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--- a/40538-8.txt
+++ b/40538-0.txt
@@ -1,38 +1,4 @@
-The Project Gutenberg EBook of Encyclopaedia Britannica, 11th Edition,
-Volume 14, Slice 1, 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 14, Slice 1
-       "Husband" to "Hydrolysis"
-
-Author: Various
-
-Release Date: August 19, 2012 [EBook #40538]
-
-Language: English
-
-Character set encoding: ISO-8859-1
-
-*** START OF THIS PROJECT GUTENBERG EBOOK ENCYC. BRITANNICA, VOL 14, SL 1 ***
-
-
-
-
-Produced by Marius Masi, Don Kretz and the Online
-Distributed Proofreading Team at http://www.pgdp.net
-
-
-
-
-
-
-
-
+*** START OF THE PROJECT GUTENBERG EBOOK 40538 ***
 
 Transcriber's notes:
 
@@ -66,7 +32,7 @@ Transcriber's notes:
       the water." 'at' amended from 'a'.
 
     ARTICLE HYDRAULICS: "But the velocity at this point was probably
-      from Howden's statements 16.58 × 40/26 = 25.5 ft. per second, an
+      from Howden's statements 16.58 × 40/26 = 25.5 ft. per second, an
       agreement as close as the approximate character of the data would
       lead us to expect." Added 'per second'.
 
@@ -83,7 +49,7 @@ Transcriber's notes:
 
   THE
 
-  ENCYCLOPÆDIA BRITANNICA
+  ENCYCLOPÆDIA BRITANNICA
 
   ELEVENTH EDITION
 
@@ -121,7 +87,7 @@ Transcriber's notes:
 
   THE
 
-  ENCYCLOPÆDIA BRITANNICA
+  ENCYCLOPÆDIA BRITANNICA
 
   A DICTIONARY OF
   ARTS, SCIENCES, LITERATURE AND GENERAL INFORMATION
@@ -133,13 +99,13 @@ Transcriber's notes:
 
   New York
 
-  Encyclopædia Britannica, Inc.
+  Encyclopædia Britannica, Inc.
   342 Madison Avenue
 
 
   Copyright, in the United States of America, 1910,
   by
-  The Encyclopædia Britannica Company.
+  The Encyclopædia Britannica Company.
 
 
      VOLUME XIV, SLICE I
@@ -224,7 +190,7 @@ THE HEADINGS OF THE ARTICLES IN THIS VOLUME SO SIGNED.
     Inscriptions: _Semitic_.
 
   A. C. G.
-    ALBERT CHARLES LEWIS GOTTHILF GÜNTHER, M.A., M.D., PH.D., F.R.S.
+    ALBERT CHARLES LEWIS GOTTHILF GÃœNTHER, M.A., M.D., PH.D., F.R.S.
 
       Keeper of Zoological Department, British Museum, 1875-1895. Gold
       Medallist, Royal Society, 1878. Author of _Catalogues of Colubrine
@@ -321,7 +287,7 @@ THE HEADINGS OF THE ARTICLES IN THIS VOLUME SO SIGNED.
     ALBRECHT SOCIN, PH.D. (1844-1899).
 
       Formerly Professor of Semitic Philology in the Universities of
-      Leipzig and Tübingen. Author of _Arabische Grammatik_; &c.
+      Leipzig and Tübingen. Author of _Arabische Grammatik_; &c.
 
     Irak-Arabi (_in part_).
 
@@ -549,10 +515,10 @@ THE HEADINGS OF THE ARTICLES IN THIS VOLUME SO SIGNED.
     Ibsen;
     Idyl.
 
-  E. Hü.
-    EMIL HÜBNER.
+  E. Hü.
+    EMIL HÃœBNER.
 
-      See the biographical article, HÜBNER, EMIL.
+      See the biographical article, HÃœBNER, EMIL.
 
     Inscriptions: _Latin_ (_in part_).
 
@@ -605,7 +571,7 @@ THE HEADINGS OF THE ARTICLES IN THIS VOLUME SO SIGNED.
 
       Professor of Ancient History in the University of Berlin. Author
       of _Geschichte des Alterthums_; _Geschichte des alten Aegyptens_;
-      _Die Israeliten und ihre Nachbarstämme_.
+      _Die Israeliten und ihre Nachbarstämme_.
 
     Hystaspes;
     Iran.
@@ -804,7 +770,7 @@ THE HEADINGS OF THE ARTICLES IN THIS VOLUME SO SIGNED.
     Hwang Ho.
 
   G. K.
-    GUSTAV KRÜGER, PH.D.
+    GUSTAV KRÃœGER, PH.D.
 
       Professor of Church History in the University of Giessen. Author
       of _Das Papstthum_; &c.
@@ -1107,11 +1073,11 @@ THE HEADINGS OF THE ARTICLES IN THIS VOLUME SO SIGNED.
     Hyacinthus.
 
   J. P. E.
-    JEAN PAUL HIPPOLYTE EMMANUEL ADHÉMAR ESMEIN.
+    JEAN PAUL HIPPOLYTE EMMANUEL ADHÉMAR ESMEIN.
 
       Professor of Law in the University of Paris. Officer of the Legion
       of Honour. Member of the Institute of France. Author of _Cours
-      élémentaire d'histoire du droit français_; &c.
+      élémentaire d'histoire du droit français_; &c.
 
     Intendant.
 
@@ -1184,7 +1150,7 @@ THE HEADINGS OF THE ARTICLES IN THIS VOLUME SO SIGNED.
     International Law: _Private_.
 
   L.
-    COUNT LÜTZOW, LITT.D. (OXON.), PH.D. (PRAGUE), F.R.G.S.
+    COUNT LÃœTZOW, LITT.D. (OXON.), PH.D. (PRAGUE), F.R.G.S.
 
       Chamberlain of H.M. the Emperor of Austria, King of Bohemia. Hon.
       Member of the Royal Society of Literature. Member of the Bohemian
@@ -1270,11 +1236,11 @@ THE HEADINGS OF THE ARTICLES IN THIS VOLUME SO SIGNED.
     Ireland: _Geography_.
 
   P. A.
-    PAUL DANIEL ALPHANDÉRY.
+    PAUL DANIEL ALPHANDÉRY.
 
-      Professor of the History of Dogma, École pratique des hautes
-      études, Sorbonne, Paris. Author of _Les Idées morales chez les
-      hétérodoxes latines au début du XIII^e. siècle_.
+      Professor of the History of Dogma, École pratique des hautes
+      études, Sorbonne, Paris. Author of _Les Idées morales chez les
+      hétérodoxes latines au début du XIII^e. siècle_.
 
     Inquisition.
 
@@ -1374,7 +1340,7 @@ THE HEADINGS OF THE ARTICLES IN THIS VOLUME SO SIGNED.
     Insectivora.
 
   R. P. S.
-    R. PHENÉ SPIERS, F.S.A., F.R.I.B.A.
+    R. PHENÉ SPIERS, F.S.A., F.R.I.B.A.
 
       Formerly Master of the Architectural School, Royal Academy,
       London. Past President of Architectural Association. Associate and
@@ -1422,7 +1388,7 @@ THE HEADINGS OF THE ARTICLES IN THIS VOLUME SO SIGNED.
     Ishmael.
 
   S. Bl.
-    SIGFUS BLÖNDAL.
+    SIGFUS BLÖNDAL.
 
       Librarian of the University of Copenhagen.
 
@@ -1511,16 +1477,16 @@ THE HEADINGS OF THE ARTICLES IN THIS VOLUME SO SIGNED.
 
       Fellow of Magdalen College, Oxford. Professor of English History,
       St David's College, Lampeter, 1880-1881. Author of _Guide du Haut
-      Dauphiné_; _The Range of the Tödi_; _Guide to Grindelwald_; _Guide
+      Dauphiné_; _The Range of the Tödi_; _Guide to Grindelwald_; _Guide
       to Switzerland_; _The Alps in Nature and in History_; &c. Editor
       of _The Alpine Journal_, 1880-1881; &c.
 
-    Hyères;
+    Hyères;
     Innsbruck;
     Interlaken;
     Iseo, Lake of;
-    Isère (_River_);
-    Isère (_Department_).
+    Isère (_River_);
+    Isère (_Department_).
 
   W. A. P.
     WALTER ALISON PHILLIPS, M.A.
@@ -1685,7 +1651,7 @@ FOOTNOTE:
 
 
 
-  ENCYCLOPÆDIA BRITANNICA
+  ENCYCLOPÆDIA BRITANNICA
 
   ELEVENTH EDITION
 
@@ -1697,8 +1663,8 @@ FOOTNOTE:
 HUSBAND, properly the "head of a household," but now chiefly used in the
 sense of a man legally joined by marriage to a woman, his "wife"; the
 legal relations between them are treated below under HUSBAND AND WIFE.
-The word appears in O. Eng. as _húsbonda_, answering to the Old
-Norwegian _húsbóndi_, and means the owner or freeholder of a _hus_, or
+The word appears in O. Eng. as _húsbonda_, answering to the Old
+Norwegian _húsbóndi_, and means the owner or freeholder of a _hus_, or
 house. The last part of the word still survives in "bondage" and
 "bondman," and is derived from _bua_, to dwell, which, like Lat.
 _colere_, means also to till or cultivate, and to have a household.
@@ -1712,7 +1678,7 @@ referring to the entangling clothes worn by a woman, and also with the
 root of _vibrare_, to tremble. These are all merely guesses, and the
 ultimate history of the word is lost. It does not appear outside
 Teutonic languages. Parallel to "husband" is "housewife," the woman
-managing a household. The earlier _húswif_ was pronounced _hussif_, and
+managing a household. The earlier _húswif_ was pronounced _hussif_, and
 this pronunciation survives in the application of the word to a small
 case containing scissors, needles and pins, cottons, &c. From this form
 also derives "hussy," now only used in a depreciatory sense of a light,
@@ -1734,7 +1700,7 @@ and adjusts freights, keeps the accounts, makes charter-parties and acts
 generally as manager of the ship's employment. Where such an agent is
 himself one of the owners of the vessel, the name of "managing owner" is
 used. The "ship's husband" or "managing owner" must register his name
-and address at the port of registry (Merchant Shipping Act 1894, § 59).
+and address at the port of registry (Merchant Shipping Act 1894, § 59).
 From the use of "husband" for a good and thrifty manager of a household,
 the verb "to husband" means to economize, to lay up a store, to save.
 
@@ -1792,7 +1758,7 @@ Europe after many centuries, during which local usages were brought
 under the influence of principles derived from the Roman law, a theory
 of marriage became established, the leading feature of which is the
 _community of goods_ between husband and wife. Describing the principle
-as it prevails in France, Story (_Conflict of Laws_, § 130) says: "This
+as it prevails in France, Story (_Conflict of Laws_, § 130) says: "This
 community or nuptial partnership (in the absence of any special
 contract) generally extends to all the movable property of the husband
 and wife, and to the fruits, income and revenue thereof.... It extends
@@ -2180,7 +2146,7 @@ of the Liverpool and Manchester railway.
 
 
 HUSS (or HUS), JOHN (c. 1373-1415), Bohemian reformer and martyr, was
-born at Hussinecz,[1] a market village at the foot of the Böhmerwald,
+born at Hussinecz,[1] a market village at the foot of the Böhmerwald,
 and not far from the Bavarian frontier, between 1373 and 1375, the exact
 date being uncertain. His parents appear to have been well-to-do Czechs
 of the peasant class. Of his early life nothing is recorded except that,
@@ -2500,7 +2466,7 @@ of honesty and freedom, of progress and of growth towards the light.
   interesting preface to _Epistolae Quaedam_, which were published in
   1537. These _Epistolae_ have been translated into French by E. de
   Bonnechose (1846), and the letters written during his imprisonment
-  have been edited by C. von Kügelgen (Leipzig, 1902).
+  have been edited by C. von Kügelgen (Leipzig, 1902).
 
   The best and most easily accessible information for the English reader
   on Huss is found in J. A. W. Neander's _Allgemeine Geschichte der
@@ -2516,17 +2482,17 @@ of honesty and freedom, of progress and of growth towards the light.
   concilii Constantiensis_, 1896); and J. Lenfant's _Histoire de la
   guerre des Hussites_ (1731) and the same writer's _Histoire du concile
   de Constance_ (1714) should be consulted. F. Palacky's _Geschichte
-  Böhmens_ (1864-1867) is also very useful. Monographs on Huss are very
-  numerous. Among them may be mentioned J. A. von Helfert, _Studien über
+  Böhmens_ (1864-1867) is also very useful. Monographs on Huss are very
+  numerous. Among them may be mentioned J. A. von Helfert, _Studien über
   Hus und Hieronymus_ (1853; this work is ultramontane in its
-  sympathies); C. von Höfler, _Hus und der Abzug der deutschen
+  sympathies); C. von Höfler, _Hus und der Abzug der deutschen
   Professoren und Studenten aus Prag_ (1864); W. Berger, _Johannes Hus
-  und König Sigmund_ (1871); E. Denis, _Huss et la guerre des Hussites_
-  (1878); P. Uhlmann, _König Sigmunds Geleit für Hus_ (1894); J.
+  und König Sigmund_ (1871); E. Denis, _Huss et la guerre des Hussites_
+  (1878); P. Uhlmann, _König Sigmunds Geleit für Hus_ (1894); J.
   Loserth, _Hus und Wiclif_ (1884), translated into English by M. J.
   Evans (1884); A. Jeep, _Gerson, Wiclefus, Hussus, inter se comparati_
   (1857); and G. von Lechler, _Johannes Hus_ (1889). See also Count
-  Lützow, _The Life and Times of John Hus_ (London, 1909).
+  Lützow, _The Life and Times of John Hus_ (London, 1909).
 
 
 FOOTNOTE:
@@ -2704,7 +2670,7 @@ his troops. The citizens of Prague laid siege to the Vysehrad, and
 towards the end of October (1420) the garrison was on the point of
 capitulating through famine. Sigismund attempted to relieve the
 fortress, but was decisively defeated by the Hussites on the 1st of
-November near the village of Pankrác. The castles of Vysehrad and
+November near the village of Pankrác. The castles of Vysehrad and
 Hradcany now capitulated, and shortly afterwards almost all Bohemia fell
 into the hands of the Hussites. Internal troubles prevented them from
 availing themselves completely of their victory. At Prague a demagogue,
@@ -2746,8 +2712,8 @@ king of Denmark, who had landed in Germany with a large force intending
 to take part in the crusade, soon returned to his own country. Free for
 a time from foreign aggression, the Hussites invaded Moravia, where a
 large part of the population favoured their creed; but, again paralysed
-by dissensions, soon returned to Bohemia. The city of Königgrätz
-(Králové Hradec), which had been under Utraquist rule, espoused the
+by dissensions, soon returned to Bohemia. The city of Königgrätz
+(Králové Hradec), which had been under Utraquist rule, espoused the
 doctrine of Tabor, and called Zizka to its aid. After several military
 successes gained by Zizka (q.v.) in 1423 and the following year, a
 treaty of peace between the Hussites was concluded on the 13th of
@@ -2838,17 +2804,17 @@ Hussite tradition in Bohemia were included in the more general name of
 "Protestants" borne by the adherents of the Reformation.
 
   All histories of Bohemia devote a large amount of space to the Hussite
-  movement. See Count Lützow, _Bohemia; an Historical Sketch_ (London,
-  1896); Palacky, _Geschichte von Böhmen_; Bachmann, _Geschichte
-  Böhmens_; L. Krummel, _Geschichte der böhmischen Reformation_ (Gotha,
+  movement. See Count Lützow, _Bohemia; an Historical Sketch_ (London,
+  1896); Palacky, _Geschichte von Böhmen_; Bachmann, _Geschichte
+  Böhmens_; L. Krummel, _Geschichte der böhmischen Reformation_ (Gotha,
   1866) and _Utraquisten und Taboriten_ (Gotha, 1871); Ernest Denis,
-  _Huss et la guerre des Hussites_ (Paris, 1878); H. Toman, _Husitské
-  Válecnictvi_ (Prague, 1898).     (L.)
+  _Huss et la guerre des Hussites_ (Paris, 1878); H. Toman, _Husitské
+  Válecnictvi_ (Prague, 1898).     (L.)
 
 
 
 
-HUSTING (O. Eng. _hústing_, from Old Norwegian _hústhing_), the "thing"
+HUSTING (O. Eng. _hústing_, from Old Norwegian _hústhing_), the "thing"
 or "ting," i.e. assembly, of the household of personal followers or
 retainers of a king, earl or chief, contrasted with the "folkmoot," the
 assembly of the whole people. "Thing" meant an inanimate object, the
@@ -2884,10 +2850,10 @@ away with this public declaration of the nomination.
 
 
 HUSUM, a town in the Prussian province of Schleswig-Holstein, in a
-fertile district 2½ m. inland from the North Sea, on the canalized
+fertile district 2½ m. inland from the North Sea, on the canalized
 Husumer Au, which forms its harbour and roadstead, 99 m. N.W. from
-Hamburg on a branch line from Tönning. Pop. (1900) 8268. It has steam
-communication with the North Frisian Islands (Nordstrand, Föhr and
+Hamburg on a branch line from Tönning. Pop. (1900) 8268. It has steam
+communication with the North Frisian Islands (Nordstrand, Föhr and
 Sylt), and is a port for the cattle trade with England. Besides a ducal
 palace and park, it possesses an Evangelical church and a gymnasium.
 Cattle markets are held weekly, and in them, as also in cereals, a
@@ -3321,7 +3287,7 @@ fundamental points of agreement between the two authors.
   general philosophy and of moral philosophy, as, for instance, in pt.
   vii. of Adam Smith's _Theory of Moral Sentiments_; Mackintosh's
   _Progress of Ethical Philosophy_; Cousin, _Cours d'histoire de la
-  philosophie morale du XVIII^e siècle_; Whewell's _Lectures on the
+  philosophie morale du XVIII^e siècle_; Whewell's _Lectures on the
   History of Moral Philosophy in England_; A. Bain's _Mental and Moral
   Science_; Noah Porter's Appendix to the English translation of
   Ueberweg's _History of Philosophy_; Sir Leslie Stephen's _History of
@@ -3424,7 +3390,7 @@ its chief interest from the _Life_ by his wife, Lucy, daughter of Sir
 Allen Apsley, written after the death of her husband but not
 published till 1806 (since often reprinted), a work not only valuable
 for the picture which it gives of the man and of the time in which he
-lived, but for the simple beauty of its style, and the naïveté with
+lived, but for the simple beauty of its style, and the naïveté with
 which the writer records her sentiments and opinions, and details the
 incidents of her private life.
 
@@ -3441,7 +3407,7 @@ HUTCHINSON, JOHN (1674-1737), English theological writer, was born at
 Spennithorne, Yorkshire, in 1674. He served as steward in several
 families of position, latterly in that of the duke of Somerset, who
 ultimately obtained for him the post of riding purveyor to the master of
-the horse, a sinecure worth about £200 a year. In 1700 he became
+the horse, a sinecure worth about £200 a year. In 1700 he became
 acquainted with Dr John Woodward (1665-1728) physician to the duke and
 author of a work entitled _The Natural History of the Earth_, to whom he
 entrusted a large number of fossils of his own collecting, along with a
@@ -3564,7 +3530,7 @@ He died at Brompton, now part of London, on the 3rd of June 1780.
 HUTCHINSON, a city and the county-seat of Reno county, Kansas, U.S.A.,
 in the broad bottom-land on the N. side of the Arkansas river. Pop.
 (1900) 9379, of whom 414 were foreign-born and 442 negroes; (1910
-census) 16,364. It is served by the Atchison, Topeka & Santa Fé, the
+census) 16,364. It is served by the Atchison, Topeka & Santa Fé, the
 Missouri Pacific and the Chicago, Rock Island & Pacific railways. The
 principal public buildings are the Federal building and the county court
 house. The city has a public library, and an industrial reformatory is
@@ -3614,7 +3580,7 @@ Humanists and Reformers. He lived with both, sympathized with both,
 though he died before the Reformation had time fully to develop. His
 life may be divided into four parts:--his youth and cloister-life
 (1488-1504); his wanderings in pursuit of knowledge (1504-1515); his
-strife with Ulrich of Württemberg (1515-1519); and his connexion with
+strife with Ulrich of Württemberg (1515-1519); and his connexion with
 the Reformation (1519-1523). Each of these periods had its own special
 antagonism, which coloured Hutten's career: in the first, his horror of
 dull monastic routine; in the second, the ill-treatment he met with at
@@ -3656,7 +3622,7 @@ Stein (d. 1515), he won the favour of the elector of Mainz, Archbishop
 Albert of Brandenburg. Here high dreams of a learned career rose on him;
 Mainz should be made the metropolis of a grand Humanist movement, the
 centre of good style and literary form. But the murder in 1515 of his
-relative Hans von Hutten by Ulrich, duke of Württemberg, changed the
+relative Hans von Hutten by Ulrich, duke of Württemberg, changed the
 whole course of his life; satire, chief refuge of the weak, became
 Hutten's weapon; with one hand he took his part in the famous _Epistolae
 obscurorum virorum_, and with the other launched scathing letters,
@@ -3717,7 +3683,7 @@ fell. He fled to Basel, where Erasmus refused to see him, both for fear
 of his loathsome diseases, and also because the beggared knight was sure
 to borrow money from him. A paper war consequently broke out between the
 two Humanists, which embittered Hutten's last days, and stained the
-memory of Erasmus. From Basel Ulrich dragged himself to Mülhausen; and
+memory of Erasmus. From Basel Ulrich dragged himself to Mülhausen; and
 when the vengeance of Erasmus drove him thence, he went to Zurich. There
 the large heart of Zwingli welcomed him; he helped him with money, and
 found him a quiet refuge with the pastor of the little isle of Ufnau on
@@ -3775,15 +3741,15 @@ Lucian.
   bitter portion of the satire. See W. Brecht, _Die Verfasser der
   Epistolae obscurorum virorum_ (1904).
 
-  For a complete catalogue of the writings of Hutten, see E. Böcking's
-  _Index Bibliographicus Huttenianus_ (1858). Böcking is also the editor
+  For a complete catalogue of the writings of Hutten, see E. Böcking's
+  _Index Bibliographicus Huttenianus_ (1858). Böcking is also the editor
   of the complete edition of Hutten's works (7 vols., 1859-1862). A
   selection of Hutten's German writings, edited by G. Balke, appeared in
   1891. Cp. S. Szamatolski, _Huttens deutsche Schriften_ (1891). The
   best biography (though it is also somewhat of a political pamphlet) is
   that of D. F. Strauss (_Ulrich von Hutten_, 1857; 4th ed., 1878;
   English translation by G. Sturge, 1874), with which may be compared
-  the older monographs by A. Wagenseil (1823), A. Bürck (1846) and J.
+  the older monographs by A. Wagenseil (1823), A. Bürck (1846) and J.
   Zeller (Paris, 1849). See also J. Deckert, _Ulrich von Huttens Leben
   und Wirken. Eine historische Skizze_ (1901).     (G. W. K.)
 
@@ -4181,7 +4147,7 @@ up the observations he had made during the voyage of the "Rattlesnake."
 He was thus enabled to produce various important memoirs, especially
 those on certain Ascidians, in which he solved the problem of
 _Appendicularia_--an organism whose place in the animal kingdom Johannes
-Müller had found himself wholly unable to assign--and on the morphology
+Müller had found himself wholly unable to assign--and on the morphology
 of the Cephalous Mollusca.
 
 Richard Owen, then the leading comparative anatomist in Great Britain,
@@ -4189,7 +4155,7 @@ was a disciple of Cuvier, and adopted largely from him the deductive
 explanation of anatomical fact from idealistic conceptions. He
 superadded the evolutionary theories of Oken, which were equally
 idealistic, but were altogether repugnant to Cuvier. Huxley would have
-none of either. Imbued with the methods of von Baer and Johannes Müller,
+none of either. Imbued with the methods of von Baer and Johannes Müller,
 his methods were purely inductive. He would not hazard any statement
 beyond what the facts revealed. He retained, however, as has been done
 by his successors, the use of archetypes, though they no longer
@@ -4208,7 +4174,7 @@ rid himself of the notion that the archetype was a property inherent in
 the group. Herbert Spencer, whose acquaintance he made in 1852, was
 unable to convert him to evolution in its widest sense (_Life_, i.
 168). He could not bring himself to acceptance of the theory--owing, no
-doubt, to his rooted aversion from à priori reasoning--without a
+doubt, to his rooted aversion from à priori reasoning--without a
 mechanical conception of its mode of operation. In his first interview
 with Darwin, which seems to have been about the same time, he expressed
 his belief "in the sharpness of the lines of demarcation between natural
@@ -4598,7 +4564,7 @@ FOOTNOTE:
 
 HUY (Lat. _Hoium_, and Flem. _Hoey_), a town of Belgium, on the right
 bank of the Meuse, at the point where it is joined by the Hoyoux. Pop.
-(1904), 14,164. It is 19 m. E. of Namur and a trifle less west of Liége.
+(1904), 14,164. It is 19 m. E. of Namur and a trifle less west of Liége.
 Huy certainly dates from the 7th century, and, according to some, was
 founded by the emperor Antoninus in A.D. 148. Its situation is
 striking, with its grey citadel crowning a grey rock, and the fine
@@ -4608,7 +4574,7 @@ equipment and partly as a prison. The ruins are still shown of the abbey
 of Neumoustier founded by Peter the Hermit on his return from the first
 crusade. He was buried there in 1115, and a statue was erected to his
 memory in the abbey grounds in 1858. Neumoustier was one of seventeen
-abbeys in this town alone dependent on the bishopric of Liége. Huy is
+abbeys in this town alone dependent on the bishopric of Liége. Huy is
 surrounded by vineyards, and the bridge which crosses the Meuse at this
 point connects the fertile Hesbaye north of the river with the rocky and
 barren Condroz south of it.
@@ -4648,7 +4614,7 @@ anagram--removed, in the case of the first, by the publication, early in
 1656, of the little tract _De Saturni luna observatio nova_; but
 retained, as regards the second, until 1659, when in the _Systema
 Saturnium_ the varying appearances of the so-called "triple planet" were
-clearly explained as the phases of a ring inclined at an angle of 28° to
+clearly explained as the phases of a ring inclined at an angle of 28° to
 the ecliptic. Huygens was also in 1656 the first effective observer of
 the Orion nebula; he delineated the bright region still known by his
 name, and detected the multiple character of its nuclear star. His
@@ -4673,7 +4639,7 @@ made respectively in November and December 1668.
 Huygens had before this time fixed his abode in France. In 1665 Colbert
 made to him on behalf of Louis XIV. an offer too tempting to be
 refused, and between the following year and 1681 his residence in the
-philosophic seclusion of the Bibliothèque du Roi was only interrupted by
+philosophic seclusion of the Bibliothèque du Roi was only interrupted by
 two short visits to his native country. His _magnum opus_ dates from
 this period. The _Horologium oscillatorium_, published with a dedication
 to his royal patron in 1673, contained original discoveries sufficient
@@ -4721,7 +4687,7 @@ undulations. This resolution of the original wave is the well-known
 fundamental laws of optics, and to assign the correct construction for
 the direction of the extraordinary ray in uniaxial crystals. These
 investigations, together with his discovery of the "wonderful
-phenomenon" of polarization, are recorded in his _Traité de la lumière_,
+phenomenon" of polarization, are recorded in his _Traité de la lumière_,
 published at Leiden in 1690, but composed in 1678. In the appended
 treatise _Sur la Cause de la pesanteur_, he rejected gravitation as a
 universal quality of matter, although admitting the Newtonian theory of
@@ -4760,25 +4726,25 @@ the merits of his competitors.
   exercitationes mathematicae et philosophicae_ (the Hague, 1833).
 
   The publication of a monumental edition of the letters and works of
-  Huygens was undertaken at the Hague by the _Société Hollandaise des
+  Huygens was undertaken at the Hague by the _Société Hollandaise des
   Sciences_, with the heading _Oeuvres de Christian Huygens_ (1888),
   &c. Ten quarto volumes, comprising the whole of his correspondence,
   had already been issued in 1905. A biography of Huygens was prefixed
-  to his _Opera varia_ (1724); his _Éloge_ in the character of a French
+  to his _Opera varia_ (1724); his _Éloge_ in the character of a French
   academician was printed by J. A. N. Condorcet in 1773. Consult
   further: P. J. Uylenbroek, _Oratio de fratribus Christiano atque
   Constantino Hugenio_ (Groningen, 1838); P. Harting, _Christiaan
   Huygens in zijn Leven en Werken geschetzt_ (Groningen, 1868); J. B. J.
   Delambre, _Hist. de l'astronomie moderne_ (ii. 549); J. E. Montucla,
-  _Hist. des mathématiques_ (ii. 84, 412, 549); M. Chasles, _Aperçu
-  historique sur l'origine des méthodes en géometrie_, pp. 101-109; E.
-  Dühring, _Kritische Geschichte der allgemeinen Principien der
+  _Hist. des mathématiques_ (ii. 84, 412, 549); M. Chasles, _Aperçu
+  historique sur l'origine des méthodes en géometrie_, pp. 101-109; E.
+  Dühring, _Kritische Geschichte der allgemeinen Principien der
   Mechanik_, Abschnitt (ii. 120, 163, iii. 227); A. Berry, _A Short
   History of Astronomy_, p. 200; R. Wolf, _Geschichte der Astronomie_,
   passim; Houzeau, _Bibliographie astronomique_ (ii. 169); F. Kaiser,
   _Astr. Nach._ (xxv. 245, 1847); _Tijdschrift voor de Wetenschappen_
   (i. 7, 1848); _Allgemeine deutsche Biographie_ (M. B. Cantor); J. C.
-  Poggendorff, _Biog. lit. Handwörterbuch_.     (A. M. C.)
+  Poggendorff, _Biog. lit. Handwörterbuch_.     (A. M. C.)
 
 
 
@@ -4917,42 +4883,42 @@ HUYSMANS, JORIS KARL (1848-1907), French novelist, was born at Paris on
 the 5th of February 1848. He belonged to a family of artists of Dutch
 extraction; he entered the ministry of the interior, and was pensioned
 after thirty years' service. His earliest venture in literature, _Le
-Drageoir à épices_ (1874), contained stories and short prose poems
+Drageoir à épices_ (1874), contained stories and short prose poems
 showing the influence of Baudelaire. _Marthe_ (1876), the life of a
 courtesan, was published in Brussels, and Huysmans contributed a story,
-"Sac au dos," to _Les Soirées de Médan_, the collection of stories of
+"Sac au dos," to _Les Soirées de Médan_, the collection of stories of
 the Franco-German war published by Zola. He then produced a series of
 novels of everyday life, including _Les Soeurs Vatard_ (1879), _En
-Ménage_ (1881), and _À vau-l'eau_ (1882), in which he outdid Zola in
+Ménage_ (1881), and _À vau-l'eau_ (1882), in which he outdid Zola in
 minute and uncompromising realism. He was influenced, however, more
 directly by Flaubert and the brothers de Goncourt than by Zola. In
 _L'Art moderne_ (1883) he gave a careful study of impressionism and in
-_Certains_ (1889) a series of studies of contemporary artists, _À
+_Certains_ (1889) a series of studies of contemporary artists, _À
 Rebours_ (1884), the history of the morbid tastes of a decadent
 aristocrat, des Esseintes, created a literary sensation, its caricature
 of literary and artistic symbolism covering much of the real beliefs of
-the leaders of the aesthetic revolt. In _Là-Bas_ Huysmans's most
+the leaders of the aesthetic revolt. In _Là-Bas_ Huysmans's most
 characteristic hero, Durtal, makes his appearance. Durtal is occupied in
 writing the life of Gilles de Rais; the insight he gains into Satanism
 is supplemented by modern Parisian students of the black art; but
 already there are signs of a leaning to religion in the sympathetic
 figures of the religious bell-ringer of Saint Sulpice and his wife. _En
 Route_ (1895) relates the strange conversion of Durtal to mysticism and
-Catholicism in his retreat to La Trappe. In _La Cathédrale_ (1898),
+Catholicism in his retreat to La Trappe. In _La Cathédrale_ (1898),
 Huysmans's symbolistic interpretation of the cathedral of Chartres, he
 develops his enthusiasm for the purity of Catholic ritual. The life of
 _Sainte Lydwine de Schiedam_ (1901), an exposition of the value of
 suffering, gives further proof of his conversion; and _L'Oblat_ (1903)
 describes Durtal's retreat to the Val des Saints, where he is attached
 as an oblate to a Benedictine monastery. Huysmans was nominated by
-Edmond de Goncourt as a member of the Académie des Goncourt. He died as
+Edmond de Goncourt as a member of the Académie des Goncourt. He died as
 a devout Catholic, after a long illness of cancer in the palate on the
 13th of May 1907. Before his death he destroyed his unpublished MSS. His
 last book was _Les Foules de Lourdes_ (1906).
 
   See Arthur Symons, _Studies in two Literatures_ (1897) and _The
-  Symbolist Movement in Literature_ (1899); Jean Lionnet in _L'Évolution
-  des idées_ (1903); Eugène Gilbert in _France et Belgique_ (1905); J.
+  Symbolist Movement in Literature_ (1899); Jean Lionnet in _L'Évolution
+  des idées_ (1903); Eugène Gilbert in _France et Belgique_ (1905); J.
   Sargeret in _Les Grands convertis_ (1906).
 
 
@@ -5010,9 +4976,9 @@ the Chinese. It rises among the Kuenlun mountains in central Asia, its
 head-waters being in close proximity to those of the Yangtsze-Kiang. It
 has a total length of about 2400 m. and drains an area of approximately
 400,000 sq. m. The main stream has its source in two lakes named
-Tsaring-nor and Oring-nor, lying about 35° N., 97° E., and after flowing
+Tsaring-nor and Oring-nor, lying about 35° N., 97° E., and after flowing
 with a south-easterly course it bends sharply to the north-west and
-north, entering China in the province of Kansuh in lat. 36°. After
+north, entering China in the province of Kansuh in lat. 36°. After
 passing Lanchow-fu, the capital of this province, the river takes an
 immense sweep to the north and north-east, until it encounters the
 rugged barrier ranges that here run north and south through the
@@ -5117,17 +5083,17 @@ have been always subject to Mercian supremacy, and possibly it was
 separated from Wessex in the time of Edwin. The first kings of whom we
 read were two brothers, Eanhere and Eanfrith, probably contemporaries of
 Wulfhere. They were followed by a king named Osric, a contemporary of
-Æthelred, and he by a king Oshere. Oshere had three sons who reigned
-after him, Æthelheard, Æthelweard and Æthelric. The two last named
+Æthelred, and he by a king Oshere. Oshere had three sons who reigned
+after him, Æthelheard, Æthelweard and Æthelric. The two last named
 appear to have been reigning in the year 706. At the beginning of Offa's
 reign we again find the kingdom ruled by three brothers, named Eanberht,
 Uhtred and Aldred, the two latter of whom lived until about 780. After
 them the title of king seems to have been given up. Their successor
-Æthelmund, who was killed in a campaign against Wessex in 802, is
+Æthelmund, who was killed in a campaign against Wessex in 802, is
 described only as an earl. The district remained in possession of the
 rulers of Mercia until the fall of that kingdom. Together with the rest
 of English Mercia it submitted to King Alfred about 877-883 under Earl
-Æthelred, who possibly himself belonged to the Hwicce. No genealogy or
+Æthelred, who possibly himself belonged to the Hwicce. No genealogy or
 list of kings has been preserved, and we do not know whether the dynasty
 was connected with that of Wessex or Mercia.
 
@@ -5250,7 +5216,7 @@ for which is regulated in some respects by fashion.
   or 8 in. with the same material or with fibre or soil; and when the
   roots are well developed, which will take from six to eight weeks,
   they may be removed to a frame, and gradually exposed to light, and
-  then placed in a forcing pit in a heat of from 60 to 70°. When the
+  then placed in a forcing pit in a heat of from 60 to 70°. When the
   flowers are fairly open, they may be removed to the greenhouse or
   conservatory.
 
@@ -5405,7 +5371,7 @@ Scephrus, both of whom are connected with Apollo Agyieus.
   See L. R. Farnell, _Cults of the Greek States_, vol. iv. (1907), pp.
   125 foll., 264 foll.; J. G. Frazer, _Adonis, Attis, Osiris_ (1906),
   bk. ii. ch. 7; S. Wide, _Lakonische Kulte_, p. 290; E. Rhode,
-  _Psyche_, 3rd ed. i. 137 foll.; Roscher, _Lexikon d. griech. u. röm.
+  _Psyche_, 3rd ed. i. 137 foll.; Roscher, _Lexikon d. griech. u. röm.
   Myth._, s.v. "Hyakinthos" (Greve); L. Preller, _Griechische Mythol._
   4th ed. i. 248 foll.     (J. M. M.)
 
@@ -5425,7 +5391,7 @@ and Aethra; their number varies between two and seven. As a reward for
 having brought up Zeus at Dodona and taken care of the infant Dionysus
 Hyes, whom they conveyed to Ino (sister of his mother Semele) at Thebes
 when his life was threatened by Lycurgus, they were translated to heaven
-and placed among the stars (Hyginus, _Poët. astron._ ii. 21). Another
+and placed among the stars (Hyginus, _Poët. astron._ ii. 21). Another
 form of the story combines them with the Pleiades. According to this
 they were twelve (or fifteen) sisters, whose brother Hyas was killed by
 a snake while hunting in Libya (Ovid, _Fasti_, v. 165; Hyginus, _Fab._
@@ -5463,7 +5429,7 @@ died at Cambridge on the 15th of January 1902.
   Cephalopoda_ (1883); _Larval Theory of the Origin of Cellular Tissue_
   (1884); _Genesis of the Arietidae_ (1889); and _Phylogeny of an
   acquired characteristic_ (1894). He wrote the section on Cephalopoda
-  in Karl von Zittel's _Paläontologie_ (1900), and his well-known study
+  in Karl von Zittel's _Paläontologie_ (1900), and his well-known study
   on the fossil pond snails of Steinheim ("The Genesis of the Tertiary
   Species of Planorbis at Steinheim") appeared in the _Memoirs_ of the
   Boston Natural History Society in 1880. He was one of the founders and
@@ -5476,7 +5442,7 @@ HYBLA, the name of several cities In Sicily. The best known
 historically, though its exact site is uncertain, is Hybla Major, near
 (or by some supposed to be identical with) Megara Hyblaea (q.v.):
 another Hybla, known as Hybla Minor or Galeatis, is represented by the
-modern Paternò; while the site of Hybla Heraea is to be sought near
+modern Paternò; while the site of Hybla Heraea is to be sought near
 Ragusa.
 
 
@@ -5510,12 +5476,12 @@ G. Gmelin towards the end of the 17th century; the next is that of Thomas
 Fairchild, who in the second decade of the 18th century, produced the
 cross which is still grown in gardens under the name of "Fairchild's
 Sweet William." Linnaeus made many experiments in the cross-fertilization
-of plants and produced several hybrids, but Joseph Gottlieb Kölreuter
+of plants and produced several hybrids, but Joseph Gottlieb Kölreuter
 (1733-1806) laid the first real foundation of our scientific knowledge of
 the subject. Later on Thomas Andrew Knight, a celebrated English
 horticulturist, devoted much successful labour to the improvement of
 fruit trees and vegetables by crossing. In the second quarter of the 19th
-century C. F. Gärtner made and published the results of a number of
+century C. F. Gärtner made and published the results of a number of
 experiments that had not been equalled by any earlier worker. Next came
 Charles Darwin, who first in the _Origin of Species_, and later in _Cross
 and Self-Fertilization of Plants_, subjected the whole question to a
@@ -5612,7 +5578,7 @@ genera is not infrequent.
   experiments with Lepidopterous insects, and has obtained a very large
   series of hybrids, of which he has kept careful record. Lepidopterists
   generally begin to suspect that many curious forms offered by dealers
-  as new species are products got by crossing known species. Apellö has
+  as new species are products got by crossing known species. Apellö has
   succeeded with Teleostean fish; Gebhardt and others with Amphibia.
   Elliot and Suchetet have studied carefully the question of
   hybridization occurring normally among birds, and have got together a
@@ -5680,7 +5646,7 @@ palps in male spiders have a similar result.
   secured by artificial means, the development of the hybrid may stop at
   an early stage. Thus hybrids between the urchin and the starfish,
   animals belonging to different classes, reached only the stage of the
-  pluteus larva. A. D. Apellö, experimenting with Teleostean fish, found
+  pluteus larva. A. D. Apellö, experimenting with Teleostean fish, found
   that very often impregnation and segmentation occurred, but that the
   development broke down immediately afterwards. W. Gebhardt, crossing
   _Rana esculenta_ with _R. arvalis_, found that the cleavage of the
@@ -5803,7 +5769,7 @@ favour of zebra disposition and against zebra shape and marking.
 Ewart's experiments and his discussion of them also throw important
 light on the general relation of hybrids to their parents. He found that
 the coloration and pattern of his zebra hybrids resembled far more those
-of the Somali or Grévy's zebra than those of their sire--a Burchell's
+of the Somali or Grévy's zebra than those of their sire--a Burchell's
 zebra. In a general discussion of the stripings of horses, asses and
 zebras, he came to the conclusion that the Somali zebra represented the
 older type, and that therefore his zebra hybrids furnished important
@@ -5968,33 +5934,33 @@ the root of the phenomena of hybridism, and that Darwin was justified in
 supposing it to lie outside the sphere of natural selection and to be a
 fundamental fact of living matter.
 
-  AUTHORITIES.--Apellö, "Über einige Resultate der Kreuzbefruchtung bei
+  AUTHORITIES.--Apellö, "Über einige Resultate der Kreuzbefruchtung bei
   Knochenfischen," _Bergens mus. aarbog_ (1894); Bateson, "Hybridization
   and Cross-breeding," _Journal of the Royal Horticultural Society_
   (1900); J. L. Bonhote, "Hybrid Ducks," _Proc. Zool. Soc. of London_
   (1905), p. 147; Boveri, article "Befruchtung," in _Ergebnisse der
   Anatomie und Entwickelungsgeschichte von Merkel und Bonnet_, i.
-  385-485; Cornevin et Lesbre, "Étude sur un hybride issu d'une mule
-  féconde et d'un cheval," _Rev. Sci._ li. 144; Charles Darwin, _Origin
+  385-485; Cornevin et Lesbre, "Étude sur un hybride issu d'une mule
+  féconde et d'un cheval," _Rev. Sci._ li. 144; Charles Darwin, _Origin
   of Species_ (1859), _The Effects of Cross and Self-Fertilization in
   the Vegetable Kingdom_ (1878); Delage, _La Structure du protoplasma et
-  les théories sur l'hérédité_ (1895, with a literature); de Vries, "The
+  les théories sur l'hérédité_ (1895, with a literature); de Vries, "The
   Law of Disjunction of Hybrids," _Comptes rendus_ (1900), p. 845;
   Elliot, _Hybridism_; Escherick, "Die biologische Bedeutung der
-  Genitalabhänge der Insecten," _Verh. z. B. Wien_, xlii. 225; Ewart,
+  Genitalabhänge der Insecten," _Verh. z. B. Wien_, xlii. 225; Ewart,
   _The Penycuik Experiments_ (1899); Focke, _Die Pflanzen-Mischlinge_
   (1881); Foster-Melliar, _The Book of the Rose_ (1894); C. F. Gaertner,
   various papers in _Flora_, 1828, 1831, 1832, 1833, 1836, 1847, on
-  "Bastard-Pflanzen"; Gebhardt, "Über die Bastardirung von _Rana
+  "Bastard-Pflanzen"; Gebhardt, "Ãœber die Bastardirung von _Rana
   esculenta_ mit _R. arvalis_," _Inaug. Dissert._ (Breslau, 1894); G.
-  Mendel, "Versuche über Pflanzen-Hybriden," _Verh. Natur. Vereins in
-  Brünn_ (1865), pp. 1-52; Morgan, "Experimental Studies," _Anat. Anz._
+  Mendel, "Versuche über Pflanzen-Hybriden," _Verh. Natur. Vereins in
+  Brünn_ (1865), pp. 1-52; Morgan, "Experimental Studies," _Anat. Anz._
   (1893), p. 141; id. p. 803; G. J. Romanes, "Physiological Selection,"
   _Jour. Linn. Soc._ xix. 337; H. Scherren, "Notes on Hybrid Bears,"
   _Proc. Zool. Soc. of London_ (1907), p. 431; Saunders, _Proc. Roy.
-  Soc._ (1897), lxii. 11; Standfuss, "Études de zoologie expérimentale,"
-  _Arch. Sci. Nat._ vi. 495; Suchetet, "Les Oiseaux hybrides rencontrés
-  à l'état sauvage," _Mém. Soc. Zool._ v. 253-525, and vi. 26-45;
+  Soc._ (1897), lxii. 11; Standfuss, "Études de zoologie expérimentale,"
+  _Arch. Sci. Nat._ vi. 495; Suchetet, "Les Oiseaux hybrides rencontrés
+  à l'état sauvage," _Mém. Soc. Zool._ v. 253-525, and vi. 26-45;
   Vernon, "The Relation between the Hybrid and Parent Forms of Echinoid
   Larvae," _Proc. Roy. Soc._ lxv. 350; Wallace, _Darwinism_ (1889);
   Weismann, _The Germ-Plasm_ (1893).     (P. C. M)
@@ -6005,19 +5971,19 @@ fundamental fact of living matter.
 HYDANTOIN (glycolyl urea),
 
                  [beta] [alpha]
-                  / NH · CH2
+                  / NH · CH2
   C3H4N2O2 or CO <          ,
-                  \ NH · CO
+                  \ NH · CO
                   [gamma]
 
-the ureïde of glycollic acid, may be obtained by heating allantoin or
+the ureïde of glycollic acid, may be obtained by heating allantoin or
 alloxan with hydriodic acid, or by heating bromacetyl urea with
-alcoholic ammonia. It crystallizes in needles, melting at 216° C.
+alcoholic ammonia. It crystallizes in needles, melting at 216° C.
 
 When hydrolysed with baryta water yields hydantoic (glycoluric)acid,
-H2N·CO·NH·CH2·CO2H, which is readily soluble in hot water, and on
+H2N·CO·NH·CH2·CO2H, which is readily soluble in hot water, and on
 heating with hydriodic acid decomposes into ammonia, carbon dioxide and
-glycocoll, CH2·NH2·CO2·H. Many substituted hydantoins are known; the
+glycocoll, CH2·NH2·CO2·H. Many substituted hydantoins are known; the
 [alpha]-alkyl hydantoins are formed on fusion of aldehyde- or
 ketone-cyanhydrins with urea, the [beta]-alkyl hydantoins from the
 fusion of mono-alkyl glycocolls with urea, and the [gamma]-alkyl
@@ -6089,7 +6055,7 @@ Clarendon, the historian, to the Bodleian Library at Oxford.
 
   See Lord Clarendon, _The Life of Edward, Earl of Clarendon_ (3 vols.,
   Oxford, 1827); Edward Foss, _The Judges of England_ (London,
-  1848-1864); Anthony à Wood, _Athenae oxonienses_ (London, 1813-1820);
+  1848-1864); Anthony à Wood, _Athenae oxonienses_ (London, 1813-1820);
   Samuel Pepys, _Diary and Correspondence_, edited by Lord Braybrooke (4
   vols., London, 1854).
 
@@ -6152,7 +6118,7 @@ orientalibus libri II._ (1694).
 
 
 HYDE, a market town and municipal borough in the Hyde parliamentary
-division of Cheshire, England, 7½ m. E. of Manchester, by the Great
+division of Cheshire, England, 7½ m. E. of Manchester, by the Great
 Central railway. Pop. (1901) 32,766. It lies in the densely populated
 district in the north-east of the county, on the river Tame, which here
 forms the boundary of Cheshire with Lancashire. To the east the outlying
@@ -6169,13 +6135,13 @@ the manor as early as the reign of John. The borough, incorporated in
 
 
 HYDE DE NEUVILLE, JEAN GUILLAUME, BARON (1776-1857), French politician,
-was born at La Charité-sur-Loire (Nièvre) on the 24th of January 1776,
+was born at La Charité-sur-Loire (Nièvre) on the 24th of January 1776,
 the son of Guillaume Hyde, who belonged to an English family which had
 emigrated with the Stuarts after the rebellion of 1745. He was only
-seventeen when he successfully defended a man denounced by Fouché before
+seventeen when he successfully defended a man denounced by Fouché before
 the revolutionary tribunal of Nevers. From 1793 onwards he was an active
 agent of the exiled princes; he took part in the Royalist rising in
-Berry in 1796, and after the _coup d'état_ of the 18th Brumaire
+Berry in 1796, and after the _coup d'état_ of the 18th Brumaire
 (November 9, 1799) tried to persuade Bonaparte to recall the Bourbons.
 An accusation of complicity in the infernal machine conspiracy of
 1800-1801 was speedily retracted, but Hyde de Neuville retired to the
@@ -6188,7 +6154,7 @@ ambassador at Washington, where he negotiated a commercial treaty. On
 his return in 1821 he declined the Constantinople embassy, and in
 November 1822 was elected deputy for Cosne. Shortly afterwards he was
 appointed French ambassador at Lisbon, where his efforts to oust British
-influence culminated, in connexion with the _coup d'état_ of Dom Miguel
+influence culminated, in connexion with the _coup d'état_ of Dom Miguel
 (April 30, 1824), in his suggestion to the Portuguese minister to invite
 the armed intervention of Great Britain. It was assumed that this would
 be refused, in view of the loudly proclaimed British principle of
@@ -6199,7 +6165,7 @@ government of Paris, which disapproved of the Portuguese constitution.
 This destroyed his influence at Lisbon, and he returned to Paris to take
 his seat in the Chamber of Deputies. In spite of his pronounced
 Royalism, he now showed Liberal tendencies, opposed the policy of
-Villèle's cabinet, and in 1828 became a member of the moderate
+Villèle's cabinet, and in 1828 became a member of the moderate
 administration of Martignac as minister of marine. In this capacity he
 showed active sympathy with the cause of Greek independence. During the
 Polignac ministry (1829-1830) he was again in opposition, being a firm
@@ -6208,7 +6174,7 @@ entered an all but solitary protest against the exclusion of the
 legitimate line of the Bourbons from the throne, and resigned his seat.
 He died in Paris on the 28th of May 1857.
 
-  His _Mémoires et souvenirs_ (3 vols., 1888), compiled from his notes
+  His _Mémoires et souvenirs_ (3 vols., 1888), compiled from his notes
   by his nieces, the vicomtesse de Bardonnet and the baronne Laurenceau,
   are of great interest for the Revolution and the Restoration.
 
@@ -6218,7 +6184,7 @@ He died in Paris on the 28th of May 1857.
 HYDE PARK, a small township of Norfolk county, Massachusetts, U.S.A.,
 about 8 m. S.W. of the business centre of Boston. Pop. (1890) 10,193;
 (1900) 13,244, of whom 3805 were foreign-born; (1910 census) 15,507. Its
-area is about 4½ sq. m. It is traversed by the New York, New Haven &
+area is about 4½ sq. m. It is traversed by the New York, New Haven &
 Hartford railway, which has large repair shops here, and by the Neponset
 river and smaller streams. The township contains the villages of Hyde
 Park, Readville (in which there is the famous "Weil" trotting-track),
@@ -6277,8 +6243,8 @@ Hyderabad city into Rajputana.
 HYDERABAD, HAIDARABAD, also known as the Nizam's Dominions, the
 principal native state of India in extent, population and political
 importance; area, 82,698 sq. m.; pop. (1901) 11,141,142, showing a
-decrease of 3.4% in the decade; estimated revenue 4½ crores of Hyderabad
-rupees (£2,500,000). The state occupies a large portion of the eastern
+decrease of 3.4% in the decade; estimated revenue 4½ crores of Hyderabad
+rupees (£2,500,000). The state occupies a large portion of the eastern
 plateau of the Deccan. It is bounded on the north and north-east by
 Berar, on the south and south-east by Madras, and on the west by Bombay.
 The country presents much variety of surface and feature; but it may be
@@ -6366,14 +6332,14 @@ Imperial Service Troops, which now form the contribution of the native
 chiefs to the defence of India. On the occasion of the Panjdeh incident
 in 1885 he made an offer of money and men, and subsequently on the
 occasion of Queen Victoria's Jubilee in 1887 he offered 20 lakhs
-(£130,000) annually for three years for the purpose of frontier defence.
+(£130,000) annually for three years for the purpose of frontier defence.
 It was finally decided that the native chiefs should maintain small but
 well-equipped bodies of infantry and cavalry for imperial defence. For
 many years past the Hyderabad finances were in a very unhealthy
 condition, the expenditure consistently outran the revenue, and the
 nobles, who held their tenure under an obsolete feudal system, vied
 with each other in ostentatious extravagance. But in 1902, on the
-revision of the Berar agreement, the nizam received 25 lakhs (£167,000)
+revision of the Berar agreement, the nizam received 25 lakhs (£167,000)
 a year for the rent of Berar, thus substituting a fixed for a
 fluctuating source of income, and a British financial adviser was
 appointed for the purpose of reorganizing the resources of the state.
@@ -6423,7 +6389,7 @@ Hyderabad is an important centre of general trade, and there is a cotton
 mill in its vicinity. The city is supplied with water from two notable
 works, the Husain Sagar and the Mir Alam, both large lakes retained by
 great dams. Secunderabad, the British military cantonment, is situated
-5½ m. N. of the residency; it includes Bolaram, the former headquarters
+5½ m. N. of the residency; it includes Bolaram, the former headquarters
 of the Hyderabad contingent.
 
 
@@ -6479,7 +6445,7 @@ by the Mahrattas in 1772, claimed British assistance, but in vain; this
 breach of faith stung him to fury, and thenceforward he and his son did
 not cease to thirst for vengeance. His time came when in 1778 the
 British, on the declaration of war with France, resolved to drive the
-French out of India. The capture of Mahé on the coast of Malabar in
+French out of India. The capture of Mahé on the coast of Malabar in
 1779, followed by the annexation of lands belonging to a dependent of
 his own, gave him the needed pretext. Again master of all that the
 Mahrattas had taken from him, and with empire extended to the Kistna, he
@@ -6506,7 +6472,7 @@ suddenly at Chittur in December 1782.
   Ali see the _History of Hyder Naik_, written by Mir Hussein Ali Khan
   Kirmani (translated from the Persian by Colonel Miles, and published
   by the Oriental Translation Fund), and the curious work written by M.
-  Le Maître de La Tour, commandant of his artillery (_Histoire
+  Le Maître de La Tour, commandant of his artillery (_Histoire
   d'Hayder-Ali Khan_, Paris, 1783). For the whole life and times see
   Wilks, _Historical Sketches of the South of India_ (1810-1817);
   Aitchison's Treaties, vol. v. (2nd ed., 1876); and Pearson, _Memoirs
@@ -6568,16 +6534,16 @@ about 22,000 people in the island, and of these 10,000 were seafarers.
 At the time of the outbreak of the war of Greek independence the total
 population was 28,190, of whom 16,460 were natives and the rest
 foreigners. One of their chief families, the Konduriotti, was worth
-£2,000,000. Into the struggle the Hydriotes flung themselves with rare
+£2,000,000. Into the struggle the Hydriotes flung themselves with rare
 enthusiasm and devotion, and the final deliverance of Greece was mainly
 due to the service rendered by their fleets.
 
-  See Pouqueville, _Voy. de la Grèce_, vol. vi.; Antonios Miaoules,
-  [Greek: Hypomnêma peri tês nêsou Hydras] (Munich, 1834); Id. [Greek:
-  Sunoptikê historia tôn naumachiôn dia tôn ploiôn tôn triôn nêsôn,
-  Hydras, Petsôn kai Psarôn] (Nauplia, 1833); Id. [Greek: Historia tês
-  nêsou Hydras] (Athens, 1874); G. D. Kriezes, [Greek: Historia tês
-  nêsou Hydras] (Patras, 1860).
+  See Pouqueville, _Voy. de la Grèce_, vol. vi.; Antonios Miaoules,
+  [Greek: Hypomnêma peri tês nêsou Hydras] (Munich, 1834); Id. [Greek:
+  Sunoptikê historia tôn naumachiôn dia tôn ploiôn tôn triôn nêsôn,
+  Hydras, Petsôn kai Psarôn] (Nauplia, 1833); Id. [Greek: Historia tês
+  nêsou Hydras] (Athens, 1874); G. D. Kriezes, [Greek: Historia tês
+  nêsou Hydras] (Patras, 1860).
 
 
 
@@ -6627,18 +6593,18 @@ variable, the range in magnitude being 4.5 to 6.
 
 
 
-HYDRACRYLIC ACID (ethylene lactic acid), CH2OH·CH2·CO2H. an organic
+HYDRACRYLIC ACID (ethylene lactic acid), CH2OH·CH2·CO2H. an organic
 oxyacid prepared by acting with silver oxide and water on
 [beta]-iodopropionic acid, or from ethylene by the addition of
 hypochlorous acid, the addition product being then treated with
 potassium cyanide and hydrolysed by an acid. It may also be prepared by
 oxidizing the trimethylene glycol obtained by the action of hydrobromic
 acid on allylbromide. It is a syrupy liquid, which on distillation is
-resolved into water and the unsaturated acrylic acid, CH2:CH·CO2H.
+resolved into water and the unsaturated acrylic acid, CH2:CH·CO2H.
 Chromic and nitric acids oxidize it to oxalic acid and carbon dioxide.
-Hydracrylic aldehyde, CH2OH·CH2·CHO, was obtained in 1904 by J. U. Nef
+Hydracrylic aldehyde, CH2OH·CH2·CHO, was obtained in 1904 by J. U. Nef
 (_Ann._ 335, p. 219) as a colourless oil by heating acrolein with water.
-Dilute alkalis convert it into crotonaldehyde, CH3·CH:CH·CHO.
+Dilute alkalis convert it into crotonaldehyde, CH3·CH:CH·CHO.
 
 
 
@@ -6724,7 +6690,7 @@ anhydrous. Compounds embraced by the second definition are more usually
 termed _hydroxides_, since at one time they were regarded as
 combinations of an oxide with water, for example, calcium oxide or lime
 when slaked with water yielded calcium hydroxide, written formerly as
-CaO·H20. The general formulae of hydroxides are: M^iOH, M^(ii)(OH)2,
+CaO·H20. The general formulae of hydroxides are: M^iOH, M^(ii)(OH)2,
 M^(iii)(OH)3, M^(iv)(OH)4, &c., corresponding to the oxides M2^iO,
 M^(ii)O, M2^(iii)O3, M^(iv)O2, &c., the Roman index denoting the valency
 of the element. There is an important difference between non-metallic
@@ -6743,14 +6709,14 @@ VIB and VIIB of the periodic table.
 
 
 
-HYDRAULICS (Gr. [Greek: hydôr], water, and [Greek: aulos], a pipe), the
+HYDRAULICS (Gr. [Greek: hydôr], water, and [Greek: aulos], a pipe), the
 branch of engineering science which deals with the practical
 applications of the laws of hydromechanics.
 
 
 I. THE DATA OF HYDRAULICS[1]
 
-§ 1. _Properties of Fluids._--The fluids to which the laws of practical
+§ 1. _Properties of Fluids._--The fluids to which the laws of practical
 hydraulics relate are substances the parts of which possess very great
 mobility, or which offer a very small resistance to distortion
 independently of inertia. Under the general heading Hydromechanics a
@@ -6774,7 +6740,7 @@ all directions must be the same; or, in other words, the pressure on any
 small element of surface is independent of the orientation of the
 surface.
 
-§ 2. Fluids are divided into liquids, or incompressible fluids, and
+§ 2. Fluids are divided into liquids, or incompressible fluids, and
 gases, or compressible fluids. Very great changes of pressure change the
 volume of liquids only by a small amount, and if the pressure on them is
 reduced to zero they do not sensibly dilate. In gases or compressible
@@ -6785,7 +6751,7 @@ In ordinary hydraulics, liquids are treated as absolutely
 incompressible. In dealing with gases the changes of volume which
 accompany changes of pressure must be taken into account.
 
-§ 3. Viscous fluids are those in which change of form under a continued
+§ 3. Viscous fluids are those in which change of form under a continued
 stress proceeds gradually and increases indefinitely. A very viscous
 fluid opposes great resistance to change of form in a short time, and
 yet may be deformed considerably by a small stress acting for a long
@@ -6810,7 +6776,7 @@ great to be neglected.
   be filled with liquid. The layers of liquid in contact with ab and cd
   adhere to them. The intermediate layers all offering an equal
   resistance to shearing or distortion, the rectangle of fluid abcd will
-  take the form of the parallelogram a´b´cd. Further, the resistance to
+  take the form of the parallelogram a´b´cd. Further, the resistance to
   the motion of ab may be expressed in the form
 
     R = [kappa][omega]V,   (1)
@@ -6827,11 +6793,11 @@ great to be neglected.
   dividing face will be exactly the same as before, and the resistance
   must therefore be the same. Hence,
 
-    R = [kappa]´[omega](nV).   (2)
+    R = [kappa]´[omega](nV).   (2)
 
   But equations (1) and (2) may both be expressed in one equation if
-  [kappa] and [kappa]´ are replaced by a constant varying inversely as
-  the thickness of the layer. Putting [kappa] = [mu]/T, [kappa]´ =
+  [kappa] and [kappa]´ are replaced by a constant varying inversely as
+  the thickness of the layer. Putting [kappa] = [mu]/T, [kappa]´ =
   [mu]/nT,
 
     R = [mu][omega]V/T;
@@ -6843,16 +6809,16 @@ great to be neglected.
   an expression first proposed by L. M. H. Navier. The coefficient [mu]
   is termed the coefficient of viscosity.
 
-  According to J. Clerk Maxwell, the value of [mu] for air at [theta]°
+  According to J. Clerk Maxwell, the value of [mu] for air at [theta]°
   Fahr. in pounds, when the velocities are expressed in feet per second,
   is
 
-    [mu] = 0.0000000256 (461° + [theta]);
+    [mu] = 0.0000000256 (461° + [theta]);
 
   that is, the coefficient of viscosity is proportional to the absolute
   temperature and independent of the pressure.
 
-  The value of [mu] for water at 77° Fahr. is, according to H. von
+  The value of [mu] for water at 77° Fahr. is, according to H. von
   Helmholtz and G. Piotrowski,
 
     [mu] = 0.0000188,
@@ -6862,7 +6828,7 @@ great to be neglected.
 
 [Illustration: FIG. 2.]
 
-§ 4. When a fluid flows in a very regular manner, as for instance when
+§ 4. When a fluid flows in a very regular manner, as for instance when
 It flows in a capillary tube, the velocities vary gradually at any
 moment from one point of the fluid to a neighbouring point. The layer
 adjacent to the sides of the tube adheres to it and is at rest. The
@@ -6894,7 +6860,7 @@ fluid.
 
 RELATION OF PRESSURE, DENSITY, AND TEMPERATURE OF LIQUIDS
 
-  § 5. _Units of Volume._--In practical calculations the cubic foot and
+  § 5. _Units of Volume._--In practical calculations the cubic foot and
   gallon are largely used, and in metric countries the litre and cubic
   metre (= 1000 litres). The imperial gallon is now exclusively used in
   England, but the United States have retained the old English wine
@@ -6905,15 +6871,15 @@ RELATION OF PRESSURE, DENSITY, AND TEMPERATURE OF LIQUIDS
     1 U.S. gallon = 0.1337 cub. ft.    = 0.8333 imp. gallon.
     1 litre       = 0.2201 imp. gallon = 0.2641 U.S. gallon.
 
-  _Density of Water._--Water at 53° F. and ordinary pressure contains
-  62.4 lb. per cub. ft., or 10 lb. per imperial gallon at 62° F. The
-  litre contains one kilogram of water at 4° C. or 1000 kilograms per
+  _Density of Water._--Water at 53° F. and ordinary pressure contains
+  62.4 lb. per cub. ft., or 10 lb. per imperial gallon at 62° F. The
+  litre contains one kilogram of water at 4° C. or 1000 kilograms per
   cubic metre. River and spring water is not sensibly denser than pure
-  water. But average sea water weighs 64 lb. per cub. ft. at 53° F. The
+  water. But average sea water weighs 64 lb. per cub. ft. at 53° F. The
   weight of water per cubic unit will be denoted by G. Ice free from air
   weighs 57.28 lb. per cub. ft. (Leduc).
 
-  § 6. _Compressibility of Liquids._--The most accurate experiments show
+  § 6. _Compressibility of Liquids._--The most accurate experiments show
   that liquids are sensibly compressed by very great pressures, and that
   up to a pressure of 65 atmospheres, or about 1000 lb. per sq. in., the
   compression is proportional to the pressure. The chief results of
@@ -6946,7 +6912,7 @@ RELATION OF PRESSURE, DENSITY, AND TEMPERATURE OF LIQUIDS
   diminishes as the temperature increases, while that of ether, alcohol
   and chloroform is increased.
 
-  § 7. _Change of Volume and Density of Water with Change of
+  § 7. _Change of Volume and Density of Water with Change of
   Temperature._--Although the change of volume of water with change of
   temperature is so small that it may generally be neglected in ordinary
   hydraulic calculations, yet it should be noted that there is a change
@@ -7005,14 +6971,14 @@ RELATION OF PRESSURE, DENSITY, AND TEMPERATURE OF LIQUIDS
     +-----+-------+----------+----------+
 
   The weight per cubic foot has been calculated from the values of
-  [rho], on the assumption that 1 cub. ft. of water at 39.2° Fahr. is
+  [rho], on the assumption that 1 cub. ft. of water at 39.2° Fahr. is
   62.425 lb. For ordinary calculations in hydraulics, the density of
   water (which will in future be designated by the symbol G) will be
-  taken at 62.4 lb. per cub. ft., which is its density at 53° Fahr. It
-  may be noted also that ice at 32° Fahr. contains 57.3 lb. per cub. ft.
+  taken at 62.4 lb. per cub. ft., which is its density at 53° Fahr. It
+  may be noted also that ice at 32° Fahr. contains 57.3 lb. per cub. ft.
   The values of [rho] are the densities in grammes per cubic centimetre.
 
-  § 8. _Pressure Column. Free Surface Level._--Suppose a small vertical
+  § 8. _Pressure Column. Free Surface Level._--Suppose a small vertical
   pipe introduced into a liquid at any point P (fig. 3). Then the liquid
   will rise in the pipe to a level OO, such that the pressure due to the
   column in the pipe exactly balances the pressure on its mouth. If the
@@ -7034,7 +7000,7 @@ RELATION OF PRESSURE, DENSITY, AND TEMPERATURE OF LIQUIDS
 
   RELATION OF PRESSURE, TEMPERATURE, AND DENSITY OF GASES
 
-  § 9. _Relation of Pressure, Volume, Temperature and Density in
+  § 9. _Relation of Pressure, Volume, Temperature and Density in
   Compressible Fluids._--Certain problems on the flow of air and steam
   are so similar to those relating to the flow of water that they are
   conveniently treated together. It is necessary, therefore, to state as
@@ -7050,7 +7016,7 @@ RELATION OF PRESSURE, DENSITY, AND TEMPERATURE OF LIQUIDS
   given quantity of air is a constant (Boyle's law).
 
   Let p0 be mean atmospheric pressure (2116.8 lb. per sq. ft.), V0 the
-  volume of 1 lb. of air at 32° Fahr. under the pressure p0. Then
+  volume of 1 lb. of air at 32° Fahr. under the pressure p0. Then
 
     p0V0 = 26214.   (1)
 
@@ -7059,21 +7025,21 @@ RELATION OF PRESSURE, DENSITY, AND TEMPERATURE OF LIQUIDS
     G0 = 1/V0 = 2116.8/26214 = .08075.   (2)
 
   For any other pressure p, at which the volume of 1 lb. is V and the
-  weight per cubic foot is G, the temperature being 32° Fahr.,
+  weight per cubic foot is G, the temperature being 32° Fahr.,
 
     pV = p/G = 26214; or G = p/26214.   (3)
 
   _Change of Pressure or Volume by Change of Temperature._--Let p0, V0,
   G0, as before be the pressure, the volume of a pound in cubic feet,
-  and the weight of a cubic foot in pounds, at 32° Fahr. Let p, V, G be
+  and the weight of a cubic foot in pounds, at 32° Fahr. Let p, V, G be
   the same quantities at a temperature t (measured strictly by the air
   thermometer, the degrees of which differ a little from those of a
   mercurial thermometer). Then, by experiment,
 
     pV = p0V0(460.6 + t)/(460.6 + 32) = p0V0[tau]/[tau]0,   (4)
 
-  where [tau], [tau]0 are the temperatures t and 32° reckoned from the
-  absolute zero, which is -460.6° Fahr.;
+  where [tau], [tau]0 are the temperatures t and 32° reckoned from the
+  absolute zero, which is -460.6° Fahr.;
 
     p/G = p0[tau]/G0[tau]0;   (4a)
 
@@ -7084,13 +7050,13 @@ RELATION OF PRESSURE, DENSITY, AND TEMPERATURE OF LIQUIDS
     p/G = 53.2[tau].   (5a)
 
   Or quite generally p/G = R[tau] for all gases, if R is a constant
-  varying inversely as the density of the gas at 32° F. For steam R =
+  varying inversely as the density of the gas at 32° F. For steam R =
   85.5.
 
 
 II. KINEMATICS OF FLUIDS
 
-§ 10. Moving fluids as commonly observed are conveniently classified
+§ 10. Moving fluids as commonly observed are conveniently classified
 thus:
 
 (1) _Streams_ are moving masses of indefinite length, completely or
@@ -7112,7 +7078,7 @@ definite paths in space. A chain of particles following each other along
 such a constant path may be termed a fluid filament or elementary
 stream.
 
-  § 11. _Steady and Unsteady, Uniform and Varying, Motion._--There are
+  § 11. _Steady and Unsteady, Uniform and Varying, Motion._--There are
   two quite distinct ways of treating hydrodynamical questions. We may
   either fix attention on a given mass of fluid and consider its changes
   of position and energy under the action of the stresses to which it is
@@ -7149,7 +7115,7 @@ stream.
   definite term applicable in strictness only to the condition of the
   stream bed.
 
-  § 12. _Theoretical Notions on the Motion of Water._--The actual motion
+  § 12. _Theoretical Notions on the Motion of Water._--The actual motion
   of the particles of water is in most cases very complex. To simplify
   hydrodynamic problems, simpler modes of motion are assumed, and the
   results of theory so obtained are compared experimentally with the
@@ -7159,7 +7125,7 @@ stream.
   one in which the particles initially situated in any plane cross
   section of the stream continue to be found in plane cross sections
   during the subsequent motion. Thus, if the particles in a thin plane
-  layer ab (fig. 5) are found again in a thin plane layer a´b´ after any
+  layer ab (fig. 5) are found again in a thin plane layer a´b´ after any
   interval of time, the motion is said to be motion in plane layers. In
   such motion the internal work in deforming the layer may usually be
   disregarded, and the resistance to the motion is confined to the
@@ -7199,7 +7165,7 @@ stream.
 
   [Illustration: FIG. 6.]
 
-  § 13. _Volume of Flow._--Let A (fig. 6) be any ideal plane surface, of
+  § 13. _Volume of Flow._--Let A (fig. 6) be any ideal plane surface, of
   area [omega], in a stream, normal to the direction of motion, and let
   V be the velocity of the fluid. Then the volume flowing through the
   surface A in unit time is
@@ -7208,12 +7174,12 @@ stream.
 
   Thus, if the motion is rectilinear, all the particles at any instant
   in the surface A will be found after one second in a similar surface
-  A´, at a distance V, and as each particle is followed by a continuous
-  thread of other particles, the volume of flow is the right prism AA´
+  A´, at a distance V, and as each particle is followed by a continuous
+  thread of other particles, the volume of flow is the right prism AA´
   having a base [omega] and length V.
 
   If the direction of motion makes an angle [theta] with the normal to
-  the surface, the volume of flow is represented by an oblique prism AA´
+  the surface, the volume of flow is represented by an oblique prism AA´
   (fig. 7), and in that case
 
     Q = [omega]V cos [theta].
@@ -7232,7 +7198,7 @@ stream.
 
   as the case may be.
 
-  § 14. _Principle of Continuity._--If we consider any completely
+  § 14. _Principle of Continuity._--If we consider any completely
   bounded fixed space in a moving liquid initially and finally filled
   continuously with liquid, the inflow must be equal to the outflow.
   Expressing the inflow with a positive and the outflow with a negative
@@ -7292,11 +7258,11 @@ stream.
 
     G1A1v1 = G2A2v2;
 
-  and hence, from (5a) § 9, if the temperature is constant,
+  and hence, from (5a) § 9, if the temperature is constant,
 
     p1A1v1 = p2A2v2.   (3)
 
-  § 15. _Stream Lines._--The characteristic of a perfect fluid, that is,
+  § 15. _Stream Lines._--The characteristic of a perfect fluid, that is,
   a fluid free from viscosity, is that the pressure between any two
   parts into which it is divided by a plane must be normal to the plane.
   One consequence of this is that the particles can have no rotation
@@ -7372,7 +7338,7 @@ stream.
   III. PHENOMENA OF THE DISCHARGE OF LIQUIDS FROM ORIFICES AS
   ASCERTAINABLE BY EXPERIMENTS
 
-  § 16. When a liquid issues vertically from a small orifice, it forms a
+  § 16. When a liquid issues vertically from a small orifice, it forms a
   jet which rises nearly to the level of the free surface of the liquid
   in the vessel from which it flows. The difference of level h_r (fig.
   14) is so small that it may be at once suspected to be due either to
@@ -7413,10 +7379,10 @@ stream.
   the pressure p at the orifice which produces outflow is connected with
   h by the relation p/G = h, the quantity p/G may be termed the pressure
   head at the orifice. Lastly, the velocity v is connected with h by the
-  relation v²/2g = h, so that v²/2g may be termed the head due to the
+  relation v²/2g = h, so that v²/2g may be termed the head due to the
   velocity v.
 
-  § 17. _Coefficients of Velocity and Resistance._--As the actual
+  § 17. _Coefficients of Velocity and Resistance._--As the actual
   velocity of discharge differs from [root]2gh by a small quantity, let
   the actual velocity
 
@@ -7447,10 +7413,10 @@ stream.
 
     c_v = [root]{1/(1 + c_r)}   (5)
 
-    c_r = 1/c_v² - 1   (5a)
+    c_r = 1/c_v² - 1   (5a)
 
   Thus if c_v = 0.97, then c_r = 0.0628. That is, for such an orifice
-  about 6¼% of the head is expended in overcoming frictional resistances
+  about 6¼% of the head is expended in overcoming frictional resistances
   to flow.
 
   [Illustration: FIG. 15.]
@@ -7486,18 +7452,18 @@ stream.
   is normal to a transverse section of the jet. Hence the actual
   discharge when contraction occurs is
 
-    Q_a = c_vv × c_c[omega] = c_c c_v[omega][root](2gh),
+    Q_a = c_vv × c_c[omega] = c_c c_v[omega][root](2gh),
 
   or simply, if c = c_vc_c,
 
     Q_a = c[omega][root](2gh),
 
   where c is called the _coefficient of discharge_. Thus for a
-  sharp-edged plane orifice c = 0.97 × 0.64 = 0.62.
+  sharp-edged plane orifice c = 0.97 × 0.64 = 0.62.
 
   [Illustration: FIG. 16.]
 
-  § 18. _Experimental Determination of c_v, c_c, and c._--The
+  § 18. _Experimental Determination of c_v, c_c, and c._--The
   coefficient of contraction c_c is directly determined by measuring the
   dimensions of the jet. For this purpose fixed screws of fine pitch
   (fig. 16) are convenient. These are set to touch the jet, and then the
@@ -7511,18 +7477,18 @@ stream.
   A on the parabolic path of the jet. If v_a is the velocity at the
   orifice, and t the time in which a particle moves from O to A, then
 
-    x = v_a t; y = ½gt².
+    x = v_a t; y = ½gt².
 
   Eliminating t,
 
-    v_a = [root](gx²/2y).
+    v_a = [root](gx²/2y).
 
   Then
 
-    c_v = v_a [root](2gh) = [root](x²/4yh).
+    c_v = v_a [root](2gh) = [root](x²/4yh).
 
   In the case of large orifices such as weirs, the velocity can be
-  directly determined by using a Pitot tube (§ 144).
+  directly determined by using a Pitot tube (§ 144).
 
   [Illustration: FIG. 17.]
 
@@ -7563,7 +7529,7 @@ stream.
 
   [Illustration: FIG. 19.]
 
-  § 19. _Coefficients for Bellmouths and Bellmouthed Orifices._--If an
+  § 19. _Coefficients for Bellmouths and Bellmouthed Orifices._--If an
   orifice is furnished with a mouthpiece exactly of the form of the
   contracted vein, then the whole of the contraction occurs within the
   mouthpiece, and if the area of the orifice is measured at the smaller
@@ -7589,7 +7555,7 @@ stream.
 
     Q = c(v)[omega][root](2gh) = [omega][root]{2gh/(1 + c_r}.
 
-  § 20. _Coefficients for Sharp-edged or virtually Sharp-edged
+  § 20. _Coefficients for Sharp-edged or virtually Sharp-edged
   Orifices._--There are a very large number of measurements of discharge
   from sharp-edged orifices under different conditions of head. An
   account of these and a very careful tabulation of the average values
@@ -7675,13 +7641,13 @@ stream.
 
   where h is in feet and d in inches.
 
-    _Coefficients of Discharge from Circular Orifices. Temperature 51° to
-    55°._
+    _Coefficients of Discharge from Circular Orifices. Temperature 51° to
+    55°._
 
     +-------+--------------------------------------------------------------+
     |Head in|             Diameters of Orifices in Inches (d).             |
     | feet  +------+------+------+------+------+------+------+------+------+
-    |   h.  |   1  |  1¼  |  1½  |  1¾  |   2  |  2¼  |  2½  |  2¾  |   3  |
+    |   h.  |   1  |  1¼  |  1½  |  1¾  |   2  |  2¼  |  2½  |  2¾  |   3  |
     +-------+------+------+------+------+------+------+------+------+------+
     |       |                       Coefficients (c).                      |
     |       +------+------+------+------+------+------+------+------+------+
@@ -7709,9 +7675,9 @@ stream.
     |   to   |                                                                |
     | Centre +------+------+------+------+--------+--------+--------+---------+
     |   of   |      |      |      |      |        |        |        |         |
-    |Orifice.|  4   |  2   |  1½  |  1   |   ¾    |    ½   |    ¼   |   1/8   |
+    |Orifice.|  4   |  2   |  1½  |  1   |   ¾    |    ½   |    ¼   |   1/8   |
     +--------+------+------+------+------+--------+--------+--------+---------+
-    |        | 4 ft.| 2 ft.|1½ ft.| 1 ft.|0.75 ft.|0.50 ft.|0.25 ft.|0.125 ft.|
+    |        | 4 ft.| 2 ft.|1½ ft.| 1 ft.|0.75 ft.|0.50 ft.|0.25 ft.|0.125 ft.|
     |        | high.| high.| high.| high.|  high. |  high. |  high. |  high.  |
     |  Feet. |      |      |      |      |        |        |        |         |
     |        | 1 ft.| 1 ft.| 1 ft.| 1 ft.|  1 ft. |  1 ft. |  1 ft. |  1 ft.  |
@@ -7753,7 +7719,7 @@ stream.
     |  50    |.6086 |.6060 |.6034 |.6018 | .6035  | .6050  | .6070  |  .6140  |
     +--------+------+------+------+------+--------+--------+--------+---------+
 
-  § 21. _Orifices with Edges of Sensible Thickness._--When the edges of
+  § 21. _Orifices with Edges of Sensible Thickness._--When the edges of
   the orifice are not bevelled outwards, but have a sensible thickness,
   the coefficient of discharge is somewhat altered. The following table
   gives values of the coefficient of discharge for the arrangements of
@@ -7764,7 +7730,7 @@ stream.
 
     Q = cb(H - h) [root]{2g(H + h)/2}.
 
-  § 22. _Partially Suppressed Contraction._--Since the contraction of
+  § 22. _Partially Suppressed Contraction._--Since the contraction of
   the jet is due to the convergence towards the orifice of the issuing
   streams, it will be diminished if for any portion of the edge of the
   orifice the convergence is prevented. Thus, if an internal rim or
@@ -7807,7 +7773,7 @@ stream.
   when n is the length of the edge of the orifice over which the border
   extends, and p is the whole length of edge or perimeter of the
   orifice. The following are the values of c_c, when the border extends
-  over ¼, ½, or ¾ of the whole perimeter:--
+  over ¼, ½, or ¾ of the whole perimeter:--
 
     +--------+-----------------------+--------------------+
     |        |          C_c          |        C_c         |
@@ -7826,7 +7792,7 @@ stream.
   Bornemann has shown, however, that these formulae for suppressed
   contraction are not reliable.
 
-  § 23. _Imperfect Contraction._--If the sides of the vessel approach
+  § 23. _Imperfect Contraction._--If the sides of the vessel approach
   near to the edge of the orifice, they interfere with the convergence
   of the streams to which the contraction is due, and the contraction is
   then modified. It is generally stated that the influence of the sides
@@ -7836,7 +7802,7 @@ stream.
 
   [Illustration: FIG. 22.]
 
-  § 24. _Orifices Furnished with Channels of Discharge._--These external
+  § 24. _Orifices Furnished with Channels of Discharge._--These external
   borders to an orifice also modify the contraction.
 
   The following coefficients of discharge were obtained with openings 8
@@ -7859,7 +7825,7 @@ stream.
 
   [Illustration: FIG. 23.]
 
-  § 25. _Inversion of the Jet._--When a jet issues from a horizontal
+  § 25. _Inversion of the Jet._--When a jet issues from a horizontal
   orifice, or is of small size compared with the head, it presents no
   marked peculiarity of form. But if the orifice is in a vertical
   surface, and if its dimensions are not small compared with the head,
@@ -7910,40 +7876,40 @@ stream.
   this contraction first suggested by H. Buff (1805-1878), namely, that
   it is due to surface tension.
 
-  § 26. _Influence of Temperature on Discharge of Orifices._--Professor
+  § 26. _Influence of Temperature on Discharge of Orifices._--Professor
   VV. C. Unwin found (_Phil. Mag._, October 1878, p. 281) that for
   sharp-edged orifices temperature has a very small influence on the
   discharge. For an orifice 1 cm. in diameter with heads of about 1 to
-  1½ ft. the coefficients were:--
+  1½ ft. the coefficients were:--
 
     Temperature F.      C.
-        205°          .594
-         62°          .598
+        205°          .594
+         62°          .598
 
   For a conoidal or bell-mouthed orifice 1 cm. diameter the effect of
   temperature was greater:--
 
     Temperature F.      C.
-        190°          0.987
-        130°          0.974
-         60°          0.942
+        190°          0.987
+        130°          0.974
+         60°          0.942
 
   an increase in velocity of discharge of 4% when the temperature
-  increased 130°.
+  increased 130°.
 
   J. G. Mair repeated these experiments on a much larger scale (_Proc.
-  Inst. Civ. Eng._ lxxxiv.). For a sharp-edged orifice 2½ in. diameter,
-  with a head of 1.75 ft., the coefficient was 0.604 at 57° and 0.607 at
-  179° F., a very small difference. With a conoidal orifice the
-  coefficient was 0.961 at 55° and 0.98l at 170° F. The corresponding
+  Inst. Civ. Eng._ lxxxiv.). For a sharp-edged orifice 2½ in. diameter,
+  with a head of 1.75 ft., the coefficient was 0.604 at 57° and 0.607 at
+  179° F., a very small difference. With a conoidal orifice the
+  coefficient was 0.961 at 55° and 0.98l at 170° F. The corresponding
   coefficients of resistance are 0.0828 and 0.0391, showing that the
   resistance decreases to about half at the higher temperature.
 
-  § 27. _Fire Hose Nozzles._--Experiments have been made by J. R.
+  § 27. _Fire Hose Nozzles._--Experiments have been made by J. R.
   Freeman on the coefficient of discharge from smooth cone nozzles used
-  for fire purposes. The coefficient was found to be 0.983 for ¾-in.
+  for fire purposes. The coefficient was found to be 0.983 for ¾-in.
   nozzle; 0.982 for 7/8 in.; 0.972 for 1 in.; 0.976 for 1(1/8) in.;
-  and 0.971 for 1¼ in. The nozzles were fixed on a taper play-pipe, and
+  and 0.971 for 1¼ in. The nozzles were fixed on a taper play-pipe, and
   the coefficient includes the resistance of this pipe (_Amer. Soc. Civ.
   Eng._ xxi., 1889). Other forms of nozzle were tried such as ring
   nozzles for which the coefficient was smaller.
@@ -7951,7 +7917,7 @@ stream.
 
   IV. THEORY OF THE STEADY MOTION OF FLUIDS.
 
-  § 28. The general equation of the steady motion of a fluid given under
+  § 28. The general equation of the steady motion of a fluid given under
   Hydrodynamics furnishes immediately three results as to the
   distribution of pressure in a stream which may here be assumed.
 
@@ -7978,7 +7944,7 @@ stream.
 
   DISTRIBUTION OF ENERGY IN INCOMPRESSIBLE FLUIDS.
 
-  § 29. _Application of the Principle of the Conservation of Energy to
+  § 29. _Application of the Principle of the Conservation of Energy to
   Cases of Stream Line Motion._--The external and internal work done on
   a mass is equal to the change of kinetic energy produced. In many
   hydraulic questions this principle is difficult to apply, because from
@@ -7998,8 +7964,8 @@ stream.
   intensity of pressure, and z the elevation above XX, of the elementary
   stream AB at A, and [omega]1, p1, v1, z1 the same quantities at B.
   Suppose that in a short time t the mass of fluid initially occupying
-  AB comes to A´B´. Then AA´, BB´ are equal to vt, v1t, and the volumes
-  of fluid AA´, BB´ are the equal inflow and outflow = Qt = [omega]vt =
+  AB comes to A´B´. Then AA´, BB´ are equal to vt, v1t, and the volumes
+  of fluid AA´, BB´ are the equal inflow and outflow = Qt = [omega]vt =
   [omega]1v1t, in the given time. If we suppose the filament AB
   surrounded by other filaments moving with not very different
   velocities, the frictional or viscous resistance on its surface will
@@ -8013,35 +7979,35 @@ stream.
   work. Hence the only external forces to be reckoned are gravity and
   the pressures on the ends of the stream.
 
-  The work of gravity when AB falls to A´B´ is the same as that of
-  transferring AA´ to BB´; that is, GQt(z - z1). The work of the
+  The work of gravity when AB falls to A´B´ is the same as that of
+  transferring AA´ to BB´; that is, GQt(z - z1). The work of the
   pressures on the ends, reckoning that at B negative, because it is
-  opposite to the direction of motion, is (p[omega] × vt) - (p1[omega]1
-  × v1t) = Qt(p - p1). The change of kinetic energy in the time t is the
-  difference of the kinetic energy originally possessed by AA´ and that
-  finally acquired by BB´, for in the intermediate part A´B there is no
+  opposite to the direction of motion, is (p[omega] × vt) - (p1[omega]1
+  × v1t) = Qt(p - p1). The change of kinetic energy in the time t is the
+  difference of the kinetic energy originally possessed by AA´ and that
+  finally acquired by BB´, for in the intermediate part A´B there is no
   change of kinetic energy, in consequence of the steadiness of the
-  motion. But the mass of AA´ and BB´ is GQt/g, and the change of
-  kinetic energy is therefore (GQt/g) (v1²/2 - v²/2). Equating this to
+  motion. But the mass of AA´ and BB´ is GQt/g, and the change of
+  kinetic energy is therefore (GQt/g) (v1²/2 - v²/2). Equating this to
   the work done on the mass AB,
 
-    GQt(z - z1) + Qt(p - p1) = (GQt/g)(v1²/2 - v²/2).
+    GQt(z - z1) + Qt(p - p1) = (GQt/g)(v1²/2 - v²/2).
 
   Dividing by GQt and rearranging the terms,
 
-    v²/2g + p/G + z = v1²/2g + p1/G + z1;   (1)
+    v²/2g + p/G + z = v1²/2g + p1/G + z1;   (1)
 
   or, as A and B are any two points,
 
-    v²/2g + p/G + z = constant = H.   (2)
+    v²/2g + p/G + z = constant = H.   (2)
 
-  Now v²/2g is the head due to the velocity v, p/G is the head
+  Now v²/2g is the head due to the velocity v, p/G is the head
   equivalent to the pressure, and z is the elevation above the datum
-  (see § 16). Hence the terms on the left are the total head due to
+  (see § 16). Hence the terms on the left are the total head due to
   velocity, pressure, and elevation at a given cross section of the
   filament, z is easily seen to be the work in foot-pounds which would
   be done by 1 lb. of fluid falling to the datum line, and similarly p/G
-  and v²/2g are the quantities of work which would be done by 1 lb. of
+  and v²/2g are the quantities of work which would be done by 1 lb. of
   fluid due to the pressure p and velocity v. The expression on the left
   of the equation is, therefore, the total energy of the stream at the
   section considered, per lb. of fluid, estimated with reference to the
@@ -8051,38 +8017,38 @@ stream.
   the fluid OO is taken as the datum, and -h, -h1 are the depths of A
   and B measured down from the free surface, the equation takes the form
 
-    v²/2g + p/G - h = v1²/2g + p1/G - h1;   (3)
+    v²/2g + p/G - h = v1²/2g + p1/G - h1;   (3)
 
   or generally
 
-    v²/2g + p/G - h = constant.   (3a)
+    v²/2g + p/G - h = constant.   (3a)
 
   [Illustration: FIG. 26.]
 
-  § 30. _Second Form of the Theorem of Bernoulli._--Suppose at the two
+  § 30. _Second Form of the Theorem of Bernoulli._--Suppose at the two
   sections A, B (fig. 26) of an elementary stream small vertical pipes
-  are introduced, which may be termed pressure columns (§ 8), having
+  are introduced, which may be termed pressure columns (§ 8), having
   their lower ends accurately parallel to the direction of flow. In such
   tubes the water will rise to heights corresponding to the pressures at
-  A and B. Hence b = p/G, and b´ = p1/G. Consequently the tops of the
-  pressure columns A´ and B´ will be at total heights b + c = p/G + z
-  and b´ + c´ = p1/G + z1 above the datum line XX. The difference of
+  A and B. Hence b = p/G, and b´ = p1/G. Consequently the tops of the
+  pressure columns A´ and B´ will be at total heights b + c = p/G + z
+  and b´ + c´ = p1/G + z1 above the datum line XX. The difference of
   level of the pressure column tops, or the fall of free surface level
   between A and B, is therefore
 
     [xi] = (p - p1)/G + (z - z1);
 
-  and this by equation (1), § 29 is (v1² - v²)/2g. That is, the fall of
+  and this by equation (1), § 29 is (v1² - v²)/2g. That is, the fall of
   free, surface level between two sections is equal to the difference of
-  the heights due to the velocities at the sections. The line A´B´ is
+  the heights due to the velocities at the sections. The line A´B´ is
   sometimes called the line of hydraulic gradient, though this term is
   also used in cases where friction needs to be taken into account. It
   is the line the height of which above datum is the sum of the
   elevation and pressure head at that point, and it falls below a
-  horizontal line A´´B´´ drawn at H ft. above XX by the quantities a =
-  v²/2g and a´ = v1²/2g, when friction is absent.
+  horizontal line A´´B´´ drawn at H ft. above XX by the quantities a =
+  v²/2g and a´ = v1²/2g, when friction is absent.
 
-  § 31. _Illustrations of the Theorem of Bernoulli._ In a lecture to the
+  § 31. _Illustrations of the Theorem of Bernoulli._ In a lecture to the
   mechanical section of the British Association in 1875, W. Froude gave
   some experimental illustrations of the principle of Bernoulli. He
   remarked that it was a common but erroneous impression that a fluid
@@ -8132,8 +8098,8 @@ stream.
   the right-hand cistern B (fig. 31), shooting across the free space
   between them without any waste, except that due to indirectness of aim
   and want of exact correspondence in the form of the orifices. In the
-  actual experiment there was 18 in. of head in the right and 20½ in. of
-  head in the left-hand cistern, so that about 2½ in. were wasted in
+  actual experiment there was 18 in. of head in the right and 20½ in. of
+  head in the left-hand cistern, so that about 2½ in. were wasted in
   friction. It will be seen that in the open space between the orifices
   there was no pressure, except the atmospheric pressure acting
   uniformly throughout the system.
@@ -8142,7 +8108,7 @@ stream.
 
   [Illustration: FIG. 31.]
 
-  § 32. _Venturi Meter._--An ingenious application of the variation of
+  § 32. _Venturi Meter._--An ingenious application of the variation of
   pressure and velocity in a converging and diverging pipe has been made
   by Clemens Herschel in the construction of what he terms a Venturi
   Meter for measuring the flow in water mains. Suppose that, as in fig.
@@ -8155,13 +8121,13 @@ stream.
   H, H2 be the pressure heads at those points. Since the velocity at B
   is greater than at A the pressure will be less. Neglecting friction
 
-    H1 + v²/2g = H + u²/2g,
+    H1 + v²/2g = H + u²/2g,
 
-    H1 - H = (u² - v²)/2g = ([rho]² - 1)v²/2g.
+    H1 - H = (u² - v²)/2g = ([rho]² - 1)v²/2g.
 
   Let h = H1 - H be termed the Venturi head, then
 
-    u = [root]{[rho]²·2gh/([rho]² - 1)},
+    u = [root]{[rho]²·2gh/([rho]² - 1)},
 
   from which the velocity through the throat and the discharge of the
   main can be calculated if the areas at A and B are known and h
@@ -8176,7 +8142,7 @@ stream.
 
   and the discharge of the main is
 
-    28 × 12.57 = 351 cub. ft. per sec.
+    28 × 12.57 = 351 cub. ft. per sec.
 
   [Illustration: FIG. 32.]
 
@@ -8194,7 +8160,7 @@ stream.
   Venturi head h. Consequently an experimental coefficient must be
   determined for each meter by tank measurement. The range of this
   coefficient is, however, surprisingly small. If to allow for friction,
-  u = k[root]{[rho]²/([rho]² - 1)}[root](2gh), then Herschel found
+  u = k[root]{[rho]²/([rho]² - 1)}[root](2gh), then Herschel found
   values of k from 0.97 to 1.0 for throat velocities varying from 8 to
   28 ft. per sec. The meter is extremely convenient. At Staines
   reservoirs there are two meters of this type on mains 94 in. in
@@ -8215,7 +8181,7 @@ stream.
   equilibrium. A pencil P records on a drum moved by clockwork the
   position of the disk, and from this the variation of flow is inferred.
 
-  § 33. _Pressure, Velocity and Energy in Different Stream Lines._--The
+  § 33. _Pressure, Velocity and Energy in Different Stream Lines._--The
   equation of Bernoulli gives the variation of pressure and velocity
   from point to point along a stream line, and shows that the total
   energy of the flow across any two sections is the same. Two other
@@ -8238,7 +8204,7 @@ stream.
   energy is measured, v its velocity, and p its pressure. Then, if H is
   the total energy at Q per unit of weight of fluid,
 
-    H = z + p/G + v²/2g.
+    H = z + p/G + v²/2g.
 
   Differentiating, we get
 
@@ -8258,19 +8224,19 @@ stream.
   volume is [omega] ds and its weight G[omega]ds. Hence, taking the
   components of the forces parallel to PQ--
 
-    [omega]dp = Gv²[omega] ds/g[rho] - G[omega] cos [phi] ds,
+    [omega]dp = Gv²[omega] ds/g[rho] - G[omega] cos [phi] ds,
 
   where [rho] is the radius of curvature of the stream line at Q.
   Consequently, introducing these values in (1),
 
-    dH = v² ds/g[rho] + v dv/g = (v/g)(v/[rho] + dv/ds) ds.   (2)
+    dH = v² ds/g[rho] + v dv/g = (v/g)(v/[rho] + dv/ds) ds.   (2)
 
 
   CURRENTS
 
-  § 34. _Rectilinear Current._--Suppose the motion is in parallel
+  § 34. _Rectilinear Current._--Suppose the motion is in parallel
   straight stream lines (fig. 35) in a vertical plane. Then [rho] is
-  infinite, and from eq. (2), § 33,
+  infinite, and from eq. (2), § 33,
 
      dH = v dv/g.
 
@@ -8301,17 +8267,17 @@ stream.
   The velocity would be infinite at radius 0, if the current could be
   conceived to extend to the axis. Now, if the motion is steady,
 
-    H = p1/G + v1²/2g = p2/G + v2²/2g;
-      = p2/G + r1² + v1²/r2²2g;
+    H = p1/G + v1²/2g = p2/G + v2²/2g;
+      = p2/G + r1² + v1²/r2²2g;
 
-    (p2- p1)/G = v1²(1 - r1²/r2²)/2g;   (5)
+    (p2- p1)/G = v1²(1 - r1²/r2²)/2g;   (5)
 
-    p2/G = H - r1²v1²/r2²2g.   (6)
+    p2/G = H - r1²v1²/r2²2g.   (6)
 
   Hence the pressure increases from the interior outwards, in a way
   indicated by the pressure columns in fig. 36, the curve through the
   free surfaces of the pressure columns being, in a radial section, the
-  quasi-hyperbola of the form xy² = c³. This curve is asymptotic to a
+  quasi-hyperbola of the form xy² = c³. This curve is asymptotic to a
   horizontal line, H ft. above the line from which the pressures are
   measured, and to the axis of the current.
 
@@ -8327,14 +8293,14 @@ stream.
   For such a current, the motion being horizontal, we have for all the
   circular elementary streams
 
-    H = p/G + v²/2g = constant;
+    H = p/G + v²/2g = constant;
 
     .: dH = dp/G + v dv/g = 0.   (7)
 
   Consider two stream lines at radii r and r + dr (fig. 36). Then in
-  (2), § 33, [rho] = r and ds = dr,
+  (2), § 33, [rho] = r and ds = dr,
 
-    v² dr/gr + v dv/g = 0,
+    v² dr/gr + v dv/g = 0,
 
     dv/v = -dr/r,
 
@@ -8360,33 +8326,33 @@ stream.
   according to the law stated above, and the head along each spiral
   stream line is constant.
 
-  § 35. _Forced Vortex._--If the law of motion in a rotating current is
+  § 35. _Forced Vortex._--If the law of motion in a rotating current is
   different from that in a free vortex, some force must be applied to
   cause the variation of velocity. The simplest case is that of a
   rotating current in which all the particles have equal angular
   velocity, as for instance when they are driven round by radiating
-  paddles revolving uniformly. Then in equation (2), § 33, considering
+  paddles revolving uniformly. Then in equation (2), § 33, considering
   two circular stream lines of radii r and r + dr (fig. 37), we have
   [rho] = r, ds = dr. If the angular velocity is [alpha], then v =
   [alpha]r and dv = [alpha]dr. Hence
 
-    dH = [alpha]²r dr/g + [alpha]²r dr/g = 2[alpha]²r dr/g.
+    dH = [alpha]²r dr/g + [alpha]²r dr/g = 2[alpha]²r dr/g.
 
-  Comparing this with (1), § 33, and putting dz = 0, because the motion
+  Comparing this with (1), § 33, and putting dz = 0, because the motion
   is horizontal,
 
-    dp/G + [alpha]²r dr/g = 2[alpha]²r dr/g,
+    dp/G + [alpha]²r dr/g = 2[alpha]²r dr/g,
 
-    dp/G = [alpha]²rdr/g,
+    dp/G = [alpha]²rdr/g,
 
-    p/G = [alpha]²/2g + constant.   (9)
+    p/G = [alpha]²/2g + constant.   (9)
 
   Let p1, r1, v1 be the pressure, radius and velocity of one cylindrical
   section, p2, r2, v2 those of another; then
 
-    p1/G - [alpha]²r1²/2g = p2/G - [alpha]²r2²/2g;
+    p1/G - [alpha]²r1²/2g = p2/G - [alpha]²r2²/2g;
 
-    (p2 - p1)/G = [alpha]²(r2² - r1²)/2g = (v2² - v1²)/2g.   (10)
+    (p2 - p1)/G = [alpha]²(r2² - r1²)/2g = (v2² - v1²)/2g.   (10)
 
   That is, the pressure increases from within outwards in a curve which
   in radial sections is a parabola, and surfaces of equal pressure are
@@ -8397,7 +8363,7 @@ stream.
 
   DISSIPATION OF HEAD IN SHOCK
 
-  § 36. _Relation of Pressure and Velocity in a Stream in Steady Motion
+  § 36. _Relation of Pressure and Velocity in a Stream in Steady Motion
   when the Changes of Section of the Stream are Abrupt._--When a stream
   changes section abruptly, rotating eddies are formed which dissipate
   energy. The energy absorbed in producing rotation is at once
@@ -8414,12 +8380,12 @@ stream.
   were expended internally, and assuming the stream horizontal, we
   should have
 
-    p/G + v²/2g = p1/G + v1²/2g.   (1)
+    p/G + v²/2g = p1/G + v1²/2g.   (1)
 
   But if work is expended in producing irregular eddying motion, the
   head at the section CD will be diminished.
 
-  Suppose the mass ABCD comes in a short time t to A´B´C´D´. The
+  Suppose the mass ABCD comes in a short time t to A´B´C´D´. The
   resultant force parallel to the axis of the stream is
 
     p[omega] + p0([omega]1 - [omega]) - p1[omega]1,
@@ -8432,9 +8398,9 @@ stream.
   [Illustration: FIG. 38.]
 
   The horizontal change of momentum in the same time is the difference
-  of the momenta of CDC´D´ and ABA´B´, because the amount of momentum
-  between A´B´ and CD remains unchanged if the motion is steady. The
-  volume of ABA´B´ or CDC´D´, being the inflow and outflow in the time
+  of the momenta of CDC´D´ and ABA´B´, because the amount of momentum
+  between A´B´ and CD remains unchanged if the motion is steady. The
+  volume of ABA´B´ or CDC´D´, being the inflow and outflow in the time
   t, is Qt = [omega]vt = [omega]1v1t, and the momentum of these masses
   is (G/g)Qvt and (G/g)Qv1t. The change of momentum is therefore
   (G/g)Qt(v1 - v). Equating this to the impulse,
@@ -8449,39 +8415,39 @@ stream.
 
     p/G - p1/G = v1 (v1 - v)/g;   (2)
 
-    p/G + v²/2g = p1/G + v1²/2g + (v - v1)²/2g.   (3)
+    p/G + v²/2g = p1/G + v1²/2g + (v - v1)²/2g.   (3)
 
-  This differs from the expression (1), § 29, obtained for cases where
+  This differs from the expression (1), § 29, obtained for cases where
   no sensible internal work is done, by the last term on the right. That
-  is, (v - v1)²/2g has to be added to the total head at CD, which is
-  p1/G + v1²/2g, to make it equal to the total head at AB, or (v -
-  v1)²/2g is the head lost in shock at the abrupt change of section. But
+  is, (v - v1)²/2g has to be added to the total head at CD, which is
+  p1/G + v1²/2g, to make it equal to the total head at AB, or (v -
+  v1)²/2g is the head lost in shock at the abrupt change of section. But
   (v - v1) is the relative velocity of the two parts of the stream.
   Hence, when an abrupt change of section occurs, the head due to the
-  relative velocity is lost in shock, or (v - v1)²/2g foot-pounds of
+  relative velocity is lost in shock, or (v - v1)²/2g foot-pounds of
   energy is wasted for each pound of fluid. Experiment verifies this
   result, so that the assumption that p0 = p appears to be admissible.
 
   If there is no shock,
 
-    p1/G = p/G + (v² - v1²)/2g.
+    p1/G = p/G + (v² - v1²)/2g.
 
   If there is shock,
 
     p1/G = p/G - v1(v1 - v)/g.
 
   Hence the pressure head at CD in the second case is less than in the
-  former by the quantity (v - v1)²/2g, or, putting [omega]1v1 =
+  former by the quantity (v - v1)²/2g, or, putting [omega]1v1 =
   [omega]v, by the quantity
 
-    (v²/2g)(1 - [omega]/[omega]1)².   (4)
+    (v²/2g)(1 - [omega]/[omega]1)².   (4)
 
 
   V. THEORY OF THE DISCHARGE FROM ORIFICES AND MOUTHPIECES
 
   [Illustration: FIG. 39.]
 
-  § 37. _Minimum Coefficient of Contraction. Re-entrant Mouthpiece of
+  § 37. _Minimum Coefficient of Contraction. Re-entrant Mouthpiece of
   Borda._--In one special case the coefficient of contraction can be
   determined theoretically, and, as it is the case where the convergence
   of the streams approaching the orifice takes place through the
@@ -8497,7 +8463,7 @@ stream.
   points may be taken equal to the hydrostatic pressure due to the depth
   from the free surface. Let [Omega] be the area of the mouthpiece AB,
   [omega] that of the contracted jet aa Suppose that in a short time t,
-  the mass OOaa comes to the position O´O´ a´a´; the impulse of the
+  the mass OOaa comes to the position O´O´ a´a´; the impulse of the
   horizontal external forces acting on the mass during that time is
   equal to the horizontal change of momentum.
 
@@ -8512,24 +8478,24 @@ stream.
   -p_a[Omega]. Hence the resultant horizontal force for the whole mass
   OOaa is (p_a + Gh)[Omega] - p_a[Omega] = Gh[Omega]. Its impulse in the
   time t is Gh[Omega]t. Since the motion is steady there is no change of
-  momentum between O´O´ and aa. The change of horizontal momentum is,
+  momentum between O´O´ and aa. The change of horizontal momentum is,
   therefore, the difference of the horizontal momentum lost in the space
-  OOO´O´ and gained in the space aaa´a´. In the former space there is no
+  OOO´O´ and gained in the space aaa´a´. In the former space there is no
   horizontal momentum.
 
-  The volume of the space aaa´a´ is [omega]vt; the mass of liquid in
-  that space is (G/g)[omega]vt; its momentum is (G/g)[omega]v²t.
+  The volume of the space aaa´a´ is [omega]vt; the mass of liquid in
+  that space is (G/g)[omega]vt; its momentum is (G/g)[omega]v²t.
   Equating impulse to momentum gained,
 
-    Gh[Omega] = (G/g)[omega]v²t;
+    Gh[Omega] = (G/g)[omega]v²t;
 
-    .: [omega]/[Omega] = gh/v²
+    .: [omega]/[Omega] = gh/v²
 
   But
 
-    v² = 2gh, and [omega]/[Omega] = c_c;
+    v² = 2gh, and [omega]/[Omega] = c_c;
 
-    .: [omega]/[Omega] = ½ = c_c;
+    .: [omega]/[Omega] = ½ = c_c;
 
   a result confirmed by experiment with mouthpieces of this kind. A
   similar theoretical investigation is not possible for orifices in
@@ -8543,7 +8509,7 @@ stream.
 
   [Illustration: FIG. 40.]
 
-  § 38. _Velocity of Filaments issuing in a Jet._--A jet is composed of
+  § 38. _Velocity of Filaments issuing in a Jet._--A jet is composed of
   fluid filaments or elementary streams, which start into motion at some
   point in the interior of the vessel from which the fluid is
   discharged, and gradually acquire the velocity of the jet. Let Mm,
@@ -8552,18 +8518,18 @@ stream.
   where the filaments have become parallel and exercise uniform mutual
   pressure. Take the free surface AB for datum line, and let p1, v1, h1,
   be the pressure, velocity and depth below datum at M; p, v, h, the
-  corresponding quantities at m. Then § 29, eq. (3a),
+  corresponding quantities at m. Then § 29, eq. (3a),
 
-    v1²/2g + p1/G - h1 = v²/2g + p/G - h   (1)
+    v1²/2g + p1/G - h1 = v²/2g + p/G - h   (1)
 
   But at M, since the velocity is insensible, the pressure is the
   hydrostatic pressure due to the depth; that is v1 = 0, p1 = p_a + Gh1.
   At m, p = p_a, the atmospheric pressure round the jet. Hence,
   inserting these values,
 
-    0 + p_a/G + h1 - h1 = v²/2g + p_a/G - h;
+    0 + p_a/G + h1 - h1 = v²/2g + p_a/G - h;
 
-    v²/2g = h;   (2)
+    v²/2g = h;   (2)
 
     or v = [root](2gh) = 8.025V [root]h.   (2a)
 
@@ -8580,11 +8546,11 @@ stream.
   _Case of a Submerged Orifice._--Let the orifice discharge below the
   level of the tail water. Then using the notation shown in fig. 41, we
   have at M, v1 = 0, p1 = Gh; + p_a at m, p = Gh3 + p_a. Inserting these
-  values in (3), § 29,
+  values in (3), § 29,
 
-    0 + h1 + p_a/G - h1 = v²/2g + h3 - h2 + p_a/G;
+    0 + h1 + p_a/G - h1 = v²/2g + h3 - h2 + p_a/G;
 
-    v²/2g = h2 - h3 = h,   (3)
+    v²/2g = h2 - h3 = h,   (3)
 
   where h is the difference of level of the head and tail water, and may
   be termed the _effective head_ producing flow.
@@ -8634,7 +8600,7 @@ stream.
 
   [Illustration: FIG. 43.]
 
-  § 39. _Large Rectangular Jets from Orifices in Vertical Plane
+  § 39. _Large Rectangular Jets from Orifices in Vertical Plane
   Surfaces._--Let an orifice in a vertical plane surface be so formed
   that it produces a jet having a rectangular contracted section with
   vertical and horizontal sides. Let b (fig. 43) be the breadth of the
@@ -8677,7 +8643,7 @@ stream.
 
   _Relation between the Expressions (5) and (8)._--For a rectangular
   orifice the area of the orifice is [omega] = B(H2 - H1), and the
-  depth measured to its centre is ½(H2 + H1). Putting these values in
+  depth measured to its centre is ½(H2 + H1). Putting these values in
   (5),
 
     Q1 = cB(H2 - H1) [root]{g(H2 + H1)}.
@@ -8716,7 +8682,7 @@ stream.
 
   [Illustration: FIG. 44.]
 
-  § 40. _Large Jets having a Circular Section from Orifices in a
+  § 40. _Large Jets having a Circular Section from Orifices in a
   Vertical Plane Surface._--Let fig. 44 represent the section of the
   jet, OO being the free surface level in the reservoir. The discharge
   through the horizontal strip aabb, of breadth aa = b, between the
@@ -8730,20 +8696,20 @@ stream.
     Q = |  b [root]{2g(h1 + y)} dy.
        _/0
 
-  But b = d sin [phi]; y = ½d(1 - cos [phi]); dy = ½d sin [phi] d[phi].
+  But b = d sin [phi]; y = ½d(1 - cos [phi]); dy = ½d sin [phi] d[phi].
   Let [epsilon] = d/(2h1 + d), then
                                   _
                                  /[pi]
-    Q = ½d² [root]{2g(h1 + d/2)} |  sin² [phi][root]{1 - [epsilon] cos [phi]} d[phi].
+    Q = ½d² [root]{2g(h1 + d/2)} |  sin² [phi][root]{1 - [epsilon] cos [phi]} d[phi].
                                 _/0
 
-  From eq. (5), putting [omega] = [pi]d²/4, h = h1 + d/2, c = 1 when d
+  From eq. (5), putting [omega] = [pi]d²/4, h = h1 + d/2, c = 1 when d
   is the diameter of the jet and not that of the orifice,
 
-    Q1 = ¼[pi]d² [root]{2g (h1 + d/2)},
+    Q1 = ¼[pi]d² [root]{2g (h1 + d/2)},
                     _
                    /[pi]
-    Q/Q1 = 2/[pi]  |   sin² [phi] [root]{1 - [epsilon] cos [phi]} d[phi].
+    Q/Q1 = 2/[pi]  |   sin² [phi] [root]{1 - [epsilon] cos [phi]} d[phi].
                   _/0
 
   For
@@ -8761,7 +8727,7 @@ stream.
 
   NOTCHES AND WEIRS
 
-  § 41. _Notches, Weirs and Byewashes._--A notch is an orifice extending
+  § 41. _Notches, Weirs and Byewashes._--A notch is an orifice extending
   up to the free surface level in the reservoir from which the discharge
   takes place. A weir is a structure over which the water flows, the
   discharge being in the same conditions as for a notch. The formula of
@@ -8782,13 +8748,13 @@ stream.
   Since the area of the notch opening is BH, the above formula is of the
   form
 
-    Q = c × BH × k [root](2gH),
+    Q = c × BH × k [root](2gH),
 
   where k is a factor depending on the form of the notch and expressing
   the ratio of the mean velocity of discharge to the velocity due to the
   depth H.
 
-  § 42. _Francis's Formula for Rectangular Notches._--The jet discharged
+  § 42. _Francis's Formula for Rectangular Notches._--The jet discharged
   through a rectangular notch has a section smaller than BH, (a) because
   of the fall of the water surface from the point where H is measured
   towards the weir, (b) in consequence of the crest contraction, (c) in
@@ -8813,7 +8779,7 @@ stream.
   contractions due to the fall of surface and to the crest contraction
   are proportional to the width of the jet. Hence, if cH is the
   thickness of the stream over the weir, measured at the contracted
-  section, the section of the jet will be c(l - 0.1nH)H and (§ 41) the
+  section, the section of the jet will be c(l - 0.1nH)H and (§ 41) the
   mean velocity will be 2/3 [root](2gH). Consequently the discharge
   will be given by an equation of the form
 
@@ -8825,7 +8791,7 @@ stream.
   ordinary formula. Francis found for c the mean value 0.622, the weir
   being sharp-edged.
 
-  § 43. _Triangular Notch_ (fig. 46).--Consider a lamina issuing between
+  § 43. _Triangular Notch_ (fig. 46).--Consider a lamina issuing between
   the depths h and h + dh. Its area, neglecting contraction, will be
   bdh, and the velocity at that depth is [root](2gh). Hence the
   discharge for this lamina is
@@ -8843,14 +8809,14 @@ stream.
   and total discharge of notch
                        _
                       /H
-    = Q = B[root](2g) |  (H - h)h^(½) dh/H
+    = Q = B[root](2g) |  (H - h)h^(½) dh/H
                      _/0
 
         = (4/15) B[root](2g)H^(3/2).
 
   or, introducing a coefficient to allow for contraction,
 
-    Q = (4/15)cB [root](2g) H^(½),
+    Q = (4/15)cB [root](2g) H^(½),
 
   [Illustration: FIG. 46.]
 
@@ -8862,11 +8828,11 @@ stream.
   this has been experimentally shown to be the case. Hence a triangular
   notch is more suitable for accurate gaugings than a rectangular notch.
   For a sharp-edged triangular notch Professor J. Thomson found c =
-  0.617. It will be seen, as in § 41, that since ½BH is the area of
+  0.617. It will be seen, as in § 41, that since ½BH is the area of
   section of the stream through the notch, the formula is again of the
   form
 
-    Q = c × ½BH × k[root](2gH),
+    Q = c × ½BH × k[root](2gH),
 
   where k = 8/15 is the ratio of the mean velocity in the notch to the
   velocity at the depth H. It may easily be shown that for all notches
@@ -8885,7 +8851,7 @@ stream.
     | measured |      |      |     |     |       |10 ft. long, | 3 ft.| 3 ft.| 3 ft.| 6 ft.|10 ft.|10 ft.|
     |from still| 3 ft.|10 ft.|3 ft.|6 ft.| 10 ft.| wing-boards | long,| long,| long,| long,| long,| long,|
     | Water in | long.| long.|long.|long.| long. |  making an  |level.|fall 1|fall 1|level.|level.|fall 1|
-    |Reservoir.|      |      |     |     |       |angle of 60°.|      |in 18.|in 12.|      |      |in 18.|
+    |Reservoir.|      |      |     |     |       |angle of 60°.|      |in 18.|in 12.|      |      |in 18.|
     +----------+------+------+-----+-----+-------+-------------+------+------+------+------+------+------+
     |     1    | .677 | .809 |.467 |.459 |.435[4]|    .754     | .452 | .545 | .467 |  ..  | .381 | .467 |
     |     2    | .675 | .803 |.509*|.561 |.585*  |    .675     | .482 | .546 | .533 |  ..  | .479*| .495*|
@@ -8903,18 +8869,18 @@ stream.
 
   [Illustration: FIG. 47.]
 
-  § 44. _Weir with a Broad Sloping Crest._--Suppose a weir formed with a
+  § 44. _Weir with a Broad Sloping Crest._--Suppose a weir formed with a
   broad crest so sloped that the streams flowing over it have a movement
   sensibly rectilinear and uniform (fig. 47). Let the inner edge be so
-  rounded as to prevent a crest contraction. Consider a filament aa´,
+  rounded as to prevent a crest contraction. Consider a filament aa´,
   the point a being so far back from the weir that the velocity of
   approach is negligible. Let OO be the surface level in the reservoir,
-  and let a be at a height h´´ below OO, and h´ above a´. Let h be the
+  and let a be at a height h´´ below OO, and h´ above a´. Let h be the
   distance from OO to the weir crest and e the thickness of the stream
   upon it. Neglecting atmospheric pressure, which has no influence, the
-  pressure at a is Gh´´; at a´ it is Gz. If v be the velocity at a´,
+  pressure at a is Gh´´; at a´ it is Gz. If v be the velocity at a´,
 
-    v²/2g = h´ + h´´ - z = h - e;
+    v²/2g = h´ + h´´ - z = h - e;
 
     Q = be [root]{2g(h - e)}.
 
@@ -8939,7 +8905,7 @@ stream.
 
   SPECIAL CASES OF DISCHARGE FROM ORIFICES
 
-  § 45. _Cases in which the Velocity of Approach needs to be taken into
+  § 45. _Cases in which the Velocity of Approach needs to be taken into
   Account. Rectangular Orifices and Notches._--In finding the velocity
   at the orifice in the preceding investigations, it has been assumed
   that the head h has been measured from the free surface of still water
@@ -8955,7 +8921,7 @@ stream.
   channel of approach where the velocity is u. It is obvious that a fall
   of the free surface,
 
-    [h] = u²/2g
+    [h] = u²/2g
 
   has been somewhere expended in producing the velocity u, and hence the
   true heads measured in still water would have been h1 + [h] and h2 +
@@ -8972,29 +8938,29 @@ stream.
   discharge quite simply. When, however, u is only known as a function
   of the section of the stream in the channel of approach, they become
   complicated. Let [Omega] be the sectional area of the channel where h1
-  and h2 are measured. Then u = Q/[Omega] and [h] = Q²/2g [Omega]².
+  and h2 are measured. Then u = Q/[Omega] and [h] = Q²/2g [Omega]².
 
   This value introduced in the equations above would render them
   excessively cumbrous. In cases therefore where [Omega] only is known,
   it is best to proceed by approximation. Calculate an approximate value
-  Q´ of Q by the equation
+  Q´ of Q by the equation
 
-    Q´ = (2/3)cb [root](2g) {h2^(3/2) - h1^(3/2)}.
+    Q´ = (2/3)cb [root](2g) {h2^(3/2) - h1^(3/2)}.
 
-  Then [h] = Q´²/2g[Omega]² nearly. This value of [h] introduced in the
+  Then [h] = Q´²/2g[Omega]² nearly. This value of [h] introduced in the
   equations above will give a second and much more approximate value of
   Q.
 
   [Illustration: FIG. 49.]
 
-  § 46. _Partially Submerged Rectangular Orifices and Notches._--When
+  § 46. _Partially Submerged Rectangular Orifices and Notches._--When
   the tail water is above the lower but below the upper edge of the
   orifice, the flow in the two parts of the orifice, into which it is
   divided by the surface of the tail water, takes place under different
   conditions. A filament M1m1 (fig. 49) in the upper part of the orifice
-  issues with a head h´ which may have any value between h1 and h. But a
+  issues with a head h´ which may have any value between h1 and h. But a
   filament M2m2 issuing in the lower part of the orifice has a velocity
-  due to h´´ - h´´´, or h, simply. In the upper part of the orifice the
+  due to h´´ - h´´´, or h, simply. In the upper part of the orifice the
   head is variable, in the lower constant. If Q1, Q2 are the discharges
   from the upper and lower parts of the orifice, b the width of the
   orifice, then
@@ -9030,7 +8996,7 @@ stream.
   head due to that velocity; then, adding [h] to each of the
   heads in the equations (3), and reducing, we get for a weir
 
-    Q = cb [root]{2g} [(h2 + [h]) (h + [h])^(½) - (1/3)(h + [h])^(3/2)
+    Q = cb [root]{2g} [(h2 + [h]) (h + [h])^(½) - (1/3)(h + [h])^(3/2)
       - (2/3)[h]^(3/2)];   (5)
 
   an equation which may be useful in estimating flood discharges.
@@ -9045,11 +9011,11 @@ stream.
   it occurred over a drowned weir. But the value of c in this case is
   imperfectly known.
 
-  § 47. _Bazin's Researches on Weirs._--H. Bazin has executed a long
+  § 47. _Bazin's Researches on Weirs._--H. Bazin has executed a long
   series of researches on the flow over weirs, so systematic and
   complete that they almost supersede other observations. The account of
   them is contained in a series of papers in the _Annales des Ponts et
-  Chaussées_ (October 1888, January 1890, November 1891, February 1894,
+  Chaussées_ (October 1888, January 1890, November 1891, February 1894,
   December 1896, 2nd trimestre 1898). Only a very abbreviated account
   can be given here. The general plan of the experiments was to
   establish first the coefficients of discharge for a standard weir
@@ -9058,7 +9024,7 @@ stream.
   compare the observed heads on the different weirs and to determine
   their coefficients from the discharge computed at the standard weir. A
   channel was constructed parallel to the Canal de Bourgogne, taking
-  water from it through three sluices 0.3 × 1.0 metres. The water enters
+  water from it through three sluices 0.3 × 1.0 metres. The water enters
   a masonry chamber 15 metres long by 4 metres wide where it is stilled
   and passes into the canal at the end of which is the standard weir.
   The canal has a length of 15 metres, a width of 2 metres and a depth
@@ -9072,7 +9038,7 @@ stream.
   [Illustration: FIG. 51.]
 
   _Standard Weir._--The weir crest was 3.72 ft. above the bottom of the
-  canal and formed by a plate ¼ in. thick. It was sharp-edged with free
+  canal and formed by a plate ¼ in. thick. It was sharp-edged with free
   overfall. It was as wide as the canal so that end contractions were
   suppressed, and enlargements were formed below the crest to admit air
   under the water sheet. The channel below the weir was used as a
@@ -9109,30 +9075,30 @@ stream.
   close agreement.
 
   _Influence of Velocity of Approach._--To take account of the velocity
-  of approach u it is usual to replace h in the formula by h + au²/2g
+  of approach u it is usual to replace h in the formula by h + au²/2g
   where [alpha] is a coefficient not very well ascertained. Then
 
-    Q = [mu]l (h + [alpha]u²/2g) [root]{2g(h + [alpha]u²/2g)}
-      = [mu]lh [root](2gh)(1 + [alpha]u²/2gh)^(3/2).   (2)
+    Q = [mu]l (h + [alpha]u²/2g) [root]{2g(h + [alpha]u²/2g)}
+      = [mu]lh [root](2gh)(1 + [alpha]u²/2gh)^(3/2).   (2)
 
   The original simple equation can be used if
 
-    m = [mu](1 + [alpha]u²/2gh)^(3/2)
+    m = [mu](1 + [alpha]u²/2gh)^(3/2)
 
-  or very approximately, since u²/2gh is small,
+  or very approximately, since u²/2gh is small,
 
-    m = [mu](1 + (3/2)[alpha]u²/2gh).   (3)
+    m = [mu](1 + (3/2)[alpha]u²/2gh).   (3)
 
   [Illustration: FIG. 52.]
 
   Now if p is the height of the weir crest above the bottom of the canal
   (fig. 52), u = Q/l(p + h). Replacing Q by its value in (1)
 
-    u²/2gh = Q²/{2ghl²(p + h)²} = m²{h/(p + h)}²,   (4)
+    u²/2gh = Q²/{2ghl²(p + h)²} = m²{h/(p + h)}²,   (4)
 
   so that (3) may be written
 
-    m = [mu][1 + k{h/(p + h)}²].   (5)
+    m = [mu][1 + k{h/(p + h)}²].   (5)
 
   Gaugings were made with weirs of 0.75, 0.50, 0.35, and 0.24 metres
   height above the canal bottom and the results compared with those of
@@ -9140,8 +9106,8 @@ stream.
   results leads to the following values of m in the general equation
   (1):--
 
-    m = [mu](1 + 2.5u²/2gh)
-      = [mu][1 + 0.55 {h/(p + h)}²].
+    m = [mu](1 + 2.5u²/2gh)
+      = [mu][1 + 0.55 {h/(p + h)}²].
 
   Values of [mu]--
 
@@ -9208,7 +9174,7 @@ stream.
   upstream edge or may adhere to the flat crest falling free beyond the
   down-stream edge. In the former case the condition is that of a
   sharp-edged weir and it is realized when the head is at least double
-  the width of crest. It may arise if the head is at least 1½ the width
+  the width of crest. It may arise if the head is at least 1½ the width
   of crest. Between these limits the condition of the sheet is unstable.
   When the sheet is adherent the coefficient m depends on the ratio of
   the head h to the width of crest c (fig. 53), and is given by the
@@ -9216,7 +9182,7 @@ stream.
   sharp-edged weir in similar conditions. Rounding the upstream edge
   even to a small extent modifies the discharge. If R is the radius of
   the rounding the coefficient m is increased in the ratio 1 to 1 + R/h
-  nearly. The results are limited to R less than ½ in.
+  nearly. The results are limited to R less than ½ in.
 
   _Drowned Weirs._--Let h (fig. 54) be the height of head water and h1
   that of tail water above the weir crest. Then Bazin obtains as the
@@ -9232,7 +9198,7 @@ stream.
 
   [Illustration: FIG. 56.]
 
-  § 48. _Separating Weirs._--Many towns derive their water-supply from
+  § 48. _Separating Weirs._--Many towns derive their water-supply from
   streams in high moorland districts, in which the flow is extremely
   variable. The water is collected in large storage reservoirs, from
   which an uniform supply can be sent to the town. In such cases it is
@@ -9264,13 +9230,13 @@ stream.
   level of its edges (fig. 57). Then, if a particle passes from a to b
   in t seconds,
 
-    y = ½gt², x = (2/3)[root](2gh) t;
+    y = ½gt², x = (2/3)[root](2gh) t;
 
-    .: y = (9/16)x²/h,
+    .: y = (9/16)x²/h,
 
   which gives the width x for any given difference of level y and head
   h, which the jet will just pass over the orifice. Set off ad
-  vertically and equal to ½g on any scale; af horizontally and equal to
+  vertically and equal to ½g on any scale; af horizontally and equal to
   2/3 [root](gh). Divide af, fe into an equal number of equal parts.
   Join a with the divisions on ef. The intersections of these lines with
   verticals from the divisions on af give the parabolic path of the jet.
@@ -9280,8 +9246,8 @@ stream.
 
   MOUTHPIECES--HEAD CONSTANT
 
-  § 49. _Cylindrical Mouthpieces._--When water issues from a short
-  cylindrical pipe or mouthpiece of a length at least equal to l½ times
+  § 49. _Cylindrical Mouthpieces._--When water issues from a short
+  cylindrical pipe or mouthpiece of a length at least equal to l½ times
   its smallest transverse dimension, the stream, after contraction
   within the mouthpiece, expands to fill it and issues full bore, or
   without contraction, at the point of discharge. The discharge is found
@@ -9303,17 +9269,17 @@ stream.
 
   The total head of any filament which goes to form the jet, taken at a
   point where its velocity is sensibly zero, is h + p_a/G; at EF the
-  total head is v²/2g + p/G; at GH it is v1²/2g + p1/G.
+  total head is v²/2g + p/G; at GH it is v1²/2g + p1/G.
 
   Between EF and GH there is a loss of head due to abrupt change of
-  velocity, which from eq. (3), § 36, may have the value
+  velocity, which from eq. (3), § 36, may have the value
 
-    (v - v1)²/2g.
+    (v - v1)²/2g.
 
   Adding this head lost to the head at GH, before equating it to the
   heads at EF and at the point where the filaments start into motion,--
 
-    h + p_a/G = v²/2g + p/G = v1²/2g + p1/G + (v - v1)²/2g.
+    h + p_a/G = v²/2g + p/G = v1²/2g + p1/G + (v - v1)²/2g.
 
   But [omega]v = [Omega]v1, and [omega] = c_c[Omega], if c_c is the
   coefficient of contraction within the mouthpiece. Hence
@@ -9322,11 +9288,11 @@ stream.
 
   Supposing the discharge into the air, so that p1 = p_a,
 
-    h + p_a/G = v1²/2g + p_a/G + (v1²/2g)(1/c_c - 1)²;
+    h + p_a/G = v1²/2g + p_a/G + (v1²/2g)(1/c_c - 1)²;
 
-    (v1/2g){1 + (1/c_c - 1)²} = h;
+    (v1/2g){1 + (1/c_c - 1)²} = h;
 
-    .: v1 = [root](2gh)/[root]{1 + (1/c_c - 1)²};   (1)
+    .: v1 = [root](2gh)/[root]{1 + (1/c_c - 1)²};   (1)
 
   [Illustration: FIG. 58.]
 
@@ -9335,7 +9301,7 @@ stream.
   contraction at EF. Let c_c = 0.64, the value for simple orifices, then
   the coefficient of velocity is
 
-    c_v = 1/[root]{1 + (1/c_c - 1)²} = 0.87   (2)
+    c_v = 1/[root]{1 + (1/c_c - 1)²} = 0.87   (2)
 
   The actual value of c_v, found by experiment is 0.82, which does not
   differ more from the theoretical value than might be expected if the
@@ -9349,24 +9315,24 @@ stream.
   It is easy to see from the equations that the pressure p at EF is less
   than atmospheric pressure. Eliminating v1, we get
 
-    (p_a - p)/G = ¾h nearly;   (3)
+    (p_a - p)/G = ¾h nearly;   (3)
 
   or
 
-    p = p_a - ¾Gh lb. per sq. ft.
+    p = p_a - ¾Gh lb. per sq. ft.
 
   If a pipe connected with a reservoir on a lower level is introduced
   into the mouthpiece at the part where the contraction is formed (fig.
   59), the water will rise in this pipe to a height
 
-    KL = (p_a - p)/G = ¾h nearly.
+    KL = (p_a - p)/G = ¾h nearly.
 
   If the distance X is less than this, the water from the lower
   reservoir will be forced continuously into the jet by the atmospheric
   pressure, and discharged with it. This is the crudest form of a kind
   of pump known as the jet pump.
 
-  § 50. _Convergent Mouthpieces._--With convergent mouthpieces there is
+  § 50. _Convergent Mouthpieces._--With convergent mouthpieces there is
   a contraction within the mouthpiece causing a loss of head, and a
   diminution of the velocity of discharge, as with cylindrical
   mouthpieces. There is also a second contraction of the stream outside
@@ -9386,28 +9352,28 @@ stream.
     |  Angle of  | Contraction, |   Velocity,  |  Discharge,  |
     |Convergence.|     c_c      |      c_v     |       c      |
     +------------+--------------+--------------+--------------+
-    |    0°  0´  |     .999     |     .830     |     .829     |
-    |    1° 36´  |    1.000     |     .866     |     .866     |
-    |    3° 10´  |    1.001     |     .894     |     .895     |
-    |    4° 10´  |    1.002     |     .910     |     .912     |
-    |    5° 26´  |    1.004     |     .920     |     .924     |
-    |    7° 52´  |     .998     |     .931     |     .929     |
-    |    8° 58´  |     .992     |     .942     |     .934     |
-    |   10° 20´  |     .987     |     .950     |     .938     |
-    |   12°  4´  |     .986     |     .955     |     .942     |
-    |   13° 24´  |     .983     |     .962     |     .946     |
-    |   14° 28´  |     .979     |     .966     |     .941     |
-    |   16° 36´  |     .969     |     .971     |     .938     |
-    |   19° 28´  |     .953     |     .970     |     .924     |
-    |   21°  0´  |     .945     |     .971     |     .918     |
-    |   23°  0´  |     .937     |     .974     |     .913     |
-    |   29° 58´  |     .919     |     .975     |     .896     |
-    |   40° 20´  |     .887     |     .980     |     .869     |
-    |   48° 50´  |     .861     |     .984     |     .847     |
+    |    0°  0´  |     .999     |     .830     |     .829     |
+    |    1° 36´  |    1.000     |     .866     |     .866     |
+    |    3° 10´  |    1.001     |     .894     |     .895     |
+    |    4° 10´  |    1.002     |     .910     |     .912     |
+    |    5° 26´  |    1.004     |     .920     |     .924     |
+    |    7° 52´  |     .998     |     .931     |     .929     |
+    |    8° 58´  |     .992     |     .942     |     .934     |
+    |   10° 20´  |     .987     |     .950     |     .938     |
+    |   12°  4´  |     .986     |     .955     |     .942     |
+    |   13° 24´  |     .983     |     .962     |     .946     |
+    |   14° 28´  |     .979     |     .966     |     .941     |
+    |   16° 36´  |     .969     |     .971     |     .938     |
+    |   19° 28´  |     .953     |     .970     |     .924     |
+    |   21°  0´  |     .945     |     .971     |     .918     |
+    |   23°  0´  |     .937     |     .974     |     .913     |
+    |   29° 58´  |     .919     |     .975     |     .896     |
+    |   40° 20´  |     .887     |     .980     |     .869     |
+    |   48° 50´  |     .861     |     .984     |     .847     |
     +------------+--------------+--------------+--------------+
 
   The maximum coefficient of discharge is that for a mouthpiece with a
-  convergence of 13°24´.
+  convergence of 13°24´.
 
   The values of c_v and c_c must here be determined by experiment. The
   above table gives values sufficient for practical purposes. Since the
@@ -9419,7 +9385,7 @@ stream.
 
   [Illustration: FIG. 59.]
 
-  § 51. _Divergent Conoidal Mouthpiece._--Suppose a mouthpiece so
+  § 51. _Divergent Conoidal Mouthpiece._--Suppose a mouthpiece so
   designed that there is no abrupt change in the section or velocity of
   the stream passing through it. It may have a form at the inner end
   approximately the same as that of a simple contracted vein, and may
@@ -9431,11 +9397,11 @@ stream.
   Then, since there is no loss of energy, except the small frictional
   resistance of the surface of the mouthpiece,
 
-    h + p_a/G = v²/2g + p/G = v1²/2g + p1/G.
+    h + p_a/G = v²/2g + p/G = v1²/2g + p1/G.
 
   If the jet discharges into the air, p1 = p_a; and
 
-    v1²/2g = h;
+    v1²/2g = h;
 
     v1 = [root](2gh);
 
@@ -9464,14 +9430,14 @@ stream.
 
   From the equations,
 
-    p/G = p_a/G = (v² - v1²)/2g.
+    p/G = p_a/G = (v² - v1²)/2g.
 
   Let [Omega]/[omega] = m. Then
 
     v = v1m;
 
-    p/G = p_a/G - v1²(m² - 1)/2g
-        = p_a/G - (m² - 1)h;
+    p/G = p_a/G - v1²(m² - 1)/2g
+        = p_a/G - (m² - 1)h;
 
   whence we find that p/G will become zero or negative if
 
@@ -9493,7 +9459,7 @@ stream.
   mouthpiece of area [omega], and without the expanding part,
   discharging into a vacuum.
 
-  § 52. _Jet Pump._--A divergent mouthpiece may be arranged to act as a
+  § 52. _Jet Pump._--A divergent mouthpiece may be arranged to act as a
   pump, as shown in fig. 62. The water which supplies the energy
   required for pumping enters at A. The water to be pumped enters at B.
   The streams combine at DD where the velocity is greatest and the
@@ -9514,7 +9480,7 @@ stream.
 
   DISCHARGE WITH VARYING HEAD
 
-  § 53. _Flow from a Vessel when the Effective Head varies with the
+  § 53. _Flow from a Vessel when the Effective Head varies with the
   Time._--Various useful problems arise relating to the time of emptying
   and filling vessels, reservoirs, lock chambers, &c., where the flow is
   dependent on a head which increases or diminishes during the
@@ -9564,7 +9530,7 @@ stream.
 
   PRACTICAL USE OF ORIFICES IN GAUGING WATER
 
-  § 54. If the water to be measured is passed through a known orifice
+  § 54. If the water to be measured is passed through a known orifice
   under an arrangement by which the constancy of the head is ensured,
   the amount which passes in a given time can be ascertained by the
   formulae already given. It will obviously be best to make the orifices
@@ -9603,7 +9569,7 @@ stream.
   connected by a key which can be locked by a padlock, which is under
   the control of the water company.
 
-  § 55. _Measurement of the Flow in Streams._--To determine the quantity
+  § 55. _Measurement of the Flow in Streams._--To determine the quantity
   of water flowing off the ground in small streams, which is available
   for water supply or for obtaining water power, small temporary weirs
   are often used. These may be formed of planks supported by piles and
@@ -9617,7 +9583,7 @@ stream.
 
     Q = (2/3)cbh [root](2gh)
 
-  where c = 0.62; or, better, the formula in § 42 may be used.
+  where c = 0.62; or, better, the formula in § 42 may be used.
 
   Gauging weirs are most commonly in the form of rectangular notches;
   and care should be taken that the crest is accurately horizontal, and
@@ -9685,7 +9651,7 @@ stream.
   difference of the reading at the water surface and that for the weir
   crest will be the head at the weir.
 
-  § 56. _Modules used in Irrigation._--In distributing water for
+  § 56. _Modules used in Irrigation._--In distributing water for
   irrigation, the charge for the water may be simply assessed on the
   area of the land irrigated for each consumer, a method followed in
   India; or a regulated quantity of water may be given to each consumer,
@@ -9700,7 +9666,7 @@ stream.
 
   [Illustration: FIG. 69.]
 
-  § 57. _Italian Module._--The Italian modules are masonry
+  § 57. _Italian Module._--The Italian modules are masonry
   constructions, consisting of a regulating chamber, to which water is
   admitted by an adjustable sluice from the canal. At the other end of
   the chamber is an orifice in a thin flagstone of fixed size. By means
@@ -9768,7 +9734,7 @@ stream.
   than the orifice, splaying out till it is 1.637 ft. wider than the
   orifice, and about 18 ft. in length.
 
-  § 58. _Spanish Module._--On the canal of Isabella II., which supplies
+  § 58. _Spanish Module._--On the canal of Isabella II., which supplies
   water to Madrid, a module much more perfect in principle than the
   Italian module is employed. Part of the water is supplied for
   irrigation, and as it is very valuable its strict measurement is
@@ -9787,13 +9753,13 @@ stream.
   radius of the plug at a distance h from the plane of flotation of the
   float, and Q the required discharge of the module. Then
 
-    Q = c[pi](R² - r²) [root](2gh).
+    Q = c[pi](R² - r²) [root](2gh).
 
   Taking c = 0.63,
 
-    Q = 15.88(R² - r²) [root]h;
+    Q = 15.88(R² - r²) [root]h;
 
-    r = [root]{R² - Q/15.88 [root]h}.
+    r = [root]{R² - Q/15.88 [root]h}.
 
   Choosing a value for R, successive values of r can be found for
   different values of h, and from these the curve of the plug can be
@@ -9804,7 +9770,7 @@ stream.
   is described in Sir C. Scott-Moncrieff's _Irrigation in Southern
   Europe_.
 
-  § 59. _Reservoir Gauging Basins._--In obtaining the power to store the
+  § 59. _Reservoir Gauging Basins._--In obtaining the power to store the
   water of streams in reservoirs, it is usual to concede to riparian
   owners below the reservoirs a right to a regulated supply throughout
   the year. This compensation water requires to be measured in such a
@@ -9845,7 +9811,7 @@ stream.
 
   [Illustration: FIG. 74.--Scale 1/500.]
 
-  § 60. _Professor Fleeming Jenkin's Constant Flow Valve._--In the
+  § 60. _Professor Fleeming Jenkin's Constant Flow Valve._--In the
   modules thus far described constant discharge is obtained by varying
   the area of the orifice through which the water flows. Professor F.
   Jenkin has contrived a valve in which a constant pressure head is
@@ -9873,7 +9839,7 @@ stream.
   must be constant also, and equal to w/[omega]. By making w small and
   [omega] large, the difference of pressure required to ensure the
   working of the apparatus may be made very small. Valves working with a
-  difference of pressure of ½ in. of water have been constructed.
+  difference of pressure of ½ in. of water have been constructed.
 
   [Illustration: FIG. 75.--Scale 1/24.]
 
@@ -9882,7 +9848,7 @@ stream.
 
   [Illustration: FIG. 76.]
 
-  § 61. _External Work during the Expansion of Air._--If air expands
+  § 61. _External Work during the Expansion of Air._--If air expands
   without doing any external work, its temperature remains constant.
   This result was first experimentally demonstrated by J. P. Joule. It
   leads to the conclusion that, however air changes its state, the
@@ -9963,11 +9929,11 @@ stream.
 
   [Illustration: FIG. 77.]
 
-  § 62. _Modification of the Theorem of Bernoulli for the Case of a
+  § 62. _Modification of the Theorem of Bernoulli for the Case of a
   Compressible Fluid._--In the application of the principle of work to a
   filament of compressible fluid, the internal work done by the
   expansion of the fluid, or absorbed in its compression, must be taken
-  into account. Suppose, as before, that AB (fig. 77) comes to A´B´ in a
+  into account. Suppose, as before, that AB (fig. 77) comes to A´B´ in a
   short time t. Let p1, [omega]1, v1, G1 be the pressure, sectional area
   of stream, velocity and weight of a cubic foot at A, and p2, [omega]2,
   v2, G2 the same quantities at B. Then, from the steadiness of motion,
@@ -9990,48 +9956,48 @@ stream.
 
   The work done by expansion of Wt lb. of fluid between A and B is Wt
   [int][v1 to v2] p dv. The change of kinetic energy as before is (W/2g)
-  (v2² - v1²)t. Hence, equating work to change of kinetic energy,
+  (v2² - v1²)t. Hence, equating work to change of kinetic energy,
 
                                        _
                                       /v2
-    W(z1 - z2)t + (p1/G1 - p2/G2)Wt + |   p dv = (W/2g)(v2² - v1²)t;
+    W(z1 - z2)t + (p1/G1 - p2/G2)Wt + |   p dv = (W/2g)(v2² - v1²)t;
                                      _/v1
                                                     _
                                                    /v2                                                                        /
-    .: z1 + p1/G1 + v1²/2g = z2 + p²/G2 + v2²/2g - |   p dv.   (1)
+    .: z1 + p1/G1 + v1²/2g = z2 + p²/G2 + v2²/2g - |   p dv.   (1)
                                                   _/v1
 
   Now the work of expansion per pound of fluid has already been given.
-  If the temperature is constant, we get (eq. 1a, § 61)
+  If the temperature is constant, we get (eq. 1a, § 61)
 
-    z1 + p1/G1 + v1²/2g
-      = z2 + p²/G2 + v2²/2g - (p1/G1) log_[epsilon] (G1/G2).
+    z1 + p1/G1 + v1²/2g
+      = z2 + p²/G2 + v2²/2g - (p1/G1) log_[epsilon] (G1/G2).
 
   But at constant temperature p1/G1 = p2/G2;
 
-    .: z1 + v1²/2g = z2 + v2²/2g - (p1/G1) log_[epsilon] (p1/p2),   (2)
+    .: z1 + v1²/2g = z2 + v2²/2g - (p1/G1) log_[epsilon] (p1/p2),   (2)
 
   or, neglecting the difference of level,
 
-    (v2² - v1²)/2g = (p1/G1) log_[epsilon] (p1/p2).   (2a)
+    (v2² - v1²)/2g = (p1/G1) log_[epsilon] (p1/p2).   (2a)
 
-  Similarly, if the expansion is adiabatic (eq. 2a, § 61),
+  Similarly, if the expansion is adiabatic (eq. 2a, § 61),
 
-    z1 + p1/G1 + v1²/2g = z2 + p2/G2 + v2²/2g
+    z1 + p1/G1 + v1²/2g = z2 + p2/G2 + v2²/2g
       - (p1/G1){1/([gamma] - 1)} {1 - (p2/p1)^([gamma] - 1)/[gamma]};   (3)
 
   or, neglecting the difference of level,
 
-    (v2² - v1²)/2g =
+    (v2² - v1²)/2g =
       (p1/G1)[1 + 1/([gamma] - 1){1 - (p2/p1)^([gamma]-1)/[gamma]}] - p2/G2.   (3a)
 
   It will be seen hereafter that there is a limit in the ratio p1/p2
   beyond which these expressions cease to be true.
 
-  § 63. _Discharge of Air from an Orifice._--The form of the equation of
+  § 63. _Discharge of Air from an Orifice._--The form of the equation of
   work for a steady stream of compressible fluid is
 
-    z1 + p1/G1 + v1²/2g = z2 + p2/G2 + v2²/2g -
+    z1 + p1/G1 + v1²/2g = z2 + p2/G2 + v2²/2g -
       (p1/G1){1/([gamma] - 1)} {1 - (p2/p1^([gamma] - 1)/[gamma]},
 
   the expansion being adiabatic, because in the flow of the streams of
@@ -10046,10 +10012,10 @@ stream.
   compared with that of the pressures and expansion, so that z1z2 may be
   neglected. Putting these values in the equation above--
 
-    p1/G1 = p2/G2 + v2²/2g - (p1/G1){1/([gamma] - 1)}
+    p1/G1 = p2/G2 + v2²/2g - (p1/G1){1/([gamma] - 1)}
       {1 - (p2/p1)^([gamma] - 1)/[gamma];
 
-    v2²/2g = p1/G1 - p2/G2 + (p1/G1){1/([gamma] - 1)}
+    v2²/2g = p1/G1 - p2/G2 + (p1/G1){1/([gamma] - 1)}
       {1 - (p2/p1)^([gamma] - 1)/[gamma]}
 
     = (p1/G1){[gamma]/([gamma] - 1) - (p2/p1)^([gamma] - 1)/[gamma]/([gamma] - 1)} - p2/G2.
@@ -10059,28 +10025,28 @@ stream.
     p1/G1^([gamma]) = p2/G2^([gamma])
     .: p2/G2 = (p1/G1)(p2/p1)^([gamma] - 1)/[gamma]
 
-    v2²/2g = (p1/G1){[gamma]/([gamma] - 1)} {1 - (p2/p1)^(([gamma] - 1)/[gamma]};   (1)
+    v2²/2g = (p1/G1){[gamma]/([gamma] - 1)} {1 - (p2/p1)^(([gamma] - 1)/[gamma]};   (1)
 
   or
 
-    v2²/2g = {[gamma]/([gamma] - 1)} {(p1/G1) - (p2/G2)};
+    v2²/2g = {[gamma]/([gamma] - 1)} {(p1/G1) - (p2/G2)};
 
   an equation commonly ascribed to L. J. Weisbach (_Civilingenieur_,
   1856), though it appears to have been given earlier by A. J. C. Barre
   de Saint Venant and L. Wantzel.
 
-  It has already (§ 9, eq. 4a) been seen that
+  It has already (§ 9, eq. 4a) been seen that
 
     p1/G1 = (p0/G0) ([tau]1/[tau]0)
 
   where for air p0 = 2116.8, G0 = .08075 and [tau]0 = 492.6.
 
-    v2²/2g = {p0[tau]1[gamma]/G0[tau]0([gamma] - 1)}
+    v2²/2g = {p0[tau]1[gamma]/G0[tau]0([gamma] - 1)}
       {1 - (p2/p1)^([gamma] - 1)/[gamma]};   (2)
 
   or, inserting numerical values,
 
-    v2²/2g = 183.6[tau]1 {1 - (p2/p1)^(0.29)};   (2a)
+    v2²/2g = 183.6[tau]1 {1 - (p2/p1)^(0.29)};   (2a)
 
   which gives the velocity of discharge v2 in terms of the pressure and
   absolute temperature, p1, [tau]1, in the vessel from which the air
@@ -10134,7 +10100,7 @@ stream.
     The same rounded at the inner end           0.92  " 0.93
     Conical converging mouthpieces              0.90  " 0.99
 
-  § 64. _Limit to the Application of the above Formulae._--In the
+  § 64. _Limit to the Application of the above Formulae._--In the
   formulae above it is assumed that the fluid issuing from the orifice
   expands from the pressure p1 to the pressure p2, while passing from
   the vessel to the section of the jet considered in estimating the area
@@ -10188,7 +10154,7 @@ stream.
 
   VII. FRICTION OF LIQUIDS.
 
-  § 65. When a stream of fluid flows over a solid surface, or conversely
+  § 65. When a stream of fluid flows over a solid surface, or conversely
   when a solid moves in still fluid, a resistance to the motion is
   generated, commonly termed fluid friction. It is due to the viscosity
   of the fluid, but generally the laws of fluid friction are very
@@ -10218,7 +10184,7 @@ stream.
 
   3. At low velocities of not more than 1 in. per second for water, the
   frictional resistance increases directly as the relative velocity of
-  the fluid and the surface against which it flows. At velocities of ½
+  the fluid and the surface against which it flows. At velocities of ½
   ft. per second and greater velocities, the frictional resistance is
   more nearly proportional to the square of the relative velocity.
 
@@ -10241,7 +10207,7 @@ stream.
   showed that in old and incrusted water mains the resistance was twice
   or sometimes thrice as great as in new and clean mains.
 
-  § 66. _Ordinary Expressions for Fluid Friction at Velocities not
+  § 66. _Ordinary Expressions for Fluid Friction at Velocities not
   Extremely Small._--Let f be the frictional resistance estimated in
   pounds per square foot of surface at a velocity of 1 ft. per second;
   [omega] the area of the surface in square feet; and v its velocity in
@@ -10249,13 +10215,13 @@ stream.
   in accordance with the laws stated above, the total resistance of the
   surface is
 
-    R = f[omega]v²   (1)
+    R = f[omega]v²   (1)
 
   where f is a quantity approximately constant for any given surface. If
 
     [xi] = 2gf/G,
 
-    R = [xi]G[omega]v²/2g,   (2)
+    R = [xi]G[omega]v²/2g,   (2)
 
   where [xi] is, like f, nearly constant for a given surface, and is
   termed the coefficient of friction.
@@ -10283,8 +10249,8 @@ stream.
   ft. per second. The work expended in fluid friction is therefore given
   by the equation--
 
-    Work expended = f[omega]v³ foot-pounds per second \   (3).
-                  = [xi]G[omega]v³/2g   "        "    /
+    Work expended = f[omega]v³ foot-pounds per second \   (3).
+                  = [xi]G[omega]v³/2g   "        "    /
 
   The coefficient of friction and the friction per square foot of
   surface can be indirectly obtained from observations of the discharge
@@ -10307,7 +10273,7 @@ stream.
 
   in which expression the second term is of greatest importance at very
   low velocities, and of comparatively little importance at velocities
-  over about ½ ft. per second. Values of [xi] expressed in this and
+  over about ½ ft. per second. Values of [xi] expressed in this and
   similar forms will be given in connexion with pipes and canals.
 
   All these expressions must at present be regarded as merely empirical
@@ -10317,7 +10283,7 @@ stream.
   than these expressions allow, and to depend on circumstances of which
   they do not take account.
 
-  § 67. _Coulomb's Experiments._--The first direct experiments on fluid
+  § 67. _Coulomb's Experiments._--The first direct experiments on fluid
   friction were made by Coulomb, who employed a circular disk suspended
   by a thin brass wire and oscillated in its own plane. His experiments
   were chiefly made at very low velocities. When the disk is rotated to
@@ -10334,7 +10300,7 @@ stream.
   apparatus oscillates. To this the friction disk is rigidly attached
   hanging in a vessel of water. The friction disks were from 4.7 to 7.7
   in. diameter, and they generally made one oscillation in from 20 to 30
-  seconds, through angles varying from 360° to 6°. When the velocity of
+  seconds, through angles varying from 360° to 6°. When the velocity of
   the circumference of the disk was less than 6 in. per second, the
   resistance was sensibly proportional to the velocity.
 
@@ -10351,7 +10317,7 @@ stream.
 
   [Illustration: FIG. 79.]
 
-  § 68. _Froude's Experiments._--The most important direct experiments
+  § 68. _Froude's Experiments._--The most important direct experiments
   on fluid friction at ordinary velocities are those made by William
   Froude (1810-1879) at Torquay. The method adopted in these experiments
   was to tow a board in a still water canal, the velocity and the
@@ -10424,7 +10390,7 @@ stream.
   its own direction, and cannot therefore experience so much resistance
   from it."
 
-  § 69. The following table gives a general statement of Froude's
+  § 69. The following table gives a general statement of Froude's
   results. In all the experiments in this table, the boards had a fine
   cutwater and a fine stern end or run, so that the resistance was
   entirely due to the surface. The table gives the resistances per
@@ -10487,7 +10453,7 @@ stream.
   becomes constant or nearly constant, and the friction per square foot
   is therefore nearly constant also.
 
-  § 70. _Friction of Rotating Disks._--A rotating disk is virtually a
+  § 70. _Friction of Rotating Disks._--A rotating disk is virtually a
   surface of unlimited extent and it is convenient for experiments on
   friction with different surfaces at different speeds. Experiments
   carried out by Professor W. C. Unwin (_Proc. Inst. Civ. Eng._ lxxx.)
@@ -10545,14 +10511,14 @@ stream.
   in agreement with Froude's results.
 
   Experiments with a bright brass disk showed that the friction
-  decreased with increase of temperature. The diminution between 41° and
-  130° F. amounted to 18%. In the general equation M = cN^n for any
+  decreased with increase of temperature. The diminution between 41° and
+  130° F. amounted to 18%. In the general equation M = cN^n for any
   given disk,
 
     c_t = 0.1328(1 - 0.0021t),
 
   where c_t is the value of c for a bright brass disk 0.85 ft. in
-  diameter at a temperature t° F.
+  diameter at a temperature t° F.
 
   The disks used were either polished or made rougher by varnish or by
   varnish and sand. The following table gives a comparison of the
@@ -10570,7 +10536,7 @@ stream.
 
   VIII. STEADY FLOW OF WATER IN PIPES OF UNIFORM SECTION.
 
-  § 71. The ordinary theory of the flow of water in pipes, on which all
+  § 71. The ordinary theory of the flow of water in pipes, on which all
   practical formulae are based, assumes that the variation of velocity
   at different points of any cross section may be neglected. The water
   is considered as moving in plane layers, which are driven through the
@@ -10612,37 +10578,37 @@ stream.
   against the surface of the pipe. The area of that surface is [chi]dl.
 
   The work expended in overcoming the frictional resistance per second
-  is (see § 66, eq. 3)
+  is (see § 66, eq. 3)
 
-    -[zeta]G[chi]dlv³/2g,
+    -[zeta]G[chi]dlv³/2g,
 
   or, since Q = [Omega]v,
 
-    -[zeta]G([chi]/[Omega]) Q (v²/2g) dl;
+    -[zeta]G([chi]/[Omega]) Q (v²/2g) dl;
 
   the negative sign being taken because the work is done against a
   resistance. Adding all these portions of work, and equating the result
   to zero, since the motion is uniform,--
 
-    -GQ dz - Q dp - [zeta]G([chi]/[Omega]) Q (v²/2g) dl = 0.
+    -GQ dz - Q dp - [zeta]G([chi]/[Omega]) Q (v²/2g) dl = 0.
 
   Dividing by GQ,
 
-    dz + dp/G + [zeta]([chi]/[Omega])(v²/2g) dl = 0.
+    dz + dp/G + [zeta]([chi]/[Omega])(v²/2g) dl = 0.
 
   Integrating,
 
-    z + p/G + [zeta]([chi]/[Omega])(v²/2g)l = constant.   (1)
+    z + p/G + [zeta]([chi]/[Omega])(v²/2g)l = constant.   (1)
 
-  § 72. Let A and B (fig. 81) be any two sections of the pipe for which
+  § 72. Let A and B (fig. 81) be any two sections of the pipe for which
   p, z, l have the values p1, z1, l1, and p2, z2, l2, respectively. Then
 
-    z1 + p1/G + [zeta]([chi]/[Omega])(v²/2g)l1
-      = z2 + p2/G + [zeta]([chi]/[Omega])(v²/2g)l2;
+    z1 + p1/G + [zeta]([chi]/[Omega])(v²/2g)l1
+      = z2 + p2/G + [zeta]([chi]/[Omega])(v²/2g)l2;
 
   or, if l2 - l1 = L, rearranging the terms,
 
-    [zeta]v²/2g = (1/L){(z1 + p1/G) - (z2 + p2/G)}[Omega]/[chi].   (2)
+    [zeta]v²/2g = (1/L){(z1 + p1/G) - (z2 + p2/G)}[Omega]/[chi].   (2)
 
   Suppose pressure columns introduced at A and B. The water will rise in
   those columns to the heights p1/G and p2/G due to the pressures p1 and
@@ -10664,19 +10630,19 @@ stream.
 
   Introducing these values,
 
-    [zeta]v²/2g = mh/L = mi.   (3)
+    [zeta]v²/2g = mh/L = mi.   (3)
 
   For pipes of circular section, and diameter d,
 
-    m = [Omega]/[chi] = ¼[pi]d²/[pi]d = ¼d.
+    m = [Omega]/[chi] = ¼[pi]d²/[pi]d = ¼d.
 
   Then
 
-    [zeta]v²/2g = ¼dh/L = ¼di;   (4)
+    [zeta]v²/2g = ¼dh/L = ¼di;   (4)
 
   or
 
-    h = [zeta](4L/d)(v²/2g);   (4a)
+    h = [zeta](4L/d)(v²/2g);   (4a)
 
   which shows that the head lost in friction is proportional to the head
   due to the velocity, and is found by multiplying that head by the
@@ -10685,7 +10651,7 @@ stream.
   But if C and D are at greatly different levels the excess of
   barometric pressure at C, in feet of water, must be added to p2/G.
 
-  § 73. _Hydraulic Gradient or Line of Virtual Slope._--Join CD. Since
+  § 73. _Hydraulic Gradient or Line of Virtual Slope._--Join CD. Since
   the head lost in friction is proportional to L, any intermediate
   pressure column between A and B will have its free surface on the line
   CD, and the vertical distance between CD and the pipe at any point
@@ -10715,26 +10681,26 @@ stream.
 
   [Illustration: FIG. 82.]
 
-  § 74. _Case of a Uniform Pipe connecting two Reservoirs, when all the
+  § 74. _Case of a Uniform Pipe connecting two Reservoirs, when all the
   Resistances are taken into account._--Let h (fig. 82) be the
   difference of level of the reservoirs, and v the velocity, in a pipe
   of length L and diameter d. The whole work done per second is
   virtually the removal of Q cub. ft. of water from the surface of the
   upper reservoir to the surface of the lower reservoir, that is GQh
-  foot-pounds. This is expended in three ways. (1) The head v²/2g,
-  corresponding to an expenditure of GQv²/2g foot-pounds of work, is
+  foot-pounds. This is expended in three ways. (1) The head v²/2g,
+  corresponding to an expenditure of GQv²/2g foot-pounds of work, is
   employed in giving energy of motion to the water. This is ultimately
   wasted in eddying motions in the lower reservoir. (2) A portion of
   head, which experience shows may be expressed in the form
-  [zeta]0v²/2g, corresponding to an expenditure of GQ[zeta]0v²/2g
+  [zeta]0v²/2g, corresponding to an expenditure of GQ[zeta]0v²/2g
   foot-pounds of work, is employed in overcoming the resistance at the
   entrance to the pipe. (3) As already shown the head expended in
-  overcoming the surface friction of the pipe is [zeta](4L/d)(v²/2g)
-  corresponding to GQ[zeta](4L/d)(v²/2g) foot-pounds of work. Hence
+  overcoming the surface friction of the pipe is [zeta](4L/d)(v²/2g)
+  corresponding to GQ[zeta](4L/d)(v²/2g) foot-pounds of work. Hence
 
-    GQh = GQv²/2g + GQ[zeta]0v²/2g + GQ[zeta]·4L·v²/d·2g;
+    GQh = GQv²/2g + GQ[zeta]0v²/2g + GQ[zeta]·4L·v²/d·2g;
 
-    h = (1 + [zeta]0 + [zeta]·4L/d)v²/2g.
+    h = (1 + [zeta]0 + [zeta]·4L/d)v²/2g.
                                                       (5)
     v = 8.025 [root][hd/{(1 + [zeta]0)d + 4[zeta]L}].
 
@@ -10747,8 +10713,8 @@ stream.
   necessary to take account of the first two terms in the bracket, as
   well as the third. For instance, in pipes for the supply of turbines,
   v is usually limited to 2 ft. per second, and the pipe is bellmouthed.
-  Then 1.08v²/2g = 0.067 ft. In pipes for towns' supply v may range from
-  2 to 4½ ft. per second, and then 1.5v²/2g = 0.1 to 0.5 ft. In either
+  Then 1.08v²/2g = 0.067 ft. In pipes for towns' supply v may range from
+  2 to 4½ ft. per second, and then 1.5v²/2g = 0.1 to 0.5 ft. In either
   case this amount of head is small compared with the whole virtual fall
   in the cases which most commonly occur.
 
@@ -10761,7 +10727,7 @@ stream.
 
   The equation above may be put in the form
 
-    h = (4[zeta]/d)[{(1 + [zeta]0)d/4[zeta]} + L] v²/2g;   (6)
+    h = (4[zeta]/d)[{(1 + [zeta]0)d/4[zeta]} + L] v²/2g;   (6)
 
   from which it is clear that the head expended at the mouthpiece is
   equivalent to that of a length
@@ -10773,7 +10739,7 @@ stream.
   added to the actual length of the pipe to allow for mouthpiece
   resistance in approximate calculations.
 
-  § 75. _Coefficient of Friction for Pipes discharging Water._--From the
+  § 75. _Coefficient of Friction for Pipes discharging Water._--From the
   average of a large number of experiments, the value of [zeta] for
   ordinary iron pipes is
 
@@ -10803,7 +10769,7 @@ stream.
 
     4[zeta] = [alpha] + [beta]/[root]v = 0.003598 + 0.004289/[root]v.   (8)
 
-  § 76. _Darcy's Experiments on Friction in Pipes._--All previous
+  § 76. _Darcy's Experiments on Friction in Pipes._--All previous
   experiments on the resistance of pipes were superseded by the
   remarkable researches carried out by H. P. G. Darcy (1803-1858), the
   Inspector-General of the Paris water works. His experiments were
@@ -10814,7 +10780,7 @@ stream.
 
   1. For new and clean pipes the friction varies considerably with the
   nature and polish of the surface of the pipe. For clean cast iron it
-  is about 1½ times as great as for cast iron covered with pitch.
+  is about 1½ times as great as for cast iron covered with pitch.
 
   2. The nature of the surface has less influence when the pipes are old
   and incrusted with deposits, due to the action of the water. Thus old
@@ -10874,7 +10840,7 @@ stream.
   These values of [zeta] are, however, not exact for widely differing
   velocities. To embrace all cases Darcy proposed the expression
 
-    [zeta] = ([alpha] + [alpha]1/d) + ([beta] + [beta]1/d²)/v;   (10)
+    [zeta] = ([alpha] + [alpha]1/d) + ([beta] + [beta]1/d²)/v;   (10)
 
   which is a modification of Coulomb's, including terms expressing the
   influence of the diameter and of the velocity. For clean pipes Darcy
@@ -10900,7 +10866,7 @@ stream.
   clear that it gives more accurate values of the discharge than simpler
   formulae.
 
-  § 77. _Later Investigations on Flow in Pipes._--The foregoing
+  § 77. _Later Investigations on Flow in Pipes._--The foregoing
   statement gives the theory of flow in pipes so far as it can be put in
   a simple rational form. But the conditions of flow are really more
   complicated than can be expressed in any rational form. Taking even
@@ -10929,7 +10895,7 @@ stream.
   is not exactly the square. Also in determining the form of his
   equation for [zeta] Darcy used only eight out of his seventeen series
   of experiments, and there is reason to think that some of these were
-  exceptional. Barré de Saint-Venant was the first to propose a formula
+  exceptional. Barré de Saint-Venant was the first to propose a formula
   with two constants,
 
     dh/4l = mV^n,
@@ -11137,7 +11103,7 @@ stream.
     | Incrusted cast iron  | .0440 | 1.160 | 2.0  |
     +----------------------+-------+-------+------+
 
-  § 78. _Distribution of Velocity in the Cross Section of a
+  § 78. _Distribution of Velocity in the Cross Section of a
   Pipe._--Darcy made experiments with a Pitot tube in 1850 on the
   velocity at different points in the cross section of a pipe. He
   deduced the relation
@@ -11146,9 +11112,9 @@ stream.
 
   where V is the velocity at the centre and v the velocity at radius r
   in a pipe of radius R with a hydraulic gradient i. Later Bazin
-  repeated the experiments and extended them (_Mém. de l'Académie des
+  repeated the experiments and extended them (_Mém. de l'Académie des
   Sciences_, xxxii. No. 6). The most important result was the ratio of
-  mean to central velocity. Let b = Ri/U², where U is the mean velocity
+  mean to central velocity. Let b = Ri/U², where U is the mean velocity
   in the pipe; then V/U = 1 + 9.03 [root]b. A very useful result for
   practical purposes is that at 0.74 of the radius of the pipe the
   velocity is equal to the mean velocity. Fig. 84 gives the velocities
@@ -11156,17 +11122,17 @@ stream.
 
   [Illustration: FIG. 84.]
 
-  § 79. _Influence of Temperature on the Flow through Pipes._--Very
+  § 79. _Influence of Temperature on the Flow through Pipes._--Very
   careful experiments on the flow through a pipe 0.1236 ft. in diameter
   and 25 ft. long, with water at different temperatures, have been made
   by J. G. Mair (_Proc. Inst. Civ. Eng._ lxxxiv.). The loss of head was
   measured from a point 1 ft. from the inlet, so that the loss at entry
-  was eliminated. The 1½ in. pipe was made smooth inside and to gauge,
+  was eliminated. The 1½ in. pipe was made smooth inside and to gauge,
   by drawing a mandril through it. Plotting the results logarithmically,
   it was found that the resistance for all temperatures varied very
   exactly as v^(1.795), the index being less than 2 as in other
   experiments with very smooth surfaces. Taking the ordinary equation of
-  flow h = [zeta](4L/D)(v²/2g), then for heads varying from 1 ft. to
+  flow h = [zeta](4L/D)(v²/2g), then for heads varying from 1 ft. to
   nearly 4 ft., and velocities in the pipe varying from 4 ft. to 9 ft.
   per second, the values of [zeta] were as follows:--
 
@@ -11192,16 +11158,16 @@ stream.
   where again a regular decrease of the coefficient occurs as the
   temperature rises. In experiments on the friction of disks at
   different temperatures Professor W. C. Unwin found that the resistance
-  was proportional to constant × (1 - 0.0021t) and the values of m given
+  was proportional to constant × (1 - 0.0021t) and the values of m given
   above are expressed almost exactly by the relation
 
     m = 0.000311(1 - 0.00215 t).
 
   In tank experiments on ship models for small ordinary variations of
   temperature, it is usual to allow a decrease of 3% of resistance for
-  10° F. increase of temperature.
+  10° F. increase of temperature.
 
-  § 80. _Influence of Deposits in Pipes on the Discharge. Scraping Water
+  § 80. _Influence of Deposits in Pipes on the Discharge. Scraping Water
   Mains._--The influence of the condition of the surface of a pipe on
   the friction is shown by various facts known to the engineers of
   waterworks. In pipes which convey certain kinds of water, oxidation
@@ -11231,8 +11197,8 @@ stream.
   is placed in the main by removing the cover from one of the boxes
   shown at C, D. The cover is then replaced, water pressure is admitted
   behind the plungers, and the apparatus driven through the main. At
-  Lancaster after twice scraping the discharge was increased 56½%, at
-  Oswestry 54½%. The increased discharge is due to the diminution of the
+  Lancaster after twice scraping the discharge was increased 56½%, at
+  Oswestry 54½%. The increased discharge is due to the diminution of the
   friction of the pipe by removing the roughnesses due to oxidation. The
   scraper can be easily followed when the mains are about 3 ft. deep by
   the noise it makes. The average speed of the scraper at Torquay is
@@ -11256,7 +11222,7 @@ stream.
   scraper devised by G. F. Deacon (see "Deposits in Pipes," by Professor
   J. C. Campbell Brown, _Proc. Inst. Civ. Eng._, 1903-1904).
 
-  § 81. _Flow of Water through Fire Hose._--The hose pipes used for fire
+  § 81. _Flow of Water through Fire Hose._--The hose pipes used for fire
   purposes are of very varied character, and the roughness of the
   surface varies. Very careful experiments have been made by J. R.
   Freeman (_Am. Soc. Civ. Eng._ xxi., 1889). It was noted that under
@@ -11297,7 +11263,7 @@ stream.
     |  hose         |    "    |   331   |1.1624 | 20.00 |  79.6 |
     +---------------+---------+---------+-------+-------+-------+
 
-  § 82. _Reduction of a Long Pipe of Varying Diameter to an Equivalent
+  § 82. _Reduction of a Long Pipe of Varying Diameter to an Equivalent
   Pipe of Uniform Diameter. Dupuit's Equation._--Water mains for the
   supply of towns often consist of a series of lengths, the diameter
   being the same for each length, but differing from length to length.
@@ -11323,21 +11289,21 @@ stream.
   in A due to friction is
 
     h = i1l1 + i2l2 + ...
-      = [zeta](v1²·4l1/2gd1) + [zeta](v2²·4l2/2gd2) + ...
+      = [zeta](v1²·4l1/2gd1) + [zeta](v2²·4l2/2gd2) + ...
 
   and in the uniform main
 
-    il = [zeta](v²·4l/2gd).
+    il = [zeta](v²·4l/2gd).
 
   If the mains are equivalent, as defined above,
 
-    [zeta](v²·4l/2gd) = [zeta](v1²·4l1/2gd1) + [zeta](v2²·4l2/2gd2) + ...
+    [zeta](v²·4l/2gd) = [zeta](v1²·4l1/2gd1) + [zeta](v2²·4l2/2gd2) + ...
 
   But, since the discharge is the same for all portions,
 
-    ¼[pi]d²v = ¼[pi]d1²v1 = ¼[pi]d2²v2 = ...
+    ¼[pi]d²v = ¼[pi]d1²v1 = ¼[pi]d2²v2 = ...
 
-    v1 = vd²/d1²; v2 = vd²/d2² ...
+    v1 = vd²/d1²; v2 = vd²/d2² ...
 
   Also suppose that [zeta] may be treated as constant for all the pipes.
   Then
@@ -11349,7 +11315,7 @@ stream.
   which gives the length of the equivalent uniform main which would have
   the same total loss of head for any given discharge.
 
-  § 83. _Other Losses of Head in Pipes._--Most of the losses of head in
+  § 83. _Other Losses of Head in Pipes._--Most of the losses of head in
   pipes, other than that due to surface friction against the pipe, are
   due to abrupt changes in the velocity of the stream producing eddies.
   The kinetic energy of these is deducted from the general energy of
@@ -11364,18 +11330,18 @@ stream.
 
   or, if the section is circular,
 
-    v1/v0 = (d0/d1)².
+    v1/v0 = (d0/d1)².
 
   The head lost at the abrupt change of velocity has already been shown
   to be the head due to the relative velocity of the two parts of the
   stream. Hence head lost
 
-    [h]_e = (v0 - v1)²/2g = ([omega]1/[omega]0 - 1)²v1²/2g
-          = {(d1/d0)² - 1}² v1²/2g
+    [h]_e = (v0 - v1)²/2g = ([omega]1/[omega]0 - 1)²v1²/2g
+          = {(d1/d0)² - 1}² v1²/2g
 
   or
 
-    [h]_e = [zeta]_ev1²/2g,   (1)
+    [h]_e = [zeta]_ev1²/2g,   (1)
 
   if [zeta]_e is put for the expression in brackets.
 
@@ -11399,27 +11365,27 @@ stream.
   ([omega]/c_c[omega])v = v/c1, where c_c is the coefficient of
   contraction. Then the head lost is
 
-    [h]_m = (v/c_c - v)²/2g = (1/c_c - 1)²v²/2g;
+    [h]_m = (v/c_c - v)²/2g = (1/c_c - 1)²v²/2g;
 
   and, if c_c is taken 0.64,
 
-    [h]_m = 0.316 v²/2g.   (2)
+    [h]_m = 0.316 v²/2g.   (2)
 
   The value of the coefficient of contraction for this case is, however,
   not well ascertained, and the result is somewhat modified by friction.
   For water entering a cylindrical, not bell-mouthed, pipe from a
   reservoir of indefinitely large size, experiment gives
 
-    [h]_a = 0.505 v²/2g.   (3)
+    [h]_a = 0.505 v²/2g.   (3)
 
   If there is a diaphragm at the mouth of the pipe as in fig. 89, let
   [omega]1 be the area of this orifice. Then the area of the contracted
   stream is c_c[omega]1, and the head lost is
 
-    [h]_c = {([omega]/c_c[omega]1) - 1}²v²/2g
-          = [zeta]_cv²/2g   (4)
+    [h]_c = {([omega]/c_c[omega]1) - 1}²v²/2g
+          = [zeta]_cv²/2g   (4)
 
-  if [zeta], is put for {([omega]/c_c[omega]1) - 1}². Weisbach has found
+  if [zeta], is put for {([omega]/c_c[omega]1) - 1}². Weisbach has found
   experimentally the following values of the coefficient, when the
   stream approaching the orifice was considerably larger than the
   orifice:--
@@ -11448,14 +11414,14 @@ stream.
 
   Elbows.--Weisbach considers the loss of head at elbows (fig. 91) to be
   due to a contraction formed by the stream. From experiments with a
-  pipe 1¼ in. diameter, he found the loss of head
+  pipe 1¼ in. diameter, he found the loss of head
 
-    [h]_e = [zeta]_e v²/2g;   (5)
+    [h]_e = [zeta]_e v²/2g;   (5)
 
-    [zeta]_e = 0.9457 sin² ½[phi] + 2.047 sin^4 ½[phi].
+    [zeta]_e = 0.9457 sin² ½[phi] + 2.047 sin^4 ½[phi].
 
     +------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
-    | [phi] =    | 20° | 40° | 60° | 80° | 90° | 100°| 110°| 120°| 130°| 140°|
+    | [phi] =    | 20° | 40° | 60° | 80° | 90° | 100°| 110°| 120°| 130°| 140°|
     |            |     |     |     |     |     |     |     |     |     |     |
     | [zeta]_e = |0.046|0.139|0.364|0.740|0.984|1.260|1.556|1.861|2.158|2.431|
     +------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
@@ -11470,7 +11436,7 @@ stream.
   not very satisfactorily ascertained. Weisbach obtained for the loss of
   head at a bend in a pipe of circular section
 
-    [h]_b = [zeta]_b v²/2g;   (6)
+    [h]_b = [zeta]_b v²/2g;   (6)
 
     [zeta]_b = 0.131 + 1.847(d/2[rho])^(7/2),
 
@@ -11484,7 +11450,7 @@ stream.
   water-stream, similar to that for an abrupt diminution of section
   already discussed. The loss of head may be taken as before to be
 
-    [h]_v = [zeta]_v v²/2g;   (7)
+    [h]_v = [zeta]_v v²/2g;   (7)
 
   where v is the velocity in the pipe beyond the valve and [zeta]_v a
   coefficient determined by experiment. The following are Weisbach's
@@ -11503,7 +11469,7 @@ stream.
 
     +-----------------------+----+-----+-----+-----+-----+-----+------+------+
     | Ratio of height of    |    |     |     |     |     |     |      |      |
-    |   opening to diameter | 1.0| 7/8 | 3/4 | 5/8 |  ½  | 3/8 |  ¼   | 1/5  |
+    |   opening to diameter | 1.0| 7/8 | 3/4 | 5/8 |  ½  | 3/8 |  ¼   | 1/5  |
     |   of pipe             |    |     |     |     |     |     |      |      |
     |  [omega]1/[omega] =   |1.00|0.948|.856 |.740 |.609 |.466 | .315 | .159 |
     |                       |    |     |     |     |     |     |      |      |
@@ -11518,7 +11484,7 @@ stream.
     turned = [theta].
 
     +------------+-----+-----+-----+-----+-----+-----+-----+
-    | [theta] =  |  5° | 10° | 15° | 20° | 25° | 30° | 35° |
+    | [theta] =  |  5° | 10° | 15° | 20° | 25° | 30° | 35° |
     | Ratio of   |     |     |     |     |     |     |     |
     |   cross    |.926 |.850 |.772 |.692 |.613 |.535 |.458 |
     |   sections |     |     |     |     |     |     |     |
@@ -11526,7 +11492,7 @@ stream.
     +------------+-----+-----+-----+-----+-----+-----+-----+
 
     +------------+-----+-----+-----+-----+-----+-----+-----+
-    | [theta] =  | 40° | 45° | 50° | 55° | 60° | 65° | 82° |
+    | [theta] =  | 40° | 45° | 50° | 55° | 60° | 65° | 82° |
     | Ratio of   |     |     |     |     |     |     |     |
     |  cross     |.385 |.315 |.250 |.190 |.137 |.091 |  0  |
     |  sections  |     |     |     |     |     |     |     |
@@ -11536,20 +11502,20 @@ stream.
     _Throttle Valve in a Cylindrical Pip_e (fig. 95)
 
     +------------+-----+-----+-----+-----+-----+-----+-----+-----+
-    | [theta] =  |  5° | 10° | 15° | 20° | 25° | 30° | 35° | 40° |
+    | [theta] =  |  5° | 10° | 15° | 20° | 25° | 30° | 35° | 40° |
     |            |     |     |     |     |     |     |     |     |
     | [zeta]_v = | .24 | .52 | .90 | 1.54| 2.51| 3.91| 6.22| 10.8|
     +------------+-----+-----+-----+-----+-----+-----+-----+-----+
 
     +------------+------+------+------+------+------+------+------+
-    | [theta] =  |  45° |  50° |  55° |  60° |  65° |  70° |  90° |
+    | [theta] =  |  45° |  50° |  55° |  60° |  65° |  70° |  90° |
     |            |      |      |      |      |      |      |      |
     | [zeta]_v = | 18.7 | 32.6 | 58.8 |  118 |  256 |  751 | [oo] |
     +------------+------+------+------+------+------+------+------+
 
   [Illustration: FIG. 95.]
 
-  § 84. _Practical Calculations on the Flow of Water in Pipes._--In the
+  § 84. _Practical Calculations on the Flow of Water in Pipes._--In the
   following explanations it will be assumed that the pipe is of so great
   a length that only the loss of head in friction against the surface of
   the pipe needs to be considered. In general it is one of the four
@@ -11557,16 +11523,16 @@ stream.
   loss of head h is given by the relation h = il, this need not be
   separately considered.
 
-  There are then three equations (see eq. 4, § 72, and 9a, § 76) for the
+  There are then three equations (see eq. 4, § 72, and 9a, § 76) for the
   solution of such problems as arise:--
 
     [zeta] = [alpha](1 + 1/12d);   (1)
 
   where [alpha] = 0.005 for new and = 0.01 for incrusted pipes.
 
-    [zeta]v²/2g = ¼di.   (2)
+    [zeta]v²/2g = ¼di.   (2)
 
-    Q = ¼[pi]d²v.   (3)
+    Q = ¼[pi]d²v.   (3)
 
   _Problem 1._ Given the diameter of the pipe and its virtual slope, to
   find the discharge and velocity of flow. Here d and i are given, and Q
@@ -11604,27 +11570,27 @@ stream.
   the virtual slope and velocity. Find v from (3); [zeta] from (1);
   lastly i from (2). If we combine (1) and (2) we get
 
-    i = [zeta](v²/2g) (4/d) = 2a{1 + 1/12d} v²/gd;   (5)
+    i = [zeta](v²/2g) (4/d) = 2a{1 + 1/12d} v²/gd;   (5)
 
   and, taking the mean values of [zeta] for pipes from 1 to 4 ft.
   diameter, given above, the approximate formulae are
 
-    i = 0.0003268 v²/d for new pipes
-      = 0.0006536 v²/d for incrusted pipes.   (5a)
+    i = 0.0003268 v²/d for new pipes
+      = 0.0006536 v²/d for incrusted pipes.   (5a)
 
   _Problem 4._ Given the virtual slope and the velocity, to find the
   diameter of the pipe and the discharge. The diameter is obtained from
   equations (2) and (1), which give the quadratic expression
 
-    d² - d(2[alpha]v²/gi) - [alpha]v²/6gi = 0.
+    d² - d(2[alpha]v²/gi) - [alpha]v²/6gi = 0.
 
-    .: d = [alpha]v²/gi + [root]{([alpha]v²/gi) ([alpha]v²/gi + 1/6)}.   (6)
+    .: d = [alpha]v²/gi + [root]{([alpha]v²/gi) ([alpha]v²/gi + 1/6)}.   (6)
 
   For practical purposes, the approximate equations
 
-    d = 2[alpha]v²/gi + 1/12   (6a)
-      = 0.00031 v²/i + .083 for new pipes
-      = 0.00062 v²/i + .083 for incrusted pipes
+    d = 2[alpha]v²/gi + 1/12   (6a)
+      = 0.00031 v²/i + .083 for new pipes
+      = 0.00062 v²/i + .083 for incrusted pipes
 
   are sufficiently accurate.
 
@@ -11633,7 +11599,7 @@ stream.
   occurs in designing, is the one which is least easy of direct
   solution. From equations (2) and (3) we get--
 
-    d^5 = 32[zeta]Q²/g[pi]²i.   (7)
+    d^5 = 32[zeta]Q²/g[pi]²i.   (7)
 
   If now the value of [zeta] in (1) is introduced, the equation becomes
   very cumbrous. Various approximate methods of meeting the difficulty
@@ -11642,9 +11608,9 @@ stream.
   (a) Taking the mean values of [zeta] given above for pipes of 1 to 4
   ft. diameter we get
 
-    d = [root 5](32[zeta]/g[pi]²) [root 5](Q²/i)   (8)
-      = 0.2216 [root 5](Q²/i) for new pipes
-      = 0.2541 [root 5](Q²/i) for incrusted pipes;
+    d = [root 5](32[zeta]/g[pi]²) [root 5](Q²/i)   (8)
+      = 0.2216 [root 5](Q²/i) for new pipes
+      = 0.2541 [root 5](Q²/i) for incrusted pipes;
 
   equations which are interesting as showing that when the value of
   [zeta] is doubled the diameter of pipe for a given discharge is only
@@ -11653,42 +11619,42 @@ stream.
   (b) A second method is to obtain a rough value of d by assuming [zeta]
   = [alpha]. This value is
 
-    d´ = [root 5](32Q²/g[pi]²i) [root 5][alpha]
-       = 0.6319 [root 5](Q²/i) [root 5][alpha].
+    d´ = [root 5](32Q²/g[pi]²i) [root 5][alpha]
+       = 0.6319 [root 5](Q²/i) [root 5][alpha].
 
   Then a very approximate value of [zeta] is
 
-    [zeta]´ = [alpha](1 + 1/12d´);
+    [zeta]´ = [alpha](1 + 1/12d´);
 
   and a revised value of d, not sensibly differing from the exact value,
   is
 
-    d´´ = [root 5](32Q²/g[pi]²i) [root 5][zeta]´
-        = 0.6319 [root 5](Q²/i) [root 5][zeta]´.
+    d´´ = [root 5](32Q²/g[pi]²i) [root 5][zeta]´
+        = 0.6319 [root 5](Q²/i) [root 5][zeta]´.
 
   (c) Equation 7 may be put in the form
 
-    d = [root 5](32[alpha]Q²/g[pi]²i) [root 5](1 + 1/12d).   (9)
+    d = [root 5](32[alpha]Q²/g[pi]²i) [root 5](1 + 1/12d).   (9)
 
   Expanding the term in brackets,
 
-    [root 5](1 + 1/12d) = 1 + 1/60d - 1/1800d² ...
+    [root 5](1 + 1/12d) = 1 + 1/60d - 1/1800d² ...
 
   Neglecting the terms after the second,
 
-    d = [root 5](32[alpha]/g[pi]²) [root 5](Q²/i)·{1 + 1/60d}
-      = [root 5](32a/g[pi]²) [root 5](Q²/i) + 0.01667;   (9a)
+    d = [root 5](32[alpha]/g[pi]²) [root 5](Q²/i)·{1 + 1/60d}
+      = [root 5](32a/g[pi]²) [root 5](Q²/i) + 0.01667;   (9a)
 
   and
 
-    [root 5](32a/g[pi]²) = 0.219 for new pipes
+    [root 5](32a/g[pi]²) = 0.219 for new pipes
                          = 0.252 for incrusted pipes.
 
   [Illustration: FIG. 96.]
 
   [Illustration: FIG. 97.]
 
-  § 85. _Arrangement of Water Mains for Towns' Supply._--Town mains are
+  § 85. _Arrangement of Water Mains for Towns' Supply._--Town mains are
   usually supplied oy gravitation from a service reservoir, which in
   turn is supplied by gravitation from a storage reservoir or by pumping
   from a lower level. The service reservoir should contain three days'
@@ -11713,7 +11679,7 @@ stream.
 
   [Illustration: FIG. 98.]
 
-  § 86. _Determination of the Diameters of Different Parts of a Water
+  § 86. _Determination of the Diameters of Different Parts of a Water
   Main._--When the plan of the arrangement of mains is determined upon,
   and the supply to each locality and the pressure required is
   ascertained, it remains to determine the diameters of the pipes. Let
@@ -11736,7 +11702,7 @@ stream.
   Where no other circumstance limits the loss of head to be assigned to
   a given length of main, a consideration of the safety of the main from
   fracture by hydraulic shock leads to a limitation of the velocity of
-  flow. Generally the velocity in water mains lies between 1½ and 4½ ft.
+  flow. Generally the velocity in water mains lies between 1½ and 4½ ft.
   per second. Occasionally the velocity in pipes reaches 10 ft. per
   second, and in hydraulic machinery working under enormous pressures
   even 20 ft. per second. Usually the velocity diminishes along the main
@@ -11750,7 +11716,7 @@ stream.
     Diameter in inches          4     8    12    18    24    30    36
     Velocity in feet per sec.  2.5   3.0   3.5   4.5   5.3   6.2   7.0
 
-  § 87. _Branched Pipe connecting Reservoirs at Different Levels._--Let
+  § 87. _Branched Pipe connecting Reservoirs at Different Levels._--Let
   A, B, C (fig. 98) be three reservoirs connected by the arrangement of
   pipes shown,--l1, d1, Q1, v1; l2, d2, Q2, v2; h3, d3, Q3, v3 being the
   length, diameter, discharge and velocity in the three portions of the
@@ -11769,27 +11735,27 @@ stream.
 
   To determine which case has to be dealt with in the given conditions,
   suppose the pipe from X to B closed by a sluice. Then there is a
-  simple main, and the height of free surface h´ at X can be determined.
+  simple main, and the height of free surface h´ at X can be determined.
   For this condition
 
-    h_a - h´ = [zeta](v1²/2g)(4l1/d1)
-             = 32[zeta]Q´² l1/g[pi]²d1^5;
+    h_a - h´ = [zeta](v1²/2g)(4l1/d1)
+             = 32[zeta]Q´² l1/g[pi]²d1^5;
 
-    h´ - h_c = [zeta](v3²/2g)(4l3/d3)
-             = 32[zeta]Q´²l3/g[pi]²d3^5;
+    h´ - h_c = [zeta](v3²/2g)(4l3/d3)
+             = 32[zeta]Q´²l3/g[pi]²d3^5;
 
-  where Q´ is the common discharge of the two portions of the pipe.
+  where Q´ is the common discharge of the two portions of the pipe.
   Hence
 
-    (h_a - h´)/(h´ - h_c) = l1d3^5/l3d1^5,
+    (h_a - h´)/(h´ - h_c) = l1d3^5/l3d1^5,
 
-  from which h´ is easily obtained. If then h´ is greater than hb,
+  from which h´ is easily obtained. If then h´ is greater than hb,
   opening the sluice between X and B will allow flow towards B, and the
-  case in hand is case I. If h´ is less than h_b, opening the sluice
-  will allow flow from B, and the case is case III. If h´ = h_b, the
+  case in hand is case I. If h´ is less than h_b, opening the sluice
+  will allow flow from B, and the case is case III. If h´ = h_b, the
   case is case II., and is already completely solved.
 
-  The true value of h must lie between h´ and h_b. Choose a new value of
+  The true value of h must lie between h´ and h_b. Choose a new value of
   h, and recalculate Q1, Q2, Q3. Then if
 
     Q1 > Q2 + Q3 in case I.,
@@ -11814,7 +11780,7 @@ stream.
   very distant, it is easy to approximate to values sufficiently
   accurate.
 
-  § 88. _Water Hammer._--If in a pipe through which water is flowing a
+  § 88. _Water Hammer._--If in a pipe through which water is flowing a
   sluice is suddenly closed so as to arrest the forward movement of the
   water, there is a rise of pressure which in some cases is serious
   enough to burst the pipe. This action is termed water hammer or water
@@ -11851,7 +11817,7 @@ stream.
 
   IX. FLOW OF COMPRESSIBLE FLUIDS IN PIPES
 
-  § 89. _Flow of Air in Long Pipes._--When air flows through a long
+  § 89. _Flow of Air in Long Pipes._--When air flows through a long
   pipe, by far the greater part of the work expended is used in
   overcoming frictional resistances due to the surface of the pipe. The
   work expended in friction generates heat, which for the most part must
@@ -11868,7 +11834,7 @@ stream.
   flowing along the tube is much less than it would be in adiabatic
   expansion.
 
