class="su">i</span>)</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">2&pi;i</td> <td class="denom">t<span class="su">i</span> &minus; z</td></tr></table>
+
+<p class="noind">where the points t<span class="su">i</span> are upon C; and the proof we have given of the
+existence of the limit shows that the sum S converges to &fnof;(z) uniformly
+in regard to z, when z is in R<span class="su">0</span>, so that we can suppose, when
+the subdivision of C into intervals t<span class="su">i+1</span> &minus; t<span class="su">i</span>, has been carried sufficiently
+far, that</p>
+
+<p class="center">|S &minus; &fnof;(z)| &lt; &epsilon;,</p>
+
+<p class="noind">for all points z of R<span class="su">0</span>, where &epsilon; is arbitrary and agreed upon beforehand.
+The function S is, however, a rational function of z with poles upon C,
+that is external to R<span class="su">0</span>. We can thus find a rational function differing
+arbitrarily little from S, and therefore arbitrarily little from &fnof;(z),
+for all points z of R<span class="su">0</span>, with poles at arbitrary positions outside R<span class="su">0</span>
+which can be reached by finite continuous curves lying outside R
+from the points of C.</p>
+
+<p>In particular, to take the simplest case, if C<span class="su">0</span>, C be simple closed
+polygons, and &Gamma; be a path to which C approximates by taking the
+number of sides of C continually greater, we can find a rational
+function differing arbitrarily little from &fnof;(z) for all points of R<span class="su">0</span> whose
+poles are at one finite point c external to &Gamma;. By a transformation
+of the form t &minus; c = r<span class="sp">&minus;1</span>, with the appropriate change in the rational
+function, we can suppose this point c to be at infinity, in which case
+the rational function becomes a polynomial. Suppose &epsilon;<span class="su">1</span>, &epsilon;<span class="su">2</span>, ...
+to be an indefinitely continued sequence of real positive numbers,
+converging to zero, and P<span class="su">r</span> to be the polynomial such that, within
+C<span class="su">0</span>, |P<span class="su">r</span> &minus; &fnof;(z)| &lt; &epsilon;<span class="su">r</span>; then the infinite series of polynomials</p>
+
+<p class="center">P<span class="su">1</span>(z) + {P<span class="su">2</span>(z) &minus; P<span class="su">1</span>(z)} + {P<span class="su">3</span>(z) &minus; P<span class="su">2</span>(z)} + ...,</p>
+
+<p class="noind">whose sum to n terms is P<span class="su">n</span>(z), converges for all finite values of z and
+represents &fnof;(z) within C<span class="su">0</span>.</p>
+
+<p>When C consists of a series of disconnected polygons, some of
+which may include others, and, by increasing indefinitely the number
+of sides of the polygons C, the points C become the boundary points
+&Gamma; of a region, we can suppose the poles of the rational function,
+constructed to approximate to &fnof;(z) within R<span class="su">0</span>, to be at points of &Gamma;.
+A series of rational functions of the form</p>
+
+<p class="center">H<span class="su">1</span>(z) + {H<span class="su">2</span>(z) &minus; H<span class="su">1</span>(z)} + {H<span class="su">3</span>(z) &minus; H<span class="su">2</span>(z)} + ...</p>
+
+<p class="noind">then, as before, represents &fnof;(z) within R<span class="su">0</span>. And R<span class="su">0</span> may be taken to
+coincide as nearly as desired with the interior of the region bounded
+by &Gamma;.</p>
+</div>
+
+<p>§ 11. <i>Expression of</i> (1 &minus; z)<span class="sp">&minus;1</span> <i>by means of Polynomials. Applications.</i>&mdash;We
+pursue the ideas just cursorily explained in some
+further detail.</p>
+
+<div class="condensed">
+<p>Let c be an arbitrary real positive quantity; putting the complex
+variable &zeta; = &xi; + i&eta;, enclose the points &zeta; = l, &zeta; = 1 + c by means
+of (i.) the straight lines &eta; = ±a, from &xi; = l to &xi; = 1 + c, (ii.) a semicircle
+convex to &zeta; = 0 of equation (&xi; &minus; 1)<span class="sp">2</span> + &eta;<span class="sp">2</span> = a<span class="sp">2</span>, (iii.) a semicircle
+concave to &zeta; = 0 of equation (&xi; &minus; 1 &minus; c)<span class="sp">2</span> + &eta;<span class="sp">2</span> = a<span class="sp">2</span>. The quantities
+c and a are to remain fixed. Take a positive integer r so that
+1/r (c/a) is less than unity, and put &sigma; = 1/r (c/a). Now take</p>
+
+<p class="center">c<span class="su">1</span> = 1 + c/r, c<span class="su">2</span> = 1 + 2c/r, ... c<span class="su">r</span> = 1 + c;</p>
+
+<p><span class="pagenum"><a name="page316" id="page316"></a>316</span></p>
+
+<p class="noind">if n<span class="su">1</span>, n<span class="su">2</span>, ... n<span class="su">r</span>, be positive integers, the rational function</p>
+
+<table class="math0" summary="math">
+<tr><td>1</td>
+<td rowspan="2"><span class="f150">{</span> 1 &minus; <span class="f150">(</span></td> <td>c<span class="su">1</span> &minus; 1</td>
+<td rowspan="2"><span class="f150">)</span> <span class="sp1">n<span class="su">1</span></span> <span class="f150">}</span></td></tr>
+<tr><td class="denom">1 &minus; &zeta;</td> <td class="denom">c<span class="su">1</span> &minus; &zeta;</td></tr></table>
+
+<p class="noind">is finite at &zeta; = 1, and has a pole of order n<span class="su">1</span> at &zeta; = c<span class="su">1</span>; the rational
+function</p>
+
+<table class="math0" summary="math">
+<tr><td>1</td>
+<td rowspan="2"><span class="f150">{</span> 1 &minus; <span class="f150">(</span></td> <td>c<span class="su">1</span> &minus; 1</td>
+<td rowspan="2"><span class="f150">)</span> <span class="sp1">n<span class="su">1</span></span> <span class="f150">} {</span> 1 &minus; <span class="f150">(</span></td> <td>c<span class="su">2</span> &minus; c<span class="su">1</span></td>
+<td rowspan="2"><span class="f150">)</span> <span class="sp1">n<span class="su">2</span></span> <span class="f150">}</span> <span class="sp1">n<span class="su">1</span></span></td></tr>
+<tr><td class="denom">1 &minus; &zeta;</td> <td class="denom">c<span class="su">1</span> &minus; &zeta;</td>
+<td class="denom">c<span class="su">2</span> &minus; &zeta;</td></tr></table>
+
+<p class="noind">is thus finite except for &zeta; = c<span class="su">2</span>, where it has a pole of order n<span class="su">1</span>n<span class="su">2</span>;
+finally, writing</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">x<span class="su">s</span> = <span class="f150">(</span></td> <td>c<span class="su">s</span> &minus; c<span class="su">s&minus;1</span></td>
+<td rowspan="2"><span class="f150">)</span> <span class="sp1">n<span class="su">s</span></span>,</td></tr>
+<tr><td class="denom">c<span class="su">s</span> &minus; &zeta;</td></tr></table>
+
+<p class="noind">the rational function</p>
+
+<table class="math0" summary="math"><tr><td>
+U = (1 &minus; &zeta;)<span class="sp">&minus;1</span> (1 &minus; x<span class="su">1</span>) (1 &minus; x<span class="su">2</span>)<span class="sp">n<span class="su">1</span></span> (1 &minus; x<span class="su">3</span>)<span class="sp">n<span class="su">1</span>n<span class="su">2</span></span> ... (1 &minus; x<span class="su">r</span>)<span class="sp">n<span class="su">1</span>n<span class="su">2</span> ... n<span class="su">r &minus; 1</span></span>
+</td></tr></table>
+
+<p class="noind">has a pole only at &zeta; = 1 + c, of order n<span class="su">1</span>n<span class="su">2</span> ... n<span class="su">r</span>.</p>
+
+<p>The difference (1 &minus; &zeta;)<span class="sp">&minus;1</span> &minus; U is of the form (1 &minus; &zeta;)<span class="sp">&minus;1</span>P, where P, of
+the form</p>
+
+<p class="center">1 &minus; (1 &minus; &rho;<span class="su">1</span>) (1 &minus; &rho;<span class="su">2</span>)...(1 &minus; &rho;<span class="su">k</span>),</p>
+
+<p class="noind">in which there are equalities among &rho;<span class="su">1</span>, &rho;<span class="su">2</span>, ... &rho;<span class="su">k</span>, is of the form</p>
+
+<p class="center">&Sigma;&rho;<span class="su">1</span> &minus; &Sigma;&rho;<span class="su">1</span>&rho;<span class="su">2</span> + &Sigma;&rho;<span class="su">1</span>&rho;<span class="su">2</span>&rho;<span class="su">3</span> &minus; ...;</p>
+
+<p class="noind">therefore, if |r<span class="su">i</span>| = |&rho;<span class="su">i</span>|, we have</p>
+
+<table class="math0" summary="math"><tr><td>
+|P| &lt; &Sigma; r<span class="su">1</span> + &Sigma; r<span class="su">1</span>r<span class="su">2</span> + &Sigma; r<span class="su">1</span>r<span class="su">2</span>r<span class="su">3</span> + ... &lt; (1 + r<span class="su">1</span>) (1 + r<span class="su">2</span>)...(1 + r<span class="su">k</span>) &minus; 1;
+</td></tr></table>
+
+<p class="noind">now, so long as &zeta; is without the closed curve above described round
+&zeta; = 1, &zeta; = 1 + c, we have</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">|</span></td> <td>1</td>
+<td rowspan="2"><span class="f150">|</span> &lt;</td> <td>1</td>
+<td rowspan="2">, <span class="f150">|</span></td> <td>c<span class="su">m</span> &minus; c<span class="su">m&minus;1</span></td>
+<td rowspan="2"><span class="f150">|</span> &lt;</td> <td>c/r</td>
+<td rowspan="2">&lt; &sigma;,</td></tr>
+<tr><td class="denom">1 &minus; &zeta;</td> <td class="denom">a</td>
+<td class="denom">c<span class="su">m</span> &minus; &zeta;</td> <td class="denom">a</td></tr></table>
+
+<p class="noind">and hence</p>
+
+<table class="math0" summary="math"><tr><td>
+|(1 &minus; &zeta;)<span class="sp">&minus;1</span> &minus; U| &lt; a<span class="sp">&minus;1</span> {(1 + &sigma;<span class="sp">n<span class="su">1</span></span>) (1 + &sigma;<span class="sp">n<span class="su">2</span></span>)<span class="sp">n<span class="su">1</span></span> (1 + &sigma;<span class="sp">n<span class="su">3</span></span>)<span class="sp">n<span class="su">1</span>n<span class="su">2</span></span> ... (1 + &sigma;<span class="sp">n<span class="su">r</span></span>)<span class="sp">n<span class="su">1</span>n<span class="su">2</span> ... n<span class="su">r&minus;1</span> &minus; 1</span>}.
+</td></tr></table>
+
+<p>Take an arbitrary real positive &epsilon;, and &mu;, a positive number, so that
+&epsilon;<span class="sp">mu</span> &minus; 1 &lt; &epsilon;a, then a value of n<span class="su">1</span> such that &sigma;<span class="sp">n<span class="su">1</span></span> &lt; &mu;/(1 + &mu;) and therefore
+&sigma;<span class="sp">n<span class="su">1</span></span>/(1 &minus; &sigma;<span class="sp">n<span class="su">1</span></span> &lt; &mu;, and values for n<span class="su">2</span>, n<span class="su">3</span> ... such that &sigma;<span class="sp">n<span class="su">2</span></span> &lt; 1/n<span class="su">1</span> &sigma;<span class="sp">2n<span class="su">1</span></span>,
+&sigma;<span class="sp">n<span class="su">3</span></span> &lt; 1/n<span class="su">1</span>n<span class="su">2</span> &sigma;<span class="sp">3n<span class="su">1</span></span>, ... &sigma;<span class="sp">n</span><span class="su">r</span> &lt; 1/(n<span class="su">1</span> ... n<span class="su">r&minus;1</span>) &sigma;<span class="sp">n<span class="su">r</span> n<span class="su">1</span></span>; then, as 1 + x &lt; e<span class="sp">x</span>, we have</p>
+
+<table class="math0" summary="math"><tr><td>
+|(&minus;&zeta;)<span class="sp">&minus;1</span> &minus; U| &lt; a<span class="sp">&minus;1</span> {exp (&sigma;<span class="sp">n<span class="su">1</span></span> + n<span class="su">1</span>&sigma;<span class="sp">n<span class="su">2</span></span> + n<span class="su">1</span>n<span class="su">2</span>&sigma;<span class="sp">n<span class="su">3</span></span> + ... + n<span class="su">1</span>n<span class="su">2</span> ... n<span class="su">r&minus;1</span>&sigma;<span class="sp">n<span class="su">r</span></span>) &minus; 1},
+</td></tr></table>
+
+<p class="noind">and therefore less than</p>
+
+<p class="center">a<span class="sp">&minus;1</span> {exp (&sigma;<span class="sp">n<span class="su">1</span></span> + &sigma;<span class="sp">2n<span class="su">1</span></span> + ... + &sigma;<span class="sp">n<span class="su">r</span> n<span class="su">1</span></span>) &minus; 1},</p>
+
+<p class="noind">which is less than</p>
+
+<table class="math0" summary="math">
+<tr><td>1</td>
+<td rowspan="2"><span class="f150">[</span> exp <span class="f150">(</span></td> <td>&sigma;<span class="sp">n<span class="su">1</span></span></td>
+<td rowspan="2"><span class="f150">)</span> &minus; 1 <span class="f150">]</span></td></tr>
+<tr><td class="denom">a</td> <td class="denom">1 &minus; &sigma;<span class="sp">n<span class="su">1</span></span></td></tr></table>
+
+<p class="noind">and therefore less than &epsilon;.</p>
+
+<p>The rational function U, with a pole at &zeta; = 1 + c, differs therefore
+from (1 &minus; &zeta;)<span class="sp">&minus;1</span>, for all points outside the closed region put about
+&zeta; = 1, &zeta; = l + c, by a quantity numerically less than &epsilon;. So long as
+a remains the same, r and &sigma; will remain the same, and a less value
+of &epsilon; will require at most an increase of the numbers n<span class="su">1</span>, n<span class="su">2</span>, ... n<span class="su">r</span>; but
+if a be taken smaller it may be necessary to increase r, and with this
+the complexity of the function U.</p>
+
+<p>Now put</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">z =</td> <td>c&zeta;</td>
+<td rowspan="2">, &emsp; &zeta; =</td> <td>(c + 1)z</td>
+<td rowspan="2">;</td></tr>
+<tr><td class="denom">c + 1 &minus; &zeta;</td> <td class="denom">c + z</td></tr></table>
+
+<p class="noind">thereby the points &zeta; = 0, 1, 1 + c become the points z = 0, 1, &infin;, the
+function (1 &minus; z)<span class="sp">&minus;1</span> being given by (1 &minus; z)<span class="sp">&minus;1</span> = c(c + 1)<span class="sp">&minus;1</span> (1 &minus; &zeta;)<span class="sp">&minus;1</span> + (c + 1)<span class="sp">&minus;1</span>;
+the function U becomes a rational function of z with a pole only at
+z = &infin;, that is, it becomes a polynomial in z, say [(c + 1)/c] H &minus; 1/c, where H
+is also a polynomial in z, and</p>
+
+<table class="math0" summary="math">
+<tr><td>1</td>
+<td rowspan="2">&minus; H =</td> <td>c</td>
+<td rowspan="2"><span class="f150">[</span></td> <td>1</td>
+<td rowspan="2">&minus; U <span class="f150">]</span>;</td></tr>
+<tr><td class="denom">1 &minus; z</td> <td class="denom">c + 1</td>
+<td class="denom">1 &minus; &zeta;</td></tr></table>
+
+<p class="noind">the lines &eta; = ±a become the two circles expressed, if z = x + iy, by</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">(x + c)² + y² = ±</td> <td>c(c + 1)</td>
+<td rowspan="2">y,</td></tr>
+<tr><td class="denom">a</td></tr></table>
+
+<p class="noind">the points (&eta; = 0, &xi; = 1 &minus; a), (&eta; = 0, &xi; = 1 + c + a) become respectively
+the points (y = 0, x = c(1 &minus; a)/(c + a), (y = 0, x = &minus;c(l + c + a)/a), whose
+limiting positions for a = 0 are respectively (y = 0, x = 1), (y = 0,
+x = &minus;&infin;). The circle (x + c)² + y² = c(c + 1)y/a can be written</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">y =</td> <td>(x + c)²</td>
+<td rowspan="2">+</td> <td>(x + c)<span class="sp">4</span></td>
+<td rowspan="2">{&mu; + &radic;[&mu;² &minus; (x + c)²]}<span class="sp">&minus;2</span>,</td></tr>
+<tr><td class="denom">2&mu;</td> <td class="denom">2&mu;</td></tr></table>
+
+<p class="noind">where &mu; = ½c(c + 1)/a; its ordinate y, for a given value of x, can
+therefore be supposed arbitrarily small by taking a sufficiently small.</p>
+
+<p>We have thus proved the following result; taking in the plane of z
+any finite region of which every interior and boundary point is at a
+finite distance, however short, from the points of the real axis for
+which 1 &#8924; x &#8924; &infin;, we can take a quantity a, and hence, with an
+arbitrary c, determine a number r; then corresponding to an arbitrary
+&epsilon;<span class="su">s</span>, we can determine a polynomial P<span class="su">s</span>, such that, for all points
+interior to the region, we have</p>
+
+<p class="center">|(1 &minus; z<span class="sp">&minus;1</span>) &minus; P<span class="su">s</span>| &lt; &epsilon;<span class="su">s</span>;</p>
+
+<p class="noind">thus the series of polynomials</p>
+
+<p class="center">P<span class="su">1</span> + (P<span class="su">2</span> &minus; P<span class="su">1</span>) + (P<span class="su">3</span> &minus; P<span class="su">2</span>) + ...,</p>
+
+<p class="noind">constructed with an arbitrary aggregate of real positive numbers
+&epsilon;<span class="su">1</span>, &epsilon;<span class="su">2</span>, &epsilon;<span class="su">3</span>, ... with zero as their limit, converges uniformly and
+represents (1 &minus; z)<span class="sp">&minus;1</span> for the whole region considered.</p>
+
+<p>§ 12. <i>Expansion of a Monogenic Function in Polynomials, over a
+Star Region.</i>&mdash;Now consider any monogenic function &fnof;(z) of which
+the origin is not a singular point; joining the origin to any singular
+point by a straight line, let the part of this straight line, produced
+beyond the singular point, lying between the singular point and z = &infin;,
+be regarded as a barrier in the plane, the portion of this straight line
+from the origin to the singular point being erased. Consider next
+any finite region of the plane, whose boundary points constitute a
+path of integration, in a sense previously explained, of which every
+point is at a finite distance greater than zero from each of the barriers
+before explained; we suppose this region to be such that any line
+joining the origin to a boundary point, when produced, does not
+meet the boundary again. For every point x in this region R we
+can then write</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">2&pi;i&fnof;(x) = <span class="f150">&int;</span></td> <td>&fnof;(t)</td>
+<td rowspan="2">&nbsp;</td> <td>&fnof;(t)</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">t</td> <td class="denom">1 &minus; xt<span class="sp">&minus;1</span></td></tr></table>
+
+<p class="noind">where &fnof;(x) represents a monogenic branch of the function, in case it
+be not everywhere single valued, and t is on the boundary of the
+region. Describe now another region R<span class="su">0</span> lying entirely within R,
+and let x be restricted to be within R<span class="su">0</span> or upon its boundary; then
+for any point t on the boundary of R, the points z of the plane for
+which zt<span class="sp">&minus; 1</span> is real and positive and equal to or greater than 1, being
+points for which |z| = |t| or |z| &gt; |t|, are without the region R<span class="su">0</span>, and
+not infinitely near to its boundary points. Taking then an arbitrary
+real positive &epsilon; we can determine a polynomial in xt<span class="sp">&minus; 1</span>, say P(xt<span class="sp">&minus;1</span>),
+such that for all points x in R<span class="su">0</span> we have</p>
+
+<p class="center">|(1 &minus; xt<span class="sp">&minus;1</span>)<span class="sp">&minus;1</span> &minus; P(xt<span class="sp">&minus;1</span>)| &lt; &epsilon;;</p>
+
+<p class="noind">the form of this polynomial may be taken the same for all points t
+on the boundary of R, and hence, if E be a proper variable quantity
+of modulus not greater than &epsilon;,</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">|</span> 2&pi;i&fnof;(x) &minus; <span class="f150">&int;</span></td> <td>dt</td>
+<td rowspan="2">&fnof;(t)P(xt<span class="sp">&minus;1</span>) <span class="f150">|</span> = <span class="f150">|</span> <span class="f150">&int;</span></td> <td>dt</td>
+<td rowspan="2">&fnof;(t)E <span class="f150">|</span> &#8924; &epsilon;LM,</td></tr>
+<tr><td class="denom">t</td> <td class="denom">t</td></tr></table>
+
+<p class="noind">where L is the length of the path of integration, the boundary of R,
+and M is a real positive quantity such that upon this boundary
+|t<span class="sp">&minus;1</span> &fnof;(t)| &lt; M. If now</p>
+
+<p class="center">P (xt<span class="sp">&minus;1</span>) = c<span class="su">0</span> + c<span class="su">1</span>xt<span class="sp">&minus;1</span> + ... + c<span class="su">m</span> x<span class="sp">m</span> t<span class="sp">&minus;m</span>,</p>
+
+<p class="noind">and</p>
+
+<table class="math0" summary="math">
+<tr><td>1</td>
+<td rowspan="2"><span class="f150">&int;</span> t<span class="sp">&minus;r&minus;1</span> &fnof;(t)dt = &mu;<span class="su">r</span>,</td></tr>
+<tr><td class="denom">2&pi;i</td></tr></table>
+
+<p class="noind">this gives</p>
+
+<p class="center">|&fnof;(x) &minus; {c<span class="su">0</span>&mu;<span class="su">0</span> + c<span class="su">1</span>&mu;<span class="su">1</span>x + ... + c<span class="su">m</span>&mu;<span class="su">m</span>x<span class="sp">m</span>}| &#8924; &epsilon;LM/2&pi;,</p>
+
+<p class="noind">where the quantities &mu;<span class="su">0</span>, &mu;<span class="su">1</span>, &mu;<span class="su">2</span>, ... are the coefficients in the expansion
+of &fnof;(x) about the origin.</p>
+
+<p>If then an arbitrary finite region be constructed of the kind
+explained, excluding the barriers joining the singular points of &fnof;(x)
+to x = &infin;, it is possible, corresponding to an arbitrary real positive
+number &sigma;, to determine a number m, and a polynomial Q(x), of
+order m, such that for all interior points of this region</p>
+
+<p class="center">|&fnof;(x) &minus; Q(x)| &lt; &sigma;.</p>
+
+<p>Hence as before, within this region &fnof;(x) can be represented by a
+series of polynomials, converging uniformly; when &fnof;(x) is not a
+single valued function the series represents one branch of the function.</p>
+
+<p>The same result can be obtained without the use of Cauchy&rsquo;s
+integral. We explain briefly the character of the proof. If a
+monogenic function of t, &phi;(t) be capable of expression as a power
+series in t &minus; x about a point x, for |t &minus; x| &#8924; &rho;, and for all points of this
+circle |&phi;(t)| &lt; g, we know that |&phi;<span class="sp">(n)</span>(x)| &lt; g&rho;<span class="sp">&minus;n</span>(n!). Hence, taking
+|z| &lt; <span class="spp">1</span>&frasl;<span class="suu">3</span>&rho;, and, for any assigned positive integer &mu;, taking m so that
+for n &gt; m we have (&mu; + n)<span class="sp">&mu;</span> &lt; (<span class="spp">3</span>&frasl;<span class="suu">2</span>)<span class="sp">n</span>, we have</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">|</span></td> <td>&phi;<span class="sp">(&mu; + n)</span>(x)·z<span class="sp">n</span></td>
+<td rowspan="2"><span class="f150">|</span> &lt;</td> <td>&phi;<span class="sp">(&mu; + n)</span>(x)</td>
+<td rowspan="2">(&mu; + n)<span class="sp">&mu;</span> |z|<span class="sp">n</span> &lt;</td> <td>g</td>
+<td rowspan="2"><span class="f150">(</span></td> <td>3</td>
+<td rowspan="2"><span class="f150">)</span> <span class="sp1">n</span> <span class="f150">(</span></td> <td>&rho;</td>
+<td rowspan="2"><span class="f150">)</span> <span class="sp1">n</span> &lt;</td> <td>g</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">n!</td>
+<td class="denom">(&mu; + n)!</td> <td class="denom">&rho;<span class="sp">&mu; + n</span></td>
+<td class="denom">2</td> <td class="denom">3</td> <td class="denom">&rho;<span class="sp">&mu;</span> 2<span class="sp">n</span></td></tr></table>
+
+<p class="noind">and therefore</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&phi;<span class="sp">&mu;</span> (x + z) = <span class="f150">&Sigma;</span> <span class="sp1">m</span><span class="su1">n=0</span></td> <td>&phi;<span class="sp">(&mu; + n)</span> (x)</td>
+<td rowspan="2">z<span class="sp">n</span> + &epsilon;<span class="su">&mu;</span>,</td></tr>
+<tr><td class="denom">n!</td></tr></table>
+
+<p class="noind">where</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">|</span>&epsilon;<span class="su">&mu;</span><span class="f150">|</span> &lt;</td> <td>g</td>
+<td rowspan="2"><span class="f150">&Sigma;</span> <span class="sp1">&infin;</span><span class="su1">n=m+1</span></td> <td>1</td>
+<td rowspan="2">&lt;</td> <td>g</td>
+<td rowspan="2">.</td></tr>
+<tr><td class="denom">&rho;<span class="sp">&mu;</span></td> <td class="denom">2<span class="sp">n</span></td>
+<td class="denom">&rho;<span class="sp">&mu;</span> 2<span class="sp">m</span></td></tr></table>
+
+<p>Now draw barriers as before, directed from the origin, joining the
+singular point of &phi;(z) to z = &infin;, take a finite region excluding all
+these barriers, let &rho; be a quantity less than the radii of convergence
+of all the power series developments of &phi;(z) about interior points of
+this region, so chosen moreover that no circle of radius &rho; with centre
+at an interior point of the region includes any singular point of &phi;(z),
+let g be such that |&phi;(z)| &lt; g for all circles of radius &rho; whose centres are
+interior points of the region, and, x being any interior point of the
+region, choose the positive integer n so that 1/n |x| &lt; <span class="spp">1</span>&frasl;<span class="suu">3</span>&rho;; then take the
+points a<span class="su">1</span> = x/n, a<span class="su">2</span> = 2x/n, a<span class="su">3</span> = 3x/n, ... a<span class="su">n</span> = x; it is supposed that
+the region is so taken that, whatever x may be, all these are interior
+points of the region. Then by what has been said, replacing x, z
+respectively by 0 and x/n, we have</p>
+
+<p><span class="pagenum"><a name="page317" id="page317"></a>317</span></p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&phi;<span class="sp">(&mu;)</span> (a<span class="su">1</span>) = <span class="f150">&Sigma;</span> <span class="sp1">m1</span><span class="su1">&lambda;1=0</span></td> <td>&phi;<span class="sp">(&mu; + &lambda;1)</span> (0)</td>
+<td rowspan="2"><span class="f150">(</span></td> <td>x</td>
+<td rowspan="2"><span class="f150">)</span> <span class="sp1">&lambda;1</span> + &alpha;<span class="su">&mu;</span></td></tr>
+<tr><td class="denom">&lambda;<span class="su">1</span>!</td>
+<td class="denom">n</td></tr></table>
+
+<p class="noind">with</p>
+
+<p class="center">&alpha;<span class="su">&mu;</span> &lt; g/&rho;<span class="sp">&mu;</span> 2<span class="sp">m1</span>,</p>
+
+<p class="noind">provided (&mu; + m<span class="su">1</span> + 1)<span class="su">&mu;</span> &lt; (<span class="spp">2</span>&frasl;<span class="suu">3</span>)<span class="sp">m1 + 1</span>; in fact for &mu; &#8924; 2n<span class="sp">2n&minus;2</span> it is sufficient
+to take m<span class="su">1</span> = n<span class="sp">2n</span>; by another application of the same inequality,
+replacing x, z respectively by a<span class="su">1</span> and x/n, we have</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&phi;<span class="sp">(&mu;)</span> (a<span class="su">2</span>) = <span class="f150">&Sigma;</span> <span class="sp1">m<span class="su">2</span></span><span class="su1">&lambda;<span class="su">2</span>=0</span></td>
+ <td>&phi;<span class="sp">(&mu; + &lambda;<span class="su">2</span>)</span> (a<span class="su">1</span>)</td>
+<td rowspan="2"><span class="f150">(</span></td> <td>x</td>
+<td rowspan="2"><span class="f150">)</span> <span class="sp1">&lambda;<span class="su">2</span></span> + &beta;&prime;<span class="su">&mu;</span> ,</td></tr>
+<tr><td class="denom">&lambda;<span class="su">2</span>!</td> <td class="denom">n</td></tr></table>
+
+<p class="noind">where</p>
+
+<p class="center">|&beta;&prime;<span class="su">&mu;</span>| &lt; g / &rho;<span class="sp">&mu;</span> 2<span class="sp">m</span><span class="su">2</span></p>
+
+<p class="noind">provided (&mu; + m<span class="su">2</span> + 1)<span class="sp">&mu;</span> &lt; (<span class="spp">3</span>&frasl;<span class="suu">2</span>)<span class="sp">m<span class="su">2</span></span> + 1; we take m<span class="su">2</span> = n<span class="sp">2n &minus; 2</span>, supposing
+&mu; &lt; 2n<span class="sp">2n&minus;4</span>. So long as &lambda;<span class="su">2</span> &#8924; m<span class="su">2</span> &#8924; n<span class="sp">2n&minus;2</span> and &mu; &lt; 2n<span class="sp">2n&minus;4</span> we have
+&mu; + &lambda;<span class="su">2</span> &lt; 2n<span class="sp">2n&minus;2</span>, and we can use the previous inequality to substitute
+here for &phi;<span class="sp">(&mu; + &lambda;<span class="su">2</span>)</span> (a<span class="su">1</span>). When this is done we find</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&phi;<span class="sp">(&mu;)</span> (a<span class="su">2</span>) =
+ <span class="f150">&Sigma;</span> <span class="sp1">m<span class="su">2</span></span><span class="su1">&lambda;<span class="su">2</span>=0</span>
+ <span class="f150">&Sigma;</span> <span class="sp1">m<span class="su">1</span></span><span class="su1">&lambda;<span class="su">1</span>=0</span></td>
+ <td>&phi;<span class="sp">(&mu; + &lambda;<span class="su">1</span> + &lambda;<span class="su">2</span>)</span> (0)</td>
+<td rowspan="2"><span class="f150">(</span></td> <td>x</td>
+<td rowspan="2"><span class="f150">)</span> <span class="sp1">&lambda;<span class="su">1</span> + &lambda;<span class="su">2</span></span> + &beta;<span class="su">&mu;</span> ,</td></tr>
+<tr><td class="denom">&lambda;<span class="su">1</span>! &lambda;<span class="su">2</span>!</td> <td class="denom">n</td></tr></table>
+
+<p class="noind">where |&beta;&mu;| &lt; 2g/&rho;<span class="sp">&mu;</span> 2<span class="sp">m<span class="su">2</span></span>, the numbers m<span class="su">1</span>, m<span class="su">2</span> being respectively n<span class="sp">2n</span>
+and n<span class="sp">2n&minus;2</span>.</p>
+
+<p>Applying then the original inequality to &phi;<span class="sp">(&mu;)</span> (a<span class="su">3</span>) = &phi;<span class="sp">(&mu;)</span> (a<span class="su">2</span> + x/n),
+and then using the series just obtained, we find a series for &phi;<span class="sp">(&mu;)</span> (a<span class="su">3</span>).
+This process being continued, we finally obtain</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&phi;(x) =
+ <span class="f150">&Sigma;</span> <span class="sp1">m<span class="su">1</span></span><span class="su1">&lambda;<span class="su">1</span>=0</span>
+ <span class="f150">&Sigma;</span> <span class="sp1">m<span class="su">2</span></span><span class="su1">&lambda;<span class="su">2</span>=0</span> ...
+ <span class="f150">&Sigma;</span> <span class="sp1">m<span class="su">n</span></span><span class="su1">&lambda;<span class="su">n</span>=0</span></td>
+ <td>&phi;<span class="sp">h</span> (0)</td>
+<td rowspan="2"><span class="f150">(</span></td> <td>x</td>
+<td rowspan="2"><span class="f150">)</span> <span class="sp1">h</span> + &epsilon; ,</td></tr>
+<tr><td class="denom">K</td> <td class="denom">n</td></tr></table>
+
+<p class="noind">where h = &lambda;<span class="su">1</span> + &lambda;<span class="su">2</span> + ... + &lambda;<span class="su">n</span>, K = &lambda;<span class="su">1</span>! &lambda;<span class="su">2</span>! ... &lambda;<span class="su">n</span>!,
+m<span class="su">1</span> = n<span class="sp">2n</span>, m<span class="su">2</span> = n<span class="sp">2n&minus;2</span>, ..., m<span class="su">n</span>= n², |&epsilon;| &lt; 2g/2<span class="sp">m</span><span class="su">n</span>.</p>
+
+<p>By this formula &phi;(x) is represented, with any required degree of
+accuracy, by a polynomial, within the region in question; and
+thence can be expressed as before by a series of polynomials converging
+uniformly (and absolutely) within this region.</p>
+</div>
+
+<p>§ 13. <i>Application of Cauchy&rsquo;s Theorem to the Determination of
+Definite Integrals.</i>&mdash;Some reference must be made to a method
+whereby real definite integrals may frequently be evaluated by
+use of the theorem of the vanishing of the integral of a function
+of a complex variable round a contour within which the function
+is single valued and non singular.</p>
+
+<div class="condensed">
+<p>We are to evaluate an integral <span class="f150">&int;</span> <span class="sp1">b</span><span class="su1">a</span> &fnof;(x)dx; we form a closed contour
+of which the portion of the real axis from x = a to x = b forms a part,
+and consider the integral &int;&fnof;(z)dz round this contour, supposing
+that the value of this integral can be determined along the curve
+forming the completion of the contour. The contour being supposed
+such that, within it, &fnof;(z) is a single valued and finite function of the
+complex variable z save at a finite number of isolated interior points,
+the contour integral is equal to the sum of the values of &int;&fnof;(z)dz taken
+round these points. Two instances will suffice to explain the
+method. (1) The integral <span class="f150">&int;</span> <span class="sp1">&infin;</span><span class="su1">0</span> [(tan x)/x] dx is convergent if it be understood
+to mean the limit when &epsilon;, &zeta;, &sigma;, ... all vanish of the sum of the
+integrals</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">&int;</span> <span class="sp1">1/2&pi;&minus;&epsilon;</span><span class="su1">0</span></td> <td>tan x</td>
+<td rowspan="2">dx, &emsp;<span class="f150">&int;</span> <span class="sp1">3/2&pi;&minus;&zeta;</span><span class="su1">1/2&pi;+&epsilon;</span></td> <td>tan x</td>
+<td rowspan="2">dx, &emsp;<span class="f150">&int;</span> <span class="sp1">5/2&pi;&minus;&sigma;</span><span class="su1">3/2&pi;+&zeta;</span></td> <td>tan x</td>
+<td rowspan="2">dx, ...</td></tr>
+<tr><td class="denom">x</td> <td class="denom">x</td>
+<td class="denom">x</td></tr></table>
+
+<p class="noind">Now draw a contour consisting in part of the whole of the positive
+and negative real axis from x = &minus;n&pi; to x = +n&pi;, where n is a positive
+integer, broken by semicircles of small radius whose centres are the
+points x = ±½&pi;, x = ±¾&pi;, ... , the contour containing also the lines
+x = n&pi; and x = &minus;n&pi; for values of y between 0 and n&pi; tan &alpha;, where &alpha;
+is a small fixed angle, the contour being completed by the portion
+of a semicircle of radius n&pi; sec &alpha; which lies in the upper half of the
+plane and is terminated at the points x = ±n&pi;, y = n&pi; tan &alpha;. Round
+this contour the integral <span class="f150">&int;</span> [(tan z / z)] dz has the value zero. The contributions
+to this contour integral arising from the semicircles of centres
+&minus;½(2s &minus; 1)&pi;, + ½(2s &minus; 1)&pi;, supposed of the same radius, are at once
+seen to have a sum which ultimately vanishes when the radius of the
+semicircles diminishes to zero. The part of the contour lying on
+the real axis gives what is meant by 2 <span class="f150">&int;</span> <span class="sp1">n&pi;</span><span class="su1">0</span> [(tan x / x)] dx. The contribution
+to the contour integral from the two straight portions at
+x = ±n&pi; is</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">&int;</span> <span class="sp1">n&pi; tan &alpha;</span><span class="su1">0</span> idy <span class="f150">(</span></td> <td>tan iy</td>
+<td rowspan="2">&minus;</td> <td>tan iy</td>
+<td rowspan="2"><span class="f150">)</span></td></tr>
+<tr><td class="denom">n&pi; + iy</td> <td class="denom">&minus;n&pi; + iy</td></tr></table>
+
+<p class="noind">where i tan iy, = &minus;[exp(y) &minus; exp(&minus;y)]/[exp(y) + exp(&minus;y)], is a real
+quantity which is numerically less than unity, so that the contribution
+in question is numerically less than</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">&int;</span> <span class="sp1">n&pi; tan &alpha;</span><span class="su1">0</span> dy</td> <td>2n&pi;</td>
+<td rowspan="2">, that is than 2&alpha;.</td></tr>
+<tr><td class="denom">n²&pi;² + y²</td></tr></table>
+
+<p>Finally, for the remaining part of the contour, for which, with
+R = n&pi; sec &alpha;, we have z = R(cos &theta; + i sin &theta;) = RE(i&theta;), we have</p>
+
+<table class="math0" summary="math">
+<tr><td>dz</td>
+<td rowspan="2">= id&theta;, i tan z =</td> <td>exp(&minus;R sin &theta;) E(iR cos &theta;) &minus; exp(R sin &theta;) E(&minus;iR cos &theta;)</td>
+<td rowspan="2">;</td></tr>
+<tr><td class="denom">z</td> <td class="denom">exp(&minus;R sin &theta;) E(iR cos &theta;) + exp(R sin &theta;) E(&minus;iR cos &theta;)</td></tr></table>
+
+<p class="noind">when n and therefore R is very large, the limit of this contribution
+to the contour integral is thus</p>
+
+<p class="center">&minus; <span class="f150">&int;</span> <span class="sp1">&pi;&minus;&alpha;</span><span class="su1">&alpha;</span> d&theta; = &minus; (&pi; &minus; 2&alpha;).</p>
+
+<p class="noind">Making n very large the result obtained for the whole contour is</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">2 <span class="f150">&int;</span> <span class="sp1">&infin;</span><span class="su1">0</span></td> <td>tan x</td>
+<td rowspan="2">dx &minus; (&pi; &minus; 2&alpha;) &minus; 2&alpha;&epsilon; = 0,</td></tr>
+<tr><td class="denom">x</td></tr></table>
+
+<p class="noind">where &epsilon; is numerically less than unity. Now supposing &alpha; to diminish
+to zero we finally obtain</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">&int;</span> <span class="sp1">&infin;</span><span class="su1">0</span></td> <td>tan x</td>
+<td rowspan="2">dx =</td> <td>&pi;</td>
+<td rowspan="2">.</td></tr>
+<tr><td class="denom">x</td> <td class="denom">2</td></tr></table>
+
+<p class="noind">(2) For another case, to illustrate a different point, we may take the
+integral</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">&int;</span></td> <td>z<span class="sp">a&minus;1</span></td>
+<td rowspan="2">dz,</td></tr>
+<tr><td class="denom">1 + z</td></tr></table>
+
+<p class="noind">wherein a is real quantity such that 0 &lt; a &lt; 1, and the contour consists
+of a small circle, z = rE(i&theta;), terminated at the points x = r cos &alpha;,
+y = ± r sin &alpha;, where &alpha; is small, of the two lines y = ± r sin &alpha; for
+r cos &alpha; &#8924; x &#8924; R cos &beta;, where R sin &beta; = r sin &alpha;, and finally of a large
+circle z = RE(i&phi;), terminated at the points x = R cos &beta;, y = ±R sin &beta;.
+We suppose &alpha; and &beta; both zero, and that the phase of z is zero for
+r cos a &#8924; x &#8924; R cos &beta;, y = r sin &alpha; = R sin &beta;. Then on r cos &alpha; &#8924; x &#8924; R cos &beta;,
+y = &minus;r sin &alpha;, the phase of z will be 2&pi;, and z<span class="sp">&alpha; &minus; 1</span> will be equal to
+x<span class="sp">&alpha; &minus; 1</span> exp [2&pi;i(a &minus; 1)], where x is real and positive. The two straight
+portions of the contour will thus together give a contribution</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">[1 &minus; exp(2&pi;i&alpha;)] <span class="f150">&int;</span> <span class="sp1">R cos &beta;</span><span class="su1">r cos &alpha;</span></td> <td>x<span class="sp">a&minus;1</span></td>
+<td rowspan="2">dx.</td></tr>
+<tr><td class="denom">1 + x</td></tr></table>
+
+<p class="noind">It can easily be shown that if the limit of z&fnof;(z) for z = 0 is zero, the
+integral &int;&fnof;(z)dz taken round an arc, of given angle, of a small circle
+enclosing the origin is ultimately zero when the radius of the circle
+diminishes to zero, and if the limit of z&fnof;(z) for z = &infin; is zero, the same
+integral taken round an arc, of given angle, of a large circle whose
+centre is the origin is ultimately zero when the radius of the circle
+increases indefinitely; in our case with &fnof;(z) = z<span class="sp">&alpha;&minus;1</span>/(1 + z), we have
+z&fnof;(z) = z<span class="sp">a</span>/(1 + z), which, for 0 &lt; a &lt; 1, diminishes to zero both for z = 0
+and for z = &infin;. Thus, finally the limit of the contour integral when
+r = 0, R = &infin; is</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">[1 &minus; exp(2&pi;i&alpha;)] <span class="f150">&int;</span> <span class="sp1">&infin;</span><span class="su1">0</span></td> <td>x<span class="sp">&alpha;&minus;1</span></td>
+<td rowspan="2">dx.</td></tr>
+<tr><td class="denom">1 + x</td></tr></table>
+
+<p class="noind">Within the contour &fnof;(z) is single valued, and has a pole at z = 1; at
+this point the phase of z is &pi; and z<span class="sp">a&minus;1</span> is exp [i&pi;(a &minus; 1)] or &minus; exp(i&pi;a);
+this is then the residue of &fnof;(z) at z = &minus;1; we thus have</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">[1 &minus; exp (2&pi;ia)] <span class="f150">&int;</span> <span class="sp1">&infin;</span><span class="su1">0</span></td> <td>x<span class="sp">a&minus;1</span></td>
+<td rowspan="2">dx = &minus;2&pi;i exp(i&pi;a),</td></tr>
+<tr><td class="denom">1 + x</td></tr></table>
+
+<p class="noind">that is</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">&int;</span> <span class="sp1">&infin;</span><span class="su1">0</span></td> <td>x<span class="sp">a&minus;1</span></td>
+<td rowspan="2">dx = &pi; cosec (a&pi;).</td></tr>
+<tr><td class="denom">1 + x</td></tr></table>
+</div>
+
+<p>§ 14. <i>Doubly Periodic Functions.</i>&mdash;An excellent illustration
+of the preceding principles is furnished by the theory of single
+valued functions having in the finite part of the plane no
+singularities but poles, which have two periods.</p>
+
+<div class="condensed">
+<p>Before passing to this it may be convenient to make here a few
+remarks as to the periodicity of (single valued) monogenic functions.
+To say that &fnof;(z) is periodic is to say that there exists a constant &omega;
+such that for every point z of the interior of the region of existence
+of &fnof;(z) we have &fnof;(z + &omega;) = &fnof;(z). This involves, considering all existing
+periods &omega; = &rho; + i&sigma;, that there exists a lower limit of &rho;² + &sigma;² other than
+zero; for otherwise all the differential coefficients of &fnof;(z) would be
+zero, and &fnof;(z) a constant; we can then suppose that not both &rho;
+and &sigma; are numerically less than &epsilon;, where &epsilon; &gt; &sigma;. Hence, if g be any
+real quantity, since the range (&minus;g, ... g) contains only a finite
+number of intervals of length &epsilon;, and there cannot be two periods
+&omega; = &rho; + i&sigma; such that &mu;&epsilon; &#8924; &rho; &lt; (&mu; + 1)&epsilon;, &nu;&epsilon; &#8924; &sigma; &lt; (&nu; + 1)&epsilon;, where &mu;, &nu; are
+integers, it follows that there is only a finite number of periods
+for which both &rho; and &sigma; are in the interval (&minus;g ... g). Considering
+then all the periods of the function which are real multiples of one
+period &omega;, and in particular those periods &lambda;&omega; wherein 0 &lt; &lambda; &#8924; 1, there is
+a lower limit for &lambda;, greater than zero, and therefore, since there is
+only a finite number of such periods for which the real and imaginary
+parts both lie between &minus;g and g, a least value of &lambda;, say &lambda;<span class="su">0</span>. If
+&Omega; = &lambda;<span class="su">0</span>&omega; and &lambda; = M&lambda;<span class="su">0</span> + &lambda;&prime;, where M is an integer and 0 &#8924; &lambda;&prime; &lt; &lambda;<span class="su">0</span>, any
+period &lambda;&omega; is of the form M&Omega; + &lambda;&prime;&omega;; since, however, &Omega;, M&Omega; and &lambda;&omega;
+are periods, so also is &lambda;&prime;&omega;, and hence, by the construction of &lambda;<span class="su">0</span>,
+we have &lambda;&prime; = 0; thus all periods which are real multiples of &omega; are
+expressible in the form M&Omega; where M is an integer, and &Omega; a period.</p>
+
+<p>If beside &omega; the functions have a period &omega;&prime; which is not a real
+multiple of &omega;, consider all existing periods of the form &mu;&omega; + &nu;&omega;&prime;
+wherein &mu;, &nu; are real, and of these those for which 0 &#8924; &mu; &#8924; 1, 0 &lt; &nu; &#8924; 1;
+<span class="pagenum"><a name="page318" id="page318"></a>318</span>
+as before there is a least value for &nu;, actually occurring in one or
+more periods, say in the period &Omega;&prime; = &mu;<span class="su">0</span>&omega; + &nu;<span class="su">0</span>&omega;&prime;; now take, if &mu;&omega; + &nu;&omega;&prime;
+be a period, &nu; = N&prime;&nu;<span class="su">0</span> + &nu;&prime;, where N&prime; is an integer, and 0 &#8924; &nu;&prime; &lt; &nu;<span class="su">0</span>;
+thence &mu;&omega; + &nu;&omega;&prime; = &mu;&omega; + N&prime;(&Omega;&prime; &minus; &mu;<span class="su">0</span>&omega;) + &nu;&prime;&omega;&prime;; take then &mu; &minus; N&mu;<span class="su">0</span> = N&lambda;<span class="su">0</span> + &lambda;&prime;,
+where N is an integer and &lambda;<span class="su">0</span> is as above, and 0 &#8924; &lambda;&prime; &lt; &lambda;<span class="su">0</span>; we
+thus have a period N&Omega; + N&prime;&Omega;&prime; + &lambda;&prime;&omega; + &nu;&prime;&omega;&prime;, and hence a period
+&lambda;&prime;&omega; + &nu;&prime;&omega;&prime;, wherein &lambda;&prime; &lt; &lambda;<span class="su">0</span>, &nu;&prime; &lt; &nu;<span class="su">0</span>; hence &nu;&prime; = 0 and &lambda;&prime; = 0. All
+periods of the form &mu;&omega; + &nu;&omega;&prime; are thus expressible in the form
+N&Omega; + N&prime;&Omega;&prime;, where &Omega;, &Omega;&prime; are periods and N, N&prime; are integers. But
+in fact any complex quantity, P + iQ, and in particular any other
+possible period of the function, is expressible, with &mu;, &nu; real, in the
+form &mu;&omega; + &nu;&omega;&prime;; for if &omega; = &rho; + i&sigma;, &omega;&prime; = &rho;&prime; + i&sigma;&prime;, this requires only
+P = &mu;&rho; + &nu;&rho;&prime;, Q = &mu;&sigma; + &nu;&sigma;&prime;, equations which, since &omega;&prime;/&omega; is not real,
+always give finite values for &mu; and &nu;.</p>
+
+<p>It thus appears that if a single valued monogenic function of z
+be periodic, either all its periods are real multiples of one of them,
+and then all are of the form M&Omega;, where &Omega; is a period and M is an
+integer, or else, if the function have two periods whose ratio is not
+real, then all its periods are expressible in the form N&Omega; + N&prime;&Omega;&prime;,
+where &Omega;, &Omega;&prime; are periods, and N, N&prime; are integers. In the former case,
+putting &zeta; = 2&pi;iz/&Omega;, and the function &fnof;(z) = &phi;(&zeta;), the function &phi;(&zeta;)
+has, like exp (&zeta;), the period 2&pi;i, and if we take t = exp (&zeta;) or &zeta; = &lambda;(t)
+the function is a single valued function of t. If then in particular &fnof;(z)
+is an integral function, regarded as a function of t, it has singularities
+only for t = 0 and t = &infin;, and may be expanded in the form <span class="f150">&Sigma;</span> <span class="sp1">&infin;</span><span class="su1">&minus;&infin;</span> a<span class="su">n</span> t<span class="sp">n</span>.</p>
+
+<p>Taking the case when the single valued monogenic function has
+two periods &omega;, &omega;&prime; whose ratio is not real, we can form a network
+of parallelograms covering the plane of z whose angular points are
+the points c + m&omega; + m&prime;&omega;&prime;, wherein c is some constant and m, m&prime; are
+all possible positive and negative integers; choosing arbitrarily
+one of these parallelograms, and calling it the primary parallelogram,
+all the values of which the function is at all capable occur for points
+of this primary parallelogram, any point, z&prime;, of the plane being,
+as it is called, <i>congruent</i> to a definite point, z, of the primary parallelogram,
+z&prime; &minus; z being of the form m&omega; + m&prime;&omega;&prime;, where m, m&prime; are integers.
+Such a function cannot be an integral function, since then, if, in the
+primary parallelogram |&fnof;(z)| &lt; M, it would also be the case, on a circle
+of centre the origin and radius R, that |&fnof;(z)| &lt; M, and therefore, if
+&Sigma;a<span class="su">n</span> z<span class="sp">n</span> be the expansion of the function, which is valid for an integral
+function for all finite values of z, we should have |a<span class="su">n</span>| &lt; MR<span class="sp">&minus;n</span>, which
+can be made arbitrarily small by taking R large enough. The
+function must then have singularities for finite values of z.</p>
+
+<p>We consider only functions for which these are poles. Of these
+there cannot be an infinite number in the primary parallelogram,
+since then those of these poles which are sufficiently near to one
+of the necessarily existing limiting points of the poles would be
+arbitrarily near to one another, contrary to the character of a pole.
+Supposing the constant c used in naming the corners of the parallelograms
+so chosen that no pole falls on the perimeter of a parallelogram,
+it is clear that the integral 1/(2&pi;i) <span class="f150">&int;</span>&fnof;(z) dz round the perimeter of the
+primary parallelogram vanishes; for the elements of the integral
+corresponding to two such opposite perimeter points as z, z + &omega;
+(or as z, z + &omega;&prime;) are mutually destructive. This integral is, however,
+equal to the sum of the residues of &fnof;(z) at the poles interior to the
+parallelogram. Which sum is therefore zero. There cannot therefore
+be such a function having only one pole of the first order in
+any parallelogram; we shall see that there can be such a function
+with two poles only in any parallelogram, each of the first order,
+with residues whose sum is zero, and that there can be such a function
+with one pole of the second order, having an expansion near this pole
+of the form (z-a)<span class="sp">&minus;2</span> + (power series in z &minus; a).</p>
+
+<p>Considering next the function &phi;(z) = [&fnof;(z)]<span class="sp">&minus;1</span> d&fnof;(z)/dz, it is easily seen
+that an ordinary point of &fnof;(z) is an ordinary point of &phi;(z), that a
+zero of order m for &fnof;(z) in the neighbourhood of which &fnof;(z) has a form,
+(z &minus; a)<span class="sp">m</span> multiplied by a power series, is a pole of &phi;(z) of residue m,
+and that a pole of &fnof;(z) of order n is a pole of &phi;(z) of residue &minus;n;
+manifestly &phi;(z) has the two periods of &fnof;(z). We thus infer, since the
+sum of the residues of &phi;(z) is zero, that for the function &fnof;(z), the
+sum of the orders of its vanishing at points belonging to one parallelogram,
+&Sigma;m, is equal to the sum of the orders of its poles, &Sigma;n; which is
+briefly expressed by saying that the number of its zeros is equal to
+the number of its poles. Applying this theorem to the function
+&fnof;(z) &minus; A, where A is an arbitrary constant, we have the result, that
+the function &fnof;(z) assumes the value A in one of the parallelograms
+as many times as it becomes infinite. Thus, by what is proved above,
+every conceivable complex value does arise as a value for the doubly
+periodic function &fnof;(z) in any one of its parallelograms, and in fact
+at least twice. The number of times it arises is called the <i>order</i> of the
+function; the result suggests a property of rational functions.</p>
+
+<p>Consider further the integral <span class="f150">&int;</span> z [&fnof;&prime;(z)/&fnof;(z)] dz, where &fnof;&prime;(z) = d&fnof;(z)/dz taken
+round the perimeter of the primary parallelogram; the contribution
+to this arising from two opposite perimeter points such as z and z + &omega;
+is of the form &minus;&omega; <span class="f150">&int;</span> z [&fnof;&prime;(z)/&fnof;(z)] dz, which, as z increases from z<span class="su">0</span> to z<span class="su">0</span> + &omega;&prime;, gives,
+if &lambda; denote the generalized logarithm, &minus; &omega; {&lambda; [&fnof;(z<span class="su">0</span> + &omega;&prime;)] &minus; &lambda;[&fnof;(z<span class="su">0</span>)]}, that
+is, since &fnof;(z<span class="su">0</span> + &omega;&prime;) = &fnof;(z<span class="su">0</span>), gives 2&pi;iN&omega;, where N is an integer; similarly
+the result of the integration along the other two opposite sides is of
+the form 2&pi;iN&prime;&omega;&prime;, where N&prime; is an integer. The integral, however,
+is equal to 2&pi;i times the sum of the residues of z&fnof;&prime;(z) / &fnof;(z) at the poles
+interior to the parallelogram. For a zero, of order m, of &fnof;(z) at z = a,
+the contribution to this sum is 2&pi;ima, for a pole of order n at z = b
+the contribution is &minus;2&pi;inb; we thus infer that &Sigma;ma &minus; &Sigma;nb = N&omega; + N&prime;&omega;&prime;;
+this we express in words by saying that the sum of the values of z
+where &fnof;(z) = 0 within any parallelogram is equal to the sum of the
+values of z where &fnof;(z) = &infin; save for integral multiples of the periods.
+By considering similarly the function &fnof;(z) &minus; A where A is an arbitrary
+constant, we prove that each of these sums is equal to the sum of
+the values of z where the function takes the value A in the parallelogram.</p>
+</div>
+
+<p>We pass now to the construction of a function having two
+arbitrary periods &omega;, &omega;&prime; of unreal ratio, which has a single pole
+of the second order in any one of its parallelograms.</p>
+
+<div class="condensed">
+<p>For this consider first the network of parallelograms whose corners
+are the points &Omega; = m&omega; + m&prime;&omega;&prime;, where m, m&prime; take all positive and
+negative integer values; putting a small circle about each corner
+of this network, let P be a point outside all these circles; this will
+be interior to a parallelogram whose corners in order may be denoted
+by z<span class="su">0</span>, z<span class="su">0</span> + &omega;, z<span class="su">0</span> + &omega; + &omega;&prime;, z<span class="su">0</span> + &omega;&prime;; we shall denote z<span class="su">0</span>, z<span class="su">0</span> + &omega; by A<span class="su">0</span>, B<span class="su">0</span>;
+this parallelogram &Pi;<span class="su">0</span> is surrounded by eight other parallelograms,
+forming with &Pi;<span class="su">0</span> a larger parallelogram &Pi;<span class="su">1</span>, of which one side, for
+instance, contains the points z<span class="su">0</span> &minus; &omega; &minus; &omega;&prime;, z<span class="su">0</span> &minus; &omega;&prime;, z<span class="su">0</span> &minus; &omega;&prime; + &omega;, z<span class="su">0</span> &minus; &omega;&prime; + 2&omega;,
+which we shall denote by A<span class="su">1</span>, B<span class="su">1</span>, C<span class="su">1</span>, D<span class="su">1</span>. This parallelogram &Pi;<span class="su">1</span> is
+surrounded by sixteen of the original parallelograms, forming with
+&Pi;<span class="su">1</span> a still larger parallelogram &Pi;<span class="su">2</span> of which one side, for instance,
+contains the points z<span class="su">0</span> &minus; 2&omega; &minus; 2&omega;&prime;, z<span class="su">0</span> &minus; &omega; &minus; 2&omega;&prime;, z<span class="su">0</span> &minus; 2&omega;&prime;, z<span class="su">0</span> + &omega; &minus; 2&omega;&prime;,
+z<span class="su">0</span> + 2&omega; &minus; 2&omega;&prime;, z<span class="su">0</span> + 3&omega; &minus; 2&omega;&prime;, which we shall denote by A<span class="su">2</span>, B<span class="su">2</span>, C<span class="su">2</span>, D<span class="su">2</span>,
+E<span class="su">2</span>, F<span class="su">2</span>. And so on. Now consider the sum of the inverse cubes of
+the distances of the point P from the corners of all the original
+parallelograms. The sum will contain the terms</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">S<span class="su">0</span> =</td> <td>1</td>
+<td rowspan="2">+ <span class="f150">(</span></td> <td>1</td>
+<td rowspan="2">+</td> <td>1</td>
+<td rowspan="2">+</td> <td>1</td>
+<td rowspan="2"><span class="f150">)</span> + <span class="f150">(</span></td> <td>1</td>
+<td rowspan="2">+</td> <td>1</td>
+<td rowspan="2">+ ... +</td> <td>1</td>
+<td rowspan="2"><span class="f150">)</span> + ...</td></tr>
+<tr><td class="denom">PA<span class="su">0</span><span class="sp">3</span></td> <td class="denom">PA<span class="su">1</span><span class="sp">3</span></td>
+<td class="denom">PB<span class="su">1</span><span class="sp">3</span></td> <td class="denom">PC<span class="su">1</span><span class="sp">3</span></td>
+<td class="denom">PA<span class="su">2</span><span class="sp">3</span></td> <td class="denom">PB<span class="su">2</span><span class="sp">3</span></td>
+<td class="denom">PE<span class="su">2</span><span class="sp">3</span></td></tr></table>
+
+<p class="noind">and three other sets of terms, each infinite in number, formed in a
+similar way. If the perpendiculars from P to the sides A<span class="su">0</span>B<span class="su">0</span>,
+A<span class="su">1</span>B<span class="su">1</span>C<span class="su">1</span>, A<span class="su">2</span>B<span class="su">2</span>C<span class="su">2</span>D<span class="su">2</span>E<span class="su">2</span>, and so on, be p, p + q, p + 2q and so on, the
+sum S<span class="su">0</span> is at most equal to</p>
+
+<table class="math0" summary="math">
+<tr><td>1</td>
+<td rowspan="2">+</td> <td>3</td>
+<td rowspan="2">+</td> <td>5</td>
+<td rowspan="2">+ ... +</td> <td>2n + 1</td>
+<td rowspan="2">+ ...</td></tr>
+<tr><td class="denom">p<span class="sp">3</span></td> <td class="denom">(p + q)<span class="sp">3</span></td>
+<td class="denom">(p + 2q)<span class="sp">3</span></td> <td class="denom">(p + nq)<span class="sp">3</span></td></tr></table>
+
+<p class="noind">of which the general term is ultimately, when n is large, in a ratio of
+equality with 2q<span class="sp">&minus;3</span> n<span class="sp">&minus;2</span>, so that the series S<span class="su">0</span> is convergent, as we know
+the sum &Sigma;n<span class="sp">&minus;2</span> to be; this assumes that p &ne; 0; if P be on A<span class="su">0</span>B<span class="su">0</span>
+the proof for the convergence of S<span class="su">0</span> &minus; 1/PA<span class="su">0</span><span class="sp">3</span>, is the same. Taking
+the three other sums analogous to S<span class="su">0</span> we thus reach the result that
+the series</p>
+
+<p class="center">&phi;(z) = &minus;2&Sigma; (z &minus; &Omega;)<span class="sp">&minus;3</span>,</p>
+
+<p class="noind">where &Omega; is m&omega; + m&prime;&omega;&prime;, and m, m&prime; are to take all positive and negative
+integer values, and z is any point outside small circles described with
+the points &Omega; as centres, is <i>absolutely convergent</i>. Its sum is therefore
+independent of the order of its terms. By the nature of the proof,
+which holds for all positions of z outside the small circles spoken of,
+the series is also clearly <i>uniformly convergent</i> outside these circles.
+Each term of the series being a monogenic function of z, the series may
+therefore be differentiated and integrated outside these circles, and
+represents a monogenic function. It is clearly periodic with the
+periods &omega;, &omega;&prime;; for &phi;(z + &omega;) is the same sum as &phi;(z) with the terms
+in a slightly different order. Thus &phi;(z + &omega;) = &phi;(z) and &phi;(z + &omega;&prime;) = &phi;(z).</p>
+
+<p>Consider now the function</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&fnof;(z) =</td> <td>1</td>
+<td rowspan="2">+ <span class="f150">&int;</span> <span class="sp1">z</span><span class="su1">0</span> <span class="f150">{</span> &phi;(z) +</td> <td>2</td>
+<td rowspan="2"><span class="f150">}</span> dz,</td></tr>
+<tr><td class="denom">z<span class="sp">2</span></td> <td class="denom">z<span class="sp">3</span></td></tr></table>
+
+<p class="noind">where, for the subject of integration, the area of uniform convergence
+clearly includes the point z = 0; this gives</p>
+
+<table class="math0" summary="math">
+<tr><td>d&fnof;(z)</td>
+<td rowspan="2">= &phi;(z)</td></tr>
+<tr><td class="denom">dz</td></tr></table>
+
+<p class="noind">and</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&fnof;(z) =</td> <td>1</td>
+<td rowspan="2">+ <span class="f150">&Sigma;</span><span class="sp">&prime;</span> <span class="f150">{</span></td> <td>1</td>
+<td rowspan="2">&minus;</td> <td>1</td>
+<td rowspan="2"><span class="f150">}</span> ,</td></tr>
+<tr><td class="denom">z<span class="sp">2</span></td> <td class="denom">(z &minus; &Omega;)<span class="sp">2</span></td>
+<td class="denom">&Omega;<span class="sp">2</span></td></tr></table>
+
+<p class="noind">wherein &Sigma;&prime; is a sum excluding the term for which m = 0 and m&prime; = 0.
+Hence &fnof;(z + &omega;) &minus; &fnof;(z) and &fnof;(z + &omega;&prime;) &minus; &fnof;(z) are both independent of z.
+Noticing, however, that, by its form, &fnof;(z) is an even function of z,
+and putting z = &minus;½&omega;, z = &minus;½&omega;&prime; respectively, we infer that also &fnof;(z)
+has the two periods &omega; and &omega;&prime;. In the primary parallelogram &Pi;<span class="su">0</span>,
+however, &fnof;(z) is only infinite at z = 0 in the neighbourhood of which
+its expansion is of the form z<span class="sp">&minus;2</span> + (power series in z). Thus &fnof;(z) is
+such a doubly periodic function as was to be constructed, having in
+any parallelogram of periods only one pole, of the second order.</p>
+</div>
+
+<p>It can be shown that any single valued meromorphic function
+of z with &omega; and &omega;&prime; as periods can be expressed rationally in terms
+of &fnof;(z) and &phi;(z), and that [&phi;(z)]<span class="sp">2</span> is of the form 4[&fnof;(z)]<span class="sp">3</span> + A&fnof;(z) + B,
+where A, B are constants.</p>
+
+<p><span class="pagenum"><a name="page319" id="page319"></a>319</span></p>
+
+<div class="condensed">
+<p>To prove the last of these results, we write, for |z| &lt; |&Omega;|,</p>
+
+<table class="math0" summary="math">
+<tr><td>1</td>
+<td rowspan="2">&minus;</td> <td>1</td>
+<td rowspan="2">=</td> <td>2z</td>
+<td rowspan="2">+</td> <td>3z²</td>
+<td rowspan="2">+ ...,</td></tr>
+<tr><td class="denom">(z &minus; &Omega;)²</td> <td class="denom">&Omega;²</td>
+<td class="denom">&Omega;³</td> <td class="denom">&Omega;<span class="sp">4</span></td></tr></table>
+
+<p class="noind">and hence, if &Sigma;&prime;&Omega;<span class="sp">&minus;2n</span> = &sigma;<span class="su">n</span>, since &Sigma;&prime;&Omega;<span class="sp">&minus;(2n&minus;1)</span> = 0, we have, for sufficiently
+small z greater than zero,</p>
+
+<p class="center">&fnof;(z) = z<span class="sp">&minus;2</span> + 3&sigma;<span class="su">2</span>·z<span class="sp">2</span> + 5&sigma;<span class="su">3</span>·z<span class="sp">4</span> + ...</p>
+
+<p class="noind">and</p>
+
+<p class="center">&phi;(z) = &minus;2z<span class="sp">&minus;3</span> + 6&sigma;<span class="su">2</span>·z + 20&sigma;<span class="su">3</span>·z<span class="sp">3</span> + ...;</p>
+
+<p class="noind">using these series we find that the function</p>
+
+<p class="center">F(z) = [&phi;(z)]² &minus; 4[&fnof;(z)]³ + 60&sigma;<span class="su">2</span>&fnof;(z) + 140&sigma;<span class="su">3</span></p>
+
+<p class="noind">contains no negative powers of z, being equal to a power series in z²
+beginning with a term in z². The function F(z) is, however, doubly
+periodic, with periods &omega;, &omega;&prime;, and can only be infinite when either
+&fnof;(z) or &phi;(z) is infinite; this follows from its form in &fnof;(z) and &phi;(z);
+thus in one parallelogram of periods it can be infinite only when
+z = 0; we have proved, however, that it is not infinite, but, on the
+contrary, vanishes, when z = 0. Being, therefore, never infinite for
+finite values of z it is a constant, and therefore necessarily always
+zero. Putting therefore &fnof;(z) = &zeta; and &phi;(z) = d&zeta;/dz we see that</p>
+
+<table class="math0" summary="math">
+<tr><td>dz</td>
+<td rowspan="2">= (4&zeta;³ &minus; 60&sigma;<span class="su">2</span>&zeta; &minus; 140&sigma;<span class="su">3</span>)<span class="sp">&minus;1/2</span>.</td></tr>
+<tr><td class="denom">d&zeta;</td></tr></table>
+
+<p class="noind">Historically it was in the discussion of integrals such as</p>
+
+<p class="center">&int; d&zeta; (4&zeta;³ &minus; 60&sigma;<span class="su">2</span>·&zeta; &minus; 140&sigma;<span class="su">3</span>)<span class="sp">&minus;1/2</span>,</p>
+
+<p class="noind">regarded as a branch of Integral Calculus, that the doubly periodic
+functions arose. As in the familiar case</p>
+
+<p class="center">z = <span class="f150">&int;</span> <span class="sp1">&zeta;</span><span class="su1">0</span> (1 &minus; &zeta;²)<span class="sp">&minus;1/2</span> d&zeta;,</p>
+
+<p class="noind">where &zeta; = sin z, it has proved finally to be simpler to regard &zeta; as a
+function of z. We shall come to the other point of view below,
+under § 20, <i>Elliptic Integrals</i>.</p>
+</div>
+
+<p>To prove that any doubly periodic function F(z) with periods
+&omega;, &omega;&prime;, having poles at the points z = a<span class="su">1</span>, ... z = a<span class="su">m</span> of a parallelogram,
+these being, for simplicity of explanation, supposed to be
+all of the first order, is rationally expressible in terms of &phi;(z)
+and &fnof;(z), and we proceed as follows:&mdash;</p>
+
+<div class="condensed">
+<p>Consider the expression</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&Phi;(z) =</td> <td>(&zeta;, 1)<span class="su">m</span> + &eta;(&zeta;, 1)<span class="su">m&minus;2</span></td></tr>
+<tr><td class="denom">(&zeta; &minus; A<span class="su">1</span>) (&zeta; &minus; A<span class="su">2</span>)...(&zeta; &minus; A<span class="su">m</span>)</td></tr></table>
+
+<p class="noind">where A<span class="su">s</span> = &fnof;(a<span class="su">s</span>), &zeta; is an abbreviation for &fnof;(z) and &eta; for &phi;(z), and
+(&zeta;, 1)<span class="su">m</span>, (&zeta;, 1)<span class="su">m&minus;2</span>, denote integral polynomials in &zeta;, of respective orders
+m and m &minus; 2, so that there are 2m unspecified, homogeneously
+entering, constants in the numerator. It is supposed that no one
+of the points a<span class="su">1</span>, ... a<span class="su">m</span> is one of the points m&omega; + m&prime;&omega;&prime; where f(z) = &infin;.
+The function &Phi;(z) is a monogenic function of z with the periods &omega;, &omega;&prime;,
+becoming infinite (and having singularities) only when (1) &zeta; = &infin; or
+(2) one of the factors &zeta;-A<span class="su">s</span> is zero. In a period parallelogram
+including z = 0 the first arises only for z = 0; since for &zeta; = &infin;, &eta; is in
+a finite ratio to &zeta;<span class="sp">3/2</span>; the function &Phi;(z) for &zeta; = &infin; is not infinite
+provided the coefficient of &zeta;<span class="sp">m</span> in (&zeta;, 1)<span class="su">m</span> is not zero; thus &Phi;(z) is
+regular about z = 0. When &zeta; &minus; A<span class="su">s</span> = 0, that is &fnof;(z) = f(a<span class="su">s</span>), we have
+z = ±a<span class="su">s</span> + m&omega; + m&prime;&omega;&prime;, and no other values of z, m and m&prime; being
+integers; suppose the unspecified coefficients in the numerator so
+taken that the numerator vanished to the first order in each of the
+m points &minus;a<span class="su">1</span>, &minus;a<span class="su">2</span>, ... &minus;a<span class="su">m</span>; that is, if &phi;(a<span class="su">s</span>) = B<span class="su">s</span>, and therefore
+&phi;(&minus;a<span class="su">s</span>) = &minus;B<span class="su">s</span>, so that we have the m relations</p>
+
+<p class="center">(A<span class="su">s</span>, 1)<span class="su">m</span> &minus; B<span class="su">s</span>(A<span class="su">s</span>, 1)<span class="su">m&minus;2</span> = 0;</p>
+
+<p class="noind">then the function &Phi;(z) will only have the m poles a<span class="su">1</span>, ... a<span class="su">m</span>. Denoting
+further the m zeros of F(z) by a<span class="su">1</span>&prime;, ... a<span class="su">m</span>&prime;, putting &fnof;(a<span class="su">s</span>&prime;) = A<span class="su">s</span>&prime;,
+&phi;(a<span class="su">s</span>&prime;) = B<span class="su">s</span>&prime;, suppose the coefficients of the numerator of &Phi;(z) to
+satisfy the further m &minus; 1 conditions</p>
+
+<p class="center">(A<span class="su">s</span>&prime;, 1)<span class="su">m</span> + B<span class="su">s</span>&prime; (A<span class="su">s</span>&prime;, 1)<span class="su">m&minus;2</span> = 0</p>
+
+<p class="noind">for s = 1, 2, ... (m &minus; 1). The ratios of the 2m coefficients in the
+numerator of &Phi;(z) can always be chosen so that the m + (m &minus; 1) linear
+conditions are all satisfied. Consider then the ratio</p>
+
+<p class="center">F(z) / &Phi;(z);</p>
+
+<p class="noind">it is a doubly periodic function with no singularity other than the
+one pole a<span class="su">m</span>&prime;. It is therefore a constant, the numerator of &Phi;(z)
+vanishing spontaneously in a<span class="su">m</span>&prime;. We have</p>
+
+<p class="center">F(z) = A&Phi;(z),</p>
+
+<p class="noind">where A is a constant; by which F(z) is expressed rationally in
+terms of &fnof;(z) and &phi;(z), as was desired.</p>
+
+<p>When z = 0 is a pole of F(z), say of order r, the other poles, each of
+the first order, being a<span class="su">1</span>, ... a<span class="su">m</span>, similar reasoning can be applied to
+a function</p>
+
+<table class="math0" summary="math">
+<tr><td>(&zeta;, 1)<span class="su">h</span> + &eta;(&zeta;, 1)<span class="su">k</span></td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">(&zeta; &minus; A<span class="su">1</span>) ... (&zeta; &minus; A<span class="su">m</span>)</td></tr></table>
+
+<p class="noind">where h, k are such that the greater of 2h &minus; 2m, 2k + 3 &minus; 2m is equal
+to r; the case where some of the poles a<span class="su">1</span>, ... a<span class="su">m</span> are multiple is
+to be met by introducing corresponding multiple factors in the denominator
+and taking a corresponding numerator. We give a
+solution of the general problem below, of a different form.</p>
+
+<p>One important application of the result is the theorem that the
+functions &fnof;(z + t), &phi;(z + t), which are such doubly periodic function of
+z as have been discussed, can each be expressed, so far as they depend
+on z, rationally in terms of &fnof;(z) and &phi;(z), and therefore, so far as they
+depend on z and t, rationally in terms of &fnof;(z), &fnof;(t), &phi;(z) and &phi;(t).
+It can in fact be shown, by reasoning analogous to that given above,
+that</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&fnof;(z + t) + &fnof;(z) + &fnof;(t) = ¼ <span class="f150">[</span></td> <td>&phi;(z) &minus; &phi;(t)</td>
+<td rowspan="2"><span class="f150">]</span> <span class="sp1">2</span>.</td></tr>
+<tr><td class="denom">&fnof;(z) &minus; &fnof;(t)</td></tr></table>
+
+<p>This shows that if F(z) be any single valued monogenic function
+which is doubly periodic and of meromorphic character, then
+F(z + t) is an algebraic function of F(z) and F(t). Conversely any
+single valued monogenic function of meromorphic character, F(z),
+which is such that F(z + t) is an algebraic function of F(z) and F(t),
+can be shown to be a doubly periodic function, or a function obtained
+from such by degeneration (in virtue of special relations connecting
+the fundamental constants).</p>
+
+<p>The functions &fnof;(z), &phi;(z) above are usually denoted by &real;(z), &real;&prime;(z);
+further the fundamental differential equation is usually written</p>
+
+<p class="center">(&real;&prime;z)² = 4(&real;z)³ &minus; g<span class="su">2</span>&real;z &minus; g<span class="su">3</span>,</p>
+
+<p class="noind">and the roots of the cubic on the right are denoted by e<span class="su">1</span>, e<span class="su">2</span>, e<span class="su">3</span>;
+for the odd function, &real;&prime;z, we have, for the congruent arguments
+&minus;½&omega;and ½&omega;, &real;&prime; (½&omega;) = &minus;&real;&prime; (&minus;½&omega;) = &minus;&real;&prime; (½&omega;), and hence &real;&prime; (½&omega;) = 0;
+hence we can take e<span class="su">1</span> = &real; (½&omega;), e<span class="su">2</span> = &real; (½&omega; + ½&omega;&prime;), e<span class="su">3</span> = &real; (½&omega;). It can
+then be proved that [&real;(z) &minus; e<span class="su">1</span>] [&real; (z + ½&omega;) &minus; e<span class="su">1</span>] = (e<span class="su">1</span> &minus; e<span class="su">2</span>) (e<span class="su">1</span> &minus; e<span class="su">3</span>), with
+similar equations for the other half periods. Consider more particularly
+the function &real;(z) &minus; e<span class="su">1</span>; like &real;(z) it has a pole of the second
+order at z = 0, its expansion in its neighbourhood being of the form
+z<span class="sp">&minus;2</span> (1 &minus; e<span class="su">1</span>z<span class="sp">2</span> + Az<span class="sp">4</span> + ...); having no other pole, it has therefore either
+two zeros, or a double zero in a period parallelogram (&omega;, &omega;&prime;). In fact
+near its zero ½&omega; its expansion is (x &minus; ½&omega;) &real;&prime; (½&omega;) + ½(z &minus; ½&omega;)² &real;&Prime; (½&omega;) +
+...; we have seen that &real;&prime; (½&omega;) = 0; thus it has a zero of the second
+order wherever it vanishes. Thus it appears that the square root
+[&real;(z) &minus; e<span class="su">1</span>]<span class="sp">1/2</span>, if we attach a definite sign to it for some particular value
+of z, is a single valued function of z; for it can at most have two
+values, and the only small circuits in the plane which could lead
+to an interchange of these values are those about either a pole or a
+zero, neither of which, as we have seen, has this effect; the function
+is therefore single valued for any circuit. Denoting the function,
+for a moment, by &fnof;<span class="su">1</span>(z), we have &fnof;<span class="su">1</span>(z + &omega;) = ±&fnof;<span class="su">1</span>(z), &fnof;<span class="su">1</span>(z + &omega;&prime;) = ±&fnof;<span class="su">1</span>(z);
+it can be seen by considerations of continuity that the right sign
+in either of these equations does not vary with z; not both these
+signs can be positive, since the function has only one pole, of the first
+order, in a parallelogram (&omega;, &omega;&prime;); from the expansion of &fnof;<span class="su">1</span>(z) about
+z = 0, namely z<span class="sp">&minus; 1</span> (1 &minus; ½e<span class="su">1</span>z² + ...), it follows that &fnof;<span class="su">1</span>(z) is an odd
+function, and hence &fnof;<span class="su">1</span> (&minus;½&omega;&prime;) = &minus;&fnof;<span class="su">1</span> (½&omega;&prime;), which is not zero since
+[&fnof;<span class="su">1</span> (½&omega;&prime;)]² = e<span class="su">3</span> &minus; e<span class="su">1</span>, so that we have &fnof;<span class="su">1</span> (z + &omega;&prime;) = &minus;&fnof;<span class="su">1</span>(z); an equation
+f<span class="su">1</span>(z + &omega;) = &minus;&fnof;<span class="su">1</span>(z) would then give &fnof;<span class="su">1</span>(z + &omega; + &omega;&prime;) = &fnof;<span class="su">1</span>(z), and hence
+&fnof;<span class="su">1</span>(½&omega; + ½&omega;&prime;) = &fnof;<span class="su">1</span>(&minus;½&omega; &minus; ½&omega;&prime;), of which the latter is &minus;&fnof;<span class="su">1</span>(½&omega; + ½&omega;&prime;); this
+would give &fnof;<span class="su">1</span>(½&omega; + ½&omega;&prime;) = 0, while [&fnof;<span class="su">1</span>(½&omega; + ½&omega;&prime;)]² = e<span class="su">2</span> &minus; e<span class="su">1</span>. We thus
+infer that &fnof;<span class="su">1</span>(z + &omega;) = &fnof;<span class="su">1</span>(z), &fnof;<span class="su">1</span>(z + &omega;&prime;) = &minus;&fnof;<span class="su">1</span>(z), &fnof;<span class="su">1</span>(z + &omega; + &omega;&prime;) = &minus;&fnof;<span class="su">1</span>(z).
+The function &fnof;<span class="su">1</span>(z) is thus doubly periodic with the periods &omega; and
+2&omega;&prime;; in a parallelogram of which two sides are &omega; and 2&omega;&prime; it has
+poles at z = 0, z = &omega;&prime; each of the first order, and zeros of the first
+order at z = ½&omega;, z = ½&omega; + &omega;&prime;; it is thus a doubly periodic function
+of the second order with two different poles of the first order in its
+parallelogram (&omega;, 2&omega;&prime;). We may similarly consider the functions
+&fnof;<span class="su">2</span>(z) = [&real;(z) &minus; e<span class="su">2</span>]<span class="sp">1/2</span>, &fnof;<span class="su">3</span>(z) = [&real;(z) &minus; e<span class="su">3</span>]<span class="sp">1/2</span>; they give</p>
+
+<table class="math0" summary="math">
+<tr><td>&fnof;<span class="su">2</span>(z + &omega; + &omega;&prime;) = &fnof;<span class="su">2</span>(z), &fnof;<span class="su">2</span>(z + &omega;) = &minus;&fnof;<span class="su">2</span>(z), &fnof;<span class="su">2</span>(z + &omega;&prime;) = &minus;&fnof;<span class="su">2</span>(z),</td>
+<td>&fnof;<span class="su">3</span>(z + &omega;&prime;) = &fnof;<span class="su">3</span>z, &fnof;<span class="su">3</span>(z + &omega;) = &minus;&fnof;<span class="su">3</span>(z), &fnof;<span class="su">3</span>(z + &omega; + &omega;&prime;) = &minus;&fnof;<span class="su">3</span>(z).</td></tr>
+</table>
+
+<p class="noind">Taking u = z (e<span class="su">1</span> &minus; e<span class="su">3</span>)<span class="sp">1/2</span>, with a definite determination of the constant
+(e<span class="su">1</span> &minus; e<span class="su">3</span>)<span class="sp">1/2</span>, it is usual, taking the preliminary signs so that for z = 0
+each of z&fnof;<span class="su">1</span>(z), z&fnof;<span class="su">2</span>(z), z&fnof;<span class="su">3</span>(z) is equal to +1, to put</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">sn(u) =</td> <td>(e<span class="su">1</span> &minus; e<span class="su">3</span>)<span class="sp">1/2</span></td>
+<td rowspan="2">, &emsp;cn(u) =</td> <td>&fnof;<span class="su">1</span>(z)</td>
+<td rowspan="2">, &emsp;dn(u) =</td> <td>f<span class="su">2</span>(z)</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">&fnof;<span class="su">3</span>(z)</td> <td class="denom">&fnof;<span class="su">3</span>(z)</td>
+<td class="denom">&fnof;<span class="su">3</span>(z)</td></tr></table>
+
+<table class="math0" summary="math">
+<tr><td>k² = (e<span class="su">2</span> &minus; e<span class="su">3</span>) / (e<span class="su">1</span> &minus; e<span class="su">3</span>), &emsp;K = ½&omega; (e<span class="su">1</span> &minus; e<span class="su">3</span>)<span class="sp">1/2</span>, &emsp; iK&prime; = ½&omega;&prime; (e<span class="su">1</span> &minus; e<span class="su">3</span>)<span class="sp">1/2</span>;</td></tr>
+</table>
+
+<p class="noind">thus sn(u) is an odd doubly periodic function of the second order
+with the periods 4K, 2iK, having poles of the first order at u = iK&prime;,
+u = 2K + iK&prime;, and zeros of the first order at u = 0, u = 2K; similarly
+cn(u), dn(u) are even doubly periodic functions whose periods can be
+written down, and sn²(u) + cn²(u) = 1, k²sn²(u) + dn²(u) = 1; if x = sn(u)
+we at once find, from the relations given here, that</p>
+
+<table class="math0" summary="math">
+<tr><td>du</td>
+<td rowspan="2">= [(1 &minus; x²) (1 &minus; k²x²)]<span class="sp">&minus;1/2</span>;</td></tr>
+<tr><td class="denom">dx</td></tr></table>
+
+<p class="noind">if we put x = sin&phi; we have</p>
+
+<table class="math0" summary="math">
+<tr><td>du</td>
+<td rowspan="2">= [1 &minus; k²sin²&phi;]<span class="sp">&minus;1/2</span>,</td></tr>
+<tr><td class="denom">d&phi;</td></tr></table>
+
+<p class="noind">and if we call &phi; the amplitude of u, we may write &phi; = am(u), x = sin·am(u),
+which explains the origin of the notation sn(u). Similarly
+cn(u) is an abbreviation of cos·am(u), and dn(u) of &Delta;am(u), where
+&Delta;(&phi;) meant (1 &minus; k²sin²&phi;)<span class="sp">1/2</span>. The addition equation for each of the
+functions &fnof;<span class="su">1</span>(z), &fnof;<span class="su">2</span>(z), &fnof;<span class="su">3</span>(z) is very simple, being</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&fnof;(z + t) = ½ <span class="f150">(</span></td> <td>&part;</td>
+<td rowspan="2">+</td> <td>&part;</td>
+<td rowspan="2"><span class="f150">)</span> log</td> <td>&fnof;(z) + &fnof;(t)</td>
+<td rowspan="2">=</td> <td>&fnof;(z)&fnof;&prime;(t) &minus; &fnof;(t)&fnof;&prime;(z)</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">&part;z</td> <td class="denom">&part;i</td>
+<td class="denom">&fnof;(z) &minus; &fnof;(t)</td> <td class="denom">&fnof;²(z) &minus; &fnof;²(t)</td></tr></table>
+
+<p class="noind">where f<span class="su">1</span>&prime;(z) means d&fnof;<span class="su">1</span>(z)/dz, which is equal to &minus;&fnof;<span class="su">2</span>(z)·&fnof;<span class="su">3</span>(z), and &fnof;²(z)
+<span class="pagenum"><a name="page320" id="page320"></a>320</span>
+means [&fnof;(z)]<span class="sp">2</span>. This may be verified directly by showing, if R denote
+the right side of the equation, that &part;R/&part;z = &part;R/&part;t; this will require
+the use of the differential equation</p>
+
+<p class="center">[&fnof;<span class="su">1</span>&prime;<span class="sp">(z)</span>]<span class="sp">2</span> = [&fnof;<span class="su">1</span><span class="sp">2</span>(z) + e<span class="su">1</span> &minus; e<span class="su">2</span>] [&fnof;<span class="su">1</span><span class="sp">2</span>(z) + e<span class="su">1</span> &minus; e<span class="su">3</span>],</p>
+
+<p class="noind">and in fact we find</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">(</span></td> <td>&part;<span class="sp">2</span></td>
+<td rowspan="2">&minus;</td> <td>&part;<span class="sp">2</span></td>
+<td rowspan="2"><span class="f150">)</span> log [&fnof;(z) + &fnof;(t)] = &fnof;<span class="sp">2</span>(z) &minus; &fnof;<span class="sp">2</span>(t) = <span class="f150">(</span></td> <td>&part;<span class="sp">2</span></td>
+<td rowspan="2">&minus;</td> <td>&part;<span class="sp">2</span></td>
+<td rowspan="2"><span class="f150">)</span> log [&fnof;(z) &minus; &fnof;(t)];</td></tr>
+<tr><td class="denom">&part;z<span class="sp">2</span></td> <td class="denom">dt<span class="sp">2</span></td>
+<td class="denom">&part;z<span class="sp">2</span></td> <td class="denom">dt<span class="sp">2</span></td></tr></table>
+
+<p class="noind">hence it will follow that R is a function of z + t, and R is at once seen
+to reduce to &fnof;(z) when t = 0. From this the addition equation for
+each of the functions sn(u), cn(u), dn(u) can be deduced at once;
+if s<span class="su">1</span>, c<span class="su">1</span>, d<span class="su">1</span>, s<span class="su">2</span>, c<span class="su">2</span>, d<span class="su">2</span> denote respectively sn(u<span class="su">1</span>), cn(u<span class="su">1</span>), dn(u<span class="su">1</span>), sn(u<span class="su">2</span>),
+cn(u<span class="su">2</span>), dn(u<span class="su">2</span>), they can be put into the forms</p>
+
+<table class="math0" summary="math">
+<tr><td>sn(u<span class="su">1</span> + u<span class="su">2</span>) = (s<span class="su">1</span>c<span class="su">2</span>d<span class="su">2</span> + s<span class="su">2</span>c<span class="su">1</span>d<span class="su">1</span>) / D,</td>
+<td>cn(u<span class="su">1</span> + u<span class="su">2</span>) = (c<span class="su">1</span>c<span class="su">2</span> &minus; s<span class="su">1</span>s<span class="su">2</span>d<span class="su">1</span>d<span class="su">2</span>) / D,</td>
+<td>dn(u<span class="su">1</span> + u<span class="su">2</span>) = (d<span class="su">1</span>d<span class="su">2</span> &minus; k<span class="sp">2</span>s<span class="su">1</span>s<span class="su">2</span>c<span class="su">1</span>c<span class="su">2</span>) / D,</td></tr>
+</table>
+
+<p class="noind">where</p>
+
+<p class="center">D = 1 &minus; k<span class="sp">2</span>s<span class="su">1</span><span class="sp">2</span>s<span class="su">2</span><span class="sp">2</span>.</p>
+
+<p>The introduction of the function &fnof;<span class="su">1</span>(z) is equivalent to the introduction
+of the function &real;(z; &omega;, 2&omega;&prime;) constructed from the periods
+&omega;, 2&omega;&prime; as was &real;(z) from &omega; and &omega;&prime;; denoting this function by &real;<span class="su">1</span>(z)
+and its differential coefficient by &real;&prime;<span class="su">1</span>(z), we have in fact</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&fnof;<span class="su">1</span>(z) = ½</td> <td>&real;&prime;<span class="su">1</span>(z)</td></tr>
+<tr><td class="denom">&real;<span class="su">1</span>(&omega;&prime;) &minus; &real;<span class="su">1</span>(z)</td></tr></table>
+
+<p class="noind">as we see at once by considering the zeros and poles and the limit of
+z&fnof;<span class="su">1</span>(z) when z = 0. In terms of the function &real;<span class="su">1</span>(z) the original function
+&real;(z) is expressed by</p>
+
+<p class="center">&real;(z) = &real;<span class="su">1</span>(z) + &real;<span class="su">1</span>(z + &omega;&prime;) &minus; &real;<span class="su">1</span>(&omega;&prime;),</p>
+
+<p class="noind">as a consideration of the poles and expansion near z = 0 will show.</p>
+
+<p>A function having &omega;, &omega;&prime; for periods, with poles at two arbitrary
+points a, b and zeros at a&prime;, b&prime;, where a&prime; + b&prime; = a + b save for an expression
+m&omega; + m&prime;&omega;&prime;, in which m, m&prime; are integers, is a constant multiple of</p>
+
+<table class="math0" summary="math">
+<tr><td>{&real; [z &minus; ½(a&prime; + b&prime;)] &minus; &real; [a&prime; &minus; ½(a&prime; + b&prime;)]} / {&real; [z &minus; ½(a + b)] &minus; &real; [a &minus; ½(a + b)]};</td></tr>
+</table>
+
+<p class="noind">if the expansion of this function near z = a be</p>
+
+<p class="center">&lambda;(z &minus; a)<span class="sp">&minus;1</span> + &mu; + <span class="f150">&Sigma;</span> <span class="su">n=1</span> &mu;<span class="su">n</span> (z &minus; a)<span class="sp">n</span>,</p>
+
+<p class="noind">the expansion near z = b is</p>
+
+<p class="center">&minus;&lambda; (z &minus; b)<span class="sp">&minus; 1</span> + &mu; + <span class="f150">&Sigma;</span> <span class="su">n=1</span> (&minus;1)<span class="sp">n</span> &mu;<span class="su">n</span> (z &minus; b)<span class="sp">n</span>,</p>
+
+<p class="noind">as we see by remarking that if z&prime; &minus; b = &minus;(z &minus; a) the function has the
+same value at z and z&prime;; hence the differential equation satisfied
+by the function is easily calculated in terms of the coefficients in
+the expansions.</p>
+
+<p>From the function &real;(z) we can obtain another function, termed the
+Zeta-function; it is usually denoted by &zeta;(z), and defined by</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&zeta;(z) &minus;</td> <td>1</td>
+<td rowspan="2">= <span class="f150">&int;</span> <span class="sp1">&pi;</span><span class="su1">0</span> <span class="f150">[</span></td> <td>1</td>
+<td rowspan="2">&minus; &real;(z) <span class="f150">]</span> dz = <span class="f150">&Sigma;</span><span class="sp1">&prime;</span> <span class="f150">(</span></td> <td>1</td>
+<td rowspan="2">+</td> <td>1</td>
+<td rowspan="2">+</td> <td>z</td>
+<td rowspan="2"><span class="f150">)</span>,</td></tr>
+<tr><td class="denom">z</td> <td class="denom">z<span class="sp">2</span></td>
+<td class="denom">z &minus; &Omega;</td> <td class="denom">&Omega;</td>
+<td class="denom">&Omega;<span class="sp">2</span></td></tr></table>
+
+<p class="noind">for which as before we have equations</p>
+
+<table class="math0" summary="math">
+<tr><td>&zeta;(z + &omega;) = &zeta;(z) + 2&pi;i&eta;, &emsp; &zeta;(z + &omega;&prime;) = &zeta;(z) + 2&pi;i&eta;&prime;,</td></tr>
+</table>
+
+<p class="noind">where 2&eta;, 2&eta;&prime; are certain constants, which in this case do not both
+vanish, since else &zeta;(z) would be a doubly periodic function with only
+one pole of the first order. By considering the integral</p>
+
+<p class="center">&int; &zeta;(z)dz</p>
+
+<p class="noind">round the perimeter of a parallelogram of sides &omega;, &omega;&prime; containing
+z = 0 in its interior, we find &eta;&omega;&prime; &minus; &eta;&prime;&omega; = 1, so that neither of &eta;, &eta;&prime;
+is zero. We have &zeta;&prime;(z) =&minus;&real;(z). From &zeta;(z) by means of the equation</p>
+
+<table class="math0" summary="math">
+<tr><td>&sigma;(z)</td>
+<td rowspan="2">= exp <span class="f150">{</span> <span class="f150">&int;</span> <span class="sp1">z</span><span class="su1">0</span> <span class="f150">[</span> &zeta;(x) &minus;</td> <td>1</td>
+<td rowspan="2"><span class="f150">]</span> dz <span class="f150">}</span> = &Pi;&prime; <span class="f150">[ (</span> 1 &minus;</td> <td>z</td>
+<td rowspan="2"><span class="f150">)</span> exp <span class="f150">(</span></td> <td>z</td>
+<td rowspan="2">+</td> <td>z<span class="sp">2</span></td>
+<td rowspan="2"><span class="f150">) ]</span>,</td></tr>
+<tr><td class="denom">z</td> <td class="denom">z</td>
+<td class="denom">&Omega;</td> <td class="denom">&Omega;</td>
+<td class="denom">2&Omega;<span class="sp">2</span></td></tr></table>
+
+<p class="noind">we determine an integral function &sigma;(z), termed the Sigma-function,
+having a zero of the first order at each of the points z = &Omega;; it can be
+seen to satisfy the equations</p>
+
+<table class="math0" summary="math">
+<tr> <td>&sigma;(z + &omega;)</td>
+<td rowspan="2">= &minus;exp [2&pi;i&eta;(z + ½&omega;)], &emsp; </td> <td>&sigma;(z + &omega;&prime;)</td>
+<td rowspan="2">= &minus;exp [2&pi;i&eta;&prime; (z + ½&omega;&prime;)].</td></tr>
+<tr><td class="denom">&sigma;(z)</td> <td class="denom">&sigma;(z)</td></tr></table>
+
+<p class="noind">By means of these equations, if a<span class="su">1</span> + a<span class="su">2</span> + ... + a<span class="su">m</span> = a&prime;<span class="su">1</span> + a&prime;<span class="su">2</span> + ...
++ a&prime;<span class="su">m</span>, it is readily shown that</p>
+
+<table class="math0" summary="math">
+<tr><td>&sigma;(z &minus; a&prime;<span class="su">1</span>) &sigma;(z &minus; a&prime;<span class="su">2</span>) ... &sigma;(z &minus; a&prime;<span class="su">m</span>)</td></tr>
+<tr><td class="denom">&sigma;(z &minus; a<span class="su">1</span>) &sigma;(z &minus; a<span class="su">2</span>) ... &sigma;(z &minus; a<span class="su">m</span>)</td></tr></table>
+
+<p class="noind">is a doubly periodic function having a<span class="su">1</span>, ... a<span class="su">m</span> as its simple poles,
+and a&prime;<span class="su">1</span>, ... a&prime;<span class="su">m</span> as its simple zeros. Thus the function &sigma;(z) has the
+important property of enabling us to write any meromorphic doubly
+periodic function as a product of factors each having one zero in the
+parallelogram of periods; these form a generalization of the simple
+factors, z &minus; a, which have the same utility for rational functions of z.
+We have &zeta;(z) = &sigma;&prime;(z)/&sigma;(z).</p>
+
+<p>The functions &zeta;(z), &real;(z) may be used to write any meromorphic
+doubly periodic function F(z) as a sum of terms having each only one
+pole; for if in the expansion of F(z) near a pole z = a the terms with
+negative powers of z &minus; a be</p>
+
+<p class="center">A<span class="su">1</span>(z &minus; a)<span class="sp">&minus;1</span> + A<span class="su">2</span>(z &minus; a)<span class="su">&minus;2</span> + ... + A<span class="su">m+1</span>(z &minus; a)<span class="sp">&minus;(m+1)</span>,</p>
+
+<p class="noind">then the difference</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">F(z) &minus; A<span class="su">1</span>&zeta; (z &minus; a) &minus; A<span class="su">2</span>&real; (z &minus; a) &minus; ... +</td> <td>A<span class="su">m+1</span></td>
+<td rowspan="2">(&minus;1)<span class="sp">m</span> &real;<span class="sp">m&minus;1</span> (z &minus; a)</td></tr>
+<tr><td class="denom">m!</td></tr></table>
+
+<p class="noind">will not be infinite at z = a. Adding to this a sum of further terms
+of the same form, one for each of the poles in a parallelogram of
+periods, we obtain, since the sum of the residues A is zero, a doubly
+periodic function without poles, that is, a constant; this gives the
+expression of F(z) referred to. The indefinite integral &int;F(z)dz can
+then be expressed in terms of z, functions &real;(z &minus; a) and their differential
+coefficients, functions &zeta;(z &minus; a) and functions log&sigma;(z &minus; a).</p>
+</div>
+
+<p>§ 15. <i>Potential Functions.</i> <i>Conformal Representation in
+General.</i>&mdash;Consider a circle of radius a lying within the region
+of existence of a single valued monogenic function, u + iv, of
+the complex variable z, = x + iy, the origin z = 0 being the centre
+of this circle. If z = rE(i&phi;) = r(cos&phi; + i sin&phi;) be an internal point
+of this circle we have</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">u + iv =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span></td> <td>(U + iV)</td>
+<td rowspan="2">dt,</td></tr>
+<tr><td class="denom">2&pi;i</td> <td class="denom">t &minus; z</td></tr></table>
+
+<p class="noind">where U + iV is the value of the function at a point of the circumference
+and t = aE(i&theta;); this is the same as</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">u + iv =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span></td> <td>(U + iV) [1 &minus; (r/a) E (i&theta; &minus; i&phi;)]</td>
+<td rowspan="2">d&theta;.</td></tr>
+<tr><td class="denom">2&pi;</td> <td class="denom">1 + (r/a)² &minus; 2(r/a) cos (&theta; &minus; &phi;)</td></tr></table>
+
+<p class="noind">If in the above formula we replace z by the external point
+(a²/r) E(i&phi;) the corresponding contour integral will vanish, so that
+also</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">0 =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span></td> <td>(U + iV) [(r/a)² &minus; (r/a) E (i&theta; &minus; i&phi;)]</td>
+<td rowspan="2">d&theta;;</td></tr>
+<tr><td class="denom">2&pi;</td> <td class="denom">1 + (r/a)² &minus; 2(r/a) cos (&theta; &minus; &phi;)</td></tr></table>
+
+<p class="noind">hence by subtraction we have</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">u =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span></td> <td>U(a² &minus; r²)</td>
+<td rowspan="2">d&theta;,</td></tr>
+<tr><td class="denom">2&pi;</td> <td class="denom">a² + r² &minus; 2ar cos (&theta; &minus; &phi;)</td></tr></table>
+
+<p class="noind">and a corresponding formula for v in terms of V. If O be the
+centre of the circle, Q be the interior point z, P the point aE(i&theta;)
+of the circumference, and &omega; the angle which QP makes with OQ
+produced, this integral is at once found to be the same as</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">u =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span> Ud&omega; &minus;</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span> Ud&theta;</td></tr>
+<tr><td class="denom">&pi;</td> <td class="denom">2&pi;</td></tr></table>
+
+<p class="noind">of which the second part does not depend upon the position of z,
+and the equivalence of the integrals holds for every arc of
+integration.</p>
+
+<div class="condensed">
+<p>Conversely, let U be any continuous real function on the circumference,
+U<span class="su">0</span> being the value of it at a point P<span class="su">0</span> of the circumference,
+and describe a small circle with centre at P<span class="su">0</span> cutting the given circle in
+A and B, so that for all points P of the arc AP<span class="su">0</span>B we have |U &minus; U<span class="su">0</span>| &lt; &epsilon;,
+where &epsilon; is a given small real quantity. Describe a further circle,
+centre P<span class="su">0</span> within the former, cutting the given circle in A&prime; and B&prime;,
+and let Q be restricted to lie in the small space bounded by the arc
+A&prime;P<span class="su">0</span>B&prime; and this second circle; then for all positions of P upon the
+greater arc AB of the original circle QP² is greater than a definite
+finite quantity which is not zero, say QP² &gt; D². Consider now the
+integral</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">u&prime; =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span> U</td> <td>(a² &minus; r²)</td>
+<td rowspan="2">d&theta; =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span> Ud&omega; &minus;</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span> Ud&theta;,</td></tr>
+<tr><td class="denom">2&pi;</td> <td class="denom">a² + r² &minus; 2ar cos (&theta; &minus; &phi;)</td>
+<td class="denom">&pi;</td> <td class="denom">2&pi;</td></tr></table>
+
+<p class="noind">which we evaluate as the sum of two, respectively along the small arc
+AP<span class="su">0</span>B and the greater arc AB. It is easy to verify that, for the
+whole circumference,</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">U<span class="su">0</span> =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span> U<span class="su">0</span></td> <td>a² &minus; r²</td>
+<td rowspan="2">d&theta; =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span> U<span class="su">0</span> d&omega; &minus;</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span> U<span class="su">0</span> d&theta;.</td></tr>
+<tr><td class="denom">2&pi;</td> <td class="denom">a² + r² &minus; 2ar cos (&theta; &minus; &phi;)</td>
+<td class="denom">&pi;</td> <td class="denom">2&pi;</td></tr></table>
+
+<p class="noind">Hence we can write</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">u&prime; &minus; U<span class="su">0</span> =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span> <span class="su">AP<span class="su">0</span>B</span> (U &minus; U<span class="su">0</span>)d&omega; &minus;</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span> <span class="su">AP<span class="su">0</span>B</span> (U &minus; U<span class="su">0</span>)d&theta; +</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span> <span class="su">AB</span> (U &minus; U<span class="su">0</span>)</td> <td>(a² &minus; r²)</td>
+<td rowspan="2">d&theta;.</td></tr>
+<tr><td class="denom">2&pi;</td> <td class="denom">2&pi;</td>
+<td class="denom">2&pi;</td> <td class="denom">QP²</td></tr></table>
+
+<p class="noind">If the finite angle between QA and QB be called &Phi; and the finite
+angle AOB be called &Theta;, the sum of the first two components is
+numerically less than</p>
+
+<table class="math0" summary="math">
+<tr><td>&epsilon;</td>
+<td rowspan="2">(&Phi; + &Theta;).</td></tr>
+<tr><td class="denom">2&pi;</td></tr></table>
+
+<p class="noind">If the greatest value of |(U &minus; U<span class="su">0</span>)| on the greater arc AB be called H,
+the last component is numerically less than</p>
+
+<table class="math0" summary="math">
+<tr><td>H</td>
+<td rowspan="2">(a² &minus; r²)</td></tr>
+<tr><td class="denom">D²</td></tr></table>
+
+<p class="noind">of which, when the circle, of centre P<span class="su">0</span>, passing through A&prime;B&prime; is
+sufficiently small, the factor a² &minus; r² is arbitrarily small. Thus it
+appears that u&prime; is a function of the position of Q whose limit, when Q,
+interior to the original circle, approaches indefinitely near to P<span class="su">0</span>, is
+U<span class="su">0</span>. From the form</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">u&prime; =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span> Ud&omega; &minus;</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span> Ud&theta;,</td></tr>
+<tr><td class="denom">&pi;</td> <td class="denom">2&pi;</td></tr></table>
+
+<p class="noind">since the inclination of QP to a fixed direction is, when Q varies, P
+remaining fixed, a solution of the differential equation</p>
+
+<table class="math0" summary="math">
+<tr><td>&part;²&psi;</td>
+<td rowspan="2">+</td> <td>&part;²</td>
+<td rowspan="2">= 0,</td></tr>
+<tr><td class="denom">&part;x²</td> <td class="denom">&part;y²</td></tr></table>
+
+<p class="noind">where z, = x + iy, is the point Q, we infer that u&prime; is a differentiable
+<span class="pagenum"><a name="page321" id="page321"></a>321</span>
+function satisfying this equation; indeed, when r &lt; a, we can write</p>
+
+<table class="math0" summary="math">
+<tr><td>1</td>
+<td rowspan="2"><span class="f150">&int;</span> U</td> <td>(a² &minus; r²)</td>
+<td rowspan="2">d&theta; =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span> U <span class="f150">[</span> 1 + 2</td> <td>r</td>
+<td rowspan="2">cos (&theta; &minus; &phi;) + 2</td> <td>r²</td>
+<td rowspan="2">cos 2(&theta; &minus; &phi;) + ... <span class="f150">]</span> d&theta;</td></tr>
+<tr><td class="denom">2&pi;</td> <td class="denom">a² + r² &minus; 2ar cos (&theta; &minus; &phi;)</td>
+<td class="denom">2&pi;</td> <td class="denom">a</td>
+<td class="denom">a²</td></tr></table>
+
+<p class="center">= a<span class="su">0</span> + a<span class="su">1</span>x + b<span class="su">1</span>y + a<span class="su">2</span> (x² &minus; y²) + 2b<span class="su">2</span>xy + ...,</p>
+
+<p class="noind">where</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">a<span class="su">0</span> =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span> Ud&theta;, &emsp; a<span class="su">1</span> =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span></td> <td>U cos&theta;</td>
+<td rowspan="2">d&theta;, &emsp; b<span class="su">1</span> =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span></td> <td>U sin&theta;</td>
+<td rowspan="2">d&theta;,</td></tr>
+<tr><td class="denom">2&pi;</td> <td class="denom">&pi;</td>
+<td class="denom">a</td> <td class="denom">&pi;</td>
+<td class="denom">a</td></tr></table>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">a<span class="su">2</span> =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span></td> <td>U cos 2&theta;</td>
+<td rowspan="2">d&theta;, &emsp; b<span class="su">2</span> =</td> <td>1</td>
+<td rowspan="2"><span class="f150">&int;</span></td> <td>U sin 2&theta;</td>
+<td rowspan="2">d&theta;.</td></tr>
+<tr><td class="denom">&pi;</td> <td class="denom">a²</td>
+<td class="denom">&pi;</td> <td class="denom">a²</td></tr></table>
+
+<p>In this series the terms of order n are sums, with real coefficients,
+of the various integral polynomials of dimension n which satisfy
+the equation &part;²&psi;/&part;x² + &part;²&psi;/&part;y²; the series is thus the real part of
+a power series in z, and is capable of differentiation and integration
+within its region of convergence.</p>
+
+<p>Conversely we may suppose a function, P, defined for the interior
+of a finite region R of the plane of the real variables x, y, capable
+of expression about any interior point x<span class="su">0</span>, y<span class="su">0</span> of this region by a power
+series in x &minus; x<span class="su">0</span>, y &minus; y<span class="su">0</span>, with real coefficients, these various series being
+obtainable from one of them by continuation. For any region R<span class="su">0</span>
+interior to the region specified, the radii of convergence of these
+power series will then have a lower limit greater than zero, and
+hence a finite number of these power series suffice to specify the
+function for all points interior to R<span class="su">0</span>. Each of these series, and
+therefore the function, will be differentiable; suppose that at all
+points of R<span class="su">0</span> the function satisfies the equation</p>
+
+<table class="math0" summary="math">
+<tr><td>&part;²P</td>
+<td rowspan="2">+</td> <td>&part;P²</td>
+<td rowspan="2">= 0,</td></tr>
+<tr><td class="denom">&part;x²</td> <td class="denom">&part;y²</td></tr></table>
+
+<p class="noind">we then call it a monogenic potential function. From this, save
+for an additive constant, there is defined another potential function
+by means of the equation</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">Q = <span class="f150">&int;</span> <span class="sp1">(x, y)</span> <span class="f150">(</span></td> <td>&part;P</td>
+<td rowspan="2">dy &minus;</td> <td>&part;P</td>
+<td rowspan="2">dx <span class="f150">)</span>.</td></tr>
+<tr><td class="denom">&part;x</td> <td class="denom">&part;y</td></tr></table>
+
+<p>The functions P, Q, being given by a finite number of power series,
+will be single valued in R<span class="su">0</span>, and P + iQ will be a monogenic function of
+z within R<span class="su">0</span>· In drawing this inference it is supposed that the region
+R<span class="su">0</span> is such that every closed path drawn in it is capable of being
+deformed continuously to a point lying within R<span class="su">0</span>, that is, is <i>simply
+connected</i>.</p>
+
+<p>Suppose in particular, c being any point interior to R<span class="su">0</span>, that P
+approaches continuously, as z approaches to the boundary of R,
+to the value log r, where r is the distance of c to the points of the
+perimeter of R. Then the function of z expressed by</p>
+
+<p class="center">&zeta; = (z &minus; c) exp (&minus;P &minus; iQ)</p>
+
+<p class="noind">will be developable by a power series in (z &minus; z<span class="su">0</span>) about every point z<span class="su">0</span>
+interior to R<span class="su">0</span>, and will vanish at z = c; while on the boundary of R
+it will be of constant modulus unity. Thus if it be plotted upon a
+plane of &zeta; the boundary of R will become a circle of radius unity
+with centre at &zeta;=0, this latter point corresponding to z=c. A
+closed path within R<span class="su">0</span>, passing once round z=c, will lead to a closed
+path passing once about &zeta; = 0. Thus every point of the interior of
+R will give rise to one point of the interior of the circle. The converse
+is also true, but is more difficult to prove; in fact, the differential
+coefficient d&zeta;/dz does not vanish for any point interior to R.
+This being assumed, we obtain a conformal representation of the
+interior of the region R upon the interior of a circle, in which the
+arbitrary interior point c of R corresponds to the centre of the circle,
+and, by utilizing the arbitrary constant arising in determining the
+function Q, an arbitrary point of the boundary of R corresponds to
+an arbitrary point of the circumference of the circle.</p>
+
+<p>There thus arises the problem of the determination of a real monogenic
+potential function, single valued and finite within a given
+arbitrary region, with an assigned continuous value at all points
+of the boundary of the region. When the region is circular this
+problem is solved by the integral 1/&pi; <span class="f150">&int;</span> Ud&omega; &minus; 1/&pi; <span class="f150">&int;</span> Ud&theta; previously
+given. When the region is bounded by the outermost portions
+of the circumferences of two overlapping circles, it can hence be
+proved that the problem also has a solution; more generally, consider
+a finite simply connected region, whose boundary we suppose
+to consist of a single closed path in the sense previously explained,
+ABCD; joining A to C by two non-intersecting paths AEC, AFC
+lying within the region, so that the original region may be supposed
+to be generated by the overlapping regions AECD, CFAB, of which
+the common part is AECF; suppose now the problem of determining
+a single valued finite monogenic potential function for the region
+AECD with a given continuous boundary value can be solved, and
+also the same problem for the region CFAB; then it can be shown
+that the same problem can be solved for the original area. Taking
+indeed the values assigned for the original perimeter ABCD, assume
+arbitrarily values for the path AEC, continuous with one another
+and with the values at A and C; then determine the potential function
+for the interior of AECD; this will prescribe values for the path
+CFA which will be continuous at A and C with the values originally
+proposed for ABC; we can then determine a function for the interior
+of CFAB with the boundary values so prescribed. This in its turn
+will give values for the path AEC, so that we can determine a new
+function for the interior of AECD. With the values which this
+assumes along CFA we can then again determine a new function for
+the interior of CFAB. And so on. It can be shown that these
+functions, so alternately determined, have a limit representing
+such a potential function as is desired for the interior of the original
+region ABCD. There cannot be two functions with the given
+perimeter values, since their difference would be a monogenic
+potential function with boundary value zero, which can easily be
+shown to be everywhere zero. At least two other methods have
+been proposed for the solution of the same problem.</p>
+
+<p>A particular case of the problem is that of the conformal representation
+of the interior of a closed polygon upon the upper half
+of the plane of a complex variable t. It can be shown without much
+difficulty that if a, b, c, ... be real values of t, and &alpha;, &beta;, &gamma;, ... be n
+real numbers, whose sum is n &minus; 2, the integral</p>
+
+<p class="center">z = &int; (t &minus; a)<span class="sp">&alpha;&minus;1</span> (t &minus; b)<span class="sp">&beta;&minus;1</span>  ... dt,</p>
+
+<p class="noind">as t describes the real axis, describes in the plane of z a polygon of n
+sides with internal angles equal to &alpha;&pi;, &beta;&pi;, ..., and, a proper sign
+being given to the integral, points of the upper half of the plane of t
+give rise to interior points of the polygon. Herein the points a, b, ...
+of the real axis give rise to the corners of the polygon; the condition
+&Sigma;&alpha; = n &minus; 2 ensures merely that the point t = &infin; does not correspond
+to a corner; if this condition be not regarded, an additional corner
+and side is introduced in the polygon. Conversely it can be shown
+that the conformal representation of a polygon upon the half plane
+can be effected in this way; for a polygon of given position of more
+than three sides it is necessary for this to determine the positions
+of all but three of a, b, c, ...; three of them may always be supposed
+to be at arbitrary positions, such as t = 0, t = 1, t = &infin;.</p>
+
+<p>As an illustration consider in the plane of z = x + iy, the portion
+of the imaginary axis from the origin to z = ih, where h is positive
+and less than unity; let C be this point z = ih; let BA be of length
+unity along the positive real axis, B being the origin and A the
+point z = 1; let DE be of length unity along the negative real axis,
+D being also the origin and E the point z = &minus; 1; let EFA be a
+semicircle of radius unity, F being the point z = i. If we put
+&zeta; = [(z² + h²)/(1 + h²z²)]<span class="sp">1/2</span>, with &zeta; = 1 when z = 1, the function is single
+valued within the semicircle, in the plane of z, which is slit along the
+imaginary axis from the origin to z = ih; if we plot the value of &zeta;
+upon another plane, as z describes the continuous curve ABCDE,
+&zeta; will describe the real axis from &zeta; = 1 to &zeta;  = &minus; 1, the point C giving
+&zeta; = 0, and the points B, D giving the points &zeta; = ±h. Near z = 0
+the expansion of &zeta; is &zeta; &minus; h = z² (1 &minus; h<span class="sp">4</span> / 2h) + ..., or &zeta; + h = &minus;z² (1 &minus; h<span class="sp">4</span> / 2h) + ...;
+in either case an increase of ½&pi; in the phase of z gives an increase
+of &pi; in the phase of &zeta; &minus; h or &zeta; + h. Near z = ih the expansion of &zeta; is
+&zeta; = (z &minus; ih)<span class="sp">1/2</span> [2ih/(1 &minus; h<span class="sp">4</span>)]<span class="sp">1/2</span> + ..., and an increase of 2&pi; in the phase of
+z &minus; ih also leads to an increase of &pi; in the phase of &zeta;. Then as z
+describes the semicircle EFA, &zeta; also describes a semicircle of radius
+unity, the point z = i becoming &zeta; = i. There is thus a conformal
+representation of the interior of the slit semicircle in the z-plane,
+upon the interior of the whole semicircle in the &zeta;-plane, the function</p>
+
+<p class="center">z = [(&zeta;² &minus; h²) / (1 &minus; h²&zeta;²)]<span class="sp">1/2</span></p>
+
+<p class="noind">being single valued in the latter semicircle. By means of a transformation
+t = (&zeta; + 1)² / (&zeta; &minus; 1)², the semicircle in the plane of &zeta; can
+further be conformably represented upon the upper half of the whole
+plane of t.</p>
+
+<p>As another illustration we may take the conformal representation
+of an equilateral triangle upon a half plane. Taking the elliptic
+function &real;(u) for which &real;&prime;²(u) = 4&real;³(u) &minus; 4, so that, with &epsilon; = exp (<span class="spp">2</span>&frasl;<span class="suu">3</span>&pi;i),
+we have e<span class="su">1</span> = 1, e<span class="su">2</span> = &epsilon;², e<span class="su">3</span> = &epsilon;, the half periods may be taken to be</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">½&omega; = <span class="f150">&int;</span> <span class="sp1">&infin;</span><span class="su1">1</span></td> <td>dt</td>
+<td rowspan="2">, &emsp; ½&omega;&prime; = <span class="f150">&int;</span> <span class="sp1">&infin;</span><span class="su1">e<span class="su">3</span></span></td> <td>dt</td>
+<td rowspan="2">= ½&epsilon;&omega;;</td></tr>
+<tr><td class="denom">2(t³ &minus; 1)<span class="sp">1/2</span></td> <td class="denom">2(t³ &minus; 1)<span class="sp">1/2</span></td></tr></table>
+
+<p class="noind">drawing the equilateral triangle whose vertices are O, of argument O,
+A of argument &omega;, and B of argument &omega; + &omega;&prime; = &minus;&epsilon;²&omega;, and the equilateral
+triangle whose angular points are O, B and C, of argument &omega;&prime;,
+let E, of argument <span class="spp">1</span>&frasl;<span class="suu">3</span>(2&omega; + &omega;&prime;), and D, of argument <span class="spp">1</span>&frasl;<span class="suu">3</span>(&omega; + 2&omega;&prime;), be the
+centroids of these triangles respectively, and let BE, OE, AE cut
+OA, AB, BO in K, L, H respectively, and BD, OD, CD cut OC, BC,
+OB in F, G, H respectively; then if u = &xi; + i&eta; be any point of the
+interior of the triangle OEH and v = &epsilon;u<span class="su">0</span> = &epsilon;(&xi; &minus; i&eta;) be any point of the
+interior of the triangle OHD, the points respectively of the ten
+triangles OEK, EKA, EAL, ELB, EBH, DHB, DBG, DGC, DCF,
+DFO are at once seen to be given by &minus;&epsilon;v, &omega; + &epsilon;u, &omega; &minus; &eta;²v, &omega; + &omega;&prime; + &epsilon;²u,
+&omega; + &omega;&prime; &minus; v, &omega; + &omega;&prime; &minus; u, &omega; + &omega;&prime; + &epsilon;v, &omega;&prime; &minus; &epsilon;u, &omega;&prime; + &epsilon;²v, &minus;&epsilon;²u. Further, when
+u is real, since the term &minus; 2(u + m&omega; + m&prime;&epsilon;²&omega;)<span class="sp">&minus;3</span>, which is the conjugate
+complex of &minus;2(u + m&omega; + m&prime;&epsilon;²&omega;)<span class="sp">3</span>, arises in the infinite sum
+which expresses &real;&prime;(u), namely as &minus;2(u + &mu;&omega; + &mu;&prime;&epsilon;&omega;)<span class="sp">&minus;3</span>, where
+&mu; = m &minus; m&prime;, &mu;&prime; = &minus;m&prime;, it follows that &real;&prime;(u) is real; in a similar
+way we prove that &real;&prime;(u) is pure imaginary when u is pure imaginary,
+and that &real;&prime;(u) = &real;&prime;(&epsilon;u) = &real;&prime;(&epsilon;²u), as also that for v = &epsilon;u<span class="su">0</span>, &real;&prime;(v) is the
+conjugate complex of &real;&prime;(u). Hence it follows that the variable</p>
+
+<p class="center">t = ½ i&real;&prime;(u)</p>
+
+<p><span class="pagenum"><a name="page322" id="page322"></a>322</span></p>
+
+<p class="noind">takes each real value once as u passes along the perimeter of the
+triangle ODE, being as can be shown respectively &infin;, 1, 0, &minus; 1 at O,
+D, H, E, and takes every complex value of imaginary part positive
+once in the interior of this triangle. This leads to</p>
+
+<p class="center">u = <span class="spp">1</span>&frasl;<span class="suu">3</span> i <span class="f150">&int;</span> <span class="sp1">&infin;</span><span class="su1">t</span> (t<span class="sp">2</span> &minus; 1)<span class="sp">&minus;2/3</span>dt</p>
+
+<p class="noind">in accordance with the general theory.</p>
+
+<p>It can be deduced that &tau; = t<span class="sp">2</span> represents the triangle ODH on the
+upper half plane of &tau;, and &zeta; = (i &minus; &tau;<span class="sp">&minus;1</span>)<span class="sp">1/2</span> represents similarly the
+triangle OBD.</p>
+</div>
+
+<p>§ 16. <i>Multiple valued Functions. Algebraic Functions.</i>&mdash;The
+explanations and definitions of a monogenic function hitherto
+given have been framed for the most part with a view to single
+valued functions. But starting from a power series, say in
+z &minus; c, which represents a single value at all points of its circle
+of convergence, suppose that, by means of a derived series in
+z &minus; c&prime;, where c&prime; is interior to the circle of convergence, we can
+continue the function beyond this, and then by means of a series
+derived from the first derived series we can make a further
+continuation, and so on; it may well be that when, after a
+closed circuit, we again consider points in the first circle of
+convergence, the value represented may not agree with the
+original value. One example is the case z<span class="sp">1/2</span>, for which two values
+exist for any value of z; another is the generalized logarithm
+&lambda;(z), for which there is an infinite number of values. In such
+cases, as before, the region of existence of the function consists
+of all points which can be reached by such continuations with
+power series, and the singular points, which are the limiting
+points of the point-aggregate constituting the region of existence,
+are those points in whose neighbourhood the radii of convergence
+of derived series have zero for limit. In this description the
+point z = &infin; does not occupy an exceptional position, a power
+series in z &minus; c being transformed to a series in 1/z when z is near
+enough to c by means of z &minus; c = c(1 &minus; cz<span class="sp">&minus;1</span>) [1 &minus; (1 &minus; cz<span class="sp">&minus;1</span>)]<span class="sp">&minus;1</span>, and a
+series in 1/z to a series in z &minus; c, when z is near enough to c, by
+means of 1/z = 1/c [1 + (z &minus; c / c)]<span class="sp">&minus;1</span>.</p>
+
+<div class="condensed">
+<p>The commonest case of the occurrence of multiple valued functions
+is that in which the function s satisfies an algebraic equation &fnof;(s, z) =
+p<span class="su">0</span>s<span class="sp">n</span> + p<span class="su">1</span>s<span class="sp">n&minus;1</span> + ... + p<span class="su">n</span> = 0, wherein p<span class="su">0</span>, p<span class="su">1</span>, ... p<span class="su">n</span> are integral polynomials
+in z. Assuming &fnof;(s, z) incapable of being written as a product
+of polynomials rational in s and z, and excepting values of z for
+which the polynomial coefficient of s<span class="sp">n</span> vanishes, as also the values
+of z for which beside &fnof;(s, z) = 0 we have also &part;f(s, z)/&part;s = 0, and also
+in general the point z = &infin;, the roots of this equation about any point
+z=c are given by n power series in z &minus; c. About a finite point z = c
+for which the equation &part;f(s, z)/&part;s = 0 is satisfied by one or more of the
+roots s of &fnof;(s, z) = 0, the n roots break up into a certain number of
+cycles, the r roots of a cycle being given by a set of power series in
+a radical (z &minus; c)<span class="sp">1/r</span>, these series of the cycle being obtainable from
+one another by replacing (z &minus; c)<span class="sp">1/r</span> by &omega;(z &minus; r)<span class="sp">1/r</span>, where &omega;, equal to
+exp (2&pi;ih/r), is one of the rth roots of unity. Putting then z &minus; c = t<span class="sp">r</span>
+we may say that the r roots of a cycle are given by a single power
+series in t, an increase of 2&pi; in the phase of t giving an increase of
+2&pi;r in the phase of z &minus; c. This single series in t, giving the values of
+s belonging to one cycle in the neighbourhood of z = c when the phase
+of z &minus; c varies through 2&pi;r, is to be looked upon as defining a single
+<i>place</i> among the aggregate of values of z and s which satisfy &fnof;(s, z) = 0;
+two such places may be at the same <i>point</i> (z = c, s = d) without
+coinciding, the corresponding power series for the neighbouring
+points being different. Thus for an ordinary value of z, z = c, there
+are n places for which the neighbouring values of s are given by n
+power series in z &minus; c; for a value of z for which &part;f(s, z)/&part;s = 0 there
+are less than n places. Similar remarks hold for the neighbourhood
+of z = &infin;; there may be n places whose neighbourhood is given by n
+power series in z<span class="sp">&minus; 1</span> or fewer, one of these being associated with a
+series in t, where t = (z<span class="sp">&minus;1</span>)<span class="sp">1/r</span>; the sum of the values of r which thus
+arise is always n. In general, then, we may say, with t of one of
+the forms (z &minus; c), (z &minus; c)<span class="sp">1/r</span>, z<span class="sp">&minus;1</span>, (z<span class="sp">&minus;1</span>)<span class="sp">1/r</span>. that the neighbourhood of
+any place (c, d) for which &fnof;(c, d) = 0 is given by a pair of expressions
+z = c + P(t), s = d + Q(t), where P(t) is a (particular case of a) power
+series vanishing for t = 0, and Q(t) is a power series vanishing for
+t = 0, and t vanishes at (c, d), the expression z &minus; c being replaced by
+z<span class="sp">&minus;1</span> when c is infinite, and similarly the expression s &minus; d by s<span class="sp">&minus;1</span> when
+d is infinite. The last case arises when we consider the finite values
+of z for which the polynomial coefficient of s<span class="sp">n</span> vanishes. Of such a
+pair of expressions we may obtain a continuation by writing t = t<span class="su">0</span> +
+&lambda;<span class="su">1</span>&tau; + &lambda;<span class="su">2</span>&tau;² + ..., where &tau; is a new variable and &lambda;<span class="su">1</span> is not zero;
+in particular for an ordinary finite place this equation simply becomes
+t = t<span class="su">0</span> + &tau;. It can be shown that all the pairs of power series z = c +
+P(t), s = d + Q(t) which are necessary to represent all pairs of values
+of z, s satisfying the equation &fnof;(s, z) = 0 can be obtained from one
+of them by this process of continuation, a fact which we express by
+saying that the equation &fnof;(s, z) = 0 defines a <i>monogenic algebraic
+construct</i>. With less accuracy we may say that an irreducible
+algebraic equation &fnof;(s, z) = 0 determines a single monogenic function
+s of z.</p>
+
+<p>Any rational function of z and s, where &fnof;(s, z) = 0, may be considered
+in the neighbourhood of any place (c, d) by substituting therein
+z = c + P(t), s = d + Q(t); the result is necessarily of the form t<span class="sp">m</span>H(t),
+where H(t) is a power series in t not vanishing for t=0 and m is an
+integer. If this integer is positive, the function is said to vanish
+to order m at the place; if this integer is negative, = &minus;&mu;, the function
+is infinite to order &mu; at the place. More generally, if A be an
+arbitrary constant, and, near (c, d), R(s, z) &minus;A is of the form t<span class="sp">m</span>H(t),
+where m is positive, we say that R(s, z) becomes m times equal to A
+at the place; if R(s, z) is infinite of order &mu; at the place, so also is
+R(s, z) &minus; A. It can be shown that the sum of the values of m at all
+the places, including the places z = &infin;, where R(s, z) vanishes, which
+we call the number of zeros of R(s, z) on the algebraic construct, is
+finite, and equal to the sum of the values of &mu; where R(s, z) is infinite,
+and more generally equal to the sum of the values of m where
+R(s, z) = A; this we express by saying that a rational function
+R(s, z) takes any value (including &infin;) the same number of times on
+the algebraic construct; this number is called the <i>order</i> of the
+rational function.</p>
+
+<p>That the total number of zeros of R(s, z) is finite is at once obvious,
+these values being obtainable by rational elimination of s between
+&fnof;(s, z) = 0, R(s, z) = 0. That the number is equal to the total number
+of infinities is best deduced by means of a theorem which is also of
+more general utility. Let R(s, z) be any rational function of s, z,
+which are connected by &fnof;(s, z) = 0; about any place (c, d) for which
+z = c + P(t), s = d + Q(t), expand the product</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">R(s, z)</td> <td>dz</td></tr>
+<tr><td class="denom">dt</td></tr></table>
+
+<p class="noind">in powers of t and pick out the coefficient of t<span class="sp">&minus;1</span>. There is only a
+finite number of places of this kind. The theorem is that the sum
+of these coefficients of t<span class="sp">&minus;1</span> is zero. This we express by</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">[</span> R(s, z)</td> <td>dz</td>
+<td rowspan="2"><span class="f150">]</span><span class="su">t<span class="sp">&minus;1</span></span> = 0.</td></tr>
+<tr><td class="denom">dt</td></tr></table>
+
+<p class="noind">The theorem holds for the case n=1, that is, for rational functions
+of one variable z; in that case, about any finite point we have
+z &minus; c = t, and about z = &infin; we have z<span class="sp">&minus;1</span> = t, and therefore dz/dt = &minus;t<span class="sp">&minus;2</span>;
+in that case, then, the theorem is that in any rational function of z,</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">&Sigma; (</span></td> <td>A<span class="su">1</span></td>
+<td rowspan="2">+</td> <td>A<span class="su">2</span></td>
+<td rowspan="2">+ ... +</td> <td>A<span class="su">m</span></td>
+<td rowspan="2"><span class="f150">)</span> + Pz<span class="sp">h</span> + Qz<span class="sp">h&minus;1</span> + ... + R,</td></tr>
+<tr><td class="denom">z &minus; a </td> <td class="denom">(z &minus; a)²</td>
+<td class="denom">(z &minus; a)<span class="sp">m</span></td></tr></table>
+
+<p class="noind">the sum &Sigma;A<span class="su">1</span> of the sum of the residues at the finite poles is equal
+to the coefficient of 1/z in the expansion, in ascending powers of 1/z,
+about z = &infin;; an obvious result. In general, if for a finite place
+of the algebraic construct associated with &fnof;(s, z) = 0, whose neighbourhood
+is given by z = c + t<span class="sp">r</span>, s = d + Q(t), there be a coefficient of t<span class="sp">&minus;1</span> in
+R(s, z) dz/dt, this will be r times the coefficient of t<span class="sp">&minus;r</span> in R(s, z) or
+R[d + Q(t), c + t<span class="sp">r</span>], namely will be the coefficient of t<span class="sp">&minus;r</span> in the sum of
+the r series obtainable from R [d + Q(t), c + t<span class="sp">r</span>] by replacing t by &omega;t,
+where &omega; is an rth root of unity; thus the sum of the coefficients of
+t<span class="sp">&minus;1</span> in R(s, z) dz/dt for all the places which arise for z = c, and the corresponding
+values of s, is equal to the coefficient of (z &minus; c)<span class="sp">&minus;1</span> in R(s<span class="su">1</span>, z) +
+R(s<span class="su">2</span>z) + ... + R(s<span class="su">n</span>, z), where s<span class="su">1</span>, ... s<span class="su">n</span> are the n values of s for a
+value of z near to z = c; this latter sum &Sigma; R(s<span class="su">i</span>, z) is, however, a
+rational function of z only. Similarly, near z = &infin;, for a place given
+by z<span class="sp">&minus;1</span>=t<span class="sp">r</span>, s = d + Q(t), or s<span class="sp">&minus;1</span> = Q(t), the coefficient of t<span class="sp">&minus;1</span> in R(s, z) dz/dt
+is equal to &minus;r times the coefficient of t<span class="sp">r</span> in R[d + Q(t), t<span class="sp">&minus;r</span>], that is
+equal to the negative coefficient of z<span class="sp">&minus;l</span> in the sum of the r series
+R[d + Q(&omega;t), t<span class="sp">&minus;r</span>], so that, as before, the sum of the coefficients of
+t<span class="sp">&minus;1</span> in R(s, z) dz/dt at the various places which arise for z = &infin; is equal
+to the negative coefficient of z<span class="sp">&minus; 1</span> in the same rational function of z,
+&Sigma; R(s<span class="su">i</span>, z). Thus, from the corresponding theorem for rational functions
+of one variable, the general theorem now being proved is seen to
+follow.</p>
+
+<p>Apply this theorem now to the rational function of s and z,</p>
+
+<table class="math0" summary="math">
+<tr><td>1</td>
+<td rowspan="2">&nbsp;</td> <td>dR(s, z)</td>
+<td rowspan="2">;</td></tr>
+<tr><td class="denom">R(s, z)</td> <td class="denom">dz</td></tr></table>
+
+<p class="noind">at a zero of R(s, z) near which R(s, z) = t<span class="sp">m</span>H(t), we have</p>
+
+<table class="math0" summary="math">
+<tr><td>1</td>
+<td rowspan="2">&nbsp;</td> <td>dR(s, z)</td>
+<td rowspan="2">&nbsp;</td> <td>dz</td>
+<td rowspan="2">=</td> <td>d</td>
+<td rowspan="2">{&lambda; [R(s, z)] },</td></tr>
+<tr><td class="denom">R(s, z)</td> <td class="denom">dz</td>
+<td class="denom">dt</td> <td class="denom">dt</td></tr></table>
+
+<p class="noind">where &lambda; denotes the generalized logarithmic function, that is equal
+to</p>
+
+<p class="center">mt<span class="sp">&minus;1</span> + power series in t;</p>
+
+<p class="noind">similarly at a place for which R(s, z) = t<span class="sp">&minus;&mu;</span>K(t); the theorem</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">[</span></td> <td>1</td>
+<td rowspan="2">&nbsp;</td> <td>dR(s, z)</td>
+<td rowspan="2">&nbsp;</td> <td>dz</td>
+<td rowspan="2"><span class="f150">]</span><span class="su">t<span class="sp">&minus;1</span></span> = 0</td></tr>
+<tr><td class="denom">R(s, z)</td> <td class="denom">dz</td>
+<td class="denom">dt</td></tr></table>
+
+<p class="noind">thus gives &Sigma;m = &Sigma;&mu;, or, in words, the total number of zeros of R(s, z)
+on the algebraic construct is equal to the total number of its poles.
+The same is therefore true of the function R(s, z) &minus; A, where A is an
+arbitrary constant; thus the number in question, being equal to the
+number of poles of R(s, z) &minus; A, is equal also to the number of times
+that R(s, z) = A on the algebraic construct.</p>
+
+<p><span class="pagenum"><a name="page323" id="page323"></a>323</span></p>
+
+<p>We have seen above that all single valued doubly periodic meromorphic
+functions, with the same periods, are rational functions of
+two variables s, z connected by an equation of the form s² = 4z³ +
+Az + B. Taking account of the relation connecting these variables s, z
+with the argument of the doubly periodic functions (which was above
+denoted by z), it can then easily be seen that the theorem now proved
+is a generalization of the theorem proved previously establishing for
+a doubly periodic function a definite <i>order</i>. There exists a generalization
+of another theorem also proved above for doubly periodic
+functions, namely, that the sum of the values of the argument in one
+parallelogram of periods for which a doubly periodic function takes
+a given value is independent of that value; this generalization,
+known as Abel&rsquo;s Theorem, is given § 17 below.</p>
+</div>
+
+<p>§ 17. <i>Integrals of Algebraic Functions.</i>&mdash;In treatises on Integral
+Calculus it is proved that if R(z) denote any rational function,
+an indefinite integral &int;R(z)dz can be evaluated in terms of
+rational and logarithmic functions, including the inverse trigonometrical
+functions. In generalization of this it was long ago
+discovered that if s² = az² + bz + c and R(s, z) be any rational
+function of s, z any integral &int;R(s, z)dz can be evaluated in terms
+of rational functions of s, z and logarithms of such functions;
+the simplest case is &int;s<span class="sp">&minus; 1</span>dz or &int;(az² + bz + c)<span class="sp"> &minus;1/2</span>dz. More generally
+if f(s, z) = 0 be such a relation connecting s, z that when &theta; is an
+appropriate rational function of s and z both s and z are rationally
+expressible, in virtue of &fnof;(s, z) = 0 in terms of &theta;, the integral
+&int;R(s, z)dz is reducible to a form &int;H(&theta;)d&theta;, where H(&theta;) is rational
+in &theta;, and can therefore also be evaluated by rational functions
+and logarithms of rational functions of s and z. It was natural
+to inquire whether a similar theorem holds for integrals
+&int;R(s, z)dz wherein s² is a cubic polynomial in z. The answer is
+in the negative. For instance, no one of the three integrals</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">&int;</span></td> <td>dz</td>
+<td rowspan="2">, <span class="f150">&int;</span></td> <td>zdz</td>
+<td rowspan="2">, <span class="f150">&int;</span></td> <td>dz</td></tr>
+<tr><td class="denom">s</td> <td class="denom">s</td>
+<td class="denom">(z &minus; c)s</td></tr></table>
+
+<p class="noind">can be expressed by rational and logarithms of rational functions
+of s and z; but it can be shown that every integral &int;R(s, z)dz
+can be expressed by means of integrals of these three types
+together with rational and logarithms of rational functions of
+s and z (see below under § 20, <i>Elliptic Integrals</i>). A similar
+theorem is true when s² = quartic polynomial in z; in fact when
+s² = A(z &minus; a) (z &minus; b) (z &minus; c) (z &minus; d), putting y = s(z &minus; a)<span class="sp">&minus;2</span>, x = (z &minus; a)<span class="sp">&minus;1</span>,
+we obtain y<span class="sp">2</span> = cubic polynomial in x. Much less is the theorem
+true when the fundamental relation &fnof;(s, z) = 0 is of more general
+type. There exists then, however, a very general theorem,
+known as <i>Abel&rsquo;s Theorem</i>, which may be enunciated as follows:
+Beside the rational function R(s, z) occurring in the integral
+&int;R(s, z)dz, consider another rational function H(s, z); let
+(a<span class="su">1</span>), ... (a<span class="su">m</span>) denote the places of the construct associated
+with the fundamental equation &fnof;(s, z) = 0, for which H(s, z) is
+equal to one value A, each taken with its proper multiplicity,
+and let (b<span class="su">1</span>), ... (b<span class="su">m</span>) denote the places for which H(s, z) = B,
+where B is another value; then the sum of the m integrals
+<span class="f150">&int;</span> <span class="sp1">(b<span class="su">i</span>)</span><span class="su1">(a<span class="su">i</span>)</span> R(s, z)dz is equal to the sum of the coefficients of t<span class="sp">&minus;1</span> in the
+expansions of the function</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">R(s, z)</td> <td>dz</td>
+<td rowspan="2">&lambda; <span class="f150">(</span></td> <td>H(s, z) &minus; B</td>
+<td rowspan="2"><span class="f150">)</span>,</td></tr>
+<tr><td class="denom">dt</td> <td class="denom">H(s, z) &minus; A</td></tr></table>
+
+<p class="noind">where &lambda; denotes the generalized logarithmic function, at the
+various places where the expansion of R(s, z)dz/dt contains
+negative powers of t. This fact may be obtained at once from
+the equation</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">[</span></td> <td>1</td>
+<td rowspan="2">R(s, z)</td> <td>dz</td>
+<td rowspan="2"><span class="f150">]</span><span class="su">t<span class="sp">&minus;1</span></span> = 0,</td></tr>
+<tr><td class="denom">H(s, z) &minus; &mu;</td> <td class="denom">dt</td></tr></table>
+
+<p class="noind">wherein &mu; is a constant. (For illustrations see below, under
+§ 20, <i>Elliptic Integrals</i>.)</p>
+
+<p>§ 18. <i>Indeterminateness of Algebraic Integrals.</i>&mdash;The theorem
+that the integral <span class="f150">&int;</span> <span class="sp1">x</span><span class="su1">a</span> &fnof;(z)dz is independent of the path from a to
+z, holds only on the hypothesis that any two such paths are
+equivalent, that is, taken together from the complete boundary
+of a region of the plane within which &fnof;(z) is finite and single
+valued, besides being differentiable. Suppose that these conditions
+fail only at a finite number of isolated points in the finite
+part of the plane. Then any path from a to z is equivalent,
+in the sense explained, to any other path together with closed
+paths beginning and ending at the arbitrary point a each enclosing
+one or more of the exceptional points, these closed paths being
+chosen, when &fnof;(z) is not a single valued function, so that the final
+value of &fnof;(z) at a is equal to its initial value. It is necessary for
+the statement that this condition may be capable of being
+satisfied.</p>
+
+<div class="condensed">
+<p>For instance, the integral <span class="f150">&int;</span> <span class="sp1">z</span><span class="su1">1</span> z<span class="sp">&minus;1</span>dz is liable to an additive indeterminateness
+equal to the value obtained by a closed path about z = 0,
+which is equal to 2&pi;i; if we put u = <span class="f150">&int;</span> <span class="sp1">z</span><span class="su1">1</span> z<span class="sp">&minus;1</span>dz and consider z as a
+function of u, then we must regard this function as unaffected by
+the addition of 2&pi;i to its argument u; we know in fact that
+z = exp (u) and is a single valued function of u, with the period 2&pi;i.
+Or again the integral <span class="f150">&int;</span> <span class="sp1">z</span><span class="su1">0</span> (1 + z²)<span class="sp">&minus;1</span>dz is liable to an additive indeterminateness
+equal to the value obtained by a closed path about
+either of the points z = ±i; thus if we put u = <span class="f150">&int;</span> <span class="sp1">z</span><span class="su1">0</span> (1 + z²)<span class="sp">&minus;1</span>dz, the
+function z of u is periodic with period &pi;, this being the function
+tan (u). Next we take the integral u = <span class="f150">&int;</span> <span class="sp1">(z)</span><span class="su1">(0)</span> (1 &minus; z²)<span class="sp">&minus;1/2</span>dz, agreeing that
+the upper and lower limits refer not only to definite values of z, but
+to definite values of z each associated with a definite determination
+of the sign of the associated radical (1 &minus; z²)<span class="sp">&minus;1/2</span>. We suppose 1 + z,
+1 &minus; z each to have phase zero for z = 0; then a single closed circuit
+of z = &minus;1 will lead back to z = 0 with (l &minus; z²)<span class="sp">1/2</span> = &minus;1; the additive
+indeterminateness of the integral, obtained by a closed path which
+restores the initial value of the subject of integration, may be
+obtained by a closed circuit containing both the points ±1 in its
+interior; this gives, since the integral taken about a vanishing
+circle whose centre is either of the points z = ±1 has ultimately
+the value zero, the sum</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">&int;</span> <span class="sp1">&minus;1</span><span class="su1">0</span></td> <td>dz</td>
+<td rowspan="2">+ <span class="f150">&int;</span> <span class="sp1">0</span><span class="su1">&minus;1</span></td> <td>dz</td>
+<td rowspan="2">+ <span class="f150">&int;</span> <span class="sp1">1</span><span class="su1">0</span></td> <td>dz</td>
+<td rowspan="2">+ <span class="f150">&int;</span> <span class="sp1">0</span><span class="su1">1</span></td> <td>dz</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">(1 &minus; z²)<span class="sp">1/2</span></td> <td class="denom">&minus;(1 &minus; z²)<span class="sp">1/2</span></td>
+<td class="denom">&minus;(1 &minus; z²)<span class="sp">1/2</span></td> <td class="denom">(1 &minus; z²)<span class="sp">1/2</span></td></tr></table>
+
+<p class="noind">where, in each case, (1 &minus; z²)<span class="sp">1/2</span> is real and positive; that is, it gives</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&minus;4 <span class="f150">&int;</span> <span class="sp1">1</span><span class="su1">0</span></td> <td>dz</td></tr>
+<tr><td class="denom">(1 &minus; z²)<span class="sp">1/2</span></td></tr></table>
+
+<p class="noind">or 2&pi;. Thus the additive indeterminateness of the integral is of the
+form 2k&pi;, where k is an integer, and the function z of u, which is
+sin (u), has 2&pi; for period. Take now the case</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">u = <span class="f150">&int;</span> <span class="sp1">(z)</span><span class="su1">(z<span class="su">0</span>)</span></td> <td>dz</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">&radic;{ (z &minus; a) (z &minus; b) (z &minus; c) (z &minus; d) }</td></tr></table>
+
+<p class="noind">adopting a definite determination for the phase of each of the
+factors z &minus; a, z &minus; b, z &minus; c, z &minus; d at the arbitrary point z<span class="su">0</span>, and supposing
+the upper limit to refer, not only to a definite value of z, but also
+to a definite determination of the radical under the sign of integration.
+From z<span class="su">0</span> describe a closed loop about the point z = a, consisting,
+suppose, of a straight path from z<span class="su">0</span> to a, followed by a vanishing
+circle whose centre is at a, completed by the straight path from a
+to z<span class="su">0</span>. Let similar loops be imagined for each of the points b, c, d,
+no two of these having a point in common. Let A denote the value
+obtained by the positive circuit of the first loop; this will be in fact
+equal to twice the integral taken from z<span class="su">0</span> along the straight path
+to a; for the contribution due to the vanishing circle is ultimately
+zero, and the effect of the circuit of this circle is to change the sign
+of the subject of integration. After the circuit about a, we arrive
+back at z<span class="su">0</span> with the subject of integration changed in sign; let
+B, C, D denote the values of the integral taken by the loops enclosing
+respectively b, c and d when in each case the initial determination
+of the subject of integration is that adopted in calculating
+A. If then we take a circuit from z<span class="su">0</span> enclosing both a and b but
+not either c or d, the value obtained will be A &minus; B, and on returning
+to z<span class="su">0</span> the subject of integration will have its initial value. It appears
+thus that the integral is subject to an additive indeterminateness
+equal to any one of the six differences such as A &minus; B. Of these
+there are only two linearly independent; for clearly only A &minus; B,
+A &minus; C, A &minus; D are linearly independent, and in fact, as we see by
+taking a closed circuit enclosing all of a, b, c, d, we have A &minus; B +
+C &minus; D = 0; for there is no other point in the plane beside a, b, c, d
+about which the subject of integration suffers a change of sign, and a
+circuit enclosing all of a, b, c, d may by putting z = 1/&zeta; be reduced to a
+circuit about &zeta; = 0 about which the value of the integral is zero.
+The general value of the integral for any position of z and the associated
+sign of the radical, when we start with a definite determination
+of the subject of integration, is thus seen to be of the form
+u<span class="su">0</span> + m(A &minus; B) + n(A &minus; C), where m and n are integers. The value of
+A &minus; B is independent of the position of z<span class="su">0</span>, being obtainable by a single
+closed positive circuit about a and b only; it is thus equal to twice the
+integral taken once from a to b, with a proper initial determination
+of the radical under the sign of integration. Similar remarks to the
+above apply to any integral &int; H(z)dz, in which H(z) is an algebraic
+function of z; in any such case H(z) is a rational function of z and a
+quantity s connected therewith by an irreducible rational algebraic
+<span class="pagenum"><a name="page324" id="page324"></a>324</span>
+equation &fnof;(s, z) = 0. Such an integral &fnof;K(z, s)dz is called an Abelian
+Integral.</p>
+</div>
+
+<p>§ 19. <i>Reversion of an Algebraic Integral</i>.&mdash;In a limited number of
+cases the equation u = &int; [z<span class="su">0</span> to z] H(z)dz, in which H(z) is an algebraic function
+of z, defines z as a single valued function of u. Several cases of this
+have been mentioned in the previous section; from what was
+previously proved under § 14, <i>Doubly Periodic Functions</i>, it appears
+that it is necessary for this that the integral should have at most
+two linearly independent additive constants of indeterminateness;
+for instance, for an integral</p>
+
+<p class="center">u = <span class="f150">&int;</span> <span class="sp1">z</span><span class="su1">z<span class="su">0</span></span> [(z &minus; a) (z &minus; b) (z &minus; c) (z &minus; d) (z &minus; e) (z &minus; f) ]<span class="sp">&minus;1/2</span>dz,</p>
+
+<p class="noind">there are three such constants, of the form A &minus; B, A &minus; C, A &minus; D,
+which are not connected by any linear equation with integral coefficients,
+and z is not a single valued function of u.</p>
+
+<p>§ 20. <i>Elliptic Integrals</i>.&mdash;An integral of the form &int; R(z, s)dz,
+where s denotes the square root of a quartic polynomial in z,
+which may reduce to a cubic polynomial, and R denotes a
+rational function of z and s, is called an <i>elliptic integral</i>.</p>
+
+<div class="condensed">
+<p>To each value of z belong two values of s, of opposite sign; starting,
+for some particular value of z, with a definite one of these two
+values, the sign to be attached to s for any other value of z will be
+determined by the path of integration for z. When z is in the neighbourhood
+of any finite value z<span class="su">0</span> for which the radical s is not zero,
+if we put z &minus; z<span class="su">0</span> = t, we can find s &minus; s<span class="su">0</span> = a power series in t, say
+s=s<span class="su">0</span> + Q(t); when z is in the neighbourhood of a value, a, for which
+s vanishes, if we put z = a + t², we shall obtain s = tQ(t), where Q(t) is a
+power series in t; when z is very large and s² is a quartic polynomial
+in z, if we put z<span class="sp">&minus;1</span> = t, we shall find s<span class="sp">&minus;1</span> = t²Q(t); when z is very large
+and s² is a cubic polynomial in z, if we put z<span class="sp">&minus;1</span> = t², we shall find
+s<span class="sp">&minus;l</span> = t³Q(t). By means of substitutions of these forms the character
+of the integral &int; R(z, s)dz may be investigated for any position of z;
+in any case it takes a form &int; [Ht<span class="sp">&minus;m</span> + Kt<span class="sp">&minus;m+1</span> + ... + Pt<span class="sp">&minus;1</span> + R + St + ... ]dt
+involving only a finite number of negative powers of t in the subject
+of integration. Consider first the particular case &int; s<span class="sp">&minus;1</span>dz; it is easily
+seen that neither for any finite nor for infinite values of z can negative
+powers of t enter; the integral is <i>everywhere finite</i>, and is said to be
+of <i>the first kind</i>; it can, moreover, be shown without difficulty that
+no integral &int; R(z, s)dz, save a constant multiple of &int; s<span class="sp">&minus;1</span>dz, has this
+property. Consider next, s² being of the form a<span class="su">0</span>z<span class="sp">4</span> + 4a<span class="su">1</span>z³ + ...,
+wherein a<span class="su">0</span> may be zero, the integral &int; (a<span class="su">0</span>z² + 2a<span class="su">1</span>z) s<span class="sp">&minus;1</span>dz; for any finite
+value of z this integral is easily proved to be everywhere finite;
+but for infinite values of z its value is of the form At<span class="sp">&minus;1</span> + Q(t), where
+Q(t) is a power series; denoting by &radic;a<span class="su">0</span> a particular square root of a<span class="su">0</span>
+when a<span class="su">0</span> is not zero, the integral becomes infinite for z = &infin; for both
+signs of s, the value of A being + &radic;a<span class="su">0</span> or &minus; &radic;a<span class="su">0</span> according as s is
+&radic;a<span class="su">0</span>·z² (1 + [2a<span class="su">1</span>/a<span class="su">0</span>] z<span class="sp">&minus;1</span> + ... ) or is the negative of this; hence the integral
+J<span class="su">1</span> = <span class="f150">&int;</span> ( [a<span class="su">0</span>z² + 2a<span class="su">1</span>z]/s + &radic;a<span class="su">0</span>) dz becomes infinite when z is infinite, for
+the former sign of s, its infinite term being 2&radic;a<span class="su">0</span>·t<span class="sp">&minus;1</span> or 2a<span class="su">0</span>·z,
+but does not become infinite for z infinite for the other sign of s.
+When a<span class="su">0</span> = 0 the signs of s for z = &infin; are not separated, being obtained
+one from the other by a circuit of z about an infinitely large circle,
+and the form obtained represents an integral becoming infinite as
+before for z = &infin;, its infinite part being 2&radic;a<span class="su">1</span>·t<span class="sp">&minus;1</span> or 2&radic;a<span class="su">1</span>·&radic;z. Similarly
+if z<span class="su">0</span> be any finite value of z which is not a root of the polynomial
+&fnof;(z) to which s² is equal, and s<span class="su">0</span> denotes a particular one of the determinations
+of s for z=z<span class="su">0</span>, the integral</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">J<span class="su">2</span> = <span class="f150">&int; {</span></td> <td>s²<span class="su">0</span> + ½(z &minus; z<span class="su">0</span>) &fnof;&prime;(z<span class="su">0</span>)</td>
+<td rowspan="2">+</td> <td>s<span class="su">0</span></td>
+<td rowspan="2"><span class="f150">}</span> dz,</td></tr>
+<tr><td class="denom">(z &minus; z<span class="su">0</span>)² s</td> <td class="denom">(z &minus; z<span class="su">0</span>)²</td></tr></table>
+
+<p class="noind">wherein &fnof;&prime;(z) = d&fnof;(z)/dz, becomes infinite for z = z<span class="su">0</span>, s = s<span class="su">0</span>, but not for
+z = z<span class="su">0</span>, s = &minus;s<span class="su">0</span>. its infinite term in the former case being the negative of
+2s<span class="su">0</span>(z &minus; z<span class="su">0</span>). For no other finite or infinite value of z is the integral
+infinite. If z = &theta; be a root of &fnof;(z), in which case the corresponding
+value of s is zero, the integral</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">J<span class="su">3</span> = ½&fnof;&prime;(&theta;) <span class="f150">&int;</span></td> <td>dz</td></tr>
+<tr><td class="denom">(z &minus; &theta;) s</td></tr></table>
+
+<p class="noind">becomes infinite for z=0, its infinite part being, if z &minus; &theta; = t², equal to
+&minus;[&fnof;&prime;(&theta;)]½ t<span class="sp">&minus;1</span>: and this integral is not elsewhere infinite. In each
+of these cases, of the integrals J<span class="su">1</span>, J<span class="su">2</span>, J<span class="su">3</span>, the subject of integration
+has been chosen so that when the integral is written near its point of
+infinity in the form &int;[At<span class="sp">&minus;2</span> + Bt<span class="sp">&minus;1</span> + Q(t)] dt, the coefficient B is zero,
+so that the infinity is of algebraic kind, and so that, when there are
+two signs distinguishable for the critical value of z, the integral
+becomes infinite for only one of these. An integral having only
+algebraic infinities, for finite or infinite values of z, is called an
+integral of the <i>second kind</i>, and it appears that such an integral
+can be formed with only one such infinity, that is, for an infinity
+arising only for one particular, and arbitrary, pair of values (s, z)
+satisfying the equation s² = &fnof;(z), this infinity being of the first order.
+A function having an algebraic infinity of the mth order (m &gt; 1),
+only for one sign of s when these signs are separable, at (1) z = &infin;,
+(2) z = z<span class="su">0</span>, (3) z = a, is given respectively by (s d/dz)<span class="sp">m&minus;1</span> J<span class="su">1</span>, (s d/dz)<span class="sp">m&minus;1</span> J<span class="su">2</span>,
+(s d/dz)<span class="sp">m&minus;1</span> J<span class="su">3</span>, as we easily see. If then we have any elliptic integral
+having algebraic infinities we can, by subtraction from it of an
+appropriate sum of constant multiples of J<span class="su">1</span>, J<span class="su">2</span>, J<span class="su">3</span> and their differential
+coefficients just written down, obtain, as the result, an integral
+without algebraic infinities. But, in fact, if J, J<span class="sp">1</span> denote any two
+of the three integrals J<span class="su">1</span>, J<span class="su">2</span>, J<span class="su">3</span>, there exists an equation AJ + BJ&prime; +
+C&fnof;s<span class="sp">&minus;1</span>dz = rational function of s, z, where A, B, C are properly chosen
+constants. For the rational function</p>
+
+<table class="math0" summary="math">
+<tr><td>s + s<span class="su">0</span></td>
+<td rowspan="2">+ z &radic;a<span class="su">0</span></td></tr>
+<tr><td class="denom">z &minus; z<span class="su">0</span></td></tr></table>
+
+<p>is at once found to become infinite for (z<span class="su">0</span>, s<span class="su">0</span>), not for (z<span class="su">0</span>, &minus;s<span class="su">0</span>), its
+infinite part for the first point being 2s/(z &minus; z<span class="su">0</span>), and to become
+infinite for z infinitely large, and one sign of s only when these are
+separable, its infinite part there being 2z &radic;a<span class="su">0</span> or 2 &radic;a<span class="su">1</span> &radic;z when a<span class="su">0</span> = 0.
+It does not become infinite for any other pair (z, s) satisfying the
+relation s<span class="sp">2</span> = &fnof;(z); this is in accordance with the easily verified
+equation</p>
+
+<table class="math0" summary="math">
+<tr><td>s + s<span class="su">0</span></td>
+<td rowspan="2">+ z &radic;a<span class="su">0</span> &minus; J<span class="su">1</span> + J<span class="su">2</span> + (a<span class="su">0</span>z<span class="su">0</span><span class="sp">2</span> + 2a<span class="su">1</span>z<span class="su">0</span>) <span class="f150">&int;</span></td> <td>dz</td>
+<td rowspan="2">= 0;</td></tr>
+<tr><td class="denom">z &minus; z<span class="sp">0</span></td> <td class="denom">s</td></tr></table>
+
+<p class="noind">and there exists the analogous equation</p>
+
+<table class="math0" summary="math">
+<tr><td>s</td>
+<td rowspan="2">+ z &radic;a<span class="su">0</span> &minus; J<span class="su">1</span> + J<span class="su">3</span> + (a<span class="su">0</span>&theta;<span class="sp">2</span> + 2a<span class="su">1</span>&theta;) <span class="f150">&int;</span></td> <td>dz</td>
+<td rowspan="2">.</td></tr>
+<tr><td class="denom">z &minus; &theta;</td> <td class="denom">s</td></tr></table>
+
+<p class="noind">Consider now the integral</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">P = <span class="f150">&int; (</span></td> <td>s + s<span class="su">0</span></td>
+<td rowspan="2">+ z &radic;a<span class="su">0</span> <span class="f150">)</span></td> <td>dz</td>
+<td rowspan="2">;</td></tr>
+<tr><td class="denom">z &minus; z<span class="su">0</span></td> <td class="denom">2s</td></tr></table>
+
+<p class="noind">this is at once found to be infinite, for finite values of z, only for
+(z<span class="su">0</span>, s<span class="su">0</span>), its infinite part being log (z &minus; z<span class="su">0</span>), and for z = &infin;, for one sign
+of s only when these are separable, its infinite part being &minus;log t,
+that is &minus;log z when a<span class="su">0</span> &ne; 0, and &minus;log (z<span class="sp">1/2</span>) when a<span class="su">0</span> = 0. And, if
+&fnof;(&theta;) = 0, the integral</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">P<span class="su">1</span> = <span class="f150">&int; (</span></td> <td>s</td>
+<td rowspan="2">+ z &radic;a<span class="su">0</span> <span class="f150">)</span></td> <td>dz</td></tr>
+<tr><td class="denom">z &minus; &theta;</td> <td class="denom">2s</td></tr></table>
+
+<p class="noind">is infinite at z = &theta;, s = 0 with an infinite part log t, that is log (z &minus; &theta;)<span class="sp">1/2</span>,
+is not infinite for any other finite value of z, and is infinite like P for
+z = &infin;. An integral possessing such logarithmic infinities is said
+to be of the third kind.</p>
+
+<p>Hence it appears that any elliptic integral, by subtraction from
+it of an appropriate sum formed with constant multiples of the
+integral J<span class="su">3</span> and the rational functions of the form (s d/dz)<span class="sp">m&minus;1</span> J<span class="su">1</span>
+with constant multiples of integrals such as P or P<span class="su">1</span>, with constant
+multiples of the integral u = &int;s<span class="sp">&minus;1</span>dz, and with rational functions,
+can be reduced to an integral H becoming infinite only for z = &infin;,
+for one sign of s only when these are separable, its infinite part being
+of the form A log t, that is, A log z or A log (z<span class="sp">1/2</span>). Such an integral
+H = &int;R(z, s)dz does not exist, however, as we at once find by writing
+R(z, s) = P(z) + sQ(z), where P(z), Q(z) are rational functions of z,
+and examining the forms possible for these in order that the integral
+may have only the specified infinity. An analogous theorem holds
+for rational functions of z and s; there exists no rational function
+which is finite for finite values of z and is infinite only for z = &infin;
+for one sign of s and to the first order only; but there exists a
+rational function infinite in all to the first order for each of two or
+more pairs (z, s), however they may be situated, or infinite to the
+second order for an arbitrary pair (z, s); and any rational function
+may be formed by a sum of constant multiples of functions such as</p>
+
+<table class="math0" summary="math">
+<tr><td>s + s<span class="su">0</span></td>
+<td rowspan="2">+ z &radic;a<span class="su">0</span> or</td> <td>s</td>
+<td rowspan="2">+ z &radic;a<span class="su">0</span></td></tr>
+<tr><td class="denom">z &minus; z<span class="su">0</span></td> <td class="denom">z &minus; &theta;</td></tr></table>
+
+<p class="noind">and their differential coefficients.</p>
+
+<p>The consideration of elliptic integrals is therefore reducible to
+that of the three</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">u = <span class="f150">&int;</span></td> <td>dz</td>
+<td rowspan="2">, &emsp; J = <span class="f150">&int; (</span></td> <td>a<span class="su">0</span>z<span class="sp">2</span> + 2a<span class="su">1</span>z</td>
+<td rowspan="2">+ z &radic;a<span class="su">0</span> <span class="f150">)</span> dz, &emsp; P = <span class="f150">&int; (</span></td> <td>s + s<span class="su">0</span></td>
+<td rowspan="2">+ z &radic;a<span class="su">0</span> <span class="f150">)</span></td> <td>dz</td></tr>
+<tr><td class="denom">s</td> <td class="denom">s</td>
+<td class="denom">z &minus; z<span class="su">0</span></td> <td class="denom">2s</td></tr></table>
+
+<p class="noind">respectively of the first, second and third kind. Now the equation
+s<span class="sp">2</span> = a<span class="su">0</span>z<span class="sp">4</span> + ... = a<span class="su">0</span> (z &minus; &theta;) (z &minus; &phi;) (z &minus; &psi;) (z &minus; &chi;), by putting</p>
+
+<p class="center">y = 2s (z &minus; &theta;)<span class="sp">&minus;2</span> [a<span class="su">0</span> (&theta; &minus; &phi;) (&theta; &minus; &psi;) (&theta; &minus; &chi;) ]<span class="sp">&minus;1/2</span></p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">x =</td> <td>1</td>
+<td rowspan="2">+</td> <td>1</td>
+<td rowspan="2"><span class="f150">(</span></td> <td>1</td>
+<td rowspan="2">+</td> <td>1</td>
+<td rowspan="2">+</td> <td>1</td>
+<td rowspan="2"><span class="f150">)</span></td></tr>
+<tr><td class="denom">z &minus; &theta;</td> <td class="denom">3</td>
+<td class="denom">&theta; &minus; &phi;</td> <td class="denom">&theta; &minus; &psi;</td>
+<td class="denom">&theta; &minus; &chi;</td></tr></table>
+
+<p class="noind">is at once reduced to the form y<span class="sp">2</span> = 4x<span class="sp">3</span> &minus; g<span class="su">2</span>x &minus; g<span class="su">3</span> = 4(x &minus; e<span class="su">1</span>) (x &minus; e<span class="su">2</span>) (x &minus; e<span class="su">3</span>),
+say; and these equations enable us to express s and z rationally
+in terms of x and y. It is therefore sufficient to consider three
+elliptic integrals</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">u = <span class="f150">&int;</span></td> <td>dx</td>
+<td rowspan="2">, &emsp; J = <span class="f150">&int;</span></td> <td>xdx</td>
+<td rowspan="2">, &emsp; P = <span class="f150">&int;</span></td> <td>y + y<span class="su">0</span></td>
+<td rowspan="2">&nbsp;</td> <td>dx</td>
+<td rowspan="2">.</td></tr>
+<tr><td class="denom">y</td> <td class="denom">y</td>
+<td class="denom">x &minus; x<span class="su">0</span></td> <td class="denom">2y</td></tr></table>
+
+<p class="noind">Of these consider the first, putting</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">u = <span class="f150">&int;</span> <span class="sp1">(&infin;)</span><span class="su1">(x)</span></td> <td>dx</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">y</td></tr></table>
+
+<p class="noind">where the limits involve not only a value for x, but a definite sign
+for the radical y. When x is very large, if we put x<span class="sp">&minus;1</span> = t<span class="sp">2</span>, y<span class="sp">&minus;1</span> =
+2t<span class="sp">3</span> (1 &minus; ¼ g<span class="su">2</span>t<span class="sp">4</span> &minus; ¼ g<span class="su">3</span>t<span class="sp">6</span>)<span class="sp">&minus;1/2</span>, we have</p>
+
+<p class="center">u = <span class="f150">&int;</span> <span class="sp1">t</span><span class="su1">0</span> (1 + <span class="spp">1</span>&frasl;<span class="suu">8</span> g<span class="su">2</span>t<span class="sp">4</span> + ... ) dt = t + <span class="spp">1</span>&frasl;<span class="suu">40</span> g<span class="su">2</span>t<span class="sp">5</span> + ...,</p>
+
+<p><span class="pagenum"><a name="page325" id="page325"></a>325</span></p>
+
+<p class="noind">whereby a definite power series in u, valid for sufficiently small value
+of u, is found for t, and hence a definite power series for x, of the form</p>
+
+<p class="center">x = u<span class="sp">&minus;2</span> + <span class="spp">1</span>&frasl;<span class="suu">20</span> g<span class="su">2</span>u<span class="sp">2</span> + ...</p>
+
+<p>Let this expression be valid for 0 &lt; |u| &lt; R, and the function defined
+thereby, which has a pole of the second order for u=0, be denoted
+by &phi;(u). In the range in question it is single valued and satisfies the
+differential equation</p>
+
+<p class="center">[&phi;&prime;(u)]<span class="sp">2</span> = 4[&phi;(u)]<span class="sp">3</span> &minus; g<span class="su">2</span>&phi;(u) &minus; g<span class="su">3</span>;</p>
+
+<p class="noind">in terms of it we can write x = &phi;(u), y = &minus; &phi;&prime;(u), and, &phi;&prime;(u) being an
+odd function, the sign attached to y in the original integral for x = &infin;
+is immaterial. Now for any two values u, v in the range in question
+consider the function</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">F(u, v) = ¼ <span class="f150">[</span></td> <td>&phi;&prime;(u) &minus; &phi;&prime;(v)</td>
+<td rowspan="2"><span class="f150">]</span><span class="sp1">2</span> &minus; &phi;(u) &minus; &phi;(v);</td></tr>
+<tr><td class="denom">&phi;(u) &minus; &phi;(v)</td></tr></table>
+
+<p class="noind">it is at once seen, from the differential equation, to be such that
+&part;F/&part;u = &part;F/&part;v; it is therefore a function of u + v; supposing
+|u + v| &lt; R we infer therefore, by putting v = 0, that</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&phi;(u + v) = ¼ <span class="f150">[</span></td> <td>&phi;&prime;(u) &minus; &phi;&prime;(v)</td>
+<td rowspan="2"><span class="f150">]</span><span class="sp1">2</span> &minus; &phi;(u) &minus; &phi;(v).</td></tr>
+<tr><td class="denom">&phi;(u) &minus; &phi;(v)</td></tr></table>
+
+<p class="noind">By repetition of this equation we infer that if u<span class="su">1</span>, ... u<span class="su">n</span> be any arguments
+each of which is in absolute value less than R, whose sum is also
+in absolute value less than R, then &phi;(u<span class="su">1</span> + ... + u<span class="su">n</span>) is a rational
+function of the 2n functions &phi;(u<span class="su">s</span>), &phi;&prime;(u<span class="su">s</span>); and hence, if |u| &lt; R,
+that</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&phi;(u) = H <span class="f150">[</span> &phi; <span class="f150">(</span></td> <td>u</td>
+<td rowspan="2"><span class="f150">)</span>, &emsp; &phi;&prime; <span class="f150">(</span></td> <td>u</td>
+<td rowspan="2"><span class="f150">) ]</span>,</td></tr>
+<tr><td class="denom">n</td> <td class="denom">n</td></tr></table>
+
+<p class="noind">where H is some rational function of the arguments &phi;(u/n), &phi;&prime;(u/n).
+In fact, however, so long as |u/n| &lt; R, each of the functions &phi;(u/n),
+&phi;&prime;(u/n) is single valued and without singularity save for the pole at
+u=0; and a rational function of single valued functions, each of
+which has no singularities other than poles in a certain region, is
+also a single valued function without singularities other than poles in
+this region. We infer, therefore, that the function of u expressed by
+H [&phi;(u/n), &phi;&prime;(u/n)] is single valued and without singularities other
+than poles so long as |u| &lt; nR; it agrees with &phi;(u) when |u| &lt; R, and
+hence furnishes a continuation of this function over the extended
+range |u| &lt; nR. Moreover, from the method of its derivation, it
+satisfies the differential equation [&phi;&prime;(u)]<span class="sp">2</span> = 4[&phi;(u)]<span class="sp">3</span> &minus; g<span class="su">2</span>&phi;(u) &minus; g<span class="su">3</span>. This
+equation has therefore one solution which is a single valued monogenic
+function with no singularities other than poles for any finite
+part of the plane, having in particular for u = 0, a pole of the second
+order; and the method adopted for obtaining this near u=0 shows
+that the differential equation has no other such solution. This,
+however, is not the only solution which is a single valued meromorphic
+function, a the functions &phi;(u + &alpha;), wherein &alpha; is arbitrary,
+being such. Taking now any range of values of u, from u = 0,
+and putting for any value of u, x = &phi;(u), y = &minus;&phi;&prime;(u), so that
+y<span class="sp">2</span>=4x<span class="sp">3</span>-g<span class="su">2</span>x-g<span class="su">3</span>, we clearly have</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">u = <span class="f150">&int;</span> <span class="sp1">(&infin;)</span><span class="su1">(x, y)</span></td> <td>dx</td>
+<td rowspan="2">;</td></tr>
+<tr><td class="denom">y</td></tr></table>
+
+<p class="noind">conversely if x<span class="su">0</span> = &phi;(u<span class="su">0</span>), y<span class="su">0</span> = &minus;&phi;&prime;(u<span class="su">0</span>) and &xi;, &eta; be any values satisfying
+&eta;<span class="su">2</span> = 4&xi;<span class="sp">2</span> &minus; g<span class="su">2</span>&xi; &minus; g<span class="su">3</span>, which are sufficiently near respectively to x<span class="su">0</span>, y<span class="su">0</span>,
+while v is defined by</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">v &minus; u<span class="su">0</span> = &minus; <span class="f150">&int;</span> <span class="sp1">(&xi;, &eta;)</span><span class="su1">(x<span class="su">0</span>, y<span class="su">0</span>)</span></td> <td>d&xi;</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">&eta;</td></tr></table>
+
+<p class="noind">then &xi;, &eta; are respectively &phi;(v) and &minus;&phi;&prime;(v); for this equation leads
+to an expansion for &xi; &minus; x<span class="su">0</span> in terms of v = u<span class="su">0</span> and only one such expansion,
+and this is obtained by the same work as would be necessary
+to expand &phi;(v) when v is near to u<span class="su">0</span>; the function &phi;(u) can therefore
+be continued by the help of this equation, from v = u<span class="su">0</span>, provided
+the lower limit of |&xi; &minus; x<span class="su">0</span>| necessary for the expansions is not zero
+in the neighbourhood of any value (x<span class="su">0</span>, y<span class="su">0</span>). In fact the function &phi;(u)
+can have only a finite number of poles in any finite part of the plane
+of u; each of these can be surrounded by a small circle, and in the
+portion of the finite part of the plane of u which is outside these
+circles, the lower limit of the radii of convergence of the expansions
+of &phi;(u) is greater than zero; the same will therefore be the case
+for the lower limit of the radii |&xi; &minus; x<span class="su">0</span>| necessary for the continuations
+spoken of above provided that the values of (&xi;, &eta;) considered do not
+lead to infinitely increasing values of v; there does not exist, however,
+any definite point (&xi;<span class="su">0</span>, &eta;<span class="su">0</span>) in the neighbourhood of which the
+integral <span class="f150">&int;</span>&nbsp;<span class="sp1">(&xi;, &eta;)</span><span class="su1">(x<span class="su">0</span>, y<span class="su">0</span>)</span> d&xi;/&eta; increases indefinitely, it is only by a path of infinite
+length that the integral can so increase. We infer therefore that
+if (&xi;, &eta;) be any point, where &eta;<span class="su">2</span> = 4&xi;<span class="sp">3</span> &minus; g<span class="su">2</span>&xi; &minus; g<span class="su">3</span>, and v be defined by</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">v = <span class="f150">&int;</span> <span class="sp1">(&infin;)</span><span class="su1">(&xi;, &eta;)</span></td> <td>dx</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">y</td></tr></table>
+
+<p class="noind">then &xi; = &phi;(v) and &eta; = &minus;&phi;&prime;(v). Thus this equation determines (&xi;, &eta;)
+without ambiguity. In particular the additive indeterminatenesses
+of the integral obtained by closed circuits of the point of integration
+are periods of the function &phi;(u); by considerations advanced above
+it appears that these periods are sums of integral multiples of two
+which may be taken to be</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&omega; = 2 <span class="f150">&int;</span> <span class="sp1">&infin;</span><span class="su1">e<span class="su">1</span></span></td> <td>dx</td>
+<td rowspan="2">, &emsp; &omega;&prime; = 2 <span class="f150">&int;</span> <span class="sp1">&infin;</span><span class="su1">e<span class="su">3</span></span></td> <td>dx</td>
+<td rowspan="2">;</td></tr>
+<tr><td class="denom">y</td> <td class="denom">y</td></tr></table>
+
+<p class="noind">these quantities cannot therefore have a real ratio, for else, being
+periods of a monogenic function, they would, as we have previously
+seen, be each integral multiples of another period; there would
+then be a closed path for (x, y), starting from an arbitrary point
+(x<span class="su">0</span>, y<span class="su">0</span>), other than one enclosing two of the points (e<span class="su">1</span>, 0), (e<span class="su">2</span>, 0),
+(e<span class="su">3</span>, 0), (&infin;, &infin;), which leads back to the initial point (x<span class="su">0</span>, y<span class="su">0</span>), which is
+impossible. On the whole, therefore, it appears that the function
+&phi;(u) agrees with the function &real;(u) previously discussed, and the
+discussion of the elliptic integrals can be continued in the manner
+given under § 14, <i>Doubly Periodic Functions</i>.</p>
+</div>
+
+<p>§ 21. <i>Modular Functions.</i>&mdash;One result of the previous theory
+is the remarkable fact that if</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&omega; = 2 <span class="f150">&int;</span> <span class="sp1">&infin;</span><span class="su1">e<span class="su">1</span></span></td> <td>dx</td>
+<td rowspan="2">, &emsp; &omega;&prime; = 2 <span class="f150">&int;</span> <span class="sp1">&infin;</span><span class="su1">e<span class="su">3</span></span></td> <td>dx</td>
+<td rowspan="2">;</td></tr>
+<tr><td class="denom">y</td> <td class="denom">y</td></tr></table>
+
+<p class="noind">where y<span class="sp">2</span> = 4(x &minus; e<span class="su">1</span>) (x &minus; e<span class="su">2</span>) (x &minus; e<span class="su">3</span>), then we have</p>
+
+<p class="center">e<span class="su">1</span> = (½&omega;)<span class="sp">&minus;2</span> + &Sigma;&prime; {[(m + ½) &omega; + m&prime;&omega;&prime;]<span class="sp">&minus;2</span> &minus; [m&omega; + m&prime;&omega;&prime;]<span class="sp">&minus;2</span>},</p>
+
+<p class="noind">and a similar equation for e<span class="su">3</span>, where the summation refers to
+all integer values of m and m&prime; other than the one pair m = 0,
+m&prime; = 0. This, with similar results, has led to the consideration
+of functions of the complex ratio &omega;&prime;/&omega;.</p>
+
+<div class="condensed">
+<p>It is easy to see that the series for &real;(u), u<span class="sp">&minus;2</span> + &Sigma;&prime;[(u + m&omega; + m&prime;&omega;&prime;)<span class="sp">2</span> &minus;
+(m&omega; + m&prime;&omega;&prime;)<span class="sp">2</span>], is unaffected by replacing &omega;, &omega;&prime; by two quantities &Omega;, &Omega;&prime;
+equal respectively to p&omega; + q&omega;&prime;, p&prime;&omega;&prime; + q&prime;&omega;&prime;, where p, q, p&prime;, q&prime; are any
+integers for which pq&prime; &minus; p&prime;q = ±1; further it can be proved that all
+substitutions with integer coefficients &Omega; = p&omega; + q&omega;&prime;, &Omega;&prime; = p&prime;&omega; + q&prime;&omega;&prime;,
+wherein pq&prime; &minus; p&prime;q = 1, can be built up by repetitions of the two particular
+substitutions (&Omega; =  &minus;&omega;&prime;, &Omega;&prime; = &omega;), (&Omega; = &omega;, &Omega;&prime; = &omega; + &omega;&prime;). Consider
+the function of the ratio &omega;&prime;/&omega; expressed by</p>
+
+<p class="center">h = &minus;&real; (½&omega;&prime;) / &real;(½&omega;);</p>
+
+<p class="noind">it is at once seen from the properties of the function &real;(u) that by
+the two particular substitutions referred to we obtain the corresponding
+substitutions for h expressed by</p>
+
+<p class="center">h&prime; = 1/h, &emsp; h&prime; = 1 &minus; h;</p>
+
+<p class="noind">thus, by all the integer substitutions &Omega; = p&omega; + q&omega;&prime;, &Omega;&prime; = p&prime;&omega; + q&prime;&omega;&prime;, in
+which pq&prime; &minus; p&prime;q = 1, the function h can only take one of the six values
+h, 1/h, 1 &minus; h, 1/(1 &minus; h), h/(h &minus; 1), (h &minus; 1)/h, which are the roots of an
+equation in &theta;,</p>
+
+<table class="math0" summary="math">
+<tr><td>(1 &minus; &theta; + &theta;<span class="sp">2</span>)<span class="sp">3</span></td>
+<td rowspan="2">=</td> <td>(1 &minus; h + h<span class="sp">2</span>)<span class="sp">3</span></td>
+<td rowspan="2">;</td></tr>
+<tr><td class="denom">&theta;<span class="sp">2</span>(1 &minus; &theta;)<span class="sp">2</span></td> <td class="denom">h<span class="sp">2</span>(1 &minus; h)<span class="sp">2</span></td></tr></table>
+
+<p class="noind">the function of &tau;, = &omega;&prime;/&omega;, expressed by the right side, is thus
+unaltered by every one of the substitutions &tau;&prime; = (p&prime; + q&prime;&tau; / p + q&tau;), wherein
+p, q, p&prime;, q&prime; are integers having pq&prime; &minus; p&prime;q = 1. If the imaginary part
+&sigma;, of &tau;, which we may write &tau; = &rho; + i&sigma;, is positive, the imaginary part
+of &tau;&prime;, which is equal to &sigma;(pq&prime; &minus; p&prime;q)/[(p + q&rho;)<span class="sp">2</span> + q<span class="sp">2</span>&sigma;<span class="sp">2</span>], is also positive;
+suppose &sigma; to be positive; it can be shown that the upper half of the
+infinite plane of the complex variable &tau; can be divided into regions,
+all bounded by arcs of circles (or straight lines), no two of these
+regions overlapping, such that any substitution of the kind under
+consideration, &tau;&prime; = (p&prime; + q&prime;&tau;)/(p + q&tau;) leads from an arbitrary point &tau;,
+of one of these regions, to a point &tau;&prime; of another; taking &tau; = &rho; + i&sigma;,
+one of these regions may be taken to be that for which  &minus;½ &lt; &rho; &lt; ½,
+&rho;<span class="sp">2</span> + &sigma;<span class="sp">2</span> &gt; 1, together with the points for which &rho; is negative on the
+curves limiting this region; then every other region is obtained
+from this so-called fundamental region by one and only one of the
+substitutions &tau; = (p&prime; + q&prime;&tau;)/(p + q&tau;), and hence by a definite combination
+of the substitutions &tau;&prime; = &minus;1/&tau;, &tau;&prime; = 1 + &tau;. Upon the infinite half
+plane of &tau;, the function considered above,</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">z(&tau;) = <span class="spp">4</span>&frasl;<span class="suu">27</span></td> <td>[&real;<span class="sp">2</span> (½&omega;) + &real; (z(½&omega;) &real; (½&omega;&prime;) + &real;<span class="sp">2</span> (½&omega;&prime;)]<span class="sp">3</span></td>
+<td rowspan="2"></td></tr>
+<tr><td class="denom">&real;<span class="sp">2</span> (½&omega;) &real;<span class="sp">2</span> (½&omega;&prime;) [&real; (½&omega;) + &real; (½&omega;&prime;]<span class="sp">2</span></td></tr></table>
+
+<p class="noind">is a single valued monogenic function, whose only essential singularities
+are the points &tau;&prime; = (p&prime; + q&prime;&tau;)/(p + q&tau;) for which &tau; = &infin;, namely
+those for which &tau;&prime; is any real rational value; the real axis is thus a
+line over which the function z(&tau;) cannot be continued, having an
+essential singularity in every arc of it, however short; in the fundamental
+region, z(&tau;) has thus only the single essential singularity,
+r = &rho; + i&sigma;, where &sigma; = &infin;; in this fundamental region z(&tau;) takes any
+assigned complex value just once, the relation z(&tau;&prime;) = z(&tau;) requiring,
+as can be shown, that &tau;&prime; is of the form (p&prime; + q&prime;&tau;)/(p + q&tau;), in which
+p, q, p&prime;, q&prime; are integers with pq&prime; &minus; p&prime;q = 1; the function z(&tau;) has thus
+a similar behaviour in every other of the regions. The division of
+the plane into regions is analogous to the division of the plane,
+in the case of doubly periodic functions, into parallelograms; in that
+case we considered only functions without essential singularities,
+and in each of the regions the function assumed every complex value
+twice, at least. Putting, as another function of &tau;, J(&tau;) = z(&tau;) [z(&tau;) &minus; 1],
+it can be shown that J(&tau;) = 0 for &tau; = exp (<span class="spp">2</span>&frasl;<span class="suu">3</span>&pi;i), that J(&tau;) = 1 for &tau; = i,
+these being values of &tau; on the boundary of the fundamental region;
+like z(&tau;) it has an essential singularity for &tau; = &rho; + i&sigma;, &sigma; = + &infin;. In the
+<span class="pagenum"><a name="page326" id="page326"></a>326</span>
+theory of linear differential equations it is important to consider the
+inverse function &tau;(J); this is infinitely many valued, having a cycle
+of three values for circulation of J about J = 0 (the circuit of this
+point leading to a linear substitution for &tau; of period 3, such as
+&tau;&prime; = &minus;(1 + &tau;)<span class="sp">&minus;1</span>), having a cycle of two values about J = 1 (the circuit
+leading to a linear substitution for &tau; of period 2, such as &tau;&prime; = &minus;&tau;<span class="sp">&minus;1</span>),
+and having a cycle of infinitely many values about J = &infin; (the circuit
+leading to a linear substitution for &tau; which is not periodic, such as
+&tau;&prime; = 1 + &tau;). These are the only singularities for the function &tau;(J).
+Each of the functions</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">[J(&tau;)]<span class="sp">1/3</span>, &emsp; [J(&tau;) &minus; 1]<span class="sp">1/2</span>, &emsp; <span class="f150">[</span> &minus;</td> <td>&real; (½&omega;) + 2&real; (½&omega;&prime;)</td>
+<td rowspan="2"><span class="f150">]</span><span class="sp1">1/8</span>,</td></tr>
+<tr><td class="denom">&real; (½&omega;) &minus; &real; (½)&omega;&prime;)</td></tr></table>
+
+<p class="noind">beside many others (see below), is a single valued function of &tau;,
+and is expressible without ambiguity in terms of the single valued
+function of &tau;,</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&eta;(&tau;) = exp <span class="f150">(</span></td> <td>i&pi;&tau;</td>
+<td rowspan="2"><span class="f150">) &Pi;</span> <span class="sp1">&infin;</span><span class="su1">n=1</span> [1 &minus; exp (2i&pi;n&tau;)] = exp <span class="f150">(</span></td> <td>i&pi;&tau;</td>
+<td rowspan="2"><span class="f150">) &Sigma;</span> <span class="sp1">&infin;</span><span class="su1">m=&minus;&infin;</span> (&minus;1)<span class="sp">m</span> exp [(3m<span class="sp">2</span> + m) i&pi;&tau;].</td></tr>
+<tr><td class="denom">12</td> <td class="denom">12</td></tr></table>
+
+<p>It should be remarked, however, that &eta;(&tau;) is not unaltered by all
+the substitutions we have considered; in fact</p>
+
+<p class="center">&eta;(&minus;&tau;<span class="sp">&minus;1</span>) = (&minus;i&tau;) ½&eta; (&tau;), &emsp; &eta;(1 + &tau;) = exp (<span class="spp">1</span>&frasl;<span class="suu">12</span> i&pi;) &eta;(&tau;).</p>
+
+<p>The aggregate of the substitutions &tau;&prime; = (p&prime; + q&prime;&tau;)/(p + q&tau;), wherein
+p, q, p&prime;, q&prime; are integers with pq&prime; &minus; p&prime;q = 1, represents a <i>Group</i>; the
+function J(&tau;), unaltered by all these substitutions, is called a <i>Modular
+Function</i>. More generally any function unaltered by all the substitutions
+of a group of linear substitutions of its variable is called an
+<i>Automorphic Function</i>. A rational function, of its variable h, of this
+character, is the function (1 &minus; h + h<span class="sp">2</span>)<span class="sp">3</span> h<span class="sp">&minus;2</span>(1 &minus; h)<span class="sp">&minus;2</span> presenting itself
+incidentally above; and there are other rational functions with a
+similar property, the group of substitutions belonging to any one
+of these being, what is a very curious fact, associable with that of
+the rotations of one of the regular solids, about an axis through its
+centre, which bring the solid into coincidence with itself. Other
+automorphic functions are the double periodic functions already
+discussed; these, as we have seen, enable us to solve the algebraic
+equation y<span class="sp">2</span> = 4x<span class="sp">3</span> &minus; g<span class="su">2</span>x &minus; g<span class="su">3</span> (and in fact many other algebraic equations,
+see below, under § 23, <i>Geometrical Applications of Elliptic
+Functions</i>) in terms of single valued functions x = &real;(u), y = &minus;&real;&prime;(u).
+A similar utility, of a more extended kind, belongs to automorphic
+functions in general; but it can be shown that such functions
+necessarily have an infinite number of essential singularities except
+for the simplest cases.</p>
+
+<p>The modular function J(&tau;) considered above, unaltered by the
+group of linear substitutions &tau;&prime; = (p&prime; + q&prime;&tau;) / (p + q&tau;), where p, q, p&prime;, q&prime;
+are integers with pq&prime; &minus; p&prime;q = 1, may be taken as the independent
+variable x of a differential equation of the third order, of the form</p>
+
+<table class="math0" summary="math">
+<tr><td>s&Prime;&prime;</td>
+<td rowspan="2">&minus;</td> <td>3</td>
+<td rowspan="2"><span class="f150">(</span></td> <td>s&Prime;</td>
+<td rowspan="2"><span class="f150">)</span><span class="sp1">2</span> =</td> <td>1 &minus; &alpha;<span class="sp">2</span></td>
+<td rowspan="2">+</td> <td>1 &minus; &beta;<span class="sp">2</span></td>
+<td rowspan="2">+</td> <td>&alpha;<span class="sp">2</span> + &beta;<span class="sp">2</span> &minus; &gamma;<span class="sp">2</span> &minus; 1</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">s&prime;</td> <td class="denom">2</td>
+<td class="denom">s&prime;</td> <td class="denom">2(x &minus; 1)<span class="sp">2</span></td>
+<td class="denom">2x<span class="sp">2</span></td> <td class="denom">2x (x &minus; 1)</td></tr></table>
+
+<p class="noind">where s&prime; = ds/dx, &amp;c., of which the dependent variable s is equal to &tau;.
+A differential equation of this form is satisfied by the quotient of
+two independent integrals of the linear differential equation of the
+second order satisfied by the hypergeometric functions. If the
+solution of the differential equation for s be written s(&alpha;,&beta;,&gamma;, x),
+we have in fact &tau; = s(½, <span class="spp">1</span>&frasl;<span class="suu">3</span>, 0, J). If we introduce also the function
+of &tau; given by</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&lambda; =</td> <td>2&real; (½&omega;&prime;) + &real; (½&omega;)</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">&real; (½&omega;&prime;) &minus; &real; (½&omega;)</td></tr></table>
+
+<p class="noind">we similarly have &tau; = s(0, 0, 0, &lambda;); this function &lambda; is a single valued
+function of &tau;, which is also a modular function, being unaltered by a
+group of integral substitutions also of the form &tau;&prime; = (p&prime; + q&prime;&tau;)/(p + q&tau;),
+with pq&prime; &minus; p&prime;q = 1, but with the restriction that p&prime; and q are even
+integers, and therefore p and q&prime; are odd integers. This group is
+thus a subgroup of the general modular group, and is in fact of the
+kind called a self-conjugate subgroup. As in the general case this
+subgroup is associated with a subdivision of the plane into regions
+of which any one is obtained from a particular region, called the
+fundamental region, by a particular one of the substitutions of the
+subgroup. This fundamental region, putting &tau; = &rho; + i&sigma;, may be
+taken to be that given by &minus;1 &lt; &rho; &lt; 1, (&rho; + ½)<span class="sp">2</span> + &sigma;<span class="sp">2</span> &gt; ¼, (&rho; &minus; ½)<span class="sp">2</span> + &sigma;<span class="sp">2</span> &gt; ¼,
+and is built up of six of the regions which arose for the general
+modular group associated with J(&tau;). Within this fundamental
+region, &lambda; takes every complex value just once, except the values
+&lambda; = 0, 1, &infin;, which arise only at the angular points &tau; = 0, &tau; = &infin;, &tau; = &minus; 1
+and the equivalent point &tau; = 1; these angular points are essential
+singularities for the function &lambda;(&tau;). For &lambda;(&tau;) as for J(&tau;), the region of
+existence is the upper half plane of &tau;, there being an essential singularity
+in every length of the real axis, however short.</p>
+
+<p>If, beside the plane of &tau;, we take a plane to represent the values of
+&lambda;, the function &tau; = s(0, 0, 0, &lambda;) being considered thereon, the values of
+&tau; belonging to the interior of the fundamental region of the &tau;-plane
+considered above, will require the consideration of the whole of the
+&lambda;-plane taken once with the exception of the portions of the real
+axis lying between &minus;&infin; and 0 and between 1 and +&infin;, the two
+sides of the first portion corresponding to the circumferences of the
+&tau;-plane expressed by (&rho; + ½)<span class="sp">2</span> + &sigma;<span class="sp">2</span> = ¼, (&rho; &minus; ½)<span class="sp">2</span> + &sigma;<span class="sp">2</span> = ¼, while the two
+sides of the latter portion, for which &lambda; is real and &gt; 1, correspond
+to the lines of the &tau;-plane expressed by &rho; = ±1. The line for
+which &lambda; is real, positive and less than unity corresponds to the
+imaginary axis of the &tau;-plane, lying in the interior of the fundamental
+region. All the values of &tau; = s(0, 0, 0, &lambda;) may then be derived
+from those belonging to the fundamental region of the &tau;-plane by
+making &lambda; describe a proper succession of circuits about the points
+&lambda; = 0, &lambda; = 1; any such circuit subjects &tau; to a linear substitution
+of the subgroup of &tau; considered, and corresponds to a change of &tau;
+from a point of the fundamental region to a corresponding point
+of one of the other regions.</p>
+</div>
+
+<p>§ 22. <i>A Property of Integral Functions deduced from the Theory
+of Modular Functions</i>.&mdash;Consider now the function exp(z),
+for finite values of z; for such values of z, exp(z) never vanishes,
+and it is impossible to assign a closed circuit for z in the finite
+part of the plane of z which will make the function &lambda; = exp(z)
+pass through a closed succession of values in the plane of &lambda;
+having &lambda; = 0 in its interior; the function s[0, 0, 0, exp(z)],
+however z vary in the finite part of the plane, will therefore never
+be subjected to those linear substitutions imposed upon
+s(0, 0, 0, &lambda;) by a circuit of &lambda; about &lambda; = 0; more generally, if
+&phi;(z) be an integral function of z, never becoming either zero or
+unity for finite values of z, the function &lambda; = &phi;(z), however z vary
+in the finite part of the plane, will never make, in the plane of &lambda;,
+a circuit about either &lambda; = 0 or &lambda; = 1, and s(0, 0, 0, &lambda;), that is
+s[0, 0, 0, &phi;(z)], will be single valued for all finite values of z;
+it will moreover remain finite, and be monogenic. In other
+words, s[0, 0, 0, &phi;(z)] is also an integral function&mdash;whose imaginary
+part, moreover, by the property of s(0, 0, 0, &lambda;), remains positive
+for all finite values of z. In that case, however, exp {is[0, 0, 0, &phi;(z)]}
+would also be an integral function of z with modulus less than
+unity for all finite values of z. If, however, we describe a circle
+of radius R in the z plane, and consider the greatest value of the
+modulus of an integral function upon this circle, this certainly
+increases indefinitely as R increases. We can infer therefore
+that <i>an integral function &phi;(z) which does not vanish for any finite
+value of z, takes the value unity and hence</i> (by considering the
+function A<span class="sp">&minus;1</span>&phi;(z)) <i>takes every other value for some definite value
+of z</i>; or, an integral function for which both the equations
+&phi;(z) = A, &phi;(z) = B are unsatisfied by definite values of z, does not
+exist, A and B being arbitrary constants.</p>
+
+<div class="condensed">
+<p>A similar theorem can be proved in regard to the values assumed
+by the function &phi;(z) for points z of modulus greater than R, however
+great R may be, also with the help of modular functions. In general
+terms it may be stated that it is a very exceptional thing for an
+integral function not to assume every complex value an infinite
+number of times.</p>
+
+<p>Another application of modular functions is to prove that the
+function s(&alpha;, &beta;, &gamma;, &lambda;) is a single valued function of &tau; = s(0, 0, 0, &lambda;);
+for, putting &tau;&prime; = (&tau; &minus; i)/(&tau; + i), the values of &tau;&prime; which correspond to the
+singular points &lambda; = 0, 1, &infin; of s(&alpha;, &beta;, &gamma;, &lambda;), though infinite in number,
+all lie on the circumference of the circle |&tau;&prime;| = 1, within which therefore
+s(&alpha;, &beta;, &gamma;, x) is expressible in a form <span class="f150">&Sigma;</span> <span class="sp1">&infin;</span><span class="su1">n=0</span> a<span class="su">n</span>&tau;&prime;<span class="sp">n</span>. More generally any
+monogenic function of &lambda; which is single valued save for circuits of
+the points &lambda; = 0, 1, &infin;, is a single valued function of &tau; = s(0, 0, 0, &lambda;).
+Identifying &lambda; with the square of the modulus in Legendre&rsquo;s form of
+the elliptical integral, we have &tau; = iK&prime;/K, where</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">K = <span class="f150">&int;</span> <span class="sp1">1</span><span class="su1">0</span></td> <td>dt</td>
+<td rowspan="2">, &emsp; K&prime; = <span class="f150">&int;</span> <span class="sp1">1</span><span class="su1">0</span></td> <td>dt</td>
+<td rowspan="2">;</td></tr>
+<tr><td class="denom">&radic;[1 &minus; t<span class="sp">2</span>] [1 &minus; &lambda;t<span class="sp">2</span>]</td> <td class="denom">&radic;[1 &minus; t<span class="sp">2</span>] [1 &minus; (1 &minus; &lambda;) t<span class="sp">2</span>]</td></tr></table>
+
+<p class="noind">functions such as &lambda;<span class="sp">1/4</span>, (1 &minus; &lambda;)<span class="sp">1/4</span>, [&lambda;(1 &minus; &lambda;)]<span class="sp">1/4</span>, which have only &lambda; = 0, 1, &infin;
+as singular points, were expressed by Jacobi as power series in q = e<span class="sp">i&pi;&tau;</span>,
+and therefore, at least for a limited range of values of &tau;, as single
+valued functions of &tau;; it follows by the theorem given that any
+product of a root of &lambda; and a root of 1 &minus; &lambda; is a single valued function
+of &tau;. More generally the differential equation</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">x(1 &minus; x)</td> <td>d<span class="sp">2</span>y </td>
+<td rowspan="2">+ [&gamma; &minus; (&alpha; + &beta; + 1)x]</td> <td>dy</td>
+<td rowspan="2">&minus; &alpha;&beta;&gamma; = 0</td></tr>
+<tr><td class="denom">dx<span class="sp">2</span></td> <td class="denom">dx</td></tr></table>
+
+<p class="noind">may be solved by expressing both the independent and dependent
+variables as single valued functions of a single variable &tau;, the expression
+for the independent variable being x = &lambda;(&tau;).</p>
+</div>
+
+<p>§ 23. <i>Geometrical Applications of Elliptic Functions.</i>&mdash;Consider
+any irreducible algebraic equation rational in x, y, f(x, y) = 0, of
+such a form that the equation represents a plane curve of order
+n with ½n(n &minus; 3) double points; taking upon this curve n&minus; 3
+arbitrary fixed points, draw through these and the double
+points the most general curve of order n &minus; 2; this will intersect
+<span class="pagenum"><a name="page327" id="page327"></a>327</span>
+&fnof; in n(n &minus; 2) &minus; n(n &minus; 3) &minus; (n &minus; 3) = 3 other points, and will contain
+homogeneously at least ½(n &minus; 1)n &minus; ½n(n &minus; 3) &minus;(n &minus; 3) = 3 arbitrary
+constants, and so will be of the form &lambda;&phi; + &lambda;<span class="su">1</span>&phi;<span class="su">1</span> + &lambda;<span class="su">2</span>&phi;<span class="su">2</span> +
+... = 0, wherein &lambda;<span class="su">3</span>, &lambda;<span class="su">4</span>, ... are in general zero. Put now
+&xi; = &phi;<span class="su">1</span>/&phi;, &eta; = &phi;<span class="su">2</span>/&phi; and eliminate x, y between these equations and
+&fnof;(x, y) = 0, so obtaining a rational irreducible equation F(&xi;, &eta;) = 0,
+representing a further plane curve. To any point (x, y) of &fnof; will
+then correspond a definite point (&xi;, &eta;) of F.</p>
+
+<div class="condensed">
+<p>For a general position of (x, y) upon &fnof; the equations
+&phi;<span class="su">1</span>(x&prime;, x&prime;)/&phi;(x&prime;, x&prime;) = &phi;<span class="su">1</span>(x, y)/&phi;(x, y), &phi;<span class="su">2</span>(x&prime;, x&prime;)/&phi;(x&prime;, x&prime;) = &phi;<span class="su">2</span>(x, y)/&phi;(x, y),
+subject to &fnof;(x&prime;, x&prime;) = 0, will have the same number of solutions (x&prime;, x&prime;);
+if their only solution is x&prime; = x, x&prime; = y, then to any position (&xi;, &eta;) of F
+will conversely correspond only one position (x, y) of &fnof;. If these
+equations have another solution beside (x, y), then any curve
+&lambda;&phi; + &lambda;<span class="su">1</span>&phi;<span class="su">1</span> + &lambda;<span class="su">2</span>&phi;<span class="su">2</span> = 0 which passes (through the double points of &fnof;
+and) through the n &minus; 2 points of &fnof; constituted by the fixed n&minus; 3
+points and a point (x<span class="su">0</span>, y<span class="su">0</span>), will necessarily pass through a further
+point, say (x<span class="su">0</span>&prime;, y<span class="su">0</span>&prime;), and will have only one further intersection with
+&fnof;; such a curve, with the n &minus; 2 assigned points, beside the double
+points, of &fnof;, will be of the form &mu;&psi; + &mu;<span class="su">1</span>&psi;<span class="su">1</span> + ... = 0, where &mu;<span class="su">2</span>, &mu;<span class="su">3</span>, ...
+are generally zero; considering the curves &psi; + t&psi;<span class="su">1</span> = 0, for variable t,
+one of these passes through a further arbitrary point of &fnof;, by choosing
+t properly, and conversely an arbitrary value of t determines a single
+further point of &fnof;; the co-ordinates of the points of &fnof; are thus
+rational functions of a parameter t, which is itself expressible rationally
+by the co-ordinates of the point; it can be shown algebraically
+that such a curve has not ½(n &minus; 3)n but ½(n &minus; 3)n + 1 double points.
+We may therefore assume that to every point of F corresponds
+only one point of &fnof;, and there is a birational transformation between
+these curves; the coefficients in this transformation will involve
+rationally the co-ordinates of the n&minus; 3 fixed points taken upon &fnof;,
+that is, at the least, by taking these to be consecutive points, will
+involve the co-ordinates of one point of &fnof;, and will not be rational
+in the coefficients of &fnof; unless we can specify a point of &fnof; whose co-ordinates
+are rational in these. The curve F is intersected by a
+straight line a&xi; + b&eta; + c = 0 in as many points as the number of
+unspecified intersections of &fnof; with a&phi; + b&phi;<span class="su">1</span> + c&phi;<span class="su">2</span> = 0, that is, 3; or F
+will be a cubic curve, without double points.</p>
+
+<p>Such a cubic curve has at least one point of inflection Y, and if a
+variable line YPQ be drawn through Y to cut the curve again in P
+and Q, the locus of a point R such that YR is the harmonic mean of
+YP and YQ, is easily proved to be a straight line. Take now a
+triangle of reference for homogeneous co-ordinates XYZ, of which
+this straight line is Y = 0, and the inflexional tangent at Y is Z = 0;
+the equation of the cubic curve will then be of the form</p>
+
+<p class="center">ZY² = aX³ + bX²Z + cXZ² + dZ³;</p>
+
+<p class="noind">by putting X equal to &lambda;X + &mu;Z, that is, choosing a suitable line
+through Y to be X = 0, and choosing &lambda; properly, this is reduced to
+the form</p>
+
+<p class="center">ZY² = 4X³ &minus; g<span class="su">2</span>XZ² &minus; g<span class="su">3</span>Z³,</p>
+
+<p class="noind">of which a representation is given, valid for every point, in terms of
+the elliptic functions &real;(u), &real;&prime;(u), by taking X = Z&real;(u), Y = Z&real;&prime;(u).
+The value of u belonging to any point is definite save for sums of
+integral multiples of the periods of the elliptic functions, being
+given by</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">u = <span class="f150">&int;</span> <span class="sp1">(x)</span><span class="su1">(&infin;)</span></td> <td>ZdX &minus; XdZ</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">ZY</td></tr></table>
+
+<p class="noind">where (&infin;) denotes the point of inflection.</p>
+
+<p>It thus appears that the co-ordinates of any point of a plane curve,
+&fnof;, of order n with ½(n &minus; 3)n double points are expressible as elliptic
+functions, there being, save for periods, a definite value of the argument
+u belonging to every point of the curve. It can then be shown
+that if a variable curve, &phi;, of order m be drawn, passing through
+the double points of the curve, the values of the argument u at the
+remaining intersections of &phi; with &fnof;, have a sum which is unaffected
+by variation of the coefficients of &phi;, save for additive aggregates
+of the periods. In virtue of the birational transformation this
+theorem can be deduced from the theorem that if any straight line
+cut the cubic y² = 4x³ &minus; g<span class="su">2</span>x &minus; g<span class="su">3</span>, in points (u<span class="su">1</span>), (u<span class="su">2</span>), (u<span class="su">3</span>), the sum
+u<span class="su">1</span> + u<span class="su">2</span> + u<span class="su">3</span> is zero, or a period; or the general theorem is a corollary
+from Abel&rsquo;s theorem proved under § 17, <i>Integrals of Algebraic
+Functions</i>. To prove the result directly for the cubic we remark
+that the variation of one of the intersections (x, y) of the cubic
+with the straight line y = mx + n, due to a variation &delta;m, &delta;n in m
+and n, is obtained by differentiation of the equation for the three
+abscissae, namely the equation</p>
+
+<p class="center">F(x) = 4x³ &minus; g<span class="su">2</span>x &minus; g<span class="su">3</span> &minus; (mx + n)² = 0,</p>
+
+<p class="noind">and is thus given by</p>
+
+<table class="math0" summary="math">
+<tr><td>dx</td>
+<td rowspan="2">=</td> <td>x&delta;m + &delta;n</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">y</td> <td class="denom">F&prime;(x)</td></tr></table>
+
+<p class="noind">and the sum of three such fractions as that on the right for the three
+roots of F(x) = 0 is zero; hence u<span class="su">1</span> + u<span class="su">2</span> + u<span class="su">3</span> is independent of the
+straight line considered; if in particular this become the inflexional
+tangent each of u<span class="su">1</span>, u<span class="su">2</span>, u<span class="su">3</span> vanishes. It may be remarked in passing
+that x<span class="su">1</span> + x<span class="su">2</span> + x<span class="su">3</span> = ¼m², and hence is ¼ {(y<span class="su">1</span> &minus; y<span class="su">2</span>)/(x<span class="su">1</span> &minus; x<span class="su">2</span>)}²; so that we
+have another proof of the addition equation for the function &real;(u).
+From this theorem for the cubic curve many of its geometrical
+properties, as for example those of its inflections, the properties of
+inscribed polygons, of the three kinds of corresponding points, and
+the theory of residuation, are at once obvious. And similar results
+hold for the curve of order n with ½(n &minus; 3)n double points.</p>
+</div>
+
+<p>§ 24. <i>Integrals of Algebraic Functions in Connexion with the
+Theory of Plane Curves.</i>&mdash;The developments which have been
+explained in connexion with elliptic functions may enable the
+reader to appreciate the vastly more extensive theory similarly
+arising for any algebraical irrationality, &fnof;(x, y) = o.</p>
+
+<div class="condensed">
+<p>The algebraical integrals &int; R(x, y)dx associated with this may as
+before be divided into those of the <i>first kind</i>, which have no infinities,
+those of the <i>second kind</i>, possessing only algebraical infinities,
+and those of the <i>third kind</i>, for which logarithmic infinities enter.
+Here there is a certain number, p, greater than unity, of linearly
+independent integrals of the first kind; and this number p is unaltered
+by any birational transformation of the fundamental equation
+&fnof;(x, y) = 0; a rational function can be constructed with poles of the
+first order at p + 1 arbitrary positions (x, y), satisfying &fnof;(x, y) = 0,
+but not with a fewer number unless their positions are chosen
+properly, a property we found for the case p = 1; and p is the number
+of linearly independent curves of order n &minus; 3 passing through the
+double points of the curve of order n expressed by &fnof;(x, y) = 0. Again
+any integral of the second kind can be expressed as a sum of p
+integrals of this kind, with poles of the first order at arbitrary
+positions, together with rational functions and integrals of the first
+kind; and an integral of the second kind can be found with one
+pole of the first order of arbitrary position, and an integral of the
+third kind with two logarithmic infinities, also of arbitrary position;
+the corresponding properties for p = 1 are proved above.</p>
+
+<p>There is, however, a difference of essential kind in regard to the
+inversion of integrals of the first kind; if u = &int;R(x, y)dx be such an
+integral, it can be shown, in common with all algebraic integrals
+associated with &fnof;(x, y) = 0, to have 2p linearly independent additive
+constants of indeterminateness; the upper limit of the integral
+cannot therefore, as we have shown, be a single valued function
+of the value of the integral. The corresponding theorem, if &int;R<span class="su">i</span>(x, y)dx
+denote one of the integrals of the first kind, is that the p equations</p>
+
+<p class="center">&int; R<span class="su">i</span> (x<span class="su">1</span>, y<span class="su">1</span>)dx<span class="su">1</span> + ... + &int; R<span class="su">i</span> (x<span class="su">p</span>, y<span class="su">p</span>)dx<span class="su">p</span> = u<span class="su">i</span>,</p>
+
+<p class="noind">determine the rational symmetric functions of the p positions (x<span class="su">1</span>, y<span class="su">1</span>),
+... (x<span class="su">p</span>, y<span class="su">p</span>) as single valued functions of the p variables, u<span class="su">1</span>, ... u<span class="su">p</span>.
+It is thus necessary to enter into the theory of functions of several
+independent variables; and the equation &fnof;(x, y) = 0 is thus not,
+in this way, capable of solution by single valued functions of one
+variable. That solution in fact is to be sought with the help of
+automorphic functions, which, however, as has been remarked,
+have, for p &gt; 1, an infinite number of essential singularities.</p>
+</div>
+
+<p>§ 25. <i>Monogenic Functions of Several Independent Variables.</i>&mdash;A
+monogenic function of several independent complex variables
+u<span class="su">i</span>, ... u<span class="su">p</span> is to be regarded as given by an aggregate of power
+series all obtainable by continuation from any one of them in a
+manner analogous to that before explained in the case of one
+independent variable. The singular points, defined as the
+limiting points of the range over which such continuation is
+possible, may either be <i>poles</i>, or <i>polar points of indetermination</i>,
+or <i>essential singularities</i>.</p>
+
+<div class="condensed">
+<p>A pole is a point (u<span class="sp">(0)</span><span class="su">1</span>, ... u<span class="sp">(0)</span><span class="su">p</span>) in the neighbourhood of which the
+function is expressible as a quotient of converging power series in
+u<span class="su">1</span> &minus; u<span class="sp">(0)</span><span class="su">1</span> ... u<span class="su">p</span> &minus; u<span class="sp">(0)</span><span class="su">p</span>; of these the denominator series D must
+vanish at (u<span class="sp">(0)</span><span class="su">1</span>, ... u<span class="sp">(0)</span><span class="su">p</span>), since else the fraction is expressible as a
+power series and the point is not a singular point, but the numerator
+series N must not also vanish at (u<span class="sp">(0)</span><span class="su">1</span>, ... u<span class="sp">(0)</span><span class="su">p</span>), or if it does, it must
+be possible to write D = MD<span class="su">0</span>, N = MN<span class="su">0</span>, where M is a converging
+power series vanishing at (u<span class="sp">(0)</span><span class="su">1</span>, ...u<span class="sp">(0)</span><span class="su">p</span>), and N<span class="su">0</span> is a converging power
+series, in (u<span class="su">1</span> &minus; u<span class="sp">(0)</span><span class="su">1</span> ... u<span class="su">p</span> &minus; u<span class="sp">(0)</span><span class="su">p</span>), not so vanishing. A polar point
+of indetermination is a point about which the function can be
+expressed as a quotient of two converging power series, both of
+which vanish at the point. As in such a simple case as (Ax + By)/
+(ax + by), about x = 0, y = 0, it can be proved that then the function
+can be made to approach to any arbitrarily assigned value by
+making the variables u<span class="su">1</span>, ... u<span class="su">p</span> approach to u<span class="sp">(0)</span><span class="su">1</span>, ... u<span class="sp">(0)</span><span class="su">p</span> by a proper
+path. It is the necessary existence of such polar points of indetermination,
+which in case p &gt; 2 are not merely isolated points,
+which renders the theory essentially more difficult than that of
+functions of one variable. An essential singularity is any which
+does not come under one of the two former descriptions and includes
+very various possibilities. A point at infinity in this theory is one
+for which any one of the variables u<span class="su">1</span>, ... u<span class="su">p</span> is indefinitely great;
+such points are brought under the preceding definitions by means
+<span class="pagenum"><a name="page328" id="page328"></a>328</span>
+of the convention that for u<span class="sp">(0)</span><span class="su">i</span> = &infin;, the difference u<span class="su">i</span>  &minus; u<span class="sp">(0)</span><span class="su">i</span> is to be
+understood to stand for u<span class="sp">&minus;1</span><span class="su">i</span>. This being so, a single valued function
+of u<span class="su">1</span>, ... u<span class="su">p</span> without essential singularities for infinite or finite values
+of the variables can be shown, by induction, to be, as in the case of
+p = 1, necessarily a rational function of the variables. A function
+having no singularities for finite values of all the variables is as before
+called an integral function; it is expressible by a power series
+converging for all finite values of the variables; a single valued
+function having for finite values of the variables no singularities
+other than poles or polar points of indetermination is called a
+meromorphic function; as for p = 1 such a function can be expressed
+as a quotient of two integral functions having no common zero
+point other than the points of indetermination of the function;
+but the proof of this theorem is difficult.</p>
+
+<p>The single valued functions which occur, as explained above, in
+the inversion of algebraic integrals of the first kind, for p &gt; 1, are
+meromorphic. They must also be periodic, unaffected that is when
+the variables u<span class="su">1</span>, ... u<span class="su">p</span> are <i>simultaneously</i> increased each by a
+proper constant, these being the additive constants of indeterminateness
+for the p integrals &int; R<span class="su">i</span>(x, y)dx arising when (x, y) makes a closed
+circuit, the same for each integral. The theory of such single valued
+meromorphic periodic functions is simpler than that of meromorphic
+functions of several variables in general, as it is sufficient to consider
+only finite values of the variables; it is the natural extension of
+the theory of doubly periodic functions previously discussed. It
+can be shown to reduce, though the proof of this requires considerable
+developments of which we cannot speak, to the theory of a single
+integral function of u<span class="su">1</span>, ... u<span class="su">p</span>, called the <i>Theta Function</i>. This is
+expressible as a series of positive and negative integral powers of
+quantities exp (c<span class="su">1</span>u<span class="su">1</span>), exp (c<span class="su">2</span>u<span class="su">2</span>), ... exp (c<span class="su">p</span>u<span class="su">p</span>), wherein c<span class="su">1</span>, ... c<span class="su">p</span> are
+proper constants; for p = 1 this theta function is essentially the
+same as that above given under a different form (see § 14, <i>Doubly
+Periodic Functions</i>), the function &sigma;(u). In the case of p = 1, all
+meromorphic functions periodic with the same two periods have
+been shown to be rational functions of two of them connected by a
+single algebraic equation; in the same way all meromorphic functions
+of p variables, periodic with the same sets of simultaneous periods,
+2p sets in all, can be shown to be expressible rationally in terms of
+p + 1 such periodic functions connected by a single algebraic equation.
+Let x<span class="su">1</span>, ... x<span class="su">p</span>, y denote p + 1 such functions; then each of the partial
+derivatives dx<span class="su">i</span>/&part;u<span class="su">i</span> will equally be a meromorphic function of the
+same periods, and so expressible rationally in terms of x<span class="su">1</span>, ... x<span class="su">p</span>, y;
+thus there will exist p equations of the form</p>
+
+<p class="center">dx<span class="su">i</span> = R<span class="su">1</span>du<span class="su">1</span> + ... + R<span class="su">p</span>du<span class="su">p</span>,</p>
+
+<p class="noind">and hence p equations of the form</p>
+
+<p class="center">du<span class="su">i</span> = H<span class="su">i, 1</span>dx<span class="su">1</span> + ... + H<span class="su">i, p</span>dx<span class="su">p</span>,</p>
+
+<p class="noind">wherein H<span class="su">i, j</span> are rational functions of x<span class="su">1</span>, ... x<span class="su">p</span>, y, these being connected
+by a fundamental algebraic (rational) equation, say &fnof;(x<span class="su">1</span>, ... x<span class="su">p</span>, y)
+= 0. This then is the generalized form of the corresponding equation
+for p = 1.</p>
+</div>
+
+<p>§ 26. <i>Multiply-Periodic Functions and the Theory of Surfaces.</i>&mdash;The
+theory of algebraic integrals &int; R(x, y)dx, wherein x, y are
+connected by a rational equation &fnof;(x, y) = 0, has developed
+concurrently with the theory of algebraic curves; in particular
+the existence of the number p invariant by all birational transformations
+is one result of an extensive theory in which curves
+capable of birational correspondence are regarded as equivalent;
+this point of view has made possible a general theory of what
+might otherwise have remained a collection of isolated theorems.</p>
+
+<div class="condensed">
+<p>In recent years developments have been made which point to
+a similar unity of conception as possible for surfaces, or indeed for
+algebraic constructs of any number of dimensions. These developments
+have been in two directions, at first followed independently,
+but now happily brought into the most intimate connexion. On the
+analytical side, E. Picard has considered the possibility of classifying
+integrals of the form &int;(Rds + Sdy), belonging to a surface &fnof;(x, y, z)
+= 0, wherein R and S are rational functions of x, y, z, according as
+they are (1) everywhere finite, (2) have poles, which then lie along
+curves upon the surface, or (3) have logarithmic infinities, also then
+lying along curves, and has brought the theory to a high degree
+of perfection. On the geometrical side A. Clebsch and M.
+Noether, and more recently the Italian school, have considered the
+geometrical characteristics of a surface which are unaltered by birational
+transformation. It was first remarked that for surfaces of
+order n there are associated surfaces of order n &minus; 4, having properties
+in relation thereto analogous to those of curves of order n &minus; 3 for a
+plane curve of order n; if such a surface &fnof;(x, y, z) = 0 have a double
+curve with triple points triple also for the surface, and &phi;(x, y, z) = 0
+be a surface of order n &minus; 4 passing through the double curve, the
+double integral</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">&int; &int;</span></td> <td>&phi; dx dy</td></tr>
+<tr><td class="denom">&part;f/&part;z</td></tr></table>
+
+<p class="noind">is everywhere finite; and, the most general everywhere finite
+integral of this form remains invariant in a birational transformation
+of the surface &fnof;, the theorem being capable of generalization to
+algebraic constructs of any number of dimensions. The number of
+linearly independent surfaces of order n &minus; 4, possessing the requisite
+particularity in regard to the singular lines and points of the surface,
+is thus a number invariant by birational transformation, and
+the equality of these numbers for two surfaces is a necessary condition
+of their being capable of such transformation. The number
+of surfaces of order m having the assigned particularity in regard to
+the singular points and lines of the fundamental surface can be given
+by a formula for a surface of given singularity; but the value of this
+formula for m = n &minus; 4 is not in all cases equal to the actual number
+of surfaces of order n &minus; 4 with the assigned particularity, and for a
+cone (or ruled surface) is in fact negative, being the negative of the
+deficiency of the plane section of the cone. Nevertheless this
+number for m = n &minus; 4 is also found to be invariant for birational
+transformation. This number, now denoted by p<span class="su">a</span>, is then a second
+invariant of birational transformation. The former number, of
+actual surfaces of order n &minus; 4 with the assigned particularity in regard
+to the singularities of the surface, is now denoted by p<span class="su">g</span>. The
+difference p<span class="su">g</span> &minus; p<span class="su">a</span>, which is never negative, is a most important
+characteristic of a surface. When it is zero, as in the case of the
+general surface of order n, and in a vast number of other ordinary
+cases, the surface is called regular.</p>
+
+<p>On a plane algebraical curve we may consider linear series of sets
+of points, obtained by the intersection with it of curves &lambda;&phi; + &lambda;<span class="su">1</span>&phi;<span class="su">1</span> +
+... = 0, wherein &lambda;, &lambda;<span class="su">1</span>, ... are variable coefficients; such a series
+consists of the sets of points where a rational function of given poles,
+belonging to the construct &fnof;(x, y) = 0, has constant values. And we
+may consider series of sets of points determined by variable curves
+whose coefficients are algebraical functions, not necessarily rational
+functions, of parameters. Similarly on a surface we may consider
+linear systems of curves, obtained by the intersection with the
+given surface of variable surfaces &lambda;&phi; + &lambda;<span class="su">1</span>&phi;<span class="su">1</span> + ... = 0, and may
+consider algebraic systems, of which the individual curve is given
+by variable surfaces whose coefficients are algebraical, not necessarily
+rational, functions of parameters. Of a linear series upon a plane
+curve there are two numbers manifestly invariant in birational
+transformation, the <i>order</i>, which is the number of points forming a
+set of the series, and the <i>dimension</i>, which is the number of parameters
+&lambda;<span class="su">1</span>/&lambda;, &lambda;<span class="su">2</span>/&lambda;, ... entering linearly in the equation of the series.
+The series is <i>complete</i> when it is not contained in a series of the same
+order but of higher dimension. So for a linear system of curves
+upon a surface, we have three invariants for birational transformation;
+the <i>order</i>, being in the number of variable intersections of two
+curves of the system, the <i>dimension</i>, being the number of linear
+parameters &lambda;<span class="su">1</span>/&lambda;, &lambda;<span class="su">2</span>/&lambda;, ... in the equation for the system, and the
+<i>deficiency</i> of the individual curves of the system. Upon any curve
+of the linear system the other curves of the system define a linear
+series, called the <i>characteristic</i> series; but even when the linear
+system is complete, that is, not contained in another linear system
+of the same order and higher dimension, it does not follow that the
+characteristic series is complete; it may be contained in a series whose
+dimension is greater by p<span class="su">g</span> &minus; p<span class="su">a</span> than its own dimension. When this
+is so it can be shown that the linear system of curves is contained
+in an algebraic system whose dimension is greater by p<span class="su">g</span> &minus; p<span class="su">a</span> than the
+dimension of the linear system. The extra p = p<span class="su">g</span> &minus; p<span class="su">a</span> variable parameters
+so entering may be regarded as the independent co-ordinates
+of an algebraic construct &fnof;(y, x<span class="su">1</span>, ... x<span class="su">p</span>) = 0; this construct has the
+property that its co-ordinates are single valued meromorphic
+functions of p variables, which are periodic, possessing 2p systems
+of periods; the p variables are expressible in the forms</p>
+
+<p class="center">u<span class="su">i</span> = &int; R<span class="su">1</span>(x, y) dx<span class="su">1</span> + ... + R<span class="su">p</span>(x, y) dx<span class="su">p</span>,</p>
+
+<p class="noind">wherein R<span class="su">i</span>(x, y) denotes a rational function of x<span class="su">1</span>, ... x<span class="su">p</span> and y.
+The original surface has correspondingly p integrals of the form
+&int;(R dx + S dy), wherein R, S are rational in x, y, z, which are everywhere
+finite; and it can be shown that it has no other such integrals.
+From this point of view, then, the number p, = p<span class="su">g</span> &minus; p<span class="su">a</span> is, for a surface,
+analogous to the deficiency of a plane curve; another analogy
+arises in the comparison of the theorems: for a plane curve of zero
+deficiency there exists no algebraic series of sets of points which
+does not consist of sets belonging to a linear series; for a surface for
+which p<span class="su">g</span> &minus; p<span class="su">a</span> = 0 there exists no algebraic system of curves not
+contained in a linear system.</p>
+
+<p>But whereas for a plane curve of deficiency zero, the co-ordinates
+of the points of the curve are rational functions of a single parameter,
+it is not necessarily the case that for a surface having p<span class="su">g</span> &minus; p<span class="su">a</span> = 0 the
+co-ordinates of the points are rational functions of two parameters;
+it is necessary that p<span class="su">g</span> &minus; p<span class="su">a</span> = 0, but this is not sufficient. For surfaces,
+beside the p<span class="su">g</span> linearly independent surfaces of order n &minus; 4
+having a definite particularity at the singularities of the surface, it is
+useful to consider surfaces of order k(n &minus; 4), also having each a
+definite particularity at the singularities, the number of these, not
+containing the original surface as component, which are linearly
+independent, is denoted by P<span class="su">k</span>. It can then be stated that a sufficient
+condition for a surface to be rational consists of the two conditions
+p<span class="su">a</span> = 0, P<span class="su">2</span> = 0. More generally it becomes a problem to classify
+surfaces according to the values of the various numbers which are
+invariant under birational transformation, and to determine for
+each the simplest form of surface to which it is birationally equivalent.
+Thus, for example, the hyperelliptic surface discussed by Humbert,
+<span class="pagenum"><a name="page329" id="page329"></a>329</span>
+of which the co-ordinates are meromorphic functions of two variables
+of the simplest kind, with four sets of periods, is characterized by
+p<span class="su">g</span> = 1, p<span class="su">a</span> = &minus;1; or again, any surface possessing a linear system of
+curves of which the order exceeds twice the deficiency of the individual
+curves diminished by two, is reducible by birational transformation
+to a ruled surface or is a rational surface. But beyond
+the general statement that much progress has already been made
+in this direction, of great interest to the student of the theory of
+functions, nothing further can be added here.</p>
+
+<p><span class="sc">Bibliography.</span>&mdash;The learner will find a lucid introduction to the
+theory in E. Goursat, <i>Cours d&rsquo;analyse mathématique</i>, t. ii. (Paris,
+1905), or, with much greater detail, in A.R. Forsyth, <i>Theory of
+Functions of a Complex Variable</i> (2nd ed., Cambridge, 1900); for
+logical rigour in the more difficult theorems, he should consult
+W.F. Osgood, <i>Lehrbuch der Functionentheorie</i>, Bd. i. (Leipzig, 1906-1907);
+for greater precision in regard to the necessary quasi-geometrical
+axioms, beside the indications attempted here, he should
+consult W.H. Young, <i>The Theory of Sets of Points</i> (Cambridge,
+1906), chs. viii.-xiii., and C. Jordan, <i>Cours d&rsquo;analyse</i>, t. i. (Paris,
+1893), chs. i., ii.; a comprehensive account of the <i>Theory of Functions
+of Real Variables</i> is by E.W. Hobson (Cambridge, 1907). Of the
+theory regarded as based after Weierstrass upon the theory of power
+series, there is J. Harkness and F. Morley, <i>Introduction to the Theory
+of Analytic Functions</i> (London, 1898), an elementary treatise;
+for the theory of the convergence of series there is also T.J. I&rsquo;A.
+Bromwich, <i>An Introduction to the Theory of Infinite Series</i> (London,
+1908); but the student should consult the collected works of Weierstrass
+(Berlin, 1894 ff.), and the writings of Mittag-Leffler in the early
+volumes of the <i>Acta mathematica</i>; earlier expositions of the theory
+of functions on the basis of power series are in C. Méray, <i>Leçons
+nouvelles sur l&rsquo;analyse infinitésimale</i> (Paris, 1894), and in Lagrange&rsquo;s
+books on the Theory of Functions. An account of the theory of
+potential in its applications to the present theory is found in most
+treatises; in particular consult E. Picard, <i>Traité d&rsquo;analyse</i>, t. ii.
+(Paris, 1893). For elliptic functions there is an introductory book,
+P. Appell and E. Lacour, <i>Principes de la théorie des fonctions elliptiques
+et applications</i> (Paris, 1897), beside the treatises of G.H. Halphen,
+<i>Traité des fonctions elliptiques et de leurs applications</i> (three parts,
+Paris, 1886 ff.), and J. Tannery et J. Molk, <i>Éléments de la théorie
+des fonctions elliptiques</i> (Paris, 1893 ff.); a book, A.G. Greenhill,
+<i>The Applications of Elliptic Functions</i> (London, 1892), shows how
+the functions enter in problems of many kinds. For modular
+functions there is an extensive treatise, F. Klein and R. Fricke,
+<i>Theorie der elliptischen Modulfunctionen</i> (Leipzig, 1890); see also
+the most interesting smaller volume, F. Klein, <i>Über das Ikosaeder</i>
+(Leipzig, 1884) (also obtainable in English). For the theory of
+Riemann&rsquo;s surface, and algebraic integrals, an interesting introduction
+is P. Appeil and E. Goursat, <i>Théorie des fonctions algébriques
+et de leurs intégrales</i>; for Abelian functions see also H. Stahl, <i>Theorie
+der Abel&rsquo;schen Functionen</i> (Leipzig, 1896), and H.F. Baker, <i>An
+Introduction to the Theory of Multiply Periodic Functions</i> (Cambridge,
+1907), and H.F. Baker, <i>Abel&rsquo;s Theorem and the Allied Theory, including
+the Theory of the Theta Functions</i> (Cambridge, 1897); for
+theta functions of one variable a standard work is C.G. Jacobi,
+<i>Fundamenta nova, &amp;c.</i> (Königsberg, 1828); for the general theory
+of theta functions, consult W. Wirtinger, <i>Untersuchungen über Theta-Functionen</i>
+(Leipzig, 1895). For a history of the theory of algebraic
+functions consult A. Brill and M. Noether, <i>Die Entwicklung der
+Theorie der algebraischen Functionen in älterer und neuerer Zeit,
+Bericht der deutschen Mathematiker-Vereinigung</i> (1894); and for a
+special theory of algebraic functions, K. Hensel and G. Landsberg,
+<i>Theorie der algebraischen Function u.s.w.</i> (Leipzig, 1902). The
+student will, of course, consult also Riemann&rsquo;s and Weierstrass&rsquo;s
+<i>Ges. Werke</i>. For the applications to geometry in general an important
+contribution, of permanent value, is E. Picard and G. Simart,
+<i>Théorie des fonctions algébriques de deux variables indépendantes</i>
+(Paris, 1897-1906). This work contains, as Note v. t. ii. p. 485, a
+valuable summary by MM. Castelnuovo and Enriques, <i>Sur quelques
+résultats nouveaux dans la théorie des surfaces algébriques</i>, containing
+many references to the numerous memoirs to be found, for the most
+part, in the transactions of scientific societies and the mathematical
+journals of Italy.</p>
+
+<p>Beside the books above enumerated there exists an unlimited
+number of individual memoirs, often of permanent importance
+and only imperfectly, or too elaborately, reproduced in the pages
+of the volumes in which the student will find references to them.