-  § 90. _Differential Equation of the Steady Motion of Air Flowing in a
+  § 90. _Differential Equation of the Steady Motion of Air Flowing in a
   Long Pipe of Uniform Section._--When air expands at a constant
   absolute temperature [tau], the relation between the pressure p in
   pounds per square foot and the density or weight per cubic foot G is
@@ -11877,7 +11843,7 @@ stream.
     p/G = c[tau],   (1)
 
   where c = 53.15. Taking [tau] = 521, corresponding to a temperature of
-  60° Fahr.,
+  60° Fahr.,
 
     c[tau] = 27690 foot-pounds.   (2)
 
@@ -11902,30 +11868,30 @@ stream.
   Consider a short length dl of the pipe limited by sections A0, A1 at a
   distance dl (fig. 99). Let p, u be the pressure and velocity at A0, p
   + dp and u + du those at A1. Further, suppose that in a very short
-  time dt the mass of air between A0A1 comes to A´0A´1 so that A0A´0 =
-  udt and A1A´1 = (u + du)dt1. Let [Omega] be the section, and m the
+  time dt the mass of air between A0A1 comes to A´0A´1 so that A0A´0 =
+  udt and A1A´1 = (u + du)dt1. Let [Omega] be the section, and m the
   hydraulic mean radius of the pipe, and W the weight of air flowing
   through the pipe per second.
 
   From the steadiness of the motion the weight of air between the
-  sections A0A´0, and A1A´1 is the same. That is,
+  sections A0A´0, and A1A´1 is the same. That is,
 
     W dt = G[Omega]u dt = G[Omega](u + du) dt.
 
   By analogy with liquids the head lost in friction is, for the length
-  dl (see § 72, eq. 3), [zeta](u²/2g)(dl/m). Let H = u²/2g. Then the
+  dl (see § 72, eq. 3), [zeta](u²/2g)(dl/m). Let H = u²/2g. Then the
   head lost is [zeta](H/m)dl; and, since Wdt lb. of air flow through the
   pipe in the time considered, the work expended in friction is
   -[zeta](H/m)Wdl dt. The change of kinetic energy in dt seconds is the
-  difference of the kinetic energy of A0A´0 and A1A´1, that is,
+  difference of the kinetic energy of A0A´0 and A1A´1, that is,
 
-    (W/g) dt {(u + du)² - u²}/2 = (W/g)u du dt = W dH dt.
+    (W/g) dt {(u + du)² - u²}/2 = (W/g)u du dt = W dH dt.
 
   The work of expansion when [Omega]udt cub. ft. of air at a pressure p
   expand to [Omega](u + du)dt cub. ft. is [Omega]p du dt. But from (3a)
   u = c[tau]W/[Omega]p, and therefore
 
-    du/dp = -c[tau]W/[Omega]p².
+    du/dp = -c[tau]W/[Omega]p².
 
   And the work done by expansion is -(c[tau]W/p)dpdt.
 
@@ -11957,14 +11923,14 @@ stream.
 
   and
 
-    H = u²/2g = c²[tau]²W²/2g[Omega]²p²,
+    H = u²/2g = c²[tau]²W²/2g[Omega]²p²,
 
-    .: dH/H + (2g[Omega]²p/c[tau]W²) dp + [zeta] dl/m = 0.   (4a)
+    .: dH/H + (2g[Omega]²p/c[tau]W²) dp + [zeta] dl/m = 0.   (4a)
 
   For tubes of uniform section m is constant; for steady motion W is
   constant; and for isothermal expansion [tau] is constant. Integrating,
 
-    log H + g[Omega]²p²/W²c[tau] + [zeta]l/m = constant;   (5)
+    log H + g[Omega]²p²/W²c[tau] + [zeta]l/m = constant;   (5)
 
   for
 
@@ -11974,37 +11940,37 @@ stream.
 
     l = l, let H = H1, and p = p1.
 
-  log (H1/H0) + (g[Omega]²}/W²c[tau]) (p1² - p0²) + [zeta]l/m = 0. (5a)
+  log (H1/H0) + (g[Omega]²}/W²c[tau]) (p1² - p0²) + [zeta]l/m = 0. (5a)
   where p0 is the greater pressure and p1 the less, and the flow is from
   A0 towards A1.
 
   By replacing W and H,
 
-    log (p0/p1) + (gc[tau]/u0²p0²)(p1² - p0² + [zeta]l/m = 0  (6)
+    log (p0/p1) + (gc[tau]/u0²p0²)(p1² - p0² + [zeta]l/m = 0  (6)
 
   Hence the initial velocity in the pipe is
 
-    u0 = [root][{gc[tau](p0² - p1²)} / {p0²([zeta]l/m + log (p0/p1)}].   (7)
+    u0 = [root][{gc[tau](p0² - p1²)} / {p0²([zeta]l/m + log (p0/p1)}].   (7)
 
   When l is great, log p0/p1 is comparatively small, and then
 
-    u0 = [root][(gc[tau]m/[zeta]l) {(p0² - p1²)/p0²}],   (7a)
+    u0 = [root][(gc[tau]m/[zeta]l) {(p0² - p1²)/p0²}],   (7a)
 
   a very simple and easily used expression. For pipes of circular
   section m = d/4, where d is the diameter:--
 
-    u0 = [root][(gc[tau]d/4[zeta]l) {(p0² - p1²)/p0²}];   (7b)
+    u0 = [root][(gc[tau]d/4[zeta]l) {(p0² - p1²)/p0²}];   (7b)
 
   or approximately
 
     u0 = (1.1319 - 0.7264 p1/p0) [root](gc[tau]d/4[zeta]l).   (7c)
 
-  § 91. _Coefficient of Friction for Air._--A discussion by Professor
+  § 91. _Coefficient of Friction for Air._--A discussion by Professor
   Unwin of the experiments by Culley and Sabine on the rate of
   transmission of light carriers through pneumatic tubes, in which there
   is steady flow of air not sensibly affected by any resistances other
   than surface friction, furnished the value [zeta] = .007. The pipes
-  were lead pipes, slightly moist, 2¼ in. (0.187 ft.) in diameter, and
+  were lead pipes, slightly moist, 2¼ in. (0.187 ft.) in diameter, and
   in lengths of 2000 to nearly 6000 ft.
 
   In some experiments on the flow of air through cast-iron pipes A.
@@ -12048,18 +12014,18 @@ stream.
   neglect the variation of level of the pipe. For that case we may
   neglect the work done by expansion, and then
 
-    z0 - z1 - p0/G0 - p1/G1 - [zeta](v²/2g)(l/m) = 0,   (10)
+    z0 - z1 - p0/G0 - p1/G1 - [zeta](v²/2g)(l/m) = 0,   (10)
 
   precisely equivalent to the equation for the flow of water, z0 and z1
   being the elevations of the two ends of the pipe above any datum, p0
   and p1 the pressures, G0 and G1 the densities, and v the mean velocity
   in the pipe. This equation may be used for the flow of coal gas.
 
-  § 92. _Distribution of Pressure in a Pipe in which Air is
+  § 92. _Distribution of Pressure in a Pipe in which Air is
   Flowing._--From equation (7a) it results that the pressure p, at l ft.
   from that end of the pipe where the pressure is p0, is
 
-    p = p0 [root](1 - [zeta]lu0²/mgc[tau]);   (11)
+    p = p0 [root](1 - [zeta]lu0²/mgc[tau]);   (11)
 
   which is of the form
 
@@ -12097,26 +12063,26 @@ stream.
 
   [Illustration: FIG. 101.]
 
-  § 93. _Weight of Air Flowing per Second._--The weight of air
+  § 93. _Weight of Air Flowing per Second._--The weight of air
   discharged per second is (equation 3a)--
 
     W = [Omega]u0p0/c[tau].
 
   From equation (7b), for a pipe of circular section and diameter d,
 
-    W = ¼[pi] [root](gd^5(p0² - p1²)/[zeta]lc[tau]),
-      = .611[root](d^5(p0² - p1²)/[zeta]l[tau]).   (13)
+    W = ¼[pi] [root](gd^5(p0² - p1²)/[zeta]lc[tau]),
+      = .611[root](d^5(p0² - p1²)/[zeta]l[tau]).   (13)
 
   Approximately
 
-    W = (.6916 p0 - .4438 p1)(d^5/[zeta]l[tau])^½.   (13a)
+    W = (.6916 p0 - .4438 p1)(d^5/[zeta]l[tau])^½.   (13a)
 
-  § 94. _Application to the Case of Pneumatic Tubes for the Transmission
+  § 94. _Application to the Case of Pneumatic Tubes for the Transmission
   of Messages._--In Paris, Berlin, London, and other towns, it has been
   found cheaper to transmit messages in pneumatic tubes than to
   telegraph by electricity. The tubes are laid underground with easy
   curves; the messages are made into a roll and placed in a light felt
-  carrier, the resistance of which in the tubes in London is only ¾ oz.
+  carrier, the resistance of which in the tubes in London is only ¾ oz.
   A current of air forced into the tube or drawn through it propels the
   carrier. In most systems the current of air is steady and continuous,
   and the carriers are introduced or removed without materially altering
@@ -12131,39 +12097,39 @@ stream.
 
   From (4a) neglecting dH/H, and putting m = d/4,
 
-    dl = g d[Omega]²p dp/2[zeta]W²cr.
+    dl = g d[Omega]²p dp/2[zeta]W²cr.
 
   From (1) and (3)
 
     u = Wc[tau]/p[Omega];
 
-    dl/u = g d[Omega]³p² dp/2[zeta]W³c²[tau]²;
+    dl/u = g d[Omega]³p² dp/2[zeta]W³c²[tau]²;
        _
       /p0
-  t = |   g d[Omega]³p² dp/2[zeta]W³c²[tau]²,
+  t = |   g d[Omega]³p² dp/2[zeta]W³c²[tau]²,
      _/p1
 
-    = gd[Omega]³(p0³ - p1³)/6[zeta]W³c²[tau]².   (14)
+    = gd[Omega]³(p0³ - p1³)/6[zeta]W³c²[tau]².   (14)
 
   But
 
     W = p0u0[Omega]/c[tau];
 
-    .: t = gdc[tau](p0³ - p1³)/6[zeta]p0³u0³,
+    .: t = gdc[tau](p0³ - p1³)/6[zeta]p0³u0³,
 
-         = [zeta]^(½)l^(3/2)(p0³ - p1³)/6(gc[tau]d)^(½)(p0² - p1²)^(3/2);   (15)
+         = [zeta]^(½)l^(3/2)(p0³ - p1³)/6(gc[tau]d)^(½)(p0² - p1²)^(3/2);   (15)
 
-  If [tau] = 521°, corresponding to 60° F.,
+  If [tau] = 521°, corresponding to 60° F.,
 
-    t = .001412 [zeta]^(½)l^(3/2)(p0³ - p1³)/d^(½)(p0² - p1²)^(3/2);   (15a)
+    t = .001412 [zeta]^(½)l^(3/2)(p0³ - p1³)/d^(½)(p0² - p1²)^(3/2);   (15a)
 
   which gives the time of transmission in terms of the initial and final
   pressures and the dimensions of the tube.
 
   _Mean Velocity of Transmission._--The mean velocity is l/t; or, for
-  [tau] = 521°,
+  [tau] = 521°,
 
-    u_mean = 0.708 [root]{d(p0² - p1²)^(3/2)/[zeta]l(p0³ - p1³)}.   (16)
+    u_mean = 0.708 [root]{d(p0² - p1²)^(3/2)/[zeta]l(p0³ - p1³)}.   (16)
 
   The following table gives some results:--
 
@@ -12186,7 +12152,7 @@ stream.
   diminished indefinitely._--If in the last equation there be put p1 =
   0, then
 
-   u´_mean = 0.708 [root](d/[zeta]l);
+   u´_mean = 0.708 [root](d/[zeta]l);
 
   where the velocity is independent of the pressure p0 at the other end,
   a result which apparently must be absurd. Probably for long pipes, as
@@ -12196,7 +12162,7 @@ stream.
 
   X. FLOW IN RIVERS AND CANALS
 
-  § 95. _Flow of Water in Open Canals and Rivers._--When water flows in
+  § 95. _Flow of Water in Open Canals and Rivers._--When water flows in
   a pipe the section at any point is determined by the form of the
   boundary. When it flows in an open channel with free upper surface,
   the section depends on the velocity due to the dynamical conditions.
@@ -12232,7 +12198,7 @@ stream.
   common velocity equal to the mean velocity of the stream. On this
   hypothesis, a plane layer abab (fig. 102) between sections normal to
   the direction of motion is treated as sliding down the channel to
-  a´a´b´b´ without deformation. The component of the weight parallel to
+  a´a´b´b´ without deformation. The component of the weight parallel to
   the channel bed balances the friction against the channel, and in
   estimating the friction the velocity of rubbing is taken to be the
   mean velocity of the stream. In actual streams, however, the velocity
@@ -12249,10 +12215,10 @@ stream.
 
   [Illustration: FIG. 102.]
 
-  § 96. _Steady Flow of Water with Uniform Velocity in Channels of
-  Constant Section._--Let aa´, bb´ (fig. 103) be two cross sections
+  § 96. _Steady Flow of Water with Uniform Velocity in Channels of
+  Constant Section._--Let aa´, bb´ (fig. 103) be two cross sections
   normal to the direction of motion at a distance dl. Since the mass
-  aa´bb´ moves uniformly, the external forces acting on it are in
+  aa´bb´ moves uniformly, the external forces acting on it are in
   equilibrium. Let [Omega] be the area of the cross sections, [chi] the
   wetted perimeter, pq + qr + rs, of a section. Then the quantity m =
   [Omega]/[chi] is termed the hydraulic mean depth of the section. Let v
@@ -12262,13 +12228,13 @@ stream.
 
   [Illustration: FIG. 103.]
 
-  The external forces acting on aa´bb´ parallel to the direction of
-  motion are three:--(a) The pressures on aa´ and bb´, which are equal
+  The external forces acting on aa´bb´ parallel to the direction of
+  motion are three:--(a) The pressures on aa´ and bb´, which are equal
   and opposite since the sections are equal and similar, and the mean
   pressures on each are the same. (b) The component of the weight W of
   the mass in the direction of motion, acting at its centre of gravity
-  g. The weight of the mass aa´bb´ is G[Omega]dl, and the component of
-  the weight in the direction of motion is G[Omega]dl × the cosine of
+  g. The weight of the mass aa´bb´ is G[Omega]dl, and the component of
+  the weight in the direction of motion is G[Omega]dl × the cosine of
   the angle between Wg and ab, that is, G[Omega]dl cos abc = G[Omega]dl
   bc/ab = G[Omega]idl. (c) There is the friction of the stream on the
   sides and bottom of the channel. This is proportional to the area
@@ -12281,9 +12247,9 @@ stream.
 
     f(v)/G = [Omega]i/[chi] = mi.   (1)
 
-  But it has been already shown (§ 66) that f(v) = [zeta]Gv²/2g,
+  But it has been already shown (§ 66) that f(v) = [zeta]Gv²/2g,
 
-    .: [zeta]v²/2g = mi.   (2)
+    .: [zeta]v²/2g = mi.   (2)
 
   This may be put in the form
 
@@ -12308,13 +12274,13 @@ stream.
   simple and long-known approximate formula for the mean velocity of a
   stream--
 
-    v = ¼ ½ [root](2mf).   (3)
+    v = ¼ ½ [root](2mf).   (3)
 
   The flow down the stream per second, or discharge of the stream, is
 
     Q = [Omega]v = [Omega]c [root](mi).   (4)
 
-  § 97. _Coefficient of Friction for Open Channels._--Various
+  § 97. _Coefficient of Friction for Open Channels._--Various
   expressions have been proposed for the coefficient of friction for
   channels as for pipes. Weisbach, giving attention chiefly to the
   variation of the coefficient of friction with the velocity, proposed
@@ -12329,7 +12295,7 @@ stream.
   This gives the following values at different velocities:--
 
     +----------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
-    | v =      |  0.3  |  0.5  |  0.7  |  1    |  1½   |   2   |   3   |   5   |   7   |  10   |  15   |
+    | v =      |  0.3  |  0.5  |  0.7  |  1    |  1½   |   2   |   3   |   5   |   7   |  10   |  15   |
     |          |       |       |       |       |       |       |       |       |       |       |       |
     | [zeta] = |0.01215|0.01025|0.00944|0.00883|0.00836|0.00812|0.90788|0.00769|0.00761|0.00755|0.00750|
     +----------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
@@ -12337,7 +12303,7 @@ stream.
   In using this value of [zeta] when v is not known, it is best to
   proceed by approximation.
 
-  § 98. _Darcy and Bazin's Expression for the Coefficient of
+  § 98. _Darcy and Bazin's Expression for the Coefficient of
   Friction._--Darcy and Bazin's researches have shown that [zeta] varies
   very greatly for different degrees of roughness of the channel bed,
   and that it also varies with the dimensions of the channel. They give
@@ -12423,7 +12389,7 @@ stream.
     |   [oo]   |    148    |   131    |   117   |   108    |     91       |
     +----------+-----------+----------+---------+----------+--------------+
 
-  § 99. _Ganguillet and Kutter's Modified Darcy Formula._--Starting from
+  § 99. _Ganguillet and Kutter's Modified Darcy Formula._--Starting from
   the general expression v = c[root]mi, Ganguillet and Kutter examined
   the variations of c for a wider variety of cases than those discussed
   by Darcy and Bazin. Darcy and Bazin's experiments were confined to
@@ -12605,23 +12571,23 @@ stream.
   Mississippi, and there is strong reason for doubting the accuracy of
   these results.
 
-  § 100. _Bazin's New Formula._--Bazin subsequently re-examined all the
+  § 100. _Bazin's New Formula._--Bazin subsequently re-examined all the
   trustworthy gaugings of flow in channels and proposed a modification
   of the original Darcy formula which appears to be more satisfactory
-  than any hitherto suggested (_Étude d'une nouvelle formule_, Paris,
+  than any hitherto suggested (_Étude d'une nouvelle formule_, Paris,
   1898). He points out that Darcy's original formula, which is of the
-  form mi/v² = [alpha] + [beta]/m, does not agree with experiments on
+  form mi/v² = [alpha] + [beta]/m, does not agree with experiments on
   channels as well as with experiments on pipes. It is an objection to
-  it that if m increases indefinitely the limit towards which mi/v²
+  it that if m increases indefinitely the limit towards which mi/v²
   tends is different for different values of the roughness. It would
   seem that if the dimensions of a canal are indefinitely increased the
   variation of resistance due to differing roughness should vanish. This
-  objection is met if it is assumed that [root](mi/v²) = [alpha] +
-  [beta]/[root]m, so that if a is a constant mi/v² tends to the limit a
+  objection is met if it is assumed that [root](mi/v²) = [alpha] +
+  [beta]/[root]m, so that if a is a constant mi/v² tends to the limit a
   when m increases. A very careful discussion of the results of gaugings
   shows that they can be expressed more satisfactorily by this new
   formula than by Ganguillet and Kutter's. Putting the equation in the
-  form [zeta]v²/2g = mi, [zeta] = 0.002594(1 + [gamma]/[root]m), where
+  form [zeta]v²/2g = mi, [zeta] = 0.002594(1 + [gamma]/[root]m), where
   [gamma] has the following values:--
 
       I. Very smooth sides, cement, planed plank, [gamma] = 0.109
@@ -12631,7 +12597,7 @@ stream.
       V. Canals in earth in ordinary condition              2.353
      VI. Canals in earth exceptionally rough                3.168
 
-  § 101. _The Vertical Velocity Curve._--If at each point along a
+  § 101. _The Vertical Velocity Curve._--If at each point along a
   vertical representing the depth of a stream, the velocity at that
   point is plotted horizontally, the curve obtained is the vertical
   velocity curve and it has been shown by many observations that it
@@ -12656,7 +12622,7 @@ stream.
 
   [Illustration: FIG. 104.]
 
-  § 102. _Curves or Contours of Equal Velocity._--If velocities are
+  § 102. _Curves or Contours of Equal Velocity._--If velocities are
   observed at a number of points at different widths and depths in a
   stream, it is possible to draw curves on the cross section through
   points at which the velocity is the same. These represent contours of
@@ -12665,7 +12631,7 @@ stream.
   the contours of equal velocity in a rectangular channel, from one of
   Bazin's gaugings.
 
-  § 103. _Experimental Observations on the Vertical Velocity Curve._--A
+  § 103. _Experimental Observations on the Vertical Velocity Curve._--A
   preliminary difficulty arises in observing the velocity at a given
   point in a stream because the velocity rapidly varies, the motion not
   being strictly steady. If an average of several velocities at the same
@@ -12685,7 +12651,7 @@ stream.
   river gaugings the depth d_z at the centre of the stream has been
   found to vary from 0 to 0.3d.
 
-  § 104. _Influence of the Wind._--In the experiments on the Mississippi
+  § 104. _Influence of the Wind._--In the experiments on the Mississippi
   the vertical velocity curve in calm weather was found to agree fairly
   with a parabola, the greatest velocity being at (3/10)ths of the depth
   of the stream from the surface. With a wind blowing down stream the
@@ -12736,13 +12702,13 @@ stream.
   at (3/10)ths of the total depth from the surface for all conditions of
   the stream.
 
-  Let h´ be the depth of the axis of the parabola, m the hydraulic mean
+  Let h´ be the depth of the axis of the parabola, m the hydraulic mean
   depth, f the number expressing the force of the wind, which may range
   from +10 to -10, positive if the wind is up stream, negative if it is
   down stream. Then Humphreys and Abbot find their results agree with
   the expression
 
-    h´/m = 0.317 ± 0.06f.
+    h´/m = 0.317 ± 0.06f.
 
   Fig. 106 shows the parabolic velocity curves according to the American
   observers for calm weather, and for an up- or down-stream wind of a
@@ -12767,15 +12733,15 @@ stream.
   little greater than, the mean velocity on a vertical. If v_(md) is the
   mid-depth velocity, then on the average v_m = 0.98v_(md).
 
-  § 105. _Mean Velocity on a Vertical from Two Velocity
+  § 105. _Mean Velocity on a Vertical from Two Velocity
   Observations._--A. J. C. Cunningham, in gaugings on the Ganges canal,
   found the following useful results. Let v0 be the surface, v_m the
   mean, and v_(xd) the velocity at the depth xd; then
 
-    v_m = ¼[v0 + 3v_(2/3d)]
-        = ½[v_(.211)^d + v_(.789)^d].
+    v_m = ¼[v0 + 3v_(2/3d)]
+        = ½[v_(.211)^d + v_(.789)^d].
 
-  § 106. _Ratio of Mean to Greatest Surface Velocity, for the whole
+  § 106. _Ratio of Mean to Greatest Surface Velocity, for the whole
   Cross Section in Trapezoidal Channels._--It is often very important to
   be able to deduce the mean velocity, and thence the discharge, from
   observation of the greatest surface velocity. The simplest method of
@@ -12796,7 +12762,7 @@ stream.
     v_m = c [root](mi),
 
   where c is a coefficient, the values of which have been already given
-  in the table in § 98. Hence
+  in the table in § 98. Hence
 
     v_m = cv0/(c + 25.4).
 
@@ -12833,7 +12799,7 @@ stream.
 
   [Illustration: FIG. 107.]
 
-  § 107. _River Bends._--In rivers flowing in alluvial plains, the
+  § 107. _River Bends._--In rivers flowing in alluvial plains, the
   windings which already exist tend to increase in curvature by the
   scouring away of material from the outer bank and the deposition of
   detritus along the inner bank. The sinuosities sometimes increase till
@@ -12876,18 +12842,18 @@ stream.
   The dotted line AB shows the direction of motion of floating particles
   on the surface of the stream.
 
-  § 108. _Discharge of a River when flowing at different Depths._--When
+  § 108. _Discharge of a River when flowing at different Depths._--When
   frequent observations must be made on the flow of a river or canal,
   the depth of which varies at different times, it is very convenient to
   have to observe the depth only. A formula can be established giving
   the flow in terms of the depth. Let Q be the discharge in cubic feet
   per second; H the depth of the river in some straight and uniform
-  part. Then Q = aH + bH², where the constants a and b must be found by
+  part. Then Q = aH + bH², where the constants a and b must be found by
   preliminary gaugings in different conditions of the river. M. C.
-  Moquerey found for part of the upper Saône, Q = 64.7H + 8.2H² in
-  metric measures, or Q = 696H + 26.8H² in English measures.
+  Moquerey found for part of the upper Saône, Q = 64.7H + 8.2H² in
+  metric measures, or Q = 696H + 26.8H² in English measures.
 
-  § 109. _Forms of Section of Channels._--The simplest form of section
+  § 109. _Forms of Section of Channels._--The simplest form of section
   for channels is the semicircular or nearly semicircular channel (fig.
   109), a form now often adopted from the facility with which it can be
   executed in concrete. It has the advantage that the rubbing surface is
@@ -12904,7 +12870,7 @@ stream.
   breadth, b0 the top breadth, d the depth, and let the slope of the
   sides be n horizontal to 1 vertical. Then the area of section is
   [Omega] = (b + nd)d = (b0 - nd)d, and the wetted perimeter [chi] = b +
-  2d[root](n² + 1).
+  2d[root](n² + 1).
 
   [Illustration: FIG. 110.]
 
@@ -12917,11 +12883,11 @@ stream.
   being the section of a navigation canal and the latter the section of
   an irrigation canal.
 
-  § 110. _Channels of Circular Section._--The following short table
+  § 110. _Channels of Circular Section._--The following short table
   facilitates calculations of the discharge with different depths of
   water in the channel. Let r be the radius of the channel section; then
   for a depth of water = [kappa]r, the hydraulic mean radius is [mu]r
-  and the area of section of the waterway [nu]r², where [kappa], [mu],
+  and the area of section of the waterway [nu]r², where [kappa], [mu],
   and [nu] have the following values:--
 
     +---------------------------------+------+-----+-----+-----+-----+-----+-----+-----+----+----+----+----+----+----+----+-----+-----+-----+-----+-----+-----+
@@ -12937,7 +12903,7 @@ stream.
 
   [Illustration: FIG. 112.--Scale 80 ft. = 1 in.]
 
-  § 111. _Egg-Shaped Channels or Sewers._--In sewers for discharging
+  § 111. _Egg-Shaped Channels or Sewers._--In sewers for discharging
   storm water and house drainage the volume of flow is extremely
   variable; and there is a great liability for deposits to be left when
   the flow is small, which are not removed during the short periods when
@@ -12954,12 +12920,12 @@ stream.
 
   [Illustration: FIG. 113.]
 
-  § 112. _Problems on Channels in which the Flow is Steady and at
-  Uniform Velocity._--The general equations given in §§ 96, 98 are
+  § 112. _Problems on Channels in which the Flow is Steady and at
+  Uniform Velocity._--The general equations given in §§ 96, 98 are
 
     [zeta] = [alpha](1 + [beta]/m);   (1)
 
-    [zeta]v²/2g = mi;   (2)
+    [zeta]v²/2g = mi;   (2)
 
     Q = [Omega]v.   (3)
 
@@ -12979,7 +12945,7 @@ stream.
 
   [Illustration: FIG. 114.]
 
-  Since m lies generally between the limits m = d and m = ½d, where d is
+  Since m lies generally between the limits m = d and m = ½d, where d is
   the depth of the stream, and since, moreover, the velocity varies as
   [root](m) so that an error in the value of m leads only to a much less
   error in the value of the velocity calculated from it, we may proceed
@@ -12990,7 +12956,7 @@ stream.
   second value of v, and from that a second value for [Omega]. Repeat
   the process till the successive values of m approximately coincide.
 
-  § 113. _Problem IV. Most Economical Form of Channel for given Side
+  § 113. _Problem IV. Most Economical Form of Channel for given Side
   Slopes._--Suppose the channel is to be trapezoidal in section (fig.
   114), and that the sides are to have a given slope. Let the
   longitudinal slope of the stream be given, and also the mean velocity.
@@ -13004,44 +12970,44 @@ stream.
 
     [Omega] = (b + nd)d;
 
-    [chi] = b + 2d [root](n² + 1).
+    [chi] = b + 2d [root](n² + 1).
 
   Both [Omega] and [chi] are to be minima. Differentiating, and equating
   to zero.
 
     (db/dd + n)d + b + nd = 0,
 
-    db/dd + 2[root](n² + 1) = 0;
+    db/dd + 2[root](n² + 1) = 0;
 
   eliminating db/dd,
 
-    {n - 2[root](n² + 1)}d + b + nd = 0;
+    {n - 2[root](n² + 1)}d + b + nd = 0;
 
-    b = 2 {[root](n² + 1) - n}d.
+    b = 2 {[root](n² + 1) - n}d.
 
   But
 
-    [Omega]/[chi] = (b + nd)d/{b + 2d [root](n² + 1)}.
+    [Omega]/[chi] = (b + nd)d/{b + 2d [root](n² + 1)}.
 
   Inserting the value of b,
 
-    m = [Omega]/[chi] = {2d[root](n² + 1) - nd}/
-      {4d [root](n² + 1) - 2nd} = ½d.
+    m = [Omega]/[chi] = {2d[root](n² + 1) - nd}/
+      {4d [root](n² + 1) - 2nd} = ½d.
 
   That is, with given side slopes, the section is least for a given
   discharge when the hydraulic mean depth is half the actual depth.
 
   A simple construction gives the form of the channel which fulfils this
-  condition, for it can be shown that when m = ½d the sides of the
+  condition, for it can be shown that when m = ½d the sides of the
   channel are tangential to a semicircle drawn on the water line.
 
   Since
 
-    [Omega]/[chi] = ½d,
+    [Omega]/[chi] = ½d,
 
   therefore
 
-    [Omega] = ½[chi]d.   (1)
+    [Omega] = ½[chi]d.   (1)
 
   Let ABCD be the channel (fig. 115); from E the centre of AD drop
   perpendiculars EF, EG, EH on the sides.
@@ -13051,13 +13017,13 @@ stream.
     AB = CD = a; BC = b; EF = EH = c; and EG = d.
 
     [Omega] = area AEB + BEC + CED,
-            = ac + ½bd.
+            = ac + ½bd.
 
     [chi] = 2a + b.
 
   Putting these values in (1),
 
-    ac + ½bd = (a + ½b)d; and hence c = d.
+    ac + ½bd = (a + ½b)d; and hence c = d.
 
   [Illustration: FIG. 115.]
 
@@ -13080,7 +13046,7 @@ stream.
 
     [Omega]/d = b + d cot [beta];   (2)
 
-    [Omega]/d² = b/d + cot [beta].   (3)
+    [Omega]/d² = b/d + cot [beta].   (3)
 
   From (1) and (2),
 
@@ -13088,11 +13054,11 @@ stream.
 
   This will be a minimum for
 
-    d[chi]/dd = [Omega]/d² + cot[beta] - 2/sin [beta] = 0,
+    d[chi]/dd = [Omega]/d² + cot[beta] - 2/sin [beta] = 0,
 
   or
 
-    [Omega]/d² = 2 cosec. [beta] - cot [beta].   (4)
+    [Omega]/d² = 2 cosec. [beta] - cot [beta].   (4)
 
   or
 
@@ -13100,10 +13066,10 @@ stream.
 
   From (3) and (4),
 
-    b/d = 2(1 - cos [beta])/sin [beta] = 2 tan ½[beta].
+    b/d = 2(1 - cos [beta])/sin [beta] = 2 tan ½[beta].
 
   _Proportions of Channels of Maximum Discharge for given Area and Side
-  Slopes. Depth of channel = d; Hydraulic mean depth = ½d; Area of
+  Slopes. Depth of channel = d; Hydraulic mean depth = ½d; Area of
   section =_ [Omega].
 
     +-------------+-----------+--------+----------+---------+------------+
@@ -13112,27 +13078,27 @@ stream.
     |             |  Horizon. | Slopes.| [Omega]. |  Width. |of each Side|
     |             |           |        |          |         |   Slope.   |
     +-------------+-----------+--------+----------+---------+------------+
-    | Semicircle  |    ..     |   ..   | 1.571 d² |    0    |    2 d     |
-    | Semi-hexagon|  60°  0´  | 3  : 5 | 1.732 d² | 1.155 d |  2.310 d   |
-    | Semi-square |  90°  0´  | 0  : 1 |   2 d²   |  2 d    |    2 d     |
-    |             |  75° 58´  | 1  : 4 | 1.812 d² | 1.562 d |  2.062 d   |
-    |             |  63° 26´  | 1  : 2 | 1.736 d² | 1.236 d |  2.236 d   |
-    |             |  53°  8´  | 3  : 4 | 1.750 d² |    d    |  2.500 d   |
-    |             |  45°  0´  | 1  : 1 | 1.828 d² | 0.828 d |  2.828 d   |
-    |             |  38° 40´  | 1¼ : 1 | 1.952 d² | 0.702 d |  3.202 d   |
-    |             |  33° 42´  | 1½ : 1 | 2.106 d² | 0.606 d |  3.606 d   |
-    |             |  29° 44´  | 1¾ : 1 | 2.282 d² | 0.532 d |  4.032 d   |
-    |             |  26° 34´  | 2  : 1 | 2.472 d² | 0.472 d |  4.472 d   |
-    |             |  23° 58´  | 2¼ : 1 | 2.674 d² | 0.424 d |  4.924 d   |
-    |             |  21° 48´  | 2½ : 1 | 2.885 d² | 0.385 d |  5.385 d   |
-    |             |  19° 58´  | 2¾ : 1 | 3.104 d² | 0.354 d |  5.854 d   |
-    |             |  18° 26´  | 3  : 1 | 3.325 d² | 0.325 d |  6.325 d   |
+    | Semicircle  |    ..     |   ..   | 1.571 d² |    0    |    2 d     |
+    | Semi-hexagon|  60°  0´  | 3  : 5 | 1.732 d² | 1.155 d |  2.310 d   |
+    | Semi-square |  90°  0´  | 0  : 1 |   2 d²   |  2 d    |    2 d     |
+    |             |  75° 58´  | 1  : 4 | 1.812 d² | 1.562 d |  2.062 d   |
+    |             |  63° 26´  | 1  : 2 | 1.736 d² | 1.236 d |  2.236 d   |
+    |             |  53°  8´  | 3  : 4 | 1.750 d² |    d    |  2.500 d   |
+    |             |  45°  0´  | 1  : 1 | 1.828 d² | 0.828 d |  2.828 d   |
+    |             |  38° 40´  | 1¼ : 1 | 1.952 d² | 0.702 d |  3.202 d   |
+    |             |  33° 42´  | 1½ : 1 | 2.106 d² | 0.606 d |  3.606 d   |
+    |             |  29° 44´  | 1¾ : 1 | 2.282 d² | 0.532 d |  4.032 d   |
+    |             |  26° 34´  | 2  : 1 | 2.472 d² | 0.472 d |  4.472 d   |
+    |             |  23° 58´  | 2¼ : 1 | 2.674 d² | 0.424 d |  4.924 d   |
+    |             |  21° 48´  | 2½ : 1 | 2.885 d² | 0.385 d |  5.385 d   |
+    |             |  19° 58´  | 2¾ : 1 | 3.104 d² | 0.354 d |  5.854 d   |
+    |             |  18° 26´  | 3  : 1 | 3.325 d² | 0.325 d |  6.325 d   |
     +-------------+-----------+--------+----------+---------+------------+
 
     Half the top width is the length of each side slope. The wetted
     perimeter is the sum of the top and bottom widths.
 
-  § 114. _Form of Cross Section of Channel in which the Mean Velocity is
+  § 114. _Form of Cross Section of Channel in which the Mean Velocity is
   Constant with Varying Discharge._--In designing waste channels from
   canals, and in some other cases, it is desirable that the mean
   velocity should be restricted within narrow limits with very different
@@ -13173,15 +13139,15 @@ stream.
     ---------------------- = ---- = k
     Increment of perimeter    ds
 
-    y²dx² = k²ds² = k²(dx² + dy²) and dx = k dy/[root](y² - k²).
+    y²dx² = k²ds² = k²(dx² + dy²) and dx = k dy/[root](y² - k²).
 
   Integrating,
 
-    x = k log_[epsilon] {y + [root](y² - k²)} + constant;
+    x = k log_[epsilon] {y + [root](y² - k²)} + constant;
 
   and, since y = b/2 when x = 0,
 
-    x = k log_[epsilon] [{y + [root](y² - k²)}/{½b + [root](¼b² - k²)}].
+    x = k log_[epsilon] [{y + [root](y² - k²)}/{½b + [root](¼b² - k²)}].
 
   Assuming values for y, the values of x can be found and the curve
   drawn.
@@ -13194,7 +13160,7 @@ stream.
   STEADY MOTION OF WATER IN OPEN CHANNELS OF VARYING CROSS SECTION AND
   SLOPE
 
-  § 115. In every stream the discharge of which is constant, or may be
+  § 115. In every stream the discharge of which is constant, or may be
   regarded as constant for the time considered, the velocity at
   different places depends on the slope of the bed. Except at certain
   exceptional points the velocity will be greater as the slope of the
@@ -13248,32 +13214,32 @@ stream.
 
   The mass of fluid passing through the element of section [omega], in
   [theta] seconds, is (G/g)[omega]v[theta], and its kinetic energy is
-  (G/2g)[omega]v³[theta]. For the whole section, the kinetic energy of
+  (G/2g)[omega]v³[theta]. For the whole section, the kinetic energy of
   the mass A0B0C0D0 passing in [theta] seconds is
 
-    (G[theta]/2g)[Sigma][omega]v³
-      = (G[theta]/2g)[Sigma][omega](u0³ + 3u0²w + 3u0² + w³),
-      = (G[theta]/2g){u0³[Omega] + [Sigma][omega]w²(3u0 + w)}.
+    (G[theta]/2g)[Sigma][omega]v³
+      = (G[theta]/2g)[Sigma][omega](u0³ + 3u0²w + 3u0² + w³),
+      = (G[theta]/2g){u0³[Omega] + [Sigma][omega]w²(3u0 + w)}.
 
   The factor 3u0 + w is equal to 2u0 + v, a quantity necessarily
-  positive. Consequently [Sigma][omega]v³ > [Omega]0u0³, and
+  positive. Consequently [Sigma][omega]v³ > [Omega]0u0³, and
   consequently the kinetic energy of A0B0C0D0 is greater than
 
-    (G[theta]/2g)[Omega]0u0³ or (G[theta])/2g)Qu0²,
+    (G[theta]/2g)[Omega]0u0³ or (G[theta])/2g)Qu0²,
 
   which would be its value if all the particles passing the section had
   the same velocity u0. Let the kinetic energy be taken at
 
-    [alpha](G[theta]/2g)[Omega]0u0³ = [alpha](G[theta]/2g)Qu0²,
+    [alpha](G[theta]/2g)[Omega]0u0³ = [alpha](G[theta]/2g)Qu0²,
 
   where [alpha] is a corrective factor, the value of which was estimated
-  by J. B. C. J. Bélanger at 1.1.[6] Its precise value is not of great
+  by J. B. C. J. Bélanger at 1.1.[6] Its precise value is not of great
   importance.
 
   In a similar way we should obtain for the kinetic energy of A1B1C1D1
   the expression
 
-    [alpha](G[theta]/2g)[Omega]1u1³ = [alpha](G[theta]/2g)Qu1²,
+    [alpha](G[theta]/2g)[Omega]1u1³ = [alpha](G[theta]/2g)Qu1²,
 
   where [Omega]1, u1 are the section and mean velocity at A1B1, and
   where a may be taken to have the same value as before without any
@@ -13282,7 +13248,7 @@ stream.
   Hence the change of kinetic energy in the whole mass A0B0A1B1 in
   [theta] seconds is
 
-    [alpha](G[theta]/2g) Q (u1² - u0²).   (1)
+    [alpha](G[theta]/2g) Q (u1² - u0²).   (1)
 
   _Motive Work of the Weight and Pressures._--Consider a small filament
   a0a1 which comes in [theta] seconds to c0c1. The work done by gravity
@@ -13306,49 +13272,49 @@ stream.
     GzQ[theta].   (2)
 
   _Work expended in Overcoming the Friction of the Stream Bed._--Let
-  A´B´, A´´B´´ be two cross sections at distances s and s + ds from
+  A´B´, A´´B´´ be two cross sections at distances s and s + ds from
   A0B0. Between these sections the velocity may be treated as uniform,
   because by hypothesis the changes of velocity from section to section
   are gradual. Hence, to this short length of stream the equation for
   uniform motion is applicable. But in that case the work in overcoming
-  the friction of the stream bed between A´B´ and A´´B´´ is
+  the friction of the stream bed between A´B´ and A´´B´´ is
 
-    GQ[theta][zeta](u²/2g)([chi]/[Omega]) ds,
+    GQ[theta][zeta](u²/2g)([chi]/[Omega]) ds,
 
   where u, [chi], [Omega] are the mean velocity, wetted perimeter, and
-  section at A´B´. Hence the whole work lost in friction from A0B0 to
+  section at A´B´. Hence the whole work lost in friction from A0B0 to
   A1B1 will be
                _
               / l
-    GQ[theta] |   [zeta](u²/2g)([chi]/[Omega]) ds.   (3)
+    GQ[theta] |   [zeta](u²/2g)([chi]/[Omega]) ds.   (3)
              _/ 0
 
   Equating the work given in (2) and (3) to the change of kinetic energy
   given in (1),
 
-    [alpha](GQ[theta]/2g)(u1² - u0²)
+    [alpha](GQ[theta]/2g)(u1² - u0²)
                                 _
                                / l
-      = GQz[theta] - GQ[theta] |   [zeta](u²/2g)([chi]/[Omega]) ds;
+      = GQz[theta] - GQ[theta] |   [zeta](u²/2g)([chi]/[Omega]) ds;
                               _/ 0
                                     _
                                    / l
-    .: z = [alpha](u1² - u0²)/2g + |   [zeta](u²/2g)([chi]/[Omega]) ds.
+    .: z = [alpha](u1² - u0²)/2g + |   [zeta](u²/2g)([chi]/[Omega]) ds.
                                   _/ 0
 
   [Illustration: FIG. 120.]
 
-  § 116. _Fundamental Differential Equation of Steady Varied
+  § 116. _Fundamental Differential Equation of Steady Varied
   Motion._--Suppose the equation just found to be applied to an
   indefinitely short length ds of the stream, limited by the end
   sections ab, a1b1, taken for simplicity normal to the stream bed (fig.
   120). For that short length of stream the fall of surface level, or
   difference of level of a and a1, may be written dz. Also, if we write
-  u for u0, and u + du for u1, the term (u0² - u1²)/2g becomes udu/g.
+  u for u0, and u + du for u1, the term (u0² - u1²)/2g becomes udu/g.
   Hence the equation applicable to an indefinitely short length of the
   stream is
 
-    dz = udu/g + ([chi]/[Omega])[zeta](u²/2g) ds.   (1)
+    dz = udu/g + ([chi]/[Omega])[zeta](u²/2g) ds.   (1)
 
   From this equation some general conclusions may be arrived at as to
   the form of the longitudinal section of the stream, but, as the
@@ -13358,12 +13324,12 @@ stream.
   _Modification of the Formula for the Restricted Case of a Stream
   flowing in a Prismatic Stream Bed of Constant Slope._--Let i be the
   constant slope of the bed. Draw ad parallel to the bed, and ac
-  horizontal. Then dz is sensibly equal to a´c. The depths of the
-  stream, h and h + dh, are sensibly equal to ab and a´b´, and therefore
-  dh = a´d. Also cd is the fall of the bed in the distance ds, and is
+  horizontal. Then dz is sensibly equal to a´c. The depths of the
+  stream, h and h + dh, are sensibly equal to ab and a´b´, and therefore
+  dh = a´d. Also cd is the fall of the bed in the distance ds, and is
   equal to ids. Hence
 
-    dz = a´c = cd - a´d = i ds - dh.   (2)
+    dz = a´c = cd - a´d = i ds - dh.   (2)
 
   Since the motion is steady--
 
@@ -13382,9 +13348,9 @@ stream.
 
   Putting the values of du and dz found in (2) and (3) in equation (1),
 
-    i ds - dh = -(u²x/g[Omega]) dh + ([chi]/[Omega])[zeta](u²/2g) ds.
+    i ds - dh = -(u²x/g[Omega]) dh + ([chi]/[Omega])[zeta](u²/2g) ds.
 
-    dh/ds = {i - ([chi]/[Omega]) [zeta] (u²/2g)}/{1 - (u²/g)(x/[Omega])}.   (4)
+    dh/ds = {i - ([chi]/[Omega]) [zeta] (u²/2g)}/{1 - (u²/g)(x/[Omega])}.   (4)
 
   _Further Restriction to the Case of a Stream of Rectangular Section
   and of Indefinite Width._--The equation might be discussed in the form
@@ -13393,9 +13359,9 @@ stream.
   if [chi] is large compared with h, [Omega]/[chi] = xh/x = h nearly.
   Then equation (4) becomes
 
-    dh/ds = i(1 - [zeta]u²/2gih)/(1 - u²/gh).   (5)
+    dh/ds = i(1 - [zeta]u²/2gih)/(1 - u²/gh).   (5)
 
-  § 117. _General Indications as to the Form of Water Surface furnished
+  § 117. _General Indications as to the Form of Water Surface furnished
   by Equation_ (5).--Let A0A1 (fig. 121) be the water surface, B0B1 the
   bed in a longitudinal section of the stream, and ab any section at a
   distance s from B0, the depth ab being h. Suppose B0B1, B0A0 taken as
@@ -13407,9 +13373,9 @@ stream.
   is parallel to the bed, as in cases of uniform motion. But from
   equation (4)
 
-    dh/ds = 0, if i - ([chi]/[Omega])[zeta](u²/2g) = 0;
+    dh/ds = 0, if i - ([chi]/[Omega])[zeta](u²/2g) = 0;
 
-    .: [zeta](u²/2g) = ([Omega]/[chi])i = mi,
+    .: [zeta](u²/2g) = ([Omega]/[chi])i = mi,
 
   which is the well-known general equation for uniform motion, based on
   the same assumptions as the equation for varied steady motion now
@@ -13420,16 +13386,16 @@ stream.
 
   Consider the possible changes of value of the fraction
 
-    (1 - [zeta]u²/2gih)/(1 - u²/gh).
+    (1 - [zeta]u²/2gih)/(1 - u²/gh).
 
   As h tends towards the limit 0, and consequently u is large, the
   numerator tends to the limit -[oo]. On the other hand if h = [oo], in
   which case u is small, the numerator becomes equal to 1. For a value H
   of h given by the equation
 
-    1 - [zeta]u²/2giH = 0,
+    1 - [zeta]u²/2giH = 0,
 
-    H = [zeta]u²/2gi,
+    H = [zeta]u²/2gi,
 
   we fall upon the case of uniform motion. The results just stated may
   be tabulated thus:--
@@ -13441,10 +13407,10 @@ stream.
   Next consider the denominator. If h becomes very small, in which case
   u must be very large, the denominator tends to the limit -[oo]. As h
   becomes very large and u consequently very small, the denominator
-  tends to the limit 1. For h = u²/g, or u = [root](gh), the denominator
+  tends to the limit 1. For h = u²/g, or u = [root](gh), the denominator
   becomes zero. Hence, tabulating these results as before:--
 
-    For h = 0, u²/g, > u²/g, [oo],
+    For h = 0, u²/g, > u²/g, [oo],
 
   the denominator becomes
 
@@ -13452,7 +13418,7 @@ stream.
 
   [Illustration: FIG. 122.]
 
-  § 118. _Case_ 1.--Suppose h > u²/g, and also h > H, or the depth
+  § 118. _Case_ 1.--Suppose h > u²/g, and also h > H, or the depth
   greater than that corresponding to uniform motion. In this case dh/ds
   is positive, and the stream increases in depth in the direction of
   flow. In fig. 122 let B0B1 be the bed, C0C1 a line parallel to the bed
@@ -13462,7 +13428,7 @@ stream.
   approaches more and more nearly the value H, and therefore dh/ds
   approaches the limit 0, or the surface of the stream is asymptotic to
   C0C1. Going down stream h increases and u diminishes, the numerator
-  and denominator of the fraction (1 - [zeta]u²/2gih)/(1 -u²/gh) both
+  and denominator of the fraction (1 - [zeta]u²/2gih)/(1 -u²/gh) both
   tend towards the limit 1, and dh/ds to the limit i. That is, the
   surface of the stream tends to become asymptotic to a horizontal line
   D0D1.
@@ -13472,7 +13438,7 @@ stream.
   The raising of the water surface above the level C0C1 is termed the
   backwater due to the weir.
 
-  § 119. _Case_ 2.--Suppose h > u²/g, and also h < H. Then dh/ds is
+  § 119. _Case_ 2.--Suppose h > u²/g, and also h < H. Then dh/ds is
   negative, and the stream is diminishing in depth in the direction of
   flow. In fig. 123 let B0B1 be the stream bed as before; C0C1 a line
   drawn parallel to B0B1 at a height above it equal to H. By hypothesis
@@ -13480,8 +13446,8 @@ stream.
   been shown to diminish from B0 towards B1. Going up stream h
   approaches the limit H, and dh/ds tends to the limit zero. That is, up
   stream A0A1 is asymptotic to C0C1. Going down stream h diminishes and
-  u increases; the inequality h>u²/g diminishes; the denominator of the
-  fraction (1 - [zeta]u²/2gih)/(1 - u²/gh) tends to the limit zero, and
+  u increases; the inequality h>u²/g diminishes; the denominator of the
+  fraction (1 - [zeta]u²/2gih)/(1 - u²/gh) tends to the limit zero, and
   consequently dh/ds tends to [infinity]. That is, down stream A0A1
   tends to a direction perpendicular to the bed. Before, however, this
   limit was reached the assumptions on which the general equation is
@@ -13527,20 +13493,20 @@ stream.
   produced, and by suitably choosing the height of the weir this might
   be made to agree approximately with the intended level AA.
 
-  § 120. _Case_ 3.--Suppose a stream flowing uniformly with a depth
-  h<u²/g. For a stream in uniform motion [zeta]u²/2g = mi, or if the
+  § 120. _Case_ 3.--Suppose a stream flowing uniformly with a depth
+  h<u²/g. For a stream in uniform motion [zeta]u²/2g = mi, or if the
   stream is of indefinitely great width, so that m = H, then
-  [zeta]u²/2g = iH, and H = [zeta]u²/2gi. Consequently the condition
+  [zeta]u²/2g = iH, and H = [zeta]u²/2gi. Consequently the condition
   stated above involves that
 
-    [zeta]u²/2gi < u²/g, or that i > [zeta]/2.
+    [zeta]u²/2gi < u²/g, or that i > [zeta]/2.
 
   If such a stream is interfered with by the construction of a weir
   which raises its level, so that its depth at the weir becomes h1 >
-  u²/g, then for a portion of the stream the depth h will satisfy the
-  conditions h < u²/g and h > H, which are not the same as those assumed in the two
+  u²/g, then for a portion of the stream the depth h will satisfy the
+  conditions h < u²/g and h > H, which are not the same as those assumed in the two
   previous cases. At some point of the stream above the weir the depth h
-  becomes equal to u²/g, and at that point dh/ds becomes infinite, or
+  becomes equal to u²/g, and at that point dh/ds becomes infinite, or
   the surface of the stream is normal to the bed. It is obvious that at
   that point the influence of internal friction will be too great to be
   neglected, and the general equation will cease to represent the true
@@ -13584,7 +13550,7 @@ stream.
 
   STANDING WAVES
 
-  § 121. The formation of a standing wave was first observed by Bidone.
+  § 121. The formation of a standing wave was first observed by Bidone.
   Into a small rectangular masonry channel, having a slope of 0.023 ft.
   per foot, he admitted water till it flowed uniformly with a depth of
   0.2 ft. He then placed a plank across the stream which raised the
@@ -13593,10 +13559,10 @@ stream.
   from it. At that point the depth suddenly increased from 0.2 ft. to
   0.56 ft. The velocity of the stream in the part unaffected by the
   obstruction was 5.54 ft. per second. Above the point where the abrupt
-  change of depth occurred u² = 5.54² = 30.7, and gh = 32.2 × 0.2 =
-  6.44; hence u² was > gh. Just below the abrupt change of depth u =
-  5.54 × 0.2/0.56 = 1.97; u² = 3.88; and gh = 32.2 × 0.56 = 18.03; hence
-  at this point u² < gh. Between these two points, therefore, u² = gh;
+  change of depth occurred u² = 5.54² = 30.7, and gh = 32.2 × 0.2 =
+  6.44; hence u² was > gh. Just below the abrupt change of depth u =
+  5.54 × 0.2/0.56 = 1.97; u² = 3.88; and gh = 32.2 × 0.56 = 18.03; hence
+  at this point u² < gh. Between these two points, therefore, u² = gh;
   and the condition for the production of a standing wave occurred.
 
   [Illustration: FIG. 126.]
@@ -13605,7 +13571,7 @@ stream.
   represent the longitudinal section of a stream and ab, cd cross
   sections normal to the bed, which for the short distance considered
   may be assumed horizontal. Suppose the mass of water abcd to come to
-  a´b´c´d´ in a short time t; and let u0, u1 be the velocities at ab and
+  a´b´c´d´ in a short time t; and let u0, u1 be the velocities at ab and
   cd, [Omega]0, [Omega]1 the areas of the cross sections. The force
   causing change of momentum in the mass abcd estimated horizontally is
   simply the difference of the pressures on ab and cd. Putting h0, h1
@@ -13613,48 +13579,48 @@ stream.
   from the free water surface, the force is G(h0[Omega]0 - h1[Omega]1)
   pounds, and the impulse in t seconds is G (h0[Omega]0 - h1[Omega]1) t
   second pounds. The horizontal change of momentum is the difference of
-  the momenta of cdc´d´ and aba´b´; that is,
+  the momenta of cdc´d´ and aba´b´; that is,
 
-    (G/g)([Omega]1u1² - [Omega]0u0²)t.
+    (G/g)([Omega]1u1² - [Omega]0u0²)t.
 
   Hence, equating impulse and change of momentum,
 
-    G(h0[Omega]0 - h1[Omega]1)t = (G/g)([Omega]1u1² - [Omega]0u0²)t;
+    G(h0[Omega]0 - h1[Omega]1)t = (G/g)([Omega]1u1² - [Omega]0u0²)t;
 
-    .: h0[Omega]0 - h1[Omega]1 = ([Omega]1u1² - [Omega]0u0²)/g.   (1)
+    .: h0[Omega]0 - h1[Omega]1 = ([Omega]1u1² - [Omega]0u0²)/g.   (1)
 
   For simplicity let the section be rectangular, of breadth B and depths
-  H0 and H1, at the two cross sections considered; then h0 = ½H0, and h1
-  = ½H1. Hence
+  H0 and H1, at the two cross sections considered; then h0 = ½H0, and h1
+  = ½H1. Hence
 
-    H0² - H1² = (2/g)(H1u1² - H0u0²).
+    H0² - H1² = (2/g)(H1u1² - H0u0²).
 
   But, since [Omega]0u0 = [Omega]1u1, we have
 
-    u1² = u0²H0²/H1²,
+    u1² = u0²H0²/H1²,
 
-    H0² - H1² = (2u0²/g)(H0²/H1 - H0).   (2)
+    H0² - H1² = (2u0²/g)(H0²/H1 - H0).   (2)
 
   This equation is satisfied if H0 = H1, which corresponds to the case
   of uniform motion. Dividing by H0 - H1, the equation becomes
 
-    (H1/H0)(H0 + H1) = 2u0²/g;   (3)
+    (H1/H0)(H0 + H1) = 2u0²/g;   (3)
 
-    .: H1 = [root](2u0²H0/g + ¼H0²) - ½H0.   (4)
+    .: H1 = [root](2u0²H0/g + ¼H0²) - ½H0.   (4)
 
   In Bidone's experiment u0 = 5.54, and H0 = 0.2. Hence H1 = 0.52, which
   agrees very well with the observed height.
 
   [Illustration: FIG. 127.]
 
-  § 122. A standing wave is frequently produced at the foot of a weir.
+  § 122. A standing wave is frequently produced at the foot of a weir.
   Thus in the ogee falls originally constructed on the Ganges canal a
   standing wave was observed as shown in fig. 127. The water falling
   over the weir crest A acquired a very high velocity on the steep slope
   AB, and the section of the stream at B became very small. It easily
-  happened, therefore, that at B the depth h < u²/g. In flowing along
+  happened, therefore, that at B the depth h < u²/g. In flowing along
   the rough apron of the weir the velocity u diminished and the depth h
-  increased. At a point C, where h became equal to u²/g, the conditions
+  increased. At a point C, where h became equal to u²/g, the conditions
   for producing the standing wave occurred. Beyond C the free surface
   abruptly rose to the level corresponding to uniform motion with the
   assigned slope of the lower reach of the canal.
@@ -13674,15 +13640,15 @@ stream.
   similar flood, that is 16.58 ft. per second. Now, taking the depth on
   the down stream face of the pier at 26 ft., the velocity necessary for
   the production of a standing wave would be u = [root](gh) =
-  [root](32.2 × 26) = 29 ft. per second nearly. But the velocity at this
-  point was probably from Howden's statements 16.58 × {40/26} = 25.5 ft.
+  [root](32.2 × 26) = 29 ft. per second nearly. But the velocity at this
+  point was probably from Howden's statements 16.58 × {40/26} = 25.5 ft.
   per second, an agreement as close as the approximate character of the
   data would lead us to expect.
 
 
   XI. ON STREAMS AND RIVERS
 
-  § 123. _Catchment Basin._--A stream or river is the channel for the
+  § 123. _Catchment Basin._--A stream or river is the channel for the
   discharge of the available rainfall of a district, termed its
   catchment basin. The catchment basin is surrounded by a ridge or
   watershed line, continuous except at the point where the river finds
@@ -13706,7 +13672,7 @@ stream.
     | Naked unfissured mountains  |   .55 to .60    |      40 to 45      |
     +-----------------------------+-----------------+--------------------+
 
-  § 124. _Flood Discharge._--The flood discharge can generally only be
+  § 124. _Flood Discharge._--The flood discharge can generally only be
   determined by examining the greatest height to which floods have been
   known to rise. To produce a flood the rainfall must be heavy and
   widely distributed, and to produce a flood of exceptional height the
@@ -13755,7 +13721,7 @@ stream.
   rivers.
 
   In some of the tank projects in India, the flood discharge has been
-  calculated from the formula D = C[3root]n², where D is the discharge
+  calculated from the formula D = C[3root]n², where D is the discharge
   in cubic yards per hour from n square miles of basin. The constant C
   was taken = 61,523 in the designs for the Ekrooka tank, = 75,000 on
   Ganges and Godavery works, and = 10,000 on Madras works.
@@ -13764,7 +13730,7 @@ stream.
 
   [Illustration: FIG. 130.]
 
-  § 125. _Action of a Stream on its Bed._--If the velocity of a stream
+  § 125. _Action of a Stream on its Bed._--If the velocity of a stream
   exceeds a certain limit, depending on its size, and on the size,
   heaviness, form and coherence of the material of which its bed is
   composed, it scours its bed and carries forward the materials. The
@@ -13788,13 +13754,13 @@ stream.
   represented by ac. In a deeper stream such as that in fig. 130, the
   average height to which particles are lifted, and, since the rate of
   vertical fall through the water may be assumed the same as before, the
-  average distance a´c´ of transport will be greater. Consequently,
+  average distance a´c´ of transport will be greater. Consequently,
   although the scouring action may be identical in the two streams, the
   velocity of transport of material down stream is greater as the depth
   of the stream is greater. The effect is that the deep stream excavates
   its bed more rapidly than the shallow stream.
 
-  § 126. _Bottom Velocity at which Scour commences._--The following
+  § 126. _Bottom Velocity at which Scour commences._--The following
   bottom velocities were determined by P. L. G. Dubuat to be the maximum
   velocities consistent with stability of the stream bed for different
   materials.
@@ -13834,7 +13800,7 @@ stream.
 
   The following table of velocities which should not be exceeded in
   channels is given in the _Ingenieurs Taschenbuch_ of the Verein
-  "Hütte":--
+  "Hütte":--
 
     +--------------------------------+---------+---------+---------+
     |                                | Surface |  Mean   | Bottom  |
@@ -13850,7 +13816,7 @@ stream.
     | Hard rocks                     |  14.00  |  12.15  |  10.36  |
     +--------------------------------+---------+---------+---------+
 
-  § 127. _Regime of a River Channel._--A river channel is said to be in
+  § 127. _Regime of a River Channel._--A river channel is said to be in
   a state of regime, or stability, when it changes little in draught or
   form in a series of years. In some rivers the deepest part of the
   channel changes its position perpetually, and is seldom found in the
@@ -13876,12 +13842,12 @@ stream.
   constantly going on. This is more likely to happen if by artificial
   means the erosion of the banks is prevented. If a river flows in soil
   incapable of resisting its tendency to scour it is necessarily sinuous
-  (§ 107), for the slightest deflection of the current to either side
+  (§ 107), for the slightest deflection of the current to either side
   begins an erosion which increases progressively till a considerable
   bend is formed. If such a river is straightened it becomes sinuous
   again unless its banks are protected from scour.
 
-  § 128. _Longitudinal Section of River Bed._--The declivity of rivers
+  § 128. _Longitudinal Section of River Bed._--The declivity of rivers
   decreases from source to mouth. In their higher parts rapid and
   torrential, flowing over beds of gravel or boulders, they enlarge in
   volume by receiving affluent streams, their slope diminishes, their
@@ -13908,7 +13874,7 @@ stream.
   stability the velocity of the river in these circumstances is constant
   from source to mouth; (2) suppose the sections of the river at all
   points are similar, so that, b being the breadth of the river at any
-  point, its hydraulic mean depth is ab and its section is cb², where a
+  point, its hydraulic mean depth is ab and its section is cb², where a
   and c are constants applicable to all parts of the river; (3) let us
   further assume that the discharge increases uniformly in consequence
   of the supply from affluents, so that, if l is the length of the river
@@ -13922,14 +13888,14 @@ stream.
   source is at A; and take A for the origin of vertical and horizontal
   coordinates. Let C be a point whose ordinates are x and y, and let the
   river at C have the breadth b, the slope i, and the velocity v. Since
-  velocity × area of section = discharge, vcb² = kl, or b =
+  velocity × area of section = discharge, vcb² = kl, or b =
   [root](kl/cv).
 
   Hydraulic mean depth = ab = a [root](kl/cv).
 
-  But, by the ordinary formula for the flow of rivers, mi = [zeta]v²;
+  But, by the ordinary formula for the flow of rivers, mi = [zeta]v²;
 
-    .: i = [zeta]v²/m = ([zeta]v^(5/2)/a) [root](c/kl).
+    .: i = [zeta]v²/m = ([zeta]v^(5/2)/a) [root](c/kl).
 
   But i is the tangent of the angle which the curve at C makes with the
   axis of X, and is therefore = dy/dx. Also, as the slope is small, l =
@@ -13943,7 +13909,7 @@ stream.
 
   or
 
-    y² = constant × x;
+    y² = constant × x;
 
   so that the curve is a common parabola, of which the axis is
   horizontal and the vertex at the source. This may be considered an
@@ -13951,7 +13917,7 @@ stream.
   less, with exceptions due to the varying hardness of their beds, and
   the irregular manner in which their volume increases.
 
-  § 129. _Surface Level of River._--The surface level of a river is a
+  § 129. _Surface Level of River._--The surface level of a river is a
   plane changing constantly in position from changes in the volume of
   water discharged, and more slowly from changes in the river bed, and
   the circumstances affecting the drainage into the river.
@@ -13985,7 +13951,7 @@ stream.
   navigable level may be taken to be that at which the river begins to
   overflow its banks.
 
-  § 130. _Relative Value of Different Materials for Submerged
+  § 130. _Relative Value of Different Materials for Submerged
   Works._--That the power of water to remove and transport different
   materials depends on their density has an important bearing on the
   selection of materials for submerged works. In many cases, as in the
@@ -14014,7 +13980,7 @@ stream.
     | Masonry              |   116-144    |  53.6-81.6   |
     +----------------------+--------------+--------------+
 
-  § 131. _Inundation Deposits from a River._--When a river carrying silt
+  § 131. _Inundation Deposits from a River._--When a river carrying silt
   periodically overflows its banks, it deposits silt over the area
   flooded, and gradually raises the surface of the country. The silt is
   deposited in greatest abundance where the water first leaves the
@@ -14035,7 +14001,7 @@ stream.
   surface by a weir or annicut gives a command of level which permits
   the water to be conveyed to any part of the district.
 
-  § 132. _Deltas._--The name delta was originally given to the [Greek:
+  § 132. _Deltas._--The name delta was originally given to the [Greek:
   Delta]-shaped portion of Lower Egypt, included between seven branches
   of the Nile. It is now given to the whole of the alluvial tracts round
   river mouths formed by deposition of sediment from the river, where
@@ -14056,7 +14022,7 @@ stream.
   134), and one of these may in time become the main channel of the
   river.
 
-  § 133. _Field Operations preliminary to a Study of River
+  § 133. _Field Operations preliminary to a Study of River
   Improvement._--There are required (1) a plan of the river, on which
   the positions of lines of levelling and cross sections are marked; (2)
   a longitudinal section and numerous cross sections of the river; (3) a
@@ -14074,7 +14040,7 @@ stream.
 
   [Illustration: FIG. 134.]
 
-  § 134. _Cross Sections_--A stake is planted flush with the water, and
+  § 134. _Cross Sections_--A stake is planted flush with the water, and
   its level relatively to some point on the line of levels is
   determined. Then the depth of the water is determined at a series of
   points (if possible at uniform distances) in a line starting from the
@@ -14112,7 +14078,7 @@ stream.
   perimeter [chi]; and from these the hydraulic mean depth m can be
   calculated.
 
-  § 135. _Measurement of the Discharge of Rivers._--The area of cross
+  § 135. _Measurement of the Discharge of Rivers._--The area of cross
   section multiplied by the mean velocity gives the discharge of the
   stream. The height of the river with reference to some fixed mark
   should be noted whenever the velocity is observed, as the velocity and
@@ -14126,7 +14092,7 @@ stream.
 
   INSTRUMENTS FOR MEASURING THE VELOCITY OF WATER
 
-  § 136. _Surface Floats_ are convenient for determining the surface
+  § 136. _Surface Floats_ are convenient for determining the surface
   velocities of a stream, though their use is difficult near the banks.
   The floats may be small balls of wood, of wax or of hollow metal, so
   loaded as to float nearly flush with the water surface. To render
@@ -14134,7 +14100,7 @@ stream.
   the Seine, cork balls 1(3/4) in. diameter were used, loaded to float
   flush with the water, and provided with a stem. In A. J. C.
   Cunningham's observations at Roorkee, the floats were thin circular
-  disks of English deal, 3 in. diameter and ¼ in. thick. For
+  disks of English deal, 3 in. diameter and ¼ in. thick. For
   observations near the banks, floats 1 in. diameter and 1/8 in. thick
   were used. To render them visible a tuft of cotton wool was used
   loosely fixed in a hole at the centre.
@@ -14148,7 +14114,7 @@ stream.
   the size and rapidity of the river. In the Roorkee experiments a
   length of run of 50 ft. was found best for the central two-fifths of
   the width, and 25 ft. for the remainder, except very close to the
-  banks, where the run was made 12½ ft. only. The longer the run the
+  banks, where the run was made 12½ ft. only. The longer the run the
   less is the proportionate error of the time observations, but on the
   other hand the greater the deviation of the floats from a straight
   course parallel to the axis of the stream. To mark the precise
@@ -14188,7 +14154,7 @@ stream.
 
   [Illustration: FIG. 137.]
 
-  § 137. _Sub-surface Floats._--The velocity at different depths below
+  § 137. _Sub-surface Floats._--The velocity at different depths below
   the surface of a stream may be obtained by sub-surface floats, used
   precisely in the same way as surface floats. The most usual
   arrangement is to have a large float, of slightly greater density than
@@ -14216,7 +14182,7 @@ stream.
 
   [Illustration: FIG. 139.]
 
-  § 138. _Twin Floats._--Suppose two equal and similar floats (fig. 139)
+  § 138. _Twin Floats._--Suppose two equal and similar floats (fig. 139)
   connected by a wire. Let one float be a little lighter and the other a
   little heavier than water. Then the velocity of the combined floats
   will be the mean of the surface velocity and the velocity at the depth
@@ -14225,7 +14191,7 @@ stream.
   velocity at the depth to which the lower float is sunk, the velocity
   of the combined floats will be
 
-    v = ½(v_s + v_d).
+    v = ½(v_s + v_d).
 
   Consequently, if v is observed, and v_s determined by an experiment
   with a single float,
@@ -14237,7 +14203,7 @@ stream.
 
   [Illustration: FIG. 140.]
 
-  § 139. _Velocity Rods._--Another form of float is shown in fig. 140.
+  § 139. _Velocity Rods._--Another form of float is shown in fig. 140.
   This consists of a cylindrical rod loaded at the lower end so as to
   float nearly vertical in water. A wooden rod, with a metal cap at the
   bottom in which shot can be placed, answers better than anything else,
@@ -14248,7 +14214,7 @@ stream.
   stream, gives directly the mean velocity of the whole vertical section
   in which it floats.
 
-  § 140. _Revy's Current Meter._--No instrument has been so much used in
+  § 140. _Revy's Current Meter._--No instrument has been so much used in
   directly determining the velocity of a stream at a given point as the
   screw current meter. Of this there are a dozen varieties at least. As
   an example of the instrument in its simplest form, Revy's meter may be
@@ -14307,7 +14273,7 @@ stream.
 
   [Illustration: FIG. 142.]
 
-  § 141. _The Harlacher Current Meter._--In this the ordinary counting
+  § 141. _The Harlacher Current Meter._--In this the ordinary counting
   apparatus is abandoned. A worm drives a worm wheel, which makes an
   electrical contact once for each 100 rotations of the worm. This
   contact gives a signal above water. With this arrangement, a series of
@@ -14323,7 +14289,7 @@ stream.
   also the battery. The magnet exposes and withdraws a coloured disk at
   an opening in the cover of the box.
 
-  § 142. _Amsler Laffon Current Meter._--A very convenient and accurate
+  § 142. _Amsler Laffon Current Meter._--A very convenient and accurate
   current meter is constructed by Amsler Laffon of Schaffhausen. This
   can be used on a rod, and put into and out of gear by a ratchet. The
   peculiarity in this case is that there is a double ratchet, so that
@@ -14350,7 +14316,7 @@ stream.
 
   [Illustration: FIG. 143.]
 
-  § 143. _Determination of the Coefficients of the Current
+  § 143. _Determination of the Coefficients of the Current
   Meter._--Suppose a series of observations has been made by towing the
   meter in still water at different speeds, and that it is required to
   ascertain from these the constants of the meter. If v is the velocity
@@ -14372,20 +14338,20 @@ stream.
 
     [Sigma]nv = n1v1 + n2v2 + ...
 
-    [Sigma]n² = n1² + n2² + ...
+    [Sigma]n² = n1² + n2² + ...
 
-    [[Sigma]n]² = [n1 + n2 + ...]²
+    [[Sigma]n]² = [n1 + n2 + ...]²
 
   Then for the determination of the constants [alpha] and [beta] in (1),
   by the method of least squares--
 
-              [Sigma]n²[Sigma]v - [Sigma]n[Sigma]nv
+              [Sigma]n²[Sigma]v - [Sigma]n[Sigma]nv
     [alpha] = -------------------------------------,
-                     m[Sigma]n² - [[Sigma]n]²
+                     m[Sigma]n² - [[Sigma]n]²
 
              m[Sigma]nv - [Sigma]v[Sigma]n
     [beta] = -----------------------------.
-                m[Sigma]n² - [[Sigma]n]²
+                m[Sigma]n² - [[Sigma]n]²
 
   [Illustration: FIG. 144.]
 
@@ -14394,31 +14360,31 @@ stream.
   the resistance of ship models is ascertained. In that case the data
   are found with exceptional accuracy.
 
-  § 144. Darcy Gauge or modified Pitot Tube.--A very old instrument for
+  § 144. Darcy Gauge or modified Pitot Tube.--A very old instrument for
   measuring velocities, invented by Henri Pitot in 1730 (_Histoire de
-  l'Académie des Sciences_, 1732, p. 376), consisted simply of a
+  l'Académie des Sciences_, 1732, p. 376), consisted simply of a
   vertical glass tube with a right-angled bend, placed so that its mouth
   was normal to the direction of flow (fig. 145).
 
   [Illustration: FIG. 145.]
 
   The impact of the stream on the mouth of the tube balances a column in
-  the tube, the height of which is approximately h = v²/2g, where v is
+  the tube, the height of which is approximately h = v²/2g, where v is
   the velocity at the depth x. Placed with its mouth parallel to the
   stream the water inside the tube is nearly at the same level as the
   surface of the stream, and turned with the mouth down stream, the
-  fluid sinks a depth h´ = v²/2g nearly, though the tube in that case
+  fluid sinks a depth h´ = v²/2g nearly, though the tube in that case
   interferes with the free flow of the liquid and somewhat modifies the
   result. Pitot expanded the mouth of the tube so as to form a funnel or
   bell mouth. In that case he found by experiment
 
-    h = 1.5v²/2g.
+    h = 1.5v²/2g.
 
   But there is more disturbance of the stream. Darcy preferred to make
   the mouth of the tube very small to avoid interference with the
   stream and to check oscillations of the water column. Let the
   difference of level of a pair of tubes A and B (fig. 145) be taken to
-  be h = kv²/2g, then k may be taken to be a corrective coefficient
+  be h = kv²/2g, then k may be taken to be a corrective coefficient
   whose value in well-shaped instruments is very nearly unity. By
   placing his instrument in front of a boat towed through water Darcy
   found k = 1.034; by placing the instrument in a stream the velocity of
@@ -14475,7 +14441,7 @@ stream.
   in some of his experiments took several readings, and deduced the
   velocity from the mean of the highest and lowest.
 
-  § 145. _Perrodil Hydrodynamometer._--This consists of a frame abcd
+  § 145. _Perrodil Hydrodynamometer._--This consists of a frame abcd
   (fig. 147) placed vertically in the stream, and of a height not less
   than the stream's depth. The two vertical members of this frame are
   connected by cross bars, and united above water by a circular bar,
@@ -14523,16 +14489,16 @@ stream.
 
   where E_t is the modulus of elasticity for torsion, and I the polar
   moment of inertia of the section of the rod. If the rod is of circular
-  section, I = ½[pi]r^4. Let R be the radius of the disk, and b its
+  section, I = ½[pi]r^4. Let R be the radius of the disk, and b its
   leverage, or the distance of its centre from the axis of the torsion
   rod. The moment of the pressure of the water on the disk is
 
-    Fb = kb(G/2g)[pi]R²v²,
+    Fb = kb(G/2g)[pi]R²v²,
 
   where G is the heaviness of water and k an experimental coefficient.
   Then
 
-    E_t I[alpha]/l = kb(G/2g)[pi]R²v².
+    E_t I[alpha]/l = kb(G/2g)[pi]R²v².
 
   For any given instrument,
 
@@ -14550,7 +14516,7 @@ stream.
     3rd   "      0.210     0.66
 
   For a thin circular plate, the coefficient k = 1.12. In the actual
-  instrument the torsion rod was a brass wire 0.06 in. diameter and 6½
+  instrument the torsion rod was a brass wire 0.06 in. diameter and 6½
   ft. long. Supposing [alpha] measured in degrees, we get by calculation
 
     v = 0.335 [root][alpha]; 0.115 [root][alpha]; 0.042 [root][alpha].
@@ -14562,8 +14528,8 @@ stream.
   for the coefficient c, in the formula v = c [root][alpha],
 
     1st disk, c =  0.3126 for velocities of 3 to 16  ft.
-    2nd   "        0.1177  "       "        1¼ to 3¼  "
-    3rd   "        0.0349  "       "    less than 1¼  "
+    2nd   "        0.1177  "       "        1¼ to 3¼  "
+    3rd   "        0.0349  "       "    less than 1¼  "
 
   The instrument is preferable to the current meter in giving the
   velocity in terms of a single observed quantity, the angle of torsion,
@@ -14586,7 +14552,7 @@ stream.
 
   PROCESSES FOR GAUGING STREAMS
 
-  § 146. _Gauging by Observation of the Maximum Surface Velocity._--The
+  § 146. _Gauging by Observation of the Maximum Surface Velocity._--The
   method of gauging which involves the least trouble is to determine the
   surface velocity at the thread of the stream, and to deduce from it
   the mean velocity of the whole cross section. The maximum surface
@@ -14603,7 +14569,7 @@ stream.
     Destrem and De Prony, experiments on the Neva    0.78
     Boileau, experiments on canals                   0.82
     Baumgartner, experiments on the Garonne          0.80
-    Brünings (mean)                                  0.85
+    Brünings (mean)                                  0.85
     Cunningham, Solani aqueduct                      0.823
 
   Various formulae, either empirical or based on some theory of the
@@ -14627,9 +14593,9 @@ stream.
   velocity can be obtained by simply observing the depth of the stream,
   and from this the mean velocity and discharge can be calculated. Let z
   be the depth of the stream, and v_o the surface velocity, both measured
-  at the thread of the stream. Then v_o² = cz; where c is a constant
+  at the thread of the stream. Then v_o² = cz; where c is a constant
   which for the Solani aqueduct had the values 1.9 to 2, the depths
-  being 6 to 10 ft., and the velocities 3½ to 4½ ft. Without any
+  being 6 to 10 ft., and the velocities 3½ to 4½ ft. Without any
   assumption of a formula, however, the surface velocities, or still
   better the mean velocities, for different conditions of the stream may
   be plotted on a diagram in which the abscissae are depths and the
@@ -14638,7 +14604,7 @@ stream.
   stream, without the need of making any new float or current meter
   observations.
 
-  § 147. _Mean Velocity determined by observing a Series of Surface
+  § 147. _Mean Velocity determined by observing a Series of Surface
   Velocities._--The ratio of the mean velocity to the surface velocity
   in one longitudinal section is better ascertained than the ratio of
   the central surface velocity to the mean velocity of the whole cross
@@ -14699,7 +14665,7 @@ stream.
 
   The ratio of the surface velocity to the mean velocity in the same
   vertical can be ascertained from the formulae for the vertical
-  velocity curve already given (§ 101). Exner, in _Erbkam's Zeitschrift_
+  velocity curve already given (§ 101). Exner, in _Erbkam's Zeitschrift_
   for 1875, gave the following convenient formula. Let v be the mean and
   V the surface velocity in any given vertical longitudinal section, the
   depth of which is h
@@ -14712,7 +14678,7 @@ stream.
   velocity has simply to be multiplied by the area of the compartment to
   which it belongs.
 
-  § 148. _Mean Velocity of the Stream from a Series of Mid Depth
+  § 148. _Mean Velocity of the Stream from a Series of Mid Depth
   Velocities._--In the gaugings of the Mississippi it was found that the
   mid depth velocity differed by only a very small quantity from the
   mean velocity in the vertical section, and it was uninfluenced by
@@ -14726,7 +14692,7 @@ stream.
   the river is divided. The discharge is the sum of the products of the
   observed mean mid depth velocities and the areas of the compartments.
 
-  § 149. _P. P. Boileau's Process for Gauging Streams._--Let U be the
+  § 149. _P. P. Boileau's Process for Gauging Streams._--Let U be the
   mean velocity at a given section of a stream, V the maximum velocity,
   or that of the principal filament, which is generally a little below
   the surface, W and w the greatest and least velocities at the surface.
@@ -14755,7 +14721,7 @@ stream.
   from a horizontal surface velocity curve, obtained from a series of
   float observations.
 
-  § 150. _Direct Determination of the Mean Velocity by a Current Meter
+  § 150. _Direct Determination of the Mean Velocity by a Current Meter
   or Darcy Gauge._--The only method of determining the mean velocity at
   a cross section of a stream which involves no assumption of the ratio
   of the mean velocity to other quantities is this--a plank bridge is
@@ -14775,7 +14741,7 @@ stream.
 
   [Illustration: FIG. 149.]
 
-  § 151. _A. R. Harlacher's Graphic Method of determining the Discharge
+  § 151. _A. R. Harlacher's Graphic Method of determining the Discharge
   from a Series of Current Meter Observations._--Let ABC (fig. 149) be
   the cross section of a river at which a complete series of current
   meter observations have been taken. Let I., II., III ... be the
@@ -14816,11 +14782,11 @@ stream.
   limited by successive planes passing through the contour curves, will
   be
 
-    ½x([Omega]0 + [Omega]1), ½x([Omega]1 + [Omega]2), and so on.
+    ½x([Omega]0 + [Omega]1), ½x([Omega]1 + [Omega]2), and so on.
 
   Consequently the discharge is
 
-    Q = x{½([Omega]0 + [Omega]_n) + [Omega]1 = [Omega]2 + ... + [Omega](n-1)}.
+    Q = x{½([Omega]0 + [Omega]_n) + [Omega]1 = [Omega]2 + ... + [Omega](n-1)}.
 
   The areas [Omega]0, [Omega]1 ... are easily ascertained by means of
   the polar planimeter. A slight difficulty arises in the part of the
@@ -14828,7 +14794,7 @@ stream.
   height which is not exactly x, and a form more rounded than the other
   layers and less like a conical frustum. The volume of this may be
   estimated separately, and taken to be the area of its base (the area
-  [Omega]_n) multiplied by 1/3 to ½ its height.
+  [Omega]_n) multiplied by 1/3 to ½ its height.
 
   [Illustration: FIG. 151.]
 
@@ -14852,7 +14818,7 @@ stream.
 
 HYDRAULIC MACHINES
 
-§ 152. Hydraulic machines may be broadly divided into two classes: (1)
+§ 152. Hydraulic machines may be broadly divided into two classes: (1)
 _Motors_, in which water descending from a higher to a lower level, or
 from a higher to a lower pressure, gives up energy which is available
 for mechanical operations; (2) _Pumps_, in which the energy of a steam
@@ -14899,7 +14865,7 @@ transmitted electrically are not included.
 
   XII. IMPACT AND REACTION OF WATER
 
-  § 153. When a stream of fluid in steady motion impinges on a solid
+  § 153. When a stream of fluid in steady motion impinges on a solid
   surface, it presses on the surface with a force equal and opposite to
   that by which the velocity and direction of motion of the fluid are
   changed. Generally, in problems on the impact of fluids, it is
@@ -14955,13 +14921,13 @@ transmitted electrically are not included.
 
   Let Q be the volume, and GQ the weight of the fluid impinging per
   second, and let v1 be the initial velocity of the fluid before
-  striking the surface. Then GQv1²/2g is the original kinetic energy of
+  striking the surface. Then GQv1²/2g is the original kinetic energy of
   Q cub. ft. of fluid, and the efficiency of the stream considered as an
   arrangement for moving the solid surface is
 
-    [eta] = Tu/(GQv1²/2g).
+    [eta] = Tu/(GQv1²/2g).
 
-  § 154. _Jet deviated entirely in one Direction.--Geometrical Solution_
+  § 154. _Jet deviated entirely in one Direction.--Geometrical Solution_
   (fig. 153).--Suppose a jet of water impinges on a surface ac with a
   velocity ab, and let it be wholly deviated in planes parallel to the
   figure. Also let ae be the velocity and direction of motion of the
@@ -14989,40 +14955,40 @@ transmitted electrically are not included.
 
   SPECIAL CASES
 
-  § 155. (1) _A Jet impinges on a plane surface at rest, in a direction
+  § 155. (1) _A Jet impinges on a plane surface at rest, in a direction
   normal to the plane_ (fig. 154).--Let a jet whose section is [omega]
   impinge with a velocity v on a plane surface at rest, in a direction
   normal to the plane. The particles approach the plane, are gradually
   deviated, and finally flow away parallel to the plane, having then no
   velocity in the original direction of the jet. The quantity of water
   impinging per second is [omega]v. The pressure on the plane, which is
-  equal to the change of momentum per second, is P = (G/g)[omega]v².
+  equal to the change of momentum per second, is P = (G/g)[omega]v².
 
   [Illustration: FIG. 154.]
 
   (2) _If the plane is moving in the direction of the jet with the
-  velocity_ ±u, the quantity impinging per second is [omega](v ± u).
-  The momentum of this quantity before impact is (G/g)[omega](v ± u)v.
-  After impact, the water still possesses the velocity ±u in the
+  velocity_ ±u, the quantity impinging per second is [omega](v ± u).
+  The momentum of this quantity before impact is (G/g)[omega](v ± u)v.
+  After impact, the water still possesses the velocity ±u in the
   direction of the jet; and the momentum, in that direction, of so much
   water as impinges in one second, after impact, is
-  ±(G/g)[omega](v ± u)u. The pressure on the plane, which is the change
+  ±(G/g)[omega](v ± u)u. The pressure on the plane, which is the change
   of momentum per second, is the difference of these quantities or P =
-  (G/g)[omega](v ± u)². This differs from the expression obtained in
+  (G/g)[omega](v ± u)². This differs from the expression obtained in
   the previous case, in that the relative velocity of the water and
-  plane v ± u is substituted for v. The expression may be written P = 2
-  × G × [omega](v ± u)²/2g, where the last two terms are the volume of
+  plane v ± u is substituted for v. The expression may be written P = 2
+  × G × [omega](v ± u)²/2g, where the last two terms are the volume of
   a prism of water whose section is the area of the jet and whose length
   is the head due to the relative velocity. The pressure on the plane is
   twice the weight of that prism of water. The work done when the plane
   is moving in the same direction as the jet is Pu = (G/g)[omega](v -
-  u)²u foot-pounds per second. There issue from the jet [omega]v cub.
+  u)²u foot-pounds per second. There issue from the jet [omega]v cub.
   ft. per second, and the energy of this quantity before impact is
-  (G/2g)[omega]v³. The efficiency of the jet is therefore [eta] = 2(v -
-  u)²u/v³. The value of u which makes this a maximum is found by
+  (G/2g)[omega]v³. The efficiency of the jet is therefore [eta] = 2(v -
+  u)²u/v³. The value of u which makes this a maximum is found by
   differentiating and equating the differential coefficient to zero:--
 
-    d[eta]/du = 2(v² - 4vu + 3u²)/v³ = 0;
+    d[eta]/du = 2(v² - 4vu + 3u²)/v³ = 0;
 
     .: u = v or (1/3)v.
 
@@ -15036,15 +15002,15 @@ transmitted electrically are not included.
   are introduced at short intervals at the same point, the quantity of
   water impinging on the series will be [omega]v instead of [omega](v -
   u), and the whole pressure = (G/g)[omega]v(v - u). The work done is
-  (G/g)[omega]vu(v - u). The efficiency [eta] = (G/g)[omega]vu(v - u) ÷
-  (G/2g)[omega]v³ = 2u(v - u)/v². This becomes a maximum for d[eta]/du =
-  2(v - 2u) = 0, or u = ½v, and the [eta] = ½. This result is often used
+  (G/g)[omega]vu(v - u). The efficiency [eta] = (G/g)[omega]vu(v - u) ÷
+  (G/2g)[omega]v³ = 2u(v - u)/v². This becomes a maximum for d[eta]/du =
+  2(v - 2u) = 0, or u = ½v, and the [eta] = ½. This result is often used
   as an approximate expression for the velocity of greatest efficiency
   when a jet of water strikes the floats of a water wheel. The work
   wasted in this case is half the whole energy of the jet when the
   floats run at the best speed.
 
-  § 156. (4) _Case of a Jet impinging on a Concave Cup Vane_, velocity
+  § 156. (4) _Case of a Jet impinging on a Concave Cup Vane_, velocity
   of water v, velocity of vane in the same direction u (fig. 155),
   weight impinging per second = Gw(v - u).
 
@@ -15055,9 +15021,9 @@ transmitted electrically are not included.
   the cup, and -(v - u) when leaving it. Hence its absolute velocity
   when leaving the cup is u - (v - u) = 2u - v. The change of momentum
   per second = (G/g)[omega](v - u) {v - (2u - v)} = 2(G/g)[omega](v -
-  u)². Comparing this with case 2, it is seen that the pressure on a
+  u)². Comparing this with case 2, it is seen that the pressure on a
   hemispherical cup is double that on a flat plane. The work done on the
-  cup = 2(G/g)[omega] (v - u)²u foot-pounds per second. The efficiency
+  cup = 2(G/g)[omega] (v - u)²u foot-pounds per second. The efficiency
   of the jet is greatest when v = 3u; in that case the efficiency =
   {16/27}.
 
@@ -15070,7 +15036,7 @@ transmitted electrically are not included.
 
   [Illustration: FIG. 156.]
 
-  § 157. (5) _Case of a Flat Vane oblique to the Jet_ (fig. 156).--This
+  § 157. (5) _Case of a Flat Vane oblique to the Jet_ (fig. 156).--This
   case presents some difficulty. The water spreading on the plane in all
   directions from the point of impact, different particles leave the
   plane with different absolute velocities. Let AB = v = velocity of
@@ -15083,7 +15049,7 @@ transmitted electrically are not included.
   impact, but AE is destroyed. Hence AE represents the entire change of
   velocity due to impact and the direction of that change. The pressure
   on the plane is in the direction AE, and its amount is = mass of water
-  impinging per second × AE.
+  impinging per second × AE.
 
   Let DAE = [theta], and let AD = v_r. Then AE = v_r cos [theta]; DE =
   v_r sin [theta]. If Q is the volume of water impinging on the plane
@@ -15128,32 +15094,32 @@ transmitted electrically are not included.
   [alpha]. Inserting this in the formulae above, we get
 
          G    [omega]
-    N = --- ----------- (v cos [alpha] - u cos [delta])²;   (1)
+    N = --- ----------- (v cos [alpha] - u cos [delta])²;   (1)
          g  cos [alpha]
 
          G  [omega] cos [delta]
-    P = --- ------------------- (v cos [alpha] - u cos [delta])²;   (2)
+    P = --- ------------------- (v cos [alpha] - u cos [delta])²;   (2)
          g      cos [alpha]
 
           G           cos [delta]
-    Pu = --- [omega]u ----------- (v cos [alpha] - u cos [delta])².   (3)
+    Pu = --- [omega]u ----------- (v cos [alpha] - u cos [delta])².   (3)
           g           cos [alpha]
 
   Three cases may be distinguished:--
 
-  (a) The plane is at rest. Then u = 0, N = (G/g)[omega]v² cos [alpha];
+  (a) The plane is at rest. Then u = 0, N = (G/g)[omega]v² cos [alpha];
   and the work done on the plane and the efficiency of the jet are zero.
 
   (b) The plane moves parallel to the jet. Then [delta] = [alpha], and
-  Pu = (G/g)[omega]u cos²[alpha](v - u)², which is a maximum when u =
+  Pu = (G/g)[omega]u cos²[alpha](v - u)², which is a maximum when u =
   1/3 v.
 
-  When u = 1/3 v then Pu max. = 4/27 (G/g)[omega]v³ cos² [alpha], and
-  the efficiency = [eta] = 4/9 cos² [alpha].
+  When u = 1/3 v then Pu max. = 4/27 (G/g)[omega]v³ cos² [alpha], and
+  the efficiency = [eta] = 4/9 cos² [alpha].
 
-  (c) The plane moves perpendicularly to the jet. Then [delta] = 90° -
+  (c) The plane moves perpendicularly to the jet. Then [delta] = 90° -
   [alpha]; cos [delta] = sin [alpha]; and Pu = G/g [omega]u (sin
-  [alpha]/cos [alpha]) (v cos [alpha] - u sin [alpha])². This is a
+  [alpha]/cos [alpha]) (v cos [alpha] - u sin [alpha])². This is a
   maximum when u = 1/3 v cos [alpha].
 
   When u = 1/3 v cos [alpha], the maximum work and the efficiency are
@@ -15161,7 +15127,7 @@ transmitted electrically are not included.
 
   [Illustration: FIG. 159.]
 
-  § 158. _Best Form of Vane to receive Water._--When water impinges
+  § 158. _Best Form of Vane to receive Water._--When water impinges
   normally or obliquely on a plane, it is scattered in all directions
   after impact, and the work carried away by the water is then generally
   lost, from the impossibility of dealing afterwards with streams of
@@ -15183,7 +15149,7 @@ transmitted electrically are not included.
 
   [Illustration: FIG. 160.]
 
-  § 159. _Floats of Poncelet Water Wheels._--Let AC (fig. 160) represent
+  § 159. _Floats of Poncelet Water Wheels._--Let AC (fig. 160) represent
   the direction of a thin horizontal stream of water having the velocity
   v. Let AB be a curved float moving horizontally with velocity u. The
   relative motion of water and float is then initially horizontal, and
@@ -15195,13 +15161,13 @@ transmitted electrically are not included.
   u)/g seconds the float moving with the velocity u comes to the
   position A1B1, and during this time a particle of water received at A
   and gliding up the float with the relative velocity v - u, attains a
-  height DE = (v - u)²/2g. At E the water comes to relative rest. It
+  height DE = (v - u)²/2g. At E the water comes to relative rest. It
   then descends along the float, and when after 2(v - u)/g seconds the
   float has come to A2B2 the water will again have reached the lip at A2
   and will quit it tangentially, that is, in the direction CA2, with a
   relative velocity -(v - u) = -[root](2gDE) acquired under the
   influence of gravity. The absolute velocity of the water leaving the
-  float is therefore u - (v - u) = 2u - v. If u = ½v, the water will
+  float is therefore u - (v - u) = 2u - v. If u = ½v, the water will
   drop off the bucket deprived of all energy of motion. The whole of the
   work of the jet must therefore have been expended in driving the
   float. The water will have been received without shock and discharged
@@ -15209,11 +15175,11 @@ transmitted electrically are not included.
   that case the floats move over an arc of a large circle; the stream of
   water has considerable thickness (about 8 in.); in order to get the
   water into and out of the wheel, it is then necessary that the lip of
-  the float should make a small angle (about 15°) with the direction of
+  the float should make a small angle (about 15°) with the direction of
   its motion. The water quits the wheel with a little of its energy of
   motion remaining.
 
-  § 160. _Pressure on a Curved Surface when the Water is deviated wholly
+  § 160. _Pressure on a Curved Surface when the Water is deviated wholly
   in one Direction._--When a jet of water impinges on a curved surface
   in such a direction that it is received without shock, the pressure on
   the surface is due to its gradual deviation from its first direction.
@@ -15232,19 +15198,19 @@ transmitted electrically are not included.
   unchanged during contact with the surface, because the deviating force
   is at each point perpendicular to the direction of motion. The water
   is deviated through an angle BCD = AOB = [phi]. Each particle of water
-  of weight p exerts radially a centrifugal force pv²/rg. Let the
+  of weight p exerts radially a centrifugal force pv²/rg. Let the
   thickness of the stream = t ft. Then the weight of water resting on
   unit of surface = Gt lb.; and the normal pressure per unit of surface
-  = n = Gtv²/gr. The resultant of the radial pressures uniformly
+  = n = Gtv²/gr. The resultant of the radial pressures uniformly
   distributed from A to B will be a force acting in the direction OC
   bisecting AOB, and its magnitude will equal that of a force of
   intensity = n, acting on the projection of AB on a plane perpendicular
-  to the direction OC. The length of the chord AB = 2r sin ½[phi]; let b
+  to the direction OC. The length of the chord AB = 2r sin ½[phi]; let b
   = breadth of the surface perpendicular to the plane of the figure. The
   resultant pressure on surface
 
-                  [phi]   Gt v²     G           [phi]
-    = R = 2rb sin ----- × --.-- = 2--- btv² sin -----,
+                  [phi]   Gt v²     G           [phi]
+    = R = 2rb sin ----- × --.-- = 2--- btv² sin -----,
                     2     g  r      g             2
 
   which is independent of the radius of curvature. It may be inferred
@@ -15256,29 +15222,29 @@ transmitted electrically are not included.
   (fig. 162) is found by combining the relative velocity BD = v - u
   tangential to the surface with the velocity BE = u of the surface. The
   intensity of normal pressure, as in the last case, is (G/g)t(v -
-  u)²/r. The resultant normal pressure R = 2(G/g)bt(v - u)² sin ½[phi].
+  u)²/r. The resultant normal pressure R = 2(G/g)bt(v - u)² sin ½[phi].
   This resultant pressure may be resolved into two components P and L,
   one parallel and the other perpendicular to the direction of the
   vane's motion. The former is an effort doing work on the vane. The
   latter is a lateral force which does no work.
 
-    P = R sin ½[phi] = (G/g) bt (v - u)² (1 - cos [phi]);
+    P = R sin ½[phi] = (G/g) bt (v - u)² (1 - cos [phi]);
 
-    L = R cos ½[phi] = (G/g) bt (v - u)² sin [phi].
+    L = R cos ½[phi] = (G/g) bt (v - u)² sin [phi].
 
   [Illustration: FIG. 162.]
 
-  The work done by the jet on the vane is Pu = (G/g)btu(v - u)²(1 - cos
+  The work done by the jet on the vane is Pu = (G/g)btu(v - u)²(1 - cos
   [phi]), which is a maximum when u = 1/3 v. This result can also be
   obtained by considering that the work done on the plane must be equal
   to the energy lost by the water, when friction is neglected.
 
-  If [phi] = 180°, cos [phi] = -1, 1 - cos [phi] = 2; then P =
-  2(G/g)bt(v - u)², the same result as for a concave cup.
+  If [phi] = 180°, cos [phi] = -1, 1 - cos [phi] = 2; then P =
+  2(G/g)bt(v - u)², the same result as for a concave cup.
 
   [Illustration: FIG. 163.]
 
-  § 161. _Position which a Movable Plane takes in Flowing Water._--When
+  § 161. _Position which a Movable Plane takes in Flowing Water._--When
   a rectangular plane, movable about an axis parallel to one of its
   sides, is placed in an indefinite current of fluid, it takes a
   position such that the resultant of the normal pressures on the two
@@ -15293,25 +15259,25 @@ transmitted electrically are not included.
     +-----------+-------------+--------------+
     |           |Larger plane.|Smaller Plane.|
     +-----------+-------------+--------------+
-    | a/b = 1.0 |[phi] = ...  |[phi] = 90°   |
-    |       0.9 |        75°  |        72½°  |
-    |       0.8 |        60°  |        57°   |
-    |       0.7 |        48°  |        43°   |
-    |       0.6 |        25°  |        29°   |
-    |       0.5 |        13°  |        13°   |
-    |       0.4 |         8°  |         6½°  |
-    |       0.3 |         6°  |        ..    |
-    |       0.2 |         4°  |        ..    |
+    | a/b = 1.0 |[phi] = ...  |[phi] = 90°   |
+    |       0.9 |        75°  |        72½°  |
+    |       0.8 |        60°  |        57°   |
+    |       0.7 |        48°  |        43°   |
+    |       0.6 |        25°  |        29°   |
+    |       0.5 |        13°  |        13°   |
+    |       0.4 |         8°  |         6½°  |
+    |       0.3 |         6°  |        ..    |
+    |       0.2 |         4°  |        ..    |
     +-----------+-------------+--------------+
 
-  § 162. _Direct Action distinguished from Reaction_ (Rankine, _Steam
-  Engine_, § 147).
+  § 162. _Direct Action distinguished from Reaction_ (Rankine, _Steam
+  Engine_, § 147).
 
   The pressure which a jet exerts on a vane can be distinguished into
   two parts, viz.:--
 
   (1) The pressure arising from changing the direct component of the
-  velocity of the water into the velocity of the vane. In fig. 153, §
+  velocity of the water into the velocity of the vane. In fig. 153, §
   154, ab cos bae is the direct component of the water's velocity, or
   component in the direction of motion of vane. This is changed into the
   velocity ae of the vane. The pressure due to direct impulse is then
@@ -15324,23 +15290,23 @@ transmitted electrically are not included.
   (2) The term reaction is applied to the additional action due to the
   direction and velocity with which the water glances off the vane. It
   is this which is diminished by the friction between the water and the
-  vane. In Case 2, § 160, the direct pressure is
+  vane. In Case 2, § 160, the direct pressure is
 
-    P1 = Gbt(v - u)²/g.
+    P1 = Gbt(v - u)²/g.
 
   That due to reaction is
 
-    P2 = -Gbt(v - u)² cos [phi]/g.
+    P2 = -Gbt(v - u)² cos [phi]/g.
 
-  If [phi] < 90°, the direct component of the water's motion is not
+  If [phi] < 90°, the direct component of the water's motion is not
   wholly converted into the velocity of the vane, and the whole
-  pressure due to direct impulse is not obtained. If [phi] > 90°, cos
+  pressure due to direct impulse is not obtained. If [phi] > 90°, cos
   [phi] is negative and an additional pressure due to reaction is
   obtained.
 
   [Illustration: FIG. 164.]
 
-  § 163. _Jet Propeller._--In the case of vessels propelled by a jet of
+  § 163. _Jet Propeller._--In the case of vessels propelled by a jet of
   water (fig. 164), driven sternwards from orifices at the side of the
   vessel, the water, originally at rest outside the vessel, is drawn
   into the ship and caused to move with the forward velocity V of the
@@ -15353,7 +15319,7 @@ transmitted electrically are not included.
 
   The energy carried away by the water
 
-    = ½(G/g)[Omega]v (v - V)².   (1)
+    = ½(G/g)[Omega]v (v - V)².   (1)
 
   The useful work done on the ship
 
@@ -15362,7 +15328,7 @@ transmitted electrically are not included.
   Adding (1) and (2), we get the whole work expended on the water,
   neglecting friction:--
 
-    W = ½(G/g)[Omega]v (v² - V²).
+    W = ½(G/g)[Omega]v (v² - V²).
 
   Hence the efficiency of the jet propeller is
 
@@ -15379,7 +15345,7 @@ transmitted electrically are not included.
 
   [Illustration: FIG. 165.]
 
-  § 164. _Pressure of a Steady Stream in a Uniform Pipe on a Plane
+  § 164. _Pressure of a Steady Stream in a Uniform Pipe on a Plane
   normal to the Direction of Motion._--Let CD (fig. 165) be a plane
   placed normally to the stream which, for simplicity, may be supposed
   to flow horizontally. The fluid filaments are deviated in front of the
@@ -15403,23 +15369,23 @@ transmitted electrically are not included.
   Let p0, p1, p2 be the pressures at the three sections. Applying
   Bernoulli's theorem to the sections A0A0 and A1A1,
 
-    p0   v²   p1   v1²
+    p0   v²   p1   v1²
     -- + -- = -- + ---.
     G    2g   G    2g
 
   Also, for the sections A1A1 and A2A2, allowing that the head due to
   the relative velocity v1 - v is lost in shock:--
 
-    p1   v1²    p2    v²   (v1 - v)²
+    p1   v1²    p2    v²   (v1 - v)²
     -- + --- =  --  + -- + ---------;
     G    2g     G     2g      2g
 
-    .: p0 - p2 = G(v1 - v)²/2g;   (2)
+    .: p0 - p2 = G(v1 - v)²/2g;   (2)
 
   or, introducing the value in (1),
 
-              G   /        [Omega]            \²
-    p0 - p2 = -- ( ----------------------- - 1 ) v²   (3)
+              G   /        [Omega]            \²
+    p0 - p2 = -- ( ----------------------- - 1 ) v²   (3)
               2g  \c_c ([Omega] - [omega])    /
 
   Now the external forces in the direction of motion acting on the mass
@@ -15429,7 +15395,7 @@ transmitted electrically are not included.
 
     (p0 - p2)[Omega] - R = 0;
 
-                     /         [Omega]           \² v²
+                     /         [Omega]           \² v²
     .: R = G[Omega] ( ----------------------- - 1 ) --;   (4)
                      \c_c ([Omega] - [omega])    /  2g
 
@@ -15439,13 +15405,13 @@ transmitted electrically are not included.
   For a given plane the expression in brackets diminishes as [Omega]
   increases. If [Omega]/[omega] = [rho], the equation (4) becomes
                      _                            _
-                 v² |       /     [rho]         \² |
+                 v² |       /     [rho]         \² |
     R = G[omega] -- |[rho] ( --------------- - 1 ) |,   (4a)
                  2g |_      \c_c ([rho] - 1)    / _|
 
   which is of the form
 
-    R = G[omega](v²/2g)K,
+    R = G[omega](v²/2g)K,
 
   where K depends only on the ratio of the sections of the stream and
   plane.
@@ -15453,7 +15419,7 @@ transmitted electrically are not included.
   For example, let c_c = 0.85, a value which is probable, if we allow
   that the sides of the pipe act as internal borders to an orifice. Then
 
-               /        [rho]      \²
+               /        [rho]      \²
     K = [rho] ( 1.176 --------- - 1 ).
                \      [rho] - 1    /
 
@@ -15477,7 +15443,7 @@ transmitted electrically are not included.
   when the stream is very much larger than the plane. Hence, in the
   expression
 
-    R = KG[omega]v²/2g,
+    R = KG[omega]v²/2g,
 
   K must be determined by experiment in each special case. For a
   cylindrical body putting [omega] for the section, c_c for the
@@ -15492,12 +15458,12 @@ transmitted electrically are not included.
 
   Then
 
-    R = K1G[omega]v²/2g,
+    R = K1G[omega]v²/2g,
 
   where
 
                 _                                           _
-               |  /  [rho]  \²  / 1     \²  /  [rho]      \² |
+               |  /  [rho]  \²  / 1     \²  /  [rho]      \² |
     K1 = [rho] | ( --------- ) ( --- - 1 ) ( --------- - 1 ) |.
                |_ \[rho] - 1/   \c_c    /   \[rho] - 1    / _|
 
@@ -15506,7 +15472,7 @@ transmitted electrically are not included.
 
   [Illustration: FIG. 166.]
 
-  § 165. _Distribution of Pressure on a Surface on which a Jet impinges
+  § 165. _Distribution of Pressure on a Surface on which a Jet impinges
   normally._--The principle of momentum gives readily enough the total
   or resultant pressure of a jet impinging on a plane surface, but in
   some cases it is useful to know the distribution of the pressure. The
@@ -15545,7 +15511,7 @@ transmitted electrically are not included.
   towards the interior of the jet, being subjected to a pressure greater
   than atmospheric pressure, will attain a less velocity, and so much
   less as they are nearer the centre of the jet. But the pressure can
-  in no case exceed the pressure v²/2g or h measured in feet of water,
+  in no case exceed the pressure v²/2g or h measured in feet of water,
   or the direction of motion of the water would be reversed, and there
   would be reflux. Hence the maximum intensity of the pressure of the
   jet on the plane is h ft. of water. If the pressure curve is drawn
@@ -15574,7 +15540,7 @@ transmitted electrically are not included.
   surface struck by a jet have been made by J. S. Beresford (_Prof.
   Papers on Indian Engineering_, No. cccxxii.), with a view to afford
   information as to the forces acting on the aprons of weirs.
-  Cylindrical jets ½ in. to 2 in. diameter, issuing from a vessel in
+  Cylindrical jets ½ in. to 2 in. diameter, issuing from a vessel in
   which the water level was constant, were allowed to fall vertically on
   a brass plate 9 in. in diameter. A small hole in the brass plate
   communicated by a flexible tube with a vertical pressure column.
@@ -15584,7 +15550,7 @@ transmitted electrically are not included.
   at that point of the area struck by the jet. When the aperture was
   exactly in the axis of the jet, the pressure column was very nearly
   level with the free surface in the reservoir supplying the jet; that
-  is, the pressure was very nearly v²/2g. As the aperture moved away
+  is, the pressure was very nearly v²/2g. As the aperture moved away
   from the axis of the jet, the pressure diminished, and it became
   insensibly small at a distance from the axis of the jet about equal to
   the diameter of the jet. Hence, roughly, the pressure due to the jet
@@ -15676,7 +15642,7 @@ transmitted electrically are not included.
   As the general form of the pressure curve has been already indicated,
   it may be assumed that its equation is of the form
 
-    y = ab^(-x²).
+    y = ab^(-x²).
 
   But it has already been shown that for x = 0, y = h, hence a = h. To
   determine the remaining constant, the other condition may be used,
@@ -15688,11 +15654,11 @@ transmitted electrically are not included.
         _/0
                 _
                /[oo]
-      = 2[pi]h |    b^(-x²)x dx
+      = 2[pi]h |    b^(-x²)x dx
               _/0
                         _      _
                        |        |[oo]
-      = ([pi]h/log_eb) |-b^(-x²)|
+      = ([pi]h/log_eb) |-b^(-x²)|
                        |_      _|0
 
       = [pi]h/log_e b.
@@ -15704,14 +15670,14 @@ transmitted electrically are not included.
     log_e b = ([pi]/2[omega]) [root](h/h1).
 
   Putting the value of b in (2) in eq. (1), and also r for the radius of
-  the jet at the orifice, so that [omega] = [pi]r², the equation to the
+  the jet at the orifice, so that [omega] = [pi]r², the equation to the
   pressure curve is
 
-                              h  x²
-    y = h[epsilon]^(-½) [root]-- --.
-                              h1 r²
+                              h  x²
+    y = h[epsilon]^(-½) [root]-- --.
+                              h1 r²
 
-  § 166. _Resistance of a Plane moving through a Fluid, or Pressure of a
+  § 166. _Resistance of a Plane moving through a Fluid, or Pressure of a
   Current on a Plane._--When a thin plate moves through the air, or
   through an indefinitely large mass of still water, in a direction
   normal to its surface, there is an excess of pressure on the anterior
@@ -15720,7 +15686,7 @@ transmitted electrically are not included.
   plate, G the density of the fluid, h the height due to the velocity,
   then the total resistance is expressed by the equation
 
-    R = fG[Omega]v²/2g pounds = fG[Omega]h;
+    R = fG[Omega]v²/2g pounds = fG[Omega]h;
 
   where f is a coefficient having about the value 1.3 for a plate moving
   in still fluid, and 1.8 for a current impinging on a fixed plane,
@@ -15765,7 +15731,7 @@ transmitted electrically are not included.
   in part or wholly due to centrifugal action.
 
   P. L. G. Dubuat (1734-1809) made experiments on a plane 1 ft. square,
-  moved in a straight line in water at 3 to 6½ ft. per second. Calling m
+  moved in a straight line in water at 3 to 6½ ft. per second. Calling m
   the coefficient of excess of pressure in front, and n the coefficient
   of deficiency of pressure behind, so that f = m + n, he found the
   following values:--
@@ -15788,7 +15754,7 @@ transmitted electrically are not included.
 
   [Illustration: FIG. 169.]
 
-  § 167. _Stanton's Experiments on the Pressure of Air on Surfaces._--At
+  § 167. _Stanton's Experiments on the Pressure of Air on Surfaces._--At
   the National Physical Laboratory, London, T. E. Stanton carried out a
   series of experiments on the distribution of pressure on surfaces in a
   current of air passing through an air trunk. These were on a small
@@ -15801,20 +15767,20 @@ transmitted electrically are not included.
   side of the central section. Similarly aeb is the distribution of
   pressure on the windward and afb on the leeward side of a diagonal
   section. The intensity of pressure at the centre of the plate on the
-  windward side was in all cases p = Gv²/2g lb. per sq. ft., where G is
+  windward side was in all cases p = Gv²/2g lb. per sq. ft., where G is
   the weight of a cubic foot of air and v the velocity of the current in
   ft. per sec. On the leeward side the negative pressure is uniform
   except near the edges, and its value depends on the form of the plate.
-  For a circular plate the pressure on the leeward side was 0.48 Gv²/2g
-  and for a rectangular plate 0.66 Gv²/2g. For circular or square plates
-  the resultant pressure on the plate was P = 0.00126 v² lb. per sq. ft.
+  For a circular plate the pressure on the leeward side was 0.48 Gv²/2g
+  and for a rectangular plate 0.66 Gv²/2g. For circular or square plates
+  the resultant pressure on the plate was P = 0.00126 v² lb. per sq. ft.
   where v is the velocity of the current in ft. per sec. On a long
   narrow rectangular plate the resultant pressure was nearly 60% greater
   than on a circular plate. In later tests on larger planes in free air,
   Stanton found resistances 18% greater than those observed with small
   planes in the air trunk.
 
-  § 168. _Case when the Direction of Motion is oblique to the
+  § 168. _Case when the Direction of Motion is oblique to the
   Plane._--The determination of the pressure between a fluid and surface
   in this case is of importance in many practical questions, for
   instance, in assigning the load due to wind pressure on sloping and
@@ -15848,15 +15814,15 @@ transmitted electrically are not included.
 
   A simpler and more convenient expression given by Colonel Duchemin is
 
-    R = 2P sin² [phi]/(1 + sin² [phi]).
+    R = 2P sin² [phi]/(1 + sin² [phi]).
 
   Consequently, the total pressure between the fluid and plane is
 
-    N = 2P sin [phi]/(1 + sin² [phi]) = 2P/(cosec [phi] + sin [phi]),
+    N = 2P sin [phi]/(1 + sin² [phi]) = 2P/(cosec [phi] + sin [phi]),
 
   and the lateral force is
 
-    L = 2P sin [phi] cos [phi]/(1 + sin² [phi]).
+    L = 2P sin [phi] cos [phi]/(1 + sin² [phi]).
 
   In 1872 some experiments were made for the Aeronautical Society on the
   pressure of air on oblique planes. These plates, of 1 to 2 ft. square,
@@ -15872,12 +15838,12 @@ transmitted electrically are not included.
   pressure on a normal surface:--
 
     +-----------------------------------+-------+-------+-------+------+
-    | Angle between Plane and Direction |  15°  |  20°  |  60°  |  90° |
+    | Angle between Plane and Direction |  15°  |  20°  |  60°  |  90° |
     |   of Blast                        |       |       |       |      |
     +-----------------------------------+-------+-------+-------+------+
     | Horizontal pressure R             | 0.4   | 0.61  | 2.73  | 3.31 |
     | Lateral pressure L                | 1.6   | 1.96  | 1.26  |  ..  |
-    | Normal pressure [root](L² + R²)   | 1.65  | 2.05  | 3.01  | 3.31 |
+    | Normal pressure [root](L² + R²)   | 1.65  | 2.05  | 3.01  | 3.31 |
     | Normal pressure by Duchemin's rule| 1.605 | 2.027 | 3.276 | 3.31 |
     +-----------------------------------+-------+-------+-------+------+
 
@@ -15914,7 +15880,7 @@ and gearing of a mill. With the motor is usually combined regulating
 machinery for adjusting the power and speed to the work done. This may
 be controlled in some cases by automatic governing machinery.
 
-§ 169. _Water Motors with Artificial Sources of Energy._--The great
+§ 169. _Water Motors with Artificial Sources of Energy._--The great
 convenience and simplicity of water motors has led to their adoption in
 certain cases, where no natural source of water power is available. In
 these cases, an artificial source of water power is created by using a
@@ -15926,7 +15892,7 @@ arrangements are most useful where a continuously acting steam engine
 stores up energy by pumping the water, while the work done by the
 hydraulic engines is done intermittently.
 
-  § 170. _Energy of a Water-fall._--Let H_t be the total fall of level
+  § 170. _Energy of a Water-fall._--Let H_t be the total fall of level
   from the point where the water is taken from a natural stream to the
   point where it is discharged into it again. Of this total fall a
   portion, which can be estimated independently, is expended in
@@ -15948,7 +15914,7 @@ hydraulic engines is done intermittently.
   volume described is Q cubic feet per second. Then the work done will
   be pQ = GHQ foot-pounds per second as before. (c) Or lastly, the water
   may be allowed to acquire the velocity v = [root](2gH) by its descent.
-  The kinetic energy of Q cubic feet will then be ½GQv²/g = GQH, and if
+  The kinetic energy of Q cubic feet will then be ½GQv²/g = GQH, and if
   the water is allowed to impinge on surfaces suitably curved which
   bring it finally to rest, it will impart to these the same energy as
   in the previous cases. Motors which receive energy mainly in the three
@@ -15959,12 +15925,12 @@ hydraulic engines is done intermittently.
   h3 = H, then, apart from energy wasted by friction or leakage or
   imperfection of the machine, the work done will be
 
-    GQh1 + pQ + (G/g) Q (v²/2g) = GQH foot pounds,
+    GQh1 + pQ + (G/g) Q (v²/2g) = GQH foot pounds,
 
   the same as if the water acted simply by its weight while descending H
   ft.
 
-§ 171. _Site for Water Motor._--Wherever a stream flows from a higher to
+§ 171. _Site for Water Motor._--Wherever a stream flows from a higher to
 a lower level it is possible to erect a water motor. The amount of power
 obtainable depends on the available head and the supply of water. In
 choosing a site the engineer will select a portion of the stream where
@@ -15985,7 +15951,7 @@ reservoirs or fed from glaciers are less variable than streams depending
 directly on rainfall, and are therefore advantageous for water-power
 purposes.
 
-  § 172. _Water Power at Holyoke, U.S.A._--About 85 m. from the mouth of
+  § 172. _Water Power at Holyoke, U.S.A._--About 85 m. from the mouth of
   the Connecticut river there was a fall of about 60 ft. in a short
   distance, forming what were called the Grand Rapids, below which the
   river turned sharply, forming a kind of peninsula on which the city of
@@ -16006,7 +15972,7 @@ purposes.
   The charge for the power water is at the rate of 20s. per h.p. per
   annum.
 
-§ 173. _Action of Water in a Water Motor._--Water motors may be divided
+§ 173. _Action of Water in a Water Motor._--Water motors may be divided
 into water-pressure engines, water-wheels and turbines.
 
 Water-pressure engines are machines with a cylinder and piston or ram,
@@ -16047,7 +16013,7 @@ adaptability to varying conditions of working.
 
 _Water-pressure Engines._
 
-§ 174. In these the water acts by pressure either due to the height of
+§ 174. In these the water acts by pressure either due to the height of
 the column in a supply pipe descending from a high-level reservoir, or
 created by pumping. Pressure engines were first used in mine-pumping on
 waterfalls of greater height than could at that time be utilized by
@@ -16120,7 +16086,7 @@ have not achieved much success. Where pressure engines are used
 simplicity is generally a first consideration, and economy is of less
 importance.
 
-  § 175. _Efficiency of Pressure Engines._--It is hardly possible to
+  § 175. _Efficiency of Pressure Engines._--It is hardly possible to
   form a theoretical expression for the efficiency of pressure engines,
   but some general considerations are useful. Consider the case of a
   long stroke hydraulic ram, which has a fairly constant velocity v
@@ -16128,25 +16094,25 @@ importance.
   of the stroke. Let r be the ratio of area of ram to area of valve
   passage, a ratio which may vary in ordinary cases from 4 to 12. Then
   the loss in shock of the water entering the cylinder will be (r -
-  1)²v²/2g in ft. of head. The friction in the supply pipe is also
-  proportional to v². The energy carried away in exhaust will be
-  proportional to v². Hence the total hydraulic losses may be taken to
-  be approximately [zeta]v²/2g ft., where [zeta] is a coefficient
+  1)²v²/2g in ft. of head. The friction in the supply pipe is also
+  proportional to v². The energy carried away in exhaust will be
+  proportional to v². Hence the total hydraulic losses may be taken to
+  be approximately [zeta]v²/2g ft., where [zeta] is a coefficient
   depending on the proportions of the machine. Let f be the friction of
   the ram packing and mechanism reckoned in lb. per sq. ft. of ram area.
   Then if the supply-pipe pressure driving the machine is p lb. per sq.
   ft., the effective working pressure will be
 
-    p - G[zeta]v²/2g - f lb. per sq. ft.
+    p - G[zeta]v²/2g - f lb. per sq. ft.
 
   Let A be the area of the ram in sq. ft., v its velocity in ft. per
   sec. The useful work done will be
 
-    (p - G[zeta]v²/2g - f)Av ft. lb. per sec.,
+    (p - G[zeta]v²/2g - f)Av ft. lb. per sec.,
 
   and the efficiency of the machine will be
 
-    [eta] = (p - G[zeta]v²/2g - f)/p.
+    [eta] = (p - G[zeta]v²/2g - f)/p.
 
   This shows that the efficiency increases with the pressure p, and
   diminishes with the speed v, other things being the same. If in
@@ -16163,7 +16129,7 @@ importance.
 
 [Illustration: FIG. 171.]
 
-§ 176. _Direct-Acting Hydraulic Lift_ (fig. 171).--This is the simplest
+§ 176. _Direct-Acting Hydraulic Lift_ (fig. 171).--This is the simplest
 of all kinds of hydraulic motor. A cage W is lifted directly by water
 pressure acting in a cylinder C, the length of which is a little greater
 than the lift. A ram or plunger R of the same length is attached to the
@@ -16196,7 +16162,7 @@ endless rope. The lift works under 73 ft. of head, and lifts 1350 lb at
   k = 0.00393 if the leathers are new or badly lubricated;
     = 0.00262 if the leathers are in good condition and well lubricated.
 
-  Since the total pressure on the ram is P = ¼[pi]d²p, the fraction of
+  Since the total pressure on the ram is P = ¼[pi]d²p, the fraction of
   the total pressure expended in overcoming the friction of the leathers
   is F/P = .005/d to .0033/d, d being in feet.
 
@@ -16216,14 +16182,14 @@ endless rope. The lift works under 73 ft. of head, and lifts 1350 lb at
 
     P2 = G(H_b - h)[Omega] + W + R - B + w(S - h) - wh - F.
 
-  If w = ½ G[Omega], P1 and P2 are constant throughout the stroke; and
+  If w = ½ G[Omega], P1 and P2 are constant throughout the stroke; and
   the moving force in ascending and descending is the same, if
 
     B = W + R + wS - G[Omega](H - H_b)/2.
 
   Using the values just found for w and B,
 
-    P1 = P2 = ½G[Omega](H - H_b) - F.
+    P1 = P2 = ½G[Omega](H - H_b) - F.
 
   Let W + R + wS + B = U, and let P be the constant accelerating force
   acting on the system, then the acceleration is (P/U)g. The velocity at
@@ -16231,11 +16197,11 @@ endless rope. The lift works under 73 ft. of head, and lifts 1350 lb at
 
     v = [root](2PgS/U);
 
-  and the mean velocity of ascent is ½v.
+  and the mean velocity of ascent is ½v.
 
 [Illustration: FIG. 172.]
 
-§ 177. _Armstrong's Hydraulic Jigger._--This is simply a single-acting
+§ 177. _Armstrong's Hydraulic Jigger._--This is simply a single-acting
 hydraulic cylinder and ram, provided with sheaves so as to give motion
 to a wire rope or chain. It is used in various forms of lift and crane.
 Fig. 172 shows the arrangement. A hydraulic ram or plunger B works in a
@@ -16248,7 +16214,7 @@ three pairs of pulleys the free end of the rope has a movement equal to
 six times the stroke of the ram, the force exerted being in the inverse
 proportion.
 
-§ 178. _Rotative Hydraulic Engines._--Valve-gear mechanism similar in
+§ 178. _Rotative Hydraulic Engines._--Valve-gear mechanism similar in
 principle to that of steam engines can be applied to actuate the
 admission and discharge valves, and the pressure engine is then
 converted into a continuously-acting motor.
@@ -16265,8 +16231,8 @@ converted into a continuously-acting motor.
   .5. Let v be the mean velocity of the piston, then its diameter d is
   given by the relation
 
-    Q = [pi]d²v/4 in double-acting engines,
-      = [pi]d²v/8 in single-acting engines.
+    Q = [pi]d²v/4 in double-acting engines,
+      = [pi]d²v/8 in single-acting engines.
 
   If there are n cylinders put Q/n for Q in these equations.
 
@@ -16280,7 +16246,7 @@ the driving effort on the crank pin is very uniform.
 
 [Illustration: FIG. 173.]
 
-  _Brotherhood Hydraulic Engine._--Three cylinders at angles of 120°
+  _Brotherhood Hydraulic Engine._--Three cylinders at angles of 120°
   with each other are formed in one casting with the frame. The
   plungers are hollow trunks, and the connecting rods abut in
   cylindrical recesses in them and are connected to a common crank pin.
@@ -16290,7 +16256,7 @@ the driving effort on the crank pin is very uniform.
   an admission or exhaust port. The blank parts of the circular valve
   close the admission and exhaust ports alternately. The fixed valve
   face is of lignum vitae in a metal recess, and the revolving valve of
-  gun-metal. In the case of a small capstan engine the cylinders are 3½
+  gun-metal. In the case of a small capstan engine the cylinders are 3½
   in. diameter and 3 in. stroke. At 40 revs. per minute, the piston
   speed is 31 ft. per minute. The ports are 1 in. diameter or 1/12 of
   the piston area, and the mean velocity in the ports 6.4 ft. per sec.
@@ -16350,10 +16316,10 @@ the driving effort on the crank pin is very uniform.
     Weight lifted,  Chain   427   633   745   857   969  1081  1193
       in lb.         only
 
-    Water used, in    7½     10    14    16    17    20    21    22
+    Water used, in    7½     10    14    16    17    20    21    22
       gallons
 
-§ 179. _Accumulator Machinery._--It has already been pointed out that it
+§ 179. _Accumulator Machinery._--It has already been pointed out that it
 is in some cases convenient to use a steam engine to create an
 artificial head of water, which is afterwards employed in driving
 water-pressure machinery. Where power is required intermittently, for
@@ -16413,7 +16379,7 @@ do not require to be of large size, as the pressure is so great.
   in., is
 
     [pi]
-    ---- p d²S foot-pounds.
+    ---- p d²S foot-pounds.
      4
 
   Thus, if the ram is 9 in., the stroke 20 ft., and the pressure 800 lb.
@@ -16423,7 +16389,7 @@ do not require to be of large size, as the pressure is so great.
   the pumping engine replaces water as soon as it is drawn off, the
   working capacity of the accumulator is very much greater than this.
   Tweddell found that an accumulator charged at 1250 lb. discharged at
-  1225 lb. per sq. in. Hence the friction was equivalent to 12½ lb. per
+  1225 lb. per sq. in. Hence the friction was equivalent to 12½ lb. per
   sq. in. and the efficiency 98%.
 
   When a very great pressure is required a differential accumulator
@@ -16431,8 +16397,8 @@ do not require to be of large size, as the pressure is so great.
   ends of the cylinder, but is of different diameters at the two ends, A
   and B. Hence if d1, d2 are the diameters of the ram in inches and p
   the required pressure in lb. per sq. in., the load required is
-  ¼p[pi](d1² - d2²). An accumulator of this kind used with riveting
-  machines has d1 = 5½ in., d2 = 4¾ in. The pressure is 2000 lb. per sq.
+  ¼p[pi](d1² - d2²). An accumulator of this kind used with riveting
+  machines has d1 = 5½ in., d2 = 4¾ in. The pressure is 2000 lb. per sq.
   in. and the load 5.4 tons.
 
   [Illustration: FIG. 178.]
@@ -16451,7 +16417,7 @@ do not require to be of large size, as the pressure is so great.
 
 _Water Wheels._
 
-§ 180. _Overshot and High Breast Wheels._--When a water fall ranges
+§ 180. _Overshot and High Breast Wheels._--When a water fall ranges
 between 10 and 70 ft. and the water supply is from 3 to 25 cub. ft. per
 second, it is possible to construct a bucket wheel on which the water
 acts chiefly by its weight. If the variation of the head-water level
@@ -16482,7 +16448,7 @@ supply is given to the wheel in all positions of the head-water level.
   If the peripheral velocity of the water wheel is too great, water is
   thrown out of the buckets before reaching the bottom of the fall. In
   practice, the circumferential velocity of water wheels of the kind now
-  described is from 4½ to 10 ft. per second, about 6 ft. being the usual
+  described is from 4½ to 10 ft. per second, about 6 ft. being the usual
   velocity of good iron wheels not of very small size. In order that the
   water may enter the buckets easily, it must have a greater velocity
   than the wheel. Usually the velocity of the water at the point where
@@ -16490,7 +16456,7 @@ supply is given to the wheel in all positions of the head-water level.
   this it must enter the wheel at a point 16 to 27 in. below the
   head-water level. Hence the diameter of an overshot wheel may be
 
-    D = H - 1(1/3) to H - 2¼ ft.
+    D = H - 1(1/3) to H - 2¼ ft.
 
   Overshot and high breast wheels work badly in backwater, and hence if
   the tail-water level varies, it is better to reduce the diameter of
@@ -16503,7 +16469,7 @@ supply is given to the wheel in all positions of the head-water level.
   Let v be the peripheral velocity of the wheel. Then the capacity of
   that portion of the wheel which passes the sluice in one second is
 
-    Q1 = vb(Dd - d²)/D
+    Q1 = vb(Dd - d²)/D
        = v b d nearly,
 
   b being the breadth of the wheel between the shrouds. If, however,
@@ -16525,9 +16491,9 @@ supply is given to the wheel in all positions of the head-water level.
   the thickness of the sheet of water entering.
 
   For a wooden bucket (fig. 180, A), take ab = distance between two
-  buckets on periphery of wheel. Make ed = ½ eb and bc = 6/5 to 5/4
+  buckets on periphery of wheel. Make ed = ½ eb and bc = 6/5 to 5/4
   ab. Join cd. For an iron bucket (fig. 180, B), take ed = 1/3 eb; bc =
-  6/5 ab. Draw cO making an angle of 10° to 15° with the radius at c.
+  6/5 ab. Draw cO making an angle of 10° to 15° with the radius at c.
   On Oc take a centre giving a circular arc passing near d, and round
   the curve into the radial part of the bucket de.
 
@@ -16553,13 +16519,13 @@ working.
 
 [Illustration: FIG. 181.]
 
-§ 181. _Poncelet Water Wheel._--When the fall does not exceed 6 ft., the
+§ 181. _Poncelet Water Wheel._--When the fall does not exceed 6 ft., the
 best water motor to adopt in many cases is the Poncelet undershot water
 wheel. In this the water acts very nearly in the same way as in a
 turbine, and the Poncelet wheel, although slightly less efficient than
 the best turbines, in normal conditions of working, is superior to most
 of them when working with a reduced supply of water. A general notion of
-the action of the water on a Poncelet wheel has already been given in §
+the action of the water on a Poncelet wheel has already been given in §
 159. Fig. 181 shows its construction. The water penned back between the
 side walls of the wheel pit is allowed to flow to the wheel under a
 movable sluice, at a velocity nearly equal to the velocity due to the
@@ -16584,9 +16550,9 @@ nearly the whole of its original kinetic energy.
   cast iron with flanges to receive the buckets. The buckets may be of
   iron 1/8 in. thick bolted to the flanges with 5/16 in. bolts.
 
-  Let H´ be the fall measured from the free surface of the head-water to
+  Let H´ be the fall measured from the free surface of the head-water to
   the point F where the mean layer enters the wheel; then the velocity
-  at which the water enters is v = [root](2gH´), and the best
+  at which the water enters is v = [root](2gH´), and the best
   circumferential velocity of the wheel is V = 0.55f to 0.6v. The number
   of rotations of the wheel per second is N = V/[pi]D. The thickness
   of the sheet of water entering the wheel is very important. The best
@@ -16609,14 +16575,14 @@ nearly the whole of its original kinetic energy.
   wheels. One of the simplest is that shown in figs. 181, 182.
 
   Let OA (fig. 181) be the vertical radius of the wheel. Set off OB, OD
-  making angles of 15° with OA. Then BD may be the length of the close
+  making angles of 15° with OA. Then BD may be the length of the close
   breasting fitted to the wheel. Draw the bottom of the head face BC at
-  a slope of 1 in 10. Parallel to this, at distances ½e and e, draw EF
+  a slope of 1 in 10. Parallel to this, at distances ½e and e, draw EF
   and GH. Then EF is the mean layer and GH the surface layer entering
-  the wheel. Join OF, and make OFK = 23°. Take FK = 0.5 to 0.7 H. Then K
+  the wheel. Join OF, and make OFK = 23°. Take FK = 0.5 to 0.7 H. Then K
   is the centre from which the bucket curve is struck and KF is the
   radius. The depth of the shrouds must be sufficient to prevent the
-  water from rising over the top of the float. It is ½H to 2/3 H. The
+  water from rising over the top of the float. It is ½H to 2/3 H. The
   number of buckets is not very important. They are usually 1 ft. apart
   on the circumference of the wheel.
 
@@ -16633,12 +16599,12 @@ nearly the whole of its original kinetic energy.
 
 _Turbines._
 
-§ 182. The name turbine was originally given in France to any water
+§ 182. The name turbine was originally given in France to any water
 motor which revolved in a horizontal plane, the axis being vertical. The
 rapid development of this class of motors dates from 1827, when a prize
-was offered by the Société d'Encouragement for a motor of this kind,
+was offered by the Société d'Encouragement for a motor of this kind,
 which should be an improvement on certain wheels then in use. The prize
-was ultimately awarded to Benoît Fourneyron (1802-1867), whose turbine,
+was ultimately awarded to Benoît Fourneyron (1802-1867), whose turbine,
 but little modified, is still constructed.
 
 _Classification of Turbines._--In some turbines the whole available
@@ -16716,7 +16682,7 @@ were placed at the bottom of the fall.
     \_________________________________\/_______________________________/
                Simple turbines; twin turbines; compound turbines.
 
-  § 183. _The Simple Reaction Wheel._--It has been shown, in § 162,
+  § 183. _The Simple Reaction Wheel._--It has been shown, in § 162,
   that, when water issues from a vessel, there is a reaction on the
   vessel tending to cause motion in a direction opposite to that of the
   jet. This principle was applied in a rotating water motor at a very
@@ -16740,18 +16706,18 @@ were placed at the bottom of the fall.
   when the machine rotates the water in the arms rotates also, and is in
   the condition of a forced vortex, all the particles having the same
   angular velocity. Consequently the pressure in the arms at the
-  orifices is H + [alpha]²r²/2g ft. of water, and the velocity of
-  discharge through the orifices is v = [root](2gH + [alpha]²r²). If the
+  orifices is H + [alpha]²r²/2g ft. of water, and the velocity of
+  discharge through the orifices is v = [root](2gH + [alpha]²r²). If the
   total area of the orifices is [omega], the quantity discharged from
   the wheel per second is
 
-    Q = [omega]v = [omega] [root](2gH + [alpha]²r²).
+    Q = [omega]v = [omega] [root](2gH + [alpha]²r²).
 
   While the water passes through the orifices with the velocity v, the
   orifices are moving in the opposite direction with the velocity
   [alpha]r. The absolute velocity of the water is therefore
 
-    v - [alpha]r = [root](2gH + [alpha]²r²) - [alpha]r.
+    v - [alpha]r = [root](2gH + [alpha]²r²) - [alpha]r.
 
   The momentum generated per second is (GQ/g)(v - [alpha]r), which is
   numerically equal to the force driving the motor at the radius r. The
@@ -16762,15 +16728,15 @@ were placed at the bottom of the fall.
   The work expended by the water fall is GQH foot-pounds per second.
   Consequently the efficiency of the motor is
 
-            (v - [alpha]r) [alpha]r   {[root]{2gH + [alpha]²r²]} - [alpha]r} [alpha]r
+            (v - [alpha]r) [alpha]r   {[root]{2gH + [alpha]²r²]} - [alpha]r} [alpha]r
     [eta] = ----------------------- = -----------------------------------------------.
                       gH                                    gH
 
   Let
 
-                                             gH         g²H²
-    [root]{2gH + [alpha]²r²} = [alpha]r + -------- - ----------- ...
-                                          [alpha]r   2[alpha]³r³
+                                             gH         g²H²
+    [root]{2gH + [alpha]²r²} = [alpha]r + -------- - ----------- ...
+                                          [alpha]r   2[alpha]³r³
 
   then
 
@@ -16785,40 +16751,40 @@ were placed at the bottom of the fall.
   best efficiency is reached when [alpha]r = [root](2gH). Then the
   efficiency apart from friction is
 
-    [eta] = {[root](2[alpha]²r²) - [alpha]r} [alpha]r/gH
-          = 0.414 [alpha]²r²/gH = 0.828,
+    [eta] = {[root](2[alpha]²r²) - [alpha]r} [alpha]r/gH
+          = 0.414 [alpha]²r²/gH = 0.828,
 
   about 17% of the energy of the fall being carried away by the water
   discharged. The actual efficiency realized appears to be about 60%, so
   that about 21% of the energy of the fall is lost in friction, in
   addition to the energy carried away by the water.
 
-  § 184. _General Statement of Hydrodynamical Principles necessary for
+  § 184. _General Statement of Hydrodynamical Principles necessary for
   the Theory of Turbines._
 
   (a) When water flows through any pipe-shaped passage, such as the
   passage between the vanes of a turbine wheel, the relation between the
-  changes of pressure and velocity is given by Bernoulli's theorem (§
+  changes of pressure and velocity is given by Bernoulli's theorem (§
   29). Suppose that, at a section A of such a passage, h1 is the
   pressure measured in feet of water, v1 the velocity, and z1 the
   elevation above any horizontal datum plane, and that at a section B
   the same quantities are denoted by h2, v2, z2. Then
 
-    h1 - h2 = (v2² - v1²)/2g + z2 - z1.   (1)
+    h1 - h2 = (v2² - v1²)/2g + z2 - z1.   (1)
 
   If the flow is horizontal, z2 = z1; and
 
-    h1 - h2 = (v2² - v1²)/2g.   (la)
+    h1 - h2 = (v2² - v1²)/2g.   (la)
 
   (b) When there is an abrupt change of section of the passage, or an
   abrupt change of section of the stream due to a contraction, then, in
   applying Bernoulli's equation allowance must be made for the loss of
-  head in shock (§ 36). Let v1, v2 be the velocities before and after
+  head in shock (§ 36). Let v1, v2 be the velocities before and after
   the abrupt change, then a stream of velocity v1 impinges on a stream
   at a velocity v2, and the relative velocity is v1 - v2. The head lost
-  is (v1 - v2)²/2g. Then equation (1a) becomes
+  is (v1 - v2)²/2g. Then equation (1a) becomes
 
-    h1 - h2 = (v1² - v2²)/2g - (v1 - v2)²/2g = v2(v1 - v2)/g   (2)
+    h1 - h2 = (v1² - v2²)/2g - (v1 - v2)²/2g = v2(v1 - v2)/g   (2)
 
   [Illustration: FIG. 184.]
 
@@ -16875,7 +16841,7 @@ were placed at the bottom of the fall.
 
     T = Ma = (GQ/g)(w1r1 - w2r2) [alpha] foot-pounds per second.   (5)
 
-  § 185. _Total and Available Fall._--Let H_t be the total difference of
+  § 185. _Total and Available Fall._--Let H_t be the total difference of
   level from the head-water to the tail-water surface. Of this total
   head a portion is expended in overcoming the resistances of the head
   race, tail race, supply pipe, or other channel conveying the water.
@@ -16894,7 +16860,7 @@ were placed at the bottom of the fall.
   for a head H - [h], but the efficiency of the turbine for the
   head H.
 
-  § 186. _Gross Efficiency and Hydraulic Efficiency of a Turbine._--Let
+  § 186. _Gross Efficiency and Hydraulic Efficiency of a Turbine._--Let
   T_d be the useful work done by the turbine, in foot-pounds per second,
   T_t the work expended in friction of the turbine shaft, gearing, &c.,
   a quantity which varies with the local conditions in which the turbine
@@ -16947,7 +16913,7 @@ were placed at the bottom of the fall.
 
 [Illustration: FIG. 189.]
 
-§ 187. _General Description of a Reaction Turbine._--Professor James
+§ 187. _General Description of a Reaction Turbine._--Professor James
 Thomson's inward flow or vortex turbine has been selected as the type of
 reaction turbines. It is one of the best in normal conditions of
 working, and the mode of regulation introduced is decidedly superior to
@@ -16961,7 +16927,7 @@ on entering the case distributes itself through a rectangular supply
 chamber SC, from which it finds its way equally to the four guide-blade
 passages G, G, G, G. In these passages it acquires a velocity about
 equal to that due to half the fall, and is directed into the wheel at an
-angle of about 10° or 12° with the tangent to its circumference. The
+angle of about 10° or 12° with the tangent to its circumference. The
 wheel W receives the water in equal proportions from each guide-blade
 passage. It consists of a centre plate p (fig. 189) keyed on the shaft
 aa, which passes through stuffing boxes on the suction pipes. On each
@@ -17002,7 +16968,7 @@ very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal.
 
   [Illustration: FIG. 191.]
 
-  § 188. _Hydraulic Power at Niagara._--The largest development of
+  § 188. _Hydraulic Power at Niagara._--The largest development of
   hydraulic power is that at Niagara. The Niagara Falls Power Company
   have constructed two power houses on the United States side, the first
   with 10 turbines of 5000 h.p. each, and the second with 10 turbines of
@@ -17026,13 +16992,13 @@ very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal.
   35,000 h.p. and are constructing another to furnish 100,000 h.p. The
   mean flow of the Niagara river is about 222,000 cub. ft. per second
   with a fall of 160 ft. The works in progress if completed will utilize
-  650,000 h.p. and require 48,000 cub. ft. per second or 21½% of the
+  650,000 h.p. and require 48,000 cub. ft. per second or 21½% of the
   mean flow of the river (Unwin, "The Niagara Falls Power Stations,"
   _Proc. Inst. Mech. Eng._, 1906).
 
   [Illustration: FIG. 192.]
 
-  § 189. _Different Forms of Turbine Wheel._--The wheel of a turbine or
+  § 189. _Different Forms of Turbine Wheel._--The wheel of a turbine or
   part of the machine on which the water acts is an annular space,
   furnished with curved vanes dividing it into passages exactly or
   roughly rectangular in cross section. For radial flow turbines the
@@ -17050,7 +17016,7 @@ very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal.
 
   [Illustration: FIG. 193.]
 
-  § 190. _Velocity of Whirl and Velocity of Flow._--Let acb (fig. 193)
+  § 190. _Velocity of Whirl and Velocity of Flow._--Let acb (fig. 193)
   be the path of the particles of water in a turbine wheel. That path
   will be in a plane normal to the axis of rotation in radial flow
   turbines, and on a cylindrical surface in axial flow turbines. At any
@@ -17090,7 +17056,7 @@ very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal.
 
   and, for an axial flow turbine,
 
-    [Omega]_o = [Omega]_i = [pi](r2² - r1²).   (12c)
+    [Omega]_o = [Omega]_i = [pi](r2² - r1²).   (12c)
 
   [Illustration: FIG. 194.]
 
@@ -17121,7 +17087,7 @@ very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal.
 
     In inward flow turbines,  u_o = u_i = 0.125 [root](2gH).
 
-  § 191. _Speed of the Wheel._--The best speed of the wheel depends
+  § 191. _Speed of the Wheel._--The best speed of the wheel depends
   partly on the frictional losses, which the ordinary theory of turbines
   disregards. It is best, therefore, to assume for V_o and V_i values
   which experiment has shown to be most advantageous.
@@ -17158,19 +17124,19 @@ very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal.
   the angles the wheel vanes make with the inlet and outlet surfaces;
   then
 
-    v_o² = [root](v_(ro)² + V_o² - 2V_o v_(ro) cos [phi])
+    v_o² = [root](v_(ro)² + V_o² - 2V_o v_(ro) cos [phi])
 
-    v_i = [root](v_(ri)² + V_o² - 2V_i v_(ri) cos [theta]),   (13)
+    v_i = [root](v_(ri)² + V_o² - 2V_i v_(ri) cos [theta]),   (13)
 
   equations which may be used to determine [phi] and [theta].
 
   [Illustration: FIG. 195.]
 
-  § 192. _Condition determining the Angle of the Vanes at the Outlet
+  § 192. _Condition determining the Angle of the Vanes at the Outlet
   Surface of the Wheel._--It has been shown that, when the water leaves
   the wheel, it should have no tangential velocity, if the efficiency is
   to be as great as possible; that is, w_o = 0. Hence, from (10), cos
-  [beta] = 0, [beta] = 90°, U_o = V_o, and the direction of the water's
+  [beta] = 0, [beta] = 90°, U_o = V_o, and the direction of the water's
   motion is normal to the outlet surface of the wheel, radial in radial
   flow, and axial in axial flow turbines.
 
@@ -17185,7 +17151,7 @@ very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal.
   flow u_o and velocity of the wheel V_o are known. When [phi] is thus
   determined,
 
-    v_(ro) = U_o cosec [phi] = V_o [root](1 + u_o²/V_o²).   (14a)
+    v_(ro) = U_o cosec [phi] = V_o [root](1 + u_o²/V_o²).   (14a)
 
   _Correction of the Angle [phi] to allow for Thickness of Vanes._--In
   determining [phi], it is most convenient to calculate its value
@@ -17196,13 +17162,13 @@ very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal.
 
   Let
 
-    [phi]´ = tan^(-1)(u_o/V_o) = tan^(-1)(Q/[Omega]_o V_o)
+    [phi]´ = tan^(-1)(u_o/V_o) = tan^(-1)(Q/[Omega]_o V_o)
 
   be the first or approximate value of [phi], and let t be the
   thickness, and n the number of wheel vanes which reach the outlet
   surface of the wheel. As the vanes cut the outlet surface
-  approximately at the angle [phi]´, their width measured on that
-  surface is t cosec [phi]´. Hence the space occupied by the vanes on
+  approximately at the angle [phi]´, their width measured on that
+  surface is t cosec [phi]´. Hence the space occupied by the vanes on
   the outlet surface is
 
   For
@@ -17218,7 +17184,7 @@ very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal.
 
     [phi] = tan [Q/V_o ([Omega]_o - [omega]) ].   (16)
 
-  § 193. _Head producing Velocity with which the Water enters the
+  § 193. _Head producing Velocity with which the Water enters the
   Wheel._--Consider the variation of pressure in a wheel passage, which
   satisfies the condition that the sections change so gradually that
   there is no loss of head in shock. When the flow is in a horizontal
@@ -17248,33 +17214,33 @@ very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal.
   Bernoulli's theorem, the change of pressure due to flow through the
   wheel passages is given by the equation
 
-    h´_i + v_(ri)²/2g = h´_o + v_(ro)²/2g;
+    h´_i + v_(ri)²/2g = h´_o + v_(ro)²/2g;
 
-    h´_i - h´_o = (v_(ro)² - v_(ri)²)/2g.
+    h´_i - h´_o = (v_(ro)² - v_(ri)²)/2g.
 
   The variation of pressure due to rotation in a forced vortex is
 
-    h´´_i - h´´_o = (V_i² - V_o²)/2g.
+    h´´_i - h´´_o = (V_i² - V_o²)/2g.
 
   Consequently the whole difference of pressure at the inlet and outlet
   surfaces of the wheel is
 
-    h_i - h_o = h´_i + h´´_i - h´_o - h´´_o
-       = (V_i² - V_o²)/2g + (v_(ro)² - v_(ri)²)/2g.   (17)
+    h_i - h_o = h´_i + h´´_i - h´_o - h´´_o
+       = (V_i² - V_o²)/2g + (v_(ro)² - v_(ri)²)/2g.   (17)
 
   _Case 1. Axial Flow Turbines._--V_i = V_o; and the first term on the
   right, in equation 17, disappears. Adding, however, the work of
   gravity due to a fall of d ft. in passing through the wheel,
 
-    h_i - h_o = (v_(ro)² - v_(ri)²)/2g - d.   (17a)
+    h_i - h_o = (v_(ro)² - v_(ri)²)/2g - d.   (17a)
 
   _Case 2. Outward Flow Turbines._--The inlet radius is less than the
-  outlet radius, and (V_i² - V_o²)/2g is negative. The centrifugal head
+  outlet radius, and (V_i² - V_o²)/2g is negative. The centrifugal head
   diminishes the pressure at the inlet surface, and increases the
   velocity with which the water enters the wheel. This somewhat
   increases the frictional loss of head. Further, if the wheel varies in
-  velocity from variations in the useful work done, the quantity (V_i² -
-  V_o²)/2g increases when the turbine speed increases, and vice versa.
+  velocity from variations in the useful work done, the quantity (V_i² -
+  V_o²)/2g increases when the turbine speed increases, and vice versa.
   Consequently the flow into the turbine increases when the speed
   increases, and diminishes when the speed diminishes, and this again
   augments the variation of speed. The action of the centrifugal head in
@@ -17303,42 +17269,42 @@ very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal.
   [h], of this h_i - h_o is expended in overcoming the pressure
   in the wheel, the velocity of flow into the wheel is
 
-    v_i = c_v[root]{2g(H - [h] - (V_i² - V_o²/2g + (v{r0}² - v_(ri)²)/2g)},   (18)
+    v_i = c_v[root]{2g(H - [h] - (V_i² - V_o²/2g + (v{r0}² - v_(ri)²)/2g)},   (18)
 
   where c_v may be taken 0.96.
 
   From (14a),
 
-    v{r0} = V_o [root](1 + u_o²/V_o²).
+    v{r0} = V_o [root](1 + u_o²/V_o²).
 
   It will be shown immediately that
 
     v_(ri) = u_i cosec [theta];
 
-  or, as this is only a small term, and [theta] is on the average 90°,
+  or, as this is only a small term, and [theta] is on the average 90°,
   we may take, for the present purpose, v_(ri) = u_i nearly.
 
   Inserting these values, and remembering that for an axial flow turbine
   V_i = V_o, [h] = 0, and the fall d in the wheel is to be
   added,
                      _                                        _
-                    |     /    V_i²  /    u_o² \    u_i²    \  |
+                    |     /    V_i²  /    u_o² \    u_i²    \  |
     v_i = c_v[root] | 2g ( H - ---- ( 1 + ----  ) + ---- - d ) |.
-                    |_    \     2g   \    V_o² /     2g     / _|
+                    |_    \     2g   \    V_o² /     2g     / _|
 
   For an outward flow turbine,
                      _                                           _
-                    |     /          V_i²  /    u_o² \    u_i² \  |
+                    |     /          V_i²  /    u_o² \    u_i² \  |
     v_i = c_v[root] | 2g ( H - [h] - ---- ( 1 + ----  ) + ----  ) |.
-                    |_    \           2g   \    V_i² /     2g  / _|
+                    |_    \           2g   \    V_i² /     2g  / _|
 
   For an inward flow turbine,
                      _                                     _
-                    |    {     V_i²  /    u_o² \    u_i² }  |
+                    |    {     V_i²  /    u_o² \    u_i² }  |
     v_i = c_v[root] | 2g { H - ---- ( 1 + ----  ) + ---- }  |.
-                    |_   {      2g   \    V_i² /     2g  } _|
+                    |_   {      2g   \    V_i² /     2g  } _|
 
-  § 194. _Angle which the Guide-Blades make with the Circumference of
+  § 194. _Angle which the Guide-Blades make with the Circumference of
   the Wheel._--At the moment the water enters the wheel, the radial
   component of the velocity is u_i, and the velocity is v_i. Hence, if
   [gamma] is the angle between the guide-blades and a tangent to the
@@ -17351,7 +17317,7 @@ very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal.
 
   [Illustration: FIG. 196.]
 
-  § 195. _Condition determining the Angle of the Vanes at the Inlet
+  § 195. _Condition determining the Angle of the Vanes at the Inlet
   Surface of the Wheel._--The single condition necessary to be satisfied
   at the inlet surface of the wheel is that the water should enter the
   wheel without shock. This condition is satisfied if the direction of
@@ -17365,7 +17331,7 @@ very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal.
   angle between v_(ri) and V_i is the angle [theta] which the vanes
   should make with the inlet surface of the wheel.
 
-  § 196. _Example of the Method of designing a Turbine. Professor James
+  § 196. _Example of the Method of designing a Turbine. Professor James
   Thomson's Inward Flow Turbine._--
 
   Let
@@ -17400,7 +17366,7 @@ very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal.
     d_o = r_o.
 
   If, to obtain considerable steadying action of the centrifugal head,
-  r_i = 2r_o, then d_i = ½d_o.
+  r_i = 2r_o, then d_i = ½d_o.
 
   _Speed of the Wheel._--Let V_i = 0.66 [root](2gH), or the speed due to
   half the fall nearly. Then the number of rotations of the turbine per
@@ -17416,15 +17382,15 @@ very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal.
 
     Tan[phi] = u_o/V_o = 0.125/0.33 = .3788;
 
-    [phi] = 21º nearly.
+    [phi] = 21º nearly.
 
   If this value is revised for the vane thickness it will ordinarily
-  become about 25º.
+  become about 25º.
 
   _Velocity with which the Water enters the Wheel._--The head producing
   the velocity is
 
-    H - (V_i²/2g) (1 + u_o²/V_i²) + u_i²/2g
+    H - (V_i²/2g) (1 + u_o²/V_i²) + u_i²/2g
       = H {1 - .4356 (1 + 0.0358) + .0156}
       = 0.5646H.
 
@@ -17436,7 +17402,7 @@ very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal.
 
     Sin [gamma] = u_i/v_i = 0.125/0.721 = 0.173;
 
-    [gamma] = 10° nearly.
+    [gamma] = 10° nearly.
 
   _Tangential Velocity of Water entering Wheel._
 
@@ -17446,11 +17412,11 @@ very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal.
 
     Cot [theta] = (w_i - V_i)/u_i = (.7101 - .66)/.125 = .4008;
 
-    [theta] = 68° nearly.
+    [theta] = 68° nearly.
 
   _Hydraulic Efficiency of Wheel._
 
-    [eta] = w_iV_i/gH = .7101 × .66 × 2
+    [eta] = w_iV_i/gH = .7101 × .66 × 2
           = 0.9373.
 
   This, however, neglects the friction of wheel covers and leakage. The
@@ -17459,7 +17425,7 @@ very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal.
 
 _Impulse and Partial Admission Turbines._
 
-§ 197. The principal defect of most turbines with complete admission is
+§ 197. The principal defect of most turbines with complete admission is
 the imperfection of the arrangements for working with less than the
 normal supply. With many forms of reaction turbine the efficiency is
 considerably reduced when the regulating sluices are partially
@@ -17525,7 +17491,7 @@ be kept down to a manageable value.
 
 [Illustration: FIG. 199.]
 
-  § 198. _General Description of an Impulse Turbine or Turbine with Free
+  § 198. _General Description of an Impulse Turbine or Turbine with Free
   Deviation._--Fig. 197 shows a general sectional elevation of a Girard
   turbine, in which the flow is axial. The water, admitted above a
   horizontal floor, passes down through the annular wheel containing the
@@ -17566,15 +17532,15 @@ be kept down to a manageable value.
 
   As an example of a partial admission radial flow impulse turbine, a
   100 h.p. turbine at Immenstadt may be taken. The fall varies from 538
-  to 570 ft. The external diameter of the wheel is 4½ ft., and its
+  to 570 ft. The external diameter of the wheel is 4½ ft., and its
   internal diameter 3 ft. 10 in. Normal speed 400 revs. per minute.
   Water is discharged into the wheel by a single nozzle, shown in fig.
   202 with its regulating apparatus and some of the vanes. The water
-  enters the wheel at an angle of 22° with the direction of motion, and
-  the final angle of the wheel vanes is 20°. The efficiency on trial was
+  enters the wheel at an angle of 22° with the direction of motion, and
+  the final angle of the wheel vanes is 20°. The efficiency on trial was
   from 75 to 78%.
 
-  § 199. _Theory of the Impulse Turbine._--The theory of the impulse
+  § 199. _Theory of the Impulse Turbine._--The theory of the impulse
   turbine does not essentially differ from that of the reaction turbine,
   except that there is no pressure in the wheel opposing the discharge
   from the guide-blades. Hence the velocity with which the water enters
@@ -17587,7 +17553,7 @@ be kept down to a manageable value.
   Q_m be the maximum supply of water, r1, r2 the internal and external
   radii of the wheel at the inlet surface; then
 
-    u_i = Q_m/{[pi](r2² - r1²)}.
+    u_i = Q_m/{[pi](r2² - r1²)}.
 
   The value of u_i may be about 0.45 [root]{2g(H - [eta][h])},
   whence r1, r2 can be determined.
@@ -17596,7 +17562,7 @@ be kept down to a manageable value.
 
     sin [gamma] = u_i/v_i = 0.45/0.94 = .48;
 
-    [gamma] = 29°.
+    [gamma] = 29°.
 
   The value of u_i should, however, be corrected for the space occupied
   by the guide-blades.
@@ -17613,7 +17579,7 @@ be kept down to a manageable value.
 
     cot [theta] = (w_i - V_i)/u_i = (0.82 - 0.5)/0.45 = .71;
 
-    [theta] = 55°.
+    [theta] = 55°.
 
   The relative velocity of the water striking the vane at the inlet edge
   is v_(ri) = u_i cosec[theta] = 1.22 u_i. This relative velocity remains
@@ -17623,7 +17589,7 @@ be kept down to a manageable value.
 
   If the final velocity of the water is axial, then
 
-    cos [phi] = V_o/v_(ro) = V_i/v_(ri) = 0.5/(1.22 × 0.45) = cos 24º 23´.
+    cos [phi] = V_o/v_(ro) = V_i/v_(ri) = 0.5/(1.22 × 0.45) = cos 24º 23´.
 
   This should be corrected for the vane thickness. Neglecting this, u_o
   = v_(ro) sin [phi] = v_(ri) sin [phi] = u_i cosec [theta] sin [phi] =
@@ -17634,7 +17600,7 @@ be kept down to a manageable value.
 
   [Illustration: FIG. 203.]
 
-  § 200. _Pelton Wheel._--In the mining district of California about
+  § 200. _Pelton Wheel._--In the mining district of California about
   1860 simple impulse wheels were used, termed hurdy-gurdy wheels. The
   wheels rotated in a vertical plane, being supported on a horizontal
   axis. Round the circumference were fixed flat vanes which were struck
@@ -17670,7 +17636,7 @@ be kept down to a manageable value.
   At the Comstock mines, Nevada, there is a 36-in. Pelton wheel made of
   a solid steel disk with phosphor bronze buckets riveted to the rim.
   The head is 2100 ft. and the wheel makes 1150 revolutions per minute,
-  the peripheral velocity being 180 ft. per sec. With a ½-in. nozzle the
+  the peripheral velocity being 180 ft. per sec. With a ½-in. nozzle the
   wheel uses 32 cub. ft. of water per minute and develops 100 h.p. At
   the Chollarshaft, Nevada, there are six Pelton wheels on a fall of
   1680 ft. driving electrical generators. With 5/8-in. nozzles each
@@ -17678,7 +17644,7 @@ be kept down to a manageable value.
 
   [Illustration: FIG. 205]
 
-  § 201. _Theory of the Pelton Wheel._--Suppose a jet with a velocity v
+  § 201. _Theory of the Pelton Wheel._--Suppose a jet with a velocity v
   strikes tangentially a curved vane AB (fig. 205) moving in the same
   direction with the velocity u. The water will flow over the vane with
   the relative velocity v - u and at B will have the tangential
@@ -17689,18 +17655,18 @@ be kept down to a manageable value.
   = u - (v - u) cos [alpha]. Hence if Q is the quantity of water
   reaching the vane per second the change of momentum per second in the
   direction of the vane's motion is (GQ/g)[v - {u - (v - u) cos
-  [alpha]}] = (GQ/g)(v - u)(1 + cos [alpha]). If a = 0°, cos [alpha] =
+  [alpha]}] = (GQ/g)(v - u)(1 + cos [alpha]). If a = 0°, cos [alpha] =
   1, and the change of momentum per second, which is equal to the effort
   driving the vane, is P = 2(GQ/g)(v - u). The work done on the vane is
   Pu = 2(GQ/g)(v - u)u. If a series of vanes are interposed in
   succession, the quantity of water impinging on the vanes per second is
   the total discharge of the nozzle, and the energy expended at the
-  nozzle is GQv²/2g. Hence the efficiency of the arrangement is, when
-  [alpha] = 0°, neglecting friction,
+  nozzle is GQv²/2g. Hence the efficiency of the arrangement is, when
+  [alpha] = 0°, neglecting friction,
 
-    [eta] = 2Pu/GQv² = 4(v - u)u/v²,
+    [eta] = 2Pu/GQv² = 4(v - u)u/v²,
 
-  which is a maximum and equal to unity if u = ½v. In that case the
+  which is a maximum and equal to unity if u = ½v. In that case the
   whole energy of the jet is usefully expended in driving the series of
   vanes. In practice [alpha] cannot be quite zero or the water leaving
   one vane would strike the back of the next advancing vane. Fig. 203
@@ -17709,7 +17675,7 @@ be kept down to a manageable value.
   of the vane. The best velocity of the vane is very approximately half
   the velocity of the jet.
 
-  § 202. _Regulation of the Pelton Wheel._--At first Pelton wheels were
+  § 202. _Regulation of the Pelton Wheel._--At first Pelton wheels were
   adjusted to varying loads merely by throttling the supply. This method
   involves a total loss of part of the head at the sluice or throttle
   valve. In addition as the working head is reduced, the relation
@@ -17725,7 +17691,7 @@ be kept down to a manageable value.
   the aperture of the nozzle. Such a needle can be controlled by an
   ordinary governor.
 
-§ 203. _General Considerations on the Choice of a Type of Turbine._--The
+§ 203. _General Considerations on the Choice of a Type of Turbine._--The
 circumferential speed of any turbine is necessarily a fraction of the
 initial velocity of the water, and therefore is greater as the head is
 greater. In reaction turbines with complete admission the number of
@@ -17764,9 +17730,9 @@ these or any combination can be used according to the state of the
 water. With a high fall the turbine of largest radius only is used, and
 the speed of rotation is less than with a turbine of smaller radius. On
 the other hand, as the fall decreases the inner turbines are used either
-singly or together, according to the power required. At the Zürich
-waterworks there are turbines of 90 h.p. on a fall varying from 10½ ft.
-to 4¾ ft. The power and speed are kept constant. Each turbine has three
+singly or together, according to the power required. At the Zürich
+waterworks there are turbines of 90 h.p. on a fall varying from 10½ ft.
+to 4¾ ft. The power and speed are kept constant. Each turbine has three
 concentric rings. The outermost ring gives 90 h.p. with 105 cub. ft. per
 second and the maximum fall. The outer and middle compartments give the
 same power with 140 cub. ft. per second and a fall of 7 ft. 10 in. All
@@ -17777,7 +17743,7 @@ fall of 7 ft., and 80.7% with all the rings working.
 
 [Illustration: FIG. 206.]
 
-§ 204. _Speed Governing._--When turbines are used to drive dynamos
+§ 204. _Speed Governing._--When turbines are used to drive dynamos
 direct, the question of speed regulation is of great importance. Steam
 engines using a light elastic fluid can be easily regulated by governors
 acting on throttle or expansion valves. It is different with water
@@ -17814,7 +17780,7 @@ head.
 
 [Illustration: FIG. 207.]
 
-§ 205. _The Hydraulic Ram._--The hydraulic ram is an arrangement by
+§ 205. _The Hydraulic Ram._--The hydraulic ram is an arrangement by
 which a quantity of water falling a distance h forces a portion of the
 water to rise to a height h1, greater than h. It consists of a supply
 reservoir (A, fig. 207), into which the water enters from some natural
@@ -17842,7 +17808,7 @@ water which is pumped passes through this valve into the air vessel a,
 from which it flows by the delivery pipe in a regular stream into the
 cistern to which the water is to be raised. In the vertical chamber
 behind the outer valve a small air vessel is formed, and into this
-opens an aperture ¼ in. in diameter, made in a brass screw plug b. The
+opens an aperture ¼ in. in diameter, made in a brass screw plug b. The
 hole is reduced to 1/16 in. in diameter at the outer end of the plug
 and is closed by a small valve opening inwards. Through this, during the
 rebound after each stroke of the ram, a small quantity of air is sucked
@@ -17877,7 +17843,7 @@ ordinary pump valves.
 
 PUMPS
 
-§ 206. The different classes of pumps correspond almost exactly to the
+§ 206. The different classes of pumps correspond almost exactly to the
 different classes of water motors, although the mechanical details of
 the construction are somewhat different. They are properly reversed
 water motors. Ordinary reciprocating pumps correspond to water-pressure
@@ -17914,7 +17880,7 @@ replaced by an elastic diaphragm, alternately depressed into and raised
 out of a cylinder.
 
 As single-acting pumps give an intermittent discharge three are
-generally used on cranks at 120°. But with all pumps the variation of
+generally used on cranks at 120°. But with all pumps the variation of
 velocity of discharge would cause great waste of work in the delivery
 pipes when they are long, and even danger from the hydraulic ramming
 action of the long column of water. An air vessel is interposed between
@@ -17942,7 +17908,7 @@ efficiency rose to from 28 to 57%, or on the average, with 50 to 100 ft.
 of lift, about 50%. A large pump with barrels 18 in. diameter, at speeds
 under 60 ft. per minute, gave the following results:--
 
-  Lift in feet    14½   34    47
+  Lift in feet    14½   34    47
   Efficiency     .46   .66   .70
 
 The very large steam-pumps employed for waterworks, with 150 ft. or more
@@ -17957,7 +17923,7 @@ varying rate of pumping usually required. Messrs Hayward Tyler have
 introduced a mechanism for varying the stroke of the pumps (Sinclair's
 patent) from full stroke to nil, without stopping the pumps.
 
-§ 207. _Centrifugal Pump._--For large volumes of water on lifts not
+§ 207. _Centrifugal Pump._--For large volumes of water on lifts not
 exceeding about 60 ft. the most convenient pump is the centrifugal pump.
 Recent improvements have made it available also for very high lifts. It
 consists of a wheel or fan with curved vanes enclosed in an annular
@@ -18018,7 +17984,7 @@ from the pump case.
 
 [Illustration: FIG. 210.]
 
-  § 208. _Design and Proportions of a Centrifugal Pump._--The design of
+  § 208. _Design and Proportions of a Centrifugal Pump._--The design of
   the pump disk is very simple. Let r_i, r_o be the radii of the inlet
   and outlet surfaces of the pump disk, d_i, d_o the clear axial width
   at those radii. The velocity of flow through the pump may be taken
@@ -18043,7 +18009,7 @@ from the pump case.
 
   and
 
-    d_o = d_i or ½d_i
+    d_o = d_i or ½d_i
 
   according as the disk is parallel-sided or coned. The water enters the
   wheel radially with the velocity u_i, and
@@ -18068,7 +18034,7 @@ from the pump case.
     v_i = u_i                                        \
     w_i = 0                                           > (4)
     tan[theta] = u_i/V_i                              |
-    v_(ri) = u_i cosec [theta] = [root](u_i² + V_i²) /
+    v_(ri) = u_i cosec [theta] = [root](u_i² + V_i²) /
 
   If the pump is raising less or more than its proper quantity, [theta]
   will not satisfy the last condition, and there is then some loss of
@@ -18078,23 +18044,23 @@ from the pump case.
 
     v_(ro) = u_o cosec [phi]                       \
     w_o = V_o - u_o cot [phi]                       > (5)
-    v_o = [root]{u_o² + (V - _o - u_o cot [phi])²} /
+    v_o = [root]{u_o² + (V - _o - u_o cot [phi])²} /
 
   _Variation of Pressure in the Pump Disk._--Precisely as in the case of
   turbines, it can be shown that the variation of pressure between the
   inlet and outlet surfaces of the pump is
 
-    h_o - h_i = (V_o² - V_i²)/2g - (v_(ro)² - v_(ri)²)/2g.
+    h_o - h_i = (V_o² - V_i²)/2g - (v_(ro)² - v_(ri)²)/2g.
 
   Inserting the values of v_(ro), v_(ri) in (4) and (5), we get for
   normal conditions of working
 
-    h_o -h_i = (V_o² - V_i²)/2g - u_o² cosec² [phi]/2g + (u_i² + V_i²)/2g
-      = V_o²/2g - u_o² cosec² [phi]/2g + u_i²/2g.   (6)
+    h_o -h_i = (V_o² - V_i²)/2g - u_o² cosec² [phi]/2g + (u_i² + V_i²)/2g
+      = V_o²/2g - u_o² cosec² [phi]/2g + u_i²/2g.   (6)
 
   _Hydraulic Efficiency of the Pump._--Neglecting disk friction, journal
   friction, and leakage, the efficiency of the pump can be found in the
-  same way as that of turbines (§ 186). Let M be the moment of the
+  same way as that of turbines (§ 186). Let M be the moment of the
   couple rotating the pump, and [alpha] its angular velocity; w_o, r_o
   the tangential velocity of the water and radius at the outlet surface;
   w_i, r_i the same quantities at the inlet surface. Q being the
@@ -18116,7 +18082,7 @@ from the pump case.
 
     [eta] = GQH/M[alpha] = gH/w_o r_o[alpha] = gH/w_o V_o.   (7)
 
-  § 209. Case 1. _Centrifugal Pump with no Whirlpool Chamber._--When no
+  § 209. Case 1. _Centrifugal Pump with no Whirlpool Chamber._--When no
   special provision is made to utilize the energy of motion of the water
   leaving the wheel, and the pump discharges directly into a chamber in
   which the water is flowing to the discharge pipe, nearly the whole of
@@ -18126,35 +18092,35 @@ from the pump case.
   v_s. The radial component of v_o is almost necessarily wasted. From
   the tangential component there is a gain of pressure
 
-    (w_o² - v_s²)/2g - (w_o - v_s)²/2g
+    (w_o² - v_s²)/2g - (w_o - v_s)²/2g
       = v_s(w_o - v_s)g,
 
   which will be small, if v_s is small compared with w_o. Its greatest
-  value, if v_s = ½w_o, is ½w_o²/2g, which will always be a small part
+  value, if v_s = ½w_o, is ½w_o²/2g, which will always be a small part
   of the whole head. Suppose this neglected. The whole variation of
-  pressure in the pump disk then balances the lift and the head u_i²/2g
+  pressure in the pump disk then balances the lift and the head u_i²/2g
   necessary to give the initial velocity of flow in the eye of the
   wheel.
 
-    u_i²/2g + H = V_o²/2g - u_o² cosec² [phi]/2g + u_i²/2g,
+    u_i²/2g + H = V_o²/2g - u_o² cosec² [phi]/2g + u_i²/2g,
 
-    H = V_o²/2g - u_o² cosec² [phi]/2g
+    H = V_o²/2g - u_o² cosec² [phi]/2g
 
   or
 
-    V_o = [root](2gH + u_o² cosec² [phi]).   (8)
+    V_o = [root](2gH + u_o² cosec² [phi]).   (8)
 
   and the efficiency of the pump is, from (7),
 
     [eta] = gH/V_o w_o = gH/{V (V_o - n_o cot [phi])},
 
-    = (V_o² - u_o² cosec² [phi])/{2V_o (V_o - u_o cot [phi]) },   (9).
+    = (V_o² - u_o² cosec² [phi])/{2V_o (V_o - u_o cot [phi]) },   (9).
 
-  For [phi] = 90°,
+  For [phi] = 90°,
 
-    [eta] = (V_o² - u_o²)/2V_o²,
+    [eta] = (V_o² - u_o²)/2V_o²,
 
-  which is necessarily less than ½. That is, half the work expended in
+  which is necessarily less than ½. That is, half the work expended in
   driving the pump is wasted. By recurving the vanes, a plan introduced
   by Appold, the efficiency is increased, because the velocity v_o of
   discharge from the pump is diminished. If [phi] is very small,
@@ -18172,17 +18138,17 @@ from the pump case.
 
     [phi]    [eta]      V_o
 
-     90°      0.47     1.03 [root](2gH)
-     45°      0.56     1.06       "
-     30°      0.65     1.12       "
-     20°      0.73     1.24       "
-     10°      0.84     1.75       "
+     90°      0.47     1.03 [root](2gH)
+     45°      0.56     1.06       "
+     30°      0.65     1.12       "
+     20°      0.73     1.24       "
+     10°      0.84     1.75       "
 
-  [phi] cannot practically be made less than 20°; and, allowing for the
+  [phi] cannot practically be made less than 20°; and, allowing for the
   frictional losses neglected, the efficiency of a pump in which [phi] =
-  20° is found to be about .60.
+  20° is found to be about .60.
 
-  § 210. Case 2. _Pump with a Whirlpool Chamber_, as in fig.
+  § 210. Case 2. _Pump with a Whirlpool Chamber_, as in fig.
   210.--Professor James Thomson first suggested that the energy of the
   water after leaving the pump disk might be utilized, if a space were
   left in which a free vortex could be formed. In such a free vortex the
@@ -18190,9 +18156,9 @@ from the pump case.
   vortex chamber is, putting r_o, r_w for the radii to the outlet
   surface of wheel and to outside of free vortex,
 
-    v_o²  /    r_o² \    v_o²  /      \
-    ---- ( 1 - ----  ) = ---- ( 1 - k² ),
-     2g   \    r_w² /     2g   \      /
+    v_o²  /    r_o² \    v_o²  /      \
+    ---- ( 1 - ----  ) = ---- ( 1 - k² ),
+     2g   \    r_w² /     2g   \      /
 
   if
 
@@ -18200,33 +18166,33 @@ from the pump case.
 
   The lift is then, adding this to the lift in the last case,
 
-    H = {V_o² - u_o² cosec² [phi] + v_o²(1 - k²)}/2g.
+    H = {V_o² - u_o² cosec² [phi] + v_o²(1 - k²)}/2g.
 
   But
 
-    v_o² = V_o² - 2V_o u_o cot [phi] + u_o² cosec² [phi];
+    v_o² = V_o² - 2V_o u_o cot [phi] + u_o² cosec² [phi];
 
-    .: H = {(2 - k²)V_o² - 2kV_o u_o cot [phi] - k²u_o² cosec² [phi]}/2g.   (10)
+    .: H = {(2 - k²)V_o² - 2kV_o u_o cot [phi] - k²u_o² cosec² [phi]}/2g.   (10)
 
   Putting this in the expression for the efficiency, we find a
   considerable increase of efficiency. Thus with
 
-    [phi] = 90° and         k = ½, [eta] = 7/8 nearly,
+    [phi] = 90° and         k = ½, [eta] = 7/8 nearly,
 
-    [phi] a small angle and k = ½, [eta] = 1 nearly.
+    [phi] a small angle and k = ½, [eta] = 1 nearly.
 
   With this arrangement of pump, therefore, the angle at the outer ends
   of the vanes is of comparatively little importance. A moderate angle
-  of 30° or 40° may very well be adopted. The following numerical values
+  of 30° or 40° may very well be adopted. The following numerical values
   of the velocity of the circumference of the pump have been obtained by
-  taking k = ½, and u_o = 0.25 [root](2gH).
+  taking k = ½, and u_o = 0.25 [root](2gH).
 
     [phi]      V_o
 
-     90°      .762 [root](2gH)
-     45°      .842      "
-     30°      .911      "
-     20°     1.023      "
+     90°      .762 [root](2gH)
+     45°      .842      "
+     30°      .911      "
+     20°     1.023      "
 
   The quantity of water to be pumped by a centrifugal pump necessarily
   varies, and an adjustment for different quantities of water cannot
@@ -18249,14 +18215,14 @@ from the pump case.
   quantity of water is discussed in a paper in the _Proc. Inst. Civ.
   Eng._ vol. 53.
 
-§ 211. _High Lift Centrifugal Pumps._--It has long been known that
+§ 211. _High Lift Centrifugal Pumps._--It has long been known that
 centrifugal pumps could be worked in series, each pump overcoming a part
 of the lift. This method has been perfected, and centrifugal pumps for
 very high lifts with great efficiency have been used by Sulzer and
 others. C. W. Darley (_Proc. Inst. Civ. Eng._, supplement to vol. 154,
 p. 156) has described some pumps of this new type driven by Parsons
 steam turbines for the water supply of Sydney, N.S.W. Each pump was
-designed to deliver 1½ million gallons per twenty-four hours against a
+designed to deliver 1½ million gallons per twenty-four hours against a
 head of 240 ft. at 3300 revs. per minute. Three pumps in series give
 therefore a lift of 720 ft. The pump consists of a central double-sided
 impeller 12 in. diameter. The water entering at the bottom divides and
@@ -18286,15 +18252,15 @@ Newcastle:--
   | Water h.p.                          |  252  |  235  |  326  |  239  |
   +-------------------------------------+-------+-------+-------+-------+
 
-In trial IV. the steam was superheated 95° F. From other trials under
+In trial IV. the steam was superheated 95° F. From other trials under
 the same conditions as trial I. the Parsons turbine uses 15.6 lb. of
 steam per brake h.p. hour, so that the combined efficiency of turbine
 and pumps is about 56%, a remarkably good result.
 
 [Illustration: FIG. 212.]
 
-§ 212. _Air-Lift Pumps._--An interesting and simple method of pumping by
-compressed air, invented by Dr J. Pohlé of Arizona, is likely to be very
+§ 212. _Air-Lift Pumps._--An interesting and simple method of pumping by
+compressed air, invented by Dr J. Pohlé of Arizona, is likely to be very
 useful in certain cases. Suppose a rising main placed in a deep bore
 hole in which there is a considerable depth of water. Air compressed to
 a sufficient pressure is conveyed by an air pipe and introduced at the
@@ -18308,12 +18274,12 @@ must be the point at which air is injected. Fig. 212 shows an airlift
 pump constructed for W. H. Maxwell at the Tunbridge Wells waterworks.
 There is a two-stage steam air compressor, compressing air to from 90 to
 100 lb. per sq. in. The bore hole is 350 ft. deep, lined with steel
-pipes 15 in. diameter for 200 ft. and with perforated pipes 13½ in.
+pipes 15 in. diameter for 200 ft. and with perforated pipes 13½ in.
 diameter for the lower 150 ft. The rest level of the water is 96 ft.
 from the ground-level, and the level when pumping 32,000 gallons per
 hour is 120 ft. from the ground-level. The rising main is 7 in.
 diameter, and is carried nearly to the bottom of the bore hole and to 20
-ft. above the ground-level. The air pipe is 2½ in. diameter. In a trial
+ft. above the ground-level. The air pipe is 2½ in. diameter. In a trial
 run 31,402 gallons per hour were raised 133 ft. above the level in the
 well. Trials of the efficiency of the system made at San Francisco with
 varying conditions will be found in a paper by E. A. Rix (_Journ. Amer.
@@ -18329,7 +18295,7 @@ It is useful for clearing a boring of sand and may be advantageously
 used permanently when a boring is in sand or gravel which cannot be kept
 out of the bore hole. The initial cost is small.
 
-§ 213. _Centrifugal Fans._--Centrifugal fans are constructed similarly
+§ 213. _Centrifugal Fans._--Centrifugal fans are constructed similarly
 to centrifugal pumps, and are used for compressing air to pressures not
 exceeding 10 to 15 in. of water-column. With this small variation of
 pressure the variation of volume and density of the air may be neglected
@@ -18344,14 +18310,14 @@ case of the important Guibal fans used in mine ventilation.
   64.4 ft. of air at average atmospheric pressure = 5.2lb. per sq. ft.
 
   Roughly the pressure-head produced in a fan without means of utilizing
-  the kinetic energy of discharge would be v²/2g ft. of air, or 0.00024
-  v² in. of water, where v is the velocity of the tips of the fan blades
+  the kinetic energy of discharge would be v²/2g ft. of air, or 0.00024
+  v² in. of water, where v is the velocity of the tips of the fan blades
   in feet per second. If d is the diameter of the fan and t the width at
   the external circumference, then [pi]dt is the discharge area of the
   fan disk. If Q is the discharge in cub. ft. per sec., u = Q/[pi]dt is
   the radial velocity of discharge which is numerically equal to the
   discharge per square foot of outlet in cubic feet per second. As both
-  the losses in the fan and the work done are roughly proportional to u²
+  the losses in the fan and the work done are roughly proportional to u²
   in fans of the same type, and are also proportional to the gauge
   pressure p, then if the losses are to be a constant percentage of the
   work done u may be taken proportional to [root]p. In ordinary cases u
@@ -18372,8 +18338,8 @@ case of the important Guibal fans used in mine ventilation.
   the kinetic energy of the air in the discharge pipe is not
   inconsiderable compared with the work done in compression. If w is the
   velocity of the air where the discharge pressure is measured, the air
-  carries away w²/2g foot-pounds per lb. of air as kinetic energy. In Q
-  cubic feet or 0.0807 Qlb. the kinetic energy is 0.00125 Qw²
+  carries away w²/2g foot-pounds per lb. of air as kinetic energy. In Q
+  cubic feet or 0.0807 Qlb. the kinetic energy is 0.00125 Qw²
   foot-pounds per second.
 
   The efficiency of fans is reckoned in two ways. If B.H.P. is the
@@ -18385,7 +18351,7 @@ case of the important Guibal fans used in mine ventilation.
   On the other hand, if the kinetic energy in the delivery pipe is taken
   as part of the useful work the efficiency is
 
-    [eta]2 = (5.2 pQ + 0.00125 Qw²)/550 B.H.P.
+    [eta]2 = (5.2 pQ + 0.00125 Qw²)/550 B.H.P.
 
   Although the theory above is a rough one it agrees sufficiently with
   experiment, with some merely numerical modifications.
@@ -18427,11 +18393,11 @@ case of the important Guibal fans used in mine ventilation.
   following approximate rules. Let p_c be the compression pressure and q
   the volume discharged per second per square foot of outlet area of
   fan. Then the total gauge pressure due to pressure of compression and
-  velocity of discharge is approximately: p = p_c + 0.0004 q² in. of
+  velocity of discharge is approximately: p = p_c + 0.0004 q² in. of
   water, so that if p_c is given, p can be found approximately. The
   pressure p depends on the circumferential speed v of the fan disk--
 
-    p = 0.00025 v² in. of water
+    p = 0.00025 v² in. of water
 
     v = 63 [root]p ft. per sec.
 
@@ -18462,8 +18428,8 @@ FOOTNOTES:
   [1] Except where other units are given, the units throughout this
     article are feet, pounds, pounds per sq. ft., feet per second.
 
-  [2] _Journal de M. Liouville_, t. xiii. (1868); _Mémoires de
-    l'Académie, des Sciences de l'Institut de France_, t. xxiii., xxiv.
+  [2] _Journal de M. Liouville_, t. xiii. (1868); _Mémoires de
+    l'Académie, des Sciences de l'Institut de France_, t. xxiii., xxiv.
     (1877).
 
   [3] The following theorem is taken from a paper by J. H. Cotterill,
@@ -18487,9 +18453,9 @@ FOOTNOTES:
 
 
 
-HYDRAZINE (DIAMIDOGEN), N2H4 or H2 N·NH2, a compound of hydrogen and
+HYDRAZINE (DIAMIDOGEN), N2H4 or H2 N·NH2, a compound of hydrogen and
 nitrogen, first prepared by Th. Curtius in 1887 from diazo-acetic ester,
-N2CH·CO2C2H5. This ester, which is obtained by the action of potassium
+N2CH·CO2C2H5. This ester, which is obtained by the action of potassium
 nitrate on the hydrochloride of amidoacetic ester, yields on hydrolysis
 with hot concentrated potassium hydroxide an acid, which Curtius
 regarded as C3H3N6(CO2H)3, but which A. Hantzsch and O. Silberrad
@@ -18504,7 +18470,7 @@ by reducing potassium dinitrososulphonate in ice cold water by means of
 sodium amalgam:--
 
   KSO3 \           KSO3 \
-        > N·NO -->       > N·NH2 --> K2SO4 + N2H4.
+        > N·NO -->       > N·NH2 --> K2SO4 + N2H4.
     KO /              H /
 
 P. J. Schestakov (_J. Russ. Phys. Chem. Soc._, 1905, 37, p. 1) obtained
@@ -18512,21 +18478,21 @@ hydrazine by oxidizing urea with sodium hypochlorite in the presence of
 benzaldehyde, which, by combining with the hydrazine, protected it from
 oxidation. F. Raschig (German Patent 198307, 1908) obtained good yields
 by oxidizing ammonia with sodium hypochlorite in solutions made viscous
-with glue. Free hydrazine is a colourless liquid which boils at 113.5°
-C., and solidifies about 0° C. to colourless crystals; it is heavier
+with glue. Free hydrazine is a colourless liquid which boils at 113.5°
+C., and solidifies about 0° C. to colourless crystals; it is heavier
 than water, in which it dissolves with rise of temperature. It is
 rapidly oxidized on exposure, is a strong reducing agent, and reacts
 vigorously with the halogens. Under certain conditions it may be
 oxidized to azoimide (A. W. Browne and F. F. Shetterly, _J. Amer. C.S._,
 1908, p. 53). By fractional distillation of its aqueous solution
-hydrazine hydrate N2H4·H2O (or perhaps H2N·NH3OH), a strong base, is
+hydrazine hydrate N2H4·H2O (or perhaps H2N·NH3OH), a strong base, is
 obtained, which precipitates the metals from solutions of copper and
 silver salts at ordinary temperatures. It dissociates completely in a
-vacuum at 143°, and when heated under atmospheric pressure to 183° it
+vacuum at 143°, and when heated under atmospheric pressure to 183° it
 decomposes into ammonia and nitrogen (A. Scott, _J. Chem. Soc._, 1904,
-85, p. 913). The sulphate N2H4·H2SO4, crystallizes in tables which are
+85, p. 913). The sulphate N2H4·H2SO4, crystallizes in tables which are
 slightly soluble in cold water and readily soluble in hot water; it is
-decomposed by heating above 250° C. with explosive evolution of gas and
+decomposed by heating above 250° C. with explosive evolution of gas and
 liberation of sulphur. By the addition of barium chloride to the
 sulphate, a solution of the hydrochloride is obtained, from which the
 crystallized salt may be obtained on evaporation.
@@ -18546,14 +18512,14 @@ crystallized salt may be obtained on evaporation.
   phenylhydrazine potassium sulphite. This salt is then hydrolysed by
   heating it with hydrochloric acid--
 
-    C6H5N2Cl + K2SO3 = KCl + C6H5N2·SO3K,
+    C6H5N2Cl + K2SO3 = KCl + C6H5N2·SO3K,
 
-    C6H5N2·SO3K + 2H = C6H5·NH·NH·SO3K,
+    C6H5N2·SO3K + 2H = C6H5·NH·NH·SO3K,
 
-    C6H5NH·NH·SO3K + HCl + H2O = C6H5·NH·NH2·HCl + KHSO4.
+    C6H5NH·NH·SO3K + HCl + H2O = C6H5·NH·NH2·HCl + KHSO4.
 
   Phenylhydrazine is a colourless oily liquid which turns brown on
-  exposure. It boils at 241° C., and melts at 17.5° C. It is slightly
+  exposure. It boils at 241° C., and melts at 17.5° C. It is slightly
   soluble in water, and is strongly basic, forming well-defined salts
   with acids. For the detection of substances containing the carbonyl
   group (such for example as aldehydes and ketones) phenylhydrazine is a
@@ -18561,10 +18527,10 @@ crystallized salt may be obtained on evaporation.
   of water and the formation of well-defined hydrazones (see ALDEHYDES,
   KETONES and SUGARS). It is a strong reducing agent; it precipitates
   cuprous oxide when heated with Fehling's solution, nitrogen and
-  benzene being formed at the same time--C6H5·NH·NH2 + 2CuO = Cu2O + N2
+  benzene being formed at the same time--C6H5·NH·NH2 + 2CuO = Cu2O + N2
   + H2O + C6H5. By energetic reduction of phenylhydrazine (e.g. by use
   of zinc dust and hydrochloric acid), ammonia and aniline are
-  produced--C6H5NH·NH2 + 2H = C6H5NH2 + NH3. It is also a most important
+  produced--C6H5NH·NH2 + 2H = C6H5NH2 + NH3. It is also a most important
   synthetic reagent. It combines with aceto-acetic ester to form
   phenylmethylpyrazolone, from which antipyrine (q.v.) may be obtained.
   Indoles (q.v.) are formed by heating certain hydrazones with anhydrous
@@ -18603,7 +18569,7 @@ namely, organic chemistry.
 
 
 
-HYDROCELE (Gr. [Greek: hydôr], water, and [Greek: kêlê], tumour), the
+HYDROCELE (Gr. [Greek: hydôr], water, and [Greek: kêlê], tumour), the
 medical term for any collection of fluid other than pus or blood in the
 neighbourhood of the testis or cord. The fluid is usually serous.
 Hydrocele may be congenital or arise in the middle-aged without apparent
@@ -18619,7 +18585,7 @@ is incised, the tunica partly removed and the cavity drained.
 
 
 
-HYDROCEPHALUS (Gr. [Greek: hydôr], water, and [Greek: kephalê], head), a
+HYDROCEPHALUS (Gr. [Greek: hydôr], water, and [Greek: kephalê], head), a
 term applied to disease of the brain which is attended with excessive
 effusion of fluid into its cavities. It exists in two forms--_acute_ and
 _chronic hydrocephalus_. Acute hydrocephalus is another name for
@@ -18686,13 +18652,13 @@ the most rational and successful.     (E. O.*)
 HYDROCHARIDEAE, in botany, a natural order of Monocotyledons, belonging
 to the series Helobieae. They are water-plants, represented in Britain
 by frog-bit (_Hydrocharis Morsusranae_) and water-soldier (_Stratiotes
-aloïdes_). The order contains about fifty species in fifteen genera,
+aloïdes_). The order contains about fifty species in fifteen genera,
 twelve of which occur in fresh water while three are marine: and
 includes both floating and submerged forms. _Hydrocharis_ floats on the
 surface of still water, and has rosettes of kidney-shaped leaves, from
 among which spring the flower-stalks; stolons bearing new leaf-rosettes
 are sent out on all sides, the plant thus propagating itself on the same
-way as the strawberry. _Stratiotes aloïdes_ has a rosette of stiff
+way as the strawberry. _Stratiotes aloïdes_ has a rosette of stiff
 sword-like leaves, which when the plant is in flower project above the
 surface; it is also stoloniferous, the young rosettes sinking to the
 bottom at the beginning of winter and rising again to the surface in the
@@ -18751,7 +18717,7 @@ flowers of _Halophila_ are submerged and apetalous.
   8, 9, Floral diagrams of male and female flowers respectively.
   s, Rudimentary stamens.]
 
-[Illustration: FIG. 2.--_Vallisneria spiralis_--Eel grass--about ¼
+[Illustration: FIG. 2.--_Vallisneria spiralis_--Eel grass--about ¼
 natural size. A, Female plant; B, Male plant.]
 
 [Illustration: FIG. 3.]
@@ -18770,7 +18736,7 @@ discussed under CHLORINE, and its manufacture under ALKALI MANUFACTURE.
 
 
 
-HYDRODYNAMICS (Gr. [Greek: hydôr], water, [Greek: dynamis], strength),
+HYDRODYNAMICS (Gr. [Greek: hydôr], water, [Greek: dynamis], strength),
 the branch of hydromechanics which discusses the motion of fluids (see
 HYDROMECHANICS).
 
@@ -18778,12 +18744,12 @@ HYDROMECHANICS).
 
 
 HYDROGEN [symbol H, atomic weight 1.008 (o = 16)], one of the chemical
-elements. Its name is derived from Gr. [Greek: hydôr], water, and
+elements. Its name is derived from Gr. [Greek: hydôr], water, and
 [Greek: gennaein], to produce, in allusion to the fact that water is
 produced when the gas burns in air. Hydrogen appears to have been
 recognized by Paracelsus in the 16th century; the combustibility of the
 gas was noticed by Turquet de Mayenne in the 17th century, whilst in
-1700 N. Lémery showed that a mixture of hydrogen and air detonated on
+1700 N. Lémery showed that a mixture of hydrogen and air detonated on
 the application of a light. The first definite experiments concerning
 the nature of hydrogen were made in 1766 by H. Cavendish, who showed
 that it was formed when various metals were acted upon by dilute
@@ -18807,10 +18773,10 @@ may be prepared by the electrolysis of acidulated water, by the
 decomposition of water by various metals or metallic hydrides, and by
 the action of many metals on acids or on bases. The alkali metals and
 alkaline earth metals decompose water at ordinary temperatures;
-magnesium begins to react above 70° C., and zinc at a dull red heat. The
+magnesium begins to react above 70° C., and zinc at a dull red heat. The
 decomposition of steam by red hot iron has been studied by H.
 Sainte-Claire Deville (_Comptes rendus_, 1870, 70, p. 1105) and by H.
-Debray (ibid., 1879, 88, p. 1341), who found that at about 1500° C. a
+Debray (ibid., 1879, 88, p. 1341), who found that at about 1500° C. a
 condition of equilibrium is reached. H. Moissan (_Bull. soc. chim._,
 1902, 27, p. 1141) has shown that potassium hydride decomposes cold
 water, with evolution of hydrogen, KH + H2O = KOH + H2. Calcium hydride
@@ -18818,8 +18784,8 @@ or hydrolite, prepared by passing hydrogen over heated calcium,
 decomposes water similarly, 1 gram giving 1 litre of gas; it has been
 proposed as a commercial source (Prats Aymerich, _Abst. J.C.S._, 1907,
 ii. p. 543), as has also aluminium turnings moistened with potassium
-cyanide and mercuric chloride, which decomposes water regularly at 70°,
-1 gram giving 1.3 litres of gas (Mauricheau-Beaupré, _Comptes rendus_,
+cyanide and mercuric chloride, which decomposes water regularly at 70°,
+1 gram giving 1.3 litres of gas (Mauricheau-Beaupré, _Comptes rendus_,
 1908, 147, p. 310). Strontium hydride behaves similarly. In preparing
 the gas by the action of metals on acids, dilute sulphuric or
 hydrochloric acid is taken, and the metals commonly used are zinc or
@@ -18836,22 +18802,22 @@ is prepared by the action of superheated steam on incandescent coke (see
 F. Hembert and Henry, _Comptes rendus_, 1885, 101, p. 797; A. Naumann
 and C. Pistor, _Ber._, 1885, 18, p. 1647), or by the electrolysis of a
 dilute solution of caustic soda (C. Winssinger, _Chem. Zeit._, 1898,
-22, p. 609; "Die Elektrizitäts-Aktiengesellschaft," _Zeit. f.
+22, p. 609; "Die Elektrizitäts-Aktiengesellschaft," _Zeit. f.
 Elektrochem._, 1901, 7, p. 857). In the latter method a 15% solution of
 caustic soda is used, and the electrodes are made of iron; the cell is
 packed in a wooden box, surrounded with sand, so that the temperature is
-kept at about 70° C.; the solution is replenished, when necessary, with
+kept at about 70° C.; the solution is replenished, when necessary, with
 distilled water. The purity of the gas obtained is about 97%.
 
 Pure hydrogen is a tasteless, colourless and odourless gas of specific
 gravity 0.06947 (air = 1) (Lord Rayleigh, _Proc. Roy. Soc._, 1893, p.
-319). It may be liquefied, the liquid boiling at -252.68° C. to -252.84°
-C., and it has also been solidified, the solid melting at -264° C. (J.
+319). It may be liquefied, the liquid boiling at -252.68° C. to -252.84°
+C., and it has also been solidified, the solid melting at -264° C. (J.
 Dewar, _Comptes rendus_, 1899, 129, p. 451; _Chem. News_, 1901, 84, p.
 49; see also LIQUID GASES). The specific heat of gaseous hydrogen (at
 constant pressure) is 3.4041 (water = 1), and the ratio of the specific
 heat at constant pressure to the specific heat at constant volume is
-1.3852 (W. C. Röntgen, _Pogg. Ann._, 1873, 148, p. 580). On the spectrum
+1.3852 (W. C. Röntgen, _Pogg. Ann._, 1873, 148, p. 580). On the spectrum
 see SPECTROSCOPY. Hydrogen is only very slightly soluble in water. It
 diffuses very rapidly through a porous membrane, and through some metals
 at a red heat (T. Graham, _Proc. Roy. Soc._, 1867, 15, p. 223; H.
@@ -18872,7 +18838,7 @@ Chem. Soc._, 1902, 18, p. 40) has shown that perfectly dry hydrogen will
 not unite with perfectly dry oxygen. Hydrogen combines with fluorine,
 even at very low temperatures, with great violence; it also combines
 with carbon, at the temperature of the electric arc. The alkali metals
-when warmed in a current of hydrogen, at about 360° C., form hydrides of
+when warmed in a current of hydrogen, at about 360° C., form hydrides of
 composition RH (R = Na, K, Rb, Cs), (H. Moissan, _Bull. soc. chim._,
 1902, 27, p. 1141); calcium and strontium similarly form hydrides CaH2,
 SrH2 at a dull red heat (A. Guntz, _Comptes rendus_, 1901, 133, p.
@@ -18893,7 +18859,7 @@ Hydrogen combines with oxygen to form two definite compounds, namely,
 water (q.v.), H2O, and hydrogen peroxide, H2O2, whilst the existence of
 a third oxide, ozonic acid, has been indicated.
 
-_Hydrogen peroxide_, H2O2, was discovered by L. J. Thénard in 1818
+_Hydrogen peroxide_, H2O2, was discovered by L. J. Thénard in 1818
 (_Ann. chim. phys._, 8, p. 306). It occurs in small quantities in the
 atmosphere. It may be prepared by passing a current of carbon dioxide
 through ice-cold water, to which small quantities of barium peroxide are
@@ -18914,7 +18880,7 @@ solution is cooled, filtered, and baryta water is added until a faint
 permanent white precipitate of hydrated barium peroxide appears; the
 solution is now filtered, and a concentrated solution of baryta water is
 added to the filtrate, when a crystalline precipitate of hydrated barium
-peroxide, BaO2·H2O, is thrown down. This is filtered off and well washed
+peroxide, BaO2·H2O, is thrown down. This is filtered off and well washed
 with water. The above methods give a dilute aqueous solution of hydrogen
 peroxide, which may be concentrated somewhat by evaporation over
 sulphuric acid in vacuo. H. P. Talbot and H. R. Moody (_Jour. Anal.
@@ -18945,17 +18911,17 @@ strength that it contains two molecules of water to one molecule of
 sulphuric acid (M. Berthelot, _Comptes rendus_, 1878, 86, p. 71).
 
 The anhydrous hydrogen peroxide obtained by Wolffenstein boils at
-84-85°C. (68 mm.); its specific gravity is 1.4996 (1.5° C.). It is very
+84-85°C. (68 mm.); its specific gravity is 1.4996 (1.5° C.). It is very
 explosive (W. Spring, _Zeit. anorg. Chem._, 1895, 8, p. 424). The
 explosion risk seems to be most marked in the preparations which have
-been extracted with ether previous to distillation, and J. W. Brühl
+been extracted with ether previous to distillation, and J. W. Brühl
 (_Ber._, 1895, 28, p. 2847) is of opinion that a very unstable, more
 highly oxidized product is produced in small quantity in the process.
 The solid variety prepared by Staedel forms colourless, prismatic
-crystals which melt at -2° C.; it is decomposed with explosive violence
+crystals which melt at -2° C.; it is decomposed with explosive violence
 by platinum sponge, and traces of manganese dioxide. The dilute aqueous
 solution is very unstable, giving up oxygen readily, and decomposing
-with explosive violence at 100° C. An aqueous solution containing more
+with explosive violence at 100° C. An aqueous solution containing more
 than 1.5% hydrogen peroxide reacts slightly acid. Towards lupetidin [aa'
 dimethyl piperidine, C5H9N(CH3)2] hydrogen peroxide acts as a dibasic
 acid (A. Marcuse and R. Wolffenstein, _Ber._, 1901, 34, p. 2430; see
@@ -18966,7 +18932,7 @@ Orndorff and J. White, _Amer. Chem. Journ._, 1893, 15, p. 347.] Hydrogen
 peroxide behaves very frequently as a powerful oxidizing agent; thus
 lead sulphide is converted into lead sulphate in presence of a dilute
 aqueous solution of the peroxide, the hydroxides of the alkaline earth
-metals are converted into peroxides of the type MO2·8H2O, titanium
+metals are converted into peroxides of the type MO2·8H2O, titanium
 dioxide is converted into the trioxide, iodine is liberated from
 potassium iodide, and nitrites (in alkaline solution) are converted into
 acid-amides (B. Radziszewski, _Ber._, 1884, 17, p. 355). In many cases
@@ -18994,8 +18960,8 @@ salts, together with the corresponding bromine and iodine compounds,
 liberate oxygen violently from hydrogen peroxide, giving hydrochloric,
 hydrobromic and hydriodic acids (S. Tanatar, _Ber._, 1899, 32, p. 1013).
 
-  On the constitution of hydrogen peroxide see C. F. Schönbein, _Jour.
-  prak. Chem._, 1858-1868; M. Traube, _Ber._, 1882-1889; J. W. Brühl,
+  On the constitution of hydrogen peroxide see C. F. Schönbein, _Jour.
+  prak. Chem._, 1858-1868; M. Traube, _Ber._, 1882-1889; J. W. Brühl,
   _Ber._, 1895, 28, p. 2847; 1900, 33, p. 1709; S. Tanatar, _Ber._,
   1903, 36, p. 1893.
 
@@ -19008,7 +18974,7 @@ hydrobromic and hydriodic acids (S. Tanatar, _Ber._, 1899, 32, p. 1013).
   2K3Fe(CN)6 + 2KOH + H2O2 = 2K4Fe(CN)6 + 2H2O + O2; or by oxidizing
   arsenious acid in alkaline solution with the peroxide and back
   titration of the excess of arsenious acid with standard iodine (B.
-  Grützner, _Arch. der Pharm._, 1899, 237, p. 705). It may be recognized
+  Grützner, _Arch. der Pharm._, 1899, 237, p. 705). It may be recognized
   by the violet coloration it gives when added to a very dilute solution
   of potassium bichromate in the presence of hydrochloric acid; by the
   orange-red colour it gives with a solution of titanium dioxide in
@@ -19025,7 +18991,7 @@ hydrobromic and hydriodic acids (S. Tanatar, _Ber._, 1899, 32, p. 1013).
 
 
 
-HYDROGRAPHY (Gr. [Greek: hydôr], water, and [Greek: graphein], to
+HYDROGRAPHY (Gr. [Greek: hydôr], water, and [Greek: graphein], to
 write), the science dealing with all the waters of the earth's surface,
 including the description of their physical features and conditions; the
 preparation of charts and maps showing the position of lakes, rivers,
@@ -19041,9 +19007,9 @@ the admiralty (see CHART).
 
 
 
-HYDROLYSIS (Gr. [Greek: hydôr], water, [Greek: luein], to loosen), in
+HYDROLYSIS (Gr. [Greek: hydôr], water, [Greek: luein], to loosen), in
 chemistry, a decomposition brought about by water after the manner shown
-in the equation R·X + H·OH = R·H + X·OH. Modern research has proved that
+in the equation R·X + H·OH = R·H + X·OH. Modern research has proved that
 such reactions are not occasioned by water acting as H2O, but really by
 its ions (hydrions and hydroxidions), for the velocity is proportional
 (in accordance with the law of chemical mass action) to the
@@ -19062,359 +19028,4 @@ fats, i.e. glyceryl esters of organic acids, into glycerin and a soap
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       The Project Gutenberg eBook of Encyclop&aelig;dia Britannica, Volume XIV Slice I - Husband to Hydrolysis.
@@ -162,45 +162,7 @@
     </style>
    </head>
 <body>
-
-
-<pre>
-
-The Project Gutenberg EBook of Encyclopaedia Britannica, 11th Edition,
-Volume 14, Slice 1, 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 14, Slice 1
-       "Husband" to "Hydrolysis"
-
-Author: Various
-
-Release Date: August 19, 2012 [EBook #40538]
-
-Language: English
-
-Character set encoding: ISO-8859-1
-
-*** START OF THIS PROJECT GUTENBERG EBOOK ENCYC. BRITANNICA, VOL 14, SL 1 ***
-
-
-
-
-Produced by Marius Masi, Don Kretz and the Online
-Distributed Proofreading Team at http://www.pgdp.net
-
-
-
-
-
-
-</pre>
-
+<div>*** START OF THE PROJECT GUTENBERG EBOOK 40538 ***</div>
 
 <table border="0" cellpadding="10" style="background-color: #dcdcdc; color: #696969; " summary="Transcriber's note">
 <tr>
@@ -430,7 +392,7 @@ Sub-Librarian of the Bodleian Library, Oxford. Fellow of Magdalen College.</td>
 
 <tr> <td class="tc1">A. C. G.</td>
 
-  <td class="tc2"><span class="sc">Albert Charles Lewis Gotthilf Günther, M.A., M.D., Ph.D., F.R.S.</span><br />
+  <td class="tc2"><span class="sc">Albert Charles Lewis Gotthilf Günther, M.A., M.D., Ph.D., F.R.S.</span><br />
 
 Keeper of Zoological Department, British Museum, 1875-1895. Gold Medallist,
 Royal Society, 1878. Author of <i>Catalogues of Colubrine Snakes, Batrachia Salientia,
@@ -534,7 +496,7 @@ See the biographical article, <span class="sc"><a href="#artlinks">Newton, Alfre
 
   <td class="tc2"><span class="sc">Albrecht Socin, Ph.D.</span> (1844-1899).<br />
 
-Formerly Professor of Semitic Philology in the Universities of Leipzig and Tübingen.
+Formerly Professor of Semitic Philology in the Universities of Leipzig and Tübingen.
 Author of <i>Arabische Grammatik</i>; &amp;c.</td>
 
    <td class="tc4 cl"><p><b>Irak-Arabi</b> (<i>in part</i>).</p></td></tr>
@@ -779,11 +741,11 @@ See the biographical article, <span class="sc"><a href="#artlinks">Gosse, Edmund
 <p><b>Ibsen;</b></p>
 <p><b>Idyl.</b></p></td></tr>
 
-<tr> <td class="tc1">E. Hü.</td>
+<tr> <td class="tc1">E. Hü.</td>
 
-  <td class="tc2"><span class="sc">Emil Hübner.</span><br />
+  <td class="tc2"><span class="sc">Emil Hübner.</span><br />
 
-See the biographical article, <span class="sc"><a href="#artlinks">Hübner, Emil</a></span>.</td>
+See the biographical article, <span class="sc"><a href="#artlinks">Hübner, Emil</a></span>.</td>
 
    <td class="tc4 cl"><p><b>Inscriptions:</b> <i>Latin</i> (<i>in part</i>).</p></td></tr>
 
@@ -840,7 +802,7 @@ of Greek Historical Inscriptions</i>; &amp;c.</td>
   <td class="tc2"><span class="sc">Eduard Meyer, Ph.D., D.Litt.</span>(Oxon.), LL.D.<br />
 
 Professor of Ancient History in the University of Berlin. Author of <i>Geschichte des
-Alterthums</i>; <i>Geschichte des alten Aegyptens</i>; <i>Die Israeliten und ihre Nachbarstämme</i>.</td>
+Alterthums</i>; <i>Geschichte des alten Aegyptens</i>; <i>Die Israeliten und ihre Nachbarstämme</i>.</td>
 
    <td class="tc4 cl"><p><b>Hystaspes;</b></p>
 <p><b>Iran.</b></p></td></tr>
@@ -1048,7 +1010,7 @@ Shanghai.</td>
 
 <tr> <td class="tc1">G. K.</td>
 
-  <td class="tc2"><span class="sc">Gustav Krüger, Ph.D.</span><br />
+  <td class="tc2"><span class="sc">Gustav Krüger, Ph.D.</span><br />
 
 Professor of Church History in the University of Giessen. Author of <i>Das Papstthum</i>;
 &amp;c.</td>
@@ -1369,11 +1331,11 @@ College (University of London). Joint-editor of Grote&rsquo;s <i>History of Gree
 
 <tr> <td class="tc1">J. P. E.</td>
 
-  <td class="tc2"><span class="sc">Jean Paul Hippolyte Emmanuel Adhémar Esmein.</span><br />
+  <td class="tc2"><span class="sc">Jean Paul Hippolyte Emmanuel Adhémar Esmein.</span><br />
 
 Professor of Law in the University of Paris. Officer of the Legion of Honour.
-Member of the Institute of France. Author of <i>Cours élémentaire d&rsquo;histoire du droit
-français</i>; &amp;c.</td>
+Member of the Institute of France. Author of <i>Cours élémentaire d&rsquo;histoire du droit
+français</i>; &amp;c.</td>
 
    <td class="tc4 cl"><p><b>Intendant.</b></p></td></tr>
 
@@ -1450,7 +1412,7 @@ Law, or the Conflict of Laws: Chapters on the Principles of International Law</i
 
 <tr> <td class="tc1">L.</td>
 
-  <td class="tc2"><span class="sc">Count Lützow, Litt.D. (Oxon.), Ph.D. (Prague), F.R.G.S.</span><br />
+  <td class="tc2"><span class="sc">Count Lützow, Litt.D. (Oxon.), Ph.D. (Prague), F.R.G.S.</span><br />
 
 Chamberlain of H.M. the Emperor of Austria, King of Bohemia. Hon. Member
 of the Royal Society of Literature. Member of the Bohemian Academy; &amp;c.
@@ -1542,11 +1504,11 @@ British Association.</td>
 
 <tr> <td class="tc1">P. A.</td>
 
-  <td class="tc2"><span class="sc">Paul Daniel Alphandéry.</span><br />
+  <td class="tc2"><span class="sc">Paul Daniel Alphandéry.</span><br />
 
-Professor of the History of Dogma, École pratique des hautes études, Sorbonne,
-Paris. Author of <i>Les Idées morales chez les hétérodoxes latines au début du XIII<span class="sp">e</span>.
-siècle</i>.</td>
+Professor of the History of Dogma, École pratique des hautes études, Sorbonne,
+Paris. Author of <i>Les Idées morales chez les hétérodoxes latines au début du XIII<span class="sp">e</span>.
+siècle</i>.</td>
 
    <td class="tc4 cl"><p><b>Inquisition.</b></p></td></tr>
 
@@ -1656,7 +1618,7 @@ all Lands</i>; &amp;c.</td>
 
 <tr> <td class="tc1">R. P. S.</td>
 
-  <td class="tc2"><span class="sc">R. Phené Spiers, F.S.A., F.R.I.B.A.</span><br />
+  <td class="tc2"><span class="sc">R. Phené Spiers, F.S.A., F.R.I.B.A.</span><br />
 
 Formerly Master of the Architectural School, Royal Academy, London. Past
 President of Architectural Association. Associate and Fellow of King&rsquo;s College,
@@ -1706,7 +1668,7 @@ Testament History</i>; <i>Religion of Ancient Palestine</i>; &amp;c.</td>
 
 <tr> <td class="tc1">S. Bl.</td>
 
-  <td class="tc2"><span class="sc">Sigfus Blöndal.</span><br />
+  <td class="tc2"><span class="sc">Sigfus Blöndal.</span><br />
 
 Librarian of the University of Copenhagen.</td>
 
@@ -1795,16 +1757,16 @@ Author of <i>History of Icelandic Geography</i>; <i>Geological Map of Iceland</i
   <td class="tc2"><span class="sc">Rev. William Augustus Brevoort Coolidge, M.A., F.R.G.S., Ph.D.</span>(Bern).<br />
 
 Fellow of Magdalen College, Oxford. Professor of English History, St David&rsquo;s
-College, Lampeter, 1880-1881. Author of <i>Guide du Haut Dauphiné</i>; <i>The Range
-of the Tödi</i>; <i>Guide to Grindelwald</i>; <i>Guide to Switzerland</i>; <i>The Alps in Nature and in
+College, Lampeter, 1880-1881. Author of <i>Guide du Haut Dauphiné</i>; <i>The Range
+of the Tödi</i>; <i>Guide to Grindelwald</i>; <i>Guide to Switzerland</i>; <i>The Alps in Nature and in
 History</i>; &amp;c. Editor of <i>The Alpine Journal</i>, 1880-1881; &amp;c.</td>
 
-   <td class="tc4 cl"><p><b>Hyères;</b></p>
+   <td class="tc4 cl"><p><b>Hyères;</b></p>
 <p><b>Innsbruck;</b></p>
 <p><b>Interlaken;</b></p>
 <p><b>Iseo, Lake of;</b></p>
-<p><b>Isère</b> (<i>River</i>);</p>
-<p><b>Isère</b> (<i>Department</i>).</p></td></tr>
+<p><b>Isère</b> (<i>River</i>);</p>
+<p><b>Isère</b> (<i>Department</i>).</p></td></tr>
 
 <tr> <td class="tc1">W. A. P.</td>
 
@@ -2017,8 +1979,8 @@ See the biographical article. <span class="sc"><a href="#artlinks">Hunter, Sir W
 chiefly used in the sense of a man legally joined by marriage to
 a woman, his &ldquo;wife&rdquo;; the legal relations between them are
 treated below under <span class="sc"><a href="#artlinks">Husband and Wife</a></span>. The word appears
-in O. Eng. as <i>húsbonda</i>, answering to the Old Norwegian
-<i>húsbóndi</i>, and means the owner or freeholder of a <i>hus</i>, or house.
+in O. Eng. as <i>húsbonda</i>, answering to the Old Norwegian
+<i>húsbóndi</i>, and means the owner or freeholder of a <i>hus</i>, or house.
 The last part of the word still survives in &ldquo;bondage&rdquo; and &ldquo;bondman,&rdquo;
 and is derived from <i>bua</i>, to dwell, which, like Lat. <i>colere</i>,
 means also to till or cultivate, and to have a household. &ldquo;Wife,&rdquo;
@@ -2033,7 +1995,7 @@ by a woman, and also with the root of <i>vibrare</i>, to tremble.
 These are all merely guesses, and the ultimate history of the
 word is lost. It does not appear outside Teutonic languages.
 Parallel to &ldquo;husband&rdquo; is &ldquo;housewife,&rdquo; the woman managing
-a household. The earlier <i>húswif</i> was pronounced <i>hussif</i>, and
+a household. The earlier <i>húswif</i> was pronounced <i>hussif</i>, and
 this pronunciation survives in the application of the word to
 a small case containing scissors, needles and pins, cottons, &amp;c.
 From this form also derives &ldquo;hussy,&rdquo; now only used in a depreciatory
@@ -2059,7 +2021,7 @@ employment. Where such an agent is himself one of the owners
 of the vessel, the name of &ldquo;managing owner&rdquo; is used. The
 &ldquo;ship&rsquo;s husband&rdquo; or &ldquo;managing owner&rdquo; must register his
 name and address at the port of registry (Merchant Shipping
-Act 1894, § 59). From the use of &ldquo;husband&rdquo; for a good and
+Act 1894, § 59). From the use of &ldquo;husband&rdquo; for a good and
 thrifty manager of a household, the verb &ldquo;to husband&rdquo; means
 to economize, to lay up a store, to save.</p>
 
@@ -2123,7 +2085,7 @@ usages were brought under the influence of principles derived
 from the Roman law, a theory of marriage became established,
 the leading feature of which is the <i>community of goods</i> between
 husband and wife. Describing the principle as it prevails in
-France, Story (<i>Conflict of Laws</i>, § 130) says: &ldquo;This community
+France, Story (<i>Conflict of Laws</i>, § 130) says: &ldquo;This community
 or nuptial partnership (in the absence of any special contract)
 generally extends to all the movable property of the husband
 and wife, and to the fruits, income and revenue thereof....
@@ -2548,7 +2510,7 @@ opening of the Liverpool and Manchester railway.</p>
 <hr class="art" />
 <p><span class="bold">HUSS<a name="ar5" id="ar5"></a></span> (or <span class="sc">Hus</span>), JOHN (<i>c.</i> 1373-1415), Bohemian reformer and
 martyr, was born at Hussinecz,<a name="fa1b" id="fa1b" href="#ft1b"><span class="sp">1</span></a> a market village at the foot of
-the Böhmerwald, and not far from the Bavarian frontier, between
+the Böhmerwald, and not far from the Bavarian frontier, between
 1373 and 1375, the exact date being uncertain. His parents
 appear to have been well-to-do Czechs of the peasant class.
 Of his early life nothing is recorded except that, notwithstanding
@@ -2910,7 +2872,7 @@ Brumfels in 1524; and Luther wrote an interesting preface to
 <i>Epistolae Quaedam</i>, which were published in 1537. These <i>Epistolae</i>
 have been translated into French by E. de Bonnechose (1846), and
 the letters written during his imprisonment have been edited by
-C. von Kügelgen (Leipzig, 1902).</p>
+C. von Kügelgen (Leipzig, 1902).</p>
 
 <p>The best and most easily accessible information for the English
 reader on Huss is found in J. A. W. Neander&rsquo;s <i>Allgemeine Geschichte
@@ -2925,17 +2887,17 @@ H. von der Haardt in his <i>Magnum Constantiense concilium</i>, vol. vi.,
 1700; and by H. Finke in his <i>Acta concilii Constantiensis</i>, 1896);
 and J. Lenfant&rsquo;s <i>Histoire de la guerre des Hussites</i> (1731) and the same
 writer&rsquo;s <i>Histoire du concile de Constance</i> (1714) should be consulted.
-F. Palacky&rsquo;s <i>Geschichte Böhmens</i> (1864-1867) is also very useful.
+F. Palacky&rsquo;s <i>Geschichte Böhmens</i> (1864-1867) is also very useful.
 Monographs on Huss are very numerous. Among them may be
-mentioned J. A. von Helfert, <i>Studien über Hus und Hieronymus</i>
-(1853; this work is ultramontane in its sympathies); C. von Höfler,
+mentioned J. A. von Helfert, <i>Studien über Hus und Hieronymus</i>
+(1853; this work is ultramontane in its sympathies); C. von Höfler,
 <i>Hus und der Abzug der deutschen Professoren und Studenten aus Prag</i>
-(1864); W. Berger, <i>Johannes Hus und König Sigmund</i> (1871);
-E. Denis, <i>Huss et la guerre des Hussites</i> (1878); P. Uhlmann, <i>König
-Sigmunds Geleit für Hus</i> (1894); J. Loserth, <i>Hus und Wiclif</i> (1884),
+(1864); W. Berger, <i>Johannes Hus und König Sigmund</i> (1871);
+E. Denis, <i>Huss et la guerre des Hussites</i> (1878); P. Uhlmann, <i>König
+Sigmunds Geleit für Hus</i> (1894); J. Loserth, <i>Hus und Wiclif</i> (1884),
 translated into English by M. J. Evans (1884); A. Jeep, <i>Gerson,
 Wiclefus, Hussus, inter se comparati</i> (1857); and G. von Lechler,
-<i>Johannes Hus</i> (1889). See also Count Lützow, <i>The Life and Times of
+<i>Johannes Hus</i> (1889). See also Count Lützow, <i>The Life and Times of
 John Hus</i> (London, 1909).</p>
 </div>
 
@@ -3135,7 +3097,7 @@ The citizens of Prague laid siege to the Vy&#353;ehrad, and towards
 the end of October (1420) the garrison was on the point of
 capitulating through famine. Sigismund attempted to relieve
 the fortress, but was decisively defeated by the Hussites on
-the 1st of November near the village of Pankrác. The castles
+the 1st of November near the village of Pankrác. The castles
 of Vy&#353;ehrad and Hrad&#269;any now capitulated, and shortly afterwards
 almost all Bohemia fell into the hands of the Hussites.
 Internal troubles prevented them from availing themselves
@@ -3185,7 +3147,7 @@ take part in the crusade, soon returned to his own country.
 Free for a time from foreign aggression, the Hussites invaded
 Moravia, where a large part of the population favoured their
 creed; but, again paralysed by dissensions, soon returned
-to Bohemia. The city of Königgrätz (Králové Hradec), which
+to Bohemia. The city of Königgrätz (Králové Hradec), which
 had been under Utraquist rule, espoused the doctrine of Tabor,
 and called &#381;i&#382;ka to its aid. After several military successes
 gained by &#381;i&#382;ka (<i>q.v.</i>) in 1423 and the following year, a treaty
@@ -3292,18 +3254,18 @@ Reformation.</p>
 
 <div class="condensed">
 <p>All histories of Bohemia devote a large amount of space to the
-Hussite movement. See Count Lützow, <i>Bohemia; an Historical
-Sketch</i> (London, 1896); Palacky, <i>Geschichte von Böhmen</i>; Bachmann,
-<i>Geschichte Böhmens</i>; L. Krummel, <i>Geschichte der böhmischen
+Hussite movement. See Count Lützow, <i>Bohemia; an Historical
+Sketch</i> (London, 1896); Palacky, <i>Geschichte von Böhmen</i>; Bachmann,
+<i>Geschichte Böhmens</i>; L. Krummel, <i>Geschichte der böhmischen
 Reformation</i> (Gotha, 1866) and <i>Utraquisten und Taboriten</i> (Gotha,
 1871); Ernest Denis, <i>Huss et la guerre des Hussites</i> (Paris, 1878);
-H. Toman, <i>Husitské Vále&#269;nictvi</i> (Prague, 1898).</p>
+H. Toman, <i>Husitské Vále&#269;nictvi</i> (Prague, 1898).</p>
 </div>
 <div class="author">(L.)</div>
 
 
 <hr class="art" />
-<p><span class="bold">HUSTING<a name="ar8" id="ar8"></a></span> (O. Eng. <i>hústing</i>, from Old Norwegian <i>hústhing</i>),
+<p><span class="bold">HUSTING<a name="ar8" id="ar8"></a></span> (O. Eng. <i>hústing</i>, from Old Norwegian <i>hústhing</i>),
 the &ldquo;thing&rdquo; or &ldquo;ting,&rdquo; <i>i.e.</i> assembly, of the household of
 personal followers or retainers of a king, earl or chief, contrasted
 with the &ldquo;folkmoot,&rdquo; the assembly of the whole people. &ldquo;Thing&rdquo;
@@ -3344,9 +3306,9 @@ did away with this public declaration of the nomination.</p>
 <p><span class="bold">HUSUM,<a name="ar9" id="ar9"></a></span> a town in the Prussian province of Schleswig-Holstein,
 in a fertile district 2<span class="spp">1</span>&frasl;<span class="suu">2</span> m. inland from the North Sea, on the
 canalized Husumer Au, which forms its harbour and roadstead,
-99 m. N.W. from Hamburg on a branch line from Tönning.
+99 m. N.W. from Hamburg on a branch line from Tönning.
 Pop. (1900) 8268. It has steam communication with the
-North Frisian Islands (Nordstrand, Föhr and Sylt), and is a
+North Frisian Islands (Nordstrand, Föhr and Sylt), and is a
 port for the cattle trade with England. Besides a ducal palace
 and park, it possesses an Evangelical church and a gymnasium.
 Cattle markets are held weekly, and in them, as also in cereals,
@@ -3796,7 +3758,7 @@ important of the modern schools of ethics (see especially art. <span class="sc">
 of general philosophy and of moral philosophy, as, for instance, in
 pt. vii. of Adam Smith&rsquo;s <i>Theory of Moral Sentiments</i>; Mackintosh&rsquo;s
 <i>Progress of Ethical Philosophy</i>; Cousin, <i>Cours d&rsquo;histoire de la
-philosophie morale du XVIII<span class="sp">e</span> siècle</i>; Whewell&rsquo;s <i>Lectures on the
+philosophie morale du XVIII<span class="sp">e</span> siècle</i>; Whewell&rsquo;s <i>Lectures on the
 History of Moral Philosophy in England</i>; A. Bain&rsquo;s <i>Mental and Moral
 Science</i>; Noah Porter&rsquo;s Appendix to the English translation of
 Ueberweg&rsquo;s <i>History of Philosophy</i>; Sir Leslie Stephen&rsquo;s <i>History of
@@ -3914,7 +3876,7 @@ September 1664. His career draws its chief interest from the
 after the death of her husband but not published till 1806 (since
 often reprinted), a work not only valuable for the picture which
 it gives of the man and of the time in which he lived, but for
-the simple beauty of its style, and the naïveté with which the
+the simple beauty of its style, and the naïveté with which the
 writer records her sentiments and opinions, and details the
 incidents of her private life.</p>
 
@@ -3933,7 +3895,7 @@ was born at Spennithorne, Yorkshire, in 1674. He served as
 steward in several families of position, latterly in that of the
 duke of Somerset, who ultimately obtained for him the post
 of riding purveyor to the master of the horse, a sinecure worth
-about £200 a year. In 1700 he became acquainted with Dr
+about £200 a year. In 1700 he became acquainted with Dr
 John Woodward (1665-1728) physician to the duke and author
 of a work entitled <i>The Natural History of the Earth</i>, to whom he
 entrusted a large number of fossils of his own collecting, along
@@ -4071,7 +4033,7 @@ historian, see M. C. Tyler&rsquo;s <i>Literary History of the American Revolutio
 Kansas, U.S.A., in the broad bottom-land on the N. side of
 the Arkansas river. Pop. (1900) 9379, of whom 414 were
 foreign-born and 442 negroes; (1910 census) 16,364. It
-is served by the Atchison, Topeka &amp; Santa Fé, the Missouri
+is served by the Atchison, Topeka &amp; Santa Fé, the Missouri
 Pacific and the Chicago, Rock Island &amp; Pacific railways. The
 principal public buildings are the Federal building and the county
 court house. The city has a public library, and an industrial
@@ -4126,7 +4088,7 @@ with both, sympathized with both, though he died before the
 Reformation had time fully to develop. His life may be divided
 into four parts:&mdash;his youth and cloister-life (1488-1504); his
 wanderings in pursuit of knowledge (1504-1515); his strife
-with Ulrich of Württemberg (1515-1519); and his connexion
+with Ulrich of Württemberg (1515-1519); and his connexion
 with the Reformation (1519-1523). Each of these periods
 had its own special antagonism, which coloured Hutten&rsquo;s career:
 in the first, his horror of dull monastic routine; in the second,
@@ -4173,7 +4135,7 @@ of Mainz, Archbishop Albert of Brandenburg. Here high
 dreams of a learned career rose on him; Mainz should be made
 the metropolis of a grand Humanist movement, the centre of
 good style and literary form. But the murder in 1515 of his
-relative Hans von Hutten by Ulrich, duke of Württemberg,
+relative Hans von Hutten by Ulrich, duke of Württemberg,
 changed the whole course of his life; satire, chief refuge of the
 weak, became Hutten&rsquo;s weapon; with one hand he took his
 part in the famous <i>Epistolae obscurorum virorum</i>, and with
@@ -4244,7 +4206,7 @@ fear of his loathsome diseases, and also because the beggared
 knight was sure to borrow money from him. A paper war
 consequently broke out between the two Humanists, which
 embittered Hutten&rsquo;s last days, and stained the memory of
-Erasmus. From Basel Ulrich dragged himself to Mülhausen;
+Erasmus. From Basel Ulrich dragged himself to Mülhausen;
 and when the vengeance of Erasmus drove him thence, he went
 to Zurich. There the large heart of Zwingli welcomed him;
 he helped him with money, and found him a quiet refuge with
@@ -4306,8 +4268,8 @@ which he attributes in the main to him. To him is due the more
 serious and severe tone of that bitter portion of the satire. See
 W. Brecht, <i>Die Verfasser der Epistolae obscurorum virorum</i> (1904).</p>
 
-<p>For a complete catalogue of the writings of Hutten, see E. Böcking&rsquo;s
-<i>Index Bibliographicus Huttenianus</i> (1858). Böcking is also the editor
+<p>For a complete catalogue of the writings of Hutten, see E. Böcking&rsquo;s
+<i>Index Bibliographicus Huttenianus</i> (1858). Böcking is also the editor
 of the complete edition of Hutten&rsquo;s works (7 vols., 1859-1862). A
 selection of Hutten&rsquo;s German writings, edited by G. Balke, appeared
 in 1891. Cp. S. Szamatolski, <i>Huttens deutsche Schriften</i> (1891).
@@ -4315,7 +4277,7 @@ The best biography (though it is also somewhat of a political
 pamphlet) is that of D. F. Strauss (<i>Ulrich von Hutten</i>, 1857;
 4th ed., 1878; English translation by G. Sturge, 1874), with
 which may be compared the older monographs by A. Wagenseil
-(1823), A. Bürck (1846) and J. Zeller (Paris, 1849). See also
+(1823), A. Bürck (1846) and J. Zeller (Paris, 1849). See also
 J. Deckert, <i>Ulrich von Huttens Leben und Wirken. Eine historische
 Skizze</i> (1901).</p>
 </div>
@@ -4770,7 +4732,7 @@ he had made during the voyage of the &ldquo;Rattlesnake.&rdquo; He was
 thus enabled to produce various important memoirs, especially
 those on certain Ascidians, in which he solved the problem
 of <i>Appendicularia</i>&mdash;an organism whose place in the animal
-kingdom Johannes Müller had found himself wholly unable
+kingdom Johannes Müller had found himself wholly unable
 to assign&mdash;and on the morphology of the Cephalous Mollusca.</p>
 
 <p>Richard Owen, then the leading comparative anatomist in
@@ -4779,7 +4741,7 @@ him the deductive explanation of anatomical fact from idealistic
 conceptions. He superadded the evolutionary theories of
 Oken, which were equally idealistic, but were altogether repugnant
 to Cuvier. Huxley would have none of either. Imbued
-with the methods of von Baer and Johannes Müller, his methods
+with the methods of von Baer and Johannes Müller, his methods
 were purely inductive. He would not hazard any statement
 beyond what the facts revealed. He retained, however, as has
 been done by his successors, the use of archetypes, though they
@@ -4800,7 +4762,7 @@ was a property inherent in the group. Herbert Spencer, whose
 acquaintance he made in 1852, was unable to convert him to
 evolution in its widest sense (<i>Life</i>, i. 168). He could not bring
 himself to acceptance of the theory&mdash;owing, no doubt, to his
-rooted aversion from à priori reasoning&mdash;without a mechanical
+rooted aversion from à priori reasoning&mdash;without a mechanical
 conception of its mode of operation. In his first interview
 with Darwin, which seems to have been about the same time,
 he expressed his belief &ldquo;in the sharpness of the lines of demarcation
@@ -5218,7 +5180,7 @@ founded on careful research and of great value.</p>
 <p><span class="bold">HUY<a name="ar24" id="ar24"></a></span> (Lat. <i>Hoium</i>, and Flem. <i>Hoey</i>), a town of Belgium,
 on the right bank of the Meuse, at the point where it is joined
 by the Hoyoux. Pop. (1904), 14,164. It is 19 m. E. of Namur
-and a trifle less west of Liége. Huy certainly dates from the
+and a trifle less west of Liége. Huy certainly dates from the
 7th century, and, according to some, was founded by the emperor
 <span class="pagenum"><a name="page21" id="page21"></a>21</span>
 Antoninus in <span class="scs">A.D.</span> 148. Its situation is striking, with its grey
@@ -5230,7 +5192,7 @@ of Neumoustier founded by Peter the Hermit on his return
 from the first crusade. He was buried there in 1115, and a
 statue was erected to his memory in the abbey grounds in
 1858. Neumoustier was one of seventeen abbeys in this town
-alone dependent on the bishopric of Liége. Huy is surrounded
+alone dependent on the bishopric of Liége. Huy is surrounded
 by vineyards, and the bridge which crosses the Meuse at this
 point connects the fertile Hesbaye north of the river with the
 rocky and barren Condroz south of it.</p>
@@ -5273,7 +5235,7 @@ publication, early in 1656, of the little tract <i>De Saturni luna
 observatio nova</i>; but retained, as regards the second, until
 1659, when in the <i>Systema Saturnium</i> the varying appearances
 of the so-called &ldquo;triple planet&rdquo; were clearly explained as the
-phases of a ring inclined at an angle of 28° to the ecliptic. Huygens
+phases of a ring inclined at an angle of 28° to the ecliptic. Huygens
 was also in 1656 the first effective observer of the Orion nebula;
 he delineated the bright region still known by his name, and
 detected the multiple character of its nuclear star. His application
@@ -5300,7 +5262,7 @@ made respectively in November and December 1668.</p>
 <p>Huygens had before this time fixed his abode in France.
 In 1665 Colbert made to him on behalf of Louis XIV. an offer
 too tempting to be refused, and between the following year and
-1681 his residence in the philosophic seclusion of the Bibliothèque
+1681 his residence in the philosophic seclusion of the Bibliothèque
 du Roi was only interrupted by two short visits to his native
 country. His <i>magnum opus</i> dates from this period. The
 <i>Horologium oscillatorium</i>, published with a dedication to his
@@ -5354,7 +5316,7 @@ he was enabled to prove the fundamental laws of optics, and
 to assign the correct construction for the direction of the extraordinary
 ray in uniaxial crystals. These investigations, together
 with his discovery of the &ldquo;wonderful phenomenon&rdquo; of polarization,
-are recorded in his <i>Traité de la lumière</i>, published at
+are recorded in his <i>Traité de la lumière</i>, published at
 Leiden in 1690, but composed in 1678. In the appended
 treatise <i>Sur la Cause de la pesanteur</i>, he rejected gravitation as
 a universal quality of matter, although admitting the Newtonian
@@ -5397,25 +5359,25 @@ Hugenii aliorumque seculi XVII. virorum celebrium exercitationes
 mathematicae et philosophicae</i> (the Hague, 1833).</p>
 
 <p>The publication of a monumental edition of the letters and works
-of Huygens was undertaken at the Hague by the <i>Société Hollandaise
+of Huygens was undertaken at the Hague by the <i>Société Hollandaise
 des Sciences</i>, with the heading <i>&OElig;uvres de Christian Huygens</i> (1888),
 &amp;c. Ten quarto volumes, comprising the whole of his correspondence,
 had already been issued in 1905. A biography of Huygens was
-prefixed to his <i>Opera varia</i> (1724); his <i>Éloge</i> in the character of a
+prefixed to his <i>Opera varia</i> (1724); his <i>Éloge</i> in the character of a
 French academician was printed by J. A. N. Condorcet in 1773.
 Consult further: P. J. Uylenbroek, <i>Oratio de fratribus Christiano
 atque Constantino Hugenio</i> (Groningen, 1838); P. Harting, <i>Christiaan
 Huygens in zijn Leven en Werken geschetzt</i> (Groningen, 1868); J. B. J.
 Delambre, <i>Hist. de l&rsquo;astronomie moderne</i> (ii. 549); J. E. Montucla,
-<i>Hist. des mathématiques</i> (ii. 84, 412, 549); M. Chasles, <i>Aperçu historique
-sur l&rsquo;origine des méthodes en géometrie</i>, pp. 101-109; E. Dühring,
+<i>Hist. des mathématiques</i> (ii. 84, 412, 549); M. Chasles, <i>Aperçu historique
+sur l&rsquo;origine des méthodes en géometrie</i>, pp. 101-109; E. Dühring,
 <i>Kritische Geschichte der allgemeinen Principien der Mechanik</i>,
 Abschnitt (ii. 120, 163, iii. 227); A. Berry, <i>A Short History of
 Astronomy</i>, p. 200; R. Wolf, <i>Geschichte der Astronomie</i>, passim;
 Houzeau, <i>Bibliographie astronomique</i> (ii. 169); F. Kaiser, <i>Astr. Nach.</i>
 (xxv. 245, 1847); <i>Tijdschrift voor de Wetenschappen</i> (i. 7, 1848);
 <i>Allgemeine deutsche Biographie</i> (M. B. Cantor); J. C. Poggendorff,
-<i>Biog. lit. Handwörterbuch</i>.</p>
+<i>Biog. lit. Handwörterbuch</i>.</p>
 </div>
 <div class="author">(A. M. C.)</div>
 
@@ -5574,23 +5536,23 @@ European continent.</p>
 was born at Paris on the 5th of February 1848. He belonged
 to a family of artists of Dutch extraction; he entered the
 ministry of the interior, and was pensioned after thirty years&rsquo;
-service. His earliest venture in literature, <i>Le Drageoir à épices</i>
+service. His earliest venture in literature, <i>Le Drageoir à épices</i>
 (1874), contained stories and short prose poems showing the
 influence of Baudelaire. <i>Marthe</i> (1876), the life of a courtesan,
 was published in Brussels, and Huysmans contributed a story,
-&ldquo;Sac au dos,&rdquo; to <i>Les Soirées de Médan</i>, the collection of stories
+&ldquo;Sac au dos,&rdquo; to <i>Les Soirées de Médan</i>, the collection of stories
 of the Franco-German war published by Zola. He then produced
 a series of novels of everyday life, including <i>Les S&oelig;urs
-Vatard</i> (1879), <i>En Ménage</i> (1881), and <i>À vau-l&rsquo;eau</i> (1882), in which
+Vatard</i> (1879), <i>En Ménage</i> (1881), and <i>À vau-l&rsquo;eau</i> (1882), in which
 he outdid Zola in minute and uncompromising realism. He
 was influenced, however, more directly by Flaubert and the
 brothers de Goncourt than by Zola. In <i>L&rsquo;Art moderne</i> (1883)
 he gave a careful study of impressionism and in <i>Certains</i> (1889)
-a series of studies of contemporary artists, <i>À Rebours</i> (1884),
+a series of studies of contemporary artists, <i>À Rebours</i> (1884),
 the history of the morbid tastes of a decadent aristocrat, des
 Esseintes, created a literary sensation, its caricature of literary
 and artistic symbolism covering much of the real beliefs of the
-leaders of the aesthetic revolt. In <i>Là-Bas</i> Huysmans&rsquo;s most
+leaders of the aesthetic revolt. In <i>Là-Bas</i> Huysmans&rsquo;s most
 characteristic hero, Durtal, makes his appearance. Durtal
 is occupied in writing the life of Gilles de Rais; the insight
 he gains into Satanism is supplemented by modern Parisian
@@ -5598,7 +5560,7 @@ students of the black art; but already there are signs of a
 leaning to religion in the sympathetic figures of the religious
 bell-ringer of Saint Sulpice and his wife. <i>En Route</i> (1895) relates
 the strange conversion of Durtal to mysticism and Catholicism
-in his retreat to La Trappe. In <i>La Cathédrale</i> (1898), Huysmans&rsquo;s
+in his retreat to La Trappe. In <i>La Cathédrale</i> (1898), Huysmans&rsquo;s
 symbolistic interpretation of the cathedral of Chartres, he
 develops his enthusiasm for the purity of Catholic ritual. The
 life of <i>Sainte Lydwine de Schiedam</i> (1901), an exposition of
@@ -5606,7 +5568,7 @@ the value of suffering, gives further proof of his conversion;
 and <i>L&rsquo;Oblat</i> (1903) describes Durtal&rsquo;s retreat to the Val des
 Saints, where he is attached as an oblate to a Benedictine
 monastery. Huysmans was nominated by Edmond de Goncourt
-as a member of the Académie des Goncourt. He died
+as a member of the Académie des Goncourt. He died
 as a devout Catholic, after a long illness of cancer in the palate
 on the 13th of May 1907. Before his death he destroyed his
 unpublished MSS. His last book was <i>Les Foules de Lourdes</i>
@@ -5614,8 +5576,8 @@ unpublished MSS. His last book was <i>Les Foules de Lourdes</i>
 
 <div class="condensed">
 <p>See Arthur Symons, <i>Studies in two Literatures</i> (1897) and <i>The
-Symbolist Movement in Literature</i> (1899); Jean Lionnet in <i>L&rsquo;Évolution
-des idées</i> (1903); Eugène Gilbert in <i>France et Belgique</i> (1905);
+Symbolist Movement in Literature</i> (1899); Jean Lionnet in <i>L&rsquo;Évolution
+des idées</i> (1903); Eugène Gilbert in <i>France et Belgique</i> (1905);
 J. Sargeret in <i>Les Grands convertis</i> (1906).</p>
 </div>
 
@@ -5678,10 +5640,10 @@ mountains in central Asia, its head-waters being in close
 proximity to those of the Yangtsze-Kiang. It has a total
 length of about 2400 m. and drains an area of approximately
 400,000 sq. m. The main stream has its source in two lakes
-named Tsaring-nor and Oring-nor, lying about 35° N., 97° E.,
+named Tsaring-nor and Oring-nor, lying about 35° N., 97° E.,
 and after flowing with a south-easterly course it bends sharply
 to the north-west and north, entering China in the province
-of Kansuh in lat. 36°. After passing Lanchow-fu, the capital
+of Kansuh in lat. 36°. After passing Lanchow-fu, the capital
 of this province, the river takes an immense sweep to the north
 and north-east, until it encounters the rugged barrier ranges
 that here run north and south through the provinces of Shansi
@@ -5794,18 +5756,18 @@ to Mercian supremacy, and possibly it was separated from
 Wessex in the time of Edwin. The first kings of whom we read
 were two brothers, Eanhere and Eanfrith, probably contemporaries
 of Wulfhere. They were followed by a king named Osric,
-a contemporary of Æthelred, and he by a king Oshere. Oshere
-had three sons who reigned after him, Æthelheard, Æthelweard
-and Æthelric. The two last named appear to have been reigning
+a contemporary of Æthelred, and he by a king Oshere. Oshere
+had three sons who reigned after him, Æthelheard, Æthelweard
+and Æthelric. The two last named appear to have been reigning
 in the year 706. At the beginning of Offa&rsquo;s reign we again find
 the kingdom ruled by three brothers, named Eanberht, Uhtred
 and Aldred, the two latter of whom lived until about 780. After
 them the title of king seems to have been given up. Their
-successor Æthelmund, who was killed in a campaign against
+successor Æthelmund, who was killed in a campaign against
 Wessex in 802, is described only as an earl. The district remained
 in possession of the rulers of Mercia until the fall of that
 kingdom. Together with the rest of English Mercia it submitted
-to King Alfred about 877-883 under Earl Æthelred, who possibly
+to King Alfred about 877-883 under Earl Æthelred, who possibly
 himself belonged to the Hwicce. No genealogy or list of kings
 has been preserved, and we do not know whether the dynasty
 was connected with that of Wessex or Mercia.</p>
@@ -5939,7 +5901,7 @@ in an open place on a dry hard bed of ashes, and be covered over to a
 depth of 6 or 8 in. with the same material or with fibre or soil; and
 when the roots are well developed, which will take from six to eight
 weeks, they may be removed to a frame, and gradually exposed to
-light, and then placed in a forcing pit in a heat of from 60 to 70°.
+light, and then placed in a forcing pit in a heat of from 60 to 70°.
 When the flowers are fairly open, they may be removed to the greenhouse
 or conservatory.</p>
 
@@ -6107,7 +6069,7 @@ both of whom are connected with Apollo Agyieus.</p>
 <p>See L. R. Farnell, <i>Cults of the Greek States</i>, vol. iv. (1907), pp. 125
 foll., 264 foll.; J. G. Frazer, <i>Adonis, Attis, Osiris</i> (1906), bk. ii.
 ch. 7; S. Wide, <i>Lakonische Kulte</i>, p. 290; E. Rhode, <i>Psyche</i>,
-3rd ed. i. 137 foll.; Roscher, <i>Lexikon d. griech. u. röm. Myth.</i>, <i>s.v.</i>
+3rd ed. i. 137 foll.; Roscher, <i>Lexikon d. griech. u. röm. Myth.</i>, <i>s.v.</i>
 &ldquo;Hyakinthos&rdquo; (Greve); L. Preller, <i>Griechische Mythol.</i> 4th ed.
 i. 248 foll.</p>
 </div>
@@ -6129,7 +6091,7 @@ two and seven. As a reward for having brought up Zeus at
 Dodona and taken care of the infant Dionysus Hyes, whom they
 conveyed to Ino (sister of his mother Semele) at Thebes when his
 life was threatened by Lycurgus, they were translated to heaven
-and placed among the stars (Hyginus, <i>Poët. astron.</i> ii. 21).
+and placed among the stars (Hyginus, <i>Poët. astron.</i> ii. 21).
 Another form of the story combines them with the Pleiades.
 According to this they were twelve (or fifteen) sisters, whose
 brother Hyas was killed by a snake while hunting in Libya
@@ -6170,7 +6132,7 @@ He died at Cambridge on the 15th of January 1902.</p>
 Cephalopoda</i> (1883); <i>Larval Theory of the Origin of Cellular Tissue</i>
 (1884); <i>Genesis of the Arietidae</i> (1889); and <i>Phylogeny of an acquired
 characteristic</i> (1894). He wrote the section on Cephalopoda in
-Karl von Zittel&rsquo;s <i>Paläontologie</i> (1900), and his well-known study on
+Karl von Zittel&rsquo;s <i>Paläontologie</i> (1900), and his well-known study on
 the fossil pond snails of Steinheim (&ldquo;The Genesis of the Tertiary
 Species of Planorbis at Steinheim&rdquo;) appeared in the <i>Memoirs</i> of the
 Boston Natural History Society in 1880. He was one of the founders
@@ -6183,7 +6145,7 @@ and editors of the <i>American Naturalist</i>.</p>
 historically, though its exact site is uncertain, is Hybla Major,
 near (or by some supposed to be identical with) Megara Hyblaea
 (<i>q.v.</i>): another Hybla, known as Hybla Minor or Galeatis, is
-represented by the modern Paternò; while the site of Hybla
+represented by the modern Paternò; while the site of Hybla
 Heraea is to be sought near Ragusa.</p>
 
 
@@ -6220,12 +6182,12 @@ in the second decade of the 18th century, produced the cross
 which is still grown in gardens under the name of &ldquo;Fairchild&rsquo;s
 Sweet William.&rdquo; Linnaeus made many experiments in the
 cross-fertilization of plants and produced several hybrids, but
-Joseph Gottlieb Kölreuter (1733-1806) laid the first real foundation
+Joseph Gottlieb Kölreuter (1733-1806) laid the first real foundation
 of our scientific knowledge of the subject. Later on Thomas
 Andrew Knight, a celebrated English horticulturist, devoted
 much successful labour to the improvement of fruit trees and
 vegetables by crossing. In the second quarter of the 19th
-century C. F. Gärtner made and published the results of a number
+century C. F. Gärtner made and published the results of a number
 of experiments that had not been equalled by any earlier worker.
 Next came Charles Darwin, who first in the <i>Origin of Species</i>,
 and later in <i>Cross and Self-Fertilization of Plants</i>, subjected the
@@ -6328,7 +6290,7 @@ series of experiments with Lepidopterous insects, and has obtained a
 very large series of hybrids, of which he has kept careful record.
 Lepidopterists generally begin to suspect that many curious forms
 offered by dealers as new species are products got by crossing known
-species. Apellö has succeeded with Teleostean fish; Gebhardt and
+species. Apellö has succeeded with Teleostean fish; Gebhardt and
 others with Amphibia. Elliot and Suchetet have studied carefully
 the question of hybridization occurring normally among birds, and
 have got together a very large body of evidence. Among the cases
@@ -6399,7 +6361,7 @@ when the actual impregnation of the egg is possible naturally, or has
 been secured by artificial means, the development of the hybrid may
 stop at an early stage. Thus hybrids between the urchin and the
 starfish, animals belonging to different classes, reached only the
-stage of the pluteus larva. A. D. Apellö, experimenting with
+stage of the pluteus larva. A. D. Apellö, experimenting with
 Teleostean fish, found that very often impregnation and segmentation
 occurred, but that the development broke down immediately
 afterwards. W. Gebhardt, crossing <i>Rana esculenta</i> with <i>R. arvalis</i>,
@@ -6535,7 +6497,7 @@ undoubtedly agree more with the wild sire.&rdquo;</p>
 <p>Ewart&rsquo;s experiments and his discussion of them also throw
 important light on the general relation of hybrids to their
 parents. He found that the coloration and pattern of his
-zebra hybrids resembled far more those of the Somali or Grévy&rsquo;s
+zebra hybrids resembled far more those of the Somali or Grévy&rsquo;s
 zebra than those of their sire&mdash;a Burchell&rsquo;s zebra. In a general
 discussion of the stripings of horses, asses and zebras, he came
 to the conclusion that the Somali zebra represented the older
@@ -6718,34 +6680,34 @@ sphere of natural selection and to be a fundamental fact of
 living matter.</p>
 
 <div class="condensed">
-<p><span class="sc">Authorities.</span>&mdash;Apellö, &ldquo;Über einige Resultate der Kreuzbefruchtung
+<p><span class="sc">Authorities.</span>&mdash;Apellö, &ldquo;Über einige Resultate der Kreuzbefruchtung
 bei Knochenfischen,&rdquo; <i>Bergens mus. aarbog</i> (1894);
 Bateson, &ldquo;Hybridization and Cross-breeding,&rdquo; <i>Journal of the Royal
 Horticultural Society</i> (1900); J. L. Bonhote, &ldquo;Hybrid Ducks,&rdquo; <i>Proc.
 Zool. Soc. of London</i> (1905), p. 147; Boveri, article &ldquo;Befruchtung,&rdquo;
 in <i>Ergebnisse der Anatomie und Entwickelungsgeschichte von Merkel
-und Bonnet</i>, i. 385-485; Cornevin et Lesbre, &ldquo;Étude sur un hybride
-issu d&rsquo;une mule féconde et d&rsquo;un cheval,&rdquo; <i>Rev. Sci.</i> li. 144; Charles
+und Bonnet</i>, i. 385-485; Cornevin et Lesbre, &ldquo;Étude sur un hybride
+issu d&rsquo;une mule féconde et d&rsquo;un cheval,&rdquo; <i>Rev. Sci.</i> li. 144; Charles
 Darwin, <i>Origin of Species</i> (1859), <i>The Effects of Cross and Self-Fertilization
 in the Vegetable Kingdom</i> (1878); Delage, <i>La Structure
-du protoplasma et les théories sur l&rsquo;hérédité</i> (1895, with a literature);
+du protoplasma et les théories sur l&rsquo;hérédité</i> (1895, with a literature);
 de Vries, &ldquo;The Law of Disjunction of Hybrids,&rdquo; <i>Comptes rendus</i>
 (1900), p. 845; Elliot, <i>Hybridism</i>; Escherick, &ldquo;Die biologische
-Bedeutung der Genitalabhänge der Insecten,&rdquo; <i>Verh. z. B. Wien</i>, xlii.
+Bedeutung der Genitalabhänge der Insecten,&rdquo; <i>Verh. z. B. Wien</i>, xlii.
 225; Ewart, <i>The Penycuik Experiments</i> (1899); Focke, <i>Die
 Pflanzen-Mischlinge</i> (1881); Foster-Melliar, <i>The Book of the Rose</i>
 (1894); C. F. Gaertner, various papers in <i>Flora</i>, 1828, 1831, 1832,
-1833, 1836, 1847, on &ldquo;Bastard-Pflanzen&rdquo;; Gebhardt, &ldquo;Über die
+1833, 1836, 1847, on &ldquo;Bastard-Pflanzen&rdquo;; Gebhardt, &ldquo;Ãœber die
 Bastardirung von <i>Rana esculenta</i> mit <i>R. arvalis</i>,&rdquo; <i>Inaug. Dissert.</i>
-(Breslau, 1894); G. Mendel, &ldquo;Versuche über Pflanzen-Hybriden,&rdquo;
-<i>Verh. Natur. Vereins in Brünn</i> (1865), pp. 1-52; Morgan, &ldquo;Experimental
+(Breslau, 1894); G. Mendel, &ldquo;Versuche über Pflanzen-Hybriden,&rdquo;
+<i>Verh. Natur. Vereins in Brünn</i> (1865), pp. 1-52; Morgan, &ldquo;Experimental
 Studies,&rdquo; <i>Anat. Anz.</i> (1893), p. 141; id. p. 803; G. J.
 Romanes, &ldquo;Physiological Selection,&rdquo; <i>Jour. Linn. Soc.</i> xix. 337;
 H. Scherren, &ldquo;Notes on Hybrid Bears,&rdquo; <i>Proc. Zool. Soc. of
 London</i> (1907), p. 431; Saunders, <i>Proc. Roy. Soc.</i> (1897), lxii. 11;
-Standfuss, &ldquo;Études de zoologie expérimentale,&rdquo; <i>Arch. Sci. Nat.</i>
-vi. 495; Suchetet, &ldquo;Les Oiseaux hybrides rencontrés à l&rsquo;état
-sauvage,&rdquo; <i>Mém. Soc. Zool.</i> v. 253-525, and vi. 26-45; Vernon,
+Standfuss, &ldquo;Études de zoologie expérimentale,&rdquo; <i>Arch. Sci. Nat.</i>
+vi. 495; Suchetet, &ldquo;Les Oiseaux hybrides rencontrés à l&rsquo;état
+sauvage,&rdquo; <i>Mém. Soc. Zool.</i> v. 253-525, and vi. 26-45; Vernon,
 &ldquo;The Relation between the Hybrid and Parent Forms of Echinoid
 Larvae,&rdquo; <i>Proc. Roy. Soc.</i> lxv. 350; Wallace, <i>Darwinism</i> (1889);
 Weismann, <i>The Germ-Plasm</i> (1893).</p>
@@ -6757,16 +6719,16 @@ Weismann, <i>The Germ-Plasm</i> (1893).</p>
 <p><span class="bold">HYDANTOIN<a name="ar39" id="ar39"></a></span> (glycolyl urea),
 C<span class="su">3</span>H<span class="su">4</span>N<span class="su">2</span>O<span class="su">2</span> or
 <img style="width:130px; height:70px; vertical-align: middle;" src="images/img29.jpg" alt="" />
-the ureïde of glycollic acid, may be obtained by heating allantoin
+the ureïde of glycollic acid, may be obtained by heating allantoin
 or alloxan with hydriodic acid, or by heating bromacetyl urea
 with alcoholic ammonia. It crystallizes in needles, melting
-at 216° C.</p>
+at 216° C.</p>
 
 <p>When hydrolysed with baryta water yields hydantoic
 <span class="pagenum"><a name="page30" id="page30"></a>30</span>
-(glycoluric)acid, H<span class="su">2</span>N·CO·NH·CH<span class="su">2</span>·CO<span class="su">2</span>H, which is readily soluble
+(glycoluric)acid, H<span class="su">2</span>N·CO·NH·CH<span class="su">2</span>·CO<span class="su">2</span>H, which is readily soluble
 in hot water, and on heating with hydriodic acid decomposes
-into ammonia, carbon dioxide and glycocoll, CH<span class="su">2</span>·NH<span class="su">2</span>·CO<span class="su">2</span>·H.
+into ammonia, carbon dioxide and glycocoll, CH<span class="su">2</span>·NH<span class="su">2</span>·CO<span class="su">2</span>·H.
 Many substituted hydantoins are known; the &alpha;-alkyl hydantoins
 are formed on fusion of aldehyde- or ketone-cyanhydrins
 with urea, the &beta;-alkyl hydantoins from the fusion of mono-alkyl
@@ -6846,7 +6808,7 @@ Lord Clarendon, the historian, to the Bodleian Library at Oxford.</p>
 <div class="condensed">
 <p>See Lord Clarendon, <i>The Life of Edward, Earl of Clarendon</i> (3 vols.,
 Oxford, 1827); Edward Foss, <i>The Judges of England</i> (London,
-1848-1864); Anthony à Wood, <i>Athenae oxonienses</i> (London, 1813-1820);
+1848-1864); Anthony à Wood, <i>Athenae oxonienses</i> (London, 1813-1820);
 Samuel Pepys, <i>Diary and Correspondence</i>, edited by Lord
 Braybrooke (4 vols., London, 1854).</p>
 </div>
@@ -6935,14 +6897,14 @@ John. The borough, incorporated in 1881, is under a mayor,
 
 <hr class="art" />
 <p><span class="bold">HYDE DE NEUVILLE, JEAN GUILLAUME,<a name="ar43" id="ar43"></a></span> <span class="sc">Baron</span> (1776-1857),
-French politician, was born at La Charité-sur-Loire
-(Nièvre) on the 24th of January 1776, the son of Guillaume
+French politician, was born at La Charité-sur-Loire
+(Nièvre) on the 24th of January 1776, the son of Guillaume
 Hyde, who belonged to an English family which had emigrated
 with the Stuarts after the rebellion of 1745. He was only seventeen
-when he successfully defended a man denounced by Fouché
+when he successfully defended a man denounced by Fouché
 before the revolutionary tribunal of Nevers. From 1793 onwards
 he was an active agent of the exiled princes; he took part in the
-Royalist rising in Berry in 1796, and after the <i>coup d&rsquo;état</i> of the
+Royalist rising in Berry in 1796, and after the <i>coup d&rsquo;état</i> of the
 18th Brumaire (November 9, 1799) tried to persuade Bonaparte
 to recall the Bourbons. An accusation of complicity in the
 infernal machine conspiracy of 1800-1801 was speedily retracted,
@@ -6957,7 +6919,7 @@ a commercial treaty. On his return in 1821 he declined the
 Constantinople embassy, and in November 1822 was elected
 deputy for Cosne. Shortly afterwards he was appointed French
 ambassador at Lisbon, where his efforts to oust British influence
-culminated, in connexion with the <i>coup d&rsquo;état</i> of Dom Miguel
+culminated, in connexion with the <i>coup d&rsquo;état</i> of Dom Miguel
 (April 30, 1824), in his suggestion to the Portuguese minister
 to invite the armed intervention of Great Britain. It was assumed
 that this would be refused, in view of the loudly proclaimed
@@ -6969,7 +6931,7 @@ disapproved of the Portuguese constitution. This destroyed
 his influence at Lisbon, and he returned to Paris to take his
 seat in the Chamber of Deputies. In spite of his pronounced
 Royalism, he now showed Liberal tendencies, opposed the
-policy of Villèle&rsquo;s cabinet, and in 1828 became a member of the
+policy of Villèle&rsquo;s cabinet, and in 1828 became a member of the
 moderate administration of Martignac as minister of marine.
 In this capacity he showed active sympathy with the cause of
 Greek independence. During the Polignac ministry (1829-1830)
@@ -6980,7 +6942,7 @@ line of the Bourbons from the throne, and resigned his seat.
 He died in Paris on the 28th of May 1857.</p>
 
 <div class="condensed">
-<p>His <i>Mémoires et souvenirs</i> (3 vols., 1888), compiled from his notes
+<p>His <i>Mémoires et souvenirs</i> (3 vols., 1888), compiled from his notes
 by his nieces, the vicomtesse de Bardonnet and the baronne Laurenceau,
 are of great interest for the Revolution and the Restoration.</p>
 </div>
@@ -7055,7 +7017,7 @@ into Rajputana.</p>
 Dominions, the principal native state of India in extent, population
 and political importance; area, 82,698 sq. m.; pop.
 (1901) 11,141,142, showing a decrease of 3.4% in the decade;
-estimated revenue 4<span class="spp">1</span>&frasl;<span class="suu">2</span> crores of Hyderabad rupees (£2,500,000).
+estimated revenue 4<span class="spp">1</span>&frasl;<span class="suu">2</span> crores of Hyderabad rupees (£2,500,000).
 The state occupies a large portion of the eastern plateau of the
 Deccan. It is bounded on the north and north-east by Berar,
 on the south and south-east by Madras, and on the west by
@@ -7155,7 +7117,7 @@ of the Imperial Service Troops, which now form the contribution
 of the native chiefs to the defence of India. On the occasion
 of the Panjdeh incident in 1885 he made an offer of money and
 men, and subsequently on the occasion of Queen Victoria&rsquo;s
-Jubilee in 1887 he offered 20 lakhs (£130,000) annually for three
+Jubilee in 1887 he offered 20 lakhs (£130,000) annually for three
 years for the purpose of frontier defence. It was finally decided
 that the native chiefs should maintain small but well-equipped
 bodies of infantry and cavalry for imperial defence. For many
@@ -7164,7 +7126,7 @@ condition, the expenditure consistently outran the revenue,
 and the nobles, who held their tenure under an obsolete feudal
 system, vied with each other in ostentatious extravagance.
 But in 1902, on the revision of the Berar agreement, the nizam
-received 25 lakhs (£167,000) a year for the rent of Berar, thus
+received 25 lakhs (£167,000) a year for the rent of Berar, thus
 substituting a fixed for a fluctuating source of income, and
 a British financial adviser was appointed for the purpose of
 reorganizing the resources of the state.</p>
@@ -7284,7 +7246,7 @@ but in vain; this breach of faith stung him to fury, and
 thenceforward he and his son did not cease to thirst for vengeance.
 His time came when in 1778 the British, on the declaration of
 war with France, resolved to drive the French out of India.
-The capture of Mahé on the coast of Malabar in 1779, followed
+The capture of Mahé on the coast of Malabar in 1779, followed
 by the annexation of lands belonging to a dependent of his own,
 gave him the needed pretext. Again master of all that the
 Mahrattas had taken from him, and with empire extended to the
@@ -7315,7 +7277,7 @@ series (1893). For the personal character and administration of
 Hyder Ali see the <i>History of Hyder Naik</i>, written by Mir Hussein Ali
 Khan Kirmani (translated from the Persian by Colonel Miles, and
 published by the Oriental Translation Fund), and the curious work
-written by M. Le Maître de La Tour, commandant of his artillery
+written by M. Le Maître de La Tour, commandant of his artillery
 (<i>Histoire d&rsquo;Hayder-Ali Khan</i>, Paris, 1783). For the whole life and
 times see Wilks, <i>Historical Sketches of the South of India</i> (1810-1817);
 Aitchison&rsquo;s Treaties, vol. v. (2nd ed., 1876); and Pearson, <i>Memoirs
@@ -7383,18 +7345,18 @@ of south Russia more especially they derived great wealth. In
 10,000 were seafarers. At the time of the outbreak of the war of
 Greek independence the total population was 28,190, of whom
 16,460 were natives and the rest foreigners. One of their chief
-families, the Konduriotti, was worth £2,000,000. Into the
+families, the Konduriotti, was worth £2,000,000. Into the
 struggle the Hydriotes flung themselves with rare enthusiasm
 and devotion, and the final deliverance of Greece was mainly
 due to the service rendered by their fleets.</p>
 
 <div class="condensed">
-<p>See Pouqueville, <i>Voy. de la Grèce</i>, vol. vi.; Antonios Miaoules,
-<span class="grk" title="Hypomnêma peri tês nêsou Hydras">&#8025;&#960;&#972;&#956;&#957;&#951;&#956;&#945; &#960;&#949;&#961;&#8054; &#964;&#8134;&#962; &#957;&#942;&#963;&#959;&#965; &#8029;&#948;&#961;&#945;&#962;</span> (Munich, 1834); Id. <span class="grk" title="Sunoptikê historia
-tôn naumachiôn dia tôn ploiôn tôn triôn nêsôn, Hydras, Petsôn kai Psarôn">&#931;&#965;&#957;&#959;&#960;&#964;&#953;&#954;&#8052; &#7985;&#963;&#964;&#959;&#961;&#943;&#945;
+<p>See Pouqueville, <i>Voy. de la Grèce</i>, vol. vi.; Antonios Miaoules,
+<span class="grk" title="Hypomnêma peri tês nêsou Hydras">&#8025;&#960;&#972;&#956;&#957;&#951;&#956;&#945; &#960;&#949;&#961;&#8054; &#964;&#8134;&#962; &#957;&#942;&#963;&#959;&#965; &#8029;&#948;&#961;&#945;&#962;</span> (Munich, 1834); Id. <span class="grk" title="Sunoptikê historia
+tôn naumachiôn dia tôn ploiôn tôn triôn nêsôn, Hydras, Petsôn kai Psarôn">&#931;&#965;&#957;&#959;&#960;&#964;&#953;&#954;&#8052; &#7985;&#963;&#964;&#959;&#961;&#943;&#945;
 &#964;&#8182;&#957; &#957;&#945;&#965;&#956;&#945;&#967;&#953;&#8182;&#957; &#948;&#953;&#8048; &#964;&#8182;&#957; &#960;&#955;&#959;&#943;&#969;&#957; &#964;&#8182;&#957; &#964;&#961;&#943;&#969;&#957; &#957;&#942;&#963;&#969;&#957;, &#8029;&#948;&#961;&#945;&#962;, &#928;&#941;&#964;&#963;&#969;&#957; &#954;&#945;&#8054; &#936;&#945;&#961;&#8182;&#957;</span>
-(Nauplia, 1833); Id. <span class="grk" title="Historia tês nêsou Hydras">&#7993;&#963;&#964;&#959;&#961;&#943;&#945; &#964;&#8134;&#962; &#957;&#942;&#963;&#959;&#965; &#8029;&#948;&#961;&#945;&#962;</span> (Athens, 1874); G. D.
-Kriezes, <span class="grk" title="Historia tês nêsou Hydras">&#7993;&#963;&#964;&#961;&#943;&#945; &#964;&#8134;&#962; &#957;&#942;&#963;&#959;&#965; &#8029;&#948;&#961;&#945;&#962;</span> (Patras, 1860).</p>
+(Nauplia, 1833); Id. <span class="grk" title="Historia tês nêsou Hydras">&#7993;&#963;&#964;&#959;&#961;&#943;&#945; &#964;&#8134;&#962; &#957;&#942;&#963;&#959;&#965; &#8029;&#948;&#961;&#945;&#962;</span> (Athens, 1874); G. D.
+Kriezes, <span class="grk" title="Historia tês nêsou Hydras">&#7993;&#963;&#964;&#961;&#943;&#945; &#964;&#8134;&#962; &#957;&#942;&#963;&#959;&#965; &#8029;&#948;&#961;&#945;&#962;</span> (Patras, 1860).</p>
 </div>
 
 
@@ -7449,7 +7411,7 @@ variable, the range in magnitude being 4.5 to 6.</p>
 
 
 <hr class="art" />
-<p><span class="bold">HYDRACRYLIC ACID<a name="ar52" id="ar52"></a></span> (ethylene lactic acid), CH<span class="su">2</span>OH·CH<span class="su">2</span>·CO<span class="su">2</span>H.
+<p><span class="bold">HYDRACRYLIC ACID<a name="ar52" id="ar52"></a></span> (ethylene lactic acid), CH<span class="su">2</span>OH·CH<span class="su">2</span>·CO<span class="su">2</span>H.
 an organic oxyacid prepared by acting with silver oxide and
 water on &beta;-iodopropionic acid, or from ethylene by the addition
 of hypochlorous acid, the addition product being then treated
@@ -7457,12 +7419,12 @@ with potassium cyanide and hydrolysed by an acid. It may
 also be prepared by oxidizing the trimethylene glycol obtained
 by the action of hydrobromic acid on allylbromide. It is a
 syrupy liquid, which on distillation is resolved into water and
-the unsaturated acrylic acid, CH<span class="su">2</span>:CH·CO<span class="su">2</span>H. Chromic and
+the unsaturated acrylic acid, CH<span class="su">2</span>:CH·CO<span class="su">2</span>H. Chromic and
 nitric acids oxidize it to oxalic acid and carbon dioxide.
-Hydracrylic aldehyde, CH<span class="su">2</span>OH·CH<span class="su">2</span>·CHO, was obtained in 1904
+Hydracrylic aldehyde, CH<span class="su">2</span>OH·CH<span class="su">2</span>·CHO, was obtained in 1904
 by J. U. Nef (<i>Ann.</i> 335, p. 219) as a colourless oil by heating
 acrolein with water. Dilute alkalis convert it into crotonaldehyde,
-CH<span class="su">3</span>·CH:CH·CHO.</p>
+CH<span class="su">3</span>·CH:CH·CHO.</p>
 
 
 <hr class="art" />
@@ -7554,7 +7516,7 @@ embraced by the second definition are more usually
 termed <i>hydroxides</i>, since at one time they were regarded as combinations
 of an oxide with water, for example, calcium oxide or
 lime when slaked with water yielded calcium hydroxide, written
-formerly as CaO·H<span class="su">2</span>0. The general formulae of hydroxides
+formerly as CaO·H<span class="su">2</span>0. The general formulae of hydroxides
 are: M<span class="sp">i</span>OH, M<span class="sp">ii</span>(OH)<span class="su">2</span>, M<span class="sp">iii</span>(OH)<span class="su">3</span>, M<span class="sp">iv</span>(OH)<span class="su">4</span>, &amp;c., corresponding
 to the oxides M<span class="su">2</span><span class="sp">i</span>O, M<span class="sp">ii</span>O, M<span class="su">2</span><span class="sp">iii</span>O<span class="su">3</span>, M<span class="sp">iv</span>O<span class="su">2</span>, &amp;c., the Roman index
 denoting the valency of the element. There is an important
@@ -7576,13 +7538,13 @@ of the periodic table.</p>
 
 
 <hr class="art" />
-<p><span class="bold">HYDRAULICS<a name="ar56" id="ar56"></a></span> (Gr. <span class="grk" title="hydôr">&#8021;&#948;&#969;&#961;</span>, water, and <span class="grk" title="aulos">&#945;&#8016;&#955;&#972;&#962;</span>, a pipe), the branch
+<p><span class="bold">HYDRAULICS<a name="ar56" id="ar56"></a></span> (Gr. <span class="grk" title="hydôr">&#8021;&#948;&#969;&#961;</span>, water, and <span class="grk" title="aulos">&#945;&#8016;&#955;&#972;&#962;</span>, a pipe), the branch
 of engineering science which deals with the practical applications
 of the laws of hydromechanics.</p>
 
 <p class="pt2 center">I. THE DATA OF HYDRAULICS<a name="fa1f" id="fa1f" href="#ft1f"><span class="sp">1</span></a></p>
 
-<p>§ 1. <i>Properties of Fluids.</i>&mdash;The fluids to which the laws of
+<p>§ 1. <i>Properties of Fluids.</i>&mdash;The fluids to which the laws of
 practical hydraulics relate are substances the parts of which
 possess very great mobility, or which offer a very small resistance
 to distortion independently of inertia. Under the general
@@ -7607,7 +7569,7 @@ at any point in a fluid the pressure in all directions must be the
 same; or, in other words, the pressure on any small element
 of surface is independent of the orientation of the surface.</p>
 
-<p>§ 2. Fluids are divided into liquids, or incompressible fluids,
+<p>§ 2. Fluids are divided into liquids, or incompressible fluids,
 and gases, or compressible fluids. Very great changes of pressure
 change the volume of liquids only by a small amount, and if
 the pressure on them is reduced to zero they do not sensibly
@@ -7620,7 +7582,7 @@ incompressible. In dealing with gases the changes of volume
 which accompany changes of pressure must be taken into
 account.</p>
 
-<p>§ 3. Viscous fluids are those in which change of form under a
+<p>§ 3. Viscous fluids are those in which change of form under a
 continued stress proceeds gradually and increases indefinitely.
 A very viscous fluid opposes great resistance to change of form
 in a short time, and yet may be deformed considerably by a
@@ -7689,15 +7651,15 @@ of the layer. Putting &kappa; = &mu;/T, &kappa;&prime; = &mu;/nT,</p>
 <p class="noind">an expression first proposed by L. M. H. Navier. The coefficient &mu; is
 termed the coefficient of viscosity.</p>
 
-<p>According to J. Clerk Maxwell, the value of &mu; for air at &theta;° Fahr. in
+<p>According to J. Clerk Maxwell, the value of &mu; for air at &theta;° Fahr. in
 pounds, when the velocities are expressed in feet per second, is</p>
 
-<p class="center">&mu; = 0.000 000 025 6 (461° + &theta;);</p>
+<p class="center">&mu; = 0.000 000 025 6 (461° + &theta;);</p>
 
 <p class="noind">that is, the coefficient of viscosity is proportional to the absolute
 temperature and independent of the pressure.</p>
 
-<p>The value of &mu; for water at 77° Fahr. is, according to H. von
+<p>The value of &mu; for water at 77° Fahr. is, according to H. von
 Helmholtz and G. Piotrowski,</p>
 
 <p class="center">&mu; = 0.000 018 8,</p>
@@ -7710,7 +7672,7 @@ with increase of temperature.</p>
 <tr><td class="figright1"><img style="width:328px; height:242px" src="images/img35b.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 2.</span></td></tr></table>
 
-<p>§ 4. When a fluid flows in a very regular manner, as for instance
+<p>§ 4. When a fluid flows in a very regular manner, as for instance
 when It flows in a capillary tube, the velocities vary gradually
 at any moment from
 one point of the fluid
@@ -7755,7 +7717,7 @@ hindered by the viscosity of the fluid.</p>
 <p class="pt1 center"><span class="sc">Relation of Pressure, Density, and Temperature
 of Liquids</span></p>
 
-<p>§ 5. <i>Units of Volume.</i>&mdash;In practical calculations the cubic foot
+<p>§ 5. <i>Units of Volume.</i>&mdash;In practical calculations the cubic foot
 and gallon are largely used, and in metric countries the litre and
 cubic metre (= 1000 litres). The imperial gallon is now exclusively
 used in England, but the United States have retained the old English
@@ -7770,15 +7732,15 @@ wine gallon.</p>
 <tr><td class="tcl">1 litre</td> <td class="tcl">= 0.2201 imp. gallon</td> <td class="tcl">= 0.2641 U.S. gallon.</td></tr>
 </table>
 
-<p><i>Density of Water.</i>&mdash;Water at 53° F. and ordinary pressure contains
-62.4 &#8468; per cub. ft., or 10 &#8468; per imperial gallon at 62° F. The litre
-contains one kilogram of water at 4° C. or 1000 kilograms per cubic
+<p><i>Density of Water.</i>&mdash;Water at 53° F. and ordinary pressure contains
+62.4 &#8468; per cub. ft., or 10 &#8468; per imperial gallon at 62° F. The litre
+contains one kilogram of water at 4° C. or 1000 kilograms per cubic
 metre. River and spring water is not sensibly denser than pure
-water. But average sea water weighs 64 &#8468; per cub. ft. at 53° F.
+water. But average sea water weighs 64 &#8468; per cub. ft. at 53° F.
 The weight of water per cubic unit will be denoted by G. Ice free
 from air weighs 57.28 &#8468; per cub. ft. (Leduc).</p>
 
-<p>§ 6. <i>Compressibility of Liquids.</i>&mdash;The most accurate experiments
+<p>§ 6. <i>Compressibility of Liquids.</i>&mdash;The most accurate experiments
 show that liquids are sensibly compressed by very great pressures,
 and that up to a pressure of 65 atmospheres, or about 1000 &#8468; per
 sq. in., the compression is proportional to the pressure. The chief
@@ -7802,17 +7764,17 @@ elasticity of volume. With the notation of the differential calculus,</p>
 <tr><td class="tccm allb">&nbsp;</td> <td class="tccm allb">Canton.</td> <td class="tccm allb">Oersted.</td> <td class="tccm allb">Colladon<br />and Sturm.</td> <td class="tccm allb">Regnault.</td></tr>
 
 <tr><td class="tcl lb rb">Water</td> <td class="tcr rb">45,990,000</td> <td class="tcr rb">45,900,000</td> <td class="tcr rb">42,660,000</td> <td class="tcr rb">44,000,000</td></tr>
-<tr><td class="tcl lb rb">Sea water</td> <td class="tcr rb">52,900,000</td> <td class="tcc rb">··</td> <td class="tcc rb">··</td> <td class="tcc rb">··</td></tr>
-<tr><td class="tcl lb rb">Mercury</td> <td class="tcr rb">705,300,000</td> <td class="tcc rb">··</td> <td class="tcr rb">626,100,000</td> <td class="tcr rb">604,500,000</td></tr>
-<tr><td class="tcl lb rb">Oil</td> <td class="tcr rb">44,090,000</td> <td class="tcc rb">··</td> <td class="tcc rb">··</td> <td class="tcc rb">··</td></tr>
-<tr><td class="tcl lb rb bb">Alcohol</td> <td class="tcr rb bb">32,060,000</td> <td class="tcc rb bb">··</td> <td class="tcr rb bb">23,100,000</td> <td class="tcc rb bb">··</td></tr>
+<tr><td class="tcl lb rb">Sea water</td> <td class="tcr rb">52,900,000</td> <td class="tcc rb">··</td> <td class="tcc rb">··</td> <td class="tcc rb">··</td></tr>
+<tr><td class="tcl lb rb">Mercury</td> <td class="tcr rb">705,300,000</td> <td class="tcc rb">··</td> <td class="tcr rb">626,100,000</td> <td class="tcr rb">604,500,000</td></tr>
+<tr><td class="tcl lb rb">Oil</td> <td class="tcr rb">44,090,000</td> <td class="tcc rb">··</td> <td class="tcc rb">··</td> <td class="tcc rb">··</td></tr>
+<tr><td class="tcl lb rb bb">Alcohol</td> <td class="tcr rb bb">32,060,000</td> <td class="tcc rb bb">··</td> <td class="tcr rb bb">23,100,000</td> <td class="tcc rb bb">··</td></tr>
 </table>
 
 <p>According to the experiments of Grassi, the compressibility of
 water diminishes as the temperature increases, while that of ether,
 alcohol and chloroform is increased.</p>
 
-<p>§ 7. <i>Change of Volume and Density of Water with Change of Temperature.</i>&mdash;Although
+<p>§ 7. <i>Change of Volume and Density of Water with Change of Temperature.</i>&mdash;Although
 the change of volume of water with change of
 temperature is so small that it may generally be neglected in ordinary
 hydraulic calculations, yet it should be noted that there is a change
@@ -7869,14 +7831,14 @@ of Units</i>.</p>
 </table>
 
 <p>The weight per cubic foot has been calculated from the values of
-&rho;, on the assumption that 1 cub. ft. of water at 39.2° Fahr. is 62.425 &#8468;.
+&rho;, on the assumption that 1 cub. ft. of water at 39.2° Fahr. is 62.425 &#8468;.
 For ordinary calculations in hydraulics, the density of water (which
 will in future be designated by the symbol G) will be taken at 62.4 &#8468;
-per cub. ft., which is its density at 53° Fahr. It may be noted also
-that ice at 32° Fahr. contains 57.3 &#8468; per cub. ft. The values of &rho;
+per cub. ft., which is its density at 53° Fahr. It may be noted also
+that ice at 32° Fahr. contains 57.3 &#8468; per cub. ft. The values of &rho;
 are the densities in grammes per cubic centimetre.</p>
 
-<p>§ 8. <i>Pressure Column. Free Surface Level.</i>&mdash;Suppose a small
+<p>§ 8. <i>Pressure Column. Free Surface Level.</i>&mdash;Suppose a small
 vertical pipe introduced into a liquid at any point P (fig. 3). Then
 the liquid will rise in the pipe to a level OO, such that the pressure
 due to the column in the pipe exactly balances the pressure on its
@@ -7902,7 +7864,7 @@ at P.</p>
 <tr><td class="figright1"><img style="width:260px; height:232px" src="images/img36.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 3.</span></td></tr></table>
 
-<p>§ 9. <i>Relation of Pressure, Volume, Temperature and Density in
+<p>§ 9. <i>Relation of Pressure, Volume, Temperature and Density in
 Compressible Fluids.</i>&mdash;Certain problems on the flow of air and
 steam are so similar to
 those relating to the flow
@@ -7927,7 +7889,7 @@ the product of the pressure p and volume V of a given quantity of
 air is a constant (Boyle&rsquo;s law).</p>
 
 <p>Let p<span class="su">0</span> be mean atmospheric pressure (2116.8 &#8468; per sq. ft.), V<span class="su">0</span>
-the volume of 1 &#8468; of air at 32° Fahr. under the pressure p<span class="su">0</span>. Then</p>
+the volume of 1 &#8468; of air at 32° Fahr. under the pressure p<span class="su">0</span>. Then</p>
 
 <p class="center">p<span class="su">0</span>V<span class="su">0</span> = 26214.</p>
 <div class="author">(1)</div>
@@ -7938,14 +7900,14 @@ the volume of 1 &#8468; of air at 32° Fahr. under the pressure p<span class="su"
 <div class="author">(2)</div>
 
 <p class="noind">For any other pressure p, at which the volume of 1 &#8468; is V and the
-weight per cubic foot is G, the temperature being 32° Fahr.,</p>
+weight per cubic foot is G, the temperature being 32° Fahr.,</p>
 
 <p class="center">pV = p/G = 26214; or G = p/26214.</p>
 <div class="author">(3)</div>
 
 <p><i>Change of Pressure or Volume by Change of Temperature.</i>&mdash;Let p<span class="su">0</span>,
 V<span class="su">0</span>, G<span class="su">0</span>, as before be the pressure, the volume of a pound in cubic feet,
-and the weight of a cubic foot in pounds, at 32° Fahr. Let p, V, G
+and the weight of a cubic foot in pounds, at 32° Fahr. Let p, V, G
 be the same quantities at a temperature t (measured strictly by the
 air thermometer, the degrees of which differ a little from those of
 a mercurial thermometer). Then, by experiment,</p>
@@ -7953,8 +7915,8 @@ a mercurial thermometer). Then, by experiment,</p>
 <p class="center">pV = p<span class="su">0</span>V<span class="su">0</span> (460.6 + t) / (460.6 + 32) = p<span class="su">0</span>V<span class="su">0</span>&tau;/&tau;<span class="su">0</span>,</p>
 <div class="author">(4)</div>
 
-<p class="noind">where &tau;, &tau;<span class="su">0</span> are the temperatures t and 32° reckoned from the absolute
-zero, which is &minus;460.6° Fahr.;</p>
+<p class="noind">where &tau;, &tau;<span class="su">0</span> are the temperatures t and 32° reckoned from the absolute
+zero, which is &minus;460.6° Fahr.;</p>
 
 <p class="center">p/G = p<span class="su">0</span>&tau;/G<span class="su">0</span>&tau;<span class="su">0</span>;</p>
 <div class="author1">(4a)</div>
@@ -7968,12 +7930,12 @@ zero, which is &minus;460.6° Fahr.;</p>
 <div class="author1">(5a)</div>
 
 <p class="noind">Or quite generally p/G = R&tau; for all gases, if R is a constant varying
-inversely as the density of the gas at 32° F. For steam R = 85.5.</p>
+inversely as the density of the gas at 32° F. For steam R = 85.5.</p>
 </div>
 
 <p class="pt2 center">II. KINEMATICS OF FLUIDS</p>
 
-<p>§ 10. Moving fluids as commonly observed are conveniently
+<p>§ 10. Moving fluids as commonly observed are conveniently
 classified thus:</p>
 
 <p>(1) <i>Streams</i> are moving masses of indefinite length, completely
@@ -7997,7 +7959,7 @@ each other along such a constant path may be termed a fluid
 filament or elementary stream.</p>
 
 <div class="condensed">
-<p>§ 11. <i>Steady and Unsteady, Uniform and Varying, Motion.</i>&mdash;There
+<p>§ 11. <i>Steady and Unsteady, Uniform and Varying, Motion.</i>&mdash;There
 are two quite distinct ways of treating hydrodynamical questions.
 We may either fix attention on a given mass of fluid and consider
 its changes of position and energy under the action of the stresses
@@ -8041,7 +8003,7 @@ is a definite term applicable to the motion of the water, the other a
 less definite term applicable in strictness only to the condition of
 the stream bed.</p>
 
-<p>§ 12. <i>Theoretical Notions on the Motion of Water.</i>&mdash;The actual
+<p>§ 12. <i>Theoretical Notions on the Motion of Water.</i>&mdash;The actual
 motion of the particles of water is in most cases very complex. To
 simplify hydrodynamic problems, simpler modes of motion are
 assumed, and the results of theory so obtained are compared experimentally
@@ -8101,7 +8063,7 @@ actual more or less varying motions, the motion of the stream
 might be treated as steady stream line or steady laminar
 motion.</p>
 
-<p>§ 13. <i>Volume of Flow.</i>&mdash;Let A (fig. 6) be any ideal plane surface,
+<p>§ 13. <i>Volume of Flow.</i>&mdash;Let A (fig. 6) be any ideal plane surface,
 of area &omega;, in a stream, normal to the direction of motion, and let V
 be the velocity of the fluid. Then the volume flowing through the
 surface A in unit time is</p>
@@ -8135,7 +8097,7 @@ volume of flow is</p>
 
 <p class="noind">as the case may be.</p>
 
-<p>§ 14. <i>Principle of Continuity.</i>&mdash;If we consider any completely
+<p>§ 14. <i>Principle of Continuity.</i>&mdash;If we consider any completely
 bounded fixed space in a moving liquid initially and finally filled
 continuously with liquid, the inflow must be equal to the outflow.
 Expressing the inflow with a positive and the outflow with a negative
@@ -8198,7 +8160,7 @@ of inflow and outflow are</p>
 
 <p class="center">G<span class="su">1</span>A<span class="su">1</span>v<span class="su">1</span> = G<span class="su">2</span>A<span class="su">2</span>v<span class="su">2</span>;</p>
 
-<p class="noind">and hence, from (5a) § 9, if the temperature is constant,</p>
+<p class="noind">and hence, from (5a) § 9, if the temperature is constant,</p>
 
 <p class="center">p<span class="su">1</span>A<span class="su">1</span>v<span class="su">1</span> = p<span class="su">2</span>A<span class="su">2</span>v<span class="su">2</span>.</p>
 <div class="author">(3)</div>
@@ -8219,7 +8181,7 @@ of inflow and outflow are</p>
 <tr><td class="figright1"><img style="width:156px; height:262px" src="images/img38c.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 13.</span></td></tr></table>
 
-<p>§ 15. <i>Stream Lines.</i>&mdash;The characteristic of a perfect fluid, that is,
+<p>§ 15. <i>Stream Lines.</i>&mdash;The characteristic of a perfect fluid, that is,
 a fluid free from viscosity, is that the pressure between any two parts
 into which it is divided by a plane must be normal to the plane.
 One consequence of this is that the particles can have no rotation
@@ -8295,7 +8257,7 @@ ORIFICES AS ASCERTAINABLE BY EXPERIMENTS</p>
 <tr><td class="figright1"><img style="width:306px; height:398px" src="images/img38d.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 14.</span></td></tr></table>
 
-<p>§ 16. When a liquid issues vertically from a small orifice, it forms
+<p>§ 16. When a liquid issues vertically from a small orifice, it forms
 a jet which rises nearly to the level of the free surface of the liquid
 in the vessel from which
 it flows. The difference
@@ -8355,7 +8317,7 @@ the pressure head at the orifice. Lastly, the velocity v is connected
 with h by the relation v<span class="sp">2</span>/2g = h, so that v<span class="sp">2</span>/2g may be termed the
 head due to the velocity v.</p>
 
-<p>§ 17. <i>Coefficients of Velocity and Resistance.</i>&mdash;As the actual velocity
+<p>§ 17. <i>Coefficients of Velocity and Resistance.</i>&mdash;As the actual velocity
 of discharge differs from &radic;<span class="ov">2gh</span> by a small quantity, let the actual
 velocity</p>
 
@@ -8450,7 +8412,7 @@ to a transverse section of the
 jet. Hence the actual discharge
 when contraction occurs is</p>
 
-<p class="center">Q<span class="su">a</span> = c<span class="su">v</span>v × c<span class="su">c</span>&omega; = c<span class="su">c</span>c<span class="su">v</span>&omega; &radic;(2gh),</p>
+<p class="center">Q<span class="su">a</span> = c<span class="su">v</span>v × c<span class="su">c</span>&omega; = c<span class="su">c</span>c<span class="su">v</span>&omega; &radic;(2gh),</p>
 
 <p class="noind">or simply, if c = c<span class="su">v</span>c<span class="su">c</span>,</p>
 
@@ -8458,10 +8420,10 @@ when contraction occurs is</p>
 
 <p class="noind">where c is called the <i>coefficient
 of discharge</i>. Thus for a sharp-edged
-plane orifice c = 0.97 ×
+plane orifice c = 0.97 ×
 0.64 = 0.62.</p>
 
-<p>§ 18. <i>Experimental Determination
+<p>§ 18. <i>Experimental Determination
 of</i> c<span class="su">v</span>, c<span class="su">c</span>, <i>and</i> c.&mdash;The coefficient
 of contraction c<span class="su">c</span> is
 directly determined by measuring
@@ -8490,7 +8452,7 @@ then</p>
 <p class="center">c<span class="su">v</span> = v<span class="su">a</span> &radic; (2gh) = &radic; (x<span class="sp">2</span>/4yh).</p>
 
 <p>In the case of large orifices such as weirs, the velocity can be
-directly determined by using a Pitot tube (§ 144).</p>
+directly determined by using a Pitot tube (§ 144).</p>
 
 <table class="flt" style="float: right; width: 430px;" summary="Illustration">
 <tr><td class="figright1"><img style="width:378px; height:285px" src="images/img39c.jpg" alt="" /></td></tr>
@@ -8553,7 +8515,7 @@ orifice is the same</p>
 <tr><td class="figcenter"><img style="width:473px; height:160px" src="images/img39e.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 19.</span></td></tr></table>
 
-<p>§ 19. <i>Coefficients for Bellmouths and Bellmouthed Orifices.</i>&mdash;If an
+<p>§ 19. <i>Coefficients for Bellmouths and Bellmouthed Orifices.</i>&mdash;If an
 orifice is furnished with a mouthpiece exactly of the form of the
 contracted vein, then the whole of the contraction occurs within
 the mouthpiece, and if the area of the orifice is measured at the
@@ -8580,7 +8542,7 @@ c<span class="su">c</span> = 1, c = c<span class="su">v</span>; and therefore</p
 
 <p class="center">Q = c<span class="su">v</span>&omega; &radic; (2gh) = &omega; &radic; { 2gh / (1 + c<span class="su">r</span> }.</p>
 
-<p>§ 20. <i>Coefficients for Sharp-edged or virtually Sharp-edged Orifices.</i>&mdash;There
+<p>§ 20. <i>Coefficients for Sharp-edged or virtually Sharp-edged Orifices.</i>&mdash;There
 are a very large number of measurements of discharge from
 sharp-edged orifices under different conditions of head. An account
 of these and a very careful tabulation of the average values of the
@@ -8662,7 +8624,7 @@ the results agree with the formula</p>
 <p class="noind">where h is in feet and d in inches.</p>
 
 <p class="pt1 center"><i>Coefficients of Discharge from Circular Orifices.
-Temperature 51° to 55°.</i></p>
+Temperature 51° to 55°.</i></p>
 
 <table class="ws" summary="Contents">
 <tr><td class="tccm allb" rowspan="2">Head in<br />feet<br />h.</td> <td class="tccm allb" colspan="9">Diameters of Orifices in Inches (d).</td></tr>
@@ -8735,7 +8697,7 @@ in Vertical Plane Surfaces.</i></p>
 <tr><td class="tcc lb rb bb">50&emsp;</td> <td class="tcc rb bb">.6086</td> <td class="tcc rb bb">.6060</td> <td class="tcc rb bb">.6034</td> <td class="tcc rb bb">.6018</td> <td class="tcc rb bb">.6035</td> <td class="tcc rb bb">.6050</td> <td class="tcc rb bb">.6070</td> <td class="tcc rb bb">.6140</td></tr>
 </table>
 
-<p>§ 21. <i>Orifices with Edges of Sensible Thickness.</i>&mdash;When the edges of
+<p>§ 21. <i>Orifices with Edges of Sensible Thickness.</i>&mdash;When the edges of
 the orifice are not bevelled outwards, but have a sensible thickness,
 the coefficient of discharge is somewhat altered. The following
 table gives values of the coefficient of discharge for the arrangements
@@ -8746,7 +8708,7 @@ The heads were measured immediately over the orifice. In this case,</p>
 
 <p class="center">Q = cb (H  &minus; h) &radic; { 2g(H + h)/2 }.</p>
 
-<p>§ 22. <i>Partially Suppressed Contraction.</i>&mdash;Since the contraction of
+<p>§ 22. <i>Partially Suppressed Contraction.</i>&mdash;Since the contraction of
 the jet is due to the convergence towards the orifice of the issuing
 streams, it will be diminished if for any portion of the edge of the
 orifice the convergence is prevented. Thus, if an internal rim or
@@ -8810,7 +8772,7 @@ however, that these formulae
 for suppressed contraction
 are not reliable.</p>
 
-<p>§ 23. <i>Imperfect Contraction.</i>&mdash;If
+<p>§ 23. <i>Imperfect Contraction.</i>&mdash;If
 the sides of
 the vessel approach near
 to the edge of the orifice,
@@ -8832,7 +8794,7 @@ are imperfectly known.</p>
 <tr><td class="figcenter"><img style="width:957px; height:205px" src="images/img41c.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 22.</span></td></tr></table>
 
-<p>§ 24. <i>Orifices Furnished with Channels of Discharge.</i>&mdash;These external
+<p>§ 24. <i>Orifices Furnished with Channels of Discharge.</i>&mdash;These external
 borders to an orifice also modify the contraction.</p>
 
 <p>The following coefficients of discharge were obtained with openings
@@ -8856,7 +8818,7 @@ borders to an orifice also modify the contraction.</p>
 <tr><td class="figcenter"><img style="width:400px; height:531px" src="images/img41d.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 23.</span></td></tr></table>
 
-<p>§ 25. <i>Inversion of the Jet.</i>&mdash;When a jet issues from a horizontal
+<p>§ 25. <i>Inversion of the Jet.</i>&mdash;When a jet issues from a horizontal
 orifice, or is of small size compared with the head, it presents no
 marked peculiarity of form. But if the orifice is in a vertical surface,
 and if its dimensions are not small compared with the head,
@@ -8920,7 +8882,7 @@ previous sheets. Lord Rayleigh accepts an explanation of this contraction
 first suggested by H. Buff (1805-1878), namely, that it is
 due to surface tension.</p>
 
-<p>§ 26. <i>Influence of Temperature on Discharge of Orifices.</i>&mdash;Professor
+<p>§ 26. <i>Influence of Temperature on Discharge of Orifices.</i>&mdash;Professor
 VV. C. Unwin found (<i>Phil. Mag.</i>, October 1878, p. 281) that for
 sharp-edged orifices temperature has a very small influence on the
 discharge. For an orifice 1 cm. in diameter with heads of about
@@ -8928,8 +8890,8 @@ discharge. For an orifice 1 cm. in diameter with heads of about
 
 <table class="ws" style="clear: both;" summary="Contents">
 <tr><td class="tcc">Temperature F.</td> <td class="tcc"><i>C.</i></td></tr>
-<tr><td class="tcc">205°</td> <td class="tcc">.594</td></tr>
-<tr><td class="tcc">&ensp;62°</td> <td class="tcc">.598</td></tr>
+<tr><td class="tcc">205°</td> <td class="tcc">.594</td></tr>
+<tr><td class="tcc">&ensp;62°</td> <td class="tcc">.598</td></tr>
 </table>
 
 <p class="noind">For a conoidal or bell-mouthed orifice 1 cm. diameter the effect of
@@ -8937,24 +8899,24 @@ temperature was greater:&mdash;</p>
 
 <table class="ws" summary="Contents">
 <tr><td class="tcc">Temperature F.</td> <td class="tcc"><i>C.</i></td></tr>
-<tr><td class="tcc">190°</td> <td class="tcc">0.987</td></tr>
-<tr><td class="tcc">130°</td> <td class="tcc">0.974</td></tr>
-<tr><td class="tcc">&ensp;60°</td> <td class="tcc">0.942</td></tr>
+<tr><td class="tcc">190°</td> <td class="tcc">0.987</td></tr>
+<tr><td class="tcc">130°</td> <td class="tcc">0.974</td></tr>
+<tr><td class="tcc">&ensp;60°</td> <td class="tcc">0.942</td></tr>
 </table>
 
 <p class="noind">an increase in velocity of discharge of 4% when the temperature
-increased 130°.</p>
+increased 130°.</p>
 
 <p>J. G. Mair repeated these experiments on a much larger scale
 (<i>Proc. Inst. Civ. Eng.</i> lxxxiv.). For a sharp-edged orifice 2<span class="spp">1</span>&frasl;<span class="suu">2</span> in.
-diameter, with a head of 1.75 ft., the coefficient was 0.604 at 57°
-and 0.607 at 179° F., a very small difference. With a conoidal
-orifice the coefficient was 0.961 at 55° and 0.98l at 170° F. The
+diameter, with a head of 1.75 ft., the coefficient was 0.604 at 57°
+and 0.607 at 179° F., a very small difference. With a conoidal
+orifice the coefficient was 0.961 at 55° and 0.98l at 170° F. The
 corresponding coefficients of resistance are 0.0828 and 0.0391,
 showing that the resistance decreases to about half at the higher
 temperature.</p>
 
-<p>§ 27. <i>Fire Hose Nozzles.</i>&mdash;Experiments have been made by J. R.
+<p>§ 27. <i>Fire Hose Nozzles.</i>&mdash;Experiments have been made by J. R.
 Freeman on the coefficient of discharge from smooth cone nozzles
 used for fire purposes. The coefficient was found to be 0.983 for <span class="spp">3</span>&frasl;<span class="suu">4</span>-in.
 nozzle; 0.982 for <span class="spp">7</span>&frasl;<span class="suu">8</span> in.; 0.972 for 1 in.; 0.976 for 1<span class="spp">1</span>&frasl;<span class="suu">8</span> in.; and
@@ -8965,7 +8927,7 @@ for which the coefficient was smaller.</p>
 
 <p class="pt2 center">IV. THEORY OF THE STEADY MOTION OF FLUIDS.</p>
 
-<p>§ 28. The general equation of the steady motion of a fluid given
+<p>§ 28. The general equation of the steady motion of a fluid given
 under Hydrodynamics furnishes immediately three results as to the
 distribution of pressure in a stream which may here be assumed.</p>
 
@@ -8991,7 +8953,7 @@ section, the distribution of pressure is the same as in a fluid at rest.</p>
 
 <p class="pt1 center sc">Distribution of Energy in Incompressible Fluids.</p>
 
-<p>§ 29. <i>Application of the Principle of the Conservation of Energy to
+<p>§ 29. <i>Application of the Principle of the Conservation of Energy to
 Cases of Stream Line Motion.</i>&mdash;The external and internal work
 done on a mass is equal to the change of kinetic energy produced.
 In many hydraulic questions this principle is difficult to apply, because
@@ -9032,7 +8994,7 @@ gravity and the pressures on the ends of the stream.</p>
 <p>The work of gravity when AB falls to A&prime;B&prime; is the same as that of
 transferring AA&prime; to BB&prime;; that is, GQt (z &minus; z<span class="su">1</span>). The work of the
 pressures on the ends, reckoning that at B negative, because it is
-opposite to the direction of motion, is (p&omega; × vt) &minus; (p<span class="su">1</span>&omega;<span class="su">1</span> × v<span class="su">1</span>t) =
+opposite to the direction of motion, is (p&omega; × vt) &minus; (p<span class="su">1</span>&omega;<span class="su">1</span> × v<span class="su">1</span>t) =
 Qt(p &minus; p<span class="su">1</span>). The change of kinetic energy in the time t is the difference
 of the kinetic energy originally possessed by AA&prime; and that
 finally acquired by BB&prime;, for in the intermediate part A&prime;B there is
@@ -9054,7 +9016,7 @@ work done on the mass AB,</p>
 <div class="author">(2)</div>
 
 <p class="noind">Now v<span class="sp">2</span>/2g is the head due to the velocity v, p/G is the head equivalent
-to the pressure, and z is the elevation above the datum (see § 16).
+to the pressure, and z is the elevation above the datum (see § 16).
 Hence the terms on the left are the total head due to velocity,
 pressure, and elevation at a given cross section of the filament, z is
 easily seen to be the work in foot-pounds which would be done
@@ -9083,10 +9045,10 @@ form</p>
 <tr><td class="figcenter"><img style="width:465px; height:289px" src="images/img43a.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 26.</span></td></tr></table>
 
-<p>§ 30. <i>Second Form of the Theorem of Bernoulli.</i>&mdash;Suppose at the
+<p>§ 30. <i>Second Form of the Theorem of Bernoulli.</i>&mdash;Suppose at the
 two sections A, B (fig. 26) of an elementary stream small vertical
 pipes are introduced, which may be termed pressure columns
-(§ 8), having their lower ends accurately parallel to the direction of
+(§ 8), having their lower ends accurately parallel to the direction of
 flow. In such tubes the water will rise to heights corresponding to
 the pressures at A and B. Hence b = p/G, and b&prime; = p<span class="su">1</span>/G. Consequently
 the tops of the pressure columns A&prime; and B&prime; will be at
@@ -9096,7 +9058,7 @@ the fall of free surface level between A and B, is therefore</p>
 
 <p class="center">&xi; = (p &minus; p<span class="su">1</span>) / G + (z &minus; z<span class="su">1</span>);</p>
 
-<p class="noind">and this by equation (1), § 29 is (v<span class="su">1</span><span class="sp">2</span> &minus; v<span class="sp">2</span>)/2g. That is, the fall of
+<p class="noind">and this by equation (1), § 29 is (v<span class="su">1</span><span class="sp">2</span> &minus; v<span class="sp">2</span>)/2g. That is, the fall of
 free, surface level between two sections is equal to the difference
 of the heights due to the velocities at the sections. The line A&prime;B&prime;
 is sometimes called the line of hydraulic gradient, though this
@@ -9106,7 +9068,7 @@ sum of the elevation and pressure head at that point, and it falls
 below a horizontal line A&Prime;B&Prime; drawn at H ft. above XX by the
 quantities a = v<span class="sp">2</span>/2g and a&prime; = v<span class="su">1</span><span class="sp">2</span>/2g, when friction is absent.</p>
 
-<p>§ 31. <i>Illustrations of the Theorem of Bernoulli.</i> In a lecture to
+<p>§ 31. <i>Illustrations of the Theorem of Bernoulli.</i> In a lecture to
 the mechanical section of the British Association in 1875, W. Froude
 gave some experimental illustrations of the principle of Bernoulli.
 He remarked that it was a common but erroneous impression that
@@ -9188,7 +9150,7 @@ pressure acting uniformly throughout the system.</p>
 <tr><td class="figcenter"><img style="width:438px; height:245px" src="images/img43f.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 31.</span></td></tr></table>
 
-<p>§ 32. <i>Venturi Meter.</i>&mdash;An ingenious application of the variation
+<p>§ 32. <i>Venturi Meter.</i>&mdash;An ingenious application of the variation
 of pressure and velocity in a converging and diverging pipe has been
 made by Clemens Herschel in the construction of what he terms a
 Venturi Meter for measuring the flow in water mains. Suppose that,
@@ -9224,7 +9186,7 @@ areas are 12.57 and 113.1 sq. in., and &rho; = 9,</p>
 
 <p class="noind">and the discharge of the main is</p>
 
-<p class="center">28 × 12.57 = 351 cub. ft. per sec.</p>
+<p class="center">28 × 12.57 = 351 cub. ft. per sec.</p>
 
 <table class="nobctr" style="clear: both;" summary="Illustration">
 <tr><td class="figcenter"><img style="width:529px; height:243px" src="images/img44a.jpg" alt="" /></td></tr>
@@ -9282,7 +9244,7 @@ the larger area the velocity is less. It finds, therefore, a new position
 of equilibrium. A pencil P records on a drum moved by clockwork
 the position of the disk, and from this the variation of flow is inferred.</p>
 
-<p>§ 33. <i>Pressure, Velocity and Energy in Different Stream Lines.</i>&mdash;The
+<p>§ 33. <i>Pressure, Velocity and Energy in Different Stream Lines.</i>&mdash;The
 equation of Bernoulli gives the variation of pressure and velocity
 from point to point along a stream line, and shows that the total
 energy of the flow across any two sections is the same. Two other
@@ -9339,9 +9301,9 @@ introducing these values in (1),</p>
 
 <p class="pt1 center sc">Currents</p>
 
-<p>§ 34. <i>Rectilinear Current.</i>&mdash;Suppose the motion is in parallel
+<p>§ 34. <i>Rectilinear Current.</i>&mdash;Suppose the motion is in parallel
 straight stream lines (fig. 35) in a vertical plane. Then &rho; is infinite,
-and from eq. (2), § 33,</p>
+and from eq. (2), § 33,</p>
 
 <p class="center">dH = v dv/g.</p>
 
@@ -9419,7 +9381,7 @@ the circular elementary streams</p>
 <div class="author">(7)</div>
 
 <p>Consider two stream lines at radii r and r + dr (fig. 36). Then in
-(2), § 33, &rho; = r and ds = dr,</p>
+(2), § 33, &rho; = r and ds = dr,</p>
 
 <p class="center">v<span class="sp">2</span> dr/gr + v dv/g = 0,</p>
 
@@ -9448,18 +9410,18 @@ The water flows spirally outwards, its velocity diminishing and its
 pressure increasing according to the law stated above, and the head
 along each spiral stream line is constant.</p>
 
-<p>§ 35. <i>Forced Vortex.</i>&mdash;If the law of motion in a rotating current is
+<p>§ 35. <i>Forced Vortex.</i>&mdash;If the law of motion in a rotating current is
 different from that in a free vortex, some force must be applied to
 cause the variation of velocity. The simplest case is that of a
 rotating current in which all the particles have equal angular velocity,
 as for instance when they are driven round by radiating paddles
-revolving uniformly. Then in equation (2), § 33, considering two
+revolving uniformly. Then in equation (2), § 33, considering two
 circular stream lines of radii r and r + dr (fig. 37), we have &rho; = r,
 ds = dr. If the angular velocity is &alpha;, then v = &alpha;r and dv = &alpha;dr. Hence</p>
 
 <p class="center">dH = &alpha;<span class="sp">2</span>r dr/g + &alpha;<span class="sp">2</span>r dr/g = 2&alpha;<span class="sp">2</span>r dr/g.</p>
 
-<p class="noind">Comparing this with (1), § 33, and putting dz = 0, because the motion
+<p class="noind">Comparing this with (1), § 33, and putting dz = 0, because the motion
 is horizontal,</p>
 
 <p class="center">dp/G + &alpha;<span class="sp">2</span>r dr/g = 2&alpha;<span class="sp">2</span>r dr/g,</p>
@@ -9487,7 +9449,7 @@ are paraboloids of revolution (fig. 37).</p>
 
 <p class="pt1 center sc">Dissipation of Head in Shock</p>
 
-<p>§ 36. <i>Relation of Pressure and Velocity in a Stream in Steady
+<p>§ 36. <i>Relation of Pressure and Velocity in a Stream in Steady
 Motion when the Changes of Section of the Stream are Abrupt.</i>&mdash;When
 a stream changes section abruptly, rotating eddies are formed
 which dissipate energy. The energy absorbed in producing rotation
@@ -9559,7 +9521,7 @@ path of the stream. Then (since Q = &omega;<span class="su">1</span>v<span class
 <p class="center">p/G + v<span class="sp">2</span>/2g = p<span class="su">1</span>/G + v<span class="su">1</span><span class="sp">2</span>/2g + (v &minus; v<span class="su">1</span>)<span class="sp">2</span> / 2g.</p>
 <div class="author">(3)</div>
 
-<p class="noind">This differs from the expression (1), § 29, obtained for cases where
+<p class="noind">This differs from the expression (1), § 29, obtained for cases where
 no sensible internal work is done, by the last term on the right.
 That is, (v &minus; v<span class="su">1</span>)<span class="sp">2</span> / 2g has to be added to the total head at CD, which
 is p<span class="su">1</span>/G + v<span class="su">1</span><span class="sp">2</span>/2g, to make it equal to the total head at AB, or (v &minus; v<span class="su">1</span>)<span class="sp">2</span> / 2g
@@ -9592,7 +9554,7 @@ MOUTHPIECES</p>
 <tr><td class="figright1"><img style="width:338px; height:420px" src="images/img46b.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 39.</span></td></tr></table>
 
-<p>§ 37. <i>Minimum Coefficient of Contraction. Re-entrant Mouthpiece
+<p>§ 37. <i>Minimum Coefficient of Contraction. Re-entrant Mouthpiece
 of Borda.</i>&mdash;In one special case the coefficient of contraction
 can be determined
 theoretically, and, as
@@ -9677,7 +9639,7 @@ little from the theoretical value, 0.5, given above.</p>
 <tr><td class="caption"><span class="sc">Fig. 40.</span></td>
 <td class="caption"><span class="sc">Fig. 41.</span></td></tr></table>
 
-<p>§ 38. <i>Velocity of Filaments issuing in a Jet.</i>&mdash;A jet is composed
+<p>§ 38. <i>Velocity of Filaments issuing in a Jet.</i>&mdash;A jet is composed
 of fluid filaments or elementary streams, which start into motion at
 some point in the
 interior of the vessel
@@ -9699,7 +9661,7 @@ parallel and
 exercise uniform mutual pressure. Take the free surface AB for
 datum line, and let p<span class="su">1</span>, v<span class="su">1</span>, h<span class="su">1</span>, be the pressure, velocity and depth
 below datum at M; p, v, h, the corresponding quantities at m.
-Then § 29, eq. (3a),</p>
+Then § 29, eq. (3a),</p>
 
 <p class="center">v<span class="su">1</span><span class="sp">2</span>/2g + p<span class="su">1</span>/G &minus; h<span class="su">1</span> = v<span class="sp">2</span>/2g + p/G &minus; h</p>
 <div class="author">(1)</div>
@@ -9739,7 +9701,7 @@ Orifice.</i>&mdash;Let the orifice
 discharge below the level
 of the tail water. Then
 using the notation shown in fig. 41, we have at M, v<span class="su">1</span> = 0, p<span class="su">1</span> = Gh; + p<span class="su">a</span>
-at m, p = Gh<span class="su">3</span> + p<span class="su">a</span>. Inserting these values in (3), § 29,</p>
+at m, p = Gh<span class="su">3</span> + p<span class="su">a</span>. Inserting these values in (3), § 29,</p>
 
 <p class="center">0 + h<span class="su">1</span> + p<span class="su">a</span>/G &minus; h<span class="su">1</span> = v<span class="sp">2</span>/2g + h<span class="su">3</span> &minus; h<span class="su">2</span>2 + p<span class="su">a</span>/G;</p>
 
@@ -9813,7 +9775,7 @@ not sensibly the same.</p>
 <tr><td class="figright1"><img style="width:351px; height:231px" src="images/img47b.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 43.</span></td></tr></table>
 
-<p>§ 39. <i>Large Rectangular Jets from Orifices in Vertical Plane Surfaces.</i>&mdash;Let
+<p>§ 39. <i>Large Rectangular Jets from Orifices in Vertical Plane Surfaces.</i>&mdash;Let
 an orifice in a vertical plane surface be so formed that it
 produces a jet having
 a rectangular contracted
@@ -9907,7 +9869,7 @@ which are in question.</p>
 <tr><td class="figcenter"><img style="width:385px; height:187px" src="images/img47c.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 44.</span></td></tr></table>
 
-<p>§ 40. <i>Large Jets having a Circular Section from Orifices in a Vertical
+<p>§ 40. <i>Large Jets having a Circular Section from Orifices in a Vertical
 Plane Surface.</i>&mdash;Let fig. 44 represent the section of the jet, OO being
 the free surface level in the reservoir. The discharge through the
 horizontal strip aabb, of breadth aa = b, between the depths h<span class="su">1</span> + y
@@ -9945,7 +9907,7 @@ parts of the orifice is taken into account, is very small.</p>
 
 <p class="pt1 center sc">Notches and Weirs</p>
 
-<p>§ 41. <i>Notches, Weirs and Byewashes.</i>&mdash;A notch is an orifice extending
+<p>§ 41. <i>Notches, Weirs and Byewashes.</i>&mdash;A notch is an orifice extending
 up to the free surface level in the reservoir from which the
 discharge takes place. A weir is a structure over which the water
 flows, the discharge being in the same conditions as for a notch.
@@ -9967,7 +9929,7 @@ point where the velocity of the water is very small.</p>
 <p>Since the area of the notch opening is BH, the above formula is
 of the form</p>
 
-<p class="center">Q = c × BH × k &radic;(2gH),</p>
+<p class="center">Q = c × BH × k &radic;(2gH),</p>
 
 <p class="noind">where k is a factor depending on the form of the notch and expressing
 the ratio of the mean velocity of discharge to the velocity due to the
@@ -9977,7 +9939,7 @@ depth H.</p>
 <tr><td class="figright1"><img style="width:325px; height:530px" src="images/img48a.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 45.</span></td></tr></table>
 
-<p>§ 42. <i>Francis&rsquo;s Formula for Rectangular Notches.</i>&mdash;The jet discharged
+<p>§ 42. <i>Francis&rsquo;s Formula for Rectangular Notches.</i>&mdash;The jet discharged
 through a rectangular notch has a section smaller than BH,
 (<i>a</i>) because of the fall of the water surface from the point where H
 <span class="pagenum"><a name="page48" id="page48"></a>48</span>
@@ -10024,7 +9986,7 @@ width of the jet is l &minus; 0.1nH, where n is the number of end contractions
 of the stream. The contractions due to the fall of surface and to the
 crest contraction are proportional to the width of the jet. Hence, if cH
 is the thickness of the stream over the weir, measured at the contracted
-section, the section of the jet will be c(l &minus; 0.1nH)H and (§ 41) the
+section, the section of the jet will be c(l &minus; 0.1nH)H and (§ 41) the
 mean velocity will be <span class="spp">2</span>&frasl;<span class="suu">3</span> &radic;(2gH). Consequently the discharge will
 be given by an equation of the form</p>
 
@@ -10037,7 +9999,7 @@ much more nearly constant for different values of l and h than in
 the ordinary formula. Francis found for c the mean value 0.622,
 the weir being sharp-edged.</p>
 
-<p>§ 43. <i>Triangular Notch</i> (fig. 46).&mdash;Consider a lamina issuing between
+<p>§ 43. <i>Triangular Notch</i> (fig. 46).&mdash;Consider a lamina issuing between
 the depths h and h + dh. Its area, neglecting contraction, will
 be bdh, and the velocity at that depth is &radic;(2gh). Hence the discharge
 for this lamina is</p>
@@ -10084,11 +10046,11 @@ to be the case.
 Hence a triangular
 notch is more suitable for accurate gaugings than a rectangular
 notch. For a sharp-edged triangular notch Professor J. Thomson
-found c = 0.617. It will be seen, as in § 41, that since <span class="spp">1</span>&frasl;<span class="suu">2</span>BH is the
+found c = 0.617. It will be seen, as in § 41, that since <span class="spp">1</span>&frasl;<span class="suu">2</span>BH is the
 area of section of the stream through the notch, the formula is
 again of the form</p>
 
-<p class="center">Q = c × <span class="spp">1</span>&frasl;<span class="suu">2</span>BH × k &radic;(2gH),</p>
+<p class="center">Q = c × <span class="spp">1</span>&frasl;<span class="suu">2</span>BH × k &radic;(2gH),</p>
 
 <p class="noind">where k = <span class="spp">8</span>&frasl;<span class="suu">15</span> is the ratio of the mean velocity in the notch to the
 velocity at the depth H. It may easily be shown that for all notches
@@ -10102,7 +10064,7 @@ is very strongly marked.</i></p>
 <tr><td class="tccm allb f80" rowspan="2">Heads in<br />inches<br />measured<br />from still<br />Water in<br />Reservoir.</td> <td class="tccm allb f80" colspan="2">Sharp Edge.</td> <td class="tccm allb f80" colspan="4">Planks 2 in. thick,<br />square on Crest.</td> <td class="tccm allb f80" colspan="6">Crests 3 ft. wide.</td></tr>
 
 <tr><td class="tccm allb f80">3 ft. long.</td> <td class="tccm allb f80">10 ft. long.</td> <td class="tccm allb f80">3 ft. long.</td> <td class="tccm allb f80">6 ft. long.</td> <td class="tccm allb f80">10 ft. long.</td>
-  <td class="tccm allb f80">10 ft. long,<br />wing-boards<br />making an<br />angle of 60°.</td>
+  <td class="tccm allb f80">10 ft. long,<br />wing-boards<br />making an<br />angle of 60°.</td>
   <td class="tccm allb f80">3 ft. long.<br />level.</td> <td class="tccm allb f80">3 ft. long,<br />fall 1 in 18.</td>
   <td class="tccm allb f80">3 ft. long,<br />fall 1 in 12.</td> <td class="tccm allb f80">6 ft. long.<br />level.</td>
   <td class="tccm allb f80">10 ft. long.<br />level.</td> <td class="tccm allb f80">10 ft. long,<br />fall 1 in 18.</td></tr>
@@ -10125,7 +10087,7 @@ is very strongly marked.</i></p>
 <tr><td class="figcenter"><img style="width:458px; height:151px" src="images/img48c.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 47.</span></td></tr></table>
 
-<p>§ 44. <i>Weir with a Broad Sloping Crest.</i>&mdash;Suppose a weir formed
+<p>§ 44. <i>Weir with a Broad Sloping Crest.</i>&mdash;Suppose a weir formed
 with a broad crest so sloped that the streams flowing over it have a
 movement sensibly rectilinear and uniform (fig. 47). Let the inner
 edge be so rounded as to prevent a crest contraction. Consider a
@@ -10162,7 +10124,7 @@ to the ordinary weir formula with c = 0.577.</p>
 
 <p class="pt1 center sc">Special Cases of Discharge from Orifices</p>
 
-<p>§ 45. <i>Cases in which the Velocity of Approach needs to be taken
+<p>§ 45. <i>Cases in which the Velocity of Approach needs to be taken
 into Account.</i> <i>Rectangular Orifices and Notches.</i>&mdash;In finding the
 velocity at the orifice in the preceding investigations, it has been
 assumed that the head h has been measured from the free surface
@@ -10215,7 +10177,7 @@ above will give a second and much more approximate value of Q.</p>
 <tr><td class="figcenter"><img style="width:459px; height:279px" src="images/img49b.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 49.</span></td></tr></table>
 
-<p>§ 46. <i>Partially Submerged Rectangular Orifices and Notches.</i>&mdash;When
+<p>§ 46. <i>Partially Submerged Rectangular Orifices and Notches.</i>&mdash;When
 the tail water is above the lower but below the upper edge
 of the orifice, the flow in the two parts of the orifice, into which it
 is divided by the surface of the tail water, takes place under different
@@ -10285,11 +10247,11 @@ a drowned weir. But the
 value of c in this case is
 imperfectly known.</p>
 
-<p>§ 47. <i>Bazin&rsquo;s Researches on
+<p>§ 47. <i>Bazin&rsquo;s Researches on
 Weirs.</i>&mdash;H. Bazin has executed a long series of researches on the
 flow over weirs, so systematic and complete that they almost
 supersede other observations. The account of them is contained
-in a series of papers in the <i>Annales des Ponts et Chaussées</i>
+in a series of papers in the <i>Annales des Ponts et Chaussées</i>
 (October 1888, January 1890, November 1891, February 1894,
 December 1896, 2nd trimestre 1898). Only a very abbreviated
 account can be given here. The general plan of the experiments
@@ -10300,7 +10262,7 @@ flow, to compare the observed heads on the different weirs and
 to determine their coefficients from the discharge computed at
 the standard weir. A channel was constructed parallel to the
 Canal de Bourgogne, taking water from it through three sluices
-0.3 × 1.0 metres. The water enters a masonry chamber 15 metres
+0.3 × 1.0 metres. The water enters a masonry chamber 15 metres
 long by 4 metres wide where it is stilled and passes into the canal
 at the end of which is the standard weir. The canal has a length
 of 15 metres, a width of 2 metres and a depth of 0.6 metres. From
@@ -10514,7 +10476,7 @@ when the sheet is
 free and the weir
 of the same height.</p>
 
-<p>§ 48. <i>Separating
+<p>§ 48. <i>Separating
 Weirs.</i>&mdash;Many
 towns derive their
 water-supply from
@@ -10574,7 +10536,7 @@ the divisions on af give the parabolic path of the jet.</p>
 
 <p class="pt1 center sc">Mouthpieces&mdash;Head Constant</p>
 
-<p>§ 49. <i>Cylindrical Mouthpieces.</i>&mdash;When water issues from a short
+<p>§ 49. <i>Cylindrical Mouthpieces.</i>&mdash;When water issues from a short
 cylindrical pipe or mouthpiece of a length at least equal to l<span class="spp">1</span>&frasl;<span class="suu">2</span> times
 its smallest transverse dimension, the stream, after contraction within
 the mouthpiece, expands to fill it and issues full bore, or without
@@ -10600,7 +10562,7 @@ at a point where its velocity is sensibly zero, is h + p<span class="su">a</span
 total head is v<span class="sp">2</span>/2g + p/G; at GH it is v<span class="su">1</span><span class="sp">2</span>/2g + p<span class="su">1</span>/G.</p>
 
 <p>Between EF and GH there is a loss of head due to abrupt change
-of velocity, which from eq. (3), § 36, may have the value</p>
+of velocity, which from eq. (3), § 36, may have the value</p>
 
 <p class="center">(v &minus; v<span class="su">1</span>)<span class="sp">2</span>/2g.</p>
 
@@ -10675,7 +10637,7 @@ will be forced continuously into the jet by the atmospheric pressure,
 and discharged with it. This is the crudest form of a kind of pump
 known as the jet pump.</p>
 
-<p>§ 50. <i>Convergent Mouthpieces.</i>&mdash;With convergent mouthpieces
+<p>§ 50. <i>Convergent Mouthpieces.</i>&mdash;With convergent mouthpieces
 there is a contraction within the mouthpiece causing a loss of head,
 and a diminution of the velocity of discharge, as with cylindrical
 mouthpieces. There is also a second contraction of the stream outside
@@ -10694,28 +10656,28 @@ orifice = 0.05085 ft. Length of mouthpiece = 2.6 Diameters.</i></p>
 <table class="ws" summary="Contents">
 <tr><td class="tccm allb">Angle of<br />Convergence.</td> <td class="tccm allb">Coefficient of<br />Contraction,<br />c<span class="su">c</span></td> <td class="tccm allb">Coefficient of<br />Velocity,<br />c<span class="su">v</span></td> <td class="tccm allb">Coefficient of<br />Discharge,<br />c</td></tr>
 
-<tr><td class="tcc lb rb">&ensp;0° &ensp;0&prime;</td> <td class="tcc rb">&ensp;.999</td> <td class="tcc rb">.830</td> <td class="tcc rb">.829</td></tr>
-<tr><td class="tcc lb rb">&ensp;1° 36&prime;</td> <td class="tcc rb">1.000</td> <td class="tcc rb">.866</td> <td class="tcc rb">.866</td></tr>
-<tr><td class="tcc lb rb">&ensp;3° 10&prime;</td> <td class="tcc rb">1.001</td> <td class="tcc rb">.894</td> <td class="tcc rb">.895</td></tr>
-<tr><td class="tcc lb rb">&ensp;4° 10&prime;</td> <td class="tcc rb">1.002</td> <td class="tcc rb">.910</td> <td class="tcc rb">.912</td></tr>
-<tr><td class="tcc lb rb">&ensp;5° 26&prime;</td> <td class="tcc rb">1.004</td> <td class="tcc rb">.920</td> <td class="tcc rb">.924</td></tr>
-<tr><td class="tcc lb rb">&ensp;7° 52&prime;</td> <td class="tcc rb">&ensp;.998</td> <td class="tcc rb">.931</td> <td class="tcc rb">.929</td></tr>
-<tr><td class="tcc lb rb">&ensp;8° 58&prime;</td> <td class="tcc rb">&ensp;.992</td> <td class="tcc rb">.942</td> <td class="tcc rb">.934</td></tr>
-<tr><td class="tcc lb rb">10° 20&prime;</td> <td class="tcc rb">&ensp;.987</td> <td class="tcc rb">.950</td> <td class="tcc rb">.938</td></tr>
-<tr><td class="tcc lb rb">12° 4&prime;</td> <td class="tcc rb">&ensp;.986</td> <td class="tcc rb">.955</td> <td class="tcc rb">.942</td></tr>
-<tr><td class="tcc lb rb">13° 24&prime;</td> <td class="tcc rb">&ensp;.983</td> <td class="tcc rb">.962</td> <td class="tcc rb">.946</td></tr>
-<tr><td class="tcc lb rb">14° 28&prime;</td> <td class="tcc rb">&ensp;.979</td> <td class="tcc rb">.966</td> <td class="tcc rb">.941</td></tr>
-<tr><td class="tcc lb rb">16° 36&prime;</td> <td class="tcc rb">&ensp;.969</td> <td class="tcc rb">.971</td> <td class="tcc rb">.938</td></tr>
-<tr><td class="tcc lb rb">19° 28&prime;</td> <td class="tcc rb">&ensp;.953</td> <td class="tcc rb">.970</td> <td class="tcc rb">.924</td></tr>
-<tr><td class="tcc lb rb">21° &ensp;0&prime;</td> <td class="tcc rb">&ensp;.945</td> <td class="tcc rb">.971</td> <td class="tcc rb">.918</td></tr>
-<tr><td class="tcc lb rb">23° &ensp;0&prime;</td> <td class="tcc rb">&ensp;.937</td> <td class="tcc rb">.974</td> <td class="tcc rb">.913</td></tr>
-<tr><td class="tcc lb rb">29° 58&prime;</td> <td class="tcc rb">&ensp;.919</td> <td class="tcc rb">.975</td> <td class="tcc rb">.896</td></tr>
-<tr><td class="tcc lb rb">40° 20&prime;</td> <td class="tcc rb">&ensp;.887</td> <td class="tcc rb">.980</td> <td class="tcc rb">.869</td></tr>
-<tr><td class="tcc lb rb bb">48° 50&prime;</td> <td class="tcc rb bb">&ensp;.861</td> <td class="tcc rb bb">.984</td> <td class="tcc rb bb">.847</td></tr>
+<tr><td class="tcc lb rb">&ensp;0° &ensp;0&prime;</td> <td class="tcc rb">&ensp;.999</td> <td class="tcc rb">.830</td> <td class="tcc rb">.829</td></tr>
+<tr><td class="tcc lb rb">&ensp;1° 36&prime;</td> <td class="tcc rb">1.000</td> <td class="tcc rb">.866</td> <td class="tcc rb">.866</td></tr>
+<tr><td class="tcc lb rb">&ensp;3° 10&prime;</td> <td class="tcc rb">1.001</td> <td class="tcc rb">.894</td> <td class="tcc rb">.895</td></tr>
+<tr><td class="tcc lb rb">&ensp;4° 10&prime;</td> <td class="tcc rb">1.002</td> <td class="tcc rb">.910</td> <td class="tcc rb">.912</td></tr>
+<tr><td class="tcc lb rb">&ensp;5° 26&prime;</td> <td class="tcc rb">1.004</td> <td class="tcc rb">.920</td> <td class="tcc rb">.924</td></tr>
+<tr><td class="tcc lb rb">&ensp;7° 52&prime;</td> <td class="tcc rb">&ensp;.998</td> <td class="tcc rb">.931</td> <td class="tcc rb">.929</td></tr>
+<tr><td class="tcc lb rb">&ensp;8° 58&prime;</td> <td class="tcc rb">&ensp;.992</td> <td class="tcc rb">.942</td> <td class="tcc rb">.934</td></tr>
+<tr><td class="tcc lb rb">10° 20&prime;</td> <td class="tcc rb">&ensp;.987</td> <td class="tcc rb">.950</td> <td class="tcc rb">.938</td></tr>
+<tr><td class="tcc lb rb">12° 4&prime;</td> <td class="tcc rb">&ensp;.986</td> <td class="tcc rb">.955</td> <td class="tcc rb">.942</td></tr>
+<tr><td class="tcc lb rb">13° 24&prime;</td> <td class="tcc rb">&ensp;.983</td> <td class="tcc rb">.962</td> <td class="tcc rb">.946</td></tr>
+<tr><td class="tcc lb rb">14° 28&prime;</td> <td class="tcc rb">&ensp;.979</td> <td class="tcc rb">.966</td> <td class="tcc rb">.941</td></tr>
+<tr><td class="tcc lb rb">16° 36&prime;</td> <td class="tcc rb">&ensp;.969</td> <td class="tcc rb">.971</td> <td class="tcc rb">.938</td></tr>
+<tr><td class="tcc lb rb">19° 28&prime;</td> <td class="tcc rb">&ensp;.953</td> <td class="tcc rb">.970</td> <td class="tcc rb">.924</td></tr>
+<tr><td class="tcc lb rb">21° &ensp;0&prime;</td> <td class="tcc rb">&ensp;.945</td> <td class="tcc rb">.971</td> <td class="tcc rb">.918</td></tr>
+<tr><td class="tcc lb rb">23° &ensp;0&prime;</td> <td class="tcc rb">&ensp;.937</td> <td class="tcc rb">.974</td> <td class="tcc rb">.913</td></tr>
+<tr><td class="tcc lb rb">29° 58&prime;</td> <td class="tcc rb">&ensp;.919</td> <td class="tcc rb">.975</td> <td class="tcc rb">.896</td></tr>
+<tr><td class="tcc lb rb">40° 20&prime;</td> <td class="tcc rb">&ensp;.887</td> <td class="tcc rb">.980</td> <td class="tcc rb">.869</td></tr>
+<tr><td class="tcc lb rb bb">48° 50&prime;</td> <td class="tcc rb bb">&ensp;.861</td> <td class="tcc rb bb">.984</td> <td class="tcc rb bb">.847</td></tr>
 </table>
 
 <p>The maximum coefficient of discharge is that for a mouthpiece
-with a convergence of 13°24&prime;.</p>
+with a convergence of 13°24&prime;.</p>
 
 <p><span class="pagenum"><a name="page52" id="page52"></a>52</span></p>
 
@@ -10741,7 +10703,7 @@ product c<span class="su">c</span> c<span class="su">v</span>, and consequently
 the discharge,
 is a maximum.</p>
 
-<p>§ 51. <i>Divergent Conoidal
+<p>§ 51. <i>Divergent Conoidal
 Mouthpiece.</i>&mdash;Suppose
 a mouthpiece so
 designed that there is
@@ -10839,7 +10801,7 @@ mouthpiece of this kind is</p>
 of area &omega;, and without the expanding part, discharging into
 a vacuum.</p>
 
-<p>§ 52. <i>Jet Pump.</i>&mdash;A divergent mouthpiece may be arranged to act
+<p>§ 52. <i>Jet Pump.</i>&mdash;A divergent mouthpiece may be arranged to act
 as a pump, as shown in fig. 62. The water which supplies the energy
 required for pumping enters at A. The water to be pumped enters
 at B. The streams combine at DD where the velocity is greatest
@@ -10863,7 +10825,7 @@ which the water is pumped.</p>
 
 <p class="pt1 center sc">Discharge with Varying Head</p>
 
-<p>§ 53. <i>Flow from a Vessel when the Effective Head varies with the
+<p>§ 53. <i>Flow from a Vessel when the Effective Head varies with the
 Time.</i>&mdash;Various useful problems arise relating to the time of emptying
 and filling vessels, reservoirs, lock chambers, &amp;c., where the flow
 is dependent on a head which increases or diminishes during the
@@ -10916,7 +10878,7 @@ with the time.</p>
 
 <p class="pt1 center sc">Practical Use of Orifices in Gauging Water</p>
 
-<p>§ 54. If the water to be measured is passed through a known orifice
+<p>§ 54. If the water to be measured is passed through a known orifice
 under an arrangement by which the constancy of the head is ensured,
 the amount which passes in a given time can be ascertained by the
 formulae already given. It will obviously be best to make the
@@ -10969,7 +10931,7 @@ consumer for emptying the pipes. The one on the left and the
 measuring cock are connected by a key which can be locked by a
 padlock, which is under the control of the water company.</p>
 
-<p>§ 55. <i>Measurement of the Flow in Streams.</i>&mdash;To determine the
+<p>§ 55. <i>Measurement of the Flow in Streams.</i>&mdash;To determine the
 quantity of water flowing off the ground in small streams, which is
 available for water supply or for obtaining water power, small
 temporary weirs are often used. These may be formed of planks
@@ -10984,7 +10946,7 @@ is, for a rectangular notch of breadth b,</p>
 
 <p class="center">Q = <span class="spp">2</span>&frasl;<span class="suu">3</span> cbh &radic;<span class="ov">2gh</span></p>
 
-<p class="noind">where c = 0.62; or, better, the formula in § 42 may be used.</p>
+<p class="noind">where c = 0.62; or, better, the formula in § 42 may be used.</p>
 
 <p>Gauging weirs are most commonly in the form of rectangular
 notches; and care should be taken that the crest is accurately
@@ -11081,7 +11043,7 @@ first be set accurately level with the weir crest, and a reading taken.
 Then the difference of the reading at the water surface and that
 for the weir crest will be the head at the weir.</p>
 
-<p>§ 56. <i>Modules used in Irrigation.</i>&mdash;In distributing water for
+<p>§ 56. <i>Modules used in Irrigation.</i>&mdash;In distributing water for
 irrigation, the charge for the water may be simply assessed on the
 area of the land irrigated for each consumer, a method followed in
 India; or a regulated quantity of water may be given to each
@@ -11098,7 +11060,7 @@ the variation of level in the irrigating channel.</p>
 <tr><td class="figcenter"><img style="width:468px; height:204px" src="images/img54a.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 69.</span></td></tr></table>
 
-<p>§ 57. <i>Italian Module.</i>&mdash;The Italian modules are masonry constructions,
+<p>§ 57. <i>Italian Module.</i>&mdash;The Italian modules are masonry constructions,
 consisting of a regulating chamber, to which water is admitted
 by an adjustable sluice from the canal. At the other end of the
 chamber is an orifice in a thin flagstone of fixed size. By means
@@ -11172,7 +11134,7 @@ the water in the chamber. The water is discharged into an open
 channel 0.655 ft. wider than the orifice, splaying out till it is 1.637
 ft. wider than the orifice, and about 18 ft. in length.</p>
 
-<p>§ 58. <i>Spanish Module.</i>&mdash;On the canal of Isabella II., which supplies
+<p>§ 58. <i>Spanish Module.</i>&mdash;On the canal of Isabella II., which supplies
 water to Madrid, a module much more perfect in principle than the
 Italian module is employed. Part of the water is supplied for irrigation,
 and as it is very valuable its
@@ -11217,7 +11179,7 @@ involves a great sacrifice of level between the canal and the fields.
 The module is described in Sir C. Scott-Moncrieff&rsquo;s <i>Irrigation in
 Southern Europe</i>.</p>
 
-<p>§ 59. <i>Reservoir Gauging Basins.</i>&mdash;In obtaining the power to store
+<p>§ 59. <i>Reservoir Gauging Basins.</i>&mdash;In obtaining the power to store
 the water of streams in reservoirs, it is usual to concede to riparian
 <span class="pagenum"><a name="page55" id="page55"></a>55</span>
 owners below the reservoirs a right to a regulated supply throughout
@@ -11265,7 +11227,7 @@ large scale.</p>
 <tr><td class="figcenter"><img style="width:476px; height:781px" src="images/img55c.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 74.</span>&mdash;Scale <span class="spp">1</span>&frasl;<span class="suu">500</span>.</td></tr></table>
 
-<p>§ 60. <i>Professor Fleeming Jenkin&rsquo;s Constant Flow Valve.</i>&mdash;In the
+<p>§ 60. <i>Professor Fleeming Jenkin&rsquo;s Constant Flow Valve.</i>&mdash;In the
 modules thus far described constant discharge is obtained by varying
 the area of the orifice through which the water flows. Professor
 F. Jenkin has contrived a valve in which a constant pressure head
@@ -11306,7 +11268,7 @@ with a difference of pressure of <span class="spp">1</span>&frasl;<span class="s
 <tr><td class="figright1"><img style="width:308px; height:324px" src="images/img56b.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 76.</span></td></tr></table>
 
-<p>§ 61. <i>External Work during the Expansion of Air.</i>&mdash;If air expands
+<p>§ 61. <i>External Work during the Expansion of Air.</i>&mdash;If air expands
 without doing any external work, its temperature remains constant.
 This result was first
 experimentally demonstrated
@@ -11403,7 +11365,7 @@ volumes per pound, we get for the work of expansion</p>
 <tr><td class="figright1"><img style="width:264px; height:93px" src="images/img56c.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 77.</span></td></tr></table>
 
-<p>§ 62. <i>Modification of the Theorem of Bernoulli for the Case of a
+<p>§ 62. <i>Modification of the Theorem of Bernoulli for the Case of a
 Compressible Fluid.</i>&mdash;In the application of the principle of work to a
 filament of compressible fluid, the internal work done by the expansion
 of the fluid, or absorbed
@@ -11447,7 +11409,7 @@ Wt <span class="f150">&int;</span><span class="sp1">v<span class="su">2</span></
 <div class="author">(1)</div>
 
 <p class="noind">Now the work of expansion per pound of fluid has already been
-given. If the temperature is constant, we get (eq. 1a, § 61)</p>
+given. If the temperature is constant, we get (eq. 1a, § 61)</p>
 
 <p class="center">Z<span class="su">1</span> + P<span class="su">1</span>/G<span class="su">1</span> + v<span class="su">1</span><span class="sp">2</span>/2g = z<span class="su">2</span> + p<span class="sp">2</span>/G<span class="su">2</span> + v<span class="su">2</span><span class="sp">2</span>/2g &minus; (p<span class="su">1</span>/G<span class="su">1</span>) log<span class="su">&epsilon;</span> (G<span class="su">1</span>/G<span class="su">2</span>).</p>
 
@@ -11461,7 +11423,7 @@ given. If the temperature is constant, we get (eq. 1a, § 61)</p>
 <p class="center">(v<span class="su">2</span><span class="sp">2</span> &minus; v<span class="su">1</span><span class="sp">2</span>) / 2g = (p<span class="su">1</span>/G<span class="su">1</span>) log<span class="su">&epsilon;</span> (p<span class="su">1</span>/p<span class="su">2</span>).</p>
 <div class="author1">(2a)</div>
 
-<p class="noind">Similarly, if the expansion is adiabatic (eq. 2a, § 61),</p>
+<p class="noind">Similarly, if the expansion is adiabatic (eq. 2a, § 61),</p>
 
 <p class="center">z<span class="su">1</span> + p<span class="su">1</span>/G<span class="su">1</span> + v<span class="su">1</span><span class="sp">2</span>/2g = z<span class="su">2</span> + p<span class="su">2</span>/G<span class="su">2</span> + v<span class="su">2</span><span class="sp">2</span>/2g &minus; (p<span class="su">1</span>/G<span class="su">1</span>)
  {1/(&gamma; &minus; 1) } {1 &minus; (p<span class="su">2</span>/p<span class="su">1</span>)<span class="sp">(&gamma;&minus;1)/&gamma;</span>};</p>
@@ -11475,7 +11437,7 @@ given. If the temperature is constant, we get (eq. 1a, § 61)</p>
 <p class="noind">It will be seen hereafter that there is a limit in the ratio p<span class="su">1</span>/p<span class="su">2</span> beyond
 which these expressions cease to be true.</p>
 
-<p>§ 63. <i>Discharge of Air from an Orifice.</i>&mdash;The form of the equation
+<p>§ 63. <i>Discharge of Air from an Orifice.</i>&mdash;The form of the equation
 of work for a steady stream of compressible fluid is</p>
 
 <p class="center">z<span class="su">1</span> + p<span class="su">1</span>/G<span class="su">1</span> + v<span class="su">1</span><span class="sp">2</span>/2g = z<span class="su">2</span> + p<span class="su">2</span>/G<span class="su">2</span> + v<span class="su">2</span><span class="sp">2</span>/2g &minus;
@@ -11516,7 +11478,7 @@ may be neglected. Putting these values in the equation above&mdash;</p>
 1856), though it appears to have been given earlier by A. J. C. Barre
 de Saint Venant and L. Wantzel.</p>
 
-<p>It has already (§ 9, eq. 4a) been seen that</p>
+<p>It has already (§ 9, eq. 4a) been seen that</p>
 
 <p class="center">p<span class="su">1</span>/G<span class="su">1</span> = (p<span class="su">0</span>/G<span class="su">0</span>) (&tau;<span class="su">1</span>/&tau;<span class="su">0</span>)</p>
 
@@ -11587,7 +11549,7 @@ c:&mdash;</p>
 <tr><td class="tcl">Conical converging mouthpieces</td> <td class="tcl">0.90</td> <td class="tcc">&rdquo;</td> <td class="tcl">0.99</td></tr>
 </table>
 
-<p>§ 64. <i>Limit to the Application of the above Formulae.</i>&mdash;In the
+<p>§ 64. <i>Limit to the Application of the above Formulae.</i>&mdash;In the
 formulae above it is assumed that the fluid issuing from the orifice
 expands from the pressure p<span class="su">1</span> to the pressure p<span class="su">2</span>, while passing from
 the vessel to the section of the jet considered in estimating the area
@@ -11642,7 +11604,7 @@ paper (<i>Civilingenieur</i>, 1871), and Fliegner&rsquo;s papers (<i>ibid.</i>,
 
 <p class="pt2 center">VII. FRICTION OF LIQUIDS.</p>
 
-<p>§ 65. When a stream of fluid flows over a solid surface, or conversely
+<p>§ 65. When a stream of fluid flows over a solid surface, or conversely
 when a solid moves in still fluid, a resistance to the motion
 is generated, commonly termed fluid friction. It is due to the viscosity
 of the fluid, but generally the laws of fluid friction are very
@@ -11695,7 +11657,7 @@ practice. H. P. G. Darcy&rsquo;s experiments, for instance, showed that
 in old and incrusted water mains the resistance was twice or sometimes
 thrice as great as in new and clean mains.</p>
 
-<p>§ 66. <i>Ordinary Expressions for Fluid Friction at Velocities not
+<p>§ 66. <i>Ordinary Expressions for Fluid Friction at Velocities not
 Extremely Small.</i>&mdash;Let f be the frictional resistance estimated in
 pounds per square foot of surface at a velocity of 1 ft. per second;
 &omega; the area of the surface in square feet; and v its velocity in feet
@@ -11782,7 +11744,7 @@ to vary through wider limits than these
 expressions allow, and to depend on circumstances of which they do
 not take account.</p>
 
-<p>§ 67. <i>Coulomb&rsquo;s Experiments.</i>&mdash;The first direct experiments on
+<p>§ 67. <i>Coulomb&rsquo;s Experiments.</i>&mdash;The first direct experiments on
 fluid friction were made by Coulomb, who employed a circular disk
 suspended by a thin brass wire and oscillated in its own plane. His
 experiments were chiefly made at very low velocities. When the
@@ -11811,7 +11773,7 @@ and they generally
 made one oscillation
 in from 20 to 30 seconds,
 through angles varying
-from 360° to 6°. When
+from 360° to 6°. When
 the velocity of the circumference
 of the disk
 was less than 6 in. per
@@ -11830,7 +11792,7 @@ ft., at a velocity of 10 ft. per second, the difference of resistance,
 measured on the difference of area, was 0.339 &#8468; per square foot.
 Also the resistance varied as the 1.949th power of the velocity.</p>
 
-<p>§ 68. <i>Froude&rsquo;s Experiments.</i>&mdash;The most important direct experiments
+<p>§ 68. <i>Froude&rsquo;s Experiments.</i>&mdash;The most important direct experiments
 on fluid friction at ordinary velocities are those made by
 William Froude (1810-1879) at Torquay. The method adopted in
 these experiments was to tow a board in a still water canal, the
@@ -11915,7 +11877,7 @@ against stationary water, but against water partially moving in its
 own direction, and cannot therefore experience so much resistance
 from it.&rdquo;</p>
 
-<p>§ 69. The following table gives a general statement of Froude&rsquo;s
+<p>§ 69. The following table gives a general statement of Froude&rsquo;s
 results. In all the experiments in this table, the boards had a fine
 cutwater and a fine stern end or run, so that the resistance was
 entirely due to the surface. The table gives the resistances per
@@ -11976,7 +11938,7 @@ water and that diffused. The velocity of the current accompanying
 the board becomes constant or nearly constant, and the friction per
 square foot is therefore nearly constant also.</p>
 
-<p>§ 70. <i>Friction of Rotating Disks.</i>&mdash;A rotating disk is virtually a
+<p>§ 70. <i>Friction of Rotating Disks.</i>&mdash;A rotating disk is virtually a
 surface of unlimited extent and it is convenient for experiments on
 friction with different surfaces at different speeds. Experiments
 carried out by Professor W. C. Unwin (<i>Proc. Inst. Civ. Eng.</i> lxxx.)
@@ -12034,14 +11996,14 @@ Froude&rsquo;s results.</p>
 
 <p>Experiments with a bright brass disk showed
 that the friction decreased with increase of
-temperature. The diminution between 41°
-and 130° F. amounted to 18%. In the general
+temperature. The diminution between 41°
+and 130° F. amounted to 18%. In the general
 equation M = cN<span class="sp">n</span> for any given disk,</p>
 
 <p class="center">c<span class="su">t</span> = 0.1328 (1 &minus; 0.0021t),</p>
 
 <p class="noind">where c<span class="su">t</span> is the value of c for a bright brass
-disk 0.85 ft. in diameter at a temperature t° F.</p>
+disk 0.85 ft. in diameter at a temperature t° F.</p>
 
 <p>The disks used were either polished or made rougher by varnish
 or by varnish and sand. The following table gives a comparison of
@@ -12061,7 +12023,7 @@ the results obtained with the disks and Froude&rsquo;s results on planks
 <p class="pt2 center">VIII. STEADY FLOW OF WATER IN PIPES OF
 UNIFORM SECTION.</p>
 
-<p>§ 71. The ordinary theory of the flow of water in pipes, on which
+<p>§ 71. The ordinary theory of the flow of water in pipes, on which
 all practical formulae are based, assumes that the variation of velocity
 at different points of any cross section may be neglected. The
 water is considered as moving in plane layers, which are driven
@@ -12115,7 +12077,7 @@ volume Q is</p>
 against the surface of the pipe. The area of that surface is &chi;dl.</p>
 
 <p>The work expended in overcoming the frictional resistance per
-second is (see § 66, eq. 3)</p>
+second is (see § 66, eq. 3)</p>
 
 <p class="center">&minus;&zeta;G&chi; dl v<span class="sp">3</span>/2g,</p>
 
@@ -12140,7 +12102,7 @@ result to zero, since the motion is uniform,&mdash;</p>
 <p class="center">z + p/G + &zeta; (&chi;/&Omega;) (v<span class="sp">2</span>/2g) l = constant.</p>
 <div class="author">(1)</div>
 
-<p>§ 72. Let A and B (fig. 81) be any two sections of the pipe for
+<p>§ 72. Let A and B (fig. 81) be any two sections of the pipe for
 which p, z, l have the values p<span class="su">1</span>, z<span class="su">1</span>, l<span class="su">1</span>, and p<span class="su">2</span>, z<span class="su">2</span>, l<span class="su">2</span>, respectively.
 Then</p>
 
@@ -12198,7 +12160,7 @@ pressure at C and D is the same, and this is usually nearly the case.
 But if C and D are at greatly different levels the excess of barometric
 pressure at C, in feet of water, must be added to p<span class="su">2</span>/G.</p>
 
-<p>§ 73. <i>Hydraulic Gradient or Line of Virtual Slope.</i>&mdash;Join CD.
+<p>§ 73. <i>Hydraulic Gradient or Line of Virtual Slope.</i>&mdash;Join CD.
 Since the head lost in friction is proportional to L, any intermediate
 pressure column between A and B will have its free surface on the
 line CD, and the vertical distance between CD and the pipe at any
@@ -12230,7 +12192,7 @@ error of practical importance.</p>
 <tr><td class="figcenter"><img style="width:471px; height:165px" src="images/img60b.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 82.</span></td></tr></table>
 
-<p>§ 74. <i>Case of a Uniform Pipe connecting two Reservoirs, when all the
+<p>§ 74. <i>Case of a Uniform Pipe connecting two Reservoirs, when all the
 Resistances are taken into account.</i>&mdash;Let h (fig. 82) be the difference
 of level of the reservoirs, and v the velocity, in a pipe of length L
 and diameter d. The whole work done per second is virtually the
@@ -12247,10 +12209,10 @@ entrance to the pipe. (3) As already shown the head expended in
 overcoming the surface friction of the pipe is &zeta;(4L/d) (v<span class="sp">2</span>/2g) corresponding
 to GQ&zeta; (4L/d) (v<span class="sp">2</span>/2g) foot-pounds of work. Hence</p>
 
-<p class="center">GQh = GQv<span class="sp">2</span>/2g + GQ&zeta;<span class="su">0</span>v<span class="sp">2</span>/2g + GQ&zeta;·4L·v<span class="sp">2</span>/d·2g;</p>
+<p class="center">GQh = GQv<span class="sp">2</span>/2g + GQ&zeta;<span class="su">0</span>v<span class="sp">2</span>/2g + GQ&zeta;·4L·v<span class="sp">2</span>/d·2g;</p>
 
 <table class="reg" summary="poem"><tr><td> <div class="poemr">
-<p>h = (1 + &zeta;<span class="su">0</span> + &zeta;·4L/d) v<span class="sp">2</span>/2g.</p>
+<p>h = (1 + &zeta;<span class="su">0</span> + &zeta;·4L/d) v<span class="sp">2</span>/2g.</p>
 <p>v = 8.025 &radic; [hd / {(1 + &zeta;<span class="su">0</span>)d + 4&zeta;L} ].</p>
 </div> </td></tr></table>
 <div class="author">(5)</div>
@@ -12290,7 +12252,7 @@ equivalent to the mouthpiece is 37.6d nearly. This may be added
 to the actual length of the pipe to allow for mouthpiece resistance
 in approximate calculations.</p>
 
-<p>§ 75. <i>Coefficient of Friction for Pipes discharging Water.</i>&mdash;From the
+<p>§ 75. <i>Coefficient of Friction for Pipes discharging Water.</i>&mdash;From the
 average of a large number of experiments, the value of &zeta; for ordinary
 iron pipes is</p>
 
@@ -12323,7 +12285,7 @@ form</p>
 
 <p><span class="pagenum"><a name="page61" id="page61"></a>61</span></p>
 
-<p>§ 76. <i>Darcy&rsquo;s Experiments on Friction in Pipes.</i>&mdash;All previous
+<p>§ 76. <i>Darcy&rsquo;s Experiments on Friction in Pipes.</i>&mdash;All previous
 experiments on the resistance of pipes were superseded by the remarkable
 researches carried out by H. P. G. Darcy (1803-1858), the
 Inspector-General of the Paris water works. His experiments were
@@ -12425,7 +12387,7 @@ cumbrous, its form is not rationally justifiable and it is not at all
 clear that it gives more accurate values of the discharge than simpler
 formulae.</p>
 
-<p>§ 77. <i>Later Investigations on Flow in Pipes.</i>&mdash;The foregoing statement
+<p>§ 77. <i>Later Investigations on Flow in Pipes.</i>&mdash;The foregoing statement
 gives the theory of flow in pipes so far as it can be put in a
 simple rational form. But the conditions of flow are really more
 complicated than can be expressed in any rational form. Taking
@@ -12454,7 +12416,7 @@ fluid friction show that the power of the velocity to which the
 resistance is proportional is not exactly the square. Also in determining
 the form of his equation for &zeta; Darcy used only eight out of his
 seventeen series of experiments, and there is reason to think that some
-of these were exceptional. Barré de Saint-Venant was the first to
+of these were exceptional. Barré de Saint-Venant was the first to
 propose a formula with two constants,</p>
 
 <p class="center">dh/4l = mV<span class="sp">n</span>,</p>
@@ -12627,7 +12589,7 @@ in other cases.</p>
 
 <p class="pt1 center"><i>General Mean Values of Constants.</i></p>
 
-<p>The general formula (Hagen&rsquo;s)&mdash;h/l = mv<span class="sp">n</span>/d<span class="sp">x</span>·2g&mdash;can therefore be
+<p>The general formula (Hagen&rsquo;s)&mdash;h/l = mv<span class="sp">n</span>/d<span class="sp">x</span>·2g&mdash;can therefore be
 taken to fit the results with convenient closeness, if the following
 mean values of the coefficients are taken, the unit being a metre:&mdash;</p>
 
@@ -12664,7 +12626,7 @@ following are the values of the coefficients:&mdash;</p>
 <tr><td class="tcl lb rb bb">Incrusted cast iron</td> <td class="tcc rb bb">.0440</td> <td class="tcc rb bb">1.160</td> <td class="tcc rb bb">2.0&ensp;</td></tr>
 </table>
 
-<p>§ 78. <i>Distribution of Velocity in the Cross Section of a Pipe.</i>&mdash;Darcy
+<p>§ 78. <i>Distribution of Velocity in the Cross Section of a Pipe.</i>&mdash;Darcy
 made experiments with a Pitot tube in 1850 on the velocity at
 different points in the cross section of a pipe. He deduced the
 relation</p>
@@ -12673,7 +12635,7 @@ relation</p>
 
 <p class="noind">where V is the velocity at the centre and v the velocity at radius r in
 a pipe of radius R with a hydraulic gradient i. Later Bazin repeated
-the experiments and extended them (<i>Mém. de l&rsquo;Académie des Sciences</i>,
+the experiments and extended them (<i>Mém. de l&rsquo;Académie des Sciences</i>,
 xxxii. No. 6). The most important result was the ratio of mean to
 central velocity. Let b = Ri/U<span class="sp">2</span>, where U is the mean velocity in the
 pipe; then V/U = 1 + 9.03 &radic;b. A very useful result for practical
@@ -12685,7 +12647,7 @@ as determined by Bazin.</p>
 <tr><td class="figcenter"><img style="width:340px; height:344px" src="images/img63a.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 84.</span></td></tr></table>
 
-<p>§ 79. <i>Influence of Temperature on the Flow through Pipes.</i>&mdash;Very
+<p>§ 79. <i>Influence of Temperature on the Flow through Pipes.</i>&mdash;Very
 careful experiments on the flow through a pipe 0.1236 ft. in diameter
 and 25 ft. long, with water at different temperatures, have been
 made by J. G. Mair (<i>Proc. Inst. Civ. Eng.</i> lxxxiv.). The loss of head
@@ -12725,16 +12687,16 @@ temperature are practically constant&mdash;</p>
 <p class="noind">where again a regular decrease of the coefficient occurs as the
 temperature rises. In experiments on the friction of disks at
 different temperatures Professor W. C. Unwin found that the resistance
-was proportional to constant × (1 &minus; 0.0021t) and the values
+was proportional to constant × (1 &minus; 0.0021t) and the values
 of m given above are expressed almost exactly by the relation</p>
 
 <p class="center">m = 0.000311 (1 &minus; 0.00215 t).</p>
 
 <p>In tank experiments on ship models for small ordinary variations
 of temperature, it is usual to allow a decrease of 3% of resistance for
-10° F. increase of temperature.</p>
+10° F. increase of temperature.</p>
 
-<p>§ 80. <i>Influence of Deposits in Pipes on the Discharge. Scraping
+<p>§ 80. <i>Influence of Deposits in Pipes on the Discharge. Scraping
 Water Mains.</i>&mdash;The influence of the condition of the surface of a pipe
 on the friction is shown by various facts known to the engineers of
 waterworks. In pipes which convey certain kinds of water, oxidation
@@ -12793,7 +12755,7 @@ a kind of brush scraper devised by G. F. Deacon (see &ldquo;Deposits in
 Pipes,&rdquo; by Professor J. C. Campbell Brown, <i>Proc. Inst. Civ. Eng.</i>,
 1903-1904).</p>
 
-<p>§ 81. <i>Flow of Water through Fire Hose.</i>&mdash;The hose pipes used for
+<p>§ 81. <i>Flow of Water through Fire Hose.</i>&mdash;The hose pipes used for
 fire purposes are of very varied character, and the roughness of the
 surface varies. Very careful experiments have been made by J. R.
 Freeman (<i>Am. Soc. Civ. Eng.</i> xxi., 1889). It was noted that under
@@ -12831,7 +12793,7 @@ hydraulic gradient. Then v = n &radic;(ri).</p>
  <tr><td class="tcc rb bb">&rdquo;</td> <td class="tcc rb bb">331</td> <td class="tcc rb bb">1.1624</td> <td class="tcc rb bb">20.00</td> <td class="tcc rb bb">&ensp;79.6</td></tr>
 </table>
 
-<p>§ 82. <i>Reduction of a Long Pipe of Varying Diameter to an Equivalent
+<p>§ 82. <i>Reduction of a Long Pipe of Varying Diameter to an Equivalent
 Pipe of Uniform Diameter. Dupuit&rsquo;s Equation.</i>&mdash;Water mains for
 the supply of towns often consist of a series of lengths, the diameter
 being the same for each length, but differing from length to length.
@@ -12862,16 +12824,16 @@ head in A due to friction is</p>
 
 <table class="reg" summary="poem"><tr><td> <div class="poemr">
 <p>h = i<span class="su">1</span>l<span class="su">1</span> + i<span class="su">2</span>l<span class="su">2</span> + ...</p>
-<p class="i05">= &zeta; (v<span class="su">1</span><span class="sp">2</span> · 4l<span class="su">1</span>/2gd<span class="su">1</span>) + &zeta; (v<span class="su">2</span><span class="sp">2</span> · 4l<span class="su">2</span>/2gd<span class="su">2</span>) + ...</p>
+<p class="i05">= &zeta; (v<span class="su">1</span><span class="sp">2</span> · 4l<span class="su">1</span>/2gd<span class="su">1</span>) + &zeta; (v<span class="su">2</span><span class="sp">2</span> · 4l<span class="su">2</span>/2gd<span class="su">2</span>) + ...</p>
 </div> </td></tr></table>
 
 <p class="noind">and in the uniform main</p>
 
-<p class="center">il = &zeta; (v<span class="sp">2</span> · 4l/2gd).</p>
+<p class="center">il = &zeta; (v<span class="sp">2</span> · 4l/2gd).</p>
 
 <p class="noind">If the mains are equivalent, as defined above,</p>
 
-<p class="center">&zeta; (v<span class="sp">2</span> · 4l/2gd) = &zeta; (v<span class="su">1</span><span class="sp">2</span> · 4l<span class="su">1</span>/2gd<span class="su">1</span>) + &zeta; (v<span class="su">2</span><span class="sp">2</span> · 4l<span class="su">2</span>/2gd<span class="su">2</span>) + ...</p>
+<p class="center">&zeta; (v<span class="sp">2</span> · 4l/2gd) = &zeta; (v<span class="su">1</span><span class="sp">2</span> · 4l<span class="su">1</span>/2gd<span class="su">1</span>) + &zeta; (v<span class="su">2</span><span class="sp">2</span> · 4l<span class="su">2</span>/2gd<span class="su">2</span>) + ...</p>
 
 <p class="noind">But, since the discharge is the same for all portions,</p>
 
@@ -12895,7 +12857,7 @@ have the same total loss of head for any given discharge.</p>
 <tr><td class="figright1"><img style="width:242px; height:117px" src="images/img64b.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 87.</span></td></tr></table>
 
-<p>§ 83. <i>Other Losses of Head in Pipes.</i>&mdash;Most of the losses of head in
+<p>§ 83. <i>Other Losses of Head in Pipes.</i>&mdash;Most of the losses of head in
 pipes, other than that due to surface friction against the pipe, are due
 to abrupt changes in the velocity of the stream producing eddies.
 The kinetic energy of these is deducted from the general energy of
@@ -13006,7 +12968,7 @@ with a pipe 1<span class="spp">1</span>&frasl;<span class="suu">4</span> in. dia
 <p class="center">&zeta;<span class="su">e</span> = 0.9457 sin<span class="sp">2</span> <span class="spp">1</span>&frasl;<span class="suu">2</span>&phi; + 2.047 sin<span class="sp">4</span> <span class="spp">1</span>&frasl;<span class="suu">2</span>&phi;.</p>
 
 <table class="ws" summary="Contents">
-<tr><td class="tcr lb rb tb">&phi; =</td> <td class="tcc rb tb">20°</td> <td class="tcc rb tb">40°</td> <td class="tcc rb tb">60°</td> <td class="tcc rb tb">80°</td> <td class="tcc rb tb">90°</td> <td class="tcc rb tb">100°</td> <td class="tcc rb tb">110°</td> <td class="tcc rb tb">120°</td> <td class="tcc rb tb">130°</td> <td class="tcc rb tb">140°</td></tr>
+<tr><td class="tcr lb rb tb">&phi; =</td> <td class="tcc rb tb">20°</td> <td class="tcc rb tb">40°</td> <td class="tcc rb tb">60°</td> <td class="tcc rb tb">80°</td> <td class="tcc rb tb">90°</td> <td class="tcc rb tb">100°</td> <td class="tcc rb tb">110°</td> <td class="tcc rb tb">120°</td> <td class="tcc rb tb">130°</td> <td class="tcc rb tb">140°</td></tr>
 <tr><td class="tcr lb rb bb">&zeta;<span class="su">&epsilon;</span> =</td> <td class="tcc rb bb">0.046</td> <td class="tcc rb bb">0.139</td> <td class="tcc rb bb">0.364</td> <td class="tcc rb bb">0.740</td> <td class="tcc rb bb">0.984</td> <td class="tcc rb bb">1.260</td> <td class="tcc rb bb">1.556</td> <td class="tcc rb bb">1.861</td> <td class="tcc rb bb">2.158</td> <td class="tcc rb bb">2.431</td></tr>
 </table>
 
@@ -13080,13 +13042,13 @@ Section at sluice = &omega;<span class="su">1</span> in pipe = &omega;.</p>
 is turned = &theta;.</p>
 
 <table class="ws" summary="Contents">
-<tr><td class="tcc lb rb tb">&theta; =</td> <td class="tcc rb tb">5°</td> <td class="tcc rb tb">10°</td> <td class="tcc rb tb">15°</td> <td class="tcc rb tb">20°</td> <td class="tcc rb tb">25°</td> <td class="tcc rb tb">30°</td> <td class="tcc rb tb">35°</td></tr>
+<tr><td class="tcc lb rb tb">&theta; =</td> <td class="tcc rb tb">5°</td> <td class="tcc rb tb">10°</td> <td class="tcc rb tb">15°</td> <td class="tcc rb tb">20°</td> <td class="tcc rb tb">25°</td> <td class="tcc rb tb">30°</td> <td class="tcc rb tb">35°</td></tr>
 <tr><td class="tcc lb rb">Ratio of<br />cross<br />sections</td> <td class="tccm rb">.926</td> <td class="tccm rb">.850</td> <td class="tccm rb">.772</td> <td class="tccm rb">.692</td> <td class="tccm rb">.613</td> <td class="tccm rb">.535</td> <td class="tccm rb">.458</td></tr>
 <tr><td class="tcc lb rb bb">&zeta;<span class="su">v</span> =</td> <td class="tcc rb bb">.05</td> <td class="tcc rb bb">.29</td> <td class="tcc rb bb">.75</td> <td class="tcc rb bb">1.56</td> <td class="tcc rb bb">3.10</td> <td class="tcc rb bb">5.47</td> <td class="tcc rb bb">9.68</td></tr>
 </table>
 
 <table class="ws" summary="Contents">
-<tr><td class="tcc lb rb tb">&theta; =</td> <td class="tcc rb tb">40°</td> <td class="tcc rb tb">45°</td> <td class="tcc rb tb">50°</td> <td class="tcc rb tb">55°</td> <td class="tcc rb tb">60°</td> <td class="tcc rb tb">65°</td> <td class="tcc rb tb">82°</td></tr>
+<tr><td class="tcc lb rb tb">&theta; =</td> <td class="tcc rb tb">40°</td> <td class="tcc rb tb">45°</td> <td class="tcc rb tb">50°</td> <td class="tcc rb tb">55°</td> <td class="tcc rb tb">60°</td> <td class="tcc rb tb">65°</td> <td class="tcc rb tb">82°</td></tr>
 <tr><td class="tcc lb rb">Ratio of<br />cross<br />sections</td> <td class="tccm rb">.385</td> <td class="tccm rb">.315</td> <td class="tccm rb">.250</td> <td class="tccm rb">.190</td> <td class="tccm rb">.137</td> <td class="tccm rb">.091</td> <td class="tccm rb">0</td></tr>
 <tr><td class="tcc lb rb bb">&zeta;<span class="su">v</span> =</td> <td class="tcc rb bb">17.3</td> <td class="tcc rb bb">31.2</td> <td class="tcc rb bb">52.6</td> <td class="tcc rb bb">106</td> <td class="tcc rb bb">206</td> <td class="tcc rb bb">486</td> <td class="tcc rb bb">&infin;</td></tr>
 </table>
@@ -13094,12 +13056,12 @@ is turned = &theta;.</p>
 <p><i>Throttle Valve in a Cylindrical Pipe</i> (fig. 95)</p>
 
 <table class="ws" summary="Contents">
-<tr><td class="tcc lb rb tb">&theta; =</td> <td class="tcc rb tb">5°</td> <td class="tcc rb tb">10°</td> <td class="tcc rb tb">15°</td> <td class="tcc rb tb">20°</td> <td class="tcc rb tb">25°</td> <td class="tcc rb tb">30°</td> <td class="tcc rb tb">35°</td> <td class="tcc rb tb">40°</td></tr>
+<tr><td class="tcc lb rb tb">&theta; =</td> <td class="tcc rb tb">5°</td> <td class="tcc rb tb">10°</td> <td class="tcc rb tb">15°</td> <td class="tcc rb tb">20°</td> <td class="tcc rb tb">25°</td> <td class="tcc rb tb">30°</td> <td class="tcc rb tb">35°</td> <td class="tcc rb tb">40°</td></tr>
 <tr><td class="tcc lb rb bb">&zeta;<span class="su">v</span> =</td> <td class="tcc rb bb">.24</td> <td class="tcc rb bb">.52</td> <td class="tcc rb bb">.90</td> <td class="tcc rb bb">1.54</td> <td class="tcc rb bb">2.51</td> <td class="tcc rb bb">3.91</td> <td class="tcc rb bb">6.22</td> <td class="tcc rb bb">10.8</td></tr>
 </table>
 
 <table class="ws" summary="Contents">
-<tr><td class="tcc lb rb tb">&theta; =</td> <td class="tcc rb tb">45°</td> <td class="tcc rb tb">50°</td> <td class="tcc rb tb">55°</td> <td class="tcc rb tb">60°</td> <td class="tcc rb tb">65°</td> <td class="tcc rb tb">70°</td> <td class="tcc rb tb">90°</td></tr>
+<tr><td class="tcc lb rb tb">&theta; =</td> <td class="tcc rb tb">45°</td> <td class="tcc rb tb">50°</td> <td class="tcc rb tb">55°</td> <td class="tcc rb tb">60°</td> <td class="tcc rb tb">65°</td> <td class="tcc rb tb">70°</td> <td class="tcc rb tb">90°</td></tr>
 <tr><td class="tcc lb rb bb">&zeta;<span class="su">v</span> =</td> <td class="tcc rb bb">18.7</td> <td class="tcc rb bb">32.6</td> <td class="tcc rb bb">58.8</td> <td class="tcc rb bb">118</td> <td class="tcc rb bb">256</td> <td class="tcc rb bb">751</td> <td class="tcc rb bb">&infin;</td></tr>
 </table>
 
@@ -13107,7 +13069,7 @@ is turned = &theta;.</p>
 <tr><td class="figright1"><img style="width:269px; height:117px" src="images/img65e.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 95.</span></td></tr></table>
 
-<p>§ 84. <i>Practical Calculations on the Flow of Water in Pipes.</i>&mdash;In
+<p>§ 84. <i>Practical Calculations on the Flow of Water in Pipes.</i>&mdash;In
 the following explanations it will be assumed that the pipe is of so
 great a length that only the
 loss of head in friction against
@@ -13121,7 +13083,7 @@ the relation h = il, this need
 not be separately considered.</p>
 
 <p>There are then three equations
-(see eq. 4, § 72, and 9a, § 76) for the solution of such problems
+(see eq. 4, § 72, and 9a, § 76) for the solution of such problems
 as arise:&mdash;</p>
 
 <p class="center">&zeta; = &alpha; (1 + 1/12d);</p>
@@ -13266,7 +13228,7 @@ form</p>
 <p class="noind">Neglecting the terms after the second,</p>
 
 <table class="reg" summary="poem"><tr><td> <div class="poemr">
-<p>d = <span class="sp">5</span>&radic; (32&alpha; / g&pi;<span class="sp">2</span>) <span class="sp">5</span>&radic; (Q<span class="sp">2</span>/i) · {1 + 1/60d}</p>
+<p>d = <span class="sp">5</span>&radic; (32&alpha; / g&pi;<span class="sp">2</span>) <span class="sp">5</span>&radic; (Q<span class="sp">2</span>/i) · {1 + 1/60d}</p>
 <p class="i05">= <span class="sp">5</span>&radic; (32&alpha; / g&pi;<span class="sp">2</span>) <span class="sp">5</span>&radic; (Q<span class="sp">2</span>/i) + 0.01667;</p>
 </div> </td></tr></table>
 <div class="author1">(9a)</div>
@@ -13286,7 +13248,7 @@ form</p>
 <tr><td class="figcenter"><img style="width:763px; height:307px" src="images/img66b.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 97.</span></td></tr></table>
 
-<p>§ 85. <i>Arrangement of Water Mains
+<p>§ 85. <i>Arrangement of Water Mains
 for Towns&rsquo; Supply.</i>&mdash;Town mains are
 usually supplied oy gravitation from
 a service reservoir, which in turn is
@@ -13315,7 +13277,7 @@ should be calculated for 50 gallons per head per day.</p>
 <tr><td class="figcenter"><img style="width:773px; height:242px" src="images/img66c.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 98.</span></td></tr></table>
 
-<p>§ 86. <i>Determination of the Diameters of Different Parts of a Water
+<p>§ 86. <i>Determination of the Diameters of Different Parts of a Water
 Main.</i>&mdash;When the plan of the arrangement of mains is determined
 upon, and the supply to each locality and the pressure required is
 ascertained, it remains to determine the diameters of the pipes. Let
@@ -13354,7 +13316,7 @@ for towns&rsquo; supply:&mdash;</p>
 <tr><td class="tcl">Velocity in feet per sec.</td> <td class="tcc">2.5</td> <td class="tcc">3.0</td> <td class="tcc">3.5</td> <td class="tcc">4.5</td> <td class="tcc">5.3</td> <td class="tcc">6.2</td> <td class="tcc">7.0</td></tr>
 </table>
 
-<p>§ 87. <i>Branched Pipe connecting Reservoirs at Different Levels.</i>&mdash;Let
+<p>§ 87. <i>Branched Pipe connecting Reservoirs at Different Levels.</i>&mdash;Let
 A, B, C (fig. 98) be three reservoirs connected by the arrangement of
 pipes shown,&mdash;l<span class="su">1</span>, d<span class="su">1</span>, Q<span class="su">1</span>, v<span class="su">1</span>; l<span class="su">2</span>, d<span class="su">2</span>, Q<span class="su">2</span>, v<span class="su">2</span>; h<span class="su">3</span>,
 d<span class="su">3</span>, Q<span class="su">3</span>, v<span class="su">3</span> being the
@@ -13427,7 +13389,7 @@ value of h, and recalculate Q<span class="su">1</span>, Q<span class="su">2</spa
 <p>Since the limits between which h can vary are in practical cases not
 very distant, it is easy to approximate to values sufficiently accurate.</p>
 
-<p>§ 88. <i>Water Hammer.</i>&mdash;If in a pipe through which water is flowing
+<p>§ 88. <i>Water Hammer.</i>&mdash;If in a pipe through which water is flowing
 a sluice is suddenly closed so as to arrest the forward movement of
 the water, there is a rise of pressure which in some cases is serious
 enough to burst the pipe. This action is termed water hammer or
@@ -13463,7 +13425,7 @@ be quite suddenly closed, this appears to be a reasonable allowance
 
 <p class="pt2 center">IX. FLOW OF COMPRESSIBLE FLUIDS IN PIPES</p>
 
-<p>§ 89. <i>Flow of Air in Long Pipes.</i>&mdash;When air flows through a long
+<p>§ 89. <i>Flow of Air in Long Pipes.</i>&mdash;When air flows through a long
 pipe, by far the greater part of the work expended is used in overcoming
 frictional resistances due to the surface of the pipe. The
 work expended in friction generates heat, which for the most part
@@ -13480,7 +13442,7 @@ used for the transmission of messages, by R. S. Culley and R. Sabine
 the air flowing along the tube is much less than it would be in adiabatic
 expansion.</p>
 
-<p>§ 90. <i>Differential Equation of the Steady Motion of Air Flowing in
+<p>§ 90. <i>Differential Equation of the Steady Motion of Air Flowing in
 a Long Pipe of Uniform Section.</i>&mdash;When air expands at a constant
 absolute temperature &tau;, the relation between the pressure p in
 pounds per square foot and the density or weight per cubic foot G
@@ -13490,7 +13452,7 @@ is given by the equation</p>
 <div class="author">(1)</div>
 
 <p class="noind">where c = 53.15. Taking &tau; = 521, corresponding to a temperature of
-60° Fahr.,</p>
+60° Fahr.,</p>
 
 <p class="center">c&tau; = 27690 foot-pounds.</p>
 <div class="author">(2)</div>
@@ -13536,7 +13498,7 @@ sections A<span class="su">0</span>A&prime;<span class="su">0</span>, and A<span
 <p class="center">W dt = G&Omega;u dt = G&Omega; (u + du) dt.</p>
 
 <p>By analogy with liquids the head lost in friction is, for the length
-dl (see § 72, eq. 3), &zeta; (u<span class="sp">2</span>/2g) (dl/m). Let H = u<span class="sp">2</span>/2g. Then the head
+dl (see § 72, eq. 3), &zeta; (u<span class="sp">2</span>/2g) (dl/m). Let H = u<span class="sp">2</span>/2g. Then the head
 lost is &zeta;(H/m)dl; and, since Wdt &#8468; of air flow through the
 pipe in the time considered, the work expended in friction is
 &minus;&zeta; (H/m)W dl dt. The change of kinetic energy in dt seconds is the
@@ -13630,7 +13592,7 @@ section m = d/4, where d is the diameter:&mdash;</p>
 <p class="center">u<span class="su">0</span> = (1.1319 &minus; 0.7264 p<span class="su">1</span>/p<span class="su">0</span>) &radic; (gc&tau;d / 4&zeta; l).</p>
 <div class="author1">(7c)</div>
 
-<p>§ 91. <i>Coefficient of Friction for Air.</i>&mdash;A discussion by Professor
+<p>§ 91. <i>Coefficient of Friction for Air.</i>&mdash;A discussion by Professor
 Unwin of the experiments by Culley and Sabine on the rate of
 transmission of light carriers through pneumatic tubes, in which
 there is steady flow of air not sensibly affected by any resistances
@@ -13691,7 +13653,7 @@ p<span class="su">0</span> and p<span class="su">1</span> the pressures, G<span
 velocity in the pipe. This equation may be used for the flow of
 coal gas.</p>
 
-<p>§ 92. <i>Distribution of Pressure in a Pipe in which Air is Flowing.</i>&mdash;From
+<p>§ 92. <i>Distribution of Pressure in a Pipe in which Air is Flowing.</i>&mdash;From
 equation (7a) it results that the pressure p, at l ft. from that
 end of the pipe where the pressure is p<span class="su">0</span>, is</p>
 
@@ -13741,7 +13703,7 @@ the pressure is least.</p>
 <tr><td class="figcenter"><img style="width:469px; height:221px" src="images/img68b.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 101.</span></td></tr></table>
 
-<p>§ 93. <i>Weight of Air Flowing per Second.</i>&mdash;The weight of air discharged
+<p>§ 93. <i>Weight of Air Flowing per Second.</i>&mdash;The weight of air discharged
 per second is (equation 3a)&mdash;</p>
 
 <p class="center">W = &Omega;u<span class="su">0</span>p<span class="su">0</span> / c&tau;.</p>
@@ -13759,7 +13721,7 @@ per second is (equation 3a)&mdash;</p>
 <p class="center">W = (.6916p<span class="su">0</span> &minus; .4438p<span class="su">1</span>) (d<span class="sp">5</span> / &zeta; l&tau;)<span class="sp">1/2</span>.</p>
 <div class="author1">(13a)</div>
 
-<p>§ 94. <i>Application to the Case of Pneumatic Tubes for the Transmission
+<p>§ 94. <i>Application to the Case of Pneumatic Tubes for the Transmission
 of Messages.</i>&mdash;In Paris, Berlin, London, and other towns, it
 has been found cheaper to transmit messages in pneumatic tubes
 than to telegraph by electricity. The tubes are laid underground
@@ -13796,7 +13758,7 @@ from 0 to l,</p>
  = &zeta;<span class="sp">1/2</span> l<span class="sp">3/2</span> (p<span class="su">0</span><span class="sp">3</span> &minus; p<span class="su">1</span><span class="sp">3</span>) / 6(gc&tau;d)<span class="sp">1/2</span> (p<span class="su">0</span><span class="sp">2</span> &minus; p<span class="su">1</span><span class="sp">2</span>)<span class="sp">3/2</span>;</p>
 <div class="author">(15)</div>
 
-<p class="noind">If &tau; = 521°, corresponding to 60° F.,</p>
+<p class="noind">If &tau; = 521°, corresponding to 60° F.,</p>
 
 <p class="center">t = .001412 &zeta;<span class="sp">1/2</span> l<span class="sp">3/2</span> (p<span class="su">0</span><span class="sp">3</span> &minus; p<span class="su">1</span><span class="sp">3</span>) / d<span class="sp">1/2</span> (p<span class="su">0</span><span class="sp">2</span> &minus; p<span class="su">1</span><span class="sp">2</span>)<span class="sp">3/2</span>;</p>
 <div class="author1">(15a)</div>
@@ -13805,7 +13767,7 @@ from 0 to l,</p>
 pressures and the dimensions of the tube.</p>
 
 <p><i>Mean Velocity of Transmission.</i>&mdash;The mean velocity is l/t; or, for
-&tau; = 521°,</p>
+&tau; = 521°,</p>
 
 <p class="center">u<span class="su">mean</span> = 0.708 &radic; {d (p<span class="su">0</span><span class="sp">2</span> &minus; p<span class="su">1</span><span class="sp">2</span>)<span class="sp">3/2</span> / &zeta; l (p<span class="su">0</span><span class="sp">3</span> &minus; p<span class="su">1</span><span class="sp">3</span>)}.</p>
 <div class="author">(16)</div>
@@ -13838,7 +13800,7 @@ terminal pressures for which the formula is applicable.</p>
 
 <p class="pt2 center">X. FLOW IN RIVERS AND CANALS</p>
 
-<p>§ 95. <i>Flow of Water in Open Canals and Rivers.</i>&mdash;When water
+<p>§ 95. <i>Flow of Water in Open Canals and Rivers.</i>&mdash;When water
 flows in a pipe the section at any point is determined by the form
 of the boundary. When it flows in an open channel with free upper
 surface, the section depends on the velocity due to the dynamical
@@ -13899,7 +13861,7 @@ hypotheses, but at present they are not practically so
 reliable, and are more complicated than the formulae obtained in
 the manner described above.</p>
 
-<p>§ 96. <i>Steady Flow of Water with Uniform Velocity in Channels of
+<p>§ 96. <i>Steady Flow of Water with Uniform Velocity in Channels of
 Constant Section.</i>&mdash;Let aa&prime;, bb&prime; (fig. 103) be two cross sections normal
 to the direction of motion at a distance dl. Since the mass aa&prime;bb&prime;
 moves uniformly, the external forces acting on it are in equilibrium.
@@ -13920,7 +13882,7 @@ equal and opposite since the sections are equal and similar, and the
 mean pressures on each are the same. (<i>b</i>) The component of the
 weight W of the mass in the direction of motion, acting at its centre
 of gravity g. The weight of the mass aa&prime;bb&prime; is G&Omega; dl, and the component
-of the weight in the direction of motion is G&Omega;dl × the cosine of
+of the weight in the direction of motion is G&Omega;dl × the cosine of
 the angle between Wg and ab, that is, G&Omega;dl cos abc = G&Omega; dl bc/ab =
 G&Omega;idl. (<i>c</i>) There is the friction of the stream on the sides and
 bottom of the channel. This is proportional to the area &chi;dl of
@@ -13932,7 +13894,7 @@ the friction is &minus;&chi; dl &fnof;(v). Equating the sum of the forces to zer
  &fnof;(v) / G = &Omega;i / &chi; = mi.</p>
 <div class="author">(1)</div>
 