+The German <i>Encyclopaedia of Mathematics</i>, and the Royal Society&rsquo;s
+<i>Reference Catalogue of Current Scientific Literature, Pure Mathematics</i>,
+published yearly, should also be consulted.</p>
+</div>
+<div class="author">(H. F. Ba.)</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1ga" id="ft1ga" href="#fa1ga"><span class="fn">1</span></a> The word &ldquo;function&rdquo; (from Lat. <i>fungi</i>, to perform) has many
+uses, with the fundamental sense of an activity special or proper
+to an office, business or profession, or to an organ of an animal or
+plant, the definite work for which the organ is an apparatus. From
+the use of the word, as in the Italian <i>funzione</i>, for a ceremony of
+the Roman Church, &ldquo;function&rdquo; is often employed for a public
+ceremony of any kind, and loosely of a social entertainment or
+gathering.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FUNDY, BAY OF,<a name="ar71" id="ar71"></a></span> an inlet of the North Atlantic, separating
+New Brunswick from Nova Scotia. It is 145 m. long and 48 m.
+wide at the mouth, but gradually narrows towards the head,
+where it divides into Chignecto Bay to the north, which subdivides
+into Shepody Bay and Cumberland Basin (the French
+Beaubassin), and Minas Channel, leading into Minas Basin, to
+the east and south. Off its western shore opens Passamaquoddy
+Bay, a magnificent sheet of deep water with good anchorage,
+receiving the waters of the St Croix river and forming part of
+the boundary between New Brunswick and the state of Maine,
+The Bay of Fundy is remarkable for the great rise and fall of
+the tide, which at the head of the bay has been known to reach
+62 ft. In Passamaquoddy Bay the rise and fall is about 25 ft.,
+which gradually increases toward the narrow upper reaches.
+At spring tides the water in the Bay of Fundy is 19 ft. higher
+than it is in Bay Verte, in Northumberland Strait, only 15 m.
+distant. Though the bay is deep, navigation is rendered
+dangerous by the violence and rapidity of the tide, and in summer
+by frequent fogs. At low tide, at such points as Moncton or
+Amherst, only an expanse of red mud can be seen, and the tide
+rushes in a bore or crest from 3 to 6 ft. in height. Large areas
+of fertile marshes are situated at the head of the bay, and the
+remains of a submerged forest show that the land has subsided
+in the latest geological period at least 40 ft. The bay receives
+the waters of the St Croix and St John rivers, and has numerous
+harbours, of which the chief are St Andrews (on Passamaquoddy
+Bay) and St John in New Brunswick, and Digby and Annapolis
+(on an inlet known as Annapolis Basin) in Nova Scotia. It was
+first explored by the Sieur de Monts (d. <i>c.</i> 1628) in 1604 and
+named by him La Baye Française.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUNERAL RITES,<a name="ar72" id="ar72"></a></span> the ceremonies associated with different
+methods of disposing of the dead. (See also <span class="sc"><a href="#artlinks">Burial and Burial
+Acts</a></span>; <span class="sc"><a href="#artlinks">Cemetery</a></span>; and <span class="sc"><a href="#artlinks">Cremation</a></span>.) In general we have little
+record, except in their tombs, of races which, in a past measured
+not merely by hundreds but by thousands of years, occupied
+the earth; and exploration of these often furnishes our only
+clue to the religions, opinions, customs, institutions and arts of
+long vanished societies. In the case of the great culture folks
+of antiquity, the Babylonians, Egyptians, Hindus, Persians,
+Greeks and Romans, we have, besides their monuments, the
+evidence of their literatures, and so can know nearly as much of
+their rites as we do of our own. The rites of modern savages
+not only help us to interpret prehistoric monuments, but explain
+peculiarities in our own rituals and in those of the culture folks
+of the past of which the significance was lost or buried under
+etiological myths. We must not then confine ourselves to the
+rites of a few leading races, neglecting their less fortunate
+brethren who have never achieved civilization. It is better to
+try to classify the rites of all races alike according as they embody
+certain leading conceptions of death, certain fears, hopes, beliefs
+entertained about the dead, about their future, and their relations
+with the living.</p>
+
+<div class="condensed">
+<p>The main ideas, then, underlying funeral rites may roughly be
+enumerated as follows:</p>
+
+<p>1. The pollution or taboo attaching to a corpse.</p>
+
+<p>2. Mourning.</p>
+
+<p>3. The continued life of the dead as evinced in the housing and
+equipment of the dead, in the furnishing of food for them, and in the
+orientation and posture assigned to the body.</p>
+
+<p>4. Communion with the dead in a funeral feast and otherwise.</p>
+
+<p>5. Sacrifice for the dead and expiation of their sins.</p>
+
+<p>6. Death witchery.</p>
+
+<p>7. Protection of the dead from ghouls.</p>
+
+<p>8. Fear of ghosts.</p>
+</div>
+
+<p>1. A dead body is unclean, and the uncleanness extends
+to things and persons which touch it. Hence the Jewish law
+(Num. v. 2) enacted that &ldquo;whoever is unclean by the dead
+shall be put outside the camp, that they defile not the camp
+in the midst whereof the Lord dwells.&rdquo; Such persons were
+unclean until the even, and might not eat of the holy things
+unless they bathed their flesh in water. A high priest might on
+no account &ldquo;go in to any dead body&rdquo; (Lev. xxi. 11). Why
+a corpse is so widely tabooed is not certain; but it is natural to
+see one reason in the corruption which in warm climates soon
+sets in. The common experience that where one has died
+another is likely to do so may also have contributed, though, of
+course, there was no scientific idea of infection. The old Persian
+scriptures are full of this taboo. He who has touched a corpse is
+&ldquo;powerless in mind, tongue and hand&rdquo; (<i>Zend Avesta</i> in <i>Sacred
+Books of the East</i>, pt. i. p. 120), and the paralysis is inflicted by
+the innumerable <i>drugs</i> or evil spirits which invest a corpse.
+Fire and earth, being alike creations of the good and pure god
+<span class="pagenum"><a name="page330" id="page330"></a>330</span>
+Ahuramazda, a body must not be burned or buried; and so the
+ancient Persians and their descendants the Parsees build Dakmas
+or &ldquo;towers of silence&rdquo; on hill-tops far from human habitations.
+Inside these the corpses are laid on a flagged terrace which
+drains into a central pit. Twice a year the bones, picked clean
+by dogs and birds of prey, are collected in the pit, and when it
+is full another tower is built. In ancient times perhaps the
+bodies of the magi or priests alone were exposed at such expense;
+the common folk were covered with wax and laid in the earth,
+the wax saving the earth from pollution. In Rome and Greece
+the corpse was buried by night, lest it should pollute the sunlight;
+and a trough of water was set at the door of the house of death
+that men might purify themselves when they came out, before
+mixing in general society. Priests and magistrates in Rome
+might not meet or look on a corpse, for they were thereby
+rendered unclean and incapable of fulfilling their official duties
+without undergoing troublesome rites of purification. At a
+Roman funeral, when the remains had been laid in the tomb,
+all present were sprinkled with lustral water from a branch of
+olive or laurel called <i>aspergillum</i>; and when they had gone
+home they were asperged afresh and stepped over a fire. The
+house was also swept out with a broom, probably lest the ghost
+of the dead should be lying about the floor. Many races, to
+avoid pollution, destroy the house and property of the deceased.
+Thus the Navahos pull down the hut in which he died, leaving its
+ruins on the ground; but if it be an expensive hut, a shanty
+is extemporized alongside, into which the dying man is transferred
+before death. No one will use the timbers of a hut so
+ruined. A burial custom of the Solomon Islands, noted by
+R.H. Codrington (<i>The Melanesians</i>, p. 255), may be dictated
+by the same scruple. There &ldquo;the mourners having hung up a
+dead man&rsquo;s arms on his house make great lamentations; all
+remains afterwards untouched, the house goes to ruin, mantled,
+as time goes on, with the vines of the growing yams, a picturesque
+and indeed, perhaps, a touching sight; for these things are not
+set up that they may in a ghostly manner accompany their
+former owner.&rdquo; H. Oldenberg (<i>Religion des Veda</i>, p. 426) describes
+how Hindus shave themselves and cut off their nails after a
+death, at the same time that they wash, renew the hearth fire,
+and furnish themselves with new vessels. For the hair and
+nails may harbour pollution, just as the medieval Greeks believed
+that evil spirits could lurk in a man&rsquo;s beard (Leo Allatius, <i>De
+opinionibus quorundam Graecorum</i>). The dead man&rsquo;s body
+is shorn and the nails cut for a kindred reason; for it must be
+purified as much as can be before it is burned as an offering on
+the pyre and before he enters on a new sphere of existence.</p>
+
+<p>2. We are accustomed to regard mourning costume as primarily
+an outward sign of our grief. Originally, however, the special
+garb seems to have been intended to warn the general public
+that persons so attired were unclean. In ancient Rome mourners
+stayed at home and avoided all feasts and amusements; laying
+aside gold, purple and jewels, they wore black dresses called
+<i>lugubria</i> or even skins. They cut neither hair nor beard, nor
+lighted fire. Under the emperors women began to wear white.
+On the west coast of Africa negroes wear white, on the Gold
+Coast red. The Chinese wear hemp, which is cheap, for mourning
+dress must as a rule be destroyed when the season of grief is
+past to get rid of the taboo. Among the Aruntas of Australia
+the wives of a dead man smear themselves with white pipe-clay
+until the last ceremonies are finished, sometimes adding ashes&mdash;this
+not to conceal themselves from the ghost (which may partly
+be the aim of some mourning costumes), but to show the ghost
+that they are duly sorrowing for their loss. These widows must
+not talk except on their hands for a whole year. &ldquo;Among the
+Maoris,&rdquo; says Frazer (<i>Golden Bough</i>, i. 323), &ldquo;anyone who had
+handled a corpse, helped to convey it to the grave, or touched a
+dead man&rsquo;s bones; was cut off from all intercourse and almost
+all communication with mankind. He could not enter any
+house, or come into contact with any person or thing, without
+utterly bedevilling them. He might not even touch food with
+his hands, which had become so frightfully tabooed or unclean
+as to be quite useless. Food would be set for him on the ground,
+and he would then sit or kneel down, and, with his hands carefully
+held behind his back, would gnaw at it as best he could.&rdquo; Often
+a degraded outcast was kept in a village to feed mourners. Such
+a taboo is strictly similar to those which surround a sacred chief
+or his property, a menstruous woman or a homicide, rendering
+them dangerous to themselves and to all who approach them.</p>
+
+<p>3. Primitive folk cannot conceive of a man&rsquo;s soul surviving
+apart from his body, nor of another life as differing from this,
+and the dead must continue to enjoy what they had here.
+Accordingly the Patagonians kill horses at the grave that the
+dead may ride to <i>Alhuemapu</i>, or country of the dead. After a
+year they collect a chief&rsquo;s bones, arrange them, tie them together
+and dress them in his best garments with beads and feathers.
+Then they lay him with his weapons in a square pit, round
+which dead horses are placed set upright on their feet by stakes.
+As late as 1781 in Poland F. Casimir&rsquo;s horse was slain and buried
+with him. In the Caucasus a Christian lady&rsquo;s jewels are buried
+with her. The Hindus used to burn a man&rsquo;s widow on his pyre,
+because he could not do without her; and St Boniface commends
+the self-sacrifice of the Wend widows who in his day burned
+themselves alive on their husbands&rsquo; pyres.</p>
+
+<p>The tumuli met with all over the north of Europe (in the
+Orkneys alone 2000 remain) are regular houses of the dead,
+models of those they occupied in life. The greater the dignity
+of the deceased, the loftier was his barrow. Silbury hill is
+170 ft. high; the tomb of Alyattes, father of Croesus, was a
+fourth of a league round; the Pyramids are still the largest
+buildings in existence; at Oberea in Tahiti is a barrow 267 ft.
+long, 87 wide and 44 high. Some Eskimo just leave a dead
+man&rsquo;s body in his house, and shut it up, often leaving by his
+side a dog&rsquo;s head to guide him on his last journey, along with
+his tools and kayak. The Sea Dyaks set a chief adrift in his war
+canoe with his weapons. So in Norse story Hake &ldquo;was laid
+wounded on a ship with the dead men and arms; the ship was
+taken out to sea and set on fire.&rdquo; The Viking was regularly
+buried in his ship or boat under a great mound. He sailed
+after death to Valhalla. In the ship was laid a stone as anchor
+and the tools, clothes, weapons and treasures of the dead. The
+Egyptians, whose land was the gift of the river Nile, equally
+believed that the dead crossed over water, and fashioned the
+hearse in the form of a boat. Hence perhaps was derived the
+Greek myth of Charon and the Styx, and the custom, which still
+survives in parts of Europe, of placing a coin in the mouth of the
+dead with which to pay the ferryman. The Egyptians placed
+in the tomb books of a kind to guide the dead to the next world.
+The Copts in a later age did the same, and to this custom we owe
+the recovery in Egypt of much ancient literature. The Armenians
+till lately buried with a priest his missal or gospel.</p>
+
+<p>In Egyptian entombments of the XIIth to the XIVth dynasties
+were added above the sepulchres what Professor Petrie terms soul-houses,
+viz. small models of houses furnished with couch and
+table, &amp;c., for the use of the <i>ka</i> or double whenever it might wish
+to come above ground and partake of meats and drinks. They
+recall, in point of size, the hut-urns of the Etruscans, but the
+latter had another use, for they contain incinerated remains.
+Etruscan tombs, like those of Egypt and Asia Minor, were made
+to resemble the dwelling-houses of the living, and furnished with
+coffered ceilings, panelled walls, couches, stools, easy chairs with
+footstools attached, all hewn out of the living rock (Dennis,
+<i>Cities and Cemeteries of Etruria</i>, vol i. p. lxx.).</p>
+
+<p>Of the old Peruvian mummies in the Kircherian Museum at
+Rome, several are of women with babies in their arms, whence
+it is evident that a mother had her suckling buried with her;
+it would console her in the next world and could hardly survive
+her in this. The practice of burying ornaments, tools and
+weapons with the dead characterizes the inhumations of the
+Quaternary epoch, as if in that dim and remote age death was
+already regarded as the portal of another life closely resembling
+this. The cups, tools, weapons, ornaments and other articles
+deposited with the dead are often carefully broken or turned
+upside down and inside out; for the soul or <i>manes</i> of objects is
+liberated by such fracture or inversion and so passes into the
+<span class="pagenum"><a name="page331" id="page331"></a>331</span>
+dead man&rsquo;s use and possession. For the same reason where the
+dead are burned, their properties are committed to the flames.
+The ghost of the warrior has a ghostly sword and buckler to
+fight with and a ghostly cup to drink from, and he is also nourished
+by the impalpable odour and reek of the animal victims sacrificed
+over his grave. Instead of valuable objects cheap images and
+models are often substituted; and why not, if the mere ghosts
+of the things are all that the wraith can enjoy? Thus Marco
+Polo (ii. 76) describes how in the land of Kinsay (Hang-chau)
+&ldquo;the friends and relations make a great mourning for the
+deceased, and clothe themselves in hempen garments, and follow
+the corpse, playing on a variety of instruments and singing
+hymns to their idols. And when they come to the burning place
+they take representations of things cut out of parchment, such
+as caparisoned horses, male and female slaves, camels, armour,
+suits of cloth of gold (and money), in great quantities, and these
+things they put on the fire along with the corpse so that they
+are all burned with it. And they tell you that the dead man
+shall have all these slaves and animals of which the effigies are
+burned, alive in flesh and blood, and the money in gold, at his
+disposal in the next world; and that the instruments which
+they have caused to be played at his funeral, and the idol hymns
+that have been chaunted shall also be produced again to welcome
+him in the next world.&rdquo; The manufacture of such paper <i>simulacra</i>
+for consumption at funerals is still an important industry
+in Chinese cities. The ancient Egyptians, assured that a man&rsquo;s
+<i>ka</i> or double shall revivify his body, took pains to guard the
+flesh from corruption, steeping the corpse in natron and stuffing
+it with spices. A body so prepared is called a mummy (<i>q.v.</i>),
+and the custom was already of a hoary antiquity in 3200 <span class="scs">B.C.</span>,
+when the oldest dated mummy we have was made. The bowels,
+removed in the process, were placed in jars over the corpse in the
+tomb, together with writing tablets, books, musical instruments,
+&amp;c., of the dead. Cemeteries also remain full of mummies of
+crocodiles, cats, fish, cows and other sacred animals. The
+Greeks settled in Egypt learned to mummify their dead, but
+the custom was abhorrent to the Jews, although the Christian
+belief in the resurrection of the flesh must have been formed to
+a large extent under Egyptian influence. Half the superiority of
+the Jewish to other ancient religions lay in this, that it prescribed
+no funeral rites other than the simplest inhumation.</p>
+
+<p>The dead all over the world and from remote antiquity have
+been laid not anyhow in the earth, but with the feet and face
+towards the region in which their future will be spent; the
+Samoans and Fijians towards the far west whither their souls
+have preceded them; the Guarayos with head turned eastwards
+because their god Tamoi has in that quarter &ldquo;his happy hunting
+grounds where the dead will meet again&rdquo; (Tylor, <i>Prim. Cult.</i>
+ii. 422). The legend is that Christ was buried with His head to
+the west, and the church follows the custom, more ancient than
+itself, of laying the dead looking to the East, because that is
+the attitude of prayer, and because at the last trump they will
+hurry eastwards. So in Eusebius (<i>Hist. Eccl.</i> 430.19) a martyr
+explains to his pagan judge that the heavenly Jerusalem, the
+fatherland of the pious, lay exactly in the east at the rising place
+of the sun. Where the body is laid out straight it is difficult to
+discern the presence of any other idea than that it is at rest. In
+Scandinavian barrows, <i>e.g.</i> in the one opened at Goldhavn in
+1830, the skeletons have been found seated on a low stone bench
+round the wall of the grave chamber facing its opening, which
+always looks south or east, never north. Here the dead were
+continuing the drinking bouts they enjoyed on earth.</p>
+
+<p>The Peruvians mummified their dead and placed them jointed
+and huddled up with knees to chin, looking toward the sunset,
+with the hands held before the face. In the oldest prehistoric
+tombs along the Nile the bodies are doubled up in the same
+position. It would seem as if in these and numerous other
+similar cases the dead were deliberately given in their graves
+the attitude of a foetus in the womb, and, as Dr Budge remarks
+(<i>Egyptian Ideas of the Future Life</i>, London, 1899, p. 162), &ldquo;we
+may perhaps be justified in seeing in this custom the symbol
+of a hope that, as the child is born from this position into the
+world, so might the deceased be born into the life beyond the
+grave.&rdquo; The late Quaternary skeletons of the Mentone cave
+were laid in a layer of ferrugineous earth specially laid down for
+them, and have contracted a red colour therefrom. Many other
+prehistoric skeletons found in Italy have a reddish colour, perhaps
+for the same reason, or because, as often to-day, the bones were
+stripped of flesh and painted. Ambrose relates that the skeletons
+of the martyrs Gervasius and Protasius, which he found and
+deposited <span class="scs">A.D.</span> 386 under the altar of his new basilica in Milan,
+were <i>mirae magnitudinis ut prisca aetas ferebat</i>, and were also
+coloured red. He imagined the red to be the remains of the
+martyrs&rsquo; blood! <i>Hic sanguis clamat coloris indicio.</i> Salomon
+Reinach has rightly divined that what Ambrose really hit upon
+was a prehistoric tomb. Red earth was probably chosen as a
+medium in which to lay a corpse because demons flee from red.
+Sacred trees and stones are painted red, and for the most solemn
+of their rites savages bedaub themselves with red clay. It is
+a favourite taboo colour.</p>
+
+<p>4. A feast is an essential feature of every primitive funeral,
+and in the Irish &ldquo;wake&rdquo; it still survives. A dead man&rsquo;s soul
+or double has to be fed at the tomb itself, perhaps to keep it
+from prowling about the homes of the survivors in search of
+victuals; and such food must also be supplied to the dead at
+stated intervals for months or years. Many races leave a
+narrow passage or tube open down to the cavity in which the
+corpse lies, and through it pour down drinks for the dead.
+Traces of such tubes are visible in the prehistoric tombs of the
+British Isles. However, such provision of food is not properly
+a funeral feast unless the survivors participate. In the Eastern
+churches and in Russia the departed are thus fed on the ninth,
+twelfth and fortieth days from death. &ldquo;Ye appease the shades
+of the dead with wine and meals,&rdquo; was the charge levelled at
+the Catholics by the 4th-century Manichaeans, and it has hardly
+ceased to be true even now after the lapse of sixteen centuries.
+The funeral feast proper, however, is either a meal of communion
+with or in the dead, which accompanies interment, or a banquet
+off the flesh of victims slain in atonement of the dead man&rsquo;s
+sins. Some anthropologists see in the common meal held at the
+grave &ldquo;the pledge and witness of the unity of the kin, the chief
+means, if not of making, at least of repairing and renewing it.&rdquo;<a name="fa1g" id="fa1g" href="#ft1g"><span class="sp">1</span></a>
+The flesh provided at these banquets is occasionally that of the
+dead man himself; Herodotus and Strabo in antiquity relate
+this of several half-civilized races in the East and West, and a
+similar story is told by Marco Polo of certain Tatars. Nor
+among modern savages are funeral feasts off the flesh of the dead
+unknown, and they seem to be intended to effect and renew a
+sacramental union or kinship of the living with the dead. The
+Uaupes in the Amazons incinerate a corpse a month after death,
+pound up the ashes, and mix them with their fermented drink.
+They believe that the virtues of the dead will thus be passed on
+to his survivors. The life of the tribe is kept inside the tribe
+and not lost. Such cannibal sacraments, however, are rare, and,
+except in a very few cases, the evidence for them weak. The
+slaying and eating of animal victims, however, at the tomb is universal
+and bears several meanings, separately or all at once. The
+animals may be slain in order that their ghosts may accompany
+the deceased in his new life. This significance we have already
+dwelt upon. Or it is believed that the shade feeds upon them,
+as the shades came up from Hades and lapped up out of a trench
+the blood of the animals slain by Ulysses. The survivors by
+eating the flesh of a victim, whose blood and soul the dead thus
+consume, sacramentally confirm the mystic tie of blood kinship
+with the dead. Or lastly, the victim may be offered for the sins
+of the dead. His sins are even supposed to be transferred into
+it and eaten by the priest. Such expiatory sacrifices of animals
+for the dead survive in the Christian churches of Armenia, Syria
+and of the East generally. Their vicarious character is emphasized
+in the prayers which accompany them, but the popular understanding
+of them probably combines all the meanings above
+enumerated. It has been suggested by Robertson Smith
+(<i>Religion of the Semites</i>, 336) that the world-wide customs of
+<span class="pagenum"><a name="page332" id="page332"></a>332</span>
+tearing the hair, rending the garments, and cutting and wounding
+the body were originally intended to establish a life-bond between
+the dead and the living. The survivors, he argues, in leaving
+portions of their hair and garments, and yet more by causing
+their own blood to stream over the corpse from self-inflicted
+wounds, by cutting off a finger and throwing it into the grave,
+leave what is eminently their own with the dead, so drawing
+closer their tie with him. Conversely, many savages daub themselves
+with the blood and other effluences of their dead kinsmen,
+and explain their custom by saying that in this way a portion
+of the dead is incorporated in themselves. Often the survivors,
+especially the widows, attach the bones or part of them to their
+persons and wear them, or at least keep them in their houses.
+The retention of the locks of the deceased and of parts of his
+dress is equally common. There is also another side to such
+customs. Having in their possession bits of the dead, and being
+so far in communion with him, the survivors are surer of his
+friendship. They have ensured themselves against ghosts who
+are apt to be by nature envious and mischievous. But whatever
+their original significance, the tearing of cheeks and hair and
+garments and cutting with knives are mostly expressions of real
+sorrow, and, as Robertson Smith remarks, of deprecation and
+supplication to an angry god or spirit. It must not be supposed
+that the savage or ancient man feels less than ourselves the
+poignancy of loss.</p>
+
+<p>6. Death-witchery has close parallels in the witch and heretic
+hunts of the Christians, but, happily for us, only flourishes
+to-day among savages. Sixty % of the deaths which occur in
+West Africa are, according to Miss Mary Kingsley&mdash;a credible
+witness&mdash;believed to be due to witchcraft and sorcery. The
+blacks regard old age or effusion of blood as the sole legitimate
+causes of death. All ordinary diseases are in their opinion due
+to private magic on the part of neighbours, just as a widespread
+epidemic marks the active hatred &ldquo;of some great outraged nature
+spirit, not of a mere human dabbler in devils.&rdquo;<a name="fa2g" id="fa2g" href="#ft2g"><span class="sp">2</span></a> Similarly in
+Christian countries an epidemic is set down to the wrath of a God
+offended by the presence of Jews, Arians and other heretics.
+The duty of an African witch-doctor is to find out who bewitched
+the deceased, just as it was of an inquisitor to discover the
+heretic. Every African post-mortem accordingly involves the
+murder of the person or persons who bewitched the dead man
+and caused him to die. The death-rate by these means is nearly
+doubled; but, since the use of poison against an obnoxious
+neighbour is common, the right person is occasionally executed.
+It is also well for neighbours not to quarrel, for, if they do and
+one of them dies of smallpox, the other is likely to be slain as
+a witch, and his lungs, liver and spleen impaled on a pole at the
+entrance of the village. It is the same case with the Australian
+blacks: &ldquo;no such thing as natural death is realized by the
+native; a man who dies has of necessity been killed by some
+other man, or perhaps even by a woman, and sooner or
+later that man or woman will be attacked. In the normal
+condition of the tribe every death meant the killing of another
+individual.&rdquo;<a name="fa3g" id="fa3g" href="#ft3g"><span class="sp">3</span></a></p>
+
+<p>7. Lastly, a primitive interment guards against the double
+risk of the ghost haunting the living and of ghouls or vampires
+taking possession of the corpse. The latter end is likely to be
+achieved if the body is cremated, for then there is no nidus to
+harbour the demon; but whether, in the remote antiquity to
+which belong many barrows containing incinerated remains,
+this motive worked, cannot be ascertained. The Indo-European
+race seems to have cremated at an early epoch, perhaps before
+the several races of East and West separated. In Christian
+funeral rites many prayers are for the protection of the body
+from violation by vampires, and it would seem as if such a motive
+dictated the architectural solidity of some ancient tombs.
+Christian graves were for protection regularly sealed with the
+cross; and the following is a characteristic prayer from the old
+Armenian rite for the burial of a layman:</p>
+
+<div class="condensed">
+<p>&ldquo;Preserve, Almighty Lord, this man&rsquo;s spirit with all saints and
+with all lovers of Thy holy name. And do Thou seal and guard the
+sepulchre of Thy servant, Thou who shuttest up the depths and
+sealest them with Thy almighty right hand ... so let the seal of
+Thy Lordship abide unmoved upon this man&rsquo;s dwelling-place and
+upon the shrine which guards Thy servant. And <i>let not any filthy
+and unclean devil dare to approach him, such as assail the body and
+souls of the heathen</i>, who possess not the birth of the holy font, and
+have not the dread seal laid upon their graves.&rdquo;</p>
+</div>
+
+<p>A terrible and revolting picture of the superstitious belief in
+ghouls which violate Christian tombs is given by Leo Allatius
+(who held it) in his tract <i>De opinionibus quorundam Graecorum</i>
+(Paris, 1646). It was probably the fear of such demonic assaults
+on the dead that inspired the insanitary custom of burying the
+dead under the floors of churches, and as near as possible to the
+altar. In the Greek Church this practice was happily forbidden
+by the code of Justinian as well as by the older law in the case of
+churches consecrated with <i>Encaenia</i> and deposition of relics.
+In the Armenian Church the same rule holds, and Ephrem Syrus
+in his testament particularly forbade his body to be laid within
+a church. Such prohibitions, however, are a witness to the
+tendency in question.</p>
+
+<p>The custom of lighting candles round a dead body and watching
+at its side all night was originally due to the belief that a corpse,
+like a person asleep, is specially liable to the assaults of demons.
+The practice of tolling a bell at death must have had a similar
+origin, for it was a common medieval belief that the sound of a
+consecrated bell drives off the demons which when a man dies
+gather near in the air to waylay his fleeting soul. For a like
+reason the consecrated bread of the Eucharist was often buried
+with believers, and St Basil is said to have specially consecrated
+a Host to be placed in his coffin.</p>
+
+<p>8. Some of the rites described under the previous heads may be
+really inspired by the fear of the dead haunting the living, but
+it must be kept in mind that the taboo attaching to a dead body
+is one thing and fear of a ghost another. A corpse is buried or
+burned, or scaffolded on a tree, a tower or a house-top, in order
+to get it out of the way and shield society from the dangerous
+infection of its taboo; but ghosts <i>quâ</i> ghosts need not be feared
+and a kinsman&rsquo;s ghost usually is not. On the contrary, it is fed
+and consoled with everything it needs, is asked not to go away
+but to stay, is in a thousand ways assured of the sorrow and
+sympathy of the survivors. Even if the body be eaten, it is
+merely to keep the soul of the deceased inside the circle of
+kinsmen, and Strabo asserts that the ancient Irish and Massagetae
+regarded it as a high honour to be so consumed by relatives.
+In Santa Cruz in Melanesia they keep the bones for arrow heads
+and store a skull in a box and set food before it &ldquo;saying that
+this is the man himself&rdquo; (R.H. Codrington, <i>The Melanesians</i>,
+p. 264), or the skull and jaw bone are kept and &ldquo;are
+called <i>mangite</i>, which are <i>saka</i>, hot with spiritual power, and by
+means of which the help of the <i>lio&rsquo;a</i>, the powerful ghost of the
+man whose relics these are, can be obtained&rdquo; (<i>ibid.</i> p. 262).
+Here we have the savage analogue to Christian relics. So the
+Australian natives make pointing sticks out of the small bones of
+the arm, with which to bewitch enemies.</p>
+
+<p>We may conclude then that in the most primitive societies,
+where blood-kinship is the only social tie and root of social custom
+it is the shades, not of kinsmen, but of strangers, who as such
+are enemies, that are dangerous and uncanny. In more developed
+societies, however, all ghosts alike are held to be so; and if a
+ghost walks it is because its body has not been properly interred
+or because its owner was a malefactor. Still, even allowing for
+this, it remains true that for a friendly ghost the proper place is
+the grave and not the homes of the living, and accordingly the
+Aruntas with cries of <i>Wah! Wah!</i> with wearing of fantastic
+head-dresses, wild dancing and beating of the air with hands and
+weapons &ldquo;drive the spirit away from the old camp which it is
+supposed to haunt,&rdquo; and which has been set fire to, and hunt
+it at a run into the grave prepared, and there stamp it down into
+the earth. &ldquo;The loud shouting of the men and women shows him
+that they do not wish to be frightened by him in his present
+state, and that they will be angry with him if he does not rest.&rdquo;
+<span class="pagenum"><a name="page333" id="page333"></a>333</span>
+(Spencer and Gillen, <i>Native Tribes of Central Australia</i>, p. 508).
+In Mesopotamia cemeteries have been discovered where the
+sepulchral jars were set upside down, clearly by way of hindering
+the ghosts from escaping into the upper world. In the Dublin
+museum we see specimens of ancient Celtic tombs showing the
+same peculiarity. For a like reason perhaps the name of the
+dead must among the Aruntas not be uttered, nor the grave
+approached, by certain classes of kinsmen. The same repugnance
+to naming the dead exists all over the world, and leads survivors
+who share the dead man&rsquo;s name to adopt another, at least for a
+time. If the dead man&rsquo;s name was that of a plant, tree, animal
+or stream, that too is changed. Here is a potent cause of linguistic
+change, that also renders any historical tradition impossible.
+The survivors seem to fear that the ghost will come when he
+hears his name called; but it also hangs together with the taboo
+which hedges round the dead as it does kings, chieftains and
+priests.</p>
+
+<div class="condensed">
+<p><span class="sc">Authorities.</span>&mdash;B. Spencer and F.J. Gillen, <i>The Native Tribes
+of Central Australia</i> (London, 1899); F.B. Jevons, <i>Introduction to
+History of Religion</i> (London, 1896); E.S. Hartland, <i>The Legend of
+Perseus</i>, vol. ii.; J.G. Frazer, <i>The Golden Bough</i> (London, 1900);
+L.W. Faraday, &ldquo;Custom and Belief in the Icelandic Sagas,&rdquo; in
+<i>Folk-lore</i>, vol. xvii. No. 4; E.B. Tylor, <i>Primitive Culture</i> (London,
+1903); E.A. W. Budge, <i>The Mummy</i> (Cambridge, 1893); C. Royer,
+&ldquo;Les Rites funéraires aux époques préhistoriques,&rdquo; <i>Revue d&rsquo;anthropologie</i>
+(1876); Forrer, <i>Über die Totenbestattung bei den Pfahlbauern</i>
+(Ausland, 1885); J. Lubbock, <i>Origin of Civilization</i> (London, 1875)
+and <i>Prehistoric Times</i> (London, 1865); L.A. Muratori, &ldquo;De antiquis
+Christianorum sepulchris,&rdquo; <i>Anecd. Graeca</i> (Padua, 1709); Onaphr.
+Panvinius, <i>De ritu sepeliendi mortuos apua veteres Christianos</i>, reprinted
+in Volbeding&rsquo;s <i>Thesaurus</i> (Leipzig, 1841).</p>
+</div>
+<div class="author">(F. C. C.)</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1g" id="ft1g" href="#fa1g"><span class="fn">1</span></a> E.S. Hartland, <i>Legend of Perseus</i> (1895), ii. 278.</p>
+
+<p><a name="ft2g" id="ft2g" href="#fa2g"><span class="fn">2</span></a> Mary Kingsley, <i>West African Studies</i> (1901), p. 178.</p>
+
+<p><a name="ft3g" id="ft3g" href="#fa3g"><span class="fn">3</span></a> B. Spencer and F.J. Gillen, <i>The Native Tribes of Central Australia</i>
+(1899), p. 48.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FUNGI<a name="ar73" id="ar73"></a></span> (pl. of Lat. <i>fungus</i>, a mushroom), the botanical name
+covering in the broad sense all the lower cellular Cryptogams
+devoid of chlorophyll, which arise from spores, and the thallus
+of which is either unicellular or composed of branched or unbranched
+tubes or cell-filaments (hyphae) with apical growth,
+or of more or less complex wefted sheets or tissue-like masses
+of such (mycelium). The latter may in certain cases attain large
+dimensions, and even undergo cell-divisions in their interior,
+resulting in the development of true tissues. The spores, which
+may be uni- or multicellular, are either abstricted free from
+the ends of hyphae (acrogenous), or formed from segments in
+their course (<i>chlamydospores</i>) or from protoplasm in their interior
+(endogenous). The want of chlorophyll restricts their mode of
+life&mdash;which is rarely aquatic&mdash;since they are therefore unable
+to decompose the carbon dioxide of the atmosphere, and renders
+them dependent on other plants or (rarely) animals for their
+carbonaceous food-materials. These they obtain usually in the
+form of carbohydrates from the dead remains of other organisms,
+or in this or other forms from the living cells of their hosts;
+in the former case they are termed saprophytes, in the latter
+parasites. While some moulds (<i>Penicillium</i>, <i>Aspergillus</i>) can
+utilize almost any organic food-materials, other fungi are more
+restricted in their choice&mdash;<i>e.g.</i> insect-parasites, horn- and
+feather-destroying fungi and parasites generally. It was
+formerly the custom to include with the Fungi the Schizomycetes
+or Bacteria, and the Myxomycetes or Mycetozoa; but the
+peculiar mode of growth and division, the cilia, spores and other
+peculiarities of the former, and the emission of naked amoeboid
+masses of protoplasm, which creep and fuse to streaming plasmodia,
+with special modes of nutrition and spore-formation of
+the latter, have led to their separation as groups of organisms
+independent of the true Fungi. On the other hand, lichens,
+previously regarded as autonomous plants, are now known to
+be dual organisms&mdash;fungi symbiotic with algae.</p>
+
+<p>The number of species in 1889 was estimated by Saccardo at
+about 32,000, but of these 8500 were so-called <i>Fungi imperfecti</i>&mdash;<i>i.e.</i>
+forms of which we only know certain stages, such as conidia,
+pycnidia, &amp;c., and which there are reasons for regarding as merely
+the corresponding stages of higher forms. Saccardo also included
+about 400 species of Myxomycetes and 650 of Schizomycetes.
+Allowing for these and for the cases, undoubtedly not few,
+where one and the same fungus has been described under different
+names, we obtain Schroeter&rsquo;s estimate (in 1892) of 20,000 species.
+In illustration of the very different estimates that have been
+made, however, may be mentioned that of De Bary in 1872 of
+150,000 species, and that of Cooke in 1895 of 40,000, and Massee
+in 1899 of over 50,000 species, the fact being that no sufficient
+data are as yet to hand for any accurate census. As regards their
+geographical distribution, fungi, like flowering plants, have no
+doubt their centres of origin and of dispersal; but we must not
+forget that every exchange of wood, wheat, fruits, plants,
+animals, or other commodities involves transmission of fungi
+from one country to another; while the migrations of birds and
+other animals, currents of air and water, and so forth, are particularly
+efficacious in transmitting these minute organisms. Against
+this, of course, it may be argued that parasitic forms can only go
+where their hosts grow, as is proved to be the case by records
+concerning the introduction of <i>Puccinia malvacearum</i>, <i>Peronospora
+viticola</i>, <i>Hemileia vastatrix</i>, &amp;c. Some fungi&mdash;<i>e.g.</i> moulds
+and yeasts&mdash;appear to be distributed all over the earth. That
+the north temperate regions appear richest in fungi may be due
+only to the fact that North America and Europe have been
+much more thoroughly investigated than other countries; it is
+certain that the tropics are the home of very numerous species.
+Again, the accuracy of the statement that the fleshy Agaricini,
+Polyporei, <i>Pezizae</i>, &amp;c., are relatively rarer in the tropics may
+depend on the fact that they are more difficult to collect and
+remit for identification than the abundantly recorded woody
+and coriaceous forms of these regions. When we remember
+that many parts of the world are practically unexplored as
+regards fungi, and that new species are constantly being discovered
+in the United States, Australia and northern Europe&mdash;the
+best explored of all&mdash;it is clear that no very accurate census
+of fungi can as yet be made, and no generalizations of value as
+to their geographical distribution are possible.</p>
+
+<p>The existence of fossil fungi is undoubted, though very few
+of the identifications can be relied on as regards species or genera.
+They extend back beyond the Carboniferous, where they occur
+as hyphae, &amp;c., preserved in the fossil woods, but the best specimens
+are probably those in amber and in siliceous petrifactions
+of more recent origin.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:600px; height:489px" src="images/img333.jpg" alt="" /></td></tr>
+<tr><td class="tcl f90"><span class="sc">Fig. 1.</span>&mdash;1, <i>Peronospora parasitica</i> (De Bary). Mycelium with
+haustoria (<i>h</i>); 2, <i>Erysiphe</i>; A and B, mycelium (<i>m</i>), with haustoria
+(<i>h</i>). (After De Bary.)</td></tr></table>
+
+<div class="condensed">
+<p class="pt2"><i>Organs.</i>&mdash;Individual hyphae or their branches often exhibit
+specializations of form. In many Basidiomycetes minute branches
+arise below the septa; their tips curve over the outside of the latter,
+and fuse with the cell above just beyond it, forming a <i>clamp-connexion</i>.
+Many parasitic hyphae put out minute lateral branches,
+which pierce the cell-wall of the host and form a peg-like (<i>Trichosphaeria</i>),
+sessile (<i>Cystopus</i>), or stalked (<i>Hemileia</i>), knot-like, or a
+more or less branched (<i>Peronospora</i>) or coiled (<i>Protomyces</i>) haustorium.
+In <i>Rhizopus</i> certain hyphae creep horizontally on the surface of the
+substratum, and then anchor their tips to it by means of a tuft of
+short branches (<i>appressorium</i>), the walls of which soften and gum
+<span class="pagenum"><a name="page334" id="page334"></a>334</span>
+themselves to it, then another branch shoots out from the tuft and
+repeats the process, like a strawberry-runner. Appressoria are
+also formed by some parasitic fungi, as a minute flattening of the tip
+of a very short branch (<i>Erysiphe</i>), or the swollen end of any hypha
+which comes in contact with the surface of the host (<i>Piptocephalis</i>,
+<i>Syncephalis</i>), haustoria piercing in each case the cell-wall below.
+In <i>Botrytis</i> the appressoria assume the form of dense tassels of short
+branches. In <i>Arthrobotrys</i> side-branches of the mycelium sling themselves
+around the host (<i>Tylenchus</i>) much as tendrils round a support.</p>
+
+<p>Many fungi (<i>Phallus</i>, <i>Agaricus</i>, <i>Fumago</i>, &amp;c.) when strongly
+growing put out ribbon-like or cylindrical cords, or sheet-like
+mycelial plates of numerous parallel hyphae, all growing together
+equally, and fusing by anastomoses, and in this way extend long
+distances in the soil, or over the surfaces of leaves, branches, &amp;c.
+These mycelial strands may be white and tender, or the outer
+hyphae may be hard and black, and very often the resemblance of
+the subterranean forms to a root is so marked that they are termed
+rhizomorphs. The outermost hyphae may even put forth thinner
+hyphae, radiating into the soil like root-hairs, and the convergent
+tips may be closely appressed and so divided by septa as to resemble
+the root-apex of a higher plant (<i>Armillaria mellea</i>).</p>
+
+<p><i>Sclerotia.</i>&mdash;Fungi, like other plants, are often found to store up
+large quantities of reserve materials (oil, glycogen, carbohydrates,
+&amp;c.) in special parts of their vegetative tissues, where they lie
+accumulated between a period of active assimilation and one of
+renewed activity, forming reserves to be consumed particularly
+during the formation of large fructifications. These reserve stores
+may be packed away in single hyphae or in swollen cells, but the
+hyphae containing them are often gathered into thick cords or
+mycelial strands (<i>Phallus</i>, mushroom, &amp;c.), or flattened and anastomosing
+ribbons and plates, often containing several kinds of hyphae
+(<i>Merulius lacrymans</i>). In other cases the strands undergo differentiation
+into an outer layer with blackened, hardened cell-walls
+and a core of ordinary hyphae, and are then termed rhizomorphs
+(<i>Armillaria mellea</i>), capable not only of extending the fungus in
+the soil, like roots, but also of lying dormant, protected by the
+outer casing. Such aggregations of hyphae frequently become
+knotted up into dense masses of interwoven and closely packed
+hyphae, varying in size from that of a pin&rsquo;s head or a pea (<i>Peziza</i>,
+<i>Coprinus</i>) to that of a man&rsquo;s fist or head, and weighing 10 to 25 &#8468;
+or more (<i>Polyporus Mylittae</i>, <i>P. tumulosus</i>, <i>Lentinus Woermanni</i>,
+<i>P. Sapurema</i>, &amp;c.). The interwoven hyphae fuse and branch
+copiously, filling up all interstices. They also undergo cutting
+up by numerous septa into short cells, and these often divide again
+in all planes, so that a pseudoparenchyma results, the walls of
+which may be thickened and swollen internally, or hardened and
+black on the exterior. In many cases the swollen cell-walls serve
+as reserves, and sometimes the substance is so thickly deposited in
+strata as to obliterate the lumen, and the hyphae become nodular
+(<i>Polyporus sacer</i>, <i>P. rhinoceros</i>, <i>Lentinus Woermanni</i>). The various
+sclerotia, if kept moist, give rise to the fructifications of the fungi
+concerned, much as a potato tuber does to a potato plant, and in
+the same way the reserve materials are consumed. They are
+principally Polyporei, Agaricini, Pezizae; none are known among
+the Phycomycetes, Uredineae or Ustilagineae. The functions of
+mycelial strands, rhizomorphs and sclerotia are not only to collect
+and store materials, but also to extend the fungus, and in many
+cases similar strands act as organs of attack. The same functions
+of storage in advance of fructification are also exercised by the
+stromata so common in Ascomycetes.</p>
+
+<p><i>Tissue Differentiations.</i>&mdash;The simpler mycelia consist of hyphae
+all alike and thin-walled, or merely differing in the diameter of the
+branches of various orders, or in their relations to the environment,
+some plunging into the substratum like roots, others remaining on
+its surface, and others (aerial hyphae) rising into the air. Such
+hyphae may be multicellular, or they may consist of simple tubes
+with numerous nuclei and no septa (<i>Phycomycetes</i>), and are then
+non-cellular. In the more complex tissue-bodies of higher fungi,
+however, we find considerable differences in the various layers or
+strands of hyphae.</p>
+
+<p>An epidermis-like or cortical protective outer layer is very common,
+and is usually characterized by the close septation of the densely
+interwoven hyphae and the thickening and dark colour of their
+outer walls (sclerotia, <i>Xylaria</i>, &amp;c.). Fibre-like hyphae with
+the lumen almost obliterated by the thick walls occur in mycelial
+cords (<i>Merulius</i>). Latex-tubes abound in the tissues of <i>Lactarius</i>,
+<i>Stereum</i>, <i>Mycena</i>, <i>Fistulina</i>, filled with white or coloured milky
+fluids, and Istvanffvi has shown that similar tubes with fluid or
+oily contents are widely spread in other Hymenomycetes. Sometimes
+fatty oil or watery sap is found in swollen hyphal ends, or
+such tubes contain coloured sap. Cystidia and paraphyses may be
+also classed here. In <i>Merulius lacrymans</i> Hartig has observed
+thin-walled hyphae with large lumina, the septa of which are perforated
+like those of sieve-tubes.</p>
+
+<p>As regards its composition, the cell-wall of fungi exhibits variations
+of the same kind as those met with in higher plants. While
+the fundamental constituent is a cellulose in many Mucorini and
+other Phycomycetes, in others bodies like pectose, callose, &amp;c.,
+commonly occur, and Wisselingh&rsquo;s researches show that chitin, a
+gluco-proteid common in animals, forms the main constituent in
+many cases, and is probably deposited directly as such, though, like
+the other substances, it may be mixed with cellulose. As in other
+cell-walls, so here the older membranes may be altered by deposits
+of various substances, such as resin, calcium oxalate, colouring
+matters; or more profoundly altered throughout, or in definite
+layers, by lignification, suberization (<i>Trametes</i>, <i>Daedalea</i>), or swelling
+to a gelatinous mucilage (<i>Tremella</i>, <i>Gymnosporangium</i>), while cutinization
+of the outer layers is common. One of the most striking
+alterations of cell-walls is that termed <i>carbonization</i>, in which the
+substance gradually turns black, hard and brittle, as if charred&mdash;<i>e.g.</i>
+<i>Xylaria</i>, <i>Ustulina</i>, some sclerotia. At the other extreme the
+cell-walls of many lichen-fungi are soft and colourless, but turn
+blue in iodine, as does starch. The young cell-wall is always tenuous
+and flexible, and may remain so throughout, but in many cases
+thickenings and structural differentiations, as well as the changes
+referred to above, alter the primary wall considerably. Such
+thickening may be localized, and <i>pits</i> (<i>e.g.</i> <i>Uredospores</i>, septa of
+Basidiomycetes), <i>spirals</i>, <i>reticulations</i>, <i>rings</i>, &amp;c. (capillitium fibres
+of <i>Podaxon</i>, <i>Calostoma</i>, <i>Battarrea</i>), occur as in the vessels of higher
+plants, while sculptured networks, pittings and so forth are as
+common on fungus-spores as they are on pollen grains.</p>
+
+<p><i>Cell-Contents.</i>&mdash;The cells of fungi, in addition to protoplasm,
+nuclei and sap-vacuoles, like other vegetable cells, contain formed
+and amorphous bodies of various kinds. Among those directly
+visible to the microscope are oil drops, often coloured (<i>Uredineae</i>)
+crystals of calcium oxalate (<i>Phallus</i>, <i>Russula</i>), proteid crystals
+(<i>Mucor</i>, <i>Pilobolus</i>, &amp;c.) and resin (Polyporei). The oidia of Erysipheae
+contain fibrosin bodies and the hyphae of Saprolegnieae
+cellulin bodies, but starch apparently never occurs. Invisible to the
+microscope, but rendered visible by reagents, are glycogen, <i>Mucor</i>,
+Ascomycetes, yeast, &amp;c. In addition to these cell-contents we
+have good indirect evidence of the existence of large series of other
+bodies, such as proteids, carbohydrates, organic acids, alkaloids,
+enzymes, &amp;c. These must not be confounded with the numerous
+substances obtained by chemical analysis of masses of the fungus,
+as there is often no proof of the manner of occurrence of such bodies,
+though we may conclude with a good show of probability that
+some of them also exist preformed in the living cell. Such are
+sugars (glucose, mannite, &amp;c.), acids (acetic, citric and a whole series
+of lichen-acids), ethereal oils and resinous bodies, often combined
+with the intense colours of fungi and lichens, and a number of
+powerful alkaloid poisons, such as muscarin (<i>Amanita</i>), ergotin
+(<i>Claviceps</i>), &amp;c.</p>
+
+<p>Among the enzymes already extracted from fungi are <i>invertases</i>
+(yeasts, moulds, &amp;c.), which split cane-sugar and other complex
+sugars with hydrolysis into simpler sugars such as dextrose and
+levulose; <i>diastases</i>, which convert starches into sugars (<i>Aspergillus</i>,
+&amp;c.); <i>cytases</i>, which dissolve cellulose similarly (<i>Botrytis</i>, &amp;c.);
+<i>peptases</i>, using the term as a general one for all enzymes which
+convert proteids into peptones and other bodies (<i>Penicillium</i>, &amp;c.);
+lipases, which break up fatty oils (<i>Empusa</i>, <i>Phycomyces</i>, &amp;c.);
+oxydases, which bring about the oxidations and changes of colour
+observed in <i>Boletus</i>, and <i>zymase</i>, extracted by Buchner from yeast,
+which brings about the conversion of sugar into alcohol and carbon-dioxide.
+That such enzymes are formed in the protoplasm is
+evident from the behaviour of hyphae, which have been observed
+to pierce cell-membranes, the chitinous coats of insects, artificial
+collodion films and layers of wax, &amp;c. That a fungus can secrete
+more than one enzyme, according to the materials its hyphae
+have to attack, has been shown by the extraction of diastase,
+inulase, trehalase, invertase, maltase, raffinase, malizitase, emulsin,
+trypsin and lipase from <i>Aspergillus</i> by Bourquelot, and similar
+events occur in other fungi. The same fact is indicated by the wide
+range of organic substances which can be utilized by <i>Penicillium</i>
+and other moulds, and by the behaviour of parasitic fungi which
+destroy various cell-contents and tissues. Many of the coloured
+pigments of fungi are fixed in the cell-walls or excreted to the outside
+(<i>Peziza aeruginosa</i>). Matruchot has used them for staining
+the living protoplasm of other fungi by growing the two together.
+Striking instances of coloured mycella are afforded by <i>Corticium
+sanguineum</i>, blood-red; <i>Elaphomyces Leveillei</i>, yellow-green;
+<i>Chlorosplenium aeruginosum</i>, verdigris green; and the <i>Dematei</i>,
+brown or black.</p>
+
+<p><i>Nuclei.</i>&mdash;Although many fungi have been regarded as devoid of
+nuclei, and all have not as yet been proved to contain them, the
+numerous investigations of recent years have revealed them in the
+cells of all forms thoroughly examined, and we are justified in
+concluding that the nucleus is as essential to the cell of a fungus
+as to that of other organisms. The hyphae of many contain
+numerous, even hundreds of nuclei (Phycomycetes); those of others
+have several (<i>Aspergillus</i>) in each segment, or only two (<i>Exoascus</i>)
+or one (<i>Erysiphe</i>) in each cell. Even the isolated cells of the yeast
+plant have each one nucleus. As a rule the nuclei of the mycelium
+are very minute (1.5-2 &mu; in <i>Phycomyces</i>), but those of many asci
+and spores are large and easily rendered visible. As with other
+plants, so in fungi the essential process of fertilization consists in the
+fusion of two nuclei, but owing to the absence of well-marked sexual
+organs from many fungi, a peculiar interest attaches to certain
+nuclear fusions in the vegetative cells or in young spores of many
+forms. Thus in Ustilagineae the chlamydospores, and in Uredineae
+<span class="pagenum"><a name="page335" id="page335"></a>335</span>
+the teleutospores, each contain two nuclei when young, which
+fuse as the spores mature. In young asci a similar fusion of two
+nuclei occurs, and also in basidia, in each case the nucleus of the
+ascus or of the basidium resulting from the fusion subsequently
+giving rise by division to the nuclei of the ascospores and basidiospores
+respectively. The significance of these fusions will be discussed
+under the various groups. Nuclear division is usually
+accompanied by all the essential features of karyokinesis.</p>
+
+<p><i>Spores.</i>&mdash;No agreement has ever been arrived at regarding the
+consistent use of the term spore. This is apparently owing to the
+facts that too much has been attempted in the definition, and that
+differences arise according as we aim at a morphological or a physiological
+definition. Physiologically, any cell or group of cells separated
+off from a hypha or unicellular fungus, and capable of itself
+growing out&mdash;germinating&mdash;to reproduce the fungus, is a spore; but
+it is evident that so wide a definition does not exclude the ordinary
+vegetative cells of sprouting fungi, such as yeasts, or small sclerotium
+like cell-aggregates of forms like <i>Coniothecium</i>. Morphologically
+considered, spores are marked by peculiarities of form, size, colour,
+place of origin, definiteness in number, mode of preparation, and so
+forth, such that they can be distinguished more or less sharply from
+the hyphae which produce them. The only physiological peculiarity
+exhibited in common by all spores is that they germinate and
+initiate the production of a new fungus-plant. Whether a spore
+results from the sexual union of two similar gametes (zygospore)
+or from the fertilization of an egg-cell by the protoplasm of a
+male organ (oospore); or is developed asexually as a motile
+(zoospore) or a quiescent body cut off from a hypha (conidium) or
+developed along its course (oidium or chlamydospore), or in its
+protoplasm (endospore), are matters of importance which have their
+uses in the classification and terminology of spores, though in many
+respects they are largely of academic interest.</p>
+
+<table class="flt" style="float: right; width: 330px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:275px; height:600px" src="images/img335a.jpg" alt="" /></td></tr>
+<tr><td class="caption1"><span class="sc">Fig.</span> 2.&mdash;<i>Peronospora parasitica</i>
+(De Bary). Conidiophore
+with conidia.</td></tr></table>
+
+<p>Klebs has attempted to divide spores into three categories as
+follows: (1) kinospores, arising by relatively simple cell-divisions
+and subserving rapid dissemination and propagation, <i>e.g.</i> zoospores,
+conidia, endogonidia, stylospores, &amp;c.; (2) paulospores, due to
+simple rearrangement of cell-contents, and subserving the persistence
+of the fungus through periods of exigency, <i>e.g.</i> gemmae, chlamydospores,
+resting-cells, cysts, &amp;c.; (3) carpospores, produced by a
+more or less complex formative process, often in special fructifications,
+and subserving either or both multiplication and persistence,
+<i>e.g.</i> zygospores, oospores, brand-spores, aecidiospores, ascospores,
+basidiospores, &amp;c. Little or nothing is gained by these definitions,
+however, which are especially physiological. In practice these
+various kinds of spores of fungi receive further special names in the
+separate groups, and names, moreover,
+which will appear, to those
+unacquainted with the history,
+to have been given without any
+consistency or regard to general
+principles; nevertheless, for ordinary
+purposes these names are far
+more useful in most cases, owing
+to their descriptive character, than
+the proposed new names, which
+have been only partially accepted.</p>
+
+<p><i>Sporophores.</i>&mdash;In some of the
+simpler fungi the spores are not
+borne on or in hyphae which can
+be distinguished from the vegetative
+parts or mycelium, but in
+the vast majority of cases the
+sporogenous hyphae either ascend
+free into the air or radiate into
+the surrounding water as distinct
+branches, or are grouped into
+special columns, cushions, layers
+or complex masses obviously
+different in colour, consistency,
+shape and other characters from
+the parts which gather up and
+assimilate the food-materials. The
+term &ldquo;receptacle&rdquo; sometimes
+applied to these spore-bearing
+hyphae is better replaced by sporophore.
+The sporophore is obsolete
+when the spore-bearing hyphae
+are not sharply distinct from the
+mycelium, simple when the constituent
+hyphae are isolated, and
+compound when the latter are
+conjoined. The chief distinctive characters of the sporogenous
+hyphae are their orientation, usually vertical; their limited apical
+growth; their peculiar branching, form, colour, contents, consistency;
+and their spore-production. According to the characters
+of the last, we might theoretically divide them into conidiophores,
+sporangiophores, gametophores, oidiophores, &amp;c.; but since the two
+latter rarely occur, and more than one kind of spore or spore-case
+may occur on a sporophore, it is impossible to carry such a scheme
+fully into practice.</p>
+
+<p>A simple sporophore may be merely a single short hypha, the end
+of which stops growing and becomes cut off as a conidium by the
+formation of a septum, which then splits and allows the conidium
+to fall. More generally the hypha below the septum grows forwards
+again, and repeats this process several times before the terminal
+conidium falls, and so a chain of conidia results, the oldest of which
+terminates the series (<i>Erysiphe</i>); when the primary branch has
+thus formed a basipetal series, branches may arise from below and
+again repeat this process, thus forming a tuft (<i>Penicillium</i>). Or the
+primary hypha may first swell at its apex, and put forth a series of
+short peg-like branches (<i>sterigmata</i>) from the increased surface thus
+provided, each of which develops a similar basipetal chain of conidia
+(<i>Aspergillus</i>), and various combinations of these processes result in
+the development of numerous varieties of exquisitely branched
+sporophores of this type (<i>Botrytis</i>, <i>Botryosporium</i>, <i>Verticillium</i>, &amp;c.).</p>
+
+<table class="pic" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter" colspan="2"><img style="width:600px; height:566px" src="images/img335b.jpg" alt="" /></td></tr>
+<tr><td class="caption" colspan="2"><span class="sc">Fig. 3.</span>&mdash;<i>Cystopus candidus</i>.</td></tr>
+
+<tr><td class="f90" style="width: 50%; vertical-align: top;">
+<p>A. <i>a</i>, Conidia.</p>
+<p>&emsp; <i>b</i>, Conidiophores.</p>
+<p>&emsp; <i>c</i>, Conidium emitting zoospores.</p>
+<p>&emsp; <i>d</i>, Free zoospore.</p>
+<p>B.<i>og</i>, Oogonium.</p></td>
+
+<td class="f90" style="width: 50%; vertical-align: top;">
+<p>&emsp; <i>os</i>, Oosphere.</p>
+<p>&emsp; <i>an</i>, Antheridium.</p>
+<p>C. Formation of zoospores by oospores.</p>
+<p>&emsp; <i>z</i>, Free zoospores.</p>
+<p>&emsp;&emsp; (After De Bary.)</p></td></tr></table>
+
+<p class="pt2">A second type is developed as follows: the primary hypha forms
+a septum below its apex as before, and the terminal conidium, thus
+abstricted, puts out a branch at its apex, which starts as a mere
+point and rapidly swells to a second conidium; this repeats the
+process, and so on, so that we now have a chain of conidia developed
+in acropetal succession, the oldest being below, and, as in <i>Penicillium</i>,
+&amp;c., branches put forth lower down may repeat the process (<i>Hormodendron</i>).
+In all these cases we may speak of simple conidiophores.
+The simple sporophore does not necessarily terminate in conidia,
+however. In <i>Mucor</i>, for example, the end of the primary hypha
+swells into a spheroidal head (sporangium), the protoplasm of which
+undergoes segmentation into more or less numerous globular masses,
+each of which secretes an enveloping cell-wall and becomes a spore
+(endospore), and branched systems of sporangia may arise as before
+(<i>Thamnidium</i>). Such may be termed sporangiophores. In <i>Sporodinia</i>
+the branches give rise also to short branches, which meet and
+fuse their contents to form zygospores. In Peronospora, Saprolegnia,
+&amp;c., the ends of the branches swell up into sporangia, which develop
+zoospores in their interior (zoosporangia), or their contents become
+oospheres, which may be fertilized by the contents of other branches
+(antheridia) and so form egg-cases (oogonia). Since in such cases
+the sporophore bears sexual cells, they may be conveniently termed
+gametophores.</p>
+
+<p>Compound sporophores arise when any of the branched or unbranched
+types of spore-bearing hyphae described above ascend
+into the air in consort, and are more or less crowded into definite
+layers, cushions, columns or other complex masses. The same laws
+apply to the individual hyphae and their branches as to simple
+sporophores, and as long as the conidia, sporangia, gametes, &amp;c.,
+are borne on their external surfaces, it is quite consistent to speak
+of these as compound sporophores, &amp;c., in the sense described, however
+complex they may become. Among the simplest cases are
+the sheet-like aggregates of sporogenous hyphae in <i>Puccinia</i>, <i>Uromyces</i>,
+&amp;c., or of basidia in <i>Exobasidium</i>, <i>Corticium</i>, &amp;c., or of asci in
+<i>Exoascus</i>, <i>Ascocorticium</i>, &amp;c. In the former, where the layer is small,
+it is often termed a sorus, but where, as in the latter, the sporogenous
+layer is extensive, and spread out more or less sheet-like on
+the supporting tissues, it is more frequently termed a hymenium.
+Another simple case is that of the columnar aggregates of sporogenous
+hyphae in forms like <i>Stilbum</i>, <i>Coremium</i>, &amp;c. These lead
+<span class="pagenum"><a name="page336" id="page336"></a>336</span>
+us to cases where the main mass of the sporophore forms a supporting
+tissue of closely crowded or interwoven hyphae, the sporogenous
+terminal parts of the hyphae being found at the periphery or apical
+regions only. Here we have the cushion-like type (stroma) of
+<i>Nectria</i> and many Pyrenomycetes, the clavate &ldquo;receptacle&rdquo; of
+<i>Clavaria</i>, &amp;c., passing into the complex forms met with in <i>Sparassis</i>,
+<i>Xylaria</i>, <i>Polyporei</i>, and <i>Agaricini</i>, &amp;c. In these cases the compound
+sporophore is often termed the hymenophore, and its various parts
+demand special names (pileus, stipes, gills, pores, &amp;c.) to denote
+peculiarities of distribution of the hymenium over the surface.</p>
+
+<p>Other series of modifications arise in which the tissues corresponding
+to the stroma invest the sporogenous hyphal ends, and thus
+enclose the spores, asci, basidia, &amp;c., in a cavity. In the simplest
+case the stroma, after bearing its crop of conidia or oidia, develops
+ascogenous branches in the loosened meshes of its interior (<i>e.g.</i>
+<i>Onygena</i>). Another simple case is where the plane or slightly convex
+surface of the stroma rises at its margins and overgrows the sporogenous
+hyphal ends, so that the spores, asci, &amp;c., come to lie in the
+depression of a cavity&mdash;<i>e.g.</i> <i>Solenia</i>, <i>Cyphella</i>&mdash;and even simpler
+cases are met with in <i>Mortierella</i>, where the zygospore is invested by
+the overgrowth of a dense mat of closely branching hyphae, and in
+<i>Gymnoascus</i>, where a loose mat of similarly barren hyphae covers
+in the tufts of asci as they develop.</p>
+
+<p>In such examples as the above we may regard the hymenium
+(<i>Solenia</i>, <i>Cyphella</i>), zygospores, or asci as truly invested by later
+growth, but in the vast majority of cases the processes which result
+in the enclosure of the spores, asci, &amp;c., in a &ldquo;fructification&rdquo; are
+much more involved, inasmuch as the latter is developed in the
+interior of hyphal tissues, which are by no means obviously homologous
+with a stroma. Thus in <i>Penicillium</i>, <i>Eurotium</i>, <i>Erysiphe</i>,
+&amp;c., hyphal ends which are the initials of ascogenous branches, are
+invested by closely packed branches at an early stage of development,
+and the asci develop inside what has by that time become
+a complete investment. Whether a true sexual process precedes
+these processes or not does not affect the present question, the
+point being that the resulting spheroidal &ldquo;fructification&rdquo; (cleistocarp,
+perithecium) has a definite wall of its own not directly comparable
+with a stroma. In other cases (<i>Hypomyces</i>, <i>Nectria</i>) the
+perithecia arise on an already mature stroma, while yet more numerous
+examples can be given (<i>Poronia</i>, <i>Hypoxylon</i>, <i>Claviceps</i>, &amp;c.)
+where the perithecia originate below the surface of a stroma formed
+long before. Similarly with the various types of conidial or oidial
+&ldquo;fructifications,&rdquo; termed pycnidia, spermogonia, aecidia, &amp;c. In
+the simplest of these cases&mdash;<i>e.g.</i> <i>Fumago</i>&mdash;a single mycelial cell
+divides by septa in all three planes until a more or less solid clump
+results. Then a hollow appears in the centre owing to the more
+rapid extension of the outer parts, and into this hollow the cells
+lining it put forth short sporogenous branches, from the tips of
+which the spores (stylospores, conidia, spermatia) are abstricted. In
+a similar way are developed the pycnidia of <i>Cicinnobolus</i>, <i>Pleospora</i>,
+<i>Cucurbitaria</i>, <i>Leptosphaeria</i> and others. In other cases (<i>Diplodia</i>,
+<i>Aecidium</i>, &amp;c.) conidial or oidial &ldquo;fructifications&rdquo; arise by a number
+of hyphae interweaving themselves into a knot, as if they were
+forming a Sclerotium. The outer parts of the mass then differentiate
+as a wall or investment, and the interior becomes a hollow, into
+which hyphal ends grow and abstrict the spores. Much more
+complicated are the processes in a large series of &ldquo;fructifications,&rdquo;
+where the mycelium first develops a densely packed mass of hyphae,
+all alike, in which labyrinths of cavities subsequently form by
+separation of hyphae in the previously homogeneous mass, and the
+hymenium covers the walls of these cavities and passages as with a
+lining layer. Meanwhile differences in consistency appear in various
+strata, and a dense outer protective layer (peridium), soft gelatinous
+layers, and so on are formed, the whole eventually attaining great
+complexity&mdash;<i>e.g.</i> puff-balls, earth-stars and various <i>Phalloideae</i>.</p>
+
+<p><i>Spore-Distribution.</i>&mdash;Ordinary conidia and similarly abstricted
+dry spores are so minute, light and numerous that their dispersal
+is ensured by any current of air or water, and we also know that
+rats and other burrowing animals often carry them on their fur;
+similarly with birds, insects, slugs, worms, &amp;c., on claws, feathers,
+proboscides, &amp;c., or merely adherent to the slimy body. In addition
+to these accidental modes of dispersal, however, there is a series of
+interesting adaptations on the part of the fungus itself. Passing
+over the locomotor activity of zoospores (<i>Pythium</i>, <i>Peronospora</i>,
+<i>Saprolegnia</i>) we often find spores held under tension in sporangia
+(<i>Pilobolus</i>) or in asci (<i>Peziza</i>) until ripe, and then forcibly shot out
+by the sudden rupture of the sporangial wall under the pressure of
+liquid behind&mdash;mechanism comparable to that of a pop-gun, if we
+suppose air replaced by watery sap. Even a single conidium, held
+tense to the last moment by the elastic cell-wall, may be thus shot
+forward by a spurt of liquid under pressure in the hypha abstricting
+it (<i>e.g.</i> <i>Empusa</i>), and similarly with <i>basidiospores</i> (<i>Coprinus</i>,
+<i>Agaricus</i>, &amp;c.). A more complicated case is illustrated by <i>Sphaerobolus</i>,
+where the entire mass of spores, enclosed in its own peridium,
+is suddenly shot up into the air like a bomb from a mortar by the
+elastic retroversion of a peculiar layer which, up to the last moment,
+surrounded the bomb, and then suddenly splits above, turns inside
+out, and drives the former as a projectile from a gun. Gelatinous
+or mucilaginous degenerations of cell-walls are frequently employed
+in the interests of spore dispersal. The mucilage surrounding
+endospores of <i>Mucor</i>, conidia of <i>Empusa</i>, &amp;c., serves to gum the spore
+to animals. Such gums are formed abundantly in pycnidia, and,
+absorbing water, swell and carry out the spores in long tendrils,
+which emerge for days and dry as they reach the air, the glued spores
+gradually being set free by rain, wind, &amp;c. In oidial chains (<i>Sclerotinia</i>)
+a minute double wedge of wall-substance arises in the middle
+lamella between each pair of contiguous oidia, and by its enlargement
+splits the separating lamella. These disjunctors serve as points of
+application for the elastic push of the swelling spore-ends, and as
+the connecting outer lamella of cell-wall suddenly gives way, the
+spores are jerked asunder. In many cases the slimy masses of
+spermatia (<i>Uredineae</i>), conidia (<i>Claviceps</i>), basidiospores (<i>Phallus</i>,
+<i>Coprinus</i>), &amp;c., emit more or less powerful odours, which attract
+flies or other insects, and it has been shown that bees carry the
+fragrant oidia of <i>Sclerotinia</i> to the stigma of <i>Vaccinium</i> and infect
+it, and that flies carry away the foetid spores of <i>Phallus</i>, just as
+pollen is dispersed by such insects. Whether the strong odour of
+trimethylamine evolved by the spores of <i>Tilletia</i> attracts insects is
+not known.</p>
+
+<p>The recent observations and exceedingly ingenious experiments of
+Falck have shown that the sporophores of the Basidiomycetes&mdash;especially
+the large sporophores of such forms as <i>Boletus</i>, <i>Polyporus</i>&mdash;contain
+quantities of reserve combustible material which are burnt
+up by the active metabolism occurring when the fruit-body is ripe.
+By this means the temperature of the sporophore is raised and the
+difference between it and the surrounding air may be one of several
+degrees. As a result convection currents are produced in the air
+which are sufficient to catch the basidiospores in their fall and carry
+them, away from the regions of comparative atmospheric stillness
+near the ground, to the upper air where more powerful air-currents
+can bring about their wide distribution.</p>
+</div>
+
+<p><i>Classification.</i>&mdash;It has been accepted for some time now that
+the majority of the fungi proper fall into three main groups,
+the Phycomycetes, Ascomycetes and Basidiomycetes, the
+Schizomycetes and Myxomycetes (Mycetozoa) being considered
+as independent groups not coming under the true fungi.</p>
+
+<p>The chief schemes of classification put forward in detail have
+been those of P.A. Saccardo (1882-1892), of Oskar Brefeld and
+Von Tavel (1892), of P.E.L. Van Tieghem (1893) and of J.
+Schroeter (1892). The scheme of Brefeld, which was based on
+the view that the Ascomycetes and Basidiomycetes were completely
+asexual and that these two groups had been derived
+from one division (Zygomycetes) of the Phycomycetes, has been
+very widely accepted. The recent work of the last twelve years
+has shown, however, that the two higher groups of fungi exhibit
+distinct sexuality, of either a normal or reduced type, and has
+also rendered very doubtful the view of the origin of these two
+groups from the Phycomycetes. The real difficulty of classification
+of the fungi lies in the polyphyletic nature of the group.
+There is very little doubt that the primitive fungi have been
+derived by degradation from the lower algae. It appears,
+however, that such a degradation has occurred not only once
+in evolution but on several occasions, so that we have in the
+Phycomycetes not a series of naturally related forms, but groups
+which have arisen perfectly independently of one another from
+various groups of the algae. It is also possible in the absence
+of satisfactory intermediate forms that the Ascomycetes and
+Basidiomycetes have also been derived from the algae independently
+of the Phycomycetes, and perhaps of one another.</p>
+
+<p>A natural classification on these lines would obviously be very
+complicated, so that in the present state of our knowledge it
+will be best to retain the three main groups mentioned above,
+bearing in mind that the Phycomycetes especially are far from
+being a natural group. The following gives a tabular survey of
+the scheme adopted in the present article:</p>
+
+<div class="condensed">
+<p><span class="sc">A. Phycomycetes.</span> Alga-like fungi with unicellular thallus
+and well-marked sexual organs.</p>
+
+<div class="list">
+<p><span class="sc">Class I.</span>&mdash;Oomycetes. Mycelium usually well developed, but
+sometimes poor or absent. Sexual reproduction by oogonia
+and antheridia; asexual reproduction by zoospores or
+conidia.</p>
+</div>
+
+<div class="list1">
+<p>1. Monoblepharidineae. Mycelium present, antheridia with
+antherozoids, oogonium with single oosphere: Monoblepharidaceae.</p>
+
+<p>2. Peronosporineae. Mycelium present; antheridia but no
+antherozoids; oogonia with one or more oospheres:
+Peronosporaceae, Saprolegniaceae.</p>
+
+<p>3. Chytridineae. Mycelium poorly developed or absent;
+oogonia and antheridia (without antherozoids) known in
+some cases; zoospores common: Chytridiaceae. Ancylistaceae.</p>
+</div>
+
+<p><span class="pagenum"><a name="page337" id="page337"></a>337</span></p>
+
+<div class="list">
+<p><span class="sc">Class II.</span>&mdash;Zygomycetes. Mycelium well developed; sexual reproduction
+by zygospores; asexual reproduction by sporangia
+and conidia.</p>
+</div>
+
+<div class="list1">
+<p>1. Mucorineae. Sexual reproduction as above, asexual by
+sporangia or conidia or both: Mucoraceae. Mortierellaceae,
+Chaetocladiaceae, Piptocephalidaceae.</p>
+
+<p>2. Entomophthorineae. Sexual reproduction typical but
+with sometimes inequality of the fusing gametes (gametangia ?):
+Entomophthoraceae.</p>
+</div>
+
+<p>B. <span class="sc">Higher Fungi.</span> Fungi with segmental thallus; sexual
+reproduction sometimes with typical antheridia and oogonia
+(ascogonia) but usually much reduced.</p>
+
+<div class="list">
+<p><span class="sc">Class I.</span>&mdash;Ustilaginales. Forms with septate thallus, and reproduction
+by chlamydospores which on germination produce
+sporidia; sexuality doubtful.</p>
+
+<p><span class="sc">Class II.</span>&mdash;Ascomycetes. Thallus septate; spores developed
+in special type of sporangium, the ascus, the number of spores
+being usually eight. Sexual reproduction sometimes typical,
+usually reduced.</p>
+</div>
+
+<div class="list1">
+<p>Exoascineae, Saccharomycetineae, Perisporinea, Discomycetes,
+Pyrenomycetes, Tuberineae, Laboulbeniineae.</p>
+</div>
+
+<div class="list">
+<p><span class="sc">Class III.</span>&mdash;Basidiales. Thallus septate. Conidia (basidiospores)
+borne in fours on a special conidiophore, the basidium.
+Sexual reproduction always much reduced.</p>
+</div>
+
+<div class="list1">
+<p>1. Uredineae. Life-history in some cases very complex and
+with well-marked sexual process and alternation of generations,
+in others much reduced; basidium (promycelium)
+derived usually from a thick-walled spore (teleutospore).</p>
+
+<p>2. Basidiomycetes. Life-history always very simple, no well-marked
+alternation of generations; basidium borne
+directly on the mycelium.</p>
+</div>
+
+<div class="list2">
+<p>(A) Protobasidiomycetes. Basidia septate.
+Auriculariaceae, Pilacreaceae, Tremellinaceae.</p>
+
+<p>(B) Autobasidiomycetes. Basidia non-septate.
+Hymenomycetes, Gasteromycetes.</p>
+</div></div>
+
+<p>A. <span class="sc">Phycomycetes.</span>&mdash;Most of the recent work of importance
+in this group deals with the cytology of sexual reproduction and
+of spore-formation, and the effect of external conditions on the
+production of reproductive organs.</p>
+
+<div class="condensed">
+<p><i>Monoblepharidaceae</i> consists of a very small group of aquatic
+forms living on fallen twigs in ponds and ditches. Only one genus,
+<i>Monoblepharis</i>, can certainly be placed here, though a somewhat
+similar genus, <i>Myrioblepharis</i>, with a peculiar multiciliate zoospore
+like that of Vaucheria, is provisionally placed in the same group.
+<i>Monoblepharis</i> was first described by Cornu in 1871, but from that
+time until 1895 when Roland Thaxter described several species
+from America the genus was completely lost sight of. <i>Monoblepharis</i>
+has oogonia with single oospheres and antheridia developing a few
+amoeboid uniciliate antherozoids; these creep to the opening of the
+oogonium and then swim in. The resemblance between this genus
+and <i>Oedogonium</i> among the algae is very striking, as is also that of
+<i>Myrioblepharis</i> and <i>Vaucheria</i>.</p>
+
+<p><i>Peronosporaceae</i> are a group of endophytic parasites&mdash;about 100
+species&mdash;of great importance as comprising the agents of &ldquo;damping
+off&rdquo; disease (<i>Pythium</i>), vine-mildew (<i>Plasmopara</i>), potato disease
+(Phytophthora), onion-mildew (<i>Peronospora</i>). <i>Pythium</i> is a semi-aquatic
+form attacking seedlings which are too plentifully supplied
+with water; its hyphae penetrate the cell-walls and rapidly destroy
+the watery tissues of the living plant; then the fungus lives in the
+dead remains. When the free ends of the hyphae emerge again into
+the air they swell up into spherical bodies which may either fall
+off and behave as conidia, each putting out a germ-tube and infecting
+the host; or the germ-tube itself swells up into a zoosporangium
+which develops a number of zoospores. In the rotting tissues
+branches of the older mycelium similarly swell up and form antheridia
+and oogonia (fig. 4). The contents of the antheridium are not set
+free, but that organ penetrates the oogonium by means of a narrow
+outgrowth, the fertilizing tube, and a male nucleus then passes over
+into the single oosphere, which at first multinucleate becomes uninucleate
+before fertilization. <i>Pythium</i> is of interest as illustrating
+the dependence of zoospore-formation on conditions and the indeterminate
+nature of conidia. The other genera are more purely
+parasitic; the mycelium usually sends haustoria into the cells of
+the host and puts out branched, aerial conidiophores through the
+stomata, the branches of which abstrict numerous &ldquo;conidia&rdquo;;
+these either germinate directly or their contents break up into
+zoospores (fig. 5). The development of the &ldquo;conidia&rdquo; as true
+conidial spores or as zoosporangia may occur in one and the same
+species (<i>Cystopus candidus</i>, <i>Phytophthora infestans</i>) as in <i>Pythium</i>
+described above; in other cases the direct conidial germination is
+characteristic of genera&mdash;<i>e.g.</i> <i>Peronospora</i>; while others emit
+zoospores&mdash;<i>e.g.</i> <i>Plasmopara</i>, &amp;c. In <i>Cystopus</i> (<i>Albugo</i>) the &ldquo;conidia&rdquo;
+are abstricted in basipetal chain-like series from the ends of hyphae
+which come to the surface in tufts and break through the epidermis
+as white pustules. Each &ldquo;conidium&rdquo; contains numerous nuclei
+and is really a zoosporangium, as after dispersal it breaks up into a
+number of zoospores. The Peronosporaceae reproduce themselves
+sexually by means of antheridia and oogonia as described in <i>Pythium</i>.
+In <i>Cystopus Bliti</i> the oosphere contains numerous nuclei, and all
+the male nuclei from the antheridium pass into it, the male and
+female nuclei then fusing in pairs. We thus have a process of
+&ldquo;multiple fertilization&rdquo;; the oosphere really represents a large
+number of undifferentiated gametes and has been termed a coenogamete.
+Between <i>Cystopus Bliti</i> on the one hand and <i>Pythium de
+Baryanum</i> on the other a number of cytologically intermediate
+forms are known. The oospore on germination usually gives origin
+to a zoosporangium, but may form directly a germ tube which infects
+the host.</p>
+
+<table class="pic" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter" colspan="2"><img style="width:500px; height:482px" src="images/img337a.jpg" alt="" /></td></tr>
+<tr><td class="tcl f80" colspan="2">From Strasburger&rsquo;s <i>Lehrbuch der Botanik</i>, by permission of Gustav Fischer.</td></tr>
+<tr><td class="caption" colspan="2"><span class="sc">Fig. 4.</span>&mdash;Fertilization of the Peronosporeae. After Wager.</td></tr>
+
+<tr><td class="f90" style="width: 50%; vertical-align: top;">
+<p>1, <i>Peronospora parasitica</i>. Young
+multinucleate oogonium (<i>og</i>)
+and antheridium (<i>an</i>).</p>
+
+<p>2, <i>Albugo candida</i>. Oogonium
+with the central uninucleate
+oosphere and the fertilizing
+tube (<i>a</i>) of the antheridium
+which introduces the male
+nucleus.</p></td>
+
+<td class="f90" style="width: 50%; vertical-align: top;">
+<p>3, The same. Fertilized egg-cell
+(<i>o</i>) surrounded by the
+periplasm (<i>p</i>).</p></td></tr></table>
+
+<table class="pic pt2" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter" colspan="2"><img style="width:500px; height:615px" src="images/img337b.jpg" alt="" /></td></tr>
+<tr><td class="caption" colspan="2"><span class="sc">Fig. 5.</span>&mdash;<i>Phytophthora infestans</i>. Fungus of Potato Disease.</td></tr>
+
+<tr><td class="f90" style="width: 50%; vertical-align: top;">
+<p>A, B, Section of Leaf of Potato
+with sporangiophores of <i>Phytophthora
+infestans</i> passing
+through the stomata D, on
+the under surface of the leaf.</p>
+
+<p>E, Sporangia.</p>
+
+<p>F, G, H, J, Further development
+of the sporangia.</p></td>
+
+<td class="f90" style="width: 50%; vertical-align: top;">
+<p>K, Germination of the zoospores
+formed in the sporangia.</p>
+
+<p>L, M, N, Fertilization of the
+oogonium and development of
+the oospore in <i>Peronospora</i>.</p></td></tr></table>
+
+<p class="pt2"><i>Saprolegniaceae</i> are aquatic forms found growing usually on dead
+insects lying in water but occasionally on living fish (<i>e.g.</i> the salmon
+disease associated with <i>Saprolegnia ferax</i>). The chief genera are
+<span class="pagenum"><a name="page338" id="page338"></a>338</span>
+<i>Saprolegnia, Achlya, Pythiopsis, Dictyuchus, Aplanes.</i> Motile zoospores
+which escape from the zoosporangium are present except in Aplanes.
+The sexual reproduction shows all transitions between forms which
+are normally sexual, like the Peronosporaceae, to forms in which
+no antheridium is developed and the oospheres develop parthenogenetically.
+The oogonia, unlike the Peronosporaceae, contain more
+than one oosphere. Klebs has shown that the development of
+zoosporangia or of oogonia and pollinodia respectively in <i>Saprolegnia</i>
+is dependent on the external conditions; so long as a continued
+stream of suitable food-material is ensured the mycelium grows on
+without forming reproductive organs, but directly the supplies of
+nitrogenous and carbonaceous food fall below a certain degree of
+concentration sporangia are developed. Further reduction of the
+supplies of food effects the formation of oogonia. This explains the
+sequence of events in the case of a <i>Saprolegnia</i>-mycelium radiating
+from a dead fly in water. Those parts nearest the fly and best
+supplied develop barren hyphae only; in a zone at the periphery,
+where the products of putrefaction dissolved in the water form a
+dilute but easily accessible supply, the zoosporangia are developed
+in abundance; oogonia, however, are only formed in the depths of
+this radiating mycelium, where the supplies of available food
+materials are least abundant.</p>
+
+<p><i>Chytridineae.</i>&mdash;These parasitic and minute, chiefly aquatic, forms
+may be looked upon as degenerate Oomycetes, since a sexual process
+and feeble unicellular mycelium occur in some; or they may be
+regarded as series of primitive forms leading up to higher members.
+There is no means of deciding the question. They are usually
+included in Oomycetes, but their simple structure, minute size,
+usually uniciliate zoospores, and their negative characters would
+justify their retention as a separate group. It contains less than
+200 species, chiefly parasitic on or in algae and other water-plants
+or animals, of various kinds, or in other fungi, seedlings, pollen and
+higher plants. They are often devoid of hyphae, or put forth fine
+protoplasmic filaments into the cells of their hosts. After absorbing
+the cell-contents of the latter, which it does in a few hours or days,
+the fungus puts out a sporangium, the contents of which break up
+into numerous minute swarm-spores, usually one-ciliate, rarely
+two-ciliate. Any one of these soon comes to rest on a host-cell,
+and either pierces it and empties its contents into its cavity, where
+the further development occurs (<i>Olpidium</i>), or merely sends in
+delicate protoplasmic filaments (<i>Rhizophydium</i>) or a short hyphal
+tube of, at most, two or three cells, which acts as a haustorium,
+the further development taking place outside the cell-wall of the
+host (<i>Chytridium</i>). In some cases resting spores are formed inside
+the host (<i>Chytridium</i>), and give rise to zoosporangia on germination.
+In a few species a sexual process is described, consisting in
+the conjugation of similar cells (<i>Zygochytrium</i>) or the union of
+two dissimilar ones (<i>Polyphagus</i>). In the development of distinct
+antheridial and oogonial cells the allied Ancylistineae show
+close alliances to <i>Pythium</i> and the Oomycetes. On the other hand,
+the uniciliate zoospores of <i>Polyphagus</i> have slightly amoeboid
+movements, and in this and the pseudopodium-like nature of the
+protoplasmic processes, such forms suggest resemblances to the
+Myxomycetes. Opinions differ as to whether the Chytridineae are degraded
+or primitive forms, and the group still needs critical revision.
+Many new forms will doubtless be discovered, as they are rarely
+collected on account of their minuteness. Some forms cause damping
+off of seedlings&mdash;<i>e.g.</i> <i>Olpidium Brassicae</i>; others discoloured spots
+and even tumour-like swellings&mdash;<i>e.g.</i> <i>Synchytium Scabiosae</i>, <i>S.
+Succisae</i>, <i>Urophlyctis</i>, &amp;c., on higher plants. Analogies have been
+pointed out between Chytridiaceae and unicellular algae, such as
+Chlorosphaeraceae, Protococcaceae, &ldquo;Palmellaceae,&rdquo; &amp;c., some of
+which are parasitic, and suggestions may be entertained as to
+possible origin from such algae.</p>
+
+<p>The <i>Zygomycetes</i>, of which about 200 species are described, are
+especially important from a theoretical standpoint, since they furnished
+the series whence Brefeld derived the vast majority of the
+fungi. They are characterized especially by the zygospores, but
+the asexual organs (sporangia) exhibit interesting series of changes,
+beginning with the typical sporangium of <i>Mucor</i> containing numerous
+endospores, passing to cases where, as in <i>Thamnidium</i>, these are
+accompanied with more numerous small sporangia (sporangioles)
+containing few spores, and thence to <i>Chaetocladium</i> and <i>Piptocephalis</i>,
+where the sporangioles form but one spore and fall and germinate
+as a whole; that is to say, the monosporous sporangium has become
+a conidium, and Brefeld regarded these and similar series of changes
+as explaining the relation of ascus to conidium in higher fungi.
+According to his view, the ascus is in effect the sporangium with
+several spores, the conidium the sporangiole with but one spore,
+and that not loose but fused with the sporangiole wall. On this
+basis, with other interesting morphological comparisons, Brefeld
+erected his hypothesis, now untenable, that the Ascomycetes and
+Basidiomycetes diverge from the Zygomycetes, the former having
+particularly specialized the ascus (sporangial) mode of reproduction,
+the latter having specialized the conidial (indehiscent one-spored
+sporangiole) mode. In addition to sporangia and the conidial spores
+referred to, some Mucorini show a peculiar mode of vegetative
+reproduction by means of gemmae or chlamydospores&mdash;<i>i.e.</i> short
+segments of the hyphae become stored with fatty reserves and act
+as spores. The gemmae formed on submerged Mucors may bud like
+a yeast, and even bring about alcoholic fermentation in a saccharine
+solution.</p>
+
+<table class="flt" style="float: right; width: 400px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:350px; height:578px" src="images/img338.jpg" alt="" /></td></tr>
+<tr><td class="caption80">From Strasburger&rsquo;s <i>Lehrbuch der Botanik</i>, by
+permission of Gustav Fischer.</td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 6.</span>&mdash;<i>Mucor Mucedo.</i> Different
+stages in the formation and germination
+of the zygospore. (After Brefeld,
+1-4. 5 from v. Tavel, <i>Pilze</i>.)</td></tr>
+
+<tr><td class="caption1">
+<p>1, Two conjugating branches in contact.</p>
+<p>2, Septation of the conjugating cells (<i>a</i>)
+    from the suspensors (<i>b</i>).</p>
+<p>3, More advanced stage, the conjugating
+    cells (<i>a</i>) are still distinct from
+    one another; the warty thickenings
+    of their walls have commenced to
+    form.</p>
+<p>4, Ripe zygospore (<i>b</i>) between the suspensors
+(<i>a</i>).</p>
+<p>5, Germinating zygospore with a germ-tube
+    bearing a sporangium.</p></td></tr></table>
+
+<p>The segments of the hyphae in this group usually contain several
+nuclei. At the time of sporangial formation the protoplasm with
+numerous nuclei streams into the swollen end of the sporangiophore
+and there becomes cut off by a cell-wall to form the sporangium.
+The protoplasm then becomes cut up by a series of clefts into a
+number of smaller and smaller pieces which are unicellular in
+<i>Pilobolus</i>, multicellular in <i>Sporodinia</i>. These then become surrounded
+by a cell-wall and form the spores. This mode of spore-formation
+is totally different from that in the ascus; hence one of
+the difficulties of the acceptance of Brefeld&rsquo;s view of the homology
+of ascus and sporangium. The cytology of zygospore-formation is
+not known in detail;
+the so-called gametes
+which fuse are multinucleate
+and are no doubt
+of the nature of gametangia.
+The fate of these
+nuclei is doubtful, probably
+they fuse in pairs
+(fig. 6).</p>
+
+<p>Blakeslee has lately
+made some very important
+observations of the
+Zygomycetes. It is well
+known that while in some
+forms, <i>e.g.</i> <i>Spordinia</i>,
+zygospores are easily obtained,
+in others, <i>e.g.</i> most
+species of <i>Mucor</i>, they
+are very erratic in their
+appearance. This has now
+been explained by
+Blakeslee, who finds that
+the Mucorinae can be
+divided into two groups,
+termed homothallic and
+heterothallic respectively.
+In the first group zygospores
+can arise by the
+union of branches from
+the <i>same</i> mycelium and
+so can be produced by the
+growth from a single spore;
+this group includes <i>Spordinia
+grandis</i>, <i>Spinellus
+fusiger</i>, some species of
+<i>Mucor</i>, &amp;c. The majority
+of forms, however, fall
+into the heterothallic
+group, in which the association
+of branches from
+two mycelia <i>different in
+nature</i> is necessary for the
+formation of zygospores.
+These structures cannot
+then be produced from the
+product of a single spore
+nor even from the thalli
+derived from <i>any</i> two
+spores. The two kinds of
+thalli Blakeslee considers
+to have a differentiation
+of the nature of sex and
+he distinguishes them as (+) and (&minus;) forms; the former being
+usually distinguished by a somewhat greater luxuriance of growth.</p>
+
+<p>The classification of the Mucorini depends on the prevalence and
+characters of the conidia, and of the sporangia and zygospores&mdash;<i>e.g.</i>
+the presence or absence of a columella in the former, the formation
+of an investment round the latter. Most genera are saprophytes,
+but some&mdash;<i>Chaetocladium</i>, <i>Piptocephalis</i>&mdash;are parasites on other
+Mucorini, and one or two are associated casually with the rotting
+of tomatoes and other fruits, bulbs, &amp;c., the fleshy parts of which
+are rapidly destroyed if once the hyphae gain entrance. Even more
+important is the question of mycosis in man and other animals,
+referred to species of <i>Mucor</i>, and investigated by Lucet and Costantin.
+Klebs has concluded that transpiration is the important
+factor in determining the formation of sporangia, while zygote-development
+depends on totally different conditions; these results
+have been called in question by Falck.</p>
+
+<p>The <i>Entomophthoraceae</i> contain three genera, <i>Empusa</i>, <i>Entomophthora</i>
+and <i>Basidiobolus</i>. The two first genera consist of forms
+which are parasitic on insects. <i>Empusa Muscae</i> causes the well-known
+epidemic in house-flies during the autumn; the dead, affected
+flies are often found attached to the window surrounded by a white
+halo of conidia. <i>B. ranarum</i> is found in the alimentary canal of the
+frog and growing on its excrement. In these three genera the conidia
+are cast off with a jerk somewhat in the same way as the sporangium
+of <i>Pilobolus</i>.</p>
+</div>
+
+<p><span class="pagenum"><a name="page339" id="page339"></a>339</span></p>
+
+<p>B. <span class="sc">Higher Fungi.</span>&mdash;Now that Brefeld&rsquo;s view of the origin
+of these forms from the Zygomycetes has been overthrown,
+the relationship of the higher and lower forms of fungi is left
+in obscurity. The term <i>Eumycetes</i> is sometimes applied to this
+group to distinguish them from the Phycomycetes, but as the
+same name is also applied to the fungi as a whole to differentiate
+them from the Mycetozoa and Bacteria, the term had best be
+dropped. The Higher Fungi fall into three groups: the <i>Ustilaginales</i>,
+of doubtful position, and the two very sharply marked
+groups <i>Basidiales</i> and <i>Ascomycetes</i>.</p>
+
+<table class="flt" style="float: right; width: 350px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:300px; height:371px" src="images/img339a.jpg" alt="" /></td></tr>
+<tr><td class="caption80">From Vine&rsquo;s <i>Students&rsquo; Text Book of
+Botany</i>, by permission of Swan Sonnenschein
+&amp; Co.</td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 7.</span>&mdash;Germinating resting-gonidia.
+A, of <i>Ustilago
+receptaculorum</i>; B, of <i>Tilletia
+Caries</i>.</td></tr>
+<tr><td class="caption1">
+<p><i>sp</i>, The gonidium.</p>
+<p><i>pm</i>, The promycelium.</p>
+<p><i>d</i>,  The sporidia: in B the
+     sporidia have coalesced
+     in pairs at <i>v</i>.</p></td></tr></table>
+
+<div class="condensed">
+<p>I. <i>Ustilaginales.</i>&mdash;This includes two families Ustilaginaceae
+(smuts) and Tilletiaceae (bunts). The bunts and smuts which
+damage our grain and fodder plants comprise about 400 species of
+internal parasites, found in all countries on herbaceous plants, and
+especially on Monocotyledons. They are remarkable for their dark
+spores developed in gall-like excrescences on the leaves, stems, &amp;c.,
+or in the fruits of the host. The discovery of the yeast-conidia of
+these fungi, and their thorough investigation by Brefeld, have
+thrown new lights on the group, as also have the results elucidating
+the nature of the ordinary dark spores&mdash;smuts, bunt, &amp;c.&mdash;which by
+their mode of origin and development are chlamydospores. When
+the latter germinate a slender &ldquo;promycelium&rdquo; is put out; in
+<i>Ustilago</i> and its allies this is transversely septate, and bears lateral
+conidia (sporidia); in <i>Tilletia</i> and its allies non-septate, and bears
+a terminal tuft of conidia (sporidia) (fig. 7). Brefeld regarded the
+promycelium as a kind of <i>basidium</i>, bearing lateral or terminal
+conidia (comparable to <i>basidiospores</i>),
+but since the number of
+basidiospores is not fixed, and the
+basidium has not yet assumed very
+definite morphological characters,
+Brefeld termed the group <i>Hemibasidii</i>,
+and regarded them as a half-way
+stage in the evolution of the
+true Basidiomycetes from Phycomycetes,
+the <i>Tilletia</i> type leading
+to the true basidium (Autobasidium),
+the <i>Ustilago</i> type to the protobasidium,
+with lateral spores; but this
+view is based on very poor evidence,
+so that it is best to place these forms
+as a separate group, the <i>Ustilaginales</i>.
+The yeast-conidia, which bud off
+from the conidia or their resulting
+mycelium when sown in nutrient
+solutions, are developed in successive
+crops by budding exactly as
+in the yeast plant, but they cannot
+ferment sugar solutions. It is the
+rapid spread of these yeast-conidia
+in manure and soil waters which
+makes it so difficult to get rid of
+smuts, &amp;c., in the fields, and they,
+like the ordinary conidia, readily
+infect the seedling wheat, oats,
+barley or other cereals. Infection
+in these cases occurs in the seedling
+at the place where root and shoot
+meet, and the infecting hypha having entered the plant goes on living
+in it and growing up with it as if it had no parasitic action at all. When
+the flowers form, however, the mycelium sends hyphae into the young
+ovaries and rapidly replaces the stores of sugar and starch, &amp;c.,
+which would have gone to make the grain, by the soot-like mass of
+spores so well known as smut, &amp;c. These spores adhere to the grain,
+and unless destroyed, by &ldquo;steeping&rdquo; or other treatment, are sown
+with it, and again produce sporidia and yeast-conidia which infect
+the seedlings. In other species the infection occurs through the
+style of the flower, but the fungus after reaching the ovule develops
+no further during that year but remains dormant in the embryo
+of the seed. On germination, however, the fungus behaves in the
+same way as one which has entered in the seedling stage. The
+cytology of these forms is very little known; Dangeard states that
+there is a fusion of two nuclei in the chlamydospore, but this requires
+confirmation. Apart from this observation there is no other trace
+of sexuality in the group.</p>
+
+<p>II. <i>Ascomycetes.</i>&mdash;This, except in the case of a few of the simpler
+forms, is a very sharply marked group characterized by a special
+type of sporangium, the ascus. In the development of the ascus we
+find two nuclei at the base which fuse together to form the single
+nucleus of the young <i>ascus</i>. The single nucleus divides by three
+successive divisions to form eight nuclei lying free in the protoplasm
+of the ascus. Then by a special method, described first by Harper,
+a mass of protoplasm is cut out round each nucleus; thus eight
+uninucleate ascospores are formed by free-cell formation. The
+protoplasm remaining over is termed <i>epiplasm</i> and often contains
+glycogen (fig. 8). In some cases nuclear division is carried further
+before spore-formation occurs, and the number of spores is then 16,
+32 and 64, &amp;c.; in a few cases the number of spores is less than
+eight by abortion of some of the eight nuclei. The ascus is thus one
+of the most sharply characterized structures among the fungi.</p>
+
+<table class="flt" style="float: right; width: 280px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:230px; height:313px" src="images/img339b.jpg" alt="" /></td></tr>
+<tr><td class="caption80">From Strasburger&rsquo;s <i>Lehrbuch der
+Botanik</i>, by permission of Gustav
+Fischer.</td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 8.</span>&mdash;Development of the
+Ascus.</td></tr>
+<tr><td class="caption1">
+<p><i>A-C</i>, <i>Pyronema confluens</i>.
+(After Harper.)</p>
+
+<p><i>D</i>, Young ascus of <i>Boudiera</i>
+with eight spores.
+(After Claussen.)</p></td></tr></table>
+
+<p>In some forms we find definite male and female sexual organs
+(<i>Sphaerotheca</i>, <i>Pyronema</i>, &amp;c.), in others the antheridium is abortive
+or absent, but the ascogonium (oogonium) is still present and the
+female nuclei fuse in pairs (<i>Lachnea
+stercorea</i>, <i>Humaria granulata</i>, <i>Ascobolus
+furfuraceus</i>); while in other
+forms ascogonium and antheridium
+are both absent and fusion occurs
+between vegetative nuclei (<i>Humaria
+rutilans</i>, and probably the majority
+of other forms). In other cases the
+sexual fusion is apparently absent
+altogether, as in <i>Exoascus</i>. In the first
+case (fig. 9) we have a true sexual
+process, while in the second and third
+cases we have a <i>reduced</i> sexual process
+in which the fusion of other nuclei
+has replaced the fusion of the normal
+male and female nuclei. It is to be
+noted that all the forms exhibit the
+fusion of nuclei in the ascus, so that
+those with the normal or reduced
+sexual process described above have
+two nuclear fusions in their life-history.
+The advantage or significance
+of the second (ascus) fusion is
+not clearly understood.</p>
+
+<p>The group of the Hemiasci was
+founded by Brefeld to include forms
+which were supposed to be a connecting
+link between Phycomycetes and
+Ascomycetes. As mentioned before,
+the connexion between these two groups is very doubtful, and the derivation
+of the ascus from an ordinary sporangium of the Zygomycetes
+cannot be accepted. The majority of the forms which were formerly
+included in this group have been shown to be either true Phycomycetes
+(like <i>Ascoidea</i>) or true Ascomycetes (like <i>Thelebolus</i>). <i>Eremascus</i> and
+<i>Dipodascus</i>, which are often placed among the Hemiasci, possibly do
+not belong to the Ascomycetes series at all.</p>
+
+<table class="pic" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter" colspan="2"><img style="width:550px; height:422px" src="images/img339c.jpg" alt="" /></td></tr>
+<tr><td class="tcl f80" colspan="2">From Strasburger&rsquo;s <i>Lehrbuch der Botanik</i>, by permission of Gustav Fischer.</td></tr>
+<tr><td class="caption" colspan="2">Fig. 9.&mdash;<i>Sphaerotheca Castagnei</i>. Fertilization and Development
+of the Perithecium. (After Harper.)</td></tr>
+
+<tr><td class="f90" style="width: 50%; vertical-align: top;">
+<p>1,  Oogonium (<i>og</i>) with the antheridial
+    branch (<i>az</i>) applied to its surface</p>
+
+<p>2,  Separation of antheridium
+    (<i>an</i>).</p>
+
+<p>3,  Passage of the antheridial
+    nucleus towards that of the
+    oogonium.</p></td>
+
+<td class="f90" style="width: 50%; vertical-align: top;">
+<p>4,  Union of the nuclei.</p>
+
+<p>5,  Fertilized oogonium surrounded
+    by two layers of
+    hyphae derived from the
+    stalk-cell (<i>st</i>).</p>
+
+<p>6,  The multicellular ascogonium
+    derived by division from the
+    oogonium; the terminal cell
+    with the two nuclei (<i>as</i>)
+    gives rise to the ascus.</p></td></tr></table>
+
+<p class="pt2"><i>Exoascaceae</i> are a small group of doubtful extent here used to
+include <i>Exoascus</i>, <i>Taphrina</i>, <i>Ascorticium</i> and <i>Endomyces</i>. The
+mycelium is very much reduced in extent. The asci are borne
+directly on the mycelium and are therefore fully exposed, being
+devoid from the beginning of any investment. The <i>Taphrineae</i>,
+which include <i>Exoascus</i> and <i>Taphrina</i>, are important parasites&mdash;<i>e.g.</i>
+pocket-plums and witches&rsquo; brooms on birches, &amp;c., are due to
+their action (fig. 10). <i>Exoascus</i> and <i>Ascorticium</i> present interesting
+parallels to <i>Exobasidium</i> and <i>Corticium</i> among the Basidiomycetes.</p>
+
+<table class="flt" style="float: right; width: 380px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:330px; height:407px" src="images/img340.jpg" alt="" /></td></tr>
+<tr><td class="caption80">From Strasburger&rsquo;s <i>Lehrbuch der
+Botanik</i>, by permission of Gustav Fischer.</td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 10.</span>&mdash;<i>Taphrina Pruni.</i>
+Transverse section through the
+epidermis of an infected plum.
+Four ripe asci, <i>a</i><span class="su">1</span>, <i>a</i><span class="su">2</span>, with eight
+spores, <i>a</i><span class="su">3</span>, <i>a</i><span class="su">4</span>, with yeast-like
+conidia abstricted from the spores.
+After Sadebeck.</td></tr>
+<tr><td class="caption1"><p>st, Stalk-cells of the asci.</p>
+<p>m, Filaments of the mycelium cut transversely.</p>
+<p>cut, Cuticle.</p>
+<p>sp, Epidermis.</p></td></tr></table>
+
+<p><i>Saccharomycetaceae</i> include the well-known yeasts which belong
+mainly to the genus <i>Saccharomyces</i>. They are characterized by
+their unicellular nature, their power of rapid budding, their capacity
+for fermenting various sugars, and their power of forming endogenous
+<span class="pagenum"><a name="page340" id="page340"></a>340</span>
+spores. The sporangium with its endogenous spores has been
+compared with an ascus, and on these grounds the group is placed
+among the Ascomycetes&mdash;a very doubtful association. The group
+has attained an importance of late even beyond that to which it was
+brought by Pasteur&rsquo;s researches on alcoholic fermentation, chiefly
+owing to the exact results of the investigations of Hansen, who
+first applied the methods of pure cultures to the study of these
+organisms, and showed that many of the inconsistencies hitherto
+existing in the literature were
+due to the coexistence in the
+cultures of several species or
+races of yeasts morphologically
+almost indistinguishable, but
+physiologically very different.
+About fifty species of <i>Saccharomyces</i>
+are described more or less
+completely, but since many of
+these cannot be distinguished
+by the microscope, and some
+have been found to develop
+physiological races or varieties
+under special conditions of
+growth, the limits are still far
+too ill-defined for complete
+botanical treatment of the genus.
+A typical yeast is able to develop
+new cells by budding when submerged
+in a saccharine solution,
+and to ferment the sugar&mdash;<i>i.e.</i>
+so to break up its molecules that,
+apart from small quantities used
+for its own substance, masses of
+it out of all proportion to the
+mass of yeast used become
+resolved into other bodies, such
+as carbon dioxide and alcohol,
+the process requiring little or
+no oxygen. Brefeld regards the
+budding process as the formation
+of conidia. Under other
+conditions, of which the temperature
+is an important one, the
+nucleus in the yeast-cell divides,
+and each daughter-nucleus again,
+and four spores are formed in the mother cell, a process obviously comparable
+to the typical development of ascospores in an ascus. Under
+yet other conditions the quiescent yeast-cells floating on the surface
+of the fermented liquor grow out into elongated sausage-shaped or
+cylindrical cells and branching cell-series, which mat together into
+mycelium-like veils. At the bottom of the fermented liquor the
+cells often obtain fatty contents and thick walls, and behave as
+resting cells (chlamydospores). The characters employed by experts
+for determining a species of yeast are the sum of its peculiarities as
+regards form and size: the shapes, colours, consistency, &amp;c., of
+the colonies grown on certain definite media; the optimum temperature
+for spore-formation, and for the development of the
+&ldquo;veils&rdquo;; and the behaviour as regards the various sugars.</p>
+
+<p>The following summary of some of the principal characteristics
+of half-a-dozen species will serve to show how such peculiarities can
+be utilized for systematic purposes:</p>
+
+<table class="ws" summary="Contents">
+
+<tr><td class="tccm allb" rowspan="2">Species.</td> <td class="tccm allb" colspan="2">Optimum Temperature for</td> <td class="tccm allb" colspan="3">Characters of</td> <td class="tccm allb" rowspan="2">Sugars Fermented and<br />Products, &amp;c.</td></tr>
+<tr><td class="tccm allb">Spores.</td> <td class="tccm allb">Veils.</td> <td class="tccm allb">Fermentation.</td> <td class="tccm allb">Cells.</td> <td class="tccm allb">Spores.</td></tr>
+
+<tr><td class="tcl lb rb"><i>S. cereviseae I</i>.</td> <td class="tcc rb">30°</td> <td class="tcc rb">20°-28°</td> <td class="tcc rb">High</td> <td class="tcl rb">Rounded</td> <td class="tcl rb">Globoid</td> <td class="tclm rb cl" rowspan="3">Inverts maltose and saccharose<br />&emsp; and form alcohol 4-6 vol. %.</td></tr>
+<tr><td class="tcl lb rb"><i>S. Pastorianus I</i></td> <td class="tcc rb">27°-5°</td> <td class="tcc rb">26°-28°</td> <td class="tcc rb">Low</td> <td class="tcl rb">Rounded</td> <td class="tcl rb">Globoid</td></tr>
+<tr><td class="tcl lb rb"><i>S. ellipsoideus</i></td> <td class="tcc rb">25°</td> <td class="tcc rb">33°-34°</td> <td class="tcc rb">Low</td> <td class="tcl rb">Rounded</td> <td class="tcl rb">Globoid</td></tr>
+<tr><td class="tcl lb rb"><i>S. anomalus</i></td> <td class="tcc rb">28°-31°</td> <td class="tcc rb">?</td> <td class="tcc rb">High</td> <td class="tcl rb">Elliptical</td> <td class="tcl rb">Hat-shaped</td> <td class="tcl rb">Ditto, and evolves a fragrant ether.</td></tr>
+<tr><td class="tcl lb rb"><i>S. Ludwigii</i></td> <td class="tcc rb">30°-31°</td> <td class="tcc rb">?</td> <td class="tcc rb">?</td> <td class="tcl rb">Elongated</td> <td class="tcl rb">Globoid</td> <td class="tcl rb">Will not invert maltose.</td></tr>
+<tr><td class="tcl lb rb bb"><i>S. membranaefaciens</i></td> <td class="tcc rb bb">30°</td> <td class="tcc rb bb">?</td> <td class="tcc rb bb">High</td> <td class="tcl rb bb">Elongated</td> <td class="tcl rb bb">Globoid</td> <td class="tcl rb bb">Inverts neither maltose nor saccharose.</td></tr>
+</table>
+
+<p>Two questions of great theoretical importance have been raised
+over and over again in connexion with yeasts, namely, (1) the
+morphological one as to whether yeasts are merely degraded forms
+of higher fungi, as would seem implied by their tendency to form
+elongated, hypha-like cells in the veils, and their development
+of &ldquo;ascospores&rdquo; as well as by the wide occurrence of yeast-like
+&ldquo;sprouting forms&rdquo; in other fungi (<i>e.g.</i> <i>Mucor</i>, Exoasci, Ustilagineae,
+higher Ascomycetes and Basidiomycetes); and (2) the question as
+to the physiological nature and meaning of fermentation. With
+regard to the first question no satisfactory proof has as yet been
+given that Saccharomycetes are derivable by culture from any
+higher form, the recent statements to that effect not having been
+confirmed. At the same time there are strong grounds for insisting
+on the resemblances between <i>Endomyces</i>, a hyphal fungus bearing
+yeast-like asci, and such a form as <i>Saccharomyces anomalus</i>. Concerning
+the second question, the recent investigations of Buchner
+and others have shown that a ferment (zymase) can be extracted
+from yeast-cells which causes sugar to break up into carbon dioxide
+and alcohol. It has since been shown by Buchner and Albert that
+yeast-cells which have been killed by alcohol and ether, or with
+acetone, still retain the enzyme. Such material is far more active
+than the zymase obtained originally by Buchner from the expressed
+juice of yeast-cells. Thus alcoholic fermentation is brought into line
+with the other fermentations.</p>
+
+<p><i>Schizosaccharomyces</i> includes a few species in which the cells do
+not &ldquo;bud&rdquo; but become elongated and then divide transversely.
+In the formation of sporangia two cells fuse together by means of
+outgrowths, in a manner very similar to that of <i>Spirogyra</i>; sometimes,
+however, the wall between two cells merely breaks down. The
+fused cell becomes a sporangium, and in it eight spores are developed.
+In certain cases single cells develop parthenogenetically, without
+fusion, each cell producing, however, only four spores. In <i>Zygosaccharomyces</i>
+described by Barker (1901) we have a form of the
+usual sprouting type, but here again there is a fusion of two cells to
+form a sporangium.</p>
+
+<p><i>Cytology.</i>&mdash;The study of the nucleus of yeast-cells is rendered
+difficult by the presence of other deeply staining granules termed by
+Guillermond <i>metachromatic granules</i>. These have often been mistaken
+for nuclei and have to be carefully distinguished by differential
+stains. In the process of budding the nucleus divides apparently
+by a process of direct division. In the formation of spores the nucleus
+of the cell divides, the protoplasm collects round the nuclei to form
+the spores by free-cell formation; the protoplasm (epiplasm) not
+used in this process becomes disorganized. A fusion of nuclei was
+originally described by Jansens and Leblanc, but it was observed
+neither by Wager nor Guillermond and is probably absent. In
+<i>Schizosaccharomyces</i> and <i>Zygosaccharomyces</i>, however, we have a
+fusion of nuclei in connexion with the conjugation of cells which
+precedes sporangium-formation. The theory may be put forward
+that the ordinary forms have been derived from sexual forms like
+<i>Schizosaccharomyces</i> and <i>Zygosaccharomyces</i> by a loss of sexuality,
+the sporangium being formed parthenogenetically without any
+nuclear fusion. This suggests a possible relationship to <i>Eremascus</i>,
+which can only doubtfully be placed in the Ascomycetes (<i>vide supra</i>).</p>
+
+<p><i>Carpoascomycetes.</i>&mdash;The other divisions of the Ascomycetes may
+be distinguished as Carpoascomycetes because they do not bear
+the asci free on the mycelium but enclosed in definite fruit bodies
+or ascocarps. The ascocarps can be distinguished into two portions,
+a mass of sterile or vegetative hyphae forming the main mass of the
+fruit body, and surrounding the fertile ascogenous hyphae which
+bear at their ends the asci. When the ascogonium (female organ)
+is present the ascogenous hyphae arise from it, with or without its
+previous fusion with an antheridium. In other cases the ascogenous
+hyphae arise directly from the vegetative hyphae. In connexion
+with this condition of reduction a fusion of nuclei has been observed
+in <i>Humaria rutilans</i> and is probably of frequent occurrence. The
+asci may be derived from the terminal cell of the branches of the
+ascogenous hyphae, but usually they are derived from the penultimate
+cell, the tip curving over to form the so-called crozier. By
+this means the ascus cell is brought uppermost, and after the fusion
+of the two nuclei it develops enormously and produces the ascospores.
+The ascospores escape from the asci in various ways, sometimes by
+a special ejaculation-mechanism. The Ascomycetes, at least the
+Carpoascomycetes, exhibit a well-marked alternation of sexual and
+asexual generations. The ordinary mycelium is the gametophyte
+since it bears the ascogonia and antheridia when present; the
+ascogenous hyphae with their asci represent the sporophyte since
+they are derived from the fertilized ascogonium. The matter is
+complicated by the apogamous transition from gametophyte to
+sporophyte in the absence of the ascogonium; also by the fact that
+there are normally two fusions in the life-history as mentioned
+earlier. If there are two fusions one would expect two reductions,
+and Harper has suggested that the division of the nuclei into eight
+in the ascus, instead of into four spores as in most reduction processes,
+is associated with a <i>double</i> reduction process in the ascus.
+Miss Fraser in <i>Humaria rutilans</i> finds two reductions: a normal
+synaptic reduction in the first nuclear division of the ascus, and a
+peculiar reduction division termed <i>brachymeiosis</i> in the third ascus
+division.</p>
+
+<p>Various types of ascocarp are characteristic of the different
+divisions of the Carpoascomycetes: the cleistothecium, apothecium
+and perithecium.</p>
+
+<p><span class="pagenum"><a name="page341" id="page341"></a>341</span></p>
+
+<p><i>Perisporineae.</i>&mdash;This includes two chief families, Erysiphaceae
+and Perisporiaceae. They are characterized by an ascocarp without
+any opening to the exterior, the ascospores being set free by the
+decay or rupture of the ascocarp wall; such a fruit-body is termed
+a <i>cleistothecium</i> (cleistocarp). The Erysiphaceae are a sharply
+marked group of forms which live as parasites. They form a superficial
+mycelium on the surface of the plant, the hyphae not usually
+penetrating the tissues but merely sending haustoria into the epidermal
+cells. Only in rare cases is the mycelium intercellular.
+Owing to their appearance they go by the popular name of mildews.
+<i>Sphaerotheca Humuli</i> is the well known hop-mildew, <i>Sphaerotheca
+Mors-Uvae</i> is the gooseberry mildew, the recent advent of which
+has led to special legislation in Great Britain to prevent its spreading,
+as when rampant it makes the culture of gooseberries impossible.
+<i>Erysiphe</i>, <i>Uncinula</i> and <i>Phyllactinia</i> are other well-known genera.
+The form of the fruit body, the difference and the nature of special
+outgrowths upon it&mdash;the appendages&mdash;are characteristic of the
+various genera. Besides peritheca the members of the Erysiphaceae
+possess conidia borne in simple chains. De Bary brought forward
+very strong evidence for the origin of the ascocarp in <i>Sphaerotheca</i>
+and <i>Erysiphe</i> by a sexual process, but Harper in 1895 was the first
+to prove conclusively, by the observation of the nuclear fusion, that
+there was a definite fertilization in <i>Sphaerotheca Humuli</i> by the
+fusion of a male (antheridial) nucleus with a female, ascogonial
+(oogonial) nucleus. Since then Harper has shown that the same
+process occurs in <i>Erysiphe</i> and <i>Phyllactinia</i>.</p>
+
+<table class="pic" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter" colspan="2"><img style="width:600px; height:640px" src="images/img341a.jpg" alt="" /></td></tr>
+<tr><td class="caption" colspan="2"><span class="sc">Fig. 11.</span>&mdash;Development of <i>Eurotium repens</i>. (After De Bary.)</td></tr>
+
+<tr><td class="f90" style="width: 50%; vertical-align: top;">
+<p>A, Small portion of mycelium
+with conidiophore (<i>c</i>), and
+archicarp (<i>as</i>).</p>
+
+<p>B, The spiral archicarp (<i>as</i>),
+with the antheridium (<i>p</i>).</p>
+
+<p>D, The same, beginning to be
+surrounded by the hyphae
+forming the perithecium wall.</p>
+
+<p>D, The perithecium.</p></td>
+
+<td class="f90" style="width: 50%; vertical-align: top;">
+<p>E, F, Sections of young perithecia.</p>
+
+<p><i>w</i>, Parietal cells.</p>
+
+<p><i>f</i>, Pseudo-parenchyma.</p>
+
+<p><i>as</i>, Ascogonium.</p>
+
+<p>G, An ascus.</p>
+
+<p>H, An ascospore.</p></td></tr></table>
+
+<p class="pt2">The Perisporiaceae are saprophytic forms, the two chief genera
+being <i>Aspergillus</i> and <i>Penicillium</i>. The blue-green mould <i>P.
+crustaceum</i> and the green mould <i>A. herbariorium</i> (= <i>Eurotium
+herbariorum</i>) are extraordinarily widely distributed, moulds being
+found on almost any food-material which is exposed to the air.
+They have characteristic conidiophores bearing numerous conidia,
+and also cleistothecia which are spherical in form and yellowish in
+colour. The latter arise from the crown of a spirally coiled archicarp
+(bearing an ascogonium at its end) and a straight antheridium.
+Vegetative hyphae then grow up and surround these and enclose
+them in a continuous sheath of plectenchyma (fig. 11). It has lately
+been shown by Fraser and Chambers that in <i>Eurotium</i> both
+ascogonium and antheridium contain a number of nuclei (<i>i.e.</i> are
+coenogametes), but that the antheridium disorganizes without
+passing its contents into the ascogonium. There is apparently a
+reduced sexual process by the fusion of the ascogonial (female)
+nuclei in pairs. <i>Aspergillus Oryzae</i> plays an important part in
+saccharifying the starch of rice, maize, &amp;c., by means of the abundant
+diastase it secretes, and, in symbiosis with a yeast which ferments
+the sugar formed, has long been used by the Japanese for the preparation
+of the alcoholic liquor saké. The process has now been
+successfully introduced into European commerce.</p>
+
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter" style="vertical-align: bottom;"><img style="width:230px; height:214px" src="images/img341b.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:350px; height:395px" src="images/img341c.jpg" alt="" /></td></tr>
+<tr><td class="tcl f80">From Strasburger&rsquo;s <i>Lehrbuch
+der Botanik</i>, by permission
+of Gustav Fischer.</td>
+<td class="caption"><span class="sc">Fig. 13.</span>&mdash;<i>Ascobolus furfuraceus.</i>
+Diagrammatic section of the fructification.
+(After Janczewski.)</td></tr>
+
+<tr><td class="caption"><span class="sc">Fig. 12.</span>&mdash;<i>Peziza aurantiaca.</i>
+(After Krombholz,
+nat. size.)</td>
+<td class="tcl f90">
+<p>&emsp; <i>m</i>, Mycelium.</p>
+<p>&emsp; <i>c</i>, Archicarp.</p>
+<p>&emsp; <i>l</i>, Pollinodium.</p>
+<p>&emsp; <i>s</i>, Ascogenous filaments.</p>
+<p>&emsp; <i>a</i>, Asri.</p>
+<p>&emsp; <i>r</i>, <i>p</i>, The sterile tissue from which the paraphyses <i>h</i> spring.</p></td></tr></table>
+
+<p class="pt2"><i>Discomycetes.</i>&mdash;Used in its widest sense this includes the
+Hysteriaceae, Phacidiaceae, Helvellaceae, &amp;c. The group is
+characterized in general by the possession of an ascocarp which,
+though usually a completely closed structure during the earlier
+stages of development, at maturity opens out to form a bowl or
+saucer-shaped organ, thus completely exposing the layer of asci
+which forms the hymenium. Such an ascocarp goes by the name of
+<i>apothecium</i>. Owing to the shape of the fruit-body many of these
+forms are known as cup-fungi, the cup or apothecium often attaining
+a large size, sometimes several inches across (fig. 12). Functional
+male and female organs have been shown to exist in <i>Pyronema</i> and
+<i>Boudiera</i>; in <i>Lachnea stercorea</i>
+both ascogonia and antheridia
+are present, but the antheridium
+is non-functional, the ascogonial
+(female) nuclei fusing in pairs;
+this is also the case in <i>Humaria
+granulata</i> and <i>Ascobolus furfuraceus</i>,
+where the antheridium is
+entirely absent. In <i>H. rutilans</i>,
+however, both sexual organs are
+absent and the ascogenous
+hyphae arise apogamously from
+the ordinary hyphae of the mycelim.
+In all these cases the
+ascogonium and antheridium contain numerous nuclei; they are
+to be looked upon as gametangia in which there is no differentiation
+of gametes, and since they act as single gametes they are termed
+coenogametes. In some forms as in <i>Ascobolus</i> the ascogonium is
+multicellular, the various cells
+communicating by pores in
+the transverse walls (fig. 13).</p>
+
+<table class="flt" style="float: right; width: 350px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:300px; height:490px" src="images/img341d.jpg" alt="" /></td></tr>
+<tr><td class="caption80">From Strasburger&rsquo;s <i>Lehrbuch der Botanik</i>,
+by permission of Gustav Fischer.</td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 14.</span>&mdash;Perithecium of Podospora
+fimiseda in longitudinal section. After v. Tavel.</td></tr>
+<tr><td class="caption1">
+<p><i>s</i>, Asci.</p>
+<p><i>a</i>, Paraphyses.</p>
+<p><i>e</i>, Periphyses.</p>
+<p><i>m</i>, Mycelial hyphae.</p></td></tr></table>
+
+<p>In the Helvellaceae there is
+no apothecium but a large
+irregular fruit body which at
+maturity bears the asci on its
+surface. The development is
+only slightly known, but there
+is some evidence for believing
+that the fruit-body is closed in
+its very early stages.</p>
+
+<p>The genus <i>Peziza</i> (in its
+widest sense) may be taken as
+the type of the group. Most
+of them grow on living plants
+or on dead vegetable remains,
+very often on fallen wood; a
+number, however, are found
+growing on earth which is rich
+in humus. The genus <i>Sclerotinia</i>
+may be mentioned here;
+a number of forms have been
+investigated by Woronin. The
+conidia are fragrant and are
+carried by bees to the stigma
+of the bilberry; here they
+germinate with the pollen and
+the hyphae pass with the pollen
+tubes down the style; the
+former infect the ovules and
+produce sclerotia, therein reducing
+the fruits to a mummified
+condition. From the
+sclerotia later the apothecium
+develops. One species, <i>S.
+heteroica</i>, is <i>heteroecious</i>; the
+ascospores infecting the leaves of <i>Vaccinium uliginosum</i>, while the
+conidia which then arise infect only <i>Ledum palustre</i>. This is the
+only case of heteroecism known in the vegetable kingdom outside
+the Uredineae.</p>
+
+<p><i>Pyrenomycetes.</i>&mdash;This is an extraordinarily large and varied group
+of forms which mostly live parasitically or saprophytically on
+vegetable tissue, but a few are parasitic on insect-larvae. The group
+<span class="pagenum"><a name="page342" id="page342"></a>342</span>
+is characterized by a special type of ascocarp, the <i>perithecium</i>.
+This is typically of a flask-shaped form opening with a small pore at
+the top. The asci live at the bottom often mixed with paraphyses,
+while the upper &ldquo;neck&rdquo; of the flask is lined with special hyphae,
+the periphyses, which aid in the ejection of the spores (fig. 14).
+The simpler forms bear the perithecia directly on the mycelium, but
+the more highly developed forms often bear them on a special
+mycelial development&mdash;the stroma, which is often of large size and
+special shape and colour, and of dense consistence. The cytological
+details of development of the perithecia are not well known; most
+of them appear to develop their ascogenous hyphae in an apogamous
+way without any connexion with an ascogonium. Besides the
+special ascocarps, accessory reproductive organs are known in the
+majority of cases in the form of conidia.</p>
+
+<p><i>Tuberineae.</i>&mdash;These are a small group of fungi including the well-known
+truffles. They are found living saprophytically (in part
+parasitically) underground in forests. The asci are developed in
+the large dense fruit bodies (cleistothecia) and the spores escape by
+the decay of the wall. The fruit-body is of complicated structure,
+but its early stages of development are not known. Many of the
+fruit-bodies have a pleasant flavour and are eaten under the name of
+truffles (<i>Tuber brumale</i> and other species). The exact life-history
+of the truffle is not known.</p>
+
+<table class="flt" style="float: left; width: 300px;" summary="Illustration">
+<tr><td class="figleft1"><img style="width:220px; height:266px" src="images/img342a.jpg" alt="" /></td></tr>
+<tr><td class="caption80">From Strasburger&rsquo;s <i>Lehrbuch der Botanik</i>,
+by permission of Gustav Fischer.</td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 15.</span>&mdash;<i>Armillaria mellea.</i> (After
+Ruhland.)</td></tr>
+<tr><td class="caption1">
+<p>A, Young basidium with the two
+primary nuclei.</p>
+
+<p>B, After fusion of the two nuclei.
+<i>Hypholoma appendiculatum</i>.</p>
+
+<p>C, A basidium before the four
+nuclei derived from the secondary
+nucleus of the basidium
+have passed into the four
+basidiospores.</p>
+
+<p>D, Passage of a nucleus through
+the sterigma into the basidiospore.</p></td></tr></table>
+
+<p><i>Laboulbeniineae</i> are a group of about 150 species of fungi found
+on insects, especially beetles, and principally known from the researches
+of Thaxter in America. The plant is a small, dark brown,
+erect structure (receptacle) of a few cells, and 1-10 mm. high, attached
+to the insect by the lowermost end (foot), and easily mistaken for a
+hair or similar appendage of the insect. The receptacle ends above
+in appendages, each consisting of one or a few cells, some of which
+are the male organs, others the female organs, and others again may
+be barren hairs. The male organ (antheridium) consists of a few
+cells, the terminal one of which either abstricts from its end, or emits
+from its interior the non-motile spermatia, reminding us of those
+of the Florideae. The female organ is essentially a flask-shaped
+structure; the neck of the flask growing out as the trichogyne, and
+the belly composed of an axial carpogenic cell surrounded by investing
+cells, and with one cell (trichophoric) between it and the trichogyne.
+These three elements&mdash;trichogyne, trichophoric cell, and
+carpogenic cell&mdash;are regarded as the procarp. The spermatia have
+been shown by Thaxter to fuse with the trichogyne, after which the
+axial cell below (carpogenic cell) undergoes divisions, and ultimately
+forms asci containing ascospores, while cells investing this form a
+perithecium, the whole structure reminding us essentially of the
+fructification of a Pyrenomycete. Many modifications in details
+occur, and the plants may be
+dioecious. No injury is done to
+the infested insects. It has lately
+been shown that there is a fusion
+of nuclei in connexion with ascus
+formation, so that there can be
+no doubt of the position of this
+extraordinary group of plants
+among the Ascomycetes. The
+various cells of these organisms
+are connected by large pits
+which are traversed by thick
+protoplasmic threads connecting
+one cell with the next. In this
+point and in their method of
+fertilization the Laboulbeniineae
+suggest a possible relationship
+of Ascomycetes and the Red
+Algae.</p>
+
+<p><i>Basidiales.</i>&mdash;This very large
+group of plants is characterized
+by the possession of a special
+type of conidiophore&mdash;the basidium,
+which gives its name to
+the group. The basidium is
+a unicellular or multicellular
+structure from which four basidiospores
+arise as outgrowths;
+it starts as a binucleate structure,
+but soon, like the ascus, becomes
+uninucleate by the fusion of the
+two nuclei. Then two successive
+nuclear divisions occur resulting
+in the formation of four nuclei
+which later migrate respectively into the four basidiospores (fig. 15).
+The Basidiales are further characterized by the complete loss of
+normal sexuality, but at some time or other in the life-history
+there takes place an association of two nuclei in a cell; the two
+nuclei are derived from separate cells or possibly in some cases are
+sister nuclei of the same cell. The two nuclei when once associated
+are termed &ldquo;conjugate&rdquo; nuclei, and they always divide at the same
+time, a half of each passing into each cell. This conjugate condition
+is finally brought to a close by the nuclear fusion in the basidium.
+Between the nuclear association and the nuclear fusion in the
+basidium many thousands of cell generations may be intercalated.
+This nuclear association of equivalent nuclei apparently represents
+a reduced sexual process (like the fusion of female nuclei in <i>Humaria
+granulata</i> and of vegetative nuclei in <i>H. rutilans</i>, among the Ascomycetes)
+in which, however, the actual fusion (normally, in a sexual
+process, occurring immediately after association) is delayed until
+the formation of the basidium. During the tetrad division in the
+basidium nuclear reduction occurs. There is thus in all the Basidiales
+an alternation of generations, obscured, however, by the apogamous
+transition from the gametophyte to sporophyte. The sporophyte
+may be considered to begin at the stage of nuclear association and
+end with the nuclear reduction in the basidium.</p>
+
+<table class="pic" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter" colspan="2"><img style="width:550px; height:705px" src="images/img342b.jpg" alt="" /></td></tr>
+<tr><td class="caption" colspan="2"><span class="sc">Fig. 16.</span>&mdash;<i>Puccinia graminis.</i></td></tr>
+
+<tr><td class="f90" style="width: 50%; vertical-align: top;">
+<p>A, Mass of teleutospores (<i>t</i>) on a
+    leaf of couch-grass.</p>
+
+<p><i>e</i>, Epidermis ruptured.</p>
+
+<p><i>b</i>, Sub-epidermal fibres. (After
+    De Bary.)</p></td>
+
+<td class="f90" style="width: 50%; vertical-align: top;">
+<p>B, Part of vertical section
+    through leaf of Berberis
+    vulgaris, with <i>a</i>, aecidium
+    fruits, <i>p</i>, peridium, and <i>sp</i>,
+    spermogonia. (After Sachs.)</p>
+
+<p>C, Mass of uredospores (<i>ur</i>),
+    with one teleutospore (<i>t</i>).</p>
+
+<p><i>sh</i>, Sub-hymenial hyphae. (After
+    De Bary.)</p></td></tr></table>
+
+<p class="pt2"><i>Uredineae.</i>&mdash;This is a large group of about 2000 forms. They are
+all intercellular parasites living mostly on the leaves of higher
+plants. Owing to the presence of oily globules of an orange-yellow
+or rusty-red colour in their hyphae and spores they are termed
+Rust-Fungi. They are distinguished from the other fungi and the
+rest of the Basidiales by the great variety of the spores and the
+great elaboration of the life-history to be found in many cases.
+Five different kinds of spores may be present&mdash;teleutospores,
+sporidia (= basidiospores), aecidiospores, spermatia and uredospores
+(fig. 16). The teleutospore, with the sporidia which arise from it,
+is always present, and the division into genera is based chiefly on
+its characters. The teleutospore puts forth on germination a four-celled
+structure, the promycelium or basidium, and this bears later
+four sporidia or basidiospores, one on each cell. When the sporidia
+infect a plant the mycelium so produced gives origin to aecidiospores
+and spermatia; the aecidiospores on infection produce a mycelium
+which bears uredospores and later teleutospores. This is the life-history
+of the most complicated forms, of the so-called <i>eu</i> forms.
+In the <i>opsis</i> forms the uredospores are absent, the mycelium from the
+aecidiospores producing directly the teleutospores. In <i>brachy</i> and
+<i>hemi</i> the aecidiospores are absent, the mycelium from the sporidia
+giving origin directly to the uredospores; the former possess spermatia,
+in the latter they are absent. In <i>lepto</i> and <i>micro</i> forms both
+aecidiospores and uredospores are absent, the sporidia producing a
+mycelium which gives rise directly to teleutospores; in the <i>lepto</i>
+forms the teleutospores can germinate directly, in the <i>micro</i> forms
+only after a period of rest. We have thus a series showing a progressive
+reduction in the complexity of the life-history, the <i>lepto</i> and
+<i>micro</i> forms having a life-history like that of the Basidiomycetes.
+The <i>eu</i> and <i>opsis</i> forms may exhibit the remarkable phenomenon
+of heteroecism, <i>i.e.</i> the dependence of the fungus on two distinct
+host-plants for the completion of the life-history. Heteroecism
+is very common in this group and is now known in over one hundred
+and fifty species. In all cases of heteroecism the sporidia infect
+one host leading to the production of aecidiospores and spermatia
+(if present), while the aecidiospores are only able to infect another
+<span class="pagenum"><a name="page343" id="page343"></a>343</span>
+host on which the uredospores (if present) and the teleutospores
+are developed. A few examples are appended:</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcc allb">Species.</td> <td class="tcc allb">Teleutospores on</td> <td class="tcc allb">Aecidiospores on</td></tr>
+
+<tr><td class="tcl lb rb"><i>Coleosporium Senecionis</i></td> <td class="tcl rb"><i>Pinus</i></td> <td class="tcl rb"><i>Senecio</i></td></tr>
+<tr><td class="tcl lb rb"><i>Melampsora Rostrupi</i></td> <td class="tcl rb"><i>Populus</i></td> <td class="tcl rb"><i>Mecurialis</i></td></tr>
+<tr><td class="tcl lb rb"><i>Pucciniastrum Goeppertiana</i></td> <td class="tcl rb"><i>Vaccinium</i></td> <td class="tcl rb"><i>Abies</i></td></tr>
+<tr><td class="tcl lb rb"><i>Gymnosporangium Sabinae</i></td> <td class="tcl rb"><i>Juniperus</i></td> <td class="tcl rb"><i>Pyrus</i></td></tr>
+<tr><td class="tcl lb rb"><i>Uromyces Pisi</i></td> <td class="tcl rb"><i>Pisum, &amp;c.</i></td> <td class="tcl rb"><i>Euphorbia</i></td></tr>
+<tr><td class="tcl lb rb"><i>Puccinia graminis</i></td> <td class="tcl rb"><i>Triticum, &amp;c.</i></td> <td class="tcl rb"><i>Berberis</i></td></tr>
+<tr><td class="tcl lb rb"><i>P. dispersa</i></td> <td class="tcl rb"><i>Secale, &amp;c.</i></td> <td class="tcl rb"><i>Anchusa</i></td></tr>
+<tr><td class="tcl lb rb"><i>P. coronata</i></td> <td class="tcl rb"><i>Agrostis</i></td> <td class="tcl rb"><i>Rhamnus</i></td></tr>
+<tr><td class="tcl lb rb"><i>P. Ari-Phalaridis</i></td> <td class="tcl rb"><i>Phalaris</i></td> <td class="tcl rb"><i>Arum</i></td></tr>
+<tr><td class="tcl lb rb"><i>P. Caricis</i></td> <td class="tcl rb"><i>Carex</i></td> <td class="tcl rb"><i>Urtica</i></td></tr>
+<tr><td class="tcl lb rb"><i>Cronartium Ribicola</i></td> <td class="tcl rb"><i>Ribes</i></td> <td class="tcl rb"><i>Pinus</i></td></tr>
+<tr><td class="tcl lb rb bb"><i>Chrysomyxa Rhododendri</i></td> <td class="tcl rb bb"><i>Rhododendron</i></td> <td class="tcl rb bb"><i>Picea</i></td></tr>
+</table>
+
+<p class="noind">Some of the Uredineae also exhibit the peculiarity of the development
+of biologic forms within a single morphological species, sometimes
+termed specialization of parasitism; this will be dealt with
+later under the section Physiology.</p>
+
+<table class="flt" style="float: right; width: 300px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:220px; height:426px" src="images/img343a.jpg" alt="" /></td></tr>
+<tr><td class="caption80">From Strasburger&rsquo;s <i>Lehrbuch der Botanik</i>,
+by permission of Gustav Fischer.</td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 17.</span>&mdash;<i>Phragmidium Violaceum.</i>
+(After Blackman.)</td></tr>
+<tr><td class="caption1">
+<p>A, Portion of a young aecidium.</p>
+
+<p><i>st</i>, Sterile cell.</p>
+
+<p><i>a</i>, Fertile cells; at <i>a</i><span class="su">2</span> the
+    passage of a nucleus from
+    the adjoining cell is seen.</p>
+
+<p>B, Formation of the first spore-mother-cell
+    (<i>sm</i>), from the
+    basal cell (<i>a</i>) of one of the
+    rows of spores.</p>
+
+<p>C, A further stage in which
+    from sm<span class="su">1</span> the first aecidiospore
+    (<i>a</i>) and the intercalary
+    cell (<i>z</i>) have arisen.</p>
+
+<p><i>sm</i><span class="su">2</span>, The second spore-mother-cell.</p>
+
+<p>D, Ripe aecidiospore</p></td></tr></table>
+
+<p><i>Cytology of Uredineae.</i>&mdash;The study of the nuclear behaviour of
+the cells of the Uredineae has thrown great light on the question of
+sexuality. This group like the rest of the Basidiales exhibits an
+association of nuclei at some
+point in its life-history, but
+unlike the case of the Basidiomycetes
+the point of association
+in the Uredineae is very well
+defined in all those forms which
+possess aecidiospores. We find
+thus that in the <i>eu</i> and <i>opsis</i>
+forms the association of nuclei
+takes place at the base of the
+aecidium which produces the
+aecidiospores. There we find
+an association of nuclei either
+by the fusion of two similar cells
+as described by Christmann or
+by the migration of the nucleus
+of a vegetative cell into a special
+cell of the aecidium. After this
+association the nuclei continue
+in the conjugate condition so
+that the aecidiospores, the uredospore-bearing
+mycelium, the
+uredospores and the young
+teleutospores all contain two
+paired nuclei in their cells (fig.
+17). Before the teleutospore
+reaches maturity the nuclei fuse,
+and the uninucleate condition
+then continues again until aecidium
+formation. In the <i>hemi</i>,
+<i>brachy</i>, <i>micro</i> and <i>lepto</i> forms,
+which possess no aecidium, we
+find that the association takes
+place at various points in the
+ordinary mycelium but always
+before the formation of the
+uredospores in the <i>hemi</i> and
+<i>brachy</i> forms, and before the
+formation of teleutospores in
+<i>micro</i> and <i>lepto</i> form. Whether
+the association of nuclei in the
+ordinary mycelium takes place
+by the migration of a nucleus
+from one cell to another or
+whether two daughter nuclei
+become conjugate in one cell,
+is not yet clear. The most
+reasonable interpretation of the
+spermatia is that they are
+abortive male cells. They have
+never been found to cause infection,
+and they have not the characters of conidia; the large
+size of their nuclei, the reduction of their cytoplasm and the
+absence of reserve material and their thin cell wall all point to their
+being male gametes. Although in the forms without aecidia the
+two generations are not sharply marked off from one another, we
+may look up the generation with single nuclei in the cells as the
+gametophyte and that with conjugate nuclei as the sporophyte.
+The subjoined diagram will indicate the relationship of the forms.</p>
+
+<p><i>Basidiomycetes.</i>&mdash;This group is characterized by its greatly reduced
+life-history as compared with that of the <i>eu</i> forms among the Uredineae.
+All the forms have the same life-history as the <i>lepto</i> forms
+of that group, so that there is no longer any trace of sexual organs.
+There is also a further reduction in that the basidium is not derived
+from a teleutospore but is borne directly on the mycelium. Formerly,
+before the relationship of promycelium and basidium were understood,
+the Uredineae were considered as quite independent of the
+Basidiomycetes. Later, however, these Uredineae were placed as a
+mere subdivision of the Basidiomycetes. Although the Uredineae
+clearly lead on to the Basidiomycetes, yet owing to their retaining
+in many cases definite traces of sexual organs they are clearly a more
+primitive group. Their marked parasitic habit also separates them
+off, so that they are best included with the Basidiomycetes in a larger
+cohort which may
+be called Basidiales.
+Most of
+Basidiomycetes
+are characterized
+by the large sporophore
+on which the
+basidia with its
+basidiospores are
+borne.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:500px; height:495px" src="images/img343b.jpg" alt="" /></td></tr>
+<tr><td class="tcl f80">From <i>Annals of Botany</i>, by permission of the Clarendon Press.</td></tr>
+<tr><td class="caption"><span class="sc">Fig. 18.</span></td></tr></table>
+
+<p>It must be
+clearly borne in
+mind that though
+the Basidiomycetes
+show no
+traces of differentiated
+sexual
+organs yet, like
+the <i>micro</i> and <i>lepto</i>
+forms of the Uredineae,
+they still
+show (in the association
+of nuclei
+and later fusion of
+nuclei in the basidium),
+a reduced
+fertilization which denotes their derivation, through the Uredineae,
+from more typically sexual forms. No one has yet made out in any
+form the exact way in which the association of nuclei takes place in the
+group. The mycelium is always found to contain conjugate nuclei
+before the formation of basidia, but the point at which the conjugate
+condition arises seems very variable. Miss Nichols finds that it
+occurs very soon after the germination of the spore in <i>Coprinus</i>, but
+no fusion of cells or migration of nuclei was to be observed.</p>
+
+<table class="pic" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter" colspan="2"><img style="width:600px; height:511px" src="images/img343c.jpg" alt="" /></td></tr>
+<tr><td class="caption" colspan="2"><span class="sc">Fig. 19.</span>&mdash;Amanita muscaria.</td></tr>
+
+<tr><td class="f90" style="width: 50%; vertical-align: top;">
+<p>A, The young plant.</p>
+<p>B, The mature plant.</p>
+<p>C, Longitudinal section of mature plant.</p>
+<p><i>p</i>, The <i>pileus</i>.</p></td>
+
+<td class="f90" style="width: 50%; vertical-align: top;">
+<p><i>g</i>, The gills.</p>
+<p><i>a</i>, The <i>annulus</i>, or remnant of <i>velum partiale</i>,</p>
+<p><i>v</i>, Remains of <i>volva</i> or <i>velum universale</i>.</p>
+<p><i>s</i>, The stalk.</p></td></tr></table>
+
+<p class="pt2"><i>Protobasidiomycetes.</i>&mdash;This, by far the smaller division of Basidiomycetes,
+includes those forms which have a septate basidium. There
+are three families&mdash;Auriculariaceae, Pilacreaceae and Tremellinaceae.
+The first named contains a small number of forms with the basidium
+divided like the promycelium of the Uredineae. They are characterized
+by their gelatinous consistence and large size of their sporophore.
+<i>Hirneola</i> (<i>Auricularia</i>) <i>Auricula-Judae</i> is the well-known
+Jew&rsquo;s Ear, so named from the resemblance of the sporophore to a
+human ear.</p>
+
+<p>The Pilacreaceae are a family found by Brefeld to contain the genus
+<i>Pilacre</i>. <i>P. Petersii</i> has a transversely divided basidium as in
+<i>Auriculariaceae</i>, but the basidia are surrounded with a peridium-like
+sheath. The <i>Tremellinaceae</i> are characterized by the possession of
+basidia which are divided by two <i>vertical</i> walls at right angles to
+one another. From each of the four segments in the case of <i>Tremella</i>
+a long outgrowth arises which reaches to the surface of the hymenium
+<span class="pagenum"><a name="page344" id="page344"></a>344</span>
+and bears the basidiospores. In <i>Dacryomyces</i> only two outgrowths
+and two spores are produced.</p>
+
+<p><i>Autobasidiomycetes</i>.&mdash;In this by far the larger division of the
+Basidiomycetes the basidia are undivided and the four basidiospores
+are borne on short sterigmata nearly always at the apex of the
+basidium. The group may be divided into two main divisions,
+<i>Hymenomycetes</i> and <i>Gasteromycetes</i>.</p>
+
+<table class="flt" style="float: right; width: 380px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:330px; height:269px" src="images/img344.jpg" alt="" /></td></tr>
+<tr><td class="caption1"><span class="sc">Fig.</span> 20.&mdash;<i>Agaricus mucidus</i>. Portion
+of hymenium. <i>s</i>, Sporidia; <i>st</i>, sterigmata;
+<i>g</i>, sterile cells; <i>c</i>, cystidium, with operculum
+<i>o</i>.</td></tr></table>
+
+<p><i>Hymenomycetes</i> are a very large group containing over 11,000
+species, most of which live in soil rich in humus or on fallen wood
+or stems, a few only being parasites. In the simplest forms (<i>e.g.</i>
+<i>Exobasidium</i>) the basidia are borne directly on the ordinary
+mycelium, but in the majority of cases the basidia are found developed
+in layers (hymenium) on special sporophores of characteristic
+form in the various groups. In these sporophores (such
+as the well-known toadstools and mushrooms where the ordinary
+vegetative mycelium is underground) we have structures specially
+developed for bearing the basidiospores and protecting them from
+rain, &amp;c., and for the distribution of the spores&mdash;see earlier part of
+article on distribution of spores (figs. 19 and 20). The underground
+mycelium in many cases
+spreads wider and wider
+each year, often in a
+circular manner, and the
+sporophores springing
+from it appear in the
+form of a ring&mdash;the so-called
+fairy rings. <i>Armillaria
+melleus</i> and
+<i>Polyporus annosus</i> are
+examples of parasitic
+forms which attack and
+destroy living trees,
+while <i>Merulius lacrymans</i> is the well-known
+&ldquo;dry rot&rdquo; fungus.</p>
+
+<p><i>Gasteromycetes</i> are
+characterized by having
+closed sporophores or
+fruit-bodies which only
+open after the spores are
+ripe and then often merely by a small pore. The fruit-bodies are of
+very various shapes, showing a differentiation into an outer <i>peridium</i>
+and an inner spore-bearing mass, the <i>gleba</i>. The gleba is usually
+differentiated into a number of chambers which are lined directly
+by the hymenium (basidial layer), or else the chambers contain an
+interwoven mass of hyphae, the branches of which bear the basidia.
+By the breaking down of the inner tissues the spores often come
+to lie as a loose powdery mass in the interior of the hollow fruit-body,
+mixed sometimes with a capillitium. The best-known genera
+are <i>Bovista, Lycoperdon</i> (puff-ball) <i>Scleroderma, Geaster</i> (earth-star,
+<i>q.v.</i>). In the last-named genus the peridium is double and the outer
+layer becomes ruptured and spreads out in the form of star-shaped
+pieces; the inner layer, however, merely opens at the apex by a
+small pore.</p>
+
+<p>The most complex members of the Gasteromycetes belong to the
+<i>Phalloideae</i>, which is sometimes placed as a distinct division of the
+Autobasidiomycetes. <i>Phallus impudicus</i>, the stink-horn, is occasionally
+found growing in woods in Britain. The fruit-body before it
+ruptures may reach the size of a hen&rsquo;s egg and is white in colour;
+from this there grows out a hollow cylindrical structure which can
+be distinguished at the distance of several yards by its disgusting
+odour. It is highly poisonous.</p>
+</div>
+
+<p><i>Physiology</i>.&mdash;The physiology of the fungi comes under the
+head of that of plants generally, and the works of Pfeffer, Sachs,
+Vines, Darwin and Klebs may be consulted for details. But
+we may refer generally here to certain phenomena peculiar to
+these plants, the life-actions of which are restricted and specialized
+by their peculiar dependence on organic supplies of carbon and
+nitrogen, so that most fungi resemble the colourless cells of higher
+plants in their nutrition. Like these they require water, small
+but indispensable quantities of salts of potassium, magnesium,
+sulphur and phosphorus, and supplies of carbonaceous and
+nitrogenous materials in different stages of complexity in the
+different cases. Like these, also, they respire oxygen, and are
+independent of light; and their various powers of growth,
+secretion, and general metabolism, irritability, and response to
+external factors show similar specific variations in both cases.
+It is quite a mistake to suppose that, apart from the chlorophyll
+function, the physiology of the fungus-cell is fundamentally
+different from that of ordinary plant-cells. Nevertheless,
+certain biological phenomena in fungi are especially pronounced,
+and of these the following require particular notice.</p>
+
+<div class="condensed">
+<p><i><span class="correction" title="amended from Parasatism">Parasitism</span>.</i> &mdash;Some fungi, though able to live as saprophytes,
+occasionally enter the body of living plants, and are thus termed
+facultative parasites. The occasion may be a wound (<i>e.g.</i> <i>Nectria</i>,
+<i>Dasyscypha</i>, &amp;c.), or the enfeeblement of the tissues of the host, or
+invigoration of the fungus, the mycelium of which then becomes
+strong enough to overcome the host&rsquo;s resistance (<i>Botrytis</i>). Many
+fungi, however, cannot complete their life-history apart from the
+host-plant. Such <i>obligate</i> parasites may be epiphytic (<i>Erysipheae</i>),
+the mycelium remaining on the outside and at most merely sending
+haustoria into the epidermal cells, or endophytic (<i>Uredineae</i>,
+<i>Ustilagineae</i>, &amp;c.), when the mycelium is entirely inside the organs
+of the host. An epiphytic fungus is not necessarily a parasite,
+however, as many saprophytes (moulds, &amp;c.) germinate and develop
+a loose mycelium on living leaves, but only enter and destroy the
+tissues after the leaf has fallen; in some cases, however, these
+saprophytic epiphytes can do harm by intercepting light and air
+from the leaf (<i>Fumago</i>, &amp;c.), and such cases make it difficult to
+draw the line between saprophytism and parasitism. Endophytic
+parasites may be intracellular, when the fungus or its mycelium
+plunges into the cells and destroys their contents directly (<i>Olpidium</i>,
+<i>Lagenidium</i>, <i>Sclerotinia</i>, &amp;c.), but they are far more frequently
+intercellular, at any rate while young, the mycelium growing in the
+lacunae between the cells (<i>Peronospora</i>, <i>Uredineae</i>) into which it
+may send short (<i>Cystopus</i>), or long and branched (<i>Peronospora
+Calotheca</i>) haustoria, or it extends in the middle lamella (<i>Ustilago</i>),
+or even in the solid substance of the cell-wall (<i>Botrytis</i>). No sharp
+lines can be drawn, however, since many mycelia are intercellular at
+first and subsequently become intracellular (<i>Ustilagineae</i>), and the
+various stages doubtless depend on the degrees of resistance which
+the host tissues are able to offer. Similar gradations are observed
+in the direct effect of the parasite on the host, which may be local
+(<i>Hemileia</i>) when the mycelium never extends far from the point of
+infection, or general (<i>Phytophthora</i>) when it runs throughout the
+plant. Destructive parasites rapidly ruin the whole plant-body
+(<i>Pythium</i>), whereas restrained parasites only tax the host slightly,
+and ill effects may not be visible for a long time, or only when the
+fungus is epidemic (<i>Rhytisma</i>). A parasite may be restricted during
+a long incubation-period, however, and rampant and destructive
+later (<i>Ustilago</i>). The latter fact, as well as the extraordinary
+fastidiousness, so to speak, of parasites in their choice of hosts or of
+organs for attack, point to reactions on the part of the host-plant,
+as well as capacities on that of the parasite, which may be partly
+explained in the light of what we now know regarding enzymes and
+chemotropism. Some parasites attack many hosts and almost any
+tissue or organ (<i>Botrytis cinerea</i>), others are restricted to one family
+(<i>Cystopus Candidus</i>) or genus (<i>Phytophthora infestans</i>) or even
+species (<i>Pucciniastrum Padi</i>), and it is customary to speak of root-parasites,
+leaf-parasites, &amp;c., in expression of the fact that a given
+parasite occurs only on such organs&mdash;<i>e.g.</i> <i>Dematophora necatrix</i> on
+roots, <i>Calyptospora Goeppertiana</i> on stems, <i>Ustilago Scabiosae</i> in
+anthers, <i>Claviceps purpurea</i> in ovaries, &amp;c. Associated with these
+relations are the specializations which parasites show in regard to
+the age of the host. Many parasites can enter a seedling, but are
+unable to attack the same host when older&mdash;<i>e.g.</i> <i>Pythium</i>, <i>Phytophthora
+omnivora</i>.</p>
+
+<p><i>Chemotropism.</i>&mdash;Taken in conjunction with Pfeffer&rsquo;s beautiful discovery
+that certain chemicals exert a distinct attractive influence
+on fungus hyphae (<i>chemotropism</i>), and the results of Miyoshi&rsquo;s
+experimental application of it, the phenomena of enzyme-secretion
+throw considerable light on the processes of infection and parasitism
+of fungi. Pfeffer showed that certain substances in definite concentrations
+cause the tips of hyphae to turn towards them; other
+substances, though not innutritious, repel them, as also do nutritious
+bodies if too highly concentrated. Marshall Ward showed that the
+hyphae of <i>Botrytis</i> pierce the cell-walls of a lily by secreting a cytase
+and dissolving a hole through the membrane. Miyoshi then demonstrated
+that if <i>Botrytis</i> is sown in a lamella of gelatine, and this
+lamella is superposed on another similar one to which a chemotropic
+substance is added, the tips of the hyphae at once turn from the
+former and enter the latter. If a thin cellulose membrane is interposed
+between the lamellae, the hyphae nevertheless turn chemotropically
+from the one lamella to the other and pierce the cellulose
+membrane in the process. The hyphae will also dissolve their way
+through a lamella of collodion, paraffin, parchment paper, elder-pith,
+or even cork or the wing of a fly, to do which it must excrete very
+different enzymes. If the membrane is of some impermeable
+substance, like gold leaf, the hyphae cannot dissolve its way through,
+but the tip finds the most minute pore and traverses the barrier
+by means of it, as it does a stoma on a leaf We may hence conclude
+that a parasitic hyphae pierces some plants or their stomata and
+refuses to enter others, because in the former case there are chemotropically
+attractive substances present which are absent from the
+latter, or are there replaced by repellent poisonous or protective
+substances such as enzymes or antitoxins.</p>
+
+<p><i>Specialization of Parasitism.</i>&mdash;The careful investigations of recent
+years have shown that in several groups of fungi we cannot be
+content to distinguish as units morphologically different species,
+but we are compelled to go deeper and analyse further the species.
+It has been shown especially in the <i>Uredineae</i> and <i>Erysiphaceae</i> that
+many forms which can hardly be distinguished morphologically,
+or which cannot be differentiated at all by structural characters, are
+not really homogeneous but consist of a number of forms which are
+<span class="pagenum"><a name="page345" id="page345"></a>345</span>
+sharply distinguishable by their infecting power. Eriksson found,
+for example, that the well-known species <i>Puccinia graminis</i> could be
+split up into a number of forms which though morphologically
+similar were physiologically distinct. He found that the species
+really consisted of six distinct races, each having a more or less
+narrow range of grasses on which it can live. The six races he named
+<i>P. graminis Secalis</i>, <i>Tritici</i>, <i>Avenae</i>, <i>Airae</i>, <i>Agrostis</i>, <i>Poae</i>. The
+first named will grow on rye and barley but not on wheat or oat.
+The form <i>Tritici</i> is the least sharply marked and will grow on wheat,
+barley, rye and oat but not on the other grasses. The form <i>Avenae</i>
+will grow on oat and many grasses but not on the other three cereals
+mentioned. The last three forms grow only on the genera <i>Aira</i>,
+<i>Agrostis</i> and <i>Poa</i> respectively. All these forms have of course their
+aecidium-stage on the barberry. The terms biologic forms, biological
+species, physiological species, physiological races, specialized forms
+have all been applied to these; perhaps the term biologic forms is
+the most satisfactory. A similar specialization has been observed
+by Marshall Ward in the <i>Puccinia</i> parasitic on species of <i>Bromus</i>,
+and by Neger, Marchal and especially Salmon in the Erysiphaceae.
+In the last-named family the single morphological species <i>Erysiphe
+graminis</i> is found growing on the cereals, barley, oat, wheat, rye
+and a number of wild grasses (such as <i>Poa</i>, <i>Bromus</i>, <i>Dactylis</i>). On
+each of these host-plants the fungus has become specialized so that
+the form on barley cannot infect the other three cereals or the wild
+grasses and so on. Just as the uredospores and aecidiospores both
+show these specialized characters in the case of <i>Puccinia graminis</i>
+so we find that both the conidia and ascospores of <i>E. graminis</i> show
+this phenomenon. Salmon has further shown in investigating the
+relation of <i>E. graminis</i> to various species of the genus, <i>Bromus</i>, that
+certain species may act as &ldquo;bridging species,&rdquo; enabling the transfer
+of a biologic form to a host-plant which it cannot normally infect.
+Thus the biologic form on <i>B. racemosus</i> cannot infect <i>B. commutatus</i>.
+If, however, conidia from <i>B. racemosus</i> are sown on <i>B. hordaceus</i>,
+the conidia which develop on that plant are now able to infect
+<i>B. commutatus</i>; thus <i>B. hordaceus</i> acts as a bridging species. Salmon
+also found that injury of a leaf by mechanical means, by heat, by
+anaesthetics, &amp;c., would affect the immunity of the plant and allow
+infection by conidia which was not able to enter a normal leaf. The
+effect of the abnormal conditions is probably to stop the production
+of, or weaken or destroy the protective enzymes or antitoxins, the
+presence of which normally confers immunity on the leaf.</p>
+
+<p><i>Symbiosis.</i>&mdash;The remarkable case of life in common first observed
+in lichens, where a fungus and an alga unite to form a compound
+organism&mdash;the lichen&mdash;totally different from either, has now been
+proved to be universal in these plants, and lichens are in all cases
+merely algae enmeshed in the interwoven hyphae of fungi (see
+LICHENS). This dualism, where the one constituent (alga) furnishes
+carbohydrates, and the other (fungus) ensures a supply of mineral
+matters, shade and moisture, has been termed <i>symbiosis</i>. Since
+then numerous other cases of symbiosis have been demonstrated.
+Many trees are found to have their smaller roots invaded by fungi
+and deformed by their action, but so far from these being injurious,
+experiments go to show that this mycorhiza (fungus-root) is
+necessary for the well-being of the tree. This is also the case with
+numerous other plants of moors and woodlands&mdash;<i>e.g.</i> Ericaceae,
+Pyrolaceae, Gentianaceae, Orchidaceae, ferns, &amp;c. Recent
+experiments have shown that the difficulties of getting orchid
+seeds to germinate are due to the absence of the necessary fungus,
+which must be in readiness to infect the young seedling immediately <span class="correction" title="added after">after</span>
+it emerges from the seed. The well-known failures with rhododendrons,
+heaths, &amp;c., in ordinary garden soils are also explained by
+the need of the fungus-infected peat for their roots. The rôle of the
+fungus appears to be to supply materials from the leaf-mould around,
+in forms which ordinary root-hairs are incapable of providing for
+the plant; in return the latter supports the fungus at slight expense
+from its abundant stores of reserve materials. Numerous other
+cases of symbiosis have been discovered among the fungi of fermentation,
+of which those between <i>Aspergillus</i> and yeast in saké
+manufacture, and between yeasts and bacteria in kephir and in the
+ginger-beer plant are best worked out. For cases of symbiosis see
+<span class="sc"><a href="#artlinks">Bacteriology</a></span>.</p>
+
+<p><span class="sc">Authorities.</span>&mdash;<i>General</i>: Engler and Prantl, <i>Die natürlichen
+Pflanzenfamilien</i>, i. Teil (1892 onwards); Zopf, <i>Die Pilze</i> (Breslau,
+1890); De Bary, <i>Comparative Morphology of Fungi</i>, &amp;c. (Oxford,
+1887); von Tafel, <i>Vergleichende Morphologie der Pilze</i> (Jena, 1892);
+Brefeld, <i>Unters. aus dem Gesamtgebiete der Mykologie</i>, Heft i. 13
+(1872-1905); Lotsy, <i>Vorträge über botanische Stammesgeschichte</i>
+(Jena, 1907). <i>Distribution</i>, &amp;c.: Cooke, <i>Introduction to the Study
+of Fungi</i> (London, 1895); Felix in <i>Zeitschr. d. deutsch. geologisch.
+Gesellsch.</i> (1894-1896); Staub, <i>Sitzungsber. d. bot. Sec. d. Kgl.
+ungarischen naturwiss. Gesellsch. zu Budapest</i> (1897). <i>Anatomy</i>,
+&amp;c.: Bommer, &ldquo;Sclerotes et cordons mycéliens,&rdquo; <i>Mém. de l&rsquo;Acad.
+Roy. de Belg.</i> (1894); Mangin, &ldquo;Observ. sur la membrane des
+mucorinées,&rdquo; <i>Journ. de Bot.</i> (1899); Zimmermann, <i>Die Morph.
+und Physiologie des Pflanzenzellkernes</i> (Jena, 1896); Wisselingh,
+&ldquo;Microchem. Unters. über die Zellwände d. Fungi,&rdquo; <i>Pringsh.
+Jahrb.</i> B. 31, p. 619 (1898); Istvanffvi, &ldquo;Unters. über die phys.
+Anat. der Pilze,&rdquo; <i>Prings. Jahrb.</i> (1896). <i>Spore Distribution</i>: Fulton,
+&ldquo;Dispersal of the Spores of Fungi by Insects,&rdquo; <i>Ann. Bot.</i> (1889);
+Falck, &ldquo;Die Sporenverbreitung bei den Basidiomyceten,&rdquo; <i>Beitr.
+zur Biol. d. Pflanzen</i>, ix. (1904). <i>Spores and Sporophores</i>: Zopf,
+<i>Die Pilze</i>; also the works of von Tafel and Brefeld. <i>Classification</i>:
+van Tieghem, <i>Journ. de bot.</i> p. 77 (1893), and the works of Brefeld,
+Engler and Prantl, von Tafel, Saccardo and Lotsy already cited,
+<i>Oomycetes</i>: Wager, &ldquo;On the Fertilization of <i>Peronospora parasitica</i>,&rdquo;
+<i>Ann. Bot.</i> vol. xiv. (1900); Stevens, &ldquo;The Compound
+Oosphere of <i>Albugo Bliti</i>,&rdquo; <i>Bot. Gaz.</i> vol. 28 (1899); &ldquo;Gametogenesis
+and Fertilization in <i>Albugo</i>,&rdquo; <i>ibid</i>. vol. 32 (1901);
+Miyake, &ldquo;The Fertilization of <i>Pythium de Baryanum</i>,&rdquo; <i>Ann. of Bot.</i>
+vol. xv. (1901); Trow, &ldquo;On Fertilization in the Saprolegnieae,&rdquo;
+<i>Ann. of Bot.</i> vol. xviii. (1904); Thaxter, &ldquo;New and Peculiar Aquatic
+Fungi,&rdquo; <i>Bot. Gaz.</i> vol. 20 (1895); Lagerheim, &ldquo;Unters. über die
+Monoblepharideae,&rdquo; <i>Bih. Svenska Vet. Acad. Handlingar</i>, 25.
+Afd. iii. (1900); Woronin, &ldquo;Beitrag zur Kenntnis der Monoblepharideen,&rdquo;
+<i>Mém. de l&rsquo;Acad. Imp. d. Sc. de St-Pétersbourg</i>, 8 sér.
+vol. 16 (1902). <i>Zygomycetes</i>: Harper, &ldquo;Cell-division in Sporangia
+and Asci,&rdquo; <i>Ann. Bot.</i> vol. xiii. (1899); Klebs, <i>Die Bedingungen der
+Fortpflanzung</i>, &amp;c. (Jena, 1896), and &ldquo;Zur Physiologie der Fortpflanzung&rdquo;
+<i>Prings. Jahr.</i> (1898 and 1899), &ldquo;Über <i>Sporodinia
+grandis</i>,&rdquo; <i>Bot. Zeit.</i> (1902); Falck, &ldquo;Die Bedingungen der Zygotenbildung
+bei Sporodinia grandis,&rdquo; Cohn&rsquo;s Beitr. z. Biol. d. Pflanzen,
+Bd. 8 (1902); Gruber &ldquo;Verhalten der Zellkerne in den Zygosporen
+von <i>Sporodinia grandis</i>,&rdquo; <i>Ber. d. deutschen bot. Ges.</i> Bd. 19 (1901);
+Blakeslee, &ldquo;Sexual Reproduction in the Mucorineae,&rdquo; <i>Proc. Am.
+Acad.</i> (1904); &ldquo;Zygospore germination in the Mucorineae,&rdquo; <i>Annales
+mycologici</i> (1906). <i>Ustilagineae</i>: Plowright, <i>British Uredineae and
+Ustilagineae</i> (London, 1889); Massee, <i>British Fungi</i> (Phycomycetes
+and Ustilagineae) (London, 1891); Brefeld, <i>Unters. aus dem
+Gesamtgeb. der Mykol.</i> Hefte xi. and xii.; and Falck, &ldquo;Die Bluteninfektion
+bei den Brandpilzen,&rdquo; ibid. Heft xiii. 1905; Dangeard, &ldquo;La
+Reproduction sexuelle des Ustilaginées,&rdquo; C.R., Oct. 9, 1893;
+Maire, &ldquo;Recherches cytologiques et taxonomiques sur les Basidiomyceten,&rdquo;
+<i>Annexé au Bull. de la Soc. Mycol. de France</i> (1902).
+<i>Saccharomycetaceae</i>: Jorgensen, <i>The Micro-organisms of Fermentation</i>
+(1899); Barker, <i>Ann. of Bot.</i> vol. xiv. (1901); &ldquo;On Spore-formation
+among the Saccharomycetes,&rdquo; <i>Journ. of the Fed. Institute
+of Brewing</i>, vol. 8 (1902); Guillermond, <i>Recherches cytologiques
+sur lés levures</i> (Paris, 1902); Hansen, <i>Centralbl. f. Bakt. u. Parasitenp.</i>
+Abt. ii. Bd. 12 (1904). <i>Exoascaceae</i>: Giesenhagen, &ldquo;<i>Taphrina,
+Exoascus, Magnusiella</i>&rdquo; (complete literature given), <i>Bot.
+Zeit.</i> Bd. 7 (1901). <i>Erysiphaceae</i>: Harper, &ldquo;Die Entwicklung des
+Perithecium bei <i>Sphaerotheca castagnei</i>,&rdquo; <i>Ber. d. deut bot Ges.</i> (1896);
+&ldquo;Sexual Reproduction and the Organization of the Nucleus in certain
+Mildews,&rdquo; <i>Publ. Carnegie Institution</i> (Washington, 1906); Blackman
+&amp; Fraser, &ldquo;Fertilization in <i>Sphaerotheca</i>,&rdquo; <i>Ann. of Bot.</i> (1905).
+<i>Perisporiaceae</i>: Brefeld, <i>Untersuchungen aus dem Gesamtgeb. der
+Mykol.</i> Heft 10 (1891); Fraser and Chamber, <i>Annales mycologici</i>
+(1907). <i>Discomycetes</i>: Harper, &ldquo;Über das Verhalten der Kerne bei
+Ascomyceten,&rdquo; <i>Jahr. f. wiss. Bot.</i> Bd. 29 (1890); &ldquo;Sexual Reproduction
+in <i>Pyronema confluens</i>,&rdquo; <i>Ann. of Bot.</i> 14 (1900); Claussen,
+&ldquo;Zur Entw. der Ascomyceten,&rdquo; Boudiera, Bot. Zeit. Bd. 63 (1905);
+Dangeard, &ldquo;Sur le <i>Pyronema confluens</i>,&rdquo; <i>Le Botaniste</i>, 9 série (1903)
+(and numerous papers in same journal earlier and later); Ramlow,
+&ldquo;Zur Entwick. von <i>Thelebolus stercoren</i>,&rdquo; <i>Bot. Zeit.</i> (1906); Woronin,
+&ldquo;Über die Sclerotienkrankheit der Vaccineen Beeren,&rdquo; <i>Mem. de
+l&rsquo;Acad. Imp. des Sciences de St-Pétersbourg</i>, 7 série, 36 (1888);
+Dittrich, &ldquo;Zur Entwickelungsgeschichte der Helvellineen,&rdquo; Cohn&rsquo;s
+<i>Beitr. z. Biol. d. Pflanzen</i> (1892). <i>Pyrenomycetes</i>: Fisch, &ldquo;Beitr.
+z. Entwickelungsgeschichte einiger Ascomyceten,&rdquo; <i>Bot. Zeit.</i>
+(1882); Frank, &ldquo;Über einige neue u. weniger bekannte Pflanzkrankh.,&rdquo;
+<i>Landw. Jahrb.</i> Bd. 12 (1883); Ward, &ldquo;<i>Onygena
+equina</i>, a horn-destroying fungus,&rdquo; <i>Phil. Trans.</i>, vol. 191
+(1899); Dawson, &ldquo;On the Biology of Poroniapunctata,&rdquo; Ann. of
+Bot. 14 (1900). <i>Tuberineae</i>: Buchholtz, &ldquo;Zur Morphologie u.
+Systematik der Fungi hypogaei,&rdquo; <i>Ann. Mycol.</i> Bd. 1 (1903);
+Fischer in Engler and Prantl, <i>Die natürlichen Pflanzenfamilien</i>
+(1896). <i>Laboulbeniineae</i>: Thaxter, &ldquo;Monograph of the Laboulbeniaceae,&rdquo;
+<i>Mem. Amer. Acad. of Arts and Sciences</i>, vol. 12 (1895).
+<i>Uredineae</i>: Eriksson and Henning, <i>Die Getreideroste</i> (Stockholm,
+1896); Eriksson, <i>Botan. Gaz.</i> vol. 25 (1896); &ldquo;On the Vegetative
+Life of some Uredineae,&rdquo; Ann. of Bot. (1905); Klebahn, <i>Die wirtwechselnden
+Rostpilze</i> (Berlin, 1904); Sapin-Trouffy, &ldquo;Recherches
+histologiques sur la famille des Urédinées,&rdquo; <i>Le Botaniste</i> (1896-1897);
+Blackman, &ldquo;On the Fertilization, Alternation of Generations and
+General Cytology of the Uredineae,&rdquo; <i>Ann. of Bot.</i> vol. 18 (1904);
+Blackman and Fraser, &ldquo;Further Studies on the Sexuality of Uredineae,&rdquo;
+<i>Ann. of Bot.</i> vol. 20 (1906); Christman, &ldquo;Sexual Reproduction
+of Rusts,&rdquo; <i>Ann. of Bot.</i> vol. 20 (1906); Ward, &ldquo;The
+Brooms and their Rust Fungus,&rdquo; <i>Ann. of Bot.</i> vol. 15 (1901).
+<i>Basidiomycetes</i>: Dangeard, &ldquo;La Reprod. sexuelle des Basidiomycètes,&rdquo;
+<i>Le Botaniste</i> (1894 and 1900); Maire, &ldquo;Recherches
+cytologiques et taxonomiques sur les Basidiomycètes,&rdquo; <i>Annexe du
+Bull. de la Soc. Mycol. de France</i> (1902); Möller, &ldquo;Protobasidiomyceten,&rdquo;
+<i>Schimper&rsquo;s Mitt. aus den Tropen</i>, Heft 8 (Jena, 1895);
+Nichols, &ldquo;The Nature and Origin of the Binucleated Cells in certain
+Basidiomycetes,&rdquo; <i>Trans. Wisconsin Acad. of Sciences</i>, vol. 15
+(1905); Wager, &ldquo;The Sexuality of the Fungi,&rdquo; <i>Ann. of Bot.</i> 13
+(1899); Woronin, &ldquo;<i>Exobasidium Vaccinii</i>,&rdquo; <i>Verh. Naturf. Ges. zu
+Freiburg</i>, Bd. 4 (1867). <i>Fermentation</i>: Buchner, &ldquo;Gährung ohne Hefezellen,&rdquo;
+<i>Bot. Zeit.</i> Bd. 18 (1898); Albert, <i>Cent. f. Bakt.</i> Bd. 17 (1901);
+<span class="pagenum"><a name="page346" id="page346"></a>346</span>
+Green, <i>The Soluble Ferments and Fermentation</i> (Cambridge, 1899).
+<i>Parasitism</i>: &ldquo;On some Relations between Host and Parasite,&rdquo;
+<i>Proc. Roy. Soc</i>. vol. 47 (1890); &ldquo;A Lily Disease,&rdquo; <i>Ann. of Botany</i>,
+vol. 2 (1888); Eriksson &amp; Hennings, <i>Die Getreideroste (vide supra</i>);
+Ward, &ldquo;On the Question of Predisposition and Immunity in Plants,&rdquo;
+<i>Proc. Cambridge Phil. Soc</i>. vol. 11 (1902); also <i>Annals of Bot</i>.
+vol. 16 (1902) and vol. 19 (1905); Neger, &ldquo;Beitr. z. Biol. d.
+Erysipheen&rdquo; <i>Flora</i>, Bde. 88 and 90 (1901-1902); Salmon, &ldquo;Cultural
+Experiments with &lsquo;Biologic Forms&rsquo; of the Erysiphaceae,&rdquo; <i>Phil.
+Trans</i>. (1904); &ldquo;On Erysiphe graminis and its adaptative parasitism
+within the genus, <i>Bromus</i>,&rdquo; <i>Ann. Mycol</i>. vol. 11 (1904), also <i>Ann.
+of Bot</i>. vol. 19 (1905). <i>Symbiosis</i>: Ward, &ldquo;The Ginger-Beer
+Plant,&rdquo; <i>Phil. Trans. Roy. Soc</i>. (1892); &ldquo;Symbiosis,&rdquo; <i>Ann. of Bot</i>. 13
+(1899); Shalk, &ldquo;Der Sinn der Mykorrhizenbildung,&rdquo; <i>Jahrb. f.
+wiss. Bot</i>. Bd. 34 (1900); Bernard, &ldquo;On some Different Cases of
+Germination,&rdquo; <i>Gardener&rsquo;s Chronicle</i> (1900); Pierce, <i>Publ. Univ.
+California</i> (1900).</p>
+</div>
+<div class="author">(H. M. W.; V. H. B.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">FUNJ<a name="ar74" id="ar74"></a></span> (<span class="sc">Funniyeh, Fung, Fungha</span>), a very mixed negroid
+race, occupying parts of Sennar and the hilly country to the
+south between the White and Blue Niles. They traditionally
+come from west of the White Nile and are affiliated by some to
+the Kordofan Nubas, by others, more justifiably, to the negro
+Shilluks. These Funj, who became the dominant race in Sennar
+in the 15th century, almost everywhere assimilated the speech,
+religion and habits of the Arabs settled in that region. Until
+the 19th century they were one of the most powerful of African
+peoples in the eastern Sudan. About the end of the 15th century
+they overthrew the kingdom of Aloa, between the two Niles,
+and conquered the neighbouring peoples of the Sudan, Nubia
+and even Kordofan. The Funj had mixed much with the Arabs
+before their conquests, and had been converted to Islam. But
+they were still in many ways savages, for James Bruce (who
+traversed the district in 1772) says that their most famous
+king, Malek-el-Gahman, preferred human liver to any other
+food, and the Belgian traveller E. Pruyssenaere (1826-1864)
+found them still performing pagan rites on their sacred Mount
+Gula. Ernst Marno declared that as late as 1870 the most
+southern branch of the race, the Boruns, a non-Arabic speaking
+tribe, were cannibals. The Funj kings were content with
+levying tribute on their neighbours, and in this loose way Shendi,
+Berber and Dongola were once tributary. The Arab viziers
+gradually absorbed all power, the Funj sovereignty becoming
+nominal; and in 1821 the Egyptians easily destroyed the Funj
+domination. To-day the Funj are few, and represent no real
+type. They are a bright, hospitable folk. Many of them are
+skilful surgeons and go far afield in their work. The fellahin,
+indeed, call surgeons &ldquo;Senaari&rdquo; (men of Sennar). See further
+<span class="sc"><a href="#artlinks">Sennar</a></span> and <span class="sc"><a href="#artlinks">Sudan</a></span> (Anglo-Egyptian).</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUNKIA<a name="ar75" id="ar75"></a></span>, in botany, a genus of rather handsome, hardy,
+herbaceous plants belonging to the natural order Liliaceae,
+and natives of China and Japan. They are tuberous, with
+broadly ovate or heart-shaped leaves and racemes of white or
+pale lilac, drooping, funnel-shaped flowers. They are useful
+for the borders of a shrubbery, the lawn or rock-work, or may
+be grown in pots for the greenhouse. The plants are propagated
+by dividing the crowns in autumn or when growth begins in
+spring.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUNNEL<a name="ar76" id="ar76"></a></span> (through an O. Fr. <i>founil</i>, found in Breton, from
+Lat. <i>infundibulum</i>, that through which anything is poured,
+from <i>fundere</i>, to pour), a vessel shaped like a cone having a small
+tube at the apex through which powder, liquid, &amp;c., may be
+easily passed into another vessel with a small opening. The
+term is used in metal-casting of the hole through which the
+metal is poured into a mould, and in anatomy and zoology of an
+<i>infundibulum</i> or funnel-shaped organ. The word is thus used
+generally of any shaft or passage to convey light, air or smoke,
+as of the chimney of an engine or a steam-boat, or the flue of an
+ordinary chimney. It is also used of a shaft or channel in rocks,
+and in the decoying of wild-fowl is applied to the cone-shaped
+passage leading from a pond and covered with a net, a &ldquo;funnel-net,&rdquo;
+into which the birds are decoyed.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUR<a name="ar77" id="ar77"></a></span> (connected with O. Fr. <i>forre</i>, a sheath or case; so &ldquo;an
+outer covering&rdquo;), the name specially given to the covering of
+the skin in certain animals which are natives of the colder
+climates, lying alongside of another and longer covering, called
+the overhair. The fur differs from the overhair, in that it is
+soft, silky, curly, downy and barbed lengthwise, while the
+overhair is straight, smooth and comparatively rigid. These
+properties of fur constitute its essential value for felting purposes,
+and mark its difference from wool and silk; the first, after some
+slight preparation by the aid of hot water, readily unites its
+fibres into a strong and compact mass; the others can best be
+managed by spinning and weaving.</p>
+
+<p>On the living animal the overhair keeps the fur filaments
+apart, prevents their tendency to felt, and protects them from
+injury&mdash;thus securing to the animal an immunity from cold and
+storm; while, as a matter of fact, this very overhair, though of
+an humbler name, is most generally the beauty and pride of the
+pelt, and marks its chief value with the furrier. We arrive
+thus at two distinct and opposite uses and values of fur. Regarded
+as useful for felt it is denominated staple fur, while with
+respect to its use with and on the pelt it is called fancy fur.</p>
+
+<p><i>History.</i>&mdash;The manufacture of fur into a felt is of comparatively
+modern origin, while the use of fur pelts as a covering for the
+body, for the couch, or for the tent is coeval with the earliest
+history of all northern tribes and nations. Their use was not
+simply a barbarous expedient to defend man from the rigours
+of an arctic winter; woven wool alone cannot, in its most perfect
+form, accomplish this. The pelt or skin is requisite to keep out
+the piercing wind and driving storm, while the fur and overhair
+ward off the cold; and &ldquo;furs&rdquo; are as much a necessity to-day
+among more northern peoples as they ever were in the days of
+barbarism. With them the providing of this necessary covering
+became the first purpose of their toil; subsequently it grew
+into an object of barter and traffic, at first among themselves,
+and afterwards with their neighbours of more temperate climes;
+and with the latter it naturally became an article of fashion,
+of ornament and of luxury. This, in brief, has been the history
+of its use in China, Tatary, Russia, Siberia and North America,
+and at present the employment of fancy furs among civilized
+nations has grown to be more extensive than at any former period.</p>
+
+<p>The supply of this demand in earlier times led to such severe
+competition as to terminate in tribal pillages and even national
+wars; and in modern times it has led to commercial ventures
+on the part of individuals and companies, the account of which,
+told in its plainest form, reads like the pages of romance. Furs
+have constituted the price of redemption for royal captives,
+the gifts of emperors and kings, and the peculiar badge of state
+functionaries. At the present day they vie with precious gems
+and gold as ornaments and garniture for wealth and fashion;
+but by their abundance, and the cheapness of some varieties,
+they have recently come within the reach of men of moderate
+incomes. The history of furs can be read in Marco Polo, as
+he grows eloquent with the description of the rich skins of the
+khan of Tatary; in the early fathers of the church, who lament
+their introduction into Rome and Byzantium as an evidence of
+barbaric and debasing luxury; in the political history of Russia,
+stretching out a powerful arm over Siberia to secure her rich
+treasures; in the story of the French occupation of Canada,
+and the ascent of the St Lawrence to Lake Superior, and the
+subsequent contest to retain possession against England; in
+the history of early settlements of New England, New York
+and Virginia; in Irving&rsquo;s <i>Astoria</i>; in the records of the Hudson&rsquo;s
+Bay Company; and in the annals of the fairs held at Nizhniy
+Novgorod and Leipzig. Here it may suffice to give some account
+of the present condition of the trade in fancy furs. The collection
+of skins is now chiefly a matter of private enterprise. Few, if
+any, monopolies exist.</p>
+
+<p><i>Natural Supplies.</i>&mdash;We are dependent upon the Carnivora,
+Rodentia, Ungulata and Marsupialia for our supplies of furs,
+the first two classes being by far of the greatest importance. The
+Carnivora include bears, wolverines, wolves, raccoons, foxes,
+sables, martens, skunks, kolinskis, fitch, fishers, ermines, cats,
+sea otters, fur seals, hair seals, lions, tigers, leopards, lynxes,
+jackals, &amp;c. The Rodentia include beavers, nutrias, musk-rats
+or musquash, marmots, hamsters, chinchillas, hares, rabbits,
+squirrels, &amp;c. The Ungulata include Persian, Astrachan, Crimean,
+<span class="pagenum"><a name="page347" id="page347"></a>347</span>
+Chinese and Tibet lambs, mouflon, guanaco, goats, ponies, &amp;c.
+The Marsupialia include opossums, wallabies and kangaroos.
+These, of course, could be subdivided, but for general purposes
+of the fur trade the above is deemed sufficient.</p>
+
+<p>The question frequently arises, not only for those interested
+in the production of fur apparel, but for those who derive so
+much comfort and pleasure from its use, whether the supply of
+fur-bearing animals is likely to be exhausted. Although it is
+a fact that the demand is ever increasing, and that some of the
+rarer animals are decreasing in numbers, yet on the other hand
+some kinds of furs are occasionally neglected through vagaries of
+fashion, which give nature an opportunity to replenish their
+source. These respites are, however, becoming fewer every day,
+and what were formerly the most neglected kinds of furs are
+becoming more and more sought after. The supply of some of
+the most valuable, such as sable, silver and natural black fox,
+sea otter and ermine, which are all taken from animals of a more
+or less shy nature, does very gradually decrease with persistent
+hunting and the encroachment of man upon the districts where
+they live, but the climate of these vast regions is so cold and
+inhospitable that the probabilities of man ever permanently
+inhabiting them in numbers sufficient to scare away or exterminate
+the fur-bearing wild animals is unlikely. Besides these
+there are many useful, though commonplace, fur-bearing animals
+like mink, musquash, skunk, raccoon, opossum, hamster, rabbit,
+hares and moles, that thrive by depredations upon cultivated
+land. Some of these are reared upon extensive wild farms.
+In addition there are domestic fur-bearing animals, such as
+Persian, Astrachan and Chinese lambs, and goats, easily bred
+and available.</p>
+
+<p>With regard to the rearing of the Persian lamb, there is a
+prevalent idea that the skins of the unborn lamb are frequently
+used; this, however, is a mistake. A few such skins have been
+taken, but they are too delicate to be of any service. The youngest,
+known as &ldquo;broadtails,&rdquo; are killed when a few days old, but for
+the well-developed curly fur, the lambs must be six or seven weeks
+old. During these weeks their bodies are covered with leather
+so that the fur may develop in close, light and clean curls. The
+experiment has been tried of rearing rare, wild, fur-bearing
+animals in captivity, and although climatic conditions and food
+have been precisely as in their natural environment, the fur has
+been poor in quality and bad in colour, totally unlike that taken
+from animals in the wild state. The sensation of fear or the restriction
+of movement and the obtaining of food without exertion
+evidently prevent the normal development of the creature.</p>
+
+<p>In mountainous districts in the more temperate zones some
+good supplies are found. Chinchillas and nutrias are obtained
+from South America, whence come also civet cats, jaguars,
+ocelots and pumas. Opossums and wallabies, good useful furs,
+come from Australia and New Zealand. The martens, foxes
+and otters imported from southern Europe and southern Asia,
+are very mixed in quality, and the majority are poor compared
+with those of Canada and the north.</p>
+
+<p>Certain characteristics In the skin reveal to the expert from
+what section of territory they come, but in classifying them it
+is considered sufficient to mention territories only.</p>
+
+<p>Some of the poorer sorts of furs, such as hamster, marmot,
+Chinese goats and lambs, Tatar ponies, weasels, kaluga, various
+monkeys, antelopes, foxes, otters, jackals and others from the
+warmer zones, which until recently were neglected on account
+of their inferior quality of colour, by the better class of the trade,
+are now being deftly dressed or dyed in Europe and America,
+and good effects are produced, although the lack of quality when
+compared with the better furs from colder climates which possess
+full top hair, close underwool and supple leathers, is readily
+manifest. It is only the pressure of increasing demand that makes
+marketable hard pelts with harsh brittle hair of nondescript
+hue, and these would, naturally, be the last to attract the notice
+of dealers.</p>
+
+<p>As it is impossible that we shall ever discover any new fur-bearing
+animals other than those we know, it behoves responsible
+authorities to enforce close seasons and restrictions, as to the
+sex and age, in the killing for the purpose of equalizing the
+numbers of the catches. As evidence of indiscriminate slaughter
+the case of the American buffaloes may be cited. At one time
+thousands of buffalo skins were obtainable and provided material
+for most useful coats and rugs for rough wear in cold regions,
+but to-day only a herd or so of the animals remain, and in
+captivity.</p>
+
+<p>The majority of animals taken for their fur are trapped or
+snared, the gun being avoided as much as possible in order that
+the coat may be quite undamaged. Many weary hours are
+spent in setting baits, traps and wires, and, frequently, when
+the hunter retraces his steps to collect the quarry it is only to
+find it gone, devoured by some large animal that has visited
+his traps before him. After the skins have been carefully
+removed&mdash;the sooner after death the better for the subsequent
+condition of the fur&mdash;they are lightly tacked out, pelt outwards,
+and, without being exposed to the sun or close contact with a
+fire, allowed to dry in a hut or shady place where there is some
+warmth or movement of air. With the exception of sealskins,
+which are pickled in brine, all raw skins come to the various
+trade markets simply dried like this.</p>
+
+<p><i>Quality and Colour.</i>&mdash;The best fur is obtained by killing
+animals when the winter is at its height and the colder the season
+the better its quality and colour. Fur skins taken out of season
+are indifferent, and the hair is liable to shed itself freely; a
+good furrier will, however, reject such faulty specimens in the
+manufacturing. The finest furs are obtained from the Arctic
+and northern regions, and the lower the latitude the less full and
+silky the fur, till, at the torrid zone, fur gives place to harsh hair
+without any underwool. The finest and closest wools are
+possessed by the amphibious Carnivora and Rodentia, viz. seals,
+otters, beavers, nutrias and musquash, the beauty of which is
+not seen until after the stiff water or top hairs are pulled out
+or otherwise removed. In this class of animal the underneath
+wool of the belly is thicker than that of the back, while the
+opposite is true of those found on the land. The sea otter, one
+of the richest and rarest of furs, especially for men&rsquo;s wear, is an
+exception to this unhairing process, which it does not require,
+the hair being of the same length as the wool, silky and bright,
+quite the reverse of the case of other aquatic animals.</p>
+
+<p>Of sealskins there are two distinct classes, the fur seals and the
+hair seals. The latter have no growth of fur under the stiff top
+hair and are killed, with few exceptions (generally of the marbled
+seals), on account of the oil and leather they yield. The best
+fur seals are found off the Alaska coast and down as far south
+as San Francisco.</p>
+
+<p>It is found that in densely wooded districts furs are darker in
+colour than in exposed regions, and that the quality of wool and
+hair is softer and more silky than those from bare tracts of country,
+where nature exacts from its creatures greater efforts to secure
+food, thereby developing stronger limbs and a consequently
+coarser body covering.</p>
+
+<p>As regards density of colour the skunk or black marten has
+the blackest fur, and some cats of the domestic kind, specially
+reared for their fur, are nearly black. Black bears have occasionally
+very black coats, but the majority have a brownish underwool.
+The natural black fox is a member of the silver fox
+family and is very rare, the skins bringing a high price. Most
+silver foxes have dark necks and in some the dark shade runs a
+quarter, half-way, or three-quarters, or even the whole length
+of the skin, but it is rather of a brownish hue. Some Russian
+sables are of a very dense bluish brown almost a black, which is
+the origin undoubtedly of the term &ldquo;sables,&rdquo; while some, from
+one district in particular, have a quantity of silver hairs, evenly
+interspersed in the fur, a peculiarity which has nothing to do
+with age. The best sea otters have very dark coats which are
+highly esteemed, a few with silver hairs in parts; where these
+are equally and evenly spread the skins are very valuable. Otters
+and beavers that run dark in the hair or wool are more valuable
+than the paler ones, the wools of which are frequently touched
+with a chemical to produce a golden shade. This is also done
+with nutrias after unhairing. The darker sorts of mink,
+<span class="pagenum"><a name="page348" id="page348"></a>348</span>
+musquash, raccoon and wolverine are more valuable than the
+paler skins.</p>
+
+<p><i>Collective Supplies and Sales.</i>&mdash;There are ten large American
+and Canadian companies with extensive systems for gathering
+the annual hauls of skins from the far-scattered trappers. These
+are the Hudson&rsquo;s Bay Co., Russian Fur Co., Alaska Commercial
+Co., North American Commercial Co., Russian Sealskin Co.,
+Harmony Fur Co., Royal Greenland Fur Co., American Fur Co.,
+Missouri Co. and Pacific Co. Most of the raw skins are forwarded
+to about half-a-dozen brokers in London, who roughly sort them
+in convenient lots, issuing catalogues to the traders of the world,
+and after due time for examination of the goods by intending
+purchasers, the lots are sold by public auction. The principal
+sales of general furs are held in London in January and March,
+smaller offerings being made in June and October; while the
+bulk of fur sealskins is sold separately in December. The
+Hudson&rsquo;s Bay Co.&rsquo;s sales take place before the others, and, as
+no reserves are placed on any lot, the results are taken as exactly
+indicating current values. While many buyers from America
+and Russia are personally in attendance at the sales, many more
+are represented by London and Leipzig agents who buy for them
+upon commission. In addition to the fur skins coming from
+North America vast numbers from Russia, Siberia, China, Japan,
+Australia and South America are offered during the same periods
+at public auction. Fairs are also held in Siberia, Russia and
+Germany for the distribution of fur skins as follows:&mdash;</p>
+
+<table class="ws f90" summary="Contents">
+<tr><td class="tcl">January:</td> <td class="tcl">Frankfort-on-the-Oder</td> <td class="tcl">Small collection of provincial produce,<br /> &emsp; such as otter, fox, fitch and marten.</td></tr>
+<tr><td class="tcl">February:</td> <td class="tcl">Irbit, Siberia</td> <td class="tcl">General Russian furs.</td></tr>
+<tr><td class="tcl">Easter:</td> <td class="tcl">Leipzig, Germany</td> <td class="tcl">General furs.</td></tr>
+<tr><td class="tcl">August:</td> <td class="tcl">Nizhniy Novgorod, Russia</td> <td class="tcl">Persian lamb and general furs.</td></tr>
+<tr><td class="tcl">August:</td> <td class="tcl">Kiakhta, Siberia</td> <td class="tcl">Chinese furs and ermine.</td></tr>
+<tr><td class="tcl">December:</td> <td class="tcl">Ishim, Siberia</td> <td class="tcl">Chiefly squirrels.</td></tr>
+</table>
+
+<p>Of course there are many transactions, generally in the cheaper
+and coarser kinds of furs, used only in central Europe, Russia
+and Asia which in no way interest the London market, and there
+are many direct consignments of skins from collectors in America
+and Russia to London, New York and Leipzig merchants. But
+the bulk of the fine furs of the world is sold at the large public
+trade auction sales in London. The chief exceptions are the
+Persian and Astrachan lambs, which are bought at the Russian
+fairs, and are dressed and dyed in Leipzig, and the ermine and
+Russian squirrels, which are dressed and manufactured into
+linings either in Russia or Germany before offered for sale to the
+wholesale merchants or manufacturers.</p>
+
+<p>The annual collection of fur skins varies considerably in
+quantity according to the demand and to the good or bad climatic
+conditions of the season; and it is impossible to give a complete
+record, as many skins are used in the country of their origin or
+exported direct to merchants. But a fairly exact statement of
+the numbers sold in the great public trade auction sales in
+London during the year 1905-1906 is herewith set out.</p>
+
+<table class="ws f90" summary="Contents">
+<tr><td class="tcc"><i>Year ending 31st of March 1906.</i></td> <td class="tcc">Total Number<br />of Skins.</td></tr>
+
+<tr><td class="tcl cl">Badger</td> <td class="tcr cl">28,634</td></tr>
+<tr><td class="tcl">Badger, Japanese</td> <td class="tcr">6,026</td></tr>
+<tr><td class="tcl cl">Bear</td> <td class="tcr cl">18,576</td></tr>
+<tr><td class="tcl">Beaver</td> <td class="tcr">80,514</td></tr>
+<tr><td class="tcl cl">Cat, Civet</td> <td class="tcr cl">157,915</td></tr>
+<tr><td class="tcl">Cat, House</td> <td class="tcr">126,703</td></tr>
+<tr><td class="tcl cl">Cat, Wild</td> <td class="tcr cl">32,253</td></tr>
+<tr><td class="tcl">Chinchilla (La Plata), known also as Bastard</td> <td class="tcr">43,578</td></tr>
+<tr><td class="tcl cl">Chinchilla Peruvian finest</td> <td class="tcr cl">5,603</td></tr>
+<tr><td class="tcl">Deer, Chinese</td> <td class="tcr">124,355</td></tr>
+<tr><td class="tcl cl">Ermine</td> <td class="tcr cl">40,641</td></tr>
+<tr><td class="tcl">Fisher</td> <td class="tcr">5,949</td></tr>
+<tr><td class="tcl cl">Fitch</td> <td class="tcr cl">77,578</td></tr>
+<tr><td class="tcl">Fox, Blue</td> <td class="tcr">1,893</td></tr>
+<tr><td class="tcl cl">Fox, Cross</td> <td class="tcr cl">10,276</td></tr>
+<tr><td class="tcl">Fox, Grey</td> <td class="tcr">59,561</td></tr>
+<tr><td class="tcl cl">Fox, Japanese</td> <td class="tcr cl">81,429</td></tr>
+<tr><td class="tcl">Fox, Kit</td> <td class="tcr">4,023</td></tr>
+<tr><td class="tcl cl">Fox, Red</td> <td class="tcr cl">158,961</td></tr>
+<tr><td class="tcl">Fox, Silver</td> <td class="tcr">2,510</td></tr>
+<tr><td class="tcl cl">Fox, White</td> <td class="tcr cl">27,463</td></tr>
+<tr><td class="tcl">Goats, Chinese</td> <td class="tcr">261,190</td></tr>
+<tr><td class="tcl cl">Hares</td> <td class="tcr cl">41,256</td></tr>
+<tr><td class="tcl">Kangaroo</td> <td class="tcr">7,115</td></tr>
+<tr><td class="tcl cl">Kid, Chinese linings and skins equal to</td> <td class="tcr cl">5,080,047</td></tr>
+<tr><td class="tcl">Kolinsky</td> <td class="tcr">114,251</td></tr>
+<tr><td class="tcl cl">Lamb, Mongolian linings and skins equal to</td> <td class="tcr cl">214,072</td></tr>
+<tr><td class="tcl">Lamb, Slink linings and skins equal to</td> <td class="tcr">167,372</td></tr>
+<tr><td class="tcl cl">Lamb, Tibet linings and skins equal to</td> <td class="tcr cl">794,130</td></tr>
+<tr><td class="tcl">Leopard</td> <td class="tcr">3,574</td></tr>
+<tr><td class="tcl cl">Lynx</td> <td class="tcr cl">88,822</td></tr>
+<tr><td class="tcl">Marmot, linings and skins equal to</td> <td class="tcr">1,600,600</td></tr>
+<tr><td class="tcl cl">Marten, Baum</td> <td class="tcr cl">4,573</td></tr>
+<tr><td class="tcl">Marten,  Japanese</td> <td class="tcr">16,461</td></tr>
+<tr><td class="tcl cl">Marten,  Stone</td> <td class="tcr cl">12,939</td></tr>
+<tr><td class="tcl">Mink, Canadian and American</td> <td class="tcr">299,254</td></tr>
+<tr><td class="tcl cl">Mink, Japanese</td> <td class="tcr cl">360,373</td></tr>
+<tr><td class="tcl">Mouflon</td> <td class="tcr">23,594</td></tr>
+<tr><td class="tcl cl">Musk-rat or Musquash, Brown</td> <td class="tcr cl">5,126,339</td></tr>
+<tr><td class="tcl">Musk-rat or Musquash, Black</td> <td class="tcr">41,788</td></tr>
+<tr><td class="tcl cl">Nutria</td> <td class="tcr cl">82,474</td></tr>
+<tr><td class="tcl">Opossum, American</td> <td class="tcr">902,065</td></tr>
+<tr><td class="tcl cl">Opossum,  Australian</td> <td class="tcr cl">4,161,685</td></tr>
+<tr><td class="tcl">Otter, River</td> <td class="tcr">21,235</td></tr>
+<tr><td class="tcl cl">Otter, Sea</td> <td class="tcr cl">522</td></tr>
+<tr><td class="tcl">Raccoon</td> <td class="tcr">310,712</td></tr>
+<tr><td class="tcl cl">Sable, Canadian and American</td> <td class="tcr cl">97,282</td></tr>
+<tr><td class="tcl">Sable, Japanese</td> <td class="tcr">556</td></tr>
+<tr><td class="tcl cl">Sable,  Russian</td> <td class="tcr cl">26,399</td></tr>
+<tr><td class="tcl">Seals, Fur</td> <td class="tcr">77,000</td></tr>
+<tr><td class="tcl cl">Seals, Hair</td> <td class="tcr cl">31,943</td></tr>
+<tr><td class="tcl">Skunk</td> <td class="tcr">1,068,408</td></tr>
+<tr><td class="tcl cl">Squirrel</td> <td class="tcr cl">194,596</td></tr>
+<tr><td class="tcl">Squirrel Linings each averaging 126 skins</td> <td class="tcr">1,982,736</td></tr>
+<tr><td class="tcl cl">Tiger</td> <td class="tcr cl">392</td></tr>
+<tr><td class="tcl">Wallaby</td> <td class="tcr">60,956</td></tr>
+<tr><td class="tcl cl">Wolf</td> <td class="tcr cl">56,642</td></tr>
+<tr><td class="tcl">Wolverine</td> <td class="tcr">1,726</td></tr>
+<tr><td class="tcl cl">Wombat</td> <td class="tcr cl">193,625</td></tr>
+</table>
+
+<p>A brief account of the different qualities of the pelts, with
+some general remarks as to their customary uses, follows. The
+prices quoted are subject to constant fluctuation and represent
+purely trade prices for bulk, and it should be explained that the
+very great variations are due to different sizes, qualities and
+colours, and moreover are only <i>first cost</i>, before skins are dressed
+and prepared. These preparations are in some cases expensive,
+and there is generally a considerable percentage of waste. The
+prices cannot be taken as a guide to the wholesale price of a
+single and finished skin, but simply as <i>relative</i> value.</p>
+
+<p>The fullest and darkest skins of each kind are the most valuable,
+and, in cases of bluish grey or white, the fuller, clearer and
+brighter are the more expensive. A few albinos are found in
+every species, but whatever their value to a museum, they are of
+little commercial importance. Some odd lots of skins arrive
+designated simply as &ldquo;sundries,&rdquo; so no classification is possible,
+and this will account for the absence of a few names of skins of
+which the imports are insignificant in quantity, or are received
+direct by the wholesale merchants.</p>
+
+<div class="condensed">
+<p class="pt2 center"><i>Names, Qualities and Uses of Pelts.</i><a name="fa1h" id="fa1h" href="#ft1h"><span class="sp">1</span></a></p>
+
+<p><span class="sc">Astrachan.</span>&mdash;See <i>Lambs</i>, below.</p>
+
+<p><span class="sc">Badger.</span>&mdash;Size 2 × 1 ft. American sorts have coarse thick underwool
+of a pale fawn or stone colour with a growth of longer black
+and white hairs, 3 or 4 in. long; a very durable but clumsy fur.
+The best skins are exported to France, Spain and Italy, and used for
+carriage rugs and military purposes. Asiatic, including Japanese,
+skins are more woolly. Russian and Prussian kinds are coarser and
+darker, and used mostly for brush trade. Value 6d. to 19s.</p>
+
+<p><span class="sc">Bear, Australian.</span>&mdash;See <i>Wombat</i>, below.</p>
+
+<p><span class="sc">Bear, Black.</span>&mdash;Size 6 × 3 ft. Fine dark brown underwool with
+bright black and flowing top hair 4 in. long. Cubs are nearly as long
+in the hair although only about half the size and not only softer and
+better, but have the advantage of being very much lighter in pelt.
+Widely distributed in North America, the best come from Canada,
+are costly and are used for military caps, boas, muffs, trimmings,
+carriage rugs and coachmen&rsquo;s capes, and the fur wears exceedingly
+well. Value 17s. 6d. to 86s. Those from East India and warm
+climates are harsh, poor and only fit for floor rugs.</p>
+
+<p><span class="sc">Bear, Brown.</span>&mdash;Size 6 × 3 ft. Similar in quality to the black,
+but far more limited in number; the colours range from light yellow
+to a rich dark brown. The best come from Hudson Bay territory
+and are valuable. Used for muffs, trimmings, boas, and carriage
+<span class="pagenum"><a name="page349" id="page349"></a>349</span>
+rugs. Inferior sorts, almost grizzly in effect and some very pale,
+are found in Europe and Asia and are mostly used locally. In India
+there is a species called Isabelline bear, which was formerly imported
+to Great Britain, but does not now arrive in any quantity worth
+mentioning. Value 10s. 6d. to 60s., Isabelline sort 10s. 6d. to 78s.</p>
+
+<p><span class="sc">Bear, Grizzly.</span>&mdash;Size 8 × 4 ft. Coarse hair, heavy pelt, mostly
+dark yellowish and brown colours, only found in western parts of
+United States, Russia and Siberia. Used as carriage rugs and floor
+rugs, most durable for latter purpose and of fine effect. They are
+about half the value of brown bear. Value 15s. to 54s.</p>
+
+<p><span class="sc">Bear, Isabelline.</span>&mdash;See <i>Bear</i>, <i>Brown</i>, above.</p>
+
+<p><span class="sc">Bear, White.</span>&mdash;Size 10 × 5 ft. The largest of all bears. Short
+close hair except on flanks, colour white to yellow. An inhabitant
+of the Arctic circle, best from Greenland. Used for floor rugs, very
+durable; and very white specimens are valuable. Value 20s. to 520s.</p>
+
+<p><span class="sc">Beaver.</span> Size 3 × 2 ft. The largest of rodents, it possesses a
+close underwool of bluish-brown hue, nearly an inch in depth, with
+coarse, bright, black or reddish-brown top hair, 3 in. long. Found
+widely in North America. After being unhaired the darkest wools
+are the most valuable, although many people prefer the bright,
+lighter brown tones. Used for collars, cuffs, boas, muffs, trimmings,
+coat linings and carriage aprons, and is of a most durable nature, in
+addition to having a rich and good appearance. Value 10s. to
+39s. 6d.</p>
+
+<p><span class="sc">Broadtail.</span>&mdash;See <i>Lambs</i>, below.</p>
+
+<p><span class="sc">Caracal.</span>&mdash;A small lynx from India, the fur very poor, seldom
+imported.</p>
+
+<p><span class="sc">Caracul.</span>&mdash;See <i>Goats</i> and <i>Lambs</i>, below.</p>
+
+<p><span class="sc">Cat, Civet.</span>&mdash;Size 9 × 4½ in., short, thick and dark underwool
+with silky black top hair with irregular and unique white markings.
+It is similar to skunk, but is much lighter in weight, softer and less
+full, without any disagreeable odour. Used for coat linings it is
+very warm and durable. A few come from China, but the fur is
+yellowish-grey, slightly spotted and worth little. Value 1s. 1d.
+to 1s. 11d.</p>
+
+<p><span class="sc">Cat, House, &amp;c.</span>&mdash;18 × 9 in., mostly black and dark brown,
+imported from Holland, Bavaria, America and Russia, where they
+are reared for their coats. The best, from Holland, are used for coat
+linings. Although in colour, weight and warmth they are excellent,
+the fur is apt to become loose and to fall off with friction of wear.
+The black are known as genet, although the true genet is a spotted
+wild cat. Wild sorts of the tabby order are coarser, and not so good
+and silky in effect as when domestically reared. Value of the
+black sorts 2d. to 3s. Wild 9d. to 14s. Some small wild cats, very
+poor flat fur of a pale fawn colour with yellow spots, are imported
+from Australia and used for linings. Value 5½d. to 1s. 1d.</p>
+
+<p><span class="sc">Cheetah.</span>&mdash;Size of a small leopard and similar in colour, but has
+black spots in lieu of rings. Only a few are now imported, which are
+used for mats. Value 2s. 6d. to 18s.</p>
+
+<p><span class="sc">Chinchilla, Peruvian</span> and <span class="sc">Bolivian.</span>&mdash;Size 12 × 7 in., fur 1 to
+1¼ in. deep. Delicate blue-grey with black shadings, one of nature&rsquo;s
+most beautiful productions, though not a durable one. Used for
+ladies&rsquo; coats, stoles, muffs, hats and trimmings. Yearly becoming
+scarcer and most costly. Value 8s. 6d. to 56s. 8d.</p>
+
+<p><span class="sc">Chinchilla, La Plata</span>, incorrectly named and known in the trade
+as &ldquo;bastard chinchilla,&rdquo; size 9 × 4 in., in a similar species, but owing
+to lower altitudes and warmer climatic conditions of habitation
+is smaller, with shorter and less beautiful fur, the underwool colour
+being darker and the top colour less pure. Used exactly as the
+better kind, and the picked skins are most effective. As with the
+best sort it is not serviceable for constant wear. Value 4s. 2d. to
+27s. 6d.</p>
+
+<p><span class="sc">Chinchillone.</span>&mdash;Size 13 × 8 in., obtained also from South America.
+Fur is longer and weaker and poorer and yellower than chinchilla.
+Probably a crossbred animal, very limited importation. Value
+3s. 6d. to 16s. 8d.</p>
+
+<p><span class="sc">Deer, Chinese</span> and <span class="sc">East Indian.</span>&mdash;Small, light, pelted skins,
+the majority of which are used for mats. Reindeer and other
+varieties are of little interest for use other than trophy mats.
+Thousands are taken for the leather trade. Value of Chinese 1s. 2d.
+to 1s. 6d. each.</p>
+
+<p><span class="sc">Dog.</span>&mdash;The only dogs that are used in the fur trade in civilized
+countries are those imported from China, which are heavy and
+coarse, and only used in the cheaper trade, chiefly for rugs. Value
+6d. to 1s.</p>
+
+<p><span class="sc">Dog Wolf.</span>&mdash;See <i>Wolf</i>, below.</p>
+
+<p><span class="sc">Ermine.</span>&mdash;Size 12 × 2½ in. Underwool short and even, with a shade
+longer top hair. Pelt light and close in texture, and durable. In
+the height of winter the colour is pure white with exception of the
+tip of tail, which is quite black. Supplies are obtained from Siberia
+and America. Best are from Ishim in Siberia. Used for cloak
+linings, stoles, muffs and trimmings, also for embellishment of
+British state, parliamentary and legal robes. When this fur is
+symmetrically spotted with black lamb pieces it is styled miniver,
+in which form it is used at the grand coronation functions of British
+sovereigns. Value 1s. 3d. to 8s. 6d.</p>
+
+<p><span class="sc">Fisher.</span>&mdash;Size 30 × 12 in., tail 12 to 18 in. long, the largest of the
+martens; has a dark shaded deep underwool with fine, glossy, dark
+and strong top hair 2 in. or more long. Best obtained from British
+America. The tails are almost black and make up most handsomely
+into trimmings, muffs, &amp;c. Tails worked separately in these forms are
+as rich and fine and more durable than any other fur suitable for a
+like purpose. The fur of the skin itself is something like a dark
+silky raccoon, but is not as attractive as the tails. Value 12s. to 46s.</p>
+
+<p><span class="sc">Fitch.</span>&mdash;Size 12 × 3 in., of the marten species, also known as the
+pole cat. Yellow underwool 1/3 in. deep, black top hair, 1½ to 1¾ in.
+long, very fine and open in growth, and not close as in martens.
+Largest skins come from Denmark, Holland and Germany. The
+Russian are smaller, but more silky and, as now dyed, make a cheap
+and fair substitute for sable. They are excellent for linings of
+ladies&rsquo; coats, being of light weight and fairly strong in the pelt.
+English mayors&rsquo; and civic officials&rsquo; robes are frequently trimmed
+with this fur in lieu of sable. Value of the German variety 2s. to
+5s. 6d. and of the Russian 7d. to 1s. 4d.</p>
+
+<p><span class="sc">Fox, Blue.</span>&mdash;Size 24 × 8 in. Underwool thick and long. Top
+hair fine and not so plentiful as in other foxes. Found in Alaska,
+Hudson Bay territory, Archangel and Greenland. Although called
+blue, the colour is a slaty or drab tone. Those from Archangel are
+more silky and of a smoky bluish colour and are the most valuable.
+These are scarce and consequently dear. The white foxes that are
+dyed smoke and celestial blue are brilliant and totally unlike the
+browner shades of this fox. Value 34s. to 195s.</p>
+
+<p><span class="sc">Fox, Common.</span>&mdash;The variation of size and quality is considerable,
+and the colour is anything from grey to red. In Great Britain the
+animal is now only regarded for the sport it provides. On the
+European continent, however, some hundreds of thousands of skins,
+principally German, Russian and Norwegian, are sold annually,
+for home use, and for dyeing and exportation, chiefly to the United
+States. The qualities do not compare with those species found in
+North America and the Arctic circle. The Asiatic, African and
+South American varieties are, with the exception of those taken in
+the mountains, poorly furred and usually brittle and therefore of no
+great service. No commercial value can be quoted.</p>
+
+<p><span class="sc">Fox, Cross.</span>&mdash;Size 20 × 7 in., are about as large as the silver and
+generally have a pale yellowish or orange tone with some silvery
+points and a darkish cross marking on the shoulders. Some are very
+similar to the pale red fox from the North-West of America and a
+few are exceptionally large. The darkest and best come from
+Labrador and Hudson Bay, and the ordinary sorts from the north-west
+of the United States and, as with silver and other kinds, the
+quality is inferior when taken from warmer latitudes. Value 10s. 6d.
+to 60s.</p>
+
+<p><span class="sc">Fox, grey.</span>&mdash;Size 27 × 10 in. Has a close dark drab underwool
+with yellowish grizzly, grey, regular and coarse top hair. The
+majority used for the trade come from Virginia and the southern
+and western parts of the United States. Those from the west are
+larger than the average, with more fur of a brighter tone. The fur
+is fairly serviceable for carriage rugs, the leather being stout, but its
+harshness of quality and nondescript colour does not contribute to
+make it a favourite. Value 9d. to 4s. 9d.</p>
+
+<p><span class="sc">Fox, Japanese.</span>&mdash;See <i>Fox, Red</i>, and <i>Raccoon</i>, below.</p>
+
+<p><span class="sc">Fox, Kit.</span>&mdash;Size 20 × 6 in. The underwool is short and soft, as
+is also the top hair, which is of very pale grey mixed with some
+yellowish-white hair. It is the smallest of foxes, and is found in
+Canada and the northern section of the United States. It is similar
+in colour and quality to the prairie fox and to many kinds from the
+warmer zones, such as from Turkey, eastern Asia and elsewhere.
+Value 1s. 3d. to 5s. 6d.</p>
+
+<p><span class="sc">Fox, Red.</span>&mdash;Size 24 × 8 in., though a few kinds are much larger.
+The underwool is long and soft and the hair plentiful and strong.
+It is found widely in the northern parts of America and in smaller
+numbers south of the United States, also in China, Japan and
+Australia. The colours vary from pale yellowish to a dark red,
+some being very brilliant. Those of Kamschatka are rich and fine in
+quality. Farther north, especially near the sea, the fur is coarse.
+Where the best coloured skins are not used for carriage rugs they are
+extensively dyed, and badger and other white hairs are inserted
+to resemble silver fox. They are also dyed a sable colour. The
+skins, being the strongest of foxes&rsquo;, both in the fur and pelt, are
+serviceable. The preparations in imitation of the natural black and
+silver sorts are very good and attractive. Value 1s. to 41s.</p>
+
+<p><span class="sc">Fox, Silver.</span> Size 30 × 10 in. Underwool close and fine. Top
+hair black to silvery, 3 in. long. The fur upon the necks usually
+runs dark, almost black, and in some cases the fur is black half-way
+down the length of the skin, in rarer cases three-quarters of the
+length and, in the most exceptional instances, the whole length,
+and when this is the case they are known as &ldquo;Natural Black Foxes&rdquo;
+and fetch enormous prices. The even silvery sorts are highly
+esteemed, and the fur is one of the most effective and precious.
+The finest are taken in Labrador. The farther south they are found,
+the poorer and coarser the fur. The brush has invariably a white
+tip. Value £1 to £320.</p>
+
+<p><span class="sc">Fox, White.</span>&mdash;Size 20 × 7 in. Animals of this species are generally
+small in size and inhabit the extreme northern sections of Hudson
+Bay, Newfoundland, Greenland, Labrador and Siberia. The
+Canadian are silky in nature and inclined to a creamy colour, while
+the Siberian are more woolly and rather whiter. Those taken in
+central Asia near or in Chinese territory are poorer and yellowish.
+The underwool in all sorts is generally of a bluish-grey tone, but the
+top hair in the depth of winter is usually full enough in quantity to
+<span class="pagenum"><a name="page350" id="page350"></a>350</span>
+hide any such variation. Those skins in which the underwool is
+quite white are rare and much more expensive. In summer specimens
+of this species, as with other white furred animals, have slightly
+discoloured coats. The skins that are not perfectly white are dyed
+jet black, dark or light smoke, violet-blue, blue-grey, and also in
+imitation of the drab shades of the natural blue. Value 18s. to 66s.</p>
+
+<p><span class="sc">Genet.</span>&mdash;Size 10 × 4 in. The genet proper is a small white spotted
+cat found in Europe, but the quantity is too small to be of commercial
+interest. The name has been adopted for the black cats used so
+much in the trade. (See <i>Cats</i>, above.) Value 1s. to 6s. 6d.</p>
+
+<p><span class="sc">Goats.</span>&mdash;Size varies greatly. The European, Arabian and East
+Indian kinds are seldom used for rugs, the skins are chiefly dressed
+as leather for books and furniture, and the kids for boots and gloves,
+and the finer wool and hair are woven into various materials. Many
+from Russia are dyed black for floor and carriage rugs; the hair is
+brittle, with poor underwool and not very durable; the cost, however,
+is small. The Chinese export thousands of similar skins in black,
+grey and white, usually ready dressed and made into rugs of two
+skins each. A great many are dyed black and brown, in imitation
+of bear, and are used largely in the western parts of the United
+States and Canada for sleigh and carriage rugs. Many are used for
+their leather. Thousands of the kids are also dyed black and worked
+into cross-shaped pieces, in which shape they are largely exported
+to Germany, France, Great Britain and America, and sold by the
+retail as caracal, kid or caracul. The grey ones are in good demand
+for motor coats. The word caracul has been adopted from the
+Turkish and signifies black-eared. See also <i>Lambs, caracul</i>. Value
+of Chinese white 3s. 6d. to 6s. 6d.: grey, 4s. to 6s. 9d.</p>
+
+<p>The Angora from the heights of central Asia Minor has curly,
+fleecy, silky, white wool, 4 to 7 in. long. The fur is not used in Great
+Britain, as formerly, and the greater quantity, known as mohair,
+is now imported for purposes of weaving. This species of goat was
+some years since introduced into Cape Colony, but its wool is not
+so good as the Asiatic breed. Good business, however, is done with
+the product, but chiefly for leather. Value 4s. to 12s. 6d.</p>
+
+<p>The Mongolian goat has a very soft silk underwool, and after the
+long top hair is removed it is dressed and imported and erroneously
+named mouflon. The colour is a light fawn, but it is so pale that it
+lends itself to be dyed any colour. It was popular some years since
+in the cheaper trade, but it is not now much seen in England. Value
+2s. to 6s.</p>
+
+<p>The Tibet goat is similar to the Angora in the fineness of its wool,
+and many are used in the making of cashmere shawls. The Tibet
+lamb so largely imported and used for children&rsquo;s wear is often miscalled
+Tibet goat. Value 3s. to 7s. 6d.</p>
+
+<p><span class="sc">Guanaco.</span>&mdash;Size 30 × 15 in. Is a species of goat found in Patagonia
+and other parts of South America. It has a very long neck and
+exceedingly soft woolly fur of a light reddish-fawn colour with very
+white flanks. It is usually imported in small quantities, native
+dressed, and ready made into rugs. The dressing is hard and
+brittle. If the skins are dressed in Europe they afford a very comfortable
+rug, though a very marked one in effect. They have a
+similar wool to the vicuna, but coarser and redder; both are largely
+used in South America. Value 1s. to 4s. 6d.</p>
+
+<p><span class="sc">Hamster.</span>&mdash;Size 8 × 3½ in. A destructive rodent, is found in
+great numbers in Russia and Germany. The fur is very flat and poor,
+of a yellowish pale brown with a little marking of black. Being
+of a light weight it is used for linings. Value 3d. to 1s.</p>
+
+<p><span class="sc">Hare.</span>&mdash;Size 24 × 9 in. The common hare of Europe does not
+much interest the furrier, the fur being chiefly used by makers of
+hatters&rsquo; felt. The white hares, however, of Russia, Siberia and other
+regions in the Arctic circle are very largely used in the cheaper trade
+of Europe, America and the British colonies. The fur is of the
+whitest when killed in winter, and that upon the flanks of the animal
+is very much longer than that upon its back. The flanks are usually
+cut off and made into muffs and stoles. The hair is, however, brittle
+and is not at all durable. This fur is dyed jet black and various
+shades of brown and grey, and manufactured into articles for the
+small drapers and for exportation. The North American hares
+are also dyed black and brown and used in the same way. Value
+of white 2d. to 5d.</p>
+
+<p><span class="sc">Jackal.</span>&mdash;Size 2 to 3 ft. long. Is found in India and north and
+south Africa. Indian are light brown and reddish, those from the
+Cape are dark grey and rather silvery. Few are imported. Fur
+generally poor and harsh, only suitable for carriage rugs. Value
+1s. to 3s. 6d.</p>
+
+<p><span class="sc">Jaguar.</span>&mdash;Size 7 to 10 ft. long. Is found in Mexico and British
+Honduras. The markings are an irregular ring formation with a
+spot in the centre. Leopards have rings only and cheetahs solid
+spots. Suitable only for hearth-rugs. Supply very limited. Value
+5s. to 45s.</p>
+
+<p><span class="sc">Kaluga.</span>&mdash;See <i>Souslik</i>, below.</p>
+
+<p><span class="sc">Kangaroo.</span>&mdash;The sizes vary considerably, some being huge,
+others quite small. The larger varieties, viz. the red and the great,
+do not usually interest furriers, the fur being harsh and poor without
+underwool. They are tanned for the leather trade. The sorts used
+for carriage aprons, coat linings and the outside of motor coats
+include: blue kangaroo, bush kangaroo, bridled kangaroo, wallaroo,
+yellow kangaroo, rock wallaby, swamp wallaby and short-tailed
+wallaby. Many of the swamp sort are dyed to imitate skunk and
+look well. Generally the colours are yellowish or brown. Some are
+dark brown as in the swamp, which being strong are suitable for
+motor coats. The rock wallabies are soft and woolly and often of a
+pretty bluish tone, and make moderately useful carriage rugs and
+perambulator aprons. The redder and browner sorts are also good
+for rugs as they are thick in the pelt. On the European continent
+many of these are dyed. The best of the lighter weights are frequently
+insufficiently strong in the hair to stand the friction of wear
+in a coat lining. Value, kangaroo 9d. to 3s., wallaby 1½ d. to 5s. 3d.,
+wallaroo 1s. to 5s. 6d.</p>
+
+<p><span class="sc">Kids.</span>&mdash;See <i>Goats</i>, above.</p>
+
+<p><span class="sc">Kolinsky.</span>&mdash;Size 12 × 2½ in. Is one of the marten tribe. The
+underwool is short and rather weak, but regular, as is also the top
+hair; the colour is usually yellow. They have been successfully
+dyed and used as a substitute for sable. They are found in Siberia,
+Amoor, China and Japan, but the best are from Siberia. They are
+light in weight and therefore suitable for linings of coats. The tails
+are used for artists&rsquo; &ldquo;sable&rdquo; brushes. The fur has often been
+designated as red or Tatar sable. Value 1s. 6d. to 4s. 6d.</p>
+
+<p><span class="sc">Lambs.</span>&mdash;The sorts that primarily interest the fur trade in Europe
+and America are those from south Russia, Persia and Afghanistan,
+which are included under the following wholesale or retail commercial
+terms: Persian lamb, broadtail, astrachan, Shiraz, Bokharan
+and caracul lamb. With the public the general term astrachan is an
+old one, embracing all the above curly sorts; the flatter kinds, as broadtail
+and caracul lamb, have always been named separately. The
+Persian lambs, size 18 × 9 in., are the finest and the best of them.
+When dressed and dyed they should have regular, close and bright
+curl, varying from a small to a very large one, and if of equal size,
+regularity, tightness and brightness, the value is comparatively a
+matter of fancy. Those that are dull and loose, or very coarse and
+flat in the curl, are of far less market value.</p>
+
+<p>All the above enumerated lambs are naturally a rusty black or
+brown, and with very few exceptions are dyed a jet black. Lustre,
+however, cannot be imparted unless the wool was originally of a
+silky nature. Broadtails, size 10 × 5 in., are the very young of the
+Persian sheep, and are killed before the wool has time to develop
+beyond the flat wavy state which can be best compared to a piece
+of moiré silk. They are naturally exceedingly light in weight, and
+those that are of an even pattern, possessing a lustrous sheen, are
+costly. There is, notwithstanding, a great demand for these from
+the fashionable world, as not only are they very effective, but being
+so flat in the wool the figure of the wearer can be shown as perfectly
+as in a garment made of silk. It cannot be regarded as an economical
+fur, as the pelt is too delicate to resist hard wear.</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcl">Persian Lamb</td> <td class="tcl">price 12s. 6d.</td> <td class="tcl">to 25s.</td></tr>
+<tr><td class="tcl">Broadtail</td> <td class="tcl">price 10s.</td> <td class="tcl">to 35s.</td></tr>
+</table>
+
+<p class="noind">Astrachan, Shiraz and Bokharan lambs, size 22 by 9 in., are of a
+coarser, looser curl, and chiefly used for coat linings, while the
+Persians are used for outside of garments, collars, cuffs, stoles, muffs,
+hats and trimmings and gloves. The so-called caracul lambs, size
+12 × 6 in., are the very young of the astrachan sheep, and the pick
+of them are almost as effective as broadtails, although less fine in the
+texture. See also remarks as to caracul kid under Goats, above.</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcl">Astrachan</td> <td class="tcl">price 1s.</td> <td class="tcl">to 5s. 6d.</td></tr>
+<tr><td class="tcl">Caracul Lamb</td> <td class="tcl">price  2s. 6d</td> <td class="tcl">to 10s. 6d.</td></tr>
+<tr><td class="tcl">Shiraz</td> <td class="tcl">price 4s. 6d</td> <td class="tcl">to 10s.</td></tr>
+<tr><td class="tcl">Bokharan</td> <td class="tcl">price 1s. 6d</td> <td class="tcl">to 3s. 6d.</td></tr>
+</table>
+
+<p class="noind">Grey lambs, size 24 × 10 in., are obtained from the Crimea and known
+in the trade as &ldquo;crimmers.&rdquo; They are of a similar nature to the
+caracul lambs, but looser in curl, ranging from a very light to a
+dark grey. The best are the pale bluish greys, and are chiefly used
+for ladies&rsquo; coats, stoles, muffs and hats. Price 2s. to 6s. Mongolian
+lambs, size 24 × 15 in., are of a short wavy loose curl, creamy white
+colour, and are usually exported from China dressed, the majority
+being ready-made into cross-shaped coats or linings. They are used
+principally for linings of good evening wraps for ladies. Price 1s.
+to 2s. 6d. Slink lambs come from South America and China. The
+former are very small and generally those that are stillborn. They
+have a particularly thin pelt with very close wool of minute curl.
+The China sorts are much larger. The smallest are used for glove
+linings and the others for opera cloak linings. Price 1s. to 6s. 6d.</p>
+
+<p><span class="sc">Leopard.</span>&mdash;Size 3 to 6 ft. long. There are several kinds, the chief
+being the snow or ounce, Chinese, Bengal, Persian, East Indian and
+African. The first variety inhabit the Himalayas and are beautifully
+covered with a deep soft fur quite long compared to the flat harsh
+hair of the Bengal sort. The colours are pale orange and white with
+very dark markings, a strong contrast making a fine effect. Most
+artists prize these skins above all others. The Chinese are of a
+medium orange brown colour, but full in fur. The East Indian are
+less full and not so dark. The Bengal are dark and medium in colour,
+short and hard hair, but useful for floor rugs, as they do not hold the
+dust like the fuller and softer hair of the kinds previously named.
+They are also used for drummers&rsquo; aprons and saddle cloths in the
+Indian army. The African are small with pale lemon colour grounds
+very closely marked with black spots on the skin, the strong contrast
+making a pleasing effect. Occasionally, where something very
+marked is wanted, skating jackets and carriage aprons are made
+<span class="pagenum"><a name="page351" id="page351"></a>351</span>
+from the softest and flattest of skins, but usually they are made into
+settee covers, floor rugs and foot muffs. Value 2s. to 40s.</p>
+
+<p><span class="sc">Lion.</span>&mdash;Size 5 to 6 ft. long. These skins are found in Africa,
+Arabia and part of India, and are every year becoming scarcer.
+They are only used for floor rugs, and the males are more highly
+esteemed on account of the set-off of the mane. Value, lions&rsquo; £10
+to £100; lionesses&rsquo; £5 to £25.</p>
+
+<p><span class="sc">Lynx.</span>&mdash;Size 45 × 20 in. The underwool is thinner than fox, but
+the top hair is fine, silky and flowing, 4 in. long, of a pale grey,
+slightly mottled with fine streaks and dark spots. The fur upon the
+flanks is longer and white with very pronounced markings of dark
+spots, and this part of the skin is generally worked separately from
+the rest and is very effective for gown trimmings. Where the colour
+is of a sandy and reddish hue the value is far less than where it is
+of a bluish tone. They inhabit North America as far south as
+California, also Norway and Sweden. Those from the Hudson Bay
+district and Sweden are the best and are very similar. Those taken
+in Central Asia are mostly used locally. For attire the skins manufactured
+in Europe are generally dyed black or brown, in which
+state it has a similar appearance to dyed fox, but having less thick
+underwool and finer hair flows freely. The finest skins when dyed
+black are used very largely in America in place of the dyed black
+fox so fashionable for mourning wear in Great Britain and France.
+The British Hussar busbies are made of the dark brown lynx, and it
+is the free silky easy movement of the fur with the least disturbance
+in the atmosphere that gives it such a pleasing effect. It is used
+for rugs in its natural state and also in Turkey as trimmings for
+garments. Value 13s. 6d. to 56s.</p>
+
+<p><span class="sc">Lynx Cat</span> or <span class="sc">Bay Lynx.</span>&mdash;Is about half the size and depth of fur
+of a lynx proper, and inhabits the central United States. It is a
+flat and reddish fur compared to the lynx and is suitable for cheap
+carriage aprons. A few come from Canada and are of better quality.
+Value 5s. to 15s.</p>
+
+<p><span class="sc">Marmot.</span>&mdash;Size 18 × 12 in. Is a rodent and is found in considerable
+numbers in the south of Prussia. The fur is a yellowish brown and
+rather harsh and brittle and has no underwool. Since, however,
+the value of all good furs has advanced, dyers and manufacturers
+have made very successful efforts with this fur. The Viennese have
+been particularly successful, and their method has been to dye the
+skins a good brown and then not put in the dark stripes, which
+exist in sable and mink, until the garment or article is finished, thus
+obtaining as perfectly symmetrical effects as if the articles were
+made of small skins instead of large ones. Marmots are also found
+in North America, Canada and China; the best, however, come from
+Russia. It should always be a cheap fur, having so few good qualities
+to recommend it. Value 9d. to 2s. 6d.</p>
+
+<p><span class="sc">Marten, American.</span>&mdash;See <i>Sable</i>, below.</p>
+
+<p><span class="sc">Marten, Baum.</span>&mdash;Size 16 × 5 in. Is sometimes called the pine
+marten, and is found in quantity in the wooded and mountainous
+districts of Russia, Norway, Germany and Switzerland. It possesses
+a thick underwool with strong top hair, and ranges from a pale to a
+dark bluish brown. The best, from Norway, are very durable and
+of good appearance and an excellent substitute for American sable.
+The tails when split into two or three, with small strips of narrow
+tape so as to separate the otherwise dense fur, formerly made very
+handsome sets of trimmings, ties and muffs, and the probabilities
+are, as with other fashions, such use will have its period of revival.
+Value 6s. to 85s.</p>
+
+<p><span class="sc">Marten, Black.</span>&mdash;See <i>Skunk</i>, below.</p>
+
+<p><span class="sc">Marten, Japanese.</span>&mdash;Size 16 × 5 in. Is of a woolly nature with
+rather coarse top hair and quite yellow in colour. It is dyed for
+the cheap trade for boas and muffs, but it is not an attractive fur
+at the best of times. It lacks a silky, bright and fresh appearance,
+and therefore is unlikely to be in great demand, except where economy
+is an object. Value 6s. 6d. to 18s. 6d.</p>
+
+<p><span class="sc">Marten, Stone.</span>&mdash;Size and quality similar to the baum; the
+colour, however, of the underwool is a stony white and the top hair
+is very dark, almost black. They live in rocky and stony districts.
+Skins of a pale bluish tone are generally used in their natural state
+for stoles, boas and muffs, but the less clear coloured skins are dyed
+in beautiful shades similar in density to the dark and valuable sables
+from Russia, and are the most effective skins that can be purchased
+at a reasonable price. The tails have also been worked, in the
+manner explained with regard to the baum marten, as sets of trimmings
+and in other forms. Stone martens are found in Russia,
+Bosnia, Turkey, Greece, Germany, the Alps and France. The
+Bosnian and the French are the best in colour. The Asiatic sorts are
+less woolly, but being silky are useful when dyed. There are many
+from Afghanistan and India which are too poor to interest the
+European markets. Value 7s. 6d. to 26s.</p>
+
+<p><span class="sc">Mink.</span>&mdash;Size 16 × 5 in. Is of the amphibious class and is found
+throughout North America and in Russia, China and Japan. The
+underwool is short, close and even, as is also the top hair, which is
+very strong. The best skins are very dark and are obtained from
+Nova Scotia. In the central states of America the colour is a good
+brown, but in the north-west and south-west the fur is coarse and
+generally pale. It is very durable for linings, and is an economical
+substitute for sable for coats, capes, boas and trimmings. Values
+have greatly increased, and the fur possessing good qualities as to
+colour and durability will doubtless always be in good request.
+The Russian species is dark but flat and poor in quality, and the
+Chinese and Japanese are so pale that they are invariably dyed.
+These, however, are of very inferior nature. Value of American
+3s. 3d. to 40s., Japanese 3d. to 2s. 3d.</p>
+
+<p><span class="sc">Mole</span>.&mdash;Size 3½ × 2½ in. Moles are plentiful in the British Isles
+and Europe, and owing to their lovely velvety coats of exquisite
+blue shade and to the dearness of other furs are much in demand.
+Though the fur is cheap in itself, the expense of dressing and working
+up these little skins is considerable, and they possess the unique
+charm of an exceptional colour with little weight of pelt; the quality
+of resistance to friction is, however, so slight as to make them expensive
+in wear. The best are the dark blue from the Fen district of
+Cambridgeshire in England. Value ½d. to 2d.</p>
+
+<p><span class="sc">Mongolian Lambs</span>.&mdash;See <i>Lambs</i>, above.</p>
+
+<p><span class="sc">Monkey, Black</span>.&mdash;Size 18 × 10 in. Among the species of monkeys
+only one interests to any extent the fur trade, and that is the black
+monkey taken on the west coast of Africa (<i>Colobus satanas</i>). The
+hair is very long, very black and bright with no underwool, and the
+white pelt of the base of the hair, by reason of the great contrast of
+colour, is very noticeable. The skins were in 1850 very fashionable
+in England for stoles, muffs and trimmings, and in America also as
+recently as 1890. They are now mostly bought for Germany and
+the continent. Value 6d. to 1s. 6d.</p>
+
+<p><span class="sc">Mouflon</span>.&mdash;Size 30 × 15 in. Is a sheep found in Russia and
+Corsica and now very little in demand, and but few are imported
+into Great Britain. Many Mongolian goats with the long hairs
+pulled out are sold as mouflon. Value 4s. to 10s. 6d.</p>
+
+<p><span class="sc">Musk-Ox</span>.&mdash;Size 6 × 3 ft. These animals have a dense coat of
+fine, long brown wool, with very long dark brown hair on the head,
+flanks and tail, and, in the centre, a peculiar pale oval marking.
+There is no other fur that is so thick, and it is eminently suitable
+for sleighing rugs, for which purpose it is highly prized in Canada.
+The musk-ox inhabits the north part of Greenland and part of
+Canada, but in very limited numbers. Value 10s. to 130s.</p>
+
+<p><span class="sc">Musquash</span> or <span class="sc">Musk-Rat, Brown</span> and <span class="sc">Black Russian</span>.&mdash;Size
+12 × 8 in. A very prolific rodent of the amphibious class obtained
+from Canada and the United States, similar in habit to the English
+vole, with a fairly thick and even brown underwool and rather
+strong top dark hair of medium density. It is a very useful fur for
+men&rsquo;s coat linings and ladies&rsquo; driving or motoring coats, being
+warm, durable and not too heavy. If the colour were less motley
+and the joins between the skins could be made less noticeable, it
+would be largely in demand for stoles, ties and muffs. As it is, this
+fur is only used for these smaller articles for the cheaper trade. It
+has, however, of later years been &ldquo;unhaired,&rdquo; the underwool clipped
+very even and then dyed seal colour, in which way very useful and
+attractive garments are supplied at less than half the cost of the
+cheaper sealskins. They do not wear as well, however, as the pelt
+and the wool are not of a strength comparable to those of sealskin.
+With care, however, such a garment lasts sufficiently long to warrant
+the present outlay. Value 5½d. to 1s. 9d.</p>
+
+<p>There is a so-called black variety found in Delaware and New
+Jersey, but the number is very small compared to the brown species.
+They are excellent for men&rsquo;s coat linings and the outside of ladies&rsquo;
+coats, for stoles, muffs, collars and cuffs. Value 10d. to 3s. 7d.</p>
+
+<p>The Russian musquash is very small, 7 × 4 in., and is limited in
+numbers compared to the brown. Only a few thousands are imported
+to London. It is of a very pretty silvery-blue shade of even
+wool with very little silky top hair, having silvery-white sides and
+altogether a very marked effect. The odour, however, even after
+dressing is rather pungent of musk, which is generally an objection.
+Value 4s. to 6s. 6d.</p>
+
+<p><span class="sc">Nutria</span>.&mdash;Size 20 × 12 in. Is a rodent known in natural history
+as the coypu, about half the size of a beaver, and when unhaired has
+not more than half, generally less, the depth of fur, which is also
+not so close. Formerly the fur was only used for hatters&rsquo; felt, but
+with the rise in prices of furs these skins have been more carefully
+removed and&mdash;with improved dressing, unhairing and silvering
+processes&mdash;the best provides a very effective and suitable fur for
+ladies&rsquo; coats, capes, stoles, muffs, hats and gloves, while the lower
+qualities make very useful, light-weighted and inexpensive linings
+for men&rsquo;s or women&rsquo;s driving coats. It is also dyed sealskin colour,
+but its woolly nature renders it less effective than the more silky
+musquash. They are obtained from the northern part of South
+America. Value is. 6d. to 6s. 6d.</p>
+
+<p><span class="sc">Ocelot</span>.&mdash;Size 36 × 13 in. Is of the nature of a leopard and
+prettily marked with stripes and oblong spots. Only a few are now
+imported from South America for carriage aprons or mats. The
+numbers are very limited. Value 1s. to 2s. 6d.</p>
+
+<p><span class="sc">Opossum, American</span>.&mdash;Size 18 × 10 in. Is a marsupial, a class
+with this exception not met with out of Australia. The underwool
+is of a very close frizzy nature, and nearly white, with long bluish
+grey mixed with some black top hair. It is only found in the central
+sections of the United States. About 1870 in England it was dyed
+dark brown or black and used for boas, muffs and trimmings, but
+until recently has been neglected on the continent. With, however,
+recent experiments in brown and skunk coloured dyes, it bids fair
+to become a popular fur. Value 2½d. to 5s. 6d.</p>
+
+<p><span class="sc">Opossum, Australian</span>.&mdash;Size 16 × 8 in. Is a totally different
+nature of fur to the American. Although it has wool and top hair,
+<span class="pagenum"><a name="page352" id="page352"></a>352</span>
+the latter is so sparse and fine that the coat may be considered as
+one of close even wool. The colour varies according to the district
+of origin, from a blue grey to yellow with reddish tones. Those
+from the neighbourhood of Sydney are light clear blue, while those
+from Victoria are dark iron grey and stronger in the wool. These
+animals are most prolific and evidently increasing in numbers.
+Their fur is pretty, warm and as yet inexpensive, and is useful for
+rugs, coat linings, stoles, muffs, trimmings and perambulator aprons.
+The worst coloured ones are frequently dyed black and brown.
+The most pleasing natural grey come from Adelaide. The reddest
+are the cheapest. Value 3¾d. to 3s. 6d.</p>
+
+<p><span class="sc">Opossum, Ringtailed</span>.&mdash;Size 7 × 4 in. Has a very short close and
+dark grey wool, some being almost black. There are but a few
+thousands imported, and being so flat they are only of use for coat
+linings, but they are very warm and light in weight. Value 6d.
+to 10d.</p>
+
+<p><span class="sc">Opossum, Tasmanian</span> (grey and black).&mdash;Size 20 × 10 in. Is of a
+similar description, but darker and stronger in the wool and larger.
+Besides these there are some very rich brown skins which were
+formerly in such request in Europe, especially Russia, that undue
+killing occurred until 1899, when the government stopped for a time
+the taking of any of this class. They are excellent for carriage
+aprons, being not only very light in weight and warm, but handsome.
+Value 2s. 6d. to 8s. 6d.</p>
+
+<p><span class="sc">Otter, River</span>.&mdash;The size varies considerably, as does the underwool
+and the top hair, according to the country of origin. There
+are few rivers in the world where they do not live. But it is in the
+colder northern regions that they are found in the greatest numbers
+and with the best fur or underwool, the top hair, which, with the
+exception of the scarce and very rich dark brown specimens they
+have in common with most aquatic animals, is pulled out before the
+skins are manufactured. Most of the best river otter comes from
+Canada and the United States and averages 36 × 18 in. in size. Skins
+from Germany and China are smaller, and shorter in the wool. The
+colours of the under wools of river otters vary, some being very
+dark, others almost yellow. Both as a fur and as a pelt it is extremely
+strong, but owing to its short and close wool it is usually made up
+for the linings, collars and cuffs of men&rsquo;s coats. A large number of
+skins, after unhairing, is dyed seal colour and used in America.
+Those from hot climates are very poor in quality. Value 28s. to 118s.</p>
+
+<p><span class="sc">Otter, Sea</span>.&mdash;Size 50 × 25 in. Possesses one of the most beautiful
+of coats. Unlike other aquatic animals the skin undergoes no process
+of unhairing, the fur being of a rich dense silky wool with the softest
+and shortest of water hairs. The colours vary from pale grey brown
+to a rich black, and many have even or uneven sprinkling of white
+or silvery-white hairs. The blacker the wool and the more regular
+the silver points, the more valuable the skin. Sea otters are, unfortunately,
+decreasing in numbers, while the demand is increasing.
+The fur is most highly esteemed in Russia and China; in the latter
+country it is used to trim mandarins&rsquo; state robes. In Europe and
+America it is much used for collar, long facings and cuffs of a gentleman&rsquo;s
+coat; such a set may cost from £200 to £600, and in all probability
+will soon cost more. Taking into consideration the size,
+it is not so costly as the natural black fox, or the darkest Russian
+sable, which is now the most expensive of all. The smaller and young
+sea otters of a grey or brown colour are of small value compared to
+the large dark and silvery ones. Value £10 to £220. A single skin
+has been known to fetch £400.</p>
+
+<p><span class="sc">Ounce</span>.&mdash;See <i>Leopard</i>, above.</p>
+
+<p><span class="sc">Persian Lambs</span>.&mdash;See <i>Lambs</i>, above.</p>
+
+<p><span class="sc">Platypus</span>.&mdash;Size 12 × 8 in. One of the most singular of fur-bearing
+animals, being the link between bird and beast. It has fur
+similar to otter, is of aquatic habits, being web-footed with spurs of
+a cock and the bill of a duck. The skins are not obtained in any
+numbers, but being brought over by travellers as curiosities and
+used for muffs, collars and cuffs, &amp;c., they are included here for
+reference. Value 2s. to 3s. 6d.</p>
+
+<p><i>Pony</i> or <i>Tatar Foal</i>.&mdash;Size 36 × 20 in. These skins are of
+comparatively recent importation to the civilized world. They are
+obtained from the young of the numerous herds of wild horses that
+roam over the plains of Turkestan. The coat is usually a shade of
+brown, sometimes greyish, fairly bright and with a suggestion of
+waviness. Useful for motor coats. Value 3s. to 10s. 6d.</p>
+
+<p><span class="sc">Puma</span>.&mdash;Size 4½ × 3 ft. Is a native of South America, similar to
+a lion in habits and colour of coat. The hair and pelt is, however, of
+less strength, and only a few are now used for floor rugs. Value
+5s. to 10s.</p>
+
+<p><span class="sc">Raccoon</span>.&mdash;Size 20 × 12 in. Is an animal varying considerably
+in size and in quality and colour of fur, according to the part of
+North America in which it is found. In common parlance, it may
+be described as a species of wild dog with close affinity to the bear.
+The underwool is 1 to 1½ in. deep, pale brown, with long top hairs
+of a dark and silvery-grey mixture of a grizzly type, the best having
+a bluish tone and the cheapest a yellowish or reddish-brown. A
+limited number of very dark and black sorts exist and are highly
+valued for trimmings. The very finest skins are chiefly used for
+stoles and muffs, and the general run for coachmen&rsquo;s capes and
+carriage rugs, which are very handsome when the tails, which are
+marked with rings of dark and light fur alternately, are left on.
+Raccoons are used in enormous quantities in Canada for men&rsquo;s
+coats, the fur outside. The poorer qualities are extensively bought
+and made up in a similar way for Austria-Hungary and Germany.
+These make excellent linings for coats or footsacks for open driving
+in very cold climates. The worst coloured skins are dyed black or
+brown and are used for British military busbies, or caps, stoles,
+boas, muffs and coachmen&rsquo;s capes. The best skins come from the
+northern parts of the United States. A smaller and poorer species
+inhabits South America, and a very few are found in the north of
+India, but these do not interest the European trade. From Japan
+a similar animal is obtained in smaller quantities with very good
+but longer fur, of yellowish motley light-brown shades. It is more
+often imported and sold as Japanese fox, but its resemblance to
+the fur of the American raccoon is so marked as to surely identify
+it. When dyed dark blue or skunk colour it is good-looking and is
+sold widely in Europe. Raccoon skins are also frequently unhaired,
+and if the underwool is of good quality the effect is similar to beaver.
+It is the most useful fur for use in America or Russia, having a full
+quantity of fur which will retain heat. Value 10d. to 26s.</p>
+
+<p><span class="sc">Sable, American</span> and <span class="sc">Canadian.</span>&mdash;Size 17 × 5 in. The skins are
+sold in the trade sale as martens, but as there are many that are of a
+very dark colour and the majority are almost as silky as the Russian
+sable, the retail trade has for generations back applied the term of
+sable to this fur. The prevailing colour is a medium brown, and
+many are quite yellow. The dyeing of these very pale skins has
+been for so long well executed that it has been possible to make
+very good useful and effective articles of them at a moderate price
+compared to Russian sable. The finest skins are found in the East
+Main and the Esquimaux Bay, in the Hudson&rsquo;s Bay Company&rsquo;s
+districts, and the poorest in Alaska. They are not found very far
+south of the northern boundary of the United States. The best
+skins are excellent in quality, colour and effect, and wear well.
+Value 27s. 3d. to 290s.</p>
+
+<p><span class="sc">Sable, Chinese</span> and <span class="sc">Japanese.</span>&mdash;Size 14 × 4½ in. These are
+similar to the Amur skins previously referred to, but of much poorer
+quality and generally only suitable for linings. The very palest
+skins are dyed and made by the Chinese into mandarins&rsquo; coats, in
+which form they are found in the London trade sales, but being
+overdressed they are inclined to be loose in the hair and the colour
+of the dye is not good. The Japanese kind are imported raw, but
+are few in numbers, very pale and require dyeing. Value 15s. to
+150s.</p>
+
+<p><span class="sc">Sable, Russian.</span>&mdash;Size 15 × 5 in. These skins belong to a species
+of marten, very similar to the European and American, but much
+more silky in the nature of their fur. They have long been known
+as &ldquo;sables,&rdquo; doubtless owing to the density of colour to which
+many of them attain, and they have always been held in the highest
+esteem by connoisseurs as possessing a combination of rare qualities.
+The underwool is close, fine and very soft, the top hair is regular,
+fine, silky and flowing, varying from 1½ to 2½ in. in depth. In
+colour they range from a pale stony or yellowish shade to a rich dark
+brown, almost black with a bluish tone. The pelts are exceedingly
+fine and close in texture and, although of little weight, are very
+durable, and articles made of them produce a sensation of warmth
+immediately they are put upon the body.</p>
+
+<p>The Yakutsk, Okhotsk and Kamschatka sorts are good, the last
+being the largest and fullest furred, but of less density of colour than
+the others. Many from other districts are pale or yellowish brown,
+and those from Saghalien are poor in quality. The most valuable
+are the darkest from Yakutsk in Siberia, particularly those that have
+silvery hairs evenly distributed over the skin. These however are
+exceedingly scarce, and when a number are required to match for
+a large garment, considerable time may be necessary to collect them.
+This class of skin is the most expensive fur in the world, reckoning
+values by a square foot unit.</p>
+
+<p>The Amur skins are paler, but often of a pretty bluish stony tone
+with many frequently interspersed silvery hairs. The quality
+too is lower, that is, the fur is not so close or deep, but they are very
+effective, particularly for close-fitting garments, as they possess the
+least appearance of bulk. The paler skins from all districts in Siberia
+are now cleverly coloured or &ldquo;topped,&rdquo; that is, just the tips of the
+hair are stained dark, and it is only an expert who can detect them
+from perfectly natural shades. If this colouring process is properly
+executed it remains fairly fast. Notwithstanding the reported
+rights of the Russian imperial authorities over some regions with
+respect to these and other valuable fur-bearing animals, there are in
+addition to the numbers regularly sent to the trade auction sales
+in London many good parcels of raw skins to be easily bought direct,
+provided price is not the first consideration. Value 25s. to 980s.</p>
+
+<p><span class="sc">Seal, Fur.</span>&mdash;Sizes range from 24 × 15 in. to 55 × 25 in., the width
+being taken at the widest part of the skin after preparation. The
+centre of the skin between the fins is very narrow and the skins taper
+at each end, particularly at the tail. The very small pups are of a
+beautiful quality, but too tiny to make into garments, and, as the aim
+of a good furrier is to avoid all lateral or cross seams, skins are
+selected that are the length of the garment that is to be made. The
+most useful skins for coats are the large pups 42 in. long, and the
+quality is very good and uniform. The largest skins, known in the
+trade as &ldquo;wigs,&rdquo; which range up to 8 ft. in length, are uneven and
+weak in the fur, and hunters do not seek to obtain them. The supply
+of the best sort is chiefly from the North Pacific, viz. Pribilof
+<span class="pagenum"><a name="page353" id="page353"></a>353</span>
+Islands, Alaska, north-west coast of America, Copper Island of the
+Aleutian group near to Kamschatka, Robben Island and Japan.
+Other kinds are taken from the South Pacific and South Atlantic
+Oceans, around Cape Horn, the Falkland Islands up to Lobos
+Islands at the entrance of the La Plata river, off the Cape of Good
+Hope and Crozet Isles. With, however, the exception of the pick
+of the Lobos Island seals the fur of the southern sea seals is very
+poor and only suitable for the cheapest market. Formerly many
+skins were obtained from New Zealand and Australia, but the
+importation is now small and the quality not good. The preparation
+of seal skin occupies a longer time than any other fur skin, but its
+fine rich effect when finished and its many properties of warmth
+and durability well repay it. Value 10s. to 232s.</p>
+
+<p><span class="sc">Seal, Hair.</span>&mdash;There are several varieties of these seals in the seas
+stretching north from Scotland, around Newfoundland, Greenland
+and the north-west coast of America, and they are far more numerous
+than fur seals. Generally they have coarse rigid hair and none
+possess any underwool. They are taken principally for the oil and
+leather they yield. Some of the better haired sorts are dyed black
+and brown and used for men&rsquo;s motor coats when quite a waterproof
+garment is wanted, and they are used also for this quality in China.
+The young of the Greenland seals are called whitecoats on account
+of the early growth being of a yellowish white colour; the hair is
+¾ to 1 in. long, and at this early stage of their life is soft compared to
+that of the older seals. These fur skins are dyed black or dark brown
+and are used for military caps and hearth-rugs. Value 2s. to 15s.
+There are fewer hair seals in the southern than in the northern seas.</p>
+
+<p><span class="sc">Sheep.</span>&mdash;Vary much in size and in quality of wool. Many of the
+domestic kind in central and northern Europe and Canada are used
+for drivers&rsquo; and peasants&rsquo; coat linings, &amp;c. In Great Britain many
+coats of the home-reared sheep, having wools two and a half to five
+inches long, are dyed various colours and used as floor rugs. Skins
+with very short wool are dyed black and used for military saddle-cloths.
+The bulk, however, is used in the wool trade. The Hungarian
+peasants are very fond of their natural brown sheep coats,
+the leather side of which is not lined, but embellished by a very close
+fancy embroidery, worked upon the leather itself; these garments
+are reversible, the fur being worn inside when the weather is cold.
+Chinese sheep are largely used for cheap rugs. Value of English
+sheep from 3s. to 10s.</p>
+
+<p><span class="sc">Skunk</span> or <span class="sc">Black Marten.</span>&mdash;Size 15 × 8 in. The underwool is
+full and fairly close with glossy, flowing top hair about 2½ in. long.
+The majority have two stripes of white hair, extending the whole
+length of the skin, but these are cut out by the manufacturing
+furrier and sold to the dealers in pieces for exportation. The animals
+are found widely spread throughout North and South America.
+The skins which are of the greatest interest to the European trade
+are those from North America, the South American species being
+small, coarse and generally brown. The best skins come from Ohio
+and New York. If it were not for its disagreeable odour, skunk
+would be worth much more than the usual market value, as it is
+naturally the blackest fur, silky in appearance and most durable.
+The improved dressing processes have to a large extent removed the
+naturally pungent scent. The fur is excellent for stoles, boas,
+collars, cuffs, muffs and trimmings. Value 1s. 6d. to 11s.</p>
+
+<p><span class="sc">Souslik.</span>&mdash;Size 7 in. × 2¼. Is a small rodent found in the south
+of Russia and also in parts of America. It has very short hair and is
+a poor fur even for the cheapest linings, which is the only use to
+which the skin could be put. It is known as kaluga when imported
+in ready-made linings from Russia where the skins are dressed and
+worked in an inferior way. Value 1d. to 3d.</p>
+
+<p><span class="sc">Squirrel.</span>&mdash;Size 10 × 5 in. This measurement refers to the
+Russian and Siberian sorts, which are the only kind imported for
+the fur. The numerous other species are too poor in their coats
+to attract notice from fur dealers. The back of the Russian squirrel
+has an even close fur varying from a clear bluish-grey to a reddish-brown,
+the bellies in the former being of a flat quality and white,
+in the latter yellowish. The backs are worked into linings separately,
+as are the bellies or &ldquo;locks.&rdquo; The pelts, although very light, are
+tough and durable, hence their good reputation for linings for
+ladies&rsquo; walking or driving coats. The best skins also provide excellent
+material for coats, capes, stoles, ties, collars, cuffs, gloves, muffs,
+hoods and light-weight carriage aprons. The tails are dark and very
+small, and when required for ends of boas three or four are made as
+one. Value per skin from 2½d. to 1s. 1d.</p>
+
+<p><span class="sc">Tibet Lamb.</span>&mdash;Size 27 × 13 in. These pretty animals have a long,
+very fine, silky and curly fleece of a creamy white. The majority
+are consigned to the trade auction sales in London ready dressed
+and worked into cross-shaped coats, and the remainder, a fourth of
+the total, come as dressed skins. They are excellent for trimmings
+of evening mantles and for children&rsquo;s ties, muffs and perambulator
+aprons. The fur is too long and bulky for linings. Value per skin
+from 4s. 6d. to 8s. 6d.</p>
+
+<p><span class="sc">Tiger.</span>&mdash;Size varies considerably, largest about 10 ft. from nose
+to root of tail. Tigers are found throughout India, Turkestan,
+China, Mongolia and the East Indies. The coats of the Bengal kind
+are short and of a dark orange brown with black stripes, those
+from east or further India are similar in colour, but longer in the hair,
+while those from north of the Himalayas and the mountains of China
+are not only huge in size, but have a very long soft hair of delicate
+orange brown with very white flanks, and marked generally with the
+blackest of stripes. The last are of a noble appearance and exceedingly
+scarce. They all make handsome floor rugs.</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcl">Value of the Indian</td> <td class="tcl">from  £3 to £15.</td></tr>
+<tr><td class="tcl">Value of the Chinese</td> <td class="tcl">from £10 to £65.</td></tr>
+</table>
+
+<p><span class="sc">Vicuna</span> is a species of long-necked sheep native to South America,
+bearing some resemblance to the guanaco, but the fur is shorter,
+closer and much finer. The colour is a pale golden-brown and the
+fur is held in great repute in South America for carriage rugs. The
+supply is evidently small as the prices are high. There is scarcely
+a commercial quotation in London, few coming in except from
+private sources. 2s. 6d. to 5s. 6d. may be considered as the average
+value.</p>
+
+<p><span class="sc">Wallaby.</span>&mdash;See <i>Kangaroo</i>, above.</p>
+
+<p><span class="sc">Wallaroo.</span>&mdash;See <i>Kangaroo</i>, above.</p>
+
+<p><span class="sc">Wolf.</span>&mdash;Size 50 × 25 in. Is closely allied to the dog tribe and,
+like the jackals, is found through a wide range of the world,&mdash;North
+and South America, Europe and Asia. Good supplies are available
+from North America and Siberia and a very few from China. The
+best are the full furred ones of a very pale bluish-grey with fine
+flowing black top hair, which are obtained from the Hudson Bay
+district. Those from the United States and Asia are harsher in
+quality and browner. A few black American specimens come into
+the market, but usually the quality is poor compared to the lighter
+furred animal. The Siberian is smaller than the North American
+and the Russian still smaller. Besides the wolf proper a large number
+of prairie or dog wolves from America and Asia are used for cheaper
+rugs. In size they are less than half that of a large wolf and are of
+a motley sandy colour. Numbers of the Russian are retained for
+home use. The finest wolves are very light weighted and most
+suitable for carriage aprons, in fact, ideal for the purpose, though
+lacking the strength of some other furs.</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcl">Wolves</td> <td class="tcl">value 2s. 6d.</td> <td class="tcl">to 64s.</td></tr>
+<tr><td class="tcl">Dog wolves</td> <td class="tcl">value 1s.</td> <td class="tcl">to  2s. 6d.</td></tr>
+</table>
+
+<p><span class="sc">Wolverine.</span>&mdash;Size 16 × 18 in. Is native to America, Siberia,
+Russia and Scandinavia and generally partakes of the nature of a
+bear. The underwool is full and thick with strong and bright top
+hair about 2½ in. long. The colour is of two or three shades of brown
+in one skin, the centre being an oval dark saddle, edged as it were
+with quite a pale tone and merging to a darker one towards the
+flanks. This peculiar character alone stamps it as a distinguished
+fur, in addition to which it has the excellent advantage of being the
+most durable fur for carriage aprons, as well as the richest in colour.
+It is not prolific, added to which it is very difficult to match a number
+of skins in quality as well as colour. Hence it is an expensive fur,
+but its excellent qualities make it valuable. The darkest of the
+least coarse skins are worth the most. Prices from 6s. to 37s.</p>
+
+<p><span class="sc">Wombat</span>, <span class="sc">Koala</span> or Australian Bear.&mdash;Size 20 × 12 in. Has
+light grey or brown close thick wool half an inch deep without any top
+hair, with a rather thick spongy pelt. It is quite inexpensive and
+only suitable for cheap rough coats, carriage rugs, perambulator
+aprons and linings for footbags. The coats are largely used in
+western America and Canada. Value 3d. to 1s. 8½d.</p>
+</div>
+
+<p><i>Preparing and Dressing.</i>&mdash;A furrier or skin merchant must
+possess a good eye for colour to be successful, the difference in
+value on this subtle matter solely (in the rarer precious sorts,
+especially sables, natural black, silver and blue fox, sea otters,
+chinchillas, fine mink, &amp;c.) being so considerable that not only a
+practised but an intuitive sense of colour is necessary to accurately
+determine the exact merits of every skin. In addition to
+this a knowledge is required of what the condition of a pelt
+should be; a good judge knows by experience whether a skin
+will turn out soft and strong, after dressing, and whether the
+hair is in the best condition of strength and beauty. The dressing
+of the pelt or skin that is to be preserved for fur is totally different
+to the making of leather; in the latter tannic acid is used, but
+never should be with a fur skin, as is so often done by natives of
+districts where a regular fur trade is not carried on. The results
+of applying tannic acid are to harden the pelt and discolour
+and weaken the fur. The best methods for dressing fur skins
+are those of a tawer or currier, the aim being to retain all the
+natural oil in the pelt, in order to preserve the natural colour
+of the fur, and to render the pelt as supple as possible. Generally
+the skins are placed in an alkali bath, then by hand with a blunt
+wooden instrument the moisture of the pelt is worked out and
+it is drawn carefully to and fro over a straight, dull-edged knife
+to remove any superfluous flesh and unevenness. Special grease
+is then rubbed in and the skin placed in a machine which softly
+and continuously beats in the softening mixture, after which it
+is put into a slowly revolving drum, fitted with wooden paddles,
+partly filled with various kinds of fine hard sawdust according
+to the nature of the furs dealt with. This process with a moderate
+degree of heat thoroughly cleans it of external greasy matter,
+<span class="pagenum"><a name="page354" id="page354"></a>354</span>
+and all that is necessary before manufacturing is to gently tap
+the fur upon a leather cushion stuffed with horsehair with smooth
+canes of a flexibility suited to the strength of the fur. After
+dressing most skins alter in shape and decrease in size.</p>
+
+<p>With regard to the merits of European dressing, it may be
+fairly taken that English, German and French dressers have
+specialities of excellence. In England, for instance, the dressing
+of sables, martens, foxes, otters, seals, bears, lions, tigers and
+leopards is first rate; while with skunk, mink, musquash,
+chinchillas, beavers, lambs and squirrels, the Germans show
+better results, particularly in the last. The pelt after the German
+dressing is dry, soft and white, which is due to a finishing process
+where meal is used, thus they compare favourably with the
+moister and consequently heavier English finish. In France they
+do well with cheaper skins, such as musquash, rabbit and hare,
+which they dye in addition to dressing. Russian dressing is
+seldom reliable; not only is there an unpleasant odour, but in
+damp weather the pelts often become clammy, which is due to
+the saline matter in the dressing mixture. Chinese dressing is
+white and supple, but contains much powder, which is disagreeable
+and difficult to get rid of, and in many instances the skin
+is rendered so thin that the roots of the fur are weakened, which
+means that it is liable to shed itself freely, when subject to
+ordinary friction in handling or wearing. American and Canadian
+dressing is gradually improving, but hitherto their results have
+been inferior to the older European methods.</p>
+
+<p>In the case of seal and beaver skins the process is a much more
+difficult one, as the water or hard top hairs have to be removed
+by hand after the pelt has been carefully rendered moist and
+warm. With seal skins the process is longer than with any other
+fur preparation and the series of processes engage many
+specialists, each man being constantly kept upon one section of
+the work. The skins arrive simply salted. After being purchased
+at the auction sales they are washed, then stretched upon a
+hoop, when all blubber and unnecessary flesh is removed, and
+the pelt is reduced to an equal thickness, but not so thin as it is
+finally rendered. Subsequently the hard top hairs are taken out
+as in the case of otters and beavers and the whole thoroughly
+cleaned in the revolving drums. The close underwool, which is
+of a slightly wavy nature and mostly of a pale drab colour, is
+then dyed by repeated applications of a rich dark brown colour,
+one coat after another, each being allowed to thoroughly dry
+before the next is put on, till the effect is almost a lustrous black
+on the top. The whole is again put through the cleaning process
+and evenly reduced in thickness by revolving emery wheels,
+and eventually finished off in the palest buff colour.</p>
+
+<p>The English dye for seals is to-day undoubtedly the best; its
+constituents are more or less of a trade secret, but the principal ingredients
+comprise gall nuts, copper dust, camphor and antimony,
+and it would appear after years of careful watching that the
+atmosphere and particularly the water of London are partly
+responsible for good and lasting results. The Paris dyers do
+excellent work in this direction, but the colour is not so durable,
+probably owing to a less pure water. In America of late, strides
+have been made in seal dyeing, but preference is still given to
+London work. In Paris, too, they obtain beautiful results in the
+&ldquo;topping&rdquo; or colouring Russian sables and the Germans are
+particularly successful in dyeing Persian lambs black and foxes
+in all blue, grey, black and smoke colours and in the insertion of
+white hairs in imitation of the real silver fox. Small quantities
+of good beaver are dyed in Russia occasionally, and white hairs
+put in so well that an effect similar to sea otter is obtained.</p>
+
+<p>The process of inserting white hairs is called in the trade
+&ldquo;pointing, &ldquo;and is either done by stitching them in with a needle
+or by adhesive caoutchouc.</p>
+
+<p>The Viennese are successful in dyeing marmot well, and their
+cleverness in colouring it with a series of stripes to represent the
+natural markings of sable which has been done after the garments
+have been made, so as to obtain symmetry of lines, has secured
+for them a large trade among the dealers of cheap furs in England
+and the continent.</p>
+
+<p><i>Manufacturing Methods and Specialities.</i>&mdash;In the olden times
+the Skinners&rsquo; Company of the city of London was an association
+of furriers and skin dressers established under royal charter
+granted by Edward III. At that period the chief concern of
+the body was to prevent buyers from being imposed upon by
+sellers who were much given to offering old furs as new; a century
+later the Skinners&rsquo; Company received other charters empowering
+them to inspect not only warehouses and open markets, but
+workrooms. In 1667 they were given power to scrutinize the
+preparing of rabbit or cony wool for the wool trade and the
+registration of the then customary seven years&rsquo; apprenticeship.
+To-day all these privileges and powers are in abeyance, and the
+interest that they took in the fur trade has been gradually
+transferred to the leather-dressing craft.</p>
+
+<p>The work done by English furriers was generally good, but
+since about 1865 has considerably improved on account of the
+influx of German workmen, who have long been celebrated
+for excellent fur work, being In their own country obliged to
+satisfy officially appointed experts and to obtain a certificate
+of capacity before they can be there employed. The French
+influence upon the trade has been, and still is, primarily one of
+style and combination of colour, bad judgment in which will mar
+the beauty of the most valuable furs. It is a recognized law
+among high-class furriers that furs should be simply arranged,
+that is, that an article should consist of one fur or of two furs
+of a suitable contrast, to which lace may be in some cases added
+with advantage. As illustrative of this, it may be explained that
+any brown tone of fur such as sable, marten, mink, black marten,
+beaver, nutria, &amp;c., will go well upon black or very dark-brown
+furs, while those of a white or grey nature, such as ermine, white
+lamb, chinchilla, blue fox, silver fox, opossum, grey squirrel, grey
+lamb, will set well upon seal or black furs, as Persian lamb,
+broadtail, astrachan, caracul lamb, &amp;c. White is also permissible
+upon some light browns and greys, but brown motley colours
+and greys should never be in contrast. One neutralizes the other
+and the effect is bad. The qualities, too have to be considered&mdash;the
+fulness of one, the flatness of the other, or the coarseness or
+fineness of the furs. The introduction of a third fur in the same
+garment or indiscriminate selection of colours of silk linings,
+braids, buttons, &amp;c., often spoils an otherwise good article.</p>
+
+<p>With regard to the natural colours of furs, the browns that
+command the highest prices are those that are of a bluish rather
+than a reddish tendency. With greys it is those that are bluish,
+not yellow, and with white those that are purest, and with black
+the most dense, that are most esteemed and that are the rarest.</p>
+
+<p>Perhaps for ingenuity and the latest methods of manipulating
+skins in the manufacturing of furs the Americans lead the way,
+but as fur cutters are more or less of a roving and cosmopolitan
+character the larger fur businesses in London, Berlin, Vienna,
+St Petersburg, Paris and New York are guided by the same
+thorough and comparatively advanced principles.</p>
+
+<p>During the period just mentioned the tailors&rsquo; methods of
+scientific pattern cutting have been adopted by the leading
+furriers in place of the old chance methods of fur cutters, so that
+to-day a fur garment may be as accurately and gracefully fitted
+as plush or velvet, and with all good houses a material pattern
+is fitted and approved before the skins are cut.</p>
+
+<p>Through the advent of German and American fur sewing-machines
+since about 1890 fur work has been done better and
+cheaper. There are, however, certain parts of a garment, such as
+the putting in of sleeves and placing on of collars, &amp;c., that can
+only be sewn by hand. For straight seams the machines are
+excellent, making as neat a seam as is found in glove work, unless,
+of course, the pelts are especially heavy, such as bears and sheep
+rugs.</p>
+
+<p>A very great feature of German and Russian work is the fur
+linings called rotondes, sacques or plates, which are made for
+their home use and exportation chiefly to Great Britain, America
+and France.</p>
+
+<p>In Weissenfels, near Leipzig, the dressing of Russian grey
+squirrel and the making it into linings is a gigantic industry, and
+is the principal support of the place. After the dressing process
+the backs of the squirrels are made up separately from the under
+<span class="pagenum"><a name="page355" id="page355"></a>355</span>
+and thinner white and grey parts, the first being known as squirrel-back
+and the other as squirrel-lock linings. A few linings are
+made from entire skins and others are made from the quite white
+pieces, which in some instances are spotted with the black ear
+tips of the animals to resemble ermine. The smaller and uneven
+pieces of heads and legs are made up into linings, so there is
+absolutely no waste. Similar work is done in Russia on almost
+as extensive a scale, but neither the dressing nor the work is
+so good as the German.</p>
+
+<p>The majority of heads, gills or throats, sides or flanks, paws
+and pieces of skins cut up in the fur workshops of Great Britain,
+America and France, weighing many tons, are chiefly exported
+to Leipzig, and made up in neighbouring countries and Greece,
+where labour can be obtained at an alarmingly low rate. Although
+the sewing, which is necessarily done by hand, the sections
+being of so unequal and tortuous a character, is rather roughly
+executed, the matching of colours and qualities is excellent.
+The enormous quantities of pieces admit of good selection and
+where odd colours prevail in a lining it is dyed. Many squirrel-lock
+linings are dyed blue and brown and used for the outside
+of cheap garments. They are of little weight, warm and effective,
+but not of great durability.</p>
+
+<p>The principal linings are as follows: Sable sides, sable heads
+and paws, sable gills, mink sides, heads and gills, marten sides,
+heads and gills, Persian lamb pieces and paws, caracul lamb
+pieces or paws, musquash sides and heads, nutria sides, genet
+pieces, raccoon sides or flanks, fox sides, kolinski whole skins, and
+small rodents as kaluga and hamster. The white stripes cut out
+of skunks are made into rugs.</p>
+
+<p>Another great source of inexpensive furs is China, and for
+many years past enormous quantities of dressed furs, many of
+which are made up in the form of linings and Chinese loose-shaped
+garments, have been imported by England, Germany
+and France for the lower class of business; the garments are only
+regarded as so much fur and are reworked. With, however, the
+exception of the best white Tibet lambs, the majority of Chinese
+furs can only be regarded as inferior material. While the work
+is often cleverly done as to matching and manipulation of the
+pelt which is very soft, there are great objections in the odour
+and the brittleness or weakness of the fur. One of the most
+remarkable results of the European intervention in the Boxer
+rising in China (1900) was the absurd price paid for so-called
+&ldquo;loot&rdquo; of furs, particularly in mandarins&rsquo; coats of dyed and
+natural fox skins and pieces, and natural ermine, poor in quality
+and yellowish in colour; from three to ten times their value
+was paid for them when at the same time huge parcels of similar
+quality were warehoused in the London docks, because purchasers
+could not be found for them.</p>
+
+<p>With regard to Japanese furs, there is little to commend them.
+The best are a species of raccoon usually sold as fox, and, being
+of close long quality of fur, they are serviceable for boas, collars,
+muffs and carriage aprons. The sables, martens, minks and
+otters are poor in quality, and all of a very yellow colour and
+they are generally dyed for the cheap trade. A small number
+of very pretty guanaco and vicuna carriage rugs are imported
+into Europe, and many come through travellers and private
+sources, but generally they are so badly dressed that they are
+quite brittle upon the leather side. Similar remarks are applicable
+to opossum rugs made in Australia. From South
+Africa a quantity of jackal, hyena, fox, leopard and sheep
+karosses, <i>i.e.</i> a peculiarly shaped rug or covering used by native
+chiefs, is privately brought over. The skins are invariably tanned
+and beautifully sewn, the furs are generally flat in quality and
+not very strong in the hair, and are retained&rsquo; more as curiosities
+than for use as a warm covering.</p>
+
+<p><i>Hatters&rsquo; Furs and Cloths and Shawls.</i>&mdash;The hat trade is largely
+interested in the fur piece trade, the best felt hats being made
+from beaver and musquash wool and the cheaper sorts from nutria,
+hare and rabbit wools. For weaving, the most valuable pieces
+are mohair taken from the angora and vicuna. They are limited
+in quantity and costly, and the trade depends upon various
+sorts of other sheep and goat wools for the bulk of its productions.</p>
+
+<p><i>Frauds and Imitations.</i>&mdash;The opportunities for cheating in
+the fur trade are very considerable, and most serious frauds
+have been perpetrated in the selling of sables that have been
+coloured or &ldquo;topped&rdquo;; that is, just the tips of the hairs stained
+dark to represent more expensive skins. It is only by years of
+experience that some of these colourings can be detected. Where
+the skins are heavily dyed it is comparatively easy to see the
+difference between a natural and a dyed colour, as the underwool
+and top hair become almost alike and the leather is also dark,
+whereas in natural skins the base of the underwool is much
+paler than the top, or of a different colour, and the leather Is
+white unless finished in a pale reddish tone as is sometimes
+the case when mahogany sawdust is used in the final cleaning.
+As has been explained, sable is a term applied for centuries past
+to the darker sorts of the Russian Siberian martens, and for years
+past the same term has been bestowed by the retail trade upon
+the American and Canadian martens. The baum and stone
+martens caught in France, the north of Turkey and Norway
+are of the same family, but coarser in underwool and the top
+hair is less in quantity and not so silky. The kolinski, or as it
+is sometimes styled Tatar sable, is the animal, the tail of which
+supplies hair for artists&rsquo; brushes. This is also of the marten
+species and has been frequently offered, when dyed dark, as have
+baum and stone martens, as Russian sables. Hares, too, are
+dyed a sable colour and advertised as sable. The fur, apart
+from a clumsy appearance, is so brittle, however, as to be of
+scarcely any service whatever.</p>
+
+<p>Among the principal imitations of other furs is musquash,
+out of which the top hair has been pulled and the undergrowth
+of wool clipped and dyed exactly the same colour as is used for
+seal, which is then offered as seal or red river seal. Its durability,
+however, is far less than that of seal. Rabbit is prepared and
+dyed and frequently offered as &ldquo;electric sealskin.&rdquo; Nutria also
+is prepared to represent sealskin, and in its natural colour, after
+the long hairs are plucked out, it is sold as otter or beaver. The
+wool is, however, poor compared to the otter and beaver, and the
+pelt thin and in no way comparable to them in strength. White
+hares are frequently sold as white fox, but the fur is weak, brittle
+and exceedingly poor compared to fox and possesses no thick
+underwool. Foxes, too, and badger are dyed a brownish black,
+and white hairs inserted to imitate silver fox, but the white hairs
+are too coarse and the colour too dense to mislead any one who
+knows the real article. But if sold upon its own merits, pointed
+fox is a durable fur.</p>
+
+<p>Garments made of sealskin pieces and Persian lamb pieces
+are frequently sold as if they were made of solid skins, the term
+&ldquo;pieces&rdquo; being simply suppressed. The London Chamber of
+Commerce have issued to the British trade a notice that any
+misleading term in advertising and all attempts at deception are
+illegal, and offenders are liable under the Merchandise Marks
+Act 1887.</p>
+
+<div class="condensed">
+<p>The most usual misnaming of manufactured furs is as follow:&mdash;</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcl cl">Musquash, pulled and dyed</td> <td class="tcl cl">Sold as seal.</td></tr>
+<tr><td class="tcl">Nutria, pulled and dyed</td> <td class="tcl">Sold as seal.</td></tr>
+<tr><td class="tcl cl">Nutria, pulled and natural</td> <td class="tcl cl">Sold as beaver.</td></tr>
+<tr><td class="tcl">Rabbit, sheared and dyed</td> <td class="tcl">Sold as seal or electric seal.</td></tr>
+<tr><td class="tcl cl">Otter, pulled and dyed</td> <td class="tcl cl">Sold as seal.</td></tr>
+<tr><td class="tcl">Marmot, dyed</td> <td class="tcl">Sold as mink or sable.</td></tr>
+<tr><td class="tcl cl">Fitch, dyed</td> <td class="tcl cl">Sold as sable.</td></tr>
+<tr><td class="tcl">Rabbit, dyed</td> <td class="tcl">Sold as sable or French sable.</td></tr>
+<tr><td class="tcl cl">Hare, dyed</td> <td class="tcl cl">Sold as sable, or fox, or lynx.</td></tr>
+<tr><td class="tcl">Musquash, dyed</td> <td class="tcl">Sold as mink or sable.</td></tr>
+<tr><td class="tcl cl">Wallaby, dyed</td> <td class="tcl cl">Sold as skunk.</td></tr>
+<tr><td class="tcl">White Rabbit</td> <td class="tcl">Sold as ermine.</td></tr>
+<tr><td class="tcl cl">White Rabbit, dyed</td> <td class="tcl cl">Sold as chinchilla.</td></tr>
+<tr><td class="tcl">White Hare, dyed or natural</td> <td class="tcl">Sold as fox, foxaline, and other similar names.</td></tr>
+<tr><td class="tcl cl">Goat, dyed</td> <td class="tcl cl">Sold as bear, leopard, &amp;c.</td></tr>
+<tr><td class="tcl">Dyed manufactured articles of all kinds</td> <td class="tcl">Sold as &ldquo;natural.&rdquo;</td></tr>
+<tr><td class="tcl cl">White hairs inserted in foxes and sables</td> <td class="tcl cl">Sold as real or natural furs.</td></tr>
+<tr><td class="tcl">Kids</td> <td class="tcl">Sold as lamb or broadtails.</td></tr>
+<tr><td class="tcl cl">American sable</td> <td class="tcl cl">Sold as real Russian sable.</td></tr>
+<tr><td class="tcl">Mink</td> <td class="tcl">Sold as sable.</td></tr>
+</table>
+</div>
+
+<p><i>The Preservation of Furs.</i>&mdash;For many years raw sealskins
+<span class="pagenum"><a name="page356" id="page356"></a>356</span>
+have been preserved in cold storage, but it is only within a
+recent period, owing to the difficulty there was in obtaining
+the necessary perfectly dry atmosphere, that dressed and made-up
+furs have been preserved by freezing. Furs kept in such a condition
+are not only immune from the ravages of the larvae of
+moth, but all the natural oils in the pelt and fur are conserved,
+so that its colour and life are prolonged, and the natural deterioration
+is arrested. Sunlight has a tendency to bleach furs and to
+encourage the development of moth eggs, therefore continued
+exposure is to be avoided. When furs are wetted by rain they
+should be well shaken and allowed to dry in a current of air
+without exposure to sun or open fire.</p>
+
+<p>Where a freezing store for furs is not accessible, furs should be
+well shaken and afterwards packed in linen and kept in a perfectly
+cool dry place, and examined in the summer at periods of
+not less than five weeks. Naphthalene and the usual malodorous
+powders are not only very disagreeable, but quite useless. Any
+chemical that is strong enough to destroy the life in a moth egg
+would also be sufficiently potent to injure the fur itself. In
+England moth life is practically continuous all the year round,
+that is, as regards those moths that attack furs, though the
+destructive element exists to a far greater extent during spring
+and summer.</p>
+
+<div class="condensed">
+<p class="pt2 center"><i>Comparative Durability of Various Furs and Weight of Unlined
+Skins per Square Foot.</i></p>
+
+<p>The following estimates of durability refer to the use of fur when
+made up &ldquo;hair outside&rdquo; in garments or stoles, not as a lining.
+The durability of fur used as linings, which is affected by other
+conditions, is set forth separately. Otter, with its water hairs
+removed, the strongest of furs for external use, is, in this table, taken
+as the standard at 100 and other furs marked accordingly:&mdash;</p>
+
+<p class="pt1 center"><i>The Precious Furs.</i></p>
+
+<table class="ws" summary="Contents">
+
+<tr><td class="tccm allb">&nbsp;</td> <td class="tccm allb">Points of<br />Durability.</td> <td class="tccm allb"><a name="fa2h" id="fa2h" href="#ft2h"><span class="sp">2</span></a> Weight<br />in oz. per<br />sq. ft.</td></tr>
+
+<tr><td class="tcl lb rb">Sable</td> <td class="tcr rb">60</td> <td class="tcc rb">2½</td></tr>
+<tr><td class="tcl lb rb">Sea</td> <td class="tcr rb">75</td> <td class="tcc rb">3</td></tr>
+<tr><td class="tcl lb rb">Fox, Silver or Black</td> <td class="tcr rb">40</td> <td class="tcc rb">3</td></tr>
+<tr><td class="tcl lb rb">Fox, White</td> <td class="tcr rb">20</td> <td class="tcc rb">3</td></tr>
+<tr><td class="tcl lb rb">Ermine</td> <td class="tcr rb">25</td> <td class="tcc rb">1¼</td></tr>
+<tr><td class="tcl lb rb">Chinchilla</td> <td class="tcr rb">15</td> <td class="tcc rb">1½</td></tr>
+<tr><td class="tcl lb rb bb">Sea-otter (for stoles or collars)</td> <td class="tcr rb bb">100</td> <td class="tcc rb bb">4¼</td></tr>
+</table>
+
+
+<p class="pt1 center"><i>The Less Valuable Furs.</i></p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tccm allb">&nbsp;</td> <td class="tccm allb">Points of<br />Durability.</td> <td class="tccm allb">Weight<br />in oz. per<br />sq. ft.</td></tr>
+
+<tr><td class="tcl lb rb">Sable &ldquo;topped,&rdquo; <i>i.e.</i> top hairs coloured</td> <td class="tcr rb">55</td> <td class="tcc rb">2½</td></tr>
+<tr><td class="tcl lb rb">Sable tinted, <i>i.e.</i> fur all coloured.</td> <td class="tcr rb">50</td> <td class="tcc rb">2½</td></tr>
+<tr><td class="tcl lb rb">Baum Marten, natural</td> <td class="tcr rb">65</td> <td class="tcc rb">2¾</td></tr>
+<tr><td class="tcl lb rb">Baum Marten, tinted</td> <td class="tcr rb">45</td> <td class="tcc rb">2¾</td></tr>
+<tr><td class="tcl lb rb">Stone Marten</td> <td class="tcr rb">40</td> <td class="tcc rb">2¾</td></tr>
+<tr><td class="tcl lb rb">Nutria</td> <td class="tcr rb">27</td> <td class="tcc rb">3¼</td></tr>
+<tr><td class="tcl lb rb">Musquash, natural</td> <td class="tcr rb">37</td> <td class="tcc rb">3¼</td></tr>
+<tr><td class="tcl lb rb">Musquash, water hairs removed, sheared and seal finished.</td> <td class="tcr rb">33</td> <td class="tcc rb">3¼</td></tr>
+<tr><td class="tcl lb rb">Skunk</td> <td class="tcr rb">70</td> <td class="tcc rb">2¾</td></tr>
+<tr><td class="tcl lb rb">Mink</td> <td class="tcr rb">70</td> <td class="tcc rb">3¼</td></tr>
+<tr><td class="tcl lb rb">Lynx, natural</td> <td class="tcr rb">25</td> <td class="tcc rb">2¾</td></tr>
+<tr><td class="tcl lb rb">Lynx, tinted black</td> <td class="tcr rb">20</td> <td class="tcc rb">2¾</td></tr>
+<tr><td class="tcl lb rb">Marmot, tinted</td> <td class="tcr rb">10</td> <td class="tcc rb">3</td></tr>
+<tr><td class="tcl lb rb">Fox, tinted black</td> <td class="tcr rb">25</td> <td class="tcc rb">3</td></tr>
+<tr><td class="tcl lb rb">Fox, tinted blue</td> <td class="tcr rb">20</td> <td class="tcc rb">3</td></tr>
+<tr><td class="tcl lb rb">Opossum</td> <td class="tcr rb">37</td> <td class="tcc rb">3</td></tr>
+<tr><td class="tcl lb rb">Otter (with water hairs)</td> <td class="tcr rb">100</td> <td class="tcc rb">4</td></tr>
+<tr><td class="tcl lb rb">Otter (water hairs removed)</td> <td class="tcr rb">95</td> <td class="tcc rb">3<span class="spp">15</span>&frasl;<span class="suu">16</span></td></tr>
+<tr><td class="tcl lb rb">Beaver (water hairs cut level with fur)</td> <td class="tcr rb">90</td> <td class="tcc rb">4</td></tr>
+<tr><td class="tcl lb rb">Beaver (water hairs removed)</td> <td class="tcr rb">85</td> <td class="tcc rb">3<span class="spp">15</span>&frasl;<span class="suu">16</span></td></tr>
+<tr><td class="tcl lb rb">Moleskin</td> <td class="tcr rb">7</td> <td class="tcc rb">1¾</td></tr>
+<tr><td class="tcl lb rb">Persian Lamb</td> <td class="tcr rb">65</td> <td class="tcc rb">3¼</td></tr>
+<tr><td class="tcl lb rb">Grey Lamb</td> <td class="tcr rb">30</td> <td class="tcc rb">3¼</td></tr>
+<tr><td class="tcl lb rb">Broadtail</td> <td class="tcr rb">15</td> <td class="tcc rb">2¼</td></tr>
+<tr><td class="tcl lb rb">Caracul Kid</td> <td class="tcr rb">10</td> <td class="tcc rb">3¼</td></tr>
+<tr><td class="tcl lb rb">Caracul Lamb</td> <td class="tcr rb">15</td> <td class="tcc rb">3¼</td></tr>
+<tr><td class="tcl lb rb">Squirrel</td> <td class="tcr rb">25</td> <td class="tcc rb">1¾</td></tr>
+<tr><td class="tcl lb rb">Hare</td> <td class="tcr rb">5</td> <td class="tcc rb">1¾</td></tr>
+<tr><td class="tcl lb rb bb">Rabbit</td> <td class="tcr rb bb">5</td> <td class="tcc rb bb">2¼</td></tr>
+</table>
+
+<p class="pt1 center"><i>Quantities of Fur needed, in Square Feet.</i></p>
+
+<p>The &ldquo;Paris Model&rdquo; figure is the basis of these estimates for
+ladies&rsquo; garments, the standard measurements being height 5 ft.
+6 in., waist 23 in., bust 38 in.</p>
+
+<table class="ws" summary="Contents">
+<tr><td>&nbsp;</td> <td class="tcc">Sq. Ft.<br />(approximate).</td></tr>
+
+<tr><td class="tcl cl">Straight stole ½ length (just below the waist line)</td> <td class="tcc cl">2¾</td></tr>
+<tr><td class="tcl">Straight stole ¾ length (just below the knee)</td> <td class="tcc">3¾</td></tr>
+<tr><td class="tcl cl">Stole, broad enough at the neck to cover the top of arm ¾ length</td> <td class="tcc cl">5</td></tr>
+<tr><td class="tcl">The same, full length (to hem of skirt)</td> <td class="tcc">6</td></tr>
+<tr><td class="tcl cl">Eton jacket, without collar</td> <td class="tcc cl">13</td></tr>
+<tr><td class="tcl">Plain cape, 15 in. long</td> <td class="tcc">6½</td></tr>
+<tr><td class="tcl cl">Deep cape, 30 in. long</td> <td class="tcc cl">15</td></tr>
+<tr><td class="tcl">Full cape with broad stole front, ¾ length</td> <td class="tcc">15</td></tr>
+<tr><td class="tcl cl">Inverness cape (to knee)</td> <td class="tcc cl">25</td></tr>
+<tr><td class="tcl">Double-breasted, straight, semi-fitting coat, covering hips</td> <td class="tcc">16</td></tr>
+<tr><td class="tcl cl">Double-breasted sacque jacket, 36 in. long, full sleeves</td> <td class="tcc cl">20</td></tr>
+<tr><td class="tcl">Same, 30 in. long</td> <td class="tcc">18</td></tr>
+<tr><td class="tcl cl">Same, 22 in. long</td> <td class="tcc cl">15</td></tr>
+<tr><td class="tcl">Long, full, shawl cape with points at back and front, well below knee</td> <td class="tcc">15</td></tr>
+<tr><td class="tcl cl">Shorter shawl cape</td> <td class="tcc cl">16</td></tr>
+<tr><td class="tcl">Motoring or driving coat, ¾ length</td> <td class="tcc">22</td></tr>
+<tr><td class="tcl cl">Motoring or driving coat, full length</td> <td class="tcc cl">27</td></tr>
+</table>
+
+<p class="pt1 center"><i>Weight and Durability of Furs for Men&rsquo;s Coat Linings.</i></p>
+
+<p>Otter with the water hairs removed, the strongest fur suited for
+linings, is here taken as the standard.</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tccm allb">&nbsp;</td> <td class="tccm allb">Points of<br />Durability.</td> <td class="tccm allb">Weight<br />in oz. per<br />sq. ft.</td></tr>
+
+<tr><td class="tcl lb rb">Otter (the water hairs removed)</td> <td class="tcr rb">100</td> <td class="tcc rb">3<span class="spp">15</span>&frasl;<span class="suu">16</span></td></tr>
+<tr><td class="tcl lb rb">Beaver (the water hairs removed)</td> <td class="tcr rb">90</td> <td class="tcc rb">3<span class="spp">15</span>&frasl;<span class="suu">16</span></td></tr>
+<tr><td class="tcl lb rb">Mink</td> <td class="tcr rb">90</td> <td class="tcc rb">3¼</td></tr>
+<tr><td class="tcl lb rb">Sealskin</td> <td class="tcr rb">75</td> <td class="tcc rb">3</td></tr>
+<tr><td class="tcl lb rb">Raccoon</td> <td class="tcr rb">75</td> <td class="tcc rb">4½</td></tr>
+<tr><td class="tcl lb rb">Persian lamb or astrachan</td> <td class="tcr rb">70</td> <td class="tcc rb">3¼</td></tr>
+<tr><td class="tcl lb rb">Sable</td> <td class="tcr rb">65</td> <td class="tcc rb">2½</td></tr>
+<tr><td class="tcl lb rb">Musquash</td> <td class="tcr rb">55</td> <td class="tcc rb">3½</td></tr>
+<tr><td class="tcl lb rb">Nutria</td> <td class="tcr rb">40</td> <td class="tcc rb">3¼</td></tr>
+<tr><td class="tcl lb rb">Grey Opossum</td> <td class="tcr rb">40</td> <td class="tcc rb">3</td></tr>
+<tr><td class="tcl lb rb">Wallaby</td> <td class="tcr rb">30</td> <td class="tcc rb">3¾</td></tr>
+<tr><td class="tcl lb rb">Squirrel</td> <td class="tcr rb">30</td> <td class="tcc rb">1¾</td></tr>
+<tr><td class="tcl lb rb">Hamster</td> <td class="tcr rb">15</td> <td class="tcc rb">1¼</td></tr>
+<tr><td class="tcl lb rb bb">Rabbit</td> <td class="tcr rb bb">10</td> <td class="tcc rb bb">2¼</td></tr>
+</table>
+
+<p class="pt1 center"><i>Durability and Weight of Linings for Ladies&rsquo; Coats or Wraps.</i></p>
+
+<p>Sable gills, the strongest fur suited for ladies&rsquo; linings, is taken as
+the standard.</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tccm allb">&nbsp;</td> <td class="tccm allb">Points of<br />Durability.</td> <td class="tccm allb">Weight<br />in oz. per<br />sq. ft.</td></tr>
+
+<tr><td class="tcl lb rb">Sable gills</td> <td class="tcr rb">100</td> <td class="tcc rb">2<span class="spp">7</span>&frasl;<span class="suu">8</span></td></tr>
+<tr><td class="tcl lb rb">Sable</td> <td class="tcr rb">85</td> <td class="tcc rb">2½</td></tr>
+<tr><td class="tcl lb rb">Sable paws</td> <td class="tcr rb">64</td> <td class="tcc rb">1<span class="spp">5</span>&frasl;<span class="suu">8</span></td></tr>
+<tr><td class="tcl lb rb">Ermine</td> <td class="tcr rb">57</td> <td class="tcc rb">1¼</td></tr>
+<tr><td class="tcl lb rb">Squirrel back</td> <td class="tcr rb">50</td> <td class="tcc rb">1¾</td></tr>
+<tr><td class="tcl lb rb">Squirrel heads</td> <td class="tcr rb">36</td> <td class="tcc rb">2½</td></tr>
+<tr><td class="tcl lb rb">Squirrel lock</td> <td class="tcr rb">21</td> <td class="tcc rb">1<span class="spp">3</span>&frasl;<span class="suu">16</span></td></tr>
+<tr><td class="tcl lb rb">Hamster</td> <td class="tcr rb">10</td> <td class="tcc rb">1¼</td></tr>
+<tr><td class="tcl lb rb bb">Rabbit</td> <td class="tcr rb bb">7</td> <td class="tcc rb bb">2¼</td></tr>
+</table>
+
+<p class="pt1 center"><i>Durability and Weight of Motoring Furs made up with Fur outside.</i></p>
+
+<p>Otter with the water hairs, the strongest fur suited for motoring
+garments, is taken as the standard.</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tccm allb">&nbsp;</td> <td class="tccm allb">Points of<br />Durability.</td> <td class="tccm allb">Weight<br />in oz. per<br />sq. ft.</td></tr>
+
+<tr><td class="tcl lb rb">Otter (with water hairs)</td> <td class="tcr rb">100</td> <td class="tcc rb">4</td></tr>
+<tr><td class="tcl lb rb">Sealskin, marble</td> <td class="tcr rb">80</td> <td class="tcc rb">3</td></tr>
+<tr><td class="tcl lb rb">&rdquo;Hair Sealskin&rdquo; (tinted) with water hairs (a special variety of seal)</td> <td class="tcr rb">75</td> <td class="tcc rb">3¼</td></tr>
+<tr><td class="tcl lb rb">Raccoon</td> <td class="tcr rb">65</td> <td class="tcc rb">4½</td></tr>
+<tr><td class="tcl lb rb bb">Russian Pony</td> <td class="tcr rb bb">35</td> <td class="tcc rb bb">2<span class="spp">5</span>&frasl;<span class="suu">8</span></td></tr>
+</table>
+
+<p><span class="pagenum"><a name="page357" id="page357"></a>357</span></p>
+
+<p class="pt1 center"><i>Durability and Weight of Furs for Rugs and Foot-sacks.</i></p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tccm allb">&nbsp;</td> <td class="tccm allb">Points of<br />Durability.</td> <td class="tccm allb">Weight<br />in oz. per<br />sq. ft.</td></tr>
+
+<tr><td class="tcl lb rb">Wolverine</td> <td class="tcr rb">100</td> <td class="tcc rb">6</td></tr>
+<tr><td class="tcl lb rb">Bear (black or brown natural)</td> <td class="tcr rb">94</td> <td class="tcc rb">7</td></tr>
+<tr><td class="tcl lb rb">Bear (tinted black)</td> <td class="tcr rb">88</td> <td class="tcc rb">7½</td></tr>
+<tr><td class="tcl lb rb">Beaver</td> <td class="tcr rb">88</td> <td class="tcc rb">4</td></tr>
+<tr><td class="tcl lb rb">Raccoon</td> <td class="tcr rb">77</td> <td class="tcc rb">4½</td></tr>
+<tr><td class="tcl lb rb">Opossum</td> <td class="tcr rb">61</td> <td class="tcc rb">3</td></tr>
+<tr><td class="tcl lb rb">Wolf</td> <td class="tcr rb">50</td> <td class="tcc rb">6½</td></tr>
+<tr><td class="tcl lb rb">Jackal</td> <td class="tcr rb">27</td> <td class="tcc rb">4½</td></tr>
+<tr><td class="tcl lb rb">Australian Bear</td> <td class="tcr rb">16</td> <td class="tcc rb">6</td></tr>
+<tr><td class="tcl lb rb bb">Goat</td> <td class="tcr rb bb">11</td> <td class="tcc rb bb">4<span class="spp">1</span>&frasl;<span class="suu">6</span></td></tr>
+</table>
+
+<p>Wolverine, the strongest fur suited for rugs and foot-sacks, is
+taken as the standard.</p>
+
+<p>For a rug about 20 to 25 sq. ft. of fur are needed, for a foot-sack
+14½.</p>
+</div>
+<div class="author">(W. S. P.)</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1h" id="ft1h" href="#fa1h"><span class="fn">1</span></a> The measurements given are from nose to root of tail of average
+large sizes after the dressing process, which has a shrinking tendency.
+The depths of fur quoted are the greatest, but there are plenty of
+good useful skins possessing a lesser depth.</p>
+
+<p><a name="ft2h" id="ft2h" href="#fa2h"><span class="fn">2</span></a> Stout, old-fashioned boxcloth is almost the only cloth that
+(after a soft, heavy lining has been added to it) affords even two-thirds
+as much protection against cold as does fur. It weighs
+4.273 oz. per sq. ft. more than the heaviest of coat-furs, and is so
+rigid as to be uncomfortable, while the subtileness of fur makes it
+&ldquo;kind&rdquo; to the body.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FURAZANES<a name="ar78" id="ar78"></a></span> (<i>furo</i>&mdash;a.a&prime;&mdash;<i>diazoles</i>), organic compounds obtained
+by heating the glyoximes (dioximes of ortho-diketones)
+with alkalis or ammonia. Dimethylfurazane is prepared by
+heating dimethylglyoxime with excess of ammonia for six hours
+at 165° C. (L. Wolff, <i>Ber.</i>, 1895, 28, p. 70). It is a liquid (at
+ordinary temperature) which boils at 156° C. (744 mm.).
+Potassium permanganate oxidizes it first to methylfurazane-carboxylic
+acid and then to furazanedicarboxylic acid. Methyl-ethylfurazane
+and diphenylfurazane are also known. By
+warming oxyfurazane acetic acid with excess of potassium permanganate
+to 100° C. oxyfurazanecarboxylic acid is obtained
+(A. Hantzsch and J. Urbahn, <i>Ber.</i>, 1895, 28, p. 764). It crystallizes
+in prisms, which melt at 175° C. Furazanecarboxylic
+acid is prepared by the action of a large excess of potassium
+permanganate on a hot solution of furazanepropionic acid.
+It melts at 107º C, and dissolves in caustic soda, with a deep
+yellow colour and formation of nitrosocyanacetic acid (L. Wolff
+and P.F. Ganz, <i>Ber.</i>, 1891, 24, p. 1167). Furoxane is an oxide
+of furazane, considered by H. Wieland to be identical with
+glyoxime peroxide; Kekulés dibromnitroacetonitrile is dibromfuroxane.</p>
+
+<p>The formulae of the compounds above mentioned are:</p>
+
+<div class="center pt2"><img style="width:550px; height:74px; vertical-align: middle;" src="images/img357a.jpg" alt="" /></div>
+
+
+
+<hr class="art" />
+<p><span class="bold">FURETIÈRE, ANTOINE<a name="ar79" id="ar79"></a></span> (1619-1688), French scholar and
+miscellaneous writer, was born in Paris on the 28th of December
+1619. He first studied law, and practised for a time as an
+advocate, but eventually took orders and after various preferments
+became abbé of Chalivoy in the diocese of Bourges in
+1662. In his leisure moments he devoted himself to letters, and
+in virtue of his satires&mdash;<i>Nouvelle Allégorique, ou histoire des
+derniers troubles arrivés au royaume d&rsquo;éloquence</i> (1658); <i>Voyage de
+Mercure</i> (1653)&mdash;he was admitted a member of the French
+Academy in 1662. That learned body had long promised a
+complete dictionary of the French tongue; and when they
+heard that Furetière was on the point of issuing a work of a
+similar nature, they interfered, alleging that he had purloined
+from their stores, and that they possessed the exclusive privilege
+of publishing such a book. After much bitter recrimination
+on both sides the offender was expelled in 1685; but for this
+act of injustice he took a severe revenge in his satire, <i>Couches
+de l&rsquo;académie</i> (Amsterdam, 1687). His <i>Dictionnaire universel</i>
+was posthumously published in 1690 (Rotterdam, 2 vols.).
+It was afterwards revised and improved by the Protestant
+jurist, Henri Basnage de Beauval (1656-1710), who published his
+edition (3 vols.) in 1701; and it was only superseded by the
+compilation known as the <i>Dictionnaire de Trévoux</i> (Paris, 3 vols.,
+1704; 7th ed., 8 vols., 1771), which was in fact little more than a
+reimpression of Basnage&rsquo;s edition. Furetière is perhaps even
+better known as the author of <i>Le Roman bourgeois</i> (1666). It
+cast ridicule on the fashionable romances of Mlle de Scudéry
+and of La Calprenède, and is of interest as descriptive of the
+everyday life of his times. There is no element of burlesque,
+as in Scarron&rsquo;s <i>Roman comique</i>, but the author contents himself
+with stringing together a number of episodes and portraits,
+obviously drawn from life, without much attempt at sequence.
+The book was edited in 1854 by Edward Fournier and Charles
+Asselineau and by P. Jannet.</p>
+
+<div class="condensed">
+<p>The <i>Fureteriana</i>, which appeared in Paris eight years after
+Furetière&rsquo;s death, which took place on the 14th of May 1688, is a
+collection of but little value.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FURFOOZ<a name="ar80" id="ar80"></a></span>, a village some 10 m. from Dinant in the Ardennes,
+Belgium. Three caves containing prehistoric remains were here
+excavated in 1872. Of these the <i>Trou de Frontal</i> is the most
+famous. In it were found human skeletons with brachycephalic
+skulls, associated with animal bones, those of the reindeer being
+particularly plentiful. Among the skeletons was discovered
+an oval vase of pottery. The Furfooz type of mankind is believed
+to date from the close of the Quaternary age. G. de Mortillet
+dates the type in the Robenhausen epoch of the Neolithic
+period. His theory is that the bones are those of men of that
+period buried in what had been a cave-dwelling of the Madelenian
+epoch.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FURFURANE<a name="ar81" id="ar81"></a></span>, or <span class="sc">Furane</span>, C<span class="su">4</span>H<span class="su">4</span>O, a colourless liquid boiling
+at 32° C., found in the distillation products of pine wood. It
+was first synthetically prepared by H. Limpricht (<i>Ann.</i>, 1873,
+165, p. 281) by distilling barium mucate with soda lime, pyromucic
+acid C<span class="su">4</span>H<span class="su">3</span>O·CO<span class="su">2</span>H being formed, which, on further loss
+of carbon dioxide, yielded furfurane. A. Henniger (<i>Ann. chim.
+phys.</i>, 1886 [2], 7, p. 220), by distilling erthyrite with formic
+acid, obtained a dihydrofurfurane</p>
+
+<p class="center">C<span class="su">4</span>H<span class="su">6</span>(OH)<span class="su">4</span> + 2H<span class="su">2</span>CO<span class="su">2</span> = C<span class="su">4</span>H<span class="su">6</span>O + CO + CO<span class="su">2</span> + 4H<span class="su">2</span>O,</p>
+
+<p class="noind">which, on treatment with phosphorus pentachloride, yielded
+furfurane. Furfurane is insoluble in water and possesses a
+characteristic smell. It does not react with sodium or with
+phenylhydrazine, but yields dye-stuffs with isatin and phenanthrenequinone.
+It reacts violently with hydrochloric acid,
+producing a brown amorphous substance. Methyl and phenyl
+derivatives have been prepared by C. Paal (<i>Ber.</i>, 1884, 17, p.
+915). Paal prepared acetonyl acetophenone by condensing
+sodium acetoacetate with phenacylbromide, and this substance
+on dehydration yields &alpha;&alpha;&prime;-phenylmethylfurfurane, the acetonyl
+acetophenone probably reacting in the tautomeric &ldquo;enolic&rdquo; form,</p>
+
+<table class="math0" summary="math">
+<tr><td>CH<span class="su">3</span>·CO·CHNa·COOR + C<span class="su">6</span>H<span class="su">5</span>·CO·CH<span class="su">2</span>Br =
+  CH<span class="su">3</span>·CO·CH(CH<span class="su">2</span>COC<span class="su">6</span>H<span class="su">5</span>)·COOR.</td></tr>
+</table>
+
+<p class="noind">This ester readily hydrolyses, and the acid formed yields acetonyl
+acetophenone (by loss of carbon dioxide), which then on dehydration
+yields the furfurane derivative, thus</p>
+
+<div class="center ptb2"><img style="width:550px; height:40px; vertical-align: middle;" src="images/img357b.jpg" alt="" /></div>
+
+<p class="noind">L. Knorr (<i>Ber.</i>, 1889, 22, p. 158) obtained diacetosuccinic ester
+by condensing sodium acetoacetate with iodine, and by dehydrating
+the ester he prepared &alpha;&alpha;&prime;-dimethylfurfurane &beta;&beta;&prime;-dicarboxylic
+acid (carbopyrotritaric acid), which on distillation
+yields &alpha;&alpha;&prime;-dimethylfurfurane as a liquid boiling at 94° C. Paal
+also obtained this compound by using monochloracetone in the
+place of phenacylbromide. By the distillation of mucic acid
+or isosaccharic acid, furfurane-&alpha;-carboxylic acid (pyromucic
+acid), C<span class="su">4</span>H<span class="su">3</span>O·CO<span class="su">2</span>H, is obtained; it crystallizes in needles or
+leaflets, and melts at 134° C.</p>
+
+<p><i>Furfurol</i> (furol), C<span class="su">4</span>H<span class="su">3</span>O·CHO, is the aldehyde of pyromucic
+acid, and is formed on distilling bran, sugar, wood and most
+carbohydrates with dilute sulphuric acid, or by distilling
+the pentoses with hydrochloric acid. It is a colourless liquid
+which boils at 162° C., and is moderately soluble in water;
+it turns brown on exposure to air and has a characteristic
+aromatic smell. It shows all the usual properties of an aldehyde,
+forming a bisulphite compound, an oxime and a hydrazone;
+whilst it can be reduced to the corresponding furfuryl alcohol by
+means of sodium amalgam, and oxidized to pyromucic acid by
+means of silver oxide. It also shows all the condensation reactions
+of benzaldehyde (<i>q.v.</i>); condensing with aldehydes
+and ketones in the presence of caustic soda to form more
+complex aldehydes and ketones with unsaturated side chains,
+<span class="pagenum"><a name="page358" id="page358"></a>358</span>
+such as furfuracrolein, C<span class="su">4</span>H<span class="su">3</span>O·CH:CH·CHO, and furfuracetone,
+C<span class="su">4</span>H<span class="su">3</span>O·CH:CH·CO·CH<span class="su">3</span>. With alcoholic potassium cyanide
+It changes to furoin, C<span class="su">4</span>H<span class="su">3</span>O·CHOH·CO·C<span class="su">4</span>H<span class="su">3</span>O, which can be
+oxidized to furil, C<span class="su">4</span>H<span class="su">3</span>O·CO·CO·C<span class="su">4</span>H<span class="su">3</span>O, whilst alcoholic potash
+converts it into furfuryl alcohol. With fatty acids and acid
+anhydrides it gives the &ldquo;Perkin&rdquo; reaction (see <span class="sc"><a href="#artlinks">Cinnamic Acid</a></span>).
+Furfurol is shown to have its aldehydic group in the <i>a</i> position,
+by conversion into furfurpropionic acid, C<span class="su">4</span>H<span class="su">3</span>O·CH<span class="su">2</span>·CH<span class="su">2</span>·CO<span class="su">2</span>H,
+which on oxidation by bromine water and subsequent reduction
+of the oxidized product is converted into <i>n</i>-pimelic acid,
+HO<span class="su">2</span>C(CH<span class="su">2</span>)<span class="su">5</span>CO<span class="su">2</span>H. Furfurol in minute quantities can be
+detected by the red colour it forms with a solution of aniline
+acetate.</p>
+
+<div class="condensed">
+<p>Furfurane&mdash;&alpha;&alpha;&prime;-dicarboxylic acid or dehydromucic acid,
+C<span class="su">4</span>H<span class="su">2</span>O(CO<span class="su">2</span>H)<span class="su">2</span>, is formed when mucic acid is heated with hydrochloric
+acid at 100° C. On being heated, it loses carbon dioxide
+and gives pyromucic acid. By digesting acetoacetic ester with
+sodium succinate and acetic anhydride, methronic acid, C<span class="su">8</span>H<span class="su">8</span>O<span class="su">5</span>,
+is obtained; for the constitution of this acid, see L. Knorr, <i>Ber.</i>,
+1889, 22, p. 152, and R. Fittig, <i>Ann.</i>, 1889, 259, p. 166.</p>
+
+<p>Di- and tetrahydrofurfurane compounds are also known (see
+A. Lipp, <i>Ber.</i>, 1889, 22, p. 1196; W.H. Perkin, junr. <i>Journ. Chem.
+Soc.</i>, 1899, 57, p. 944; and S. Ruhemann, <i>ibid.</i>, 1896, 69, p. 1383).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FURIES<a name="ar82" id="ar82"></a></span> (Lat. <i>Furiae</i>, also called <span class="sc">Dirae</span>), in Roman mythology
+an adaptation of the Greek Erinyes (<i>q.v.</i>), with whom they
+are generally identical. A special aspect of them in Virgil is
+that of agents employed by the higher gods to stir up mischief,
+strife and hatred upon earth. Mention may here be made of
+an old Italian deity Furina (or Furrina), whose worship fell
+early into disuse, and who was almost forgotten in the time of
+Varro. By the mythologists of Cicero&rsquo;s time the name was
+connected with the verb <i>furere</i> and the noun <i>furia</i>, which in the
+plural (not being used in the singular in this sense) was accepted
+as the equivalent of the Greek Erinyes. But it is more probably
+related to <i>furvus</i>, <i>fuscus</i>, and signifies one of the spirits of darkness,
+who watched over men&rsquo;s lives and haunted their abodes.
+This goddess had her own special priest, a grove across the Tiber
+where Gaius Gracchus was slain, and a festival on the 25th of
+July. Authorities differ as to the existence of more than one
+goddess called Furina, and their identity with the Forinae
+mentioned in two inscriptions found at Rome (<i>C.I.L.</i> vi.
+422 and 10,200).</p>
+
+
+<hr class="art" />
+<p><span class="bold">FURLONG<a name="ar83" id="ar83"></a></span> (from the O. Eng. <i>furlang</i>, <i>i.e.</i> &ldquo;furrow-long&rdquo;),
+a measure of length, originally the length of a furrow in the
+&ldquo;common field&rdquo; system. As the field in this system was
+generally taken to be a square, 10 acres in extent, and as the
+acre varied in different districts and at different times, the
+&ldquo;furlong&rdquo; also varied. The side of a square containing 10
+statute acres is 220 yds. or 40 poles, which was the usually
+accepted length of the furlong. This is also the length of <span class="spp">1</span>&frasl;<span class="suu">8</span>th of
+the statute mile. &ldquo;Furlong&rdquo; was as early as the 9th century
+used to translate the Latin <i>stadium</i>, <span class="spp">1</span>&frasl;<span class="suu">8</span>th of the Roman mile.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FURNACE<a name="ar84" id="ar84"></a></span>, a contrivance for the production and utilization
+of heat by the combustion of fuel. The word is common to all
+the Romance tongues, appearing in more or less modified forms
+of the Latin <i>fornax</i>. But in all those languages the word has a
+more extended meaning than in English, as it covers every
+variety of heating apparatus; while here, in addition to furnaces
+proper, we distinguish other varieties as <i>ovens</i>, <i>stoves</i> and <i>kilns</i>.
+The first of these, in the form <i>Ofen</i>, is used in German as a general
+term like the French <i>four</i>; but in English it has been restricted
+to those apparatus in which only a moderate temperature,
+usually below a red heat, is produced in a close chamber. Our
+bakers&rsquo; ovens, hot-air ovens or stoves, annealing ovens for glass
+or metal, &amp;c., would all be called <i>fours</i> in French and <i>Öfen</i> in
+German, in common with furnaces of all kinds. Stove, an
+equivalent of oven, is from the German <i>Stube</i>, <i>i.e.</i> a heated room,
+and is commonly so understood; but is also applied to open
+fire-places, which appears to be somewhat of a departure from
+the original signification.</p>
+
+<p>Furnaces are constructed according to many different patterns
+with varying degrees of complexity in arrangement; but all
+may be considered as combining three essential parts, namely,
+the fire-place in which the fuel is consumed, the heated chamber,
+laboratory, hearth or working bed, as it is variously called,
+where the heat is applied to the special work for which the furnace
+is designed, and the apparatus for producing rapid combustion
+by the supply of air under pressure to the fire. In the simplest
+cases the functions of two or more of these parts may be combined
+into one, as in the smith&rsquo;s forge, where the fire-place and heating
+chamber are united, the iron being placed among the coals, only
+the air for burning being supplied under pressure from a blowing
+engine by a second special contrivance, the tuyere, tuiron,
+twyer or blast-pipe; but in the more refined modern furnaces,
+where great economy of fuel is an object, the different functions
+are distributed over separate and distinct apparatus, the fuel
+being converted into gas in one, dried in another, and heated
+in a third, before arriving at the point of combustion in the
+working chamber of the furnace proper.</p>
+
+<div class="condensed">
+<p>Furnaces may be classified according as the products of combustion
+are employed (1) only for heating purposes, or (2) both for
+heating and bringing about some chemical change. The furnaces
+employed for steam-raising or for heating buildings are invariably
+of the first type (see <span class="sc"><a href="#artlinks">Boiler</a></span> and <span class="sc"><a href="#artlinks">Heating</a></span>), while those employed
+in metallurgy are generally of the second. The essential difference
+in construction is that in the first class the substances heated do
+not come into contact with either the fuel or the furnace gases,
+whereas in the second they do. Metallurgical furnaces of the first
+class are termed crucible, muffle or retort furnaces, and of the
+second shaft and reverberatory furnaces. The following is a detailed
+subdivision:&mdash;</p>
+
+<p>(1) Fuel and substance in contact.</p>
+
+<div class="list">
+   <p>(<i>a</i>) Height of furnace greater than diameter = shaft furnaces.</p>
+</div>
+
+<div class="list1">
+       <p>(&alpha;) No blast = kilns.</p>
+
+       <p>(&beta;) With blast = blast furnaces.</p>
+</div>
+
+<div class="list">
+   <p>(<i>b</i>) Height not much greater than diameter = hearth furnaces.</p>
+</div>
+
+<p>(2) Substance heated by products of combustion = reverberatory
+      furnaces.</p>
+
+<div class="list">
+   <p>(<i>a</i>) Charge not melted = roasting or calcining furnaces.</p>
+
+   <p>(<i>b</i>) Charge melted = melting furnaces.</p>
+</div>
+
+<p>(3) Substance is not directly heated by the fuel or by the products
+      of combustion.</p>
+
+<div class="list">
+   <p>(<i>a</i>) Heating chamber fixed and forming part of furnace =
+        muffle furnaces.</p>
+
+   <p>(<i>b</i>) Crucible furnaces.</p>
+
+   <p>(<i>c</i>) Retort furnaces.</p>
+</div>
+
+<p>Another classification may be based upon the nature of the heating
+agent, according as it is coal (or some similar combustible) oil, gas
+or electricity. In this article the general principles of metallurgical
+furnaces will be treated; the subject of gas- and oil-heated furnaces
+is treated in the article Fuel, and of the electric furnace in the
+article Electrometallurgy. For special furnaces reference should
+be made to the articles on the industry concerned, <i>e.g.</i> <span class="sc"><a href="#artlinks">Glass</a></span>, <span class="sc"><a href="#artlinks">Gas</a></span>,
+§ <span class="sc"><a href="#artlinks">Manufacture</a></span>, &amp;c.</p>
+</div>
+
+<p><i>Shaft, Blast and Hearth Furnaces.</i>&mdash;The blast furnace in its
+simplest form is among the oldest, if not the oldest, of metallurgical
+contrivances. In the old copper-smelting district of
+Arabia Petraea, clay blast-pipes dating back to the earlier
+dynasties of ancient Egypt have been found buried in slag heaps;
+and in India the native smiths and iron-workers continue to use
+furnaces of similar types. These, when reduced to their most
+simple expression, are mere basin-shaped hollows in the ground,
+containing ignited charcoal and the substances to be heated,
+the fire being urged by a blast of air blown in through one or
+more nozzles from a bellows at or near the top. They are
+essentially the same as the smith&rsquo;s forge. This class of furnace
+is usually known as an open fire or hearth, and is represented in
+a more advanced stage of development by the Catalan, German
+and Walloon forges formerly used in the production of malleable
+iron.</p>
+
+<table class="flt" style="float: right; width: 350px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:300px; height:272px" src="images/img359a.jpg" alt="" /></td></tr>
+<tr><td class="caption1"> <span class="sc">Fig. 1.</span>&mdash;Elevation of Catalan
+Forge.</td></tr></table>
+
+<div class="condensed">
+<p>Fig. 1 represents a Catalan forge. The cavity in the ground is
+represented by a pit of square or rectangular section lined with
+brick or stone of a kind not readily acted on by heat, about 1½ or
+2 ft. deep, usually somewhat larger above than below, with a tuyere
+or blast-pipe of copper penetrating one of the walls near the top,
+with a considerable downward inclination, so that the air meets
+the fuel some way down. In iron-smelting the ore is laid in a heap
+upon the fuel (charcoal) filling up the hearth, and is gradually brought
+to the metallic state by the reducing action of the carbon monoxide
+formed at the tuyere. The metal sinks through the ignited fuel,
+forming, in the hearth, a spongy mass or ball, which is lifted out by
+the smelters at the end of each operation, and carried to the forge
+hammer. The earthy matters form a fusible glass or slag melt, and
+<span class="pagenum"><a name="page359" id="page359"></a>359</span>
+collect at the lowest point of the hearth, whence they are removed
+by opening a hole pierced through the front wall at the bottom.
+The active portion of such a furnace is essentially that above the
+blast-pipe, the function of the lower part being merely the collection
+of the reduced metal; the fire may therefore be regarded as burning
+in an unconfined space, with the waste of a large amount of its
+heating power. By continuing the walls of the hearth above the
+tuyere, into a shaft or stack either
+of the same or some other section,
+we obtain a furnace of increased
+capacity, but with no greater
+power of consuming fuel, in which
+the material to be treated can be
+heated up gradually by loading it
+into the stack, alternately with
+layers of fuel, the charge descending
+regularly to the point of combustion,
+and absorbing a proportion
+of the heat of the flame
+that went to waste in the open
+fire. This principle is capable of
+very wide extension, the blast
+furnace being mainly limited in
+height by the strength the column
+of materials or &ldquo;burden&rdquo; has to
+resist crushing, under the weight due to the head adopted, and the
+power of the blowing engine to supply blast of sufficient density
+to overcome the resistance of the closely packed materials to the
+free passage of the spent gases. The consuming power of the
+furnace or the rate at which it can burn the fuel supplied is measured
+by the number of tuyeres and their section.</p>
+</div>
+
+<p>The development of blast furnaces is practically the development
+of iron-smelting. The profile has been very much varied
+at different times. The earliest examples were square or rectangular
+in horizontal section, but the general tendency of modern
+practice is to substitute round sections, their construction being
+facilitated by the use of specially moulded bricks which have
+entirely superseded the sandstone blocks formerly used. The
+vertical section, on the other hand, is subject to considerable
+variation according to the work to which the furnace is applied.
+Where the operation is simply one of fusion, as in the iron-founder&rsquo;s
+cupola, in which there is no very great change in volume
+in the materials on their descent to the tuyeres, the stack is nearly
+or quite straight-sided; but when, as is the case with the smelting
+of iron ores with limestone flux, a large proportion of volatile
+matter has to be removed in the process, a wall of varying
+inclination is used, so that the body of the furnace is formed of
+two dissimilar truncated cones, joined by their bases, the lower
+one passing downwards into a short, nearly cylindrical,
+position. For further consideration of this subject see <span class="sc"><a href="#artlinks">Iron
+and Steel</a></span>.</p>
+
+<p><i>Hearth furnaces</i> are employed in certain metallurgical operations,
+<i>e.g.</i> in the air-reduction process for smelting lead ores.
+The principle is essentially that of the Catalan forge. Such
+furnaces are very wasteful, and have little to recommend them
+(see Schnabel, Metallurgy, 1905, vol. 1. p. 409).</p>
+
+<p><i>Reverberatory Furnaces.</i>&mdash;Blast furnaces are, from the intimate
+contact between the burden to be smelted and the fuel, the least
+wasteful of heat; but their use supposes the possibility of obtaining
+fuel of good quality and free from sulphur or other substances
+likely to deteriorate the metal produced. In all cases, therefore,
+where it is desired to do the work out of contact with the solid
+fuel, the operation of burning or heat-producing must be performed
+in a special fire-place or combustion chamber, the body
+of flame and heated gas being afterwards made to act upon the
+surface of the material exposed in a broad thin layer in the
+working bed or laboratory of the furnace by reverberation from
+the low vaulted roof covering the bed. Such furnaces are known
+by the general name of reverberatory or reverbatory furnaces,
+also as air or wind furnaces, to distinguish them from those
+worked with compressed air or blast.</p>
+
+<p>Originally the term cupola was used for the reverberatory
+furnace, but in the course of time it has changed its meaning,
+and is now given to a small blast furnace such as that used by
+iron-founders&mdash;reverberatory smelting furnaces in the same
+trade being called air furnaces.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:640px; height:365px" src="images/img359b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 2.</span>&mdash;Longitudinal section of Reverberatory Furnace.</td></tr></table>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:650px; height:384px" src="images/img359c.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 3.</span>&mdash;Reverberatory Furnace (horizontal section).</td></tr></table>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:650px; height:715px" src="images/img359d.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 4.</span>&mdash;Reverberatory Furnace (elevation at flue end).</td></tr></table>
+
+<div class="condensed">
+<p>Figs. 2, 3 and 4 represent a reverberatory furnace such as is used
+for the fusion of copper ores for regulus, and may be taken as generally
+representing its class. The fire-place A is divided from the
+working bed B by a low wall C known as the fire bridge, and at the
+opposite end there is sometimes, though not invariably, a second
+bridge of less height called the flue bridge D. A short diagonal flue
+or up-take E conveys the current of spent flame to the chimney
+F, which is of square section, diminishing by steps at two or three
+different heights, and provided at the top with a covering plate or
+damper G, which may be raised or lowered by a chain reaching to
+the ground, and serves for regulating the speed of the exhaust gases,
+and thereby the draught of air through the fire. Where several
+furnaces are connected with the same chimney stack, the damper
+takes the form of a sliding plate in the mouth of the connecting flue,
+so that the draught in one may be modified without affecting the
+others. The fire bridge is partially protected against the intense
+<span class="pagenum"><a name="page360" id="page360"></a>360</span>
+heat of the body of flame issuing through the fire arch by a passage
+to which the air has free access. The material to be melted is
+introduced into the furnace from the hoppers HH through the
+charging holes in the roof. When melted the products separate on
+the bed (which is made of closely packed sand or other infusible
+substances), according to their density; the lighter earthy matters
+forming an upper layer of slag are drawn out by the slag hole K at
+the flue end into an iron wagon or bogie, while the metal subsides
+to the bottom of the bed, and at the termination of the operation
+is run out by the tap hole L into moulds or granulated into water.
+The opposite opening M is the working door, through which the tool
+for stirring the charge is introduced. It is covered by a plate
+suspended to a lever, similar to that seen in the end elevation (fig. 4)
+in front of the slag hole.</p>
+</div>
+
+<p>According to the purposes to which they are applied, reverberatory
+furnaces may be classed into two groups, namely, fusion
+or melting furnaces, and calcining or wasting furnaces, also
+called calciners. The former have a very extended application
+in many branches of industry, being used by both founders and
+smelters in the fusion of metals; in the concentration of poor
+metallic compounds by fusion into regulus; in the reduction
+of lead and tin ores; for refining copper and silver; and for
+making malleable iron by the puddling processes and welding.
+Calcining furnaces have a less extended application, being
+chiefly employed in the conversion of metallic sulphides into
+oxides by continued exposure to the action of air at a temperature
+far below that of fusion, or into chlorides by roasting with common
+salt. As some of these substances (for example, lead sulphide
+and copper pyrites) are readily fusible when first heated, but
+become more refractory as part of the sulphur is dissipated and
+oxygen takes its place, it is important that the heat should be
+very carefully regulated at first, otherwise the mass may become
+clotted or fritted together, and the oxidizing effect of the air soon
+ceases unless the fritted masses be broken small again. This is
+generally done by making the bed of the furnace very long in
+proportion to its breadth and to the fire-grate area, which may
+be the more easily done as a not inconsiderable amount of heat
+is given out during the oxidation of the ore&mdash;such increased
+length being often obtained by placing two or even three working
+beds one above the other, and allowing the flame to pass over them
+in order from below upwards. Such calciners are used especially
+in roasting zinc blende into zinc oxide, and in the conversion of
+copper sulphides into chlorides in the wet extraction process. In
+some processes of lead-smelting, where the minerals treated
+contain sand, the long calciner is provided with a melting bottom
+close to the fire-place, so that the desulphurized ore leaves the
+furnace as a glassy slag or silicate, which is subsequently reduced
+to the metallic state by fusion with fluxes in blast furnaces.
+Reverberatory furnaces play an important part in the manufacture
+of sodium carbonate; descriptions and illustrations are
+given in the article <span class="sc"><a href="#artlinks">Alkali Manufacture</a></span>.</p>
+
+<p><i>Muffle, Crucible and Retort Furnaces.</i>&mdash;A third class of furnaces
+is so arranged that the work is done by indirect heating; that
+is, the material under treatment, whether subjected to calcination,
+fusion or any other process, is not brought in contact either
+with fuel or flame, but is raised to the proper temperature by
+exposure in a chamber heated externally by the products of
+combustion. These are known as muffle or chamber furnaces;
+and by supposing the crucibles or retorts to represent similar
+chambers of only temporary duration, the ordinary pot melting
+air furnaces, and those for the reduction of zinc ores or the
+manufacture of coal gas, may be included in the same category.
+These are almost invariably air furnaces, though sometimes air
+under pressure is used, as, for example, in the combustion of
+small anthracitic coal, where a current of air from a fan-blower
+is sometimes blown under the grate to promote combustion.
+Types of muffle furnaces are figured in the article <span class="sc"><a href="#artlinks">Annealing,
+Hardening and Tempering</a></span>.</p>
+
+<p><i>Furnace Materials.</i>&mdash;The materials used in the construction
+of furnaces are divisible into two classes, namely, ordinary and
+refractory or fire-resisting. The former are used principally as
+casing, walls, pillars or other supporting parts of the structure,
+and includes ordinary red or yellow bricks, clay-slate, granite
+and most building stones; the latter are reserved for the parts
+immediately in contact with the fuel and flame, such as the
+lining of the fire-place, the arches, roof and flues, the lower part
+if not the whole of the chimney lining in reverberatory furnaces,
+and the whole of the internal walls of blast furnaces. Among
+such substances are fireclay and firebricks, certain sandstones,
+silica in the form of ganister, and Dinas stone and bricks, ferric
+oxide and alumina, carbon (as coke and graphite), magnesia,
+lime and chromium oxide&mdash;their relative importance being
+indicated by their order, the last two or three indeed being only
+of limited use.</p>
+
+<p>The most essential point in good fireclays, or in the bricks
+or other objects made from them, is the power of resisting
+fusion at the highest heat to which they may be exposed. This
+supposes them to be free from metallic oxides forming easily
+fusible compounds with silica, such as lime or iron, the presence
+of the former even in comparatively small proportion being very
+detrimental. As clays they must be sufficiently plastic to be
+readily moulded, but at the same time possess sufficient stiffness
+not to contract too strongly in drying, whereby the objects
+produced would be liable to be warped or cracked before firing.
+In most cases, however, the latter tendency is guarded against,
+in making up the paste for moulding, by adding to the fresh
+clay a certain proportion of burnt material of the same kind,
+such as old bricks or potsherds, ground to a coarse powder.
+Coke dust or graphite is used for the same purpose in crucible
+making (see <span class="sc"><a href="#artlinks">Firebrick</a></span>).</p>
+
+<div class="condensed">
+<p>The most highly valued fireclays are derived from the Coal
+Measures. Among the chief localities are the neighbourhood of
+Stourbridge in Worcestershire and Stannington near Sheffield,
+which supply most of the materials for crucibles used in steel and
+brass melting, and the pots for glass houses; Newcastle-on-Tyne
+and Glenboig near Glasgow, where heavy blast furnace and other
+firebricks, gas retorts, &amp;c., are made in large quantities. Coarse-grained
+but very strong firebricks are also made of the waste of
+china clay works.</p>
+
+<p>In Belgium the clay raised at Andenne is very largely used for
+making retorts for zinc furnaces. The principal French fireclays
+are derived from the Tertiary strata in the south, and more nearly
+resemble porcelain clays than those of the Coal Measures. They
+give wares of remarkably fine texture and surface, combined with
+high refractory character.</p>
+
+<p>In Germany, Ips and Passau on the Danube, and Gross Almerode
+in Hesse, are the best known localities producing fireclay goods, the
+crucibles from the last-mentioned place, known as Hessian crucibles,
+going all over the world. These, though not showing a great resistance
+to extreme heat, are very slightly affected by sudden alternations
+in heating, as they may be plunged cold into a strongly heated
+furnace without cracking, a treatment to which French and Stourbridge
+pots cannot be subjected with safety.</p>
+</div>
+
+<p>Plumbago or graphite is largely used in the production of
+crucibles, not in the pure state but in admixture with fireclay;
+the proportion of the former varies with the quality from 25 to
+nearly 50%. These are the most enduring of all crucibles, the
+best lasting out 70 or 80 meltings in brass foundries, about 50
+with bronze, and 8 to 10 in steel-melting.</p>
+
+<p>Silica is used in furnace-building in the forms of sand, ganister,
+a finely ground sandstone from the Coal Measures of Yorkshire,
+and the analogous substance known as Dinas clay, which is
+really nearly pure silica, containing at most about 2½% of bases.
+Dinas clay is found at various places in the Vale of Neath in
+South Wales, in the form of a loose disintegrated sandstone,
+which is crushed between rollers, mixed with about 1% of lime,
+and moulded into bricks that are fired in kilns at a very high
+temperature. These bricks are specially used for the roof, fire
+arches, and other parts subjected to intense heat in reverberatory
+steel-melting furnaces, and, although infusible under
+ordinary conditions, are often fairly melted by the heat without
+fluxing or corrosion after a certain amount of exposure. Ganister,
+a slightly plastic siliceous sand, is similarly used for the lining
+of Bessemer steel converters; it is found in the neighbourhood
+of Sheffield.</p>
+
+<p>Alumina as a refractory material is chiefly used in the form
+of bauxite, but its applications are somewhat special. It has
+been found to stand well for the linings of rotatory puddling
+furnaces, where, under long-continued heating, it changes into
+a substance as hard and infusible as natural emery. In the
+<span class="pagenum"><a name="page361" id="page361"></a>361</span>
+Paris Exhibition of 1878 bricks very hard and dense in character,
+said to be of pure alumina, were exhibited by Muller &amp; Co. of
+Paris, as well as bricks of magnesia, the latter being specially
+remarkable for their great weight. They are intended for use
+at the extreme temperatures obtainable in steel furnaces, or
+for the melting of platinum before the oxy-hydrogen blowpipe.
+For the latter purpose, however, lime is generally used; but as
+this substance has only small stability, it is usually bedded in a
+casing of firebrick. Oxide of chromium and chrome iron ore
+have been proposed as refractory crucible materials. The former
+may be used as a bed for melting platinum in the same way as
+lime or magnesia, without affecting the quality of the metal.</p>
+
+<p>Ferric oxide, though not strictly infusible, is largely used as a
+protecting lining for furnaces in which malleable iron is made,
+a portion of the ore being reduced and recovered in the process.
+In an oxidizing atmosphere it is indifferent to silica, and therefore
+siliceous bricks containing a considerable proportion of ferric
+oxide, when used in flues of boilers, brewers&rsquo; coppers, &amp;c. and
+similar situations, are perfectly fire-resisting so long as the heated
+gas contains a large proportion of unconsumed air. The red
+firebricks known as Windsor bricks, which are practically
+similar in composition to soft red sandstone, are of this character.</p>
+
+<p>The electric furnace has led to the discovery of several
+important materials, which have been employed as furnace
+linings. Carborundum (<i>q.v.</i>) was applied by Engels in 1899,
+firebricks being washed with carborundum paste and then baked.
+Siloxicon, a compound of carbon, silicon and oxygen, formed
+from carbon and silica in the electric furnace, was patented by
+E.G. Acheson in 1903. It is very refractory, and is applied by
+mixing with water and some bond, such as sodium silicate or
+gas-tar. An amorphous, soft silicon carbide, also formed in the
+electric furnace, was patented by B. Talbot in 1899. For basic
+linings, magnesia crystallized in the electric furnace is being
+extensively used, replacing dolomite to some extent (see E.
+Kilburn Scott, &ldquo;Refractory Materials for Furnace Linings,&rdquo;
+<i>Faraday Soc.</i>, 1906, p. 289).</p>
+
+<div class="condensed">
+<p><i>Furnace Construction.</i>&mdash;In the construction of furnaces provision
+has to be made for the unequal expansion of the different parts under
+the effect of heat. This is especially necessary in the case of reverberatory
+furnaces, which are essentially weak structures, and
+therefore require to be bound together by complicated systems of
+tie rods and uprights or buck staves. The latter are very commonly
+made of old flat bottom rails, laid with the flat of the flange against
+the wall. Puddling furnaces are usually entirely cased with iron
+plates, and blast furnaces with hoops round each course of the stack,
+or in those of thinner constructions the firebrick work is entirely
+enclosed in a wrought iron casing or jacket. Such parts as may be
+subjected to extreme heat and the fretting action of molten material,
+as the tuyere and slag breasts of blast furnaces, and the fire bridges
+and bed plates of reverberatory furnaces, are often made in cast
+iron with double walls, a current of water or air being kept circulating
+through the intermediate space. In this way the metal, owing to
+its high conductivity and low specific heat as compared to that of
+water, is kept at a temperature far below its melting point if the
+water is renewed quickly enough. It is of course necessary in such
+cases that the circulation shall be perfectly free, in order to prevent
+the accumulation of steam under pressure in the interior of the
+casting. This method has received considerable extension, notably
+in furnace-smelting of iron ores containing manganese, where the
+entire hearth is often completely water-cased, and in some lead
+furnaces where no firebrick lining is used, the lower part of the
+furnace stack being a mere double iron box cooled by water sufficiently
+to keep a coating of slag adhering to the inner shell which
+prevents the metal from being acted upon.</p>
+
+<p><i>Mechanical Furnaces.</i>&mdash;The introduction and withdrawal of the
+charges in fusion furnaces is effected by gravitation, the solid masses
+of raw ore, fuel and flux being thrown in at the top, and flowing
+out of the furnace at the taphole or slag run at the bottom. Vertical
+kilns, such as those used for burning limestone, are worked in a
+similar manner&mdash;the raw stone going in at the top, and the burnt
+product falling through holes in the bottom when allowed to do so.
+With reverberatory calciners, however, where the work is done
+upon a horizontal bed, a considerable amount of hand labour is
+expended in raking out the charge when finished, and in drawing
+slags from fusion furnaces; and more particularly in the puddling
+process of refining iron the amount of manual exertion required is
+very much greater. To diminish the item of expenditure on this
+head, various kinds of mechanical furnaces have been adopted, all
+of which can be classified under three heads of gravitating furnaces,
+mechanical stirrers and revolving furnaces.</p>
+
+<p>1. In <i>gravitating furnaces</i> the bed is laid at a slope just within the
+angle of repose of the charge, which is introduced at the upper end,
+and is pushed down the slope by fresh material, when necessary,
+in the contrary direction to the flame which enters at the lower end.
+Gerstenhofer&rsquo;s pyrites burner is a furnace of this class. It has a tall
+vertical chamber heated from below, and traversed by numerous
+narrow horizontal cross bars at different heights. The ore in fine
+powder is fed in at the top, through a hopper, in a regular thin
+stream, by a pair of rollers, and in falling lodges on the flats of the
+bars, forming a talus upon each of the height corresponding to the
+angle of rest of the material, which is, however, at short intervals
+removed to lower levels by the arrival of fresh ore from above. In
+this way a very large surface is exposed to the heat, and the ore, if
+containing sufficient sulphur to maintain the combustion, is perfectly
+burned when it arrives at the bottom; if, however, it is imperfectly
+sized or damp, or if it contains much earthy matter, the result is
+not very satisfactory. There are many other furnaces in which the
+same principle is utilized.</p>
+
+<p>2. <i>Mechanical stirrers</i> constitute a second division of mechanical
+furnaces, in which the labour of rabbling or stirring the charges is
+performed by combinations of levers and wheel-work taking motion
+from a rotating shaft, and more or less perfectly imitating the action
+of hand labour. They are almost entirely confined to puddling
+furnaces.</p>
+
+<p>3. <i>Revolving furnaces</i>, the third and most important division of
+mechanical furnaces, are of two kinds. The first of these resemble
+an ordinary reverberatory furnace by having a flat bed which,
+however, has the form of a circular disk mounted on a central shaft,
+and receives a slow movement of rotation from a water-wheel or
+other motor, so that every part of the surface is brought successively
+under the action of the fire, the charge being stirred and ultimately
+removed by passing under a series of fixed scraper arms placed above
+the surface at various points. Brunton&rsquo;s calciner, used in the &ldquo;burning&rdquo;
+of the pyritic minerals associated with tin ore, is a familiar
+example of this type. The hearth may either rotate on an inclined
+axis, so that the path of its surface is oblique to that of the flame,
+or the working part may be a hollow cylinder, between the fireplace
+and flue, with its axis horizontal or nearly so, whose inner surface
+represents the working bed, mounted upon friction rollers, and
+receiving motion from a special steam-engine by means of a central
+belt of spur gearing. Furnaces of the second kind were first used in
+alkali works for the conversion of sulphate into carbonate of sodium
+in the process known as black ash fusion, but have since been applied
+to other processes. As calciners they are used in tin mines and for
+the chlorination of silver ores. Mechanical furnaces are figured in
+the article <span class="sc"><a href="#artlinks">Alkali Manufacture</a></span>.</p>
+
+<p><i>Use of Heated Air.</i>&mdash;The calorific intensity of fuel is found to be
+very considerably enhanced, if the combustion be effected with air
+previously heated to any temperature between that of boiling water
+and a dull red heat, the same effect being observed both with solid
+and gaseous fuel. The latter, especially when brought to the burning
+point at a high temperature, produces a heat that can be resisted
+by the most refractory substances only, such as silica, alumina and
+magnesia. This is attained in the regenerative furnace of Siemens,
+detailed consideration of which belongs more properly to the subject
+of iron.</p>
+
+<p><i>Economy of Waste Heat.</i>&mdash;In every system of artificial heating, the
+amount of heat usefully applied is but a small proportion of that
+developed by combustion. Even under the most advantageous
+application, that of evaporation of water in a steam boiler where the
+gases of the fire have to travel through a great length of flues bounded
+by thin iron surfaces of great heat-absorbing capacity, the temperature
+of the current at the chimney is generally much above that
+required to maintain an active draught in the fireplace; and other
+tubes containing water, often in considerable numbers, forming the
+so-called fuel economizers, may often be interposed between the
+boiler and the chimney with marked advantage as regards saving
+of fuel. In reverberatory and air furnaces used in the different
+operations of iron manufacture, where an extremely high temperature
+has to be maintained in spaces of comparatively small extent, such
+as the beds of puddling, welding and steel-melting furnaces, the
+temperature of the exhaust gases is exceedingly high, and if allowed
+to pass directly into the chimney they appear as a great body of
+flame at the top. It is now general to save a portion of this heat by
+passing the flame through flues of steam boilers, air-heating apparatus,
+or both&mdash;so that the steam required for the necessary operations
+of the forge and heated blast for the furnace itself may be obtained
+without further expenditure of fuel. The most perfect method of
+utilizing the waste heat hitherto applied is that of the Siemens regenerator,
+in which the spent gases are made to travel through
+chambers, known as regenerators or recuperators of heat, containing
+a quantity of thin firebricks piled into a cellular mass so as to offer
+a very large heat-absorbing surface, whereby their temperature is
+very considerably reduced, and they arrive at the chimney at a heat
+not exceeding 300 or 400 degrees. As soon as the bricks have become
+red hot, the current is diverted to an adjacent chamber or pair of
+chambers, and the acquired heat is removed by a current of cool
+gas or air passing towards the furnace, where it arrives at a temperature
+sufficiently high to ensure the greatest possible heating
+effect in combustion.</p>
+
+<p><span class="pagenum"><a name="page362" id="page362"></a>362</span></p>
+
+<p>In iron-smelting blast furnaces the waste gases are of considerable
+fuel value, and may render important services if properly applied.
+Owing to the conditions of the work, which require the maintenance
+of a sensibly reducing atmosphere, they contain a very notable
+proportion of carbonic oxide, and are drawn off by large wrought iron
+tubes near the top of the furnace and conveyed by branch pipes
+to the different boilers and air-heating apparatus, which are now
+entirely heated by the combustion of such gases, or mixed with air
+and exploded in gas engines. Formerly they were allowed to burn
+to waste at the mouth of a short chimney place above the furnace
+top, forming a huge body of flame, which was one of the most
+striking features of the Black Country landscape at night.</p>
+
+<p><i>Laboratory and Portable Furnaces.</i>&mdash;Small air-furnaces with hot
+plates or sand bath flues were formerly much employed in chemical
+laboratories, as well as small blast furnaces for crucibles heated with
+charcoal or coke. The use of such furnaces has very considerably
+diminished, owing to the general introduction of coal-gas for heating
+purposes in laboratories, which has been rendered possible by the
+invention of the Bunsen burner, in which the mixture of air and gas
+giving the least luminous but most powerfully heating flame is
+effected automatically by the effluent gas. These burners, or
+modifications of them, have also been applied to muffle furnaces,
+which are convenient when only a few assays have to be made&mdash;the
+furnace being a mere clay shell and soon brought to a working
+temperature; but the fuel is too expensive to allow of their being
+used habitually or on a large scale. Petroleum, or rather the heavy
+oils obtained in tar refineries, having an equal or superior heating
+power to coal-gas, may also be used in laboratories for producing
+high temperatures. The oil is introduced in a thin stream upon a
+series of inclined and channelled bars, where it is almost immediately
+volatilized and burnt by air flowing in through parallel orifices.
+Furnaces of this kind may be used for melting cast iron or bronze
+in small quantities, and were employed by H. Sainte Claire Deville
+in experiments in the metallurgy of the platinum group of metals.</p>
+
+<p>Sefstrom&rsquo;s blast furnace, used in Sweden for the assay of iron ores,
+is a convenient form of portable furnace applied to melting in
+crucibles. It consists of a sheet-iron cylinder about 8 or 9 in. in
+diameter, within which is fixed one of smaller size lined with fireclay.
+The space between the two cylinders serves as a heater and
+distributor for the blast, which is introduced through the nozzle at
+the bottom, and enters the furnace through a series of several small
+tuyeres arranged round the inner lining. Charcoal is the fuel used,
+and the crucibles stand upon the bottom of the clay lining. When
+a large body of fuel is required, the cylinder can be lengthened by
+an iron hoop which fits over the top ring. Deville&rsquo;s portable blast
+furnace is very similar in principle to the above, but the body of the
+furnace is formed of a single cast iron cylinder lined with fireclay,
+closed below by a cast iron plate perforated by a ring of small holes&mdash;a
+hemispherical basin below forming the air-heating chamber.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FURNEAUX, TOBIAS<a name="ar85" id="ar85"></a></span> (1735-1781), English navigator, was
+born at Swilly near Plymouth on the 21st of August 1735. He
+entered the royal navy, and was employed on the French and
+African coasts and in the West Indies during the latter part of the
+Seven Years&rsquo; War (1760-1763). He served as second lieutenant
+of the &ldquo;Dolphin&rdquo; under Captain Samuel Wallis on the latter&rsquo;s
+voyage round the globe (August 1766-May 1768); was made
+a commander in November 1771; and commanded the &ldquo;Adventure&rdquo;
+which accompanied Captain Cook (in the &ldquo;Resolution&rdquo;)
+in Cook&rsquo;s second voyage. On this expedition Furneaux
+was twice separated from his leader (February 8-May 19, 1773;
+October 22, 1773-July 14, 1774, the date of his return to
+England). On the former occasion he explored a great part of
+the south and east coasts of Tasmania, and made the earliest
+British chart of the same. Most of his names here survive;
+Cook, visiting this shore-line on his third voyage, confirmed
+Furneaux&rsquo;s account and delineation of it (with certain minor
+criticisms and emendations), and named after him the islands
+in Banks Straits, opening into Bass&rsquo;s Straits, and the group now
+known as the Low Archipelago. After the &ldquo;Adventure&rdquo; was
+finally separated from the &ldquo;Resolution&rdquo; off New Zealand in
+October 1773, Furneaux returned home alone, bringing with him
+Omai of Ulaietea. This first South Sea Islander seen in the
+British Isles returned to his home with Cook in 1776-1777.
+Furneaux was made a captain in 1775, and commanded the
+&ldquo;Syren&rdquo; in the British attack of the 28th of June 1776 upon
+Charleston, South Carolina. His successful efforts to introduce
+domestic animals and potatoes into the South Sea Islands are
+worthy of note. He died at Swilly on the 19th of September
+1781.</p>
+
+<div class="condensed">
+<p>See Hawkesworth&rsquo;s <i>Narrative of Wallis&rsquo; Voyage</i>; Captain Cook&rsquo;s
+<i>Narrative of his Second Voyage</i>; also T. Furneaux&rsquo;s life by Rev.
+Henry Furneaux in the <i>Dictionary of National Biography</i>.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FURNES<a name="ar86" id="ar86"></a></span> (Flem. <i>Veurne</i>), an old-fashioned little town amid
+the dunes near the coast in West Flanders, Belgium, about
+26 m. S.W. of Bruges. Pop. (1904) 6099. It is the centre of a
+considerable area extending to the French frontier, and its
+market is an important one for the disposal of corn, stock, hops
+and dairy produce. During the Norman raids Furnes was
+destroyed, and the present town was built by Baldwin Bras de
+Fer, first count of Flanders, about the year 870. At the height
+of the prosperity of the Flemish communes in the 14th century
+there were dependent on the barony of Furnes not fewer than
+fifty-two rich villages, but these have all disappeared, partly
+no doubt as the consequence of repeated French invasions down
+to the end of the 18th century, but chiefly through the encroachment
+of the sea followed by the accumulation of sand along the
+whole of this portion of the coast. Furnes contains many
+curious old houses and the church of St Walburga, which is a
+fine survival of the 13th century with some older portions. The
+old church and buildings, grouped round the Grand Place, which
+is the scene of the weekly market, present a quaint picture
+which is perhaps not to be equalled in the country. Near Furnes
+on the seashore is the fashionable bathing place called La Panne.</p>
+
+<p>Furnes one day a year becomes a centre of attraction to all
+the people of Flanders. This is the last Sunday in July, when the
+fête of Calvary and the Crucifixion is celebrated. Of all popular
+festivities in Belgium this is the nearest approach to the old
+Passion Play. The whole story of Christ is told with great
+precision by means of succeeding groups which typify the different
+phases of the subject. The people of Furnes pose as Roman
+soldiers or Jewish priests, as the apostles or mere spectators,
+while the women put on long black veils so that they may figure
+in the procession as the just women.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FURNESS, HORACE HOWARD<a name="ar87" id="ar87"></a></span> (1833-&emsp;&emsp;), American
+Shakespearian scholar, was born in Philadelphia on the 2nd of
+November 1833, being the son of William Henry Furness (1802-1896)
+minister of the First Unitarian church in that city, a
+powerful preacher and writer. He graduated at Harvard in
+1854, and was admitted to the bar in 1859, but soon devoted
+himself to the study of Shakespeare. He accumulated a collection
+of illustrative material of great richness and extent, and brought
+out in 1871 the first volume of a new Variorum edition, designed
+to represent and summarize the conclusions of the best authorities
+in all languages&mdash;textual, critical and annotative. The volumes
+appeared as follows: <i>Romeo and Juliet</i> (1871); <i>Macbeth</i> (1873)
+(revised edition, 1903); <i>Hamlet</i> (2 vols., 1877); <i>King Lear</i>
+(1880); <i>Othello</i> (1886); <i>The Merchant of Venice</i> (1888); <i>As You
+Like It</i> (1890); <i>The Tempest</i> (1892); <i>A Midsummer Night&rsquo;s
+Dream</i> (1895); <i>The Winter&rsquo;s Tale</i> (1898); <i>Much Ado about
+Nothing</i> (1899); <i>Twelfth Night</i> (1901); <i>Love&rsquo;s Labour&rsquo;s Lost</i>
+(1904). The edition has been generally accepted as a thorough
+and scholarly piece of work; its chief fault is that, beginning
+with <i>Othello</i> (1858), the editor used the First Folio text as his
+basis, while in others he makes the text of the Cambridge (Globe)
+editors his foundation. His wife, Helen Kate Furness (1837-1883),
+compiled <i>A Concordance to the Poems of Shakespeare</i> (1872).</p>
+
+
+<hr class="art" />
+<p><span class="bold">FURNESS<a name="ar88" id="ar88"></a></span>, a district of Lancashire, England, separated from
+the major portion of the county by Morecambe Bay. It is
+bounded S.E. by this inlet of the Irish Sea, S.W. by the sea,
+W. by the Duddon estuary and Cumberland, and N. and E. by
+Westmorland. Its area is about 250 sq. m. It forms the greater
+part of the North Lonsdale parliamentary division of Lancashire,
+and contains the parliamentary borough of Barrow-in-Furness.
+The surface is almost entirely hilly. The northern half is included
+in the celebrated Lake District, and contains such eminences
+as the Old Man of Coniston and Wetherlam. Apart from the
+Duddon, which forms part of the western boundary, the principal
+rivers are the Leven and Crake, flowing southward into a common
+estuary in Morecambe Bay. The Leven drains Windermere
+and the Crake Coniston Lake. The usage of the term &ldquo;Lake
+District,&rdquo; however, tends to limit the name of Furness in common
+thought to the district south of the Lakes, where several of the
+place-names are suffixed with that of the district, as Barrow-in-Farness,
+Dalton-in-Furness, Broughton-in-Furness. Between
+<span class="pagenum"><a name="page363" id="page363"></a>363</span>
+the Duddon and Morecambe Bay lies Walney Island, 8 m. in
+length, and in the shallow strait between it and the mainland
+are several smaller islands. That part of Furness which forms a
+peninsula between the Leven estuary and Morecambe Bay, and
+the Duddon estuary, is rich in hematite iron ore, which has been
+worked from very early times. It was known and smelted by
+British and Romans, and by the monks of Furness Abbey and
+Conishead Priory, both in the district. It was owing to the
+existence of this ore that the town of Barrow grew up in the 19th
+century; at first as a port from which the ore was exported to
+South Wales, while later furnaces were established on the spot,
+and acquired additional importance on the introduction of the
+Bessemer process, which requires a non-phosphoric ore such as
+is found here. The hematite is also worked at Ulverston, Askam,
+Dalton and elsewhere, but the furnaces now depend in part
+upon ore imported from Spain. The supposed extension of the
+ore under the sands of the Duddon estuary led to the construction
+of a sea wall to facilitate the working. The district is served
+by the main line of the Furness railway, from Carnforth (junction
+with the London &amp; North-Western railway), passing the pleasant
+watering-place of Grange, and approximately following the
+coast by Ulverston, Dalton and Barrow, with branches to Lake
+Side, Windermere, and to Coniston.</p>
+
+<p>Apart from its industrial importance and scenic attractions,
+Furness has an especial interest on account of its famous abbey.
+The ruins of this, beautifully situated in a wooded
+valley, are extensive, and mainly of fine transitional
+<span class="sidenote">Furness Abbey.</span>
+Norman and Early English date, acquiring additional
+picturesqueness from the warm colour of the red sandstone
+of which they are built. The abbey of Furness, otherwise
+Furdenesia or the further <i>nese</i> (promontory), which was dedicated
+to St Mary, was founded in 1127 by a small body of monks
+belonging to the Benedictine order of Savigny. In 1124 they
+had settled at Tulketh, near Preston, but migrated in 1127 to
+Furness under the auspices of Stephen, count of Boulogne,
+afterwards king, at that time lord of the liberty of Furness.
+In 1148 the brotherhood joined the Cistercian order. Stephen
+granted to the monks the lordship of Furness, and his charter
+was confirmed by Henry I., Henry II. and subsequent kings.
+The abbot&rsquo;s power throughout the lordship was almost absolute;
+he had a market and fair at Dalton, was free from service to the
+county and wapentake, and held a sheriff&rsquo;s tourn. By a succession
+of gifts the abbey became one of the richest in England
+and was the largest Cistercian foundation in the kingdom. At
+the Dissolution its revenues amounted to between £750 and
+£800 a year, exclusive of meadows, pastures, fisheries, mines,
+mills and salt works, and the wealth of the monks enabled them
+to practise a regal hospitality. The abbot was one of the twenty
+Cistercian abbots summoned to the parliament of 1264, but was
+not cited after 1330, as he did not hold of the king <i>in capite per
+baroniam</i>. The abbey founded several offshoot houses, one of
+the most important being Rushen Abbey in the Isle of Man. In
+1535 the royal commissioners visited the abbey and reported
+four of its inmates, including the abbot, for incontinence. In
+1536 the abbot was charged with complicity in the Pilgrimage
+of Grace, and on the 7th of April 1537, under compulsion,
+surrendered the abbey to the king. A few monks were granted
+pensions, and the abbot was endowed with the profits of the
+rectory of Dalton, valued at £33, 6s. 8d. per annum. In 1540
+the estates and revenues were annexed by act of parliament to
+the Duchy of Lancaster. About James I.&rsquo;s reign the site and
+territories were alienated to the Prestons of Preston-Patrick,
+from whom they descended to the dukes of Devonshire.</p>
+
+<p>Conishead Priory, near Ulverston, an Augustinian foundation
+of the reign of Henry II., has left no remains, but of the priory
+of Cartmel (1188) the fine church is still in use. It is a cruciform
+structure of transitional Norman and later dates, its central
+tower having the upper storey set diagonally upon the lower.
+The chancel contains some superb Jacobean carved oak screens,
+with stalls of earlier date.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FURNISS, HARRY<a name="ar89" id="ar89"></a></span> (1854-&emsp;&emsp;), British caricaturist and
+illustrator, was born at Wexford, Ireland, of English and Scottish
+parents. He was educated in Dublin, and in his schooldays
+edited a <i>Schoolboy&rsquo;s Punch</i> in close imitation of the original.
+He came to London when he was nineteen, and began to draw
+for the illustrated papers, being for some years a regular contributor
+to the <i>Illustrated London News</i>. His first drawing in <i>Punch</i>
+appeared in 1880, and he joined its staff in 1884. He illustrated
+Lucy&rsquo;s &ldquo;Diary of Toby, M.P.,&rdquo; in <i>Punch</i>, where his political
+caricatures became a popular feature. Among his other successes
+were a series of &ldquo;Puzzle Heads,&rdquo; and his annual &ldquo;Royal
+Academy guy&rsquo;d.&rdquo; In <i>Royal Academy Antics</i> (1890) he published
+a volume of caricatures of the work of leading artists. He
+resigned from the staff of <i>Punch</i> in 1894, produced for a short
+time a weekly comic paper <i>Lika Joko</i>, and in 1898 began a
+humorous monthly, <i>Fair Game</i>; but these were short-lived.
+Among the numerous books he illustrated were James Payn&rsquo;s
+<i>Talk of the Town</i>, Lewis Carroll&rsquo;s <i>Sylvie and Bruno</i>, Gilbert à
+Beckett&rsquo;s <i>Comic Blackstone</i>, G.E. Farrow&rsquo;s <i>Wallypug Book</i>,
+and his own novel, <i>Poverty Bay</i> (1905). <i>Our Joe, his great Fight</i>
+(1903), was a collection of original cartoons. His volume of
+reminiscences, <i>Confessions of a Caricaturist</i> (1901), was followed
+by <i>Harry Furniss at Home</i> (1904). In 1905 he published <i>How to
+draw in Pen and Ink</i>, and produced the first number of <i>Harry
+Furniss&rsquo;s Christmas Annual</i>.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FURNITURE<a name="ar90" id="ar90"></a></span> (from &ldquo;furnish,&rdquo; Fr. <i>fournir</i>), a general term
+of obscure origin, used to describe the chattels and fittings required
+to adapt houses and other buildings for use. Wood,
+ivory, precious stones, bronze, silver and gold have been used
+from the most ancient times in the construction or for the
+decoration of furniture. The kinds of objects required for
+furniture have varied according to the changes of manners and
+customs, as well as with reference to the materials at the command
+of the workman, in different climates and countries.
+Of really ancient furniture there are very few surviving examples,
+partly by reason of the perishable materials of which it was usually
+constructed; and partly because, however great may have been
+the splendour of Egypt, however consummate the taste of Greece,
+however luxurious the life of Rome, the number of household
+appliances was very limited. The chair, the couch, the table,
+the bed, were virtually the entire furniture of early peoples,
+whatever the degree of their civilization, and so they remained
+until the close of what are known in European history as the
+middle ages. During the long empire-strewn centuries which
+intervened between the lapse of Egypt and the obliteration of
+Babylon, the extinction of Greece and the dismemberment of
+Rome and the great awakening of the Renaissance, household
+comfort developed but little. The Ptolemies were as well lodged
+as the Plantagenets, and peoples who spent their lives in the
+open air, going to bed in the early hours of darkness, and rising
+as soon as it was light, needed but little household furniture.</p>
+
+<p>Indoor life and the growth of sedentary habits exercised a
+powerful influence upon the development of furniture. From
+being splendid, or at least massive, and exceedingly sparse and
+costly, it gradually became light, plentiful and cheap. In the
+ancient civilizations, as in the periods when our own was slowly
+growing, household plenishings, save in the rudest and most
+elementary forms, were the privilege of the great&mdash;no person
+of mean degree could have obtained, or would have dared to
+use if he could, what is now the commonest object in every
+house, the chair (<i>q.v.</i>). Sparse examples of the furniture of
+Egypt, Nineveh, Greece and Rome are to be found in museums;
+but our chief sources of information are mural and sepulchral
+paintings and sculptures. The Egyptians used wooden furniture
+carved and gilded, covered with splendid textiles, and supported
+upon the legs of wild animals; they employed chests and coffers
+as receptacles for clothes, valuables and small objects generally.
+Wild animals and beasts of the chase were carved upon the
+furniture of Nineveh also; the lion, the bull and the ram were
+especially characteristic. The Assyrians were magnificent in
+their household appointments; their tables and couches were
+inlaid with ivory and precious metals. Cedar and ebony were
+much used by these great Eastern peoples, and it is probable that
+they were familiar with rosewood, walnut and teak. Solomon&rsquo;s
+<span class="pagenum"><a name="page364" id="page364"></a>364</span>
+bed was of cedar of Lebanon. Greek furniture was essentially
+Oriental in form; the more sumptuous varieties were of bronze,
+damascened with gold and silver. The Romans employed Greek
+artists and workmen and absorbed or adapted many of their
+mobiliary fashions, especially in chairs and couches. The Roman
+tables were of splendid marbles or rare woods. In the later
+ages of the empire, in Rome and afterwards in Constantinople,
+gold and silver were plentifully used in furniture; such indeed
+was the abundance of these precious metals that even cooking
+utensils and common domestic vessels were made of them.</p>
+
+<p>The architectural features so prominent in much of the
+medieval furniture begin in these Byzantine and late Roman
+thrones and other seats. These features became paramount as
+Pointed architecture became general in Europe, and scarcely
+less so during the Renaissance. Most of the medieval furniture,
+chests, seats, trays, &amp;c., of Italian make were richly gilt and
+painted. In northern Europe carved oak was more generally
+used. State seats in feudal halls were benches with ends carved
+in tracery, backs panelled or hung with cloths (called cloths of
+estate), and canopies projecting above. Bedsteads were square
+frames, the testers of panelled wood, resting on carved posts.
+Chests of oak carved with panels of tracery, or of Italian cypress
+(when they could be imported), were used to hold and to carry
+clothes, tapestries, &amp;c., to distant castles and manor houses;
+for house furniture, owing to its scarcity and cost, had to be
+moved from place to place. Copes and other ecclesiastical
+vestments were kept in chests with ornamental lock plates and
+iron hinges. The splendour of most feudal houses depended
+on pictorial tapestries which could be packed and carried from
+place to place. Wardrobes were rooms fitted for the reception
+of dresses, as well as for spices and other valuable stores. Excellent
+carving in relief was executed on caskets, which were of
+wood or of ivory, with painting and gilding, and decorated with
+delicate hinge and lock metal-work. The general subjects of
+sculpture were taken from legends of the saints or from metrical
+romances. Renaissance art made a great change in architecture,
+and this change was exemplified in furniture. Cabinets (<i>q.v.</i>) and
+panelling took the outlines of palaces and temples. In Florence,
+Rome, Venice, Milan and other capitals of Italy, sumptuous
+cabinets, tables, chairs, chests, &amp;c., were made to the orders
+of the native princes. Vasari (<i>Lives of Painters</i>) speaks of
+scientific diagrams and mathematical problems illustrated in
+costly materials, by the best artists of the day, on furniture made
+for the Medici family. The great extent of the rule of Charles V.
+helped to give a uniform training to artists from various countries
+resorting to Italy, so that cabinets, &amp;c., which were made in
+vast numbers in Spain, Flanders and Germany, can hardly be
+distinguished from those executed in Italy. Francis I. and
+Henry VIII. encouraged the revived arts in their respective
+dominions. <i>Pietra dura</i>, or inlay of hard pebbles, agate, lapis
+lazuli, and other stones, ivory carved and inlaid, carved and gilt
+wood, marquetry or veneering with thin woods, tortoise-shell,
+brass, &amp;c., were used in making sumptuous furniture during the
+first period of the Renaissance. Subjects of carving or relief
+were generally drawn from the theological and cardinal virtues,
+from classical mythology, from the seasons, months, &amp;c. Carved
+altarpieces and woodwork in churches partook of the change in
+style.</p>
+
+<p>The great period of furniture in almost every country was,
+however, unquestionably the 18th century. That century saw
+many extravagances in this, as in other forms of art, but on the
+whole it saw the richest <i>floraison</i> of taste, and the widest sense
+of invention. This is the more remarkable since the furniture
+of the 17th century has often been criticized as heavy and coarse.
+The criticism is only partly justified. Throughout the first three-quarters
+of the period between the accession of James I. and
+that of Queen Anne, massiveness and solidity were the distinguishing
+characteristics of all work. Towards the reign of
+James II., however, there came in one of the most pleasing and
+elegant styles ever known in England. Nearly a generation
+before then Boulle was developing in France the splendid and
+palatial method of inlay which, although he did not invent it,
+is inseparably associated with his name. We owe it perhaps to
+the fact that France, as the neighbour of Italy, was touched
+more immediately by the Renaissance than England that the
+reign of heaviness came earlier to an end in that country than on
+the other side of the Channel. But there is a heaviness which is
+pleasing as well as one which is forbidding, and much of the
+furniture made in England any time after the middle of the
+17th century was highly attractive. If English furniture of
+the Stuart period be not sought after to the same extent as that
+of a hundred years later, it is yet highly prized and exceedingly
+decorative. Angularity it often still possessed, but generally
+speaking its elegance of form and richness of upholstering lent
+it an attraction which not long before had been entirely lacking.
+Alike in France and in England, the most attractive achievements
+of the cabinetmaker belong to the 18th century&mdash;English Queen
+Anne and early Georgian work is universally charming; the
+regency and the reigns of Louis XV. and XVI. formed a period
+of the greatest artistic splendour. The inspiration of much of
+the work of the great English school was derived from France,
+although the gropings after the Chinese taste and the earlier
+Gothic manner were mainly indigenous. The French styles of the
+century, which began with excessive flamboyance, closed before
+the Revolution with a chaste perfection of detail which is perhaps
+more delightful than anything that has ever been done in
+furniture. In the achievements of Riesener, David Röntgen,
+Gouthière, Oeben and Rousseau de la Rottière we have the high-water
+mark of craftsmanship. The marquetry of the period,
+although not always beautiful in itself, was executed with
+extraordinary smoothness and finish; the mounts of gilded
+bronze, which were the leading characteristic of most of the work
+of the century, were finished with a minute delicacy of touch
+which was until then unknown, and has never been rivalled since.
+If the periods of Francis I. and Henry II., of Louis XIV. and
+the regency produced much that was sumptuous and even elegant,
+that of Louis XVI., while men&rsquo;s minds were as yet undisturbed
+by violent political convulsions, stands out as, on the whole,
+the one consummate era in the annals of furniture. Times of
+great achievement are almost invariably followed directly by
+those in which no tall thistles grow and in which every little
+shrub is magnified to the dimensions of a forest tree; and the
+so-called &ldquo;empire style&rdquo; which had begun even while the last
+monarch of the <i>ancien régime</i> still reigned, lacked alike the graceful
+conception and the superb execution of the preceding style.
+Heavy and usually uninspired, it was nurtured in tragedy and
+perished amid disaster. Yet it is a profoundly interesting style,
+both by reason of the classical roots from which it sprang and
+the attempt, which it finally reflected, to establish new ideas in
+every department of life. Founded upon the wreck of a lingering
+feudalism it reached back to Rome and Greece, and even to
+Egypt. If it is rarely charming, it is often impressive by its
+severity. Mahogany, satinwood and other rich timbers were
+characteristic of the style of the end of the 18th century;
+rosewood was most commonly employed for the choicer work
+of the beginning of the 19th. Bronze mounts were in high
+favour, although their artistic character varied materially.</p>
+
+<p>Previously to the middle of the 18th century the only cabinetmaker
+who gained sufficient personal distinction to have had
+his name preserved was André Charles Boulle; beginning with
+that period France and England produced many men whose
+renown is hardly less than that of artists in other media. With
+Chippendale there arose a marvellously brilliant school of English
+cabinetmakers, in which the most outstanding names are those
+of Sheraton, Heppelwhite, Shearer and the Adams. But if the
+school was splendid it was lamentably short-lived, and the 19th
+century produced no single name in the least worthy to be
+placed beside these giants. Whether, in an age of machinery,
+much room is left for fine individual execution may be doubted,
+and the manufacture of furniture now, to a great extent, takes
+place in large factories both in England and on the continent.
+Owing to the necessary subdivision of labour in these
+establishments, each piece of furniture passes through numerous
+distinct workshops. The master and a few artificers formerly
+<span class="pagenum"><a name="page365" id="page365"></a>365</span>
+superintended each piece of work, which, therefore, was never
+far removed from the designer&rsquo;s eye. Though accomplished
+artists are retained by the manufacturers of London, Paris and
+other capitals, there can no longer be the same relation between
+the designer and his work. Many operations in these modern
+factories are carried on by machinery. This, though an economy
+of labour, entails loss of artistic effect. The chisel and the knife
+are no longer in such cases guided and controlled by the sensitive
+touch of the human hand.</p>
+
+<p class="pt2 noind f90 sc">Plate I.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+
+<tr><td>
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:183px; height:255px" src="images/img364a.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:179px; height:254px" src="images/img364b.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:179px; height:249px" src="images/img364c.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:180px; height:250px" src="images/img364c1.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 1.</span>&mdash;Venetian Folding Chair of
+carved and gilt walnut, leather
+back and seat; about 1530.</td>
+<td class="caption"><span class="sc">Fig. 2.</span>&mdash;Oak Arm-chair. English,
+17th century.</td>
+<td class="caption"><span class="sc">Fig. 3.</span>&mdash;Arm-chair, solid seat, cane
+back; about 1660.</td>
+<td class="caption"><span class="sc">Fig. 4.</span>&mdash;Arm-chair, stuffed back and
+seat; about 1650.</td></tr></table></td></tr>
+
+<tr><td>
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:114px; height:258px" src="images/img364d.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:352px; height:262px" src="images/img364e.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:122px; height:260px" src="images/img364f.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 5.</span>&mdash;Painted and carved High-Back
+Chair; about 1660.</td>
+<td class="caption"><span class="sc">Fig. 6.</span>&mdash;Carved Walnut Chairs. English, early 18th century.
+The arm-chair is inlaid.</td>
+<td class="caption"><span class="sc">Fig. 7.</span>&mdash;Walnut Chair; about 1710.</td></tr></table></td></tr>
+
+<tr><td>
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:166px; height:254px" src="images/img364g.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:194px; height:252px" src="images/img364h.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:161px; height:250px" src="images/img364i.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:160px; height:252px" src="images/img364j.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 8.</span>&mdash;Carved Mahogany Chair
+in the style of Chippendale; 2nd
+half of 18th century.</td>
+<td class="caption"><span class="sc">Fig. 9.</span>&mdash;Carved Mahogany Arm-chair,
+in the style of Chippendale, with
+ribbon pattern.</td>
+<td class="caption"><span class="sc">Fig. 10.</span>&mdash;Carved and Inlaid Mahogany
+Chair, in the style of Hepplewhite;
+late 18th century.</td>
+<td class="caption"><span class="sc">Fig. 11.</span>&mdash;Mahogany Chair in the
+style of Sheraton; about 1780.</td></tr></table></td></tr>
+
+<tr><td>
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:198px; height:268px" src="images/img364k.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:205px; height:264px" src="images/img364l.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:194px; height:268px" src="images/img364m.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:206px; height:265px" src="images/img364n.jpg" alt="" /></td></tr>
+<tr><td class="caption">Fig. 12.&mdash;Painted and gilt Arm-chair
+with cane seat, in the style of
+Adam; about 1790.</td>
+<td class="caption"><span class="sc">Fig. 13.</span>&mdash;Arm-chair of carved and gilt
+wood with stuffed back, seat and
+arms. French, Louis XV. style.</td>
+<td class="caption"><span class="sc">Fig. 14.</span>&mdash;Mahogany Arm-chair. Empire
+style, early 19th century, said to have
+belonged to the Bonaparte family.</td>
+<td class="caption"><span class="sc">Fig. 15.</span>&mdash;Painted and gilt Beech Chair.
+English, about 1800.</td></tr></table></td></tr>
+</table>
+
+<p class="pt2 noind f90 sc">Plate II.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+
+<tr><td>
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:376px; height:210px" src="images/img365a.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:371px; height:211px" src="images/img365b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 1.</span>&mdash;Front of Oak Coffer with wrought iron bands.
+French, 2nd half of 13th century.</td>
+<td class="caption"><span class="sc">Fig. 2.</span>&mdash;English Oak Chest, dated 1637.</td></tr></table></td></tr>
+
+<tr><td>
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:370px; height:191px" src="images/img365c.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:368px; height:186px" src="images/img365d.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 3.</span>&mdash;Italian (Florentine) Coffer of Wood with gilt arabesque
+stucco ornament, about 1480.</td>
+<td class="caption"><span class="sc">Fig. 4.</span>&mdash;Italian &ldquo;Cassone&rdquo; or Marriage Coffer, 13th century.
+Carved and gilt wood with painted front and ends.</td></tr></table></td></tr>
+
+<tr><td>
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:461px; height:264px" src="images/img365e.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:274px; height:270px" src="images/img365f.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 5.</span>&mdash;Walnut Table with expanding leaves. Swiss, 17th century.</td>
+<td class="caption"><span class="sc">Fig. 6.</span>&mdash;Oak Gate-Legged Table. English,
+17th century.</td></tr></table></td></tr>
+
+<tr><td>
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:369px; height:233px" src="images/img365g.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:366px; height:235px" src="images/img365h.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 7.</span>&mdash;Writing Table. French, end of Louis XV. period.
+Riesener marquetry, ormolu mounts and Sèvres plaques.</td>
+<td class="caption"><span class="sc">Fig. 8.</span>&mdash;Painted Satin-Wood Tables, in the style of Sheraton,
+about 1790.</td></tr>
+<tr><td class="caption f80" colspan="2">(The above are in the Victoria and Albert Museum, except Fig. 8, which were in the Bethnal Green Exhibition, 1892.)</td></tr></table></td></tr>
+</table>
+
+<p class="pt2 noind f90 sc">Plate III.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+
+<tr><td>
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:244px; height:316px" src="images/img366a.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:367px; height:316px" src="images/img366b.jpg" alt="" /></td></tr>
+<tr><td class="caption">1. CARVED OAK SIDEBOARD. English, 17th century. Victoria and Albert
+Museum.</td>
+<td class="caption">2. CARVED OAK COURT CUPBOARD. English, early 17th
+century. Victoria and Albert Museum.</td></tr></table></td></tr>
+
+<tr><td>
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:349px; height:269px" src="images/img366c.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:221px; height:260px" src="images/img366d.jpg" alt="" /></td></tr>
+<tr><td class="caption">3. EBONY CARVED CABINET. The interior
+decorated with inlaid ivory and coloured
+woods; French or Dutch, middle of 17th
+century. Victoria and Albert Museum.</td>
+<td class="caption">4. VENEERED CHEST OF DRAWERS. About
+1690. Lent to Bethnal Green Exhibition by
+Sir Spencer Ponsonby-Fane, G.C.B.</td></tr></table></td></tr>
+
+<tr><td>
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:263px; height:384px" src="images/img366e.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:257px; height:384px" src="images/img366f.jpg" alt="" /></td></tr>
+<tr><td class="caption">5. EBONY ARMOIRE. With tortoise-shell
+panels inlaid with brass and other
+metals, and ormolu mountings. Designed
+by Bérain, and executed by André
+Boulle. French, Louis XIV. period.
+Victoria and Albert Museum.</td>
+<td class="caption">6. GLASS-FRONTED BOOKCASE AND CABINET. Of
+mahogany. In the style of Sheraton, about 1790. Lent
+to the Bethnal Green Exhibition by the late Vincent J. Robinson,
+C.I.E.</td></tr></table></td></tr>
+</table>
+
+<p class="pt2 noind f90 sc">Plate IV.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+
+<tr><td>
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:371px; height:263px" src="images/img367a.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:368px; height:262px" src="images/img367b.jpg" alt="" /></td></tr>
+<tr><td class="caption">1. COMMODE OF PINE. With marquetry of brass, ebony, tortoise-shell,
+mother-of-pearl, ivory, and green-stained bone. &ldquo;Boulle&rdquo; work with
+designs in the style of Bérain. French, late period of Louis XIV.</td>
+<td class="caption">2. COMMODE. With panels of Japanese lacquer and ormolu mountings,
+in the style of Caffieri. French, Louis XV. period.</td></tr></table></td></tr>
+
+<tr><td>
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:246px; height:314px" src="images/img367c.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:251px; height:317px" src="images/img367d.jpg" alt="" /></td></tr>
+<tr><td class="caption">3. TABLE OF KING AND TULIP WOODS. With ormolu mountings.
+Louis XV. period.</td>
+<td class="caption">4. ESCRITOIRE À TOILETTE. Formerly belonging to Marie Antoinette.
+Of tulip and sycamore woods inlaid with other coloured woods, ormolu
+mounts. Louis XV. period.</td></tr></table></td></tr>
+
+<tr><td>
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:296px; height:394px" src="images/img367e.jpg" alt="" /></td>
+<td class="figcenter"><img style="width:290px; height:394px" src="images/img367f.jpg" alt="" /></td></tr>
+<tr><td class="caption">5. FOUR-POST BEDSTEAD. Of oak inlaid
+with bog-oak and holly, from the &ldquo;Inlaid Room&rdquo;
+at Sizergh Castle, Westmorland. Latter half of
+sixteenth century.</td>
+<td class="caption">6. CARVED AND GILT BEDSTEAD. With
+blue silk damask coverings and hangings.
+French, late 18th century. Louis XVI. period.</td></tr>
+<tr><td class="caption f80" colspan="2">From the Victoria and Albert Museum, S. Kensington.</td></tr></table></td></tr>
+</table>
+
+<p class="pt2 noind f90 sc">Plate V.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:730px; height:550px" src="images/img368a.jpg" alt="" /></td></tr>
+<tr><td class="figcenter"><img style="width:731px; height:544px" src="images/img368b.jpg" alt="" /></td></tr>
+<tr><td class="tcl f80"><i>Photo, Mansell &amp; Co.</i></td></tr>
+<tr><td class="caption">THE &ldquo;BUREAU DU ROI,&rdquo; MADE FOR LOUIS XV., NOW IN THE LOUVRE. For description, see <span class="sc">Desk</span>.</td></tr></table>
+
+<p>A decided, if not always intelligent, effort to devise a new
+style in furniture began during the last few years of the 19th
+century, which gained the name of &ldquo;<i>l&rsquo;art nouveau</i>.&rdquo; Its pioneers
+professed to be free from all old traditions and to seek inspiration
+from nature alone. Happily nature is less forbidding than many
+of these interpretations of it, and much of the &ldquo;new art&rdquo; is a
+remarkable exemplification of the impossibility of altogether
+ignoring traditional forms. The style was not long in degenerating
+into extreme extravagance. Perhaps the most striking consequence
+of this effort has been, especially in England, the
+revival of the use of oak. Lightly polished, or waxed, the cheap
+foreign oaks often produce very agreeable results, especially
+when there is applied to them a simple inlay of boxwood and
+stained holly, or a modern form of pewter. The simplicity of
+these English forms is in remarkable contrast to the tortured
+and ungainly outlines of continental seekers after a conscious
+and unpleasing &ldquo;originality.&rdquo;</p>
+
+<p>Until a very recent period the most famous collections of
+historic furniture were to be found in such French museums as
+the Louvre, Cluny and the Garde Meuble. Now, however, they
+are rivalled, if not surpassed, by the magnificent collections of
+the Victoria and Albert Museum at South Kensington, and the
+Wallace collection at Hertford House, London. The latter, in
+conjunction with the Jones bequest at South Kensington, forms
+the finest of all gatherings of French furniture of the great
+periods, notwithstanding that in the Bureau du Roi the Louvre
+possesses the most magnificent individual example in existence.
+In America there are a number of admirable collections representative
+of the graceful and homely &ldquo;colonial furniture&rdquo;
+made in England and the United States during the Queen Anne
+and Georgian periods.</p>
+
+<div class="condensed">
+<p>See also the separate articles in this work on particular forms of
+furniture. The literature of the subject has become very extensive,
+and it is needless to multiply here the references to books. Perrot
+and Chipiez, in their great <i>Histoire de l&rsquo;art dans l&rsquo;antiquité</i> (1882
+et seq.) deal with ancient times, and A. de Champeaux, in <i>Le Meuble</i>
+(1885), with the middle ages and later period; English furniture is
+admirably treated by Percy Macquoid in his <i>History of English
+Furniture</i> (1905); and Lady Dilke&rsquo;s <i>French Furniture in the 18th
+Century</i> (1901), and Luke Vincent Lockwood&rsquo;s <i>Colonial Furniture in
+America</i> (1901), should also be consulted.</p>
+</div>
+<div class="author">(J. P. B.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">FURNIVALL, FREDERICK JAMES<a name="ar91" id="ar91"></a></span> (1825-1910), English
+philologist and editor, was born at Egham, Surrey, on the 4th
+of February 1825, the son of a surgeon. He was called to the bar
+in 1849, but his attention was soon diverted to philological
+studies and social problems. He gave Frederick Denison Maurice
+valuable assistance in the Christian Socialist movement, and was
+one of the founders of the Working Men&rsquo;s College. For half a
+century he indefatigably promoted the study of early English
+literature, partly by his own work as editor, and still more
+efficaciously by the agency of the numerous learned societies
+of which he was both founder and director, especially the Early
+English Text Society (1864), which has been of inestimable
+service in promoting the study of early and middle English.
+He also established and conducted the Chaucer, Ballad, New
+Shakespeare and Wyclif Societies, and at a later period societies
+for the special study of Browning and Shelley. He edited texts
+for the Early English Text Society, for the Roxburghe Club
+and the Rolls Series; but his most important labours were
+devoted to Chaucer, whose study he as an editor greatly assisted
+by his &ldquo;Six-Text&rdquo; edition of the <i>Canterbury Tales</i>, and other
+publications of the Chaucer Society. He was the honorary
+secretary of the Philological Society, and was one of the original
+promoters of the Oxford <i>New English Dictionary</i>. He co-operated
+with its first editor, Herbert Coleridge, and after his death
+was for some time principal editor during the preliminary period
+of the collection of material. The completion of his half-century
+of labour was acknowledged in 1900 by a handsome testimonial,
+including the preparation by his friends of a volume of philological
+essays specially dedicated to him, <i>An English Miscellany</i>
+(Oxford, 1901), and a considerable donation to the Early English
+Text Society. Dr Furnivall was always an enthusiastic oarsman,
+and till the end kept up his interest in rowing; with John
+Beesley in 1845 he introduced the new type of narrow sculling
+boat, and in 1886 started races on the Thames for sculling fours
+and sculling eights. He died on the 2nd of July 1910.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FURSE, CHARLES WELLINGTON<a name="ar92" id="ar92"></a></span> (1868-1904), English
+painter, born at Staines, the son of the Rev. C.W. Furse, archdeacon
+of Westminster, was descended collaterally from Sir
+Joshua Reynolds, and in his short span of life achieved such
+rare excellence as a portrait and figure painter that he forms an
+important link in the chain of British portraiture which extends
+from the time when Van Dyck was called to the court of Charles I.
+to our own day. His talent was precocious; at the age of seven
+he gave indications of it in a number of drawings illustrating
+Scott&rsquo;s novels. He entered the Slade school in 1884, winning the
+Slade scholarship in the following year, and completed his education
+at Julian&rsquo;s <i>atelier</i> in Paris. Hard worker as he was, his
+activity was frequently interrupted by spells of illness, for he had
+developed signs of consumption when he was still attending the
+Slade school. An important canvas called &ldquo;Cain&rdquo; was his first
+contribution (1888) to the Royal Academy, to the associateship
+of which he was elected in the year of his death. For some years
+before he had been a staunch supporter of the New English Art
+Club, to the exhibitions of which he was a regular contributor.
+He was married in October 1900 to Katherine, daughter of John
+Addington Symonds. His fondness for sport and of an open-air
+life found expression in his art and introduced a new, fresh and
+vigorous note into portraiture. There is never a suggestion of
+the studio or of the fatiguing pose in his portraits. The sitters
+appear unconscious of being painted, and are generally seen in
+the pursuit of their favourite outdoor sport or pastime, in the
+full enjoyment of life. Such are the &ldquo;Diana of the Uplands,&rdquo;
+the &ldquo;Lord Roberts&rdquo; and &ldquo;The Return from the Ride&rdquo; at the
+Tate Gallery; the four children in the &ldquo;Cubbing with the York
+and Ainsty,&rdquo; &ldquo;The Lilac Gown,&rdquo; &ldquo;Mr and Mrs Oliver Fishing&rdquo;
+and the portrait of Lord Charles Beresford. Most of these
+pictures, and indeed nearly all the work completed in the few
+years of Furse&rsquo;s activity, show a pronounced decorative tendency.
+His sense of space, composition and decorative design can best
+be judged by his admirable mural decorations for Liverpool
+town hall, executed between 1899 and 1902. A memorial exhibition
+of Furse&rsquo;s paintings and sketches was held at the Burlington
+Fine Arts Club in 1906.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FÜRST, JULIUS<a name="ar93" id="ar93"></a></span> (1805-1873), German Orientalist, was born
+of Jewish parents at Zerkowo in Posen, on the 12th of May 1805.
+He studied philosophy and philology at Berlin, and oriental
+literature at Posen, Breslau and Halle. In 1857 he was appointed
+to a lectureship at the university of Leipzig, and he was promoted
+to a professorship in 1864, which he held until his death at Leipzig
+on the 9th of February 1873. Among his writings may be
+mentioned <i>Lehrgebäude der aramäischen Idiome</i> (Leipzig, 1835);
+<i>Librorum sacrorum Veteris Testamenti concordantiae Hebraicae
+atque Chaldaicae</i> (Leipzig, 1837-1840); <i>Hebräisches und chaldäisches
+Wörterbuch</i> (1851, English translation by S. Davidson 1867);
+<i>Kultur und Literaturgeschichte der Juden in Asien</i> (1849). Fürst
+also edited a valuable <i>Bibliotheca Judaica</i> (Leipzig, 1849-1863),
+and was the author of some other works of minor importance.
+From 1840 to 1851 he was editor of <i>Der Orient</i>, a journal devoted
+to the language, literature, history and antiquities of the Jews.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FÜRSTENBERG,<a name="ar94" id="ar94"></a></span> the name of two noble houses of Germany.</p>
+
+<p>1. The more important is in possession of a mediatized principality
+in the district of the Black Forest and the Upper Danube,
+which comprises the countship of Heiligenberg, about 7 m. to
+the N. of the Lake of Constance, the landgraviates of Stühlingen
+and Baar, and the lordships of Jungnau, Trochtelfingen, Hausen
+<span class="pagenum"><a name="page366" id="page366"></a>366</span>
+and Möskirch or Messkirch. The territory is discontinuous;
+and as it lies partly in Baden, partly in Württemberg, and partly
+in the Prussian province of Sigmaringen, the head of the family
+is an hereditary member of the first chamber of Baden and of
+the chamber of peers in Württemberg and in Prussia. The
+relations of the principality with Baden are defined by the treaty
+of May 1825, and its relations with Württemberg by the royal
+declaration of 1839. The <i>Stammort</i> or ancestral seat of the
+family is Fürstenberg in the Black Forest, about 13 m. N. of
+Schaffhausen, but the principal residence of the present representatives
+of the main line is at Donaueschingen.</p>
+
+<p>The family of Fürstenberg claims descent from a certain
+Count Unruoch, a contemporary of Charlemagne, but their
+authentic pedigree is only traceable to Egino II., count of
+Urach, who died before 1136. In 1218 his successors inherited
+the possessions of the house of Zähringen in the Baar district
+of the Black Forest, where they built the town and castle of
+Fürstenberg. Of the two sons of Egino V. of Urach, Conrad,
+the elder, inherited the Breisgau and founded the line of the
+counts of Freiburg, while the younger, Heinrich (1215-1284),
+received the territories lying in the Kinzigthal and Baar, and
+from 1250 onward styled himself first lord, then count, of
+Fürstenberg. His territories were subsequently divided among
+several branches of his descendants, though temporarily reunited
+under Count Friedrich III., whose wife, Anna, heiress
+of the last count of Wardenberg, brought him the countship of
+Heiligenberg and lordships of Jungnau and Trochtelfingen in
+1534. On Friedrich&rsquo;s death (1559) his territories were divided
+between his two sons, Joachim and Christof I. Of these the
+former founded the line of Heiligenberg, the latter that of
+Kinzigthal. The Kinzigthal branch was again subdivided in
+the 17th century between the two sons of Christof II. (d. 1614),
+the elder, Wratislaw II. (d. 1642), founding the line of Mösskirch,
+the younger, Friedrich Rudolf (d. 1655), that of Stühlingen.
+The Heiligenberg branch received an accession of dignity by the
+elevation of Count Hermann Egon (d. 1674) to the rank of prince
+of the Empire in 1664, but his line became extinct with the
+death of his son Prince Anton Egon, favourite of King Augustus
+the Strong and regent of Saxony, in 1716. The heads of both
+the Mösskirch and Stühlingen lines were now raised to the
+dignity of princes of the Empire (1716). The Mösskirch branch
+died out with Prince Karl Friedrich (d. 1744); the territories
+of the Stühlingen branch had been divided on the death of
+Count Prosper Ferdinand (1662-1704) between his two sons,
+Joseph Wilhelm Ernst (1699-1762) and Ludwig August Egon
+(1705-1759). The first of these was created prince of the Empire
+on the 10th of December 1716, and founded the princely line
+of the Swabian Fürstenbergs; in 1772 he obtained from the
+emperor Francis I. for all his legitimate sons and their descendants
+the right to bear, instead of the style of landgrave, that of
+prince, which had so far been confined to the reigning head of
+the family. Ludwig, on the other hand, founded the family of
+the landgraves of Fürstenberg, who, since their territories lay
+in Austria and Moravia, were known as the &ldquo;cadet line in
+Austria.&rdquo; The princely line became extinct with the death
+of Karl Joachim in 1804, and the inheritance passed to the
+Bohemian branch of the Austrian cadet line in the person of
+Karl Egon II. (see below). Two years later the principality
+was mediatized.</p>
+
+<p>In 1909 there were two branches of the princely house of
+Fürstenberg: (1) the main branch, that of Fürstenberg-Donaueschingen,
+the head of which was Prince Maximilian Egon (b.
+1863), who succeeded his cousin Karl Egon III. in 1896; (2)
+that of Fürstenberg-Königshof, in Bohemia, the head of which
+was Prince Emil Egon (b. 1876), chamberlain and secretary of
+legation to the Austro-Hungarian embassy in London (1907).
+The cadet line of the landgraves of Fürstenberg is now extinct,
+its last representative having been the landgrave Joseph Friedrich
+Ernst of Fürstenberg-Weitra (1860-1896), son of the
+landgrave Ernst (1816-1889) by a morganatic marriage. He
+was not recognized as <i>ebenbürtig</i> by the family. The landgraves
+of Fürstenberg were in 1909 represented only by the landgravines
+Theresa (b. 1839) and Gabrielle (b. 1844), daughters of the
+landgrave Johann Egon (1802-1879).</p>
+
+<p>From the days of Heinrich of Urach, a relative and notable
+supporter of Rudolph of Habsburg, the Fürstenbergs have
+played a stirring part in German history as statesmen, ecclesiastics
+and notably soldiers. There was a popular saying that
+&ldquo;the emperor fights no great battle but a Fürstenberg falls.&rdquo;
+In the Heiligenberg line the following may be more particularly
+noticed.</p>
+
+<p><span class="sc">Franz Egon</span> (1625-1682), bishop of Strassburg, was the elder
+son of Egon VII., count of Fürstenberg (1588-1635), who served
+with distinction as a Bavarian general in the Thirty Years&rsquo; War.
+He began life as a soldier in the imperial service, but on the
+elevation of his friend Maximilian Henry of Bavaria to the
+electorate of Cologne in 1650, he went to his court and embraced
+the ecclesiastical career. He soon gained a complete ascendancy
+over the weak-minded elector, and, with his brother William
+Egon (see below), was mainly instrumental in making him the
+tool of the aggressive policy of Louis XIV. of France. Ecclesiastical
+preferments were heaped upon him. As a child he had
+been appointed to a canonry of Cologne; to these he added
+others at Strassburg, Liége, Hildesheim and Spires; he became
+also suffragan bishop and dean of Cologne and provost of Hildesheim,
+and in 1663 bishop of Strassburg. Later he was also
+prince-abbot of Lüders and Murbach and abbot of Stablo and
+Malmedy. On the conclusion of a treaty between the emperor
+and the elector of Cologne, on the 11th of May 1674, Franz was
+deprived of all his preferments in Germany, and was compelled
+to take refuge in France. He was, however, amnestied with his
+brother William by a special article of the treaty of Nijmwegen
+(1679), whereupon he returned to Cologne. After the French
+occupation of Strassburg (1681) he took up his residence there
+and died on the 1st of April 1682.</p>
+
+<p>His brother <span class="sc">William Egon</span> (1629-1704), bishop of Strassburg,
+began his career as a soldier in the French service. He went to
+the court of the elector of Cologne at the same time as Franz
+Egon, whose zeal for the cause of Louis XIV. of France he shared.
+In 1672 the intrigues of the two Fürstenbergs had resulted in a
+treaty of offensive alliance between the French monarchy and
+the electorate of Cologne, and, the brothers being regarded by
+the Imperialists as the main cause of this disaster, William was
+seized by imperial soldiers in the monastery of St Pantaleon at
+Cologne, hurried off to Vienna and there tried for his life. He
+was saved by the intervention of the papal nuncio, but was kept
+in prison till the signature of the treaty of Nijmwegen (1679).
+As a reward for his services Louis XIV. appointed him bishop
+of Strassburg in succession to his brother in 1682, in 1686 obtained
+for him from Pope Innocent XI. the cardinal&rsquo;s hat, and in 1688
+succeeded in obtaining his election as coadjutor-archbishop of
+Cologne and successor to the elector Maximilian Henry. At the
+instance of the emperor, however, the pope interposed his veto;
+the canons followed the papal lead, and, the progress of the
+Allies against Louis XIV. depriving him of all prospect of
+success, William Egon retired to France. Here he took up his
+abode at his abbey of St Germain des Près near Paris, where he
+died on the 10th of April 1704.</p>
+
+<p>In the Stühlingen line the most notable was <span class="sc">Karl Egon</span>
+(1796-1854), prince of Fürstenberg, the son of Prince Karl
+Alois of Fürstenberg, a general in the Austrian service, who was
+killed at the battle of Loptingen on the 25th of March 1799.
+In 1804 he inherited the Swabian principality of Fürstenberg
+and all the possessions of the family except the Moravian estates.
+He studied at Freiburg and Würzburg, and in 1815 accompanied
+Prince Schwarzenberg to Paris as staff-officer. In 1817 he came
+of age, and in the following year married the princess Amalie
+of Baden. By the mediatization of his principality in 1806 the
+greater part of his vast estates had fallen under the sovereignty
+of the grand-duke of Baden, and Prince Fürstenberg took a
+conspicuous part in the upper house of the grand-duchy. In
+politics he distinguished himself by a liberalism rare in a great
+German noble, carrying through by his personal influence with
+his peers the abolition of tithes and feudal dues and stanchly
+<span class="pagenum"><a name="page367" id="page367"></a>367</span>
+advocating the freedom of the press. He was not less distinguished
+by his large charities: among other foundations he
+established a hospital at Donaueschingen. For the industrial
+development of the country, too, he did much, and proved himself
+also a notable patron of the arts. His palace of Donaueschingen,
+with its collections of paintings, engravings and coins, was a
+centre of culture, where poets, painters and musicians met with
+princely entertainment. He died on the 14th of September
+1869, and was succeeded by his son Karl Egon II. (1820-1892),
+with the death of whose son, Karl Egon III., in 1896, the title
+and estates passed to Prince Maximilian Egon, head of the cadet
+line of Fürstenberg-Pürglitz.</p>
+
+<div class="condensed">
+<p>See Münch, <i>Gesch. des Hauses und des Landes Fürstenberg</i>, 4 vols.
+(Aix-la-Chapelle, 1829-1847); S. Riezler, <i>Gesch. des fürstlichen
+Hauses Fürstenberg bis 1507</i> (Tübingen, 1883); <i>Fürstenbergisches
+Urkundenbuch</i>, edited by S. Riezler and F.L. Baumann, vols. i.-vii.
+(Tübingen, 1877-1891), continued <i>s. tit. Mitteilungen aus dem
+fürstlich. Fürstenbergischem Archiv</i> by Baumann and G. Tumbült,
+2 vols. (ib. 1899-1902); Stokvis, <i>Manuel d&rsquo;histoire</i> (Leiden, 1890-1893);
+<i>Almanach de Gotha; Allgemeine deutsche Biographie</i>.</p>
+</div>
+
+<p>2. The second Fürstenberg family has its possessions in
+Westphalia and the country of the Rhine, and takes its name
+from the castle of Fürstenberg on the Ruhr. The two most
+remarkable men whom it has produced are Franz Friedrich
+Wilhelm, freiherr von Fürstenberg, and Franz Egon, count von
+Fürstenberg-Stammheim. The former (1728-1810) became
+ultimately vicar-general of the prince-bishop of Münster, and
+effected a great number of important reforms in the administration
+of the country, besides doing much for its educational
+and industrial development. The latter (1797-1859) was an
+enthusiastic patron of art, who zealously advocated the completion
+of the Cologne cathedral, and erected the beautiful church
+of St Apollinaris near Remagen on the Rhine. He was a member
+of the Prussian Upper House in 1849, collaborated in founding
+the <i>Preussisches Wochenblatt</i>, and was an ardent defender of
+Catholic interests. His son, Count Gisbert von Fürstenberg-Stammheim
+(b. 1836), was in 1909 head of the Rhenish line of
+the house of Fürstenberg.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FÜRSTENWALDE,<a name="ar95" id="ar95"></a></span> a town of Germany, in the Prussian
+province of Brandenburg, on the right bank of the Spree, and
+on the railway from Berlin to Frankfort-on-Oder, 28 m. E. of
+the former city. Pop. (1905) 20,498. Its beautiful cathedral
+church contains several old monuments. The industries are
+important, including, besides brewing and malting, manufactures
+of starch, vinegar, electric lamps and gas-fittings, stoves, &amp;c.,
+iron-founding and wool-weaving. Fürstenwalde is one of the
+oldest towns of Brandenburg. From 1385 it was the seat of
+the bishop of Lebus, whose bishopric was incorporated with
+the electorate of Brunswick in 1595.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FÜRTH,<a name="ar96" id="ar96"></a></span> a manufacturing town of Germany, in the kingdom
+of Bavaria, at the confluence of the Pegnitz with the Regnitz,
+5 m. N.W. from Nuremberg by rail, at the junction of lines to
+Hof and Würzburg. Pop. (1885) 35,455; (1905) 60,638. It is
+a modern town in appearance, with broad streets and palatial
+business houses. Of its four Evangelical churches, the old St
+Michaeliskirche is a handsome structure; but its chief edifices
+are the new town hall, with a tower 175 ft. high and the
+magnificent synagogue. The Jews have also a high school,
+which enjoys a great reputation. There are besides a classical,
+a wood-carving and an agricultural school and a library. Fürth
+is the seat of several important industries; particularly, the
+production of chromolithographs and picture-books, the manufacture
+of mirrors and mirror-frames, bronze and gold-leaf wares,
+pencils, toys, haberdashery, optical instruments, silver work,
+turnery, chicory, machinery, fancy boxes and cases, and an
+extensive trade is carried on in these goods as also in hops,
+metals, wool, groceries and coal. A large annual fair is held
+at Michaelmas and lasts for eleven days. The earliest railway
+in Germany was that between Nuremberg and Fürth (opened
+on the 7th of December 1835).</p>
+
+<p>Fürth was founded, according to tradition, by Charlemagne,
+who erected a chapel there. It was for a time a <i>Vogtei</i> (advocateship)
+under the burgraves of Nuremberg, but about 1314 it was
+bequeathed to the see of Bamberg, and in 1806 it came into
+the possession of Bavaria. In 1632 Gustavus Adolphus besieged
+it in vain, and in 1634 it was pillaged and burnt by the Croats.
+It owes its rise to prosperity to the tolerance it meted out to the
+Jews, who found here an asylum from the oppression under
+which they suffered in Nuremberg.</p>
+
+<div class="condensed">
+<p>See Fronmüller, <i>Chronik der Stadt Fürth</i> (1887).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FURTWÄNGLER, ADOLF<a name="ar97" id="ar97"></a></span> (1853-1907), German archaeologist,
+was born at Freiburg im Breisgau, and was educated there,
+at Leipzig and at Munich, where he was a pupil of H. Brunn,
+whose comparative method in art-criticism he much developed.
+He took part in the excavations at Olympia in 1878, became
+an assistant in the Berlin Museum in 1880, and professor at
+Berlin (1884) and later at Munich. His latest excavation work
+was at Aegina. He was a prolific writer, with a prodigious
+knowledge and memory, and a most ingenious and confident
+critic; and his work not only dominated the field of archaeological
+criticism but also raised its standing both at home and abroad.
+Among his numerous publications the most important were a
+volume on the bronzes found at Olympia, vast works on ancient
+gems and Greek vases, and the invaluable <i>Masterpieces of
+Greek Sculpture</i> (English translation by Eugénie Strong). He
+died at Athens on the 10th of October 1907.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FURZE,<a name="ar98" id="ar98"></a></span> <span class="sc">Gorse</span> or <span class="sc">Whin</span>; botanical name <i>Ulex</i> (Ger.
+<i>Stechginster</i>, Fr. <i>ajonc</i>), a genus of thorny papilionaceous
+shrubs, of few species, confined to west and central Europe and
+north-west Africa. Common furze, <i>U. europaeus</i>, is found on
+heaths and commons in western Europe from Denmark to Italy
+and Greece, and in the Canaries and Azores, and is abundant
+in nearly all parts of the British Isles. It grows to a height
+of 2-6 ft.; it has hairy stems, and the smaller branches end each
+in a spine; the leaves, sometimes lanceolate on the lowermost
+branches, are mostly represented by spines from 2 to 6 lines long,
+and branching at their base; and the flowers, about three-quarters
+of an inch in length, have a shaggy, yellowish-olive calyx, with two
+small ovate bracts at its base, and appear in early spring and
+late autumn. They are yellow and sweet-scented and visited by
+bees. The pods are few-seeded; their crackling as they burst
+may often be heard in hot weather. This species comprises the
+varieties <i>vulgaris</i>, or <i>U. europaeus</i> proper, which has spreading
+branches, and strong, many-ridged spines, and <i>strictus</i> (Irish
+furze), with erect branches, and slender 4-edged spines. The
+other British species of furze is <i>U. nanus</i>, dwarf furze, a native
+of Belgium, Spain and the west of France; it is a procumbent
+plant, less hairy than <i>U. europaeus</i>, with smaller and more
+orange-coloured flowers, which spring from the primary spines,
+and have a nearly smooth calyx, with minute basal bracts.
+Furze, or gorse, is sometimes employed for fences.</p>
+
+<p>Notwithstanding its formidable spines, the young shoots
+yield a palatable and nutritious winter forage for horses and
+cattle. To fit it for this purpose it must be chopped and bruised
+to destroy the spines. This is sometimes done in a primitive
+and laborious way by laying the gorse upon a block of wood and
+beating it with a mallet, flat at one end and armed with crossed
+knife-edges at the other, by the alternate use of which it is
+bruised and chopped. There are now a variety of machines
+by which this is done rapidly and efficiently, and which are in
+use where this kind of forage is used to any extent. The agricultural
+value of this plant has often been over-rated by theoretical
+writers. In the case of very poor, dry soils it does, however,
+yield much valuable food at a season when green forage is not
+otherwise to be had. It is on this account of importance to
+dairymen; and to them it has this further recommendation,
+that cows fed upon it give much rich milk, which is free from
+any unpleasant flavour. To turn it to good account, it
+must be sown in drills, kept clean by hoeing, and treated
+as a regular green crop. If sown in March, on land fitly prepared
+and afterwards duly cared for, it is ready for use in the
+autumn of the following year. A succession of cuttings of
+proper age is obtained for several years from the same field.
+It is cut by a short stout scythe, and must be brought
+from the field daily; for when put in a heap after being
+<span class="pagenum"><a name="page368" id="page368"></a>368</span>
+chopped and bruised it heats rapidly. It is given to horses and
+cows in combination with chopped hay or straw. An acre will
+produce about 2000 faggots of green two-year-old gorse, weighing
+20 &#8468; each.</p>
+
+<p>This plant is invaluable in mountain sheep-walks. The
+rounded form of the furze bushes that are met with in such
+situations shows how diligently the annual growth, as far as it
+is accessible, is nibbled by the sheep. The food and shelter
+afforded to them in snowstorms by clusters of such bushes is
+of such importance that the wonder is our sheep farmers do not
+bestow more pains to have it in adequate quantity. Young
+plants of whin are so kept down by the sheep that they can
+seldom attain to a profitable size unless protected by a fence
+for a few years. In various parts of England it is cut for fuel.
+The ashes contain a large proportion of alkali, and are a good
+manure, especially for peaty land.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUSARO, LAGO,<a name="ar99" id="ar99"></a></span> a lake of Campania, Italy, ½ m. W. of Baia,
+and 1 m. S. of the acropolis of Cumae. It is the ancient <i>Acherusia
+palus</i>, separated from the sea on the W. by a line of sandhills.
+It may have been the harbour of Cumae in early antiquity.
+In the 1st century <span class="scs">A.D.</span> an artificial outlet was dug for it at its
+S. end, with a tunnel, lined with <i>opus reticulatum</i> and brick,
+under the hill of Torregaveta. This hill is covered with the
+remains of a large villa, which is almost certainly that of Servilius
+Vatia, described by Seneca (<i>Epist.</i> 55). There are remains of
+other villas on the shores of the lake. Oyster cultivation is
+carried on there.</p>
+
+<div class="condensed">
+<p>See J. Beloch, <i>Campanien</i> (2nd ed., Breslau, 1890), 188.</p>
+</div>
+<div class="author">(T. As.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">FUSELI, HENRY<a name="ar100" id="ar100"></a></span> (1741-1825), English painter and writer on
+art, of German-Swiss family, was born at Zürich in Switzerland
+on the 7th of February 1741; he himself asserted in 1745, but
+this appears to have been a mere whim. He was the second
+child in a family of eighteen. His father was John Caspar
+Füssli, of some note as a painter of portraits and landscapes,
+and author of Lives of the <i>Helvetic Painters</i>. This parent
+destined his son for the church, and with this view sent him to
+the Caroline college of his native town, where he received an
+excellent classical education. One of his schoolmates there
+was Lavater, with whom he formed an intimate friendship.</p>
+
+<p>After taking orders in 1761 Fuseli was obliged to leave his
+country for a while in consequence of having aided Lavater to
+expose an unjust magistrate, whose family was still powerful
+enough to make its vengeance felt. He first travelled through
+Germany, and then, in 1765, visited England, where he supported
+himself for some time by miscellaneous writing: there was a
+sort of project of promoting through his means a regular literary
+communication between England and Germany. He became
+in course of time acquainted with Sir Joshua Reynolds, to whom
+he showed his drawings. By Sir Joshua&rsquo;s advice he then devoted
+himself wholly to art. In 1770 he made an art-pilgrimage to
+Italy, where he remained till 1778, changing his name from
+Füssli to Fuseli, as more Italian-sounding. Early in 1779 he
+returned to England, taking Zürich on his way. He found a
+commission awaiting him from Alderman Boydell, who was then
+organizing his celebrated Shakespeare gallery. Fuseli painted
+a number of pieces for this patron, and about this time published
+an English edition of Lavater&rsquo;s work on physiognomy. He likewise
+gave Cowper some valuable assistance in preparing the
+translation of Homer. In 1788 Fuseli married Miss Sophia
+Rawlins (who it appears was originally one of his models, and who
+proved an affectionate wife), and he soon after became an
+associate of the Royal Academy. Two years later he was promoted
+to the grade of Academician. In 1799 he exhibited a
+series of paintings from subjects furnished by the works of
+Milton, with a view to forming a Milton gallery corresponding
+to Boydell&rsquo;s Shakespeare gallery. The number of the Milton
+paintings was forty-seven, many of them very large; they were
+executed at intervals within nine years. This exhibition, which
+closed in 1800, proved a failure as regards profit. In 1799 also
+he was appointed professor of painting to the Academy. Four
+years afterwards he was chosen keeper, and resigned his professorship;
+but he resumed it in 1810, and continued to hold
+both offices till his death. In 1805 he brought out an edition of
+Pilkington&rsquo;s <i>Lives of the Painters</i>, which, however, did not add
+much to his reputation. Canova, when on his visit to England,
+was much taken with Fuseli&rsquo;s works, and on returning to Rome
+in 1817 caused him to be elected a member of the first class in
+the Academy of St Luke. Fuseli, after a life of uninterrupted
+good health, died at Putney Hill on the 16th of April 1825,
+at the advanced age of eighty-four, and was buried in the crypt
+of St Paul&rsquo;s cathedral. He was comparatively rich at his death,
+though his professional gains had always appeared to be meagre.</p>
+
+<p>As a painter, Fuseli had a daring invention, was original,
+fertile in resource, and ever aspiring after the highest forms
+of excellence. His mind was capable of grasping and realizing
+the loftiest conceptions, which, however, he often spoiled on the
+canvas by exaggerating the due proportions of the parts, and
+throwing his figures into attitudes of fantastic and over-strained
+contortion. He delighted to select from the region of the supernatural,
+and pitched everything upon an ideal scale, believing
+a certain amount of exaggeration necessary in the higher branches
+of historical painting. &ldquo;Damn Nature! she always puts me
+out,&rdquo; was his characteristic exclamation. In this theory he was
+confirmed by the study of Michelangelo&rsquo;s works and the marble
+statues of the Monte Cavallo, which, when at Rome, he used
+often to contemplate in the evening, relieved against a murky
+sky or illuminated by lightning. But this idea was by him
+carried out to an excess, not only in the forms, but also in the
+attitudes of his figures; and the violent and intemperate action
+which he often displays destroys the grand effect which many
+of his pieces would otherwise produce. A striking illustration
+of this occurs in his famous picture of &ldquo;Hamlet breaking from
+his Attendants to follow the Ghost&rdquo;: Hamlet, it has been said,
+looks as though he would burst his clothes with convulsive
+cramps in all his muscles. This intemperance is the grand defect
+of nearly all Fuseli&rsquo;s compositions. On the other hand, his
+paintings are never either languid or cold. His figures are full
+of life and earnestness, and seem to have an object in view
+which they follow with rigid intensity. Like Rubens he excelled
+in the art of setting his figures in motion. Though the lofty and
+terrible was his proper sphere, Fuseli had a fine perception of the
+ludicrous. The grotesque humour of his fairy scenes, especially
+those taken from <i>A Midsummer-Night&rsquo;s Dream</i>, is in its way not
+less remarkable than the poetic power of his more ambitious
+works. As a colourist Fuseli has but small claims to distinction.
+He scorned to set a palette as most artists do; he merely dashed
+his tints recklessly over it. Not unfrequently he used his paints
+in the form of a dry powder, which he rubbed up with his pencil
+with oil, or turpentine, or gold size, regardless of the quantity,
+and depending for accident on the general effect. This recklessness
+may perhaps be explained by the fact that he did not paint
+in oil till he was twenty-five years of age. Despite these drawbacks
+he possessed the elements of a great painter.</p>
+
+<p>Fuseli painted more than 200 pictures, but he exhibited only
+a minority of them. His earliest painting represented &ldquo;Joseph
+interpreting the Dreams of the Baker and Butler&rdquo;; the first
+to excite particular attention was the &ldquo;Nightmare,&rdquo; exhibited
+in 1782. He produced only two portraits. His sketches or
+designs numbered about 800; they have admirable qualities of
+invention and design, and are frequently superior to his paintings.</p>
+
+<p>His general powers of mind were large. He was a thorough
+master of French, Italian, English and German, and could write
+in all these tongues with equal facility and vigour, though he
+preferred German as the vehicle of his thoughts. His writings
+contain passages of the best art-criticism that English literature
+can show. The principal work is his series of <i>Lectures</i> in the
+Royal Academy, twelve in number, commenced in 1801.</p>
+
+<div class="condensed">
+<p>Many interesting anecdotes of Fuseli, and his relations to contemporary
+artists, are given in his <i>Life</i> by John Knowles, who also
+edited his works in 3 vols. 8vo, London, 1831.</p>
+</div>
+<div class="author">(W. M. R.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">FUSEL OIL<a name="ar101" id="ar101"></a></span> (from the Ger. <i>Fusel</i>, bad spirits), the name applied
+to the volatile oily liquids, of a nauseous fiery taste and smell,
+which are obtained in the rectification of spirituous liquors made
+by the fermentation of grain, potatoes, the marc of grapes, and
+<span class="pagenum"><a name="page369" id="page369"></a>369</span>
+other material, and which, as they are of higher boiling point
+than ethyl alcohol, occur in largest quantity in the last portions
+of the distillate. Besides ethyl or ordinary alcohol, and amyl
+alcohol, which are present in them all, there have been found in
+fusel oil several other bodies of the C<span class="su">n</span>H<span class="su">2n+1</span>·OH series, also
+certain ethers, and members of the C<span class="su">n</span>H<span class="su">2n+1</span>·CO<span class="su">2</span>H series of
+fatty acids. Normal propyl alcohol is contained in the fusel
+oil of the marc brandy of the south of France, and isoprimary
+butyl alcohol in that of beet-root molasses. The chief constituent
+of the fusel oil procured in the manufacture of alcohol from
+potatoes and grain, usually known as fusel oil and potato-spirit,
+is isoprimary amyl alcohol, or isobutylcarbinol. Ordinary fusel
+oil yields also an isomeric amyl alcohol (active amyl alcohol)
+boiling at about 128°. Variable quantities of fusel oil, less or
+greater according to the stage of ripening, exist in commercial
+spirits (see <span class="sc"><a href="#artlinks">Spirits</a></span>).</p>
+
+<p>Fusel oil and its chief constituent, amyl alcohol, are direct
+nerve poisons. In small doses it causes only thirst and headache,
+with furred tongue and some excitement. In large doses it is
+a convulsent poison. Impure beverages induce all the graver
+neurotic and visceral disorders in alcoholism; and, like fusel
+oil, furfurol and the essence of absinthe, are convulsent poisons.
+Pure ethyl alcohol intoxication, indeed, is rarely seen, being
+modified in the case of spirits by the higher alcohols contained
+in fusel oil. According to Rabuteau the toxic properties of the
+higher alcohols increase with their molecular weight and boiling
+point. Richet considers that the fusel oil contained in spirits
+constitutes the chief danger in the consumption of alcoholic
+beverages. The expert can immediately detect the peculiarly
+virulent characters of the mixed intoxication due to the consumption
+of spirits containing a large percentage of fusel oil.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUSIBLE METAL,<a name="ar102" id="ar102"></a></span> a term applied to certain alloys, generally
+composed of bismuth, lead and tin, which possess the property of
+melting at comparatively low temperatures. Newton&rsquo;s fusible
+metal (named after Sir Isaac Newton) contains 50 parts of
+bismuth, 31.25 of lead and 18.75 of tin; that of Jean Darcet
+(1725-1801), 50 parts of bismuth with 25 each of lead and tin;
+and that of Valentin Rose the elder, 50 of bismuth with 28.1 of
+lead and 24.1 of tin. These melt between 91° and 95° C. The
+addition of cadmium gives still greater fusibility; in Wood&rsquo;s
+metal, for instance, which is Darcet&rsquo;s metal with half the tin
+replaced by cadmium, the melting point is lowered to 66°-71° C.;
+while another described by Lipowitz and containing 15 parts of
+bismuth, 8 of lead, 4 of tin and 3 of cadmium, softens at about
+55° and is completely liquid a little above 60°. By the addition
+of mercury to Darcet&rsquo;s metal the melting point may be reduced
+so low as 45°. These fusible metals have the peculiarity of expanding
+as they cool; Rose&rsquo;s metal, for instance, remains pasty
+for a considerable range of temperature below its fusing point,
+contracts somewhat rapidly from 80° to 55°, expands from 55°
+to 35°, and contracts again from 35° to 0°. For this reason they
+may be used for taking casts of anatomical specimens or making
+<i>clichés</i> from wood-blocks, the expansion on cooling securing
+sharp impressions. By suitable modification in the proportions
+of the components, a series of alloys can be made which melt
+at various temperatures above the boiling point of water; for
+example, with 8 parts of bismuth, 8 of lead and 3 of tin the
+melting point is 123°, and with 8 of bismuth, 30 of lead and 24 of
+tin it is 172°. With tin and lead only in equal proportions it is
+241°. Such alloys are used for making the fusible plugs inserted
+in the furnace-crowns of steam boilers, as a safeguard in the event
+of the water-level being allowed to fall too low. When this
+happens the plug being no longer covered with water is heated
+to such a temperature that it melts and allows the contents of
+the boiler to escape into the furnace. In automatic fire-sprinklers
+the orifices of the pipes are closed with fusible metal, which melts
+and liberates the water when, owing to an outbreak of fire in
+the room, the temperature rises above a predetermined limit.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUSILIER,<a name="ar103" id="ar103"></a></span> originally (in French about 1670, in English about
+1680) the name of a soldier armed with a light flintlock musket
+called the fusil; now a regimental designation. Various forms
+of flintlock small arms had been used in warfare since the middle
+of the 16th century. At the time of the English civil war (1642-1652)
+the term &ldquo;firelock&rdquo; was usually employed to distinguish
+these weapons from the more common matchlock musket. The
+special value of the firelock in armies of the 17th century lay
+in the fact that the artillery of the time used open powder barrels
+for the service of the guns, making it unsafe to allow lighted
+matches in the muskets of the escort. Further, a military escort
+was required, not only for the protection, but also for the
+surveillance of the artillerymen of those days. Companies of
+&ldquo;firelocks&rdquo; were therefore organized for these duties, and out of
+these companies grew the &ldquo;fusiliers&rdquo; who were employed in
+the same way in the wars of Louis XIV. In the latter part of
+the Thirty Years&rsquo; War (1643) fusiliers were simply mounted
+troops armed with the fusil, as carabiniers were with the carbine.
+But the escort companies of artillery came to be known by the
+name shortly afterwards, and the regiment of French Royal
+Fusiliers, organized in 1671 by Vauban, was considered the model
+for Europe. The general adoption of the flintlock musket and
+the suppression of the pike in the armies of Europe put an end
+to the original special duties of fusiliers, and they were subsequently
+employed to a large extent in light infantry work,
+perhaps on account of the greater individual aptitude for
+detached duties naturally shown by soldiers who had never been
+restricted to a fixed and unchangeable place in the line of battle.
+The senior fusilier regiment in the British service, the (7th)
+Royal Fusiliers (City of London Regiment), was formed on the
+French model in 1685; the 5th foot (now Northumberland
+Fusiliers), senior to the 7th in the army, was not at that time
+a fusilier regiment. The distinctive head-dress of fusiliers in the
+British service is a fur cap, generally resembling, but smaller
+than and different in details from, that of the Foot Guards.</p>
+
+<p>In Germany the name &ldquo;fusilier&rdquo; is borne by certain infantry
+regiments and by one battalion in each grenadier regiment.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUSION,<a name="ar104" id="ar104"></a></span> the term generally applied to the melting of a solid
+substance, or the change of state of aggregation from the solid
+to the liquid. The term &ldquo;liquefaction&rdquo; is frequently employed
+in the same sense, but is often restricted to the condensation
+of a gas or vapour. The converse process of freezing or solidification,
+the change from the liquid to the solid state, is subject to
+the same laws, and must be considered together with fusion.
+The solution of a solid in a foreign liquid, and the deposition or
+crystallization of a solid from a solution, are so closely related
+to the fusion of a pure substance, that it will also be necessary
+to consider some of the analogies which they present.</p>
+
+<p>1. <i>General Phenomena.</i>&mdash;There are two chief varieties of the
+process of fusion, namely, crystalline and amorphous, which are
+in many ways distinct, although it is possible to find intermediate
+cases which partake of the characteristics of both. The melting
+of ice may be taken as a typical case of crystalline fusion. The
+passage from rigid solid to mobile liquid occurs at a definite
+surface without any intermediate stage or plastic condition.
+The change takes place at a definite temperature, the fusing or
+freezing point (abbreviated F.P.), and requires the addition
+of a definite quantity of heat to the solid, which is called the
+latent heat of fusion. There is also in general a considerable
+change of volume during fusion, which amounts in the case of
+ice to a contraction of 9%. Typical cases of amorphous solidification
+are those of silica, glass, plastic sulphur, pitch, alcohol and
+many organic liquids. In this type the liquid gradually becomes
+more and more viscous as the temperature falls, and ultimately
+attains the rigidity characteristic of a solid, without any definite
+freezing point or latent heat. The condition of the substance
+remains uniform throughout, if its temperature is uniform;
+there is no separation into the two distinct phases of solid
+and liquid, and there is no sudden change of volume at any
+temperature.</p>
+
+<p>A change or transition from one crystalline form to another
+may occur in the solid state with evolution or absorption of
+heat at a definite temperature, and is analogous to the change
+from solid to liquid, but usually takes place more slowly owing
+to the small molecular mobility of the solid state. Thus
+rhombic sulphur when heated passes slowly at 95.6° C. into the
+<span class="pagenum"><a name="page370" id="page370"></a>370</span>
+monosymmetric form which melts at 120°, but if heated rapidly
+the rhombic form melts at 114.5. The two forms, rhombic and
+monosymmetric, can exist in equilibrium at 95.6°, the transition
+point at which they have the same vapour pressure. Similarly
+a solid solution of carbon in iron, when cooled slowly, passes
+at about 700° C., with considerable evolution of heat, into the
+form of &ldquo;pearlite,&rdquo; which is soft when cold, but if rapidly chilled
+the carbon remains in solution and the steel is very hard (see
+also <span class="sc"><a href="#artlinks">Alloys</a></span>).</p>
+
+<p>In the case of crystalline fusion it is necessary to distinguish
+two cases, the homogeneous and the heterogeneous. In the first
+case the composition of the solid and liquid phases are the same,
+and the temperature remains constant during the whole process
+of fusion. In the second case the solid and liquid phases differ
+in composition; that of the liquid phase changes continuously,
+and the temperature does not remain constant during the fusion.
+The first case comprises the fusion of pure substances, and
+that of eutectics, or cryohydrates; the second is the general
+case of an alloy or a solution. These have been very fully
+studied and their phenomena greatly elucidated in recent
+years.</p>
+
+<p>There is also a sub-variety of amorphous fusion, which may
+be styled colloid or gelatinous, and may be illustrated by the
+behaviour of solutions of water in gelatin. Many of these jellies
+melt at a fairly definite temperature on heating, and coagulate or
+set at a definite temperature on cooling. But in some cases the
+process is not reversible, and there is generally marked hysteresis,
+the temperature of setting and other phenomena depending on
+the rate of cooling. This case has not yet been fully worked out;
+but it appears probable that in many cases the jelly possesses
+a spongy framework of solid, holding liquid in its meshes or
+interstices. It might be regarded as a case of &ldquo;heterogeneous&rdquo;
+amorphous fusion, in which the liquid separates into two phases
+of different composition, one of which solidifies before the other.
+The two phases cannot, as a rule, be distinguished optically,
+but it is generally possible to squeeze out some of the liquid
+phase when the jelly has set, which proves that the substance
+is not really homogeneous. In very complicated mixtures, such
+as acid lavas or slags containing a large proportion of silica,
+amorphous and crystalline solidification may occur together.
+In this case the crystals separate first during the process of
+cooling, the mother liquor increases gradually in viscosity, and
+finally sets as an amorphous ground-mass or matrix, in which
+crystals of different kinds and sizes, formed at different stages
+of the cooling, remain embedded. The formation of crystals
+in an amorphous solid after it has set is also of frequent
+occurrence. It is termed devitrification, but is a very slow
+process unless the solid is in a plastic state.</p>
+
+<p>2. <i>Homogeneous Crystalline Fusion.</i>&mdash;The fusion of a solid of
+this type is characterized most clearly by the perfect constancy
+of temperature during the process. In fact, the law of constant
+temperature, which is generally stated as the first of the so-called
+&ldquo;laws of fusion,&rdquo; does not strictly apply except to this case.
+The constancy of the F.P. of a pure substance is so characteristic
+that change of the F.P. is often one of the most convenient tests
+of the presence of foreign material. In the case of substances
+like ice, which melt at a low temperature and are easily obtained
+in large quantities in a state of purity, the point of fusion may
+be very accurately determined by observing the temperature
+of an intimate mixture of the solid and liquid while slowly
+melting as it absorbs heat from surrounding bodies. But in the
+majority of cases it is more convenient to observe the freezing
+point as the liquid is cooled. By this method it is possible to
+ensure perfect uniformity of temperature throughout the mass
+by stirring the liquid continuously during the process of freezing,
+whereas it is difficult to ensure uniformity of temperature in
+melting a solid, however gradually the heat is supplied, unless
+the solid can be mixed with the liquid. It is also possible to
+observe the F.P. in other ways, as by noting the temperature
+at the moment of the breaking of a wire, of the stoppage of a
+stirrer, or of the maximum rate of change of volume, but these
+methods are generally less certain in their indications than the
+point of greatest constancy of temperature in the case of homogeneous
+crystalline solids.</p>
+
+<div class="condensed">
+<p class="pt2 center"><i>Fusing Points of Common Metals</i></p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcl">Mercury</td> <td class="tcr rb">&minus;38.8°</td> <td class="tcl">Antimony</td> <td class="tcr">630°</td></tr>
+<tr><td class="tcl">Potassium</td> <td class="tcr rb">62.5°</td> <td class="tcl">Aluminium</td> <td class="tcr">655°</td></tr>
+<tr><td class="tcl">Sodium</td> <td class="tcr rb">95.6°</td> <td class="tcl">Silver</td> <td class="tcr">962°</td></tr>
+<tr><td class="tcl">Tin</td> <td class="tcr rb">231.9°</td> <td class="tcl">Gold</td> <td class="tcr">1064°</td></tr>
+<tr><td class="tcl">Bismuth</td> <td class="tcr rb">269.2°</td> <td class="tcl">Copper</td> <td class="tcr">1082°</td></tr>
+<tr><td class="tcl">Cadmium</td> <td class="tcr rb">320.7°</td> <td class="tcl">Nickel</td> <td class="tcr">1427°</td></tr>
+<tr><td class="tcl">Lead</td> <td class="tcr rb">327.7°</td> <td class="tcl">Palladium</td> <td class="tcr">1535°</td></tr>
+<tr><td class="tcl">Zinc</td> <td class="tcr rb">419.0°</td> <td class="tcl">Platinum</td> <td class="tcr">1710°</td></tr>
+</table></div>
+
+<p>The above table contains some of the most recent values of
+fusing points of metals determined (except the first three and
+the last three) with platinum thermometers. The last three
+values are those obtained by extrapolation with platinum-rhodium
+and platinum-iridium couples. (See Harker, <i>Proc.
+Roy. Soc.</i> A 76, p. 235, 1905.) Some doubt has recently been
+raised with regard to the value for platinum, which is much
+lower than that previously accepted, namely 1775°.</p>
+
+<p>3. <i>Superfusion, Supersaturation.</i>&mdash;It is generally possible to
+cool a liquid several degrees below its normal freezing point
+without a separation of crystals, especially if it is protected
+from agitation, which would assist the molecules to rearrange
+themselves. A liquid in this state is said to be &ldquo;undercooled&rdquo;
+or &ldquo;superfused.&rdquo; The phenomenon is even more familiar in
+the case of solutions (<i>e.g.</i> sodium sulphate or acetate) which may
+remain in the &ldquo;metastable&rdquo; condition for an indefinite time
+if protected from dust, &amp;c. The introduction into the liquid
+under this condition of the smallest fragment of the crystal,
+with respect to which the solution is supersaturated, will produce
+immediate crystallization, which will continue until the
+temperature is raised to the saturation point by the liberation
+of the latent heat of fusion. The constancy of temperature at
+the normal freezing point is due to the equilibrium of exchange
+existing between the liquid and solid. Unless both solid and
+liquid are present, there is no condition of equilibrium, and the
+temperature is indeterminate.</p>
+
+<p>It has been shown by H.A. Miers (<i>Jour. Chem. Soc.</i>, 1906, 89,
+p. 413) that for a supersaturated solution in metastable equilibrium
+there is an inferior limit of temperature, at which it passes
+into the &ldquo;labile&rdquo; state, <i>i.e.</i> spontaneous crystallization occurs
+throughout the mass in a fine shower. This seems to be analogous
+to the fine misty condensation which occurs in a supersaturated
+vapour in the absence of nuclei (see <span class="sc"><a href="#artlinks">Vaporization</a></span>) when the
+supersaturation exceeds a certain limit.</p>
+
+<div class="condensed">
+<p>4. <i>Effect of Pressure on the F.P.</i>&mdash;The effect of pressure on the
+fusing-point depends on the change of volume during fusion. Substances
+which expand on <i>freezing</i>, like ice, have their freezing points
+lowered by increase of pressure; substances which expand on
+<i>fusing</i>, like wax, have their melting points raised by pressure.
+In each case the effect of pressure is to retard increase of volume.
+This effect was first predicted by James Thomson on the analogy
+of the effect of pressure on the boiling point, and was numerically
+verified by Lord Kelvin in the case of ice, and later by Bunsen in
+the case of paraffin and spermaceti. The equation by which the
+change of the F.P. is calculated may be proved by a simple application
+of the Carnot cycle, exactly as in the case of vapour and liquid.
+(See <span class="sc"><a href="#artlinks">Thermodynamics</a></span>.) If L be the latent heat of fusion in
+mechanical units, v&prime; the volume of unit mass of the solid, and v&Prime;
+that of the liquid, the work done in an elementary Carnot cycle of
+range d&theta; will be dp(v&Prime; &minus; v&prime;), if dp is the increase of pressure required
+to produce a change d&theta; in the F.P. Since the ratio of the work-difference
+or cycle-area to the heat-transferred L must be equal to
+d&theta;/&theta;, we have the relation</p>
+
+<p class="center">d&theta;/dp = &theta; (v&Prime; &minus; v&prime;)/L.</p>
+<div class="author">(1)</div>
+
+<p class="noind">The sign of d&theta;, the change of the F.P., is the same as that of the
+change of volume (v&Prime; &minus; v&prime;). Since the change of volume seldom
+exceeds 0.1 c.c. per gramme, the change of the F.P. per atmosphere
+is so small that it is not as a rule necessary to take account of variations
+of atmospheric pressure in observing a freezing point. A
+variation of 1 cm. in the height of the barometer would correspond
+to a change of .0001° C. only in the F.P. of ice. This is far beyond the
+limits of accuracy of most observations. Although the effect of
+pressure is so small, it produces, as is well known, remarkable
+results in the motion of glaciers, the moulding and regelation of
+ice, and many other phenomena. It has also been employed to
+explain the apparent inversion of the order of crystallization in
+rocks like granite, in which the arrangement of the crystals indicates
+that the quartz matrix solidified subsequently to the crystals of
+<span class="pagenum"><a name="page371" id="page371"></a>371</span>
+felspar, mica or hornblende embedded in it, although the quartz
+has a higher melting point. It is contended that under enormous
+pressure the freezing points of the more fusible constituents might
+be raised above that of the quartz, if the latter is less affected by
+pressure. Thus Bunsen found the F.P. of paraffin wax 1.4° C.
+below that of spermaceti at atmospheric pressure. At 100 atmospheres
+the two melted at the same temperature. At higher pressures
+the paraffin would solidify first. The effect of pressure on the
+silicates, however, is much smaller, and it is not so easy to explain
+a change of several hundred degrees in the F.P. It seems more
+likely in this particular case that the order of crystallization depends
+on the action of superheated water or steam at high temperatures
+and pressures, which is well known to exert a highly solvent and
+metamorphic action on silicates.</p>
+
+<p>5. <i>Variation of Latent Heat.</i>&mdash;C.C. Person in 1847 endeavoured to
+show by the application of the first law of thermodynamics that
+the increase of the latent heat per degree should be equal to the
+difference (s&Prime; &minus; s&prime;) between the specific heats of the liquid and solid.
+If, for instance, water at 0° C. were first frozen and then cooled to
+&minus;t° C., the heat abstracted per gramme would be (L&prime; + s&prime;t) calories.
+But if the water were first cooled to &minus;t° C., and then frozen at &minus;t°C.,
+by abstracting heat L&Prime;, the heat abstracted would be L&Prime; + s&Prime;t.
+Assuming that the heat abstracted should be the same in the two
+cases, we evidently obtain L&prime; &minus; L&Prime; = (s&Prime; &minus; s&prime;)t. This theory has been
+approximately verified by Petterson, by observing the freezing of a
+liquid cooled below its normal F.P. (<i>Jour. Chem. Soc.</i> 24, p. 151).
+But his method does not represent the true variation of the latent
+heat with temperature, since the freezing, in the case of a superfused
+liquid, really takes place at the normal freezing point. A quantity
+of heat s&Prime;t is abstracted in cooling to &minus;t, (L&Prime; &minus; s&Prime;t) in raising to 0°
+and freezing at 0°, and s&rsquo;t in cooling the ice to -t. The latent heat
+L&Prime; at &minus;t does not really enter into the experiment. In order to
+make the liquid freeze at a different temperature, it is necessary to
+subject it to pressure, and the effect of the pressure on the latent
+heat cannot be neglected. The entropy of a liquid &phi;&Prime; at its F.P.
+reckoned from any convenient zero &phi;<span class="su">0</span> in the solid state may be
+represented by the expression</p>
+
+<p class="center">&phi;&Prime; &minus; &phi;<span class="su">0</span> = &int; s&prime;d&theta;/&theta; + L/&theta;.</p>
+<div class="author">(2)</div>
+
+<p class="noind">Since &theta;d&phi;&Prime;/d&theta; = s&Prime;, we obtain by differentiation the relation</p>
+
+<p class="center">dL/d&theta; = s&Prime; &minus; s&prime; + L/&theta;,</p>
+<div class="author">(3)</div>
+
+<p class="noind">which is exactly similar to the equation for the specific heat of a
+vapour maintained in the saturated condition. If we suppose that
+the specific heats s&prime; and s&Prime; of the solid and liquid at equilibrium
+pressure are nearly the same as those ordinarily observed at constant
+pressure, the relation (3) differs from that of Person only by
+the addition of the term L/&theta;. Since s&Prime; is greater than s&prime; in all cases
+hitherto investigated, and L/&theta; is necessarily positive, it is clear that
+the latent heat of fusion must increase with rise of temperature, or
+diminish with fall of temperature. It is possible to imagine the F.P.
+so lowered by pressure (positive or negative) that the latent heat
+should vanish, in which case we should probably obtain a continuous
+passage from the liquid to the solid state similar to that which
+occurs in the case of amorphous substances. According to equation
+(3), the rate of change of the latent heat of water is approximately
+0.80 calorie per degree at 0° C. (as compared with 0.50, Person),
+if we assume s&Prime; = 1, and s&prime; = 0.5. Putting (s&Prime; &minus; s&prime;) = 0.5 in equation
+(2), we find L = 0 at &minus;160° C. approximately, but no stress can be
+laid on this estimate, as the variation of (s&Prime; &minus; s&prime;) is so uncertain.</p>
+</div>
+
+<table class="flt" style="float: right; width: 360px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:307px; height:351px" src="images/img371a.jpg" alt="" /></td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 1.</span>&mdash;F.P. or Solubility
+Curve: simple case.</td></tr></table>
+
+<p>6. <i>Freezing of Solutions and Alloys.</i>&mdash;The phenomena of
+freezing of heterogeneous crystalline mixtures may be illustrated
+by the case of aqueous solutions and of metallic solutions or
+alloys, which have been most widely studied. The usual effect
+of an impurity, such as salt or sugar in solution in water, is to
+lower the freezing point, so that no crystallization occurs until
+the temperature has fallen below the normal F.P. of the pure
+solvent, the depression of F.P. being nearly proportional to the
+concentration of the solution. When freezing begins, the solvent
+generally separates out from the solution in the pure state. This
+separation of the solvent involves an increase in the strength
+of the remaining solution, so that the temperature does not
+remain constant during the freezing, but continues to fall as
+more of the solvent is separated. There is a perfectly definite
+relation between temperature and concentration at each stage
+of the process, which may be represented in the form of a curve
+as AC in fig. 1, called the freezing point curve. The equilibrium
+temperature, at the surface of contact between the solid and
+liquid, depends only on the composition of the liquid phase and
+not at all on the quantity of solid present. The abscissa of the
+F.P. curve represents the composition of that portion of the
+original solution which remains liquid at any temperature. If
+instead of starting with a dilute solution we start with a strong
+solution represented by a point N, and cool it as shown by the
+vertical line ND, a point D is generally reached at which the
+solution becomes &ldquo;saturated.&rdquo; The dissolved substance or
+&ldquo;solute&rdquo; then separates out as the solution is further cooled,
+and the concentration diminishes with fall of temperature in
+a definite relation, as indicated by the curve CB, which is called
+the solubility curve. Though often called by different names,
+the two curves AC and CB are
+essentially of a similar nature.
+To take the case of an aqueous
+solution of salt as an example,
+along CB the solution is saturated
+with respect to salt, along
+AC the solution is saturated with
+respect to ice. When the point
+C is reached along either curve,
+the solution is saturated with
+respect to both salt and ice.
+The concentration cannot vary
+further, and the temperature
+remains constant, while the salt
+and ice crystallize out together,
+maintaining the exact proportions
+in which they exist in the solution. The resulting solid was
+termed a cryohydrate by F. Guthrie, but it is really an intimate
+mixture of two kinds of crystals, and not a chemical compound
+or hydrate containing the constituents in chemically equivalent
+proportions. The lowest temperature attainable by means of a
+freezing mixture is the temperature of the F.P. of the corresponding
+cryohydrate. In a mixture of salt and ice with the least
+trace of water a saturated brine is quickly formed, which dissolves
+the ice and falls rapidly in temperature, owing to the absorption
+of the latent heat of fusion. So long as both ice and salt are
+present, if the mixture is well stirred, the solution must necessarily
+become saturated with respect to both ice and salt, and this can
+only occur at the cryohydric temperature, at which the two
+curves of solubility intersect.</p>
+
+<p>The curves in fig. 1 also illustrate the simplest type of freezing
+point curve in the case of alloys of two metals A and B which
+do not form mixed crystals or chemical compounds. The alloy
+corresponding to the cryohydrate, possessing the lowest melting
+point, is called the eutectic alloy, as it is most easily cast and
+worked. It generally possesses a very fine-grained structure,
+and is not a chemical compound. (See <span class="sc"><a href="#artlinks">Alloys</a></span>.)</p>
+
+<table class="flt" style="float: right; width: 310px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:256px; height:349px" src="images/img371b.jpg" alt="" /></td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 2.</span>&mdash;Cooling Curves
+of Alloys: typical case.</td></tr></table>
+
+<p>To obtain a complete F.P. curve even for a binary alloy is a
+laborious and complicated process, but the information contained
+in such a curve is often very valuable. It is necessary to operate
+with a number of different alloys of suitably chosen composition,
+and to observe the freezing points of each separately. Each alloy
+should also be analysed after the process if there is any risk of
+its composition having been altered by oxidation or otherwise.
+The freezing points are generally best
+determined by observing the gradual
+cooling of a considerable mass, which
+is well stirred so long as it remains
+liquid. The curve of cooling may most
+conveniently be recorded, either photographically,
+using a thermocouple and
+galvanometer, as in the method of Sir
+W. Roberts-Austen, or with pen and
+ink, if a platinum thermometer is available,
+according to the method put in
+practice by C.T. Heycock and F.H.
+Neville. A typical set of curves obtained
+in this manner is shown in fig. 2. When
+the pure metal A in cooling reaches its
+F.P. the temperature suddenly becomes
+stationary, and remains accurately constant for a considerable
+period. Often it falls slightly below the F.P. owing to super-fusion,
+but rises to the F.P. and remains constant as soon as
+freezing begins. The second curve shows the cooling of A with
+10% of another metal B added. The freezing begins at a lower
+temperature with the separation of pure A. The temperature
+<span class="pagenum"><a name="page372" id="page372"></a>372</span>
+no longer remains constant during freezing, but falls more and
+more rapidly as the proportion of B in the liquid increases.
+When the eutectic temperature is reached there is a second
+F.P. or arrest at which the whole of the remaining liquid solidifies.
+With 20% of B the first F.P. is further lowered, and the temperature
+falls faster. The eutectic F.P. is of longer duration, but
+still at the same temperature. For an alloy of the composition
+of the eutectic itself there is no arrest until the eutectic temperature
+is reached, at which the whole solidifies without change of
+temperature. There is a great advantage in recording these
+curves automatically, as the primary arrest is often very slight,
+and difficult to observe in any other way.</p>
+
+<div class="condensed">
+<p>7. <i>Change of Solubility with Temperature.</i>&mdash;The lowering of the
+F.P. of a solution with increase of concentration, as shown by the
+F.P. or solubility curves, may be explained and calculated by
+equation (1) in terms of the osmotic pressure of the dissolved substance
+by analogy with the effect of mechanical pressure. It is
+possible in salt solutions to strain out the salt mechanically by a
+suitable filter or &ldquo;semi-permeable membrane,&rdquo; which permits the
+water to pass, but retains the salt. To separate 1 gramme of
+salt requires the performance of work PV against the osmotic
+pressure P, where V is the corresponding diminution in the volume
+of the solution. In dilute solutions, to which alone the following
+calculation can be applied, the volume V is the reciprocal of the
+concentration C of the solution in grammes per unit volume, and
+the osmotic pressure P is equal to that of an equal number of molecules
+of gas in the same space, and may be deduced from the usual
+equation of a gas,</p>
+
+<p class="center">P = R&theta; / VM = R&theta;C / M,      </p>
+<div class="author">(4)</div>
+
+<p class="noind">where M is the molecular weight of the salt in solution, &theta; the absolute
+temperature, and R a constant which has the value 8.32 joules,
+or nearly 2 calories, per degree C. It is necessary to consider
+two cases, corresponding to the curves CB and AB in fig. 1, in
+which the solution is saturated with respect to salt and water
+respectively. To facilitate description we take the case of a salt
+dissolved in water, but similar results apply to solutions in other
+liquids and alloys of metals.</p>
+
+<p>(<i>a</i>) If unit mass of salt is separated in the solid state from a saturated
+solution of salt (curve CB) by forcing out through a semi-permeable
+membrane against the osmotic pressure P the corresponding
+volume of water V in which it is dissolved, the heat evolved
+is the latent heat of saturated solution of the salt Q together with
+the work done PV. Writing (Q + PV) for L, and V for (v&Prime; &minus; v&prime;) in
+equation (1), and substituting P for p, we obtain</p>
+
+<p class="center">Q + PV = V&theta;dP / d&theta;,</p>
+<div class="author">(5)</div>
+
+<p class="noind">which is equivalent to equation (1), and may be established by
+similar reasoning. Substituting for P and V in terms of C from
+equation (4), if Q is measured in calories, R = 2, and we obtain</p>
+
+<p class="center">QC = 2&theta;²dC / d&theta;,</p>
+<div class="author">(6)</div>
+
+<p class="noind">which may be integrated, assuming Q constant, with the result</p>
+
+<p class="center">2log<span class="su">e</span>C&Prime; / C&prime; = Q / &theta;&prime; &minus; Q / &theta;&Prime;,</p>
+<div class="author">(7)</div>
+
+<p class="noind">where C&prime;, C&Prime; are the concentrations of the saturated solution corresponding
+to the temperatures &theta;&prime; and &theta;&Prime;. This equation may be
+employed to calculate the latent heat of solution Q from two observations
+of the solubility. It follows from these equations that
+Q is of the same sign as dC/d&theta;, that is to say, the solubility increases
+with rise of temperature if heat is absorbed in the formation of the
+saturated solution, which is the usual case. If, on the other hand,
+heat is liberated on solution, as in the case of caustic potash or
+sulphate of calcium, the solubility diminishes with rise of temperature.</p>
+
+<p>(<i>b</i>) In the case of a solution saturated with respect to ice (curve
+AC), if one gramme of water having a volume v is separated by freezing,
+we obtain a precisely similar equation to (5), but with L the latent
+heat of fusion of water instead of Q, and v instead of V. If the
+solution is dilute, we may neglect the external work Pv in comparison
+with L, and also the heat of dilution, and may write P/t for dP/d&theta;,
+where t is the depression of the F.P. below that of the pure solvent.
+Substituting for P in terms of V from equation (4), we obtain</p>
+
+<p class="center">t = 2&theta;²v / LVM = 2&theta;²w / LWM,</p>
+<div class="author">(8)</div>
+
+<p class="noind">where W is the weight of water and w that of salt in a given volume
+of solution. If M grammes of salt are dissolved in 100 of water,
+w = M and W = 100. The depression of the F.P. in this case is
+called by van &lsquo;t Hoff the &ldquo;Molecular Depression of the F.P.&rdquo; and
+is given by the simple formula</p>
+
+<p class="center">t = .02&theta;² / L.</p>
+<div class="author">(9)</div>
+
+<p class="noind">Equation (8) may be used to calculate L or M, if either is known,
+from observations of t, &theta; and w/W. The results obtained are
+sufficiently approximate to be of use in many cases in spite of the
+rather liberal assumptions and approximations effected in the
+course of the reasoning. In any case the equations give a simple
+theoretical basis with which to compare experimental data in order
+to estimate the order of error involved in the assumptions. We
+may thus estimate the variation of the osmotic pressure from the
+value given by the gaseous equation, as the concentration of the
+solution or the molecular dissociation changes. The most uncertain
+factor in the formula is the molecular weight M, since the
+molecule in solution may be quite different from that denoted by
+the chemical formula of the solid. In many cases the molecule of
+a metal in dilute solution in another metal is either monatomic, or
+forms a compound molecule with the solvent containing one atom
+of the dissolved metal, in which case the molecular depression is
+given by putting the atomic weight for M. In other cases, as
+Cu, Hg, Zn, in solution in cadmium, the depression of the F.P.
+per atom, according to Heycock and Neville, is only half as great,
+which would imply a diatomic molecule. Similarly As and Au in
+Cd appear to be triatomic, and Sn in Pb tetratomic. Intermediate
+cases may occur in which different molecules exist together in
+equilibrium in proportions which vary according to the temperature
+and concentration. The most familiar case is that of an electrolyte,
+in which the molecule of the dissolved substance is partly dissociated
+into ions. In such cases the degree of dissociation may be estimated
+by observing the depression of the F.P., but the results obtained
+cannot always be reconciled with those deduced by other methods,
+such as measurement of electrical conductivity, and there are many
+difficulties which await satisfactory interpretation.</p>
+
+<p>Exactly similar relations to (8) and (9) apply to changes of boiling
+point or vapour pressure produced by substances in solution (see
+<span class="sc"><a href="#artlinks">Vaporization</a></span>), the laws of which are very closely connected with
+the corresponding phenomena of fusion; but the consideration of
+the vapour phase may generally be omitted in dealing with the fusion
+of mixtures where the vapour pressure of either constituent is small.</p>
+</div>
+
+<table class="flt" style="float: right; width: 430px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:372px; height:235px" src="images/img372.jpg" alt="" /></td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 3.</span>&mdash;Solubility Curves of
+Hydrates.</td></tr></table>
+
+<p>8. <i>Hydrates.</i>&mdash;The simple case of a freezing point curve,
+illustrated in fig. 1, is generally modified by the occurrence
+of compounds of a character analogous to hydrates of soluble
+salts, in which the dissolved substance combines with one or
+more molecules of the solvent. These hydrates may exist as
+compound molecules in the solution, but their composition
+cannot be demonstrated unless they can be separated in the solid
+state. Corresponding to each crystalline hydrate there is generally
+a separate branch of the solubility curve along which the
+crystals of the hydrate are in equilibrium with the saturated
+solution. At any given temperature the hydrate possessing the
+least solubility is the most stable. If two are present in contact
+with the same solution, the more soluble will dissolve, and the
+less soluble will be formed at its expense until the conversion
+is complete. The two hydrates cannot be in equilibrium with the
+same solution except at the temperature at which their solubilities
+are equal, <i>i.e.</i> at the point where the corresponding curves
+of solubility intersect. This temperature is called the &ldquo;Transition
+Point.&rdquo; In the case of ZnSO<span class="su">4</span>, as shown in fig. 3, the heptahydrate,
+with seven molecules of water, is the least soluble
+hydrate at ordinary temperatures,
+and is generally
+deposited from saturated
+solutions. Above 39° C.,
+however, the hexahydrate,
+with six molecules, is less
+soluble, and a rapid conversion
+of the hepta- into the
+hexahydrate occurs if the
+former is heated above the
+transition point. The solubility
+of the hexahydrate is
+greater than that of the heptahydrate below 39°, but increases
+more slowly with rise of temperature. At about 80° C.
+the hexahydrate gives place to the monohydrate, which
+dissolves in water with evolution of heat, and diminishes in
+solubility with rise of temperature. Intermediate hydrates
+exist, but they are more soluble, and cannot be readily isolated.
+Both the mono- and hexahydrates are capable of existing in
+equilibrium with saturated solutions at temperatures far below
+their transition points, provided that the less soluble hydrate
+is not present in the crystalline form. The solubility curves can
+therefore be traced, as in fig. 3, over an extended range of temperature.
+The equilibrium of each hydrate with the solvent,
+considered separately, would present a diagram of two branches
+similar to fig. 1, but as a rule only a small portion of each curve
+can be realized, and the complete solubility curve, as experimentally
+determined, is composed of a number of separate
+pieces corresponding to the ranges of minimum solubility of
+different hydrates. Failure to recognize this, coupled with the
+<span class="pagenum"><a name="page373" id="page373"></a>373</span>
+fact that in strong and viscous solutions the state of equilibrium
+is but slowly attained, is the probable explanation of the remarkable
+discrepancies existing in many recorded data of solubility.</p>
+
+<div class="condensed">
+<p class="pt2 center"><i>Transition Points of Hydrates.</i></p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcl">Na<span class="su">2</span>CrO<span class="su">4</span>·10H<span class="su">2</span>O</td> <td class="tcc rb">19.9°</td>
+  <td class="tcl">NaBr·2H<span class="su">2</span>0</td> <td class="tcc">50.7°</td></tr>
+
+<tr><td class="tcl">Na<span class="su">2</span>SO<span class="su">4</span>·10H<span class="su">2</span>O</td> <td class="tcc rb">32.4°</td>
+  <td class="tcl">MnCl<span class="su">2</span>·4H<span class="su">2</span>O</td> <td class="tcc">57.8°</td></tr>
+
+<tr><td class="tcl">Na<span class="su">2</span>CO<span class="su">3</span>·10H<span class="su">2</span>O</td> <td class="tcc rb">35.1°</td>
+  <td class="tcl">Na<span class="su">3</span>PO<span class="su">4</span>·12H<span class="su">2</span>O</td> <td class="tcc">73.4°</td></tr>
+
+<tr><td class="tcl">Na<span class="su">2</span>S<span class="su">2</span>O<span class="su">3</span>·5H<span class="su">2</span>O</td> <td class="tcc rb">48.0°</td>
+  <td class="tcl">Ba(OH)<span class="su">2</span>·8H<span class="su">2</span>O</td> <td class="tcc">77.9°</td></tr>
+</table></div>
+
+<p>The transition points of the hydrates given in the above list
+(Richards, <i>Proc. Amer. Acad.</i>, 1899, 34, p. 277) afford well-marked
+constant temperatures which can be utilized as fixed
+points for experimental purposes.</p>
+
+<p>9. <i>Formation of Mixed Crystals.</i>&mdash;An important exception
+to the general type already described, in which the addition of a
+dissolved substance lowers the F.P. of the solvent, is presented
+by the formation of mixed crystals, or &ldquo;solid solutions,&rdquo; in
+which the solvent and solute occur mixed in varying proportions.
+This isomorphous replacement of one substance by another, in
+the same crystal with little or no change of form, has long been
+known and studied in the case of minerals and salts, but the
+relations between composition and melting-point have seldom
+been investigated, and much still remains obscure. In this case
+the process of freezing does not necessitate the performance of
+work of separation of the constituents of the solution, the F.P.
+is not necessarily depressed, and the effect cannot be calculated
+by the usual formula for dilute solutions. One of the simplest
+types of F.P. curve which may result from the occurrence of
+mixed crystals is illustrated by the case of alloys of gold and
+silver, or gold and platinum, in which the F.P. curve is nearly
+a straight line joining the freezing-points of the constituents.
+The equilibrium between the solid and liquid, in both of which
+the two metals are capable of mixing in all proportions, bears in
+this case an obvious and close analogy to the equilibrium between
+a mixed liquid (<i>e.g.</i> alcohol and water) and its vapour. In the
+latter case, as is well known, the vapour will contain a larger
+proportion of the more volatile constituent. Similarly in the case
+of the formation of mixed crystals, the liquid should contain
+a larger proportion of the more fusible constituent than the solid
+with which it is in equilibrium. The composition of the crystals
+which are being deposited at any moment will, therefore,
+necessarily change as solidification proceeds, following the
+change in the composition of the liquid, and the temperature
+will fall until the last portions of the liquid to solidify will consist
+chiefly of the more fusible constituent, at the F.P. of which the
+solidification will be complete. If, however, as seems to be
+frequently the case, the composition of the solid and liquid phases
+do not greatly differ from each other, the greater part of the
+solidification will occur within a comparatively small range of
+temperature, and the initial F.P. of the alloy will be well marked.
+It is possible in this case to draw a second curve representing
+the composition of the <i>solid</i> phase which is in equilibrium with
+the liquid at any temperature. This curve will not represent the
+average composition of the crystals, but that of the outer coating
+only which is in equilibrium with the liquid at the moment.
+H.W.B. Roozeboom (<i>Zeit. Phys. Chem.</i> xxx. p. 385) has
+attempted to classify some of the possible cases which may
+occur in the formation of mixed crystals on the basis of J.W.
+Gibbs&rsquo;s thermodynamic potential, the general properties of which
+may be qualitatively deduced from a consideration of observed
+phenomena. But although this method may enable us to classify
+different types, and even to predict results in a qualitative
+manner, it does not admit of numerical calculation similar to
+equation (8), as the Gibbs&rsquo;s function itself is of a purely abstract
+nature and its form is unknown. There is no doubt that the
+formation of mixed crystals may explain many apparent
+anomalies in the study of F.P. curves. The whole subject has
+been most fruitful of results in recent years, and appears full of
+promise for the future.</p>
+
+<div class="condensed">
+<p>For further details in this particular branch the reader may consult
+a report by Neville (<i>Brit. Assoc. Rep.</i>, 1900), which contains numerous
+references to original papers by Roberts-Austen, Le Chatelier,
+Roozeboom and others. For the properties of solutions see <span class="sc"><a href="#artlinks">Solution</a></span>.</p>
+</div>
+<div class="author">(H. L. C.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">FÜSSEN,<a name="ar105" id="ar105"></a></span> a town of Germany, in the kingdom of Bavaria, at
+the foot of the Alps (Tirol), on the Lech, 2500 ft. above the sea,
+with a branch line to Oberdorf on the railway to Augsburg. Pop.
+4000. It has six Roman Catholic churches, a Franciscan monastery
+and a castle. Rope-making is an important industry.
+The castle, lying on a rocky eminence, is remarkable for the
+peace signed here on the 22nd of April 1745 between the elector
+Maximilian III., Joseph of Bavaria and Maria Theresa. Two
+miles to the S.E., immediately on the Austrian frontier, romantically
+situated on a rock overlooking the Schwanensee, is the
+magnificent castle of Hohenschwangau, and a little to the north,
+on the site of an old castle, that of Neuschwanstein, built by
+Louis II. of Bavaria.</p>
+
+<div class="condensed">
+<p>See H. Feistle, <i>Füssen und Umgebung</i> (1898).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FUST, JOHANN<a name="ar106" id="ar106"></a></span> (&emsp;&emsp;?-1466), early German printer, belonged
+to a rich and respectable burgher family of Mainz, which is known
+to have flourished from 1423, and to have held many civil and
+religious offices. The name was always written Fust, but in
+1506 Johann Schöffer, in dedicating the German translation of
+Livy to the emperor Maximilian, called his grandfather Faust,
+and thenceforward the family assumed this name, and the Fausts
+of Aschaffenburg, an old and quite distinct family, placed
+Johann Fust in their pedigree. Johann&rsquo;s brother Jacob, a
+goldsmith, was one of the burgomasters in 1462, when Mainz
+was stormed and sacked by the troops of Count Adolf of Nassau,
+on which occasion he seems to have perished (see a document,
+dated May 8, 1463, published by Wyss in <i>Quartalbl. des hist.
+Vereins für Hessen</i>, 1879, p. 24). There is no evidence that, as
+is commonly asserted, Johann Fust was a goldsmith, but he
+appears to have been a money-lender or banker. On account of
+his connexion with Gutenberg (<i>q.v.</i>), he has been represented
+by some as the inventor of printing, and the instructor as well as
+the partner of Gutenberg, by others as his patron and benefactor,
+who saw the value of his discovery and supplied him with means
+to carry it out, whereas others paint him as a greedy and
+crafty speculator, who took advantage of Gutenberg&rsquo;s necessity
+and robbed him of the fruits of his invention. However this may
+be, the Helmasperger document of November 6, 1455, shows
+that Fust advanced money to Gutenberg (apparently 800
+guilders in 1450, and another 800 in 1452) for carrying on his
+work, and that Fust, in 1455, brought a suit against Gutenberg
+to recover the money he had lent, claiming 2020 (more correctly
+2026) guilders for principal and interest. It appears that he had
+not paid in the 300 guilders a year which he had undertaken to
+furnish for expenses, wages, &amp;c., and, according to Gutenberg,
+had said that he had no intention of claiming interest. The suit
+was apparently decided in Fust&rsquo;s favour, November 6, 1455,
+in the refectory of the Barefooted Friars of Mainz, when Fust
+made oath that he himself had borrowed 1550 guilders and
+given them to Gutenberg. There is no evidence that Fust, as
+is usually supposed, removed the portion of the printing materials
+covered by his mortgage to his own house, and carried on printing
+there with the aid of Peter Schöffer, of Gernsheim (who is known
+to have been a scriptor at Paris in 1449), to whom, probably
+about 1455,<a name="fa1i" id="fa1i" href="#ft1i"><span class="sp">1</span></a> he gave his only daughter Dyna or Christina in
+marriage. Their first publication was the Psalter, August 14,
+1457, a folio of 350 pages, the first printed book with a complete
+date, and remarkable for the beauty of the large initials printed
+each in two colours, red and blue, from types made in two
+pieces.<a name="fa2i" id="fa2i" href="#ft2i"><span class="sp">2</span></a> The Psalter was reprinted with the same types, 1459
+(August 29), 1490, 1502 (Schöffer&rsquo;s last publication) and 1516.
+Fust and Schöffer&rsquo;s other works are given below.<a name="fa3i" id="fa3i" href="#ft3i"><span class="sp">3</span></a> In 1464 Adolf
+<span class="pagenum"><a name="page374" id="page374"></a>374</span>
+of Nassau appointed for the parish of St Quintin three <i>Baumeisters</i>
+(master-builders) who were to choose twelve chief parishioners
+as assistants for life. One of the first of these &ldquo;Vervaren,&rdquo;
+who were named on May-day 1464, was Johannes Fust, and in
+1467 Adam von Hochheim was chosen instead of &ldquo;the late&rdquo;
+(<i>selig</i>) Johannes Fust. Fust is said to have gone to Paris in 1466
+and to have died of the plague, which raged there in August and
+September. He certainly was in Paris on the 4th of July, when
+he gave Louis de Lavernade of the province of Forez, then
+chancellor of the duke of Bourbon and first president of the
+parliament of Toulouse, a copy of his second edition of Cicero,
+as appears from a note in Lavernade&rsquo;s own hand at the end of
+the book, which is now in the library of Geneva. But nothing
+further is known than that on the 30th of October, probably
+in 1471, an annual mass was instituted for him by Peter Schöffer,
+Conrad Henlif (for Henekes, or Henckis, Schöffer&rsquo;s partner?
+who married Fust&rsquo;s widow about 1468<a name="fa4i" id="fa4i" href="#ft4i"><span class="sp">4</span></a>) and Johann Fust (the
+son), in the abbey-church of St Victor of Paris, where he was
+buried; and that Peter Schöffer founded a similar memorial
+service for Fust in 1473 in the church of the Dominicans at
+Mainz (Bockenheimer, <i>Gesch. der Stadt Mainz</i>, iv. 15).</p>
+
+<p>Fust was formerly often confused with the famous magician
+Dr Johann Faust, who, though an historical figure, had nothing
+to do with him (see <span class="sc"><a href="#artlinks">Faust</a></span>).</p>
+
+<div class="condensed">
+<p>See further the articles <span class="sc"><a href="#artlinks">Gutenberg</a></span> and <span class="sc"><a href="#artlinks">Typography</a></span>.</p>
+</div>
+<div class="author">(J. H. H.)</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1i" id="ft1i" href="#fa1i"><span class="fn">1</span></a> This date is uncertain; some place the marriage in 1453 or soon
+after, others about 1464. It is probable that Fust alluded to this
+relationship when he spoke of Schöffer as <i>pueri mei</i> in the colophons
+of Cicero&rsquo;s <i>De officiis</i> of 1465 and 1466.</p>
+
+<p><a name="ft2i" id="ft2i" href="#fa2i"><span class="fn">2</span></a> This method was patented in England by Solomon Henry in
+1780, and by Sir William Congreve in 1819.</p>
+
+<p><a name="ft3i" id="ft3i" href="#fa3i"><span class="fn">3</span></a> (3) Durandus, <i>Rationale divinorum officiorum</i> (1459), folio, 160
+leaves; (4) the <i>Clementine Constitutions</i>, with the gloss of Johannes
+Andreae (1460), 51 leaves; (5) <i>Biblia Sacra Latina</i> (1462), folio,
+2 vols., 242 and 239 leaves, 48 lines to a full page; (6) the Sixth
+Book of Decretals, with Andreae&rsquo;s gloss, 17th December 1465, folio,
+141 leaves; (7) Cicero, <i>De officiis</i> (1465). 4to, 88 leaves, the first
+edition of a Latin classic and the first book containing Greek characters,
+while in the colophon Fust for the first time calls Schöffer
+&ldquo;puerum suum&rdquo;; (8) the same, 4th February 1466; (9) <i>Grammatica
+rhytmica</i> (1466), folio, 11 leaves. They also printed in 1461-1462
+several papal bulls, proclamations of Adolf of Nassau, &amp;c. Nothing
+is known to have appeared for three years after the storming and
+capture of Mainz in 1462.</p>
+
+<p><a name="ft4i" id="ft4i" href="#fa4i"><span class="fn">4</span></a> Some confusion in the history of the Fust family has arisen
+since the publication of Bernard&rsquo;s <i>Orig. de l&rsquo;imprimerie</i> (1853).