-<p class="noind">But it has been already shown (§ 66) that &fnof;(v) = &zeta;Gv<span class="sp">2</span>/2g,</p>
+<p class="noind">But it has been already shown (§ 66) that &fnof;(v) = &zeta;Gv<span class="sp">2</span>/2g,</p>
 
 <p class="center">&there4; &zeta;v<span class="sp">2</span> / 2g = mi.</p>
 <div class="author">(2)</div>
@@ -13970,7 +13932,7 @@ is</p>
 <p class="center">Q = &Omega;v = &Omega;c &radic; (mi).</p>
 <div class="author">(4)</div>
 
-<p>§ 97. <i>Coefficient of Friction for Open Channels.</i>&mdash;Various expressions
+<p>§ 97. <i>Coefficient of Friction for Open Channels.</i>&mdash;Various expressions
 have been proposed for the coefficient of friction for
 channels as for pipes. Weisbach, giving attention chiefly to the
 variation of the coefficient of friction with the velocity, proposed an
@@ -13993,7 +13955,7 @@ expression of the form</p>
 <p>In using this value of &zeta; when v is not known, it is best to proceed
 by approximation.</p>
 
-<p>§ 98. <i>Darcy and Bazin&rsquo;s Expression for the Coefficient of Friction.</i>&mdash;Darcy
+<p>§ 98. <i>Darcy and Bazin&rsquo;s Expression for the Coefficient of Friction.</i>&mdash;Darcy
 and Bazin&rsquo;s researches have shown that &zeta; varies very greatly
 for different degrees of roughness of the channel bed, and that it
 also varies with the dimensions of the channel. They give for &zeta; an
@@ -14072,7 +14034,7 @@ mean depths as are likely to occur in practical calculations:&mdash;</p>
 <tr><td class="tcc lb rb bb">&infin;</td> <td class="tcc rb bb">148</td> <td class="tcc rb bb">131</td> <td class="tcc rb bb">117</td> <td class="tcc rb bb">108</td> <td class="tcc rb bb">91&ensp;</td></tr>
 </table>
 
-<p>§ 99. <i>Ganguillet and Kutter&rsquo;s Modified Darcy Formula.</i>&mdash;Starting
+<p>§ 99. <i>Ganguillet and Kutter&rsquo;s Modified Darcy Formula.</i>&mdash;Starting
 from the general expression v = c&radic;mi, Ganguillet and Kutter
 examined the variations of c for a wider variety of cases than those
 discussed by Darcy and Bazin. Darcy and Bazin&rsquo;s experiments
@@ -14256,10 +14218,10 @@ The term involving the slope was introduced to secure agreement
 with some early experiments on the Mississippi, and there is strong
 reason for doubting the accuracy of these results.</p>
 
-<p>§ 100. <i>Bazin&rsquo;s New Formula.</i>&mdash;Bazin subsequently re-examined
+<p>§ 100. <i>Bazin&rsquo;s New Formula.</i>&mdash;Bazin subsequently re-examined
 all the trustworthy gaugings of flow in channels and proposed a
 modification of the original Darcy formula which appears to be
-more satisfactory than any hitherto suggested (<i>Étude d&rsquo;une nouvelle
+more satisfactory than any hitherto suggested (<i>Étude d&rsquo;une nouvelle
 formule</i>, Paris, 1898). He points out that Darcy&rsquo;s original formula,
 which is of the form mi/v<span class="sp">2</span> = &alpha; + &beta;/m, does not agree with experiments
 on channels as well as with experiments on pipes. It is an objection
@@ -14283,7 +14245,7 @@ mi, &zeta; = 0.002594 (1 + &gamma;/&radic; m), where &gamma; has the following v
 <tr><td class="tcr">VI.</td> <td class="tcl">Canals in earth exceptionally rough</td> <td class="tcc">3.168</td></tr>
 </table>
 
-<p>§ 101. <i>The Vertical Velocity Curve.</i>&mdash;If at each point along a
+<p>§ 101. <i>The Vertical Velocity Curve.</i>&mdash;If at each point along a
 vertical representing the depth of a stream, the velocity at that
 point is plotted horizontally, the curve obtained is the vertical
 velocity curve and it has been shown by many observations that
@@ -14314,7 +14276,7 @@ form of the horizontal velocity curve
 is roughly similar to the section of
 the stream.</p>
 
-<p>§ 102. <i>Curves or Contours of Equal
+<p>§ 102. <i>Curves or Contours of Equal
 Velocity.</i>&mdash;If velocities are observed
 at a number of points at different
 widths and depths in a stream, it is
@@ -14328,7 +14290,7 @@ the vertical and horizontal velocity curves and the contours of
 equal velocity in a rectangular channel, from one of Bazin&rsquo;s
 gaugings.</p>
 
-<p>§ 103. <i>Experimental Observations on the Vertical Velocity Curve.</i>&mdash;A
+<p>§ 103. <i>Experimental Observations on the Vertical Velocity Curve.</i>&mdash;A
 preliminary difficulty arises in observing the velocity at a given
 point in a stream because the velocity rapidly varies, the motion
 not being strictly steady. If an average of several velocities at the
@@ -14350,7 +14312,7 @@ found not at the surface but at some distance below it. In various
 river gaugings the depth d<span class="su">z</span> at the centre of the stream has been found
 to vary from 0 to 0.3d.</p>
 
-<p>§ 104. <i>Influence of the Wind.</i>&mdash;In the experiments on the Mississippi
+<p>§ 104. <i>Influence of the Wind.</i>&mdash;In the experiments on the Mississippi
 the vertical velocity curve in calm weather was found to agree
 fairly with a parabola, the greatest velocity being at <span class="spp">3</span>&frasl;<span class="suu">10</span>ths of the
 depth of the stream from the surface. With a wind blowing down
@@ -14408,7 +14370,7 @@ may range from +10 to &minus;10, positive if the wind is up stream,
 negative if it is down stream. Then Humphreys and Abbot find
 their results agree with the expression</p>
 
-<p class="center">h&prime; / m = 0.317 ± 0.06f.</p>
+<p class="center">h&prime; / m = 0.317 ± 0.06f.</p>
 
 <p class="noind">Fig. 106 shows the parabolic velocity curves according to the
 American observers for calm weather, and for an up- or down-stream
@@ -14435,7 +14397,7 @@ of observations by various observers gave the mean velocity at from
 to, but a little greater than, the mean velocity on a vertical. If
 v<span class="su">md</span> is the mid-depth velocity, then on the average v<span class="su">m</span> = 0.98v<span class="su">md</span>.</p>
 
-<p>§ 105. <i>Mean Velocity on a Vertical from Two Velocity Observations.</i>&mdash;A.
+<p>§ 105. <i>Mean Velocity on a Vertical from Two Velocity Observations.</i>&mdash;A.
 J. C. Cunningham, in gaugings on the Ganges canal, found the
 following useful results. Let v<span class="su">0</span> be the surface, v<span class="su">m</span> the mean, and
 v<span class="su">xd</span> the velocity at the depth xd; then</p>
@@ -14443,7 +14405,7 @@ v<span class="su">xd</span> the velocity at the depth xd; then</p>
 <p class="center">v<span class="su">m</span> = <span class="spp">1</span>&frasl;<span class="suu">4</span> (v<span class="su">0</span> + 3v<span class="su">2/3d</span> )<br />
 = <span class="spp">1</span>&frasl;<span class="suu">2</span> (v<span class="su">.211</span><span class="sp">d</span> + v<span class="su">.789</span><span class="sp">d</span> ).</p>
 
-<p>§ 106. <i>Ratio of Mean to Greatest Surface Velocity, for the whole
+<p>§ 106. <i>Ratio of Mean to Greatest Surface Velocity, for the whole
 Cross Section in Trapezoidal Channels.</i>&mdash;It is often very important
 to be able to deduce the mean velocity, and thence the discharge,
 from observation of the greatest surface velocity. The simplest
@@ -14464,7 +14426,7 @@ v<span class="su">m</span> the mean velocity of the stream. Then, according to B
 <p class="center">v<span class="su">m</span> = c &radic; (mi),</p>
 
 <p class="noind">where c is a coefficient, the values of which have been already given
-in the table in § 98. Hence</p>
+in the table in § 98. Hence</p>
 
 <p class="center">v<span class="su">m</span> = cv<span class="su">0</span> / (c + 25.4).</p>
 
@@ -14500,7 +14462,7 @@ in the table in § 98. Hence</p>
 <tr><td class="figright1"><img style="width:324px; height:307px" src="images/img72a.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 107.</span></td></tr></table>
 
-<p>§ 107. <i>River Bends.</i>&mdash;In rivers flowing in alluvial plains, the windings
+<p>§ 107. <i>River Bends.</i>&mdash;In rivers flowing in alluvial plains, the windings
 which already exist tend to increase in curvature by the scouring
 away of material from the outer bank and the deposition of detritus
 along the inner bank. The sinuosities sometimes increase till a
@@ -14567,7 +14529,7 @@ show the directions of flow immediately in contact with the sides
 and bottom. The dotted line AB shows the direction of motion of
 floating particles on the surface of the stream.</p>
 
-<p>§ 108. <i>Discharge of a River when flowing at different Depths.</i>&mdash;When
+<p>§ 108. <i>Discharge of a River when flowing at different Depths.</i>&mdash;When
 frequent observations must be made on the flow of a river
 or canal, the depth of which varies at different times, it is very
 convenient to have to observe the depth only. A formula can be
@@ -14576,10 +14538,10 @@ discharge in cubic feet per second; H the depth of the river in some
 straight and uniform part. Then Q = aH + bH<span class="sp">2</span>, where the constants
 a and b must be found by preliminary gaugings in different conditions
 of the river. M. C. Moquerey found for part of the upper
-Saône, Q = 64.7H + 8.2H<span class="sp">2</span> in metric measures, or Q = 696H + 26.8H<span class="sp">2</span>
+Saône, Q = 64.7H + 8.2H<span class="sp">2</span> in metric measures, or Q = 696H + 26.8H<span class="sp">2</span>
 in English measures.</p>
 
-<p>§ 109. <i>Forms of Section of Channels.</i>&mdash;The simplest form of section
+<p>§ 109. <i>Forms of Section of Channels.</i>&mdash;The simplest form of section
 for channels is the semicircular or nearly semicircular channel (fig.
 109), a form now often adopted from the facility with which it can be
 executed in concrete. It has the advantage that the rubbing surface
@@ -14614,7 +14576,7 @@ commonly adopted.</p>
 former being the section of a navigation canal and the latter the
 section of an irrigation canal.</p>
 
-<p>§ 110. <i>Channels of Circular Section.</i>&mdash;The following short table
+<p>§ 110. <i>Channels of Circular Section.</i>&mdash;The following short table
 facilitates calculations of the discharge with different depths of water
 in the channel. Let r be the radius of the channel section; then
 for a depth of water = &kappa;r, the hydraulic mean radius is &mu;r and the
@@ -14641,7 +14603,7 @@ following values:&mdash;</p>
 <tr><td class="figright1"><img style="width:325px; height:297px" src="images/img73b.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 113.</span></td></tr></table>
 
-<p>§ 111. <i>Egg-Shaped Channels or Sewers.</i>&mdash;In sewers for discharging
+<p>§ 111. <i>Egg-Shaped Channels or Sewers.</i>&mdash;In sewers for discharging
 storm water and house drainage the volume of flow is extremely
 variable; and there is a great liability for deposits to be left when
 the flow is small, which are not removed during the short periods
@@ -14663,12 +14625,12 @@ numbers marked on the
 figure being proportional
 numbers.</p>
 
-<p>§ 112. <i>Problems on
+<p>§ 112. <i>Problems on
 Channels in which the
 Flow is Steady and at
 Uniform Velocity.</i>&mdash;The
 general equations given
-in §§ 96, 98 are</p>
+in §§ 96, 98 are</p>
 
 <p class="center">&zeta; = &alpha;(1 + &beta;/m);</p>
 <div class="author">(1)</div>
@@ -14712,7 +14674,7 @@ the process till the successive
 values of m approximately
 coincide.</p>
 
-<p>§ 113. <i>Problem IV. Most
+<p>§ 113. <i>Problem IV. Most
 Economical Form of Channel
 for given Side Slopes.</i>&mdash;Suppose
 the channel is to be
@@ -14856,25 +14818,25 @@ Area of section =</i> &Omega;.</p>
 <tr><td class="tcl allb">&nbsp;</td> <td class="tccm allb f80">Inclination<br />of Sides to<br />Horizon.</td> <td class="tccm allb f80">Ratio of<br />Side<br />Slopes.</td> <td class="tccm allb f80">Area of<br />Section &Omega;.</td> <td class="tccm allb f80">Bottom<br />Width.</td> <td class="tccm allb f80">Top width =<br />twice length<br />of each Side<br />Slope.</td></tr>
 
 <tr><td class="tcl lb rb">Semicircle</td> <td class="tcc rb">..</td> <td class="tcc rb">..</td> <td class="tcc rb">1.571d<span class="sp">2</span></td> <td class="tcc rb">0</td> <td class="tcc rb">2d</td></tr>
-<tr><td class="tcl lb rb">Semi-hexagon</td> <td class="tcc rb">60°&ensp;  &ensp;0&prime;</td> <td class="tcc rb">3&ensp;  : 5</td> <td class="tcc rb">1.732d<span class="sp">2</span></td> <td class="tcc rb">1.155d</td> <td class="tcc rb">2.310d</td></tr>
-<tr><td class="tcl lb rb">Semi-square</td> <td class="tcc rb">90°&ensp;  &ensp;0&prime;</td> <td class="tcc rb">0&ensp;  : 1</td> <td class="tcc rb">2d<span class="sp">2</span></td> <td class="tcc rb">2d</td> <td class="tcc rb">2d</td></tr>
-<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">75°&ensp; 58&prime;</td> <td class="tcc rb">1&ensp;  : 4</td> <td class="tcc rb">1.812d<span class="sp">2</span></td> <td class="tcc rb">1.562d</td> <td class="tcc rb">2.062d</td></tr>
-<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">63°&ensp; 26&prime;</td> <td class="tcc rb">1&ensp;  : 2</td> <td class="tcc rb">1.736d<span class="sp">2</span></td> <td class="tcc rb">1.236d</td> <td class="tcc rb">2.236d</td></tr>
-<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">53°&ensp;  &ensp;8&prime;</td> <td class="tcc rb">3&ensp;  : 4</td> <td class="tcc rb">1.750d<span class="sp">2</span></td> <td class="tcc rb">d</td> <td class="tcc rb">2.500d</td></tr>
-<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">45°&ensp;  &ensp;0&prime;</td> <td class="tcc rb">1&ensp;  : 1</td> <td class="tcc rb">1.828d<span class="sp">2</span></td> <td class="tcc rb">0.828d</td> <td class="tcc rb">2.828d</td></tr>
-<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">38°&ensp; 40&prime;</td> <td class="tcc rb">1<span class="spp">1</span>&frasl;<span class="suu">4</span> : 1</td> <td class="tcc rb">1.952d<span class="sp">2</span></td> <td class="tcc rb">0.702d</td> <td class="tcc rb">3.202d</td></tr>
-<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">33°&ensp; 42&prime;</td> <td class="tcc rb">1<span class="spp">1</span>&frasl;<span class="suu">2</span> : 1</td> <td class="tcc rb">2.106d<span class="sp">2</span></td> <td class="tcc rb">0.606d</td> <td class="tcc rb">3.606d</td></tr>
-<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">29°&ensp; 44&prime;</td> <td class="tcc rb">1<span class="spp">3</span>&frasl;<span class="suu">4</span> : 1</td> <td class="tcc rb">2.282d<span class="sp">2</span></td> <td class="tcc rb">0.532d</td> <td class="tcc rb">4.032d</td></tr>
-<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">26°&ensp; 34&prime;</td> <td class="tcc rb">2&ensp; : 1</td> <td class="tcc rb">2.472d<span class="sp">2</span></td> <td class="tcc rb">0.472d</td> <td class="tcc rb">4.472d</td></tr>
-<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">23°&ensp; 58&prime;</td> <td class="tcc rb">2<span class="spp">1</span>&frasl;<span class="suu">4</span> : 1</td> <td class="tcc rb">2.674d<span class="sp">2</span></td> <td class="tcc rb">0.424d</td> <td class="tcc rb">4.924d</td></tr>
-<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">21°&ensp; 48&prime;</td> <td class="tcc rb">2<span class="spp">1</span>&frasl;<span class="suu">2</span> : 1</td> <td class="tcc rb">2.885d<span class="sp">2</span></td> <td class="tcc rb">0.385d</td> <td class="tcc rb">5.385d</td></tr>
-<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">19°&ensp; 58&prime;</td> <td class="tcc rb">2<span class="spp">3</span>&frasl;<span class="suu">4</span> : 1</td> <td class="tcc rb">3.104d<span class="sp">2</span></td> <td class="tcc rb">0.354d</td> <td class="tcc rb">5.854d</td></tr>
-<tr><td class="tcl lb rb bb">&nbsp;</td> <td class="tcc rb bb">18°&ensp; 26&prime;</td> <td class="tcc rb bb">3&ensp;  : 1</td> <td class="tcc rb bb">3.325d<span class="sp">2</span></td> <td class="tcc rb bb">0.325d</td> <td class="tcc rb bb">6.325d</td></tr>
+<tr><td class="tcl lb rb">Semi-hexagon</td> <td class="tcc rb">60°&ensp;  &ensp;0&prime;</td> <td class="tcc rb">3&ensp;  : 5</td> <td class="tcc rb">1.732d<span class="sp">2</span></td> <td class="tcc rb">1.155d</td> <td class="tcc rb">2.310d</td></tr>
+<tr><td class="tcl lb rb">Semi-square</td> <td class="tcc rb">90°&ensp;  &ensp;0&prime;</td> <td class="tcc rb">0&ensp;  : 1</td> <td class="tcc rb">2d<span class="sp">2</span></td> <td class="tcc rb">2d</td> <td class="tcc rb">2d</td></tr>
+<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">75°&ensp; 58&prime;</td> <td class="tcc rb">1&ensp;  : 4</td> <td class="tcc rb">1.812d<span class="sp">2</span></td> <td class="tcc rb">1.562d</td> <td class="tcc rb">2.062d</td></tr>
+<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">63°&ensp; 26&prime;</td> <td class="tcc rb">1&ensp;  : 2</td> <td class="tcc rb">1.736d<span class="sp">2</span></td> <td class="tcc rb">1.236d</td> <td class="tcc rb">2.236d</td></tr>
+<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">53°&ensp;  &ensp;8&prime;</td> <td class="tcc rb">3&ensp;  : 4</td> <td class="tcc rb">1.750d<span class="sp">2</span></td> <td class="tcc rb">d</td> <td class="tcc rb">2.500d</td></tr>
+<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">45°&ensp;  &ensp;0&prime;</td> <td class="tcc rb">1&ensp;  : 1</td> <td class="tcc rb">1.828d<span class="sp">2</span></td> <td class="tcc rb">0.828d</td> <td class="tcc rb">2.828d</td></tr>
+<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">38°&ensp; 40&prime;</td> <td class="tcc rb">1<span class="spp">1</span>&frasl;<span class="suu">4</span> : 1</td> <td class="tcc rb">1.952d<span class="sp">2</span></td> <td class="tcc rb">0.702d</td> <td class="tcc rb">3.202d</td></tr>
+<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">33°&ensp; 42&prime;</td> <td class="tcc rb">1<span class="spp">1</span>&frasl;<span class="suu">2</span> : 1</td> <td class="tcc rb">2.106d<span class="sp">2</span></td> <td class="tcc rb">0.606d</td> <td class="tcc rb">3.606d</td></tr>
+<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">29°&ensp; 44&prime;</td> <td class="tcc rb">1<span class="spp">3</span>&frasl;<span class="suu">4</span> : 1</td> <td class="tcc rb">2.282d<span class="sp">2</span></td> <td class="tcc rb">0.532d</td> <td class="tcc rb">4.032d</td></tr>
+<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">26°&ensp; 34&prime;</td> <td class="tcc rb">2&ensp; : 1</td> <td class="tcc rb">2.472d<span class="sp">2</span></td> <td class="tcc rb">0.472d</td> <td class="tcc rb">4.472d</td></tr>
+<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">23°&ensp; 58&prime;</td> <td class="tcc rb">2<span class="spp">1</span>&frasl;<span class="suu">4</span> : 1</td> <td class="tcc rb">2.674d<span class="sp">2</span></td> <td class="tcc rb">0.424d</td> <td class="tcc rb">4.924d</td></tr>
+<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">21°&ensp; 48&prime;</td> <td class="tcc rb">2<span class="spp">1</span>&frasl;<span class="suu">2</span> : 1</td> <td class="tcc rb">2.885d<span class="sp">2</span></td> <td class="tcc rb">0.385d</td> <td class="tcc rb">5.385d</td></tr>
+<tr><td class="tcl lb rb">&nbsp;</td> <td class="tcc rb">19°&ensp; 58&prime;</td> <td class="tcc rb">2<span class="spp">3</span>&frasl;<span class="suu">4</span> : 1</td> <td class="tcc rb">3.104d<span class="sp">2</span></td> <td class="tcc rb">0.354d</td> <td class="tcc rb">5.854d</td></tr>
+<tr><td class="tcl lb rb bb">&nbsp;</td> <td class="tcc rb bb">18°&ensp; 26&prime;</td> <td class="tcc rb bb">3&ensp;  : 1</td> <td class="tcc rb bb">3.325d<span class="sp">2</span></td> <td class="tcc rb bb">0.325d</td> <td class="tcc rb bb">6.325d</td></tr>
 <tr><td class="tcc" colspan="6">Half the top width is the length of each side slope. The wetted<br />
 perimeter is the sum of the top and bottom widths.</td></tr>
 </table>
 
-<p>§ 114. <i>Form of Cross Section of Channel in which the Mean Velocity
+<p>§ 114. <i>Form of Cross Section of Channel in which the Mean Velocity
 is Constant with Varying Discharge.</i>&mdash;In designing waste channels
 from canals, and in some other cases, it is desirable that the mean
 velocity should be restricted within narrow limits with very different
@@ -14936,7 +14898,7 @@ rapid flattening of the side slopes is remarkable.</p>
 <p class="pt1 center sc">Steady Motion of Water in Open Channels of Varying
 Cross Section and Slope</p>
 
-<p>§ 115. In every stream the discharge of which is constant, or may
+<p>§ 115. In every stream the discharge of which is constant, or may
 be regarded as constant for the time considered, the velocity at
 different places depends on the slope of the bed. Except at certain
 exceptional points the velocity will be greater as the slope of the
@@ -15018,7 +14980,7 @@ the same velocity u<span class="su">0</span>. Let the kinetic energy be taken at
 <p class="center">&alpha; (G&theta; / 2g) &Omega;<span class="su">0</span>u<span class="su">0</span><span class="sp">3</span> = &alpha; (G&theta; / 2g) Qu<span class="su">0</span><span class="sp">2</span>,</p>
 
 <p class="noind">where &alpha; is a corrective factor, the value of which was estimated by
-J. B. C. J. Bélanger at 1.1.<a name="fa6f" id="fa6f" href="#ft6f"><span class="sp">6</span></a> Its precise value is not of great importance.</p>
+J. B. C. J. Bélanger at 1.1.<a name="fa6f" id="fa6f" href="#ft6f"><span class="sp">6</span></a> Its precise value is not of great importance.</p>
 
 <p>In a similar way we should obtain for the kinetic energy of
 A<span class="su">1</span>B<span class="su">1</span>C<span class="su">1</span>D<span class="su">1</span> the expression</p>
@@ -15087,7 +15049,7 @@ energy given in (1),</p>
 <tr><td class="figcenter"><img style="width:435px; height:228px" src="images/img75a.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 120.</span></td></tr></table>
 
-<p>§ 116. <i>Fundamental Differential Equation of Steady Varied Motion.</i>&mdash;Suppose
+<p>§ 116. <i>Fundamental Differential Equation of Steady Varied Motion.</i>&mdash;Suppose
 the equation just found to be applied to an indefinitely
 short length ds of the stream, limited by the end sections ab, a<span class="su">1</span>b<span class="su">1</span>,
 taken for simplicity normal to the stream bed (fig. 120). For that
@@ -15148,7 +15110,7 @@ becomes</p>
 <p class="center">dh/ds = i (1 &minus; &zeta;u<span class="sp">2</span> / 2gih) / (1 &minus; u<span class="sp">2</span>/gh).</p>
 <div class="author">(5)</div>
 
-<p>§ 117. <i>General Indications as to the Form of Water Surface furnished
+<p>§ 117. <i>General Indications as to the Form of Water Surface furnished
 by Equation</i> (5).&mdash;Let A<span class="su">0</span>A<span class="su">1</span> (fig. 121) be the water surface,
 B<span class="su">0</span>B<span class="su">1</span> the bed in a longitudinal section of the stream, and ab any
 section at a distance s from B<span class="su">0</span>, the depth ab being h. Suppose
@@ -15207,7 +15169,7 @@ before:&mdash;</p>
 <tr><td class="figcenter"><img style="width:443px; height:220px" src="images/img75c.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 122.</span></td></tr></table>
 
-<p>§ 118. <i>Case</i> 1.&mdash;Suppose h &gt; u<span class="sp">2</span>/g, and also h &gt; H, or the depth
+<p>§ 118. <i>Case</i> 1.&mdash;Suppose h &gt; u<span class="sp">2</span>/g, and also h &gt; H, or the depth
 greater than that corresponding to uniform motion. In this case
 dh/ds is positive, and the stream increases in depth in the direction
 of flow. In fig. 122 let B<span class="su">0</span>B<span class="su">1</span> be the bed, C<span class="su">0</span>C<span class="su">1</span> a line parallel to the
@@ -15233,7 +15195,7 @@ termed the backwater due to the weir.</p>
 <tr><td class="figright1"><img style="width:387px; height:172px" src="images/img76b.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 124.</span></td></tr></table>
 
-<p>§ 119. <i>Case</i> 2.&mdash;Suppose h &gt; u<span class="sp">2</span>/g, and also h &lt; H. Then dh/ds is
+<p>§ 119. <i>Case</i> 2.&mdash;Suppose h &gt; u<span class="sp">2</span>/g, and also h &lt; H. Then dh/ds is
 <span class="pagenum"><a name="page76" id="page76"></a>76</span>
 negative, and the stream is diminishing in depth in the direction of
 flow. In fig. 123 let B<span class="su">0</span>B<span class="su">1</span> be the stream bed as before; C<span class="su">0</span>C<span class="su">1</span> a line
@@ -15308,7 +15270,7 @@ approximately with the intended level AA.</p>
 <tr><td class="figcenter"><img style="width:496px; height:272px" src="images/img76c.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 125.</span></td></tr></table>
 
-<p>§ 120. <i>Case</i> 3.&mdash;Suppose a stream flowing uniformly with a depth
+<p>§ 120. <i>Case</i> 3.&mdash;Suppose a stream flowing uniformly with a depth
 h &lt; u<span class="sp">2</span>/g. For a stream in uniform motion &zeta;u<span class="sp">2</span>/2g = mi, or if the
 stream is of indefinitely great width, so that m = H, then &zeta;u<span class="sp">2</span>/2g = iH,
 and H = &zeta;u<span class="sp">2</span>/2gi. Consequently the condition stated above involves
@@ -15362,7 +15324,7 @@ production of a standing wave may occur.</p>
 
 <p class="pt1 center sc">Standing Waves</p>
 
-<p>§ 121. The formation of a standing wave was first observed by
+<p>§ 121. The formation of a standing wave was first observed by
 Bidone. Into a small rectangular masonry channel, having a slope
 of 0.023 ft. per foot, he admitted water till it flowed uniformly with
 a depth of 0.2 ft. He then placed a plank across the stream which
@@ -15372,9 +15334,9 @@ point 15 ft. from it. At that point the depth suddenly increased
 from 0.2 ft. to 0.56 ft. The velocity of the stream in the part unaffected
 by the obstruction was 5.54 ft. per second. Above the point
 where the abrupt change of depth occurred u<span class="sp">2</span> = 5.54<span class="sp">2</span> = 30.7, and
-gh = 32.2 × 0.2 = 6.44; hence u<span class="sp">2</span> was &gt; gh. Just below the abrupt
-change of depth u = 5.54 × 0.2/0.56 = 1.97; u<span class="sp">2</span> = 3.88; and gh =
-32.2 × 0.56 = 18.03; hence at this point u<span class="sp">2</span> &lt; gh. Between these two
+gh = 32.2 × 0.2 = 6.44; hence u<span class="sp">2</span> was &gt; gh. Just below the abrupt
+change of depth u = 5.54 × 0.2/0.56 = 1.97; u<span class="sp">2</span> = 3.88; and gh =
+32.2 × 0.56 = 18.03; hence at this point u<span class="sp">2</span> &lt; gh. Between these two
 points, therefore, u<span class="sp">2</span> = gh; and the condition for the production of a
 standing wave occurred.</p>
 
@@ -15436,7 +15398,7 @@ which agrees very well with the observed height.</p>
 <tr><td class="figcenter"><img style="width:475px; height:145px" src="images/img77a.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 127.</span></td></tr></table>
 
-<p>§ 122. A standing wave is frequently produced at the foot of
+<p>§ 122. A standing wave is frequently produced at the foot of
 a weir. Thus in the ogee falls originally constructed on the Ganges
 canal a standing wave was observed as shown in fig. 127. The water
 falling over the weir crest A acquired a very high velocity on the
@@ -15479,16 +15441,16 @@ of the pier at 26 ft., the
 velocity necessary for the
 production of a standing
 wave would be u = &radic; (gh)
-= &radic; (32.2 × 26) = 29 ft.
+= &radic; (32.2 × 26) = 29 ft.
 per second nearly. But
 the velocity at this
-point was probably from Howden&rsquo;s statements 16.58 × <span class="spp">40</span>&frasl;<span class="suu">26</span> = 25.5
+point was probably from Howden&rsquo;s statements 16.58 × <span class="spp">40</span>&frasl;<span class="suu">26</span> = 25.5
 ft. <span class="correction" title="added per second">per second</span>, an agreement as close as the approximate character of the
 data would lead us to expect.</p>
 
 <p class="pt2 center" style="clear: both;">XI. ON STREAMS AND RIVERS</p>
 
-<p>§ 123. <i>Catchment Basin.</i>&mdash;A stream or river is the channel for the
+<p>§ 123. <i>Catchment Basin.</i>&mdash;A stream or river is the channel for the
 discharge of the available rainfall of a district, termed its catchment
 basin. The catchment basin is surrounded by a ridge or watershed
 line, continuous except at the point where the river finds an outlet.
@@ -15508,7 +15470,7 @@ average rainfall on the catchment basin (Tiefenbacher).</p>
 <tr><td class="tcl lb rb bb">Naked unfissured mountains</td> <td class="tcc rb bb">.55 to .60</td> <td class="tcc rb bb">40 to 45</td></tr>
 </table>
 
-<p>§ 124. <i>Flood Discharge.</i>&mdash;The flood discharge can generally only be
+<p>§ 124. <i>Flood Discharge.</i>&mdash;The flood discharge can generally only be
 determined by examining the greatest height to which floods have
 been known to rise. To produce a flood the rainfall must be heavy
 and widely distributed, and to produce a flood of exceptional height
@@ -15567,7 +15529,7 @@ Ganges and Godavery works, and = 10,000 on Madras works.</p>
 <tr><td class="figright1"><img style="width:327px; height:128px" src="images/img77d.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 130.</span></td></tr></table>
 
-<p>§ 125. <i>Action of a Stream on its Bed.</i>&mdash;If the velocity of a stream
+<p>§ 125. <i>Action of a Stream on its Bed.</i>&mdash;If the velocity of a stream
 exceeds a certain limit, depending on its size, and on the size, heaviness,
 form and coherence of the
 material of which its bed is composed,
@@ -15610,7 +15572,7 @@ streams, the velocity of transport of material down stream is greater
 as the depth of the stream is greater. The effect is that the deep
 stream excavates its bed more rapidly than the shallow stream.</p>
 
-<p>§ 126. <i>Bottom Velocity at which Scour commences.</i>&mdash;The following
+<p>§ 126. <i>Bottom Velocity at which Scour commences.</i>&mdash;The following
 bottom velocities were determined by P. L. G. Dubuat to be the
 maximum velocities consistent with stability of the stream bed for
 different materials.</p>
@@ -15649,7 +15611,7 @@ obtained:&mdash;</p>
 
 <p>The following table of velocities which should not be exceeded
 in channels is given in the <i>Ingenieurs Taschenbuch</i> of the Verein
-&ldquo;Hütte&rdquo;:&mdash;</p>
+&ldquo;Hütte&rdquo;:&mdash;</p>
 
 <table class="ws" summary="Contents">
 <tr><td class="tcc allb">&nbsp;</td> <td class="tcc allb">Surface<br />Velocity.</td> <td class="tcc allb">Mean<br />Velocity.</td> <td class="tcc allb">Bottom<br />Velocity.</td></tr>
@@ -15664,7 +15626,7 @@ in channels is given in the <i>Ingenieurs Taschenbuch</i> of the Verein
 <tr><td class="tcl lb rb bb">Hard rocks</td> <td class="tcc rb bb">14.00</td> <td class="tcc rb bb">12.15</td> <td class="tcc rb bb">10.36</td></tr>
 </table>
 
-<p>§ 127. <i>Regime of a River Channel.</i>&mdash;A river channel is said to be in
+<p>§ 127. <i>Regime of a River Channel.</i>&mdash;A river channel is said to be in
 a state of regime, or stability, when it changes little in draught or
 form in a series of years. In some rivers the deepest part of the
 channel changes its position perpetually, and is seldom found in the
@@ -15694,13 +15656,13 @@ the silting at another. In that case the general regime is permanent,
 though alteration is constantly going on. This is more likely to
 happen if by artificial means the erosion of the banks is prevented.
 If a river flows in soil incapable of resisting its tendency to scour
-it is necessarily sinuous (§ 107), for the slightest deflection of the
+it is necessarily sinuous (§ 107), for the slightest deflection of the
 current to either side begins an erosion which increases progressively
 till a considerable bend is formed. If such a river is
 straightened it becomes sinuous again unless its banks are protected
 from scour.</p>
 
-<p>§ 128. <i>Longitudinal Section of River Bed.</i>&mdash;The declivity of rivers
+<p>§ 128. <i>Longitudinal Section of River Bed.</i>&mdash;The declivity of rivers
 decreases from source to mouth. In their higher parts rapid and
 torrential, flowing over beds of gravel or boulders, they enlarge in
 volume by receiving affluent streams, their slope diminishes, their
@@ -15750,7 +15712,7 @@ vertical and horizontal coordinates. Let C be a point whose ordinates
 are x and y, and let the river at C have the breadth b, the slope i,
 and the velocity v.</p>
 
-<p class="noind">Since velocity × area of section = discharge, vcb<span class="sp">2</span> = kl, or b = &radic; (kl/cv).</p>
+<p class="noind">Since velocity × area of section = discharge, vcb<span class="sp">2</span> = kl, or b = &radic; (kl/cv).</p>
 
 <p class="noind">Hydraulic mean depth = ab = a &radic; (kl/cv).</p>
 
@@ -15770,7 +15732,7 @@ l = AC = AD = x nearly.</p>
 
 <p class="noind">or</p>
 
-<p class="center">y<span class="sp">2</span> = constant × x;</p>
+<p class="center">y<span class="sp">2</span> = constant × x;</p>
 
 <p class="noind">so that the curve is a common parabola, of which the axis is horizontal
 and the vertex at the source. This may be considered an
@@ -15779,7 +15741,7 @@ more or less, with exceptions due to the varying
 hardness of their beds, and the irregular manner in
 which their volume increases.</p>
 
-<p>§ 129. <i>Surface Level of River.</i>&mdash;The surface level of a
+<p>§ 129. <i>Surface Level of River.</i>&mdash;The surface level of a
 river is a plane changing constantly in position from
 changes in the volume of water discharged, and more
 slowly from changes in the river bed, and the circumstances
@@ -15818,7 +15780,7 @@ under bridges becoming insufficient. Ordinarily the highest
 navigable level may be taken to be that at which the river begins to
 overflow its banks.</p>
 
-<p>§ 130. <i>Relative Value of Different Materials for Submerged Works.</i>&mdash;That
+<p>§ 130. <i>Relative Value of Different Materials for Submerged Works.</i>&mdash;That
 the power of water to remove and transport different materials
 depends on their density has an important bearing on the selection
 of materials for submerged works. In many cases, as in the aprons
@@ -15846,7 +15808,7 @@ V &#8468;.</p>
 <tr><td class="tcl lb rb bb">Masonry</td> <td class="tcc rb bb">116-144</td> <td class="tcc rb bb">53.6-81.6</td></tr>
 </table>
 
-<p>§ 131. <i>Inundation Deposits from a River.</i>&mdash;When a river carrying
+<p>§ 131. <i>Inundation Deposits from a River.</i>&mdash;When a river carrying
 silt periodically overflows its banks, it deposits silt over the area
 flooded, and gradually raises the surface of the country. The silt is
 deposited in greatest abundance where the water first leaves the
@@ -15869,7 +15831,7 @@ country in this case is very easy; a comparatively slight raising of
 the river surface by a weir or annicut gives a command of level
 which permits the water to be conveyed to any part of the district.</p>
 
-<p>§ 132. <i>Deltas.</i>&mdash;The name delta was originally given to the &Delta;-shaped
+<p>§ 132. <i>Deltas.</i>&mdash;The name delta was originally given to the &Delta;-shaped
 portion of Lower Egypt, included between seven branches of
 the Nile. It is now given to the whole of the alluvial tracts round
 river mouths formed by deposition of sediment from the river, where
@@ -15890,7 +15852,7 @@ of shoals at its mouth, and the river tends to form new bifurcations
 AC or AD (fig. 134), and one of these may in time become the main
 channel of the river.</p>
 
-<p>§ 133. <i>Field Operations preliminary to a Study of River Improvement.</i>&mdash;There
+<p>§ 133. <i>Field Operations preliminary to a Study of River Improvement.</i>&mdash;There
 are required (1) a plan of the river, on which the
 positions of lines of levelling and cross sections are marked; (2) a
 longitudinal section and numerous cross sections of the river; (3) a
@@ -15910,7 +15872,7 @@ observations, two on each side of the river.</p>
 <tr><td class="figcenter"><img style="width:456px; height:320px" src="images/img79b.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 134.</span></td></tr></table>
 
-<p>§ 134. <i>Cross Sections</i>&mdash;A stake is planted flush with the water, and
+<p>§ 134. <i>Cross Sections</i>&mdash;A stake is planted flush with the water, and
 its level relatively to some point on the line of levels is determined.
 Then the depth of the water is determined at a series of points (if
 possible at uniform distances) in a line starting from the stake and
@@ -15961,7 +15923,7 @@ From the section can be measured the sectional area of the stream
 &Omega; and its wetted perimeter &chi;; and from these the hydraulic mean
 depth m can be calculated.</p>
 
-<p>§ 135. <i>Measurement of the Discharge of Rivers.</i>&mdash;The area of cross
+<p>§ 135. <i>Measurement of the Discharge of Rivers.</i>&mdash;The area of cross
 section multiplied by the mean velocity gives the discharge of the
 stream. The height of the river with reference to some fixed mark
 should be noted whenever the velocity is observed, as the velocity
@@ -15974,7 +15936,7 @@ than one method should be used.</p>
 
 <p class="pt1 center sc">Instruments for Measuring the Velocity of Water</p>
 
-<p>§ 136. <i>Surface Floats</i> are convenient for determining the surface
+<p>§ 136. <i>Surface Floats</i> are convenient for determining the surface
 velocities of a stream, though their use is difficult near the banks.
 The floats may be small balls of wood, of wax or of hollow metal, so
 loaded as to float nearly flush with the water surface. To render
@@ -16050,7 +16012,7 @@ and in some cases to the nearest quarter second.</p>
 <tr><td class="figright1"><img style="width:213px; height:275px" src="images/img80b.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 137.</span></td></tr></table>
 
-<p>§ 137. <i>Sub-surface Floats.</i>&mdash;The velocity at different depths below
+<p>§ 137. <i>Sub-surface Floats.</i>&mdash;The velocity at different depths below
 the surface of a stream may be obtained by sub-surface floats, used
 precisely in the same way as surface floats. The most usual arrangement
 is to have a large float, of slightly greater density than water,
@@ -16089,7 +16051,7 @@ slice of cork, which serves as the surface float.</p>
 <tr><td class="caption"><span class="sc">Fig. 138.</span></td>
 <td class="caption"><span class="sc">Fig. 139.</span></td></tr></table>
 
-<p>§ 138. <i>Twin Floats.</i>&mdash;Suppose two equal and similar floats (fig. 139)
+<p>§ 138. <i>Twin Floats.</i>&mdash;Suppose two equal and similar floats (fig. 139)
 connected by a wire. Let one float be a little lighter and the other
 a little heavier than water. Then the velocity of the combined
 floats will be the mean of the surface velocity and the velocity at the
@@ -16112,7 +16074,7 @@ the sub-surface float.</p>
 <tr><td class="figright1"><img style="width:206px; height:342px" src="images/img80e.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 140.</span></td></tr></table>
 
-<p>§ 139. <i>Velocity Rods.</i>&mdash;Another form of float is shown in fig. 140.
+<p>§ 139. <i>Velocity Rods.</i>&mdash;Another form of float is shown in fig. 140.
 This consists of a cylindrical rod loaded at the lower end so as to
 float nearly vertical in water. A wooden rod, with a metal cap at the
 bottom in which shot can be placed,
@@ -16127,7 +16089,7 @@ sinks nearly to the bed of the stream,
 gives directly the mean velocity of the
 whole vertical section in which it floats.</p>
 
-<p>§ 140. <i>Revy&rsquo;s Current Meter.</i>&mdash;No instrument
+<p>§ 140. <i>Revy&rsquo;s Current Meter.</i>&mdash;No instrument
 has been so much used in
 directly determining the velocity of a
 stream at a given point as the screw
@@ -16200,7 +16162,7 @@ and stopped by hand.</p>
 <tr><td class="figright1"><img style="width:159px; height:606px" src="images/img81b.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 142.</span></td></tr></table>
 
-<p>§ 141. <i>The Harlacher Current Meter.</i>&mdash;In
+<p>§ 141. <i>The Harlacher Current Meter.</i>&mdash;In
 this the ordinary counting apparatus is abandoned.
 A worm drives a worm wheel, which
 makes an electrical contact once for each 100
@@ -16224,7 +16186,7 @@ small metal box containing also the battery.
 The magnet exposes and withdraws a coloured
 disk at an opening in the cover of the box.</p>
 
-<p>§ 142. <i>Amsler Laffon Current Meter.</i>&mdash;A
+<p>§ 142. <i>Amsler Laffon Current Meter.</i>&mdash;A
 very convenient and accurate current meter
 is constructed by Amsler Laffon of Schaffhausen.
 This can be used on a rod, and
@@ -16256,7 +16218,7 @@ used as a sounding instrument.</p>
 <tr><td class="figcenter"><img style="width:470px; height:859px" src="images/img81c.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 143.</span></td></tr></table>
 
-<p>§ 143. <i>Determination of the Coefficients of the Current Meter.</i>&mdash;Suppose
+<p>§ 143. <i>Determination of the Coefficients of the Current Meter.</i>&mdash;Suppose
 a series of observations has been made by towing the meter in
 still water at different speeds, and that it is required to ascertain from
 these the constants of the meter. If v is the velocity of the water and
@@ -16309,9 +16271,9 @@ determined by towing them in R. E. Froude&rsquo;s experimental tank in
 which the resistance of ship models is ascertained. In that case the
 data are found with exceptional accuracy.</p>
 
-<p>§ 144. Darcy Gauge or modified Pitot Tube.&mdash;A very old instrument
+<p>§ 144. Darcy Gauge or modified Pitot Tube.&mdash;A very old instrument
 for measuring velocities, invented by Henri Pitot in 1730
-(<i>Histoire de l&rsquo;Académie des Sciences</i>, 1732, p. 376), consisted simply
+(<i>Histoire de l&rsquo;Académie des Sciences</i>, 1732, p. 376), consisted simply
 of a vertical glass tube with a right-angled bend, placed so that its
 mouth was normal to the direction of flow (fig. 145).</p>
 
@@ -16428,7 +16390,7 @@ constant, but varies a little from moment to moment. Darcy in
 some of his experiments took several readings, and deduced the
 velocity from the mean of the highest and lowest.</p>
 
-<p>§ 145. <i>Perrodil Hydrodynamometer.</i>&mdash;This consists of a frame
+<p>§ 145. <i>Perrodil Hydrodynamometer.</i>&mdash;This consists of a frame
 abcd (fig. 147) placed vertically in the stream, and of a height not
 less than the stream&rsquo;s depth. The two vertical members of this
 frame are connected by cross bars, and united above water by a
@@ -16558,7 +16520,7 @@ indications of very low velocities.</p>
 
 <p class="pt1 center sc">Processes for Gauging Streams</p>
 
-<p>§ 146. <i>Gauging by Observation of the Maximum Surface Velocity.</i>&mdash;The
+<p>§ 146. <i>Gauging by Observation of the Maximum Surface Velocity.</i>&mdash;The
 method of gauging which involves the least trouble is to determine
 the surface velocity at the thread of the stream, and to deduce
 from it the mean velocity of the whole cross section. The maximum
@@ -16577,7 +16539,7 @@ values:&mdash;</p>
 <tr><td class="tcl">Destrem and De Prony, experiments on the Neva</td> <td class="tcl">0.78</td></tr>
 <tr><td class="tcl">Boileau, experiments on canals</td> <td class="tcl">0.82</td></tr>
 <tr><td class="tcl">Baumgartner, experiments on the Garonne</td> <td class="tcl">0.80</td></tr>
-<tr><td class="tcl">Brünings (mean)</td> <td class="tcl">0.85</td></tr>
+<tr><td class="tcl">Brünings (mean)</td> <td class="tcl">0.85</td></tr>
 <tr><td class="tcl">Cunningham, Solani aqueduct</td> <td class="tcl">0.823</td></tr>
 </table>
 
@@ -16615,7 +16577,7 @@ found would then always give the velocity for any observed depth of
 the stream, without the need of making any new float or current
 meter observations.</p>
 
-<p>§ 147. <i>Mean Velocity determined by observing a Series of Surface
+<p>§ 147. <i>Mean Velocity determined by observing a Series of Surface
 Velocities.</i>&mdash;The ratio of the mean velocity to the surface velocity
 in one longitudinal section is better ascertained than the ratio of
 the central surface velocity to the mean velocity of the whole cross
@@ -16691,7 +16653,7 @@ very calm weather.</p>
 
 <p>The ratio of the surface velocity to the mean velocity in the same
 vertical can be ascertained from the formulae for the vertical velocity
-curve already given (§ 101). Exner, in <i>Erbkam&rsquo;s Zeitschrift</i> for 1875,
+curve already given (§ 101). Exner, in <i>Erbkam&rsquo;s Zeitschrift</i> for 1875,
 gave the following convenient formula. Let v be the mean and V
 the surface velocity in any given vertical longitudinal section, the
 depth of which is h</p>
@@ -16704,7 +16666,7 @@ which the rod floats. No formula of reduction is then necessary.
 The observed velocity has simply to be multiplied by the area of
 the compartment to which it belongs.</p>
 
-<p>§ 148. <i>Mean Velocity of the Stream from a Series of Mid Depth
+<p>§ 148. <i>Mean Velocity of the Stream from a Series of Mid Depth
 Velocities.</i>&mdash;In the gaugings of the Mississippi it was found that
 the mid depth velocity differed by only a very small quantity from
 the mean velocity in the vertical section, and it was uninfluenced by
@@ -16719,7 +16681,7 @@ into which the river is divided. The discharge is the sum of
 the products of the observed mean mid depth velocities and the
 areas of the compartments.</p>
 
-<p>§ 149. <i>P. P. Boileau&rsquo;s Process for Gauging Streams.</i>&mdash;Let U be the
+<p>§ 149. <i>P. P. Boileau&rsquo;s Process for Gauging Streams.</i>&mdash;Let U be the
 mean velocity at a given section of a stream, V the maximum velocity,
 or that of the principal filament, which is generally a little below the
 surface, W and w the greatest and least velocities at the surface.
@@ -16748,7 +16710,7 @@ the mean velocity of the stream. More conveniently W, w, and U
 can be measured from a horizontal surface velocity curve, obtained
 from a series of float observations.</p>
 
-<p>§ 150. <i>Direct Determination of the Mean Velocity by a Current Meter
+<p>§ 150. <i>Direct Determination of the Mean Velocity by a Current Meter
 or Darcy Gauge.</i>&mdash;The only method of determining the mean velocity
 at a cross section of a stream which involves no assumption of the
 ratio of the mean velocity to other quantities is this&mdash;a plank
@@ -16774,7 +16736,7 @@ on shore.</p>
 <tr><td class="figright1"><img style="width:327px; height:129px" src="images/img85a.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 150.</span></td></tr></table>
 
-<p>§ 151. <i>A. R. Harlacher&rsquo;s Graphic Method of determining the Discharge
+<p>§ 151. <i>A. R. Harlacher&rsquo;s Graphic Method of determining the Discharge
 from a Series of Current Meter Observations.</i>&mdash;Let ABC (fig.
 149) be the cross section of a river at which a complete series of
 current meter observations have been taken. Let I., II., III., ... be
@@ -16859,7 +16821,7 @@ with the mean velocity of the stream.</p>
 
 <p class="pt2 center sc">Hydraulic Machines</p>
 
-<p>§ 152. Hydraulic machines may be broadly divided into two
+<p>§ 152. Hydraulic machines may be broadly divided into two
 classes: (1) <i>Motors</i>, in which water descending from a higher
 to a lower level, or from a higher to a lower pressure, gives up
 energy which is available for mechanical operations; (2) <i>Pumps</i>,
@@ -16912,7 +16874,7 @@ transmitted electrically are not included.</p>
 <p class="pt2 center">XII. IMPACT AND REACTION OF WATER</p>
 
 <div class="condensed">
-<p>§ 153. When a stream of fluid in steady motion impinges on a
+<p>§ 153. When a stream of fluid in steady motion impinges on a
 solid surface, it presses on the surface with a force equal and opposite
 to that by which the velocity and direction of motion of the fluid
 are changed. Generally, in problems on the impact of fluids, it is
@@ -16980,7 +16942,7 @@ for moving the solid surface is</p>
 
 <p class="center">&eta; = Tu / (GQv<span class="su">1</span><span class="sp">2</span> / 2g).</p>
 
-<p>§ 154. <i>Jet deviated entirely in one Direction.&mdash;Geometrical Solution</i>
+<p>§ 154. <i>Jet deviated entirely in one Direction.&mdash;Geometrical Solution</i>
 (fig. 153).&mdash;Suppose a jet of water impinges on a surface ac with a
 velocity ab, and let it be wholly deviated in planes parallel to the
 figure. Also let ae be the velocity and direction of motion of the
@@ -17012,7 +16974,7 @@ and parallel to the initial and final directions of relative motion.</p>
 <tr><td class="figright1"><img style="width:182px; height:313px" src="images/img86c.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 154.</span></td></tr></table>
 
-<p>§ 155. (1) <i>A Jet impinges on a plane surface at rest, in a direction
+<p>§ 155. (1) <i>A Jet impinges on a plane surface at rest, in a direction
 normal to the plane</i> (fig. 154).&mdash;Let a jet whose section is &omega; impinge
 with a velocity v on a plane surface at rest,
 in a direction normal to the plane. The
@@ -17026,20 +16988,20 @@ the change of momentum per second, is
 P = (G/g) &omega;v<span class="sp">2</span>.</p>
 
 <p>(2) <i>If the plane is moving in the direction
-of the jet with the velocity</i> ±u, the quantity
-impinging per second is &omega;(v ± u). The
+of the jet with the velocity</i> ±u, the quantity
+impinging per second is &omega;(v ± u). The
 momentum of this quantity before impact
-is (G/g)&omega;(v ± u)v. After impact, the water
-still possesses the velocity ±u in the
+is (G/g)&omega;(v ± u)v. After impact, the water
+still possesses the velocity ±u in the
 direction of the jet; and the momentum,
 in that direction, of so much water as
 impinges in one second, after impact, is
-±(G/g) &omega; (v ± u)u. The pressure on the
+±(G/g) &omega; (v ± u)u. The pressure on the
 plane, which is the change of momentum
-per second, is the difference of these quantities or P = (G/g) &omega; (v ± u)<span class="sp">2</span>.
+per second, is the difference of these quantities or P = (G/g) &omega; (v ± u)<span class="sp">2</span>.
 This differs from the expression obtained in the previous case,
-in that the relative velocity of the water and plane v ± u is substituted
-for v. The expression may be written P = 2 × G × &omega; (v ± u)<span class="sp">2</span>/2g,
+in that the relative velocity of the water and plane v ± u is substituted
+for v. The expression may be written P = 2 × G × &omega; (v ± u)<span class="sp">2</span>/2g,
 where the last two terms are the volume of a prism of water whose
 section is the area of the jet and whose length is the head due
 to the relative velocity. The pressure on the plane is twice the
@@ -17066,14 +17028,14 @@ and equating the differential coefficient to zero:&mdash;</p>
 are introduced at short intervals at the same point, the quantity of
 water impinging on the series will be &omega;v instead of &omega;(v &minus; u), and the
 whole pressure = (G/g) &omega;v (v &minus; u). The work done is (G/g)&omega;vu (v &minus; u).
-The efficiency &eta; = (G/g) &omega;vu (v &minus; u) ÷ (G/2g) &omega;v<span class="sp">3</span> = 2u(v-u)/v<span class="sp">2</span>. This becomes
+The efficiency &eta; = (G/g) &omega;vu (v &minus; u) ÷ (G/2g) &omega;v<span class="sp">3</span> = 2u(v-u)/v<span class="sp">2</span>. This becomes
 a maximum for d&eta;/du = 2(v &minus; 2u) = 0, or u = <span class="spp">1</span>&frasl;<span class="suu">2</span>v, and the &eta; = <span class="spp">1</span>&frasl;<span class="suu">2</span>.
 This result is often used as an approximate expression for the velocity
 of greatest efficiency when a jet of water strikes the floats of a water
 wheel. The work wasted in this case is half the whole energy of the
 jet when the floats run at the best speed.</p>
 
-<p>§ 156. (4) <i>Case of a Jet impinging on a Concave Cup Vane</i>, velocity
+<p>§ 156. (4) <i>Case of a Jet impinging on a Concave Cup Vane</i>, velocity
 of water v, velocity of vane in the same direction u (fig. 155), weight
 impinging per second = Gw (v &minus; u).</p>
 
@@ -17111,7 +17073,7 @@ cups.</p>
 <tr><td class="figcenter"><img style="width:402px; height:174px" src="images/img87b.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 156.</span></td></tr></table>
 
-<p>§ 157. (5) <i>Case of a Flat Vane oblique to the Jet</i> (fig. 156).&mdash;This case
+<p>§ 157. (5) <i>Case of a Flat Vane oblique to the Jet</i> (fig. 156).&mdash;This case
 presents some difficulty. The water spreading on the plane in all
 directions from the point of impact, different particles leave the plane
 with different absolute velocities. Let AB = v = velocity of water,
@@ -17124,7 +17086,7 @@ the plane. On the assumption that friction is insensible, DE is
 unaffected by impact, but AE is destroyed. Hence AE represents
 the entire change of velocity due to impact and the direction of
 that change. The pressure on the plane is in the direction AE, and
-its amount is = mass of water impinging per second × AE.</p>
+its amount is = mass of water impinging per second × AE.</p>
 
 <p>Let DAE = &theta;, and let AD = v<span class="su">r</span>. Then AE = v<span class="su">r</span> cos &theta;; DE = v<span class="su">r</span> sin &theta;.
 If Q is the volume of water impinging on the plane per second,
@@ -17211,7 +17173,7 @@ work done on the plane and the efficiency of the jet are zero.</p>
 <p>When u = <span class="spp">1</span>&frasl;<span class="suu">3</span>v then Pu max. = <span class="spp">4</span>&frasl;<span class="suu">27</span>(G/g)&omega;v<span class="sp">3</span> cos<span class="sp">2</span>&alpha;, and the efficiency
 = &eta; = <span class="spp">4</span>&frasl;<span class="suu">9</span>cos<span class="sp">2</span>&alpha;.</p>
 
-<p>(<i>c</i>) The plane moves perpendicularly to the jet. Then &delta; = 90° &minus; &alpha;;
+<p>(<i>c</i>) The plane moves perpendicularly to the jet. Then &delta; = 90° &minus; &alpha;;
 cos &delta; = sin &alpha;; and Pu = G/g &omega;u (sin &alpha; / cos &alpha;) (v cos &alpha; &minus; u sin &alpha;)<span class="sp">2</span>. This is a maximum
 when u = <span class="spp">1</span>&frasl;<span class="suu">3</span>v cos &alpha;.</p>
 
@@ -17222,7 +17184,7 @@ same as in the last case.</p>
 <tr><td class="figcenter"><img style="width:439px; height:244px" src="images/img87e.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 159.</span></td></tr></table>
 
-<p>§ 158. <i>Best Form of Vane to receive Water.</i>&mdash;When water impinges
+<p>§ 158. <i>Best Form of Vane to receive Water.</i>&mdash;When water impinges
 normally or obliquely on a plane, it is scattered in all directions
 after impact, and the work carried away by the water is then generally
 lost, from the impossibility of dealing afterwards with streams of
@@ -17247,7 +17209,7 @@ direction AB. This is sometimes expressed by saying that the vane
 <tr><td class="figcenter"><img style="width:478px; height:124px" src="images/img88a.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 160.</span></td></tr></table>
 
-<p>§ 159. <i>Floats of Poncelet Water Wheels.</i>&mdash;Let AC (fig. 160) represent
+<p>§ 159. <i>Floats of Poncelet Water Wheels.</i>&mdash;Let AC (fig. 160) represent
 the direction of a thin horizontal stream of water having the
 velocity v. Let AB be a curved float moving horizontally with
 velocity u. The relative motion of water and float is then initially
@@ -17273,11 +17235,11 @@ without velocity. This is the principle of the Poncelet wheel, but
 in that case the floats move over an arc of a large circle; the stream
 of water has considerable thickness (about 8 in.); in order to get
 the water into and out of the wheel, it is then necessary that the lip
-of the float should make a small angle (about 15°) with the direction
+of the float should make a small angle (about 15°) with the direction
 of its motion. The water quits the wheel with a little of its energy of
 motion remaining.</p>
 
-<p>§ 160. <i>Pressure on a Curved Surface when the Water is deviated
+<p>§ 160. <i>Pressure on a Curved Surface when the Water is deviated
 wholly in one Direction.</i>&mdash;When a jet of water impinges on a curved
 surface in such a direction that it is received without shock, the
 pressure on the surface is due to its gradual deviation from its first
@@ -17319,8 +17281,8 @@ of the figure. The resultant pressure on surface</p>
 
 <table class="math0" summary="math">
 <tr><td rowspan="2">= R = 2rb sin</td> <td>&phi;</td>
-<td rowspan="2">×</td> <td>Gt</td>
-<td rowspan="2">·</td> <td>v<span class="sp">2</span></td>
+<td rowspan="2">×</td> <td>Gt</td>
+<td rowspan="2">·</td> <td>v<span class="sp">2</span></td>
 <td rowspan="2">= 2</td> <td>G</td>
 <td rowspan="2">btv<span class="sp">2</span> sin</td> <td>&phi;</td>
 <td rowspan="2">,</td></tr>
@@ -17360,10 +17322,10 @@ which is a maximum when u = <span class="spp">1</span>&frasl;<span class="suu">3
 obtained by considering that the work done on the plane must be
 equal to the energy lost by the water, when friction is neglected.</p>
 
-<p>If &phi; = 180°, cos &phi; = &minus;1, 1 &minus; cos &phi; = 2; then P = 2(G/g) bt (v &minus; u)<span class="sp">2</span>,
+<p>If &phi; = 180°, cos &phi; = &minus;1, 1 &minus; cos &phi; = 2; then P = 2(G/g) bt (v &minus; u)<span class="sp">2</span>,
 the same result as for a concave cup.</p>
 
-<p>§ 161. <i>Position which a Movable Plane takes in Flowing Water.</i>&mdash;When
+<p>§ 161. <i>Position which a Movable Plane takes in Flowing Water.</i>&mdash;When
 a rectangular plane, movable about an axis parallel to one of
 its sides, is placed in an indefinite
 current of fluid, it
@@ -17386,26 +17348,26 @@ table:&mdash;</p>
 <table class="ws" summary="Contents">
 <tr><td class="tcc allb">&nbsp;</td> <td class="tcc allb">Larger plane.</td> <td class="tcc allb">Smaller Plane.</td></tr>
 
-<tr><td class="tcr lb rb">a/b = 1.0</td> <td class="tcr rb">&phi; = ...</td> <td class="tcr rb">&phi; = 90°</td></tr>
-<tr><td class="tcr lb rb">0.9</td> <td class="tcr rb">75°</td> <td class="tcr rb">72<span class="spp">1</span>&frasl;<span class="suu">2</span>°</td></tr>
-<tr><td class="tcr lb rb">0.8</td> <td class="tcr rb">60°</td> <td class="tcr rb">57°</td></tr>
-<tr><td class="tcr lb rb">0.7</td> <td class="tcr rb">48°</td> <td class="tcr rb">43°</td></tr>
-<tr><td class="tcr lb rb">0.6</td> <td class="tcr rb">25°</td> <td class="tcr rb">29°</td></tr>
-<tr><td class="tcr lb rb">0.5</td> <td class="tcr rb">13°</td> <td class="tcr rb">13°</td></tr>
-<tr><td class="tcr lb rb">0.4</td> <td class="tcr rb">8°</td> <td class="tcr rb">6<span class="spp">1</span>&frasl;<span class="suu">2</span>°</td></tr>
-<tr><td class="tcr lb rb">0.3</td> <td class="tcr rb">6°</td> <td class="tcc rb">..</td></tr>
-<tr><td class="tcr lb rb bb">0.2</td> <td class="tcr rb bb">4°</td> <td class="tcc rb bb">..</td></tr>
+<tr><td class="tcr lb rb">a/b = 1.0</td> <td class="tcr rb">&phi; = ...</td> <td class="tcr rb">&phi; = 90°</td></tr>
+<tr><td class="tcr lb rb">0.9</td> <td class="tcr rb">75°</td> <td class="tcr rb">72<span class="spp">1</span>&frasl;<span class="suu">2</span>°</td></tr>
+<tr><td class="tcr lb rb">0.8</td> <td class="tcr rb">60°</td> <td class="tcr rb">57°</td></tr>
+<tr><td class="tcr lb rb">0.7</td> <td class="tcr rb">48°</td> <td class="tcr rb">43°</td></tr>
+<tr><td class="tcr lb rb">0.6</td> <td class="tcr rb">25°</td> <td class="tcr rb">29°</td></tr>
+<tr><td class="tcr lb rb">0.5</td> <td class="tcr rb">13°</td> <td class="tcr rb">13°</td></tr>
+<tr><td class="tcr lb rb">0.4</td> <td class="tcr rb">8°</td> <td class="tcr rb">6<span class="spp">1</span>&frasl;<span class="suu">2</span>°</td></tr>
+<tr><td class="tcr lb rb">0.3</td> <td class="tcr rb">6°</td> <td class="tcc rb">..</td></tr>
+<tr><td class="tcr lb rb bb">0.2</td> <td class="tcr rb bb">4°</td> <td class="tcc rb bb">..</td></tr>
 </table>
 
-<p>§ 162. <i>Direct Action distinguished from Reaction</i> (Rankine, <i>Steam
-Engine</i>, § 147).</p>
+<p>§ 162. <i>Direct Action distinguished from Reaction</i> (Rankine, <i>Steam
+Engine</i>, § 147).</p>
 
 <p>The pressure which a jet exerts on a vane can be distinguished
 into two parts, viz&there4;&mdash;</p>
 
 <p>(1) The pressure arising from changing the direct component of
 the velocity of the water into the velocity of the vane. In fig.
-153, § 154, ab cos bae is the direct component of the water&rsquo;s velocity,
+153, § 154, ab cos bae is the direct component of the water&rsquo;s velocity,
 or component in the direction of motion of vane. This is changed
 into the velocity ae of the vane. The pressure due to direct impulse
 is then</p>
@@ -17418,7 +17380,7 @@ producing pressure on the vane.</p>
 <p>(2) The term reaction is applied to the additional action due to
 the direction and velocity with which the water glances off the
 vane. It is this which is diminished by the friction between the
-water and the vane. In Case 2, § 160, the direct pressure is</p>
+water and the vane. In Case 2, § 160, the direct pressure is</p>
 
 <p class="center">P<span class="su">1</span> = Gbt (v &minus; u)<span class="sp">2</span> / g.</p>
 
@@ -17426,17 +17388,17 @@ water and the vane. In Case 2, § 160, the direct pressure is</p>
 
 <p class="center">P<span class="su">2</span> = &minus;Gbt (v &minus; u)<span class="sp">2</span> cos &phi; / g.</p>
 
-<p>If &phi; &lt; 90°, the direct component of the water&rsquo;s motion is not
+<p>If &phi; &lt; 90°, the direct component of the water&rsquo;s motion is not
 wholly converted into the velocity of the vane, and the whole
 <span class="pagenum"><a name="page89" id="page89"></a>89</span>
-pressure due to direct impulse is not obtained. If &phi; &gt; 90°, cos &phi; is
+pressure due to direct impulse is not obtained. If &phi; &gt; 90°, cos &phi; is
 negative and an additional pressure due to reaction is obtained.</p>
 
 <table class="flt" style="float: right; width: 250px;" summary="Illustration">
 <tr><td class="figright1"><img style="width:203px; height:139px" src="images/img89a.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 164.</span></td></tr></table>
 
-<p>§ 163. <i>Jet Propeller.</i>&mdash;In the case of vessels propelled by a jet of
+<p>§ 163. <i>Jet Propeller.</i>&mdash;In the case of vessels propelled by a jet of
 water (fig. 164), driven sternwards from orifices at the side of the
 vessel, the water, originally at rest outside
 the vessel, is drawn into the ship
@@ -17485,7 +17447,7 @@ about <span class="spp">2</span>&frasl;<span class="suu">3</span>.</p>
 <tr><td class="figcenter"><img style="width:474px; height:204px" src="images/img89b.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 165.</span></td></tr></table>
 
-<p>§ 164. <i>Pressure of a Steady Stream in a Uniform Pipe on a Plane
+<p>§ 164. <i>Pressure of a Steady Stream in a Uniform Pipe on a Plane
 normal to the Direction of Motion.</i>&mdash;Let CD (fig. 165) be a plane
 placed normally to the stream which, for simplicity, may be supposed
 to flow horizontally. The fluid filaments are deviated in
@@ -17652,7 +17614,7 @@ Hence there is less pressure on the cylinder than on the thin plane.</p>
 <tr><td class="figright1"><img style="width:234px; height:211px" src="images/img89c.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 166.</span></td></tr></table>
 
-<p>§ 165. <i>Distribution of Pressure on a Surface on which a Jet impinges
+<p>§ 165. <i>Distribution of Pressure on a Surface on which a Jet impinges
 normally.</i>&mdash;The principle of momentum gives readily enough the
 total or resultant pressure of a jet impinging on a plane surface, but
 in some cases it is useful to know the distribution of the pressure.
@@ -17851,7 +17813,7 @@ curve is</p>
 
 <p class="center">y = h&epsilon;<span class="sp">&minus;1/2</span> &radic;<span class="ov">(h / h</span><span class="su">1</span>) (x<span class="sp">2</span> / r<span class="sp">2</span>).</p>
 
-<p>§ 166. <i>Resistance of a Plane moving through a Fluid, or Pressure
+<p>§ 166. <i>Resistance of a Plane moving through a Fluid, or Pressure
 of a Current on a Plane.</i>&mdash;When a thin plate moves through the
 air, or through an indefinitely large mass of still water, in a direction
 normal to its surface, there is an excess of pressure on the anterior
@@ -17932,7 +17894,7 @@ being f = 1.834, a result agreeing well with Dubuat.</p>
 <tr><td class="figright1"><img style="width:216px; height:315px" src="images/img91a.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 169.</span></td></tr></table>
 
-<p>§ 167. <i>Stanton&rsquo;s Experiments on the Pressure of Air on Surfaces.</i>&mdash;At
+<p>§ 167. <i>Stanton&rsquo;s Experiments on the Pressure of Air on Surfaces.</i>&mdash;At
 the National Physical Laboratory, London, T. E. Stanton carried
 out a series of experiments on the distribution of pressure on surfaces
 in a current of air passing through an air trunk. These were on a
@@ -17968,7 +17930,7 @@ greater than on a circular plate. In later tests on larger planes in
 free air, Stanton found resistances 18% greater than those observed
 with small planes in the air trunk.</p>
 
-<p>§ 168. <i>Case when the Direction of Motion is oblique to the Plane.</i>&mdash;The
+<p>§ 168. <i>Case when the Direction of Motion is oblique to the Plane.</i>&mdash;The
 determination of the pressure between a fluid and surface in this
 case is of importance in many practical questions, for instance, in
 assigning the load due to wind pressure on sloping and curved roofs,
@@ -18034,7 +17996,7 @@ Duchemin&rsquo;s rule. These last values are obtained by taking P = 3.31,
 the observed pressure on a normal surface:&mdash;</p>
 
 <table class="ws" summary="Contents">
-<tr><td class="tcc allb">Angle between Plane and Direction of Blast</td> <td class="tcc allb">15°</td> <td class="tcc allb">20°</td> <td class="tcc allb">60°</td> <td class="tcc allb">90°</td></tr>
+<tr><td class="tcc allb">Angle between Plane and Direction of Blast</td> <td class="tcc allb">15°</td> <td class="tcc allb">20°</td> <td class="tcc allb">60°</td> <td class="tcc allb">90°</td></tr>
 
 <tr><td class="tcl lb rb">Horizontal pressure R</td> <td class="tcl rb">0.4</td> <td class="tcl rb">0.61</td> <td class="tcl rb">2.73</td> <td class="tcc rb">3.31</td></tr>
 <tr><td class="tcl lb rb">Lateral pressure L</td> <td class="tcl rb">1.6</td> <td class="tcl rb">1.96</td> <td class="tcl rb">1.26</td> <td class="tcc rb">..</td></tr>
@@ -18079,7 +18041,7 @@ automatic governing machinery.</p>
 
 <p><span class="pagenum"><a name="page92" id="page92"></a>92</span></p>
 
-<p>§ 169. <i>Water Motors with Artificial Sources of Energy.</i>&mdash;The
+<p>§ 169. <i>Water Motors with Artificial Sources of Energy.</i>&mdash;The
 great convenience and simplicity of water motors has led to their
 adoption in certain cases, where no natural source of water
 power is available. In these cases, an artificial source of water
@@ -18093,7 +18055,7 @@ steam engine stores up energy by pumping the water, while the
 work done by the hydraulic engines is done intermittently.</p>
 
 <div class="condensed">
-<p>§ 170. <i>Energy of a Water-fall.</i>&mdash;Let H<span class="su">t</span> be the total fall of level from
+<p>§ 170. <i>Energy of a Water-fall.</i>&mdash;Let H<span class="su">t</span> be the total fall of level from
 the point where the water is taken from a natural stream to the
 point where it is discharged into it again. Of this total fall a portion,
 which can be estimated independently, is expended in overcoming
@@ -18132,7 +18094,7 @@ of the machine, the work done will be</p>
 H ft.</p>
 </div>
 
-<p>§ 171. <i>Site for Water Motor.</i>&mdash;Wherever a stream flows from
+<p>§ 171. <i>Site for Water Motor.</i>&mdash;Wherever a stream flows from
 a higher to a lower level it is possible to erect a water motor.
 The amount of power obtainable depends on the available head
 and the supply of water. In choosing a site the engineer will
@@ -18156,7 +18118,7 @@ streams depending directly on rainfall, and are therefore advantageous
 for water-power purposes.</p>
 
 <div class="condensed">
-<p>§ 172. <i>Water Power at Holyoke, U.S.A.</i>&mdash;About 85 m. from the
+<p>§ 172. <i>Water Power at Holyoke, U.S.A.</i>&mdash;About 85 m. from the
 mouth of the Connecticut river there was a fall of about 60 ft. in
 a short distance, forming what were called the Grand Rapids, below
 which the river turned sharply, forming a kind of peninsula on which
@@ -18178,7 +18140,7 @@ effective. The charge for the power water is at the rate of 20s. per
 h.p. per annum.</p>
 </div>
 
-<p>§ 173. <i>Action of Water in a Water Motor.</i>&mdash;Water motors may
+<p>§ 173. <i>Action of Water in a Water Motor.</i>&mdash;Water motors may
 be divided into water-pressure engines, water-wheels and
 turbines.</p>
 
@@ -18223,7 +18185,7 @@ conditions of working.</p>
 
 <p class="pt1 center"><i>Water-pressure Engines.</i></p>
 
-<p>§ 174. In these the water acts by pressure either due to the
+<p>§ 174. In these the water acts by pressure either due to the
 height of the column in a supply pipe descending from a high-level
 reservoir, or created by pumping. Pressure engines were
 first used in mine-pumping on waterfalls of greater height than
@@ -18304,7 +18266,7 @@ success. Where pressure engines are used simplicity is generally
 a first consideration, and economy is of less importance.</p>
 
 <div class="condensed">
-<p>§ 175. <i>Efficiency of Pressure Engines.</i>&mdash;It is hardly possible to form
+<p>§ 175. <i>Efficiency of Pressure Engines.</i>&mdash;It is hardly possible to form
 a theoretical expression for the efficiency of pressure engines, but
 some general considerations are useful. Consider the case of a long
 stroke hydraulic ram, which has a fairly constant velocity v during
@@ -18356,7 +18318,7 @@ engines probably not more than
 50% and that only when fully loaded.</p>
 </div>
 
-<p>§ 176. <i>Direct-Acting Hydraulic
+<p>§ 176. <i>Direct-Acting Hydraulic
 Lift</i> (fig. 171).&mdash;This is the
 simplest of all kinds of hydraulic
 motor. A cage W is lifted directly
@@ -18471,7 +18433,7 @@ constant)</p>
 <tr><td class="figleft1"><img style="width:133px; height:443px" src="images/img94a.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 172.</span></td></tr></table>
 
-<p>§ 177. <i>Armstrong&rsquo;s Hydraulic Jigger.</i>&mdash;This is simply a single-acting
+<p>§ 177. <i>Armstrong&rsquo;s Hydraulic Jigger.</i>&mdash;This is simply a single-acting
 hydraulic cylinder and ram, provided with sheaves so
 as to give motion to a wire rope or chain. It is used in various
 forms of lift and crane. Fig. 172 shows the arrangement. A
@@ -18489,7 +18451,7 @@ free end of the rope has a movement equal
 to six times the stroke of the ram, the force
 exerted being in the inverse proportion.</p>
 
-<p>§ 178. <i>Rotative Hydraulic Engines.</i>&mdash;Valve-gear
+<p>§ 178. <i>Rotative Hydraulic Engines.</i>&mdash;Valve-gear
 mechanism similar in principle to that
 of steam engines can be applied to actuate
 the admission and discharge valves, and the
@@ -18535,7 +18497,7 @@ effort on the crank pin is very uniform.</p>
 <tr><td class="caption"><span class="sc">Fig. 175.</span></td></tr></table>
 
 <div class="condensed">
-<p><i>Brotherhood Hydraulic Engine.</i>&mdash;Three cylinders at angles of 120°
+<p><i>Brotherhood Hydraulic Engine.</i>&mdash;Three cylinders at angles of 120°
 with each other are formed in one casting with the frame. The
 plungers are hollow trunks, and the connecting rods abut in
 cylindrical recesses in them and are connected to a common crank
@@ -18647,7 +18609,7 @@ was 22 ft. and the water pressure in the cylinders 80 &#8468; per sq. in.</p>
 </table>
 </div>
 
-<p>§ 179. <i>Accumulator Machinery.</i>&mdash;It has already been pointed
+<p>§ 179. <i>Accumulator Machinery.</i>&mdash;It has already been pointed
 out that it is in some cases convenient to use a steam engine
 to create an artificial head of water, which is afterwards employed
 in driving water-pressure machinery. Where power is required
@@ -18795,7 +18757,7 @@ upper cylinder.</p>
 
 <p class="pt1 center"><i>Water Wheels.</i></p>
 
-<p>§ 180. <i>Overshot and High Breast Wheels.</i>&mdash;When
+<p>§ 180. <i>Overshot and High Breast Wheels.</i>&mdash;When
 a water fall ranges between 10
 and 70 ft. and the water supply is from 3
 to 25 cub. ft. per second, it is possible to
@@ -18887,7 +18849,7 @@ long as possible, and the width of opening of the buckets should be
 buckets on periphery of wheel. Make ed = <span class="spp">1</span>&frasl;<span class="suu">2</span> eb and bc = <span class="spp">6</span>&frasl;<span class="suu">5</span> to <span class="spp">5</span>&frasl;<span class="suu">4</span> ab.
 Join cd. For an iron bucket (fig. 180, B), take ed = <span class="spp">1</span>&frasl;<span class="suu">3</span>eb; bc = <span class="spp">6</span>&frasl;<span class="suu">5</span>ab.
 Draw cO making an
-angle of 10° to 15° with
+angle of 10° to 15° with
 the radius at c. On Oc
 take a centre giving a
 circular arc passing
@@ -18926,7 +18888,7 @@ are still working.</p>
 <tr><td class="figcenter"><img style="width:473px; height:249px" src="images/img96c.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 181.</span></td></tr></table>
 
-<p>§ 181. <i>Poncelet Water Wheel.</i>&mdash;When the fall does not exceed
+<p>§ 181. <i>Poncelet Water Wheel.</i>&mdash;When the fall does not exceed
 6 ft., the best water motor to adopt in many cases is the Poncelet
 undershot water wheel. In this the water acts very nearly in the
 same way as in a turbine, and the Poncelet wheel, although
@@ -18934,7 +18896,7 @@ slightly less efficient than the best turbines, in normal conditions
 of working, is superior to most of them when working with
 a reduced supply of water. A general notion of the action
 of the water on a Poncelet wheel has already been given in
-§ 159. Fig. 181 shows its construction. The water penned back
+§ 159. Fig. 181 shows its construction. The water penned back
 between the side walls of the wheel pit is allowed to flow to the
 wheel under a movable sluice, at a velocity nearly equal to the
 velocity due to the whole fall. The water is guided down a slope
@@ -18986,11 +18948,11 @@ the wheel is made about 4 in. greater than b.</p>
 wheels. One of the simplest is that shown in figs. 181, 182.</p>
 
 <p>Let OA (fig. 181) be the vertical radius of the wheel. Set off OB,
-OD making angles of 15° with OA. Then BD may be the length of
+OD making angles of 15° with OA. Then BD may be the length of
 the close breasting fitted to the wheel. Draw the bottom of the
 head face BC at a slope of 1 in 10. Parallel to this, at distances <span class="spp">1</span>&frasl;<span class="suu">2</span>e
 and e, draw EF and GH. Then EF is the mean layer and GH the
-surface layer entering the wheel. Join OF, and make OFK = 23°.
+surface layer entering the wheel. Join OF, and make OFK = 23°.
 Take FK = 0.5 to 0.7 H. Then K is the centre from which the
 bucket curve is struck and KF is the radius. The depth of the
 shrouds must be sufficient to prevent the water from rising over the
@@ -19013,13 +18975,13 @@ and V the velocity of the wheel.</p>
 
 <p class="pt1 center"><i>Turbines.</i></p>
 
-<p>§ 182. The name turbine was originally given in France to
+<p>§ 182. The name turbine was originally given in France to
 any water motor which revolved in a horizontal plane, the axis
 being vertical. The rapid development of this class of motors
-dates from 1827, when a prize was offered by the Société
+dates from 1827, when a prize was offered by the Société
 d&rsquo;Encouragement for a motor of this kind, which should be
 an improvement on certain wheels then in use. The prize
-was ultimately awarded to Benoît Fourneyron (1802-1867),
+was ultimately awarded to Benoît Fourneyron (1802-1867),
 whose turbine, but little modified, is still constructed.</p>
 
 <p><i>Classification of Turbines.</i>&mdash;In some turbines the whole
@@ -19105,7 +19067,7 @@ the same as if the turbine were placed at the bottom of the fall.</p>
 <tr><td class="figright1"><img style="width:211px; height:256px" src="images/img97b.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 183.</span></td></tr></table>
 
-<p>§ 183. <i>The Simple Reaction Wheel.</i>&mdash;It has been shown, in § 162,
+<p>§ 183. <i>The Simple Reaction Wheel.</i>&mdash;It has been shown, in § 162,
 that, when water issues from a vessel, there is a reaction on the
 vessel tending to cause motion in a
 direction opposite to that of the jet.
@@ -19191,13 +19153,13 @@ discharged. The actual efficiency realized appears to be about 60%,
 so that about 21% of the energy of the fall is lost in friction, in
 addition to the energy carried away by the water.</p>
 
-<p class="center">§ 184. <i>General Statement of Hydrodynamical Principles necessary for
+<p class="center">§ 184. <i>General Statement of Hydrodynamical Principles necessary for
 the Theory of Turbines.</i></p>
 
 <p>(<i>a</i>) When water flows through any pipe-shaped passage, such as
 the passage between the vanes of a turbine wheel, the relation between
 the changes of pressure and velocity is given by Bernoulli&rsquo;s
-theorem (§ 29). Suppose that, at a section A of such a passage, h<span class="su">1</span>
+theorem (§ 29). Suppose that, at a section A of such a passage, h<span class="su">1</span>
 is the pressure measured in feet of water, v<span class="su">1</span> the velocity, and z<span class="su">1</span> the
 elevation above any horizontal datum plane, and that at a section
 B the same quantities are denoted by h<span class="su">2</span>, v<span class="su">2</span>, z<span class="su">2</span>. Then</p>
@@ -19212,7 +19174,7 @@ B the same quantities are denoted by h<span class="su">2</span>, v<span class="s
 <p>(<i>b</i>) When there is an abrupt change of section of the passage, or
 an abrupt change of section of the stream due to a contraction, then,
 in applying Bernoulli&rsquo;s equation allowance must be made for the
-loss of head in shock (§ 36). Let v<span class="su">1</span>, v<span class="su">2</span> be the velocities before and
+loss of head in shock (§ 36). Let v<span class="su">1</span>, v<span class="su">2</span> be the velocities before and
 after the abrupt change, then a stream of velocity v<span class="su">1</span> impinges on a
 stream at a velocity v<span class="su">2</span>, and the relative velocity is v<span class="su">1</span> &minus; v<span class="su">2</span>. The
 head lost is (v<span class="su">1</span> &minus; v<span class="su">2</span>)<span class="sp">2</span>/2g. Then equation (1a) becomes</p>
@@ -19291,7 +19253,7 @@ water on the wheel is</p>
 <p class="center">T = Ma = (GQ/g) (w<span class="su">1</span>r<span class="su">1</span> &minus; w<span class="su">2</span>r<span class="su">2</span>) &alpha; foot-pounds per second.</p>
 <div class="author">(5)</div>
 
-<p>§ 185. <i>Total and Available Fall.</i>&mdash;Let H<span class="su">t</span> be the total difference of
+<p>§ 185. <i>Total and Available Fall.</i>&mdash;Let H<span class="su">t</span> be the total difference of
 level from the head-water to the tail-water surface. Of this total
 head a portion is expended in overcoming the resistances of the head
 race, tail race, supply pipe, or other channel conveying the water.
@@ -19309,7 +19271,7 @@ belonging to the turbine itself. In that case the velocities of the
 water in the turbine should be calculated for a head H &minus; &#615;, but the
 efficiency of the turbine for the head H.</p>
 
-<p>§ 186. <i>Gross Efficiency and Hydraulic Efficiency of a Turbine.</i>&mdash;Let
+<p>§ 186. <i>Gross Efficiency and Hydraulic Efficiency of a Turbine.</i>&mdash;Let
 T<span class="su">d</span> be the useful work done by the turbine, in foot-pounds per
 second, T<span class="su">t</span> the work expended in friction of the turbine shaft,
 gearing, &amp;c., a quantity which varies with the local conditions in
@@ -19373,7 +19335,7 @@ the theory of turbines. It was first given by Reiche (<i>Turbinenbaues</i>,
 <tr><td class="figright1"><img style="width:336px; height:521px" src="images/img100a.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 189.</span></td></tr></table>
 
-<p>§ 187. <i>General Description of a Reaction Turbine.</i>&mdash;Professor
+<p>§ 187. <i>General Description of a Reaction Turbine.</i>&mdash;Professor
 James Thomson&rsquo;s inward flow or vortex turbine has been
 selected as the type of reaction turbines. It is one of the best
 in normal conditions of working, and the mode of regulation
@@ -19389,7 +19351,7 @@ on entering the case distributes itself through a rectangular
 supply chamber SC, from which it finds its way equally to the
 four guide-blade passages G, G, G, G. In these passages it
 acquires a velocity about equal to that due to half the fall, and is
-directed into the wheel at an angle of about 10° or 12° with the
+directed into the wheel at an angle of about 10° or 12° with the
 tangent to its circumference. The wheel W receives the water
 in equal proportions from each guide-blade passage. It consists
 of a centre plate p (fig. 189) keyed on the shaft aa, which passes
@@ -19459,7 +19421,7 @@ are the worm and wheel for working the guide-blade gear.</p>
 <tr><td class="figcenter"><img style="width:514px; height:405px" src="images/img100c.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 191.</span></td></tr></table>
 
-<p>§ 188. <i>Hydraulic Power at Niagara.</i>&mdash;The largest development of
+<p>§ 188. <i>Hydraulic Power at Niagara.</i>&mdash;The largest development of
 hydraulic power is that at Niagara. The Niagara Falls Power
 Company have constructed two power houses on the United States
 side, the first with 10 turbines of 5000 h.p. each, and the second
@@ -19492,7 +19454,7 @@ Stations,&rdquo; <i>Proc. Inst. Mech. Eng.</i>, 1906).</p>
 <tr><td class="figcenter"><img style="width:987px; height:241px" src="images/img100d.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 192.</span></td></tr></table>
 
-<p>§ 189. <i>Different Forms of Turbine Wheel.</i>&mdash;The wheel of a turbine
+<p>§ 189. <i>Different Forms of Turbine Wheel.</i>&mdash;The wheel of a turbine
 or part of the machine on which the water acts is an annular space,
 furnished with curved vanes dividing it into passages exactly or
 roughly rectangular in cross section. For radial flow turbines the
@@ -19512,7 +19474,7 @@ concentric cylinders.</p>
 <tr><td class="figright1"><img style="width:324px; height:237px" src="images/img101a.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 193.</span></td></tr></table>
 
-<p>§ 190. <i>Velocity of Whirl and Velocity of Flow.</i>&mdash;Let acb (fig. 193)
+<p>§ 190. <i>Velocity of Whirl and Velocity of Flow.</i>&mdash;Let acb (fig. 193)
 be the path of the particles of water in a turbine wheel. That
 path will be in a
 plane normal to the
@@ -19613,7 +19575,7 @@ losses in the wheel passages are a small fraction of the total head.</p>
 <tr><td class="tcl">In inward flow turbines,</td> <td class="tcl">u<span class="su">o</span> = u<span class="su">i</span> = 0.125 &radic;<span class="ov">(2gH)</span>.</td></tr>
 </table>
 
-<p>§ 191. <i>Speed of the Wheel.</i>&mdash;The best speed of the wheel depends
+<p>§ 191. <i>Speed of the Wheel.</i>&mdash;The best speed of the wheel depends
 partly on the frictional losses, which the ordinary theory of turbines
 disregards. It is best, therefore, to assume for V<span class="su">o</span> and V<span class="su">i</span> values
 which experiment has shown to be most advantageous.</p>
@@ -19659,7 +19621,7 @@ the wheel vanes make with the inlet and outlet surfaces; then</p>
 <tr><td class="figright1"><img style="width:337px; height:279px" src="images/img101c.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 195.</span></td></tr></table>
 
-<p>§ 192. <i>Condition determining the Angle of the Vanes at the Outlet
+<p>§ 192. <i>Condition determining the Angle of the Vanes at the Outlet
 Surface of the Wheel.</i>&mdash;It has been shown that, when the water leaves
 the wheel, it should
 have no tangential
@@ -19668,7 +19630,7 @@ is to be as
 great as possible;
 that is, w<span class="su">o</span> = 0. Hence,
 from (10), cos &beta; = 0,
-&beta; = 90°, U<span class="su">o</span> = V<span class="su">o</span>, and
+&beta; = 90°, U<span class="su">o</span> = V<span class="su">o</span>, and
 the direction of the
 water&rsquo;s motion is
 normal to the outlet
@@ -19726,7 +19688,7 @@ be</p>
 <p class="center">&phi; = tan [Q / V<span class="su">o</span> (&Omega;<span class="su">o</span> &minus; &omega;) ].</p>
 <div class="author">(16)</div>
 
-<p>§ 193. <i>Head producing Velocity with which the Water enters the
+<p>§ 193. <i>Head producing Velocity with which the Water enters the
 Wheel.</i>&mdash;Consider the variation of pressure in a wheel passage,
 which satisfies the condition that the sections change so gradually
 that there is no loss of head in shock. When the flow is in a horizontal
@@ -19827,7 +19789,7 @@ wheel, the velocity of flow into the wheel is</p>
 
 <p class="center">v<span class="su">ri</span> = u<span class="su">i</span> cosec &theta;;</p>
 
-<p class="noind">or, as this is only a small term, and &theta; is on the average 90°, we
+<p class="noind">or, as this is only a small term, and &theta; is on the average 90°, we
 may take, for the present purpose, v<span class="su">ri</span> = u<span class="su">i</span> nearly.</p>
 
 <p>Inserting these values, and remembering that for an axial flow
@@ -19861,7 +19823,7 @@ turbine V<span class="su">i</span> = V<span class="su">o</span>, &#615; = 0, and
 <tr><td class="denom">2g</td> <td class="denom">V<span class="su">i</span><span class="sp">2</span></td>
 <td class="denom">2g</td></tr></table>
 
-<p>§ 194. <i>Angle which the Guide-Blades make with the Circumference
+<p>§ 194. <i>Angle which the Guide-Blades make with the Circumference
 of the Wheel.</i>&mdash;At the moment the water enters the wheel, the
 radial component of the velocity is u<span class="su">i</span>, and the velocity is v<span class="su">i</span>. Hence,
 if &gamma; is the angle between the guide-blades and a tangent to the
@@ -19876,7 +19838,7 @@ of the guide-blades.</p>
 <tr><td class="figright1"><img style="width:346px; height:230px" src="images/img102.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 196.</span></td></tr></table>
 
-<p>§ 195. <i>Condition determining the Angle of the Vanes at the Inlet
+<p>§ 195. <i>Condition determining the Angle of the Vanes at the Inlet
 Surface of the Wheel.</i>&mdash;The single condition necessary to be satisfied
 at the inlet surface of
 the wheel is that the
@@ -19900,7 +19862,7 @@ of the wheel. Completing the parallelogram, v<span class="su">ri</span> is the d
 relative motion. Hence the angle between v<span class="su">ri</span> and V<span class="su">i</span> is the angle &theta;
 which the vanes should make with the inlet surface of the wheel.</p>
 
-<p>§ 196. <i>Example of the Method of designing a Turbine. Professor
+<p>§ 196. <i>Example of the Method of designing a Turbine. Professor
 James Thomson&rsquo;s Inward Flow Turbine.</i>&mdash;</p>
 
 <table class="reg" summary="poem"><tr><td> <div class="poemr">
@@ -19952,10 +19914,10 @@ second is</p>
 
 <p class="center">Tan &phi; = u<span class="su">o</span> / V<span class="su">o</span> = 0.125 / 0.33 = .3788;</p>
 
-<p class="center">&phi; = 21º nearly.</p>
+<p class="center">&phi; = 21º nearly.</p>
 
 <p>If this value is revised for the vane thickness it will ordinarily
-become about 25º.</p>
+become about 25º.</p>
 
 <p><i>Velocity with which the Water enters the Wheel.</i>&mdash;The head producing
 the velocity is</p>
@@ -19974,7 +19936,7 @@ the velocity is</p>
 
 <p class="center">Sin &gamma; = u<span class="su">i</span> / v<span class="su">i</span> = 0.125 / 0.721 = 0.173;</p>
 
-<p class="center">&gamma; = 10° nearly.</p>
+<p class="center">&gamma; = 10° nearly.</p>
 
 <p><i>Tangential Velocity of Water entering Wheel.</i></p>
 
@@ -19984,12 +19946,12 @@ the velocity is</p>
 
 <p class="center">Cot &theta; = (w<span class="su">i</span> &minus; V<span class="su">i</span>) / u<span class="su">i</span> = (.7101 &minus; .66) / .125 = .4008;</p>
 
-<p class="center">&theta; = 68° nearly.</p>
+<p class="center">&theta; = 68° nearly.</p>
 
 <p><i>Hydraulic Efficiency of Wheel.</i></p>
 
 <table class="reg" summary="poem"><tr><td> <div class="poemr">
-<p>&eta; = w<span class="su">i</span>V<span class="su">i</span> / gH = .7101 × .66 × 2</p>
+<p>&eta; = w<span class="su">i</span>V<span class="su">i</span> / gH = .7101 × .66 × 2</p>
 <p class="i05">= 0.9373.</p>
 </div> </td></tr></table>
 
@@ -19999,7 +19961,7 @@ The efficiency from experiment has been found to be 0.75 to 0.80.</p>
 
 <p class="pt1 center"><i>Impulse and Partial Admission Turbines.</i></p>
 
-<p>§ 197. The principal defect of most turbines with complete
+<p>§ 197. The principal defect of most turbines with complete
 admission is the imperfection of the arrangements for working
 with less than the normal supply. With many forms of reaction
 turbine the efficiency is considerably reduced when the regulating
@@ -20078,7 +20040,7 @@ velocity, and may be kept down to a manageable value.</p>
 <td class="caption"><span class="sc">Fig. 199.</span></td></tr></table>
 
 <div class="condensed">
-<p>§ 198. <i>General Description of an Impulse Turbine or Turbine with
+<p>§ 198. <i>General Description of an Impulse Turbine or Turbine with
 Free Deviation.</i>&mdash;Fig. 197 shows a general sectional elevation of a
 Girard turbine, in
 which the flow is
@@ -20160,17 +20122,17 @@ its internal diameter 3 ft. 10 in. Normal speed 400 revs. per minute.
 Water is discharged into the wheel by a single nozzle, shown in fig.
 202 with its regulating apparatus and some of the vanes. The water
 enters the wheel
-at an angle of 22°
+at an angle of 22°
 with the direction
 of motion,
 and the final
 angle of the wheel
-vanes is 20°. The
+vanes is 20°. The
 efficiency on trial
 was from 75 to
 78%.</p>
 
-<p>§ 199. <i>Theory
+<p>§ 199. <i>Theory
 of the Impulse
 Turbine.</i>&mdash;The
 theory of the impulse
@@ -20202,7 +20164,7 @@ determined.</p>
 
 <p class="center">sin &gamma; = u<span class="su">i</span> / v<span class="su">i</span> = 0.45 / 0.94 = .48;</p>
 
-<p class="center">&gamma; = 29°.</p>
+<p class="center">&gamma; = 29°.</p>
 
 <p class="noind">The value of u<span class="su">i</span> should, however, be corrected for the space occupied
 by the guide-blades.</p>
@@ -20219,7 +20181,7 @@ by the guide-blades.</p>
 
 <p class="center">cot &theta; = (w<span class="su">i</span> &minus; V<span class="su">i</span>) / u<span class="su">i</span> = (0.82 &minus; 0.5) / 0.45 = .71;</p>
 
-<p class="center">&theta; = 55°.</p>
+<p class="center">&theta; = 55°.</p>
 
 <p>The relative velocity of the water striking the vane at the inlet
 edge is v<span class="su">ri</span> = u<span class="su">i</span> cosec &theta; = 1.22u<span class="su">i</span>. This relative velocity remains
@@ -20229,7 +20191,7 @@ Also in an axial flow turbine V<span class="su">o</span> = V<span class="su">i</
 
 <p>If the final velocity of the water is axial, then</p>
 
-<p class="center">cos &phi; = V<span class="su">o</span> / v<span class="su">ro</span> = V<span class="su">i</span> / v<span class="su">ri</span> = 0.5 / (1.22 × 0.45) = cos 24º 23&prime;.</p>
+<p class="center">cos &phi; = V<span class="su">o</span> / v<span class="su">ro</span> = V<span class="su">i</span> / v<span class="su">ri</span> = 0.5 / (1.22 × 0.45) = cos 24º 23&prime;.</p>
 
 <p class="noind">This should be corrected for the vane thickness. Neglecting this,
 u<span class="su">o</span> = v<span class="su">ro</span> sin &phi; = v<span class="su">ri</span> sin &phi; = u<span class="su">i</span> cosec &theta; sin &phi; = 0.5u<span class="su">i</span>. The discharging area
@@ -20242,7 +20204,7 @@ in the section (fig. 199).</p>
 <tr><td class="figright1"><img style="width:160px; height:124px" src="images/img104d.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 203.</span></td></tr></table>
 
-<p>§ 200. <i>Pelton Wheel.</i>&mdash;In the mining district of California about
+<p>§ 200. <i>Pelton Wheel.</i>&mdash;In the mining district of California about
 1860 simple impulse wheels were used, termed hurdy-gurdy wheels.
 The wheels rotated in a vertical plane, being supported on a horizontal
 axis. Round the circumference were fixed flat vanes which
@@ -20295,7 +20257,7 @@ each develops 125 h.p.</p>
 <tr><td class="figright1"><img style="width:305px; height:274px" src="images/img105a.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 205</span></td></tr></table>
 
-<p>§ 201. <i>Theory of the Pelton Wheel.</i>&mdash;Suppose a jet with a velocity
+<p>§ 201. <i>Theory of the Pelton Wheel.</i>&mdash;Suppose a jet with a velocity
 v strikes tangentially a curved vane AB (fig. 205) moving in the
 same direction with the velocity u. The water will flow over the
 vane with the relative velocity v &minus; u and at B will have the tangential
@@ -20311,7 +20273,7 @@ per second the change of
 momentum per second in
 the direction of the vane&rsquo;s
 motion is (GQ/g) [v &minus; {u &minus; (v &minus; u) cos &alpha;}] = (GQ/g) (v &minus; u) (1 + cos &alpha;).
-If a = 0°, cos &alpha; = 1, and the change
+If a = 0°, cos &alpha; = 1, and the change
 of momentum per second,
 which is equal to the
 effort driving the vane, is
@@ -20323,7 +20285,7 @@ in succession, the
 quantity of water impinging
 on the vanes per second is the total discharge of the nozzle,
 and the energy expended at the nozzle is GQv<span class="sp">2</span>/2g. Hence the
-efficiency of the arrangement is, when &alpha; = 0°, neglecting friction,</p>
+efficiency of the arrangement is, when &alpha; = 0°, neglecting friction,</p>
 
 <p class="center">&eta; = 2Pu / GQv<span class="sp">2</span> = 4 (v &minus; u) u/v<span class="sp">2</span>,</p>
 
@@ -20336,7 +20298,7 @@ vane on each side in a direction nearly parallel to the direction of
 motion of the vane. The best velocity of the vane is very approximately
 half the velocity of the jet.</p>
 
-<p>§ 202. <i>Regulation of the Pelton Wheel.</i>&mdash;At first Pelton wheels were
+<p>§ 202. <i>Regulation of the Pelton Wheel.</i>&mdash;At first Pelton wheels were
 adjusted to varying loads merely by throttling the supply. This
 method involves a total loss of part of the head at the sluice or
 throttle valve. In addition as the working head is reduced, the
@@ -20353,7 +20315,7 @@ occupy more or less of the aperture of the nozzle. Such a needle can
 be controlled by an ordinary governor.</p>
 </div>
 
-<p>§ 203. <i>General Considerations on the Choice of a Type of
+<p>§ 203. <i>General Considerations on the Choice of a Type of
 Turbine.</i>&mdash;The circumferential speed of any turbine is necessarily
 a fraction of the initial velocity of the water, and therefore is
 greater as the head is greater. In reaction turbines with complete
@@ -20397,7 +20359,7 @@ the state of the water. With a high fall the turbine of largest
 radius only is used, and the speed of rotation is less than with a
 turbine of smaller radius. On the other hand, as the fall decreases
 the inner turbines are used either singly or together, according
-to the power required. At the Zürich waterworks there are
+to the power required. At the Zürich waterworks there are
 turbines of 90 h.p. on a fall varying from 10<span class="spp">1</span>&frasl;<span class="suu">2</span> ft. to 4<span class="spp">3</span>&frasl;<span class="suu">4</span> ft. The
 power and speed are kept constant. Each turbine has three
 concentric rings. The outermost ring gives 90 h.p. with 105
@@ -20413,7 +20375,7 @@ tests the efficiency was 74% with the outer ring working alone,
 <tr><td class="figcenter"><img style="width:433px; height:723px" src="images/img105b.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 206.</span></td></tr></table>
 
-<p>§ 204. <i>Speed Governing.</i>&mdash;When turbines are used to drive
+<p>§ 204. <i>Speed Governing.</i>&mdash;When turbines are used to drive
 dynamos direct, the question of speed regulation is of great importance.
 Steam engines using a light elastic fluid can be easily
 regulated by governors acting on throttle or expansion valves.
@@ -20456,7 +20418,7 @@ if the pressure is in excess of that due to the head.</p>
 <tr><td class="figcenter"><img style="width:691px; height:212px" src="images/img106a.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 207.</span></td></tr></table>
 
-<p>§ 205. <i>The Hydraulic Ram.</i>&mdash;The hydraulic ram is an arrangement
+<p>§ 205. <i>The Hydraulic Ram.</i>&mdash;The hydraulic ram is an arrangement
 by which a quantity of water falling a distance h forces
 a portion of the water to rise to a height h<span class="su">1</span>, greater than h.
 It consists of a supply reservoir (A, fig. 207), into which the water
@@ -20543,7 +20505,7 @@ pump valves.</p>
 
 <p class="pt2 center sc">Pumps</p>
 
-<p>§ 206. The different classes of pumps correspond
+<p>§ 206. The different classes of pumps correspond
 almost exactly to the different classes
 of water motors, although the mechanical
 details of the construction are somewhat
@@ -20587,7 +20549,7 @@ plunger is replaced by an elastic diaphragm, alternately depressed
 into and raised out of a cylinder.</p>
 
 <p>As single-acting pumps give an intermittent discharge three
-are generally used on cranks at 120°. But with all pumps the
+are generally used on cranks at 120°. But with all pumps the
 variation of velocity of discharge would cause great waste of work
 in the delivery pipes when they are long, and even danger from
 the hydraulic ramming action of the long column of water.
@@ -20637,7 +20599,7 @@ Messrs Hayward Tyler have introduced a mechanism for varying
 the stroke of the pumps (Sinclair&rsquo;s patent) from full stroke
 to nil, without stopping the pumps.</p>
 
-<p>§ 207. <i>Centrifugal Pump.</i>&mdash;For large volumes of water on
+<p>§ 207. <i>Centrifugal Pump.</i>&mdash;For large volumes of water on
 lifts not exceeding about 60 ft. the most convenient pump is
 the centrifugal pump. Recent improvements have made it
 available also for very high lifts. It consists of a wheel or fan
@@ -20708,7 +20670,7 @@ air from the pump case.</p>
 <tr><td class="caption"><span class="sc">Fig. 210.</span></td></tr></table>
 
 <div class="condensed">
-<p>§ 208. <i>Design and Proportions of a Centrifugal Pump.</i>&mdash;The design
+<p>§ 208. <i>Design and Proportions of a Centrifugal Pump.</i>&mdash;The design
 of the pump disk is very simple. Let r<span class="su">i</span>, r<span class="su">o</span> be the radii of the inlet
 and outlet surfaces of the pump disk, d<span class="su">i</span>, d<span class="su">o</span> the clear axial width at
 those radii. The velocity of flow through the pump may be taken
@@ -20808,7 +20770,7 @@ conditions of working</p>
 
 <p><i>Hydraulic Efficiency of the Pump.</i>&mdash;Neglecting disk friction,
 journal friction, and leakage, the efficiency of the pump can be found
-in the same way as that of turbines (§ 186). Let M be the moment
+in the same way as that of turbines (§ 186). Let M be the moment
 of the couple rotating the pump, and &alpha; its angular velocity;
 w<span class="su">o</span>, r<span class="su">o</span>
 the tangential velocity of the water and radius at the outlet
@@ -20833,7 +20795,7 @@ efficiency is</p>
 <p class="center">&eta; = GQH / M&alpha; = gH / w<span class="su">o</span>r<span class="su">o</span>&alpha; = gH / w<span class="su">o</span>V<span class="su">o</span>.</p>
 <div class="author">(7)</div>
 
-<p>§ 209. Case 1. <i>Centrifugal Pump with no Whirlpool Chamber.</i>&mdash;When
+<p>§ 209. Case 1. <i>Centrifugal Pump with no Whirlpool Chamber.</i>&mdash;When
 no special provision is made to utilize the energy of motion of
 the water leaving the wheel, and the pump discharges directly into a
 chamber in which the water is flowing to the discharge pipe, nearly
@@ -20869,7 +20831,7 @@ wheel.</p>
  = (V<span class="su">o</span><span class="sp">2</span> &minus; u<span class="su">o</span><span class="sp">2</span> cosec<span class="sp">2</span> &phi;) / {2V<span class="su">o</span> (V<span class="su">o</span> &minus; u<span class="su">o</span> cot &phi;) },</p>
 <div class="author">(9)</div>
 
-<p class="noind">For &phi; = 90°,</p>
+<p class="noind">For &phi; = 90°,</p>
 
 <p class="center">&eta; = (V<span class="su">o</span><span class="sp">2</span> &minus; u<span class="su">o</span><span class="sp">2</span>) / 2V<span class="su">o</span><span class="sp">2</span>,</p>
 
@@ -20894,18 +20856,18 @@ efficiency and the circumferential velocity of the pump:&mdash;</p>
 <table class="ws" summary="Contents">
 <tr><td class="tcc">&phi;</td> <td class="tcc">&eta;</td> <td class="tcc">V<span class="su">o</span></td></tr>
 
-<tr><td class="tcc">90°</td> <td class="tcc">0.47</td> <td class="tcl">1.03 &radic;<span class="ov">2gH</span></td></tr>
-<tr><td class="tcc">45°</td> <td class="tcc">0.56</td> <td class="tcl">1.06&emsp;&rdquo;</td></tr>
-<tr><td class="tcc">30°</td> <td class="tcc">0.65</td> <td class="tcl">1.12&emsp;&rdquo;</td></tr>
-<tr><td class="tcc">20°</td> <td class="tcc">0.73</td> <td class="tcl">1.24&emsp;&rdquo;</td></tr>
-<tr><td class="tcc">10°</td> <td class="tcc">0.84</td> <td class="tcl">1.75&emsp;&rdquo;</td></tr>
+<tr><td class="tcc">90°</td> <td class="tcc">0.47</td> <td class="tcl">1.03 &radic;<span class="ov">2gH</span></td></tr>
+<tr><td class="tcc">45°</td> <td class="tcc">0.56</td> <td class="tcl">1.06&emsp;&rdquo;</td></tr>
+<tr><td class="tcc">30°</td> <td class="tcc">0.65</td> <td class="tcl">1.12&emsp;&rdquo;</td></tr>
+<tr><td class="tcc">20°</td> <td class="tcc">0.73</td> <td class="tcl">1.24&emsp;&rdquo;</td></tr>
+<tr><td class="tcc">10°</td> <td class="tcc">0.84</td> <td class="tcl">1.75&emsp;&rdquo;</td></tr>
 </table>
 
-<p class="noind">&phi; cannot practically be made less than 20°; and, allowing for the
-frictional losses neglected, the efficiency of a pump in which &phi; = 20° is
+<p class="noind">&phi; cannot practically be made less than 20°; and, allowing for the
+frictional losses neglected, the efficiency of a pump in which &phi; = 20° is
 found to be about .60.</p>
 
-<p>§ 210. Case 2. <i>Pump with a Whirlpool Chamber</i>, as in fig. 210.&mdash;Professor
+<p>§ 210. Case 2. <i>Pump with a Whirlpool Chamber</i>, as in fig. 210.&mdash;Professor
 James Thomson first suggested that the energy of the water
 after leaving the pump disk might be utilized, if a space were left
 in which a free vortex could be formed. In such a free vortex the
@@ -20940,24 +20902,24 @@ of wheel and to outside of free vortex,</p>
 increase of efficiency. Thus with</p>
 
 <table class="ws" summary="Contents">
-<tr><td class="tcl">&phi; = 90° and</td> <td class="tcl">k = <span class="spp">1</span>&frasl;<span class="suu">2</span>,</td> <td class="tcl">&eta; = <span class="spp">7</span>&frasl;<span class="suu">8</span> nearly,</td></tr>
+<tr><td class="tcl">&phi; = 90° and</td> <td class="tcl">k = <span class="spp">1</span>&frasl;<span class="suu">2</span>,</td> <td class="tcl">&eta; = <span class="spp">7</span>&frasl;<span class="suu">8</span> nearly,</td></tr>
 
 <tr><td class="tcl">&phi; a small angle and</td> <td class="tcl">k = <span class="spp">1</span>&frasl;<span class="suu">2</span>,</td> <td class="tcl">&eta; = 1 nearly.</td></tr>
 </table>
 
 <p class="noind">With this arrangement of pump, therefore, the angle at the outer
 ends of the vanes is of comparatively little importance. A moderate
-angle of 30° or 40° may very well be adopted. The following
+angle of 30° or 40° may very well be adopted. The following
 numerical values of the velocity of the circumference of the pump
 have been obtained by taking k = <span class="spp">1</span>&frasl;<span class="suu">2</span>, and u<span class="su">o</span> = 0.25&radic;(2gH).</p>
 
 <table class="ws" summary="Contents">
 <tr><td class="tcc">&phi;</td> <td class="tcc">V<span class="su">o</span></td></tr>
 
-<tr><td class="tcc">90°</td> <td class="tcl">&ensp;.762 &radic;<span class="ov">2gH</span></td></tr>
-<tr><td class="tcc">45°</td> <td class="tcl">&ensp;.842&emsp;&rdquo;</td></tr>
-<tr><td class="tcc">30°</td> <td class="tcl">&ensp;.911&emsp;&rdquo;</td></tr>
-<tr><td class="tcc">20°</td> <td class="tcl">1.023&emsp;&rdquo;</td></tr>
+<tr><td class="tcc">90°</td> <td class="tcl">&ensp;.762 &radic;<span class="ov">2gH</span></td></tr>
+<tr><td class="tcc">45°</td> <td class="tcl">&ensp;.842&emsp;&rdquo;</td></tr>
+<tr><td class="tcc">30°</td> <td class="tcl">&ensp;.911&emsp;&rdquo;</td></tr>
+<tr><td class="tcc">20°</td> <td class="tcl">1.023&emsp;&rdquo;</td></tr>
 </table>
 
 <p>The quantity of water to be pumped by a centrifugal pump necessarily
@@ -20982,7 +20944,7 @@ or more than the normal quantity of water is discussed in a paper in
 the <i>Proc. Inst. Civ. Eng.</i> vol. 53.</p>
 </div>
 
-<p>§ 211. <i>High Lift Centrifugal Pumps.</i>&mdash;It has long been known
+<p>§ 211. <i>High Lift Centrifugal Pumps.</i>&mdash;It has long been known
 that centrifugal pumps could be worked in series, each pump
 overcoming a part of the lift. This method has been perfected,
 and centrifugal pumps for very high lifts with great efficiency
@@ -21020,7 +20982,7 @@ the results of tests made at Newcastle:&mdash;</p>
 <tr><td class="tcl lb bb">Water h.p.</td> <td class="tcr rb bb">&nbsp;</td> <td class="tcc rb bb">252</td> <td class="tcc rb bb">235</td> <td class="tcc rb bb">326</td> <td class="tcc rb bb">239</td></tr>
 </table>
 
-<p>In trial IV. the steam was superheated 95° F. From other
+<p>In trial IV. the steam was superheated 95° F. From other
 trials under the same conditions as trial I. the Parsons turbine
 uses 15.6 &#8468; of steam per brake h.p. hour, so that the combined
 efficiency of turbine and pumps is about 56%, a remarkably
@@ -21030,8 +20992,8 @@ good result.</p>
 <tr><td class="figright1"><img style="width:376px; height:707px" src="images/img109.jpg" alt="" /></td></tr>
 <tr><td class="caption"><span class="sc">Fig. 212.</span></td></tr></table>
 
-<p>§ 212. <i>Air-Lift Pumps.</i>&mdash;An interesting and simple method of
-pumping by compressed air, invented by Dr J. Pohlé of Arizona,
+<p>§ 212. <i>Air-Lift Pumps.</i>&mdash;An interesting and simple method of
+pumping by compressed air, invented by Dr J. Pohlé of Arizona,
 is likely to be very useful in certain cases. Suppose a rising
 main placed in a deep bore hole in which there is a considerable
 depth of water. Air compressed to a sufficient pressure is conveyed
@@ -21099,7 +21061,7 @@ and may be advantageously used permanently when a boring
 is in sand or gravel which cannot be kept out of the bore hole.
 The initial cost is small.</p>
 
-<p>§ 213. <i>Centrifugal Fans.</i>&mdash;Centrifugal fans are constructed
+<p>§ 213. <i>Centrifugal Fans.</i>&mdash;Centrifugal fans are constructed
 similarly to centrifugal pumps, and are used for compressing
 air to pressures not exceeding 10 to 15 in. of water-column.
 With this small variation of pressure the variation of volume
@@ -21242,7 +21204,7 @@ form of the empirical results.</p>
 <p><a name="ft1f" id="ft1f" href="#fa1f"><span class="fn">1</span></a> Except where other units are given, the units throughout this
 article are feet, pounds, pounds per sq. ft., feet per second.</p>
 
-<p><a name="ft2f" id="ft2f" href="#fa2f"><span class="fn">2</span></a> <i>Journal de M. Liouville</i>, t. xiii. (1868); <i>Mémoires de l&rsquo;Académie,
+<p><a name="ft2f" id="ft2f" href="#fa2f"><span class="fn">2</span></a> <i>Journal de M. Liouville</i>, t. xiii. (1868); <i>Mémoires de l&rsquo;Académie,
 des Sciences de l&rsquo;Institut de France</i>, t. xxiii., xxiv. (1877).</p>
 
 <p><a name="ft3f" id="ft3f" href="#fa3f"><span class="fn">3</span></a> The following theorem is taken from a paper by J. H. Cotterill,
@@ -21267,9 +21229,9 @@ on v<span class="su">2</span>, and the statement above is no longer true.</p>
 
 
 <hr class="art" />
-<p><span class="bold">HYDRAZINE<a name="ar57" id="ar57"></a></span> (<span class="sc">Diamidogen</span>), N<span class="su">2</span>H<span class="su">4</span> or H<span class="su">2</span> N·NH<span class="su">2</span>, a compound
+<p><span class="bold">HYDRAZINE<a name="ar57" id="ar57"></a></span> (<span class="sc">Diamidogen</span>), N<span class="su">2</span>H<span class="su">4</span> or H<span class="su">2</span> N·NH<span class="su">2</span>, a compound
 of hydrogen and nitrogen, first prepared by Th. Curtius in 1887
-from diazo-acetic ester, N<span class="su">2</span>CH·CO<span class="su">2</span>C<span class="su">2</span>H<span class="su">5</span>. This ester, which is
+from diazo-acetic ester, N<span class="su">2</span>CH·CO<span class="su">2</span>C<span class="su">2</span>H<span class="su">5</span>. This ester, which is
 obtained by the action of potassium nitrate on the hydrochloride
 of amidoacetic ester, yields on hydrolysis with hot concentrated
 potassium hydroxide an acid, which Curtius regarded as
@@ -21295,23 +21257,23 @@ in the presence of benzaldehyde, which, by combining with the
 hydrazine, protected it from oxidation. F. Raschig (German
 Patent 198307, 1908) obtained good yields by oxidizing ammonia
 with sodium hypochlorite in solutions made viscous with glue.
-Free hydrazine is a colourless liquid which boils at 113.5° C.,
-and solidifies about 0° C. to colourless crystals; it is heavier
+Free hydrazine is a colourless liquid which boils at 113.5° C.,
+and solidifies about 0° C. to colourless crystals; it is heavier
 than water, in which it dissolves with rise of temperature. It
 is rapidly oxidized on exposure, is a strong reducing agent, and
 reacts vigorously with the halogens. Under certain conditions
 it may be oxidized to azoimide (A. W. Browne and F. F.
 Shetterly, <i>J. Amer. C.S.</i>, 1908, p. 53). By fractional distillation
-of its aqueous solution hydrazine hydrate N<span class="su">2</span>H<span class="su">4</span>·H<span class="su">2</span>O
-(or perhaps H<span class="su">2</span>N·NH<span class="su">3</span>OH), a strong base, is obtained, which
+of its aqueous solution hydrazine hydrate N<span class="su">2</span>H<span class="su">4</span>·H<span class="su">2</span>O
+(or perhaps H<span class="su">2</span>N·NH<span class="su">3</span>OH), a strong base, is obtained, which
 precipitates the metals from solutions of copper and silver
 salts at ordinary temperatures. It dissociates completely in a
-vacuum at 143°, and when heated under atmospheric pressure
-to 183° it decomposes into ammonia and nitrogen (A. Scott,
-<i>J. Chem. Soc.</i>, 1904, 85, p. 913). The sulphate N<span class="su">2</span>H<span class="su">4</span>·H<span class="su">2</span>SO<span class="su">4</span>,
+vacuum at 143°, and when heated under atmospheric pressure
+to 183° it decomposes into ammonia and nitrogen (A. Scott,
+<i>J. Chem. Soc.</i>, 1904, 85, p. 913). The sulphate N<span class="su">2</span>H<span class="su">4</span>·H<span class="su">2</span>SO<span class="su">4</span>,
 crystallizes in tables which are slightly soluble in cold water
 and readily soluble in hot water; it is decomposed by heating
-above 250° C. with explosive evolution of gas and liberation of
+above 250° C. with explosive evolution of gas and liberation of
 sulphur. By the addition of barium chloride to the sulphate, a
 solution of the hydrochloride is obtained, from which the
 crystallized salt may be obtained on evaporation.</p>
@@ -21333,15 +21295,15 @@ by zinc dust and acetic acid to phenylhydrazine potassium sulphite.
 This salt is then hydrolysed by heating it with hydrochloric acid&mdash;</p>
 
 <table class="reg" summary="poem"><tr><td> <div class="poemr">
-<p>C<span class="su">6</span>H<span class="su">5</span>N<span class="su">2</span>Cl + K<span class="su">2</span>SO<span class="su">3</span> = KCl + C<span class="su">6</span>H<span class="su">5</span>N<span class="su">2</span>·SO<span class="su">3</span>K,</p>
+<p>C<span class="su">6</span>H<span class="su">5</span>N<span class="su">2</span>Cl + K<span class="su">2</span>SO<span class="su">3</span> = KCl + C<span class="su">6</span>H<span class="su">5</span>N<span class="su">2</span>·SO<span class="su">3</span>K,</p>
 
-<p>C<span class="su">6</span>H<span class="su">5</span>N<span class="su">2</span>·SO<span class="su">3</span>K + 2H = C<span class="su">6</span>H<span class="su">5</span>·NH·NH·SO<span class="su">3</span>K,</p>
+<p>C<span class="su">6</span>H<span class="su">5</span>N<span class="su">2</span>·SO<span class="su">3</span>K + 2H = C<span class="su">6</span>H<span class="su">5</span>·NH·NH·SO<span class="su">3</span>K,</p>
 
-<p>C<span class="su">6</span>H<span class="su">5</span>NH·NH·SO<span class="su">3</span>K + HCl + H<span class="su">2</span>O = C<span class="su">6</span>H<span class="su">5</span>·NH·NH<span class="su">2</span>·HCl + KHSO<span class="su">4</span>.</p>
+<p>C<span class="su">6</span>H<span class="su">5</span>NH·NH·SO<span class="su">3</span>K + HCl + H<span class="su">2</span>O = C<span class="su">6</span>H<span class="su">5</span>·NH·NH<span class="su">2</span>·HCl + KHSO<span class="su">4</span>.</p>
 </div> </td></tr></table>
 
 <p>Phenylhydrazine is a colourless oily liquid which turns brown on
-exposure. It boils at 241° C., and melts at 17.5° C. It is slightly
+exposure. It boils at 241° C., and melts at 17.5° C. It is slightly
 soluble in water, and is strongly basic, forming well-defined salts
 with acids. For the detection of substances containing the carbonyl
 group (such for example as aldehydes and ketones) phenylhydrazine
@@ -21350,9 +21312,9 @@ elimination of water and the formation of well-defined hydrazones
 (see <span class="sc"><a href="#artlinks">Aldehydes</a></span>, <span class="sc"><a href="#artlinks">Ketones</a></span> and <span class="sc"><a href="#artlinks">Sugars</a></span>). It is a strong reducing
 agent; it precipitates cuprous oxide when heated with Fehling&rsquo;s
 solution, nitrogen and benzene being formed at the same
-time&mdash;C<span class="su">6</span>H<span class="su">5</span>·NH·NH<span class="su">2</span> + 2CuO = Cu<span class="su">2</span>O + N<span class="su">2</span> + H<span class="su">2</span>O + C<span class="su">6</span>H<span class="su">5</span>. By energetic reduction
+time&mdash;C<span class="su">6</span>H<span class="su">5</span>·NH·NH<span class="su">2</span> + 2CuO = Cu<span class="su">2</span>O + N<span class="su">2</span> + H<span class="su">2</span>O + C<span class="su">6</span>H<span class="su">5</span>. By energetic reduction
 of phenylhydrazine (<i>e.g.</i> by use of zinc dust and hydrochloric
-acid), ammonia and aniline are produced&mdash;C<span class="su">6</span>H<span class="su">5</span>NH·NH<span class="su">2</span> + 2H =
+acid), ammonia and aniline are produced&mdash;C<span class="su">6</span>H<span class="su">5</span>NH·NH<span class="su">2</span> + 2H =
 C<span class="su">6</span>H<span class="su">5</span>NH<span class="su">2</span> + NH<span class="su">3</span>. It is also a most important synthetic reagent.
 It combines with aceto-acetic ester to form phenylmethylpyrazolone,
 from which antipyrine (<i>q.v.</i>) may be obtained. Indoles (<i>q.v.</i>) are
@@ -21395,7 +21357,7 @@ organic chemistry.</p>
 
 
 <hr class="art" />
-<p><span class="bold">HYDROCELE<a name="ar60" id="ar60"></a></span> (Gr. <span class="grk" title="hydôr">&#8021;&#948;&#969;&#961;</span>, water, and <span class="grk" title="kêlê">&#954;&#942;&#955;&#951;</span>, tumour), the
+<p><span class="bold">HYDROCELE<a name="ar60" id="ar60"></a></span> (Gr. <span class="grk" title="hydôr">&#8021;&#948;&#969;&#961;</span>, water, and <span class="grk" title="kêlê">&#954;&#942;&#955;&#951;</span>, tumour), the
 medical term for any collection of fluid other than pus or blood
 in the neighbourhood of the testis or cord. The fluid is usually
 serous. Hydrocele may be congenital or arise in the middle-aged
@@ -21412,7 +21374,7 @@ drained.</p>
 
 
 <hr class="art" />
-<p><span class="bold">HYDROCEPHALUS<a name="ar61" id="ar61"></a></span> (Gr. <span class="grk" title="hydôr">&#8021;&#948;&#969;&#961;</span>, water, and <span class="grk" title="kephalê">&#954;&#949;&#966;&#945;&#955;&#8052;</span>, head),
+<p><span class="bold">HYDROCEPHALUS<a name="ar61" id="ar61"></a></span> (Gr. <span class="grk" title="hydôr">&#8021;&#948;&#969;&#961;</span>, water, and <span class="grk" title="kephalê">&#954;&#949;&#966;&#945;&#955;&#8052;</span>, head),
 a term applied to disease of the brain which is attended
 with excessive effusion of fluid into its cavities. It exists
 in two forms&mdash;<i>acute</i> and <i>chronic hydrocephalus</i>. Acute hydrocephalus
@@ -21501,7 +21463,7 @@ plant.</td></tr>
 <p><span class="bold">HYDROCHARIDEAE,<a name="ar62" id="ar62"></a></span> in botany, a natural order of Monocotyledons,
 belonging to the series Helobieae. They are water-plants,
 represented in Britain by frog-bit (<i>Hydrocharis Morsusranae</i>)
-and water-soldier (<i>Stratiotes aloïdes</i>). The order contains
+and water-soldier (<i>Stratiotes aloïdes</i>). The order contains
 about fifty species in fifteen genera, twelve of which occur in
 fresh water while three are marine: and includes both floating
 and submerged forms.
@@ -21518,7 +21480,7 @@ on all sides, the plant
 thus propagating itself
 on the same way as
 the strawberry.
-<i>Stratiotes aloïdes</i> has a
+<i>Stratiotes aloïdes</i> has a
 rosette of stiff sword-like
 leaves, which when
 the plant is in flower
@@ -21649,19 +21611,19 @@ manufacture under <span class="sc"><a href="#artlinks">Alkali Manufacture</a></s
 
 
 <hr class="art" />
-<p><span class="bold">HYDRODYNAMICS<a name="ar64" id="ar64"></a></span> (Gr. <span class="grk" title="hydôr">&#8021;&#948;&#969;&#961;</span>, water, <span class="grk" title="dynamis">&#948;&#973;&#957;&#945;&#956;&#953;&#962;</span>, strength),
+<p><span class="bold">HYDRODYNAMICS<a name="ar64" id="ar64"></a></span> (Gr. <span class="grk" title="hydôr">&#8021;&#948;&#969;&#961;</span>, water, <span class="grk" title="dynamis">&#948;&#973;&#957;&#945;&#956;&#953;&#962;</span>, strength),
 the branch of hydromechanics which discusses the motion of
 fluids (see <span class="sc"><a href="#artlinks">Hydromechanics</a></span>).</p>
 
 
 <hr class="art" />
 <p><span class="bold">HYDROGEN<a name="ar65" id="ar65"></a></span> [symbol H, atomic weight 1.008 (o = 16)], one
-of the chemical elements. Its name is derived from Gr. <span class="grk" title="hydôr">&#8021;&#948;&#969;&#961;</span>,
+of the chemical elements. Its name is derived from Gr. <span class="grk" title="hydôr">&#8021;&#948;&#969;&#961;</span>,
 water, and <span class="grk" title="gennaein">&#947;&#949;&#957;&#957;&#940;&#949;&#953;&#957;</span>, to produce, in allusion to the fact that
 water is produced when the gas burns in air. Hydrogen appears
 to have been recognized by Paracelsus in the 16th century;
 the combustibility of the gas was noticed by Turquet de Mayenne
-in the 17th century, whilst in 1700 N. Lémery showed that a
+in the 17th century, whilst in 1700 N. Lémery showed that a
 mixture of hydrogen and air detonated on the application of
 a light. The first definite experiments concerning the nature
 of hydrogen were made in 1766 by H. Cavendish, who showed
@@ -21689,11 +21651,11 @@ of acidulated water, by the decomposition of water by
 various metals or metallic hydrides, and by the action of many
 metals on acids or on bases. The alkali metals and alkaline earth
 metals decompose water at ordinary temperatures; magnesium
-begins to react above 70° C., and zinc at a dull red heat. The
+begins to react above 70° C., and zinc at a dull red heat. The
 decomposition of steam by red hot iron has been studied by
 H. Sainte-Claire Deville (<i>Comptes rendus</i>, 1870, 70, p. 1105)
 and by H. Debray (<i>ibid.</i>, 1879, 88, p. 1341), who found that at
-about 1500° C. a condition of equilibrium is reached. H. Moissan
+about 1500° C. a condition of equilibrium is reached. H. Moissan
 (<i>Bull. soc. chim.</i>, 1902, 27, p. 1141) has shown that potassium
 hydride decomposes cold water, with evolution of hydrogen,
 KH + H<span class="su">2</span>O = KOH + H<span class="su">2</span>. Calcium hydride or hydrolite, prepared
@@ -21702,7 +21664,7 @@ similarly, 1 gram giving 1 litre of gas; it has been proposed
 as a commercial source (Prats Aymerich, <i>Abst. J.C.S.</i>, 1907, ii.
 p. 543), as has also aluminium turnings moistened with potassium
 cyanide and mercuric chloride, which decomposes water regularly
-at 70°, 1 gram giving 1.3 litres of gas (Mauricheau-Beaupré,
+at 70°, 1 gram giving 1.3 litres of gas (Mauricheau-Beaupré,
 <i>Comptes rendus</i>, 1908, 147, p. 310). Strontium hydride behaves
 similarly. In preparing the gas by the action of metals on
 acids, dilute sulphuric or hydrochloric acid is taken, and the
@@ -21721,25 +21683,25 @@ by the action of superheated steam on incandescent coke (see
 F. Hembert and Henry, <i>Comptes rendus</i>, 1885, 101, p. 797;
 A. Naumann and C. Pistor, <i>Ber.</i>, 1885, 18, p. 1647), or by the
 electrolysis of a dilute solution of caustic soda (C. Winssinger,
-<i>Chem. Zeit.</i>, 1898, 22, p. 609; &ldquo;Die Elektrizitäts-Aktiengesellschaft,&rdquo;
+<i>Chem. Zeit.</i>, 1898, 22, p. 609; &ldquo;Die Elektrizitäts-Aktiengesellschaft,&rdquo;
 <i>Zeit. f. Elektrochem.</i>, 1901, 7, p. 857). In the latter
 method a 15% solution of caustic soda is used, and the
 electrodes are made of iron; the cell is packed in a wooden
 box, surrounded with sand, so that the temperature is kept
-at about 70° C.; the solution is replenished, when necessary,
+at about 70° C.; the solution is replenished, when necessary,
 with distilled water. The purity of the gas obtained is about
 97%.</p>
 
 <p>Pure hydrogen is a tasteless, colourless and odourless gas of
 specific gravity 0.06947 (air = 1) (Lord Rayleigh, <i>Proc. Roy. Soc.</i>,
-1893, p. 319). It may be liquefied, the liquid boiling at &minus;252.68°
-C. to &minus;252.84° C., and it has also been solidified, the solid melting
-at &minus;264° C. (J. Dewar, <i>Comptes rendus</i>, 1899, 129, p. 451;
+1893, p. 319). It may be liquefied, the liquid boiling at &minus;252.68°
+C. to &minus;252.84° C., and it has also been solidified, the solid melting
+at &minus;264° C. (J. Dewar, <i>Comptes rendus</i>, 1899, 129, p. 451;
 <i>Chem. News</i>, 1901, 84, p. 49; see also <span class="sc"><a href="#artlinks">Liquid Gases</a></span>). The
 specific heat of gaseous hydrogen (at constant pressure) is
 3.4041 (water = 1), and the ratio of the specific heat at constant
 pressure to the specific heat at constant volume is 1.3852 (W. C.
-Röntgen, <i>Pogg. Ann.</i>, 1873, 148, p. 580). On the spectrum see
+Röntgen, <i>Pogg. Ann.</i>, 1873, 148, p. 580). On the spectrum see
 <span class="sc"><a href="#artlinks">Spectroscopy</a></span>. Hydrogen is only very slightly soluble in water.
 It diffuses very rapidly through a porous membrane, and through
 some metals at a red heat (T. Graham, <i>Proc. Roy. Soc.</i>, 1867, 15,
@@ -21762,7 +21724,7 @@ shown that perfectly dry hydrogen will not unite with perfectly
 dry oxygen. Hydrogen combines with fluorine, even at very low
 temperatures, with great violence; it also combines with carbon,
 at the temperature of the electric arc. The alkali metals when
-warmed in a current of hydrogen, at about 360° C., form hydrides
+warmed in a current of hydrogen, at about 360° C., form hydrides
 of composition RH (R = Na, K, Rb, Cs), (H. Moissan, <i>Bull. soc.
 chim.</i>, 1902, 27, p. 1141); calcium and strontium similarly
 form hydrides CaH<span class="su">2</span>, SrH<span class="su">2</span> at a dull red heat (A. Guntz, <i>Comptes
@@ -21787,7 +21749,7 @@ namely, water (<i>q.v.</i>), H<span class="su">2</span>O, and hydrogen peroxide,
 H<span class="su">2</span>O<span class="su">2</span>, whilst the existence of a third oxide, ozonic acid, has been
 indicated.</p>
 
-<p><i>Hydrogen peroxide</i>, H<span class="su">2</span>O<span class="su">2</span>, was discovered by L. J. Thénard in
+<p><i>Hydrogen peroxide</i>, H<span class="su">2</span>O<span class="su">2</span>, was discovered by L. J. Thénard in
 1818 (<i>Ann. chim. phys.</i>, 8, p. 306). It occurs in small quantities
 in the atmosphere. It may be prepared by passing a current of
 carbon dioxide through ice-cold water, to which small quantities
@@ -21811,7 +21773,7 @@ added until a faint permanent white precipitate of hydrated
 barium peroxide appears; the solution is now filtered, and a
 concentrated solution of baryta water is added to the filtrate,
 when a crystalline precipitate of hydrated barium peroxide,
-BaO<span class="su">2</span>·H<span class="su">2</span>O, is thrown down. This is filtered off and well washed
+BaO<span class="su">2</span>·H<span class="su">2</span>O, is thrown down. This is filtered off and well washed
 with water. The above methods give a dilute aqueous solution
 of hydrogen peroxide, which may be concentrated somewhat
 by evaporation over sulphuric acid in vacuo. H. P. Talbot and
@@ -21846,18 +21808,18 @@ sulphuric acid (M. Berthelot, <i>Comptes rendus</i>, 1878, 86,
 p. 71).</p>
 
 <p>The anhydrous hydrogen peroxide obtained by Wolffenstein
-boils at 84-85°C. (68 mm.); its specific gravity is 1.4996 (1.5° C.).
+boils at 84-85°C. (68 mm.); its specific gravity is 1.4996 (1.5° C.).
 It is very explosive (W. Spring, <i>Zeit. anorg. Chem.</i>, 1895, 8,
 p. 424). The explosion risk seems to be most marked in the
 preparations which have been extracted with ether previous to
-distillation, and J. W. Brühl (<i>Ber.</i>, 1895, 28, p. 2847) is of opinion
+distillation, and J. W. Brühl (<i>Ber.</i>, 1895, 28, p. 2847) is of opinion
 that a very unstable, more highly oxidized product is produced
 in small quantity in the process. The solid variety prepared by
-Staedel forms colourless, prismatic crystals which melt at &minus;2° C.;
+Staedel forms colourless, prismatic crystals which melt at &minus;2° C.;
 it is decomposed with explosive violence by platinum sponge, and
 traces of manganese dioxide. The dilute aqueous solution is
 very unstable, giving up oxygen readily, and decomposing with
-explosive violence at 100° C. An aqueous solution containing
+explosive violence at 100° C. An aqueous solution containing
 more than 1.5% hydrogen peroxide reacts slightly acid. Towards
 lupetidin [aa&prime; dimethyl piperidine, C<span class="su">5</span>H<span class="su">9</span>N(CH<span class="su">3</span>)<span class="su">2</span>] hydrogen
 peroxide acts as a dibasic acid (A. Marcuse and R. Wolffenstein,
@@ -21870,7 +21832,7 @@ behaves very frequently as a powerful oxidizing agent; thus
 lead sulphide is converted into lead sulphate in presence of a
 dilute aqueous solution of the peroxide, the hydroxides of the
 alkaline earth metals are converted into peroxides of the type
-MO<span class="su">2</span>·8H<span class="su">2</span>O, titanium dioxide is converted into the trioxide,
+MO<span class="su">2</span>·8H<span class="su">2</span>O, titanium dioxide is converted into the trioxide,
 iodine is liberated from potassium iodide, and nitrites (in alkaline
 solution) are converted into acid-amides (B. Radziszewski, <i>Ber.</i>,
 1884, 17, p. 355). In many cases it is found that hydrogen
@@ -21902,9 +21864,9 @@ hydrobromic and hydriodic acids (S. Tanatar, <i>Ber.</i>, 1899,
 32, p. 1013).</p>
 
 <div class="condensed">
-<p>On the constitution of hydrogen peroxide see C. F. Schönbein,
+<p>On the constitution of hydrogen peroxide see C. F. Schönbein,
 <i>Jour. prak. Chem.</i>, 1858-1868; M. Traube, <i>Ber.</i>, 1882-1889; J. W.
-Brühl, <i>Ber.</i>, 1895, 28, p. 2847; 1900, 33, p. 1709; S. Tanatar, <i>Ber.</i>,
+Brühl, <i>Ber.</i>, 1895, 28, p. 2847; 1900, 33, p. 1709; S. Tanatar, <i>Ber.</i>,
 1903, 36, p. 1893.</p>
 
 <p>Hydrogen peroxide finds application as a bleaching agent, as an
@@ -21916,7 +21878,7 @@ acid solution; with potassium ferricyanide in alkaline solution,
 2K<span class="su">3</span>Fe(CN)<span class="su">6</span> + 2KOH + H<span class="su">2</span>O<span class="su">2</span> = 2K<span class="su">4</span>Fe(CN)<span class="su">6</span> + 2H<span class="su">2</span>O + O<span class="su">2</span>; or by oxidizing
 arsenious acid in alkaline solution with the peroxide and
 back titration of the excess of arsenious acid with standard iodine
-(B. Grützner, <i>Arch. der Pharm.</i>, 1899, 237, p. 705). It may be
+(B. Grützner, <i>Arch. der Pharm.</i>, 1899, 237, p. 705). It may be
 recognized by the violet coloration it gives when added to a very
 dilute solution of potassium bichromate in the presence of hydrochloric
 acid; by the orange-red colour it gives with a solution of
@@ -21933,7 +21895,7 @@ acid, produced according to the reaction O<span class="su">3</span> + H<span cla
 
 
 <hr class="art" />
-<p><span class="bold">HYDROGRAPHY<a name="ar66" id="ar66"></a></span> (Gr. <span class="grk" title="hydôr">&#8021;&#948;&#969;&#961;</span>, water, and <span class="grk" title="graphein">&#947;&#961;&#940;&#966;&#949;&#953;&#957;</span>, to write),
+<p><span class="bold">HYDROGRAPHY<a name="ar66" id="ar66"></a></span> (Gr. <span class="grk" title="hydôr">&#8021;&#948;&#969;&#961;</span>, water, and <span class="grk" title="graphein">&#947;&#961;&#940;&#966;&#949;&#953;&#957;</span>, to write),
 the science dealing with all the waters of the earth&rsquo;s surface,
 including the description of their physical features and conditions;
 the preparation of charts and maps showing the position
@@ -21949,9 +21911,9 @@ the admiralty (see <span class="sc"><a href="#artlinks">Chart</a></span>).</p>
 
 
 <hr class="art" />
-<p><span class="bold">HYDROLYSIS<a name="ar67" id="ar67"></a></span> (Gr. <span class="grk" title="hydôr">&#8021;&#948;&#969;&#961;</span>, water, <span class="grk" title="luein">&#955;&#973;&#949;&#953;&#957;</span>, to loosen), in chemistry,
+<p><span class="bold">HYDROLYSIS<a name="ar67" id="ar67"></a></span> (Gr. <span class="grk" title="hydôr">&#8021;&#948;&#969;&#961;</span>, water, <span class="grk" title="luein">&#955;&#973;&#949;&#953;&#957;</span>, to loosen), in chemistry,
 a decomposition brought about by water after the manner shown
-in the equation R·X + H·OH = R·H + X·OH. Modern research
+in the equation R·X + H·OH = R·H + X·OH. Modern research
 has proved that such reactions are not occasioned by water
 acting as H<span class="su">2</span>O, but really by its ions (hydrions and hydroxidions),
 for the velocity is proportional (in accordance with the law of
@@ -21965,382 +21927,7 @@ glyceryl esters of organic acids, into glycerin and a soap (see
 
 <hr class="art" />
 
-
-
-
-
-
-
-
-<pre>
-
-
-
-
-
-End of the Project Gutenberg EBook of Encyclopaedia Britannica, 11th
-Edition, Volume 14, Slice 1, by Various
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-</pre>
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+<div>*** END OF THE PROJECT GUTENBERG EBOOK 40538 ***</div>
 </body>
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-The Project Gutenberg EBook of Encyclopaedia Britannica, 11th Edition,
-Volume 14, Slice 1, 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 14, Slice 1
-       "Husband" to "Hydrolysis"
-
-Author: Various
-
-Release Date: August 19, 2012 [EBook #40538]
-
-Language: English
-
-Character set encoding: ASCII
-
-*** START OF THIS PROJECT GUTENBERG EBOOK ENCYC. BRITANNICA, VOL. 14, SL 1 ***
-
-
-
-
-Produced by Marius Masi, Don Kretz and the Online
-Distributed Proofreading Team at http://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) The following typographical errors have been corrected:
-
-    ARTICLE HUSS: "This appointment had a deep influence on the already
-      vigorous religious life of Huss himself ..." 'appointment' amended
-      from 'appoinment'.
-
-    ARTICLE HYACINTH: "... the wild hyacinth of western North America,
-      Camassia esculenta." 'America' amended from 'Amercia'.
-
-    ARTICLE HYDRAULICS: "Fig. 74 shows an arrangement designed for the
-      Manchester water works. The water enters from the reservoir at
-      chamber A, the object of which is to still the irregular motion of
-      the water." 'at' amended from 'a'.
-
-    ARTICLE HYDRAULICS: "But the velocity at this point was probably
-      from Howden's statements 16.58 X 40/26 = 25.5 ft. per second, an
-      agreement as close as the approximate character of the data would
-      lead us to expect." Added 'per second'.
-
-    ARTICLE HYDRAULICS: "... as the velocity and area of cross section
-      are different in different states of the river." 'different'
-      amended from 'differest'.
-
-    ARTICLE HYDROGEN: "... for example, formic, glycollic, lactic,
-      tartaric, malic, benzoic and other organic acids are readily
-      oxidized in the presence of ferrous sulphate ..." 'glycollic'
-      amended from 'glygollic'.
-
-
-
-  THE
-
-  ENCYCLOPAEDIA BRITANNICA
-
-  ELEVENTH EDITION
-
-
-
-
-  FIRST  edition, published in three    volumes, 1768-1771.
-  SECOND    "        "        ten          "     1777-1784.
-  THIRD     "        "        eighteen     "     1788-1797.
-  FOURTH    "        "        twenty       "     1801-1810.
-  FIFTH     "        "        twenty       "     1815-1817.
-  SIXTH     "        "        twenty       "     1823-1824.
-  SEVENTH   "        "        twenty-one   "     1830-1842.
-  EIGHTH    "        "        twenty-two   "     1853-1860.
-  NINTH     "        "        twenty-five  "     1875-1889.
-  TENTH     "   ninth edition and eleven
-                  supplementary volumes,         1902-1903.
-  ELEVENTH  "  published in twenty-nine volumes, 1910-1911.
-
-
-  COPYRIGHT
-
-  in all countries subscribing to the Bern Convention
-
-  by
-
-  THE CHANCELLOR, MASTERS AND SCHOLARS
-  of the
-  UNIVERSITY OF CAMBRIDGE
-
-  _All rights reserved_
-
-
-
-
-  THE
-
-  ENCYCLOPAEDIA BRITANNICA
-
-  A DICTIONARY OF
-  ARTS, SCIENCES, LITERATURE AND GENERAL INFORMATION
-
-  ELEVENTH EDITION
-
-  VOLUME XIV
-  HUSBAND to ITALIC
-
-  New York
-
-  Encyclopaedia Britannica, Inc.
-  342 Madison Avenue
-
-
-  Copyright, in the United States of America, 1910,
-  by
-  The Encyclopaedia Britannica Company.
-
-
-     VOLUME XIV, SLICE I
-
-    Husband to Hydrolysis
-
-
-
-
-ARTICLES IN THIS SLICE:
-
-
-  HUSBAND                               HYADES
-  HUSBAND AND WIFE                      HYATT, ALPHEUS
-  HUSHI                                 HYBLA
-  HUSKISSON, WILLIAM                    HYBRIDISM
-  HUSS                                  HYDANTOIN
-  HUSSAR                                HYDE (17th century English family)
-  HUSSITES                              HYDE, THOMAS
-  HUSTING                               HYDE (market town)
-  HUSUM                                 HYDE DE NEUVILLE, JEAN GUILLAUME
-  HUTCHESON, FRANCIS                    HYDE PARK
-  HUTCHINSON, ANNE                      HYDERABAD (city of India)
-  HUTCHINSON, JOHN (puritan soldier)    HYDERABAD (state of India)
-  HUTCHINSON, JOHN (theological writer) HYDERABAD (capital of Hyderabad)
-  HUTCHINSON, SIR JONATHAN              HYDER ALI
-  HUTCHINSON, THOMAS                    HYDRA (island of Greece)
-  HUTCHINSON (Kansas, U.S.A.)           HYDRA (legendary monster)
-  HUTTEN, PHILIPP VON                   HYDRA (constellation)
-  HUTTEN, ULRICH VON                    HYDRACRYLIC ACID
-  HUTTER, LEONHARD                      HYDRANGEA
-  HUTTON, CHARLES                       HYDRASTINE
-  HUTTON, JAMES                         HYDRATE
-  HUTTON, RICHARD HOLT                  HYDRAULICS
-  HUXLEY, THOMAS HENRY                  HYDRAZINE
-  HUY                                   HYDRAZONE
-  HUYGENS, CHRISTIAAN                   HYDROCARBON
-  HUYGENS, SIR CONSTANTIJN              HYDROCELE
-  HUYSMANS (Flemish painters)           HYDROCEPHALUS
-  HUYSMANS, JORIS KARL                  HYDROCHARIDEAE
-  HUYSUM, JAN VAN                       HYDROCHLORIC ACID
-  HWANG HO                              HYDRODYNAMICS
-  HWICCE                                HYDROGEN
-  HYACINTH (flower)                     HYDROGRAPHY
-  HYACINTH (gem-stone)                  HYDROLYSIS
-  HYACINTHUS
-
-
-
-
-INITIALS USED IN VOLUME XI. TO IDENTIFY INDIVIDUAL CONTRIBUTORS,[1] WITH
-THE HEADINGS OF THE ARTICLES IN THIS VOLUME SO SIGNED.
-
-
-
-
-  A. Ba.
-    ADOLFO BARTOLI (1833-1894).
-
-      Formerly Professor of Literature at the Istituto di studi
-      superiori at Florence. Author of Storia della letteratura
-      Italiana; &c.
-
-    Italian Literature (_in part_).
-
-  A. Bo.*
-    AUGUSTE BOUDINHON, D.D., D.C.L.
-
-      Professor of Canon Law at the Catholic University of Paris.
-      Honorary Canon of Paris. Editor of the _Canoniste contemporain_.
-
-    Index Librorum Prohibitorum;
-    Infallibility.
-
-  A. Cy.
-    ARTHUR ERNEST COWLEY, M.A., LITT.D.
-
-      Sub-Librarian of the Bodleian Library, Oxford. Fellow of Magdalen
-      College.
-
-    Ibn Gabirol;
-    Inscriptions: _Semitic_.
-
-  A. C. G.
-    ALBERT CHARLES LEWIS GOTTHILF GUNTHER, M.A., M.D., PH.D., F.R.S.
-
-      Keeper of Zoological Department, British Museum, 1875-1895. Gold
-      Medallist, Royal Society, 1878. Author of _Catalogues of Colubrine
-      Snakes, Batrachia Salientia, and Fishes in the British Museum_;
-      _Reptiles of British India_; _Fishes of Zanzibar_; _Reports on the
-      "Challenger" Fishes_; &c.
-
-    Ichthyology (_in part_).
-
-  A. E. G.*
-    REV. ALFRED ERNEST GARVIE, M.A., D.D.
-
-      Principal of New College, Hampstead. Member of the Board of
-      Theology and the Board of Philosophy, London University. Author of
-      _Studies in the inner Life of Jesus_; &c.
-
-    Immortality;
-    Inspiration.
-
-  A. E. H. L.
-    AUGUSTUS EDWARD HOUGH LOVE, M.A., D.SC., F.R.S.
-
-      Sedleian Professor of Natural Philosophy in the University of
-      Oxford. Hon. Fellow of Queen's College, Oxford; formerly Fellow of
-      St John's College, Cambridge. Secretary to the London Mathematical
-      Society.
-
-    Infinitesimal Calculus.
-
-  A. F. C.
-    ALEXANDER FRANCIS CHAMBERLAIN, A.M., PH.D.
-
-      Assistant Professor of Anthropology, Clark University, Worcester,
-      Massachusetts. Member of American Antiquarian Society; Hon. Member
-      of American Folk-lore Society. Author of _The Child and Childhood
-      in Folk Thought_.
-
-    Indians, North American.
-
-  A. G.
-    MAJOR ARTHUR GEORGE FREDERICK GRIFFITHS (d. 1908).
-
-      H.M. Inspector of Prisons, 1878-1896. Author of _The Chronicles of
-      Newgate_; _Secrets of the Prison House_; &c.
-
-    Identification.
-
-  A. Ge.
-    SIR ARCHIBALD GEIKIE, LL.D.
-
-      See the biographical article, GEIKIE, SIR A.
-
-    Hutton, James.
-
-  A. Go.*
-    REV. ALEXANDER GORDON, M.A.
-
-      Lecturer on Church History in the University of Manchester.
-
-    Illuminati.
-
-  A. G. G.
-    SIR ALFRED GEORGE GREENHILL, M.A., F.R.S.
-
-      Formerly Professor of Mathematics in the Ordnance College,
-      Woolwich. Author of _Differential and Integral Calculus with
-      Applications_; _Hydrostatics_; _Notes on Dynamics_; &c.
-
-    Hydromechanics.
-
-  A. H.-S.
-    SIR A. HOUTUM-SCHINDLER, C.I.E.
-
-      General in the Persian Army. Author of _Eastern Persian Irak_.
-
-    Isfahan (_in part_).
-
-  A. M. C.
-    AGNES MARY CLERKE.
-
-      See the biographical article, CLERKE, A. M.
-
-    Huygens, Christiaan.
-
-  A. N.
-    ALFRED NEWTON, F.R.S.
-
-      See the biographical article, NEWTON, ALFRED.
-
-    Ibis;
-    Icterus.
-
-  A. So.
-    ALBRECHT SOCIN, PH.D. (1844-1899).
-
-      Formerly Professor of Semitic Philology in the Universities of
-      Leipzig and Tubingen. Author of _Arabische Grammatik_; &c.
-
-    Irak-Arabi (_in part_).
-
-  A. S. Wo.
-    ARTHUR SMITH WOODWARD, LL.D., F.R.S.
-
-      Keeper of Geology, Natural History Museum, South Kensington.
-      Secretary of the Geological Society, London.
-
-    Ichthyosaurus;
-    Iguanodon.
-
-  A. W. H.*
-    ARTHUR WILLIAM HOLLAND.
-
-      Formerly Scholar of St John's College, Oxford. Bacon Scholar of
-      Gray's Inn, 1900.
-
-    Imperial Cities;
-    Instrument of Government.
-
-  A. W. Po.
-    ALFRED WILLIAM POLLARD, M.A.
-
-      Assistant Keeper of Printed Books, British Museum. Fellow of
-      King's College, London. Hon. Secretary Bibliographical Society.
-      Editor of _Books about Books_ and _Bibliographica_. Joint-editor
-      of The Library. Chief Editor of the "Globe" _Chaucer_.
-
-    Incunabula.
-
-  A. W. R.
-    ALEXANDER WOOD RENTON, M.A., LL.B.
-
-      Puisne judge of the Supreme Court of Ceylon. Editor of
-      _Encyclopaedia of the Laws of England_.
-
-    Inebriety, Law of;
-    Insanity: _Law_.
-
-  C. F. A.
-    CHARLES FRANCIS ATKINSON.
-
-      Formerly Scholar of Queen's College, Oxford. Captain, 1st City of
-      London (Royal Fusiliers). Author of _The Wilderness and Cold
-      Harbour_.
-
-    Infantry;
-    Italian Wars.
-
-  C. G.
-    COLONEL CHARLES GRANT.
-
-      Formerly Inspector of Military Education in India.
-
-    India: _Costume_.
-
-  C. H. Ha.
-    CARLTON HUNTLEY HAYES, A.M., PH.D.
-
-      Assistant Professor of History at Columbia University, New York
-      City. Member of the American Historical Association.
-
-    Innocent V., VIII.
-
-  C. Ll. M.
-    CONWAY LLOYD MORGAN, LL.D., F.R.S.
-
-      Professor of Psychology at the University of Bristol. Principal of
-      University College, Bristol, 1887-1909. Author of _Animal Life and
-      Intelligence_; _Habit and Instinct_.
-
-    Instinct;
-    Intelligence in Animals.
-
-  C. R. B.
-    CHARLES RAYMOND BEAZLEY, M.A., D.LITT., F.R.G.S., F.R.HIST.S.
-
-      Professor of Modern History in the University of Birmingham.
-      Formerly Fellow of Merton College, Oxford; and University Lecturer
-      in the History of Geography. Lothian Prizeman, Oxford, 1889.
-      Lowell Lecturer, Boston, 1908. Author of _Henry the Navigator_;
-      _The Dawn of Modern Geography_; &c.
-
-    Ibn Batuta (_in part_);
-    Idrisi.
-
-  C. S.*
-    CARLO SALVIONI.
-
-      Professor of Classical and Romance Languages, University of Milan.
-
-    Italian Language (_in part_).
-
-  C. T. L.
-    CHARLTON THOMAS LEWIS, PH.D. (1834-1904).
-
-      Formerly Lecturer on Life Insurance, Harvard and Columbia
-      Universities, and on Principles of Insurance, Cornell University.
-      Author of _History of Germany_; _Essays_; _Addresses_; &c.
-
-    Insurance (_in part_).
-
-  C. We.
-    CECIL WEATHERLY.
-
-      Formerly Scholar of Queen's College, Oxford. Barrister-at-Law,
-      Inner Temple.
-
-    Infant Schools.
-
-  D. B. Ma.
-    DUNCAN BLACK MACDONALD, M.A., D.D.
-
-      Professor of Semitic Languages, Hartford Theological Seminary,
-      U.S.A. Author of _Development of Muslim Theology, Jurisprudence
-      and Constitutional Theory_; _Selection from Ibn Khaldum_;
-      _Religious Attitude and Life in Islam_; &c.
-
-    Imam.
-
-  D. G. H.
-    DAVID GEORGE HOGARTH, M.A.
-
-      Keeper of the Ashmolean Museum, Oxford. Fellow of Magdalen
-      College, Oxford. Fellow of the British Academy. Excavated at
-      Paphos, 1888; Naucratis, 1899 and 1903; Ephesus, 1904-1905;
-      Assiut, 1906-1907; Director, British School at Athens, 1897-1900;
-      Director, Cretan Exploration Fund, 1899.
-
-    Ionia (_in part_);
-    Isauria.
-
-  D. H.
-    DAVID HANNAY.
-
-      Formerly British Vice-Consul at Barcelona. Author of _Short
-      History of Royal Navy, 1217-1688_; _Life of Emilio Castelar_; &c.
-
-    Impressment.
-
-  D. F. T.
-    DONALD FRANCIS TOVEY.
-
-      Author of _Essays in Musical Analysis_; comprising _The Classical
-      Concerto_, _The Goldberg Variations_, and analyses of many other
-      classical works.
-
-    Instrumentation.
-
-  D. S. M.
-    DUGALD SUTHERLAND MACCOLL, M.A., LL.D.
-
-      Keeper of the National Gallery of British Art (Tate Gallery).
-      Lecturer on the History of Art, University College, London; Fellow
-      of University College, London. Author of Nineteenth Century Art;
-      &c.
-
-    Impressionism.
-
-  E. A. M.
-    EDWARD ALFRED MINCHIN, M.A., F.Z.S.
-
-      Professor of Protozoology in the University of London. Formerly
-      Fellow of Merton College, Oxford; and Lecturer on Comparative
-      Anatomy in the University of Oxford. Author of "Sponges and
-      Sporozoa" in Lankester's _Treatise on Zoology_; &c.
-
-    Hydromedusae;
-    Hydrozoa.
-
-  E. Br.
-    ERNEST BARKER, M.A.
-
-      Fellow and Lecturer in Modern History, St John's College, Oxford.
-      Formerly Fellow and Tutor of Merton College. Craven Scholar, 1895.
-
-    Imperial Chamber.
-
-  E. Bra.
-    EDWIN BRAMWELL, M.B., F.R.C.P., F.R.S. (Edin.).
-
-      Assistant Physician, Royal Infirmary, Edinburgh.
-
-    Hysteria (_in part_).
-
-  E. C. B.
-    RIGHT REV. EDWARD CUTHBERT BUTLER, O.S.B., D.LITT.
-
-      Abbot of Downside Abbey, Bath. Author of "The Lausiac History of
-      Palladius" in _Cambridge Texts and Studies_.
-
-    Imitation of Christ.
-
-  E. C. Q.
-    EDMUND CROSBY QUIGGIN, M.A.
-
-      Fellow, Lecturer in Modern History, and Monro Lecturer in Celtic,
-      Gonville and Caius College, Cambridge.
-
-    Ireland: _Early History_.
-
-  E. F. S.
-    EDWARD FAIRBROTHER STRANGE.
-
-      Assistant Keeper, Victoria and Albert Museum, South Kensington.
-      Member of Council, Japan Society. Author of numerous works on art
-      subjects. Joint-editor of Bell's "Cathedral" Series.
-
-    Illustration: _Technical Developments_.
-
-  E. F. S. D.
-    LADY DILKE.
-
-      See the biographical article: DILKE, SIR C. W., BART.
-
-    Ingres.
-
-  E. G.
-    EDMUND GOSSE, LL.D.
-
-      See the biographical article, GOSSE, EDMUND.
-
-    Huygens, Sir Constantijn;
-    Ibsen;
-    Idyl.
-
-  E. Hu.
-    EMIL HUBNER.
-
-      See the biographical article, HUBNER, EMIL.
-
-    Inscriptions: _Latin_ (_in part_).
-
-  E. H. B.
-    SIR EDWARD HERBERT BUNBURY, BART., M.A., F.R.G.S. (d. 1895).
-
-      M.P. for Bury St Edmunds, 1847-1852. Author of a _History of
-      Ancient Geography_; &c.
-
-    Ionia (_in part_).
-
-  E. H. M.
-    ELLIS HOVELL MINNS, M.A.
-
-      Lecturer and Assistant Librarian, and formerly Fellow, Pembroke
-      College, Cambridge University Lecturer in Palaeography.
-
-    Iazyges;
-    Issedones.
-
-  E. H. P.
-    EDWARD HENRY PALMER, M.A.
-
-      See the biographical article, PALMER, E. H.
-
-    Ibn Khaldun (_in part_).
-
-  E. K.
-    EDMUND KNECHT, PH.D., M.SC.TECH.(Manchester), F.I.C.
-
-      Professor of Technological Chemistry, Manchester University. Head
-      of Chemical Department, Municipal School of Technology,
-      Manchester. Examiner in Dyeing, City and Guilds of London
-      Institute. Author of _A Manual of Dyeing_; &c. Editor of J_ournal
-      of the Society of Dyers and Colourists_.
-
-    Indigo.
-
-  E. L. H.
-    THE RIGHT REV. THE BISHOP OF LINCOLN (EDWARD LEE HICKS).
-
-      Honorary Fellow of Corpus Christi College, Oxford. Formerly Canon
-      Residentiary of Manchester. Fellow and Tutor of Corpus Christi
-      College. Author of _Manual of Greek Historical Inscriptions_; &c.
-
-    Inscriptions: Greek (_in part_).
-
-  Ed. M.
-    EDUARD MEYER, PH.D., D.LITT.(Oxon.), LL.D.
-
-      Professor of Ancient History in the University of Berlin. Author
-      of _Geschichte des Alterthums_; _Geschichte des alten Aegyptens_;
-      _Die Israeliten und ihre Nachbarstamme_.
-
-    Hystaspes;
-    Iran.
-
-  E. M. T.
-    SIR EDWARD MAUNDE THOMPSON, G.C.B., I.S.O., D.C.L., LITT.D., LL.D.
-
-      Director and Principal Librarian, British Museum, 1898-1909.
-      Sandars Reader in Bibliography, Cambridge, 1895-1896. Hon. Fellow
-      of University College, Oxford. Correspondent of the Institute of
-      France and of the Royal Prussian Academy of Sciences. Author of
-      _Handbook of Greek and Latin Palaeography_. Editor of _Chronicon
-      Angliae_. Joint-editor of publications of the Palaeographical
-      Society, the New Palaeographical Society, and of the Facsimile of
-      the Laurentian Sophocles.
-
-    Illuminated MSS.
-
-  E. O.*
-    EDMUND OWEN, M.B., F.R.C.S., LL.D., D.SC.
-
-      Consulting Surgeon to St Mary's Hospital, London, and to the
-      Children's Hospital, Great Ormond Street; late Examiner in Surgery
-      at the Universities of Cambridge, Durham and London. Author of _A
-      Manual of Anatomy for Senior Students_.
-
-    Hydrocephalus.
-
-  F. A. F.
-    FRANK ALBERT FETTER, PH.D.
-
-      Professor of Political Economy and Finance, Cornell University.
-      Member of the State Board of Charities. Author of _The Principles
-      of Economics_; &c.
-
-    Interstate Commerce.
-
-  F. C. C.
-    FREDERICK CORNWALLIS CONYBEARE, M.A., D.TH.(Giessen).
-
-      Fellow of the British Academy. Formerly Fellow of University
-      College, Oxford. Author of _The Ancient Armenian Texts of
-      Aristotle_; _Myth, Magic and Morals_; &c.
-
-    Iconoclasts;
-    Image Worship.
-
-  F. G. M. B.
-    FREDERICK GEORGE MEESON BECK, M.A.
-
-      Fellow and Lecturer in Classics, Clare College, Cambridge.
-
-    Hwicce.
-
-  F. J. H.
-    FRANCIS JOHN HAVERFIELD, M.A., LL.D., F.S.A.
-
-      Camden Professor of Ancient History in the University of Oxford.
-      Fellow of Brasenose College. Fellow of the British Academy.
-      Formerly Censor, Student, Tutor and Librarian of Christ Church,
-      Oxford. Ford's Lecturer, 1906-1907. Author of Monographs on Roman
-      History, especially Roman Britain; &c.
-
-    Icknield Street.
-
-  F. Ll. G.
-    FRANCIS LLEWELLYN GRIFFITH, M.A., PH.D., F.S.A.
-
-      Reader in Egyptology, Oxford University. Editor of the
-      Archaeological Survey and Archaeological Reports of the Egypt
-      Exploration Fund. Fellow of Imperial German Archaeological
-      Institute.
-
-    Hyksos;
-    Isis.
-
-  F. P.*
-    FREDERICK PETERSON, M.D., PH.D.
-
-      Professor of Psychiatry, Columbia University. President of New
-      York State Commission in Lunacy, 1902-1906. Author of _Mental
-      Diseases_; &c.
-
-    Insanity: _Hospital Treatment._
-
-  F. S. P.
-    FRANCIS SAMUEL PHILBRICK, A.M., PH.D.
-
-      Formerly Fellow of Nebraska State University, and Scholar and
-      Resident Fellow of Harvard University. Member of American
-      Historical Association.
-
-    Independence, Declaration of.
-
-  F. Wa.
-    FRANCIS WATT, M.A.
-
-      Barrister-at-Law, Middle Temple. Author of _Law's Lumber Room_.
-
-    Inn and Innkeeper.
-
-  F. W. R.*
-    FREDERICK WILLIAM RUDLER, I.S.O., F.G.S.
-
-      Curator and Librarian of the Museum of Practical Geology, London,
-      1879-1902. President of the Geologists' Association, 1887-1889.
-
-    Hyacinth
-    Iolite.
-
-  F. Y. P.
-    FREDERICK YORK POWELL, D.C.L., LL.D.
-
-      See the biographical article, POWELL, FREDERICK YORK.
-
-    Iceland: _History_, and _Ancient Literature_.
-
-  G. A. B.
-    GEORGE A. BOULENGER, F.R.S., D.SC., PH.D.
-
-      In charge of the collections of Reptiles and Fishes, Department of
-      Zoology, British Museum. Vice-President of the Zoological Society
-      of London.
-
-    Ichthyology (_in part_).
-
-  G. A. Gr.
-    GEORGE ABRAHAM GRIERSON, C.I.E., PH.D., D.LITT.(Dublin).
-
-      Member of the Indian Civil Service, 1873-1903. In charge of
-      Linguistic Survey of India, 1898-1902. Gold Medallist, Royal
-      Asiatic Society, 1909. Vice-President of the Royal Asiatic
-      Society. Formerly Fellow of Calcutta University. Author of _The
-      Languages of India_; &c.
-
-    Indo-Aryan Languages.
-
-  G. A. J. C.
-    GRENVILLE ARTHUR JAMES COLE.
-
-      Director of the Geological Survey of Ireland. Professor of
-      Geology, Royal College of Science for Ireland, Dublin. Author of
-      _Aids in Practical Geology_; &c.
-
-    Ireland: _Geology_.
-
-  G. B.
-    SIR GEORGE CHRISTOPHER MOLESWORTH BIRDWOOD, K.C.I.E.
-
-      See the biographical article, BIRDWOOD, SIR G. C. M.
-
-    Incense.
-
-  G. F. H.*
-    GEORGE FRANCIS HILL, M.A.
-
-      Assistant in Department of Coins and Medals, British Museum.
-      Author of _Sources for Greek History 478-431_ B.C.; _Handbook of
-      Greek and Roman Coins_; &c.
-
-    Inscriptions: Greek (_in part_).
-
-  G. G. Co.
-    GEORGE GORDON COULTON, M.A.
-
-      Birkbeck Lecturer in Ecclesiastical History, Trinity College,
-      Cambridge. Author of _Medieval Studies_; _Chaucer and his
-      England_; &c.
-
-    Indulgence.
-
-  G. H. C.
-    GEORGE HERBERT CARPENTER, B.SC. (Lond.).
-
-      Professor of Zoology in the Royal College of Science, Dublin.
-      Author of _Insects: their Structure and Life_.
-
-    Hymenoptera;
-    Ichneumon-Fly;
-    Insect.
-
-  G. I. A.
-    GRAZIADIO I. ASCOLI.
-
-      Senator of the Kingdom of Italy. Professor of Comparative Grammar
-      at the University of Milan. Author of _Codice Islandese_; &c.
-
-    Italian Language (_in part_).
-
-  G. J.
-    GEORGE JAMIESON, C.M.G., M.A.
-
-      Formerly Consul-General at Shanghai, and Consul and Judge of the
-      Supreme Court, Shanghai.
-
-    Hwang Ho.
-
-  G. K.
-    GUSTAV KRUGER, PH.D.
-
-      Professor of Church History in the University of Giessen. Author
-      of _Das Papstthum_; &c.
-
-    Irenaeus.
-
-  G. P. M.
-    GEORGE PERCIVAL MUDGE, A.R.C.S., F.Z.S.
-
-      Lecturer on Biology, London Hospital Medical College, and London
-      School of Medicine for Women, University of London. Author of _A
-      Text Book of Zoology_; &c.
-
-    Incubation and Incubators.
-
-  G. W. K.
-    VERY REV. GEORGE WILLIAM KITCHIN, M.A., D.D., F.S.A.
-
-      Dean of Durham, and Warden of the University of Durham. Hon.
-      Student of Christ Church, Oxford. Fellow of King's College,
-      London. Dean of Winchester, 1883-1894. Author of _A History of
-      France_; &c.
-
-    Hutten, Ulrich von.
-
-  G. W. T.
-    REV. GRIFFITHES WHEELER THATCHER, M.A., B.D.
-
-      Warden of Camden College, Sydney, N.S.W. Formerly Tutor in Hebrew
-      and Old Testament History at Mansfield College, Oxford. Author of
-      a _Commentary on Judges_; _An Arabic Grammar_; &c.
-
-    Ibn 'Abd Rabbihi;
-    Ibn 'Arabi;
-    Ibn Athir;
-    Ibn Duraid;
-    Ibn Faradi;
-    Ibn Farid;
-    Ibn Hazm;
-    Ibn Hisham;
-    Ibn Ishaq;
-    Ibn Jubair;
-    Ibn Khaldun (_in part_);
-    Ibn Khallikan;
-    Ibn Qutaiba;
-    Ibn Sa'd;
-    Ibn Tufail;
-    Ibn Usaibi'a;
-    Ibrahim Al-Mausili.
-
-  H. Ch.
-    HUGH CHISHOLM, M.A.
-
-      Formerly Scholar of Corpus Christi College, Oxford. Editor the
-      11th edition of the _Encyclopaedia Britannica_; Co-editor of the
-      10th edition.
-
-    Iron Mask;
-    Ismail.
-
-  H. C. R.
-    SIR HENRY CRESWICKE RAWLINSON, BART., K.C.B.
-
-      See the biographical article, RAWLINSON, SIR HENRY CRESWICKE.
-
-    Isfahan: _History_.
-
-  H. L. H.
-    HARRIET L. HENNESSY, M.D., (Brux.) L.R.C.P.I., L.R.C.S.I.
-
-    Infancy;
-    Intestinal Obstruction.
-
-  H. M. H.
-    HENRY MARION HOWE, A.M., LL.D.
-
-      Professor of Metallurgy, Columbia University. Author of
-      _Metallurgy of Steel_; &c.
-
-    Iron and Steel.
-
-  H. N. D.
-    HENRY NEWTON DICKSON, M.A., D.SC., F.R.G.S.
-
-      Professor of Geography, University College, Reading. Author of
-      _Elementary Meteorology_; _Papers on Oceanography_; &c.
-
-    Indian Ocean.
-
-  H. O.
-    HERMANN OELSNER, M.A., PH.D.
-
-      Taylorian Professor of the Romance Languages in University of
-      Oxford. Member of Council of the Philological Society. Author of
-      _A History of Provencal Literature_; &c.
-
-    Italian Literature (_in part_).
-
-  H. St.
-    HENRY STURT, M.A.
-
-      Author of _Idola Theatri_; _The Idea of a Free Church_; and
-      _Personal Idealism_.
-
-    Induction.
-
-  H. T. A.
-    REV. HERBERT THOMAS ANDREWS.
-
-      Professor of New Testament Exegesis, New College, London. Author
-      of the "Commentary on Acts" in the _Westminster New Testament_;
-      _Handbook on the Apocryphal Books_ in the "Century Bible."
-
-    Ignatius.
-
-  H. Y.
-    SIR HENRY YULE, K.C.S.I., C.B.
-
-      See the biographical article, YULE, SIR HENRY.
-
-    Ibn Batuta (_in part_).
-
-  I. A.
-    ISRAEL ABRAHAMS, M.A.
-
-      Reader in Talmudic and Rabbinic Literature in the University of
-      Cambridge. Formerly President, Jewish Historical Society in
-      England. Author of _A Short History of Jewish Literature_; _Jewish
-      Life in the Middle Ages_; &c.
-
-    Ibn Tibbon;
-    Immanuel Ben Solomon.
-
-  J. A. F.
-    JOHN AMBROSE FLEMING, M.A., F.R.S., D.SC.
-
-      Pender Professor of Electrical Engineering in the University of
-      London. Fellow of University College, London. Formerly Fellow of
-      St John's College, Cambridge, and Lecturer on Applied Mechanics in
-      the University. Author of _Magnets and Electric Currents_.
-
-    Induction Coil.
-
-  J. Bs.
-    JAMES BURGESS, C.I.E., LL.D., F.R.S.(Edin.), F.R.G.S.,
-    HON.A.R.I.B.A.
-
-      Formerly Director General of Archaeological Survey of India.
-      Author of _Archaeological Survey of Western India_. Editor of
-      Fergusson's _History of Indian Architecture_.
-
-    Indian Architecture.
-
-  J. B. T.
-    SIR JOHN BATTY TUKE, KT., M.D., F.R.S.(Edin.), D.SC., LL.D.
-
-      President of the Neurological Society of the United Kingdom.
-      Medical Director of New Saughton Hall Asylum, Edinburgh. M.P. for
-      the Universities of Edinburgh and St Andrews, 1900-1910.
-
-    Hysteria (_in part_);
-    Insanity: _Medical._
-
-  J. C. H.
-    RIGHT REV. JOHN CUTHBERT HEDLEY, O.S.B., D.D.
-
-      R.C. Bishop of Newport. Author of _The Holy Eucharist_; &c.
-
-    Immaculate Conception.
-
-  J. C. Van D.
-    JOHN CHARLES VAN DYKE.
-
-      Professor of the History of Art, Rutgers College, New Brunswick,
-      N.J. Formerly Editor of _The Studio and Art Review_. Author of
-      _Art for Art's Sake_; _History of Painting_; _Old English
-      Masters_; &c.
-
-    Inness, George.
-
-  J. C. W.
-    JAMES CLAUDE WEBSTER.
-
-      Barrister-at-Law, Middle Temple.
-
-    Inns of Court.
-
-  J. D. B.
-    JAMES DAVID BOURCHIER, M.A., F.R.G.S.
-
-      King's College, Cambridge. Correspondent of _The Times_ in
-      South-Eastern Europe. Commander of the Orders of Prince Danilo of
-      Montenegro and of the Saviour of Greece, and Officer of the Order
-      of St Alexander of Bulgaria.
-
-    Ionian Islands.
-
-  J. F. F.
-    JOHN FAITHFULL FLEET, C.I.E., PH.D.
-
-      Commissioner of Central and Southern Divisions of Bombay,
-      1891-1897. Author of _Inscriptions of the Early Gupta Kings_; &c.
-
-    Inscriptions: _Indian_.
-
-  J. F.-K.
-    JAMES FITZMAURICE-KELLY, LITT.D., F.R.HIST.S.
-
-      Gilmour Professor of Spanish Language and Literature, Liverpool
-      University. Norman McColl Lecturer, Cambridge University. Fellow
-      of the British Academy. Member of the Royal Spanish Academy.
-      Knight Commander of the Order of Alphonso XII. Author of A History
-      of Spanish Literature; &c.
-
-    Isla, J. F. de.
-
-  J. G. K.
-    JOHN GRAHAM KERR, M.A., F.R.S.
-
-      Regius Professor of Zoology in the University of Glasgow. Formerly
-      Demonstrator in Animal Morphology in the University of Cambridge.
-      Fellow of Christ's College, Cambridge, 1898-1904. Walsingham
-      Medallist, 1898. Neill Prizeman, Royal Society of Edinburgh, 1904.
-
-    Ichthyology (_in part_).
-
-  J. G. Sc.
-    SIR JAMES GEORGE SCOTT, K.C.I.E.
-
-      Superintendent and Political Officer, Southern Shan States. Author
-      of _Burma, a Handbook_; _The Upper Burma Gazetteer_; &c.
-
-    Irrawaddy.
-
-  J. H. A. H.
-    JOHN HENRY ARTHUR HART, M.A.
-
-      Fellow, Theological Lecturer and Librarian, St John's College,
-      Cambridge.
-
-    Hyrcanus.
-
-  J. H. Mu.
-    JOHN HENRY MUIRHEAD, M.A., LL.D.
-
-      Professor of Philosophy in the University of Birmingham. Author of
-      _Elements of Ethics_; _Philosophy and Life_; &c. Editor of
-      _Library of Philosophy_.
-
-    Idealism.
-
-  J. H. Be.
-    VERY REV. JOHN HENRY BERNARD, M.A., D.D., D.C.L.
-
-      Dean of St Patrick's Cathedral, Dublin. Archbishop King's
-      Professor of Divinity and formerly Fellow of Trinity College,
-      Dublin. Joint-editor of the Irish _Liber Hymnorum_; &c.
-
-    Ireland, Church of.
-
-  J. H. van't H.
-    JACOBUS HENRICUS VAN'T HOFF, LL.D., D.SC., D.M.
-
-      See the biographical article VAN'T HOFF, JACOBUS HENRICUS.
-
-    Isomerism.
-
-  J. L. M.
-    JOHN LYNTON MYRES, M.A., F.S.A., F.R.G.S.
-
-      Wykeham Professor of Ancient History in the University of Oxford.
-      Formerly Gladstone Professor of Greek and Lecturer in Ancient
-      Geography, University of Liverpool. Lecturer in Classical
-      Archaeology in University of Oxford.
-
-    Iberians;
-    Ionians.
-
-  J. Mn.
-    JOHN MACPHERSON, M.D.
-
-      Formerly Inspector-General of Hospitals, Bengal.
-
-    Insanity: _Medical_ (_in part_).
-
-  J. M. A. de L.
-    JEAN MARIE ANTOINE DE LANESSAN.
-
-      See the biographical article, LANESSAN, J. M. A. DE.
-
-    Indo-China, French (_in part_).
-
-  J. M. M.
-    JOHN MALCOLM MITCHELL.
-
-      Sometime Scholar of Queen's College, Oxford. Lecturer in Classics,
-      East London College (University of London). Joint-editor of
-      Grote's _History of Greece_.
-
-    Hyacinthus.
-
-  J. P. E.
-    JEAN PAUL HIPPOLYTE EMMANUEL ADHEMAR ESMEIN.
-
-      Professor of Law in the University of Paris. Officer of the Legion
-      of Honour. Member of the Institute of France. Author of _Cours
-      elementaire d'histoire du droit francais_; &c.
-
-    Intendant.
-
-  J. P. Pe.
-    REV. JOHN PUNNETT PETERS, PH.D., D.D.
-
-      Canon Residentiary, Cathedral of New York. Formerly Professor of
-      Hebrew in the University of Pennsylvania. Director of the
-      University Expedition to Babylonia, 1888-1895. Author of _Nippur,
-      or Explorations and Adventures on the Euphrates_.
-
-    Irak-Arabi (_in part_).
-
-  J. S. Bl.
-    JOHN SUTHERLAND BLACK, M.A., LL.D.
-
-      Assistant Editor of the 9th edition of the _Encyclopaedia
-      Britannica_. Joint-editor of the _Encyclopaedia Biblica_.
-
-    Huss, John.
-
-  J. S. Co.
-    JAMES SUTHERLAND COTTON, M.A.
-
-      Editor of the _Imperial Gazetteer of India_. Hon. Secretary of the
-      Egyptian Exploration Fund. Formerly Fellow and Lecturer of Queen's
-      College, Oxford. Author of _India_; &c.
-
-    India: _Geography and Statistics (in part); History (in part)_;
-    Indore.
-
-  J. S. F.
-    JOHN SMITH FLETT, D.SC., F.G.S.
-
-      Petrographer to the Geological Survey. Formerly Lecturer on
-      Petrology in Edinburgh University. Neill Medallist of the Royal
-      Society of Edinburgh. Bigsby Medallist of the Geological Society
-      of London.
-
-    Itacolumite.
-
-  J. T. Be.
-    John Thomas Bealby.
-
-      Joint-author of Stanford's _Europe_. Formerly Editor of the
-      _Scottish Geographical Magazine_. Translator of Sven Hedin's
-      _Through Asia, Central Asia and Tibet_; &c.
-
-    Irkutsk (_in part_).
-
-  J. V.*
-    JULES VIARD.
-
-      Archivist at the National Archives, Paris. Officer of Public
-      Instruction. Author of _La France sous Philippe VI. de Valois_;
-      &c.
-
-    Isabella of Bavaria.
-
-  Jno. W.
-    JOHN WESTLAKE, K.C., LL.D.
-
-      Professor of International Law, Cambridge, 1888-1908. One of the
-      Members for the United Kingdom of International Court of
-      Arbitration under the Hague Convention, 1900-1906. Bencher of
-      Lincoln's Inn. Author of _A Treatise on Private International Law,
-      or the Conflict of Laws: Chapters on the Principles of
-      International Law_, pt. i. "Peace," pt. ii. "War."
-
-    International Law: _Private_.
-
-  L.
-    COUNT LUTZOW, LITT.D. (OXON.), PH.D. (PRAGUE), F.R.G.S.
-
-      Chamberlain of H.M. the Emperor of Austria, King of Bohemia. Hon.
-      Member of the Royal Society of Literature. Member of the Bohemian
-      Academy; &c. Author of _Bohemia, a Historical Sketch_; _The
-      Historians of Bohemia_ (Ilchester Lecture, Oxford, 1904); _The
-      Life and Times of John Hus_; &c.
-
-    Hussites.
-
-  L. C. B.
-    LEWIS CAMPBELL BRUCE, M.D., F.R.C.P.
-
-      Author of _Studies in Clinical Psychiatry_.
-
-    Insanity: _Medical_ (_in part_).
-
-  L. Ho.
-    LAURENCE HOUSMAN.
-
-      See the biographical article, HOUSMAN, L.
-
-    Illustration (_in part_).
-
-  L. J. S.
-    LEONARD JAMES SPENCER, M.A.
-
-      Assistant in Department of Mineralogy, British Museum. Formerly
-      Scholar of Sidney Sussex College, Cambridge, and Harkness Scholar.
-      Editor of the _Mineralogical Magazine_.
-
-    Hypersthene;
-    Ilmenite.
-
-  L. T. D.
-    SIR LEWIS TONNA DIBDIN, M.A., D.C.L., F.S.A.
-
-      Dean of the Arches; Master of the Faculties; and First Church
-      Estates Commissioner. Bencher of Lincoln's Inn. Author of
-      _Monasticism in England_; &c.
-
-    Incense: _Ritual Use._
-
-  M. Ha.
-    MARCUS HARTOG, M.A., D.SC., F.L.S.
-
-      Professor of Zoology, University College, Cork. Author of
-      "Protozoa" in _Cambridge Natural History_; and papers for various
-      scientific journals.
-
-    Infusoria.
-
-  M. Ja.
-    MORRIS JASTROW, JUN., PH.D.
-
-      Professor of Semitic Languages, University of Pennsylvania, U.S.A.
-      Author of _Religion of the Babylonians and Assyrians_; &c.
-
-    Ishtar.
-
-  M. O. B. C.
-    MAXIMILIAN OTTO BISMARCK CASPARI, M.A.
-
-      Reader in Ancient History at London University. Lecturer in Greek
-      at Birmingham University, 1905-1908.
-
-    Irene (752-803).
-
-  N. M.
-    NORMAN MCLEAN, M.A.
-
-      Fellow, Lecturer and Librarian of Christ's College, Cambridge.
-      University Lecturer in Aramaic. Examiner for the Oriental
-      Languages Tripos and the Theological Tripos at Cambridge.
-
-    Isaac of Antioch.
-
-  O. J. R. H.
-    OSBERT JOHN RADCLIFFE HOWARTH, M.A.
-
-      Christ Church, Oxford. Geographical Scholar, 1901. Assistant
-      Secretary of the British Association.
-
-    Ireland: _Geography_.
-
-  P. A.
-    PAUL DANIEL ALPHANDERY.
-
-      Professor of the History of Dogma, Ecole pratique des hautes
-      etudes, Sorbonne, Paris. Author of _Les Idees morales chez les
-      heterodoxes latines au debut du XIII^e. siecle_.
-
-    Inquisition.
-
-  P. A. K.
-    PRINCE PETER ALEXEIVITCH KROPOTKIN.
-
-      See the biographical article, KROPOTKIN, PRINCE P. A.
-
-    Irkutsk (_in part_).
-
-  P. C. M.
-    PETER CHALMERS MITCHELL, M.A., F.R.S., F.Z.S., D.SC., LL.D.
-
-      Secretary to the Zoological Society of London. University
-      Demonstrator in Comparative Anatomy and Assistant to Linacre
-      Professor at Oxford, 1888-1891. Examiner in Zoology to the
-      University of London, 1903. Author of _Outlines of Biology_; &c.
-
-    Hybridism.
-
-  P. Gi.
-    PETER GILES, M.A., LL.D., LITT.D.
-
-      Fellow and Classical Lecturer of Emmanuel College, Cambridge, and
-      University Reader in Comparative Philology. Formerly Secretary of
-      the Cambridge Philological Society. Author of _Manual of
-      Comparative Philology_; &c.
-
-    I;
-    Indo-European Languages.
-
-  P. Sm.
-    PRESERVED SMITH, PH.D.
-
-      Rufus B. Kellogg Fellow, Amherst College, Amherst, Mass.
-
-    Innocent I., II.
-
-  R.
-    THE RIGHT HON. LORD RAYLEIGH.
-
-      See the biographical article, RAYLEIGH, 3RD BARON.
-
-    Interference of Light.
-
-  R. A. S. M.
-    ROBERT ALEXANDER STEWART MACALISTER, M.A., F.S.A.
-
-      St John's College, Cambridge. Director of Excavations for the
-      Palestine Exploration Fund.
-
-    Idumaea.
-
-  R. Ba.
-    RICHARD BAGWELL, M.A., LL.D.
-
-      Commissioner of National Education for Ireland. Author of _Ireland
-      under the Tudors_; _Ireland under the Stuarts_.
-
-    Ireland: _Modern History_.
-
-  R. C. J.
-    SIR RICHARD CLAVERHOUSE JEBB, D.C.L., LL.D.
-
-      See the biographical article, JEBB, SIR RICHARD CLAVERHOUSE.
-
-    Isaeus;
-    Isocrates.
-
-  R. G.
-    RICHARD GARNETT. LL.D.
-
-      See the biographical article, GARNETT, RICHARD.
-
-    Irving, Washington.
-
-  R. H. C.
-    REV. ROBERT HENRY CHARLES, M.A., D.D., D.LITT.
-
-      Grinfield Lecturer, and Lecturer in Biblical Studies, Oxford.
-      Fellow of the British Academy. Formerly Professor of Biblical
-      Greek, Trinity College, Dublin. Author of _Critical History of the
-      Doctrine of a Future Life_; _Book of Jubilees_; &c.
-
-    Isaiah, Ascension of.
-
-  R. L.*
-    RICHARD LYDEKKER, F.R.S., F.Z.S., F.G.S.
-
-      Member of the Staff of the Geological Survey of India 1874-1882.
-      Author of _Catalogues of Fossil Mammals, Reptiles and Birds in the
-      British Museum_; _The Deer of all Lands_; &c.
-
-    Hyracoidea;
-    Ibex (_in part_);
-    Indri;
-    Insectivora.
-
-  R. P. S.
-    R. PHENE SPIERS, F.S.A., F.R.I.B.A.
-
-      Formerly Master of the Architectural School, Royal Academy,
-      London. Past President of Architectural Association. Associate and
-      Fellow of King's College, London. Corresponding Member of the
-      Institute of France. Editor of Fergusson's _History of
-      Architecture_. Author of _Architecture; East and West_; &c.
-
-    Hypaethros.
-
-  R. S. C.
-    ROBERT SEYMOUR CONWAY, M.A., D.LITT.(CANTAB.).
-
-      Professor of Latin and Indo-European Philology in the University
-      of Manchester. Formerly Professor of Latin in University College,
-      Cardiff; and Fellow of Gonville and Caius College, Cambridge.
-      Author of _The Italic Dialects_.
-
-    Iguvium;
-    Iovilae.
-
-  S.
-    THE RIGHT HON. THE EARL OF SELBORNE.
-
-      See the biographical article, SELBORNE, 1ST EARL OF.
-
-    Hymns.
-
-  R. Tr.
-    ROLAND TRUSLOVE, M.A.
-
-      Formerly Scholar of Christ Church, Oxford. Dean, Fellow and
-      Lecturer in Classics at Worcester College, Oxford.
-
-    Indo-China, French (_in part_).
-
-  S. A. C.
-    STANLEY ARTHUR COOK, M.A.
-
-      Lecturer in Hebrew and Syriac, and formerly Fellow, Gonville and
-      Caius College, Cambridge. Editor for Palestine Exploration Fund.
-      Author of _Glossary of Aramaic Inscriptions_; _The Laws of Moses
-      and the Code of Hammurabi_; _Critical Notes on Old Testament
-      History_; _Religion of Ancient Palestine_; &c.
-
-    Ishmael.
-
-  S. Bl.
-    SIGFUS BLONDAL.
-
-      Librarian of the University of Copenhagen.
-
-    Iceland: _Recent Literature_.
-
-  T. As.
-    THOMAS ASHBY, M.A., D.LITT. (Oxon.).
-
-      Director of British School of Archaeology at Rome. Formerly
-      Scholar of Christ Church, Oxford. Craven Fellow, 1897. Conington
-      Prizeman, 1906. Member of the Imperial German Archaeological
-      Institute.
-
-    Interamna Lirenas;
-    Ischia.
-
-  T. A. I.
-    THOMAS ALLAN INGRAM, M.A., LL.D.
-
-      Trinity College, Dublin.
-
-    Illegitimacy;
-    Insurance (_in part_).
-
-  T. Ba.
-    SIR THOMAS BARCLAY, M.P.
-
-      Member of the Institute of International Law. Member of the
-      Supreme Council of the Congo Free State. Officer of the Legion of
-      Honour. Author of _Problems of International Practice and
-      Diplomacy_; &c. M.P. for Blackburn, 1910.
-
-    Immunity;
-    International Law.
-
-  T. F.
-    REV. THOMAS FOWLER, M.A., D.D., LL.D. (1832-1904).
-
-      President of Corpus Christi College, Oxford, 1881-1904. Honorary
-      Fellow of Lincoln College. Professor of Logic, 1873-1888.
-      Vice-Chancellor of the University of Oxford, 1899-1901. Author of
-      _Elements of Deductive Logic_; _Elements of Inductive Logic_;
-      _Locke_ ("English Men of Letters"); _Shaftesbury and Hutcheson_
-      ("English Philosophers"); &c.
-
-    Hutcheson, Francis (_in part_).
-
-  T. F. C.
-    THEODORE FREYLINGHUYSEN COLLIER, PH.D.
-
-      Assistant Professor of History, Williams College, Williamstown,
-      Mass., U.S.A.
-
-    Innocent IX.-XIII.
-
-  T. H. H.*
-    COLONEL SIR THOMAS HUNGERFORD HOLDICH, K.C.M.G., K.C.I.E.,
-    HON.D.SC.
-
-      Superintendent, Frontier Surveys, India, 1892-1898. Gold
-      Medallist, R.G.S., London, 1887. Author of _The Indian
-      Borderland_; _The Countries of the King's Award_; _India_;
-      _Tibet_; &c.
-
-    Indus.
-
-  T. K. C.
-    REV. THOMAS KELLY CHEYNE, D.D.
-
-      See the biographical article, CHEYNE, T. K.
-
-    Isaiah.
-
-  Th. T.
-    THORVALDUR THORODDSEN.
-
-      Icelandic Expert and Explorer. Honorary Professor in the
-      University of Copenhagen. Author of _History of Icelandic
-      Geography_; _Geological Map of Iceland_; &c.
-
-    Iceland: _Geography and Statistics_.
-
-  W. A. B. C.
-    REV. WILLIAM AUGUSTUS BREVOORT COOLIDGE, M.A., F.R.G.S.,
-    PH.D.(Bern).
-
-      Fellow of Magdalen College, Oxford. Professor of English History,
-      St David's College, Lampeter, 1880-1881. Author of _Guide du Haut
-      Dauphine_; _The Range of the Todi_; _Guide to Grindelwald_; _Guide
-      to Switzerland_; _The Alps in Nature and in History_; &c. Editor
-      of _The Alpine Journal_, 1880-1881; &c.
-
-    Hyeres;
-    Innsbruck;
-    Interlaken;
-    Iseo, Lake of;
-    Isere (_River_);
-    Isere (_Department_).
-
-  W. A. P.
-    WALTER ALISON PHILLIPS, M.A.
-
-      Formerly Exhibitioner of Merton College and Senior Scholar of St
-      John's College, Oxford. Author of _Modern Europe_; &c.
-
-    Innocent III., IV.
-
-  W. C. U.
-    WILLIAM CAWTHORNE UNWIN, LL.D., F.R.S., M.INST.C.E., M.INST.M.E.,
-    A.R.I.B.A.
-
-      Emeritus Professor, Central Technical College, City and Guilds of
-      London Institute. Author of _Wrought Iron Bridges and Roofs_;
-      _Treatise on Hydraulics_; &c.
-
-    Hydraulics.
-
-  W. F. C.
-    WILLIAM FEILDEN CRAIES, M.A.
-
-      Barrister-at-Law, Inner Temple. Lecturer on Criminal Law, King's
-      College, London. Editor of Archbold's _Criminal Pleading_ (23rd
-      edition).
-
-    Indictment.
-
-  W. F. Sh.
-    WILLIAM FLEETWOOD SHEPPARD, M.A.
-
-      Senior Examiner in the Board of Education, London. Formerly Fellow
-      of Trinity College, Cambridge. Senior Wrangler, 1884.
-
-    Interpolation.
-
-  W. G.
-    WILLIAM GARNETT, M.A., D.C.L.
-
-      Educational Adviser to the London County Council. Formerly Fellow
-      and Lecturer of St John's College, Cambridge. Principal and
-      Professor of Mathematics, Durham College of Science,
-      Newcastle-on-Tyne. Author of _Elementary Dynamics_; &c.
-
-    Hydrometer.
-
-  W. Go.
-    WILLIAM GOW, M.A., PH.D.
-
-      Secretary of the British and Foreign Marine Insurance Co. Ltd.,
-      Liverpool. Lecturer on Marine Insurance at University College,
-      Liverpool. Author of _Marine Insurance_; &c.
-
-    Insurance: _Marine_.
-
-  W. H. F.
-    SIR WILLIAM HENRY FLOWER, F.R.S.
-
-      See the biographical article, FLOWER, SIR W. H.
-
-    Ibex (_in part_).
-
-  W. H. Po.
-    W. HALDANE PORTER.
-
-      Barrister-at-Law, Middle Temple.
-
-    Ireland: _Statistics and Administration_.
-
-  W. Ma.
-    SIR WILLIAM MARKBY, K.C.I.E.
-
-      See the biographical article, MARKBY, SIR WILLIAM.
-
-    Indian Law.
-
-  W. McD.
-    WILLIAM MCDOUGALL, M.A.
-
-      Wilde Reader in Mental Philosophy in the University of Oxford.
-      Formerly Fellow of St John's College, Cambridge.
-
-    Hypnotism.
-
-  W. M. L.
-    WALLACE MARTIN LINDSAY, M.A., LITT.D., LL.D.
-
-      Professor of Humanity, University of St Andrews. Fellow of the
-      British Academy. Formerly Fellow of Jesus College, Oxford. Author
-      of _Handbook of Latin Inscriptions_; _The Latin Language_; &c.
-
-    Inscriptions: _Latin_ (_in part_).
-
-  W. M. Ra.
-    SIR WILLIAM MITCHELL RAMSAY, LITT.D., D.C.L.
-
-      See the biographical article, RAMSAY, SIR W. MITCHELL.
-
-    Iconium.
-
-  W. R. So.
-    WILLIAM RITCHIE SORLEY, M.A., LITT.D., LL.D.
-
-      Professor of Moral Philosophy in the University of Cambridge.
-      Fellow of King's College, Cambridge. Fellow of the British
-      Academy. Formerly Fellow of Trinity College. Author of _The Ethics
-      of Naturalism_; _The Interpretation of Evolution_; &c.
-
-    Iamblichus.
-
-  W. T. T.-D.
-    SIR WILLIAM TURNER THISELTON-DYER, F.R.S., K.C.M.G., C.I.E.,
-    D.SC., LL.D., PH.D., F.L.S.
-
-      Hon. Student of Christ Church, Oxford. Director, Royal Botanic
-      Gardens, Kew, 1885-1905. Botanical Adviser to Secretary of State
-      for Colonies, 1902-1906. Joint-author of _Flora of Middlesex_.
-      Editor of _Flora Capenses_ and _Flora of Tropical Africa_.
-
-    Huxley.
-
-  W. Wn.
-    WILLIAM WATSON, D.SC., F.R.S., A.R.C.S.
-
-      Assistant Professor of Physics, Royal College of Science, London.
-      Vice-President of the Physical Society. Author of _A Text Book of
-      Practical Physics_; &c.
-
-    Inclinometer.
-
-  W. W. H.
-    SIR WILLIAM WILSON HUNTER.
-
-      See the biographical article. HUNTER, SIR WILLIAM WILSON.
-
-    India: _History (in part); Geography and Statistics (in part)._
-
-
-
-
-  PRINCIPAL UNSIGNED ARTICLES
-
-  Husband and Wife.   Image.           Ink.
-  Hyacinth.           Impeachment.     Inkerman.
-  Hyderabad.          Income Tax.      International, The.
-  Hydrogen.           Indiana.         Intestacy.
-  Hydropathy.         Indian Mutiny.   Inverness-shire.
-  Hydrophobia.        Indicator.       Investiture.
-  Ice.                Infant.          Iodine.
-  Ice-Yachting.       Infanticide.     Iowa.
-  Idaho.              Infinite.        Ipecacuanha.
-  Illinois.           Influenza.       Iris.
-  Illumination.       Inheritance.     Iron.
-  Illyria.            Injunction.      Irrigation.
-
-
-FOOTNOTE:
-
-  [1] A complete list, showing all individual contributors, appears in
-    the final volume.
-
-
-
-
-  ENCYCLOPAEDIA BRITANNICA
-
-  ELEVENTH EDITION
-
-  VOLUME XIV
-
-
-
-
-HUSBAND, properly the "head of a household," but now chiefly used in the
-sense of a man legally joined by marriage to a woman, his "wife"; the
-legal relations between them are treated below under HUSBAND AND WIFE.
-The word appears in O. Eng. as _husbonda_, answering to the Old
-Norwegian _husbondi_, and means the owner or freeholder of a _hus_, or
-house. The last part of the word still survives in "bondage" and
-"bondman," and is derived from _bua_, to dwell, which, like Lat.
-_colere_, means also to till or cultivate, and to have a household.
-"Wife," in O. Eng. _wif_, appears in all Teutonic languages except
-Gothic; cf. Ger. _Weib_, Dutch _wijf_, &c., and meant originally simply
-a female, "woman" itself being derived from _wifman_, the pronunciation
-of the plural _wimmen_ still preserving the original _i_. Many
-derivations of "wife" have been given; thus it has been connected with
-the root of "weave," with the Gothic _waibjan_, to fold or wrap up,
-referring to the entangling clothes worn by a woman, and also with the
-root of _vibrare_, to tremble. These are all merely guesses, and the
-ultimate history of the word is lost. It does not appear outside
-Teutonic languages. Parallel to "husband" is "housewife," the woman
-managing a household. The earlier _huswif_ was pronounced _hussif_, and
-this pronunciation survives in the application of the word to a small
-case containing scissors, needles and pins, cottons, &c. From this form
-also derives "hussy," now only used in a depreciatory sense of a light,
-impertinent girl. Beyond the meaning of a husband as a married man, the
-word appears in connexion with agriculture, in "husbandry" and
-"husbandman." According to some authorities "husbandman" meant
-originally in the north of England a holder of a "husbandland," a
-manorial tenant who held two ox-gangs or virgates, and ranked next below
-the yeoman (see J. C. Atkinson in _Notes and Queries_, 6th series, vol.
-xii., and E. Bateson, _History of Northumberland_, ii., 1893). From the
-idea of the manager of a household, "husband" was in use transferred to
-the manager of an estate, and the title was held by certain officials,
-especially in the great trading companies. Thus the "husband" of the
-East India Company looked after the interests of the company at the
-custom-house. The word in this sense is practically obsolete, but it
-still appears in "ship's husband," an agent of the owners of a ship who
-looks to the proper equipping of the vessel, and her repairs, procures
-and adjusts freights, keeps the accounts, makes charter-parties and acts
-generally as manager of the ship's employment. Where such an agent is
-himself one of the owners of the vessel, the name of "managing owner" is
-used. The "ship's husband" or "managing owner" must register his name
-and address at the port of registry (Merchant Shipping Act 1894, S 59).
-From the use of "husband" for a good and thrifty manager of a household,
-the verb "to husband" means to economize, to lay up a store, to save.
-
-
-
-
-HUSBAND AND WIFE, LAW RELATING TO. For the modes in which the relation
-of husband and wife may be constituted and dissolved, see MARRIAGE and
-DIVORCE. The present article will deal only with the effect of marriage
-on the legal position of the spouses. The person chiefly affected is the
-wife, who probably in all political systems becomes subject, in
-consequence of marriage, to some kind of disability. The most favourable
-system scarcely leaves her as free as an unmarried woman; and the most
-unfavourable subjects her absolutely to the authority of her husband. In
-modern times the effect of marriage on property is perhaps the most
-important of its consequences, and on this point the laws of different
-states show wide diversity of principles.
-
-The history of Roman law exhibits a transition from an extreme theory to
-its opposite. The position of the wife in the earliest Roman household
-was regulated by the law of _Manus_. She fell under the "hand" of her
-husband,--became one of his family, along with his sons and daughters,
-natural or adopted, and his slaves. The dominion which, so far as the
-children was concerned, was known as the _patria potestas_, was, with
-reference to the wife, called the _manus_. The subject members of the
-family, whether wife or children, had, broadly speaking, no rights of
-their own. If this institution implied the complete subjection of the
-wife to the husband, it also implied a much closer bond of union between
-them than we find in the later Roman law. The wife on her husband's
-death succeeded, like the children, to freedom and a share of the
-inheritance. _Manus_, however, was not essential to a legal marriage;
-its restraints were irksome and unpopular, and in course of time it
-ceased to exist, leaving no equivalent protection of the stability of
-family life. The later Roman marriage left the spouses comparatively
-independent of each other. The distance between the two modes of
-marriage may be estimated by the fact that, while under the former
-the wife was one of the husband's immediate heirs, under the latter she
-was called to the inheritance only after his kith and kin had been
-exhausted, and only in preference to the treasury. It seems doubtful how
-far she had, during the continuance of marriage, a legal right to
-enforce aliment from her husband, although if he neglected her she had
-the unsatisfactory remedy of an easy divorce. The law, in fact,
-preferred to leave the parties to arrange their mutual rights and
-obligations by private contracts. Hence the importance of the law of
-settlements (_Dotes_). The _Dos_ and the _Donatio ante nuptias_ were
-settlements by or on behalf of the husband or wife, during the
-continuance of the marriage, and the law seems to have looked with some
-jealousy on gifts made by one to the other in any less formal way, as
-possibly tainted with undue influence. During the marriage the husband
-had the administration of the property.
-
-The _manus_ of the Roman law appears to be only one instance of an
-institution common to all primitive societies. On the continent of
-Europe after many centuries, during which local usages were brought
-under the influence of principles derived from the Roman law, a theory
-of marriage became established, the leading feature of which is the
-_community of goods_ between husband and wife. Describing the principle
-as it prevails in France, Story (_Conflict of Laws_, S 130) says: "This
-community or nuptial partnership (in the absence of any special
-contract) generally extends to all the movable property of the husband
-and wife, and to the fruits, income and revenue thereof.... It extends
-also to all immovable property of the husband and wife acquired during
-the marriage, but not to such immovable property as either possessed at
-the time of the marriage, or which came to them afterwards by title of
-succession or by gift. The property thus acquired by this nuptial
-partnership is liable to the debts of the parties existing at the time
-of the marriage; to the debts contracted by the husband during the
-community, or by the wife during the community with the consent of the
-husband; and to debts contracted for the maintenance of the family....
-The husband alone is entitled to administer the property of the
-community, and he may alien, sell or mortgage it without the concurrence
-of the wife." But he cannot dispose by will of more than his share of
-the common property, nor can he part with it gratuitously _inter vivos_.
-The community is dissolved by death (natural or civil), divorce,
-separation of body or separation of property. On separation of body or
-of property the wife is entitled to the full control of her movable
-property, but cannot alien her immovable property, without her husband's
-consent or legal authority. On the death of either party the property is
-divided in equal moieties between the survivor and the heirs of the
-deceased.
-
-_Law of England._--The English common law as usual followed its own
-course in dealing with this subject, and in no department were its rules
-more entirely insular and independent. The text writers all assumed two
-fundamental principles, which between them established a system of
-rights totally unlike that just described. Husband and wife were said to
-be one person in the eye of the law--_unica persona, quia caro una et
-sanguis unus_. Hence a man could not grant or give anything to his wife,
-because she was himself, and if there were any compacts between them
-before marriage they were dissolved by the union of persons. Hence, too,
-the old rule of law, now greatly modified, that husband and wife could
-not be allowed to give evidence against each other, in any trial, civil
-or criminal. The unity, however, was one-sided only; it was the wife who
-was merged in the husband, not the husband in the wife. And when the
-theory did not apply, the disabilities of "coverture" suspended the
-active exercise of the wife's legal faculties. The old technical
-phraseology described husband and wife as _baron_ and _feme_; the rights
-of the husband were baronial rights. From one point of view the wife was
-merged in the husband, from another she was as one of his vassals. A
-curious example is the immunity of the wife in certain cases from
-punishment for crime committed in the presence and on the presumed
-coercion of the husband. "So great a favourite," says Blackstone, "is
-the female sex of the laws of England."
-
-The application of these principles with reference to the property of
-the wife, and her capacity to contract, may now be briefly traced.
-
-The _freehold property_ of the wife became vested in the husband and
-herself during the coverture, and he had the management and the profits.
-If the wife had been in actual possession at any time during the
-marriage of an estate of inheritance, and if there had been a child of
-the marriage capable of inheriting, then the husband became entitled on
-his wife's death to hold the estate for his own life as tenant by the
-_curtesy of England_ (_curialitas_).[1] Beyond this, however, the
-husband's rights did not extend, and the wife's heir at last succeeded
-to the inheritance. The wife could not part with her real estate without
-the concurrence of the husband; and even so she must be examined apart
-from her husband, to ascertain whether she freely and voluntarily
-consented to the deed.
-
-With regard to personal property, it passed absolutely at common law to
-the husband. Specific things in the possession of the wife (_choses_ in
-possession) became the property of the husband at once; things not in
-possession, but due and recoverable from others (_choses_ in action),
-might be recovered by the husband. A _chose_ in action not reduced into
-actual possession, when the marriage was dissolved by death, reverted to
-the wife if she was the survivor; if the husband survived he could
-obtain possession by taking out letters of administration. A _chose_ in
-action was to be distinguished from a specific thing which, although the
-property of the wife, was for the time being in the hands of another. In
-the latter case the property was in the wife, and passed at once to the
-husband; in the former the wife had a mere _jus in personam_, which the
-husband might enforce if he chose, but which was still capable of
-reverting to the wife if the husband died without enforcing it.
-
-The _chattels real_ of the wife (i.e., personal property, dependent on,
-and partaking of, the nature of realty, such as leaseholds) passed to
-the husband, subject to the wife's right of survivorship, unless barred
-by the husband by some act done during his life. A disposition by will
-did not bar the wife's interest; but any disposition _inter vivos_ by
-the husband was valid and effective.
-
-The courts of equity, however, greatly modified the rules of the common
-law by the introduction of the wife's _separate estate_, i.e. property
-settled to the wife for her separate use, independently of her husband.
-The principle seems to have been originally admitted in a case of actual
-separation, when a fund was given for the maintenance of the wife while
-living apart from her husband. And the conditions under which separate
-estate might be enjoyed had taken the Court of Chancery many generations
-to develop. No particular form of words was necessary to create a
-separate estate, and the intervention of trustees, though common, was
-not necessary. A clear intention to deprive the husband of his common
-law rights was sufficient to do so. In such a case a married woman was
-entitled to deal with her property as if she was unmarried, although the
-earlier decisions were in favour of requiring her binding engagements to
-be in writing or under seal. But it was afterwards held that any
-engagements, clearly made with reference to the separate estate, would
-bind that estate, exactly as if the woman had been a _feme sole_.
-Connected with the doctrine of separate use was the equitable
-contrivance of _restraint on anticipation_ with which later legislation
-has not interfered, whereby property might be so settled to the separate
-use of a married woman that she could not, during coverture, alienate it
-or anticipate the income. No such restraint is recognized in the ease of
-a man or of a _feme sole_, and it depends entirely on the separate
-estate; and the separate estate has its existence only during coverture,
-so that a woman to whom such an estate is given may dispose of it so
-long as she is unmarried, but becomes bound by the restraint as soon as
-she is married. In yet another way the court of Chancery interfered to
-protect the interests of married women. When a husband sought the
-aid of that court to get possession of his wife's _choses_ in action, he
-was required to make a provision for her and her children out of the
-fund sought to be recovered. This is called the wife's _equity to a
-settlement_, and is said to be based on the original maxim of Chancery
-jurisprudence, that "he who seeks equity must do equity." Two other
-property interests of minor importance are recognised. The wife's
-_pin-money_ is a provision for the purchase of clothes and ornaments
-suitable to her husband's station, but it is not an absolute gift to the
-separate use of the wife; and a wife surviving her husband cannot claim
-for more than one year's arrears of pin-money. _Paraphernalia_ are
-jewels and other ornaments given to the wife by her husband for the
-purpose of being worn by her, but not as her separate property. The
-husband may dispose of them by act _inter vivos_ but not by will, unless
-the will confers other benefits on the wife, in which case she must
-elect between the will and the paraphernalia. She may also on the death
-of the husband claim paraphernalia, provided all creditors have been
-satisfied, her right being superior to that of any legatee.
-
-The corresponding interest of the wife in the property of the husband is
-much more meagre and illusory. Besides a general right to maintenance at
-her husband's expense, she has at common law a right to dower (q.v.) in
-her husband's lands, and to a _pars rationabilis_ (third) of his
-personal estate, if he dies intestate. The former, which originally was
-a solid provision for widows, has by the ingenuity of conveyancers, as
-well as by positive enactment, been reduced to very slender dimensions.
-It may be destroyed by a mere declaration to that effect on the part of
-the husband, as well as by his conveyance of the land or by his will.
-
-The common practice of regulating the rights of husband, wife and
-children by marriage settlements obviates the hardships of the common
-law--at least for the women of the wealthier classes. The legislature by
-the Married Women's Property Acts of 1870, 1874, 1882 (which repealed
-and consolidated the acts of 1870 and 1874), 1893 and 1907 introduced
-very considerable changes. The chief provisions of the Married Women's
-Property Act 1882, which enormously improved the position of women
-unprotected by marriage settlement, are, shortly, that a married woman
-is capable of acquiring, holding and disposing of by will or otherwise,
-any real and personal property, in the same manner as if she were a
-_feme sole_, without the intervention of any trustee. The property of a
-woman married after the beginning of the act, whether belonging to her
-at the time of marriage or acquired after marriage, is held by her as a
-_feme sole_. The same is the case with property acquired after the
-beginning of the act by a woman married before the act. After marriage a
-woman remains liable for antenuptial debts and liabilities, and as
-between her and her husband, in the absence of contract to the contrary,
-her separate property is deemed primarily liable. The husband is only
-liable to the extent of property acquired from or through his wife. The
-act also contained provisions as to stock, investment, insurance,
-evidence and other matters. The effect of the act was to render obsolete
-the law as to what created a separate use or a reduction into possession
-of _choses_ in action, as to equity to a settlement, as to fraud on the
-husband's marital rights, and as to the inability of one of two married
-persons to give a gift to the other. Also, in the case of a gift to a
-husband and wife in terms which would make them joint tenants if
-unmarried, they no longer take as one person but as two. The act
-contained a special saving of existing and future settlements; a
-settlement being still necessary where it is desired to secure only the
-enjoyment of the income to the wife and to provide for children. The act
-by itself would enable the wife, without regard to family claims,
-instantly to part with the whole of any property which might come to
-her. Restraint on anticipation was preserved by the act, subject to the
-liability of such property for antenuptial debts, and to the power given
-by the Conveyancing Act 1881 to bind a married woman's interest
-notwithstanding a clause of restraint. The Married Women's Property Act
-of 1893 repealed two clauses in the act of 1882, the exact bearing of
-which had been a matter of controversy. It provided specifically that
-every contract thereinafter entered into by a married woman, otherwise
-than as an agent, should be deemed to be a contract entered into by her
-with respect to and be binding upon her separate property, whether she
-was or was not in fact possessed of or entitled to any separate property
-at the time when she entered into such contract, that it should bind all
-separate property which she might at any time or thereafter be possessed
-of or entitled to, and that it should be enforceable by process of law
-against all property which she might thereafter, while discovert, be
-possessed of or entitled to. The act of 1907 enabled a married woman,
-without her husband, to dispose of or join in disposing of, real or
-personal property held by her solely or jointly as trustee or personal
-representative, in like manner as if she were a _feme sole_. It also
-provided that a settlement or agreement for settlement whether before or
-after marriage, respecting the property of the woman, should not be
-valid unless executed by her if she was of full age or confirmed by her
-after she attained full age. The Married Women's Property Act 1908
-removed a curious anomaly by enacting that a married woman having
-separate property should be equally liable with single women and widows
-for the maintenance of parents who are in receipt of poor relief.
-
-The British colonies generally have adopted the principles of the
-English acts of 1882 and 1893.
-
-  _Law of Scotland._--The law of Scotland differs less from English law
-  than the use of a very different terminology would lead us to suppose.
-  The phrase _communio bonorum_ has been employed to express the
-  interest which the spouses have in the _movable_ property of both, but
-  its use has been severely censured as essentially inaccurate and
-  misleading. It has been contended that there was no real community of
-  goods, and no partnership or societas between the spouses. The wife's
-  movable property, with certain exceptions, and subject to special
-  agreements, became as absolutely the property of the husband as it did
-  in English law. The notion of a _communio_ was, however, favoured by
-  the peculiar rights of the wife and children on the dissolution of the
-  marriage. Previous to the Intestate Movable Succession (Scotland) Act
-  1855 the law stood as follows. The fund formed by the movable property
-  of both spouses may be dealt with by the husband as he pleases during
-  life; it is increased by his acquisitions and diminished by his debts.
-  The respective shares contributed by husband and wife return on the
-  dissolution of the marriage to them or their representatives if the
-  marriage be dissolved within a year and a day, and without a living
-  child. Otherwise the division is into two or three shares, according
-  as children are existing or not at the dissolution of the marriage. On
-  the death of the husband, his children take one-third (called
-  _legitim_), the widow takes one-third (_jus relictae_), and the
-  remaining one-third (the _dead part_) goes according to his will or to
-  his next of kin. If there be no children, the _jus relictae_ and the
-  dead's part are each one-half. If the wife die before the husband, her
-  representatives, whether children or not, are creditors for the value
-  of her share. The statute above-mentioned, however, enacts that "where
-  a wife shall predecease her husband, the next of kin, executors or
-  other representatives of such wife, whether testate or intestate,
-  shall have no right to any share of the goods in communion; nor shall
-  any legacy or bequest or testamentary disposition thereof by such
-  wife, affect or attach to the said goods or any portion thereof." It
-  also abolishes the rule by which the shares revert if the marriage
-  does not subsist for a year and a day. Several later acts apply to
-  Scotland some of the principles of the English Married Women's
-  Property Acts. These are the Married Women's Property (Scotland) Act
-  1877, which protects the earnings, &c., of wives, and limits the
-  husband's liability for antenuptial debts of the wife, the Married
-  Women's Policies of Assurance (Scotland) Act 1880, which enables a
-  woman to contract for a policy of assurance for her separate use, and
-  the Married Women's Property (Scotland) Act 1881, which abolished the
-  _jus mariti_.
-
-  A wife's _heritable_ property does not pass to the husband on
-  marriage, but he acquires a right to the administration and profits.
-  His courtesy, as in English law, is also recognized. On the other
-  hand, a widow has a _terce_ or life-rent of a third part of the
-  husband's heritable estate, unless she has accepted a conventional
-  provision.
-
-  _Continental Europe._--Since 1882 English legislation in the matter of
-  married women's property has progressed from perhaps the most backward
-  to the foremost place in Europe. By a curious contrast, the only two
-  European countries where, in the absence of a settlement to the
-  contrary, independence of the wife's property was recognized, were
-  Russia and Italy. But there is now a marked tendency towards
-  contractual emancipation. Sweden adopted a law on this subject in
-  1874, Denmark in 1880, Norway in 1888. Germany followed, the Civil
-  Code which came into operation in 1900 (Art. 1367) providing that the
-  wife's wages or earnings shall form part of her _Vorbehaltsgut_ or
-  separate property, which a previous article (1365) placed beyond
-  the husband's control. As regards property accruing to the wife in
-  Germany by succession, will or gift _inter vivos_, it is only separate
-  property where the donor has deliberately stipulated exclusion of the
-  husband's right.
-
-  In France it seemed as if the system of community of property was
-  ingrained in the institutions of the country. But a law of 1907 has
-  brought France into line with other countries. This law gives a
-  married woman sole control over earnings from her personal work and
-  savings therefrom. She can with such money acquire personalty or
-  realty, over the former of which she has absolute control. But if she
-  abuses her rights by squandering her money or administering her
-  property badly or imprudently the husband may apply to the court to
-  have her freedom restricted.
-
-  _American Law._--In the United States, the revolt against the common
-  law theory of husband and wife was carried farther than in England,
-  and legislation early tended in the direction of absolute equality
-  between the sexes. Each state has, however, taken its own way and
-  selected its own time for introducing modifications of the existing
-  law, so that the legislation on this subject is now exceedingly
-  complicated and difficult. James Schouler (_Law of Domestic
-  Relations_) gives an account of the general result in the different
-  states to which reference may be made. The peculiar system of
-  Homestead Laws in many of the states (see HOMESTEAD and EXEMPTION
-  LAWS) constitutes an inalienable provision for the wife and family of
-  the householder.
-
-
-FOOTNOTE:
-
-  [1] Curtesy or courtesy has been explained by legal writers as
-    "arising _by favour_ of the law of England." The word has nothing to
-    do with courtesy in the sense of complaisance.
-
-
-
-
-HUSHI (Rumanian _Husi_), the capital of the department of Falciu,
-Rumania; on a branch of the Jassy-Galatz railway, 9 m. W. of the river
-Pruth and the Russian frontier. Pop. (1900) 15,404, about one-fourth
-being Jews. Hushi is an episcopal see. The cathedral was built in 1491
-by Stephen the Great of Moldavia. There are no important manufactures,
-but a large fair is held annually in September for the sale of
-live-stock, and wine is produced in considerable quantities. Hushi is
-said to have been founded in the 15th century by a colony of Hussites,
-from whom its name is derived. The treaty of the Pruth between Russia
-and Turkey was signed here in 1711.
-
-
-
-
-HUSKISSON, WILLIAM (1770-1830), English statesman and financier, was
-descended from an old Staffordshire family of moderate fortune, and was
-born at Birch Moreton, Worcestershire, on the 11th of March 1770. Having
-been placed in his fourteenth year under the charge of his maternal
-great-uncle Dr Gem, physician to the English embassy at Paris, in 1783
-he passed his early years amidst a political fermentation which led him
-to take a deep interest in politics. Though he approved of the French
-Revolution, his sympathies were with the more moderate party, and he
-became a member of the "club of 1789," instituted to support the new
-form of constitutional monarchy in opposition to the anarchical attempts
-of the Jacobins. He early displayed his mastery of the principles of
-finance by a _Discours_ delivered in August 1790 before this society, in
-regard to the issue of assignats by the government. The _Discours_
-gained him considerable reputation, but as it failed in its purpose he
-withdrew from the society. In January 1793 he was appointed by Dundas to
-an office created to direct the execution of the Aliens Act; and in the
-discharge of his delicate duties he manifested such ability that in 1795
-he was appointed under-secretary at war. In the following year he
-entered parliament as member for Morpeth, but for a considerable period
-he took scarcely any part in the debates. In 1800 he inherited a fortune
-from Dr Gem. On the retirement of Pitt in 1801 he resigned office, and
-after contesting Dover unsuccessfully he withdrew for a time into
-private life. Having in 1804 been chosen to represent Liskeard, he was
-on the restoration of the Pitt ministry appointed secretary of the
-treasury, holding office till the dissolution of the ministry after the
-death of Pitt in January 1806. After being elected for Harwich in 1807,
-he accepted the same office under the duke of Portland, but he withdrew
-from the ministry along with Canning in 1809. In the following year he
-published a pamphlet on the currency system, which confirmed his
-reputation as the ablest financier of his time; but his free-trade
-principles did not accord with those of his party. In 1812 he was
-returned for Chichester. When in 1814 he re-entered the public service,
-it was only as chief commissioner of woods and forests, but his
-influence was from this time very great in the commercial and financial
-legislation of the country. He took a prominent part in the corn-law
-debates of 1814 and 1815; and in 1819 he presented a memorandum to Lord
-Liverpool advocating a large reduction in the unfunded debt, and
-explaining a method for the resumption of cash payments, which was
-embodied in the act passed the same year. In 1821 he was a member of the
-committee appointed to inquire into the causes of the agricultural
-distress then prevailing, and the proposed relaxation of the corn laws
-embodied in the report was understood to have been chiefly due to his
-strenuous advocacy. In 1823 he was appointed president of the board of
-trade and treasurer of the navy, and shortly afterwards he received a
-seat in the cabinet. In the same year he was returned for Liverpool as
-successor to Canning, and as the only man who could reconcile the Tory
-merchants to a free trade policy. Among the more important legislative
-changes with which he was principally connected were a reform of the
-Navigation Acts, admitting other nations to a full equality and
-reciprocity of shipping duties; the repeal of the labour laws; the
-introduction of a new sinking fund; the reduction of the duties on
-manufactures and on the importation of foreign goods, and the repeal of
-the quarantine duties. In accordance with his suggestion Canning in 1827
-introduced a measure on the corn laws proposing the adoption of a
-sliding scale to regulate the amount of duty. A misapprehension between
-Huskisson and the duke of Wellington led to the duke proposing an
-amendment, the success of which caused the abandonment of the measure by
-the government. After the death of Canning in the same year Huskisson
-accepted the secretaryship of the colonies under Lord Goderich, an
-office which he continued to hold in the new cabinet formed by the duke
-of Wellington in the following year. After succeeding with great
-difficulty in inducing the cabinet to agree to a compromise on the corn
-laws, Huskisson finally resigned office in May 1829 on account of a
-difference with his colleagues in regard to the disfranchisement of East
-Retford. On the 15th of September of the following year he was
-accidentally killed by a locomotive engine while present at the opening
-of the Liverpool and Manchester railway.
-
-  See the _Life of Huskisson_, by J. Wright (London, 1831).
-
-
-
-
-HUSS (or HUS), JOHN (c. 1373-1415), Bohemian reformer and martyr, was
-born at Hussinecz,[1] a market village at the foot of the Bohmerwald,
-and not far from the Bavarian frontier, between 1373 and 1375, the exact
-date being uncertain. His parents appear to have been well-to-do Czechs
-of the peasant class. Of his early life nothing is recorded except that,
-notwithstanding the early loss of his father, he obtained a good
-elementary education, first at Hussinecz, and afterwards at the
-neighbouring town of Prachaticz. At, or only a very little beyond, the
-usual age he entered the recently (1348) founded university of Prague,
-where he became bachelor of arts in 1393, bachelor of theology in 1394,
-and master of arts in 1396. In 1398 he was chosen by the Bohemian
-"nation" of the university to an examinership for the bachelor's degree;
-in the same year he began to lecture also, and there is reason to
-believe that the philosophical writings of Wycliffe, with which he had
-been for some years acquainted, were his text-books. In October 1401 he
-was made dean of the philosophical faculty, and for the half-yearly
-period from October 1402 to April 1403 he held the office of rector of
-the university. In 1402 also he was made rector or curate
-(_capellarius_) of the Bethlehem chapel, which had in 1391 been erected
-and endowed by some zealous citizens of Prague for the purpose of
-providing good popular preaching in the Bohemian tongue. This
-appointment had a deep influence on the already vigorous religious life
-of Huss himself; and one of the effects of the earnest and independent
-study of Scripture into which it led him was a profound conviction of
-the great value not only of the philosophical but also of the
-theological writings of Wycliffe.
-
-This newly-formed sympathy with the English reformer did not, in the
-first instance at least, involve Huss in any conscious opposition to the
-established doctrines of Catholicism, or in any direct conflict with the
-authorities of the church; and for several years he continued to
-act in full accord with his archbishop (Sbynjek, or Sbynko, of
-Hasenburg). Thus in 1405 he, with other two masters, was commissioned to
-examine into certain reputed miracles at Wilsnack, near Wittenberg,
-which had caused that church to be made a resort of pilgrims from all
-parts of Europe. The result of their report was that all pilgrimage
-thither from the province of Bohemia was prohibited by the archbishop on
-pain of excommunication, while Huss, with the full sanction of his
-superior, gave to the world his first published writing, entitled _De
-Omni Sanguine Christi Glorificato_, in which he declaimed in no measured
-terms against forged miracles and ecclesiastical greed, urging
-Christians at the same time to desist from looking for sensible signs of
-Christ's presence, but rather to seek Him in His enduring word. More
-than once also Huss, together with his friend Stanislaus of Znaim, was
-appointed to be synod preacher, and in this capacity he delivered at the
-provincial councils of Bohemia many faithful admonitions. As early as
-the 28th of May 1403, it is true, there had been held a university
-disputation about the new doctrines of Wycliffe, which had resulted in
-the condemnation of certain propositions presumed to be his; five years
-later (May 20, 1408) this decision had been refined into a declaration
-that these, forty-five in number, were not to be taught in any
-heretical, erroneous or offensive sense. But it was only slowly that the
-growing sympathy of Huss with Wycliffe unfavourably affected his
-relations with his colleagues in the priesthood. In 1408, however, the
-clergy of the city and archiepiscopal diocese of Prague laid before the
-archbishop a formal complaint against Huss, arising out of strong
-expressions with regard to clerical abuses of which he had made use in
-his public discourses; and the result was that, having been first
-deprived of his appointment as synodal preacher, he was, after a vain
-attempt to defend himself in writing, publicly forbidden the exercise of
-any priestly function throughout the diocese. Simultaneously with these
-proceedings in Bohemia, negotiations had been going on for the removal
-of the long-continued papal schism, and it had become apparent that a
-satisfactory solution could only be secured if, as seemed not
-impossible, the supporters of the rival popes, Benedict XIII. and
-Gregory XII., could be induced, in view of the approaching council of
-Pisa, to pledge themselves to a strict neutrality. With this end King
-Wenceslaus of Bohemia had requested the co-operation of the archbishop
-and his clergy, and also the support of the university, in both
-instances unsuccessfully, although in the case of the latter the
-Bohemian "nation," with Huss at its head, had only been overborne by the
-votes of the Bavarians, Saxons and Poles. There followed an expression
-of nationalist and particularistic as opposed to ultramontane and also
-to German feeling, which undoubtedly was of supreme importance for the
-whole of the subsequent career of Huss. In compliance with this feeling
-a royal edict (January 18, 1409) was issued, by which, in alleged
-conformity with Paris usage, and with the original charter of the
-university, the Bohemian "nation" received three votes, while only one
-was allotted to the other three "nations" combined; whereupon all the
-foreigners, to the number of several thousands, almost immediately
-withdrew from Prague, an occurrence which led to the formation shortly
-afterwards of the university of Leipzig.
-
-It was a dangerous triumph for Huss; for his popularity at court and in
-the general community had been secured only at the price of clerical
-antipathy everywhere and of much German ill-will. Among the first
-results of the changed order of things were on the one hand the election
-of Huss (October 1409) to be again rector of the university, but on the
-other hand the appointment by the archbishop of an inquisitor to inquire
-into charges of heretical teaching and inflammatory preaching brought
-against him. He had spoken disrespectfully of the church, it was said,
-had even hinted that Antichrist might be found to be in Rome, had
-fomented in his preaching the quarrel between Bohemians and Germans, and
-had, notwithstanding all that had passed, continued to speak of Wycliffe
-as both a pious man and an orthodox teacher. The direct result of this
-investigation is not known, but it is impossible to disconnect from it
-the promulgation by Pope Alexander V., on the 20th of December 1409, of
-a bull which ordered the abjuration of all Wycliffite heresies and the
-surrender of all his books, while at the same time--a measure specially
-levelled at the pulpit of Bethlehem chapel--all preaching was prohibited
-except in localities which had been by long usage set apart for that
-use. This decree, as soon as it was published in Prague (March 9, 1410),
-led to much popular agitation, and provoked an appeal by Huss to the
-pope's better informed judgment; the archbishop, however, resolutely
-insisted on carrying out his instructions, and in the following July
-caused to be publicly burned, in the courtyard of his own palace,
-upwards of 200 volumes of the writings of Wycliffe, while he pronounced
-solemn sentence of excommunication against Huss and certain of his
-friends, who had in the meantime again protested and appealed to the new
-pope (John XXIII.). Again the populace rose on behalf of their hero,
-who, in his turn, strong in the conscientious conviction that "in the
-things which pertain to salvation God is to be obeyed rather than man,"
-continued uninterruptedly to preach in the Bethlehem chapel, and in the
-university began publicly to defend the so-called heretical treatises of
-Wycliffe, while from king and queen, nobles and burghers, a petition was
-sent to Rome praying that the condemnation and prohibition in the bull
-of Alexander V. might be quashed. Negotiations were carried on for some
-months, but in vain; in March 1411 the ban was anew pronounced upon Huss
-as a disobedient son of the church, while the magistrates and
-councillors of Prague who had favoured him were threatened with a
-similar penalty in ease of their giving him a contumacious support.
-Ultimately the whole city, which continued to harbour him, was laid
-under interdict; yet he went on preaching, and masses were celebrated as
-usual, so that at the date of Archbishop Sbynko's death in September
-1411, it seemed as if the efforts of ecclesiastical authority had
-resulted in absolute failure.
-
-The struggle, however, entered on a new phase with the appearance at
-Prague in May 1412 of the papal emissary charged with the proclamation
-of the papal bulls by which a religious war was decreed against the
-excommunicated King Ladislaus of Naples, and indulgence was promised to
-all who should take part in it, on terms similar to those which had been
-enjoyed by the earlier crusaders to the Holy Land. By his bold and
-thorough-going opposition to this mode of procedure against Ladislaus,
-and still more by his doctrine that indulgence could never be sold
-without simony, and could not be lawfully granted by the church except
-on condition of genuine contrition and repentance, Huss at last isolated
-himself, not only from the archiepiscopal party under Albik of
-Unitschow, but also from the theological faculty of the university, and
-especially from such men as Stanislaus of Znaim and Stephen Paletz, who
-until then had been his chief supporters. A popular demonstration, in
-which the papal bulls had been paraded through the streets with
-circumstances of peculiar ignominy and finally burnt, led to
-intervention by Wenceslaus on behalf of public order; three young men,
-for having openly asserted the unlawfulness of the papal indulgence
-after silence had been enjoined, were sentenced to death (June 1412);
-the excommunication against Huss was renewed, and the interdict again
-laid on all places which should give him shelter--a measure which now
-began to be more strictly regarded by the clergy, so that in the
-following December Huss had no alternative but to yield to the express
-wish of the king by temporarily withdrawing from Prague. A provincial
-synod, held at the instance of Wenceslaus in February 1413, broke up
-without having reached any practical result; and a commission appointed
-shortly afterwards also failed to bring about a reconciliation between
-Huss and his adversaries. The so-called heretic meanwhile spent his time
-partly at Kozihradek, some 45 m. south of Prague, and partly at
-Krakowitz in the immediate neighbourhood of the capital, occasionally
-giving a course of open-air preaching, but finding his chief employment
-in maintaining that copious correspondence of which some precious
-fragments still are extant, and in the composition of the treatise, _De
-Ecclesia_, which subsequently furnished most of the material for the
-capital charges brought against him, and was formerly considered
-the most important of his works, though it is mainly a transcript of
-Wycliffe's work of the same name.
-
-During the year 1413 the arrangements for the meeting of a general
-council at Constance were agreed upon between Sigismund and Pope John
-XXIII. The objects originally contemplated had been the restoration of
-the unity of the church and its reform in head and members; but so great
-had become the prominence of Bohemian affairs that to these also a first
-place in the programme of the approaching oecumenical assembly required
-to be assigned, and for their satisfactory settlement the presence of
-Huss was necessary. His attendance was accordingly requested, and the
-invitation was willingly accepted as giving him a long-wished-for
-opportunity both of publicly vindicating himself from charges which he
-felt to be grievous, and of loyally making confession for Christ. He set
-out from Bohemia on the 14th of October 1414, not, however, until he had
-carefully ordered all his private affairs, with a presentiment, which he
-did not conceal, that in all probability he was going to his death. The
-journey, which appears to have been undertaken with the usual passport,
-and under the protection of several powerful Bohemian friends (John of
-Chlum, Wenceslaus of Duba, Henry of Chlum) who accompanied him, was a
-very prosperous one; and at almost all the halting-places he was
-received with a consideration and enthusiastic sympathy which he had
-hardly expected to meet with anywhere in Germany. On the 3rd of November
-he arrived at Constance; shortly afterwards there was put into his hands
-the famous imperial "safe conduct," the promise of which had been one of
-his inducements to quit the comparative security he had enjoyed in
-Bohemia. This safe conduct, which had been frequently printed, stated
-that Huss should, whatever judgment might be passed on him, be allowed
-to return freely to Bohemia. This by no means provided for his immunity
-from punishment. If faith to him had not been broken he would have been
-sent back to Bohemia to be punished by his sovereign, the king of
-Bohemia. The treachery of King Sigismund is undeniable, and was indeed
-admitted by the king himself. The safe conduct was probably indeed given
-by him to entice Huss to Constance. On the 4th of December the pope
-appointed a commission of three bishops to investigate the case against
-the heretic, and to procure witnesses; to the demand of Huss that he
-might be permitted to employ an agent in his defence a favourable answer
-was at first given, but afterwards even this concession to the forms of
-justice was denied. While the commission was engaged in the prosecution
-of its enquiries, the flight of Pope John XXIII. took place on the 20th
-of March, an event which furnished a pretext for the removal of Huss
-from the Dominican convent to a more secure and more severe place of
-confinement under the charge of the bishop of Constance at Gottlieben on
-the Rhine. On the 4th of May the temper of the council on the doctrinal
-questions in dispute was fully revealed in its unanimous condemnation of
-Wycliffe, especially of the so-called "forty-five articles" as
-erroneous, heretical, revolutionary. It was not, however, until the 5th
-of June that the case of Huss came up for hearing; the meeting, which
-was an exceptionally full one, took place in the refectory of the
-Franciscan cloister. Autograph copies of his work _De Ecclesia_ and of
-the controversial tracts which he had written against Paletz and
-Stanislaus of Znaim having been acknowledged by him, the extracted
-propositions on which the prosecution based their charge of heresy were
-read; but as soon as the accused began to enter upon his defence, he was
-assailed by violent outcries, amidst which it was impossible for him to
-be heard, so that he was compelled to bring his speech to an abrupt
-close, which he did with the calm remark: "In such a council as this I
-had expected to find more propriety, piety and order." It was found
-necessary to adjourn the sitting until the 7th of June, on which
-occasion the outward decencies were better observed, partly no doubt
-from the circumstance that Sigismund was present in person. The
-propositions which had been extracted from the _De Ecclesia_ were again
-brought up, and the relations between Wycliffe and Huss were discussed,
-the object of the prosecution being to fasten upon the latter the
-charge of having entirely adopted the doctrinal system of the former,
-including especially a denial of the doctrine of transubstantiation. The
-accused repudiated the charge of having abandoned the Catholic doctrine,
-while expressing hearty admiration and respect for the memory of
-Wycliffe. Being next asked to make an unqualified submission to the
-council, he expressed himself as unable to do so, while stating his
-willingness to amend his teaching wherever it had been shown to be
-false. With this the proceedings of the day were brought to a close. On
-the 8th of June the propositions extracted from the _De Ecclesia_ were
-again taken up with some fulness of detail; some of these he repudiated
-as incorrectly given, others he defended; but when asked to make a
-general recantation he steadfastly declined, on the ground that to do so
-would be a dishonest admission of previous guilt. Among the propositions
-he could heartily abjure was that relating to transubstantiation; among
-those he felt constrained unflinchingly to maintain was one which had
-given great offence, to the effect that Christ, not Peter, is the head
-of the church to whom ultimate appeal must be made. The council,
-however, showed itself inaccessible to all his arguments and
-explanations, and its final resolution, as announced by Pierre d'Ailly,
-was threefold: first, that Huss should humbly declare that he had erred
-in all the articles cited against him; secondly, that he should promise
-on oath neither to hold nor teach them in the future; thirdly, that he
-should publicly recant them. On his declining to make this submission he
-was removed from the bar. Sigismund himself gave it as his opinion that
-it had been clearly proved by many witnesses that the accused had taught
-many pernicious heresies, and that even should he recant he ought never
-to be allowed to preach or teach again or to return to Bohemia, but that
-should he refuse recantation there was no remedy but the stake. During
-the next four weeks no effort was spared to shake the determination of
-Huss; but he steadfastly refused to swerve from the path which
-conscience had once made clear. "I write this," says he, in a letter to
-his friends at Prague, "in prison and in chains, expecting to-morrow to
-receive sentence of death, full of hope in God that I shall not swerve
-from the truth, nor abjure errors imputed to me by false witnesses." The
-sentence he expected was pronounced on the 6th of July in the presence
-of Sigismund and a full sitting of the council; once and again he
-attempted to remonstrate, but in vain, and finally he betook himself to
-silent prayer. After he had undergone the ceremony of degradation with
-all the childish formalities usual on such occasions, his soul was
-formally consigned by all those present to the devil, while he himself
-with clasped hands and uplifted eyes reverently committed it to Christ.
-He was then handed over to the secular arm, and immediately led to the
-place of execution, the council meanwhile proceeding unconcernedly with
-the rest of its business for the day. Many incidents recorded in the
-histories make manifest the meekness, fortitude and even cheerfulness
-with which he went to his death. After he had been tied to the stake and
-the faggots had been piled, he was for the last time urged to recant,
-but his only reply was: "God is my witness that I have never taught or
-preached that which false witnesses have testified against me. He knows
-that the great object of all my preaching and writing was to convert men
-from sin. In the truth of that gospel which hitherto I have written,
-taught and preached, I now joyfully die." The fire was then kindled, and
-his voice as it audibly prayed in the words of the "Kyrie Eleison" was
-soon stifled in the smoke. When the flames had done their office, the
-ashes that were left and even the soil on which they lay were carefully
-removed and thrown into the Rhine.
-
-Not many words are needed to convey a tolerably adequate estimate of the
-character and work of the "pale thin man in mean attire," who in
-sickness and poverty thus completed the forty-sixth year of a busy life
-at the stake. The value of Huss as a scholar was formerly underrated.
-The publication of his _Super IV. Sententiarum_ has proved that he was a
-man of profound learning. Yet his principal glory will always be founded
-on his spiritual teaching. It might not be easy to formulate
-precisely the doctrines for which he died, and certainly some of them,
-as, for example, that regarding the church, were such as many
-Protestants even would regard as unguarded and difficult to harmonize
-with the maintenance of external church order; but his is undoubtedly
-the honour of having been the chief intermediary in handing on from
-Wycliffe to Luther the torch which kindled the Reformation, and of
-having been one of the bravest of the martyrs who have died in the cause
-of honesty and freedom, of progress and of growth towards the light.
-     (J. S. Bl.)
-
-  The works of Huss are usually classed under four heads: the dogmatical
-  and polemical, the homiletical, the exegetical and the epistolary. In
-  the earlier editions of his works sufficient care was not taken to
-  distinguish between his own writings and those of Wycliffe and others
-  who were associated with him. In connexion with his sermons it is
-  worthy of note that by means of them and by his public teaching
-  generally Huss exercised a considerable influence not only on the
-  religious life of his time, but on the literary development of his
-  native tongue. The earliest collected edition of his works, _Historia
-  et monumenta Joannis Hus et Hieronymi Pragensis_, was published at
-  Nuremberg in 1558 and was reprinted with a considerable quantity of
-  new matter at Frankfort in 1715. A Bohemian edition of the works has
-  been edited by K. J. Erben (Prague, 1865-1868), and the _Documenta J.
-  Hus vitam, doctrinam, causam in Constantiensi concilio_ (1869), edited
-  by F. Palacky, is very valuable. More recently _Joannis Hus. Opera
-  omnia_ have been edited by W. Flojshaus (Prague, 1904 fol.). The
-  _De Ecclesia_ was published by Ulrich von Hutten in 1520; other
-  controversial writings by Otto Brumfels in 1524; and Luther wrote an
-  interesting preface to _Epistolae Quaedam_, which were published in
-  1537. These _Epistolae_ have been translated into French by E. de
-  Bonnechose (1846), and the letters written during his imprisonment
-  have been edited by C. von Kugelgen (Leipzig, 1902).
-
-  The best and most easily accessible information for the English reader
-  on Huss is found in J. A. W. Neander's _Allgemeine Geschichte der
-  christlichen Religion und Kirche_, translated by J. Torrey
-  (1850-1858); in G. von Lechler's _Wiclif und die Vorgeschichte der
-  Reformation_, translated by P. Lorimer (1878); in H. H. Milman's
-  _History of Latin Christianity_, vol. viii. (1867); and in M.
-  Creighton's _History of the Papacy_ (1897). Among the earlier
-  authorities is the _Historia Bohemica_ of Aeneas Sylvius (1475). The
-  _Acta_ of the council of Constance (published by P. Labbe in his
-  _Concilia_, vol. xvi., 1731; by H. von der Haardt in his _Magnum
-  Constantiense concilium_, vol. vi., 1700; and by H. Finke in his _Acta
-  concilii Constantiensis_, 1896); and J. Lenfant's _Histoire de la
-  guerre des Hussites_ (1731) and the same writer's _Histoire du concile
-  de Constance_ (1714) should be consulted. F. Palacky's _Geschichte
-  Bohmens_ (1864-1867) is also very useful. Monographs on Huss are very
-  numerous. Among them may be mentioned J. A. von Helfert, _Studien uber
-  Hus und Hieronymus_ (1853; this work is ultramontane in its
-  sympathies); C. von Hofler, _Hus und der Abzug der deutschen
-  Professoren und Studenten aus Prag_ (1864); W. Berger, _Johannes Hus
-  und Konig Sigmund_ (1871); E. Denis, _Huss et la guerre des Hussites_
-  (1878); P. Uhlmann, _Konig Sigmunds Geleit fur Hus_ (1894); J.
-  Loserth, _Hus und Wiclif_ (1884), translated into English by M. J.
-  Evans (1884); A. Jeep, _Gerson, Wiclefus, Hussus, inter se comparati_
-  (1857); and G. von Lechler, _Johannes Hus_ (1889). See also Count
-  Lutzow, _The Life and Times of John Hus_ (London, 1909).
-
-
-FOOTNOTE:
-
-  [1] From which the name Huss, or more properly Hus, an abbreviation
-    adopted by himself about 1396, is derived. Prior to that date he was
-    invariably known as Johann Hussynecz, Hussinecz, Hussenicz or de
-    Hussynecz.
-
-
-
-
-HUSSAR, originally the name of a soldier belonging to a corps of light
-horse raised by Matthias Corvinus, king of Hungary, in 1458, to fight
-against the Turks. The Magyar _huszar_, from which the word is derived,
-was formerly connected with the Magyar _husz_, twenty, and was explained
-by a supposed raising of the troops by the taking of each twentieth man.
-According to the _New English Dictionary_ the word is an adaptation of
-the Italian _corsaro_, corsair, a robber, and is found in 15th-century
-documents coupled with _praedones_. The hussar was the typical Hungarian
-cavalry soldier, and, in the absence of good light cavalry in the
-regular armies of central and western Europe, the name and character of
-the hussars gradually spread into Prussia, France, &c. Frederick the
-Great sent Major H. J. von Zieten to study the work of this type of
-cavalry in the Austrian service, and Zieten so far improved on the
-Austrian model that he defeated his old teacher, General Baranyai, in an
-encounter between the Prussian and Austrian hussars at Rothschloss in
-1741. The typical uniform of the Hungarian hussar was followed with
-modifications in other European armies. It consisted of a busby or a
-high cylindrical cloth cap, jacket with heavy braiding, and a dolman or
-pelisse, a loose coat worn hanging from the left shoulder. The hussar
-regiments of the British army were converted from light dragoons at the
-following dates: 7th (1805), 10th and 15th (1806), 18th (1807, and
-again on revival after disbandment, 1858), 8th (1822), 11th (1840), 20th
-(late 2nd Bengal European Cavalry) (1860), 13th, 14th, and 19th (late
-1st Bengal European Cavalry) (1861). The 21st Lancers were hussars from
-1862 to 1897.
-
-
-
-
-HUSSITES, the name given to the followers of John Huss (1369-1415), the
-Bohemian reformer. They were at first often called Wycliffites, as the
-theological theories of Huss were largely founded on the teachings of
-Wycliffe. Huss indeed laid more stress on church reform than on
-theological controversy. On such matters he always writes as a disciple
-of Wycliffe. The Hussite movement may be said to have sprung from three
-sources, which are however closely connected. Bohemia, which had first
-received Christianity from the East, was from geographical and other
-causes long but very loosely connected with the Church of Rome. The
-connexion became closer at the time when the schism with its violent
-controversies between the rival pontiffs, waged with the coarse
-invective customary to medieval theologians, had brought great discredit
-on the papacy. The terrible rapacity of its representatives in Bohemia,
-which increased in proportion as it became more difficult to obtain
-money from western countries such as England and France, caused general
-indignation; and this was still further intensified by the gross
-immorality of the Roman priests. The Hussite movement was also a
-democratic one, an uprising of the peasantry against the landowners at a
-period when a third of the soil belonged to the clergy. Finally national
-enthusiasm for the Slavic race contributed largely to its importance.
-The towns, in most cases creations of the rulers of Bohemia who had
-called in German immigrants, were, with the exception of the "new town"
-of Prague, mainly German; and in consequence of the regulations of the
-university, Germans also held almost all the more important
-ecclesiastical offices--a condition of things greatly resented by the
-natives of Bohemia, which at this period had reached a high degree of
-intellectual development.
-
-The Hussite movement assumed a revolutionary character as soon as the
-news of the death of Huss reached Prague. The knights and nobles of
-Bohemia and Moravia, who were in favour of church reform, sent to the
-council at Constance (September 2nd, 1415) a protest, known as the
-"_protestatio Bohemorum_" which condemned the execution of Huss in the
-strongest language. The attitude of Sigismund, king of the Romans, who
-sent threatening letters to Bohemia declaring that he would shortly
-"drown all Wycliffites and Hussites," greatly incensed the people.
-Troubles broke out in various parts of Bohemia, and many Romanist
-priests were driven from their parishes. Almost from the first the
-Hussites were divided into two sections, though many minor divisions
-also arose among them. Shortly before his death Huss had accepted a
-doctrine preached during his absence by his adherents at Prague, namely
-that of "utraquism," i.e. the obligation of the faithful to receive
-communion in both kinds (_sub utraque specie_). This doctrine became the
-watchword of the moderate Hussites who were known as the Utraquists or
-Calixtines (_calix_, the chalice), in Bohemian, _podoboji_; while the
-more advanced Hussites were soon known as the Taborites, from the city
-of Tabor that became their centre.
-
-Under the influence of his brother Sigismund, king of the Romans, King
-Wenceslaus endeavoured to stem the Hussite movement. A certain number of
-Hussites lead by Nicolas of Hus--no relation of John Huss--left Prague.
-They held meetings in various parts of Bohemia, particularly at Usti,
-near the spot where the town of Tabor was founded soon afterwards. At
-these meetings Sigismund was violently denounced, and the people
-everywhere prepared for war. In spite of the departure of many prominent
-Hussites the troubles at Prague continued. On the 30th of July 1419,
-when a Hussite procession headed by the priest John of Zelivo (in Ger.
-Selau) marched through the streets of Prague, stones were thrown at the
-Hussites from the windows of the town-hall of the "new town." The
-people, headed by John Zizka (1376-1424), threw the burgomaster and
-several town-councillors, who were the instigators of this outrage, from
-the windows and they were immediately killed by the crowd. On hearing
-this news King Wenceslaus was seized with an apoplectic fit, and died a
-few days afterwards. The death of the king resulted in renewed troubles
-in Prague and in almost all parts of Bohemia. Many Romanists, mostly
-Germans--for they had almost all remained faithful to the papal
-cause--were expelled from the Bohemian cities. In Prague, in November
-1419, severe fighting took place between the Hussites and the
-mercenaries whom Queen Sophia (widow of Wenceslaus and regent after the
-death of her husband) had hurriedly collected. After a considerable part
-of the city had been destroyed a truce was concluded on the 13th of
-November. The nobles, who though favourable to the Hussite cause yet
-supported the regent, promised to act as mediators with Sigismund; while
-the citizens of Prague consented to restore to the royal forces the
-castle of Vysehrad, which had fallen into their hands. Zizka, who
-disapproved of this compromise, left Prague and retired to Plzen
-(Pilsen). Unable to maintain himself there he marched to southern
-Bohemia, and after defeating the Romanists at Sudomer--the first pitched
-battle of the Hussite wars--he arrived at Usti, one of the earliest
-meeting-places of the Hussites. Not considering its situation
-sufficiently strong, he moved to the neighbouring new settlement of the
-Hussites, to which the biblical name of Tabor was given. Tabor soon
-became the centre of the advanced Hussites, who differed from the
-Utraquists by recognizing only two sacraments--Baptism and
-Communion--and by rejecting most of the ceremonial of the Roman Church.
-The ecclesiastical organization of Tabor had a somewhat puritanic
-character, and the government was established on a thoroughly democratic
-basis. Four captains of the people (_hejtmane_) were elected, one of
-whom was Zizka; and a very strictly military discipline was instituted.
-
-Sigismund, king of the Romans, had, by the death of his brother
-Wenceslaus without issue, acquired a claim on the Bohemian crown; though
-it was then, and remained till much later, doubtful whether Bohemia was
-an hereditary or an elective monarchy. A firm adherent of the Church of
-Rome, Sigismund was successful in obtaining aid from the pope. Martin V.
-issued a bull on the 17th of March 1420 which proclaimed a crusade "for
-the destruction of the Wycliffites, Hussites and all other heretics in
-Bohemia." The vast army of crusaders, with which were Sigismund and many
-German princes, and which consisted of adventurers attracted by the hope
-of pillage from all parts of Europe, arrived before Prague on the 30th
-of June and immediately began the siege of the city, which had, however,
-soon to be abandoned (see [VZ]I[VZ]KA, JOHN). Negotiations took place
-for a settlement of the religious differences. The united Hussites
-formulated their demands in a statement known as the "articles of
-Prague." This document, the most important of the Hussite period, runs
-thus in the wording of the contemporary chronicler, Laurence of
-Brezova:--
-
-  I. The word of God shall be preached and made known in the kingdom of
-  Bohemia freely and in an orderly manner by the priests of the Lord....
-
-  II. The sacrament of the most Holy Eucharist shall be freely
-  administered in the two kinds, that is bread and wine, to all the
-  faithful in Christ who are not precluded by mortal sin--according to
-  the word and disposition of Our Saviour.
-
-  III. The secular power over riches and worldly goods which the clergy
-  possesses in contradiction to Christ's precept, to the prejudice of
-  its office and to the detriment of the secular arm, shall be taken and
-  withdrawn from it, and the clergy itself shall be brought back to the
-  evangelical rule and an apostolic life such as that which Christ and
-  his apostles led....
-
-  IV. All mortal sins, and in particular all public and other disorders,
-  which are contrary to God's law shall in every rank of life be duly
-  and judiciously prohibited and destroyed by those whose office it is.
-
-These articles, which contain the essence of the Hussite doctrine, were
-rejected by Sigismund, mainly through the influence of the papal
-legates, who considered them prejudicial to the authority of the Roman
-see. Hostilities therefore continued. Though Sigismund had retired from
-Prague, the castles of Vysehrad and Hradcany remained in possession of
-his troops. The citizens of Prague laid siege to the Vysehrad, and
-towards the end of October (1420) the garrison was on the point of
-capitulating through famine. Sigismund attempted to relieve the
-fortress, but was decisively defeated by the Hussites on the 1st of
-November near the village of Pankrac. The castles of Vysehrad and
-Hradcany now capitulated, and shortly afterwards almost all Bohemia fell
-into the hands of the Hussites. Internal troubles prevented them from
-availing themselves completely of their victory. At Prague a demagogue,
-the priest John of Zelivo, for a time obtained almost unlimited
-authority over the lower classes of the townsmen; and at Tabor a
-communistic movement (that of the so-called Adamites) was sternly
-suppressed by Zizka. Shortly afterwards a new crusade against the
-Hussites was undertaken. A large German army entered Bohemia, and in
-August 1421 laid siege to the town of Zatec (Saaz). The crusaders hoped
-to be joined in Bohemia by King Sigismund, but that prince was detained
-in Hungary. After an unsuccessful attempt to storm Zatec the crusaders
-retreated somewhat ingloriously, on hearing that the Hussite troops were
-approaching. Sigismund only arrived in Bohemia at the end of the year
-1421. He took possession of the town of Kutna Hora (Kuttenberg), but was
-decisively defeated by Zizka at Nemecky Brod (Deutschbrod) on the 6th of
-January 1422. Bohemia was now again for a time free from foreign
-intervention, but internal discord again broke out caused partly by
-theological strife, partly by the ambition of agitators. John of Zelivo
-was on the 9th of March 1422 arrested by the town council of Prague and
-decapitated. There were troubles at Tabor also, where a more advanced
-party opposed Zizka's authority. Bohemia obtained a temporary respite
-when, in 1422, Prince Sigismund Korybutovic of Poland became for a short
-time ruler of the country. His authority was recognized by the Utraquist
-nobles, the citizens of Prague, and the more moderate Taborites,
-including Zizka. Korybutovic, however, remained but a short time in
-Bohemia; after his departure civil war broke out, the Taborites opposing
-in arms the more moderate Utraquists, who at this period are also called
-by the chroniclers the "Praguers," as Prague was their principal
-stronghold. On the 27th of April 1423, Zizka now again leading, the
-Taborites defeated at Horic the Utraquist army under Cenek of
-Wartemberg; shortly afterwards an armistice was concluded at
-Konopist.
-
-Papal influence had meanwhile succeeded in calling forth a new crusade
-against Bohemia, but it resulted in complete failure. In spite of the
-endeavours of their rulers, the Slavs of Poland and Lithuania did not
-wish to attack the kindred Bohemians; the Germans were prevented by
-internal discord from taking joint action against the Hussites; and the
-king of Denmark, who had landed in Germany with a large force intending
-to take part in the crusade, soon returned to his own country. Free for
-a time from foreign aggression, the Hussites invaded Moravia, where a
-large part of the population favoured their creed; but, again paralysed
-by dissensions, soon returned to Bohemia. The city of Koniggratz
-(Kralove Hradec), which had been under Utraquist rule, espoused the
-doctrine of Tabor, and called Zizka to its aid. After several military
-successes gained by Zizka (q.v.) in 1423 and the following year, a
-treaty of peace between the Hussites was concluded on the 13th of
-September 1424 at Liben, a village near Prague, now part of that city.
-
-In 1426 the Hussites were again attacked by foreign enemies. In June of
-that year their forces, led by Prokop the Great--who took the command of
-the Taborites shortly after Zizka's death in October 1424--and Sigismund
-Korybutovic, who had returned to Bohemia, signally defeated the Germans
-at Aussig (Usti nad Labem). After this great victory, and another at
-Tachau in 1427, the Hussites repeatedly invaded Germany, though they
-made no attempt to occupy permanently any part of the country.
-
-The almost uninterrupted series of victories of the Hussites now
-rendered vain all hope of subduing them by force of arms. Moreover, the
-conspicuously democratic character of the Hussite movement caused the
-German princes, who were afraid that such views might extend to
-their own countries, to desire peace. Many Hussites, particularly the
-Utraquist clergy, were also in favour of peace. Negotiations for this
-purpose were to take place at the oecumenical council which had been
-summoned to meet at Basel on the 3rd of March 1431. The Roman see
-reluctantly consented to the presence of heretics at this council, but
-indignantly rejected the suggestion of the Hussites that members of the
-Greek Church, and representatives of all Christian creeds, should also
-be present. Before definitely giving its consent to peace negotiations,
-the Roman Church determined on making a last effort to reduce the
-Hussites to subjection. On the 1st of August 1431 a large army of
-crusaders, under Frederick, margrave of Brandenburg, whom Cardinal
-Cesarini accompanied as papal legate, crossed the Bohemian frontier; on
-the 14th of August it reached the town of Domazlice (Tauss); but on
-the arrival of the Hussite army under Prokop the crusaders immediately
-took to flight, almost without offering resistance.
-
-On the 15th of October the members of the council, who had already
-assembled at Basel, issued a formal invitation to the Hussites to take
-part in its deliberations. Prolonged negotiations ensued; but finally a
-Hussite embassy, led by Prokop and including John of Rokycan, the
-Taborite bishop Nicolas of Pelhrimov, the "English Hussite," Peter
-Payne and many others, arrived at Basel on the 4th of January 1433. It
-was found impossible to arrive at an agreement. Negotiations were not,
-however, broken off; and a change in the political situation of Bohemia
-finally resulted in a settlement. In 1434 war again broke out between
-the Utraquists and the Taborites. On the 30th of May of that year the
-Taborite army, led by Prokop the Great and Prokop the Less, who both
-fell in the battle, was totally defeated and almost annihilated at
-Lipan. The moderate party thus obtained the upper hand; and it
-formulated its demands in a document which was finally accepted by the
-Church of Rome in a slightly modified form, and which is known as "the
-compacts." The compacts, mainly founded on the articles of Prague,
-declare that:--
-
-  1. The Holy Sacrament is to be given freely in both kinds to all
-  Christians in Bohemia and Moravia, and to those elsewhere who adhere
-  to the faith of these two countries.
-
-  2. All mortal sins shall be punished and extirpated by those whose
-  office it is so to do.
-
-  3. The word of God is to be freely and truthfully preached by the
-  priests of the Lord, and by worthy deacons.
-
-  4. The priests in the time of the law of grace shall claim no
-  ownership of worldly possessions.
-
-On the 5th of July 1436 the compacts were formally accepted and signed
-at Iglau, in Moravia, by King Sigismund, by the Hussite delegates, and
-by the representatives of the Roman Church. The last-named, however,
-refused to recognize as archbishop of Prague, John of Rokycan, who had
-been elected to that dignity by the estates of Bohemia. The Utraquist
-creed, frequently varying in its details, continued to be that of the
-established church of Bohemia till all non-Roman religious services were
-prohibited shortly after the battle of the White Mountain in 1620. The
-Taborite party never recovered from its defeat at Lipan, and after the
-town of Tabor had been captured by George of Podebrad in 1452 Utraquist
-religious worship was established there. The Bohemian brethren, whose
-intellectual originator was Peter Chelcicky, but whose actual founders
-were Brother Gregory, a nephew of Archbishop Rokycan, and Michael,
-curate of Zamberk, to a certain extent continued the Taborite
-traditions, and in the 15th and 16th centuries included most of the
-strongest opponents of Rome in Bohemia. J. A. Komensky (Comenius), a
-member of the brotherhood, claimed for the members of his church that
-they were the genuine inheritors of the doctrines of Hus. After the
-beginning of the German Reformation many Utraquists adopted to a large
-extent the doctrines of Luther and Calvin; and in 1567 obtained the
-repeal of the compacts, which no longer seemed sufficiently
-far-reaching. From the end of the 16th century the inheritors of the
-Hussite tradition in Bohemia were included in the more general name of
-"Protestants" borne by the adherents of the Reformation.
-
-  All histories of Bohemia devote a large amount of space to the Hussite
-  movement. See Count Lutzow, _Bohemia; an Historical Sketch_ (London,
-  1896); Palacky, _Geschichte von Bohmen_; Bachmann, _Geschichte
-  Bohmens_; L. Krummel, _Geschichte der bohmischen Reformation_ (Gotha,
-  1866) and _Utraquisten und Taboriten_ (Gotha, 1871); Ernest Denis,
-  _Huss et la guerre des Hussites_ (Paris, 1878); H. Toman, _Husitske
-  Valecnictvi_ (Prague, 1898).     (L.)
-
-
-
-
-HUSTING (O. Eng. _husting_, from Old Norwegian _husthing_), the "thing"
-or "ting," i.e. assembly, of the household of personal followers or
-retainers of a king, earl or chief, contrasted with the "folkmoot," the
-assembly of the whole people. "Thing" meant an inanimate object, the
-ordinary meaning at the present day, also a cause or suit, and an
-assembly; a similar development of meaning is found in the Latin _res_.
-The word still appears in the names of the legislative assemblies of
-Norway, the _Storthing_ and of Iceland, the _Althing_. "Husting," or
-more usually in the plural "hustings," was the name of a court of the
-city of London. This court was formerly the county court for the city
-and was held before the lord mayor, the sheriffs and aldermen, for pleas
-of land, common pleas and appeals from the sheriffs. It had probate
-jurisdiction and wills were registered. All this jurisdiction has long
-been obsolete, but the court still sits occasionally for registering
-gifts made to the city. The charter of Canute (1032) contains a
-reference to "hustings" weights, which points to the early establishment
-of the court. It is doubtful whether courts of this name were held in
-other towns, but John Cowell (1554-1611) in his _Interpreter_ (1601)
-s.v., "Hustings," says that according to Fleta there were such courts at
-Winchester, York, Lincoln, Sheppey and elsewhere, but the passage from
-Fleta, as the _New English Dictionary_ points out, does not necessarily
-imply this (11. lv. _Habet etiam Rex curiam in civitatibus ... et in
-locis ... sicut in Hustingis London, Winton, &c._). The ordinary use of
-"hustings" at the present day for the platform from which a candidate
-speaks at a parliamentary or other election, or more widely for a
-political candidate's election campaign, is derived from the application
-of the word, first to the platform in the Guildhall on which the London
-court was held, and next to that from which the public nomination of
-candidates for a parliamentary election was formerly made, and from
-which the candidate addressed the electors. The Ballot Act of 1872 did
-away with this public declaration of the nomination.
-
-
-
-
-HUSUM, a town in the Prussian province of Schleswig-Holstein, in a
-fertile district 2(1/2) m. inland from the North Sea, on the canalized
-Husumer Au, which forms its harbour and roadstead, 99 m. N.W. from
-Hamburg on a branch line from Tonning. Pop. (1900) 8268. It has steam
-communication with the North Frisian Islands (Nordstrand, Fohr and
-Sylt), and is a port for the cattle trade with England. Besides a ducal
-palace and park, it possesses an Evangelical church and a gymnasium.
-Cattle markets are held weekly, and in them, as also in cereals, a
-lively export trade is done. There are also extensive oyster fisheries,
-the property of the state, the yield during the season being very
-considerable. Husum is the birthplace of Johann Georg Forchhammer
-(1794-1865), the mineralogist, Peter Wilhelm Forchhammer (1801-1894),
-the archaeologist, and Theodore Storm (1817-1888), the poet, to the last
-of whom a monument has been erected here.
-
-Husum is first mentioned in 1252, and its first church was built in
-1431. Wisby rights were granted it in 1582, and in 1603 it received
-municipal privileges from the duke of Holstein. It suffered greatly from
-inundations in 1634 and 1717.
-
-  See Christiansen, _Die Geschichte Husums_ (Husum, 1903); and
-  Henningsen, _Das Stiftungsbuch der Stadt Husum_ (Husum, 1904).
-
-
-
-
-HUTCHESON, FRANCIS (1694-1746), English philosopher, was born on the 8th
-of August 1694. His birthplace was probably the townland of Drumalig, in
-the parish of Saintfield and county of Down, Ireland.[1] Though the
-family had sprung from Ayrshire, in Scotland, both his father and
-grandfather were ministers of dissenting congregations in the north of
-Ireland. Hutcheson was educated partly by his grandfather, partly at an
-academy, where according to his biographer, Dr Leechman, he was taught
-"the ordinary scholastic philosophy which was in vogue in those
-days." In 1710 he entered the university of Glasgow, where he spent six
-years, at first in the study of philosophy, classics and general
-literature, and afterwards in the study of theology. On quitting the
-university, he returned to the north of Ireland, and received a licence
-to preach. When, however, he was about to enter upon the pastorate of a
-small dissenting congregation he changed his plans on the advice of a
-friend and opened a private academy in Dublin. In Dublin his literary
-attainments gained him the friendship of many prominent inhabitants.
-Among these was Archbishop King (author of the _De origine mali_), who
-resisted all attempts to prosecute Hutcheson in the archbishop's court
-for keeping a school without the episcopal licence. Hutcheson's
-relations with the clergy of the Established Church, especially with the
-archbishops of Armagh and Dublin, Hugh Boulter (1672-1742) and William
-King (1650-1729), seem to have been most cordial, and his biographer, in
-speaking of "the inclination of his friends to serve him, the schemes
-proposed to him for obtaining promotion," &c., probably refers to some
-offers of preferment, on condition of his accepting episcopal
-ordination. These offers, however, were unavailing.
-
-While residing in Dublin, Hutcheson published anonymously the four
-essays by which he is best known, namely, the _Inquiry concerning
-Beauty, Order, Harmony and Design_, the _Inquiry concerning Moral Good
-and Evil_, in 1725, the _Essay on the Nature and Conduct of the Passions
-and Affections_ and _Illustrations upon the Moral Sense_, in 1728. The
-alterations and additions made in the second edition of these Essays
-were published in a separate form in 1726. To the period of his Dublin
-residence are also to be referred the _Thoughts on Laughter_ (a
-criticism of Hobbes) and the Observations on the _Fable of the Bees_,
-being in all six letters contributed to _Hibernicus' Letters_, a
-periodical which appeared, in Dublin (1725-1727, 2nd ed. 1734). At the
-end of the same period occurred the controversy in the _London Journal_
-with Gilbert Burnet (probably the second son of Dr Gilbert Burnet,
-bishop of Salisbury); on the "True Foundation of Virtue or Moral
-Goodness." All these letters were collected in one volume (Glasgow,
-1772).
-
-In 1729 Hutcheson succeeded his old master, Gershom Carmichael, in the
-chair of moral philosophy in the university of Glasgow. It is curious
-that up to this time all his essays and letters had been published
-anonymously, though their authorship appears to have been well known. In
-1730 he entered on the duties of his office, delivering an inaugural
-lecture (afterwards published), _De naturali hominum socialitate_. It
-was a great relief to him after the drudgery of school work to secure
-leisure for his favourite studies; "non levi igitur laetitia commovebar
-cum almam matrem Academiam me, suum olim alumnum, in libertatem
-asseruisse audiveram." Yet the works on which Hutcheson's reputation
-rests had already been published.
-
-The remainder of his life he devoted to his professorial duties. His
-reputation as a teacher attracted many young men, belonging to
-dissenting families, from England and Ireland, and he enjoyed a
-well-deserved popularity among both his pupils and his colleagues.
-Though somewhat quick-tempered, he was remarkable for his warm feelings
-and generous impulses. He was accused in 1738 before the Glasgow
-presbytery for "following two false and dangerous doctrines: first, that
-the standard of moral goodness was the promotion of the happiness of
-others; and second, that we could have a knowledge of good and evil
-without and prior to a knowledge of God" (Rae, _Life of Adam Smith_,
-1895). The accusation seems to have had no result.
-
-In addition to the works named, the following were published during
-Hutcheson's lifetime: a pamphlet entitled _Considerations on Patronage_
-(1735); _Philosophiae moralis institutio compendiaria, ethices et
-jurisprudentiae naturalis elementa continens, lib. iii._ (Glasgow,
-1742); _Metaphysicae synopsis ontologiam et pneumatologiam complectens_
-(Glasgow, 1742). The last work was published anonymously. After his
-death, his son, Francis Hutcheson (c. 1722-1773), author of a number of
-popular songs (e.g. "As Colin one evening," "Jolly Bacchus," "Where
-Weeping Yews"), published much the longest, though by no means the most
-interesting, of his works, _A System of Moral Philosophy, in Three
-Books_ (2 vols., London, 1755). To this is prefixed a life of the
-author, by Dr William Leechman (1706-1785), professor of divinity in the
-university of Glasgow. The only remaining work assigned to Hutcheson is
-a small treatise on _Logic_ (Glasgow, 1764). This compendium, together
-with the _Compendium of Metaphysics_, was republished at Strassburg in
-1722.
-
-Thus Hutcheson dealt with metaphysics, logic and ethics. His importance
-is, however, due almost entirely to his ethical writings, and among
-these primarily to the four essays and the letters published during his
-residence in Dublin. His standpoint has a negative and a positive
-aspect; he is in strong opposition to Thomas Hobbes and Bernard de
-Mandeville, and in fundamental agreement with Shaftesbury (Anthony
-Ashley Cooper, 3rd earl of Shaftesbury), whose name he very properly
-coupled with his own on the title-page of the first two essays. There
-are no two names, perhaps, in the history of English moral philosophy,
-which stand in a closer connexion. The analogy drawn between beauty and
-virtue, the functions assigned to the moral sense, the position that the
-benevolent feelings form an original and irreducible part of our nature,
-and the unhesitating adoption of the principle that the test of virtuous
-action is its tendency to promote the general welfare are obvious and
-fundamental points of agreement between the two authors.
-
-  I. _Ethics._--According to Hutcheson, man has a variety of senses,
-  internal as well as external, reflex as well as direct, the general
-  definition of a sense being "any determination of our minds to receive
-  ideas independently on our will, and to have perceptions of pleasure
-  and pain" (_Essay on the Nature and Conduct of the Passions_, sect.
-  1). He does not attempt to give an exhaustive enumeration of these
-  "senses," but, in various parts of his works, he specifies, besides
-  the five external senses commonly recognized (which, he rightly hints,
-  might be added to),--(1) consciousness, by which each man has a
-  perception of himself and of all that is going on in his own mind
-  (_Metaph. Syn._ pars i. cap. 2); (2) the sense of beauty (sometimes
-  called specifically "an internal sense"); (3) a public sense, or
-  sensus communis, "a determination to be pleased with the happiness of
-  others and to be uneasy at their misery"; (4) the moral sense, or
-  "moral sense of beauty in actions and affections, by which we perceive
-  virtue or vice, in ourselves or others"; (5) a sense of honour, or
-  praise and blame, "which makes the approbation or gratitude of others
-  the necessary occasion of pleasure, and their dislike, condemnation or
-  resentment of injuries done by us the occasion of that uneasy
-  sensation called shame"; (6) a sense of the ridiculous. It is plain,
-  as the author confesses, that there may be "other perceptions,
-  distinct from all these classes," and, in fact, there seems to be no
-  limit to the number of "senses" in which a psychological division of
-  this kind might result.
-
-  Of these "senses" that which plays the most important part in
-  Hutcheson's ethical system is the "moral sense." It is this which
-  pronounces immediately on the character of actions and affections,
-  approving those which are virtuous, and disapproving those which are
-  vicious. "His principal design," he says in the preface to the two
-  first treatises, "is to show that human nature was not left quite
-  indifferent in the affair of virtue, to form to itself observations
-  concerning the advantage or disadvantage of actions, and accordingly
-  to regulate its conduct. The weakness of our reason, and the
-  avocations arising from the infirmity and necessities of our nature,
-  are so great that very few men could ever have formed those long
-  deductions of reasons which show some actions to be in the whole
-  advantageous to the agent, and their contraries pernicious. The Author
-  of nature has much better furnished us for a virtuous conduct than our
-  moralists seem to imagine, by almost as quick and powerful
-  instructions as we have for the preservation of our bodies. He has
-  made virtue a lovely form, to excite our pursuit of it, and has given
-  us strong affections to be the springs of each virtuous action."
-  Passing over the appeal to final causes involved in this and similar
-  passages, as well as the assumption that the "moral sense" has had no
-  growth or history, but was "implanted" in man exactly in the condition
-  in which it is now to be found among the more civilized races, an
-  assumption common to the systems of both Hutcheson and Butler, it may
-  be remarked that this use of the term "sense" has a tendency to
-  obscure the real nature of the process which goes on in an act of
-  moral judgment. For, as is so clearly established by Hume, this act
-  really consists of two parts: one an act of deliberation, more or less
-  prolonged, resulting in an intellectual judgment; the other a reflex
-  feeling, probably instantaneous, of satisfaction at actions which we
-  denominate good, of dissatisfaction at those which we denominate bad.
-  By the intellectual part of this process we refer the action or habit
-  to a certain class; but no sooner is the intellectual process
-  completed than there is excited in us a feeling similar to that
-  which myriads of actions and habits of the same class, or deemed to be
-  of the same class, have excited in us on former occasions. Now,
-  supposing the latter part of this process to be instantaneous, uniform
-  and exempt from error, the former certainly is not. All mankind may,
-  apart from their selfish interests, approve that which is virtuous or
-  makes for the general good, but surely they entertain the most widely
-  divergent opinions, and, in fact, frequently arrive at directly
-  opposite conclusions as to particular actions and habits. This obvious
-  distinction is undoubtedly recognized by Hutcheson in his analysis of
-  the mental process preceding moral action, nor does he invariably
-  ignore it, even when treating of the moral approbation or
-  disapprobation which is subsequent on action. None the less, it
-  remains true that Hutcheson, both by his phraseology, and by the
-  language in which he describes the process of moral approbation, has
-  done much to favour that loose, popular view of morality which,
-  ignoring the necessity of deliberation and reflection, encourages
-  hasty resolves and unpremeditated judgments. The term "moral sense"
-  (which, it may be noticed, had already been employed by Shaftesbury,
-  not only, as Dr Whewell appears to intimate, in the margin, but also
-  in the text of his _Inquiry_), if invariably coupled with the term
-  "moral judgment," would be open to little objection; but, taken alone,
-  as designating the complex process of moral approbation, it is liable
-  to lead not only to serious misapprehension but to grave practical
-  errors. For, if each man's decisions are solely the result of an
-  immediate intuition of the moral sense, why be at any pains to test,
-  correct or review them? Or why educate a faculty whose decisions are
-  infallible? And how do we account for differences in the moral
-  decisions of different societies, and the observable changes in a
-  man's own views? The expression has, in fact, the fault of most
-  metaphorical terms: it leads to an exaggeration of the truth which it
-  is intended to suggest.
-
-  But though Hutcheson usually describes the moral faculty as acting
-  instinctively and immediately, he does not, like Butler, confound the
-  moral faculty with the moral standard. The test or criterion of right
-  action is with Hutcheson, as with Shaftesbury, its tendency to promote
-  the general welfare of mankind. He thus anticipates the utilitarianism
-  of Bentham--and not only in principle, but even in the use of the
-  phrase "the greatest happiness for the greatest number" (_Inquiry
-  concerning Moral Good and Evil_, sect. 3).
-
-  It is curious that Hutcheson did not realize the inconsistency of this
-  external criterion with his fundamental ethical principle. Intuition
-  has no possible connexion with an empirical calculation of results,
-  and Hutcheson in adopting such a criterion practically denies his
-  fundamental assumption.
-
-  As connected with Hutcheson's virtual adoption of the utilitarian
-  standard may be noticed a kind of moral algebra, proposed for the
-  purpose of "computing the morality of actions." This calculus occurs
-  in the _Inquiry concerning Moral Good and Evil_, sect. 3.
-
-
-    Benevolence.
-
-  The most distinctive of Hutcheson's ethical doctrines still remaining
-  to be noticed is what has been called the "benevolent theory" of
-  morals. Hobbes had maintained that all our actions, however disguised
-  under apparent sympathy, have their roots in self-love. Hutcheson not
-  only maintains that benevolence is the sole and direct source of many
-  of our actions, but, by a not unnatural recoil, that it is the only
-  source of those actions of which, on reflection, we approve.
-  Consistently with this position, actions which flow from self-love
-  only are pronounced to be morally indifferent. But surely, by the
-  common consent of civilized men, prudence, temperance, cleanliness,
-  industry, self-respect and, in general, the "personal virtues," are
-  regarded, and rightly regarded, as fitting objects of moral
-  approbation. This consideration could hardly escape any author,
-  however wedded to his own system, and Hutcheson attempts to extricate
-  himself from the difficulty by laying down the position that a man may
-  justly regard himself as a part of the rational system, and may thus
-  "be, in part, an object of his own benevolence" (Ibid.),--a curious
-  abuse of terms, which really concedes the question at issue. Moreover,
-  he acknowledges that, though self-love does not merit approbation,
-  neither, except in its extreme forms, does it merit condemnation,
-  indeed the satisfaction of the dictates of self-love is one of the
-  very conditions of the preservation of society. To press home the
-  inconsistencies involved in these various statements would be a
-  superfluous task.
-
-  The vexed question of liberty and necessity appears to be carefully
-  avoided in Hutcheson's professedly ethical works. But, in the
-  _Synopsis metaphysicae_, he touches on it in three places, briefly
-  stating both sides of the question, but evidently inclining to that
-  which he designates as the opinion of the Stoics in opposition to what
-  he designates as the opinion of the Peripatetics. This is
-  substantially the same as the doctrine propounded by Hobbes and Locke
-  (to the latter of whom Hutcheson refers in a note), namely, that our
-  will is determined by motives in conjunction with our general
-  character and habit of mind, and that the only true liberty is the
-  liberty of acting as we will, not the liberty of willing as we will.
-  Though, however, his leaning is clear, he carefully avoids
-  dogmatizing, and deprecates the angry controversies to which the
-  speculations on this subject had given rise.
-
-  It is easy to trace the influence of Hutcheson's ethical theories on
-  the systems of Hume and Adam Smith. The prominence given by these
-  writers to the analysis of moral action and moral approbation, with
-  the attempt to discriminate the respective provinces of the reason and
-  the emotions in these processes, is undoubtedly due to the influence
-  of Hutcheson. To a study of the writings of Shaftesbury and Hutcheson
-  we might, probably, in large measure, attribute the unequivocal
-  adoption of the utilitarian standard by Hume, and, if this be the
-  case, the name of Hutcheson connects itself, through Hume, with the
-  names of Priestley, Paley and Bentham. Butler's _Sermons_ appeared in
-  1726, the year after the publication of Hutcheson's two first essays,
-  and the parallelism between the "conscience" of the one writer and the
-  "moral sense" of the other is, at least, worthy of remark.
-
-  II. _Mental Philosophy._--In the sphere of mental philosophy and logic
-  Hutcheson's contributions are by no means so important or original as
-  in that of moral philosophy. They are interesting mainly as a link
-  between Locke and the Scottish school. In the former subject the
-  influence of Locke is apparent throughout. All the main outlines of
-  Locke's philosophy seem, at first sight, to be accepted as a matter of
-  course. Thus, in stating his theory of the moral sense, Hutcheson is
-  peculiarly careful to repudiate the doctrine of innate ideas (see, for
-  instance, _Inquiry concerning Moral Good and Evil_, sect. 1 ad fin.,
-  and sect. 4; and compare _Synopsis Metaphysicae_, pars i. cap. 2). At
-  the same time he shows more discrimination than does Locke in
-  distinguishing between the two uses of this expression, and between
-  the legitimate and illegitimate form of the doctrine (Syn. Metaph.
-  pars i. cap. 2). All our ideas are, as by Locke, referred to external
-  or internal sense, or, in other words, to sensation and reflection
-  (see, for instance, _Syn. Metaph._ pars i. cap. 1; _Logicae Compend._
-  pars i. cap. 1; _System of Moral Philosophy_, bk. i. ch. 1). It is,
-  however, a most important modification of Locke's doctrine, and one
-  which connects Hutcheson's mental philosophy with that of Reid, when
-  he states that the ideas of extension, figure, motion and rest "are
-  more properly ideas accompanying the sensations of sight and touch
-  than the sensations of either of these senses"; that the idea of self
-  accompanies every thought, and that the ideas of number, duration and
-  existence accompany every other idea whatsoever (see _Essay on the
-  Nature and Conduct of the Passions_, sect. i. art. 1; _Syn. Metaph._
-  pars i. cap. 1, pars ii. cap. 1; Hamilton on Reid, p. 124, note).
-  Other important points in which Hutcheson follows the lead of Locke
-  are his depreciation of the importance of the so-called laws of
-  thought, his distinction between the primary and secondary qualities
-  of bodies, the position that we cannot know the inmost essences of
-  things ("intimae rerum naturae sive essentiae"), though they excite
-  various ideas in us, and the assumption that external things are known
-  only through the medium of ideas (_Syn. Metaph._ pars i. cap. 1),
-  though, at the same time, we are assured of the existence of an
-  external world corresponding to these ideas. Hutcheson attempts to
-  account for our assurance of the reality of an external world by
-  referring it to a natural instinct (_Syn. Metaph._ pars i. cap. 1). Of
-  the correspondence or similitude between our ideas of the primary
-  qualities of things and the things themselves God alone can be
-  assigned as the cause. This similitude has been effected by Him
-  through a law of nature. "Haec prima qualitatum primariarum perceptio,
-  sive mentis actio quaedam sive passio dicatur, non alia similitudinis
-  aut convenientiae inter ejusmodi ideas et res ipsas causa assignari
-  posse videtur, quam ipse Deus, qui certa naturae lege hoc efficit, ut
-  notiones, quae rebus praesentibus excitantur, sint ipsis similes, aut
-  saltem earum habitudines, si non veras quantitates, depingant" (pars
-  ii. cap. 1). Locke does speak of God "annexing" certain ideas to
-  certain motions of bodies; but nowhere does he propound a theory so
-  definite as that here propounded by Hutcheson, which reminds us at
-  least as much of the speculations of Malebranche as of those of Locke.
-
-  Amongst the more important points in which Hutcheson diverges from
-  Locke is his account of the idea of personal identity, which he
-  appears to have regarded as made known to us directly by
-  consciousness. The distinction between body and mind, _corpus_ or
-  _materia_ and _res cogitans_, is more emphatically accentuated by
-  Hutcheson than by Locke. Generally, he speaks as if we had a direct
-  consciousness of mind as distinct from body (see, for instance, _Syn.
-  Metaph._ pars ii. cap. 3), though, in the posthumous work on _Moral
-  Philosophy_, he expressly states that we know mind as we know body "by
-  qualities immediately perceived though the substance of both be
-  unknown" (bk. i. ch. 1). The distinction between perception proper and
-  sensation proper, which occurs by implication though it is not
-  explicitly worked out (see Hamilton's _Lectures on Metaphysics_, Lect.
-  24; Hamilton's edition of _Dugald Stewart's Works_, v. 420), the
-  imperfection of the ordinary division of the external senses into five
-  classes, the limitation of consciousness to a special mental faculty
-  (severely criticized in Sir W. Hamilton's _Lectures on Metaphysics_,
-  Lect. xii.) and the disposition to refer on disputed questions of
-  philosophy not so much to formal arguments as to the testimony of
-  consciousness and our natural instincts are also amongst the points in
-  which Hutcheson supplemented or departed from the philosophy of Locke.
-  The last point can hardly fail to suggest the "common-sense
-  philosophy" of Reid.
-
-  Thus, in estimating Hutcheson's position, we find that in particular
-  questions he stands nearer to Locke, but in the general spirit of his
-  philosophy he seems to approach more closely to his Scottish
-  successors.
-
-  The short _Compendium of Logic_, which is more original than such
-  works usually are, is remarkable chiefly for the large
-  proportion of psychological matter which it contains. In these parts
-  of the book Hutcheson mainly follows Locke. The technicalities of the
-  subject are passed lightly over, and the book is readable. It may be
-  specially noticed that he distinguishes between the mental result and
-  its verbal expression [idea--term; judgment--proposition], that he
-  constantly employs the word "idea," and that he defines logical truth
-  as "convenientia signorum cum rebus significatis" (or "propositionis
-  convenientia cum rebus ipsis," _Syn. Metaph._ pars i. cap 3), thus
-  implicitly repudiating a merely formal view of logic.
-
-  III. _Aesthetics._--Hutcheson may further be regarded as one of the
-  earliest modern writers on aesthetics. His speculations on this
-  subject are contained in the _Inquiry concerning Beauty, Order,
-  Harmony and Design_, the first of the two treatises published in 1725.
-  He maintains that we are endowed with a special sense by which we
-  perceive beauty, harmony and proportion. This is a _reflex_ sense,
-  because it presupposes the action of the external senses of sight and
-  hearing. It may be called an internal sense, both in order to
-  distinguish its perceptions from the mere perceptions of sight and
-  hearing, and because "in some other affairs, where our external senses
-  are not much concerned, we discern a sort of beauty, very like in many
-  respects to that observed in sensible objects, and accompanied with
-  like pleasure" (_Inquiry, &c._, sect. 1). The latter reason leads him
-  to call attention to the beauty perceived in universal truths, in the
-  operations of general causes and in moral principles and actions.
-  Thus, the analogy between beauty and virtue, which was so favourite a
-  topic with Shaftesbury, is prominent in the writings of Hutcheson
-  also. Scattered up and down the treatise there are many important and
-  interesting observations which our limits prevent us from noticing.
-  But to the student of mental philosophy it may be specially
-  interesting to remark that Hutcheson both applies the principle of
-  association to explain our ideas of beauty and also sets limits to its
-  application, insisting on there being "a natural power of perception
-  or sense of beauty in objects, antecedent to all custom, education or
-  example" (see _Inquiry, &c._, sects. 6, 7; Hamilton's _Lectures on
-  Metaphysics_, Lect. 44 ad fin.).
-
-  Hutcheson's writings naturally gave rise to much controversy. To say
-  nothing of minor opponents, such as "Philaretus" (Gilbert Burnet,
-  already alluded to), Dr John Balguy (1686-1748), prebendary of
-  Salisbury, the author of two tracts on "The Foundation of Moral
-  Goodness," and Dr John Taylor (1694-1761) of Norwich, a minister of
-  considerable reputation in his time (author of _An Examination of the
-  Scheme of Morality advanced by Dr Hutcheson_), the essays appear to
-  have suggested, by antagonism, at least two works which hold a
-  permanent place in the literature of English ethics--Butler's
-  _Dissertation on the Nature of Virtue_, and Richard Price's _Treatise
-  of Moral Good and Evil_ (1757). In this latter work the author
-  maintains, in opposition to Hutcheson, that actions are _in
-  themselves_ right or wrong, that right and wrong are simple ideas
-  incapable of analysis, and that these ideas are perceived immediately
-  by the understanding. We thus see that, not only directly but also
-  through the replies which it called forth, the system of Hutcheson, or
-  at least the system of Hutcheson combined with that of Shaftesbury,
-  contributed, in large measure, to the formation and development of
-  some of the most important of the modern schools of ethics (see
-  especially art. ETHICS).
-
-  AUTHORITIES.--Notices of Hutcheson occur in most histories, both of
-  general philosophy and of moral philosophy, as, for instance, in pt.
-  vii. of Adam Smith's _Theory of Moral Sentiments_; Mackintosh's
-  _Progress of Ethical Philosophy_; Cousin, _Cours d'histoire de la
-  philosophie morale du XVIII^e siecle_; Whewell's _Lectures on the
-  History of Moral Philosophy in England_; A. Bain's _Mental and Moral
-  Science_; Noah Porter's Appendix to the English translation of
-  Ueberweg's _History of Philosophy_; Sir Leslie Stephen's _History of
-  English Thought in the Eighteenth Century_, &c. See also Martineau,
-  _Types of Ethical Theory_ (London, 1902); W. R. Scott, _Francis
-  Hutcheson_ (Cambridge, 1900); Albee, _History of English
-  Utilitarianism_ (London, 1902); T. Fowler, _Shaftesbury and Hutcheson_
-  (London, 1882); J. McCosh, _Scottish Philosophy_ (New York, 1874). Of
-  Dr Leechman's _Biography_ of Hutcheson we have already spoken. J.
-  Veitch gives an interesting account of his professorial work in
-  Glasgow, _Mind_, ii. 209-212.     (T. F.; X.)
-
-
-FOOTNOTE:
-
-  [1] See _Belfast Magazine_ for August 1813.
-
-
-
-
-HUTCHINSON, ANNE (c. 1600-1643), American religious enthusiast, leader
-of the "Antinomians" in New England, was born in Lincolnshire, England,
-about 1600. She was the daughter of a clergyman named Francis Marbury,
-and, according to tradition, was a cousin of John Dryden. She married
-William Hutchinson, and in 1634 emigrated to Boston, Massachusetts, as a
-follower and admirer of the Rev. John Cotton. Her orthodoxy was
-suspected and for a time she was not admitted to the church, but soon
-she organized meetings among the Boston women, among whom her
-exceptional ability and her services as a nurse had given her great
-influence; and at these meetings she discussed and commented upon recent
-sermons and gave expression to her own theological views. The meetings
-became increasingly popular, and were soon attended not only by the
-women but even by some of the ministers and magistrates, including
-Governor Henry Vane. At these meetings she asserted that she, Cotton and
-her brother-in-law, the Rev. John Wheelwright--whom she was trying to
-make second "teacher" in the Boston church--were under a "covenant of
-grace," that they had a special inspiration, a "peculiar indwelling of
-the Holy Ghost," whereas the Rev. John Wilson, the pastor of the Boston
-church, and the other ministers of the colony were under a "covenant of
-works." Anne Hutchinson was, in fact, voicing a protest against the
-legalism of the Massachusetts Puritans, and was also striking at the
-authority of the clergy in an intensely theocratic community. In such a
-community a theological controversy inevitably was carried into secular
-politics, and the entire colony was divided into factions. Mrs
-Hutchinson was supported by Governor Vane, Cotton, Wheelwright and the
-great majority of the Boston church; opposed to her were Deputy-Governor
-John Winthrop, Wilson and all of the country magistrates and churches.
-At a general fast, held late in January 1637, Wheelwright preached a
-sermon which was taken as a criticism of Wilson and his friends. The
-strength of the parties was tested at the General Court of Election of
-May 1637, when Winthrop defeated Vane for the governorship. Cotton
-recanted, Vane returned to England in disgust, Wheelwright was tried and
-banished and the rank and file either followed Cotton in making
-submission or suffered various minor punishments. Mrs Hutchinson was
-tried (November 1637) by the General Court chiefly for "traducing the
-ministers," and was sentenced to banishment; later, in March 1638, she
-was tried before the Boston church and was formally excommunicated. With
-William Coddington (d. 1678), John Clarke and others, she established a
-settlement on the island of Aquidneck (now Rhode Island) in 1638. Four
-years later, after the death of her husband, she settled on Long Island
-Sound near what is now New Rochelle, Westchester county, New York, and
-was killed in an Indian rising in August 1643, an event regarded in
-Massachusetts as a manifestation of Divine Providence. Anne Hutchinson
-and her followers were called "Antinomians," probably more as a term of
-reproach than with any special reference to her doctrinal theories; and
-the controversy in which she was involved is known as the "Antinomian
-Controversy."
-
-  See C. F. Adams, _Antinomianism in the Colony of Massachusetts Bay_,
-  vol. xiv. of the Prince Society Publications (Boston, 1894); and
-  _Three Episodes of Massachusetts History_ (Boston and New York, 1896).
-
-
-
-
-HUTCHINSON, JOHN (1615-1664), Puritan soldier, son of Sir Thomas
-Hutchinson of Owthorpe, Nottinghamshire, and of Margaret, daughter of
-Sir John Byron of Newstead, was baptized on the 18th of September 1615.
-He was educated at Nottingham and Lincoln schools and at Peterhouse,
-Cambridge, and in 1637 he entered Lincoln's Inn. On the outbreak of the
-great Rebellion he took the side of the Parliament, and was made in 1643
-governor of Nottingham Castle, which he defended against external
-attacks and internal divisions, till the triumph of the parliamentary
-cause. He was chosen member for Nottinghamshire in March 1646, took the
-side of the Independents, opposed the offers of the king at Newport, and
-signed the death-warrant. Though a member at first of the council of
-state, he disapproved of the subsequent political conduct of Cromwell
-and took no further part in politics during the lifetime of the
-protector. He resumed his seat in the recalled Long Parliament in May
-1659, and followed Monk in opposing Lambert, believing that the former
-intended to maintain the commonwealth. He was returned to the Convention
-Parliament for Nottingham but expelled on the 9th of June 1660, and
-while not excepted from the Act of Indemnity was declared incapable of
-holding public office. In October 1663, however, he was arrested upon
-suspicion of being concerned in the Yorkshire plot, and after a rigorous
-confinement in the Tower of London, of which he published an account
-(reprinted in the Harleian _Miscellany_, vol. iii.), and in Sandown
-Castle, Kent, he died on the 11th of September 1664. His career draws
-its chief interest from the _Life_ by his wife, Lucy, daughter of Sir
-Allen Apsley, written after the death of her husband but not
-published till 1806 (since often reprinted), a work not only valuable
-for the picture which it gives of the man and of the time in which he
-lived, but for the simple beauty of its style, and the naivete with
-which the writer records her sentiments and opinions, and details the
-incidents of her private life.
-
-  See the edition of Lucy Hutchinson's _Memoirs of the Life of Colonel
-  Hutchinson_ by C. H. Firth (1885); _Brit. Mus. Add. MSS._ 25,901 (a
-  fragment of the Life), also _Add. MSS._ 19, 333, 36,247 f. 51; _Notes
-  and Queries_, 7, ser. iii. 25, viii. 422; _Monk's Contemporaries_, by
-  Guizot.
-
-
-
-
-HUTCHINSON, JOHN (1674-1737), English theological writer, was born at
-Spennithorne, Yorkshire, in 1674. He served as steward in several
-families of position, latterly in that of the duke of Somerset, who
-ultimately obtained for him the post of riding purveyor to the master of
-the horse, a sinecure worth about L200 a year. In 1700 he became
-acquainted with Dr John Woodward (1665-1728) physician to the duke and
-author of a work entitled _The Natural History of the Earth_, to whom he
-entrusted a large number of fossils of his own collecting, along with a
-mass of manuscript notes, for arrangement and publication. A
-misunderstanding as to the manner in which these should be dealt with
-was the immediate occasion of the publication by Hutchinson in 1724 of
-_Moses's Principia_, part i., in which Woodward's _Natural History_ was
-bitterly ridiculed, his conduct with regard to the mineralogical
-specimens not obscurely characterized, and a refutation of the Newtonian
-doctrine of gravitation seriously attempted. It was followed by part ii.
-in 1727, and by various other works, including _Moses's Sine Principio_,
-1730; _The Confusion of Tongues and Trinity of the Gentiles_, 1731;
-_Power Essential and Mechanical, or what power belongs to God and what
-to his creatures, in which the design of Sir I. Newton and Dr Samuel
-Clarke is laid open_, 1732; _Glory or Gravity_, 1733; _The Religion of
-Satan, or Antichrist Delineated_, 1736. He taught that the Bible
-contained the elements not only of true religion but also of all
-rational philosophy. He held that the Hebrew must be read without
-points, and his interpretation rested largely on fanciful symbolism.
-Bishop George Home of Norwich was during some of his earlier years an
-avowed Hutchinsonian; and William Jones of Nayland continued to be so to
-the end of his life.
-
-  A complete edition of his publications, edited by Robert Spearman and
-  Julius Bate, appeared in 1748 (12 vols.); an _Abstract_ of these
-  followed in 1753; and a _Supplement_, with _Life_ by Spearman
-  prefixed, in 1765.
-
-
-
-
-HUTCHINSON, SIR JONATHAN (1828-   ), English surgeon and pathologist, was
-born on the 23rd of July 1828 at Selby, Yorkshire, his parents belonging
-to the Society of Friends. He entered St Bartholomew's Hospital, became
-a member of the Royal College of Surgeons in 1850 (F.R.C.S. 1862), and
-rapidly gained reputation as a skilful operator and a scientific
-inquirer. He was president of the Hunterian Society in 1869 and 1870,
-professor of surgery and pathology at the College of Surgeons from 1877
-to 1882, president of the Pathological Society, 1879-1880, of the
-Ophthalmological Society, 1883, of the Neurological Society, 1887, of
-the Medical Society, 1890, and of the Royal Medical and Chirurgical in
-1894-1896. In 1889 he was president of the Royal College of Surgeons. He
-was a member of two Royal Commissions, that of 1881 to inquire into the
-provision for smallpox and fever cases in the London hospitals, and that
-of 1889-1896 on vaccination and leprosy. He also acted as honorary
-secretary to the Sydenham Society. His activity in the cause of
-scientific surgery and in advancing the study of the natural sciences
-was unwearying. His lectures on neuro-pathogenesis, gout, leprosy,
-diseases of the tongue, &c., were full of original observation; but his
-principal work was connected with the study of syphilis, on which he
-became the first living authority. He was the founder of the London
-Polyclinic or Postgraduate School of Medicine; and both in his native
-town of Selby and at Haslemere, Surrey, he started (about 1890)
-educational museums for popular instruction in natural history. He
-published several volumes on his own subjects, was editor of the
-quarterly _Archives of Surgery_, and was given the Hon. LL.D. degree by
-both Glasgow and Cambridge. After his retirement from active
-consultative work he continued to take great interest in the question of
-leprosy, asserting the existence of a definite connexion between this
-disease and the eating of salted fish. He received a knighthood in 1908.
-
-
-
-
-HUTCHINSON, THOMAS (1711-1780), the last royal governor of the province
-of Massachusetts, son of a wealthy merchant of Boston, Mass., was born
-there on the 9th of September 1711. He graduated at Harvard in 1727,
-then became an apprentice in his father's counting-room, and for several
-years devoted himself to business. In 1737 he began his public career as
-a member of the Boston Board of Selectmen, and a few weeks later he was
-elected to the General Court of Massachusetts Bay, of which he was a
-member until 1740 and again from 1742 to 1749, serving as speaker in
-1747, 1748 and 1749. He consistently contended for a sound financial
-system, and vigorously opposed the operations of the "Land Bank" and the
-issue of pernicious bills of credit. In 1748 he carried through the
-General Court a bill providing for the cancellation and redemption of
-the outstanding paper currency. Hutchinson went to England in 1740 as
-the representative of Massachusetts in a boundary dispute with New
-Hampshire. He was a member of the Massachusetts Council from 1749 to
-1756, was appointed judge of probate in 1752 and was chief justice of
-the superior court of the province from 1761 to 1769, was
-lieutenant-governor from 1758 to 1771, acting as governor in the latter
-two years, and from 1771 to 1774 was governor. In 1754 he was a delegate
-from Massachusetts to the Albany Convention, and, with Franklin, was a
-member of the committee appointed to draw up a plan of union. Though he
-recognized the legality of the Stamp Act of 1765, he considered the
-measure inexpedient and impolitic and urged its repeal, but his attitude
-was misunderstood; he was considered by many to have instigated the
-passage of the Act, and in August 1765 a mob sacked his Boston residence
-and destroyed many valuable manuscripts and documents. He was acting
-governor at the time of the "Boston Massacre" in 1770, and was virtually
-forced by the citizens of Boston, under the leadership of Samuel Adams,
-to order the removal of the British troops from the town. Throughout the
-pre-Revolutionary disturbances in Massachusetts he was the
-representative of the British ministry, and though he disapproved of
-some of the ministerial measures he felt impelled to enforce them and
-necessarily incurred the hostility of the Whig or Patriot element. In
-1774, upon the appointment of General Thomas Gage as military governor
-he went to England, and acted as an adviser to George III. and the
-British ministry on American affairs, uniformly counselling moderation.
-He died at Brompton, now part of London, on the 3rd of June 1780.
-
-  He wrote _A Brief Statement of the Claim of the Colonies_ (1764); a
-  _Collection of Original Papers relative to the History of
-  Massachusetts Bay_ (1769), reprinted as _The Hutchinson Papers_ by the
-  Prince Society in 1865; and a judicious, accurate and very valuable
-  _History of the Province of Massachusetts Bay_ (vol. i., 1764, vol.
-  ii., 1767, and vol. iii., 1828). His _Diary and Letters, with an
-  Account of his Administration_, was published at Boston in 1884-1886.
-
-  See James K. Hosmer's _Life of Thomas Hutchinson_ (Boston, 1896), and
-  a biographical chapter in John Fiske's _Essays Historical and
-  Literary_ (New York, 1902). For an estimate of Hutchinson as an
-  historian, see M. C. Tyler's _Literary History of the American
-  Revolution_ (New York, 1897).
-
-
-
-
-HUTCHINSON, a city and the county-seat of Reno county, Kansas, U.S.A.,
-in the broad bottom-land on the N. side of the Arkansas river. Pop.
-(1900) 9379, of whom 414 were foreign-born and 442 negroes; (1910
-census) 16,364. It is served by the Atchison, Topeka & Santa Fe, the
-Missouri Pacific and the Chicago, Rock Island & Pacific railways. The
-principal public buildings are the Federal building and the county court
-house. The city has a public library, and an industrial reformatory is
-maintained here by the state. Hutchinson is situated in a stock-raising,
-fruit-growing and farming region (the principal products of which are
-wheat, Indian corn and fodder), with which it has a considerable
-wholesale trade. An enormous deposit of rock salt underlies the city and
-its vicinity, and Hutchinson's principal industry is the
-manufacture (by the open-pan and grainer processes) and the shipping of
-salt; the city has one of the largest salt plants in the world. Among
-the other manufactures are flour, creamery products, soda-ash,
-straw-board, planing-mill products and packed meats. Natural gas is
-largely used as a factory fuel. The city's factory product was valued at
-$2,031,048 in 1905, an increase of 31.8% since 1900. Hutchinson was
-chartered as a city In 1871.
-
-
-
-
-HUTTEN, PHILIPP VON (c. 1511-1546), German knight, was a relative of
-Ulrich von Hutten and passed some of his early years at the court of the
-emperor Charles V. Later he joined the band of adventurers which under
-Georg Hohermuth, or George of Spires, sailed to Venezuela, or Venosala
-as Hutten calls it, with the object of conquering and exploiting this
-land in the interests of the Augsburg family of Welser. The party landed
-at Coro in February 1535 and Hutten accompanied Hohermuth on his long
-and toilsome expedition into the interior in search of treasure. After
-the death of Hohermuth in December 1540 he became captain-general of
-Venezuela. Soon after this event he vanished into the interior,
-returning after five years of wandering to find that a Spaniard, Juan de
-Caravazil, or Caravajil, had been appointed governor in his absence.
-With his travelling companion, Bartholomew Welser the younger, he was
-seized by Caravazil in April 1546 and the two were afterwards put to
-death.
-
-  Hutten left some letters, and also a narrative of the earlier part of
-  his adventures, this _Zeitung aus India Junkher Philipps von Hutten_
-  being published in 1785.
-
-
-
-
-HUTTEN, ULRICH VON (1488-1523), was born on the 21st of April 1488, at
-the castle of Steckelberg, near Fulda, in Hesse. Like Erasmus or
-Pirckheimer, he was one of those men who form the bridge between
-Humanists and Reformers. He lived with both, sympathized with both,
-though he died before the Reformation had time fully to develop. His
-life may be divided into four parts:--his youth and cloister-life
-(1488-1504); his wanderings in pursuit of knowledge (1504-1515); his
-strife with Ulrich of Wurttemberg (1515-1519); and his connexion with
-the Reformation (1519-1523). Each of these periods had its own special
-antagonism, which coloured Hutten's career: in the first, his horror of
-dull monastic routine; in the second, the ill-treatment he met with at
-Greifswald; in the third, the crime of Duke Ulrich; in the fourth, his
-disgust with Rome and with Erasmus. He was the eldest son of a poor and
-not undistinguished knightly family. As he was mean of stature and
-sickly his father destined him for the cloister, and he was sent to the
-Benedictine house at Fulda; the thirst for learning there seized on him,
-and in 1505 he fled from the monastic life, and won his freedom with the
-sacrifice of his worldly prospects, and at the cost of incurring his
-father's undying anger. From the Fulda cloister he went first to
-Cologne, next to Erfurt, and then to Frankfort-on-Oder on the opening in
-1506 of the new university of that town. For a time he was in Leipzig,
-and in 1508 we find him a shipwrecked beggar on the Pomeranian coast. In
-1509 the university of Greifswald welcomed him, but here too those who
-at first received him kindly became his foes; the sensitive
-ill-regulated youth, who took the liberties of genius, wearied his
-burgher patrons; they could not brook the poet's airs and vanity, and
-ill-timed assertions of his higher rank. Wherefore he left Greifswald,
-and as he went was robbed of clothes and books, his only baggage, by the
-servants of his late friends; in the dead of winter, half starved,
-frozen, penniless, he reached Rostock. Here again the Humanists received
-him gladly, and under their protection he wrote against his Greifswald
-patrons, thus beginning the long list of his satires and fierce attacks
-on personal or public foes. Rostock could not hold him long; he wandered
-on to Wittenberg and Leipzig, and thence to Vienna, where he hoped to
-win the emperor Maximilian's favour by an elaborate national poem on the
-war with Venice. But neither Maximilian nor the university of Vienna
-would lift a hand for him, and he passed into Italy, where, at Pavia, he
-sojourned throughout 1511 and part of 1512. In the latter year his
-studies were interrupted by war; in the siege of Pavia by papal troops
-and Swiss, he was plundered by both sides, and escaped, sick and
-penniless, to Bologna; on his recovery he even took service as a private
-soldier in the emperor's army.
-
-This dark period lasted no long time; in 1514 he was again in Germany,
-where, thanks to his poetic gifts and the friendship of Eitelwolf von
-Stein (d. 1515), he won the favour of the elector of Mainz, Archbishop
-Albert of Brandenburg. Here high dreams of a learned career rose on him;
-Mainz should be made the metropolis of a grand Humanist movement, the
-centre of good style and literary form. But the murder in 1515 of his
-relative Hans von Hutten by Ulrich, duke of Wurttemberg, changed the
-whole course of his life; satire, chief refuge of the weak, became
-Hutten's weapon; with one hand he took his part in the famous _Epistolae
-obscurorum virorum_, and with the other launched scathing letters,
-eloquent Ciceronian orations, or biting satires against the duke. Though
-the emperor was too lazy and indifferent to smite a great prince, he
-took Hutten under his protection and bestowed on him the honour of a
-laureate crown in 1517. Hutten, who had meanwhile revisited Italy, again
-attached himself to the electoral court at Mainz; and he was there when
-in 1518 his friend Pirckheimer wrote, urging him to abandon the court
-and dedicate himself to letters. We have the poet's long reply, in an
-epistle on his "way of life," an amusing mixture of earnestness and
-vanity, self-satisfaction and satire; he tells his friend that his
-career is just begun, that he has had twelve years of wandering, and
-will now enjoy himself a while in patriotic literary work; that he has
-by no means deserted the humaner studies, but carries with him a little
-library of standard books. Pirckheimer in his burgher life may have ease
-and even luxury; he, a knight of the empire, how can he condescend to
-obscurity? He must abide where he can shine.
-
-In 1519 he issued in one volume his attacks on Duke Ulrich, and then,
-drawing sword, took part in the private war which overthrew that prince;
-in this affair he became intimate with Franz von Sickingen, the champion
-of the knightly order (Ritterstand). Hutten now warmly and openly
-espoused the Lutheran cause, but he was at the same time mixed up in the
-attempt of the "Ritterstand" to assert itself as the militia of the
-empire against the independence of the German princes. Soon after this
-time he discovered at Fulda a copy of the manifesto of the emperor Henry
-IV. against Hildebrand, and published it with comments as an attack on
-the papal claims over Germany. He hoped thereby to interest the new
-emperor Charles V., and the higher orders in the empire, in behalf of
-German liberties; but the appeal failed. What Luther had achieved by
-speaking to cities and common folk in homely phrase, because he touched
-heart and conscience, that the far finer weapons of Hutten failed to
-effect, because he tried to touch the more cultivated sympathies and
-dormant patriotism of princes and bishops, nobles and knights. And so he
-at once gained an undying name in the republic of letters and ruined his
-own career. He showed that the artificial verse-making of the Humanists
-could be connected with the new outburst of genuine German poetry. The
-Minnesinger was gone; the new national singer, a Luther or a Hans Sachs,
-was heralded by the stirring lines of Hutten's pen. These have in them a
-splendid natural swing and ring, strong and patriotic, though
-unfortunately addressed to knight and landsknecht rather than to the
-German people.
-
-The poet's high dream of a knightly national regeneration had a rude
-awakening. The attack on the papacy, and Luther's vast and sudden
-popularity, frightened Elector Albert, who dismissed Hutten from his
-court. Hoping for imperial favour, he betook himself to Charles V.; but
-that young prince would have none of him. So he returned to his friends,
-and they rejoiced greatly to see him still alive; for Pope Leo X. had
-ordered him to be arrested and sent to Rome, and assassins dogged his
-steps. He now attached himself more closely to Franz von Sickingen and
-the knightly movement. This also came to a disastrous end in the capture
-of the Ebernberg, and Sickingen's death; the higher nobles had
-triumphed; the archbishops avenged themselves on Lutheranism as
-interpreted by the knightly order. With Sickingen Hutten also finally
-fell. He fled to Basel, where Erasmus refused to see him, both for fear
-of his loathsome diseases, and also because the beggared knight was sure
-to borrow money from him. A paper war consequently broke out between the
-two Humanists, which embittered Hutten's last days, and stained the
-memory of Erasmus. From Basel Ulrich dragged himself to Mulhausen; and
-when the vengeance of Erasmus drove him thence, he went to Zurich. There
-the large heart of Zwingli welcomed him; he helped him with money, and
-found him a quiet refuge with the pastor of the little isle of Ufnau on
-the Zurich lake. There the frail and worn-out poet, writing swift satire
-to the end, died at the end of August or beginning of September 1523 at
-the age of thirty-five. He left behind him some debts due to
-compassionate friends; he did not even own a single book, and all his
-goods amounted to the clothes on his back, a bundle of letters, and that
-valiant pen which had fought so many a sharp battle, and had won for the
-poor knight-errant a sure place in the annals of literature.
-
-Ulrich von Hutten is one of those men of genius at whom propriety is
-shocked, and whom the mean-spirited avoid. Yet through his short and
-buffeted life he was befriended, with wonderful charity and patience, by
-the chief leaders of the Humanist movement. For, in spite of his
-irritable vanity, his immoral life and habits, his odious diseases, his
-painful restlessness, Hutten had much in him that strong men could love.
-He passionately loved the truth, and was ever open to all good
-influences. He was a patriot, whose soul soared to ideal schemes and a
-grand utopian restoration of his country. In spite of all, his was a
-frank and noble nature; his faults chiefly the faults of genius
-ill-controlled, and of a life cast in the eventful changes of an age of
-novelty. A swarm of writings issued from his pen; at first the smooth
-elegance of his Latin prose and verse seemed strangely to miss his real
-character; he was the Cicero and Ovid of Germany before he became its
-Lucian.
-
-  His chief works were his _Ars versificandi_ (1511); the _Nemo_ (1518);
-  a work on the _Morbus Gallicus_ (1519); the volume of Steckelberg
-  complaints against Duke Ulrich (including his four _Ciceronian
-  Orations_, his Letters and the _Phalarismus_) also in 1519; the
-  _Vadismus_ (1520); and the controversy with Erasmus at the end of his
-  life. Besides these were many admirable poems in Latin and German. It
-  is not known with certainty how far Hutten was the parent of the
-  celebrated _Epistolae obscurorum virorum_, that famous satire on
-  monastic ignorance as represented by the theologians of Cologne with
-  which the friends of Reuchlin defended him. At first the
-  cloister-world, not discerning its irony, welcomed the work as a
-  defence of their position; though their eyes were soon opened by the
-  favour with which the learned world received it. The _Epistolae_ were
-  eagerly bought up; the first part (41 letters) appeared at the end of
-  1515; early in 1516 there was a second edition; later in 1516 a third,
-  with an appendix of seven letters; in 1517 appeared the second part
-  (62 letters), to which a fresh appendix of eight letters was subjoined
-  soon after. In 1909 the Latin text of the _Epistolae_ with an English
-  translation was published by F. G. Stokes. Hutten, in a letter
-  addressed to Robert Crocus, denied that he was the author of the book,
-  but there is no doubt as to his connexion with it. Erasmus was of
-  opinion that there were three authors, of whom Crotus Rubianus was the
-  originator of the idea, and Hutten a chief contributor. D. F. Strauss,
-  who dedicates to the subject a chapter of his admirable work on
-  Hutten, concludes that he had no share in the first part, but that his
-  hand is clearly visible in the second part, which he attributes in the
-  main to him. To him is due the more serious and severe tone of that
-  bitter portion of the satire. See W. Brecht, _Die Verfasser der
-  Epistolae obscurorum virorum_ (1904).
-
-  For a complete catalogue of the writings of Hutten, see E. Bocking's
-  _Index Bibliographicus Huttenianus_ (1858). Bocking is also the editor
-  of the complete edition of Hutten's works (7 vols., 1859-1862). A
-  selection of Hutten's German writings, edited by G. Balke, appeared in
-  1891. Cp. S. Szamatolski, _Huttens deutsche Schriften_ (1891). The
-  best biography (though it is also somewhat of a political pamphlet) is
-  that of D. F. Strauss (_Ulrich von Hutten_, 1857; 4th ed., 1878;
-  English translation by G. Sturge, 1874), with which may be compared
-  the older monographs by A. Wagenseil (1823), A. Burck (1846) and J.
-  Zeller (Paris, 1849). See also J. Deckert, _Ulrich von Huttens Leben
-  und Wirken. Eine historische Skizze_ (1901).     (G. W. K.)
-
-
-
-
-HUTTER, LEONHARD (1563-1616), German Lutheran theologian, was born at
-Nellingen near Ulm in January 1563. From 1581 he studied at the
-universities of Strassburg, Leipzig, Heidelberg and Jena. In 1594 he
-began to give theological lectures at Jena, and in 1596 accepted a call
-as professor of theology at Wittenberg, where he died on the 23rd of
-October 1616. Hutter was a stern champion of Lutheran orthodoxy, as set
-down in the confessions and embodied in his own _Compendium locorum
-theologicorum_ (1610; reprinted 1863), being so faithful to his master
-as to win the title of "Luther redonatus."
-
-  In reply to Rudolf Hospinian's _Concordia discors_ (1607), he wrote a
-  work, rich in historical material but one-sided in its apologetics,
-  _Concordia concors_ (1614), defending the formula of Concord, which he
-  regarded as inspired. His _Irenicum vere christianum_ is directed
-  against David Pareus (1548-1622), professor primarius at Heidelberg,
-  who in _Irenicum sive de unione et synodo Evangelicorum_ (1614) had
-  pleaded for a reconciliation of Lutheranism and Calvinism; his
-  _Calvinista aulopoliticus_ (1610) was written against the "damnable
-  Calvinism" which was becoming prevalent in Holstein and Brandenburg.
-  Another work, based on the formula of Concord, was entitled _Loci
-  communes theologici_.
-
-
-
-
-HUTTON, CHARLES (1737-1823), English mathematician, was born at
-Newcastle-on-Tyne on the 14th of August 1737. He was educated in a
-school at Jesmond, kept by Mr Ivison, a clergyman of the church of
-England. There is reason to believe, on the evidence of two pay-bills,
-that for a short time in 1755 and 1756 Hutton worked in Old Long Benton
-colliery; at any rate, on Ivison's promotion to a living, Hutton
-succeeded to the Jesmond school, whence, in consequence of increasing
-pupils, he removed to Stote's Hall. While he taught during the day at
-Stote's Hall, he studied mathematics in the evening at a school in
-Newcastle. In 1760 he married, and began tuition on a larger scale in
-Newcastle, where he had among his pupils John Scott, afterwards Lord
-Eldon, chancellor of England. In 1764 he published his first work, _The
-Schoolmaster's Guide, or a Complete System of Practical Arithmetic_,
-which in 1770 was followed by his _Treatise on Mensuration both in
-Theory and Practice_. In 1772 appeared a tract on _The Principles of
-Bridges_, suggested by the destruction of Newcastle bridge by a high
-flood on the 17th of November 1771. In 1773 he was appointed professor
-of mathematics at the Royal Military Academy, Woolwich, and in the
-following year he was elected F.R.S. and reported on Nevil Maskelyne's
-determination of the mean density and mass of the earth from
-measurements taken in 1774-1776 at Mount Schiehallion in Perthshire.
-This account appeared in the _Philosophical Transactions_ for 1778, was
-afterwards reprinted in the second volume of his _Tracts on Mathematical
-and Philosophical Subjects_, and procured for Hutton the degree of LL.D.
-from the university of Edinburgh. He was elected foreign secretary to
-the Royal Society in 1779, but his resignation in 1783 was brought about
-by the president Sir Joseph Banks, whose behaviour to the mathematical
-section of the society was somewhat high-handed (see Kippis's
-_Observations on the late Contests in the Royal Society_, London, 1784).
-After his _Tables of the Products and Powers of Numbers_, 1781, and his
-_Mathematical Tables_, 1785, he issued, for the use of the Royal
-Military Academy, in 1787 _Elements of Conic Sections_, and in 1798 his
-_Course of Mathematics_. His _Mathematical and Philosophical
-Dictionary_, a valuable contribution to scientific biography, was
-published in 1795 (2nd ed., 1815), and the four volumes of _Recreations
-in Mathematics and Natural Philosophy_, mostly a translation from the
-French, in 1803. One of the most laborious of his works was the
-abridgment, in conjunction with G. Shaw and R. Pearson, of the
-_Philosophical Transactions_. This undertaking, the mathematical and
-scientific parts of which fell to Hutton's share, was completed in 1809,
-and filled eighteen volumes quarto. His name first appears in the
-_Ladies' Diary_ (a poetical and mathematical almanac which was begun in
-1704, and lasted till 1871) in 1764; ten years later he was appointed
-editor of the almanac, a post which he retained till 1817. Previously he
-had begun a small periodical, _Miscellanea Mathematica_, which extended
-only to thirteen numbers; subsequently he published in five volumes _The
-Diarian Miscellany_, which contained large extracts from the _Diary_. He
-resigned his professorship in 1807, and died on the 27th of January
-1823.
-
-  See John Bruce, _Charles Hutton_ (Newcastle, 1823).
-
-
-
-
-HUTTON, JAMES (1726-1797), Scottish geologist, was born in Edinburgh on
-the 3rd of June 1726. Educated at the high school and university of his
-native city, he acquired while a student a passionate love of scientific
-inquiry. He was apprenticed to a lawyer, but his employer advised that a
-more congenial profession should be chosen for him. The young apprentice
-chose medicine as being nearest akin to his favourite pursuit of
-chemistry. He studied for three years at Edinburgh, and completed his
-medical education in Paris, returning by the Low Countries, and taking
-his degree of doctor of medicine at Leiden in 1749. Finding, however,
-that there seemed hardly any opening for him, he abandoned the medical
-profession, and, having inherited a small property in Berwickshire from
-his father, resolved to devote himself to agriculture. He then went to
-Norfolk to learn the practical work of farming, and subsequently
-travelled in Holland, Belgium and the north of France. During these
-years he began to study the surface of the earth, gradually shaping in
-his mind the problem to which he afterwards devoted his energies. In the
-summer of 1754 he established himself on his own farm in Berwickshire,
-where he resided for fourteen years, and where he introduced the most
-improved forms of husbandry. As the farm was brought into excellent
-order, and as its management, becoming more easy, grew less interesting,
-he was induced to let it, and establish himself for the rest of his life
-in Edinburgh. This took place about the year 1768. He was unmarried, and
-from this period until his death in 1797 he lived with his three
-sisters. Surrounded by congenial literary and scientific friends he
-devoted himself to research.
-
-At that time geology in any proper sense of the term did not exist.
-Mineralogy, however, had made considerable progress. But Hutton had
-conceived larger ideas than were entertained by the mineralogists of his
-day. He desired to trace back the origin of the various minerals and
-rocks, and thus to arrive at some clear understanding of the history of
-the earth. For many years he continued to study the subject. At last, in
-the spring of the year 1785, he communicated his views to the recently
-established Royal Society of Edinburgh in a paper entitled _Theory of
-the Earth, or an Investigation of the Laws Observable in the
-Composition, Dissolution and Restoration of Land upon the Globe_. In
-this remarkable work the doctrine is expounded that geology is not
-cosmogony, but must confine itself to the study of the materials of the
-earth; that everywhere evidence may be seen that the present rocks of
-the earth's surface have been in great part formed out of the waste of
-older rocks; that these materials having been laid down under the sea
-were there consolidated under great pressure, and were subsequently
-disrupted and upheaved by the expansive power of subterranean heat; that
-during these convulsions veins and masses of molten rock were injected
-into the rents of the dislocated strata; that every portion of the
-upraised land, as soon as exposed to the atmosphere, is subject to
-decay; and that this decay must tend to advance until the whole of the
-land has been worn away and laid down on the sea-floor, whence future
-upheavals will once more raise the consolidated sediments into new land.
-In some of these broad and bold generalizations Hutton was anticipated
-by the Italian geologists; but to him belongs the credit of having first
-perceived their mutual relations, and combined them in a luminous
-coherent theory based upon observation.
-
-It was not merely the earth to which Hutton directed his attention. He
-had long studied the changes of the atmosphere. The same volume in which
-his _Theory of the Earth_ appeared contained also a _Theory of Rain_,
-which was read to the Royal Society of Edinburgh in 1784. He contended
-that the amount of moisture which the air can retain in solution
-increases with augmentation of temperature, and, therefore, that on the
-mixture of two masses of air of different temperatures a portion of the
-moisture must be condensed and appear in visible form. He investigated
-the available data regarding rainfall and climate in different regions
-of the globe, and came to the conclusion that the rainfall is everywhere
-regulated by the humidity of the air on the one hand, and the causes
-which promote mixtures of different aerial currents in the higher
-atmosphere on the other.
-
-The vigour and versatility of his genius may be understood from the
-variety of works which, during his thirty years' residence in Edinburgh,
-he gave to the world. In 1792 he published a quarto volume entitled
-_Dissertations on different Subjects in Natural Philosophy_, in which he
-discussed the nature of matter, fluidity, cohesion, light, heat and
-electricity. Some of these subjects were further illustrated by him in
-papers read before the Royal Society of Edinburgh. He did not restrain
-himself within the domain of physics, but boldly marched into that of
-metaphysics, publishing three quarto volumes with the title _An
-Investigation of the Principles of Knowledge, and of the Progress of
-Reason--from Sense to Science and Philosophy_. In this work he developed
-the idea that the external world, as conceived by us, is the creation of
-our own minds influenced by impressions from without, that there is no
-resemblance between our picture of the outer world and the reality, yet
-that the impressions produced upon our minds, being constant and
-consistent, become as much realities to us as if they precisely
-resembled things actually existing, and, therefore, that our moral
-conduct must remain the same as if our ideas perfectly corresponded to
-the causes producing them. His closing years were devoted to the
-extension and republication of his _Theory of the Earth_, of which two
-volumes appeared in 1795. A third volume, necessary to complete the
-work, was left by him in manuscript, and is referred to by his
-biographer John Playfair. A portion of the MS. of this volume, which had
-been given to the Geological Society of London by Leonard Horner, was
-published by the Society in 1899, under the editorship of Sir A. Geikie.
-The rest of the manuscript appears to be lost. Soon afterwards Hutton
-set to work to collect and systematize his numerous writings on
-husbandry, which he proposed to publish under the title of _Elements of
-Agriculture_. He had nearly completed this labour when an incurable
-disease brought his active career to a close on the 26th of March 1797.
-
-  It is by his _Theory of the Earth_ that Hutton will be remembered with
-  reverence while geology continues to be cultivated. The author's
-  style, however, being somewhat heavy and obscure, the book did not
-  attract during his lifetime so much attention as it deserved. Happily
-  for science Hutton numbered among his friends John Playfair (q.v.),
-  professor of mathematics in the university of Edinburgh, whose
-  enthusiasm for the spread of Hutton's doctrine was combined with a
-  rare gift of graceful and luminous exposition. Five years after
-  Hutton's death he published a volume, _Illustrations of the Huttonian
-  Theory of the Earth_, in which he gave an admirable summary of that
-  theory, with numerous additional illustrations and arguments. This
-  work is justly regarded as one of the classical contributions to
-  geological literature. To its influence much of the sound progress of
-  British geology must be ascribed. In the year 1805 a biographical
-  account of Hutton, written by Playfair, was published in vol. v. of
-  the _Transactions of the Royal Society of Edinburgh_.     (A. Ge.)
-
-
-
-
-HUTTON, RICHARD HOLT (1826-1897), English writer and theologian, son of
-Joseph Hutton, Unitarian minister at Leeds, was born at Leeds on the 2nd
-of June 1826. His family removed to London in 1835, and he was educated
-at University College School and University College, where he began a
-lifelong friendship with Walter Bagehot, of whose works he afterwards was
-the editor; he took the degree in 1845, being awarded the gold medal for
-philosophy. Meanwhile he had also studied for short periods at Heidelberg
-and Berlin, and in 1847 he entered Manchester New College with the idea
-of becoming a minister like his father, and studied there under James
-Martineau. He did not, however, succeed in obtaining a call to any
-church, and for some little time his future was unsettled. He married in
-1851 his cousin, Anne Roscoe, and became joint-editor with J. L. Sanford
-of the _Inquirer_, the principal Unitarian organ. But his innovations and
-his unconventional views about stereotyped Unitarian doctrines caused
-alarm, and in 1853 he resigned. His health had broken down, and he
-visited the West Indies, where his wife died of yellow fever. In 1855
-Hutton and Bagehot became joint-editors of the _National Review_, a new
-monthly, and conducted it for ten years. During this time Hutton's
-theological views, influenced largely by Coleridge, and more directly by
-F. W. Robertson and F. D. Maurice, gradually approached more and more to
-those of the Church of England, which he ultimately joined. His interest
-in theology was profound, and he brought to it a spirituality of outlook
-and an aptitude for metaphysical inquiry and exposition which added a
-singular attraction to his writings. In 1861 he joined Meredith Townsend
-as joint-editor and part proprietor of the _Spectator_, then a well-known
-liberal weekly, which, however, was not remunerative from the business
-point of view. Hutton took charge of the literary side of the paper, and
-by degrees his own articles became and remained up to the last one of the
-best-known features of serious and thoughtful English journalism. The
-_Spectator_, which gradually became a prosperous property, was his
-pulpit, in which unwearyingly he gave expression to his views,
-particularly on literary, religious and philosophical subjects, in
-opposition to the agnostic and rationalistic opinions then current in
-intellectual circles, as popularized by Huxley. A man of fearless
-honesty, quick and catholic sympathies, broad culture, and many friends
-in intellectual and religious circles, he became one of the most
-influential journalists of the day, his fine character and conscience
-earning universal respect and confidence. He was an original member of
-the Metaphysical Society (1869). He was an anti-vivisectionist, and a
-member of the royal commission (1875) on that subject. In 1858 he had
-married Eliza Roscoe, a cousin of his first wife; she died early in 1897,
-and Hutton's own death followed on the 9th of September of the same year.
-
-  Among his other publications may be mentioned _Essays, Theological and
-  Literary_ (1871; revised 1888), and _Criticisms on Contemporary
-  Thought and Thinkers_ (1894); and his opinions may be studied
-  compendiously in the selections from his _Spectator_ articles
-  published in 1899 under the title of _Aspects of Religious and
-  Scientific Thought_.
-
-
-
-
-HUXLEY, THOMAS HENRY (1825-1895), English biologist, was born on the 4th
-of May 1825 at Ealing, where his father, George Huxley, was senior
-assistant-master in the school of Dr Nicholas. This was an establishment
-of repute, and is at any rate remarkable for having produced two men
-with so little in common in after life as Huxley and Cardinal Newman.
-The cardinal's brother, Francis William, had been "captain" of the
-school in 1821. Huxley was a seventh child (as his father had also
-been), and the youngest who survived infancy. Of Huxley's ancestry no
-more is ascertainable than in the case of most middle-class families. He
-himself thought it sprang from the Cheshire Huxleys of Huxley Hall.
-Different branches migrated south, one, now extinct, reaching London,
-where its members were apparently engaged in commerce. They established
-themselves for four generations at Wyre Hall, near Edmonton, and one was
-knighted by Charles II. Huxley describes his paternal race as "mainly
-Iberian mongrels, with a good dash of Norman and a little Saxon."[1]
-From his father he thought he derived little except a quick temper and
-the artistic faculty which proved of great service to him and reappeared
-in an even more striking degree in his daughter, the Hon. Mrs Collier.
-"Mentally and physically," he wrote, "I am a piece of my mother." Her
-maiden name was Rachel Withers. "She came of Wiltshire people," he adds,
-and describes her as "a typical example of the Iberian variety." He
-tells us that "her most distinguishing characteristic was rapidity of
-thought.... That peculiarity has been passed on to me in full strength"
-(_Essays_, i. 4). One of the not least striking facts in Huxley's life
-is that of education in the formal sense he received none. "I had two
-years of a pandemonium of a school (between eight and ten), and after
-that neither help nor sympathy in any intellectual direction till I
-reached manhood" (_Life_, ii. 145). After the death of Dr Nicholas the
-Ealing school broke up, and Huxley's father returned about 1835 to his
-native town, Coventry, where he had obtained a small appointment. Huxley
-was left to his own devices; few histories of boyhood could offer any
-parallel. At twelve he was sitting up in bed to read Hutton's _Geology_.
-His great desire was to be a mechanical engineer; it ended in his
-devotion to "the mechanical engineering of living machines." His
-curiosity in this direction was nearly fatal; a _post-mortem_ he was
-taken to between thirteen and fourteen was followed by an illness which
-seems to have been the starting-point of the ill-health which pursued
-him all through life. At fifteen he devoured Sir William Hamilton's
-_Logic_, and thus acquired the taste for metaphysics, which he
-cultivated to the end. At seventeen he came under the influence of
-Thomas Carlyle's writings. Fifty years later he wrote: "To make things
-clear and get rid of cant and shows of all sorts. This was the lesson I
-learnt from Carlyle's books when I was a boy, and it has stuck by me all
-my life" (_Life_, ii. 268). Incidentally they led him to begin to learn
-German; he had already acquired French. At seventeen Huxley, with his
-elder brother James, commenced regular medical studies at Charing Cross
-Hospital, where they had both obtained scholarships. He studied under
-Wharton Jones, a physiologist who never seems to have attained the
-reputation he deserved. Huxley said of him: "I do not know that I ever
-felt so much respect for a teacher before or since" (_Life_, i. 20). At
-twenty he passed his first M.B. examination at the University of London,
-winning the gold medal for anatomy and physiology; W. H. Ransom, the
-well-known Nottingham physician, obtaining the exhibition. In 1845 he
-published, at the suggestion of Wharton Jones, his first scientific
-paper, demonstrating the existence of a hitherto unrecognized layer in
-the inner sheath of hairs, a layer that has been known since as
-"Huxley's layer."
-
-Something had to be done for a livelihood, and at the suggestion of a
-fellow-student, Mr (afterwards Sir Joseph) Fayrer, he applied for an
-appointment in the navy. He passed the necessary examination, and at the
-same time obtained the qualification of the Royal College of Surgeons.
-He was "entered on the books of Nelson's old ship, the 'Victory,' for
-duty at Haslar Hospital." Its chief, Sir John Richardson, who was a
-well-known Arctic explorer and naturalist, recognized Huxley's ability,
-and procured for him the post of surgeon to H.M.S. "Rattlesnake," about
-to start for surveying work in Torres Strait. The commander, Captain
-Owen Stanley, was a son of the bishop of Norwich and brother of Dean
-Stanley, and wished for an officer with some scientific knowledge.
-Besides Huxley the "Rattlesnake" also carried a naturalist by
-profession, John Macgillivray, who, however, beyond a dull narrative of
-the expedition, accomplished nothing. The "Rattlesnake" left England on
-the 3rd of December 1846, and was ordered home after the lamented death
-of Captain Stanley at Sydney, to be paid off at Chatham on the 9th of
-November 1850. The tropical seas teem with delicate surface-life, and to
-the study of this Huxley devoted himself with unremitting devotion. At
-that time no known methods existed by which it could be preserved for
-study in museums at home. He gathered a magnificent harvest in the
-almost unreaped field, and the conclusions he drew from it were the
-beginning of the revolution in zoological science which he lived to see
-accomplished.
-
-Baron Cuvier (1769-1832), whose classification still held its ground,
-had divided the animal kingdom into four great _embranchements_. Each of
-these corresponded to an independent archetype, of which the "idea" had
-existed in the mind of the Creator. There was no other connexion between
-these classes, and the "ideas" which animated them were, as far as one
-can see, arbitrary. Cuvier's groups, without their theoretical basis,
-were accepted by K. E. von Baer (1792-1876). The "idea" of the group, or
-archetype, admitted of endless variation within it; but this was
-subordinate to essential conformity with the archetype, and hence Cuvier
-deduced the important principle of the "correlation of parts," of which
-he made such conspicuous use in palaeontological reconstruction.
-Meanwhile the "Naturphilosophen," with J. W. Goethe (1749-1832) and L.
-Oken (1779-1851), had in effect grasped the underlying principle of
-correlation, and so far anticipated evolution by asserting the
-possibility of deriving specialized from simpler structures. Though they
-were still hampered by idealistic conceptions, they established
-morphology. Cuvier's four great groups were Vertebrata, Mollusca,
-Articulata and Radiata. It was amongst the members of the last
-class that Huxley found most material ready to his hand in the seas of
-the tropics. It included organisms of the most varied kind, with nothing
-more in common than that their parts were more or less distributed round
-a centre. Huxley sent home "communication after communication to the
-Linnean Society," then a somewhat somnolent body, "with the same result
-as that obtained by Noah when he sent the raven out of the ark"
-(_Essays_, i. 13). His important paper, _On the Anatomy and the
-Affinities of the Family of Medusae_, met with a better fate. It was
-communicated by the bishop of Norwich to the Royal Society, and printed
-by it in the _Philosophical Transactions_ in 1849. Huxley united, with
-the Medusae, the Hydroid and Sertularian polyps, to form a class to
-which he subsequently gave the name of Hydrozoa. This alone was no
-inconsiderable feat for a young surgeon who had only had the training of
-the medical school. But the ground on which it was done has led to
-far-reaching theoretical developments. Huxley realized that something
-more than superficial characters were necessary in determining the
-affinities of animal organisms. He found that all the members of the
-class consisted of two membranes enclosing a central cavity or stomach.
-This is characteristic of what are now called the Coelenterata. All
-animals higher than these have been termed Coelomata; they possess a
-distinct body-cavity in addition to the stomach. Huxley went further
-than this, and the most profound suggestion in his paper is the
-comparison of the two layers with those which appear in the germ of the
-higher animals. The consequences which have flowed from this prophetic
-generalization of the _ectoderm_ and _endoderm_ are familiar to every
-student of evolution. The conclusion was the more remarkable as at the
-time he was not merely free from any evolutionary belief, but actually
-rejected it. The value of Huxley's work was immediately recognized. On
-returning to England in 1850 he was elected a Fellow of the Royal
-Society. In the following year, at the age of twenty-six, he not merely
-received the Royal medal, but was elected on the council. With
-absolutely no aid from any one he had placed himself in the front rank
-of English scientific men. He secured the friendship of Sir J. D. Hooker
-and John Tyndall, who remained his lifelong friends. The Admiralty
-retained him as a nominal assistant-surgeon, in order that he might work
-up the observations he had made during the voyage of the "Rattlesnake."
-He was thus enabled to produce various important memoirs, especially
-those on certain Ascidians, in which he solved the problem of
-_Appendicularia_--an organism whose place in the animal kingdom Johannes
-Muller had found himself wholly unable to assign--and on the morphology
-of the Cephalous Mollusca.
-
-Richard Owen, then the leading comparative anatomist in Great Britain,
-was a disciple of Cuvier, and adopted largely from him the deductive
-explanation of anatomical fact from idealistic conceptions. He
-superadded the evolutionary theories of Oken, which were equally
-idealistic, but were altogether repugnant to Cuvier. Huxley would have
-none of either. Imbued with the methods of von Baer and Johannes Muller,
-his methods were purely inductive. He would not hazard any statement
-beyond what the facts revealed. He retained, however, as has been done
-by his successors, the use of archetypes, though they no longer
-represented fundamental "ideas" but generalizations of the essential
-points of structure common to the individuals of each class. He had not
-wholly freed himself, however, from archetypal trammels. "The doctrine,"
-he says, "that every natural group is organized after a definite
-archetype ... seems to me as important for zoology as the doctrine of
-definite proportions for chemistry." This was in 1853. He further
-stated: "There is no progression from a lower to a higher type, but
-merely a more or less complete evolution of one type" (_Phil. Trans._,
-1853, p. 63). As Chalmers Mitchell points out, this statement is of
-great historical interest. Huxley definitely uses the word "evolution,"
-and admits its existence _within_ the great groups. He had not, however,
-rid himself of the notion that the archetype was a property inherent in
-the group. Herbert Spencer, whose acquaintance he made in 1852, was
-unable to convert him to evolution in its widest sense (_Life_, i.
-168). He could not bring himself to acceptance of the theory--owing, no
-doubt, to his rooted aversion from a priori reasoning--without a
-mechanical conception of its mode of operation. In his first interview
-with Darwin, which seems to have been about the same time, he expressed
-his belief "in the sharpness of the lines of demarcation between natural
-groups," and was received with a humorous smile (_Life_, i. 169).
-
-The naval medical service exists for practical purposes. It is not
-surprising, therefore, that after his three years' nominal employment
-Huxley was ordered on active service. Though without private means of
-any kind, he resigned. The navy, however, retains the credit of having
-started his scientific career as well as that of Hooker and Darwin.
-Huxley was now thrown on his own resources, the immediate prospects of
-which were slender enough. As a matter of fact, he had not to wait many
-months. His friend, Edward Forbes, was appointed to the chair of natural
-history in Edinburgh, and in July 1854 he succeeded him as lecturer at
-the School of Mines and as naturalist to the Geological Survey in the
-following year. The latter post he hesitated at first to accept, as he
-"did not care for fossils" (_Essays_, i. 15). In 1855 he married Miss H.
-A. Heathorn, whose acquaintance he had made in Sydney. They were engaged
-when Huxley could offer nothing but the future promise of his ability.
-The confidence of his devoted helpmate was not misplaced, and her
-affection sustained him to the end, after she had seen him the recipient
-of every honour which English science could bestow. His most important
-research belonging to this period was the Croonian Lecture delivered
-before the Royal Society in 1858 on "The Theory of the Vertebrate
-Skull." In this he completely and finally demolished, by applying as
-before the inductive method, the idealistic, if in some degree
-evolutionary, views of its origin which Owen had derived from Goethe and
-Oken. This finally disposed of the "archetype," and may be said once for
-all to have liberated the English anatomical school from the deductive
-method.
-
-In 1859 _The Origin of Species_ was published. This was a momentous
-event in the history of science, and not least for Huxley. Hitherto he
-had turned a deaf ear to evolution. "I took my stand," he says, "upon
-two grounds: firstly, that ... the evidence in favour of transmutation
-was wholly insufficient; and secondly, that no suggestion respecting the
-causes of the transmutation assumed, which had been made, was in any way
-adequate to explain the phenomena" (_Life_, i. 168). Huxley had studied
-Lamarck "attentively," but to no purpose. Sir Charles Lyell "was the
-chief agent in smoothing the road for Darwin. For consistent
-uniformitarianism postulates evolution as much in the organic as in the
-inorganic world" (l.c.); and Huxley found in Darwin what he had failed
-to find in Lamarck, an intelligible hypothesis good enough as a working
-basis. Yet with the transparent candour which was characteristic of him,
-he never to the end of his life concealed the fact that he thought it
-wanting in rigorous proof. Darwin, however, was a naturalist; Huxley was
-not. He says: "I am afraid there is very little of the genuine
-naturalist in me. I never collected anything, and species-work was
-always a burden to me; what I cared for was the architectural and
-engineering part of the business" (_Essays_, i. 7). But the solution of
-the problem of organic evolution must work upwards from the initial
-stages, and it is precisely for the study of these that "species-work"
-is necessary. Darwin, by observing the peculiarities in the distribution
-of the plants which he had collected in the Galapagos, was started on
-the path that led to his theory. Anatomical research had only so far led
-to transcendental hypothesis, though in Huxley's hands it had cleared
-the decks of that lumber. He quotes with approval Darwin's remark that
-"no one has a right to examine the question of species who has not
-minutely described many" (_Essays_, ii. 283). The rigorous proof which
-Huxley demanded was the production of species sterile to one another by
-selective breeding (_Life_, i. 193). But this was a misconception of the
-question. Sterility is a physiological character, and the specific
-differences which the theory undertook to account for are
-morphological; there is no necessary nexus between the two. Huxley,
-however, felt that he had at last a secure grip of evolution. He warned
-Darwin: "I will stop at no point as long as clear reasoning will carry
-me further" (_Life_, i. 172). Owen, who had some evolutionary
-tendencies, was at first favourably disposed to Darwin's theory, and
-even claimed that he had to some extent anticipated it in his own
-writings. But Darwin, though he did not thrust it into the foreground,
-never flinched from recognizing that man could not be excluded from his
-theory. "Light will be thrown on the origin of man and his history"
-(_Origin_, ed. i. 488). Owen could not face the wrath of fashionable
-orthodoxy. In his Rede Lecture he endeavoured to save the position by
-asserting that man was clearly marked off from all other animals by the
-anatomical structure of his brain. This was actually inconsistent with
-known facts, and was effectually refuted by Huxley in various papers and
-lectures, summed up in 1863 in _Man's Place in Nature_. This "monkey
-damnification" of mankind was too much even for the "veracity" of
-Carlyle, who is said to have never forgiven it. Huxley had not the
-smallest respect for authority as a basis for belief, scientific or
-otherwise. He held that scientific men were morally bound "to try all
-things and hold fast to that which is good" (_Life_, ii. 161). Called
-upon in 1862, in the absence of the president, to deliver the
-presidential address to the Geological Society, he disposed once for all