+On p. 262, vol. i. he gave an extract from the correspondence between
+Oberlin and Bodmann (now preserved in the Paris Nat. Library),
+from which it would appear that Peter Schöffer was the son-in-law,
+not of Johann Fust, but of a brother of his, Conrad Fust. Of the
+latter, however, no other trace has been found, and he is no doubt
+a fiction of F.J. Bodmann, who, partly basing himself on the
+&ldquo;Conrad&rdquo; (Henlif, or Henckis) mentioned above, added the rest
+to gratify Oberlin (see Wyss in <i>Quartalblätter des hist. Vereins für
+Hessen</i>, 1879, p. 17).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FUSTEL DE COULANGES, NUMA DENIS<a name="ar107" id="ar107"></a></span> (1830-1889), French
+historian, was born in Paris on the 18th of March 1830, of Breton
+descent. After studying at the École Normale Supérieure he
+was sent to the French school at Athens in 1853, directed some
+excavations in Chios, and wrote an historical account of the
+island. After his return he filled various educational offices,
+and took his doctor&rsquo;s degree with two theses, <i>Quid Vestae cultus
+in institutis veterum privatis publicisque valuerit</i> and <i>Polybe,
+ou la Grèce conquise par les Romains</i> (1858). In these works
+his distinctive qualities were already revealed. His minute
+knowledge of the language of the Greek and Roman institutions,
+coupled with his low estimate of the conclusions of contemporary
+scholars, led him to go direct to the original texts, which he read
+without political or religious bias. When, however, he had
+succeeded in extracting from the sources a general idea that
+seemed to him clear and simple, he attached himself to it as if to
+the truth itself, employing dialectic of the most penetrating,
+subtle and even paradoxical character in his deduction of the
+logical consequences. From 1860 to 1870 he was professor of
+history at the faculty of letters at Strassburg, where he had a
+brilliant career as a teacher, but never yielded to the influence
+exercised by the German universities in the field of classical and
+Germanic antiquities.</p>
+
+<p>It was at Strassburg that he published his remarkable volume
+<i>La Cité antique</i> (1864), in which he showed forcibly the part
+played by religion in the political and social evolution of Greece
+and Rome. Although his making religion the sole factor of this
+evolution was a perversion of the historical facts, the book was
+so consistent throughout, so full of ingenious ideas, and written
+in so striking a style, that it ranks as one of the masterpieces of
+the French language in the 19th century. By this literary
+merit Fustel set little store, but he clung tenaciously to his
+theories. When he revised the book in 1875, his modifications
+were very slight, and it is conceivable that, had he recast it,
+as he often expressed the desire to do in the last years of his life,
+he would not have abandoned any part of his fundamental
+thesis. The work is now largely superseded.</p>
+
+<p>Fustel de Coulanges was the most conscientious of men, the
+most systematic and uncompromising of historians. Appointed
+to a lectureship at the École Normale Supérieure in February
+1870, to a professorship at the Paris faculty of letters in 1875,
+and to the chair of medieval history created for him at the
+Sorbonne in 1878, he applied himself to the study of the political
+institutions of ancient France. The invasion of France by
+the German armies during the war of 1870-71 attracted his
+attention to the Germanic invasions under the Roman Empire.
+Pursuing the theory of J.B. Dubos, but singularly transforming
+it, he maintained that those invasions were not marked by the
+violent and destructive character usually attributed to them;
+that the penetration of the German barbarians into Gaul was a
+slow process; that the Germans submitted to the imperial
+administration; that the political institutions of the Merovingians
+had their origins in the Roman laws at least as much as, if not
+more than, in German usages; and, consequently, that there was
+no conquest of Gaul by the Germans. This thesis he sustained
+brilliantly in his <i>Histoire des institutions politiques de l&rsquo;ancienne
+France</i>, the first volume of which appeared in 1874. It was the
+author&rsquo;s original intention to complete this work in four volumes,
+but as the first volume was keenly attacked in Germany as well
+as in France, Fustel was forced in self-defence to recast the book
+entirely. With admirable conscientiousness he re-examined
+all the texts and wrote a number of dissertations, of which,
+though several (<i>e.g.</i> those on the Germanic mark and on the
+<i>allodium</i> and <i>beneficium</i>) were models of learning and sagacity,
+all were dominated by his general idea and characterized by a
+total disregard for the results of such historical disciplines as
+diplomatic. From this crucible issued an entirely new work,
+less well arranged than the original, but richer in facts and
+critical comments. The first volume was expanded into three
+volumes, <i>La Gaule romaine</i> (1891), <i>L&rsquo;Invasion germanique et
+la fin de l&rsquo;empire</i> (1891) and <i>La Monarchie franque</i> (1888), followed
+by three other volumes, <i>L&rsquo;Alleu et le domaine rural pendant
+l&rsquo;époque mérovingienne</i> (1889), <i>Les Origines du système féodal:
+le bénéfice et le patronat ...</i> (1890) and <i>Les Transformations de
+la royauté pendant l&rsquo;époque carolingienne</i> (1892). Thus, in six
+volumes, he had carried the work no farther than the Carolingian
+period. The result of this enormous labour, albeit worthy of a
+great historian, clearly showed that the author lacked all sense
+of historical proportion. He was a diligent seeker after the truth,
+and was perfectly sincere when he informed a critic of the exact
+number of &ldquo;truths&rdquo; he had discovered, and when he remarked
+to one of his pupils a few days before his death, &ldquo;Rest assured
+that what I have written in my book is the truth.&rdquo; Such superb
+self-confidence can accomplish much, and it undoubtedly helped
+to form Fustel&rsquo;s talent and to give to his style that admirable
+concision which subjugates even when it fails to convince;
+but a student instinctively distrusts an historian who settles the
+most controverted problems with such impassioned assurance.
+The dissertations not embodied in his great work were collected
+by himself and (after his death) by his pupil, Camille Jullian,
+and published as volumes of miscellanies: <i>Recherches sur
+quelques problèmes d&rsquo;histoire</i> (1885), dealing with the Roman
+colonate, the land system in Normandy, the Germanic mark, and
+the judiciary organization in the kingdom of the Franks;
+<i>Nouvelles recherches sur quelques problèmes d&rsquo;histoire</i> (1891);
+and <i>Questions historiques</i> (1893), which contains his paper on
+Chios and his thesis on Polybius.</p>
+
+<p>His life was devoted almost entirely to his teaching and his
+books. In 1875 he was elected member of the Académie des
+Sciences Morales, and in 1880 reluctantly accepted the post
+of director of the École Normale. Without intervening personally
+in French politics, he took a keen interest in the questions of
+administration and social reorganization arising from the fall
+of the imperialist régime and the disasters of the war. He wished
+<span class="pagenum"><a name="page375" id="page375"></a>375</span>
+the institutions of the present to approximate more closely to
+those of the past, and devised for the new French constitution a
+body of reforms which reflected the opinions he had formed
+upon the democracy at Rome and in ancient France. But these
+were dreams which did not hold him long, and he would have
+been scandalized had he known that his name was subsequently
+used as the emblem of a political and religious party. He died
+at Massy (Seine-et-Oise) on the 12th of September 1889. Throughout
+his historical career&mdash;at the École Normale and the Sorbonne
+and in his lectures delivered to the empress Eugénie&mdash;his sole
+aim was to ascertain the truth, and in the defence of truth his
+polemics against what he imagined to be the blindness and
+insincerity of his critics sometimes assumed a character of harshness
+and injustice. But, in France at least, these critics were
+the first to render justice to his learning, his talents and his
+disinterestedness.</p>
+
+<div class="condensed">
+<p>See Paul Guiraud, <i>Fustel de Coulanges</i> (1896); H. d&rsquo;Arbois de
+Jubainville, <i>Deux Manières d&rsquo;écrire l&rsquo;histoire: critique de Bossuet,
+d&rsquo;Augustin Thierry et de Fustel de Coulanges</i> (1896); and Gabriel
+Monod, <i>Portraits et souvenirs</i> (1897).</p>
+</div>
+<div class="author">(C. B.*)</div>
+
+
+<hr class="art" />
+<p><span class="bold">FUSTIAN,<a name="ar108" id="ar108"></a></span> a term which includes a variety of heavy woven
+cotton fabrics, chiefly prepared for men&rsquo;s wear. It embraces
+plain twilled cloth called jean, and cut fabrics similar to velvet,
+known as velveteen, moleskin, corduroy, &amp;c. The term was
+once applied to a coarse cloth made of cotton and flax; now,
+fustians are usually of cotton and dyed various colours. In the
+reign of Edward III. the name was given to a woollen fabric.
+The name is said to be derived from El-Fustat, a suburb of Cairo,
+where it was first made; and certainly a kind of cloth has long
+been known under that name. In a petition to parliament,
+<i>temp.</i> Philip and Mary, &ldquo;fustian of Naples&rdquo; is mentioned. In
+the 13th and 14th centuries priests&rsquo; robes and women&rsquo;s dresses
+were made of fustian, but though dresses are still made from
+some kinds the chief use is for labourers&rsquo; clothes.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUSTIC<a name="ar109" id="ar109"></a></span> (Fr. <i>fustoc</i>, from Arab. <i>fustuq</i>, Gr. <span class="grk" title="pistakê">&#960;&#953;&#963;&#964;&#940;&#954;&#951;</span>, pistachio)
+<span class="sc">Yellow Wood</span> or <span class="sc">Old Fustic</span>, a dye-stuff consisting of the
+wood of <i>Chlorophora tinctoria</i>, a large tree of the natural order
+Moraceae, growing in the West Indies and tropical America.
+Fustic occurs in commerce in blocks, which are brown without,
+and of a brownish-yellow within. It is sometimes employed for
+inlaid work. The dye-stuff termed young fustic or Zante fustic,
+and also Venetian sumach, is the wood of <i>Rhus cotinus</i> (fustet,
+or smoke tree), a southern European and Asiatic shrub of the
+natural order Anacardiaceae, called by Gerarde &ldquo;red sumach,&rdquo;
+and apparently the &ldquo;coccygia&rdquo; and &ldquo;cotinus&rdquo; of Pliny (<i>Nat.
+Hist.</i> xiii. 41, xvi. 30). Its colouring matter is fisetin, C<span class="su">15</span>H<span class="su">10</span>O<span class="su">6</span>,
+which was synthesized by S. von Kostanecki (<i>Ber.</i>, 1904, 37,
+p. 384). (See <span class="sc"><a href="#artlinks">Dyeing</a></span>.)</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUTURES,<a name="ar110" id="ar110"></a></span> a term used in the produce markets for purchases
+or sales of commodities to be completed at a future date, as
+opposed to cash or &ldquo;spot&rdquo; transactions, which are settled
+immediately. See <span class="sc"><a href="#artlinks">Market</a></span>, and (for a detailed discussion of
+the question as affecting cotton) <span class="sc"><a href="#artlinks">Cotton</a></span>: <i>Marketing and Supply</i>.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FUX, JOHANN JOSEPH<a name="ar111" id="ar111"></a></span> (1660-1741), Austrian musician,
+was born at Hirtenfeld (Styria) in 1660. Of his youth and
+early training nothing is known. In 1696 he was organist at one
+of the principal churches of Vienna, and in 1698 was appointed
+by the emperor Leopold I. as his &ldquo;imperial court-composer,&rdquo;
+with a salary of about £6 a month. At the court of Leopold and
+of his successors Joseph I. and Charles VI., Fux remained for
+the rest of his life. To his various court dignities that of organist
+at St Stephen&rsquo;s cathedral was added in 1704. He married the
+daughter of the government secretary Schnitzbaum. As a
+proof of the high favour in which he was held by the art-loving
+Charles VI., it is told that at the coronation of that emperor
+as king of Bohemia in 1723 an opera, <i>La Constanza e la Fortezza</i>,
+especially composed by Fux for the occasion, was given at
+Prague in an open-air theatre. Fux at the time was suffering
+from gout, but the emperor had him carried in a litter all the
+way from Vienna, and gave him a seat in the imperial box.
+Fux died at Vienna on the 13th of February 1741. His life,
+although passed in the great world, was eventless, and his only
+troubles arose from the intrigues of his Italian rivals at court.
+Of the numerous operas which Fux wrote it is unnecessary to
+speak. They do not essentially differ from the style of the
+Italian <i>opera seria</i> of the time. Of greater importance are his
+sacred compositions, psalms, motets, oratorios and masses,
+the celebrated <i>Missa Canonica</i> amongst the latter. It is an all
+but unparalleled <i>tour de force</i> of learned musicianship, being
+written entirely in that most difficult of contrapuntal devices&mdash;the
+canon. As a contrapuntist and musical scholar generally,
+Fux was unsurpassed by any of his contemporaries, and his
+great theoretical work, the <i>Gradus ad Parnassum</i>, long
+remained by far the most thorough treatment of counterpoint
+and its various developments. The title of the original
+Latin edition is <i>Gradus ad Parnassum sive manuductio ad
+compositionem musicae regularem, methoda nova ac certa nondum
+ante tam exacta ordine in lucem edita, elaborata a Joanne Josepho
+Fux</i> (Vienna, 1715). It was translated into most European
+languages during the 18th century, and is still studied by
+musicians interested in the history of their art. The expenses
+of the publication were defrayed by the emperor Charles VI.</p>
+
+<div class="condensed">
+<p>Fux&rsquo;s biography was published by Ludwig von Köchel (Vienna,
+1871). It is based on minute original research and contains, amongst
+other valuable materials, a complete catalogue of the composer&rsquo;s
+numerous works.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">FUZE<a name="ar112" id="ar112"></a></span> or <span class="sc">Fuse</span>, an appliance for firing explosives in blasting
+operations, military shells, &amp;c. (see <span class="sc"><a href="#artlinks">Blasting</a></span> and <span class="sc"><a href="#artlinks">Ammunition</a></span>,
+§ <i>Shell</i>). The spelling is not governed by authority, but modern
+convenience has dictated the adoption of the &ldquo;z&rdquo; by military
+engineers as a general rule, in order to distinguish this sense
+from that of melting by heat (see below). The word, according
+to the <i>New English Dictionary</i>, is one of the forms in which the
+Lat. <i>fusus</i>, spindle, has been adapted through Romanic into
+English, the ordinary fuze taking the shape of a spindle-like
+tube. Similarly the term &ldquo;fusee&rdquo; (Fr. <i>fusée</i>, spindle full of tow,
+Late Lat. <i>fusata</i>) is applied to a coned spindle sometimes used in
+the wheel train of watches and spring clocks to equalize the action
+of the mainspring (see <span class="sc"><a href="#artlinks">Watch</a></span>); and the application of the same
+term to a special kind of match may also be due to its resemblance
+to a spindle. Again, in heraldry, another form, &ldquo;fusil,&rdquo; derived
+through the French from a Late Lat. diminutive (<i>fusillus</i> or
+<i>fusellus</i>) of this same <i>fusus</i>, is used of a bearing, an elongated
+lozenge. According to other etymological authorities, however
+(see Skeat, <i>Etym. Dict.</i>, 1898), &ldquo;fuze&rdquo; or &ldquo;fuse,&rdquo; and &ldquo;fusee&rdquo;
+in the sense of match, are all forms derived through the Fr. fusil,
+from Late Lat. <i>focile</i>, steel for striking fire from a flint, from Lat.
+<i>focus</i>, hearth. The Fr. <i>fusil</i> and English &ldquo;fusil&rdquo; were thus
+transferred to the &ldquo;firelock,&rdquo; <i>i.e.</i> the light musket of the 17th
+century (see <span class="sc"><a href="#artlinks">Fusilier</a></span>).</p>
+
+<p>In electrical engineering a &ldquo;fuse&rdquo; (always so spelled) is a
+safety device, commonly consisting of a strip or wire of easily
+fusible metal, which melts and thus interrupts the circuit of
+which it forms part, whenever that circuit, through some accident
+or derangement, is caused to carry a current larger than that
+for which it is intended. In this sense the word must be connected
+with <i>fusus</i>, the past participle of Lat. <i>fundere</i>, to pour,
+whence comes the verb &ldquo;fuse,&rdquo; to melt by heat, often used
+figuratively in the sense of blend, mix.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FYNE, LOCH,<a name="ar113" id="ar113"></a></span> an inlet of the sea, Argyllshire, Scotland.
+From the head, 6 m. above Inveraray, to the mouth on the Sound
+of Bute, it has a south-westerly and then southerly trend and
+is 44 m. long, its width varying from ¼ m. to 6 m. It receives the
+Fyne, Shira, Aray and many other streams, and, on the western
+side, gives off Lochs Shira, Gair, Gilp (with Ardrishaig, the
+Crinan Canal and Lochgilphead) and East Tarbert (with Tarbert
+village). The glens debouching on the lake are Fyne, Shira,
+Aray, Kinglas and Hell&rsquo;s Glen. The coast generally is picturesque
+and in many parts well wooded. All vessels using the Crinan
+Canal navigate the loch to and from Ardrishaig, and there are
+daily excursions during the season, as far up as Inveraray.
+There are ferries at St Catherine&rsquo;s and Otter, and piers at Tarbert,
+Ardrishaig, Kilmory, Crarae, Furnace, Inveraray, Strachur and
+elsewhere. The industries comprise granite quarrying at Furnace
+<span class="pagenum"><a name="page376" id="page376"></a>376</span>
+and Crarae, distilling at Ardrishaig, gunpowder-making at
+Furnace and Kilfinan, and, above all, fishing. Haddock, whiting
+and codling are taken, and the famous &ldquo;Loch Fyne herrings&rdquo;
+command the highest price in the market.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FYRD,<a name="ar114" id="ar114"></a></span> the name given to the English army, or militia, during
+the Anglo-Saxon period (see <span class="sc"><a href="#artlinks">Army</a></span>, 60). It is first mentioned
+in the <i>Anglo-Saxon Chronicle</i> under the date 605. The ealdorman,
+or sheriff, of the shire was probably charged with the duty of
+calling out and leading the fyrd, which appears always to have
+retained a local character, as during the time of the Danish
+invasions we read of the fyrd of Kent, of Somerset and of
+Devon. As attendance at the fyrd was included in the <i>trinoda
+necessitas</i> it was compulsory on all holders of land; but that
+it was not confined to them is shown by the following extract
+from the laws of Ine, king of the West Saxons, dated about
+690, which prescribes the penalty for the serious offence of
+neglecting the fyrd: &ldquo;If a <i>gesithcund</i> man owning land neglect
+the fyrd, let him pay 120 shillings, and forfeit his land; one not
+owning land 60 shillings; a ceorlish man 30 shillings as <i>fyrdwite</i>.&rdquo;
+The fyrd was gradually superseded by the gathering of the
+thegns and their retainers, but it was occasionally called out for
+defensive purposes even after the Norman Conquest.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FYT, JOHANNES<a name="ar115" id="ar115"></a></span> (1609-1661), Belgian animal painter, was
+born at Antwerp and christened on the 19th of August 1609.
+He was registered apprentice to Hans van den Berghe in 1621.
+Professionally van den Berghe was a restorer of old pictures
+rather than a painter of new ones. At twenty Johannes Fyt
+entered the gild of St Luke as a master, and from that time
+till his death in 1661 he produced a vast number of pictures
+in which the bold facility of Snyders is united to the powerful
+effects of Rembrandt, and harmonies of gorgeous tone are not
+less conspicuous than freedom of touch and a true semblance
+of nature. There never was such a master of technical processes
+as Fyt in the rendering of animal life in its most varied forms.
+He may have been less correct in outline, less bold in action
+than Snyders, but he was much more skilful and more true in
+the reproduction of the coat of deer, dogs, greyhounds, hares
+and monkeys, whilst in realizing the plumage of peacocks,
+woodcocks, ducks, hawks, and cocks and hens, he had not his
+equal, nor was any artist even of the Dutch school more effective
+in relieving his compositions with accessories of tinted cloth,
+porcelain ware, vases and fruit. He was not clever at figures,
+and he sometimes trusted for these to the co-operation of Cornelius
+Schut or Willeborts, whilst his architectural backgrounds
+were sometimes executed by Quellyn. &ldquo;Silenus amongst
+Fruit and Flowers,&rdquo; in the Harrach collection at Vienna, &ldquo;Diana
+and her Nymphs with the Produce of the Chase,&rdquo; in the Belvedere
+at Vienna, and &ldquo;Dead Game and Fruit in front of a Triumphal
+Arch,&rdquo; belonging to Baron von Rothschild at Vienna, are
+specimens of the co-operation respectively of Schut, Willeborts
+and Quellyn. They are also Fyt&rsquo;s masterpieces. The earliest
+dated work of the master is a cat grabbing at a piece of dead
+poultry near a hare and birds, belonging to Baron Cetto at
+Munich, and executed in 1644. The latest is a &ldquo;Dead Snipe
+with Ducks,&rdquo; of 1660, sold with the Jäger collection at Cologne
+in 1871. Great power is shown in the bear and boar hunts at
+Munich and Ravensworth castle. A &ldquo;Hunted Roedeer with
+Dogs in the Water,&rdquo; in the Berlin Museum, has some of the life
+and more of the roughness of Snyders, but lacks variety of tint
+and finish. A splendid specimen is the Page and Parrot near a
+table covered with game, guarded by a dog staring at a monkey,
+in the Wallace collection. With the needle and the brush
+Fyt was equally clever. He etched 16 plates, and those representing
+dogs are of their kind unique.</p>
+
+
+<hr class="art" />
+<p><span class="bold">FYZABAD,<a name="ar116" id="ar116"></a></span> or <span class="sc">Faizabad</span>, a city, district and division of
+British India in the United Provinces. The city stands on the
+left bank of the river Gogra, 78 m. by rail E. of Lucknow. Pop.
+(1901) 75,085. To the E. of Fyzabad, and now forming a
+suburb, is the ancient site of Ajodhya(<i>q.v.</i>). Fyzabad was
+founded about 1730 by Sa&rsquo;adat Ali Khan, the first nawab
+wazir of Oudh, who built a hunting-lodge here. It received its
+present name in the reign of his successor; and Shuja-ud-daula,
+the third nawab, laid out a large town and fortified it, and here
+he was buried. It was afterwards the residence of the Begums
+of Oudh, famous in connexion with the impeachment of Warren
+Hastings. When the court of Oudh was removed to Lucknow
+in 1775 all the leading merchants and bankers abandoned the
+place. At the census of 1869 Fyzabad contained only 37,804
+inhabitants; but it is now again advancing in prosperity and
+population. On the outbreak of the Mutiny in 1857, the cantonment
+contained two regiments of infantry, a squadron of cavalry,
+and a light field battery of artillery&mdash;all natives. Owing to
+their threatening demeanour after the Meerut massacre, many
+of the European women and children were sheltered by one of
+the great landholders of Oudh, and others were sent to less
+disturbed parts of the country. The troops rose, as was anticipated,
+and although they at first permitted their officers to take
+boats and proceed towards Dinapur, a message was afterwards
+sent to a rebel force lower down the river to intercept the fugitives.
+Of four boats, one, having passed the rebels unnoticed, succeeded
+in reaching Dinapur safely. Of those in the other three boats,
+one alone escaped. Fyzabad is now a station for European
+as well as for native troops. It is the headquarters of a brigade
+in the 8th division of the northern army. There is a government
+college. Sugar-refining and trade in agricultural produce are
+important.</p>
+
+<p><span class="sc">The District of Fyzabad</span>, lying between the two great rivers
+Gogra and Gumti, has an area of 1740 sq. m. It is entirely
+alluvial and well wooded, and has a good climate. Pop. (1901)
+1,225,374, an increase of .7% in the decade. The district is
+traversed throughout its length by the Oudh and Rohilkhand
+railway from Lucknow to Benares, with a branch to Allahabad.
+Tanda, with a population in 1901 of 19,853, has the largest
+production of cotton goods in Oudh.</p>
+
+<p>The <span class="sc">Division of Fyzabad</span> has an area of 12,113 sq. m., and
+comprises the six districts of Fyzabad, Gonda, Bahraich,
+Sultanpur, Partabgarh and Bara Banki. Pop. (1901) 6,855,991,
+an increase of 2% in the decade.</p>
+
+<hr class="art" />
+
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
+End of the Project Gutenberg EBook of Encyclopaedia Britannica, 11th
+Edition, Volume 11, Slice 3, by Various
+
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@@ -0,0 +1,21115 @@
+The Project Gutenberg EBook of Encyclopaedia Britannica, 11th Edition,
+Volume 11, Slice 3, by Various
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 3
+       "Frost" to "Fyzabad"
+
+Author: Various
+
+Release Date: August 13, 2011 [EBook #37064]
+
+Language: English
+
+Character set encoding: ASCII
+
+*** START OF THIS PROJECT GUTENBERG EBOOK ENCYC. BRITANNICA, VOL 11, SL 3 ***
+
+
+
+
+Produced by Marius Masi, Don Kretz and the Online
+Distributed Proofreading Team at https://www.pgdp.net
+
+
+
+
+
+
+
+
+Transcriber's notes:
+
+(1) Numbers following letters (without space) like C2 were originally
+      printed in subscript. Letter subscripts are preceded by an
+      underscore, like C_n.
+
+(2) Characters following a carat (^) were printed in superscript.
+
+(3) Side-notes were relocated to function as titles of their respective
+      paragraphs.
+
+(4) Macrons and breves above letters and dots below letters were not
+      inserted.
+
+(5) [root] stands for the root symbol; [alpha], [beta], etc. for greek
+      letters.
+
+(6) RN stands for Real Number symbol and (Pd) for Partial derivative
+      symbol
+
+(7) The following typographical errors have been corrected:
+
+    ARTICLE FRUIT: "The covering of the seed is marked i. n is the
+      nucellus or perisperm, enclosing the embryo-sac es, in which the
+      endosperm is formed." 'in' amended from 'is'.
+
+    ARTICLE FRUIT: "It occupies the whole cavity of the embryo-sac, or
+      is formed only at certain portions of it, at the apex, as in
+      Rhinanthus, ..." 'occupies' amended from 'occupied'.
+
+    ARTICLE FUEL: "Owing to the siliceous nature of the ash of straw,
+      it is desirable to have a means of clearing the grate bars from
+      slags and clinkers at short intervals, and to use a steam jet to
+      clear the tubes from similar deposits." 'straw' amended from
+      'sraw'.
+
+    ARTICLE FUEL: "In a research upon the heating power and other
+      properties of coal for naval use, carried out by the German
+      admiralty, the results tabulated below were obtained with coals
+      from different localities." 'from' amended from 'form'.
+
+    ARTICLE FUEL: "C + 2H2O = CO2 + 2H2" '+' amended from '='.
+
+    ARTICLE FULHAM: "The principal thoroughfares are Fulham Palace Road
+      running S. from Hammersmith, Fulham Road and King's Road, W. from
+      Chelsea, converging and leading to Putney Bridge over the Thames;
+      ..." 'converging' amended from 'coverging'.
+
+    ARTICLE FULLER, THOMAS: "Their eldest child, John, baptized at
+      Broadwindsor by his father, 6th June 1641, was afterwards rector of
+      Sidney Sussex College, edited the Worthies of England, 1662, and
+      became rector of Great Wakering, Essex, where he died in 1687."
+      added 'rector'.
+
+    ARTICLE FUNCTION: "When Taylor's theorem leads to a representation
+      of the function by means of an infinite series, the function is
+      said to be "analytic" (cf. S 21)." 'Taylor's' amended from
+      'Talyor's'.
+
+    ARTICLE FUNCTION: "or a series which converges uniformly may be
+      integrated term by term." 'uniformly' amended from 'unformly'.
+
+    ARTICLE FUNGI: "Parasitism.--Some fungi, though able to live as
+      saprophytes, occasionally enter the body of living plants, and are
+      thus termed facultative parasites." 'Parasitism' amended from
+      'Parasatism'.
+
+    ARTICLE FUNGI: "Recent experiments have shown that the difficulties
+      of getting orchid seeds to germinate are due to the absence of the
+      necessary fungus, which must be in readiness to infect the young
+      seedling immediately after it emerges from the seed." added
+      'after'.
+
+
+
+
+          ENCYCLOPAEDIA BRITANNICA
+
+  A DICTIONARY OF ARTS, SCIENCES, LITERATURE
+           AND GENERAL INFORMATION
+
+              ELEVENTH EDITION
+
+
+           VOLUME XI, SLICE III
+
+             FROST to FYZABAD
+
+
+
+
+ARTICLES IN THIS SLICE:
+
+
+  FROST                             FULMAR
+  FROSTBITE                         FULMINIC ACID
+  FROSTBURG                         FULTON, ROBERT
+  FROTHINGHAM, OCTAVIUS BROOKS      FULTON (Missouri, U.S.A.)
+  FROUDE, JAMES ANTHONY             FULTON (New York, U.S.A.)
+  FRUCTOSE                          FUM
+  FRUGONI, CARLO INNOCENZIO MARIA   FUMARIC AND MALEIC ACIDS
+  FRUIT                             FUMAROLE
+  FRUIT AND FLOWER FARMING          FUMIGATION
+  FRUMENTIUS                        FUMITORY
+  FRUNDSBERG, GEORG VON             FUNCHAL
+  FRUSTUM                           FUNCTION
+  FRUYTIERS, PHILIP                 FUNDY, BAY OF
+  FRY                               FUNERAL RITES
+  FRY, SIR EDWARD                   FUNGI
+  FRY, ELIZABETH                    FUNJ
+  FRYXELL, ANDERS                   FUNKIA
+  FUAD PASHA                        FUNNEL
+  FUCHOW                            FUR
+  FUCHS, JOHANN NEPOMUK VON         FURAZANES
+  FUCHS, LEONHARD                   FURETIERE, ANTOINE
+  FUCHSIA                           FURFOOZ
+  FUCHSINE                          FURFURANE
+  FUCINO, LAGO DI                   FURIES
+  FUEL                              FURLONG
+  FUENTE OVEJUNA                    FURNACE
+  FUENTERRABIA                      FURNEAUX, TOBIAS
+  FUERO                             FURNES
+  FUERTEVENTURA                     FURNESS, HORACE HOWARD
+  FUGGER                            FURNESS
+  FUGITIVE SLAVE LAWS               FURNISS, HARRY
+  FUGLEMAN                          FURNITURE
+  FUGUE                             FURNIVALL, FREDERICK JAMES
+  FUHRICH, JOSEPH VON               FURSE, CHARLES WELLINGTON
+  FUJI                              FURST, JULIUS
+  FU-KIEN                           FURSTENBERG
+  FUKUI                             FURSTENWALDE
+  FUKUOKA                           FURTH
+  FULA                              FURTWANGLER, ADOLF
+  FULCHER OF CHARTRES               FURZE
+  FULDA                             FUSARO, LAGO
+  FULGENTIUS, FABIUS PLANCIADES     FUSELI, HENRY
+  FULGINIAE                         FUSEL OIL
+  FULGURITE                         FUSIBLE METAL
+  FULHAM                            FUSILIER
+  FULK (king of Jerusalem)          FUSION
+  FULK (archbishop of Reims)        FUSSEN
+  FULKE, WILLIAM                    FUST, JOHANN
+  FULK NERRA                        FUSTEL DE COULANGES, NUMA DENIS
+  FULLEBORN, GEORG GUSTAV           FUSTIAN
+  FULLER, ANDREW                    FUSTIC
+  FULLER, GEORGE                    FUTURES
+  FULLER, MARGARET                  FUX, JOHANN JOSEPH
+  FULLER, MELVILLE WESTON           FUZE
+  FULLER, THOMAS                    FYNE, LOCH
+  FULLER, WILLIAM                   FYRD
+  FULLER'S EARTH                    FYT, JOHANNES
+  FULLERTON, LADY GEORGIANA         FYZABAD
+
+
+
+
+FROST (a common Teutonic word, cf. Dutch, _vorst_, Ger. _Frost_, from
+the common Teutonic verb meaning "to freeze," Dutch, _vriezen_, Ger.
+_frieren_; the Indo-European root is seen in Lat. _pruina_, hoar-frost,
+cf. _prurire_, to itch, burn, _pruna_, burning coal, Sansk. _plush_, to
+burn), in meteorology, the act, or agent of the process, of freezing;
+hence the terms "hoar-frost" and "white-frost" applied to visible frozen
+vapour formed on exposed surfaces. A frost can only occur when the
+surface temperature falls below 32 deg. F., the freezing-point of water;
+if the temperature be between 28 deg. and 32 deg. it is a "light frost,"
+if below 28 deg. it is a "heavy," "killing" or "black frost"; the term
+"black frost" is also used when no hoar-frost is present. The number of
+degrees below freezing-point is termed "degrees of frost." As soon as a
+mass of air is cooled to its dew-point, water begins to be precipitated
+in the form of rain, dew, snow or hail. Hoarfrost is only formed at the
+immediate surface of the land if the latter be at a temperature below 32
+deg., and this may occur even when the temperature of the air a few feet
+above the ground is 12 deg.-16 deg. above the freezing-point. The
+heaviest hoar-frosts are formed under weather conditions similar to
+those under which the heaviest summer dews occur, namely, clear and calm
+nights, when there is no cloud to impede the radiation of heat from the
+surface of the land, which thereby becomes rapidly and completely
+cooled. The danger of frost is minimized when the soil is very moist, as
+for example after 10-12 mm. of rain; and it is a practice in America to
+flood fields on the receipt of a frost warning, radiation being checked
+by the light fog sheets which develop over moist soils, just as a
+cloud-layer in the upper atmosphere impedes radiation on a grand scale.
+A layer of smoke will also impede radiation locally, and to this end
+smoky fires are sometimes lit in such positions that the smoke may drift
+over planted ground which it is desirable to preserve from frost.
+Similarly, frost may occur in open country when a town, protected by its
+smoke-cloud above, is free of it. In a valley with fairly high and steep
+flanks frost sometimes occurs locally at the bottom, because the layer
+of air cooled by contact with the cold surface of the higher ground is
+heavier than that not so cooled, and therefore tends to flow or settle
+downwards along the slope of the land. When meteorological
+considerations point to a frost, an estimate of the night temperature
+may be obtained by multiplying the difference between the readings of
+the wet and dry bulb thermometer by 2.5 and subtracting the result from
+the dry bulb temperature. This rule applies when the evening air is at
+about 50 deg. and 30.1 in. pressure, the sky being clear. An instrument
+has been devised in France for the prediction of frost. It consists of a
+wet bulb and a dry bulb thermometer, mounted on a board on which is also
+a scale of lines corresponding to degrees of the dry bulb, and a pointer
+traversing a scale graduated according to degrees of the wet bulb.
+Observations for the night are taken about half an hour before sunset.
+By means of the pointer and scale, the point may be found at which the
+line of the dry-bulb reading meets the pointer set to the reading of the
+wet bulb. The scale is further divided by colours so that the observed
+point may fall within one of three zones, indicating certain frost,
+probable frost or no probability of frost.
+
+
+
+
+FROSTBITE, a form of mortification (q.v.), due to the action of extreme
+cold in cutting off the blood-supply from the fingers, toes, nose, ears,
+&c. In comparatively trifling forms it occurs as "chaps" and
+"chilblains," but the term frostbite is usually applied only to more
+severe cases, where the part affected becomes in danger of gangrene. An
+immediate application of snow, or ice-water, will restore the
+circulation; the application of heat would cause inflammation. But if
+the mortification has gone too far for the circulation to be restored,
+the part will be lost, and surgical treatment may be necessary.
+
+
+
+
+FROSTBURG, a town of Allegany county, Maryland, U.S.A., 11 m. W. of
+Cumberland. Pop. (1890) 3804; (1900) 5274 (578 foreign-born and 236
+negroes); (1910) 6028. It is served by the Cumberland & Pennsylvania
+railway and the Cumberland & Westernport electric railway. The town is
+about 2000 ft. above sea-level on a plateau between the Great Savage and
+Dans mountains, and its delightful scenery and air have made it
+attractive as a summer resort. It is the seat of the second state normal
+school, opened in 1904. Frostburg is in the midst of the coal region of
+the state, and is itself almost completely undermined; it has planing
+mills and manufactures large quantities of fire-brick. The municipality
+owns and operates its waterworks. Natural gas is piped to Frostburg from
+the West Virginia fields, 120 m. away. Frostburg was first settled in
+1812; was called Mount Pleasant until about 1830, when the present name
+was substituted in honour of Meshech Frost, one of the town's founders;
+and was incorporated in 1870.
+
+
+
+
+FROTHINGHAM, OCTAVIUS BROOKS (1822-1895), American clergyman and author,
+was born in Boston on the 26th of November 1822, son of Nathaniel
+Langdon Frothingham (1793-1870), a prominent Unitarian preacher of
+Boston, and through his mother's family related to Phillips Brooks. He
+graduated from Harvard College in 1843 and from the Divinity School in
+1846. He was pastor of the North Unitarian church of Salem,
+Massachusetts, in 1847-1855. From 1855 to 1860 he was pastor of a new
+Unitarian society in Jersey City, where he gave up the Lord's Supper,
+thinking that it ministered to self-satisfaction; and it was as a
+radical Unitarian that he became pastor of another young church in New
+York City in 1860. Indeed in 1864 he was recognized as leader of the
+radicals after his reply to Dr Hedge's address to the graduating
+students of the Divinity School on _Anti-Supernaturalism in the Pulpit_.
+In 1865, when he had practically given up "transcendentalism," his
+church building was sold and his congregation began to worship in Lyric
+Hall under the name of the Independent Liberal Church; in 1875 they
+removed to the Masonic Temple, but four years later ill-health compelled
+Frothingham's resignation, and the church dissolved. Paralysis
+threatened him and he never fully recovered his health; in 1881 he
+returned to Boston, where he died on the 27th of November 1895. To this
+later period of his life belongs his best literary work. While he was in
+New York he was for a time art critic of the _Tribune_. Always himself
+on the unpopular side and an able but thoroughly fair critic of the
+majority, he habitually under-estimated his own worth; he was not only
+an anti-slavery leader when abolition was not popular even in New
+England, and a radical and rationalist when it was impossible for him to
+stay conveniently in the Unitarian Church, but he was the first
+president of the National Free Religious Association (1867) and an early
+and ardent disciple of Darwin and Spencer. To his radical views he was
+always faithful. It is a mistake to say that he grew more conservative
+in later years; but his judgment grew more generous and catholic. He was
+a greater orator than man of letters, and his sermons in New York were
+delivered to large audiences, averaging one thousand at the Masonic
+Temple, and were printed each week; in eloquence and in the charm of his
+spoken word he was probably surpassed in his day by none save George
+William Curtis. Personally he seemed cold and distant, partly because of
+his impressive appearance, and partly because of his own modesty, which
+made him backward in seeking friendships.
+
+  His principal published works are: _Stories from the Life of the
+  Teacher_ (1863), _A Child's Book of Religion_ (1866), and other works
+  of religious teaching for children; several volumes of sermons;
+  _Beliefs of Unbelievers_ (1876), _The Cradle of the Christ: a Study in
+  Primitive Christianity_ (1877), _The Spirit of New Faith_ (1877), _The
+  Rising and the Setting Faith_ (1878), and other expositions of the
+  "new faith" he preached; _Life of Theodore Parker_ (1874),
+  _Transcendentalism in New England_ (1876), which is largely
+  biographical, _Gerrit Smith, a Biography_ (1878), _George Ripley_
+  (1882), in the "American Men of Letters" series, _Memoir of William
+  Henry Channing_ (1886), _Boston Unitarianism, 1820-1850_ (1890),
+  really a biography of his father; and _Recollections and Impressions,
+  1822-1890_ (1891).
+
+
+
+
+FROUDE, JAMES ANTHONY (1818-1894), English historian, son of R.H.
+Froude, archdeacon of Totnes, was born at Dartington, Devon, on the 23rd
+of April 1818. He was educated at Westminster and Oriel College, Oxford,
+then the centre of the ecclesiastical revival. He obtained a second
+class and the chancellor's English essay prize, and was elected a fellow
+of Exeter College (1842). His elder brother, Richard Hurrell Froude
+(1803-1836), had been one of the leaders of the High Church movement at
+Oxford. Froude joined that party and helped J.H. Newman, afterwards
+cardinal, in his _Lives of the English Saints_. He was ordained deacon
+in 1845. By that time his religious opinions had begun to change, he
+grew dissatisfied with the views of the High Church party, and came
+under the influence of Carlyle's teaching. Signs of this change first
+appeared publicly in his _Shadows of the Clouds_, a volume containing
+two stories of a religious sort, which he published in 1847 under the
+pseudonym of "Zeta," and his complete desertion of his party was
+declared a year later in his _Nemesis of Faith_, an heretical and
+unpleasant book, of which the earlier part seems to be autobiographical.
+
+On the demand of the college he resigned his fellowship at Oxford, and
+mainly at least supported himself by writing, contributing largely to
+_Fraser's Magazine_ and the _Westminster Review_. The excellence of his
+style was soon generally recognized. The first two volumes of his
+_History of England from the Fall of Wolsey to the Defeat of the Spanish
+Armada_ appeared in 1856, and the work was completed in 1870. As an
+historian he is chiefly remarkable for literary excellence, for the art
+with which he represents his conception of the past. He condemns a
+scientific treatment of history and disregards its philosophy. He held
+that its office was simply to record human actions and that it should be
+written as a drama. Accordingly he gives prominence to the personal
+element in history. His presentations of character and motives, whether
+truthful or not, are undeniably fine; but his doctrine that there should
+be "no theorizing" about history tended to narrow his survey, and
+consequently he sometimes, as in his remarks on the foreign policy of
+Elizabeth, seems to misapprehend the tendencies of a period on which he
+is writing.
+
+Froude's work is often marred by prejudice and incorrect statements. He
+wrote with a purpose. The keynote of his _History_ is contained in his
+assertion that the Reformation was "the root and source of the expansive
+force which has spread the Anglo-Saxon race over the globe." Hence he
+overpraises Henry VIII. and others who forwarded the movement, and
+speaks too harshly of some of its opponents. So too, in his _English in
+Ireland_ (1872-1874), which was written to show the futility of attempts
+to conciliate the Irish, he aggravates all that can be said against the
+Irish, touches too lightly on English atrocities, and writes unjustly of
+the influence of Roman Catholicism. A strong anti-clerical prejudice is
+manifest in his historical work generally, and is doubtless the result
+of the change in his views on Church matters and his abandonment of the
+clerical profession. Carlyle's influence on him may be traced both in
+his admiration for strong rulers and strong government, which led him to
+write as though tyranny and brutality were excusable, and in his
+independent treatment of character. His rehabilitation of Henry VIII.
+was a useful protest against the idea that the king was a mere
+sanguinary profligate, but his representation of him as the self-denying
+minister of his people's will is erroneous, and is founded on the false
+theory that the preambles of the acts of Henry's parliaments represented
+the opinions of the educated laymen of England. As an advocate he
+occasionally forgets that sobriety of judgment and expression become an
+historian. He was not a judge of evidence, and seems to have been
+unwilling to admit the force of any argument or the authority of any
+statement which militated against his case. In his _Divorce of Catherine
+of Aragon_ (1891) he made an unfortunate attempt to show that certain
+fresh evidence on the subject, brought forward by Dr Gairdner, Dr
+Friedmann and others, was not inconsistent with the views which he has
+expressed in his _History_ nearly forty years before. He worked
+diligently at original manuscript authorities at Simancas, the Record
+Office and Hatfield House; but he used his materials carelessly, and
+evidently brought to his investigation of them a mind already made up as
+to their significance. His _Life of Caesar_ (1879), a glorification of
+imperialism, betrays an imperfect acquaintance with Roman politics and
+the life of Cicero; and of his two pleasant books of travel, _The
+English in the West Indies_ (1888) shows that he made little effort to
+master his subject, and _Oceana_ (1886), the record of a tour in
+Australia and New Zealand, among a multitude of other blunders, notes
+the prosperity of the working-classes in Adelaide at the date of his
+visit, when, in fact, owing to a failure in the wheat-crop, hundreds
+were then living on charity. He was constitutionally inaccurate, and
+seems to have been unable to represent the exact sense of a document
+which lay before him, or even to copy from it correctly. Historical
+scholars ridiculed his mistakes, and Freeman, the most violent of his
+critics, never let slip a chance of hitting at him in the _Saturday
+Review_. Froude's temperament was sensitive, and he suffered from these
+attacks, which were often unjust and always too savage in tone. The
+literary quarrel between him and Freeman excited general interest when
+it blazed out in a series of articles which Freeman wrote in the
+_Contemporary Review_ (1878-1879) on Froude's _Short Study_ of Thomas
+Becket.
+
+Notwithstanding its defects, Froude's _History_ is a great achievement;
+it presents an important and powerful account of the Reformation period
+in England, and lays before us a picture of the past magnificently
+conceived, and painted in colours which will never lose their freshness
+and beauty. As with Froude's work generally, its literary merit is
+remarkable; it is a well-balanced and orderly narrative, coherent in
+design and symmetrical in execution. Though it is perhaps needlessly
+long, the thread of the story is never lost amid a crowd of details;
+every incident is made subordinate to the general idea, appears in its
+appropriate place, and contributes its share to the perfection of the
+whole. The excellence of its form is matched by the beauty of its style,
+for Froude was a master of English prose. The most notable
+characteristic of his style is its graceful simplicity; it is never
+affected or laboured; his sentences are short and easy, and follow one
+another naturally. He is always lucid. He was never in doubt as to his
+own meaning, and never at a loss for the most appropriate words in which
+to express it. Simple as his language is, it is dignified and worthy of
+its subject. Nowhere perhaps does his style appear to more advantage
+than in his four series of essays entitled _Short Studies on Great
+Subjects_ (1867-1882), for it is seen there unfettered by the
+obligations of narrative. Yet his narrative is admirably told. For the
+most part flowing easily along, it rises on fit occasions to splendour,
+picturesque beauty or pathos. Few more brilliant pieces of historical
+writing exist than his description of the coronation procession of Anne
+Boleyn through the streets of London, few more full of picturesque power
+than that in which he relates how the spire of St Paul's was struck by
+lightning; and to have once read is to remember for ever the touching
+and stately words in which he compares the monks of the London
+Charterhouse preparing for death with the Spartans at Thermopylae.
+Proofs of his power in the sustained narration of stirring events are
+abundant; his treatment of the Pilgrimage of Grace, of the sea fight at
+St Helens and the repulse of the French invasion, and of the murder of
+Rizzio, are among the most conspicuous examples of it. Nor is he less
+successful when recording pathetic events, for his stories of certain
+martyrdoms, and of the execution of Mary queen of Scots, are told with
+exquisite feeling and in language of well-restrained emotion. And his
+characters are alive. We may not always agree with his portraiture, but
+the men and women whom he saw exist for us instinct with the life with
+which he endows them and animated by the motives which he attributes to
+them. His successes must be set against his failures. At the least he
+wrote a great history, one which can never be disregarded by future
+writers on his period, be their opinions what they may; which attracts
+and delights a multitude of readers, and is a splendid example of
+literary form and grace in historical composition.
+
+The merits of his work met with full recognition. Each instalment of his
+_History_, in common with almost everything which he wrote, was widely
+read, and in spite of some adverse criticisms was received with eager
+applause. In 1868 he was elected rector of St Andrews University,
+defeating Disraeli by a majority of fourteen. He was warmly welcomed in
+the United States, which he visited in 1872, but the lectures on Ireland
+which he delivered there caused much dissatisfaction. On the death of
+his adversary Freeman in 1892, he was appointed, on the recommendation
+of Lord Salisbury, to succeed him as regius professor of modern history
+at Oxford. Except to a few Oxford men, who considered that historical
+scholarship should have been held to be a necessary qualification for
+the office, his appointment gave general satisfaction. His lectures on
+Erasmus and other 16th-century subjects were largely attended. With some
+allowance for the purpose for which they were originally written, they
+present much the same characteristics as his earlier historical books.
+His health gave way in the summer of 1894, and he died on the 20th of
+October.
+
+His long life was full of literary work. Besides his labours as an
+author, he was for fourteen years editor of _Fraser's Magazine_. He was
+one of Carlyle's literary executors, and brought some sharp criticism
+upon himself by publishing Carlyle's _Reminiscences_ and the _Memorials
+of Jane Welsh Carlyle_, for they exhibited the domestic life and
+character of his old friend in an unpleasant light. Carlyle had given
+the manuscripts to him, telling him that he might publish them if he
+thought it well to do so, and at the close of his life agreed to their
+publication. Froude therefore declared that in giving them to the world
+he was carrying out his friend's wish by enabling him to make a
+posthumous confession of his faults. Besides publishing these
+manuscripts he wrote a _Life of Carlyle_. His earlier study of Irish
+history afforded him suggestions for a historical novel entitled _The
+Two Chiefs of Dunboy_ (1889). In spite of one or two stirring scenes it
+is a tedious book, and its personages are little more than machines for
+the enunciation of the author's opinions and sentiments. Though Froude
+had some intimate friends he was generally reserved. When he cared to
+please, his manners and conversation were charming. Those who knew him
+well formed a high estimate of his ability in practical affairs. In 1874
+Lord Carnarvon, then colonial secretary, sent Froude to South Africa to
+report on the best means of promoting a confederation of its colonies
+and states, and in 1875 he was again sent to the Cape as a member of a
+proposed conference to further confederation. Froude's speeches in South
+Africa were rather injudicious, and his mission was a failure (see SOUTH
+AFRICA: _History_). He was twice married. His first wife, a daughter of
+Pascoe Grenfell and sister of Mrs Charles Kingsley, died in 1860; his
+second, a daughter of John Warre, M.P. for Taunton, died in 1874.
+
+  Froude's _Life_, by Herbert Paul, was published in 1905.     (W. Hu.)
+
+
+
+
+FRUCTOSE, LAEVULOSE, or FRUIT-SUGAR, a carbohydrate of the formula
+C6H12O6. It is closely related to ordinary d-glucose, with which it
+occurs in many fruits, starches and also in honey. It is a hydrolytic
+product of inulin, from which it may be prepared; but it is more usual
+to obtain it from "invert sugar," the mixture obtained by hydrolysing
+cane sugar with sulphuric acid. Cane sugar then yields a syrupy mixture
+of glucose and fructose, which, having been freed from the acid and
+concentrated, is mixed with water, cooled in ice and calcium hydroxide
+added. The fructose is precipitated as a saccharate, which is filtered,
+suspended in water and decomposed by carbon dioxide. The liquid is
+filtered, the filtrate concentrated, and the syrup so obtained washed
+with cold alcohol. On cooling the fructose separates. It may be obtained
+as a syrup, as fine, silky needles, a white crystalline powder, or as a
+granular crystalline, somewhat hygroscopic mass. When anhydrous it melts
+at about 95 deg. C. It is readily soluble in water and in dilute alcohol,
+but insoluble in absolute alcohol. It is sweeter than cane sugar and is
+more easily assimilated. It has been employed under the name diabetin as
+a sweetening agent for diabetics, since it does not increase the
+sugar-content of the urine; other medicinal applications are in phthisis
+(mixed with quassia or other bitter), and for children suffering from
+tuberculosis or scrofula in place of cane sugar or milk-sugar.
+
+Chemically, fructose is an oxyketone or ketose, its structural formula
+being CH2OH.(CH.OH)3.CO.CH2OH; this result followed from its conversion
+by H. Kiliani into methylbutylacetic acid. The form described above is
+_laevo_-rotatory, but it is termed d-fructose, since it is related to
+d-glucose. Solutions exhibit mutarotation, fresh solutions having a
+specific rotation of -104.0 deg., which gradually diminishes to -92 deg.
+It was synthesized by Emil Fischer, who found the synthetic sugar which
+he named [alpha]-acrose to be (d + l)-fructose, and by splitting this
+mixture he obtained both the d and l forms. Fructose resembles d-glucose
+in being fermentable by yeast (it is the one ketose which exhibits this
+property), and also in its power of reducing alkaline copper and silver
+solutions; this latter property is assigned to the readiness with which
+hydroxyl and ketone groups in close proximity suffer oxidation. For the
+structural (stereochemical) relations of fructose see SUGAR.
+
+
+
+
+FRUGONI, CARLO INNOCENZIO MARIA (1692-1768), Italian poet, was born at
+Genoa on the 21st of November 1692. He was originally destined for the
+church and at the age of fifteen, in opposition to his strong wishes,
+was shut up in a convent; but although in the following year he was
+induced to pronounce monastic vows, he had no liking for this life. He
+acquired considerable reputation as an elegant writer both of Latin and
+Italian prose and verse; and from 1716 to 1724 he filled the chairs of
+rhetoric at Brescia, Rome, Genoa, Bologna and Modena successively,
+attracting by his brilliant fluency a large number of students at each
+university. Through Cardinal Bentivoglio he was recommended to Antonio
+Farnese, duke of Parma, who appointed him his poet laureate; and he
+remained at the court of Parma until the death of Antonio, after which
+he returned to Genoa. Shortly afterwards, through the intercession of
+Bentivoglio, he obtained from the pope the remission of his monastic
+vows, and ultimately succeeded in recovering a portion of his paternal
+inheritance. After the peace of Aix-la-Chapelle he returned to the court
+of Parma, and there devoted the later years of his life chiefly to
+poetical composition. He died on the 20th of December 1768. As a poet
+Frugoni was one of the best of the school of the Arcadian Academy, and
+his lyrics and pastorals had great facility and elegance.
+
+  His collected works were published at Parma in 10 vols. in 1799, and a
+  more complete edition appeared at Lucca in the same year in 15 vols. A
+  selection from his works was published at Brescia in 1782, in 4 vols.
+
+
+
+
+FRUIT (through the French from the Lat. _fructus_; _frui_, to enjoy), in
+its widest sense, any product of the soil that can be enjoyed by man or
+animals; the word is so used constantly in the Bible, and extended, as a
+Hebraism, to offspring or progeny of man and of animals, in such
+expressions as "the fruit of the body," "of the womb," "fruit of thy
+cattle" (Deut. xxviii. 4), &c., and generally to the product of any
+action or effort. Between this wide and frequently figurative use of the
+word and its application in the strict botanical sense treated below,
+there is a popular meaning, regarding the objects denoted by the word
+entirely from the standpoint of edibility, and differentiating them
+roughly from those other products of the soil, which, regarded
+similarly, are known as vegetables. In this sense "fruit" is applied to
+such seed-envelopes of plants as are edible, either raw or cooked, and
+are usually sweet, juicy or of a refreshing flavour. But applications of
+the word in this sense are apt to be loose and shifting according to the
+fashion of the time.
+
+Fruit, in the botanical sense, is developed from the flower as the
+result of fertilization of the ovule. After fertilization various
+changes take place in the parts of the flower. Those more immediately
+concerned in the process, the anther and stigma, rapidly wither and
+decay, while the filaments and style often remain for some time; the
+floral envelopes become dry, the petals fall, and the sepals are either
+deciduous, or remain persistent in an altered form; the ovary becomes
+enlarged, forming the _pericarp_; and the ovules are developed as the
+seeds, containing the embryo-plant. The term fruit is strictly applied
+to the mature pistil or ovary, with the seeds in its interior; but it
+often includes other parts of the flower, such as the bracts and floral
+envelopes. Thus the fruit of the hazel and oak consists of the ovary
+enveloped by the bracts; that of the apple and pear, of the ovary and
+floral receptacle; and that of the pine-apple, of the whole
+inflorescence. Such fruits are sometimes distinguished as _pseudocarps_.
+In popular language, the fruit includes all those parts which exhibit a
+striking change as the result of fertilization. In general, the fruit is
+not ripened unless fertilization has been effected; but cases occur as
+the result of cultivation in which the fruit swells and becomes to all
+appearance perfect, while no seeds are produced. Thus, there are
+seedless oranges, grapes and pineapples. When the ovules are
+unfertilized, it is common to find that the ovary withers and does not
+come to maturity; but in the case of bananas, plantains and bread-fruit,
+the non-development of seeds seems to lead to a larger growth and a
+greater succulence of fruit.
+
+  The fruit, like the ovary, may be formed of a single carpel or of
+  several. It may have one cell or cavity, being _unilocular_; or many,
+  _multilocular_, &c. The number and nature of the divisions depend on
+  the number of carpels and the extent to which their edges are folded
+  inwards. The appearances presented by the ovary do not always remain
+  permanent in the fruit. Great changes are observed to take place, not
+  merely as regards the increased size of the ovary, its softening or
+  hardening, but also in its internal structure, owing to the
+  suppression, additional formation or enlargement of parts. Thus, in
+  the ash (fig. 1) an ovary with two cells, each containing an ovule
+  attached to a central placenta, is changed into a unilocular fruit
+  with one seed; one ovule becomes abortive, while the other, g,
+  gradually enlarging until the septum is pushed to one side, unites
+  with the walls of the cell, and the placenta appears to be parietal.
+  In the oak and hazel, an ovary with three and two cells respectively,
+  and two ovules in each, produces a one-celled fruit with one seed. In
+  the coco-nut, a trilocular and triovular ovary produces a one-celled,
+  one-seeded fruit. This abortion may depend on the pressure caused by
+  the development of certain ovules, or it may proceed from
+  non-fertilization of all the ovules and consequent non-enlargement of
+  the carpels. Again, by the growth of the placenta, or the folding
+  inwards of parts of the carpels, divisions occur in the fruit which
+  did not exist in the ovary. In _Cathartocarpus Fistula_ a one-celled
+  ovary is changed into a fruit having each of its seeds in a separate
+  cell, in consequence of spurious dissepiments being produced
+  horizontal from the inner wall of the ovary. In flax (_Linum_) by the
+  folding inwards of the back of the carpels a five-celled ovary becomes
+  a ten-celled fruit. In _Astragalus_ the folding inwards of the dorsal
+  suture converts a one-celled ovary into a two-celled fruit; and in
+  _Oxytropis_ the folding of the ventral suture gives rise to a similar
+  change. The development of cellular or pulpy matter, and the
+  enlargement of parts not forming whorls of the flower, frequently
+  alter the appearance of the fruit, and render it difficult to discover
+  its formation. In the gooseberry (fig. 29), grape, guava, tomato and
+  pomegranate, the seeds nestle in pulp formed by the placentas. In the
+  orange the pulpy matter surrounding the seeds is formed by succulent
+  cells, which are produced from the inner partitioned lining of the
+  pericarp. In the strawberry the receptacle becomes succulent, and
+  bears the mature carpels on its convex surface (fig. 2); in the rose
+  there is a fleshy hollow receptacle which bears the carpels on its
+  concave surface (fig. 3). In the juniper the scaly bracts grow up
+  round the seeds and become succulent, and in the fig (fig. 4) the
+  receptacle becomes succulent and encloses an inflorescence.
+
+  [Illustration:
+
+    Fig. 1.--Samara or winged fruit of Ash (_Fraxinus_). 1, Entire, with
+    its wing a; 2, lower portion cut transversely, to show that it
+    consists of two cells; one of which, l, is abortive, and is reduced
+    to a very small cavity, while the other is much enlarged and filled
+    with a seed g.
+
+    Fig. 2.--Fruit of the Strawberry (_Fragaria vesca_), consisting of
+    an enlarged succulent receptacle, bearing on its surface the small
+    dry seed-like fruits (achenes). (After Duchartre.)
+
+    From Strasburger's _Lehrbuch der Botanik_, by permission of Gustav
+    Fischer.
+
+    Fig. 3.--Fruit of the Rose cut vertically. s', Fleshy hollowed
+    receptacle; s, persistent sepals; _fr_, ripe carpels; e, stamens,
+    withered.
+
+    Fig. 4.--Peduncle of Fig (_Ficus Carica_), ending in a hollow
+    receptacle enclosing numerous male and female flowers.
+
+    Fig. 5.--Fruit of Cherry (_Prunus Cerasus_) in longitudinal section.
+    ep, Epicarp; m, mesocarp; en, endocarp.
+
+    From Strasburger's _Lehrbuch der Botanik_, by permission of Gustav
+    Fischer.]
+
+  The pericarp consists usually of three layers, the external, or
+  _epicarp_ (fig. 5, ep); the middle, or _mesocarp_, m; and the
+  internal, or _endocarp_, _en_. These layers are well seen in such a
+  fruit as the peach, plum or cherry, where they are separable one from
+  the other; in them the epicarp forms what is commonly called the skin;
+  the mesocarp, much developed, forms the flesh or pulp, and hence has
+  sometimes been called _sarcocarp_; while the endocarp, hardened by the
+  production of woody cells, forms the _stone_ or _putamen_ immediately
+  covering the kernel or seed. The pulpy matter found in the interior of
+  fruits, such as the gooseberry, grape and others, is formed from the
+  placentas, and must not be confounded with the sarcocarp. In some
+  fruits, as in the nut, the three layers become blended together and
+  are indistinguishable. In bladder senna (_Colutea arborescens_) the
+  pericarp retains its leaf-like appearance, but in most cases it
+  becomes altered both in consistence and in colour. Thus in the date
+  the epicarp is the outer brownish skin, the pulpy matter is the
+  mesocarp or sarcocarp, and the thin papery-like lining is the endocarp
+  covering the hard seed. In the medlar the endocarp becomes of a stony
+  hardness. In the melon the epicarp and endocarp are very thin, while
+  the mesocarp forms the bulk of the fruit, differing in texture and
+  taste in its external and internal parts. The rind of the orange
+  consists of epicarp and mesocarp, while the endocarp forms partitions
+  in the interior, filled with pulpy cells. The part of the pericarp
+  attached to the peduncle is the base, and the point where the style or
+  stigma existed is the apex. This latter is not always the apparent
+  apex, as in the case of the ovary; it may be lateral or even basilar.
+  The style sometimes remains in a hardened form, rendering the fruit
+  _apiculate_; at other times it falls off, leaving only traces of its
+  existence. The presence of the style or stigma serves to distinguish
+  certain single-seeded pericarps from seeds.
+
+  [Illustration:
+
+    FIG. 6.--Seed-vessel or capsule of Campion, opening by ten teeth at
+    the apex. The calyx c is seen surrounding the seed-vessel.
+
+    FIG. 7.--Capsule of Poppy, opening by pores p, under the radiating
+    peltate stigma s.]
+
+
+    Dehiscence of fruits.
+
+  When the fruit is mature and the seeds are ripe, the carpels usually
+  give way either at the ventral or dorsal suture or at both, and so
+  allow the seeds to escape. The fruit in this case is _dehiscent_. But
+  some fruits are _indehiscent_, falling to the ground entire, and the
+  seeds eventually reaching the soil by their decay. By dehiscence the
+  pericarp becomes divided into different pieces, or _valves_, the fruit
+  being univalvular, bivalvular or multivalvular, &c., according as
+  there are one, two or many valves. The splitting extends the whole
+  length of the fruit, or is partial, the valves forming teeth at the
+  apex, as in the order Caryophyllaceae (fig. 6). Sometimes the valves
+  are detached only at certain points, and thus dehiscence takes place
+  by pores at the apex, as in poppy (fig. 7), or at the base, as in
+  _Campanula_. Indehiscent fruits are either dry, as the nut, or fleshy,
+  as the cherry and apple. They are formed of one or several carpels. In
+  the former case they usually contain only a single seed, which may
+  become so incorporated with the pericarp as to appear to be naked, as
+  in the grain of wheat and generally in grasses. In such cases the
+  presence of the remains of style or stigma determines their true
+  nature.
+
+  [Illustration:
+
+    FIG. 8.--Dry dehiscent fruit. The pod (legume) of the Pea; r, the
+    dorsal suture; b, the ventral; c, calyx; s, seeds.
+
+    From Vines' _Students' Text-Book of Botany_, by permission of Swan
+    Sonnenschein & Co.
+
+    FIG. 9.--(1) Fruit or capsule of Meadow Saffron (_Colchicum
+    autumnale_), dehiscing along the septa (septicidally); (2) same cut
+    across, showing the three chambers with the seeds attached along the
+    middle line (axile placentation).
+
+    FIG. 10.--Diagram to illustrate the septicidal dehiscence in a
+    pentalocular capsule. The loculaments l correspond to the number of
+    the carpels, which separate by splitting through the septa, s.
+
+    FIG. 11.--The seed vessel (capsule) of the Flower-de-Luce (_Iris_),
+    opening in a loculicidal manner. The three valves bear the septa in
+    the centre, and the opening takes place through the back of the
+    loculaments. Each valve is formed by the halves of contiguous
+    carpels.
+
+    FIG. 12.--Diagram to illustrate loculicidal dehiscence. The
+    loculaments l, split at the back, and the valves separate, bearing
+    the septa s on their centres.
+
+    FIG. 13.--Diagram to illustrate septifragal dehiscence, in which the
+    dehiscence takes place through the back of the loculaments l, and
+    the valves separate from the septa s, which are left attached to the
+    placentas in the centre.]
+
+  Dehiscent fruits, when composed of single carpels, may open by the
+  ventral suture only, as in the paeony, hellebore, _Aquilegia_ (fig.
+  28) and _Caltha_; by the dorsal suture only, as in magnolias and some
+  _Proteaceae_, or by both together, as in the pea (fig. 8) and bean; in
+  these cases the dehiscence is _sutural_. When composed of several
+  united carpels, two types of dehiscence occur--a longitudinal and a
+  transverse. In the longitudinal the separation may take place by the
+  dissepiments throughout their length, so that the fruit is resolved
+  into its original carpels, and each valve represents a carpel, as in
+  rhododendron, _Colchicum_, &c.; this dehiscence, in consequence of
+  taking place through the septum, is called _septicidal_ (figs. 9, 10).
+  The valves separate from their commissure, or central line of union,
+  carrying the placentas with them, or they leave the latter in the
+  centre, so as to form with the axis a column of a cylindrical, conical
+  or prismatic shape. Dehiscence is _loculicidal_ when the union between
+  the edges of the carpels is persistent, and they dehisce by the dorsal
+  suture, or through the back of the loculaments, as in the lily and
+  iris (figs. 11, 12). In these cases each valve consists of a half of
+  each of two contiguous carpels. The placentas either remain united to
+  the axis, or they separate from it, being attached to the septa on the
+  valves. When the outer walls of the carpels break off from the septa,
+  leaving them attached to the central column, the dehiscence is said to
+  be _septifragal_ (fig. 13), and where, as in _Linum catharticum_ and
+  _Calluna_, the splitting takes place first of all in a septicidal
+  manner, the fruit is described as _septicidally septifragal_; while in
+  other cases, as in thorn apple (_Datura Stramonium_), where the
+  splitting is at first loculicidal, the dehiscence is _loculicidally
+  septifragal_. In all those forms the separation of the valves takes
+  place either from above downwards or from below upwards. In
+  _Saxifraga_ a splitting for a short distance of the ventral sutures of
+  the carpels takes place, so that a large apical pore is formed. In the
+  fruit of Cruciferae, as wallflower (fig. 14), the valves separate from
+  the base of the fruit, leaving a central _replum_, or frame, which
+  supports the false septum formed by a prolongation from the parietal
+  placentas on opposite sides of the fruit, extending between the
+  ventral sutures of the carpels. In Orchidaceae (fig. 15) the pericarp,
+  when ripe, separates into three valves in a loculicidal manner, but
+  the midribs of the carpels, to which the placentas are attached, often
+  remain adherent to the axis both at the apex and base after the valves
+  bearing the seeds have fallen. The other type of dehiscence is
+  transverse, or _circumscissile_, when the upper part of the united
+  carpels falls off in the form of a lid or operculum, as in _Anagallis_
+  and in henbane (_Hyoscyamus_) (fig. 16).
+
+  [Illustration:
+
+    FIG. 14.--Siliqua or seed-vessel of Wallflower (_Cheiranthus
+    Cheiri_), opening by two valves, which separate from the base
+    upwards, leaving the seeds attached to the dissepiment which is
+    supported by the replum.
+
+    From Strasburger's _Lehrbuch der Botanik_, by permission of Gustav
+    Fischer.
+
+    FIG. 15.--Capsule of an Orchid (_Xylobium_). v, valve.
+
+    FIG. 16.--Seed-vessel of _Anagallisarvensis_, opening by
+    circumscissile dehiscence.
+
+    From Strasburger's _Lehrbuch der Botanik_, by permission of Gustav
+    Fischer.
+
+    FIG. 17.--Lomentum of _Hedysarum_ which, when ripe, separates
+    transversely into single-seeded portions or mericarps.
+
+    FIG. 18.--Fruit of _Geranium pratense_, after splitting.]
+
+  Sometimes the axis is prolonged beyond the base of the carpels, as in
+  the mallow and castor-oil plant, the carpels being united to it
+  throughout their length by their faces, and separating from it without
+  opening. In the Umbelliferae the two carpels separate from the lower
+  part of the axis, and remain attached by their apices to a
+  prolongation of it, called a _carpophore_ or _podocarp_, which splits
+  into two (fig. 25) and suspends them; hence the fruit is termed a
+  _cremocarp_, which divides into two _mericarps_. The general term
+  _schizocarp_ is applied to all dry fruits, which break up into two or
+  more one-seeded indehiscent mericarps, as in _Hedysarum_ (fig. 17). In
+  the order Geraniaceae the styles remain attached to a central column,
+  and the mericarps separate from below upwards, before dehiscing by
+  their ventral suture (fig. 18). Carpels which separate one from
+  another in this manner are called _cocci_. They are well seen in the
+  order Euphorbiaceae, where there are usually three such carpels, and
+  the fruit is termed tricoccus. In many of them, as _Hura crepitans_,
+  the cocci separate with great force and elasticity. In many leguminous
+  plants, such as _Ornithopus_, _Hedysarum_ (fig. 17), _Entada_,
+  _Coronilla_ and the gum-arabic plant (_Acacia arabica_), the fruit
+  becomes a schizocarp by the formation of transverse partitions from
+  the folding in of the sides of the pericarp, and distinct separations
+  taking place at these partitions.
+
+  Fruits are formed by one flower, or are the product of several flowers
+  combined. In the former case they are either _apocarpous_, of one
+  mature carpel or of several separate free carpels; or _syncarpous_, of
+  several carpels, more or less completely united. When the fruit is
+  composed of the ovaries of several flowers united, it is usual to find
+  the bracts and floral envelopes also joined with them, so as to form
+  one mass; hence such fruits are known as multiple, confluent or
+  _anthocarpous_. The term simple is applied to fruits which are formed
+  by the ovary of a single flower, whether they are composed of one or
+  several carpels, and whether these carpels are separate or combined.
+
+  [Illustration: From Vines' _Students' Text-Book of Botany_, by
+  permission of Swan Sonnenschein & Co.
+
+    FIG. 19.--Dry one-seeded fruit of dock (_Rumex_) cut vertically. ov,
+    Pericarp formed from ovary wall; s, seed; e, endosperm; pl, embryo
+    with radicle pointing upwards and cotyledons downwards--enlarged.
+
+    FIG. 20.--Achene of _Ranunculus arvensis_ in longitudinal section;
+    e, endosperm; pl, embryo. (After Baillon, enlarged.)
+
+    From Strasburger's _Lehrbuch der Botanik_, by permission of Gustav
+    Fischer.
+
+    FIG. 21.--Fruit of Common Sycamore (_Acer Pseudoplatanus_), dividing
+    into two mericarps m; s, pedicel; fl, wings (nat. size).]
+
+
+    Dispersal of fruit or seed.
+
+  The object of the fruit in the economy of the plant is the protection
+  and nursing of the developing seed and the dispersion of the ripe
+  seeds. Hence, generally, one-seeded fruits are indehiscent, while
+  fruits containing more than one seed open to allow of the dispersal of
+  the seeds over as wide an area as possible. The form, colour,
+  structure and method of dehiscence of fruits and the form of the
+  contained seeds are intimately associated with the means of dispersal,
+  which fall into several categories. (1) By a mechanism residing in the
+  fruit. Thus many fruits open suddenly when they are dry, and the seeds
+  are ejected by the twisting or curving of the valves, or in some other
+  way; e.g. in gorse, by the spiral curving of the valves; in
+  _Impatiens_, by the twisting of the cocci; in squirting cucumber, by
+  the pressure exerted on the pulpy contents by the walls of the
+  pericarp. (2) By aid of various external agencies such as water.
+  Fruits or seeds are sometimes sufficiently buoyant to float for a long
+  time on sea- or fresh-water; e.g. coco-nut, by means of its thick,
+  fibrous coat (mesocarp), is carried hundreds of miles in the sea, the
+  tough, leathery outer coat (epicarp) preventing it from becoming
+  water-soaked. Fruits and seeds of West Indian plants are thrown up on
+  the coasts of north-west Europe, having been carried by the Gulf
+  Stream, and will often germinate; many are rendered buoyant by
+  air-containing cavities, and the embryo is protected from the seawater
+  by the tough coat of fruit or seed. Water-lily seeds are surrounded
+  with a spongy tissue when set free from the fruit, and float for some
+  distance before dropping to the bottom. (3) The most general agent in
+  the dispersal of seeds is the wind or currents of air--the fruit or
+  seed being rendered buoyant by wing-developments as in fruits of ash
+  (fig. 1) or maple (fig. 21), seeds of pines and firs, or many members
+  of the order Bignoniaceae; or hair-developments as in fruits of
+  clematis, where the style forms a feathery appendage, fruits of many
+  Compositae (dandelion, thistle, &c.), which are crowned by a plumose
+  pappus, or seeds of willow and poplar, or _Asclepias_ (fig. 36), which
+  bear tufts of silky hairs; to this category belong bladder-like
+  fruits, such as bladder-senna, which are easily rolled by the wind, or
+  cases like the so-called rose of Jericho, a small cruciferous plant
+  (_Anastatica hierocuntica_), where the plant dries up after developing
+  its fruits and becomes detached from the ground; the branches curl
+  inwards, and the whole plant is rolled over the dry ground by the
+  wind. The wind also aids the dispersal of the seeds in the case of
+  fruits which open by small teeth (many Caryophyllaceae [fig. 6]) or
+  pores (poppy [fig. 7], _Campanula_, &c.); the seeds are in these cases
+  small and numerous, and are jerked through the pores when the
+  capsules, which are generally borne on long, dry stems or stalks, are
+  shaken by the wind. (4) In other cases members of the animal world aid
+  in seed-dispersal. Fruits often bear stiff hairs or small hooks, which
+  cling to the coat of an animal or the feathers of a bird; such are
+  fruits of cleavers (_Galium Aparine_), a common hedge-row plant,
+  _Ranunculus arvensis_ (fig. 20), carrot, _Geum_, &c.; or the fruit or
+  seed has an often bright-coloured, fleshy covering, which is sought by
+  birds as food, as in stone-fruits such as plum, cherry (fig. 5), &c.,
+  where the seed is protected from injury in the mouth or stomach of the
+  animal by the hard endocarp; or the hips of the rose (fig. 3), where
+  the succulent scarlet "fruit" (the swollen receptacle) envelops a
+  number of small dry true fruits (achenes), which cling by means of
+  stiff hairs to the beak of the bird.
+
+  [Illustration:
+
+    FIG. 22.--Vertical section of a grain of wheat, showing embryo below
+    at the base of the endosperm e; s, scutellum separating embryo from
+    endosperm; f.l, foliage leaf; p.s, sheath of plumule; p.r, primary
+    root; s.p.r, sheath of primary root.
+
+    FIG. 23.--Fruit of Comfrey (_Symphytum_) surrounded by persistent
+    calyx, c. The style s appears to arise from the base of the carpels,
+    enlarged.
+
+    FIG. 24.--Ovary of _Foeniculum officinale_ with pendulous ovules, in
+    longitudinal section. (After Berg and Schmidt, magnified.)
+
+    From Strasburger's _Lehrbuch der Botanik_, by permission of Gustav
+    Fischer.
+
+    FIG. 25.--Fruit of _Carum Carui_. A, Ovary of the flower; B, ripe
+    fruit. The two carpels have separated so as to form two mericarps
+    (m). Part of the septum constitutes the carpophore (a). p, Top of
+    flower-stalk; d, disk on top of ovary; n, stigma.
+
+    From Vines' _Students' Text-Book of Botany_, by permission of Swan
+    Sonnenschein & Co.]
+
+
+    Forms of fruit.
+
+  Simple fruits have either a _dry_ or _succulent_ pericarp. The
+  _achene_ is a dry, one-seeded, indehiscent fruit, the pericarp of
+  which is closely applied to the seed, but separable from it. It is
+  solitary, forming a single fruit, as in the dock (fig. 19) and in the
+  cashew, where it is supported on a fleshy peduncle; or _aggregate_, as
+  in _Ranunculus_ (fig. 20), where several achenes are placed on a
+  common elevated receptacle. In the strawberry the achenes (fig. 2) are
+  aggregated on a convex succulent receptacle. In the rose they are
+  supported on a concave receptacle (fig. 3), and in the fig the
+  succulent receptacle completely encloses the achenes (fig. 4). In
+  _Dorstenia_ the achenes are situated on a flat or slightly concave
+  receptacle. Hence what in common language are called the seeds of the
+  strawberry, rose and fig, are in reality ripe carpels. The styles
+  occasionally remain attached to the achenes in the form of feathery
+  appendages, as in _Clematis_. In Compositae, the fruit is an inferior
+  achene (_cypsela_), to which the pappus (modified calyx) remains
+  adherent. Such is also the nature of the fruit in Dipsacaceae (e.g.
+  scabious). When the pericarp is thin, and appears like a bladder
+  surrounding the seed, the achene is termed a _utricle_, as in
+  Amarantaceae. When the pericarp is extended in the form of a winged
+  appendage, a _samara_ or _samaroid achene_ is produced, as in the ash
+  (fig. 1) and common sycamore (fig. 21). In these cases there are
+  usually two achenes united, one of which, however, as in _Fraxinus_
+  (fig. 1), may be abortive. The wing surrounds the fruit longitudinally
+  in the elm. When the pericarp becomes so incorporated with the seed as
+  to be inseparable from it, as in grains of wheat (fig. 22), maize,
+  oats and other grasses, then the name _caryopsis_ is given. The
+  one-seeded portions (mericarps) of schizocarps often take the form of
+  achenes, e.g. the mericarps of the mallows or of umbellifers (figs.
+  24, 25). In Labiatae and Boraginaceae (e.g. comfrey, fig. 23), where
+  the bicarpellary ovary becomes our one-seeded portions in the fruit,
+  the partial fruits are of the nature of achenes or nutlets according
+  to the texture (leathery or hard) of the pericarp.
+
+  [Illustration: From Strasburger's _Lehrbuch der Botanik_, by
+  permission of Gustav Fischer.
+
+    FIG. 26.--Cupule of _Quercus Aegilops_. cp, cupule; gl, fruit.
+    (After Duchartre.)]
+
+  The _nut_ or _glans_ is a dry one-celled indehiscent fruit with a
+  hardened pericarp, often surrounded by bracts at the base, and, when
+  mature, containing only one seed. In the young state the ovary often
+  contains two or more ovules, but only one comes to maturity. It is
+  illustrated by the fruits of the hazel and chestnut, which are covered
+  by leafy bracts, in the form of a _husk_, and by the acorn, in which
+  the bracts and receptacle form a _cupula_ or _cup_ (fig. 26). The
+  parts of the pericarp of the nut are united so as to appear one. In
+  common language the term nut is very vaguely applied both to fruit and
+  seeds.
+
+  The _drupe_ is a succulent usually one-seeded indehiscent fruit, with
+  a pericarp easily distinguishable into epicarp, mesocarp and endocarp.
+  This term is applied to such fruits as the cherry (fig. 5), peach,
+  plum, apricot or mango. The endocarp is usually hard, forming the
+  stone (putamen) of the fruit, which encloses the kernel or seed. The
+  mesocarp is generally pulpy and succulent, so as to be truly a
+  sarcocarp, as in the peach, but it is sometimes of a tough texture, as
+  in the almond, and at other times is more or less fibrous, as in the
+  coco-nut. In the almond there are often two ovules formed, only one of
+  which comes to perfection. In the raspberry and bramble several small
+  drupes or _drupels_ are aggregated so as to constitute an _etaerio_.
+
+  The _follicle_ is a dry unilocular many-seeded fruit, formed from one
+  carpel and dehiscing by the ventral suture. It is rare to meet with a
+  solitary follicle forming the fruit. There are usually several
+  aggregated together, either in a whorl on a shortened receptacle, as
+  in hellebore, aconite, larkspur, columbine (figs. 27, 28) or the order
+  Crassulaceae, or in a spiral manner on an elongated receptacle, as in
+  _Magnolia_ and _Banksia_. Occasionally, follicles dehisce by the
+  dorsal suture, as in _Magnolia grandiflora_ and _Banksia_.
+
+  [Illustration:
+
+    FIG. 27.--Fruit of Columbine (_Aquilegia_), formed of five
+    follicles.
+
+    FIG. 28.--Single follicle, showing dehiscence by the ventral suture.
+
+    FIG. 29.--Transverse section of berry of Gooseberry, showing the
+    seeds attached to the parietal placentas and immersed in pulp, which
+    is formed partly from the endocarp, partly from the seed-coat.
+
+    FIG. 30.--Section of the fruit of the Apple (_Pyrus Malus_), or
+    pome, consisting of a fleshy covering formed by the floral
+    receptacle and the true fruit or core with five cavities with
+    seeds.]
+
+  The _legume_ or _pod_ is a dry monocarpellary unilocular many-seeded
+  fruit, formed from one carpel, dehiscing both by the ventral and the
+  dorsal suture. It characterizes leguminous plants, as the bean and pea
+  (fig. 8). In the bladder-senna it forms an inflated legume. In some
+  Leguminosae, as _Arachis_, _Cathartocarpus Fistula_ and the tamarind,
+  the fruit must be considered a legume, although it does not dehisce.
+  The first of these plants produces its fruit underground, and is
+  called earth-nut; the second has a partitioned legume and is
+  schizocarpic; and both the second and third have pulpy matter
+  surrounding the seeds. Some legumes are schizocarpic by the formation
+  of constrictions externally. Such a form is the _lomentum_ or
+  _lomentaceous legume_ of _Hedysarum_ (fig. 17), _Coronilla_,
+  _Ornithopus_, _Entada_ and of some Acacias. In _Medicago_ the legume
+  ~~ is twisted like a snail, and in _Caesalpinia coriaria_, or
+  Divi-divi, it is vermiform or curved like a worm. Sometimes the number
+  of seeds is reduced, as in _Erythrina monosperma_ and _Geoffroya
+  superba_, which are one-seeded, and in _Pterocarpus_ and _Dalbergia_,
+  which are two-seeded.
+
+  [Illustration: FIG. 31.--Transverse section of the fruit of the Melon
+  (_Cucumis Melo_), showing the placentas with the seeds attached to
+  them. The three carpels forming the pepo are separated by partitions.
+  From the centre processes pass outwards, ending in the curved
+  placenta.
+
+  The _berry_ (_bacca_) is a term applied generally to all fruits with
+  seeds immersed in pulp, and includes fruits of very various origin. In
+  _Actaea_ (baneberry) or _Berberis_ (barberry) it is derived from a
+  single free carpel; generally, however, it is the product of a
+  syncarpous ovary, which is superior, as in grape or potato, or
+  inferior, as in gooseberry (fig. 29) or currant. In the pomegranate
+  there is a peculiar baccate many-celled inferior fruit, having a tough
+  rind, enclosing two rows of carpels placed one above the other. The
+  seeds are immersed in pulp, and are attached irregularly to the wall,
+  base and centre of the loculi. In the baobab there is a multilocular
+  syncarpous fruit, in which the seeds are immersed in pulp.
+
+  The _pepo_, another indehiscent syncarpous fruit, is illustrated by
+  the fruit of the gourd, melon (fig. 31) and other Cucurbitaceae. It is
+  formed of three carpels, surmounted by the calyx; the rind is thick
+  and fleshy, and there are three or more seed-bearing parietal
+  placentas, either surrounding a central cavity or prolonged inwards
+  into it. The fruit of the papaw resembles the pepo, but the calyx is
+  not superior.
+
+  The _hesperidium_ is the name given to such indehiscent fleshy
+  syncarpous fruits as the orange, lemon and shaddock, in which the
+  epicarp and mesocarp form a separable rind, and the endocarp sends
+  prolongations inwards, forming triangular divisions, to the inner
+  angle of which the seeds are attached, pulpy cells being developed
+  around them from the wall. Both pepo and hesperidium may be considered
+  as modifications of the berry.
+
+  The _pome_ (fig. 30), seen in the apple, pear, quince, medlar and
+  hawthorn, is a fleshy indehiscent syncarpous fruit, in the formation
+  of which the receptacle takes part. The outer succulent part is the
+  swollen receptacle, the horny core being the true fruit developed from
+  the usually five carpels and enclosing the seeds. In the medlar the
+  core (or true pericarp) is of a stony hardness, while the outer
+  succulent covering is open at the summit. The pome somewhat resembles
+  the fruit of the rose (fig. 3), where the succulent receptacle
+  surrounds a number of separate achenes.
+
+  The name _capsule_ is applied generally to all dry syncarpous fruits,
+  which dehisce by valves. It may thus be unilocular or multilocular,
+  one- or many-seeded. The true valvular capsule is observed in
+  _Colchicum_ (fig. 9), lily and iris (fig. 11). The _porose capsule_ is
+  seen in the poppy (fig. 7), _Antirrhinum_ and _Campanula_. In
+  _Campanula_ the pores occur at the base of the capsule, which becomes
+  inverted when ripe. When the capsule opens by a lid, or by
+  circumscissile dehiscence, it is called a _pyxidium_, as in pimpernel
+  (_Anagallis arvensis_) (fig. 16), henbane and monkey-pot (_Lecythis_).
+  The capsule assumes a screw-like form in _Helicteres_, and a star-like
+  form in star-anise (_Illicium anisatum_). In certain instances the
+  cells of the capsule separate from each other, and open with
+  elasticity to scatter the seeds. This kind of capsule is met with in
+  the sandbox tree (_Hura crepitans_) and other Euphorbiaceae, where the
+  cocci, containing each a single seed, burst asunder with force; and in
+  Geraniaceae, where the cocci, each containing, when mature, usually
+  one seed, separate from the carpophore, become curved upwards by their
+  adherent styles, and open by the ventral suture (fig. 18).
+
+  The _siliqua_ is a dry syncarpous bilocular many-seeded fruit, formed
+  from two carpels, with a false septum, dehiscing by two valves from
+  below upwards, the valves separating from the placentas and leaving
+  them united by the septum (fig. 32). The seeds are attached on both
+  sides of the septum, either in one row or in two. When the fruit is
+  long and narrow it is a _siliqua_ (fig. 14); when broad and short,
+  _silicula_ (fig. 33). It occurs in cruciferous plants, as wallflower,
+  cabbage and cress. In _Glaucium_ and _Eschscholtzia_ (Papaveraceae)
+  the dissepiment is of a spongy nature. It may become transversely
+  constricted (_lomentaceous_), as in radish (_Raphanus_) and sea-kale,
+  and it may be reduced, as in woad (_Isatis_), to a one-seeded
+  condition.
+
+  It sometimes happens that the ovaries of two flowers unite so as to
+  form a double fruit (_syncarp_). This may be seen in many species of
+  honeysuckle. But the fruits which are now to be considered consist
+  usually of the floral envelopes, as well as the ovaries of several
+  flowers united into one, and are called _multiple_ or _confluent_. The
+  term _anthocarpous_ has also been applied as indicating that the
+  floral envelopes as well as the carpels are concerned in the formation
+  of the fruit.
+
+  The _sorosis_ is a succulent multiple fruit formed by the confluence
+  of a spike of flowers, as in the fruit of the pine-apple (fig. 34),
+  the bread-fruit and jack-fruit. Similarly the fruit of the mulberry
+  represents a catkin-like inflorescence.
+
+  The _syconus_ is an anthocarpous fruit, in which the receptacle
+  completely encloses numerous flowers and becomes succulent. The fig
+  (fig. 4) is of this nature, and what are called its seeds are the
+  achenes of the numerous flowers scattered over the succulent hollowed
+  receptacle. In _Dorstenia_ the axis is less deeply hollowed, and of a
+  harder texture, the fruit exhibiting often very anomalous forms.
+
+  The _strobilus_, or _cone_, is a seed-bearing spike, more or less
+  elongated, covered with scales, each of which may be regarded as
+  representing a separate flower, and has often two seeds at its base;
+  the seeds are naked, no ovary being present. This fruit is seen in the
+  cones of firs, spruces, larches and cedars, which have received the
+  name of Coniferae, or cone-bearers, on this account. Cone-like fruit
+  is also seen in most Cycadaceae. The scales of the strobilus are
+  sometimes thick and closely united, so as to form a more or less
+  angular and rounded mass, as in the cypress; while in the juniper they
+  become fleshy, and are so incorporated as to form a globular fruit
+  like a berry. The dry fruit of the cypress and the succulent fruit of
+  the juniper have received the name of _galbulus_. In the hop the fruit
+  is called also a strobilus, but in it the scales are thin and
+  membranous, and the seeds are not naked but are contained in
+  pericarps.
+
+  [Illustration:
+
+    FIG. 32.--Honesty (_Lunaria biennis_), showing the septum after the
+    carpels have fallen away.
+
+    From Strasburger's _Lehrbuch der Botanik_, by permission of Gustav
+    Fischer.
+
+    FIG. 33.--Silicula or pouch of shepherd's purse (_Capsella_),
+    opening by two folded valves, which separate from above downwards.
+    The partition is narrow, hence the silicula is angustiseptal.
+
+    From Strasburger's _Lehrbuch der Botanik_, by permission of Gustav
+    Fischer.
+
+    FIG. 34.--Fruit of the pine-apple (_Ananassa sativa_), developed
+    from a spike of numerous flowers with bracts, united so as to form a
+    collective or anthocarpous fruit. The crown of the pine-apple, c,
+    consists of a series of empty bracts prolonged beyond the fruit.]
+
+  The same causes which produce alterations in the other parts of the
+  flower give rise to anomalous appearances in the fruit. The carpels,
+  in place of bearing seeds, are sometimes changed into leaves, with
+  lobes at their margins. Leaves are sometimes produced from the upper
+  part of the fruit. In the genus _Citrus_, to which the orange and
+  lemon belong, it is very common to meet with a separation of the
+  carpels, so as to produce what are called horned oranges and fingered
+  citrons. In this case a syncarpous fruit has a tendency to become
+  apocarpous. In the orange we occasionally find a supernumerary row of
+  carpels produced, giving rise to the appearance of small and imperfect
+  oranges enclosed within the original one; the navel orange is of this
+  nature. It sometimes happens that, by the union of flowers, double
+  fruits are produced. Occasionally a double fruit is produced, not by
+  the incorporation of two flowers, but by the abnormal development of a
+  second carpel in the flower.
+
+    _Arrangement of Fruits._
+
+    A. True fruits--developed from the ovary alone.
+        1. Pericarp not fleshy or fibrous.
+            i. Indehiscent--not opening to allow the escape of the
+                seeds--generally one-seeded. Achene; caryopsis; cypsela;
+                nut; schizocarp.
+            ii. Dehiscent--the pericarp splits to allow the escape of the
+                seeds--generally many-seeded. Follicle; legume; siliqua;
+                capsule.
+        2. Pericarp generally differentiated into distinct layers, one
+            of which is succulent or fibrous. Drupe; berry.
+    B. Pseudocarps--the development extends beyond the ovary. Pome;
+    syconus; sorosis.
+
+  _The Seed._--The _seed_ is formed from the ovule as the result of
+  fertilization. It is contained in a seed-vessel formed from the ovary
+  in the plants called _angiospermous_; while in _gymnospermous_
+  plants, such as Coniferae and Cycadaceae, it is naked, or, in other
+  words, has no true pericarp. It sometimes happens in Angiosperms, that
+  the seed-vessel is ruptured at an early period of growth, so that the
+  seeds become more or less exposed during their development; this
+  occurs in mignonette, where the capsule opens at the apex, and in
+  _Cuphea_, where the placenta bursts through the ovary and floral
+  envelopes, and appears as an erect process bearing the young seeds.
+  After fertilization the ovule is greatly changed, in connexion with
+  the formation of the embryo. In the embryo-sac of most Angiosperms
+  (q.v.) there is a development of cellular tissue, the endosperm, more
+  or less filling the embryo-sac. In Gymnosperms (q.v.) the endosperm is
+  formed preparatory to fertilization. The fertilized egg enlarges and
+  becomes multicellular, forming the embryo. The embryo-sac enlarges
+  greatly, displacing gradually the surrounding nucellus, which
+  eventually forms merely a thin layer around the sac, or completely
+  disappears. The remainder of the nucellus and the integuments of the
+  ovules form the seed-coats. In some cases (fig. 35) a delicate inner
+  coat or _tegmen_ can be distinguished from a tougher outer coat or
+  _testa_; often, however, the layers are not thus separable. The
+  consistency of the seed-coat, its thickness, the character of its
+  surface, &c., vary widely, the variations being often closely
+  associated with the environment or with the means of seed-dispersal.
+  An account of the development of the seed from the ovule will be found
+  in the article ANGIOSPERMS. When the pericarp is dehiscent the
+  seed-covering is of a strong and often rough character; but when the
+  pericarp is indehiscent and encloses the seed for a long period, the
+  outer seed-coat is thin and soft. The cells of the testa are often
+  coloured, and have projections and appendages of various kinds. Thus
+  in _Abrus precatorius_ and _Adenanthera pavonina_ it is of a bright
+  red colour; in French beans it is beautifully mottled; in the almond
+  it is veined; in the tulip and primrose it is rough; in the snapdragon
+  it is marked with depressions; in cotton and _Asclepias_ (fig. 36) it
+  has hairs attached to it; and in mahogany, _Bignonia_, and the pines
+  and firs it is expanded in the form of wing-like appendages (fig. 37).
+  In _Collomia_, _Acanthodium_, _Cobaea scandens_ and other seeds, it
+  contains spiral cells, from which, when moistened with water, the
+  fibres uncoil in a beautiful manner; and in flax (_Linum_) and others
+  the cells are converted into mucilage. These structural peculiarities
+  of the testa in different plants have relation to the scattering of
+  the seed and its germination upon a suitable nidus. But in some plants
+  the pericarps assume structures which subserve the same purpose; this
+  especially occurs in small pericarps enclosing single seeds, as
+  achenes, caryopsides, &c. Thus in Compositae and valerian, the pappose
+  limb of the calyx forms a parachute to the pericarp; in Labiatae and
+  some Compositae spiral cells are formed in the epicarp; and the
+  epicarp is prolonged as a wing in _Fraxinus_ (fig. 1) and _Acer_ (fig.
+  21).
+
+  [Illustration:
+
+    FIG. 35.--Seed of Pea (_Pisum_) with one cotyledon removed. c,
+    Remaining cotyledon; ch, chalaza-point at which the nourishing
+    vessels enter; e, tegmen or inner coat; f, funicle or stalk; g,
+    plumule of embryo; m, micropyle; pl, placenta; r, radicle of embryo;
+    t, tigellum or stalk between root and plumule; te, testa.
+
+    FIG. 36.--Seed of _Asclepias_, with a cluster of hairs arising from
+    the edges of the micropyle.]
+
+  Sometimes there is an additional covering to the seed, formed after
+  fertilization, to which the name _arillus_ has been given (fig. 38).
+  This is seen in the passion-flower, where the covering arises from the
+  placenta or extremity of the funicle at the base of the ovule and
+  passes upwards towards the apex, leaving the micropyle uncovered. In
+  the nutmeg and spindle tree this additional coat is formed from above
+  downwards, constituting in the former case a laciniated scarlet
+  covering called _mace_. In such instances it has been called an
+  _arillode_ (fig. 39). This arillode, after growing downwards, may be
+  reflected upwards so as to cover the micropyle. The fleshy scarlet
+  covering formed around the naked seed in the yew is by some considered
+  of the nature of an aril. On the testa, at various points, there are
+  produced at times other cellular bodies, to which the name of
+  _strophioles_, or _caruncles_, has been given, the seeds being
+  strophiolate or carunculate. These tumours may occur near the base of
+  the seed, as in _Polygala_, or at the apex, as in Castor-oil plant
+  (_Ricinus_); or they may occur in the course of the raphe, as in
+  blood-root (_Sanguinaria_) and _Asarabacca_. The funicles of the
+  ovules frequently attain a great length in the seed, and in some
+  magnolias, when the fruit dehisces, they appear as long scarlet cords
+  suspending the seeds outside. The hilum or umbilicus of the seed is
+  usually well marked, as a scar of varying size; in the calabar bean
+  and in some species of Mucuna and Dolichos it extends along a large
+  portion of the edge of the seed; it frequently exhibits marked
+  colours, being black in the bean, white in many species of Phaseolus,
+  &c. The micropyle (fig. 35, m) of the seed may be recognizable by the
+  naked eye, as in the pea and bean tribe, _Iris_, &c., or it may be
+  very minute or microscopic. It indicates the true apex of the seed,
+  and is important as marking the point to which the root of the embryo
+  is directed. At the micropyle in the bean is observed a small process
+  of integument, which, when the young plant sprouts, is pushed up like
+  a lid; it is called the _embryotega_. The chalaza (fig. 38, ch) is
+  often of a different colour from the rest of the seed. In the orange
+  (fig. 40) it is of a reddish-brown colour, and is easily recognized at
+  one end of the seed when the integuments are carefully removed. In
+  anatropal seeds the raphe forms a distinct ridge along one side of the
+  seed (fig. 41).
+
+  The position of the seed as regards the pericarp resembles that of the
+  ovule in the ovary, and the same terms are applied--erect, ascending,
+  pendulous, suspended, curved, &c. These terms have no reference to the
+  mode in which the fruit is attached to the axis. Thus the seed may be
+  erect while the fruit itself is pendent, in the ordinary meaning of
+  that term. The part of the seed next the axis or the ventral suture is
+  its face, the opposite side being the back. Seeds exhibit great
+  varieties of form. They may be flattened laterally (_compressed_), or
+  from above downwards (_depressed_). They may be round, oval,
+  triangular, polygonal, rolled up like a snail, as in _Physostemon_, or
+  coiled up like a snake, as in _Ophiocaryon paradoxum_.
+
+  [Illustration:
+
+    FIG. 37.--Seed of Pine (_Pinus_), with a membranous appendage w to
+    the testa, called a wing.
+
+    FIG. 38.--Young anatropal seed of the white Water-lily (_Nymphaea
+    alba_), cut vertically. It is attached to the placenta by the
+    funicle f, cellular prolongations from which form an aril a a. The
+    vessels of the cord are prolonged to the base of the nucellus n by
+    means of the raphe r. The base of the nucellus is indicated by the
+    chalaza ch, while the apex is at the micropyle m. The covering of
+    the seed is marked i. n is the nucellus or perisperm, enclosing the
+    embryo-sac es, in which the endosperm is formed. The embryo e, with
+    its suspensor, is contained in the sac, the radicle pointing to the
+    micropyle m.
+
+    FIG. 39.--Arillode a, or false aril, of the Spindle-tree
+    (_Euonymus_), arising from the micropyle f.
+
+    FIG. 40.--Anatropal seed of the Orange (_Citrus Aurantium_) opened
+    to show the chalaza c, which forms a brown spot at one end.
+
+    FIG. 41.--Entire anatropal seed of the Orange (_Citrus Aurantium_),
+    with its rugose or wrinkled testa, and the raphe r ramifying in the
+    thickness of the testa on one side.]
+
+  The endosperm formed in the embryo-sac of angiosperms after
+  fertilization, and found previous to it in gymnosperms, consists of
+  cells containing nitrogenous and starchy or fatty matter, destined for
+  the nutriment of the embryo. It occupies the whole cavity of the
+  embryo-sac, or is formed only at certain portions of it, at the apex,
+  as in _Rhinanthus_, at the base, as in _Vaccinium_, or in the middle,
+  as in _Veronica_. As the endosperm increases in size along with the
+  embryo-sac and the embryo, the substance of the original nucellus of
+  the ovule is gradually absorbed. Sometimes, however, as in Musaceae,
+  Cannaceae, Zingiberaceae, no endosperm is formed; the cells of the
+  original nucellus, becoming filled with food-materials for the embryo,
+  are not absorbed, but remain surrounding the embryo-sac with the
+  embryo, and constitute the _perisperm_. Again, in other plants, as
+  Nymphaeaceae (fig. 38) and Piperaceae, both endosperm and perisperm
+  are present. It was from observations on cases such as these that old
+  authors, imagining a resemblance betwixt the plant-ovule and the
+  animal ovum, applied the name _albumen_ to the outer nutrient mass or
+  perisperm, and designated the endosperm as _vitellus_. The term
+  albumen is very generally used as including all the nutrient matter
+  stored up in the seed, but it would be advisable to discard the name
+  as implying a definite chemical substance. There is a large class of
+  plants in which although at first after fertilization a mass of
+  endosperm is formed, yet, as the embryo increases in size, the
+  nutrient matter from the endospermic cells passes out from them, and
+  is absorbed by the cells of the embryo plant. In the mature seed, in
+  such cases, there is no separate mass of tissue containing nutrient
+  food-material apart from the embryo itself. Such a seed is said to be
+  _exalbuminous_, as in Compositae, Cruciferae and most Leguminosae
+  (e.g. pea, fig. 35). When either endosperm or perisperm or both are
+  present the seed is said to be _albuminous_.
+
+  [Illustration: FIG. 42.--The dicotyledonous embryo of the Pea laid
+  open. c, c, The two fleshy cotyledons, or seed-lobes, which remain
+  under ground when the plant sprouts; r, the radicular extremity of the
+  axis whence the root arises; t, the axis (hypocotyl) bearing the young
+  stalk and leaves g (plumule), which lie in a depression of the
+  cotyledons f.]
+
+  The albumen varies much in its nature and consistence, and furnishes
+  important characters. It may be farinaceous or mealy, consisting
+  chiefly of cells filled with starch, as in cereal grains, where it is
+  abundant; fleshy or cartilaginous, consisting of thicker cells which
+  are still soft, as in the coco-nut, and which sometimes contain oil,
+  as in the oily albumen of _Croton_, _Ricinus_ and poppy; horny, when
+  the cell-walls are slightly thickened and capable of distension, as in
+  date and coffee; the cell-walls sometimes become greatly thickened,
+  filling up the testa as a hard mass, as in vegetable ivory
+  (_Phytelephas_). The albumen may be uniform throughout, or it may
+  present a mottled appearance, as in the nutmeg, the seeds of Anonaceae
+  and some Palms, where it is called _ruminated_. This mottled
+  appearance is due to a protrusion of a dark lamella of the integument
+  between folded protuberances of albumen. A cavity is sometimes left in
+  the centre which is usually filled with fluid, as in the coco-nut. The
+  relative size of the embryo and of the endosperm varies much. In
+  Monocotyledons the embryo is usually small, and the endosperm large,
+  and the same is true in the case of coffee and many other plants
+  amongst Dicotyledons. The opposite is the case in other plants, as in
+  the Labiatae, Plumbaginaceae, &c.
+
+  The embryo consists of an axis bearing the _cotyledons_ (fig. 42, c),
+  or the first leaves of the plant. To that part of this axis
+  immediately beneath the cotyledons the terms _hypocotyl_, _caulicle_
+  or _tigellum_ (t) have been applied, and continuous backwards with it
+  is the young root or _radicle_ (r), the descending axis, their point
+  of union being the collar or neck. The terminal growing bud of the
+  axis is called the _plumule_ or _gemmule_ (g), and represents the
+  ascending axis. The radicular extremity points towards the micropyle,
+  while the cotyledonary extremity is pointed towards the base of the
+  ovule or the chalaza. Hence, by ascertaining the position of the
+  micropyle and chalaza, the two extremities of the embryo can in
+  general be discovered. It is in many cases difficult to recognize the
+  parts in an embryo; thus in _Cuscuta_, the embryo appears as an
+  elongated axis without divisions; and in _Caryocar_ the mass of the
+  embryo is made up by the radicular extremity and hypocotyl, in a
+  groove of which the cotyledonary extremity lies embedded (fig. 52). In
+  some monocotyledonous embryos, as in Orchidaceae, the embryo is a
+  cellular mass showing no parts. In parasitic plants also which form no
+  chlorophyll, as _Orobanche_, _Monotropa_, &c., the embryo remains
+  without differentiation, consisting merely of a mass of cells until
+  the ripening of the seed. When the embryo is surrounded by the
+  endosperm on all sides except its radicular extremity it is internal
+  (see figs. 19, 20); when lying outside the endosperm, and only coming
+  into contact with it at certain points, it is external, as in grasses
+  (e.g. wheat, fig. 22). When the embryo follows the direction of the
+  axis of the seed, it is axile or axial (fig. 43); when it is not in
+  the direction of the axis, it becomes abaxile or abaxial. In
+  campylotropal seeds the embryo is curved, and in place of being
+  embedded in endosperm, is frequently external to it, following the
+  concavity of the seed (fig. 44), and becoming peripherical, with the
+  chalaza situated in the curvature of the embryo, as in
+  Caryophyllaceae.
+
+  It has been already stated that the radicle of the embryo is directed
+  to the micropyle, and the cotyledons to the chalaza. In some cases, by
+  the growth of the integuments, the former is turned round so as not to
+  correspond with the apex of the nucellus, and then the embryo has the
+  radicle directed to one side, and is called excentric, as is seen in
+  Primulaceae, Plantaginaceae and many palms, especially the date. The
+  position of the embryo in different kinds of seeds varies. In an
+  orthotropal seed the embryo is inverted or _antitropal_, the radicle
+  pointing to the apex of the seed, or to the part opposite the hilum.
+  Again, in an anatropal seed the embryo is erect or _homotropal_ (fig.
+  43), the radicle being directed to the base of the seed. In curved or
+  campylotropal seeds the embryo is folded so that its radicular and
+  cotyledonary extremities are approximated, and it becomes
+  _amphitropal_ (fig. 44). In this instance the seed may be
+  exalbuminous, and the embryo may be folded on itself; or albuminous,
+  the embryo surrounding more or less completely the endosperm and being
+  peripherical. According to the mode in which the seed is attached to
+  the pericarp, the radicle may be directed upwards or downwards, or
+  laterally, as regards the ovary. In an orthotropal seed attached to
+  the base of the pericarp it is superior, as also in a suspended
+  anatropal seed. In other anatropal seeds the radicle is inferior. When
+  the seed is horizontal as regards the pericarp, the radicle is either
+  centrifugal, when it points to the outer wall of the ovary; or
+  centripetal, when it points to the axis or inner wall of the ovary.
+  These characters are of value for purposes of classification, as they
+  are often constant in large groups of genera.
+
+  Plants in which there are two cotyledons produced in the embryo are
+  _dicotyledonous_. The two cotyledons thus formed are opposite to each
+  other (figs. 42 and 45), but are not always of the same size. Thus, in
+  Abronia and other members of the order Nyctaginaceae, one of them is
+  smaller than the other (often very small), and in _Carapa guianensis_
+  there appears to be only one, in consequence of the intimate union
+  which takes place between the two. The union between the cotyledonary
+  leaves may continue after the young plant begins to germinate. Such
+  embryos have been called _pseudomonocotyledonous_. The texture of the
+  cotyledons varies. They may be thick, as in the pea (fig. 42),
+  exhibiting no traces of venation, with their flat internal surfaces in
+  contact, and their backs more or less convex; or they may be in the
+  form of thin and delicate laminae, flattened on both sides, and having
+  distinct venation, as in _Ricinus_, _Jatropha_, _Euonymus_, &c. The
+  cotyledons usually form the greater part of the mature embryo, and
+  this is remarkably well seen in such exalbuminous seeds as the bean
+  and pea.
+
+  [Illustration:
+
+    FIG. 43.--Seed of Pansy (_Viola tricolor_) cut vertically. The
+    embryo pl is axial, in the midst of fleshy endosperm al. The seed is
+    anatropal, and the embryo is homotropal; the cotyledons co point to
+    the base of the nucellus or chalaza ch, while the radicle, or the
+    other extremity of the embryo, points to the micropyle, close to the
+    hilum h. The hilum or base of the seed, and the chalaza or base of
+    the nucellus are united by means of the raphe r.
+
+    FIG. 44.--Seed of the Red Campion (_Lychnis_), cut vertically,
+    showing the peripheral embryo, with its two cotyledons and its
+    radicle. The embryo is curved round the albumen, so that its
+    cotyledons and radicle both come near the hilum (_amphitropal_).
+
+    FIG. 45.--Mature dicotyledonous embryo of the Almond, with one of
+    the cotyledons removed. r, Radicle; t, young stem or caulicle; c,
+    one of the cotyledons left; i, line of insertion of the cotyledon
+    which has been removed; g, plumule.
+
+    FIG. 46.--Exalbuminous seed of Wallflower (Cheiranthus) cut
+    vertically. The radicle r is folded on the edges of the cotyledons c
+    which are accumbent.
+
+    FIG. 47.--Transverse section of the seed of the Wallflower
+    (_Cheiranthus_), showing the radicle r folded on the edges of the
+    accumbent cotyledons c.
+
+    FIG. 48.--Transverse section of the seed of the Dame's Violet
+    (_Hesperis_). The radicle r is folded on the back of the cotyledons
+    c, which are said to be incumbent.]
+
+  Cotyledons are usually entire and sessile. But they occasionally
+  become lobed, as in the walnut and the lime; or petiolate, as in
+  _Geranium molle_; or auriculate, as in the ash. Like leaves in the
+  bud, cotyledons may be either applied directly to each other, or may
+  be folded in various ways. In geranium the cotyledons are twisted and
+  doubled; in convolvulus they are corrugated; and in the potato and in
+  _Bunias_, they are spiral,--the same terms being applied as to the
+  foliage leaves. The radicle and cotyledons are either straight or
+  variously curved. Thus, in some cruciferous plants, as the wallflower,
+  the cotyledons are applied by their faces, and the radicle (figs. 46,
+  47) is folded on their edges, so as to be lateral; the cotyledons are
+  here _accumbent_. In others, as _Hesperis_, the cotyledons (fig. 48)
+  are applied to each other by their faces, and the radicle, r, is
+  folded on their back, so as to be dorsal, and the cotyledons are
+  _incumbent_. Again, the cotyledons are _conduplicate_ when the radicle
+  is dorsal, and enclosed between their folds. In other divisions the
+  radicle is folded in a spiral manner, and the cotyledons follow the
+  same course.
+
+  In many gymnosperms more than two cotyledons are present, and they are
+  arranged in a whorl. This occurs in Coniferae, especially in the pine,
+  fir (fig. 49), spruce and larch, in which six, nine, twelve and even
+  fifteen have been observed. They are linear, and resemble in their
+  form and mode of development the clustered or fasciculated leaves of
+  the larch. Plants having numerous cotyledons are termed
+  _polycotyledonous_. In species of _Streptocarpus_ the cotyledons are
+  permanent, and act the part of leaves. One of them is frequently
+  largely developed, while the other is small or abortive.
+
+  [Illustration:
+
+    FIG. 49.--Polycotylodonous embryo of the Pine (_Pinus_) beginning to
+    sprout. t, Hypocotyl; r, radicle. The cotyledons c are numerous.
+    Within the cotyledons the primordial leaves are seen, constituting
+    the plumule or first bud of the plant.
+
+    FIG. 50.--Embryo of a species of Arrow-grass (_Triglochin_), showing
+    a uniform conical mass, with a slit s near the lower part. The
+    cotyledon c envelops the young bud, which protrudes at the slit
+    during germination. The radicle is developed from the lower part of
+    the axis r.
+
+    FIG. 51.--Grain of wheat (_Triticum_) germinating, showing (b) the
+    cotyledon and (c) the rootlets surrounded by their sheaths
+    (_coleorrhizae_).
+
+    FIG. 52.--Embryo of _Caryocar_. t, Thick hypocotyl, forming nearly
+    the whole mass, becoming narrowed and curved at its extremity, and
+    applied to the groove s. In the figure this narrowed portion is
+    slightly separated from the groove; c, two rudimentary cotyledons.]
+
+  In those plants in which there is only a single cotyledon in the
+  embryo, hence called _monocotyledonous_, the embryo usually has a
+  cylindrical form more or less rounded at the extremities, or elongated
+  and fusiform, often oblique. The axis is usually very short compared
+  with the cotyledon, which in general encloses the plumule by its lower
+  portion, and exhibits on one side a small slit which indicates the
+  union of the edges of the vaginal or sheathing portion of the leaf
+  (fig. 50). In grasses, by the enlargement of the embryo in a
+  particular direction, the endosperm is pushed on one side, and thus
+  the embryo comes to lie outside at the base of the endosperm (figs.
+  22, 51). The lamina of the cotyledon is not developed. Upon the side
+  of the embryo next the endosperm and enveloping it is a large
+  shield-shaped body, termed the _scutellum_. This is an outgrowth from
+  the base of the cotyledon, enveloping more or less the cotyledon and
+  plumule, in some cases, as in maize, completely investing it; in other
+  cases, as in rice, merely sending small prolongations over its
+  anterior face at the apex. By others this scutellum is considered as
+  the true cotyledon, and the sheathing structure covering the plumule
+  is regarded as a ligule or axillary stipule (see GRASSES). In many
+  aquatic monocotyledons (e.g. _Potamogeton_, _Ruppia_ and others) there
+  is a much-developed hypocotyl, which forms the greater part of the
+  embryo and acts as a store of nutriment in germination; these are
+  known as _macropodous_ embryos. A similar case is that of _Caryocar_
+  among Dicotyledons, where the swollen hypocotyl occupies most of the
+  embryo (fig. 52). In some grasses, as oats and rice, a projection of
+  cellular tissue is seen upon the side of the embryo opposite to the
+  scutellum, that is, on the anterior side. This has been termed the
+  _epiblast_. It is very large in rice. This by some was considered the
+  rudimentary second cotyledon; but is now generally regarded as an
+  outgrowth of the sheath of the true cotyledon.     (A. B. R.)
+
+
+
+
+FRUIT AND FLOWER FARMING. The different sorts of fruits and flowers are
+dealt with in articles under their own headings, to which reference may
+be made; and these give the substantial facts as to their cultivation.
+See also the article HORTICULTURE.
+
+
+TABLE I.--_Extent of Orchards in Great Britain in each Year, 1887 to
+1901._
+
+  +------+---------++------+---------++------+---------+
+  | Year.|  Acres. || Year.|  Acres. || Year.|  Acres. |
+  +------+---------++------+---------++------+---------+
+  | 1887 | 202,234 || 1892 | 208,950 || 1897 | 224,116 |
+  | 1888 | 199,178 || 1893 | 211,664 || 1898 | 226,059 |
+  | 1889 | 199,897 || 1894 | 214,187 || 1899 | 228,603 |
+  | 1890 | 202,305 || 1895 | 218,428 || 1900 | 232,129 |
+  | 1891 | 209,996 || 1896 | 221,254 || 1901 | 234,660 |
+  +------+---------++------+---------++------+---------+
+
+
+TABLE II.--_Areas under Orchards in England, Wales and Scotland--Acres._
+
+  +------+----------+--------+---------+--------------+
+  | Year.| England. | Wales. |Scotland.|Great Britain.|
+  +------+----------+--------+---------+--------------+
+  | 1896 | 215,642  |  3677  |  1935   |   221,254    |
+  | 1897 | 218,261  |  3707  |  2148   |   224,116    |
+  | 1898 | 220,220  |  3690  |  2149   |   226,059    |
+  | 1899 | 222,712  |  3666  |  2225   |   228,603    |
+  | 1900 | 226,164  |  3695  |  2270   |   232,129    |
+  | 1901 | 228,580  |  3767  |  2313   |   234,660    |
+  | 1908 | 244,430  |  3577  |  2290   |   250,297    |
+  +------+----------+--------+---------+--------------+
+
+
+GREAT BRITAIN
+
+The extent of the fruit industry may be gathered from the figures for
+the acreage of land under cultivation in orchards and small fruit
+plantations. The Board of Agriculture returns concerning the orchard
+areas of Great Britain showed a continuous expansion year by year from
+199,178 acres in 1888 to 234,660 acres in 1901, as will be learnt from
+Table I. There was, it is true, an exception in 1892, but the decline in
+that year is explained by the circumstance that since 1891 the
+agricultural returns have been collected only from holdings of more than
+one acre, whereas they were previously obtained from all holdings of a
+quarter of an acre or more. As there are many holdings of less than an
+acre in extent upon which fruit is grown, and as fruit is largely raised
+also in suburban and other gardens which do not come into the returns,
+it may be taken for granted that the actual extent of land devoted to
+fruit culture exceeds that which is indicated by the official figures.
+In the Board of Agriculture returns up to June 1908, 308,000 acres are
+stated to be devoted to fruit cultivation of all kinds in Great Britain.
+Table II. shows that the expansion of the orchard area of Great Britain
+is mainly confined to England, for it has slightly decreased in Wales
+and Scotland. The acreage officially returned as under orchards is that
+of arable or grass land which is also used for fruit trees of any kind.
+Conditions of soil and climate determine the irregular distribution of
+orchards in Great Britain. The dozen counties which possess the largest
+extent of orchard land all lie in the south or west of the island.
+According to the returns for 1908 (excluding small fruit areas) they
+were the following:--
+
+  +----------+--------++-----------+--------++----------+------+
+  |  County. | Acres. ||  County.  | Acres. ||  County. |Acres.|
+  +----------+--------++-----------+--------++----------+------+
+  | Kent     | 32,751 || Worcester | 23,653 || Salop    | 4685 |
+  | Devon    | 27,200 || Gloucester| 20,424 || Dorset   | 4464 |
+  | Hereford | 28,316 || Cornwall  |  5,415 || Monmouth | 3914 |
+  | Somerset | 25,279 || Middlesex |  5,300 || Wilts    | 3630 |
+  +----------+--------++-----------+--------++----------+------+
+
+Leaving out of consideration the county of Kent, which grows a greater
+variety of fruit than any of the others, the counties of Devon,
+Hereford, Somerset, Worcester and Gloucester have an aggregate orchard
+area of 124,872 acres. These five counties of the west and south-west of
+England--constituting in one continuous area what is essentially the
+cider country of Great Britain--embrace therefore rather less than half
+of the entire orchard area of the island, while Salop, Monmouth and
+Wilts have about 300 less than they had a few years ago. Five English
+counties have less than 1000 acres each of orchards, namely, the county
+of London, and the northern counties of Cumberland, Westmorland,
+Northumberland and Durham. Rutland has just over 100 acres. The largest
+orchard areas in Wales are in the two counties adjoining
+Hereford--Brecon with 1136 acres and Radnor with 727 acres; at the other
+extreme is Anglesey, with a decreasing orchard area of only 22 acres. Of
+the Scottish counties, Lanark takes the lead with 1285 acres, Perth,
+Stirling and Haddington following with 684 and 129 acres respectively.
+Ayr and Midlothian are the only other counties possessing 100 acres or
+more of orchards, whilst Kincardine, Orkney and Shetland return no
+orchard area, and Banff, Bute, Kinross, Nairn, Peebles, Sutherland and
+Wigtown return less than 10 acres each. It may be added that in 1908
+Jersey returned 1090 acres of orchards, Guernsey, &c., 144 acres, and
+the Isle of Man, 121 acres; the two last-named places showing a decline
+as compared with eight years previously.
+
+Outside the cider counties proper of England, the counties in which
+orchards for commercial fruit-growing have increased considerably in
+recent years include Berks, Buckingham, Cambridge, Essex, Lincoln,
+Middlesex, Monmouth, Norfolk, Oxford, Salop, Sussex, Warwick and Wilts.
+Apples are the principal fruit grown in the western and south-western
+counties, pears also being fairly common. In parts of Gloucestershire,
+however, and in the Evesham and Pershore districts of Worcestershire,
+plum orchards exist. Plums are almost as largely grown as apples in
+Cambridgeshire. Large quantities of apples, plums, damsons, cherries,
+and a fair quantity of pears are grown for the market in Kent, whilst
+apples, plums and pears predominate in Middlesex. In many counties
+damsons are cultivated around fruit plantations to shelter the latter
+from the wind.
+
+Of small fruit (currants, gooseberries, strawberries, raspberries, &c.)
+no return was made of the acreage previous to 1888, in which year it was
+given as 36,724 acres for Great Britain. In 1889 it rose to 41,933
+acres.
+
+Later figures are shown in Table III. It will be observed that, owing to
+corrections made in the enumeration in 1897, a considerable reduction in
+the area is recorded for that year, and presumably the error then
+discovered existed in all the preceding returns. The returns for 1907
+gave the acreage of small fruit as 82,175 acres, and in 1908 at 84,880
+acres--an area more than double that of 1889.
+
+
+TABLE III.--_Areas of Small Fruit in Great Britain._
+
+  +-------+--------+-------+--------+-------+--------+
+  | Year. | Acres. | Year. | Acres. | Year. | Acres. |
+  +-------+--------+-------+--------+-------+--------+
+  | 1890  | 46,234 | 1894  | 68,415 | 1898  | 69,753 |
+  | 1891  | 58,704 | 1895  | 74,547 | 1899  | 71,526 |
+  | 1892  | 62,148 | 1896  | 76,245 | 1900  | 73,780 |
+  | 1893  | 65,487 | 1897  | 69,792 | 1901  | 74,999 |
+  +-------+--------+-------+--------+-------+--------+
+
+
+TABLE IV.--_Areas under Small Fruit in England, Wales and
+Scotland--Acres._
+
+  +-------+----------+--------+-----------+----------------+
+  | Year. | England. | Wales. | Scotland. | Great Britain. |
+  +-------+----------+--------+-----------+----------------+
+  | 1898  |  63,438  |  1044  |   5271    |     69,753     |
+  | 1899  |  64,867  |  1106  |   5553    |     71,526     |
+  | 1900  |  66,749  |  1109  |   5922    |     73,780     |
+  | 1901  |  67,828  |  1092  |   6079    |     74,999     |
+  | 1908  |  75,750  |  1200  |   7930    |     84,880     |
+  +-------+----------+--------+-----------+----------------+
+
+There has undoubtedly been a considerable expansion, rather than a
+contraction, of small fruit plantations since 1896. The acreage of small
+fruit in Great Britain is about one-third that of the orchards. As may
+be seen in Table IV., it is mainly confined to England, though Scotland
+has over 4000 more acres of small fruit than of orchards. About
+one-third of the area of small fruit in England belongs to Kent alone,
+that county having returned 24,137 acres in 1908. Cambridge now ranks
+next with 6878 acres, followed by Norfolk with 5876 acres,
+Worcestershire with 4852 acres, Middlesex with 4163 acres, Hants with
+3320 acres and Essex with 2150 acres. It should be remarked that between
+1900 and 1908 Cambridgeshire had almost doubled its area of small
+fruits, from 3740 to 6878 acres; whilst both Norfolk and Worcestershire
+in 1908 had larger areas devoted to small fruits than Middlesex--in
+which county there had been a decrease of about 400 acres during the
+same period. The largest county area of small fruit in Wales is 806
+acres in Denbighshire, and in Scotland 2791 acres in Perthshire, 2259
+acres in Lanarkshire, followed by 412 acres in Forfarshire. The only
+counties in Great Britain which make no return under the head of small
+fruit are Orkney and Shetland; and Sutherland only gives 2-1/2 acres. It
+is hardly necessary to say that considerable areas of small fruit, in
+kitchen gardens and elsewhere, find no place in the official returns,
+which, however, include small fruit grown between and under orchard
+trees.
+
+Gooseberries are largely grown in most small fruit districts. Currants
+are less widely cultivated, but the red currant is more extensively
+grown than the black, the latter having suffered seriously from the
+ravages of the black currant mite. Kent is the great centre for
+raspberries and for strawberries, though, in addition, the latter fruit
+is largely grown in Cambridgeshire (2411 acres), Hampshire (2327 acres),
+Norfolk (2067 acres) and Worcestershire (1273 acres). Essex,
+Lincolnshire, Cheshire, Cornwall and Middlesex each has more than 500
+acres devoted to strawberry cultivation.
+
+The following statement from returns for 1908 shows the area under
+different kinds of fruit in 1907 and 1908 in Great Britain, and also
+whether there had been an increase or decrease:
+
+  +-----------------+---------+---------+-------------+
+  |                 |  1907.  |  1908.  | Increase or |
+  |                 |         |         |  Decrease.  |
+  +-----------------+---------+---------+-------------+
+  |                 |  Acres. |  Acres. |    Acres.   |
+  | Small Fruit--   |         |         |             |
+  |   Strawberries  |  27,827 |  28,815 |   + 988     |
+  |   Raspberries   |   8,878 |   9,323 |   + 445     |
+  |   Currants and  |         |         |             |
+  |    Gooseberries |  25,590 |  26,241 |   + 651     |
+  |   Other kinds   |  19,880 |  20,501 |   + 621     |
+  |                 +---------+---------+-------------+
+  |                 |  82,175 |  84,880 |   +2705     |
+  |                 +---------+---------+-------------+
+  | Orchards--      |         |         |             |
+  |   Apples        | 172,643 | 172,751 |   + 108     |
+  |   Pears         |   8,911 |   9,604 |   + 693     |
+  |   Cherries      |  12,027 |  11,868 |   - 159     |
+  |   Plums         |  14,901 |  15,683 |   + 782     |
+  |   Other kinds   |  41,694 |  40,391 |   -1303     |
+  |                 +---------+---------+-------------+
+  |                 | 250,176 | 250,297 |   + 121     |
+  +-----------------+---------+---------+-------------+
+
+It appears from the Board of Agriculture returns that 27,433 acres of
+small fruit was grown in orchards, so that the total extent of land
+under fruit cultivation in Great Britain at the end of 1908 was about
+308,000 acres.
+
+There are no official returns as to the acreage devoted to orchard
+cultivation in Ireland. The figures relating to small fruit, moreover,
+extend back only to 1899, when the area under this head was returned as
+4809 acres, which became 4359 acres in 1900 and 4877 acres in 1901. In
+most parts of the country there are districts favourable to the culture
+of small fruits, such as strawberries, raspberries, gooseberries and
+currants, and of top fruits, such as apples, pears, plums and damsons.
+The only localities largely identified with fruit culture as an industry
+are the Drogheda district and the Armagh district. In the former all the
+kinds named are grown except strawberries, the speciality being
+raspberries, which are marketed in Dublin, Belfast and Liverpool. In the
+Armagh district, again, all the kinds named are grown, but in this case
+strawberries are the speciality, the markets utilized being Richhill,
+Belfast, and those in Scotland. In the Drogheda district the grower
+bears the cost of picking, packing and shipping, but he cannot estimate
+his net returns until his fruit is on the market. Around Armagh the
+Scottish system prevails--that is, the fruit is sold while growing, the
+buyer being responsible for the picking and marketing.
+
+The amount of fruit imported into the United Kingdom has such an
+important bearing on the possibilities of the industry that the
+following figures also may be useful:
+
+  The quantities of apples, pears, plums, cherries and grapes imported
+  in the raw condition into the United Kingdom in each year, 1892 to
+  1901, are shown in Table V. Previous to 1892 apples only were
+  separately enumerated. Up to 1899 inclusive the quantities were given
+  in bushels, but in 1900 a change was made to hundred-weights. This
+  renders the quantities in that and subsequent years not directly
+  comparable with those in earlier years, but the comparison of the
+  values, which are also given in the table, continues to hold good. The
+  figures for 1908 have been added to show the increase that had taken
+  place. In some years the value of imported apples exceeds the
+  aggregate value of the pears, plums, cherries and grapes imported. The
+  extreme values for apples shown in the table are L844,000 in 1893 and
+  L2,079,000 in 1908. Grapes rank next to apples in point of value, and
+  over the seventeen years the amount ranged between L394,000 in 1892
+  and L728,000 in 1908. On the average, the annual outlay on imported
+  pears is slightly in excess of that on plums. The extremes shown are
+  L167,000 in 1895 and L515,000 in 1908. In the case of plums, the
+  smallest outlay tabulated is L166,000 in 1895, whilst the largest is
+  L498,000 in 1897. The amounts expended upon imported cherries varied
+  between L96,000 in 1895 and L308,000 in 1900. In 1900 apricots and
+  peaches, imported raw, previously included with raw plums, were for
+  the first time separately enumerated, the import into the United
+  Kingdom for that year amounting to 13,689 cwt., valued at L25,846; in
+  1901 the quantity was 13,463 cwt. and the value L32,350. The latter
+  rose in 1908 to L60,000. In 1900, also, currants, gooseberries and
+  strawberries, hitherto included in unenumerated raw fruit, were
+  likewise for the first time separately returned. Of raw currants the
+  import was 64,462 cwt., valued at L87,170 (1908, L121,850); of raw
+  gooseberries 26,045 cwt., valued at L14,626 (1908, L25,520); and of
+  raw strawberries, 52,225 cwt., valued at L85,949. In 1907 only 44,000
+  cwt. of strawberries were imported. In 1901 the quantities and values
+  were respectively--currants, 70,402 cwt., L75,308; gooseberries,
+  21,735 cwt., L11,420; strawberries, 38,604 cwt., L51,290. Up to 1899
+  the imports of tomatoes were included amongst unenumerated raw
+  vegetables, so that the quantity was not separately ascertainable. For
+  1900 the import of tomatoes was 833,032 cwt., valued at L792,339,
+  which is equivalent to a fraction under 2-1/2d. per lb. For 1901 the
+  quantity was 793,991 cwt., and the value L734,051; for 1906, there
+  were 1,124,700 cwt., valued at L953,475; for 1907, 1,135,499 cwt.,
+  valued at L1,020,805; and for 1908, 1,160,283 cwt., valued at
+  L955,983.
+
+
+  TABLE V.--_Imports of Raw Apples, Pears, Plums, Cherries and Grapes
+  into the United Kingdom, 1892 to 1901. Quantities in Thousands of
+  Bushels (thousands of cwt. in 1900 and 1901). Values in Thousands of
+  Pounds Sterling._
+
+    +------+-------------------------------------------------+
+    |      |                  Quantities.                    |
+    | Year.+---------+--------+--------+-----------+---------+
+    |      | Apples. | Pears. | Plums. | Cherries. | Grapes. |
+    +------+---------+--------+--------+-----------+---------+
+    | 1892 |  4515   |   637  |   413  |    217    |   762   |
+    | 1893 |  3460   |   915  |   777  |    346    |   979   |
+    | 1894 |  4969   |  1310  |   777  |    311    |   833   |
+    | 1895 |  3292   |   407  |   401  |    196    |   865   |
+    | 1896 |  6177   |   483  |   560  |    219    |   883   |
+    | 1897 |  4200   |  1052  |  1044  |    312    |   994   |
+    | 1898 |  3459   |   492  |   922  |    402    |  1136   |
+    | 1899 |  3861   |   572  |   558  |    281    |  1158   |
+    | 1900 |  2129*  |   477* |   423* |    243*   |   593*  |
+    | 1901 |  1830*  |   349* |   264* |    213*   |   680*  |
+    +------+---------+--------+--------+-----------+---------+
+    |                         Values.                        |
+    +------+---------+--------+--------+-----------+---------+
+    | 1892 |  1354   |   297  |   200  |    135    |   394   |
+    | 1893 |   844   |   347  |   332  |    195    |   530   |
+    | 1894 |  1389   |   411  |   302  |    167    |   470   |
+    | 1895 |   960   |   167  |   166  |     96    |   487   |
+    | 1896 |  1582   |   207  |   242  |    106    |   443   |
+    | 1897 |  1187   |   378  |   498  |    178    |   495   |
+    | 1898 |  1108   |   222  |   435  |    231    |   550   |
+    | 1899 |  1186   |   266  |   294  |    154    |   588   |
+    | 1900 |  1225   |   367  |   393  |    308    |   595   |
+    | 1901 |  1183   |   296  |   244  |    214    |   695   |
+    | 1908 |  2079   |   515  |   428  |    235    |   728   |
+    +------+---------+--------+--------+-----------+---------+
+      * Thousands of cwts.
+
+  In 1908 the outlay of the United Kingdom upon imported raw fruits,
+  such as can easily be produced at home, was L4,195,654, made up as
+  follows:
+
+    Apples      L2,079,703  |  Plums                L428,966
+    Grapes         728,026  |  Currants              121,852
+    Pears          515,914  |  Apricots and peaches   60,141
+    Cherries       235,523  |  Gooseberries           25,529
+
+  In addition about L280,000 was spent upon "unenumerated" raw fruit,
+  and L560,000 on nuts other than almonds "used as fruit," which would
+  include walnuts and filberts, both produced at home. It is certain,
+  therefore, that the expenditure on imported fruits, such as are grown
+  within the limits of the United Kingdom, exceeds four millions
+  sterling per annum. The remainder of the outlay on imported fruit in
+  1908, amounting to over L5,000,000, was made up of L2,269,651 for
+  oranges, L471,713 for lemons, L1,769,249 for bananas, and L560,301 for
+  almond-nuts; these cannot be grown on an industrial scale in the
+  British Isles.
+
+  It may be interesting to note the source of some of these imported
+  fruits. The United States and Canada send most of the apples, the
+  quantity for 1907 being 1,413,000 cwt. and 1,588,000 cwt.
+  respectively, while Australia contributes 280,000 cwt. Plums come
+  chiefly from France (200,000 cwt.), followed with 38,000 cwt. from
+  Germany and 28,000 cwt. from the Netherlands. Pears are imported
+  chiefly from France (204,000 cwt.) and Belgium (176,000); but the
+  Netherlands send 52,000 cwt., and the United States 24,000 cwt. The
+  great bulk of imported tomatoes comes from the Canary Islands, the
+  quantity in 1907 being 604,692 cwt. The Channel Islands also sent
+  223,800 cwt., France 115,500 cwt., Spain 169,000 cwt., and Portugal a
+  long way behind with 11,700 cwt. Most of the strawberries imported
+  come from France (33,800 cwt.) and the Netherlands (10,300 cwt.).
+
+_Fruit-growing in Kent._--Kent is by far the largest fruit-growing
+county in England. For centuries that county has been famous for its
+fruit, and appears to have been the centre for the distribution of trees
+and grafts throughout the country. The cultivation of fruit land upon
+farms in many parts of Kent has always been an important feature in its
+agriculture. An excellent description of this noteworthy characteristic
+of Kentish farming is contained in a comprehensive paper on the
+agriculture of Kent by Mr Charles Whitehead,[1] whose remarks, with
+various additions and modifications, are here reproduced.
+
+  Where the conditions are favourable, especially in East and Mid Kent,
+  there is a considerable acreage of fruit land attached to each farm,
+  planted with cherry, apple, pear, plum and damson trees, and with bush
+  fruits, or soft fruits as they are sometimes called, including
+  gooseberries, currants, raspberries, either with or without standard
+  trees, and strawberries, and filberts and cob-nuts in Mid Kent. This
+  acreage has largely increased, and will no doubt continue to increase,
+  as, on the whole, fruit-growing has been profitable and has materially
+  benefited those fortunate enough to have fruit land on their farms.
+  There are also cultivators who grow nothing but fruit. These are
+  principally in the district of East Kent, between Rochester and
+  Canterbury, and in the district of Mid Kent near London, and they
+  manage their fruit land, as a rule, better than farmers, as they give
+  their undivided attention to it and have more technical knowledge. But
+  there has been great improvement of late in the management of fruit
+  land, especially of cherry and apple orchards, the grass of which is
+  fed off by animals having corn or cake, or the land is well manured.
+  Apple trees are grease-banded and sprayed systematically by advanced
+  fruit-growers to prevent or check the attacks of destructive insects.
+  Far more attention is being paid to the selection of varieties of
+  apples and pears having colour, size, flavour, keeping qualities, and
+  other attributes to meet the tastes of the public, and to compete with
+  the beautiful fruit that comes from the United States and Canada.
+
+  Of the various kinds of apples at present grown in Kent mention should
+  be made of Mr Gladstone, Beauty of Bath, Devonshire Quarrenden, Lady
+  Sudely, Yellow Ingestre and Worcester Pearmain. These are dessert
+  apples ready to pick in August and September, and are not stored. For
+  storing, King of the Pippins, Cox's Orange Pippin (the best dessert
+  apple in existence), Cox's Pomona, Duchess, Favourite, Gascoyne's
+  Scarlet Seedling, Court Pendu Plat, Baumann's Red Reinette, Allington
+  Pippin, Duke of Devonshire and Blenheim Orange. Among kitchen apples
+  for selling straight from the trees the most usually planted are Lord
+  Grosvenor, Lord Suffield, Keswick Codlin, Early Julian, Eclinville
+  Seedling, Pott's Seedling, Early Rivers, Grenadier, Golden Spire,
+  Stirling Castle and Domino. For storing, the cooking sorts favoured
+  now are Stone's or Loddington, Warner's King, Wellington, Lord Derby,
+  Queen Caroline, Tower of Glamis, Winter Queening, Lucombe's Seedling,
+  Bismarck, Bramley's Seedling, Golden Noble and Lane's Prince Albert.
+  Almost all these will flourish equally as standards, pyramids and
+  bushes. Among pears are Hessle, Clapp's Favourite, William's Bon
+  Chretien, Beurre de Capiaumont, Fertility, Beurre Riche, Chissel,
+  Beurre Clairgeau, Louise Bonne of Jersey, Doyenne du Comice and Vicar
+  of Winkfield. Among plums, Rivers's Early Prolific, Tsar, Belgian
+  Purple, Black Diamond, Kentish Bush Plum, Pond's Seedling, Magnum
+  Bonum and Victoria are mainly cultivated. The damson known as Farleigh
+  Prolific, or Crittenden's, is most extensively grown throughout the
+  county, and usually yields large crops, which make good prices. As a
+  case in point, purchasers were offering to contract for quantities of
+  this damson at L20 per ton in May of 1899, as the prospects of the
+  yield were unsatisfactory. On the other hand, in one year recently
+  when the crop was abnormally abundant, some of the fruit barely paid
+  the expenses of sending to market. The varieties of cherries most
+  frequently grown are Governor Wood, Knight's Early Black, Frogmore
+  Blackheart, Black Eagle, Waterloo, Amberheart, Bigarreau, Napoleon
+  Bigarreau and Turk. A variety of cherry known as the Kentish cherry,
+  of a light red colour and fine subacid flavour, is much grown in Kent
+  for drying and cooking purposes. Another cherry, similar in colour and
+  quality, which comes rather late, known as the Flemish, is also
+  extensively cultivated, as well as the very dark red large Morello,
+  used for making cherry brandy. These three varieties are grown
+  extensively as pyramids, and the last-named also on walls and sides of
+  buildings. Sometimes the cherry crop is sold by auction to dealers,
+  who pick, pack and consign the fruit to market. Large prices are often
+  made, as much as L80 per acre being not uncommon. The crop on a large
+  cherry orchard in Mid Kent has been sold for more than L100 per acre.
+
+  Where old standard trees have been long neglected and have become
+  overgrown by mosses and lichens, the attempts made to improve them
+  seldom succeed. The introduction of bush fruit trees dwarfed by
+  grafting on the Paradise stock has been of much advantage to fruit
+  cultivators, as they come into bearing in two or three years, and are
+  more easily cultivated, pruned, sprayed and picked than standards.
+  Many plantations of these bush trees have been formed in Kent of
+  apples, pears and plums. Half standards and pyramids have also been
+  planted of these fruits, as well as of cherries. Bushes of
+  gooseberries and currants, and clumps or stools of raspberry canes,
+  have been planted to a great extent in many parts of the East and Mid
+  divisions of Kent, but not much in the Weald, where apples are
+  principally grown. Sometimes fruit bushes are put in alternate rows
+  with bush of standard trees of apple, pear, plum or damson, or they
+  are planted by themselves. The distances apart for planting are
+  generally for cherry and apple trees on grass 30 ft. by 30 ft.; for
+  standard apples and pear trees from 20 ft. to 24 ft. upon arable land,
+  with bush fruit, as gooseberries and currants, under them. These are
+  set 6 ft. by 6 ft. apart, and 5 ft. by 2 ft. for raspberries, and
+  strawberries 2 ft. 6 in. to 3 ft. by 1 ft. 6 in. to 1 ft. 3 in. apart.
+  On some fruit farms bush or dwarf trees--apples, pears, plums--are
+  planted alone, at distances varying from 8 ft. to 10 ft. apart, giving
+  from 485 to 680 bush trees per acre, nothing being grown between them
+  except perhaps strawberries or vegetables during the first two or
+  three years. It is believed that this is the best way of ensuring
+  fruit of high quality and colour. Another arrangement consists in
+  putting standard apple or pear trees 30 ft. apart (48 trees per acre),
+  and setting bush trees of apples or pears 15 ft. apart between them;
+  these latter come quickly into bearing, and are removed when the
+  standards are fully grown. Occasionally gooseberry or currant bushes,
+  or raspberry canes or strawberry plants, are set between the bush
+  trees, and taken away directly they interfere with the growth of
+  these. Half standard apple or plum trees are set triangularly 15 ft.
+  apart, and strawberry plants at a distance of 1-1/2 ft. from plant to
+  plant and 2-1/2 ft. from row to row. Or currant or gooseberry bushes
+  are set between the half standards, and strawberry plants between
+  these.
+
+  These systems involve high farming. The manures used are London
+  manure, where hops are not grown, and bone meal, super-phosphate,
+  rags, shoddy, wool-waste, fish refuse, nitrate of soda, kainit and
+  sulphate of ammonia. Where hops are grown the London manure is wanted
+  for them. Fruit plantations are always dug by hand with the Kent spud.
+  Fruit land is never ploughed, as in the United States and Canada. The
+  soil is levelled down with the "Canterbury" hoe, and then the
+  plantations are kept free from weeds with the ordinary draw or "plate"
+  hoe. The best fruit farmers spray fruit trees regularly in the early
+  spring, and continue until the blossoms come out, with quassia and
+  soft soap and paraffin emulsions, and a very few with Paris green
+  only, where there is no under fruit, in order to prevent and check the
+  constant attacks of the various caterpillars and other insect pests.
+  This is a costly and laborious process, but it pays well, as a rule.
+  The fallacy that fruit trees on grass land require no manure, and that
+  the grass may be allowed to grow up to their trunks without any harm,
+  is exploding, and many fruit farmers are well manuring their grass
+  orchards and removing the grass for some distance round the stems,
+  particularly where the trees are young.
+
+  Strawberries are produced in enormous quantities in the northern part
+  of the Mid Kent district round the Crays, and from thence to
+  Orpington; also near Sandwich, and to some extent near Maidstone.
+  Raspberry canes have been extensively put in during the last few
+  years, and in some seasons yield good profits. There is a very great
+  and growing demand for all soft fruits for jam-making, and prices are
+  fairly good, taking an average of years, notwithstanding the heavy
+  importations from France, Belgium, Holland, Spain and Italy. The
+  extraordinary increase in the national demand for jam and other fruit
+  preserves has been of great benefit to Kent fruit producers. The
+  cheapness of duty-free sugar, as compared with sugar paying duty in
+  the United States and other large fruit-producing countries, afforded
+  one of the very few advantages possessed by British cultivators, but
+  the reimposition of the sugar duty in the United Kingdom in 1901 has
+  modified the position in this respect. Jam factories were established
+  in several parts of Kent about 1889 or 1890, but most of them
+  collapsed either from want of capital or from bad management. There
+  are still a few remaining, principally in connexion with large fruit
+  farms. One of these is at Swanley, whose energetic owners farm nearly
+  2000 acres of fruit land in Kent. The fruit grown by them that will
+  not make satisfactory prices in a fresh raw state is made into jam, or
+  if time presses it is first made into pulp, and kept until the
+  opportunity comes for making it into jam. In this factory there are
+  fifteen steam-jacketed vats in one row, and six others for candied
+  peel. A season's output on a recent occasion comprised about 3500 tons
+  of jam, 850 tons of candied peel and 750 gross (108,000 bottles) of
+  bottled fruit. A great deal of the fruit preserved is purchased,
+  whilst much of that grown on the farms is sold. A strigging machine is
+  employed, which does as much work as fifty women in taking currants
+  off their strigs or stalks. Black currant pulp is stored in casks till
+  winter, when there is time to convert it into jam. Strawberries cannot
+  be pulped to advantage, but it is otherwise with raspberries, the pulp
+  of which is largely made. Apricots for jam are obtained chiefly from
+  France and Spain. There is another flourishing factory near
+  Sittingbourne worked on the same lines. It is very advantageous to
+  fruit farmers to have jam factories in connexion with their farms or
+  to have them near, as they can thoroughly grade their fruit, and send
+  only the best to market, thus ensuring a high reputation for its
+  quality. Carriage is saved, which is a serious charge, though railway
+  rates from Kent to the great manufacturing towns and to Scotland are
+  very much less proportionally than those to London, and consequently
+  Kent growers send increasing quantities to these distant markets,
+  where prices are better, not being so directly interfered with by
+  imported fruit, which generally finds its way to London.
+
+  Kentish fruit-growers are becoming more particular in picking,
+  grading, packing and storing fruit, as well as in marketing it. A
+  larger quantity of fruit is now carefully stored, and sent to selected
+  markets as it ripens, or when there is an ascertained demand, as it is
+  found that if it is consigned to market direct from the trees there
+  must frequently be forced sales and competition with foreign fruit
+  that is fully matured and in good order. It was customary formerly for
+  Kentish growers to consign all their fruit to the London markets; now
+  a good deal of it is sent to Manchester, Birmingham, Liverpool,
+  Sheffield, Newcastle and other large cities. Some is sent even to
+  Edinburgh and Glasgow. Many large growers send no fruit to London now.
+  It is by no means uncommon for growers to sell their fruit crops on
+  the trees or bushes by auction or private treaty, or to contract to
+  supply a stipulated quantity of specified fruit, say of currants,
+  raspberries or strawberries, to jam manufacturers. There is a
+  considerable quantity of fruit, such as grapes, peaches, nectarines,
+  grown under glass, and this kind of culture tends to increase.
+
+  Filberts and cob-nuts are a special product of Kent, in the
+  neighbourhood of Maidstone principally, and upon the Ragstone soils,
+  certain conditions of soil and situation being essential for their
+  profitable production. A part of the filbert and cob-nut crop is
+  picked green in September, as they do well for dessert, though their
+  kernels are not large or firm, and it pays to sell them green, as they
+  weigh more heavily. One grower in Mid Kent has 100 acres of nuts, and
+  has grown 100 tons in a good year. The average price of late years has
+  been about 5d. per lb., which would make the gross return of the 100
+  acres amount to L4660. Kentish filberts have long been proverbial for
+  their excellence. Cobs are larger and look better for dessert, though
+  their flavour is not so fine. They are better croppers, and are now
+  usually planted. This cultivation is not much extending, as it is very
+  long before the trees come into full bearing. The London market is
+  supplied entirely with these nuts from Kent, and there is some demand
+  in America for them. Filbert and cob trees are most closely pruned.
+  All the year's growth is cut away except the very finest young wood,
+  which the trained eye of the tree-cutter sees at a glance is
+  blossom-bearing. The trees are kept from 5-1/2 to 7 ft. high upon
+  stems from 1-1/2 to 2 ft. high, and are trained so as to form a cup of
+  from 7 to 8 ft. in diameter.
+
+  There seems no reason to expect any decrease in the acreage of fruit
+  land in Kent, and if the improvement in the selection of varieties and
+  in the general management continues it will yet pay. A hundred years
+  ago every one was grubbing fruit land in order that hops might be
+  planted, and for this many acres of splendid cherry orchards were
+  sacrificed. Now the disposition is to grub hop plants and substitute
+  apples, plums, or small fruit or cherry trees.
+
+  _Fruit-growing in other Districts._--The large fruit plantations in
+  the vicinity of London are to be found mostly in the valley of the
+  Thames, around such centres as Brentford, Isleworth, Twickenham,
+  Heston, Hounslow, Cranford and Southall. All varieties of orchard
+  trees, but mostly apples, pears, and plums and small fruit, are grown
+  in these districts, the nearness of which to the metropolitan fruit
+  market at Covent Garden is of course an advantage. Some of the
+  orchards are old, and are not managed on modern principles. They
+  contain, moreover, varieties of fruit many of which are out of date
+  and would not be employed in establishing new plantations. In the
+  better-managed grounds the antiquated varieties have been removed, and
+  their places taken by newer and more approved types. In addition to
+  apples, pears, plums, damsons, cherries and quinces as top fruit,
+  currants, gooseberries and raspberries are grown as bottom fruit.
+  Strawberries are extensively grown in some of the localities, and in
+  favourable seasons outdoor tomatoes are ripened and marketed.
+
+  Fruit is extensively grown in Cambridgeshire and adjacent counties in
+  the east of England. A leading centre is Cottenham, where the Lower
+  Greensand crops out and furnishes one of the best of soils for
+  fruit-culture. In Cottenham about a thousand acres are devoted to
+  fruit, and nearly the same acreage to asparagus, which is, however,
+  giving place to fruit. Currants, gooseberries and strawberries are the
+  most largely grown, apples, plums and raspberries following. Of
+  varieties of plums the Victoria is first in favour, and then Rivers's
+  Early Prolific, Tsar and Gisborne. London is the chief market, as it
+  receives about half the fruit sent away, whilst a considerable
+  quantity goes to Manchester, and some is sent to a neighbouring jam
+  factory at Histon, where also a moderate acreage of fruit is grown.
+  Another fruit-growing centre in Cambridgeshire is at Willingham,
+  where--besides plums, gooseberries and raspberries--outdoor tomatoes
+  are a feature. Greengages are largely grown near Cambridge. Wisbech is
+  the centre of an extensive fruit district, situated partly in
+  Cambridgeshire and partly in Norfolk. Gooseberries, strawberries and
+  raspberries are largely grown, and as many as 80 tons of the
+  first-named fruit have been sent away from Wisbech station in a single
+  day. In the fruit-growing localities of Huntingdonshire apples, plums
+  and gooseberries are the most extensively grown, but pears,
+  greengages, cherries, currants, strawberries and raspberries are also
+  cultivated. As illustrating variations in price, it may be mentioned
+  that about the year 1880 the lowest price for gooseberries was L10 per
+  ton, whereas it has since been down to L4. Huntingdonshire fruit is
+  sent chiefly to Yorkshire, Scotland and South Wales, but railway
+  freights are high.
+
+  Essex affords a good example of successful fruit-farming at Tiptree
+  Heath, near Kelvedon, where under one management about 260 acres out
+  of a total of 360 are under fruit. The soil, a stiff loam, grows
+  strawberries to perfection, and 165 acres are allotted to this fruit.
+  The other principal crops are 43 acres of raspberries and 30 acres of
+  black currants, besides which there are small areas of red currants,
+  gooseberries, plums, damsons, greengages, cherries, apples, quinces
+  and blackberries. The variety of strawberry known as the Small Scarlet
+  is a speciality here, and it occupies 55 acres, as it makes the best
+  of jam. The Paxton, Royal Sovereign and Noble varieties are also
+  grown. Strawberries stand for six or seven years on this farm, and
+  begin to yield well when two years old. A jam factory is worked in
+  conjunction with the fruit farm. Pulp is not made except when there is
+  a glut of fruit. Perishable fruit intended for whole-fruit preserves
+  is never held over after it is gathered. The picking of strawberries
+  begins at 4 A.M., and the first lot is made into jam by 6 A.M.
+
+  Hampshire, like Cambridgeshire and Norfolk, are the only counties in
+  which the area of small fruit exceeds that of orchards. The returns
+  for 1908 show that Hampshire had 3320 acres of small fruit to 2236
+  acres of orchards; Cambridge had 6878 acres of small fruit to 5221 of
+  orchards; and Norfolk had 5876 acres of small fruit against 5188 acres
+  of orchards. Compared with twenty years previously, the acreage of
+  small fruit had trebled. This is largely due in Hampshire to the
+  extension of strawberry culture in the Southampton district, where the
+  industry is in the hands of many small growers, few of whom cultivate
+  more than 20 acres each. Sarisbury and Botley are the leading parishes
+  in which the business is carried on. Most of the strawberry holdings
+  are from half an acre to 5 acres in extent, a few are from 5 to 10
+  acres, fewer still from 10 to 20 acres and only half-a-dozen over that
+  limit. Runners from one-year plants are used for planting, being found
+  more fruitful than those from older plants. Peat-moss manure from
+  London stables is much used, but artificial manures are also employed
+  with good results. Shortly after flowering the plants are bedded down
+  with straw at the rate of about 25 cwt. per acre. Picking begins some
+  ten days earlier than in Kent, at a date between 1st June and 15th
+  June. The first week's gathering is sent mostly to London, but
+  subsequently the greater part of the fruit goes to the Midlands and to
+  Scotland and Ireland.
+
+  In recent years fruit-growing has much increased in South
+  Worcestershire, in the vicinity of Evesham and Pershore. Hand-lights
+  are freely used in the market gardens of this district for the
+  protection of cucumbers and vegetable marrows, besides which tomatoes
+  are extensively grown out of doors. At one time the egg plum and the
+  Worcester damson were the chief fruit crops, apples and cherries
+  ranking next, pears being grown to only a moderate extent. According
+  to the 1908 returns, however, apples come first, plums second, pears
+  third and cherries fourth. In a prolific season a single tree of the
+  Damascene or Worcester damson will yield from 400 to 500 lb. of
+  fruit. There is a tendency to grow plum trees in the bush shape, as
+  they are less liable than standards to injury from wind. The manures
+  used include soot, fish guano, blood manure and phosphates--basic slag
+  amongst the last-named. In the Pershore district, where there is a jam
+  factory, plums are the chief tree fruit, whilst most of the orchard
+  apples and pears are grown for cider and perry. Gooseberries are a
+  feature, as are also strawberries, red and black currants and a few
+  white, but raspberries are little grown. The soil, a strong or medium
+  loam of fair depth, resting on clay, is so well adapted to plums that
+  trees live for fifty years. In order to check the ravages of the
+  winter moth, plum and apple trees are grease-banded at the beginning
+  of October and again at the end of March. The trees are also sprayed
+  when necessary with insecticidal solutions. Pruning is done in the
+  autumn. An approved distance apart at which to grow plum trees is 12
+  ft. by 12 ft. In the Earl of Coventry's fruit plantation, 40 acres in
+  extent, at Croome Court, plums and apples are planted alternately, the
+  bottom fruit being black currants, which are less liable to injury
+  from birds than are red currants or gooseberries. Details concerning
+  the methods of cultivation of fruit and flowers in various parts of
+  England, the varieties commonly grown, the expenditure involved, and
+  allied matters, will be found in Mr W.E. Bear's papers in the _Journal
+  of the Royal Agricultural Society_ in 1898 and 1899.
+
+  Apart altogether from market gardening and commercial fruit-growing,
+  it must be borne in mind that an enormous business is done in the
+  raising of young fruit-trees every year. Hundreds of thousands of
+  apples, pears, plums, cherries, peaches, nectarines and apricots are
+  budded or grafted each year on suitable stocks. They are trained in
+  various ways, and are usually fit for sale the third year. These young
+  trees replace old ones in private and commercial gardens, and are also
+  used to establish new plantations in different parts of the kingdom.
+
+  _The Woburn Experimental Fruit Farm._--The establishment in 1894 of
+  the experimental fruit farm at Ridgmont, near Woburn, Beds, has
+  exercised a healthy influence upon the progress and development of
+  fruit-farming in England. The farm was founded and carried on by the
+  public-spirited enterprise of the Duke of Bedford and Mr Spencer U.
+  Pickering, the latter acting as director. The main object of the
+  experimental station was "to ascertain facts relative to the culture
+  of fruit, and to increase our knowledge of, and to improve our
+  practice in, this industry." The farm is 20 acres in extent, and
+  occupies a field which up to June 1894 had been used as arable land
+  for the ordinary rotation of farm crops. The soil is a sandy loam 9 or
+  10 in. deep, resting on a bed of Oxford Clay. Although it contains a
+  large proportion of sand, the land would generally be termed very
+  heavy, and the water often used to stand on it in places for weeks
+  together in a wet season. The tillage to which the ground was
+  subjected for the purposes of the fruit farm much improved its
+  character, and in dry weather it presents as good a tilth as could be
+  desired. Chemical analyses of the soil from different parts of the
+  field show such wide differences that it is admitted to be by no means
+  an ideal one for experimental purposes. Without entering upon further
+  details, it may be useful to give a summary of the chief results
+  obtained.
+
+  Apples have been grown and treated in a variety of ways, but of the
+  different methods of treatment careless planting, coupled with
+  subsequent neglect, has given the most adverse results, the crop of
+  fruit being not 5% of that from trees grown normally. Of the separate
+  deleterious items constituting total neglect, by far the most
+  effective was the growth of weeds on the surface; careless planting,
+  absence of manure, and the omission of trenching all had comparatively
+  little influence on the results. A set of trees that had been
+  carelessly planted and neglected, but subsequently tended in the early
+  part of 1896, were in the autumn of that year only 10% behind their
+  normally-treated neighbours, thus demonstrating that the response to
+  proper attention is prompt. The growth of grass around young apple
+  trees produced a very striking effect, the injury being much greater
+  than that due to weeds. It is possible, however, that in wet years the
+  ill-effects of both grass and weeds would be less than in dry seasons.
+  Nevertheless, the grass-grown trees, after five years, were scarcely
+  bigger than when planted, and the actual increase in weight which they
+  showed during that time was about eighteen times smaller than in the
+  case of similar trees in tilled ground. It is believed that one of the
+  main causes of the ill-effects is the large increase in the
+  evaporation of water from the soil which is known to be produced by
+  grass, the trees being thereby made to suffer from drought, with
+  constant deprivation of other nourishment as well. That grass growing
+  round young apple trees is deleterious was a circumstance known to
+  many horticulturists, but the extent to which it interferes with the
+  development of the trees had never before been realized. Thousands of
+  pounds are annually thrown away in England through want of knowledge
+  of this fact. Yet trees will flourish in grass under certain
+  conditions. Whether the dominant factor is the age (or size) of the
+  tree has been investigated by grassing over trees which have hitherto
+  been in the open ground, and the results appear to indicate that the
+  grass is as deleterious to the older trees as it was to the younger
+  ones. Again, it appears to have been demonstrated that young apple
+  trees, at all events in certain soils, require but little or no manure
+  in the early stages of their existence, so that in this case also
+  large sums must be annually wasted upon manurial dressings which
+  produce no effects. The experiments have dealt with dwarf trees of
+  Bramley, Cox and Potts, six trees of each variety constituting one
+  investigation. Some of the experiments were repeated with Stirling
+  Castle, and others with standard trees of Bramley, Cox and Lane's
+  Prince Albert. All were planted in 1894-1895, the dwarfs being then
+  three years old and the standards four. In each experiment the
+  "normal" treatment is altered in some one particular, this normal
+  treatment consisting of planting the trees carefully in trenched
+  ground, and subsequently keeping the surface clean; cutting back after
+  planting, pruning moderately in autumn, and shortening the growths
+  when it appeared necessary in summer; giving in autumn a dressing of
+  mixed mineral manures, and in February one of nitrate of soda, this
+  dressing being probably equivalent to one of 12 tons of dung per acre.
+  In the experiments on branch treatment, the bad effects of omitting to
+  cut the trees back on planting, or to prune them subsequently, is
+  evident chiefly in the straggling and bad shape of the resulting
+  trees, but such trees also are not so vigorous as they should be. The
+  quantity of fruit borne, however, is in excess of the average. The
+  check on the vigour and growth of a tree by cutting or injuring its
+  roots is in marked contrast with the effects of a similar interference
+  with the branches. Trees which had been root-pruned each year were in
+  1898 little more than half as big as the normal trees, whilst those
+  root-pruned every second year were about two-thirds as big as the
+  normal. The crops borne by these trees were nevertheless heavy in
+  proportion to the size of the trees. Such frequent root-pruning is
+  not, of course, a practice which should be adopted. It was found that
+  trees which had been carefully lifted every other year and replanted
+  at once experienced no ill-effects from the operation; but in a case
+  where the trees after being lifted had been left in a shed for three
+  days before replanting--which would reproduce to a certain extent the
+  conditions experienced when trees are sent out from a
+  nursery--material injury was suffered, these trees after four years
+  being 28% smaller than similar ones which had not been replanted. Sets
+  of trees planted respectively in November, January and March have, on
+  the whole, shown nothing in favour of any of these different times for
+  planting purposes. Some doubt is thrown on the accepted view that
+  there is a tendency, at any rate with young apple and pear trees, to
+  fruit in alternate seasons.
+
+  Strawberries of eighty-five different varieties have been experimented
+  with, each variety being represented in 1900 by plants of five
+  different ages, from one to five years. In 1896 and 1898 the crops of
+  fruit were about twice as heavy as in 1897 and 1899, but it has not
+  been found possible to correlate these variations with the
+  meteorological records of the several seasons. Taking the average of
+  all the varieties, the relative weights of crop per plant, when these
+  are compared with the two-year-old plants in the same season, are, for
+  the five ages of one to five years, 31, 100, 122, 121 and 134,
+  apparently showing that the bearing power increases rapidly up to two
+  years, less rapidly up to three years, after which age it remains
+  practically constant. The relative average size of the berries shows a
+  deterioration with the age of the plant. The comparative sizes from
+  plants of one to five years old were 115, 100, 96, 91 and 82
+  respectively. If the money value of the crop is taken to be directly
+  dependent on its total weight, and also on the size of the fruits, the
+  relative values of the crop for the different ages would be 34, 100,
+  117, 111 and 110, so that, on the Ridgmont ground, strawberry plants
+  could be profitably retained up to five years and probably longer. As
+  regards what may be termed the order of merit of different varieties
+  of strawberries, it appears that even small differences in position
+  and treatment cause large variations, not only in the features of the
+  crop generally, but also in the relative behaviour of the different
+  varieties. The relative cropping power of the varieties under
+  apparently similar conditions may often be expressed by a number five
+  or tenfold as great in one case as in the other. A comparison of the
+  relative behaviour of the same varieties in different seasons is
+  attended by similar variations. The varying sensitiveness of different
+  varieties of strawberry plants to small and undefinable differences in
+  circumstances is indeed one of the most important facts brought to
+  light in the experiments.
+
+  _Fruit Culture in Ireland._--The following figures have been kindly
+  supplied by the Irish Board of Agriculture, and deal with the acreage
+  under fruit culture in Ireland up to the end of the year 1907.
+
+    1. _Orchard Fruit_--       Statute Acres.
+        Apples                     5829
+        Pears                       224
+        Plums                       223
+        Damsons                     138
+        Other kinds                 129
+                                   ----
+                      Total        6543
+
+    2. _Small Fruit_--
+        Currants, black             234
+        Currants, red and white     159
+        Gooseberries                675
+        Raspberries                 374
+        Strawberries                994
+        Mixed fruit                2470
+                                   ----
+                      Total        4906
+
+  It therefore appears that while Ireland grows only about
+  one-thirty-third the quantity of apples that England does, it is
+  nevertheless nearly 5000 acres ahead of Scotland and about 2000 acres
+  ahead of Wales. It grows 41 times fewer pears than England, but still
+  is ahead of Scotland and a long way ahead of Wales in this fruit.
+  There are 70 times fewer plums grown in Ireland than in England, and
+  about the same in Scotland, while Wales does very little indeed. In
+  small fruit Ireland is a long way behind Scotland in the culture of
+  strawberries and raspberries, although with currants and gooseberries
+  it is very close. Considering the climate, and the fact that there
+  are, according to the latest available returns, over 62,000 holdings
+  above 1 acre but not exceeding 5 acres (having a total of 224,000
+  acres), it is possible fruit culture may become more prevalent than it
+  has been in the past.
+
+_The Flower-growing Industry._--During the last two or three decades of
+the 19th century a very marked increase in flower production occurred in
+England. Notably was this the case in the neighbourhood of London,
+where, within a radius of 15 or 20 m., the fruit crops, which had
+largely taken the place of garden vegetables, were themselves ousted in
+turn to satisfy the increasing demand for land for flower cultivation.
+No flower has entered more largely into the development of the industry
+than the narcissus or daffodil, of which there are now some 600
+varieties. Comparatively few of these, however, are grown for market
+purposes, although all are charming from the amateur point of view. On
+some flower farms a dozen or more acres are devoted to narcissi alone,
+the production of bulbs for sale as well as of flowers for market being
+the object of the growers.
+
+In the London district the country in the Thames valley west of the
+metropolis is as largely occupied by flower farms as it is by fruit
+farms--in fact, the cultivation of flowers is commonly associated with
+that of fruit. In the vicinity of Richmond narcissi are extensively
+grown, as they also are more to the west in the Long Ditton district,
+and likewise around Twickenham, Isleworth, Hounslow, Feltham and
+Hampton. Roses come more into evidence in the neighbourhood of Hounslow,
+Cranford, Hillingdon and Uxbridge, and in some gardens daffodils and
+roses occupy alternate rows. In this district also such flowers as
+herbaceous paeonies, Spanish irises, German irises, Christmas roses,
+lilies of the valley, chrysanthemums, foxgloves, hollyhocks,
+wallflowers, carnations, &c., are extensively grown in many market
+gardens. South of London is the Mitcham country, long noted for its
+production of lavender. The incessant growth of the lavender plant upon
+the same land, however, has led to the decline of this industry, which
+has been largely transferred to districts in the counties of Bedford,
+Essex and Hertford. At Mitcham, nevertheless, mixed flowers are very
+largely grown for the supply of the metropolis, and one farm alone has
+nearly 100 acres under flowers and glass-houses. Chrysanthemums, asters,
+Iceland poppies, gaillardias, pansies, bedding calceolarias, zonal
+pelargoniums and other plants are cultivated in immense quantities. At
+Swanley and Eynsford, in Kent, flowers are extensively cultivated in
+association with fruit and vegetables. Narcissi, chrysanthemums,
+violets, carnations, campanulas, roses, pansies, irises, sweet peas, and
+many other flowers are here raised, and disposed of in the form both of
+cut flowers and of plants.
+
+The Scilly Isles are important as providing the main source of supply of
+narcissi to the English markets in the early months of the year. This
+trade arose almost by accident, for it was about the year 1865 that a
+box of narcissi sent to Covent Garden Market, London, realized L1; and
+the knowledge of this fact getting abroad, the farmers of the isles
+began collecting wild bulbs from the fields in order to cultivate them
+and increase their stocks. Some ten years, however, elapsed before the
+industry promised to become remunerative. In 1885 a Bulb and Flower
+Association was established to promote the industrial growth of flowers.
+The exports of flowers in that year reached 65 tons, and they steadily
+increased until 1893, when they amounted to 450 tons. A slight decline
+followed, but in 1896 the quantity exported was no less than 514 tons.
+This would represent upwards of 3-1/2 million bunches of flowers,
+chiefly narcissi and anemones. Rather more than 500 acres are devoted to
+flower-growing in the isles, by far the greater part of this area being
+assigned to narcissi, whilst anemones, gladioli, marguerites, arum
+lilies, Spanish irises, pinks and wallflowers are cultivated on a much
+smaller scale. The great advantage enjoyed by the Scilly flower-growers
+is earliness of production, due to climatic causes; the soil, moreover,
+is well suited to flower culture and there is an abundance of sunshine.
+The long journey to London is somewhat of a drawback, in regard to both
+time and freight, but the earliness of the flowers more than compensates
+for this. Open-air narcissi are usually ready at the beginning of
+January, and the supply is maintained in different varieties up to the
+middle or end of May. The narcissus bulbs are usually planted in
+October, 4 in. by 3 in. apart for the smaller sorts and 6 in. by 4 to 6
+in. for the larger. A compost of farmyard manure, seaweed, earth and
+road scrapings is the usual dressing, but nitrate of soda, guano and
+bones are also occasionally employed. A better plan, perhaps, is to
+manure heavily the previous crop, frequently potatoes, no direct
+manuring then being needed for the bulbs, these not being left in the
+ground more than two or three years. The expenses of cultivation are
+heavy, the cost of bulbs alone--of which it requires nearly a quarter of
+a million of the smaller varieties, or half as many of the largest, to
+plant an acre--being considerable. The polyanthus varieties of narcissus
+are likely to continue the most remunerative to the flower-growers of
+Scilly, as they flourish better in these isles than on the mainland.
+
+In the district around the Wash, in the vicinity of such towns as
+Wisbech, Spalding and Boston, the industrial culture of bulbs and
+flowers underwent great expansion in the period between 1880 and 1909.
+At Wisbech one concern alone has a farm of some 900 acres, devoted
+chiefly to flowers and fruit, the soil being a deep fine alluvium. Roses
+are grown here, one field containing upwards of 100,000 trees. Nearly 20
+acres are devoted to narcissi, which are grown for the bulbs and also,
+together with tulips, for cut flowers. Carnations are cultivated both
+in the field and in pots. Cut flowers are sent out in large quantities,
+neatly and effectively packed, the parcel post being mainly employed as
+a means of distribution. In the neighbourhood of Spalding crocuses and
+snowdrops are less extensively grown than used to be the case. On one
+farm, however, upwards of 20 acres are devoted to narcissi alone, whilst
+gladioli, lilies and irises are grown on a smaller scale. Around Boston
+narcissi are also extensively grown for the market, both bulbs and cut
+blooms being sold. The bulbs are planted 3 in. apart in rows, the latter
+being 9 in. apart, and are allowed to stand from two to four years.
+
+  The imports of fresh flowers into the United Kingdom were not
+  separately shown prior to 1900. In that year, however, their value
+  amounted to L200,585, in 1901 to L225,011, in 1906 to L233,884, in
+  1907 to L233,641, and in 1908 to L229,802, so that the trade showed a
+  fairly steady condition. From the monthly totals quoted in Table VI.
+  it would appear that the trade sinks to its minimum dimensions in the
+  four months July to October inclusive, and that after September the
+  business continually expands up to April, subsequent to which
+  contraction again sets in. About one-half of the trade belongs
+  practically to the three months of February, March and April.
+
+
+  TABLE VI.--_Values of Fresh Flowers imported into the United Kingdom._
+
+    +-----------+----------+----------+----------+
+    |   Month.  |   1906.  |   1907.  |   1908.  |
+    +-----------+----------+----------+----------+
+    | January   |  L31,035 |  L18,545 |  L29,180 |
+    | February  |   34,647 |   25,541 |   30,541 |
+    | March     |   50,232 |   42,611 |   35,185 |
+    | April     |   30,809 |   50,418 |   42,681 |
+    | May       |   22,980 |   21,767 |   23,129 |
+    | June      |   17,641 |   18,358 |   16,904 |
+    | July      |    3,386 |    4,509 |    3,467 |
+    | August    |    1,646 |    1,539 |    1,081 |
+    | September |      852 |      736 |      953 |
+    | October   |    4,481 |    3,180 |    4,504 |
+    | November  |   17,506 |   15,763 |   15,097 |
+    | December  |   18,669 |   30,674 |   27,080 |
+    |           +----------+----------+----------+
+    |    Total  | L233,884 | L233,641 | L229,802 |
+    +-----------+----------+----------+----------+
+
+_Hothouse Culture of Fruit and Flowers._--The cultivation of fruit and
+flowers under glass has increased enormously since about the year 1880,
+especially in the neighbourhood of London, where large sums of money
+have been sunk in the erection and equipment of hothouses. In the parish
+of Cheshunt, Herts, alone there are upwards of 130 acres covered with
+glass, and between that place on the north and London on the south
+extensive areas of land are similarly utilized. In Middlesex, in the
+north, in the districts of Edmonton, Enfield, Ponders End and Finchley,
+and in the west from Isleworth to Hampton, Feltham, Hillingdon, Sipson
+and Uxbridge, many crops are now cultivated under glass. At Erith,
+Swanley, and other places in Kent, as also at Worthing, in Sussex,
+glass-house culture has much extended. A careful estimate puts the area
+of industrial hothouses in England at about 1200 acres, but it is
+probably much more than this. Most of the greenhouses are fixtures, but
+in some parts of the kingdom structures that move on rails and wheels
+are used, to enable the ground to be prepared in the open for one crop
+while another is maturing under glass. The leading products are grapes,
+tomatoes and cucumbers, the last-named two being true fruits from the
+botanist's point of view, though commercially included with vegetables.
+To these may be added on the same ground dwarf or French beans, and
+runner or climbing beans. Peaches, nectarines and strawberries are
+largely grown under glass, and, in private hothouses--from which the
+produce is used mainly for household consumption, and which are not
+taken into consideration here--pineapples, figs and other fruit.
+Conservative estimates indicate the average annual yield of hothouse
+grapes to be about 12 tons per acre and of tomatoes 20 tons. The greater
+part of the space in the hothouses is assigned to fruit, but whilst some
+houses are devoted exclusively to flowers, in others, where fruit is the
+main object, flowers are forced in considerable quantities in winter and
+early spring. The flowers grown under glass include tulips, hyacinths,
+primulas, cyclamens, spiraeas, mignonettes, fuchsias, calceolarias,
+roses, chrysanthemums, daffodils, arum lilies or callas, liliums,
+azaleas, eucharises, camellias, stephanotis, tuberoses, bouvardias,
+gardenias, heaths or ericas, poinsettias, lilies of the valley, zonal
+pelargoniums, tuberous and fibrous rooted begonias, and many others.
+There is an increasing demand for foliage hothouse plants, such as
+ferns, palms, crotons, aspidistras, araucarias, dracaenas, India-rubber
+plants, aralias, grevilleas, &c. Berried plants like solanums and
+aucubas also find a ready sale, while the ornamental kinds of asparagus
+such as _sprengeri_ and _plumosus_ nanus, are ever in demand for
+trailing decorations, as well as myrsiphyilum. Special mention must be
+made of the winter or perpetual flowering carnations which are now grown
+by hundreds of thousands in all parts of the kingdom for decorative work
+during the winter season. The converse of forcing plants into early
+blossom is adopted with such an important crop as lily of the valley.
+During the summer season the crowns are placed in refrigerators with
+about 2 degrees of frost, and quantities are taken out as required every
+week and transferred to the greenhouse to develop. Tomatoes are grown
+largely in houses exclusively occupied by them, in which case two and
+sometimes three crops can be gathered in the year. In the Channel
+Islands, where potatoes grown under glass are lifted in April and May,
+in order to secure the high prices of the early markets, tomato
+seedlings are planted out from boxes into the ground as quickly as the
+potatoes are removed, the tomato planter working only a few rows behind
+the potato digger. The trade in imported tomatoes is so considerable
+that home growers are well justified in their endeavours to meet the
+demand more fully with native produce, whether raised under glass or in
+the open. Tomatoes were not separately enumerated in the imports
+previous to 1900. It has already been stated that in 1900 the raw
+tomatoes imported amounted to 833,032 cwt., valued at L792,339, and in
+1901 to 793,991 cwt., valued at L734,051. From the monthly quantities
+given in Table VII., it would appear that the imports are largest in
+June, July and August, about one-half of the year's total arriving
+during those three months. It is too early in June and July for
+home-grown outdoor tomatoes to enter into competition with the imported
+product, but home-grown hothouse tomatoes should be qualified to
+challenge this trade.
+
+
+TABLE VII.--_Quantities of Tomatoes imported into the United Kingdom._
+
+  +-----------+-----------+------------+------------+
+  | Month.    |   1906.   |    1907.   |    1908.   |
+  +-----------+-----------+------------+------------+
+  | January   |    61,940 |     56,022 |     73,409 |
+  | February  |    58,187 |     58,289 |     69,350 |
+  | March     |   106,458 |     98,028 |     86,928 |
+  | April     |   103,273 |    109,057 |     74,917 |
+  | May       |    67,933 |    114,041 |     88,901 |
+  | June      |    62,906 |    144,379 |    127,793 |
+  | July      |   238,362 |    150,907 |    171,978 |
+  | August    |   180,046 |    102,600 |    124,757 |
+  | September |   114,860 |    101,198 |    119,224 |
+  | October   |    52,678 |     67,860 |     75,722 |
+  | November  |    41,513 |     66,522 |     74,292 |
+  | December  |    36,316 |     66,591 |     73,012 |
+  |           +-----------+------------+------------+
+  |   Total   | 1,124,472 |  1,135,494 |  1,160,283 |
+  |           +-----------+------------+------------+
+  |   Value   |  L953,475 | L1,135,499 | L1,160,283 |
+  +-----------+-----------+------------+------------+
+
+An important feature of modern flower growing is the production and
+cultivation of what are known as "hardy herbaceous perennials." Some
+2000 or 3000 different species and varieties of these are now raised in
+special nurseries; and during the spring, summer and autumn seasons
+magnificent displays are to be seen not only in the markets but at the
+exhibitions in London and at the great provincial shows held throughout
+the kingdom. The production of many of these perennials is so easy that
+amateurs in several instances have taken it up as a business hobby; and
+in some cases, chiefly through advertising in the horticultural press,
+very lucrative concerns have been established.
+
+Ornamental flowering trees and shrubs constitute another feature of
+modern gardening. These are grown and imported by thousands chiefly for
+their sprays of blossom or foliage, and for planting in large or small
+gardens, public parks, &c., for landscape effect. Indeed there is
+scarcely an easily grown plant from the northern or southern temperate
+zones that does not now find a place in the nursery or garden, provided
+it is sufficiently attractive to sell for its flowers, foliage or
+appearance.
+
+_Conditions of the Fruit and Flower growing Industries._--As regards
+open-air fruit-growing, the outlook for new ventures is perhaps brighter
+than in the hothouse industry, not--as Mr Bear has pointed out--because
+the area of fruit land in England is too small, but because the level of
+efficiency, from the selection of varieties to the packing and marketing
+of the produce, is very much lower in the former than in the latter
+branch of enterprise. In other words, whereas the practice of the
+majority of hothouse nurserymen is so skilled, so up-to-date, and so
+entirely under high pressure that a new competitor, however well
+trained, will find it difficult to rise above mediocrity, the converse
+is true of open-air fruit-growers. Many, and an increasing proportion,
+of the latter are thoroughly efficient in all branches of their
+business, and are in possession of plantations of the best market
+varieties of fruit, well cultivated, pruned and otherwise managed. But
+the extent of fruit plantations completely up to the mark in relation to
+varieties and treatment of trees and bushes, and in connexion with which
+the packing and marketing of the produce are equally satisfactory, is
+small in proportion to the total fruit area of the country. Information
+concerning the best treatment of fruit trees has spread widely in recent
+years, and old plantations, as a rule, suffer from the neglect or errors
+of the past, however skilful their present holders may be. Although the
+majority of professional market fruit-growers may be well up to the
+standard in skill, there are numerous contributors to the fruit supply
+who are either ignorant of the best methods of cultivation and marketing
+or careless in their application. The bad condition of the great
+majority of farm orchards is notorious, and many landowners, farmers and
+amateur gardeners who have planted fruit on a more or less extensive
+scale have mismanaged their undertakings. For these reasons new growers
+of open-air fruit for market have opportunities of succeeding by means
+of superiority to the majority of those with whom they will compete,
+provided that they possess the requisite knowledge, energy and capital.
+It has been asserted on sound authority that there is no chance of
+success for fruit-growers except in districts favourable as regards
+soil, climate and nearness to a railway or a good market; and, even
+under these conditions, only for men who have had experience in the
+industry and are prepared to devote their unremitting attention to it.
+Most important is it to a beginner that he should ascertain the
+varieties of fruit that flourish best in his particular district.
+Certain kinds seem to do well or fairly well in all parts of the
+country; others, whilst heavy croppers in some localities, are often
+unsatisfactory in others.
+
+As has been intimated, there is probably in England less room for
+expansion of fruit culture under glass than in the open. The large
+increase of glass-houses in modern times appears to have brought the
+supply of hothouse produce, even at greatly reduced prices, at least up
+to the level of the demand; and as most nurserymen continue to extend
+their expanse of glass, the prospect for new competitors is not a bright
+one. Moreover, the vast scale upon which some of the growers conduct the
+hothouse industry puts small producers at a great disadvantage, not only
+because the extensive producers can grow grapes and other fruit more
+economically than small growers--with the possible exception of those
+who do all or nearly all their own work--but also, and still more,
+because the former have greater advantages in transporting and marketing
+their fruit. There has, in recent years, been a much greater fall in the
+prices of hothouse than of open-air fruit, especially under the existing
+system of distribution, which involves the payment by consumers of 50 to
+100% more in prices than growers receive. The best openings for new
+nurseries are probably not where they are now to be found in large
+groups, and especially not in the neighbourhood of London, but in
+suitable spots near the great centres of population in the Midlands and
+the North, or big towns elsewhere not already well supplied with
+nurseries. By such a selection of a locality the beginner may build up a
+retail trade in hothouse fruit, or at least a trade with local
+fruiterers and grocers, thus avoiding railway charges and salesmen's
+commissions to a great extent, though it may often be advantageous to
+send certain kinds of produce to a distant market. Above all, a man who
+has no knowledge of the hothouse industry should avoid embarking his
+capital in it, trusting himself in the hands of a foreman, as experience
+shows that such a venture usually leads to disaster. Some years of
+training in different nurseries are desirable for any young man who is
+desirous of becoming a grower of hothouse fruits or flowers.
+
+There can be no doubt that flower-growing is greatly extending in
+England, and that competition among home growers is becoming more
+severe. Foreign supplies of flowers have increased, but not nearly as
+greatly in proportion as home supplies, and it seems clear that home
+growers have gained ground in relation to their foreign rivals, except
+with respect to flowers for the growth of which foreigners have
+extraordinary natural advantages. There seems some danger of the home
+culture of the narcissus being over-done, and the florists'
+chrysanthemum appears to be produced in excess of the demand. Again, in
+the production of violets the warm and sunny South of France has an
+advantage not possessed by England, whilst Holland, likewise for
+climatic reasons, maintains her hold upon the hyacinth and tulip trade.
+Whether the production of flowers as a whole is gaining ground upon the
+demand or not is a difficult question to answer. It is true that the
+prices of flowers have fallen generally; but production, at any rate
+under glass, has been cheapened, and if a fair profit can be obtained,
+the fall in prices, without which the existing consumption of flowers
+would be impossible, does not necessarily imply over-production. There
+is some difference of opinion among growers upon this point; but nearly
+all agree that profits are now so small that production on a large scale
+is necessary to provide a fair income. Industrial flower-growing affords
+such a wide scope for the exercise of superior skill, industry and
+alertness, that it is not surprising to find some who are engaged in it
+doing remarkably well to all appearance, while others are struggling on
+and hardly paying their way. That a man with only a little capital,
+starting in a small way, has many disadvantages is certain; also, that
+his chance of saving money and extending his business quickly is much
+smaller than it was. To the casual looker-on, who knows nothing of the
+drudgery of the industry, flower-growing seems a delightful method of
+getting a living. That it is an entrancing pursuit there is no doubt;
+but it is equally true that it is a very arduous one, requiring careful
+forethought, ceaseless attention and abundant energy. Fortunately for
+those who might be tempted, without any knowledge of the industry, to
+embark capital in it, flower-growing, if at all comprehensive in scope,
+so obviously requires a varied and extensive technical knowledge,
+combined with good commercial ability, that any one can see that a
+thorough training is necessary to a man who intends to adopt it as a
+business, especially if hothouse flowers are to be produced.
+
+  The market for fruit, and more especially for flowers, is a fickle
+  one, and there is nearly always some uncertainty as to the course of
+  prices. The perishable nature of soft fruit and cut flowers renders
+  the markets very sensitive to anything in the nature of a glut, the
+  occurrence of which is usually attended with disastrous results to
+  producers. Foreign competition, moreover, has constantly to be faced,
+  and it is likely to increase rather than diminish. French growers have
+  a great advantage over the open-air cultivators of England, for the
+  climate enables them to get their produce into the markets early in
+  the season, when the highest prices are obtainable. The geographical
+  advantage which France enjoys in being so near to England is, however,
+  considerably discounted by the increasing facilities for cold storage
+  in transit, both by rail and sea. The development of such facilities
+  permits of the retail sale in England of luscious fruit as fresh and
+  attractive as when it was gathered beneath the sunny skies of
+  California. In the case of flowers, fashion is an element not to be
+  ignored. Flowers much in request in one season may meet with very
+  little demand in another, and it is difficult for the producer to
+  anticipate the changes which caprice may dictate. Even for the same
+  kind of flower the requirements are very uncertain, and the white
+  blossom which is all the rage in one season may be discarded in favour
+  of one of another colour in the next. The sale of fresh flowers for
+  church decoration at Christmas and Easter has reached enormous
+  dimensions. The irregularity in the date of the festival, however,
+  causes some inconvenience to growers. If it falls very early the great
+  bulk of suitable flowers may not be sufficiently forward for sale,
+  whilst a late Easter may find the season too far advanced. The trade
+  in cut flowers, therefore, is generally attended by uncertainty, and
+  often by anxiety.     (W. FR.; J. WS.)
+
+
+UNITED STATES
+
+In the United States horticulture and market gardening have now assumed
+immense proportions. In a country of over 3,000,000 sq. m., stretching
+from the Atlantic to the Pacific on the one hand, and from the Gulf of
+Mexico to the great northern lakes and the Dominion of Canada on the
+other, a great variation of climatic conditions is not unnatural. From a
+horticultural point of view there are practically two well-defined
+regions: (1) that to the east of the Rocky Mountains across to the
+Atlantic, where the climate is more like that of eastern Asia than of
+western Europe so far as rainfall, temperature and seasonable conditions
+are concerned; (2) that to the west of the Rockies, known as the Pacific
+coast region, where the climate is somewhat similar to that of western
+Europe. It may be added that in the northern states--in Washington,
+Montana, North Dakota, Minnesota, Wisconsin, &c.--the winters are often
+very severe, while the southern states practically enjoy a temperature
+somewhat similar to that of the Riviera. Indeed the range of temperature
+between the extreme northern states and the extreme southern may vary as
+much as 120 deg. F. The great aim of American gardeners, therefore, has
+been to find out or to produce the kinds of fruits, flowers and
+vegetables that are likely to flourish in different parts of this
+immense country.
+
+_Fruit Culture._--There is probably no country in the world where so
+many different kinds of fruit can be grown with advantage to the nation
+as in the United States. In the temperate regions apples, pears and
+plums are largely grown, and orchards of these are chiefly to be found
+in the states of New York, Massachusetts, Pennsylvania, Michigan,
+Missouri, Colorado, and also in northern Texas, Arkansas and N.
+California. To these may be added cranberries and quinces, which are
+chiefly grown in the New England states. The quinces are not a crop of
+first-rate importance, but as much as 800,000 bushels of cranberries are
+grown each year. The peach orchards are assuming great proportions, and
+are chiefly to be found in Georgia and Texas, while grapes are grown
+throughout the Republic from east to west in all favourable localities.
+Oranges, lemons and citrons are more or less extensively grown in
+Florida and California, and in these regions what are known as Japanese
+or "Kelsey" plums (forms of _Prunus triflora_) are also grown as
+marketable crops. Pomegranates are not yet largely grown, but it is
+possible their culture will develop in southern Texas and Louisiana,
+where the climate is tempered by the waters of the Gulf of Mexico.
+Tomatoes are grown in most parts of the country so easily that there is
+frequently a glut; while the strawberry region extends from Florida to
+Virginia, Pennsylvania and other states--thus securing a natural
+succession from south to north for the various great market centres.
+
+Of the fruits mentioned apples are undoubtedly the most important. Not
+only are the American people themselves supplied with fresh fruit, but
+immense quantities are exported to Europe--Great Britain alone absorbing
+as much as 1,430,000 cwt. in 1908. The varieties originally grown were
+of course those taken or introduced from Europe by the early settlers.
+Since the middle of the 19th century great changes have been brought
+about, and the varieties mostly cultivated now are distinctly American.
+They have been raised by crossing and intercrossing the most suitable
+European forms with others since imported from Russia. In the extreme
+northern states indeed, where it is essential to have apple trees that
+will stand the severest winters, the Russian varieties crossed with the
+berry crab of eastern Europe (_Pyrus baccata_) have produced a race
+eminently suited to that particular region. The individual fruits are
+not very large, but the trees are remarkably hardy. Farther south larger
+fruited varieties are grown, and among these may be noted Baldwins,
+Newton pippins, Spitzenbergs and Rhode Island greening. Apple orchards
+are numerous in the State of New York, where it is estimated that over
+100,000 acres are devoted to them. In the hilly regions of Missouri,
+Arkansas and Colorado there are also great plantations of apples. The
+trees, however, are grown on different principles from those in New York
+State. In the latter state apple trees with ordinary care live to more
+than 100 years of age and produce great crops; in the other states,
+however, an apple tree is said to be middle-aged at 20, decrepit at 30
+and practically useless at 40 years of age. They possess the advantage,
+however, of bearing early and heavily.
+
+Until the introduction of the cold-storage system, about the year 1880,
+America could hardly be regarded as a commercial fruit-growing country.
+Since then, however, owing to the great improvements made in railway
+refrigerating vans and storage houses, immense quantities of fruit can
+be despatched in good condition to any part of the world; or they can be
+kept at home in safety until such time as the markets of Chicago, New
+York, Boston, Baltimore, Philadelphia, &c., are considered favourable
+for their reception.
+
+Apple trees are planted at distances varying from 25 ft. to 30 ft. apart
+in the middle western states, to 40 ft. to 50 ft. apart in New York
+State. Here and there, however, in some of the very best orchards the
+trees are planted 60 ft. apart every way. Each tree thus has a chance to
+develop to its utmost limits, and as air and light reach it better, a
+far larger fruit-bearing surface is secured. Actual experience has shown
+that trees planted at 60 ft. apart--about 28 to the acre--produce more
+fruit by 43 bushels than trees at 30 ft. apart--i.e. about 48 to the
+acre.
+
+Until recent years pruning as known to English and French gardeners was
+practically unknown. There was indeed no great necessity for it, as the
+trees, not being cramped for space, threw their branches outwards and
+upwards, and thus rarely become overcrowded. When practised, however,
+the operation could scarcely be called pruning; lopping or trimming
+would be more accurate descriptions.
+
+Apple orchards are not immune from insect pests and fungoid diseases,
+and an enormous business is now done in spraying machines and various
+insecticides. It pays to spray the trees, and figures have been given to
+show that orchards that have been sprayed four times have produced an
+average income of L211 per acre against L103 per acre from unsprayed
+orchards.
+
+The spring frosts are also troublesome, and in the Colorado and other
+orchards the process known as "smudging" is now adopted to save the
+crops. This consists in placing 20 or 30, or even more, iron or tin pots
+to an acre, each pot containing wooden chips soaked in tar (or pitch)
+mixed with kerosene. Whenever the thermometer shows 3 or 4 degrees of
+frost the smudge-pots are lighted. A dense white smoke then arises and
+is diffused throughout the orchards, enveloping the blossoming heads of
+the trees in a dense cloud. This prevents the frost from killing the
+tender pistils in the blossoms, and when several smudge-pots are alight
+at the same time the temperature of the orchard is raised two or three
+degrees. This work has generally to be done between 3 and 5 A.M., and
+the growers naturally have an anxious time until all danger is over. The
+failure to attend to smudging, even on one occasion, may result in the
+loss of the entire crop of plums, apples or pears.
+
+Next to apples perhaps peaches are the most important fruit crop. The
+industry is chiefly carried on in Georgia, Texas and S. Carolina, and on
+a smaller scale in some of the adjoining states. Peaches thus flourish
+in regions that are quite unsuitable for apples or pears. In many
+orchards in Georgia, where over 3,000,000 acres have been planted, there
+are as many as 100,000 peach trees; while some of the large fruit
+companies grow as many as 365,000. In one place in West Virginia there
+is, however, a peach orchard containing 175,000 trees, and in Missouri
+another company has 3 sq. m. devoted to peach culture. As a rule the
+crops do well. Sometimes, however, a disease known as the "yellows"
+makes sad havoc amongst them, and scarcely a fruit is picked in an
+orchard which early in the season gave promise of a magnificent crop.
+
+Plums are an important crop in many states. Besides the European
+varieties and those that have been raised by crossing with American
+forms, there is now a growing trade done in Japanese plums. The largest
+of these is popularly known as "Kelseys," named after John Kelsey, who
+raised the first fruit in 1876 from trees brought to California in 1870.
+Sometimes the fruits are 3 in. in diameter, and like most of the
+Japanese varieties are more heart-shaped and pointed than plums of
+European origin. One apparent drawback to the Kelsey plum is its
+irregularity in ripening. It has been known in some years to be quite
+ripe in June, while in others the fruits are still green in October.
+
+Pears are much grown in such states as Massachusetts, New York,
+Pennsylvania, Missouri and California; while bush fruits like currants,
+gooseberries and raspberries find large spaces devoted in most of the
+middle and northern states. Naturally a good deal of crossing and
+intercrossing has taken place amongst the European and American forms of
+these fruits, but so far as gooseberries are concerned no great advance
+seems to have been made in securing varieties capable of resisting the
+devastating gooseberry mildew.
+
+Other fruits of more or less commercial value are oranges, lemons and
+citrons, chiefly in Florida. Lemons are practically a necessity to the
+American people, owing to the heat of the summers, when cool and
+refreshing drinks with an agreeable acidulous taste are in great demand.
+The pomelo (grape-fruit) is a kind of lemon with a thicker rind and a
+more acid flavour. At one time its culture was confined to Florida, but
+of recent years it has found its way into Californian orchards.
+Notwithstanding the prevailing mildness of the climate in both
+California and Florida, the crops of oranges, lemons, citrons, &c., are
+sometimes severely injured by frosts when in blossom.
+
+Other fruits likely to be heard of in the future are the kaki or
+persimmon, the loquat, which is already grown in Louisiana, as well as
+the pomegranate.
+
+Great aid and encouragement are given by the government to the progress
+of American fruit-growing, and by the experiments that are being
+constantly carried out and tabulated at Cornell University and by the
+U.S.A. department of agriculture.
+
+_Flower Culture._--So far as flowers are concerned there appears to be
+little difference between the kinds of plants grown in the United States
+and in England, France, Belgium, Germany, Holland, &c. Indeed there is a
+great interchange of new varieties of plants between Europe and America,
+and modifications in systems of culture are being gradually introduced
+from one side of the Atlantic to the other. The building of greenhouses
+for commercial purposes is perhaps on a somewhat different scale from
+that in England, but there are probably no extensive areas of glass such
+as are to be seen north of London from Enfield Highway to Broxburne. Hot
+water apparatus differs merely in detail, although most of the boilers
+used resemble those on the continent of Europe rather than in England.
+Great business is done in bulbs--mostly imported from Holland--stove and
+greenhouse plants, hardy perennials, orchids, ferns of the "fancy" and
+"dagger" types of Nephrolepis, and in carnations and roses. Amongst the
+latter thousands of such varieties as Beauty, Liberty, Killarney,
+Richmond and Bride are grown, and realize good prices as a rule in the
+markets. Carnations of the winter-flowering or "perpetual" type have
+long been grown in America, and enormous prices have been given for
+individual plants on certain occasions, rivalling the fancy prices paid
+in England for certain orchids. The American system of carnation-growing
+has quite captivated English cultivators, and new varieties are being
+constantly raised in both countries. Chrysanthemums are another great
+feature of American florists, and sometimes during the winter season a
+speculative grower will send a living specimen to one of the London
+exhibitions in the hope of booking large orders for cuttings of it later
+on. Sweet peas, dahlias, lilies of the valley, arum lilies and indeed
+every flower that is popular in England is equally popular in America,
+and consequently is largely grown.
+
+  _Vegetables._--So far as these are concerned, potatoes, cabbages,
+  cauliflowers, beans of all kinds, cucumbers, tomatoes (already
+  referred to under fruits), musk-melons, lettuces, radishes, endives,
+  carrots, &c.; are naturally grown in great quantities, not only in the
+  open air, but also under glass. The French system of intensive
+  cultivation as practised on hot beds of manure round Paris is
+  practically unknown at present. In the southern states there would be
+  no necessity to practise it, but in the northern ones it is likely to
+  attract attention.     (J. Ws.)
+
+
+FOOTNOTE:
+
+  [1] _Jour. Roy. Agric. Soc._, 1899.
+
+
+
+
+FRUMENTIUS (c. 300-c. 360), the founder of the Abyssinian church,
+traditionally identified in Abyssinian literature with Abba Salama or
+Father of Peace (but see ETHIOPIA), was a native of Phoenicia. According
+to the 4th-century historian Rufinus (x. 9), who gives Aedesius himself
+as his authority, a certain Tyrian, Meropius, accompanied by his kinsmen
+Frumentius and Aedesius, set out on an expedition to "India," but fell
+into the hands of Ethiopians on the shore of the Red Sea and, with his
+ship's crew, was put to death. The two young men were taken to the king
+at Axum, where they were well treated and in time obtained great
+influence. With the help of Christian merchants who visited the country
+Frumentius gave Christianity a firm footing, which was strengthened when
+in 326 he was consecrated bishop by Athanasius of Alexandria, who in his
+_Epistola ad Constantinum_ mentions the consecration, and gives some
+details of the history of Frumentius's mission. Later witnesses speak of
+his fidelity to the homoousian during the Arian controversies. Aedesius
+returned to Tyre, where he was ordained presbyter.
+
+
+
+
+FRUNDSBERG, GEORG VON (1473-1528), German soldier, was born at
+Mindelheim on the 24th of September 1473. He fought for the German king
+Maximilian I. against the Swiss in 1499, and in the same year was among
+the imperial troops sent to assist Ludovico Sforza, duke of Milan,
+against the French. Still serving Maximilian, he took part in 1504 in
+the war over the succession to the duchy of Bavaria-Landshut, and
+afterwards fought in the Netherlands. Convinced of the necessity of a
+native body of trained infantry Frundsberg assisted Maximilian to
+organize the _Landsknechte_ (q.v.), and subsequently at the head of
+bands of these formidable troops he was of great service to the Empire
+and the Habsburgs. In 1509 he shared in the war against Venice, winning
+fame for himself and his men; and after a short visit to Germany
+returned to Italy, where in 1513 and 1514 he gained fresh laurels by his
+enterprises against the Venetians and the French. Peace being made, he
+returned to Germany, and at the head of the infantry of the Swabian
+league assisted to drive Ulrich of Wurttemberg from his duchy in 1519.
+At the diet of Worms in 1521 he spoke words of encouragement to Luther,
+and when the struggle between France and the Empire was renewed he took
+part in the invasion of Picardy, and then proceeding to Italy brought
+the greater part of Lombardy under the influence of Charles V. through
+his victory at Bicocca in April 1522. He was partly responsible for the
+great victory over the French at Pavia in February 1525, and, returning
+to Germany, he assisted to suppress the Peasant revolt, using on this
+occasion, however, diplomacy as well as force. When the war in Italy was
+renewed Frundsberg raised an army at his own expense, and skilfully
+surmounting many difficulties, joined the constable de Bourbon near
+Piacenza and marched towards Rome. Before he reached the city, however,
+his unpaid troops showed signs of mutiny, and their leader, stricken
+with illness and unable to pacify them, gave up his command. Returning
+to Germany, he died at Mindelheim on the 20th of August 1528. He was a
+capable and chivalrous soldier, and a devoted servant of the Habsburgs.
+His son Caspar (1500-1536) and his grandson Georg (d. 1586) were both
+soldiers of some distinction. With the latter's death the family became
+extinct.
+
+  See Adam Reissner, _Historia Herrn Georgs und Herrn Kaspars von
+  Frundsberg_ (Frankfort, 1568). A German translation of this work was
+  published at Frankfort in 1572. F.W. Barthold, _Georg von Frundsberg_
+  (Hamburg, 1833); J. Heilmann, _Kriegsgeschichte von Bayern, Franken,
+  Pfalz und Schwaben_ (Munich, 1868).
+
+
+
+
+
+FRUSTUM (Latin for a "piece broken off"), a term in geometry for the
+part of a solid figure, such as a cone or pyramid, cut off by a plane
+parallel to the base, or lying between two parallel planes; and hence in
+architecture a name given to the drum of a column.
+
+
+
+
+FRUYTIERS, PHILIP (1627-1666), Flemish painter and engraver, was a pupil
+of the Jesuits' college at Antwerp in 1627, and entered the Antwerp gild
+of painters without a fee in 1631. He is described in the register of
+that institution as "illuminator, painter and engraver." The current
+account of his life is "that he worked exclusively in water colours, yet
+was so remarkable in this branch of his art for arrangement, drawing,
+and especially for force and clearness of colour, as to excite the
+admiration of Rubens, whom he portrayed with all his family." The truth
+is that he was an artist of the most versatile talents, as may be judged
+from the fact that in 1646 he executed an Assumption with figures of
+life size, and four smaller pictures in oil, for the church of St
+Jacques at Antwerp, for which he received the considerable sum of 1150
+florins. Unhappily no undoubted production of his hand has been
+preserved. All that we can point to with certainty is a series of etched
+plates, chiefly portraits, which are acknowledged to have been
+powerfully and skilfully handled. If, however, we search the portfolios
+of art collections on the European continent, we sometimes stumble upon
+miniatures on vellum, drawn with great talent and coloured with
+extraordinary brilliancy. In form they quite recall the works of Rubens,
+and these, it may be, are the work of Philip Fruytiers.
+
+
+
+
+FRY, the name of a well-known English Quaker family, originally living
+in Wiltshire. About the middle of the 18th century JOSEPH FRY
+(1728-1787), a doctor, settled in Bristol, where he acquired a large
+practice, but eventually abandoned medicine for commerce. He became
+interested in china-making, soap-boiling and type-founding businesses in
+Bristol, and in a chemical works at Battersea, all of which ventures
+proved very profitable. The type-founding business was subsequently
+removed to London and conducted by his son Edmund. Joseph Fry, however,
+is best remembered as the founder of the great Bristol firm of J.S. Fry
+& Sons, chocolate manufacturers. He purchased the chocolate-making
+patent of William Churchman and on it laid the foundations of the
+present large business. After his death the Bristol chocolate factory
+was carried on with increasing success by his widow and by his son,
+JOSEPH STORRS FRY (1767-1835).
+
+In 1795 a new and larger factory was built in Union Street, Bristol,
+which still forms the centre of the firm's premises, and in 1798 a
+Watt's steam-engine was purchased and the cocoa-beans ground by steam.
+On the death of Joseph Storrs Fry his three sons, Joseph (1795-1879),
+Francis, and Richard (1807-1878) became partners in the firm, the
+control being mainly in the hands of FRANCIS FRY (1803-1886). Francis
+Fry was in every way a remarkable character. The development of the
+business to its modern enormous proportion was chiefly his work, but
+this did not exhaust his activities. He took a principal part in the
+introduction of railways to the west of England, and in 1852 drew up a
+scheme for a general English railway parcel service. He was an ardent
+bibliographer, taking a special interest in early English Bibles, of
+which he made in the course of a long life a large and striking
+collection, and of the most celebrated of which he published facsimiles
+with bibliographical notes. Francis Fry died in 1886, and his son
+Francis J. Fry and nephew Joseph Storrs Fry carried on the business,
+which in 1896 was for family reasons converted into a private limited
+company, Joseph Storrs Fry being chairman and all the directors members
+of the Fry family.
+
+
+
+
+FRY, SIR EDWARD (1827-   ), English judge, second son of Joseph Fry
+(1795-1879), was born at Bristol on the 4th of November 1827, and
+educated at University College, London, and London University. He was
+called to the bar in 1854 and was made a Q.C. in 1869, practising in the
+rolls court and becoming recognized as a leading equity lawyer. In 1877
+he was raised to the bench and knighted. As chancery judge he will be
+remembered for his careful interpretations and elucidations of the
+Judicature Acts, then first coming into operation. In 1883 he was made a
+lord justice of appeal, but resigned in 1892; and subsequently his
+knowledge of equity and talents for arbitration were utilized by the
+British government from time to time in various special directions,
+particularly as chairman of many commissions. He was also one of the
+British representatives at the Paris North Sea Inquiry Commission
+(1905), and was appointed a member of the Hague Permanent Arbitration
+Court. He wrote _A Treatise on the Specific Performance of Public
+Contracts_ (London, 1858, and many subsequent editions).
+
+
+
+
+FRY, ELIZABETH (1780-1845), English philanthropist, and, after Howard,
+the chief promoter of prison reform in Europe, was born in Norwich on
+the 21st of May 1780. Her father, John Gurney, afterwards of Earlham
+Hall, a wealthy merchant and banker, represented an old family which for
+some generations had belonged to the Society of Friends. While still a
+girl she gave many indications of the benevolence of disposition,
+clearness and independence of judgment, and strength of purpose, for
+which she was afterwards so distinguished; but it was not until after
+she had entered her eighteenth year that her religion assumed a decided
+character, and that she was induced, under the preaching of the American
+Quaker, William Savery, to become an earnest and enthusiastic though
+never fanatical "Friend." In August 1800 she became the wife of Joseph
+Fry, a London merchant.
+
+Amid increasing family cares she was unwearied in her attention to the
+poor and the neglected of her neighbourhood; and in 1811 she was
+acknowledged by her co-religionists as a "minister," an honour and
+responsibility for which she was undoubtedly qualified, not only by
+vigour of intelligence and warmth of heart, but also by an altogether
+unusual faculty of clear, fluent and persuasive speech. Although she had
+made several visits to Newgate prison as early as February 1813, it was
+not until nearly four years afterwards that the great public work of her
+life may be said to have begun. The association for the Improvement of
+the Female Prisoners in Newgate was formed in April 1817. Its aim was
+the much-needed establishment of some of what are now regarded as the
+first principles of prison discipline, such as entire separation of the
+sexes, classification of criminals, female supervision for the women,
+and adequate provision for their religious and secular instruction, as
+also for their useful employment. The ameliorations effected by this
+association, and largely by the personal exertions of Mrs Fry, soon
+became obvious, and led to a rapid extension of similar methods to other
+places. In 1818 she, along with her brother, visited the prisons of
+Scotland and the north of England; and the publication (1819) of the
+notes of this tour, as also the cordial recognition of the value of her
+work by the House of Commons committee on the prisons of the metropolis,
+led to a great increase of her correspondence, which now extended to
+Italy, Denmark and Russia, as well as to all parts of the United
+Kingdom. Through a visit to Ireland, which she made in 1827, she was led
+to direct her attention to other houses of detention besides prisons;
+and her observations resulted in many important improvements in the
+British hospital system, and in the treatment of the insane. In 1838 she
+visited France, and besides conferring with many of the leading prison
+officials, she personally visited most of the houses of detention in
+Paris, as well as in Rouen, Caen and some other places. In the following
+year she obtained an official permission to visit all the prisons in
+that country; and her tour, which extended from Boulogne and Abbeville
+to Toulouse and Marseilles, resulted in a report which was presented to
+the minister of the interior and the prefect of police. Before returning
+to England she had included Geneva, Zurich, Stuttgart and
+Frankfort-on-Main in her inspection. The summer of 1840 found her
+travelling through Belgium, Holland and Prussia on the same mission; and
+in 1841 she also visited Copenhagen. In 1842, through failing health,
+Mrs Fry was compelled to forgo her plans for a still more widely
+extended activity, but had the satisfaction of hearing from almost every
+quarter of Europe that the authorities were giving increased practical
+effect to her suggestions. In 1844 she was seized with a lingering
+illness, of which she died on the 12th of October 1845. She was
+survived by a numerous family, the youngest of whom was born in 1822.
+
+Two interesting volumes of _Memoirs, with Extracts from her Journals and
+Letters_, edited by two of her daughters, were published in 1847. See
+also _Elizabeth Fry_, by G. King Lewis (1910).
+
+
+
+
+FRYXELL, ANDERS (1795-1881), Swedish historian, was born at Hesselskog,
+Dalsland, Sweden, on the 7th of February 1795. He was educated at
+Upsala, took holy orders in 1820, was made a doctor of philosophy in
+1821, and in 1823 began to publish the great work of his life, the
+_Stories from Swedish History_. He did not bring this labour to a close
+until, fifty-six years later, he published the forty-sixth and crowning
+volume of his vast enterprise. Fryxell, as a historian, appealed to
+every class by the picturesqueness of his style and the breadth of his
+research; he had the gift of awakening to an extraordinary degree the
+national sense in his readers. In 1824 he published his _Swedish
+Grammar_, which was long without a rival. In 1833 he received the title
+of professor, and in 1835 he was appointed to the incumbency of Sunne,
+in the diocese of Karlstad, where he resided for the remainder of his
+life. In 1840 he was elected to the Swedish Academy in succession to the
+poet Wallin (1779-1839). In 1847 Fryxell received from his bishop
+permission to withdraw from all the services of the Church, that he
+might devote himself without interruption to historical investigation.
+Among his numerous minor writings are prominent his _Characteristics of
+Sweden between 1592 and 1600_ (1830), his _Origins of the Inaccuracy
+with which the History of Sweden in Catholic Times has been Treated_
+(1847), and his _Contributions to the Literary History of Sweden_. It is
+now beginning to be seen that the abundant labours of Fryxell were
+rather of a popular than of a scientific order, and although their
+influence during his lifetime was unbounded, it is only fair to later
+and exacter historians to admit that they threaten to become obsolete in
+more than one direction. On the 21st of March 1881 Anders Fryxell died
+at Stockholm, and in 1884 his daughter Eva Fryxell (born 1829) published
+from his MS. an interesting _History of My History_, which was really a
+literary autobiography and displays the persistency and tirelessness of
+his industry.     (E. G.)
+
+
+
+
+FUAD PASHA (1815-1869), Turkish statesman, was the son of the
+distinguished poet Kecheji-zade Izzet Molla. He was educated at the
+medical school and was at first an army surgeon. About 1836 he entered
+the civil service as an official of the foreign ministry. He became
+secretary of the embassy in London; was employed on special missions in
+the principalities and at St Petersburg (1848), and was sent to Egypt as
+special commissioner in 1851. In that year he became minister for
+foreign affairs, a post to which he was appointed also on four
+subsequent occasions and which he held at the time of his death. During
+the Crimean War he commanded the troops on the Greek frontier and
+distinguished himself by his bravery. He was Turkish delegate at the
+Paris conference of 1856; was charged with a mission to Syria in 1860;
+grand vizier in 1860 and 1861, and also minister of war. He accompanied
+the sultan Abd-ul-Aziz on his journey to Egypt and Europe, when the
+freedom of the city of London was conferred on him. He died at Nice
+(whither he had been ordered for his health) in 1869. Fuad was renowned
+for his boldness and promptness of decision, as well as for his ready
+wit and his many bons mots. Generally regarded as the partisan of a
+pro-English policy, he rendered most valuable service to his country by
+his able management of the foreign relations of Turkey, and not least by
+his efficacious settlement of affairs in Syria after the massacres of
+1860.
+
+
+
+
+FUCHOW, FU-CHAU, FOOCHOW, a city of China, capital of the province of
+Fu-kien, and one of the principal ports open to foreign commerce. In the
+local dialect it is called Hokchiu. It is situated on the river Min,
+about 35 m. from the sea, in 26 deg. 5' N. and 119 deg. 20' E., 140 m.
+N. of Amoy and 280 S. of Hang-chow. The city proper, lying nearly 3 m.
+from the north bank of the river, is surrounded by a wall about 30 ft.
+high and 12 ft. thick, which makes a circuit of upwards of 5 m. and is
+pierced by seven gateways surrounded by tall fantastic watch-towers.
+The whole district between the city and the river, the island of
+Nantai, and the southern banks of the Min are occupied by extensive
+suburbs; and the river itself bears a large floating population.
+Communication from bank to bank is afforded by a long stone bridge
+supported by forty solid stone piers in its northern section and by nine
+in its southern. The most remarkable establishment of Fuchow is the
+arsenal situated about 3 m. down the stream at Pagoda Island, where the
+sea-going vessels usually anchor. It was founded in 1867, and is
+conducted under the direction of French engineers according to European
+methods. In 1870 it employed about 1000 workmen besides fifty European
+superintendents, and between that date and 1880 it turned out about 20
+or 30 small gunboats. In 1884 it was partially destroyed by the French
+fleet, and for a number of years the workshops and machinery were
+allowed to stand idle and go to decay. On the 1st of August 1895 an
+attack was made on the English mission near the city of Ku-chang, 120 m.
+west of Fuchow, on which occasion nine missionaries, of whom eight were
+ladies, were massacred. The port was opened to European commerce in
+1842; and in 1853 the firm of Russell and Co. shipped the first cargoes
+of tea from Fuchow to Europe and America. The total trade in foreign
+vessels in 1876 was imports to the value of L1,531,617, and exports to
+the value of L3,330,489. In 1904 the imports amounted to L1,440,351, and
+the exports to L1,034,436. The number of vessels that entered in 1876
+was 275, and of these 211 were British, 27 German, 11 Danish and 9
+American. While in 1904, 480 vessels entered the port, 216 of which were
+British. A large trade is carried on by the native merchants in timber,
+paper, woollen and cotton goods, oranges and olives; but the foreign
+houses mainly confine themselves to opium and tea. Commercial
+intercourse with Australia and New Zealand is on the increase. The
+principal imports, besides opium, are shirtings, T-cloths, lead and tin,
+medicines, rice, tobacco, and beans and peas. Two steamboat lines afford
+regular communication with Hong-Kong twice a month. The town is the seat
+of several important missions, of which the first was founded in 1846.
+That supported by the American board had in 1876 issued 1,3000,000
+copies of Chinese books and tracts.
+
+
+
+
+FUCHS, JOHANN NEPOMUK VON (1774-1856), German chemist and mineralogist,
+was born at Mattenzell, near Brennberg in the Bavarian Forest, on the
+15th of May 1774. In 1807 he became professor of chemistry and
+mineralogy at the university of Landshut, and in 1823 conservator of the
+mineralogical collections at Munich, where he was appointed professor of
+mineralogy three years later, on the removal thither of the university
+of Landshut. He retired in 1852, was ennobled by the king of Bavaria in
+1854, and died at Munich on the 5th of March 1856. His name is chiefly
+known for his mineralogical observations and for his work on soluble
+glass.
+
+  His collected works, including _Uber den Einfluss der Chemie und
+  Mineralogie_ (1824), _Die Naturgeschichte des Mineralreichs_ (1842),
+  _Uber die Theorien der Erde_ (1844), were published at Munich in 1856.
+
+
+
+
+FUCHS, LEONHARD (1501-1566), German physician and botanist, was born at
+Wembdingen in Bavaria on the 17th of January 1501. He attended school at
+Heilbronn and Erfurt, and in 1521 graduated at the university of
+Ingolstadt. About the same time he espoused the doctrines of the
+Reformation. Having in 1524 received his diploma as doctor of medicine,
+he practised for two years in Munich. He became in 1526 professor of
+medicine at Ingolstadt, and in 1528 physician to the margrave of
+Anspach. In Anspach he was the means of saving the lives of many during
+the epidemic locally known as the "English sweating-sickness." By the
+duke of Wurttemberg he was, in 1535, appointed to the professorship of
+medicine at the university of Tubingen, a post held by him till his
+death on the 10th of May 1566. Fuchs was an advocate of the Galenic
+school of medicine, and published several Latin translations of
+treatises by its founder and by Hippocrates. But his most important
+publication was _De historia stirpium commentarii insignes_ (Basel,
+1542), a work illustrated with more than five hundred excellent outline
+illustrations, including figures of the common foxglove and of another
+species of the genus _Digitalis_, which was so named by him.
+
+
+
+
+FUCHSIA, so named by Plumier in honour of the botanist Leonhard Fuchs, a
+genus of plants of the natural order Onagraceae, characterized by
+entire, usually opposite leaves, pendent flowers, a funnel-shaped,
+brightly coloured, quadripartite, deciduous calyx, 4 petals, alternating
+with the calycine segments, 8, rarely 10, exserted stamens, a long
+filiform style, an inferior ovary, and fruit, a fleshy ovoid many-seeded
+berry. All the members of the genus, with the exception of the New
+Zealand species, _F. excorticata, F. Colensoi_ and _F. procumbens_, are
+natives of Central and South America--occurring in the interior of
+forests or in damp and shady mountainous situations. The various species
+differ not a little in size as well as in other characters; some, as _F.
+verrucosa_, being dwarf shrubs; others, as _F. arborescens_ and _F.
+apetala_, attaining a height of 12 to 16 ft., and having stems several
+inches in diameter. Plumier, in his _Nova plantarum Americanarum genera_
+(p. 14, tab. 14, Paris, 1703), gave a description of a species of
+fuchsia, the first known, under the name of _Fuchsia triphylla, flore
+coccineo_, and a somewhat conventional outline figure of the same plant
+was published at Amsterdam in 1757 by Burmann. In the _Histoire des
+plantes medicinales_ of the South American traveller Feuillee (p. 64,
+pl. XLVII.), written in 1709-1711, and published by him with his
+_Journal_, Paris, 1725, the name _Thilco_ is applied to a species of
+fuchsia from Chile, which is described, though not evidently so figured,
+as having a pentamerous calyx. The _F. coccinea_ of Alton (fig.) (see
+J.D. Hooker, in _Journal Linnean Soc_., Botany, vol. x. p. 458, 1867),
+the first species of fuchsia cultivated in England, where it was long
+confined to the greenhouse, was brought from South America by Captain
+Firth in 1788 and placed in Kew Gardens. Of this species Mr Lee, a
+nurseryman at Hammersmith, soon afterwards obtained an example, and
+procured from it by means of cuttings several hundred plants, which he
+sold at a guinea each. In 1823 _F. macrostemma_ and _F. gracilis_, and
+during the next two or three years several other species, were
+introduced into England; but it was not until about 1837, or soon after
+florists had acquired _F. fulgens_, that varieties of interest began to
+make their appearance. The numerous hybrid forms now existing are the
+result chiefly of the intercrossing of that or other long-flowered with
+globose-flowered plants. _F. Venus-victrix_, raised by Mr Gulliver,
+gardener to the Rev. S. Marriott of Horsemonden, Kent, and sold in 1822
+to Messrs Cripps, was the earliest white-sepalled fuchsia. The first
+fuchsia with a white corolla was produced about 1853 by Mr Storey. In
+some varieties the blossoms are variegated, and in others they are
+double. There appears to be very little limit to the number of forms to
+be obtained by careful cultivation and selection. To hybridize, the
+flower as soon as it opens is emasculated, and it is then fertilized
+with pollen from some different flower.
+
+[Illustration: _Fuchsia coccinea_. 1, Flower cut open after removal of
+sepals; 2, fruit; 3, floral diagram.]
+
+Ripe seed is sown either in autumn or about February or March in light,
+rich, well-drained mould, and is thinly covered with sandy soil and
+watered. A temperature of 70 deg. to 75 deg. Fahr. has been found
+suitable for raising. The seedlings are pricked off into shallow pots or
+pans, and when 3 in. in height are transferred to 3-in. pots, and are
+then treated the same as plants from cuttings. Fuchsias may be grafted
+as readily as camellias, preferably by the splice or whip method, the
+apex of a young shoot being employed as a scion; but the easiest and
+most usual method of propagation is by cuttings. The most expeditious
+way to procure these is to put plants in heat in January, and to take
+their shoots when 3 in. in length. For summer flowering in England they
+are best made about the end of August, and should be selected from the
+shortest-jointed young wood. They root readily in a compost of loam and
+silver-sand if kept close and sprinkled for a short time. In from two to
+three weeks they may be put into 3-in. pots containing a compost of
+equal parts of rich loam, silver-sand and leaf-mould. They are
+subsequently moved from the frame or bed, first to a warm and shady, and
+then to a more airy part of the greenhouse. In January a little
+artificial heat may be given, to be gradually increased as the days
+lengthen. The side-shoots are generally pruned when they have made three
+or four joints, and for bushy plants the leader is stopped soon after
+the first potting. Care is taken to keep the plants as near the glass as
+possible, and shaded from bright sunshine, also to provide them
+plentifully with water, except at the time of shifting, when the roots
+should be tolerably dry. For the second potting a suitable soil is a
+mixture of well-rotted cow-dung or old hotbed mould with leaf-mould and
+sandy peat, and to promote drainage a little peat-moss may be placed
+immediately over the crocks in the lower part of the pot. Weak liquid
+manure greatly promotes the advance of the plants, and should be
+regularly supplied twice or thrice a week during the flowering season.
+After this, water is gradually withheld from them, and they may be
+placed in the open air to ripen their wood.
+
+Among the more hardy or half-hardy plants for inside borders are
+varieties of the Chilean species, _F. macrostemma_ (or _F.
+magellanica_), a shrub 6 to 12 ft. high with a scarlet calyx, such as
+_F. m. globosa, F. m. gracilis_; one of the most graceful and hardy of
+these, a hybrid _F. riccartoni_, was raised at Riccarton, near
+Edinburgh, in 1830. For inside culture may be mentioned _F. boliviana_
+(Bolivia), 2 to 4 ft. high, with rich crimson flowers with a
+trumpet-shaped tube; _F. corymbiflora_ (Peru), 4 to 6 ft. high, with
+scarlet flowers nearly 2 in. long in long terminal clusters; F. fulgens
+(Mexico), 4 to 6 ft., with drooping apical clusters of scarlet flowers;
+_F. microphylla_ (Central America), with small leaves and small scarlet
+funnel-shaped flowers, the petals deep red; _F. procumbens_ (New
+Zealand), a pretty little creeper, the small flowers of which are
+succeeded by oval magenta-crimson berries which remain on for months;
+and _F. splendens_ (Mexico), 6 ft. high, with very showy scarlet and
+green flowers. But these cannot compare in beauty or freedom of blossom
+with the numerous varieties raised by gardeners. The nectar of fuchsia
+flowers has been shown to contain nearly 78% of cane sugar, the
+remainder being fruit sugar. The berries of some fuchsias are subacid or
+sweet and edible. From certain species a dye is obtainable. The
+so-called "native fuchsias" of southern and eastern Australia are plants
+of the genus _Correa_, natural order Rutaceae.
+
+
+
+
+FUCHSINE, or MAGENTA, a red dye-stuff consisting of a mixture of the
+hydrochlorides or acetates of pararosaniline and rosaniline. It was
+obtained in 1856 by J. Natanson (_Ann_., 1856, 98, p. 297) by the action
+of ethylene chloride on aniline, and by A.W. Hofmann in 1858 from
+aniline and carbon tetrachloride. It is prepared by oxidizing "aniline
+for red" (a mixture of aniline and ortho- and para-toluidine) with
+arsenic acid (H. Medlock, _Dingler's Poly. Jour_., 1860, 158, p. 146);
+by heating aniline for red with nitrobenzene, concentrated hydrochloric
+acid and iron (Coupier, _Ber_., 1873, 6, p. 423); or by condensing
+formaldehyde with aniline and ortho-toluidine and oxidizing the mixture.
+It forms small crystals, showing a brilliant green reflex, and is
+soluble in water and alcohol with formation of a deep red solution. It
+dyes silk, wool and leather direct, and cotton after mordanting with
+tannin and tartar emetic (see DYEING). An aqueous solution of fuchsine
+is decolorized on the addition of sulphurous acid, the easily soluble
+fuchsine sulphurous acid being formed. This solution is frequently used
+as a test reagent for the detection of aldehydes, giving, in most cases,
+a red coloration on the addition of a small quantity of the aldehyde.
+
+  The constitution of the fuchsine bases (pararosaniline and rosaniline)
+  was determined by E. and O. Fischer in 1878 (_Ann_., 1878, 194, p.
+  242); A.W. Hofmann having previously shown that oxidation of pure
+  aniline alone or of pure toluidine yielded no fuchsine, whilst
+  oxidation of a mixture of aniline and para-toluidine gave rise to the
+  fine red dye-stuff para-fuchsine (pararosaniline hydrochloride)
+
+    CH3.C6H4NH2 + 2C6H5NH2 + 3O = HO.C(C6H4NH2)3 + 2H2O.
+                                  Colour base (pararosaniline).
+
+    HO.C(C6H4NH2)3.HCl = H2O + (H2N.C6H4)2C : C6H4 : NH2Cl.
+                                  Pararosaniline hydrochloride.
+
+  A. Rosenstiehl (_Jahres_., 1869, p. 693) found also that different
+  rosanilines were obtained according to whether ortho- or
+  para-toluidine was oxidized with aniline; and he gave the name
+  rosaniline to the one obtained from aniline and ortho-toluidine,
+  reserving the term pararosaniline for the other. E. and O. Fischer
+  showed that these compounds were derivatives of triphenylmethane and
+  tolyldiphenylmethane respectively. Pararosaniline was reduced to the
+  corresponding leuco compound (paraleucaniline), from which by
+  diazotization and boiling with alcohol, the parent hydrocarbon was
+  obtained
+
+    (H2N.C5H4)2C : C6H4:NH2Cl --> HC(C6H4NH2.HCl)3 --> HC(C6H4N2Cl3)
+    Pararosaniline hydrochloride.  Paraleucaniline.
+
+                                                      --> HC(C6H5)3.
+                                                   Triphenylmethane.
+
+  The reverse series of operations was also carried out by the Fischers,
+  triphenylmethane being nitrated, and the nitro compound then reduced
+  to triaminotriphenylmethane or paraleucaniline, which on careful
+  oxidation is converted into the dye-stuff. A similar series of
+  reactions was carried out with rosaniline, which was shown to be the
+  corresponding derivative of tolyldiphenylmethane.
+
+  The free pararosaniline, C19H19N3O, and rosaniline, C20H21N3O, may be
+  obtained by precipitating solutions of their salts with a caustic
+  alkali, colourless precipitates being obtained, which crystallize from
+  hot water in the form of needles or plates. The position of the amino
+  groups in pararosaniline was determined by the work of H. Caro and C.
+  Graebe (_Ber_., 1878, II, p. 1348) and of E. and O. Fischer (_Ber._,
+  1880, 13, p. 2204) as follows: Nitrous acid converts pararosaniline
+  into aurin, which when superheated with water yields
+  para-dioxybenzophenone. As the hydroxyl groups in aurin correspond to
+  the amino groups in pararosaniline, two of these in the latter
+  compound must be in the para position. The third is also in the para
+  position; for if benzaldehyde be condensed with aniline, condensation
+  occurs in the para position, for the compound formed may be converted
+  into para-dioxybenzophenone,
+
+    C6H5CHO --> C6H5CH(C6H4NH2)2 --> C6H5CH(C6H4OH)2 --> CO(C6H4OH)2;
+
+  but if para-nitrobenzaldehyde be used in the above reaction and the
+  resulting nitro compound NO2.C6H4.CH(C6H4NH2)2 be reduced, then
+  pararosaniline is the final product, and consequently the third amino
+  group occupies the para position. Many derivatives of pararosaniline
+  and rosaniline are known, in which the hydrogen atoms of the amino
+  groups are replaced by alkyl groups; this has the effect of producing
+  a blue or violet shade, which becomes deeper as the number of groups
+  increases (see DYEING).
+
+
+
+
+FUCINO, LAGO DI [Lat. _Lacus Fucinus_], a lake bed of the Abruzzi,
+Italy, in the province of Aquila, 2 m. E. of the town of Avezzano. The
+lake was 37 m. in circumference and 65 ft. deep. From the lack of an
+outlet, the level of the lake was subject to great variations, often
+fraught with disastrous consequences. As early as A.D. 52 the emperor
+Claudius, realizing a project of Julius Caesar, constructed a tunnel
+3-1/2 m. long, with 40 shafts at intervals, by which the surplus waters
+found an outlet to the Liris (or Garigliano). No less than 30,000
+workmen were employed for eleven years in driving this tunnel. In the
+following reign the tunnel was allowed to fall into disrepair, but was
+repaired by Trajan. When, however, it finally went out of use is
+uncertain. The various attempts made to reopen it from 1240 onwards were
+unsuccessful. By 1852 the lake had gradually risen until it was 30 ft.
+above its original level, and had become a source of danger to the
+surrounding countryside. A company undertook to drain it on condition of
+becoming proprietors of the site when dry; in 1854, however, the rights
+and privileges were purchased by Prince Giulio Torlonia (d. 1886), the
+great Roman banker, who carried on the work at his own expense until, in
+1876, the lake was finally drained at the cost of some L1,700,000. The
+reclaimed area is 12-1/2 m. long, 7 m. broad, and is cultivated by
+families from the Torlonia estates. The outlet by which it was drained
+is 4 m. long and 24 sq. yds. in section.
+
+  See A. Brisse and L. de Rotron, _Le Dessechement du lac Fucin, execute
+  par S.E. le Prince A. Torlonia_ (Rome, 1876).     (T. As.)
+
+
+
+
+FUEL (O. Fr. _feuaile_, popular Lat. _focalia_, from _focus_, hearth,
+fire), a term applicable to all substances that can be usefully employed
+for the production of heat by combustion. Any element or combination of
+elements susceptible of oxidation may under appropriate conditions be
+made to burn; but only those that ignite at a moderate initial
+temperature and burn with comparative rapidity, and, what is practically
+of more importance, are obtainable in quantity at moderate prices, can
+fairly be regarded as fuels. The elementary substances that can be so
+classed are primarily hydrogen, carbon and sulphur, while others finding
+more special applications are silicon, phosphorus, and the more readily
+oxidizable metals, such as iron, manganese, aluminium and magnesium.
+More important, however, than the elements are the carbohydrates or
+compounds of carbon, oxygen and hydrogen, which form the bulk of the
+natural fuels, wood, peat and coal, as well as of their liquid and
+gaseous derivatives--coal-gas, coal-tar, pitch, oil, &c., which have
+high values as fuel. Carbon in the elementary form has its nearest
+representative in the carbonized fuels, charcoal from wood and coke from
+coal.
+
+
+_Solid Fuels._
+
+  Wood.
+
+Wood may be considered as having the following average composition when
+in the air-dried state: Carbon, 39.6; hydrogen, 4.8; oxygen, 34.8; ash,
+1.0; water, 20%. When it is freshly felled, the water may be from 18 to
+50%. Air-dried or even green wood ignites readily when a considerable
+surface is exposed to the kindling flame, but in large masses with
+regular or smooth surfaces it is often difficult to get it to burn. When
+previously torrefied or scorched by heating to a temperature of about
+200 deg., at which incipient charring is set up, it is exceedingly
+inflammable. The ends of imperfectly charred boughs from the charcoal
+heaps in this condition are used in Paris and other large towns in
+France for kindling purposes, under the name of _fumerons_. The
+inflammability, however, varies with the density,--the so-called hard
+woods, oak, beech and maple, taking fire less readily than the softer,
+and, more especially, the coniferous varieties rich in resin. The
+calorific power of absolutely dry woods may as an average be taken at
+about 4000 units, and when air-dried, i.e. containing 25% of water, at
+2800 to 3000 units. Their evaporative values, i.e. the quantities of
+water evaporated by unit weight, are 3.68 and 4.44.
+
+Wood being essentially a flaming fuel is admirably adapted for use with
+heat-receiving surfaces of large extent, such as locomotive and marine
+boilers, and is also very clean in use. The absence of all cohesion in
+the cinders or unburnt carbonized residue causes a large amount of
+ignited particles to be projected from the chimney, when a rapid draught
+is used, unless special spark-catchers of wire gauze or some analogous
+contrivance are used. When burnt in open fireplaces the volatile
+products given off in the apartment on the first heating have an acrid
+penetrating odour, which is, however, very generally considered to be
+agreeable. Owing to the large amount of water present, no very high
+temperatures can be obtained by the direct combustion of wood, and to
+produce these for metallurgical purposes it is necessary to convert it
+previously either into charcoal or into inflammable gas.
+
+
+  Peat.
+
+Peat includes a great number of substances of very unequal fuel value,
+the most recently formed spongy light brown kind approximating in
+composition to wood, while the dense pitchy brown compact substance,
+obtained from the bottom of bogs of ancient formation, may be compared
+with lignite or even in some instances with coal. Unlike wood, however,
+it contains incombustible matter in variable but large quantity, from 5
+to 15% or even more. Much of this, when the amount is large, is often
+due to sand mechanically intermixed; when air-dried the proportion of
+water is from 8 to 20%. When these constituents are deducted the average
+composition may be stated to be--carbon, 52 to 66; hydrogen, 4.7 to
+7.4; oxygen, 28 to 39; and nitrogen, 1.5 to 3%. Average air-dried peat
+may be taken as having a calorific value of 3000 to 3500 units, and when
+dried at 100 deg. C., and with a minimum of ash (4 to 5%), at about 5200
+units, or from a quarter to one-third more than that of an equal weight
+of wood. The lighter and more spongy varieties of peat when air-dried
+are exceedingly inflammable, firing at a temperature of 200 deg. C.; the
+denser pulpy kinds ignite less readily when in the natural state, and
+often require a still higher temperature when prepared by pulping and
+compression or partial carbonization. Most kinds burn with a red smoky
+flame, developing a very strong odour, which, however, has its admirers
+in the same way that wood smoke has. This arises from the destructive
+distillation of imperfectly carbonized organic matter. The ash, like
+that of wood, is light and powdery, except when much sand is present,
+when it is of a denser character.
+
+Peat is principally found in high latitudes, on exposed high tablelands
+and treeless areas in more temperate climates, and in the valleys of
+slow-flowing rivers,--as in Ireland, the west of Scotland, the tableland
+of Bavaria, the North German plain, and parts of the valleys of the
+Somme, Oise and a few other rivers in northern France. A principal
+objection to its use is its extreme bulk, which for equal evaporative
+effect is from 8 to 18 times that of coal. Various methods have been
+proposed, and adopted more or less successfully, for the purpose of
+increasing the density of raw peat by compression, either with or
+without pulping; the latter process gives the heaviest products, but the
+improvement is scarcely sufficient to compensate for the cost.
+
+
+  Lignite.
+
+Lignite or brown coal is of intermediate character between peat and coal
+proper. The best kinds are undistinguishable in quality from
+free-burning coals, and the lowest earthy kinds are not equal to average
+peat. When freshly raised, the proportion of water may be from 45 to 50%
+and even more, which is reduced from 28 to 20% by exposure to dry air.
+Most varieties, however, when fully dried, break up into powder, which
+considerably diminishes their utility as fuel, as they cannot be
+consolidated by coking. Lignite dust may, however, be compacted into
+serviceable blocks for burning, by pressure in machines similar to those
+used for brickmaking, either in the wet state as raised from the mines
+or when kiln-dried at 200 deg. C. This method was adopted to a very large
+extent in Prussian Saxony. The calorific value varies between 3500 and
+5000 units, and the evaporative factor from 2.16 when freshly raised to
+5.84 for the best kinds of lignite when perfectly dried.
+
+
+  Other natural fuels.
+
+Of the other natural fuels, apart from coal (q.v.), the most important
+is so-called vegetable refuse, such as cotton stalks, brushwood, straw,
+and the woody residue of sugar-cane after the extraction of the
+saccharine juice known as megasse or cane trash. These are extensively
+used in countries where wood and coal are scarce, usually for providing
+steam in the manufactures where they arise, e.g. straw for thrashing,
+cotton stalks for ploughing, irrigating, or working presses, and cane
+trash for boiling down sugar or driving the cane mill. According to J.
+Head (_Proc. Inst. of Civil Engineers_, vol. xlviii. p. 75), the
+evaporative values of 1 lb. of these different articles when burnt in a
+tubular boiler are--coal, 8 lb.; dry peat, 4 lb.; dry wood, 3.58-3.52
+lb.; cotton stalks or megasse, 3.2-2.7 lb.; straw, 2.46-2.30 lb.
+Owing to the siliceous nature of the ash of straw, it is desirable to
+have a means of clearing the grate bars from slags and clinkers at short
+intervals, and to use a steam jet to clear the tubes from similar
+deposits.
+
+The common fuel of India and Egypt is derived from the dung of camels
+and oxen, moulded into thin cakes, and dried in the sun. It has a very
+low heating power, and in burning gives off acrid ammoniacal smoke and
+vapour.
+
+Somewhat similar are the tan cakes made from spent tanners' bark, which
+are used to some extent in eastern France and in Germany. They are made
+by moulding the spent bark into cakes, which are then slowly dried by
+exposure to the air. Their effect is about equivalent to 80 and 30% of
+equal weights of wood and coal respectively.
+
+Sulphur, phosphorus and silicon, the other principal combustible
+elements, are only of limited application as fuels. The first is used in
+the liquidation of sulphur-bearing rocks. The ore is piled into large
+heaps, which are ignited at the bottom, a certain proportion, from
+one-fourth to one-third, of the sulphur content being sacrificed, in
+order to raise the mass to a sufficient temperature to allow the
+remainder to melt and run down to the collecting basin. Another
+application is in the so-called "pyritic smelting," where ores of copper
+(q.v.) containing iron pyrites, FeS2, are smelted with appropriate
+fluxes in a hot blast, without preliminary roasting, the sulphur and
+iron of the pyrites giving sufficient heat by oxidation to liquefy both
+slag and metal. Phosphorus, which is of value from its low igniting
+point, receives its only application in the manufacture of lucifer
+matches. The high temperature produced by burning phosphorus is in part
+due to the product of combustion (phosphoric acid) being solid, and
+therefore there is less heat absorbed than would be the case with a
+gaseous product. The same effect is observed in a still more striking
+manner with silicon, which in the only special case of its application
+to the production of heat, namely, in the Bessemer process of
+steel-making, gives rise to an enormous increase of temperature in the
+metal, sufficient indeed to keep the iron melted. The absolute calorific
+value of silicon is lower than that of carbon, but the product of
+combustion (silica) being non-volatile at all furnace temperatures, the
+whole of the heat developed is available for heating the molten iron,
+instead of a considerable part being consumed in the work of
+volatilization, as is the case with carbonic oxide, which burns to waste
+in the air.
+
+
+    Calorific power.
+
+  _Assay and Valuation of Carbonaceous Fuels._--The utility or value of
+  a fuel depends upon two principal factors, namely, its calorific power
+  and its calorific intensity or pyrometric effect, that is, the
+  sensible temperature of the products of combustion. The first of these
+  is constant for any particular product of combustion independently of
+  the method by which the burning is effected, whether by oxygen, air or
+  a reducible metallic oxide. It is most conveniently determined in the
+  laboratory by measuring the heat evolved during the combustion of a
+  given weight of the fuel. The method of Lewis Thompson is one of the
+  most useful. The calorimeter consists of a copper cylinder in which a
+  weighed quantity of coal intimately mixed with 10-12 parts of a
+  mixture of 3 parts of potassium chlorate and 1 of potassium nitrate is
+  deflagrated under a copper case like a diving-bell, placed at the
+  bottom of a deep glass jar filled with a known weight of water. The
+  mixture is fired by a fuse of lamp-cotton previously soaked in a nitre
+  solution and dried. The gases produced by the combustion rising
+  through the water are cooled, with a corresponding increase of
+  temperature in the latter, so that the difference between the
+  temperature observed before and after the experiment measures the heat
+  evolved. The instrument is so constructed that 30 grains (2 grammes)
+  of coal are burnt in 29,010 grains of water, or in the proportion of 1
+  to 937, these numbers being selected that the observed rise of
+  temperature in Fahrenheit degrees corresponds to the required
+  evaporative value in pounds, subject only to a correction for the
+  amount of heat absorbed by the mass of the instrument, for which a
+  special coefficient is required and must be experimentally determined.
+  The ordinary bomb calorimeter is also used. An approximate method is
+  based upon the reduction of lead oxide by the carbon and hydrogen of
+  the coal, the amount of lead reduced affording a measure of the oxygen
+  expended, whence the heating power may be calculated, 1 part of pure
+  carbon being capable of producing 34-1/2 times its weight of lead. The
+  operation is performed by mixing the weighed sample with a large
+  excess of litharge in a crucible, and exposing it to a bright red heat
+  for a short time. After cooling, the crucible is broken and the
+  reduced button of lead is cleaned and weighed. The results obtained by
+  this method are less accurate with coals containing much disposable
+  hydrogen and iron pyrites than with those approximating to anthracite,
+  as the heat equivalent of the hydrogen in excess of that required to
+  form water with the oxygen of the coal is calculated as carbon, while
+  it is really about four times as great. Sulphur in iron pyrites also
+  acts as a reducing agent upon litharge, and increases the apparent
+  effect in a similar manner.
+
+  The evaporative power of a coal found by the above methods, and also
+  by calculating the separate calorific factors of the components as
+  determined by the chemical analysis, is always considerably above that
+  obtained by actual combustion under a steam boiler, as in the latter
+  case numerous sources of loss, such as imperfect combustion of gases,
+  loss of unburnt coal in cinders, &c., come into play, which cannot be
+  allowed for in laboratory experiments. It is usual, therefore, to
+  determine the value of a coal by the combustion of a weighed quantity
+  in the furnace of a boiler, and measuring the amount of water
+  evaporated by the heat developed.
+
+  In a research upon the heating power and other properties of coal for
+  naval use, carried out by the German admiralty, the results tabulated
+  below were obtained with coals from different localities.
+
+    +-----------------------+-----------+------------+-----------+------------------+
+    |                       | Slag left |  Ashes in  |  Soot in  | Water evaporated |
+    |                       | in Grate. |   Ashpit.  |   Flues.  | by 1 lb. of Coal.|
+    +-----------------------+-----------+------------+-----------+------------------+
+    | Westphalian gas coals | 0.33-6.42 | 2.83- 6.53 | 0.32-0.46 |   6.60-7.45 lb.  |
+    |  Do. bituminous coals | 0.98-9.10 | 1.97- 9.63 | 0.24-0.88 |   7.30-8.66      |
+    |  Do. dry coals        | 1.93-5.70 | 4.37-10.63 | 0.24-0.48 |   7.03-8.51      |
+    | Silesian coals        | 0.92-1.30 | 3.15- 3.50 | 0.24-0.30 |   6.73-7.10      |
+    | Welsh steam coals     | 1.20-4.07 | 4.07       | 0.32      |   8.41           |
+    | Newcastle coals       | 1.92      | 2.57       | 0.35      |   7.28           |
+    +-----------------------+-----------+------------+-----------+------------------+
+
+  The heats of combustion of elements and compounds will be found in
+  most of the larger works on physical and chemical constants; a
+  convenient series is given in the _Annuaire du Bureau des Longitudes_,
+  appearing in alternate years. The following figures for the principal
+  fuel elements are taken from the issue for 1908; they are expressed in
+  gramme "calories" or heat units, signifying the weight of water in
+  grammes that can be raised 1 deg. C. in temperature by the combustion
+  of 1 gramme of the substance, when it is oxidized to the condition
+  shown in the second column:
+
+    +----------------+---------------------------------+-----------+
+    |    Element.    |      Product of Combustion.     | Calories. |
+    +----------------+---------------------------------+-----------+
+    | Hydrogen     \ | Water, H2O, condensed to liquid |  34,500   |
+    |              / |      "      as vapour           |  29,650   |
+    | Carbon--       |                                 |           |
+    |   Diamond      | Carbon Dioxide, CO2             |   7,868   |
+    |   Graphite     |    "      "                     |   7,900   |
+    |   Amorphous    |    "      "                     |   8,133   |
+    | Silicon--      |                                 |           |
+    |   Amorphous    | Silicon Dioxide, SiO2           |   6,414   |
+    |   Crystallized |    "      "                     |   6,570   |
+    | Phosphorus     | Phosphoric pentoxide, P2O5      |   5,958   |
+    | Sulphur        | Sulphur dioxide, SO2, gaseous   |   2,165   |
+    +----------------+---------------------------------+-----------+
+
+  The results may also be expressed in terms of the atomic equivalent of
+  the combustible by multiplying the above values by the atomic weight
+  of the substance, 12 for carbon, 28 for silicon, &c.
+
+  In all fuels containing hydrogen the calorific value as found by the
+  calorimeter is higher than that obtainable under working conditions by
+  an amount equal to the latent heat of volatilization of water which
+  reappears as heat when the vapour is condensed, though under ordinary
+  conditions of use the vapour passes away uncondensed. This gives rise
+  to the distinction of higher and lower calorific values for such
+  substances, the latter being those generally used in practice. The
+  differences for the more important compound gaseous fuels are as
+  follows:--
+
+                             Calorific Value.
+                            Higher.      Lower.
+    Acetylene, C2H2         11,920      11,500
+    Ethylene, C2H4          11,880      11,120
+    Methane, CH4            13,240      11,910
+    Carbon monoxide, CO      2,440       2,440
+
+
+    Caloric intensity.
+
+  The calorific intensity or pyrometric effect of any particular fuel
+  depends upon so many variable elements that it cannot be determined
+  except by actual experiment. The older method was to multiply the
+  weight of the products of combustion by their specific heats, but this
+  gave untrustworthy results as a rule, on account of two
+  circumstances--the great increase in specific heat at high
+  temperatures in compound gases such as water and carbon dioxide, and
+  their instability when heated to 1800 deg. or 2000 deg. At such
+  temperatures dissociation to a notable extent takes place, especially
+  with the latter substance, which is also readily reduced to carbon
+  monoxide when brought in contact with carbon at a red heat--a change
+  which is attended with a large heat absorption. This effect is higher
+  with soft kinds of carbon, such as charcoal or soft coke, than with
+  dense coke, gas retort carbon or graphite. These latter substances,
+  therefore, are used when an intense local heat is required, as for
+  example, in the Deville furnace, to which air is supplied under
+  pressure. Such a method is, however, only of very special application,
+  the ordinary method being to supply air to the fire in excess of that
+  required to burn the fuel to prevent the reduction of the carbon
+  dioxide. The volume of flame, however, is increased by inert gas, and
+  there is a proportionate diminution of the heating effect. Under the
+  most favourable conditions, when the air employed has been previously
+  raised to a high temperature and pressure, the highest attainable
+  flame temperature from carbonaceous fuel seems to be about 2100
+  deg.-2300 deg. C.; this is realized in the bright spots or "eyes" of
+  the tuyeres of blast furnaces.
+
+  Very much higher temperatures may be reached when the products of
+  combustion are not volatile, and the operation can be effected by
+  using the fuel and oxidizing agent in the proportions exactly
+  required for perfect combustion and intimately mixed. These
+  conditions are met in the "Thermit" process of Goldschmidt, where
+  finely divided aluminium is oxidized by the oxide of some similar
+  metal, such as iron, manganese or chromium, the reaction being started
+  by a primer of magnesium and barium peroxide. The reaction is so
+  rapidly effected that there is an enormous rise in temperature,
+  estimated to be 5400 deg. F. (3000 deg. C.), which is sufficient to
+  melt the most refractory metals, such as chromium. The slag consists
+  of alumina which crystallizes in the forms of corundum and ruby, and
+  is utilized as an abrasive under the name of corubin.
+
+  The chemical examination includes the determination of (1) moisture,
+  (2) ash, (3) coke, (4) volatile matter, (5) fixed carbon in coke, (6)
+  sulphur, (7) chlorine, (8) phosphorus. Moisture is determined by
+  noting the loss in weight when a sample is heated at 100 deg. for
+  about one hour. The ash is determined by heating a sample in a muffle
+  furnace until all the combustible matter has been burnt off. The ash,
+  which generally contains silica, oxides of the alkaline earths, ferric
+  oxide (which gives the ash a red colour), sulphur, &c., is analysed by
+  the ordinary gravimetric methods. The determination of coke is very
+  important on account of the conclusions concerning the nature of the
+  coal which it permits to be drawn. A sample is finely powdered and
+  placed in a covered porcelain crucible, which is surrounded by an
+  outer one, the space between them being packed with small coke. The
+  crucibles are heated in a wind furnace for 1 to 1-1/2 hours, then
+  allowed to cool, the inner crucible removed, and the coke weighed. The
+  coke may be (1) pulverulent, (2) slightly fritted, (3) spongy and
+  swelled, (4) compact. Pulverulent cokes indicate a non-caking
+  bituminous coal, rich in oxygen if the amount be below 60%, but if the
+  amount be very much less it generally indicates a lignite; if the
+  amount be above 80% it indicates an anthracite containing little
+  oxygen or hydrogen. A fritted coke indicates a slightly coking coal,
+  while the spongy appearance points to a highly coking coal which has
+  been partly fused in the furnace. A compact coke is yielded by good
+  coking coals, and is usually large in amount. The volatile matters are
+  determined as the loss of weight on coking less the amount of
+  moisture. The "fixed carbon" is the carbon retained in the coke, which
+  contains in addition the ash already determined. The fixed carbon is
+  therefore the difference between the coke and the ash, and may be
+  determined from these figures; or it may be determined directly by
+  burning off the coke in a muffle and noting the loss in weight.
+  Sulphur may be present as (1) organic sulphur, (2) as iron pyrites or
+  other sulphides, (3) as the sulphates of calcium, aluminium and other
+  metals; but the amount is generally so small that only the total
+  sulphur is determined. This is effected by heating a mixture of the
+  fuel with lime and sodium carbonate in a porcelain dish to redness in
+  a muffle until all the carbonaceous matter has been burnt off. The
+  residue, which contains the sulphur as calcium sulphate, is
+  transferred to a beaker containing water to which a little bromine has
+  been added. Hydrochloric acid is carefully added, the liquid filtered
+  and the residue washed. To the filtrate ammonia is added, and then
+  barium chloride, which precipitates the sulphur as barium sulphate.
+  Sulphur existing in the form of sulphates may be removed by washing a
+  sample with boiling water and determining the sulphuric acid in the
+  solution. The washed sample is then fused in the usual way to
+  determine the proportion of sulphur existing as iron pyrites. The
+  distinction between sulphur present as sulphate and sulphide is of
+  importance in the examination of coals intended for iron smelting, as
+  the sulphates of the earthy metals are reduced by the gases of the
+  furnace to sulphides, which pass into the slag without affecting the
+  quality of the iron produced, while the sulphur of the metallic
+  sulphides in the ash acts prejudicially upon the metal. Coals for
+  gas-making should contain little sulphur, as the gases produced in the
+  combustion are noxious and have very corrosive properties. Chlorine is
+  rarely determined, but when present in quantity it corrodes copper and
+  brass boiler tubes, with which consequently chlorine-bearing coals
+  cannot be used. The element is determined by fusing with soda lime in
+  a muffle, dissolving the residue in water and precipitating with
+  silver nitrate. Phosphorus is determined in the ash by fusing it with
+  a mixture of sodium and potassium carbonates, extracting the residue
+  with hydrochloric acid, and twice evaporating to dryness with the same
+  acid. The residue is dissolved in hydrochloric acid, a few drops of
+  ferric chloride added, and then ammonia in excess. The precipitate of
+  ferric phosphate is then treated as in the ordinary estimation of
+  phosphates. If it be necessary to determine the absolute amount of
+  carbon and hydrogen in a fuel, the dried sample is treated with copper
+  oxide as in the ordinary estimation of these elements in organic
+  compounds.     (H. B.)
+
+
+_Liquid Fuel._
+
+Vegetable oil is not used for fuel except for laboratory purposes,
+partly because its constituent parts are less adaptable for combustion
+under the conditions necessary for steam-raising, but chiefly because of
+the commercial difficulty of producing it with sufficient economy to
+compete with mineral fuel either solid or liquid.
+
+The use of petroleum as fuel had long been recognized as a scientific
+possibility, and some attempts had been made to adopt it in practice
+upon a commercial scale, but the insufficiency, and still more the
+irregularity, of the supplies prevented it from coming into practical
+use to any important extent until about 1898, when discoveries of oil
+specially adapted by chemical composition for fuel purposes changed the
+aspect of the situation. These discoveries of special oil were made
+first in Borneo and later in Texas, and experience in treating the oils
+from both localities has shown that while not less adapted to produce
+kerosene or illuminating oil, they are better adapted to produce fuel
+oil than either the Russian or the Pennsylvanian products. Texas oil did
+not hold its place in the market for long, because the influx of water
+into the wells lowered their yield, but discoveries of fuel oil in
+Mexico have come later and will help to maintain the balance of the
+world's supply, although this is still a mere fraction of the assured
+supply of coal.
+
+With regard to the chemical properties of petroleum, it is not necessary
+to say more in the present place than that the lighter and more volatile
+constituents, known commercially as naphtha and benzene, must be removed
+by distillation in order to leave a residue composed principally of
+hydrocarbons which, while containing the necessary carbon for
+combustion, shall be sufficiently free from volatile qualities to avoid
+premature ignition and consequent danger of explosion. Attempts have
+been made to use crude oil for fuel purposes, and these have had some
+success in the neighbourhood of the oil wells and under boilers of
+unusually good ventilation both as regards their chimneys and the
+surroundings of their stokeholds; but for reasons both of commerce and
+of safety it is not desirable to use crude oil where some distillation
+is possible. The more complete the process of distillation, and the
+consequent removal of the volatile constituents, the higher the
+flash-point, and the more turgid and viscous is the fuel resulting; and
+if the process is carried to an extreme, the residue or fuel becomes
+difficult to ignite by the ordinary process of spraying or atomizing
+mechanically at the moment immediately preceding combustion. The
+proportions which have been found to work efficiently in practice are as
+follows:--
+
+  Carbon             88.00 %
+  Hydrogen           10.75 %
+  Oxygen              1.25 %
+                   ---------
+        Total       100
+
+The standards of safety for liquid fuel as determined by flash-point are
+not yet finally settled, and are changing from time to time. The British
+admiralty require a flash-point of 270 deg. F., and to this high
+standard, and the consequent viscosity of the fuel used by vessels in
+the British fleet, may partly be attributed the low rate of combustion
+that was at first found possible in them. The German admiralty have
+fixed a flash-point of 187 deg. F., and have used oil of this standard
+with perfect safety, and at the same time with much higher measure of
+evaporative duty than has been attained in British war-vessels. In the
+British mercantile marine Lloyd's Register has permitted fuel with a
+flash-point as low as 150 deg. F. as a minimum, and no harm has
+resulted. The British Board of Trade, the department of the government
+which controls the safety of passenger vessels, has fixed a higher
+standard upon the basis of a minimum of 185 deg. In the case of
+locomotives the flash-point as a standard of safety is of less
+importance than in the case of stationary or marine boilers, because the
+storage is more open, and the ventilation, both of the storage tanks and
+the boilers during combustion, much more perfect than in any other class
+of steam-boilers.
+
+The process of refining by distillation is also necessary to reduce two
+impurities which greatly retard storage and combustion, i.e. water and
+sulphur. Water is found in all crude petroleum as it issues from the
+wells, and sulphur exists in important quantities in oil from the Texas
+wells. Its removal was at first found very expensive, but there no
+longer exists difficulty in this respect, and large quantities of
+petroleum fuel practically free from sulphur are now regularly exported
+from Texas to New York and to Europe.
+
+Water mixed with fuel is in intimate mechanical relation, and frequently
+so remains in considerable quantities even after the process of
+distillation. It is in fact so thoroughly mixed as to form an emulsion.
+The effect of feeding such a mixture into a furnace is extremely
+injurious, because the water must be decomposed chemically into its
+constituents, hydrogen and oxygen, thus absorbing a large quantity of
+heat which would otherwise be utilized for evaporation. Water also
+directly delays combustion by producing from the jet a long, dull, red
+flame instead of a short bright, white flame, and the process of
+combustion, which should take place by vaporization of the oil near the
+furnace mouth, is postponed and transferred to the upper part of the
+combustion-box, the tubes, and even the base of the chimney, producing
+loss of heat and injury to the boiler structure. The most effective
+means of ridding the fuel of this dangerous impurity is by heat and
+settlement. The coefficients of expansion of water and oil by heat are
+substantially different, and a moderate rise of temperature therefore
+separates the particles and precipitates the water, which is easily
+drawn off--leaving the oil available for use. The heating and
+precipitation are usually performed upon a patented system of settling
+tanks and heating apparatus known as the Flannery-Boyd system, which has
+proved itself indispensable for the successful use at sea of petroleum
+fuel containing any large proportion of water.
+
+
+  Progress of liquid fuel.
+
+The laboratory and mechanical use of petroleum for fuel has already been
+referred to, but it was not until the year 1870 that petroleum was
+applied upon a wider and commercial scale. In the course of distillation
+of Russian crude petroleum for the production of kerosene or lamp oil,
+large quantities of refuse were produced--known by the Russian name of
+_astatki_--and these were found an incumbrance and useless for any
+commercial purpose. To a Russian oil-refiner gifted with mechanical
+instinct and the genius for invention occurred the idea of utilizing the
+waste product as fuel by spraying or atomizing it with steam, so that,
+the thick and sluggish fluid being broken up into particles, the air
+necessary for combustion could have free access to it. The earliest
+apparatus for this purpose was a simple piece of gas-tube, into which
+the thick oil was fed; by another connexion steam at high pressure was
+admitted to an inner and smaller tube, and, the end of the tube nearest
+to the furnace being open, the pressure of the steam blew the oil into
+the furnace, and by its velocity broke it up into spray. The apparatus
+worked with success from the first. Experience pointed out the proper
+proportionate sizes for the inlets of steam and oil, the proper pressure
+for the steam, and the proportionate sizes for the orifices of admission
+to the furnaces, as well as the sizes of air-openings and best
+arrangements of fire-bricks in the furnaces themselves; and what had
+been a waste product now became a by-product of great value. Practically
+all the steam power in South Russia, both for factories and navigation
+of the inland seas and rivers, is now raised from _astatki_ fuel.
+
+In the Far East, including Burma and parts of China and Japan, the use
+of liquid fuel spread rapidly during the years 1899, 1900 and 1901,
+owing entirely to the development of the Borneo oil-fields by the
+enterprise of Sir Marcus Samuel and the large British corporation known
+as the Shell Transport and Trading Company, of which he is the head.
+This corporation has since amalgamated with the Royal Dutch Petroleum
+Company controlling the extensive wells in Dutch Borneo, and together
+they supply large quantities of liquid fuel for use in the Far East. In
+the United States of America liquid fuel is not only used for
+practically the whole of the manufacturing and locomotive purposes of
+the state of Texas, but factories in New York, and a still larger number
+in California, are now discarding the use of coal and adopting
+petroleum, because it is more economical in its consumption and also
+more easily handled in transit, and saves nearly all the labour of
+stoking. So far the supplies for China and Japan have been exported from
+Borneo, but the discoveries of new oil-fields in California, of a
+character specially adapted for fuel, have encouraged the belief that it
+may be possible to supply Chile and Peru and other South American
+countries, where coal is extremely expensive, with Californian fuel; and
+it has also found its way across the Pacific to Japan. There are
+believed to be large deposits in West Africa, but in the meantime the
+only sources of supply to those parts of Africa where manufacture is
+progressing, i.e. South Africa and Egypt, are the oil-fields of Borneo
+and Texas, from which the import has well begun, from Texas to
+Alexandria via the Mediterranean, and from Borneo to Cape Town via
+Singapore.
+
+In England, notwithstanding the fact that there exist the finest
+coal-fields in the world, there has been a surprising development of the
+use of petroleum as fuel. The Great Eastern railway adapted 120
+locomotive engines to its use, and these ran with regularity and success
+both on express passenger and goods trains until the increase in price
+due to short supply compelled a return to coal fuel. The London,
+Brighton & South Coast railway also began the adaptation of some of
+their locomotive engines, but discontinued the use of liquid fuel from
+the same cause. Several large firms of contractors and cement
+manufacturers, chiefly on the banks of the Thames, made the same
+adaptations which proved mechanically successful, but were not continued
+when the price of liquid fuel increased with the increased demand.
+
+[Illustration: FIG. 1.--Holden Burner.]
+
+
+  Economy of liquid fuel.
+
+The chief factors of economy are the greater calorific value of oil than
+coal (about 16 lb. of water per lb. of oil fuel evaporated from a
+temperature of 212 deg. F.), not only in laboratory practice, but in
+actual use on a large scale, and the saving of labour both in transit
+from the source of supply to the place of use and in the act of stoking
+the furnaces. The use of cranes, hand labour with shovels, wagons and
+locomotives, horses and carts, is unavoidable for the transit of coal;
+and labour to trim the coal, to stoke it when under combustion, and to
+handle the residual ashes, are all indispensable to steam-raising by
+coal. On the other hand, a system of pipes and pumps, and a limited
+quantity of skilled labour to manage them, is all that is necessary for
+the transit and combustion of petroleum fuel; and it is certain that
+even in England will be found places which, from topographical and other
+circumstances, will use petroleum more economically than coal as fuel
+for manufacturing purposes under reasonable conditions of price for the
+fuel.
+
+[Illustration: FIG. 2.--Rusden and Eeles Burner.]
+
+The theoretical calorific value of oil fuel is more nearly realized in
+practice than the theoretical calorific value of coal, because the
+facilities for complete combustion, due to the artificial admixture of
+the air by the atomizing process, are greater in the case of oil than
+coal, and for this reason, among others, the practical evaporative
+results are proportionately higher with liquid fuel. In some cases the
+work done in a steam-engine by 2 tons of coal has been performed by 1
+ton of oil fuel, but in others the proportions have been as 3 to 2, and
+these latter can be safely relied on in practice as a minimum. This
+saving, combined with the savings of labour and transit already
+explained, will in the near future make the use of liquid fuel
+compulsory, except in places so near to coal-fields that the cost of
+coal becomes sufficiently low to counterbalance the savings in weight of
+fuel consumed and in labour in handling it. In some locomotives on the
+Great Eastern railway the consumption of oil and coal for the same
+development of horse-power was as 17 lb. oil is to 35 lb. coal; all,
+however, did not realize so high a result.
+
+
+  Liquid fuel in locomotives.
+
+The mechanical apparatus for applying petroleum to steam-raising in
+locomotives is very simple. The space in the tender usually occupied by
+coal is closed up by steel-plating closely riveted and tested, so as to
+form a storage tank. From this tank a feed-pipe is led to a burner of
+the combined steam-and-oil type already indicated, and this burner is so
+arranged as to enter a short distance inside the furnace mouth. The
+ordinary fire-bars are covered with a thin layer of coal, which starts
+the ignition in the first place, and the whole apparatus is ready for
+work. The burner best adapted for locomotive practice is the Holden
+Burner (fig. 1), which was used on the Great Eastern railway. The
+steam-pipe is connected at A, the oil-pipe at B, and the hand-wheels C
+and D are for the adjustment of the internal orifices according to the
+rate of combustion required. The nozzle E is directed towards the
+furnace, and the external ring FF, supplied by the small pipe G and the
+by-pass valve H, projects a series of steam jets into the furnace,
+independent of the injections of atomized fuel, and so induces an
+artificial inrush of air for the promotion of combustion. This type of
+burner has also been tried on stationary boilers and on board ship. It
+works well, although the great consumption of steam by the supplementary
+ring is a difficulty at sea, where the water lost by the consumption of
+steam cannot easily be made up.
+
+
+  Liquid fuel at sea.
+
+Although the application of the new fuel for land and locomotive boilers
+has already been large, the practice at sea has been far more extensive.
+The reason is chiefly to be found in the fact that although the sources
+of supply are at a distance from Great Britain, yet they are in
+countries to whose neighbourhood British steamships regularly trade, and
+in which British naval squadrons are regularly stationed, so that the
+advantages of adopting liquid fuel have been more immediate and the
+economy more direct. The certainty of continuous supply of the fuel and
+the wide distribution of storage stations have so altered the conditions
+that the general adoption of the new fuel for marine purposes becomes a
+matter of urgency for the statesman, the merchant and the engineer. None
+of these can afford to neglect the new conditions, lest they be noted
+and acted upon by their competitors. Storage for supply now exists at a
+number of sea ports: London, Barrow, Southampton, Amsterdam, Copenhagen,
+New Orleans, Savannah, New York, Philadelphia, Singapore, Hong Kong,
+Madras, Colombo, Suez, Hamburg, Port Arthur, Rangoon, Calcutta, Bombay,
+Alexandria, Bangkok, Saigon, Penang, Batavia, Surabaya, Amoy, Swatow,
+Fuchow, Shanghai, Hankow, Sydney, Melbourne, Adelaide, Zanzibar,
+Mombasa, Yokohama, Kobe and Nagasaki; also in South African and South
+American ports.
+
+[Illustration: FIG. 3.--Storage of Liquid Fuel on Oil-carrying Steamers
+(Flannery-Boyd System).]
+
+The British admiralty have undertaken experiments with liquid fuel at
+sea, and at the same time investigations of the possibility of supply
+from sources within the regions of the British empire. There is an
+enormous supply of shale under the north-eastern counties of England,
+but no oil that can be pumped--still less oil with a pressure above it
+so as to "gush" like the wells in America--and the only sources of
+liquid supply under the British flag appear to be in Burma and Trinidad.
+The Borneo fields are not under British control, although developed
+entirely by British capital. The Italian admiralty have fitted several
+large warships with boiler apparatus to burn petroleum. The German
+admiralty are regularly using liquid fuel on the China station. The
+Dutch navy have fitted coal fuel and liquid fuel furnaces in
+combination, so that the smaller powers required may be developed by
+coal alone, and the larger powers by supplementing coal fuel with oil
+fuel. The speeds of some vessels of the destroyer type have by this
+means been accelerated nearly two knots.
+
+[Illustration: FIG. 4.--Installation on ss. "Trochas."]
+
+[Illustration: FIG. 5.--Details of Furnace, Meyer System.]
+
+[Illustration: FIG. 6.--Details of Exterior Elongation of Furnace, Meyer
+System.]
+
+
+  Advantages in warships.
+
+The questions which govern the use of fuel in warships are more largely
+those of strategy and fighting efficiency than economy of evaporation.
+Indeed, the cost of constructing and maintaining in fighting efficiency
+a modern warship is so great that the utmost use strategically must be
+obtained from the vessel, and in this comparison the cost of fuel is
+relatively so small an item that its increase or decrease may be
+considered almost a negligible quantity. The desideratum in a warship is
+to obtain the greatest fighting efficiency based on the thickest
+armour, the heaviest and most numerous guns, the highest maximum speed,
+and, last and not least, the greatest range of effective action based
+upon the maximum supplies of fuel, provisions and other consumable
+stores that the ship can carry. Now, if by changing the type of fuel it
+be possible to reduce its weight by 30%, and to abolish the stokers, who
+are usually more than half the ship's company, the weight saved will be
+represented not merely by the fuel, but by the consumable stores
+otherwise necessary for the stokers. Conversely, the radius of effective
+action of the ship will be doubled as regards consumable stores if the
+crew be halved, and will be increased by 50% if the same weight of fuel
+be carried in the form of liquid instead of coal. In space the gain by
+using oil fuel is still greater, and 36 cubic feet of oil as stored are
+equal in practical calorific value to 67 cubic feet of coal according to
+the allowance usual for ship's bunkering. On the other hand, coal has
+been relied upon, when placed in the side bunkers of unarmoured ships,
+as a protection against shot and shell, and this advantage, if it really
+exists, could not be claimed in regard to liquid fuel.
+
+Recent experiments in coaling warships at sea have not been very
+successful, as the least bad weather has prevented the safe transmission
+of coal bags from the collier to the ship. The same difficulty does not
+exist for oil fuel, which has been pumped through flexible tubing from
+one ship to the other even in comparatively rough weather.
+Smokelessness, so important a feature of sea strategy, has not always
+been attained by liquid fuel, but where the combustion is complete, by
+reason of suitable furnace arrangements and careful management, there is
+no smoke. The great drawback, however, to the use of liquid fuel in fast
+small vessels is the confined space allotted to the boilers, such
+confinement being unavoidable in view of the high power concentrated in
+a small hull. The British admiralty's experiments, however, have gone
+far to solve the problem, and the quantity of oil which can be consumed
+by forced draught in confined boilers now more nearly equals the
+quantity of coal consumed under similar conditions. All recent vessels
+built for the British navy are so constructed that the spaces between
+their double bottoms are oil-tight and capable of storing liquid fuel in
+the tanks so formed. Most recent battleships and cruisers have also
+liquid fuel furnace fittings, and in 1910 it already appeared probable
+that the use of oil fuel in warships would rapidly develop.
+
+In view of recent accusations of insufficiency of coal storage in
+foreign naval depots, by reason of the allegation that coal so stored
+quickly perishes, it is interesting to note that liquid fuel may be
+stored in tanks for an indefinite time without any deterioration
+whatever.
+
+
+  Advantages in merchant ships.
+
+In the case of merchant steamers large progress has also been made. The
+Shell Transport and Trading Company have twenty-one vessels successfully
+navigating in all parts of the world and using liquid fuel. The
+Hamburg-American Steamship Company have four large vessels similarly
+fitted for oil fuel, which, however, differ in furnace arrangements, as
+will be hereafter described, although using coal when the fluctuation of
+the market renders that the more economical fuel. One of the large
+American transatlantic lines is adopting liquid fuel, and French,
+German, Danish and American mercantile vessels are also beginning to use
+it in considerable amounts.
+
+In the case of very large passenger steamers, such as those of 20 knots
+and upwards in the Atlantic trade, the saving in cost of fuel is
+trifling compared with the advantage arising from the greater weight and
+space available for freight. Adopting a basis of 3 to 2 as between coal
+consumption and oil consumption, there is an increase of 1000 tons of
+dead weight cargo in even a medium-sized Atlantic steamer, and a
+collateral gain of about 100,000 cub. ft. of measurement cargo, by
+reason of the ordinary bunkers being left quite free, and the oil being
+stored in the double bottom spaces hitherto unutilized except for the
+purpose of water ballast. The cleanliness and saving of time from
+bunkering by the use of oil fuel is also an important factor in
+passenger ships, whilst considerable additional speed is obtainable. The
+cost of the installation, however, is very considerable, as it includes
+not only burners and pipes for the furnaces, but also the construction
+of oil-tight tanks, with pumps and numerous valves and pipe connexions.
+
+[Illustration: FIG. 7.--Furnace on ss. "Ferdinand Laeisz." A, it is
+proposed to do away with this ring of brickwork as being useless; B, it
+is proposed to fill this space up, thus continuing lining of furnace to
+combustion chamber, and also to fit protection bricks in way of saddle
+plate.]
+
+[Illustration: FIG. 8.--Fuel Tanks, &c., of ss. "Murex."]
+
+[Illustration: FIG. 9.--Furnace Gear of ss. "Murex."]
+
+  Fig. 2 shows a burner of Rusden and Eeles' patent as generally used on
+  board ships for the purpose of injecting the oil. A is a movable cap
+  holding the packing B, which renders the annular spindle M oil and
+  steam tight. E is the outer casing containing the steam jacket from
+  which the steam, after being fed through the steam-supply pipe G,
+  passes into the annular space surrounding the spindle P. It will be
+  seen that if the spindle P be travelled inwards by turning the handle
+  N, the orifice at the nozzle RR will be opened so as to allow the
+  steam to flow out radially. If at the same time the annular spindle M
+  be drawn inwards by revolving the handle L, the oil which passes
+  through the supply pipe F will also have emission at RR, and, coming
+  in contact with the outflowing steam, will be pulverized and sprayed
+  into the furnace. Fig. 3 is a profile and plan of a steamer adapted
+  for carrying oil in bulk, and showing all the storage arrangements for
+  handling liquid fuel. Fig. 4 shows the interior arrangement of the
+  boiler furnace of the steamship "Trocas." A is broken fire-brick
+  resting on the ordinary fire-bars, B is a brick bridge, C a casing of
+  fire-brick intended to protect the riveted seam immediately above it
+  from the direct impact of the flame, and D is a lining of fire-brick
+  at the back of the combustion-box, also intended to protect the
+  plating from the direct impact of the petroleum flame. The arrangement
+  of the furnace on the Meyer system is shown in fig. 5, where E is an
+  annular projection built at the mouth of the furnace, and BB are
+  spiral passages for heating the air before it passes into the furnace.
+  Fig. 6 shows the rings CC and details of the casting which forms the
+  projection or exterior elongation of the furnace. The brickwork
+  arrangement adopted for the double-ended boilers on the
+  Hamburg-American Steamship Company's "Ferdinand Laeisz" is represented
+  in fig. 7. The whole furnace is lined with fire-brick, and the burner
+  is mounted upon a circular disk plate which covers the mouth of the
+  furnace. The oil is injected not by steam pulverization, but by
+  pressure due to a steam-pump. The oil is heated to about 60 deg. C.
+  before entering the pump, and further heated to 90 deg. C. after
+  leaving the pump. It is then filtered, and passes to the furnace
+  injector C at about 30-lb. pressure; and its passage through this
+  injector and the spiral passages of which it consists pulverizes the
+  oil into spray, in which form it readily ignites on reaching the
+  interior of the furnace. The injector is on the Korting principle,
+  that is, it atomizes by fracture of the liquid oil arising from its
+  own momentum under pressure. The advantage of this system as compared
+  with the steam-jet system is the saving of fresh water, the
+  abstraction of which is so injurious to the boiler by the formation of
+  scale.
+
+  [Illustration: FIG. 10.--Section through Furnace of ss. "Murex."]
+
+  The general arrangement of the fuel tanks and filling pipes on the ss.
+  "Murex" is shown in fig. 8; and fig. 9 represents the furnace gear of
+  the same vessel, A being the steam-pipe, B the oil-pipe, C the
+  injector, D the swivel upon which the injector is hung so that it may
+  be swung clear of the furnace, E the fire-door, and F the handle for
+  adjusting the injector. In fig. 10, which represents a section of the
+  furnace, H is a fire-brick pier and K a fire-brick baffling bridge.
+
+  It is found in practice that to leave out the fire-bars ordinarily
+  used for coal produces a better result with liquid fuel than the
+  alternative system of keeping them in place and protecting them by a
+  layer of broken fire-brick.
+
+  Boilers fitted upon all the above systems have been run for thousands
+  of miles without trouble. In new construction it is desirable to give
+  larger combustion chambers and longer and narrower boiler tubes than
+  in the case of boilers intended for the combustion of coal alone.
+       (F. F.*)
+
+
+_Gaseous Fuel._
+
+Strictly speaking, much, and sometimes even most, of the heating
+effected by solid or liquid fuel is actually performed by the gases
+given off during the combustion. We speak, however, of gaseous fuel only
+in those cases where we supply a combustible gas from the outset, or
+where we produce from ordinary solid (or liquid) fuel in one place a
+stream of combustible gas which is burned in another place, more or less
+distant from that where it has been generated.
+
+  The various descriptions of gaseous fuel employed in practice may be
+  classified under the following heads:
+
+  I. Natural Gas.
+
+  II. Combustible Gases obtained as by-products in various technical
+        operations.
+
+  III. Coal Gas (Illuminating Gas).
+
+  IV. Combustible Gases obtained by the partial combustion of coal, &c.
+
+I. _Natural Gas._--From time immemorial it has been known that in some
+parts of the Caucasus and of China large quantities of gases issue from
+the soil, sometimes under water, which can be lighted and burn with a
+luminous flame. The "eternal fires" of Baku belong to this class. In
+coal-mines frequently similar streams of gas issue from the coal; these
+are called "blowers," and when they are of somewhat regular occurrence
+are sometimes conducted away in pipes and used for underground lighting.
+As a regular source of heating power, however, natural gas is employed
+only in some parts of the United States, especially in Pennsylvania,
+Kansas, Ohio and West Virginia, where it always occurs in the
+neighbourhood of coal and petroleum fields. The first public mention of
+it was made in 1775, but it was not till 1821 that it was turned to use
+at Fredonia, N.Y. In Pennsylvania natural gas was discovered in 1859,
+but at first very little use was made of it. Its industrial employment
+dates only from 1874, and became of great importance about ten years
+later. Nobody ever doubted that the gas found in these localities was an
+accumulation of many ages and that, being tapped by thousands of
+bore-holes, it must rapidly come to an end. This assumption was
+strengthened by the fact that the "gas-wells," which at first gave out
+the gas at a pressure of 700 or 800, sometimes even of 1400 lb. per sq.
+in., gradually showed a more and more diminishing pressure and many of
+them ceased to work altogether. About the year 1890 the belief was
+fairly general that the stock of natural gas would soon be entirely
+exhausted. Indeed, the value of the annual production of natural gas in
+the United States, computed as its equivalent of coal, was then
+estimated at twenty-one million dollars, in 1895 at twelve millions, in
+1899 at eleven and a half millions. But the output rose again to a value
+of twenty-seven millions in 1901, and to fifty million dollars in 1907.
+Mostly the gas, derived from upwards of 10,000 gas-wells, is now
+artificially compressed to a pressure of 300 or 400 lb. per sq. in. by
+means of steam-power or gas motors, fed by the gas itself, and is
+conveyed over great distances in iron pipes, from 9 or 10 to 36 in. in
+diameter. In 1904 nearly 30,000 m. of pipe lines were in operation. In
+1907 the quantity of natural gas consumed in the United States (nearly
+half of which was in Pennsylvania) was 400,000 million cub. ft., or
+nearly 3 cub. m. Canada (Ontario) also produces some natural gas,
+reaching a maximum of about $746,000 in 1907.
+
+The principal constituent of natural gas is always methane, CH4, of
+which it contains from 68.4 to 94.0% by volume. Those gases which
+contain less methane contain all the more hydrogen, viz. 2.9 to 29.8%.
+There is also some ethylene, ethane and carbon monoxide, rarely
+exceeding 2 or 3%. The quantity of incombustible gases--oxygen, carbon
+dioxide, nitrogen--ranges from mere traces to about 5%. The density is
+from 0.45 to 0.55. The heating power of 1000 cub. ft. of natural gas is
+equal to from 80 to 120 lb., on the average 100 lb., of good coal, but
+it is really worth much more than this proportion would indicate, as it
+burns completely, without smoke or ashes, and without requiring any
+manual labour. It is employed for all domestic and for most industrial
+purposes.
+
+The origin of natural gas is not properly understood, even now. The most
+natural assumption is, of course, that its formation is connected with
+that of the petroleum always found in the same neighbourhood, the latter
+principally consisting of the higher-boiling aliphatic hydrocarbons of
+the methane series. But whence do they both come? Some bring them into
+connexion with the formation of coal, others with the decomposition of
+animal remains, others with that of _diatomaceae_, &c., and even an
+inorganic origin of both petroleum and natural gas has been assumed by
+chemists of the rank of D.I. Mendeleeff and H. Moissan.
+
+II. _Gases obtained as By-products._--There are two important cases in
+which gaseous by-products are utilized as fuel; both are intimately
+connected with the manufacture of iron, but in a very different way, and
+the gases are of very different composition.
+
+(a) _Blast-furnace Gases._--The gases issuing from the mouths of
+blast-furnaces (see IRON AND STEEL) were first utilized in 1837 by Faber
+du Faur, at Wasseralfingen. Their use became more extensive after 1860,
+and practically universal after 1870. The volume of gas given off per
+ton of iron made is about 158,000 cub. ft. Its percentage composition by
+volume is:
+
+  Carbon monoxide    21.6  to  29.0,  mostly about  26%
+  Hydrogen            1.8   "   6.3,    "      "     3%
+  Methane             0.1   "   0.8,    "      "   0.5%
+  Carbon dioxide      6     "  12,      "      "   9.5%
+  Nitrogen           51     "  60,      "      "  56  %
+  Steam               5     "  12,      "      "   5  %
+                                                  -----
+                                                 100  %
+
+There is always a large amount of mechanically suspended flue-dust in
+this gas. It is practically equal to a poor producer-gas (see below),
+and is everywhere used, first for heating the blast in Cowper stoves or
+similar apparatus, and secondly for raising all the steam required for
+the operation of the blast-furnace, that is, for driving the
+blowing-engines, hoisting the materials, &c. Where the iron ore is
+roasted previously to being fed into the furnace, this can also be done
+by this gas, but in some cases the waste in using it is so great that
+there is not enough left for the last purpose. The calorific power of
+this gas per cubic foot is from 80 to 120 B.Th.U.
+
+Since about 1900 a great advance has been made in this field. Instead of
+burning the blast-furnace gas under steam boilers and employing the
+steam for producing mechanical energy, the gas is directly burned in
+gas-motors on the explosion principle. Thus upwards of three times the
+mechanical energy is obtained in comparison with the indirect way
+through the steam boiler. After all the power required for the
+operations of the blast-furnace has been supplied, there is a surplus of
+from 10 to 20 h.p. for each ton of pig-iron made, which may be applied
+to any other purpose.
+
+(b) _Coke-oven Gases._--Where the coking of coal is performed in the old
+beehive ovens or similar apparatus the gas issuing at the mouth of the
+ovens is lost. The attempts at utilizing the gases in such cases have
+not been very successful. It is quite different where coke is
+manufactured in the same way as illuminating gas, viz. by the
+destructive distillation of coal in closed apparatus (retorts), heated
+from the outside. This industry, which is described in detail in G.
+Lunge's _Coal-Tar and Ammonia_ (4th ed., 1909), originated in France,
+but has spread far more in Germany, where more than half of the coke
+produced is made by it; in the United Kingdom and the United States its
+progress has been much slower, but there also it has long been
+recognized as the only proper method. The output of coke is increased by
+about 15% in comparison with the beehive ovens, as the heat required for
+the process of distillation is not produced by burning part of the coal
+itself (as in the beehive ovens), but by burning part of the gas. The
+quality of the coke for iron-making is quite as good as that of beehive
+coke, although it differs from it in appearance. Moreover, the gases can
+be made to yield their ammonia, their tar, and even their benzene
+vapours, the value of which products sometimes exceeds that of the coke
+itself. And after all this there is still an excess of gas available for
+any other purpose.
+
+As the principle of distilling the coal is just the same, whether the
+object is the manufacture of coal gas proper or of coke as the main
+product, although there is much difference in the details of the
+manufacture, it follows that the quality of the gas is very similar in
+both cases, so far as its heating value is concerned. Of course this
+heating value is less where the benzene has been extracted from
+coke-oven gas, since this compound is the richest heat-producer in the
+gas. This is, however, of minor importance in the present case, as there
+is only about 1% benzene in these gases.
+
+The composition of coke-oven gases, after the extraction of the ammonia
+and tar, is about 53% hydrogen, 36% methane, 6% carbon monoxide, 2%
+ethylene and benzene, 0.5% sulphuretted hydrogen, 1.5% carbon dioxide,
+1% nitrogen.
+
+III. _Coal Gas (Illuminating Gas)._--Although ordinary coal gas is
+primarily manufactured for illuminating purposes, it is also extensively
+used for cooking, frequently also for heating domestic rooms, baths,
+&c., and to some extent also for industrial operations on a small scale,
+where cleanliness and exact regulation of the work are of particular
+importance. In chemical laboratories it is preferred to every other kind
+of fuel wherever it is available. The manufacture of coal gas being
+described elsewhere in this work (see GAS, S _Manufacture_), we need
+here only point out that it is obtained by heating bituminous coal in
+fireclay retorts and purifying the products of this destructive
+distillation by cooling, washing and other operations. The residual gas,
+the ordinary composition of which is given in the table below, amounts
+to about 10,000 cub. ft. for a ton of coal, and represents about 21% of
+its original heating value, 56.5% being left in the coke, 5.5% in the
+tar and 17% being lost. As we must deduct from the coke that quantity
+which is required for the heating of the retorts, and which, even when
+good gas producers are employed, amounts to 12% of the weight of the
+coal, or 10% of its heat value, the total loss of heat rises to 27%.
+Taking, further, into account the cost of labour, the wear and tear, and
+the capital interest on the plant, coal gas must always be an expensive
+fuel in comparison with coal itself, and cannot be thought of as a
+general substitute for the latter. But in many cases the greater expense
+of the coal gas is more than compensated by its easy distribution, the
+facility and cleanliness of its application, the general freedom from
+the mechanical loss, unavoidable in the case of coal fires, the
+prevention of black smoke and so forth. The following table shows the
+average composition of coal gas by volume and weight, together with the
+heat developed by its single constituents, the latter being expressed in
+kilogram-calories per cub. metre (0.252 kilogram-calories = 1 British
+heat unit; 1 cub. metre = 35.3 cub. ft.; therefore 0.1123 calories per
+cub. metre = 1 British heat unit per cub. foot).
+
+  +----------------------+----------+----------+------------+--------------+------------+
+  |                      |          |          | Heat-value |  Heat-value  | Heat-value |
+  |    Constituents.     |  Volume  |  Weight  | per Cubic  | per Quantity |  per cent. |
+  |                      | per cent.| per cent.|   Metre    | contained in |  of Total. |
+  |                      |          |          |  Calories. |  1 Cub. Met. |            |
+  +----------------------+----------+----------+-----------+---------------+------------+
+  | Hydrogen, H2         |   47     |    7.4   |   2,582    |     1213     |    22.8    |
+  | Methane, CH4         |   34     |   42.8   |   8,524    |     2898     |    54.5    |
+  | Carbon monoxide, CO  |    9     |   19.9   |   3,043    |      273     |     5.1    |
+  | Benzene vapour, C6H6 |    1.2   |    7.4   |  33,815    |      405     |     7.7    |
+  | Ethylene, C2H4       |    3.8   |    8.4   |  13,960    |      530     |     9.9    |
+  | Carbon dioxide, CO2  |    2.5   |    8.6   |     ..     |       ..     |      ..    |
+  | Nitrogen, N2         |    2.5   |    5.5   |     ..     |       ..     |      ..    |
+  |                      +----------+----------+------------+--------------+------------+
+  |        Total         |  100.0   |  100.0   |     ..     |     5319     |   100.0    |
+  +----------------------+----------+----------+------------+--------------+------------+
+
+One cubic metre of such gas weighs 568 grammes. _Rich gas_, or gas made
+by the destructive distillation of certain bituminous schists, of oil,
+&c., contains much more of the heavy hydrocarbons, and its heat-value is
+therefore much higher than the above. The carburetted water gas, very
+generally made in America, and sometimes employed in England for mixing
+with coal gas, is of varying composition; its heat-value is generally
+rather less than that of coal gas (see below).
+
+IV. _Combustible Gases produced by the Partial Combustion of Coal,
+&c._--These form by far the most important kind of gaseous fuel. When
+coal is submitted to destructive distillation to produce the
+illuminating gas described in the preceding paragraph, only a
+comparatively small proportion of the heating value of the coal (say, a
+sixth or at most a fifth part) is obtained in the shape of gaseous fuel,
+by far the greater proportion remaining behind in the shape of coke.
+
+An entirely different class of gaseous fuels comprises those produced by
+the incomplete combustion of the total carbon contained in the raw
+material, where the result is a mixture of gases which, being capable of
+combining with more oxygen, can be burnt and employed for heating
+purposes. Apart from some descriptions of waste gases belonging to this
+class (of which the most notable are those from blast-furnaces), we must
+distinguish two ways of producing such gaseous fuels entirely different
+in principle, though sometimes combined in one operation. The incomplete
+combustion of carbon may be brought about by means of atmospheric
+oxygen, by means of water, or by a simultaneous combination of these two
+actions. In the first case the chemical reaction is
+
+  C + O= CO       (a);
+
+the nitrogen accompanying the oxygen in the atmospheric air necessarily
+remains mixed with carbon monoxide, and the resulting gases, which
+always contain some carbon dioxide, some products of the destructive
+distillation of the coal, &c., are known as _producer gas_ or _Siemens
+gas_. In the second case the chemical reaction is mainly
+
+  C + H2O = CO + H2   (b);
+
+that is to say, the carbon is converted into monoxide and the hydrogen
+is set free. As both of these substances can combine with oxygen, and as
+there is no atmospheric nitrogen to deal with, the resulting gas (_water
+gas_) is, apart from a few impurities, entirely combustible. Another
+kind of water gas is formed by the reaction
+
+  C + 2H2O = CO2 + 2H2   (c),
+
+but this reaction, which converts all the carbon into the incombustible
+form of CO2, is considered as an unwelcome, although never entirely
+avoidable, concomitant of (b).
+
+The reaction by which water gas is produced being endothermic (as we
+shall see), this gas cannot be obtained except by introducing the
+balance of energy in another manner. This might be done by heating the
+apparatus from without, but as this method would be uneconomical, the
+process is carried out by alternating the endothermic production of
+water gas with the exothermic combustion of carbon by atmospheric air.
+Pure water gas is not, therefore, made by a continuous process, but
+alternates with the production of other gases, combustible or not. But
+instead of constantly interrupting the process in this way, a continuous
+operation may be secured by simultaneously carrying on both the
+reactions (a) and (b) in such proportions that the heat generated by (a)
+at least equals the heat absorbed by (b). For this purpose the apparatus
+is fed at the same time with atmospheric air and with a certain quantity
+of steam, preferably in a superheated state. Gaseous mixtures of this
+kind have been made, more or less intentionally, for a long time past.
+One of the best known of them, intended less for the purpose of serving
+as ordinary fuel than for that of driving machinery, is the Dowson gas.
+
+An advantage common to all kinds of gaseous fuel, which indeed forms the
+principal reason why it is intentionally produced from solid fuel, in
+spite of inevitable losses in the course of the operation, is the
+following. The combustion of solid fuel (coal, &c.) cannot be carried on
+with the theoretically necessary quantity of atmospheric air, but
+requires a considerable excess of the latter, at least 50%, sometimes
+100% and more. This is best seen from the analyses of smoke gases. If
+all the oxygen of the air were converted into CO2 and H2O, the amount of
+CO2 in the smoke gases should be in the case of pure carbon nearly 21
+volumes %, as carbon dioxide occupies the same volume as oxygen; while
+ordinary coal, where the hydrogen takes up a certain quantity of oxygen
+as well, should show about 18.5% CO2. But the best smoke gases of steam
+boilers show only 12 or 13%, much more frequently only 10% CO2, and
+gases from reverberatory furnaces often show less than 5%. This means
+that the volume of the smoke gases escaping into the air is from 1-1/2
+to 2 times (in the case of high-temperature operations often 4 times)
+greater than the theoretical minimum; and as these gases always carry
+off a considerable quantity of heat, the loss of heat is all the greater
+the less complete is the utilization of the oxygen and the higher the
+temperature of the operation. This explains why, in the case of the
+best-constructed steam-boiler fires provided with heat economizers,
+where the smoke gases are deprived of most of their heat, the proportion
+of the heat value of the fuel actually utilized may rise to 70 or even
+75%, while in some metallurgical operations, in glass-making and similar
+cases, it may be below 5%.
+
+One way of overcoming this difficulty to a certain extent is to reduce
+the solid fuel to a very fine powder, which can be intimately mixed with
+the air so that the consumption of the latter is only very slightly in
+excess of the theoretical quantity; but this process, which has been
+only recently introduced on a somewhat extended scale, involves much
+additional expense and trouble, and cannot as yet be considered a real
+success. Generally, too, it is far less easily applied than gaseous
+fuel. The latter can be readily and intimately mixed with the exact
+quantity of air that is required and distributed in any suitable way,
+and much of the waste heat can be utilized for a preliminary heating of
+the air and the gas to be burned by means of "recuperators."
+
+We shall now describe the principal classes of gaseous fuel, produced by
+the partial combustion of coal.
+
+A. _Producer Gas, Siemens Gas._--As we have seen above, this gas is made
+by the incomplete combustion of fuel. The materials generally employed
+for its production are anthracite, coke or other fuels which are not
+liable to cake during the operation, and thus stop the draught or
+otherwise disturb the process, but by special measures also bituminous
+coal, lignite, peat and other fuel may be utilized for gas producers.
+The fuel is arranged in a deep layer, generally from 4 ft. up to 10 ft.,
+and the air is introduced from below, either by natural draught or by
+means of a blast, and either by a grate or only by a slit in the wall of
+the "gas producer." Even if the primary action taking place at the
+entrance of the air consisted in the complete combustion of the carbon
+to dioxide, CO2, the latter, in rising through the high column of
+incandescent fuel, must be reduced to monoxide: CO2 + C = 2CO. But as
+the temperature in the producer rises rather high, and as in ordinary
+circumstances the action of oxygen on carbon above 1000 deg. C. consists
+almost entirely in the direct formation of CO, we may regard this
+compound as primarily formed in the hotter parts of the gas-producer. It
+is true that ordinary producer gas always contains more or less CO2, but
+this may be formed higher up by air entering through leakages in the
+apparatus. If we ignore the hydrogen contained in the fuel, the
+theoretical composition of producer gas would be 33.3% CO and 66.7% N,
+both by volume and weight. Its weight per cubic metre is 1.251 grammes,
+and its heat value 1013 calories per cubic metre, or less than one-fifth
+of the heat-value of coal gas. Practically, however, producer gas
+contains a small percentage of gases, increasing its heat-value, like
+hydrogen, methane, &c., but on the other hand it is never free from
+carbon dioxide to the extent of from 2 to 8%. Its heat-value may
+therefore range between 800 and 1100 calories per cubic metre. Even when
+taking as the basis of our calculation a theoretical gas of 33.3% CO, we
+find that there is a great loss of heat-value in the manufacture of this
+gas. Thermochemistry teaches us that the reaction C + O develops 29.5%
+of the heat produced by the complete oxidation of C to CO2, thus leaving
+only 70.5% for the stage CO + O = CO2. If, therefore, the gas given off
+in the producer is allowed to cool down to ordinary temperature, nearly
+30% of the heat-value of the coal is lost by radiation. If, however, the
+gas producer is built in close proximity to the place where the
+combustion takes place, so that the gas does not lose very much of its
+heat, the loss is correspondingly less. Even then there is no reason why
+this mode of burning the fuel, i.e. first with "primary air" in the
+producer (C + O = CO), then with "secondary air" in the furnace (CO + O
+= CO2), should be preferred to the direct complete burning of the fuel
+on a grate, unless the above-mentioned advantage is secured, viz.
+reduction of the smoke gases to a minimum by confining the supply of air
+as nearly as possible to that required for the formation of CO2, which
+is only possible by producing an intimate mixture of the producer gas
+with the secondary air. The advantage in question is not very great
+where the heat of the smoke gases can be very fully utilized, e.g. in
+well-constructed steam boilers, salt-pans and the like, and as a matter
+of fact gas producers have not found much use in such cases. But a very
+great advantage is attained in high-temperature operations, where the
+smoke gases escape very hot, and where it is on that account
+all-important to confine their quantity to a minimum.
+
+It is precisely in these cases that another requirement frequently comes
+in, viz. the production at a given point of a higher temperature than is
+easily attained by ordinary fires. Gas-firing lends itself very well to
+this end, as it is easily combined with a preliminary heating up of the
+air, and even of the gas itself, by means of "recuperators." The
+original and best-known form of these, due to Siemens Brothers, consists
+of two brick chambers filled with loosely stacked fire-bricks in such
+manner that any gases passed through the chambers must seek their way
+through the interstices left between the bricks, by which means a
+thorough interchange of temperature takes place. The smoke gases,
+instead of escaping directly into the atmosphere, are made to pass
+through one of these chambers, giving up part of their heat to the
+brickwork. After a certain time the draught is changed by means of
+valves, the smoke gases are passed through another chamber, and the cold
+air intended to feed the combustion is made to pass through the first
+chamber, where it takes up heat from the white-hot bricks, and is thus
+heated up to a bright red heat until the chamber is cooled down too far,
+when the draughts are again reversed. Sometimes the producer gas itself
+is heated up in this manner (especially when it has been cooled down by
+travelling a long distance); in that case four recuperator chambers must
+be provided instead of two. Another class of recuperators is not founded
+on the alternating system, but acts continuously; the smoke gases travel
+always in the same direction in flues contiguous to other flues or pipes
+in which the air flows in the opposite direction, an interchange of heat
+taking place through the walls of the flues or pipes. Here the surface
+of contact must be made very large if a good effect is to be produced.
+In both cases not merely is a saving effected of all the calories which
+are abstracted by the cold air from the recuperator, but as less fuel
+has to be burned to get a given effect, the quantity of smoke gas is
+reduced. For details and other producer gases, see GAS, II. _For Fuel
+and Power._
+
+Gas-firing in the manner just described can be brought about by very
+simple means, viz. by lowering the fire-grate of an ordinary fire-place
+to at least 4 ft. below the fire-bridge, and by introducing the air
+partly below the grate and partly behind the fire-place, at or near the
+point where the greatest heat is required. Usually, however, more
+elaborate apparatus is employed, some of which we shall describe below.
+Gas-firing has now become universal in some of the most important
+industries and nearly so in others. The present extension of
+steel-making and other branches of metallurgy is intimately connected
+with this system, as is the modern method of glass-making, of heating
+coal gas retorts and so forth.
+
+The composition of producer gas differs considerably, principally
+according to the material from which it is made. Analyses of ordinary
+producer gas (not such as falls under the heading of "semi-water gas,"
+see _sub_ C) by volume show 22 to 33% CO, 1 to 7% CO2, 0.5 to 2% H2, 0.5
+to 3% hydrocarbons, and 64 to 68% N2.
+
+B. _Water Gas._--The reaction of steam on highly heated carbonaceous
+matter was first observed by Felice Fontana in 1780. This was four years
+before Henry Cavendish isolated hydrogen from water, and thirteen years
+before William Murdoch made illuminating gas by the distillation of
+coal, so that it was no wonder that Fontana's laboratory work was soon
+forgotten. Nor had the use of carburetted water gas, as introduced by
+Donovan in 1830 for illuminating purposes, more than a very short life.
+More important is the fact that during nine years the illumination of
+the town of Narbonne was carried on by incandescent platinum wire,
+heated by water gas, where also internally heated generators were for
+the first time regularly employed. The Narbonne process was abandoned in
+1865, and for some time no real progress was made in this field in
+Europe. But in America, T.S.C. Lowe, Strong, Tessie du Motay and others
+took up the matter, the first permanent success being obtained by the
+introduction (1873) of Lowe's system at Phoenixville, Pa. In the United
+States the abundance of anthracite, as well as of petroleum naphtha,
+adapted for carburetting the gas, secures a great commercial advantage
+to this kind of illuminant over coal gas, so that now three-fourths of
+all American gas-works employ carburetted water gas. In Europe the
+progress of this industry was naturally much less rapid, but here also
+since 1882, when the apparatus of Lowe and Dwight was introduced in the
+town of Essen, great improvements have been worked out, principally by
+E. Blass, and by these improvements water gas obtained a firm footing
+also for certain heating purposes. The American process for making
+carburetted water gas, as an auxiliary to ordinary coal gas, was first
+introduced by the London Gas Light and Coke Company on a large scale in
+1890.
+
+Water gas in its original state is called "blue gas," because it burns
+with a blue, non-luminous flame, which produces a very high temperature.
+According to the equation C + H2O = CO + H2, this gas consists
+theoretically of equal volumes of carbon monoxide and hydrogen. We shall
+presently see why it is impossible to avoid the presence of a little
+carbon dioxide and other gases, but we shall for the moment treat of
+water gas as if it were composed according to the above equation. The
+reaction C + H2O = CO + H2 is endothermic, that is, its thermal value is
+negative. One gram-molecule of carbon produces 97 great calories (1
+great calorie or kilogram-calorie = 1000 gram-calories) when burning to
+CO2, and this is of course the maximum effect obtainable from this
+source. If the same gram-molecule of carbon is used for making water
+gas, that is, CO + H2, the heat produced by the combustion of the
+product is 68.4 + 57.6 = 126 great calories, an apparent surplus of 29
+calories, which cannot be got out of nothing. This is made evident by
+another consideration. In the above reaction C is not burned to CO2, but
+to CO, a reaction which produces 28.6 calories per gram-molecule. But as
+the oxygen is furnished from water, which must first be decomposed by
+the expenditure of energy, we must introduce this amount, 68.5 calories
+in the case of liquid water, or 57.6 calories in the case of steam, as a
+negative quantity, and the difference, viz. + 28.6 - 57.6 = 29 great
+calories, represents the amount of heat to be expended from another
+source in order to bring about the reaction of one gram-molecule of
+carbon on one gram-molecule of H2O in the shape of steam. This explains
+why steam directed upon incandescent coal will produce water gas only
+for a very short time: even a large mass of coal will quickly be cooled
+down so much that at first a gas of different composition is formed and
+soon the process will cease altogether. We can avoid this result by
+carrying on the process in a retort heated from without by an ordinary
+coal fire, and all the early water gas apparatus was constructed in this
+way; but such a method is very uneconomical, and was long ago replaced
+by a process first patented by J. and T.N. Kirkham in 1854, and very
+much improved by successive inventors. This process consists in
+conducting the operation in an upright brick shaft, charged with
+anthracite, coke or other suitable fuel. This shaft resembles an
+ordinary gas producer, but it differs in being worked, not in a
+continuous manner, which, as shown above, would be impossible, but by
+alternately blowing air and steam through the coal for periods of a few
+minutes each. During the first phase, when carbon is burned by
+atmospheric oxygen, and thereby heat is produced, this heat, or rather
+that part of it which is not carried away by radiation and by the
+products of combustion on leaving the apparatus, is employed in raising
+the temperature of the remaining mass of fuel, and is thus available for
+the second phase, in which the reaction (b) C + H2O = CO + H2 goes on
+with the abstraction of a corresponding amount of heat from the
+incandescent fuel, so that the latter rapidly cools down, and the
+process must be reversed by blowing in air and so forth. The formation
+of exactly equal volumes of carbon monoxide and hydrogen goes on only at
+temperatures over 1200 deg. C., that is, for a very few minutes. Even at
+1100 deg. C. a little CO2 can be proved to exist in the gas, and at 900
+deg. its proportion becomes too high to allow the process to go on.
+About 650 deg. C. the CO has fallen to a minimum, and the reaction is
+now essentially (c) C + 2H2O = CO2 + 2H2; soon after the temperature of
+the mass will have fallen to such a low point that the steam passes
+through it without any perceptible action. The gas produced by reaction
+(c) contains only two-thirds of combustible matter, and is on that
+account less valuable than proper water gas formed by reaction (b);
+moreover, it requires the generation of twice the amount of steam, and
+its presence is all the less desirable since it must soon lead to a
+total cessation of the process. In ordinary circumstances it is evident
+that the more steam is blown in during a unit of time, the sooner
+reaction (c) will set in; on the other hand, the more heat has been
+accumulated in the producer the longer can the blowing-in of steam be
+continued.
+
+The process of making water gas consequently comprises two alternating
+operations, viz. first "blowing-up" by means of a current of air, by
+which the heat of the mass of fuel is raised to about 1200 deg. C.; and,
+secondly "steaming," by injecting a current of (preferably superheated)
+steam until the temperature of the fuel had fallen to about 900 deg. C.,
+and too much carbon dioxide appears in the product. During the steaming
+the gas is carried off by a special conduit into a scrubber, where the
+dust mechanically carried away in the current is washed out, and the gas
+is at the same time cooled down nearly to the ordinary temperature. It
+is generally stored in a gas-holder, from which it is conducted away as
+required. It is never quite free from nitrogen, as the producer at the
+beginning of steaming contains much of this gas, together with CO or
+CO2. The proportion of hydrogen may exceed 50%, in consequence of
+reaction (c) setting in at the close of the steaming. Ordinary "blue"
+water gas, if, as usual, made from coke or anthracite, contains 48-52%
+H2, 40-41% CO, 1-5% CO2, 4-5% N2, and traces of hydrocarbons, especially
+methane. If made from bituminous coal, it contains more of the latter.
+If "carburetted" (a process which increases its volume 50% and more) by
+the vapours from superheated petroleum naphtha, the proportion of CO
+ranges about 25%, with about as much methane, and from 10 to 15% of
+"illuminants" (heavy hydrocarbons). The latter, of course, greatly
+enhance the fuel-value of the gas. Pure water gas would possess the
+following fuel-value per cubic metre:
+
+  0.5 cub. met. H2 = 1291 calories
+  0.5  "    "   CO = 1522    "
+                     ----
+                     2813    "
+
+Ordinary "blue" water gas has a fuel-value of at least 2500 calories.
+Carburetted water gas, which varies very much in its percentage of
+hydrocarbons, sometimes reaches nearly the heat-value of coal gas, but
+such gas is only in exceptional cases used for heating purposes.
+
+We must now turn to the "blowing-up" stage of the process. Until
+recently it was assumed that during this stage the combustion of carbon
+cannot be carried on beyond the formation of carbon monoxide, for as the
+gas-producer must necessarily contain a deep layer of fuel (generally
+about 6 to 10 ft.), any CO2 formed at first would be reduced to CO; and
+it was further assumed that hardly any CO2 would be formed from the
+outset, as the temperature of the apparatus is too high for this
+reaction to take place. But as the combustion of C to CO produces only
+about 30% of the heat produced when C is burned into CO2, the quantity
+of fuel consumed for "blowing-up" is very large, and in fact
+considerably exceeds that consumed in "steaming." There is, of course, a
+further loss by radiation and minor sources, and the result is that 1
+kilogram of carbon yields only about 1.2 cub. met. of water gas. Each
+period of blowing-up generally occupies from 8 to 12 minutes, that of
+steaming only 4 or 5 minutes. This low yield of water gas until quite
+recently appeared to be unavoidable, and the only question seemed to be
+whether and to what extent the gas formed during blowing-up, which is in
+fact identical with ordinary producer gas (Siemens gas), could be
+utilized. In America, where the water gas is mostly employed for
+illuminating purposes, at least part of the blowing-up gas is utilized
+for heating the apparatus in which the naphtha is volatilized and the
+vapours are "fixed" by superheating. This process, however, never
+utilizes anything like the whole of the blowing-up gas, nor can this be
+effected by raising and superheating the steam necessary for the second
+operation; indeed, the employment of this gas for raising steam is not
+very easy, owing to the irregularities of and constant interruptions in
+the supply. In some systems the gas made during the blowing-up stage is
+passed through chambers, loosely filled with bricks, like Siemens
+recuperators, where it is burned by "secondary" air: the heat thus
+imparted to the brickwork is utilized by passing through the
+recuperator, and thus superheating, the steam required for the next
+steaming operation. In many cases, principally where no carburetting is
+practised, the blowing-up gas is simply burned at the mouth of the
+producer, and is thus altogether lost; and in no case can it be utilized
+without great waste. A very important improvement in this respect was
+effected by C. Dellwik and E. Fleischer. They found that the view that
+it is unavoidable to burn the carbon to monoxide during the blowing-up
+holds good only for the pressure of blast formerly applied. This did not
+much exceed that which is required for overcoming the frictional
+resistance within the producer. If, however, the pressure is
+considerably increased, and the height of the column of fuel reduced,
+both of these conditions being strictly regulated in accordance with the
+result desired, it is easy to attain a combustion of the carbon to
+dioxide, with only traces of monoxide, in spite of the high temperature.
+Evidently the excess of oxygen coming into contact with each particle of
+carbon in a given unit of time produces other conditions of chemical
+equilibrium than those existing at lower pressures. At any rate,
+experience has shown that by this process, in which the full heat-value
+of carbon is utilized during the blowing-up stage, the time of
+heating-up can be reduced from 10 to 1-1/2 or 2 minutes, and the
+steaming can be prolonged from 4 or 5 to 8 or 10 minutes, with the
+result that twice the quantity of water gas is obtained, viz. upwards of
+2 cub. metres from 1 kilogram of carbon.
+
+The application of water gas as a fuel mainly depends upon the high
+temperatures which it is possible to attain by its aid, and these are
+principally due to the circumstance that it forms a much smaller flame
+than coal gas, not to speak of Siemens gas, which contains at most 33%
+of combustible matter against 90% or more in water gas. The latter
+circumstance also allows the gas to be conducted and distributed in
+pipes of moderate dimensions. Its application, apart from its use as an
+illuminant (with which we are not concerned here), was formerly retarded
+by its high cost in comparison with Siemens gas and other sources of
+heat, but as this state of affairs has been changed by the modern
+improvements, its use is rapidly extending, especially for metallurgical
+purposes.
+
+C. _Mixed Gas (Semi-Water Gas)._--This class is sometimes called Dowson
+gas, irrespective of its method of production, although it was made and
+extensively used a long time before J.E. Dowson constructed his
+apparatus for generating such a gas principally for driving gas-engines.
+By a combination of the processes for generating Siemens gas and water
+gas, it is produced by injecting into a gas-producer at the same time a
+certain quantity of air and a corresponding quantity of steam, the
+latter never exceeding the amount which can be decomposed by the
+heat-absorbing reaction, C + H2O = CO + H2, at the expense of the heat
+generated by the action of the air in the reaction C + O = CO. Such gas
+used to be frequently obtained in an accidental way by introducing
+liquid water or steam into an ordinary gas-producer for the purpose of
+facilitating its working by avoiding an excessive temperature, such as
+might cause the rapid destruction of the brickwork and the fusion of the
+ashes of the fuel into troublesome cakes. It was soon found that by
+proceeding in this way a certain advantage could be gained in regard to
+the consumption of fuel, as the heat abstracted by the steam from the
+brickwork and the fuel itself was usefully employed for decomposing
+water, its energy thus reappearing in the shape of a combustible gas. It
+is hardly necessary to mention explicitly that the total heat obtained
+by any such process from a given quantity of carbon (or hydrogen) can in
+no case exceed that which is generated by direct combustion; some
+inventors, however, whether inadvertently or intentionally, have
+actually represented this to be possible, in manifest violation of the
+law of the conservation of energy.
+
+Roughly speaking, this gas may be said to be produced by the combination
+of the reactions, described _sub_ A and B, to the joint reaction: 2C + O
++ H2O = 2CO + H2. The decomposition of H2O (applied in the shape of
+steam) absorbs 57.6 gram calories, the formation of 2CO produces 59 gram
+calories; hence there is a small positive excess of 1.4 calories at
+disposal. This in reality would not be sufficient to cover the loss by
+radiation, &c.; hence rather more free oxygen (i.e. atmospheric air)
+must be employed than is represented by the above equation. All this
+free oxygen is, of course, accompanied by nearly four times its volume
+of nitrogen.
+
+The mixed gas thus obtained differs very much in composition, but is
+always much richer in hydrogen (of which it contains sometimes as much
+as 20%) and poorer in carbon monoxide (sometimes down to 20%) than
+Siemens gas; generally it contains more of CO2 than the latter. The
+proportion of nitrogen is always less, about 50%. It is therefore a more
+concentrated fuel than Siemens gas, and better adapted to the driving of
+gas-engines. It scarcely costs more to make than ordinary Siemens gas,
+except where the steam is generated and superheated in special
+apparatus, as is done in the Dowson producer, which, on the other hand,
+yields a correspondingly better gas. As is natural, its properties are
+some way between those of Siemens gas and of water gas; but they
+approach more nearly the former, both as to costs and as to fuel-value,
+and also as to the temperatures reached in combustion. This is easily
+understood if we consider that gas of just the same description can be
+obtained by mixing one volume of real water gas with the four volumes of
+Siemens gas made during the blowing-up stage--an operation which is
+certainly too expensive for practical use.
+
+A modification of this gas is the _Mond gas_, which is made, according
+to Mond's patent, by means of such an excess of steam that most of the
+nitrogen of the coke is converted into ammonia (Grouven's reaction). Of
+course much of this steam passes on undecomposed, and the quantity of
+the gas is greatly increased by the reaction C + 2H2O = CO2 + 2H2; hence
+the fuel-value of this gas is less than that of semi-water gas made in
+other ways. Against this loss must be set the gain of ammonia which is
+recovered by means of an arrangement of coolers and scrubbers, and,
+except at very low prices of ammonia, the profit thus made is probably
+more than sufficient to cover the extra cost. But as the process
+requires very large and expensive plant, and its profits would vanish in
+the case of the value of ammonia becoming much lower (a result which
+would very probably follow if it were somewhat generally introduced), it
+cannot be expected to supplant the other descriptions of gaseous fuel to
+more than a limited extent.
+
+Semi-water gas is especially adapted for the purpose of driving
+gas-engines on the explosive principle (gas-motors). Ordinary
+producer-gas is too poor for this purpose in respect of heating power;
+moreover, owing to the prevalence of carbon monoxide, it does not light
+quickly enough. These defects are sufficiently overcome in semi-water
+gas by the larger proportion of hydrogen contained in it. For the
+purpose in question the gas should be purified from tar and ashes, and
+should also be cooled down before entering the gas-engine. The Dowson
+apparatus and others are constructed on this principle.
+
+_Air Gas._--By forcing air over or through volatile inflammable liquids
+a gaseous mixture can be obtained which burns with a bright flame and
+which can be used for illumination. Its employment for heating purposes
+is quite exceptional, e.g. in chemical laboratories, and we abstain,
+therefore, from describing any of the numerous appliances, some of them
+bearing very fanciful names, which have been devised for its
+manufacture.     (G. L.)
+
+
+
+
+FUENTE OVEJUNA [_Fuenteovejuna_], a town of Spain, in the province of
+Cordova; near the sources of the river Guadiato, and on the Fuente del
+Arco-Belmez-Cordova railway. Pop. (1900) 11,777. Fuente Ovejuna is built
+on a hill, in a well-irrigated district, which, besides producing an
+abundance of wheat, wine, fruit and honey, also contains argentiferous
+lead mines and stone quarries. Cattle-breeding is an important local
+industry, and leather, preserved meat, soap and flour are manufactured.
+The parish church formerly belonged to the knights of Calatrava (c.
+1163-1486).
+
+
+
+
+FUENTERRABIA (formerly sometimes written _Fontarabia_; Lat. _Fons
+Rapidus_), a town of northern Spain, in the province of Guipuzcoa; on
+the San Sebastian-Bayonne railway; near the Bay of Biscay and on the
+French frontier. Pop. (1870) about 750; (1900) 4345. Fuenterrabia stands
+on the slope of a hill on the left bank of the river Bidassoa, and near
+the point where its estuary begins. Towards the close of the 19th
+century the town became popular as a summer resort for visitors from the
+interior of Spain, and, in consequence, its appearance underwent many
+changes and much of its early prosperity returned. Hotels and villas
+were built in the new part of the town that sprang up outside the
+picturesque walled fortress, and there is quite a contrast between the
+part inside the heavy, half-ruined ramparts, with its narrow, steep
+streets and curious gable-roofed houses, its fine old church and castle
+and its massive town hall, and the new suburbs and fishermen's quarter
+facing the estuary of the Bidassoa. Many industries flourish on the
+outskirts of the town, including rope and net manufactures, flour mills,
+saw mills, mining railways, paper mills.
+
+Fuenterrabia formerly possessed considerable strategic importance, and
+it has frequently been taken and retaken in wars between France and
+Spain. The rout of Charlemagne in 778, which has been associated with
+Fontarabia, by Milton (_Paradise Lost_, i. 587), is generally understood
+to have taken place not here but at Roncesvalles (q.v.), which is nearly
+40 m. E.S.E. Unsuccessful attempts to seize Fuenterrabia were made by
+the French troops in 1476 and again in 1503. In a subsequent campaign
+(1521) these were more successful, but the fortress was retaken in 1524.
+The prince of Conde sustained a severe repulse under its walls in 1638,
+and it was on this occasion that the town received from Philip IV. the
+rank of city (_muy noble, muy leal, y muy valerosa ciudad_, "most noble,
+most loyal, and most valiant city"), a privilege which involved some
+measure of autonomy. After a severe siege, Fuenterrabia surrendered to
+the duke of Berwick and his French troops in 1719; and in 1794 it again
+fell into the hands of the French, who so dismantled it that it has
+never since been reckoned by the Spaniards among their fortified places.
+It was by the ford opposite Fuenterrabia that the duke of Wellington, on
+the 8th of October 1813, successfully forced a passage into France in
+the face of an opposing army commanded by Marshal Soult. Severe fighting
+also took place here during the Carlist War in 1837.
+
+
+
+
+FUERO, a Spanish term, derived from the Latin _forum_. The Castillan use
+of the word in the sense of a right, privilege or charter is most
+probably to be traced to the Roman _conventus juridici_, otherwise known
+as _jurisdictiones_ or _fora_, which in Pliny's time were already
+numerous in the Iberian peninsula. In each of these provincial _fora_
+the Roman magistrate, as is well known, was accustomed to pay all
+possible deference to the previously established common law of the
+district; and it was the privilege of every free subject to demand that
+he should be judged in accordance with the customs and usages of his
+proper forum. This was especially true in the case of the inhabitants of
+those towns which were in possession of the _jus italicum_. It is not,
+indeed, demonstrable, but there are many presumptions, besides some
+fragments of direct evidence, which make it more than probable that the
+old administrative arrangements both of the provinces and of the towns,
+but especially of the latter, remained practically undisturbed at the
+period of the Gothic occupation of Spain.[1] The Theodosian Code and the
+Breviary of Alaric alike seem to imply a continuance of the municipal
+system which had been established by the Romans; nor does the later Lex
+Visigothorum, though avowedly designed in some points to supersede the
+Roman law, appear to have contemplated any marked interference with the
+former _fora_, which were still to a large extent left to be regulated
+in the administration of justice by unwritten, immemorial, local custom.
+Little is known of the condition of the subject populations of the
+peninsula during the Arab occupation; but we are informed that the
+Christians were, sometimes at least, judged according to their own laws
+in separate tribunals presided over by Christian judges;[2] and the mere
+fact of the preservation of the name _alcalde_, an official whose
+functions corresponded so closely to those of the _judex_ or _defensor
+civitatis_, is fitted to suggest that the old municipal _fora_, if much
+impaired, were not even then in all cases wholly destroyed. At all
+events when the word _forum_[3] begins to appear for the first time in
+documents of the 10th century in the sense of a liberty or privilege,
+it is generally implied that the thing so named is nothing new. The
+earliest extant written fuero is probably that which was granted to the
+province and town of Leon by Alphonso V. in 1020. It emanated from the
+king in a general council of the kingdom of Leon and Castile, and
+consisted of two separate parts; in the first 19 chapters were contained
+a series of statutes which were to be valid for the kingdom at large,
+while the rest of the document was simply a municipal charter.[4] But in
+neither portion does it in any sense mark a new legislative departure,
+unless in so far as it marks the beginning of the era of written
+charters for towns. The "fuero general" does not profess to supersede
+the _consuetudines antiquorum jurium_ or Chindaswint's codification of
+these in the Lex Visigothorum; the "fuero municipal" is really for the
+most part but a resuscitation of usages formerly established, a
+recognition and definition of liberties and privileges that had long
+before been conceded or taken for granted. The right of the burgesses to
+self-government and self-taxation is acknowledged and confirmed, they,
+on the other hand, being held bound to a constitutional obedience and
+subjection to the sovereign, particularly to the payment of definite
+imperial taxes, and the rendering of a certain amount of military
+service (as the ancient municipia had been). Almost contemporaneous with
+this fuero of Leon was that granted to Najera (Naxera) by Sancho el
+Mayor of Navarre (_ob._ 1035), and confirmed, in 1076, by Alphonso
+VI.[5] Traces of others of perhaps even an earlier date are occasionally
+to be met with. In the fuero of Cardena, for example, granted by
+Ferdinand I. in 1039, reference is made to a previous forum Burgense
+(Burgos), which, however, has not been preserved, if, indeed, it ever
+had been reduced to writing at all. The phraseology of that of Sepulveda
+(1076) in like manner points back to an indefinitely remote
+antiquity.[6] Among the later fueros of the 11th century, the most
+important are those of Jaca (1064) and of Logrono (1095). The former of
+these, which was distinguished by the unusual largeness of its
+concessions, and by the careful minuteness of its details, rapidly
+extended to many places in the neighbourhood, while the latter charter
+was given also to Miranda by Alphonso VI., and was further extended in
+1181 by Sancho el Sabio of Navarre to Vitoria, thus constituting one of
+the earliest written _fora_ of the "Provincias Vascongadas." In the
+course of the 12th and 13th centuries the number of such documents
+increased very rapidly; that of Toledo especially, granted to the
+Mozarabic population in 1101, but greatly enlarged and extended by
+Alphonso VII. (1118) and succeeding sovereigns, was used as a basis for
+many other Castilian fueros. Latterly the word fuero came to be used in
+Castile in a wider sense than before, as meaning a general code of laws;
+thus about the time of Saint Ferdinand the old Lex Visigothorum, then
+translated for the first time into the vernacular, was called the Fuero
+Juzgo, a name which was soon retranslated into the barbarous Latin of
+the period as Forum Judicum;[7] and among the compilations of Alphonso
+the Learned in like manner were an _Espejo de Fueros_ and also the
+_Fuero de las leyes_, better known perhaps as the _Fuero Real_. The
+famous code known as the _Ordenamiento Real de Alcala_, or _Fuero Viejo
+de Castilla_, dates from a still later period. As the power of the
+Spanish crown was gradually concentrated and consolidated, royal
+pragmaticas began to take the place of constitutional laws; the local
+fueros of the various districts slowly yielded before the superior force
+of imperialism; and only those of Navarre and the Basque provinces (see
+BASQUES) have had sufficient vitality to enable them to survive to
+comparatively modern times. While actually owning the lordship of the
+Castilian crown since about the middle of the 14th century, these
+provinces rigidly insisted upon compliance with their consuetudinary
+law, and especially with that which provided that the _senor_, before
+assuming the government, should personally appear before the assembly
+and swear to maintain the ancient constitutions. Each of the provinces
+mentioned had distinct sets of fueros, codified at different periods,
+and varying considerably as to details; the main features, however, were
+the same in all. Their rights, after having been recognized by
+successive Spanish sovereigns from Ferdinand the Catholic to Ferdinand
+VII., were, at the death of the latter in 1833, set aside by the
+government of Castanos. The result was a civil war, which terminated in
+a renewed acknowledgment of the fueros by Isabel II. (1839). The
+provisional government of 1868 also promised to respect them, and
+similar pledges were given by the governments which succeeded. In
+consequence, however, of the Carlist rising of 1873-1876, the Basque
+fueros were finally extinguished in 1876. The history of the _Foraes_ of
+the Portuguese towns, and of the _Fors du Bearn_, is precisely analogous
+to that of the fueros of Castile.
+
+  Among the numerous works that more or less expressly deal with this
+  subject, that of Marina (_Ensayo historico-critico sobre la antigua
+  legislacion y principales cuerpos legales de los reynos de Leon y
+  Castilla_) still continues to hold a high place. Reference may also be
+  made to Colmeiro's _Curso de derecho politico segun la historia de
+  Leon y de Castilla_ (Madrid, 1873); to Schafer's _Geschichte von
+  Spanien_, ii. 418-428, iii. 293 seq.; and to Hallam's _Middle Ages_,
+  c. iv.
+
+
+FOOTNOTES:
+
+  [1] The nature of the evidence may be gathered from Savigny, _Gesch.
+    d. rom. Rechts_. See especially i. pp. 154, 259 seq.
+
+  [2] Compare Lembke u. Schafer, _Geschichte von Spanien_, i. 314; ii.
+    117.
+
+  [3] Or rather _forus_. See Ducange, s.v.
+
+  [4] Cap. xx. begins: "Constituimus etiam ut Legionensis civitas, quae
+    depopulata fuit a Sarracenis in diebus patris mei Veremundi regis,
+    repopulatur _per hos foros subscriptos_."
+
+  [5] "Mando et concedo et confirmo ut ista civitas cum sua plebe et
+    cum omnibus suis pertinentiis sub tali lege et sub tali foro maneat
+    per saecula cuncta. Amen. Isti sunt fueros quae habuerunt in Naxera
+    in diebus Sanctii regis et Gartiani regis."
+
+  [6] "Ego Aldefonsus rex et uxor mea Agnes confirmamus ad
+    Septempublica suo foro quod habuit in tempore antiquo de avolo meo et
+    in tempore comitum Ferrando Gonzalez et comite Garcia Ferdinandez et
+    comite Domno Santio."
+
+  [7] This Latin is later even than that of Ferdinand, whose words are:
+    "Statuo et mando quod Liber Judicum, quo ego misi Cordubam,
+    translatetur in vulgarem et vocetur forum de Corduba ... et quod per
+    saecula cuncta sit pro foro et nullus sit ausus istud forum aliter
+    appellare nisi forum de Corduba, et jubeo et mando quod omnis morator
+    et populator ... veniet ad judicium et ad forum de Corduba."
+
+
+
+
+FUERTEVENTURA, an island in the Atlantic Ocean, forming part of the
+Spanish archipelago of the Canary Islands (q.v.). Pop. (1900) 11,669;
+area 665 sq. m. Fuerteventura lies between Lanzarote and Grand Canary.
+It has a length of 52 m., and an average width of 12 m. Though less
+mountainous than the other islands, its aspect is barren. There are only
+two springs of fresh water, and these are confined to one valley. Lava
+streams and other signs of volcanic action abound, but there has been no
+igneous activity since the Spaniards took possession. At each extremity
+of the island are high mountains, which send off branches along the
+coast so as to enclose a large arid plain. The highest peak reaches 2500
+ft. In external appearance, climate and productions, Fuerteventura
+greatly resembles Lanzarote. An interval of three years without rain has
+been known. Oliva (pop. 1900, 2464) is the largest town. A smaller place
+in the centre of the island named Betancuria (586) is the administrative
+capital. Cabras (1000) on the eastern coast is the chief port.
+Dromedaries are bred here.
+
+
+
+
+FUGGER, the name of a famous German family of merchants and bankers. The
+founder of the family was Johann Fugger, a weaver at Graben, near
+Augsburg, whose son, Johann, settled in Augsburg probably in 1367. The
+younger Johann added the business of a merchant to that of a weaver, and
+through his marriage with Clara Widolph became a citizen of Augsburg.
+After a successful career he died in 1408, leaving two sons, Andreas and
+Jakob, who greatly extended the business which they inherited from their
+father. Andreas, called the "rich Fugger," had several sons, among them
+being Lukas, who was very prominent in the municipal politics of
+Augsburg and who was very wealthy until he was ruined by the repudiation
+by the town of Louvain of a great debt owing to him, and Jakob, who was
+granted the right to bear arms in 1452, and who founded the family of
+Fugger vom Reh--so called from the first arms of the Fuggers, a roe
+(_Reh_) or on a field azure--which became extinct on the death of his
+great-grandson, Ulrich, in 1583. Johann Fugger's son, Jakob, died in
+1469, and three of his seven sons, Ulrich (1441-1510), Georg (1453-1506)
+and Jakob (1459-1525), men of great resource and industry, inherited the
+family business and added enormously to the family wealth. In 1473
+Ulrich obtained from the emperor Frederick III. the right to bear arms
+for himself and his brothers, and about the same time he began to act
+as the banker of the Habsburgs, a connexion destined to bring fame and
+fortune to his house. Under the lead of Jakob, who had been trained for
+business in Venice, the Fuggers were interested in silver mines in Tirol
+and copper mines in Hungary, while their trade in spices, wool and silk
+extended to almost all parts of Europe. Their wealth enabled them to
+make large loans to the German king, Maximilian I., who pledged to them
+the county of Kirchberg, the lordship of Weissenhorn and other lands,
+and bestowed various privileges upon them. Jakob built the castle of
+Fuggerau in Tirol, and erected the Fuggerei at Augsburg, a collection of
+106 dwellings, which were let at low rents to poor people and which
+still exist. Jakob Fugger and his two nephews, Ulrich (d. 1525) and
+Hieronymus (d. 1536), the sons of Ulrich, died without direct heirs, and
+the family was continued by Georg's sons, Raimund (1489-1535) and Anton
+(1493-1560), under whom the Fuggers attained the summit of their wealth
+and influence.
+
+Jakob Fugger's florins had contributed largely to the election of
+Charles V. to the imperial throne in 1519, and his nephews and heirs
+maintained close and friendly relations with the great emperor. In
+addition to lending him large sums of money, they farmed his valuable
+quicksilver mines at Almaden, his silver mines at Guadalcanal, the great
+estates of the military orders which had passed into his hands, and
+other parts of his revenue as king of Spain; receiving in return several
+tokens of the emperor's favour. In 1530 Raimund and Anton were granted
+the imperial dignity of counts of Kirchberg and Weissenhorn, and
+obtained full possession of these mortgaged properties; in 1534 they
+were given the right of coining money; and in 1541 received rights of
+jurisdiction over their lands. During the diet of Augsburg in 1530
+Charles V. was the guest of Anton Fugger at his house in the Weinmarkt,
+and the story relates how the merchant astonished the emperor by
+lighting a fire of cinnamon with an imperial bond for money due to him.
+This incident forms the subject of a picture by Carl Becker which is in
+the National Gallery at Berlin. Continuing their mercantile career, the
+Fuggers brought the new world within the sphere of their operations, and
+also carried on an extensive and lucrative business in farming
+indulgences. Moreover, both brothers found time to acquire landed
+property, and were munificent patrons of literature and art. When Anton
+died he is said to have been worth 6,000,000 florins, besides a vast
+amount of property in Europe, Asia and America; and before this time the
+total wealth of the family had been estimated at 63,000,000 florins. The
+Fuggers were devotedly attached to the Roman Catholic Church, which
+benefited from their liberality. Jakob had been made a count palatine
+(_Pfalzgraf_) and had received other marks of favour from Pope Leo X.,
+and several members of the family had entered the church; one, Raimund's
+son, Sigmund, becoming bishop of Regensburg.
+
+In addition to the bishop, three of Raimund Fugger's sons attained some
+degree of celebrity. Johann Jakob (1516-1575), was the author of
+_Wahrhaftigen Beschreibung des osterreichischen und habsburgischen
+Nahmens_, which was largely used by S. von Bircken in his _Spiegel der
+Ehren des Erzhauses Osterreich_ (Nuremberg, 1668), and of a _Geheim
+Ernbuch des Fuggerischen Geschlechtes_. He was also a patron of art, and
+a distinguished counsellor of Duke Albert IV. of Bavaria. After the
+death of his son Konstantin, in 1627, this branch of the family was
+divided into three lines, which became extinct in 1738, 1795 and 1846
+respectively. Another of Raimund's sons was Ulrich (1526-1584), who,
+after serving Pope Paul III. at Rome, became a Protestant. Hated on this
+account by the other members of his family, he took refuge in the
+Rhenish Palatinate; greatly interested in the Greek classics, he
+occupied himself in collecting valuable manuscripts, which he bequeathed
+to the university of Heidelberg. Raimund's other son was Georg (d.
+1579), who inherited the countships of Kirchberg and Weissenhorn, and
+founded a branch of the family which still exists, its present head
+being Georg, Count Fugger of Kirchberg and Weissenhorn (b. 1850).
+
+Anton Fugger left three sons, Marcus (1529-1597), Johann (d. 1598) and
+Jakob (d. 1598), all of whom left male issue. Marcus was the author of
+a book on horse-breeding, _Wie und wo man ein Gestut von guten edeln
+Kriegsrossen aufrichten soll_ (1578), and of a German translation of the
+_Historia ecclesiastica_ of Nicephorus Callistus. He founded the
+Nordendorf branch of the family, which became extinct on the death of
+his grandson, Nicolaus, in 1676. Another grandson of Marcus was Franz
+Fugger (1612-1664), who served under Wallenstein during the Thirty
+Years' War, and was afterwards governor of Ingolstadt. He was killed at
+the battle of St Gotthard on the 1st of August 1664.
+
+Johann Fugger had three sons, Christoph (d. 1615) and Marcus (d. 1614),
+who founded the families of Fugger-Glott and Fugger-Kirchheim
+respectively, and Jakob, bishop of Constance from 1604 until his death
+in 1626. Christoph's son, Otto Heinrich (1592-1644), was a soldier of
+some distinction and a knight of the order of the Golden Fleece. He was
+one of the most active of the Bavarian generals during the Thirty Years'
+War, and acted as governor of Augsburg, where his rule aroused much
+discontent. The family of Kirchheim died out in 1672. That of Glott was
+divided into several branches by the sons of Otto Heinrich and of his
+brother Johann Ernst (d. 1628). These lines, however, have gradually
+become extinct except the eldest line, represented in 1909 by Karl
+Ernst, Count Fugger of Glott (b. 1859). Anton Fugger's third son Jakob,
+the founder of the family of Wellenburg, had two sons who left issue,
+but in 1777 the possessions of this branch of the family were again
+united by Anselm Joseph (d. 1793), Count Fugger of Babenhausen. In 1803
+Anselm's son, Anselm Maria (d. 1821), was made a prince of the Holy
+Roman Empire, the title of Prince Fugger of Babenhausen being borne by
+his direct descendant Karl (b. 1861). On the fall of the empire in 1806
+the lands of the Fuggers, which were held directly of the empire, were
+mediatized under Bavaria and Wurttemberg. The heads of the three
+existing branches of the Fuggers are all hereditary members of the
+Bavarian Upper House.
+
+Augsburg has many interesting mementoes of the Fuggers, including the
+family burial-chapel in the church of St Anna; the Fugger chapel in the
+church of St Ulrich and St Afra; the Fuggerhaus, still in the possession
+of one branch of the family; and a statue of Johann Jakob Fugger.
+
+  In 1593 a collection of portraits of the Fuggers, engraved by
+  Dominique Custos of Antwerp, was issued at Augsburg. Editions with 127
+  portraits appeared in 1618 and 1620, the former accompanied by a
+  genealogy in Latin, the latter by one in German. Another edition of
+  this _Pinacotheca Fuggerorum_, published at Vienna in 1754, includes
+  139 portraits. See _Chronik der Familie Fugger vom Jahre 1599_, edited
+  by C. Meyer (Munich, 1902); A. Geiger, _Jakob Fugger, 1459-1525_
+  (Regensburg, 1895); A. Schulte, _Die Fugger in Rom, 1495-1523_
+  (Leipzig, 1904); R. Ehrenberg, _Das Zeitalter der Fugger_ (Jena,
+  1896); K. Habler, _Die Geschichte der Fuggerschen Handlung in Spanien_
+  (Weimar, 1897); A. Stauber, _Das Haus Fugger_ (Augsburg, 1900); and M.
+  Jansen, _Die Anfange der Fugger_ (Leipzig, 1907).
+
+
+
+
+FUGITIVE SLAVE LAWS, a term applied in the United States to the Statutes
+passed by Congress in 1793 and 1850 to provide for the return of negro
+slaves who escaped from one state into another or into a public
+territory. A fugitive slave clause was inserted in the Articles of
+Confederation of the New England Confederation of 1643, providing for
+the return of the fugitive upon the certificate of one magistrate in the
+jurisdiction out of which the said servant fled--no trial by jury being
+provided for. This seems to have been the only instance of an
+inter-colonial provision for the return of fugitive slaves; there were,
+indeed, not infrequent escapes by slaves from one colony to another, but
+it was not until after the growth of anti-slavery sentiment and the
+acquisition of western territory, that it became necessary to adopt a
+uniform method for the return of fugitive slaves. Such provision was
+made in the Ordinance of 1787 (for the Northwest Territory), which in
+Article VI. provided that in the case of "any person escaping into the
+same [the Northwest Territory] from whom labor or service is lawfully
+claimed in any one of the original states, such fugitive may be lawfully
+reclaimed and conveyed to the person claiming his or her labor or
+service as aforesaid." An agreement of the sort was necessary to
+persuade the slave-holding states to union, and in the Federal
+Constitution, Article IV., Section II., it is provided that "no person
+held to service or labor in one state, under the laws thereof, escaping
+into another, shall, in consequence of any law or regulation therein, be
+discharged from such service or labor, but shall be delivered up on
+claim of the party to whom such service or labour may be due."
+
+The first specific legislation on the subject was enacted on the 12th of
+February 1793, and like the Ordinance for the Northwest Territory and
+the section of the Constitution quoted above, did not contain the word
+"slave"; by its provisions any Federal district or circuit judge or any
+state magistrate was authorized to decide finally and without a jury
+trial the status of an alleged fugitive. The measure soon met with
+strong opposition in the northern states, and Personal Liberty Laws were
+passed to hamper officials in the execution of the law; Indiana in 1824
+and Connecticut in 1828 providing jury trial for fugitives who appealed
+from an original decision against them. In 1840 New York and Vermont
+extended the right of trial by jury to fugitives and provided them with
+attorneys. As early as the first decade of the 19th century individual
+dissatisfaction with the law of 1793 had taken the form of systematic
+assistance rendered to negroes escaping from the South to Canada or New
+England--the so-called "Underground Railroad."[1] The decision of the
+Supreme Court of the United States in the case of _Prigg_ v.
+_Pennsylvania_ in 1842 (16 Peters 539), that state authorities could not
+be forced to act in fugitive slave cases, but that national authorities
+must carry out the national law, was followed by legislation in
+Massachusetts (1843), Vermont (1843), Pennsylvania (1847) and Rhode
+Island (1848), forbidding state officials to help enforce the law and
+refusing the use of state gaols for fugitive slaves. The demand from the
+South for more effective Federal legislation was voiced in the second
+fugitive slave law, drafted by Senator J.M. Mason of Virginia, and
+enacted on the 18th of September 1850 as a part of the Compromise
+Measures of that year. Special commissioners were to have concurrent
+jurisdiction with the U.S. circuit and district courts and the inferior
+courts of Territories in enforcing the law; fugitives could not testify
+in their own behalf; no trial by jury was provided; penalties were
+imposed upon marshals who refused to enforce the law or from whom a
+fugitive should escape, and upon individuals who aided negroes to
+escape; the marshal might raise a _posse comitatus_; a fee of $10 was
+paid to the commissioner when his decision favoured the claimant and
+only $5 when it favoured the fugitive; and both the fact of the escape
+and the identity of the fugitive were to be determined on purely _ex
+parte_ testimony. The severity of this measure led to gross abuses and
+defeated its purpose; the number of abolitionists increased, the
+operations of the Underground Railroad became more efficient, and new
+Personal Liberty Laws were enacted in Vermont (1850), Connecticut
+(1854), Rhode Island (1854), Massachusetts (1855), Michigan (1855),
+Maine (1855 and 1857), Kansas (1858) and Wisconsin (1858). These
+Personal Liberty Laws forbade justices and judges to take cognizance of
+claims, extended the _habeas corpus_ act and the privilege of jury trial
+to fugitives, and punished false testimony severely. The supreme court
+of Wisconsin went so far (1859) as to declare the Fugitive Slave Law
+unconstitutional. These state laws were one of the grievances officially
+referred to by South Carolina (in Dec. 1860) as justifying her secession
+from the Union. Attempts to carry into effect the law of 1850 aroused
+much bitterness. The arrests of Sims and of Shadrach in Boston in 1851;
+of "Jerry" M'Henry, in Syracuse, New York, in the same year; of Anthony
+Burns in 1854, in Boston; and of the two Garner families in 1856, in
+Cincinnati, with other cases arising under the Fugitive Slave Law of
+1850, probably had as much to do with bringing on the Civil War as did
+the controversy over slavery in the Territories.
+
+With the beginning of the Civil War the legal status of the slave was
+changed by his master's being in arms. General B.F. Butler, in May 1861,
+declared negro slaves contraband of war. A confiscation bill was passed
+in August 1861 discharging from his service or labour any slave employed
+in aiding or promoting any insurrection against the government of the
+United States. By an act of the 17th of July 1862 any slave of a
+disloyal master who was in territory occupied by northern troops was
+declared _ipso facto_ free. But for some time the Fugitive Slave Law was
+considered still to hold in the case of fugitives from masters in the
+border states who were loyal to the Union government, and it was not
+until the 28th of June 1864 that the Act of 1850 was repealed.
+
+  See J.F. Rhodes, _History of the United States from the Compromise of
+  1850_, vols. i. and ii. (New York, 1893); and M.G. M'Dougall,
+  _Fugitive Slaves, 1619-1865_ (Boston, 1891).
+
+
+FOOTNOTE:
+
+  [1] The precise amount of organization in the Underground Railroad
+    cannot be definitely ascertained because of the exaggerated use of
+    the figure of railroading in the documents of the "presidents" of the
+    road, Robert Purvis and Levi Coffin, and of its many "conductors,"
+    and their discussion of the "packages" and "freight" shipped by them.
+    The system reached from Kentucky and Virginia across Ohio, and from
+    Maryland across Pennsylvania and New York, to New England and Canada,
+    and as early as 1817 a group of anti-slavery men in southern Ohio had
+    helped to Canada as many as 1000 slaves. The Quakers of Pennsylvania
+    possibly began the work of the mysterious Underground Railroad; the
+    best known of them was Thomas Garrett (1789-1871), a native of
+    Pennsylvania, who, in 1822, removed to Wilmington, Delaware, where he
+    was convicted in 1848 on four counts under the Fugitive Slave Law and
+    was fined $8000; he is said to have helped 2700 slaves to freedom.
+    The most picturesque figure of the Underground Railroad was Harriet
+    Tubman (c. 1820), called by her friend, John Brown, "General" Tubman,
+    and by her fellow negroes "Moses." She made about a score of trips
+    into the South, bringing out with her 300 negroes altogether. At one
+    time a reward of $40,000 was offered for her capture. She was a
+    mystic, with remarkable clairvoyant powers, and did great service as
+    a nurse, a spy and a scout in the Civil War. Levi Coffin (1798-1877),
+    a native of North Carolina (whose cousin, Vestal Coffin, had
+    established before 1819 a "station" of the Underground near what is
+    now Guilford College, North Carolina), in 1826 settled in Wayne
+    County, Ohio; his home at New Garden (now Fountain City) was the
+    meeting point of three "lines" from Kentucky; and in 1847 he removed
+    to Cincinnati, where his labours in bringing slaves out of the South
+    were even more successful. It has been argued that the Underground
+    Railroad delayed the final decision of the slavery question, inasmuch
+    as it was a "safety valve"; for, without it, the more intelligent and
+    capable of the negro slaves would, it is asserted, have become the
+    leaders of insurrections in the South, and would not have been
+    removed from the places where they could have done most damage.
+    Consult William Still, _The Underground Railroad_ (Philadelphia,
+    1872), a collection of anecdotes by a negro agent of the Pennsylvania
+    Anti-Slavery Society, and of the Philadelphia branch of the Railroad;
+    and the important and scholarly work of Wilbur H. Siebert, _The
+    Underground Railroad from Slavery to Freedom_ (New York, 1898).
+
+
+
+
+FUGLEMAN (from the Ger. _Flugelmann_, the man on the _Flugel_ or wing),
+properly a military term for a soldier who is selected to act as
+"guide," and posted generally on the flanks with the duty of directing
+the march in the required line, or of giving the time, &c., to the
+remainder of the unit, which conforms to his movements, in any military
+exercise. The word is then applied to a ringleader or one who takes the
+lead in any movement or concerted movement.
+
+
+
+
+FUGUE (Lat. _fuga_, flight), in music, the mutual "pursuit" of voices or
+parts. It was, up to the end of the 16th century, if not later, the name
+applied to two art-forms. (A) _Fuga ligata_ was the exact reproduction
+by one or more voices of the statement of a leading part. The
+reproducing voice (_comes_) was seldom if ever written out, for all
+differences between it and the _dux_ were rigidly systematic; e.g. it
+was an exact inversion, or exactly twice as slow, or to be sung
+backwards, &c. &c. Hence, a rule or _canon_ was given, often in
+enigmatic form, by which the _comes_ was deduced from the _dux_: and so
+the term _canon_ became the appropriate name for the form itself, and is
+still retained. (B) A composition in which the canonic style was
+cultivated without canonic restriction was, in the 16th century, called
+_fuga ricercata_ or simply a _ricercare_, a term which is still used by
+Bach as a title for the fugues in _Das musikalische Opfer_.
+
+The whole conception of fugue, rightly understood, is one of the most
+important in music, and the reasons why some contrapuntal compositions
+are called fugues, while others are not, are so trivial, technically as
+well as aesthetically, that we have preferred to treat the subject
+separately under the general heading of CONTRAPUNTAL FORMS, reserving
+only technical terms for definition here.
+
+(i.) If in the beginning or "exposition" the material with which the
+opening voice accompanies the answer is faithfully reproduced as the
+accompaniment to subsequent entries of the subject, it is called a
+_countersubject_ (see COUNTERPOINT, under sub-heading _Double
+Counterpoint_). Obviously the process may be carried further, the first
+countersubject going on to a second when the subject enters in the third
+part and so on. The term is also applied to new subjects appearing later
+in the fugue in combination (immediate or destined) with the original
+subject. Cherubini, holding the doctrine that a fugue cannot have more
+than one subject, insists on applying the term to the less prominent of
+the subjects of what are commonly called double fugues, i.e. fugues
+which begin with two parts and two subjects simultaneously, and so also
+with _triple_ and _quadruple fugues_.
+
+(ii.) _Episodes_ are passages separating the entries of the subject.[1]
+Episodes are usually developed from the material of the subject and
+countersubjects; they are very rarely independent, but then
+conspicuously so.
+
+(iii.) _Stretto_, the overlapping of subject and answer, is a resource
+the possibilities of which may be exemplified by the setting of the
+words _omnes generationes_ in Bach's _Magnificat_ (see BACH).
+
+(iv.) The distinction between _real_ and _tonal_ fugue, which is still
+sometimes treated as a thing of great historical and technical
+importance, is really a mere detail resulting from the fact that a
+violent oscillation between the keys of tonic and dominant is no part of
+the function of a fugal exposition, so that the answer is (especially in
+its first notes and in points that tend to shift the key) not so much a
+transposition of the subject to the key of the dominant as an adaptation
+of it from the tonic part to the dominant part of the scale, or vice
+versa; in short, the answer is as far as possible _on_ the dominant, not
+_in_ the dominant. The modifications this principle produces in the
+answer (which have been happily described as resembling
+"fore-shortening") are the only distinctive marks of tonal fugue; and
+the text-books are half filled with the attempt to reduce them from
+matters of ear to rules of thumb, which rules, however, have the merit
+(unusual in those of the academic fugue) of being founded on observation
+of the practice of great masters. But the same principle as often as not
+produces answers that are exact transpositions of the subject; and so
+the only kind of real fugue (i.e. fugue with an exact answer) that could
+rightly be contrasted with tonal fugue would be that in which the answer
+ought to be tonal but is not. It must be admitted that tonal answers are
+rare in the modal music of the 16th century, though their melodic
+principles are of yet earlier date; still, though tonal fugue does not
+become usual until well on in the 17th century, the idea that it is a
+separate species is manifestly absurd, unless the term simply means
+"fugue in modern tonality or key," whatever the answer may be.
+
+The term "answer" is usually reserved for those entries of the subject
+that are placed in what may be called the "complementary" position of
+the scale, whether they are "tonally" modified or not. Thus the order of
+entries in the exposition of the first fugue of the _Wohltemp_. _Klav_.
+is subject, answer, answer, subject; a departure from the usual rule
+according to which subject and answer are strictly alternate in the
+exposition.
+
+In conclusion we may remind the reader of the most accurate as well as
+the most vivid description ever given of the essentials of a fugue, in
+the famous lines in _Paradise Lost_, book xi.
+
+              "His volant touch,
+  Instinct through all proportions, low and high,
+  Fled and pursued transverse the resonant fugue."
+
+It is hard to realize that this description of organ-music was written
+in no classical period of instrumental polyphony, but just half-way
+between the death of Frescobaldi and the birth of Bach. Every word is a
+definition, both retrospective and prophetic; and in "transverse" we see
+all that Sir Frederick Gore Ouseley expresses in his popular distinction
+between the "perpendicular" or homophonic style in which harmony is
+built up in chords, and the "horizontal" or polyphonic style in which it
+is woven in threads of independent melody.   (D. F. T.)
+
+
+FOOTNOTE:
+
+  [1] An episode occurring during the exposition is sometimes called
+    _codetta_, a distinction the uselessness of which at once appears on
+    an analysis of Bach's 2nd fugue in the _Wohltemp_. _Klav_. (the term
+    codetta is more correctly applied to notes filling in a gap between
+    subject and its first answer, but such a gap is rare in good
+    examples).
+
+
+
+
+FUHRICH, JOSEPH VON (1800-1876), Austrian painter, was born at Kratzau
+in Bohemia on the 9th of February 1800. Deeply impressed as a boy by
+rude pictures adorning the wayside chapels of his native country, his
+first attempt at composition was a sketch of the Nativity for the
+festival of Christmas in his father's house. He lived to see the day
+when, becoming celebrated as a composer of scriptural episodes, his
+sacred subjects were transferred in numberless repetitions to the
+roadside churches of the Austrian state, where humble peasants thus
+learnt to admire modern art reviving the models of earlier ages. Fuhrich
+has been fairly described as a "Nazarene," a romantic religious artist
+whose pencil did more than any other to restore the old spirit of Durer
+and give new shape to countless incidents of the gospel and scriptural
+legends. Without the power of Cornelius or the grace of Overbeck, he
+composed with great skill, especially in outline. His mastery of
+distribution, form, movement and expression was considerable. In its
+peculiar way his drapery was perfectly cast. Essentially creative as a
+landscape draughtsman, he had still no feeling for colour; and when he
+produced monumental pictures he was not nearly so successful as when
+designing subjects for woodcuts. Fuhrich's fame extended far beyond the
+walls of the Austrian capital, and his illustrations to Tieck's
+_Genofeva_, the Lord's Prayer, the Triumph of Christ, the Road to
+Bethlehem, the Succession of Christ according to Thomas a Kempis, the
+Prodigal Son, and the verses of the Psalter, became well known. His
+Prodigal Son, especially, is remarkable for the fancy with which the
+spirit of evil is embodied in a figure constantly recurring, and like
+that of Mephistopheles exhibiting temptation in a human yet demoniacal
+shape. Fuhrich became a pupil at the Academy of Prague in 1816. His
+first inspiration was derived from the prints of Durer and the Faust of
+Cornelius, and the first fruit of this turn of study was the Genofeva
+series. In 1826 he went to Rome, where he added three frescoes to those
+executed by Cornelius and Overbeck in the Palazzo Massimi. His subjects
+were taken from the life of Tasso, and are almost solitary examples of
+his talent in this class of composition. In 1831 he finished the Triumph
+of Christ now in the Raczynski palace at Berlin. In 1834 he was made
+custos and in 1841 professor of composition in the Academy of Vienna.
+After this he completed the monumental pictures of the church of St
+Nepomuk, and in 1854-1861 the vast series of wall paintings which cover
+the inside of the Lerchenfeld church at Vienna. In 1872 he was pensioned
+and made a knight of the order of Franz Joseph; 1875 is the date of his
+illustrations to the Psalms. He died on the 13th of March 1876.
+
+  His autobiography was published in 1875, and a memoir by his son Lucas
+  in 1886.
+
+
+
+
+FUJI (Fuji-san, Fujiyama, Fusiyama), a celebrated mountain of Japan,
+standing W.S.W. of Tokyo, its base being about 70 m. by rail from that
+city. It rises to a height of 12,395 ft. and its southern slopes reach
+the shore of Suruga Bay. It is a cone of beautifully simple form, the
+more striking to view because it stands isolated; but its summit is not
+conical, being broken by a crater some 2000 ft. in diameter, for Fuji is
+a quiescent volcano. Small outbursts of steam are still to be observed
+at some points. An eruption is recorded so lately as the first decade of
+the 18th century. The mountain is the resort of great numbers of
+pilgrims (see also JAPAN).
+
+
+
+
+FU-KIEN (formerly MIN), a south-eastern province of China, bounded N. by
+the province of Cheh-kiang, S. by that of Kwang-tung, W. by that of
+Kiang-si and E. by the sea. It occupies an area of 53,480 sq. m. and its
+population is estimated at 20,000,000. The provincial capital is Fuchow
+Fu, and it is divided into eleven prefectures, besides that ruled over
+by the prefect of the capital city. Fu-kien is generally mountainous,
+being overspread by the Nan-shan ranges, which run a general course of
+N.E. and S.W. The principal river is the Min, which is formed by the
+junction, in the neighbourhood of the city of Yen-p'ing Fu, of three
+rivers, namely, the Nui-si, which takes its rise in the mountains on the
+western frontier in the prefecture of Kien-ning Fu, the Fuh-tun Ki, the
+source of which is found in the district of Kwang-tsih in the north-west
+of the province, and the Ta-shi-ki (Shao Ki), which rises in the
+mountains in the western district of Ning-hwa. From Yen-p'ing Fu the
+river takes a south-easterly course, and after passing along the south
+face of the city of Fuchow Fu, empties itself into the sea about 30 m.
+below that town. Its upper course is narrow and rocky and abounds in
+rapids, but as it approaches Fuchow Fu the channel widens and the
+current becomes slow and even. Its depth is very irregular, and it is
+navigable only by native boats of a small class. Two other rivers flow
+into the sea near Amoy, neither of which, however, is navigable for any
+distance from its mouth owing to the shallows and rapids with which they
+abound. Thirty-five miles inland from Amoy stands the city of Chang
+Chow, famous for the bridge which there spans the Kin-lung river. This
+bridge is 800 ft. long, and consists of granite monoliths stretching
+from one abutment to another. The soil of the province is, as its name,
+"Happy Establishment," indicates, very productive, and the scenery is of
+a rich and varied character. Most of the hills are covered with verdure,
+and the less rugged are laid out in terraces. The principal products of
+the province are tea, of which the best kind is that known as Bohea,
+which takes its name, by a mispronunciation, from the Wu-e Mountains, in
+the prefecture of Kien-ning Fu, where it is grown; grains of various
+kinds, oranges, plantins, lichis, bamboo, ginger, gold, silver, lead,
+tin, iron, salt (both marine and rock), deers' horns, beeswax, sugar,
+fish, birds' nests, medicine, paper, cloth, timber, &c. Fu-kien has
+three open ports, Fuchow Fu opened in 1842, Amoy opened to trade in the
+same year and Funing. The latter port was only opened to foreign trade
+in 1898, but in 1904 it imported and exported goods to the value of
+L7668 and L278,160 respectively.
+
+
+
+
+FUKUI, a town of Japan in the province of Echizen, Nippon, near the west
+coast, 20 m. N. by E. of Wakasa Bay. It lies in a volcanic district much
+exposed to earthquakes, and suffered severely during the disturbances of
+1891-1892, when a chasm over 40 m. long was opened across the Neo valley
+from Fukui to Katabira. But Fukui subsequently revived, and is now in a
+flourishing condition, with several local industries, especially the
+manufacture of paper, and an increasing population exceeding 50,000.
+Fukui has railway communication. There are ruins of a castle of the
+Daimios of Echizen.
+
+
+
+
+FUKUOKA, a town on the north-west coast of the island of Kiushiu, Japan,
+in the province of Chikuzen, 90 m. N.N.E. of Nagasaki by rail. Pop.
+about 72,000. With Hakata, on the opposite side of a small coast stream,
+it forms a large centre of population, with an increasing export trade
+and several local industries. Of these the most important is
+silk-weaving, and Hakata especially is noted for its durable silk
+fabrics. Fukuoka was formerly the residence of the powerful daimio of
+Chikuzen, and played a conspicuous part in the medieval history of
+Japan; the renowned temple of Yeiyas in the district was destroyed by
+fire during the revolution of 1868. There are several other places of
+this name in Japan, the most important being Fukuoka in the province of
+Mutsu, North Nippon, a railway station on the main line from Tokyo to
+Aimori Ura Bay. Pop. about 5000.
+
+
+
+
+FULA (FULBE, FELLATAH or PEULS), a numerous and powerful African people,
+spread over an immense region from Senegal nearly to Darfur. Strictly
+they have no country of their own, and nowhere form the whole of the
+population, though nearly always the dominant native race. They are most
+numerous in Upper Senegal and in the countries under French sway
+immediately south of Senegambia, notably Futa Jallon. Farther east they
+rule, subject to the control of the French, Segu and Massena, countries
+on both banks of the upper Niger, to the south-west of Timbuktu. The
+districts within the great bend of the Niger have a large Fula
+population. East of that river Sokoto and its tributary emirates are
+ruled by Fula princes, subject to the control of the British Nigerian
+administration. Fula are settled in Bornu, Bagirmi, Wadai and the upper
+Nile Valley,[1] but have no political power in those countries. Their
+most southerly emirate is Adamawa, the country on both sides of the
+upper Benue. In this vast region of distribution the Fula populations
+are most dense towards the west and north, most scattered towards the
+east and south. Originally herdsmen in the western and central Sudan,
+they extended their sway east of the Niger, under the leadership of
+Othman Dan Fodio, during the early years of the 19th century, and having
+subdued the Hausa states, founded the empire of Sokoto with the vassal
+emirates of Kano, Gando, Nupe, Adamawa, &c.
+
+The question of the ethnic affinities of the Fula has given rise to an
+enormous amount of speculation, but the most reasonable theory is that
+they are a mixture of Berber and Negro. This is now the most generally
+accepted theory. Certainly there is no reason to connect them with the
+ancient Egyptians. In the district of Senegal known as Fuladugu or "Fula
+Land," where the purest types of the race are found, the people are of a
+reddish brown or light chestnut colour, with oval faces, ringlety or
+even smooth hair, never woolly, straight and even aquiline noses,
+delicately shaped lips and regular features quite differentiating them
+from the Negro type. Like most conquering races the Fula are, however,
+not of uniform physique, in many districts approximating to the local
+type. They nevertheless maintain throughout their widespread territory a
+certain national solidarity, thanks to common speech, traditions and
+usages. The ruling caste of the Fula differs widely in character from
+the herdsmen of the western Sudan. The latter are peaceable, inoffensive
+and abstemious. They are mainly monogamous, and by rigidly abstaining
+from foreign marriages have preserved racial purity. The ruling caste in
+Nigeria, on the other hand, despise their pastoral brethren, and through
+generations of polygamy with the conquered tribes have become more
+Negroid in type, black, burly and coarse featured. Love of luxury, pomp
+and finery is their chief characteristic. Taken as a whole, the Fula
+race is distinguished by great intelligence, frankness of disposition
+and strength of character. As soldiers they are renowned almost
+exclusively as cavalry; and the race has produced several leaders
+possessed of much strategical skill. Besides the ordinary Negro weapons,
+they use iron spears with leatherbound handles and swords. They are
+generally excellent rulers, stern but patient and just. The Nigerian
+emirs acquired, however, an evil reputation during the 19th century as
+slave raiders. They have long been devout Mahommedans, and mosques and
+schools exist in almost all their towns. Tradition says that of old
+every Fula boy and girl was a scholar; but during the decadence of their
+power towards the close of the 19th century education was not highly
+valued. Power seems to have somewhat spoilt this virile race, but such
+authorities as Sir Frederick Lugard believe them still capable of a
+great future.
+
+The Fula language has as yet found no place in any African linguistic
+family. In its rudiments it is akin to the Hamito-Semitic group. It
+possesses two grammatical genders, not masculine and feminine, but the
+human and the non-human; the adjective agrees in assonance with its
+noun, and euphony plays a great part in verbal and nominal inflections.
+In some ways resembling the Negro dialects, it betrays non-Negroid
+influences in the use of suffixes. The name of the people has many
+variations. Fulbe or Fula (sing. Pullo, Peul) is the Mandingan name,
+Follani the Hausa, Fellatah the Kanuri, Fullan the Arab, and Fulde on
+the Benue. Like the name Abate, "white," given them in Kororofa, all
+these seem to refer to their light reddish hue.
+
+  See F. Ratzel, _History of Mankind_ (English ed., London, 1896-1898);
+  Sir F. Lugard, "Northern Nigeria," in _Geographical Journal_ (July
+  1904); Grimai de Guirodon, _Les Puls_ (1887); E.A. Brackenbury, _A
+  Short Vocabulary of the Fulani Language_ (Zungeru, 1907); the articles
+  NIGERIA and SOKOTO and authorities there cited.
+
+
+FOOTNOTE:
+
+  [1] Sir Wm. Wallace in a report on Northern Nigeria ("Colonial
+    Office" series, No. 551, 1907) calls attention to the exodus "of
+    thousands of Fulani of all sorts, but mostly Mellawa, from the French
+    Middle Niger," and states that the majority of the emigrants are
+    settling in the Nile valley.
+
+
+
+
+FULCHER (or FOUCHER) OF CHARTRES (1058-c. 1130), French chronicler, was
+a priest who was present at the council of Clermont in 1095, and
+accompanied Robert II., duke of Normandy, on the first crusade in 1096.
+Having spent some time in Italy and taken part in the fighting on the
+way to the Holy Land, he became chaplain to Baldwin, who was chosen king
+of Jerusalem in 1100, and lived with Baldwin at Edessa and then at
+Jerusalem. He accompanied this king on several warlike expeditions, but
+won more lasting fame by writing his _Historia Hierosolymitana_ or
+_Gesta Francorum Jerusalem expugnantium_, one of the most trustworthy
+sources for the history of the first crusade. In its final form it is
+divided into three books, and covers the period between the council of
+Clermont and 1127, and the author only gives details of events which he
+himself had witnessed. It was used by William of Tyre. Fulcher died
+after 1127, probably at Jerusalem. He has been confused with Foucher of
+Mongervillier (d. 1171), abbot of St-Pere-en-Vallee at Chartres, and
+also with another person of the same name who distinguished himself at
+the siege of Antioch in 1098.
+
+  The _Historia_, but in an incomplete form, was first published by J.
+  Bongars in the _Gesta Dei per Francos_ (Hanover, 1611). The best
+  edition is in tome iii. of the _Recueil des historiens des croisades,
+  Historiens occidentaux_ (Paris, 1866); and there is a French
+  translation in tome xxiv. of Guizot's _Collection des memoires
+  relatifs a l'histoire de France_ (Paris, 1823-1835).
+
+  See H. von Sybel, _Geschichte des ersten Kreuzzuges_ (Leipzig, 1881);
+  and A. Molinier, _Les Sources de l'histoire de France_, tome ii.
+  (Paris, 1902).
+
+
+
+
+FULDA, a town and episcopal see of Germany, in the Prussian province of
+Hesse-Nassau, between the Rhon and the Vogel-Gebirge, 69 m. N.E. from
+Frankfort-on-Main on the railway to Bebra. Although irregularly built
+the town is pleasantly situated, and contains two fine squares, on one
+of which stands a fine statue of St Boniface. The present cathedral was
+built at the beginning of the 18th century on the model of St Peter's at
+Rome, but it has an ancient crypt, which contains the bones of St
+Boniface and was restored in 1892. Opposite the cathedral is the former
+monastery of St Michael, now the episcopal palace. The Michaelskirche,
+attached to it, is a small round church built, in imitation of the Holy
+Sepulchre, in 822 and restored in 1853. Of other buildings may be
+mentioned the Library, with upwards of 80,000 printed books and many
+valuable MSS., the stately palace with its gardens and orangery, the
+former Benedictine nunnery (founded 1625, and now used as a seminary),
+and the Minorite friary (1238) now used as a furniture warehouse. Among
+the secular buildings are the fine _Schloss_, the _Bibliothek_, the town
+hall and the post office. There are several schools, a hospital founded
+in the 13th century, and some new artillery barracks. Many industries
+are carried on in Fulda. These include weaving and dyeing, the
+manufacture of linen, plush and other textiles and brewing. There are
+also railway works in the town. A large trade is done in cattle and
+grain, many markets being held here. Fine views are obtained from
+several hills in the neighbourhood, among these being the Frauenberg,
+the Petersberg and the Kalvarienberg.
+
+Fulda owes its existence to its famous abbey. It became a town in 1208,
+and during the middle ages there were many struggles between the abbots
+and the townsfolk. During the Peasants' War it was captured by the
+rebels and during the Seven Years' War by the Hanoverians. It came
+finally into the possession of Prussia in 1866. From 1734 to 1804 Fulda
+was the seat of a university, and latterly many assemblies of German
+bishops have been held in the town.
+
+The great Benedictine abbey of Fulda occupies the place in the
+ecclesiastical history of Germany which Monte Cassino holds in Italy, St
+Gall in South Germany, Corvey in Saxony, Tours in France and Iona in
+Scotland. Founded in 744 at the instigation of St Boniface by his pupil
+Sturm, who was the first abbot, it became the centre of a great
+missionary work. It was liberally endowed with land by the princes of
+the Carolingian house and others, and soon became one of the most famous
+and wealthy establishments of its kind. About 968 the pope declared that
+its abbot was primate of all the abbots in Germany and Gaul, and later
+he became a prince of the Empire. Fulda was specially famous for its
+school, which was the centre of the theological learning of the early
+middle ages. Among the teachers here were Alcuin, Hrabanus Maurus, who
+was abbot from 822 to 842, and Walafrid Strabo. Early in the 10th
+century the monastery was reformed by introducing monks from Scotland,
+who were responsible for restoring in its old strictness the Benedictine
+rule. Later the abbey lost some of its lands and also its high position,
+and some time before the Reformation the days of its glory were over.
+Johann von Henneberg, who was abbot from 1529 to 1541, showed some
+sympathy with the teaching of the reformers, but the Counter-Reformation
+made great progress here under Abbot Balthasar von Dernbach. Gustavus
+Adolphus gave the abbey as a principality to William, landgrave of
+Hesse, but William's rule only lasted for ten years. In 1752 the abbot
+was raised to the rank of a bishop, and Fulda ranked as a
+prince-bishopric. This was secularized in 1802, and in quick succession
+it belonged to the prince of Orange, the king of France and the
+grand-duchy of Frankfort. In 1816 the greater part of the principality
+was ceded by Prussia to Hesse-Cassel, a smaller portion being united
+with Bavaria. Sharing the fate of Hesse-Cassel, this larger portion was
+annexed by Prussia in 1866. In 1829 a new bishopric was founded at
+Fulda.
+
+  For the town see A. Hartmann, _Zeitgeschichte von Fulda_ (Fulda,
+  1895); J. Schneider, _Fuhrer durch die Stadt Fulda_ (Fulda, 1899); and
+  _Chronik von Fulda und dessen Umgebungen_ (1839). For the history of
+  the abbey see Gegenbaur, _Das Kloster Fulda im Karolinger Zeitalter_
+  (Fulda, 1871-1874); Arndt, _Geschichte des Hochstifts Fulda_ (Fulda,
+  1860); and the _Fuldaer Geschichtsblatter_ (1902 fol.).
+
+
+
+
+FULGENTIUS, FABIUS PLANCIADES, Latin grammarian, a native of Africa,
+flourished in the first half of the 6th (or the last part of the 5th)
+century A.D. He is to be distinguished from Fulgentius, bishop of Ruspe
+(468-533), to whom he was probably related, and also from the bishop's
+pupil and biographer, Fulgentius Ferrandus. Four extant works are
+attributed to him. (1) _Mythologiarum libri iii._, dedicated to a
+certain Catus, a presbyter of Carthage, containing 75 myths briefly
+told, and then explained in the mystical and allegorical manner of the
+Stoics and Neoplatonists. For this purpose the author generally invokes
+the aid of etymologies which, borrowed from the philosophers, are highly
+absurd. As a Christian, Fulgentius sometimes (but less frequently than
+might have been expected) quotes the Bible by the side of the
+philosophers, to give a Christian colouring to the moral lesson. (2)
+_Expositio Vergilianae continentiae (continentia_ = contents), a sort of
+appendix to (1), dedicated to Catus. The poet himself appears to the
+author and explains the twelve books of the _Aeneid_ as a picture of
+human life. The three words _arma_ (= virtus), _vir_ (= sapientia),
+_primus_ (= princeps) in the first line represent respectively
+_substantia corporalis, sensualis, ornans_. Book i. symbolizes the birth
+and early childhood of man (the shipwreck of Aeneas denotes the peril of
+birth), book vi. the plunge into the depths of wisdom. (3) _Expositio
+sermonum antiquorum_, explanations of 63 rare and obsolete words,
+supported by quotations (sometimes from authors and works that never
+existed). It is much inferior to the similar work of Nonius, with which
+it is often edited. (4) _Liber absque litteris de aetatibus mundi et
+hominis_. In the MS. heading of this work, the name of the author is
+given as Fabius Claudius Gordianus Fulgentius (Claudius is the name of
+the father, and Gordianus that of the grandfather of the bishop, to whom
+some attribute the work). The title _Absque litteris_ indicates that one
+letter of the alphabet is wholly omitted in each successive book (A in
+bk. i., B in bk. ii.). Only 14 books are preserved. The matter is
+chiefly taken from sacred history. In addition to these, Fulgentius
+speaks of early poetical attempts after the manner of Anacreon, and of a
+work called _Physiologus_, dealing with medical questions, and including
+a discussion of the mystical signification of the numbers 7 and 9.
+Fulgentius is a representative of the so-called late African style,
+taking for his models Apuleius, Tertullian and Martianus Capella. His
+language is bombastic, affected and incorrect, while the lengthy and
+elaborate periods make it difficult to understand his meaning.
+
+  See the edition of the four works by R. Helm (1898, Teubner series);
+  also M. Zink, _Der Mytholog Fulgentius_ (1867); E. Jungmann, "De
+  Fulgentii aetate et scriptis," in _Acta Societatis Philologae
+  Lipsiensis_, i. (1871); A. Ebert, _Allgemeine Geschichte der Litt. des
+  Mittelalters_, i.; article "Fulgentius" by C.F. Bohr in Ersch and
+  Gruber's _Allgemeine Encyklopadie_; Teuffel-Schwabe, _History of Roman
+  Literature_ (Eng. trans.).
+
+
+
+
+FULGINIAE (mod. _Foligno_), an ancient town of Umbria, Italy, on the
+later line of the Via Flaminia, 15 m. S. of Nuceria. It appears to have
+been of comparatively late origin, inasmuch as it had no city walls,
+but, in imperial times especially, owing to its position on the new line
+of the Via Flaminia, it must have increased in importance as being the
+point of departure of roads to Perusia and to Picenum over the pass of
+Plestia. It appears to have had an amphitheatre, and three bridges over
+the Topino are attributed to the Roman period. Three miles to the N.
+lies the independent community of Forum Flaminii, the site of which is
+marked by the church of S. Giovanni Profiamma, at or near which the
+newer line of the Via Flaminia rejoined the older. It was no doubt
+founded by the builder of the road, C. Flaminius, consul in 220 B.C.
+(See FOLIGNO and FLAMINIA, VIA.)     (T. As.)
+
+
+
+
+FULGURITE (from Lat. _fulgur_, lightning), in petrology, the name given
+to rocks which have been fused on the surface by lightning, and to the
+characteristic holes in rocks formed by the same agency. When lightning
+strikes the naked surfaces of rocks, the sudden rise of temperature may
+produce a certain amount of fusion, especially when the rocks are dry
+and the electricity is not readily conducted away. Instances of this
+have been observed on Ararat and on several mountains in the Alps,
+Pyrenees, &c. A thin glassy crust, resembling a coat of varnish, is
+formed; its thickness is usually not more than one-eighth of an inch,
+and it may be colourless, white or yellow. When examined under the
+microscope, it usually shows no crystallization, and contains minute
+bubbles due to the expansion of air or other gases in the fused
+pellicle. Occasionally small microliths may appear, but this is uncommon
+because so thin a film would cool with extreme rapidity. The minerals of
+the rock beneath are in some cases partly fused, but the more refractory
+often appear quite unaffected. The glass has arisen from the melting of
+the most fusible ingredients alone.
+
+Another type of fulgurite is commonest in dry sands and takes the shape
+of vertical tubes which may be nearly half an inch in diameter.
+Generally they are elliptical in cross section, or flattened by the
+pressure exerted by the surrounding sand on the fulgurite at a time when
+it was still very hot and plastic. These tubes are often vertical and
+may run downwards for several feet through the sand, branching and
+lessening as they descend. Tubular perforations in hard rocks have been
+noted also, but these are short and probably follow original cracks. The
+glassy material contains grains of sand and many small round or
+elliptical cavities, the long axes of which are radial. Minerals like
+felspar and mica are fused more readily than quartz, but analysis shows
+that some fulgurite glasses are very rich in silica, which perhaps was
+dissolved in the glass rather than simply fused. The central cavity of
+the tube and the bubbles in its walls point to the expansion of the
+gases (air, water, &c.) in the sand by sudden and extreme heating. Very
+fine threads of glass project from the surface of the tube as if fused
+droplets had been projected outwards with considerable force. Where the
+quartz grains have been greatly heated but not melted they become white
+and semi-opaque, but where they are in contact with the glass they
+usually show partial solution. Occasionally crystallization has begun
+before the glass solidified, and small microliths, the nature of which
+is undeterminable, occur in streams and wisps in the clear hyaline
+matrix.     (J. S. F.)
+
+
+
+
+FULHAM, a western metropolitan borough of London, England, bounded N.W.
+by Hammersmith, N.E. by Kensington, E. by Chelsea, and S.E., S. and S.W.
+by the river Thames. Pop. (1901) 137,289. The principal thoroughfares
+are Fulham Palace Road running S. from Hammersmith, Fulham Road and
+King's Road, W. from Chelsea, converging and leading to Putney Bridge
+over the Thames; North End Road between Hammersmith and Fulham Roads;
+Lillie Road between South Kensington and Fulham Palace Road; and
+Wandsworth Bridge Road leading S. from New King's Road to Wandsworth
+Bridge. In the north Fulham includes the residential district known as
+West Kensington, and farther south that of Walham Green. The manor house
+or palace of the bishops of London stands in grounds, beautifully
+planted and surrounded by a moat, believed to be a Danish work, near the
+river west of Putney Bridge. Its oldest portion is the picturesque
+western quadrangle, built by Bishop Fitzjames (1506-1522). The parish
+church of All Saints, between the bridge and the grounds, was erected in
+1881 from designs by Sir Arthur Blomfield. The fine old monuments from
+the former building, dating from the 16th to the 18th centuries, are
+mostly preserved, and in the churchyard are the memorials of several
+bishops of London and of Theodore Hook (1841). The public recreation
+grounds include the embankment and gardens between the river and the
+palace grounds, and there are also two well-known enclosures used for
+sports within the borough. Of these Hurlingham Park is the headquarters
+of the Hurlingham Polo Club and a fashionable resort; and Queen's Club,
+West Kensington, has tennis and other courts for the use of members, and
+is also the scene of important football matches, and of the athletic
+meetings between Oxford and Cambridge Universities, and those between
+the English and American Universities held in England. In Seagrave Road
+is the Western fever hospital. The parliamentary borough of Fulham
+returns one member. The borough council consists of a mayor, 6 aldermen
+and 36 councillors. Area, 1703.5 acres.
+
+Fulham, or in its earliest form _Fullanham_, is uncertainly stated to
+signify "the place" either "of fowls" or "of dirt." The manor is said to
+have been given to Bishop Erkenwald about the year 691 for himself and
+his successors in the see of London, and Holinshed relates that the
+Bishop of London was lodging in his manor place in 1141 when Geoffrey de
+Mandeville, riding out from the Tower of London, took him prisoner. At
+the Commonwealth the manor was temporarily out of the bishops' hands,
+being sold to Colonel Edmund Harvey. There is no record of the first
+erection of a parish church, but the first known rector was appointed in
+1242, and a church probably existed a century before this. The earliest
+part of the church demolished in 1881, however, did not date farther
+back than the 15th century. In 879 Danish invaders, sailing up the
+Thames, wintered at Fulham and Hammersmith. Near the former wooden
+Putney Bridge, built in 1729 and replaced in 1886, the earl of Essex
+threw a bridge of boats across the river in 1642 in order to march his
+army in pursuit of Charles I., who thereupon fell back on Oxford.
+Margravine Road recalls the existence of Bradenburg House, a riverside
+mansion built by Sir Nicholas Crispe in the time of Charles I., used as
+the headquarters of General Fairfax in 1647 during the civil wars, and
+occupied in 1792 by the margrave of Bradenburg-Anspach and Bayreuth and
+his wife, and in 1820 by Caroline, consort of George IV.
+
+
+
+
+FULK, king of Jerusalem (b. 1092), was the son of Fulk IV., count of
+Anjou, and his wife Bertrada (who ultimately deserted her husband and
+became the mistress of Philip I. of France). He became count of Anjou in
+1109, and considerably added to the prestige of his house. In particular
+he showed himself a doughty opponent to Henry I. of England, against
+whom he continually supported Louis VI. of France, until in 1127 Henry
+won him over by betrothing his daughter Matilda to Fulk's son Geoffrey
+Plantagenet. Already in 1120 Fulk had visited the Holy Land, and become
+a close friend of the Templars. On his return he assigned to the order
+of the Templars an annual subsidy, while he also maintained two knights
+in the Holy Land for a year. In 1128 he was preparing to return to the
+East, when he received an embassy from Baldwin II., king of Jerusalem,
+who had no male heir to succeed him, offering his daughter Melisinda in
+marriage, with the right of eventual succession to the kingdom. Fulk
+readily accepted the offer; and in 1129 he came and was married to
+Melisinda, receiving the towns of Acre and Tyre as her dower. In 1131,
+at the age of thirty-nine, he became king of Jerusalem. His reign is not
+marked by any considerable events: the kingdom which had reached its
+zenith under Baldwin II., and did not begin to decline till the capture
+of Edessa in the reign of Baldwin III., was quietly prosperous under his
+rule. In the beginning of his reign he had to act as regent of Antioch,
+and to provide a husband, Raymund of Poitou, for the infant heiress
+Constance. But the great problem with which he had to deal was the
+progress of the atabeg Zengi of Mosul. In 1137 he was beaten near Barin,
+and escaping into the fort was surrounded and forced to capitulate. A
+little later, however, he greatly improved his position by strengthening
+his alliance with the vizier of Damascus, who also had to fear the
+progress of Zengi (1140); and in this way he was able to capture the
+fort of Banias, to the N. of Lake Tiberias. Fulk also strengthened the
+kingdom on the south; while his butler, Paganus, planted the fortress of
+Krak to the south of the Dead Sea, and helped to give the kingdom an
+access towards the Red Sea, he himself constructed Blanche Garde and
+other forts on the S.W. to overawe the garrison of Ascalon, which was
+still held by the Mahommedans, and to clear the road towards Egypt.
+Twice in Fulk's reign the eastern emperor, John Comnenus, appeared in
+northern Syria (1137 and 1142); but his coming did not affect the king,
+who was able to decline politely a visit which the emperor proposed to
+make to Jerusalem. In 1143 he died, leaving two sons, who both became
+kings, as Baldwin III. and Amalric I.
+
+Fulk continued the tradition of good statesmanship and sound
+churchmanship which Baldwin I. and Baldwin II. had begun. William of
+Tyre speaks of him as a fine soldier, an able politician, and a good son
+of the church, and only blames him for partiality to his friends, and a
+forgetfulness of names and faces, which placed him at a disadvantage and
+made him too dependent on his immediate intimates. Little, perhaps, need
+be made of these censures: the real fault of Fulk was his neglect to
+envisage the needs of the northern principalities, and to head a
+combined resistance to the rising power of Zengi of Mosul.
+
+  His reign in Jerusalem is narrated by R. Rohricht (_Geschichte des
+  Konigreichs Jerusalem_, Innsbruck, 1898), and has been made the
+  subject of a monograph by G. Dodu (_De Fulconis Hierosolymitani
+  regno_, Paris, 1894).     (E. Br.)
+
+
+
+
+FULK (d. 900), archbishop of Reims, and partisan of Charles the Simple
+in his struggle with Odo, count of Paris, was elected to the see as
+archbishop in 883 upon the death of Hincmar. In 887 he was engaged in a
+struggle with the Normans who invaded his territories. Upon the
+deposition of Charles the Fat he sided with Charles the Simple in his
+contest for the West Frankish dominions against Count Odo of Paris, and
+crowned him king in his own metropolitan church at Reims after most of
+the nobles had gone over to Odo (893). Upon the death of Odo he
+succeeded in having Charles recognized as king by a majority of the West
+Frankish nobility. In 892 he obtained special privileges for his
+province from Pope Formosus, who promised that thereafter, when the
+archbishopric became vacant, the revenues should not be enjoyed by
+anyone while the vacancy existed, but should be reserved for the new
+incumbent, provided the election took place within the canonical limit
+of three months. From 898 until his death he held the office of
+chancellor, which for some time afterwards was regularly filled by the
+archbishop of Reims. In his efforts to keep the wealthy abbeys and
+benefices of the church out of the hands of the nobles, he incurred the
+hatred of Baldwin, count of Flanders, who secured his assassination on
+the 17th of June 900, a crime which the weak Carolingian monarch left
+unpunished.
+
+  Fulk left some letters, which are collected in Migne, _Patrologia
+  Latina_, vol. cxxxi. 11-14.
+
+
+
+
+FULKE, WILLIAM (1538-1589), Puritan divine, was born in London and
+educated at Cambridge. After studying law for six years, he became a
+fellow at St John's College, Cambridge, in 1564. He took a leading part
+in the "vestiarian" controversy, and persuaded the college to discard
+the surplice. In consequence he was expelled from St. John's for a
+time, but in 1567 he became Hebrew lecturer and preacher there. After
+standing unsuccessfully for the headship of the college in 1569, he
+became chaplain to the earl of Leicester, and received from him the
+livings of Warley, in Essex, and Dennington in Suffolk. In 1578 he was
+elected master of Pembroke Hall, Cambridge. As a Puritan
+controversialist he was remarkably active; in 1580 the bishop of Ely
+appointed him to defend puritanism against the Roman Catholics, Thomas
+Watson, ex-bishop of Lincoln (1513-1584), and John Feckenham, formerly
+abbot of Westminster, and in 1581 he was one of the disputants with the
+Jesuit, Edmund Campion, while in 1582 he was among the clergy selected
+by the privy council to argue against any papist. His numerous polemical
+writings include _A Defense of the sincere true Translations of the
+holie Scriptures into the English tong_ (London, 1583), and confutations
+of Thomas Stapleton (1535-1598), Cardinal Allen and other Roman Catholic
+controversialists.
+
+
+
+
+FULK NERRA (c. 970-1040), count of Anjou, eldest son of Count Geoffrey
+I., "Grisegonelle" (Grey Tunic) and Adela of Vermandois, was born about
+970 and succeeded his father in the countship of Anjou on the 21st of
+July 987. He was successful in repelling the attacks of the count of
+Rennes and laying the foundations of the conquest of Touraine (see
+ANJOU). In this connexion he built a great number of strong castles,
+which has led in modern times to his being called "the great builder."
+He also founded several religious houses, among them the abbeys of
+Beaulieu, near Loches (c. 1007), of Saint-Nicholas at Angers (1020) and
+of Ronceray at Angers (1028), and, in order to expiate his crimes of
+violence, made three pilgrimages to the Holy Land (in 1002-1003, c. 1008
+and in 1039). On his return from the third of these journeys he died at
+Metz in Lorraine on the 21st of June 1040. By his first marriage, with
+Elizabeth, daughter of Bouchard le Venerable, count of Vendome, he had a
+daughter, Adela, who married Boon of Nevers and transmitted to her
+children the countship of Vendome. Elizabeth having died in 1000, Fulk
+married Hildegarde of Lorraine, by whom he had a son, Geoffrey Martel
+(q.v.), and a daughter Ermengarde, who married Geoffrey, count of
+Gatinais, and was the mother of Geoffrey "le Barbu" (the Bearded) and of
+Fulk "le Rechin" (see ANJOU).
+
+  See Louis Halphen, _Le Comte d'Anjou au XI^e siecle_ (Paris, 1906).
+  The biography of Fulk Nerra by Alexandre de Salies, _Histoire de
+  Foulques Nerra_ (Angers, 1874) is confused and uncritical. A very
+  summary biography is given by Celestin Port, _Dictionnaire historique,
+  geographique et biographique de Maine-et-Loire_ (3 vols.,
+  Paris-Angers, 1874-1878), vol. ii. pp. 189-192, and there is also a
+  sketch in Kate Norgate, _England under the Angevin Kings_ (2 vols.,
+  London, 1887), vol. i. ch. iii.     (L. H.*)
+
+
+
+
+FULLEBORN, GEORG GUSTAV (1769-1803), German philosopher, philologist and
+miscellaneous writer, was born at Glogau, Silesia, on the 2nd of March
+1769, and died at Breslau on the 6th of February 1803. He was educated
+at the University of Halle, and was made doctor of philosophy in
+recognition of his thesis _De Xenophane, Zenone et Gorgia_. He took
+diaconal orders in 1791, but almost immediately became professor of
+classics at Breslau. His philosophical works include annotations to
+Garve's translation of the _Politics_ of Aristotle (1799-1800), and a
+large share in the _Beitrage zur Geschichte der Philosophie_ (published
+in twelve parts between 1791 and 1799), in which he collaborated with
+Forberg, Reinhold and Niethammer. In philology he wrote _Encyclopaedia
+philologica sive primae lineae Isagoges in antiquorum studia_ (1798; 2nd
+ed., 1805); _Kurze Theorie des lateinischen Stils_ (1793); _Leitfaden
+der Rhetorik_ (1802); and an annotated edition of the _Satires_ of
+Persius. Under the pseudonym "Edelwald Justus" he published several
+collections of popular tales--_Bunte Blatter_ (1795); _Kleine Schriften
+zur Unterhaltung_ (1798); _Nebenstunden_ (1799). After his death were
+published _Taschenbuch fur Brunnengaste_ (1806) and _Kanzelreden_
+(1807). He was a frequent contributor to the press, where his writings
+were very popular.
+
+  See Schummel, _Gedachtnisrede_ (1803) and _Garve und Fulleborn_;
+  Meusel, _Gelehrtes Teutschland_, vol. ii.
+
+
+
+
+FULLER, ANDREW (1754-1815), English Baptist divine, was born on the 6th
+of February 1754, at Wicken in Cambridgeshire. In his boyhood and youth
+he worked on his father's farm. In his seventeenth year he became a
+member of the Baptist church at Soham, and his gifts as an exhorter met
+with so much approval that, in the spring of 1775, he was called and
+ordained as pastor of that congregation. In 1782 he removed to Kettering
+in Northamptonshire, where he became friendly with some of the most
+eminent ministers of the denomination. Before leaving Soham he had
+written the substance of a treatise in which he had sought to counteract
+the prevailing Baptist hyper-Calvinism which, "admitting nothing
+spiritually good to be the duty of the unregenerate, and nothing to be
+addressed to them in a way of exhortation excepting what related to
+external obedience," had long perplexed his own mind. This work he
+published, under the title _The Gospel worthy of all Acceptation_, soon
+after his settlement in Kettering; and although it immediately involved
+him in a somewhat bitter controversy which lasted for nearly twenty
+years, it was ultimately successful in considerably modifying the views
+prevalent among English dissenters. In 1793 he published a treatise,
+_The Calvinistic and Socinian systems examined and compared as to their
+moral tendency_, in which he rebutted the accusation of antinomianism
+levelled by the Socinians against those who over-emphasized the
+doctrines of free grace. This work, along with another against Deism,
+entitled _The Gospel its own Witness_, is regarded as the production on
+which his reputation as a theologian mainly rests. Fuller also published
+an admirable _Memoir of the Rev. Samuel Pearce_, of Birmingham, and a
+volume of _Expository Lectures in Genesis_, besides a considerable
+number of smaller pieces, chiefly sermons and pamphlets, which were
+issued in a collected form after his death. He was a man of forceful
+character, more prominent on the practical side of religion than on the
+devotional, and accordingly not pre-eminently successful in his local
+ministry. His great work was done in connexion with the Baptist
+Missionary Society, formed at Kettering in 1792, of which he was
+secretary until his death on the 7th of May 1815. Both Princeton and
+Yale, U.S.A., conferred on him the degree of D. D., but he never used
+it.
+
+  Several editions of his collected works have appeared, and a _Memoir_,
+  principally compiled from his own papers, was published about a year
+  after his decease by Dr Ryland, his most intimate friend and coadjutor
+  in the affairs of the Baptist mission. There is also a biography by
+  the Rev. J.W. Morris (1816); and his son prefixed a memoir to an
+  edition of his chief works in Bohn's Standard Library (1852).
+
+
+
+
+FULLER, GEORGE (1822-1884), American figure and portrait painter, was
+born at Deerfield, Massachusetts, in 1822. At the age of twenty he
+entered the studio of the sculptor H.K. Brown, at Albany, New York,
+where he drew from the cast and modelled heads. Having attained some
+proficiency he went about the country painting portraits, settling at
+length in Boston, where he studied the works of the earlier Americans,
+Stuart, Copley and Allston. After three years in that city, and twelve
+in New York, where in 1857 he was elected a member of the National
+Academy of Design, he went to Europe for a brief visit and for study.
+During all this time his work had received little recognition and
+practically no financial encouragement, and on his return he settled on
+the family farm at Deerfield, where he continued to work in his own way
+with no thought of the outside world. In 1876, however, he was forced by
+pressing needs to dispose of his work, and he sent some pictures to a
+dealer in Boston, where he met with immediate success, financial and
+artistic, and for the remaining eight years of his life he never lacked
+patrons. He died in Boston on the 21st of March 1884. He was a poetic
+painter, and a dreamer of delicate fancies and quaint, intangible phases
+of nature, his canvases being usually enveloped in a brown mist that
+renders the outlines vague. Among his noteworthy canvases are: "The
+Turkey Pasture," "Romany Girl," "And she was a Witch," "Nydia,"
+"Winifred Dysart" and "The Quadroon."
+
+
+
+
+FULLER, MARGARET, Marchioness Ossoli (1810-1850), American authoress,
+eldest child of Timothy Fuller (1778-1835), a lawyer and politician of
+some eminence, was born at Cambridgeport, Massachusetts, on the 23rd of
+May 1810. Her education was conducted by her father, who, she states,
+made the mistake of thinking to "gain time by bringing forward the
+intellect as early as possible," the consequence being "a premature
+development of brain that made her a youthful prodigy by day, and by
+night a victim of spectral illusions, nightmare and somnambulism." At
+six years she began to read Latin, and at a very early age she had
+selected as her favourite authors Shakespeare, Cervantes and Moliere.
+Soon the great amount of study exacted of her ceased to be a burden, and
+reading became a habit and a passion. Having made herself familiar with
+the masterpieces of French, Italian and Spanish literature, she in 1833
+began the study of German, and within the year had read some of the
+masterpieces of Goethe, Korner, Novalis and Schiller.
+
+After her father's death in 1835 she went to Boston to teach languages,
+and in 1837 she was chosen principal teacher in the Green Street school,
+Providence, Rhode Island, where she remained till 1839. From this year
+until 1844 she stayed at different places in the immediate neighbourhood
+of Boston, forming an intimate acquaintance with the colonists of Brook
+Farm, and numbering among her closest friends R.W. Emerson, Nathaniel
+Hawthorne and W.H. Channing. In 1839 she published a translation of
+Eckermann's _Conversations with Goethe_, which was followed in 1842 by a
+translation of the correspondence between Karoline von Gunderode and
+Bettina von Arnim, entitled _Gunderode_. Aided by R.W. Emerson and
+George Ripley, she in 1840 started _The Dial_, a poetical and
+philosophical magazine representing the opinions and aims of the New
+England Transcendentalists. This journal she continued to edit for two
+years, and while in Boston she also conducted conversation classes for
+ladies in which philosophical and social subjects were discussed with a
+somewhat over-accentuated earnestness. These meetings may be regarded as
+perhaps the beginning of the modern movement in behalf of women's
+rights. R.W. Emerson, who had met her as early as 1836, thus describes
+her appearance: "She was then twenty-six years old. She had a face and
+frame that would indicate fulness and tenacity of life. She was rather
+under the middle height; her complexion was fair, with strong fair hair.
+She was then, as always, carefully and becomingly dressed, and of
+ladylike self-possession. For the rest her appearance had nothing
+prepossessing. Her extreme plainness, a trick of incessantly opening and
+shutting her eyelids, the nasal tone of her voice, all repelled; and I
+said to myself we shall never get far." On better acquaintance this
+unprepossessing exterior seemed, however, to melt away, and her
+inordinate self-esteem to be lost in the depth and universality of her
+sympathy. She possessed an almost irresistible power of winning the
+intellectual and moral confidence of those with whom she came in
+contact, and "applied herself to her companion as the sponge applies
+itself to water." She obtained from each the best they had to give. It
+was indeed more as a conversationalist than as a writer that she earned
+the title of the Priestess of Transcendentalism. It was her intimate
+friends who admired her most. Smart and pungent though she is as a
+writer, the apparent originality of her views depends more on
+eccentricity than either intellectual depth or imaginative vigour. In
+1844 she removed to New York at the desire of Horace Greeley to write
+literary criticism for _The Tribune_, and in 1846 she published a
+selection from her articles on contemporary authors in Europe and
+America, under the title _Papers on Literature and Art_. The same year
+she paid a visit to Europe, passing some time in England and France, and
+finally taking up her residence in Italy. There she was married in
+December 1847 to the marquis Giovanni Angelo Ossoli, a friend of
+Mazzini. During 1848-1849 she was present with her husband in Rome, and
+when the city was besieged she, at the request of Mazzini, took charge
+of one of the two hospitals while her husband fought on the walls. In
+May 1850, along with her husband and infant son, she embarked at Leghorn
+for America, but when they had all but reached their destination the
+vessel was wrecked on Fire Island beach on the 16th of June, and the
+Ossolis were among the passengers who perished.
+
+  _Life Without and Life Within_ (Boston, 1860) is a collection of
+  essays, poems, &c., supplementary to her _Collected Works_, printed in
+  1855. See the _Autobiography of Margaret Fuller Ossoli_, with
+  additional memoirs by J.F. Clarke, R.W. Emerson and W.H. Channing (2
+  vols., Boston, 1852); also _Margaret Fuller (Marchesa Ossoli)_, by
+  Julia Ward Howe (1883), in the "Eminent Women" series; _Margaret
+  Fuller Ossoli_ (Boston, 1884), by Thomas Wentworth Higginson in the
+  "American Men of Letters" series, which is based largely on unedited
+  material; and _The Love Letters of Margaret Fuller, 1845-1846_ (London
+  and New York, 1903), with an introduction by Julia Ward Howe.
+
+
+
+
+FULLER, MELVILLE WESTON (1833-1910), American jurist, chief justice of
+the Supreme Court of the United States, was born at Augusta, Maine, on
+the 11th of February 1833. After graduating at Bowdoin College in 1853
+he spent a year at the Harvard Law School, and in 1855 began the
+practice of law at Augusta, where he was an associate-editor of a
+Democratic paper, _The Age_, and served in the city council and as city
+attorney. In 1856 he removed to Chicago, Illinois, where he continued to
+practise until 1888, rising to a high position at the bar of the
+Northwest. For some years he was active in Democratic politics, being a
+member of the Illinois Constitutional Convention in 1862 and of the
+State House of Representatives from 1863 to 1865. He was a delegate to
+various National conventions of his party, and in that of 1876 placed
+Thomas A. Hendricks in nomination for the presidency. In 1888, by
+President Cleveland's appointment, he succeeded Morrison R. Waite as
+chief-justice of the Supreme Court of the United States. In 1899 he was
+appointed by President McKinley a member of the arbitration commission
+at Paris to settle the Venezuela-British Guiana boundary dispute.
+
+
+
+
+FULLER, THOMAS (1608-1661), English divine and historian, eldest son of
+Thomas Fuller, rector of Aldwincle St Peter's, Northamptonshire, was
+born at his father's rectory and was baptized on the 19th of June 1608.
+Dr John Davenant, bishop of Salisbury, was his uncle and godfather.
+According to Aubrey, Fuller was "a boy of pregnant wit." At thirteen he
+was admitted to Queens' College, Cambridge, then presided over by Dr
+John Davenant. His cousin, Edward Davenant, was a tutor in the same
+college. He was apt and quick in study; and in Lent 1624-1625 he became
+B.A. and in July 1628 M.A. Being overlooked in an election of fellows of
+his college, he was removed by Bishop Davenant to Sidney Sussex College,
+November 1628. In 1630 he received from Corpus Christi College the
+curacy of St Benet's, Cambridge.
+
+Fuller's quaint and humorous oratory soon attracted attention. He
+published in 1631 a poem on the subject of David and Bathsheba, entitled
+_David's Hainous Sinne, Heartie Repentance, Heavie Punishment_. In June
+of the same year his uncle gave him a prebend in Salisbury, where his
+father, who died in the following year, held a canonry. The rectory of
+Broadwindsor, Dorsetshire, then in the diocese of Bristol, was his next
+preferment (1634); and on the 11th of June 1635 he proceeded B.D. At
+Broadwindsor he compiled _The Historie of the Holy Warre_ (1639), a
+history of the crusades, and _The Holy State and the Prophane State_
+(1642). This work describes the holy state as existing in the family and
+in public life, gives rules of conduct, model "characters" for the
+various professions and profane biographies. It was perhaps the most
+popular of all his writings. He was in 1640 elected proctor for Bristol
+in the memorable convocation of Canterbury, which assembled with the
+Short Parliament. On the sudden dissolution of the latter he joined
+those who urged that convocation should likewise dissolve as usual. That
+opinion was overruled; and the assembly continued to sit by virtue of a
+royal writ. Fuller has left in his _Church History_ a valuable account
+of the proceedings of this synod, for sitting in which he was fined
+L200, which, however, was never exacted. His first published volume of
+sermons appeared in 1640 under the title of _Joseph's party-coloured
+Coat_, which contains many of his quaint utterances and odd conceits.
+His grosser mannerisms of style, derived from the divines of the former
+generation, disappeared for the most part in his subsequent discourses.
+
+About 1640 he had married Eleanor, daughter of Hugh Grove of Chisenbury,
+Wiltshire. She died in 1641. Their eldest child, John, baptized at
+Broadwindsor by his father, 6th June 1641, was afterwards rector of
+Sidney Sussex College, edited the _Worthies of England_, 1662, and
+became rector of Great Wakering, Essex, where he died in 1687.
+
+At Broadwindsor, early in the year 1641, Thomas Fuller, his curate Henry
+Sanders, the church wardens, and others, nine persons altogether,
+certified that their parish, represented by 242 grown-up male persons,
+had taken the Protestation ordered by the speaker of the Long
+Parliament. Fuller was not formally dispossessed of his living and
+prebend on the triumph of the Presbyterian party, but he relinquished
+both preferments about this time. For a short time he preached with
+success at the Inns of Court, and thence removed, at the invitation of
+the master of the Savoy (Dr Balcanqual) and the brotherhood of that
+foundation, to be lecturer at their chapel of St Mary Savoy. Some of the
+best discourses of the witty preacher were delivered at the Savoy to
+audiences which extended into the chapel-yard. In one he set forth with
+searching and truthful minuteness the hindrances to peace, and urged the
+signing of petitions to the king at Oxford, and to the parliament, to
+continue their care in advancing an accommodation. In his _Appeal of
+Injured Innocence_ Fuller says that he was once deputed to carry a
+petition to the king at Oxford. This has been identified with a petition
+entrusted to Sir Edward Wardour, clerk of the pells, Dr Dukeson, "Dr
+Fuller," and four or five others from the city of Westminster and the
+parishes contiguous to the Savoy. A pass was granted by the House of
+Lords, on the 2nd of January 1643, for an equipage of two coaches, four
+or six horses and eight or ten attendants. On the arrival of the
+deputation at Uxbridge, on the 4th of January, officers of the
+Parliamentary army stopped the coaches and searched the gentlemen; and
+they found upon the latter "two scandalous books arraigning the
+proceedings of the House," and letters with ciphers to Lord Viscount
+Falkland and the Lord Spencer. Ultimately a joint order of both Houses
+remanded the party; and Fuller and his friends suffered a brief
+imprisonment. The Westminster Petition, notwithstanding, reached the
+king's hands; and it was published with the royal reply (see J.E.
+Bailey, _Life of Thomas Fuller_, pp. 245 _et seq._). When it was
+expected, three months later, that a favourable result would attend the
+negotiations at Oxford, Fuller preached a sermon at Westminster Abbey,
+on the 27th of March 1643, on the anniversary of Charles I.'s accession,
+on the text, "Yea, let him take all, so my Lord the King return in
+peace." On Wednesday, the 26th of July, he preached on church
+reformation, satirizing the religious reformers, and maintaining that
+only the Supreme Power could initiate reforms.
+
+He was now obliged to leave London, and in August 1643 he joined the
+king at Oxford. He lived in a hired chamber at Lincoln College for 17
+weeks. Thence he put forth a witty and effective reply to John
+Saltmarsh, who had attacked his views on ecclesiastical reform. Fuller
+subsequently published by royal request a sermon preached on the 10th of
+May 1644, at St Mary's, Oxford, before the king and Prince Charles,
+called _Jacob's Vow_.
+
+The spirit of Fuller's preaching, always characterized by calmness and
+moderation, gave offence to the high royalists, who charged him with
+lukewarmness in their cause. To silence unjust censures he became
+chaplain to the regiment of Sir Ralph Hopton. For the first five years
+of the war, as he said, when excusing the non-appearance of his _Church
+History_, "I had little list or leisure to write, fearing to be made a
+history, and shifting daily for my safety. All that time I could not
+live to study, who did only study to live." After the defeat of Hopton
+at Cheriton Down, Fuller retreated to Basing House. He took an active
+part in its defence, and his life with the troops caused him to be
+afterwards regarded as one of "the great cavalier parsons." In his
+marches with his regiment round about Oxford and in the west, he devoted
+much time to the collection of details, from churches, old buildings,
+and the conversation of ancient gossips, for his _Church-History_ and
+_Worthies of England_. He compiled in 1645 a small volume of prayers and
+meditations,--the _Good Thoughts in Bad Times_,--which, set up and
+printed in the besieged city of Exeter, whither he had retired, was
+called by himself "the first fruits of Exeter press." It was inscribed
+to Lady Dalkeith, governess to the infant princess, Henrietta Anne (b.
+1644), to whose household he was attached as chaplain. The corporation
+gave him the Bodleian lectureship on the 21st of March 1645/6, and he
+held it until the 17th of June following, soon after the surrender of
+the city to the parliament. _The Fear of losing the Old Light_ (1646)
+was his farewell discourse to his Exeter friends. Under the Articles of
+Surrender Fuller made his composition with the government at London, his
+"delinquency" being that he had been present in the king's garrisons. In
+_Andronicus, or the Unfortunate Politician_ (1646), partly authentic and
+partly fictitious, he satirized the leaders of the Revolution; and for
+the comfort of sufferers by the war he issued (1647) a second devotional
+manual, entitled _Good Thoughts in Worse Times_, abounding in fervent
+aspirations, and drawing moral lessons in beautiful language out of the
+events of his life or the circumstances of the time. In grief over his
+losses, which included his library and manuscripts (his "upper and
+nether millstone"), and over the calamities of the country, he wrote his
+work on the _Cause and Cure of a Wounded Conscience_ (1647). It was
+prepared at Boughton House in his native county, where he and his son
+were entertained by Edward Lord Montagu, who had been one of his
+contemporaries at the university and had taken the side of the
+parliament.
+
+For the next few years of his life Fuller was mainly dependent upon his
+dealings with booksellers, of whom he asserted that none had ever lost
+by him. He made considerable progress in an English translation from the
+MS. of the _Annales_ of his friend Archbishop Ussher. Amongst his
+benefactors it is curious to find Sir John Danvers of Chelsea, the
+regicide. Fuller in 1647 began to preach at St Clement's, Eastcheap, and
+elsewhere in the capacity of lecturer. While at St Clement's he was
+suspended; but speedily recovering his freedom, he preached wherever he
+was invited. At Chelsea, where also he occasionally officiated, he
+covertly preached a sermon on the death of Charles I., but he did not
+break with his Roundhead patrons. James Hay, 2nd earl of Carlisle, made
+him his chaplain, and presented him in 1648 or 1649 to the curacy of
+Waltham Abbey. His possession of the living was in jeopardy on the
+appointment of Cromwell's "Tryers"; but he evaded their inquisitorial
+questions by his ready wit. He was not disturbed at Waltham in 1655,
+when the Protector's edict prohibited the adherents of the late king
+from preaching. Lionel, 3rd earl of Middlesex, who lived at Copt Hall,
+near Waltham, gave him what remained of the books of the lord treasurer
+his father; and through the good offices of the marchioness of Hertford,
+part of his own pillaged library was restored to him. Fuller was thus
+able to prosecute his literary labours, producing successively his
+descriptive geography of the Holy Land, called _A Pisgah-Sight of
+Palestine_ (1650), and his _Church-History of Britain_ (1655), from the
+birth of Jesus Christ until the year 1648. With the _Church-History_ was
+printed _The History of the University of Cambridge since the Conquest_
+and _The History of Waltham Abbey_. These works were furthered in no
+slight degree by his connexion with Sion College, London, where he had a
+chamber, as well for the convenience of the press as of his city
+lectureships. The _Church-History_ was angrily attacked by Dr P. Heylyn,
+who, in the spirit of High-Churchmanship, wished, as he said, to
+vindicate the truth, the church and the injured clergy. About 1652
+Fuller married his second wife, Mary Roper, youngest sister of Thomas,
+Viscount Baltinglass, by whom he had several children. At the Oxford Act
+of 1657, Robert South, who was _Terrae filius_, lampooned Fuller, whom
+he described in this _Oratio_ as living in London, ever scribbling and
+each year bringing forth new _folia_ like a tree. At length, continues
+South, the _Church-History_ came forth with its 166 dedications to
+wealthy and noble friends; and with this huge volume under one arm, and
+his wife (said to be little of stature) on the other, he ran up and
+down the streets of London, seeking at the houses of his patrons
+invitations to dinner, to be repaid by his dull jests at table.
+
+His last and best patron was George Berkeley, 1st Earl Berkeley
+(1628-1698), of Cranford House, Middlesex, whose chaplain he was, and
+who gave him Cranford rectory (1658). To this nobleman Fuller's reply to
+Heylyn's _Examen Historicum_, called _The Appeal of Injured Innocence_
+(1659), was inscribed. At the end of the _Appeal_ is an epistle "to my
+loving friend Dr Peter Heylyn," conceived in the admirable Christian
+spirit which characterized all Fuller's dealings with controversialists.
+"Why should _Peter_," he asked, "fall out with _Thomas_, both being
+disciples to the same Lord and Master? I assure you, sir, whatever you
+conceive to the contrary, I am cordial to the cause of the English
+Church, and my hoary hairs will go down to the grave in sorrow for her
+sufferings."
+
+In _An Alarum to the Counties of England and Wales_ (1660) Fuller argued
+for a free and full parliament--free from force, as he expressed it, as
+well as from abjurations or previous engagements. _Mixt Contemplations
+in Better Times_ (1660), dedicated to Lady Monk, tendered advice in the
+spirit of its motto, "Let your moderation be known to all men: the Lord
+is at hand." There is good reason to suppose that Fuller was at the
+Hague immediately before the Restoration, in the retinue of Lord
+Berkeley, one of the commissioners of the House of Lords, whose last
+service to his friend was to interest himself in obtaining him a
+bishopric. _A Panegyrick to His Majesty on his Happy Return_ was the
+last of Fuller's verse-efforts. On the 2nd of August, by royal letters,
+he was admitted D.D. at Cambridge. He resumed his lectures at the Savoy,
+where Samuel Pepys heard him preach; but he preferred his conversation
+or his books to his sermons. Fuller's last promotion was that of
+chaplain in extraordinary to Charles II. In the summer of 1661 he
+visited the west in connexion with the business of his prebend, which
+had been restored to him. On Sunday, the 12th of August, while preaching
+at the Savoy, he was seized with typhus fever, and died at his new
+lodgings in Covent Garden on the 16th of August. He was buried in
+Cranford church, where a mural tablet was afterwards set up on the north
+side of the chancel, with an epitaph which contains a conceit worthy of
+his own pen, to the effect that while he was endeavouring (viz. in _The
+Worthies_) to give immortality to others, he himself attained it.
+
+Fuller's wit and vivacious good-humour made him a favourite with men of
+both sides, and his sense of humour kept him from extremes. Probably
+Heylyn and South had some excuse for their attitude towards his very
+moderate politics. "By his particular temper and management," said
+Echard (_Hist. of England_, iii. 71), "he weathered the late great storm
+with more success than many other great men." He was known as "a perfect
+walking library." The strength of his memory was proverbial, and some
+amusing anecdotes are connected with it.
+
+His writings were the product of a highly original mind. He had a
+fertile imagination and a happy faculty of illustration. Antithetic and
+axiomatic sentences abound in his pages, embodying literally the wisdom
+of the many in the wit of one. He was "quaint," and something more.
+"Wit," said Coleridge, in a well-known eulogy, "was the stuff and
+substance of Fuller's intellect. It was the element, the earthen base,
+the material which he worked in; and this very circumstance has
+defrauded him of his due praise for the practical wisdom of the
+thoughts, for the beauty and variety of the truths, into which he shaped
+the stuff. Fuller was incomparably the most sensible, the least
+prejudiced, great man of an age that boasted a galaxy of great men"
+(_Literary Remains_, vol. ii. (1836), pp. 389-390). This opinion was
+formed after the perusal of the _Church-History_. That work and _The
+History of the Worthies of England_ are unquestionably Fuller's greatest
+efforts. They embody the collections of an entire life; and since his
+day they have been the delight of many readers. The _Holy State_ has
+taken rank amongst the best books of "characters." Charles Lamb made
+some selections from Fuller, and had a profound admiration for the
+"golden works" of the "dear, fine, silly old angel." Since Lamb's time,
+mainly through the appreciative criticisms of S.T. Coleridge, Robert
+Southey and others, Fuller's works have received much attention.
+
+  There is an elaborate account of the life and writings of Fuller by
+  William Oldys in the _Biographia Britannica_, vol. iii. (1750), based
+  on Fuller's own works and the anonymous _Life of ... Dr Thomas Fuller_
+  (1661; reprinted in a volume of selections by A.L.J. Gosset, 1893).
+  The completest account of him is _The Life of Thomas Fuller, with
+  Notices of his Books, his Kinsmen and his Friends_ (1874), by J.E.
+  Bailey, who gives a detailed bibliography (pp. 713-762) of his works.
+  _The Worthies of England_ was reprinted by John Nichols (1811) and by
+  P.A. Nuttall (1840). His _Collected Sermons_ were edited by J.E.
+  Bailey and W.E.A. Axon in 1891. Fuller's quaint wit lends itself to
+  selection, and there are several modern volumes of extracts from his
+  works.
+
+
+
+
+FULLER, WILLIAM (1670-c. 1717), English impostor, was born at Milton in
+Kent on the 20th of September 1670. His paternity is doubtful, but he
+was related to the family of Herbert. After 1688 he served James II.'s
+queen, Mary of Modena, and the Jacobites, seeking at the same time to
+gain favour with William III.; and after associating with Titus Oates,
+being imprisoned for debt and pretending to reveal Jacobite plots, the
+House of Commons in 1692 declared he was an "imposter, cheat and false
+accuser." Having stood in the pillory he was again imprisoned until
+1695, when he was released; and at this time he took the opportunity to
+revive the old and familiar story that Mary of Modena was not the mother
+of the prince of Wales. In 1701 he published his autobiographical _Life
+of William Fuller_ and some _Original Letters of the late King James_.
+Unable to prove the assertions made in his writings he was put in the
+pillory, whipped and fined. He died, probably in prison, about 1717.
+Fuller's other writings are _Mr William Fuller's trip to Bridewell, with
+a full account of his barbarous usage in the pillory; The sincere and
+hearty confession of Mr William Fuller_ (1704); and _An humble appeal to
+the impartial judgment of all parties in Great Britain_ (1716).
+
+  He must be distinguished from WILLIAM FULLER (1608-1675), dean of St
+  Patrick's (1660), bishop of Limerick (1663), and bishop of Lincoln
+  (1667), the friend of Samuel Pepys; and also from William Fuller (c.
+  1580-1659), dean of Ely and later dean of Durham.
+
+
+
+
+FULLER'S EARTH (Ger. _Walkererde_, Fr. _terre a foulon_, _argile
+smectique_)--so named from its use by fullers as an absorbent of the
+grease and oil of cloth,--a clay-like substance, which from its
+variability is somewhat difficult to define. In colour it is most often
+greenish, olive-green or greenish-grey; on weathering it changes to a
+brown tint or it may bleach. As a rule it falls to pieces when placed in
+water and is not markedly plastic; when dry it adheres strongly to the
+tongue; since, however, these properties are possessed by many clays
+that do not exhibit detergent qualities, the only test of value lies in
+the capacity to absorb grease or clarify oil. Fuller's earth has a
+specific gravity of 1.7-2.4, and a shining streak; it is usually
+unctuous to the touch. Microscopically, it consists of minute
+irregular-shaped particles of a mineral that appears to be the result of
+a chloritic or talcose alteration of a felspar. The small size of most
+of the grains, less than .07 mm., makes their determination almost
+impossible. Chemical analysis shows that the peculiar properties of this
+earth are due to its physical rather than its chemical nature.
+
+  The following analyses of the weathered and unweathered condition of
+  the earth from Nutfield, Surrey, represent the composition of one of
+  the best known varieties:--
+
+    Blue Earth (dried at 100 deg. C.).
+
+    Insoluble residue  69.96  | Insoluble residue--
+    Fe2O3               2.48  |   SiO2            62.81
+    Al2O3               3.46  |   Al2O3            3.46
+    CaO                 5.87  |   Fe2O3            1.30
+    MgO                 1.41  |   CaO              1.53
+    P2O5                0.27  |   MgO              0.86
+    SO3                 0.05  |                   -----
+    NaCl                0.05  |                   69.96
+    K2O                 0.74  |                   =====
+    H2O (combined)     15.57  |
+                       -----  |
+                       99.86  |
+                       =====  |
+
+
+    Yellow Earth (dried at 100 deg. C.).
+
+    Insoluble residue  76.13  | Insoluble residue--
+    Fe2O3               2.41  |   SiO2            59.37
+    Al2O3               1.77  |   Al2O3           10.05
+    CaO                 4.31  |   Fe2O3            3.86
+    MgO                 1.05  |   CaO              1.86
+    P2O5                0.14  |   MgO              1.04
+    SO3                 0.07  |                   -----
+    NaCl                0.14  |                   76.18
+    K2O                 0.84  |                   =====
+    H2O (combined)     13.19  |
+                      ------  |
+                      100.05  |
+                      ======  |
+
+  (Analysis by P.G. Sanford, _Geol. Mag._, 1889, 6, pp. 456, 526.)
+
+  Of other published analyses, not a few show a lower silica content
+  (44%, 50%), along with a higher proportion of alumina (11%, 23%).
+
+Fuller's earth may occur on any geological horizon; at Nutfield in
+Surrey, England, it is in the Cretaceous formations; at Midford near
+Bath it is of Jurassic age; at Bala, North Wales, it occurs in
+Ordovician strata; in Saxony it appears to be the decomposition product
+of a diabasic rock. In America it is found in California in rocks
+ranging from Cretaceous to Pleistocene age; in S. Dakota, Custer county
+and elsewhere a yellow, gritty earth of Jurassic age is worked; in
+Florida and Georgia occurs a brittle, whitish earth of Oligocene age.
+Other deposits are worked in Arkansas, Texas, Colorado, Massachusetts
+and South Carolina.
+
+Fuller's earth is either mined or dug in the open according to local
+circumstances. It is then dried in the sun or by artificial heat and
+transported in small lumps in sacks. In other cases it is ground to a
+fine powder after being dried; or it is first roughly ground and made
+into a slurry with water, which is allowed to carry off the finer from
+the coarser particles and deposit them in a creamy state in suitable
+tanks. After consolidation this fine material is dried artificially on
+drying floors, broken into lumps, and packed for transport. The use of
+fuller's earth for cleansing wool and cloth has greatly decreased, but
+the demand for the material is as great or greater than it ever was. It
+is now used very largely in the filtration of mineral oils, and also for
+decolourizing certain vegetable oils. It is employed in the formation of
+certain soaps and cleansing preparations.
+
+The term "Fuller's Earth" has a special significance in geology, for it
+was applied by W. Smith in 1799 to certain clays in the neighbourhood of
+Bath, and the use of the expression is still retained by English
+geologists, either in this form or in the generalized "Fullonian." The
+Fullonian lies at the base of the Great Oolite or Bathonian series, but
+its palaeontological characters place it between that series and the
+underlying Inferior Oolite. The zonal fossils are _Perisphinctes
+arbustigerus_ and _Macrocephalus subcontractus_ with _Ostrea acuminata_,
+_Rhynchonella concinna_ and _Goniomya angulifera_. The formation is in
+part the equivalent of the "Vesulien" of J. Marcou (Vesoul in
+Haute-Saone). In Dorsetshire and Somersetshire, where it is best
+developed, it is represented by an Upper Fuller's Earth Clay, the
+Fuller's Earth Rock (an impersistent earthy limestone, usually
+fossiliferous), and the Lower Fuller's Earth Clay. Commercial fuller's
+earth has been obtained only from the Upper Clay. In eastern
+Gloucestershire and northern Oxfordshire the Fuller's Earth passes
+downwards without break into the Inferior Oolite; northward it dies out
+about Chipping Norton in Oxfordshire and passes laterally into the
+Stonesfield Slates series; in the midland counties it may perhaps be
+represented by the "Upper Estuarine Series." In parts of Dorsetshire the
+clays have been used for brickmaking and the limestone (rock) for local
+buildings.
+
+  See H.B. Woodward, "Jurassic Rocks of Great Britain," vol. iv. (1894),
+  _Mem. Geol. Survey_ (London).     [J. A. H.]
+
+
+
+
+FULLERTON, LADY GEORGIANA CHARLOTTE (1812-1885), English novelist and
+philanthropist, youngest daughter of the 1st Earl Granville, was born at
+Tixall Hall in Staffordshire on the 23rd of September 1812. In 1833 she
+married Alexander George Fullerton, then an Irish officer in the guards.
+After living in Paris for some eight years she and her husband
+accompanied Lord Granville to Cannes and thence to Rome. In 1843 her
+husband entered the Roman Catholic church, and in the following year
+Lady Georgiana Fullerton published her first novel, _Ellen Middleton_,
+which attracted W.E. Gladstone's attention in the _English Review_. In
+1846 she entered the Roman Catholic church. The death of her only son in
+1854 plunged her in grief, and she continued to wear mourning until the
+end of her life. In 1856 she became one of the third order of St
+Francis, and thenceforward devoted herself to charitable work. In
+conjunction with Miss Taylor she founded the religious community known
+as "The Poor Servants of the Mother of God Incarnate," and she also took
+an active part in bringing to England the sisters of St Vincent of Paul.
+Her philanthropic work is described in Mrs Augustus Craven's work _Lady
+Georgiana Fullerton, sa vie et ses [oe]uvres_ (Paris, 1888), which was
+translated into English by Henry James Coleridge. She died at
+Bournemouth on the 19th of January 1885. Among her other novels were
+_Grantley Manor_ (1847), _Lady Bird_ (1852), and _Too Strange not to be
+True_ (1864).
+
+
+
+
+FULMAR, from the Gaelic _Fulmaire_, the _Fulmarus glacialis_ of modern
+ornithologists, one of the largest of the petrels (_Procellariidae_) of
+the northern hemisphere, being about the size of the common gull (_Larus
+canus_) and not unlike it in general coloration, except that its
+primaries are grey instead of black. This bird, which ranges over the
+North Atlantic, is seldom seen on the European side below lat. 53 deg.
+N., but on the American side comes habitually to lat. 45 deg. or even
+lower. In the Pacific it is represented by a scarcely separable form,
+_F. glupischa_. It has been commonly believed to have two
+breeding-places in the British Islands, namely, St Kilda and South
+Barra; but, according to Robert Gray (_Birds of the West of Scotland_,
+p. 499), it has abandoned the latter since 1844, though still breeding
+in Skye. Northward it established itself about 1838 on Myggenaes Holm,
+one of the Faeroes, while it has several stations off the coast of
+Iceland and Spitsbergen, as well as at Bear Island. Its range towards
+the pole seems to be only bounded by open water, and it is the constant
+attendant upon all who are employed in the whale and seal fisheries,
+showing the greatest boldness in approaching boats and ships, and
+feeding on the offal obtained from them. By British seamen it is
+commonly called the "molly mawk"[1] (corrupted from _Mallemuck_), and is
+extremely well known to them, its flight, as it skims over the waves,
+first with a few beats of the wings and then gliding for a long way,
+being very peculiar. It only visits the land to deposit its single white
+egg, which is laid on a rocky ledge, where a shallow nest is made in the
+turf and lined with a little dried grass. Many of its breeding-places
+are a most valuable property to those who live near them and take the
+eggs and young, which, from the nature of the locality, are only to be
+had at a hazardous risk of life. In St Kilda a large number of the young
+are killed in one week of August, the only time when, by the custom of
+the community, they are allowed to be taken. These, after the oil is
+extracted from them, serve the islanders with food for the winter. The
+oil has been chemically analysed and found to be a fish-oil, and to
+possess nearly all the qualities of that obtained from the liver of the
+cod, with a lighter specific gravity. It, however, has an extremely
+strong scent, which is said by those who have visited St Kilda to
+pervade every thing and person on the island, and is certainly retained
+by an egg or skin of the bird for many years. Whenever a live example is
+seized in the hand it ejects a considerable quantity of this oil from
+its mouth.
+
+
+FOOTNOTE:
+
+  [1] A name misapplied in the southern hemisphere to _Diomedea
+    melanophrys_, one of the albatrosses.
+
+
+
+
+FULMINIC ACID, HCNO or H2C2N2O2, an organic acid isomeric with cyanic
+and cyanuric acids; its salts, termed fulminates, are very explosive and
+are much employed as detonators. The free acid, which is obtained by
+treating the salts with acids, is an oily liquid smelling like prussic
+acid; it is very explosive, and the vapour is poisonous to about the
+same degree as that of prussic acid. The first fulminate prepared was
+the "fulminating silver" of L.G. Brugnatelli, who found in 1798 that if
+silver be dissolved in nitric acid and the solution added to spirits of
+wine, a white, highly explosive powder was obtained. This substance is
+to be distinguished from the black "fulminating silver" obtained by
+C.L. Berthollet in 1788 by acting with ammonia on precipitated silver
+oxide. The next salt to be obtained was the mercuric salt, which was
+prepared in 1799 by Edward Charles Howard, who substituted mercury for
+silver in Brugnatelli's process. A similar method is that of J. von
+Liebig (1823), who heated a mixture of alcohol, nitric acid and mercuric
+nitrate; the salt is largely manufactured by processes closely
+resembling the last. A laboratory method is to mix solutions of sodium
+nitromethane, CH2:NO(ONa), and mercuric chloride, a yellow basic salt
+being formed at the same time. Mercuric fulminate is less explosive than
+the silver salt, and forms white needles (with 1/2H2O) which are
+tolerably soluble in water. The use of mercuric fulminate as a detonator
+dates from about 1814, when the explosive cap was invented. It is still
+the commonest detonator, but it is now usually mixed with other
+substances; the British service uses for percussion caps 6 parts of
+fulminate, 6 of potassium chlorate and 4 of antimony sulphide, and for
+time fuses 4 parts of fulminate, 6 of potassium chlorate and 4 of
+antimony sulphide, the mixture being damped with a shellac varnish; for
+use in blasting, a home office order of 1897 prescribes a mixture of 4
+parts of fulminate and 1 of potassium chlorate. In 1900 Bielefeldt found
+that a fulminate placed on top of an aromatic nitro compound, such as
+trinitrotoluene, formed a useful detonator; this discovery has been
+especially taken advantage of in Germany, in which country detonators of
+this nature are being largely employed. Tetranitromethylaniline (tetryl)
+has also been employed (Brit. Pat. 13340 of 1905). It has been proposed
+to replace fulminate by silver azoimide (Wohler & Matter, Brit. Pat.
+4468 of 1908), and by lead azoimide (Hyronimus, Brit. Pat. 1819 of
+1908).
+
+  The constitution of fulminic acid has been investigated by many
+  experimenters, but apparently without definitive results. The
+  researches of Liebig (1823), Liebig and Gay-Lussac (1824), and of
+  Liebig again in 1838 showed the acid to be isomeric with cyanic acid,
+  and probably (HCNO)2, since it gave mixed and acid salts. Kekule, in
+  1858, concluded that it was nitroacetonitrile, NO2.CH2.CN, a view
+  opposed by Steiner (1883), E. Divers and M. Kawakita (1884), R. Scholl
+  (1890), and by J.U. Nef (1894), who proposed the formulae:
+
+    C : N.OH        / N : CH      CH : N.O
+    ..           O /      .       .           C : N.OH.
+    C : N.OH,       \ N : C.OH,   CH : N.0,
+
+     Steiner,        Divers,       Scholl,      Nef.
+
+  The formulae of Kekule, Divers and Armstrong have been discarded, and
+  it remains to be shown whether Nef's carbonyloxime formula (or the
+  bimolecular formula of Steiner) or Scholl's glyoxime peroxide formula
+  is correct. There is some doubt as to the molecular formula of
+  fulminic acid. The existence of double salts, and the observations of
+  L. Wohler and K. Theodorovits (_Ber._, 1905, 38, p. 345), that only
+  compounds containing two carbon atoms yielded fulminates, points to
+  (HCNO)2; on the other hand, Wohler (_loc. cit._ p. 1351) found that
+  cryoscopic and electric conductivity measurements showed sodium
+  fulminate to be NaCNO. Nef based his formula, which involves bivalent
+  carbon, on many reactions; in particular, that silver fulminate with
+  hydrochloric acid gave salts of formylchloridoxime, which with water
+  gave hydroxylamine and formic acid, thus
+
+                      // NOAg         // N.OH
+    C : NO OAg -> HC //       --> HC //       --> H.CO2H + H2N.OH,
+                     \   Cl          \   OH
+
+  and also on the production from sodium nitromethane and mercuric
+  chloride, thus CH2 : NO.Ohg --> H2O + C : NOhg(hg = 1/2Hg). H. Wieland
+  and F.C. Palazzo (1907) support this formula, finding that methyl
+  nitrolic acid, NO2.CH : N.OH, yielded under certain conditions
+  fulminic acid, and vice versa (Palazzo, 1907). M.Z. Jowitschitsch
+  (_Ann._, 1906, 347, p. 233) inclines to Scholl's formula; he found
+  that the synthetic silver salt of glyoxime peroxide resembled silver
+  fulminate in yielding hydroxylamine with hydrochloric acid, but
+  differed in being less explosive, and in being soluble in nitric acid.
+  H. Wieland and his collaborators regard "glyoxime peroxide" as an
+  oxide of furazane (q.v.), and have shown that a close relationship
+  exists between the nitrile oxides, furoxane, and fulminic acid (see
+  Ann. Rep., London Chem. Soc., 1909, p. 84). _Fulminuric acid_,
+  (HCNO)3, obtained by Liebig by boiling mercuric fulminate with water,
+  was synthesized in 1905 by C. Ulpiani and L. Bernardini (_Gazetta_,
+  iii. 35, p. 7), who regard it as NO2.CH(CN).CO.NH2. It deflagrates at
+  145 deg., and forms a characteristic cuprammonium salt.
+
+  The early history of mercuric fulminate and a critical account of its
+  application as a detonator is given in _The Rise and Progress of the
+  British Explosives Industry_ (International Congress of Applied
+  Chemistry, 1909). The manufacture and modern aspects are treated in
+  Oscar Guttmann, _The Manufacture of Explosives_, and _Manufacture of
+  Explosives, Twenty Years' Progress_ (1909).
+
+
+
+
+FULTON, ROBERT (1765-1815), American engineer, was born in 1765 in
+Little Britain (now Fulton, Lancaster county), Pa. His parents were
+Irish, and so poor that they could afford him only a very scanty
+education. At an early age he was bound apprentice to a jeweller in
+Philadelphia, but subsequently adopted portrait and landscape painting
+as his profession. In his twenty-second year, with the object of
+studying with his countryman, Benjamin West, he went to England, and
+there became acquainted with the duke of Bridgewater, Earl Stanhope and
+James Watt. Partly by their influence he was led to devote his attention
+to engineering, especially in connexion with canal construction; he
+obtained an English patent in 1794 for superseding canal locks by
+inclined planes, and in 1796 he published a _Treatise on the Improvement
+of Canal Navigation_. He then took up his residence in Paris, where he
+projected the first panorama ever exhibited in that city, and
+constructed a submarine boat, the "Nautilus," which was tried in Brest
+harbour in 1801 before a commission appointed by Napoleon I., and by the
+aid of which he was enabled to blow up a small vessel with a torpedo. It
+was at Paris also in 1803 that he first succeeded in propelling a boat
+by steam-power, thus realizing a design which he had conceived ten years
+previously. Returning to America he continued his experiments with
+submarine explosives, but failed to convince either the English, French
+or United States governments of the adequacy of his methods. With steam
+navigation he had more success. In association with Robert R. Livingston
+(q.v.), who in 1798 had been granted the exclusive right to navigate the
+waters of New York state with steam-vessels, he constructed the
+"Clermont," which, engined by Boulton & Watt of Birmingham, began to ply
+on the Hudson between New York and Albany in 1807. The privilege
+obtained by Livingston in 1798 was granted jointly to Fulton and
+Livingston in 1803, and by an act passed in 1808 the monopoly was
+secured to them and their associates for a period depending on the
+number of steamers constructed, but limited to a maximum of thirty
+years. In 1814-1815, on behalf of the United States government, he
+constructed the "Fulton," a vessel of 38 tons with central
+paddle-wheels, which was the first steam warship. He died at New York on
+the 24th of February 1815. Among Fulton's inventions were machines for
+spinning flax, for making ropes, and for sawing and polishing marble.
+
+  See C.D. Colden, _Life of Robert Fulton_ (New York, 1817); Robert H.
+  Thurston, _History of the Growth of the Steam-Engine_ (New York,
+  1878); George H. Preble, _Chronological History of Steam Navigation_
+  (Philadelphia, 1883); and Mrs A.C. Sutcliffe, _Robert Fulton and the
+  Clermont_ (New York, 1909).
+
+
+
+
+FULTON, a city and the county-seat of Callaway county, Missouri, U.S.A.,
+25 m. N.E. of Jefferson City. Pop. (1890) 4314; (1900) 4883 (1167
+negroes); (1910) 5228. It is served by the Chicago & Alton railway. The
+city has an important stock market and manufactures fire-brick and
+pottery. At Fulton are the Westminster College (Presbyterian, founded in
+1853), the Synodical College for Young Women (Pres., founded in 1871),
+the William Woods College for Girls (Christian Church, 1890), and the
+Missouri school for the deaf (1851). Here, too, is a state hospital for
+the insane (1847), the first institution of the kind in Missouri. The
+place was laid out as a town in 1825 and named Volney, but in honour of
+Robert Fulton the present name was adopted a little later. Fulton was
+incorporated in 1859.
+
+
+
+
+FULTON, a city of Oswego county, New York, U.S.A., on the right bank of
+the Oswego river, about 10 m. S. by E. of Oswego. Pop. (1900) 5281;
+(1905, state census) 8847; (1910) 10,480. Fulton is served by the
+Delaware, Lackawanna & Western, the New York Central & Hudson River, and
+the New York, Ontario & Western railways, by electric railway to Oswego
+and Syracuse and by the Oswego Canal. The city has a Carnegie library.
+Ample water-power is furnished by the Oswego river, which here flows in
+a series of rapids, and the manufactures are many in kind. On the 3rd of
+July 1756, on an island (afterward called Battle Island) 4 m. N. of the
+present city of Fulton, a British force of about 300 under Captain John
+Bradstreet (1711-1774) defeated an attacking force of French and Indians
+(numbering about 700) under De Villiers. Soon after this, Bradstreet
+built a fort within the present limits of Fulton. The first civilian
+settler came in 1793, and the first survey (which included only a part
+of the subsequent village) was made in 1815. Fulton was incorporated as
+a village in 1835, and in April 1902 was combined with the village of
+Oswego Falls (pop. in 1900, 2925) and was chartered as a city.
+
+
+
+
+FUM, or FUNJ HWANG, one of the four symbolical creatures which in
+Chinese mythology are believed to keep watch and ward over the Celestial
+Empire. It was begotten by fire, was born in the Hill of the Sun's Halo,
+and its body bears inscribed on it the five cardinal virtues. It has the
+breast of a goose, the hindquarters of a stag, a snake's neck, a fish's
+tail, a fowl's forehead, a duck's down, the marks of a dragon, the back
+of a tortoise, the face of a swallow, the beak of a cock, is about six
+cubits high, and perches only on the woo-tung tree. The appearance of
+Fum heralds an age of universal virtue. Its figure is that which is
+embroidered on the dresses of some mandarins.
+
+
+
+
+FUMARIC AND MALEIC ACIDS, two isomeric unsaturated acids of composition
+C4H4O4. _Fumaric acid_ is found in fumitory (_Fumaria officinalis_), in
+various fungi (_Agaricus piperatus_, &c.), and in Iceland moss. It is
+obtained by heating malic acid alone to 150 deg. C., or by heating it
+with hydrochloric acid (V. Dessaignes, _Jahresb_., 1856, p. 463) or with
+a large quantity of hydrobromic acids (A. Kekule, _Ann._, 1864, 130, p.
+21). It may also be obtained by boiling monobromsuccinic acid with
+water; by the action of dichloracetic acid and water on silver malonate
+(T. Komnenos, _Ann._, 1883, 218, p. 169); by the cyanide synthesis from
+acetylene di-iodide; and by heating maleic acid to 210 deg. C. (Z.
+Skraup, _Monats. f. Chemie_, 1891, 12, p. 112). It crystallizes in small
+prisms or needles, and is practically insoluble in cold water. It
+sublimes to some extent at about 200 deg. C., being partially converted
+into maleic anhydride and water, the reaction becoming practically
+quantitative if dehydrating agents be used. Reducing agents (zinc and
+caustic alkali, hydriodic acid, sodium amalgam, &c.) convert it into
+succinic acid. Bromine converts it into dibromsuccinic acid. Potassium
+permanganate oxidizes it to racemic acid (A. Kekule and R. Anschutz,
+_Ber._, 1881, 14, p. 713). By long-continued heating with caustic soda
+at 100 deg. C. it is converted into inactive malic acid.
+
+_Maleic acid_ is obtained by distilling malic or fumaric acids; by
+heating fumaric acid with acetyl chloride to 100 deg. C; or by the
+hydrolysis of trichlorphenomalic acid ([beta]-trichloraceto-acrylic
+acid) [A. Kekule, _Ann._, 1884, 223, p. 185]. It crystallizes in
+monoclinic prisms, which are easily soluble in water, melt at 130 deg.
+C., and boil at 160 deg. C., decomposing into water and maleic
+anhydride. When heated with concentrated hydrobromic or hydriodic acids,
+it is converted into fumaric acid. It yields an anilide; oxidation
+converts it into mesotartaric acid. Maleic anhydride is obtained by
+distilling fumaric acid with phosphorus pentoxide. It forms triclinic
+crystals which melt at 60 deg. C. and boil at 196 deg. C.
+
+  Both acids are readily esterified by the action of alkyl halides on
+  their silver salts, and the maleic ester is readily transformed into
+  the fumaric ester by warming with iodine, the same result being
+  obtained by esterification of maleic acid in alcoholic solution by
+  means of hydrochloric acid. Both acids yield acetylene by the
+  electrolysis of aqueous solutions of their alkali salts, and on
+  reduction both yield succinic acid, whilst by the addition of
+  hydrobromic acid they both yield monobromsuccinic acid (R. Fittig,
+  _Ann._, 1877, 188, p. 98). From these results it follows that the two
+  acids are structurally identical, and the isomerism has consequently
+  to be explained on other grounds. This was accomplished by W.
+  Wislicenus ["Uber die raumliche Anordnung der Atome," &c., _Trans, of
+  the Saxon Acad. of Sciences_ (Math. Phys. Section), 1887, p. 14] by an
+  extension of the van't Hoff hypothesis (see STEREO-ISOMERISM). The
+  formulae of the acids are written thus:
+
+    HC.CO2H                    HC.CO2H
+    ..        Maleic acid.       ..      Fumaric acid.
+    HC.CO2H                 HO2C.C.H
+
+  These account for maleic acid readily yielding an anhydride, whereas
+  fumaric acid does not, and for the behaviour of the acids towards
+  bromine, fumaric acid yielding ordinary dibromsuccinic acid, and
+  maleic acid the isomeric isodibromsuccinic acid.
+
+
+
+
+FUMAROLE, a vent from which volcanic vapours issue, named indirectly
+from the Lat. _fumariolum_, a smoke-hole. The vapours from fumaroles
+were studied first by R.W. Bunsen, on his visit to Iceland, and
+afterwards by H. Sainte-Claire Deville and other chemists and geologists
+in France, who examined the vapours from Santorin, Etna, &c. The hottest
+vapours issue from dry fumaroles, at temperatures of at least 500 deg.
+C., and consist chiefly of anhydrous chlorides, notably sodium chloride.
+The acid fumaroles yield vapours of lower temperature (300 deg. to 400
+deg.) containing much water vapour, with hydrogen chloride and sulphur
+dioxide. The alkaline fumaroles are still cooler, though above 100 deg.,
+and evolve ammonium chloride with other vapours. Cold fumaroles, below
+100 deg., discharge principally aqueous vapour, with carbon dioxide, and
+perhaps hydrogen sulphide. The fumaroles of Mont Pele in Martinique
+during the eruption of 1902 were examined by A. Lacroix, and the vapours
+analysed by H. Moissan, who found that they consisted chiefly of water
+vapour, with hydrogen chloride, sulphur, carbon dioxide, carbon
+monoxide, methane, hydrogen, nitrogen, oxygen and argon. These vapours
+issued at a temperature of about 400 deg. Armand Gautier has pointed out
+that these gases are practically of the same composition as those which
+he obtained on heating granite and certain other rocks. (See VOLCANO).
+
+
+
+
+FUMIGATION (from Lat. _fumigare_, to smoke), the process of producing
+smoke or fumes, as by burning sulphur, frankincense, tobacco, &c.,
+whether as a ceremony of incantation, or for perfuming a room, or for
+purposes of disinfection or destruction of vermin. In medicine the term
+has been used of the exposure of the body, or a portion of it, to fumes
+such as those of nitre, sal-ammoniac, mercury, &c.; fumigation, by the
+injection of tobacco smoke into the great bowel, was a recognized
+procedure in the 18th century for the resuscitation of the apparently
+drowned. "Fumigated" or "fumed" oak is oak which has been darkened by
+exposure to ammonia vapour.
+
+
+
+
+FUMITORY, in botany, the popular name for the British species of
+_Fumaria_, a genus of small, branched, often climbing annual herbs with
+much-divided leaves and racemes of small flowers. The flowers are
+tubular with a spurred base, and in the British species are pink to
+purplish in colour. They are weeds of cultivation growing in fields and
+waste places. _F. capreolata_ climbs by means of twisting petioles. In
+past times fumitory was in esteem for its reputed cholagogue and other
+medicinal properties; and in England, boiled in water, milk or whey, it
+was used as a cosmetic. The root of the allied species (_Corydalis cava_
+or _tuberosa_) is known as _radix aristolochia_, and has been used
+medicinally for various cutaneous and other disorders, in doses of 10 to
+30 grains. Some eleven alkaloids have been isolated from it. The herbage
+of _Fumaria officinalis_ and _F. racemosa_ is used in China under the
+name of _Tsze-hwa-ti-ting_ as an application for glandular swellings,
+carbuncles and abscesses, and was formerly valued in jaundice, and in
+cases of accidental swallowing of the beard of grain (see F. Porter
+Smith, _Contrib. towards the Mat. Medica ... of China_, p. 99, 1871).
+The name fumitory, Latin _fumus terrae_, has been supposed to be derived
+from the fact that its juice irritates the eyes like smoke (see Fuchs,
+_De historia stirpium_, p. 338, 1542); but _The Grete Herball_, cap.
+clxix., 1529, fol., following the _De simplici medicina_ of Platearius,
+fo. xciii. (see in _Nicolai Praepositi dispensatorium ad aromatarios_,
+1536), says: "It is called Fumus terre fume or smoke of the erthe
+bycause it is engendred of a cours fumosyte rysynge frome the erthe in
+grete quantyte lyke smoke: this grosse or cours fumosyte of the erthe
+wyndeth and wryeth out: and by workynge of the ayre and sonne it turneth
+into this herbe."
+
+
+
+
+FUNCHAL, the capital of the Portuguese archipelago of the Madeiras; on
+the south coast of Madeira, in 32 deg. 37' N. and 16 deg. 54' W. Pop.
+(1900) 20,850. Funchal is the see of a bishop, in the archiepiscopal
+province of Lisbon; it is also the administrative centre of the
+archipelago, and the residence of the governor and foreign consuls. The
+city has an attractive appearance from the sea. Its whitewashed houses,
+in their gardens full of tropical plants, are built along the curving
+shore of Funchal Bay, and on the lower slopes of an amphitheatre of
+mountains, which form a background 4000 ft. high. Numerous country
+houses (_quintas_), with terraced gardens, vineyards and sugar-cane
+plantations occupy the surrounding heights. Three mountain streams
+traverse the city through deep channels, which in summer are dry, owing
+to the diversion of the water for irrigation. A small fort, on an
+isolated rock off shore, guards the entrance to the bay, and a larger
+and more powerfully armed fort crowns an eminence inland. The chief
+buildings include the cathedral, Anglican and Presbyterian churches,
+hospitals, opera-house, museum and casino. There are small public
+gardens and a meteorological observatory. In the steep and narrow
+streets, which are lighted by electricity, wheeled traffic is
+impossible; sledges drawn by oxen, and other primitive conveyances are
+used instead (see MADEIRA). In winter the fine climate and scenery
+attract numerous invalids and other visitors, for whose accommodation
+there are good hotels; many foreigners engaged in the coal and wine
+trades also reside here permanently. The majority of these belong to the
+British community, which was first established here in the 18th century.
+Funchal is the headquarters of Madeiran industry and commerce (see
+MADEIRA). It has no docks and no facilities for landing passengers or
+goods; vessels are obliged to anchor in the roadstead, which, however,
+is sheltered from every wind except the south. Funchal is connected by
+cable with Carcavellos (for Lisbon), Porthcurnow (for Falmouth, England)
+and St Vincent in the Cape Verde Islands (for Pernambuco, Brazil).
+
+
+
+
+FUNCTION,[1] in mathematics, a variable number the value of which
+depends upon the values of one or more other variable numbers. The
+theory of functions is conveniently divided into (I.) Functions of Real
+Variables, wherein real, and only real, numbers are involved, and (II.)
+Functions of Complex Variables, wherein complex or imaginary numbers are
+involved.
+
+
+I. FUNCTIONS OF REAL VARIABLES
+
+1. _Historical._--The word function, defined in the above sense, was
+introduced by Leibnitz in a short note of date 1694 concerning the
+construction of what we now call an "envelope" (_Leibnizens
+mathematische Schriften_, edited by C.I. Gerhardt, Bd. v. p. 306), and
+was there used to denote a variable length related in a defined way to a
+variable point of a curve. In 1698 James Bernoulli used the word in a
+special sense in connexion with some isoperimetric problems (Joh.
+Bernoulli, _Opera_, t. i. p. 255). He said that when it is a question of
+selecting from an infinite set of like curves that one which best
+fulfils some function, then of two curves whose intersection determines
+the thing sought one is always the "line of the function" (_Linea
+functionis_). In 1718 John Bernoulli (_Opera_, t. ii. p. 241) defined a
+"function of a variable magnitude" as a quantity made up in any way of
+this variable magnitude and constants; and in 1730 (Opera, t. iii. p.
+174) he noted a distinction between "algebraic" and "transcendental"
+functions. By the latter he meant integrals of algebraic functions. The
+notation [f](x) for a function of a variable x was introduced by
+Leonhard Euler in 1734 (_Comm. Acad. Petropol._ t. vii. p. 186), in
+connexion with the theorem of the interchange of the order of
+differentiations. The notion of functionality or functional relation of
+two magnitudes was thus of geometrical origin; but a function soon came
+to be regarded as an analytical expression, not necessarily an algebraic
+expression, containing the variable or variables. Thus we may have
+rational integral algebraic functions such as _ax_^2 + _bx_ + c, or
+rational algebraic functions which are not integral, such as
+
+  a1x^n + a2x^(n - 1) + ... + a_n
+  -------------------------------,
+  b1x^m + b2x^(m - 1) + ... + b_m
+
+or irrational algebraic functions, such as [root]x, or, more generally
+the algebraic functions that are determined implicitly by an algebraic
+equation, as, for instance,
+
+  [f]_n(x, y) + [f]_(n - 1) (x, y) + ... + [f]0 = 0
+
+where [f]_n(x, y), ... mean homogeneous expressions in x and y having
+constant coefficients, and having the degrees indicated by the suffixes,
+and [f]0 is a constant. Or again we may have trigonometrical functions,
+such as sin x and tan x, or inverse trigonometrical functions, such as
+sin^(-1)x, or exponential functions, such as e^x and a^x, or logarithmic
+functions, such as log x and log (1 + x). We may have these functional
+symbols combined in various ways, and thus there arises a great number
+of functions. Further we may have functions of more than one variable,
+as, for instance, the expression xy/(x^2 + y^2), in which both x and y
+are regarded as variable. Such functions were introduced into analysis
+somewhat unsystematically as the need for them arose, and the later
+developments of analysis led to the introduction of other classes of
+functions.
+
+2. _Graphic Representation._--In the case of a function of one variable
+x, any value of x and the corresponding value y of the function can be
+the co-ordinates of a point in a plane. To any value of x there
+corresponds a point N on the axis of x, in accordance with the rule that
+x is the abscissa of N. The corresponding value of y determines a point
+P in accordance with the rule that x is the abscissa and y the ordinate
+of P. The ordinate y gives the value of the function which corresponds
+to that value of the variable x which is specified by N; and it may be
+described as "the value of the function at N." Since there is a
+one-to-one correspondence of the points N and the numbers x, we may also
+describe the ordinate as "the value of the function at x." In simple
+cases the aggregate of the points P which are determined by any
+particular function (of one variable) is a curve, called the "graph of
+the function" (see S 14). In like manner a function of two variables
+defines a surface.
+
+3. _The Variable._--Graphic methods of representation, such as those
+just described, enabled mathematicians to deal with irrational values of
+functions and variables at the time when there was no theory of
+irrational numbers other than Euclid's theory of incommensurables. In
+that theory an irrational number was the ratio of two incommensurable
+geometric magnitudes. In the modern theory of number irrational numbers
+are defined in a purely arithmetical manner, independent of the
+measurement of any quantities or magnitudes, whether geometric or of any
+other kind. The definition is effected by means of the system of
+_ordinal_ numbers (see NUMBER). When this formal system is established,
+the theory of measurement may be founded upon it; and, in particular,
+the co-ordinates of a point are defined as numbers (not lengths), which
+are assigned in accordance with a rule. This rule involves the
+measurement of lengths. The theory of functions can be developed without
+any reference to graphs, or co-ordinates or lengths. The process by
+which analysis has been freed from any consideration of measurable
+quantities has been called the "arithmetization of analysis." In the
+theory so developed, the variable upon which a function depends is
+always to be regarded as a number, and the corresponding value of the
+function is also a number. Any reference to points or co-ordinates is to
+be regarded as a picturesque mode of expression, pointing to a possible
+application of the theory to geometry. The development of "arithmetized
+analysis" in the 19th century is associated with the name of Karl
+Weierstrass.
+
+All possible values of a variable are numbers. In what follows we shall
+confine our attention to the case where the numbers are real. When
+complex numbers are introduced, instead of real ones, the theory of
+functions receives a wide extension, which is accompanied by appropriate
+limitations (see below, II. Functions of Complex Variables). The set of
+all real numbers forms a _continuum_. In fact the notion of a
+one-dimensional continuum first becomes precise in virtue of the
+establishment of the system of real numbers.
+
+4. _Domain of a Variable.--Theory of Aggregates._--The notion of a
+"variable" is that of a number to which we may assign at pleasure any
+one of the values that belong to some chosen set, or _aggregate_, of
+numbers; and this set, or aggregate, is called the "domain of the
+variable." This domain may be an "interval," that is to say it may
+consist of two terminal numbers, all the numbers between them and no
+others. When this is the case the number is said to be "continuously
+variable." When the domain consists of all real numbers, the variable is
+said to be "unrestricted." A domain which consists of all the real
+numbers which exceed some fixed number may be described as an "interval
+unlimited towards the right"; similarly we may have an interval
+"unlimited towards the left."
+
+  In more complicated cases we must have some rule or process for
+  assigning the aggregate of numbers which constitute the domain of a
+  variable. The methods of definition of particular types of aggregates,
+  and the theorems relating to them, form a branch of analysis called
+  the "theory of aggregates" (_Mengenlehre, Theorie des ensembles,
+  Theory of sets of points_). The notion of an "aggregate" in general
+  underlies the system of ordinal numbers. An aggregate is said to be
+  "infinite" when it is possible to effect a one-to-one correspondence
+  of all its elements to some of its elements. For example, we may make
+  all the integers correspond to the even integers, by making 1
+  correspond to 2, 2 to 4, and generally n to 2n. The aggregate of
+  positive integers is an infinite aggregate. The aggregates of all
+  rational numbers and of all real numbers and of points on a line are
+  other examples of infinite aggregates. An aggregate whose elements are
+  real numbers is said to "extend to infinite values" if, after any
+  number N, however great, is specified, it is possible to find in the
+  aggregate numbers which exceed N in absolute value. Such an aggregate
+  is always infinite. The "neighbourhood of a number (or point) a for a
+  positive number h" is the aggregate of all numbers (or points) x for
+  which the absolute value of x - a denoted by |x - a|, does not exceed
+  h.
+
+5. _General Notion of Functionality._--A function of one variable was
+for a long time commonly regarded as the ordinate of a curve; and the
+two notions (1) that which is determined by a curve supposed drawn, and
+(2) that which is determined by an analytical expression supposed
+written down, were not for a long time clearly distinguished. It was for
+this reason that Fourier's discovery that a single analytical expression
+is capable of representing (in different parts of an interval) what
+would in his time have been called different functions so profoundly
+struck mathematicians (S 23). The analysts who, in the middle of the
+19th century, occupied themselves with the theory of the convergence of
+Fourier's series were led to impose a restriction on the character of a
+function in order that it should admit of such representation, and thus
+the door was opened for the introduction of the general notion of
+functional dependence. This notion may be expressed as follows: We have
+a variable number, y, and another variable number, x, a domain of the
+variable x, and a rule for assigning one or more definite values to y
+when x is any point in the domain; then y is said to be a "function" of
+the variable x, and x is called the "argument" of the function.
+According to this notion a function is, as it were, an indefinitely
+extended table, like a table of logarithms; to each point in the domain
+of the argument there correspond values for the function, but it remains
+arbitrary what values the function is to have at any such point.
+
+  For the specification of any particular function two things are
+  requisite: (1) a statement of the values of the variable, or of the
+  aggregate of points, to which values of the function are to be made to
+  correspond, i.e. of the "domain of the argument"; (2) a rule for
+  assigning the value or values of the function that correspond to any
+  point in this domain. We may refer to the second of these two
+  essentials as "the rule of calculation." The relation of functions to
+  analytical expressions may then be stated in the form that the rule of
+  calculation is: "Give the function the value of the expression at any
+  point at which the expression has a determinate value," or again more
+  generally, "Give the function the value of the expression at all
+  points of a definite aggregate included in the domain of the
+  argument." The former of these is the rule of those among the earlier
+  analysts who regarded an analytical expression and a function as the
+  same thing, and their usage may be retained without causing confusion
+  and with the advantage of brevity, the analytical expression serving
+  to specify the domain of the argument as well as the rule of
+  calculation, e.g. we may speak of "the function 1/x." This function is
+  defined by the analytical expression 1/x at all points except the
+  point x = 0. But in complicated cases separate statements of the
+  domain of the argument and the rule of calculation cannot be dispensed
+  with. In general, when the rule of calculation is determined as above
+  by an analytical expression at any aggregate of points, the function
+  is said to be "represented" by the expression at those points.
+
+  When the rule of calculation assigns a single definite value for a
+  function at each point in the domain of the argument the function is
+  "uniform" or "one-valued." In what follows it is to be understood that
+  all the functions considered are one-valued, and the values assigned
+  by the rule of calculation real. In the most important cases the
+  domain of the argument of a function of one variable is an interval,
+  with the possible exception of isolated points.
+
+6. _Limits._--Let [f](x) be a function of a variable number x; and let a
+be a point such that there are points of the domain of the argument x in
+the neighbourhood of a for any number h, however small. If there is a
+number L which has the property that, after any positive number
+[epsilon], however small, has been specified, it is possible to find a
+positive number h, so that |L - [f](x)| < [epsilon] for all points x of
+the domain (other than a) for which |x-a| < h, then L is the "limit of
+[f](x) at the point a." The condition for the existence of L is that,
+after the positive number [epsilon] has been specified, it must be
+possible to find a positive number h, so that |[f](x') - [f](x)| <
+[epsilon] for all points x and x' of the domain (other than a) for which
+|x - a| < h and |x' - a| < h.
+
+It is a fundamental theorem that, when this condition is satisfied,
+there exists a perfectly definite number L which is the limit of [f](x)
+at the point a as defined above. The limit of [f](x) at the point a is
+denoted by Lt_(x = a)[f](x), or by lim_(x = a)[f](x).
+
+  If [f](x) is a function of one variable x in a domain which extends to
+  infinite values, and if, after [epsilon] has been specified, it is
+  possible to find a number N, so that |[f](x') - [f](x)| <[epsilon] for
+  all values of x and x' which are in the domain and exceed N, then
+  there is a number L which has the property that |[f](x) - L| <
+  [epsilon] for all such values of x. In this case [f](x) has a limit L
+  at x = [oo]. In like manner [f](x) may have a limit at x = -[oo]. This
+  statement includes the case where the domain of the argument consists
+  exclusively of positive integers. The values of the function then form
+  a "sequence," u1, u2, ... u_n, ..., and this sequence can have a limit
+  at n = [oo].
+
+  The principle common to the above definitions and theorems is called,
+  after P. du Bois Reymond, "the general principle of convergence to a
+  limit."
+
+  It must be understood that the phrase "x = [oo]" does not mean that x
+  takes some particular value which is infinite. There is no such value.
+  The phrase always refers to a limiting process in which, as the
+  process is carried out, the variable number x increases without limit:
+  it may, as in the above example of a sequence, increase by taking
+  successively the values of all the integral numbers; in other cases it
+  may increase by taking the values that belong to any domain which
+  "extends to infinite values."
+
+  A very important type of limits is furnished by _infinite series_.
+  When a sequence of numbers u1, u2, ... u_n, ... is given, we may form
+  a new sequence s1, s2, ... s_n, ... from it by the rules s1 = u1, s2 =
+  u1 + u2, ... s_n = u1 + u2 + ... + u_n or by the equivalent rules s1 =
+  u, s_n - s_(n - 1) = u_n(n = 2, 3, ...). If the new sequence has a
+  limit at n = [oo], this limit is called the "sum of the infinite
+  series" u1 + u2 + ..., and the series is said to be "convergent" (see
+  SERIES).
+
+  A function which has not a limit at a point a may be such that, if a
+  certain aggregate of points is chosen out of the domain of the
+  argument, and the points x in the neighbourhood of a are restricted to
+  belong to this aggregate, then the function has a limit at a. For
+  example, sin(1/x) has limit zero at 0 if x is restricted to the
+  aggregate 1/[pi], 1/2[pi], ... 1/n[pi], ... or to the aggregate
+  1/2[pi], 2/5[pi], ... n/(n^2 + 1)[pi], ..., but if x takes all values
+  in the neighbourhood of 0, sin (1/x) has not a limit at 0. Again,
+  there may be a limit at a if the points x in the neighbourhood of a
+  are restricted by the condition that x - a is positive; then we have a
+  "limit on the right" at a; similarly we may have a "limit on the left"
+  at a point. Any such limit is described as a "limit for a restricted
+  domain." The limits on the left and on the right are denoted by [f](a
+  - 0) and [f](a + 0).
+
+  The limit L of [f](x) at a stands in no necessary relation to the
+  value of [f](x) at a. If the point a is in the domain of the argument,
+  the value of [f](x) at a is assigned by the rule of calculation, and
+  may be different from L. In case [f](a) = L the limit is said to be
+  "attained." If the point a is not in the domain of the argument, there
+  is no value for [f](x) at a. In the case where [f](x) is defined for
+  all points in an interval containing a, except the point a, and has a
+  limit L at a, we may arbitrarily annex the point a to the domain of
+  the argument and assign to [f](a) the value L; the function may then
+  be said to be "extrinsically defined." The so-called "indeterminate
+  forms" (see INFINITESIMAL CALCULUS) are examples.
+
+7. _Superior and Inferior Limits; Infinities._--The value of a function
+at every point in the domain of its argument is finite, since, by
+definition, the value can be assigned, but this does not necessarily
+imply that there is a number N which exceeds all the values (or is less
+than all the values). It may happen that, however great a number N we
+take, there are among the values of the function numbers which exceed N
+(or are less than -N).
+
+If a number can be found which is greater than every value of the
+function, then either ([alpha]) there is one value of the function
+which exceeds all the others, or ([beta]) there is a number S which
+exceeds every value of the function but is such that, however small a
+positive number [epsilon] we take, there are values of the function
+which exceed S -[epsilon]. In the case ([alpha]) the function has a
+greatest value; in case ([beta]) the function has a "superior limit" S,
+and then there must be a point a which has the property that there are
+points of the domain of the argument, in the neighbourhood of a for any
+h, at which the values of the function differ from S by less than
+[epsilon]. Thus S is the limit of the function at a, either for the
+domain of the argument or for some more restricted domain. If a is in
+the domain of the argument, and if, after omission of a, there is a
+superior limit S which is in this way the limit of the function at a, if
+further [f](a) = S, then S is the greatest value of the function: in
+this case the greatest value is a limit (at any rate for a restricted
+domain) which is attained; it may be called a "superior limit which is
+attained." In like manner we may have a "smallest value" or an "inferior
+limit," and a smallest value may be an "inferior limit which is
+attained."
+
+  All that has been said here may be adapted to the description of
+  greatest values, superior limits, &c., of a function in a restricted
+  domain contained in the domain of the argument. In particular, the
+  domain of the argument may contain an interval; and therein the
+  function may have a superior limit, or an inferior limit, which is
+  attained. Such a limit is a _maximum_ value or a _minimum_ value of
+  the function.
+
+  Again, if, after any number N, however great, has been specified, it
+  is possible to find points of the domain of the argument at which the
+  value of the function exceeds N, the values of the function are said
+  to have an "infinite superior limit," and then there must be a point a
+  which has the property that there are points of the domain, in the
+  neighbourhood of a for any h, at which the value of the function
+  exceeds N. If the point a is in the domain of the argument the
+  function is said to "tend to become infinite" at a; it has of course a
+  finite value at a. If the point a is not in the domain of the argument
+  the function is said to "become infinite" at a; it has of course no
+  value at a. In like manner we may have a (negatively) infinite
+  inferior limit. Again, after any number N, however great, has been
+  specified and a number h found, so that all the values of the
+  function, at points in the neighbourhood of a for h, exceed N in
+  absolute value, all these values may have the same sign; the function
+  is then said to become, or to tend to become, "determinately
+  (positively or negatively) infinite"; otherwise it is said to become
+  or to tend to become, "indeterminately infinite."
+
+  All the infinities that occur in the theory of functions are of the
+  nature of variable finite numbers, with the single exception of the
+  infinity of an infinite aggregate. The latter is described as an
+  "actual infinity," the former as "improper infinities." There is no
+  "actual infinitely small" corresponding to the actual infinity. The
+  only "infinitely small" is zero. All "infinite values" are of the
+  nature of superior and inferior limits which are not attained.
+
+8. _Increasing and Decreasing Functions._--A function [f](x) of one
+variable x, defined in the interval between a and b, is "increasing
+throughout the interval" if, whenever x and x' are two numbers in the
+interval and x' > x, then [f](x') > [f](x); the function "never
+decreases throughout the interval" if, x' and x being as before, [f](x')
+> [f](x). Similarly for decreasing functions, and for functions which
+never increase throughout an interval. A function which either never
+increases or never diminishes throughout an interval is said to be
+"monotonous throughout" the interval. If we take in the above definition
+b > a, the definition may apply to a function under the restriction that
+x' is not b and x is not a; such a function is "monotonous within" the
+interval. In this case we have the theorem that the function (if it
+never decreases) has a limit on the left at b and a limit on the right
+at a, and these are the superior and inferior limits of its values at
+all points within the interval (the ends excluded); the like holds
+_mutatis mutandis_ if the function never increases. If the function is
+monotonous throughout the interval, [f](b) is the greatest (or least)
+value of [f](x) in the interval; and if [f](b) is the limit of [f](x) on
+the left at b, such a greatest (or least) value is an example of a
+superior (or inferior) limit which is attained. In these cases the
+function tends continually to its limit.
+
+  These theorems and definitions can be extended, with obvious
+  modifications, to the cases of a domain which is not an interval, or
+  extends to infinite values. By means of them we arrive at sufficient,
+  but not necessary, criteria for the existence of a limit; and these
+  are frequently easier to apply than the general principle of
+  convergence to a limit (S 6), of which principle they are particular
+  cases. For example, the function represented by x log (1/x)
+  continually diminishes when 1/e > x > 0 and x diminishes towards
+  zero, and it never becomes negative. It therefore has a limit on the
+  right at x = 0. This limit is zero. The function represented by x sin
+  (1/x) does not continually diminish towards zero as x diminishes
+  towards zero, but is sometimes greater than zero and sometimes less
+  than zero in any neighbourhood of x = 0, however small. Nevertheless,
+  the function has the limit zero at x = 0.
+
+9. _Continuity of Functions._--A function [f](x) of one variable x is
+said to be continuous at a point a if (1) [f](x) is defined in an
+interval containing a; (2) [f](x) has a limit at a; (3) [f](a) is equal
+to this limit. The limit in question must be a limit for continuous
+variation, not for a restricted domain. If [f](x) has a limit on the
+left at a and [f](a) is equal to this limit, the function may be said to
+be "continuous to the left" at a; similarly the function may be
+"continuous to the right" at a.
+
+A function is said to be "continuous throughout an interval" when it is
+continuous at every point of the interval. This implies continuity to
+the right at the smaller end-value and continuity to the left at the
+greater end-value. When these conditions at the ends are not satisfied
+the function is said to be continuous "within" the interval. By a
+"continuous function" of one variable we always mean a function which is
+continuous throughout an interval.