-of one of the principles accepted by geologists, that similar fossils in
-distinct regions indicated that the strata containing them were
-contemporary. All that could be concluded, he pointed out, was that the
-general order of succession was the same. In 1854 Huxley had refused the
-post of palaeontologist to the Geological Survey; but the fossils for
-which he then said that he "did not care" soon acquired importance in
-his eyes, as supplying evidence for the support of the evolutionary
-theory. The thirty-one years during which he occupied the chair of
-natural history at the School of Mines were largely occupied with
-palaeontological research. Numerous memoirs on fossil fishes established
-many far-reaching morphological facts. The study of fossil reptiles led
-to his demonstrating, in the course of lectures on birds, delivered at
-the College of Surgeons in 1867, the fundamental affinity of the two
-groups which he united under the title of Sauropsida. An incidental
-result of the same course was his proposed rearrangement of the
-zoological regions into which P. L. Sclater had divided the world in
-1857. Huxley anticipated, to a large extent, the results at which
-botanists have since arrived: he proposed as primary divisions,
-Arctogaea--to include the land areas of the northern hemisphere--and
-Notogaea for the remainder. Successive waves of life originated in and
-spread from the northern area, the survivors of the more ancient types
-finding successively a refuge in the south. Though Huxley had accepted
-the Darwinian theory as a working hypothesis, he never succeeded in
-firmly grasping it in detail. He thought "evolution might conceivably
-have taken place without the development of groups possessing the
-characters of species" (_Essays_, v. 41). His palaeontological
-researches ultimately led him to dispense with Darwin. In 1892 he wrote:
-"The doctrine of evolution is no speculation, but a generalization of
-certain facts ... classed by biologists under the heads of Embryology
-and of Palaeontology" (_Essays_, v. 42). Earlier in 1881 he had asserted
-even more emphatically that if the hypothesis of evolution "had not
-existed, the palaeontologist would have had to invent it" (_Essays_, iv.
-44).
-
-From 1870 onwards he was more and more drawn away from scientific
-research by the claims of public duty. Some men yield the more readily
-to such demands, as their fulfilment is not unaccompanied by public
-esteem. But he felt, as he himself said of Joseph Priestley, "that he
-was a man and a citizen before he was a philosopher, and that the duties
-of the two former positions are at least as imperative as those of the
-latter" (_Essays_, iii. 13). From 1862 to 1884 he served on no less than
-ten Royal Commissions, dealing in every case with subjects of great
-importance, and in many with matters of the gravest moment to the
-community. He held and filled with invariable dignity and distinction
-more public positions than have perhaps ever fallen to the lot of a
-scientific man in England. From 1871 to 1880 he was a secretary of the
-Royal Society. From 1881 to 1885 he was president. For honours he cared
-little, though they were within his reach; it is said that he might have
-received a peerage. He accepted, however, in 1892, a Privy
-Councillorship, at once the most democratic and the most aristocratic
-honour accessible to an English citizen. In 1870 he was president of the
-British Association at Liverpool, and in the same year was elected a
-member of the newly constituted London School Board. He resigned the
-latter position in 1872, but in the brief period during which he acted,
-probably more than any man, he left his mark on the foundations of
-national elementary education. He made war on the scholastic methods
-which wearied the mind in merely taxing the memory; the children were to
-be prepared to take their place worthily in the community. Physical
-training was the basis; domestic economy, at any rate for girls, was
-insisted upon, and for all some development of the aesthetic sense by
-means of drawing and singing. Reading, writing and arithmetic were the
-indispensable tools for acquiring knowledge, and intellectual discipline
-was to be gained through the rudiments of physical science. He insisted
-on the teaching of the Bible partly as a great literary heritage, partly
-because he was "seriously perplexed to know by what practical measures
-the religious feeling, which is the essential basis of conduct, was to
-be kept up, in the present utterly chaotic state of opinion in these
-matters, without its use" (_Essays_, iii. 397). In 1872 the School of
-Mines was moved to South Kensington, and Huxley had, for the first time
-after eighteen years, those appliances for teaching beyond the lecture
-room, which to the lasting injury of the interests of biological science
-in Great Britain had been withheld from him by the short-sightedness of
-government. Huxley had only been able to bring his influence to bear
-upon his pupils by oral teaching, and had had no opportunity by personal
-intercourse in the laboratory of forming a school. He was now able to
-organize a system of instruction for classes of elementary teachers in
-the general principles of biology, which indirectly affected the
-teaching of the subject throughout the country.
-
-The first symptoms of physical failure to meet the strain of the
-scientific and public duties demanded of him made some rest imperative,
-and he took a long holiday in Egypt. He still continued for some years
-to occupy himself mainly with vertebrate morphology. But he seemed to
-find more interest and the necessary mental stimulus to exertion in
-lectures, public addresses and more or less controversial writings. His
-health, which had for a time been fairly restored, completely broke down
-again in 1885. In 1890 he removed from London to Eastbourne, where after
-a painful illness he died on the 29th of June 1895.
-
-  The latter years of Huxley's life were mainly occupied with
-  contributions to periodical literature on subjects connected with
-  philosophy and theology. The effect produced by these on popular
-  opinion was profound. This was partly due to his position as a man of
-  science, partly to his obvious earnestness and sincerity, but in the
-  main to his strenuous and attractive method of exposition. Such
-  studies were not wholly new to him, as they had more or less engaged
-  his thoughts from his earliest days. That his views exhibit some
-  process of development and are not wholly consistent was, therefore,
-  to be expected, and for this reason it is not easy to summarize them
-  as a connected body of teaching. They may be found perhaps in their
-  most systematic form in the volume on _Hume_ published in 1879.
-
-  Huxley's general attitude to the problems of theology and philosophy
-  was technically that of scepticism. "I am," he wrote, "too much of a
-  sceptic to deny the possibility of anything" (_Life_, ii. 127). "Doubt
-  is a beneficent demon" (_Essays_, ix. 56). He was anxious,
-  nevertheless, to avoid the accusation of Pyrrhonism (_Life_, ii. 280),
-  but the Agnosticism which he defined to express his position in 1869
-  suggests the Pyrrhonist _Aphasia_. The only approach to certainty
-  which he admitted lay in the order of nature. "The conception of the
-  constancy of the order of nature has become the dominant idea of
-  modern thought.... Whatever may be man's speculative doctrines, it is
-  quite certain that every intelligent person guides his life and risks
-  his fortune upon the belief that the order of nature is constant, and
-  that the chain of natural causation is never broken." He adds,
-  however, that "it by no means necessarily follows that we are
-  justified in expanding this generalization into the infinite past"
-  (_Essays_, iv. 47, 48). This was little more than a pious
-  reservation, as evolution implies the principle of continuity (l.c. p.
-  55). Later he stated his belief even more absolutely: "If there is
-  anything in the world which I do firmly believe in, it is the
-  universal validity of the law of causation, but that universality
-  cannot be proved by any amount of experience" (_Essays_, ix. 121). The
-  assertion that "There is only one method by which intellectual truth
-  can be reached, whether the subject-matter of investigation belongs to
-  the world of physics or to the world of consciousness" (_Essays_, ix.
-  126) laid him open to the charge of materialism, which he vigorously
-  repelled. His defence, when he rested it on the imperfection of the
-  physical analysis of matter and force (l.c. p. 131), was irrelevant;
-  he was on sounder ground when he contended with Berkeley "that our
-  certain knowledge does not extend beyond our states of consciousness"
-  (l.c. p. 130). "Legitimate materialism, that is, the extension of the
-  conceptions and of the methods of physical science to the highest as
-  well as to the lowest phenomena of vitality, is neither more nor less
-  than a sort of shorthand idealism" (_Essays_, i. 194). While "the
-  substance of matter is a metaphysical unknown quality of the existence
-  of which there is no proof ... the non-existence of a substance of
-  mind is equally arguable; ... the result ... is the reduction of the
-  All to co-existences and sequences of phenomena beneath and beyond
-  which there is nothing cognoscible" (_Essays_, ix. 66). Hume had
-  defined a miracle as a "violation of the laws of nature." Huxley
-  refused to accept this. While, on the one hand, he insists that "the
-  whole fabric of practical life is built upon our faith in its
-  continuity" (_Hume_, p. 129), on the other "nobody can presume to say
-  what the order of nature must be"; this "knocks the bottom out of all
-  a priori objections either to ordinary 'miracles' or to the efficacy
-  of prayer" (_Essays_, v. 133). "If by the term miracles we mean only
-  extremely wonderful events, there can be no just ground for denying
-  the possibility of their occurrence" (_Hume_, p. 134). Assuming the
-  chemical elements to be aggregates of uniform primitive matter, he saw
-  no more theoretical difficulty in water being turned into alcohol in
-  the miracle at Cana, than in sugar undergoing a similar conversion
-  (_Essays_, v. 81). The credibility of miracles with Huxley is a
-  question of evidence. It may be remarked that a scientific explanation
-  is destructive of the supernatural character of a miracle, and that
-  the demand for evidence may be so framed as to preclude the
-  credibility of any historical event. Throughout his life theology had
-  a strong attraction, not without elements of repulsion, for Huxley.
-  The circumstances of his early training, when Paley was the "most
-  interesting Sunday reading allowed him when a boy" (_Life_, ii. 57),
-  probably had something to do with both. In 1860 his beliefs were
-  apparently theistic: "Science seems to me to teach in the highest and
-  strongest manner the great truth which is embodied in the Christian
-  conception of entire surrender to the will of God" (_Life_, i. 219).
-  In 1885 he formulates "the perfect ideal of religion" in a passage
-  which has become almost famous: "In the 8th century B.C. in the heart
-  of a world of idolatrous polytheists, the Hebrew prophets put forth a
-  conception of religion which appears to be as wonderful an inspiration
-  of genius as the art of Pheidias or the science of Aristotle. 'And
-  what doth the Lord require of thee, but to do justly, and to love
-  mercy, and to walk humbly with thy God'" (_Essays_, iv. 161). Two
-  years later he was writing: "That there is no evidence of the
-  existence of such a being as the God of the theologians is true
-  enough" (_Life_, ii. 162). He insisted, however, that "atheism is on
-  purely philosophical grounds untenable" (l.c.). His theism never
-  really advanced beyond the recognition of "the passionless
-  impersonality of the unknown and unknowable, which science shows
-  everywhere underlying the thin veil of phenomena" (_Life_, i. 239). In
-  other respects his personal creed was a kind of scientific Calvinism.
-  There is an interesting passage in an essay written in 1892, "An
-  Apologetic Eirenicon," which has not been republished, which
-  illustrates this: "It is the secret of the superiority of the best
-  theological teachers to the majority of their opponents that they
-  substantially recognize these realities of things, however strange the
-  forms in which they clothe their conceptions. The doctrines of
-  predestination, of original sin, of the innate depravity of man and
-  the evil fate of the greater part of the race, of the primacy of Satan
-  in this world, of the essential vileness of matter, of a malevolent
-  Demiurgus subordinate to a benevolent Almighty, who has only lately
-  revealed himself, faulty as they are, appear to me to be vastly nearer
-  the truth than the 'liberal' popular illusions that babies are all
-  born good, and that the example of a corrupt society is responsible
-  for their failure to remain so; that it is given to everybody to reach
-  the ethical ideal if he will only try; that all partial evil is
-  universal good, and other optimistic figments, such as that which
-  represents 'Providence' under the guise of a paternal philanthropist,
-  and bids us believe that everything will come right (according to our
-  notions) at last." But his "slender definite creed," R. H. Hutton, who
-  was associated with him in the Metaphysical Society, thought--and no
-  doubt rightly--in no respect "represented the cravings of his larger
-  nature."
-
-  From 1880 onwards till the very end of his life, Huxley was
-  continuously occupied in a controversial campaign against orthodox
-  beliefs. As Professor W. F. R. Weldon justly said of his earlier
-  polemics: "They were certainly among the principal agents in winning a
-  larger measure of toleration for the critical examination of
-  fundamental beliefs, and for the free expression of honest reverent
-  doubt." He threw Christianity overboard bodily and with little
-  appreciation of its historic effect as a civilizing agency. He
-  thought that "the exact nature of the teachings and the convictions of
-  Jesus is extremely uncertain" (_Essays_, v. 348). "What we are usually
-  pleased to call religion nowadays is, for the most part, Hellenized
-  Judaism" (_Essays_, iv. 162). His final analysis of what "since the
-  second century, has assumed to itself the title of Orthodox
-  Christianity" is a "varying compound of some of the best and some of
-  the worst elements of Paganism and Judaism, moulded in practice by the
-  innate character of certain people of the Western world" (_Essays_, v.
-  142). He concludes "That this Christianity is doomed to fall is, to my
-  mind, beyond a doubt; but its fall will neither be sudden nor speedy"
-  (l.c.). He did not omit, however, to do justice to "the bright side of
-  Christianity," and was deeply impressed with the life of Catherine of
-  Siena. Failing Christianity, he thought that some other "hypostasis of
-  men's hopes" will arise (_Essays_, v. 254). His latest speculations on
-  ethical problems are perhaps the least satisfactory of his writings.
-  In 1892 he wrote: "The moral sense is a very complex affair--dependent
-  in part upon associations of pleasure and pain, approbation and
-  disapprobation, formed by education in early youth, but in part also
-  on an innate sense of moral beauty and ugliness (how originated need
-  not be discussed), which is possessed by some people in great
-  strength, while some are totally devoid of it" (_Life_, ii. 305). This
-  is an intuitional theory, and he compares the moral with the aesthetic
-  sense, which he repeatedly declares to be intuitive; thus: "All the
-  understanding in the world will neither increase nor diminish the
-  force of the intuition that this is beautiful and this is ugly"
-  (_Essays_, ix. 80). In the Romanes Lecture delivered in 1894, in which
-  this passage occurs, he defines "law and morals" to be "restraints
-  upon the struggle for existence between men in society." It follows
-  that "the ethical process is in opposition to the cosmic process," to
-  which the struggle for existence belongs (_Essays_, ix. 31).
-  Apparently he thought that the moral sense in its origin was
-  intuitional and in its development utilitarian. "Morality commenced
-  with society" (_Essays_, v. 52). The "ethical process" is the "gradual
-  strengthening of the social bond" (_Essays_, ix. 35). "The cosmic
-  process has no sort of relation to moral ends" (l.c. p. 83); "of moral
-  purpose I see no trace in nature. That is an article of exclusive
-  human manufacture" (_Life_, ii. 268). The cosmic process Huxley
-  identified with evil, and the ethical process with good; the two are
-  in necessary conflict. "The reality at the bottom of the doctrine of
-  original sin" is the "innate tendency to self-assertion" inherited by
-  man from the cosmic order (_Essays_, ix. 27). "The actions we call
-  sinful are part and parcel of the struggle for existence" (_Life_, ii.
-  282). "The prospect of attaining untroubled happiness" is "an
-  illusion" (_Essays_, ix. 44), and the cosmic process in the long run
-  will get the best of the contest, and "resume its sway" when evolution
-  enters on its downward course (l.c. p. 45). This approaches pure
-  pessimism, and though in Huxley's view the "pessimism of Schopenhauer
-  is a nightmare" (_Essays_, ix. 200), his own philosophy of life is not
-  distinguishable, and is often expressed in the same language. The
-  cosmic order is obviously non-moral (_Essays_, ix. 197). That it is,
-  as has been said, immoral is really meaningless. Pain and suffering
-  are affections which imply a complex nervous organization, and we are
-  not justified in projecting them into nature external to ourselves.
-  Darwin and A. R. Wallace disagreed with Huxley in seeing rather the
-  joyous than the suffering side of nature. Nor can it be assumed that
-  the descending scale of evolution will reproduce the ascent, or that
-  man will ever be conscious of his doom.
-
-  As has been said, Huxley never thoroughly grasped the Darwinian
-  principle. He thought "transmutation may take place without
-  transition" (_Life_, i. 173). In other words, that evolution is
-  accomplished by leaps and not by the accumulation of small variations.
-  He recognized the "struggle for existence" but not the gradual
-  adjustment of the organism to its environment which is implied in
-  "natural selection." In highly civilized societies he thought that the
-  former was at an end (_Essays_, ix. 36) and had been replaced by the
-  "struggle for enjoyment" (l.c. p. 40). But a consideration of the
-  stationary population of France might have shown him that the effect
-  in the one case may be as restrictive as in the other. So far from
-  natural selection being in abeyance under modern social conditions,
-  "it is," as Professor Karl Pearson points out, "something we run up
-  against at once, almost as soon as we examine a mortality table"
-  (_Biometrika_, i. 76). The inevitable conclusion, whether we like it
-  or not, is that the future evolution of humanity is as much a part of
-  the cosmic process as its past history, and Huxley's attempt to shut
-  the door on it cannot be maintained scientifically.
-
-  AUTHORITIES.--_Life and Letters of Thomas Henry Huxley_, by his son
-  Leonard Huxley (2 vols., 1900); _Scientific Memoirs of T. H. Huxley_
-  (4 vols., 1898-1901); _Collected Essays_ by T. H. Huxley (9 vols.,
-  1898); _Thomas Henry Huxley, a Sketch of his Life and Work_, by P.
-  Chalmers Mitchell, M.A. (Oxon., 1900); a critical study founded on
-  careful research and of great value.     (W. T. T.-D.)
-
-
-FOOTNOTE:
-
-  [1] _Nature_, lxiii. 127.
-
-
-
-
-HUY (Lat. _Hoium_, and Flem. _Hoey_), a town of Belgium, on the right
-bank of the Meuse, at the point where it is joined by the Hoyoux. Pop.
-(1904), 14,164. It is 19 m. E. of Namur and a trifle less west of Liege.
-Huy certainly dates from the 7th century, and, according to some, was
-founded by the emperor Antoninus in A.D. 148. Its situation is
-striking, with its grey citadel crowning a grey rock, and the fine
-collegiate church (with a 13th-century gateway) of Notre Dame built
-against it. The citadel is now used partly as a depot of military
-equipment and partly as a prison. The ruins are still shown of the abbey
-of Neumoustier founded by Peter the Hermit on his return from the first
-crusade. He was buried there in 1115, and a statue was erected to his
-memory in the abbey grounds in 1858. Neumoustier was one of seventeen
-abbeys in this town alone dependent on the bishopric of Liege. Huy is
-surrounded by vineyards, and the bridge which crosses the Meuse at this
-point connects the fertile Hesbaye north of the river with the rocky and
-barren Condroz south of it.
-
-
-
-
-HUYGENS, CHRISTIAAN (1629-1695), Dutch mathematician, mechanician,
-astronomer and physicist, was born at the Hague on the 14th of April
-1629. He was the second son of Sir Constantijn Huygens. From his father
-he received the rudiments of his education, which was continued at
-Leiden under A. Vinnius and F. van Schooten, and completed in the
-juridical school of Breda. His mathematical bent, however, soon diverted
-him from legal studies, and the perusal of some of his earliest theorems
-enabled Descartes to predict his future greatness. In 1649 he
-accompanied the mission of Henry, count of Nassau, to Denmark, and in
-1651 entered the lists of science as an assailant of the unsound system
-of quadratures adopted by Gregory of St Vincent. This first essay
-(_Exetasis quadraturae circuli_, Leiden, 1651) was quickly succeeded by
-his _Theoremata de quadratura hyperboles, ellipsis, et circuli_; while,
-in a treatise entitled _De circuli magnitudine inventa_, he made, three
-years later, the closest approximation so far obtained to the ratio of
-the circumference to the diameter of a circle.
-
-Another class of subjects was now to engage his attention. The
-improvement of the telescope was justly regarded as a _sine qua non_ for
-the advancement of astronomical knowledge. But the difficulties
-interposed by spherical and chromatic aberration had arrested progress
-in that direction until, in 1655, Huygens, working with his brother
-Constantijn, hit upon a new method of grinding and polishing lenses. The
-immediate results of the clearer definition obtained were the detection
-of a satellite to Saturn (the sixth in order of distance from its
-primary), and the resolution into their true form of the abnormal
-appendages to that planet. Each discovery in turn was, according to the
-prevailing custom, announced to the learned world under the veil of an
-anagram--removed, in the case of the first, by the publication, early in
-1656, of the little tract _De Saturni luna observatio nova_; but
-retained, as regards the second, until 1659, when in the _Systema
-Saturnium_ the varying appearances of the so-called "triple planet" were
-clearly explained as the phases of a ring inclined at an angle of 28 deg. to
-the ecliptic. Huygens was also in 1656 the first effective observer of
-the Orion nebula; he delineated the bright region still known by his
-name, and detected the multiple character of its nuclear star. His
-application of the pendulum to regulate the movement of clocks sprang
-from his experience of the need for an exact measure of time in
-observing the heavens. The invention dates from 1656; on the 16th of
-June 1657 Huygens presented his first "pendulum-clock" to the
-states-general; and the _Horologium_, containing a description of the
-requisite mechanism, was published in 1658.
-
-His reputation now became cosmopolitan. As early as 1655 the university
-of Angers had distinguished him with an honorary degree of doctor of
-laws. In 1663, on the occasion of his second visit to England, he was
-elected a fellow of the Royal Society, and imparted to that body in
-January 1669 a clear and concise statement of the laws governing the
-collision of elastic bodies. Although these conclusions were arrived at
-independently, and, as it would seem, several years previous to their
-publication, they were in great measure anticipated by the
-communications on the same subject of John Wallis and Christopher Wren,
-made respectively in November and December 1668.
-
-Huygens had before this time fixed his abode in France. In 1665 Colbert
-made to him on behalf of Louis XIV. an offer too tempting to be
-refused, and between the following year and 1681 his residence in the
-philosophic seclusion of the Bibliotheque du Roi was only interrupted by
-two short visits to his native country. His _magnum opus_ dates from
-this period. The _Horologium oscillatorium_, published with a dedication
-to his royal patron in 1673, contained original discoveries sufficient
-to have furnished materials for half a dozen striking disquisitions. His
-solution of the celebrated problem of the "centre of oscillation" formed
-in itself an important event in the history of mechanics. Assuming as an
-axiom that the centre of gravity of any number of interdependent bodies
-cannot rise higher than the point from which it fell, he arrived, by
-anticipating in the particular case the general principle of the
-conservation of _vis viva_, at correct although not strictly
-demonstrated conclusions. His treatment of the subject was the first
-successful attempt to deal with the dynamics of a system. The
-determination of the true relation between the length of a pendulum and
-the time of its oscillation; the invention of the theory of evolutes;
-the discovery, hence ensuing, that the cycloid is its own evolute, and
-is strictly isochronous; the ingenious although practically inoperative
-idea of correcting the "circular error" of the pendulum by applying
-cycloidal cheeks to clocks--were all contained in this remarkable
-treatise. The theorems on the composition of forces in circular motion
-with which it concluded formed the true prelude to Newton's _Principia_,
-and would alone suffice to establish the claim of Huygens to the highest
-rank among mechanical inventors.
-
-In 1681 he finally severed his French connexions, and returned to
-Holland. The harsher measures which about that time began to be adopted
-towards his co-religionists in France are usually assigned as the motive
-of this step. He now devoted himself during six years to the production
-of lenses of enormous focal distance, which, mounted on high poles, and
-connected with the eye-piece by means of a cord, formed what were called
-"aerial telescopes." Three of his object-glasses, of respectively 123,
-180 and 210 ft. focal length, are in the possession of the Royal
-Society. He also succeeded in constructing an almost perfectly
-achromatic eye-piece, still known by his name. But his researches in
-physical optics constitute his chief title-deed to immortality. Although
-Robert Hooke in 1668 and Ignace Pardies in 1672 had adopted a vibratory
-hypothesis of light, the conception was a mere floating possibility
-until Huygens provided it with a sure foundation. His powerful
-scientific imagination enabled him to realize that all the points of a
-wave-front originate partial waves, the aggregate effect of which is to
-reconstitute the primary disturbance at the subsequent stages of its
-advance, thus accomplishing its propagation; so that each primary
-undulation is the envelope of an indefinite number of secondary
-undulations. This resolution of the original wave is the well-known
-"Principle of Huygens," and by its means he was enabled to prove the
-fundamental laws of optics, and to assign the correct construction for
-the direction of the extraordinary ray in uniaxial crystals. These
-investigations, together with his discovery of the "wonderful
-phenomenon" of polarization, are recorded in his _Traite de la lumiere_,
-published at Leiden in 1690, but composed in 1678. In the appended
-treatise _Sur la Cause de la pesanteur_, he rejected gravitation as a
-universal quality of matter, although admitting the Newtonian theory of
-the planetary revolutions. From his views on centrifugal force he
-deduced the oblate figure of the earth, estimating its compression,
-however, at little more than one-half its actual amount.
-
-Huygens never married. He died at the Hague on the 8th of June 1695,
-bequeathing his manuscripts to the university of Leiden, and his
-considerable property to the sons of his younger brother. In character
-he was as estimable as he was brilliant in intellect. Although, like
-most men of strong originative power, he assimilated with difficulty the
-ideas of others, his tardiness sprang rather from inability to depart
-from the track of his own methods than from reluctance to acknowledge
-the merits of his competitors.
-
-  In addition to the works already mentioned, his _Cosmotheoros_--a
-  speculation concerning the inhabitants of the planets--was
-  printed posthumously at the Hague in 1698, and appeared almost
-  simultaneously in an English translation. A volume entitled _Opera
-  posthuma_ (Leiden, 1703) contained his "Dioptrica," in which the ratio
-  between the respective focal lengths of object-glass and eye-glass is
-  given as the measure of magnifying power, together with the shorter
-  essays _De vitris figurandis_, _De corona et parheliis_, &c. An early
-  tract _De ratiociniis in ludo aleae_, printed in 1657 with Schooten's
-  _Exercitationes mathematicae_, is notable as one of the first formal
-  treatises on the theory of probabilities; nor should his
-  investigations of the properties of the cissoid, logarithmic and
-  catenary curves be left unnoticed. His invention of the spiral
-  watch-spring was explained in the _Journal des savants_ (Feb. 25,
-  1675). An edition of his works was published by G. J.'s Gravesande, in
-  four quarto volumes entitled _Opera varia_ (Leiden, 1724) and _Opera
-  reliqua_ (Amsterdam, 1728). His scientific correspondence was edited
-  by P. J. Uylenbroek from manuscripts preserved at Leiden, with the
-  title _Christiani Hugenii aliorumque seculi XVII. virorum celebrium
-  exercitationes mathematicae et philosophicae_ (the Hague, 1833).
-
-  The publication of a monumental edition of the letters and works of
-  Huygens was undertaken at the Hague by the _Societe Hollandaise des
-  Sciences_, with the heading _Oeuvres de Christian Huygens_ (1888),
-  &c. Ten quarto volumes, comprising the whole of his correspondence,
-  had already been issued in 1905. A biography of Huygens was prefixed
-  to his _Opera varia_ (1724); his _Eloge_ in the character of a French
-  academician was printed by J. A. N. Condorcet in 1773. Consult
-  further: P. J. Uylenbroek, _Oratio de fratribus Christiano atque
-  Constantino Hugenio_ (Groningen, 1838); P. Harting, _Christiaan
-  Huygens in zijn Leven en Werken geschetzt_ (Groningen, 1868); J. B. J.
-  Delambre, _Hist. de l'astronomie moderne_ (ii. 549); J. E. Montucla,
-  _Hist. des mathematiques_ (ii. 84, 412, 549); M. Chasles, _Apercu
-  historique sur l'origine des methodes en geometrie_, pp. 101-109; E.
-  Duhring, _Kritische Geschichte der allgemeinen Principien der
-  Mechanik_, Abschnitt (ii. 120, 163, iii. 227); A. Berry, _A Short
-  History of Astronomy_, p. 200; R. Wolf, _Geschichte der Astronomie_,
-  passim; Houzeau, _Bibliographie astronomique_ (ii. 169); F. Kaiser,
-  _Astr. Nach._ (xxv. 245, 1847); _Tijdschrift voor de Wetenschappen_
-  (i. 7, 1848); _Allgemeine deutsche Biographie_ (M. B. Cantor); J. C.
-  Poggendorff, _Biog. lit. Handworterbuch_.     (A. M. C.)
-
-
-
-
-HUYGENS, SIR CONSTANTIJN (1596-1687), Dutch poet and diplomatist, was
-born at the Hague on the 4th of September 1596. His father, Christiaan
-Huygens, was secretary to the state council, and a man of great
-political importance. At the baptism of the child, the city of Breda was
-one of his sponsors, and the admiral Justinus van Nassau the other. He
-was trained in every polite accomplishment, and before he was seven
-could speak French with fluency. He was taught Latin by Johannes
-Dedelus, and soon became a master of classic versification. He developed
-not only extraordinary intellectual gifts but great physical beauty and
-strength, and was one of the most accomplished athletes and gymnasts of
-his age; his skill in playing the lute and in the arts of painting and
-engraving attracted general attention before he began to develop his
-genius as a writer. In 1616 he proceeded, with his elder brother, to the
-university of Leiden. He stayed there only one year, and in 1618 went to
-London with the English ambassador Dudley Carleton; he remained in
-London for some months, and then went to Oxford, where he studied for
-some time in the Bodleian Library, and to Woodstock, Windsor and
-Cambridge; he was introduced at the English court, and played the lute
-before James I. The most interesting feature of this visit was the
-intimacy which sprang up between the young Dutch poet and Dr Donne, for
-whose genius Huygens preserved through life an unbounded admiration. He
-returned to Holland in company with the English contingent of the synod
-of Dort, and in 1619 he proceeded to Venice in the diplomatic service of
-his country; on his return he nearly lost his life by a foolhardy
-exploit, namely, the scaling of the topmost spire of Strassburg
-cathedral. In 1621 he published one of his most weighty and popular
-poems, his _Batava Tempe_, and in the same year he proceeded again to
-London, as secretary to the ambassador, Wijngaerdan, but returned in
-three months. His third diplomatic visit to England lasted longer, from
-the 5th of December 1621 to the 1st of March 1623. During his absence,
-his volume of satires, _'t Costelick Mal_, dedicated to Jacob Cats,
-appeared at the Hague. In the autumn of 1622 he was knighted by James I.
-He published a large volume of miscellaneous poems in 1625 under the
-title of _Otiorum libri sex_; and in the same year he was appointed
-private secretary to the stadholder. In 1627 Huygens married Susanna
-van Baerle, and settled at the Hague; four sons and a daughter were born
-to them. In 1630 Huygens was called to a seat in the privy council, and
-he continued to exercise political power with wisdom and vigour for many
-years, under the title of the lord of Zuylichem. In 1634 he is supposed
-to have completed his long-talked-of version of the poems of Donne,
-fragments of which exist. In 1637 his wife died, and he immediately
-began to celebrate the virtues and pleasures of their married life in
-the remarkable didactic poem called _Dagwerck_, which was not published
-till long afterwards. From 1639 to 1641 he occupied himself by building
-a magnificent house and garden outside the Hague, and by celebrating
-their beauties in a poem entitled _Hofwijck_, which was published in
-1653. In 1647 he wrote his beautiful poem of _Oogentroost_ or "Eye
-Consolation," to gratify his blind friend Lucretia van Trollo. He made
-his solitary effort in the dramatic line in 1657, when he brought out
-his comedy of _Trijntje Cornelis Klacht_, which deals, in rather broad
-humour, with the adventures of the wife of a ship's captain at Zaandam.
-In 1658 he rearranged his poems, and issued them with many additions,
-under the title of _Corn Flowers_. He proposed to the government that
-the present highway from the Hague to the sea at Scheveningen should be
-constructed, and during his absence on a diplomatic mission to the
-French court in 1666 the road was made as a compliment to the venerable
-statesman, who expressed his gratitude in a descriptive poem entitled
-_Zeestraet_. Huygens edited his poems for the last time in 1672, and
-died in his ninety-first year, on the 28th of March 1687. He was buried,
-with the pomp of a national funeral, in the church of St Jacob, on the
-4th of April. His second son, Christiaan, the eminent astronomer, is
-noticed separately.
-
-  Constantijn Huygens is the most brilliant figure in Dutch literary
-  history. Other statesmen surpassed him in political influence, and at
-  least two other poets surpassed him in the value and originality of
-  their writings. But his figure was more dignified and splendid, his
-  talents were more varied, and his general accomplishments more
-  remarkable than those of any other person of his age, the greatest age
-  in the history of the Netherlands. Huygens is the _grand seigneur_ of
-  the republic, the type of aristocratic oligarchy, the jewel and
-  ornament of Dutch liberty. When we consider his imposing character and
-  the positive value of his writings, we may well be surprised that he
-  has not found a modern editor. It is a disgrace to Dutch scholarship
-  that no complete collection of the writings of Huygens exists. His
-  autobiography, _De vita propria sermonum libri duo_, did not see the
-  light until 1817, and his remarkable poem, _Cluyswerck_, was not
-  printed until 1841. As a poet Huygens shows a finer sense of form than
-  any other early Dutch writer; the language, in his hands, becomes as
-  flexible as Italian. His epistles and lighter pieces, in particular,
-  display his metrical ease and facility to perfection.     (E. G.)
-
-
-
-
-HUYSMANS, the name of four Flemish painters who matriculated in the
-Antwerp gild in the 17th century. Cornelis the elder, apprenticed in
-1633, passed for a mastership in 1636, and remained obscure. Jacob,
-apprenticed to Frans Wouters in 1650, wandered to England towards the
-close of the reign of Charles II., and competed with Lely as a
-fashionable portrait painter. He executed a portrait of the queen,
-Catherine of Braganza, now in the national portrait gallery, and Horace
-Walpole assigns to him the likeness of Lady Bellasys, catalogued at
-Hampton Court as a work of Lely. His portrait of Izaak Walton in the
-National Gallery shows a disposition to imitate the styles of Rubens and
-Van Dyke. According to most accounts he died in London in 1696. Jan
-Baptist Huysmans, born at Antwerp in 1654, matriculated in 1676-1677,
-and died there in 1715-1716. He was younger brother to Cornelis Huysmans
-the second, who was born at Antwerp in 1648, and educated by Gaspar de
-Wit and Jacob van Artois. Of Jan Baptist little or nothing has been
-preserved, except that he registered numerous apprentices at Antwerp,
-and painted a landscape dated 1697 now in the Brussels museum. Cornelis
-the second is the only master of the name of Huysmans whose talent was
-largely acknowledged. He received lessons from two artists, one of whom
-was familiar with the Roman art of the Poussins, whilst the other
-inherited the scenic style of the school of Rubens. He combined the two
-in a rich, highly coloured, and usually effective style, which, however,
-was not free from monotony. Seldom attempting anything but woodside
-views with fancy backgrounds, half Italian, half Flemish, he painted
-with great facility, and left numerous examples behind. At the outset of
-his career he practised at Malines, where he married in 1682, and there
-too he entered into some business connexion with van der Meulen, for
-whom he painted some backgrounds. In 1706 he withdrew to Antwerp, where
-he resided till 1717, returning then to Malines, where he died on the
-1st of June 1727.
-
-  Though most of his pictures were composed for cabinets rather than
-  churches, he sometimes emulated van Artois in the production of large
-  sacred pieces, and for many years his "Christ on the Road to Emmaus"
-  adorned the choir of Notre Dame of Malines. In the gallery of Nantes,
-  where three of his small landscapes are preserved, there hangs an
-  "Investment of Luxembourg," by van der Meulen, of which he is known to
-  have laid in the background. The national galleries of London and
-  Edinburgh contain each one example of his skill. Blenheim, too, and
-  other private galleries in England, possess one or more of his
-  pictures. But most of his works are on the European continent.
-
-
-
-
-HUYSMANS, JORIS KARL (1848-1907), French novelist, was born at Paris on
-the 5th of February 1848. He belonged to a family of artists of Dutch
-extraction; he entered the ministry of the interior, and was pensioned
-after thirty years' service. His earliest venture in literature, _Le
-Drageoir a epices_ (1874), contained stories and short prose poems
-showing the influence of Baudelaire. _Marthe_ (1876), the life of a
-courtesan, was published in Brussels, and Huysmans contributed a story,
-"Sac au dos," to _Les Soirees de Medan_, the collection of stories of
-the Franco-German war published by Zola. He then produced a series of
-novels of everyday life, including _Les Soeurs Vatard_ (1879), _En
-Menage_ (1881), and _A vau-l'eau_ (1882), in which he outdid Zola in
-minute and uncompromising realism. He was influenced, however, more
-directly by Flaubert and the brothers de Goncourt than by Zola. In
-_L'Art moderne_ (1883) he gave a careful study of impressionism and in
-_Certains_ (1889) a series of studies of contemporary artists, _A
-Rebours_ (1884), the history of the morbid tastes of a decadent
-aristocrat, des Esseintes, created a literary sensation, its caricature
-of literary and artistic symbolism covering much of the real beliefs of
-the leaders of the aesthetic revolt. In _La-Bas_ Huysmans's most
-characteristic hero, Durtal, makes his appearance. Durtal is occupied in
-writing the life of Gilles de Rais; the insight he gains into Satanism
-is supplemented by modern Parisian students of the black art; but
-already there are signs of a leaning to religion in the sympathetic
-figures of the religious bell-ringer of Saint Sulpice and his wife. _En
-Route_ (1895) relates the strange conversion of Durtal to mysticism and
-Catholicism in his retreat to La Trappe. In _La Cathedrale_ (1898),
-Huysmans's symbolistic interpretation of the cathedral of Chartres, he
-develops his enthusiasm for the purity of Catholic ritual. The life of
-_Sainte Lydwine de Schiedam_ (1901), an exposition of the value of
-suffering, gives further proof of his conversion; and _L'Oblat_ (1903)
-describes Durtal's retreat to the Val des Saints, where he is attached
-as an oblate to a Benedictine monastery. Huysmans was nominated by
-Edmond de Goncourt as a member of the Academie des Goncourt. He died as
-a devout Catholic, after a long illness of cancer in the palate on the
-13th of May 1907. Before his death he destroyed his unpublished MSS. His
-last book was _Les Foules de Lourdes_ (1906).
-
-  See Arthur Symons, _Studies in two Literatures_ (1897) and _The
-  Symbolist Movement in Literature_ (1899); Jean Lionnet in _L'Evolution
-  des idees_ (1903); Eugene Gilbert in _France et Belgique_ (1905); J.
-  Sargeret in _Les Grands convertis_ (1906).
-
-
-
-
-HUYSUM, JAN VAN (1682-1749), Dutch painter, was born at Amsterdam in
-1682, and died in his native city on the 8th of February 1749. He was
-the son of Justus van Huysum, who is said to have been expeditious in
-decorating doorways, screens and vases. A picture by this artist is
-preserved in the gallery of Brunswick, representing Orpheus and the
-Beasts in a wooded landscape, and here we have some explanation of his
-son's fondness for landscapes of a conventional and Arcadian kind; for
-Jan van Huysum, though skilled as a painter of still life, believed
-himself to possess the genius of a landscape painter. Half his pictures
-in public galleries are landscapes, views of imaginary lakes and
-harbours with impossible ruins and classic edifices, and woods of tall
-and motionless trees--the whole very glossy and smooth, and entirely
-lifeless. The earliest dated work of this kind is that of 1717, in the
-Louvre, a grove with maidens culling flowers near a tomb, ruins of a
-portico, and a distant palace on the shores of a lake bounded by
-mountains.
-
-It is doubtful whether any artist ever surpassed van Huysum in
-representing fruit and flowers. It has been said that his fruit has no
-savour and his flowers have no perfume--in other words, that they are
-hard and artificial--but this is scarcely true. In substance fruit and
-flower are delicate and finished imitations of nature in its more subtle
-varieties of matter. The fruit has an incomparable blush of down, the
-flowers have a perfect delicacy of tissue. Van Huysum, too, shows
-supreme art in relieving flowers of various colours against each other,
-and often against a light and transparent background. He is always
-bright, sometimes even gaudy. Great taste and much grace and elegance
-are apparent in the arrangement of bouquets and fruit in vases adorned
-with bas reliefs or in baskets on marble tables. There is exquisite and
-faultless finish everywhere. But what van Huysum has not is the breadth,
-the bold effectiveness, and the depth of thought of de Heem, from whom
-he descends through Abraham Mignon.
-
-  Some of the finest of van Huysum's fruit and flower pieces have been
-  in English private collections: those of 1723 in the earl of
-  Ellesmere's gallery, others of 1730-1732 in the collections of Hope
-  and Ashburton. One of the best examples is now in the National Gallery
-  (1736-1737). No public museum has finer and more numerous specimens
-  than the Louvre, which boasts of four landscapes and six panels with
-  still life; then come Berlin and Amsterdam with four fruit and flower
-  pieces; then St Petersburg, Munich, Hanover, Dresden, the Hague,
-  Brunswick, Vienna, Carlsruhe and Copenhagen.
-
-
-
-
-HWANG HO [HOANG HO], the second largest river in China. It is known to
-foreigners as the Yellow river--a name which is a literal translation of
-the Chinese. It rises among the Kuenlun mountains in central Asia, its
-head-waters being in close proximity to those of the Yangtsze-Kiang. It
-has a total length of about 2400 m. and drains an area of approximately
-400,000 sq. m. The main stream has its source in two lakes named
-Tsaring-nor and Oring-nor, lying about 35 deg. N., 97 deg. E., and after flowing
-with a south-easterly course it bends sharply to the north-west and
-north, entering China in the province of Kansuh in lat. 36 deg. After
-passing Lanchow-fu, the capital of this province, the river takes an
-immense sweep to the north and north-east, until it encounters the
-rugged barrier ranges that here run north and south through the
-provinces of Shansi and Chihli. By these ranges it is forced due south
-for 500 m., forming the boundary between the provinces of Shansi and
-Shensi, until it finds an outlet eastwards at Tung Kwan--a pass which
-for centuries has been renowned as the gate of Asia, being indeed the
-sole commercial passage between central China and the West. At Tung Kwan
-the river is joined by its only considerable affluent in China proper,
-the Wei (Wei-ho), which drains the large province of Shensi, and the
-combined volume of water continues its way at first east and then
-north-east across the great plain to the sea. At low water in the winter
-season the discharge is only about 36,000 cub. ft. per second, whereas
-during the summer flood it reaches 116,000 ft. or more. The amount of
-sediment carried down is very large, though no accurate observations
-have been made. In the account of Lord Macartney's embassy, which
-crossed the Yellow river in 1792, it was calculated to be 17,520 million
-cub. ft. a year, but this is considered very much over the mark. Two
-reasons, however, combine to render it probable that the sedimentary
-matter is very large in proportion to the volume of water: the first
-being the great fall, and the consequently rapid current over two-thirds
-of the river's course; the second that the drainage area is nearly all
-covered with deposits of loess, which, being very friable, readily gives
-way before the rainfall and is washed down in large quantity. The
-ubiquity of this loess or yellow earth, as the Chinese call it, has in
-fact given its name both to the river which carries it in solution and
-to the sea (the Yellow Sea) into which it is discharged. It is
-calculated by Dr Guppy (_Journal of China Branch of Royal Asiatic
-Society_, vol. xvi.) that the sediment brought down by the three
-northern rivers of China, viz., the Yangtsze, the Hwang-ho and the
-Peiho, is 24,000 million cub. ft. per annum, and is sufficient to fill
-up the whole of the Yellow Sea and the Gulf of Pechili in the space of
-about 36,000 years.
-
-  Unlike the Yangtsze, the Hwang-ho is of no practical value for
-  navigation. The silt and sand form banks and bars at the mouth, the
-  water is too shallow in winter and the current is too strong in
-  summer, and, further, the bed of the river is continually shifting. It
-  is this last feature which has earned for the river the name "China's
-  sorrow." As the silt-laden waters debouch from the rocky bed of the
-  upper reaches on to the plains, the current slackens, and the coarser
-  detritus settles on the bottom. By degrees the bed rises, and the
-  people build embankments to prevent the river from overflowing. As the
-  bed rises the embankments must be raised too, until the stream is
-  flowing many feet above the level of the surrounding country. As time
-  goes on the situation becomes more and more dangerous; finally, a
-  breach occurs, and the whole river pours over the country, carrying
-  destruction and ruin with it. If the breach cannot be repaired the
-  river leaves its old channel entirely and finds a new exit to the sea
-  along the line of least resistance. Such in brief has been the story
-  of the river since the dawn of Chinese history. At various times it
-  has discharged its waters alternately on one side or the other of the
-  great mass of mountains forming the promontory of Shantung, and by
-  mouths as far apart from each other as 500 m. At each change it has
-  worked havoc and disaster by covering the cultivated fields with 2 or
-  3 ft. of sand and mud.
-
-  A great change in the river's course occurred in 1851, when a breach
-  was made in the north embankment near Kaifengfu in Honan. At this
-  point the river bed was some 25 ft. above the plain; the water
-  consequently forsook the old channel entirely and poured over the
-  level country, finally seizing on the bed of a small river called the
-  Tsing, and thereby finding an exit to the sea. Since that time the new
-  channel thus carved out has remained the proper course of the river,
-  the old or southerly channel being left quite dry. It required some
-  fifteen or more years to repair damages from this outbreak, and to
-  confine the stream by new embankments. After that there was for a time
-  comparative immunity from inundations, but in 1882 fresh outbursts
-  again began. The most serious of all took place in 1887, when it
-  appeared probable that there would be again a permanent change in the
-  river's course. By dint of great exertions, however, the government
-  succeeded in closing the breach, though not till January 1889, and not
-  until there had been immense destruction of life and property. The
-  outbreak on this occasion occurred, as all the more serious outbreaks
-  have done, in Honan, a few miles west of the city of Kaifengfu. The
-  stream poured itself over the level and fertile country to the
-  southwards, sweeping whole villages before it, and converting the
-  plain into one vast lake. The area affected was not less than 50,000
-  sq. m. and the loss of life was computed at over one million. Since
-  1887 there have been a series of smaller outbreaks, mostly at points
-  lower down and in the neighbourhood of Chinanfu, the capital of
-  Shantung. These perpetually occurring disasters entail a heavy expense
-  on the government; and from the mere pecuniary point of view it would
-  well repay them to call in the best foreign engineering skill
-  available, an expedient, however, which has not commended itself to
-  the Chinese authorities.     (G. J.)
-
-
-
-
-HWICCE, one of the kingdoms of Anglo-Saxon Britain. Its exact dimensions
-are unknown; they probably coincided with those of the old diocese of
-Worcester, the early bishops of which bore the title "Episcopus
-Hwicciorum." It would therefore include Worcestershire, Gloucestershire
-except the Forest of Dean, the southern half of Warwickshire, and the
-neighbourhood of Bath. The name Hwicce survives in Wychwood in
-Oxfordshire and Whichford in Warwickshire. These districts, or at all
-events the southern portion of them, were according to the _Anglo-Saxon
-Chronicle_, _s.a._ 577, originally conquered by the West Saxons under
-Ceawlin. In later times, however, the kingdom of the Hwicce appears to
-have been always subject to Mercian supremacy, and possibly it was
-separated from Wessex in the time of Edwin. The first kings of whom we
-read were two brothers, Eanhere and Eanfrith, probably contemporaries of
-Wulfhere. They were followed by a king named Osric, a contemporary of
-Aethelred, and he by a king Oshere. Oshere had three sons who reigned
-after him, Aethelheard, Aethelweard and Aethelric. The two last named
-appear to have been reigning in the year 706. At the beginning of Offa's
-reign we again find the kingdom ruled by three brothers, named Eanberht,
-Uhtred and Aldred, the two latter of whom lived until about 780. After
-them the title of king seems to have been given up. Their successor
-Aethelmund, who was killed in a campaign against Wessex in 802, is
-described only as an earl. The district remained in possession of the
-rulers of Mercia until the fall of that kingdom. Together with the rest
-of English Mercia it submitted to King Alfred about 877-883 under Earl
-Aethelred, who possibly himself belonged to the Hwicce. No genealogy or
-list of kings has been preserved, and we do not know whether the dynasty
-was connected with that of Wessex or Mercia.
-
-  See Bede, _Historia eccles._ (edited by C. Plummer) iv. 13 (Oxford,
-  1896); W. de G. Birch, _Cartularium Saxonicum_, 43, 51, 76, 85, 116,
-  117, 122, 163, 187, 232, 233, 238 (Oxford, 1885-1889).
-       (F. G. M. B.)
-
-
-
-
-HYACINTH (Gr. hyakinthos), also called JACINTH (through Ital.
-_giacinto_), one of the most popular of spring garden flowers. It was in
-cultivation prior to 1597, at which date it is mentioned by Gerard. Rea
-in 1665 mentions several single and double varieties as being then in
-English gardens, and Justice in 1754 describes upwards of fifty
-single-flowered varieties, and nearly one hundred double-flowered ones,
-as a selection of the best from the catalogues of two then celebrated
-Dutch growers. One of the Dutch sorts, called La Reine de Femmes, a
-single white, is said to have produced from thirty-four to thirty-eight
-flowers in a spike, and on its first appearance to have sold for 50
-guilders a bulb; while one called Overwinnaar, or Conqueror, a double
-blue, sold at first for 100 guilders, Gloria Mundi for 500 guilders, and
-Koning Saloman for 600 guilders. Several sorts are at that date
-mentioned as blooming well in water-glasses. Justice relates that he
-himself raised several very valuable double-flowered kinds from seeds,
-which many of the sorts he describes are noted for producing freely.
-
-The original of the cultivated hyacinth, _Hyacinthus orientalis_, a
-native of Greece and Asia Minor, is by comparison an insignificant
-plant, bearing on a spike only a few small, narrow-lobed, washy blue
-flowers, resembling in form those of our common blue-bell. So great has
-been the improvement effected by the florists, and chiefly by the Dutch,
-that the modern hyacinth would scarcely be recognized as the descendant
-of the type above referred to, the spikes being long and dense, composed
-of a large number of flowers; the spikes produced by strong bulbs not
-unfrequently measure 6 to 9 in. in length and from 7 to 9 in. in
-circumference, with the flowers closely set on from bottom to top. Of
-late years much improvement has been effected in the size of the
-individual flowers and the breadth of their recurving lobes, as well as
-in securing increased brilliancy and depth of colour.
-
-The peculiarities of the soil and climate of Holland are so very
-favourable to their production that Dutch florists have made a specialty
-of the growth of those and other bulbous-rooted flowers. Hundreds of
-acres are devoted to the growth of hyacinths in the vicinity of Haarlem,
-and bring in a revenue of several hundreds of thousands of pounds. Some
-notion of the vast number imported into England annually may be formed
-from the fact that, for the supply of flowering plants to Covent Garden,
-one market grower alone produces from 60,000 to 70,000 in pots under
-glass, their blooming period being accelerated by artificial heat, and
-extending from Christmas onwards until they bloom naturally in the open
-ground.
-
-In the spring flower garden few plants make a more effective display
-than the hyacinth. Dotted in clumps in the flower borders, and arranged
-in masses of well-contrasted colours In beds in the flower garden, there
-are no flowers which impart during their season--March and April--a
-gayer tone to the parterre. The bulbs are rarely grown a second time,
-either for indoor or outdoor culture, though with care they might be
-utilized for the latter purpose; and hence the enormous numbers which
-are procured each recurring year from Holland.
-
-The first hyacinths were single-flowered, but towards the close of the
-17th century double-flowered ones began to appear, and till a recent
-period these bulbs were the most esteemed. At the present time, however,
-the single-flowered sorts are in the ascendant, as they produce more
-regular and symmetrical spikes of blossom, the flowers being closely set
-and more or less horizontal in direction, while most of the double sorts
-have the bells distant and dependent, so that the spike is loose and by
-comparison ineffective. For pot culture, and for growth in
-water-glasses especially, the single-flowered sorts are greatly to be
-preferred. Few if any of the original kinds are now in cultivation, a
-succession of new and improved varieties having been raised, the demand
-for which is regulated in some respects by fashion.
-
-  The hyacinth delights in a rich light sandy soil. The Dutch
-  incorporate freely with their naturally light soil a compost
-  consisting of one-third coarse sea or river sand, one-third rotten cow
-  dung without litter and one-third leaf-mould. The soil thus renovated
-  retains its qualities for six or seven years, but hyacinths are not
-  planted upon the same place for two years successively, intermediary
-  crops of narcissus, crocus or tulips being taken. A good compost for
-  hyacinths is sandy loam, decayed leaf-mould, rotten cow dung and sharp
-  sand in equal parts, the whole being collected and laid up in a heap
-  and turned over occasionally. Well-drained beds made up of this soil,
-  and refreshed with a portion of new compost annually, would grow the
-  hyacinth to perfection. The best time to plant the bulbs is towards
-  the end of September and during October; they should be arranged in
-  rows, 6 to 8 in. asunder, there being four rows in each bed. The bulbs
-  should be sunk about 4 to 6 in. deep, with a small quantity of clean
-  sand placed below and around each of them. The beds should be covered
-  with decayed tan-bark, coco-nut fibre or half-rotten dung litter. As
-  the flower-stems appear, they are tied to rigid but slender stakes to
-  preserve them from accident. If the bulbs are at all prized, the stems
-  should be broken off as soon as the flowering is over, so as not to
-  exhaust the bulbs; the leaves, however, must be allowed to grow on
-  till matured, but as soon as they assume a yellow colour, the bulbs
-  are taken up, the leaves cut off near their base, and the bulbs laid
-  out in a dry, airy, shady place to ripen, after which they are cleaned
-  of loose earth and skin, ready for storing. It is the practice in
-  Holland, about a month after the bloom, or when the tips of the leaves
-  assume a withered appearance, to take up the bulbs, and to lay them
-  sideways on the ground, covering them with an inch or two of earth.
-  About three weeks later they are again taken up and cleaned. In the
-  store-room they should be kept dry, well-aired and apart from each
-  other.
-
-  Few plants are better adapted than the hyacinth for pot culture as
-  greenhouse decorative plants; and by the aid of forcing they may be
-  had in bloom as early as Christmas. They flower fairly well in 5-in.
-  pots, the stronger bulbs in 6-in. pots. To bloom at Christmas, they
-  should be potted early in September, in a compost resembling that
-  already recommended for the open-air beds; and, to keep up a
-  succession of bloom, others should be potted at intervals of a few
-  weeks till the middle or end of November. The tops of the bulbs should
-  be about level with the soil, and if a little sand is put immediately
-  around them so much the better. The pots should be set in an open
-  place on a dry hard bed of ashes, and be covered over to a depth of 6
-  or 8 in. with the same material or with fibre or soil; and when the
-  roots are well developed, which will take from six to eight weeks,
-  they may be removed to a frame, and gradually exposed to light, and
-  then placed in a forcing pit in a heat of from 60 to 70 deg. When the
-  flowers are fairly open, they may be removed to the greenhouse or
-  conservatory.
-
-  The hyacinth may be very successfully grown in glasses for ornament in
-  dwelling-houses. The glasses are filled to the neck with rain or even
-  tap water, a few lumps of charcoal being dropped into them. The bulbs
-  are placed in the hollow provided for them, so that their base just
-  touches the water. This may be done in September or October. They are
-  then set in a dark cupboard for a few weeks till roots are freely
-  produced, and then gradually exposed to light. The early-flowering
-  single white Roman hyacinth, a small-growing pure white variety,
-  remarkable for its fragrance, is well adapted for forcing, as it can
-  be had in bloom if required by November. For windows it grows well in
-  the small glasses commonly used for crocuses; and for decorative
-  purposes should be planted about five bulbs in a 5-in. pot, or in pans
-  holding a dozen each. If grown for cut flowers it can be planted
-  thickly in boxes of any convenient size. It is highly esteemed during
-  the winter months by florists.
-
-  The Spanish hyacinth (_H. amethystinus_) and _H. azureus_ are charming
-  little bulbs for growing in masses in the rock garden or front of the
-  flower border. The older botanists included in the genus _Hyacinthus_
-  species of _Muscari_, _Scilla_ and other genera of bulbous Liliaceae,
-  and the name of hyacinth is still popularly applied to several other
-  bulbous plants. Thus _Muscari botryoides_ is the grape hyacinth, 6
-  in., blue or white, the handsomest; _M. moschatum_, the musk hyacinth,
-  10 in., has peculiar livid greenish-yellow flowers and a strong musky
-  odour; _M. comosum_ var. _monstrosum_, the feather hyacinth, bears
-  sterile flowers broken up into a featherlike mass; _M. racemosum_, the
-  starch hyacinth, is a native with deep blue plum-scented flowers. The
-  Cape hyacinth is _Galtonia candicans_, a magnificent border plant, 3-4
-  ft. high, with large drooping white bell-shaped flowers; the star
-  hyacinth, _Scilla amoena_; the Peruvian hyacinth or Cuban lily, _S.
-  peruviana_, a native of the Mediterranean region, to which Linnaeus
-  gave the species name _peruviana_ on a mistaken assumption of its
-  origin; the wild hyacinth or blue-bell, known variously as _Endymion
-  nonscriptum_, _Hyacinthus nonscriptus_ or _Scilla nutans_; the wild
-  hyacinth of western North America, _Camassia esculenta_. They all
-  flourish in good garden soil of a gritty nature.
-
-
-
-
-HYACINTH, or JACINTH, in mineralogy, a variety of zircon (q.v.) of
-yellowish red colour, used as a gem-stone. The _hyacinthus_ of ancient
-writers must have been our sapphire, or blue corundum, while the
-hyacinth of modern mineralogists may have been the stone known as
-_lyncurium_ ([Greek: lynkourion]). The Hebrew word _leshem_, translated
-ligure in the Authorized Version (Ex. xxviii. 19), from the [Greek:
-ligyrion] of the Septuagint, appears in the Revised Version as jacinth,
-but with a marginal alternative of amber. Both jacinth and amber may be
-reddish yellow, but their identification is doubtful. As our jacinth
-(zircon) is not known in ancient Egyptian work, Professor Flinders
-Petrie has suggested that the _leshem_ may have been a yellow quartz, or
-perhaps agate. Some old English writers describe the jacinth as yellow,
-whilst others refer to it as a blue stone, and the _hyacinthus_ of some
-authorities seems undoubtedly to have been our sapphire. In Rev. xx. 20
-the Revised Version retains the word jacinth, but gives sapphire as an
-alternative.
-
-Most of the gems known in trade as hyacinth are only garnets--generally
-the deep orange-brown hessonite or cinnamon-stone--and many of the
-antique engraved stones reputed to be hyacinth are probably garnets. The
-difference may be detected optically, since the garnet is singly and the
-hyacinth doubly refracting; moreover the specific gravity affords a
-simple means of diagnosis, that of garnet being only about 3.7, whilst
-hyacinth may have a density as high as 4.7. Again, it was shown many
-years ago by Sir A. H. Church that most hyacinths, when examined by the
-spectroscope, show a series of dark absorption bands, due perhaps to the
-presence of some rare element such as uranium or erbium.
-
-Hyacinth is not a common mineral. It occurs, with other zircons, in the
-gem-gravels of Ceylon, and very fine stones have been found as pebbles
-at Mudgee in New South Wales. Crystals of zircon, with all the typical
-characters of hyacinth, occur at Expailly, Le Puy-en-Velay, in Central
-France, but they are not large enough for cutting. The stones which have
-been called Compostella hyacinths are simply ferruginous quartz from
-Santiago de Compostella in Spain.     (F. W. R.*)
-
-
-
-
-HYACINTHUS,[1] in Greek mythology, the youngest son of the Spartan king
-Amyclas, who reigned at Amyclae (so Pausanias iii. 1. 3, iii. 19. 5; and
-Apollodorus i. 3. 3, iii. 10. 3). Other stories make him son of Oebalus,
-of Eurotas, or of Pierus and the nymph Clio (see Hyginus, _Fabulae_,
-271; Lucian, _De saltatione_, 45, and _Dial. deor._ 14). According to
-the general story, which is probably late and composite, his great
-beauty attracted the love of Apollo, who killed him accidentally when
-teaching him to throw the _discus_ (quoit); others say that Zephyrus (or
-Boreas) out of jealousy deflected the quoit so that it hit Hyacinthus on
-the head and killed him. According to the representation on the tomb at
-Amyclae (Pausanias, _loc. cit._) Hyacinthus was translated into heaven
-with his virgin sister Polyboea. Out of his blood there grew the flower
-known as the hyacinth, the petals of which were marked with the mournful
-exclamation AI, AI, "alas" (cf. "that sanguine flower inscribed with
-woe"). This Greek hyacinth cannot have been the flower which now bears
-the name: it has been identified with a species of iris and with the
-larkspur (_Delphinium Aiacis_), which appear to have the markings
-described. The Greek hyacinth was also said to have sprung from the
-blood of Ajax. Evidently the Greek authorities confused both the flowers
-and the traditions.
-
-The death of Hyacinthus was celebrated at Amyclae by the second most
-important of Spartan festivals, the Hyacinthia, which took place in the
-Spartan month Hecatombeus. What month this was is not certain. Arguing
-from Xenophon (_Hell._ iv. 5) we get May; assuming that the Spartan
-Hecatombeus is the Attic Hecatombaion, we get July; or again it may be
-the Attic Scirophorion, June. At all events the Hyacinthia was an early
-summer festival. It lasted three days, and the rites gradually passed
-from mourning for Hyacinthus to rejoicings in the majesty of Apollo,
-the god of light and warmth, and giver of the ripe fruits of the earth
-(see a passage from Polycrates, _Laconica_, quoted by Athenaeus 139 d;
-criticized by L. R. Farnell, _Cults of the Greek States_, iv. 266
-foll.). This festival is clearly connected with vegetation, and marks
-the passage from the youthful verdure of spring to the dry heat of
-summer and the ripening of the corn.
-
-The precise relation which Apollo bears to Hyacinthus is obscure. The
-fact that at Tarentum a Hyacinthus tomb is ascribed by Polybius to
-Apollo Hyacinthus (not Hyacinthius) has led some to think that the
-personalities are one, and that the hero is merely an emanation from the
-god; confirmation is sought in the Apolline appellation [Greek:
-tetracheir], alleged by Hesychius to have been used in Laconia, and
-assumed to describe a composite figure of Apollo-Hyacinthus. Against
-this theory is the essential difference between the two figures.
-Hyacinthus is a chthonian vegetation god whose worshippers are afflicted
-and sorrowful; Apollo, though interested in vegetation, is never
-regarded as inhabiting the lower world, his death is not celebrated in
-any ritual, his worship is joyous and triumphant, and finally the
-Amyclean Apollo is specifically the god of war and song. Moreover,
-Pausanias describes the monument at Amyclae as consisting of a rude
-figure of Apollo standing on an altar-shaped base which formed the tomb
-of Hyacinthus. Into the latter offerings were put for the hero before
-gifts were made to the god.
-
-On the whole it is probable that Hyacinthus belongs originally to the
-pre-Dorian period, and that his story was appropriated and woven into
-their own Apollo myth by the conquering Dorians. Possibly he may be the
-apotheosis of a pre-Dorian king of Amyclae. J. G. Frazer further
-suggests that he may have been regarded as spending the winter months in
-the underworld and returning to earth in the spring when the "hyacinth"
-blooms. In this case his festival represents perhaps both the Dorian
-conquest of Amyclae and the death of spring before the ardent heat of
-the summer sun, typified as usual by the _discus_ (quoit) with which
-Apollo is said to have slain him. With the growth of the hyacinth from
-his blood should be compared the oriental stories of violets springing
-from the blood of Attis, and roses and anemones from that of Adonis. As
-a youthful vegetation god, Hyacinthus may be compared with Linus and
-Scephrus, both of whom are connected with Apollo Agyieus.
-
-  See L. R. Farnell, _Cults of the Greek States_, vol. iv. (1907), pp.
-  125 foll., 264 foll.; J. G. Frazer, _Adonis, Attis, Osiris_ (1906),
-  bk. ii. ch. 7; S. Wide, _Lakonische Kulte_, p. 290; E. Rhode,
-  _Psyche_, 3rd ed. i. 137 foll.; Roscher, _Lexikon d. griech. u. rom.
-  Myth._, s.v. "Hyakinthos" (Greve); L. Preller, _Griechische Mythol._
-  4th ed. i. 248 foll.     (J. M. M.)
-
-
-FOOTNOTE:
-
-  [1] The word is probably derived from an Indo-European root, meaning
-    "youthful," found in Latin, Greek, English and Sanskrit. Some have
-    suggested that the first two letters are from [Greek: uein], to rain,
-    (cf. Hyades).
-
-
-
-
-HYADES ("the rainy ones"), in Greek mythology, the daughters of Atlas
-and Aethra; their number varies between two and seven. As a reward for
-having brought up Zeus at Dodona and taken care of the infant Dionysus
-Hyes, whom they conveyed to Ino (sister of his mother Semele) at Thebes
-when his life was threatened by Lycurgus, they were translated to heaven
-and placed among the stars (Hyginus, _Poet. astron._ ii. 21). Another
-form of the story combines them with the Pleiades. According to this
-they were twelve (or fifteen) sisters, whose brother Hyas was killed by
-a snake while hunting in Libya (Ovid, _Fasti_, v. 165; Hyginus, _Fab._
-192). They lamented him so bitterly that Zeus, out of compassion,
-changed them into stars--five into the Hyades, at the head of the
-constellation of the Bull, the remainder into the Pleiades. Their name
-is derived from the fact that the rainy season commenced when they rose
-at the same time as the sun (May 7-21); the original conception of them
-is that of the fertilizing principle of moisture. The Romans derived the
-name from [Greek: us] (pig), and translated it by _Suculae_ (Cicero, _De
-nat. deorum_, ii. 43).
-
-
-
-
-HYATT, ALPHEUS (1838-1902), American naturalist, was born at Washington,
-D.C., on the 5th of April 1838. From 1858 to 1862 he studied at Harvard,
-where he had Louis Agassiz for his master, and in 1863 he served as a
-volunteer in the Civil War, attaining the rank of captain. In 1867 he
-was appointed curator of the Essex Institute at Salem, and in 1870
-became professor of zoology and palaeontology at the Massachusetts
-Institute of Technology (resigned 1888), and custodian of the Boston
-Society of Natural History (curator in 1881). In 1886 he was appointed
-assistant for palaeontology in the Cambridge museum of comparative
-anatomy, and in 1889 was attached to the United States Geological Survey
-as palaeontologist for the Trias and Jura. He was the chief founder of
-the American Society of Naturalists, of which he acted as first
-president in 1883, and he also took a leading part in establishing the
-marine biological laboratories at Annisquam and Woods Hole, Mass. He
-died at Cambridge on the 15th of January 1902.
-
-  His works include _Observations on Fresh-water Polyzoa_ (1866);
-  _Fossil Cephalopods of the Museum of Comparative Zoology_ (1872);
-  _Revision of North American Porifera_ (1875-1877); _Genera of Fossil
-  Cephalopoda_ (1883); _Larval Theory of the Origin of Cellular Tissue_
-  (1884); _Genesis of the Arietidae_ (1889); and _Phylogeny of an
-  acquired characteristic_ (1894). He wrote the section on Cephalopoda
-  in Karl von Zittel's _Palaontologie_ (1900), and his well-known study
-  on the fossil pond snails of Steinheim ("The Genesis of the Tertiary
-  Species of Planorbis at Steinheim") appeared in the _Memoirs_ of the
-  Boston Natural History Society in 1880. He was one of the founders and
-  editors of the _American Naturalist_.
-
-
-
-
-HYBLA, the name of several cities In Sicily. The best known
-historically, though its exact site is uncertain, is Hybla Major, near
-(or by some supposed to be identical with) Megara Hyblaea (q.v.):
-another Hybla, known as Hybla Minor or Galeatis, is represented by the
-modern Paterno; while the site of Hybla Heraea is to be sought near
-Ragusa.
-
-
-
-
-HYBRIDISM. The Latin word _hybrida_, _hibrida_ or _ibrida_ has been
-assumed to be derived from the Greek [Greek: hybris], an insult or
-outrage, and a hybrid or mongrel has been supposed to be an outrage on
-nature, an unnatural product. As a general rule animals and plants
-belonging to distinct species do not produce offspring when crossed with
-each other, and the term hybrid has been employed for the result of a
-fertile cross between individuals of different species, the word mongrel
-for the more common result of the crossing of distinct varieties. A
-closer scrutiny of the facts, however, makes the term hybridism less
-isolated and more vague. The words species and genus, and still more
-subspecies and variety, do not correspond with clearly marked and
-sharply defined zoological categories, and no exact line can be drawn
-between the various kinds of crossings from those between individuals
-apparently identical to those belonging to genera universally recognized
-as distinct. Hybridism therefore grades into mongrelism, mongrelism into
-cross-breeding, and cross-breeding into normal pairing, and we can say
-little more than that the success of the union is the more unlikely or
-more unnatural the further apart the parents are in natural affinity.
-
-The interest in hybridism was for a long time chiefly of a practical
-nature, and was due to the fact that hybrids are often found to present
-characters somewhat different from those of either parent. The leading
-facts have been known in the case of the horse and ass from time
-immemorial. The earliest recorded observation of a hybrid plant is by J.
-G. Gmelin towards the end of the 17th century; the next is that of Thomas
-Fairchild, who in the second decade of the 18th century, produced the
-cross which is still grown in gardens under the name of "Fairchild's
-Sweet William." Linnaeus made many experiments in the cross-fertilization
-of plants and produced several hybrids, but Joseph Gottlieb Kolreuter
-(1733-1806) laid the first real foundation of our scientific knowledge of
-the subject. Later on Thomas Andrew Knight, a celebrated English
-horticulturist, devoted much successful labour to the improvement of
-fruit trees and vegetables by crossing. In the second quarter of the 19th
-century C. F. Gartner made and published the results of a number of
-experiments that had not been equalled by any earlier worker. Next came
-Charles Darwin, who first in the _Origin of Species_, and later in _Cross
-and Self-Fertilization of Plants_, subjected the whole question to a
-critical examination, reviewed the known facts and added many to them.
-
-  Darwin's conclusions were summed up by G. J. Romanes in the 9th
-  edition of this _Encyclopaedia_ as follows:--
-
-  1. The laws governing the production of hybrids are identical, or
-  nearly identical, in the animal and vegetable kingdoms.
-
-  2. The sterility which so generally attends the crossing of two
-  specific forms is to be distinguished as of two kinds, which, although
-  often confounded by naturalists, are in reality quite distinct.
-  For the sterility may obtain between the two parent species when first
-  crossed, or it may first assert itself in their hybrid progeny. In the
-  latter case the hybrids, although possibly produced without any
-  appearance of infertility on the part of their parent species,
-  nevertheless prove more or less infertile among themselves, and also
-  with members of either parent species.
-
-  3. The degree of both kinds of infertility varies in the case of
-  different species, and in that of their hybrid progeny, from absolute
-  sterility up to complete fertility. Thus, to take the case of plants,
-  "when pollen from a plant of one family is placed on the stigma of a
-  plant of a distinct family, it exerts no more influence than so much
-  inorganic dust. From this absolute zero of fertility, the pollen of
-  different species, applied to the stigma of some one species of the
-  same genus, yields a perfect gradation in the number of seeds
-  produced, up to nearly complete, or even quite complete, fertility;
-  so, in hybrids themselves, there are some which never have produced,
-  and probably never would produce, even with the pollen of the pure
-  parents, a single fertile seed; but in some of these cases a first
-  trace of fertility may be detected, by the pollen of one of the pure
-  parent species causing the flower of the hybrid to wither earlier than
-  it otherwise would have done; and the early withering of the flower is
-  well known to be a sign of incipient fertilization. From this extreme
-  degree of sterility we have self-fertilized hybrids producing a
-  greater and greater number of seeds up to perfect fertility."
-
-  4. Although there is, as a rule, a certain parallelism, there is no
-  fixed relation between the degree of sterility manifested by the
-  parent species when crossed and that which is manifested by their
-  hybrid progeny. There are many cases in which two pure species can be
-  crossed with unusual facility, while the resulting hybrids are
-  remarkably sterile; and, contrariwise, there are species which can
-  only be crossed with extreme difficulty, though the hybrids, when
-  produced, are very fertile. Even within the limits of the same genus,
-  these two opposite cases may occur.
-
-  5. When two species are reciprocally crossed, i.e. male A with female
-  B, and male B with female A, the degree of sterility often differs
-  greatly in the two cases. The sterility of the resulting hybrids may
-  differ likewise.
-
-  6. The degree of sterility of first crosses and of hybrids runs, to a
-  certain extent, parallel with the systematic affinity of the forms
-  which are united. "For species belonging to distinct genera can
-  rarely, and those belonging to distinct families can never, be
-  crossed. The parallelism, however, is far from complete; for a
-  multitude of closely allied species will not unite, or unite with
-  extreme difficulty, whilst other species, widely different from each
-  other, can be crossed with perfect facility. Nor does the difficulty
-  depend on ordinary constitutional differences; for annual and
-  perennial plants, deciduous and evergreen trees, plants flowering at
-  different seasons, inhabiting different stations, and naturally living
-  under the most opposite climates, can often be crossed with ease. The
-  difficulty or facility apparently depends exclusively on the sexual
-  constitution of the species which are crossed, or on their sexual
-  elective affinity."
-
-There are many new records as to the production of hybrids.
-Horticulturists have been extremely active and successful in their
-attempts to produce new flowers or new varieties of vegetables by
-seminal or graft-hybrids, and any florist's catalogue or the account of
-any special plant, such as is to be found in Foster-Melliar's _Book of
-the Rose_, is in great part a history of successful hybridization. Much
-special experimental work has been done by botanists, notably by de
-Vries, to the results of whose experiments we shall recur. Experiments
-show clearly that the obtaining of hybrids is in many cases merely a
-matter of taking sufficient trouble, and the successful crossing of
-genera is not infrequent.
-
-  Focke, for instance, cites cases where hybrids were obtained between
-  _Brassica_ and _Raphanus_, _Galium_ and _Asperula_, _Campanula_ and
-  _Phyteuma_, _Verbascum_ and _Celsia_. Among animals, new records and
-  new experiments are almost equally numerous. Boveri has crossed
-  _Echinus microtuberculatus_ with _Sphaerechinus granularis_. Thomas
-  Hunt Morgan even obtained hybrids between Asterias, a starfish, and
-  _Arbacia_, a sea-urchin, a cross as remote as would be that between a
-  fish and a mammal. Vernon got many hybrids by fertilizing the eggs of
-  _Strongylocentrotus lividus_ with the sperm of _Sphaerechinus
-  granularis_. Standfuss has carried on an enormous series of
-  experiments with Lepidopterous insects, and has obtained a very large
-  series of hybrids, of which he has kept careful record. Lepidopterists
-  generally begin to suspect that many curious forms offered by dealers
-  as new species are products got by crossing known species. Apello has
-  succeeded with Teleostean fish; Gebhardt and others with Amphibia.
-  Elliot and Suchetet have studied carefully the question of
-  hybridization occurring normally among birds, and have got together a
-  very large body of evidence. Among the cases cited by Elliot the most
-  striking are that of the hybrid between _Colaptes cafer_ and _C.
-  auratus_, which occurs over a very wide area of North America and is
-  known as _C. hybridus_, and the hybrid between _Euplocamus lineatus_
-  and _E. horsfieldi_, which appears to be common in Assam. St M.
-  Podmore has produced successful crosses between the wood-pigeon
-  (_Columba palumbus_) and a domesticated variety of the rock pigeon
-  (_C. livia_). Among mammals noteworthy results have been obtained by
-  Professor Cossar Ewart, who has bred nine zebra hybrids by crossing
-  mares of various sizes with a zebra stallion, and who has studied in
-  addition three hybrids out of zebra mares, one sired by a donkey, the
-  others by ponies. Crosses have been made between the common rabbit
-  (_Lepus cuniculus_) and the guinea-pig (_Cavia cobaya_), and examples
-  of the results have been exhibited in the Zoological Gardens of
-  Sydney, New South Wales. The Carnivora generally are very easy to
-  hybridize, and many successful experiments have been made with animals
-  in captivity. Karl Hagenbeck of Hamburg has produced crosses between
-  the lion (_Felis leo_) and the tiger (_F. tigris_). What was probably
-  a "tri-hybrid" in which lion, leopard and jaguar were mingled was
-  exhibited by a London showman in 1908. Crosses between various species
-  of the smaller cats have been fertile on many occasions. The black
-  bear (_Ursus americanus_) and the European brown bear (_U. arctos_)
-  bred in the London Zoological Gardens in 1859, but the three cubs did
-  not reach maturity. Hybrids between the brown bear and the
-  grizzly-bear (_U. horribilis_) have been produced in Cologne, whilst
-  at Halle since 1874 a series of successful matings of polar (_U.
-  maritimus_) and brown bears have been made. Examples of these hybrid
-  bears have been exhibited by the London Zoological Society. The London
-  Zoological Society has also successfully mated several species of
-  antelopes, for instance, the water-bucks _Kobus ellipsiprymnus_ and
-  _K. unctuosus_, and Selous's antelope _Limnotragus selousi_ with _L.
-  gratus_.
-
-The causes militating against the production of hybrids have also
-received considerable attention. Delage, discussing the question, states
-that there is a general proportion between sexual attraction and
-zoological affinity, and in many cases hybrids are not naturally
-produced simply from absence of the stimulus to sexual mating, or
-because of preferential mating within the species or variety. In
-addition to differences of habit, temperament, time of maturity, and so
-forth, gross structural differences may make mating impossible. Thus
-Escherick contends that among insects the peculiar structure of the
-genital appendages makes cross-impregnation impossible, and there is
-reason to believe that the specific peculiarities of the modified sexual
-palps in male spiders have a similar result.
-
-  The difficulties, however, may not exist, or may be overcome by
-  experiment, and frequently it is only careful management that is
-  required to produce crossing. Thus it has been found that when the
-  pollen of one species does not succeed in fertilizing the ovules of
-  another species, yet the reciprocal cross may be successful; that is
-  to say, the pollen of the second species may fertilize the ovules of
-  the first. H. M. Vernon, working with sea-urchins, found that the
-  obtaining of hybrids depended on the relative maturity of the sexual
-  products. The difficulties in crossing apparently may extend to the
-  chemiotaxic processes of the actual sexual cells. Thus when the
-  spermatozoa of an urchin were placed in a drop of seawater containing
-  ripe eggs of an urchin and of a starfish, the former eggs became
-  surrounded by clusters of the male cells, while the latter appeared to
-  exert little attraction for the alien germ-cells. Finally, when the
-  actual impregnation of the egg is possible naturally, or has been
-  secured by artificial means, the development of the hybrid may stop at
-  an early stage. Thus hybrids between the urchin and the starfish,
-  animals belonging to different classes, reached only the stage of the
-  pluteus larva. A. D. Apello, experimenting with Teleostean fish, found
-  that very often impregnation and segmentation occurred, but that the
-  development broke down immediately afterwards. W. Gebhardt, crossing
-  _Rana esculenta_ with _R. arvalis_, found that the cleavage of the
-  ovum was normal, but that abnormality began with the gastrula, and
-  that development soon stopped. In a very general fashion there appears
-  to be a parallel between the zoological affinity and the extent to
-  which the incomplete development of the hybrid proceeds.
-
-As to the sterility of hybrids _inter se_, or with either of the parent
-forms, information is still wanted. Delage, summing up the evidence in a
-general way, states that mongrels are more fertile and stronger than
-their parents, while hybrids are at least equally hardy but less
-fertile. While many of the hybrid products of horticulturists are
-certainly infertile, others appear to be indefinitely fertile.
-
-  Focke, it is true, states that the hybrids between _Primula auricula_
-  and _P. hirsuta_ are fertile for many generations, but not
-  indefinitely so; but, while this may be true for the particular case,
-  there seems no reason to doubt that many plant hybrids are quite
-  fertile. In the case of animals the evidence is rather against
-  fertility. Standfuss, who has made experiments lasting over many
-  years, and who has dealt with many genera of Lepidoptera, obtained no
-  fertile hybrid females, although he found that hybrid males paired
-  readily and successfully with pure-bred females of the parent races.
-  Elliot, dealing with birds, concluded that no hybrids were
-  fertile with one another beyond the second generation, but thought
-  that they were fertile with members of the parent races. Wallace, on
-  the other hand, cites from Quatrefages the case of hybrids between the
-  moths _Bombyx cynthia_ and _B. arrindia_, which were stated to be
-  fertile _inter se_ for eight generations. He also states that hybrids
-  between the sheep and goat have a limited fertility _inter se_.
-  Charles Darwin, however, had evidence that some hybrid pheasants were
-  completely fertile, and he himself interbred the progeny of crosses
-  between the common and Chinese geese, whilst there appears to be no
-  doubt as to the complete fertility of the crosses between many species
-  of ducks, J. L. Bonhote having interbred in various crosses for
-  several generations the mallard (_Anas boschas_), the Indian spot-bill
-  duck (_A. poecilorhyncha_), the New Zealand grey duck (_A.
-  superciliosa_) and the pin-tail (_Dafila acuta_). Podmore's pigeon
-  hybrids were fertile _inter se_, a specimen having been exhibited at
-  the London Zoological Gardens. The hybrids between the brown and polar
-  bears bred at Halle proved to be fertile, both with one of the parent
-  species and with one another.
-
-  Cornevin and Lesbre state that in 1873 an Arab mule was fertilized in
-  Africa by a stallion, and gave birth to female offspring which she
-  suckled. All three were brought to the Jardin d'Acclimatation in
-  Paris, and there the mule had a second female colt to the same father,
-  and subsequently two male colts in succession to an ass and to a
-  stallion. The female progeny were fertilized, but their offspring were
-  feeble and died at birth. Cossar Ewart gives an account of a recent
-  Indian case in which a female mule gave birth to a male colt. He
-  points out, however, that many mistakes have been made about the
-  breeding of hybrids, and is not altogether inclined to accept this
-  supposed case. Very little has been published with regard to the most
-  important question, as to the actual condition of the sexual organs
-  and cells in hybrids. There does not appear to be gross anatomical
-  defect to account for the infertility of hybrids, but microscopical
-  examination in a large number of cases is wanted. Cossar Ewart, to
-  whom indeed much of the most interesting recent work on hybrids is
-  due, states that in male zebra-hybrids the sexual cells were immature,
-  the tails of the spermatozoa being much shorter than those of the
-  similar cells in stallions and zebras. He adds, however, that the male
-  hybrids he examined were young, and might not have been sexually
-  mature. He examined microscopically the ovary of a female zebra-hybrid
-  and found one large and several small Graafian follicles, in all
-  respects similar to those in a normal mare or female zebra. A careful
-  study of the sexual organs in animal and plant hybrids is very much to
-  be desired, but it may be said that so far as our present knowledge
-  goes there is not to be expected any obvious microscopical cause of
-  the relative infertility of hybrids.
-
-The relative variability of hybrids has received considerable attention
-from many writers. Horticulturists, as Bateson has written, are "aware
-of the great and striking variations which occur in so many orders of
-plants when hybridization is effected." The phrase has been used
-"breaking the constitution of a plant" to indicate the effect produced
-in the offspring of a hybrid union, and the device is frequently used by
-those who are seeking for novelties to introduce on the market. It may
-be said generally that hybrids are variable, and that the products of
-hybrids are still more variable. J. L. Bonhote found extreme variations
-amongst his hybrid ducks. Y. Delage states that in reciprocal crosses
-there is always a marked tendency for the offspring to resemble the male
-parents; he quotes from Huxley that the mule, whose male parent is an
-ass, is more like the ass, and that the hinny, whose male parent is a
-horse, is more like the horse. Standfuss found among Lepidoptera that
-males were produced much more often than females, and that these males
-paired readily. The freshly hatched larvae closely resembled the larvae
-of the female parent, but in the course of growth the resemblance to the
-male increased, the extent of the final approximation to the male
-depending on the relative phylogenetic age of the two parents, the
-parent of the older species being prepotent. In reciprocal pairing, he
-found that the male was able to transmit the characters of the parents
-in a higher degree. Cossar Ewart, in relation to zebra hybrids, has
-discussed the matter of resemblance to parents in very great detail, and
-fuller information must be sought in his writings. He shows that the
-wild parent is not necessarily prepotent, although many writers have
-urged that view. He described three hybrids bred out of a zebra mare by
-different horses, and found in all cases that the resemblance to the
-male or horse parent was more profound. Similarly, zebra-donkey hybrids
-out of zebra mares bred in France and in Australia were in characters
-and disposition far more like the donkey parents. The results which he
-obtained in the hybrids which he bred from a zebra stallion and
-different mothers were more variable, but there was rather a balance in
-favour of zebra disposition and against zebra shape and marking.
-
-  "Of the nine zebra-horse hybrids I have bred," he says, "only two in
-  their make and disposition take decidedly after the wild parent. As
-  explained fully below, all the hybrids differ profoundly in the plan
-  of their markings from the zebra, while in their ground colour they
-  take after their respective dams or the ancestors of their dams far
-  more than after the zebra--the hybrid out of the yellow and white
-  Iceland pony, e.g. instead of being light in colour, as I anticipated,
-  is for the most part of a dark dun colour, with but indistinct
-  stripes. The hoofs, mane and tail of the hybrids are at the most
-  intermediate, but this is perhaps partly owing to reversion towards
-  the ancestors of these respective dams. In their disposition and
-  habits they all undoubtedly agree more with the wild sire."
-
-Ewart's experiments and his discussion of them also throw important
-light on the general relation of hybrids to their parents. He found that
-the coloration and pattern of his zebra hybrids resembled far more those
-of the Somali or Grevy's zebra than those of their sire--a Burchell's
-zebra. In a general discussion of the stripings of horses, asses and
-zebras, he came to the conclusion that the Somali zebra represented the
-older type, and that therefore his zebra hybrids furnished important
-evidence of the effect of crossing in producing reversion to ancestral
-type. The same subject has of course been discussed at length by Darwin,
-in relation to the cross-breeding of varieties of pigeons; but the
-modern experimentalists who are following the work of Mendel interpret
-reversion differently (see MENDELISM).
-
-_Graft-Hybridism._--It is well known that, when two varieties or allied
-species are grafted together, each retains its distinctive characters.
-But to this general, if not universal, rule there are on record several
-alleged exceptions, in which either the scion is said to have partaken
-of the qualities of the stock, the stock of the scion, or each to have
-affected the other. Supposing any of these influences to have been
-exerted, the resulting product would deserve to be called a
-graft-hybrid. It is clearly a matter of great interest to ascertain
-whether such formation of hybrids by grafting is really possible; for,
-if even one instance of such formation could be unequivocally proved, it
-would show that sexual and asexual reproduction are essentially
-identical.
-
-The cases of alleged graft-hybridism are exceedingly few, considering
-the enormous number of grafts that are made every year by
-horticulturists, and have been so made for centuries. Of these cases the
-most celebrated are those of Adam's laburnum (_Cytisus Adami_) and the
-bizzarria orange. Adam's laburnum is now flourishing in numerous places
-throughout Europe, all the trees having been raised as cuttings from the
-original graft, which was made by inserting a bud of the purple laburnum
-into a stock of the yellow. M. Adam, who made the graft, has left on
-record that from it there sprang the existing hybrid. There can be no
-question as to the truly hybrid character of the latter--all the
-peculiarities of both parent species being often blended in the same
-raceme, flower or even petal; but until the experiment shall have been
-successfully repeated there must always remain a strong suspicion that,
-notwithstanding the assertion and doubtless the belief of M. Adam, the
-hybrid arose as a cross in the ordinary way of seminal reproduction.
-Similarly, the bizzarria orange, which is unquestionably a hybrid
-between the bitter orange and the citron--since it presents the
-remarkable spectacle of these two different fruits blended into one--is
-stated by the gardener who first succeeded in producing it to have
-arisen as a graft-hybrid; but here again a similar doubt, similarly due
-to the need of corroboration, attaches to the statement. And the same
-remark applies to the still more wonderful case of the so-called
-trifacial orange, which blends three distinct kinds of fruit in one, and
-which is said to have been produced by artificially splitting and
-uniting the seeds taken from the three distinct species, the fruits of
-which now occur blended in the triple hybrid.
-
-The other instances of alleged graft-hybridism are too numerous to be
-here noticed in detail; they refer to jessamine, ash, hazel, vine,
-hyacinth, potato, beet and rose. Of these the cases of the vine, beet
-and rose are the strongest as evidence of graft-hybridization, from the
-fact that some of them were produced as the result of careful
-experiments made by very competent experimentalists. On the whole, the
-results of some of these experiments, although so few in number, must be
-regarded as making out a strong case in favour of the possibility of
-graft-hybridism. For it must always be remembered that, in experiments
-of this kind, negative evidence, however great in amount, may be
-logically dissipated by a single positive result.
-
-_Theory of Hybridism._--Charles Darwin was interested in hybridism as an
-experimental side of biology, but still more from the bearing of the
-facts on the theory of the origin of species. It is obvious that
-although hybridism is occasionally possible as an exception to the
-general infertility of species inter se, the exception is still more
-minimized when it is remembered that the hybrid progeny usually display
-some degree of sterility. The main facts of hybridism appear to lend
-support to the old doctrine that there are placed between all species
-the barriers of mutual sterility. The argument for the fixity of species
-appears still stronger when the general infertility of species crossing
-is contrasted with the general fertility of the crossing of natural and
-artificial varieties. Darwin himself, and afterwards G. J. Romanes,
-showed, however, that the theory of natural selection did not require
-the possibility of the commingling of specific types, and that there was
-no reason to suppose that the mutation of species should depend upon
-their mutual crossing. There existed more than enough evidence, and this
-has been added to since, to show that infertility with other species is
-no criterion of a species, and that there is no exact parallel between
-the degree of affinity between forms and their readiness to cross. The
-problem of hybridism is no more than the explanation of the generally
-reduced fertility of remoter crosses as compared with the generally
-increased fertility of crosses between organisms slightly different.
-Darwin considered and rejected the view that the inter-sterility of
-species could have been the result of natural selection.
-
-  "At one time it appeared to me probable," he wrote (_Origin of
-  Species_, 6th ed. p. 247), "as it has to others, that the sterility of
-  first crosses and of hybrids might have been slowly acquired through
-  the natural selection of slightly lessened degrees of fertility,
-  which, like any other variation, spontaneously appeared in certain
-  individuals of one variety when crossed with those of another variety.
-  For it would clearly be advantageous to two varieties or incipient
-  species if they could be kept from blending, on the same principle
-  that, when man is selecting at the same time two varieties, it is
-  necessary that he should keep them separate. In the first place, it
-  may be remarked that species inhabiting distinct regions are often
-  sterile when crossed; now it could clearly have been of no advantage
-  to such separated species to have been rendered mutually sterile and,
-  consequently, this could not have been effected through natural
-  selection; but it may perhaps be argued that, if a species were
-  rendered sterile with some one compatriot, sterility with other
-  species would follow as a necessary contingency. In the second place,
-  it is almost as much opposed to the theory of natural selection as to
-  that of special creation, that in reciprocal crosses the male element
-  of one form should have been rendered utterly impotent on a second
-  form, whilst at the same time the male element of this second form is
-  enabled freely to fertilize the first form; for this peculiar state of
-  the reproductive system could hardly have been advantageous to either
-  species."
-
-Darwin came to the conclusion that the sterility of crossed species must
-be due to some principle quite independent of natural selection. In his
-search for such a principle he brought together much evidence as to the
-instability of the reproductive system, pointing out in particular how
-frequently wild animals in captivity fail to breed, whereas some
-domesticated races have been so modified by confinement as to be fertile
-together although they are descended from species probably mutually
-infertile. He was disposed to regard the phenomena of differential
-sterility as, so to speak, by-products of the process of evolution. G.
-J. Romanes afterwards developed his theory of physiological selection,
-in which he supposed that the appearance of differential fertility
-within a species was the starting-point of new species; certain
-individuals by becoming fertile only _inter se_ proceeded along lines of
-modification diverging from the lines followed by other members of the
-species. Physiological selection in fact would operate in the same
-fashion as geographical isolation; if a portion of a species separated
-on an island tends to become a new species, so also a portion separated
-by infertility with the others would tend to form a new species.
-According to Romanes, therefore, mutual infertility was the
-starting-point, not the result, of specific modification. Romanes,
-however, did not associate his interesting theory with a sufficient
-number of facts, and it has left little mark on the history of the
-subject. A. R. Wallace, on the other hand, has argued that sterility
-between incipient species may have been increased by natural selection
-in the same fashion as other favourable variations are supposed to have
-been accumulated. He thought that "some slight degree of infertility was
-a not infrequent accompaniment of the external differences which always
-arise in a state of nature between varieties and incipient species."
-
-Weismann concluded, from an examination of a series of plant hybrids,
-that from the same cross hybrids of different character may be obtained,
-but that the characters are determined at the moment of fertilization;
-for he found that all the flowers on the same hybrid plant resembled one
-another in the minutest details of colour and pattern. Darwin already
-had pointed to the act of fertilization as the determining point, and it
-is in this direction that the theory of hybridism has made the greatest
-advance.
-
-The starting-point of the modern views comes from the experiments and
-conclusions on plant hybrids made by Gregor Mendel and published in
-1865. It is uncertain if Darwin had paid attention to this work;
-Romanes, writing in the 9th edition of this _Encyclopaedia_, cited it
-without comment. First H. de Vries, then W. Bateson and a series of
-observers returned to the work of Mendel (see MENDELISM), and made it
-the foundation of much experimental work and still more theory. It is
-still too soon to decide if the confident predictions of the Mendelians
-are justified, but it seems clear that a combination of Mendel's
-numerical results with Weismann's (see HEREDITY) conception of the
-particulate character of the germ-plasm, or hereditary material, is at
-the root of the phenomena of hybridism, and that Darwin was justified in
-supposing it to lie outside the sphere of natural selection and to be a
-fundamental fact of living matter.
-
-  AUTHORITIES.--Apello, "Uber einige Resultate der Kreuzbefruchtung bei
-  Knochenfischen," _Bergens mus. aarbog_ (1894); Bateson, "Hybridization
-  and Cross-breeding," _Journal of the Royal Horticultural Society_
-  (1900); J. L. Bonhote, "Hybrid Ducks," _Proc. Zool. Soc. of London_
-  (1905), p. 147; Boveri, article "Befruchtung," in _Ergebnisse der
-  Anatomie und Entwickelungsgeschichte von Merkel und Bonnet_, i.
-  385-485; Cornevin et Lesbre, "Etude sur un hybride issu d'une mule
-  feconde et d'un cheval," _Rev. Sci._ li. 144; Charles Darwin, _Origin
-  of Species_ (1859), _The Effects of Cross and Self-Fertilization in
-  the Vegetable Kingdom_ (1878); Delage, _La Structure du protoplasma et
-  les theories sur l'heredite_ (1895, with a literature); de Vries, "The
-  Law of Disjunction of Hybrids," _Comptes rendus_ (1900), p. 845;
-  Elliot, _Hybridism_; Escherick, "Die biologische Bedeutung der
-  Genitalabhange der Insecten," _Verh. z. B. Wien_, xlii. 225; Ewart,
-  _The Penycuik Experiments_ (1899); Focke, _Die Pflanzen-Mischlinge_
-  (1881); Foster-Melliar, _The Book of the Rose_ (1894); C. F. Gaertner,
-  various papers in _Flora_, 1828, 1831, 1832, 1833, 1836, 1847, on
-  "Bastard-Pflanzen"; Gebhardt, "Uber die Bastardirung von _Rana
-  esculenta_ mit _R. arvalis_," _Inaug. Dissert._ (Breslau, 1894); G.
-  Mendel, "Versuche uber Pflanzen-Hybriden," _Verh. Natur. Vereins in
-  Brunn_ (1865), pp. 1-52; Morgan, "Experimental Studies," _Anat. Anz._
-  (1893), p. 141; id. p. 803; G. J. Romanes, "Physiological Selection,"
-  _Jour. Linn. Soc._ xix. 337; H. Scherren, "Notes on Hybrid Bears,"
-  _Proc. Zool. Soc. of London_ (1907), p. 431; Saunders, _Proc. Roy.
-  Soc._ (1897), lxii. 11; Standfuss, "Etudes de zoologie experimentale,"
-  _Arch. Sci. Nat._ vi. 495; Suchetet, "Les Oiseaux hybrides rencontres
-  a l'etat sauvage," _Mem. Soc. Zool._ v. 253-525, and vi. 26-45;
-  Vernon, "The Relation between the Hybrid and Parent Forms of Echinoid
-  Larvae," _Proc. Roy. Soc._ lxv. 350; Wallace, _Darwinism_ (1889);
-  Weismann, _The Germ-Plasm_ (1893).     (P. C. M)
-
-
-
-
-HYDANTOIN (glycolyl urea),
-
-                 [beta] [alpha]
-                  / NH . CH2
-  C3H4N2O2 or CO <          ,
-                  \ NH . CO
-                  [gamma]
-
-the ureide of glycollic acid, may be obtained by heating allantoin or
-alloxan with hydriodic acid, or by heating bromacetyl urea with
-alcoholic ammonia. It crystallizes in needles, melting at 216 deg. C.
-
-When hydrolysed with baryta water yields hydantoic (glycoluric)acid,
-H2N.CO.NH.CH2.CO2H, which is readily soluble in hot water, and on
-heating with hydriodic acid decomposes into ammonia, carbon dioxide and
-glycocoll, CH2.NH2.CO2.H. Many substituted hydantoins are known; the
-[alpha]-alkyl hydantoins are formed on fusion of aldehyde- or
-ketone-cyanhydrins with urea, the [beta]-alkyl hydantoins from the
-fusion of mono-alkyl glycocolls with urea, and the [gamma]-alkyl
-hydantoins from the action of alkalis and alkyl iodides on the
-[alpha]-compounds. [gamma]-Methyl hydantoin has been obtained as a
-splitting product of caffeine (E. Fischer, _Ann._, 1882, 215, p. 253).
-
-
-
-
-HYDE, the name of an English family distinguished in the 17th century.
-Robert Hyde of Norbury, Cheshire, had several sons, of whom the third
-was Lawrence Hyde of Gussage St Michael, Dorsetshire. Lawrence's son
-Henry was father of Edward Hyde, earl of Clarendon (q.v.), whose second
-son by his second wife was Lawrence, earl of Rochester (q.v.); another
-son was Sir Lawrence Hyde, attorney-general to Anne of Denmark, James
-I.'s consort; and a third son was Sir Nicholas Hyde (d. 1631),
-chief-justice of England. Sir Nicholas entered parliament in 1601 and
-soon became prominent as an opponent of the court, though he does not
-appear to have distinguished himself in the law. Before long, however,
-he deserted the popular party, and in 1626 he was employed by the duke
-of Buckingham in his defence to impeachment by the Commons; and in the
-following year he was appointed chief-justice of the king's bench, in
-which office it fell to him to give judgment in the celebrated case of
-Sir Thomas Darnell and others who had been committed to prison on
-warrants signed by members of the privy council, which contained no
-statement of the nature of the charge against the prisoners. In answer
-to the writ of _habeas corpus_ the attorney-general relied on the
-prerogative of the crown, supported by a precedent of Queen Elizabeth's
-reign. Hyde, three other judges concurring, decided in favour of the
-crown, but without going so far as to declare the right of the crown to
-refuse indefinitely to show cause against the discharge of the
-prisoners. In 1629 Hyde was one of the judges who condemned Eliot,
-Holles and Valentine for conspiracy in parliament to resist the king's
-orders; refusing to admit their plea that they could not be called upon
-to answer out of parliament for acts done in parliament. Sir Nicholas
-Hyde died in August 1631.
-
-Sir Lawrence Hyde, attorney-general to Anne of Denmark, had eleven sons,
-four of whom were men of some mark. Henry was an ardent royalist who
-accompanied Charles II. to the continent, and returning to England was
-beheaded in 1650; Alexander (1598-1667) became bishop of Salisbury in
-1665; Edward (1607-1659) was a royalist divine who was nominated dean of
-Windsor in 1658, but died before taking up the appointment, and who was
-the author of many controversial works in Anglican theology; and Robert
-(1595-1665) became recorder of Salisbury and represented that borough in
-the Long Parliament, in which he professed royalist principles, voting
-against the attainder of Strafford. Having been imprisoned and deprived
-of his recordership by the parliament in 1645/6, Robert Hyde gave refuge
-to Charles II. on his flight from Worcester in 1651, and on the
-Restoration he was knighted and made a judge of the common pleas. He
-died in 1665. Henry Hyde (1672-1753), only son of Lawrence, earl of
-Rochester, became 4th earl of Clarendon and 2nd earl of Rochester, both
-of which titles became extinct at his death. He was in no way
-distinguished, but his wife Jane Hyde, countess of Clarendon and
-Rochester (d. 1725), was a famous beauty celebrated by the homage of
-Swift, Prior and Pope, and by the groundless scandal of Lady Mary
-Wortley Montagu. Two of her daughters, Jane, countess of Essex, and
-Catherine, duchess of Queensberry, were also famous beauties of the
-reign of Queen Anne. Her son, Henry Hyde (1710-1753), known as Viscount
-Cornbury, was a Tory and Jacobite member of parliament, and an intimate
-friend of Bolingbroke, who addressed to him his _Letters on the Study
-and Use of History_, and _On the Spirit of Patriotism_. In 1750 Lord
-Cornbury was created Baron Hyde of Hindon, but, as he predeceased his
-father, this title reverted to the latter and became extinct at his
-death. Lord Cornbury was celebrated as a wit and a conversationalist.
-By his will he bequeathed the papers of his great-grandfather, Lord
-Clarendon, the historian, to the Bodleian Library at Oxford.
-
-  See Lord Clarendon, _The Life of Edward, Earl of Clarendon_ (3 vols.,
-  Oxford, 1827); Edward Foss, _The Judges of England_ (London,
-  1848-1864); Anthony a Wood, _Athenae oxonienses_ (London, 1813-1820);
-  Samuel Pepys, _Diary and Correspondence_, edited by Lord Braybrooke (4
-  vols., London, 1854).
-
-
-
-
-HYDE, THOMAS (1636-1703), English Orientalist, was born at Billingsley,
-near Bridgnorth, in Shropshire, on the 29th of June 1636. He inherited
-his taste for linguistic studies, and received his first lessons in some
-of the Eastern tongues, from his father, who was rector of the parish.
-In his sixteenth year Hyde entered King's College, Cambridge, where,
-under Wheelock, professor of Arabic, he made rapid progress in Oriental
-languages, so that, after only one year of residence, he was invited to
-London to assist Brian Walton in his edition of the _Polyglott Bible_.
-Besides correcting the Arabic, Persic and Syriac texts for that work,
-Hyde transcribed into Persic characters the Persian translation of the
-Pentateuch, which had been printed in Hebrew letters at Constantinople
-in 1546. To this work, which Archbishop Ussher had thought well-nigh
-impossible even for a native of Persia, Hyde appended the Latin version
-which accompanies it in the _Polyglott_. In 1658 he was chosen Hebrew
-reader at Queen's College, Oxford, and in 1659, in consideration of his
-erudition in Oriental tongues, he was admitted to the degree of M.A. In
-the same year he was appointed under-keeper of the Bodleian Library, and
-in 1665 librarian-in-chief. Next year he was collated to a prebend at
-Salisbury, and in 1673 to the archdeaconry of Gloucester, receiving the
-degree of D.D. shortly afterwards. In 1691 the death of Edward Pococke
-opened up to Hyde the Laudian professorship of Arabic; and in 1697, on
-the deprivation of Roger Altham, he succeeded to the regius chair of
-Hebrew and a canonry of Christ Church. Under Charles II., James II. and
-William III. Hyde discharged the duties of Eastern interpreter to the
-court. Worn out by his unremitting labours, he resigned his
-librarianship in 1701, and died at Oxford on the 18th of February 1703.
-Hyde, who was one of the first to direct attention to the vast treasures
-of Oriental antiquity, was an excellent classical scholar, and there was
-hardly an Eastern tongue accessible to foreigners with which he was not
-familiar. He had even acquired Chinese, while his writings are the best
-testimony to his mastery of Turkish, Arabic, Syriac, Persian, Hebrew and
-Malay.
-
-In his chief work, _Historia religionis veterum Persarum_ (1700), he
-made the first attempt to correct from Oriental sources the errors of
-the Greek and Roman historians who had described the religion of the
-ancient Persians. His other writings and translations comprise _Tabulae
-longitudinum et latitudinum stellarum fixarum ex observatione principis
-Ulugh Beighi_ (1665), to which his notes have given additional value;
-_Quatuor evangelia et acta apostolorum lingua Malaica, caracteribus
-Europaeis_ (1677); _Epistola de mensuris et ponderibus serum sive
-sinensium_ (1688), appended to Bernard's _De mensuris et ponderibus
-antiquis; Abraham Peritsol itinera mundi_ (1691); and _De ludis
-orientalibus libri II._ (1694).
-
-  With the exception of the _Historia religionis_, which was republished
-  by Hunt and Costard in 1760, the writings of Hyde, including some
-  unpublished MSS., were collected and printed by Dr Gregory Sharpe in
-  1767 under the title _Syntagma dissertationum quas olim ... Thomas
-  Hyde separatim edidit_. There is a life of the author prefixed. Hyde
-  also published a catalogue of the Bodleian Library in 1674.
-
-
-
-
-HYDE, a market town and municipal borough in the Hyde parliamentary
-division of Cheshire, England, 7(1/2) m. E. of Manchester, by the Great
-Central railway. Pop. (1901) 32,766. It lies in the densely populated
-district in the north-east of the county, on the river Tame, which here
-forms the boundary of Cheshire with Lancashire. To the east the outlying
-hills of the Peak district of Derbyshire rise abruptly. The town has
-cotton weaving factories, spinning mills, print-works, iron foundries
-and machine works; also manufactures of hats and margarine. There are
-extensive coal mines in the vicinity. Hyde is wholly of modern growth,
-though it contains a few ancient houses, such as Newton Hall, in the
-part of the town so called. The old family of Hyde held possession of
-the manor as early as the reign of John. The borough, incorporated in
-1881, is under a mayor, 6 aldermen and 18 councillors. Area, 3081 acres.
-
-
-
-
-HYDE DE NEUVILLE, JEAN GUILLAUME, BARON (1776-1857), French politician,
-was born at La Charite-sur-Loire (Nievre) on the 24th of January 1776,
-the son of Guillaume Hyde, who belonged to an English family which had
-emigrated with the Stuarts after the rebellion of 1745. He was only
-seventeen when he successfully defended a man denounced by Fouche before
-the revolutionary tribunal of Nevers. From 1793 onwards he was an active
-agent of the exiled princes; he took part in the Royalist rising in
-Berry in 1796, and after the _coup d'etat_ of the 18th Brumaire
-(November 9, 1799) tried to persuade Bonaparte to recall the Bourbons.
-An accusation of complicity in the infernal machine conspiracy of
-1800-1801 was speedily retracted, but Hyde de Neuville retired to the
-United States, only to return after the Restoration. He was sent by
-Louis XVIII. to London to endeavour to persuade the British government
-to transfer Napoleon to a remoter and safer place of exile than the isle
-of Elba, but the negotiations were cut short by the emperor's return to
-France in March 1815. In January 1816 de Neuville became French
-ambassador at Washington, where he negotiated a commercial treaty. On
-his return in 1821 he declined the Constantinople embassy, and in
-November 1822 was elected deputy for Cosne. Shortly afterwards he was
-appointed French ambassador at Lisbon, where his efforts to oust British
-influence culminated, in connexion with the _coup d'etat_ of Dom Miguel
-(April 30, 1824), in his suggestion to the Portuguese minister to invite
-the armed intervention of Great Britain. It was assumed that this would
-be refused, in view of the loudly proclaimed British principle of
-non-intervention, and that France would then be in a position to
-undertake a duty that Great Britain had declined. The scheme broke down,
-however, owing to the attitude of the reactionary party in the
-government of Paris, which disapproved of the Portuguese constitution.
-This destroyed his influence at Lisbon, and he returned to Paris to take
-his seat in the Chamber of Deputies. In spite of his pronounced
-Royalism, he now showed Liberal tendencies, opposed the policy of
-Villele's cabinet, and in 1828 became a member of the moderate
-administration of Martignac as minister of marine. In this capacity he
-showed active sympathy with the cause of Greek independence. During the
-Polignac ministry (1829-1830) he was again in opposition, being a firm
-upholder of the charter; but after the revolution of July 1830 he
-entered an all but solitary protest against the exclusion of the
-legitimate line of the Bourbons from the throne, and resigned his seat.
-He died in Paris on the 28th of May 1857.
-
-  His _Memoires et souvenirs_ (3 vols., 1888), compiled from his notes
-  by his nieces, the vicomtesse de Bardonnet and the baronne Laurenceau,
-  are of great interest for the Revolution and the Restoration.
-
-
-
-
-HYDE PARK, a small township of Norfolk county, Massachusetts, U.S.A.,
-about 8 m. S.W. of the business centre of Boston. Pop. (1890) 10,193;
-(1900) 13,244, of whom 3805 were foreign-born; (1910 census) 15,507. Its
-area is about 4(1/2) sq. m. It is traversed by the New York, New Haven &
-Hartford railway, which has large repair shops here, and by the Neponset
-river and smaller streams. The township contains the villages of Hyde
-Park, Readville (in which there is the famous "Weil" trotting-track),
-Fairmount, Hazelwood and Clarendon Hills. Until about 1856 Hyde Park was
-a farmstead. The value of the total factory product increased from
-$4,383,959 in 1900 to $6,739,307 in 1905, or 53.7%. In 1868 Hyde Park
-was incorporated as a township, being formed of territory taken from
-Dorchester, Dedham and Milton.
-
-
-
-
-HYDERABAD, or HAIDARABAD, a city and district of British India, in the
-Sind province of Bombay. The city stands on a hill about 3 m. from the
-left bank of the Indus, and had a population in 1901 of 69,378. Upon the
-site of the present fort is supposed to have stood the ancient town of
-Nerankot, which in the 8th century submitted to Mahommed bin Kasim. In
-1768 the present city was founded by Ghulam Shah Kalhora; and it
-remained the capital of Sind until 1843, when, after the battle of
-Meeanee, it was surrendered to the British, and the capital transferred
-to Karachi. The city is built on the most northerly hills of the Ganga
-range, a site of great natural strength. In the fort, which covers an
-area of 36 acres, is the arsenal of the province, transferred thither
-from Karachi in 1861, and the palaces of the ex-mirs of Sind. An
-excellent water supply is derived from the Indus. In addition to
-manufactures of silk, gold and silver embroidery, lacquered ware and
-pottery, there are three factories for ginning cotton. There are three
-high schools, training colleges for masters and mistresses, a medical
-school, an agricultural school for village officials, and a technical
-school. The city suffered from plague in 1896-1897.
-
-The DISTRICT OF HYDERABAD has an area of 8291 sq. m., with a population
-in 1901 of 989,030, showing an increase of 15% in the decade. It
-consists of a vast alluvial plain, on the left bank of the Indus, 216 m.
-long and 48 broad. Fertile along the course of the river, it degenerates
-towards the east into sandy wastes, sparsely populated, and defying
-cultivation. The monotony is relieved by the fringe of forest which
-marks the course of the river, and by the avenues of trees that line the
-irrigation channels branching eastward from this stream. The south of
-the district has a special feature in its large natural water-courses
-(called _dhoras_) and basin-like shallows (_chhaus_), which retain the
-rains for a long time. A limestone range called the Ganga and the
-pleasant frequency of garden lands break the monotonous landscape. The
-principal crops are millets, rice, oil-seeds, cotton and wheat, which
-are dependent on irrigation, mostly from government canals. There is a
-special manufacture at Hala of glazed pottery and striped cotton cloth.
-Three railways traverse the district: (1) one of the main lines of the
-North-Western system, following the Indus valley and crossing the river
-near Hyderabad; (2) a broad-gauge branch running south to Badin, which
-will ultimately be extended to Bombay; and (3) a metre-gauge line from
-Hyderabad city into Rajputana.
-
-
-
-
-HYDERABAD, HAIDARABAD, also known as the Nizam's Dominions, the
-principal native state of India in extent, population and political
-importance; area, 82,698 sq. m.; pop. (1901) 11,141,142, showing a
-decrease of 3.4% in the decade; estimated revenue 4(1/2) crores of
-Hyderabad rupees (L2,500,000). The state occupies a large portion of the
-eastern plateau of the Deccan. It is bounded on the north and north-east
-by Berar, on the south and south-east by Madras, and on the west by
-Bombay. The country presents much variety of surface and feature; but it
-may be broadly divided into two tracts, distinguished from one another
-geologically and ethnically, which are locally known from the languages
-spoken as Telingana and Marathwara. In some parts it is mountainous,
-wooded and picturesque, in others flat and undulating. The open country
-includes lands of all descriptions, including many rich and fertile
-plains, much good land not yet brought under cultivation, and numerous
-tracts too sterile ever to be cultivated. In the north-west the
-geological formations are volcanic, consisting principally of trap, but
-in some parts of basalt; in the middle, southern and south-western parts
-the country is overlaid with gneissic formations. The territory is well
-watered, rivers being numerous, and tanks or artificial pieces of water
-abundant, especially in Telingana. The principal rivers are the
-Godavari, with its tributaries the Dudna, Manjira and Pranhita; the
-Wardha, with its tributary the Penganga; and the Kistna, with its
-tributary the Tungabhadra. The climate may be considered in general
-good; and as there are no arid bare deserts, hot winds are little felt.
-
-More than half the revenue of the state is derived from the land, and
-the development of the country by irrigation and railways has caused
-considerable expansion in this revenue, though the rate of increase in
-the decade 1891-1901 was retarded by a succession of unfavourable
-seasons. The soil is generally fertile, though in some parts it consists
-of _chilka_, a red and gritty mould little fitted for purposes of
-agriculture. The principal crops are millets of various kinds, rice,
-wheat, oil-seeds, cotton, tobacco, sugar-cane, and fruits and
-garden produce in great variety. Silk, known as _tussur_, the produce of
-a wild species of worm, is utilized on a large scale. Lac, suitable for
-use as a resin or dye, gums and oils are found in great quantities.
-Hides, raw and tanned, are articles of some importance in commerce. The
-principal exports are cotton, oil-seeds, country-clothes and hides; the
-imports are salt, grain, timber, European piece-goods and hardware. The
-mineral wealth of the state consists of coal, copper, iron, diamonds and
-gold; but the development of these resources has not hitherto been very
-successful. The only coal mine now worked is the large one at Singareni,
-with an annual out-turn of nearly half a million tons. This coal has
-enabled the nizam's guaranteed state railway to be worked so cheaply
-that it now returns a handsome profit to the state. It also gives
-encouragement to much-needed schemes of railway extension, and to the
-erection of cotton presses and of spinning and weaving mills. The
-Hyderabad-Godavari railway (opened in 1901) traverses a rich cotton
-country, and cotton presses have been erected along the line. The
-currency of the state is based on the _hali sikka_, which contains
-approximately the same weight of silver as the British rupee, but its
-exchange value fell heavily after 1893, when free coinage ceased in the
-mint. In 1904, however, a new coin (the Mahbubia rupee) was minted; the
-supply was regulated, and the rate of exchange became about 115 = 100
-British rupees. The state suffered from famine during 1900, the total
-number of persons in receipt of relief rising to nearly 500,000 in June
-of that year. The nizam met the demands for relief with great
-liberality.
-
-The nizam of Hyderabad is the principal Mahommedan ruler in India. The
-family was founded by Asaf Jah, a distinguished Turkoman soldier of the
-emperor Aurangzeb, who in 1713 was appointed subahdar of the Deccan,
-with the title of nizam-ul-mulk (regulator of the state), but eventually
-threw off the control of the Delhi court. Azaf Jah's death in 1748 was
-followed by an internecine struggle for the throne among his
-descendants, in which the British and the French took part. At one time
-the French nominee, Salabat Jang, established himself with the help of
-Bussy. But finally, in 1761, when the British had secured their
-predominance throughout southern India, Nizam Ali took his place and
-ruled till 1803. It was he who confirmed the grant of the Northern
-Circars in 1766, and joined in the two wars against Tippoo Sultan in
-1792 and 1799. The additions of territory which he acquired by these
-wars was afterwards (1800) ceded to the British, as payment for the
-subsidiary force which he had undertaken to maintain. By a later treaty
-in 1853, the districts known as Berar were "assigned" to defray the cost
-of the Hyderabad contingent. In 1857 when the Mutiny broke out, the
-attitude of Hyderabad as the premier native state and the cynosure of
-the Mahommedans in India became a matter of extreme importance; but
-Afzul-ud-Dowla, the father of the present ruler, and his famous
-minister, Sir Salar Jang, remained loyal to the British. An attack on
-the residency was repulsed, and the Hyderabad contingent displayed their
-loyalty in the field against the rebels. In 1902 by a treaty made by
-Lord Curzon, Berar was leased in perpetuity to the British government,
-and the Hyderabad contingent was merged in the Indian army. The nizam
-Mir Mahbub Ali Khan Bahadur, Asaf Jah, a direct descendant of the famous
-nizam-ul-mulk, was born on the 18th of August 1866. On the death of his
-father in 1869 he succeeded to the throne as a minor, and was invested
-with full powers in 1884. He is notable as the originator of the
-Imperial Service Troops, which now form the contribution of the native
-chiefs to the defence of India. On the occasion of the Panjdeh incident
-in 1885 he made an offer of money and men, and subsequently on the
-occasion of Queen Victoria's Jubilee in 1887 he offered 20 lakhs
-(L130,000) annually for three years for the purpose of frontier defence.
-It was finally decided that the native chiefs should maintain small but
-well-equipped bodies of infantry and cavalry for imperial defence. For
-many years past the Hyderabad finances were in a very unhealthy
-condition, the expenditure consistently outran the revenue, and the
-nobles, who held their tenure under an obsolete feudal system, vied
-with each other in ostentatious extravagance. But in 1902, on the
-revision of the Berar agreement, the nizam received 25 lakhs (L167,000)
-a year for the rent of Berar, thus substituting a fixed for a
-fluctuating source of income, and a British financial adviser was
-appointed for the purpose of reorganizing the resources of the state.
-
-  See S. H. Bilgrami and C. Willmott, _Historical and Descriptive Sketch
-  of the Nizam's Dominions_ (Bombay, 1883-1884).
-
-
-
-
-HYDERABAD or HAIDARABAD, capital of the above state, is situated on the
-right bank of the river Musi, a tributary of the Kistna, with Golconda
-to the west, and the residency and its bazaars and the British
-cantonment of Secunderabad to the north-east. It is the fourth largest
-city in India; pop. (1901) 448,466, including suburbs and cantonment.
-The city itself is in shape a parallelogram, with an area of more than 2
-sq. m. It was founded in 1589 by Mahommed Kuli, fifth of the Kutb Shahi
-kings, of whose period several important buildings remain as monuments.
-The principal of these is the Char Minar or Four Minarets (1591). The
-minarets rise from arches facing the cardinal points, and stand in the
-centre of the city, with four roads radiating from their base. The Ashur
-Khana (1594), a ceremonial building, the hospital, the Gosha Mahal
-palace and the Mecca mosque, a sombre building designed after a mosque
-at Mecca, surrounding a paved quadrangle 360 ft. square, were the other
-principal buildings of the Kutb Shahi period, though the mosque was only
-completed in the time of Aurangzeb. The city proper is surrounded by a
-stone wall with thirteen gates, completed in the time of the first
-nizam, who made Hyderabad his capital. The suburbs, of which the most
-important is Chadarghat, extend over an additional area of 9 sq. m.
-There are several fine palaces built by various nizams, and the British
-residency is an imposing building in a large park on the left bank of
-the Musi, N.E. of the city. The bazaars surrounding it, and under its
-jurisdiction, are extremely picturesque and are thronged with natives
-from all parts of India. Four bridges crossed the Musi, the most notable
-of which was the Purana Pul, of 23 arches, built in 1593. On the 27th
-and 28th of September 1908, however, the Musi, swollen by torrential
-rainfall (during which 15 in. fell in 36 hours), rose in flood to a
-height of 12 ft. above the bridges and swept them away. The damage done
-was widespread; several important buildings were involved, including the
-palace of Salar Jang and the Victoria zenana hospital, while the
-beautiful grounds of the residency were destroyed. A large and densely
-populated part of the city was wrecked, and thousands of lives were
-lost. The principal educational establishments are the Nizam college
-(first grade), engineering, law, medical, normal, industrial and
-Sanskrit schools, and a number of schools for Europeans and Eurasians.
-Hyderabad is an important centre of general trade, and there is a cotton
-mill in its vicinity. The city is supplied with water from two notable
-works, the Husain Sagar and the Mir Alam, both large lakes retained by
-great dams. Secunderabad, the British military cantonment, is situated
-5(1/2) m. N. of the residency; it includes Bolaram, the former
-headquarters of the Hyderabad contingent.
-
-
-
-
-HYDER ALI, or Haidar 'Ali (c. 1722-1782), Indian ruler and commander.
-This Mahommedan soldier-adventurer, who, followed by his son Tippoo,
-became the most formidable Asiatic rival the British ever encountered in
-India, was the great-grandson of a _fakir_ or wandering ascetic of
-Islam, who had found his way from the Punjab to Gulburga in the Deccan,
-and the second son of a _naik_ or chief constable at Budikota, near
-Kolar in Mysore. He was born in 1722, or according to other authorities
-1717. An elder brother, who like himself was early turned out into the
-world to seek his own fortune, rose to command a brigade in the Mysore
-army, while Hyder, who never learned to read or write, passed the first
-years of his life aimlessly in sport and sensuality, sometimes, however,
-acting as the agent of his brother, and meanwhile acquiring a useful
-familiarity with the tactics of the French when at the height of their
-reputation under Dupleix. He is said to have induced his brother to
-employ a Parsee to purchase artillery and small arms from the Bombay
-government, and to enrol some thirty sailors of different European
-nations as gunners, and is thus credited with having been "the first
-Indian who formed a corps of sepoys armed with firelocks and bayonets,
-and who had a train of artillery served by Europeans." At the siege of
-Devanhalli (1749) Hyder's services attracted the attention of Nanjiraj,
-the minister of the raja of Mysore, and he at once received an
-independent command; within the next twelve years his energy and ability
-had made him completely master of minister and raja alike, and in
-everything but in name he was ruler of the kingdom. In 1763 the conquest
-of Kanara gave him possession of the treasures of Bednor, which he
-resolved to make the most splendid capital in India, under his own name,
-thenceforth changed from Hyder Naik into Hyder Ali Khan Bahadur; and in
-1765 he retrieved previous defeat at the hands of the Mahrattas by the
-destruction of the Nairs or military caste of the Malabar coast, and the
-conquest of Calicut. Hyder Ali now began to occupy the serious attention
-of the Madras government, which in 1766 entered into an agreement with
-the nizam to furnish him with troops to be used against the common foe.
-But hardly had this alliance been formed when a secret arrangement was
-come to between the two Indian powers, the result of which was that
-Colonel Smith's small force was met with a united army of 80,000 men and
-100 guns. British dash and sepoy fidelity, however, prevailed, first in
-the battle of Chengam (September 3rd, 1767), and again still more
-remarkably in that of Tiruvannamalai (Trinomalai). On the loss of his
-recently made fleet and forts on the western coast, Hyder Ali now
-offered overtures for peace; on the rejection of these, bringing all his
-resources and strategy into play, he forced Colonel Smith to raise the
-siege of Bangalore, and brought his army within 5 m. of Madras. The
-result was the treaty of April 1769, providing for the mutual
-restitution of all conquests, and for mutual aid and alliance in
-defensive war; it was followed by a commercial treaty in 1770 with the
-authorities of Bombay. Under these arrangements Hyder Ali, when defeated
-by the Mahrattas in 1772, claimed British assistance, but in vain; this
-breach of faith stung him to fury, and thenceforward he and his son did
-not cease to thirst for vengeance. His time came when in 1778 the
-British, on the declaration of war with France, resolved to drive the
-French out of India. The capture of Mahe on the coast of Malabar in
-1779, followed by the annexation of lands belonging to a dependent of
-his own, gave him the needed pretext. Again master of all that the
-Mahrattas had taken from him, and with empire extended to the Kistna, he
-descended through the passes of the Ghats amid burning villages,
-reaching Conjeeveram, only 45 m. from Madras, unopposed. Not till the
-smoke was seen from St Thomas's Mount, where Sir Hector Munro commanded
-some 5200 troops, was any movement made; then, however, the British
-general sought to effect a junction with a smaller body under Colonel
-Baillie recalled from Guntur. The incapacity of these officers,
-notwithstanding the splendid courage of their men, resulted in the total
-destruction of Baillie's force of 2800 (September the 10th, 1780).
-Warren Hastings sent from Bengal Sir Eyre Coote, who, though repulsed at
-Chidambaram, defeated Hyder thrice successively in the battles of Porto
-Novo, Pollilur and Sholingarh, while Tippoo was forced to raise the
-siege of Wandiwash, and Vellore was provisioned. On the arrival of Lord
-Macartney as governor of Madras, the British fleet captured Negapatam,
-and forced Hyder Ali to confess that he could never ruin a power which
-had command of the sea. He had sent his son Tippoo to the west coast, to
-seek the assistance of the French fleet, when his death took place
-suddenly at Chittur in December 1782.
-
-  See L. B. Bowring, _Haidar Ali and Tipu Sultan_, "Rulers of India"
-  series (1893). For the personal character and administration of Hyder
-  Ali see the _History of Hyder Naik_, written by Mir Hussein Ali Khan
-  Kirmani (translated from the Persian by Colonel Miles, and published
-  by the Oriental Translation Fund), and the curious work written by M.
-  Le Maitre de La Tour, commandant of his artillery (_Histoire
-  d'Hayder-Ali Khan_, Paris, 1783). For the whole life and times see
-  Wilks, _Historical Sketches of the South of India_ (1810-1817);
-  Aitchison's Treaties, vol. v. (2nd ed., 1876); and Pearson, _Memoirs
-  of Schwartz_ (1834).
-
-
-
-
-HYDRA (or SIDRA, NIDRA, IDERO, &c.; anc. _Hydrea_), an island of Greece,
-lying about 4 m. off the S.E. coast of Argolis in the Peloponnesus, and
-forming along with the neighbouring island of Dokos (Dhoko) the Bay of
-Hydra. Pop. about 6200. The greatest length from south-west to
-north-east is about 11 m., and the area is about 21 sq. mi.; but it is
-little better than a rocky and treeless ridge with hardly a patch or two
-of arable soil. Hence the epigram of Antonios Kriezes to the queen of
-Greece: "The island produces prickly pears in abundance, splendid sea
-captains and excellent prime ministers." The highest point, Mount Ere,
-so called (according to Miaoules) from the Albanian word for wind, is
-1958 ft. high. The next in importance is known as the Prophet Elias,
-from the large convent of that name on its summit. It was there that the
-patriot Theodorus Kolokotrones was imprisoned, and a large pine tree is
-still called after him. The fact that in former times the island was
-richly clad with woods is indicated by the name still employed by the
-Turks, _Tchamliza_, the place of pines; but it is only in some favoured
-spots that a few trees are now to be found. Tradition also has it that
-it was once a well-watered island (hence the designation Hydrea), but
-the inhabitants are now wholly dependent on the rain supply, and they
-have sometimes had to bring water from the mainland. This lack of
-fountains is probably to be ascribed in part to the effect of
-earthquakes, which are not infrequent; that of 1769 continued for six
-whole days. Hydra, the chief town, is built near the middle of the
-northern coast, on a very irregular site, consisting of three hills and
-the intervening ravines. From the sea its white and handsome houses
-present a picturesque appearance, and its streets though narrow are
-clean and attractive. Besides the principal harbour, round which the
-town is built, there are three other ports on the north coast--Mandraki,
-Molo, Panagia, but none of them is sufficiently sheltered. Almost all
-the population of the island is collected in the chief town, which is
-the seat of a bishop, and has a local court, numerous churches and a
-high school. Cotton and silk weaving, tanning and shipbuilding are
-carried on, and there is a fairly active trade.
-
-Hydra was of no importance in ancient times. The only fact in its
-history is that the people of Hermione (a city on the neighbouring
-mainland now known by the common name of _Kastri_) surrendered it to
-Samian refugees, and that from these the people of Troezen received it
-in trust. It appears to be completely ignored by the Byzantine
-chroniclers. In 1580 it was chosen as a refuge by a body of Albanians
-from Kokkinyas in Troezenia; and other emigrants followed in 1590, 1628,
-1635, 1640, &c. At the close of the 17th century the Hydriotes took part
-in the reviving commerce of the Peloponnesus; and in course of time they
-extended their range. About 1716 they began to build _sakturia_ (of from
-10 to 15 tons burden), and to visit the islands of the Aegean; not long
-after they introduced the _latinadika_ (40-50 tons), and sailed as far
-as Alexandria, Constantinople, Trieste and Venice; and by and by they
-ventured to France and even America. From the grain trade of south
-Russia more especially they derived great wealth. In 1813 there were
-about 22,000 people in the island, and of these 10,000 were seafarers.
-At the time of the outbreak of the war of Greek independence the total
-population was 28,190, of whom 16,460 were natives and the rest
-foreigners. One of their chief families, the Konduriotti, was worth
-L2,000,000. Into the struggle the Hydriotes flung themselves with rare
-enthusiasm and devotion, and the final deliverance of Greece was mainly
-due to the service rendered by their fleets.
-
-  See Pouqueville, _Voy. de la Grece_, vol. vi.; Antonios Miaoules,
-  [Greek: Hypomnema peri tes nesou Hydras] (Munich, 1834); Id. [Greek:
-  Sunoptike historia ton naumachion dia ton ploion ton trion neson,
-  Hydras, Petson kai Psaron] (Nauplia, 1833); Id. [Greek: Historia tes
-  nesou Hydras] (Athens, 1874); G. D. Kriezes, [Greek: Historia tes
-  nesou Hydras] (Patras, 1860).
-
-
-
-
-HYDRA (watersnake), in Greek legend, the offspring of Typhon and
-Echidna, a gigantic monster with nine heads (the number is variously
-given), the centre one being immortal. Its haunt was a hill beneath a
-plane tree near the river Amymone, in the marshes of Lerna by Argos. The
-destruction of this Lernaean hydra was one of the twelve "labours"
-of Heracles, which he accomplished with the assistance of Iolaus.
-Finding that as soon as one head was cut off two grew up in its place,
-they burnt out the roots with firebrands, and at last severed the
-immortal head from the body, and buried it under a mighty block of rock.
-The arrows dipped by Heracles in the poisonous blood or gall of the
-monster ever afterwards inflicted fatal wounds. The generally accepted
-interpretation of the legend is that "the hydra denotes the damp, swampy
-ground of Lerna with its numerous springs ([Greek: kephalai], heads);
-its poison the miasmic vapours rising from the stagnant water; its death
-at the hands of Heracles the introduction of the culture and consequent
-purification of the soil" (Preller). A euhemeristic explanation is given
-by Palaephatus (39). An ancient king named Lernus occupied a small
-citadel named Hydra, which was defended by 50 bowmen. Heracles besieged
-the citadel and hurled firebrands at the garrison. As often as one of
-the defenders fell, two others at once stepped into his place. The
-citadel was finally taken with the assistance of the army of Iolaus and
-the garrison slain.
-
-  See Hesiod, _Theog._, 313; Euripides, _Hercules furens_, 419;
-  Pausanias ii. 37; Apollodorus ii. 5, 2; Diod. Sic. iv. 11; Roscher's
-  _Lexikon der Mythologie_. In the article GREEK ART, fig. 20 represents
-  the slaying of the Lernaean hydra by Heracles.
-
-
-
-
-HYDRA, in astronomy, a constellation of the southern hemisphere,
-mentioned by Eudoxus (4th century B.C.) and Aratus (3rd century B.C.),
-and catalogued by Ptolemy (27 stars), Tycho Brahe (19) and Hevelius
-(31). Interesting objects are: the nebula _H. IV. 27 Hydrae_, a
-planetary nebula, gaseous and whose light is about equal to an 8th
-magnitude star; [epsilon] _Hydrae_, a beautiful triple star, composed of
-two yellow stars of the 4th and 6th magnitudes, and a blue star of the
-7th magnitude; _R. Hydrae_, a long period (425 days) variable, the range
-in magnitude being from 4 to 9.7; and _U. Hydrae_, an irregularly
-variable, the range in magnitude being 4.5 to 6.
-
-
-
-
-HYDRACRYLIC ACID (ethylene lactic acid), CH2OH.CH2.CO2H. an organic
-oxyacid prepared by acting with silver oxide and water on
-[beta]-iodopropionic acid, or from ethylene by the addition of
-hypochlorous acid, the addition product being then treated with
-potassium cyanide and hydrolysed by an acid. It may also be prepared by
-oxidizing the trimethylene glycol obtained by the action of hydrobromic
-acid on allylbromide. It is a syrupy liquid, which on distillation is
-resolved into water and the unsaturated acrylic acid, CH2:CH.CO2H.
-Chromic and nitric acids oxidize it to oxalic acid and carbon dioxide.
-Hydracrylic aldehyde, CH2OH.CH2.CHO, was obtained in 1904 by J. U. Nef
-(_Ann._ 335, p. 219) as a colourless oil by heating acrolein with water.
-Dilute alkalis convert it into crotonaldehyde, CH3.CH:CH.CHO.
-
-
-
-
-HYDRANGEA, a popular flower, the plant to which the name is most
-commonly applied being _Hydrangea Hortensia_, a low deciduous shrub,
-producing rather large oval strongly-veined leaves in opposite pairs
-along the stem. It is terminated by a massive globular corymbose head of
-flowers, which remain a long period in an ornamental condition. The
-normal colour of the flowers, the majority of which have neither stamens
-nor pistil, is pink; but by the influence of sundry agents in the soil,
-such as alum or iron, they become changed to blue. There are numerous
-varieties, one of the most noteworthy being "Thomas Hogg" with pure
-white flowers. The part of the inflorescence which appears to be the
-flower is an exaggerated expansion of the sepals, the other parts being
-generally abortive. The perfect flowers are small, rarely produced in
-the species above referred to, but well illustrated by others, in which
-they occupy the inner parts of the corymb, the larger showy neuter
-flowers being produced at the circumference.
-
-There are upwards of thirty species, found chiefly in Japan, in the
-mountains of India, and in North America, and many of them are familiar
-in gardens. _H. Hortensia_ (a species long known in cultivation In China
-and Japan) is the most useful for decoration, as the head of flowers
-lasts long in a fresh state, and by the aid of forcing can be had for a
-considerable period for the ornamentation of the greenhouse and
-conservatory. Their natural flowering season is towards the end of the
-summer, but they may be had earlier by means of forcing. _H. japonica_
-is another fine conservatory plant, with foliage and habit much
-resembling the last named, but this has flat corymbs of flowers, the
-central ones small and perfect, and the outer ones only enlarged and
-neuter. This also produces pink or blue flowers under the influence of
-different soils.
-
-The Japanese species of hydrangea are sufficiently hardy to grow in any
-tolerably favourable situation, but except in the most sheltered
-localities they seldom blossom to any degree of perfection in the open
-air, the head of blossom depending on the uninjured development of a
-well-ripened terminal bud, and this growth being frequently affected by
-late spring frosts. They are much more useful for pot-culture indoors,
-and should be reared from cuttings of shoots having the terminal bud
-plump and prominent, put in during summer, these developing a single
-head of flowers the succeeding summer. Somewhat larger plants may be had
-by nipping out the terminal bud and inducing three or four shoots to
-start in its place, and these, being steadily developed and well
-ripened, should each yield its inflorescence in the following summer,
-that is, when two years old. Large plants grown in tubs and vases are
-fine subjects for large conservatories, and useful for decorating
-terrace walks and similar places during summer, being housed in winter,
-and started under glass in spring.
-
-_Hydrangea paniculata_ var. _grandiflora_ is a very handsome plant; the
-branched inflorescence under favourable circumstances is a yard or more
-in length, and consists of large spreading masses of crowded white
-neuter flowers which completely conceal the few inconspicuous fertile
-ones. The plant attains a height of 8 to 10 ft. and when in flower late
-in summer and in autumn is a very attractive object in the shrubbery.
-
-The Indian and American species, especially the latter, are quite hardy,
-and some of them are extremely effective.
-
-
-
-
-HYDRASTINE, C21H21NO6, an alkaloid found with berberine in the root of
-golden seal, _Hydrastis canadensis_, a plant indigenous to North
-America. It was discovered by Durand in 1851, and its chemistry formed
-the subject of numerous communications by E. Schmidt and M. Freund (see
-_Ann._, 1892, 271, p. 311) who, aided by P. Fritsch (_Ann._, 1895, 286,
-p. 1), established its constitution. It is related to narcotine, which
-is methoxy hydrastine. The root of golden seal is used in medicine under
-the name hydrastis rhizome, as a stomachic and nervine stimulant.
-
-
-
-
-HYDRATE, in chemistry, a compound containing the elements of water in
-combination; more specifically, a compound containing the monovalent
-hydroxyl or OH group. The first and more general definition includes
-substances containing water of crystallization; such salts are said to
-be hydrated, and when deprived of their water to be dehydrated or
-anhydrous. Compounds embraced by the second definition are more usually
-termed _hydroxides_, since at one time they were regarded as
-combinations of an oxide with water, for example, calcium oxide or lime
-when slaked with water yielded calcium hydroxide, written formerly as
-CaO.H20. The general formulae of hydroxides are: M^iOH, M^(ii)(OH)2,
-M^(iii)(OH)3, M^(iv)(OH)4, &c., corresponding to the oxides M2^iO,
-M^(ii)O, M2^(iii)O3, M^(iv)O2, &c., the Roman index denoting the valency
-of the element. There is an important difference between non-metallic
-and metallic hydroxides; the former are invariably acids (oxyacids), the
-latter are more usually basic, although acidic metallic oxides yield
-acidic hydroxides. Elements exhibiting strong basigenic or oxygenic
-characters yield the most, stable hydroxides; in other words, stable
-hydroxides are associated with elements belonging to the extreme groups
-of the periodic system, and unstable hydroxides with the central
-members. The most stable basic hydroxides are those of the alkali
-metals, viz. lithium, sodium, potassium, rubidium and caesium, and of
-the alkaline earth metals, viz. calcium, barium and strontium; the most
-stable acidic hydroxides are those of the elements placed in groups VB,
-VIB and VIIB of the periodic table.
-
-
-
-
-HYDRAULICS (Gr. [Greek: hydor], water, and [Greek: aulos], a pipe), the
-branch of engineering science which deals with the practical
-applications of the laws of hydromechanics.
-
-
-I. THE DATA OF HYDRAULICS[1]
-
-S 1. _Properties of Fluids._--The fluids to which the laws of practical
-hydraulics relate are substances the parts of which possess very great
-mobility, or which offer a very small resistance to distortion
-independently of inertia. Under the general heading Hydromechanics a
-fluid is defined to be a substance which yields continually to the
-slightest tangential stress, and hence in a fluid at rest there can be
-no tangential stress. But, further, in fluids such as water, air, steam,
-&c., to which the present division of the article relates, the
-tangential stresses that are called into action between contiguous
-portions during distortion or change of figure are always small compared
-with the weight, inertia, pressure, &c., which produce the visible
-motions it is the object of hydraulics to estimate. On the other hand,
-while a fluid passes easily from one form to another, it opposes
-considerable resistance to change of volume.
-
-It is easily deduced from the absence or smallness of the tangential
-stress that contiguous portions of fluid act on each other with a
-pressure which is exactly or very nearly normal to the interface which
-separates them. The stress must be a pressure, not a tension, or the
-parts would separate. Further, at any point in a fluid the pressure in
-all directions must be the same; or, in other words, the pressure on any
-small element of surface is independent of the orientation of the
-surface.
-
-S 2. Fluids are divided into liquids, or incompressible fluids, and
-gases, or compressible fluids. Very great changes of pressure change the
-volume of liquids only by a small amount, and if the pressure on them is
-reduced to zero they do not sensibly dilate. In gases or compressible
-fluids the volume alters sensibly for small changes of pressure, and if
-the pressure is indefinitely diminished they dilate without limit.
-
-In ordinary hydraulics, liquids are treated as absolutely
-incompressible. In dealing with gases the changes of volume which
-accompany changes of pressure must be taken into account.
-
-S 3. Viscous fluids are those in which change of form under a continued
-stress proceeds gradually and increases indefinitely. A very viscous
-fluid opposes great resistance to change of form in a short time, and
-yet may be deformed considerably by a small stress acting for a long
-period. A block of pitch is more easily splintered than indented by a
-hammer, but under the action of the mere weight of its parts acting for
-a long enough time it flattens out and flows like a liquid.
-
-[Illustration: FIG. 1.]
-
-All actual fluids are viscous. They oppose a resistance to the relative
-motion of their parts. This resistance diminishes with the velocity of
-the relative motion, and becomes zero in a fluid the parts of which are
-relatively at rest. When the relative motion of different parts of a
-fluid is small, the viscosity may be neglected without introducing
-important errors. On the other hand, where there is considerable
-relative motion, the viscosity may be expected to have an influence too
-great to be neglected.
-
-  _Measurement of Viscosity. Coefficient of Viscosity._--Suppose the
-  plane ab, fig. 1 of area [omega], to move with the velocity V
-  relatively to the surface cd and parallel to it. Let the space between
-  be filled with liquid. The layers of liquid in contact with ab and cd
-  adhere to them. The intermediate layers all offering an equal
-  resistance to shearing or distortion, the rectangle of fluid abcd will
-  take the form of the parallelogram a'b'cd. Further, the resistance to
-  the motion of ab may be expressed in the form
-
-    R = [kappa][omega]V,   (1)
-
-  where [kappa] is a coefficient the nature of which remains to be
-  determined.
-
-  If we suppose the liquid between ab and cd divided into layers as
-  shown in fig. 2, it will be clear that the stress R acts, at each
-  dividing face, forwards in the direction of motion if we consider the
-  upper layer, backwards if we consider the lower layer. Now suppose the
-  original thickness of the layer T increased to nT; if the bounding
-  plane in its new position has the velocity nV, the shearing at each
-  dividing face will be exactly the same as before, and the resistance
-  must therefore be the same. Hence,
-
-    R = [kappa]'[omega](nV).   (2)
-
-  But equations (1) and (2) may both be expressed in one equation if
-  [kappa] and [kappa]' are replaced by a constant varying inversely as
-  the thickness of the layer. Putting [kappa] = [mu]/T, [kappa]' =
-  [mu]/nT,
-
-    R = [mu][omega]V/T;
-
-  or, for an indefinitely thin layer,
-
-    R = [mu][omega]dV/dt,   (3)
-
-  an expression first proposed by L. M. H. Navier. The coefficient [mu]
-  is termed the coefficient of viscosity.
-
-  According to J. Clerk Maxwell, the value of [mu] for air at [theta]
-  deg. Fahr. in pounds, when the velocities are expressed in feet per
-  second, is
-
-    [mu] = 0.0000000256 (461 deg. + [theta]);
-
-  that is, the coefficient of viscosity is proportional to the absolute
-  temperature and independent of the pressure.
-
-  The value of [mu] for water at 77 deg. Fahr. is, according to H. von
-  Helmholtz and G. Piotrowski,
-
-    [mu] = 0.0000188,
-
-  the units being the same as before. For water [mu] decreases rapidly
-  with increase of temperature.
-
-[Illustration: FIG. 2.]
-
-S 4. When a fluid flows in a very regular manner, as for instance when
-It flows in a capillary tube, the velocities vary gradually at any
-moment from one point of the fluid to a neighbouring point. The layer
-adjacent to the sides of the tube adheres to it and is at rest. The
-layers more interior than this slide on each other. But the resistance
-developed by these regular movements is very small. If in large pipes
-and open channels there were a similar regularity of movement, the
-neighbouring filaments would acquire, especially near the sides, very
-great relative velocities. V. J. Boussinesq has shown that the central
-filament in a semicircular canal of 1 metre radius, and inclined at a
-slope of only 0.0001, would have a velocity of 187 metres per second,[2]
-the layer next the boundary remaining at rest. But before such a
-difference of velocity can arise, the motion of the fluid becomes much
-more complicated. Volumes of fluid are detached continually from the
-boundaries, and, revolving, form eddies traversing the fluid in all
-directions, and sliding with finite relative velocities against those
-surrounding them. These slidings develop resistances incomparably
-greater than the viscous resistance due to movements varying
-continuously from point to point. The movements which produce the
-phenomena commonly ascribed to fluid friction must be regarded as
-rapidly or even suddenly varying from one point to another. The internal
-resistances to the motion of the fluid do not depend merely on the
-general velocities of translation at different points of the fluid (or
-what Boussinesq terms the mean local velocities), but rather on the
-intensity at each point of the eddying agitation. The problems of
-hydraulics are therefore much more complicated than problems in which a
-regular motion of the fluid is assumed, hindered by the viscosity of the
-fluid.
-
-
-RELATION OF PRESSURE, DENSITY, AND TEMPERATURE OF LIQUIDS
-
-  S 5. _Units of Volume._--In practical calculations the cubic foot and
-  gallon are largely used, and in metric countries the litre and cubic
-  metre (= 1000 litres). The imperial gallon is now exclusively used in
-  England, but the United States have retained the old English wine
-  gallon.
-
-    1 cub. ft.    = 6.236 imp. gallons = 7.481 U.S. gallons.
-    1 imp. gallon = 0.1605 cub. ft.    = 1.200 U.S. gallons.
-    1 U.S. gallon = 0.1337 cub. ft.    = 0.8333 imp. gallon.
-    1 litre       = 0.2201 imp. gallon = 0.2641 U.S. gallon.
-
-  _Density of Water._--Water at 53 deg. F. and ordinary pressure
-  contains 62.4 lb. per cub. ft., or 10 lb. per imperial gallon at 62
-  deg. F. The litre contains one kilogram of water at 4 deg. C. or 1000
-  kilograms per cubic metre. River and spring water is not sensibly
-  denser than pure water. But average sea water weighs 64 lb. per cub.
-  ft. at 53 deg. F. The weight of water per cubic unit will be denoted
-  by G. Ice free from air weighs 57.28 lb. per cub. ft. (Leduc).
-
-  S 6. _Compressibility of Liquids._--The most accurate experiments show
-  that liquids are sensibly compressed by very great pressures, and that
-  up to a pressure of 65 atmospheres, or about 1000 lb. per sq. in., the
-  compression is proportional to the pressure. The chief results of
-  experiment are given in the following table. Let V1 be the volume of a
-  liquid in cubic feet under a pressure p1 lb. per sq. ft., and V2 its
-  volume under a pressure p2. Then the cubical compression is (V2 -
-  V1)/V1, and the ratio of the increase of pressure p2 - p1 to the
-  cubical compression is sensibly constant. That is, k = (p2 - p1)V1/(V2
-  - V1) is constant. This constant is termed the elasticity of volume.
-  With the notation of the differential calculus,
-
-             / /  dV \        dp
-    k = dp  / ( - --  ) = - V --.
-           /   \   V /        dV
-
-    _Elasticity of Volume of Liquids._
-
-    +-----------+------------+-----------+------------+------------+
-    |           |   Canton.  |  Oersted. |  Colladon  |  Regnault. |
-    |           |            |           | and Sturm. |            |
-    +-----------+------------+-----------+------------+------------+
-    | Water     | 45,990,000 | 45,900,000| 42,660,000 | 44,000,000 |
-    | Sea water | 52,900,000 |     ..    |            |     ..     |
-    | Mercury   |705,300,000 |     ..    |626,100,000 |604,500,000 |
-    | Oil       | 44,090,000 |     ..    |            |     ..     |
-    | Alcohol   | 32,060,000 |     ..    | 23,100,000 |     ..     |
-    +-----------+------------+-----------+------------+------------+
-
-  According to the experiments of Grassi, the compressibility of water
-  diminishes as the temperature increases, while that of ether, alcohol
-  and chloroform is increased.
-
-  S 7. _Change of Volume and Density of Water with Change of
-  Temperature._--Although the change of volume of water with change of
-  temperature is so small that it may generally be neglected in ordinary
-  hydraulic calculations, yet it should be noted that there is a change
-  of volume which should be allowed for in very exact calculations. The
-  values of [rho] in the following short table, which gives data enough
-  for hydraulic purposes, are taken from Professor Everett's _System of
-  Units_.
-
-    _Density of Water at Different Temperatures._
-
-    +-------------+----------+----------+
-    |             |          |    G     |
-    | Temperature.|  [rho]   |Weight of |
-    +-----+-------+Density of|1 cub. ft.|
-    |Cent.| Fahr. |  Water.  |  in lb.  |
-    +-----+-------+----------+----------+
-    |  0  |  32.0 |  .999884 |  62.417  |
-    |  1  |  33.8 |  .999941 |  62.420  |
-    |  2  |  35.6 |  .999982 |  62.423  |
-    |  3  |  37.4 | 1.000004 |  62.424  |
-    |  4  |  39.2 | 1.000013 |  62.425  |
-    |  5  |  41.0 | 1.000003 |  62.424  |
-    |  6  |  42.8 |  .999983 |  62.423  |
-    |  7  |  44.6 |  .999946 |  62.421  |
-    |  8  |  46.4 |  .999899 |  62.418  |
-    |  9  |  48.2 |  .999837 |  62.414  |
-    | 10  |  50.0 |  .999760 |  62.409  |
-    | 11  |  51.8 |  .999668 |  62.403  |
-    | 12  |  53.6 |  .999562 |  62.397  |
-    | 13  |  55.4 |  .999443 |  62.389  |
-    | 14  |  57.2 |  .999312 |  62.381  |
-    | 15  |  59.0 |  .999173 |  62.373  |
-    | 16  |  60.8 |  .999015 |  62.363  |
-    | 17  |  62.6 |  .998854 |  62.353  |
-    | 18  |  64.4 |  .998667 |  62.341  |
-    | 19  |  66.2 |  .998473 |  62.329  |
-    | 20  |  68.0 |  .998272 |  62.316  |
-    | 22  |  71.6 |  .997839 |  62.289  |
-    | 24  |  75.2 |  .997380 |  62.261  |
-    | 26  |  78.8 |  .996879 |  62.229  |
-    | 28  |  82.4 |  .996344 |  62.196  |
-    | 30  |  86   |  .995778 |  62.161  |
-    | 35  |  95   |  .99469  |  62.093  |
-    | 40  | 104   |  .99236  |  61.947  |
-    | 45  | 113   |  .99038  |  61.823  |
-    | 50  | 122   |  .98821  |  61.688  |
-    | 55  | 131   |  .98583  |  61.540  |
-    | 60  | 140   |  .98339  |  61.387  |
-    | 65  | 149   |  .98075  |  61.222  |
-    | 70  | 158   |  .97795  |  61.048  |
-    | 75  | 167   |  .97499  |  60.863  |
-    | 80  | 176   |  .97195  |  60.674  |
-    | 85  | 185   |  .96880  |  60.477  |
-    | 90  | 194   |  .96557  |  60.275  |
-    |100  | 212   |  .95866  |  59.844  |
-    +-----+-------+----------+----------+
-
-  The weight per cubic foot has been calculated from the values of
-  [rho], on the assumption that 1 cub. ft. of water at 39.2 deg. Fahr.
-  is 62.425 lb. For ordinary calculations in hydraulics, the density of
-  water (which will in future be designated by the symbol G) will be
-  taken at 62.4 lb. per cub. ft., which is its density at 53 deg. Fahr.
-  It may be noted also that ice at 32 deg. Fahr. contains 57.3 lb. per
-  cub. ft. The values of [rho] are the densities in grammes per cubic
-  centimetre.
-
-  S 8. _Pressure Column. Free Surface Level._--Suppose a small vertical
-  pipe introduced into a liquid at any point P (fig. 3). Then the liquid
-  will rise in the pipe to a level OO, such that the pressure due to the
-  column in the pipe exactly balances the pressure on its mouth. If the
-  fluid is in motion the mouth of the pipe must be supposed accurately
-  parallel to the direction of motion, or the impact of the liquid at
-  the mouth of the pipe will have an influence on the height of the
-  column. If this condition is complied with, the height h of the
-  column is a measure of the pressure at the point P. Let [omega] be the
-  area of section of the pipe, h the height of the pressure column, p
-  the intensity of pressure at P; then
-
-    p[omega] = Gh[omega] lb.,
-
-    p/G = h;
-
-  that is, h is the height due to the pressure at p. The level OO will
-  be termed the free surface level corresponding to the pressure at P.
-
-
-  RELATION OF PRESSURE, TEMPERATURE, AND DENSITY OF GASES
-
-  S 9. _Relation of Pressure, Volume, Temperature and Density in
-  Compressible Fluids._--Certain problems on the flow of air and steam
-  are so similar to those relating to the flow of water that they are
-  conveniently treated together. It is necessary, therefore, to state as
-  briefly as possible the properties of compressible fluids so far as
-  knowledge of them is requisite in the solution of these problems. Air
-  may be taken as a type of these fluids, and the numerical data here
-  given will relate to air.
-
-  [Illustration: FIG. 3.]
-
-  _Relation of Pressure and Volume at Constant Temperature._--At
-  constant temperature the product of the pressure p and volume V of a
-  given quantity of air is a constant (Boyle's law).
-
-  Let p0 be mean atmospheric pressure (2116.8 lb. per sq. ft.), V0 the
-  volume of 1 lb. of air at 32 deg. Fahr. under the pressure p0. Then
-
-    p0V0 = 26214.   (1)
-
-  If G0 is the weight per cubic foot of air in the same conditions,
-
-    G0 = 1/V0 = 2116.8/26214 = .08075.   (2)
-
-  For any other pressure p, at which the volume of 1 lb. is V and the
-  weight per cubic foot is G, the temperature being 32 deg. Fahr.,
-
-    pV = p/G = 26214; or G = p/26214.   (3)
-
-  _Change of Pressure or Volume by Change of Temperature._--Let p0, V0,
-  G0, as before be the pressure, the volume of a pound in cubic feet,
-  and the weight of a cubic foot in pounds, at 32 deg. Fahr. Let p, V, G
-  be the same quantities at a temperature t (measured strictly by the
-  air thermometer, the degrees of which differ a little from those of a
-  mercurial thermometer). Then, by experiment,
-
-    pV = p0V0(460.6 + t)/(460.6 + 32) = p0V0[tau]/[tau]0,   (4)
-
-  where [tau], [tau]0 are the temperatures t and 32 deg. reckoned from
-  the absolute zero, which is -460.6 deg. Fahr.;
-
-    p/G = p0[tau]/G0[tau]0;   (4a)
-
-    G = p[tau]0G0/p0[tau].   (5)
-
-  If p0 = 2116.8, G0 = .08075, [tau]0 = 460.6 + 32 = 492.6, then
-
-    p/G = 53.2[tau].   (5a)
-
-  Or quite generally p/G = R[tau] for all gases, if R is a constant
-  varying inversely as the density of the gas at 32 deg. F. For steam R
-  = 85.5.
-
-
-II. KINEMATICS OF FLUIDS
-
-S 10. Moving fluids as commonly observed are conveniently classified
-thus:
-
-(1) _Streams_ are moving masses of indefinite length, completely or
-incompletely bounded laterally by solid boundaries. When the solid
-boundaries are complete, the flow is said to take place in a pipe. When
-the solid boundary is incomplete and leaves the upper surface of the
-fluid free, it is termed a stream bed or channel or canal.
-
-(2) A stream bounded laterally by differently moving fluid of the same
-kind is termed a _current_.
-
-(3) A _jet_ is a stream bounded by fluid of a different kind.
-
-(4) An _eddy_, _vortex_ or _whirlpool_ is a mass of fluid the particles
-of which are moving circularly or spirally.
-
-(5) In a stream we may often regard the particles as flowing along
-definite paths in space. A chain of particles following each other along
-such a constant path may be termed a fluid filament or elementary
-stream.
-
-  S 11. _Steady and Unsteady, Uniform and Varying, Motion._--There are
-  two quite distinct ways of treating hydrodynamical questions. We may
-  either fix attention on a given mass of fluid and consider its changes
-  of position and energy under the action of the stresses to which it is
-  subjected, or we may have regard to a given fixed portion of space,
-  and consider the volume and energy of the fluid entering and leaving
-  that space.
-
-  If, in following a given path ab (fig. 4), a mass of water a has a
-  constant velocity, the motion is said to be uniform. The kinetic
-  energy of the mass a remains unchanged. If the velocity varies from
-  point to point of the path, the motion is called varying motion. If at
-  a given point a in space, the particles of water always arrive with
-  the same velocity and in the same direction, during any given time,
-  then the motion is termed steady motion. On the contrary, if at the
-  point a the velocity or direction varies from moment to moment the
-  motion is termed unsteady. A river which excavates its own bed is in
-  unsteady motion so long as the slope and form of the bed is changing.
-  It, however, tends always towards a condition in which the bed ceases
-  to change, and it is then said to have reached a condition of
-  permanent regime. No river probably is in absolutely permanent regime,
-  except perhaps in rocky channels. In other cases the bed is scoured
-  more or less during the rise of a flood, and silted again during the
-  subsidence of the flood. But while many streams of a torrential
-  character change the condition of their bed often and to a large
-  extent, in others the changes are comparatively small and not easily
-  observed.
-
-  [Illustration: FIG. 4.]
-
-  As a stream approaches a condition of steady motion, its regime
-  becomes permanent. Hence steady motion and permanent regime are
-  sometimes used as meaning the same thing. The one, however, is a
-  definite term applicable to the motion of the water, the other a less
-  definite term applicable in strictness only to the condition of the
-  stream bed.
-
-  S 12. _Theoretical Notions on the Motion of Water._--The actual motion
-  of the particles of water is in most cases very complex. To simplify
-  hydrodynamic problems, simpler modes of motion are assumed, and the
-  results of theory so obtained are compared experimentally with the
-  actual motions.
-
-  _Motion in Plane Layers._--The simplest kind of motion in a stream is
-  one in which the particles initially situated in any plane cross
-  section of the stream continue to be found in plane cross sections
-  during the subsequent motion. Thus, if the particles in a thin plane
-  layer ab (fig. 5) are found again in a thin plane layer a'b' after any
-  interval of time, the motion is said to be motion in plane layers. In
-  such motion the internal work in deforming the layer may usually be
-  disregarded, and the resistance to the motion is confined to the
-  circumference.
-
-  [Illustration: FIG. 5.]
-
-  _Laminar Motion._--In the case of streams having solid boundaries, it
-  is observed that the central parts move faster than the lateral parts.
-  To take account of these differences of velocity, the stream may be
-  conceived to be divided into thin laminae, having cross sections
-  somewhat similar to the solid boundary of the stream, and sliding on
-  each other. The different laminae can then be treated as having
-  differing velocities according to any law either observed or deduced
-  from their mutual friction. A much closer approximation to the real
-  motion of ordinary streams is thus obtained.
-
-  _Stream Line Motion._--In the preceding hypothesis, all the particles
-  in each lamina have the same velocity at any given cross section of
-  the stream. If this assumption is abandoned, the cross section of the
-  stream must be supposed divided into indefinitely small areas, each
-  representing the section of a fluid filament. Then these filaments may
-  have any law of variation of velocity assigned to them. If the motion
-  is steady motion these fluid filaments (or as they are then termed
-  _stream lines_) will have fixed positions in space.
-
-  _Periodic Unsteady Motion._--In ordinary streams with rough
-  boundaries, it is observed that at any given point the velocity varies
-  from moment to moment in magnitude and direction, but that the average
-  velocity for a sensible period (say for 5 or 10 minutes) varies very
-  little either in magnitude or velocity. It has hence been conceived
-  that the variations of direction and magnitude of the velocity are
-  periodic, and that, if for each point of the stream the mean velocity
-  and direction of motion were substituted for the actual more or less
-  varying motions, the motion of the stream might be treated as steady
-  stream line or steady laminar motion.
-
-  [Illustration: FIG. 6.]
-
-  S 13. _Volume of Flow._--Let A (fig. 6) be any ideal plane surface, of
-  area [omega], in a stream, normal to the direction of motion, and let
-  V be the velocity of the fluid. Then the volume flowing through the
-  surface A in unit time is
-
-    Q = [omega]V.   (1)
-
-  Thus, if the motion is rectilinear, all the particles at any instant
-  in the surface A will be found after one second in a similar surface
-  A', at a distance V, and as each particle is followed by a continuous
-  thread of other particles, the volume of flow is the right prism AA'
-  having a base [omega] and length V.
-
-  If the direction of motion makes an angle [theta] with the normal to
-  the surface, the volume of flow is represented by an oblique prism AA'
-  (fig. 7), and in that case
-
-    Q = [omega]V cos [theta].
-
-  [Illustration: FIG. 7.]
-
-  If the velocity varies at different points of the surface, let the
-  surface be divided into very small portions, for each of which the
-  velocity may be regarded as constant. If d[omega] is the area and v,
-  or v cos [theta], the normal velocity for this element of the surface,
-  the volume of flow is
-         _                _
-        /                /
-    Q = | v d[omega], or | v cos [theta] d[omega],
-       _/               _/
-
-  as the case may be.
-
-  S 14. _Principle of Continuity._--If we consider any completely
-  bounded fixed space in a moving liquid initially and finally filled
-  continuously with liquid, the inflow must be equal to the outflow.
-  Expressing the inflow with a positive and the outflow with a negative
-  sign, and estimating the volume of flow Q for all the boundaries,
-
-    [Sigma]Q = 0.
-
-  In general the space will remain filled with fluid if the pressure at
-  every point remains positive. There will be a break of continuity, if
-  at any point the pressure becomes negative, indicating that the stress
-  at that point is tensile. In the case of ordinary water this statement
-  requires modification. Water contains a variable amount of air in
-  solution, often about one-twentieth of its volume. This air is
-  disengaged and breaks the continuity of the liquid, if the pressure
-  falls below a point corresponding to its tension. It is for this
-  reason that pumps will not draw water to the full height due to
-  atmospheric pressure.
-
-  _Application of the Principle of Continuity to the case of a
-  Stream._--If A1, A2 are the areas of two normal cross sections of a
-  stream, and V1, V2 are the velocities of the stream at those sections,
-  then from the principle of continuity,
-
-    V1A1 = V2A2;
-
-    V1/V2 = A2/A1   (2)
-
-  that is, the normal velocities are inversely as the areas of the cross
-  sections. This is true of the mean velocities, if at each section the
-  velocity of the stream varies. In a river of varying slope the
-  velocity varies with the slope. It is easy therefore to see that in
-  parts of large cross section the slope is smaller than in parts of
-  small cross section.
-
-  If we conceive a space in a liquid bounded by normal sections at A1,
-  A2 and between A1, A2 by stream lines (fig. 8), then, as there is no
-  flow across the stream lines,
-
-    V1/V2 = A2/A1,
-
-  as in a stream with rigid boundaries.
-
-  [Illustration: FIG. 8.]
-
-  In the case of compressible fluids the variation of volume due to the
-  difference of pressure at the two sections must be taken into account.
-  If the motion is steady the weight of fluid between two cross sections
-  of a stream must remain constant. Hence the weight flowing in must be
-  the same as the weight flowing out. Let p1, p2 be the pressures, v1,
-  v2 the velocities, G1, G2 the weight per cubic foot of fluid, at cross
-  sections of a stream of areas A1, A2. The volumes of inflow and
-  outflow are
-
-    A1v1 and A2v2,
-
-  and, if the weights of these are the same,
-
-    G1A1v1 = G2A2v2;
-
-  and hence, from (5a) S 9, if the temperature is constant,
-
-    p1A1v1 = p2A2v2.   (3)
-
-  S 15. _Stream Lines._--The characteristic of a perfect fluid, that is,
-  a fluid free from viscosity, is that the pressure between any two
-  parts into which it is divided by a plane must be normal to the plane.
-  One consequence of this is that the particles can have no rotation
-  impressed upon them, and the motion of such a fluid is irrotational. A
-  stream line is the line, straight or curved, traced by a particle in a
-  current of fluid in irrotational movement. In a steady current each
-  stream line preserves its figure and position unchanged, and marks the
-  track of a stream of particles forming a fluid filament or elementary
-  stream. A current in steady irrotational movement may be conceived to
-  be divided by insensibly thin partitions following the course of the
-  stream lines into a number of elementary streams. If the positions of
-  these partitions are so adjusted that the volumes of flow in all the
-  elementary streams are equal, they represent to the mind the velocity
-  as well as the direction of motion of the particles in different parts
-  of the current, for the velocities are inversely proportional to the
-  cross sections of the elementary streams. No actual fluid is devoid of
-  viscosity, and the effect of viscosity is to render the motion of a
-  fluid sinuous, or rotational or eddying under most ordinary
-  conditions. At very low velocities in a tube of moderate size the
-  motion of water may be nearly pure stream line motion. But at some
-  velocity, smaller as the diameter of the tube is greater, the motion
-  suddenly becomes tumultuous. The laws of simple stream line motion
-  have hitherto been investigated theoretically, and from mathematical
-  difficulties have only been determined for certain simple cases.
-  Professor H. S. Hele Shaw has found means of exhibiting stream line
-  motion in a number of very interesting cases experimentally. Generally
-  in these experiments a thin sheet of fluid is caused to flow between
-  two parallel plates of glass. In the earlier experiments streams of
-  very small air bubbles introduced into the water current rendered
-  visible the motions of the water. By the use of a lantern the image of
-  a portion of the current can be shown on a screen or photographed. In
-  later experiments streams of coloured liquid at regular distances were
-  introduced into the sheet and these much more clearly marked out the
-  forms of the stream lines. With a fluid sheet 0.02 in. thick, the
-  stream lines were found to be stable at almost any required velocity.
-  For certain simple cases Professor Hele Shaw has shown that the
-  experimental stream lines of a viscous fluid are so far as can be
-  measured identical with the calculated stream lines of a perfect
-  fluid. Sir G. G. Stokes pointed out that in this case, either from the
-  thinness of the stream between its glass walls, or the slowness of the
-  motion, or the high viscosity of the liquid, or from a combination of
-  all these, the flow is regular, and the effects of inertia disappear,
-  the viscosity dominating everything. Glycerine gives the stream lines
-  very satisfactorily.
-
-  [Illustration: FIG. 9.]
-
-  [Illustration: FIG. 10.]
-
-  [Illustration: FIG. 11.]
-
-  [Illustration: FIG. 12.]
-
-  [Illustration: FIG. 13.]
-
-  Fig. 9 shows the stream lines of a sheet of fluid passing a fairly
-  shipshape body such as a screwshaft strut. The arrow shows the
-  direction of motion of the fluid. Fig. 10 shows the stream lines for a
-  very thin glycerine sheet passing a non-shipshape body, the stream
-  lines being practically perfect. Fig. 11 shows one of the earlier
-  air-bubble experiments with a thicker sheet of water. In this case the
-  stream lines break up behind the obstruction, forming an eddying wake.
-  Fig. 12 shows the stream lines of a fluid passing a sudden contraction
-  or sudden enlargement of a pipe. Lastly, fig. 13 shows the stream
-  lines of a current passing an oblique plane. H. S. Hele Shaw,
-  "Experiments on the Nature of the Surface Resistance in Pipes and on
-  Ships," _Trans. Inst. Naval Arch._ (1897). "Investigation of Stream
-  Line Motion under certain Experimental Conditions," _Trans. Inst.
-  Naval Arch._ (1898); "Stream Line Motion of a Viscous Fluid," _Report
-  of British Association_ (1898).
-
-
-  III. PHENOMENA OF THE DISCHARGE OF LIQUIDS FROM ORIFICES AS
-  ASCERTAINABLE BY EXPERIMENTS
-
-  S 16. When a liquid issues vertically from a small orifice, it forms a
-  jet which rises nearly to the level of the free surface of the liquid
-  in the vessel from which it flows. The difference of level h_r (fig.
-  14) is so small that it may be at once suspected to be due either to
-  air resistance on the surface of the jet or to the viscosity of the
-  liquid or to friction against the sides of the orifice. Neglecting for
-  the moment this small quantity, we may infer, from the elevation of
-  the jet, that each molecule on leaving the orifice possessed the
-  velocity required to lift it against gravity to the height h. From
-  ordinary dynamics, the relation between the velocity and height of
-  projection is given by the equation
-
-    v = [root](2gh).   (1)
-
-  As this velocity is nearly reached in the flow from well-formed
-  orifices, it is sometimes called the theoretical velocity of
-  discharge. This relation was first obtained by Torricelli.
-
-  [Illustration: FIG. 14.]
-
-  If the orifice is of a suitable conoidal form, the water issues in
-  filaments normal to the plane of the orifice. Let [omega] be the area
-  of the orifice, then the discharge per second must be, from eq. (1),
-
-    Q = [omega]v = [omega][root](2gh) nearly.   (2)
-
-  This is sometimes quite improperly called the theoretical discharge
-  for any kind of orifice. Except for a well-formed conoidal orifice the
-  result is not approximate even, so that if it is supposed to be based
-  on a theory the theory is a false one.
-
-  _Use of the term Head in Hydraulics._--The term _head_ is an old
-  millwright's term, and meant primarily the height through which a mass
-  of water descended in actuating a hydraulic machine. Since the water
-  in fig. 14 descends through a height h to the orifice, we may say
-  there are h ft. of head above the orifice. Still more generally any
-  mass of liquid h ft. above a horizontal plane may be said to have h
-  ft. of elevation head relatively to that datum plane. Further, since
-  the pressure p at the orifice which produces outflow is connected with
-  h by the relation p/G = h, the quantity p/G may be termed the pressure
-  head at the orifice. Lastly, the velocity v is connected with h by the
-  relation v^2/2g = h, so that v^2/2g may be termed the head due to the
-  velocity v.
-
-  S 17. _Coefficients of Velocity and Resistance._--As the actual
-  velocity of discharge differs from [root]2gh by a small quantity, let
-  the actual velocity
-
-    = v_a = c_v [root](2gh),   (3)
-
-  where c_v is a coefficient to be determined by experiment, called the
-  _coefficient of velocity_. This coefficient is found to be tolerably
-  constant for different heads with well-formed simple orifices, and it
-  very often has the value 0.97.
-
-  The difference between the velocity of discharge and the velocity due
-  to the head may be reckoned in another way. The total height h causing
-  outflow consists of two parts--one part h_e expended effectively in
-  producing the velocity of outflow, another h_r in overcoming the
-  resistances due to viscosity and friction. Let
-
-    h_r = c_r h_e,
-
-  where c{r} is a coefficient determined by experiment, and called the
-  _coefficient of resistance_ of the orifice. It is tolerably constant
-  for different heads with well-formed orifices. Then
-
-    v_a = [root](2gh_e) = [root]{2gh/(1 + c_r)}.   (4)
-
-  The relation between c_v and c_r for any orifice is easily found:--
-
-    v_a = c_v[root](2gh) = [root]{2gh/(1 + c_r)}
-
-    c_v = [root]{1/(1 + c_r)}   (5)
-
-    c_r = 1/c_v^2 - 1   (5a)
-
-  Thus if c_v = 0.97, then c_r = 0.0628. That is, for such an orifice
-  about 6(1/4)% of the head is expended in overcoming frictional
-  resistances to flow.
-
-  [Illustration: FIG. 15.]
-
-  _Coefficient of Contraction--Sharp-edged Orifices in Plane
-  Surfaces._--When a jet issues from an aperture in a vessel, it may
-  either spring clear from the inner edge of the orifice as at a or b
-  (fig. 15), or it may adhere to the sides of the orifice as at c. The
-  former condition will be found if the orifice is bevelled outwards as
-  at a, so as to be sharp edged, and it will also occur generally for a
-  prismatic aperture like b, provided the thickness of the plate in
-  which the aperture is formed is less than the diameter of the jet. But
-  if the thickness is greater the condition shown at c will occur.
-
-  When the discharge occurs as at a or b, the filaments converging
-  towards the orifice continue to converge beyond it, so that the
-  section of the jet where the filaments have become parallel is smaller
-  than the section of the orifice. The inertia of the filaments opposes
-  sudden change of direction of motion at the edge of the orifice, and
-  the convergence continues for a distance of about half the diameter of
-  the orifice beyond it. Let [omega] be the area of the orifice, and
-  c_c[omega] the area of the jet at the point where convergence ceases;
-  then c_c is a coefficient to be determined experimentally for each
-  kind of orifice, called the _coefficient of contraction_. When the
-  orifice is a sharp-edged orifice in a plane surface, the value of c_c
-  is on the average 0.64, or the section of the jet is very nearly
-  five-eighths of the area of the orifice.
-
-  _Coefficient of Discharge._--In applying the general formula Q =
-  [omega]v to a stream, it is assumed that the filaments have a common
-  velocity v normal to the section [omega]. But if the jet contracts, it
-  is at the contracted section of the jet that the direction of motion
-  is normal to a transverse section of the jet. Hence the actual
-  discharge when contraction occurs is
-
-    Q_a = c_vv X c_c[omega] = c_c c_v[omega][root](2gh),
-
-  or simply, if c = c_vc_c,
-
-    Q_a = c[omega][root](2gh),
-
-  where c is called the _coefficient of discharge_. Thus for a
-  sharp-edged plane orifice c = 0.97 X 0.64 = 0.62.
-
-  [Illustration: FIG. 16.]
-
-  S 18. _Experimental Determination of c_v, c_c, and c._--The
-  coefficient of contraction c_c is directly determined by measuring the
-  dimensions of the jet. For this purpose fixed screws of fine pitch
-  (fig. 16) are convenient. These are set to touch the jet, and then the
-  distance between them can be measured at leisure.
-
-  The coefficient of velocity is determined directly by measuring the
-  parabolic path of a horizontal jet.
-
-  Let OX, OY (fig. 17) be horizontal and vertical axes, the origin being
-  at the orifice. Let h be the head, and x, y the coordinates of a point
-  A on the parabolic path of the jet. If v_a is the velocity at the
-  orifice, and t the time in which a particle moves from O to A, then
-
-    x = v_a t; y = (1/2)gt^2.
-
-  Eliminating t,
-
-    v_a = [root](gx^2/2y).
-
-  Then
-
-    c_v = v_a [root](2gh) = [root](x^2/4yh).
-
-  In the case of large orifices such as weirs, the velocity can be
-  directly determined by using a Pitot tube (S 144).
-
-  [Illustration: FIG. 17.]
-
-  The coefficient of discharge, which for practical purposes is the most
-  important of the three coefficients, is best determined by tank
-  measurement of the flow from the given orifice in a suitable time. If
-  Q is the discharge measured in the tank per second, then
-
-    c = Q/[omega][root](2gh).
-
-  Measurements of this kind though simple in principle are not free from
-  some practical difficulties, and require much care. In fig. 18 is
-  shown an arrangement of measuring tank. The orifice is fixed in the
-  wall of the cistern A and discharges either into the waste channel BB,
-  or into the measuring tank. There is a short trough on rollers C which
-  when run under the jet directs the discharge into the tank, and when
-  run back again allows the discharge to drop into the waste channel. D
-  is a stilling screen to prevent agitation of the surface at the
-  measuring point, E, and F is a discharge valve for emptying the
-  measuring tank. The rise of level in the tank, the time of the flow
-  and the head over the orifice at that time must be exactly observed.
-
-  [Illustration: FIG. 18.]
-
-  For well made sharp-edged orifices, small relatively to the water
-  surface in the supply reservoir, the coefficients under different
-  conditions of head are pretty exactly known. Suppose the same quantity
-  of water is made to flow in succession through such an orifice and
-  through another orifice of which the coefficient is required, and when
-  the rate of flow is constant the heads over each orifice are noted.
-  Let h1, h2 be the heads, [omega]1, [omega]2 the areas of the orifices,
-  c1, c2 the coefficients. Then since the flow through each orifice is
-  the same
-
-    Q = c1[omega]1 [root](2gh1) = c2[omega]2 [root](2gh2).
-
-    c2 = c1([omega]1/[omega]2) [root](h1/h2).
-
-  [Illustration: FIG. 19.]
-
-  S 19. _Coefficients for Bellmouths and Bellmouthed Orifices._--If an
-  orifice is furnished with a mouthpiece exactly of the form of the
-  contracted vein, then the whole of the contraction occurs within the
-  mouthpiece, and if the area of the orifice is measured at the smaller
-  end, c_c must be put = 1. It is often desirable to bellmouth the ends
-  of pipes, to avoid the loss of head which occurs if this is not
-  done; and such a bellmouth may also have the form of the contracted
-  jet. Fig. 19 shows the proportions of such a bellmouth or bell-mouthed
-  orifice, which approximates to the form of the contracted jet
-  sufficiently for any practical purpose.
-
-  For such an orifice L. J. Weisbach found the following values of the
-  coefficients with different heads.
-
-    +--------------------------------+------+------+------+------+-------+
-    | Head over orifice, in ft. = h  | .66  | 1.64 |11.48 |55.77 |337.93 |
-    +--------------------------------+------+------+------+------+-------+
-    | Coefficient of velocity = c_v  | .959 | .967 | .975 | .994 |  .994 |
-    | Coefficient of resistance = c_r| .087 | .069 | .052 | .012 |  .012 |
-    +--------------------------------+------+------+------+------+-------+
-
-  As there is no contraction after the jet issues from the orifice, c_c
-  = 1, c = c_v; and therefore
-
-    Q = c(v)[omega][root](2gh) = [omega][root]{2gh/(1 + c_r}.
-
-  S 20. _Coefficients for Sharp-edged or virtually Sharp-edged
-  Orifices._--There are a very large number of measurements of discharge
-  from sharp-edged orifices under different conditions of head. An
-  account of these and a very careful tabulation of the average values
-  of the coefficients will be found in the _Hydraulics_ of the late
-  Hamilton Smith (Wiley & Sons, New York, 1886). The following short
-  table abstracted from a larger one will give a fair notion of how the
-  coefficient varies according to the most trustworthy of the
-  experiments.
-
-    _Coefficient of Discharge for Vertical Circular Orifices, Sharp-edged,
-    with free Discharge into the Air._ Q = c[omega][root](2gh).
-
-    +-----------+------------------------------------------------+
-    |   Head    |            Diameters of Orifice.               |
-    |measured to+------+------+------+------+------+------+------+
-    | Centre of | .02  | .04  | .10  | .20  | .40  | .60  | 1.0  |
-    |  Orifice. +------+------+------+------+------+------+------+
-    |           |                  Values of C.                  |
-    +-----------+------+------+------+------+------+------+------+
-    |    0.3    |  ..  | ..   | .621 |  ..  |  ..  |  ..  |  ..  |
-    |    0.4    |  ..  | .637 | .618 |  ..  |  ..  |  ..  |  ..  |
-    |    0.6    | .655 | .630 | .613 | .601 | .596 | .588 |  ..  |
-    |    0.8    | .648 | .626 | .610 | .601 | .597 | .594 | .583 |
-    |    1.0    | .644 | .623 | .608 | .600 | .598 | .595 | .591 |
-    |    2.0    | .632 | .614 | .604 | .599 | .599 | .597 | .595 |
-    |    4.0    | .623 | .609 | .602 | .599 | .598 | .597 | .596 |
-    |    8.0    | .614 | .605 | .600 | .598 | .597 | .596 | .596 |
-    |   20.0    | .601 | .599 | .596 | .596 | .596 | .596 | .594 |
-    +-----------+------+------+------+------+------+------+------+
-
-  At the same time it must be observed that differences of sharpness in
-  the edge of the orifice and some other circumstances affect the
-  results, so that the values found by different careful experimenters
-  are not a little discrepant. When exact measurement of flow has to be
-  made by a sharp-edged orifice it is desirable that the coefficient for
-  the particular orifice should be directly determined.
-
-  The following results were obtained by Dr H. T. Bovey in the
-  laboratory of McGill University.
-
-    _Coefficient of Discharge for Sharp-edged Orifices._
-
-    +----+------------------------------------------------------------------+
-    |    |                         Form of Orifice.                         |
-    |    +------+----------------+-----------------+-----------------+------+
-    |    |      |     Square.    |Rectangular Ratio|Rectangular Ratio|      |
-    |Head|      |                |  of Sides 4:1   |  of Sides 16:1  |      |
-    | in | Cir- +------+---------+---------+-------+---------+-------+ Tri- |
-    | ft.|cular.|Sides |         |  Long   | Long  |  Long   | Long  |angu- |
-    |    |      |Verti-|Diagonal |  Sides  | Sides |  Sides  | Sides | lar. |
-    |    |      | cal. |Vertical.|Vertical.| hori- |Vertical.| Hori- |      |
-    |    |      |      |         |         |zontal.|         |zontal.|      |
-    +----+------+------+---------+---------+-------+---------+-------+------+
-    |  1 | .620 | .627 |  .628   |   .642  |  .643 |   .663  |  .664 | .636 |
-    |  2 | .613 | .620 |  .628   |   .634  |  .636 |   .650  |  .651 | .628 |
-    |  4 | .608 | .616 |  .618   |   .628  |  .629 |   .641  |  .642 | .623 |
-    |  6 | .607 | .614 |  .616   |   .626  |  .627 |   .637  |  .637 | .620 |
-    |  8 | .606 | .613 |  .614   |   .623  |  .625 |   .634  |  .635 | .619 |
-    | 10 | .605 | .612 |  .613   |   .622  |  .624 |   .632  |  .633 | .618 |
-    | 12 | .604 | .611 |  .612   |   .622  |  .623 |   .631  |  .631 | .618 |
-    | 14 | .604 | .610 |  .612   |   .621  |  .622 |   .630  |  .630 | .618 |
-    | 16 | .603 | .610 |  .611   |   .620  |  .622 |   .630  |  .630 | .617 |
-    | 18 | .603 | .610 |  .611   |   .620  |  .621 |   .630  |  .629 | .616 |
-    | 20 | .603 | .609 |  .611   |   .620  |  .621 |   .629  |  .628 | .616 |
-    +----+------+------+---------+---------+-------+---------+-------+------+
-
-  The orifice was 0.196 sq. in. area and the reductions were made with g
-  = 32.176 the value for Montreal. The value of the coefficient appears
-  to increase as (perimeter) / (area) increases. It decreases as the
-  head increases. It decreases a little as the size of the orifice is
-  greater.
-
-  Very careful experiments by J. G. Mair (_Proc. Inst. Civ. Eng._
-  lxxxiv.) on the discharge from circular orifices gave the results
-  shown on top of next column.
-
-  The edges of the orifices were got up with scrapers to a sharp square
-  edge. The coefficients generally fall as the head increases and as the
-  diameter increases. Professor W. C. Unwin found that the results agree
-  with the formula
-
-    c = 0.6075 + 0.0098/[root]h - 0.0037d,
-
-  where h is in feet and d in inches.
-
-    _Coefficients of Discharge from Circular Orifices. Temperature 51
-    deg. to 55 deg._
-
-    +-------+--------------------------------------------------------------+
-    |Head in|             Diameters of Orifices in Inches (d).             |
-    | feet  +------+------+------+------+------+------+------+------+------+
-    |   h.  |   1  |1(1/4)|1(1/2)|1(3/4)|   2  |2(1/4)|2(1/2)|2(3/4)|   3  |
-    +-------+------+------+------+------+------+------+------+------+------+
-    |       |                       Coefficients (c).                      |
-    |       +------+------+------+------+------+------+------+------+------+
-    |   .75 | .616 | .614 | .616 | .610 | .616 | .612 | .607 | .607 | .609 |
-    |  1.0  | .613 | .612 | .612 | .611 | .612 | .611 | .604 | .608 | .609 |
-    |  1.25 | .613 | .614 | .610 | .608 | .612 | .608 | .605 | .605 | .606 |
-    |  1.50 | .610 | .612 | .611 | .606 | .610 | .607 | .603 | .607 | .605 |
-    |  1.75 | .612 | .611 | .611 | .605 | .611 | .605 | .604 | .607 | .605 |
-    |  2.00 | .609 | .613 | .609 | .606 | .609 | .606 | .604 | .604 | .605 |
-    +-------+------+------+------+------+------+------+------+------+------+
-
-  The following table, compiled by J. T. Fanning (_Treatise on Water
-  Supply Engineering_), gives values for rectangular orifices in
-  vertical plane surfaces, the head being measured, not immediately over
-  the orifice, where the surface is depressed, but to the still-water
-  surface at some distance from the orifice. The values were obtained by
-  graphic interpolation, all the most reliable experiments being plotted
-  and curves drawn so as to average the discrepancies.
-
-    _Coefficients of Discharge for Rectangular Orifices, Sharp-edged, in
-    Vertical Plane Surfaces._
-
-    +--------+----------------------------------------------------------------+
-    |  Head  |                  Ratio of Height to Width.                     |
-    |   to   |                                                                |
-    | Centre +------+------+------+------+--------+--------+--------+---------+
-    |   of   |      |      |      |      |        |        |        |         |
-    |Orifice.|  4   |  2   |1(1/2)|  1   |  3/4   |   1/2  |   1/4  |   1/8   |
-    +--------+------+------+------+------+--------+--------+--------+---------+
-    |        | 4 ft.| 2 ft.|1(1/2)| 1 ft.|0.75 ft.|0.50 ft.|0.25 ft.|0.125 ft.|
-    |        | high.| high.|  ft. | high.|  high. |  high. |  high. |  high.  |
-    |  Feet. |      |      | high.|      |        |        |        |         |
-    |        | 1 ft.| 1 ft.| 1 ft.| 1 ft.|  1 ft. |  1 ft. |  1 ft. |  1 ft.  |
-    |        | wide.| wide.| wide.| wide.|  wide. |  wide. |  wide. |  wide.  |
-    +--------+------+------+------+------+--------+--------+--------+---------+
-    |   0.2  |  ..  |  ..  |  ..  |  ..  |   ..   |   ..   |   ..   |  .6333  |
-    |    .3  |  ..  |  ..  |  ..  |  ..  |   ..   |   ..   | .6293  |  .6334  |
-    |    .4  |  ..  |  ..  |  ..  |  ..  |   ..   | .6140  | .6306  |  .6334  |
-    |    .5  |  ..  |  ..  |  ..  |  ..  | .6050  | .6150  | .6313  |  .6333  |
-    |    .6  |  ..  |  ..  |  ..  |.5984 | .6063  | .6156  | .6317  |  .6332  |
-    |    .7  |  ..  |  ..  |  ..  |.5994 | .6074  | .6162  | .6319  |  .6328  |
-    |    .8  |  ..  |  ..  |.6130 |.6000 | .6082  | .6165  | .6322  |  .6326  |
-    |    .9  |  ..  |  ..  |.6134 |.6006 | .6086  | .6168  | .6323  |  .6324  |
-    |   1.0  |  ..  |  ..  |.6135 |.6010 | .6090  | .6172  | .6320  |  .6320  |
-    |   1.25 |  ..  |.6188 |.6140 |.6018 | .6095  | .6173  | .6317  |  .6312  |
-    |   1.50 |  ..  |.6187 |.6144 |.6026 | .6100  | .6172  | .6313  |  .6303  |
-    |   1.75 |  ..  |.6186 |.6145 |.6033 | .6103  | .6168  | .6307  |  .6296  |
-    |   2    |  ..  |.6183 |.6144 |.6036 | .6104  | .6166  | .6302  |  .6291  |
-    |   2.25 |  ..  |.6180 |.6143 |.6029 | .6103  | .6163  | .6293  |  .6286  |
-    |   2.50 |.6290 |.6176 |.6139 |.6043 | .6102  | .6157  | .6282  |  .6278  |
-    |   2.75 |.6280 |.6173 |.6136 |.6046 | .6101  | .6155  | .6274  |  .6273  |
-    |   3    |.6273 |.6170 |.6132 |.6048 | .6100  | .6153  | .6267  |  .6267  |
-    |   3.5  |.6250 |.6160 |.6123 |.6050 | .6094  | .6146  | .6254  |  .6254  |
-    |   4    |.6245 |.6150 |.6110 |.6047 | .6085  | .6136  | .6236  |  .6236  |
-    |   4.5  |.6226 |.6138 |.6100 |.6044 | .6074  | .6125  | .6222  |  .6222  |
-    |   5    |.6208 |.6124 |.6088 |.6038 | .6063  | .6114  | .6202  |  .6202  |
-    |   6    |.6158 |.6094 |.6063 |.6020 | .6044  | .6087  | .6154  |  .6154  |
-    |   7    |.6124 |.6064 |.6038 |.6011 | .6032  | .6058  | .6110  |  .6114  |
-    |   8    |.6090 |.6036 |.6022 |.6010 | .6022  | .6033  | .6073  |  .6087  |
-    |   9    |.6060 |.6020 |.6014 |.6010 | .6015  | .6020  | .6045  |  .6070  |
-    |  10    |.6035 |.6015 |.6010 |.6010 | .6010  | .6010  | .6030  |  .6060  |
-    |  15    |.6040 |.6018 |.6010 |.6011 | .6012  | .6013  | .6033  |  .6066  |
-    |  20    |.6045 |.6024 |.6012 |.6012 | .6014  | .6018  | .6036  |  .6074  |
-    |  25    |.6048 |.6028 |.6014 |.6012 | .6016  | .6022  | .6040  |  .6083  |
-    |  30    |.6054 |.6034 |.6017 |.6013 | .6018  | .6027  | .6044  |  .6092  |
-    |  35    |.6060 |.6039 |.6021 |.6014 | .6022  | .6032  | .6049  |  .6103  |
-    |  40    |.6066 |.6045 |.6025 |.6015 | .6026  | .6037  | .6055  |  .6114  |
-    |  45    |.6054 |.6052 |.6029 |.6016 | .6030  | .6043  | .6062  |  .6125  |
-    |  50    |.6086 |.6060 |.6034 |.6018 | .6035  | .6050  | .6070  |  .6140  |
-    +--------+------+------+------+------+--------+--------+--------+---------+
-
-  S 21. _Orifices with Edges of Sensible Thickness._--When the edges of
-  the orifice are not bevelled outwards, but have a sensible thickness,
-  the coefficient of discharge is somewhat altered. The following table
-  gives values of the coefficient of discharge for the arrangements of
-  the orifice shown in vertical section at P, Q, R (fig. 20). The plan
-  of all the orifices is shown at S. The planks forming the orifice and
-  sluice were each 2 in. thick, and the orifices were all 24 in. wide.
-  The heads were measured immediately over the orifice. In this case,
-
-    Q = cb(H - h) [root]{2g(H + h)/2}.
-
-  S 22. _Partially Suppressed Contraction._--Since the contraction of
-  the jet is due to the convergence towards the orifice of the issuing
-  streams, it will be diminished if for any portion of the edge of the
-  orifice the convergence is prevented. Thus, if an internal rim or
-  border is applied to part of the edge of the orifice (fig. 21), the
-  convergence for so much of the edge is suppressed. For such cases G.
-  Bidone found the following empirical formulae applicable:--
-
-    _Table of Coefficients of Discharge for Rectangular Vertical Orifices
-    in Fig. 20._
-
-    +--------+-----------------------------------------------------------------------------------------------+
-    |Head h  |                                                                                               |
-    |above   |                                Height of Orifice, H - h, in feet                              |
-    |upper   +-----------------------+-----------------------+-----------------------+-----------------------+
-    |edge of |          1.31         |          0.66         |          0.16         |          0.10         |
-    |Orifice +-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
-    |in feet.|   P   |   Q   |   R   |   P   |   Q   |   R   |   P   |   Q   |   R   |   P   |   Q   |   R   |
-    +--------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
-    |  0.328 | 0.598 | 0.644 | 0.648 | 0.634 | 0.665 | 0.668 | 0.691 | 0.664 | 0.666 | 0.710 | 0.694 | 0.696 |
-    |   .656 | 0.609 | 0.653 | 0.657 | 0.640 | 0.672 | 0.675 | 0.685 | 0.687 | 0.688 | 0.696 | 0.704 | 0.706 |
-    |   .787 | 0.612 | 0.655 | 0.659 | 0.641 | 0.674 | 0.677 | 0.684 | 0.690 | 0.692 | 0.694 | 0.706 | 0.708 |
-    |   .984 | 0.616 | 0.656 | 0.660 | 0.641 | 0.675 | 0.678 | 0.683 | 0.693 | 0.695 | 0.692 | 0.709 | 0.711 |
-    |  1.968 | 0.618 | 0.649 | 0.653 | 0.640 | 0.676 | 0.679 | 0.678 | 0.695 | 0.697 | 0.688 | 0.710 | 0.712 |
-    |  3.28  | 0.608 | 0.632 | 0.634 | 0.638 | 0.674 | 0.676 | 0.673 | 0.694 | 0.695 | 0.680 | 0.704 | 0.705 |
-    |  4.27  | 0.602 | 0.624 | 0.626 | 0.637 | 0.673 | 0.675 | 0.672 | 0.693 | 0.694 | 0.678 | 0.701 | 0.702 |
-    |  4.92  | 0.598 | 0.620 | 0.622 | 0.637 | 0.673 | 0.674 | 0.672 | 0.692 | 0.693 | 0.676 | 0.699 | 0.699 |
-    |  5.58  | 0.596 | 0.618 | 0.620 | 0.637 | 0.672 | 0.673 | 0.672 | 0.692 | 0.693 | 0.676 | 0.698 | 0.698 |
-    |  6.56  | 0.595 | 0.615 | 0.617 | 0.636 | 0.671 | 0.672 | 0.671 | 0.691 | 0.692 | 0.675 | 0.696 | 0.696 |
-    |  9.84  | 0.592 | 0.611 | 0.612 | 0.634 | 0.669 | 0.670 | 0.668 | 0.689 | 0.690 | 0.672 | 0.693 | 0.693 |
-    +--------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
-
-  For rectangular orifices,
-
-    C_c = 0.62(1 + 0.152n/p);
-
-  and for circular orifices,
-
-    C_c = 0.62(1 + 0.128n/p);
-
-  when n is the length of the edge of the orifice over which the border
-  extends, and p is the whole length of edge or perimeter of the
-  orifice. The following are the values of c_c, when the border extends
-  over 1/4, 1/2, or 3/4 of the whole perimeter:--
-
-    +--------+-----------------------+--------------------+
-    |        |          C_c          |        C_c         |
-    |   n/p  | Rectangular Orifices. | Circular Orifices. |
-    +--------+-----------------------+--------------------+
-    |  0.25  |         0.643         |        .640        |
-    |  0.50  |         0.667         |        .660        |
-    |  0.75  |         0.691         |        .680        |
-    +--------+-----------------------+--------------------+
-
-  [Illustration: FIG. 20.]
-
-  [Illustration: FIG. 21.]
-
-  For larger values of n/p the formulae are not applicable. C. R.
-  Bornemann has shown, however, that these formulae for suppressed
-  contraction are not reliable.
-
-  S 23. _Imperfect Contraction._--If the sides of the vessel approach
-  near to the edge of the orifice, they interfere with the convergence
-  of the streams to which the contraction is due, and the contraction is
-  then modified. It is generally stated that the influence of the sides
-  begins to be felt if their distance from the edge of the orifice is
-  less than 2.7 times the corresponding width of the orifice. The
-  coefficients of contraction for this case are imperfectly known.
-
-  [Illustration: FIG. 22.]
-
-  S 24. _Orifices Furnished with Channels of Discharge._--These external
-  borders to an orifice also modify the contraction.
-
-  The following coefficients of discharge were obtained with openings 8
-  in. wide, and small in proportion to the channel of approach (fig. 22,
-  A, B, C).
-
-    +-----------+-------------------------------------------------------+
-    |   h2--h1  |                       h1 in feet.                     |
-    |  in feet  |------+-----+-----+-----+------+-----+-----+-----+-----+
-    |           |.0656 |.164 |.328 |.656 |1.640 |3.28 |4.92 |6.56 |9.84 |
-    +-----------+------+-----+-----+-----+------+-----+-----+-----+-----+
-    | A\        | .480 |.511 |.542 |.574 | .599 |.601 |.601 |.601 |.601 |
-    | B > 0.656 | .480 |.510 |.538 |.506 | .592 |.600 |.602 |.602 |.601 |
-    | C/        | .527 |.553 |.574 |.592 | .607 |.610 |.610 |.609 |.608 |
-    |           |      |     |     |     |      |     |     |     |     |
-    | A\        | .488 |.577 |.624 |.631 | .625 |.624 |.619 |.613 |.606 |
-    | B > 0.164 | .487 |.571 |.606 |.617 | .626 |.628 |.627 |.623 |.618 |
-    | C/        | .585 |.614 |.633 |.645 | .652 |.651 |.650 |.650 |.649 |
-    +-----------+------+-----+-----+-----+------+-----+-----+-----+-----+
-
-  [Illustration: FIG. 23.]
-
-  S 25. _Inversion of the Jet._--When a jet issues from a horizontal
-  orifice, or is of small size compared with the head, it presents no
-  marked peculiarity of form. But if the orifice is in a vertical
-  surface, and if its dimensions are not small compared with the head,
-  it undergoes a series of singular changes of form after leaving
-  the orifice. These were first investigated by G. Bidone (1781-1839);
-  subsequently H. G. Magnus (1802-1870) measured jets from different
-  orifices; and later Lord Rayleigh (_Proc. Roy. Soc._ xxix. 71)
-  investigated them anew.
-
-  Fig. 23 shows some forms, the upper figure giving the shape of the
-  orifices, and the others sections of the jet. The jet first contracts
-  as described above, in consequence of the convergence of the fluid
-  streams within the vessel, retaining, however, a form similar to that
-  of the orifice. Afterwards it expands into sheets in planes
-  perpendicular to the sides of the orifice. Thus the jet from a
-  triangular orifice expands into three sheets, in planes bisecting at
-  right angles the three sides of the triangle. Generally a jet from an
-  orifice, in the form of a regular polygon of n sides, forms n sheets
-  in planes perpendicular to the sides of the polygon.
-
-  Bidone explains this by reference to the simpler case of meeting
-  streams. If two equal streams having the same axis, but moving in
-  opposite directions, meet, they spread out into a thin disk normal to
-  the common axis of the streams. If the directions of two streams
-  intersect obliquely they spread into a symmetrical sheet perpendicular
-  to the plane of the streams.
-
-  [Illustration: FIG. 24.]
-
-  Let a1, a2 (fig. 24) be two points in an orifice at depths h1, h2 from
-  the free surface. The filaments issuing at a1, a2 will have the
-  different velocities [root](2gh1) and [root](2gh2). Consequently they
-  will tend to describe parabolic paths a1cb1 and a2cb2 of different