+
+  The principal properties of a continuous function are:
+
+  1. The function is practically constant throughout sufficiently small
+  intervals. This means that, after any point a of the interval has been
+  chosen, and any positive number [epsilon], however small, has been
+  specified, it is possible to find a number h, so that the difference
+  between any two values of the function in the interval between a-h and
+  a + h is less than [epsilon]. There is an obvious modification if a is
+  an end-point of the interval.
+
+  2. The continuity of the function is "uniform." This means that the
+  number h which corresponds to any [epsilon] as in (1) may be the same
+  at all points of the interval, or, in other words, that the numbers h
+  which correspond to [epsilon] for different values of a have a
+  positive inferior limit.
+
+  3. The function has a greatest value and a least value in the
+  interval, and these are superior and inferior limits which are
+  attained.
+
+  4. There is at least one point of the interval at which the function
+  takes any value between its greatest and least values in the interval.
+
+  5. If the interval is unlimited towards the right (or towards the
+  left), the function has a limit at [oo] (or at -[oo]).
+
+10. _Discontinuity of Functions._--The discontinuities of a function of
+one variable, defined in an interval with the possible exception of
+isolated points, may be classified as follows:
+
+(1) The function may become infinite, or tend to become infinite, at a
+point.
+
+(2) The function may be undefined at a point.
+
+(3) The function may have a limit on the left and a limit on the right
+at the same point; these may be different from each other, and at least
+one of them must be different from the value of the function at the
+point.
+
+(4) The function may have no limit at a point, or no limit on the left,
+or no limit on the right, at a point.
+
+  In case a function [f](x), defined as above, has no limit at a point
+  a, there are four limiting values which come into consideration.
+  Whatever positive number h we take, the values of the function at
+  points between a and a + h (a excluded) have a superior limit (or a
+  greatest value), and an inferior limit (or a least value); further, as
+  h decreases, the former never increases and the latter never
+  decreases; accordingly each of them tends to a limit. We have in this
+  way two limits on the right--the inferior limit of the superior limits
+  in diminishing neighbourhoods, and the superior limit of the inferior
+  limits in diminishing neighbourhoods. These are denoted by /{[f](a +
+  o)} and {[f](a + 0)}/, and they are called the "limits of
+  indefiniteness" on the right. Similar limits on the left are denoted
+  by /{[f](a - 0)} and {[f](a - 0)}/. Unless [f](x) becomes, or tends to
+  become, infinite at a, all these must exist, any two of them may be
+  equal, and at least one of them must be different from [f](a), if
+  [f](a) exists. If the first two are equal there is a limit on the
+  right denoted by [f](a + 0); if the second two are equal, there is a
+  limit on the left denoted by [f](a - 0). In case the function becomes,
+  or tends to become, infinite at a, one or more of these limits is
+  infinite in the sense explained in S 7; and now it is to be noted
+  that, e.g. the superior limit of the inferior limits in diminishing
+  neighbourhoods on the right of a may be negatively infinite; this
+  happens if, after any number N, however great, has been specified, it
+  is possible to find a positive number h, so that all the values of the
+  function in the interval between a and a + h (a excluded) are less
+  than -N; in such a case [f](x) tends to become negatively infinite
+  when x decreases towards a; other modes of tending to infinite limits
+  may be described in similar terms.
+
+11. _Oscillation of Functions._--The difference between the greatest and
+least of the numbers [f](a), /{[f](a + 0)}, {[f](a + 0)}/, /{[f](a -
+0)}, {[f](a - 0)}/, when they are all finite, is called the
+"oscillation" or "fluctuation" of the function [f](x) at the point a.
+This difference is the limit for h = 0 of the difference between the
+superior and inferior limits of the values of the function at points in
+the interval between a - h and a + h. The corresponding difference for
+points in a finite interval is called the "oscillation of the function
+in the interval." When any of the four limits of indefiniteness is
+infinite the oscillation is infinite in the sense explained in S 7.
+
+  For the further classification of functions we divide the domain of
+  the argument into partial intervals by means of points between the
+  end-points. Suppose that the domain is the interval between a and b.
+  Let intermediate points x1, x2 ... x{n - 1}_, be taken so that b >
+  X_(n - 1) > x_(n - 2) ... > X1 > a_. We may devise a rule by which, as
+  n increases indefinitely, all the differences b - x_(n - 1), x_(n - 1)
+  - x_(n - 2), ... x1 - a tend to zero as a limit. The interval is then
+  said to be divided into "indefinitely small partial intervals."
+
+  A function defined in an interval with the possible exception of
+  isolated points may be such that the interval can be divided into a
+  set of finite partial intervals within each of which the function is
+  monotonous (S 8). When this is the case the sum of the oscillations of
+  the function in those partial intervals is finite, provided the
+  function does not tend to become infinite. Further, in such a case the
+  sum of the oscillations will remain below a fixed number for any mode
+  of dividing the interval into indefinitely small partial intervals. A
+  class of functions may be defined by the condition that the sum of the
+  oscillations has this property, and such functions are said to have
+  "restricted oscillation." Sometimes the phrase "limited fluctuation"
+  is used. It can be proved that any function with restricted
+  oscillation is capable of being expressed as the sum of two monotonous
+  functions, of which one never increases and the other never diminishes
+  throughout the interval. Such a function has a limit on the right and
+  a limit on the left at every point of the interval. This class of
+  functions includes all those which have a finite number of maxima and
+  minima in a finite-interval, and some which have an infinite number.
+  It is to be noted that the class does not include all continuous
+  functions.
+
+12. _Differentiable Function._--The idea of the differentiation of a
+continuous function is that of a process for measuring the rate of
+growth; the increment of the function is compared with the increment of
+the variable. If _[f](x)_ is defined in an interval containing the point
+a, and _a - k_ and _a + k_ are points of the interval, the expression
+
+  [f](a + h) - [f](a)
+  -------------------         (1)
+           h
+
+represents a function of h, which we may call [phi](h), defined at all
+points of an interval for h between -k and k except the point 0. Thus
+the four limits /[phi](+0), [phi](+0)/, /[phi](-0), [phi](-0)/ exist,
+and two or more of them may be equal. When the first two are equal
+either of them is the "progressive differential coefficient" of [f](x)
+at the point a; when the last two are equal either of them is the
+"regressive differential coefficient" of [f](x) at a; when all four are
+equal the function is said to be "differentiable" at a, and either of
+them is the "differential coefficient" of [f](x) at a, or the "first
+derived function" of [f](x) at a. It is denoted by d[f](x) / dx or by
+[f]'(x). In this case [phi](h) has a definite limit at h = 0, or is
+determinately infinite at h = 0 (S 7). The four limits here in question
+are called, after Dini, the "four derivates" of [f](x) at a. In
+accordance with the notation for derived functions they may be denoted
+by
+
+  ----------              ----------
+  [f]' + (a), [f]' + (a), [f]' - (a), f' - (a).
+              ---------               --------
+
+  A function which has a finite differential coefficient at all points
+  of an interval is continuous throughout the interval, but if the
+  differential coefficient becomes infinite at a point of the interval
+  the function may or may not be continuous throughout the interval; on
+  the other hand a function may be continuous without being
+  differentiable. This result, comparable in importance, from the point
+  of view of the general theory of functions, with the discovery of
+  Fourier's theorem, is due to G.F.B. Riemann; but the failure of an
+  attempt made by Ampere to prove that every continuous function must be
+  differentiable may be regarded as the first step in the theory.
+  Examples of analytical expressions which represent continuous
+  functions that are not differentiable have been given by Riemann,
+  Weierstrass, Darboux and Dini (see S 24). The most important theorem
+  in regard to differentiable functions is the "theorem of intermediate
+  value." (See INFINITESIMAL CALCULUS.)
+
+13. _Analytic Function._--If [f](x) and its first n differential
+coefficients, denoted by[f]'(x), [f]''(x), ... [f](^n)(x), are
+continuous in the interval between a and a + h, then
+
+                                   h^2
+  [f](a + h) = [f](a) + h[f]'(a) + --- f''(a) + ...
+                                    2!
+
+      h^(n - 1)
+    + --------- [f]^(n - 1)(a) + R_n,
+       (n - 1)!
+
+where R_n may have various forms, some of which are given in the article
+INFINITESIMAL CALCULUS. This result is known as "Taylor's theorem."
+
+When Taylor's theorem leads to a representation of the function by means
+of an infinite series, the function is said to be "analytic" (cf. S 21).
+
+14. _Ordinary Function._--The idea of a curve representing a continuous
+function in an interval is that of a line which has the following
+properties: (1) the co-ordinates of a point of the curve are a value x
+of the argument and the corresponding value y of the function; (2) at
+every point the curve has a definite tangent; (3) the interval can be
+divided into a finite number of partial intervals within each of which
+the function is monotonous; (4) the property of monotony within partial
+intervals is retained after interchange of the axes of co-ordinates x
+and y. According to condition (2) y is a continuous and differentiable
+function of x, but this condition does not include conditions (3) and
+(4): there are continuous partially monotonous functions which are not
+differentiable, there are continuous differentiable functions which are
+not monotonous in any interval however small; and there are continuous,
+differentiable and monotonous functions which do not satisfy condition
+(4) (cf. S 24). A function which can be represented by a curve, in the
+sense explained above, is said to be "ordinary," and the curve is the
+graph of the function (S2). All analytic functions are ordinary, but not
+all ordinary functions are analytic.
+
+15. _Integrable Function._--The idea of integration is twofold. We may
+seek the function which has a given function as its differential
+coefficient, or we may generalize the question of finding the area of a
+curve. The first inquiry leads directly to the indefinite integral, the
+second directly to the definite integral. Following the second method we
+define "the definite integral of the function [f](x) through the
+interval between a and b" to be the limit of the sum
+
+   _n
+  \   [f](x'_r)(x_r - x_(r - 1))
+  /_
+    1
+
+when the interval is divided into ultimately indefinitely small partial
+intervals by points x1, x2, ... x_(n - 1). Here x'_r denotes any point
+in the rth partial interval, x0 is put for a, and x_n for b. It can be
+shown that the limit in question is finite and independent of the mode
+of division into partial intervals, and of the choice of the points such
+as x'_r, provided (1) the function is defined for all points of the
+interval, and does not tend to become infinite at any of them; (2) for
+any one mode of division of the interval into ultimately indefinitely
+small partial intervals, the sum of the products of the oscillation of
+the function in each partial interval and the difference of the
+end-values of that partial interval has limit zero when n is increased
+indefinitely. When these conditions are satisfied the function is said
+to be "integrable" in the interval. The numbers a and b which limit the
+interval are usually called the "lower and upper limits." We shall call
+them the "nearer and further end-values." The above definition of
+integration was introduced by Riemann in his memoir on trigonometric
+series (1854). A still more general definition has been given by
+Lebesgue. As the more general definition cannot be made intelligible
+without the introduction of some rather recondite notions belonging to
+the theory of aggregates, we shall, in what follows, adhere to Riemann's
+definition.
+
+  We have the following theorems:--
+
+  1. Any continuous function is integrable.
+
+  2. Any function with restricted oscillation is integrable.
+
+  3. A discontinuous function is integrable if it does not tend to
+  become infinite, and if the points at which the oscillation of the
+  function exceeds a given number [sigma], however small, can be
+  enclosed in partial intervals the sum of whose breadths can be
+  diminished indefinitely.
+
+  These partial intervals must be a set chosen out of some complete set
+  obtained by the process used in the definition of integration.
+
+  4. The sum or product of two integrable functions is integrable.
+
+  As regards integrable functions we have the following theorems:
+
+  1. If S and I are the superior and inferior limits (or greatest and
+  least values) of [f](x) in the interval between a and b, [int] [a to
+  b] [f](x)dx is intermediate between S(b - a) and I(b - a).
+
+  2. The integral is a continuous function of each of the end-values.
+
+  3. If the further end-value b is variable, and if [int] [a to x]
+  [f](x)_dx_ = F(x), then if [f](x) is continuous at b, F(x) is
+  differentiable at b, and F'(b) = [f](b).
+
+  4. In case [f](x) is continuous throughout the interval F(x) is
+  continuous and differentiable throughout the interval, and F'(x) =
+  [f](x) throughout the interval.
+
+  5. In case [f]'(x) is continuous throughout the interval between a and
+  b,
+      _
+     / b
+     |   [f]'(x)dx = [f](b) - [f](a).
+    _/a
+
+  6. In case [f](x) is discontinuous at one or more points of the
+  interval between a and b, in which it is integrable,
+      _
+     / x
+     |   [f](x)dx
+    _/a
+
+  is a function of x, of which the four derivates at any point of the
+  interval are equal to the limits of indefiniteness of [f](x) at the
+  point.
+
+  7. It may be that there exist functions which are differentiable
+  throughout an interval in which their differential coefficients are
+  not integrable; if, however, F(x) is a function whose differential
+  coefficient, F'(x), is integrable in an interval, then
+             _
+            / x
+    F(x) =  |   F'(x)dx + const.,
+           _/a
+
+  where a is a fixed point, and x a variable point, of the interval.
+  Similarly, if any one of the four derivates of a function is
+  integrable in an interval, all are integrable, and the integral of
+  either differs from the original function by a constant only.
+
+  The theorems (4), (6), (7) show that there is some discrepancy between
+  the indefinite integral considered as the function which has a given
+  function as its differential coefficient, and as a definite integral
+  with a variable end-value.
+
+  We have also two theorems concerning the integral of the product of
+  two integrable functions [f](x) and [phi](x); these are known as "the
+  first and second theorems of the mean." The first theorem of the mean
+  is that, if [phi](x) is one-signed throughout the interval between a
+  and b, there is a number M intermediate between the superior and
+  inferior limits, or greatest and least values, of [f](x) in the
+  interval, which has the property expressed by the equation
+       _                _
+      / b              / b
+    M |   [phi](x)dx = |   [f](x)[phi](x)dx.
+     _/a              _/a
+
+  The second theorem of the mean is that, if [f](x) is monotonous
+  throughout the interval, there is a number [xi] between a and b which
+  has the property expressed by the equation
+      _                             _                       _
+     / b                           /[xi]                   / b
+     |   [f](x)[phi](x)dx = [f](a) |   [phi](x)dx + [f](b) |    [phi](x)dx.
+    _/a                           _/a                     _/[xi]
+
+  (_See_ FOURIER'S SERIES.)
+
+16. _Improper Definite Integrals._--We may extend the idea of
+integration to cases of functions which are not defined at some point,
+or which tend to become infinite in the neighbourhood of some point, and
+to cases where the domain of the argument extends to infinite values. If
+c is a point in the interval between a and b at which [f](x) is not
+defined, we impose a restriction on the points x'_r of the definition:
+none of them is to be the point c. This comes to the same thing as
+defining [int] [a to b] [f](x)dx to be
+                 _                        _
+                / c-[epsilon]            / b
+             Lt |        [f](x)dx +   Lt |     [f](x)dx,      (1)
+               _/a                      _/c+[epsilon]'
+    [epsilon]=0             [epsilon]'=0
+
+where, to fix ideas, b is taken > a, and [epsilon] and [epsilon]' are
+positive. The same definition applies to the case where [f](x) becomes
+infinite, or tends to become infinite, at c, provided both the limits
+exist. This definition may be otherwise expressed by saying that a
+partial interval containing the point c is omitted from the interval of
+integration, and a limit taken by diminishing the breadth of this
+partial interval indefinitely; in this form it applies to the cases
+where c is a or b.
+
+Again, when the interval of integration is unlimited to the right, or
+extends to positively infinite values, we have as a definition
+    _                  _
+   / [oo]             / h
+   |   [f](x)dx =  Lt |  [f](x)dx,
+  _/a                _/a
+               h=[oo]
+
+provided this limit exists. Similar definitions apply to
+    _                   _
+   /-[oo]              / [oo]
+   |   [f](x)dx and to |      [f](x)dx.
+  _/a                 _/-[oo]
+
+All such definite integrals as the above are said to be "improper." For
+example, [int] {0 to [oo]} (sin x / x)dx is improper in two ways. It
+means
+                        _
+                       / h        sin x
+   Lt             Lt   |          ----- dx,
+  h=[oo]  [epsilon]=0 _/[epsilon]   x
+
+in which the positive number [epsilon] is first diminished indefinitely,
+and the positive number h is afterwards increased indefinitely.
+
+The "theorems of the mean" (S 15) require modification when the
+integrals are improper (see FOURIER'S SERIES).
+
+When the improper definite integral of a function which becomes, or
+tends to become, infinite, exists, the integral is said to be
+"convergent." If [f](x) tends to become infinite at a point c in the
+interval between a and b, and the expression (1) does not exist, then
+the expression [int] [a to b][f](x)_dx_, which has no value, is called a
+"divergent integral, "and it may happen that there is a definite value
+for
+      _    _                       _                    _
+     |    / c-[epsilon]           / b                    |
+  Lt |    |           [f](x) dx + |            [f](x) dx |
+     |_  _/a                     _/c+[epsilon]'         _|
+
+provided that [epsilon] and [epsilon]' are connected by some definite
+relation, and both, remaining positive, tend to limit zero. The value of
+the above limit is then called a "principal value" of the divergent
+integral. Cauchy's principal value is obtained by making [epsilon]' =
+[epsilon], i.e. by taking the omitted interval so that the infinity is
+at its middle point. A divergent integral which has one or more
+principal values is sometimes described as "semi-convergent."
+
+17. _Domain of a Set of Variables._--The numerical continuum of n
+dimensions (C_n) is the aggregate that is arrived at by attributing
+simultaneous values to each of n variables x1, x2, ... x_n, these values
+being any real numbers. The elements of such an aggregate are called
+"points," and the numbers x1, x2 ... x_n the "co-ordinates" of a point.
+Denoting in general the points (x1, x2, ... x_n) and (x'1, x'2 ... x'_n)
+by x and x', the sum of the differences |x1 - x'1| + |x2 - x'2| + ... +
+|x_n - x'_n| may be denoted by |x - x'| and called the "difference of
+the two points." We can in various ways choose out of the continuum an
+aggregate of points, which may be an infinite aggregate, and any such
+aggregate can be the "domain" of a "variable point." The domain is said
+to "extend to an infinite distance" if, after any number N, however
+great, has been specified, it is possible to find in the domain points
+of which one or more co-ordinates exceed N in absolute value. The
+"neighbourhood" of a point a for a (positive) number h is the aggregate
+constituted of all the points x, which are such that the "difference"
+denoted by |x - a| < h. If an infinite aggregate of points does not
+extend to an infinite distance, there must be at least one point a,
+which has the property that the points of the aggregate which are in the
+neighbourhood of a for any number h, however small, themselves
+constitute an infinite aggregate, and then the point a is called a
+"limiting point" of the aggregate; it may or may not be a point of the
+aggregate. An aggregate of points is "perfect" when all its points are
+limiting points of it, and all its limiting points are points of it; it
+is "connected" when, after taking any two points a, b of it, and
+choosing any positive number [epsilon], however small, a number m and
+points x', x", ... x^(m) of the aggregate can be found so that all the
+differences denoted by |x' - a|, |x" - x'|, ... |b - x^(m)| are less
+than [epsilon]. A perfect connected aggregate is a _continuum_. This is
+G. Cantor's definition.
+
+  The definition of a continuum in C_n leaves open the question of the
+  number of dimensions of the continuum, and a further explanation is
+  necessary in order to define arithmetically what is meant by a
+  "homogeneous part" H_n of C_n. Such a part would correspond to an
+  interval in C1, or to an area bounded by a simple closed contour in
+  C2; and, besides being perfect and connected, it would have the
+  following properties: (1) There are points of C_n, which are not
+  points of H_n; these form a complementary aggregate H'_n. (2) There
+  are points "within" H_n; this means that for any such point there is a
+  neighbourhood consisting exclusively of points of H_n. (3) The points
+  of H_n which do not lie "within" H_n are limiting points of H'_n; they
+  are not points of H'_n, but the neighbourhood of any such point for
+  any number h, however small, contains points within H_n and points of
+  H'_n: the aggregate of these points is called the "boundary" of H_n.
+  (4) When any two points a, b within H_n are taken, it is possible to
+  find a number [epsilon] and a corresponding number m, and to choose
+  points x', x", ... x^m, so that the neighbourhood of a for [epsilon]
+  contains x', and consists exclusively of points within H_n, and
+  similarly for x' and x", x" and x"', ... x^m and b. Condition (3)
+  would exclude such an aggregate as that of the points within and upon
+  two circles external to each other and a line joining a point on one
+  to a point on the other, and condition (4) would exclude such an
+  aggregate as that of the points within and upon two circles which
+  touch externally.
+
+18. Functions of Several Variables.--A function of several variables
+differs from a function of one variable in that the argument of the
+function consists of a set of variables, or is a variable point in a C_n
+when there are n variables. The function is definable by means of the
+domain of the argument and the rule of calculation. In the most
+important cases the domain of the argument is a homogeneous part H_n of
+C_n with the possible exception of isolated points, and the rule of
+calculation is that the value of the function in any assigned part of
+the domain of the argument is that value which is assumed at the point
+by an assigned analytical expression. The limit of a function at a point
+a is defined in the same way as in the case of a function of one
+variable.
+
+  We take a positive fraction [epsilon] and consider the neighbourhood
+  of a for h, and from this neighbourhood we exclude the point a, and we
+  also exclude any point which is not in the domain of the argument.
+  Then we take x and x' to be any two of the retained points in the
+  neighbourhood. The function [f] has a limit at a if for any positive
+  [epsilon], however small, there is a corresponding h which has the
+  property that |[f](x') - [f](x)| < [epsilon], whatever points x, x' in
+  the neighbourhood of a for h we take (a excluded). For example, when
+  there are two variables x1, x2, and both are unrestricted, the domain
+  of the argument is represented by a plane, and the values of the
+  function are correlated with the points of the plane. The function has
+  a limit at a point a, if we can mark out on the plane a region
+  containing the point a within it, and such that the difference of the
+  values of the function which correspond to any two points of the
+  region (neither of the points being a) can be made as small as we
+  please in absolute value by contracting all the linear dimensions of
+  the region sufficiently. When the domain of the argument of a function
+  of n variables extends to an infinite distance, there is a "limit at
+  an infinite distance" if, after any number [epsilon], however small,
+  has been specified, a number N can be found which is such that
+  |[f](x') - [f](x)| < [epsilon], for all points x and x' (of the
+  domain) of which one or more co-ordinates exceed N in absolute value.
+  In the case of functions of several variables great importance
+  attaches to limits for a restricted domain. The definition of such a
+  limit is verbally the same as the corresponding definition in the case
+  of functions of one variable (S 6). For example, a function of x1 and
+  x2 may have a limit at (x1 = 0, x2 = 0) if we first diminish x1
+  without limit, keeping x2 constant, and afterwards diminish x2 without
+  limit. Expressed in geometrical language, this process amounts to
+  approaching the origin along the axis of x2. The definitions of
+  superior and inferior limits, and of maxima and minima, and the
+  explanations of what is meant by saying that a function of several
+  variables becomes infinite, or tends to become infinite, at a point,
+  are almost identical verbally with the corresponding definitions and
+  explanations in the case of a function of one variable (S 7). The
+  definition of a continuous function (S 9) admits of immediate
+  extension; but it is very important to observe that a function of two
+  or more variables may be a continuous function of each of the
+  variables, when the rest are kept constant, without being a continuous
+  function of its argument. For example, a function of x and y may be
+  defined by the conditions that when x = 0 it is zero whatever value y
+  may have, and when x [/=] 0 it has the value of sin {4tan^(-1)(y/x)}.
+  When y has any particular value this function is a continuous function
+  of x, and, when x has any particular value this function is a
+  continuous function of y; but the function of x and y is discontinuous
+  at (x = 0, y = 0).
+
+19. _Differentiation and Integration._--The definition of partial
+differentiation of a function of several variables presents no
+difficulty. The most important theorems concerning differentiable
+functions are the "theorem of the total differential," the theorem of
+the interchangeability of the order of partial differentiations, and the
+extension of Taylor's theorem (see INFINITESIMAL CALCULUS).
+
+With a view to the establishment of the notion of integration through a
+domain, we must define the "extent" of the domain. Take first a domain
+consisting of the point a and all the points x for which |x - a| < 1/2h,
+where h is a chosen positive number; the extent of this domain is h^n, n
+being the number of variables; such a domain may be described as
+"square," and the number h may be called its "breadth"; it is a
+homogeneous part of the numerical continuum of n dimensions, and its
+boundary consists of all the points for which |x - a| = 1/2h. Now the
+points of any domain, which does not extend to an infinite distance, may
+be assigned to a finite number m of square domains of finite breadths,
+so that every point of the domain is either within one of these square
+domains or on its boundary, and so that no point is within two of the
+square domains; also we may devise a rule by which, as the number m
+increases indefinitely, the breadths of all the square domains are
+diminished indefinitely. When this process is applied to a homogeneous
+part, H, of the numerical continuum C_n, then, at any stage of the
+process, there will be some square domains of which all the points
+belong to H, and there will generally be others of which some, but not
+all, of the points belong to H. As the number m is increased
+indefinitely the sums of the extents of both these categories of square
+domains will tend to definite limits, which cannot be negative; when the
+second of these limits is zero the domain H is said to be "measurable,"
+and the first of these limits is its "extent"; it is independent of the
+rule adopted for constructing the square domains and contracting their
+breadths. The notion thus introduced may be adapted by suitable
+modifications to continua of lower dimensions in C_n.
+
+  The integral of a function f(x) through a measurable domain H, which
+  is a homogeneous part of the numerical continuum of n dimensions, is
+  defined in just the same way as the integral through an interval, the
+  extent of a square domain taking the place of the difference of the
+  end-values of a partial interval; and the condition of integrability
+  takes the same form as in the simple case. In particular, the
+  condition is satisfied when the function is continuous throughout the
+  domain. The definition of an integral through a domain may be adapted
+  to any domain of measurable extent. The extensions to "improper"
+  definite integrals may be made in the same way as for a function of
+  one variable; in the particular case of a function which tends to
+  become infinite at a point in the domain of integration, the point is
+  enclosed in a partial domain which is omitted from the integration,
+  and a limit is taken when the extent of the omitted partial domain is
+  diminished indefinitely; a divergent integral may have different
+  (principal) values for different modes of contracting the extent of
+  the omitted partial domain. In applications to mathematical physics
+  great importance attaches to convergent integrals and to principal
+  values of divergent integrals. For example, any component of magnetic
+  force at a point within a magnet, and the corresponding component of
+  magnetic induction at the same point are expressed by different
+  principal values of the same divergent integral. Delicate questions
+  arise as to the possibility of representing the integral of a function
+  of n variables through a domain H_n, as a repeated integral, of
+  evaluating it by successive integrations with respect to the variables
+  one at a time and of interchanging the order of such integrations.
+  These questions have been discussed very completely by C. Jordan, and
+  we may quote the result that all the transformations in question are
+  valid when the function is continuous throughout the domain.
+
+20. _Representation of Functions in General._--We have seen that the
+notion of a function is wider than the notion of an analytical
+expression, and that the same function may be "represented" by one
+expression in one part of the domain of the argument and by some other
+expression in another part of the domain (S 5). Thus there arises the
+general problem of the representation of functions. The function may be
+given by specifying the domain of the argument and the rule of
+calculation, or else the function may have to be determined in
+accordance with certain conditions; for example, it may have to satisfy
+in a prescribed domain an assigned differential equation. In either case
+the problem is to determine, when possible, a single analytical
+expression which shall have the same value as the function at all points
+in the domain of the argument. For the representation of most functions
+for which the problem can be solved recourse must be had to limiting
+processes. Thus we may utilize infinite series, or infinite products, or
+definite integrals; or again we may represent a function of one variable
+as the limit of an expression containing two variables in a domain in
+which one variable remains constant and another varies. An example of
+this process is afforded by the expression Lt_y = [oo]xy/(x^2y + 1),
+which represents a function of x vanishing at x = 0 and at all other
+values of x having the value of 1/x. The method of series falls under
+this more general process (cf. S 6). When the terms u1, u2, ... of a
+series are functions of a variable x, the sum s_n of the first n terms
+of the series is a function of x and n; and, when the series is
+convergent, its sum, which is Lt_n = [oo]s_n, can represent a function
+of x. In most cases the series converges for some values of x and not
+for others, and the values for which it converges form the "domain of
+convergence." The sum of the series represents a function in this
+domain.
+
+  The apparently more general method of representation of a function of
+  one variable as the limit of a function of two variables has been
+  shown by R. Baire to be identical in scope with the method of series,
+  and it has been developed by him so as to give a very complete account
+  of the possibility of representing functions by analytical
+  expressions. For example, he has shown that Riemann's totally
+  discontinuous function, which is equal to 1 when x is rational and to
+  0 when x is irrational, can be represented by an analytical
+  expression. An infinite process of a different kind has been adapted
+  to the problem of the representation of a continuous function by T.
+  Broden. He begins with a function having a graph in the form of a
+  regular polygon, and interpolates additional angular points in an
+  ordered sequence without limit. The representation of a function by
+  means of an infinite product falls clearly under Baire's method, while
+  the representation by means of a definite integral is analogous to
+  Broden's method. As an example of these two latter processes we may
+  cite the Gamma function [[Gamma](x)] defined for positive values of x
+  by the definite integral
+      _
+     / [oo]
+     |     e^(-t)t^(x - 1)dt,
+    _/0
+
+  or by the infinite product
+
+                                                /      x   \
+    L t_(n = [oo]) n^x/x (1 + x)(1 + 1/2x) ... ( 1 + -----  ).
+                                                \    n - 1 /
+
+  The second of these expressions avails for the representation of the
+  function at all points at which x is not a negative integer.
+
+21. _Power Series._--Taylor's theorem leads in certain cases to a
+representation of a function by an infinite series. We have under
+certain conditions (S 13)
+
+                     _n-1
+                    \    (x - a)^r
+  [f](x) = [f](a) + /_   --------- [f]^(r) (a) + R_n;
+                      r=1    r!
+
+and this becomes
+
+                     _[oo]
+                    \     (x - a)^r
+  [f](x) = [f](a) + /_    --------- [f]^(r) (a),
+                      r=1     r!
+
+provided that ([alpha]) a positive number k can be found so that at all
+points in the interval between a and a + k (except these points) [f](x)
+has continuous differential coefficients of all finite orders, and at a
+has progressive differential coefficients of all finite orders; ([beta])
+Cauchy's form of the remainder R_n, viz. [(x - a)^n / (n - 1)!] (1 -
+[theta])^(n - 1)[f]^n {a + [theta](x - a)}, has the limit zero when n
+increases indefinitely, for all values of [theta] between 0 and 1, and
+for all values of x in the interval between a and a + k, except possibly
+a + k. When these conditions are satisfied, the series (1) represents
+the function at all points of the interval between a and a + k, except
+possibly a + k, and the function is "analytic" (S 13) in this domain.
+Obvious modifications admit of extension to an interval between a and a
+- k, or between a - k and a + k. When a series of the form (1)
+represents a function it is called "the Taylor's series for the
+function."
+
+Taylor's series is a power series, i.e. a series of the form
+
+   _[oo]
+  \     a_n (x - a)^n.
+  /_
+    n=0
+
+  As regards power series we have the following theorems:
+
+  1. If the power series converges at any point except a there is a
+  number k which has the property that the series converges absolutely
+  in the interval between a - k and a + k, with the possible exception
+  of one or both end-points.
+
+  2. The power series represents a continuous function in its domain of
+  convergence (the end-points may have to be excluded).
+
+  3. This function is analytic in the domain, and the power series
+  representing it is the Taylor's series for the function.
+
+  The theory of power series has been developed chiefly from the point
+  of view of the theory of functions of complex variables.
+
+22. _Uniform Convergence._--We shall suppose that the domain of
+convergence of an infinite series of functions is an interval with the
+possible exception of isolated points. Let [f](x) be the sum of the
+series at any point x of the domain, and [f]_n(x) the sum of the first n
++ 1 terms. The condition of convergence at a point a is that, after any
+positive number [epsilon], however small, has been specified, it must be
+possible to find a number n so that |[f]_m(a) - [f]_p(a)| < [epsilon]
+for all values of m and p which exceed n. The sum, [f](a), is the limit
+of the sequence of numbers [f]_n(a) at n = [oo]. The convergence is
+said to be "uniform" in an interval if, after specification of
+[epsilon], the same number n suffices at all points of the interval to
+make |[f](x) - [f]_m(x)| < [epsilon] for all values of m which exceed n.
+The numbers n corresponding to any [epsilon], however small, are all
+finite, but, when [epsilon] is less than some fixed finite number, they
+may have an infinite superior limit (S 7); when this is the case there
+must be at least one point, a, of the interval which has the property
+that, whatever number N we take, [epsilon] can be taken so small that,
+at some point in the neighbourhood of a, n must be taken > N to make
+|[f](x) - f_m(x)| < [epsilon] when m > n; then the series does not
+converge uniformly in the neighbourhood of a. The distinction may be
+otherwise expressed thus: Choose a first and [epsilon] afterwards, then
+the number n is finite; choose [epsilon] first and allow a to vary, then
+the number n becomes a function of a, which may tend to become infinite,
+or may remain below a fixed number; if such a fixed number exists, ho
+wever small [epsilon] may be, the convergence is uniform.
+
+  For example, the series sin x - 1/2 sin 2x + {1/3} sin 3x - ... is
+  convergent for all real values of x, and, when [pi] > x > -[pi] its
+  sum is 1/2x; but, when x is but a little less than [pi], the number of
+  terms which must be taken in order to bring the sum at all near to the
+  value of 1/2x is very large, and this number tends to increase
+  indefinitely as x approaches [pi]. This series does not converge
+  uniformly in the neighbourhood of x = [pi]. Another example is
+  afforded by the series
+
+     _[oo]    nx           (n + 1)x
+    \     ---------- - ---------------- ,
+    /_    n^2x^2 + 1   (n + 1)^2x^2 + 1
+      n=0
+
+  of which the remainder after n terms is nx/(n^2x^2 + 1). If we put x =
+  1/n, for any value of n, however great, the remainder is 1/2; and the
+  number of terms required to be taken to make the remainder tend to
+  zero depends upon the value of x when x is near to zero--it must, in
+  fact, be large compared with 1/x. The series does not converge
+  uniformly in the neighbourhood of x = 0.
+
+As regards series whose terms represent continuous functions we have the
+following theorems:
+
+(1) If the series converges uniformly in an interval it represents a
+function which is continuous throughout the interval.
+
+(2) If the series represents a function which is discontinuous in an
+interval it cannot converge uniformly in the interval.
+
+(3) A series which does not converge uniformly in an interval may
+nevertheless represent a function which is continuous throughout the
+interval.
+
+(4) A power series converges uniformly in any interval contained within
+its domain of convergence, the end-points being excluded.
+
+(5) If [Sigma] (r=0 to [oo]) [f]_r(x) = [f](x) converges uniformly in
+the interval between a and b
+
+    _              _[oo]  _
+   / b            \      / b
+   |  [f](x)dx =  /_     |   [f]_r(x)dx,
+  _/ a              r=0 _/a
+
+or a series which converges uniformly may be integrated term by term.
+
+(6) If [Signa] (r=0 to [oo]) [f]'_r(x) converges uniformly in an
+interval, then [Signa] (r=o to [oo]) [f]_r(x) converges in the interval,
+and represents a continuous differentiable function, [phi](x); in fact
+we have
+
+               _[oo]
+  [phi]'(x) = \    [f]'_r(x),
+              /_
+                r=0
+
+or a series can be differentiated term by term if the series of derived
+functions converges uniformly.
+
+A series whose terms represent functions which are not continuous
+throughout an interval may converge uniformly in the interval. If
+[Signa] (r=0 to [oo]) [f]_r(x) = [f](x), is such a series, and if all
+the functions [f]_r(x) have limits at a, then [f](x) has a limit at a,
+which is [Signa] (r=0 a=0 to [oo]) Lt [f]_r(x). A similar theorem holds
+for limits on the left or on the right.
+
+23. _Fourier's Series._--An extensive class of functions admit of being
+represented by series of the form
+
+        _[oo]  /        n[pi]x           n[pi]x \
+  a0 + \      ( a_n cos ------ + b_n sin ------  ),  (i.)
+       /_      \          c                c    /
+         n=1
+
+and the rule for determining the coefficients a_n, b_n of such a series,
+in order that it may represent a given function [f](x) in the interval
+between -c and c, was given by Fourier, viz. we have
+            _                      _
+        1  / c                 1  / c           n[pi]x
+  a0 = --- |  [f](x)dx,  a_n = -- |   [f](x)cos ------ dx,
+       2c _/-c                 c _/-c             c
+           _
+          / c  1            n[pi]x
+    b_n = |    -- [f](x)sin ------ dx.
+         _/-c  c              c
+
+The interval between -c and c may be called the "periodic interval," and
+we may replace it by any other interval, e.g. that between 0 and 1,
+without any restriction of generality. When this is done the sum of the
+series takes the form
+
+           _     _r=n
+          / 1   \    [f](z)cos {2r[pi](z - x)} dz,
+   Lt     |     /_
+  n=[oo] _/0     r=-n
+
+
+and this is
+           _
+          / 1       sin {(2n + 1)(z - x)[pi]}
+    Lt    |  [f](z) ------------------------ dz.     (ii.)
+  n=[oo] _/0            sin {(z - x)[pi]}
+
+Fourier's theorem is that, if the periodic interval can be divided into
+a finite number of partial intervals within each of which the function
+is ordinary (S 14), the series represents the function within each of
+those partial intervals. In Fourier's time a function of this character
+was regarded as completely arbitrary.
+
+  By a discussion of the integral (ii.) based on the Second Theorem of
+  the Mean (S 15) it can be shown that, if [f](x) has restricted
+  oscillation in the interval (S 11), the sum of the series is equal to
+  1/2{[f](x + 0) + [f](x - 0)} at any point x within the interval, and
+  that it is equal to 1/2{[f]( + 0) + [f](1 - 0} at each end of the
+  interval. (See the article FOURIER'S SERIES.) It therefore represents
+  the function at any point of the periodic interval at which the
+  function is continuous (except possibly the end-points), and has a
+  definite value at each point of discontinuity. The condition of
+  restricted oscillation includes all the functions contemplated in the
+  statement of the theorem and some others. Further, it can be shown
+  that, in any partial interval throughout which [f](x) is continuous,
+  the series converges uniformly, and that no series of the form (i),
+  with coefficients other than those determined by Fourier's rule, can
+  represent the function at all points, except points of discontinuity,
+  in the same periodic interval. The result can be extended to a
+  function [f](x) which tends to become infinite at a finite number of
+  points a of the interval, provided (1) [f](x) tends to become
+  determinately infinite at each of the points a, (2) the improper
+  definite integral of [f](x) through the interval is convergent, (3)
+  [f](x) has not an infinite number of discontinuities or of maxima or
+  minima in the interval.
+
+24. _Representation of Continuous Functions by Series._--If the series
+for [f](x) formed by Fourier's rule converges at the point a of the
+periodic interval, and if [f](x) is continuous at a, the sum of the
+series is [f](a); but it has been proved by P. du Bois Reymond that the
+function may be continuous at a, and yet the series formed by Fourier's
+rule may be divergent at a. Thus some continuous functions do not admit
+of representation by Fourier's series. All continuous functions,
+however, admit of being represented with arbitrarily close approximation
+in either of two forms, which may be described as "terminated Fourier's
+series" and "terminated power series," according to the two following
+theorems:
+
+(1) If [f](x) is continuous throughout the interval between 0 and 2[pi],
+and if any positive number [epsilon] however small is specified, it is
+possible to find an integer n, so that the difference between the value
+of [f](x) and the sum of the first n terms of the series for [f](x),
+formed by Fourier's rule with periodic interval from 0 to 2[pi], shall
+be less than [epsilon] at all points of the interval. This result can be
+extended to a function which is continuous in any given interval.
+
+(2) If [f](x) is continuous throughout an interval, and any positive
+number [epsilon] however small is specified, it is possible to find an
+integer n and a polynomial in x of the nth degree, so that the
+difference between the value of [f](x) and the value of the polynomial
+shall be less than [epsilon] at all points of the interval.
+
+Again it can be proved that, if [f](x) is continuous throughout a given
+interval, polynomials in x of finite degrees can be found, so as to form
+an infinite series of polynomials whose sum is equal to [f](x) at all
+points of the interval. Methods of representation of continuous
+functions by infinite series of rational fractional functions have also
+been devised.
+
+  Particular interest attaches to continuous functions which are not
+  differentiable. Weierstrass gave as an example the function
+  represented by the series [Sigma] (n=0 to [oo]) a^n cos(b^[n] x[pi]),
+  where a is positive and less than unity, and b is an odd integer
+  exceeding (1 + (3/2)[pi]) / a. It can be shown that this series is
+  uniformly convergent in every interval, and that the continuous
+  function [f](x) represented by it has the property that there is, in
+  the neighbourhood of any point x0, an infinite aggregate of points x',
+  having x0 as a limiting point, for which {[f](x') - [f](x0)} / (x' -
+  x0) tends to become infinite with one sign when x' - x0 approaches
+  zero through positive values, and infinite with the opposite sign when
+  x' - x0 approaches zero through negative values. Accordingly the
+  function is not differentiable at any point. The definite integral of
+  such a function [f](x) through the interval between a fixed point and
+  a variable point x, is a continuous differentiable function F(x), for
+  which F'(x) = [f](x); and, if [f](x) is one-signed throughout any
+  interval F(x) is monotonous throughout that interval, but yet F(x)
+  cannot be represented by a curve. In any interval, however small, the
+  tangent would have to take the same direction for infinitely many
+  points, and yet there is no interval in which the tangent has
+  everywhere the same direction. Further, it can be shown that all
+  functions which are everywhere continuous and nowhere differentiable
+  are capable of representation by series of the form [Sigma][a]_n
+  [phi]_n (x), where [Sigma][a]_n is an absolutely convergent series of
+  numbers, and [phi]_n(x) is an analytic function whose absolute value
+  never exceeds unity.
+
+25. _Calculations with Divergent Series._--When the series described in
+(1) and (2) of S 24 diverge, they may, nevertheless, be used for the
+approximate numerical calculation of the values of the function,
+provided the calculation is not carried beyond a certain number of
+terms. Expansions in series which have the property of representing a
+function approximately when the expansion is not carried too far are
+called "asymptotic expansions." Sometimes they are called
+"semi-convergent series"; but this term is avoided in the best modern
+usage, because it is often used to describe series whose convergence
+depends upon the order of the terms, such as the series 1 - 1/2 + 1/3 -
+...
+
+  In general, let [f]0(x) + [f]1(x) + ... be a series of functions which
+  does not converge in a certain domain. It may happen that, if any
+  number [epsilon], however small, is first specified, a number n can
+  afterwards be found so that, at a point a of the domain, the value
+  [f](a) of a certain function [f](x) is connected with the sum of the
+  first n + 1 terms of the series by the relation |[f](a) - [Sigma] (r=0
+  to n) [f]_r(a) | < [epsilon]. It must also happen that, if any number
+  N, however great, is specified, a number n'(>n) can be found so that,
+  for all values of m which exceed n', | [Sigma](r=0 to m) [f]_r(a) | >
+  N. The divergent series [f]0(x) + [f]1(x) + ... is then an asymptotic
+  expansion for the function f(x) in the domain.
+
+  The best known example of an asymptotic expansion is Stirling's
+  formula for n! when n is large, viz.
+             _____
+            /
+    n! =  \/(2[pi]) 1/2n^(n + 1/2) e^(-n + [theta] / 12n),
+
+  where [theta] is some number lying between 0 and 1. This formula is
+  included in the asymptotic expansion for the Gamma function. We have
+  in fact
+
+    log {[Gamma](x)} = (x - 1/2) log x - x + 1/2 log 2[pi] + [~omega](x),
+
+  where [~omega](x) is the function defined by the definite integral
+                   _
+                  / [oo]
+    ~[omega](x) = |     {[1 - e^(-t)]^(-1) - t^(-1) - 1/2} t^(-1) e^(-tx)dt.
+                 _/0
+
+  The multiplier of e^(-tx) under the sign of integration can be
+  expanded in the power series
+
+     B1      B2         B3
+    ---- -  ---- t^2 + ---- t^4 - ...,
+     2!      4!         6!
+
+  where B1, B2, ... are "Bernoulli's numbers" given by the formula
+
+                               _[oo]
+                              \
+    B_m = 2.2m! (2[pi])^(-2m) /_   [r^(-2m)].
+                                r=1
+
+  When the series is integrated term by term, the right-hand member of
+  the equation for [~omega](x) takes the form
+
+     B1   1     B2   1     B3    1
+    ---- --- - ---- --- + ----  --- - ...,
+    1.2   x    3.4  x^3    5.6  x^5
+
+  This series is divergent; but, if it is stopped at any term, the
+  difference between the sum of the series so terminated and the value
+  of [~omega](x) is less than the last of the retained terms. Stirling's
+  formula is obtained by retaining the first term only. Other well-known
+  examples of asymptotic expansions are afforded by the descending
+  series for Bessel's functions. Methods of obtaining such expansions
+  for the solutions of linear differential equations of the second order
+  were investigated by G.G. Stokes (_Math. and Phys. Papers_, vol. ii.
+  p. 329), and a general theory of asymptotic expansions has been
+  developed by H. Poincare. A still more general theory of divergent
+  series, and of the conditions in which they can be used, as above, for
+  the purposes of approximate calculation has been worked out by E.
+  Borel. The great merit of asymptotic expansions is that they admit of
+  addition, subtraction, multiplication and division, term by term, in
+  the same way as absolutely convergent series, and they admit also of
+  integration term by term; that is to say, the results of such
+  operations are asymptotic expansions for the sum, difference,
+  product, quotient, or integral, as the case may be.
+
+26. _Interchange of the Order of Limiting Operations._--When we require
+to perform any limiting operation upon a function which is itself
+represented by the result of a limiting process, the question of the
+possibility of interchanging the order of the two processes always
+arises. In the more elementary problems of analysis it generally happens
+that such an interchange is possible; but in general it is not possible.
+In other words, the performance of the two processes in different orders
+may lead to two different results; or the performance of them in one of
+the two orders may lead to no result. The fact that the interchange is
+possible under suitable restrictions for a particular class of
+operations is a theorem to be proved.
+
+  Among examples of such interchanges we have the differentiation and
+  integration of an infinite series term by term (S 22), and the
+  differentiation and integration of a definite integral with respect to
+  a parameter by performing the like processes upon the subject of
+  integration (S 19). As a last example we may take the limit of the sum
+  of an infinite series of functions at a point in the domain of
+  convergence. Suppose that the series [Sigma] (r=0 to [oo]) [f]_r(x)
+  represents a function ([f]x) in an interval containing a point a, and
+  that each of the functions [f]_r(x) has a limit at a. If we first put
+  x = a, and then sum the series, we have the value [f](a); if we first
+  sum the series for any x, and afterwards take the limit of the sum at
+  x = a, we have the limit of [f](x) at a; if we first replace each
+  function [f]_r(x) by its limit at a, and then sum the series, we may
+  arrive at a value different from either of the foregoing. If the
+  function [f](x) is continuous at a, the first and second results are
+  equal; if the functions [f]_r(x) are all continuous at a, the first
+  and third results are equal; if the series is uniformly convergent,
+  the second and third results are equal. This last case is an example
+  of the interchange of the order of two limiting operations, and a
+  sufficient, though not always a necessary, condition, for the validity
+  of such an interchange will usually be found in some suitable
+  extension of the notion of uniform convergence.
+
+  AUTHORITIES.--Among the more important treatises and memoirs connected
+  with the subject are: R. Baire, _Fonctions discontinues_ (Paris,
+  1905); O. Biermann, _Analytische Functionen_ (Leipzig, 1887); E.
+  Borel, _Theorie des fonctions_ (Paris, 1898) (containing an
+  introductory account of the Theory of Aggregates), and _Series
+  divergentes_ (Paris, 1901), also _Fonctions de variables reelles_
+  (Paris, 1905); T.J. I'A. Bromwich, _Introduction to the Theory of
+  Infinite Series_ (London, 1908); H.S. Carslaw, _Introduction to the
+  Theory of Fourier's Series and Integrals_ (London, 1906); U. Dini,
+  _Functionen e. reellen Grosse_ (Leipzig, 1892), and _Serie di Fourier_
+  (Pisa, 1880); A. Genocchi u. G. Peano, _Diff.- u. Int.-Rechnung_
+  (Leipzig, 1899); J. Harkness and F. Morley, _Introduction to the
+  Theory of Analytic Functions_ (London, 1898); A. Harnack, _Diff. and
+  Int. Calculus_ (London, 1891); E.W. Hobson, _The Theory of Functions
+  of a real Variable and the Theory of Fourier's Series_ (Cambridge,
+  1907); C. Jordan, _Cours d'analyse_ (Paris, 1893-1896); L. Kronecker,
+  _Theorie d. einfachen u. vielfachen Integrale_ (Leipzig, 1894); H.
+  Lebesgue, _Lecons sur l'integration_ (Paris, 1904); M. Pasch, _Diff.-
+  u. Int.-Rechnung_ (Leipzig, 1882); E. Picard, _Traite d'analyse_
+  (Paris, 1891); O. Stolz, _Allgemeine Arithmetik_ (Leipzig, 1885), and
+  _Diff.- u. Int.-Rechnung_ (Leipzig, 1893-1899); J. Tannery, _Theorie
+  des fonctions_ (Paris, 1886); W.H. and G.C. Young, _The Theory of Sets
+  of Points_ (Cambridge, 1906); Broden, "Stetige Functionen e. reellen
+  Veranderlichen," _Crelle_, Bd. cxviii.; G. Cantor, A series of memoirs
+  on the "Theory of Aggregates" and on "Trigonometric series" in _Acta
+  Math_. tt. ii., vii., and _Math. Ann_. Bde. iv.-xxiii.; Darboux,
+  "Fonctions discontinues," _Ann. Sci. Ecole normale sup_. (2), t. iv.;
+  Dedekind, _Was sind u. was sollen d. Zahlen_? (Brunswick, 1887), and
+  _Stetigkeit u. irrationale Zahlen_ (Brunswick, 1872); Dirichlet,
+  "Convergence des series trigonometriques," _Crelle_, Bd. iv.; P. Du
+  Bois Reymond, _Allgemeine Functionentheorie_ (Tubingen, 1882), and
+  many memoirs in _Crelle_ and in _Math. Ann_.; Heine,
+  "Functionenlehre," _Crelle_, Bd. lxxiv.; J. Pierpont, _The Theory of
+  Functions of a real Variable_ (Boston, 1905); F. Klein, "Allgemeine
+  Functionsbegriff," _Math. Ann_. Bd. xxii.; W.F. Osgood, "On Uniform
+  Convergence," _Amer. J. of Math_. vol. xix.; Pincherle, "Funzioni
+  analitiche secondo Weierstrass," _Giorn. di mat_. t. xviii.;
+  Pringsheim, "Bedingungen d. Taylorschen Lehrsatzes," _Math. Ann_. Bd.
+  xliv.; Riemann, "Trigonometrische Reihe," _Ges. Werke_ (Leipzig,
+  1876); Schoenflies, "Entwickelung d. Lehre v. d.
+  Punktmannigfaltigkeiten," _Jahresber. d. deutschen Math.-Vereinigung_,
+  Bd. viii.; Study, Memoir on "Functions with Restricted Oscillation,"
+  _Math. Ann_. Bd. xlvii.; Weierstrass, Memoir on "Continuous Functions
+  that are not Differentiable," _Ges. math. Werke_, Bd. ii. p. 71
+  (Berlin, 1895), and on the "Representation of Arbitrary Functions,"
+  ibid. Bd. iii. p. 1; W.H. Young, "On Uniform and Non-uniform
+  Convergence," _Proc. London Math. Soc._ (Ser. 2) t. 6. Further
+  information and very full references will be found in the articles by
+  Pringsheim, Schoenflies and Voss in the _Encyclopadie der math.
+  Wissenschaften_, Bde. i., ii. (Leipzig, 1898, 1899).     (A. E. H. L.)
+
+
+II.--FUNCTIONS OF COMPLEX VARIABLES
+
+In the preceding section the doctrine of functionality is discussed with
+respect to real quantities; in this section the theory when complex or
+imaginary quantities are involved receives treatment. The following
+abstract explains the arrangement of the subject matter: (S 1), _Complex
+numbers_, states what a complex number is; (S 2), _Plotting of simple
+expressions involving complex numbers_, illustrates the meaning in some
+simple cases, introducing the notion of conformal representation and
+proving that an algebraic equation has complex, if not real, roots; (S
+3), _Limiting operations_, defines certain simple functions of a complex
+variable which are obtained by passing to a limit, in particular the
+exponential function, and the generalized logarithm, here denoted by
+[lambda](z); (S 4), _Functions of a complex variable in general_, after
+explaining briefly what is to be understood by a region of the complex
+plane and by a path, and expounding a logical principle of some
+importance, gives the accepted definition of a function of a complex
+variable, establishes the existence of a complex integral, and proves
+Cauchy's theorem relating thereto; (S 5), _Applications_, considers the
+differentiation and integration of series of functions of a complex
+variable, proves Laurent's theorem, and establishes the expansion of a
+function of a complex variable as a power series, leading, in (S 6),
+_Singular points_, to a definition of the region of existence and
+singular points of a function of a complex variable, and thence, in (S
+7), _Monogenic Functions_, to what the writer believes to be the
+simplest definition of a function of a complex variable, that of
+Weierstrass; (S 8), _Some elementary properties of single valued
+functions_, first discusses the meaning of a pole, proves that a single
+valued function with only poles is rational, gives Mittag-Leffler's
+theorem, and Weierstrass's theorem for the primary factors of an
+integral function, stating generalized forms for these, leading to the
+theorem of (S 9), _The construction of a monogenic function with a given
+region of existence_, with which is connected (S10), _Expression of a
+monogenic function by rational functions in a given region_, of which
+the method is applied in (S 11), _Expression of_ (1 - z)^(-1) _by
+polynomials_, to a definite example, used here to obtain (S 12), _An
+expansion of an arbitrary function by means of a series of polynomials,
+over a star region_, also obtained in the original manner of
+Mittag-Leffler; (S 13), _Application of Cauchy's theorem to the
+determination of definite integrals_, gives two examples of this method;
+(S 14), _Doubly Periodic Functions_, is introduced at this stage as
+furnishing an excellent example of the preceding principles. The reader
+who wishes to approach the matter from the point of view of Integral
+Calculus should first consult the section (S 20) below, dealing with
+_Elliptic Integrals_; (S 15), _Potential Functions, Conformal
+representation in general_, gives a sketch of the connexion of the
+theory of potential functions with the theory of conformal
+representation, enunciating the Schwarz-Christoffel theorem for the
+representation of a polygon, with the application to the case of an
+equilateral triangle; (S 16), _Multiple-valued Functions, Algebraic
+Functions_, deals for the most part with algebraic functions, proving
+the residue theorem, and establishing that an algebraic function has a
+definite Order; (S 17), _Integrals of Algebraic Functions_, enunciating
+Abel's theorem; (S 18), _Indeterminateness of Algebraic Integrals_,
+deals with the periods associated with an algebraic integral,
+establishing that for an elliptic integral the number of these is two;
+(S 19), _Reversion of an algebraic integral_, mentions a problem
+considered below in detail for an elliptic integral; (S 20), _Elliptic
+Integrals_, considers the algebraic reduction of any elliptic integral
+to one of three standard forms, and proves that the function obtained by
+reversion is single-valued; (S 21), _Modular Functions_, gives a
+statement of some of the more elementary properties of some functions of
+great importance, with a definition of Automorphic Functions, and a hint
+of the connexion with the theory of linear differential equations; (S
+22), _A property of integral functions, deduced from the theory of
+modular functions_, proves that there cannot be more than one value not
+assumed by an integral function, and gives the basis of the well-known
+expression of the modulus of the elliptic functions in terms of the
+ratio of the periods; (S 23), _Geometrical applications of Elliptic
+Functions_, shows that any plane curve of deficiency unity can be
+expressed by elliptic functions, and gives a geometrical proof of the
+addition theorem for the function RN(u); (S 24), _Integrals of Algebraic
+Functions in connexion with the theory of plane curves_, discusses the
+generalization to curves of any deficiency; (S 25), _Monogenic Functions
+of several independent variables_, describes briefly the beginnings of
+this theory, with a mention of some fundamental theorems: (S 26),
+_Multiply-Periodic Functions and the Theory of Surfaces_, attempts to
+show the nature of some problems now being actively pursued.
+
+Beside the brevity necessarily attaching to the account here given of
+advanced parts of the subject, some of the more elementary results are
+stated only, without proof, as, for instance: the monogeneity of an
+algebraic function, no reference being made, moreover, to the cases of
+differential equations whose integrals are monogenic; that a function
+possessing an algebraic addition theorem is necessarily an elliptic
+function (or a particular case of such); that any area can be
+conformally represented on a half plane, a theorem requiring further
+much more detailed consideration of the meaning of _area_ than we have
+given; while the character and properties, including the connectivity,
+of a Riemann surface have not been referred to. The theta functions are
+referred to only once, and the principles of the theory of Abelian
+Functions have been illustrated only by the developments given for
+elliptic functions.
+
+S 1. _Complex Numbers._--Complex numbers are numbers of the form x + iy,
+where x, y are ordinary real numbers, and i is a symbol imagined capable
+of combination with itself and the ordinary real numbers, by way of
+addition, subtraction, multiplication and division, according to the
+ordinary commutative, associative and distributive laws; the symbol i is
+further such that i^2 = -1.
+
+  Taking in a plane two rectangular axes Ox, Oy, we assume that every
+  point of the plane is definitely associated with two real numbers x, y
+  (its co-ordinates) and conversely; thus any point of the plane is
+  associated with a single complex number; in particular, for every
+  point of the axis Ox, for which y = O, the associated number is an
+  ordinary real number; the complex numbers thus include the real
+  numbers. The axis Ox is often called the real axis, and the axis Oy
+  the imaginary axis. If P be the point associated with the complex
+  variable z = x + iy, the distance OP be called r, and the positive
+  angle less than 2[pi] between Ox and OP be called [theta], we may
+  write z = r(cos[theta] + i sin[theta]); then r is called the modulus
+  or absolute value of z and often denoted by |z| and [theta] is called
+  the phase or amplitude of z, and often denoted by ph (z); strictly the
+  phase is ambiguous by additive multiples of 2[pi]. If z' = x' + iy' be
+  represented by P', the complex argument z' + z is represented by a
+  point P" obtained by drawing from P' a line equal to and parallel to
+  OP; the geometrical representation involves for its validity certain
+  properties of the plane; as, for instance, the equation z' + z = z +
+  z' involves the possibility of constructing a parallelogram (with OP"
+  as diagonal). It is important constantly to bear in mind, what is
+  capable of easy algebraic proof (and geometrically is Euclid's
+  proposition III. 7), that the modulus of a sum or difference of two
+  complex numbers is generally less than (and is never greater than) the
+  sum of their moduli, and is greater than (or equal to) the difference
+  of their moduli; the former statement thus holds for the sum of any
+  number of complex numbers. We shall write E(i[theta]) for cos[theta] +
+  i sin [theta]; it is at once verified that E(i[alpha]). E(i[beta]) =
+  E[i([alpha] + [beta])], so that the phase of a product of complex
+  quantities is obtained by addition of their respective phases.
+
+S 2. _Plotting and Properties of Simple Expressions involving a Complex
+Number._--If we put [zeta] = (z-i)/(z + i), and, putting [zeta] = [xi] +
+i[eta], take a new plane upon which [xi], [eta] are rectangular
+co-ordinates, the equations [xi] = (x^2 + y^2-1)/[x^2 + (y + 1)^2],
+[eta] = -2xy/[x^2 + (y + i)^2] will determine, corresponding to any
+point of the first plane, a point of the second plane. There is the one
+exception of z = -i, that is, x = 0, y = -1, of which the corresponding
+point is at infinity. It can now be easily proved that as z describes
+the real axis in its plane the point [zeta] describes once a circle of
+radius unity, with centre at [zeta] = 0, and that there is a definite
+correspondence of point to point between points in the z-plane which are
+above the real axis and points of the [zeta]-plane which are interior to
+this circle; in particular z = i corresponds to [zeta] = 0.
+
+  Moreover, [zeta] being a rational function of z, both [xi] and [eta]
+  are continuous differentiable functions of x and y, save when [zeta]
+  is infinite; writing [zeta] = [f](x, y) = [f](z - iy, y), the fact
+  that this is really independent of y leads at once to (Pd)f/(Pd)x +
+  i(Pd)[f]/(Pd)y = 0, and hence to
+
+    (Pd)[xi]   (Pd)[eta]  (Pd)[xi]     (Pd)[eta]  (Pd)^2[xi]   (Pd)^2[xi]
+    -------- = ---------, -------- = - ---------, ---------- + ---------- = 0;
+     (Pd)x       (Pd)y'    (Pd)y         (Pd)x'     (Pd)x^2      (Pd)y^2
+
+  so that [xi] is not any arbitrary function of x, y, and when [xi] is
+  known [eta] is determinate save for an additive constant. Also, in
+  virtue of these equations, if [zeta], [zeta]' be the values of [zeta]
+  corresponding to two near values of z, say z and z', the ratio
+  ([zeta]'-[zeta])/(z'- z) has a definite limit when z' = z, independent
+  of the ultimate phase of z'- z, this limit being therefore equal to
+  (Pd)[zeta]/(Pd)x, that is, (Pd)[xi]/(Pd)x + i(Pd)[eta])/(Pd)x.
+  Geometrically this fact is interpreted by saying that if two curves in
+  the z-plane intersect at a point P, at which both the differential
+  coefficients (Pd)[xi]/(Pd)x, (Pd)[eta]/(Pd)x are not zero, and P', P"
+  be two points near to P on these curves respectively, and the
+  corresponding points of the [zeta]-plane be Q, Q', Q", then (1) the
+  ratios PP"/PP', QQ"/QQ' are ultimately equal, (2) the angle P'PP" is
+  equal to Q'QQ", (3) the rotation from PP' to PP" is in the same sense
+  as from QQ' to QQ", it being understood that the axes of [xi], [eta]
+  in the one plane are related as are the axes of x, y. Thus any diagram
+  of the z-plane becomes a diagram of the [zeta]-plane with the same
+  angles; the magnification, however, which is equal to
+     _                             _
+    |  /(Pd)[xi]\^2    /(Pd)[xi]\^2 | 1/2
+    | ( -------- ) + ( -------- )   |
+    |_ \ (Pd)x  /     \  (Pd)y /   _|
+
+  varies from point to point. Conversely, it appears subsequently that
+  the expression of any copy of a diagram (say, a map) which preserves
+  angles requires the intervention of the complex variable.
+
+  As another illustration consider the case when [zeta] is a polynomial
+  in z,
+
+    [zeta] = p0 z^n + p1 z^(n - 1) + ... + p_n;
+
+  H being an arbitrary real positive number, it can be shown that a
+  radius R can be found such for every |z| > R we have |[zeta]| > H;
+  consider the lower limit of |[zeta]| for |z| < R; as [xi]^2 + [eta]^2
+  is a real continuous function of x, y for |z| < R, there is a point
+  (x, y), say (x0, y0), at which |[zeta]| is least, say equal to [rho],
+  and therefore within a circle in the [zeta]-plane whose centre is the
+  origin, of radius [rho], there are no points [zeta] representing
+  values corresponding to |z| < R. But if [zeta]0 be the value of [zeta]
+  corresponding to (x0, y0), and the expression of [zeta] - [zeta]0 near
+  z0 = x0 + iy0, in terms of z - z0, be A(z - z0)^m + B(z - z0)^(m + 1)
+  + ..., where A is not zero, to two points near to (x0, y0), say (x1,
+  y1) or z1 and z2 = z0 + (z1 - z0)(cos [pi]/m + i sin [pi]/m), will
+  correspond two points near to [zeta]0, say [zeta]1, and 2[zeta]0
+  -[zeta]'1, situated so that [zeta]0 is between them. One of these must
+  be within the circle ([rho]). We infer then that [rho] = 0, and have
+  proved that every polynomial in z vanishes for some value of z, and
+  can therefore be written as a product of factors of the form z -
+  [alpha], where [alpha] denotes a complex number. This proposition
+  alone suffices to suggest the importance of complex numbers.
+
+S 3. _Limiting Operations._--In order that a complex number [zeta] =
+[xi] + i[eta] may have a limit it is necessary and sufficient that each
+of [xi] and [eta] has a limit. Thus an infinite series w0 + w1 + w2 +
+..., whose terms are complex numbers, is convergent if the real series
+formed by taking the real parts of its terms and that formed by the
+imaginary terms are both convergent. The series is also convergent if
+the real series formed by the moduli of its terms is convergent; in that
+case the series is said to be absolutely convergent, and it can be shown
+that its sum is unaltered by taking the terms in any other order.
+Generally the necessary and sufficient condition of convergence is that,
+for a given real positive [epsilon], a number m exists such that for
+every n > m, and every positive p, the batch of terms w_n + w_(n + 1) +
+... + w_(n + p) is less than [epsilon] in absolute value. If the terms
+depend upon a complex variable z, the convergence is called _uniform_
+for a range of values of z, when the inequality holds, for the same
+[epsilon] and m, for all the points z of this range.
+
+  The infinite series of most importance are those of which the general
+  term is a_nz^n, wherein a_n is a constant, and z is regarded as
+  variable, n = 0, 1, 2, 3, ... Such a series is called a power series,
+  if a real and positive number M exists such that for z = z0 and every
+  n, |a_n z0^n| < M, a condition which is satisfied, for instance, if
+  the series converges for z = z0, then it is at once proved that the
+  series converges absolutely for every z for which |z| < |z0|, and
+  converges uniformly over every range |z| < r' for which r' < |z0|. To
+  every power series there belongs then a circle of convergence within
+  which it converges absolutely and uniformly; the function of z
+  represented by it is thus continuous within the circle (this being the
+  result of a general property of uniformly convergent series of
+  continuous functions); the sum for an interior point z is, however,
+  continuous with the sum for a point z0 on the circumference, as z
+  approaches to z0 provided the series converges for z = z0, as can be
+  shown without much difficulty. Within a common circle of convergence
+  two power series [Sigma] a_n z^n, [Sigma] b_n z^n can be multiplied
+  together according to the ordinary rule, this being a consequence of a
+  theorem for absolutely convergent series. If r1 be less than the
+  radius of convergence of a series [Sigma] a_nz^n and for |z| = r1, the
+  sum of the series be in absolute value less than a real positive
+  quantity M, it can be shown that for |z| = r1 every term is also less
+  than M in absolute value, namely, |a_n| < Mr1^(-n). If in every
+  arbitrarily small neighbourhood of z = 0 there be a point for which
+  two converging power series [Sigma]a_nz^n, [Sigma]b_n z^n agree in
+  value, then the series are identical, or a_n = b_n; thus also if
+  [Sigma]a_nz^n vanish at z = 0 there is a circle of finite radius about
+  z = 0 as centre within which no other points are found for which the
+  sum of the series is zero. Considering a power series [f](z) =
+  [Sigma]a_nz^n of radius of convergence R, if |z0| < R and we put z =
+  z0 + t with |t| < R-|z0|, the resulting series [Sigma]a_n (z0 + t)^n
+  may be regarded as a double series in z0 and t, which, since |z0| + t
+  < R, is absolutely convergent; it may then be arranged according to
+  powers of t. Thus we may write [f](z) = [Sigma]A_n t^n; hence A0 =
+  [f](z0), and we have [[f](z0 + t) - [f](z0)]/t = [Sigma](n=1) A_n
+  t^(n-l), wherein the continuous series on the right reduces to A1 for
+  t = 0; thus the ratio on the left has a definite limit when t = 0,
+  equal namely to A1 or [Sigma]na_nz0^(n - 1). In other words, the
+  original series may legitimately be differentiated at any interior
+  point z0 of its circle of convergence. Repeating this process we find
+  [f](z0 + t) = [Sigma]t^n [f]^(n) (z0)/n!, where [f]^(n) (z0) is the
+  nth differential coefficient. Repeating for this power series, in t,
+  the argument applied about z = 0 for [Sigma]a_n z^n, we infer that for
+  the series [f](z) every point which reduces it to zero is an isolated
+  point, and of such points only a finite number lie within a circle
+  which is within the circle of convergence of [f](z).
+
+  Perhaps the simplest possible power series is e^z = exp(z) = 1 +
+  z^2/2! + z^3/3! + ... of which the radius of convergence is infinite.
+  By multiplication we have exp(z).exp(z^1) = exp(z + z^1). In
+  particular when x, y are real, and z = x + iy, exp(z) = exp(x)exp(iy).
+  Now the functions
+
+    U0 = sin y, V0 = 1 - cos y, U1 = y - sin y,
+    V1 = 1/2y^2 - 1 + cos y, U2 = (1/6)y^3 - y + sin y,
+      V2 = (1/24)y^4 - 1/2y^2 + 1 - cos y, ...
+
+  all vanish for y = 0, and the differential coefficient of any one
+  after the first is the preceding one; as a function (of a real
+  variable) is increasing when its differential coefficient is positive,
+  we infer, for y positive, that each of these functions is positive;
+  proceeding to a limit we hence infer that
+
+    cos y = 1 - 1/2y^2 + (1/24)y^4 - ..., sin y = y - (1/6)y^3 +
+      (1/120)y^5 - ...,
+
+  for positive, and hence, for all values of y. We thus have exp(iy) =
+  cos y + i sin y, and exp (z) = exp (x).(cos y + i sin y). In other
+  words, the modulus of exp (z) is exp (x) and the phase is y. Hence
+  also
+
+    exp(z + 2[pi]i) = exp(x) [cos (y + 2[pi]) + i sin(y + 2[pi])],
+
+  which we express by saying that exp (z) has the period 2[pi]i, and
+  hence also the period 2k[pi]i, where k is an arbitrary integer. From
+  the fact that the constantly increasing function exp (x) can vanish
+  only for x = 0, we at once prove that exp (z) has no other periods.
+
+  Taking in the plane of z an infinite strip lying between the lines y =
+  0, y = 2[pi] and plotting the function [zeta] = exp (z) upon a new
+  plane, it follows at once from what has been said that every complex
+  value of [zeta] arises when z takes in turn all positions in this
+  strip, and that no value arises twice over. The equation [zeta] =
+  exp(z) thus defines z, regarded as depending upon [zeta], with only an
+  additive ambiguity 2k[pi]i, where k is an integer. We write z =
+  [lambda]([zeta]); when [zeta] is real this becomes the logarithm of
+  [zeta]; in general [lambda]([zeta]) = log |[zeta]| + i ph ([zeta]) +
+  2k[pi]i, where k is an integer; and when [zeta] describes a closed
+  circuit surrounding the origin the phase of [zeta] increases by 2[pi],
+  or k increases by unity. Differentiating the series for [zeta] we have
+  d[zeta]/dz = [zeta], so that z, regarded as depending upon [zeta], is
+  also differentiable, with dz/d[zeta] = [zeta]^(-1). On the other hand,
+  consider the series [zeta] - 1 - 1/2([zeta] - 1)^2 + 1/3([zeta] - 1)^3
+  - ...; it converges when [zeta] = 2 and hence converges for |[zeta] -
+  1| < 1; its differential coefficient is, however, 1 - ([zeta] - 1) +
+  ([zeta] - 1)^2 - ..., that is, (1 + [zeta] - 1)^(-1). Wherefore if
+  [phi]([zeta]) denote this series, for |[zeta] - 1| < 1, the difference
+  [lambda]([zeta]) - [phi]([zeta]), regarded as a function of [xi] and
+  [eta], has vanishing differential coefficients; if we take the value
+  of [lambda]([zeta]) which vanishes when [zeta] = 1 we infer thence
+  that for |[zeta] - 1| < 1, [lambda]([zeta]) = [Sigma][n = 1] [(-1)^(n
+  - 1)]/n ([zeta] - 1)^n. It is to be remarked that it is impossible for
+  [zeta] while subject to |[zeta] - 1| < 1 to make a circuit about the
+  origin. For values of [zeta] for which |[zeta] - 1| [not less than] 1,
+  we can also calculate [lambda]([zeta]) with the help of infinite
+  series, utilizing the fact that [lambda]([zeta][zeta]') =
+  [lambda]([zeta]) + [lambda]([zeta]').
+
+  The function [lambda]([zeta]) is required to define [zeta]^a when
+  [zeta] and a are complex numbers; this is defined as exp
+  [a[lambda]([zeta])], that is as [Sigma] (n=0) a^n[[lambda]
+  ([zeta])]^n/n!. When a is a real integer the ambiguity of
+  [lambda]([zeta]) is immaterial here, since exp [a[lambda]([zeta]) +
+  2ka[pi]i] = exp[a[lambda]([zeta])]; when a is of the form 1/q, where q
+  is a positive integer, there are q values possible for [zeta]^(1/q),
+  of the form exp [1/q [lambda]([zeta])] exp(2k[pi]i/q), with k = 0, 1,
+  ... q - 1, all other values of k leading to one of these; the qth
+  power of any one of these values is [zeta]; when a = p/q, where p, q
+  are integers without common factor, q being positive, we have
+  [zeta]^(p/q) = ([zeta]^(1/q))^p. The definition of the symbol [zeta]^a
+  is thus a generalization of the ordinary definition of a power, when
+  the numbers are real. As an example, let it be required to find the
+  meaning of i^i; the number i is of modulus unity and phase 1/2[pi];
+  thus [lambda](i) = i(1/2[pi] + 2k[pi]); thus
+
+    i^i = exp(-1/2[pi] - 2k[pi]) = exp(-1/2[pi]) exp(-2k[pi]),
+
+  is always real, but has an infinite number of values.
+
+  The function exp (z) is used also to define a generalized form of the
+  cosine and sine functions when z is complex; we write, namely, cos z =
+  1/2[exp(iz) + exp(-iz)] and sin z = -1/2i[exp(iz) - exp(-iz)]. It will
+  be found that these obey the ordinary relations holding when z is
+  real, except that their moduli are not inferior to unity. For example,
+  cos i = 1 + 1/2! + 1/4! + ... is obviously greater than unity.
+
+S4. _Of Functions of a Complex Variable in General._--We have in what
+precedes shown how to generalize the ordinary rational, algebraic and
+logarithmic functions, and considered more general cases, of functions
+expressible by power series in z. With the suggestions furnished by
+these cases we can frame a general definition. So far our use of the
+plane upon which z is represented has been only illustrative, the
+results being capable of analytical statement. In what follows this
+representation is vital to the mode of expression we adopt; as then the
+properties of numbers cannot be ultimately based upon spatial
+intuitions, it is necessary to indicate what are the geometrical ideas
+requiring elucidation.
+
+  Consider a square of side a, to whose perimeter is attached a definite
+  direction of description, which we take to be counter-clockwise;
+  another square, also of side a, may be added to this, so that there is
+  a side common; this common side being erased we have a composite
+  region with a definite direction of perimeter; to this a third square
+  of the same size may be attached, so that there is a side common to it
+  and one of the former squares, and this common side may be erased. If
+  this process be continued any number of times we obtain a region of
+  the plane bounded by one or more polygonal closed lines, no two of
+  which intersect; and at each portion of the perimeter there is a
+  definite direction of description, which is such that the region is on
+  the left of the describing point. Similarly we may construct a region
+  by piecing together triangles, so that every consecutive two have a
+  side in common, it being understood that there is assigned an upper
+  limit for the greatest side of a triangle, and a lower limit for the
+  smallest angle. In the former method, each square may be divided into
+  four others by lines through its centre parallel to its sides; in the
+  latter method each triangle may be divided into four others by lines
+  joining the middle points of its sides; this halves the sides and
+  preserves the angles. When we speak of a _region_ of the plane in
+  general, unless the contrary is stated, we shall suppose it capable of
+  being generated in this latter way by means of a finite number of
+  triangles, there being an upper limit to the length of a side of the
+  triangle and a lower limit to the size of an angle of the triangle. We
+  shall also require to speak of a _path_ in the plane; this is to be
+  understood as capable of arising as a limit of a polygonal path of
+  finite length, there being a definite direction or sense of
+  description at every point of the path, which therefore never meets
+  itself. From this the meaning of a closed path is clear. The boundary
+  points of a region form one or more closed paths, but, in general, it
+  is only in a limiting sense that the interior points of a closed path
+  are a region.
+
+  There is a logical principle also which must be referred to. We
+  frequently have cases where, about every interior or boundary, point
+  z0 of a certain region a circle can be put, say of radius r0, such
+  that for all points z of the region which are interior to this circle,
+  for which, that is, |z - z0| < r0, a certain property holds. Assuming
+  that to r0 is given the value which is the upper limit for z0, of the
+  possible values, we may call the points |z - z0| < r0, the
+  neighbourhood belonging to or _proper_ to z0, and may speak of the
+  property as the property (z, z0). The value of r0 will in general vary
+  with z0; what is in most cases of importance is the question whether
+  the lower limit of r0 for all positions is zero or greater than zero.
+  (A) This lower limit is certainly greater than zero provided the
+  property (z, z0) is of a kind which we may call extensive; such,
+  namely, that if it holds, for some position of z0 and all positions of
+  z, within a certain region, then the property (z, z1) holds within a
+  circle of radius R about any interior point z1 of this region for all
+  points z for which the circle |z - z1| = R is within the region. Also
+  in this case r0 varies continuously with z0. (B) Whether the property
+  is of this extensive character or not we can prove that the region can
+  be divided into a finite number of sub-regions such that, for every
+  one of these, the property holds, (1) for _some_ point z0 within or
+  upon the boundary of the sub-region, (2) for _every_ point z within or
+  upon the boundary of the sub-region.
+
+  We prove these statements (A), (B) in reverse order. To prove (B) let
+  a region for which the property (z, z0) holds for all points z and
+  some point z0 of the region, be called _suitable_: if each of the
+  triangles of which the region is built up be suitable, what is desired
+  is proved; if not let an unsuitable triangle be subdivided into four,
+  as before explained; if one of these subdivisions is unsuitable let it
+  be again subdivided; and so on. Either the process terminates and then
+  what is required is proved; or else we obtain an indefinitely
+  continued sequence of unsuitable triangles, each contained in the
+  preceding, which converge to a point, say [zeta]; after a certain
+  stage all these will be interior to the proper region of [zeta]; this,
+  however, is contrary to the supposition that they are all unsuitable.
+
+  We now make some applications of this result (B). Suppose a definite
+  finite real value attached to every interior or boundary point of the
+  region, say [f](x, y). It may have a finite upper limit H for the
+  region, so that no point (x, y) exists for which [f](x, y) > H, but
+  points (x, y) exist for which [f](x, y) > H - [epsilon], however small
+  [epsilon] may be; if not we say that its upper limit is infinite.
+  There is then at least one point of the region such that, for points
+  of the region within a circle about this point, the upper limit of
+  [f](x, y) is H, however small the radius of the circle be taken; for
+  if not we can put about every point of the region a circle within
+  which the upper limit of [f](x, y) is less than H; then by the result
+  (B) above the region consists of a finite number of sub-regions within
+  each of which the upper limit is less than H; this is inconsistent
+  with the hypothesis that the upper limit for the whole region is H. A
+  similar statement holds for the lower limit. A case of such a function
+  [f](x, y) is the radius r0 of the neighbourhood proper to any point
+  z0, spoken of above. We can hence prove the statement (A) above.
+
+  Suppose the property (z, z0) extensive, and, if possible, that the
+  lower limit of r0 is zero. Let then [zeta] be a point such that the
+  lower limit of r0 is zero for points z0 within a circle about [zeta]
+  however small; let r be the radius of the neighbourhood proper to
+  [zeta]; take z0 so that |z0 - [zeta]| < 1/2r; the property (z, z0),
+  being extensive, holds within a circle, centre z0, of radius r - |z0 -
+  [zeta]|, which is greater than |z0 - [zeta]|, and increases to r as
+  |z0 - [zeta]| diminishes; this being true for all points z0 near
+  [zeta], the lower limit of r0 is not zero for the neighbourhood of
+  [zeta], contrary to what was supposed. This proves (A). Also, as is
+  here shown that r0 [ = >] r - |z0-[zeta]|, may similarly be shown that
+  r [=>] r0 - |z0 - [zeta]|. Thus r0 differs arbitrarily little from r
+  when |z0-[zeta]| is sufficiently small; that is, r0 varies
+  continuously with z0. Next suppose the function [f](x, y), which has a
+  definite finite value at every point of the region considered, to be
+  continuous but not necessarily real, so that about every point z0,
+  within or upon the boundary of the region, [eta] being an arbitrary
+  real positive quantity assigned beforehand, a circle is possible, so
+  that for all points z of the region interior to this circle, we have
+  |[f](x, y) - [f](x0, y0)| < 1/2[eta], and therefore (x', y') being any
+  other point interior to this circle, |[f](x', y') - [f](x, y)| <
+  [eta]. We can then apply the result (A) obtained above, taking for the
+  neighbourhood proper to any point z0 the circular area within which,
+  for any two points (x, y), (x', y'), we have |[f](x', y') - [f](x, y)|
+  < [eta]. This is clearly an extensive property. Thus, a number r is
+  assignable, greater than zero, such that, for any two points (x, y),
+  (x', y') within a circle |z - z0| = r about any point z0, we have
+  |[f](x', y') - [f](x, y)| < [eta], and, in particular, |[f](x, y) -
+  [f](x0, y0)| < [eta], where [eta] is an arbitrary real positive
+  quantity agreed upon beforehand.
+
+  Take now any path in the region, whose extreme points are z0, z, and
+  let z1, ... z_(n - 1) be intermediate points of the path, in order;
+  denote the continuous function [f](x, y) by [f](z), and let [f]_r
+  denote any quantity such that |[f]_r - [f](z_r)| [=<] |[f](z_(r + 1))
+  - [f](z_r)|; consider the sum
+
+    (z1 - z0)[f]0 + (z2 - z1)[f]1 + ... + (z - z_(n - 1))[f](n - 1).
+
+  By the definition of a path we can suppose, n being large enough, that
+  the intermediate points z1, ... z_(n - 1) are so taken that if z_i,
+  z_(i + 1) be any two points intermediate, in order, to z_r and z_(r +
+  1), we have |z_(i + i) - z_i| < |z_(r + 1) - z_r|; we can thus suppose
+  |z1 - z0|, |z2 - z1|, ... |z - z_(n - 1)|all to converge constantly
+  to zero. This being so, we can show that the sum above has a definite
+  limit. For this it is sufficient, as in the case of an integral of a
+  function of one real variable, to prove this to be so when the
+  convergence is obtained by taking new points of division intermediate
+  to the former ones. If, however, z_(r, 1), z_(r, 2), ... z_(r, m - 1)
+  be intermediate in order to z_r and z_(r + 1), and |[f]_(r, i) -
+  [f](z_(r, i))| < |[f](z_(r, i + 1)) - [f](z_(r, i))|, the difference
+  between [Sigma](z_(r + 1) - z_r)[f]_r and
+
+    [Sigma]{(z_(r, 1) - z_r)[f]_(r, 0) + (z_(r, 2) - z{r, 1})[f]_(r, 1)
+      + ... + (z_(r + 1) - z_(r, m - 1))[f]_(r, m - 1)},
+
+  which is equal to
+
+    [Sigma]_r [Sigma]_i (z_(r, i + 1) - z_(r, i))([f]_(r, i) - [f]_r),
+
+  is, when |z_(r + 1) - z_r| is small enough, to ensure |[f](z_(r +
+  1)) - [f](z_r)| < [eta], less in absolute value than
+
+    [Sigma]2[eta] [Sigma] |z_(r, i + 1) - z{r, i}|,
+
+  which, if S be the upper limit of the perimeter of the polygon from
+  which the path is generated, is < 2[eta]S, and is therefore
+  arbitrarily small.
+
+  The limit in question is called [int](z_0 to z) [f](z)dz. In
+  particular when [f](z) = 1, it is obvious from the definition that its
+  value is z - z0; when [f](z) = z, by taking [f]_r = 1/2(z_(r + 1) -
+  z_r), it is equally clear that its value is 1/2(z^2 - z0^2); these
+  results will be applied immediately.
+
+  Suppose now that to every interior and boundary point z0 of a certain
+  region there belong two definite finite numbers [f](z0), F(z0), such
+  that, whatever real positive quantity [eta] may be, a real positive
+  number [epsilon] exists for which the condition
+
+    | [f](z) - [f](z0)         |
+    | ---------------- - F(z0) | < [eta],
+    |      z-z0                |
+
+  which we describe as the condition (z, z0), is satisfied for every
+  point z, within or upon the boundary of the region, satisfying the
+  limitation |z - z0| < [epsilon]. Then [f](z0) is called a
+  differentiable function of the complex variable z0 over this region,
+  its differential coefficient being F(z0). The function [f](z0) is thus
+  a continuous function of the real variables x0, y0, where z0 = x0 +
+  iy0, over the region; it will appear that F(z0) is also continuous and
+  in fact also a differentiable function of z0.
+
+  Supposing [eta] to be retained the same for all points z0 of the
+  region, and [sigma]0 to be the upper limit of the possible values of
+  [epsilon] for the point z0, it is to be presumed that [sigma]0 will
+  vary with z0, and it is not obvious as yet that the lower limit of the
+  values of [sigma]0 as z0 varies over the region may not be zero. We
+  can, however, show that the region can be divided into a finite number
+  of sub-regions for each of which the condition (z, z0), above, is
+  satisfied for all points z, within or upon the boundary of this
+  sub-region, for an appropriate position of z0, within or upon the
+  boundary of this sub-region. This is proved above as result (B).
+
+  Hence it can be proved that, for a differentiable function [f](z), the
+  integral [int](z_1 to z) [f](z)dz has the same value by whatever path
+  within the region we pass from z1 to z. This we prove by showing that
+  when taken round a closed path in the region the integral
+  [int][f](z)dz vanishes. Consider first a triangle over which the
+  condition (z, z0) holds, for some position of z0 and every position of
+  z, within or upon the boundary of the triangle. Then as
+
+    [f](z) = [f](z0) + (z - z0)F(z0) + [eta][theta](z - z0), where |[theta]| < 1,
+
+  we have
+      _                               _           _            _
+     /                               /           /            /
+     |[f](z)dz = [[f](z0) - z0F(z0)] |dz + F(z0) |zdz + [eta] |[theta](z - z0)dz,
+    _/                              _/          _/           _/
+
+  which, as the path is closed, is [eta] [int][theta](z-z0)dz. Now, from
+  the theorem that the absolute value of a sum is less than the sum of
+  the absolute values of the terms, this last is less, in absolute
+  value, than [eta]ap, where a is the greatest side of the triangle and
+  p is its perimeter; if [Delta] be the area of the triangle, we have
+  [Delta] = 1/2ab sin C > ([alpha]/[pi])ba, where [alpha] is the least
+  angle of the triangle, and hence a(a + b + c) < 2a(b + c) <
+  4[pi][Delta]/[alpha]; the integral [int][f](z)dz round the perimeter
+  of the triangle is thus < 4[pi][eta][Delta]/[alpha]. Now consider any
+  region made up of triangles, as before explained, in each of which the
+  condition (z, z0) holds, as in the triangle just taken. The integral
+  [int][f](z)dz round the boundary of the region is equal to the sum of
+  the values of the integral round the component triangles, and thus
+  less in absolute value than 4[pi][eta]K/[alpha], where K is the whole
+  area of the region, and [alpha] is the smallest angle of the component
+  triangles. However small [eta] be taken, such a division of the region
+  into a finite number of component triangles has been shown possible;
+  the integral round the perimeter of the region is thus arbitrarily
+  small. Thus it is actually zero, which it was desired to prove. Two
+  remarks should be added: (1) The theorem is proved only on condition
+  that the closed path of integration belongs to the region at every
+  point of which the conditions are satisfied. (2) The theorem, though
+  proved only when the region consists of triangles, holds also when the
+  boundary points of the region consist of one or more closed paths, no
+  two of which meet.
+
+  Hence we can deduce the remarkable result that the value of [f](z) at
+  any interior point of a region is expressible in terms of the value of
+  [f](z) at the boundary points. For consider in the original region the
+  function [f](z)/(z - z0), where z0 is an interior point: this
+  satisfies the same conditions as [f](z) except in the immediate
+  neighbourhood of z0. Taking out then from the original region a small
+  regular polygonal region with z0 as centre, the theorem holds for the
+  remaining portion. Proceeding to the limit when the polygon becomes a
+  circle, it appears that the integral [int] dz[f](z)/(z - z0) round the
+  boundary of the original region is equal to the same integral taken
+  counter-clockwise round a small circle having z0 as centre; on this
+  circle, however, if z - z0 = rE(i[theta]), dz/(z - z0) = id[theta],
+  and [f](z) differs arbitrarily little from f(z0) if r is sufficiently
+  small; the value of the integral round this circle is therefore,
+  ultimately, when r vanishes, equal to 2[pi]i[f](z0). Hence [f](z0) = 1
+  / 2[pi]i [int] [dt[f](t)/(t - z0)], where this integral is round the
+  boundary of the original region. From this it appears that
+                                             _
+                 [f](z) - [f](z0)     1     /  dt[f](t)
+    F(z0) = lim. ---------------- = ------  | ---------
+                      z - z0        2[pi]i _/  (t-z0)^2
+
+  also round the boundary of the original region. This form shows,
+  however, that F(z0) is a continuous, finite, differentiable function
+  of z0 over the whole interior of the original region.
+
+S 5. _Applications._--The previous results have manifold applications.
+
+  (1) If an infinite series of differentiable functions of z be
+  uniformly convergent along a certain path lying with the region of
+  definition of the functions, so that S(2) = u0(z) + u1(z) + ... + u_(n
+  - 1)(z) + R_n(z), where |R_n(z)| < [epsilon] for all points of the
+  path, we have
+      _           _            _                  _                   _
+     /z          /z           /z                 /z                  /z
+     |  S(z)dz = |  u0(z)dz + |  u1(z)dz + ... + |  u_(n - 1)(z)dz + |  R_n(z)dz,
+    _/z0        _/z0         _/z0               _/z0                _/z0
+
+  wherein, in absolute value, [int](z_0 to z) R_n(z)dz < [epsilon]L, if
+  L be the length of the path. Thus the series may be integrated, and
+  the resulting series is also uniformly convergent.
+
+  (2) If [f](x, y) be definite, finite and continuous at every point of
+  a region, and over any closed path in the region [int][f](x, y)dz = 0,
+  then [psi](z) = [int](z_0 to z) [f](x, y)dz, for interior points z0,
+  z, is a differentiable function of z, having for its differential
+  coefficient the function [f](x, y), which is therefore also a
+  differentiable function of z at interior points.
+
+  (3) Hence if the series u0(z) + u1(z) + ... to [oo] be uniformly
+  convergent over a region, its terms being differentiable functions of
+  z, then its sum S(z) is a differentiable function of z, whose
+  differential coefficient, given by (1 / 2[pi]i) [int] (2[pi]i /
+  (t - z)^2), is obtainable by differentiating the series. This theorem,
+  unlike (1), does not hold for functions of a real variable.
+
+  (4) If the region of definition of a differentiable function [f](z)
+  include the region bounded by two concentric circles of radii r, R,
+  with centre at the origin, and z0 be an interior point of this region,
+                       _                     _
+                 1    /  [f](t)dt     1     / [f](t)dt
+    [f](z0) = ------  |  -------- - ------  | --------,
+              2[pi]i _/R  t - z0    2[pi]i _/r t - z0
+
+  where the integrals are both counter-clockwise round the two
+  circumferences respectively; putting in the first (t - z0)^(-1) =
+  [Sigma]_(n=0) z0^n/t^(n + 1), and in the second (t - z0)^(-1) =
+  [Sigma]_(n=0) t^n/z0^(n + 1), we find [f](z0) = [Sigma] (-[oo] to
+  [oo]) A_nz0^n, wherein A_n = (1 / 2[pi]i) [int] [f(t) / t^(n + 1)] dt,
+  taken round any circle, centre the origin, of radius intermediate
+  between r and R. Particular cases are: ([alpha]) when the region of
+  definition of the function includes the whole interior of the outer
+  circle; then we may take r = 0, the coefficients A_n for which n < 0
+  all vanish, and the function [f](z0) is expressed for the whole
+  interior |z0| < R by a power series [Sigma] (0 to [oo]) A_n z0^n. In
+  other words, _about every interior point c of the region of definition
+  a differentiable function of z is expressible by a power series in z -
+  c; a very important result.
+
+  ([beta]) If the region of definition, though not including the origin,
+  extends to within arbitrary nearness of this on all sides, and at the
+  same time the product z^m [f](z) has a finite limit when |z|
+  diminishes to zero, all the coefficients A_n for which n < -m vanish,
+  and we have
+
+    f(z0) = A_(-m) z0^(-m) + A_(-m + 1) z0^(-m + 1)
+      + ... + A_(-1) z0^(-1) + A0 + A1z0 ... to [oo].
+
+  Such a case occurs, for instance, when [f](z) = cosec z, the number m
+  being unity.
+
+S 6. _Singular Points._--The _region of existence_ of a differentiable
+function of z is an unclosed aggregate of points, each of which is an
+interior point of a neighbourhood consisting wholly of points of the
+aggregate, at every point of which the function is definite and finite
+and possesses a unique finite differential coefficient. Every point of
+the plane, not belonging to the aggregate, which is a limiting point of
+points of the aggregate, such, that is, that points of the aggregate lie
+in every neighbourhood of this, is called a _singular point_ of the
+function.
+
+  About every interior point z0 of the region of existence the function
+  may be represented by a power series in z-z0, and the series converges
+  and represents the function over any circle centre at z0 which
+  contains no singular point in its interior. This has been proved
+  above. And it can be similarly proved, putting z = 1/[zeta], that if
+  the region of existence of the function contains all points of the
+  plane for which |z| > R, then the function is representable for all
+  such points by a power series in z^(-1) or [zeta]; in such case we say
+  that the region of existence of the function contains the point z =
+  [oo]. A series in z^(-1) has a finite limit when |z| = [oo]; a series
+  in z cannot remain finite for all points z for which |z| > R; for if,
+  for |z| = R, the sum of a power series [Sigma]a_n z^n in z is in
+  absolute value less than M, we have |a_n| < Mr(-n), and therefore, if
+  M remains finite for all values of r however great, a_n = 0. Thus the
+  region of existence of a function if it contains all finite points of
+  the plane cannot contain the point z = [oo]; such is, for instance,
+  the case of the function exp (z) = [Sigma]z^n/n!. This may be regarded
+  as a particular case of a well-known result (S 7), that the
+  circumference of convergence of any power series representing the
+  function contains at least one singular point. As an extreme case
+  functions exist whose region of existence is circular, there being a
+  singular point in every arc of the circumference, however small; for
+  instance, this is the case for the functions represented for |z| < 1
+  by the series [Sigma]_(n=0) z^m, where m = n^2, the series
+  [Sigma]_(n=0) z^m where m = n!, and the series [Sigma](n=1 to 0)
+  z^m/(m + 1)(m + 2) where m = a^n, a being a positive integer, although
+  in the last case the series actually converges for every point of the
+  circle of convergence |z| = 1. If z be a point interior to the circle
+  of convergence of a series representing the function, the series may
+  be rearranged in powers of z - z0; as z0 approaches to a singular
+  point of the function, lying on the circle of convergence, the radii
+  of convergence of these derived series in z - z0 diminish to zero;
+  when, however, a circle can be put about z0, not containing any
+  singular point of the function, but containing points outside the
+  circle of convergence of the original series, then the series in z -
+  z0 gives the value of the function for these external points. If the
+  function be supposed to be given only for the interior of the original
+  circle, by the original power series, the series in z - z0 converging
+  beyond the original circle gives what is known as an _analytical
+  continuation_ of the function. It appears from what has been proved
+  that the value of the function at all points of its region of
+  existence can be obtained from its value, supposed given by a series
+  in one original circle, by a succession of such processes of
+  analytical continuation.
+
+S 7. _Monogenic Functions._--This suggests an entirely different way of
+formulating the fundamental parts of the theory of functions of a
+complex variable, which appears to be preferable to that so far followed
+here.
+
+  Starting with a convergent power series, say in powers of z, this
+  series can be arranged in powers of z - z0, about any point z0
+  interior to its circle of convergence, and the new series converges
+  certainly for |z - z0| < r - |z0|, if r be the original radius of
+  convergence. If for every position of z0 this is the greatest radius
+  of convergence of the derived series, then the original series
+  represents a function existing only within its circle of convergence.
+  If for some position of z0 the derived series converges for |z - z0| <
+  r - |z0| + D, then it can be shown that for points z, interior to the
+  original circle, lying in the annulus r - |z0| < |z - z0| < r - |z0| +
+  D, the value represented by the derived series agrees with that
+  represented by the original series. If for another point z1 interior
+  to the original circle the derived series converges for |z - z1| < r -
+  |z1| + E, and the two circles |z - z0| = r - |z0| + D, |z - z1| = r -
+  |z1| + E have interior points common, lying beyond |z| = r, then it
+  can be shown that the values represented by these series at these
+  common points agree. Either series then can be used to furnish an
+  analytical continuation of the function as originally defined.
+  Continuing this process of continuation as far as possible, we arrive
+  at the conception of the function as defined by an aggregate of power
+  series of which every one has points of convergence common with some
+  one or more others; the whole aggregate of points of the plane which
+  can be so reached constitutes the region of existence of the function;
+  the limiting points of this region are the points in whose
+  neighbourhood the derived series have radii of convergence diminishing
+  indefinitely to zero; these are the singular points. The circle of
+  convergence of any of the series has at least one such singular point
+  upon its circumference. So regarded the function is called a
+  _monogenic_ function, the epithet having reference to the single
+  origin, by one power series, of the expressions representing the
+  function; it is also sometimes called a _monogenic analytical_
+  function, or simply an _analytical_ function; all that is necessary to
+  define it is the value of the function and of all its differential
+  coefficients, at some one point of the plane; in the method previously
+  followed here it was necessary to suppose the function differentiable
+  at every point of its region of existence. The theory of the
+  integration of a monogenic function, and Cauchy's theorem, that
+  [int][f](z)dz = 0 over a closed path, are at once deducible from the
+  corresponding results applied to a single power series for the
+  interior of its circle of convergence. There is another advantage
+  belonging to the theory of monogenic functions: the theory as
+  originally given here applies in the first instance only to single
+  valued functions; a monogenic function is by no means necessarily
+  single valued--it may quite well happen that starting from a
+  particular power series, converging over a certain circle, and
+  applying the process of analytical continuation over a closed path
+  back to an interior point of this circle, the value obtained does not
+  agree with the initial value. The notion of basing the theory of
+  functions on the theory of power series is, after Newton, largely due
+  to Lagrange, who has some interesting remarks in this regard at the
+  beginning of his _Theorie des fonctions analytiques_. He applies the
+  idea, however, primarily to functions of a real variable for which the
+  expression by power series is only of very limited validity; for
+  functions of a complex variable probably the systematization of the
+  theory owes most to Weierstrass, whose use of the word monogenic is
+  that adopted above. In what follows we generally suppose this point of
+  view to be regarded as fundamental.
+
+S 8. _Some Elementary Properties of Single Valued Functions._--A _pole_
+is a singular point of the function [f](z) which is not a singularity of
+the function 1/[f](z); this latter function is therefore, by the
+definition, capable of representation about this point, z0, by a series
+[[f](z)]^(-1 ) = [Sigma]a_n (z - z0)^n. If herein a0 is not zero we can
+hence derive a representation for [f](z) as a power series about z0,
+contrary to the hypothesis that z0 is a singular point for this
+function. Hence a0 = 0; suppose also a1 = 0, a2 = 0, ... a_(m - 1) = 0,
+but a_m [+-] 0. Then [[f](z)]^(-1) = (z - z0)^m [a_m + a_(m + 1)(z - z0)
++ ...], and hence (z - z0)^m [f](z) = a_m^(-1) + [Sigma]b_n (z - z0)^n,
+namely, the expression of [f](z) about z = z0 contains a finite number
+of negative powers of z - z0 and a (finite or) infinite number of
+positive powers. Thus a pole is always an isolated singularity.
+
+  The integral [int][f](z)dz taken by a closed circuit about the pole
+  not containing any other singularity is at once seen to be 2[pi]iA1,
+  where A1 is the coefficient of (z - z0)^(-1) in the expansion of
+  [f](z) at the pole; this coefficient has therefore a certain
+  uniqueness, and it is called the _residue of [f](z) at the pole_.
+  Considering a region in which there are no other singularities than
+  poles, all these being interior points, _the integral (1 / 2[pi]i)
+  [int][f](z)dz round the boundary of this region is equal to the sum
+  of the residues at the included poles_, a very important result. Any
+  singular point of a function which is not a pole is called an
+  _essential singularity_; if it be isolated the function is capable, in
+  the neighbourhood of this point, of approaching arbitrarily near to
+  any assigned value. For, the point being isolated, the function can be
+  represented, in its neighbourhood, as we have proved, by a series
+  [Sigma] (-[oo] to [oo]) a_n(z - z0)^n; it thus cannot remain finite in
+  the immediate neighbourhood of the point. The point is necessarily an
+  isolated essential singularity also of the function {[f](z) - A}^(-1)
+  for if this were expressible by a power series about the point, so
+  would also the function [f](z) be; as {[f](z) - A}^(-1) approaches
+  infinity, so does [f](z) approach the arbitrary value A. Similar
+  remarks apply to the point z = [oo], the function being regarded as a
+  function of [zeta] = z^(-1). In the neighbourhood of an essential
+  singularity, which is a limiting point also of poles, the function
+  clearly becomes infinite. For an essential singularity which is not
+  isolated the same result does not necessarily hold.
+
+A single valued function is said to be an _integral_ function when it
+has no singular points except z = [oo]. Such is, for instance, an
+integral polynomial, which has z = [oo] for a pole, and the functions
+exp (z) which has z = [oo] as an essential singularity. A function which
+has no singular points for finite values of z other than poles is called
+a _meromorphic_ function. If it also have a pole at z = [oo] it is a
+_rational_ function; for then, if a1, ... a_s be its finite poles, of
+orders m1; m2, ... m_s, the product (z - a1)^m1 ... (z - a_s)^m_s[f](z)
+is an integral function with a pole at infinity, capable therefore, for
+large values of z, of an expression (z^ - 1)^(-m) [Sigma]_(r=0) a_r(z^ -
+1)^r; thus (z - a1)^m1 ... (z - a_s)^m_s[f](z) is capable of a form
+[Sigma]_(r=0) b_r z^r, but z^(-m) [Sigma]_(r=0) b_r z^r remains finite
+for z = [oo]. Therefore b_(r + 1) = b_(r + 2) = ... = 0, and[f](z) is a
+rational function.
+
+  If for a single valued function F(z) every singular point in the
+  finite part of the plane is isolated there can only be a finite number
+  of these in any finite part of the plane, and they can be taken to be
+  a1, a2, a3, ... with |a1| [=<] |a2| [=<] |a3| ... and limit |a_n| =
+  [oo]. About a_s the function is expressible as [Sigma] (-[oo] to [oo])
+  A_n(z - a_s)^n; let [f]_s(z) = [Sigma] (-[oo] to 1) A^n(z - a_s)^n be
+  the sum of the negative powers in this expansion. Assuming z = 0 not
+  to be a singular point, let [f]_s(z) be expanded in powers of z, in
+  the form [Sigma]_(n=0) C_n z^n, and [mu]_s be chosen so that F_s(z) =
+  [f]_s(z) - [Sigma] (1 to [mu]_s-1) C_nz^n = [Sigma] ([mu]_s to [oo])
+  C_n z^n is, for |z| < r_s < |a_s|, less in absolute value than the
+  general term [epsilon]_s of a fore-agreed convergent series of real
+  positive terms. Then the series [phi](z) = [Sigma] (s=1 to [oo])
+  F_s(z) converges uniformly in any finite region of the plane, other
+  than at the points a_s, and is expressible about any point by a power
+  series, and near a_s, [phi](z) - f_s(z) is expressible by a power
+  series in z-a_s. Thus F(z) - [phi](z) is an integral function. In
+  particular when all the finite singularities of F(z) are poles, F(z)
+  is hereby expressed as the sum of an integral function and a series of
+  rational functions. The condition |F_s(z)| < [epsilon]_s is imposed
+  only to render the series [Sigma]F_s(z) uniformly convergent; this
+  condition may in particular cases be satisfied by a series [Sigma]
+  G_s(z) where G_s(z) = [f]_s(z) - [Sigma] (1 to [nu]_s-1) C_nz^n and
+  [nu]_s < [mu]_s. An example of the theorem is the function [pi] cot
+  [pi]z - z^(-1) for which, taking at first only half the poles,
+  [f]_s(z) = 1/(z-s); in this case the series [Sigma]F_s(z) where F_s(z)
+  = (z - s)^-1 + s^-1 is uniformly convergent; thus [pi]cot[pi]z - z^-1
+  - [Sigma] (-[oo] to [oo]) [(z - s)^-1 + s^-1], where s = 0 is excluded
+  from the summation, is an integral function. It can be proved that
+  this integral function vanishes.
+
+  Considering an integral function [f](z), if there be no finite
+  positions of z for which this function vanishes, the function
+  [lambda][[f](z)] is at once seen to be an integral function, [phi](z),
+  or [f](z) = exp[[phi](z)]; if however great R may be there be only a
+  finite number of values of z for which [f](z) vanishes, say z = a1,
+  ... a_m, then it is at once seen that [f](z) = exp [[phi](z)].(z -
+  a1)^h1...(z - a_m)^h_m, where [phi](z) is an integral function, and
+  h1, ... h_m are positive integers. If, however, [f](z) vanish for z =
+  a1, a2 ... where |a1| [=<] |a2| [=<] ... and limit |a_n| = [oo], and
+  if for simplicity we assume that z - 0 is not a zero and all the zeros
+  a1, a2, ... are of the first order, we find, by applying the preceding
+  theorem to the function (1 / [f](z)) (d[f](z) / dz), that [f](z) =
+  exp[[phi](z)] [Pi] (n=1 to [oo]) {(1 - z/a_n) exp[phi]_n(z)}, where
+  [phi](z) is an integral function, and [phi]_n(z) is an integral
+  polynomial of the form
+
+                  z      z^2            z^s
+    [phi]_n(z) = --- + ------ + ... + ------.
+                 a_n   2a^2_n         sa_n^s
+
+  The number s may be the same for all values of n, or it may increase
+  indefinitely with n; it is sufficient in any case to take s = n. In
+  particular for the function sin[pi]x / [pi]x, we have
+                         _                      _
+    sin[pi]x      [oo]  |  /    x \       / x \  |
+    -------- = [Pi]     | ( 1 - -- ) exp (  -- ) |,
+     [pi]x       -[oo]  |_ \    n /       \ n / _|
+
+  where n = 0 is excluded from the product. Or again we have
+                                 _                       _
+        1                  [oo] |  /    x \       /  x \  |
+    ---------- = xe^C_x [Pi]    | ( 1 - -- ) exp ( - -- ) |,
+    [Gamma](x)             n=1  |_ \    n /       \  n / _|
+
+  where C is a constant, and [Gamma](x) is a function expressible when x
+  is real and positive by the integral [int] (0 to [oo])
+  e^(-t) t^(x - 1)dt.
+
+  There exist interesting investigations as to the connexion of the
+  value of s above, the law of increase of the modulus of the integral
+  function [f](z), and the law of increase of the coefficients in the
+  series [f](z) = [Sigma] a_n z^n as n increases (see the bibliography
+  below under _Integral Functions_). It can be shown, moreover, that an
+  integral function actually assumes every finite complex value, save,
+  in exceptional cases, one value at most. For instance, the function
+  exp (z) assumes every finite value except zero (see below under S 21,
+  _Modular Functions_).
+
+The two theorems given above, the one, known as Mittag-Leffler's
+theorem, relating to the expression as a sum of simpler functions of a
+function whose singular points have the point z = [oo] as their only
+limiting point, the other, Weierstrass's factor theorem, giving the
+expression of an integral function as a product of factors each with
+only one zero in the finite part of the plane, may be respectively
+generalized as follows:--
+
+  I. If a1, a2, a3, ... be an infinite series of isolated points having
+  the points of the aggregate (c) as their limiting points, so that in
+  any neighbourhood of a point of (c) there exists an infinite number of
+  the points a1, a2, ..., and with every point a_i there be associated a
+  polynomial in (z - a_i)^-1, say g_i; then there exists a single valued
+  function whose region of existence excludes only the points (a) and
+  the points (c), having in a point a_i a pole whereat the expansion
+  consists of the terms g_i, together with a power series in z - a_i;
+  the function is expressible as an infinite series of terms g_i -
+  [gamma]_i, where [gamma]_i is also a rational function.
+
+  II. With a similar aggregate (a), with limiting points (c), suppose
+  with every point a_i there is associated a positive integer r_i. Then
+  there exists a single valued function whose region of existence
+  excludes only the points (c), vanishing to order r_i at the point a_i,
+  but not elsewhere, expressible in the form
+
+       [oo] /    a_n - c_n \^r_n
+    [Pi]   ( 1 - ---------  )    exp(g_n),
+       n=1  \     z - c_n  /
+
+  where with every point a_n is associated a proper point c_n of (c),
+  and
+
+                _[mu]_n
+               \       1  / a_n - c_n \^s
+    g_n = r_n  /_     -- (  ---------  ),
+                 s=1   s  \  z - c_n  /
+
+  [mu]_n being a properly chosen positive integer.
+
+  If it should happen that the points (c) determine a path dividing the
+  plane into separated regions, as, for instance, if a_n = R(1 - n^-1)
+  exp(i[pi] [root]2.n), when (c) consists of the points of the circle
+  |z| = R, the product expression above denotes different monogenic
+  functions in the different regions, not continuable into one another.
+
+S 9. _Construction of a Monogenic Function with a given Region of
+Existence._--A series of isolated points interior to a given region can
+be constructed in infinitely many ways whose limiting points are the
+boundary points of the region, or are boundary points of the region of
+such denseness that one of them is found in the neighbourhood of every
+point of the boundary, however small. Then the application of the last
+enunciated theorem gives rise to a function having no singularities in
+the interior of the region, but having a singularity in a boundary point
+in every small neighbourhood of every boundary point; this function has
+the given region as region of existence.
+
+S 10. _Expression of a Monogenic Function by means of Rational Functions
+in a given Region._--Suppose that we have a region R0 of the plane, as
+previously explained, for all the interior or boundary points of which z
+is finite, and let its boundary points, consisting of one or more closed
+polygonal paths, no two of which have a point in common, be called C0.
+Further suppose that all the points of this region, including the
+boundary points, are interior points of another region R, whose boundary
+is denoted by C. Let z be restricted to be within or upon the boundary
+of C0; let a, b, ... be finite points upon C or outside R. Then when b
+is near enough to a, the fraction (a - b)/(z - b) is arbitrarily small
+for all positions of z; say
+
+  | a - b |
+  | ----- | < [epsilon], for |a - b| < [eta];
+  | z - b |
+
+the rational function of the complex variable t,
+         _                _
+    1   |     / a - b \^n  |
+  ----- |1 - (  -----  )   |,
+  t - a |_    \ t - b /   _|
+
+in which n is a positive integer, is not infinite at t = a, but has a
+pole at t = b. By taking n large enough, the value of this function, for
+all positions z of t belonging to R0, differs as little as may be
+desired from (t - a)^-1. By taking a sum of terms such as
+
+       _              _               _
+      \      {   1   |     / a - b \^n | }^p
+  F = /_ A_p { ----- |1 - (  -----  )  | },
+             { t - a |_    \ t - b /  _| }
+
+we can thus build a rational function differing, in value, in R0, as
+little as may be desired from a given rational function
+         _
+        \
+  [f] = /_ A_p (t - a)^(-p),
+
+and differing, outside R or upon the boundary of R, from [f], in the
+fact that while [f] is infinite at t = a, F is infinite only at t = b.
+By a succession of steps of this kind we thus have the theorem that,
+given a rational function of t whose poles are outside R or upon the
+boundary of R, and an arbitrary point c outside R or upon the boundary
+of R, which can be reached by a finite continuous path outside R from
+all the poles of the rational function, we can build another rational
+function differing in R0 arbitrarily little from the former, whose poles
+are all at the point c.
+
+  Now any monogenic function [f](t) whose region of definition includes
+  C and the interior of R can be represented at all points z in R[0] by
+                      _
+               1     /  [f](t)dt
+    [f](z) = ------  |  --------,
+             2[pi]i _/   t - z
+
+  where the path of integration is C. This integral is the limit of a
+  sum
+                _
+          1    \  [f](t_i) (t_(i + 1) - t_i)
+    S = ------ /_ --------------------------,
+        2[pi]i             t_i - z
+
+  where the points t_i are upon C; and the proof we have given of the
+  existence of the limit shows that the sum S converges to [f](z)
+  uniformly in regard to z, when z is in R0, so that we can suppose,
+  when the subdivision of C into intervals t_(i + 1) - t_i, has been
+  carried sufficiently far, that
+
+    | S - [f](z) | < [epsilon],
+
+  for all points z of R0, where [epsilon] is arbitrary and agreed upon
+  beforehand. The function S is, however, a rational function of z with
+  poles upon C, that is external to R0. We can thus find a rational
+  function differing arbitrarily little from S, and therefore
+  arbitrarily little from [f](z), for all points z of R0, with poles at
+  arbitrary positions outside R0 which can be reached by finite
+  continuous curves lying outside R from the points of C.
+
+  In particular, to take the simplest case, if C0, C be simple closed
+  polygons, and [GAMMA] be a path to which C approximates by taking the
+  number of sides of C continually greater, we can find a rational
+  function differing arbitrarily little from [f](z) for all points of R0
+  whose poles are at one finite point c external to [GAMMA]. By a
+  transformation of the form t - c = r^-1, with the appropriate change
+  in the rational function, we can suppose this point c to be at
+  infinity, in which case the rational function becomes a polynomial.
+  Suppose [epsilon]1, [epsilon]2, ... to be an indefinitely continued
+  sequence of real positive numbers, converging to zero, and P_r to be
+  the polynomial such that, within C0, |P_r - [f](z)| < [epsilon]_r;
+  then the infinite series of polynomials
+
+    P1(z) + {P2(z) - P1(z)} + {P3(z) - P2(z)} + ...,
+
+  whose sum to n terms is P_n(z), converges for all finite values of z
+  and represents [f](z) within C0.
+
+  When C consists of a series of disconnected polygons, some of which
+  may include others, and, by increasing indefinitely the number of
+  sides of the polygons C, the points C become the boundary points
+  [Gamma] of a region, we can suppose the poles of the rational
+  function, constructed to approximate to [f](z) within R0, to be at
+  points of [Gamma]. A series of rational functions of the form
+
+    H1(z) + {H2(z) - H1(z)} + {H3(z) - H2(z)} + ...
+
+  then, as before, represents [f](z) within R0. And R0 may be taken to
+  coincide as nearly as desired with the interior of the region bounded
+  by [Gamma].
+
+S 11. _Expression of (1 - z)^(-1) by means of Polynomials.
+Applications._--We pursue the ideas just cursorily explained in some
+further detail.
+
+  Let c be an arbitrary real positive quantity; putting the complex
+  variable [zeta] = [xi] + i[eta], enclose the points [zeta] = l, [zeta]
+  = 1 + c by means of (i.) the straight lines [eta] = [+-]a, from [xi] =
+  l to [xi] = 1 + c, (ii.) a semicircle convex to [zeta] = 0 of equation
+  ([xi] - 1)^2 + [eta]^2 = a^2, (iii.) a semicircle concave to [zeta] =
+  0 of equation ([xi] - 1 - c)^2 + [eta]^2 = a^2. The quantities c and a
+  are to remain fixed. Take a positive integer r so that 1/r (c/a) is
+  less than unity, and put [sigma] = 1/r (c/a). Now take
+
+    c1 = 1 + c/r, c2 = 1 + 2c/r, ... c_r = 1 + c;
+
+  if n1, n2, ... n_r, be positive integers, the rational function
+                _                      _
+        1      |     /    c1 - 1   \^n1 |
+    ---------- |1 - (  -----------  )   |
+    1 - [zeta] |_    \ c1 - [zeta] /   _|
+
+  is finite at [zeta] = 1, and has a pole of order n1 at [zeta] = c1;
+  the rational function
+                _                      _   _                     _
+         1     |     /    c1 - 1   \^n1 | |     /   c2 - c1  \^n2 |^n1
+    ---------- |1 - (  ------------ )   | |1 - (  ----------- )   |
+    1 - [zeta] |_    \ c1 - [zeta] /   _| |_    \ c2 - [zeta]/   _|
+
+  is thus finite except for [zeta] = c2, where it has a pole of order
+  n1n2; finally, writing
+
+           / c_s - c_(s-1) \^n_s
+    x_s = (  -------------  ),
+           \ c_s - [zeta]  /
+
+  the rational function
+
+    U = (1 - [zeta])^(-1) (1 - x1)(1 - x2)^n1 (1 - x3)^n1n2 ...
+      (1 - x_r)^(n1n2 ... n_(r - 1))
+
+  has a pole only at [zeta] = 1 + c, of order n1n2 ... n_r.
+
+  The difference (1 - [zeta])^(-1) - U is of the form (1 -
+  [zeta])^(-1)P, where P, of the form
+
+    1 - (1 - [rho]1)(1 - [rho]2)...(1 - [rho]_k),
+
+  in which there are equalities among [rho]1, [rho]2, ... [rho]_k, is of
+  the form
+
+    [Sigma][rho]1 - [Sigma][rho]1[rho]2 + [Sigma][rho]1[rho]2[rho]3 - ...;
+
+  therefore, if |r_i| = |[rho]_i|, we have
+
+    |P| < [Sigma]r1 + [Sigma]r1r2 + [Sigma]r1r2r3 + ... <
+      (1 + r1)(1 + r2)...(1 + r_k) - 1;
+
+  now, so long as [zeta] is without the closed curve above described
+  round [zeta] = 1, [zeta] = 1 + c, we have
+
+    |     1    |    1    |c_m - c_(m-1)|   c/r
+    |----------| < ---,  |-------------| < --- < [sigma],
+    |1 - [zeta]|    a    |c_m - [zeta] |    a
+
+  and hence
+
+    |(1 - [zeta])^(-1) - U| < a^(-1) {(1 + [sigma]^n1) (1 + [sigma]^n2)^n1
+      (1 + [sigma]^n3)^n1n2 ... (1 + [sigma]^n_r)^(n1n2 ... n_(r-1)) - 1}.
+
+  Take an arbitrary real positive [epsilon], and [mu], a positive
+  number, so that [epsilon]^[mu] - 1 < [epsilon]a, then a value of n1
+  such that [sigma]^n1 < [mu]/(1 + [mu]) and therefore [sigma]^n1 / (1 -
+  [sigma]^n1 < [mu], and values for n2, n3 ... such that[sigma]^n2 <
+  1/n1 [sigma]^2n1, [sigma]^n3 < 1/n1n2 [sigma]^{3n1, ... [sigma]^n_r} <
+  1/(n1...n_(r - 1)} [sigma]^n_rn1; then, as 1 + x < e^x, we have
+  |(-[zeta])^(-1) - U| < a^-1 {exp([sigma]^n1 + n1[sigma]^n2 +
+  n1n2[sigma]^n3 + ... + n1n2...n_(r - 1)[sigma]^n_r) - 1}, and
+  therefore less than
+
+    a^(-1) {exp([sigma]^n1 + [sigma]^2n1 + ... + [sigma]^n_rn1) - 1},
+
+  which is less than
+        _                         _
+    1  |     /  [sigma]^n1  \      |
+    -- |exp ( -------------- ) - 1 |
+    a  |_    \1 - [sigma]^n1/     _|
+
+  and therefore less than [epsilon].
+
+  The rational function U, with a pole at [zeta] = 1 + c, differs
+  therefore from (1 - [zeta])^(-1), for all points outside the closed
+  region put about [zeta] = 1, [zeta] = l + c, by a quantity numerically
+  less than [epsilon]. So long as a remains the same, r and [sigma] will
+  remain the same, and a less value of [epsilon] will require at most an
+  increase of the numbers n1, n2, ... n_r; but if a be taken smaller it
+  may be necessary to increase r, and with this the complexity of the
+  function U.
+
+  Now put
+
+            c[zeta]               (c + 1)z
+    z = --------------,  [zeta] = --------;
+        c + 1 - [zeta]              c + z
+
+  thereby the points [zeta] = 0, 1, 1 + c become the points z = 0, 1,
+  [oo], the function (1 - z)^(-1) being given by (1-z)^(-1) = c(c +
+  1)^(-1)(1 - [zeta])^(-1) + (c + 1)^(-1); the function U becomes a
+  rational function of z with a pole only at z = [oo], that is, it
+  becomes a polynomial in z, say [(c + 1)/c]H - 1/c, where H is also a
+  polynomial in z, and
+                       _              _
+      1           c   |      1         |
+    ----- - H = ----- | ---------- - U |;
+    1 - z       c + 1 |_1 + [zeta]    _|
+
+  the lines [eta] = [+-]a become the two circles expressed, if z = x +
+  iy, by
+
+                           c(c + 1)
+    (x + c)^2 + y^2 = [+-] -------- y,
+                               a
+
+  the points ([eta] = 0, [xi] = 1 - a), ([eta] = 0, [xi] = 1 + c + a)
+  become respectively the points (y = 0, x = c(1 - a)/(c + a), (y = 0, x
+  = -c(l + c + a)/a), whose limiting positions for a = 0 are
+  respectively (y = 0, x = 1), (y = 0, x = -[oo]). The circle (x + c)^2 +
+  y^2 = c(c + 1)y/a can be written
+
+        (x + c)^2   (x + c)^4
+    y = --------- + --------- {[mu] + [root][[mu]^2 - (x + c)^2]}^(-2),
+          2[mu]       2[mu]
+
+  where [mu] = 1/2c(c + 1)/a; its ordinate y, for a given value of x,
+  can therefore be supposed arbitrarily small by taking a sufficiently
+  small.
+
+  We have thus proved the following result; taking in the plane of z any
+  finite region of which every interior and boundary point is at a
+  finite distance, however short, from the points of the real axis for
+  which 1 =< x =< [oo], we can take a quantity a, and hence, with an
+  arbitrary c, determine a number r; then corresponding to an arbitrary
+  [epsilon]_s, we can determine a polynomial P_s, such that, for all
+  points interior to the region, we have
+
+    |(1 - z^(-1)) - P_s| < [epsilon]_s;
+
+  thus the series of polynomials
+
+    P1 + (P2 - P1) + (P3 - P2) + ...,
+
+  constructed with an arbitrary aggregate of real positive numbers
+  [epsilon]1, [epsilon]2, [epsilon]3, ... with zero as their limit,
+  converges uniformly and represents (1-z)^(-1) for the whole region
+  considered.
+
+  S 12. _Expansion of a Monogenic Function in Polynomials, over a Star
+  Region._--Now consider any monogenic function [f](z) of which the
+  origin is not a singular point; joining the origin to any singular
+  point by a straight line, let the part of this straight line, produced
+  beyond the singular point, lying between the singular point and z =
+  [oo], be regarded as a barrier in the plane, the portion of this
+  straight line from the origin to the singular point being erased.
+  Consider next any finite region of the plane, whose boundary points
+  constitute a path of integration, in a sense previously explained, of
+  which every point is at a finite distance greater than zero from each
+  of the barriers before explained; we suppose this region to be such
+  that any line joining the origin to a boundary point, when produced,
+  does not meet the boundary again. For every point x in this region R
+  we can then write
+                    _
+                   /  dt     [f](t)
+    2[pi]i[f](x) = |  --  -----------,
+                  _/   t  1 - xt^(-1)
+
+  where [f](x) represents a monogenic branch of the function, in case it
+  be not everywhere single valued, and t is on the boundary of the
+  region. Describe now another region R0 lying entirely within R, and
+  let x be restricted to be within R0 or upon its boundary; then for any
+  point t on the boundary of R, the points z of the plane for which
+  zt^(-1) is real and positive and equal to or greater than 1, being
+  points for which |z| = |t| or |z| > |t|, are without the region R0,
+  and not infinitely near to its boundary points. Taking then an
+  arbitrary real positive [epsilon] we can determine a polynomial in
+  xt^(-1), say P(xt^(-1)), such that for all points x in R0 we have
+
+    |[1 - xt^(-1)]^(-1) - P[xt^(-1)]| < [epsilon];
+
+  the form of this polynomial may be taken the same for all points t on
+  the boundary of R, and hence, if E be a proper variable quantity of
+  modulus not greater than [epsilon],
+                     _                          _
+    |               / dt                |   |  / dt       |
+    |2[pi]i[f](x) - | --[f](t)P(xt^(-1))| = |  | --[f](t)E| <= [epsilon]LM,
+    |              _/  t                |   | _/  t       |
+
+  where L is the length of the path of integration, the boundary of R,
+  and M is a real positive quantity such that upon this boundary
+  |t^(-1)[f](t)| < M. If now
+
+    P(xt^(-1)) = c0 + c1xt^(-1) + ... + c_mx^mt^(-m),
+
+  and
+             _
+      1     /
+    ------  | t^(-r-1)[f](t)dt = [mu]_r,
+    2[pi]i _/
+
+  this gives
+
+    |[f](x) - {c0[mu]0 + c1[mu]1x + ... + c_m[mu]_mx^m}| =< [epsilon]LM/2[pi],
+
+  where the quantities [mu]0, [mu]1, [mu]2, ... are the coefficients in
+  the expansion of [f](x) about the origin.
+
+  If then an arbitrary finite region be constructed of the kind
+  explained, excluding the barriers joining the singular points of
+  [f](x) to x = [oo], it is possible, corresponding to an arbitrary real
+  positive number [sigma], to determine a number m, and a polynomial
+  Q(x), of order m, such that for all interior points of this region
+
+    |[f](x) - Q(x)| < [sigma].
+
+  Hence as before, within this region [f](x) can be represented by a
+  series of polynomials, converging uniformly; when [f](x) is not a
+  single valued function the series represents one branch of the
+  function.
+
+  The same result can be obtained without the use of Cauchy's integral.
+  We explain briefly the character of the proof. If a monogenic function
+  of t, [phi](t) be capable of expression as a power series in t-x about
+  a point x, for |t - x| =< [rho], and for all points of this circle
+  |[phi](t)| < g, we know that |[phi]^(n)(x)| < g[rho]^(-n)(n!). Hence,
+  taking |z| < 1/3[rho], and, for any assigned positive integer [mu],
+  taking m so that for n > m we have ([mu] + n)^[mu] < (3/2)^n, we have
+
+    |[phi]^(([mu] + n))(x)z^n|   [phi]^([mu] + n)(x)
+    |------------------------| < -------------------([mu] + n)^([mu])|z|^n
+    |           n!           |       ([mu] + n)!
+
+               g          /3 \     /[rho]\            g
+      < ---------------- ( -- )^n ( ----- )^n < --------------,
+        [rho]^([mu] + n)  \2 /     \  3  /      [rho]^[mu] 2^n
+
+  and therefore
+
+                           _m
+                          \   [phi]^([mu] + n)(x)
+    [phi]^([mu])(x + z) = /_  ------------------- z^n + [epsilon]_[mu],
+                            n=0         n!
+
+  where
+
+                             g        _[oo]  1          g
+    |[epsilon]_([mu])| < ----------  \      --- < --------------
+                         [rho]^[mu]  /_     2^n   [rho]^[mu] 2^m
+                                       n=m+1
+
+  Now draw barriers as before, directed from the origin, joining the
+  singular point of [phi](z) to z = [oo], take a finite region excluding
+  all these barriers, let [rho] be a quantity less than the radii of
+  convergence of all the power series developments of [phi](z) about
+  interior points of this region, so chosen moreover that no circle of
+  radius [rho] with centre at an interior point of the region includes
+  any singular point of [phi](z), let g be such that |[phi](z)| < g for
+  all circles of radius [rho] whose centres are interior points of the
+  region, and, x being any interior point of the region, choose the
+  positive integer n so that 1/n |x| 1/3 - [rho]; then take the points
+  a1 = x/n, a2 = 2x/n, a3 = 3x/n, ... a_n = x; it is supposed that the
+  region is so taken that, whatever x may be, all these are interior
+  points of the region. Then by what has been said, replacing x, z
+  respectively by 0 and x/n, we have
+
+                            _m1   [phi]^([mu] + [lambda]1)(0)  /x \^[lambda]1
+    [phi]^([mu])  (a{1}) = \      --------------------------- ( -- ) + [alpha]_[mu]
+                           /_              [lambda]{1}!        \n /
+                     [lambda]1=0
+
+  with
+
+    |[alpha]{[mu]}| < g/[rho]^[mu] 2^m1,
+
+  provided ([mu] + m1 + 1)^[mu] < (3/2)^(m1+1); in fact for [mu] =<
+  2n^(2n-2) it is sufficient to take m1 = n^2n; by another application
+  of the same inequality, replacing x, z respectively by a1 and x/n, we
+  have
+
+                         _ m2   [phi]^([mu]+[lambda]2)(a1)  /x \^[lambda]2
+    [phi]^([mu])(a2) =  \       -------------------------- ( -- )   + [beta]'_[mu],
+                        /_              [lambda]{2}!        \n /
+                  [lambda]2=0
+
+  where
+
+    |[beta]'[mu]| < g/[rho]^[mu] 2^m2
+
+  provided ([mu] + m2 + 1)^[mu] < {3/2}^(m2 + 1); we take m2 = n^(2n -
+  2), supposing [mu] < 2^(2n - 4). So long as [lambda]2 =< = m} =< n^(2n
+  - 2) and [mu] < 2n^(2n - 4) we have [mu] + [lambda]{2} < 2n^(2n - 2),
+  and we can use the previous inequality to substitute here for
+  [phi]^([mu] + [lambda]2) (a1). When this is done we find
+
+                         _ m2         _ m1 [phi]^([mu] + [lambda]1 + [lambda]2)(0)
+    [phi]^([mu])(a2) =  \            \     ---------------------------------------
+                        /_           /_             [lambda]1! [lambda]2!
+                   [lambda]2=0  [lambda]1=0
+
+       /x \ ^[lambda]1 + [lambda]2
+      ( -- )                       + [beta]_[mu],
+       \n /
+
+  where |[beta]_[mu]| < 2g/[rho]^[mu] 2^(m2), the numbers m1, m2 being
+  respectively n^2n and n^(2n - 2).
+
+  Applying then the original inequality to [phi]^([mu]) (a3) =
+  [phi]^([mu]) (a2 + x/n), and then using the series just obtained, we
+  find a series for [phi]^([mu]) (a3). This process being continued, we
+  finally obtain
+
+                _ m1        _ m2           _ m_n
+    [phi](x) = \            \       ...   \         [phi]^(h)(0) /x \^h
+               /_           /_            /_        ----------- ( -- ) + [epsilon],
+         [lambda]1=0  [lambda]2=0   [lambda]_n=0         K       \n /
+
+  where h = [lambda]1 + [lambda]2 + ... + [lambda]_n , K = [lambda]1!
+  [lambda]2! ... [lambda]_n!, m1 = n^(2n), m1 = n^(2n - 2), ... , m1 =
+  n^2, |[epsilon]| < 2g/2^(m_n).
+
+  By this formula [phi](x) is represented, with any required degree of
+  accuracy, by a polynomial, within the region in question; and thence
+  can be expressed as before by a series of polynomials converging
+  uniformly (and absolutely) within this region.
+
+S 13. _Application of Cauchy's Theorem to the Determination of Definite
+Integrals._--Some reference must be made to a method whereby real
+definite integrals may frequently be evaluated by use of the theorem of
+the vanishing of the integral of a function of a complex variable round
+a contour within which the function is single valued and non singular.
+
+  We are to evaluate an integral [int][a to b] [f](x)dx; we form a
+  closed contour of which the portion of the real axis from x = a to x =
+  b forms a part, and consider the integral [int][f](z)dz round this
+  contour, supposing that the value of this integral can be determined
+  along the curve forming the completion of the contour. The contour
+  being supposed such that, within it, [f](z) is a single valued and
+  finite function of the complex variable z save at a finite number of
+  isolated interior points, the contour integral is equal to the sum of
+  the values of [int][f](z)dz taken round these points. Two instances
+  will suffice to explain the method. (1) The integral [int][0 to [oo]]
+  (tan x)/x dx is convergent if it be understood to mean the limit when
+  [epsilon], [zeta], [sigma], ... all vanish of the sum of the integrals
+
+      _1/2[pi]-[epsilon]         _(3/2)[pi]-[zeta]            _(5/2)[pi]-[sigma]
+     /                tan x     /                  tan x     /                  tan x
+     |                ----- dx, |                  ----- dx, |                  ----- dx, ...
+    _/ 0                x      _/1/2[pi]+[epsilon]     x    _/(3/2)[pi]+[zeta]    x
+
+  Now draw a contour consisting in part of the whole of the positive and
+  negative real axis from x = -n[pi] to x = + n[pi], where n is a
+  positive integer, broken by semicircles of small radius whose centres
+  are the points x = [+-]1/2[pi], x = [+-]3/4[pi], ... , the contour
+  containing also the lines x = n[pi] and x = -n[pi] for values of y
+  between 0 and n[pi] tan [alpha], where [alpha] is a small fixed angle,
+  the contour being completed by the portion of a semicircle of radius
+  n[pi] sec [alpha] which lies in the upper half of the plane and is
+  terminated at the points x = [+-]n[pi], y = n[pi] tan [alpha]. Round
+  this contour the integral [int](tan z /z) dz has the value zero. The
+  contributions to this contour integral arising from the semicircles of
+  centres -1/2(2s - 1)[pi], + 1/2(2s - 1)[pi], supposed of the same
+  radius, are at once seen to have a sum which ultimately vanishes when
+  the radius of the semicircles diminishes to zero. The part of the
+  contour lying on the real axis gives what is meant by 2 [int][0 to
+  n[pi]](tan x / x) dx. The contribution to the contour integral from
+  the two straight portions at x = [+-]n[pi] is
+
+      _n[pi] tan [alpha]
+     /                   /  tan iy        tan iy   \
+     |              idy ( ---------- - -----------  )
+    _/ 0                 \n[pi] + iy   -n[pi] + iy /
+
+  where i tan iy, = -[exp(y) - exp(-y)]/[exp(y) + exp(-y)], is a real
+  quantity which is numerically less than unity, so that the
+  contribution in question is numerically less than
+
+      _n[pi] tan [alpha]
+     /                      2n[pi]
+     |              dy ---------------, that is than 2[alpha].
+    _/ 0               n^2[pi]^2 + y^2
+
+  Finally, for the remaining part of the contour, for which, with R =
+  n[pi] sec [alpha], we have z = R(cos [theta] + i sin [theta]) =
+  RE(i[theta]), we have
+
+    dz
+    -- = id[theta], i tan z =
+    z
+
+      exp(-R sin [theta]) E(iR cos [theta]) - exp(R sin [theta]) E(-iR cos [theta])
+      -----------------------------------------------------------------------------;
+      exp(-R sin [theta]) E(iR cos [theta]) + exp(R sin [theta]) E(-iR cos [theta])
+
+  when n and therefore R is very large, the limit of this contribution
+  to the contour integral is thus
+       _
+      / [pi]-[alpha]
+    - |             d[theta] = -([pi] - 2[alpha]).
+     _/ [alpha]
+
+  Making n very large the result obtained for the whole contour is
+       _
+      / [oo] tan x
+    2 |      ----- dx - ([pi] - 2[alpha]) - 2[alpha][epsilon] = 0;
+     _/ 0      x
+
+  where [epsilon] is numerically less than unity. Now supposing [alpha]
+  to diminish to zero we finally obtain
+      _
+     / [oo] tan x      [pi]
+     |      ----- dx = ----
+    _/  0     x         2
+
+  (2) For another case, to illustrate a different point, we may take the
+  integral
+      _
+     /  z^(a-1)
+     |  ------- dz,
+    _/   1 + z
+
+  wherein a is real quantity such that 0 < a < 1, and the contour
+  consists of a small circle, z = rE(i[theta]), terminated at the points
+  x = r cos [alpha], y = [+-] r sin [alpha], where [alpha] is small, of
+  the two lines y = [+-] r sin [alpha] for r cos [alpha] =< x =< R cos
+  [beta], where R sin [beta] = r sin [alpha], and finally of a large
+  circle z = RE(i[phi]), terminated at the points x = R cos [beta], y =
+  [+-] R sin [beta]. We suppose [alpha] and [beta] both zero, and that
+  the phase of z is zero for r cos a =< x =< R cos [beta], y = r sin
+  [alpha] = R sin [beta]. Then on r cos [alpha] =< x =< R cos [beta], y
+  = -r sin [alpha], the phase of z will be 2[pi], and z^([alpha] - 1)
+  will be equal to x^([alpha] - 1) exp (2[pi]i(a - 1)), where x is real
+  and positive. The two straight portions of the contour will thus
+  together give a contribution
+
+                               _
+                              / R cos [beta]  x^(a - 1)
+    [1 - exp (2[pi]i[alpha])] |               --------- dx.
+                             _/ r cos [alpha]   1 + x
+
+  It can easily be shown that if the limit of z[f](z) for z = 0 is zero,
+  the integral [int] [f](z)dz taken round an arc, of given angle, of a
+  small circle enclosing the origin is ultimately zero when the radius
+  of the circle diminishes to zero, and if the limit of z[f](z) for z =
+  [oo] is zero, the same integral taken round an arc, of given angle, of
+  a large circle whose centre is the origin is ultimately zero when the
+  radius of the circle increases indefinitely; in our case with [f](z) =
+  z^([alpha] - 1)/(1 + z), we have z[f](z) = z^a/(1 + z), which, for 0 <
+  a < 1, diminishes to zero both for z = 0 and for z = [oo]. Thus,
+  finally the limit of the contour integral when r = 0, R = [oo] is
+                               _
+                              / [oo]  x^([alpha] - 1)
+    [1 - exp (2[pi]i[alpha])] |       --------------- dx.
+                             _/ 0          1 + x
+
+  Within the contour [f](z) is single valued, and has a pole at z = 1;
+  at this point the phase of z is [pi] and z^(a - 1) is exp [i[pi](a -
+  1)] or - exp (i[pi]a); this is then the residue of [f](z) at z = -1;
+  we thus have
+                         _
+                        / [oo]  x^(a - 1)
+    [1 - exp (2[pi]ia)] |       --------- dx = -2[pi]i exp (i[pi]a),
+                       _/ 0       1 + x
+
+  that is
+      _
+     / [oo]  x^(a - 1)
+     |       --------- dx = [pi] cosec (a[pi]).
+    _/ 0       1 + x
+
+S 14. _Doubly Periodic Functions._--An excellent illustration of the
+preceding principles is furnished by the theory of single valued
+functions having in the finite part of the plane no singularities but
+poles, which have two periods.
+
+  Before passing to this it may be convenient to make here a few remarks
+  as to the periodicity of (single valued) monogenic functions. To say
+  that [f](z) is periodic is to say that there exists a constant [omega]
+  such that for every point z of the interior of the region of existence
+  of [f](z) we have [f](z + [omega]) = [f](z). This involves,
+  considering all existing periods [omega] = [rho] + i[sigma], that
+  there exists a lower limit of [rho]^2 + [sigma]^2 other than zero; for
+  otherwise all the differential coefficients of [f](z) would be zero,
+  and [f](z) a constant; we can then suppose that not both [rho] and
+  [sigma] are numerically less than [epsilon], where [epsilon] >
+  [sigma]. Hence, if g be any real quantity, since the range (-g, ... g)
+  contains only a finite number of intervals of length [epsilon], and
+  there cannot be two periods [omega] = [rho] + i[sigma] such that
+  [mu][epsilon] =< [rho] < ([mu] + 1)[epsilon], [nu][epsilon] =< [sigma]
+  < ([nu] + 1)[epsilon], where [mu], [nu] are integers, it follows that
+  there is only a finite number of periods for which both [rho] and
+  [sigma] are in the interval (-g ... g). Considering then all the
+  periods of the function which are real multiples of one period
+  [omega], and in particular those periods [lambda][omega] wherein 0 <
+  [lambda] =< 1, there is a lower limit for [lambda], greater than zero,
+  and therefore, since there is only a finite number of such periods for
+  which the real and imaginary parts both lie between -g and g, a least
+  value of [lambda], say [lambda]0. If [Omega] = [lambda]0[omega] and
+  [lambda] = M[lambda]0 + [lambda]', where M is an integer and 0 [< = ]
+  [lambda]' < [lambda]0, any period [lambda][omega] is of the form
+  M[Omega] + [lambda]'[omega]; since, however, [Omega], M[Omega] and
+  [lambda][omega] are periods, so also is [lambda]'[omega], and hence,
+  by the construction of [lambda]0, we have [lambda]' = 0; thus all
+  periods which are real multiples of [omega] are expressible in the
+  form M[Omega] where M is an integer, and [Omega] a period.
+
+  If beside [omega] the functions have a period [omega]' which is not a
+  real multiple of [omega], consider all existing periods of the form
+  [mu][omega] + [nu][omega]' wherein [mu], [nu] are real, and of these
+  those for which 0 [< = ] [mu] =< 1, 0 < [nu] =< 1; as before there is
+  a least value for [nu], actually occurring in one or more periods, say
+  in the period [Omega]' = [mu]0[omega] + [nu]0[omega]'; now take, if
+  [mu][omega] + [nu][omega]' be a period, [nu] = N'[nu]0 + [nu]', where
+  N' is an integer, and 0 =< [nu]' < [nu]0; thence [mu][omega] +
+  [nu][omega]' = [mu][omega] + N'([Omega]' - [mu]0[omega]) +
+  [nu]'[omega]'; take then [mu] - N[mu]0 = N[lambda]0 + [lambda]', where
+  N is an integer and [lambda]0 is as above, and 0 =< [lambda]' <
+  [lambda]0; we thus have a period N[Omega] + N'[Omega]' +
+  [lambda]'[omega] + [nu]'[omega]', and hence a period [lambda]'[omega]
+  + [nu]'[omega]', wherein [lambda]' < [lambda]0, [nu]' < [nu]0; hence
+  [nu]' = 0 and [lambda]' = 0. All periods of the form [mu][omega] +
+  [nu][omega]' are thus expressible in the form N[Omega] + N'[Omega]',
+  where [Omega], [Omega]' are periods and N, N' are integers. But in
+  fact any complex quantity, P + iQ, and in particular any other
+  possible period of the function, is expressible, with [mu], [nu] real,
+  in the form [mu][omega] + [nu][omega]'; for if [omega] = [rho] +
+  i[sigma], [omega]' = [rho]' + i[sigma]', this requires only P =
+  [mu][rho] + [nu][rho]', Q = [mu][sigma] + [nu][sigma]', equations
+  which, since [omega]'/[omega] is not real, always give finite values
+  for [mu] and [nu].
+
+  It thus appears that if a single valued monogenic function of z be
+  periodic, either all its periods are real multiples of one of them,
+  and then all are of the form M[Omega], where [Omega] is a period and M
+  is an integer, or else, if the function have two periods whose ratio
+  is not real, then all its periods are expressible in the form N[Omega]
+  + N'[Omega]', where [Omega], [Omega]' are periods, and N, N' are
+  integers. In the former case, putting [zeta] = 2[pi]iz/[Omega], and
+  the function [f](z) = [phi]([zeta]), the function [phi]([zeta]) has,
+  like exp ([zeta]), the period 2[pi]i, and if we take t = exp([zeta])
+  or [zeta] = [lambda](t) the function is a single valued function of t.
+  If then in particular [f](z) is an integral function, regarded as a
+  function of t, it has singularities only for t = 0 and t = [oo], and
+  may be expanded in the form [Sigma](-[oo] to [oo]) a_nt^n.
+
+  Taking the case when the single valued monogenic function has two
+  periods [omega], [omega]' whose ratio is not real, we can form a
+  network of parallelograms covering the plane of z whose angular points
+  are the points c + m[omega] + m'[omega]', wherein c is some constant
+  and m, m' are all possible positive and negative integers; choosing
+  arbitrarily one of these parallelograms, and calling it the primary
+  parallelogram, all the values of which the function is at all capable
+  occur for points of this primary parallelogram, any point, z', of the
+  plane being, as it is called, _congruent_ to a definite point, z, of
+  the primary parallelogram, z' - z being of the form m[omega] +
+  m'[omega]', where m, m' are integers. Such a function cannot be an
+  integral function, since then, if, in the primary parallelogram
+  |[f](z)| < M, it would also be the case, on a circle of centre the
+  origin and radius R, that |[f](z)| < M, and therefore, if
+  [Sigma]a_nz^n be the expansion of the function, which is valid for an
+  integral function for all finite values of z, we should have |a_n| <
+  MR^(-n), which can be made arbitrarily small by taking R large enough.
+  The function must then have singularities for finite values of z.
+
+  We consider only functions for which these are poles. Of these there
+  cannot be an infinite number in the primary parallelogram, since then
+  those of these poles which are sufficiently near to one of the
+  necessarily existing limiting points of the poles would be arbitrarily
+  near to one another, contrary to the character of a pole. Supposing
+  the constant c used in naming the corners of the parallelograms so
+  chosen that no pole falls on the perimeter of a parallelogram, it is
+  clear that the integral 1/(2[pi]i) [int][f](z)dz round the perimeter
+  of the primary parallelogram vanishes; for the elements of the
+  integral corresponding to two such opposite perimeter points as z, z +
+  [omega] (or as z, z + [omega]') are mutually destructive. This
+  integral is, however, equal to the sum of the residues of [f](z) at
+  the poles interior to the parallelogram. Which sum is therefore zero.
+  There cannot therefore be such a function having only one pole of the
+  first order in any parallelogram; we shall see that there can be such
+  a function with two poles only in any parallelogram, each of the first
+  order, with residues whose sum is zero, and that there can be such a
+  function with one pole of the second order, having an expansion near
+  this pole of the form (z - a)^(-2) + (power series in z - a).
+
+  Considering next the function [phi](z) = [[f](z)]^(-1) d[f](z)/dz, it
+  is easily seen that an ordinary point of [f](z) is an ordinary point
+  of [phi](z), that a zero of order m for [f](z) in the neighbourhood of
+  which [f](z) has a form, (z - a)^m multiplied by a power series, is a
+  pole of [phi](z) of residue m, and that a pole of [f](z) of order n is
+  a pole of [phi](z) of residue -n; manifestly [phi](z) has the two
+  periods of [f](z). We thus infer, since the sum of the residues of
+  [phi](z) is zero, that for the function [f](z), the sum of the orders
+  of its vanishing at points belonging to one parallelogram, [Sigma]m,
+  is equal to the sum of the orders of its poles, [Sigma]n; which is
+  briefly expressed by saying that the number of its zeros is equal to
+  the number of its poles. Applying this theorem to the function
+  [f](z) - A, where A is an arbitrary constant, we have the result, that
+  the function [f](z) assumes the value A in one of the parallelograms
+  as many times as it becomes infinite. Thus, by what is proved above,
+  every conceivable complex value does arise as a value for the doubly
+  periodic function [f](z) in any one of its parallelograms, and in fact
+  at least twice. The number of times it arises is called the _order_ of
+  the function; the result suggests a property of rational functions.
+
+  Consider further the integral [int] z [f]'(z)/[f](z) dz, where [f]'(z)
+  = d[f](z)/dz taken round the perimeter of the primary parallelogram;
+  the contribution to this arising from two opposite perimeter points
+  such as z and z + [omega] is of the form -[omega] [int] z
+  [f]'(z)/[f](z) dz, which, as z increases from z0 to z0 + [omega]',
+  gives, if [lambda] denote the generalized logarithm, -
+  [omega]{[lambda][[f](z0 + [omega]')] - [lambda][[f](z0)]}, that is,
+  since [f](z0 + [omega]') = [f](z0), gives 2[pi]iN[omega], where N is
+  an integer; similarly the result of the integration along the other
+  two opposite sides is of the form 2[pi]iN'[omega]', where N' is an
+  integer. The integral, however, is equal to 2[pi]i times the sum of
+  the residues of z[f]'(z)/[f](z) at the poles interior to the
+  parallelogram. For a zero, of order m, of [f](z) at z = a, the
+  contribution to this sum is 2[pi]ima, for a pole of order n at z = b
+  the contribution is -2[pi]inb; we thus infer that [Sigma]ma -
+  [Sigma]nb = N[omega] + N'[omega]'; this we express in words by saying
+  that the sum of the values of z where [f](z) = 0 within any
+  parallelogram is equal to the sum of the values of z where [f](z) =
+  [oo] save for integral multiples of the periods. By considering
+  similarly the function [f](z) - A where A is an arbitrary constant, we
+  prove that each of these sums is equal to the sum of the values of z
+  where the function takes the value A in the parallelogram.
+
+We pass now to the construction of a function having two arbitrary
+periods [omega], [omega]' of unreal ratio, which has a single pole of
+the second order in any one of its parallelograms.
+
+  For this consider first the network of parallelograms whose corners
+  are the points [Omega] = m[omega] + m'[omega]', where m, m' take all
+  positive and negative integer values; putting a small circle about
+  each corner of this network, let P be a point outside all these
+  circles; this will be interior to a parallelogram whose corners in
+  order may be denoted by z0, z0 + [omega], z0 + [omega] + [omega]', z0
+  + [omega]'; we shall denote z0, z0 + [omega] by A0, B0; this
+  parallelogram [Pi]0 is surrounded by eight other parallelograms,
+  forming with [Pi]0 a larger parallelogram [Pi]1, of which one side,
+  for instance, contains the points z0 - [omega] - [omega]', z0 -
+  [omega]', z0 - [omega]' + [omega], z0 - [omega]' + 2[omega], which we
+  shall denote by A1, B1, C1, D1. This parallelogram [Pi]1 is surrounded
+  by sixteen of the original parallelograms, forming with [Pi]1 a still
+  larger parallelogram [Pi]2 of which one side, for instance, contains
+  the points z0 - 2[omega] - 2[omega]', z0 - [omega] - 2[omega]', z0 -
+  2[omega]', z0 + [omega] - 2[omega]', z0 + 2[omega] - 2[omega]', z0 +
+  3[omega] - 2[omega]', which we shall denote by A2, B2, C2, D2, E2, F2.
+  And so on. Now consider the sum of the inverse cubes of the distances
+  of the point P from the corners of all the original parallelograms.
+  The sum will contain the terms
+
+           1      /  1       1       1  \     /  1       1              1  \
+    S0 = ----- + ( ----- + ----- + ----- ) + ( ----- + ----- + ... +  ----- ) +  ...
+         PA0^3    \PA1^3   PB1^3   PC1^3/     \PA2^3   PB2^3          PE2^3/
+
+  and three other sets of terms, each infinite in number, formed in a
+  similar way. If the perpendiculars from P to the sides A0B0, A1B1C1,
+  A2B2C2D2E2, and so on, be p, p + q, p + 2q and so on, the sum S0 is at
+  most equal to
+
+     1        3            5               2n + 1
+    --- + --------- + ---------- + ... + ---------- + ...
+    p^3   (p + q)^3   (p + 2q)^3         (p + nq)^3
+
+  of which the general term is ultimately, when n is large, in a ratio
+  of equality with 2q^(-3)n^(-2), so that the series S0 is convergent,
+  as we know the sum [Sigma]n^(-2) to be; this assumes that p[/ = ]0; if
+  P be on A0B0 the proof for the convergence of S0 - 1/PA0^3, is the
+  same. Taking the three other sums analogous to S0 we thus reach the
+  result that the series
+
+    [phi](z) = -2[Sigma](z - [Omega])^(-3),
+
+  where [Omega] is m[omega] + m'[omega]', and m, m' are to take all
+  positive and negative integer values, and z is any point outside small
+  circles described with the points [Omega] as centres, is _absolutely
+  convergent_. Its sum is therefore independent of the order of its
+  terms. By the nature of the proof, which holds for all positions of z
+  outside the small circles spoken of, the series is also clearly
+  _uniformly convergent_ outside these circles. Each term of the series
+  being a monogenic function of z, the series may therefore be
+  differentiated and integrated outside these circles, and represents a
+  monogenic function. It is clearly periodic with the periods [omega],
+  [omega]'; for [phi](z + [omega]) is the same sum as [phi](z) with the
+  terms in a slightly different order. Thus [phi](z + [omega]) =
+  [phi](z) and [phi](z + [omega]') = [phi](z).
+
+  Consider now the function
+                      _   _               _
+               1     / z |            2    |
+    [f](z) =  --- +  |   | [phi](z) + --   | dz,
+              z^2   _/ 0 |_           z^3 _|
+
+  where, for the subject of integration, the area of uniform convergence
+  clearly includes the point z = 0; this gives
+
+    d[f](z)
+    ------- = [phi](z)
+      dz
+
+  and
+                             _                             _
+              1             |        1             1        |
+    [f](z) = --- + [Sigma]' |  -------------- - --------    |,
+             z^2            |_ (z - [Omega])^2   [Omega]^2 _|
+
+  wherein [Sigma]' is a sum excluding the term for which m = 0 and m' =
+  0. Hence [f](z + [omega]) - [f](z) and [f](z + [omega]') - [f](z) are
+  both independent of z. Noticing, however, that, by its form, [f](z) is
+  an even function of z, and putting z = -1/2[omega], z = -1/2[omega]'
+  respectively, we infer that also [f](z) has the two periods [omega]
+  and [omega]'. In the primary parallelogram [Pi]0, however, [f](z) is
+  only infinite at z = 0 in the neighbourhood of which its expansion is
+  of the form z^(-2) + (power series in z). Thus [f](z) is such a doubly
+  periodic function as was to be constructed, having in any
+  parallelogram of periods only one pole, of the second order.
+
+It can be shown that any single valued meromorphic function of z with
+[omega] and [omega]' as periods can be expressed rationally in terms of
+[f](z) and [phi](z), and that [[phi](z)]^2 is of the form 4[[f](z)]^3 +
+A[f](z) + B, where A, B are constants.
+
+  To prove the last of these results, we write, for |z| < |[Omega]|,
+
+           1              1          2z         3z^2
+    --------------- - --------- = --------- + --------- + ...,
+    (z - [Omega])^2   [Omega]^2   [Omega]^3   [Omega]^4
+
+  and hence, if [Sigma]'[Omega]^(-2n) = [sigma]_n, since
+  [Sigma]'[Omega]^(-(2n - 1)) = 0, we have, for sufficiently small z
+  greater than zero,
+
+    [f](z) = z^(-2) + 3[sigma]2.z^2 + 5[sigma]3.z^4 + ...
+
+  and
+
+    [phi](z) = -2z^(-3) + 6[sigma]2.z + 20[sigma]3.z^3 + ...;
+
+  using these series we find that the function
+
+    F(z) = [[phi](z)]^2 - 4[[f](z)]^3 + 60[sigma]2[f](z) + 140[sigma]3
+
+  contains no negative powers of z, being equal to a power series in z^2
+  beginning with a term in z^2. The function F(z) is, however, doubly
+  periodic, with periods [omega], [omega]', and can only be infinite
+  when either [f](z) or [phi](z) is infinite; this follows from its form
+  in [f](z) and [phi](z); thus in one parallelogram of periods it can be
+  infinite only when z = 0; we have proved, however, that it is not
+  infinite, but, on the contrary, vanishes, when z = 0. Being,
+  therefore, never infinite for finite values of z it is a constant, and
+  therefore necessarily always zero. Putting therefore [f](z) = [zeta]
+  and [phi](z) = d[zeta]/dz we see that
+
+      dz
+    ------- = (4[zeta]^3 - 60[sigma]2[zeta] - 140[sigma]3)^(-1/2)
+    d[zeta]
+
+  Historically it was in the discussion of integrals such as
+      _
+     /
+     | d[zeta](4[zeta]^3 - 60[sigma]2.[zeta] - 140[sigma]3)^(-1/2),
+    _/
+
+  regarded as a branch of Integral Calculus, that the doubly periodic
+  functions arose. As in the familiar case
+         _
+        / [zeta]
+    z = |       (1 - [zeta]^2)^(-1/2) d[zeta],
+       _/ 0
+
+  where [zeta] = sin z, it has proved finally to be simpler to regard
+  [zeta] as a function of z. We shall come to the other point of view
+  below, under S 20, _Elliptic Integrals_.
+
+To prove that any doubly periodic function F(z) with periods [omega],
+[omega]', having poles at the points z = a1, ... z = a_m of a
+parallelogram, these being, for simplicity of explanation, supposed to
+be all of the first order, is rationally expressible in terms of
+[phi](z) and [f](z), and we proceed as follows:--
+
+  Consider the expression
+
+                 ([zeta], 1)_m + [eta]([zeta], 1)_(m - 2)
+    [Phi](z) =  ------------------------------------------
+                ([zeta]- A1)([zeta] - A2)...([zeta] - A_m)
+
+  where A_s = [f](a_s), [zeta] is an abbreviation for [f](z) and [eta]
+  for [phi](z), and ([zeta], 1)_m, ([zeta], 1)_(m - 2), denote integral
+  polynomials in [zeta], of respective orders m and m - 2, so that there
+  are 2m unspecified, homogeneously entering, constants in the
+  numerator. It is supposed that no one of the points a1, ... a_m is one
+  of the points m[omega] + m'[omega]' where f(z) = [oo]. The function
+  [Phi](z) is a monogenic function of z with the periods [omega],
+  [omega]', becoming infinite (and having singularities) only when (1)
+  [zeta] = [oo] or (2) one of the factors [zeta] - A_s is zero. In a
+  period parallelogram including z = 0 the first arises only for z = 0;
+  since for [zeta] = [oo], [eta] is in a finite ratio to [zeta]^(3/2);
+  the function [Phi](z) for [zeta] = [oo] is not infinite provided the
+  coefficient of [zeta]^m in ([zeta], 1)_m is not zero; thus [Phi](z) is
+  regular about z = 0. When [zeta] - A_s = 0, that is [f](z) = f(a_s),
+  we have z = [+-]a_s + m[omega] + m'[omega]', and no other values of z, m
+  and m' being integers; suppose the unspecified coefficients in the
+  numerator so taken that the numerator vanished to the first order in
+  each of the m points -a1, -a2, ... -a_m; that is, if [phi](a_s) = B_s,
+  and therefore [phi](-a_s) = -B_s, so that we have the m relations
+
+    (A_s, 1)_m - B_s(A_s, 1)_(m - 2) = 0;
+
+  then the function [Phi](z) will only have the m poles a1, ... a_m.
+  Denoting further the m zeros of F(z) by a1', ... a_m', putting
+  [f](a_s') = A_s', [phi](a_s') = B_s', suppose the coefficients of the
+  numerator of [Phi](z) to satisfy the further m-1 conditions
+
+    (A_s', 1)_m + B_s'(A_s',1)_(m - 2) = 0
+
+  for s = 1, 2, ... (m - 1). The ratios of the 2m coefficients in the
+  numerator of [Phi](z) can always be chosen so that the m + (m - 1)
+  linear conditions are all satisfied. Consider then the ratio
+
+    F(z)/[Phi](z);
+
+  it is a doubly periodic function with no singularity other than the
+  one pole a_m'. It is therefore a constant, the numerator of [Phi](z)
+  vanishing spontaneously in a_m'. We have
+
+    F(z) = A[Phi](z),
+
+  where A is a constant; by which F(z) is expressed rationally in terms
+  of [f](z) and [phi](z), as was desired.
+
+  When z = 0 is a pole of F(z), say of order r, the other poles, each of
+  the first order, being a1, ... a_m, similar reasoning can be applied
+  to a function
+
+    ([zeta], 1)_h + [eta]([zeta], 1)_k
+    ----------------------------------,
+      ([zeta] - A1)...([zeta] - A_m)
+
+  where h, k are such that the greater of 2h - 2m, 2k + 3 - 2m is equal
+  to r; the case where some of the poles a1, ... a_m are multiple is to
+  be met by introducing corresponding multiple factors in the
+  denominator and taking a corresponding numerator. We give a solution
+  of the general problem below, of a different form.
+
+  One important application of the result is the theorem that the
+  functions [f](z + t), [phi](z + t), which are such doubly periodic
+  function of z as have been discussed, can each be expressed, so far as
+  they depend on z, rationally in terms of [f](z) and [phi](z), and
+  therefore, so far as they depend on z and t, rationally in terms of
+  [f](z), [f](t), [phi](z) and [phi](t). It can in fact be shown, by
+  reasoning analogous to that given above, that
+                                        _                    _
+                                       |  [phi](z) - [phi](t) |^2
+    [f](z + t) + [f](z) + [f](t) = 1/4 |  ------------------- |.
+                                       |_   [f](z) - [f](t)  _|
+
+  This shows that if F(z) be any single valued monogenic function which
+  is doubly periodic and of meromorphic character, then F(z + t) is an
+  algebraic function of F(z) and F(t). Conversely any single valued
+  monogenic function of meromorphic character, F(z), which is such that
+  F(z + t) is an algebraic function of F(z) and F(t), can be shown to be
+  a doubly periodic function, or a function obtained from such by
+  degeneration (in virtue of special relations connecting the
+  fundamental constants).
+
+  The functions [f](z), [phi](z) above are usually denoted by RN(z),
+  RN'(z); further the fundamental differential equation is usually
+  written
+
+    (RN'z)^2 = 4(RNz)^3 - g2RNz - g3,
+
+  and the roots of the cubic on the right are denoted by e1, e2, e3; for
+  the odd function, RN'z, we have, for the congruent arguments
+  -1/2[omega]and 1/2[omega], RN'(1/2[omega]) = -RN'(-1/2[omega]) =
+  -RN'(1/2[omega]), and hence RN'(1/2[omega]) = 0; hence we can take e1
+  = RN(1/2[omega]), e2 = RN(1/2[omega] + 1/2[omega]'), e3 =
+  RN(1/2[omega]). It can then be proved that [RN(z) - e1][RN(z +
+  1/2[omega]) - e1] = (e1 - e2)(e1 - e3), with similar equations for the
+  other half periods. Consider more particularly the function RN(z) -
+  e1; like RN(z) it has a pole of the second order at z = 0, its
+  expansion in its neighbourhood being of the form z^(-2)(1 - e1z^2 +
+  Az^4 + ...); having no other pole, it has therefore either two zeros,
+  or a double zero in a period parallelogram ([omega], [omega]'). In
+  fact near its zero 1/2[omega] its expansion is (x - 1/2[omega])
+  RN'(1/2[omega]) + 1/2(z - 1/2[omega])^2 RN"(1/2[omega]) + ...; we have
+  seen that RN'(1/2[omega]) = 0; thus it has a zero of the second order
+  wherever it vanishes. Thus it appears that the square root [RN(z) -
+  e1]^1/2, if we attach a definite sign to it for some particular value
+  of z, is a single valued function of z; for it can at most have two
+  values, and the only small circuits in the plane which could lead to
+  an interchange of these values are those about either a pole or a
+  zero, neither of which, as we have seen, has this effect; the function
+  is therefore single valued for any circuit. Denoting the function, for
+  a moment, by [f]1(z), we have [f]1(z + [omega]) = [+-][f]1(z), [f]1(z
+  + [omega]') = [+-][f]1(z); it can be seen by considerations of
+  continuity that the right sign in either of these equations does not
+  vary with z; not both these signs can be positive, since the function
+  has only one pole, of the first order, in a parallelogram ([omega],
+  [omega]'); from the expansion of [f]1(z) about z = 0, namely z^(-1) (1
+  - 1/2e1z^2 + ...), it follows that [f]1(z) is an odd function, and
+  hence [f]1(-1/2[omega]') = -[f]1(1/2[omega]'), which is not zero since
+  [[f]1(1/2[omega]')]^2 = e3 - e1, so that we have [f]1(z + [omega]') =
+  -[f]1(z); an equation f1(z + [omega]) = -[f]1(z) would then give
+  [f]1(z + [omega] + [omega]') = [f]1(z), and hence [f]1(1/2[omega] +
+  1/2[omega]') = [f]1(-1/2[omega] - 1/2[omega]'), of which the latter is
+  -[f]1(1/2[omega] + 1/2[omega]'); this would give [f]1(1/2[omega] +
+  1/2[omega]') = 0, while [[f]1 (1/2[omega] + 1/2[omega]')]^2 = e2 - e1.
+  We thus infer that [f]1(z + [omega]) = [f]1(z), [f]1(z + [omega]') =
+  -[f]1(z), [f]1(z + [omega] + [omega]') = -[f]1(z). The function
+  [f]1(z) is thus doubly periodic with the periods [omega] and
+  2[omega]'; in a parallelogram of which two sides are [omega] and
+  2[omega]' it has poles at z = 0, z = [omega]' each of the first order,
+  and zeros of the first order at z = 1/2[omega], z = 1/2[omega] +
+  [omega]'; it is thus a doubly periodic function of the second order
+  with two different poles of the first order in its parallelogram
+  ([omega], 2[omega]'). We may similarly consider the functions [f]2(z)
+  = [RN(z) - e2]^1/2, [f]3(z) = [RN(z) - e3]^1/2; they give
+
+    [f]2(z + [omega] + [omega]') = [f]2(z), [f]2(z + [omega]) = -[f]2(z), [f]2(z + [omega]') = -[f]2(z),
+
+    [f]3(z + [omega]') = [f]3z, [f]3(z + [omega]) = -[f]3(z), [f]3(z + [omega] + [omega]') = -[f]3(z).
+
+  Taking u = z(e1 - e3)^1/2, with a definite determination of the
+  constant (e1 - e3)^1/2, it is usual, taking the preliminary signs so
+  that for z = 0 each of z[f]1(z), z[f]2(z), z[f]3(z) is equal to + 1,
+  to put
+
+            (e1 - e3)^1/2          [f]1(z)          f2(z)
+    sn(u) = -------------, cn(u) = -------, dn(u) = -----,
+              [f]3(z)              [f]3(z)          f3(z)
+
+    k^2 = (e2 - e3)/(e1 - e3), K = 1/2[omega](e1 - e3)^1/2, iK' = 1/2[omega]'(e1 - e3)^1/2;
+
+  thus sn(u) is an odd doubly periodic function of the second order with
+  the periods 4K, 2iK, having poles of the first order at u = iK', u =
+  2K + iK', and zeros of the first order at u = 0, u = 2K; similarly
+  cn(u), dn(u) are even doubly periodic functions whose periods can be
+  written down, and sn^2(u) + cn^2(u) = 1, k^2sn^2(u) + dn^2(u) = 1; if
+  x = sn(u) we at once find, from the relations given here, that
+
+    du
+    -- = [(1 - x^2) (1 - k^2x^2)]^(-1/2);
+    dx
+
+  if we put x = sin[phi] we have
+
+      du
+    ------ = [1 - k^2sin^2 [phi]]^(-1/2),
+    d[phi]
+
+  and if we call [phi] the amplitude of u, we may write [phi] = am(u), x
+  = sin.am(u), which explains the origin of the notation sn(u).
+  Similarly cn(u) is an abbreviation of cos.am(u), and dn(u) of
+  [Delta]am(u), where [Delta]([phi]) meant (1 - k^2sin^2 [phi])^1/2. The
+  addition equation for each of the functions [f]1(z), [f]2(z), [f]3(z)
+  is very simple, being
+
+                     /(Pd)    (Pd) \      [f](z) + [f](t)   [f](z)[f]'(t) - [f](t)[f]'(z)
+    [f](z + t) = 1/2( ----- + ----- ) log --------------- = -----------------------------,
+                     \(Pd)z   (Pd)i/      [f](z) - [f](t)         [f]^2(z) - [f]^2(t)
+
+  where f1'(z) means d[f]1(z)/dz, which is equal to -[f]2(z).[f]3(z),
+  and [f]^2(z) means [[f](z)]^2. This may be verified directly by
+  showing, if R denote the right side of the equation, that (Pd)R/(Pd)z
+  = (Pd)R/(Pd)t; this will require the use of the differential equation
+
+    [[f]1'^(z)]^2 = [[f]1^2(z) + e1 - e2] [[f]1^2(z) + e1 - e3],
+
+  and in fact we find
+
+     / (Pd)^2   (Pd)^2\
+    ( ------- - ------ ) log [[f](z) + [f](t)] = [f]^2(z) - [f]^2(t) =
+     \(Pd)z^2    dt^2 /
+
+       / (Pd)^2   (Pd)^2\
+      ( ------- - ------ ) log [[f](z) - [f](t)];
+       \(Pd)z^2    dt^2 /
+
+  hence it will follow that R is a function of z + t, and R is at once
+  seen to reduce to [f](z) when t = 0. From this the addition equation
+  for each of the functions sn(u), cn(u), dn(u) can be deduced at once;
+  if s1, c1, d1, s2, c2, d2 denote respectively sn(u1), cn(u1), dn(u1),
+  sn(u2), cn(u2), dn(u2), they can be put into the forms
+
+    sn(u1 + u2) = (s1c2d2 + s2c1d1)/D,
+
+    cn(u1 + u2) = (c1c2 - s1s2d1d2)/D,
+
+    dn(u1 + u2) = (d1d2 - k^2s1s2c1c2)/D,
+
+  where
+
+    D = 1 - k^2s1^2s2^2.
+
+  The introduction of the function [f]1(z) is equivalent to the
+  introduction of the function RN(z; [omega], 2[omega]') constructed
+  from the periods [omega], 2[omega]' as was RN(z) from [omega] and
+  [omega]'; denoting this function by RN1(z) and its differential
+  coefficient by RN'1(z), we have in fact
+
+                         RN'1(z)
+    [f]1(z) = 1/2 ----------------------
+                  RN1([omega]') - RN1(z)
+
+  as we see at once by considering the zeros and poles and the limit of
+  z[f]1(z) when z = 0. In terms of the function RN1(z) the original
+  function RN(z) is expressed by
+
+    RN(z) = RN1(z) + RN1(z + [omega]') - RN1([omega]'),
+
+  as a consideration of the poles and expansion near z = 0 will show.
+
+  A function having [omega], [omega]' for periods, with poles at two
+  arbitrary points a, b and zeros at a', b', where a' + b' = a + b save
+  for an expression m[omega] + m'[omega]', in which m, m' are integers,
+  is a constant multiple of
+
+    {RN[z - 1/2(a' + b')] - RN[a' - 1/2(a' + b')]} / {RN[z - 1/2(a + b)] - RN[a - 1/2(a + b)]};
+
+  if the expansion of this function near z = a be
+                                   _
+    [lambda](z - a)^(-1) + [mu] + \  [mu]_n(z - a)^n,
+                                  /_
+                                 n = 1
+
+  the expansion near z = b is
+                                    _
+    -[lambda](z - b)^(-1) + [mu] + \  (-1)^n [mu]_n (z - b)^n,
+                                   /_
+                                  n = 1
+
+  as we see by remarking that if z'- b = -(z - a) the function has the
+  same value at z and z'; hence the differential equation satisfied by
+  the function is easily calculated in terms of the coefficients in the
+  expansions.
+
+  From the function RN(z) we can obtain another function, termed the
+  Zeta-function; it is usually denoted by [zeta](z), and defined by
+                    _      _            _
+              1    / [pi] |   1          |      _   /     1           1          z    \
+    [zeta](z) -- = |      |  --- - RN(z) |dz = \ ' ( ----------- + ------- + --------- ),
+              z   _/ 0    |_ z^2        _|     /_   \z - [Omega]   [Omega]   [Omega]^2/
+
+  for which as before we have equations
+
+    [zeta](z + [omega]) = [zeta](z) + 2[pi]i[eta],
+    [zeta](z + [omega]') = [zeta](z) + 2[pi]i[eta]',
+
+  where 2[eta], 2[eta]' are certain constants, which in this case do not
+  both vanish, since else [zeta](z) would be a doubly periodic function
+  with only one pole of the first order. By considering the integral
+      _
+     /
+     | [zeta](z)dz
+    _/
+
+  round the perimeter of a parallelogram of sides [omega], [omega]'
+  containing z = 0 in its interior, we find [eta][omega]' -
+  [eta]'[omega] = 1, so that neither of [eta], [eta]' is zero. We have
+  [zeta]'(z) = -RN(z). From [zeta](z) by means of the equation
+                         _   _              _
+    [sigma](z)       {  / z |             1  |   }
+    ---------- = exp {  |   | [zeta](x) - -- |dz } =
+        z            { _/ 0 |_            z _|   }
+             _                                            _
+            |  /       2   \       /   z          z^2   \  |
+      [Pi]' | ( 1 - ------- ) exp ( ------- + ---------- ) |,
+            |_ \    [Omega]/       \[Omega]   2[Omega]^2/ _|
+
+  we determine an integral function [sigma](z), termed the
+  Sigma-function, having a zero of the first order at each of the points
+  z = [Omega]; it can be seen to satisfy the equations
+
+    [sigma](z + [omega])
+    -------------------- = -exp [2[pi] i[eta](z + 1/2[omega])],
+         [sigma](z)
+
+    [sigma](z + [omega]')
+    --------------------- = -exp [2[pi] i[eta]'(z + 1/2[omega]')].
+         [sigma](z)
+
+  By means of these equations, if a1 + a2 + ... + a_m = a'1 + a'2 + ...
+  + a'_m, it is readily shown that
+
+    [sigma](z - a'1)[sigma](z - a'2) ... [sigma](z - a'_m)
+    ------------------------------------------------------
+      [sigma](z - a1[sigma](z - a2) ... [sigma](z - a_m)
+
+  is a doubly periodic function having a1, ... a_m as its simple poles,
+  and a'1, ... a'_m as its simple zeros. Thus the function [sigma](z)
+  has the important property of enabling us to write any meromorphic
+  doubly periodic function as a product of factors each having one zero
+  in the parallelogram of periods; these form a generalization of the
+  simple factors, z - a, which have the same utility for rational
+  functions of z. We have [zeta](z) = [sigma]'(z)/[sigma](z).
+
+  The functions [zeta](z), RN(z) may be used to write any meromorphic
+  doubly periodic function F(z) as a sum of terms having each only one
+  pole; for if in the expansion of F(z) near a pole z = a the terms with
+  negative powers of z-a be
+
+    A1(z - a)^(-1) + A2(z - a){-2} + ... + A_(m + 1)(z - a)^(-(m + 1)),
+
+  then the difference
+
+                                                       A_(m + 1)
+    F(z) - A1[zeta](z - a) - A2[Fraktur](z - a)- ... + ---------(-1)^m RN^(m - 1)(z - a)
+                                                           m!
+
+  will not be infinite at z = a. Adding to this a sum of further terms
+  of the same form, one for each of the poles in a parallelogram of
+  periods, we obtain, since the sum of the residues A is zero, a doubly
+  periodic function without poles, that is, a constant; this gives the
+  expression of F(z) referred to. The indefinite integral [int]F(z)dz
+  can then be expressed in terms of z, functions RN(z - a) and their
+  differential coefficients, functions [zeta](z - a) and functions
+  log[sigma](z - a).
+
+S 15. _Potential Functions. Conformal Representation in
+General._--Consider a circle of radius a lying within the region of
+existence of a single valued monogenic function, u + iv, of the complex
+variable z, = x + iy, the origin z = 0 being the centre of this circle.
+If z = rE(i[phi]) = r(cos [phi] + i sin [phi]) be an internal point of
+this circle we have
+                    _
+             1     / (U + iV)
+  u + iv = ------  | -------- dt,
+           2[pi]i _/  t - z
+
+where U + iV is the value of the function at a point of the
+circumference and t = aE(i[theta]); this is the same as
+                   _
+             1    /  (U + iV) [1 - (r/a)E(i[theta] - i[phi])]
+  u + iv = -----  | ------------------------------------------ d[theta].
+           2[pi] _/ 1 + (r/a)^2 - 2(r/a) cos ([theta] - [phi])
+
+If in the above formula we replace z by the external point
+(a^2/r)E(i[phi]) the corresponding contour integral will vanish, so that
+also
+
+              _
+        1    /  (U + iV) [(r/a)^2 - (r/a)E(i[theta] - i[phi])]
+  0 = -----  |  ---------------------------------------------- d[theta];
+      2[pi] _/    1 + (r/a)^2 - 2(r/a) cos ([theta] - [phi])
+
+hence by subtraction we have
+              _
+        1    /             U(a^2 - r^2)
+  u = -----  | ------------------------------------- d[theta],
+      2[pi] _/ a^2 + r^2 - 2ar cos ([theta] - [phi])
+
+and a corresponding formula for v in terms of V. If O be the centre of
+the circle, Q be the interior point z, P the point aE(i[theta]) of the
+circumference, and [omega] the angle which QP makes with OQ produced,
+this integral is at once found to be the same as
+             _                    _
+       1    /               1    /
+  u = ----  | Ud[omega] - -----  | Ud[theta]
+      [pi] _/             2[pi] _/
+
+of which the second part does not depend upon the position of z, and the
+equivalence of the integrals holds for every arc of integration.
+
+  Conversely, let U be any continuous real function on the
+  circumference, U0 being the value of it at a point P0 of the
+  circumference, and describe a small circle with centre at P0 cutting
+  the given circle in A and B, so that for all points P of the arc AP0B
+  we have |U - U0| < [epsilon], where [epsilon] is a given small real
+  quantity. Describe a further circle, centre P0 within the former,
+  cutting the given circle in A' and B', and let Q be restricted to lie
+  in the small space bounded by the arc A'P0B' and this second circle;
+  then for all positions of P upon the greater arc AB of the original
+  circle QP^2 is greater than a definite finite quantity which is not
+  zero, say QP^2 > D^2. Consider now the integral
+                 _
+           1    /               (a^2 - r^2)
+    u' = -----  | U ------------------------------------ d[theta], =
+         2[pi] _/   a^2 + r^2 - 2ar cos ([theta] - [phi]
+
+             _                    _
+       1    /               1    /
+      ----  | Ud[omega] - -----  | Ud[theta],
+      [pi] _/             2[pi] _/
+
+  which we evaluate as the sum of two, respectively along the small arc
+  AP0B and the greater arc AB. It is easy to verify that, for the whole
+  circumference,
+                 _
+           1    /               (a^2 - r^2)
+    U0 = -----  | U0 ------------------------------------ d[theta] =
+         2[pi] _/    a^2 + r^2 - 2ar cos ([theta] - [phi]
+
+             _                     _
+       1    /                1    /
+      ----  | U0d[omega] - -----  | U0d[theta].
+      [pi] _/              2[pi] _/
+
+  Hence we can write
+                      _                                _
+                1    /                           1    /
+    u' - U0 = -----  |     (U - U0) d[omega] - -----  |    (U - U0) d[theta] +
+              2[pi] _/AP0B                     2[pi] _/AP0B
+
+              _
+        1    /           (a^2 - r^2)
+      -----  |  (U - U0) ----------- d[theta].
+      2[pi] _/AB             QP^2
+
+  If the finite angle between QA and QB be called [Phi] and the finite
+  angle AOB be called [Theta], the sum of the first two components is
+  numerically less than
+
+    [epsilon]
+    --------- ([Phi] + [Theta]).
+      2[pi]
+
+  If the greatest value of |(U - U0)| on the greater arc AB be called H,
+  the last component is numerically less than
+
+     H
+    --- (a^2 - r^2),
+    D^2
+
+  of which, when the circle, of centre P0, passing through A'B' is
+  sufficiently small, the factor a^2 - r^2 is arbitrarily small. Thus it
+  appears that u' is a function of the position of Q whose limit, when
+  Q, interior to the original circle, approaches indefinitely near to
+  P0, is U0. From the form
+                _                    _
+          1    /               1    /
+    u' = ----  | Ud[omega] - -----  | Ud[theta],
+         [pi] _/             2[pi] _/
+
+  since the inclination of QP to a fixed direction is, when Q varies, P
+  remaining fixed, a solution of the differential equation
+
+    (Pd)^2[psi]    (Pd)^2
+    ----------- + ------- = 0,
+      (Pd)x^2     (Pd)y^2
+
+  where z, = x + iy, is the point Q, we infer that u' is a
+  differentiable function satisfying this equation; indeed, when r < a,
+  we can write
+            _
+      1    /                (a^2 - r^2)
+    -----  | U ------------------------------------- d[theta]
+    2[pi] _/   a^2 + r^2 - 2ar cos ([theta] - [phi])
+                _   _                                                                  _
+          1    /   |       r                            r^2                             |
+      = -----  | U | 1 + 2 -- cos ([theta] - [phi]) + 2 --- cos 2([theta] - [phi]) + ...| d[theta]
+        2[pi] _/   |_      a                            a^2                            _|
+
+      = a0 + a1x + b1y + a2(x^2 - y^2) + 2b2xy + ...,
+
+  where
+
+                 _                       _                                   _
+           1    /                  1    / U cos[theta]                 1    / U sin[theta]
+    a0 = -----  | Ud[theta], a1 = ----  | ------------ d[theta], b1 = ----  | ------------ d[theta],
+         2[pi] _/                 [pi] _/      a                      [pi] _/       a
+
+                _                                      _
+          1    / U cos 2[theta]                 1     / U sin 2[theta]
+    a2 = ----  | -------------- d[theta], b2 = ----   | -------------- d[theta].
+         [pi] _/       a^2                      [pi] _/       a^2
+
+  In this series the terms of order n are sums, with real coefficients,
+  of the various integral polynomials of dimension n which satisfy the
+  equation (Pd)^2[psi]/(Pd)x^2 + (Pd)^2[psi]/(Pd)y^2; the series is thus
+  the real part of a power series in z, and is capable of
+  differentiation and integration within its region of convergence.
+
+  Conversely we may suppose a function, P, defined for the interior of a
+  finite region R of the plane of the real variables x, y, capable of
+  expression about any interior point x0, y0 of this region by a power
+  series in x - x0, y - y0, with real coefficients, these various series
+  being obtainable from one of them by continuation. For any region R0
+  interior to the region specified, the radii of convergence of these
+  power series will then have a lower limit greater than zero, and hence
+  a finite number of these power series suffice to specify the function
+  for all points interior to R0. Each of these series, and therefore the
+  function, will be differentiable; suppose that at all points of R0 the
+  function satisfies the equation
+
+    (Pd)^2P   (Pd)P^2
+    ------- + ------- = 0,
+    (Pd)x^2   (Pd)y^2
+
+  we then call it a monogenic potential function. From this, save for an
+  additive constant, there is defined another potential function by
+  means of the equation
+         _
+        /(x, y) /(Pd)P      (Pd)P   \
+    Q = |      ( ----- dy - ----- dx ).
+       _/       \(Pd)x      (Pd)y   /
+
+  The functions P, Q, being given by a finite number of power series,
+  will be single valued in R0, and P + iQ will be a monogenic function
+  of z within R0. In drawing this inference it is supposed that the
+  region R0 is such that every closed path drawn in it is capable of
+  being deformed continuously to a point lying within R0, that is, is
+  _simply connected_.
+
+  Suppose in particular, c being any point interior to R0, that P
+  approaches continuously, as z approaches to the boundary of R, to the
+  value log r, where r is the distance of c to the points of the
+  perimeter of R. Then the function of z expressed by
+
+    [zeta] = (z - c) exp (-P - iQ)
+
+  will be developable by a power series in (z - z0) about every point z0
+  interior to R0, and will vanish at z = c; while on the boundary of R
+  it will be of constant modulus unity. Thus if it be plotted upon a
+  plane of [zeta] the boundary of R will become a circle of radius unity
+  with centre at [zeta] = 0, this latter point corresponding to z = c. A
+  closed path within R0, passing once round z = c, will lead to a closed
+  path passing once about [zeta] = 0. Thus every point of the interior
+  of R will give rise to one point of the interior of the circle. The
+  converse is also true, but is more difficult to prove; in fact, the
+  differential coefficient d[zeta]/dz does not vanish for any point
+  interior to R. This being assumed, we obtain a conformal
+  representation of the interior of the region R upon the interior of a
+  circle, in which the arbitrary interior point c of R corresponds to
+  the centre of the circle, and, by utilizing the arbitrary constant
+  arising in determining the function Q, an arbitrary point of the
+  boundary of R corresponds to an arbitrary point of the circumference
+  of the circle.
+
+  There thus arises the problem of the determination of a real monogenic
+  potential function, single valued and finite within a given arbitrary
+  region, with an assigned continuous value at all points of the
+  boundary of the region. When the region is circular this problem is
+  solved by the integral 1/[pi] [int] Ud[omega] - 1/[pi] [int] Ud[theta]
+  previously given. When the region is bounded by the outermost portions
+  of the circumferences of two overlapping circles, it can hence be
+  proved that the problem also has a solution; more generally, consider
+  a finite simply connected region, whose boundary we suppose to consist
+  of a single closed path in the sense previously explained, ABCD;
+  joining A to C by two non-intersecting paths AEC, AFC lying within the
+  region, so that the original region may be supposed to be generated by
+  the overlapping regions AECD, CFAB, of which the common part is AECF;
+  suppose now the problem of determining a single valued finite
+  monogenic potential function for the region AECD with a given
+  continuous boundary value can be solved, and also the same problem for
+  the region CFAB; then it can be shown that the same problem can be
+  solved for the original area. Taking indeed the values assigned for
+  the original perimeter ABCD, assume arbitrarily values for the path
+  AEC, continuous with one another and with the values at A and C; then
+  determine the potential function for the interior of AECD; this will
+  prescribe values for the path CFA which will be continuous at A and C
+  with the values originally proposed for ABC; we can then determine a
+  function for the interior of CFAB with the boundary values so
+  prescribed. This in its turn will give values for the path AEC, so
+  that we can determine a new function for the interior of AECD. With
+  the values which this assumes along CFA we can then again determine a
+  new function for the interior of CFAB. And so on. It can be shown that
+  these functions, so alternately determined, have a limit representing
+  such a potential function as is desired for the interior of the
+  original region ABCD. There cannot be two functions with the given
+  perimeter values, since their difference would be a monogenic
+  potential function with boundary value zero, which can easily be shown
+  to be everywhere zero. At least two other methods have been proposed
+  for the solution of the same problem.
+
+  A particular case of the problem is that of the conformal
+  representation of the interior of a closed polygon upon the upper half
+  of the plane of a complex variable t. It can be shown without much
+  difficulty that if a, b, c, ... be real values of t, and [alpha],
+  [beta], [gamma], ... be n real numbers, whose sum is n - 2, the
+  integral
+
+         _
+        /
+    z = | (t - a)^([alpha] - 1) (t - b)^([beta] - 1)  ... dt,
+       _/
+
+  as t describes the real axis, describes in the plane of z a polygon of
+  n sides with internal angles equal to [alpha][pi], [beta][pi], ...,
+  and, a proper sign being given to the integral, points of the upper
+  half of the plane of t give rise to interior points of the polygon.
+  Herein the points a, b, ... of the real axis give rise to the corners
+  of the polygon; the condition [Sigma][alpha] = n - 2 ensures merely
+  that the point t = [oo] does not correspond to a corner; if this
+  condition be not regarded, an additional corner and side is introduced
+  in the polygon. Conversely it can be shown that the conformal
+  representation of a polygon upon the half plane can be effected in
+  this way; for a polygon of given position of more than three sides it
+  is necessary for this to determine the positions of all but three of
+  a, b, c, ...; three of them may always be supposed to be at arbitrary
+  positions, such as t = 0, t = 1, t = [oo].
+
+  As an illustration consider in the plane of z = x + iy, the portion of
+  the imaginary axis from the origin to z = ih, where h is positive and
+  less than unity; let C be this point z = ih; let BA be of length unity
+  along the positive real axis, B being the origin and A the point z =
+  1; let DE be of length unity along the negative real axis, D being
+  also the origin and E the point z = -1; let EFA be a semicircle of
+  radius unity, F being the point z = i. If we put [zeta] = [(z^2 +
+  h^2)/(1 + h^2z^2)]^1/2, with [zeta] = 1 when z = 1, the function is
+  single valued within the semicircle, in the plane of z, which is slit
+  along the imaginary axis from the origin to z = ih; if we plot the
+  value of [zeta] upon another plane, as z describes the continuous
+  curve ABCDE, [zeta] will describe the real axis from [zeta] = 1 to
+  [zeta] = -1, the point C giving [zeta] = 0, and the points B, D giving
+  the points [zeta] = [+-]h. Near z = 0 the expansion of [zeta] is
+  [zeta] - h = z^2 1 - h^4 / 2h + ..., or [zeta] + h = -z^2 (1 - h^4)/2h
+  + ...; in either case an increase of 1/2[pi] in the phase of z gives
+  an increase of [pi] in the phase of [zeta] - h or [zeta] + h. Near z =
+  ih the expansion of [zeta] is [zeta] = (z - ih)^1/2 [2ih/(1 -
+  h^4)]^1/2 + ..., and an increase of 2[pi] in the phase of z - ih also
+  leads to an increase of [pi] in the phase of [zeta]. Then as z
+  describes the semicircle EFA, [zeta] also describes a semicircle of
+  radius unity, the point z = i becoming [zeta] = i. There is thus a
+  conformal representation of the interior of the slit semicircle in the
+  z-plane, upon the interior of the whole semicircle in the
+  [zeta]-plane, the function
+
+    z = [([zeta]^2 - h^2) / (1 - h^2[zeta]^2)]^1/2
+
+  being single valued in the latter semicircle. By means of a
+  transformation t = ([zeta] + 1)^2/([zeta] - 1)^2, the semicircle in
+  the plane of [zeta] can further be conformably represented upon the
+  upper half of the whole plane of t.
+
+  As another illustration we may take the conformal representation of an
+  equilateral triangle upon a half plane. Taking the elliptic function
+  RN(u) for which RN'^2(u) = 4RN^3(u) - 4, so that, with [epsilon] = exp
+  (2/3[pi]i), we have e1 = 1, e2 = [epsilon]^2, e3 = [epsilon], the half
+  periods may be taken to be
+                  _                                   _
+                 / [oo]     dt                       / [oo]      dt
+    1/2[omega] = |     --------------, 1/2[omega]' = |     -------------- = 1/2[epsilon][omega];
+                _/ 1   2(t^3 - 1)^1/2               _/ e3  2(t^3 - 1)^1/2
+
+  drawing the equilateral triangle whose vertices are O, of argument O,
+  A of argument [omega], and B of argument [omega] + [omega]' =
+  -[epsilon]^2[omega], and the equilateral triangle whose angular points
+  are O, B and C, of argument [omega]', let E, of argument
+  {1/3}(2[omega] + [omega]'), and D, of argument 1/3([omega] +
+  2[omega]'), be the centroids of these triangles respectively, and let
+  BE, OE, AE cut OA, AB, BO in K, L, H respectively, and BD, OD, CD cut
+  OC, BC, OB in F, G, H respectively; then if u = [xi] + i[eta] be any
+  point of the interior of the triangle OEH and v = [epsilon]u0 =
+  [epsilon]([xi] - i[eta]) be any point of the interior of the triangle
+  OHD, the points respectively of the ten triangles OEK, EKA, EAL, ELB,
+  EBH, DHB, DBG, DGC, DCF, DFO are at once seen to be given by
+  -[epsilon]v, [omega] + [epsilon]u, [omega] - [eta]^2v, [omega] +
+  [omega]' + [epsilon]^2u, [omega] + [omega]' - v, [omega] + [omega]' -
+  u, [omega] + [omega]' + [epsilon]v, [omega]' - [epsilon]u, [omega]' +
+  [epsilon]^2v, -[epsilon]^2u. Further, when u is real, since the term
+  -2(u + m[omega] + m'[epsilon]^2[omega])^(-3), which is the conjugate
+  complex of -2(u + m[omega] + m'[epsilon]^2[omega])^3, arises in the
+  infinite sum which expresses RN'(u), namely as -2(u + [mu][omega] +
+  [mu]'[epsilon][omega])^(-3), where [mu] = m - m', [mu]' = -m', it
+  follows that RN'(u) is real; in a similar way we prove that RN'(u) is
+  pure imaginary when u is pure imaginary, and that RN'(u) =
+  RN'([epsilon]u) = RN'([epsilon]^2u), as also that for v = [epsilon]u0,
+  RN'(v) is the conjugate complex of RN'(u). Hence it follows that the
+  variable
+
+    t = 1/2iRN'(u)
+
+  takes each real value once as u passes along the perimeter of the
+  triangle ODE, being as can be shown respectively [oo], 1, 0, -1 at O,
+  D, H, E, and takes every complex value of imaginary part positive once
+  in the interior of this triangle. This leads to
+              _
+             / [oo]
+    u = 1/3i |     (t^2 - 1)^(-2/3) dt
+            _/ t
+
+  in accordance with the general theory.
+
+  It can be deduced that [tau] = t^2 represents the triangle ODH on the
+  upper half plane of [tau], and [zeta] = {i-[tau]^(-1)}^(1/2)
+  represents similarly the triangle OBD.
+
+S 16. _Multiple valued Functions. Algebraic Functions._--The
+explanations and definitions of a monogenic function hitherto given have
+been framed for the most part with a view to single valued functions.
+But starting from a power series, say in z - c, which represents a
+single value at all points of its circle of convergence, suppose that,
+by means of a derived series in z - c', where c' is interior to the
+circle of convergence, we can continue the function beyond this, and
+then by means of a series derived from the first derived series we can
+make a further continuation, and so on; it may well be that when, after
+a closed circuit, we again consider points in the first circle of
+convergence, the value represented may not agree with the original
+value. One example is the case z^(1/2), for which two values exist for
+any value of z; another is the generalized logarithm [Lambda] (z), for
+which there is an infinite number of values. In such cases, as before,
+the region of existence of the function consists of all points which can
+be reached by such continuations with power series, and the singular
+points, which are the limiting points of the point-aggregate
+constituting the region of existence, are those points in whose
+neighbourhood the radii of convergence of derived series have zero for
+limit. In this description the point z = [oo] does not occupy an
+exceptional position, a power series in z - c being transformed to a
+series in 1/z when z is near enough to c by means of z - c = c(1 -
+cz^(-1)) [1 - (1 - cz^(-1))]^(-1), and a series in 1/z to a series in z
+- c, when z is near enough to c, by means of
+
+  1    1   /    z - c \^(-1)
+  -- = -- ( 1 + -----  ).
+  z    c   \      c   /
+
+  The commonest case of the occurrence of multiple valued functions is
+  that in which the function s satisfies an algebraic equation [f](s, z)
+  = p_0s^n + p1s^(n - 1) + ... + p_n = 0, wherein p0, p1, ... p_n are
+  integral polynomials in z. Assuming [f](s, z) incapable of being
+  written as a product of polynomials rational in s and z, and excepting
+  values of z for which the polynomial coefficient of s^n vanishes, as
+  also the values of z for which beside [f](s, z) = 0 we have also
+  (Pd)f(s, z)/(Pd)s = 0, and also in general the point z = [oo], the
+  roots of this equation about any point z = c are given by n power
+  series in z-c. About a finite point z = c for which the equation
+  (Pd)f(s, z)/(Pd)s = 0 is satisfied by one or more of the roots s of
+  [f](s, z) = 0, the n roots break up into a certain number of cycles,
+  the r roots of a cycle being given by a set of power series in a
+  radical (z - c)^(1/r), these series of the cycle being obtainable from
+  one another by replacing (z - c)^(1/r) by [omega](z - r)^(1/r), where
+  [omega], equal to exp (2[pi]ih/r), is one of the rth roots of unity.
+  Putting then z - c = t^r we may say that the r roots of a cycle are
+  given by a single power series in t, an increase of 2[pi] in the phase
+  of t giving an increase of 2[pi]r in the phase of z - c. This single
+  series in t, giving the values of s belonging to one cycle in the
+  neighbourhood of z = c when the phase of z-c varies through 2[pi]r, is
+  to be looked upon as defining a single _place_ among the aggregate of
+  values of z and s which satisfy [f](s, z) = 0; two such places may be
+  at the same _point_ (z = c, s = d) without coinciding, the
+  corresponding power series for the neighbouring points being
+  different. Thus for an ordinary value of z, z = c, there are n places
+  for which the neighbouring values of s are given by n power series in
+  z-c; for a value of z for which (Pd)f(s, z)/(Pd)s = 0 there are less
+  than n places. Similar remarks hold for the neighbourhood of z = [oo];
+  there may be n places whose neighbourhood is given by n power series
+  in z^(-1) or fewer, one of these being associated with a series in t,
+  where t = (z^(-1))^(1/r); the sum of the values of r which thus arise
+  is always n. In general, then, we may say, with t of one of the forms
+  (z-c), (z-c)^(1/r), z^(-1), (z^(-1))^(1/r). that the neighbourhood of
+  any place (c, d) for which [f](c, d) = 0 is given by a pair of
+  expressions z = c + P(t), s = d + Q(t), where P(t) is a (particular
+  case of a) power series vanishing for t = 0, and Q(t) is a power
+  series vanishing for t = 0, and t vanishes at (c, d), the expression
+  z-c being replaced by z^(-1) when c is infinite, and similarly the
+  expression s-d by s^(-1) when d is infinite. The last case arises when
+  we consider the finite values of z for which the polynomial
+  coefficient of s^n vanishes. Of such a pair of expressions we may
+  obtain a continuation by writing t = t0 + [lambda]1[tau] +
+  [lambda]2[tau]^2 + .. , where [tau] is a new variable and [lambda]1 is
+  not zero; in particular for an ordinary finite place this equation
+  simply becomes t = t0 + [tau]. It can be shown that all the pairs of
+  power series z = c + P(t), s = d + Q(t) which are necessary to
+  represent all pairs of values of z, s satisfying the equation [f](s,
+  z) = 0 can be obtained from one of them by this process of
+  continuation, a fact which we express by saying that the equation
+  [f](s, z) = 0 defines a _monogenic algebraic construct_. With less
+  accuracy we may say that an irreducible algebraic equation [f](s, z) =
+  0 determines a single monogenic function s of z.
+
+  Any rational function of z and s, where [f](s, z) = 0, may be
+  considered in the neighbourhood of any place (c, d) by substituting
+  therein z = c + P(t), s = d + Q(t); the result is necessarily of the
+  form t^m H(t), where H(t) is a power series in t not vanishing for t =
+  0 and m is an integer. If this integer is positive, the function is
+  said to vanish to order m at the place; if this integer is negative, =
+  -[mu], the function is infinite to order [mu] at the place. More
+  generally, if A be an arbitrary constant, and, near (c, d), R(s, z) -
+  A is of the form t^mH(t), where m is positive, we say that R(s, z)
+  becomes m times equal to A at the place; if R(s, z) is infinite of
+  order [mu] at the place, so also is R(s, z) - A. It can be shown that
+  the sum of the values of m at all the places, including the places z =
+  [oo], where R(s, z) vanishes, which we call the number of zeros of
+  R(s, z) on the algebraic construct, is finite, and equal to the sum of
+  the values of [mu] where R (s, z) is infinite, and more generally
+  equal to the sum of the values of m where R(s, z) = A; this we express
+  by saying that a rational function R(s, z) takes any value (including
+  [oo]) the same number of times on the algebraic construct; this number
+  is called the _order_ of the rational function.
+
+  That the total number of zeros of R (s, z) is finite is at once
+  obvious, these values being obtainable by rational elimination of s
+  between [f](s, z) = 0, R(s, z) = 0. That the number is equal to the
+  total number of infinities is best deduced by means of a theorem which
+  is also of more general utility. Let R(s, z) be any rational function
+  of s, z, which are connected by [f](s, z) = 0; about any place (c, d)
+  for which z = c + P(t), s = d + Q(t), expand the product
+
+            dz
+    R(s, z) --
+            dt
+
+  in powers of t and pick out the coefficient of t^(-1). There is only a
+  finite number of places of this kind. The theorem is that the sum of
+  these coefficients of t^(-1) is zero. This we express by
+     _          _
+    |        dz  |
+    |R(s, z) --  |      = 0.
+    |_       dt _|t^(-1)
+
+  The theorem holds for the case n = 1, that is, for rational functions
+  of one variable z; in that case, about any finite point we have z - c
+  = t, and about z = [oo] we have z^(-1) = t, and therefore dz/dt =
+  -t^(-2); in that case, then, the theorem is that in any rational
+  function of z,
+
+     _  / A1         A2               A_m    \
+    \  ( ----- + --------- + ... + ---------  ) + Pz^h + Qz^(h - 1) + ... + R,
+    /_  \z - a   (z - a)^2         (z - a)^m /
+
+  the sum [Sigma]A1 of the sum of the residues at the finite poles is
+  equal to the coefficient of 1/z in the expansion, in ascending powers
+  of 1/z, about z = [oo]; an obvious result. In general, if for a finite
+  place of the algebraic construct associated with [f](s, z) = 0, whose
+  neighbourhood is given by z = c + t^r, s = d + Q(t), there be a
+  coefficient of t^(-1) in R(s, z)dz/dt, this will be r times the
+  coefficient of t^(-r) in R(s, z) or R[d + Q(t), c + t^r], namely will
+  be the coefficient of t^(-r) in the sum of the r series obtainable
+  from R[d + Q(t), c + t^r] by replacing t by [omega]t, where [omega] is
+  an rth root of unity; thus the sum of the coefficients of t^(-1) in
+  R(s, z)dz/dt for all the places which arise for z = c, and the
+  corresponding values of s, is equal to the coefficient of (z - c)^(-1)
+  in R(s1, z) + R(s2z) + ... + R(s_n, z), where s1, ... s_n are the n
+  values of s for a value of z near to z = c; this latter sum [Sigma]
+  R(s_i, z) is, however, a rational function of z only. Similarly, near
+  z = [oo], for a place given by z^(-1) = t^r, s = d + Q(t), or s^(-1) =
+  Q(t), the coefficient of t^(-1) in R(s, z)dz/dt is equal to -r times
+  the coefficient of t^r in R[d + Q(t), t^(-r)], that is equal to the
+  negative coefficient of z^(-l) in the sum of the r series R[d +
+  Q([omega]t), t^(-r)], so that, as before, the sum of the coefficients
+  of t^(-1) in R(s, z)dz/dt at the various places which arise for z =
+  [oo] is equal to the negative coefficient of z^(-1) in the same
+  rational function of z, [Sigma] R(s_i, z). Thus, from the
+  corresponding theorem for rational functions of one variable, the
+  general theorem now being proved is seen to follow.
+
+  Apply this theorem now to the rational function of s and z,
+
+       1    dR(s, z)
+    ------- -------;
+    R(s, z)   dz
+
+  at a zero of R(s, z) near which R(s, z) = t^mH(t), we have
+
+       1    dR(s, z) dz    d
+    ------- -------  -- = -- {[lambda] [R(s, z)]}
+    R(s, z)    dz    dt   dt
+
+  where [lambda] denotes the generalized logarithmic function, that is
+  equal to
+
+    mt^(-1) + power series in t;
+
+  similarly at a place for which R(s, z) = t^(-[mu]) K(t); the theorem
+     _                     _
+    |     1    dR(s, z) dz  |
+    |  ------- -------- --  | t^(-1) = 0
+    |_ R(s, z)    dz    dt _|
+
+  thus gives [Sigma]m = [Sigma][mu], or, in words, the total number of
+  zeros of R(s, z) on the algebraic construct is equal to the total
+  number of its poles. The same is therefore true of the function R(s,
+  z) - A, where A is an arbitrary constant; thus the number in question,
+  being equal to the number of poles of R(s, z) - A, is equal also to
+  the number of times that R(s, z) = A on the algebraic construct.
+
+  We have seen above that all single valued doubly periodic meromorphic
+  functions, with the same periods, are rational functions of two
+  variables s, z connected by an equation of the form s^2 = 4z^3 + Az +
+  B. Taking account of the relation connecting these variables s, z with
+  the argument of the doubly periodic functions (which was above denoted
+  by z), it can then easily be seen that the theorem now proved is a
+  generalization of the theorem proved previously establishing for a
+  doubly periodic function a definite _order_. There exists a
+  generalization of another theorem also proved above for doubly
+  periodic functions, namely, that the sum of the values of the argument
+  in one parallelogram of periods for which a doubly periodic function
+  takes a given value is independent of that value; this generalization,
+  known as Abel's Theorem, is given S 17 below.
+
+S 17. _Integrals of Algebraic Functions._--In treatises on Integral
+Calculus it is proved that if R(z) denote any rational function, an
+indefinite integral [int]R(z)dz can be evaluated in terms of rational
+and logarithmic functions, including the inverse trigonometrical
+functions. In generalization of this it was long ago discovered that if
+s^2 = az^2 + bz + c and R(s, z) be any rational function of s, z any
+integral [int]R(s, z)dz can be evaluated in terms of rational functions
+of s, z and logarithms of such functions; the simplest case is
+[int]s^(-1)dz or [int](az^2 + bz + c)^(-1/2)dz. More generally if f(s,
+z) = 0 be such a relation connecting s, z that when [theta] is an
+appropriate rational function of s and z both s and z are rationally
+expressible, in virtue of [f](s, z) = 0 in terms of [theta], the
+integral [int]R(s, z)dz is reducible to a form [int]H ([theta])d[theta],
+where H([theta]) is rational in [theta], and can therefore also be
+evaluated by rational functions and logarithms of rational functions of
+s and z. It was natural to inquire whether a similar theorem holds for
+integrals [int]R(s, z)dz wherein s^2 is a cubic polynomial in z. The
+answer is in the negative. For instance, no one of the three integrals
+
+    _     _      _
+   / dz  / zdz  /    dz
+   | --, | ---, | --------
+  _/ s  _/  s  _/ (z - c)s
+
+can be expressed by rational and logarithms of rational functions of s
+and z; but it can be shown that every integral [int]R(s, z)dz can be
+expressed by means of integrals of these three types together with
+rational and logarithms of rational functions of s and z (see below
+under S 20, Elliptic Integrals). A similar theorem is true when s^2 =
+quartic polynomial in z; in fact when s^2 = A(z - a)(z - b)(z - c)(z -
+d), putting y = s(z - a)^(-2), x = (z - a)^(-1), we obtain y2 = cubic
+polynomial in x. Much less is the theorem true when the fundamental
+relation [f](s, z) = 0 is of more general type. There exists then,
+however, a very general theorem, known as _Abel's Theorem_, which may be
+enunciated as follows: Beside the rational function R(s, z) occurring in
+the integral [int]R(s, z)dz, consider another rational function H(s, z);
+let (a1), ... (a_m) denote the places of the construct associated with
+the fundamental equation [f](s, z) = 0, for which H(s, z) is equal to
+one value A, each taken with its proper multiplicity, and let (b1), ...
+(b_m) denote the places for which H(s, z) = B, where B is another value;
+then the sum of the m integrals [int] [(b_i) to (a_i)] R(s, z)dz is
+equal to the sum of the coefficients of t^(-1) in the expansions of the
+function
+
+          dz           / H(s, z) - B \
+  R(s, z) -- [lambda] (  -----------  ),
+          dt           \ H(s, z) - A /
+
+where [lambda] denotes the generalized logarithmic function, at the
+various places where the expansion of R(s, z)dz/dt contains negative
+powers of t. This fact may be obtained at once from the equation
+   _                           _
+  |        1                dz  |
+  |  -------------- R(s, z) --  |      = 0,
+  |_ H(s, z) - [mu]         dt _|t^(-1)
+
+wherein [mu] is a constant. (For illustrations see below, under S 20,
+Elliptic Integrals.)
+
+S 18. _Indeterminateness of Algebraic Integrals._--The theorem that the
+integral [int][a to x] [f](z)dz is independent of the path from a to z,
+holds only on the hypothesis that any two such paths are equivalent,
+that is, taken together from the complete boundary of a region of the
+plane within which [f](z) is finite and single valued, besides being
+differentiable. Suppose that these conditions fail only at a finite
+number of isolated points in the finite part of the plane. Then any path
+from a to z is equivalent, in the sense explained, to any other path
+together with closed ~~ paths beginning and ending at the arbitrary
+point a each enclosing one or more of the exceptional points, these
+closed paths being chosen, when [f](z) is not a single valued function,
+so that the final value of [f](z) at a is equal to its initial value. It
+is necessary for the statement that this condition may be capable of
+being satisfied.
+
+  For instance, the integral [int][1 to z] z^(-1)dz is liable to an
+  additive indeterminateness equal to the value obtained by a closed
+  path about z = 0, which is equal to 2[pi]i; if we put u = [int][1 to
+  z] z^(-1)dz and consider z as a function of u, then we must regard
+  this function as unaffected by the addition of 2[pi]i to its argument
+  u; we know in fact that z = exp (u) and is a single valued function of
+  u, with the period 2[pi]i. Or again the integral [int][0 to z] (1 +
+  z^2)^(-1)dz is liable to an additive indeterminateness equal to the
+  value obtained by a closed path about either of the points z = [+-]i;
+  thus if we put u = [int][0 to z] (1 + z^2)^(-1)dz, the function z of u
+  is periodic with period [pi], this being the function tan (u). Next we
+  take the integral u = [int][(0) to (z)] (1 - z^2)^(-1/2)dz, agreeing
+  that the upper and lower limits refer not only to definite values of
+  z, but to definite values of z each associated with a definite
+  determination of the sign of the associated radical (1 - z^2)^(-1/2).
+  We suppose 1 + z, 1 - z each to have phase zero for z = 0; then a
+  single closed circuit of z = -1 will lead back to z = 0 with (l -
+  z^2)^1/2 = -1; the additive indeterminateness of the integral,
+  obtained by a closed path which restores the initial value of the
+  subject of integration, may be obtained by a closed circuit containing
+  both the points [+-]1 in its interior; this gives, since the integral
+  taken about a vanishing circle whose centre is either of the points z
+  = [+-] 1 has ultimately the value zero, the sum
+
+      _                 _                     _                     _
+     / -1     dz       / 0        dz         / 1        dz         / 0      dz
+     |   ----------- + |    -------------- + |    -------------- + |   -------------,
+    _/ 0 (1-z^2)^1/2  _/-1  -(1 - z^2)^1/2  _/ 0  -(1 - z^2)^1/2  _/ 1 (1 - z^2)^1/2
+
+  where, in each case, (1 - z^2)^1/2 is real and positive; that is, it
+  gives
+        _
+       / 1      dz
+    -4 |   -------------
+      _/ 0 (1 - z^2)^1/2
+
+  or 2[pi]. Thus the additive indeterminateness of the integral is of
+  the form 2k[pi], where k is an integer, and the function z of u, which
+  is sin (u), has 2[pi] for period. Take now the case
+         _
+        / (z)                   dz
+    u = |      ------------------------------------,
+       _/ (z0) [root]{(z - a)(z - b)(z - c)(z - d)}
+
+  adopting a definite determination for the phase of each of the factors
+  z - a, z - b, z - c, z - d at the arbitrary point z0, and supposing
+  the upper limit to refer, not only to a definite value of z, but also
+  to a definite determination of the radical under the sign of
+  integration. From z0 describe a closed loop about the point z = a,
+  consisting, suppose, of a straight path from z0 to a, followed by a
+  vanishing circle whose centre is at a, completed by the straight path
+  from a to z0. Let similar loops be imagined for each of the points b,
+  c, d, no two of these having a point in common. Let A denote the value
+  obtained by the positive circuit of the first loop; this will be in
+  fact equal to twice the integral taken from z0 along the straight path
+  to a; for the contribution due to the vanishing circle is ultimately
+  zero, and the effect of the circuit of this circle is to change the
+  sign of the subject of integration. After the circuit about a, we
+  arrive back at z0 with the subject of integration changed in sign; let
+  B, C, D denote the values of the integral taken by the loops enclosing
+  respectively b, c and d when in each case the initial determination of
+  the subject of integration is that adopted in calculating A. If then
+  we take a circuit from z0 enclosing both a and b but not either c or
+  d, the value obtained will be A - B, and on returning to z0 the
+  subject of integration will have its initial value. It appears thus
+  that the integral is subject to an additive indeterminateness equal to
+  any one of the six differences such as A - B. Of these there are only
+  two linearly independent; for clearly only A - B, A - C, A - D are
+  linearly independent, and in fact, as we see by taking a closed
+  circuit enclosing all of a, b, c, d, we have A - B + C - D = 0; for
+  there is no other point in the plane beside a, b, c, d about which the
+  subject of integration suffers a change of sign, and a circuit
+  enclosing all of a, b, c, d may by putting z = 1/[zeta] be reduced to
+  a circuit about [zeta] = 0 about which the value of the integral is
+  zero. The general value of the integral for any position of z and the
+  associated sign of the radical, when we start with a definite
+  determination of the subject of integration, is thus seen to be of the
+  form u0 + m(A - B) + n(A - C), where m and n are integers. The value
+  of A - B is independent of the position of z0, being obtainable by a
+  single closed positive circuit about a and b only; it is thus equal to
+  twice the integral taken once from a to b, with a proper initial
+  determination of the radical under the sign of integration. Similar
+  remarks to the above apply to any integral [int]H(z)dz, in which H(z)
+  is an algebraic function of z; in any such case H(z) is a rational
+  function of z and a quantity s connected therewith by an irreducible
+  rational algebraic equation [f](s, z) = 0. Such an integral [f]K(z,
+  s)dz is called an Abelian Integral.
+
+S 19. _Reversion of an Algebraic Integral._--In a limited number of
+cases the equation u = [int] [z0 to z] H(z)dz, in which H(z) is an
+algebraic function of z, defines z as a single valued function of u.
+Several cases of this have been mentioned in the previous section; from
+what was previously proved under S 14, _Doubly Periodic Functions_, it
+appears that it is necessary for this that the integral should have at
+most two linearly independent additive constants of indeterminateness;
+for instance, for an integral
+       _
+      / z
+  u = |   [(z - a)(z - b)(z - c)(z - d)(z - e)(z - f)]^(-1/2) dz,
+     _/ z0
+
+there are three such constants, of the form A - B, A - C, A - D, which
+are not connected by any linear equation with integral coefficients, and
+z is not a single valued function of u.
+
+S 20. _Elliptic Integrals._--An integral of the form [int] R(z, s)dz,
+where s denotes the square root of a quartic polynomial in z, which may
+reduce to a cubic polynomial, and R denotes a rational function of z and
+s, is called an _elliptic integral_.
+
+  To each value of z belong two values of s, of opposite sign; starting,
+  for some particular value of z, with a definite one of these two
+  values, the sign to be attached to s for any other value of z will be
+  determined by the path of integration for z. When z is in the
+  neighbourhood of any finite value z0 for which the radical s is not
+  zero, if we put z - z0 = t, we can find s - s0 = a power series in t,
+  say s = s0 + Q(t); when z is in the neighbourhood of a value, a, for
+  which s vanishes, if we put z = a + t^2, we shall obtain s = tQ(t),
+  where Q(t) is a power series in t; when z is very large and s^2 is a
+  quartic polynomial in z, if we put z^(-1) = t, we shall find s^(-1) =
+  t^2Q(t); when z is very large and s^2 is a cubic polynomial in z, if we
+  put z^(-1) = t^2, we shall find s^(-l) = t^3Q(t). By means of
+  substitutions of these forms the character of the integral [int] R(z,
+  s)dz may be investigated for any position of z; in any case it takes a
+  form [int] [Ht^(-m) + Kt^(-m + 1) + ... + Pt^(-1) + R + St + ...]dt
+  involving only a finite number of negative powers of t in the subject
+  of integration. Consider first the particular case [int] s^(-1)dz; it
+  is easily seen that neither for any finite nor for infinite values of
+  z can negative powers of t enter; the integral is _everywhere finite_,
+  and is said to be of _the first kind_; it can, moreover, be shown
+  without difficulty that no integral [int] R(z, s)dz, save a constant
+  multiple of [int] s^(-1)dz, has this property. Consider next, s^2 being
+  of the form a0z^4 + 4a1z^3 + ..., wherein a0 may be zero, the integral
+  [int] {a0z^2 + 2a1z) s^(-1)dz; for any finite value of z this integral
+  is easily proved to be everywhere finite; but for infinite values of z
+  its value is of the form At^(-1) + Q(t), where Q(t) is a power series;
+  denoting by [root]a0 a particular square root of a0 when a0 is not
+  zero, the integral becomes infinite for z = [oo] for both signs of s,
+  the value of A being + [root]a0 or - [root]a0 according as s is
+  [root]a0.z^2 (1 + [2a1/a0] z^(-1) + ...) or is the negative of this;
+  hence the integral J1 = [int] ([a0z^2 + 2a1z / s] + [root]a0)dz becomes
+  infinite when z is infinite, for the former sign of s, its infinite
+  term being 2[root]a0 t^(-1) or 2a0.z, but does not become infinite for
+  z infinite for the other sign of s. When a0 = 0 the signs of s for z =
+  [oo] are not separated, being obtained one from the other by a circuit
+  of z about an infinitely large circle, and the form obtained
+  represents an integral becoming infinite as before for z = [oo], its
+  infinite part being 2[root]a1.t^(-1) or 2[root]a1.[root]z. Similarly
+  if z0 be any finite value of z which is not a root of the polynomial
+  [f](z) to which s^2 is equal, and s0 denotes a particular one of the
+  determinations of s for z = z0, the integral
+          _
+         /  / s0^2 + 1/2(z - z0) [f]'(z0)      s0     \
+    J2 = | (  --------------------------- + ---------  ) dz,
+        _/  \        (z - z0)^2s           (z - z0)^2 /
+
+  wherein [f]'(z) = d[f](z)/dz, becomes infinite for z = z0, s = s0, but
+  not for z = z0, s = -s0. its infinite term in the former case being
+  the negative of 2s0(z - z0). For no other finite or infinite value of
+  z is the integral infinite. If z = [theta] be a root of [f](z), in
+  which case the corresponding value of s is zero, the integral
+                           _
+                          /       dz
+    J3 = 1/2[f]'([theta]) | --------------
+                         _/ (z - [theta])s
+
+  becomes infinite for z = 0, its infinite part being, if z - [theta] =
+  t^2, equal to -[[f]'([theta])] 1/2t^(-1): and this integral is not
+  elsewhere infinite. In each of these cases, of the integrals J1, J2,
+  J3, the subject of integration has been chosen so that when the
+  integral is written near its point of infinity in the form
+  [int][At^(-2) + Bt^(-1) + Q(t)]dt, the coefficient B is zero, so that
+  the infinity is of algebraic kind, and so that, when there are two
+  signs distinguishable for the critical value of z, the integral
+  becomes infinite for only one of these. An integral having only
+  algebraic infinities, for finite or infinite values of z, is called an
+  integral of the _second kind_, and it appears that such an integral
+  can be formed with only one such infinity, that is, for an infinity
+  arising only for one particular, and arbitrary, pair of values (s, z)
+  satisfying the equation s^2 = [f](z), this infinity being of the first
+  order. A function having an algebraic infinity of the mth order (m >
+  1), only for one sign of s when these signs are separable, at (1) z =
+  [oo], (2) z = z0, (3) z = a, is given respectively by (s d/dz)^(m -
+  1)J1, (s d/dz)^(m - 1) J2, (s d/dz )^(m - 1) J3, as we easily see. If
+  then we have any elliptic integral having algebraic infinities we can,
+  by subtraction from it of an appropriate sum of constant multiples of
+  J1, J2, J3 and their differential coefficients just written down,
+  obtain, as the result, an integral without algebraic infinities. But,
+  in fact, if J, J^1 denote any two of the three integrals J1, J2, J3,
+  there exists an equation AJ + BJ' + C[f]s^(-1)dz = rational function
+  of s, z, where A, B, C are properly chosen constants. For the rational
+  function
+
+    s + s0
+    ------ + z [root]a0
+    z - z0
+
+  is at once found to become infinite for (z0, s0), not for (z0, -s0),
+  its infinite part for the first point being 2s/(z - z0), and to become
+  infinite for z infinitely large, and one sign of s only when these are
+  separable, its infinite part there being 2z [root] a0 or 2 [root] a1
+  [root] z when a0 = 0. It does not become infinite for any other pair
+  (z, s) satisfying the relation s^2 = [f](z); this is in accordance
+  with the easily verified equation
+                                                       _
+    s + s0                                            / dz
+    ------- + z [root]a0 - J1 + J2 + (a0z0^2 + 2a1z0) | -- = 0;
+    z - z^0                                          _/ s
+
+  and there exists the analogous equation
+                                                                     _
+         s                                                          / dz
+    ----------- + z [root]a0 - J1 + J3 + (a0[theta]^2 + 2a1[theta]) | -- = 0.
+    z - [theta]                                                    _/ s
+
+  Consider now the integral
+          _
+         /  /s + s0                \  dz
+    P =  | ( --------- + z [root]a0 ) --;
+        _/  \z - z0                /  2s
+
+  this is at once found to be infinite, for finite values of z, only for
+  (z0, s0), its infinite part being log (z - z0), and for z = [oo], for
+  one sign of s only when these are separable, its infinite part being
+  -log t, that is -log z when a0 /= 0, and -log (z^1/2) when a0 = 0.
+  And, if [f]([theta]) = 0, the integral
+
+          _
+         /   /    s                   \  dz
+    P1 = |  ( ----------- + z [root]a0 ) --
+        _/   \z - [theta]             /  2s
+
+  is infinite at z = [theta], s = 0 with an infinite part log t, that is
+  log (z - [theta])^1/2, is not infinite for any other finite value of z,
+  and is infinite like P for z = [oo]. An integral possessing such
+  logarithmic infinities is said to be of the third kind.
+
+  Hence it appears that any elliptic integral, by subtraction from it of
+  an appropriate sum formed with constant multiples of the integral J3
+  and the rational functions of the form (s d/dz)^(m - 1) J1 with
+  constant multiples of integrals such as P or P1, with constant
+  multiples of the integral u = [int]s^(-1)dz, and with rational
+  functions, can be reduced to an integral H becoming infinite only for
+  z = [oo], for one sign of s only when these are separable, its
+  infinite part being of the form A log t, that is, A log z or A log
+  (z^1/2). Such an integral H = [int]R(z, s)dz does not exist, however,
+  as we at once find by writing R(z, s) = P(z) + sQ(z), where P(z), Q(z)
+  are rational functions of z, and examining the forms possible for
+  these in order that the integral may have only the specified infinity.
+  An analogous theorem holds for rational functions of z and s; there
+  exists no rational function which is finite for finite values of z and
+  is infinite only for z = [oo] for one sign of s and to the first order
+  only; but there exists a rational function infinite in all to the
+  first order for each of two or more pairs (z, s), however they may be
+  situated, or infinite to the second order for an arbitrary pair (z,
+  s); and any rational function may be formed by a sum of constant
+  multiples of functions such as
+
+    s + s0                      s
+    ------ + z [root]a0 or ----------- + z [root]a0
+    z - z0                 z - [theta]
+
+  and their differential coefficients.
+
+  The consideration of elliptic integrals is therefore reducible to that
+  of the three
+         _          _                                       _
+        /  dz      /  /a0z^2 + 2a1z             \          /  /s + s0             \ dz
+    u = |  --, J = | ( ------------ + z [root]a0 ) dz, P = | ( ------ + z [root]a0 )--
+       _/  s      _/  \     s                   /         _/  \z - z0             / 2s
+
+  respectively of the first, second and third kind. Now the equation s^2
+  = a0z^4 + ... = a0(z - [theta]) (z - [phi]) (z - [psi]) (z - [chi]),
+  by putting
+
+    y = 2s(z - [theta])^(-2) [a0([theta] - [phi]) ([theta] - [psi]) ([theta] - [chi])]^(-1/2)
+
+             1        1   /       1                 1                 1       \
+    x = ----------- + -- ( --------------- + -------------- + ---------------  )
+        z - [theta]   3   \[theta] - [phi]   [theta] - [psi]   [theta] - [chi]/
+
+  is at once reduced to the form y^2 = 4x^3- g2x - g3 = 4(x - e1)(x -
+  e2(x - e3), say; and these equations enable us to express s and z
+  rationally in terms of x and y. It is therefore sufficient to consider
+  three elliptic integrals
+         _          _           _
+        /  dx      /  xdx      /  y + y0  dx
+    u = |  --, J = |  ---, P = |  ------  --.
+       _/  y      _/   y      _/  x - x0  2y
+
+  Of these consider the first, putting
+         _
+        / ([oo]) dx
+    u = |        --,
+       _/ (x)    y
+
+  where the limits involve not only a value for x, but a definite sign
+  for the radical y. When x is very large, if we put x^(-1) = t^2, y^(-1)
+  = 2t^3(1 - 1/4 g2t^4 - 1/4 g3t^6)^(-1/2), we have
+          _
+         / t  /    1             \          1
+    u =  |   ( 1 + -- g2t^4 + ... )dt = t + -- g2t^5 + ...,
+        _/ 0  \    8             /          40
+
+  whereby a definite power series in u, valid for sufficiently small
+  value of u, is found for t, and hence a definite power series for x,
+  of the form
+
+    x = u^(-2) + (1/20)g2u^2 + ...
+
+  Let this expression be valid for 0 < |u| < R, and the function defined
+  thereby, which has a pole of the second order for u = 0, be denoted by
+  [phi](u). In the range in question it is single valued and satisfies
+  the differential equation
+
+    [[phi]'(u)]^2 = 4[[phi](u)]^3 - g2[phi](u) - g3;
+
+  in terms of it we can write x = [phi](u), y = -[phi]'(u), and,
+  [phi]'(u) being an odd function, the sign attached to y in the
+  original integral for x = [oo] is immaterial. Now for any two values
+  u, v in the range in question consider the function
+                   _                     _
+                  | [phi]'(u) - [phi]'(v) |^2
+    F(u, v) = 1/4 | --------------------- | - [phi](u) - [phi](v);
+                  |_ [phi](u) - [phi](v) _|
+
+  it is at once seen, from the differential equation, to be such that
+  (Pd)F/(Pd)u = (Pd)F/(Pd)v; it is therefore a function of u + v;
+  supposing |u + v| < R we infer therefore, by putting v = 0, that
+                        _                      _
+                       | [phi]'(u) - [phi]'(v)] |^2
+    [phi](u + v) = 1/4 | ---------------------  | - [phi](u) - [phi](v).
+                       |_ [phi](u) - [phi](v)  _|
+
+  By repetition of this equation we infer that if u1, ... u_n be any
+  arguments each of which is in absolute value less than R, whose sum is
+  also in absolute value less than R, then [phi](u1 + ... + u_n) is a
+  rational function of the 2n functions [phi](u_s), [phi]'(u_s); and
+  hence, if |u| < R, that
+
+    [phi](u) = H [[phi](u/n), [phi]'(u/n)],
+
+  where H is some rational function of the arguments [phi](u/n),
+  [phi]'(u/n). In fact, however, so long as |u/n| < R, each of the
+  functions [phi](u/n), [phi]'(u/n) is single valued and without
+  singularity save for the pole at u = 0; and a rational function of
+  single valued functions, each of which has no singularities other than
+  poles in a certain region, is also a single valued function without
+  singularities other than poles in this region. We infer, therefore,
+  that the function of u expressed by H[[phi](u/n), [phi]'(u/n)] is
+  single valued and without singularities other than poles so long as
+  |u| < nR; it agrees with [phi](u) when |u| < R, and hence furnishes a
+  continuation of this function over the extended range |u| < nR.
+  Moreover, from the method of its derivation, it satisfies the
+  differential equation [[phi]'(u)]^2 = 4[[phi](u)]^3 - g2[phi](u) - g3.
+  This equation has therefore one solution which is a single valued
+  monogenic function with no singularities other than poles for any
+  finite part of the plane, having in particular for u = 0, a pole of
+  the second order; and the method adopted for obtaining this near u = 0
+  shows that the differential equation has no other such solution. This,
+  however, is not the only solution which is a single valued meromorphic
+  function, a the functions [phi](u + [alpha]), wherein [alpha] is
+  arbitrary, being such. Taking now any range of values of u, from u =
+  0, and putting for any value of u, x = [phi](u), y = -[phi]'(u), so
+  that y^2 = 4x^3 - g2x - g3, we clearly have
+         _
+        / ([oo]) dx
+    u = |        --;
+       _/ (x, y) y
+
+  conversely if x0 = [phi](u0), y0 = -[phi]'(u0) and [xi], [eta] be any
+  values satisfying [eta]2 = 4[xi]^2 - g2[xi] - g3, which are
+  sufficiently near respectively to x0, y0, while v is defined by
+               _
+              / ([xi], [eta])  d[xi]
+    v - u0 = -|                -----,
+             _/ (x0, y0)       [eta]
+
+  then [xi], [eta] are respectively [phi](v) and -[phi]'(v); for this
+  equation leads to an expansion for [xi]-x0 in terms of v = u0 and only
+  one such expansion, and this is obtained by the same work as would be
+  necessary to expand [phi](v) when v is near to u0; the function
+  [phi](u) can therefore be continued by the help of this equation, from
+  v = u0, provided the lower limit of |[xi] - x0| necessary for the
+  expansions is not zero in the neighbourhood of any value (x0, y0). In
+  fact the function [phi](u) can have only a finite number of poles in
+  any finite part of the plane of u; each of these can be surrounded by
+  a small circle, and in the portion of the finite part of the plane of
+  u which is outside these circles, the lower limit of the radii of
+  convergence of the expansions of [phi](u) is greater than zero; the
+  same will therefore be the case for the lower limit of the radii |[xi]
+  - x0| necessary for the continuations spoken of above provided that
+  the values of ([xi], [eta]) considered do not lead to infinitely
+  increasing values of v; there does not exist, however, any definite
+  point ([xi]0, [eta]0) in the neighbourhood of which the integral [int]
+  [([xi], [eta]) to (x0, y0)] d[xi]/[eta] increases indefinitely, it is
+  only by a path of infinite length that the integral can so increase.
+  We infer therefore that if ([xi],[eta]) be any point, where [eta]2 =
+  4[xi]^3 - g2[xi] - g3, and v be defined by
+         _
+        / ([oo])         dx
+    v = |                -- ,
+       _/ ([xi], [eta])  y
+
+  then [xi] = [phi](v) and [eta] = -[phi]'(v). Thus this equation
+  determines ([xi], [eta]) without ambiguity. In particular the additive
+  indeterminatenesses of the integral obtained by closed circuits of the
+  point of integration are periods of the function [phi](u); by
+  considerations advanced above it appears that these periods are sums
+  of integral multiples of two which may be taken to be
+                _                        _
+               / [oo]  dx               / [oo]  dx
+    [omega] = 2|       --, [omega]' = 2 |       --;
+              _/ e1    y               _/ e3    y
+
+  these quantities cannot therefore have a real ratio, for else, being
+  periods of a monogenic function, they would, as we have previously
+  seen, be each integral multiples of another period; there would then
+  be a closed path for (x, y), starting from an arbitrary point (x0,
+  y0), other than one enclosing two of the points (e1, 0), (e2, 0), (e3,
+  0), ([oo], [oo]), which leads back to the initial point (x0, y0),
+  which is impossible. On the whole, therefore, it appears that the
+  function [phi](u) agrees with the function RN(u) previously discussed,
+  and the discussion of the elliptic integrals can be continued in the
+  manner given under S 14, _Doubly Periodic Functions_.
+
+S 21. _Modular Functions._--One result of the previous theory is the
+remarkable fact that if
+              _                        _
+             / [oo]  dx               / [oo]  dx
+  [omega] = 2|       --, [omega]' = 2 |       --,
+            _/ e1    y               _/ e3    y
+
+where y^2 = 4(x - e1) (x - e2) (x - e3), then we have
+
+  e1 = (1/2[omega])^(-2) + [Sigma]' {[(m + 1/2)[omega] + m'[omega]']^(-2) -
+    [m[omega] + m'[omega]']^(-2)},
+
+and a similar equation for e3, where the summation refers to all integer
+values of m and m' other than the one pair m = 0, m' = 0. This, with
+similar results, has led to the consideration of functions of the
+complex ratio [omega]'/[omega].
+
+  It is easy to see that the series for RN(u), u^(-2) + [Sigma] [(u +
+  m[omega] + m'[omega]')^2-(m[omega] + m'[omega]')^2], is unaffected by
+  replacing [omega], [omega]' by two quantities [Omega], [Omega]' equal
+  respectively to p[omega] + q[omega]', p'[omega]' + q'[omega]', where
+  p, q, p', q' are any integers for which pq' - p'q = [+-]1; further it
+  can be proved that all substitutions with integer coefficients [Omega]
+  = p[omega] + q[omega]', [Omega]' = p'[omega] + q'[omega]', wherein pq'
+  - p'q = 1, can be built up by repetitions of the two particular
+  substitutions ([Omega] = -[omega]', [Omega]' = [omega]), ([Omega] =
+  [omega], [Omega]' = [omega] + [omega]'). Consider the function of the
+  ratio [omega]'/[omega] expressed by
+
+    h = -RN (1/2[omega]') / RN(1/2[omega]);
+
+  it is at once seen from the properties of the function RN(u) that by
+  the two particular substitutions referred to we obtain the
+  corresponding substitutions for h expressed by
+
+    h' = 1/h, h' = 1 - h;
+
+  thus, by all the integer substitutions [Omega] = p[omega] + q[omega]',
+  [Omega]' = p'[omega] + q'[omega]', in which pq' - p'q = 1, the
+  function h can only take one of the six values h, 1/h, 1 - h, 1/(1 -
+  h), h/(h - 1), (h - 1)/h, which are the roots of an equation in
+  [theta],
+
+    (1 - [theta] + [theta]^2)^3   (1 - h + h^2)^3
+    --------------------------- = ---------------;
+      [theta]^2(1 - [theta])^2      h^2(1 - h)^2
+
+  the function of [tau], = [omega]'/[omega], expressed by the right
+  side, is thus unaltered by every one of the substitutions [tau]' = (p'
+  + q'[tau] / p + q[tau]), wherein p, q, p', q' are integers having pq'
+  - p'q = 1. If the imaginary part [sigma], of [tau], which we may write
+  [tau] = [rho] + i[sigma], is positive, the imaginary part of [tau]',
+  which is equal to [sigma](pq' - p'q)/[(p + q[rho])^2 + q^2[sigma]^2],
+  is also positive; suppose [sigma] to be positive; it can be shown that
+  the upper half of the infinite plane of the complex variable [tau] can
+  be divided into regions, all bounded by arcs of circles (or straight
+  lines), no two of these regions overlapping, such that any
+  substitution of the kind under consideration, [tau]' = (p' +
+  q'[tau])/(p + q[tau]) leads from an arbitrary point [tau], of one of
+  these regions, to a point [tau]' of another; taking [tau] = [rho] +
+  i[sigma], one of these regions may be taken to be that for which -1/2
+  < [rho] < 1/2, [rho]^2 + [sigma]^2 > 1, together with the points for
+  which [rho] is negative on the curves limiting this region; then every
+  other region is obtained from this so-called fundamental region by one
+  and only one of the substitutions [tau] = (p' + q'[tau])/(p + q[tau]),
+  and hence by a definite combination of the substitutions [tau]' =
+  -1/[tau], [tau]' = 1 + [tau]. Upon the infinite half plane of [tau],
+  the function considered above,
+
+               4  [RN^2(1/2[omega]) + RN(z(1/2[omega]) RN(1/2[omega]') + RN^2 (1/2[omega]')]^3
+    z([tau]) = -- ----------------------------------------------------------------------------
+               27    RN^2(1/2[omega]) RN^2(1/2[omega]') [RN(1/2[omega]) + RN(1/2[omega]')]^2
+
+  is a single valued monogenic function, whose only essential
+  singularities are the points [tau]' = (p' + q'[tau])/(p + q[tau]) for
+  which [tau] = [oo], namely those for which [tau]' is any real rational
+  value; the real axis is thus a line over which the function z([tau])
+  cannot be continued, having an essential singularity in every arc of
+  it, however short; in the fundamental region, z([tau]) has thus only
+  the single essential singularity, r = [rho] + i[sigma], where [sigma]
+  = [oo]; in this fundamental region z([tau]) takes any assigned complex
+  value just once, the relation z([tau]') = z([tau]) requiring, as can
+  be shown, that [tau]' is of the form (p' + q'[tau])/(p + q[tau]), in
+  which p, q, p', q' are integers with pq' - p'q = 1; the function
+  z([tau]) has thus a similar behaviour in every other of the regions.
+  The division of the plane into regions is analogous to the division of
+  the plane, in the case of doubly periodic functions, into
+  parallelograms; in that case we considered only functions without
+  essential singularities, and in each of the regions the function
+  assumed every complex value twice, at least. Putting, as another
+  function of [tau], J([tau]) = z([tau])[z([tau]) - 1], it can be shown
+  that J([tau]) = 0 for [tau] = exp (2/3[pi]i), that J([tau]) = 1 for
+  [tau] = i, these being values of [tau] on the boundary of the
+  fundamental region; like z([tau]) it has an essential singularity for
+  [tau] = [rho] + i[sigma], [sigma] = + [oo]. In the theory of linear
+  differential equations it is important to consider the inverse
+  function [tau](J); this is infinitely many valued, having a cycle of
+  three values for circulation of J about J = 0 (the circuit of this
+  point leading to a linear substitution for [tau] of period 3, such as
+  [tau]' = -(1 + [tau])^(-1)), having a cycle of two values about J = 1
+  (the circuit leading to a linear substitution for [tau] of period 2,
+  such as [tau]' = -[tau]^(-1)), and having a cycle of infinitely many
+  values about J = [oo] (the circuit leading to a linear substitution
+  for [tau] which is not periodic, such as [tau]' = 1 + [tau]). These
+  are the only singularities for the function [tau](J). Each of the
+  functions
+                                         _                                    _
+                                        |   RN(1/2[omega]) + 2RN(1/2[omega]')  |^(1/8)
+    [J([tau])]^(1/3), [J([tau])-1]^1/2, | - ---------------------------------  |     ,
+                                        |_  RN(1/2[omega]) - RN(1/2)[omega]') _|
+
+  beside many others (see below), is a single valued function of [tau],
+  and is expressible without ambiguity in terms of the single valued
+  function of [tau],
+
+                       /i[pi][tau]\    [oo]
+    [eta]([tau]) = exp( ---------- ) [Pi]   [1-exp (2i[pi]n[tau])],
+                       \    12    /     n=1
+
+                    /i[pi][tau]\   _[oo]
+              = exp(----------- ) \    (-1)^m exp [(3m^2 + m) i[pi][tau]].
+                    \    12    /  /_
+                                m = -[oo]
+
+  It should be remarked, however, that [eta]([tau]) is not unaltered by
+  all the substitutions we have considered; in fact
+
+    [eta](-[tau]^(-1)) = (-i[tau])1/2[eta]([tau]), [eta](1 + [tau]) =
+      exp (1/12 i[pi]) [eta]([tau]).
+
+  The aggregate of the substitutions [tau]' = (p' + q'[tau])/(p +
+  q[tau]), wherein p, q, p', q' are integers with pq' - p'q = 1,
+  represents a _Group_; the function J([tau]), unaltered by all these
+  substitutions, is called a _Modular Function_. More generally any
+  function unaltered by all the substitutions of a group of linear
+  substitutions of its variable is called an _Automorphic Function_. A
+  rational function, of its variable h, of this character, is the
+  function (1 - h + h^2)^3 h^(-2)(1 - h)^(-2) presenting itself
+  incidentally above; and there are other rational functions with a
+  similar property, the group of substitutions belonging to any one of
+  these being, what is a very curious fact, associable with that of the
+  rotations of one of the regular solids, about an axis through its
+  centre, which bring the solid into coincidence with itself. Other
+  automorphic functions are the double periodic functions already
+  discussed; these, as we have seen, enable us to solve the algebraic
+  equation y^2 = 4x^3 - g2x - g3 (and in fact many other algebraic
+  equations, see below, under S 23, _Geometrical Applications of
+  Elliptic Functions_) in terms of single valued functions x = RN(u), y
+  = -RN'(u). A similar utility, of a more extended kind, belongs to
+  automorphic functions in general; but it can be shown that such
+  functions necessarily have an infinite number of essential
+  singularities except for the simplest cases.
+
+  The modular function J([tau]) considered above, unaltered by the group
+  of linear substitutions [tau]' = (p' + q'[tau]) / (p + q[tau]), where
+  p, q, p', q' are integers with pq' - p'q = 1, may be taken as the
+  independent variable x of a differential equation of the third order,
+  of the form
+
+    s'''   3   /s''\^2    1 - a^2    1 - [beta]^2   [alpha]^2 + [beta]^2 - [gamma]^2 - 1
+    ---- - -- ( --- ) = ---------- + ------------ + ------------------------------------,
+     s'    2   \ s'/    2(x - 1)^2       2x^2                    2x(x - 1)
+
+  where s' = ds/dx, &c., of which the dependent variable s is equal to
+  [tau]. A differential equation of this form is satisfied by the
+  quotient of two independent integrals of the linear differential
+  equation of the second order satisfied by the hypergeometric
+  functions. If the solution of the differential equation for s be
+  written s([alpha], [beta], [gamma], x), we have in fact [tau] = s(1/2,
+  1/3, 0, J). If we introduce also the function of [tau] given by
+
+               2RN (1/2[omega]') + f V(1/2[omega])
+    [lambda] = -----------------------------------,
+                 RN(1/2[omega]') - RN(1/2[omega])
+
+  we similarly have [tau] = s(0, 0, 0, [lambda]); this function [lambda]
+  is a single valued function of [tau], which is also a modular
+  function, being unaltered by a group of integral substitutions also of
+  the form [tau]' = (p' + q'[tau])/(p + q[tau]), with pq' - p'q = 1, but
+  with the restriction that p' and q are even integers, and therefore p
+  and q' are odd integers. This group is thus a subgroup of the general
+  modular group, and is in fact of the kind called a self-conjugate
+  subgroup. As in the general case this subgroup is associated with a
+  subdivision of the plane into regions of which any one is obtained
+  from a particular region, called the fundamental region, by a
+  particular one of the substitutions of the subgroup. This fundamental
+  region, putting [tau] = [rho] + i[sigma], may be taken to be that
+  given by -1 < [rho] < 1, ([rho] + 1/2)^2 + [sigma]^2 > 1/4, ([rho] -
+  1/2)^2 + [sigma]^2 > 1/4, and is built up of six of the regions which
+  arose for the general modular group associated with J([tau]). Within
+  this fundamental region, [lambda] takes every complex value just once,
+  except the values [lambda] = 0, 1, [oo], which arise only at the
+  angular points [tau] = 0, [tau] = [oo], [tau] = -1 and the equivalent
+  point [tau] = 1; these angular points are essential singularities for
+  the function [lambda]([tau]). For [lambda]([tau]) as for J([tau]), the
+  region of existence is the upper half plane of [tau], there being an
+  essential singularity in every length of the real axis, however short.
+
+
+  If, beside the plane of [tau], we take a plane to represent the values
+  of [lambda], the function [tau] = s(0, 0, 0, [lambda]) being
+  considered thereon, the values of [tau] belonging to the interior of
+  the fundamental region of the [tau]-plane considered above, will
+  require the consideration of the whole of the [lambda]-plane taken
+  once with the exception of the portions of the real axis lying between
+  -[oo] and 0 and between 1 and + [oo], the two sides of the first
+  portion corresponding to the circumferences of the [tau]-plane
+  expressed by ([rho] + 1/2)^2 + [sigma]^2 = 1/4, ([rho] - 1/2)^2 +
+  [sigma]^2 = 1/4, while the two sides of the latter portion, for which
+  [lambda] is real and > 1, correspond to the lines of the [tau]-plane
+  expressed by [rho] = [+-]1. The line for which [lambda] is real,
+  positive and less than unity corresponds to the imaginary axis of the
+  [tau]-plane, lying in the interior of the fundamental region. All the
+  values of [tau] = s(0, 0, 0, [lambda]) may then be derived from those
+  belonging to the fundamental region of the [tau]-plane by making
+  [lambda] describe a proper succession of circuits about the points
+  [lambda] = 0, [lambda] = 1; any such circuit subjects [tau] to a
+  linear substitution of the subgroup of [tau] considered, and
+  corresponds to a change of [tau] from a point of the fundamental
+  region to a corresponding point of one of the other regions.
+
+S 22. _A Property of Integral Functions deduced from the Theory of
+Modular Functions._--Consider now the function exp(z), for finite values
+of z; for such values of z, exp(z) never vanishes, and it is impossible
+to assign a closed circuit for z in the finite part of the plane of z
+which will make the function [lambda] = exp(z) pass through a closed
+succession of values in the plane of [lambda] having [lambda] = 0 in its
+interior; the function s[0, 0, 0, exp(z)], however z vary in the finite
+part of the plane, will therefore never be subjected to those linear
+substitutions imposed upon s(0, 0, 0, [lambda]) by a circuit of [lambda]
+about [lambda] = 0; more generally, if [phi](z) be an integral function
+of z, never becoming either zero or unity for finite values of z, the
+function [lambda] = [phi](z), however z vary in the finite part of the
+plane, will never make, in the plane of [lambda], a circuit about either
+[lambda] = 0 or [lambda] = 1, and s(0, 0, 0, [lambda]), that is s[0, 0,
+0, [phi](z)], will be single valued for all finite values of z; it will
+moreover remain finite, and be monogenic. In other words, s[0, 0, 0,
+[phi](z)] is also an integral function--whose imaginary part, moreover,
+by the property of s(0, 0, 0, [lambda]), remains positive for all finite
+values of z. In that case, however, exp{is[0, 0, 0, [phi](z)]} would
+also be an integral function of z with modulus less than unity for all
+finite values of z. If, however, we describe a circle of radius R in the
+z plane, and consider the greatest value of the modulus of an integral
+function upon this circle, this certainly increases indefinitely as R
+increases. We can infer therefore that _an integral function [phi](z)
+which does not vanish for any finite value of z, takes the value unity
+and hence_ (by considering the function A^(-1)[phi](z)) _takes every
+other value for some definite value of z_; or, an integral function for
+which both the equations [phi](z) = A, [phi](z) = B are unsatisfied by
+definite values of z, does not exist, A and B being arbitrary constants.
+
+  A similar theorem can be proved in regard to the values assumed by the
+  function [phi](z) for points z of modulus greater than R, however
+  great R may be, also with the help of modular functions. In general
+  terms it may be stated that it is a very exceptional thing for an
+  integral function not to assume every complex value an infinite number
+  of times.
+
+  Another application of modular functions is to prove that the function
+  s([alpha], [beta], [gamma], [lambda]) is a single valued function of
+  [tau] = s(0, 0, 0, [lambda]); for, putting [tau]' = ([tau] - i)/([tau]
+  + i), the values of [tau]' which correspond to the singular points
+  [lambda] = 0, 1, [oo] of s([alpha], [beta], [gamma], [lambda]), though
+  infinite in number, all lie on the circumference of the circle
+  |[tau]'| = 1, within which therefore s([alpha], [beta], [gamma], x) is
+  expressible in a form [Sigma] [n = 0 to [oo]] a_n[tau]'^n. More
+  generally any monogenic function of [lambda] which is single valued
+  save for circuits of the points [lambda] = 0, 1, [oo], is a single
+  valued function of [tau] = s(0, 0, 0, [lambda]). Identifying [lambda]
+  with the square of the modulus in Legendre's form of the elliptical
+  integral, we have [tau] = iK'/K, where
+
+         _                                           _
+        /1                dt                        /1                  dt
+    K = |  ----------------------------------, K' = |  ---------------------------------------;
+       _/0  [root][1 - t^2] [1 - [lambda]t^2]      _/0 [root][1 - t^2] [1 - (1 - [lambda])t^2]
+
+  functions such as [lambda]^1/4, (1 - [lambda])^1/4, [[lambda](1 -
+  [lambda])]^1/4, which have only [lambda] = 0, 1, [oo] as singular
+  points, were expressed by Jacobi as power series in q =
+  e^(i[pi][tau]), and therefore, at least for a limited range of values
+  of [tau], as single valued functions of [tau]; it follows by the
+  theorem given that any product of a root of [lambda] and a root of 1 -
+  [lambda] is a single valued function of [tau]. More generally the
+  differential equation
+
+             d^2y                                       dy
+    x(1 - x) ---- + [[gamma] - ([alpha] + [beta] + 1)x] -- -[alpha][beta][gamma] = 0
+             dx^2                                       dx
+
+  may be solved by expressing both the independent and dependent
+  variables as single valued functions of a single variable [tau], the
+  expression for the independent variable being x = [lambda]([tau]).
+
+S 23. _Geometrical Applications of Elliptic Functions._--Consider any
+irreducible algebraic equation rational in x, y, f(x, y) = 0, of such a
+form that the equation represents a plane curve of order n with 1/2n(n
+-3) double points; taking upon this curve n-3 arbitrary fixed points,
+draw through these and the double points the most general curve of order
+n -2; this will intersect [f] in n(n - 2) - n(n - 3) - (n - 3) = 3
+other points, and will contain homogeneously at least 1/2(n - 1)n -
+1/2n(n -3) - (n - 3) = 3 arbitrary constants, and so will be of the form
+[lambda][phi] + [lambda]1[phi]1 + [lambda]2[phi]2 + ... = 0, wherein
+[lambda]3, [lambda]4, ... are in general zero. Put now [xi] =
+[phi]1/[phi], [eta] = [phi]2/[phi] and eliminate x, y between these
+equations and [f](x, y) = 0, so obtaining a rational irreducible
+equation F([xi], [eta]) = 0, representing a further plane curve. To any
+point (x, y) of [f] will then correspond a definite point ([xi], [eta])
+of F.
+
+  For a general position of (x, y) upon [f] the equations [phi]1(x',
+  y')/[phi](x', y') = [phi]1(x, y)/[phi](x, y), [phi]2(x', y')/[phi](x',
+  y') = [phi]2(x, y)/[phi](x, y), subject to [f](x', y') = 0, will have
+  the same number of solutions (x', y'); if their only solution is x' =
+  x, y' = y, then to any position ([xi],[eta]) of F will conversely
+  correspond only one position (x, y) of [f]. If these equations have
+  another solution beside (x, y), then any curve [lambda][phi] +
+  [lambda]1[phi]1 + [lambda]2[phi]2 = 0 which passes (through the double
+  points of [f] and) through the n - 2 points of [f] constituted by the
+  fixed n-3 points and a point (x0, y0), will necessarily pass through a
+  further point, say (x0', y0'), and will have only one further
+  intersection with [f]; such a curve, with the n - 2 assigned points,
+  beside the double points, of [f], will be of the form [mu][psi] +
+  [mu]1[psi]1 + ... = 0, where [mu]2, [mu]3, ... are generally zero;
+  considering the curves [psi] + t[psi]1 = 0, for variable t, one of
+  these passes through a further arbitrary point of [f], by choosing t
+  properly, and conversely an arbitrary value of t determines a single
+  further point of [f]; the co-ordinates of the points of [f] are thus
+  rational functions of a parameter t, which is itself expressible
+  rationally by the co-ordinates of the point; it can be shown
+  algebraically that such a curve has not 1/2(n - 3)n but 1/2(n - 3)n +
+  1 double points. We may therefore assume that to every point of F
+  corresponds only one point of [f], and there is a birational
+  transformation between these curves; the coefficients in this
+  transformation will involve rationally the co-ordinates of the n-3
+  fixed points taken upon [f], that is, at the least, by taking these to
+  be consecutive points, will involve the co-ordinates of one point of
+  [f], and will not be rational in the coefficients of [f] unless we can
+  specify a point of [f] whose co-ordinates are rational in these. The
+  curve F is intersected by a straight line a[xi] + b[eta] + c = 0 in as
+  many points as the number of unspecified intersections of [f] with
+  a[phi] + b[phi]1 + c[phi]2 = 0, that is, 3; or F will be a cubic
+  curve, without double points.
+
+  Such a cubic curve has at least one point of inflection Y, and if a
+  variable line YPQ be drawn through Y to cut the curve again in P and
+  Q, the locus of a point R such that YR is the harmonic mean of YP and
+  YQ, is easily proved to be a straight line. Take now a triangle of
+  reference for homogeneous co-ordinates XYZ, of which this straight
+  line is Y = 0, and the inflexional tangent at Y is Z = 0; the equation
+  of the cubic curve will then be of the form
+
+    ZY^2 = aX^3 + bX^2Z + cXZ^2 + dZ^3;
+
+  by putting X equal to [lambda]X + [mu]Z, that is, choosing a suitable
+  line through Y to be X = 0, and choosing [lambda] properly, this is
+  reduced to the form
+
+    ZY^2 = 4X^3 - g2XZ^2  -g3Z^3,
+
+  of which a representation is given, valid for every point, in terms of
+  the elliptic functions RN(u), RN'(u), by taking X = ZRN(u), Y =
+  ZRN'(u). The value of u belonging to any point is definite save for
+  sums of integral multiples of the periods of the elliptic functions,
+  being given by
+         _
+        /  (x)  ZdX - XdZ
+    u = |       ---------,
+       _/ ([oo])   ZY
+
+  where ([oo]) denotes the point of inflection.
+
+  It thus appears that the co-ordinates of any point of a plane curve,
+  [f], of order n with 1/2(n - 3)n double points are expressible as
+  elliptic functions, there being, save for periods, a definite value of
+  the argument u belonging to every point of the curve. It can then be
+  shown that if a variable curve, [phi], of order m be drawn, passing
+  through the double points of the curve, the values of the argument u
+  at the remaining intersections of [phi] with [f], have a sum which is
+  unaffected by variation of the coefficients of [phi], save for
+  additive aggregates of the periods. In virtue of the birational
+  transformation this theorem can be deduced from the theorem that if
+  any straight line cut the cubic y^2 = 4x^3 - g2x - g3, in points (u1),
+  (u2), (u3), the sum u1 + u2 + u3 is zero, or a period; or the general
+  theorem is a corollary from Abel's theorem proved under S 17,
+  _Integrals of Algebraic Functions_. To prove the result directly for
+  the cubic we remark that the variation of one of the intersections (x,
+  y) of the cubic with the straight line y = mx + n, due to a variation
+  [delta]m, [delta]n in m and n, is obtained by differentiation of the
+  equation for the three abscissae, namely the equation
+
+    F(x) = 4x^3 - g2x - g3 - (mx + n)^2 = 0,
+
+  and is thus given by
+
+    dx     x[delta]m + [delta]n
+    -- = 2 --------------------,
+    y             F'(x)
+
+  and the sum of three such fractions as that on the right for the three
+  roots of F(x) = 0 is zero; hence u1 + u2 + u3 is independent of the
+  straight line considered; if in particular this become the inflexional
+  tangent each of u1, u2, u3 vanishes. It may be remarked in passing
+  that x1 + x2 + x3 = 1/4m^2, and hence is 1/4{(y1 - y2)/(x1 - x2)}^2; so
+  that we have another proof of the addition equation for the function
+  RN(u). From this theorem for the cubic curve many of its geometrical
+  properties, as for example those of its inflections, the properties of
+  inscribed polygons, of the three kinds of corresponding points, and
+  the theory of residuation, are at once obvious. And similar results
+  hold for the curve of order n with 1/2(n - 3)n double points.
+
+S 24. _Integrals of Algebraic Functions in Connexion with the Theory of
+Plane Curves._--The developments which have been explained in connexion
+with elliptic functions may enable the reader to appreciate the vastly
+more extensive theory similarly arising for any algebraical
+irrationality, [f](x, y) = o.
+
+  The algebraical integrals [int] R(x, y)dx associated with this may as
+  before be divided into those of the _first kind_, which have no
+  infinities, those of the _second kind_, possessing only algebraical
+  infinities, and those of the _third kind_, for which logarithmic
+  infinities enter. Here there is a certain number, p, greater than
+  unity, of linearly independent integrals of the first kind; and this
+  number p is unaltered by any birational transformation of the
+  fundamental equation [f](x, y) = 0; a rational function can be
+  constructed with poles of the first order at p + 1 arbitrary positions
+  (x, y), satisfying [f](x, y) = 0, but not with a fewer number unless
+  their positions are chosen properly, a property we found for the case
+  p = 1; and p is the number of linearly independent curves of order n-3
+  passing through the double points of the curve of order n expressed by
+  [f](x, y) = 0. Again any integral of the second kind can be expressed
+  as a sum of p integrals of this kind, with poles of the first order at
+  arbitrary positions, together with rational functions and integrals of
+  the first kind; and an integral of the second kind can be found with
+  one pole of the first order of arbitrary position, and an integral of
+  the third kind with two logarithmic infinities, also of arbitrary
+  position; the corresponding properties for p = 1 are proved above.
+
+  There is, however, a difference of essential kind in regard to the
+  inversion of integrals of the first kind; if u = [int] R(x, y)dx be
+  such an integral, it can be shown, in common with all algebraic
+  integrals associated with [f](x, y) = 0, to have 2p linearly
+  independent additive constants of indeterminateness; the upper limit
+  of the integral cannot therefore, as we have shown, be a single valued
+  function of the value of the integral. The corresponding theorem, if
+  [int] R_i(x, y)dx denote one of the integrals of the first kind, is
+  that the p equations
+      _                         _
+     /                         /
+     | R_i (x1, y1)dx1 + ... + | Ri (x_p, y_p) dx_p = u_i,
+    _/                        _/
+
+  determine the rational symmetric functions of the p positions (x1,
+  y1), ... (x_p, y_p) as single valued functions of the p variables, u1,
+  ... u_p. It is thus necessary to enter into the theory of functions of
+  several independent variables; and the equation [f](x, y) = 0 is thus
+  not, in this way, capable of solution by single valued functions of
+  one variable. That solution in fact is to be sought with the help of
+  automorphic functions, which, however, as has been remarked, have, for
+  p > 1, an infinite number of essential singularities.
+
+S 25. _Monogenic Functions of Several Independent Variables._--A
+monogenic function of several independent complex variables u_i, ... u_p
+is to be regarded as given by an aggregate of power series all
+obtainable by continuation from any one of them in a manner analogous to
+that before explained in the case of one independent variable. The
+singular points, defined as the limiting points of the range over which
+such continuation is possible, may either be _poles_, or _polar points
+of indetermination_, or _essential singularities_.
+
+  A pole is a point (u1^(0), ... u_p^(0)) in the neighbourhood of which
+  the function is expressible as a quotient of converging power series
+  in u1 - u1^(0) ... u_p - u_p^(0); of these the denominator series D
+  must vanish at (u1^(0), ... u_p^(0)), since else the fraction is
+  expressible as a power series and the point is not a singular point,
+  but the numerator series N must not also vanish at (u1^(0), ...
+  u_p^(0)), or if it does, it must be possible to write D = M0, N = MN0,
+  where M is a converging power series vanishing at (u1^(0), ...
+  u_p^(0)), and N0 is a converging power series, in (u1 - u1^(0) ... u_p
+  - u_p^(0)), not so vanishing. A polar point of indetermination is a
+  point about which the function can be expressed as a quotient of two
+  converging power series, both of which vanish at the point. As in such
+  a simple case as (Ax + By) / (ax + by), about x = 0, y = 0, it can be
+  proved that then the function can be made to approach to any
+  arbitrarily assigned value by making the variables u1, ... u_p
+  approach to u1^(0), ... u_p^(0) by a proper path. It is the necessary
+  existence of such polar points of indetermination, which in case p > 2
+  are not merely isolated points, which renders the theory essentially
+  more difficult than that of functions of one variable. An essential
+  singularity is any which does not come under one of the two former
+  descriptions and includes very various possibilities. A point at
+  infinity in this theory is one for which any one of the variables u1,
+  ... u_p is indefinitely great; such points are brought under the
+  preceding definitions by means of the convention that for u_i^(0) =
+  [oo], the difference u_i - u_i^(0) is to be understood to stand for
+  u_i^(-1) . This being so, a single valued function of u1, ... u_p
+  without essential singularities for infinite or finite values of the
+  variables can be shown, by induction, to be, as in the case of p = 1,
+  necessarily a rational function of the variables. A function having no
+  singularities for finite values of all the variables is as before
+  called an integral function; it is expressible by a power series
+  converging for all finite values of the variables; a single valued
+  function having for finite values of the variables no singularities
+  other than poles or polar points of indetermination is called a
+  meromorphic function; as for p = 1 such a function can be expressed as
+  a quotient of two integral functions having no common zero point other
+  than the points of indetermination of the function; but the proof of
+  this theorem is difficult.
+
+  The single valued functions which occur, as explained above, in the
+  inversion of algebraic integrals of the first kind, for p > 1, are
+  meromorphic. They must also be periodic, unaffected that is when the
+  variables u1, ... u_p are _simultaneously_ increased each by a proper
+  constant, these being the additive constants of indeterminateness for
+  the p integrals [int] R_i(x, y)dx arising when (x, y) makes a closed
+  circuit, the same for each integral. The theory of such single valued
+  meromorphic periodic functions is simpler than that of meromorphic
+  functions of several variables in general, as it is sufficient to
+  consider only finite values of the variables; it is the natural
+  extension of the theory of doubly periodic functions previously
+  discussed. It can be shown to reduce, though the proof of this
+  requires considerable developments of which we cannot speak, to the
+  theory of a single integral function of u1, ... u_p, called the _Theta
+  Function_. This is expressible as a series of positive and negative
+  integral powers of quantities exp (c1u1), exp (c2u2), ... exp (c_p
+  u_p), wherein c1, ... c_p are proper constants; for p = 1 this theta
+  function is essentially the same as that above given under a different
+  form (see S 14, _Doubly Periodic Functions_), the function [sigma](u).
+  In the case of p = 1, all meromorphic functions periodic with the same
+  two periods have been shown to be rational functions of two of them
+  connected by a single algebraic equation; in the same way all
+  meromorphic functions of p variables, periodic with the same sets of
+  simultaneous periods, 2p sets in all, can be shown to be expressible
+  rationally in terms of p + 1 such periodic functions connected by a
+  single algebraic equation. Let x1, ... x_p, y denote p + 1 such
+  functions; then each of the partial derivatives dx_i/(Pd)u_i will
+  equally be a meromorphic function of the same periods, and so
+  expressible rationally in terms of x1, ... x_p, y; thus there will
+  exist p equations of the form
+
+    dx_i = R1 du1 + ... + R_p du_p,
+
+  and hence p equations of the form
+
+    du_i = H_(i, 1)dx1 + ... + H_(i, p)dx_p,
+
+  wherein H_(i, j) are rational functions of x1, ... x_p, y, these being
+  connected by a fundamental algebraic (rational) equation, say [f](x1,
+  ... x_p, y) = 0. This then is the generalized form of the
+  corresponding equation for p = 1.
+
+S 26. _Multiply-Periodic Functions and the Theory of Surfaces._--The
+theory of algebraic integrals [int] R(x, y)dx, wherein x, y are
+connected by a rational equation [f](x, y) = 0, has developed
+concurrently with the theory of algebraic curves; in particular the
+existence of the number p invariant by all birational transformations is
+one result of an extensive theory in which curves capable of birational
+correspondence are regarded as equivalent; this point of view has made
+possible a general theory of what might otherwise have remained a
+collection of isolated theorems.
+
+  In recent years developments have been made which point to a similar
+  unity of conception as possible for surfaces, or indeed for algebraic
+  constructs of any number of dimensions. These developments have been
+  in two directions, at first followed independently, but now happily
+  brought into the most intimate connexion. On the analytical side, E.
+  Picard has considered the possibility of classifying integrals of the
+  form [int](Rds + Sdy), belonging to a surface [f](x, y, z) = 0,
+  wherein R and S are rational functions of x, y, z, according as they
+  are (1) everywhere finite, (2) have poles, which then lie along curves
+  upon the surface, or (3) have logarithmic infinities, also then lying
+  along curves, and has brought the theory to a high degree of
+  perfection. On the geometrical side A. Clebsch and M. Noether, and
+  more recently the Italian school, have considered the geometrical
+  characteristics of a surface which are unaltered by birational
+  transformation. It was first remarked that for surfaces of order n
+  there are associated surfaces of order n-4, having properties in
+  relation thereto analogous to those of curves of order n-3 for a plane
+  curve of order n; if such a surface [f](x, y, z) = 0 have a double
+  curve with triple points triple also for the surface, and [phi](x, y,
+  z) = 0 be a surface of order n - 4 passing through the double curve,
+  the double integral
+      _  _
+     /  /  [phi] dx dy
+     |  |  -----------
+    _/ _/  (Pd)f/(Pd)z
+
+  is everywhere finite; and, the most general everywhere finite integral
+  of this form remains invariant in a birational transformation of the
+  surface [f], the theorem being capable of generalization to algebraic
+  constructs of any number of dimensions. The number of linearly
+  independent surfaces of order n - 4, possessing the requisite
+  particularity in regard to the singular lines and points of the
+  surface, is thus a number invariant by birational transformation, and
+  the equality of these numbers for two surfaces is a necessary
+  condition of their being capable of such transformation. The number of
+  surfaces of order m having the assigned particularity in regard to the
+  singular points and lines of the fundamental surface can be given by a
+  formula for a surface of given singularity; but the value of this
+  formula for m = n - 4 is not in all cases equal to the actual number
+  of surfaces of order n - 4 with the assigned particularity, and for a
+  cone (or ruled surface) is in fact negative, being the negative of the
+  deficiency of the plane section of the cone. Nevertheless this number
+  for m = n - 4 is also found to be invariant for birational
+  transformation. This number, now denoted by p_a, is then a second
+  invariant of birational transformation. The former number, of actual
+  surfaces of order n - 4 with the assigned particularity in regard to
+  the singularities of the surface, is now denoted by p_g. The
+  difference p_g - p_a, which is never negative, is a most important
+  characteristic of a surface. When it is zero, as in the case of the
+  general surface of order n, and in a vast number of other ordinary
+  cases, the surface is called regular.
+
+  On a plane algebraical curve we may consider linear series of sets of
+  points, obtained by the intersection with it of curves [lambda][phi] +
+  [lambda]1[phi]1 + ... = 0, wherein [lambda], [lambda]1, ... are
+  variable coefficients; such a series consists of the sets of points
+  where a rational function of given poles, belonging to the construct
+  [f](x, y) = 0, has constant values. And we may consider series of sets
+  of points determined by variable curves whose coefficients are
+  algebraical functions, not necessarily rational functions, of
+  parameters. Similarly on a surface we may consider linear systems of
+  curves, obtained by the intersection with the given surface of
+  variable surfaces [lambda][phi] + [lambda]1[phi]1 + ... = 0, and may
+  consider algebraic systems, of which the individual curve is given by
+  variable surfaces whose coefficients are algebraical, not necessarily
+  rational, functions of parameters. Of a linear series upon a plane
+  curve there are two numbers manifestly invariant in birational
+  transformation, the _order_, which is the number of points forming a
+  set of the series, and the _dimension_, which is the number of
+  parameters [lambda]1/[lambda], [lambda]2/[lambda], ... entering
+  linearly in the equation of the series. The series is _complete_ when
+  it is not contained in a series of the same order but of higher
+  dimension. So for a linear system of curves upon a surface, we have
+  three invariants for birational transformation; the _order_, being in
+  the number of variable intersections of two curves of the system, the
+  _dimension_, being the number of linear parameters [lambda]1/[lambda],
+  [lambda]2/[lambda], ... in the equation for the system, and the
+  _deficiency_ of the individual curves of the system. Upon any curve of
+  the linear system the other curves of the system define a linear
+  series, called the _characteristic_ series; but even when the linear
+  system is complete, that is, not contained in another linear system of
+  the same order and higher dimension, it does not follow that the
+  characteristic series is complete; it may be contained in a series
+  whose dimension is greater by p_g - p_a than its own dimension. When
+  this is so it can be shown that the linear system of curves is
+  contained in an algebraic system whose dimension is greater by p_g -
+  p_a than the dimension of the linear system. The extra p = p_g - p_a
+  variable parameters so entering may be regarded as the independent
+  co-ordinates of an algebraic construct [f](y, x1, ... x_p) = 0; this
+  construct has the property that its co-ordinates are single valued
+  meromorphic functions of p variables, which are periodic, possessing
+  2p systems of periods; the p variables are expressible in the forms
+           _
+          /
+    u_i = | R1(x, y) dx1 + ... + R_p(x, y) dx_p,
+         _/
+
+  wherein R_i(x, y) denotes a rational function of x1, ... x_p and y.
+  The original surface has correspondingly p integrals of the form
+  [int](R dx + S dy), wherein R, S are rational in x, y, z, which are
+  everywhere finite; and it can be shown that it has no other such
+  integrals. From this point of view, then, the number p, = p_g - p_a
+  is, for a surface, analogous to the deficiency of a plane curve;
+  another analogy arises in the comparison of the theorems: for a plane
+  curve of zero deficiency there exists no algebraic series of sets of
+  points which does not consist of sets belonging to a linear series;
+  for a surface for which p_g - p_a = 0 there exists no algebraic system
+  of curves not contained in a linear system.
+
+  But whereas for a plane curve of deficiency zero, the co-ordinates of
+  the points of the curve are rational functions of a single parameter,
+  it is not necessarily the case that for a surface having p_g - p_a = 0
+  the co-ordinates of the points are rational functions of two
+  parameters; it is necessary that p_g - p_a = 0, but this is not
+  sufficient. For surfaces, beside the p_g linearly independent surfaces
+  of order n - 4 having a definite particularity at the singularities of
+  the surface, it is useful to consider surfaces of order k(n - 4), also
+  having each a definite particularity at the singularities, the number
+  of these, not containing the original surface as component, which are
+  linearly independent, is denoted by P_k. It can then be stated that a
+  sufficient condition for a surface to be rational consists of the two
+  conditions p_a = 0, P2 = 0. More generally it becomes a problem to
+  classify surfaces according to the values of the various numbers which
+  are invariant under birational transformation, and to determine for
+  each the simplest form of surface to which it is birationally
+  equivalent. Thus, for example, the hyperelliptic surface discussed by
+  Humbert, of which the co-ordinates are meromorphic functions of two
+  variables of the simplest kind, with four sets of periods, is
+  characterized by p_g = 1, p_a = -1; or again, any surface possessing a
+  linear system of curves of which the order exceeds twice the
+  deficiency of the individual curves diminished by two, is reducible by
+  birational transformation to a ruled surface or is a rational surface.
+  But beyond the general statement that much progress has already been
+  made in this direction, of great interest to the student of the theory
+  of functions, nothing further can be added here.
+
+  BIBLIOGRAPHY.--The learner will find a lucid introduction to the
+  theory in E. Goursat, _Cours d'analyse mathematique_, t. ii. (Paris,
+  1905), or, with much greater detail, in A.R. Forsyth, _Theory of
+  Functions of a Complex Variable_ (2nd ed., Cambridge, 1900); for
+  logical rigour in the more difficult theorems, he should consult W.F.
+  Osgood, _Lehrbuch der Functionentheorie_, Bd. i. (Leipzig, 1906-1907);
+  for greater precision in regard to the necessary quasi-geometrical
+  axioms, beside the indications attempted here, he should consult W.H.
+  Young, _The Theory of Sets of Points_ (Cambridge, 1906), chs.
+  viii.-xiii., and C. Jordan, _Cours d'analyse_, t. i. (Paris, 1893),
+  chs. i., ii.; a comprehensive account of the _Theory of Functions of
+  Real Variables_ is by E.W. Hobson (Cambridge, 1907). Of the theory
+  regarded as based after Weierstrass upon the theory of power series,
+  there is J. Harkness and F. Morley, _Introduction to the Theory of
+  Analytic Functions_ (London, 1898), an elementary treatise; for the
+  theory of the convergence of series there is also T.J. I'A. Bromwich,
+  _An Introduction to the Theory of Infinite Series_ (London, 1908); but
+  the student should consult the collected works of Weierstrass (Berlin,
+  1894 ff.), and the writings of Mittag-Leffler in the early volumes of
+  the _Acta mathematica_; earlier expositions of the theory of functions
+  on the basis of power series are in C. Meray, _Lecons nouvelles sur
+  l'analyse infinitesimale_ (Paris, 1894), and in Lagrange's books on
+  the Theory of Functions. An account of the theory of potential in its
+  applications to the present theory is found in most treatises; in
+  particular consult E. Picard, _Traite d'analyse_, t. ii. (Paris,
+  1893). For elliptic functions there is an introductory book, P. Appell
+  and E. Lacour, _Principes de la theorie des fonctions elliptiques et
+  applications_ (Paris, 1897), beside the treatises of G.H. Halphen,
+  _Traite des fonctions elliptiques et de leurs applications_ (three
+  parts, Paris, 1886 ff.), and J. Tannery et J. Molk, _Elements de la
+  theorie des fonctions elliptiques_ (Paris, 1893 ff.); a book, A.G.
+  Greenhill, _The Applications of Elliptic Functions_ (London, 1892),
+  shows how the functions enter in problems of many kinds. For modular
+  functions there is an extensive treatise, F. Klein and R. Fricke,
+  _Theorie der elliptischen Modulfunctionen_ (Leipzig, 1890); see also
+  the most interesting smaller volume, F. Klein, _Uber das Ikosaeder_
+  (Leipzig, 1884) (also obtainable in English). For the theory of
+  Riemann's surface, and algebraic integrals, an interesting
+  introduction is P. Appeil and E. Goursat, _Theorie des fonctions
+  algebriques et de leurs integrales_; for Abelian functions see also H.
+  Stahl, _Theorie der Abel'schen Functionen_ (Leipzig, 1896), and H.F.
+  Baker, _An Introduction to the Theory of Multiply Periodic Functions_
+  (Cambridge, 1907), and H.F. Baker, _Abel's Theorem and the Allied
+  Theory, including the Theory of the Theta Functions_ (Cambridge,
+  1897); for theta functions of one variable a standard work is C.G.
+  Jacobi, _Fundamenta nova, &c._ (Konigsberg, 1828); for the general
+  theory of theta functions, consult W. Wirtinger, _Untersuchungen uber
+  Theta-Functionen_ (Leipzig, 1895). For a history of the theory of
+  algebraic functions consult A. Brill and M. Noether, _Die Entwicklung
+  der Theorie der algebraischen Functionen in alterer und neuerer Zeit,
+  Bericht der deutschen Mathematiker-Vereinigung_ (1894); and for a
+  special theory of algebraic functions, K. Hensel and G. Landsberg,
+  _Theorie der algebraischen Function u.s.w._ (Leipzig, 1902). The
+  student will, of course, consult also Riemann's and Weierstrass's
+  _Ges. Werke_. For the applications to geometry in general an important
+  contribution, of permanent value, is E. Picard and G. Simart, _Theorie
+  des fonctions algebriques de deux variables independantes_ (Paris,
+  1897-1906). This work contains, as Note v. t. ii. p. 485, a valuable
+  summary by MM. Castelnuovo and Enriques, _Sur quelques resultats
+  nouveaux dans la theorie des surfaces algebriques_, containing many
+  references to the numerous memoirs to be found, for the most part, in
+  the transactions of scientific societies and the mathematical journals
+  of Italy.
+
+  Beside the books above enumerated there exists an unlimited number of
+  individual memoirs, often of permanent importance and only
+  imperfectly, or too elaborately, reproduced in the pages of the
+  volumes in which the student will find references to them. The German
+  _Encyclopaedia of Mathematics_, and the Royal Society's _Reference
+  Catalogue of Current Scientific Literature, Pure Mathematics_,
+  published yearly, should also be consulted.     (H. F. Ba.)
+
+
+FOOTNOTE:
+
+  [1] The word "function" (from Lat. _fungi_, to perform) has many
+    uses, with the fundamental sense of an activity special or proper to
+    an office, business or profession, or to an organ of an animal or
+    plant, the definite work for which the organ is an apparatus. From
+    the use of the word, as in the Italian _funzione_, for a ceremony of
+    the Roman Church, "function" is often employed for a public ceremony
+    of any kind, and loosely of a social entertainment or gathering.
+
+
+
+
+FUNDY, BAY OF, an inlet of the North Atlantic, separating New Brunswick
+from Nova Scotia. It is 145 m. long and 48 m. wide at the mouth, but
+gradually narrows towards the head, where it divides into Chignecto Bay
+to the north, which subdivides into Shepody Bay and Cumberland Basin
+(the French Beaubassin), and Minas Channel, leading into Minas Basin, to
+the east and south. Off its western shore opens Passamaquoddy Bay, a
+magnificent sheet of deep water with good anchorage, receiving the
+waters of the St Croix river and forming part of the boundary between
+New Brunswick and the state of Maine, The Bay of Fundy is remarkable for
+the great rise and fall of the tide, which at the head of the bay has
+been known to reach 62 ft. In Passamaquoddy Bay the rise and fall is
+about 25 ft., which gradually increases toward the narrow upper reaches.
+At spring tides the water in the Bay of Fundy is 19 ft. higher than it
+is in Bay Verte, in Northumberland Strait, only 15 m. distant. Though
+the bay is deep, navigation is rendered dangerous by the violence and
+rapidity of the tide, and in summer by frequent fogs. At low tide, at
+such points as Moncton or Amherst, only an expanse of red mud can be
+seen, and the tide rushes in a bore or crest from 3 to 6 ft. in height.
+Large areas of fertile marshes are situated at the head of the bay, and
+the remains of a submerged forest show that the land has subsided in the
+latest geological period at least 40 ft. The bay receives the waters of
+the St Croix and St John rivers, and has numerous harbours, of which the
+chief are St Andrews (on Passamaquoddy Bay) and St John in New
+Brunswick, and Digby and Annapolis (on an inlet known as Annapolis
+Basin) in Nova Scotia. It was first explored by the Sieur de Monts (d.
+c. 1628) in 1604 and named by him La Baye Francaise.
+
+
+
+
+FUNERAL RITES, the ceremonies associated with different methods of
+disposing of the dead. (See also BURIAL AND BURIAL ACTS; CEMETERY; and
+CREMATION.) In general we have little record, except in their tombs, of
+races which, in a past measured not merely by hundreds but by thousands
+of years, occupied the earth; and exploration of these often furnishes
+our only clue to the religions, opinions, customs, institutions and arts
+of long vanished societies. In the case of the great culture folks of
+antiquity, the Babylonians, Egyptians, Hindus, Persians, Greeks and
+Romans, we have, besides their monuments, the evidence of their
+literatures, and so can know nearly as much of their rites as we do of
+our own. The rites of modern savages not only help us to interpret
+prehistoric monuments, but explain peculiarities in our own rituals and
+in those of the culture folks of the past of which the significance was
+lost or buried under etiological myths. We must not then confine
+ourselves to the rites of a few leading races, neglecting their less
+fortunate brethren who have never achieved civilization. It is better to
+try to classify the rites of all races alike according as they embody
+certain leading conceptions of death, certain fears, hopes, beliefs
+entertained about the dead, about their future, and their relations with
+the living.
+
+  The main ideas, then, underlying funeral rites may roughly be
+  enumerated as follows:
+
+  1. The pollution or taboo attaching to a corpse.
+
+  2. Mourning.
+
+  3. The continued life of the dead as evinced in the housing and
+  equipment of the dead, in the furnishing of food for them, and in the
+  orientation and posture assigned to the body.
+
+  4. Communion with the dead in a funeral feast and otherwise.
+
+  5. Sacrifice for the dead and expiation of their sins.
+
+  6. Death witchery.
+
+  7. Protection of the dead from ghouls.
+
+  8. Fear of ghosts.
+
+1. A dead body is unclean, and the uncleanness extends to things and
+persons which touch it. Hence the Jewish law (Num. v. 2) enacted that
+"whoever is unclean by the dead shall be put outside the camp, that they
+defile not the camp in the midst whereof the Lord dwells." Such persons
+were unclean until the even, and might not eat of the holy things unless
+they bathed their flesh in water. A high priest might on no account "go
+in to any dead body" (Lev. xxi. 11). Why a corpse is so widely tabooed
+is not certain; but it is natural to see one reason in the corruption
+which in warm climates soon sets in. The common experience that where
+one has died another is likely to do so may also have contributed,
+though, of course, there was no scientific idea of infection. The old
+Persian scriptures are full of this taboo. He who has touched a corpse
+is "powerless in mind, tongue and hand" (_Zend Avesta_ in _Sacred Books
+of the East_, pt. i. p. 120), and the paralysis is inflicted by the
+innumerable _drugs_ or evil spirits which invest a corpse. Fire and
+earth, being alike creations of the good and pure god Ahuramazda, a
+body must not be burned or buried; and so the ancient Persians and their
+descendants the Parsees build Dakmas or "towers of silence" on hill-tops
+far from human habitations. Inside these the corpses are laid on a
+flagged terrace which drains into a central pit. Twice a year the bones,
+picked clean by dogs and birds of prey, are collected in the pit, and
+when it is full another tower is built. In ancient times perhaps the
+bodies of the magi or priests alone were exposed at such expense; the
+common folk were covered with wax and laid in the earth, the wax saving
+the earth from pollution. In Rome and Greece the corpse was buried by
+night, lest it should pollute the sunlight; and a trough of water was
+set at the door of the house of death that men might purify themselves
+when they came out, before mixing in general society. Priests and
+magistrates in Rome might not meet or look on a corpse, for they were
+thereby rendered unclean and incapable of fulfilling their official
+duties without undergoing troublesome rites of purification. At a Roman
+funeral, when the remains had been laid in the tomb, all present were
+sprinkled with lustral water from a branch of olive or laurel called
+_aspergillum_; and when they had gone home they were asperged afresh and
+stepped over a fire. The house was also swept out with a broom, probably
+lest the ghost of the dead should be lying about the floor. Many races,
+to avoid pollution, destroy the house and property of the deceased. Thus
+the Navahos pull down the hut in which he died, leaving its ruins on the
+ground; but if it be an expensive hut, a shanty is extemporized
+alongside, into which the dying man is transferred before death. No one
+will use the timbers of a hut so ruined. A burial custom of the Solomon
+Islands, noted by R.H. Codrington (_The Melanesians_, p. 255), may be
+dictated by the same scruple. There "the mourners having hung up a dead
+man's arms on his house make great lamentations; all remains afterwards
+untouched, the house goes to ruin, mantled, as time goes on, with the
+vines of the growing yams, a picturesque and indeed, perhaps, a touching
+sight; for these things are not set up that they may in a ghostly manner
+accompany their former owner." H. Oldenberg (_Religion des Veda_, p.
+426) describes how Hindus shave themselves and cut off their nails after
+a death, at the same time that they wash, renew the hearth fire, and
+furnish themselves with new vessels. For the hair and nails may harbour
+pollution, just as the medieval Greeks believed that evil spirits could
+lurk in a man's beard (Leo Allatius, _De opinionibus quorundam
+Graecorum_). The dead man's body is shorn and the nails cut for a
+kindred reason; for it must be purified as much as can be before it is
+burned as an offering on the pyre and before he enters on a new sphere
+of existence.
+
+2. We are accustomed to regard mourning costume as primarily an outward
+sign of our grief. Originally, however, the special garb seems to have
+been intended to warn the general public that persons so attired were
+unclean. In ancient Rome mourners stayed at home and avoided all feasts
+and amusements; laying aside gold, purple and jewels, they wore black
+dresses called _lugubria_ or even skins. They cut neither hair nor
+beard, nor lighted fire. Under the emperors women began to wear white.
+On the west coast of Africa negroes wear white, on the Gold Coast red.
+The Chinese wear hemp, which is cheap, for mourning dress must as a rule
+be destroyed when the season of grief is past to get rid of the taboo.
+Among the Aruntas of Australia the wives of a dead man smear themselves
+with white pipe-clay until the last ceremonies are finished, sometimes
+adding ashes--this not to conceal themselves from the ghost (which may
+partly be the aim of some mourning costumes), but to show the ghost that
+they are duly sorrowing for their loss. These widows must not talk
+except on their hands for a whole year. "Among the Maoris," says Frazer
+(_Golden Bough_, i. 323), "anyone who had handled a corpse, helped to
+convey it to the grave, or touched a dead man's bones; was cut off from
+all intercourse and almost all communication with mankind. He could not
+enter any house, or come into contact with any person or thing, without
+utterly bedevilling them. He might not even touch food with his hands,
+which had become so frightfully tabooed or unclean as to be quite
+useless. Food would be set for him on the ground, and he would then sit
+or kneel down, and, with his hands carefully held behind his back, would
+gnaw at it as best he could." Often a degraded outcast was kept in a
+village to feed mourners. Such a taboo is strictly similar to those
+which surround a sacred chief or his property, a menstruous woman or a
+homicide, rendering them dangerous to themselves and to all who approach
+them.
+
+3. Primitive folk cannot conceive of a man's soul surviving apart from
+his body, nor of another life as differing from this, and the dead must
+continue to enjoy what they had here. Accordingly the Patagonians kill
+horses at the grave that the dead may ride to _Alhuemapu_, or country of
+the dead. After a year they collect a chief's bones, arrange them, tie
+them together and dress them in his best garments with beads and
+feathers. Then they lay him with his weapons in a square pit, round
+which dead horses are placed set upright on their feet by stakes. As
+late as 1781 in Poland F. Casimir's horse was slain and buried with him.
+In the Caucasus a Christian lady's jewels are buried with her. The
+Hindus used to burn a man's widow on his pyre, because he could not do
+without her; and St Boniface commends the self-sacrifice of the Wend
+widows who in his day burned themselves alive on their husbands' pyres.
+
+The tumuli met with all over the north of Europe (in the Orkneys alone
+2000 remain) are regular houses of the dead, models of those they
+occupied in life. The greater the dignity of the deceased, the loftier
+was his barrow. Silbury hill is 170 ft. high; the tomb of Alyattes,
+father of Croesus, was a fourth of a league round; the Pyramids are
+still the largest buildings in existence; at Oberea in Tahiti is a
+barrow 267 ft. long, 87 wide and 44 high. Some Eskimo just leave a dead
+man's body in his house, and shut it up, often leaving by his side a
+dog's head to guide him on his last journey, along with his tools and
+kayak. The Sea Dyaks set a chief adrift in his war canoe with his
+weapons. So in Norse story Hake "was laid wounded on a ship with the
+dead men and arms; the ship was taken out to sea and set on fire." The
+Viking was regularly buried in his ship or boat under a great mound. He
+sailed after death to Valhalla. In the ship was laid a stone as anchor
+and the tools, clothes, weapons and treasures of the dead. The
+Egyptians, whose land was the gift of the river Nile, equally believed
+that the dead crossed over water, and fashioned the hearse in the form
+of a boat. Hence perhaps was derived the Greek myth of Charon and the
+Styx, and the custom, which still survives in parts of Europe, of
+placing a coin in the mouth of the dead with which to pay the ferryman.
+The Egyptians placed in the tomb books of a kind to guide the dead to
+the next world. The Copts in a later age did the same, and to this
+custom we owe the recovery in Egypt of much ancient literature. The
+Armenians till lately buried with a priest his missal or gospel.
+
+In Egyptian entombments of the XIIth to the XIVth dynasties were added
+above the sepulchres what Professor Petrie terms soul-houses, viz. small
+models of houses furnished with couch and table, &c., for the use of the
+_ka_ or double whenever it might wish to come above ground and partake
+of meats and drinks. They recall, in point of size, the hut-urns of the
+Etruscans, but the latter had another use, for they contain incinerated
+remains. Etruscan tombs, like those of Egypt and Asia Minor, were made
+to resemble the dwelling-houses of the living, and furnished with
+coffered ceilings, panelled walls, couches, stools, easy chairs with
+footstools attached, all hewn out of the living rock (Dennis, _Cities
+and Cemeteries of Etruria_, vol i. p. lxx.).
+
+Of the old Peruvian mummies in the Kircherian Museum at Rome, several
+are of women with babies in their arms, whence it is evident that a
+mother had her suckling buried with her; it would console her in the
+next world and could hardly survive her in this. The practice of burying
+ornaments, tools and weapons with the dead characterizes the inhumations
+of the Quaternary epoch, as if in that dim and remote age death was
+already regarded as the portal of another life closely resembling this.
+The cups, tools, weapons, ornaments and other articles deposited with
+the dead are often carefully broken or turned upside down and inside
+out; for the soul or _manes_ of objects is liberated by such fracture or
+inversion and so passes into the dead man's use and possession. For the
+same reason where the dead are burned, their properties are committed to
+the flames. The ghost of the warrior has a ghostly sword and buckler to
+fight with and a ghostly cup to drink from, and he is also nourished by
+the impalpable odour and reek of the animal victims sacrificed over his
+grave. Instead of valuable objects cheap images and models are often
+substituted; and why not, if the mere ghosts of the things are all that
+the wraith can enjoy? Thus Marco Polo (ii. 76) describes how in the land
+of Kinsay (Hang-chau) "the friends and relations make a great mourning
+for the deceased, and clothe themselves in hempen garments, and follow
+the corpse, playing on a variety of instruments and singing hymns to
+their idols. And when they come to the burning place they take
+representations of things cut out of parchment, such as caparisoned
+horses, male and female slaves, camels, armour, suits of cloth of gold
+(and money), in great quantities, and these things they put on the fire
+along with the corpse so that they are all burned with it. And they tell
+you that the dead man shall have all these slaves and animals of which
+the effigies are burned, alive in flesh and blood, and the money in
+gold, at his disposal in the next world; and that the instruments which
+they have caused to be played at his funeral, and the idol hymns that
+have been chaunted shall also be produced again to welcome him in the
+next world." The manufacture of such paper _simulacra_ for consumption
+at funerals is still an important industry in Chinese cities. The
+ancient Egyptians, assured that a man's _ka_ or double shall revivify
+his body, took pains to guard the flesh from corruption, steeping the
+corpse in natron and stuffing it with spices. A body so prepared is
+called a mummy (q.v.), and the custom was already of a hoary antiquity
+in 3200 B.C., when the oldest dated mummy we have was made. The bowels,
+removed in the process, were placed in jars over the corpse in the tomb,
+together with writing tablets, books, musical instruments, &c., of the
+dead. Cemeteries also remain full of mummies of crocodiles, cats, fish,
+cows and other sacred animals. The Greeks settled in Egypt learned to
+mummify their dead, but the custom was abhorrent to the Jews, although
+the Christian belief in the resurrection of the flesh must have been
+formed to a large extent under Egyptian influence. Half the superiority
+of the Jewish to other ancient religions lay in this, that it prescribed
+no funeral rites other than the simplest inhumation.
+
+The dead all over the world and from remote antiquity have been laid not
+anyhow in the earth, but with the feet and face towards the region in
+which their future will be spent; the Samoans and Fijians towards the
+far west whither their souls have preceded them; the Guarayos with head
+turned eastwards because their god Tamoi has in that quarter "his happy
+hunting grounds where the dead will meet again" (Tylor, _Prim. Cult._
+ii. 422). The legend is that Christ was buried with His head to the
+west, and the church follows the custom, more ancient than itself, of
+laying the dead looking to the East, because that is the attitude of
+prayer, and because at the last trump they will hurry eastwards. So in
+Eusebius (_Hist. Eccl._ 430.19) a martyr explains to his pagan judge
+that the heavenly Jerusalem, the fatherland of the pious, lay exactly in
+the east at the rising place of the sun. Where the body is laid out
+straight it is difficult to discern the presence of any other idea than
+that it is at rest. In Scandinavian barrows, e.g. in the one opened at
+Goldhavn in 1830, the skeletons have been found seated on a low stone
+bench round the wall of the grave chamber facing its opening, which
+always looks south or east, never north. Here the dead were continuing
+the drinking bouts they enjoyed on earth.
+
+The Peruvians mummified their dead and placed them jointed and huddled
+up with knees to chin, looking toward the sunset, with the hands held
+before the face. In the oldest prehistoric tombs along the Nile the
+bodies are doubled up in the same position. It would seem as if in these
+and numerous other similar cases the dead were deliberately given in
+their graves the attitude of a foetus in the womb, and, as Dr Budge
+remarks (_Egyptian Ideas of the Future Life_, London, 1899, p. 162), "we
+may perhaps be justified in seeing in this custom the symbol of a hope
+that, as the child is born from this position into the world, so might
+the deceased be born into the life beyond the grave." The late
+Quaternary skeletons of the Mentone cave were laid in a layer of
+ferrugineous earth specially laid down for them, and have contracted a
+red colour therefrom. Many other prehistoric skeletons found in Italy
+have a reddish colour, perhaps for the same reason, or because, as often
+to-day, the bones were stripped of flesh and painted. Ambrose relates
+that the skeletons of the martyrs Gervasius and Protasius, which he
+found and deposited A.D. 386 under the altar of his new basilica in
+Milan, were _mirae magnitudinis ut prisca aetas ferebat_, and were also
+coloured red. He imagined the red to be the remains of the martyrs'
+blood! _Hic sanguis clamat coloris indicio._ Salomon Reinach has rightly
+divined that what Ambrose really hit upon was a prehistoric tomb. Red
+earth was probably chosen as a medium in which to lay a corpse because
+demons flee from red. Sacred trees and stones are painted red, and for
+the most solemn of their rites savages bedaub themselves with red clay.
+It is a favourite taboo colour.
+
+4. A feast is an essential feature of every primitive funeral, and in
+the Irish "wake" it still survives. A dead man's soul or double has to
+be fed at the tomb itself, perhaps to keep it from prowling about the
+homes of the survivors in search of victuals; and such food must also be
+supplied to the dead at stated intervals for months or years. Many races
+leave a narrow passage or tube open down to the cavity in which the
+corpse lies, and through it pour down drinks for the dead. Traces of
+such tubes are visible in the prehistoric tombs of the British Isles.
+However, such provision of food is not properly a funeral feast unless
+the survivors participate. In the Eastern churches and in Russia the
+departed are thus fed on the ninth, twelfth and fortieth days from
+death. "Ye appease the shades of the dead with wine and meals," was the
+charge levelled at the Catholics by the 4th-century Manichaeans, and it
+has hardly ceased to be true even now after the lapse of sixteen
+centuries. The funeral feast proper, however, is either a meal of
+communion with or in the dead, which accompanies interment, or a banquet
+off the flesh of victims slain in atonement of the dead man's sins. Some
+anthropologists see in the common meal held at the grave "the pledge and
+witness of the unity of the kin, the chief means, if not of making, at
+least of repairing and renewing it."[1] The flesh provided at these
+banquets is occasionally that of the dead man himself; Herodotus and
+Strabo in antiquity relate this of several half-civilized races in the
+East and West, and a similar story is told by Marco Polo of certain
+Tatars. Nor among modern savages are funeral feasts off the flesh of the
+dead unknown, and they seem to be intended to effect and renew a
+sacramental union or kinship of the living with the dead. The Uaupes in
+the Amazons incinerate a corpse a month after death, pound up the ashes,
+and mix them with their fermented drink. They believe that the virtues
+of the dead will thus be passed on to his survivors. The life of the
+tribe is kept inside the tribe and not lost. Such cannibal sacraments,
+however, are rare, and, except in a very few cases, the evidence for
+them weak. The slaying and eating of animal victims, however, at the
+tomb is universal and bears several meanings, separately or all at once.
+The animals may be slain in order that their ghosts may accompany the
+deceased in his new life. This significance we have already dwelt upon.
+Or it is believed that the shade feeds upon them, as the shades came up
+from Hades and lapped up out of a trench the blood of the animals slain
+by Ulysses. The survivors by eating the flesh of a victim, whose blood
+and soul the dead thus consume, sacramentally confirm the mystic tie of
+blood kinship with the dead. Or lastly, the victim may be offered for
+the sins of the dead. His sins are even supposed to be transferred into
+it and eaten by the priest. Such expiatory sacrifices of animals for the
+dead survive in the Christian churches of Armenia, Syria and of the East
+generally. Their vicarious character is emphasized in the prayers which
+accompany them, but the popular understanding of them probably combines
+all the meanings above enumerated. It has been suggested by Robertson
+Smith (_Religion of the Semites_, 336) that the world-wide customs of
+tearing the hair, rending the garments, and cutting and wounding the
+body were originally intended to establish a life-bond between the dead
+and the living. The survivors, he argues, in leaving portions of their
+hair and garments, and yet more by causing their own blood to stream
+over the corpse from self-inflicted wounds, by cutting off a finger and
+throwing it into the grave, leave what is eminently their own with the
+dead, so drawing closer their tie with him. Conversely, many savages
+daub themselves with the blood and other effluences of their dead
+kinsmen, and explain their custom by saying that in this way a portion
+of the dead is incorporated in themselves. Often the survivors,
+especially the widows, attach the bones or part of them to their persons
+and wear them, or at least keep them in their houses. The retention of
+the locks of the deceased and of parts of his dress is equally common.
+There is also another side to such customs. Having in their possession
+bits of the dead, and being so far in communion with him, the survivors
+are surer of his friendship. They have ensured themselves against ghosts
+who are apt to be by nature envious and mischievous. But whatever their
+original significance, the tearing of cheeks and hair and garments and
+cutting with knives are mostly expressions of real sorrow, and, as
+Robertson Smith remarks, of deprecation and supplication to an angry god
+or spirit. It must not be supposed that the savage or ancient man feels
+less than ourselves the poignancy of loss.
+
+6. Death-witchery has close parallels in the witch and heretic hunts of
+the Christians, but, happily for us, only flourishes to-day among
+savages. Sixty % of the deaths which occur in West Africa are, according
+to Miss Mary Kingsley--a credible witness--believed to be due to
+witchcraft and sorcery. The blacks regard old age or effusion of blood
+as the sole legitimate causes of death. All ordinary diseases are in
+their opinion due to private magic on the part of neighbours, just as a
+widespread epidemic marks the active hatred "of some great outraged
+nature spirit, not of a mere human dabbler in devils."[2] Similarly in
+Christian countries an epidemic is set down to the wrath of a God
+offended by the presence of Jews, Arians and other heretics. The duty of
+an African witch-doctor is to find out who bewitched the deceased, just
+as it was of an inquisitor to discover the heretic. Every African
+post-mortem accordingly involves the murder of the person or persons who
+bewitched the dead man and caused him to die. The death-rate by these
+means is nearly doubled; but, since the use of poison against an
+obnoxious neighbour is common, the right person is occasionally
+executed. It is also well for neighbours not to quarrel, for, if they do
+and one of them dies of smallpox, the other is likely to be slain as a
+witch, and his lungs, liver and spleen impaled on a pole at the entrance
+of the village. It is the same case with the Australian blacks: "no such
+thing as natural death is realized by the native; a man who dies has of
+necessity been killed by some other man, or perhaps even by a woman, and
+sooner or later that man or woman will be attacked. In the normal
+condition of the tribe every death meant the killing of another
+individual."[3]
+
+7. Lastly, a primitive interment guards against the double risk of the
+ghost haunting the living and of ghouls or vampires taking possession of
+the corpse. The latter end is likely to be achieved if the body is
+cremated, for then there is no nidus to harbour the demon; but whether,
+in the remote antiquity to which belong many barrows containing
+incinerated remains, this motive worked, cannot be ascertained. The
+Indo-European race seems to have cremated at an early epoch, perhaps
+before the several races of East and West separated. In Christian
+funeral rites many prayers are for the protection of the body from
+violation by vampires, and it would seem as if such a motive dictated
+the architectural solidity of some ancient tombs. Christian graves were
+for protection regularly sealed with the cross; and the following is a
+characteristic prayer from the old Armenian rite for the burial of a
+layman:
+
+  "Preserve, Almighty Lord, this man's spirit with all saints and with
+  all lovers of Thy holy name. And do Thou seal and guard the sepulchre
+  of Thy servant, Thou who shuttest up the depths and sealest them with
+  Thy almighty right hand ... so let the seal of Thy Lordship abide
+  unmoved upon this man's dwelling-place and upon the shrine which
+  guards Thy servant. And _let not any filthy and unclean devil dare to
+  approach him, such as assail the body and souls of the heathen_, who
+  possess not the birth of the holy font, and have not the dread seal
+  laid upon their graves."
+
+A terrible and revolting picture of the superstitious belief in ghouls
+which violate Christian tombs is given by Leo Allatius (who held it) in
+his tract _De opinionibus quorundam Graecorum_ (Paris, 1646). It was
+probably the fear of such demonic assaults on the dead that inspired the
+insanitary custom of burying the dead under the floors of churches, and
+as near as possible to the altar. In the Greek Church this practice was
+happily forbidden by the code of Justinian as well as by the older law
+in the case of churches consecrated with _Encaenia_ and deposition of
+relics. In the Armenian Church the same rule holds, and Ephrem Syrus in
+his testament particularly forbade his body to be laid within a church.
+Such prohibitions, however, are a witness to the tendency in question.
+
+The custom of lighting candles round a dead body and watching at its
+side all night was originally due to the belief that a corpse, like a
+person asleep, is specially liable to the assaults of demons. The
+practice of tolling a bell at death must have had a similar origin, for
+it was a common medieval belief that the sound of a consecrated bell
+drives off the demons which when a man dies gather near in the air to
+waylay his fleeting soul. For a like reason the consecrated bread of the
+Eucharist was often buried with believers, and St Basil is said to have
+specially consecrated a Host to be placed in his coffin.
+
+8. Some of the rites described under the previous heads may be really
+inspired by the fear of the dead haunting the living, but it must be
+kept in mind that the taboo attaching to a dead body is one thing and
+fear of a ghost another. A corpse is buried or burned, or scaffolded on
+a tree, a tower or a house-top, in order to get it out of the way and
+shield society from the dangerous infection of its taboo; but ghosts
+_qua_ ghosts need not be feared and a kinsman's ghost usually is not. On
+the contrary, it is fed and consoled with everything it needs, is asked
+not to go away but to stay, is in a thousand ways assured of the sorrow
+and sympathy of the survivors. Even if the body be eaten, it is merely
+to keep the soul of the deceased inside the circle of kinsmen, and
+Strabo asserts that the ancient Irish and Massagetae regarded it as a
+high honour to be so consumed by relatives. In Santa Cruz in Melanesia
+they keep the bones for arrow heads and store a skull in a box and set
+food before it "saying that this is the man himself" (R.H. Codrington,
+_The Melanesians_, p. 264), or the skull and jaw bone are kept and "are
+called _mangite_, which are _saka_, hot with spiritual power, and by
+means of which the help of the _lio'a_, the powerful ghost of the man
+whose relics these are, can be obtained" (ibid. p. 262). Here we have
+the savage analogue to Christian relics. So the Australian natives make
+pointing sticks out of the small bones of the arm, with which to bewitch
+enemies.
+
+We may conclude then that in the most primitive societies, where
+blood-kinship is the only social tie and root of social custom it is the
+shades, not of kinsmen, but of strangers, who as such are enemies, that
+are dangerous and uncanny. In more developed societies, however, all
+ghosts alike are held to be so; and if a ghost walks it is because its
+body has not been properly interred or because its owner was a
+malefactor. Still, even allowing for this, it remains true that for a
+friendly ghost the proper place is the grave and not the homes of the
+living, and accordingly the Aruntas with cries of _Wah! Wah!_ with
+wearing of fantastic head-dresses, wild dancing and beating of the air
+with hands and weapons "drive the spirit away from the old camp which it
+is supposed to haunt," and which has been set fire to, and hunt it at a
+run into the grave prepared, and there stamp it down into the earth.
+"The loud shouting of the men and women shows him that they do not wish
+to be frightened by him in his present state, and that they will be
+angry with him if he does not rest." (Spencer and Gillen, _Native
+Tribes of Central Australia_, p. 508). In Mesopotamia cemeteries have
+been discovered where the sepulchral jars were set upside down, clearly
+by way of hindering the ghosts from escaping into the upper world. In
+the Dublin museum we see specimens of ancient Celtic tombs showing the
+same peculiarity. For a like reason perhaps the name of the dead must
+among the Aruntas not be uttered, nor the grave approached, by certain
+classes of kinsmen. The same repugnance to naming the dead exists all
+over the world, and leads survivors who share the dead man's name to
+adopt another, at least for a time. If the dead man's name was that of a
+plant, tree, animal or stream, that too is changed. Here is a potent
+cause of linguistic change, that also renders any historical tradition
+impossible. The survivors seem to fear that the ghost will come when he
+hears his name called; but it also hangs together with the taboo which
+hedges round the dead as it does kings, chieftains and priests.
+
+  AUTHORITIES.--B. Spencer and F.J. Gillen, _The Native Tribes of
+  Central Australia_ (London, 1899); F.B. Jevons, _Introduction to
+  History of Religion_ (London, 1896); E.S. Hartland, _The Legend of
+  Perseus_, vol. ii.; J.G. Frazer, _The Golden Bough_ (London, 1900);
+  L.W. Faraday, "Custom and Belief in the Icelandic Sagas," in
+  _Folk-lore_, vol. xvii. No. 4; E.B. Tylor, _Primitive Culture_
+  (London, 1903); E.A. W. Budge, _The Mummy_ (Cambridge, 1893); C.
+  Royer, "Les Rites funeraires aux epoques prehistoriques," _Revue
+  d'anthropologie_ (1876); Forrer, _Uber die Totenbestattung bei den
+  Pfahlbauern_ (Ausland, 1885); J. Lubbock, _Origin of Civilization_
+  (London, 1875) and _Prehistoric Times_ (London, 1865); L.A. Muratori,
+  "De antiquis Christianorum sepulchris," _Anecd. Graeca_ (Padua, 1709);
+  Onaphr. Panvinius, _De ritu sepeliendi mortuos apua veteres
+  Christianos_, reprinted in Volbeding's _Thesaurus_ (Leipzig, 1841).
+       (F. C. C.)
+
+
+FOOTNOTES:
+
+  [1] E.S. Hartland, _Legend of Perseus_ (1895), ii. 278.
+
+  [2] Mary Kingsley, _West African Studies_ (1901), p. 178.
+
+  [3] B. Spencer and F.J. Gillen, _The Native Tribes of Central
+    Australia_ (1899), p. 48.
+
+
+
+
+FUNGI (pl. of Lat. _fungus_, a mushroom), the botanical name covering in
+the broad sense all the lower cellular Cryptogams devoid of chlorophyll,
+which arise from spores, and the thallus of which is either unicellular
+or composed of branched or unbranched tubes or cell-filaments (hyphae)
+with apical growth, or of more or less complex wefted sheets or
+tissue-like masses of such (mycelium). The latter may in certain cases
+attain large dimensions, and even undergo cell-divisions in their
+interior, resulting in the development of true tissues. The spores,
+which may be uni- or multicellular, are either abstricted free from the
+ends of hyphae (acrogenous), or formed from segments in their course
+(_chlamydospores_) or from protoplasm in their interior (endogenous).
+The want of chlorophyll restricts their mode of life--which is rarely
+aquatic--since they are therefore unable to decompose the carbon dioxide
+of the atmosphere, and renders them dependent on other plants or
+(rarely) animals for their carbonaceous food-materials. These they
+obtain usually in the form of carbohydrates from the dead remains of
+other organisms, or in this or other forms from the living cells of
+their hosts; in the former case they are termed saprophytes, in the
+latter parasites. While some moulds (_Penicillium_, _Aspergillus_) can
+utilize almost any organic food-materials, other fungi are more
+restricted in their choice--e.g. insect-parasites, horn- and
+feather-destroying fungi and parasites generally. It was formerly the
+custom to include with the Fungi the Schizomycetes or Bacteria, and the
+Myxomycetes or Mycetozoa; but the peculiar mode of growth and division,
+the cilia, spores and other peculiarities of the former, and the
+emission of naked amoeboid masses of protoplasm, which creep and fuse to
+streaming plasmodia, with special modes of nutrition and spore-formation
+of the latter, have led to their separation as groups of organisms
+independent of the true Fungi. On the other hand, lichens, previously
+regarded as autonomous plants, are now known to be dual organisms--fungi
+symbiotic with algae.
+
+The number of species in 1889 was estimated by Saccardo at about 32,000,
+but of these 8500 were so-called _Fungi imperfecti_--i.e. forms of which
+we only know certain stages, such as conidia, pycnidia, &c., and which
+there are reasons for regarding as merely the corresponding stages of
+higher forms. Saccardo also included about 400 species of Myxomycetes
+and 650 of Schizomycetes. Allowing for these and for the cases,
+undoubtedly not few, where one and the same fungus has been described
+under different names, we obtain Schroeter's estimate (in 1892) of
+20,000 species. In illustration of the very different estimates that
+have been made, however, may be mentioned that of De Bary in 1872 of
+150,000 species, and that of Cooke in 1895 of 40,000, and Massee in 1899
+of over 50,000 species, the fact being that no sufficient data are as
+yet to hand for any accurate census. As regards their geographical
+distribution, fungi, like flowering plants, have no doubt their centres
+of origin and of dispersal; but we must not forget that every exchange
+of wood, wheat, fruits, plants, animals, or other commodities involves
+transmission of fungi from one country to another; while the migrations
+of birds and other animals, currents of air and water, and so forth, are
+particularly efficacious in transmitting these minute organisms. Against
+this, of course, it may be argued that parasitic forms can only go where
+their hosts grow, as is proved to be the case by records concerning the
+introduction of _Puccinia malvacearum_, _Peronospora viticola_,
+_Hemileia vastatrix_, &c. Some fungi--e.g. moulds and yeasts--appear to
+be distributed all over the earth. That the north temperate regions
+appear richest in fungi may be due only to the fact that North America
+and Europe have been much more thoroughly investigated than other
+countries; it is certain that the tropics are the home of very numerous
+species. Again, the accuracy of the statement that the fleshy Agaricini,
+Polyporei, _Pezizae_, &c., are relatively rarer in the tropics may
+depend on the fact that they are more difficult to collect and remit for
+identification than the abundantly recorded woody and coriaceous forms
+of these regions. When we remember that many parts of the world are
+practically unexplored as regards fungi, and that new species are
+constantly being discovered in the United States, Australia and northern
+Europe--the best explored of all--it is clear that no very accurate
+census of fungi can as yet be made, and no generalizations of value as
+to their geographical distribution are possible.
+
+The existence of fossil fungi is undoubted, though very few of the
+identifications can be relied on as regards species or genera. They
+extend back beyond the Carboniferous, where they occur as hyphae, &c.,
+preserved in the fossil woods, but the best specimens are probably those
+in amber and in siliceous petrifactions of more recent origin.
+
+[Illustration: FIG. 1.--1, _Peronospora parasitica_ (De Bary). Mycelium
+with haustoria (h); 2, _Erysiphe_; A and B, mycelium (m), with haustoria
+(h). (After De Bary.)]
+
+  _Organs._--Individual hyphae or their branches often exhibit
+  specializations of form. In many Basidiomycetes minute branches arise
+  below the septa; their tips curve over the outside of the latter, and
+  fuse with the cell above just beyond it, forming a _clamp-connexion_.
+  Many parasitic hyphae put out minute lateral branches, which pierce
+  the cell-wall of the host and form a peg-like (_Trichosphaeria_),
+  sessile (_Cystopus_), or stalked (_Hemileia_), knot-like, or a more or
+  less branched (_Peronospora_) or coiled (_Protomyces_) haustorium. In
+  _Rhizopus_ certain hyphae creep horizontally on the surface of the
+  substratum, and then anchor their tips to it by means of a tuft of
+  short branches (_appressorium_), the walls of which soften and gum
+  themselves to it, then another branch shoots out from the tuft and
+  repeats the process, like a strawberry-runner. Appressoria are also
+  formed by some parasitic fungi, as a minute flattening of the tip of a
+  very short branch (_Erysiphe_), or the swollen end of any hypha which
+  comes in contact with the surface of the host (_Piptocephalis_,
+  _Syncephalis_), haustoria piercing in each case the cell-wall below.
+  In _Botrytis_ the appressoria assume the form of dense tassels of
+  short branches. In _Arthrobotrys_ side-branches of the mycelium sling
+  themselves around the host (_Tylenchus_) much as tendrils round a
+  support.
+
+  Many fungi (_Phallus_, _Agaricus_, _Fumago_, &c.) when strongly
+  growing put out ribbon-like or cylindrical cords, or sheet-like
+  mycelial plates of numerous parallel hyphae, all growing together
+  equally, and fusing by anastomoses, and in this way extend long
+  distances in the soil, or over the surfaces of leaves, branches, &c.
+  These mycelial strands may be white and tender, or the outer hyphae
+  may be hard and black, and very often the resemblance of the
+  subterranean forms to a root is so marked that they are termed
+  rhizomorphs. The outermost hyphae may even put forth thinner hyphae,
+  radiating into the soil like root-hairs, and the convergent tips may
+  be closely appressed and so divided by septa as to resemble the
+  root-apex of a higher plant (_Armillaria mellea_).
+
+  _Sclerotia._--Fungi, like other plants, are often found to store up
+  large quantities of reserve materials (oil, glycogen, carbohydrates,
+  &c.) in special parts of their vegetative tissues, where they lie
+  accumulated between a period of active assimilation and one of renewed
+  activity, forming reserves to be consumed particularly during the
+  formation of large fructifications. These reserve stores may be packed
+  away in single hyphae or in swollen cells, but the hyphae containing
+  them are often gathered into thick cords or mycelial strands
+  (_Phallus_, mushroom, &c.), or flattened and anastomosing ribbons and
+  plates, often containing several kinds of hyphae (_Merulius
+  lacrymans_). In other cases the strands undergo differentiation into
+  an outer layer with blackened, hardened cell-walls and a core of
+  ordinary hyphae, and are then termed rhizomorphs (_Armillaria
+  mellea_), capable not only of extending the fungus in the soil, like
+  roots, but also of lying dormant, protected by the outer casing. Such
+  aggregations of hyphae frequently become knotted up into dense masses
+  of interwoven and closely packed hyphae, varying in size from that of
+  a pin's head or a pea (_Peziza_, _Coprinus_) to that of a man's fist
+  or head, and weighing 10 to 25 lb. or more (_Polyporus Mylittae_, _P.
+  tumulosus_, _Lentinus Woermanni_, _P. Sapurema_, &c.). The interwoven
+  hyphae fuse and branch copiously, filling up all interstices. They
+  also undergo cutting up by numerous septa into short cells, and these
+  often divide again in all planes, so that a pseudoparenchyma results,
+  the walls of which may be thickened and swollen internally, or
+  hardened and black on the exterior. In many cases the swollen
+  cell-walls serve as reserves, and sometimes the substance is so
+  thickly deposited in strata as to obliterate the lumen, and the hyphae
+  become nodular (_Polyporus sacer_, _P. rhinoceros_, _Lentinus
+  Woermanni_). The various sclerotia, if kept moist, give rise to the
+  fructifications of the fungi concerned, much as a potato tuber does to
+  a potato plant, and in the same way the reserve materials are
+  consumed. They are principally Polyporei, Agaricini, Pezizae; none are
+  known among the Phycomycetes, Uredineae or Ustilagineae. The functions
+  of mycelial strands, rhizomorphs and sclerotia are not only to collect
+  and store materials, but also to extend the fungus, and in many cases
+  similar strands act as organs of attack. The same functions of storage
+  in advance of fructification are also exercised by the stromata so
+  common in Ascomycetes.
+
+  _Tissue Differentiations._--The simpler mycelia consist of hyphae all
+  alike and thin-walled, or merely differing in the diameter of the
+  branches of various orders, or in their relations to the environment,
+  some plunging into the substratum like roots, others remaining on its
+  surface, and others (aerial hyphae) rising into the air. Such hyphae
+  may be multicellular, or they may consist of simple tubes with
+  numerous nuclei and no septa (_Phycomycetes_), and are then
+  non-cellular. In the more complex tissue-bodies of higher fungi,
+  however, we find considerable differences in the various layers or
+  strands of hyphae.
+
+  An epidermis-like or cortical protective outer layer is very common,
+  and is usually characterized by the close septation of the densely
+  interwoven hyphae and the thickening and dark colour of their outer
+  walls (sclerotia, _Xylaria_, &c.). Fibre-like hyphae with the lumen
+  almost obliterated by the thick walls occur in mycelial cords
+  (_Merulius_). Latex-tubes abound in the tissues of _Lactarius_,
+  _Stereum_, _Mycena_, _Fistulina_, filled with white or coloured milky
+  fluids, and Istvanffvi has shown that similar tubes with fluid or oily
+  contents are widely spread in other Hymenomycetes. Sometimes fatty oil
+  or watery sap is found in swollen hyphal ends, or such tubes contain
+  coloured sap. Cystidia and paraphyses may be also classed here. In
+  _Merulius lacrymans_ Hartig has observed thin-walled hyphae with large
+  lumina, the septa of which are perforated like those of sieve-tubes.
+
+  As regards its composition, the cell-wall of fungi exhibits variations
+  of the same kind as those met with in higher plants. While the
+  fundamental constituent is a cellulose in many Mucorini and other
+  Phycomycetes, in others bodies like pectose, callose, &c., commonly
+  occur, and Wisselingh's researches show that chitin, a gluco-proteid
+  common in animals, forms the main constituent in many cases, and is
+  probably deposited directly as such, though, like the other
+  substances, it may be mixed with cellulose. As in other cell-walls, so
+  here the older membranes may be altered by deposits of various
+  substances, such as resin, calcium oxalate, colouring matters; or more
+  profoundly altered throughout, or in definite layers, by
+  lignification, suberization (_Trametes_, _Daedalea_), or swelling to a
+  gelatinous mucilage (_Tremella_, _Gymnosporangium_), while
+  cutinization of the outer layers is common. One of the most striking
+  alterations of cell-walls is that termed _carbonization_, in which the
+  substance gradually turns black, hard and brittle, as if charred--e.g.
+  _Xylaria_, _Ustulina_, some sclerotia. At the other extreme the
+  cell-walls of many lichen-fungi are soft and colourless, but turn blue
+  in iodine, as does starch. The young cell-wall is always tenuous and
+  flexible, and may remain so throughout, but in many cases thickenings
+  and structural differentiations, as well as the changes referred to
+  above, alter the primary wall considerably. Such thickening may be
+  localized, and _pits_ (e.g. _Uredospores_, septa of Basidiomycetes),
+  _spirals_, _reticulations_, _rings_, &c. (capillitium fibres of
+  _Podaxon_, _Calostoma_, _Battarrea_), occur as in the vessels of
+  higher plants, while sculptured networks, pittings and so forth are as
+  common on fungus-spores as they are on pollen grains.
+
+  _Cell-Contents._--The cells of fungi, in addition to protoplasm,
+  nuclei and sap-vacuoles, like other vegetable cells, contain formed
+  and amorphous bodies of various kinds. Among those directly visible to
+  the microscope are oil drops, often coloured (_Uredineae_) crystals of
+  calcium oxalate (_Phallus_, _Russula_), proteid crystals (_Mucor_,
+  _Pilobolus_, &c.) and resin (Polyporei). The oidia of Erysipheae
+  contain fibrosin bodies and the hyphae of Saprolegnieae cellulin
+  bodies, but starch apparently never occurs. Invisible to the
+  microscope, but rendered visible by reagents, are glycogen, _Mucor_,
+  Ascomycetes, yeast, &c. In addition to these cell-contents we have
+  good indirect evidence of the existence of large series of other
+  bodies, such as proteids, carbohydrates, organic acids, alkaloids,
+  enzymes, &c. These must not be confounded with the numerous substances
+  obtained by chemical analysis of masses of the fungus, as there is
+  often no proof of the manner of occurrence of such bodies, though we
+  may conclude with a good show of probability that some of them also
+  exist preformed in the living cell. Such are sugars (glucose, mannite,
+  &c.), acids (acetic, citric and a whole series of lichen-acids),
+  ethereal oils and resinous bodies, often combined with the intense
+  colours of fungi and lichens, and a number of powerful alkaloid
+  poisons, such as muscarin (_Amanita_), ergotin (_Claviceps_), &c.
+
+  Among the enzymes already extracted from fungi are _invertases_
+  (yeasts, moulds, &c.), which split cane-sugar and other complex sugars
+  with hydrolysis into simpler sugars such as dextrose and levulose;
+  _diastases_, which convert starches into sugars (_Aspergillus_, &c.);
+  _cytases_, which dissolve cellulose similarly (_Botrytis_, &c.);
+  _peptases_, using the term as a general one for all enzymes which
+  convert proteids into peptones and other bodies (_Penicillium_, &c.);
+  lipases, which break up fatty oils (_Empusa_, _Phycomyces_, &c.);
+  oxydases, which bring about the oxidations and changes of colour
+  observed in _Boletus_, and _zymase_, extracted by Buchner from yeast,
+  which brings about the conversion of sugar into alcohol and
+  carbon-dioxide. That such enzymes are formed in the protoplasm is
+  evident from the behaviour of hyphae, which have been observed to
+  pierce cell-membranes, the chitinous coats of insects, artificial
+  collodion films and layers of wax, &c. That a fungus can secrete more
+  than one enzyme, according to the materials its hyphae have to attack,
+  has been shown by the extraction of diastase, inulase, trehalase,
+  invertase, maltase, raffinase, malizitase, emulsin, trypsin and lipase
+  from _Aspergillus_ by Bourquelot, and similar events occur in other
+  fungi. The same fact is indicated by the wide range of organic
+  substances which can be utilized by _Penicillium_ and other moulds,
+  and by the behaviour of parasitic fungi which destroy various
+  cell-contents and tissues. Many of the coloured pigments of fungi are
+  fixed in the cell-walls or excreted to the outside (_Peziza
+  aeruginosa_). Matruchot has used them for staining the living
+  protoplasm of other fungi by growing the two together. Striking
+  instances of coloured mycella are afforded by _Corticium sanguineum_,
+  blood-red; _Elaphomyces Leveillei_, yellow-green; _Chlorosplenium
+  aeruginosum_, verdigris green; and the _Dematei_, brown or black.
+
+  _Nuclei._--Although many fungi have been regarded as devoid of nuclei,
+  and all have not as yet been proved to contain them, the numerous
+  investigations of recent years have revealed them in the cells of all
+  forms thoroughly examined, and we are justified in concluding that the
+  nucleus is as essential to the cell of a fungus as to that of other
+  organisms. The hyphae of many contain numerous, even hundreds of
+  nuclei (Phycomycetes); those of others have several (_Aspergillus_) in
+  each segment, or only two (_Exoascus_) or one (_Erysiphe_) in each
+  cell. Even the isolated cells of the yeast plant have each one
+  nucleus. As a rule the nuclei of the mycelium are very minute (1.5-2
+  [mu] in _Phycomyces_), but those of many asci and spores are large and
+  easily rendered visible. As with other plants, so in fungi the
+  essential process of fertilization consists in the fusion of two
+  nuclei, but owing to the absence of well-marked sexual organs from
+  many fungi, a peculiar interest attaches to certain nuclear fusions in
+  the vegetative cells or in young spores of many forms. Thus in
+  Ustilagineae the chlamydospores, and in Uredineae the teleutospores,
+  each contain two nuclei when young, which fuse as the spores mature.
+  In young asci a similar fusion of two nuclei occurs, and also in
+  basidia, in each case the nucleus of the ascus or of the basidium
+  resulting from the fusion subsequently giving rise by division to the
+  nuclei of the ascospores and basidiospores respectively. The
+  significance of these fusions will be discussed under the various
+  groups. Nuclear division is usually accompanied by all the essential
+  features of karyokinesis.
+
+  _Spores._--No agreement has ever been arrived at regarding the
+  consistent use of the term spore. This is apparently owing to the
+  facts that too much has been attempted in the definition, and that
+  differences arise according as we aim at a morphological or a
+  physiological definition. Physiologically, any cell or group of cells
+  separated off from a hypha or unicellular fungus, and capable of
+  itself growing out--germinating--to reproduce the fungus, is a spore;
+  but it is evident that so wide a definition does not exclude the
+  ordinary vegetative cells of sprouting fungi, such as yeasts, or small
+  sclerotium like cell-aggregates of forms like _Coniothecium_.
+  Morphologically considered, spores are marked by peculiarities of
+  form, size, colour, place of origin, definiteness in number, mode of
+  preparation, and so forth, such that they can be distinguished more or
+  less sharply from the hyphae which produce them. The only
+  physiological peculiarity exhibited in common by all spores is that
+  they germinate and initiate the production of a new fungus-plant.
+  Whether a spore results from the sexual union of two similar gametes
+  (zygospore) or from the fertilization of an egg-cell by the protoplasm
+  of a male organ (oospore); or is developed asexually as a motile
+  (zoospore) or a quiescent body cut off from a hypha (conidium) or
+  developed along its course (oidium or chlamydospore), or in its
+  protoplasm (endospore), are matters of importance which have their
+  uses in the classification and terminology of spores, though in many
+  respects they are largely of academic interest.
+
+  [Illustration: FIG. 2.--_Peronospora parasitica_ (De Bary).
+  Conidiophore with conidia.]
+
+  Klebs has attempted to divide spores into three categories as follows:
+  (1) kinospores, arising by relatively simple cell-divisions and
+  subserving rapid dissemination and propagation, e.g. zoospores,
+  conidia, endogonidia, stylospores, &c.; (2) paulospores, due to simple
+  rearrangement of cell-contents, and subserving the persistence of the
+  fungus through periods of exigency, e.g. gemmae, chlamydospores,
+  resting-cells, cysts, &c.; (3) carpospores, produced by a more or less
+  complex formative process, often in special fructifications, and
+  subserving either or both multiplication and persistence, e.g.
+  zygospores, oospores, brand-spores, aecidiospores, ascospores,
+  basidiospores, &c. Little or nothing is gained by these definitions,
+  however, which are especially physiological. In practice these various
+  kinds of spores of fungi receive further special names in the separate
+  groups, and names, moreover, which will appear, to those unacquainted
+  with the history, to have been given without any consistency or regard
+  to general principles; nevertheless, for ordinary purposes these names
+  are far more useful in most cases, owing to their descriptive
+  character, than the proposed new names, which have been only partially
+  accepted.
+
+  _Sporophores._--In some of the simpler fungi the spores are not borne
+  on or in hyphae which can be distinguished from the vegetative parts
+  or mycelium, but in the vast majority of cases the sporogenous hyphae
+  either ascend free into the air or radiate into the surrounding water
+  as distinct branches, or are grouped into special columns, cushions,
+  layers or complex masses obviously different in colour, consistency,
+  shape and other characters from the parts which gather up and
+  assimilate the food-materials. The term "receptacle" sometimes applied
+  to these spore-bearing hyphae is better replaced by sporophore. The
+  sporophore is obsolete when the spore-bearing hyphae are not sharply
+  distinct from the mycelium, simple when the constituent hyphae are
+  isolated, and compound when the latter are conjoined. The chief
+  distinctive characters of the sporogenous hyphae are their
+  orientation, usually vertical; their limited apical growth; their
+  peculiar branching, form, colour, contents, consistency; and their
+  spore-production. According to the characters of the last, we might
+  theoretically divide them into conidiophores, sporangiophores,
+  gametophores, oidiophores, &c.; but since the two latter rarely occur,
+  and more than one kind of spore or spore-case may occur on a
+  sporophore, it is impossible to carry such a scheme fully into
+  practice.
+
+  A simple sporophore may be merely a single short hypha, the end of
+  which stops growing and becomes cut off as a conidium by the formation
+  of a septum, which then splits and allows the conidium to fall. More
+  generally the hypha below the septum grows forwards again, and repeats
+  this process several times before the terminal conidium falls, and so
+  a chain of conidia results, the oldest of which terminates the series
+  (_Erysiphe_); when the primary branch has thus formed a basipetal
+  series, branches may arise from below and again repeat this process,
+  thus forming a tuft (_Penicillium_). Or the primary hypha may first
+  swell at its apex, and put forth a series of short peg-like branches
+  (_sterigmata_) from the increased surface thus provided, each of which
+  develops a similar basipetal chain of conidia (_Aspergillus_), and
+  various combinations of these processes result in the development of
+  numerous varieties of exquisitely branched sporophores of this type
+  (_Botrytis_, _Botryosporium_, _Verticillium_, &c.).
+
+  [Illustration: FIG. 3.--_Cystopus candidus_.
+
+    A. a, Conidia.
+       b, Conidiophores.
+       c, Conidium emitting zoospores.
+       d, Free zoospore.
+    B.og, Oogonium.
+      os, Oosphere.
+      an, Antheridium.
+    C. Formation of zoospores by oospores.
+       z, Free zoospores. (After De Bary.)]
+
+  A second type is developed as follows: the primary hypha forms a
+  septum below its apex as before, and the terminal conidium, thus
+  abstricted, puts out a branch at its apex, which starts as a mere
+  point and rapidly swells to a second conidium; this repeats the
+  process, and so on, so that we now have a chain of conidia developed
+  in acropetal succession, the oldest being below, and, as in
+  _Penicillium_, &c., branches put forth lower down may repeat the
+  process (_Hormodendron_). In all these cases we may speak of simple
+  conidiophores. The simple sporophore does not necessarily terminate in
+  conidia, however. In _Mucor_, for example, the end of the primary
+  hypha swells into a spheroidal head (sporangium), the protoplasm of
+  which undergoes segmentation into more or less numerous globular
+  masses, each of which secretes an enveloping cell-wall and becomes a
+  spore (endospore), and branched systems of sporangia may arise as
+  before (_Thamnidium_). Such may be termed sporangiophores. In
+  _Sporodinia_ the branches give rise also to short branches, which meet
+  and fuse their contents to form zygospores. In Peronospora,
+  Saprolegnia, &c., the ends of the branches swell up into sporangia,
+  which develop zoospores in their interior (zoosporangia), or their
+  contents become oospheres, which may be fertilized by the contents of
+  other branches (antheridia) and so form egg-cases (oogonia). Since in
+  such cases the sporophore bears sexual cells, they may be conveniently
+  termed gametophores.
+
+  Compound sporophores arise when any of the branched or unbranched
+  types of spore-bearing hyphae described above ascend into the air in
+  consort, and are more or less crowded into definite layers, cushions,
+  columns or other complex masses. The same laws apply to the individual
+  hyphae and their branches as to simple sporophores, and as long as the
+  conidia, sporangia, gametes, &c., are borne on their external
+  surfaces, it is quite consistent to speak of these as compound
+  sporophores, &c., in the sense described, however complex they may
+  become. Among the simplest cases are the sheet-like aggregates of
+  sporogenous hyphae in _Puccinia_, _Uromyces_, &c., or of basidia in
+  _Exobasidium_, _Corticium_, &c., or of asci in _Exoascus_,
+  _Ascocorticium_, &c. In the former, where the layer is small, it is
+  often termed a sorus, but where, as in the latter, the sporogenous
+  layer is extensive, and spread out more or less sheet-like on the
+  supporting tissues, it is more frequently termed a hymenium. Another
+  simple case is that of the columnar aggregates of sporogenous hyphae
+  in forms like _Stilbum_, _Coremium_, &c. These lead us to cases where
+  the main mass of the sporophore forms a supporting tissue of closely
+  crowded or interwoven hyphae, the sporogenous terminal parts of the
+  hyphae being found at the periphery or apical regions only. Here we
+  have the cushion-like type (stroma) of _Nectria_ and many
+  Pyrenomycetes, the clavate "receptacle" of _Clavaria_, &c., passing
+  into the complex forms met with in _Sparassis_, _Xylaria_,
+  _Polyporei_, and _Agaricini_, &c. In these cases the compound
+  sporophore is often termed the hymenophore, and its various parts
+  demand special names (pileus, stipes, gills, pores, &c.) to denote
+  peculiarities of distribution of the hymenium over the surface.
+
+  Other series of modifications arise in which the tissues corresponding
+  to the stroma invest the sporogenous hyphal ends, and thus enclose the
+  spores, asci, basidia, &c., in a cavity. In the simplest case the
+  stroma, after bearing its crop of conidia or oidia, develops
+  ascogenous branches in the loosened meshes of its interior (e.g.
+  _Onygena_). Another simple case is where the plane or slightly convex
+  surface of the stroma rises at its margins and overgrows the
+  sporogenous hyphal ends, so that the spores, asci, &c., come to lie in
+  the depression of a cavity--e.g. _Solenia_, _Cyphella_--and even
+  simpler cases are met with in _Mortierella_, where the zygospore is
+  invested by the overgrowth of a dense mat of closely branching hyphae,
+  and in _Gymnoascus_, where a loose mat of similarly barren hyphae
+  covers in the tufts of asci as they develop.
+
+  In such examples as the above we may regard the hymenium (_Solenia_,
+  _Cyphella_), zygospores, or asci as truly invested by later growth,
+  but in the vast majority of cases the processes which result in the
+  enclosure of the spores, asci, &c., in a "fructification" are much
+  more involved, inasmuch as the latter is developed in the interior of
+  hyphal tissues, which are by no means obviously homologous with a
+  stroma. Thus in _Penicillium_, _Eurotium_, _Erysiphe_, &c., hyphal
+  ends which are the initials of ascogenous branches, are invested by
+  closely packed branches at an early stage of development, and the asci
+  develop inside what has by that time become a complete investment.
+  Whether a true sexual process precedes these processes or not does not
+  affect the present question, the point being that the resulting
+  spheroidal "fructification" (cleistocarp, perithecium) has a definite
+  wall of its own not directly comparable with a stroma. In other cases
+  (_Hypomyces_, _Nectria_) the perithecia arise on an already mature
+  stroma, while yet more numerous examples can be given (_Poronia_,
+  _Hypoxylon_, _Claviceps_, &c.) where the perithecia originate below
+  the surface of a stroma formed long before. Similarly with the various
+  types of conidial or oidial "fructifications," termed pycnidia,
+  spermogonia, aecidia, &c. In the simplest of these cases--e.g.
+  _Fumago_--a single mycelial cell divides by septa in all three planes
+  until a more or less solid clump results. Then a hollow appears in the
+  centre owing to the more rapid extension of the outer parts, and into
+  this hollow the cells lining it put forth short sporogenous branches,
+  from the tips of which the spores (stylospores, conidia, spermatia)
+  are abstricted. In a similar way are developed the pycnidia of
+  _Cicinnobolus_, _Pleospora_, _Cucurbitaria_, _Leptosphaeria_ and
+  others. In other cases (_Diplodia_, _Aecidium_, &c.) conidial or
+  oidial "fructifications" arise by a number of hyphae interweaving
+  themselves into a knot, as if they were forming a Sclerotium. The
+  outer parts of the mass then differentiate as a wall or investment,
+  and the interior becomes a hollow, into which hyphal ends grow and
+  abstrict the spores. Much more complicated are the processes in a
+  large series of "fructifications," where the mycelium first develops a
+  densely packed mass of hyphae, all alike, in which labyrinths of
+  cavities subsequently form by separation of hyphae in the previously
+  homogeneous mass, and the hymenium covers the walls of these cavities
+  and passages as with a lining layer. Meanwhile differences in
+  consistency appear in various strata, and a dense outer protective
+  layer (peridium), soft gelatinous layers, and so on are formed, the
+  whole eventually attaining great complexity--e.g. puff-balls,
+  earth-stars and various _Phalloideae_.
+
+  _Spore-Distribution._--Ordinary conidia and similarly abstricted dry
+  spores are so minute, light and numerous that their dispersal is
+  ensured by any current of air or water, and we also know that rats and
+  other burrowing animals often carry them on their fur; similarly with
+  birds, insects, slugs, worms, &c., on claws, feathers, proboscides,
+  &c., or merely adherent to the slimy body. In addition to these
+  accidental modes of dispersal, however, there is a series of
+  interesting adaptations on the part of the fungus itself. Passing over
+  the locomotor activity of zoospores (_Pythium_, _Peronospora_,
+  _Saprolegnia_) we often find spores held under tension in sporangia
+  (_Pilobolus_) or in asci (_Peziza_) until ripe, and then forcibly shot
+  out by the sudden rupture of the sporangial wall under the pressure of
+  liquid behind--mechanism comparable to that of a pop-gun, if we
+  suppose air replaced by watery sap. Even a single conidium, held tense
+  to the last moment by the elastic cell-wall, may be thus shot forward
+  by a spurt of liquid under pressure in the hypha abstricting it (e.g.
+  _Empusa_), and similarly with _basidiospores_ (_Coprinus_, _Agaricus_,
+  &c.). A more complicated case is illustrated by _Sphaerobolus_, where
+  the entire mass of spores, enclosed in its own peridium, is suddenly
+  shot up into the air like a bomb from a mortar by the elastic
+  retroversion of a peculiar layer which, up to the last moment,
+  surrounded the bomb, and then suddenly splits above, turns inside out,
+  and drives the former as a projectile from a gun. Gelatinous or
+  mucilaginous degenerations of cell-walls are frequently employed in
+  the interests of spore dispersal. The mucilage surrounding endospores
+  of _Mucor_, conidia of _Empusa_, &c., serves to gum the spore to
+  animals. Such gums are formed abundantly in pycnidia, and, absorbing
+  water, swell and carry out the spores in long tendrils, which emerge
+  for days and dry as they reach the air, the glued spores gradually
+  being set free by rain, wind, &c. In oidial chains (_Sclerotinia_) a
+  minute double wedge of wall-substance arises in the middle lamella
+  between each pair of contiguous oidia, and by its enlargement splits
+  the separating lamella. These disjunctors serve as points of
+  application for the elastic push of the swelling spore-ends, and as
+  the connecting outer lamella of cell-wall suddenly gives way, the
+  spores are jerked asunder. In many cases the slimy masses of spermatia
+  (_Uredineae_), conidia (_Claviceps_), basidiospores (_Phallus_,
+  _Coprinus_), &c., emit more or less powerful odours, which attract
+  flies or other insects, and it has been shown that bees carry the
+  fragrant oidia of _Sclerotinia_ to the stigma of _Vaccinium_ and
+  infect it, and that flies carry away the foetid spores of _Phallus_,
+  just as pollen is dispersed by such insects. Whether the strong odour
+  of trimethylamine evolved by the spores of _Tilletia_ attracts insects
+  is not known.
+
+  The recent observations and exceedingly ingenious experiments of Falck
+  have shown that the sporophores of the Basidiomycetes--especially the
+  large sporophores of such forms as _Boletus_, _Polyporus_--contain
+  quantities of reserve combustible material which are burnt up by the
+  active metabolism occurring when the fruit-body is ripe. By this means
+  the temperature of the sporophore is raised and the difference between
+  it and the surrounding air may be one of several degrees. As a result
+  convection currents are produced in the air which are sufficient to
+  catch the basidiospores in their fall and carry them, away from the
+  regions of comparative atmospheric stillness near the ground, to the
+  upper air where more powerful air-currents can bring about their wide
+  distribution.
+
+_Classification._--It has been accepted for some time now that the
+majority of the fungi proper fall into three main groups, the
+Phycomycetes, Ascomycetes and Basidiomycetes, the Schizomycetes and
+Myxomycetes (Mycetozoa) being considered as independent groups not
+coming under the true fungi.
+
+The chief schemes of classification put forward in detail have been
+those of P.A. Saccardo (1882-1892), of Oskar Brefeld and Von Tavel
+(1892), of P.E.L. Van Tieghem (1893) and of J. Schroeter (1892). The
+scheme of Brefeld, which was based on the view that the Ascomycetes and
+Basidiomycetes were completely asexual and that these two groups had
+been derived from one division (Zygomycetes) of the Phycomycetes, has
+been very widely accepted. The recent work of the last twelve years has
+shown, however, that the two higher groups of fungi exhibit distinct
+sexuality, of either a normal or reduced type, and has also rendered
+very doubtful the view of the origin of these two groups from the
+Phycomycetes. The real difficulty of classification of the fungi lies in
+the polyphyletic nature of the group. There is very little doubt that
+the primitive fungi have been derived by degradation from the lower
+algae. It appears, however, that such a degradation has occurred not
+only once in evolution but on several occasions, so that we have in the
+Phycomycetes not a series of naturally related forms, but groups which
+have arisen perfectly independently of one another from various groups
+of the algae. It is also possible in the absence of satisfactory
+intermediate forms that the Ascomycetes and Basidiomycetes have also
+been derived from the algae independently of the Phycomycetes, and
+perhaps of one another.
+
+A natural classification on these lines would obviously be very
+complicated, so that in the present state of our knowledge it will be
+best to retain the three main groups mentioned above, bearing in mind
+that the Phycomycetes especially are far from being a natural group. The
+following gives a tabular survey of the scheme adopted in the present
+article:
+
+  A. PHYCOMYCETES. Alga-like fungi with unicellular thallus and
+  well-marked sexual organs.
+
+  CLASS I.--Oomycetes. Mycelium usually well developed, but sometimes
+  poor or absent. Sexual reproduction by oogonia and antheridia; asexual
+  reproduction by zoospores or conidia.
+
+    1. Monoblepharidineae. Mycelium present, antheridia with
+    antherozoids, oogonium with single oosphere: Monoblepharidaceae.
+
+    2. Peronosporineae. Mycelium present; antheridia but no
+    antherozoids; oogonia with one or more oospheres: Peronosporaceae,
+    Saprolegniaceae.
+
+    3. Chytridineae. Mycelium poorly developed or absent; oogonia and
+    antheridia (without antherozoids) known in some cases; zoospores
+    common: Chytridiaceae. Ancylistaceae.
+
+  CLASS II.--Zygomycetes. Mycelium well developed; sexual reproduction
+  by zygospores; asexual reproduction by sporangia and conidia.
+
+    1. Mucorineae. Sexual reproduction as above, asexual by sporangia or
+    conidia or both: Mucoraceae. Mortierellaceae, Chaetocladiaceae,
+    Piptocephalidaceae.
+
+    2. Entomophthorineae. Sexual reproduction typical but with sometimes
+    inequality of the fusing gametes (gametangia ?): Entomophthoraceae.
+
+  B. HIGHER FUNGI. Fungi with segmental thallus; sexual reproduction
+  sometimes with typical antheridia and oogonia (ascogonia) but usually
+  much reduced.
+
+  CLASS I.--Ustilaginales. Forms with septate thallus, and reproduction
+  by chlamydospores which on germination produce sporidia; sexuality
+  doubtful.
+
+  CLASS II.--Ascomycetes. Thallus septate; spores developed in special
+  type of sporangium, the ascus, the number of spores being usually
+  eight. Sexual reproduction sometimes typical, usually reduced.
+
+  Exoascineae, Saccharomycetineae, Perisporinea, Discomycetes,
+  Pyrenomycetes, Tuberineae, Laboulbeniineae.
+
+  CLASS III.--Basidiales. Thallus septate. Conidia (basidiospores) borne
+  in fours on a special conidiophore, the basidium. Sexual reproduction
+  always much reduced.
+
+    1. Uredineae. Life-history in some cases very complex and with
+    well-marked sexual process and alternation of generations, in others
+    much reduced; basidium (promycelium) derived usually from a
+    thick-walled spore (teleutospore).
+
+    2. Basidiomycetes. Life-history always very simple, no well-marked
+    alternation of generations; basidium borne directly on the mycelium.
+
+      (A) Protobasidiomycetes. Basidia septate. Auriculariaceae,
+      Pilacreaceae, Tremellinaceae.
+
+      (B) Autobasidiomycetes. Basidia non-septate. Hymenomycetes,
+      Gasteromycetes.
+
+A. PHYCOMYCETES.--Most of the recent work of importance in this group
+deals with the cytology of sexual reproduction and of spore-formation,
+and the effect of external conditions on the production of reproductive
+organs.
+
+  _Monoblepharidaceae_ consists of a very small group of aquatic forms
+  living on fallen twigs in ponds and ditches. Only one genus,
+  _Monoblepharis_, can certainly be placed here, though a somewhat
+  similar genus, _Myrioblepharis_, with a peculiar multiciliate zoospore
+  like that of Vaucheria, is provisionally placed in the same group.
+  _Monoblepharis_ was first described by Cornu in 1871, but from that
+  time until 1895 when Roland Thaxter described several species from
+  America the genus was completely lost sight of. _Monoblepharis_ has
+  oogonia with single oospheres and antheridia developing a few amoeboid
+  uniciliate antherozoids; these creep to the opening of the oogonium
+  and then swim in. The resemblance between this genus and _Oedogonium_
+  among the algae is very striking, as is also that of _Myrioblepharis_
+  and _Vaucheria_.
+
+  _Peronosporaceae_ are a group of endophytic parasites--about 100
+  species--of great importance as comprising the agents of "damping off"
+  disease (_Pythium_), vine-mildew (_Plasmopara_), potato disease
+  (Phytophthora), onion-mildew (_Peronospora_). _Pythium_ is a
+  semi-aquatic form attacking seedlings which are too plentifully
+  supplied with water; its hyphae penetrate the cell-walls and rapidly
+  destroy the watery tissues of the living plant; then the fungus lives
+  in the dead remains. When the free ends of the hyphae emerge again
+  into the air they swell up into spherical bodies which may either fall
+  off and behave as conidia, each putting out a germ-tube and infecting
+  the host; or the germ-tube itself swells up into a zoosporangium which
+  develops a number of zoospores. In the rotting tissues branches of the
+  older mycelium similarly swell up and form antheridia and oogonia
+  (fig. 4). The contents of the antheridium are not set free, but that
+  organ penetrates the oogonium by means of a narrow outgrowth, the
+  fertilizing tube, and a male nucleus then passes over into the single
+  oosphere, which at first multinucleate becomes uninucleate before
+  fertilization. _Pythium_ is of interest as illustrating the dependence
+  of zoospore-formation on conditions and the indeterminate nature of
+  conidia. The other genera are more purely parasitic; the mycelium
+  usually sends haustoria into the cells of the host and puts out
+  branched, aerial conidiophores through the stomata, the branches of
+  which abstrict numerous "conidia"; these either germinate directly or
+  their contents break up into zoospores (fig. 5). The development of
+  the "conidia" as true conidial spores or as zoosporangia may occur in
+  one and the same species (_Cystopus candidus_, _Phytophthora
+  infestans_) as in _Pythium_ described above; in other cases the direct
+  conidial germination is characteristic of genera--e.g. _Peronospora_;
+  while others emit zoospores--e.g. _Plasmopara_, &c. In _Cystopus_
+  (_Albugo_) the "conidia" are abstricted in basipetal chain-like series
+  from the ends of hyphae which come to the surface in tufts and break
+  through the epidermis as white pustules. Each "conidium" contains
+  numerous nuclei and is really a zoosporangium, as after dispersal it
+  breaks up into a number of zoospores. The Peronosporaceae reproduce
+  themselves sexually by means of antheridia and oogonia as described in
+  _Pythium_. In _Cystopus Bliti_ the oosphere contains numerous nuclei,
+  and all the male nuclei from the antheridium pass into it, the male
+  and female nuclei then fusing in pairs. We thus have a process of
+  "multiple fertilization"; the oosphere really represents a large
+  number of undifferentiated gametes and has been termed a coenogamete.
+  Between _Cystopus Bliti_ on the one hand and _Pythium de Baryanum_ on
+  the other a number of cytologically intermediate forms are known. The
+  oospore on germination usually gives origin to a zoosporangium, but
+  may form directly a germ tube which infects the host.
+
+  [Illustration: From Strasburger's _Lehrbuch der Botanik_, by
+  permission of Gustav Fischer.
+
+  FIG. 4.--Fertilization of the Peronosporeae. After Wager.
+
+    1, _Peronospora parasitica_. Young multinucleate oogonium (og) and
+    antheridium (an).
+
+    2, _Albugo candida_. Oogonium with the central uninucleate oosphere
+    and the fertilizing tube (a) of the antheridium which introduces the
+    male nucleus.
+
+    3, The same. Fertilized egg-cell (o) surrounded by the periplasm
+    (p).]
+
+  [Illustration: FIG. 5.--_Phytophthora infestans_. Fungus of Potato
+  Disease.
+
+    A, B, Section of Leaf of Potato with sporangiophores of
+    _Phytophthora infestans_ passing through the stomata D, on the under
+    surface of the leaf.
+
+    E, Sporangia.
+
+    F, G, H, J, Further development of the sporangia.
+
+    K, Germination of the zoospores formed in the sporangia.
+
+    L, M, N, Fertilization of the oogonium and development of the
+    oospore in _Peronospora_.]
+
+  _Saprolegniaceae_ are aquatic forms found growing usually on dead
+  insects lying in water but occasionally on living fish (e.g. the
+  salmon disease associated with _Saprolegnia ferax_). The chief genera
+  are _Saprolegnia, Achlya, Pythiopsis, Dictyuchus, Aplanes._ Motile
+  zoospores which escape from the zoosporangium are present except in
+  Aplanes. The sexual reproduction shows all transitions between forms
+  which are normally sexual, like the Peronosporaceae, to forms in which
+  no antheridium is developed and the oospheres develop
+  parthenogenetically. The oogonia, unlike the Peronosporaceae, contain
+  more than one oosphere. Klebs has shown that the development of
+  zoosporangia or of oogonia and pollinodia respectively in
+  _Saprolegnia_ is dependent on the external conditions; so long as a
+  continued stream of suitable food-material is ensured the mycelium
+  grows on without forming reproductive organs, but directly the
+  supplies of nitrogenous and carbonaceous food fall below a certain
+  degree of concentration sporangia are developed. Further reduction of
+  the supplies of food effects the formation of oogonia. This explains
+  the sequence of events in the case of a _Saprolegnia_-mycelium
+  radiating from a dead fly in water. Those parts nearest the fly and
+  best supplied develop barren hyphae only; in a zone at the periphery,
+  where the products of putrefaction dissolved in the water form a
+  dilute but easily accessible supply, the zoosporangia are developed in
+  abundance; oogonia, however, are only formed in the depths of this
+  radiating mycelium, where the supplies of available food materials are
+  least abundant.
+
+  _Chytridineae._--These parasitic and minute, chiefly aquatic, forms
+  may be looked upon as degenerate Oomycetes, since a sexual process and
+  feeble unicellular mycelium occur in some; or they may be regarded as
+  series of primitive forms leading up to higher members. There is no
+  means of deciding the question. They are usually included in
+  Oomycetes, but their simple structure, minute size, usually uniciliate
+  zoospores, and their negative characters would justify their retention
+  as a separate group. It contains less than 200 species, chiefly
+  parasitic on or in algae and other water-plants or animals, of various
+  kinds, or in other fungi, seedlings, pollen and higher plants. They
+  are often devoid of hyphae, or put forth fine protoplasmic filaments
+  into the cells of their hosts. After absorbing the cell-contents of
+  the latter, which it does in a few hours or days, the fungus puts out
+  a sporangium, the contents of which break up into numerous minute
+  swarm-spores, usually one-ciliate, rarely two-ciliate. Any one of
+  these soon comes to rest on a host-cell, and either pierces it and
+  empties its contents into its cavity, where the further development
+  occurs (_Olpidium_), or merely sends in delicate protoplasmic
+  filaments (_Rhizophydium_) or a short hyphal tube of, at most, two or
+  three cells, which acts as a haustorium, the further development
+  taking place outside the cell-wall of the host (_Chytridium_). In some
+  cases resting spores are formed inside the host (_Chytridium_), and
+  give rise to zoosporangia on germination. In a few species a sexual
+  process is described, consisting in the conjugation of similar cells
+  (_Zygochytrium_) or the union of two dissimilar ones (_Polyphagus_).
+  In the development of distinct antheridial and oogonial cells the
+  allied Ancylistineae show close alliances to _Pythium_ and the
+  Oomycetes. On the other hand, the uniciliate zoospores of _Polyphagus_
+  have slightly amoeboid movements, and in this and the
+  pseudopodium-like nature of the protoplasmic processes, such forms
+  suggest resemblances to the Myxomycetes. Opinions differ as to whether
+  the Chytridineae are degraded or primitive forms, and the group still
+  needs critical revision. Many new forms will doubtless be discovered,
+  as they are rarely collected on account of their minuteness. Some
+  forms cause damping off of seedlings--e.g. _Olpidium Brassicae_;
+  others discoloured spots and even tumour-like swellings--e.g.
+  _Synchytium Scabiosae_, _S. Succisae_, _Urophlyctis_, &c., on higher
+  plants. Analogies have been pointed out between Chytridiaceae and
+  unicellular algae, such as Chlorosphaeraceae, Protococcaceae,
+  "Palmellaceae," &c., some of which are parasitic, and suggestions may
+  be entertained as to possible origin from such algae.
+
+  The _Zygomycetes_, of which about 200 species are described, are
+  especially important from a theoretical standpoint, since they
+  furnished the series whence Brefeld derived the vast majority of the
+  fungi. They are characterized especially by the zygospores, but the
+  asexual organs (sporangia) exhibit interesting series of changes,
+  beginning with the typical sporangium of _Mucor_ containing numerous
+  endospores, passing to cases where, as in _Thamnidium_, these are
+  accompanied with more numerous small sporangia (sporangioles)
+  containing few spores, and thence to _Chaetocladium_ and
+  _Piptocephalis_, where the sporangioles form but one spore and fall
+  and germinate as a whole; that is to say, the monosporous sporangium
+  has become a conidium, and Brefeld regarded these and similar series
+  of changes as explaining the relation of ascus to conidium in higher
+  fungi. According to his view, the ascus is in effect the sporangium
+  with several spores, the conidium the sporangiole with but one spore,
+  and that not loose but fused with the sporangiole wall. On this basis,
+  with other interesting morphological comparisons, Brefeld erected his
+  hypothesis, now untenable, that the Ascomycetes and Basidiomycetes
+  diverge from the Zygomycetes, the former having particularly
+  specialized the ascus (sporangial) mode of reproduction, the latter
+  having specialized the conidial (indehiscent one-spored sporangiole)
+  mode. In addition to sporangia and the conidial spores referred to,
+  some Mucorini show a peculiar mode of vegetative reproduction by means
+  of gemmae or chlamydospores--i.e. short segments of the hyphae become
+  stored with fatty reserves and act as spores. The gemmae formed on
+  submerged Mucors may bud like a yeast, and even bring about alcoholic
+  fermentation in a saccharine solution.
+
+  [Illustration: From Strasburger's _Lehrbuch der Botanik_, by
+  permission of Gustav Fischer.
+
+  FIG. 6.--_Mucor Mucedo._ Different stages in the formation and
+  germination of the zygospore. (After Brefeld, 1-4. 5 from v. Tavel,
+  _Pilze_.)
+
+    1, Two conjugating branches in contact.
+
+    2, Septation of the conjugating cells (a) from the suspensors (b).
+
+    3, More advanced stage, the conjugating cells (a) are still distinct
+    from one another; the warty thickenings of their walls have
+    commenced to form.
+
+    4, Ripe zygospore (b) between the suspensors (a).
+
+    5, Germinating zygospore with a germ-tube bearing a sporangium.]
+
+  The segments of the hyphae in this group usually contain several
+  nuclei. At the time of sporangial formation the protoplasm with
+  numerous nuclei streams into the swollen end of the sporangiophore and
+  there becomes cut off by a cell-wall to form the sporangium. The
+  protoplasm then becomes cut up by a series of clefts into a number of
+  smaller and smaller pieces which are unicellular in _Pilobolus_,
+  multicellular in _Sporodinia_. These then become surrounded by a
+  cell-wall and form the spores. This mode of spore-formation is totally
+  different from that in the ascus; hence one of the difficulties of the
+  acceptance of Brefeld's view of the homology of ascus and sporangium.
+  The cytology of zygospore-formation is not known in detail; the
+  so-called gametes which fuse are multinucleate and are no doubt of the
+  nature of gametangia. The fate of these nuclei is doubtful, probably
+  they fuse in pairs (fig. 6).
+
+  Blakeslee has lately made some very important observations of the
+  Zygomycetes. It is well known that while in some forms, e.g.
+  _Spordinia_, zygospores are easily obtained, in others, e.g. most
+  species of _Mucor_, they are very erratic in their appearance. This
+  has now been explained by Blakeslee, who finds that the Mucorinae can
+  be divided into two groups, termed homothallic and heterothallic
+  respectively. In the first group zygospores can arise by the union of
+  branches from the _same_ mycelium and so can be produced by the growth
+  from a single spore; this group includes _Spordinia grandis_,
+  _Spinellus fusiger_, some species of _Mucor_, &c. The majority of
+  forms, however, fall into the heterothallic group, in which the
+  association of branches from two mycelia _different in nature_ is
+  necessary for the formation of zygospores. These structures cannot
+  then be produced from the product of a single spore nor even from the
+  thalli derived from _any_ two spores. The two kinds of thalli
+  Blakeslee considers to have a differentiation of the nature of sex and
+  he distinguishes them as ( + ) and (-) forms; the former being usually
+  distinguished by a somewhat greater luxuriance of growth.
+
+  The classification of the Mucorini depends on the prevalence and
+  characters of the conidia, and of the sporangia and zygospores--e.g.
+  the presence or absence of a columella in the former, the formation of
+  an investment round the latter. Most genera are saprophytes, but
+  some--_Chaetocladium_, _Piptocephalis_--are parasites on other
+  Mucorini, and one or two are associated casually with the rotting of
+  tomatoes and other fruits, bulbs, &c., the fleshy parts of which are
+  rapidly destroyed if once the hyphae gain entrance. Even more
+  important is the question of mycosis in man and other animals,
+  referred to species of _Mucor_, and investigated by Lucet and
+  Costantin. Klebs has concluded that transpiration is the important
+  factor in determining the formation of sporangia, while
+  zygote-development depends on totally different conditions; these
+  results have been called in question by Falck.
+
+  The _Entomophthoraceae_ contain three genera, _Empusa_,
+  _Entomophthora_ and _Basidiobolus_. The two first genera consist of
+  forms which are parasitic on insects. _Empusa Muscae_ causes the
+  well-known epidemic in house-flies during the autumn; the dead,
+  affected flies are often found attached to the window surrounded by a
+  white halo of conidia. _B. ranarum_ is found in the alimentary canal
+  of the frog and growing on its excrement. In these three genera the
+  conidia are cast off with a jerk somewhat in the same way as the
+  sporangium of _Pilobolus_.
+
+B. HIGHER FUNGI.--Now that Brefeld's view of the origin of these forms
+from the Zygomycetes has been overthrown, the relationship of the higher
+and lower forms of fungi is left in obscurity. The term _Eumycetes_ is
+sometimes applied to this group to distinguish them from the
+Phycomycetes, but as the same name is also applied to the fungi as a
+whole to differentiate them from the Mycetozoa and Bacteria, the term
+had best be dropped. The Higher Fungi fall into three groups: the
+_Ustilaginales_, of doubtful position, and the two very sharply marked
+groups _Basidiales_ and _Ascomycetes_.
+
+[Illustration: From Vine's _Students' Text Book of Botany_, by
+permission of Swan Sonnenschein & Co.
+
+FIG. 7.--Germinating resting-gonidia. A, of _Ustilago receptaculorum_;
+B, of _Tilletia Caries_.
+
+  sp, The gonidium.
+
+  pm, The promycelium.
+
+  d,  The sporidia: in B the sporidia have coalesced in pairs at v.]
+
+  I. _Ustilaginales._--This includes two families Ustilaginaceae (smuts)
+  and Tilletiaceae (bunts). The bunts and smuts which damage our grain
+  and fodder plants comprise about 400 species of internal parasites,
+  found in all countries on herbaceous plants, and especially on
+  Monocotyledons. They are remarkable for their dark spores developed in
+  gall-like excrescences on the leaves, stems, &c., or in the fruits of
+  the host. The discovery of the yeast-conidia of these fungi, and their
+  thorough investigation by Brefeld, have thrown new lights on the
+  group, as also have the results elucidating the nature of the ordinary
+  dark spores--smuts, bunt, &c.--which by their mode of origin and
+  development are chlamydospores. When the latter germinate a slender
+  "promycelium" is put out; in _Ustilago_ and its allies this is
+  transversely septate, and bears lateral conidia (sporidia); in
+  _Tilletia_ and its allies non-septate, and bears a terminal tuft of
+  conidia (sporidia) (fig. 7). Brefeld regarded the promycelium as a
+  kind of _basidium_, bearing lateral or terminal conidia (comparable to
+  _basidiospores_), but since the number of basidiospores is not fixed,
+  and the basidium has not yet assumed very definite morphological
+  characters, Brefeld termed the group _Hemibasidii_, and regarded them
+  as a half-way stage in the evolution of the true Basidiomycetes from
+  Phycomycetes, the _Tilletia_ type leading to the true basidium
+  (Autobasidium), the _Ustilago_ type to the protobasidium, with lateral
+  spores; but this view is based on very poor evidence, so that it is
+  best to place these forms as a separate group, the _Ustilaginales_.
+  The yeast-conidia, which bud off from the conidia or their resulting
+  mycelium when sown in nutrient solutions, are developed in successive
+  crops by budding exactly as in the yeast plant, but they cannot
+  ferment sugar solutions. It is the rapid spread of these yeast-conidia
+  in manure and soil waters which makes it so difficult to get rid of
+  smuts, &c., in the fields, and they, like the ordinary conidia,
+  readily infect the seedling wheat, oats, barley or other cereals.
+  Infection in these cases occurs in the seedling at the place where
+  root and shoot meet, and the infecting hypha having entered the plant
+  goes on living in it and growing up with it as if it had no parasitic
+  action at all. When the flowers form, however, the mycelium sends
+  hyphae into the young ovaries and rapidly replaces the stores of sugar
+  and starch, &c., which would have gone to make the grain, by the
+  soot-like mass of spores so well known as smut, &c. These spores
+  adhere to the grain, and unless destroyed, by "steeping" or other
+  treatment, are sown with it, and again produce sporidia and
+  yeast-conidia which infect the seedlings. In other species the
+  infection occurs through the style of the flower, but the fungus after
+  reaching the ovule develops no further during that year but remains
+  dormant in the embryo of the seed. On germination, however, the fungus
+  behaves in the same way as one which has entered in the seedling
+  stage. The cytology of these forms is very little known; Dangeard
+  states that there is a fusion of two nuclei in the chlamydospore, but
+  this requires confirmation. Apart from this observation there is no
+  other trace of sexuality in the group.
+
+  II. _Ascomycetes._--This, except in the case of a few of the simpler
+  forms, is a very sharply marked group characterized by a special type
+  of sporangium, the ascus. In the development of the ascus we find two
+  nuclei at the base which fuse together to form the single nucleus of
+  the young _ascus_. The single nucleus divides by three successive
+  divisions to form eight nuclei lying free in the protoplasm of the
+  ascus. Then by a special method, described first by Harper, a mass of
+  protoplasm is cut out round each nucleus; thus eight uninucleate
+  ascospores are formed by free-cell formation. The protoplasm remaining
+  over is termed _epiplasm_ and often contains glycogen (fig. 8). In
+  some cases nuclear division is carried further before spore-formation
+  occurs, and the number of spores is then 16, 32 and 64, &c.; in a few
+  cases the number of spores is less than eight by abortion of some of
+  the eight nuclei. The ascus is thus one of the most sharply
+  characterized structures among the fungi.
+
+  In some forms we find definite male and female sexual organs
+  (_Sphaerotheca_, _Pyronema_, &c.), in others the antheridium is
+  abortive or absent, but the ascogonium (oogonium) is still present and
+  the female nuclei fuse in pairs (_Lachnea stercorea_, _Humaria
+  granulata_, _Ascobolus furfuraceus_); while in other forms ascogonium
+  and antheridium are both absent and fusion occurs between vegetative
+  nuclei (_Humaria rutilans_, and probably the majority of other forms).
+  In other cases the sexual fusion is apparently absent altogether, as
+  in _Exoascus_. In the first case (fig. 9) we have a true sexual
+  process, while in the second and third cases we have a _reduced_
+  sexual process in which the fusion of other nuclei has replaced the
+  fusion of the normal male and female nuclei. It is to be noted that
+  all the forms exhibit the fusion of nuclei in the ascus, so that those
+  with the normal or reduced sexual process described above have two
+  nuclear fusions in their life-history. The advantage or significance
+  of the second (ascus) fusion is not clearly understood.
+
+  [Illustration: From Strasburger's _Lehrbuch der Botanik_, by
+  permission of Gustav Fischer.
+
+  FIG. 8.--Development of the Ascus.
+
+    A-C, _Pyronema confluens_. (After Harper.)
+
+    D, Young ascus of _Boudiera_ with eight spores. (After Claussen.)]
+
+  The group of the Hemiasci was founded by Brefeld to include forms
+  which were supposed to be a connecting link between Phycomycetes and
+  Ascomycetes. As mentioned before, the connexion between these two
+  groups is very doubtful, and the derivation of the ascus from an
+  ordinary sporangium of the Zygomycetes cannot be accepted. The
+  majority of the forms which were formerly included in this group have
+  been shown to be either true Phycomycetes (like _Ascoidea_) or true
+  Ascomycetes (like _Thelebolus_). _Eremascus_ and _Dipodascus_, which
+  are often placed among the Hemiasci, possibly do not belong to the
+  Ascomycetes series at all.
+
+  [Illustration: From Strasburger's _Lehrbuch der Botanik_, by
+  permission of Gustav Fischer.
+
+  Fig. 9.--_Sphaerotheca Castagnei_. Fertilization and Development of
+  the Perithecium. (After Harper.)
+
+    1, Oogonium (og) with the antheridial branch (az) applied to its
+    surface
+
+    2, Separation of antheridium (an).
+
+    3, Passage of the antheridial nucleus towards that of the oogonium.
+
+    4, Union of the nuclei.
+
+    5, Fertilized oogonium surrounded by two layers of hyphae derived
+    from the stalk-cell (st).
+
+    6, The multicellular ascogonium derived by division from the
+    oogonium; the terminal cell with the two nuclei (as) gives rise to
+    the ascus.]
+
+  _Exoascaceae_ are a small group of doubtful extent here used to
+  include _Exoascus_, _Taphrina_, _Ascorticium_ and _Endomyces_. The
+  mycelium is very much reduced in extent. The asci are borne directly
+  on the mycelium and are therefore fully exposed, being devoid from the
+  beginning of any investment. The _Taphrineae_, which include
+  _Exoascus_ and _Taphrina_, are important parasites--e.g. pocket-plums
+  and witches' brooms on birches, &c., are due to their action (fig.
+  10). _Exoascus_ and _Ascorticium_ present interesting parallels to
+  _Exobasidium_ and _Corticium_ among the Basidiomycetes.
+
+  _Saccharomycetaceae_ include the well-known yeasts which belong mainly
+  to the genus _Saccharomyces_. They are characterized by their
+  unicellular nature, their power of rapid budding, their capacity for
+  fermenting various sugars, and their power of forming endogenous
+  spores. The sporangium with its endogenous spores has been compared
+  with an ascus, and on these grounds the group is placed among the
+  Ascomycetes--a very doubtful association. The group has attained an
+  importance of late even beyond that to which it was brought by
+  Pasteur's researches on alcoholic fermentation, chiefly owing to the
+  exact results of the investigations of Hansen, who first applied the
+  methods of pure cultures to the study of these organisms, and showed
+  that many of the inconsistencies hitherto existing in the literature
+  were due to the coexistence in the cultures of several species or
+  races of yeasts morphologically almost indistinguishable, but
+  physiologically very different. About fifty species of _Saccharomyces_
+  are described more or less completely, but since many of these cannot
+  be distinguished by the microscope, and some have been found to
+  develop physiological races or varieties under special conditions of
+  growth, the limits are still far too ill-defined for complete
+  botanical treatment of the genus. A typical yeast is able to develop
+  new cells by budding when submerged in a saccharine solution, and to
+  ferment the sugar--i.e. so to break up its molecules that, apart from
+  small quantities used for its own substance, masses of it out of all
+  proportion to the mass of yeast used become resolved into other
+  bodies, such as carbon dioxide and alcohol, the process requiring
+  little or no oxygen. Brefeld regards the budding process as the
+  formation of conidia. Under other conditions, of which the temperature
+  is an important one, the nucleus in the yeast-cell divides, and each
+  daughter-nucleus again, and four spores are formed in the mother cell,
+  a process obviously comparable to the typical development of
+  ascospores in an ascus. Under yet other conditions the quiescent
+  yeast-cells floating on the surface of the fermented liquor grow out
+  into elongated sausage-shaped or cylindrical cells and branching
+  cell-series, which mat together into mycelium-like veils. At the
+  bottom of the fermented liquor the cells often obtain fatty contents
+  and thick walls, and behave as resting cells (chlamydospores). The
+  characters employed by experts for determining a species of yeast are
+  the sum of its peculiarities as regards form and size: the shapes,
+  colours, consistency, &c., of the colonies grown on certain definite
+  media; the optimum temperature for spore-formation, and for the
+  development of the "veils"; and the behaviour as regards the various
+  sugars.
+
+  [Illustration: From Strasburger's _Lehrbuch der Botanik_, by
+  permission of Gustav Fischer.
+
+  FIG. 10.--_Taphrina Pruni._ Transverse section through the epidermis
+  of an infected plum. Four ripe asci, a1, a2, with eight spores, a3,
+  a4, with yeast-like conidia abstricted from the spores. After
+  Sadebeck.
+
+    st, Stalk-cells of the asci.
+
+    m, Filaments of the mycelium cut transversely.
+
+    cut, Cuticle.
+
+    sp, Epidermis.]
+
+  The following summary of some of the principal characteristics of
+  half-a-dozen species will serve to show how such peculiarities can be
+  utilized for systematic purposes:
+
+    +---------------------+---------------------------------+----------------------------------+----------------------------------------+
+    |                     |              Optimum            |          Characters of           |                                        |
+    |      Species.       |         Temperature for         +----------+-----------+-----------+         Sugars Fermented and           |
+    |                     +----------------+----------------+ Fermenta-|   Cells.  |  Spores.  |              Products, &c.             |
+    |                     |      Spores.   |     Veils.     |   tion   |           |           |                                        |
+    +---------------------+----------------+----------------+----------+-----------+-----------+----------------------------------------+
+    |_S. cereviseae I_.   |     30 deg.    | 20 deg.-28 deg.|   High   | Rounded   | Globoid   | / Inverts maltose and saccharose and   |
+    |_S. Pastorianus I_   | 27 deg.-5 deg. | 26 deg.-28 deg.|   Low    | Rounded   | Globoid   |<    form alcohol 4-6 vol. %.           |
+    |_S. ellipsoideus_    |     25 deg.    | 33 deg.-34 deg.|   Low    | Rounded   | Globoid   | \                                      |
+    |                     |                |                |          |           |           |                                        |
+    |_S. anomalus_        | 28 deg.-31 deg.|        ?       |   High   | Elliptical| Hat-shaped| Ditto, and evolves a fragrant ether.   |
+    |                     |                |                |          |                       |                                        |
+    |_S. Ludwigii_        | 30 deg.-31 deg.|        ?       |    ?     | Elongated | Globoid   | Will not invert maltose.               |
+    |                     |                |                |          |                       |                                        |
+    |_S. membranaefaciens_|     30 deg.    |        ?       |   High   | Elongated | Globoid   | Inverts neither maltose nor saccharose.|
+    +---------------------+----------------+----------------+----------+-----------+-----------+----------------------------------------+
+
+  Two questions of great theoretical importance have been raised over
+  and over again in connexion with yeasts, namely, (1) the morphological
+  one as to whether yeasts are merely degraded forms of higher fungi, as
+  would seem implied by their tendency to form elongated, hypha-like
+  cells in the veils, and their development of "ascospores" as well as
+  by the wide occurrence of yeast-like "sprouting forms" in other fungi
+  (e.g. _Mucor_, Exoasci, Ustilagineae, higher Ascomycetes and
+  Basidiomycetes); and (2) the question as to the physiological nature
+  and meaning of fermentation. With regard to the first question no
+  satisfactory proof has as yet been given that Saccharomycetes are
+  derivable by culture from any higher form, the recent statements to
+  that effect not having been confirmed. At the same time there are
+  strong grounds for insisting on the resemblances between _Endomyces_,
+  a hyphal fungus bearing yeast-like asci, and such a form as
+  _Saccharomyces anomalus_. Concerning the second question, the recent
+  investigations of Buchner and others have shown that a ferment
+  (zymase) can be extracted from yeast-cells which causes sugar to break
+  up into carbon dioxide and alcohol. It has since been shown by Buchner
+  and Albert that yeast-cells which have been killed by alcohol and
+  ether, or with acetone, still retain the enzyme. Such material is far
+  more active than the zymase obtained originally by Buchner from the
+  expressed juice of yeast-cells. Thus alcoholic fermentation is brought
+  into line with the other fermentations.
+
+  _Schizosaccharomyces_ includes a few species in which the cells do not
+  "bud" but become elongated and then divide transversely. In the
+  formation of sporangia two cells fuse together by means of outgrowths,
+  in a manner very similar to that of _Spirogyra_; sometimes, however,
+  the wall between two cells merely breaks down. The fused cell becomes
+  a sporangium, and in it eight spores are developed. In certain cases
+  single cells develop parthenogenetically, without fusion, each cell
+  producing, however, only four spores. In _Zygosaccharomyces_ described
+  by Barker (1901) we have a form of the usual sprouting type, but here
+  again there is a fusion of two cells to form a sporangium.
+
+  _Cytology._--The study of the nucleus of yeast-cells is rendered
+  difficult by the presence of other deeply staining granules termed by
+  Guillermond _metachromatic granules_. These have often been mistaken
+  for nuclei and have to be carefully distinguished by differential
+  stains. In the process of budding the nucleus divides apparently by a
+  process of direct division. In the formation of spores the nucleus of
+  the cell divides, the protoplasm collects round the nuclei to form the
+  spores by free-cell formation; the protoplasm (epiplasm) not used in
+  this process becomes disorganized. A fusion of nuclei was originally
+  described by Jansens and Leblanc, but it was observed neither by Wager
+  nor Guillermond and is probably absent. In _Schizosaccharomyces_ and
+  _Zygosaccharomyces_, however, we have a fusion of nuclei in connexion
+  with the conjugation of cells which precedes sporangium-formation. The
+  theory may be put forward that the ordinary forms have been derived
+  from sexual forms like _Schizosaccharomyces_ and _Zygosaccharomyces_
+  by a loss of sexuality, the sporangium being formed
+  parthenogenetically without any nuclear fusion. This suggests a
+  possible relationship to _Eremascus_, which can only doubtfully be
+  placed in the Ascomycetes (_vide supra_).
+
+  _Carpoascomycetes._--The other divisions of the Ascomycetes may be
+  distinguished as Carpoascomycetes because they do not bear the asci
+  free on the mycelium but enclosed in definite fruit bodies or
+  ascocarps. The ascocarps can be distinguished into two portions, a
+  mass of sterile or vegetative hyphae forming the main mass of the
+  fruit body, and surrounding the fertile ascogenous hyphae which bear
+  at their ends the asci. When the ascogonium (female organ) is present
+  the ascogenous hyphae arise from it, with or without its previous
+  fusion with an antheridium. In other cases the ascogenous hyphae arise
+  directly from the vegetative hyphae. In connexion with this condition
+  of reduction a fusion of nuclei has been observed in _Humaria
+  rutilans_ and is probably of frequent occurrence. The asci may be
+  derived from the terminal cell of the branches of the ascogenous
+  hyphae, but usually they are derived from the penultimate cell, the
+  tip curving over to form the so-called crozier. By this means the
+  ascus cell is brought uppermost, and after the fusion of the two
+  nuclei it develops enormously and produces the ascospores. The
+  ascospores escape from the asci in various ways, sometimes by a
+  special ejaculation-mechanism. The Ascomycetes, at least the
+  Carpoascomycetes, exhibit a well-marked alternation of sexual and
+  asexual generations. The ordinary mycelium is the gametophyte since it
+  bears the ascogonia and antheridia when present; the ascogenous hyphae
+  with their asci represent the sporophyte since they are derived from
+  the fertilized ascogonium. The matter is complicated by the apogamous
+  transition from gametophyte to sporophyte in the absence of the
+  ascogonium; also by the fact that there are normally two fusions in
+  the life-history as mentioned earlier. If there are two fusions one
+  would expect two reductions, and Harper has suggested that the
+  division of the nuclei into eight in the ascus, instead of into four
+  spores as in most reduction processes, is associated with a _double_
+  reduction process in the ascus. Miss Fraser in _Humaria rutilans_
+  finds two reductions: a normal synaptic reduction in the first nuclear
+  division of the ascus, and a peculiar reduction division termed
+  _brachymeiosis_ in the third ascus division.
+
+  Various types of ascocarp are characteristic of the different
+  divisions of the Carpoascomycetes: the cleistothecium, apothecium and
+  perithecium.
+
+  _Perisporineae._--This includes two chief families, Erysiphaceae and
+  Perisporiaceae. They are characterized by an ascocarp without any
+  opening to the exterior, the ascospores being set free by the decay or
+  rupture of the ascocarp wall; such a fruit-body is termed a
+  _cleistothecium_ (cleistocarp). The Erysiphaceae are a sharply marked
+  group of forms which live as parasites. They form a superficial
+  mycelium on the surface of the plant, the hyphae not usually
+  penetrating the tissues but merely sending haustoria into the
+  epidermal cells. Only in rare cases is the mycelium intercellular.
+  Owing to their appearance they go by the popular name of mildews.
+  _Sphaerotheca Humuli_ is the well known hop-mildew, _Sphaerotheca
+  Mors-Uvae_ is the gooseberry mildew, the recent advent of which has
+  led to special legislation in Great Britain to prevent its spreading,
+  as when rampant it makes the culture of gooseberries impossible.
+  _Erysiphe_, _Uncinula_ and _Phyllactinia_ are other well-known genera.
+  The form of the fruit body, the difference and the nature of special
+  outgrowths upon it--the appendages--are characteristic of the various
+  genera. Besides peritheca the members of the Erysiphaceae possess
+  conidia borne in simple chains. De Bary brought forward very strong
+  evidence for the origin of the ascocarp in _Sphaerotheca_ and
+  _Erysiphe_ by a sexual process, but Harper in 1895 was the first to
+  prove conclusively, by the observation of the nuclear fusion, that
+  there was a definite fertilization in _Sphaerotheca Humuli_ by the
+  fusion of a male (antheridial) nucleus with a female, ascogonial
+  (oogonial) nucleus. Since then Harper has shown that the same process
+  occurs in _Erysiphe_ and _Phyllactinia_.
+
+  [Illustration: FIG. 11.--Development of _Eurotium repens_. (After De
+  Bary.)
+
+    A, Small portion of mycelium with conidiophore (c), and archicarp
+    (as).
+
+    B, The spiral archicarp (as), with the antheridium (p).
+
+    D, The same, beginning to be surrounded by the hyphae forming the
+    perithecium wall.
+
+    D, The perithecium.
+
+    E, F, Sections of young perithecia.
+
+    w, Parietal cells.
+
+    f, Pseudo-parenchyma.
+
+    as, Ascogonium.
+
+    G, An ascus.
+
+    H, An ascospore.]
+
+  The Perisporiaceae are saprophytic forms, the two chief genera being
+  _Aspergillus_ and _Penicillium_. The blue-green mould _P. crustaceum_
+  and the green mould _A. herbariorium_ ( = _Eurotium herbariorum_) are
+  extraordinarily widely distributed, moulds being found on almost any
+  food-material which is exposed to the air. They have characteristic
+  conidiophores bearing numerous conidia, and also cleistothecia which
+  are spherical in form and yellowish in colour. The latter arise from
+  the crown of a spirally coiled archicarp (bearing an ascogonium at its
+  end) and a straight antheridium. Vegetative hyphae then grow up and
+  surround these and enclose them in a continuous sheath of plectenchyma
+  (fig. 11). It has lately been shown by Fraser and Chambers that in
+  _Eurotium_ both ascogonium and antheridium contain a number of nuclei
+  (i.e. are coenogametes), but that the antheridium disorganizes without
+  passing its contents into the ascogonium. There is apparently a
+  reduced sexual process by the fusion of the ascogonial (female) nuclei
+  in pairs. _Aspergillus Oryzae_ plays an important part in
+  saccharifying the starch of rice, maize, &c., by means of the abundant
+  diastase it secretes, and, in symbiosis with a yeast which ferments
+  the sugar formed, has long been used by the Japanese for the
+  preparation of the alcoholic liquor sake. The process has now been
+  successfully introduced into European commerce.
+
+  [Illustration: From Strasburger's _Lehrbuch der Botanik_, by
+  permission of Gustav Fischer.
+
+  FIG. 12.--_Peziza aurantiaca._ (After Krombholz, nat. size.)]
+
+  [Illustration: FIG. 13.--_Ascobolus furfuraceus._ Diagrammatic section
+  of the fructification. (After Janczewski.)
+
+    m, Mycelium.
+
+    c, Archicarp.
+
+    l, Pollinodium.
+
+    s, Ascogenous filaments.
+
+    a, Asri.
+
+    r, p, The sterile tissue from which the paraphyses h spring.]
+
+  _Discomycetes._--Used in its widest sense this includes the
+  Hysteriaceae, Phacidiaceae, Helvellaceae, &c. The group is
+  characterized in general by the possession of an ascocarp which,
+  though usually a completely closed structure during the earlier stages
+  of development, at maturity opens out to form a bowl or saucer-shaped
+  organ, thus completely exposing the layer of asci which forms the
+  hymenium. Such an ascocarp goes by the name of _apothecium_. Owing to
+  the shape of the fruit-body many of these forms are known as
+  cup-fungi, the cup or apothecium often attaining a large size,
+  sometimes several inches across (fig. 12). Functional male and female
+  organs have been shown to exist in _Pyronema_ and _Boudiera_; in
+  _Lachnea stercorea_ both ascogonia and antheridia are present, but the
+  antheridium is non-functional, the ascogonial (female) nuclei fusing
+  in pairs; this is also the case in _Humaria granulata_ and _Ascobolus
+  furfuraceus_, where the antheridium is entirely absent. In _H.
+  rutilans_, however, both sexual organs are absent and the ascogenous
+  hyphae arise apogamously from the ordinary hyphae of the mycelim. In
+  all these cases the ascogonium and antheridium contain numerous
+  nuclei; they are to be looked upon as gametangia in which there is no
+  differentiation of gametes, and since they act as single gametes they
+  are termed coenogametes. In some forms as in _Ascobolus_ the
+  ascogonium is multicellular, the various cells communicating by pores
+  in the transverse walls (fig. 13).
+
+  In the Helvellaceae there is no apothecium but a large irregular fruit
+  body which at maturity bears the asci on its surface. The development
+  is only slightly known, but there is some evidence for believing that
+  the fruit-body is closed in its very early stages.
+
+  [Illustration: From Strasburger's _Lehrbuch der Botanik_, by
+  permission of Gustav Fischer.
+
+  FIG. 14.--Perithecium of Podospora fimiseda in longitudinal section
+  After v. Tavel.
+
+    s, Asci.
+
+    a, Paraphyses.
+
+    e, Periphyses.
+
+    m, Mycelial hyphae.]
+
+  The genus _Peziza_ (in its widest sense) may be taken as the type of
+  the group. Most of them grow on living plants or on dead vegetable
+  remains, very often on fallen wood; a number, however, are found
+  growing on earth which is rich in humus. The genus _Sclerotinia_ may
+  be mentioned here; a number of forms have been investigated by
+  Woronin. The conidia are fragrant and are carried by bees to the
+  stigma of the bilberry; here they germinate with the pollen and the
+  hyphae pass with the pollen tubes down the style; the former infect
+  the ovules and produce sclerotia, therein reducing the fruits to a
+  mummified condition. From the sclerotia later the apothecium develops.
+  One species, _S. heteroica_, is _heteroecious_; the ascospores
+  infecting the leaves of _Vaccinium uliginosum_, while the conidia
+  which then arise infect only _Ledum palustre_. This is the only case
+  of heteroecism known in the vegetable kingdom outside the Uredineae.
+
+  _Pyrenomycetes._--This is an extraordinarily large and varied group of
+  forms which mostly live parasitically or saprophytically on vegetable
+  tissue, but a few are parasitic on insect-larvae. The group is
+  characterized by a special type of ascocarp, the _perithecium_. This
+  is typically of a flask-shaped form opening with a small pore at the
+  top. The asci live at the bottom often mixed with paraphyses, while
+  the upper "neck" of the flask is lined with special hyphae, the
+  periphyses, which aid in the ejection of the spores (fig. 14). The
+  simpler forms bear the perithecia directly on the mycelium, but the
+  more highly developed forms often bear them on a special mycelial
+  development--the stroma, which is often of large size and special
+  shape and colour, and of dense consistence. The cytological details of
+  development of the perithecia are not well known; most of them appear
+  to develop their ascogenous hyphae in an apogamous way without any
+  connexion with an ascogonium. Besides the special ascocarps, accessory
+  reproductive organs are known in the majority of cases in the form of
+  conidia.
+
+  _Tuberineae._--These are a small group of fungi including the
+  well-known truffles. They are found living saprophytically (in part
+  parasitically) underground in forests. The asci are developed in the
+  large dense fruit bodies (cleistothecia) and the spores escape by the
+  decay of the wall. The fruit-body is of complicated structure, but its
+  early stages of development are not known. Many of the fruit-bodies
+  have a pleasant flavour and are eaten under the name of truffles
+  (_Tuber brumale_ and other species). The exact life-history of the
+  truffle is not known.
+
+  _Laboulbeniineae_ are a group of about 150 species of fungi found on
+  insects, especially beetles, and principally known from the researches
+  of Thaxter in America. The plant is a small, dark brown, erect
+  structure (receptacle) of a few cells, and 1-10 mm. high, attached to
+  the insect by the lowermost end (foot), and easily mistaken for a hair
+  or similar appendage of the insect. The receptacle ends above in
+  appendages, each consisting of one or a few cells, some of which are
+  the male organs, others the female organs, and others again may be
+  barren hairs. The male organ (antheridium) consists of a few cells,
+  the terminal one of which either abstricts from its end, or emits from
+  its interior the non-motile spermatia, reminding us of those of the
+  Florideae. The female organ is essentially a flask-shaped structure;
+  the neck of the flask growing out as the trichogyne, and the belly
+  composed of an axial carpogenic cell surrounded by investing cells,
+  and with one cell (trichophoric) between it and the trichogyne. These
+  three elements--trichogyne, trichophoric cell, and carpogenic
+  cell--are regarded as the procarp. The spermatia have been shown by
+  Thaxter to fuse with the trichogyne, after which the axial cell below
+  (carpogenic cell) undergoes divisions, and ultimately forms asci
+  containing ascospores, while cells investing this form a perithecium,
+  the whole structure reminding us essentially of the fructification of
+  a Pyrenomycete. Many modifications in details occur, and the plants
+  may be dioecious. No injury is done to the infested insects. It has
+  lately been shown that there is a fusion of nuclei in connexion with
+  ascus formation, so that there can be no doubt of the position of this
+  extraordinary group of plants among the Ascomycetes. The various cells
+  of these organisms are connected by large pits which are traversed by
+  thick protoplasmic threads connecting one cell with the next. In this
+  point and in their method of fertilization the Laboulbeniineae suggest
+  a possible relationship of Ascomycetes and the Red Algae.
+
+  [Illustration: From Strasburger's _Lehrbuch der Botanik_, by
+  permission of Gustav Fischer.
+
+  FIG. 15.--_Armillaria mellea._ (After Ruhland.)
+
+    A, Young basidium with the two primary nuclei.
+
+    B, After fusion of the two nuclei. _Hypholoma appendiculatum_.
+
+    C, A basidium before the four nuclei derived from the secondary
+    nucleus of the basidium have passed into the four basidiospores.
+
+    D, Passage of a nucleus through the sterigma into the basidiospore.]
+
+  _Basidiales._--This very large group of plants is characterized by the
+  possession of a special type of conidiophore--the basidium, which
+  gives its name to the group. The basidium is a unicellular or
+  multicellular structure from which four basidiospores arise as
+  outgrowths; it starts as a binucleate structure, but soon, like the
+  ascus, becomes uninucleate by the fusion of the two nuclei. Then two
+  successive nuclear divisions occur resulting in the formation of four
+  nuclei which later migrate respectively into the four basidiospores
+  (fig. 15). The Basidiales are further characterized by the complete
+  loss of normal sexuality, but at some time or other in the
+  life-history there takes place an association of two nuclei in a cell;
+  the two nuclei are derived from separate cells or possibly in some
+  cases are sister nuclei of the same cell. The two nuclei when once
+  associated are termed "conjugate" nuclei, and they always divide at
+  the same time, a half of each passing into each cell. This conjugate
+  condition is finally brought to a close by the nuclear fusion in the
+  basidium. Between the nuclear association and the nuclear fusion in
+  the basidium many thousands of cell generations may be intercalated.
+  This nuclear association of equivalent nuclei apparently represents a
+  reduced sexual process (like the fusion of female nuclei in _Humaria
+  granulata_ and of vegetative nuclei in _H. rutilans_, among the
+  Ascomycetes) in which, however, the actual fusion (normally, in a
+  sexual process, occurring immediately after association) is delayed
+  until the formation of the basidium. During the tetrad division in the
+  basidium nuclear reduction occurs. There is thus in all the Basidiales
+  an alternation of generations, obscured, however, by the apogamous
+  transition from the gametophyte to sporophyte. The sporophyte may be
+  considered to begin at the stage of nuclear association and end with
+  the nuclear reduction in the basidium.
+
+  [Illustration: FIG. 16.--_Puccinia graminis._
+
+    A, Mass of teleutospores (t) on a leaf of couch-grass.
+
+    e, Epidermis ruptured.
+
+    b, Sub-epidermal fibres. (After De Bary.)
+
+    B, Part of vertical section through leaf of Berberis vulgaris, with
+    a, aecidium fruits, p, peridium, and sp, spermogonia. (After Sachs.)
+
+    C, Mass of uredospores (ur), with one teleutospore (t).
+
+    sh, Sub-hymenial hyphae. (After De Bary.)]
+
+  _Uredineae._--This is a large group of about 2000 forms. They are all
+  intercellular parasites living mostly on the leaves of higher plants.
+  Owing to the presence of oily globules of an orange-yellow or
+  rusty-red colour in their hyphae and spores they are termed
+  Rust-Fungi. They are distinguished from the other fungi and the rest
+  of the Basidiales by the great variety of the spores and the great
+  elaboration of the life-history to be found in many cases. Five
+  different kinds of spores may be present--teleutospores, sporidia ( =
+  basidiospores), aecidiospores, spermatia and uredospores (fig. 16).
+  The teleutospore, with the sporidia which arise from it, is always
+  present, and the division into genera is based chiefly on its
+  characters. The teleutospore puts forth on germination a four-celled
+  structure, the promycelium or basidium, and this bears later four
+  sporidia or basidiospores, one on each cell. When the sporidia infect
+  a plant the mycelium so produced gives origin to aecidiospores and
+  spermatia; the aecidiospores on infection produce a mycelium which
+  bears uredospores and later teleutospores. This is the life-history of
+  the most complicated forms, of the so-called _eu_ forms. In the
+  _opsis_ forms the uredospores are absent, the mycelium from the
+  aecidiospores producing directly the teleutospores. In _brachy_ and
+  _hemi_ the aecidiospores are absent, the mycelium from the sporidia
+  giving origin directly to the uredospores; the former possess
+  spermatia, in the latter they are absent. In _lepto_ and _micro_ forms
+  both aecidiospores and uredospores are absent, the sporidia producing
+  a mycelium which gives rise directly to teleutospores; in the _lepto_
+  forms the teleutospores can germinate directly, in the _micro_ forms
+  only after a period of rest. We have thus a series showing a
+  progressive reduction in the complexity of the life-history, the
+  _lepto_ and _micro_ forms having a life-history like that of the
+  Basidiomycetes. The _eu_ and _opsis_ forms may exhibit the remarkable
+  phenomenon of heteroecism, i.e. the dependence of the fungus on two
+  distinct host-plants for the completion of the life-history.
+  Heteroecism is very common in this group and is now known in over one
+  hundred and fifty species. In all cases of heteroecism the sporidia
+  infect one host leading to the production of aecidiospores and
+  spermatia (if present), while the aecidiospores are only able to
+  infect another host on which the uredospores (if present) and the
+  teleutospores are developed. A few examples are appended:
+
+    +-----------------------------+------------------+------------------+
+    |           Species.          | Teleutospores on | Aecidiospores on |
+    +-----------------------------+------------------+------------------+
+    | _Coleosporium Senecionis_   | _Pinus_          |   _Senecio_      |
+    | _Melampsora Rostrupi_       | _Populus_        |   _Mecurialis_   |
+    | _Pucciniastrum Goeppertiana_| _Vaccinium_      |   _Abies_        |
+    | _Gymnosporangium Sabinae_   | _Juniperus_      |   _Pyrus_        |
+    | _Uromyces Pisi_             | _Pisum, &c._     |   _Euphorbia_    |
+    | _Puccinia graminis_         | _Triticum, &c._  |   _Berberis_     |
+    | _P. dispersa_               | _Secale, &c._    |   _Anchusa_      |
+    | _P. coronata_               | _Agrostis_       |   _Rhamnus_      |
+    | _P. Ari-Phalaridis_         | _Phalaris_       |   _Arum_         |
+    | _P. Caricis_                | _Carex_          |   _Urtica_       |
+    | _Cronartium Ribicola_       | _Ribes_          |   _Pinus_        |
+    | _Chrysomyxa Rhododendri_    | _Rhododendron_   |   _Picea_        |
+    +-----------------------------+------------------+------------------+
+
+  Some of the Uredineae also exhibit the peculiarity of the development
+  of biologic forms within a single morphological species, sometimes
+  termed specialization of parasitism; this will be dealt with later
+  under the section Physiology.
+
+  [Illustration: From Strasburger's _Lehrbuch der Botanik_, by
+  permission of Gustav Fischer.
+
+  FIG. 17.--_Phragmidium Violaceum._ (After Blackman.)
+
+    A, Portion of a young aecidium.
+
+    st, Sterile cell.
+
+    a, Fertile cells; at a2 the passage of a nucleus from the adjoining
+    cell is seen.
+
+    B, Formation of the first spore-mother-cell (sm), from the basal
+    cell (a) of one of the rows of spores.
+
+    C, A further stage in which from sm1 the first aecidiospore (a) and
+    the intercalary cell (z) have arisen.
+
+    sm2, The second spore-mother-cell.
+
+    D, Ripe aecidiospore.]
+
+  _Cytology of Uredineae._--The study of the nuclear behaviour of the
+  cells of the Uredineae has thrown great light on the question of
+  sexuality. This group like the rest of the Basidiales exhibits an
+  association of nuclei at some point in its life-history, but unlike
+  the case of the Basidiomycetes the point of association in the
+  Uredineae is very well defined in all those forms which possess
+  aecidiospores. We find thus that in the _eu_ and _opsis_ forms the
+  association of nuclei takes place at the base of the aecidium which
+  produces the aecidiospores. There we find an association of nuclei
+  either by the fusion of two similar cells as described by Christmann
+  or by the migration of the nucleus of a vegetative cell into a special
+  cell of the aecidium. After this association the nuclei continue in
+  the conjugate condition so that the aecidiospores, the
+  uredospore-bearing mycelium, the uredospores and the young
+  teleutospores all contain two paired nuclei in their cells (fig. 17).
+  Before the teleutospore reaches maturity the nuclei fuse, and the
+  uninucleate condition then continues again until aecidium formation.
+  In the _hemi_, _brachy_, _micro_ and _lepto_ forms, which possess no
+  aecidium, we find that the association takes place at various points
+  in the ordinary mycelium but always before the formation of the
+  uredospores in the _hemi_ and _brachy_ forms, and before the formation
+  of teleutospores in _micro_ and _lepto_ form. Whether the association
+  of nuclei in the ordinary mycelium takes place by the migration of a
+  nucleus from one cell to another or whether two daughter nuclei become
+  conjugate in one cell, is not yet clear. The most reasonable
+  interpretation of the spermatia is that they are abortive male cells.
+  They have never been found to cause infection, and they have not the
+  characters of conidia; the large size of their nuclei, the reduction
+  of their cytoplasm and the absence of reserve material and their thin
+  cell wall all point to their being male gametes. Although in the forms
+  without aecidia the two generations are not sharply marked off from
+  one another, we may look up the generation with single nuclei in the
+  cells as the gametophyte and that with conjugate nuclei as the
+  sporophyte. The subjoined diagram will indicate the relationship of
+  the forms.
+
+  _Basidiomycetes._--This group is characterized by its greatly reduced
+  life-history as compared with that of the _eu_ forms among the
+  Uredineae. All the forms have the same life-history as the _lepto_
+  forms of that group, so that there is no longer any trace of sexual
+  organs. There is also a further reduction in that the basidium is not
+  derived from a teleutospore but is borne directly on the mycelium.
+  Formerly, before the relationship of promycelium and basidium were
+  understood, the Uredineae were considered as quite independent of the
+  Basidiomycetes. Later, however, these Uredineae were placed as a mere
+  subdivision of the Basidiomycetes. Although the Uredineae clearly lead
+  on to the Basidiomycetes, yet owing to their retaining in many cases
+  definite traces of sexual organs they are clearly a more primitive
+  group. Their marked parasitic habit also separates them off, so that
+  they are best included with the Basidiomycetes in a larger cohort
+  which may be called Basidiales. Most of Basidiomycetes are
+  characterized by the large sporophore on which the basidia with its
+  basidiospores are borne.
+
+  [Illustration: From _Annals of Botany_, by permission of the Clarendon
+  Press.
+
+  FIG. 18.]
+
+  It must be clearly borne in mind that though the Basidiomycetes show
+  no traces of differentiated sexual organs yet, like the _micro_ and
+  _lepto_ forms of the Uredineae, they still show (in the association of
+  nuclei and later fusion of nuclei in the basidium), a reduced
+  fertilization which denotes their derivation, through the Uredineae,
+  from more typically sexual forms. No one has yet made out in any form
+  the exact way in which the association of nuclei takes place in the
+  group. The mycelium is always found to contain conjugate nuclei before
+  the formation of basidia, but the point at which the conjugate
+  condition arises seems very variable. Miss Nichols finds that it
+  occurs very soon after the germination of the spore in _Coprinus_, but
+  no fusion of cells or migration of nuclei was to be observed.
+
+  _Protobasidiomycetes._--This, by far the smaller division of
+  Basidiomycetes, includes those forms which have a septate basidium.
+  There are three families--Auriculariaceae, Pilacreaceae and
+  Tremellinaceae. The first named contains a small number of forms with
+  the basidium divided like the promycelium of the Uredineae. They are
+  characterized by their gelatinous consistence and large size of their
+  sporophore. _Hirneola_ (_Auricularia_) _Auricula-Judae_ is the
+  well-known Jew's Ear, so named from the resemblance of the sporophore
+  to a human ear.
+
+  [Illustration: FIG. 19.--_Amanita muscaria_.
+
+    A, The young plant.
+
+    B, The mature plant.
+
+    C, Longitudinal section of mature plant.
+
+    p, The _pileus_.
+
+    g, The gills.
+
+    a, The _annulus_, or remnant of _velum partiale_,
+
+    v, Remains of _volva_ or _velum universale_.
+
+    s, The stalk.]
+
+  The Pilacreaceae are a family found by Brefeld to contain the genus
+  _Pilacre_. _P. Petersii_ has a transversely divided basidium as in
+  _Auriculariaceae_, but the basidia are surrounded with a peridium-like
+  sheath. The _Tremellinaceae_ are characterized by the possession of
+  basidia which are divided by two _vertical_ walls at right angles to
+  one another. From each of the four segments in the case of _Tremella_
+  a long outgrowth arises which reaches to the surface of the hymenium
+  and bears the basidiospores. In _Dacryomyces_ only two outgrowths and
+  two spores are produced.
+
+  _Autobasidiomycetes._--In this by far the larger division of the
+  Basidiomycetes the basidia are undivided and the four basidiospores
+  are borne on short sterigmata nearly always at the apex of the
+  basidium. The group may be divided into two main divisions,
+  _Hymenomycetes_ and _Gasteromycetes_.
+
+  _Hymenomycetes_ are a very large group containing over 11,000 species,
+  most of which live in soil rich in humus or on fallen wood or stems, a
+  few only being parasites. In the simplest forms (e.g. _Exobasidium_)
+  the basidia are borne directly on the ordinary mycelium, but in the
+  majority of cases the basidia are found developed in layers (hymenium)
+  on special sporophores of characteristic form in the various groups.
+  In these sporophores (such as the well-known toadstools and mushrooms
+  where the ordinary vegetative mycelium is underground) we have
+  structures specially developed for bearing the basidiospores and
+  protecting them from rain, &c., and for the distribution of the
+  spores--see earlier part of article on distribution of spores (figs.
+  19 and 20). The underground mycelium in many cases spreads wider and
+  wider each year, often in a circular manner, and the sporophores
+  springing from it appear in the form of a ring--the so-called fairy
+  rings. _Armillaria melleus_ and _Polyporus annosus_ are examples of
+  parasitic forms which attack and destroy living trees, while _Merulius
+  lacrymans_ is the well-known "dry rot" fungus.
+
+  [Illustration: FIG. 20.--_Agaricus mucidus_. Portion of hymenium. s,
+  Sporidia; st, sterigmata; g, sterile cells; c, cystidium, with
+  operculum o.]
+
+  _Gasteromycetes_ are characterized by having closed sporophores or
+  fruit-bodies which only open after the spores are ripe and then often
+  merely by a small pore. The fruit-bodies are of very various shapes,
+  showing a differentiation into an outer _peridium_ and an inner
+  spore-bearing mass, the _gleba_. The gleba is usually differentiated
+  into a number of chambers which are lined directly by the hymenium
+  (basidial layer), or else the chambers contain an interwoven mass of
+  hyphae, the branches of which bear the basidia. By the breaking down
+  of the inner tissues the spores often come to lie as a loose powdery
+  mass in the interior of the hollow fruit-body, mixed sometimes with a
+  capillitium. The best-known genera are _Bovista, Lycoperdon_
+  (puff-ball) _Scleroderma, Geaster_ (earth-star, q.v.). In the
+  last-named genus the peridium is double and the outer layer becomes
+  ruptured and spreads out in the form of star-shaped pieces; the inner
+  layer, however, merely opens at the apex by a small pore.
+
+  The most complex members of the Gasteromycetes belong to the
+  _Phalloideae_, which is sometimes placed as a distinct division of the
+  Autobasidiomycetes. _Phallus impudicus_, the stink-horn, is
+  occasionally found growing in woods in Britain. The fruit-body before
+  it ruptures may reach the size of a hen's egg and is white in colour;
+  from this there grows out a hollow cylindrical structure which can be
+  distinguished at the distance of several yards by its disgusting
+  odour. It is highly poisonous.
+
+_Physiology._--The physiology of the fungi comes under the head of that
+of plants generally, and the works of Pfeffer, Sachs, Vines, Darwin and
+Klebs may be consulted for details. But we may refer generally here to
+certain phenomena peculiar to these plants, the life-actions of which
+are restricted and specialized by their peculiar dependence on organic
+supplies of carbon and nitrogen, so that most fungi resemble the
+colourless cells of higher plants in their nutrition. Like these they
+require water, small but indispensable quantities of salts of potassium,
+magnesium, sulphur and phosphorus, and supplies of carbonaceous and
+nitrogenous materials in different stages of complexity in the different
+cases. Like these, also, they respire oxygen, and are independent of
+light; and their various powers of growth, secretion, and general
+metabolism, irritability, and response to external factors show similar
+specific variations in both cases. It is quite a mistake to suppose
+that, apart from the chlorophyll function, the physiology of the
+fungus-cell is fundamentally different from that of ordinary
+plant-cells. Nevertheless, certain biological phenomena in fungi are
+especially pronounced, and of these the following require particular
+notice.
+
+  _Parasitism._--Some fungi, though able to live as saprophytes,
+  occasionally enter the body of living plants, and are thus termed
+  facultative parasites. The occasion may be a wound (e.g. _Nectria_,
+  _Dasyscypha_, &c.), or the enfeeblement of the tissues of the host, or
+  invigoration of the fungus, the mycelium of which then becomes strong
+  enough to overcome the host's resistance (_Botrytis_). Many fungi,
+  however, cannot complete their life-history apart from the host-plant.
+  Such _obligate_ parasites may be epiphytic (_Erysipheae_), the
+  mycelium remaining on the outside and at most merely sending haustoria
+  into the epidermal cells, or endophytic (_Uredineae_, _Ustilagineae_,
+  &c.), when the mycelium is entirely inside the organs of the host. An
+  epiphytic fungus is not necessarily a parasite, however, as many
+  saprophytes (moulds, &c.) germinate and develop a loose mycelium on
+  living leaves, but only enter and destroy the tissues after the leaf
+  has fallen; in some cases, however, these saprophytic epiphytes can do
+  harm by intercepting light and air from the leaf (_Fumago_, &c.), and
+  such cases make it difficult to draw the line between saprophytism and
+  parasitism. Endophytic parasites may be intracellular, when the fungus
+  or its mycelium plunges into the cells and destroys their contents
+  directly (_Olpidium_, _Lagenidium_, _Sclerotinia_, &c.), but they are
+  far more frequently intercellular, at any rate while young, the
+  mycelium growing in the lacunae between the cells (_Peronospora_,
+  _Uredineae_) into which it may send short (_Cystopus_), or long and
+  branched (_Peronospora Calotheca_) haustoria, or it extends in the
+  middle lamella (_Ustilago_), or even in the solid substance of the
+  cell-wall (_Botrytis_). No sharp lines can be drawn, however, since
+  many mycelia are intercellular at first and subsequently become
+  intracellular (_Ustilagineae_), and the various stages doubtless
+  depend on the degrees of resistance which the host tissues are able to
+  offer. Similar gradations are observed in the direct effect of the
+  parasite on the host, which may be local (_Hemileia_) when the
+  mycelium never extends far from the point of infection, or general
+  (_Phytophthora_) when it runs throughout the plant. Destructive
+  parasites rapidly ruin the whole plant-body (_Pythium_), whereas
+  restrained parasites only tax the host slightly, and ill effects may
+  not be visible for a long time, or only when the fungus is epidemic
+  (_Rhytisma_). A parasite may be restricted during a long
+  incubation-period, however, and rampant and destructive later
+  (_Ustilago_). The latter fact, as well as the extraordinary
+  fastidiousness, so to speak, of parasites in their choice of hosts or
+  of organs for attack, point to reactions on the part of the
+  host-plant, as well as capacities on that of the parasite, which may
+  be partly explained in the light of what we now know regarding enzymes
+  and chemotropism. Some parasites attack many hosts and almost any
+  tissue or organ (_Botrytis cinerea_), others are restricted to one
+  family (_Cystopus Candidus_) or genus (_Phytophthora infestans_) or
+  even species (_Pucciniastrum Padi_), and it is customary to speak of
+  root-parasites, leaf-parasites, &c., in expression of the fact that a
+  given parasite occurs only on such organs--e.g. _Dematophora necatrix_
+  on roots, _Calyptospora Goeppertiana_ on stems, _Ustilago Scabiosae_
+  in anthers, _Claviceps purpurea_ in ovaries, &c. Associated with these
+  relations are the specializations which parasites show in regard to
+  the age of the host. Many parasites can enter a seedling, but are
+  unable to attack the same host when older--e.g. _Pythium_,
+  _Phytophthora omnivora_.
+
+  _Chemotropism._--Taken in conjunction with Pfeffer's beautiful
+  discovery that certain chemicals exert a distinct attractive influence
+  on fungus hyphae (_chemotropism_), and the results of Miyoshi's
+  experimental application of it, the phenomena of enzyme-secretion
+  throw considerable light on the processes of infection and parasitism
+  of fungi. Pfeffer showed that certain substances in definite
+  concentrations cause the tips of hyphae to turn towards them; other
+  substances, though not innutritious, repel them, as also do nutritious
+  bodies if too highly concentrated. Marshall Ward showed that the
+  hyphae of _Botrytis_ pierce the cell-walls of a lily by secreting a
+  cytase and dissolving a hole through the membrane. Miyoshi then
+  demonstrated that if _Botrytis_ is sown in a lamella of gelatine, and
+  this lamella is superposed on another similar one to which a
+  chemotropic substance is added, the tips of the hyphae at once turn
+  from the former and enter the latter. If a thin cellulose membrane is
+  interposed between the lamellae, the hyphae nevertheless turn
+  chemotropically from the one lamella to the other and pierce the
+  cellulose membrane in the process. The hyphae will also dissolve their
+  way through a lamella of collodion, paraffin, parchment paper,
+  elder-pith, or even cork or the wing of a fly, to do which it must
+  excrete very different enzymes. If the membrane is of some impermeable
+  substance, like gold leaf, the hyphae cannot dissolve its way through,
+  but the tip finds the most minute pore and traverses the barrier by
+  means of it, as it does a stoma on a leaf We may hence conclude that a
+  parasitic hyphae pierces some plants or their stomata and refuses to
+  enter others, because in the former case there are chemotropically
+  attractive substances present which are absent from the latter, or are
+  there replaced by repellent poisonous or protective substances such as
+  enzymes or antitoxins.
+
+  _Specialization of Parasitism._--The careful investigations of recent
+  years have shown that in several groups of fungi we cannot be content
+  to distinguish as units morphologically different species, but we are
+  compelled to go deeper and analyse further the species. It has been
+  shown especially in the _Uredineae_ and _Erysiphaceae_ that many forms
+  which can hardly be distinguished morphologically, or which cannot be
+  differentiated at all by structural characters, are not really
+  homogeneous but consist of a number of forms which are sharply
+  distinguishable by their infecting power. Eriksson found, for example,
+  that the well-known species _Puccinia graminis_ could be split up into
+  a number of forms which though morphologically similar were
+  physiologically distinct. He found that the species really consisted
+  of six distinct races, each having a more or less narrow range of
+  grasses on which it can live. The six races he named _P. graminis
+  Secalis_, _Tritici_, _Avenae_, _Airae_, _Agrostis_, _Poae_. The first
+  named will grow on rye and barley but not on wheat or oat. The form
+  _Tritici_ is the least sharply marked and will grow on wheat, barley,
+  rye and oat but not on the other grasses. The form _Avenae_ will grow
+  on oat and many grasses but not on the other three cereals mentioned.
+  The last three forms grow only on the genera _Aira_, _Agrostis_ and
+  _Poa_ respectively. All these forms have of course their
+  aecidium-stage on the barberry. The terms biologic forms, biological
+  species, physiological species, physiological races, specialized forms
+  have all been applied to these; perhaps the term biologic forms is the
+  most satisfactory. A similar specialization has been observed by
+  Marshall Ward in the _Puccinia_ parasitic on species of _Bromus_, and
+  by Neger, Marchal and especially Salmon in the Erysiphaceae. In the
+  last-named family the single morphological species _Erysiphe graminis_
+  is found growing on the cereals, barley, oat, wheat, rye and a number
+  of wild grasses (such as _Poa_, _Bromus_, _Dactylis_). On each of
+  these host-plants the fungus has become specialized so that the form
+  on barley cannot infect the other three cereals or the wild grasses
+  and so on. Just as the uredospores and aecidiospores both show these
+  specialized characters in the case of _Puccinia graminis_ so we find
+  that both the conidia and ascospores of _E. graminis_ show this
+  phenomenon. Salmon has further shown in investigating the relation of
+  _E. graminis_ to various species of the genus, _Bromus_, that certain
+  species may act as "bridging species," enabling the transfer of a
+  biologic form to a host-plant which it cannot normally infect. Thus
+  the biologic form on _B. racemosus_ cannot infect _B. commutatus_. If,
+  however, conidia from _B. racemosus_ are sown on _B. hordaceus_, the
+  conidia which develop on that plant are now able to infect _B.
+  commutatus_; thus _B. hordaceus_ acts as a bridging species. Salmon
+  also found that injury of a leaf by mechanical means, by heat, by
+  anaesthetics, &c., would affect the immunity of the plant and allow
+  infection by conidia which was not able to enter a normal leaf. The
+  effect of the abnormal conditions is probably to stop the production
+  of, or weaken or destroy the protective enzymes or antitoxins, the
+  presence of which normally confers immunity on the leaf.
+
+  _Symbiosis._--The remarkable case of life in common first observed in
+  lichens, where a fungus and an alga unite to form a compound
+  organism--the lichen--totally different from either, has now been
+  proved to be universal in these plants, and lichens are in all cases
+  merely algae enmeshed in the interwoven hyphae of fungi (see LICHENS).
+  This dualism, where the one constituent (alga) furnishes
+  carbohydrates, and the other (fungus) ensures a supply of mineral
+  matters, shade and moisture, has been termed _symbiosis_. Since then
+  numerous other cases of symbiosis have been demonstrated. Many trees
+  are found to have their smaller roots invaded by fungi and deformed by
+  their action, but so far from these being injurious, experiments go to
+  show that this mycorhiza (fungus-root) is necessary for the well-being
+  of the tree. This is also the case with numerous other plants of moors
+  and woodlands--e.g. Ericaceae, Pyrolaceae, Gentianaceae, Orchidaceae,
+  ferns, &c. Recent experiments have shown that the difficulties of
+  getting orchid seeds to germinate are due to the absence of the
+  necessary fungus, which must be in readiness to infect the young
+  seedling immediately after it emerges from the seed. The well-known
+  failures with rhododendrons, heaths, &c., in ordinary garden soils are
+  also explained by the need of the fungus-infected peat for their
+  roots. The role of the fungus appears to be to supply materials from
+  the leaf-mould around, in forms which ordinary root-hairs are
+  incapable of providing for the plant; in return the latter supports
+  the fungus at slight expense from its abundant stores of reserve
+  materials. Numerous other cases of symbiosis have been discovered
+  among the fungi of fermentation, of which those between _Aspergillus_
+  and yeast in sake manufacture, and between yeasts and bacteria in
+  kephir and in the ginger-beer plant are best worked out. For cases of
+  symbiosis see BACTERIOLOGY.
+
+  AUTHORITIES.--_General_: Engler and Prantl, _Die naturlichen
+  Pflanzenfamilien_, i. Teil (1892 onwards); Zopf, _Die Pilze_ (Breslau,
+  1890); De Bary, _Comparative Morphology of Fungi_, &c. (Oxford, 1887);
+  von Tafel, _Vergleichende Morphologie der Pilze_ (Jena, 1892);
+  Brefeld, _Unters. aus dem Gesamtgebiete der Mykologie_, Heft i. 13
+  (1872-1905); Lotsy, _Vortrage uber botanische Stammesgeschichte_
+  (Jena, 1907). _Distribution_, &c.: Cooke, _Introduction to the Study
+  of Fungi_ (London, 1895); Felix in _Zeitschr. d. deutsch. geologisch.
+  Gesellsch._ (1894-1896); Staub, _Sitzungsber. d. bot. Sec. d. Kgl.
+  ungarischen naturwiss. Gesellsch. zu Budapest_ (1897). _Anatomy_, &c.:
+  Bommer, "Sclerotes et cordons myceliens," _Mem. de l'Acad. Roy. de
+  Belg._ (1894); Mangin, "Observ. sur la membrane des mucorinees,"
+  _Journ. de Bot._ (1899); Zimmermann, _Die Morph. und Physiologie des
+  Pflanzenzellkernes_ (Jena, 1896); Wisselingh, "Microchem. Unters. uber
+  die Zellwande d. Fungi," _Pringsh. Jahrb._ B. 31, p. 619 (1898);
+  Istvanffvi, "Unters. uber die phys. Anat. der Pilze," _Prings. Jahrb._
+  (1896). _Spore Distribution_: Fulton, "Dispersal of the Spores of
+  Fungi by Insects," _Ann. Bot._ (1889); Falck, "Die Sporenverbreitung
+  bei den Basidiomyceten," _Beitr. zur Biol. d. Pflanzen_, ix. (1904).
+  _Spores and Sporophores_: Zopf, _Die Pilze_; also the works of von
+  Tafel and Brefeld. _Classification_: van Tieghem, _Journ. de bot._ p.
+  77 (1893), and the works of Brefeld, Engler and Prantl, von Tafel,
+  Saccardo and Lotsy already cited, _Oomycetes_: Wager, "On the
+  Fertilization of _Peronospora parasitica_," _Ann. Bot._ vol. xiv.
+  (1900); Stevens, "The Compound Oosphere of _Albugo Bliti_," _Bot.
+  Gaz._ vol. 28 (1899); "Gametogenesis and Fertilization in _Albugo_,"
+  ibid. vol. 32 (1901); Miyake, "The Fertilization of _Pythium de
+  Baryanum_," _Ann. of Bot._ vol. xv. (1901); Trow, "On Fertilization in
+  the Saprolegnieae," _Ann. of Bot._ vol. xviii. (1904); Thaxter, "New
+  and Peculiar Aquatic Fungi," _Bot. Gaz._ vol. 20 (1895); Lagerheim,
+  "Unters. uber die Monoblepharideae," _Bih. Svenska Vet. Acad.
+  Handlingar_, 25. Afd. iii. (1900); Woronin, "Beitrag zur Kenntnis der
+  Monoblepharideen," _Mem. de l'Acad. Imp. d. Sc. de St-Petersbourg_, 8
+  ser. vol. 16 (1902). _Zygomycetes_: Harper, "Cell-division in
+  Sporangia and Asci," _Ann. Bot._ vol. xiii. (1899); Klebs, _Die
+  Bedingungen der Fortpflanzung_, &c. (Jena, 1896), and "Zur Physiologie
+  der Fortpflanzung" _Prings. Jahr._ (1898 and 1899), "Uber _Sporodinia
+  grandis_," _Bot. Zeit._ (1902); Falck, "Die Bedingungen der
+  Zygotenbildung bei Sporodinia grandis," Cohn's Beitr. z. Biol. d.
+  Pflanzen, Bd. 8 (1902); Gruber "Verhalten der Zellkerne in den
+  Zygosporen von _Sporodinia grandis_," _Ber. d. deutschen bot. Ges._
+  Bd. 19 (1901); Blakeslee, "Sexual Reproduction in the Mucorineae,"
+  _Proc. Am. Acad._ (1904); "Zygospore germination in the Mucorineae,"
+  _Annales mycologici_ (1906). _Ustilagineae_: Plowright, _British
+  Uredineae and Ustilagineae_ (London, 1889); Massee, _British Fungi_
+  (Phycomycetes and Ustilagineae) (London, 1891); Brefeld, _Unters. aus
+  dem Gesamtgeb. der Mykol._ Hefte xi. and xii.; and Falck, "Die
+  Bluteninfektion bei den Brandpilzen," ibid. Heft xiii. 1905; Dangeard,
+  "La Reproduction sexuelle des Ustilaginees," C.R., Oct. 9, 1893;
+  Maire, "Recherches cytologiques et taxonomiques sur les
+  Basidiomyceten," _Annexe au Bull. de la Soc. Mycol. de France_ (1902).
+  _Saccharomycetaceae_: Jorgensen, _The Micro-organisms of Fermentation_
+  (1899); Barker, _Ann. of Bot._ vol. xiv. (1901); "On Spore-formation
+  among the Saccharomycetes," _Journ. of the Fed. Institute of Brewing_,
+  vol. 8 (1902); Guillermond, _Recherches cytologiques sur les levures_
+  (Paris, 1902); Hansen, _Centralbl. f. Bakt. u. Parasitenp._ Abt. ii.
+  Bd. 12 (1904). _Exoascaceae_: Giesenhagen, "_Taphrina, Exoascus,
+  Magnusiella_" (complete literature given), _Bot. Zeit._ Bd. 7 (1901).
+  _Erysiphaceae_: Harper, "Die Entwicklung des Perithecium bei
+  _Sphaerotheca castagnei_," _Ber. d. deut bot Ges._ (1896); "Sexual
+  Reproduction and the Organization of the Nucleus in certain Mildews,"
+  _Publ. Carnegie Institution_ (Washington, 1906); Blackman & Fraser,
+  "Fertilization in _Sphaerotheca_," _Ann. of Bot._ (1905).
+  _Perisporiaceae_: Brefeld, _Untersuchungen aus dem Gesamtgeb. der
+  Mykol._ Heft 10 (1891); Fraser and Chamber, _Annales mycologici_
+  (1907). _Discomycetes_: Harper, "Uber das Verhalten der Kerne bei
+  Ascomyceten," _Jahr. f. wiss. Bot._ Bd. 29 (1890); "Sexual
+  Reproduction in _Pyronema confluens_," _Ann. of Bot._ 14 (1900);
+  Claussen, "Zur Entw. der Ascomyceten," Boudiera, Bot. Zeit. Bd. 63
+  (1905); Dangeard, "Sur le _Pyronema confluens_," _Le Botaniste_, 9
+  serie (1903) (and numerous papers in same journal earlier and later);
+  Ramlow, "Zur Entwick. von _Thelebolus stercoren_," _Bot. Zeit._
+  (1906); Woronin, "Uber die Sclerotienkrankheit der Vaccineen Beeren,"
+  _Mem. de l'Acad. Imp. des Sciences de St-Petersbourg_, 7 serie, 36
+  (1888); Dittrich, "Zur Entwickelungsgeschichte der Helvellineen,"
+  Cohn's _Beitr. z. Biol. d. Pflanzen_ (1892). _Pyrenomycetes_: Fisch,
+  "Beitr. z. Entwickelungsgeschichte einiger Ascomyceten," _Bot. Zeit._
+  (1882); Frank, "Uber einige neue u. weniger bekannte Pflanzkrankh.,"
+  _Landw. Jahrb._ Bd. 12 (1883); Ward, "_Onygena equina_, a
+  horn-destroying fungus," _Phil. Trans._, vol. 191 (1899); Dawson, "On
+  the Biology of Poroniapunctata," Ann. of Bot. 14 (1900). _Tuberineae_:
+  Buchholtz, "Zur Morphologie u. Systematik der Fungi hypogaei," _Ann.
+  Mycol._ Bd. 1 (1903); Fischer in Engler and Prantl, _Die naturlichen
+  Pflanzenfamilien_ (1896). _Laboulbeniineae_: Thaxter, "Monograph of
+  the Laboulbeniaceae," _Mem. Amer. Acad. of Arts and Sciences_, vol. 12
+  (1895). _Uredineae_: Eriksson and Henning, _Die Getreideroste_
+  (Stockholm, 1896); Eriksson, _Botan. Gaz._ vol. 25 (1896); "On the
+  Vegetative Life of some Uredineae," Ann. of Bot. (1905); Klebahn, _Die
+  wirtwechselnden Rostpilze_ (Berlin, 1904); Sapin-Trouffy, "Recherches
+  histologiques sur la famille des Uredinees," _Le Botaniste_
+  (1896-1897); Blackman, "On the Fertilization, Alternation of
+  Generations and General Cytology of the Uredineae," _Ann. of Bot._
+  vol. 18 (1904); Blackman and Fraser, "Further Studies on the Sexuality
+  of Uredineae," _Ann. of Bot._ vol. 20 (1906); Christman, "Sexual
+  Reproduction of Rusts," _Ann. of Bot._ vol. 20 (1906); Ward, "The
+  Brooms and their Rust Fungus," _Ann. of Bot._ vol. 15 (1901).
+  _Basidiomycetes_: Dangeard, "La Reprod. sexuelle des Basidiomycetes,"
+  _Le Botaniste_ (1894 and 1900); Maire, "Recherches cytologiques et
+  taxonomiques sur les Basidiomycetes," _Annexe du Bull. de la Soc.
+  Mycol. de France_ (1902); Moller, "Protobasidiomyceten," _Schimper's
+  Mitt. aus den Tropen_, Heft 8 (Jena, 1895); Nichols, "The Nature and
+  Origin of the Binucleated Cells in certain Basidiomycetes," _Trans.
+  Wisconsin Acad. of Sciences_, vol. 15 (1905); Wager, "The Sexuality of
+  the Fungi," _Ann. of Bot._ 13 (1899); Woronin, "_Exobasidium
+  Vaccinii_," _Verh. Naturf. Ges. zu Freiburg_, Bd. 4 (1867).
+  _Fermentation_: Buchner, "Gahrung ohne Hefezellen," _Bot. Zeit._ Bd.
+  18 (1898); Albert, _Cent. f. Bakt._ Bd. 17 (1901); Green, _The
+  Soluble Ferments and Fermentation_ (Cambridge, 1899). _Parasitism_:
+  "On some Relations between Host and Parasite," _Proc. Roy. Soc_. vol.
+  47 (1890); "A Lily Disease," _Ann. of Botany_, vol. 2 (1888); Eriksson
+  & Hennings, _Die Getreideroste (vide supra_); Ward, "On the Question
+  of Predisposition and Immunity in Plants," _Proc. Cambridge Phil.
+  Soc_. vol. 11 (1902); also _Annals of Bot_. vol. 16 (1902) and vol. 19
+  (1905); Neger, "Beitr. z. Biol. d. Erysipheen" _Flora_, Bde. 88 and 90
+  (1901-1902); Salmon, "Cultural Experiments with 'Biologic Forms' of
+  the Erysiphaceae," _Phil. Trans_. (1904); "On Erysiphe graminis and
+  its adaptative parasitism within the genus, _Bromus_," _Ann. Mycol_.
+  vol. 11 (1904), also _Ann. of Bot_. vol. 19 (1905). _Symbiosis_: Ward,
+  "The Ginger-Beer Plant," _Phil. Trans. Roy. Soc_. (1892); "Symbiosis,"
+  _Ann. of Bot_. 13 (1899); Shalk, "Der Sinn der Mykorrhizenbildung,"
+  _Jahrb. f. wiss. Bot_. Bd. 34 (1900); Bernard, "On some Different
+  Cases of Germination," _Gardener's Chronicle_ (1900); Pierce, _Publ.
+  Univ. California_ (1900).     (H. M. W.; V. H. B.)
+
+
+
+
+FUNJ (FUNNIYEH, FUNG, FUNGHA), a very mixed negroid race, occupying
+parts of Sennar and the hilly country to the south between the White and
+Blue Niles. They traditionally come from west of the White Nile and are
+affiliated by some to the Kordofan Nubas, by others, more justifiably,
+to the negro Shilluks. These Funj, who became the dominant race in
+Sennar in the 15th century, almost everywhere assimilated the speech,
+religion and habits of the Arabs settled in that region. Until the 19th
+century they were one of the most powerful of African peoples in the
+eastern Sudan. About the end of the 15th century they overthrew the
+kingdom of Aloa, between the two Niles, and conquered the neighbouring
+peoples of the Sudan, Nubia and even Kordofan. The Funj had mixed much
+with the Arabs before their conquests, and had been converted to Islam.
+But they were still in many ways savages, for James Bruce (who traversed
+the district in 1772) says that their most famous king, Malek-el-Gahman,
+preferred human liver to any other food, and the Belgian traveller E.
+Pruyssenaere (1826-1864) found them still performing pagan rites on
+their sacred Mount Gula. Ernst Marno declared that as late as 1870 the
+most southern branch of the race, the Boruns, a non-Arabic speaking
+tribe, were cannibals. The Funj kings were content with levying tribute
+on their neighbours, and in this loose way Shendi, Berber and Dongola
+were once tributary. The Arab viziers gradually absorbed all power, the
+Funj sovereignty becoming nominal; and in 1821 the Egyptians easily
+destroyed the Funj domination. To-day the Funj are few, and represent no
+real type. They are a bright, hospitable folk. Many of them are skilful
+surgeons and go far afield in their work. The fellahin, indeed, call
+surgeons "Senaari" (men of Sennar). See further SENNAR AND SUDAN
+(Anglo-Egyptian).
+
+
+
+
+FUNKIA, in botany, a genus of rather handsome, hardy, herbaceous plants
+belonging to the natural order Liliaceae, and natives of China and
+Japan. They are tuberous, with broadly ovate or heart-shaped leaves and
+racemes of white or pale lilac, drooping, funnel-shaped flowers. They
+are useful for the borders of a shrubbery, the lawn or rock-work, or may
+be grown in pots for the greenhouse. The plants are propagated by
+dividing the crowns in autumn or when growth begins in spring.
+
+
+
+
+FUNNEL (through an O. Fr. _founil_, found in Breton, from Lat.
+_infundibulum_, that through which anything is poured, from _fundere_,
+to pour), a vessel shaped like a cone having a small tube at the apex
+through which powder, liquid, &c., may be easily passed into another
+vessel with a small opening. The term is used in metal-casting of the
+hole through which the metal is poured into a mould, and in anatomy and
+zoology of an _infundibulum_ or funnel-shaped organ. The word is thus
+used generally of any shaft or passage to convey light, air or smoke, as
+of the chimney of an engine or a steam-boat, or the flue of an ordinary
+chimney. It is also used of a shaft or channel in rocks, and in the
+decoying of wild-fowl is applied to the cone-shaped passage leading from
+a pond and covered with a net, a "funnel-net," into which the birds are
+decoyed.
+
+
+
+
+FUR (connected with O. Fr. _forre_, a sheath or case; so "an outer
+covering"), the name specially given to the covering of the skin in
+certain animals which are natives of the colder climates, lying
+alongside of another and longer covering, called the overhair. The fur
+differs from the overhair, in that it is soft, silky, curly, downy and
+barbed lengthwise, while the overhair is straight, smooth and
+comparatively rigid. These properties of fur constitute its essential
+value for felting purposes, and mark its difference from wool and silk;
+the first, after some slight preparation by the aid of hot water,
+readily unites its fibres into a strong and compact mass; the others can
+best be managed by spinning and weaving.
+
+On the living animal the overhair keeps the fur filaments apart,
+prevents their tendency to felt, and protects them from injury--thus
+securing to the animal an immunity from cold and storm; while, as a
+matter of fact, this very overhair, though of an humbler name, is most
+generally the beauty and pride of the pelt, and marks its chief value
+with the furrier. We arrive thus at two distinct and opposite uses and
+values of fur. Regarded as useful for felt it is denominated staple fur,
+while with respect to its use with and on the pelt it is called fancy
+fur.
+
+_History._--The manufacture of fur into a felt is of comparatively
+modern origin, while the use of fur pelts as a covering for the body,
+for the couch, or for the tent is coeval with the earliest history of
+all northern tribes and nations. Their use was not simply a barbarous
+expedient to defend man from the rigours of an arctic winter; woven wool
+alone cannot, in its most perfect form, accomplish this. The pelt or
+skin is requisite to keep out the piercing wind and driving storm, while
+the fur and overhair ward off the cold; and "furs" are as much a
+necessity to-day among more northern peoples as they ever were in the
+days of barbarism. With them the providing of this necessary covering
+became the first purpose of their toil; subsequently it grew into an
+object of barter and traffic, at first among themselves, and afterwards
+with their neighbours of more temperate climes; and with the latter it
+naturally became an article of fashion, of ornament and of luxury. This,
+in brief, has been the history of its use in China, Tatary, Russia,
+Siberia and North America, and at present the employment of fancy furs
+among civilized nations has grown to be more extensive than at any
+former period.
+
+The supply of this demand in earlier times led to such severe
+competition as to terminate in tribal pillages and even national wars;
+and in modern times it has led to commercial ventures on the part of
+individuals and companies, the account of which, told in its plainest
+form, reads like the pages of romance. Furs have constituted the price
+of redemption for royal captives, the gifts of emperors and kings, and
+the peculiar badge of state functionaries. At the present day they vie
+with precious gems and gold as ornaments and garniture for wealth and
+fashion; but by their abundance, and the cheapness of some varieties,
+they have recently come within the reach of men of moderate incomes. The
+history of furs can be read in Marco Polo, as he grows eloquent with the
+description of the rich skins of the khan of Tatary; in the early
+fathers of the church, who lament their introduction into Rome and
+Byzantium as an evidence of barbaric and debasing luxury; in the
+political history of Russia, stretching out a powerful arm over Siberia
+to secure her rich treasures; in the story of the French occupation of
+Canada, and the ascent of the St Lawrence to Lake Superior, and the
+subsequent contest to retain possession against England; in the history
+of early settlements of New England, New York and Virginia; in Irving's
+_Astoria_; in the records of the Hudson's Bay Company; and in the annals
+of the fairs held at Nizhniy Novgorod and Leipzig. Here it may suffice
+to give some account of the present condition of the trade in fancy
+furs. The collection of skins is now chiefly a matter of private
+enterprise. Few, if any, monopolies exist.
+
+_Natural Supplies._--We are dependent upon the Carnivora, Rodentia,
+Ungulata and Marsupialia for our supplies of furs, the first two classes
+being by far of the greatest importance. The Carnivora include bears,
+wolverines, wolves, raccoons, foxes, sables, martens, skunks, kolinskis,
+fitch, fishers, ermines, cats, sea otters, fur seals, hair seals, lions,
+tigers, leopards, lynxes, jackals, &c. The Rodentia include beavers,
+nutrias, musk-rats or musquash, marmots, hamsters, chinchillas, hares,
+rabbits, squirrels, &c. The Ungulata include Persian, Astrachan,
+Crimean, Chinese and Tibet lambs, mouflon, guanaco, goats, ponies, &c.
+The Marsupialia include opossums, wallabies and kangaroos. These, of
+course, could be subdivided, but for general purposes of the fur trade
+the above is deemed sufficient.
+
+The question frequently arises, not only for those interested in the
+production of fur apparel, but for those who derive so much comfort and
+pleasure from its use, whether the supply of fur-bearing animals is
+likely to be exhausted. Although it is a fact that the demand is ever
+increasing, and that some of the rarer animals are decreasing in
+numbers, yet on the other hand some kinds of furs are occasionally
+neglected through vagaries of fashion, which give nature an opportunity
+to replenish their source. These respites are, however, becoming fewer
+every day, and what were formerly the most neglected kinds of furs are
+becoming more and more sought after. The supply of some of the most
+valuable, such as sable, silver and natural black fox, sea otter and
+ermine, which are all taken from animals of a more or less shy nature,
+does very gradually decrease with persistent hunting and the
+encroachment of man upon the districts where they live, but the climate
+of these vast regions is so cold and inhospitable that the probabilities
+of man ever permanently inhabiting them in numbers sufficient to scare
+away or exterminate the fur-bearing wild animals is unlikely. Besides
+these there are many useful, though commonplace, fur-bearing animals
+like mink, musquash, skunk, raccoon, opossum, hamster, rabbit, hares and
+moles, that thrive by depredations upon cultivated land. Some of these
+are reared upon extensive wild farms. In addition there are domestic
+fur-bearing animals, such as Persian, Astrachan and Chinese lambs, and
+goats, easily bred and available.
+
+With regard to the rearing of the Persian lamb, there is a prevalent
+idea that the skins of the unborn lamb are frequently used; this,
+however, is a mistake. A few such skins have been taken, but they are
+too delicate to be of any service. The youngest, known as "broadtails,"
+are killed when a few days old, but for the well-developed curly fur,
+the lambs must be six or seven weeks old. During these weeks their
+bodies are covered with leather so that the fur may develop in close,
+light and clean curls. The experiment has been tried of rearing rare,
+wild, fur-bearing animals in captivity, and although climatic conditions
+and food have been precisely as in their natural environment, the fur
+has been poor in quality and bad in colour, totally unlike that taken
+from animals in the wild state. The sensation of fear or the restriction
+of movement and the obtaining of food without exertion evidently prevent
+the normal development of the creature.
+
+In mountainous districts in the more temperate zones some good supplies
+are found. Chinchillas and nutrias are obtained from South America,
+whence come also civet cats, jaguars, ocelots and pumas. Opossums and
+wallabies, good useful furs, come from Australia and New Zealand. The
+martens, foxes and otters imported from southern Europe and southern
+Asia, are very mixed in quality, and the majority are poor compared with
+those of Canada and the north.
+
+Certain characteristics In the skin reveal to the expert from what
+section of territory they come, but in classifying them it is considered
+sufficient to mention territories only.
+
+Some of the poorer sorts of furs, such as hamster, marmot, Chinese goats
+and lambs, Tatar ponies, weasels, kaluga, various monkeys, antelopes,
+foxes, otters, jackals and others from the warmer zones, which until
+recently were neglected on account of their inferior quality of colour,
+by the better class of the trade, are now being deftly dressed or dyed
+in Europe and America, and good effects are produced, although the lack
+of quality when compared with the better furs from colder climates which
+possess full top hair, close underwool and supple leathers, is readily
+manifest. It is only the pressure of increasing demand that makes
+marketable hard pelts with harsh brittle hair of nondescript hue, and
+these would, naturally, be the last to attract the notice of dealers.
+
+As it is impossible that we shall ever discover any new fur-bearing
+animals other than those we know, it behoves responsible authorities to
+enforce close seasons and restrictions, as to the sex and age, in the
+killing for the purpose of equalizing the numbers of the catches. As
+evidence of indiscriminate slaughter the case of the American buffaloes
+may be cited. At one time thousands of buffalo skins were obtainable and
+provided material for most useful coats and rugs for rough wear in cold
+regions, but to-day only a herd or so of the animals remain, and in
+captivity.
+
+The majority of animals taken for their fur are trapped or snared, the
+gun being avoided as much as possible in order that the coat may be
+quite undamaged. Many weary hours are spent in setting baits, traps and
+wires, and, frequently, when the hunter retraces his steps to collect
+the quarry it is only to find it gone, devoured by some large animal
+that has visited his traps before him. After the skins have been
+carefully removed--the sooner after death the better for the subsequent
+condition of the fur--they are lightly tacked out, pelt outwards, and,
+without being exposed to the sun or close contact with a fire, allowed
+to dry in a hut or shady place where there is some warmth or movement of
+air. With the exception of sealskins, which are pickled in brine, all
+raw skins come to the various trade markets simply dried like this.
+
+_Quality and Colour._--The best fur is obtained by killing animals when
+the winter is at its height and the colder the season the better its
+quality and colour. Fur skins taken out of season are indifferent, and
+the hair is liable to shed itself freely; a good furrier will, however,
+reject such faulty specimens in the manufacturing. The finest furs are
+obtained from the Arctic and northern regions, and the lower the
+latitude the less full and silky the fur, till, at the torrid zone, fur
+gives place to harsh hair without any underwool. The finest and closest
+wools are possessed by the amphibious Carnivora and Rodentia, viz.
+seals, otters, beavers, nutrias and musquash, the beauty of which is not
+seen until after the stiff water or top hairs are pulled out or
+otherwise removed. In this class of animal the underneath wool of the
+belly is thicker than that of the back, while the opposite is true of
+those found on the land. The sea otter, one of the richest and rarest of
+furs, especially for men's wear, is an exception to this unhairing
+process, which it does not require, the hair being of the same length as
+the wool, silky and bright, quite the reverse of the case of other
+aquatic animals.
+
+Of sealskins there are two distinct classes, the fur seals and the hair
+seals. The latter have no growth of fur under the stiff top hair and are
+killed, with few exceptions (generally of the marbled seals), on account
+of the oil and leather they yield. The best fur seals are found off the
+Alaska coast and down as far south as San Francisco.
+
+It is found that in densely wooded districts furs are darker in colour
+than in exposed regions, and that the quality of wool and hair is softer
+and more silky than those from bare tracts of country, where nature
+exacts from its creatures greater efforts to secure food, thereby
+developing stronger limbs and a consequently coarser body covering.
+
+As regards density of colour the skunk or black marten has the blackest
+fur, and some cats of the domestic kind, specially reared for their fur,
+are nearly black. Black bears have occasionally very black coats, but
+the majority have a brownish underwool. The natural black fox is a
+member of the silver fox family and is very rare, the skins bringing a
+high price. Most silver foxes have dark necks and in some the dark shade
+runs a quarter, half-way, or three-quarters, or even the whole length of
+the skin, but it is rather of a brownish hue. Some Russian sables are of
+a very dense bluish brown almost a black, which is the origin
+undoubtedly of the term "sables," while some, from one district in
+particular, have a quantity of silver hairs, evenly interspersed in the
+fur, a peculiarity which has nothing to do with age. The best sea otters
+have very dark coats which are highly esteemed, a few with silver hairs
+in parts; where these are equally and evenly spread the skins are very
+valuable. Otters and beavers that run dark in the hair or wool are more
+valuable than the paler ones, the wools of which are frequently touched
+with a chemical to produce a golden shade. This is also done with
+nutrias after unhairing. The darker sorts of mink, musquash, raccoon
+and wolverine are more valuable than the paler skins.
+
+_Collective Supplies and Sales._--There are ten large American and
+Canadian companies with extensive systems for gathering the annual hauls
+of skins from the far-scattered trappers. These are the Hudson's Bay
+Co., Russian Fur Co., Alaska Commercial Co., North American Commercial
+Co., Russian Sealskin Co., Harmony Fur Co., Royal Greenland Fur Co.,
+American Fur Co., Missouri Co. and Pacific Co. Most of the raw skins are
+forwarded to about half-a-dozen brokers in London, who roughly sort them
+in convenient lots, issuing catalogues to the traders of the world, and
+after due time for examination of the goods by intending purchasers, the
+lots are sold by public auction. The principal sales of general furs are
+held in London in January and March, smaller offerings being made in
+June and October; while the bulk of fur sealskins is sold separately in
+December. The Hudson's Bay Co.'s sales take place before the others,
+and, as no reserves are placed on any lot, the results are taken as
+exactly indicating current values. While many buyers from America and
+Russia are personally in attendance at the sales, many more are
+represented by London and Leipzig agents who buy for them upon
+commission. In addition to the fur skins coming from North America vast
+numbers from Russia, Siberia, China, Japan, Australia and South America
+are offered during the same periods at public auction. Fairs are also
+held in Siberia, Russia and Germany for the distribution of fur skins as
+follows:--
+
+  January:   Frankfort-on-the-  Small collection of provincial produce,
+               Oder               such as otter, fox, fitch and marten.
+
+  February:  Irbit, Siberia     General Russian furs.
+
+  Easter:    Leipzig, Germany   General furs.
+
+  August:    Nizhniy Novgorod,  Persian lamb and general furs.
+               Russia
+
+  August:    Kiakhta, Siberia   Chinese furs and ermine.
+
+  December:  Ishim, Siberia     Chiefly squirrels.
+
+Of course there are many transactions, generally in the cheaper and
+coarser kinds of furs, used only in central Europe, Russia and Asia
+which in no way interest the London market, and there are many direct
+consignments of skins from collectors in America and Russia to London,
+New York and Leipzig merchants. But the bulk of the fine furs of the
+world is sold at the large public trade auction sales in London. The
+chief exceptions are the Persian and Astrachan lambs, which are bought
+at the Russian fairs, and are dressed and dyed in Leipzig, and the
+ermine and Russian squirrels, which are dressed and manufactured into
+linings either in Russia or Germany before offered for sale to the
+wholesale merchants or manufacturers.
+
+The annual collection of fur skins varies considerably in quantity
+according to the demand and to the good or bad climatic conditions of
+the season; and it is impossible to give a complete record, as many
+skins are used in the country of their origin or exported direct to
+merchants. But a fairly exact statement of the numbers sold in the great
+public trade auction sales in London during the year 1905-1906 is
+herewith set out.
+
+       _Year ending 31st of March 1906._      Total Number
+                                                of Skins.
+
+  Badger                                         28,634
+  Badger, Japanese                                6,026
+  Bear                                           18,576
+  Beaver                                         80,514
+  Cat, Civet                                    157,915
+  Cat, House                                    126,703
+   "   Wild                                      32,253
+  Chinchilla (La Plata), known also as Bastard   43,578
+      "      Peruvian finest                      5,603
+  Deer, Chinese                                 124,355
+  Ermine                                         40,641
+  Fisher                                          5,949
+  Fitch                                          77,578
+  Fox, Blue                                       1,893
+   "   Cross                                     10,276
+   "   Grey                                      59,561
+   "   Japanese                                  81,429
+   "   Kit                                        4,023
+   "   Red                                      158,961
+   "   Silver                                     2,510
+   "   White                                     27,463
+  Goats, Chinese                                261,190
+  Hares                                          41,256
+  Kangaroo                                        7,115
+  Kid, Chinese linings and skins equal to     5,080,047
+  Kolinsky                                      114,251
+  Lamb, Mongolian linings and skins equal to    214,072
+    "   Slink        "        "       "         167,372
+    "   Tibet        "        "       "         794,130
+  Leopard                                         3,574
+  Lynx                                           88,822
+  Marmot, linings and skins equal to          1,600,600
+  Marten, Baum                                    4,573
+    "     Japanese                               16,461
+    "     Stone                                  12,939
+  Mink, Canadian and American                   299,254
+    "   Japanese                                360,373
+  Mouflon                                        23,594
+  Musk-rat or Musquash, Brown                 5,126,339
+    "           "       Black                    41,788
+  Nutria                                         82,474
+  Opossum, American                             902,065
+    "      Australian                         4,161,685
+  Otter, River                                   21,235
+    "    Sea                                        522
+  Raccoon                                       310,712
+  Sable, Canadian and American                   97,282
+    "    Japanese                                   556
+    "    Russian                                 26,399
+  Seals, Fur                                     77,000
+    "    Hair                                    31,943
+  Skunk                                       1,068,408
+  Squirrel                                      194,596
+    "     Linings each averaging 126 skins    1,982,736
+  Tiger                                             392
+  Wallaby                                        60,956
+  Wolf                                           56,642
+  Wolverine                                       1,726
+  Wombat                                        193,625
+
+A brief account of the different qualities of the pelts, with some
+general remarks as to their customary uses, follows. The prices quoted
+are subject to constant fluctuation and represent purely trade prices
+for bulk, and it should be explained that the very great variations are
+due to different sizes, qualities and colours, and moreover are only
+_first cost_, before skins are dressed and prepared. These preparations
+are in some cases expensive, and there is generally a considerable
+percentage of waste. The prices cannot be taken as a guide to the
+wholesale price of a single and finished skin, but simply as _relative_
+value.
+
+The fullest and darkest skins of each kind are the most valuable, and,
+in cases of bluish grey or white, the fuller, clearer and brighter are
+the more expensive. A few albinos are found in every species, but
+whatever their value to a museum, they are of little commercial
+importance. Some odd lots of skins arrive designated simply as
+"sundries," so no classification is possible, and this will account for
+the absence of a few names of skins of which the imports are
+insignificant in quantity, or are received direct by the wholesale
+merchants.
+
+
+  _Names, Qualities and Uses of Pelts._[1]
+
+  ASTRACHAN.--See _Lambs_, below.
+
+  BADGER.--Size 2 X 1 ft. American sorts have coarse thick underwool of
+  a pale fawn or stone colour with a growth of longer black and white
+  hairs, 3 or 4 in. long; a very durable but clumsy fur. The best skins
+  are exported to France, Spain and Italy, and used for carriage rugs
+  and military purposes. Asiatic, including Japanese, skins are more
+  woolly. Russian and Prussian kinds are coarser and darker, and used
+  mostly for brush trade. Value 6d. to 19s.
+
+  BEAR, AUSTRALIAN.--See _Wombat_, below.
+
+  BEAR, BLACK.--Size 6 X 3 ft. Fine dark brown underwool with bright
+  black and flowing top hair 4 in. long. Cubs are nearly as long in the
+  hair although only about half the size and not only softer and better,
+  but have the advantage of being very much lighter in pelt. Widely
+  distributed in North America, the best come from Canada, are costly
+  and are used for military caps, boas, muffs, trimmings, carriage rugs
+  and coachmen's capes, and the fur wears exceedingly well. Value 17s.
+  6d. to 86s. Those from East India and warm climates are harsh, poor
+  and only fit for floor rugs.
+
+  BEAR, BROWN.--Size 6 X 3 ft. Similar in quality to the black, but far
+  more limited in number; the colours range from light yellow to a rich
+  dark brown. The best come from Hudson Bay territory and are valuable.
+  Used for muffs, trimmings, boas, and carriage rugs. Inferior sorts,
+  almost grizzly in effect and some very pale, are found in Europe and
+  Asia and are mostly used locally. In India there is a species called
+  Isabelline bear, which was formerly imported to Great Britain, but
+  does not now arrive in any quantity worth mentioning. Value 10s. 6d.
+  to 60s., Isabelline sort 10s. 6d. to 78s.
+
+  BEAR, GRIZZLY.--Size 8 X 4 ft. Coarse hair, heavy pelt, mostly dark
+  yellowish and brown colours, only found in western parts of United
+  States, Russia and Siberia. Used as carriage rugs and floor rugs, most
+  durable for latter purpose and of fine effect. They are about half the
+  value of brown bear. Value 15s. to 54s.
+
+  BEAR, ISABELLINE.--See _Bear_, _Brown_, above.
+
+  BEAR, WHITE.--Size 10 X 5 ft. The largest of all bears. Short close
+  hair except on flanks, colour white to yellow. An inhabitant of the
+  Arctic circle, best from Greenland. Used for floor rugs, very durable;
+  and very white specimens are valuable. Value 20s. to 520s.
+
+  BEAVER. Size 3 X 2 ft. The largest of rodents, it possesses a close
+  underwool of bluish-brown hue, nearly an inch in depth, with coarse,
+  bright, black or reddish-brown top hair, 3 in. long. Found widely in
+  North America. After being unhaired the darkest wools are the most
+  valuable, although many people prefer the bright, lighter brown tones.
+  Used for collars, cuffs, boas, muffs, trimmings, coat linings and
+  carriage aprons, and is of a most durable nature, in addition to
+  having a rich and good appearance. Value 10s. to 39s. 6d.
+
+  BROADTAIL.--See _Lambs_, below.
+
+  CARACAL.--A small lynx from India, the fur very poor, seldom imported.
+
+  CARACUL.--See _Goats_ and _Lambs_, below.
+
+  CAT, CIVET.--Size 9 X 4-1/2 in., short, thick and dark underwool with
+  silky black top hair with irregular and unique white markings. It is
+  similar to skunk, but is much lighter in weight, softer and less full,
+  without any disagreeable odour. Used for coat linings it is very warm
+  and durable. A few come from China, but the fur is yellowish-grey,
+  slightly spotted and worth little. Value 1s. 1d. to 1s. 11d.
+
+  CAT, HOUSE, &C.--18 X 9 in., mostly black and dark brown, imported
+  from Holland, Bavaria, America and Russia, where they are reared for
+  their coats. The best, from Holland, are used for coat linings.
+  Although in colour, weight and warmth they are excellent, the fur is
+  apt to become loose and to fall off with friction of wear. The black
+  are known as genet, although the true genet is a spotted wild cat.
+  Wild sorts of the tabby order are coarser, and not so good and silky
+  in effect as when domestically reared. Value of the black sorts 2d. to
+  3s. Wild 9d. to 14s. Some small wild cats, very poor flat fur of a
+  pale fawn colour with yellow spots, are imported from Australia and
+  used for linings. Value 5-1/2d. to 1s. 1d.
+
+  CHEETAH.--Size of a small leopard and similar in colour, but has black
+  spots in lieu of rings. Only a few are now imported, which are used
+  for mats. Value 2s. 6d. to 18s.
+
+  CHINCHILLA, PERUVIAN and BOLIVIAN.--Size 12 X 7 in., fur 1 to 1-1/4
+  in. deep. Delicate blue-grey with black shadings, one of nature's most
+  beautiful productions, though not a durable one. Used for ladies'
+  coats, stoles, muffs, hats and trimmings. Yearly becoming scarcer and
+  most costly. Value 8s. 6d. to 56s. 8d.
+
+  CHINCHILLA, LA PLATA, incorrectly named and known in the trade as
+  "bastard chinchilla," size 9 X 4 in., in a similar species, but owing
+  to lower altitudes and warmer climatic conditions of habitation is
+  smaller, with shorter and less beautiful fur, the underwool colour
+  being darker and the top colour less pure. Used exactly as the better
+  kind, and the picked skins are most effective. As with the best sort
+  it is not serviceable for constant wear. Value 4s. 2d. to 27s. 6d.
+
+  CHINCHILLONE.--Size 13 X 8 in., obtained also from South America. Fur
+  is longer and weaker and poorer and yellower than chinchilla. Probably
+  a crossbred animal, very limited importation. Value 3s. 6d. to 16s.
+  8d.
+
+  DEER, CHINESE and EAST INDIAN.--Small, light, pelted skins, the
+  majority of which are used for mats. Reindeer and other varieties are
+  of little interest for use other than trophy mats. Thousands are taken
+  for the leather trade. Value of Chinese 1s. 2d. to 1s. 6d. each.
+
+  DOG.--The only dogs that are used in the fur trade in civilized
+  countries are those imported from China, which are heavy and coarse,
+  and only used in the cheaper trade, chiefly for rugs. Value 6d. to 1s.
+
+  DOG WOLF.--See _Wolf_, below.
+
+  ERMINE.--Size 12 X 2-1/2 in. Underwool short and even, with a shade
+  longer top hair. Pelt light and close in texture, and durable. In the
+  height of winter the colour is pure white with exception of the tip of
+  tail, which is quite black. Supplies are obtained from Siberia and
+  America. Best are from Ishim in Siberia. Used for cloak linings,
+  stoles, muffs and trimmings, also for embellishment of British state,
+  parliamentary and legal robes. When this fur is symmetrically spotted
+  with black lamb pieces it is styled miniver, in which form it is used
+  at the grand coronation functions of British sovereigns. Value 1s. 3d.
+  to 8s. 6d.
+
+  FISHER.--Size 30 X 12 in., tail 12 to 18 in. long, the largest of the
+  martens; has a dark shaded deep underwool with fine, glossy, dark and
+  strong top hair 2 in. or more long. Best obtained from British
+  America. The tails are almost black and make up most handsomely into
+  trimmings, muffs, &c. Tails worked separately in these forms are as
+  rich and fine and more durable than any other fur suitable for a like
+  purpose. The fur of the skin itself is something like a dark silky
+  raccoon, but is not as attractive as the tails. Value 12s. to 46s.
+
+  FITCH.--Size 12 X 3 in., of the marten species, also known as the pole
+  cat. Yellow underwool 1/3 in. deep, black top hair, 1-1/2 to 1-3/4 in.
+  long, very fine and open in growth, and not close as in martens.
+  Largest skins come from Denmark, Holland and Germany. The Russian are
+  smaller, but more silky and, as now dyed, make a cheap and fair
+  substitute for sable. They are excellent for linings of ladies' coats,
+  being of light weight and fairly strong in the pelt. English mayors'
+  and civic officials' robes are frequently trimmed with this fur in
+  lieu of sable. Value of the German variety 2s. to 5s. 6d. and of the
+  Russian 7d. to 1s. 4d.
+
+  FOX, BLUE.--Size 24 X 8 in. Underwool thick and long. Top hair fine
+  and not so plentiful as in other foxes. Found in Alaska, Hudson Bay
+  territory, Archangel and Greenland. Although called blue, the colour
+  is a slaty or drab tone. Those from Archangel are more silky and of a
+  smoky bluish colour and are the most valuable. These are scarce and
+  consequently dear. The white foxes that are dyed smoke and celestial
+  blue are brilliant and totally unlike the browner shades of this fox.
+  Value 34s. to 195s.
+
+  FOX, COMMON.--The variation of size and quality is considerable, and
+  the colour is anything from grey to red. In Great Britain the animal
+  is now only regarded for the sport it provides. On the European
+  continent, however, some hundreds of thousands of skins, principally
+  German, Russian and Norwegian, are sold annually, for home use, and
+  for dyeing and exportation, chiefly to the United States. The
+  qualities do not compare with those species found in North America and
+  the Arctic circle. The Asiatic, African and South American varieties
+  are, with the exception of those taken in the mountains, poorly furred
+  and usually brittle and therefore of no great service. No commercial
+  value can be quoted.
+
+  FOX, CROSS.--Size 20 X 7 in., are about as large as the silver and
+  generally have a pale yellowish or orange tone with some silvery
+  points and a darkish cross marking on the shoulders. Some are very
+  similar to the pale red fox from the North-West of America and a few
+  are exceptionally large. The darkest and best come from Labrador and
+  Hudson Bay, and the ordinary sorts from the north-west of the United
+  States and, as with silver and other kinds, the quality is inferior
+  when taken from warmer latitudes. Value 10s. 6d. to 60s.
+
+  FOX, GREY.--Size 27 X 10 in. Has a close dark drab underwool with
+  yellowish grizzly, grey, regular and coarse top hair. The majority
+  used for the trade come from Virginia and the southern and western
+  parts of the United States. Those from the west are larger than the
+  average, with more fur of a brighter tone. The fur is fairly
+  serviceable for carriage rugs, the leather being stout, but its
+  harshness of quality and nondescript colour does not contribute to
+  make it a favourite. Value 9d. to 4s. 9d.
+
+  FOX, JAPANESE.--See _Fox, Red_, and _Raccoon_, below.
+
+  FOX, KIT.--Size 20 X 6 in. The underwool is short and soft, as is also
+  the top hair, which is of very pale grey mixed with some
+  yellowish-white hair. It is the smallest of foxes, and is found in
+  Canada and the northern section of the United States. It is similar in
+  colour and quality to the prairie fox and to many kinds from the
+  warmer zones, such as from Turkey, eastern Asia and elsewhere. Value
+  1s. 3d. to 5s. 6d.
+
+  FOX, RED.--Size 24 X 8 in., though a few kinds are much larger. The
+  underwool is long and soft and the hair plentiful and strong. It is
+  found widely in the northern parts of America and in smaller numbers
+  south of the United States, also in China, Japan and Australia. The
+  colours vary from pale yellowish to a dark red, some being very
+  brilliant. Those of Kamschatka are rich and fine in quality. Farther
+  north, especially near the sea, the fur is coarse. Where the best
+  coloured skins are not used for carriage rugs they are extensively
+  dyed, and badger and other white hairs are inserted to resemble silver
+  fox. They are also dyed a sable colour. The skins, being the strongest
+  of foxes', both in the fur and pelt, are serviceable. The preparations
+  in imitation of the natural black and silver sorts are very good and
+  attractive. Value 1s. to 41s.
+
+  FOX, SILVER. Size 30 X 10 in. Underwool close and fine. Top hair black
+  to silvery, 3 in. long. The fur upon the necks usually runs dark,
+  almost black, and in some cases the fur is black half-way down the
+  length of the skin, in rarer cases three-quarters of the length and,
+  in the most exceptional instances, the whole length, and when this is
+  the case they are known as "Natural Black Foxes" and fetch enormous
+  prices. The even silvery sorts are highly esteemed, and the fur is one
+  of the most effective and precious. The finest are taken in Labrador.
+  The farther south they are found, the poorer and coarser the fur. The
+  brush has invariably a white tip. Value L1 to L320.
+
+  FOX, WHITE.--Size 20 X 7 in. Animals of this species are generally
+  small in size and inhabit the extreme northern sections of Hudson Bay,
+  Newfoundland, Greenland, Labrador and Siberia. The Canadian are silky
+  in nature and inclined to a creamy colour, while the Siberian are more
+  woolly and rather whiter. Those taken in central Asia near or in
+  Chinese territory are poorer and yellowish. The underwool in all sorts
+  is generally of a bluish-grey tone, but the top hair in the depth of
+  winter is usually full enough in quantity to hide any such variation.
+  Those skins in which the underwool is quite white are rare and much
+  more expensive. In summer specimens of this species, as with other
+  white furred animals, have slightly discoloured coats. The skins that
+  are not perfectly white are dyed jet black, dark or light smoke,
+  violet-blue, blue-grey, and also in imitation of the drab shades of
+  the natural blue. Value 18s. to 66s.
+
+  GENET.--Size 10 X 4 in. The genet proper is a small white spotted cat
+  found in Europe, but the quantity is too small to be of commercial
+  interest. The name has been adopted for the black cats used so much in
+  the trade. (See CATS, above.) Value 1s. to 6s. 6d.
+
+  GOATS.--Size varies greatly. The European, Arabian and East Indian
+  kinds are seldom used for rugs, the skins are chiefly dressed as
+  leather for books and furniture, and the kids for boots and gloves,
+  and the finer wool and hair are woven into various materials. Many
+  from Russia are dyed black for floor and carriage rugs; the hair is
+  brittle, with poor underwool and not very durable; the cost, however,
+  is small. The Chinese export thousands of similar skins in black, grey
+  and white, usually ready dressed and made into rugs of two skins each.
+  A great many are dyed black and brown, in imitation of bear, and are
+  used largely in the western parts of the United States and Canada for
+  sleigh and carriage rugs. Many are used for their leather. Thousands
+  of the kids are also dyed black and worked into cross-shaped pieces,
+  in which shape they are largely exported to Germany, France, Great
+  Britain and America, and sold by the retail as caracal, kid or
+  caracul. The grey ones are in good demand for motor coats. The word
+  caracul has been adopted from the Turkish and signifies black-eared.
+  See also LAMBS, CARACUL. Value of Chinese white 3s. 6d. to 6s. 6d.:
+  grey, 4s. to 6s. 9d.
+
+  The Angora from the heights of central Asia Minor has curly, fleecy,
+  silky, white wool, 4 to 7 in. long. The fur is not used in Great
+  Britain, as formerly, and the greater quantity, known as mohair, is
+  now imported for purposes of weaving. This species of goat was some
+  years since introduced into Cape Colony, but its wool is not so good
+  as the Asiatic breed. Good business, however, is done with the
+  product, but chiefly for leather. Value 4s. to 12s. 6d.
+
+  The Mongolian goat has a very soft silk underwool, and after the long
+  top hair is removed it is dressed and imported and erroneously named
+  mouflon. The colour is a light fawn, but it is so pale that it lends
+  itself to be dyed any colour. It was popular some years since in the
+  cheaper trade, but it is not now much seen in England. Value 2s. to
+  6s.
+
+  The Tibet goat is similar to the Angora in the fineness of its wool,
+  and many are used in the making of cashmere shawls. The Tibet lamb so
+  largely imported and used for children's wear is often miscalled Tibet
+  goat. Value 3s. to 7s. 6d.