-  horizontal range, and intersecting in the point c. But since two
-  filaments cannot simultaneously flow through the same point, they must
-  exercise mutual pressure, and will be deflected out of the paths they
-  tend to describe. It is this mutual pressure which causes the
-  expansion of the jet into sheets.
-
-  Lord Rayleigh pointed out that, when the orifices are small and the
-  head is not great, the expansion of the sheets in directions
-  perpendicular to the direction of flow reaches a limit. Sections taken
-  at greater distance from the orifice show a contraction of the sheets
-  until a compact form is reached similar to that at the first
-  contraction. Beyond this point, if the jet retains its coherence,
-  sheets are thrown out again, but in directions bisecting the angles
-  between the previous sheets. Lord Rayleigh accepts an explanation of
-  this contraction first suggested by H. Buff (1805-1878), namely, that
-  it is due to surface tension.
-
-  S 26. _Influence of Temperature on Discharge of Orifices._--Professor
-  VV. C. Unwin found (_Phil. Mag._, October 1878, p. 281) that for
-  sharp-edged orifices temperature has a very small influence on the
-  discharge. For an orifice 1 cm. in diameter with heads of about 1 to
-  1(1/2) ft. the coefficients were:--
-
-    Temperature F.      C.
-       205 deg.       .594
-        62 deg.       .598
-
-  For a conoidal or bell-mouthed orifice 1 cm. diameter the effect of
-  temperature was greater:--
-
-    Temperature F.      C.
-       190 deg.        0.987
-       130 deg.        0.974
-        60 deg.        0.942
-
-  an increase in velocity of discharge of 4% when the temperature
-  increased 130 deg.
-
-  J. G. Mair repeated these experiments on a much larger scale (_Proc.
-  Inst. Civ. Eng._ lxxxiv.). For a sharp-edged orifice 2(1/2) in.
-  diameter, with a head of 1.75 ft., the coefficient was 0.604 at 57
-  deg. and 0.607 at 179 deg. F., a very small difference. With a
-  conoidal orifice the coefficient was 0.961 at 55 deg. and 0.98l at 170
-  deg. F. The corresponding coefficients of resistance are 0.0828 and
-  0.0391, showing that the resistance decreases to about half at the
-  higher temperature.
-
-  S 27. _Fire Hose Nozzles._--Experiments have been made by J. R.
-  Freeman on the coefficient of discharge from smooth cone nozzles used
-  for fire purposes. The coefficient was found to be 0.983 for (3/4)-in.
-  nozzle; 0.982 for 7/8 in.; 0.972 for 1 in.; 0.976 for 1(1/8) in.; and
-  0.971 for 1(1/4) in. The nozzles were fixed on a taper play-pipe, and
-  the coefficient includes the resistance of this pipe (_Amer. Soc. Civ.
-  Eng._ xxi., 1889). Other forms of nozzle were tried such as ring
-  nozzles for which the coefficient was smaller.
-
-
-  IV. THEORY OF THE STEADY MOTION OF FLUIDS.
-
-  S 28. The general equation of the steady motion of a fluid given under
-  Hydrodynamics furnishes immediately three results as to the
-  distribution of pressure in a stream which may here be assumed.
-
-  (a) If the motion is rectilinear and uniform, the variation of
-  pressure is the same as in a fluid at rest. In a stream flowing in an
-  open channel, for instance, when the effect of eddies produced by the
-  roughness of the sides is neglected, the pressure at each point is
-  simply the hydrostatic pressure due to the depth below the free
-  surface.
-
-  (b) If the velocity of the fluid is very small, the distribution of
-  pressure is approximately the same as in a fluid at rest.
-
-  (c) If the fluid molecules take precisely the accelerations which they
-  would have if independent and submitted only to the external forces,
-  the pressure is uniform. Thus in a jet falling freely in the air the
-  pressure throughout any cross section is uniform and equal to the
-  atmospheric pressure.
-
-  (d) In any bounded plane section traversed normally by streams which
-  are rectilinear for a certain distance on either side of the section,
-  the distribution of pressure is the same as in a fluid at rest.
-
-
-  DISTRIBUTION OF ENERGY IN INCOMPRESSIBLE FLUIDS.
-
-  S 29. _Application of the Principle of the Conservation of Energy to
-  Cases of Stream Line Motion._--The external and internal work done on
-  a mass is equal to the change of kinetic energy produced. In many
-  hydraulic questions this principle is difficult to apply, because from
-  the complicated nature of the motion produced it is difficult to
-  estimate the total kinetic energy generated, and because in some cases
-  the internal work done in overcoming frictional or viscous resistances
-  cannot be ascertained; but in the case of stream line motion it
-  furnishes a simple and important result known as Bernoulli's theorem.
-
-  [Illustration: FIG. 25.]
-
-  Let AB (fig. 25) be any one elementary stream, in a steadily moving
-  fluid mass. Then, from the steadiness of the motion, AB is a fixed
-  path in space through which a stream of fluid is constantly flowing.
-  Let OO be the free surface and XX any horizontal datum line. Let
-  [omega] be the area of a normal cross section, v the velocity, p the
-  intensity of pressure, and z the elevation above XX, of the elementary
-  stream AB at A, and [omega]1, p1, v1, z1 the same quantities at B.
-  Suppose that in a short time t the mass of fluid initially occupying
-  AB comes to A'B'. Then AA', BB' are equal to vt, v1t, and the volumes
-  of fluid AA', BB' are the equal inflow and outflow = Qt = [omega]vt =
-  [omega]1v1t, in the given time. If we suppose the filament AB
-  surrounded by other filaments moving with not very different
-  velocities, the frictional or viscous resistance on its surface will
-  be small enough to be neglected, and if the fluid is incompressible no
-  internal work is done in change of volume. Then the work done by
-  external forces will be equal to the kinetic energy produced in the
-  time considered.
-
-  The normal pressures on the surface of the mass (excluding the ends A,
-  B) are at each point normal to the direction of motion, and do no
-  work. Hence the only external forces to be reckoned are gravity and
-  the pressures on the ends of the stream.
-
-  The work of gravity when AB falls to A'B' is the same as that of
-  transferring AA' to BB'; that is, GQt(z - z1). The work of the
-  pressures on the ends, reckoning that at B negative, because it is
-  opposite to the direction of motion, is (p[omega] X vt) - (p1[omega]1
-  X v1t) = Qt(p - p1). The change of kinetic energy in the time t is the
-  difference of the kinetic energy originally possessed by AA' and that
-  finally acquired by BB', for in the intermediate part A'B there is no
-  change of kinetic energy, in consequence of the steadiness of the
-  motion. But the mass of AA' and BB' is GQt/g, and the change of
-  kinetic energy is therefore (GQt/g) (v1^2/2 - v^2/2). Equating this to
-  the work done on the mass AB,
-
-    GQt(z - z1) + Qt(p - p1) = (GQt/g)(v1^2/2 - v^2/2).
-
-  Dividing by GQt and rearranging the terms,
-
-    v^2/2g + p/G + z = v1^2/2g + p1/G + z1;   (1)
-
-  or, as A and B are any two points,
-
-    v^2/2g + p/G + z = constant = H.   (2)
-
-  Now v^2/2g is the head due to the velocity v, p/G is the head
-  equivalent to the pressure, and z is the elevation above the datum
-  (see S 16). Hence the terms on the left are the total head due to
-  velocity, pressure, and elevation at a given cross section of the
-  filament, z is easily seen to be the work in foot-pounds which would
-  be done by 1 lb. of fluid falling to the datum line, and similarly p/G
-  and v^2/2g are the quantities of work which would be done by 1 lb. of
-  fluid due to the pressure p and velocity v. The expression on the left
-  of the equation is, therefore, the total energy of the stream at the
-  section considered, per lb. of fluid, estimated with reference to the
-  datum line XX. Hence we see that in stream line motion, under
-  the restrictions named above, the total energy per lb. of fluid is
-  uniformly distributed along the stream line. If the free surface of
-  the fluid OO is taken as the datum, and -h, -h1 are the depths of A
-  and B measured down from the free surface, the equation takes the form
-
-    v^2/2g + p/G - h = v1^2/2g + p1/G - h1;   (3)
-
-  or generally
-
-    v^2/2g + p/G - h = constant.   (3a)
-
-  [Illustration: FIG. 26.]
-
-  S 30. _Second Form of the Theorem of Bernoulli._--Suppose at the two
-  sections A, B (fig. 26) of an elementary stream small vertical pipes
-  are introduced, which may be termed pressure columns (S 8), having
-  their lower ends accurately parallel to the direction of flow. In such
-  tubes the water will rise to heights corresponding to the pressures at
-  A and B. Hence b = p/G, and b' = p1/G. Consequently the tops of the
-  pressure columns A' and B' will be at total heights b + c = p/G + z
-  and b' + c' = p1/G + z1 above the datum line XX. The difference of
-  level of the pressure column tops, or the fall of free surface level
-  between A and B, is therefore
-
-    [xi] = (p - p1)/G + (z - z1);
-
-  and this by equation (1), S 29 is (v1^2 - v^2)/2g. That is, the fall
-  of free, surface level between two sections is equal to the difference
-  of the heights due to the velocities at the sections. The line A'B' is
-  sometimes called the line of hydraulic gradient, though this term is
-  also used in cases where friction needs to be taken into account. It
-  is the line the height of which above datum is the sum of the
-  elevation and pressure head at that point, and it falls below a
-  horizontal line A"B" drawn at H ft. above XX by the quantities a =
-  v^2/2g and a' = v1^2/2g, when friction is absent.
-
-  S 31. _Illustrations of the Theorem of Bernoulli._ In a lecture to the
-  mechanical section of the British Association in 1875, W. Froude gave
-  some experimental illustrations of the principle of Bernoulli. He
-  remarked that it was a common but erroneous impression that a fluid
-  exercises in a contracting pipe A (fig. 27) an excess of pressure
-  against the entire converging surface which it meets, and that,
-  conversely, as it enters an enlargement B, a relief of pressure is
-  experienced by the entire diverging surface of the pipe. Further it is
-  commonly assumed that when passing through a contraction C, there is
-  in the narrow neck an excess of pressure due to the squeezing together
-  of the liquid at that point. These impressions are in no respect
-  correct; the pressure is smaller as the section of the pipe is smaller
-  and conversely.
-
-  [Illustration: FIG. 27.]
-
-  Fig. 28 shows a pipe so formed that a contraction is followed by an
-  enlargement, and fig. 29 one in which an enlargement is followed by a
-  contraction. The vertical pressure columns show the decrease of
-  pressure at the contraction and increase of pressure at the
-  enlargement. The line abc in both figures shows the variation of free
-  surface level, supposing the pipe frictionless. In actual pipes,
-  however, work is expended in friction against the pipe; the total head
-  diminishes in proceeding along the pipe, and the free surface level is
-  a line such as ab1c1, falling below abc.
-
-  Froude further pointed out that, if a pipe contracts and enlarges
-  again to the same size, the resultant pressure on the converging part
-  exactly balances the resultant pressure on the diverging part so that
-  there is no tendency to move the pipe bodily when water flows through
-  it. Thus the conical part AB (fig. 30) presents the same projected
-  surface as HI, and the pressures parallel to the axis of the pipe,
-  normal to these projected surfaces, balance each other. Similarly the
-  pressures on BC, CD balance those on GH, EG. In the same way, in any
-  combination of enlargements and contractions, a balance of pressures,
-  due to the flow of liquid parallel to the axis of the pipe, will be
-  found, provided the sectional area and direction of the ends are the
-  same.
-
-  [Illustration: FIG. 28.]
-
-  [Illustration: FIG. 29.]
-
-  The following experiment is interesting. Two cisterns provided with
-  converging pipes were placed so that the jet from one was exactly
-  opposite the entrance to the other. The cisterns being filled very
-  nearly to the same level, the jet from the left-hand cistern A entered
-  the right-hand cistern B (fig. 31), shooting across the free space
-  between them without any waste, except that due to indirectness of aim
-  and want of exact correspondence in the form of the orifices. In the
-  actual experiment there was 18 in. of head in the right and 20(1/2)
-  in. of head in the left-hand cistern, so that about 2(1/2) in. were
-  wasted in friction. It will be seen that in the open space between the
-  orifices there was no pressure, except the atmospheric pressure acting
-  uniformly throughout the system.
-
-  [Illustration: FIG. 30.]
-
-  [Illustration: FIG. 31.]
-
-  S 32. _Venturi Meter._--An ingenious application of the variation of
-  pressure and velocity in a converging and diverging pipe has been made
-  by Clemens Herschel in the construction of what he terms a Venturi
-  Meter for measuring the flow in water mains. Suppose that, as in fig.
-  32, a contraction is made in a water main, the change of section being
-  gradual to avoid the production of eddies. The ratio [rho] of the
-  cross sections at A and B, that is at inlet and throat, is in actual
-  meters 5 to 1 to 20 to 1, and is very carefully determined by the
-  maker of the meter. Then, if v and u are the velocities at A and B, u
-  = [rho]v. Let pressure pipes be introduced at A, B and C, and let H1,
-  H, H2 be the pressure heads at those points. Since the velocity at B
-  is greater than at A the pressure will be less. Neglecting friction
-
-    H1 + v^2/2g = H + u^2/2g,
-
-    H1 - H = (u^2 - v^2)/2g = ([rho]^2 - 1)v^2/2g.
-
-  Let h = H1 - H be termed the Venturi head, then
-
-    u = [root]{[rho]^2 . 2gh/([rho]^2 - 1)},
-
-  from which the velocity through the throat and the discharge of the
-  main can be calculated if the areas at A and B are known and h
-  observed. Thus if the diameters at A and B are 4 and 12 in., the areas
-  are 12.57 and 113.1 sq. in., and [rho] = 9,
-
-    u = [root]81/80 [root](2gh) = 1.007 [root](2gh).
-
-  If the observed Venturi head is 12 ft.,
-
-    u = 28 ft. per sec.,
-
-  and the discharge of the main is
-
-    28 X 12.57 = 351 cub. ft. per sec.
-
-  [Illustration: FIG. 32.]
-
-  Hence by a simple observation of pressure difference, the flow in the
-  main at any moment can be determined. Notice that the pressure height
-  at C will be the same as at A except for a small loss h_f due to
-  friction and eddying between A and B. To get the pressure at the
-  throat very exactly Herschel surrounds it by an annular passage
-  communicating with the throat by several small holes, sometimes formed
-  in vulcanite to prevent corrosion. Though constructed to prevent
-  eddying as much as possible there is some eddy loss. The main effect
-  of this is to cause a loss of head between A and C which may vary from
-  a fraction of a foot to perhaps 5 ft. at the highest velocities at
-  which a meter can be used. The eddying also affects a little the
-  Venturi head h. Consequently an experimental coefficient must be
-  determined for each meter by tank measurement. The range of this
-  coefficient is, however, surprisingly small. If to allow for friction,
-  u = k[root]{[rho]^2/([rho]^2 - 1)}[root](2gh), then Herschel found
-  values of k from 0.97 to 1.0 for throat velocities varying from 8 to
-  28 ft. per sec. The meter is extremely convenient. At Staines
-  reservoirs there are two meters of this type on mains 94 in. in
-  diameter. Herschel contrived a recording arrangement which records the
-  variation of flow from hour to hour and also the total flow in any
-  given time. In Great Britain the meter is constructed by G. Kent, who
-  has made improvements in the recording arrangement.
-
-  [Illustration: FIG. 33.]
-
-  In the Deacon Waste Water Meter (fig. 33) a different principle is
-  used. A disk D, partly counter-balanced by a weight, is suspended in
-  the water flowing through the main in a conical chamber. The
-  unbalanced weight of the disk is supported by the impact of the water.
-  If the discharge of the main increases the disk rises, but as it rises
-  its position in the chamber is such that in consequence of the larger
-  area the velocity is less. It finds, therefore, a new position of
-  equilibrium. A pencil P records on a drum moved by clockwork the
-  position of the disk, and from this the variation of flow is inferred.
-
-  S 33. _Pressure, Velocity and Energy in Different Stream Lines._--The
-  equation of Bernoulli gives the variation of pressure and velocity
-  from point to point along a stream line, and shows that the total
-  energy of the flow across any two sections is the same. Two other
-  directions may be defined, one normal to the stream line and in the
-  plane containing its radius of curvature at any point, the other
-  normal to the stream line and the radius of curvature. For the
-  problems most practically useful it will be sufficient to consider the
-  stream lines as parallel to a vertical or horizontal plane. If the
-  motion is in a vertical plane, the action of gravity must be taken
-  into the reckoning; if the motion is in a horizontal plane, the terms
-  expressing variation of elevation of the filament will disappear.[3]
-
-  [Illustration: FIG. 34.]
-
-  Let AB, CD (fig. 34) be two consecutive stream lines, at present
-  assumed to be in a vertical plane, and PQ a normal to these lines
-  making an angle [phi] with the vertical. Let P, Q be two particles
-  moving along these lines at a distance PQ = ds, and let z be the
-  height of Q above the horizontal plane with reference to which the
-  energy is measured, v its velocity, and p its pressure. Then, if H is
-  the total energy at Q per unit of weight of fluid,
-
-    H = z + p/G + v^2/2g.
-
-  Differentiating, we get
-
-    dH = dz + dp/G + vdv/g,   (1)
-
-  for the increment of energy between Q and P. But
-
-    dz = PQ cos [phi] = ds cos [phi];
-
-    .: dH = dp/G + v dv/g + ds cos [phi],   (1a)
-
-  where the last term disappears if the motion is in a horizontal plane.
-
-  Now imagine a small cylinder of section [omega] described round PQ as
-  an axis. This will be in equilibrium under the action of its
-  centrifugal force, its weight and the pressure on its ends. But its
-  volume is [omega] ds and its weight G[omega]ds. Hence, taking the
-  components of the forces parallel to PQ--
-
-    [omega]dp = Gv^2[omega] ds/g[rho] - G[omega] cos [phi] ds,
-
-  where [rho] is the radius of curvature of the stream line at Q.
-  Consequently, introducing these values in (1),
-
-    dH = v^2 ds/g[rho] + v dv/g = (v/g)(v/[rho] + dv/ds) ds.   (2)
-
-
-  CURRENTS
-
-  S 34. _Rectilinear Current._--Suppose the motion is in parallel
-  straight stream lines (fig. 35) in a vertical plane. Then [rho] is
-  infinite, and from eq. (2), S 33,
-
-     dH = v dv/g.
-
-  Comparing this with (1) we see that
-
-    dz + dp/G = 0;
-
-    .: z + p/G = constant; (3)
-
-  or the pressure varies hydrostatically as in a fluid at rest. For two
-  stream lines in a horizontal plane, z is constant, and therefore p is
-  constant.
-
-  [Illustration: FIG. 35.]
-
-  _Radiating Current._--Suppose water flowing radially between
-  horizontal parallel planes, at a distance apart = [delta]. Conceive
-  two cylindrical sections of the current at radii r1 and r2, where the
-  velocities are v1 and v2, and the pressures p1 and p2. Since the flow
-  across each cylindrical section of the current is the same,
-
-    Q = 2[pi]r1[delta]v1 = 2[pi]r2[delta]v2
-
-    r1v1 = r2v2
-
-    r1/r2 = v2/v1.   (4)
-
-  The velocity would be infinite at radius 0, if the current could be
-  conceived to extend to the axis. Now, if the motion is steady,
-
-    H = p1/G + v1^2/2g = p2/G + v2^2/2g;
-      = p2/G + r1^2 + v1^2/r2^2 2g;
-
-    (p2- p1)/G = v1^2(1 - r1^2/r2^2)/2g;   (5)
-
-    p2/G = H - r1^2v1^2/r2^2 2g.   (6)
-
-  Hence the pressure increases from the interior outwards, in a way
-  indicated by the pressure columns in fig. 36, the curve through the
-  free surfaces of the pressure columns being, in a radial section, the
-  quasi-hyperbola of the form xy^2 = c^3. This curve is asymptotic to a
-  horizontal line, H ft. above the line from which the pressures are
-  measured, and to the axis of the current.
-
-  [Illustration: FIG. 36.]
-
-  _Free Circular Vortex._--A free circular vortex is a revolving mass of
-  water, in which the stream lines are concentric circles, and in which
-  the total head for each stream line is the same. Hence, if by any slow
-  radial motion portions of the water strayed from one stream line to
-  another, they would take freely the velocities proper to their new
-  positions under the action of the existing fluid pressures only.
-
-  For such a current, the motion being horizontal, we have for all the
-  circular elementary streams
-
-    H = p/G + v^2/2g = constant;
-
-    .: dH = dp/G + v dv/g = 0.   (7)
-
-  Consider two stream lines at radii r and r + dr (fig. 36). Then in
-  (2), S 33, [rho] = r and ds = dr,
-
-    v^2 dr/gr + v dv/g = 0,
-
-    dv/v = -dr/r,
-
-    v [oo] 1/r,   (8)
-
-  precisely as in a radiating current; and hence the distribution of
-  pressure is the same, and formulae 5 and 6 are applicable to this
-  case.
-
-  _Free Spiral Vortex._--As in a radiating and circular current the
-  equations of motion are the same, they will also apply to a vortex in
-  which the motion is compounded of these motions in any proportions,
-  provided the radial component of the motion varies inversely as the
-  radius as in a radial current, and the tangential component varies
-  inversely as the radius as in a free vortex. Then the whole velocity
-  at any point will be inversely proportional to the radius of the
-  point, and the fluid will describe stream lines having a constant
-  inclination to the radius drawn to the axis of the current. That is,
-  the stream lines will be logarithmic spirals. When water is delivered
-  from the circumference of a centrifugal pump or turbine into a
-  chamber, it forms a free vortex of this kind. The water flows spirally
-  outwards, its velocity diminishing and its pressure increasing
-  according to the law stated above, and the head along each spiral
-  stream line is constant.
-
-  S 35. _Forced Vortex._--If the law of motion in a rotating current is
-  different from that in a free vortex, some force must be applied to
-  cause the variation of velocity. The simplest case is that of a
-  rotating current in which all the particles have equal angular
-  velocity, as for instance when they are driven round by radiating
-  paddles revolving uniformly. Then in equation (2), S 33, considering
-  two circular stream lines of radii r and r + dr (fig. 37), we have
-  [rho] = r, ds = dr. If the angular velocity is [alpha], then v =
-  [alpha]r and dv = [alpha]dr. Hence
-
-    dH = [alpha]^2r dr/g + [alpha]^2r dr/g = 2[alpha]^2r dr/g.
-
-  Comparing this with (1), S 33, and putting dz = 0, because the motion
-  is horizontal,
-
-    dp/G + [alpha]^2r dr/g = 2[alpha]^2r dr/g,
-
-    dp/G = [alpha]^2rdr/g,
-
-    p/G = [alpha]^2/2g + constant.   (9)
-
-  Let p1, r1, v1 be the pressure, radius and velocity of one cylindrical
-  section, p2, r2, v2 those of another; then
-
-    p1/G - [alpha]^2r1^2/2g = p2/G - [alpha]^2r2^2/2g;
-
-    (p2 - p1)/G = [alpha]^2(r2^2 - r1^2)/2g = (v2^2 - v1^2)/2g.   (10)
-
-  That is, the pressure increases from within outwards in a curve which
-  in radial sections is a parabola, and surfaces of equal pressure are
-  paraboloids of revolution (fig. 37).
-
-  [Illustration: FIG. 37.]
-
-
-  DISSIPATION OF HEAD IN SHOCK
-
-  S 36. _Relation of Pressure and Velocity in a Stream in Steady Motion
-  when the Changes of Section of the Stream are Abrupt._--When a stream
-  changes section abruptly, rotating eddies are formed which dissipate
-  energy. The energy absorbed in producing rotation is at once
-  abstracted from that effective in causing the flow, and sooner or
-  later it is wasted by frictional resistances due to the rapid relative
-  motion of the eddying parts of the fluid. In such cases the work thus
-  expended internally in the fluid is too important to be neglected, and
-  the energy thus lost is commonly termed energy lost in shock. Suppose
-  fig. 38 to represent a stream having such an abrupt change of section.
-  Let AB, CD be normal sections at points where ordinary stream line
-  motion has not been disturbed and where it has been re-established.
-  Let [omega], p, v be the area of section, pressure and velocity at AB,
-  and [omega]1, p1, v1 corresponding quantities at CD. Then if no work
-  were expended internally, and assuming the stream horizontal, we
-  should have
-
-    p/G + v^2/2g = p1/G + v1^2/2g.   (1)
-
-  But if work is expended in producing irregular eddying motion, the
-  head at the section CD will be diminished.
-
-  Suppose the mass ABCD comes in a short time t to A'B'C'D'. The
-  resultant force parallel to the axis of the stream is
-
-    p[omega] + p0([omega]1 - [omega]) - p1[omega]1,
-
-  where p0 is put for the unknown pressure on the annular space between
-  AB and EF. The impulse of that force is
-
-    {p[omega] + p0([omega]1 - [omega]) - p1[omega]1} t.
-
-  [Illustration: FIG. 38.]
-
-  The horizontal change of momentum in the same time is the difference
-  of the momenta of CDC'D' and ABA'B', because the amount of momentum
-  between A'B' and CD remains unchanged if the motion is steady. The
-  volume of ABA'B' or CDC'D', being the inflow and outflow in the time
-  t, is Qt = [omega]vt = [omega]1v1t, and the momentum of these masses
-  is (G/g)Qvt and (G/g)Qv1t. The change of momentum is therefore
-  (G/g)Qt(v1 - v). Equating this to the impulse,
-
-    {p[omega] + p0([omega]1 - [omega]) - p1[omega]1}t = (G/g)Qt(v1 - v).
-
-  Assume that p0 = p, the pressure at AB extending unchanged through the
-  portions of fluid in contact with AE, BF which lie out of the path of
-  the stream. Then (since Q = [omega]1v1)
-
-    (p - p1) = (G/g) v1 (v1 - v);
-
-    p/G - p1/G = v1 (v1 - v)/g;   (2)
-
-    p/G + v^2/2g = p1/G + v1^2/2g + (v - v1)^2/2g.   (3)
-
-  This differs from the expression (1), S 29, obtained for cases where
-  no sensible internal work is done, by the last term on the right. That
-  is, (v - v1)^2/2g has to be added to the total head at CD, which is
-  p1/G + v1^2/2g, to make it equal to the total head at AB, or (v -
-  v1)^2/2g is the head lost in shock at the abrupt change of section.
-  But (v - v1) is the relative velocity of the two parts of the stream.
-  Hence, when an abrupt change of section occurs, the head due to the
-  relative velocity is lost in shock, or (v - v1)^2/2g foot-pounds of
-  energy is wasted for each pound of fluid. Experiment verifies this
-  result, so that the assumption that p0 = p appears to be admissible.
-
-  If there is no shock,
-
-    p1/G = p/G + (v^2 - v1^2)/2g.
-
-  If there is shock,
-
-    p1/G = p/G - v1(v1 - v)/g.
-
-  Hence the pressure head at CD in the second case is less than in the
-  former by the quantity (v - v1)^2/2g, or, putting [omega]1v1 =
-  [omega]v, by the quantity
-
-    (v^2/2g)(1 - [omega]/[omega]1)^2.   (4)
-
-
-  V. THEORY OF THE DISCHARGE FROM ORIFICES AND MOUTHPIECES
-
-  [Illustration: FIG. 39.]
-
-  S 37. _Minimum Coefficient of Contraction. Re-entrant Mouthpiece of
-  Borda._--In one special case the coefficient of contraction can be
-  determined theoretically, and, as it is the case where the convergence
-  of the streams approaching the orifice takes place through the
-  greatest possible angle, the coefficient thus determined is the
-  minimum coefficient.
-
-  Let fig. 39 represent a vessel with vertical sides, OO being the free
-  water surface, at which the pressure is p_a. Suppose the liquid issues
-  by a horizontal mouthpiece, which is re-entrant and of the greatest
-  length which permits the jet to spring clear from the inner end of the
-  orifice, without adhering to its sides. With such an orifice the
-  velocity near the points CD is negligible, and the pressure at those
-  points may be taken equal to the hydrostatic pressure due to the depth
-  from the free surface. Let [Omega] be the area of the mouthpiece AB,
-  [omega] that of the contracted jet aa Suppose that in a short time t,
-  the mass OOaa comes to the position O'O' a'a'; the impulse of the
-  horizontal external forces acting on the mass during that time is
-  equal to the horizontal change of momentum.
-
-  The pressure on the side OC of the mass will be balanced by the
-  pressure on the opposite side OE, and so for all other portions of the
-  vertical surfaces of the mass, excepting the portion EF opposite the
-  mouthpiece and the surface AaaB of the jet. On EF the pressure is
-  simply the hydrostatic pressure due to the depth, that is, (p_a + Gh).
-  On the surface and section AaaB of the jet, the horizontal resultant
-  of the pressure is equal to the atmospheric pressure p_a acting on the
-  vertical projection AB of the jet; that is, the resultant pressure is
-  -p_a[Omega]. Hence the resultant horizontal force for the whole mass
-  OOaa is (p_a + Gh)[Omega] - p_a[Omega] = Gh[Omega]. Its impulse in the
-  time t is Gh[Omega]t. Since the motion is steady there is no change of
-  momentum between O'O' and aa. The change of horizontal momentum is,
-  therefore, the difference of the horizontal momentum lost in the space
-  OOO'O' and gained in the space aaa'a'. In the former space there is no
-  horizontal momentum.
-
-  The volume of the space aaa'a' is [omega]vt; the mass of liquid in
-  that space is (G/g)[omega]vt; its momentum is (G/g)[omega]v^2t.
-  Equating impulse to momentum gained,
-
-    Gh[Omega] = (G/g)[omega]v^2t;
-
-    .: [omega]/[Omega] = gh/v^2
-
-  But
-
-    v^2 = 2gh, and [omega]/[Omega] = c_c;
-
-    .: [omega]/[Omega] = 1/2 = c_c;
-
-  a result confirmed by experiment with mouthpieces of this kind. A
-  similar theoretical investigation is not possible for orifices in
-  plane surfaces, because the velocity along the sides of the vessel in
-  the neighbourhood of the orifice is not so small that it can be
-  neglected. The resultant horizontal pressure is therefore greater than
-  Gh[Omega], and the contraction is less. The experimental values of the
-  coefficient of discharge for a re-entrant mouthpiece are 0.5149
-  (Borda), 0.5547 (Bidone), 0.5324 (Weisbach), values which differ
-  little from the theoretical value, 0.5, given above.
-
-  [Illustration: FIG. 40.]
-
-  S 38. _Velocity of Filaments issuing in a Jet._--A jet is composed of
-  fluid filaments or elementary streams, which start into motion at some
-  point in the interior of the vessel from which the fluid is
-  discharged, and gradually acquire the velocity of the jet. Let Mm,
-  fig. 40 be such a filament, the point M being taken where the velocity
-  is insensibly small, and m at the most contracted section of the jet,
-  where the filaments have become parallel and exercise uniform mutual
-  pressure. Take the free surface AB for datum line, and let p1, v1, h1,
-  be the pressure, velocity and depth below datum at M; p, v, h, the
-  corresponding quantities at m. Then S 29, eq. (3a),
-
-    v1^2/2g + p1/G - h1 = v^2/2g + p/G - h   (1)
-
-  But at M, since the velocity is insensible, the pressure is the
-  hydrostatic pressure due to the depth; that is v1 = 0, p1 = p_a + Gh1.
-  At m, p = p_a, the atmospheric pressure round the jet. Hence,
-  inserting these values,
-
-    0 + p_a/G + h1 - h1 = v^2/2g + p_a/G - h;
-
-    v^2/2g = h;   (2)
-
-    or v = [root](2gh) = 8.025V [root]h.   (2a)
-
-  [Illustration: FIG. 41.]
-
-  That is, neglecting the viscosity of the fluid, the velocity of
-  filaments at the contracted section of the jet is simply the velocity
-  due to the difference of level of the free surface in the reservoir
-  and the orifice. If the orifice is small in dimensions compared with
-  h, the filaments will all have nearly the same velocity, and if h is
-  measured to the centre of the orifice, the equation above gives the
-  mean velocity of the jet.
-
-  _Case of a Submerged Orifice._--Let the orifice discharge below the
-  level of the tail water. Then using the notation shown in fig. 41, we
-  have at M, v1 = 0, p1 = Gh; + p_a at m, p = Gh3 + p_a. Inserting these
-  values in (3), S 29,
-
-    0 + h1 + p_a/G - h1 = v^2/2g + h3 - h2 + p_a/G;
-
-    v^2/2g = h2 - h3 = h,   (3)
-
-  where h is the difference of level of the head and tail water, and may
-  be termed the _effective head_ producing flow.
-
-  [Illustration: FIG. 42.]
-
-  _Case where the Pressures are different on the Free Surface and at the
-  Orifice._--Let the fluid flow from a vessel in which the pressure is
-  p0 into a vessel in which the pressure is p, fig. 42. The pressure p0
-  will produce the same effect as a layer of fluid of thickness p0/G
-  added to the head water; and the pressure p, will produce the same
-  effect as a layer of thickness p/G added to the tail water. Hence the
-  effective difference of level, or effective head producing flow, will
-  be
-
-    h = h0 + p0/G - p/G;
-
-  and the velocity of discharge will be
-
-    v = [root][2g {h0 + (p0 - p)/G}].   (4)
-
-  We may express this result by saying that differences of pressure at
-  the free surface and at the orifice are to be reckoned as part of the
-  effective head.
-
-  Hence in all cases thus far treated the velocity of the jet is the
-  velocity due to the effective head, and the discharge, allowing for
-  contraction of the jet, is
-
-    Q = c[omega]v = c[omega] [root](2gh),   (5)
-
-  where [omega] is the area of the orifice, c[omega] the area of the
-  contracted section of the jet, and h the effective head measured to
-  the centre of the orifice. If h and [omega] are taken in feet, Q is in
-  cubic feet per second.
-
-  It is obvious, however, that this formula assumes that all the
-  filaments have sensibly the same velocity. That will be true for
-  horizontal orifices, and very approximately true in other cases, if
-  the dimensions of the orifice are not large compared with the head h.
-  In large orifices in say a vertical surface, the value of h is
-  different for different filaments, and then the velocity of different
-  filaments is not sensibly the same.
-
-
-  SIMPLE ORIFICES--HEAD CONSTANT
-
-  [Illustration: FIG. 43.]
-
-  S 39. _Large Rectangular Jets from Orifices in Vertical Plane
-  Surfaces._--Let an orifice in a vertical plane surface be so formed
-  that it produces a jet having a rectangular contracted section with
-  vertical and horizontal sides. Let b (fig. 43) be the breadth of the
-  jet, h1 and h2 the depths below the free surface of its upper and
-  lower surfaces. Consider a lamina of the jet between the depths h and
-  h + dh. Its normal section is bdh, and the velocity of discharge
-  [root](2gh). The discharge per second in this lamina is therefore
-  b[root](2gh) dh, and that of the whole jet is therefore
-         _
-        /h2
-    Q = |   b [root](2gh) dh
-       _/h1
-
-    = 2/3 b[root](2g) {h2^(3/2) - h1^(3/2)},   (6)
-
-  where the first factor on the right is a coefficient depending on the
-  form of the orifice.
-
-  Now an orifice producing a rectangular jet must itself be very
-  approximately rectangular. Let B be the breadth, H1, H2, the depths to
-  the upper and lower edges of the orifice. Put
-
-    b [h2^(3/2) - h1^(3/2)] / B [H2^(3/2) - H1^(3/2)] = c.   (7)
-
-  Then the discharge, in terms of the dimensions of the orifice, instead
-  of those of the jet, is
-
-    Q = (2/3)cB [root](2g) [H2^(3/2) - H1^(3/2)],   (8)
-
-  the formula commonly given for the discharge of rectangular orifices.
-  The coefficient c is not, however, simply the coefficient of
-  contraction, the value of which is
-
-    b(h2 - h1)/B(H2 - H1),
-
-  and not that given in (7). It cannot be assumed, therefore, that c in
-  equation (8) is constant, and in fact it is found to vary for
-  different values of B/H2 and B/H1, and must be ascertained
-  experimentally.
-
-  _Relation between the Expressions (5) and (8)._--For a rectangular
-  orifice the area of the orifice is [omega] = B(H2 - H1), and the
-  depth measured to its centre is (1/2)(H2 + H1). Putting these values
-  in (5),
-
-    Q1 = cB(H2 - H1) [root]{g(H2 + H1)}.
-
-  From (8) the discharge is
-
-    Q2 = (2/3)cB [root](2g) [H2^(3/2) - H1^(3/2)].
-
-  Hence, for the same value of c in the two cases,
-
-    Q2/Q1 = (2/3)[H2^(3/2) - H1^(3/2)] / [(H2 - H1)[root]{(H2 + H1)/2}].
-
-  Let H1/H2 = [sigma], then
-
-    Q2/Q1 = 0.9427(1 - [sigma]^(3/2)) /
-      {1 - [sigma] [root]{(1 + [sigma])}}.   (9)
-
-  If H1 varies from 0 to [infinity], [sigma]( = H1/H2) varies from 0 to
-  1. The following table gives values of the two estimates of the
-  discharge for different values of [sigma]:--
-
-    +------------------+--------+------------------+--------+
-    | H1/H2 = [sigma]. | Q2/Q1. | H1/H2 = [sigma]. | Q2/Q1. |
-    +------------------+--------+------------------+--------+
-    |       0.0        |  .943  |       0.8        |   .999 |
-    |       0.2        |  .979  |       0.9        |   .999 |
-    |       0.5        |  .995  |       1.0        |  1.000 |
-    |       0.7        |  .998  |                  |        |
-    +------------------+--------+------------------+--------+
-
-  Hence it is obvious that, except for very small values of [sigma], the
-  simpler equation (5) gives values sensibly identical with those of
-  (8). When [sigma]<0.5 it is better to use equation (8) with values of
-  c determined experimentally for the particular proportions of orifice
-  which are in question.
-
-  [Illustration: FIG. 44.]
-
-  S 40. _Large Jets having a Circular Section from Orifices in a
-  Vertical Plane Surface._--Let fig. 44 represent the section of the
-  jet, OO being the free surface level in the reservoir. The discharge
-  through the horizontal strip aabb, of breadth aa = b, between the
-  depths h1 + y and h1 + y + dy, is
-
-    dQ = b [root]{2g(h1 + y)} dy.
-
-  The whole discharge of the jet is
-         _
-        /d
-    Q = |  b [root]{2g(h1 + y)} dy.
-       _/0
-
-  But b = d sin [phi]; y = (1/2)d(1 - cos [phi]); dy = (1/2)d sin [phi]
-  d[phi]. Let [epsilon] = d/(2h1 + d), then
-
-                                       _
-                                      /[pi]
-    Q = (1/2)d^2 [root]{2g(h1 + d/2)} |  sin^2 [phi][root]{1 - [epsilon] cos [phi]} d[phi].
-                                     _/0
-
-  From eq. (5), putting [omega] = [pi]d^2/4, h = h1 + d/2, c = 1 when d
-  is the diameter of the jet and not that of the orifice,
-
-    Q1 = (1/4)[pi]d^2 [root]{2g (h1 + d/2)},
-                    _
-                   /[pi]
-    Q/Q1 = 2/[pi]  |   sin^2 [phi] [root]{1 - [epsilon] cos [phi]} d[phi].
-                  _/0
-
-  For
-
-    h1 = [infinity], [epsilon] = 0 and Q/Q1 = 1;
-
-  and for
-
-    h1 = 0, [epsilon] = 1 and Q/Q1 = 0.96.
-
-  So that in this case also the difference between the simple formula
-  (5) and the formula above, in which the variation of head at different
-  parts of the orifice is taken into account, is very small.
-
-
-  NOTCHES AND WEIRS
-
-  S 41. _Notches, Weirs and Byewashes._--A notch is an orifice extending
-  up to the free surface level in the reservoir from which the discharge
-  takes place. A weir is a structure over which the water flows, the
-  discharge being in the same conditions as for a notch. The formula of
-  discharge for an orifice of this kind is ordinarily deduced by putting
-  H1 = 0 in the formula for the corresponding orifice, obtained as in
-  the preceding section. Thus for a rectangular notch, put H1 = 0 in
-  (8). Then
-
-    Q = (2/3)cB [root](2g) H^(3/2),   (11)
-
-  where H is put for the depth to the crest of the weir or the bottom of
-  the notch. Fig. 45 shows the mode in which the discharge occurs in the
-  case of a rectangular notch or weir with a level crest. As, the free
-  surface level falls very sensibly near the notch, the head H should be
-  measured at some distance back from the notch, at a point where the
-  velocity of the water is very small.
-
-  Since the area of the notch opening is BH, the above formula is of the
-  form
-
-    Q = c X BH X k [root](2gH),
-
-  where k is a factor depending on the form of the notch and expressing
-  the ratio of the mean velocity of discharge to the velocity due to the
-  depth H.
-
-  S 42. _Francis's Formula for Rectangular Notches._--The jet discharged
-  through a rectangular notch has a section smaller than BH, (a) because
-  of the fall of the water surface from the point where H is measured
-  towards the weir, (b) in consequence of the crest contraction, (c) in
-  consequence of the end contractions. It may be pointed out that while
-  the diminution of the section of the jet due to the surface fall and
-  to the crest contraction is proportional to the length of the weir,
-  the end contractions have nearly the same effect whether the weir is
-  wide or narrow.
-
-  [Illustration: FIG. 45.]
-
-  J. B. Francis's experiments showed that a perfect end contraction,
-  when the heads varied from 3 to 24 in., and the length of the weir was
-  not less than three times the head, diminished the effective length of
-  the weir by an amount approximately equal to one-tenth of the head.
-  Hence, if l is the length of the notch or weir, and H the head
-  measured behind the weir where the water is nearly still, then the
-  width of the jet passing through the notch would be l - 0.2H, allowing
-  for two end contractions. In a weir divided by posts there may be more
-  than two end contractions. Hence, generally, the width of the jet is l
-  - 0.1nH, where n is the number of end contractions of the stream. The
-  contractions due to the fall of surface and to the crest contraction
-  are proportional to the width of the jet. Hence, if cH is the
-  thickness of the stream over the weir, measured at the contracted
-  section, the section of the jet will be c(l - 0.1nH)H and (S 41) the
-  mean velocity will be 2/3 [root](2gH). Consequently the discharge
-  will be given by an equation of the form
-
-    Q = (2/3)c (l - 0.1nH)H [root](2gH)
-      = 5.35c (l - 0.1nH) H^(3/2).
-
-  This is Francis's formula, in which the coefficient of discharge c is
-  much more nearly constant for different values of l and h than in the
-  ordinary formula. Francis found for c the mean value 0.622, the weir
-  being sharp-edged.
-
-  S 43. _Triangular Notch_ (fig. 46).--Consider a lamina issuing between
-  the depths h and h + dh. Its area, neglecting contraction, will be
-  bdh, and the velocity at that depth is [root](2gh). Hence the
-  discharge for this lamina is
-
-    b[root](2gh) dh.
-
-  But
-
-    B/b = H/(H - h); b = B(H - h)/H.
-
-  Hence discharge of lamina
-
-    = B(H - h) [root](2gh) dh/H;
-
-  and total discharge of notch
-                       _
-                      /H
-    = Q = B[root](2g) |  (H - h)h^(1/2) dh/H
-                     _/0
-
-        = (4/15) B[root](2g)H^(3/2).
-
-  or, introducing a coefficient to allow for contraction,
-
-    Q = (4/15)cB [root](2g) H^(1/2),
-
-  [Illustration: FIG. 46.]
-
-  When a notch is used to gauge a stream of varying flow, the ratio B/H
-  varies if the notch is rectangular, but is constant if the notch is
-  triangular. This led Professor James Thomson to suspect that the
-  coefficient of discharge, c, would be much more constant with
-  different values of H in a triangular than in a rectangular notch, and
-  this has been experimentally shown to be the case. Hence a triangular
-  notch is more suitable for accurate gaugings than a rectangular notch.
-  For a sharp-edged triangular notch Professor J. Thomson found c =
-  0.617. It will be seen, as in S 41, that since (1/2)BH is the area of
-  section of the stream through the notch, the formula is again of the
-  form
-
-    Q = c X (1/2)BH X k[root](2gH),
-
-  where k = 8/15 is the ratio of the mean velocity in the notch to the
-  velocity at the depth H. It may easily be shown that for all notches
-  the discharge can be expressed in this form.
-
-    _Coefficients for the Discharge over Weirs, derived from the
-    Experiments of T. E. Blackwell. When more than one experiment was
-    made with the same head, and the results were pretty uniform, the
-    resulting coefficients are marked with an (*). The effect of the
-    converging wing-boards is very strongly marked._
-
-    +----------+-------------+---------------------------------+-----------------------------------------+
-    |          |             |       Planks 2 in. thick,       |                                         |
-    | Heads in | Sharp Edge. |        square on Crest.         |            Crests 3 ft. wide.           |
-    |  inches  +------+------+-----+-----+-------+-------------+------+------+------+------+------+------+
-    | measured |      |      |     |     |       |10 ft. long, | 3 ft.| 3 ft.| 3 ft.| 6 ft.|10 ft.|10 ft.|
-    |from still| 3 ft.|10 ft.|3 ft.|6 ft.| 10 ft.| wing-boards | long,| long,| long,| long,| long,| long,|
-    | Water in | long.| long.|long.|long.| long. |  making an  |level.|fall 1|fall 1|level.|level.|fall 1|
-    |Reservoir.|      |      |     |     |       |angle of 60  |      |in 18.|in 12.|      |      |in 18.|
-    +----------+------+------+-----+-----+-------+-----deg.----+------+------+------+------+------+------+
-    |     1    | .677 | .809 |.467 |.459 |.435[4]|    .754     | .452 | .545 | .467 |  ..  | .381 | .467 |
-    |     2    | .675 | .803 |.509*|.561 |.585*  |    .675     | .482 | .546 | .533 |  ..  | .479*| .495*|
-    |     3    | .630 | .642*|.563*|.597*|.569*  |     ..      | .441 | .537 | .539 | .492*|  ..  |  ..  |
-    |     4    | .617 | .656 |.549 |.575 |.602*  |    .656     | .419 | .431 | .455 | .497*|  ..  | .515 |
-    |     5    | .602 | .650*|.588 |.601*|.609*  |    .671     | .479 | .516 |  ..  |  ..  | .518 |  ..  |
-    |     6    | .593 |  ..  |.593*|.608*|.576*  |     ..      | .501*|  ..  | .531 | .507 | .513 | .543 |
-    |     7    |  ..  |  ..  |.617*|.608*|.576*  |     ..      | .488 | .513 | .527 | .497 |  ..  |  ..  |
-    |     8    |  ..  | .581 |.606*|.590*|.548*  |     ..      | .470 | .491 |  ..  |  ..  | .468 | .507 |
-    |     9    |  ..  | .530 |.600 |.569*|.558*  |     ..      | .476 | .492*| .498 | .480*| .486 |  ..  |
-    |    10    |  ..  |  ..  |.614*|.539 |.534*  |     ..      |  ..  |  ..  |  ..  | .465*| .455 |  ..  |
-    |    12    |  ..  |  ..  | ..  |.525 |.534*  |     ..      |  ..  |  ..  |  ..  | .467*|  ..  |  ..  |
-    |    14    |  ..  |  ..  | ..  |.549*| ..    |     ..      |  ..  |  ..  |  ..  |  ..  |  ..  |  ..  |
-    +----------+------+------+-----+-----+-------+-------------+------+------+------+------+------+------+
-
-  [Illustration: FIG. 47.]
-
-  S 44. _Weir with a Broad Sloping Crest._--Suppose a weir formed with a
-  broad crest so sloped that the streams flowing over it have a movement
-  sensibly rectilinear and uniform (fig. 47). Let the inner edge be so
-  rounded as to prevent a crest contraction. Consider a filament aa',
-  the point a being so far back from the weir that the velocity of
-  approach is negligible. Let OO be the surface level in the reservoir,
-  and let a be at a height h" below OO, and h' above a'. Let h be the
-  distance from OO to the weir crest and e the thickness of the stream
-  upon it. Neglecting atmospheric pressure, which has no influence, the
-  pressure at a is Gh"; at a' it is Gz. If v be the velocity at a',
-
-    v^2/2g = h' + h" - z = h - e;
-
-    Q = be [root]{2g(h - e)}.
-
-  Theory does not furnish a value for e, but Q = 0 for e = 0 and for e =
-  h. Q has therefore a maximum for a value of e between 0 and h,
-  obtained by equating dQ/de to zero. This gives e = (2/3)h, and,
-  inserting this value,
-
-    Q = 0.385 bh [root](2gh),
-
-  as a maximum value of the discharge with the conditions assigned.
-  Experiment shows that the actual discharge is very approximately equal
-  to this maximum, and the formula is more legitimately applicable to
-  the discharge over broad-crested weirs and to cases such as the
-  discharge with free upper surface through large masonry sluice
-  openings than the ordinary weir formula for sharp-edged weirs. It
-  should be remembered, however, that the friction on the sides and
-  crest of the weir has been neglected, and that this tends to reduce a
-  little the discharge. The formula is equivalent to the ordinary weir
-  formula with c = 0.577.
-
-
-  SPECIAL CASES OF DISCHARGE FROM ORIFICES
-
-  S 45. _Cases in which the Velocity of Approach needs to be taken into
-  Account. Rectangular Orifices and Notches._--In finding the velocity
-  at the orifice in the preceding investigations, it has been assumed
-  that the head h has been measured from the free surface of still water
-  above the orifice. In many cases which occur in practice the channel
-  of approach to an orifice or notch is not so large, relatively to the
-  stream through the orifice or notch, that the velocity in it can be
-  disregarded.
-
-  [Illustration: FIG. 48.]
-
-  Let h1, h2 (fig. 48) be the heads measured from the free surface to
-  the top and bottom edges of a rectangular orifice, at a point in the
-  channel of approach where the velocity is u. It is obvious that a fall
-  of the free surface,
-
-    [h] = u^2/2g
-
-  has been somewhere expended in producing the velocity u, and hence the
-  true heads measured in still water would have been h1 + [h] and h2 +
-  [h]. Consequently the discharge, allowing for the velocity of
-  approach, is
-
-    Q = (2/3)cb [root](2g) {(h2 + [h])^(3/2) - (h1 + [h])^(3/2)}.   (1)
-
-  And for a rectangular notch for which h1 = 0, the discharge is
-
-    Q = (2/3)cb [root](2g) {(h2 + [h])^(3/2) - [h]^(3/2)}.   (2)
-
-  In cases where u can be directly determined, these formulae give the
-  discharge quite simply. When, however, u is only known as a function
-  of the section of the stream in the channel of approach, they become
-  complicated. Let [Omega] be the sectional area of the channel where h1
-  and h2 are measured. Then u = Q/[Omega] and [h] = Q^2/2g [Omega]^2.
-
-  This value introduced in the equations above would render them
-  excessively cumbrous. In cases therefore where [Omega] only is known,
-  it is best to proceed by approximation. Calculate an approximate value
-  Q' of Q by the equation
-
-    Q' = (2/3)cb [root](2g) {h2^(3/2) - h1^(3/2)}.
-
-  Then [h] = Q'^2/2g[Omega]^2 nearly. This value of [h] introduced in the
-  equations above will give a second and much more approximate value of
-  Q.
-
-  [Illustration: FIG. 49.]
-
-  S 46. _Partially Submerged Rectangular Orifices and Notches._--When
-  the tail water is above the lower but below the upper edge of the
-  orifice, the flow in the two parts of the orifice, into which it is
-  divided by the surface of the tail water, takes place under different
-  conditions. A filament M1m1 (fig. 49) in the upper part of the orifice
-  issues with a head h' which may have any value between h1 and h. But a
-  filament M2m2 issuing in the lower part of the orifice has a velocity
-  due to h" - h"', or h, simply. In the upper part of the orifice the
-  head is variable, in the lower constant. If Q1, Q2 are the discharges
-  from the upper and lower parts of the orifice, b the width of the
-  orifice, then
-
-    Q1 = (2/3)cb [root](2g) {h^(3/2) - h1^(3/2)}
-                                                  (3)
-    Q1 = cb (h2 - h) [root](2gh).
-
-  In the case of a rectangular notch or weir, h1 = 0. Inserting this
-  value, and adding the two portions of the discharge together, we get
-  for a drowned weir
-
-    Q = cb[root](2gh) (h2 - h/3),   (4)
-
-  where h is the difference of level of the head and tail water, and h2
-  is the head from the free surface above the weir to the weir crest
-  (fig. 50).
-
-  From some experiments by Messrs A. Fteley and F.P. Stearns (_Trans.
-  Am. Soc. C.E._, 1883, p. 102) some values of the coefficient c can be
-  reduced
-
-    h3/h2     c     h3/h2      c
-
-     0.1    0.629    0.7     0.578
-     0.2    0.614    0.8     0.583
-     0.3    0.600    0.9     0.596
-     0.4    0.590    0.95    0.607
-     0.5    0.582    1.00    0.628
-     0.6    0.578
-
-  If velocity of approach is taken into account, let [h] be the
-  head due to that velocity; then, adding [h] to each of the
-  heads in the equations (3), and reducing, we get for a weir
-
-    Q = cb [root]{2g} [(h2 + [h]) (h + [h])^(1/2) - (1/3)(h + [h])^(3/2)
-      - (2/3)[h]^(3/2)];   (5)
-
-  an equation which may be useful in estimating flood discharges.
-
-  [Illustration: FIG. 50.]
-
-  _Bridge Piers and other Obstructions in Streams._--When the piers of a
-  bridge are erected in a stream they create an obstruction to the flow
-  of the stream, which causes a difference of surface-level above and
-  below the pier (fig. 51). If it is necessary to estimate this
-  difference of level, the flow between the piers may be treated as if
-  it occurred over a drowned weir. But the value of c in this case is
-  imperfectly known.
-
-  S 47. _Bazin's Researches on Weirs._--H. Bazin has executed a long
-  series of researches on the flow over weirs, so systematic and
-  complete that they almost supersede other observations. The account of
-  them is contained in a series of papers in the _Annales des Ponts et
-  Chaussees_ (October 1888, January 1890, November 1891, February 1894,
-  December 1896, 2nd trimestre 1898). Only a very abbreviated account
-  can be given here. The general plan of the experiments was to
-  establish first the coefficients of discharge for a standard weir
-  without end contractions; next to establish weirs of other types in
-  series with the standard weir on a channel with steady flow, to
-  compare the observed heads on the different weirs and to determine
-  their coefficients from the discharge computed at the standard weir. A
-  channel was constructed parallel to the Canal de Bourgogne, taking
-  water from it through three sluices 0.3 X 1.0 metres. The water enters
-  a masonry chamber 15 metres long by 4 metres wide where it is stilled
-  and passes into the canal at the end of which is the standard weir.
-  The canal has a length of 15 metres, a width of 2 metres and a depth
-  of 0.6 metres. From this extends a channel 200 metres in length with a
-  slope of 1 mm. per metre. The channel is 2 metres wide with vertical
-  sides. The channels were constructed of concrete rendered with cement.
-  The water levels were taken in chambers constructed near the canal, by
-  floats actuating an index on a dial. Hook gauges were used in
-  determining the heads on the weirs.
-
-  [Illustration: FIG. 51.]
-
-  _Standard Weir._--The weir crest was 3.72 ft. above the bottom of the
-  canal and formed by a plate 1/4 in. thick. It was sharp-edged with free
-  overfall. It was as wide as the canal so that end contractions were
-  suppressed, and enlargements were formed below the crest to admit air
-  under the water sheet. The channel below the weir was used as a
-  gauging tank. Gaugings were made with the weir 2 metres in length and
-  afterwards with the weir reduced to 1 metre and 0.5 metre in length,
-  the end contractions being suppressed in all cases. Assuming the
-  general formula
-
-    Q = mlh [root](2gh),   (1)
-
-  Bazin arrives at the following values of _m_:--
-
-    _Coefficients of Discharge of Standard Weir._
-
-    +----------------+--------------+--------+
-    | Head h metres. | Head h feet. |    m   |
-    +----------------+--------------+--------+
-    |      0.05      |     .164     | 0.4485 |
-    |      0.10      |     .328     | 0.4336 |
-    |      0.15      |     .492     | 0.4284 |
-    |      0.20      |     .656     | 0.4262 |
-    |      0.25      |     .820     | 0.4259 |
-    |      0.30      |     .984     | 0.4266 |
-    |      0.35      |    1.148     | 0.4275 |
-    |      0.40      |    1.312     | 0.4286 |
-    |      0.45      |    1.476     | 0.4299 |
-    |      0.50      |    1.640     | 0.4313 |
-    |      0.55      |    1.804     | 0.4327 |
-    |      0.60      |    1.968     | 0.4341 |
-    +----------------+--------------+--------+
-
-  Bazin compares his results with those of Fteley and Stearns in 1877
-  and 1879, correcting for a different velocity of approach, and finds a
-  close agreement.
-
-  _Influence of Velocity of Approach._--To take account of the velocity
-  of approach u it is usual to replace h in the formula by h + au^2/2g
-  where [alpha] is a coefficient not very well ascertained. Then
-
-    Q = [mu]l (h + [alpha]u^2/2g) [root]{2g(h + [alpha]u^2/2g)}
-      = [mu]lh [root](2gh)(1 + [alpha]u^2/2gh)^(3/2).   (2)
-
-  The original simple equation can be used if
-
-    m = [mu](1 + [alpha]u^2/2gh)^(3/2)
-
-  or very approximately, since u^2/2gh is small,
-
-    m = [mu](1 + (3/2)[alpha]u^2/2gh).   (3)
-
-  [Illustration: FIG. 52.]
-
-  Now if p is the height of the weir crest above the bottom of the canal
-  (fig. 52), u = Q/l(p + h). Replacing Q by its value in (1)
-
-    u^2/2gh = Q^2/{2ghl^2(p + h)^2} = m^2{h/(p + h)}^2,   (4)
-
-  so that (3) may be written
-
-    m = [mu][1 + k{h/(p + h)}^2].   (5)
-
-  Gaugings were made with weirs of 0.75, 0.50, 0.35, and 0.24 metres
-  height above the canal bottom and the results compared with those of
-  the standard weir taken at the same time. The discussion of the
-  results leads to the following values of m in the general equation
-  (1):--
-
-    m = [mu](1 + 2.5u^2/2gh)
-      = [mu][1 + 0.55 {h/(p + h)}^2].
-
-  Values of [mu]--
-
-    +----------------+--------------+--------+
-    | Head h metres. | Head h feet. |  [mu]  |
-    +----------------+--------------+--------+
-    |      0.05      |     .164     | 0.4481 |
-    |      0.10      |     .328     | 0.4322 |
-    |      0.20      |     .656     | 0.4215 |
-    |      0.30      |     .984     | 0.4174 |
-    |      0.40      |    1.312     | 0.4144 |
-    |      0.50      |    1.640     | 0.4118 |
-    |      0.60      |    1.968     | 0.4092 |
-    +----------------+--------------+--------+
-
-  An approximate formula for [mu] is:
-
-    [mu] = 0.405 + 0.003/h (h in metres)
-
-    [mu] = 0.405 + 0.01/h (h in feet).
-
-  _Inclined Weirs._---Experiments were made in which the plank weir was
-  inclined up or down stream, the crest being sharp and the end
-  contraction suppressed. The following are coefficients by which the
-  discharge of a vertical weir should be multiplied to obtain the
-  discharge of the inclined weir.
-
-                                      Coefficient.
-    Inclination up stream      1 to 1     0.93
-         "           "         3 to 2     0.94
-         "           "         3 to 1     0.96
-    Vertical weir                         1.00
-    Inclination down stream    3 to 1     1.04
-         "           "         3 to 2     1.07
-         "           "         1 to 1     1.10
-         "           "         1 to 2     1.12
-         "           "         1 to 4     1.09
-
-  The coefficient varies appreciably, if h/p approaches unity, which
-  case should be avoided.
-
-  In all the preceding cases the sheet passing over the weir is detached
-  completely from the weir and its under-surface is subject to
-  atmospheric pressure. These conditions permit the most exact
-  determination of the coefficient of discharge. If the sides of the
-  canal below the weir are not so arranged as to permit the access of
-  air under the sheet, the phenomena are more complicated. So long as
-  the head does not exceed a certain limit the sheet is detached from
-  the weir, but encloses a volume of air which is at less than
-  atmospheric pressure, and the tail water rises under the sheet. The
-  discharge is a little greater than for free overfall. At greater head
-  the air disappears from below the sheet and the sheet is said to be
-  "drowned." The drowned sheet may be independent of the tail water
-  level or influenced by it. In the former case the fall is followed by
-  a rapid, terminating in a standing wave. In the latter case when the
-  foot of the sheet is drowned the level of the tail water influences
-  the discharge even if it is below the weir crest.
-
-  [Illustration: FIG. 53.]
-
-  [Illustration: FIG. 54.]
-
-  _Weirs with Flat Crests._--The water sheet may spring clear from the
-  upstream edge or may adhere to the flat crest falling free beyond the
-  down-stream edge. In the former case the condition is that of a
-  sharp-edged weir and it is realized when the head is at least double
-  the width of crest. It may arise if the head is at least 1(1/2) the
-  width of crest. Between these limits the condition of the sheet is
-  unstable. When the sheet is adherent the coefficient m depends on the
-  ratio of the head h to the width of crest c (fig. 53), and is given by
-  the equation m = m1 [0.70 + 0.185h/c], where m1 is the coefficient for
-  a sharp-edged weir in similar conditions. Rounding the upstream edge
-  even to a small extent modifies the discharge. If R is the radius of
-  the rounding the coefficient m is increased in the ratio 1 to 1 + R/h
-  nearly. The results are limited to R less than 1/2 in.
-
-  _Drowned Weirs._--Let h (fig. 54) be the height of head water and h1
-  that of tail water above the weir crest. Then Bazin obtains as the
-  approximate formula for the coefficient of discharge
-
-    m = 1.05m1 [1 + (1/5)h1/p] [root 3]{(h - h1)/h},
-
-  where as before m1 is the coefficient for a sharp-edged weir in
-  similar conditions, that is, when the sheet is free and the weir of
-  the same height.
-
-  [Illustration: FIG. 55.]
-
-  [Illustration: FIG. 56.]
-
-  S 48. _Separating Weirs._--Many towns derive their water-supply from
-  streams in high moorland districts, in which the flow is extremely
-  variable. The water is collected in large storage reservoirs, from
-  which an uniform supply can be sent to the town. In such cases it is
-  desirable to separate the coloured water which comes down the streams
-  in high floods from the purer water of ordinary flow. The latter is
-  sent into the reservoirs; the former is allowed to flow away down the
-  original stream channel, or is stored in separate reservoirs and used
-  as compensation water. To accomplish the separation of the flood and
-  ordinary water, advantage is taken of the different horizontal range
-  of the parabolic path of the water falling over a weir, as the depth
-  on the weir and, consequently, the velocity change. Fig. 55 shows one
-  of these separating weirs in the form in which they were first
-  introduced on the Manchester Waterworks; fig. 56 a more modern weir of
-  the same kind designed by Sir A. Binnie for the Bradford Waterworks.
-  When the quantity of water coming down the stream is not excessive, it
-  drops over the weir into a transverse channel leading to the
-  reservoirs. In flood, the water springs over the mouth of this channel
-  and is led into a waste channel.
-
-  It may be assumed, probably with accuracy enough for practical
-  purposes, that the particles describe the parabolas due to the mean
-  velocity of the water passing over the weir, that is, to a velocity
-
-    (2/3)[root](2gh),
-
-  where h is the head above the crest of the weir.
-
-  Let cb = x be the width of the orifice and ac = y the difference of
-  level of its edges (fig. 57). Then, if a particle passes from a to b
-  in t seconds,
-
-    y = (1/2)gt^2, x = (2/3)[root](2gh) t;
-
-    .: y = (9/16)x^2/h,
-
-  which gives the width x for any given difference of level y and head
-  h, which the jet will just pass over the orifice. Set off ad
-  vertically and equal to (1/2)g on any scale; af horizontally and equal
-  to 2/3 [root](gh). Divide af, fe into an equal number of equal parts.
-  Join a with the divisions on ef. The intersections of these lines with
-  verticals from the divisions on af give the parabolic path of the jet.
-
-  [Illustration: FIG. 57.]
-
-
-  MOUTHPIECES--HEAD CONSTANT
-
-  S 49. _Cylindrical Mouthpieces._--When water issues from a short
-  cylindrical pipe or mouthpiece of a length at least equal to l(1/2)
-  times its smallest transverse dimension, the stream, after contraction
-  within the mouthpiece, expands to fill it and issues full bore, or
-  without contraction, at the point of discharge. The discharge is found
-  to be about one-third greater than that from a simple orifice of the
-  same size. On the other hand, the energy of the fluid per unit of
-  weight is less than that of the stream from a simple orifice with the
-  same head, because part of the energy is wasted in eddies produced at
-  the point where the stream expands to fill the mouthpiece, the action
-  being something like that which occurs at an abrupt change of section.
-
-  Let fig. 58 represent a vessel discharging through a cylindrical
-  mouthpiece at the depth h from the free surface, and let the axis of
-  the jet XX be taken as the datum with reference to which the head is
-  estimated. Let [Omega] be the area of the mouthpiece, [omega] the area
-  of the stream at the contracted section EF. Let v, p be the velocity
-  and pressure at EF, and v1, p1 the same quantities at GH. If the
-  discharge is into the air, p1 is equal to the atmospheric pressure
-  p_a.
-
-  The total head of any filament which goes to form the jet, taken at a
-  point where its velocity is sensibly zero, is h + p_a/G; at EF the
-  total head is v^2/2g + p/G; at GH it is v1^2/2g + p1/G.
-
-  Between EF and GH there is a loss of head due to abrupt change of
-  velocity, which from eq. (3), S 36, may have the value
-
-    (v - v1)^2/2g.
-
-  Adding this head lost to the head at GH, before equating it to the
-  heads at EF and at the point where the filaments start into motion,--
-
-    h + p_a/G = v^2/2g + p/G = v1^2/2g + p1/G + (v - v1)^2/2g.
-
-  But [omega]v = [Omega]v1, and [omega] = c_c[Omega], if c_c is the
-  coefficient of contraction within the mouthpiece. Hence
-
-    v = [Omega]v1/[omega] = v1/c_c.
-
-  Supposing the discharge into the air, so that p1 = p_a,
-
-    h + p_a/G = v1^2/2g + p_a/G + (v1^2/2g)(1/c_c - 1)^2;
-
-    (v1/2g){1 + (1/c_c - 1)^2} = h;
-
-    .: v1 = [root](2gh)/[root]{1 + (1/c_c - 1)^2};   (1)
-
-  [Illustration: FIG. 58.]
-
-  where the coefficient on the right is evidently the coefficient of
-  velocity for the cylindrical mouthpiece in terms of the coefficient of
-  contraction at EF. Let c_c = 0.64, the value for simple orifices, then
-  the coefficient of velocity is
-
-    c_v = 1/[root]{1 + (1/c_c - 1)^2} = 0.87   (2)
-
-  The actual value of c_v, found by experiment is 0.82, which does not
-  differ more from the theoretical value than might be expected if the
-  friction of the mouthpiece is allowed for. Hence, for mouthpieces of
-  this kind, and for the section at GH,
-
-    c_v = 0.82 c_c = 1.00 c = 0.82,
-
-    Q = 0.82[Omega] [root](2gh).
-
-  It is easy to see from the equations that the pressure p at EF is less
-  than atmospheric pressure. Eliminating v1, we get
-
-    (p_a - p)/G = (3/4)h nearly;   (3)
-
-  or
-
-    p = p_a - (3/4)Gh lb. per sq. ft.
-
-  If a pipe connected with a reservoir on a lower level is introduced
-  into the mouthpiece at the part where the contraction is formed (fig.
-  59), the water will rise in this pipe to a height
-
-    KL = (p_a - p)/G = (3/4)h nearly.
-
-  If the distance X is less than this, the water from the lower
-  reservoir will be forced continuously into the jet by the atmospheric
-  pressure, and discharged with it. This is the crudest form of a kind
-  of pump known as the jet pump.
-
-  S 50. _Convergent Mouthpieces._--With convergent mouthpieces there is
-  a contraction within the mouthpiece causing a loss of head, and a
-  diminution of the velocity of discharge, as with cylindrical
-  mouthpieces. There is also a second contraction of the stream outside
-  the mouthpiece. Hence the discharge is given by an equation of the
-  form
-
-    Q = c_v c_c[Omega] [root](2gh),   (4)
-
-  where [Omega] is the area of the external end of the mouthpiece, and
-  c_c[Omega] the section of the contracted jet beyond the mouthpiece.
-
-    _Convergent Mouthpieces (Castel's Experiments).--Smallest diameter of
-    orifice = 0.05085 ft. Length of mouthpiece = 2.6 Diameters._
-
-    +----------------+--------------+--------------+--------------+
-    |                |Coefficient of|Coefficient of|Coefficient of|
-    |    Angle of    | Contraction, |   Velocity,  |  Discharge,  |
-    |  Convergence.  |     c_c      |      c_v     |       c      |
-    +----------------+--------------+--------------+--------------+
-    |    0 deg.  0'  |     .999     |     .830     |     .829     |
-    |    1 deg. 36'  |    1.000     |     .866     |     .866     |
-    |    3 deg. 10'  |    1.001     |     .894     |     .895     |
-    |    4 deg. 10'  |    1.002     |     .910     |     .912     |
-    |    5 deg. 26'  |    1.004     |     .920     |     .924     |
-    |    7 deg. 52'  |     .998     |     .931     |     .929     |
-    |    8 deg. 58'  |     .992     |     .942     |     .934     |
-    |   10 deg. 20'  |     .987     |     .950     |     .938     |
-    |   12 deg.  4'  |     .986     |     .955     |     .942     |
-    |   13 deg. 24'  |     .983     |     .962     |     .946     |
-    |   14 deg. 28'  |     .979     |     .966     |     .941     |
-    |   16 deg. 36'  |     .969     |     .971     |     .938     |
-    |   19 deg. 28'  |     .953     |     .970     |     .924     |
-    |   21 deg.  0'  |     .945     |     .971     |     .918     |
-    |   23 deg.  0'  |     .937     |     .974     |     .913     |
-    |   29 deg. 58'  |     .919     |     .975     |     .896     |
-    |   40 deg. 20'  |     .887     |     .980     |     .869     |
-    |   48 deg. 50'  |     .861     |     .984     |     .847     |
-    +----------------+--------------+--------------+--------------+
-
-  The maximum coefficient of discharge is that for a mouthpiece with a
-  convergence of 13 deg.24'.
-
-  The values of c_v and c_c must here be determined by experiment. The
-  above table gives values sufficient for practical purposes. Since the
-  contraction beyond the mouthpiece increases with the convergence, or,
-  what is the same thing, c_c diminishes, and on the other hand the loss
-  of energy diminishes, so that c_v increases with the convergence,
-  there is an angle for which the product c_c c_v, and consequently the
-  discharge, is a maximum.
-
-  [Illustration: FIG. 59.]
-
-  S 51. _Divergent Conoidal Mouthpiece._--Suppose a mouthpiece so
-  designed that there is no abrupt change in the section or velocity of
-  the stream passing through it. It may have a form at the inner end
-  approximately the same as that of a simple contracted vein, and may
-  then enlarge gradually, as shown in fig. 60. Suppose that at EF it
-  becomes cylindrical, so that the jet may be taken to be of the
-  diameter EF. Let [omega], v, p be the section, velocity and pressure
-  at CD, and [Omega], v1, p1 the same quantities at EF, p_a being as
-  usual the atmospheric pressure, or pressure on the free surface AB.
-  Then, since there is no loss of energy, except the small frictional
-  resistance of the surface of the mouthpiece,
-
-    h + p_a/G = v^2/2g + p/G = v1^2/2g + p1/G.
-
-  If the jet discharges into the air, p1 = p_a; and
-
-    v1^2/2g = h;
-
-    v1 = [root](2gh);
-
-  or, if a coefficient is introduced to allow for friction,
-
-    v1 = c_v [root](2gh);
-
-  where c_v is about 0.97 if the mouthpiece is smooth and well formed.
-
-    Q = [Omega] v1 = c_v [Omega] [root](2gh).
-
-  [Illustration: FIG. 60.]
-
-  Hence the discharge depends on the area of the stream at EF, and not
-  at all on that at CD, and the latter may be made as small as we please
-  without affecting the amount of water discharged.
-
-  There is, however, a limit to this. As the velocity at CD is greater
-  than at EF the pressure is less, and therefore less than atmospheric
-  pressure, if the discharge is into the air. If CD is so contracted
-  that p = 0, the continuity of flow is impossible. In fact the stream
-  disengages itself from the mouthpiece for some value of p greater than
-  0 (fig. 61).
-
-  [Illustration: FIG. 61.]
-
-  From the equations,
-
-    p/G = p_a/G = (v^2 - v1^2)/2g.
-
-  Let [Omega]/[omega] = m. Then
-
-    v = v1m;
-
-    p/G = p_a/G - v1^2(m^2 - 1)/2g
-        = p_a/G - (m^2 - 1)h;
-
-  whence we find that p/G will become zero or negative if
-
-    [Omega]/[omega] >= [root]{(h + p_a/G)/h}
-                     = [root]{1 + p_a/Gh};
-
-  or, putting p_a/G = 34 ft., if
-
-    [Omega]/[omega] >= [root]{(h + 34)/h}.
-
-  In practice there will be an interruption of the full bore flow with a
-  less ratio of [Omega]/[omega], because of the disengagement of air
-  from the water. But, supposing this does not occur, the maximum
-  discharge of a mouthpiece of this kind is
-
-    Q = [omega] [root]{2g(h + p_a/G)};
-
-  that is, the discharge is the same as for a well-bell-mouthed
-  mouthpiece of area [omega], and without the expanding part,
-  discharging into a vacuum.
-
-  S 52. _Jet Pump._--A divergent mouthpiece may be arranged to act as a
-  pump, as shown in fig. 62. The water which supplies the energy
-  required for pumping enters at A. The water to be pumped enters at B.
-  The streams combine at DD where the velocity is greatest and the
-  pressure least. Beyond DD the stream enlarges in section, and its
-  pressure increases, till it is sufficient to balance the head due to
-  the height of the lift, and the water flows away by the discharge pipe
-  C.
-
-  [Illustration: FIG. 62.]
-
-  Fig. 63 shows the whole arrangement in a diagrammatic way. A is the
-  reservoir which supplies the water that effects the pumping; B is the
-  reservoir of water to be pumped; C is the reservoir into which the
-  water is pumped.
-
-  [Illustration: FIG. 63.]
-
-
-  DISCHARGE WITH VARYING HEAD
-
-  S 53. _Flow from a Vessel when the Effective Head varies with the
-  Time._--Various useful problems arise relating to the time of emptying
-  and filling vessels, reservoirs, lock chambers, &c., where the flow is
-  dependent on a head which increases or diminishes during the
-  operation. The simplest of these problems is the case of filling or
-  emptying a vessel of constant horizontal section.
-
-  [Illustration: FIG. 64.]
-
-  _Time of Emptying or Filling a Vertical-sided Lock Chamber._--Suppose
-  the lock chamber, which has a water surface of [Omega] square ft., is
-  emptied through a sluice in the tail gates, of area [omega], placed
-  below the tail-water level. Then the effective head producing flow
-  through the sluice is the difference of level in the chamber and tail
-  bay. Let H (fig. 64) be the initial difference of level, h the
-  difference of level after t seconds. Let -dh be the fall of level in
-  the chamber during an interval dt. Then in the time dt the volume in
-  the chamber is altered by the amount -[Omega]dh, and the outflow from
-  the sluice in the same time is c[omega][root](2gh)dt. Hence the
-  differential equation connecting h and t is
-
-    c[omega] [root](2gh) dt + [Omega]h = 0.
-
-  For the time t, during which the initial head H diminishes to any
-  other value h,
-                                    _               _
-                                   /h              /t
-    -{[Omega]/(c[omega] [root]2g)} |  dh/[root]h = |  dt.
-                                  _/H             _/0
-
-    .: t = 2[Omega]([root]H - [root]h) / {c[omega] [root](2g)}
-         = ([Omega]/c[omega]){[root](2H/g) - [root](2h/g)}.
-
-  For the whole time of emptying, during which h diminishes from H to 0,
-
-    T = ([Omega]/c[omega]) [root](2H/g).
-
-  Comparing this with the equation for flow under a constant head, it
-  will be seen that the time is double that required for the discharge
-  of an equal volume under a constant head.
-
-  The time of filling the lock through a sluice in the head gates is
-  exactly the same, if the sluice is below the tail-water level. But if
-  the sluice is above the tail-water level, then the head is constant
-  till the level of the sluice is reached, and afterwards it diminishes
-  with the time.
-
-
-  PRACTICAL USE OF ORIFICES IN GAUGING WATER
-
-  S 54. If the water to be measured is passed through a known orifice
-  under an arrangement by which the constancy of the head is ensured,
-  the amount which passes in a given time can be ascertained by the
-  formulae already given. It will obviously be best to make the orifices
-  of the forms for which the coefficients are most accurately
-  determined; hence sharp-edged orifices or notches are most commonly
-  used.
-
-  _Water Inch._--For measuring small quantities of water circular
-  sharp-edged orifices have been used. The discharge from a circular
-  orifice one French inch in diameter, with a head of one line above the
-  top edge, was termed by the older hydraulic writers a water-inch. A
-  common estimate of its value was 14 pints per minute, or 677 English
-  cub. ft. in 24 hours. An experiment by C. Bossut gave 634 cub. ft. in
-  24 hours (see Navier's edition of _Belidor's Arch. Hydr._, p. 212).
-
-  L. J. Weisbach points out that measurements of this kind would be made
-  more accurately with a greater head over the orifice, and he proposes
-  that the head should be equal to the diameter of the orifice. Several
-  equal orifices may be used for larger discharges.
-
-  [Illustration: FIG. 65.]
-
-  _Pin Ferrules or Measuring Cocks._--To give a tolerably definite
-  supply of water to houses, without the expense of a meter, a ferrule
-  with an orifice of a definite size, or a cock, is introduced in the
-  service-pipe. If the head in the water main is constant, then a
-  definite quantity of water would be delivered in a given time. The
-  arrangement is not a very satisfactory one, and acts chiefly as a
-  check on extravagant use of water. It is interesting here chiefly as
-  an example of regulation of discharge by means of an orifice. Fig. 65
-  shows a cock of this kind used at Zurich. It consists of three cocks,
-  the middle one having the orifice of the predetermined size in a small
-  circular plate, protected by wire gauze from stoppage by impurities in
-  the water. The cock on the right hand can be used by the consumer for
-  emptying the pipes. The one on the left and the measuring cock are
-  connected by a key which can be locked by a padlock, which is under
-  the control of the water company.
-
-  S 55. _Measurement of the Flow in Streams._--To determine the quantity
-  of water flowing off the ground in small streams, which is available
-  for water supply or for obtaining water power, small temporary weirs
-  are often used. These may be formed of planks supported by piles and
-  puddled to prevent leakage. The measurement of the head may be made by
-  a thin-edged scale at a short distance behind the weir, where the
-  water surface has not begun to slope down to the weir and where the
-  velocity of approach is not high. The measurements are conveniently
-  made from a short pile driven into the bed of the river, accurately
-  level with the crest of the weir (fig. 66). Then if at any moment the
-  head is h, the discharge is, for a rectangular notch of breadth b,
-
-    Q = (2/3)cbh [root](2gh)
-
-  where c = 0.62; or, better, the formula in S 42 may be used.
-
-  Gauging weirs are most commonly in the form of rectangular notches;
-  and care should be taken that the crest is accurately horizontal, and
-  that the weir is normal to the direction of flow of the stream. If the
-  planks are thick, they should be bevelled (fig. 67), and then the edge
-  may be protected by a metal plate about (1/10)th in. thick to secure
-  the requisite accuracy of form and sharpness of edge. In permanent
-  gauging weirs, a cast steel plate is sometimes used to form the edge
-  of the weir crest. The weir should be large enough to discharge the
-  maximum volume flowing in the stream, and at the same time it is
-  desirable that the minimum head should not be too small (say half a
-  foot) to decrease the effects of errors of measurement. The section of
-  the jet over the weir should not exceed one-fifth the section of the
-  stream behind the weir, or the velocity of approach will need to be
-  taken into account. A triangular notch is very suitable for
-  measurements of this kind.
-
-  [Illustration: FIG. 66.]
-
-  If the flow is variable, the head h must be recorded at equidistant
-  intervals of time, say twice daily, and then for each 12-hour period
-  the discharge must be calculated for the mean of the heads at the
-  beginning and end of the time. As this involves a good deal of
-  troublesome calculation, E. Sang proposed to use a scale so graduated
-  as to read off the discharge in cubic feet per second. The lengths of
-  the principal graduations of such a scale are easily calculated by
-  putting Q = 1, 2, 3 ... in the ordinary formulae for notches; the
-  intermediate graduations may be taken accurately enough by subdividing
-  equally the distances between the principal graduations.
-
-  [Illustration: FIG. 67.]
-
-  [Illustration: FIG. 68.]
-
-  The accurate measurement of the discharge of a stream by means of a
-  weir is, however, in practice, rather more difficult than might be
-  inferred from the simplicity of the principle of the operation. Apart
-  from the difficulty of selecting a suitable coefficient of discharge,
-  which need not be serious if the form of the weir and the nature of
-  its crest are properly attended to, other difficulties of measurement
-  arise. The length of the weir should be very accurately determined,
-  and if the weir is rectangular its deviations from exactness of level
-  should be tested. Then the agitation of the water, the ripple on its
-  surface, and the adhesion of the water to the scale on which the head
-  is measured, are liable to introduce errors. Upon a weir 10 ft. long,
-  with 1 ft. depth of water flowing over, an error of 1-1000th of a foot
-  in measuring the head, or an error of 1-100th of a foot in measuring
-  the length of the weir, would cause an error in computing the
-  discharge of 2 cub. ft. per minute.
-
-  _Hook Gauge._--For the determination of the surface level of water,
-  the most accurate instrument is the hook gauge used first by U. Boyden
-  of Boston, in 1840. It consists of a fixed frame with scale and
-  vernier. In the instrument in fig. 68 the vernier is fixed to the
-  frame, and the scale slides vertically. The scale carries at its lower
-  end a hook with a fine point, and the scale can be raised or lowered
-  by a fine pitched screw. If the hook is depressed below the water
-  surface and then raised by the screw, the moment of its reaching the
-  water surface will be very distinctly marked, by the reflection from a
-  small capillary elevation of the water surface over the point of the
-  hook. In ordinary light, differences of level of the water of .001 of
-  a foot are easily detected by the hook gauge. If such a gauge is used
-  to determine the heads at a weir, the hook should first be set
-  accurately level with the weir crest, and a reading taken. Then the
-  difference of the reading at the water surface and that for the weir
-  crest will be the head at the weir.
-
-  S 56. _Modules used in Irrigation._--In distributing water for
-  irrigation, the charge for the water may be simply assessed on the
-  area of the land irrigated for each consumer, a method followed in
-  India; or a regulated quantity of water may be given to each consumer,
-  and the charge may be made proportional to the quantity of water
-  supplied, a method employed for a long time in Italy and other parts
-  of Europe. To deliver a regulated quantity of water from the
-  irrigation channel, arrangements termed modules are used. These are
-  constructions intended to maintain a constant or approximately
-  constant head above an orifice of fixed size, or to regulate the size
-  of the orifice so as to give a constant discharge, notwithstanding the
-  variation of level in the irrigating channel.
-
-  [Illustration: FIG. 69.]
-
-  S 57. _Italian Module._--The Italian modules are masonry
-  constructions, consisting of a regulating chamber, to which water is
-  admitted by an adjustable sluice from the canal. At the other end of
-  the chamber is an orifice in a thin flagstone of fixed size. By means
-  of the adjustable sluice a tolerably constant head above the fixed
-  orifice is maintained, and therefore there is a nearly constant
-  discharge of ascertainable amount through the orifice, into the
-  channel leading to the fields which are to be irrigated.
-
-  [Illustration: FIG. 70.--Scale 1/100.]
-
-  In fig. 69, A is the adjustable sluice by which water is admitted to
-  the regulating chamber, B is the fixed orifice through which the water
-  is discharged. The sluice A is adjusted from time to time by the canal
-  officers, so as to bring the level of the water in the regulating
-  chamber to a fixed level marked on the wall of the chamber. When
-  adjusted it is locked. Let [omega]1 be the area of the orifice through
-  the sluice at A, and [omega]2 that of the fixed orifice at B; let h1
-  be the difference of level between the surface of the water in the
-  canal and regulating chamber; h2 the head above the centre of the
-  discharging orifice, when the sluice has been adjusted and the flow
-  has become steady; Q the normal discharge in cubic feet per second.
-  Then, since the flow through the orifices at A and B is the same,
-
-    Q = c1[omega]1 [root](2gh1) = c2[omega]2 [root](2gh2),
-
-  where c1 and c2 are the coefficients of discharge suitable for the two
-  orifices. Hence
-
-    c1[omega]1/c2[omega]2 = [root](h2/h1).
-
-  If the orifice at B opened directly into the canal without any
-  intermediate regulating chamber, the discharge would increase for a
-  given change of level in the canal in exactly the same ratio.
-  Consequently the Italian module in no way moderates the fluctuations
-  of discharge, except so far as it affords means of easy adjustment
-  from time to time. It has further the advantage that the cultivator,
-  by observing the level of the water in the chamber, can always see
-  whether or not he is receiving the proper quantity of water.
-
-  On each canal the orifices are of the same height, and intended to
-  work with the same normal head, the width of the orifices being varied
-  to suit the demand for water. The unit of discharge varies on
-  different canals, being fixed in each case by legal arrangements. Thus
-  on the Canal Lodi the unit of discharge or one module of water is the
-  discharge through an orifice 1.12 ft. high, 0.12416 ft. wide, with a
-  head of 0.32 ft. above the top edge of the orifice, or .88 ft. above
-  the centre. This corresponds to a discharge of about 0.6165 cub. ft.
-  per second.
-
-  [Illustration: FIG. 71.]
-
-  In the most elaborate Italian modules the regulating chamber is arched
-  over, and its dimensions are very exactly prescribed. Thus in the
-  modules of the Naviglio Grande of Milan, shown in fig. 70, the
-  measuring orifice is cut in a thin stone slab, and so placed that the
-  discharge is into the air with free contraction on all sides. The
-  adjusting sluice is placed with its sill flush with the bottom of the
-  canal, and is provided with a rack and lever and locking arrangement.
-  The covered regulating chamber is about 20 ft. long, with a breadth
-  1.64 ft. greater than that of the discharging orifice. At precisely
-  the normal level of the water in the regulating chamber, there is a
-  ceiling of planks intended to still the agitation of the water. A
-  block of stone serves to indicate the normal level of the water in the
-  chamber. The water is discharged into an open channel 0.655 ft. wider
-  than the orifice, splaying out till it is 1.637 ft. wider than the
-  orifice, and about 18 ft. in length.
-
-  S 58. _Spanish Module._--On the canal of Isabella II., which supplies
-  water to Madrid, a module much more perfect in principle than the
-  Italian module is employed. Part of the water is supplied for
-  irrigation, and as it is very valuable its strict measurement is
-  essential. The module (fig. 72) consists of two chambers one above the
-  other, the upper chamber being in free communication with the
-  irrigation canal, and the lower chamber discharging by a culvert to
-  the fields. In the arched roof between the chambers there is a
-  circular sharp-edged orifice in a bronze plate. Hanging in this there
-  is a bronze plug of variable diameter suspended from a hollow brass
-  float. If the water level in the canal lowers, the plug descends and
-  gives an enlarged opening, and conversely. Thus a perfectly constant
-  discharge with a varying head can be obtained, provided no clogging or
-  silting of the chambers prevents the free discharge of the water or
-  the rise and fall of the float. The theory of the module is very
-  simple. Let R (fig. 71) be the radius of the fixed opening, r the
-  radius of the plug at a distance h from the plane of flotation of the
-  float, and Q the required discharge of the module. Then
-
-    Q = c[pi](R^2 - r^2) [root](2gh).
-
-  Taking c = 0.63,
-
-    Q = 15.88(R^2 - r^2) [root]h;
-
-    r = [root]{R^2 - Q/15.88 [root]h}.
-
-  Choosing a value for R, successive values of r can be found for
-  different values of h, and from these the curve of the plug can be
-  drawn. The module shown in fig. 72 will discharge 1 cubic metre per
-  second. The fixed opening is 0.2 metre diameter, and the greatest head
-  above the fixed orifice is 1 metre. The use of this module involves a
-  great sacrifice of level between the canal and the fields. The module
-  is described in Sir C. Scott-Moncrieff's _Irrigation in Southern
-  Europe_.
-
-  S 59. _Reservoir Gauging Basins._--In obtaining the power to store the
-  water of streams in reservoirs, it is usual to concede to riparian
-  owners below the reservoirs a right to a regulated supply throughout
-  the year. This compensation water requires to be measured in such a
-  way that the millowners and others interested in the matter can assure
-  themselves that they are receiving a proper quantity, and they are
-  generally allowed a certain amount of control as to the times during
-  which the daily supply is discharged into the stream.
-
-  [Illustration: FIG. 72.]
-
-  Fig. 74 shows an arrangement designed for the Manchester water works.
-  The water enters from the reservoir at chamber A, the object of which
-  is to still the irregular motion of the water. The admission is
-  regulated by sluices at b, b, b. The water is discharged by orifices
-  or notches at a, a, over which a tolerably constant head is maintained
-  by adjusting the sluices at b, b, b. At any time the millowners can
-  see whether the discharge is given and whether the proper head is
-  maintained over the orifices. To test at any time the discharge of the
-  orifices, a gauging basin B is provided. The water ordinarily flows
-  over this, without entering it, on a floor of cast-iron plates. If the
-  discharge is to be tested, the water is turned for a definite time
-  into the gauging basin, by suddenly opening and closing a sluice at c.
-  The volume of flow can be ascertained from the depth in the gauging
-  chamber. A mechanical arrangement (fig. 73) was designed for securing
-  an absolutely constant head over the orifices at a, a. The orifices
-  were formed in a cast-iron plate capable of sliding up and down,
-  without sensible leakage, on the face of the wall of the chamber. The
-  orifice plate was attached by a link to a lever, one end of which
-  rested on the wall and the other on floats f in the chamber A. The
-  floats rose and fell with the changes of level in the chamber, and
-  raised and lowered the orifice plate at the same time. This mechanical
-  arrangement was not finally adopted, careful watching of the sluices
-  at b, b, b, being sufficient to secure a regular discharge. The
-  arrangement is then equivalent to an Italian module, but on a large
-  scale.
-
-  [Illustration: FIG. 73.--Scale 1/120.]
-
-  [Illustration: FIG. 74.--Scale 1/500.]
-
-  S 60. _Professor Fleeming Jenkin's Constant Flow Valve._--In the
-  modules thus far described constant discharge is obtained by varying
-  the area of the orifice through which the water flows. Professor F.
-  Jenkin has contrived a valve in which a constant pressure head is
-  obtained, so that the orifice need not be varied (_Roy. Scot. Society_
-  _of Arts_, 1876). Fig. 75 shows a valve of this kind suitable for a
-  6-in. water main. The water arriving by the main C passes through an
-  equilibrium valve D into the chamber A, and thence through a sluice O,
-  which can be set for any required area of opening, into the
-  discharging main B. The object of the arrangement is to secure a
-  constant difference of pressure between the chambers A and B, so that
-  a constant discharge flows through the stop valve O. The equilibrium
-  valve D is rigidly connected with a plunger P loosely fitted in a
-  diaphragm, separating A from a chamber B2 connected by a pipe B1 with
-  the discharging main B. Any increase of the difference of pressure in
-  A and B will drive the plunger up and close the equilibrium valve, and
-  conversely a decrease of the difference of pressure will cause the
-  descent of the plunger and open the equilibrium valve wider. Thus a
-  constant difference of pressure is obtained in the chambers A and B.
-  Let [omega] be the area of the plunger in square feet, p the
-  difference of pressure in the chambers A and B in pounds per square
-  foot, w the weight of the plunger and valve. Then if at any moment
-  p[omega] exceeds w the plunger will rise, and if it is less than w the
-  plunger will descend. Apart from friction, and assuming the valve D to
-  be strictly an equilibrium valve, since [omega] and w are constant, p
-  must be constant also, and equal to w/[omega]. By making w small and
-  [omega] large, the difference of pressure required to ensure the
-  working of the apparatus may be made very small. Valves working with a
-  difference of pressure of 1/2 in. of water have been constructed.
-
-  [Illustration: FIG. 75.--Scale 1/24.]
-
-
-  VI. STEADY FLOW OF COMPRESSIBLE FLUIDS.
-
-  [Illustration: FIG. 76.]
-
-  S 61. _External Work during the Expansion of Air._--If air expands
-  without doing any external work, its temperature remains constant.
-  This result was first experimentally demonstrated by J. P. Joule. It
-  leads to the conclusion that, however air changes its state, the
-  internal work done is proportional to the change of temperature. When,
-  in expanding, air does work against an external resistance, either
-  heat must be supplied or the temperature falls.
-
-  To fix the conditions, suppose 1 lb. of air confined behind a piston
-  of 1 sq. ft. area (fig. 76). Let the initial pressure be p1 and the
-  volume of the air v1, and suppose this to expand to the pressure p2
-  and volume v2. If p and v are the corresponding pressure and volume at
-  any intermediate point in the expansion, the work done on the piston
-  during the expansion from v to v + dv is pdv, and the whole work
-  during the expansion from v1 to v2, represented by the area abcd, is
-      _
-     /v2
-     |   p dv.
-    _/v1
-
-  Amongst possible cases two may be selected.
-
-  _Case 1._--So much heat is supplied to the air during expansion that
-  the temperature remains constant. Hyperbolic expansion.
-
-  Then
-
-    pv = p1v1.
-
-  Work done during expansion per pound of air
-        _                _
-       /v2              /v2
-    =  |   p dv  = p1v1 |   dv/v
-      _/v1             _/v1
-
-    = p1v1 log_[epsilon] v2v1 = p1v1 log_[epsilon] p1p2.   (1)
-
-  Since the weight per cubic foot is the reciprocal of the volume per
-  pound, this may be written
-
-    (p1/G1) log_[epsilon] G1/G2.   (1a)
-
-  Then the expansion curve ab is a common hyperbola.
-
-  _Case 2._--No heat is supplied to the air during expansion. Then the
-  air loses an amount of heat equivalent to the external work done and
-  the temperature falls. Adiabatic expansion.
-
-  In this case it can be shown that
-
-    pv^[gamma] = p1v1^[gamma],
-
-  where [gamma] is the ratio of the specific heats of air at constant
-  pressure and volume. Its value for air is 1.408, and for dry steam
-  1.135.
-
-  Work done during expansion per pound of air.
-
-        _                         _
-       /v2                       /v2
-    =  |   p dv   = p1v1^[gamma] |   dv/v^[gamma]
-      _/v1                      _/v1
-
-    = - {p1v1^[gamma]/([gamma] - 1)} {1/v2^([gamma] - 1) -  1/v1^([gamma] - 1)}
-
-    = {p1v1^[gamma]/([gamma] - 1)} {1/v1^([gamma] - 1) -  1/v2^([gamma] - 1)}
-
-    = {p1v1/([gamma] - 1)} {1 - (v1/v2)^([gamma] - 1)}.   (2)
-
-  The value of p1v1 for any given temperature can be found from the data
-  already given.
-
-  As before, substituting the weights G1, G2 per cubic foot for the
-  volumes per pound, we get for the work of expansion
-
-    (p1/G1){1/([gamma] - 1)} {1 - (G2/G1)^([gamma] - 1)},   (2a)
-
-    = p1v1{1/([gamma] - 1)} {1 - (p2/p1)^([gamma] - 1)/[gamma]}.   (2b)
-
-  [Illustration: FIG. 77.]
-
-  S 62. _Modification of the Theorem of Bernoulli for the Case of a
-  Compressible Fluid._--In the application of the principle of work to a
-  filament of compressible fluid, the internal work done by the
-  expansion of the fluid, or absorbed in its compression, must be taken
-  into account. Suppose, as before, that AB (fig. 77) comes to A'B' in a
-  short time t. Let p1, [omega]1, v1, G1 be the pressure, sectional area
-  of stream, velocity and weight of a cubic foot at A, and p2, [omega]2,
-  v2, G2 the same quantities at B. Then, from the steadiness of motion,
-  the weight of fluid passing A in any given time must be equal to the
-  weight passing B:
-
-    G1[omega]1v1t = G2[omega]2v2t.
-
-  Let z1, z2 be the heights of the sections A and B above any given
-  datum. Then the work of gravity on the mass AB in t seconds is
-
-    G1[omega]1v1t(z1 - z2) = W(z1 - z2)t,
-
-  where W is the weight of gas passing A or B per second. As in the case
-  of an incompressible fluid, the work of the pressures on the ends of
-  the mass AB is
-
-    p1[omega]1v1t - p2[omega]2v2t,
-    = (p1/G1 - p2/G2)Wt.
-
-  The work done by expansion of Wt lb. of fluid between A and B is Wt
-  [int][v1 to v2] p dv. The change of kinetic energy as before is (W/2g)
-  (v2^2 - v1^2)t. Hence, equating work to change of kinetic energy,
-
-                                       _
-                                      /v2
-    W(z1 - z2)t + (p1/G1 - p2/G2)Wt + |   p dv = (W/2g)(v2^2 - v1^2)t;
-                                     _/v1
-                                                       _
-                                                      /v2                                                                        /
-    .: z1 + p1/G1 + v1^2/2g = z2 + p^2/G2 + v2^2/2g - |   p dv.   (1)
-                                                     _/v1
-
-  Now the work of expansion per pound of fluid has already been given.
-  If the temperature is constant, we get (eq. 1a, S 61)
-
-    z1 + p1/G1 + v1^2/2g
-      = z2 + p^2/G2 + v2^2/2g - (p1/G1) log_[epsilon] (G1/G2).
-
-  But at constant temperature p1/G1 = p2/G2;
-
-    .: z1 + v1^2/2g = z2 + v2^2/2g - (p1/G1) log_[epsilon] (p1/p2),   (2)
-
-  or, neglecting the difference of level,
-
-    (v2^2 - v1^2)/2g = (p1/G1) log_[epsilon] (p1/p2).   (2a)
-
-  Similarly, if the expansion is adiabatic (eq. 2a, S 61),
-
-    z1 + p1/G1 + v1^2/2g = z2 + p2/G2 + v2^2/2g
-      - (p1/G1){1/([gamma] - 1)} {1 - (p2/p1)^([gamma] - 1)/[gamma]};   (3)
-
-  or, neglecting the difference of level,
-
-    (v2^2 - v1^2)/2g =
-      (p1/G1)[1 + 1/([gamma] - 1){1 - (p2/p1)^([gamma]-1)/[gamma]}] - p2/G2.   (3a)
-
-  It will be seen hereafter that there is a limit in the ratio p1/p2
-  beyond which these expressions cease to be true.
-
-  S 63. _Discharge of Air from an Orifice._--The form of the equation of
-  work for a steady stream of compressible fluid is
-
-    z1 + p1/G1 + v1^2/2g = z2 + p2/G2 + v2^2/2g -
-      (p1/G1){1/([gamma] - 1)} {1 - (p2/p1^([gamma] - 1)/[gamma]},
-
-  the expansion being adiabatic, because in the flow of the streams of
-  air through an orifice no sensible amount of heat can be communicated
-  from outside.
-
-  Suppose the air flows from a vessel, where the pressure is p1 and the
-  velocity sensibly zero, through an orifice, into a space where the
-  pressure is p2. Let v2 be the velocity of the jet at a point where the
-  convergence of the streams has ceased, so that the pressure in the jet
-  is also p2. As air is light, the work of gravity will be small
-  compared with that of the pressures and expansion, so that z1z2 may be
-  neglected. Putting these values in the equation above--
-
-    p1/G1 = p2/G2 + v2^2/2g - (p1/G1){1/([gamma] - 1)}
-      {1 - (p2/p1)^([gamma] - 1)/[gamma];
-
-    v2^2/2g = p1/G1 - p2/G2 + (p1/G1){1/([gamma] - 1)}
-      {1 - (p2/p1)^([gamma] - 1)/[gamma]}
-
-    = (p1/G1){[gamma]/([gamma] - 1) - (p2/p1)^([gamma] - 1)/[gamma]/([gamma] - 1)} - p2/G2.
-
-  But
-
-    p1/G1^([gamma]) = p2/G2^([gamma])
-    .: p2/G2 = (p1/G1)(p2/p1)^([gamma] - 1)/[gamma]
-
-    v2^2/2g = (p1/G1){[gamma]/([gamma] - 1)} {1 - (p2/p1)^(([gamma] - 1)/[gamma]};   (1)
-
-  or
-
-    v2^2/2g = {[gamma]/([gamma] - 1)} {(p1/G1) - (p2/G2)};
-
-  an equation commonly ascribed to L. J. Weisbach (_Civilingenieur_,
-  1856), though it appears to have been given earlier by A. J. C. Barre
-  de Saint Venant and L. Wantzel.
-
-  It has already (S 9, eq. 4a) been seen that
-
-    p1/G1 = (p0/G0) ([tau]1/[tau]0)
-
-  where for air p0 = 2116.8, G0 = .08075 and [tau]0 = 492.6.
-
-    v2^2/2g = {p0[tau]1[gamma]/G0[tau]0([gamma] - 1)}
-      {1 - (p2/p1)^([gamma] - 1)/[gamma]};   (2)
-
-  or, inserting numerical values,
-
-    v2^2/2g = 183.6[tau]1 {1 - (p2/p1)^(0.29)};   (2a)
-
-  which gives the velocity of discharge v2 in terms of the pressure and
-  absolute temperature, p1, [tau]1, in the vessel from which the air
-  flows, and the pressure p2 in the vessel into which it flows.
-
-  Proceeding now as for liquids, and putting [omega] for the area of the
-  orifice and c for the coefficient of discharge, the volume of air
-  discharged per second at the pressure p2 and temperature [tau]2 is
-
-    Q2 = c[omega]v2 = c[omega] [root][(2g[gamma]p1/([gamma] - 1)G1)
-      (1 - (p2/p1)^([gamma] - 1)/[gamma])]
-
-    = 108.7c[omega] [root][[tau]1 {1 - (p2/p1)^(0.29)}].   (3)
-
-  If the volume discharged is measured at the pressure p1 and absolute
-  temperature [tau]1 in the vessel from which the air flows, let Q1 be
-  that volume; then
-
-    p1Q1^[gamma] = p2Q2^[gamma];
-
-    Q1 = (p2/p1)^(1/[gamma]) Q2;
-
-    Q1 = c[omega] [root][{2g[gamma]p1/([gamma] - 1)G1}
-      {(p2/p1)^(2/[gamma]) - (p2/p1)^([gamma] + 1)/[gamma]}].
-
-  Let
-
-    (p2/p1)^(2/[gamma]) - (p2/p1)^([gamma] - 1)/[gamma] =
-      (p2/p1)^(1.41) - (p2/p1)^(1.7) = [psi]; then
-
-    Q1 = c[omega] [root][2g[gamma]p1[psi]/([gamma] - 1)G1]
-       = 108.7c[omega] [root]([tau]1[psi]).   (4)
-
-  The weight of air at pressure p1 and temperature [tau]1 is
-
-    G1 = p1/53.2[tau]1 lb. per cubic foot.
-
-  Hence the weight of air discharged is
-
-    W = G1Q1 = c[omega] [root][2g[gamma]p1G1[psi]/([gamma] - 1)]
-      = 2.043c[omega]p1 [root]([psi]/[tau]1).   (5)
-
-  Weisbach found the following values of the coefficient of discharge
-  c:--
-
-    Conoidal mouthpieces of the form of the \
-      contracted vein with effective         >       c =
-      pressures of .23 to 1.1 atmosphere    /   0.97 to 0.99
-    Circular sharp-edged orifices               0.563 " 0.788
-    Short cylindrical mouthpieces               0.81  " 0.84
-    The same rounded at the inner end           0.92  " 0.93
-    Conical converging mouthpieces              0.90  " 0.99
-
-  S 64. _Limit to the Application of the above Formulae._--In the
-  formulae above it is assumed that the fluid issuing from the orifice
-  expands from the pressure p1 to the pressure p2, while passing from
-  the vessel to the section of the jet considered in estimating the area
-  [omega]. Hence p2 is strictly the pressure in the jet at the plane of
-  the external orifice in the case of mouthpieces, or at the plane of
-  the contracted section in the case of simple orifices. Till recently
-  it was tacitly assumed that this pressure p2 was identical with the
-  general pressure external to the orifice. R. D. Napier first
-  discovered that, when the ratio p2/p1 exceeded a value which does not
-  greatly differ from 0.5, this was no longer true. In that case the
-  expansion of the fluid down to the external pressure is not completed
-  at the time it reaches the plane of the contracted section, and the
-  pressure there is greater than the general external pressure; or, what
-  amounts to the same thing, the section of the jet where the expansion
-  is completed is a section which is greater than the area c_c[omega] of
-  the contracted section of the jet, and may be greater than the area
-  [omega] of the orifice. Napier made experiments with steam which
-  showed that, so long as p2/p1 > 0.5, the formulae above were
-  trustworthy, when p2 was taken to be the general external pressure,
-  but that, if p2/p1 < 0.5, then the pressure at the contracted section
-  was independent of the external pressure and equal to 0.5p1. Hence in
-  such cases the constant value 0.5 should be substituted in the
-  formulae for the ratio of the internal and external pressures p2/p1.
-
-  It is easily deduced from Weisbach's theory that, if the pressure
-  external to an orifice is gradually diminished, the weight of air
-  discharged per second increases to a maximum for a value of the ratio
-
-    p2/p1 = {2/([gamma] + 1)}^([gamma] - 1/[gamma])
-          = 0.527 for air
-          = 0.58 for dry steam.
-
-  For a further decrease of external pressure the discharge
-  diminishes,--a result no doubt improbable. The new view of Weisbach's
-  formula is that from the point where the maximum is reached, or not
-  greatly differing from it, the pressure at the contracted section
-  ceases to diminish.
-
-  A. F. Fliegner showed (_Civilingenieur_ xx., 1874) that for air
-  flowing from well-rounded mouthpieces there is no discontinuity of the
-  law of flow, as Napier's hypothesis implies, but the curve of flow
-  bends so sharply that Napier's rule may be taken to be a good
-  approximation to the true law. The limiting value of the ratio p2/p1,
-  for which Weisbach's formula, as originally understood, ceases to
-  apply, is for air 0.5767; and this is the number to be substituted for
-  p2/p1 in the formulae when p2/p1 falls below that value. For later
-  researches on the flow of air, reference may be made to G. A. Zeuner's
-  paper (_Civilingenieur_, 1871), and Fliegner's papers (_ibid._, 1877,
-  1878).
-
-
-  VII. FRICTION OF LIQUIDS.
-
-  S 65. When a stream of fluid flows over a solid surface, or conversely
-  when a solid moves in still fluid, a resistance to the motion is
-  generated, commonly termed fluid friction. It is due to the viscosity
-  of the fluid, but generally the laws of fluid friction are very
-  different from those of simple viscous resistance. It would appear
-  that at all speeds, except the slowest, rotating eddies are formed by
-  the roughness of the solid surface, or by abrupt changes of velocity
-  distributed throughout the fluid; and the energy expended in producing
-  these eddying motions is gradually lost in overcoming the viscosity of
-  the fluid in regions more or less distant from that where they are
-  first produced.
-
-  The laws of fluid friction are generally stated thus:--
-
-  1. The frictional resistance is independent of the pressure between
-  the fluid and the solid against which it flows. This may be verified
-  by a simple direct experiment. C. H. Coulomb, for instance, oscillated
-  a disk under water, first with atmospheric pressure acting on the
-  water surface, afterwards with the atmospheric pressure removed. No
-  difference in the rate of decrease of the oscillations was observed.
-  The chief proof that the friction is independent of the pressure is
-  that no difference of resistance has been observed in water mains and
-  in other cases, where water flows over solid surfaces under widely
-  different pressures.
-
-  2. The frictional resistance of large surfaces is proportional to the
-  area of the surface.
-
-  3. At low velocities of not more than 1 in. per second for water, the
-  frictional resistance increases directly as the relative velocity of
-  the fluid and the surface against which it flows. At velocities of 1/2
-  ft. per second and greater velocities, the frictional resistance is
-  more nearly proportional to the square of the relative velocity.
-
-  In many treatises on hydraulics it is stated that the frictional
-  resistance is independent of the nature of the solid surface. The
-  explanation of this was supposed to be that a film of fluid remained
-  attached to the solid surface, the resistance being generated between
-  this fluid layer and layers more distant from the surface. At
-  extremely low velocities the solid surface does not seem to have much
-  influence on the friction. In Coulomb's experiments a metal surface
-  covered with tallow, and oscillated in water, had exactly the same
-  resistance as a clean metal surface, and when sand was scattered over
-  the tallow the resistance was only very slightly increased. The
-  earlier calculations of the resistance of water at higher velocities
-  in iron and wood pipes and earthen channels seemed to give a similar
-  result. These, however, were erroneous, and it is now well understood
-  that differences of roughness of the solid surface very greatly
-  influence the friction, at such velocities as are common in
-  engineering practice. H. P. G. Darcy's experiments, for instance,
-  showed that in old and incrusted water mains the resistance was twice
-  or sometimes thrice as great as in new and clean mains.
-
-  S 66. _Ordinary Expressions for Fluid Friction at Velocities not
-  Extremely Small._--Let f be the frictional resistance estimated in
-  pounds per square foot of surface at a velocity of 1 ft. per second;
-  [omega] the area of the surface in square feet; and v its velocity in
-  feet per second relatively to the water in which it is immersed. Then,
-  in accordance with the laws stated above, the total resistance of the
-  surface is
-
-    R = f[omega]v^2   (1)
-
-  where f is a quantity approximately constant for any given surface. If
-
-    [xi] = 2gf/G,
-
-    R = [xi]G[omega]v^2/2g,   (2)
-
-  where [xi] is, like f, nearly constant for a given surface, and is
-  termed the coefficient of friction.
-
-  The following are average values of the coefficient of friction for
-  water, obtained from experiments on large plane surfaces, moved in an
-  indefinitely large mass of water.
-
-    +------------------------------------+--------------+-----------------+
-    |                                    | Coefficient  |    Frictional   |
-    |                                    | of Friction, |  Resistance in  |
-    |                                    |     [xi]     | lb. per sq. ft. |
-    |                                    |              |        f        |
-    +------------------------------------+--------------+-----------------+
-    |                                    |              |                 |
-    | New well-painted iron plate        |    .00489    |     .00473      |
-    | Painted and planed plank (Beaufoy) |    .00350    |     .00339      |
-    | Surface of iron ships (Rankine)    |    .00362    |     .00351      |
-    | Varnished surface (Froude)         |    .00258    |     .00250      |
-    | Fine sand surface     "            |    .00418    |     .00405      |
-    | Coarser sand surface  "            |    .00503    |     .00488      |
-    +------------------------------------+--------------+-----------------+
-
-  The distance through which the frictional resistance is overcome is v
-  ft. per second. The work expended in fluid friction is therefore given
-  by the equation--
-
-    Work expended = f[omega]v^3 foot-pounds per second \   (3).
-                  = [xi]G[omega]v^3/2g   "        "    /
-
-  The coefficient of friction and the friction per square foot of
-  surface can be indirectly obtained from observations of the discharge
-  of pipes and canals. In obtaining them, however, some assumptions as
-  to the motion of the water must be made, and it will be better
-  therefore to discuss these values in connexion with the cases to which
-  they are related.
-
-  Many attempts have been made to express the coefficient of friction in
-  a form applicable to low as well as high velocities. The older
-  hydraulic writers considered the resistance termed fluid friction to
-  be made up of two parts,--a part due directly to the distortion of the
-  mass of water and proportional to the velocity of the water relatively
-  to the solid surface, and another part due to kinetic energy imparted
-  to the water striking the roughnesses of the solid surface and
-  proportional to the square of the velocity. Hence they proposed to
-  take
-
-    [xi] = [alpha] + [beta]/v
-
-  in which expression the second term is of greatest importance at very
-  low velocities, and of comparatively little importance at velocities
-  over about 1/2 ft. per second. Values of [xi] expressed in this and
-  similar forms will be given in connexion with pipes and canals.
-
-  All these expressions must at present be regarded as merely empirical
-  expressions serving practical purposes.
-
-  The frictional resistance will be seen to vary through wider limits
-  than these expressions allow, and to depend on circumstances of which
-  they do not take account.
-
-  S 67. _Coulomb's Experiments._--The first direct experiments on fluid
-  friction were made by Coulomb, who employed a circular disk suspended
-  by a thin brass wire and oscillated in its own plane. His experiments
-  were chiefly made at very low velocities. When the disk is rotated to
-  any given angle, it oscillates under the action of its inertia and the
-  torsion of the wire. The oscillations diminish gradually in
-  consequence of the work done in overcoming the friction of the disk.
-  The diminution furnishes a means of determining the friction.
-
-  [Illustration: FIG. 78.]
-
-  Fig. 78 shows Coulomb's apparatus. LK supports the wire and disk: ag
-  is the brass wire, the torsion of which causes the oscillations; DS is
-  a graduated disk serving to measure the angles through which the
-  apparatus oscillates. To this the friction disk is rigidly attached
-  hanging in a vessel of water. The friction disks were from 4.7 to 7.7
-  in. diameter, and they generally made one oscillation in from 20 to 30
-  seconds, through angles varying from 360 deg. to 6 deg. When the
-  velocity of the circumference of the disk was less than 6 in. per
-  second, the resistance was sensibly proportional to the velocity.
-
-  _Beaufoy's Experiments._--Towards the end of the 18th century Colonel
-  Mark Beaufoy (1764-1827) made an immense mass of experiments on the
-  resistance of bodies moved through water (_Nautical and Hydraulic
-  Experiments_, London, 1834). Of these the only ones directly bearing
-  on surface friction were some made in 1796 and 1798. Smooth painted
-  planks were drawn through water and the resistance measured. For two
-  planks differing in area by 46 sq. ft., at a velocity of 10 ft. per
-  second, the difference of resistance, measured on the difference of
-  area, was 0.339 lb. per square foot. Also the resistance varied as the
-  1.949th power of the velocity.
-
-  [Illustration: FIG. 79.]
-
-  S 68. _Froude's Experiments._--The most important direct experiments
-  on fluid friction at ordinary velocities are those made by William
-  Froude (1810-1879) at Torquay. The method adopted in these experiments
-  was to tow a board in a still water canal, the velocity and the
-  resistance being registered by very ingenious recording arrangements.
-  The general arrangement of the apparatus is shown in fig. 79. AA is
-  the board the resistance of which is to be determined. B is a cutwater
-  giving a fine entrance to the plane surfaces of the board. CC is a bar
-  to which the board AA is attached, and which is suspended by a
-  parallel motion from a carriage running on rails above the still water
-  canal. G is a link by which the resistance of the board is transmitted
-  to a spiral spring H. A bar I rigidly connects the other end of the
-  spring to the carriage. The dotted lines K, L indicate the position of
-  a couple of levers by which the extension of the spring is caused to
-  move a pen M, which records the extension on a greatly increased
-  scale, by a line drawn on the paper cylinder N. This cylinder revolves
-  at a speed proportionate to that of the carriage, its motion being
-  obtained from the axle of the carriage wheels. A second pen O,
-  receiving jerks at every second and a quarter from a clock P, records
-  time on the paper cylinder. The scale for the line of resistance is
-  ascertained by stretching the spiral spring by known weights. The
-  boards used for the experiment were 3/16 in. thick, 19 in. deep, and
-  from 1 to 50 ft. in length, cutwater included. A lead keel
-  counteracted the buoyancy of the board. The boards were covered with
-  various substances, such as paint, varnish, Hay's composition,
-  tinfoil, &c., so as to try the effect of different degrees of
-  roughness of surface. The results obtained by Froude may be summarized
-  as follows:--
-
-  1. The friction per square foot of surface varies very greatly for
-  different surfaces, being generally greater as the sensible roughness
-  of the surface is greater. Thus, when the surface of the board was
-  covered as mentioned below, the resistance for boards 50 ft. long, at
-  10 ft. per second, was--
-
-    Tinfoil or varnish   0.25 lb. per sq. ft.
-    Calico               0.47     "      "
-    Fine sand            0.405    "      "
-    Coarser sand         0.488    "      "
-
-  2. The power of the velocity to which the friction is proportional
-  varies for different surfaces. Thus, with short boards 2 ft. long,
-
-    For tinfoil the resistance varied as v^(2.16).
-    For other surfaces the resistance varied as v^(2.00).
-
-  With boards 50 ft. long,
-
-    For varnish or tinfoil the resistance varied as v^(1.83).
-    For sand the resistance varied as v^(2.00).
-
-  3. The average resistance per square foot of surface was much greater
-  for short than for long boards; or, what is the same thing, the
-  resistance per square foot at the forward part of the board was
-  greater than the friction per square foot of portions more sternward.
-  Thus,
-
-                                      Mean Resistance in
-                                       lb. per sq. ft.
-    Varnished surface     2 ft. long        0.41
-                         50    "            0.25
-    Fine sand surface     2    "            0.81
-                         50    "            0.405
-
-  This remarkable result is explained thus by Froude: "The portion of
-  surface that goes first in the line of motion, in experiencing
-  resistance from the water, must in turn communicate motion to the
-  water, in the direction in which it is itself travelling. Consequently
-  the portion of surface which succeeds the first will be rubbing,
-  not against stationary water, but against water partially moving in
-  its own direction, and cannot therefore experience so much resistance
-  from it."
-
-  S 69. The following table gives a general statement of Froude's
-  results. In all the experiments in this table, the boards had a fine
-  cutwater and a fine stern end or run, so that the resistance was
-  entirely due to the surface. The table gives the resistances per
-  square foot in pounds, at the standard speed of 600 feet per minute,
-  and the power of the speed to which the friction is proportional, so
-  that the resistance at other speeds is easily calculated.
-
-    +------------+---------------------------------------------------------------------------+
-    |            |           Length of Surface, or Distance from Cutwater, in feet.          |
-    |            +------------------+------------------+------------------+------------------+
-    |            |       2 ft.      |       8 ft.      |       20 ft.     |      50 ft.      |
-    |            +------+-----+-----+------+-----+-----+------+-----+-----+------+-----+-----+
-    |            |   A  |  B  |  C  |   A  |  B  |  C  |   A  |  B  |  C  |   A  |  B  |  C  |
-    +------------+------+-----+-----+------+-----+-----+------+-----+-----+------+-----+-----+
-    | Varnish    | 2.00 | .41 |.390 | 1.85 |.325 |.264 | 1.85 |.278 |.240 | 1.83 |.250 |.226 |
-    | Paraffin   |  ..  | .38 |.370 | 1.94 |.314 |.260 | 1.93 |.271 |.237 |  ..  |  .. |  .. |
-    | Tinfoil    | 2.16 | .30 |.295 | 1.99 |.278 |.263 | 1.90 |.262 |.244 | 1.83 |.246 |.232 |
-    | Calico     | 1.93 | .87 |.725 | 1.92 |.626 |.504 | 1.89 |.531 |.447 | 1.87 |.474 |.423 |
-    | Fine sand  | 2.00 | .81 |.690 | 2.00 |.583 |.450 | 2.00 |.480 |.384 | 2.06 |.405 |.337 |
-    | Medium sand| 2.00 | .90 |.730 | 2.00 |.625 |.488 | 2.00 |.534 |.465 | 2.00 |.488 |.456 |
-    | Coarse sand| 2.00 |1.10 |.880 | 2.00 |.714 |.520 | 2.00 |.588 |.490 |  ..  |  .. |  .. |
-    +--------- --+------+-----+-----+------+-----+-----+------+-----+-----+------+-----+-----+
-
-  Columns A give the power of the speed to which the resistance is
-  approximately proportional.
-
-  Columns B give the mean resistance per square foot of the whole
-  surface of a board of the lengths stated in the table.
-
-  Columns C give the resistance in pounds of a square foot of surface at
-  the distance sternward from the cutwater stated in the heading.
-
-  Although these experiments do not directly deal with surfaces of
-  greater length than 50 ft., they indicate what would be the
-  resistances of longer surfaces. For at 50 ft. the decrease of
-  resistance for an increase of length is so small that it will make no
-  very great difference in the estimate of the friction whether we
-  suppose it to continue to diminish at the same rate or not to diminish
-  at all. For a varnished surface the friction at 10 ft. per second
-  diminishes from 0.41 to 0.32 lb. per square foot when the length is
-  increased from 2 to 8 ft., but it only diminishes from 0.278 to 0.250
-  lb. per square foot for an increase from 20 ft. to 50 ft.
-
-  If the decrease of friction sternwards is due to the generation of a
-  current accompanying the moving plane, there is not at first sight any
-  reason why the decrease should not be greater than that shown by the
-  experiments. The current accompanying the board might be assumed to
-  gain in volume and velocity sternwards, till the velocity was nearly
-  the same as that of the moving plane and the friction per square foot
-  nearly zero. That this does not happen appears to be due to the mixing
-  up of the current with the still water surrounding it. Part of the
-  water in contact with the board at any point, and receiving energy of
-  motion from it, passes afterwards to distant regions of still water,
-  and portions of still water are fed in towards the board to take its
-  place. In the forward part of the board more kinetic energy is given
-  to the current than is diffused into surrounding space, and the
-  current gains in velocity. At a greater distance back there is an
-  approximate balance between the energy communicated to the water and
-  that diffused. The velocity of the current accompanying the board
-  becomes constant or nearly constant, and the friction per square foot
-  is therefore nearly constant also.
-
-  S 70. _Friction of Rotating Disks._--A rotating disk is virtually a
-  surface of unlimited extent and it is convenient for experiments on
-  friction with different surfaces at different speeds. Experiments
-  carried out by Professor W. C. Unwin (_Proc. Inst. Civ. Eng._ lxxx.)
-  are useful both as illustrating the laws of fluid friction and as
-  giving data for calculating the resistance of the disks of turbines
-  and centrifugal pumps. Disks of 10, 15 and 20 in. diameter fixed on a
-  vertical shaft were rotated by a belt driven by an engine. They were
-  enclosed in a cistern of water between parallel top and bottom fixed
-  surfaces. The cistern was suspended by three fine wires. The friction
-  of the disk is equal to the tendency of the cistern to rotate, and
-  this was measured by balancing the cistern by a fine silk cord passing
-  over a pulley and carrying a scale pan in which weights could be
-  placed.
-
-  If [omega] is an element of area on the disk moving with the velocity
-  v, the friction on this element is f[omega]v^n, where f and n are
-  constant for any given kind of surface. Let [alpha] be the angular
-  velocity of rotation, R the radius of the disk. Consider a ring of the
-  surface between r and r + dr. Its area is 2[pi]r dr, its velocity
-  [alpha]r and the friction of this ring is f2[pi]r dr[alpha]^n r^n. The
-  moment of the friction about the axis of rotation is
-  2[pi][alpha]^n fr^(n + 2)dr, and the total moment of friction for the
-  two sides of the disk is
-                          _
-                         /R
-    M = 4[pi][alpha]^n f | r^(n+2) dr = {4[pi][alpha]^n /(n + 3)}fR^(n+3).      .
-                        _/0
-
-  If N is the number of revolutions per sec.,
-
-    M = {2^(n+2) [pi]^(n+1) N^n/(n + 3)} fR^(n+3),
-
-  and the work expended in rotating the disk is
-
-    M[alpha] = {2^(n+3)[pi]^(n+2)N^(n+1)/(n + 3)} fR^(n+3), foot lb. per sec.
-
-  The experiments give directly the values of M for the disks
-  corresponding to any speed N. From these the values of f and n can be
-  deduced, f being the friction per square foot at unit velocity. For
-  comparison with Froude's results it is convenient to calculate the
-  resistance at 10 ft. per second, which is F = f10^n.
-
-  The disks were rotated in chambers 22 in. diameter and 3, 6 and 12 in.
-  deep. In all cases the friction of the disks increased a little as the
-  chamber was made larger. This is probably due to the stilling of the
-  eddies against the surface of the chamber and the feeding back of the
-  stilled water to the disk. Hence the friction depends not only on the
-  surface of the disk but to some extent on the surface of the chamber
-  in which it rotates. If the surface of the chamber is made rougher by
-  covering with coarse sand there is also an increase of resistance.
-
-  For the smoother surfaces the friction varied as the 1.85th power of
-  the velocity. For the rougher surfaces the power of the velocity to
-  which the resistance was proportional varied from 1.9 to 2.1. This is
-  in agreement with Froude's results.
-
-  Experiments with a bright brass disk showed that the friction
-  decreased with increase of temperature. The diminution between 41 deg.
-  and 130 deg. F. amounted to 18%. In the general equation M = cN^n for
-  any given disk,
-
-    c_t = 0.1328(1 - 0.0021t),
-
-  where c_t is the value of c for a bright brass disk 0.85 ft. in
-  diameter at a temperature t deg. F.
-
-  The disks used were either polished or made rougher by varnish or by
-  varnish and sand. The following table gives a comparison of the
-  results obtained with the disks and Froude's results on planks 50 ft.
-  long. The values given are the resistances per square foot at 10 ft.
-  per sec.
-
-    _Froude's Experiments._ |          _Disk Experiments._
-                            |
-    Tinfoil surface  0.232  |   Bright brass      0.202 to 0.229
-    Varnish          0.226  |   Varnish           0.220 to 0.233
-    Fine sand        0.337  |   Fine sand              0.339
-    Medium sand      0.456  |   Very coarse sand  0.587 to 0.715
-
-
-  VIII. STEADY FLOW OF WATER IN PIPES OF UNIFORM SECTION.
-
-  S 71. The ordinary theory of the flow of water in pipes, on which all
-  practical formulae are based, assumes that the variation of velocity
-  at different points of any cross section may be neglected. The water
-  is considered as moving in plane layers, which are driven through the
-  pipe against the frictional resistance, by the difference of pressure
-  at or elevation of the ends of the pipe. If the motion is steady the
-  velocity at each cross section remains the same from moment to moment,
-  and if the cross sectional area is constant the velocity at all
-  sections must be the same. Hence the motion is uniform. The most
-  important resistance to the motion of the water is the surface
-  friction of the pipe, and it is convenient to estimate this
-  independently of some smaller resistances which will be accounted for
-  presently.
-
-  [Illustration: FIG. 80.]
-
-  In any portion of a uniform pipe, excluding for the present the ends
-  of the pipe, the water enters and leaves at the same velocity. For
-  that portion therefore the work of the external forces and of the
-  surface friction must be equal. Let fig. 80 represent a very short
-  portion of the pipe, of length dl, between cross sections at z and z +
-  dz ft. above any horizontal datum line xx, the pressures at the cross
-  sections being p and p + dp lb. per square foot. Further, let Q be the
-  volume of flow or discharge of the pipe per second, [Omega] the area
-  of a normal cross section, and [chi] the perimeter of the pipe. The Q
-  cubic feet, which flow through the space considered per second, weigh
-  GQ lb., and fall through a height -dz ft. The work done by gravity is
-  then
-
-    -GQ dz;
-
-  a positive quantity if dz is negative, and vice versa. The resultant
-  pressure parallel to the axis of the pipe is p - (p + dp) = -dp lb.
-  per square foot of the cross section. The work of this pressure on the
-  volume Q is
-
-    -Q dp.
-
-  The only remaining force doing work on the system is the friction
-  against the surface of the pipe. The area of that surface is [chi]dl.
-
-  The work expended in overcoming the frictional resistance per second
-  is (see S 66, eq. 3)
-
-    -[zeta]G[chi]dlv^3/2g,
-
-  or, since Q = [Omega]v,
-
-    -[zeta]G([chi]/[Omega]) Q (v^2/2g) dl;
-
-  the negative sign being taken because the work is done against a
-  resistance. Adding all these portions of work, and equating the result
-  to zero, since the motion is uniform,--
-
-    -GQ dz - Q dp - [zeta]G([chi]/[Omega]) Q (v^2/2g) dl = 0.
-
-  Dividing by GQ,
-
-    dz + dp/G + [zeta]([chi]/[Omega])(v^2/2g) dl = 0.
-
-  Integrating,
-
-    z + p/G + [zeta]([chi]/[Omega])(v^2/2g)l = constant.   (1)
-
-  S 72. Let A and B (fig. 81) be any two sections of the pipe for which
-  p, z, l have the values p1, z1, l1, and p2, z2, l2, respectively. Then
-
-    z1 + p1/G + [zeta]([chi]/[Omega])(v^2/2g)l1
-      = z2 + p2/G + [zeta]([chi]/[Omega])(v^2/2g)l2;
-
-  or, if l2 - l1 = L, rearranging the terms,
-
-    [zeta]v^2/2g = (1/L){(z1 + p1/G) - (z2 + p2/G)}[Omega]/[chi].   (2)
-
-  Suppose pressure columns introduced at A and B. The water will rise in
-  those columns to the heights p1/G and p2/G due to the pressures p1 and
-  p2 at A and B. Hence (z1 + p1/G) - (z2 + p2/G) is the quantity
-  represented in the figure by DE, the fall of level of the pressure
-  columns, or _virtual fall_ of the pipe. If there were no friction in
-  the pipe, then by Bernoulli's equation there would be no fall of level
-  of the pressure columns, the velocity being the same at A and B. Hence
-  DE or h is the head lost in friction in the distance AB. The quantity
-  DE/AB = h/L is termed the virtual slope of the pipe or virtual fall
-  per foot of length. It is sometimes termed very conveniently the
-  relative fall. It will be denoted by the symbol i.
-
-  [Illustration: FIG. 81.]
-
-  The quantity [Omega]/[chi] which appears in many hydraulic equations
-  is called the hydraulic mean radius of the pipe. It will be denoted by
-  m.
-
-  Introducing these values,
-
-    [zeta]v^2/2g = mh/L = mi.   (3)
-
-  For pipes of circular section, and diameter d,
-
-    m = [Omega]/[chi] = (1/4)[pi]d^2/[pi]d = (1/4)d.
-
-  Then
-
-    [zeta]v^2/2g = (1/4)dh/L = (1/4)di;   (4)
-
-  or
-
-    h = [zeta](4L/d)(v^2/2g);   (4a)
-
-  which shows that the head lost in friction is proportional to the head
-  due to the velocity, and is found by multiplying that head by the
-  coefficient 4[zeta]L/d. It is assumed above that the atmospheric
-  pressure at C and D is the same, and this is usually nearly the case.
-  But if C and D are at greatly different levels the excess of
-  barometric pressure at C, in feet of water, must be added to p2/G.
-
-  S 73. _Hydraulic Gradient or Line of Virtual Slope._--Join CD. Since
-  the head lost in friction is proportional to L, any intermediate
-  pressure column between A and B will have its free surface on the line
-  CD, and the vertical distance between CD and the pipe at any point
-  measures the pressure, exclusive of atmospheric pressure, in the pipe
-  at that point. If the pipe were laid along the line CD instead of AB,
-  the water would flow at the same velocity by gravity without any
-  change of pressure from section to section. Hence CD is termed the
-  virtual slope or hydraulic gradient of the pipe. It is the line of
-  free surface level for each point of the pipe.
-
-  If an ordinary pipe, connecting reservoirs open to the air, rises at
-  any joint above the line of virtual slope, the pressure at that point
-  is less than the atmospheric pressure transmitted through the pipe. At
-  such a point there is a liability that air may be disengaged from the
-  water, and the flow stopped or impeded by the accumulation of air. If
-  the pipe rises more than 34 ft. above the line of virtual slope, the
-  pressure is negative. But as this is impossible, the continuity of the
-  flow will be broken.
-
-  If the pipe is not straight, the line of virtual slope becomes a
-  curved line, but since in actual pipes the vertical alterations of
-  level are generally small, compared with the length of the pipe,
-  distances measured along the pipe are sensibly proportional to
-  distances measured along the horizontal projection of the pipe. Hence
-  the line of hydraulic gradient may be taken to be a straight line
-  without error of practical importance.
-
-  [Illustration: FIG. 82.]
-
-  S 74. _Case of a Uniform Pipe connecting two Reservoirs, when all the
-  Resistances are taken into account._--Let h (fig. 82) be the
-  difference of level of the reservoirs, and v the velocity, in a pipe
-  of length L and diameter d. The whole work done per second is
-  virtually the removal of Q cub. ft. of water from the surface of the
-  upper reservoir to the surface of the lower reservoir, that is GQh
-  foot-pounds. This is expended in three ways. (1) The head v^2/2g,
-  corresponding to an expenditure of GQv^2/2g foot-pounds of work, is
-  employed in giving energy of motion to the water. This is ultimately
-  wasted in eddying motions in the lower reservoir. (2) A portion of
-  head, which experience shows may be expressed in the form
-  [zeta]0v^2/2g, corresponding to an expenditure of GQ[zeta]0v^2/2g
-  foot-pounds of work, is employed in overcoming the resistance at the
-  entrance to the pipe. (3) As already shown the head expended in
-  overcoming the surface friction of the pipe is [zeta](4L/d)(v^2/2g)
-  corresponding to GQ[zeta](4L/d)(v^2/2g) foot-pounds of work. Hence
-
-    GQh = GQv^2/2g + GQ[zeta]0v^2/2g + GQ[zeta].4L.v^2/d.2g;
-
-    h = (1 + [zeta]0 + [zeta].4L/d)v^2/2g.
-                                                      (5)
-    v = 8.025 [root][hd/{(1 + [zeta]0)d + 4[zeta]L}].
-
-  If the pipe is bell-mouthed, [zeta]0 is about = .08. If the entrance
-  to the pipe is cylindrical, [zeta]0 = 0.505. Hence 1 + [zeta]0 = 1.08
-  to 1.505. In general this is so small compared with [zeta]4L/d that,
-  for practical calculations, it may be neglected; that is, the losses
-  of head other than the loss in surface friction are left out of the
-  reckoning. It is only in short pipes and at high velocities that it is
-  necessary to take account of the first two terms in the bracket, as
-  well as the third. For instance, in pipes for the supply of turbines,
-  v is usually limited to 2 ft. per second, and the pipe is bellmouthed.
-  Then 1.08v^2/2g = 0.067 ft. In pipes for towns' supply v may range
-  from 2 to 4(1/2) ft. per second, and then 1.5v^2/2g = 0.1 to 0.5 ft.
-  In either case this amount of head is small compared with the whole
-  virtual fall in the cases which most commonly occur.
-
-  When d and v or d and h are given, the equations above are solved
-  quite simply. When v and h are given and d is required, it is better
-  to proceed by approximation. Find an approximate value of d by
-  assuming a probable value for [zeta] as mentioned below. Then from
-  that value of d find a corrected value for [zeta] and repeat the
-  calculation.
-
-  The equation above may be put in the form
-
-    h = (4[zeta]/d)[{(1 + [zeta]0)d/4[zeta]} + L] v^2/2g;   (6)
-
-  from which it is clear that the head expended at the mouthpiece is
-  equivalent to that of a length
-
-    (1 + [zeta]0)d/4[zeta]
-
-  of the pipe. Putting 1 + [zeta]0 = 1.505 and [zeta] = 0.01, the length
-  of pipe equivalent to the mouthpiece is 37.6d nearly. This may be
-  added to the actual length of the pipe to allow for mouthpiece
-  resistance in approximate calculations.
-
-  S 75. _Coefficient of Friction for Pipes discharging Water._--From the
-  average of a large number of experiments, the value of [zeta] for
-  ordinary iron pipes is
-
-    [zeta] = 0.007567.   (7)
-
-  But practical experience shows that no single value can be taken
-  applicable to very different cases. The earlier hydraulicians occupied
-  themselves chiefly with the dependence of [zeta] on the velocity.
-  Having regard to the difference of the law of resistance at very low
-  and at ordinary velocities, they assumed that [zeta] might be
-  expressed in the form
-
-    [zeta] = a + [beta]/v.
-
-  The following are the best numerical values obtained for [zeta] so
-  expressed:--
-
-    +----------------------------------+----------+----------+
-    |                                  |  [alpha] |  [beta]  |
-    +----------------------------------+----------+----------+
-    | R. de Prony (from 51 experiments)| 0.006836 | 0.001116 |
-    | J. F. d'Aubuisson de Voisins     | 0.00673  | 0.001211 |
-    | J. A. Eytelwein                  | 0.005493 | 0.00143  |
-    +----------------------------------+----------+----------+
-
-  Weisbach proposed the formula
-
-    4[zeta] = [alpha] + [beta]/[root]v = 0.003598 + 0.004289/[root]v.   (8)
-
-  S 76. _Darcy's Experiments on Friction in Pipes._--All previous
-  experiments on the resistance of pipes were superseded by the
-  remarkable researches carried out by H. P. G. Darcy (1803-1858), the
-  Inspector-General of the Paris water works. His experiments were
-  carried out on a scale, under a variation of conditions, and with a
-  degree of accuracy which leaves little to be desired, and the results
-  obtained are of very great practical importance. These results may be
-  stated thus:--
-
-  1. For new and clean pipes the friction varies considerably with the
-  nature and polish of the surface of the pipe. For clean cast iron it
-  is about 1(1/2) times as great as for cast iron covered with pitch.
-
-  2. The nature of the surface has less influence when the pipes are old
-  and incrusted with deposits, due to the action of the water. Thus old
-  and incrusted pipes give twice as great a frictional resistance as new
-  and clean pipes. Darcy's coefficients were chiefly determined from
-  experiments on new pipes. He doubles these coefficients for old and
-  incrusted pipes, in accordance with the results of a very limited
-  number of experiments on pipes containing incrustations and deposits.
-
-  3. The coefficient of friction may be expressed in the form [zeta] =
-  [alpha] + [beta]/v; but in pipes which have been some time in use it
-  is sufficiently accurate to take [zeta] = [alpha]1 simply, where
-  [alpha]1 depends on the diameter of the pipe alone, but [alpha] and
-  [beta] on the other hand depend both on the diameter of the pipe and
-  the nature of its surface. The following are the values of the
-  constants.
-
-  For pipes which have been some time in use, neglecting the term
-  depending on the velocity;
-
-    [zeta] = [alpha](1 + [beta]/d).   (9)
-
-    +-------------------------------------------------+---------+------+
-    |                                                 | [alpha] |[beta]|
-    +-------------------------------------------------+---------+------+
-    | For drawn wrought-iron or smooth cast-iron pipes| .004973 | .084 |
-    | For pipes altered by light incrustations        | .00996  | .084 |
-    +-------------------------------------------------+---------+------+
-
-  These coefficients may be put in the following very simple form,
-  without sensibly altering their value:--
-
-    For clean pipes              [zeta] = .005(1 + (1/12)d)   (9a)
-    For slightly incrusted pipes [zeta] = .01(1 + (1/12)d)
-
-    _Darcy's Value of the Coefficient of Friction [zeta] for Velocities
-    not less than 4 in. per second._
-
-    +----------+------------------++----------+------------------+
-    | Diameter |     [zeta]       || Diameter |     [zeta]       |
-    | of Pipe  +--------+---------|| of Pipe  +------------------+
-    |in Inches.|  New   |Incrusted||in Inches.|  New   |Incrusted|
-    |          | Pipes. |  Pipes. ||          | Pipes. |  Pipes. |
-    +----------+--------+---------++----------+--------+---------+
-    |     2    |0.00750 |0.01500  ||    18    | .00528 | .01056  |
-    |     3    | .00667 | .01333  ||    21    | .00524 | .01048  |
-    |     4    | .00625 | .01250  ||    24    | .00521 | .01042  |
-    |     5    | .00600 | .01200  ||    27    | .00519 | .01037  |
-    |     6    | .00583 | .01167  ||    30    | .00517 | .01033  |
-    |     7    | .00571 | .01143  ||    36    | .00514 | .01028  |
-    |     8    | .00563 | .01125  ||    42    | .00512 | .01024  |
-    |     9    | .00556 | .01111  ||    48    | .00510 | .01021  |
-    |    12    | .00542 | .01083  ||    54    | .00509 | .01019  |
-    |    15    | .00533 | .01067  ||          |        |         |
-    +----------+--------+---------++----------+--------+---------+
-
-  These values of [zeta] are, however, not exact for widely differing
-  velocities. To embrace all cases Darcy proposed the expression
-
-    [zeta] = ([alpha] + [alpha]1/d) + ([beta] + [beta]1/d^2)/v;   (10)
-
-  which is a modification of Coulomb's, including terms expressing the
-  influence of the diameter and of the velocity. For clean pipes Darcy
-  found these values
-
-    [alpha]  = .004346
-    [alpha]1 = .0003992
-    [beta]   = .0010182
-    [beta]1  = .000005205.
-
-  It has become not uncommon to calculate the discharge of pipes by the
-  formula of E. Ganguillet and W. R. Kutter, which will be discussed
-  under the head of channels. For the value of c in the relation v = c
-  [root](mi), Ganguillet and Kutter take
-
-            41.6 + 1.811/n + .00281/i
-    c = ----------------------------------
-        1 + [(41.6 + .00281/i)(n/[root]m)]
-
-  where n is a coefficient depending only on the roughness of the pipe.
-  For pipes uncoated as ordinarily laid n = 0.013. The formula is very
-  cumbrous, its form is not rationally justifiable and it is not at all
-  clear that it gives more accurate values of the discharge than simpler
-  formulae.
-
-  S 77. _Later Investigations on Flow in Pipes._--The foregoing
-  statement gives the theory of flow in pipes so far as it can be put in
-  a simple rational form. But the conditions of flow are really more
-  complicated than can be expressed in any rational form. Taking even
-  selected experiments the values of the empirical coefficient [zeta]
-  range from 0.16 to 0.0028 in different cases. Hence means of
-  discriminating the probable value of [zeta] are necessary in using the
-  equations for practical purposes. To a certain extent the knowledge
-  that [zeta] decreases with the size of the pipe and increases very
-  much with the roughness of its surface is a guide, and Darcy's method
-  of dealing with these causes of variation is very helpful. But a
-  further difficulty arises from the discordance of the results of
-  different experiments. For instance F. P. Stearns and J. M. Gale both
-  experimented on clean asphalted cast-iron pipes, 4 ft. in diameter.
-  According to one set of gaugings [zeta] = .0051, and according to the
-  other [zeta] = .0031. It is impossible in such cases not to suspect
-  some error in the observations or some difference in the condition of
-  the pipes not noticed by the observers.
-
-  It is not likely that any formula can be found which will give exactly
-  the discharge of any given pipe. For one of the chief factors in any
-  such formula must express the exact roughness of the pipe surface, and
-  there is no scientific measure of roughness. The most that can be done
-  is to limit the choice of the coefficient for a pipe within certain
-  comparatively narrow limits. The experiments on fluid friction show
-  that the power of the velocity to which the resistance is proportional
-  is not exactly the square. Also in determining the form of his
-  equation for [zeta] Darcy used only eight out of his seventeen series
-  of experiments, and there is reason to think that some of these were
-  exceptional. Barre de Saint-Venant was the first to propose a formula
-  with two constants,
-
-    dh/4l = mV^n,
-
-  where m and n are experimental constants. If this is written in the
-  form
-
-    log m + n log v = log (dh/4l),
-
-  we have, as Saint-Venant pointed out, the equation to a straight line,
-  of which m is the ordinate at the origin and n the ratio of the slope.
-  If a series of experimental values are plotted logarithmically the
-  determination of the constants is reduced to finding the straight line
-  which most nearly passes through the plotted points. Saint-Venant
-  found for n the value of 1.71. In a memoir on the influence of
-  temperature on the movement of water in pipes (Berlin, 1854) by G. H.
-  L. Hagen (1797-1884) another modification of the Saint-Venant formula
-  was given. This is h/l = mv^n/d^x, which involves three experimental
-  coefficients. Hagen found n = 1.75; x = 1.25; and m was then nearly
-  independent of variations of v and d. But the range of cases examined
-  was small. In a remarkable paper in the _Trans. Roy. Soc._, 1883,
-  Professor Osborne Reynolds made much clearer the change from regular
-  stream line motion at low velocities to the eddying motion, which
-  occurs in almost all the cases with which the engineer has to deal.
-  Partly by reasoning, partly by induction from the form of
-  logarithmically plotted curves of experimental results, he arrived at
-  the general equation h/l = c(v^n/d^(3 - n))P^(2 - n), where n = l for
-  low velocities and n = 1.7 to 2 for ordinary velocities. P is a
-  function of the temperature. Neglecting variations of temperature
-  Reynold's formula is identical with Hagen's if x = 3 - n. For
-  practical purposes Hagen's form is the more convenient.
-
-    _Values of Index of Velocity._
-
-    +--------------------+---------------+----------+---------------+
-    |                    |               | Diameter |               |
-    |  Surface of Pipe.  |   Authority.  | of Pipe  |  Values of n. |
-    |                    |               |in Metres.|               |
-    +--------------------+---------------+----------+---------------+
-    | Tin plate          | Bossut        |  /.036   | 1.697 \  1.72 |
-    |                    |               |  \.054   | 1.730 /       |
-    |                    |               |          |               |
-    | Wrought iron (gas  | Hamilton Smith|  /.0159  | 1.756 \  1.75 |
-    |   pipe)            |               |  \.0267  | 1.770 /       |
-    |                    |               |          |               |
-    |                    |               |  /.014   | 1.866 \       |
-    | Lead               | Darcy         | < .027   | 1.755  > 1.77 |
-    |                    |               |  \.041   | 1.760 /       |
-    |                    |               |          |               |
-    | Clean brass        | Mair          |   .036   | 1.795    1.795|
-    |                    |               |          |               |
-    |                  / | Hamilton Smith| / .0266  | 1.760 \       |
-    | Asphalted       <  | Lampe.        |<  .4185  | 1.850  > 1.85 |
-    |                  | | W. W. Bonn    | | .306   | 1.582 |       |
-    |                  \ | Stearns       | \1.219   | 1.880 /       |
-    |                    |               |          |               |
-    | Riveted wrought \  |               | /.2776   | 1.804 \       |
-    |   iron           > | Hamilton Smith|< .3219   | 1.892  > 1.87 |
-    |                 /  |               | \.3749   | 1.852 /       |
-    |                    |               |          |               |
-    | Wrought iron (gas\ |               | /.0122   | 1.900 \       |
-    |   pipe)           >| Darcy         |< .0266   | 1.899  > 1.87 |
-    |                  / |               | \.0395   | 1.838 /       |
-    |                    |               |          |               |
-    |                    |               | /.0819   | 1.950 \       |
-    | New cast iron      | Darcy         |< .137    | 1.923  > 1.95 |
-    |                    |               | |.188    | 1.957 |       |
-    |                    |               | \.50     | 1.950 /       |
-    |                    |               |          |               |
-    |                    |               | /.0364   | 1.835 \       |
-    |                    |               | |.0801   | 2.000  > 2.00 |
-    | Cleaned cast iron  | Darcy         |< .2447   | 2.000 |       |
-    |                    |               | \.397    | 2.07  /       |
-    |                    |               |          |               |
-    |                    |               | /.0359   | 1.980 \       |
-    | Incrusted cast iron| Darcy         |< .0795   | 1.990  > 2.00 |
-    |                    |               | \.2432   | 1.990 /       |
-    +--------------------+---------------+----------+---------------+
-
-  [Illustration: FIG. 83.]
-
-  In 1886, Professor W. C. Unwin plotted logarithmically all the most
-  trustworthy experiments on flow in pipes then available.[5] Fig. 83
-  gives one such plotting. The results of measuring the slopes of the
-  lines drawn through the plotted points are given in the table.
-
-  It will be seen that the values of the index n range from 1.72 for the
-  smoothest and cleanest surface, to 2.00 for the roughest. The numbers
-  after the brackets are rounded off numbers.
-
-  The value of n having been thus determined, values of m/d^x were next
-  found and averaged for each pipe. These were again plotted
-  logarithmically in order to find a value for x. The lines were not
-  very regular, but in all cases the slope was greater than 1 to 1, so
-  that the value of x must be greater than unity. The following table
-  gives the results and a comparison of the value of x and Reynolds's
-  value 3 - n.
-
-    +-----------------------+--------+--------+-------+
-    |      Kind of Pipe.    |    n    | 3 - n |   x   |
-    +-----------------------+--------+--------+-------+
-    | Tin plate             |  1.72  |  1.28  | 1.100 |
-    | Wrought iron (Smith)  |  1.75  |  1.25  | 1.210 |
-    | Asphalted pipes       |  1.85  |  1.15  | 1.127 |
-    | Wrought iron (Darcy)  |  1.87  |  1.13  | 1.680 |
-    | Riveted wrought iron  |  1.87  |  1.13  | 1.390 |
-    | New cast iron         |  1.95  |  1.05  | 1.168 |
-    | Cleaned cast iron     |  2.00  |  1.00  | 1.168 |
-    | Incrusted cast iron   |  2.00  |  1.00  | 1.160 |
-    +-----------------------+--------+--------+-------+
-
-  With the exception of the anomalous values for Darcy's wrought-iron
-  pipes, there is no great discrepancy between the values of x and 3 -
-  n, but there is no appearance of relation in the two quantities. For
-  the present it appears preferable to assume that x is independent of
-  n.
-
-  It is now possible to obtain values of the third constant m, using the
-  values found for n and x. The following table gives the results, the
-  values of m being for metric measures.
-
-  Here, considering the great range of diameters and velocities in the
-  experiments, the constancy of m is very satisfactorily close. The
-  asphalted pipes give rather variable values. But, as some of these
-  were new and some old, the variation is, perhaps, not surprising. The
-  incrusted pipes give a value of m quite double that for new pipes but
-  that is perfectly consistent with what is known of fluid friction in
-  other cases.
-
-    +---------------+----------+-----------+----------+----------------+
-    |               | Diameter | Value of  |   Mean   |                |
-    | Kind of Pipe. |    in    |     m.    |  Value   |   Authority.   |
-    |               |  Metres. |           |   of m.  |                |
-    +---------------+----------+-----------+----------+----------------+
-    | Tin plate     |  / 0.036 | .01697 \  | .01686   | Bossut         |
-    |               |  \ 0.054 | .01676 /  |          |                |
-    |               |          |           |          |                |
-    | Wrought iron  |  / 0.016 | .01302 \  | .01310   | Hamilton Smith |
-    |               |  \ 0.027 | .01319 /  |          |                |
-    |               |          |           |          |                |
-    |               |  / 0.027 | .01749 \  |        / | Hamilton Smith |
-    |               |  | 0.306 | .02058 |  |        | | W. W. Bonn     |
-    | Asphalted     | <  0.306 | .02107  > | .01831<  | W. W. Bonn     |
-    |   pipes       |  | 0.419 | .01650 |  |        | | Lampe          |
-    |               |  | 1.219 | .01317 |  |        | | Stearns        |
-    |               |  \ 1.219 | .02107 /  |        \ | Gale           |
-    |               |          |           |          |                |
-    |               |  / 0.278 | .01370 \  |          |                |
-    |               |  | 0.322 | .01440 |  |          |                |
-    | Riveted       | <  0.375 | .01390  > | .01403   | Hamilton Smith |
-    |   wrought iron|  | 0.432 | .01368 |  |          |                |
-    |               |  \ 0.657 | .01448 /  |          |                |
-    |               |          |           |          |                |
-    |               |  / 0.082 | .01725 \  |          |                |
-    | New cast iron | <  0.137 | .01427  > | .01658   | Darcy          |
-    |               |  | 0.188 | .01734 |  |          |                |
-    |               |  \ 0.500 | .01745 /  |          |                |
-    |               |          |           |          |                |
-    | Cleaned cast  |  / 0.080 | .01979 \  |          |                |
-    |   iron        | <  0.245 | .02091  > | .01994   | Darcy          |
-    |               |  \ 0.297 | .01913 /  |          |                |
-    |               |          |           |          |                |
-    | Incrusted cast|  / 0.036 | .03693 \  |          |                |
-    |   iron        | <  0.080 | .03530  > | .03643   | Darcy          |
-    |               |  \ 0.243 | .03706 /  |          |                |
-    +---------------+----------+-----------+----------+----------------+
-
-
-  _General Mean Values of Constants._
-
-  The general formula (Hagen's)--h/l = mv^n/d^x.2g--can therefore be
-  taken to fit the results with convenient closeness, if the following
-  mean values of the coefficients are taken, the unit being a metre:--
-
-    +----------------------+-------+-------+------+
-    |     Kind of Pipe.    |   m   |   x   |   n  |
-    +----------------------+-------+-------+------+
-    | Tin plate            | .0169 | 1.10  | 1.72 |
-    | Wrought iron         | .0131 | 1.21  | 1.75 |
-    | Asphalted iron       | .0183 | 1.127 | 1.85 |
-    | Riveted wrought iron | .0140 | 1.390 | 1.87 |
-    | New cast iron        | .0166 | 1.168 | 1.95 |
-    | Cleaned cast iron    | .0199 | 1.168 | 2.0  |
-    | Incrusted cast iron  | .0364 | 1.160 | 2.0  |
-    +----------------------+-------+-------+------+
-
-  The variation of each of these coefficients is within a comparatively
-  narrow range, and the selection of the proper coefficient for any
-  given case presents no difficulty, if the character of the surface of
-  the pipe is known.
-
-  It only remains to give the values of these coefficients when the
-  quantities are expressed in English feet. For English measures the
-  following are the values of the coefficients:--
-
-    +----------------------+-------+-------+------+
-    |     Kind of Pipe.    |   m   |   x   |   n  |
-    +----------------------+-------+-------+------+
-    | Tin plate            | .0265 | 1.10  | 1.72 |
-    | Wrought iron         | .0226 | 1.21  | 1.75 |
-    | Asphalted iron       | .0254 | 1.127 | 1.85 |
-    | Riveted wrought iron | .0260 | 1.390 | 1.87 |
-    | New cast iron        | .0215 | 1.168 | 1.95 |
-    | Cleaned cast iron    | .0243 | 1.168 | 2.0  |
-    | Incrusted cast iron  | .0440 | 1.160 | 2.0  |
-    +----------------------+-------+-------+------+
-
-  S 78. _Distribution of Velocity in the Cross Section of a
-  Pipe._--Darcy made experiments with a Pitot tube in 1850 on the
-  velocity at different points in the cross section of a pipe. He
-  deduced the relation
-
-    V - v = 11.3(r^(3/2)/R) [root]i,
-
-  where V is the velocity at the centre and v the velocity at radius r
-  in a pipe of radius R with a hydraulic gradient i. Later Bazin
-  repeated the experiments and extended them (_Mem. de l'Academie des
-  Sciences_, xxxii. No. 6). The most important result was the ratio of
-  mean to central velocity. Let b = Ri/U^2, where U is the mean velocity
-  in the pipe; then V/U = 1 + 9.03 [root]b. A very useful result for
-  practical purposes is that at 0.74 of the radius of the pipe the
-  velocity is equal to the mean velocity. Fig. 84 gives the velocities
-  at different radii as determined by Bazin.
-
-  [Illustration: FIG. 84.]
-
-  S 79. _Influence of Temperature on the Flow through Pipes._--Very
-  careful experiments on the flow through a pipe 0.1236 ft. in diameter
-  and 25 ft. long, with water at different temperatures, have been made
-  by J. G. Mair (_Proc. Inst. Civ. Eng._ lxxxiv.). The loss of head was
-  measured from a point 1 ft. from the inlet, so that the loss at entry
-  was eliminated. The 1(1/2) in. pipe was made smooth inside and to gauge,
-  by drawing a mandril through it. Plotting the results logarithmically,
-  it was found that the resistance for all temperatures varied very
-  exactly as v^(1.795), the index being less than 2 as in other
-  experiments with very smooth surfaces. Taking the ordinary equation of
-  flow h = [zeta](4L/D)(v^2/2g), then for heads varying from 1 ft. to
-  nearly 4 ft., and velocities in the pipe varying from 4 ft. to 9 ft.
-  per second, the values of [zeta] were as follows:--
-
-    Temp. F.    [zeta]      |  Temp. F.     [zeta]
-       57   .0044 to .0052  |    100    .0039 to .0042
-       70   .0042 to .0045  |    110    .0037 to .0041
-       80   .0041 to .0045  |    120    .0037 to .0041
-       90   .0040 to .0045  |    130    .0035 to .0039
-                            |    160    .0035 to .0038
-
-  This shows a marked decrease of resistance as the temperature rises.
-  If Professor Osborne Reynolds's equation is assumed h = mLV^n/d^(3 -
-  n), and n is taken 1.795, then values of m at each temperature are
-  practically constant--
-
-    Temp. F.      m.    |  Temp. F.     m.
-       57     0.000276  |    100     0.000244
-       70     0.000263  |    110     0.000235
-       80     0.000257  |    120     0.000229
-       90     0.000250  |    130     0.000225
-                        |    160     0.000206
-
-  where again a regular decrease of the coefficient occurs as the
-  temperature rises. In experiments on the friction of disks at
-  different temperatures Professor W. C. Unwin found that the resistance
-  was proportional to constant X (1 - 0.0021t) and the values of m given
-  above are expressed almost exactly by the relation
-
-    m = 0.000311(1 - 0.00215 t).
-
-  In tank experiments on ship models for small ordinary variations of
-  temperature, it is usual to allow a decrease of 3% of resistance for
-  10 deg. F. increase of temperature.
-
-  S 80. _Influence of Deposits in Pipes on the Discharge. Scraping Water
-  Mains._--The influence of the condition of the surface of a pipe on
-  the friction is shown by various facts known to the engineers of
-  waterworks. In pipes which convey certain kinds of water, oxidation
-  proceeds rapidly and the discharge is considerably diminished. A main
-  laid at Torquay in 1858, 14 m. in length, consists of 10-in., 9-in.
-  and 8-in. pipes. It was not protected from corrosion by any coating.
-  But it was found to the surprise of the engineer that in eight years
-  the discharge had diminished to 51% of the original discharge. J. G.
-  Appold suggested an apparatus for scraping the interior of the pipe,
-  and this was constructed and used under the direction of William
-  Froude (see "Incrustation of Iron Pipes," by W. Ingham, _Proc. Inst.
-  Mech. Eng._, 1899). It was found that by scraping the interior of the
-  pipe the discharge was increased 56%. The scraping requires to be
-  repeated at intervals. After each scraping the discharge diminishes
-  rather rapidly to 10% and afterwards more slowly, the diminution in a
-  year being about 25%.
-
-  Fig. 85 shows a scraper for water mains, similar to Appold's but
-  modified in details, as constructed by the Glenfield Company, at
-  Kilmarnock. A is a longitudinal section of the pipe, showing the
-  scraper in place; B is an end view of the plungers, and C, D sections
-  of the boxes placed at intervals on the main for introducing or
-  withdrawing the scraper. The apparatus consists of two plungers,
-  packed with leather so as to fit the main pretty closely. On the
-  spindle of these plungers are fixed eight steel scraping blades, with
-  curved scraping edges fitting the surface of the main. The apparatus
-  is placed in the main by removing the cover from one of the boxes
-  shown at C, D. The cover is then replaced, water pressure is admitted
-  behind the plungers, and the apparatus driven through the main. At
-  Lancaster after twice scraping the discharge was increased 56(1/2)%,
-  at Oswestry 54(1/2)%. The increased discharge is due to the diminution
-  of the friction of the pipe by removing the roughnesses due to
-  oxidation. The scraper can be easily followed when the mains are about
-  3 ft. deep by the noise it makes. The average speed of the scraper at
-  Torquay is 2(1/3) m. per hour. At Torquay 49% of the deposit is iron
-  rust, the rest being silica, lime and organic matter.
-
-  [Illustration: FIG. 85. Scale 1/25.]
-
-  In the opinion of some engineers it is inadvisable to use the scraper.
-  The incrustation is only temporarily removed, and if the use of the
-  scraper is continued the life of the pipe is reduced. The only
-  treatment effective in preventing or retarding the incrustation due to
-  corrosion is to coat the pipes when hot with a smooth and perfect
-  layer of pitch. With certain waters such as those derived from the
-  chalk the incrustation is of a different character, consisting of
-  nearly pure calcium carbonate. A deposit of another character which
-  has led to trouble in some mains is a black slime containing a good
-  deal of iron not derived from the pipes. It appears to be an organic
-  growth. Filtration of the water appears to prevent the growth of the
-  slime, and its temporary removal may be effected by a kind of brush
-  scraper devised by G. F. Deacon (see "Deposits in Pipes," by Professor
-  J. C. Campbell Brown, _Proc. Inst. Civ. Eng._, 1903-1904).
-
-  S 81. _Flow of Water through Fire Hose._--The hose pipes used for fire
-  purposes are of very varied character, and the roughness of the
-  surface varies. Very careful experiments have been made by J. R.
-  Freeman (_Am. Soc. Civ. Eng._ xxi., 1889). It was noted that under
-  pressure the diameter of the hose increased sufficiently to have a
-  marked influence on the discharge. In reducing the results the true
-  diameter has been taken. Let v = mean velocity in ft. per sec.; r =
-  hydraulic mean radius or one-fourth the diameter in feet; i =
-  hydraulic gradient. Then v = n[root](ri).
-
-    +---------------+---------+---------+-------+-------+-------+
-    |               | Diameter| Gallons |       |       |       |
-    |               |    in   | (United |       |       |       |
-    |               | Inches. | States) |   i   |   v   |   n   |
-    |               |         | per min.|       |       |       |
-    +---------------+---------+---------+-------+-------+-------+
-    | Solid rubber  |  2.65   |   215   | .1863 | 12.50 | 123.3 |
-    |  hose         |    "    |   344   | .4714 | 20.00 | 124.0 |
-    |               |         |         |       |       |       |
-    | Woven cotton, |  2.47   |   200   | .2464 | 13.40 | 119.1 |
-    |  rubber lined |    "    |   299   | .5269 | 20.00 | 121.5 |
-    |               |         |         |       |       |       |
-    | Woven cotton, |  2.49   |   200   | .2427 | 13.20 | 117.7 |
-    |  rubber lined |    "    |   319   | .5708 | 21.00 | 122.1 |
-    |               |         |         |       |       |       |
-    | Knit cotton,  |  2.68   |   132   | .0809 |  7.50 | 111.6 |
-    |  rubber lined |    "    |   299   | .3931 | 17.00 | 114.8 |
-    |               |         |         |       |       |       |
-    | Knit cotton,  |  2.69   |   204   | .2357 | 11.50 | 100.1 |
-    |  rubber lined |    "    |   319   | .5165 | 18.00 | 105.8 |
-    |               |         |         |       |       |       |
-    | Woven cotton, |  2.12   |   154   | .3448 | 14.00 | 113.4 |
-    |  rubber lined |    "    |   240   | .7673 | 21.81 | 118.4 |
-    |               |         |         |       |       |       |
-    | Woven cotton, |  2.53   |    54.8 | .0261 |  3.50 |  94.3 |
-    |  rubber lined |    "    |   298   | .8264 | 19.00 |  91.0 |
-    |               |         |         |       |       |       |
-    | Unlined linen |  2.60   |    57.9 | .0414 |  3.50 |  73.9 |
-    |  hose         |    "    |   331   |1.1624 | 20.00 |  79.6 |
-    +---------------+---------+---------+-------+-------+-------+
-
-  S 82. _Reduction of a Long Pipe of Varying Diameter to an Equivalent
-  Pipe of Uniform Diameter. Dupuit's Equation._--Water mains for the
-  supply of towns often consist of a series of lengths, the diameter
-  being the same for each length, but differing from length to length.
-  In approximate calculations of the head lost in such mains, it is
-  generally accurate enough to neglect the smaller losses of head and to
-  have regard to the pipe friction only, and then the calculations may
-  be facilitated by reducing the main to a main of uniform diameter, in
-  which there would be the same loss of head. Such a uniform main will
-  be termed an equivalent main.
-
-  [Illustration: FIG. 86.]
-
-  In fig. 86 let A be the main of variable diameter, and B the
-  equivalent uniform main. In the given main of variable diameter A, let
-
-    l1, l2... be the lengths,
-    d1, d2...    the diameters,
-    v1, v2...    the velocities,
-    i1, i2...    the slopes,
-
-  for the successive portions, and let l, d, v and i be corresponding
-  quantities for the equivalent uniform main B. The total loss of head
-  in A due to friction is
-
-    h = i1l1 + i2l2 + ...
-      = [zeta](v1^2 . 4l1/2gd1) + [zeta](v2^2 . 4l2/2gd2) + ...
-
-  and in the uniform main
-
-    il = [zeta](v^2 . 4l/2gd).
-
-  If the mains are equivalent, as defined above,
-
-    [zeta](v^2 . 4l/2gd) = [zeta](v1^2 . 4l1/2gd1) + [zeta](v2^2 . 4l2/2gd2) + ...
-
-  But, since the discharge is the same for all portions,
-
-    (1/4)[pi]d^2v = (1/4)[pi]d1^2v1 = (1/4)[pi]d2^2v2 = ...
-
-    v1 = vd^2/d1^2; v2 = vd^2/d2^2 ...
-
-  Also suppose that [zeta] may be treated as constant for all the pipes.
-  Then
-
-    l/d = (d^4/d1^4)(l1/d1) + (d^4/d2^4(12/d2) + ...
-
-    l = (d^5/d1^5)l1 + (d^5/d2^5)l2 + ...
-
-  which gives the length of the equivalent uniform main which would have
-  the same total loss of head for any given discharge.
-
-  S 83. _Other Losses of Head in Pipes._--Most of the losses of head in
-  pipes, other than that due to surface friction against the pipe, are
-  due to abrupt changes in the velocity of the stream producing eddies.
-  The kinetic energy of these is deducted from the general energy of
-  translation, and practically wasted.
-
-  [Illustration: FIG. 87.]
-
-  _Sudden Enlargement of Section._--Suppose a pipe enlarges in section
-  from an area [omega]0 to an area [omega]1 (fig. 87); then
-
-    v1/v0 = [omega]0/[omega]1;
-
-  or, if the section is circular,
-
-    v1/v0 = (d0/d1)^2.
-
-  The head lost at the abrupt change of velocity has already been shown
-  to be the head due to the relative velocity of the two parts of the
-  stream. Hence head lost
-
-    [h]_e = (v0 - v1)^2/2g = ([omega]1/[omega]0 - 1)^2v1^2/2g
-          = {(d1/d0)^2 - 1}^2 v1^2/2g
-
-  or
-
-    [h]_e = [zeta]_ev1^2/2g,   (1)
-
-  if [zeta]_e is put for the expression in brackets.
-
-    +--------------+----+----+----+----+----+----+----+----+----+----+----+-----+-----+-----+-----+
-    | [omega]1/    |1.1 |1.2 |1.5 |1.7 |1.8 |1.9 |2.0 |2.5 |3.0 |3.5 |4.0 | 5.0 | 6.0 | 7.0 | 8.0 |
-    |   [omega]0 = |    |    |    |    |    |    |    |    |    |    |    |     |     |     |     |
-    | d1/d0 =      |1.05|1.10|1.22|1.30|1.34|1.38|1.41|1.58|1.73|1.87|2.00| 2.24| 2.45| 2.65| 2.83|
-    |              |    |    |    |    |    |    |    |    |    |    |    |     |     |     |     |
-    | [zeta]_e =   | .01| .04| .25| .49| .64| .81|1.00|2.25|4.00|6.25|9.00|16.00|25.00|36.0 |49.0 |
-    +--------------+----+----+----+----+----+----+----+----+----+----+----+-----+-----+-----+-----+
-
-  [Illustration: FIG. 88.]
-
-  [Illustration: FIG. 89.]
-
-  _Abrupt Contraction of Section._--When water passes from a larger to a
-  smaller section, as in figs. 88, 89, a contraction is formed, and the
-  contracted stream abruptly expands to fill the section of the pipe.
-  Let [omega] be the section and v the velocity of the stream at bb. At
-  aa the section will be c_c[omega], and the velocity
-  ([omega]/c_c[omega])v = v/c1, where c_c is the coefficient of
-  contraction. Then the head lost is
-
-    [h]_m = (v/c_c - v)^2/2g = (1/c_c - 1)^2v^2/2g;
-
-  and, if c_c is taken 0.64,
-
-    [h]_m = 0.316 v^2/2g.   (2)
-
-  The value of the coefficient of contraction for this case is, however,
-  not well ascertained, and the result is somewhat modified by friction.
-  For water entering a cylindrical, not bell-mouthed, pipe from a
-  reservoir of indefinitely large size, experiment gives
-
-    [h]_a = 0.505 v^2/2g.   (3)
-
-  If there is a diaphragm at the mouth of the pipe as in fig. 89, let
-  [omega]1 be the area of this orifice. Then the area of the contracted
-  stream is c_c[omega]1, and the head lost is
-
-    [h]_c = {([omega]/c_c[omega]1) - 1}^2v^2/2g
-          = [zeta]_cv^2/2g   (4)
-
-  if [zeta], is put for {([omega]/c_c[omega]1) - 1}^2. Weisbach has found
-  experimentally the following values of the coefficient, when the
-  stream approaching the orifice was considerably larger than the
-  orifice:--
-
-    +--------------------+-------+------+------+-----+-----+-----+-----+-----+-----+-----+
-    | [omega]1/[omega] = |  0.1  |  0.2 |  0.3 | 0.4 | 0.5 | 0.6 |0.7  | 0.8 | 0.9 | 1.0 |
-    |                    |       |      |      |     |     |     |     |     |     |     |
-    | c_c =              | .616  | .614 | .612 |.610 |.617 |.605 |.603 |.601 |.598 |.596 |
-    |                    |       |      |      |     |     |     |     |     |     |     |
-    | [zeta]_c =         | 231.7 |50.99 |19.78 |9.612|5.256|3.077|1.876|1.169|0.734|0.480|
-    +--------------------+-------+------+------+-----+-----+-----+-----+-----+-----+-----+
-
-  [Illustration: FIG. 90.]
-
-  When a diaphragm was placed in a tube of uniform section (fig. 90) the
-  following values were obtained, [omega]1 being the area of the orifice
-  and [omega] that of the pipe:--
-
-    +--------------------+-------+------+------+-----+-----+-----+-----+-----+-----+-----+
-    | [omega]1/[omega] = |  0.1  | 0.2  | 0.3  | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0 |
-    |                    |       |      |      |     |     |     |     |     |     |     |
-    | c_c =              | .624  | .632 | .643 |.659 |.681 |.712 |.755 |.813 |.892 |1.00 |
-    |                    |       |      |      |     |     |     |     |     |     |     |
-    | [xi]_c =           | 225.9 |47.77 |30.83 |7.801|1.753|1.796|.797 |.290 |.060 |.000 |
-    +--------------------+-------+------+------+-----+-----+-----+-----+-----+-----+-----+
-
-  Elbows.--Weisbach considers the loss of head at elbows (fig. 91) to be
-  due to a contraction formed by the stream. From experiments with a
-  pipe 1(1/4) in. diameter, he found the loss of head
-
-    [h]_e = [zeta]_e v^2/2g;   (5)
-
-    [zeta]_e = 0.9457 sin^2 (1/2)[phi] + 2.047 sin^4 (1/2)[phi].
-
-    +------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
-    | [phi] =    | 20  | 40  | 60  | 80  | 90  | 100 | 110 | 120 | 130 | 140 |
-    |    [deg.]  |     |     |     |     |     |     |     |     |     |     |
-    | [zeta]_e = |0.046|0.139|0.364|0.740|0.984|1.260|1.556|1.861|2.158|2.431|
-    +------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
-
-  Hence at a right-angled elbow the whole head due to the velocity very
-  nearly is lost.
-
-  [Illustration: FIG. 91.]
-
-  _Bends._--Weisbach traces the loss of head at curved bends to a
-  similar cause to that at elbows, but the coefficients for bends are
-  not very satisfactorily ascertained. Weisbach obtained for the loss of
-  head at a bend in a pipe of circular section
-
-    [h]_b = [zeta]_b v^2/2g;   (6)
-
-    [zeta]_b = 0.131 + 1.847(d/2[rho])^(7/2),
-
-  where d is the diameter of the pipe and [rho] the radius of curvature
-  of the bend. The resistance at bends is small and at present very ill
-  determined.
-
-  [Illustration: FIG. 92.]
-
-  _Valves, Cocks and Sluices._--These produce a contraction of the
-  water-stream, similar to that for an abrupt diminution of section
-  already discussed. The loss of head may be taken as before to be
-
-    [h]_v = [zeta]_v v^2/2g;   (7)
-
-  where v is the velocity in the pipe beyond the valve and [zeta]_v a
-  coefficient determined by experiment. The following are Weisbach's
-  results.
-
-  _Sluice in Pipe of Rectangular Section_ (fig. 92). Section at sluice =
-  [omega]1 in pipe = [omega].
-
-    +--------------------+----+----+----+----+----+----+----+----+----+-----+
-    | [omega]1/[omega] = |1.0 |0.9 |0.8 |0.7 |0.6 |0.5 |0.4 | 0.3| 0.2| 0.1 |
-    |                    |    |    |    |    |    |    |    |    |    |     |
-    | [zeta]_v =         |0.00|.09 |.39 |.95 |2.08|4.02|8.12|17.8|44.5| 193 |
-    +--------------------+----+----+----+----+----+----+----+----+----+-----+
-
-    _Sluice in Cylindrical Pipe_ (fig. 93).
-
-    +-----------------------+----+-----+-----+-----+-----+-----+------+------+
-    | Ratio of height of    |    |     |     |     |     |     |      |      |
-    |   opening to diameter | 1.0| 7/8 | 3/4 | 5/8 | 1/2 | 3/8 | 1/4  | 1/5  |
-    |   of pipe             |    |     |     |     |     |     |      |      |
-    |  [omega]1/[omega] =   |1.00|0.948|.856 |.740 |.609 |.466 | .315 | .159 |
-    |                       |    |     |     |     |     |     |      |      |
-    |       [zeta]_v =      |0.00|0.07 |0.26 |0.81 |2.06 |5.52 | 17.0 | 97.8 |
-    +-----------------------+----+-----+-----+-----+-----+-----+------+------+
-
-  [Illustration: FIG. 93.]
-
-  [Illustration: FIG. 94.]
-
-    _Cock in a Cylindrical Pipe_ (fig. 94). Angle through which cock is
-    turned = [theta].
-
-    +------------+--------+---------+---------+---------+---------+---------+---------+
-    | [theta] =  | 5 deg. | 10 deg. | 15 deg. | 20 deg. | 25 deg. | 30 deg. | 35 deg. |
-    | Ratio of   |        |         |         |         |         |         |         |
-    |   cross    |  .926  |  .850   |  .772   |  .692   |  .613   |  .535   |  .458   |
-    |   sections |        |         |         |         |         |         |         |
-    | [zeta]_v = |  .05   |   .29   |   .75   |  1.56   |  3.10   |  5.47   |  9.68   |
-    +------------+--------+---------+---------+---------+---------+---------+---------+
-
-    +------------+---------+---------+---------+---------+---------+---------+---------+
-    | [theta] =  | 40 deg. | 45 deg. | 50 deg. | 55 deg. | 60 deg. | 65 deg. | 82 deg. |
-    | Ratio of   |         |         |         |         |         |         |         |
-    |  cross     |  .385   |  .315   |  .250   |  .190   |  .137   |  .091   |    0    |
-    |  sections  |         |         |         |         |         |         |         |
-    | [zeta]_v = |   17.3  |   31.2  |   52.6  |  106    |  206    |  486    |  [oo]   |
-    +------------+---------+---------+---------+---------+---------+---------+---------+
-
-    _Throttle Valve in a Cylindrical Pip_e (fig. 95)
-
-    +------------+---------+---------+---------+---------+---------+---------+---------+---------+
-    | [theta] =  |  5 deg. | 10 deg. | 15 deg. | 20 deg. | 25 deg. | 30 deg. | 35 deg. | 40 deg. |
-    |            |         |         |         |         |         |         |         |         |
-    | [zeta]_v = |   .24   |   .52   |   .90   |   1.54  |   2.51  |   3.91  |   6.22  |   10.8  |
-    +------------+---------+---------+---------+---------+---------+---------+---------+---------+
-
-    +------------+----------+----------+----------+----------+----------+----------+----------+
-    | [theta] =  |  45 deg. |  50 deg. |  55 deg. |  60 deg. |  65 deg. |  70 deg. |  90 deg. |
-    |            |          |          |          |          |          |          |          |
-    | [zeta]_v = |   18.7   |   32.6   |   58.8   |    118   |    256   |    751   |   [oo]   |
-    +------------+----------+----------+----------+----------+----------+----------+----------+
-
-  [Illustration: FIG. 95.]
-
-  S 84. _Practical Calculations on the Flow of Water in Pipes._--In the
-  following explanations it will be assumed that the pipe is of so great
-  a length that only the loss of head in friction against the surface of
-  the pipe needs to be considered. In general it is one of the four
-  quantities d, i, v or Q which requires to be determined. For since the
-  loss of head h is given by the relation h = il, this need not be
-  separately considered.
-
-  There are then three equations (see eq. 4, S 72, and 9a, S 76) for the
-  solution of such problems as arise:--
-
-    [zeta] = [alpha](1 + 1/12d);   (1)
-
-  where [alpha] = 0.005 for new and = 0.01 for incrusted pipes.
-
-    [zeta]v^2/2g = (1/4)di.   (2)
-
-    Q = (1/4)[pi]d^2v.   (3)
-
-  _Problem 1._ Given the diameter of the pipe and its virtual slope, to
-  find the discharge and velocity of flow. Here d and i are given, and Q
-  and v are required. Find [zeta] from (1); then v from (2); lastly Q
-  from (3). This case presents no difficulty.
-
-  By combining equations (1) and (2), v is obtained directly:--
-
-    v = [root](gdi/2[zeta]) = [root](g/2[alpha]) [root][di/{1 + 1/12d}].   (4)
-
-    For new pipes        [root](g/2[alpha]) = 56.72
-    For incrusted pipes  = 40.13
-
-  For pipes not less than 1, or more than 4 ft. in diameter, the mean
-  values of [zeta] are
-
-    For new pipes        0.00526
-    For incrusted pipes  0.01052.
-
-  Using these values we get the very simple expressions--
-
-    v = 55.31 [root](di) for new pipes
-      = 39.11 [root](di) for incrusted pipes.   (4a)
-
-  Within the limits stated, these are accurate enough for practical
-  purposes, especially as the precise value of the coefficient [zeta]
-  cannot be known for each special case.
-
-  _Problem 2._ Given the diameter of a pipe and the velocity of flow, to
-  find the virtual slope and discharge. The discharge is given by (3);
-  the proper value of [zeta] by (1); and the virtual slope by (2). This
-  also presents no special difficulty.
-
-  _Problem 3._ Given the diameter of the pipe and the discharge, to find
-  the virtual slope and velocity. Find v from (3); [zeta] from (1);
-  lastly i from (2). If we combine (1) and (2) we get
-
-    i = [zeta](v^2/2g) (4/d) = 2a{1 + 1/12d} v^2/gd;   (5)
-
-  and, taking the mean values of [zeta] for pipes from 1 to 4 ft.
-  diameter, given above, the approximate formulae are
-
-    i = 0.0003268 v^2/d for new pipes
-      = 0.0006536 v^2/d for incrusted pipes.   (5a)
-
-  _Problem 4._ Given the virtual slope and the velocity, to find the
-  diameter of the pipe and the discharge. The diameter is obtained from
-  equations (2) and (1), which give the quadratic expression
-
-    d^2 - d(2[alpha]v^2/gi) - [alpha]v^2/6gi = 0.
-
-    .: d = [alpha]v^2/gi + [root]{([alpha]v^2/gi) ([alpha]v^2/gi + 1/6)}.   (6)
-
-  For practical purposes, the approximate equations
-
-    d = 2[alpha]v^2/gi + 1/12   (6a)
-      = 0.00031 v^2/i + .083 for new pipes
-      = 0.00062 v^2/i + .083 for incrusted pipes
-
-  are sufficiently accurate.
-
-  _Problem 5._ Given the virtual slope and the discharge, to find the
-  diameter of the pipe and velocity of flow. This case, which often
-  occurs in designing, is the one which is least easy of direct
-  solution. From equations (2) and (3) we get--
-
-    d^5 = 32[zeta]Q^2/g[pi]^2i.   (7)
-
-  If now the value of [zeta] in (1) is introduced, the equation becomes
-  very cumbrous. Various approximate methods of meeting the difficulty
-  may be used.
-
-  (a) Taking the mean values of [zeta] given above for pipes of 1 to 4
-  ft. diameter we get
-
-    d = [root 5](32[zeta]/g[pi]^2) [root 5](Q^2/i)   (8)
-      = 0.2216 [root 5](Q^2/i) for new pipes
-      = 0.2541 [root 5](Q^2/i) for incrusted pipes;
-
-  equations which are interesting as showing that when the value of
-  [zeta] is doubled the diameter of pipe for a given discharge is only
-  increased by 13%.
-
-  (b) A second method is to obtain a rough value of d by assuming [zeta]
-  = [alpha]. This value is
-
-    d' = [root 5](32Q^2/g[pi]^2i) [root 5][alpha]
-       = 0.6319 [root 5](Q^2/i) [root 5][alpha].
-
-  Then a very approximate value of [zeta] is
-
-    [zeta]' = [alpha](1 + 1/12d');
-
-  and a revised value of d, not sensibly differing from the exact value,
-  is
-
-    d" = [root 5](32Q^2/g[pi]^2i) [root 5][zeta]'
-        = 0.6319 [root 5](Q^2/i) [root 5][zeta]'.
-
-  (c) Equation 7 may be put in the form
-
-    d = [root 5](32[alpha]Q^2/g[pi]^2i) [root 5](1 + 1/12d).   (9)
-
-  Expanding the term in brackets,
-
-    [root 5](1 + 1/12d) = 1 + 1/60d - 1/1800d^2 ...
-
-  Neglecting the terms after the second,
-
-    d = [root 5](32[alpha]/g[pi]^2) [root 5](Q^2/i).{1 + 1/60d}
-      = [root 5](32a/g[pi]^2) [root 5](Q^2/i) + 0.01667;   (9a)
-
-  and
-
-    [root 5](32a/g[pi]^2) = 0.219 for new pipes
-                         = 0.252 for incrusted pipes.
-
-  [Illustration: FIG. 96.]
-
-  [Illustration: FIG. 97.]
-
-  S 85. _Arrangement of Water Mains for Towns' Supply._--Town mains are
-  usually supplied oy gravitation from a service reservoir, which in
-  turn is supplied by gravitation from a storage reservoir or by pumping
-  from a lower level. The service reservoir should contain three days'
-  supply or in important cases much more. Its elevation should be such
-  that water is delivered at a pressure of at least about 100 ft. to the
-  highest parts of the district. The greatest pressure in the mains is
-  usually about 200 ft., the pressure for which ordinary pipes and
-  fittings are designed. Hence if the district supplied has great
-  variations of level it must be divided into zones of higher and lower
-  pressure. Fig. 96 shows a district of two zones each with its service
-  reservoir and a range of pressure in the lower district from 100 to
-  200 ft. The total supply required is in England about 25 gallons per
-  head per day. But in many towns, and especially in America, the supply
-  is considerably greater, but also in many cases a good deal of the
-  supply is lost by leakage of the mains. The supply through the branch
-  mains of a distributing system is calculated from the population
-  supplied. But in determining the capacity of the mains the fluctuation
-  of the demand must be allowed for. It is usual to take the maximum
-  demand at twice the average demand. Hence if the average demand is 25
-  gallons per head per day, the mains should be calculated for 50
-  gallons per head per day.
-
-  [Illustration: FIG. 98.]
-
-  S 86. _Determination of the Diameters of Different Parts of a Water
-  Main._--When the plan of the arrangement of mains is determined upon,
-  and the supply to each locality and the pressure required is
-  ascertained, it remains to determine the diameters of the pipes. Let
-  fig. 97 show an elevation of a main ABCD ..., R being the reservoir
-  from which the supply is derived. Let NN be the datum line of the
-  levelling operations, and H_a, H_b ... the heights of the main above
-  the datum line, H_r being the height of the water surface in the
-  reservoir from the same datum. Set up next heights AA1, BB1, ...
-  representing the minimum pressure height necessary for the adequate
-  supply of each locality. Then A1B1C1D1 ... is a line which should form
-  a lower limit to the line of virtual slope. Then if heights [h]_a,
-  [h]_b, [h]_c ... are taken representing the actual losses of head in
-  each length l_a, l_b, l_c ... of the main, A0B0C0 will be the line of
-  virtual slope, and it will be obvious at what points such as D0 and
-  E0, the pressure is deficient, and a different choice of diameter of
-  main is required. For any point z in the length of the main, we have
-
-    Pressure height = H_r - H_z - ([h]_a + [h]_b + ... [h]_z).
-
-  Where no other circumstance limits the loss of head to be assigned to
-  a given length of main, a consideration of the safety of the main from
-  fracture by hydraulic shock leads to a limitation of the velocity of
-  flow. Generally the velocity in water mains lies between 1(1/2) and
-  4(1/2) ft. per second. Occasionally the velocity in pipes reaches 10
-  ft. per second, and in hydraulic machinery working under enormous
-  pressures even 20 ft. per second. Usually the velocity diminishes
-  along the main as the discharge diminishes, so as to reduce somewhat
-  the total loss of head which is liable to render the pressure
-  insufficient at the end of the main.
-
-  J. T. Fanning gives the following velocities as suitable in pipes for
-  towns' supply:--
-
-    Diameter in inches          4     8    12    18    24    30    36
-    Velocity in feet per sec.  2.5   3.0   3.5   4.5   5.3   6.2   7.0
-
-  S 87. _Branched Pipe connecting Reservoirs at Different Levels._--Let
-  A, B, C (fig. 98) be three reservoirs connected by the arrangement of
-  pipes shown,--l1, d1, Q1, v1; l2, d2, Q2, v2; h3, d3, Q3, v3 being the
-  length, diameter, discharge and velocity in the three portions of the
-  main pipe. Suppose the dimensions and positions of the pipes known and
-  the discharges required.
-
-  If a pressure column is introduced at X, the water will rise to a
-  height XR, measuring the pressure at X, and aR, Rb, Rc will be the
-  lines of virtual slope. If the free surface level at R is above b, the
-  reservoir A supplies B and C, and if R is below b, A and B supply C.
-  Consequently there are three cases:--
-
-      I. R above b; Q1 = Q2 + Q3.
-     II. R level with b; Q1 = Q3; Q2 = 0
-    III. R below b; Q1 + Q2 = Q3.
-
-  To determine which case has to be dealt with in the given conditions,
-  suppose the pipe from X to B closed by a sluice. Then there is a
-  simple main, and the height of free surface h' at X can be determined.
-  For this condition
-
-    h_a - h' = [zeta](v1^2/2g)(4l1/d1)
-             = 32[zeta]Q'^2 l1/g[pi]^2d1^5;
-
-    h' - h_c = [zeta](v3^2/2g)(4l3/d3)
-             = 32[zeta]Q'^2l3/g[pi]^2d3^5;
-
-  where Q' is the common discharge of the two portions of the pipe.
-  Hence
-
-    (h_a - h')/(h' - h_c) = l1d3^5/l3d1^5,
-
-  from which h' is easily obtained. If then h' is greater than hb,
-  opening the sluice between X and B will allow flow towards B, and the
-  case in hand is case I. If h' is less than h_b, opening the sluice
-  will allow flow from B, and the case is case III. If h' = h_b, the
-  case is case II., and is already completely solved.
-
-  The true value of h must lie between h' and h_b. Choose a new value of
-  h, and recalculate Q1, Q2, Q3. Then if
-
-    Q1 > Q2 + Q3 in case I.,
-
-  or
-
-    Q1 + Q2 > Q3 in case III.,
-
-  the value chosen for h is too small, and a new value must be chosen.
-
-  If
-
-    Q1 < Q2 + Q3 in case I.,
-
-  or
-
-    Q1 + Q2 < Q3 in case III.,
-
-  the value of h is too great.
-
-  Since the limits between which h can vary are in practical cases not
-  very distant, it is easy to approximate to values sufficiently
-  accurate.
-
-  S 88. _Water Hammer._--If in a pipe through which water is flowing a
-  sluice is suddenly closed so as to arrest the forward movement of the
-  water, there is a rise of pressure which in some cases is serious
-  enough to burst the pipe. This action is termed water hammer or water
-  ram. The fluctuation of pressure is an oscillating one and gradually
-  dies out. Care is usually taken that sluices should only be closed
-  gradually and then the effect is inappreciable. Very careful
-  experiments on water hammer were made by N. J. Joukowsky at Moscow in
-  1898 (_Stoss in Wasserleitungen_, St Petersburg, 1900), and the
-  results are generally confirmed by experiments made by E. B. Weston
-  and R. C. Carpenter in America. Joukowsky used pipes, 2, 4 and 6 in.
-  diameter, from 1000 to 2500 ft. in length. The sluice closed in 0.03
-  second, and the fluctuations of pressure were automatically
-  registered. The maximum excess pressure due to water-hammer action was
-  as follows:--
-
-    +---------------------------------+---------------------------------+
-    |       Pipe 4-in. diameter.      |       Pipe 6-in. diameter.      |
-    +--------------+------------------+--------------+------------------+
-    |   Velocity   | Excess Pressure. |   Velocity   | Excess Pressure. |
-    | ft. per sec. |  lb. per sq. in. | ft. per sec. |  lb. per sq. in. |
-    +--------------+------------------+--------------+------------------+
-    |     0.5      |        31        |     0.6      |        43        |
-    |     2.9      |       168        |     3.0      |       173        |
-    |     4.1      |       232        |     5.6      |       369        |
-    |     9.2      |       519        |     7.5      |       426        |
-    +--------------+------------------+--------------+------------------+
-
-  In some cases, in fixing the thickness of water mains, 100 lb. per sq.
-  in. excess pressure is allowed to cover the effect of water hammer.
-  With the velocities usual in water mains, especially as no valves can
-  be quite suddenly closed, this appears to be a reasonable allowance
-  (see also Carpenter, _Am. Soc. Mech. Eng._, 1893).
-
-
-  IX. FLOW OF COMPRESSIBLE FLUIDS IN PIPES
-
-  S 89. _Flow of Air in Long Pipes._--When air flows through a long
-  pipe, by far the greater part of the work expended is used in
-  overcoming frictional resistances due to the surface of the pipe. The
-  work expended in friction generates heat, which for the most part must
-  be developed in and given back to the air. Some heat may be
-  transmitted through the sides of the pipe to surrounding materials,
-  but in experiments hitherto made the amount so conducted away appears
-  to be very small, and if no heat is transmitted the air in the tube
-  must remain sensibly at the same temperature during expansion. In
-  other words, the expansion may be regarded as isothermal expansion,
-  the heat generated by friction exactly neutralizing the cooling due to
-  the work done. Experiments on the pneumatic tubes used for the
-  transmission of messages, by R. S. Culley and R. Sabine (_Proc. Inst.
-  Civ. Eng._ xliii.), show that the change of temperature of the air
-  flowing along the tube is much less than it would be in adiabatic
-  expansion.
-
-  S 90. _Differential Equation of the Steady Motion of Air Flowing in a
-  Long Pipe of Uniform Section._--When air expands at a constant
-  absolute temperature [tau], the relation between the pressure p in
-  pounds per square foot and the density or weight per cubic foot G is
-  given by the equation
-
-    p/G = c[tau],   (1)
-
-  where c = 53.15. Taking [tau] = 521, corresponding to a temperature of
-  60 deg. Fahr.,
-
-    c[tau] = 27690 foot-pounds.   (2)
-
-  The equation of continuity, which expresses the condition that in
-  steady motion the same weight of fluid, W, must pass through each
-  cross section of the stream in the unit of time, is
-
-    G[Omega]u = W = constant,   (3)
-
-  where [Omega] is the section of the pipe and u the velocity of the
-  air. Combining (1) and (3),
-
-    [Omega]up/W = c[tau] = constant.   (3a)
-
-  [Illustration: FIG. 99.]
-
-  Since the work done by gravity on the air during its flow through a
-  pipe due to variations of its level is generally small compared with
-  the work done by changes of pressure, the former may in many cases be
-  neglected.
-
-  Consider a short length dl of the pipe limited by sections A0, A1 at a
-  distance dl (fig. 99). Let p, u be the pressure and velocity at A0, p
-  + dp and u + du those at A1. Further, suppose that in a very short
-  time dt the mass of air between A0A1 comes to A'0A'1 so that A0A'0 =
-  udt and A1A'1 = (u + du)dt1. Let [Omega] be the section, and m the
-  hydraulic mean radius of the pipe, and W the weight of air flowing
-  through the pipe per second.
-
-  From the steadiness of the motion the weight of air between the
-  sections A0A'0, and A1A'1 is the same. That is,
-
-    W dt = G[Omega]u dt = G[Omega](u + du) dt.
-
-  By analogy with liquids the head lost in friction is, for the length
-  dl (see S 72, eq. 3), [zeta](u^2/2g)(dl/m). Let H = u^2/2g. Then the
-  head lost is [zeta](H/m)dl; and, since Wdt lb. of air flow through the
-  pipe in the time considered, the work expended in friction is
-  -[zeta](H/m)Wdl dt. The change of kinetic energy in dt seconds is the
-  difference of the kinetic energy of A0A'0 and A1A'1, that is,
-
-    (W/g) dt {(u + du)^2 - u^2}/2 = (W/g)u du dt = W dH dt.
-
-  The work of expansion when [Omega]udt cub. ft. of air at a pressure p
-  expand to [Omega](u + du)dt cub. ft. is [Omega]p du dt. But from (3a)
-  u = c[tau]W/[Omega]p, and therefore
-
-    du/dp = -c[tau]W/[Omega]p^2.
-
-  And the work done by expansion is -(c[tau]W/p)dpdt.
-
-  The work done by gravity on the mass between A0 and A1 is zero if the
-  pipe is horizontal, and may in other cases be neglected without great
-  error. The work of the pressures at the sections A0A1 is
-
-    p[Omega]u dt - (p + dp)[Omega](u + du) dt
-      = -(pdu + udp)[Omega] dt
-
-  But from (3a)
-
-    pu = constant,
-
-    p du + u dp = 0,
-
-  and the work of the pressures is zero. Adding together the quantities
-  of work, and equating them to the change of kinetic energy,
-
-    WDH dt = -(c[tau]W/p) dp dt - [zeta](H/m)W dl dt
-
-    dH + (c[tau]/p) dp + [zeta](H/m) dl = 0,
-
-    dH/H + (c[tau]/Hp) dp + [zeta]dl/m) = 0   (4)
-
-  But
-
-    u = c[tau]W/[Omega]p,
-
-  and
-
-    H = u^2/2g = c^2[tau]^2W^2/2g[Omega]^2p^2,
-
-    .: dH/H + (2g[Omega]^2p/c[tau]W^2) dp + [zeta] dl/m = 0.   (4a)
-
-  For tubes of uniform section m is constant; for steady motion W is
-  constant; and for isothermal expansion [tau] is constant. Integrating,
-
-    log H + g[Omega]^2p^2/W^2c[tau] + [zeta]l/m = constant;   (5)
-
-  for
-
-    l = 0, let H = H0, and p = p0;
-
-  and for
-
-    l = l, let H = H1, and p = p1.
-
-  log (H1/H0) + (g[Omega]^2}/W^2c[tau]) (p1^2 - p0^2) + [zeta]l/m = 0.
-  (5a) where p0 is the greater pressure and p1 the less, and the flow is
-  from A0 towards A1.
-
-  By replacing W and H,
-
-    log (p0/p1) + (gc[tau]/u0^2p0^2)(p1^2 - p0^2 + [zeta]l/m = 0  (6)
-
-  Hence the initial velocity in the pipe is
-
-    u0 = [root][{gc[tau](p0^2 - p1^2)} / {p0^2([zeta]l/m + log (p0/p1)}].   (7)
-
-  When l is great, log p0/p1 is comparatively small, and then
-
-    u0 = [root][(gc[tau]m/[zeta]l) {(p0^2 - p1^2)/p0^2}],   (7a)
-
-  a very simple and easily used expression. For pipes of circular
-  section m = d/4, where d is the diameter:--
-
-    u0 = [root][(gc[tau]d/4[zeta]l) {(p0^2 - p1^2)/p0^2}];   (7b)
-
-  or approximately
-
-    u0 = (1.1319 - 0.7264 p1/p0) [root](gc[tau]d/4[zeta]l).   (7c)
-
-  S 91. _Coefficient of Friction for Air._--A discussion by Professor
-  Unwin of the experiments by Culley and Sabine on the rate of
-  transmission of light carriers through pneumatic tubes, in which there
-  is steady flow of air not sensibly affected by any resistances other
-  than surface friction, furnished the value [zeta] = .007. The pipes
-  were lead pipes, slightly moist, 2(1/4) in. (0.187 ft.) in diameter,
-  and in lengths of 2000 to nearly 6000 ft.
-
-  In some experiments on the flow of air through cast-iron pipes A.
-  Arson found the coefficient of friction to vary with the velocity and
-  diameter of the pipe. Putting
-
-    [zeta] = [alpha]/v + [beta],   (8)
-
-  he obtained the following values--
-
-    +------------------+--------+-------+--------------------+
-    | Diameter of Pipe |        |       | [zeta] for 100 ft. |
-    |     in feet      | [alpha]| [beta]|   per second.      |
-    +------------------+--------+-------+--------------------+
-    |      1.64        | .00129 | .00483|      .00484        |
-    |      1.07        | .00972 | .00640|      .00650        |
-    |       .83        | .01525 | .00704|      .00719        |
-    |       .338       | .03604 | .00941|      .00977        |
-    |       .266       | .03790 | .00959|      .00997        |
-    |       .164       | .04518 | .01167|      .01212        |
-    +------------------+--------+-------+--------------------+
-
-  It is worth while to try if these numbers can be expressed in the form
-  proposed by Darcy for water. For a velocity of 100 ft. per second, and
-  without much error for higher velocities, these numbers agree fairly
-  with the formula
-
-    [zeta] = 0.005(1 + (3/10)d),   (9)
-
-  which only differs from Darcy's value for water in that the second
-  term, which is always small except for very small pipes, is larger.
-
-  Some later experiments on a very large scale, by E. Stockalper at the
-  St Gotthard Tunnel, agree better with the value
-
-    [zeta] = 0.0028(1 + (3/10)d).
-
-  These pipes were probably less rough than Arson's.
-
-  When the variation of pressure is very small, it is no longer safe to
-  neglect the variation of level of the pipe. For that case we may
-  neglect the work done by expansion, and then
-
-    z0 - z1 - p0/G0 - p1/G1 - [zeta](v^2/2g)(l/m) = 0,   (10)
-
-  precisely equivalent to the equation for the flow of water, z0 and z1
-  being the elevations of the two ends of the pipe above any datum, p0
-  and p1 the pressures, G0 and G1 the densities, and v the mean velocity
-  in the pipe. This equation may be used for the flow of coal gas.
-
-  S 92. _Distribution of Pressure in a Pipe in which Air is
-  Flowing._--From equation (7a) it results that the pressure p, at l ft.
-  from that end of the pipe where the pressure is p0, is
-
-    p = p0 [root](1 - [zeta]lu0^2/mgc[tau]);   (11)
-
-  which is of the form
-
-    p = [root](al + b)
-
-  for any given pipe with given end pressures. The curve of free surface
-  level for the pipe is, therefore, a parabola with horizontal axis.
-  Fig. 100 shows calculated curves of pressure for two of Sabine's
-  experiments, in one of which the pressure was greater than atmospheric
-  pressure, and in the other less than atmospheric pressure. The
-  observed pressures are given in brackets and the calculated pressures
-  without brackets. The pipe was the pneumatic tube between Fenchurch
-  Street and the Central Station, 2818 yds. in length. The pressures are
-  given in inches of mercury.
-
-  [Illustration: FIG. 100.]
-
-  _Variation of Velocity in the Pipe._--Let p0, u0 be the pressure and
-  velocity at a given section of the pipe; p, u, the pressure and
-  velocity at any other section. From equation (3a)
-
-    up = c[tau]W/[Omega] = constant;
-
-  so that, for any given uniform pipe,
-
-    up = u0p0,
-     u = u0p0/p;   (12)
-
-  which gives the velocity at any section in terms of the pressure,
-  which has already been determined. Fig. 101 gives the velocity curves
-  for the two experiments of Culley and Sabine, for which the pressure
-  curves have already been drawn. It will be seen that the velocity
-  increases considerably towards that end of the pipe where the pressure
-  is least.
-
-  [Illustration: FIG. 101.]
-
-  S 93. _Weight of Air Flowing per Second._--The weight of air
-  discharged per second is (equation 3a)--
-
-    W = [Omega]u0p0/c[tau].
-
-  From equation (7b), for a pipe of circular section and diameter d,
-
-    W = (1/4)[pi] [root](gd^5(p0^2 - p1^2)/[zeta]lc[tau]),
-      = .611[root](d^5(p0^2 - p1^2)/[zeta]l[tau]).   (13)
-
-  Approximately
-
-    W = (.6916 p0 - .4438 p1)(d^5/[zeta]l[tau])^(1/2).   (13a)
-
-  S 94. _Application to the Case of Pneumatic Tubes for the Transmission
-  of Messages._--In Paris, Berlin, London, and other towns, it has been
-  found cheaper to transmit messages in pneumatic tubes than to
-  telegraph by electricity. The tubes are laid underground with easy
-  curves; the messages are made into a roll and placed in a light felt
-  carrier, the resistance of which in the tubes in London is only 3/4 oz.
-  A current of air forced into the tube or drawn through it propels the
-  carrier. In most systems the current of air is steady and continuous,
-  and the carriers are introduced or removed without materially altering
-  the flow of air.
-
-  _Time of Transit through the Tube._--Putting t for the time of transit
-  from 0 to l,
-         _
-        /l
-    t = |   dl/u,
-       _/0
-
-  From (4a) neglecting dH/H, and putting m = d/4,
-
-    dl = g d[Omega]^2p dp/2[zeta]W^2cr.
-
-  From (1) and (3)
-
-    u = Wc[tau]/p[Omega];
-
-    dl/u = g d[Omega]^3p^2 dp/2[zeta]W^3c^2[tau]^2;
-       _
-      /p0
-  t = |   g d[Omega]^3p^2 dp/2[zeta]W^3c^2[tau]^2,
-     _/p1
-
-    = gd[Omega]^3(p0^3 - p1^3)/6[zeta]W^3c^2[tau]^2.   (14)
-
-  But
-
-    W = p0u0[Omega]/c[tau];
-
-    .: t = gdc[tau](p0^3 - p1^3)/6[zeta]p0^3 u0^3,
-
-         = [zeta]^(1/2)l^(3/2)(p0^3 - p1^3)/6(gc[tau]d)^(1/2)(p0^2 - p1^2)^(3/2);   (15)
-
-  If [tau] = 521 deg., corresponding to 60 deg. F.,
-
-    t = .001412 [zeta]^(1/2)l^(3/2)(p0^3 - p1^3)/d^(1/2)(p0^2 - p1^2)^(3/2);   (15a)
-
-  which gives the time of transmission in terms of the initial and final
-  pressures and the dimensions of the tube.
-
-  _Mean Velocity of Transmission._--The mean velocity is l/t; or, for
-  [tau] = 521 deg.,
-
-    u_mean = 0.708 [root]{d(p0^2 - p1^2)^(3/2)/[zeta]l(p0^3 - p1^3)}.   (16)
-
-  The following table gives some results:--
-
-    +-----------+-----------------+----------------------------------+
-    |           |    Absolute     |                                  |
-    |           |  Pressures in   |    Mean Velocities for Tubes     |
-    |           | lb. per sq. in. |       of a length in feet.       |
-    +-----------+--------+--------+------+------+------+------+------+
-    |           |   p0   |   p1   | 1000 | 2000 | 3000 | 4000 | 5000 |
-    +-----------+--------+--------+------+------+------+------+------+
-    | Vacuum    |   15   |    5   | 99.4 | 70.3 | 57.4 | 49.7 | 44.5 |
-    |   Working |   15   |   10   | 67.2 | 47.5 | 38.8 | 34.4 | 30.1 |
-    |           |        |        |      |      |      |      |      |
-    | Pressure  |   20   |   15   | 57.2 | 40.5 | 33.0 | 28.6 | 25.6 |
-    |   Working |   25   |   15   | 74.6 | 52.7 | 43.1 | 37.3 | 33.3 |
-    |           |   30   |   15   | 84.7 | 60.0 | 49.0 | 42.4 | 37.9 |
-    +-----------+-----------------+------+------+------+------+------+
-
-  _Limiting Velocity in the Pipe when the Pressure at one End is
-  diminished indefinitely._--If in the last equation there be put p1 =
-  0, then
-
-   u'_mean = 0.708 [root](d/[zeta]l);
-
-  where the velocity is independent of the pressure p0 at the other end,
-  a result which apparently must be absurd. Probably for long pipes, as
-  for orifices, there is a limit to the ratio of the initial and
-  terminal pressures for which the formula is applicable.
-
-
-  X. FLOW IN RIVERS AND CANALS
-
-  S 95. _Flow of Water in Open Canals and Rivers._--When water flows in
-  a pipe the section at any point is determined by the form of the
-  boundary. When it flows in an open channel with free upper surface,
-  the section depends on the velocity due to the dynamical conditions.
-
-  Suppose water admitted to an unfilled canal. The channel will
-  gradually fill, the section and velocity at each point gradually
-  changing. But if the inflow to the canal at its head is constant, the
-  increase of cross section and diminution of velocity at each point
-  attain after a time a limit. Thenceforward the section and velocity at
-  each point are constant, and the motion is steady, or permanent regime
-  is established.
-
-  If when the motion is steady the sections of the stream are all equal,
-  the motion is uniform. By hypothesis, the inflow [Omega]v is constant
-  for all sections, and [Omega] is constant; therefore v must be
-  constant also from section to section. The case is then one of uniform
-  steady motion. In most artificial channels the form of section is
-  constant, and the bed has a uniform slope. In that case the motion is
-  uniform, the depth is constant, and the stream surface is parallel to
-  the bed. If when steady motion is established the sections are
-  unequal, the motion is steady motion with varying velocity from
-  section to section. Ordinary rivers are in this condition, especially
-  where the flow is modified by weirs or obstructions. Short
-  unobstructed lengths of a river may be treated as of uniform section
-  without great error, the mean section in the length being put for the
-  actual sections.
-
-  In all actual streams the different fluid filaments have different
-  velocities, those near the surface and centre moving faster than those
-  near the bottom and sides. The ordinary formulae for the flow of
-  streams rest on a hypothesis that this variation of velocity may be
-  neglected, and that all the filaments may be treated as having a
-  common velocity equal to the mean velocity of the stream. On this
-  hypothesis, a plane layer abab (fig. 102) between sections normal to
-  the direction of motion is treated as sliding down the channel to
-  a'a'b'b' without deformation. The component of the weight parallel to
-  the channel bed balances the friction against the channel, and in
-  estimating the friction the velocity of rubbing is taken to be the
-  mean velocity of the stream. In actual streams, however, the velocity
-  of rubbing on which the friction depends is not the mean velocity of
-  the stream, and is not in any simple relation with it, for channels of
-  different forms. The theory is therefore obviously based on an
-  imperfect hypothesis. However, by taking variable values for the
-  coefficient of friction, the errors of the ordinary formulae are to a
-  great extent neutralized, and they may be used without leading to
-  practical errors. Formulae have been obtained based on less restricted
-  hypotheses, but at present they are not practically so reliable, and
-  are more complicated than the formulae obtained in the manner
-  described above.
-
-  [Illustration: FIG. 102.]
-
-  S 96. _Steady Flow of Water with Uniform Velocity in Channels of
-  Constant Section._--Let aa', bb' (fig. 103) be two cross sections
-  normal to the direction of motion at a distance dl. Since the mass
-  aa'bb' moves uniformly, the external forces acting on it are in
-  equilibrium. Let [Omega] be the area of the cross sections, [chi] the
-  wetted perimeter, pq + qr + rs, of a section. Then the quantity m =
-  [Omega]/[chi] is termed the hydraulic mean depth of the section. Let v
-  be the mean velocity of the stream, which is taken as the common
-  velocity of all the particles, i, the slope or fall of the stream in
-  feet, per foot, being the ratio bc/ab.
-
-  [Illustration: FIG. 103.]
-
-  The external forces acting on aa'bb' parallel to the direction of
-  motion are three:--(a) The pressures on aa' and bb', which are equal
-  and opposite since the sections are equal and similar, and the mean
-  pressures on each are the same. (b) The component of the weight W of
-  the mass in the direction of motion, acting at its centre of gravity
-  g. The weight of the mass aa'bb' is G[Omega]dl, and the component of
-  the weight in the direction of motion is G[Omega]dl X the cosine of
-  the angle between Wg and ab, that is, G[Omega]dl cos abc = G[Omega]dl
-  bc/ab = G[Omega]idl. (c) There is the friction of the stream on the
-  sides and bottom of the channel. This is proportional to the area
-  [chi]dl of rubbing surface and to a function of the velocity which may
-  be written f(v); f(v) being the friction per sq. ft. at a velocity v.
-  Hence the friction is -[chi]dl f(v). Equating the sum of the forces to
-  zero,
-
-    G[Omega]i dl - [chi]dl f(v) = 0,
-
-    f(v)/G = [Omega]i/[chi] = mi.   (1)
-
-  But it has been already shown (S 66) that f(v) = [zeta]Gv^2/2g,
-
-    .: [zeta]v^2/2g = mi.   (2)
-
-  This may be put in the form
-
-    v = [root](2g/[zeta]) [root](mi) = c [root](mi);   (2a)
-
-  where c is a coefficient depending on the roughness and form of the
-  channel.
-
-  The coefficient of friction [zeta] varies greatly with the degree of
-  roughness of the channel sides, and somewhat also with the velocity.
-  It must also be made to depend on the absolute dimensions of the
-  section, to eliminate the error of neglecting the variations of
-  velocity in the cross section. A common mean value assumed for [zeta]
-  is 0.00757. The range of values will be discussed presently.
-
-  It is often convenient to estimate the fall of the stream in feet per
-  mile, instead of in feet per foot. If f is the fall in feet per mile,
-
-    f = 5280 i.
-
-  Putting this and the above value of [zeta] in (2a), we get the very
-  simple and long-known approximate formula for the mean velocity of a
-  stream--
-
-    v = (1/4) (1/2) [root](2mf).   (3)
-
-  The flow down the stream per second, or discharge of the stream, is
-
-    Q = [Omega]v = [Omega]c [root](mi).   (4)
-
-  S 97. _Coefficient of Friction for Open Channels._--Various
-  expressions have been proposed for the coefficient of friction for
-  channels as for pipes. Weisbach, giving attention chiefly to the
-  variation of the coefficient of friction with the velocity, proposed
-  an expression of the form
-
-    [zeta] = [alpha](1 + [beta]/v),   (5)
-
-  and from 255 experiments obtained for the constants the values
-
-    [alpha] = 0.007409; [beta] = 0.1920.
-
-  This gives the following values at different velocities:--
-
-    +----------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
-    | v =      |  0.3  |  0.5  |  0.7  |  1    |1(1/2) |   2   |   3   |   5   |   7   |  10   |  15   |
-    |          |       |       |       |       |       |       |       |       |       |       |       |