+
+  GUANACO.--Size 30 X 15 in. Is a species of goat found in Patagonia and
+  other parts of South America. It has a very long neck and exceedingly
+  soft woolly fur of a light reddish-fawn colour with very white flanks.
+  It is usually imported in small quantities, native dressed, and ready
+  made into rugs. The dressing is hard and brittle. If the skins are
+  dressed in Europe they afford a very comfortable rug, though a very
+  marked one in effect. They have a similar wool to the vicuna, but
+  coarser and redder; both are largely used in South America. Value 1s.
+  to 4s. 6d.
+
+  HAMSTER.--Size 8 X 3-1/2 in. A destructive rodent, is found in great
+  numbers in Russia and Germany. The fur is very flat and poor, of a
+  yellowish pale brown with a little marking of black. Being of a light
+  weight it is used for linings. Value 3d. to 1s.
+
+  HARE.--Size 24 X 9 in. The common hare of Europe does not much
+  interest the furrier, the fur being chiefly used by makers of hatters'
+  felt. The white hares, however, of Russia, Siberia and other regions
+  in the Arctic circle are very largely used in the cheaper trade of
+  Europe, America and the British colonies. The fur is of the whitest
+  when killed in winter, and that upon the flanks of the animal is very
+  much longer than that upon its back. The flanks are usually cut off
+  and made into muffs and stoles. The hair is, however, brittle and is
+  not at all durable. This fur is dyed jet black and various shades of
+  brown and grey, and manufactured into articles for the small drapers
+  and for exportation. The North American hares are also dyed black and
+  brown and used in the same way. Value of white 2d. to 5d.
+
+  JACKAL.--Size 2 to 3 ft. long. Is found in India and north and south
+  Africa. Indian are light brown and reddish, those from the Cape are
+  dark grey and rather silvery. Few are imported. Fur generally poor and
+  harsh, only suitable for carriage rugs. Value 1s. to 3s. 6d.
+
+  JAGUAR.--Size 7 to 10 ft. long. Is found in Mexico and British
+  Honduras. The markings are an irregular ring formation with a spot in
+  the centre. Leopards have rings only and cheetahs solid spots.
+  Suitable only for hearth-rugs. Supply very limited. Value 5s. to 45s.
+
+  KALUGA.--See _Souslik_, below.
+
+  KANGAROO.--The sizes vary considerably, some being huge, others quite
+  small. The larger varieties, viz. the red and the great, do not
+  usually interest furriers, the fur being harsh and poor without
+  underwool. They are tanned for the leather trade. The sorts used for
+  carriage aprons, coat linings and the outside of motor coats include:
+  blue kangaroo, bush kangaroo, bridled kangaroo, wallaroo, yellow
+  kangaroo, rock wallaby, swamp wallaby and short-tailed wallaby. Many
+  of the swamp sort are dyed to imitate skunk and look well. Generally
+  the colours are yellowish or brown. Some are dark brown as in the
+  swamp, which being strong are suitable for motor coats. The rock
+  wallabies are soft and woolly and often of a pretty bluish tone, and
+  make moderately useful carriage rugs and perambulator aprons. The
+  redder and browner sorts are also good for rugs as they are thick in
+  the pelt. On the European continent many of these are dyed. The best
+  of the lighter weights are frequently insufficiently strong in the
+  hair to stand the friction of wear in a coat lining. Value, kangaroo
+  9d. to 3s., wallaby 1-1/2 d. to 5s. 3d., wallaroo 1s. to 5s. 6d.
+
+  KIDS.--See _Goats_, above.
+
+  KOLINSKY.--Size 12 X 2-1/2 in. Is one of the marten tribe. The
+  underwool is short and rather weak, but regular, as is also the top
+  hair; the colour is usually yellow. They have been successfully dyed
+  and used as a substitute for sable. They are found in Siberia, Amoor,
+  China and Japan, but the best are from Siberia. They are light in
+  weight and therefore suitable for linings of coats. The tails are used
+  for artists' "sable" brushes. The fur has often been designated as red
+  or Tatar sable. Value 1s. 6d. to 4s. 6d.
+
+  LAMBS.--The sorts that primarily interest the fur trade in Europe and
+  America are those from south Russia, Persia and Afghanistan, which are
+  included under the following wholesale or retail commercial terms:
+  Persian lamb, broadtail, astrachan, Shiraz, Bokharan and caracul lamb.
+  With the public the general term astrachan is an old one, embracing
+  all the above curly sorts; the flatter kinds, as broadtail and caracul
+  lamb, have always been named separately. The Persian lambs, size 18 X
+  9 in., are the finest and the best of them. When dressed and dyed they
+  should have regular, close and bright curl, varying from a small to a
+  very large one, and if of equal size, regularity, tightness and
+  brightness, the value is comparatively a matter of fancy. Those that
+  are dull and loose, or very coarse and flat in the curl, are of far
+  less market value.
+
+  All the above enumerated lambs are naturally a rusty black or brown,
+  and with very few exceptions are dyed a jet black. Lustre, however,
+  cannot be imparted unless the wool was originally of a silky nature.
+  Broadtails, size 10 X 5 in., are the very young of the Persian sheep,
+  and are killed before the wool has time to develop beyond the flat
+  wavy state which can be best compared to a piece of moire silk. They
+  are naturally exceedingly light in weight, and those that are of an
+  even pattern, possessing a lustrous sheen, are costly. There is,
+  notwithstanding, a great demand for these from the fashionable world,
+  as not only are they very effective, but being so flat in the wool the
+  figure of the wearer can be shown as perfectly as in a garment made of
+  silk. It cannot be regarded as an economical fur, as the pelt is too
+  delicate to resist hard wear.
+
+    Persian Lamb price 12s. 6d. to 25s.
+    Broadtail      "   10s.     "  35s.
+
+  Astrachan, Shiraz and Bokharan lambs, size 22 by 9 in., are of a
+  coarser, looser curl, and chiefly used for coat linings, while the
+  Persians are used for outside of garments, collars, cuffs, stoles,
+  muffs, hats and trimmings and gloves. The so-called caracul lambs,
+  size 12 X 6 in., are the very young of the astrachan sheep, and the
+  pick of them are almost as effective as broadtails, although less fine
+  in the texture. See also remarks as to caracul kid under Goats, above.
+
+    Astrachan  price 1s.    to 5s. 6d.
+    Caracul Lamb "   2s. 6d " 10s. 6d.
+    Shiraz       "   4s. 6d " 10s.
+    Bokharan     "   1s. 6d "  3s. 6d.
+
+  Grey lambs, size 24 X 10 in., are obtained from the Crimea and known
+  in the trade as "crimmers." They are of a similar nature to the
+  caracul lambs, but looser in curl, ranging from a very light to a dark
+  grey. The best are the pale bluish greys, and are chiefly used for
+  ladies' coats, stoles, muffs and hats. Price 2s. to 6s. Mongolian
+  lambs, size 24 X 15 in., are of a short wavy loose curl, creamy white
+  colour, and are usually exported from China dressed, the majority
+  being ready-made into cross-shaped coats or linings. They are used
+  principally for linings of good evening wraps for ladies. Price 1s. to
+  2s. 6d. Slink lambs come from South America and China. The former are
+  very small and generally those that are stillborn. They have a
+  particularly thin pelt with very close wool of minute curl. The China
+  sorts are much larger. The smallest are used for glove linings and the
+  others for opera cloak linings. Price 1s. to 6s. 6d.
+
+  LEOPARD.--Size 3 to 6 ft. long. There are several kinds, the chief
+  being the snow or ounce, Chinese, Bengal, Persian, East Indian and
+  African. The first variety inhabit the Himalayas and are beautifully
+  covered with a deep soft fur quite long compared to the flat harsh
+  hair of the Bengal sort. The colours are pale orange and white with
+  very dark markings, a strong contrast making a fine effect. Most
+  artists prize these skins above all others. The Chinese are of a
+  medium orange brown colour, but full in fur. The East Indian are less
+  full and not so dark. The Bengal are dark and medium in colour, short
+  and hard hair, but useful for floor rugs, as they do not hold the dust
+  like the fuller and softer hair of the kinds previously named. They
+  are also used for drummers' aprons and saddle cloths in the Indian
+  army. The African are small with pale lemon colour grounds very
+  closely marked with black spots on the skin, the strong contrast
+  making a pleasing effect. Occasionally, where something very marked is
+  wanted, skating jackets and carriage aprons are made from the softest
+  and flattest of skins, but usually they are made into settee covers,
+  floor rugs and foot muffs. Value 2s. to 40s.
+
+  LION.--Size 5 to 6 ft. long. These skins are found in Africa, Arabia
+  and part of India, and are every year becoming scarcer. They are only
+  used for floor rugs, and the males are more highly esteemed on account
+  of the set-off of the mane. Value, lions' L10 to L100; lionesses' L5
+  to L25.
+
+  LYNX.--Size 45 X 20 in. The underwool is thinner than fox, but the top
+  hair is fine, silky and flowing, 4 in. long, of a pale grey, slightly
+  mottled with fine streaks and dark spots. The fur upon the flanks is
+  longer and white with very pronounced markings of dark spots, and this
+  part of the skin is generally worked separately from the rest and is
+  very effective for gown trimmings. Where the colour is of a sandy and
+  reddish hue the value is far less than where it is of a bluish tone.
+  They inhabit North America as far south as California, also Norway and
+  Sweden. Those from the Hudson Bay district and Sweden are the best and
+  are very similar. Those taken in Central Asia are mostly used locally.
+  For attire the skins manufactured in Europe are generally dyed black
+  or brown, in which state it has a similar appearance to dyed fox, but
+  having less thick underwool and finer hair flows freely. The finest
+  skins when dyed black are used very largely in America in place of the
+  dyed black fox so fashionable for mourning wear in Great Britain and
+  France. The British Hussar busbies are made of the dark brown lynx,
+  and it is the free silky easy movement of the fur with the least
+  disturbance in the atmosphere that gives it such a pleasing effect. It
+  is used for rugs in its natural state and also in Turkey as trimmings
+  for garments. Value 13s. 6d. to 56s.
+
+  LYNX CAT or BAY LYNX.--Is about half the size and depth of fur of a
+  lynx proper, and inhabits the central United States. It is a flat and
+  reddish fur compared to the lynx and is suitable for cheap carriage
+  aprons. A few come from Canada and are of better quality. Value 5s. to
+  15s.
+
+  MARMOT.--Size 18 X 12 in. Is a rodent and is found in considerable
+  numbers in the south of Prussia. The fur is a yellowish brown and
+  rather harsh and brittle and has no underwool. Since, however, the
+  value of all good furs has advanced, dyers and manufacturers have made
+  very successful efforts with this fur. The Viennese have been
+  particularly successful, and their method has been to dye the skins a
+  good brown and then not put in the dark stripes, which exist in sable
+  and mink, until the garment or article is finished, thus obtaining as
+  perfectly symmetrical effects as if the articles were made of small
+  skins instead of large ones. Marmots are also found in North America,
+  Canada and China; the best, however, come from Russia. It should
+  always be a cheap fur, having so few good qualities to recommend it.
+  Value 9d. to 2s. 6d.
+
+  MARTEN, AMERICAN.--See _Sable_, below.
+
+  MARTEN, BAUM.--Size 16 X 5 in. Is sometimes called the pine marten,
+  and is found in quantity in the wooded and mountainous districts of
+  Russia, Norway, Germany and Switzerland. It possesses a thick
+  underwool with strong top hair, and ranges from a pale to a dark
+  bluish brown. The best, from Norway, are very durable and of good
+  appearance and an excellent substitute for American sable. The tails
+  when split into two or three, with small strips of narrow tape so as
+  to separate the otherwise dense fur, formerly made very handsome sets
+  of trimmings, ties and muffs, and the probabilities are, as with other
+  fashions, such use will have its period of revival. Value 6s. to 85s.
+
+  MARTEN, BLACK.--See _Skunk_, below.
+
+  MARTEN, JAPANESE.--Size 16 X 5 in. Is of a woolly nature with rather
+  coarse top hair and quite yellow in colour. It is dyed for the cheap
+  trade for boas and muffs, but it is not an attractive fur at the best
+  of times. It lacks a silky, bright and fresh appearance, and therefore
+  is unlikely to be in great demand, except where economy is an object.
+  Value 6s. 6d. to 18s. 6d.
+
+  MARTEN, STONE.--Size and quality similar to the baum; the colour,
+  however, of the underwool is a stony white and the top hair is very
+  dark, almost black. They live in rocky and stony districts. Skins of a
+  pale bluish tone are generally used in their natural state for stoles,
+  boas and muffs, but the less clear coloured skins are dyed in
+  beautiful shades similar in density to the dark and valuable sables
+  from Russia, and are the most effective skins that can be purchased at
+  a reasonable price. The tails have also been worked, in the manner
+  explained with regard to the baum marten, as sets of trimmings and in
+  other forms. Stone martens are found in Russia, Bosnia, Turkey,
+  Greece, Germany, the Alps and France. The Bosnian and the French are
+  the best in colour. The Asiatic sorts are less woolly, but being silky
+  are useful when dyed. There are many from Afghanistan and India which
+  are too poor to interest the European markets. Value 7s. 6d. to 26s.
+
+  MINK.--Size 16 X 5 in. Is of the amphibious class and is found
+  throughout North America and in Russia, China and Japan. The underwool
+  is short, close and even, as is also the top hair, which is very
+  strong. The best skins are very dark and are obtained from Nova
+  Scotia. In the central states of America the colour is a good brown,
+  but in the north-west and south-west the fur is coarse and generally
+  pale. It is very durable for linings, and is an economical substitute
+  for sable for coats, capes, boas and trimmings. Values have greatly
+  increased, and the fur possessing good qualities as to colour and
+  durability will doubtless always be in good request. The Russian
+  species is dark but flat and poor in quality, and the Chinese and
+  Japanese are so pale that they are invariably dyed. These, however,
+  are of very inferior nature. Value of American 3s. 3d. to 40s.,
+  Japanese 3d. to 2s. 3d.
+
+  MOLE.--Size 3-1/2 X 2-1/2 in. Moles are plentiful in the British Isles
+  and Europe, and owing to their lovely velvety coats of exquisite blue
+  shade and to the dearness of other furs are much in demand. Though the
+  fur is cheap in itself, the expense of dressing and working up these
+  little skins is considerable, and they possess the unique charm of an
+  exceptional colour with little weight of pelt; the quality of
+  resistance to friction is, however, so slight as to make them
+  expensive in wear. The best are the dark blue from the Fen district of
+  Cambridgeshire in England. Value 1/2d. to 2d.
+
+  MONGOLIAN LAMBS.--See _Lambs_, above.
+
+  MONKEY, BLACK.--Size 18 X 10 in. Among the species of monkeys only one
+  interests to any extent the fur trade, and that is the black monkey
+  taken on the west coast of Africa (_Colobus satanas_). The hair is
+  very long, very black and bright with no underwool, and the white pelt
+  of the base of the hair, by reason of the great contrast of colour, is
+  very noticeable. The skins were in 1850 very fashionable in England
+  for stoles, muffs and trimmings, and in America also as recently as
+  1890. They are now mostly bought for Germany and the continent. Value
+  6d. to 1s. 6d.
+
+  MOUFLON.--Size 30 X 15 in. Is a sheep found in Russia and Corsica and
+  now very little in demand, and but few are imported into Great
+  Britain. Many Mongolian goats with the long hairs pulled out are sold
+  as mouflon. Value 4s. to 10s. 6d.
+
+  MUSK-OX.--Size 6 X 3 ft. These animals have a dense coat of fine, long
+  brown wool, with very long dark brown hair on the head, flanks and
+  tail, and, in the centre, a peculiar pale oval marking. There is no
+  other fur that is so thick, and it is eminently suitable for sleighing
+  rugs, for which purpose it is highly prized in Canada. The musk-ox
+  inhabits the north part of Greenland and part of Canada, but in very
+  limited numbers. Value 10s. to 130s.
+
+  MUSQUASH or MUSK-RAT, BROWN and BLACK RUSSIAN.--Size 12 X 8 in. A very
+  prolific rodent of the amphibious class obtained from Canada and the
+  United States, similar in habit to the English vole, with a fairly
+  thick and even brown underwool and rather strong top dark hair of
+  medium density. It is a very useful fur for men's coat linings and
+  ladies' driving or motoring coats, being warm, durable and not too
+  heavy. If the colour were less motley and the joins between the skins
+  could be made less noticeable, it would be largely in demand for
+  stoles, ties and muffs. As it is, this fur is only used for these
+  smaller articles for the cheaper trade. It has, however, of later
+  years been "unhaired," the underwool clipped very even and then dyed
+  seal colour, in which way very useful and attractive garments are
+  supplied at less than half the cost of the cheaper sealskins. They do
+  not wear as well, however, as the pelt and the wool are not of a
+  strength comparable to those of sealskin. With care, however, such a
+  garment lasts sufficiently long to warrant the present outlay. Value
+  5-1/2d. to 1s. 9d.
+
+  There is a so-called black variety found in Delaware and New Jersey,
+  but the number is very small compared to the brown species. They are
+  excellent for men's coat linings and the outside of ladies' coats, for
+  stoles, muffs, collars and cuffs. Value 10d. to 3s. 7d.
+
+  The Russian musquash is very small, 7 X 4 in., and is limited in
+  numbers compared to the brown. Only a few thousands are imported to
+  London. It is of a very pretty silvery-blue shade of even wool with
+  very little silky top hair, having silvery-white sides and altogether
+  a very marked effect. The odour, however, even after dressing is
+  rather pungent of musk, which is generally an objection. Value 4s. to
+  6s. 6d.
+
+  NUTRIA.--Size 20 X 12 in. Is a rodent known in natural history as the
+  coypu, about half the size of a beaver, and when unhaired has not more
+  than half, generally less, the depth of fur, which is also not so
+  close. Formerly the fur was only used for hatters' felt, but with the
+  rise in prices of furs these skins have been more carefully removed
+  and--with improved dressing, unhairing and silvering processes--the
+  best provides a very effective and suitable fur for ladies' coats,
+  capes, stoles, muffs, hats and gloves, while the lower qualities make
+  very useful, light-weighted and inexpensive linings for men's or
+  women's driving coats. It is also dyed sealskin colour, but its woolly
+  nature renders it less effective than the more silky musquash. They
+  are obtained from the northern part of South America. Value is. 6d. to
+  6s. 6d.
+
+  OCELOT.--Size 36 X 13 in. Is of the nature of a leopard and prettily
+  marked with stripes and oblong spots. Only a few are now imported from
+  South America for carriage aprons or mats. The numbers are very
+  limited. Value 1s. to 2s. 6d.
+
+  OPOSSUM, AMERICAN.--Size 18 X 10 in. Is a marsupial, a class with this
+  exception not met with out of Australia. The underwool is of a very
+  close frizzy nature, and nearly white, with long bluish grey mixed
+  with some black top hair. It is only found in the central sections of
+  the United States. About 1870 in England it was dyed dark brown or
+  black and used for boas, muffs and trimmings, but until recently has
+  been neglected on the continent. With, however, recent experiments in
+  brown and skunk coloured dyes, it bids fair to become a popular fur.
+  Value 2-1/2d. to 5s. 6d.
+
+  OPOSSUM, AUSTRALIAN.--Size 16 X 8 in. Is a totally different nature of
+  fur to the American. Although it has wool and top hair, the latter is
+  so sparse and fine that the coat may be considered as one of close
+  even wool. The colour varies according to the district of origin, from
+  a blue grey to yellow with reddish tones. Those from the neighbourhood
+  of Sydney are light clear blue, while those from Victoria are dark
+  iron grey and stronger in the wool. These animals are most prolific
+  and evidently increasing in numbers. Their fur is pretty, warm and as
+  yet inexpensive, and is useful for rugs, coat linings, stoles, muffs,
+  trimmings and perambulator aprons. The worst coloured ones are
+  frequently dyed black and brown. The most pleasing natural grey come
+  from Adelaide. The reddest are the cheapest. Value 3-3/4d. to 3s. 6d.
+
+  OPOSSUM, RINGTAILED.--Size 7 X 4 in. Has a very short close and dark
+  grey wool, some being almost black. There are but a few thousands
+  imported, and being so flat they are only of use for coat linings, but
+  they are very warm and light in weight. Value 6d. to 10d.
+
+  OPOSSUM, TASMANIAN (grey and black).--Size 20 X 10 in. Is of a similar
+  description, but darker and stronger in the wool and larger. Besides
+  these there are some very rich brown skins which were formerly in such
+  request in Europe, especially Russia, that undue killing occurred
+  until 1899, when the government stopped for a time the taking of any
+  of this class. They are excellent for carriage aprons, being not only
+  very light in weight and warm, but handsome. Value 2s. 6d. to 8s. 6d.
+
+  OTTER, RIVER.--The size varies considerably, as does the underwool and
+  the top hair, according to the country of origin. There are few rivers
+  in the world where they do not live. But it is in the colder northern
+  regions that they are found in the greatest numbers and with the best
+  fur or underwool, the top hair, which, with the exception of the
+  scarce and very rich dark brown specimens they have in common with
+  most aquatic animals, is pulled out before the skins are manufactured.
+  Most of the best river otter comes from Canada and the United States
+  and averages 36 X 18 in. in size. Skins from Germany and China are
+  smaller, and shorter in the wool. The colours of the under wools of
+  river otters vary, some being very dark, others almost yellow. Both as
+  a fur and as a pelt it is extremely strong, but owing to its short and
+  close wool it is usually made up for the linings, collars and cuffs of
+  men's coats. A large number of skins, after unhairing, is dyed seal
+  colour and used in America. Those from hot climates are very poor in
+  quality. Value 28s. to 118s.
+
+  OTTER, SEA.--Size 50 X 25 in. Possesses one of the most beautiful of
+  coats. Unlike other aquatic animals the skin undergoes no process of
+  unhairing, the fur being of a rich dense silky wool with the softest
+  and shortest of water hairs. The colours vary from pale grey brown to
+  a rich black, and many have even or uneven sprinkling of white or
+  silvery-white hairs. The blacker the wool and the more regular the
+  silver points, the more valuable the skin. Sea otters are,
+  unfortunately, decreasing in numbers, while the demand is increasing.
+  The fur is most highly esteemed in Russia and China; in the latter
+  country it is used to trim mandarins' state robes. In Europe and
+  America it is much used for collar, long facings and cuffs of a
+  gentleman's coat; such a set may cost from L200 to L600, and in all
+  probability will soon cost more. Taking into consideration the size,
+  it is not so costly as the natural black fox, or the darkest Russian
+  sable, which is now the most expensive of all. The smaller and young
+  sea otters of a grey or brown colour are of small value compared to
+  the large dark and silvery ones. Value L10 to L220. A single skin has
+  been known to fetch L400.
+
+  OUNCE.--See _Leopard_, above.
+
+  PERSIAN LAMBS.--See _Lambs_, above.
+
+  PLATYPUS.--Size 12 X 8 in. One of the most singular of fur-bearing
+  animals, being the link between bird and beast. It has fur similar to
+  otter, is of aquatic habits, being web-footed with spurs of a cock and
+  the bill of a duck. The skins are not obtained in any numbers, but
+  being brought over by travellers as curiosities and used for muffs,
+  collars and cuffs, &c., they are included here for reference. Value
+  2s. to 3s. 6d.
+
+  _Pony_ or _Tatar Foal._--Size 36 X 20 in. These skins are of
+  comparatively recent importation to the civilized world. They are
+  obtained from the young of the numerous herds of wild horses that roam
+  over the plains of Turkestan. The coat is usually a shade of brown,
+  sometimes greyish, fairly bright and with a suggestion of waviness.
+  Useful for motor coats. Value 3s. to 10s. 6d.
+
+  PUMA.--Size 4-1/2 X 3 ft. Is a native of South America, similar to a
+  lion in habits and colour of coat. The hair and pelt is, however, of
+  less strength, and only a few are now used for floor rugs. Value 5s.
+  to 10s.
+
+  RACCOON.--Size 20 X 12 in. Is an animal varying considerably in size
+  and in quality and colour of fur, according to the part of North
+  America in which it is found. In common parlance, it may be described
+  as a species of wild dog with close affinity to the bear. The
+  underwool is 1 to 1-1/2 in. deep, pale brown, with long top hairs of a
+  dark and silvery-grey mixture of a grizzly type, the best having a
+  bluish tone and the cheapest a yellowish or reddish-brown. A limited
+  number of very dark and black sorts exist and are highly valued for
+  trimmings. The very finest skins are chiefly used for stoles and
+  muffs, and the general run for coachmen's capes and carriage rugs,
+  which are very handsome when the tails, which are marked with rings of
+  dark and light fur alternately, are left on. Raccoons are used in
+  enormous quantities in Canada for men's coats, the fur outside. The
+  poorer qualities are extensively bought and made up in a similar way
+  for Austria-Hungary and Germany. These make excellent linings for
+  coats or footsacks for open driving in very cold climates. The worst
+  coloured skins are dyed black or brown and are used for British
+  military busbies, or caps, stoles, boas, muffs and coachmen's capes.
+  The best skins come from the northern parts of the United States. A
+  smaller and poorer species inhabits South America, and a very few are
+  found in the north of India, but these do not interest the European
+  trade. From Japan a similar animal is obtained in smaller quantities
+  with very good but longer fur, of yellowish motley light-brown shades.
+  It is more often imported and sold as Japanese fox, but its
+  resemblance to the fur of the American raccoon is so marked as to
+  surely identify it. When dyed dark blue or skunk colour it is
+  good-looking and is sold widely in Europe. Raccoon skins are also
+  frequently unhaired, and if the underwool is of good quality the
+  effect is similar to beaver. It is the most useful fur for use in
+  America or Russia, having a full quantity of fur which will retain
+  heat. Value 10d. to 26s.
+
+  SABLE, AMERICAN and CANADIAN.--Size 17 X 5 in. The skins are sold in
+  the trade sale as martens, but as there are many that are of a very
+  dark colour and the majority are almost as silky as the Russian sable,
+  the retail trade has for generations back applied the term of sable to
+  this fur. The prevailing colour is a medium brown, and many are quite
+  yellow. The dyeing of these very pale skins has been for so long well
+  executed that it has been possible to make very good useful and
+  effective articles of them at a moderate price compared to Russian
+  sable. The finest skins are found in the East Main and the Esquimaux
+  Bay, in the Hudson's Bay Company's districts, and the poorest in
+  Alaska. They are not found very far south of the northern boundary of
+  the United States. The best skins are excellent in quality, colour and
+  effect, and wear well. Value 27s. 3d. to 290s.
+
+  SABLE, CHINESE and JAPANESE.--Size 14 X 4-1/2 in. These are similar to
+  the Amur skins previously referred to, but of much poorer quality and
+  generally only suitable for linings. The very palest skins are dyed
+  and made by the Chinese into mandarins' coats, in which form they are
+  found in the London trade sales, but being overdressed they are
+  inclined to be loose in the hair and the colour of the dye is not
+  good. The Japanese kind are imported raw, but are few in numbers, very
+  pale and require dyeing. Value 15s. to 150s.
+
+  SABLE, RUSSIAN.--Size 15 X 5 in. These skins belong to a species of
+  marten, very similar to the European and American, but much more silky
+  in the nature of their fur. They have long been known as "sables,"
+  doubtless owing to the density of colour to which many of them attain,
+  and they have always been held in the highest esteem by connoisseurs
+  as possessing a combination of rare qualities. The underwool is close,
+  fine and very soft, the top hair is regular, fine, silky and flowing,
+  varying from 1-1/2 to 2-1/2 in. in depth. In colour they range from a
+  pale stony or yellowish shade to a rich dark brown, almost black with
+  a bluish tone. The pelts are exceedingly fine and close in texture
+  and, although of little weight, are very durable, and articles made of
+  them produce a sensation of warmth immediately they are put upon the
+  body.
+
+  The Yakutsk, Okhotsk and Kamschatka sorts are good, the last being the
+  largest and fullest furred, but of less density of colour than the
+  others. Many from other districts are pale or yellowish brown, and
+  those from Saghalien are poor in quality. The most valuable are the
+  darkest from Yakutsk in Siberia, particularly those that have silvery
+  hairs evenly distributed over the skin. These however are exceedingly
+  scarce, and when a number are required to match for a large garment,
+  considerable time may be necessary to collect them. This class of skin
+  is the most expensive fur in the world, reckoning values by a square
+  foot unit.
+
+  The Amur skins are paler, but often of a pretty bluish stony tone with
+  many frequently interspersed silvery hairs. The quality too is lower,
+  that is, the fur is not so close or deep, but they are very effective,
+  particularly for close-fitting garments, as they possess the least
+  appearance of bulk. The paler skins from all districts in Siberia are
+  now cleverly coloured or "topped," that is, just the tips of the hair
+  are stained dark, and it is only an expert who can detect them from
+  perfectly natural shades. If this colouring process is properly
+  executed it remains fairly fast. Notwithstanding the reported rights
+  of the Russian imperial authorities over some regions with respect to
+  these and other valuable fur-bearing animals, there are in addition to
+  the numbers regularly sent to the trade auction sales in London many
+  good parcels of raw skins to be easily bought direct, provided price
+  is not the first consideration. Value 25s. to 980s.
+
+  SEAL, FUR.--Sizes range from 24 X 15 in. to 55 X 25 in., the width
+  being taken at the widest part of the skin after preparation. The
+  centre of the skin between the fins is very narrow and the skins taper
+  at each end, particularly at the tail. The very small pups are of a
+  beautiful quality, but too tiny to make into garments, and, as the aim
+  of a good furrier is to avoid all lateral or cross seams, skins are
+  selected that are the length of the garment that is to be made. The
+  most useful skins for coats are the large pups 42 in. long, and the
+  quality is very good and uniform. The largest skins, known in the
+  trade as "wigs," which range up to 8 ft. in length, are uneven and
+  weak in the fur, and hunters do not seek to obtain them. The supply of
+  the best sort is chiefly from the North Pacific, viz. Pribilof
+  Islands, Alaska, north-west coast of America, Copper Island of the
+  Aleutian group near to Kamschatka, Robben Island and Japan. Other
+  kinds are taken from the South Pacific and South Atlantic Oceans,
+  around Cape Horn, the Falkland Islands up to Lobos Islands at the
+  entrance of the La Plata river, off the Cape of Good Hope and Crozet
+  Isles. With, however, the exception of the pick of the Lobos Island
+  seals the fur of the southern sea seals is very poor and only suitable
+  for the cheapest market. Formerly many skins were obtained from New
+  Zealand and Australia, but the importation is now small and the
+  quality not good. The preparation of seal skin occupies a longer time
+  than any other fur skin, but its fine rich effect when finished and
+  its many properties of warmth and durability well repay it. Value 10s.
+  to 232s.
+
+  SEAL, HAIR.--There are several varieties of these seals in the seas
+  stretching north from Scotland, around Newfoundland, Greenland and the
+  north-west coast of America, and they are far more numerous than fur
+  seals. Generally they have coarse rigid hair and none possess any
+  underwool. They are taken principally for the oil and leather they
+  yield. Some of the better haired sorts are dyed black and brown and
+  used for men's motor coats when quite a waterproof garment is wanted,
+  and they are used also for this quality in China. The young of the
+  Greenland seals are called whitecoats on account of the early growth
+  being of a yellowish white colour; the hair is 3/4 to 1 in. long, and
+  at this early stage of their life is soft compared to that of the
+  older seals. These fur skins are dyed black or dark brown and are used
+  for military caps and hearth-rugs. Value 2s. to 15s. There are fewer
+  hair seals in the southern than in the northern seas.
+
+  SHEEP.--Vary much in size and in quality of wool. Many of the domestic
+  kind in central and northern Europe and Canada are used for drivers'
+  and peasants' coat linings, &c. In Great Britain many coats of the
+  home-reared sheep, having wools two and a half to five inches long,
+  are dyed various colours and used as floor rugs. Skins with very short
+  wool are dyed black and used for military saddle-cloths. The bulk,
+  however, is used in the wool trade. The Hungarian peasants are very
+  fond of their natural brown sheep coats, the leather side of which is
+  not lined, but embellished by a very close fancy embroidery, worked
+  upon the leather itself; these garments are reversible, the fur being
+  worn inside when the weather is cold. Chinese sheep are largely used
+  for cheap rugs. Value of English sheep from 3s. to 10s.
+
+  SKUNK or BLACK MARTEN.--Size 15 X 8 in. The underwool is full and
+  fairly close with glossy, flowing top hair about 2-1/2 in. long. The
+  majority have two stripes of white hair, extending the whole length of
+  the skin, but these are cut out by the manufacturing furrier and sold
+  to the dealers in pieces for exportation. The animals are found widely
+  spread throughout North and South America. The skins which are of the
+  greatest interest to the European trade are those from North America,
+  the South American species being small, coarse and generally brown.
+  The best skins come from Ohio and New York. If it were not for its
+  disagreeable odour, skunk would be worth much more than the usual
+  market value, as it is naturally the blackest fur, silky in appearance
+  and most durable. The improved dressing processes have to a large
+  extent removed the naturally pungent scent. The fur is excellent for
+  stoles, boas, collars, cuffs, muffs and trimmings. Value 1s. 6d. to
+  11s.
+
+  SOUSLIK.--Size 7 in. X 2-1/4. Is a small rodent found in the south of
+  Russia and also in parts of America. It has very short hair and is a
+  poor fur even for the cheapest linings, which is the only use to which
+  the skin could be put. It is known as kaluga when imported in
+  ready-made linings from Russia where the skins are dressed and worked
+  in an inferior way. Value 1d. to 3d.
+
+  SQUIRREL.--Size 10 X 5 in. This measurement refers to the Russian and
+  Siberian sorts, which are the only kind imported for the fur. The
+  numerous other species are too poor in their coats to attract notice
+  from fur dealers. The back of the Russian squirrel has an even close
+  fur varying from a clear bluish-grey to a reddish-brown, the bellies
+  in the former being of a flat quality and white, in the latter
+  yellowish. The backs are worked into linings separately, as are the
+  bellies or "locks." The pelts, although very light, are tough and
+  durable, hence their good reputation for linings for ladies' walking
+  or driving coats. The best skins also provide excellent material for
+  coats, capes, stoles, ties, collars, cuffs, gloves, muffs, hoods and
+  light-weight carriage aprons. The tails are dark and very small, and
+  when required for ends of boas three or four are made as one. Value
+  per skin from 2-1/2d. to 1s. 1d.
+
+  TIBET LAMB.--Size 27 X 13 in. These pretty animals have a long, very
+  fine, silky and curly fleece of a creamy white. The majority are
+  consigned to the trade auction sales in London ready dressed and
+  worked into cross-shaped coats, and the remainder, a fourth of the
+  total, come as dressed skins. They are excellent for trimmings of
+  evening mantles and for children's ties, muffs and perambulator
+  aprons. The fur is too long and bulky for linings. Value per skin from
+  4s. 6d. to 8s. 6d.
+
+  TIGER.--Size varies considerably, largest about 10 ft. from nose to
+  root of tail. Tigers are found throughout India, Turkestan, China,
+  Mongolia and the East Indies. The coats of the Bengal kind are short
+  and of a dark orange brown with black stripes, those from east or
+  further India are similar in colour, but longer in the hair, while
+  those from north of the Himalayas and the mountains of China are not
+  only huge in size, but have a very long soft hair of delicate orange
+  brown with very white flanks, and marked generally with the blackest
+  of stripes. The last are of a noble appearance and exceedingly scarce.
+  They all make handsome floor rugs.
+
+    Value of the Indian       from  L3 to L15.
+      "     "    Chinese        "  L10 to L65.
+
+  VICUNA is a species of long-necked sheep native to South America,
+  bearing some resemblance to the guanaco, but the fur is shorter,
+  closer and much finer. The colour is a pale golden-brown and the fur
+  is held in great repute in South America for carriage rugs. The supply
+  is evidently small as the prices are high. There is scarcely a
+  commercial quotation in London, few coming in except from private
+  sources. 2s. 6d. to 5s. 6d. may be considered as the average value.
+
+  WALLABY.--See _Kangaroo_, above.
+
+  WALLAROO.--See _Kangaroo_, above.
+
+  WOLF.--Size 50 X 25 in. Is closely allied to the dog tribe and, like
+  the jackals, is found through a wide range of the world,--North and
+  South America, Europe and Asia. Good supplies are available from North
+  America and Siberia and a very few from China. The best are the full
+  furred ones of a very pale bluish-grey with fine flowing black top
+  hair, which are obtained from the Hudson Bay district. Those from the
+  United States and Asia are harsher in quality and browner. A few black
+  American specimens come into the market, but usually the quality is
+  poor compared to the lighter furred animal. The Siberian is smaller
+  than the North American and the Russian still smaller. Besides the
+  wolf proper a large number of prairie or dog wolves from America and
+  Asia are used for cheaper rugs. In size they are less than half that
+  of a large wolf and are of a motley sandy colour. Numbers of the
+  Russian are retained for home use. The finest wolves are very light
+  weighted and most suitable for carriage aprons, in fact, ideal for the
+  purpose, though lacking the strength of some other furs.
+
+    Wolves       value  2s. 6d. to 64s.
+    Dog wolves     "    1s.     to  2s. 6d.
+
+  WOLVERINE.--Size 16 X 18 in. Is native to America, Siberia, Russia and
+  Scandinavia and generally partakes of the nature of a bear. The
+  underwool is full and thick with strong and bright top hair about
+  2-1/2 in. long. The colour is of two or three shades of brown in one
+  skin, the centre being an oval dark saddle, edged as it were with
+  quite a pale tone and merging to a darker one towards the flanks. This
+  peculiar character alone stamps it as a distinguished fur, in addition
+  to which it has the excellent advantage of being the most durable fur
+  for carriage aprons, as well as the richest in colour. It is not
+  prolific, added to which it is very difficult to match a number of
+  skins in quality as well as colour. Hence it is an expensive fur, but
+  its excellent qualities make it valuable. The darkest of the least
+  coarse skins are worth the most. Prices from 6s. to 37s.
+
+  WOMBAT, KOALA or Australian Bear.--Size 20 X 12 in. Has light grey or
+  brown close thick wool half an inch deep without any top hair, with a
+  rather thick spongy pelt. It is quite inexpensive and only suitable
+  for cheap rough coats, carriage rugs, perambulator aprons and linings
+  for footbags. The coats are largely used in western America and
+  Canada. Value 3d. to 1s. 8-1/2d.
+
+_Preparing and Dressing._--A furrier or skin merchant must possess a
+good eye for colour to be successful, the difference in value on this
+subtle matter solely (in the rarer precious sorts, especially sables,
+natural black, silver and blue fox, sea otters, chinchillas, fine mink,
+&c.) being so considerable that not only a practised but an intuitive
+sense of colour is necessary to accurately determine the exact merits of
+every skin. In addition to this a knowledge is required of what the
+condition of a pelt should be; a good judge knows by experience whether
+a skin will turn out soft and strong, after dressing, and whether the
+hair is in the best condition of strength and beauty. The dressing of
+the pelt or skin that is to be preserved for fur is totally different to
+the making of leather; in the latter tannic acid is used, but never
+should be with a fur skin, as is so often done by natives of districts
+where a regular fur trade is not carried on. The results of applying
+tannic acid are to harden the pelt and discolour and weaken the fur. The
+best methods for dressing fur skins are those of a tawer or currier, the
+aim being to retain all the natural oil in the pelt, in order to
+preserve the natural colour of the fur, and to render the pelt as supple
+as possible. Generally the skins are placed in an alkali bath, then by
+hand with a blunt wooden instrument the moisture of the pelt is worked
+out and it is drawn carefully to and fro over a straight, dull-edged
+knife to remove any superfluous flesh and unevenness. Special grease is
+then rubbed in and the skin placed in a machine which softly and
+continuously beats in the softening mixture, after which it is put into
+a slowly revolving drum, fitted with wooden paddles, partly filled with
+various kinds of fine hard sawdust according to the nature of the furs
+dealt with. This process with a moderate degree of heat thoroughly
+cleans it of external greasy matter, and all that is necessary before
+manufacturing is to gently tap the fur upon a leather cushion stuffed
+with horsehair with smooth canes of a flexibility suited to the strength
+of the fur. After dressing most skins alter in shape and decrease in
+size.
+
+With regard to the merits of European dressing, it may be fairly taken
+that English, German and French dressers have specialities of
+excellence. In England, for instance, the dressing of sables, martens,
+foxes, otters, seals, bears, lions, tigers and leopards is first rate;
+while with skunk, mink, musquash, chinchillas, beavers, lambs and
+squirrels, the Germans show better results, particularly in the last.
+The pelt after the German dressing is dry, soft and white, which is due
+to a finishing process where meal is used, thus they compare favourably
+with the moister and consequently heavier English finish. In France they
+do well with cheaper skins, such as musquash, rabbit and hare, which
+they dye in addition to dressing. Russian dressing is seldom reliable;
+not only is there an unpleasant odour, but in damp weather the pelts
+often become clammy, which is due to the saline matter in the dressing
+mixture. Chinese dressing is white and supple, but contains much powder,
+which is disagreeable and difficult to get rid of, and in many instances
+the skin is rendered so thin that the roots of the fur are weakened,
+which means that it is liable to shed itself freely, when subject to
+ordinary friction in handling or wearing. American and Canadian dressing
+is gradually improving, but hitherto their results have been inferior to
+the older European methods.
+
+In the case of seal and beaver skins the process is a much more
+difficult one, as the water or hard top hairs have to be removed by hand
+after the pelt has been carefully rendered moist and warm. With seal
+skins the process is longer than with any other fur preparation and the
+series of processes engage many specialists, each man being constantly
+kept upon one section of the work. The skins arrive simply salted. After
+being purchased at the auction sales they are washed, then stretched
+upon a hoop, when all blubber and unnecessary flesh is removed, and the
+pelt is reduced to an equal thickness, but not so thin as it is finally
+rendered. Subsequently the hard top hairs are taken out as in the case
+of otters and beavers and the whole thoroughly cleaned in the revolving
+drums. The close underwool, which is of a slightly wavy nature and
+mostly of a pale drab colour, is then dyed by repeated applications of a
+rich dark brown colour, one coat after another, each being allowed to
+thoroughly dry before the next is put on, till the effect is almost a
+lustrous black on the top. The whole is again put through the cleaning
+process and evenly reduced in thickness by revolving emery wheels, and
+eventually finished off in the palest buff colour.
+
+The English dye for seals is to-day undoubtedly the best; its
+constituents are more or less of a trade secret, but the principal
+ingredients comprise gall nuts, copper dust, camphor and antimony, and
+it would appear after years of careful watching that the atmosphere and
+particularly the water of London are partly responsible for good and
+lasting results. The Paris dyers do excellent work in this direction,
+but the colour is not so durable, probably owing to a less pure water.
+In America of late, strides have been made in seal dyeing, but
+preference is still given to London work. In Paris, too, they obtain
+beautiful results in the "topping" or colouring Russian sables and the
+Germans are particularly successful in dyeing Persian lambs black and
+foxes in all blue, grey, black and smoke colours and in the insertion of
+white hairs in imitation of the real silver fox. Small quantities of
+good beaver are dyed in Russia occasionally, and white hairs put in so
+well that an effect similar to sea otter is obtained.
+
+The process of inserting white hairs is called in the trade "pointing,
+"and is either done by stitching them in with a needle or by adhesive
+caoutchouc.
+
+The Viennese are successful in dyeing marmot well, and their cleverness
+in colouring it with a series of stripes to represent the natural
+markings of sable which has been done after the garments have been made,
+so as to obtain symmetry of lines, has secured for them a large trade
+among the dealers of cheap furs in England and the continent.
+
+_Manufacturing Methods and Specialities._--In the olden times the
+Skinners' Company of the city of London was an association of furriers
+and skin dressers established under royal charter granted by Edward III.
+At that period the chief concern of the body was to prevent buyers from
+being imposed upon by sellers who were much given to offering old furs
+as new; a century later the Skinners' Company received other charters
+empowering them to inspect not only warehouses and open markets, but
+workrooms. In 1667 they were given power to scrutinize the preparing of
+rabbit or cony wool for the wool trade and the registration of the then
+customary seven years' apprenticeship. To-day all these privileges and
+powers are in abeyance, and the interest that they took in the fur trade
+has been gradually transferred to the leather-dressing craft.
+
+The work done by English furriers was generally good, but since about
+1865 has considerably improved on account of the influx of German
+workmen, who have long been celebrated for excellent fur work, being In
+their own country obliged to satisfy officially appointed experts and to
+obtain a certificate of capacity before they can be there employed. The
+French influence upon the trade has been, and still is, primarily one of
+style and combination of colour, bad judgment in which will mar the
+beauty of the most valuable furs. It is a recognized law among
+high-class furriers that furs should be simply arranged, that is, that
+an article should consist of one fur or of two furs of a suitable
+contrast, to which lace may be in some cases added with advantage. As
+illustrative of this, it may be explained that any brown tone of fur
+such as sable, marten, mink, black marten, beaver, nutria, &c., will go
+well upon black or very dark-brown furs, while those of a white or grey
+nature, such as ermine, white lamb, chinchilla, blue fox, silver fox,
+opossum, grey squirrel, grey lamb, will set well upon seal or black
+furs, as Persian lamb, broadtail, astrachan, caracul lamb, &c. White is
+also permissible upon some light browns and greys, but brown motley
+colours and greys should never be in contrast. One neutralizes the other
+and the effect is bad. The qualities, too have to be considered--the
+fulness of one, the flatness of the other, or the coarseness or fineness
+of the furs. The introduction of a third fur in the same garment or
+indiscriminate selection of colours of silk linings, braids, buttons,
+&c., often spoils an otherwise good article.
+
+With regard to the natural colours of furs, the browns that command the
+highest prices are those that are of a bluish rather than a reddish
+tendency. With greys it is those that are bluish, not yellow, and with
+white those that are purest, and with black the most dense, that are
+most esteemed and that are the rarest.
+
+Perhaps for ingenuity and the latest methods of manipulating skins in
+the manufacturing of furs the Americans lead the way, but as fur cutters
+are more or less of a roving and cosmopolitan character the larger fur
+businesses in London, Berlin, Vienna, St Petersburg, Paris and New York
+are guided by the same thorough and comparatively advanced principles.
+
+During the period just mentioned the tailors' methods of scientific
+pattern cutting have been adopted by the leading furriers in place of
+the old chance methods of fur cutters, so that to-day a fur garment may
+be as accurately and gracefully fitted as plush or velvet, and with all
+good houses a material pattern is fitted and approved before the skins
+are cut.
+
+Through the advent of German and American fur sewing-machines since
+about 1890 fur work has been done better and cheaper. There are,
+however, certain parts of a garment, such as the putting in of sleeves
+and placing on of collars, &c., that can only be sewn by hand. For
+straight seams the machines are excellent, making as neat a seam as is
+found in glove work, unless, of course, the pelts are especially heavy,
+such as bears and sheep rugs.
+
+A very great feature of German and Russian work is the fur linings
+called rotondes, sacques or plates, which are made for their home use
+and exportation chiefly to Great Britain, America and France.
+
+In Weissenfels, near Leipzig, the dressing of Russian grey squirrel and
+the making it into linings is a gigantic industry, and is the principal
+support of the place. After the dressing process the backs of the
+squirrels are made up separately from the under and thinner white and
+grey parts, the first being known as squirrel-back and the other as
+squirrel-lock linings. A few linings are made from entire skins and
+others are made from the quite white pieces, which in some instances are
+spotted with the black ear tips of the animals to resemble ermine. The
+smaller and uneven pieces of heads and legs are made up into linings, so
+there is absolutely no waste. Similar work is done in Russia on almost
+as extensive a scale, but neither the dressing nor the work is so good
+as the German.
+
+The majority of heads, gills or throats, sides or flanks, paws and
+pieces of skins cut up in the fur workshops of Great Britain, America
+and France, weighing many tons, are chiefly exported to Leipzig, and
+made up in neighbouring countries and Greece, where labour can be
+obtained at an alarmingly low rate. Although the sewing, which is
+necessarily done by hand, the sections being of so unequal and tortuous
+a character, is rather roughly executed, the matching of colours and
+qualities is excellent. The enormous quantities of pieces admit of good
+selection and where odd colours prevail in a lining it is dyed. Many
+squirrel-lock linings are dyed blue and brown and used for the outside
+of cheap garments. They are of little weight, warm and effective, but
+not of great durability.
+
+The principal linings are as follows: Sable sides, sable heads and paws,
+sable gills, mink sides, heads and gills, marten sides, heads and gills,
+Persian lamb pieces and paws, caracul lamb pieces or paws, musquash
+sides and heads, nutria sides, genet pieces, raccoon sides or flanks,
+fox sides, kolinski whole skins, and small rodents as kaluga and
+hamster. The white stripes cut out of skunks are made into rugs.
+
+Another great source of inexpensive furs is China, and for many years
+past enormous quantities of dressed furs, many of which are made up in
+the form of linings and Chinese loose-shaped garments, have been
+imported by England, Germany and France for the lower class of business;
+the garments are only regarded as so much fur and are reworked. With,
+however, the exception of the best white Tibet lambs, the majority of
+Chinese furs can only be regarded as inferior material. While the work
+is often cleverly done as to matching and manipulation of the pelt which
+is very soft, there are great objections in the odour and the
+brittleness or weakness of the fur. One of the most remarkable results
+of the European intervention in the Boxer rising in China (1900) was the
+absurd price paid for so-called "loot" of furs, particularly in
+mandarins' coats of dyed and natural fox skins and pieces, and natural
+ermine, poor in quality and yellowish in colour; from three to ten times
+their value was paid for them when at the same time huge parcels of
+similar quality were warehoused in the London docks, because purchasers
+could not be found for them.
+
+With regard to Japanese furs, there is little to commend them. The best
+are a species of raccoon usually sold as fox, and, being of close long
+quality of fur, they are serviceable for boas, collars, muffs and
+carriage aprons. The sables, martens, minks and otters are poor in
+quality, and all of a very yellow colour and they are generally dyed for
+the cheap trade. A small number of very pretty guanaco and vicuna
+carriage rugs are imported into Europe, and many come through travellers
+and private sources, but generally they are so badly dressed that they
+are quite brittle upon the leather side. Similar remarks are applicable
+to opossum rugs made in Australia. From South Africa a quantity of
+jackal, hyena, fox, leopard and sheep karosses, i.e. a peculiarly shaped
+rug or covering used by native chiefs, is privately brought over. The
+skins are invariably tanned and beautifully sewn, the furs are generally
+flat in quality and not very strong in the hair, and are retained' more
+as curiosities than for use as a warm covering.
+
+_Hatters' Furs and Cloths and Shawls._--The hat trade is largely
+interested in the fur piece trade, the best felt hats being made from
+beaver and musquash wool and the cheaper sorts from nutria, hare and
+rabbit wools. For weaving, the most valuable pieces are mohair taken
+from the angora and vicuna. They are limited in quantity and costly, and
+the trade depends upon various sorts of other sheep and goat wools for
+the bulk of its productions.
+
+_Frauds and Imitations._--The opportunities for cheating in the fur
+trade are very considerable, and most serious frauds have been
+perpetrated in the selling of sables that have been coloured or
+"topped"; that is, just the tips of the hairs stained dark to represent
+more expensive skins. It is only by years of experience that some of
+these colourings can be detected. Where the skins are heavily dyed it is
+comparatively easy to see the difference between a natural and a dyed
+colour, as the underwool and top hair become almost alike and the
+leather is also dark, whereas in natural skins the base of the underwool
+is much paler than the top, or of a different colour, and the leather Is
+white unless finished in a pale reddish tone as is sometimes the case
+when mahogany sawdust is used in the final cleaning. As has been
+explained, sable is a term applied for centuries past to the darker
+sorts of the Russian Siberian martens, and for years past the same term
+has been bestowed by the retail trade upon the American and Canadian
+martens. The baum and stone martens caught in France, the north of
+Turkey and Norway are of the same family, but coarser in underwool and
+the top hair is less in quantity and not so silky. The kolinski, or as
+it is sometimes styled Tatar sable, is the animal, the tail of which
+supplies hair for artists' brushes. This is also of the marten species
+and has been frequently offered, when dyed dark, as have baum and stone
+martens, as Russian sables. Hares, too, are dyed a sable colour and
+advertised as sable. The fur, apart from a clumsy appearance, is so
+brittle, however, as to be of scarcely any service whatever.
+
+Among the principal imitations of other furs is musquash, out of which
+the top hair has been pulled and the undergrowth of wool clipped and
+dyed exactly the same colour as is used for seal, which is then offered
+as seal or red river seal. Its durability, however, is far less than
+that of seal. Rabbit is prepared and dyed and frequently offered as
+"electric sealskin." Nutria also is prepared to represent sealskin, and
+in its natural colour, after the long hairs are plucked out, it is sold
+as otter or beaver. The wool is, however, poor compared to the otter and
+beaver, and the pelt thin and in no way comparable to them in strength.
+White hares are frequently sold as white fox, but the fur is weak,
+brittle and exceedingly poor compared to fox and possesses no thick
+underwool. Foxes, too, and badger are dyed a brownish black, and white
+hairs inserted to imitate silver fox, but the white hairs are too coarse
+and the colour too dense to mislead any one who knows the real article.
+But if sold upon its own merits, pointed fox is a durable fur.
+
+Garments made of sealskin pieces and Persian lamb pieces are frequently
+sold as if they were made of solid skins, the term "pieces" being simply
+suppressed. The London Chamber of Commerce have issued to the British
+trade a notice that any misleading term in advertising and all attempts
+at deception are illegal, and offenders are liable under the Merchandise
+Marks Act 1887.
+
+  The most usual misnaming of manufactured furs is as follow:--
+
+  Musquash, pulled and dyed      Sold as seal.
+  Nutria, pulled and dyed        Sold as seal.
+  Nutria, pulled and natural     Sold as beaver.
+  Rabbit, sheared and dyed       Sold as seal or electric seal.
+  Otter, pulled and dyed         Sold as seal.
+  Marmot, dyed                   Sold as mink or sable.
+  Fitch, dyed                    Sold as sable.
+  Rabbit, dyed                   Sold as sable or French sable.
+  Hare, dyed                     Sold as sable, or fox, or lynx.
+  Musquash, dyed                 Sold as mink or sable.
+  Wallaby, dyed                  Sold as skunk.
+  White Rabbit                   Sold as ermine.
+  White Rabbit, dyed             Sold as chinchilla.
+  White Hare, dyed or natural    Sold as fox, foxaline, and
+                                   other similar names.
+  Goat, dyed                     Sold as bear, leopard, &c.
+  Dyed manufactured articles of
+    all kinds                    Sold as "natural."
+  White hairs inserted in foxes
+    and sables                   Sold as real or natural furs.
+  Kids                           Sold as lamb or broadtails.
+  American sable                 Sold as real Russian sable.
+  Mink                           Sold as sable.
+
+_The Preservation of Furs._--For many years raw sealskins have been
+preserved in cold storage, but it is only within a recent period, owing
+to the difficulty there was in obtaining the necessary perfectly dry
+atmosphere, that dressed and made-up furs have been preserved by
+freezing. Furs kept in such a condition are not only immune from the
+ravages of the larvae of moth, but all the natural oils in the pelt and
+fur are conserved, so that its colour and life are prolonged, and the
+natural deterioration is arrested. Sunlight has a tendency to bleach
+furs and to encourage the development of moth eggs, therefore continued
+exposure is to be avoided. When furs are wetted by rain they should be
+well shaken and allowed to dry in a current of air without exposure to
+sun or open fire.
+
+Where a freezing store for furs is not accessible, furs should be well
+shaken and afterwards packed in linen and kept in a perfectly cool dry
+place, and examined in the summer at periods of not less than five
+weeks. Naphthalene and the usual malodorous powders are not only very
+disagreeable, but quite useless. Any chemical that is strong enough to
+destroy the life in a moth egg would also be sufficiently potent to
+injure the fur itself. In England moth life is practically continuous
+all the year round, that is, as regards those moths that attack furs,
+though the destructive element exists to a far greater extent during
+spring and summer.
+
+  _Comparative Durability of Various Furs and Weight of Unlined Skins
+  per Square Foot._
+
+  The following estimates of durability refer to the use of fur when
+  made up "hair outside" in garments or stoles, not as a lining. The
+  durability of fur used as linings, which is affected by other
+  conditions, is set forth separately. Otter, with its water hairs
+  removed, the strongest of furs for external use, is, in this table,
+  taken as the standard at 100 and other furs marked accordingly:--
+
+
+  _The Precious Furs._
+
+    +---------------------------------------+-------------+------------+
+    |                                       |  Points of  | [2]Weight  |
+    |                                       | Durability. | in oz. per |
+    |                                       |             |   sq. ft.  |
+    +---------------------------------------+-------------+------------+
+    | Sable                                 |      60     |     2-1/2  |
+    | Sea                                   |      75     |     3      |
+    | Fox, Silver or Black                  |      40     |     3      |
+    |  "   White                            |      20     |     3      |
+    | Ermine                                |      25     |     1-1/4  |
+    | Chinchilla                            |      15     |     1-1/2  |
+    | Sea-otter (for stoles or collars)     |     100     |     4-1/4  |
+    +---------------------------------------+-------------+------------+
+
+
+  _The Less Valuable Furs._
+
+    +----------------------------------------+-------------+------------+
+    |                                        |  Points of  |   Weight   |
+    |                                        | Durability. | in oz. per |
+    |                                        |             |   sq. ft.  |
+    +----------------------------------------+-------------+------------+
+    | Sable "topped," i.e. top hairs coloured|      55     |    2-1/2   |
+    |   "  tinted, i.e. fur all coloured.    |      50     |    2-1/2   |
+    | Baum Marten, natural                   |      65     |    2-3/4   |
+    |  "     "     tinted                    |      45     |    2-3/4   |
+    | Stone Marten                           |      40     |    2-3/4   |
+    | Nutria                                 |      27     |    3-1/4   |
+    | Musquash, natural                      |      37     |    3-1/4   |
+    |    "   water hairs removed, sheared    |             |            |
+    |         and seal finished.             |      33     |    3-1/4   |
+    | Skunk                                  |      70     |    2-3/4   |
+    | Mink                                   |      70     |    3-1/4   |
+    | Lynx, natural                          |      25     |    2-3/4   |
+    |  "  tinted black                       |      20     |    2-3/4   |
+    | Marmot, tinted                         |      10     |    3       |
+    | Fox, tinted black                      |      25     |    3       |
+    |  "     "    blue                       |      20     |    3       |
+    | Opossum                                |      37     |    3       |
+    | Otter (with water hairs)               |     100     |    4       |
+    |   "  (water hairs removed)             |      95     |    3-15/16 |
+    | Beaver (water hairs cut level with fur)|      90     |    4       |
+    |   "  (water hairs removed).            |      85     |    3-15/16 |
+    | Moleskin                               |       7     |    1-3/4   |
+    | Persian Lamb                           |      65     |    3-1/4   |
+    | Grey     "                             |      30     |    3-1/4   |
+    | Broadtail                              |      15     |    2-1/4   |
+    | Caracul Kid                            |      10     |    3-1/4   |
+    |    "   Lamb                            |      15     |    3-1/4   |
+    | Squirrel                               |      25     |    1-3/4   |
+    | Hare                                   |       5     |    1-3/4   |
+    | Rabbit                                 |       5     |    2-1/4   |
+    +----------------------------------------+-------------+------------+
+
+
+  _Quantities of Fur needed, in Square Feet._
+
+  The "Paris Model" figure is the basis of these estimates for ladies'
+  garments, the standard measurements being height 5 ft. 6 in., waist 23
+  in., bust 38 in.
+
+                                                             Sq. Ft.
+                                                         (approximate).
+
+    Straight stole 1/2 length (just below the waist line)      2-3/4
+    Straight stole 3/4 length (just below the knee)            3-3/4
+    Stole, broad enough at the neck to cover the top of
+      arm 3/4 length                                           5
+    The same, full length (to hem of skirt)                    6
+    Eton jacket, without collar                               13
+    Plain cape, 15 in. long                                    6-1/2
+    Deep cape, 30 in. long                                    15
+    Full cape with broad stole front, 3/4 length              15
+    Inverness cape (to knee)                                  25
+    Double-breasted, straight, semi-fitting coat, covering
+      hips                                                    16
+    Double-breasted sacque jacket, 36 in. long, full sleeves  20
+    Same, 30 in. long                                         18
+    Same, 22 in. long                                         15
+    Long, full, shawl cape with points at back and front,
+      well below knee                                         15
+    Shorter shawl cape                                        16
+    Motoring or driving coat, 3/4 length                      22
+    Motoring or driving coat, full length                     27
+
+
+  _Weight and Durability of Furs for Men's Coat Linings._
+
+  Otter with the water hairs removed, the strongest fur suited for
+  linings, is here taken as the standard.
+
+    +---------------------------------+-----------+-------------+
+    |                                 | Points of |    Weight   |
+    |                                 |Durability.| in oz. per  |
+    |                                 |           |   sq. ft.   |
+    +---------------------------------+-----------+-------------+
+    | Otter (the water hairs removed) |    100    |    3-15/16  |
+    | Beaver     "      "             |     90    |    3-15/16  |
+    | Mink                            |     90    |    3-1/4    |
+    | Sealskin                        |     75    |    3        |
+    | Raccoon                         |     75    |    4-1/2    |
+    | Persian lamb or astrachan       |     70    |    3-1/4    |
+    | Sable                           |     65    |    2-1/2    |
+    | Musquash                        |     55    |    3-1/2    |
+    | Nutria                          |     40    |    3-1/4    |
+    | Grey Opossum                    |     40    |    3        |
+    | Wallaby                         |     30    |    3-3/4    |
+    | Squirrel                        |     30    |    1-3/4    |
+    | Hamster                         |     15    |    1-1/4    |
+    | Rabbit                          |     10    |    2-1/4    |
+    +---------------------------------+-----------+-------------+
+
+
+  _Durability and Weight of Linings for Ladies' Coats or Wraps._
+
+  Sable gills, the strongest fur suited for ladies' linings, is taken as
+  the standard.
+
+    +---------------------------------+-----------+-------------+
+    |                                 | Points of |    Weight   |
+    |                                 |Durability.| in oz. per  |
+    |                                 |           |   sq. ft.   |
+    +---------------------------------+-----------+-------------+
+    | Sable gills                     |    100    |    2-7/8    |
+    | Sable                           |     85    |    2-1/2    |
+    | Sable paws                      |     64    |    1-5/8    |
+    | Ermine                          |     57    |    1-1/4    |
+    | Squirrel back                   |     50    |    1-3/4    |
+    | Squirrel heads                  |     36    |    2-1/2    |
+    | Squirrel lock                   |     21    |    1-3/16   |
+    | Hamster                         |     10    |    1-1/4    |
+    | Rabbit                          |      7    |    2-1/4    |
+    +---------------------------------+-----------+-------------+
+
+
+  _Durability and Weight of Motoring Furs made up with Fur outside._
+
+  Otter with the water hairs, the strongest fur suited for motoring
+  garments, is taken as the standard.
+
+    +-------------------------------------+-----------+-------------+
+    |                                     | Points of |    Weight   |
+    |                                     |Durability.| in oz. per  |
+    |                                     |           |   sq. ft.   |
+    +-------------------------------------+-----------+-------------+
+    | Otter (with water hairs)            |    100    |     4       |
+    | Sealskin, marble                    |     80    |     3       |
+    | "Hair Sealskin" (tinted) with water |           |             |
+    |   hairs (a special variety of seal) |     75    |     3-1/4   |
+    | Raccoon                             |     65    |     4-1/2   |
+    | Russian Pony                        |     35    |     2-5/8   |
+    +-------------------------------------+-----------+-------------+
+
+
+  _Durability and Weight of Furs for Rugs and Foot-sacks._
+
+    +-------------------------------------+-----------+-------------+
+    |                                     | Points of |    Weight   |
+    |                                     |Durability.| in oz. per  |
+    |                                     |           |   sq. ft.   |
+    +-------------------------------------+-----------+-------------+
+    | Wolverine                           |    100    |     6       |
+    | Bear (black or brown natural)       |     94    |     7       |
+    | Bear (tinted black)                 |     88    |     7-1/2   |
+    | Beaver                              |     88    |     4       |
+    | Raccoon                             |     77    |     4-1/2   |
+    | Opossum                             |     61    |     3       |
+    | Wolf                                |     50    |     6-1/2   |
+    | Jackal                              |     27    |     4-1/2   |
+    | Australian Bear                     |     16    |     6       |
+    | Goat                                |     11    |     4-1/6   |
+    +-------------------------------------+-----------+-------------+
+
+  Wolverine, the strongest fur suited for rugs and foot-sacks, is taken
+  as the standard.
+
+  For a rug about 20 to 25 sq. ft. of fur are needed, for a foot-sack
+  14-1/2.     (W. S. P.)
+
+
+FOOTNOTES:
+
+  [1] The measurements given are from nose to root of tail of average
+    large sizes after the dressing process, which has a shrinking
+    tendency. The depths of fur quoted are the greatest, but there are
+    plenty of good useful skins possessing a lesser depth.
+
+  [2] Stout, old-fashioned boxcloth is almost the only cloth that
+    (after a soft, heavy lining has been added to it) affords even
+    two-thirds as much protection against cold as does fur. It weighs
+    4.273 oz. per sq. ft. more than the heaviest of coat-furs, and is so
+    rigid as to be uncomfortable, while the subtileness of fur makes it
+    "kind" to the body.
+
+
+
+
+FURAZANES (_furo_--a.a'--_diazoles_), organic compounds obtained by
+heating the glyoximes (dioximes of ortho-diketones) with alkalis or
+ammonia. Dimethylfurazane is prepared by heating dimethylglyoxime with
+excess of ammonia for six hours at 165 deg. C. (L. Wolff, _Ber._, 1895,
+28, p. 70). It is a liquid (at ordinary temperature) which boils at 156
+deg. C. (744 mm.). Potassium permanganate oxidizes it first to
+methylfurazane-carboxylic acid and then to furazanedicarboxylic acid.
+Methyl-ethylfurazane and diphenylfurazane are also known. By warming
+oxyfurazane acetic acid with excess of potassium permanganate to 100
+deg. C. oxyfurazanecarboxylic acid is obtained (A. Hantzsch and J.
+Urbahn, _Ber._, 1895, 28, p. 764). It crystallizes in prisms, which melt
+at 175 deg. C. Furazanecarboxylic acid is prepared by the action of a
+large excess of potassium permanganate on a hot solution of
+furazanepropionic acid. It melts at 107 deg. C, and dissolves in caustic
+soda, with a deep yellow colour and formation of nitrosocyanacetic acid
+(L. Wolff and P.F. Ganz, _Ber._, 1891, 24, p. 1167). Furoxane is an
+oxide of furazane, considered by H. Wieland to be identical with
+glyoxime peroxide; Kekules dibromnitroacetonitrile is dibromfuroxane.
+
+The formulae of the compounds above mentioned are:
+
+  HC:N\        CH3.C:N\             HC:N\         HC--CH \
+   .   O           .   O             .   O        ..  .   O
+  HC:N/        CH3.C:N/         HO2C.C:N/         N.O.N  /
+
+  Furazane.   Dimethyl-     Furazanecarboxylic   Furoxane.
+              furazane.            acid.
+
+
+
+
+FURETIERE, ANTOINE (1619-1688), French scholar and miscellaneous writer,
+was born in Paris on the 28th of December 1619. He first studied law,
+and practised for a time as an advocate, but eventually took orders and
+after various preferments became abbe of Chalivoy in the diocese of
+Bourges in 1662. In his leisure moments he devoted himself to letters,
+and in virtue of his satires--_Nouvelle Allegorique, ou histoire des
+derniers troubles arrives au royaume d'eloquence_ (1658); _Voyage de
+Mercure_ (1653)--he was admitted a member of the French Academy in 1662.
+That learned body had long promised a complete dictionary of the French
+tongue; and when they heard that Furetiere was on the point of issuing a
+work of a similar nature, they interfered, alleging that he had
+purloined from their stores, and that they possessed the exclusive
+privilege of publishing such a book. After much bitter recrimination on
+both sides the offender was expelled in 1685; but for this act of
+injustice he took a severe revenge in his satire, _Couches de
+l'academie_ (Amsterdam, 1687). His _Dictionnaire universel_ was
+posthumously published in 1690 (Rotterdam, 2 vols.). It was afterwards
+revised and improved by the Protestant jurist, Henri Basnage de Beauval
+(1656-1710), who published his edition (3 vols.) in 1701; and it was
+only superseded by the compilation known as the _Dictionnaire de
+Trevoux_ (Paris, 3 vols., 1704; 7th ed., 8 vols., 1771), which was in
+fact little more than a reimpression of Basnage's edition. Furetiere is
+perhaps even better known as the author of _Le Roman bourgeois_ (1666).
+It cast ridicule on the fashionable romances of Mlle de Scudery and of
+La Calprenede, and is of interest as descriptive of the ~~ everyday
+life of his times. There is no element of burlesque, as in Scarron's
+_Roman comique_, but the author contents himself with stringing together
+a number of episodes and portraits, obviously drawn from life, without
+much attempt at sequence. The book was edited in 1854 by Edward Fournier
+and Charles Asselineau and by P. Jannet.
+
+  The _Fureteriana_, which appeared in Paris eight years after
+  Furetiere's death, which took place on the 14th of May 1688, is a
+  collection of but little value.
+
+
+
+
+FURFOOZ, a village some 10 m. from Dinant in the Ardennes, Belgium.
+Three caves containing prehistoric remains were here excavated in 1872.
+Of these the _Trou de Frontal_ is the most famous. In it were found
+human skeletons with brachycephalic skulls, associated with animal
+bones, those of the reindeer being particularly plentiful. Among the
+skeletons was discovered an oval vase of pottery. The Furfooz type of
+mankind is believed to date from the close of the Quaternary age. G. de
+Mortillet dates the type in the Robenhausen epoch of the Neolithic
+period. His theory is that the bones are those of men of that period
+buried in what had been a cave-dwelling of the Madelenian epoch.
+
+
+
+
+FURFURANE, or FURANE, C4H4O, a colourless liquid boiling at 32 deg. C.,
+found in the distillation products of pine wood. It was first
+synthetically prepared by H. Limpricht (_Ann._, 1873, 165, p. 281) by
+distilling barium mucate with soda lime, pyromucic acid C4H3O.CO2H being
+formed, which, on further loss of carbon dioxide, yielded furfurane. A.
+Henniger (_Ann. chim. phys._, 1886 [2], 7, p. 220), by distilling
+erthyrite with formic acid, obtained a dihydrofurfurane
+
+  C4H6(OH)4 + 2H2CO2 = C4H6O + CO+CO2 + 4H2O,
+
+which, on treatment with phosphorus pentachloride, yielded furfurane.
+Furfurane is insoluble in water and possesses a characteristic smell. It
+does not react with sodium or with phenylhydrazine, but yields
+dye-stuffs with isatin and phenanthrenequinone. It reacts violently with
+hydrochloric acid, producing a brown amorphous substance. Methyl and
+phenyl derivatives have been prepared by C. Paal (_Ber._, 1884, 17, p.
+915). Paal prepared acetonyl acetophenone by condensing sodium
+acetoacetate with phenacylbromide, and this substance on dehydration
+yields [alpha][alpha]'-phenylmethylfurfurane, the acetonyl acetophenone
+probably reacting in the tautomeric "enolic" form,
+
+  CH3.CO.CHNa.COOR + C6H5.CO.CH2Br = CH3.CO.CH(CH2COC6H5).COOR.
+
+This ester readily hydrolyses, and the acid formed yields acetonyl
+acetophenone (by loss of carbon dioxide), which then on dehydration
+yields the furfurane derivative, thus
+
+          CH--CH                         CH--CH
+        //      \\                     //     \\
+  CH3.C           C.C6H5 = H2O + CH3.C          C.C6H5.
+        \       /                      \___ ___/
+          OH  OH                           O
+
+L. Knorr (_Ber._, 1889, 22, p. 158) obtained diacetosuccinic ester by
+condensing sodium acetoacetate with iodine, and by dehydrating the ester
+he prepared [alpha][alpha]'-dimethylfurfurane [beta][beta]'-dicarboxylic
+acid (carbopyrotritaric acid), which on distillation yields
+[alpha][alpha]'-dimethylfurfurane as a liquid boiling at 94 deg. C. Paal
+also obtained this compound by using monochloracetone in the place of
+phenacylbromide. By the distillation of mucic acid or isosaccharic acid,
+furfurane-[alpha]-carboxylic acid (pyromucic acid), C4H3O.CO2H, is
+obtained; it crystallizes in needles or leaflets, and melts at 134 deg.
+C.
+
+_Furfurol_ (furol), C4H3O.CHO, is the aldehyde of pyromucic acid, and is
+formed on distilling bran, sugar, wood and most carbohydrates with
+dilute sulphuric acid, or by distilling the pentoses with hydrochloric
+acid. It is a colourless liquid which boils at 162 deg. C., and is
+moderately soluble in water; it turns brown on exposure to air and has a
+characteristic aromatic smell. It shows all the usual properties of an
+aldehyde, forming a bisulphite compound, an oxime and a hydrazone;
+whilst it can be reduced to the corresponding furfuryl alcohol by means
+of sodium amalgam, and oxidized to pyromucic acid by means of silver
+oxide. It also shows all the condensation reactions of benzaldehyde
+(q.v.); condensing with aldehydes and ketones in the presence of caustic
+soda to form more complex aldehydes and ketones with unsaturated side
+chains, such as furfuracrolein, C4H3O.CH:CH.CHO, and furfuracetone,
+C4H3O.CH:CH.CO.CH3. With alcoholic potassium cyanide It changes to
+furoin, C4H3O.CHOH.CO.C4H3O, which can be oxidized to furil,
+C4H3O.CO.CO.C4H3O, whilst alcoholic potash converts it into furfuryl
+alcohol. With fatty acids and acid anhydrides it gives the "Perkin"
+reaction (see CINNAMIC ACID). Furfurol is shown to have its aldehydic
+group in the a position, by conversion into furfurpropionic acid,
+C4H3O.CH2.CH2.CO2H, which on oxidation by bromine water and subsequent
+reduction of the oxidized product is converted into n-pimelic acid,
+HO2C(CH2)5CO2H. Furfurol in minute quantities can be detected by the red
+colour it forms with a solution of aniline acetate.
+
+  Furfurane--[alpha][alpha]'-dicarboxylic acid or dehydromucic acid,
+  C4H2O(CO2H)2, is formed when mucic acid is heated with hydrochloric
+  acid at 100 deg. C. On being heated, it loses carbon dioxide and gives
+  pyromucic acid. By digesting acetoacetic ester with sodium succinate
+  and acetic anhydride, methronic acid, C8H8O5, is obtained; for the
+  constitution of this acid, see L. Knorr, _Ber._, 1889, 22, p. 152, and
+  R. Fittig, Ann., 1889, 259, p. 166.
+
+  Di- and tetrahydrofurfurane compounds are also known (see A. Lipp,
+  Ber., 1889, 22, p. 1196; W.H. Perkin, junr. _Journ. Chem. Soc._, 1899,
+  57, p. 944; and S. Ruhemann, ibid., 1896, 69, p. 1383).
+
+
+
+
+FURIES (Lat. _Furiae_, also called DIRAE), in Roman mythology an
+adaptation of the Greek Erinyes (q.v.), with whom they are generally
+identical. A special aspect of them in Virgil is that of agents employed
+by the higher gods to stir up mischief, strife and hatred upon earth.
+Mention may here be made of an old Italian deity Furina (or Furrina),
+whose worship fell early into disuse, and who was almost forgotten in
+the time of Varro. By the mythologists of Cicero's time the name was
+connected with the verb _furere_ and the noun _furia_, which in the
+plural (not being used in the singular in this sense) was accepted as
+the equivalent of the Greek Erinyes. But it is more probably related to
+_furvus_, _fuscus_, and signifies one of the spirits of darkness, who
+watched over men's lives and haunted their abodes. This goddess had her
+own special priest, a grove across the Tiber where Gaius Gracchus was
+slain, and a festival on the 25th of July. Authorities differ as to the
+existence of more than one goddess called Furina, and their identity
+with the Forinae mentioned in two inscriptions found at Rome (_C.I.L._
+vi. 422 and 10,200).
+
+
+
+
+FURLONG (from the O. Eng. _furlang_, i.e. "furrow-long"), a measure of
+length, originally the length of a furrow in the "common field" system.
+As the field in this system was generally taken to be a square, 10 acres
+in extent, and as the acre varied in different districts and at
+different times, the "furlong" also varied. The side of a square
+containing 10 statute acres is 220 yds. or 40 poles, which was the
+usually accepted length of the furlong. This is also the length of
+{1/8}th of the statute mile. "Furlong" was as early as the 9th century
+used to translate the Latin _stadium_, 1/8th of the Roman mile.
+
+
+
+
+FURNACE, a contrivance for the production and utilization of heat by the
+combustion of fuel. The word is common to all the Romance tongues,
+appearing in more or less modified forms of the Latin _fornax_. But in
+all those languages the word has a more extended meaning than in
+English, as it covers every variety of heating apparatus; while here, in
+addition to furnaces proper, we distinguish other varieties as _ovens_,
+_stoves_ and _kilns_. The first of these, in the form _Ofen_, is used in
+German as a general term like the French _four_; but in English it has
+been restricted to those apparatus in which only a moderate temperature,
+usually below a red heat, is produced in a close chamber. Our bakers'
+ovens, hot-air ovens or stoves, annealing ovens for glass or metal, &c.,
+would all be called _fours_ in French and _Ofen_ in German, in common
+with furnaces of all kinds. Stove, an equivalent of oven, is from the
+German _Stube_, i.e. a heated room, and is commonly so understood; but
+is also applied to open fire-places, which appears to be somewhat of a
+departure from the original signification.
+
+Furnaces are constructed according to many different patterns with
+varying degrees of complexity in arrangement; but all may be considered
+as combining three essential parts, namely, the fire-place in which the
+fuel is consumed, the heated chamber, laboratory, hearth or working bed,
+as it is variously called, where the heat is applied to the special work
+for which the furnace is designed, and the apparatus for producing rapid
+combustion by the supply of air under pressure to the fire. In the
+simplest cases the functions of two or more of these parts may be
+combined into one, as in the smith's forge, where the fire-place and
+heating chamber are united, the iron being placed among the coals, only
+the air for burning being supplied under pressure from a blowing engine
+by a second special contrivance, the tuyere, tuiron, twyer or
+blast-pipe; but in the more refined modern furnaces, where great economy
+of fuel is an object, the different functions are distributed over
+separate and distinct apparatus, the fuel being converted into gas in
+one, dried in another, and heated in a third, before arriving at the
+point of combustion in the working chamber of the furnace proper.
+
+  Furnaces may be classified according as the products of combustion are
+  employed (1) only for heating purposes, or (2) both for heating and
+  bringing about some chemical change. The furnaces employed for
+  steam-raising or for heating buildings are invariably of the first
+  type (see BOILER and HEATING), while those employed in metallurgy are
+  generally of the second. The essential difference in construction is
+  that in the first class the substances heated do not come into contact
+  with either the fuel or the furnace gases, whereas in the second they
+  do. Metallurgical furnaces of the first class are termed crucible,
+  muffle or retort furnaces, and of the second shaft and reverberatory
+  furnaces. The following is a detailed subdivision:--
+
+  (1) Fuel and substance in contact.
+     (a) Height of furnace greater than diameter = shaft furnaces.
+         ([alpha]) No blast = kilns.
+         ([beta]) With blast = blast furnaces.
+     (b) Height not much greater than diameter = hearth furnaces.
+
+  (2) Substance heated by products of combustion = reverberatory
+        furnaces.
+     (a) Charge not melted = roasting or calcining furnaces.
+     (b) Charge melted = melting furnaces.
+
+  (3) Substance is not directly heated by the fuel or by the products
+        of combustion.
+     (a) Heating chamber fixed and forming part of furnace = muffle
+           furnaces.
+     (b) Crucible furnaces.
+     (c) Retort furnaces.
+
+Another classification may be based upon the nature of the heating
+agent, according as it is coal (or some similar combustible) oil, gas or
+electricity. In this article the general principles of metallurgical
+furnaces will be treated; the subject of gas- and oil-heated furnaces is
+treated in the article Fuel, and of the electric furnace in the article
+Electrometallurgy. For special furnaces reference should be made to the
+articles on the industry concerned, e.g. GLASS, GAS, S MANUFACTURE, &c.
+
+_Shaft, Blast and Hearth Furnaces._--The blast furnace in its simplest
+form is among the oldest, if not the oldest, of metallurgical
+contrivances. In the old copper-smelting district of Arabia Petraea,
+clay blast-pipes dating back to the earlier dynasties of ancient Egypt
+have been found buried in slag heaps; and in India the native smiths and
+iron-workers continue to use furnaces of similar types. These, when
+reduced to their most simple expression, are mere basin-shaped hollows
+in the ground, containing ignited charcoal and the substances to be
+heated, the fire being urged by a blast of air blown in through one or
+more nozzles from a bellows at or near the top. They are essentially the
+same as the smith's forge. This class of furnace is usually known as an
+open fire or hearth, and is represented in a more advanced stage of
+development by the Catalan, German and Walloon forges formerly used in
+the production of malleable iron.
+
+[Illustration: FIG. 1.--Elevation of Catalan Forge.]
+
+  Fig. 1 represents a Catalan forge. The cavity in the ground is
+  represented by a pit of square or rectangular section lined with brick
+  or stone of a kind not readily acted on by heat, about 1-1/2 or 2 ft.
+  deep, usually somewhat larger above than below, with a tuyere or
+  blast-pipe of copper penetrating one of the walls near the top, with a
+  considerable downward inclination, so that the air meets the fuel some
+  way down. In iron-smelting the ore is laid in a heap upon the fuel
+  (charcoal) filling up the hearth, and is gradually brought to the
+  metallic state by the reducing action of the carbon monoxide formed at
+  the tuyere. The metal sinks through the ignited fuel, forming, in the
+  hearth, a spongy mass or ball, which is lifted out by the smelters at
+  the end of each operation, and carried to the forge hammer. The earthy
+  matters form a fusible glass or slag melt, and collect at the lowest
+  point of the hearth, whence they are removed by opening a hole pierced
+  through the front wall at the bottom. The active portion of such a
+  furnace is essentially that above the blast-pipe, the function of the
+  lower part being merely the collection of the reduced metal; the fire
+  may therefore be regarded as burning in an unconfined space, with the
+  waste of a large amount of its heating power. By continuing the walls
+  of the hearth above the tuyere, into a shaft or stack either of the
+  same or some other section, we obtain a furnace of increased capacity,
+  but with no greater power of consuming fuel, in which the material to
+  be treated can be heated up gradually by loading it into the stack,
+  alternately with layers of fuel, the charge descending regularly to
+  the point of combustion, and absorbing a proportion of the heat of the
+  flame that went to waste in the open fire. This principle is capable
+  of very wide extension, the blast furnace being mainly limited in
+  height by the strength the column of materials or "burden" has to
+  resist crushing, under the weight due to the head adopted, and the
+  power of the blowing engine to supply blast of sufficient density to
+  overcome the resistance of the closely packed materials to the free
+  passage of the spent gases. The consuming power of the furnace or the
+  rate at which it can burn the fuel supplied is measured by the number
+  of tuyeres and their section.
+
+The development of blast furnaces is practically the development of
+iron-smelting. The profile has been very much varied at different times.
+The earliest examples were square or rectangular in horizontal section,
+but the general tendency of modern practice is to substitute round
+sections, their construction being facilitated by the use of specially
+moulded bricks which have entirely superseded the sandstone blocks
+formerly used. The vertical section, on the other hand, is subject to
+considerable variation according to the work to which the furnace is
+applied. Where the operation is simply one of fusion, as in the
+iron-founder's cupola, in which there is no very great change in volume
+in the materials on their descent to the tuyeres, the stack is nearly or
+quite straight-sided; but when, as is the case with the smelting of iron
+ores with limestone flux, a large proportion of volatile matter has to
+be removed in the process, a wall of varying inclination is used, so
+that the body of the furnace is formed of two dissimilar truncated
+cones, joined by their bases, the lower one passing downwards into a
+short, nearly cylindrical, position. For further consideration of this
+subject see IRON AND STEEL.
+
+_Hearth furnaces_ are employed in certain metallurgical operations, e.g.
+in the air-reduction process for smelting lead ores. The principle is
+essentially that of the Catalan forge. Such furnaces are very wasteful,
+and have little to recommend them (see Schnabel, Metallurgy, 1905, vol.
+1. p. 409).
+
+_Reverberatory Furnaces._--Blast furnaces are, from the intimate contact
+between the burden to be smelted and the fuel, the least wasteful of
+heat; but their use supposes the possibility of obtaining fuel of good
+quality and free from sulphur or other substances likely to deteriorate
+the metal produced. In all cases, therefore, where it is desired to do
+the work out of contact with the solid fuel, the operation of burning or
+heat-producing must be performed in a special fire-place or combustion
+chamber, the body of flame and heated gas being afterwards made to act
+upon the surface of the material exposed in a broad thin layer in the
+working bed or laboratory of the furnace by reverberation from the low
+vaulted roof covering the bed. Such furnaces are known by the general
+name of reverberatory or reverbatory furnaces, also as air or wind
+furnaces, to distinguish them from those worked with compressed air or
+blast.
+
+Originally the term cupola was used for the reverberatory furnace, but
+in the course of time it has changed its meaning, and is now given to a
+small blast furnace such as that used by iron-founders--reverberatory
+smelting furnaces in the same trade being called air furnaces.
+
+[Illustration: FIG. 2.--Longitudinal section of Reverberatory Furnace.]
+
+[Illustration: FIG. 3.--Reverberatory Furnace (horizontal section).]
+
+[Illustration: FIG. 4.--Reverberatory Furnace (elevation at flue end).]
+
+  Figs. 2, 3 and 4 represent a reverberatory furnace such as is used for
+  the fusion of copper ores for regulus, and may be taken as generally
+  representing its class. The fire-place A is divided from the working
+  bed B by a low wall C known as the fire bridge, and at the opposite
+  end there is sometimes, though not invariably, a second bridge of less
+  height called the flue bridge D. A short diagonal flue or up-take E
+  conveys the current of spent flame to the chimney F, which is of
+  square section, diminishing by steps at two or three different
+  heights, and provided at the top with a covering plate or damper G,
+  which may be raised or lowered by a chain reaching to the ground, and
+  serves for regulating the speed of the exhaust gases, and thereby the
+  draught of air through the fire. Where several furnaces are connected
+  with the same chimney stack, the damper takes the form of a sliding
+  plate in the mouth of the connecting flue, so that the draught in one
+  may be modified without affecting the others. The fire bridge is
+  partially protected against the intense heat of the body of flame
+  issuing through the fire arch by a passage to which the air has free
+  access. The material to be melted is introduced into the furnace from
+  the hoppers HH through the charging holes in the roof. When melted the
+  products separate on the bed (which is made of closely packed sand or
+  other infusible substances), according to their density; the lighter
+  earthy matters forming an upper layer of slag are drawn out by the
+  slag hole K at the flue end into an iron wagon or bogie, while the
+  metal subsides to the bottom of the bed, and at the termination of the
+  operation is run out by the tap hole L into moulds or granulated into
+  water. The opposite opening M is the working door, through which the
+  tool for stirring the charge is introduced. It is covered by a plate
+  suspended to a lever, similar to that seen in the end elevation (fig.
+  4) in front of the slag hole.
+
+According to the purposes to which they are applied, reverberatory
+furnaces may be classed into two groups, namely, fusion or melting
+furnaces, and calcining or wasting furnaces, also called calciners. The
+former have a very extended application in many branches of industry,
+being used by both founders and smelters in the fusion of metals; in the
+concentration of poor metallic compounds by fusion into regulus; in the
+reduction of lead and tin ores; for refining copper and silver; and for
+making malleable iron by the puddling processes and welding. Calcining
+furnaces have a less extended application, being chiefly employed in the
+conversion of metallic sulphides into oxides by continued exposure to
+the action of air at a temperature far below that of fusion, or into
+chlorides by roasting with common salt. As some of these substances (for
+example, lead sulphide and copper pyrites) are readily fusible when
+first heated, but become more refractory as part of the sulphur is
+dissipated and oxygen takes its place, it is important that the heat
+should be very carefully regulated at first, otherwise the mass may
+become clotted or fritted together, and the oxidizing effect of the air
+soon ceases unless the fritted masses be broken small again. This is
+generally done by making the bed of the furnace very long in proportion
+to its breadth and to the fire-grate area, which may be the more easily
+done as a not inconsiderable amount of heat is given out during the
+oxidation of the ore--such increased length being often obtained by
+placing two or even three working beds one above the other, and allowing
+the flame to pass over them in order from below upwards. Such calciners
+are used especially in roasting zinc blende into zinc oxide, and in the
+conversion of copper sulphides into chlorides in the wet extraction
+process. In some processes of lead-smelting, where the minerals treated
+contain sand, the long calciner is provided with a melting bottom close
+to the fire-place, so that the desulphurized ore leaves the furnace as a
+glassy slag or silicate, which is subsequently reduced to the metallic
+state by fusion with fluxes in blast furnaces. Reverberatory furnaces
+play an important part in the manufacture of sodium carbonate;
+descriptions and illustrations are given in the article ALKALI
+MANUFACTURE.
+
+_Muffle, Crucible and Retort Furnaces._--A third class of furnaces is so
+arranged that the work is done by indirect heating; that is, the
+material under treatment, whether subjected to calcination, fusion or
+any other process, is not brought in contact either with fuel or flame,
+but is raised to the proper temperature by exposure in a chamber heated
+externally by the products of combustion. These are known as muffle or
+chamber furnaces; and by supposing the crucibles or retorts to represent
+similar chambers of only temporary duration, the ordinary pot melting
+air furnaces, and those for the reduction of zinc ores or the
+manufacture of coal gas, may be included in the same category. These are
+almost invariably air furnaces, though sometimes air under pressure is
+used, as, for example, in the combustion of small anthracitic coal,
+where a current of air from a fan-blower is sometimes blown under the
+grate to promote combustion. Types of muffle furnaces are figured in the
+article ANNEALING, HARDENING AND TEMPERING.
+
+_Furnace Materials._--The materials used in the construction of furnaces
+are divisible into two classes, namely, ordinary and refractory or
+fire-resisting. The former are used principally as casing, walls,
+pillars or other supporting parts of the structure, and includes
+ordinary red or yellow bricks, clay-slate, granite and most building
+stones; the latter are reserved for the parts immediately in contact
+with the fuel and flame, such as the lining of the fire-place, the
+arches, roof and flues, the lower part if not the whole of the chimney
+lining in reverberatory furnaces, and the whole of the internal walls of
+blast furnaces. Among such substances are fireclay and firebricks,
+certain sandstones, silica in the form of ganister, and Dinas stone and
+bricks, ferric oxide and alumina, carbon (as coke and graphite),
+magnesia, lime and chromium oxide--their relative importance being
+indicated by their order, the last two or three indeed being only of
+limited use.
+
+The most essential point in good fireclays, or in the bricks or other
+objects made from them, is the power of resisting fusion at the highest
+heat to which they may be exposed. This supposes them to be free from
+metallic oxides forming easily fusible compounds with silica, such as
+lime or iron, the presence of the former even in comparatively small
+proportion being very detrimental. As clays they must be sufficiently
+plastic to be readily moulded, but at the same time possess sufficient
+stiffness not to contract too strongly in drying, whereby the objects
+produced would be liable to be warped or cracked before firing. In most
+cases, however, the latter tendency is guarded against, in making up the
+paste for moulding, by adding to the fresh clay a certain proportion of
+burnt material of the same kind, such as old bricks or potsherds, ground
+to a coarse powder. Coke dust or graphite is used for the same purpose
+in crucible making (see FIREBRICK).
+
+  The most highly valued fireclays are derived from the Coal Measures.
+  Among the chief localities are the neighbourhood of Stourbridge in
+  Worcestershire and Stannington near Sheffield, which supply most of
+  the materials for crucibles used in steel and brass melting, and the
+  pots for glass houses; Newcastle-on-Tyne and Glenboig near Glasgow,
+  where heavy blast furnace and other firebricks, gas retorts, &c., are
+  made in large quantities. Coarse-grained but very strong firebricks
+  are also made of the waste of china clay works.
+
+  In Belgium the clay raised at Andenne is very largely used for making
+  retorts for zinc furnaces. The principal French fireclays are derived
+  from the Tertiary strata in the south, and more nearly resemble
+  porcelain clays than those of the Coal Measures. They give wares of
+  remarkably fine texture and surface, combined with high refractory
+  character.
+
+  In Germany, Ips and Passau on the Danube, and Gross Almerode in Hesse,
+  are the best known localities producing fireclay goods, the crucibles
+  from the last-mentioned place, known as Hessian crucibles, going all
+  over the world. These, though not showing a great resistance to
+  extreme heat, are very slightly affected by sudden alternations in
+  heating, as they may be plunged cold into a strongly heated furnace
+  without cracking, a treatment to which French and Stourbridge pots
+  cannot be subjected with safety.
+
+Plumbago or graphite is largely used in the production of crucibles, not
+in the pure state but in admixture with fireclay; the proportion of the
+former varies with the quality from 25 to nearly 50%. These are the most
+enduring of all crucibles, the best lasting out 70 or 80 meltings in
+brass foundries, about 50 with bronze, and 8 to 10 in steel-melting.
+
+Silica is used in furnace-building in the forms of sand, ganister, a
+finely ground sandstone from the Coal Measures of Yorkshire, and the
+analogous substance known as Dinas clay, which is really nearly pure
+silica, containing at most about 2-1/2% of bases. Dinas clay is found at
+various places in the Vale of Neath in South Wales, in the form of a
+loose disintegrated sandstone, which is crushed between rollers, mixed
+with about 1% of lime, and moulded into bricks that are fired in kilns
+at a very high temperature. These bricks are specially used for the
+roof, fire arches, and other parts subjected to intense heat in
+reverberatory steel-melting furnaces, and, although infusible under
+ordinary conditions, are often fairly melted by the heat without fluxing
+or corrosion after a certain amount of exposure. Ganister, a slightly
+plastic siliceous sand, is similarly used for the lining of Bessemer
+steel converters; it is found in the neighbourhood of Sheffield.
+
+Alumina as a refractory material is chiefly used in the form of bauxite,
+but its applications are somewhat special. It has been found to stand
+well for the linings of rotatory puddling furnaces, where, under
+long-continued heating, it changes into a substance as hard and
+infusible as natural emery. In the Paris Exhibition of 1878 bricks very
+hard and dense in character, said to be of pure alumina, were exhibited
+by Muller & Co. of Paris, as well as bricks of magnesia, the latter
+being specially remarkable for their great weight. They are intended for
+use at the extreme temperatures obtainable in steel furnaces, or for the
+melting of platinum before the oxy-hydrogen blowpipe. For the latter
+purpose, however, lime is generally used; but as this substance has only
+small stability, it is usually bedded in a casing of firebrick. Oxide of
+chromium and chrome iron ore have been proposed as refractory crucible
+materials. The former may be used as a bed for melting platinum in the
+same way as lime or magnesia, without affecting the quality of the
+metal.
+
+Ferric oxide, though not strictly infusible, is largely used as a
+protecting lining for furnaces in which malleable iron is made, a
+portion of the ore being reduced and recovered in the process. In an
+oxidizing atmosphere it is indifferent to silica, and therefore
+siliceous bricks containing a considerable proportion of ferric oxide,
+when used in flues of boilers, brewers' coppers, &c. and similar
+situations, are perfectly fire-resisting so long as the heated gas
+contains a large proportion of unconsumed air. The red firebricks known
+as Windsor bricks, which are practically similar in composition to soft
+red sandstone, are of this character.
+
+The electric furnace has led to the discovery of several important
+materials, which have been employed as furnace linings. Carborundum
+(q.v.) was applied by Engels in 1899, firebricks being washed with
+carborundum paste and then baked. Siloxicon, a compound of carbon,
+silicon and oxygen, formed from carbon and silica in the electric
+furnace, was patented by E.G. Acheson in 1903. It is very refractory,
+and is applied by mixing with water and some bond, such as sodium
+silicate or gas-tar. An amorphous, soft silicon carbide, also formed in
+the electric furnace, was patented by B. Talbot in 1899. For basic
+linings, magnesia crystallized in the electric furnace is being
+extensively used, replacing dolomite to some extent (see E. Kilburn
+Scott, "Refractory Materials for Furnace Linings," _Faraday Soc._, 1906,
+p. 289).
+
+  _Furnace Construction._--In the construction of furnaces provision has
+  to be made for the unequal expansion of the different parts under the
+  effect of heat. This is especially necessary in the case of
+  reverberatory furnaces, which are essentially weak structures, and
+  therefore require to be bound together by complicated systems of tie
+  rods and uprights or buck staves. The latter are very commonly made of
+  old flat bottom rails, laid with the flat of the flange against the
+  wall. Puddling furnaces are usually entirely cased with iron plates,
+  and blast furnaces with hoops round each course of the stack, or in
+  those of thinner constructions the firebrick work is entirely enclosed
+  in a wrought iron casing or jacket. Such parts as may be subjected to
+  extreme heat and the fretting action of molten material, as the tuyere
+  and slag breasts of blast furnaces, and the fire bridges and bed
+  plates of reverberatory furnaces, are often made in cast iron with
+  double walls, a current of water or air being kept circulating through
+  the intermediate space. In this way the metal, owing to its high
+  conductivity and low specific heat as compared to that of water, is
+  kept at a temperature far below its melting point if the water is
+  renewed quickly enough. It is of course necessary in such cases that
+  the circulation shall be perfectly free, in order to prevent the
+  accumulation of steam under pressure in the interior of the casting.
+  This method has received considerable extension, notably in
+  furnace-smelting of iron ores containing manganese, where the entire
+  hearth is often completely water-cased, and in some lead furnaces
+  where no firebrick lining is used, the lower part of the furnace stack
+  being a mere double iron box cooled by water sufficiently to keep a
+  coating of slag adhering to the inner shell which prevents the metal
+  from being acted upon.
+
+  _Mechanical Furnaces._--The introduction and withdrawal of the charges
+  in fusion furnaces is effected by gravitation, the solid masses of raw
+  ore, fuel and flux being thrown in at the top, and flowing out of the
+  furnace at the taphole or slag run at the bottom. Vertical kilns, such
+  as those used for burning limestone, are worked in a similar
+  manner--the raw stone going in at the top, and the burnt product
+  falling through holes in the bottom when allowed to do so. With
+  reverberatory calciners, however, where the work is done upon a
+  horizontal bed, a considerable amount of hand labour is expended in
+  raking out the charge when finished, and in drawing slags from fusion
+  furnaces; and more particularly in the puddling process of refining
+  iron the amount of manual exertion required is very much greater. To
+  diminish the item of expenditure on this head, various kinds of
+  mechanical furnaces have been adopted, all of which can be classified
+  under three heads of gravitating furnaces, mechanical stirrers and
+  revolving furnaces.
+
+  1. In _gravitating furnaces_ the bed is laid at a slope just within
+  the angle of repose of the charge, which is introduced at the upper
+  end, and is pushed down the slope by fresh material, when necessary,
+  in the contrary direction to the flame which enters at the lower end.
+  Gerstenhofer's pyrites burner is a furnace of this class. It has a
+  tall vertical chamber heated from below, and traversed by numerous
+  narrow horizontal cross bars at different heights. The ore in fine
+  powder is fed in at the top, through a hopper, in a regular thin
+  stream, by a pair of rollers, and in falling lodges on the flats of
+  the bars, forming a talus upon each of the height corresponding to the
+  angle of rest of the material, which is, however, at short intervals
+  removed to lower levels by the arrival of fresh ore from above. In
+  this way a very large surface is exposed to the heat, and the ore, if
+  containing sufficient sulphur to maintain the combustion, is perfectly
+  burned when it arrives at the bottom; if, however, it is imperfectly
+  sized or damp, or if it contains much earthy matter, the result is not
+  very satisfactory. There are many other furnaces in which the same
+  principle is utilized.
+
+  2. _Mechanical stirrers_ constitute a second division of mechanical
+  furnaces, in which the labour of rabbling or stirring the charges is
+  performed by combinations of levers and wheel-work taking motion from
+  a rotating shaft, and more or less perfectly imitating the action of
+  hand labour. They are almost entirely confined to puddling furnaces.
+
+  3. _Revolving furnaces_, the third and most important division of
+  mechanical furnaces, are of two kinds. The first of these resemble an
+  ordinary reverberatory furnace by having a flat bed which, however,
+  has the form of a circular disk mounted on a central shaft, and
+  receives a slow movement of rotation from a water-wheel or other
+  motor, so that every part of the surface is brought successively under
+  the action of the fire, the charge being stirred and ultimately
+  removed by passing under a series of fixed scraper arms placed above
+  the surface at various points. Brunton's calciner, used in the
+  "burning" of the pyritic minerals associated with tin ore, is a
+  familiar example of this type. The hearth may either rotate on an
+  inclined axis, so that the path of its surface is oblique to that of
+  the flame, or the working part may be a hollow cylinder, between the
+  fireplace and flue, with its axis horizontal or nearly so, whose inner
+  surface represents the working bed, mounted upon friction rollers, and
+  receiving motion from a special steam-engine by means of a central
+  belt of spur gearing. Furnaces of the second kind were first used in
+  alkali works for the conversion of sulphate into carbonate of sodium
+  in the process known as black ash fusion, but have since been applied
+  to other processes. As calciners they are used in tin mines and for
+  the chlorination of silver ores. Mechanical furnaces are figured in
+  the article ALKALI MANUFACTURE.
+
+  _Use of Heated Air._--The calorific intensity of fuel is found to be
+  very considerably enhanced, if the combustion be effected with air
+  previously heated to any temperature between that of boiling water and
+  a dull red heat, the same effect being observed both with solid and
+  gaseous fuel. The latter, especially when brought to the burning point
+  at a high temperature, produces a heat that can be resisted by the
+  most refractory substances only, such as silica, alumina and magnesia.
+  This is attained in the regenerative furnace of Siemens, detailed
+  consideration of which belongs more properly to the subject of iron.
+
+  _Economy of Waste Heat._--In every system of artificial heating, the
+  amount of heat usefully applied is but a small proportion of that
+  developed by combustion. Even under the most advantageous application,
+  that of evaporation of water in a steam boiler where the gases of the
+  fire have to travel through a great length of flues bounded by thin
+  iron surfaces of great heat-absorbing capacity, the temperature of the
+  current at the chimney is generally much above that required to
+  maintain an active draught in the fireplace; and other tubes
+  containing water, often in considerable numbers, forming the so-called
+  fuel economizers, may often be interposed between the boiler and the
+  chimney with marked advantage as regards saving of fuel. In
+  reverberatory and air furnaces used in the different operations of
+  iron manufacture, where an extremely high temperature has to be
+  maintained in spaces of comparatively small extent, such as the beds
+  of puddling, welding and steel-melting furnaces, the temperature of
+  the exhaust gases is exceedingly high, and if allowed to pass directly
+  into the chimney they appear as a great body of flame at the top. It
+  is now general to save a portion of this heat by passing the flame
+  through flues of steam boilers, air-heating apparatus, or both--so
+  that the steam required for the necessary operations of the forge and
+  heated blast for the furnace itself may be obtained without further
+  expenditure of fuel. The most perfect method of utilizing the waste
+  heat hitherto applied is that of the Siemens regenerator, in which the
+  spent gases are made to travel through chambers, known as regenerators
+  or recuperators of heat, containing a quantity of thin firebricks
+  piled into a cellular mass so as to offer a very large heat-absorbing
+  surface, whereby their temperature is very considerably reduced, and
+  they arrive at the chimney at a heat not exceeding 300 or 400 degrees.
+  As soon as the bricks have become red hot, the current is diverted to
+  an adjacent chamber or pair of chambers, and the acquired heat is
+  removed by a current of cool gas or air passing towards the furnace,
+  where it arrives at a temperature sufficiently high to ensure the
+  greatest possible heating effect in combustion.
+
+  In iron-smelting blast furnaces the waste gases are of considerable
+  fuel value, and may render important services if properly applied.
+  Owing to the conditions of the work, which require the maintenance of
+  a sensibly reducing atmosphere, they contain a very notable proportion
+  of carbonic oxide, and are drawn off by large wrought iron tubes near
+  the top of the furnace and conveyed by branch pipes to the different
+  boilers and air-heating apparatus, which are now entirely heated by
+  the combustion of such gases, or mixed with air and exploded in gas
+  engines. Formerly they were allowed to burn to waste at the mouth of a
+  short chimney place above the furnace top, forming a huge body of
+  flame, which was one of the most striking features of the Black
+  Country landscape at night.
+
+  _Laboratory and Portable Furnaces._--Small air-furnaces with hot
+  plates or sand bath flues were formerly much employed in chemical
+  laboratories, as well as small blast furnaces for crucibles heated
+  with charcoal or coke. The use of such furnaces has very considerably
+  diminished, owing to the general introduction of coal-gas for heating
+  purposes in laboratories, which has been rendered possible by the
+  invention of the Bunsen burner, in which the mixture of air and gas
+  giving the least luminous but most powerfully heating flame is
+  effected automatically by the effluent gas. These burners, or
+  modifications of them, have also been applied to muffle furnaces,
+  which are convenient when only a few assays have to be made--the
+  furnace being a mere clay shell and soon brought to a working
+  temperature; but the fuel is too expensive to allow of their being
+  used habitually or on a large scale. Petroleum, or rather the heavy
+  oils obtained in tar refineries, having an equal or superior heating
+  power to coal-gas, may also be used in laboratories for producing high
+  temperatures. The oil is introduced in a thin stream upon a series of
+  inclined and channelled bars, where it is almost immediately
+  volatilized and burnt by air flowing in through parallel orifices.
+  Furnaces of this kind may be used for melting cast iron or bronze in
+  small quantities, and were employed by H. Sainte Claire Deville in
+  experiments in the metallurgy of the platinum group of metals.
+
+  Sefstrom's blast furnace, used in Sweden for the assay of iron ores,
+  is a convenient form of portable furnace applied to melting in
+  crucibles. It consists of a sheet-iron cylinder about 8 or 9 in. in
+  diameter, within which is fixed one of smaller size lined with
+  fireclay. The space between the two cylinders serves as a heater and
+  distributor for the blast, which is introduced through the nozzle at
+  the bottom, and enters the furnace through a series of several small
+  tuyeres arranged round the inner lining. Charcoal is the fuel used,
+  and the crucibles stand upon the bottom of the clay lining. When a
+  large body of fuel is required, the cylinder can be lengthened by an
+  iron hoop which fits over the top ring. Deville's portable blast
+  furnace is very similar in principle to the above, but the body of the
+  furnace is formed of a single cast iron cylinder lined with fireclay,
+  closed below by a cast iron plate perforated by a ring of small
+  holes--a hemispherical basin below forming the air-heating chamber.
+
+
+
+
+FURNEAUX, TOBIAS (1735-1781), English navigator, was born at Swilly near
+Plymouth on the 21st of August 1735. He entered the royal navy, and was
+employed on the French and African coasts and in the West Indies during
+the latter part of the Seven Years' War (1760-1763). He served as second
+lieutenant of the "Dolphin" under Captain Samuel Wallis on the latter's
+voyage round the globe (August 1766-May 1768); was made a commander in
+November 1771; and commanded the "Adventure" which accompanied Captain
+Cook (in the "Resolution") in Cook's second voyage. On this expedition
+Furneaux was twice separated from his leader (February 8-May 19, 1773;
+October 22, 1773-July 14, 1774, the date of his return to England). On
+the former occasion he explored a great part of the south and east
+coasts of Tasmania, and made the earliest British chart of the same.
+Most of his names here survive; Cook, visiting this shore-line on his
+third voyage, confirmed Furneaux's account and delineation of it (with
+certain minor criticisms and emendations), and named after him the
+islands in Banks Straits, opening into Bass's Straits, and the group now
+known as the Low Archipelago. After the "Adventure" was finally
+separated from the "Resolution" off New Zealand in October 1773,
+Furneaux returned home alone, bringing with him Omai of Ulaietea. This
+first South Sea Islander seen in the British Isles returned to his home
+with Cook in 1776-1777. Furneaux was made a captain in 1775, and
+commanded the "Syren" in the British attack of the 28th of June 1776
+upon Charleston, South Carolina. His successful efforts to introduce
+domestic animals and potatoes into the South Sea Islands are worthy of
+note. He died at Swilly on the 19th of September 1781.
+
+  See Hawkesworth's _Narrative of Wallis' Voyage_; Captain Cook's
+  _Narrative of his Second Voyage_; also T. Furneaux's life by Rev.
+  Henry Furneaux in the _Dictionary of National Biography_.
+
+
+
+
+
+FURNES (Flem. _Veurne_), an old-fashioned little town amid the dunes
+near the coast in West Flanders, Belgium, about 26 m. S.W. of Bruges.
+Pop. (1904) 6099. It is the centre of a considerable area extending to
+the French frontier, and its market is an important one for the disposal
+of corn, stock, hops and dairy produce. During the Norman raids Furnes
+was destroyed, and the present town was built by Baldwin Bras de Fer,
+first count of Flanders, about the year 870. At the height of the
+prosperity of the Flemish communes in the 14th century there were
+dependent on the barony of Furnes not fewer than fifty-two rich
+villages, but these have all disappeared, partly no doubt as the
+consequence of repeated French invasions down to the end of the 18th
+century, but chiefly through the encroachment of the sea followed by the
+accumulation of sand along the whole of this portion of the coast.
+Furnes contains many curious old houses and the church of St Walburga,
+which is a fine survival of the 13th century with some older portions.
+The old church and buildings, grouped round the Grand Place, which is
+the scene of the weekly market, present a quaint picture which is
+perhaps not to be equalled in the country. Near Furnes on the seashore
+is the fashionable bathing place called La Panne.
+
+Furnes one day a year becomes a centre of attraction to all the people
+of Flanders. This is the last Sunday in July, when the fete of Calvary
+and the Crucifixion is celebrated. Of all popular festivities in Belgium
+this is the nearest approach to the old Passion Play. The whole story of
+Christ is told with great precision by means of succeeding groups which
+typify the different phases of the subject. The people of Furnes pose as
+Roman soldiers or Jewish priests, as the apostles or mere spectators,
+while the women put on long black veils so that they may figure in the
+procession as the just women.
+
+
+
+
+FURNESS, HORACE HOWARD (1833-   ), American Shakespearian scholar, was
+born in Philadelphia on the 2nd of November 1833, being the son of
+William Henry Furness (1802-1896) minister of the First Unitarian church
+in that city, a powerful preacher and writer. He graduated at Harvard in
+1854, and was admitted to the bar in 1859, but soon devoted himself to
+the study of Shakespeare. He accumulated a collection of illustrative
+material of great richness and extent, and brought out in 1871 the first
+volume of a new Variorum edition, designed to represent and summarize
+the conclusions of the best authorities in all languages--textual,
+critical and annotative. The volumes appeared as follows: _Romeo and
+Juliet_ (1871); _Macbeth_ (1873) (revised edition, 1903); _Hamlet_ (2
+vols., 1877); _King Lear_ (1880); _Othello_ (1886); _The Merchant of
+Venice_ (1888); _As You Like It_ (1890); _The Tempest_ (1892); _A
+Midsummer Night's Dream_ (1895); _The Winter's Tale_ (1898); _Much Ado
+about Nothing_ (1899); _Twelfth Night_ (1901); _Love's Labour's Lost_
+(1904). The edition has been generally accepted as a thorough and
+scholarly piece of work; its chief fault is that, beginning with
+_Othello_ (1858), the editor used the First Folio text as his basis,
+while in others he makes the text of the Cambridge (Globe) editors his
+foundation. His wife, Helen Kate Furness (1837-1883), compiled _A
+Concordance to the Poems of Shakespeare_ (1872).
+
+
+
+
+FURNESS, a district of Lancashire, England, separated from the major
+portion of the county by Morecambe Bay. It is bounded S.E. by this inlet
+of the Irish Sea, S.W. by the sea, W. by the Duddon estuary and
+Cumberland, and N. and E. by Westmorland. Its area is about 250 sq. m.
+It forms the greater part of the North Lonsdale parliamentary division
+of Lancashire, and contains the parliamentary borough of
+Barrow-in-Furness. The surface is almost entirely hilly. The northern
+half is included in the celebrated Lake District, and contains such
+eminences as the Old Man of Coniston and Wetherlam. Apart from the
+Duddon, which forms part of the western boundary, the principal rivers
+are the Leven and Crake, flowing southward into a common estuary in
+Morecambe Bay. The Leven drains Windermere and the Crake Coniston Lake.
+The usage of the term "Lake District," however, tends to limit the name
+of Furness in common thought to the district south of the Lakes, where
+several of the place-names are suffixed with that of the district, as
+Barrow-in-Farness, Dalton-in-Furness, Broughton-in-Furness. Between the
+Duddon and Morecambe Bay lies Walney Island, 8 m. in length, and in the
+shallow strait between it and the mainland are several smaller islands.
+That part of Furness which forms a peninsula between the Leven estuary
+and Morecambe Bay, and the Duddon estuary, is rich in hematite iron ore,
+which has been worked from very early times. It was known and smelted by
+British and Romans, and by the monks of Furness Abbey and Conishead
+Priory, both in the district. It was owing to the existence of this ore
+that the town of Barrow grew up in the 19th century; at first as a port
+from which the ore was exported to South Wales, while later furnaces
+were established on the spot, and acquired additional importance on the
+introduction of the Bessemer process, which requires a non-phosphoric
+ore such as is found here. The hematite is also worked at Ulverston,
+Askam, Dalton and elsewhere, but the furnaces now depend in part upon
+ore imported from Spain. The supposed extension of the ore under the
+sands of the Duddon estuary led to the construction of a sea wall to
+facilitate the working. The district is served by the main line of the
+Furness railway, from Carnforth (junction with the London &
+North-Western railway), passing the pleasant watering-place of Grange,
+and approximately following the coast by Ulverston, Dalton and Barrow,
+with branches to Lake Side, Windermere, and to Coniston.
+
+
+  Furness Abbey.
+
+Apart from its industrial importance and scenic attractions, Furness has
+an especial interest on account of its famous abbey. The ruins of this,
+beautifully situated in a wooded valley, are extensive, and mainly of
+fine transitional Norman and Early English date, acquiring additional
+picturesqueness from the warm colour of the red sandstone of which they
+are built. The abbey of Furness, otherwise Furdenesia or the further
+_nese_ (promontory), which was dedicated to St Mary, was founded in 1127
+by a small body of monks belonging to the Benedictine order of Savigny.
+In 1124 they had settled at Tulketh, near Preston, but migrated in 1127
+to Furness under the auspices of Stephen, count of Boulogne, afterwards
+king, at that time lord of the liberty of Furness. In 1148 the
+brotherhood joined the Cistercian order. Stephen granted to the monks
+the lordship of Furness, and his charter was confirmed by Henry I.,
+Henry II. and subsequent kings. The abbot's power throughout the
+lordship was almost absolute; he had a market and fair at Dalton, was
+free from service to the county and wapentake, and held a sheriff's
+tourn. By a succession of gifts the abbey became one of the richest in
+England and was the largest Cistercian foundation in the kingdom. At the
+Dissolution its revenues amounted to between L750 and L800 a year,
+exclusive of meadows, pastures, fisheries, mines, mills and salt works,
+and the wealth of the monks enabled them to practise a regal
+hospitality. The abbot was one of the twenty Cistercian abbots summoned
+to the parliament of 1264, but was not cited after 1330, as he did not
+hold of the king _in capite per baroniam_. The abbey founded several
+offshoot houses, one of the most important being Rushen Abbey in the
+Isle of Man. In 1535 the royal commissioners visited the abbey and
+reported four of its inmates, including the abbot, for incontinence. In
+1536 the abbot was charged with complicity in the Pilgrimage of Grace,
+and on the 7th of April 1537, under compulsion, surrendered the abbey to
+the king. A few monks were granted pensions, and the abbot was endowed
+with the profits of the rectory of Dalton, valued at L33, 6s. 8d. per
+annum. In 1540 the estates and revenues were annexed by act of
+parliament to the Duchy of Lancaster. About James I.'s reign the site
+and territories were alienated to the Prestons of Preston-Patrick, from
+whom they descended to the dukes of Devonshire.
+
+Conishead Priory, near Ulverston, an Augustinian foundation of the reign
+of Henry II., has left no remains, but of the priory of Cartmel (1188)
+the fine church is still in use. It is a cruciform structure of
+transitional Norman and later dates, its central tower having the upper
+storey set diagonally upon the lower. The chancel contains some superb
+Jacobean carved oak screens, with stalls of earlier date.
+
+
+
+
+FURNISS, HARRY (1854-   ), British caricaturist and illustrator, was
+born at Wexford, Ireland, of English and Scottish parents. He was
+educated in Dublin, and in his schooldays edited a _Schoolboy's Punch_
+in close imitation of the original. He came to London when he was
+nineteen, and began to draw for the illustrated papers, being for some
+years a regular contributor to the _Illustrated London News_. His first
+drawing in _Punch_ appeared in 1880, and he joined its staff in 1884. He
+illustrated Lucy's "Diary of Toby, M.P.," in _Punch_, where his
+political caricatures became a popular feature. Among his other
+successes were a series of "Puzzle Heads," and his annual "Royal Academy
+guy'd." In _Royal Academy Antics_ (1890) he published a volume of
+caricatures of the work of leading artists. He resigned from the staff
+of _Punch_ in 1894, produced for a short time a weekly comic paper _Lika
+Joko_, and in 1898 began a humorous monthly, _Fair Game_; but these were
+short-lived. Among the numerous books he illustrated were James Payn's
+_Talk of the Town_, Lewis Carroll's _Sylvie and Bruno_, Gilbert a
+Beckett's _Comic Blackstone_, G.E. Farrow's _Wallypug Book_, and his own
+novel, _Poverty Bay_ (1905). _Our Joe, his great Fight_ (1903), was a
+collection of original cartoons. His volume of reminiscences,
+_Confessions of a Caricaturist_ (1901), was followed by _Harry Furniss
+at Home_ (1904). In 1905 he published _How to draw in Pen and Ink_, and
+produced the first number of _Harry Furniss's Christmas Annual_.
+
+
+
+
+FURNITURE (from "furnish," Fr. _fournir_), a general term of obscure
+origin, used to describe the chattels and fittings required to adapt
+houses and other buildings for use. Wood, ivory, precious stones,
+bronze, silver and gold have been used from the most ancient times in
+the construction or for the decoration of furniture. The kinds of
+objects required for furniture have varied according to the changes of
+manners and customs, as well as with reference to the materials at the
+command of the workman, in different climates and countries. Of really
+ancient furniture there are very few surviving examples, partly by
+reason of the perishable materials of which it was usually constructed;
+and partly because, however great may have been the splendour of Egypt,
+however consummate the taste of Greece, however luxurious the life of
+Rome, the number of household appliances was very limited. The chair,
+the couch, the table, the bed, were virtually the entire furniture of
+early peoples, whatever the degree of their civilization, and so they
+remained until the close of what are known in European history as the
+middle ages. During the long empire-strewn centuries which intervened
+between the lapse of Egypt and the obliteration of Babylon, the
+extinction of Greece and the dismemberment of Rome and the great
+awakening of the Renaissance, household comfort developed but little.
+The Ptolemies were as well lodged as the Plantagenets, and peoples who
+spent their lives in the open air, going to bed in the early hours of
+darkness, and rising as soon as it was light, needed but little
+household furniture.
+
+Indoor life and the growth of sedentary habits exercised a powerful
+influence upon the development of furniture. From being splendid, or at
+least massive, and exceedingly sparse and costly, it gradually became
+light, plentiful and cheap. In the ancient civilizations, as in the
+periods when our own was slowly growing, household plenishings, save in
+the rudest and most elementary forms, were the privilege of the
+great--no person of mean degree could have obtained, or would have dared
+to use if he could, what is now the commonest object in every house, the
+chair (q.v.). Sparse examples of the furniture of Egypt, Nineveh, Greece
+and Rome are to be found in museums; but our chief sources of
+information are mural and sepulchral paintings and sculptures. The
+Egyptians used wooden furniture carved and gilded, covered with splendid
+textiles, and supported upon the legs of wild animals; they employed
+chests and coffers as receptacles for clothes, valuables and small
+objects generally. Wild animals and beasts of the chase were carved upon
+the furniture of Nineveh also; the lion, the bull and the ram were
+especially characteristic. The Assyrians were magnificent in their
+household appointments; their tables and couches were inlaid with ivory
+and precious metals. Cedar and ebony were much used by these great
+Eastern peoples, and it is probable that they were familiar with
+rosewood, walnut and teak. Solomon's bed was of cedar of Lebanon. Greek
+furniture was essentially Oriental in form; the more sumptuous varieties
+were of bronze, damascened with gold and silver. The Romans employed
+Greek artists and workmen and absorbed or adapted many of their
+mobiliary fashions, especially in chairs and couches. The Roman tables
+were of splendid marbles or rare woods. In the later ages of the empire,
+in Rome and afterwards in Constantinople, gold and silver were
+plentifully used in furniture; such indeed was the abundance of these
+precious metals that even cooking utensils and common domestic vessels
+were made of them.
+
+The architectural features so prominent in much of the medieval
+furniture begin in these Byzantine and late Roman thrones and other
+seats. These features became paramount as Pointed architecture became
+general in Europe, and scarcely less so during the Renaissance. Most of
+the medieval furniture, chests, seats, trays, &c., of Italian make were
+richly gilt and painted. In northern Europe carved oak was more
+generally used. State seats in feudal halls were benches with ends
+carved in tracery, backs panelled or hung with cloths (called cloths of
+estate), and canopies projecting above. Bedsteads were square frames,
+the testers of panelled wood, resting on carved posts. Chests of oak
+carved with panels of tracery, or of Italian cypress (when they could be
+imported), were used to hold and to carry clothes, tapestries, &c., to
+distant castles and manor houses; for house furniture, owing to its
+scarcity and cost, had to be moved from place to place. Copes and other
+ecclesiastical vestments were kept in chests with ornamental lock plates
+and iron hinges. The splendour of most feudal houses depended on
+pictorial tapestries which could be packed and carried from place to
+place. Wardrobes were rooms fitted for the reception of dresses, as well
+as for spices and other valuable stores. Excellent carving in relief was
+executed on caskets, which were of wood or of ivory, with painting and
+gilding, and decorated with delicate hinge and lock metal-work. The
+general subjects of sculpture were taken from legends of the saints or
+from metrical romances. Renaissance art made a great change in
+architecture, and this change was exemplified in furniture. Cabinets
+(q.v.) and panelling took the outlines of palaces and temples. In
+Florence, Rome, Venice, Milan and other capitals of Italy, sumptuous
+cabinets, tables, chairs, chests, &c., were made to the orders of the
+native princes. Vasari (_Lives of Painters_) speaks of scientific
+diagrams and mathematical problems illustrated in costly materials, by
+the best artists of the day, on furniture made for the Medici family.
+The great extent of the rule of Charles V. helped to give a uniform
+training to artists from various countries resorting to Italy, so that
+cabinets, &c., which were made in vast numbers in Spain, Flanders and
+Germany, can hardly be distinguished from those executed in Italy.
+Francis I. and Henry VIII. encouraged the revived arts in their
+respective dominions. _Pietra dura_, or inlay of hard pebbles, agate,
+lapis lazuli, and other stones, ivory carved and inlaid, carved and gilt
+wood, marquetry or veneering with thin woods, tortoise-shell, brass,
+&c., were used in making sumptuous furniture during the first period of
+the Renaissance. Subjects of carving or relief were generally drawn from
+the theological and cardinal virtues, from classical mythology, from the
+seasons, months, &c. Carved altarpieces and woodwork in churches partook
+of the change in style.
+
+The great period of furniture in almost every country was, however,
+unquestionably the 18th century. That century saw many extravagances in
+this, as in other forms of art, but on the whole it saw the richest
+_floraison_ of taste, and the widest sense of invention. This is the
+more remarkable since the furniture of the 17th century has often been
+criticized as heavy and coarse. The criticism is only partly justified.
+Throughout the first three-quarters of the period between the accession
+of James I. and that of Queen Anne, massiveness and solidity were the
+distinguishing characteristics of all work. Towards the reign of James
+II., however, there came in one of the most pleasing and elegant styles
+ever known in England. Nearly a generation before then Boulle was
+developing in France the splendid and palatial method of inlay which,
+although he did not invent it, is inseparably associated with his name.
+We owe it perhaps to the fact that France, as the neighbour of Italy,
+was touched more immediately by the Renaissance than England that the
+reign of heaviness came earlier to an end in that country than on the
+other side of the Channel. But there is a heaviness which is pleasing as
+well as one which is forbidding, and much of the furniture made in
+England any time after the middle of the 17th century was highly
+attractive. If English furniture of the Stuart period be not sought
+after to the same extent as that of a hundred years later, it is yet
+highly prized and exceedingly decorative. Angularity it often still
+possessed, but generally speaking its elegance of form and richness of
+upholstering lent it an attraction which not long before had been
+entirely lacking. Alike in France and in England, the most attractive
+achievements of the cabinetmaker belong to the 18th century--English
+Queen Anne and early Georgian work is universally charming; the regency
+and the reigns of Louis XV. and XVI. formed a period of the greatest
+artistic splendour. The inspiration of much of the work of the great
+English school was derived from France, although the gropings after the
+Chinese taste and the earlier Gothic manner were mainly indigenous. The
+French styles of the century, which began with excessive flamboyance,
+closed before the Revolution with a chaste perfection of detail which is
+perhaps more delightful than anything that has ever been done in
+furniture. In the achievements of Riesener, David Rontgen, Gouthiere,
+Oeben and Rousseau de la Rottiere we have the high-water mark of
+craftsmanship. The marquetry of the period, although not always
+beautiful in itself, was executed with extraordinary smoothness and
+finish; the mounts of gilded bronze, which were the leading
+characteristic of most of the work of the century, were finished with a
+minute delicacy of touch which was until then unknown, and has never
+been rivalled since. If the periods of Francis I. and Henry II., of
+Louis XIV. and the regency produced much that was sumptuous and even
+elegant, that of Louis XVI., while men's minds were as yet undisturbed
+by violent political convulsions, stands out as, on the whole, the one
+consummate era in the annals of furniture. Times of great achievement
+are almost invariably followed directly by those in which no tall
+thistles grow and in which every little shrub is magnified to the
+dimensions of a forest tree; and the so-called "empire style" which had
+begun even while the last monarch of the _ancien regime_ still reigned,
+lacked alike the graceful conception and the superb execution of the
+preceding style. Heavy and usually uninspired, it was nurtured in
+tragedy and perished amid disaster. Yet it is a profoundly interesting
+style, both by reason of the classical roots from which it sprang and
+the attempt, which it finally reflected, to establish new ideas in every
+department of life. Founded upon the wreck of a lingering feudalism it
+reached back to Rome and Greece, and even to Egypt. If it is rarely
+charming, it is often impressive by its severity. Mahogany, satinwood
+and other rich timbers were characteristic of the style of the end of
+the 18th century; rosewood was most commonly employed for the choicer
+work of the beginning of the 19th. Bronze mounts were in high favour,
+although their artistic character varied materially.
+
+Previously to the middle of the 18th century the only cabinetmaker who
+gained sufficient personal distinction to have had his name preserved
+was Andre Charles Boulle; beginning with that period France and England
+produced many men whose renown is hardly less than that of artists in
+other media. With Chippendale there arose a marvellously brilliant
+school of English cabinetmakers, in which the most outstanding names are
+those of Sheraton, Heppelwhite, Shearer and the Adams. But if the school
+was splendid it was lamentably short-lived, and the 19th century
+produced no single name in the least worthy to be placed beside these
+giants. Whether, in an age of machinery, much room is left for fine
+individual execution may be doubted, and the manufacture of furniture
+now, to a great extent, takes place in large factories both in England
+and on the continent. Owing to the necessary subdivision of labour in
+these establishments, each piece of furniture passes through numerous
+distinct workshops. The master and a few artificers formerly
+superintended each piece of work, which, therefore, was never far
+removed from the designer's eye. Though accomplished artists are
+retained by the manufacturers of London, Paris and other capitals, there
+can no longer be the same relation between the designer and his work.
+Many operations in these modern factories are carried on by machinery.
+This, though an economy of labour, entails loss of artistic effect. The
+chisel and the knife are no longer in such cases guided and controlled
+by the sensitive touch of the human hand.
+
+[Illustration: PLATE I.
+
+  FIG. 1.--Venetian Folding Chair of carved and gilt walnut, leather
+  back and seat; about 1530.
+
+  FIG. 2.--Oak Arm-chair. English, 17th century.
+
+  FIG. 3.--Arm-chair, solid seat, cane back; about 1660.
+
+  FIG. 4.--Arm-chair, stuffed back and seat; about 1650.
+
+  FIG. 5.--Painted and carved High-Back Chair; about 1660.
+
+  FIG. 6.--Carved Walnut Chairs. English, early 18th century. The
+  arm-chair is inlaid.
+
+  FIG. 7.--Walnut Chair; about 1710.
+
+  FIG. 8.--Carved Mahogany Chair in the style of Chippendale; 2nd half
+  of 18th century.
+
+  FIG. 9.--Carved Mahogany Arm-chair, in the style of Chippendale, with
+  ribbon pattern.
+
+  FIG. 10.--Carved and Inlaid Mahogany Chair, in the style of
+  Hepplewhite; late 18th century.
+
+  FIG. 11.--Mahogany Chair in the style of Sheraton; about 1780.
+
+  Fig. 12.--Painted and gilt Arm-chair with cane seat, in the style of
+  Adam; about 1790.
+
+  FIG. 13.--Arm-chair of carved and gilt wood with stuffed back, seat
+  and arms. French, Louis XV. style.
+
+  FIG. 14.--Mahogany Arm-chair. Empire style, early 19th century, said
+  to have belonged to the Bonaparte family.
+
+  FIG. 15.--Painted and gilt Beech Chair. English, about 1800.]
+
+[Illustration: PLATE II.
+
+  FIG. 1.--Front of Oak Coffer with wrought iron bands. French, 2nd half
+  of 13th century.
+
+  FIG. 2.--English Oak Chest, dated 1637.
+
+  FIG. 3.--Italian (Florentine) Coffer of Wood with gilt arabesque
+  stucco ornament, about 1480.
+
+  FIG. 4.--Italian "Cassone" or Marriage Coffer, 13th century. Carved
+  and gilt wood with painted front and ends.
+
+  FIG. 5.--Walnut Table with expanding leaves. Swiss, 17th century.
+
+  FIG. 6.--Oak Gate-Legged Table. English, 17th century.
+
+  FIG. 7.--Writing Table. French, end of Louis XV. period. Riesener
+  marquetry, ormolu mounts and Sevres plaques.
+
+  FIG. 8.--Painted Satin-Wood Tables, in the style of Sheraton, about
+  1790.
+
+  (The above are in the Victoria and Albert Museum, except Fig. 8, which
+  were in the Bethnal Green Exhibition, 1892.)]
+
+[Illustration: PLATE III.
+
+  1. CARVED OAK SIDEBOARD. English, 17th century. Victoria and Albert
+  Museum.
+
+  2. CARVED OAK COURT CUPBOARD. English, early 17th century. Victoria
+  and Albert Museum.
+
+  3. EBONY CARVED CABINET. The interior decorated with inlaid ivory and
+  coloured woods; French or Dutch, middle of 17th century. Victoria and
+  Albert Museum.
+
+  4. VENEERED CHEST OF DRAWERS. About 1690. Lent to Bethnal Green
+  Exhibition by Sir Spencer Ponsonby-Fane, G.C.B.
+
+  5. EBONY ARMOIRE. With tortoise-shell panels inlaid with brass and
+  other metals, and ormolu mountings. Designed by Berain, and executed
+  by Andre Boulle. French, Louis XIV. period. Victoria and Albert
+  Museum.
+
+  6. GLASS-FRONTED BOOKCASE AND CABINET. Of mahogany. In the style of
+  Sheraton, about 1790. Lent to the Bethnal Green Exhibition by the late
+  Vincent J. Robinson, C.I.E.]
+
+[Illustration: PLATE IV.
+
+  1. COMMODE OF PINE. With marquetry of brass, ebony, tortoise-shell,
+  mother-of-pearl, ivory, and green-stained bone. "Boulle" work with
+  designs in the style of Berain. French, late period of Louis XIV.
+
+  2. COMMODE. With panels of Japanese lacquer and ormolu mountings, in
+  the style of Caffieri. French, Louis XV. period.
+
+  3. TABLE OF KING AND TULIP WOODS. With ormolu mountings. Louis XV.
+  period.
+
+  4. ESCRITOIRE A TOILETTE. Formerly belonging to Marie Antoinette. Of
+  tulip and sycamore woods inlaid with other coloured woods, ormolu
+  mounts. Louis XV. period.
+
+  5. FOUR-POST BEDSTEAD. Of oak inlaid with bog-oak and holly, from the
+  "Inlaid Room" at Sizergh Castle, Westmorland. Latter half of sixteenth
+  century.
+
+  6. CARVED AND GILT BEDSTEAD. With blue silk damask coverings and
+  hangings. French, late 18th century. Louis XVI. period.
+
+  From the Victoria and Albert Museum, S. Kensington.]
+
+[Illustration: PLATE V.
+
+  _Photo, Mansell & Co._
+
+  THE "BUREAU DU ROI," MADE FOR LOUIS XV., NOW IN THE LOUVRE. For
+  description, see DESK.]
+
+A decided, if not always intelligent, effort to devise a new style in
+furniture began during the last few years of the 19th century, which
+gained the name of "_l'art nouveau_." Its pioneers professed to be free
+from all old traditions and to seek inspiration from nature alone.
+Happily nature is less forbidding than many of these interpretations of
+it, and much of the "new art" is a remarkable exemplification of the
+impossibility of altogether ignoring traditional forms. The style was
+not long in degenerating into extreme extravagance. Perhaps the most
+striking consequence of this effort has been, especially in England, the
+revival of the use of oak. Lightly polished, or waxed, the cheap foreign
+oaks often produce very agreeable results, especially when there is
+applied to them a simple inlay of boxwood and stained holly, or a modern
+form of pewter. The simplicity of these English forms is in remarkable
+contrast to the tortured and ungainly outlines of continental seekers
+after a conscious and unpleasing "originality."
+
+Until a very recent period the most famous collections of historic
+furniture were to be found in such French museums as the Louvre, Cluny
+and the Garde Meuble. Now, however, they are rivalled, if not surpassed,
+by the magnificent collections of the Victoria and Albert Museum at
+South Kensington, and the Wallace collection at Hertford House, London.
+The latter, in conjunction with the Jones bequest at South Kensington,
+forms the finest of all gatherings of French furniture of the great
+periods, notwithstanding that in the Bureau du Roi the Louvre possesses
+the most magnificent individual example in existence. In America there
+are a number of admirable collections representative of the graceful and
+homely "colonial furniture" made in England and the United States during
+the Queen Anne and Georgian periods.
+
+  See also the separate articles in this work on particular forms of
+  furniture. The literature of the subject has become very extensive,
+  and it is needless to multiply here the references to books. Perrot
+  and Chipiez, in their great _Histoire de l'art dans l'antiquite_ (1882
+  et seq.) deal with ancient times, and A. de Champeaux, in _Le Meuble_
+  (1885), with the middle ages and later period; English furniture is
+  admirably treated by Percy Macquoid in his _History of English
+  Furniture_ (1905); and Lady Dilke's _French Furniture in the 18th
+  Century_ (1901), and Luke Vincent Lockwood's _Colonial Furniture in
+  America_ (1901), should also be consulted.     (J. P. B.)
+
+
+
+
+FURNIVALL, FREDERICK JAMES (1825-1910), English philologist and editor,
+was born at Egham, Surrey, on the 4th of February 1825, the son of a
+surgeon. He was called to the bar in 1849, but his attention was soon
+diverted to philological studies and social problems. He gave Frederick
+Denison Maurice valuable assistance in the Christian Socialist movement,
+and was one of the founders of the Working Men's College. For half a
+century he indefatigably promoted the study of early English literature,
+partly by his own work as editor, and still more efficaciously by the
+agency of the numerous learned societies of which he was both founder
+and director, especially the Early English Text Society (1864), which
+has been of inestimable service in promoting the study of early and
+middle English. He also established and conducted the Chaucer, Ballad,
+New Shakespeare and Wyclif Societies, and at a later period societies
+for the special study of Browning and Shelley. He edited texts for the
+Early English Text Society, for the Roxburghe Club and the Rolls Series;
+but his most important labours were devoted to Chaucer, whose study he
+as an editor greatly assisted by his "Six-Text" edition of the
+_Canterbury Tales_, and other publications of the Chaucer Society. He
+was the honorary secretary of the Philological Society, and was one of
+the original promoters of the Oxford _New English Dictionary_. He
+co-operated with its first editor, Herbert Coleridge, and after his
+death was for some time principal editor during the preliminary period
+of the collection of material. The completion of his half-century of
+labour was acknowledged in 1900 by a handsome testimonial, including the
+preparation by his friends of a volume of philological essays specially
+dedicated to him, _An English Miscellany_ (Oxford, 1901), and a
+considerable donation to the Early English Text Society. Dr Furnivall
+was always an enthusiastic oarsman, and till the end kept up his
+interest in rowing; with John Beesley in 1845 he introduced the new type
+of narrow sculling boat, and in 1886 started races on the Thames for
+sculling fours and sculling eights. He died on the 2nd of July 1910.
+
+
+
+
+FURSE, CHARLES WELLINGTON (1868-1904), English painter, born at Staines,
+the son of the Rev. C.W. Furse, archdeacon of Westminster, was descended
+collaterally from Sir Joshua Reynolds, and in his short span of life
+achieved such rare excellence as a portrait and figure painter that he
+forms an important link in the chain of British portraiture which
+extends from the time when Van Dyck was called to the court of Charles
+I. to our own day. His talent was precocious; at the age of seven he
+gave indications of it in a number of drawings illustrating Scott's
+novels. He entered the Slade school in 1884, winning the Slade
+scholarship in the following year, and completed his education at
+Julian's _atelier_ in Paris. Hard worker as he was, his activity was
+frequently interrupted by spells of illness, for he had developed signs
+of consumption when he was still attending the Slade school. An
+important canvas called "Cain" was his first contribution (1888) to the
+Royal Academy, to the associateship of which he was elected in the year
+of his death. For some years before he had been a staunch supporter of
+the New English Art Club, to the exhibitions of which he was a regular
+contributor. He was married in October 1900 to Katherine, daughter of
+John Addington Symonds. His fondness for sport and of an open-air life
+found expression in his art and introduced a new, fresh and vigorous
+note into portraiture. There is never a suggestion of the studio or of
+the fatiguing pose in his portraits. The sitters appear unconscious of
+being painted, and are generally seen in the pursuit of their favourite
+outdoor sport or pastime, in the full enjoyment of life. Such are the
+"Diana of the Uplands," the "Lord Roberts" and "The Return from the
+Ride" at the Tate Gallery; the four children in the "Cubbing with the
+York and Ainsty," "The Lilac Gown," "Mr and Mrs Oliver Fishing" and the
+portrait of Lord Charles Beresford. Most of these pictures, and indeed
+nearly all the work completed in the few years of Furse's activity, show
+a pronounced decorative tendency. His sense of space, composition and
+decorative design can best be judged by his admirable mural decorations
+for Liverpool town hall, executed between 1899 and 1902. A memorial
+exhibition of Furse's paintings and sketches was held at the Burlington
+Fine Arts Club in 1906.
+
+
+
+
+FURST, JULIUS (1805-1873), German Orientalist, was born of Jewish
+parents at Zerkowo in Posen, on the 12th of May 1805. He studied
+philosophy and philology at Berlin, and oriental literature at Posen,
+Breslau and Halle. In 1857 he was appointed to a lectureship at the
+university of Leipzig, and he was promoted to a professorship in 1864,
+which he held until his death at Leipzig on the 9th of February 1873.
+Among his writings may be mentioned _Lehrgebaude der aramaischen Idiome_
+(Leipzig, 1835); _Librorum sacrorum Veteris Testamenti concordantiae
+Hebraicae atque Chaldaicae_ (Leipzig, 1837-1840); _Hebraisches und
+chaldaisches Worterbuch_ (1851, English translation by S. Davidson
+1867); _Kultur und Literaturgeschichte der Juden in Asien_ (1849). Furst
+also edited a valuable _Bibliotheca Judaica_ (Leipzig, 1849-1863), and
+was the author of some other works of minor importance. From 1840 to
+1851 he was editor of _Der Orient_, a journal devoted to the language,
+literature, history and antiquities of the Jews.
+
+
+
+
+FURSTENBERG, the name of two noble houses of Germany.
+
+1. The more important is in possession of a mediatized principality in
+the district of the Black Forest and the Upper Danube, which comprises
+the countship of Heiligenberg, about 7 m. to the N. of the Lake of
+Constance, the landgraviates of Stuhlingen and Baar, and the lordships
+of Jungnau, Trochtelfingen, Hausen and Moskirch or Messkirch. The
+territory is discontinuous; and as it lies partly in Baden, partly in
+Wurttemberg, and partly in the Prussian province of Sigmaringen, the
+head of the family is an hereditary member of the first chamber of Baden
+and of the chamber of peers in Wurttemberg and in Prussia. The relations
+of the principality with Baden are defined by the treaty of May 1825,
+and its relations with Wurttemberg by the royal declaration of 1839. The
+_Stammort_ or ancestral seat of the family is Furstenberg in the Black
+Forest, about 13 m. N. of Schaffhausen, but the principal residence of
+the present representatives of the main line is at Donaueschingen.
+
+The family of Furstenberg claims descent from a certain Count Unruoch, a
+contemporary of Charlemagne, but their authentic pedigree is only
+traceable to Egino II., count of Urach, who died before 1136. In 1218
+his successors inherited the possessions of the house of Zahringen in
+the Baar district of the Black Forest, where they built the town and
+castle of Furstenberg. Of the two sons of Egino V. of Urach, Conrad, the
+elder, inherited the Breisgau and founded the line of the counts of
+Freiburg, while the younger, Heinrich (1215-1284), received the
+territories lying in the Kinzigthal and Baar, and from 1250 onward
+styled himself first lord, then count, of Furstenberg. His territories
+were subsequently divided among several branches of his descendants,
+though temporarily reunited under Count Friedrich III., whose wife,
+Anna, heiress of the last count of Wardenberg, brought him the countship
+of Heiligenberg and lordships of Jungnau and Trochtelfingen in 1534. On
+Friedrich's death (1559) his territories were divided between his two
+sons, Joachim and Christof I. Of these the former founded the line of
+Heiligenberg, the latter that of Kinzigthal. The Kinzigthal branch was
+again subdivided in the 17th century between the two sons of Christof
+II. (d. 1614), the elder, Wratislaw II. (d. 1642), founding the line of
+Mosskirch, the younger, Friedrich Rudolf (d. 1655), that of Stuhlingen.
+The Heiligenberg branch received an accession of dignity by the
+elevation of Count Hermann Egon (d. 1674) to the rank of prince of the
+Empire in 1664, but his line became extinct with the death of his son
+Prince Anton Egon, favourite of King Augustus the Strong and regent of
+Saxony, in 1716. The heads of both the Mosskirch and Stuhlingen lines
+were now raised to the dignity of princes of the Empire (1716). The
+Mosskirch branch died out with Prince Karl Friedrich (d. 1744); the
+territories of the Stuhlingen branch had been divided on the death of
+Count Prosper Ferdinand (1662-1704) between his two sons, Joseph Wilhelm
+Ernst (1699-1762) and Ludwig August Egon (1705-1759). The first of these
+was created prince of the Empire on the 10th of December 1716, and
+founded the princely line of the Swabian Furstenbergs; in 1772 he
+obtained from the emperor Francis I. for all his legitimate sons and
+their descendants the right to bear, instead of the style of landgrave,
+that of prince, which had so far been confined to the reigning head of
+the family. Ludwig, on the other hand, founded the family of the
+landgraves of Furstenberg, who, since their territories lay in Austria
+and Moravia, were known as the "cadet line in Austria." The princely
+line became extinct with the death of Karl Joachim in 1804, and the
+inheritance passed to the Bohemian branch of the Austrian cadet line in
+the person of Karl Egon II. (see below). Two years later the
+principality was mediatized.
+
+In 1909 there were two branches of the princely house of Furstenberg:
+(1) the main branch, that of Furstenberg-Donaueschingen, the head of
+which was Prince Maximilian Egon (b. 1863), who succeeded his cousin
+Karl Egon III. in 1896; (2) that of Furstenberg-Konigshof, in Bohemia,
+the head of which was Prince Emil Egon (b. 1876), chamberlain and
+secretary of legation to the Austro-Hungarian embassy in London (1907).
+The cadet line of the landgraves of Furstenberg is now extinct, its last
+representative having been the landgrave Joseph Friedrich Ernst of
+Furstenberg-Weitra (1860-1896), son of the landgrave Ernst (1816-1889)
+by a morganatic marriage. He was not recognized as _ebenburtig_ by the
+family. The landgraves of Furstenberg were in 1909 represented only by
+the landgravines Theresa (b. 1839) and Gabrielle (b. 1844), daughters
+of the landgrave Johann Egon (1802-1879).
+
+From the days of Heinrich of Urach, a relative and notable supporter of
+Rudolph of Habsburg, the Furstenbergs have played a stirring part in
+German history as statesmen, ecclesiastics and notably soldiers. There
+was a popular saying that "the emperor fights no great battle but a
+Furstenberg falls." In the Heiligenberg line the following may be more
+particularly noticed.
+
+FRANZ EGON (1625-1682), bishop of Strassburg, was the elder son of Egon
+VII., count of Furstenberg (1588-1635), who served with distinction as a
+Bavarian general in the Thirty Years' War. He began life as a soldier in
+the imperial service, but on the elevation of his friend Maximilian
+Henry of Bavaria to the electorate of Cologne in 1650, he went to his
+court and embraced the ecclesiastical career. He soon gained a complete
+ascendancy over the weak-minded elector, and, with his brother William
+Egon (see below), was mainly instrumental in making him the tool of the
+aggressive policy of Louis XIV. of France. Ecclesiastical preferments
+were heaped upon him. As a child he had been appointed to a canonry of
+Cologne; to these he added others at Strassburg, Liege, Hildesheim and
+Spires; he became also suffragan bishop and dean of Cologne and provost
+of Hildesheim, and in 1663 bishop of Strassburg. Later he was also
+prince-abbot of Luders and Murbach and abbot of Stablo and Malmedy. On
+the conclusion of a treaty between the emperor and the elector of
+Cologne, on the 11th of May 1674, Franz was deprived of all his
+preferments in Germany, and was compelled to take refuge in France. He
+was, however, amnestied with his brother William by a special article of
+the treaty of Nijmwegen (1679), whereupon he returned to Cologne. After
+the French occupation of Strassburg (1681) he took up his residence
+there and died on the 1st of April 1682.
+
+His brother WILLIAM EGON (1629-1704), bishop of Strassburg, began his
+career as a soldier in the French service. He went to the court of the
+elector of Cologne at the same time as Franz Egon, whose zeal for the
+cause of Louis XIV. of France he shared. In 1672 the intrigues of the
+two Furstenbergs had resulted in a treaty of offensive alliance between
+the French monarchy and the electorate of Cologne, and, the brothers
+being regarded by the Imperialists as the main cause of this disaster,
+William was seized by imperial soldiers in the monastery of St Pantaleon
+at Cologne, hurried off to Vienna and there tried for his life. He was
+saved by the intervention of the papal nuncio, but was kept in prison
+till the signature of the treaty of Nijmwegen (1679). As a reward for
+his services Louis XIV. appointed him bishop of Strassburg in succession
+to his brother in 1682, in 1686 obtained for him from Pope Innocent XI.
+the cardinal's hat, and in 1688 succeeded in obtaining his election as
+coadjutor-archbishop of Cologne and successor to the elector Maximilian
+Henry. At the instance of the emperor, however, the pope interposed his
+veto; the canons followed the papal lead, and, the progress of the
+Allies against Louis XIV. depriving him of all prospect of success,
+William Egon retired to France. Here he took up his abode at his abbey
+of St Germain des Pres near Paris, where he died on the 10th of April
+1704.
+
+In the Stuhlingen line the most notable was KARL EGON (1796-1854),
+prince of Furstenberg, the son of Prince Karl Alois of Furstenberg, a
+general in the Austrian service, who was killed at the battle of
+Loptingen on the 25th of March 1799. In 1804 he inherited the Swabian
+principality of Furstenberg and all the possessions of the family except
+the Moravian estates. He studied at Freiburg and Wurzburg, and in 1815
+accompanied Prince Schwarzenberg to Paris as staff-officer. In 1817 he
+came of age, and in the following year married the princess Amalie of
+Baden. By the mediatization of his principality in 1806 the greater part
+of his vast estates had fallen under the sovereignty of the grand-duke
+of Baden, and Prince Furstenberg took a conspicuous part in the upper
+house of the grand-duchy. In politics he distinguished himself by a
+liberalism rare in a great German noble, carrying through by his
+personal influence with his peers the abolition of tithes and feudal
+dues and stanchly advocating the freedom of the press. He was not less
+distinguished by his large charities: among other foundations he
+established a hospital at Donaueschingen. For the industrial development
+of the country, too, he did much, and proved himself also a notable
+patron of the arts. His palace of Donaueschingen, with its collections
+of paintings, engravings and coins, was a centre of culture, where
+poets, painters and musicians met with princely entertainment. He died
+on the 14th of September 1869, and was succeeded by his son Karl Egon
+II. (1820-1892), with the death of whose son, Karl Egon III., in 1896,
+the title and estates passed to Prince Maximilian Egon, head of the
+cadet line of Furstenberg-Purglitz.
+
+  See Munch, _Gesch. des Hauses und des Landes Furstenberg_, 4 vols.
+  (Aix-la-Chapelle, 1829-1847); S. Riezler, _Gesch. des furstlichen
+  Hauses Furstenberg bis 1507_ (Tubingen, 1883); _Furstenbergisches
+  Urkundenbuch_, edited by S. Riezler and F.L. Baumann, vols. i.-vii.
+  (Tubingen, 1877-1891), continued _s. tit. Mitteilungen aus dem
+  furstlich. Furstenbergischem Archiv_ by Baumann and G. Tumbult, 2
+  vols. (ib. 1899-1902); Stokvis, _Manuel d'histoire_ (Leiden,
+  1890-1893); _Almanach de Gotha; Allgemeine deutsche Biographie_.
+
+2. The second Furstenberg family has its possessions in Westphalia and
+the country of the Rhine, and takes its name from the castle of
+Furstenberg on the Ruhr. The two most remarkable men whom it has
+produced are Franz Friedrich Wilhelm, freiherr von Furstenberg, and
+Franz Egon, count von Furstenberg-Stammheim. The former (1728-1810)
+became ultimately vicar-general of the prince-bishop of Munster, and
+effected a great number of important reforms in the administration of
+the country, besides doing much for its educational and industrial
+development. The latter (1797-1859) was an enthusiastic patron of art,
+who zealously advocated the completion of the Cologne cathedral, and
+erected the beautiful church of St Apollinaris near Remagen on the
+Rhine. He was a member of the Prussian Upper House in 1849, collaborated
+in founding the _Preussisches Wochenblatt_, and was an ardent defender
+of Catholic interests. His son, Count Gisbert von Furstenberg-Stammheim
+(b. 1836), was in 1909 head of the Rhenish line of the house of
+Furstenberg.
+
+
+
+
+FURSTENWALDE, a town of Germany, in the Prussian province of
+Brandenburg, on the right bank of the Spree, and on the railway from
+Berlin to Frankfort-on-Oder, 28 m. E. of the former city. Pop. (1905)
+20,498. Its beautiful cathedral church contains several old monuments.
+The industries are important, including, besides brewing and malting,
+manufactures of starch, vinegar, electric lamps and gas-fittings,
+stoves, &c., iron-founding and wool-weaving. Furstenwalde is one of the
+oldest towns of Brandenburg. From 1385 it was the seat of the bishop of
+Lebus, whose bishopric was incorporated with the electorate of Brunswick
+in 1595.
+
+
+
+
+FURTH, a manufacturing town of Germany, in the kingdom of Bavaria, at
+the confluence of the Pegnitz with the Regnitz, 5 m. N.W. from Nuremberg
+by rail, at the junction of lines to Hof and Wurzburg. Pop. (1885)
+35,455; (1905) 60,638. It is a modern town in appearance, with broad
+streets and palatial business houses. Of its four Evangelical churches,
+the old St Michaeliskirche is a handsome structure; but its chief
+edifices are the new town hall, with a tower 175 ft. high and the
+magnificent synagogue. The Jews have also a high school, which enjoys a
+great reputation. There are besides a classical, a wood-carving and an
+agricultural school and a library. Furth is the seat of several
+important industries; particularly, the production of chromolithographs
+and picture-books, the manufacture of mirrors and mirror-frames, bronze
+and gold-leaf wares, pencils, toys, haberdashery, optical instruments,
+silver work, turnery, chicory, machinery, fancy boxes and cases, and an
+extensive trade is carried on in these goods as also in hops, metals,
+wool, groceries and coal. A large annual fair is held at Michaelmas and
+lasts for eleven days. The earliest railway in Germany was that between
+Nuremberg and Furth (opened on the 7th of December 1835).
+
+Furth was founded, according to tradition, by Charlemagne, who erected a
+chapel there. It was for a time a _Vogtei_ (advocateship) under the
+burgraves of Nuremberg, but about 1314 it was bequeathed to the see of
+Bamberg, and in 1806 it came into the possession of Bavaria. In 1632
+Gustavus Adolphus besieged it in vain, and in 1634 it was pillaged and
+burnt by the Croats. It owes its rise to prosperity to the tolerance it
+meted out to the Jews, who found here an asylum from the oppression
+under which they suffered in Nuremberg.
+
+  See Fronmuller, _Chronik der Stadt Furth_ (1887).
+
+
+
+
+FURTWANGLER, ADOLF (1853-1907), German archaeologist, was born at
+Freiburg im Breisgau, and was educated there, at Leipzig and at Munich,
+where he was a pupil of H. Brunn, whose comparative method in
+art-criticism he much developed. He took part in the excavations at
+Olympia in 1878, became an assistant in the Berlin Museum in 1880, and
+professor at Berlin (1884) and later at Munich. His latest excavation
+work was at Aegina. He was a prolific writer, with a prodigious
+knowledge and memory, and a most ingenious and confident critic; and his
+work not only dominated the field of archaeological criticism but also
+raised its standing both at home and abroad. Among his numerous
+publications the most important were a volume on the bronzes found at
+Olympia, vast works on ancient gems and Greek vases, and the invaluable
+_Masterpieces of Greek Sculpture_ (English translation by Eugenie
+Strong). He died at Athens on the 10th of October 1907.
+
+
+
+
+FURZE, GORSE or WHIN; botanical name _Ulex_ (Ger. _Stechginster_, Fr.
+_ajonc_), a genus of thorny papilionaceous shrubs, of few species,
+confined to west and central Europe and north-west Africa. Common furze,
+_U. europaeus_, is found on heaths and commons in western Europe from
+Denmark to Italy and Greece, and in the Canaries and Azores, and is
+abundant in nearly all parts of the British Isles. It grows to a height
+of 2-6 ft.; it has hairy stems, and the smaller branches end each in a
+spine; the leaves, sometimes lanceolate on the lowermost branches, are
+mostly represented by spines from 2 to 6 lines long, and branching at
+their base; and the flowers, about three-quarters of an inch in length,
+have a shaggy, yellowish-olive calyx, with two small ovate bracts at its
+base, and appear in early spring and late autumn. They are yellow and
+sweet-scented and visited by bees. The pods are few-seeded; their
+crackling as they burst may often be heard in hot weather. This species
+comprises the varieties _vulgaris_, or _U. europaeus_ proper, which has
+spreading branches, and strong, many-ridged spines, and _strictus_
+(Irish furze), with erect branches, and slender 4-edged spines. The
+other British species of furze is _U. nanus_, dwarf furze, a native of
+Belgium, Spain and the west of France; it is a procumbent plant, less
+hairy than _U. europaeus_, with smaller and more orange-coloured
+flowers, which spring from the primary spines, and have a nearly smooth
+calyx, with minute basal bracts. Furze, or gorse, is sometimes employed
+for fences.
+
+Notwithstanding its formidable spines, the young shoots yield a
+palatable and nutritious winter forage for horses and cattle. To fit it
+for this purpose it must be chopped and bruised to destroy the spines.
+This is sometimes done in a primitive and laborious way by laying the
+gorse upon a block of wood and beating it with a mallet, flat at one end
+and armed with crossed knife-edges at the other, by the alternate use of
+which it is bruised and chopped. There are now a variety of machines by
+which this is done rapidly and efficiently, and which are in use where
+this kind of forage is used to any extent. The agricultural value of
+this plant has often been over-rated by theoretical writers. In the case
+of very poor, dry soils it does, however, yield much valuable food at a
+season when green forage is not otherwise to be had. It is on this
+account of importance to dairymen; and to them it has this further
+recommendation, that cows fed upon it give much rich milk, which is free
+from any unpleasant flavour. To turn it to good account, it must be sown
+in drills, kept clean by hoeing, and treated as a regular green crop. If
+sown in March, on land fitly prepared and afterwards duly cared for, it
+is ready for use in the autumn of the following year. A succession of
+cuttings of proper age is obtained for several years from the same
+field. It is cut by a short stout scythe, and must be brought from the
+field daily; for when put in a heap after being chopped and bruised it
+heats rapidly. It is given to horses and cows in combination with
+chopped hay or straw. An acre will produce about 2000 faggots of green
+two-year-old gorse, weighing 20 lb. each.
+
+This plant is invaluable in mountain sheep-walks. The rounded form of
+the furze bushes that are met with in such situations shows how
+diligently the annual growth, as far as it is accessible, is nibbled by
+the sheep. The food and shelter afforded to them in snowstorms by
+clusters of such bushes is of such importance that the wonder is our
+sheep farmers do not bestow more pains to have it in adequate quantity.
+Young plants of whin are so kept down by the sheep that they can seldom
+attain to a profitable size unless protected by a fence for a few years.
+In various parts of England it is cut for fuel. The ashes contain a
+large proportion of alkali, and are a good manure, especially for peaty
+land.
+
+
+
+
+FUSARO, LAGO, a lake of Campania, Italy, 1/2 m. W. of Baia, and 1 m. S.
+of the acropolis of Cumae. It is the ancient _Acherusia palus_,
+separated from the sea on the W. by a line of sandhills. It may have
+been the harbour of Cumae in early antiquity. In the 1st century A.D. an
+artificial outlet was dug for it at its S. end, with a tunnel, lined
+with _opus reticulatum_ and brick, under the hill of Torregaveta. This
+hill is covered with the remains of a large villa, which is almost
+certainly that of Servilius Vatia, described by Seneca (_Epist._ 55).
+There are remains of other villas on the shores of the lake. Oyster
+cultivation is carried on there.
+
+  See J. Beloch, _Campanien_ (2nd ed., Breslau, 1890), 188.     (T. As.)
+
+
+
+
+FUSELI, HENRY (1741-1825), English painter and writer on art, of
+German-Swiss family, was born at Zurich in Switzerland on the 7th of
+February 1741; he himself asserted in 1745, but this appears to have
+been a mere whim. He was the second child in a family of eighteen. His
+father was John Caspar Fussli, of some note as a painter of portraits
+and landscapes, and author of Lives of the _Helvetic Painters_. This
+parent destined his son for the church, and with this view sent him to
+the Caroline college of his native town, where he received an excellent
+classical education. One of his schoolmates there was Lavater, with whom
+he formed an intimate friendship.
+
+After taking orders in 1761 Fuseli was obliged to leave his country for
+a while in consequence of having aided Lavater to expose an unjust
+magistrate, whose family was still powerful enough to make its vengeance
+felt. He first travelled through Germany, and then, in 1765, visited
+England, where he supported himself for some time by miscellaneous
+writing: there was a sort of project of promoting through his means a
+regular literary communication between England and Germany. He became in
+course of time acquainted with Sir Joshua Reynolds, to whom he showed
+his drawings. By Sir Joshua's advice he then devoted himself wholly to
+art. In 1770 he made an art-pilgrimage to Italy, where he remained till
+1778, changing his name from Fussli to Fuseli, as more Italian-sounding.
+Early in 1779 he returned to England, taking Zurich on his way. He found
+a commission awaiting him from Alderman Boydell, who was then organizing
+his celebrated Shakespeare gallery. Fuseli painted a number of pieces
+for this patron, and about this time published an English edition of
+Lavater's work on physiognomy. He likewise gave Cowper some valuable
+assistance in preparing the translation of Homer. In 1788 Fuseli married
+Miss Sophia Rawlins (who it appears was originally one of his models,
+and who proved an affectionate wife), and he soon after became an
+associate of the Royal Academy. Two years later he was promoted to the
+grade of Academician. In 1799 he exhibited a series of paintings from
+subjects furnished by the works of Milton, with a view to forming a
+Milton gallery corresponding to Boydell's Shakespeare gallery. The
+number of the Milton paintings was forty-seven, many of them very large;
+they were executed at intervals within nine years. This exhibition,
+which closed in 1800, proved a failure as regards profit. In 1799 also
+he was appointed professor of painting to the Academy. Four years
+afterwards he was chosen keeper, and resigned his professorship; but he
+resumed it in 1810, and continued to hold both offices till his death.
+In 1805 he brought out an edition of Pilkington's _Lives of the
+Painters_, which, however, did not add much to his reputation. Canova,
+when on his visit to England, was much taken with Fuseli's works, and on
+returning to Rome in 1817 caused him to be elected a member of the first
+class in the Academy of St Luke. Fuseli, after a life of uninterrupted
+good health, died at Putney Hill on the 16th of April 1825, at the
+advanced age of eighty-four, and was buried in the crypt of St Paul's
+cathedral. He was comparatively rich at his death, though his
+professional gains had always appeared to be meagre.
+
+As a painter, Fuseli had a daring invention, was original, fertile in
+resource, and ever aspiring after the highest forms of excellence. His
+mind was capable of grasping and realizing the loftiest conceptions,
+which, however, he often spoiled on the canvas by exaggerating the due
+proportions of the parts, and throwing his figures into attitudes of
+fantastic and over-strained contortion. He delighted to select from the
+region of the supernatural, and pitched everything upon an ideal scale,
+believing a certain amount of exaggeration necessary in the higher
+branches of historical painting. "Damn Nature! she always puts me out,"
+was his characteristic exclamation. In this theory he was confirmed by
+the study of Michelangelo's works and the marble statues of the Monte
+Cavallo, which, when at Rome, he used often to contemplate in the
+evening, relieved against a murky sky or illuminated by lightning. But
+this idea was by him carried out to an excess, not only in the forms,
+but also in the attitudes of his figures; and the violent and
+intemperate action which he often displays destroys the grand effect
+which many of his pieces would otherwise produce. A striking
+illustration of this occurs in his famous picture of "Hamlet breaking
+from his Attendants to follow the Ghost": Hamlet, it has been said,
+looks as though he would burst his clothes with convulsive cramps in all
+his muscles. This intemperance is the grand defect of nearly all
+Fuseli's compositions. On the other hand, his paintings are never either
+languid or cold. His figures are full of life and earnestness, and seem
+to have an object in view which they follow with rigid intensity. Like
+Rubens he excelled in the art of setting his figures in motion. Though
+the lofty and terrible was his proper sphere, Fuseli had a fine
+perception of the ludicrous. The grotesque humour of his fairy scenes,
+especially those taken from _A Midsummer-Night's Dream_, is in its way
+not less remarkable than the poetic power of his more ambitious works.
+As a colourist Fuseli has but small claims to distinction. He scorned to
+set a palette as most artists do; he merely dashed his tints recklessly
+over it. Not unfrequently he used his paints in the form of a dry
+powder, which he rubbed up with his pencil with oil, or turpentine, or
+gold size, regardless of the quantity, and depending for accident on the
+general effect. This recklessness may perhaps be explained by the fact
+that he did not paint in oil till he was twenty-five years of age.
+Despite these drawbacks he possessed the elements of a great painter.
+
+Fuseli painted more than 200 pictures, but he exhibited only a minority
+of them. His earliest painting represented "Joseph interpreting the
+Dreams of the Baker and Butler"; the first to excite particular
+attention was the "Nightmare," exhibited in 1782. He produced only two
+portraits. His sketches or designs numbered about 800; they have
+admirable qualities of invention and design, and are frequently superior
+to his paintings.
+
+His general powers of mind were large. He was a thorough master of
+French, Italian, English and German, and could write in all these
+tongues with equal facility and vigour, though he preferred German as
+the vehicle of his thoughts. His writings contain passages of the best
+art-criticism that English literature can show. The principal work is
+his series of _Lectures_ in the Royal Academy, twelve in number,
+commenced in 1801.
+
+  Many interesting anecdotes of Fuseli, and his relations to
+  contemporary artists, are given in his _Life_ by John Knowles, who
+  also edited his works in 3 vols. 8vo, London, 1831.     (W. M. R.)
+
+
+
+
+FUSEL OIL (from the Ger. _Fusel_, bad spirits), the name applied to the
+volatile oily liquids, of a nauseous fiery taste and smell, which are
+obtained in the rectification of spirituous liquors made by the
+fermentation of grain, potatoes, the marc of grapes, and other
+material, and which, as they are of higher boiling point than ethyl
+alcohol, occur in largest quantity in the last portions of the
+distillate. Besides ethyl or ordinary alcohol, and amyl alcohol, which
+are present in them all, there have been found in fusel oil several
+other bodies of the C_n H_(2n + 1).OH series, also certain ethers, and
+members of the C_n H_(2n + 1).CO2H series of fatty acids. Normal propyl
+alcohol is contained in the fusel oil of the marc brandy of the south of
+France, and isoprimary butyl alcohol in that of beet-root molasses. The
+chief constituent of the fusel oil procured in the manufacture of
+alcohol from potatoes and grain, usually known as fusel oil and
+potato-spirit, is isoprimary amyl alcohol, or isobutylcarbinol. Ordinary
+fusel oil yields also an isomeric amyl alcohol (active amyl alcohol)
+boiling at about 128 deg. Variable quantities of fusel oil, less or
+greater according to the stage of ripening, exist in commercial spirits
+(see SPIRITS).
+
+Fusel oil and its chief constituent, amyl alcohol, are direct nerve
+poisons. In small doses it causes only thirst and headache, with furred
+tongue and some excitement. In large doses it is a convulsent poison.
+Impure beverages induce all the graver neurotic and visceral disorders
+in alcoholism; and, like fusel oil, furfurol and the essence of
+absinthe, are convulsent poisons. Pure ethyl alcohol intoxication,
+indeed, is rarely seen, being modified in the case of spirits by the
+higher alcohols contained in fusel oil. According to Rabuteau the toxic
+properties of the higher alcohols increase with their molecular weight
+and boiling point. Richet considers that the fusel oil contained in
+spirits constitutes the chief danger in the consumption of alcoholic
+beverages. The expert can immediately detect the peculiarly virulent
+characters of the mixed intoxication due to the consumption of spirits
+containing a large percentage of fusel oil.
+
+
+
+
+FUSIBLE METAL, a term applied to certain alloys, generally composed of
+bismuth, lead and tin, which possess the property of melting at
+comparatively low temperatures. Newton's fusible metal (named after Sir
+Isaac Newton) contains 50 parts of bismuth, 31.25 of lead and 18.75 of
+tin; that of Jean Darcet (1725-1801), 50 parts of bismuth with 25 each
+of lead and tin; and that of Valentin Rose the elder, 50 of bismuth with
+28.1 of lead and 24.1 of tin. These melt between 91 deg. and 95 deg. C.
+The addition of cadmium gives still greater fusibility; in Wood's metal,
+for instance, which is Darcet's metal with half the tin replaced by
+cadmium, the melting point is lowered to 66 deg.-71 deg. C.; while
+another described by Lipowitz and containing 15 parts of bismuth, 8 of
+lead, 4 of tin and 3 of cadmium, softens at about 55 deg. and is
+completely liquid a little above 60 deg. By the addition of mercury to
+Darcet's metal the melting point may be reduced so low as 45 deg. These
+fusible metals have the peculiarity of expanding as they cool; Rose's
+metal, for instance, remains pasty for a considerable range of
+temperature below its fusing point, contracts somewhat rapidly from 80
+deg. to 55 deg., expands from 55 deg. to 35 deg., and contracts again
+from 35 deg. to 0 deg. For this reason they may be used for taking casts
+of anatomical specimens or making _cliches_ from wood-blocks, the
+expansion on cooling securing sharp impressions. By suitable
+modification in the proportions of the components, a series of alloys
+can be made which melt at various temperatures above the boiling point
+of water; for example, with 8 parts of bismuth, 8 of lead and 3 of tin
+the melting point is 123 deg., and with 8 of bismuth, 30 of lead and 24
+of tin it is 172 deg. With tin and lead only in equal proportions it is
+241 deg. Such alloys are used for making the fusible plugs inserted in
+the furnace-crowns of steam boilers, as a safeguard in the event of the
+water-level being allowed to fall too low. When this happens the plug
+being no longer covered with water is heated to such a temperature that
+it melts and allows the contents of the boiler to escape into the
+furnace. In automatic fire-sprinklers the orifices of the pipes are
+closed with fusible metal, which melts and liberates the water when,
+owing to an outbreak of fire in the room, the temperature rises above a
+predetermined limit.
+
+
+
+
+FUSILIER, originally (in French about 1670, in English about 1680) the
+name of a soldier armed with a light flintlock musket called the fusil;
+now a regimental designation. Various forms of flintlock small arms had
+been used in warfare since the middle of the 16th century. At the time
+of the English civil war (1642-1652) the term "firelock" was usually
+employed to distinguish these weapons from the more common matchlock
+musket. The special value of the firelock in armies of the 17th century
+lay in the fact that the artillery of the time used open powder barrels
+for the service of the guns, making it unsafe to allow lighted matches
+in the muskets of the escort. Further, a military escort was required,
+not only for the protection, but also for the surveillance of the
+artillerymen of those days. Companies of "firelocks" were therefore
+organized for these duties, and out of these companies grew the
+"fusiliers" who were employed in the same way in the wars of Louis XIV.
+In the latter part of the Thirty Years' War (1643) fusiliers were simply
+mounted troops armed with the fusil, as carabiniers were with the
+carbine. But the escort companies of artillery came to be known by the
+name shortly afterwards, and the regiment of French Royal Fusiliers,
+organized in 1671 by Vauban, was considered the model for Europe. The
+general adoption of the flintlock musket and the suppression of the pike
+in the armies of Europe put an end to the original special duties of
+fusiliers, and they were subsequently employed to a large extent in
+light infantry work, perhaps on account of the greater individual
+aptitude for detached duties naturally shown by soldiers who had never
+been restricted to a fixed and unchangeable place in the line of battle.
+The senior fusilier regiment in the British service, the (7th) Royal
+Fusiliers (City of London Regiment), was formed on the French model in
+1685; the 5th foot (now Northumberland Fusiliers), senior to the 7th in
+the army, was not at that time a fusilier regiment. The distinctive
+head-dress of fusiliers in the British service is a fur cap, generally
+resembling, but smaller than and different in details from, that of the
+Foot Guards.
+
+In Germany the name "fusilier" is borne by certain infantry regiments
+and by one battalion in each grenadier regiment.
+
+
+
+
+FUSION, the term generally applied to the melting of a solid substance,
+or the change of state of aggregation from the solid to the liquid. The
+term "liquefaction" is frequently employed in the same sense, but is
+often restricted to the condensation of a gas or vapour. The converse
+process of freezing or solidification, the change from the liquid to the
+solid state, is subject to the same laws, and must be considered
+together with fusion. The solution of a solid in a foreign liquid, and
+the deposition or crystallization of a solid from a solution, are so
+closely related to the fusion of a pure substance, that it will also be
+necessary to consider some of the analogies which they present.
+
+1. _General Phenomena._--There are two chief varieties of the process of
+fusion, namely, crystalline and amorphous, which are in many ways
+distinct, although it is possible to find intermediate cases which
+partake of the characteristics of both. The melting of ice may be taken
+as a typical case of crystalline fusion. The passage from rigid solid to
+mobile liquid occurs at a definite surface without any intermediate
+stage or plastic condition. The change takes place at a definite
+temperature, the fusing or freezing point (abbreviated F.P.), and
+requires the addition of a definite quantity of heat to the solid, which
+is called the latent heat of fusion. There is also in general a
+considerable change of volume during fusion, which amounts in the case
+of ice to a contraction of 9%. Typical cases of amorphous solidification
+are those of silica, glass, plastic sulphur, pitch, alcohol and many
+organic liquids. In this type the liquid gradually becomes more and more
+viscous as the temperature falls, and ultimately attains the rigidity
+characteristic of a solid, without any definite freezing point or latent
+heat. The condition of the substance remains uniform throughout, if its
+temperature is uniform; there is no separation into the two distinct
+phases of solid and liquid, and there is no sudden change of volume at
+any temperature.
+
+A change or transition from one crystalline form to another may occur in
+the solid state with evolution or absorption of heat at a definite
+temperature, and is analogous to the change from solid to liquid, but
+usually takes place more slowly owing to the small molecular mobility of
+the solid state. Thus rhombic sulphur when heated passes slowly at 95.6
+deg. C. into the monosymmetric form which melts at 120 deg., but if
+heated rapidly the rhombic form melts at 114.5. The two forms, rhombic
+and monosymmetric, can exist in equilibrium at 95.6 deg., the transition
+point at which they have the same vapour pressure. Similarly a solid
+solution of carbon in iron, when cooled slowly, passes at about 700 deg.
+C., with considerable evolution of heat, into the form of "pearlite,"
+which is soft when cold, but if rapidly chilled the carbon remains in
+solution and the steel is very hard (see also ALLOYS).
+
+In the case of crystalline fusion it is necessary to distinguish two
+cases, the homogeneous and the heterogeneous. In the first case the
+composition of the solid and liquid phases are the same, and the
+temperature remains constant during the whole process of fusion. In the
+second case the solid and liquid phases differ in composition; that of
+the liquid phase changes continuously, and the temperature does not
+remain constant during the fusion. The first case comprises the fusion
+of pure substances, and that of eutectics, or cryohydrates; the second
+is the general case of an alloy or a solution. These have been very
+fully studied and their phenomena greatly elucidated in recent years.
+
+There is also a sub-variety of amorphous fusion, which may be styled
+colloid or gelatinous, and may be illustrated by the behaviour of
+solutions of water in gelatin. Many of these jellies melt at a fairly
+definite temperature on heating, and coagulate or set at a definite
+temperature on cooling. But in some cases the process is not reversible,
+and there is generally marked hysteresis, the temperature of setting and
+other phenomena depending on the rate of cooling. This case has not yet
+been fully worked out; but it appears probable that in many cases the
+jelly possesses a spongy framework of solid, holding liquid in its
+meshes or interstices. It might be regarded as a case of "heterogeneous"
+amorphous fusion, in which the liquid separates into two phases of
+different composition, one of which solidifies before the other. The two
+phases cannot, as a rule, be distinguished optically, but it is
+generally possible to squeeze out some of the liquid phase when the
+jelly has set, which proves that the substance is not really
+homogeneous. In very complicated mixtures, such as acid lavas or slags
+containing a large proportion of silica, amorphous and crystalline
+solidification may occur together. In this case the crystals separate
+first during the process of cooling, the mother liquor increases
+gradually in viscosity, and finally sets as an amorphous ground-mass or
+matrix, in which crystals of different kinds and sizes, formed at
+different stages of the cooling, remain embedded. The formation of
+crystals in an amorphous solid after it has set is also of frequent
+occurrence. It is termed devitrification, but is a very slow process
+unless the solid is in a plastic state.
+
+2. _Homogeneous Crystalline Fusion._--The fusion of a solid of this type
+is characterized most clearly by the perfect constancy of temperature
+during the process. In fact, the law of constant temperature, which is
+generally stated as the first of the so-called "laws of fusion," does
+not strictly apply except to this case. The constancy of the F.P. of a
+pure substance is so characteristic that change of the F.P. is often one
+of the most convenient tests of the presence of foreign material. In the
+case of substances like ice, which melt at a low temperature and are
+easily obtained in large quantities in a state of purity, the point of
+fusion may be very accurately determined by observing the temperature of
+an intimate mixture of the solid and liquid while slowly melting as it
+absorbs heat from surrounding bodies. But in the majority of cases it is
+more convenient to observe the freezing point as the liquid is cooled.
+By this method it is possible to ensure perfect uniformity of
+temperature throughout the mass by stirring the liquid continuously
+during the process of freezing, whereas it is difficult to ensure
+uniformity of temperature in melting a solid, however gradually the heat
+is supplied, unless the solid can be mixed with the liquid. It is also
+possible to observe the F.P. in other ways, as by noting the temperature
+at the moment of the breaking of a wire, of the stoppage of a stirrer,
+or of the maximum rate of change of volume, but these methods are
+generally less certain in their indications than the point of greatest
+constancy of temperature in the case of homogeneous crystalline solids.
+
+  _Fusing Points of Common Metals_
+
+  Mercury     -38.8 deg.     Antimony     630 deg.
+  Potassium    62.5 deg.     Aluminium    655 deg.
+  Sodium       95.6 deg.     Silver       962 deg.
+  Tin         231.9 deg.     Gold        1064 deg.
+  Bismuth     269.2 deg.     Copper      1082 deg.
+  Cadmium     320.7 deg.     Nickel      1427 deg.
+  Lead        327.7 deg.     Palladium   1535 deg.
+  Zinc        419.0 deg.     Platinum    1710 deg.
+
+The above table contains some of the most recent values of fusing points
+of metals determined (except the first three and the last three) with
+platinum thermometers. The last three values are those obtained by
+extrapolation with platinum-rhodium and platinum-iridium couples. (See
+Harker, _Proc. Roy. Soc._ A 76, p. 235, 1905.) Some doubt has recently
+been raised with regard to the value for platinum, which is much lower
+than that previously accepted, namely 1775 deg.
+
+3. _Superfusion, Supersaturation._--It is generally possible to cool a
+liquid several degrees below its normal freezing point without a
+separation of crystals, especially if it is protected from agitation,
+which would assist the molecules to rearrange themselves. A liquid in
+this state is said to be "undercooled" or "superfused." The phenomenon
+is even more familiar in the case of solutions (e.g. sodium sulphate or
+acetate) which may remain in the "metastable" condition for an
+indefinite time if protected from dust, &c. The introduction into the
+liquid under this condition of the smallest fragment of the crystal,
+with respect to which the solution is supersaturated, will produce
+immediate crystallization, which will continue until the temperature is
+raised to the saturation point by the liberation of the latent heat of
+fusion. The constancy of temperature at the normal freezing point is due
+to the equilibrium of exchange existing between the liquid and solid.
+Unless both solid and liquid are present, there is no condition of
+equilibrium, and the temperature is indeterminate.
+
+It has been shown by H.A. Miers (_Jour. Chem. Soc._, 1906, 89, p. 413)
+that for a supersaturated solution in metastable equilibrium there is an
+inferior limit of temperature, at which it passes into the "labile"
+state, i.e. spontaneous crystallization occurs throughout the mass in a
+fine shower. This seems to be analogous to the fine misty condensation
+which occurs in a supersaturated vapour in the absence of nuclei (see
+VAPORIZATION) when the supersaturation exceeds a certain limit.
+
+  4. _Effect of Pressure on the F.P._--The effect of pressure on the
+  fusing-point depends on the change of volume during fusion. Substances
+  which expand on _freezing_, like ice, have their freezing points
+  lowered by increase of pressure; substances which expand on _fusing_,
+  like wax, have their melting points raised by pressure. In each case
+  the effect of pressure is to retard increase of volume. This effect
+  was first predicted by James Thomson on the analogy of the effect of
+  pressure on the boiling point, and was numerically verified by Lord
+  Kelvin in the case of ice, and later by Bunsen in the case of paraffin
+  and spermaceti. The equation by which the change of the F.P. is
+  calculated may be proved by a simple application of the Carnot cycle,
+  exactly as in the case of vapour and liquid. (See THERMODYNAMICS.) If
+  L be the latent heat of fusion in mechanical units, v' the volume of
+  unit mass of the solid, and v" that of the liquid, the work done in
+  an elementary Carnot cycle of range d[theta] will be dp(v"- v'), if
+  dp is the increase of pressure required to produce a change d[theta]
+  in the F.P. Since the ratio of the work-difference or cycle-area to
+  the heat-transferred L must be equal to d[theta]/[theta], we have the
+  relation
+
+    d[theta]/dp = [theta](v" - v')/L.   (1)
+
+  The sign of d[theta], the change of the F.P., is the same as that of
+  the change of volume (v" - v'). Since the change of volume seldom
+  exceeds 0.1 c.c. per gramme, the change of the F.P. per atmosphere is
+  so small that it is not as a rule necessary to take account of
+  variations of atmospheric pressure in observing a freezing point. A
+  variation of 1 cm. in the height of the barometer would correspond to
+  a change of .0001 deg. C. only in the F.P. of ice. This is far beyond
+  the limits of accuracy of most observations. Although the effect of
+  pressure is so small, it produces, as is well known, remarkable
+  results in the motion of glaciers, the moulding and regelation of ice,
+  and many other phenomena. It has also been employed to explain the
+  apparent inversion of the order of crystallization in rocks like
+  granite, in which the arrangement of the crystals indicates that the
+  quartz matrix solidified subsequently to the crystals of felspar,
+  mica or hornblende embedded in it, although the quartz has a higher
+  melting point. It is contended that under enormous pressure the
+  freezing points of the more fusible constituents might be raised above
+  that of the quartz, if the latter is less affected by pressure. Thus
+  Bunsen found the F.P. of paraffin wax 1.4 deg. C. below that of
+  spermaceti at atmospheric pressure. At 100 atmospheres the two melted
+  at the same temperature. At higher pressures the paraffin would
+  solidify first. The effect of pressure on the silicates, however, is
+  much smaller, and it is not so easy to explain a change of several
+  hundred degrees in the F.P. It seems more likely in this particular
+  case that the order of crystallization depends on the action of
+  superheated water or steam at high temperatures and pressures, which
+  is well known to exert a highly solvent and metamorphic action on
+  silicates.
+
+  5. _Variation of Latent Heat._--C.C. Person in 1847 endeavoured to
+  show by the application of the first law of thermodynamics that the
+  increase of the latent heat per degree should be equal to the
+  difference (s"- s') between the specific heats of the liquid and
+  solid. If, for instance, water at 0 deg. C. were first frozen and then
+  cooled to -t deg. C., the heat abstracted per gramme would be (L'+
+  s't) calories. But if the water were first cooled to -t deg. C., and
+  then frozen at -t deg.C., by abstracting heat L", the heat abstracted
+  would be L" + s"t. Assuming that the heat abstracted should be the
+  same in the two cases, we evidently obtain L'- L" = (s"- s')t. This
+  theory has been approximately verified by Petterson, by observing the
+  freezing of a liquid cooled below its normal F.P. (_Jour. Chem. Soc._
+  24, p. 151). But his method does not represent the true variation of
+  the latent heat with temperature, since the freezing, in the case of a
+  superfused liquid, really takes place at the normal freezing point. A
+  quantity of heat s"t is abstracted in cooling to -t, (L"- s"t) in
+  raising to 0 deg. and freezing at 0 deg., and s't in cooling the ice
+  to -t. The latent heat L" at -t does not really enter into the
+  experiment. In order to make the liquid freeze at a different
+  temperature, it is necessary to subject it to pressure, and the effect
+  of the pressure on the latent heat cannot be neglected. The entropy of
+  a liquid [phi]" at its F.P. reckoned from any convenient zero [phi]0
+  in the solid state may be represented by the expression
+
+                       _
+                      /
+   [phi]" - [phi]0 =  | s'd[theta] / [theta] + L / [theta].  (2)
+                     _/
+
+  Since [theta]d[phi]"/d[theta] = s", we obtain by differentiation the
+  relation
+
+    dL / d[theta] = s"- s' + L / [theta],   (3)
+
+  which is exactly similar to the equation for the specific heat of a
+  vapour maintained in the saturated condition. If we suppose that the
+  specific heats s' and s'' of the solid and liquid at equilibrium
+  pressure are nearly the same as those ordinarily observed at constant
+  pressure, the relation (3) differs from that of Person only by the
+  addition of the term L/[theta]. Since s" is greater than s' in all
+  cases hitherto investigated, and L/[theta] is necessarily positive, it
+  is clear that the latent heat of fusion must increase with rise of
+  temperature, or diminish with fall of temperature. It is possible to
+  imagine the F.P. so lowered by pressure (positive or negative) that
+  the latent heat should vanish, in which case we should probably obtain
+  a continuous passage from the liquid to the solid state similar to
+  that which occurs in the case of amorphous substances. According to
+  equation (3), the rate of change of the latent heat of water is
+  approximately 0.80 calorie per degree at 0 deg. C. (as compared with
+  0.50, Person), if we assume s" = 1, and s' = 0.5. Putting (s" - s') =
+  0.5 in equation (2), we find L = 0 at -160 deg. C. approximately, but
+  no stress can be laid on this estimate, as the variation of (s" - s')
+  is so uncertain.
+
+6. _Freezing of Solutions and Alloys._--The phenomena of freezing of
+heterogeneous crystalline mixtures may be illustrated by the case of
+aqueous solutions and of metallic solutions or alloys, which have been
+most widely studied. The usual effect of an impurity, such as salt or
+sugar in solution in water, is to lower the freezing point, so that no
+crystallization occurs until the temperature has fallen below the normal
+F.P. of the pure solvent, the depression of F.P. being nearly
+proportional to the concentration of the solution. When freezing begins,
+the solvent generally separates out from the solution in the pure state.
+This separation of the solvent involves an increase in the strength of
+the remaining solution, so that the temperature does not remain constant
+during the freezing, but continues to fall as more of the solvent is
+separated. There is a perfectly definite relation between temperature
+and concentration at each stage of the process, which may be represented
+in the form of a curve as AC in fig. 1, called the freezing point curve.
+The equilibrium temperature, at the surface of contact between the solid
+and liquid, depends only on the composition of the liquid phase and not
+at all on the quantity of solid present. The abscissa of the F.P. curve
+represents the composition of that portion of the original solution
+which remains liquid at any temperature. If instead of starting with a
+dilute solution we start with a strong solution represented by a point
+N, and cool it as shown by the vertical line ND, a point D is generally
+reached at which the solution becomes "saturated." The dissolved
+substance or "solute" then separates out as the solution is further
+cooled, and the concentration diminishes with fall of temperature in a
+definite relation, as indicated by the curve CB, which is called the
+solubility curve. Though often called by different names, the two curves
+AC and CB are essentially of a similar nature. To take the case of an
+aqueous solution of salt as an example, along CB the solution is
+saturated with respect to salt, along AC the solution is saturated with
+respect to ice. When the point C is reached along either curve, the
+solution is saturated with respect to both salt and ice. The
+concentration cannot vary further, and the temperature remains constant,
+while the salt and ice crystallize out together, maintaining the exact
+proportions in which they exist in the solution. The resulting solid was
+termed a cryohydrate by F. Guthrie, but it is really an intimate mixture
+of two kinds of crystals, and not a chemical compound or hydrate
+containing the constituents in chemically equivalent proportions. The
+lowest temperature attainable by means of a freezing mixture is the
+temperature of the F.P. of the corresponding cryohydrate. In a mixture
+of salt and ice with the least trace of water a saturated brine is
+quickly formed, which dissolves the ice and falls rapidly in
+temperature, owing to the absorption of the latent heat of fusion. So
+long as both ice and salt are present, if the mixture is well stirred,
+the solution must necessarily become saturated with respect to both ice
+and salt, and this can only occur at the cryohydric temperature, at
+which the two curves of solubility intersect.
+
+[Illustration: FIG. 1.--F.P. or Solubility Curve: simple case.]
+
+The curves in fig. 1 also illustrate the simplest type of freezing point
+curve in the case of alloys of two metals A and B which do not form
+mixed crystals or chemical compounds. The alloy corresponding to the
+cryohydrate, possessing the lowest melting point, is called the eutectic
+alloy, as it is most easily cast and worked. It generally possesses a
+very fine-grained structure, and is not a chemical compound. (See
+ALLOYS.)
+
+[Illustration: FIG. 2.--Cooling Curves of Alloys: typical case.]
+
+To obtain a complete F.P. curve even for a binary alloy is a laborious
+and complicated process, but the information contained in such a curve
+is often very valuable. It is necessary to operate with a number of
+different alloys of suitably chosen composition, and to observe the
+freezing points of each separately. Each alloy should also be analysed
+after the process if there is any risk of its composition having been
+altered by oxidation or otherwise. The freezing points are generally
+best determined by observing the gradual cooling of a considerable mass,
+which is well stirred so long as it remains liquid. The curve of cooling
+may most conveniently be recorded, either photographically, using a
+thermocouple and galvanometer, as in the method of Sir W.
+Roberts-Austen, or with pen and ink, if a platinum thermometer is
+available, according to the method put in practice by C.T. Heycock and
+F.H. Neville. A typical set of curves obtained in this manner is shown
+in fig. 2. When the pure metal A in cooling reaches its F.P. the
+temperature suddenly becomes stationary, and remains accurately constant
+for a considerable period. Often it falls slightly below the F.P. owing
+to super-fusion, but rises to the F.P. and remains constant as soon as
+freezing begins. The second curve shows the cooling of A with 10% of
+another metal B added. The freezing begins at a lower temperature with
+the separation of pure A. The temperature no longer remains constant
+during freezing, but falls more and more rapidly as the proportion of B
+in the liquid increases. When the eutectic temperature is reached there
+is a second F.P. or arrest at which the whole of the remaining liquid
+solidifies. With 20% of B the first F.P. is further lowered, and the
+temperature falls faster. The eutectic F.P. is of longer duration, but
+still at the same temperature. For an alloy of the composition of the
+eutectic itself there is no arrest until the eutectic temperature is
+reached, at which the whole solidifies without change of temperature.
+There is a great advantage in recording these curves automatically, as
+the primary arrest is often very slight, and difficult to observe in any
+other way.
+
+  7. _Change of Solubility with Temperature._--The lowering of the F.P.
+  of a solution with increase of concentration, as shown by the F.P. or
+  solubility curves, may be explained and calculated by equation (1) in
+  terms of the osmotic pressure of the dissolved substance by analogy
+  with the effect of mechanical pressure. It is possible in salt
+  solutions to strain out the salt mechanically by a suitable filter or
+  "semi-permeable membrane," which permits the water to pass, but
+  retains the salt. To separate 1 gramme of salt requires the
+  performance of work PV against the osmotic pressure P, where V is the
+  corresponding diminution in the volume of the solution. In dilute
+  solutions, to which alone the following calculation can be applied,
+  the volume V is the reciprocal of the concentration C of the solution
+  in grammes per unit volume, and the osmotic pressure P is equal to
+  that of an equal number of molecules of gas in the same space, and may
+  be deduced from the usual equation of a gas,
+
+    P = R[theta] / VM = R[theta]C / M,   (4)
+
+  where M is the molecular weight of the salt in solution, [theta] the
+  absolute temperature, and R a constant which has the value 8.32
+  joules, or nearly 2 calories, per degree C. It is necessary to
+  consider two cases, corresponding to the curves CB and AB in fig. 1,
+  in which the solution is saturated with respect to salt and water
+  respectively. To facilitate description we take the case of a salt
+  dissolved in water, but similar results apply to solutions in other
+  liquids and alloys of metals.
+
+  (a) If unit mass of salt is separated in the solid state from a
+  saturated solution of salt (curve CB) by forcing out through a
+  semi-permeable membrane against the osmotic pressure P the
+  corresponding volume of water V in which it is dissolved, the heat
+  evolved is the latent heat of saturated solution of the salt Q
+  together with the work done PV. Writing (Q + PV) for L, and V for (v"
+  - v') in equation (1), and substituting P for p, we obtain
+
+    Q + PV = V[theta]dP / d[theta],   (5)
+
+  which is equivalent to equation (1), and may be established by similar
+  reasoning. Substituting for P and V in terms of C from equation (4),
+  if Q is measured in calories, R = 2, and we obtain
+
+    QC = 2[theta]^2dC / d[theta],   (6)
+
+  which may be integrated, assuming Q constant, with the result
+
+    2log_eC" / C' = Q / [theta]' - Q / [theta]",   (7)
+
+  where C', C" are the concentrations of the saturated solution
+  corresponding to the temperatures [theta]' and [theta]". This
+  equation may be employed to calculate the latent heat of solution Q
+  from two observations of the solubility. It follows from these
+  equations that Q is of the same sign as dC/d[theta], that is to say,
+  the solubility increases with rise of temperature if heat is absorbed
+  in the formation of the saturated solution, which is the usual case.
+  If, on the other hand, heat is liberated on solution, as in the case
+  of caustic potash or sulphate of calcium, the solubility diminishes
+  with rise of temperature.
+
+  (b) In the case of a solution saturated with respect to ice (curve
+  AC), if one gramme of water having a volume v is separated by
+  freezing, we obtain a precisely similar equation to (5), but with L
+  the latent heat of fusion of water instead of Q, and v instead of V.
+  If the solution is dilute, we may neglect the external work Pv in
+  comparison with L, and also the heat of dilution, and may write P/t
+  for dP/d[theta], where t is the depression of the F.P. below that of
+  the pure solvent. Substituting for P in terms of V from equation (4),
+  we obtain
+
+    t = 2[theta]^2v / LVM = 2[theta]^2w / LWM,   (8)
+
+  where W is the weight of water and w that of salt in a given volume of
+  solution. If M grammes of salt are dissolved in 100 of water, w = M
+  and W = 100. The depression of the F.P. in this case is called by van
+  't Hoff the "Molecular Depression of the F.P." and is given by the
+  simple formula
+
+    t = .02[theta]^2 / L.   (9)
+
+  Equation (8) may be used to calculate L or M, if either is known, from
+  observations of t, [theta] and w/W. The results obtained are
+  sufficiently approximate to be of use in many cases in spite of the
+  rather liberal assumptions and approximations effected in the course
+  of the reasoning. In any case the equations give a simple theoretical
+  basis with which to compare experimental data in order to estimate the
+  order of error involved in the assumptions. We may thus estimate the
+  variation of the osmotic pressure from the value given by the gaseous
+  equation, as the concentration of the solution or the molecular
+  dissociation changes. The most uncertain factor in the formula is the
+  molecular weight M, since the molecule in solution may be quite
+  different from that denoted by the chemical formula of the solid. In
+  many cases the molecule of a metal in dilute solution in another metal
+  is either monatomic, or forms a compound molecule with the solvent
+  containing one atom of the dissolved metal, in which case the
+  molecular depression is given by putting the atomic weight for M. In
+  other cases, as Cu, Hg, Zn, in solution in cadmium, the depression of
+  the F.P. per atom, according to Heycock and Neville, is only half as
+  great, which would imply a diatomic molecule. Similarly As and Au in
+  Cd appear to be triatomic, and Sn in Pb tetratomic. Intermediate cases
+  may occur in which different molecules exist together in equilibrium
+  in proportions which vary according to the temperature and
+  concentration. The most familiar case is that of an electrolyte, in
+  which the molecule of the dissolved substance is partly dissociated
+  into ions. In such cases the degree of dissociation may be estimated
+  by observing the depression of the F.P., but the results obtained
+  cannot always be reconciled with those deduced by other methods, such
+  as measurement of electrical conductivity, and there are many
+  difficulties which await satisfactory interpretation.
+
+  Exactly similar relations to (8) and (9) apply to changes of boiling
+  point or vapour pressure produced by substances in solution (see
+  VAPORIZATION), the laws of which are very closely connected with the
+  corresponding phenomena of fusion; but the consideration of the vapour
+  phase may generally be omitted in dealing with the fusion of mixtures
+  where the vapour pressure of either constituent is small.
+
+[Illustration: FIG. 3.--Solubility Curves of Hydrates.]
+
+8. _Hydrates._--The simple case of a freezing point curve, illustrated
+in fig. 1, is generally modified by the occurrence of compounds of a
+character analogous to hydrates of soluble salts, in which the dissolved
+substance combines with one or more molecules of the solvent. These
+hydrates may exist as compound molecules in the solution, but their
+composition cannot be demonstrated unless they can be separated in the
+solid state. Corresponding to each crystalline hydrate there is
+generally a separate branch of the solubility curve along which the
+crystals of the hydrate are in equilibrium with the saturated solution.
+At any given temperature the hydrate possessing the least solubility is
+the most stable. If two are present in contact with the same solution,
+the more soluble will dissolve, and the less soluble will be formed at
+its expense until the conversion is complete. The two hydrates cannot be
+in equilibrium with the same solution except at the temperature at which
+their solubilities are equal, i.e. at the point where the corresponding
+curves of solubility intersect. This temperature is called the
+"Transition Point." In the case of ZnSO4, as shown in fig. 3, the
+heptahydrate, with seven molecules of water, is the least soluble
+hydrate at ordinary temperatures, and is generally deposited from
+saturated solutions. Above 39 deg. C., however, the hexahydrate, with six
+molecules, is less soluble, and a rapid conversion of the hepta- into
+the hexahydrate occurs if the former is heated above the transition
+point. The solubility of the hexahydrate is greater than that of the
+heptahydrate below 39 deg., but increases more slowly with rise of
+temperature. At about 80 deg. C. the hexahydrate gives place to the
+monohydrate, which dissolves in water with evolution of heat, and
+diminishes in solubility with rise of temperature. Intermediate hydrates
+exist, but they are more soluble, and cannot be readily isolated. Both
+the mono- and hexahydrates are capable of existing in equilibrium with
+saturated solutions at temperatures far below their transition points,
+provided that the less soluble hydrate is not present in the crystalline
+form. The solubility curves can therefore be traced, as in fig. 3, over
+an extended range of temperature. The equilibrium of each hydrate with
+the solvent, considered separately, would present a diagram of two
+branches similar to fig. 1, but as a rule only a small portion of each
+curve can be realized, and the complete solubility curve, as
+experimentally determined, is composed of a number of separate pieces
+corresponding to the ranges of minimum solubility of different hydrates.
+Failure to recognize this, coupled with the fact that in strong and
+viscous solutions the state of equilibrium is but slowly attained, is
+the probable explanation of the remarkable discrepancies existing in
+many recorded data of solubility.
+
+  _Transition Points of Hydrates._
+
+  Na2CrO4.10H2O   19.9 deg.     NaBr.2H20      50.7 deg.
+  Na2SO4.10H2O    32.4 deg.     MnCl2.4H2O     57.8 deg.
+  Na2CO3.10H2O    35.1 deg.     Na3PO4.12H2O   73.4 deg.
+  Na2S2O3.5H2O    48.0 deg.     Ba(OH)2.8H2O   77.9 deg.
+
+The transition points of the hydrates given in the above list (Richards,
+_Proc. Amer. Acad._, 1899, 34, p. 277) afford well-marked constant
+temperatures which can be utilized as fixed points for experimental
+purposes.
+
+9. _Formation of Mixed Crystals._--An important exception to the general
+type already described, in which the addition of a dissolved substance
+lowers the F.P. of the solvent, is presented by the formation of mixed
+crystals, or "solid solutions," in which the solvent and solute occur
+mixed in varying proportions. This isomorphous replacement of one
+substance by another, in the same crystal with little or no change of
+form, has long been known and studied in the case of minerals and salts,
+but the relations between composition and melting-point have seldom been
+investigated, and much still remains obscure. In this case the process
+of freezing does not necessitate the performance of work of separation
+of the constituents of the solution, the F.P. is not necessarily
+depressed, and the effect cannot be calculated by the usual formula for
+dilute solutions. One of the simplest types of F.P. curve which may
+result from the occurrence of mixed crystals is illustrated by the case
+of alloys of gold and silver, or gold and platinum, in which the F.P.
+curve is nearly a straight line joining the freezing-points of the
+constituents. The equilibrium between the solid and liquid, in both of
+which the two metals are capable of mixing in all proportions, bears in
+this case an obvious and close analogy to the equilibrium between a
+mixed liquid (e.g. alcohol and water) and its vapour. In the latter
+case, as is well known, the vapour will contain a larger proportion of
+the more volatile constituent. Similarly in the case of the formation of
+mixed crystals, the liquid should contain a larger proportion of the
+more fusible constituent than the solid with which it is in equilibrium.
+The composition of the crystals which are being deposited at any moment
+will, therefore, necessarily change as solidification proceeds,
+following the change in the composition of the liquid, and the
+temperature will fall until the last portions of the liquid to solidify
+will consist chiefly of the more fusible constituent, at the F.P. of
+which the solidification will be complete. If, however, as seems to be
+frequently the case, the composition of the solid and liquid phases do
+not greatly differ from each other, the greater part of the
+solidification will occur within a comparatively small range of
+temperature, and the initial F.P. of the alloy will be well marked. It
+is possible in this case to draw a second curve representing the
+composition of the _solid_ phase which is in equilibrium with the liquid
+at any temperature. This curve will not represent the average
+composition of the crystals, but that of the outer coating only which is
+in equilibrium with the liquid at the moment. H.W.B. Roozeboom (_Zeit.
+Phys. Chem._ xxx. p. 385) has attempted to classify some of the possible
+cases which may occur in the formation of mixed crystals on the basis of
+J.W. Gibbs's thermodynamic potential, the general properties of which
+may be qualitatively deduced from a consideration of observed phenomena.
+But although this method may enable us to classify different types, and
+even to predict results in a qualitative manner, it does not admit of
+numerical calculation similar to equation (8), as the Gibbs's function
+itself is of a purely abstract nature and its form is unknown. There is
+no doubt that the formation of mixed crystals may explain many apparent
+anomalies in the study of F.P. curves. The whole subject has been most
+fruitful of results in recent years, and appears full of promise for the
+future.
+
+  For further details in this particular branch the reader may consult a
+  report by Neville (_Brit. Assoc. Rep._, 1900), which contains numerous
+  references to original papers by Roberts-Austen, Le Chatelier,
+  Roozeboom and others. For the properties of solutions see SOLUTION.
+       (H. L. C.)
+
+
+
+
+
+FUSSEN, a town of Germany, in the kingdom of Bavaria, at the foot of the
+Alps (Tirol), on the Lech, 2500 ft. above the sea, with a branch line to
+Oberdorf on the railway to Augsburg. Pop. 4000. It has six Roman
+Catholic churches, a Franciscan monastery and a castle. Rope-making is
+an important industry. The castle, lying on a rocky eminence, is
+remarkable for the peace signed here on the 22nd of April 1745 between
+the elector Maximilian III., Joseph of Bavaria and Maria Theresa. Two
+miles to the S.E., immediately on the Austrian frontier, romantically
+situated on a rock overlooking the Schwanensee, is the magnificent
+castle of Hohenschwangau, and a little to the north, on the site of an
+old castle, that of Neuschwanstein, built by Louis II. of Bavaria.
+
+  See H. Feistle, _Fussen und Umgebung_ (1898).
+
+
+
+
+FUST, JOHANN (   ?-1466), early German printer, belonged to a rich and
+respectable burgher family of Mainz, which is known to have flourished
+from 1423, and to have held many civil and religious offices. The name
+was always written Fust, but in 1506 Johann Schoffer, in dedicating the
+German translation of Livy to the emperor Maximilian, called his
+grandfather Faust, and thenceforward the family assumed this name, and
+the Fausts of Aschaffenburg, an old and quite distinct family, placed
+Johann Fust in their pedigree. Johann's brother Jacob, a goldsmith, was
+one of the burgomasters in 1462, when Mainz was stormed and sacked by
+the troops of Count Adolf of Nassau, on which occasion he seems to have
+perished (see a document, dated May 8, 1463, published by Wyss in
+_Quartalbl. des hist. Vereins fur Hessen_, 1879, p. 24). There is no
+evidence that, as is commonly asserted, Johann Fust was a goldsmith, but
+he appears to have been a money-lender or banker. On account of his
+connexion with Gutenberg (q.v.), he has been represented by some as the
+inventor of printing, and the instructor as well as the partner of
+Gutenberg, by others as his patron and benefactor, who saw the value of
+his discovery and supplied him with means to carry it out, whereas
+others paint him as a greedy and crafty speculator, who took advantage
+of Gutenberg's necessity and robbed him of the fruits of his invention.
+However this may be, the Helmasperger document of November 6, 1455,
+shows that Fust advanced money to Gutenberg (apparently 800 guilders in
+1450, and another 800 in 1452) for carrying on his work, and that Fust,
+in 1455, brought a suit against Gutenberg to recover the money he had
+lent, claiming 2020 (more correctly 2026) guilders for principal and
+interest. It appears that he had not paid in the 300 guilders a year
+which he had undertaken to furnish for expenses, wages, &c., and,
+according to Gutenberg, had said that he had no intention of claiming
+interest. The suit was apparently decided in Fust's favour, November 6,
+1455, in the refectory of the Barefooted Friars of Mainz, when Fust made
+oath that he himself had borrowed 1550 guilders and given them to
+Gutenberg. There is no evidence that Fust, as is usually supposed,
+removed the portion of the printing materials covered by his mortgage to
+his own house, and carried on printing there with the aid of Peter
+Schoffer, of Gernsheim (who is known to have been a scriptor at Paris in
+1449), to whom, probably about 1455,[1] he gave his only daughter Dyna
+or Christina in marriage. Their first publication was the Psalter,
+August 14, 1457, a folio of 350 pages, the first printed book with a
+complete date, and remarkable for the beauty of the large initials
+printed each in two colours, red and blue, from types made in two
+pieces.[2] The Psalter was reprinted with the same types, 1459 (August
+29), 1490, 1502 (Schoffer's last publication) and 1516. Fust and
+Schoffer's other works are given below.[3] In 1464 Adolf of Nassau
+appointed for the parish of St Quintin three _Baumeisters_
+(master-builders) who were to choose twelve chief parishioners as
+assistants for life. One of the first of these "Vervaren," who were
+named on May-day 1464, was Johannes Fust, and in 1467 Adam von Hochheim
+was chosen instead of "the late" (_selig_) Johannes Fust. Fust is said
+to have gone to Paris in 1466 and to have died of the plague, which
+raged there in August and September. He certainly was in Paris on the
+4th of July, when he gave Louis de Lavernade of the province of Forez,
+then chancellor of the duke of Bourbon and first president of the
+parliament of Toulouse, a copy of his second edition of Cicero, as
+appears from a note in Lavernade's own hand at the end of the book,
+which is now in the library of Geneva. But nothing further is known than
+that on the 30th of October, probably in 1471, an annual mass was
+instituted for him by Peter Schoffer, Conrad Henlif (for Henekes, or
+Henckis, Schoffer's partner? who married Fust's widow about 1468[4]) and
+Johann Fust (the son), in the abbey-church of St Victor of Paris, where
+he was buried; and that Peter Schoffer founded a similar memorial
+service for Fust in 1473 in the church of the Dominicans at Mainz
+(Bockenheimer, _Gesch. der Stadt Mainz_, iv. 15).
+
+Fust was formerly often confused with the famous magician Dr Johann
+Faust, who, though an historical figure, had nothing to do with him (see
+FAUST).
+
+  See further the articles GUTENBERG and TYPOGRAPHY.     (J. H. H.)
+
+
+FOOTNOTES:
+
+  [1] This date is uncertain; some place the marriage in 1453 or soon
+    after, others about 1464. It is probable that Fust alluded to this
+    relationship when he spoke of Schoffer as _pueri mei_ in the
+    colophons of Cicero's _De officiis_ of 1465 and 1466.
+
+  [2] This method was patented in England by Solomon Henry in 1780, and
+    by Sir William Congreve in 1819.
+
+  [3] (3) Durandus, _Rationale divinorum officiorum_ (1459), folio, 160
+    leaves; (4) the _Clementine Constitutions_, with the gloss of
+    Johannes Andreae (1460), 51 leaves; (5) _Biblia Sacra Latina_ (1462),
+    folio, 2 vols., 242 and 239 leaves, 48 lines to a full page; (6) the
+    Sixth Book of Decretals, with Andreae's gloss, 17th December 1465,
+    folio, 141 leaves; (7) Cicero, _De officiis_ (1465). 4to, 88 leaves,
+    the first edition of a Latin classic and the first book containing
+    Greek characters, while in the colophon Fust for the first time calls
+    Schoffer "puerum suum"; (8) the same, 4th February 1466; (9)
+    _Grammatica rhytmica_ (1466), folio, 11 leaves. They also printed in
+    1461-1462 several papal bulls, proclamations of Adolf of Nassau, &c.
+    Nothing is known to have appeared for three years after the storming
+    and capture of Mainz in 1462.
+
+  [4] Some confusion in the history of the Fust family has arisen since
+    the publication of Bernard's _Orig. de l'imprimerie_ (1853). On p.
+    262, vol. i. he gave an extract from the correspondence between
+    Oberlin and Bodmann (now preserved in the Paris Nat. Library), from
+    which it would appear that Peter Schoffer was the son-in-law, not of
+    Johann Fust, but of a brother of his, Conrad Fust. Of the latter,
+    however, no other trace has been found, and he is no doubt a fiction
+    of F.J. Bodmann, who, partly basing himself on the "Conrad" (Henlif,
+    or Henckis) mentioned above, added the rest to gratify Oberlin (see
+    Wyss in _Quartalblatter des hist. Vereins fur Hessen_, 1879, p. 17).
+
+
+
+
+FUSTEL DE COULANGES, NUMA DENIS (1830-1889), French historian, was born
+in Paris on the 18th of March 1830, of Breton descent. After studying at
+the Ecole Normale Superieure he was sent to the French school at Athens
+in 1853, directed some excavations in Chios, and wrote an historical
+account of the island. After his return he filled various educational
+offices, and took his doctor's degree with two theses, _Quid Vestae
+cultus in institutis veterum privatis publicisque valuerit_ and _Polybe,
+ou la Grece conquise par les Romains_ (1858). In these works his
+distinctive qualities were already revealed. His minute knowledge of the
+language of the Greek and Roman institutions, coupled with his low
+estimate of the conclusions of contemporary scholars, led him to go
+direct to the original texts, which he read without political or
+religious bias. When, however, he had succeeded in extracting from the
+sources a general idea that seemed to him clear and simple, he attached
+himself to it as if to the truth itself, employing dialectic of the most
+penetrating, subtle and even paradoxical character in his deduction of
+the logical consequences. From 1860 to 1870 he was professor of history
+at the faculty of letters at Strassburg, where he had a brilliant career
+as a teacher, but never yielded to the influence exercised by the German
+universities in the field of classical and Germanic antiquities.
+
+It was at Strassburg that he published his remarkable volume _La Cite
+antique_ (1864), in which he showed forcibly the part played by religion
+in the political and social evolution of Greece and Rome. Although his
+making religion the sole factor of this evolution was a perversion of
+the historical facts, the book was so consistent throughout, so full of
+ingenious ideas, and written in so striking a style, that it ranks as
+one of the masterpieces of the French language in the 19th century. By
+this literary merit Fustel set little store, but he clung tenaciously to
+his theories. When he revised the book in 1875, his modifications were
+very slight, and it is conceivable that, had he recast it, as he often
+expressed the desire to do in the last years of his life, he would not
+have abandoned any part of his fundamental thesis. The work is now
+largely superseded.
+
+Fustel de Coulanges was the most conscientious of men, the most
+systematic and uncompromising of historians. Appointed to a lectureship
+at the Ecole Normale Superieure in February 1870, to a professorship at
+the Paris faculty of letters in 1875, and to the chair of medieval
+history created for him at the Sorbonne in 1878, he applied himself to
+the study of the political institutions of ancient France. The invasion
+of France by the German armies during the war of 1870-71 attracted his
+attention to the Germanic invasions under the Roman Empire. Pursuing the
+theory of J.B. Dubos, but singularly transforming it, he maintained that
+those invasions were not marked by the violent and destructive character
+usually attributed to them; that the penetration of the German
+barbarians into Gaul was a slow process; that the Germans submitted to
+the imperial administration; that the political institutions of the
+Merovingians had their origins in the Roman laws at least as much as, if
+not more than, in German usages; and, consequently, that there was no
+conquest of Gaul by the Germans. This thesis he sustained brilliantly in
+his _Histoire des institutions politiques de l'ancienne France_, the
+first volume of which appeared in 1874. It was the author's original
+intention to complete this work in four volumes, but as the first volume
+was keenly attacked in Germany as well as in France, Fustel was forced
+in self-defence to recast the book entirely. With admirable
+conscientiousness he re-examined all the texts and wrote a number of
+dissertations, of which, though several (e.g. those on the Germanic mark
+and on the _allodium_ and _beneficium_) were models of learning and
+sagacity, all were dominated by his general idea and characterized by a
+total disregard for the results of such historical disciplines as
+diplomatic. From this crucible issued an entirely new work, less well
+arranged than the original, but richer in facts and critical comments.
+The first volume was expanded into three volumes, _La Gaule romaine_
+(1891), _L'Invasion germanique et la fin de l'empire_ (1891) and _La
+Monarchie franque_ (1888), followed by three other volumes, _L'Alleu et
+le domaine rural pendant l'epoque merovingienne_ (1889), _Les Origines
+du systeme feodal: le benefice et le patronat ..._ (1890) and _Les
+Transformations de la royaute pendant l'epoque carolingienne_ (1892).
+Thus, in six volumes, he had carried the work no farther than the
+Carolingian period. The result of this enormous labour, albeit worthy of
+a great historian, clearly showed that the author lacked all sense of
+historical proportion. He was a diligent seeker after the truth, and was
+perfectly sincere when he informed a critic of the exact number of
+"truths" he had discovered, and when he remarked to one of his pupils a
+few days before his death, "Rest assured that what I have written in my
+book is the truth." Such superb self-confidence can accomplish much, and
+it undoubtedly helped to form Fustel's talent and to give to his style
+that admirable concision which subjugates even when it fails to
+convince; but a student instinctively distrusts an historian who settles
+the most controverted problems with such impassioned assurance. The
+dissertations not embodied in his great work were collected by himself
+and (after his death) by his pupil, Camille Jullian, and published as
+volumes of miscellanies: _Recherches sur quelques problemes d'histoire_
+(1885), dealing with the Roman colonate, the land system in Normandy,
+the Germanic mark, and the judiciary organization in the kingdom of the
+Franks; _Nouvelles recherches sur quelques problemes d'histoire_ (1891);
+and _Questions historiques_ (1893), which contains his paper on Chios
+and his thesis on Polybius.
+
+His life was devoted almost entirely to his teaching and his books. In
+1875 he was elected member of the Academie des Sciences Morales, and in
+1880 reluctantly accepted the post of director of the Ecole Normale.
+Without intervening personally in French politics, he took a keen
+interest in the questions of administration and social reorganization
+arising from the fall of the imperialist regime and the disasters of the
+war. He wished the institutions of the present to approximate more
+closely to those of the past, and devised for the new French
+constitution a body of reforms which reflected the opinions he had
+formed upon the democracy at Rome and in ancient France. But these were
+dreams which did not hold him long, and he would have been scandalized
+had he known that his name was subsequently used as the emblem of a
+political and religious party. He died at Massy (Seine-et-Oise) on the
+12th of September 1889. Throughout his historical career--at the Ecole
+Normale and the Sorbonne and in his lectures delivered to the empress
+Eugenie--his sole aim was to ascertain the truth, and in the defence of
+truth his polemics against what he imagined to be the blindness and
+insincerity of his critics sometimes assumed a character of harshness
+and injustice. But, in France at least, these critics were the first to
+render justice to his learning, his talents and his disinterestedness.
+
+  See Paul Guiraud, _Fustel de Coulanges_ (1896); H. d'Arbois de
+  Jubainville, _Deux Manieres d'ecrire l'histoire: critique de Bossuet,
+  d'Augustin Thierry et de Fustel de Coulanges_ (1896); and Gabriel
+  Monod, _Portraits et souvenirs_ (1897).     (C. B.*)
+
+
+
+
+FUSTIAN, a term which includes a variety of heavy woven cotton fabrics,
+chiefly prepared for men's wear. It embraces plain twilled cloth called
+jean, and cut fabrics similar to velvet, known as velveteen, moleskin,
+corduroy, &c. The term was once applied to a coarse cloth made of cotton
+and flax; now, fustians are usually of cotton and dyed various colours.
+In the reign of Edward III. the name was given to a woollen fabric. The
+name is said to be derived from El-Fustat, a suburb of Cairo, where it
+was first made; and certainly a kind of cloth has long been known under
+that name. In a petition to parliament, _temp._ Philip and Mary,
+"fustian of Naples" is mentioned. In the 13th and 14th centuries
+priests' robes and women's dresses were made of fustian, but though
+dresses are still made from some kinds the chief use is for labourers'
+clothes.
+
+
+
+
+FUSTIC (Fr. _fustoc_, from Arab. _fustuq_, Gr. [Greek: pistake],
+pistachio) YELLOW WOOD or OLD FUSTIC, a dye-stuff consisting of the wood
+of _Chlorophora tinctoria_, a large tree of the natural order Moraceae,
+growing in the West Indies and tropical America. Fustic occurs in
+commerce in blocks, which are brown without, and of a brownish-yellow
+within. It is sometimes employed for inlaid work. The dye-stuff termed
+young fustic or Zante fustic, and also Venetian sumach, is the wood of
+_Rhus cotinus_ (fustet, or smoke tree), a southern European and Asiatic
+shrub of the natural order Anacardiaceae, called by Gerarde "red
+sumach," and apparently the "coccygia" and "cotinus" of Pliny (_Nat.
+Hist._ xiii. 41, xvi. 30). Its colouring matter is fisetin, C15H10O6,
+which was synthesized by S. von Kostanecki (_Ber._, 1904, 37, p. 384).
+(See DYEING.)
+
+
+
+
+FUTURES, a term used in the produce markets for purchases or sales of
+commodities to be completed at a future date, as opposed to cash or
+"spot" transactions, which are settled immediately. See MARKET, and (for
+a detailed discussion of the question as affecting cotton) COTTON:
+_Marketing and Supply_.
+
+
+
+
+FUX, JOHANN JOSEPH (1660-1741), Austrian musician, was born at
+Hirtenfeld (Styria) in 1660. Of his youth and early training nothing is
+known. In 1696 he was organist at one of the principal churches of
+Vienna, and in 1698 was appointed by the emperor Leopold I. as his
+"imperial court-composer," with a salary of about L6 a month. At the
+court of Leopold and of his successors Joseph I. and Charles VI., Fux
+remained for the rest of his life. To his various court dignities that
+of organist at St Stephen's cathedral was added in 1704. He married the
+daughter of the government secretary Schnitzbaum. As a proof of the high
+favour in which he was held by the art-loving Charles VI., it is told
+that at the coronation of that emperor as king of Bohemia in 1723 an
+opera, _La Constanza e la Fortezza_, especially composed by Fux for the
+occasion, was given at Prague in an open-air theatre. Fux at the time
+was suffering from gout, but the emperor had him carried in a litter all
+the way from Vienna, and gave him a seat in the imperial box. Fux died
+at Vienna on the 13th of February 1741. His life, although passed in the
+great world, was eventless, and his only troubles arose from the
+intrigues of his Italian rivals at court. Of the numerous operas which
+Fux wrote it is unnecessary to speak. They do not essentially differ
+from the style of the Italian _opera seria_ of the time. Of greater
+importance are his sacred compositions, psalms, motets, oratorios and
+masses, the celebrated _Missa Canonica_ amongst the latter. It is an all
+but unparalleled _tour de force_ of learned musicianship, being written
+entirely in that most difficult of contrapuntal devices--the canon. As a
+contrapuntist and musical scholar generally, Fux was unsurpassed by any
+of his contemporaries, and his great theoretical work, the _Gradus ad
+Parnassum_, long remained by far the most thorough treatment of
+counterpoint and its various developments. The title of the original
+Latin edition is _Gradus ad Parnassum sive manuductio ad compositionem
+musicae regularem, methoda nova ac certa nondum ante tam exacta ordine
+in lucem edita, elaborata a Joanne Josepho Fux_ (Vienna, 1715). It was
+translated into most European languages during the 18th century, and is
+still studied by musicians interested in the history of their art. The
+expenses of the publication were defrayed by the emperor Charles VI.
+
+  Fux's biography was published by Ludwig von Kochel (Vienna, 1871). It
+  is based on minute original research and contains, amongst other
+  valuable materials, a complete catalogue of the composer's numerous
+  works.
+
+
+
+
+FUZE or FUSE, an appliance for firing explosives in blasting operations,
+military shells, &c. (see BLASTING and AMMUNITION, S SHELL). The
+spelling is not governed by authority, but modern convenience has
+dictated the adoption of the "z" by military engineers as a general
+rule, in order to distinguish this sense from that of melting by heat
+(see below). The word, according to the _New English Dictionary_, is one
+of the forms in which the Lat. _fusus_, spindle, has been adapted
+through Romanic into English, the ordinary fuze taking the shape of a
+spindle-like tube. Similarly the term "fusee" (Fr. _fusee_, spindle full
+of tow, Late Lat. _fusata_) is applied to a coned spindle sometimes used
+in the wheel train of watches and spring clocks to equalize the action
+of the mainspring (see WATCH); and the application of the same term to a
+special kind of match may also be due to its resemblance to a spindle.
+Again, in heraldry, another form, "fusil," derived through the French
+from a Late Lat. diminutive (_fusillus_ or _fusellus_) of this same
+_fusus_, is used of a bearing, an elongated lozenge. According to other
+etymological authorities, however (see Skeat, _Etym. Dict._, 1898),
+"fuze" or "fuse," and "fusee" in the sense of match, are all forms
+derived through the Fr. fusil, from Late Lat. _focile_, steel for
+striking fire from a flint, from Lat. _focus_, hearth. The Fr. _fusil_
+and English "fusil" were thus transferred to the "firelock," i.e. the
+light musket of the 17th century (see FUSILIER).
+
+In electrical engineering a "fuse" (always so spelled) is a safety
+device, commonly consisting of a strip or wire of easily fusible metal,
+which melts and thus interrupts the circuit of which it forms part,
+whenever that circuit, through some accident or derangement, is caused
+to carry a current larger than that for which it is intended. In this
+sense the word must be connected with _fusus_, the past participle of
+Lat. _fundere_, to pour, whence comes the verb "fuse," to melt by heat,
+often used figuratively in the sense of blend, mix.
+
+
+
+
+FYNE, LOCH, an inlet of the sea, Argyllshire, Scotland. From the head, 6
+m. above Inveraray, to the mouth on the Sound of Bute, it has a
+south-westerly and then southerly trend and is 44 m. long, its width
+varying from 1/4 m. to 6 m. It receives the Fyne, Shira, Aray and many
+other streams, and, on the western side, gives off Lochs Shira, Gair,
+Gilp (with Ardrishaig, the Crinan Canal and Lochgilphead) and East
+Tarbert (with Tarbert village). The glens debouching on the lake are
+Fyne, Shira, Aray, Kinglas and Hell's Glen. The coast generally is
+picturesque and in many parts well wooded. All vessels using the Crinan
+Canal navigate the loch to and from Ardrishaig, and there are daily
+excursions during the season, as far up as Inveraray. There are ferries
+at St Catherine's and Otter, and piers at Tarbert, Ardrishaig, Kilmory,
+Crarae, Furnace, Inveraray, Strachur and elsewhere. The industries
+comprise granite quarrying at Furnace and Crarae, distilling at
+Ardrishaig, gunpowder-making at Furnace and Kilfinan, and, above all,
+fishing. Haddock, whiting and codling are taken, and the famous "Loch
+Fyne herrings" command the highest price in the market.
+
+
+
+
+FYRD, the name given to the English army, or militia, during the
+Anglo-Saxon period (see ARMY, 60). It is first mentioned in the
+_Anglo-Saxon Chronicle_ under the date 605. The ealdorman, or sheriff,
+of the shire was probably charged with the duty of calling out and
+leading the fyrd, which appears always to have retained a local
+character, as during the time of the Danish invasions we read of the
+fyrd of Kent, of Somerset and of Devon. As attendance at the fyrd was
+included in the _trinoda necessitas_ it was compulsory on all holders of
+land; but that it was not confined to them is shown by the following
+extract from the laws of Ine, king of the West Saxons, dated about 690,
+which prescribes the penalty for the serious offence of neglecting the
+fyrd: "If a _gesithcund_ man owning land neglect the fyrd, let him pay
+120 shillings, and forfeit his land; one not owning land 60 shillings; a
+ceorlish man 30 shillings as _fyrdwite_." The fyrd was gradually
+superseded by the gathering of the thegns and their retainers, but it
+was occasionally called out for defensive purposes even after the Norman
+Conquest.
+
+
+
+
+FYT, JOHANNES (1609-1661), Belgian animal painter, was born at Antwerp
+and christened on the 19th of August 1609. He was registered apprentice
+to Hans van den Berghe in 1621. Professionally van den Berghe was a
+restorer of old pictures rather than a painter of new ones. At twenty
+Johannes Fyt entered the gild of St Luke as a master, and from that time
+till his death in 1661 he produced a vast number of pictures in which
+the bold facility of Snyders is united to the powerful effects of
+Rembrandt, and harmonies of gorgeous tone are not less conspicuous than
+freedom of touch and a true semblance of nature. There never was such a
+master of technical processes as Fyt in the rendering of animal life in
+its most varied forms. He may have been less correct in outline, less
+bold in action than Snyders, but he was much more skilful and more true
+in the reproduction of the coat of deer, dogs, greyhounds, hares and
+monkeys, whilst in realizing the plumage of peacocks, woodcocks, ducks,
+hawks, and cocks and hens, he had not his equal, nor was any artist even
+of the Dutch school more effective in relieving his compositions with
+accessories of tinted cloth, porcelain ware, vases and fruit. He was not
+clever at figures, and he sometimes trusted for these to the
+co-operation of Cornelius Schut or Willeborts, whilst his architectural
+backgrounds were sometimes executed by Quellyn. "Silenus amongst Fruit
+and Flowers," in the Harrach collection at Vienna, "Diana and her Nymphs
+with the Produce of the Chase," in the Belvedere at Vienna, and "Dead
+Game and Fruit in front of a Triumphal Arch," belonging to Baron von
+Rothschild at Vienna, are specimens of the co-operation respectively of
+Schut, Willeborts and Quellyn. They are also Fyt's masterpieces. The
+earliest dated work of the master is a cat grabbing at a piece of dead
+poultry near a hare and birds, belonging to Baron Cetto at Munich, and
+executed in 1644. The latest is a "Dead Snipe with Ducks," of 1660,
+sold with the Jager collection at Cologne in 1871. Great power is shown
+in the bear and boar hunts at Munich and Ravensworth castle. A "Hunted
+Roedeer with Dogs in the Water," in the Berlin Museum, has some of the
+life and more of the roughness of Snyders, but lacks variety of tint and
+finish. A splendid specimen is the Page and Parrot near a table covered
+with game, guarded by a dog staring at a monkey, in the Wallace
+collection. With the needle and the brush Fyt was equally clever. He
+etched 16 plates, and those representing dogs are of their kind unique.
+
+
+
+
+FYZABAD, or FAIZABAD, a city, district and division of British India in
+the United Provinces. The city stands on the left bank of the river
+Gogra, 78 m. by rail E. of Lucknow. Pop. (1901) 75,085. To the E. of
+Fyzabad, and now forming a suburb, is the ancient site of Ajodhya
+(q.v.). Fyzabad was founded about 1730 by Sa'adat Ali Khan, the first
+nawab wazir of Oudh, who built a hunting-lodge here. It received its
+present name in the reign of his successor; and Shuja-ud-daula, the
+third nawab, laid out a large town and fortified it, and here he was
+buried. It was afterwards the residence of the Begums of Oudh, famous in
+connexion with the impeachment of Warren Hastings. When the court of
+Oudh was removed to Lucknow in 1775 all the leading merchants and
+bankers abandoned the place. At the census of 1869 Fyzabad contained
+only 37,804 inhabitants; but it is now again advancing in prosperity and
+population. On the outbreak of the Mutiny in 1857, the cantonment
+contained two regiments of infantry, a squadron of cavalry, and a light
+field battery of artillery--all natives. Owing to their threatening
+demeanour after the Meerut massacre, many of the European women and
+children were sheltered by one of the great landholders of Oudh, and
+others were sent to less disturbed parts of the country. The troops
+rose, as was anticipated, and although they at first permitted their
+officers to take boats and proceed towards Dinapur, a message was
+afterwards sent to a rebel force lower down the river to intercept the
+fugitives. Of four boats, one, having passed the rebels unnoticed,
+succeeded in reaching Dinapur safely. Of those in the other three boats,
+one alone escaped. Fyzabad is now a station for European as well as for
+native troops. It is the headquarters of a brigade in the 8th division
+of the northern army. There is a government college. Sugar-refining and
+trade in agricultural produce are important.
+
+THE DISTRICT OF FYZABAD, lying between the two great rivers Gogra and
+Gumti, has an area of 1740 sq. m. It is entirely alluvial and well
+wooded, and has a good climate. Pop. (1901) 1,225,374, an increase of
+.7% in the decade. The district is traversed throughout its length by
+the Oudh and Rohilkhand railway from Lucknow to Benares, with a branch
+to Allahabad. Tanda, with a population in 1901 of 19,853, has the
+largest production of cotton goods in Oudh.
+
+The DIVISION OF FYZABAD has an area of 12,113 sq. m., and comprises the
+six districts of Fyzabad, Gonda, Bahraich, Sultanpur, Partabgarh and
+Bara Banki. Pop. (1901) 6,855,991, an increase of 2% in the decade.
+
+
+
+
+
+
+End of the Project Gutenberg EBook of Encyclopaedia Britannica, 11th
+Edition, Volume 11, Slice 3, by Various
+
+*** END OF THIS PROJECT GUTENBERG EBOOK ENCYC. BRITANNICA, VOL 11, SL 3 ***
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