-    | [zeta] = |0.01215|0.01025|0.00944|0.00883|0.00836|0.00812|0.90788|0.00769|0.00761|0.00755|0.00750|
-    +----------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
-
-  In using this value of [zeta] when v is not known, it is best to
-  proceed by approximation.
-
-  S 98. _Darcy and Bazin's Expression for the Coefficient of
-  Friction._--Darcy and Bazin's researches have shown that [zeta] varies
-  very greatly for different degrees of roughness of the channel bed,
-  and that it also varies with the dimensions of the channel. They give
-  for [zeta] an empirical expression (similar to that for pipes) of the
-  form
-
-    [zeta] = a(1 + [beta]/m);   (6)
-
-  where m is the hydraulic mean depth. For different kinds of channels
-  they give the following values of the coefficient of friction:--
-
-    +-------------------------------------------------+--------+------+
-    |                 Kind of Channel.                | [alpha]|[beta]|
-    +-------------------------------------------------+--------+------+
-    |  I. Very smooth channels, sides of smooth       |        |      |
-    |       cement or planed timber                   | .00294 | 0.10 |
-    | II. Smooth channels, sides of ashlar, brickwork,|        |      |
-    |       planks                                    | .00373 | 0.23 |
-    |III. Rough channels, sides of rubble masonry or  |        |      |
-    |       pitched with stone                        | .00471 | 0.82 |
-    | IV. Very rough canals in earth                  | .00549 | 4.10 |
-    |  V. Torrential streams encumbered with detritus | .00785 | 5.74 |
-    +-------------------------------------------------+--------+------+
-
-  The last values (Class V.) are not Darcy and Bazin's, but are taken
-  from experiments by Ganguillet and Kutter on Swiss streams.
-
-  The following table very much facilitates the calculation of the mean
-  velocity and discharge of channels, when Darcy and Bazin's value of
-  the coefficient of friction is used. Taking the general formula for
-  the mean velocity already given in equation (2a) above,
-
-    v = c [root](mi),
-
-  where c = [root](2g/[zeta]), the following table gives values of c for
-  channels of different degrees of roughness, and for such values of the
-  hydraulic mean depths as are likely to occur in practical
-  calculations:--
-
-  Values of c in v = c[root](mi), deduced from Darcy and Bazin's Values.
-
-    +----------+-----------+----------+---------+----------+--------------+
-    |          |Very Smooth|  Smooth  |  Rough  |Very Rough| Excessively  |
-    |   Mean   | Channels, | Channels,|Channels,| Channels,|Rough Channels|
-    |Depth = m.|  Cement.  |Ashlar or | Rubble  |Canals in | encumbered   |
-    |          |           |Brickwork.| Masonry.|  Earth.  |with Detritus.|
-    +----------+-----------+----------+---------+----------+--------------+
-    |     .25  |    125    |    95    |    57   |    26    |     18.5     |
-    |     .5   |    135    |   110    |    72   |    36    |     25.6     |
-    |     .75  |    139    |   116    |    81   |    42    |     30.8     |
-    |    1.0   |    141    |   119    |    87   |    48    |     34.9     |
-    |    1.5   |    143    |   122    |    94   |    56    |     41.2     |
-    |    2.0   |    144    |   124    |    98   |    62    |     46.0     |
-    |    2.5   |    145    |   126    |   101   |    67    |     ..       |
-    |    3.0   |    145    |   126    |   104   |    70    |     53       |
-    |    3.5   |    146    |   127    |   105   |    73    |     ..       |
-    |    4.0   |    146    |   128    |   106   |    76    |     58       |
-    |    4.5   |    146    |   128    |   107   |    78    |     ..       |
-    |    5.0   |    146    |   128    |   108   |    80    |     62       |
-    |    5.5   |    146    |   129    |   109   |    82    |     ..       |
-    |    6.0   |    147    |   129    |   110   |    84    |     65       |
-    |    6.5   |    147    |   129    |   110   |    85    |     ..       |
-    |    7.0   |    147    |   129    |   110   |    86    |     67       |
-    |    7.5   |    147    |   129    |   111   |    87    |     ..       |
-    |    8.0   |    147    |   130    |   111   |    88    |     69       |
-    |    8.5   |    147    |   130    |   112   |    89    |     ..       |
-    |    9.0   |    147    |   130    |   112   |    90    |     71       |
-    |    9.5   |    147    |   130    |   112   |    90    |     ..       |
-    |   10.0   |    147    |   130    |   112   |    91    |     72       |
-    |   11     |    147    |   130    |   113   |    92    |     ..       |
-    |   12     |    147    |   130    |   113   |    93    |     74       |
-    |   13     |    147    |   130    |   113   |    94    |     ..       |
-    |   14     |    147    |   130    |   113   |    95    |     ..       |
-    |   15     |    147    |   130    |   114   |    96    |     77       |
-    |   16     |    147    |   130    |   114   |    97    |     ..       |
-    |   17     |    147    |   130    |   114   |    97    |     ..       |
-    |   18     |    147    |   130    |   114   |    98    |     ..       |
-    |   20     |    147    |   131    |   114   |    98    |     80       |
-    |   25     |    148    |   131    |   115   |   100    |     ..       |
-    |   30     |    148    |   131    |   115   |   102    |     83       |
-    |   40     |    148    |   131    |   116   |   103    |     85       |
-    |   50     |    148    |   131    |   116   |   104    |     86       |
-    |   [oo]   |    148    |   131    |   117   |   108    |     91       |
-    +----------+-----------+----------+---------+----------+--------------+
-
-  S 99. _Ganguillet and Kutter's Modified Darcy Formula._--Starting from
-  the general expression v = c[root]mi, Ganguillet and Kutter examined
-  the variations of c for a wider variety of cases than those discussed
-  by Darcy and Bazin. Darcy and Bazin's experiments were confined to
-  channels of moderate section, and to a limited variation of slope.
-  Ganguillet and Kutter brought into the discussion two very distinct
-  and important additional series of results. The gaugings of the
-  Mississippi by A. A. Humphreys and H. L. Abbot afford data of
-  discharge for the case of a stream of exceptionally large section and
-  or very low slope. On the other hand, their own measurements of the
-  flow in the regulated channels of some Swiss torrents gave data for
-  cases in which the inclination and roughness of the channels were
-  exceptionally great. Darcy and Bazin's experiments alone were
-  conclusive as to the dependence of the coefficient c on the dimensions
-  of the channel and on its roughness of surface. Plotting values of c
-  for channels of different inclination appeared to indicate that it
-  also depended on the slope of the stream. Taking the Mississippi data
-  only, they found
-
-    c = 256 for an inclination of 0.0034 per thousand,
-      = 154      "       "        0.02         "
-
-  so that for very low inclinations no constant value of c independent
-  of the slope would furnish good values of the discharge. In small
-  rivers, on the other hand, the values of c vary little with the slope.
-  As regards the influence of roughness of the sides of the channel a
-  different law holds. For very small channels differences of roughness
-  have a great influence on the discharge, but for very large channels
-  different degrees of roughness have but little influence, and for
-  indefinitely large channels the influence of different degrees of
-  roughness must be assumed to vanish. The coefficients given by Darcy
-  and Bazin are different for each of the classes of channels of
-  different roughness, even when the dimensions of the channel are
-  infinite. But, as it is much more probable that the influence of the
-  nature of the sides diminishes indefinitely as the channel is larger,
-  this must be regarded as a defect in their formula.
-
-  Comparing their own measurements in torrential streams in Switzerland
-  with those of Darcy and Bazin, Ganguillet and Kutter found that the
-  four classes of coefficients proposed by Darcy and Bazin were
-  insufficient to cover all cases. Some of the Swiss streams gave
-  results which showed that the roughness of the bed was markedly
-  greater than in any of the channels tried by the French engineers. It
-  was necessary therefore in adopting the plan of arranging the
-  different channels in classes of approximately similar roughness to
-  increase the number of classes. Especially an additional class was
-  required for channels obstructed by detritus.
-
-  To obtain a new expression for the coefficient in the formula
-
-    v = [root](2g/[zeta]) [root](mi) = c [root](mi),
-
-  Ganguillet and Kutter proceeded in a purely empirical way. They found
-  that an expression of the form
-
-    c = [alpha]/(1 + [beta]/[root]m)
-
-  could be made to fit the experiments somewhat better than Darcy's
-  expression. Inverting this, we get
-
-    1/c = 1/[alpha] + [beta]/[alpha] [root]m,
-
-  an equation to a straight line having 1/[root]m for abscissa, 1/c for
-  ordinate, and inclined to the axis of abscissae at an angle the
-  tangent of which is [beta]/[alpha].
-
-  Plotting the experimental values of 1/c and 1/[root]m, the points so
-  found indicated a curved rather than a straight line, so that [beta]
-  must depend on [alpha]. After much comparison the following form was
-  arrived at--
-
-    c = (A + l/n)/(1 + An/[root]m),
-
-  where n is a coefficient depending only on the roughness of the sides
-  of the channel, and A and l are new coefficients, the value of which
-  remains to be determined. From what has been already stated, the
-  coefficient c depends on the inclination of the stream, decreasing as
-  the slope i increases.
-
-  Let
-
-    A = a + p/i.
-
-  Then
-
-    c = (a + l/n + p/i)/{1 + (a + p/i)n/[root]m},
-
-  the form of the expression for c ultimately adopted by Ganguillet and
-  Kutter.
-
-  For the constants a, l, p Ganguillet and Kutter obtain the values 23,
-  1 and 0.00155 for metrical measures, or 41.6, 1.811 and 0.00281 for
-  English feet. The coefficient of roughness n is found to vary from
-  0.008 to 0.050 for either metrical or English measures.
-
-  The most practically useful values of the coefficient of roughness n
-  are given in the following table:--
-
-              Nature of Sides of Channel.               Coefficient of
-                                                         Roughness n.
-    Well-planed timber                                     0.009
-    Cement plaster                                         0.010
-    Plaster of cement with one-third sand                  0.011
-    Unplaned planks                                        0.012
-    Ashlar and brickwork                                   0.013
-    Canvas on frames                                       0.015
-    Rubble masonry                                         0.017
-    Canals in very firm gravel                             0.020
-    Rivers and canals in perfect order, free from stones \
-      or weeds                                           / 0.025
-    Rivers and canals in moderately good order, not      \
-      quite free from stones and weeds                   / 0.030
-    Rivers and canals in bad order, with weeds and       \
-      detritus                                           / 0.035
-    Torrential streams encumbered with detritus            0.050
-
-  Ganguillet and Kutter's formula is so cumbrous that it is difficult to
-  use without the aid of tables.
-
-  Lowis D'A. Jackson published complete and extensive tables for
-  facilitating the use of the Ganguillet and Kutter formula (_Canal and
-  Culvert Tables_, London, 1878). To lessen calculation he puts the
-  formula in this form:--
-
-    M = n(41.6 + 0.00281/i);
-
-    v = ([root]m/n) {(M + 1.811)/(M + [root]m)} [root](mi).
-
-  The following table gives a selection of values of M, taken from
-  Jackson's tables:--
-
-    +--------+--------------------------------------------------------------+
-    |        |                     Values of M for n =                      |
-    |  i =   +--------+--------+--------+--------+--------+--------+--------+
-    |        |  0.010 |  0.012 |  0.015 |  0.017 |  0.020 |  0.025 |  0.030 |
-    +--------+--------+--------+--------+--------+--------+--------+--------+
-    | .00001 | 3.2260 | 3.8712 | 4.8390 | 5.4842 | 6.4520 | 8.0650 | 9.6780 |
-    | .00002 | 1.8210 | 2.1852 | 2.7315 | 3.0957 | 3.6420 | 4.5525 | 5.4630 |
-    | .00004 | 1.1185 | 1.3422 | 1.6777 | 1.9014 | 2.2370 | 2.7962 | 3.3555 |
-    | .00006 | 0.8843 | 1.0612 | 1.3264 | 1.5033 | 1.7686 | 2.2107 | 2.6529 |
-    | .00008 | 0.7672 | 0.9206 | 1.1508 | 1.3042 | 1.5344 | 1.9180 | 2.3016 |
-    | .00010 | 0.6970 | 0.8364 | 1.0455 | 1.1849 | 1.3940 | 1.7425 | 2.0910 |
-    | .00025 | 0.5284 | 0.6341 | 0.7926 | 0.8983 | 1.0568 | 1.3210 | 1.5852 |
-    | .00050 | 0.4722 | 0.5666 | 0.7083 | 0.8027 | 0.9444 | 1.1805 | 1.4166 |
-    | .00075 | 0.4535 | 0.5442 | 0.6802 | 0.7709 | 0.9070 | 1.1337 | 1.3605 |
-    | .00100 | 0.4441 | 0.5329 | 0.6661 | 0.7550 | 0.8882 | 1.1102 | 1.3323 |
-    | .00200 | 0.4300 | 0.5160 | 0.6450 | 0.7310 | 0.8600 | 1.0750 | 1.2900 |
-    | .00300 | 0.4254 | 0.5105 | 0.6381 | 0.7232 | 0.8508 | 1.0635 | 1.2762 |
-    +--------+--------+--------+--------+--------+--------+--------+--------+
-
-  A difficulty in the use of this formula is the selection of the
-  coefficient of roughness. The difficulty is one which no theory will
-  overcome, because no absolute measure of the roughness of stream beds
-  is possible. For channels lined with timber or masonry the difficulty
-  is not so great. The constants in that case are few and sufficiently
-  defined. But in the case of ordinary canals and rivers the case is
-  different, the coefficients having a much greater range. For
-  artificial canals in rammed earth or gravel n varies from 0.0163 to
-  0.0301. For natural channels or rivers n varies from 0.020 to 0.035.
-
-  In Jackson's opinion even Kutter's numerous classes of channels seem
-  inadequately graduated, and he proposes for artificial canals the
-  following classification:--
-
-      I. Canals in very firm gravel, in perfect order      n = 0.02
-     II. Canals in earth, above the average in order       n = 0.0225
-    III. Canals in earth, in fair order                    n = 0.025
-     IV. Canals in earth, below the average in order       n = 0.0275
-      V. Canals in earth, in rather bad order, partially\
-           overgrown with weeds and obstructed by        > n = 0.03
-           detritus.                                    /
-
-  Ganguillet and Kutter's formula has been considerably used partly from
-  its adoption in calculating tables for irrigation work in India. But
-  it is an empirical formula of an unsatisfactory form. Some engineers
-  apparently have assumed that because it is complicated it must be more
-  accurate than simpler formulae. Comparison with the results of
-  gaugings shows that this is not the case. The term involving the slope
-  was introduced to secure agreement with some early experiments on the
-  Mississippi, and there is strong reason for doubting the accuracy of
-  these results.
-
-  S 100. _Bazin's New Formula._--Bazin subsequently re-examined all the
-  trustworthy gaugings of flow in channels and proposed a modification
-  of the original Darcy formula which appears to be more satisfactory
-  than any hitherto suggested (_Etude d'une nouvelle formule_, Paris,
-  1898). He points out that Darcy's original formula, which is of the
-  form mi/v^2 = [alpha] + [beta]/m, does not agree with experiments on
-  channels as well as with experiments on pipes. It is an objection to
-  it that if m increases indefinitely the limit towards which mi/v^2
-  tends is different for different values of the roughness. It would
-  seem that if the dimensions of a canal are indefinitely increased the
-  variation of resistance due to differing roughness should vanish. This
-  objection is met if it is assumed that [root](mi/v^2) = [alpha] +
-  [beta]/[root]m, so that if a is a constant mi/v^2 tends to the limit a
-  when m increases. A very careful discussion of the results of gaugings
-  shows that they can be expressed more satisfactorily by this new
-  formula than by Ganguillet and Kutter's. Putting the equation in the
-  form [zeta]v^2/2g = mi, [zeta] = 0.002594(1 + [gamma]/[root]m), where
-  [gamma] has the following values:--
-
-      I. Very smooth sides, cement, planed plank, [gamma] = 0.109
-     II. Smooth sides, planks, brickwork                    0.290
-    III. Rubble masonry sides                               0.833
-     IV. Sides of very smooth earth, or pitching            1.539
-      V. Canals in earth in ordinary condition              2.353
-     VI. Canals in earth exceptionally rough                3.168
-
-  S 101. _The Vertical Velocity Curve._--If at each point along a
-  vertical representing the depth of a stream, the velocity at that
-  point is plotted horizontally, the curve obtained is the vertical
-  velocity curve and it has been shown by many observations that it
-  approximates to a parabola with horizontal axis. The vertex of the
-  parabola is at the level of the greatest velocity. Thus in fig. 104 OA
-  is the vertical at which velocities are observed; v0 is the surface;
-  v_z the maximum and v_d the bottom velocity. B C D is the vertical
-  velocity curve which corresponds with a parabola having its vertex at
-  C. The mean velocity at the vertical is
-
-    v_m = (1/3)[2v_z + v_d + (d_z/d)(v0 - v_d)].
-
-  _The Horizontal Velocity Curve._--Similarly if at each point along a
-  horizontal representing the width of the stream the velocities are
-  plotted, a curve is obtained called the horizontal velocity curve. In
-  streams of symmetrical section this is a curve symmetrical about the
-  centre line of the stream. The velocity varies little near the centre
-  of the stream, but very rapidly near the banks. In unsymmetrical
-  sections the greatest velocity is at the point where the stream is
-  deepest, and the general form of the horizontal velocity curve is
-  roughly similar to the section of the stream.
-
-  [Illustration: FIG. 104.]
-
-  S 102. _Curves or Contours of Equal Velocity._--If velocities are
-  observed at a number of points at different widths and depths in a
-  stream, it is possible to draw curves on the cross section through
-  points at which the velocity is the same. These represent contours of
-  a solid, the volume of which is the discharge of the stream per
-  second. Fig. 105 shows the vertical and horizontal velocity curves and
-  the contours of equal velocity in a rectangular channel, from one of
-  Bazin's gaugings.
-
-  S 103. _Experimental Observations on the Vertical Velocity Curve._--A
-  preliminary difficulty arises in observing the velocity at a given
-  point in a stream because the velocity rapidly varies, the motion not
-  being strictly steady. If an average of several velocities at the same
-  point is taken, or the average velocity for a sensible period of time,
-  this average is found to be constant. It may be inferred that though
-  the velocity at a point fluctuates about a mean value, the
-  fluctuations being due to eddying motions superposed on the general
-  motion of the stream, yet these fluctuations produce effects which
-  disappear in the mean of a series of observations and, in calculating
-  the volume of flow, may be disregarded.
-
-  [Illustration: FIG. 105.]
-
-  In the next place it is found that in most of the best observations on
-  the velocity in streams, the greatest velocity at any vertical is
-  found not at the surface but at some distance below it. In various
-  river gaugings the depth d_z at the centre of the stream has been
-  found to vary from 0 to 0.3d.
-
-  S 104. _Influence of the Wind._--In the experiments on the Mississippi
-  the vertical velocity curve in calm weather was found to agree fairly
-  with a parabola, the greatest velocity being at (3/10)ths of the depth
-  of the stream from the surface. With a wind blowing down stream the
-  surface velocity is increased, and the axis of the parabola approaches
-  the surface. On the contrary, with a wind blowing up stream the
-  surface velocity is diminished, and the axis of the parabola is
-  lowered, sometimes to half the depth of the stream. The American
-  observers drew from their observations the conclusion that there was
-  an energetic retarding action at the surface of a stream like that due
-  to the bottom and sides. If there were such a retarding action the
-  position of the filament of maximum velocity below the surface would
-  be explained.
-
-  It is not difficult to understand that a wind acting on surface
-  ripples or waves should accelerate or retard the surface motion of the
-  stream, and the Mississippi results may be accepted so far as showing
-  that the surface velocity of a stream is variable when the mean
-  velocity of the stream is constant. Hence observations of surface
-  velocity by floats or otherwise should only be made in very calm
-  weather. But it is very difficult to suppose that, in still air, there
-  is a resistance at the free surface of the stream at all analogous to
-  that at the sides and bottom. Further, in very careful experiments, P.
-  P. Boileau found the maximum velocity, though raised a little above
-  its position for calm weather, still at a considerable distance below
-  the surface, even when the wind was blowing down stream with a
-  velocity greater than that of the stream, and when the action of the
-  air must have been an accelerating and not a retarding action. A much
-  more probable explanation of the diminution of the velocity at and
-  near the free surface is that portions of water, with a diminished
-  velocity from retardation by the sides or bottom, are thrown off in
-  eddying masses and mingle with the rest of the stream. These eddying
-  masses modify the velocity in all parts of the stream, but have their
-  greatest influence at the free surface. Reaching the free surface they
-  spread out and remain there, mingling with the water at that level and
-  diminishing the velocity which would otherwise be found there.
-
-  _Influence of the Wind on the Depth at which the Maximum Velocity is
-  found._--In the gaugings of the Mississippi the vertical velocity
-  curve was found to agree well with a parabola having a horizontal axis
-  at some distance below the water surface, the ordinate of the parabola
-  at the axis being the maximum velocity of the section. During the
-  gaugings the force of the wind was registered on a scale ranging from
-  0 for a calm to 10 for a hurricane. Arranging the velocity curves in
-  three sets--(1) with the wind blowing up stream, (2) with the wind
-  blowing down stream, (3) calm or wind blowing across stream--it was
-  found that an upstream wind lowered, and a down-stream wind raised,
-  the axis of the parabolic velocity curve. In calm weather the axis was
-  at (3/10)ths of the total depth from the surface for all conditions of
-  the stream.
-
-  Let h' be the depth of the axis of the parabola, m the hydraulic mean
-  depth, f the number expressing the force of the wind, which may range
-  from +10 to -10, positive if the wind is up stream, negative if it is
-  down stream. Then Humphreys and Abbot find their results agree with
-  the expression
-
-    h'/m = 0.317 [+-] 0.06f.
-
-  Fig. 106 shows the parabolic velocity curves according to the American
-  observers for calm weather, and for an up- or down-stream wind of a
-  force represented by 4.
-
-  [Illustration: FIG. 106.]
-
-  It is impossible at present to give a theoretical rule for the
-  vertical velocity curve, but in very many gaugings it has been found
-  that a parabola with horizontal axis fits the observed results fairly
-  well. The mean velocity on any vertical in a stream varies from 0.85
-  to 0.92 of the surface velocity at that vertical, and on the average
-  if v0 is the surface and v_m the mean velocity at a vertical v_m =
-  6/7 v0, a result useful in float gauging. On any vertical there is a
-  point at which the velocity is equal to the mean velocity, and if this
-  point were known it would be useful in gauging. Humphreys and Abbot in
-  the Mississippi found the mean velocity at 0.66 of the depth; G. H. L.
-  Hagen and H. Heinemann at 0.56 to 0.58 of the depth. The mean of
-  observations by various observers gave the mean velocity at from 0.587
-  to 0.62 of the depth, the average of all being almost exactly 0.6 of
-  the depth. The mid-depth velocity is therefore nearly equal to, but a
-  little greater than, the mean velocity on a vertical. If v_(md) is the
-  mid-depth velocity, then on the average v_m = 0.98v_(md).
-
-  S 105. _Mean Velocity on a Vertical from Two Velocity
-  Observations._--A. J. C. Cunningham, in gaugings on the Ganges canal,
-  found the following useful results. Let v0 be the surface, v_m the
-  mean, and v_(xd) the velocity at the depth xd; then
-
-    v_m = (1/4)[v0 + 3v_(2/3d)]
-        = (1/2)[v_(.211)^d + v_(.789)^d].
-
-  S 106. _Ratio of Mean to Greatest Surface Velocity, for the whole
-  Cross Section in Trapezoidal Channels._--It is often very important to
-  be able to deduce the mean velocity, and thence the discharge, from
-  observation of the greatest surface velocity. The simplest method of
-  gauging small streams and channels is to observe the greatest surface
-  velocity by floats, and thence to deduce the mean velocity. In general
-  in streams of fairly regular section the mean velocity for the whole
-  section varies from 0.7 to 0.85 of the greatest surface velocity. For
-  channels not widely differing from those experimented on by Bazin, the
-  expression obtained by him for the ratio of surface to mean velocity
-  may be relied on as at least a good approximation to the truth. Let v0
-  be the greatest surface velocity, v_m the mean velocity of the stream.
-  Then, according to Bazin,
-
-    v_m = v0 - 25.4 [root](mi).
-
-  But
-
-    v_m = c [root](mi),
-
-  where c is a coefficient, the values of which have been already given
-  in the table in S 98. Hence
-
-    v_m = cv0/(c + 25.4).
-
-    _Values of Coefficient c/(c + 25.4) in the Formula v_m = cv0/(c +
-    25.4)._
-
-    +----------+---------+----------+---------+----------+----------+
-    |Hydraulic |  Very   |  Smooth  |  Rough  |Very Rough| Channels |
-    |Mean Depth| Smooth  |Channels. |Channels.| Channels.|encumbered|
-    |   = m.   |Channels.|Ashlar or | Rubble  | Canals in|   with   |
-    |          | Cement. |Brickwork.| Masonry.|  Earth.  | Detritus.|
-    +----------+---------+----------+---------+----------+----------+
-    |          |         |          |         |          |          |
-    |    0.25  |   .83   |   .79    |   .69   |   .51    |   .42    |
-    |    0.5   |   .84   |   .81    |   .74   |   .58    |   .50    |
-    |    0.75  |   .84   |   .82    |   .76   |   .63    |   .55    |
-    |    1.0   |   .85   |    ..    |   .77   |   .65    |   .58    |
-    |    2.0   |    ..   |   .83    |   .79   |   .71    |   .64    |
-    |    3.0   |    ..   |    ..    |   .80   |   .73    |   .67    |
-    |    4.0   |    ..   |    ..    |   .81   |   .75    |   .70    |
-    |    5.0   |    ..   |    ..    |    ..   |   .76    |   .71    |
-    |    6.0   |    ..   |   .84    |    ..   |   .77    |   .72    |
-    |    7.0   |    ..   |    ..    |    ..   |   .78    |   .73    |
-    |    8.0   |    ..   |    ..    |    ..   |    ..    |    ..    |
-    |    9.0   |    ..   |    ..    |   .82   |    ..    |   .74    |
-    |   10.0   |    ..   |    ..    |    ..   |    ..    |    ..    |
-    |   15.0   |    ..   |    ..    |    ..   |   .79    |   .75    |
-    |   20.0   |    ..   |    ..    |    ..   |   .80    |   .76    |
-    |   30.0   |    ..   |    ..    |   .82   |    ..    |   .77    |
-    |   40.0   |    ..   |    ..    |    ..   |    ..    |    ..    |
-    |   50.0   |    ..   |    ..    |    ..   |    ..    |    ..    |
-    |   [oo]   |    ..   |    ..    |    ..   |    ..    |   .79    |
-    +----------+---------+----------+---------+----------+----------+
-
-  [Illustration: FIG. 107.]
-
-  S 107. _River Bends._--In rivers flowing in alluvial plains, the
-  windings which already exist tend to increase in curvature by the
-  scouring away of material from the outer bank and the deposition of
-  detritus along the inner bank. The sinuosities sometimes increase till
-  a loop is formed with only a narrow strip of land between the two
-  encroaching branches of the river. Finally a "cut off" may occur, a
-  waterway being opened through the strip of land and the loop left
-  separated from the stream, forming a horseshoe shaped lagoon or marsh.
-  Professor James Thomson pointed out (_Proc. Roy. Soc._, 1877, p. 356;
-  _Proc. Inst. of Mech. Eng._, 1879, p. 456) that the usual supposition
-  is that the water tending to go forwards in a straight line rushes
-  against the outer bank and scours it, at the same time creating
-  deposits at the inner bank. That view is very far from a complete
-  account of the matter, and Professor Thomson gave a much more
-  ingenious account of the action at the bend, which he completely
-  confirmed by experiment.
-
-  [Illustration: FIG. 108.]
-
-  When water moves round a circular curve under the action of gravity
-  only, it takes a motion like that in a free vortex. Its velocity is
-  greater parallel to the axis of the stream at the inner than at the
-  outer side of the bend. Hence the scouring at the outer side and the
-  deposit at the inner side of the bend are not due to mere difference
-  of velocity of flow in the general direction of the stream; but, in
-  virtue of the centrifugal force, the water passing round the bend
-  presses outwards, and the free surface in a radial cross section has a
-  slope from the inner side upwards to the outer side (fig. 108). For
-  the greater part of the water flowing in curved paths, this difference
-  of pressure produces no tendency to transverse motion. But the water
-  immediately in contact with the rough bottom and sides of the channel
-  is retarded, and its centrifugal force is insufficient to balance the
-  pressure due to the greater depth at the outside of the bend. It
-  therefore flows inwards towards the inner side of the bend, carrying
-  with it detritus which is deposited at the inner bank. Conjointly with
-  this flow inwards along the bottom and sides, the general mass of
-  water must flow outwards to take its place. Fig. 107 shows the
-  directions of flow as observed in a small artificial stream, by means
-  of light seeds and specks of aniline dye. The lines CC show the
-  directions of flow immediately in contact with the sides and bottom.
-  The dotted line AB shows the direction of motion of floating particles
-  on the surface of the stream.
-
-  S 108. _Discharge of a River when flowing at different Depths._--When
-  frequent observations must be made on the flow of a river or canal,
-  the depth of which varies at different times, it is very convenient to
-  have to observe the depth only. A formula can be established giving
-  the flow in terms of the depth. Let Q be the discharge in cubic feet
-  per second; H the depth of the river in some straight and uniform
-  part. Then Q = aH + bH^2, where the constants a and b must be found by
-  preliminary gaugings in different conditions of the river. M. C.
-  Moquerey found for part of the upper Saone, Q = 64.7H + 8.2H^2 in
-  metric measures, or Q = 696H + 26.8H^2 in English measures.
-
-  S 109. _Forms of Section of Channels._--The simplest form of section
-  for channels is the semicircular or nearly semicircular channel (fig.
-  109), a form now often adopted from the facility with which it can be
-  executed in concrete. It has the advantage that the rubbing surface is
-  less in proportion to the area than in any other form.
-
-  [Illustration: FIG. 109.]
-
-  Wooden channels or flumes, of which there are examples on a large
-  scale in America, are rectangular in section, and the same form is
-  adopted for wrought and cast-iron aqueducts. Channels built with
-  brickwork or masonry may be also rectangular, but they are often
-  trapezoidal, and are always so if the sides are pitched with masonry
-  laid dry. In a trapezoidal channel, let b (fig. 110) be the bottom
-  breadth, b0 the top breadth, d the depth, and let the slope of the
-  sides be n horizontal to 1 vertical. Then the area of section is
-  [Omega] = (b + nd)d = (b0 - nd)d, and the wetted perimeter [chi] = b +
-  2d[root](n^2 + 1).
-
-  [Illustration: FIG. 110.]
-
-  When a channel is simply excavated in earth it is always originally
-  trapezoidal, though it becomes more or less rounded in course of time.
-  The slope of the sides then depends on the stability of the earth, a
-  slope of 2 to 1 being the one most commonly adopted.
-
-  Figs. 111, 112 show the form of canals excavated in earth, the former
-  being the section of a navigation canal and the latter the section of
-  an irrigation canal.
-
-  S 110. _Channels of Circular Section._--The following short table
-  facilitates calculations of the discharge with different depths of
-  water in the channel. Let r be the radius of the channel section; then
-  for a depth of water = [kappa]r, the hydraulic mean radius is [mu]r
-  and the area of section of the waterway [nu]r^2, where [kappa], [mu],
-  and [nu] have the following values:--
-
-    +---------------------------------+------+-----+-----+-----+-----+-----+-----+-----+----+----+----+----+----+----+----+-----+-----+-----+-----+-----+-----+
-    | Depth of water in   \ [kappa] = |.01   |.05  |.10  |.15  |.20  |.25  |.30  |.35  |.40 |.45 |.50 |.55 |.60 |.65 |.70 |.75  |.80  |.85  |.90  |.95  |1.0  |
-    |   terms of radius   /           |      |     |     |     |     |     |     |     |    |    |    |    |    |    |    |     |     |     |     |     |     |
-    | Hydraulic mean depth\ [mu]    = |.00668|.0321|.0523|.0963|.1278|.1574|.1852|.2142|.242|.269|.293|.320|.343|.365|.387|.408 |.429 |.449 |.466 |.484 |.500 |
-    |   in terms of radius/           |      |     |     |     |     |     |     |     |    |    |    |    |    |    |    |     |     |     |     |     |     |
-    | Waterway in terms of\ [nu]    = |.00189|.0211|.0598|.1067|.1651|.228 |.294 |.370 |.450|.532|.614|.709|.795|.885|.979|1.075|1.175|1.276|1.371|1.470|1.571|
-    |   square of radius  /           |      |     |     |     |     |     |     |     |    |    |    |    |    |    |    |     |     |     |     |     |     |
-    +---------------------------------+------+-----+-----+-----+-----+-----+-----+-----+----+----+----+----+----+----+----+-----+-----+-----+-----+-----+-----+
-
-  [Illustration: FIG. 111.--Scale 20 ft. = 1 in.]
-
-  [Illustration: FIG. 112.--Scale 80 ft. = 1 in.]
-
-  S 111. _Egg-Shaped Channels or Sewers._--In sewers for discharging
-  storm water and house drainage the volume of flow is extremely
-  variable; and there is a great liability for deposits to be left when
-  the flow is small, which are not removed during the short periods when
-  the flow is large. The sewer in consequence becomes choked. To obtain
-  uniform scouring action, the velocity of flow should be constant or
-  nearly so; a complete uniformity of velocity cannot be obtained with
-  any form of section suitable for sewers, but an approximation to
-  uniform velocity is obtained by making the sewers of oval section.
-  Various forms of oval have been suggested, the simplest being one in
-  which the radius of the crown is double the radius of the invert, and
-  the greatest width is two-thirds the height. The section of such a
-  sewer is shown in fig. 113, the numbers marked on the figure being
-  proportional numbers.
-
-  [Illustration: FIG. 113.]
-
-  S 112. _Problems on Channels in which the Flow is Steady and at
-  Uniform Velocity._--The general equations given in SS 96, 98 are
-
-    [zeta] = [alpha](1 + [beta]/m);   (1)
-
-    [zeta]v^2/2g = mi;   (2)
-
-    Q = [Omega]v.   (3)
-
-  _Problem I._--Given the transverse section of stream and discharge, to
-  find the slope. From the dimensions of the section find [Omega] and m;
-  from (1) find [zeta], from (3) find v, and lastly from (2) find i.
-
-  _Problem II._--Given the transverse section and slope, to find the
-  discharge. Find v from (2), then Q from (3).
-
-  _Problem III._--Given the discharge and slope, and either the breadth,
-  depth, or general form of the section of the channel, to determine its
-  remaining dimensions. This must generally be solved by approximations.
-  A breadth or depth or both are chosen, and the discharge calculated.
-  If this is greater than the given discharge, the dimensions are
-  reduced and the discharge recalculated.
-
-  [Illustration: FIG. 114.]
-
-  Since m lies generally between the limits m = d and m = (1/2)d, where
-  d is the depth of the stream, and since, moreover, the velocity varies
-  as [root](m) so that an error in the value of m leads only to a much
-  less error in the value of the velocity calculated from it, we may
-  proceed thus. Assume a value for m, and calculate v from it. Let v1 be
-  this first approximation to v. Then Q/v1 is a first approximation to
-  [Omega], say [Omega]1. With this value of [Omega] design the section
-  of the channel; calculate a second value for m; calculate from it a
-  second value of v, and from that a second value for [Omega]. Repeat
-  the process till the successive values of m approximately coincide.
-
-  S 113. _Problem IV. Most Economical Form of Channel for given Side
-  Slopes._--Suppose the channel is to be trapezoidal in section (fig.
-  114), and that the sides are to have a given slope. Let the
-  longitudinal slope of the stream be given, and also the mean velocity.
-  An infinite number of channels could be found satisfying the
-  foregoing conditions. To render the problem determinate, let it be
-  remembered that, since for a given discharge [Omega][oo] [cube
-  root][chi], other things being the same, the amount of excavation will
-  be least for that channel which has the least wetted perimeter. Let d
-  be the depth and b the bottom width of the channel, and let the sides
-  slope n horizontal to 1 vertical (fig. 114), then
-
-    [Omega] = (b + nd)d;
-
-    [chi] = b + 2d [root](n^2 + 1).
-
-  Both [Omega] and [chi] are to be minima. Differentiating, and equating
-  to zero.
-
-    (db/dd + n)d + b + nd = 0,
-
-    db/dd + 2[root](n^2 + 1) = 0;
-
-  eliminating db/dd,
-
-    {n - 2[root](n^2 + 1)}d + b + nd = 0;
-
-    b = 2 {[root](n^2 + 1) - n}d.
-
-  But
-
-    [Omega]/[chi] = (b + nd)d/{b + 2d [root](n^2 + 1)}.
-
-  Inserting the value of b,
-
-    m = [Omega]/[chi] = {2d[root](n^2 + 1) - nd}/
-      {4d [root](n^2 + 1) - 2nd} = (1/2)d.
-
-  That is, with given side slopes, the section is least for a given
-  discharge when the hydraulic mean depth is half the actual depth.
-
-  A simple construction gives the form of the channel which fulfils this
-  condition, for it can be shown that when m = (1/2)d the sides of the
-  channel are tangential to a semicircle drawn on the water line.
-
-  Since
-
-    [Omega]/[chi] = (1/2)d,
-
-  therefore
-
-    [Omega] = (1/2)[chi]d.   (1)
-
-  Let ABCD be the channel (fig. 115); from E the centre of AD drop
-  perpendiculars EF, EG, EH on the sides.
-
-  Let
-
-    AB = CD = a; BC = b; EF = EH = c; and EG = d.
-
-    [Omega] = area AEB + BEC + CED,
-            = ac + (1/2)bd.
-
-    [chi] = 2a + b.
-
-  Putting these values in (1),
-
-    ac + (1/2)bd = (a + (1/2)b)d; and hence c = d.
-
-  [Illustration: FIG. 115.]
-
-  That is, EF, EG, EH are all equal, hence a semicircle struck from E
-  with radius equal to the depth of the stream will pass through F and H
-  and be tangential to the sides of the channel.
-
-  [Illustration: FIG. 116.]
-
-  To draw the channel, describe a semicircle on a horizontal line with
-  radius = depth of channel. The bottom will be a horizontal tangent of
-  that semicircle, and the sides tangents drawn at the required side
-  slopes.
-
-  The above result may be obtained thus (fig. 116):--
-
-    [chi] = b + 2d/sin [beta].   (1)
-
-    [Omega] = d(b + d cot [beta]);
-
-    [Omega]/d = b + d cot [beta];   (2)
-
-    [Omega]/d^2 = b/d + cot [beta].   (3)
-
-  From (1) and (2),
-
-    [chi] = [Omega]/d - d cot [beta] + 2d/sin [beta].
-
-  This will be a minimum for
-
-    d[chi]/dd = [Omega]/d^2 + cot[beta] - 2/sin [beta] = 0,
-
-  or
-
-    [Omega]/d^2 = 2 cosec. [beta] - cot [beta].   (4)
-
-  or
-
-    d = [root]{[Omega] sin [beta]/(2 - cos [beta])}.
-
-  From (3) and (4),
-
-    b/d = 2(1 - cos [beta])/sin [beta] = 2 tan (1/2)[beta].
-
-  _Proportions of Channels of Maximum Discharge for given Area and Side
-  Slopes. Depth of channel = d; Hydraulic mean depth = (1/2)d; Area of
-  section =_ [Omega].
-
-    +-------------+---------------+------------+-----------+---------+------------+
-    |             |  Inclination  |  Ratio of  |  Area of  |         |Top width = |
-    |             |  of Sides to  |    Side    |  Section  |  Bottom |twice length|
-    |             |    Horizon.   |   Slopes.  |  [Omega]. |  Width. |of each Side|
-    |             |               |            |           |         |   Slope.   |
-    +-------------+---------------+------------+-----------+---------+------------+
-    | Semicircle  |      ..       |     ..     | 1.571 d^2 |    0    |    2 d     |
-    | Semi-hexagon|  60 deg.  0'  |     3  : 5 | 1.732 d^2 | 1.155 d |  2.310 d   |
-    | Semi-square |  90 deg.  0'  |     0  : 1 |   2 d^2   |  2 d    |    2 d     |
-    |             |  75 deg. 58'  |     1  : 4 | 1.812 d^2 | 1.562 d |  2.062 d   |
-    |             |  63 deg. 26'  |     1  : 2 | 1.736 d^2 | 1.236 d |  2.236 d   |
-    |             |  53 deg.  8'  |     3  : 4 | 1.750 d^2 |    d    |  2.500 d   |
-    |             |  45 deg.  0'  |     1  : 1 | 1.828 d^2 | 0.828 d |  2.828 d   |
-    |             |  38 deg. 40'  | 1(1/4) : 1 | 1.952 d^2 | 0.702 d |  3.202 d   |
-    |             |  33 deg. 42'  | 1(1/2) : 1 | 2.106 d^2 | 0.606 d |  3.606 d   |
-    |             |  29 deg. 44'  | 1(3/4) : 1 | 2.282 d^2 | 0.532 d |  4.032 d   |
-    |             |  26 deg. 34'  |     2  : 1 | 2.472 d^2 | 0.472 d |  4.472 d   |
-    |             |  23 deg. 58'  | 2(1/4) : 1 | 2.674 d^2 | 0.424 d |  4.924 d   |
-    |             |  21 deg. 48'  | 2(1/2) : 1 | 2.885 d^2 | 0.385 d |  5.385 d   |
-    |             |  19 deg. 58'  | 2(3/4) : 1 | 3.104 d^2 | 0.354 d |  5.854 d   |
-    |             |  18 deg. 26'  |     3  : 1 | 3.325 d^2 | 0.325 d |  6.325 d   |
-    +-------------+---------------+------------+-----------+---------+------------+
-
-    Half the top width is the length of each side slope. The wetted
-    perimeter is the sum of the top and bottom widths.
-
-  S 114. _Form of Cross Section of Channel in which the Mean Velocity is
-  Constant with Varying Discharge._--In designing waste channels from
-  canals, and in some other cases, it is desirable that the mean
-  velocity should be restricted within narrow limits with very different
-  volumes of discharge. In channels of trapezoidal form the velocity
-  increases and diminishes with the discharge. Hence when the discharge
-  is large there is danger of erosion, and when it is small of silting
-  or obstruction by weeds. A theoretical form of section for which the
-  mean velocity would be constant can be found, and, although this is
-  not very suitable for practical purposes, it can be more or less
-  approximated to in actual channels.
-
-  Let fig. 117 represent the cross section of the channel. From the
-  symmetry of the section, only half the channel need be considered. Let
-  obac be any section suitable for the minimum flow, and let it be
-  required to find the curve beg for the upper part of the channel so
-  that the mean velocity shall be constant. Take o as origin of
-  coordinates, and let de, fg be two levels of the water above ob.
-
-  [Illustration: FIG. 117.]
-
-  Let
-
-    ob = b/2; de = y, fg = y + dy, od = x, of = x + dx; eg = ds.
-
-  The condition to be satisfied is that
-
-    v = c [root](mi)
-
-  should be constant, whether the water-level is at ob, de, or fg.
-  Consequently
-
-    m = constant = k
-
-  for all three sections, and can be found from the section obac. Hence
-  also
-
-     Increment of section    y dx
-    ---------------------- = ---- = k
-    Increment of perimeter    ds
-
-    y^2dx^2 = k^2ds^2 = k^2(dx^2 + dy^2) and dx = k dy/[root](y^2 - k^2).
-
-  Integrating,
-
-    x = k log_[epsilon] {y + [root](y^2 - k^2)} + constant;
-
-  and, since y = b/2 when x = 0,
-
-    x = k log_[epsilon] [{y + [root](y^2 - k^2)}/{(1/2)b + [root]((1/4)b^2 - k^2)}].
-
-  Assuming values for y, the values of x can be found and the curve
-  drawn.
-
-  The figure has been drawn for a channel the minimum section of which
-  is a half hexagon of 4 ft. depth. Hence k = 2; b = 9.2; the rapid
-  flattening of the side slopes is remarkable.
-
-
-  STEADY MOTION OF WATER IN OPEN CHANNELS OF VARYING CROSS SECTION AND
-  SLOPE
-
-  S 115. In every stream the discharge of which is constant, or may be
-  regarded as constant for the time considered, the velocity at
-  different places depends on the slope of the bed. Except at certain
-  exceptional points the velocity will be greater as the slope of the
-  bed is greater, and, as the velocity and cross section of the stream
-  vary inversely, the section of the stream will be least where the
-  velocity and slope are greatest. If in a stream of tolerably uniform
-  slope an obstruction such as a weir is built, that will cause an
-  alteration of flow similar to that of an alteration of the slope of
-  the bed for a greater or less distance above the weir, and the
-  originally uniform cross section of the stream will become a varied
-  one. In such cases it is often of much practical importance to
-  determine the longitudinal section of the stream.
-
-  The cases now considered will be those in which the changes of
-  velocity and cross section are gradual and not abrupt, and in which
-  the only internal work which needs to be taken into account is that
-  due to the friction of the stream bed, as in cases of uniform motion.
-  Further, the motion will be supposed to be steady, the mean velocity
-  at each given cross section remaining constant, though it varies from
-  section to section along the course of the stream.
-
-  [Illustration: FIG. 118.]
-
-  Let fig. 118 represent a longitudinal section of the stream, A0A1
-  being the water surface, B0B1 the stream bed. Let A0B0, A1B1 be cross
-  sections normal to the direction of flow. Suppose the mass of water
-  A0B0A1B1 comes in a short time [theta] to C0D0C1D1, and let the work
-  done on the mass be equated to its change of kinetic energy during
-  that period. Let l be the length A0A1 of the portion of the stream
-  considered, and z the fall, of surface level in that distance. Let Q
-  be the discharge of the stream per second.
-
-  [Illustration: FIG. 119.]
-
-  _Change of Kinetic Energy._--At the end of the time [theta] there are
-  as many particles possessing the same velocities in the space C0D0A1B1
-  as at the beginning. The change of kinetic energy is therefore the
-  difference of the kinetic energies of A0B0C0D0 and A1B1C1D1.
-
-  Let fig. 119 represent the cross section A0B0, and let [omega] be a
-  small element of its area at a point where the velocity is v. Let
-  [Omega]0 be the whole area of the cross section and u0 the mean
-  velocity for the whole cross section. From the definition of mean
-  velocity we have
-
-    u0 = [Sigma][omega]v/[Omega]0.
-
-  Let v = u0 + w, where w is the difference between the velocity at the
-  small element [omega] and the mean velocity. For the whole cross
-  section, [Sigma][omega]w = 0.
-
-  The mass of fluid passing through the element of section [omega], in
-  [theta] seconds, is (G/g)[omega]v[theta], and its kinetic energy is
-  (G/2g)[omega]v^3[theta]. For the whole section, the kinetic energy of
-  the mass A0B0C0D0 passing in [theta] seconds is
-
-    (G[theta]/2g)[Sigma][omega]v^3
-      = (G[theta]/2g)[Sigma][omega](u0^3 + 3u0^2w + 3u0^2 + w^3),
-      = (G[theta]/2g){u0^3[Omega] + [Sigma][omega]w^2(3u0 + w)}.
-
-  The factor 3u0 + w is equal to 2u0 + v, a quantity necessarily
-  positive. Consequently [Sigma][omega]v^3 > [Omega]0u0^3, and
-  consequently the kinetic energy of A0B0C0D0 is greater than
-
-    (G[theta]/2g)[Omega]0u0^3 or (G[theta])/2g)Qu0^2,
-
-  which would be its value if all the particles passing the section had
-  the same velocity u0. Let the kinetic energy be taken at
-
-    [alpha](G[theta]/2g)[Omega]0u0^3 = [alpha](G[theta]/2g)Qu0^2,
-
-  where [alpha] is a corrective factor, the value of which was estimated
-  by J. B. C. J. Belanger at 1.1.[6] Its precise value is not of great
-  importance.
-
-  In a similar way we should obtain for the kinetic energy of A1B1C1D1
-  the expression
-
-    [alpha](G[theta]/2g)[Omega]1 u1^3 = [alpha](G[theta]/2g)Q u1^2,
-
-  where [Omega]1, u1 are the section and mean velocity at A1B1, and
-  where a may be taken to have the same value as before without any
-  important error.
-
-  Hence the change of kinetic energy in the whole mass A0B0A1B1 in
-  [theta] seconds is
-
-    [alpha](G[theta]/2g) Q (u1^2 - u0^2).   (1)
-
-  _Motive Work of the Weight and Pressures._--Consider a small filament
-  a0a1 which comes in [theta] seconds to c0c1. The work done by gravity
-  during that movement is the same as if the portion a0c0 were carried
-  to a1c1. Let dQ[theta] be the volume of a0c0 or a1c1, and y0, y1 the
-  depths of a0, a1 from the surface of the stream. Then the volume
-  dQ[theta] or GdQ[theta] pounds falls through a vertical height z + y1
-  - y0, and the work done by gravity is
-
-    G dQ[theta](z + y1 - y0).
-
-  Putting p_a for atmospheric pressure, the whole pressure per unit of
-  area at a0 is Gy0 + p_a, and that at a1 is - (Gy1 + p_a). The work of
-  these pressures is
-
-    G(y0 + p_a/G - y1 - p_a/G) dQ[theta] = G(y0 - y1) dQ[theta].
-
-  Adding this to the work of gravity, the whole work is GzdQ[theta]; or,
-  for the whole cross section,
-
-    GzQ[theta].   (2)
-
-  _Work expended in Overcoming the Friction of the Stream Bed._--Let
-  A'B', A"B" be two cross sections at distances s and s + ds from
-  A0B0. Between these sections the velocity may be treated as uniform,
-  because by hypothesis the changes of velocity from section to section
-  are gradual. Hence, to this short length of stream the equation for
-  uniform motion is applicable. But in that case the work in overcoming
-  the friction of the stream bed between A'B' and A"B" is
-
-    GQ[theta][zeta](u^2/2g)([chi]/[Omega]) ds,
-
-  where u, [chi], [Omega] are the mean velocity, wetted perimeter, and
-  section at A'B'. Hence the whole work lost in friction from A0B0 to
-  A1B1 will be
-               _
-              / l
-    GQ[theta] |   [zeta](u^2/2g)([chi]/[Omega]) ds.   (3)
-             _/ 0
-
-  Equating the work given in (2) and (3) to the change of kinetic energy
-  given in (1),
-
-    [alpha](GQ[theta]/2g)(u1^2 - u0^2)
-                                _
-                               / l
-      = GQz[theta] - GQ[theta] |   [zeta](u^2/2g)([chi]/[Omega]) ds;
-                              _/ 0
-                                      _
-                                     / l
-    .: z = [alpha](u1^2 - u0^2)/2g + |   [zeta](u^2/2g)([chi]/[Omega]) ds.
-                                    _/ 0
-
-  [Illustration: FIG. 120.]
-
-  S 116. _Fundamental Differential Equation of Steady Varied
-  Motion._--Suppose the equation just found to be applied to an
-  indefinitely short length ds of the stream, limited by the end
-  sections ab, a1b1, taken for simplicity normal to the stream bed (fig.
-  120). For that short length of stream the fall of surface level, or
-  difference of level of a and a1, may be written dz. Also, if we write
-  u for u0, and u + du for u1, the term (u0^2 - u1^2)/2g becomes udu/g.
-  Hence the equation applicable to an indefinitely short length of the
-  stream is
-
-    dz = udu/g + ([chi]/[Omega])[zeta](u^2/2g) ds.   (1)
-
-  From this equation some general conclusions may be arrived at as to
-  the form of the longitudinal section of the stream, but, as the
-  investigation is somewhat complicated, it is convenient to simplify it
-  by restricting the conditions of the problem.
-
-  _Modification of the Formula for the Restricted Case of a Stream
-  flowing in a Prismatic Stream Bed of Constant Slope._--Let i be the
-  constant slope of the bed. Draw ad parallel to the bed, and ac
-  horizontal. Then dz is sensibly equal to a'c. The depths of the
-  stream, h and h + dh, are sensibly equal to ab and a'b', and therefore
-  dh = a'd. Also cd is the fall of the bed in the distance ds, and is
-  equal to ids. Hence
-
-    dz = a'c = cd - a'd = i ds - dh.   (2)
-
-  Since the motion is steady--
-
-    Q = [Omega]u = constant.
-
-  Differentiating,
-
-    [Omega] du + u d[Omega] = 0;
-
-    .:du = -u d[Omega]/[Omega].
-
-  Let x be the width of the stream, then d[Omega] = xdh very nearly.
-  Inserting this value,
-
-    du = -(ux/[Omega]) dh.   (3)
-
-  Putting the values of du and dz found in (2) and (3) in equation (1),
-
-    i ds - dh = -(u^2x/g[Omega]) dh + ([chi]/[Omega])[zeta](u^2/2g) ds.
-
-    dh/ds = {i - ([chi]/[Omega]) [zeta] (u^2/2g)}/{1 - (u^2/g)(x/[Omega])}.   (4)
-
-  _Further Restriction to the Case of a Stream of Rectangular Section
-  and of Indefinite Width._--The equation might be discussed in the form
-  just given, but it becomes a little simpler if restricted in the way
-  just stated. For, if the stream is rectangular, [chi]h = [Omega], and
-  if [chi] is large compared with h, [Omega]/[chi] = xh/x = h nearly.
-  Then equation (4) becomes
-
-    dh/ds = i(1 - [zeta]u^2/2gih)/(1 - u^2/gh).   (5)
-
-  S 117. _General Indications as to the Form of Water Surface furnished
-  by Equation_ (5).--Let A0A1 (fig. 121) be the water surface, B0B1 the
-  bed in a longitudinal section of the stream, and ab any section at a
-  distance s from B0, the depth ab being h. Suppose B0B1, B0A0 taken as
-  rectangular coordinate axes, then dh/ds is the trigonometric tangent
-  of the angle which the surface of the stream at a makes with the axis
-  B0B1. This tangent dh/ds will be positive, if the stream is increasing
-  in depth in the direction B0B1; negative, if the stream is diminishing
-  in depth from B0 towards B1. If dh/ds = 0, the surface of the stream
-  is parallel to the bed, as in cases of uniform motion. But from
-  equation (4)
-
-    dh/ds = 0, if i - ([chi]/[Omega])[zeta](u^2/2g) = 0;
-
-    .: [zeta](u^2/2g) = ([Omega]/[chi])i = mi,
-
-  which is the well-known general equation for uniform motion, based on
-  the same assumptions as the equation for varied steady motion now
-  being considered. The case of uniform motion is therefore a limiting
-  case between two different kinds of varied motion.
-
-  [Illustration: FIG. 121.]
-
-  Consider the possible changes of value of the fraction
-
-    (1 - [zeta]u^2/2gih)/(1 - u^2/gh).
-
-  As h tends towards the limit 0, and consequently u is large, the
-  numerator tends to the limit -[oo]. On the other hand if h = [oo], in
-  which case u is small, the numerator becomes equal to 1. For a value H
-  of h given by the equation
-
-    1 - [zeta]u^2/2giH = 0,
-
-    H = [zeta]u^2/2gi,
-
-  we fall upon the case of uniform motion. The results just stated may
-  be tabulated thus:--
-
-    For h = 0, H, > H, [oo],
-
-  the numerator has the value -[oo], 0, > 0, 1.
-
-  Next consider the denominator. If h becomes very small, in which case
-  u must be very large, the denominator tends to the limit -[oo]. As h
-  becomes very large and u consequently very small, the denominator
-  tends to the limit 1. For h = u^2/g, or u = [root](gh), the
-  denominator becomes zero. Hence, tabulating these results as before:--
-
-    For h = 0, u^2/g, > u^2/g, [oo],
-
-  the denominator becomes
-
-    -[oo], 0, > 0, 1.
-
-  [Illustration: FIG. 122.]
-
-  S 118. _Case_ 1.--Suppose h > u^2/g, and also h > H, or the depth
-  greater than that corresponding to uniform motion. In this case dh/ds
-  is positive, and the stream increases in depth in the direction of
-  flow. In fig. 122 let B0B1 be the bed, C0C1 a line parallel to the bed
-  and at a height above it equal to H. By hypothesis, the surface A0A1
-  of the stream is above C0C1, and it has just been shown that the depth
-  of the stream increases from B0 towards B1. But going up stream h
-  approaches more and more nearly the value H, and therefore dh/ds
-  approaches the limit 0, or the surface of the stream is asymptotic to
-  C0C1. Going down stream h increases and u diminishes, the numerator
-  and denominator of the fraction (1 - [zeta]u^2/2gih)/(1 -u^2/gh) both
-  tend towards the limit 1, and dh/ds to the limit i. That is, the
-  surface of the stream tends to become asymptotic to a horizontal line
-  D0D1.
-
-  The form of water surface here discussed is produced when the flow of
-  a stream originally uniform is altered by the construction of a weir.
-  The raising of the water surface above the level C0C1 is termed the
-  backwater due to the weir.
-
-  S 119. _Case_ 2.--Suppose h > u^2/g, and also h < H. Then dh/ds is
-  negative, and the stream is diminishing in depth in the direction of
-  flow. In fig. 123 let B0B1 be the stream bed as before; C0C1 a line
-  drawn parallel to B0B1 at a height above it equal to H. By hypothesis
-  the surface A0A1 of the stream is below C0C1, and the depth has just
-  been shown to diminish from B0 towards B1. Going up stream h
-  approaches the limit H, and dh/ds tends to the limit zero. That is, up
-  stream A0A1 is asymptotic to C0C1. Going down stream h diminishes and
-  u increases; the inequality h>u^2/g diminishes; the denominator of the
-  fraction (1 - [zeta]u^2/2gih)/(1 - u^2/gh) tends to the limit zero, and
-  consequently dh/ds tends to [infinity]. That is, down stream A0A1
-  tends to a direction perpendicular to the bed. Before, however, this
-  limit was reached the assumptions on which the general equation is
-  based would cease to be even approximately true, and the equation
-  would cease to be applicable. The filaments would have a relative
-  motion, which would make the influence of internal friction in the
-  fluid too important to be neglected. A stream surface of this form may
-  be produced if there is an abrupt fall in the bed of the stream (fig.
-  124).
-
-  [Illustration: FIG. 123.]
-
-  [Illustration: FIG. 124.]
-
-  [Illustration: FIG. 125.]
-
-  On the Ganges canal, as originally constructed, there were abrupt
-  falls precisely of this kind, and it appears that the lowering of the
-  water surface and increase of velocity which such falls occasion, for
-  a distance of some miles up stream, was not foreseen. The result was
-  that, the velocity above the falls being greater than was intended,
-  the bed was scoured and considerable damage was done to the works.
-  "When the canal was first opened the water was allowed to pass freely
-  over the crests of the overfalls, which were laid on the level of the
-  bed of the earthen channel; erosion of bed and sides for some miles up
-  rapidly followed, and it soon became apparent that means must be
-  adopted for raising the surface of the stream at those points (that
-  is, the crests of the falls). Planks were accordingly fixed in the
-  grooves above the bridge arches, or temporary weirs were formed over
-  which the water was allowed to fall; in some cases the surface of the
-  water was thus raised above its normal height, causing a backwater in
-  the channel above" (Crofton's _Report on the Ganges Canal_, p. 14).
-  Fig. 125 represents in an exaggerated form what probably occurred, the
-  diagram being intended to represent some miles' length of the canal
-  bed above the fall. AA parallel to the canal bed is the level
-  corresponding to uniform motion with the intended velocity of the
-  canal. In consequence of the presence of the ogee fall, however, the
-  water surface would take some such form as BB, corresponding to Case 2
-  above, and the velocity would be greater than the intended velocity,
-  nearly in the inverse ratio of the actual to the intended depth. By
-  constructing a weir on the crest of the fall, as shown by dotted
-  lines, a new water surface CC corresponding to Case 1 would be
-  produced, and by suitably choosing the height of the weir this might
-  be made to agree approximately with the intended level AA.
-
-  S 120. _Case_ 3.--Suppose a stream flowing uniformly with a depth h <
-  u^2/g. For a stream in uniform motion [zeta]u^2/2g = mi, or if the
-  stream is of indefinitely great width, so that m = H, then
-  [zeta]u^2/2g = iH, and H = [zeta]u^2/2gi. Consequently the condition
-  stated above involves that
-
-    [zeta]u^2/2gi < u^2/g, or that i > [zeta]/2.
-
-  If such a stream is interfered with by the construction of a weir
-  which raises its level, so that its depth at the weir becomes h1 >
-  u^2/g, then for a portion of the stream the depth h will satisfy the
-  conditions h < u^2/g and h > H, which are not the same as those assumed in the two
-  previous cases. At some point of the stream above the weir the depth h
-  becomes equal to u^2/g, and at that point dh/ds becomes infinite, or
-  the surface of the stream is normal to the bed. It is obvious that at
-  that point the influence of internal friction will be too great to be
-  neglected, and the general equation will cease to represent the true
-  conditions of the motion of the water. It is known that, in cases such
-  as this, there occurs an abrupt rise of the free surface of the
-  stream, or a standing wave is formed, the conditions of motion in
-  which will be examined presently.
-
-  It appears that the condition necessary to give rise to a standing
-  wave is that i > [zeta]/2. Now [zeta] depends for different channels
-  on the roughness of the channel and its hydraulic mean depth. Bazin
-  calculated the values of [zeta] for channels of different degrees of
-  roughness and different depths given in the following table, and the
-  corresponding minimum values of i for which the exceptional case of
-  the production of a standing wave may occur.
-
-    +-----------------------------+----------------+-------------------------+
-    |                             |  Slope below   |  Standing Wave Formed.  |
-    |                             |which a Standing|                         |
-    |   Nature of Bed of Stream.  |    Wave is     +-------------+-----------+
-    |                             | impossible in  |Slope in feet|Least Depth|
-    |                             | feet peer foot.|  per foot.  |  in feet. |
-    +-----------------------------+----------------+-------------+-----------+
-    |                             |                |  / 0.002    |   0.262   |
-    | Very smooth cemented surface|    0.00147     | <  0.003    |    .098   |
-    |                             |                |  \ 0.004    |    .065   |
-    |                             |                |             |           |
-    |                             |                |  / 0.003    |    .394   |
-    | Ashlar or brickwork         |    0.00186     | <  0.004    |    .197   |
-    |                             |                |  \ 0.006    |    .098   |
-    |                             |                |             |           |
-    |                             |                |  / 0.004    |   1.181   |
-    | Rubble masonry              |    0.00235     | <  0.006    |    .525   |
-    |                             |                |  \ 0.010    |    .262   |
-    |                             |                |             |           |
-    |                             |                |  / 0.006    |   3.478   |
-    | Earth                       |    0.00275     | <  0.010    |   1.542   |
-    |                             |                |  \ 0.015    |    .919   |
-    +-----------------------------+----------------+-------------+-----------+
-
-
-  STANDING WAVES
-
-  S 121. The formation of a standing wave was first observed by Bidone.
-  Into a small rectangular masonry channel, having a slope of 0.023 ft.
-  per foot, he admitted water till it flowed uniformly with a depth of
-  0.2 ft. He then placed a plank across the stream which raised the
-  level just above the obstruction to 0.95 ft. He found that the stream
-  above the obstruction was sensibly unaffected up to a point 15 ft.
-  from it. At that point the depth suddenly increased from 0.2 ft. to
-  0.56 ft. The velocity of the stream in the part unaffected by the
-  obstruction was 5.54 ft. per second. Above the point where the abrupt
-  change of depth occurred u^2 = 5.54^2 = 30.7, and gh = 32.2 X 0.2 =
-  6.44; hence u^2 was > gh. Just below the abrupt change of depth u =
-  5.54 X 0.2/0.56 = 1.97; u^2 = 3.88; and gh = 32.2 X 0.56 = 18.03; hence
-  at this point u^2 < gh. Between these two points, therefore, u^2 = gh;
-  and the condition for the production of a standing wave occurred.
-
-  [Illustration: FIG. 126.]
-
-  The change of level at a standing wave may be found thus. Let fig. 126
-  represent the longitudinal section of a stream and ab, cd cross
-  sections normal to the bed, which for the short distance considered
-  may be assumed horizontal. Suppose the mass of water abcd to come to
-  a'b'c'd' in a short time t; and let u0, u1 be the velocities at ab and
-  cd, [Omega]0, [Omega]1 the areas of the cross sections. The force
-  causing change of momentum in the mass abcd estimated horizontally is
-  simply the difference of the pressures on ab and cd. Putting h0, h1
-  for the depths of the centres of gravity of ab and cd measured down
-  from the free water surface, the force is G(h0[Omega]0 - h1[Omega]1)
-  pounds, and the impulse in t seconds is G (h0[Omega]0 - h1[Omega]1) t
-  second pounds. The horizontal change of momentum is the difference of
-  the momenta of cdc'd' and aba'b'; that is,
-
-    (G/g)([Omega]1u1^2 - [Omega]0u0^2)t.
-
-  Hence, equating impulse and change of momentum,
-
-    G(h0[Omega]0 - h1[Omega]1)t = (G/g)([Omega]1u1^2 - [Omega]0u0^2)t;
-
-    .: h0[Omega]0 - h1[Omega]1 = ([Omega]1u1^2 - [Omega]0u0^2)/g.   (1)
-
-  For simplicity let the section be rectangular, of breadth B and depths
-  H0 and H1, at the two cross sections considered; then h0 = (1/2)H0,
-  and h1 = (1/2)H1. Hence
-
-    H0^2 - H1^2 = (2/g)(H1u1^2 - H0u0^2).
-
-  But, since [Omega]0u0 = [Omega]1u1, we have
-
-    u1^2 = u0^2H0^2/H1^2,
-
-    H0^2 - H1^2 = (2u0^2/g)(H0^2/H1 - H0).   (2)
-
-  This equation is satisfied if H0 = H1, which corresponds to the case
-  of uniform motion. Dividing by H0 - H1, the equation becomes
-
-    (H1/H0)(H0 + H1) = 2u0^2/g;   (3)
-
-    .: H1 = [root](2u0^2H0/g + (1/4)H0^2) - (1/2)H0.   (4)
-
-  In Bidone's experiment u0 = 5.54, and H0 = 0.2. Hence H1 = 0.52, which
-  agrees very well with the observed height.
-
-  [Illustration: FIG. 127.]
-
-  S 122. A standing wave is frequently produced at the foot of a weir.
-  Thus in the ogee falls originally constructed on the Ganges canal a
-  standing wave was observed as shown in fig. 127. The water falling
-  over the weir crest A acquired a very high velocity on the steep slope
-  AB, and the section of the stream at B became very small. It easily
-  happened, therefore, that at B the depth h < u^2/g. In flowing along
-  the rough apron of the weir the velocity u diminished and the depth h
-  increased. At a point C, where h became equal to u^2/g, the conditions
-  for producing the standing wave occurred. Beyond C the free surface
-  abruptly rose to the level corresponding to uniform motion with the
-  assigned slope of the lower reach of the canal.
-
-  [Illustration: FIG. 128.]
-
-  A standing wave is sometimes formed on the down stream side of bridges
-  the piers of which obstruct the flow of the water. Some interesting
-  cases of this kind are described in a paper on the "Floods in the
-  Nerbudda Valley" in the _Proc. Inst. Civ. Eng._ vol. xxvii. p. 222, by
-  A. C. Howden. Fig. 128 is compiled from the data given in that paper.
-  It represents the section of the stream at pier 8 of the Towah
-  Viaduct, during the flood of 1865. The ground level is not exactly
-  given by Howden, but has been inferred from data given on another
-  drawing. The velocity of the stream was not observed, but the author
-  states it was probably the same as at the Gunjal river during a
-  similar flood, that is 16.58 ft. per second. Now, taking the depth on
-  the down stream face of the pier at 26 ft., the velocity necessary for
-  the production of a standing wave would be u = [root](gh) =
-  [root](32.2 X 26) = 29 ft. per second nearly. But the velocity at this
-  point was probably from Howden's statements 16.58 X {40/26} = 25.5 ft.
-  per second, an agreement as close as the approximate character of the
-  data would lead us to expect.
-
-
-  XI. ON STREAMS AND RIVERS
-
-  S 123. _Catchment Basin._--A stream or river is the channel for the
-  discharge of the available rainfall of a district, termed its
-  catchment basin. The catchment basin is surrounded by a ridge or
-  watershed line, continuous except at the point where the river finds
-  an outlet. The area of the catchment basin may be determined from a
-  suitable contoured map on a scale of at least 1 in 100,000. Of the
-  whole rainfall on the catchment basin, a part only finds its way to
-  the stream. Part is directly re-evaporated, part is absorbed by
-  vegetation, part may escape by percolation into neighbouring
-  districts. The following table gives the relation of the average
-  stream discharge to the average rainfall on the catchment basin
-  (Tiefenbacher).
-
-    +-----------------------------+-----------------+--------------------+
-    |                             |Ratio of average |Loss by Evaporation,|
-    |                             |   Discharge to  | &c., in per cent of|
-    |                             |average Rainfall.|   total Rainfall.  |
-    +-----------------------------+-----------------+--------------------+
-    | Cultivated land and spring- |                 |                    |
-    |   forming declivities.      |    .3 to .33    |      67 to 70      |
-    | Wooded hilly slopes.        |   .35 to .45    |      55 to 65      |
-    | Naked unfissured mountains  |   .55 to .60    |      40 to 45      |
-    +-----------------------------+-----------------+--------------------+
-
-  S 124. _Flood Discharge._--The flood discharge can generally only be
-  determined by examining the greatest height to which floods have been
-  known to rise. To produce a flood the rainfall must be heavy and
-  widely distributed, and to produce a flood of exceptional height the
-  duration of the rainfall must be so great that the flood waters of the
-  most distant affluents reach the point considered, simultaneously with
-  those from nearer points. The larger the catchment basin the less
-  probable is it that all the conditions tending to produce a maximum
-  discharge should simultaneously occur. Further, lakes and the river
-  bed itself act as storage reservoirs during the rise of water level
-  and diminish the rate of discharge, or serve as flood moderators. The
-  influence of these is often important, because very heavy rain storms
-  are in most countries of comparatively short duration. Tiefenbacher
-  gives the following estimate of the flood discharge of streams in
-  Europe:--
-
-                                         Flood discharge of Streams
-                                         per Second per Square Mile
-                                             of Catchment Basin.
-
-    In flat country                           8.7 to 12.5 cub. ft.
-    In hilly districts                       17.5 to 22.5    "
-    In moderately mountainous districts      36.2 to 45.0    "
-    In very mountainous districts            50.0 to 75.0    "
-
-  It has been attempted to express the decrease of the rate of flood
-  discharge with the increase of extent of the catchment basin by
-  empirical formulae. Thus Colonel P. P. L. O'Connell proposed the
-  formula y = M [root]x, where M is a constant called the modulus of the
-  river, the value of which depends on the amount of rainfall, the
-  physical characters of the basin, and the extent to which the floods
-  are moderated by storage of the water. If M is small for any given
-  river, it shows that the rainfall is small, or that the permeability
-  or slope of the sides of the valley is such that the water does not
-  drain rapidly to the river, or that lakes and river bed moderate the
-  rise of the floods. If values of M are known for a number of rivers,
-  they may be used in inferring the probable discharge of other similar
-  rivers. For British rivers M varies from 0.43 for a small stream
-  draining meadow land to 37 for the Tyne. Generally it is about 15 or
-  20. For large European rivers M varies from 16 for the Seine to 67.5
-  for the Danube. For the Nile M = 11, a low value which results from
-  the immense length of the Nile throughout which it receives no
-  affluent, and probably also from the influence of lakes. For different
-  tributaries of the Mississippi M varies from 13 to 56. For various
-  Indian rivers it varies from 40 to 303, this variation being due to
-  the great variations of rainfall, slope and character of Indian
-  rivers.
-
-  In some of the tank projects in India, the flood discharge has been
-  calculated from the formula D = C[3root]n^2, where D is the discharge
-  in cubic yards per hour from n square miles of basin. The constant C
-  was taken = 61,523 in the designs for the Ekrooka tank, = 75,000 on
-  Ganges and Godavery works, and = 10,000 on Madras works.
-
-  [Illustration: FIG. 129.]
-
-  [Illustration: FIG. 130.]
-
-  S 125. _Action of a Stream on its Bed._--If the velocity of a stream
-  exceeds a certain limit, depending on its size, and on the size,
-  heaviness, form and coherence of the material of which its bed is
-  composed, it scours its bed and carries forward the materials. The
-  quantity of material which a given stream can carry in suspension
-  depends on the size and density of the particles in suspension, and is
-  greater as the velocity of the stream is greater. If in one part of
-  its course the velocity of a stream is great enough to scour the bed
-  and the water becomes loaded with silt, and in a subsequent part of
-  the river's course the velocity is diminished, then part of the
-  transported material must be deposited. Probably deposit and scour go
-  on simultaneously over the whole river bed, but in some parts the rate
-  of scour is in excess of the rate of deposit, and in other parts the
-  rate of deposit is in excess of the rate of scour. Deep streams appear
-  to have the greatest scouring power at any given velocity. It is
-  possible that the difference is strictly a difference of transporting,
-  not of scouring action. Let fig. 129 represent a section of a stream.
-  The material lifted at a will be diffused through the mass of the
-  stream and deposited at different distances down stream. The average
-  path of a particle lifted at a will be some such curve as abc, and the
-  average distance of transport each time a particle is lifted will be
-  represented by ac. In a deeper stream such as that in fig. 130, the
-  average height to which particles are lifted, and, since the rate of
-  vertical fall through the water may be assumed the same as before, the
-  average distance a'c' of transport will be greater. Consequently,
-  although the scouring action may be identical in the two streams, the
-  velocity of transport of material down stream is greater as the depth
-  of the stream is greater. The effect is that the deep stream excavates
-  its bed more rapidly than the shallow stream.
-
-  S 126. _Bottom Velocity at which Scour commences._--The following
-  bottom velocities were determined by P. L. G. Dubuat to be the maximum
-  velocities consistent with stability of the stream bed for different
-  materials.
-
-  Darcy and Bazin give, for the relation of the mean velocity v_m and
-  bottom velocity v_b.
-
-    v_m = v_b + 10.87 [root](mi).
-
-  But
-
-    [root]mi = v_m [root]([zeta]/2g);
-
-    .: v_m = v_b/(1 - 10.87 [root]([zeta]/2g)).
-
-  Taking a mean value for [zeta], we get
-
-    v_m = 1.312 v_b,
-
-  and from this the following values of the mean velocity are
-  obtained:--
-
-    +-----------------------+---------------+-------------+
-    |                       |Bottom Velocity|Mean Velocity|
-    |                       |     = v_b.    |    = v_m.   |
-    +-----------------------+---------------+-------------+
-    | 1. Soft earth         |     0.25      |     .33     |
-    | 2. Loam               |     0.50      |     .65     |
-    | 3. Sand               |     1.00      |    1.30     |
-    | 4. Gravel             |     2.00      |    2.62     |
-    | 5. Pebbles            |     3.40      |    4.46     |
-    | 6. Broken stone, flint|     4.00      |    5.25     |
-    | 7. Chalk, soft shale  |     5.00      |    6.56     |
-    | 8. Rock in beds       |     6.00      |    7.87     |
-    | 9. Hard rock.         |    10.00      |   13.12     |
-    +-----------------------+---------------+-------------+
-
-  The following table of velocities which should not be exceeded in
-  channels is given in the _Ingenieurs Taschenbuch_ of the Verein
-  "Hutte":--
-
-    +--------------------------------+---------+---------+---------+
-    |                                | Surface |  Mean   | Bottom  |
-    |                                |Velocity.|Velocity.|Velocity.|
-    +--------------------------------+---------+---------+---------+
-    | Slimy earth or brown clay      |    .49  |    .36  |    .26  |
-    | Clay                           |    .98  |    .75  |    .52  |
-    | Firm sand                      |   1.97  |   1.51  |   1.02  |
-    | Pebbly bed                     |   4.00  |   3.15  |   2.30  |
-    | Boulder bed                    |   5.00  |   4.03  |   3.08  |
-    | Conglomerate of slaty fragments|   7.28  |   6.10  |   4.90  |
-    | Stratified rocks               |   8.00  |   7.45  |   6.00  |
-    | Hard rocks                     |  14.00  |  12.15  |  10.36  |
-    +--------------------------------+---------+---------+---------+
-
-  S 127. _Regime of a River Channel._--A river channel is said to be in
-  a state of regime, or stability, when it changes little in draught or
-  form in a series of years. In some rivers the deepest part of the
-  channel changes its position perpetually, and is seldom found in the
-  same place in two successive years. The sinuousness of the river also
-  changes by the erosion of the banks, so that in time the position of
-  the river is completely altered. In other rivers the change from year
-  to year is very small, but probably the regime is never perfectly
-  stable except where the rivers flow over a rocky bed.
-
-  [Illustration: FIG. 131.]
-
-  If a river had a constant discharge it would gradually modify its bed
-  till a permanent regime was established. But as the volume discharged
-  is constantly changing, and therefore the velocity, silt is deposited
-  when the velocity decreases, and scour goes on when the velocity
-  increases in the same place. When the scouring and silting are
-  considerable, a perfect balance between the two is rarely established,
-  and hence continual variations occur in the form of the river and the
-  direction of its currents. In other cases, where the action is less
-  violent, a tolerable balance may be established, and the deepening of
-  the bed by scour at one time is compensated by the silting at another.
-  In that case the general regime is permanent, though alteration is
-  constantly going on. This is more likely to happen if by artificial
-  means the erosion of the banks is prevented. If a river flows in soil
-  incapable of resisting its tendency to scour it is necessarily sinuous
-  (S 107), for the slightest deflection of the current to either side
-  begins an erosion which increases progressively till a considerable
-  bend is formed. If such a river is straightened it becomes sinuous
-  again unless its banks are protected from scour.
-
-  S 128. _Longitudinal Section of River Bed._--The declivity of rivers
-  decreases from source to mouth. In their higher parts rapid and
-  torrential, flowing over beds of gravel or boulders, they enlarge in
-  volume by receiving affluent streams, their slope diminishes, their
-  bed consists of smaller materials, and finally they reach the sea.
-  Fig. 131 shows the length in miles, and the surface fall in feet per
-  mile, of the Tyne and its tributaries.
-
-  The decrease of the slope is due to two causes. (1) The action of the
-  transporting power of the water, carrying the smallest debris the
-  greatest distance, causes the bed to be less stable near the mouth
-  than in the higher parts of the river; and, as the river adjusts its
-  slope to the stability of the bed by scouring or increasing its
-  sinuousness when the slope is too great, and by silting or
-  straightening its course if the slope is too small, the decreasing
-  stability of the bed would coincide with a decreasing slope. (2) The
-  increase of volume and section of the river leads to a decrease of
-  slope; for the larger the section the less slope is necessary to
-  ensure a given velocity.
-
-  The following investigation, though it relates to a purely arbitrary
-  case, is not without interest. Let it be assumed, to make the
-  conditions definite--(1) that a river flows over a bed of uniform
-  resistance to scour, and let it be further assumed that to maintain
-  stability the velocity of the river in these circumstances is constant
-  from source to mouth; (2) suppose the sections of the river at all
-  points are similar, so that, b being the breadth of the river at any
-  point, its hydraulic mean depth is ab and its section is cb^2, where a
-  and c are constants applicable to all parts of the river; (3) let us
-  further assume that the discharge increases uniformly in consequence
-  of the supply from affluents, so that, if l is the length of the river
-  from its source to any given point, the discharge there will be kl,
-  where k is another constant applicable to all points in the course of
-  the river.
-
-  [Illustration: FIG. 132.]
-
-  Let AB (fig. 132) be the longitudinal section of the river, whose
-  source is at A; and take A for the origin of vertical and horizontal
-  coordinates. Let C be a point whose ordinates are x and y, and let the
-  river at C have the breadth b, the slope i, and the velocity v. Since
-  velocity X area of section = discharge, vcb^2 = kl, or b =
-  [root](kl/cv).
-
-  Hydraulic mean depth = ab = a [root](kl/cv).
-
-  But, by the ordinary formula for the flow of rivers, mi = [zeta]v^2;
-
-    .: i = [zeta]v^2/m = ([zeta]v^(5/2)/a) [root](c/kl).
-
-  But i is the tangent of the angle which the curve at C makes with the
-  axis of X, and is therefore = dy/dx. Also, as the slope is small, l =
-  AC = AD = x nearly.
-
-    .: dy/dx = ([zeta]v^(5/2)/a) [root](c/kx);
-
-  and, remembering that v is constant,
-
-    y = (2[zeta]v^(5/2)/a) [root](cx/k);
-
-  or
-
-    y^2 = constant X x;
-
-  so that the curve is a common parabola, of which the axis is
-  horizontal and the vertex at the source. This may be considered an
-  ideal longitudinal section, to which actual rivers approximate more or
-  less, with exceptions due to the varying hardness of their beds, and
-  the irregular manner in which their volume increases.
-
-  S 129. _Surface Level of River._--The surface level of a river is a
-  plane changing constantly in position from changes in the volume of
-  water discharged, and more slowly from changes in the river bed, and
-  the circumstances affecting the drainage into the river.
-
-  For the purposes of the engineer, it is important to determine (1) the
-  extreme low water level, (2) the extreme high water or flood level,
-  and (3) the highest navigable level.
-
-  1. _Low Water Level_ cannot be absolutely known, because a river
-  reaches its lowest level only at rare intervals, and because
-  alterations in the cultivation of the land, the drainage, the removal
-  of forests, the removal or erection of obstructions in the river bed,
-  &c., gradually alter the conditions of discharge. The lowest level of
-  which records can be found is taken as the conventional or approximate
-  low water level, and allowance is made for possible changes.
-
-  2. _High Water or Flood Level._--The engineer assumes as the highest
-  flood level the highest level of which records can be obtained. In
-  forming a judgment of the data available, it must be remembered that
-  the highest level at one point of a river is not always simultaneous
-  with the attainment of the highest level at other points, and that
-  the rise of a river in flood is very different in different parts of
-  its course. In temperate regions, the floods of rivers seldom rise
-  more than 20 ft. above low-water level, but in the tropics the rise of
-  floods is greater.
-
-  3. _Highest Navigable Level._--When the river rises above a certain
-  level, navigation becomes difficult from the increase of the velocity
-  of the current, or from submersion of the tow paths, or from the
-  headway under bridges becoming insufficient. Ordinarily the highest
-  navigable level may be taken to be that at which the river begins to
-  overflow its banks.
-
-  S 130. _Relative Value of Different Materials for Submerged
-  Works._--That the power of water to remove and transport different
-  materials depends on their density has an important bearing on the
-  selection of materials for submerged works. In many cases, as in the
-  aprons or floorings beneath bridges, or in front of locks or falls,
-  and in the formation of training walls and breakwaters by _pierres
-  perdus_, which have to resist a violent current, the materials of
-  which the structures are composed should be of such a size and weight
-  as to be able individually to resist the scouring action of the water.
-  The heaviest materials will therefore be the best; and the different
-  value of materials in this respect will appear much more striking, if
-  it is remembered that all materials lose part of their weight in
-  water. A block whose volume is V cubic feet, and whose density in air
-  is w lb. per cubic foot, weighs in air wV lb., but in water only
-  (w--62.4) V lb.
-
-    +----------------------+-----------------------------+
-    |                      | Weight of a Cub. Ft. in lb. |
-    |                      +--------------+--------------+
-    |                      |    In Air.   |   In Water.  |
-    +----------------------+--------------+--------------+
-    | Basalt               |    187.3     |    124.9     |
-    | Brick                |    130.0     |     67.6     |
-    | Brickwork            |    112.0     |     49.6     |
-    | Granite and limestone|    170.0     |    107.6     |
-    | Sandstone            |    144.0     |     81.6     |
-    | Masonry              |   116-144    |  53.6-81.6   |
-    +----------------------+--------------+--------------+
-
-  S 131. _Inundation Deposits from a River._--When a river carrying silt
-  periodically overflows its banks, it deposits silt over the area
-  flooded, and gradually raises the surface of the country. The silt is
-  deposited in greatest abundance where the water first leaves the
-  river. It hence results that the section of the country assumes a
-  peculiar form, the river flowing in a trough along the crest of a
-  ridge, from which the land slopes downwards on both sides. The silt
-  deposited from the water forms two wedges, having their thick ends
-  towards the river (fig. 133).
-
-  [Illustration: FIG. 133.]
-
-  This is strikingly the case with the Mississippi, and that river is
-  now kept from flooding immense areas by artificial embankments or
-  levees. In India, the term _deltaic segment_ is sometimes applied to
-  that portion of a river running through deposits formed by inundation,
-  and having this characteristic section. The irrigation of the country
-  in this case is very easy; a comparatively slight raising of the river
-  surface by a weir or annicut gives a command of level which permits
-  the water to be conveyed to any part of the district.
-
-  S 132. _Deltas._--The name delta was originally given to the [Greek:
-  Delta]-shaped portion of Lower Egypt, included between seven branches
-  of the Nile. It is now given to the whole of the alluvial tracts round
-  river mouths formed by deposition of sediment from the river, where
-  its velocity is checked on its entrance to the sea. The characteristic
-  feature of these alluvial deltas is that the river traverses them, not
-  in a single channel, but in two or many bifurcating branches. Each
-  branch has a tract of the delta under its influence, and gradually
-  raises the surface of that tract, and extends it seaward. As the delta
-  extends itself seaward, the conditions of discharge through the
-  different branches change. The water finds the passage through one of
-  the branches less obstructed than through the others; the velocity and
-  scouring action in that branch are increased; in the others they
-  diminish. The one channel gradually absorbs the whole of the water
-  supply, while the other branches silt up. But as the mouth of the new
-  main channel extends seaward the resistance increases both from the
-  greater length of the channel and the formation of shoals at its
-  mouth, and the river tends to form new bifurcations AC or AD (fig.
-  134), and one of these may in time become the main channel of the
-  river.
-
-  S 133. _Field Operations preliminary to a Study of River
-  Improvement._--There are required (1) a plan of the river, on which
-  the positions of lines of levelling and cross sections are marked; (2)
-  a longitudinal section and numerous cross sections of the river; (3) a
-  series of gaugings of the discharge at different points and in
-  different conditions of the river.
-
-  _Longitudinal Section._--This requires to be carried out with great
-  accuracy. A line of stakes is planted, following the sinuosities of
-  the river, and chained and levelled. The cross sections are referred
-  to the line of stakes, both as to position and direction. The
-  determination of the surface slope is very difficult, partly from its
-  extreme smallness, partly from oscillation of the water. Cunningham
-  recommends that the slope be taken in a length of 2000 ft. by four
-  simultaneous observations, two on each side of the river.
-
-  [Illustration: FIG. 134.]
-
-  S 134. _Cross Sections_--A stake is planted flush with the water, and
-  its level relatively to some point on the line of levels is
-  determined. Then the depth of the water is determined at a series of
-  points (if possible at uniform distances) in a line starting from the
-  stake and perpendicular to the thread of the stream. To obtain these,
-  a wire may be stretched across with equal distances marked on it by
-  hanging tags. The depth at each of these tags may be obtained by a
-  light wooden staff, with a disk-shaped shoe 4 to 6 in. in diameter. If
-  the depth is great, soundings may be taken by a chain and weight. To
-  ensure the wire being perpendicular to the thread of the stream, it is
-  desirable to stretch two other wires similarly graduated, one above
-  and the other below, at a distance of 20 to 40 yds. A number of floats
-  being then thrown in, it is observed whether they pass the same
-  graduation on each wire.
-
-  [Illustration: FIG. 135.]
-
-  For large and rapid rivers the cross section is obtained by sounding
-  in the following way. Let AC (fig. 135) be the line on which soundings
-  are required. A base line AB is measured out at right angles to AC,
-  and ranging staves are set up at AB and at D in line with AC. A boat
-  is allowed to drop down stream, and, at the moment it comes in line
-  with AD, the lead is dropped, and an observer in the boat takes, with
-  a box sextant, the angle AEB subtended by AB. The sounding line may
-  have a weight of 14 lb. of lead, and, if the boat drops down stream
-  slowly, it may hang near the bottom, so that the observation is made
-  instantly. In extensive surveys of the Mississippi observers with
-  theodolites were stationed at A and B. The theodolite at A was
-  directed towards C, that at B was kept on the boat. When the boat came
-  on the line AC, the observer at A signalled, the sounding line was
-  dropped, and the observer at B read off the angle ABE. By repeating
-  observations a number of soundings are obtained, which can be plotted
-  in their proper position, and the form of the river bed drawn by
-  connecting the extremities of the lines. From the section can be
-  measured the sectional area of the stream [Omega] and its wetted
-  perimeter [chi]; and from these the hydraulic mean depth m can be
-  calculated.
-
-  S 135. _Measurement of the Discharge of Rivers._--The area of cross
-  section multiplied by the mean velocity gives the discharge of the
-  stream. The height of the river with reference to some fixed mark
-  should be noted whenever the velocity is observed, as the velocity and
-  area of cross section are different in different states of the river.
-  To determine the mean velocity various methods may be adopted; and,
-  since no method is free from liability to error, either from the
-  difficulty of the observations or from uncertainty as to the ratio of
-  the mean velocity to the velocity observed, it is desirable that more
-  than one method should be used.
-
-
-  INSTRUMENTS FOR MEASURING THE VELOCITY OF WATER
-
-  S 136. _Surface Floats_ are convenient for determining the surface
-  velocities of a stream, though their use is difficult near the banks.
-  The floats may be small balls of wood, of wax or of hollow metal, so
-  loaded as to float nearly flush with the water surface. To render
-  them visible they may have a vertical painted stem. In experiments on
-  the Seine, cork balls 1(3/4) in. diameter were used, loaded to float
-  flush with the water, and provided with a stem. In A. J. C.
-  Cunningham's observations at Roorkee, the floats were thin circular
-  disks of English deal, 3 in. diameter and 1/4 in. thick. For
-  observations near the banks, floats 1 in. diameter and 1/8 in. thick
-  were used. To render them visible a tuft of cotton wool was used
-  loosely fixed in a hole at the centre.
-
-  The velocity is obtained by allowing the float to be carried down, and
-  noting the time of passage over a measured length of the stream. If v
-  is the velocity of any float, t the time of passing over a length l,
-  then v = l/t. To mark out distinctly the length of stream over which
-  the floats pass, two ropes may be stretched across the stream at a
-  distance apart, which varies usually from 50 to 250 ft., according to
-  the size and rapidity of the river. In the Roorkee experiments a
-  length of run of 50 ft. was found best for the central two-fifths of
-  the width, and 25 ft. for the remainder, except very close to the
-  banks, where the run was made 12(1/2) ft. only. The longer the run the
-  less is the proportionate error of the time observations, but on the
-  other hand the greater the deviation of the floats from a straight
-  course parallel to the axis of the stream. To mark the precise
-  position at which the floats cross the ropes, Cunningham used short
-  white rope pendants, hanging so as nearly to touch the surface of the
-  water. In this case the streams were 80 to 180 ft. in width. In wider
-  streams the use of ropes to mark the length of run is impossible, and
-  recourse must be had to box sextants or theodolites to mark the path
-  of the floats.
-
-  [Illustration: FIG. 136.]
-
-  Let AB (fig. 136) be a measured base line strictly parallel to the
-  thread of the stream, and AA1, BB1 lines at right angles to AB marked
-  out by ranging rods at A1 and B1. Suppose observers stationed at A and
-  B with sextants or theodolites, and let CD be the path of any float
-  down stream. As the float approaches AA1, the observer at B keeps it
-  on the cross wire of his instrument. The observer at A observes the
-  instant of the float reaching the line AA1, and signals to B who then
-  reads off the angle ABC. Similarly, as the float approaches BB1, the
-  observer at A keeps it in sight, and when signalled to by B reads the
-  angle BAD. The data so obtained are sufficient for plotting the path
-  of the float and determining the distances AC, BD.
-
-  The time taken by the float in passing over the measured distance may
-  be observed by a chronograph, started as the float passes the upper
-  rope or line, and stopped when it passes the lower. In Cunningham's
-  observations two chronometers were sometimes used, the time of passing
-  one end of the run being noted on one, and that of passing the other
-  end of the run being noted on the other. The chronometers were
-  compared immediately before the observations. In other cases a single
-  chronometer was used placed midway of the run. The moment of the
-  floats passing the ends of the run was signalled to a time-keeper at
-  the chronometer by shouting. It was found quite possible to count the
-  chronometer beats to the nearest half second, and in some cases to the
-  nearest quarter second.
-
-  [Illustration: FIG. 137.]
-
-  S 137. _Sub-surface Floats._--The velocity at different depths below
-  the surface of a stream may be obtained by sub-surface floats, used
-  precisely in the same way as surface floats. The most usual
-  arrangement is to have a large float, of slightly greater density than
-  water, connected with a small and very light surface float. The motion
-  of the combined arrangement is not sensibly different from that of the
-  large float, and the small surface float enables an observer to note
-  the path and velocity of the sub-surface float. The instrument is,
-  however, not free from objection. If the large submerged float is made
-  of very nearly the same density as water, then it is liable to be
-  thrown upwards by very slight eddies in the water, and it does not
-  maintain its position at the depth at which it is intended to float.
-  On the other hand, if the large float is made sensibly heavier than
-  water, the indicating or surface float must be made rather large, and
-  then it to some extent influences the motion of the submerged float.
-  Fig. 137 shows one form of sub-surface float. It consists of a couple
-  of tin plates bent at a right angle and soldered together at the
-  angle. This is connected with a wooden ball at the surface by a very
-  thin wire or cord. As the tin alone makes a heavy submerged float, it
-  is better to attach to the tin float some pieces of wood to diminish
-  its weight in water. Fig. 138 shows the form of submerged float used
-  by Cunningham. It consists of a hollow metal ball connected to a
-  slice of cork, which serves as the surface float.
-
-  [Illustration: FIG. 138.]
-
-  [Illustration: FIG. 139.]
-
-  S 138. _Twin Floats._--Suppose two equal and similar floats (fig. 139)
-  connected by a wire. Let one float be a little lighter and the other a
-  little heavier than water. Then the velocity of the combined floats
-  will be the mean of the surface velocity and the velocity at the depth
-  at which the heavier float swims, which is determined by the length of
-  the connecting wire. Thus if v_s is the surface velocity and v_d the
-  velocity at the depth to which the lower float is sunk, the velocity
-  of the combined floats will be
-
-    v = (1/2)(v_s + v_d).
-
-  Consequently, if v is observed, and v_s determined by an experiment
-  with a single float,
-
-    v_d = 2v - v_s
-
-  According to Cunningham, the twin float gives better results than the
-  sub-surface float.
-
-  [Illustration: FIG. 140.]
-
-  S 139. _Velocity Rods._--Another form of float is shown in fig. 140.
-  This consists of a cylindrical rod loaded at the lower end so as to
-  float nearly vertical in water. A wooden rod, with a metal cap at the
-  bottom in which shot can be placed, answers better than anything else,
-  and sometimes the wooden rod is made in lengths, which can be screwed
-  together so as to suit streams of different depths. A tuft of cotton
-  wool at the top serves to make the float more easily visible. Such a
-  rod, so adjusted in length that it sinks nearly to the bed of the
-  stream, gives directly the mean velocity of the whole vertical section
-  in which it floats.
-
-  S 140. _Revy's Current Meter._--No instrument has been so much used in
-  directly determining the velocity of a stream at a given point as the
-  screw current meter. Of this there are a dozen varieties at least. As
-  an example of the instrument in its simplest form, Revy's meter may be
-  selected. This is an ordinary screw meter of a larger size than usual,
-  more carefully made, and with its details carefully studied (figs.
-  141, 142). It was designed after experience in gauging the great South
-  American rivers. The screw, which is actuated by the water, is 6 in.
-  in diameter, and is of the type of the Griffiths screw used in ships.
-  The hollow spherical boss serves to make the weight of the screw
-  sensibly equal to its displacement, so that friction is much reduced.
-  On the axis aa of the screw is a worm which drives the counter. This
-  consists of two worm wheels g and h fixed on a common axis. The worm
-  wheels are carried on a frame attached to the pin l. By means of a
-  string attached to l they can be pulled into gear with the worm, or
-  dropped out of gear and stopped at any instant. A nut m can be screwed
-  up, if necessary, to keep the counter permanently in gear. The worm is
-  two-threaded, and the worm wheel g has 200 teeth. Consequently it
-  makes one rotation for 100 rotations of the screw, and the number of
-  rotations up to 100 is marked by the passage of the graduations on its
-  edge in front of a fixed index. The second worm wheel has 196 teeth,
-  and its edge is divided into 49 divisions. Hence it falls behind the
-  first wheel one division for a complete rotation of the latter. The
-  number of hundreds of rotations of the screw are therefore shown by
-  the number of divisions on h passed over by an index fixed to g. One
-  difficulty in the use of the ordinary screw meter is that particles of
-  grit, getting into the working parts, very sensibly alter the
-  friction, and therefore the speed of the meter. Revy obviates this by
-  enclosing the counter in a brass box with a glass face. This box is
-  filled with pure water, which ensures a constant coefficient of
-  friction for the rubbing parts, and prevents any mud or grit finding
-  its way in. In order that the meter may place itself with the axis
-  parallel to the current, it is pivoted on a vertical axis and directed
-  by a large vane shown in fig. 142. To give the vane more
-  directing power the vertical axis is nearer the screw than in ordinary
-  meters, and the vane is larger. A second horizontal vane is attached
-  by the screws x, x, the object of which is to allow the meter to rest
-  on the ground without the motion of the screw being interfered with.
-  The string or wire for starting and stopping the meter is carried
-  through the centre of the vertical axis, so that the strain on it may
-  not tend to pull the meter oblique to the current. The pitch of the
-  screw is about 9 in. The screws at x serve for filling the meter with
-  water. The whole apparatus is fixed to a rod (fig. 142), of a length
-  proportionate to the depth, or for very great depths it is fixed to a
-  weighted bar lowered by ropes, a plan invented by Revy. The instrument
-  is generally used thus. The reading of the counter is noted, and it is
-  put out of gear. The meter is then lowered into the water to the
-  required position from a platform between two boats, or better from a
-  temporary bridge. Then the counter is put into gear for one, two or
-  five minutes. Lastly, the instrument is raised and the counter again
-  read. The velocity is deduced from the number of rotations in unit
-  time by the formulae given below. For surface velocities the counter
-  may be kept permanently in gear, the screw being started and stopped
-  by hand.
-
-  [Illustration: FIG. 141.]
-
-  [Illustration: FIG. 142.]
-
-  S 141. _The Harlacher Current Meter._--In this the ordinary counting
-  apparatus is abandoned. A worm drives a worm wheel, which makes an
-  electrical contact once for each 100 rotations of the worm. This
-  contact gives a signal above water. With this arrangement, a series of
-  velocity observations can be made, without removing the instrument
-  from the water, and a number of practical difficulties attending the
-  accurate starting and stopping of the ordinary counter are entirely
-  got rid of. Fig. 143 shows the meter. The worm wheel z makes one
-  rotation for 100 of the screw. A pin moving the lever x makes the
-  electrical contact. The wires b, c are led through a gas pipe B; this
-  also serves to adjust the meter to any required position on the wooden
-  rod dd. The rudder or vane is shown at WH. The galvanic current acts
-  on the electromagnet m, which is fixed in a small metal box containing
-  also the battery. The magnet exposes and withdraws a coloured disk at
-  an opening in the cover of the box.
-
-  S 142. _Amsler Laffon Current Meter._--A very convenient and accurate
-  current meter is constructed by Amsler Laffon of Schaffhausen. This
-  can be used on a rod, and put into and out of gear by a ratchet. The
-  peculiarity in this case is that there is a double ratchet, so that
-  one pull on the string puts the counter into gear and a second puts it
-  out of gear. The string may be slack during the action of the meter,
-  and there is less uncertainty than when the counter has to be held in
-  gear. For deep streams the meter A is suspended by a wire with a heavy
-  lenticular weight below (fig. 144). The wire is payed out from a small
-  winch D, with an index showing the depth of the meter, and passes over
-  a pulley B. The meter is in gimbals and is directed by a conical
-  rudder which keeps it facing the stream with its axis horizontal.
-  There is an electric circuit from a battery C through the meter, and a
-  contact is made closing the circuit every 100 revolutions. The moment
-  the circuit closes a bell rings. By a subsidiary arrangement, when the
-  foot of the instrument, 0.3 metres below the axis of the meter,
-  touches the ground the circuit is also closed and the bell rings. It
-  is easy to distinguish the continuous ring when the ground is reached
-  from the short ring when the counter signals. A convenient winch for
-  the wire is so graduated that if set when the axis of the meter is at
-  the water surface it indicates at any moment the depth of the meter
-  below the surface. Fig. 144 shows the meter as used on a boat. It is a
-  very convenient instrument for obtaining the velocity at different
-  depths and can also be used as a sounding instrument.
-
-  [Illustration: FIG. 143.]
-
-  S 143. _Determination of the Coefficients of the Current
-  Meter._--Suppose a series of observations has been made by towing the
-  meter in still water at different speeds, and that it is required to
-  ascertain from these the constants of the meter. If v is the velocity
-  of the water and n the observed number of rotations per second, let
-
-    v = [alpha] + [beta]n   (1)
-
-  where [alpha] and [beta] are constants. Now let the meter be towed
-  over a measured distance L, and let N be the revolutions of the meter
-  and t the time of transit. Then the speed of the meter relatively to
-  the water is L/t = v feet per second, and the number of revolutions
-  per second is N/t = n. Suppose m observations have been made in this
-  way, furnishing corresponding values of v and n, the speed in each
-  trial being as uniform as possible,
-
-    [Sigma]n = n1 + n2 + ...
-
-    [Sigma]v = v1 + v2 + ...
-
-    [Sigma]nv = n1v1 + n2v2 + ...
-
-    [Sigma]n^2 = n1^2 + n2^2 + ...
-
-    [[Sigma]n]^2 = [n1 + n2 + ...]^2
-
-  Then for the determination of the constants [alpha] and [beta] in (1),
-  by the method of least squares--
-
-              [Sigma]n^2[Sigma]v - [Sigma]n[Sigma]nv
-    [alpha] = --------------------------------------,
-                     m[Sigma]n^2 - [[Sigma]n]^2
-
-             m[Sigma]nv - [Sigma]v[Sigma]n
-    [beta] = -----------------------------.
-               m[Sigma]n^2 - [[Sigma]n]^2
-
-  [Illustration: FIG. 144.]
-
-  In a few cases the constants for screw current meters have been
-  determined by towing them in R. E. Froude's experimental tank in which
-  the resistance of ship models is ascertained. In that case the data
-  are found with exceptional accuracy.
-
-  S 144. Darcy Gauge or modified Pitot Tube.--A very old instrument for
-  measuring velocities, invented by Henri Pitot in 1730 (_Histoire de
-  l'Academie des Sciences_, 1732, p. 376), consisted simply of a
-  vertical glass tube with a right-angled bend, placed so that its mouth
-  was normal to the direction of flow (fig. 145).
-
-  [Illustration: FIG. 145.]
-
-  The impact of the stream on the mouth of the tube balances a column in
-  the tube, the height of which is approximately h = v^2/2g, where v is
-  the velocity at the depth x. Placed with its mouth parallel to the
-  stream the water inside the tube is nearly at the same level as the
-  surface of the stream, and turned with the mouth down stream, the
-  fluid sinks a depth h' = v^2/2g nearly, though the tube in that case
-  interferes with the free flow of the liquid and somewhat modifies the
-  result. Pitot expanded the mouth of the tube so as to form a funnel or
-  bell mouth. In that case he found by experiment
-
-    h = 1.5v^2/2g.
-
-  But there is more disturbance of the stream. Darcy preferred to make
-  the mouth of the tube very small to avoid interference with the
-  stream and to check oscillations of the water column. Let the
-  difference of level of a pair of tubes A and B (fig. 145) be taken to
-  be h = kv^2/2g, then k may be taken to be a corrective coefficient
-  whose value in well-shaped instruments is very nearly unity. By
-  placing his instrument in front of a boat towed through water Darcy
-  found k = 1.034; by placing the instrument in a stream the velocity of
-  which had been ascertained by floats, he found k = 1.006; by readings
-  taken in different parts of the section of a canal in which a known
-  volume of water was flowing, he found k = 0.993. He believed the first
-  value to be too high in consequence of the disturbance caused by the
-  boat. The mean of the other two values is almost exactly unity
-  (_Recherches hydrauliques_, Darcy and Bazin, 1865, p. 63). W. B.
-  Gregory used somewhat differently formed Pitot tubes for which the k =
-  1 (_Am. Soc. Mech. Eng._, 1903, 25). T. E. Stanton used a Pitot tube
-  in determining the velocity of an air current, and for his instrument
-  he found k = 1.030 to k = 1.032 ("On the Resistance of Plane Surfaces
-  in a Current of Air," _Proc. Inst. Civ. Eng._, 1904, 156).
-
-  One objection to the Pitot tube in its original form was the great
-  difficulty and inconvenience of reading the height h in the immediate
-  neighbourhood of the stream surface. This is obviated in the Darcy
-  gauge, which can be removed from the stream to be read.
-
-  Fig. 146 shows a Darcy gauge. It consists of two Pitot tubes having
-  their mouths at right angles. In the instrument shown, the two tubes,
-  formed of copper in the lower part, are united into one for strength,
-  and the mouths of the tubes open vertically and horizontally. The
-  upper part of the tubes is of glass, and they are provided with a
-  brass scale and two verniers b, b. The whole instrument is supported
-  on a vertical rod or small pile AA, the fixing at B permitting the
-  instrument to be adjusted to any height on the rod, and at the same
-  time allowing free rotation, so that it can be held parallel to the
-  current. At c is a two-way cock, which can be opened or closed by
-  cords. If this is shut, the instrument can be lifted out of the stream
-  for reading. The glass tubes are connected at top by a brass fixing,
-  with a stop cock a, and a flexible tube and mouthpiece m. The use of
-  this is as follows. If the velocity is required at a point near the
-  surface of the stream, one at least of the water columns would be
-  below the level at which it could be read. It would be in the copper
-  part of the instrument. Suppose then a little air is sucked out by the
-  tube m, and the cock a closed, the two columns will be forced up an
-  amount corresponding to the difference between atmospheric pressure
-  and that in the tubes. But the difference of level will remain
-  unaltered.
-
-  When the velocities to be measured are not very small, this instrument
-  is an admirable one. It requires observation only of a single linear
-  quantity, and does not require any time observation. The law
-  connecting the velocity and the observed height is a rational one, and
-  it is not absolutely necessary to make any experiments on the
-  coefficient of the instrument. If we take v = k[root](2gh), then it
-  appears from Darcy's experiments that for a well-formed instrument k
-  does not sensibly differ from unity. It gives the velocity at a
-  definite point in the stream. The chief difficulty arises from the
-  fact that at any given point in a stream the velocity is not
-  absolutely constant, but varies a little from moment to moment. Darcy
-  in some of his experiments took several readings, and deduced the
-  velocity from the mean of the highest and lowest.
-
-  S 145. _Perrodil Hydrodynamometer._--This consists of a frame abcd
-  (fig. 147) placed vertically in the stream, and of a height not less
-  than the stream's depth. The two vertical members of this frame are
-  connected by cross bars, and united above water by a circular bar,
-  situated in the vertical plane and carrying a horizontal graduated
-  circle ef. This whole system is movable round its axis, being
-  suspended on a pivot at g connected with the fixed support mn. Other
-  horizontal arms serve as guides. The central vertical rod gr forms a
-  torsion rod, being fixed at r to the frame abcd, and, passing freely
-  upwards through the guides, it carries a horizontal needle moving
-  over the graduated circle ef. The support g, which carries the
-  apparatus, also receives in a tubular guide the end of the torsion rod
-  gr and a set screw for fixing the upper end of the torsion rod when
-  necessary. The impulse of the stream of water is received on a
-  circular disk x, in the plane of the torsion rod and the frame abcd.
-  To raise and lower the apparatus easily, it is not fixed directly to
-  the rod mn, but to a tube kl sliding on mn.
-
-  [Illustration: FIG. 146.]
-
-  Suppose the apparatus arranged so that the disk x is at that level in
-  the stream where the velocity is to be determined. The plane abcd is
-  placed parallel to the direction of motion of the water. Then the disk
-  x (acting as a rudder) will place itself parallel to the stream on the
-  down stream side of the frame. The torsion rod will be unstrained, and
-  the needle will be at zero on the graduated circle. If, then, the
-  instrument is turned by pressing the needle, till the plane abcd of
-  the disk and the zero of the graduated circle is at right angles to
-  the stream, the torsion rod will be twisted through an angle which
-  measures the normal impulse of the stream on the disk x. That angle
-  will be given by the distance of the needle from zero. Observation
-  shows that the velocity of the water at a given point is not constant.
-  It varies between limits more or less wide. When the apparatus is
-  nearly in its right position, the set screw at g is made to clamp the
-  torsion spring. Then the needle is fixed, and the apparatus carrying
-  the graduated circle oscillates. It is not, then, difficult to note
-  the mean angle marked by the needle.
-
-  [Illustration: FIG. 147.]
-
-  Let r be the radius of the torsion rod, l its length from the needle
-  over ef to r, and [alpha] the observed torsion angle. Then the moment
-  of the couple due to the molecular forces in the torsion rod is
-
-    M = E_t I[alpha]/l;
-
-  where E_t is the modulus of elasticity for torsion, and I the polar
-  moment of inertia of the section of the rod. If the rod is of circular
-  section, I = (1/2)[pi]r^4. Let R be the radius of the disk, and b its
-  leverage, or the distance of its centre from the axis of the torsion
-  rod. The moment of the pressure of the water on the disk is
-
-    Fb = kb(G/2g)[pi]R^2v^2,
-
-  where G is the heaviness of water and k an experimental coefficient.
-  Then
-
-    E_t I[alpha]/l = kb(G/2g)[pi]R^2v^2.
-
-  For any given instrument,
-
-    v = c [root][alpha],
-
-  where c is a constant coefficient for the instrument.
-
-  The instrument as constructed had three disks which could be used at
-  will. Their radii and leverages were in feet
-
-                  R =      b =
-
-    1st disk     0.052     0.16
-    2nd   "      0.105     0.32
-    3rd   "      0.210     0.66
-
-  For a thin circular plate, the coefficient k = 1.12. In the actual
-  instrument the torsion rod was a brass wire 0.06 in. diameter and
-  6(1/2) ft. long. Supposing [alpha] measured in degrees, we get by
-  calculation
-
-    v = 0.335 [root][alpha]; 0.115 [root][alpha]; 0.042 [root][alpha].
-
-  Very careful experiments were made with the instrument. It was fixed
-  to a wooden turning bridge, revolving over a circular channel of 2 ft.
-  width, and about 76 ft. circumferential length. An allowance was made
-  for the slight current produced in the channel. These experiments gave
-  for the coefficient c, in the formula v = c [root][alpha],
-
-    1st disk, c =  0.3126 for velocities of 3 to 16        ft.
-    2nd   "        0.1177  "       "      1(1/4) to 3(1/4)  "
-    3rd   "        0.0349  "       "    less than 1(1/4)    "
-
-  The instrument is preferable to the current meter in giving the
-  velocity in terms of a single observed quantity, the angle of torsion,
-  while the current meter involves the observation of two quantities,
-  the number of rotations and the time. The current meter, except in
-  some improved forms, must be withdrawn from the water to read the
-  result of each experiment, and the law connecting the velocity and
-  number of rotations of a current meter is less well-determined than
-  that connecting the pressure on a disk and the torsion of the wire of
-  a hydrodynamometer.
-
-  The Pitot tube, like the hydrodynamometer, does not require a time
-  observation. But, where the velocity is a varying one, and
-  consequently the columns of water in the Pitot tube are oscillating,
-  there is room for doubt as to whether, at any given moment of closing
-  the cock, the difference of level exactly measures the impulse of the
-  stream at the moment. The Pitot tube also fails to give measurable
-  indications of very low velocities.
-
-
-  PROCESSES FOR GAUGING STREAMS
-
-  S 146. _Gauging by Observation of the Maximum Surface Velocity._--The
-  method of gauging which involves the least trouble is to determine the
-  surface velocity at the thread of the stream, and to deduce from it
-  the mean velocity of the whole cross section. The maximum surface
-  velocity may be determined by floats or by a current meter.
-  Unfortunately the ratio of the maximum surface to the mean velocity is
-  extremely variable. Thus putting v_o for the surface velocity at the
-  thread of the stream, and v_m for the mean velocity of the whole cross
-  section, v_m/v_o has been found to have the following values:--
-
-                                                     v_m/v_o
-
-    De Prony, experiments on small wooden channels   0.8164
-    Experiments on the Seine                         0.62
-    Destrem and De Prony, experiments on the Neva    0.78
-    Boileau, experiments on canals                   0.82
-    Baumgartner, experiments on the Garonne          0.80
-    Brunings (mean)                                  0.85
-    Cunningham, Solani aqueduct                      0.823
-
-  Various formulae, either empirical or based on some theory of the
-  vertical and horizontal velocity curves, have been proposed for
-  determining the ratio v_m/v_o. Bazin found from his experiments the
-  empirical expression
-
-    v_m = v_o - 25.4 [root](mi);
-
-  where m is the hydraulic mean depth and i the slope of the stream.
-
-  In the case of irrigation canals and rivers, it is often important to
-  determine the discharge either daily or at other intervals of time,
-  while the depth and consequently the mean velocity is varying.
-  Cunningham (_Roorkee Prof. Papers_, iv. 47), has shown that, for a
-  given part of such a stream, where the bed is regular and of permanent
-  section, a simple formula may be found for the variation of the
-  central surface velocity with the depth. When once the constants of
-  this formula have been determined by measuring the central surface
-  velocity and depth, in different conditions of the stream, the surface
-  velocity can be obtained by simply observing the depth of the stream,
-  and from this the mean velocity and discharge can be calculated. Let z
-  be the depth of the stream, and v_o the surface velocity, both measured
-  at the thread of the stream. Then v_o^2 = cz; where c is a constant
-  which for the Solani aqueduct had the values 1.9 to 2, the depths
-  being 6 to 10 ft., and the velocities 3(1/2) to 4(1/2) ft. Without any
-  assumption of a formula, however, the surface velocities, or still
-  better the mean velocities, for different conditions of the stream may
-  be plotted on a diagram in which the abscissae are depths and the
-  ordinates velocities. The continuous curve through points so found
-  would then always give the velocity for any observed depth of the
-  stream, without the need of making any new float or current meter
-  observations.
-
-  S 147. _Mean Velocity determined by observing a Series of Surface
-  Velocities._--The ratio of the mean velocity to the surface velocity
-  in one longitudinal section is better ascertained than the ratio of
-  the central surface velocity to the mean velocity of the whole cross
-  section. Suppose the river divided into a number of compartments by
-  equidistant longitudinal planes, and the surface velocity observed in
-  each compartment. From this the mean velocity in each compartment and
-  the discharge can be calculated. The sum of the partial discharges
-  will be the total discharge of the stream. When wires or ropes can be
-  stretched across the stream, the compartments can be marked out by
-  tags attached to them. Suppose two such ropes stretched across the
-  stream, and floats dropped in above the upper rope. By observing
-  within which compartment the path of the float lies, and noting the
-  time of transit between the ropes, the surface velocity in each
-  compartment can be ascertained. The mean velocity in each compartment
-  is 0.85 to 0.91 of the surface velocity in that compartment. Putting k
-  for this ratio, and v1, v2 ... for the observed velocities, in
-  compartments of area [Omega]1, [Omega]2 ... then the total discharge
-  is
-
-    Q = k([Omega]1v1 + [Omega]2v2 + ... ).
-
-  If several floats are allowed to pass over each compartment, the mean
-  of all those corresponding to one compartment is to be taken as the
-  surface velocity of that compartment.
-
-  [Illustration: FIG. 148.]
-
-  This method is very applicable in the case of large streams or rivers
-  too wide to stretch a rope across. The paths of the floats are then
-  ascertained in this way. Let fig. 148 represent a portion of the
-  river, which should be straight and free from obstructions. Suppose a
-  base line AB measured parallel to the thread of the stream, and let
-  the mean cross section of the stream be ascertained either by sounding
-  the terminal cross sections AE, BF, or by sounding a series of
-  equidistant cross sections. The cross sections are taken at right
-  angles to the base line. Observers are placed at A and B with
-  theodolites or box sextants. The floats are dropped in from a boat
-  above AE, and picked up by another boat below BF. An observer with a
-  chronograph or watch notes the time in which each float passes from AE
-  to BF. The method of proceeding is this. The observer A sets his
-  theodolite in the direction AE, and gives a signal to drop a float. B
-  keeps his instrument on the float as it comes down. At the moment the
-  float arrives at C in the line AE, the observer at A calls out. B
-  clamps his instrument and reads off the angle ABC, and the time
-  observer begins to note the time of transit. B now points his
-  instrument in the direction BF, and A keeps the float on the cross
-  wire of his instrument. At the moment the float arrives at D in the
-  line BF, the observer B calls out, A clamps his instrument and reads
-  off the angle BAD, and the time observer notes the time of transit
-  from C to D. Thus all the data are determined for plotting the path CD
-  of the float and determining its velocity. By dropping in a series of
-  floats, a number of surface velocities can be determined. When all
-  these have been plotted, the river can be divided into convenient
-  compartments. The observations belonging to each compartment are then
-  averaged, and the mean velocity and discharge calculated. It is
-  obvious that, as the surface velocity is greatly altered by wind,
-  experiments of this kind should be made in very calm weather.
-
-  The ratio of the surface velocity to the mean velocity in the same
-  vertical can be ascertained from the formulae for the vertical
-  velocity curve already given (S 101). Exner, in _Erbkam's Zeitschrift_
-  for 1875, gave the following convenient formula. Let v be the mean and
-  V the surface velocity in any given vertical longitudinal section, the
-  depth of which is h
-
-    v/V = (1 + 0.1478 [root]h)/(1 + 0.2216 [root]h).
-
-  If vertical velocity rods are used instead of common floats, the mean
-  velocity is directly determined for the vertical section in which the
-  rod floats. No formula of reduction is then necessary. The observed
-  velocity has simply to be multiplied by the area of the compartment to
-  which it belongs.
-
-  S 148. _Mean Velocity of the Stream from a Series of Mid Depth
-  Velocities._--In the gaugings of the Mississippi it was found that the
-  mid depth velocity differed by only a very small quantity from the
-  mean velocity in the vertical section, and it was uninfluenced by
-  wind. If therefore a series of mid depth velocities are determined by
-  double floats or by a current meter, they may be taken to be the mean
-  velocities of the compartments in which they occur, and no formula of
-  reduction is necessary. If floats are used, the method is precisely
-  the same as that described in the last paragraph for surface floats.
-  The paths of the double floats are observed and plotted, and the mean
-  taken of those corresponding to each of the compartments into which
-  the river is divided. The discharge is the sum of the products of the
-  observed mean mid depth velocities and the areas of the compartments.
-
-  S 149. _P. P. Boileau's Process for Gauging Streams._--Let U be the
-  mean velocity at a given section of a stream, V the maximum velocity,
-  or that of the principal filament, which is generally a little below
-  the surface, W and w the greatest and least velocities at the surface.
-  The distance of the principal filament from the surface is generally
-  less than one-fourth of the depth of the stream; W is a little less
-  than V; and U lies between W and w. As the surface velocities change
-  continuously from the centre towards the sides there are at the
-  surface two filaments having a velocity equal to U. The determination
-  of the position of these filaments, which Boileau terms the gauging
-  filaments, cannot be effected entirely by theory. But, for sections of
-  a stream in which there are no abrupt changes of depth, their position
-  can be very approximately assigned. Let [Delta] and l be the
-  horizontal distances of the surface filament, having the velocity W,
-  from the gauging filament, which has the velocity U, and from the bank
-  on one side. Then
-
-    [Delta]/l = c^4 [root]{(W + 2w)/7(W - w)},
-
-  c being a numerical constant. From gaugings by Humphreys and Abbot,
-  Bazin and Baumgarten, the values c = 0.919, 0.922 and 0.925 are
-  obtained. Boileau adopts as a mean value 0.922. Hence, if W and w are
-  determined by float gauging or otherwise, [Delta] can be found, and
-  then a single velocity observation at [Delta] ft. from the filament of
-  maximum velocity gives, without need of any reduction, the mean
-  velocity of the stream. More conveniently W, w, and U can be measured
-  from a horizontal surface velocity curve, obtained from a series of
-  float observations.
-
-  S 150. _Direct Determination of the Mean Velocity by a Current Meter
-  or Darcy Gauge._--The only method of determining the mean velocity at
-  a cross section of a stream which involves no assumption of the ratio
-  of the mean velocity to other quantities is this--a plank bridge is
-  fixed across the stream near its surface. From this, velocities are
-  observed at a sufficient number of points in the cross section of the
-  stream, evenly distributed over its area. The mean of these is the
-  true mean velocity of the stream. In Darcy and Bazin's experiments on
-  small streams, the velocity was thus observed at 36 points in the
-  cross section.
-
-  When the stream is too large to fix a bridge across it, the
-  observations may be taken from a boat, or from a couple of boats with
-  a gangway between them, anchored successively at a series of points
-  across the width of the stream. The position of the boat for each
-  series of observations is fixed by angular observations to a base line
-  on shore.
-
-  [Illustration: FIG. 149.]
-
-  S 151. _A. R. Harlacher's Graphic Method of determining the Discharge
-  from a Series of Current Meter Observations._--Let ABC (fig. 149) be
-  the cross section of a river at which a complete series of current
-  meter observations have been taken. Let I., II., III ... be the
-  verticals at different points of which the velocities were measured.
-  Suppose the depths at I., II., III., ... (fig. 149), set off as
-  vertical ordinates in fig. 150, and on these vertical ordinates
-  suppose the velocities set off horizontally at their proper depths.
-  Thus, if v is the measured velocity at the depth h from the surface in
-  fig. 149, on vertical marked III., then at III. in fig. 150 take cd =
-  h and ac = v. Then d is a point in the vertical velocity curve for the
-  vertical III., and, all the velocities for that ordinate being
-  similarly set off, the curve can be drawn. Suppose all the vertical
-  velocity curves I.... V. (fig. 150), thus drawn. On each of these
-  figures draw verticals corresponding to velocities of x, 2x, 3x ...
-  ft. per second. Then for instance cd at III. (fig. 150) is the depth
-  at which a velocity of 2x ft. per second existed on the vertical III.
-  in fig. 149 and if cd is set off at III. in fig. 149 it gives a point
-  in a curve passing through points of the section where the velocity
-  was 2x ft. per second. Set off on each of the verticals in fig. 149
-  all the depths thus found in the corresponding diagram in fig. 150.
-  Curves drawn through the corresponding points on the verticals are
-  curves of equal velocity.
-
-  [Illustration: FIG. 150.]
-
-  The discharge of the stream per second may be regarded as a solid
-  having the cross section of the river (fig. 149) as a base, and cross
-  sections normal to the plane of fig. 149 given by the diagrams in fig.
-  150. The curves of equal velocity may therefore be considered as
-  contour lines of the solid whose volume is the discharge of the stream
-  per second. Let [Omega]0 be the area of the cross section of the
-  river, [Omega]1, [Omega]2 ... the areas contained by the successive
-  curves of equal velocity, or, if these cut the surface of the stream,
-  by the curves and that surface. Let x be the difference of velocity
-  for which the successive curves are drawn, assumed above for
-  simplicity at 1 ft. per second. Then the volume of the successive
-  layers of the solid body whose volume represents the discharge,
-  limited by successive planes passing through the contour curves, will
-  be
-
-    (1/2)x([Omega]0 + [Omega]1), (1/2)x([Omega]1 + [Omega]2), and so on.
-
-  Consequently the discharge is
-
-    Q = x{(1/2)([Omega]0 + [Omega]_n) + [Omega]1 = [Omega]2 + ... + [Omega](n-1)}.
-
-  The areas [Omega]0, [Omega]1 ... are easily ascertained by means of
-  the polar planimeter. A slight difficulty arises in the part of the
-  solid lying above the last contour curve. This will have generally a
-  height which is not exactly x, and a form more rounded than the other
-  layers and less like a conical frustum. The volume of this may be
-  estimated separately, and taken to be the area of its base (the area
-  [Omega]_n) multiplied by 1/3 to 1/2 its height.
-
-  [Illustration: FIG. 151.]
-
-  Fig. 151 shows the results of one of Harlacher's gaugings worked out
-  in this way. The upper figure shows the section of the river and the
-  positions of the verticals at which the soundings and gaugings were
-  taken. The lower gives the curves of equal velocity, worked out from
-  the current meter observations, by the aid of vertical velocity
-  curves. The vertical scale in this figure is ten times as great as in
-  the other. The discharge calculated from the contour curves is 14.1087
-  cubic metres per second. In the lower figure some other interesting
-  curves are drawn. Thus, the uppermost dotted curve is the curve
-  through points at which the maximum velocity was found; it shows that
-  the maximum velocity was always a little below the surface, and at a
-  greater depth at the centre than at the sides. The next curve shows
-  the depth at which the mean velocity for each vertical was found. The
-  next is the curve of equal velocity corresponding to the mean velocity
-  of the stream; that is, it passes through points in the cross section
-  where the velocity was identical with the mean velocity of the stream.
-
-
-HYDRAULIC MACHINES
-
-S 152. Hydraulic machines may be broadly divided into two classes: (1)
-_Motors_, in which water descending from a higher to a lower level, or
-from a higher to a lower pressure, gives up energy which is available
-for mechanical operations; (2) _Pumps_, in which the energy of a steam
-engine or other motor is expended in raising water from a lower to a
-higher level. A few machines such as the ram and jet pump combine the
-functions of motor and pump. It may be noted that constructively pumps
-are essentially reversed motors. The reciprocating pump is a reversed
-pressure engine, and the centrifugal pump a reversed turbine. Hydraulic
-machine tools are in principle motors combined with tools, and they now
-form an important special class.
-
-Water under pressure conveyed in pipes is a convenient and economical
-means of transmitting energy and distributing it to many scattered
-working points. Hence large and important hydraulic systems are adopted
-in which at a central station water is pumped at high pressure into
-distributing mains, which convey it to various points where it actuates
-hydraulic motors operating cranes, lifts, dock gates, and in some cases
-riveting and shearing machines. In this case the head driving the
-hydraulic machinery is artificially created, and it is the convenience of
-distributing power in an easily applied form to distant points which
-makes the system advantageous. As there is some unavoidable loss in
-creating an artificial head this system is most suitable for driving
-machines which work intermittently (see POWER TRANSMISSION). The
-development of electrical methods of transmitting and distributing energy
-has led to the utilization of many natural waterfalls so situated as to
-be useless without such a means of transferring the power to points where
-it can be conveniently applied. In some cases, as at Niagara, the
-hydraulic power can only be economically developed in very large units,
-and it can be most conveniently subdivided and distributed by
-transformation into electrical energy. Partly from the development of new
-industries such as paper-making from wood pulp and electro-metallurgical
-processes, which require large amounts of cheap power, partly from the
-facility with which energy can now be transmitted to great distances
-electrically, there has been a great increase in the utilization of
-water-power in countries having natural waterfalls. According to the
-twelfth census of the United States the total amount of water-power
-reported as used in manufacturing establishments in that country was
-1,130,431 h.p. in 1870; 1,263,343 h.p. in 1890; and 1,727,258 h.p. in
-1900. The increase was 8.4% in the decade 1870-1880, 3.1% in 1880-1890,
-and no less than 36.7% in 1890-1900. The increase is the more striking
-because in this census the large amounts of hydraulic power which are
-transmitted electrically are not included.
-
-
-  XII. IMPACT AND REACTION OF WATER
-
-  S 153. When a stream of fluid in steady motion impinges on a solid
-  surface, it presses on the surface with a force equal and opposite to
-  that by which the velocity and direction of motion of the fluid are
-  changed. Generally, in problems on the impact of fluids, it is
-  necessary to neglect the effect of friction between the fluid and the
-  surface on which it moves.
-
-  _During Impact the Velocity of the Fluid relatively to the Surface on
-  which it impinges remains unchanged in Magnitude._--Consider a mass of
-  fluid flowing in contact with a solid surface also in motion, the
-  motion of both fluid and solid being estimated relatively to the
-  earth. Then the motion of the fluid may be resolved into two parts,
-  one a motion equal to that of the solid, and in the same direction,
-  the other a motion relatively to the solid. The motion which the fluid
-  has in common with the solid cannot at all be influenced by the
-  contact. The relative component of the motion of the fluid can only be
-  altered in direction, but not in magnitude. The fluid moving in
-  contact with the surface can only have a relative motion parallel to
-  the surface, while the pressure between the fluid and solid, if
-  friction is neglected, is normal to the surface. The pressure
-  therefore can only deviate the fluid, without altering the magnitude
-  of the relative velocity. The unchanged common component and, combined
-  with it, the deviated relative component give the resultant final
-  velocity, which may differ greatly in magnitude and direction from the
-  initial velocity.
-
-  From the principle of momentum, the impulse of any mass of fluid
-  reaching the surface in any given time is equal to the change of
-  momentum estimated in the same direction. The pressure between the
-  fluid and surface, in any direction, is equal to the change of
-  momentum in that direction of so much fluid as reaches the surface in
-  one second. If P_a is the pressure in any direction, m the mass of
-  fluid impinging per second, v_a the change of velocity in the
-  direction of P_a due to impact, then
-
-    P_a = mv_a.
-
-  If v1 (fig. 152) is the velocity and direction of motion before
-  impact, v2 that after impact, then v is the total change of motion due
-  to impact. The resultant pressure of the fluid on the surface is in
-  the direction of v, and is equal to v multiplied by the mass impinging
-  per second. That is, putting P for the resultant pressure,
-
-    P = mv.
-
-  Let P be resolved into two components, N and T, normal and tangential
-  to the direction of motion of the solid on which the fluid impinges.
-  Then N is a lateral force producing a pressure on the supports of the
-  solid, T is an effort which does work on the solid. If u is the
-  velocity of the solid, Tu is the work done per second by the fluid in
-  moving the solid surface.
-
-  [Illustration: FIG. 152.]
-
-  Let Q be the volume, and GQ the weight of the fluid impinging per
-  second, and let v1 be the initial velocity of the fluid before
-  striking the surface. Then GQv1^2/2g is the original kinetic energy of
-  Q cub. ft. of fluid, and the efficiency of the stream considered as an
-  arrangement for moving the solid surface is
-
-    [eta] = Tu/(GQv1^2/2g).
-
-  S 154. _Jet deviated entirely in one Direction.--Geometrical Solution_
-  (fig. 153).--Suppose a jet of water impinges on a surface ac with a
-  velocity ab, and let it be wholly deviated in planes parallel to the
-  figure. Also let ae be the velocity and direction of motion of the
-  surface. Join eb; then the water moves with respect to the surface in
-  the direction and with the velocity eb. As this relative velocity is
-  unaltered by contact with the surface, take cd = eb, tangent to the
-  surface at c, then cd is the relative motion of the water with respect
-  to the surface at c. Take df equal and parallel to ae. Then fc
-  (obtained by compounding the relative motion of water to surface and
-  common velocity of water and surface) is the absolute velocity and
-  direction of the water leaving the surface. Take ag equal and parallel
-  to fc. Then, since ab is the initial and ag the final velocity and
-  direction of motion, gb is the total change of motion of the water.
-  The resultant pressure on the plane is in the direction gb. Join eg.
-  In the triangle gae, ae is equal and parallel to df, and ag to fc.
-  Hence eg is equal and parallel to cd. But cd = eb = relative motion of
-  water and surface. Hence the change of motion of the water is
-  represented in magnitude and direction by the third side of an
-  isosceles triangle, of which the other sides are equal to the relative
-  velocity of the water and surface, and parallel to the initial and
-  final directions of relative motion.
-
-  [Illustration: FIG. 153.]
-
-
-  SPECIAL CASES
-
-  S 155. (1) _A Jet impinges on a plane surface at rest, in a direction
-  normal to the plane_ (fig. 154).--Let a jet whose section is [omega]
-  impinge with a velocity v on a plane surface at rest, in a direction
-  normal to the plane. The particles approach the plane, are gradually
-  deviated, and finally flow away parallel to the plane, having then no
-  velocity in the original direction of the jet. The quantity of water
-  impinging per second is [omega]v. The pressure on the plane, which is
-  equal to the change of momentum per second, is P = (G/g)[omega]v^2.
-
-  [Illustration: FIG. 154.]
-
-  (2) _If the plane is moving in the direction of the jet with the
-  velocity_ [+-]u, the quantity impinging per second is [omega](v [+-]
-  u). The momentum of this quantity before impact is (G/g)[omega](v [+-]
-  u)v. After impact, the water still possesses the velocity [+-]u in the
-  direction of the jet; and the momentum, in that direction, of so much
-  water as impinges in one second, after impact, is [+-](G/g)[omega](v
-  [+-] u)u. The pressure on the plane, which is the change of momentum
-  per second, is the difference of these quantities or P =
-  (G/g)[omega](v [+-] u)^2. This differs from the expression obtained in
-  the previous case, in that the relative velocity of the water and
-  plane v [+-] u is substituted for v. The expression may be written P =
-  2 X G X [omega](v [+-] u)^2/2g, where the last two terms are the
-  volume of a prism of water whose section is the area of the jet and
-  whose length is the head due to the relative velocity. The pressure on
-  the plane is twice the weight of that prism of water. The work done
-  when the plane is moving in the same direction as the jet is Pu =
-  (G/g)[omega](v - u)^2u foot-pounds per second. There issue from the
-  jet [omega]v cub. ft. per second, and the energy of this quantity
-  before impact is (G/2g)[omega]v^3. The efficiency of the jet is
-  therefore [eta] = 2(v - u)^2u/v^3. The value of u which makes this a
-  maximum is found by differentiating and equating the differential
-  coefficient to zero:--
-
-    d[eta]/du = 2(v^2 - 4vu + 3u^2)/v^3 = 0;
-
-    .: u = v or (1/3)v.
-
-  The former gives a minimum, the latter a maximum efficiency.
-
-  Putting u = (1/3)v in the expression above,
-
-    [eta] max. = 8/27.
-
-  (3) If, instead of one plane moving before the jet, a series of planes
-  are introduced at short intervals at the same point, the quantity of
-  water impinging on the series will be [omega]v instead of [omega](v -
-  u), and the whole pressure = (G/g)[omega]v(v - u). The work done is
-  (G/g)[omega]vu(v - u). The efficiency [eta] = (G/g)[omega]vu(v - u) /
-  (G/2g)[omega]v^3 = 2u(v - u)/v^2. This becomes a maximum for d[eta]/du
-  = 2(v - 2u) = 0, or u = (1/2)v, and the [eta] = 1/2. This result is
-  often used as an approximate expression for the velocity of greatest
-  efficiency when a jet of water strikes the floats of a water wheel.
-  The work wasted in this case is half the whole energy of the jet when
-  the floats run at the best speed.
-
-  S 156. (4) _Case of a Jet impinging on a Concave Cup Vane_, velocity
-  of water v, velocity of vane in the same direction u (fig. 155),
-  weight impinging per second = Gw(v - u).
-
-  [Illustration: FIG. 155.]
-
-  If the cup is hemispherical, the water leaves the cup in a direction
-  parallel to the jet. Its relative velocity is v - u when approaching
-  the cup, and -(v - u) when leaving it. Hence its absolute velocity
-  when leaving the cup is u - (v - u) = 2u - v. The change of momentum
-  per second = (G/g)[omega](v - u) {v - (2u - v)} = 2(G/g)[omega](v -
-  u)^2. Comparing this with case 2, it is seen that the pressure on a
-  hemispherical cup is double that on a flat plane. The work done on the
-  cup = 2(G/g)[omega] (v - u)^2u foot-pounds per second. The efficiency
-  of the jet is greatest when v = 3u; in that case the efficiency =
-  {16/27}.
-
-  If a series of cup vanes are introduced in front of the jet, so that
-  the quantity of water acted upon is [omega]v instead of [omega](v -
-  u), then the whole pressure on the chain of cups is (G/g)[omega]v{v -
-  (2u - v)} = 2(G/g)[omega]v(v - u). In this case the efficiency is
-  greatest when v = 2u, and the maximum efficiency is unity, or all the
-  energy of the water is expended on the cups.
-
-  [Illustration: FIG. 156.]
-
-  S 157. (5) _Case of a Flat Vane oblique to the Jet_ (fig. 156).--This
-  case presents some difficulty. The water spreading on the plane in all
-  directions from the point of impact, different particles leave the
-  plane with different absolute velocities. Let AB = v = velocity of
-  water, AC = u = velocity of plane. Then, completing the parallelogram,
-  AD represents in magnitude and direction the relative velocity of
-  water and plane. Draw AE normal to the plane and DE parallel to the
-  plane. Then the relative velocity AD may be regarded as consisting of
-  two components, one AE normal, the other DE parallel to the plane. On
-  the assumption that friction is insensible, DE is unaffected by
-  impact, but AE is destroyed. Hence AE represents the entire change of
-  velocity due to impact and the direction of that change. The pressure
-  on the plane is in the direction AE, and its amount is = mass of water
-  impinging per second X AE.
-
-  Let DAE = [theta], and let AD = v_r. Then AE = v_r cos [theta]; DE =
-  v_r sin [theta]. If Q is the volume of water impinging on the plane
-  per second, the change of momentum is (G/g)Qv_r cos [theta]. Let AC =
-  u = velocity of the plane, and let AC make the angle CAE = [delta]
-  with the normal to the plane. The velocity of the plane in the
-  direction AE = u cos [delta]. The work of the jet on the plane =
-  (G/g)Qv_r cos [theta] u cos [delta]. The same problem may be thus
-  treated algebraically (fig. 157). Let BAF = [alpha], and CAF =
-  [delta]. The velocity v of the water may be decomposed into AF = v cos
-  [alpha] normal to the plane, and FB = v sin [alpha] parallel to the
-  plane. Similarly the velocity of the plane = u = AC = BD can be
-  decomposed into BG = FE = u cos [delta] normal to the plane, and DG =
-  u sin [delta] parallel to the plane. As friction is neglected, the
-  velocity of the water parallel to the plane is unaffected by the
-  impact, but its component v cos [alpha] normal to the plane becomes
-  after impact the same as that of the plane, that is, u cos [delta].
-  Hence the change of velocity during impact = AE = v cos [alpha] - u
-  cos [delta]. The change of momentum per second, and consequently the
-  normal pressure on the plane is N = (G/g) Q(v cos [alpha] - u cos
-  [delta]). The pressure in the direction in which the plane is moving
-  is P = N cos [delta] = (G/g)Q (v cos [alpha] - u cos [delta]) cos
-  [delta], and the work done on the plane is Pu = (G/g)Q(v cos [alpha] -
-  u cos [delta]) u cos [delta], which is the same expression as before,
-  since AE = v_r cos [theta] = v cos [alpha] - u cos [delta].
-
-  [Illustration: FIG. 157.]
-
-  [Illustration: FIG. 158.]
-
-  In one second the plane moves so that the point A (fig. 158) comes to
-  C, or from the position shown in full lines to the position shown in
-  dotted lines. If the plane remained stationary, a length AB = v of the
-  jet would impinge on the plane, but, since the plane moves in the same
-  direction as the jet, only the length HB = AB - AH impinges on the
-  plane.
-
-  But AH = AC cos [delta]/ cos [alpha] = u cos [delta]/ cos [alpha], and
-  therefore HB = v - u cos [delta]/ cos [alpha]. Let [omega] = sectional
-  area of jet; volume impinging on plane per second = Q = [omega](v - u
-  cos [delta]/cos [alpha]) = [omega](v cos [alpha] - u cos [delta])/ cos
-  [alpha]. Inserting this in the formulae above, we get
-
-         G    [omega]
-    N = --- ----------- (v cos [alpha] - u cos [delta])^2;   (1)
-         g  cos [alpha]
-
-         G  [omega] cos [delta]
-    P = --- ------------------- (v cos [alpha] - u cos [delta])^2;   (2)
-         g      cos [alpha]
-
-          G           cos [delta]
-    Pu = --- [omega]u ----------- (v cos [alpha] - u cos [delta])^2.   (3)
-          g           cos [alpha]
-
-  Three cases may be distinguished:--
-
-  (a) The plane is at rest. Then u = 0, N = (G/g)[omega]v^2 cos [alpha];
-  and the work done on the plane and the efficiency of the jet are zero.
-
-  (b) The plane moves parallel to the jet. Then [delta] = [alpha], and
-  Pu = (G/g)[omega]u cos^2[alpha](v - u)^2, which is a maximum when u =
-  1/3 v.
-
-  When u = 1/3 v then Pu max. = 4/27 (G/g)[omega]v^3 cos^2 [alpha], and
-  the efficiency = [eta] = 4/9 cos^2 [alpha].
-
-  (c) The plane moves perpendicularly to the jet. Then [delta] = 90 deg.
-  - [alpha]; cos [delta] = sin [alpha]; and Pu = G/g [omega]u (sin
-  [alpha]/cos [alpha]) (v cos [alpha] - u sin [alpha])^2. This is a
-  maximum when u = 1/3 v cos [alpha].
-
-  When u = 1/3 v cos [alpha], the maximum work and the efficiency are
-  the same as in the last case.
-
-  [Illustration: FIG. 159.]
-
-  S 158. _Best Form of Vane to receive Water._--When water impinges
-  normally or obliquely on a plane, it is scattered in all directions
-  after impact, and the work carried away by the water is then generally
-  lost, from the impossibility of dealing afterwards with streams of
-  water deviated in so many directions. By suitably forming the vane,
-  however, the water may be entirely deviated in one direction, and the
-  loss of energy from agitation of the water is entirely avoided.
-
-  Let AB (fig. 159) be a vane, on which a jet of water impinges at the
-  point A and in the direction AC. Take AC = v = velocity of water, and
-  let AD represent in magnitude and direction the velocity of the vane.
-  Completing the parallelogram, DC or AE represents the direction in
-  which the water is moving relatively to the vane. If the lip of the
-  vane at A is tangential to AE, the water will not have its direction
-  suddenly changed when it impinges on the vane, and will therefore have
-  no tendency to spread laterally. On the contrary it will be so
-  gradually deviated that it will glide up the vane in the direction AB.
-  This is sometimes expressed by saying that the vane _receives the
-  water without shock_.
-
-  [Illustration: FIG. 160.]
-
-  S 159. _Floats of Poncelet Water Wheels._--Let AC (fig. 160) represent
-  the direction of a thin horizontal stream of water having the velocity
-  v. Let AB be a curved float moving horizontally with velocity u. The
-  relative motion of water and float is then initially horizontal, and
-  equal to v - u.
-
-  In order that the float may receive the water without shock, it is
-  necessary and sufficient that the lip of the float at A should be
-  tangential to the direction AC of relative motion. At the end of (v -
-  u)/g seconds the float moving with the velocity u comes to the
-  position A1B1, and during this time a particle of water received at A
-  and gliding up the float with the relative velocity v - u, attains a
-  height DE = (v - u)^2/2g. At E the water comes to relative rest. It
-  then descends along the float, and when after 2(v - u)/g seconds the
-  float has come to A2B2 the water will again have reached the lip at A2
-  and will quit it tangentially, that is, in the direction CA2, with a
-  relative velocity -(v - u) = -[root](2gDE) acquired under the
-  influence of gravity. The absolute velocity of the water leaving the
-  float is therefore u - (v - u) = 2u - v. If u = (1/2)v, the water will
-  drop off the bucket deprived of all energy of motion. The whole of the
-  work of the jet must therefore have been expended in driving the
-  float. The water will have been received without shock and discharged
-  without velocity. This is the principle of the Poncelet wheel, but in
-  that case the floats move over an arc of a large circle; the stream of
-  water has considerable thickness (about 8 in.); in order to get the
-  water into and out of the wheel, it is then necessary that the lip of
-  the float should make a small angle (about 15 deg.) with the direction
-  of its motion. The water quits the wheel with a little of its energy
-  of motion remaining.
-
-  S 160. _Pressure on a Curved Surface when the Water is deviated wholly
-  in one Direction._--When a jet of water impinges on a curved surface
-  in such a direction that it is received without shock, the pressure on
-  the surface is due to its gradual deviation from its first direction.
-  On any portion of the area the pressure is equal and opposite to the
-  force required to cause the deviation of so much water as rests on
-  that surface. In common language, it is equal to the centrifugal force
-  of that quantity of water.
-
-  [Illustration: FIG. 161.]
-
-  _Case 1. Surface Cylindrical and Stationary._--Let AB (fig. 161) be
-  the surface, having its axis at O and its radius = r. Let the water
-  impinge at A tangentially, and quit the surface tangentially at B.
-  Since the surface is at rest, v is both the absolute velocity of the
-  water and the velocity relatively to the surface, and this remains
-  unchanged during contact with the surface, because the deviating force
-  is at each point perpendicular to the direction of motion. The water
-  is deviated through an angle BCD = AOB = [phi]. Each particle of water
-  of weight p exerts radially a centrifugal force pv^2/rg. Let the
-  thickness of the stream = t ft. Then the weight of water resting on
-  unit of surface = Gt lb.; and the normal pressure per unit of surface
-  = n = Gtv^2/gr. The resultant of the radial pressures uniformly
-  distributed from A to B will be a force acting in the direction OC
-  bisecting AOB, and its magnitude will equal that of a force of
-  intensity = n, acting on the projection of AB on a plane perpendicular
-  to the direction OC. The length of the chord AB = 2r sin (1/2)[phi];
-  let b = breadth of the surface perpendicular to the plane of the
-  figure. The resultant pressure on surface
-
-                  [phi]   Gt v^2     G            [phi]
-    = R = 2rb sin ----- X --.--- = 2--- btv^2 sin -----,
-                    2     g   r      g              2
-
-  which is independent of the radius of curvature. It may be inferred
-  that the resultant pressure is the same for any curved surface of the
-  same projected area, which deviates the water through the same angle.
-
-  _Case 2. Cylindrical Surface moving in the Direction AC with Velocity
-  u._--The relative velocity = v - u. The final velocity BF (fig. 162)
-  is found by combining the relative velocity BD = v - u tangential to
-  the surface with the velocity BE = u of the surface. The intensity of
-  normal pressure, as in the last case, is (G/g)t(v - u)^2/r. The
-  resultant normal pressure R = 2(G/g)bt(v - u)^2 sin (1/2)[phi]. This
-  resultant pressure may be resolved into two components P and L, one
-  parallel and the other perpendicular to the direction of the vane's
-  motion. The former is an effort doing work on the vane. The latter is
-  a lateral force which does no work.
-
-    P = R sin (1/2)[phi] = (G/g) bt (v - u)^2 (1 - cos [phi]);
-
-    L = R cos (1/2)[phi] = (G/g) bt (v - u)^2 sin [phi].
-
-  [Illustration: FIG. 162.]
-
-  The work done by the jet on the vane is Pu = (G/g)btu(v - u)^2(1 - cos
-  [phi]), which is a maximum when u = 1/3 v. This result can also be
-  obtained by considering that the work done on the plane must be equal
-  to the energy lost by the water, when friction is neglected.
-
-  If [phi] = 180 deg., cos [phi] = -1, 1 - cos [phi] = 2; then P =
-  2(G/g)bt(v - u)^2, the same result as for a concave cup.
-
-  [Illustration: FIG. 163.]
-
-  S 161. _Position which a Movable Plane takes in Flowing Water._--When
-  a rectangular plane, movable about an axis parallel to one of its
-  sides, is placed in an indefinite current of fluid, it takes a
-  position such that the resultant of the normal pressures on the two
-  sides of the axis passes through the axis. If, therefore, planes
-  pivoted so that the ratio a/b (fig. 163) is varied are placed in
-  water, and the angle they make with the direction of the stream is
-  observed, the position of the resultant of the pressures on the plane
-  is determined for different angular positions. Experiments of this
-  kind have been made by Hagen. Some of his results are given in the
-  following table:--
-
-    +-----------+---------------+--------------------+
-    |           | Larger plane. |   Smaller Plane.   |
-    +-----------+---------------+--------------------+
-    | a/b = 1.0 |[phi] = ...    |[phi] = 90 deg.     |
-    |       0.9 |      75 deg.  |        72(1/2) deg.|
-    |       0.8 |      60 deg.  |        57 deg.     |
-    |       0.7 |      48 deg.  |        43 deg.     |
-    |       0.6 |      25 deg.  |        29 deg.     |
-    |       0.5 |      13 deg.  |        13 deg.     |
-    |       0.4 |       8 deg.  |         6(1/2) deg.|
-    |       0.3 |       6 deg.  |        ..          |
-    |       0.2 |       4 deg.  |        ..          |
-    +-----------+-------------+----------------------+
-
-  S 162. _Direct Action distinguished from Reaction_ (Rankine, _Steam
-  Engine_, S 147).
-
-  The pressure which a jet exerts on a vane can be distinguished into
-  two parts, viz.:--
-
-  (1) The pressure arising from changing the direct component of the
-  velocity of the water into the velocity of the vane. In fig. 153, S
-  154, ab cos bae is the direct component of the water's velocity, or
-  component in the direction of motion of vane. This is changed into the
-  velocity ae of the vane. The pressure due to direct impulse is then
-
-    P1 = GQ(ab cos bae - ae)/g.
-
-  For a flat vane moving normally, this direct action is the only action
-  producing pressure on the vane.
-
-  (2) The term reaction is applied to the additional action due to the
-  direction and velocity with which the water glances off the vane. It
-  is this which is diminished by the friction between the water and the
-  vane. In Case 2, S 160, the direct pressure is
-
-    P1 = Gbt(v - u)^2/g.
-
-  That due to reaction is
-
-    P2 = -Gbt(v - u)^2 cos [phi]/g.
-
-  If [phi] < 90 deg., the direct component of the water's motion is not
-  wholly converted into the velocity of the vane, and the whole
-  pressure due to direct impulse is not obtained. If [phi] > 90 deg.,
-  cos [phi] is negative and an additional pressure due to reaction is
-  obtained.
-
-  [Illustration: FIG. 164.]
-
-  S 163. _Jet Propeller._--In the case of vessels propelled by a jet of
-  water (fig. 164), driven sternwards from orifices at the side of the
-  vessel, the water, originally at rest outside the vessel, is drawn
-  into the ship and caused to move with the forward velocity V of the
-  ship. Afterwards it is projected sternwards from the jets with a
-  velocity v relatively to the ship, or v - V relatively to the earth.
-  If [Omega] is the total sectional area of the jets, [Omega]v is the
-  quantity of water discharged per second. The momentum generated per
-  second in a sternward direction is (G/g)[Omega]v(v - V), and this is
-  equal to the forward acting reaction P which propels the ship.
-
-  The energy carried away by the water
-
-    = (1/2)(G/g)[Omega]v (v - V)^2.   (1)
-
-  The useful work done on the ship
-
-    PV = (G/g)[Omega]v (v - V)V.   (2)
-
-  Adding (1) and (2), we get the whole work expended on the water,
-  neglecting friction:--
-
-    W = (1/2)(G/g)[Omega]v (v^2 - V^2).
-
-  Hence the efficiency of the jet propeller is
-
-    PV/W = 2V/(v + V).   (3)
-
-  This increases towards unity as v approaches V. In other words, the
-  less the velocity of the jets exceeds that of the ship, and therefore
-  the greater the area of the orifice of discharge, the greater is the
-  efficiency of the propeller.
-
-  In the "Waterwitch" v was about twice V. Hence in this case the
-  theoretical efficiency of the propeller, friction neglected, was about
-  2/3.
-
-  [Illustration: FIG. 165.]
-
-  S 164. _Pressure of a Steady Stream in a Uniform Pipe on a Plane
-  normal to the Direction of Motion._--Let CD (fig. 165) be a plane
-  placed normally to the stream which, for simplicity, may be supposed
-  to flow horizontally. The fluid filaments are deviated in front of the
-  plane, form a contraction at A1A1, and converge again, leaving a mass
-  of eddying water behind the plane. Suppose the section A0A0 taken at a
-  point where the parallel motion has not begun to be disturbed, and
-  A2A2 where the parallel motion is re-established. Then since the same
-  quantity of water with the same velocity passes A0A0, A2A2 in any
-  given time, the external forces produce no change of momentum on the
-  mass A0A0A2A2, and must therefore be in equilibrium. If [Omega] is the
-  section of the stream at A0A0 or A2A2, and [omega] the area of the
-  plate CD, the area of the contracted section of the stream at A1A1
-  will be c_c([Omega] - [omega]), where c_c is the coefficient of
-  contraction. Hence, if v is the velocity at A0A0 or A2A2, and v1 the
-  velocity at A1A1,
-
-    v[Omega] = c_c v([Omega] - [omega]);
-
-    .:v1 = v[Omega]/c_c ([Omega] - [omega]).   (1)
-
-  Let p0, p1, p2 be the pressures at the three sections. Applying
-  Bernoulli's theorem to the sections A0A0 and A1A1,
-
-    p0   v^2   p1   v1^2
-    -- + --- = -- + ----.
-    G    2g    G     2g
-
-  Also, for the sections A1A1 and A2A2, allowing that the head due to
-  the relative velocity v1 - v is lost in shock:--
-
-    p1   v1^2    p2    v^2   (v1 - v)^2
-    -- + ---- =  --  + --- + ----------;
-    G     2g     G     2g        2g
-
-    .: p0 - p2 = G(v1 - v)^2/2g;   (2)
-
-  or, introducing the value in (1),
-
-              G   /        [Omega]            \^2
-    p0 - p2 = -- ( ----------------------- - 1 ) v^2   (3)
-              2g  \c_c ([Omega] - [omega])    /
-
-  Now the external forces in the direction of motion acting on the mass
-  A0A0A2A2 are the pressures p0[Omega]1 - p2[Omega] at the ends, and the
-  reaction -R of the plane on the water, which is equal and opposite to
-  the pressure of the water on the plane. As these are in equilibrium,
-
-    (p0 - p2)[Omega] - R = 0;
-
-                     /         [Omega]           \^2 v^2
-    .: R = G[Omega] ( ----------------------- - 1 )  ---;   (4)
-                     \c_c ([Omega] - [omega])    /   2g
-
-  an expression like that for the pressure of an isolated jet on an
-  indefinitely extended plane, with the addition of the term in
-  brackets, which depends only on the areas of the stream and the plane.
-  For a given plane the expression in brackets diminishes as [Omega]
-  increases. If [Omega]/[omega] = [rho], the equation (4) becomes
-                      _                             _
-                 v^2 |       /     [rho]         \^2 |
-    R = G[omega] --- |[rho] ( --------------- - 1 )  |,   (4a)
-                 2g  |_      \c_c ([rho] - 1)    /  _|
-
-  which is of the form
-
-    R = G[omega](v^2/2g)K,
-
-  where K depends only on the ratio of the sections of the stream and
-  plane.
-
-  For example, let c_c = 0.85, a value which is probable, if we allow
-  that the sides of the pipe act as internal borders to an orifice. Then
-
-               /        [rho]      \^2
-    K = [rho] ( 1.176 --------- - 1 ).
-               \      [rho] - 1    /
-
-    [rho] =        K =
-
-       1        [infinity]
-       2           3.66
-       3           1.75
-       4           1.29
-       5           1.10
-      10            .94
-      50           2.00
-     100           3.50
-
-  The assumption that the coefficient of contraction c_c is constant for
-  different values of [rho] is probably only true when [rho] is not very
-  large. Further, the increase of K for large values of [rho] is
-  contrary to experience, and hence it may be inferred that the
-  assumption that all the filaments have a common velocity v1 at the
-  section A1A1 and a common velocity v at the section A2A2 is not true
-  when the stream is very much larger than the plane. Hence, in the
-  expression
-
-    R = KG[omega]v^2/2g,
-
-  K must be determined by experiment in each special case. For a
-  cylindrical body putting [omega] for the section, c_c for the
-  coefficient of contraction, c_c([Omega] - [omega]) for the area of the
-  stream at A1A1,
-
-    v1 = v[Omega]/c_c([Omega] - [omega]); v2 = v[Omega]/([Omega] - [omega]);
-
-  or, putting [rho] = [Omega]/[omega],
-
-    v1 = v[rho]/c_c ([rho] - 1), v2 = v[rho]/([rho] - 1).
-
-  Then
-
-    R = K1G[omega]v^2/2g,
-
-  where
-
-                _                                            _
-               |  /  [rho]  \^2 / 1     \^2 /  [rho]      \^2 |
-    K1 = [rho] | ( --------- ) ( --- - 1 ) ( --------- - 1 )  |.
-               |_ \[rho] - 1/   \c_c    /   \[rho] - 1    /  _|
-
-  Taking c_c = 0.85 and [rho] = 4, K1 = 0.467, a value less than before.
-  Hence there is less pressure on the cylinder than on the thin plane.
-
-  [Illustration: FIG. 166.]
-
-  S 165. _Distribution of Pressure on a Surface on which a Jet impinges
-  normally._--The principle of momentum gives readily enough the total
-  or resultant pressure of a jet impinging on a plane surface, but in
-  some cases it is useful to know the distribution of the pressure. The
-  problem in the case in which the plane is struck normally, and the jet
-  spreads in all directions, is one of great complexity, but even in
-  that case the maximum intensity of the pressure is easily assigned.
-  Each layer of water flowing from an orifice is gradually deviated
-  (fig. 166) by contact with the surface, and during deviation exercises
-  a centrifugal pressure towards the axis of the jet. The force exerted
-  by each small mass of water is normal to its path and inversely as the
-  radius of curvature of the path. Hence the greatest pressure on the
-  plane must be at the axis of the jet, and the pressure must decrease
-  from the axis outwards, in some such way as is shown by the curve of
-  pressure in fig. 167, the branches of the curve being probably
-  asymptotic to the plane.
-
-  For simplicity suppose the jet is a vertical one. Let h1 (fig. 167) be
-  the depth of the orifice from the free surface, and v1 the velocity of
-  discharge. Then, if [omega] is the area of the orifice, the quantity
-  of water impinging on the plane is obviously
-
-    Q = [omega]v1 = [omega] [root](2gh1);
-
-  that is, supposing the orifice rounded, and neglecting the coefficient
-  of discharge.
-
-  The velocity with which the fluid reaches the plane is, however,
-  greater than this, and may reach the value
-
-    v = [root](2gh);
-
-  where h is the depth of the plane below the free surface. The external
-  layers of fluid subjected throughout, after leaving the orifice, to
-  the atmospheric pressure will attain the velocity v, and will flow
-  away with this velocity unchanged except by friction. The layers
-  towards the interior of the jet, being subjected to a pressure greater
-  than atmospheric pressure, will attain a less velocity, and so much
-  less as they are nearer the centre of the jet. But the pressure can
-  in no case exceed the pressure v^2/2g or h measured in feet of water,
-  or the direction of motion of the water would be reversed, and there
-  would be reflux. Hence the maximum intensity of the pressure of the
-  jet on the plane is h ft. of water. If the pressure curve is drawn
-  with pressures represented by feet of water, it will touch the free
-  water surface at the centre of the jet.
-
-  [Illustration: FIG. 167.]
-
-  Suppose the pressure curve rotated so as to form a solid of
-  revolution. The weight of water contained in that solid is the total
-  pressure of the jet on the surface, which has already been determined.
-  Let V = volume of this solid, then GV is its weight in pounds.
-  Consequently
-
-    GV = (G/g)[omega]v1v;
-
-    V = 2[omega] [root](hh1).
-
-  We have already, therefore, two conditions to be satisfied by the
-  pressure curve.
-
-  [Illustration: FIG. 168.--Curves of Pressure of Jets impinging
-  normally on a Plane.]
-
-  Some very interesting experiments on the distribution of pressure on a
-  surface struck by a jet have been made by J. S. Beresford (_Prof.
-  Papers on Indian Engineering_, No. cccxxii.), with a view to afford
-  information as to the forces acting on the aprons of weirs.
-  Cylindrical jets 1/2 in. to 2 in. diameter, issuing from a vessel in
-  which the water level was constant, were allowed to fall vertically on
-  a brass plate 9 in. in diameter. A small hole in the brass plate
-  communicated by a flexible tube with a vertical pressure column.
-  Arrangements were made by which this aperture could be moved 1/20
-  in. at a time across the area struck by the jet. The height of the
-  pressure column, for each position of the aperture, gave the pressure
-  at that point of the area struck by the jet. When the aperture was
-  exactly in the axis of the jet, the pressure column was very nearly
-  level with the free surface in the reservoir supplying the jet; that
-  is, the pressure was very nearly v^2/2g. As the aperture moved away
-  from the axis of the jet, the pressure diminished, and it became
-  insensibly small at a distance from the axis of the jet about equal to
-  the diameter of the jet. Hence, roughly, the pressure due to the jet
-  extends over an area about four times the area of section of the jet.
-
-  Fig. 168 shows the pressure curves obtained in three experiments with
-  three jets of the sizes shown, and with the free surface level in the
-  reservoir at the heights marked.
-
-    +------------------------------------------------------+
-    |          Experiment 1. Jet .475 in. diameter.        |
-    +----------------+------------------+------------------+
-    |  Height from   |   Distance from  |                  |
-    |  Free Surface  |    Axis of Jet   |   Pressure in.   |
-    | to Brass Plate |    in inches.    | inches of Water. |
-    |   in inches.   |                  |                  |
-    +----------------+------------------+------------------+
-    |       43       |        0         |       40.5       |
-    |        "       |        .05       |       39.40      |
-    |        "       |        .1        |     37.5-39.5    |
-    |        "       |        .15       |       35         |
-    |        "       |        .2        |     33.5-37      |
-    |        "       |        .25       |       31         |
-    |        "       |        .3        |      21-27       |
-    |        "       |        .35       |       21         |
-    |        "       |        .4        |       14         |
-    |        "       |        .45       |        8         |
-    |        "       |        .5        |        3.5       |
-    |        "       |        .55       |        1         |
-    |        "       |        .6        |        0.5       |
-    |        "       |        .65       |        0         |
-    +----------------+------------------+------------------+
-    |         Experiment 2. Jet .988 in. diameter.         |
-    +----------------+------------------+------------------+
-    |      42.15     |         0        |       42         |
-    |        "       |        .05       |       41.9       |
-    |        "       |        .1        |    41.5-41.8     |
-    |        "       |        .15       |       41         |
-    |        "       |        .2        |       40.3       |
-    |        "       |        .25       |       39.2       |
-    |        "       |        .3        |       37.5       |
-    |        "       |        .35       |       34.8       |
-    |        "       |        .45       |       27         |
-    |      42.25     |        .5        |       23         |
-    |        "       |        .55       |       18.5       |
-    |        "       |        .6        |       13         |
-    |        "       |        .65       |        8.3       |
-    |        "       |        .7        |        5         |
-    |        "       |        .75       |        3         |
-    |        "       |        .8        |        2.2       |
-    |      42.15     |        .85       |        1.6       |
-    |        "       |        .95       |        1         |
-    +----------------+------------------+------------------+
-    |         Experiment 3. Jet 19.5 in. diameter.         |
-    +----------------+------------------+------------------+
-    |      27.15     |         0        |       26.9       |
-    |        "       |        .08       |       26.9       |
-    |        "       |        .13       |       26.8       |
-    |        "       |        .18       |     26.5-26.6    |
-    |        "       |        .23       |     26.4-26.5    |
-    |        "       |        .28       |     26.3-26.6    |
-    |       27       |        .33       |       26.2       |
-    |        "       |        .38       |       25.9       |
-    |        "       |        .43       |       25.5       |
-    |        "       |        .48       |       25         |
-    |        "       |        .53       |       24.5       |
-    |        "       |        .58       |       24         |
-    |        "       |        .63       |       23.3       |
-    |        "       |        .68       |       22.5       |
-    |        "       |        .73       |       21.8       |
-    |        "       |        .78       |       21         |
-    |        "       |        .83       |       20.3       |
-    |        "       |        .88       |       19.3       |
-    |        "       |        .93       |       18         |
-    |        "       |        .98       |       17         |
-    |      26.5      |       1.13       |       13.5       |
-    |        "       |       1.18       |       12.5       |
-    |        "       |       1.23       |       10.8       |
-    |        "       |       1.28       |        9.5       |
-    |        "       |       1.33       |        8         |
-    |        "       |       1.38       |        7         |
-    |        "       |       1.43       |        6.3       |
-    |        "       |       1.48       |        5         |
-    |        "       |       1.53       |        4.3       |
-    |        "       |       1.58       |        3.5       |
-    |        "       |       1.9        |        2         |
-    +----------------+------------------+------------------+
-
-  As the general form of the pressure curve has been already indicated,
-  it may be assumed that its equation is of the form
-
-    y = ab^(-x^2).
-
-  But it has already been shown that for x = 0, y = h, hence a = h. To
-  determine the remaining constant, the other condition may be used,
-  that the solid formed by rotating the pressure curve represents the
-  total pressure on the plane. The volume of the solid is
-          _
-         /[oo]
-    V =  |    2[pi]xy dx
-        _/0
-                _
-               /[oo]
-      = 2[pi]h |    b^(-x^2)x dx
-              _/0
-                        _       _
-                       |         |[oo]
-      = ([pi]h/log_eb) |-b^(-x^2)|
-                       |_       _|0
-
-      = [pi]h/log_e b.
-
-  Using the condition already stated,
-
-    2[omega] [root](hh1) = [pi]h/log_e b,
-
-    log_e b = ([pi]/2[omega]) [root](h/h1).
-
-  Putting the value of b in (2) in eq. (1), and also r for the radius of
-  the jet at the orifice, so that [omega] = [pi]r^2, the equation to the
-  pressure curve is
-
-                                h  x^2
-    y = h[epsilon]^(-1/2) [root]-- ---.
-                                h1 r^2
-
-  S 166. _Resistance of a Plane moving through a Fluid, or Pressure of a
-  Current on a Plane._--When a thin plate moves through the air, or
-  through an indefinitely large mass of still water, in a direction
-  normal to its surface, there is an excess of pressure on the anterior
-  face and a diminution of pressure on the posterior face. Let v be the
-  relative velocity of the plate and fluid, [Omega] the area of the
-  plate, G the density of the fluid, h the height due to the velocity,
-  then the total resistance is expressed by the equation
-
-    R = fG[Omega]v^2/2g pounds = fG[Omega]h;
-
-  where f is a coefficient having about the value 1.3 for a plate moving
-  in still fluid, and 1.8 for a current impinging on a fixed plane,
-  whether the fluid is air or water. The difference in the value of the
-  coefficient in the two cases is perhaps due to errors of experiment.
-  There is a similar resistance to motion in the case of all bodies of "
-  _unfair_ " form, that is, in which the surfaces over which the water
-  slides are not of gradual and continuous curvature.
-
-  The stress between the fluid and plate arises chiefly in this way.
-  The streams of fluid deviated in front of the plate, supposed for
-  definiteness to be moving through the fluid, receive from it forward
-  momentum. Portions of this forward moving water are thrown off
-  laterally at the edges of the plate, and diffused through the
-  surrounding fluid, instead of falling to their original position
-  behind the plate. Other portions of comparatively still water are
-  dragged into motion to fill the space left behind the plate; and there
-  is thus a pressure less than hydrostatic pressure at the back of the
-  plate. The whole resistance to the motion of the plate is the sum of
-  the excess of pressure in front and deficiency of pressure behind.
-  This resistance is independent of any friction or viscosity in the
-  fluid, and is due simply to its inertia resisting a sudden change of
-  direction at the edge of the plate.
-
-  Experiments made by a whirling machine, in which the plate is fixed on
-  a long arm and moved circularly, gave the following values of the
-  coefficient _f_. The method is not free from objection, as the
-  centrifugal force causes a flow outwards across the plate.
-
-    +---------------+------------------------+
-    |  Approximate  |      Values of f.      |
-    | Area of Plate +------+-------+---------+
-    |   in sq. ft.  |Borda.|Hutton.|Thibault.|
-    +---------------+------+-------+---------+
-    |     0.13      | 1.39 |  1.24 |   ..    |
-    |     0.25      | 1.49 |  1.43 |  1.525  |
-    |     0.63      | 1.64 |   ..  |   ..    |
-    |     1.11      |  ..  |   ..  |  1.784  |
-    +---------------+------+-------+---------+
-
-  There is a steady increase of resistance with the size of the plate,
-  in part or wholly due to centrifugal action.
-
-  P. L. G. Dubuat (1734-1809) made experiments on a plane 1 ft. square,
-  moved in a straight line in water at 3 to 6(1/2) ft. per second.
-  Calling m the coefficient of excess of pressure in front, and n the
-  coefficient of deficiency of pressure behind, so that f = m + n, he
-  found the following values:--
-
-    m = 1; n = 0.433; f = 1.433.
-
-  The pressures were measured by pressure columns. Experiments by A. J.
-  Morin (1795-1880), G. Piobert (1793-1871) and I. Didion (1798-1878) on
-  plates of 0.3 to 2.7 sq. ft. area, drawn vertically through water,
-  gave f = 2.18; but the experiments were made in a reservoir of
-  comparatively small depth. For similar plates moved through air they
-  found f = 1.36, a result more in accordance with those which precede.
-
-  For a fixed plane in a moving current of water E. Mariotte found f =
-  1.25. Dubuat, in experiments in a current of water like those
-  mentioned above, obtained the values m = 1.186; n = 0.670; f = 1.856.
-  Thibault exposed to wind pressure planes of 1.17 and 2.5 sq. ft. area,
-  and found f to vary from 1.568 to 2.125, the mean value being f =
-  1.834, a result agreeing well with Dubuat.
-
-  [Illustration: FIG. 169.]
-
-  S 167. _Stanton's Experiments on the Pressure of Air on Surfaces._--At
-  the National Physical Laboratory, London, T. E. Stanton carried out a
-  series of experiments on the distribution of pressure on surfaces in a
-  current of air passing through an air trunk. These were on a small
-  scale but with exceptionally accurate means of measurement. These
-  experiments differ from those already given in that the plane is small
-  relatively to the cross section of the current (_Proc. Inst. Civ.
-  Eng._ clvi., 1904). Fig. 169 shows the distribution of pressure on a
-  square plate. ab is the plate in vertical section. acb the
-  distribution of pressure on the windward and adb that on the leeward
-  side of the central section. Similarly aeb is the distribution of
-  pressure on the windward and afb on the leeward side of a diagonal
-  section. The intensity of pressure at the centre of the plate on the
-  windward side was in all cases p = Gv^2/2g lb. per sq. ft., where G is
-  the weight of a cubic foot of air and v the velocity of the current in
-  ft. per sec. On the leeward side the negative pressure is uniform
-  except near the edges, and its value depends on the form of the plate.
-  For a circular plate the pressure on the leeward side was 0.48 Gv^2/2g
-  and for a rectangular plate 0.66 Gv^2/2g. For circular or square plates
-  the resultant pressure on the plate was P = 0.00126 v^2 lb. per sq. ft.
-  where v is the velocity of the current in ft. per sec. On a long
-  narrow rectangular plate the resultant pressure was nearly 60% greater
-  than on a circular plate. In later tests on larger planes in free air,
-  Stanton found resistances 18% greater than those observed with small
-  planes in the air trunk.
-
-  S 168. _Case when the Direction of Motion is oblique to the
-  Plane._--The determination of the pressure between a fluid and surface
-  in this case is of importance in many practical questions, for
-  instance, in assigning the load due to wind pressure on sloping and
-  curved roofs, and experiments have been made by Hutton, Vince, and
-  Thibault on planes moved circularly through air and water on a
-  whirling machine.
-
-  [Illustration: FIG. 170.]
-
-  Let AB (fig. 170) be a plane moving in the direction R making an angle
-  [phi] with the plane. The resultant pressure between the fluid and the
-  plane will be a normal pressure N. The component R of this normal
-  pressure is the resistance to the motion of the plane and the other
-  component L is a lateral force resisted by the guides which support
-  the plane. Obviously
-
-    R = N sin [phi];
-
-    L = N cos [phi].
-
-  In the case of wind pressure on a sloping roof surface, R is the
-  horizontal and L the vertical component of the normal pressure.
-
-  In experiments with the whirling machine it is the resistance to
-  motion, R, which is directly measured. Let P be the pressure on a
-  plane moved normally through a fluid. Then, for the same plane
-  inclined at an angle [phi] to its direction of motion, the resistance
-  was found by Hutton to be
-
-    R = P(sin [phi])^{1.842 cos [phi]}.
-
-  A simpler and more convenient expression given by Colonel Duchemin is
-
-    R = 2P sin^2 [phi]/(1 + sin^2 [phi]).
-
-  Consequently, the total pressure between the fluid and plane is
-
-    N = 2P sin [phi]/(1 + sin^2 [phi]) = 2P/(cosec [phi] + sin [phi]),
-
-  and the lateral force is
-
-    L = 2P sin [phi] cos [phi]/(1 + sin^2 [phi]).
-
-  In 1872 some experiments were made for the Aeronautical Society on the
-  pressure of air on oblique planes. These plates, of 1 to 2 ft. square,
-  were balanced by ingenious mechanism designed by F. H. Wenham and
-  Spencer Browning, in such a manner that both the pressure in the
-  direction of the air current and the lateral force were separately
-  measured. These planes were placed opposite a blast from a fan issuing
-  from a wooden pipe 18 in. square. The pressure of the blast varied
-  from 6/10 to 1 in. of water pressure. The following are the results
-  given in pounds per square foot of the plane, and a comparison of the
-  experimental results with the pressures given by Duchemin's rule.
-  These last values are obtained by taking P = 3.31, the observed
-  pressure on a normal surface:--
-
-    +-----------------------------------+-------+-------+-------+------+
-    | Angle between Plane and Direction |   15  |   20  |   60  |  90  |
-    |   of Blast                        |  deg. |  deg. |  deg. | deg. |
-    +-----------------------------------+-------+-------+-------+------+
-    | Horizontal pressure R             | 0.4   | 0.61  | 2.73  | 3.31 |
-    | Lateral pressure L                | 1.6   | 1.96  | 1.26  |  ..  |
-    | Normal pressure [root](L^2 + R^2) | 1.65  | 2.05  | 3.01  | 3.31 |
-    | Normal pressure by Duchemin's rule| 1.605 | 2.027 | 3.276 | 3.31 |
-    +-----------------------------------+-------+-------+-------+------+
-
-
-WATER MOTORS
-
-In every system of machinery deriving energy from a natural waterfall
-there exist the following parts:--
-
-1. A supply channel or head race, leading the water from the highest
-accessible level to the site of the machine. This may be an open channel
-of earth, masonry or wood, laid at as small a slope as is consistent
-with the delivery of the necessary supply of water, or it may be a
-closed cast or wrought-iron pipe, laid at the natural slope of the
-ground, and about 3 ft. below the surface. In some cases part of the
-head race is an open channel, part a closed pipe. The channel often
-starts from a small storage reservoir, constructed near the stream
-supplying the water motor, in which the water accumulates when the motor
-is not working. There are sluices or penstocks by which the supply can
-be cut off when necessary.
-
-2. Leading from the motor there is a tail race, culvert, or discharge
-pipe delivering the water after it has done its work at the lowest
-convenient level.
-
-3. A waste channel, weir, or bye-wash is placed at the origin of the
-head race, by which surplus water, in floods, escapes.
-
-4. The motor itself, of one of the kinds to be described presently,
-which either overcomes a useful resistance directly, as in the case of a
-ram acting on a lift or crane chain, or indirectly by actuating
-transmissive machinery, as when a turbine drives the shafting, belting
-and gearing of a mill. With the motor is usually combined regulating
-machinery for adjusting the power and speed to the work done. This may
-be controlled in some cases by automatic governing machinery.
-
-S 169. _Water Motors with Artificial Sources of Energy._--The great
-convenience and simplicity of water motors has led to their adoption in
-certain cases, where no natural source of water power is available. In
-these cases, an artificial source of water power is created by using a
-steam-engine to pump water to a reservoir at a great elevation, or to
-pump water into a closed reservoir in which there is great pressure. The
-water flowing from the reservoir through hydraulic engines gives back
-the energy expended, less so much as has been wasted by friction. Such
-arrangements are most useful where a continuously acting steam engine
-stores up energy by pumping the water, while the work done by the
-hydraulic engines is done intermittently.
-
-  S 170. _Energy of a Water-fall._--Let H_t be the total fall of level
-  from the point where the water is taken from a natural stream to the
-  point where it is discharged into it again. Of this total fall a
-  portion, which can be estimated independently, is expended in
-  overcoming the resistances of the head and tail races or the supply
-  and discharge pipes. Let this portion of head wasted be [h]_r. Then
-  the available head to work the motor is H = H_t - [h]_r. It is this
-  available head which should be used in all calculations of the
-  proportions of the motor. Let Q be the supply of water per second.
-  Then GQH foot-pounds per second is the gross available work of the
-  fall. The power of the fall may be utilized in three ways. (a) The GQ
-  pounds of water may be placed on a machine at the highest level, and
-  descending in contact with it a distance of H ft., the work done will
-  be (neglecting losses from friction or leakage) GQH foot-pounds per
-  second. (b) Or the water may descend in a closed pipe from the higher
-  to the lower level, in which case, with the same reservation as
-  before, the pressure at the foot of the pipe will be p = GH pounds per
-  square foot. If the water with this pressure acts on a movable piston
-  like that of a steam engine, it will drive the piston so that the
-  volume described is Q cubic feet per second. Then the work done will
-  be pQ = GHQ foot-pounds per second as before. (c) Or lastly, the water
-  may be allowed to acquire the velocity v = [root](2gH) by its descent.
-  The kinetic energy of Q cubic feet will then be (1/2)GQv^2/g = GQH,
-  and if the water is allowed to impinge on surfaces suitably curved
-  which bring it finally to rest, it will impart to these the same
-  energy as in the previous cases. Motors which receive energy mainly in
-  the three ways described in (a), (b), (c) may be termed gravity,
-  pressure and inertia motors respectively. Generally, if Q ft. per
-  second of water act by weight through a distance h1, at a pressure p
-  due to h2 ft. of fall, and with a velocity v due to h3 ft. of fall, so
-  that h1 + h2 + h3 = H, then, apart from energy wasted by friction or
-  leakage or imperfection of the machine, the work done will be
-
-    GQh1 + pQ + (G/g) Q (v^2/2g) = GQH foot pounds,
-
-  the same as if the water acted simply by its weight while descending H
-  ft.
-
-S 171. _Site for Water Motor._--Wherever a stream flows from a higher to
-a lower level it is possible to erect a water motor. The amount of power
-obtainable depends on the available head and the supply of water. In
-choosing a site the engineer will select a portion of the stream where
-there is an abrupt natural fall, or at least a considerable slope of the
-bed. He will have regard to the facility of constructing the channels
-which are to convey the water, and will take advantage of any bend in
-the river which enables him to shorten them. He will have accurate
-measurements made of the quantity of water flowing in the stream, and he
-will endeavour to ascertain the average quantity available throughout
-the year, the minimum quantity in dry seasons, and the maximum for which
-bye-wash channels must be provided. In many cases the natural fall can
-be increased by a dam or weir thrown across the stream. The engineer
-will also examine to what extent the head will vary in different
-seasons, and whether it is necessary to sacrifice part of the fall and
-give a steep slope to the tail race to prevent the motor being drowned
-by backwater in floods. Streams fed from lakes which form natural
-reservoirs or fed from glaciers are less variable than streams depending
-directly on rainfall, and are therefore advantageous for water-power
-purposes.
-
-  S 172. _Water Power at Holyoke, U.S.A._--About 85 m. from the mouth of
-  the Connecticut river there was a fall of about 60 ft. in a short
-  distance, forming what were called the Grand Rapids, below which the
-  river turned sharply, forming a kind of peninsula on which the city of
-  Holyoke is built. In 1845 the magnitude of the water-power available
-  attracted attention, and it was decided to build a dam across the
-  river. The ordinary flow of the river is 6000 cub. ft. per sec.,
-  giving a gross power of 30,000 h.p. In dry seasons the power is 20,000
-  h.p., or occasionally less. From above the dam a system of canals
-  takes the water to mills on three levels. The first canal starts with
-  a width of 140 ft. and depth of 22 ft., and supplies the highest
-  range of mills. A second canal takes the water which has driven
-  turbines in the highest mills and supplies it to a second series of
-  mills. There is a third canal on a still lower level supplying the
-  lowest mills. The water then finds its way back to the river. With the
-  grant of a mill site is also leased the right to use the water-power.
-  A mill-power is defined as 38 cub. ft. of water per sec. during 16
-  hours per day on a fall of 20 ft. This gives about 60 h.p. effective.
-  The charge for the power water is at the rate of 20s. per h.p. per
-  annum.
-
-S 173. _Action of Water in a Water Motor._--Water motors may be divided
-into water-pressure engines, water-wheels and turbines.
-
-Water-pressure engines are machines with a cylinder and piston or ram,
-in principle identical with the corresponding part of a steam-engine.
-The water is alternately admitted to and discharged from the cylinder,
-causing a reciprocating action of the piston or plunger. It is admitted
-at a high pressure and discharged at a low one, and consequently work is
-done on the piston. The water in these machines never acquires a high
-velocity, and for the most part the kinetic energy of the water is
-wasted. The useful work is due to the difference of the pressure of
-admission and discharge, whether that pressure is due to the weight of a
-column of water of more or less considerable height, or is artificially
-produced in ways to be described presently.
-
-Water-wheels are large vertical wheels driven by water falling from a
-higher to a lower level. In most water-wheels, the water acts directly
-by its weight loading one side of the wheel and so causing rotation. But
-in all water-wheels a portion, and in some a considerable portion, of
-the work due to gravity is first employed to generate kinetic energy in
-the water; during its action on the water-wheel the velocity of the
-water diminishes, and the wheel is therefore in part driven by the
-impulse due to the change of the water's momentum. Water-wheels are
-therefore motors on which the water acts, partly by weight, partly by
-impulse.
-
-Turbines are wheels, generally of small size compared with water wheels,
-driven chiefly by the impulse of the water. Before entering the moving
-part of the turbine, the water is allowed to acquire a considerable
-velocity; during its action on the turbine this velocity is diminished,
-and the impulse due to the change of momentum drives the turbine.
-
-In designing or selecting a water motor it is not sufficient to consider
-only its efficiency in normal conditions of working. It is generally
-quite as important to know how it will act with a scanty water supply or
-a diminished head. The greatest difference in water motors is in their
-adaptability to varying conditions of working.
-
-
-_Water-pressure Engines._
-
-S 174. In these the water acts by pressure either due to the height of
-the column in a supply pipe descending from a high-level reservoir, or
-created by pumping. Pressure engines were first used in mine-pumping on
-waterfalls of greater height than could at that time be utilized by
-water wheels. Usually they were single acting, the water-pressure
-lifting the heavy pump rods which then made the return or pumping stroke
-by their own weight. To avoid losses by fluid friction and shock the
-velocity of the water in the pipes and passages was restricted to from 3
-to 10 ft. per second, and the mean speed of plunger to 1 ft. per second.
-The stroke was long and the number of strokes 3 to 6 per minute. The
-pumping lift being constant, such engines worked practically always at
-full load, and the efficiency was high, about 84%. But they were
-cumbrous machines. They are described in Weisbach's _Mechanics of
-Engineering_.
-
-The convenience of distributing energy from a central station to
-scattered working-points by pressure water conveyed in pipes--a system
-invented by Lord Armstrong--has already been mentioned. This system has
-led to the development of a great variety of hydraulic pressure engines
-of very various types. The cost of pumping the pressure water to some
-extent restricts its use to intermittent operations, such as working
-lifts and cranes, punching, shearing and riveting machines, forging and
-flanging presses. To keep down the cost of the distributing mains
-very high pressures are adopted, generally 700 lb. per sq. in. or 1600
-ft. of head or more.
-
-In a large number of hydraulic machines worked by water at high
-pressure, especially lifting machines, the motor consists of a direct,
-single acting ram and cylinder. In a few cases double-acting pistons and
-cylinders are used; but they involve a water-tight packing of the piston
-not easily accessible. In some cases pressure engines are used to obtain
-rotative movement, and then two double-acting cylinders or three
-single-acting cylinders are used, driving a crank shaft. Some
-double-acting cylinders have a piston rod half the area of the piston.
-The pressure water acts continuously on the annular area in front of the
-piston. During the forward stroke the pressure on the front of the
-piston balances half the pressure on the back. During the return stroke
-the pressure on the front is unopposed. The water in front of the piston
-is not exhausted, but returns to the supply pipe. As the frictional
-losses in a fluid are independent of the pressure, and the work done
-increases directly as the pressure, the percentage loss decreases for
-given velocities of flow as the pressure increases. Hence for
-high-pressure machines somewhat greater velocities are permitted in the
-passages than for low-pressure machines. In supply mains the velocity is
-from 3 to 6 ft. per second, in valve passages 5 to 10 ft. per second, or
-in extreme cases 20 ft. per second, where there is less object in
-economizing energy. As the water is incompressible, slide valves must
-have neither lap nor lead, and piston valves are preferable to ordinary
-slide valves. To prevent injurious compression from exhaust valves
-closing too soon in rotative engines with a fixed stroke, small
-self-acting relief valves are fitted to the cylinder ends, opening
-outwards against the pressure into the valve chest. Imprisoned water can
-then escape without over-straining the machines.
-
-In direct single-acting lift machines, in which the stroke is fixed, and
-in rotative machines at constant speed it is obvious that the cylinder
-must be filled at each stroke irrespective of the amount of work to be
-done. The same amount of water is used whether much or little work is
-done, or whether great or small weights are lifted. Hence while pressure
-engines are very efficient at full load, their efficiency decreases as
-the load decreases. Various arrangements have been adopted to diminish
-this defect in engines working with a variable load. In lifting
-machinery there is sometimes a double ram, a hollow ram enclosing a
-solid ram. By simple arrangements the solid ram only is used for small
-loads, but for large loads the hollow ram is locked to the solid ram,
-and the two act as a ram of larger area. In rotative engines the case is
-more difficult. In Hastie's and Rigg's engines the stroke is
-automatically varied with the load, increasing when the load is large
-and decreasing when it is small. But such engines are complicated and
-have not achieved much success. Where pressure engines are used
-simplicity is generally a first consideration, and economy is of less
-importance.
-
-  S 175. _Efficiency of Pressure Engines._--It is hardly possible to
-  form a theoretical expression for the efficiency of pressure engines,
-  but some general considerations are useful. Consider the case of a
-  long stroke hydraulic ram, which has a fairly constant velocity v
-  during the stroke, and valves which are fairly wide open during most
-  of the stroke. Let r be the ratio of area of ram to area of valve
-  passage, a ratio which may vary in ordinary cases from 4 to 12. Then
-  the loss in shock of the water entering the cylinder will be (r -
-  1)^2v^2/2g in ft. of head. The friction in the supply pipe is also
-  proportional to v^2. The energy carried away in exhaust will be
-  proportional to v^2. Hence the total hydraulic losses may be taken to
-  be approximately [zeta]v^2/2g ft., where [zeta] is a coefficient
-  depending on the proportions of the machine. Let f be the friction of
-  the ram packing and mechanism reckoned in lb. per sq. ft. of ram area.
-  Then if the supply-pipe pressure driving the machine is p lb. per sq.
-  ft., the effective working pressure will be
-
-    p - G[zeta]v^2/2g - f lb. per sq. ft.
-
-  Let A be the area of the ram in sq. ft., v its velocity in ft. per
-  sec. The useful work done will be
-
-    (p - G[zeta]v^2/2g - f)Av ft. lb. per sec.,
-
-  and the efficiency of the machine will be
-
-    [eta] = (p - G[zeta]v^2/2g - f)/p.
-
-  This shows that the efficiency increases with the pressure p, and
-  diminishes with the speed v, other things being the same. If in
-  regulating the engine for varying load the pressure is throttled,
-  part of the available head is destroyed at the throttle valve, and p
-  in the bracket above is reduced. Direct-acting hydraulic lifts,
-  without intermediate gearing, may have an efficiency of 95% during the
-  working stroke. If a hydraulic jigger is used with ropes and sheaves
-  to change the speed of the ram to the speed of the lift, the
-  efficiency may be only 50%. E. B. Ellington has given the efficiency
-  of lifts with hydraulic balance at 85% during the working stroke.
-  Large pressure engines have an efficiency of 85%, but small rotative
-  engines probably not more than 50% and that only when fully loaded.
-
-[Illustration: FIG. 171.]
-
-S 176. _Direct-Acting Hydraulic Lift_ (fig. 171).--This is the simplest
-of all kinds of hydraulic motor. A cage W is lifted directly by water
-pressure acting in a cylinder C, the length of which is a little greater
-than the lift. A ram or plunger R of the same length is attached to the
-cage. The water-pressure admitted by a cock to the cylinder forces up
-the ram, and when the supply valve is closed and the discharge valve
-opened, the ram descends. In this case the ram is 9 in. diameter, with a
-stroke of 49 ft. It consists of lengths of wrought-iron pipe screwed
-together perfectly water-tight, the lower end being closed by a
-cast-iron plug. The ram works in a cylinder 11 in. diameter of 9 ft.
-lengths of flanged cast-iron pipe. The ram passes water-tight through
-the cylinder cover, which is provided with double hat leathers to
-prevent leakage outwards or inwards. As the weight of the ram and cage
-is much more than sufficient to cause a descent of the cage, part of the
-weight is balanced. A chain attached to the cage passes over a pulley at
-the top of the lift, and carries at its free end a balance weight B,
-working in T iron guides. Water is admitted to the cylinder from a 4-in.
-supply pipe through a two-way slide, worked by a rack, spindle and
-endless rope. The lift works under 73 ft. of head, and lifts 1350 lb at
-2 ft. per second. The efficiency is from 75 to 80%.
-
-  The principal prejudicial resistance to the motion of a ram of this
-  kind is the friction of the cup leathers, which make the joint between
-  the cylinder and ram. Some experiments by John Hick give for the
-  friction of these leathers the following formula. Let F = the total
-  friction in pounds; d = diameter of ram in ft.; p = water-pressure in
-  pounds per sq. ft.; k a coefficient.
-
-  F = k p d
-
-  k = 0.00393 if the leathers are new or badly lubricated;
-    = 0.00262 if the leathers are in good condition and well lubricated.
-
-  Since the total pressure on the ram is P = (1/4)[pi]d^2p, the fraction
-  of the total pressure expended in overcoming the friction of the
-  leathers is F/P = .005/d to .0033/d, d being in feet.
-
-  Let H be the height of the pressure column measured from the free
-  surface of the supply reservoir to the bottom of the ram in its lowest
-  position, H_b the height from the discharge reservoir to the same
-  point, h the height of the ram above its lowest point at any moment, S
-  the length of stroke, [Omega] the area of the ram, W the weight of
-  cage, R the weight of ram, B the weight of balance weight, w the
-  weight of balance chain per foot run, F the friction of the cup
-  leather and slides. Then, neglecting fluid friction, if the ram is
-  rising the accelerating force is
-
-    P1 = G(H - h)[Omega] - R - W + B - w(S - h) + wh - F,
-
-  and if the ram is descending
-
-    P2 = G(H_b - h)[Omega] + W + R - B + w(S - h) - wh - F.
-
-  If w = 1/2 G[Omega], P1 and P2 are constant throughout the stroke; and
-  the moving force in ascending and descending is the same, if
-
-    B = W + R + wS - G[Omega](H - H_b)/2.
-
-  Using the values just found for w and B,
-
-    P1 = P2 = (1/2)G[Omega](H - H_b) - F.
-
-  Let W + R + wS + B = U, and let P be the constant accelerating force
-  acting on the system, then the acceleration is (P/U)g. The velocity at
-  the end of the stroke is (assuming the friction to be constant)
-
-    v = [root](2PgS/U);
-
-  and the mean velocity of ascent is (1/2)v.
-
-[Illustration: FIG. 172.]
-
-S 177. _Armstrong's Hydraulic Jigger._--This is simply a single-acting
-hydraulic cylinder and ram, provided with sheaves so as to give motion
-to a wire rope or chain. It is used in various forms of lift and crane.
-Fig. 172 shows the arrangement. A hydraulic ram or plunger B works in a
-stationary cylinder A. Ram and cylinder carry sets of sheaves over which
-passes a chain or rope, fixed at one end to the cylinder, and at the
-other connected over guide pulleys to a lift or crane. For each pair of
-pulleys, one on the cylinder and one on the ram, the movement of the
-free end of the rope is doubled compared with that of the ram. With
-three pairs of pulleys the free end of the rope has a movement equal to
-six times the stroke of the ram, the force exerted being in the inverse
-proportion.
-
-S 178. _Rotative Hydraulic Engines._--Valve-gear mechanism similar in
-principle to that of steam engines can be applied to actuate the
-admission and discharge valves, and the pressure engine is then
-converted into a continuously-acting motor.
-
-  Let H be the available fall to work the engine after deducting the
-  loss of head in the supply and discharge pipes, Q the supply of water
-  in cubic feet per second, and [eta] the efficiency of the engine. Then
-  the horse-power of the engine is
-
-    H.P. = [eta]GQH/550.
-
-  The efficiency of large slow-moving pressure engines is [eta] = .66 to
-  .8. In small motors of this kind probably [eta] is not greater than
-  .5. Let v be the mean velocity of the piston, then its diameter d is
-  given by the relation
-
-    Q = [pi]d^2v/4 in double-acting engines,
-      = [pi]d^2v/8 in single-acting engines.
-
-  If there are n cylinders put Q/n for Q in these equations.
-
-Small rotative pressure engines form extremely convenient motors for
-hoists, capstans or winches, and for driving small machinery. The
-single-acting engine has the advantage that the pressure of the piston
-on the crank pin is always in one direction; there is then no knocking
-as the dead centres are passed. Generally three single-acting cylinders
-are used, so that the engine will readily start in all positions, and
-the driving effort on the crank pin is very uniform.
-
-[Illustration: FIG. 173.]
-
-  _Brotherhood Hydraulic Engine._--Three cylinders at angles of 120 deg.
-  with each other are formed in one casting with the frame. The
-  plungers are hollow trunks, and the connecting rods abut in
-  cylindrical recesses in them and are connected to a common crank pin.
-  A circular valve disk with concentric segmental ports revolves at the
-  same rate as the crank over ports in the valve face common to the
-  three cylinders. Each cylinder is always in communication with either
-  an admission or exhaust port. The blank parts of the circular valve
-  close the admission and exhaust ports alternately. The fixed valve
-  face is of lignum vitae in a metal recess, and the revolving valve of
-  gun-metal. In the case of a small capstan engine the cylinders are
-  3(1/2) in. diameter and 3 in. stroke. At 40 revs. per minute, the
-  piston speed is 31 ft. per minute. The ports are 1 in. diameter or
-  1/12 of the piston area, and the mean velocity in the ports 6.4 ft.
-  per sec. With 700 lb. per sq. in. water pressure and an efficiency of
-  50%, the engine is about 3 h.p. A common arrangement is to have three
-  parallel cylinders acting on a three-throw crank shaft, the cylinders
-  oscillating on trunnions.
-
-  _Hastie's Engine._--Fig. 173 shows a similar engine made by Messrs
-  Hastie of Greenock. G, G, G are the three plungers which pass out of
-  the cylinders through cup leathers, and act on the same crank pin. A
-  is the inlet pipe which communicates with the cock B. This cock
-  controls the action of the engine, being so constructed that it acts
-  as a reversing valve when the handle C is in its extreme positions and
-  as a brake when in its middle position. With the handle in its middle
-  position, the ports of the cylinders are in communication with the
-  exhaust. Two passages are formed in the framing leading from the cock
-  B to the ends of the cylinders, one being in communication with the
-  supply pipe A, the other with the discharge pipe Q. These passages end
-  as shown at E. The oscillation of the cylinders puts them alternately
-  in communication with each of these passages, and thus the water is
-  alternately admitted and exhausted.
-
-  [Illustration: FIG. 174.]
-
-  [Illustration: FIG. 175.]
-
-  In any ordinary rotative engine the length of stroke is invariable.
-  Consequently the consumption of water depends simply on the speed of
-  the engine, irrespective of the effort overcome. If the power of the
-  engine must be varied without altering the number of rotations, then
-  the stroke must be made variable. Messrs Hastie have contrived an
-  exceedingly ingenious method of varying the stroke automatically, in
-  proportion to the amount of work to be done (fig. 174). The crank pin
-  I is carried in a slide H moving in a disk M. In this is a double cam
-  K acting on two small steel rollers J, L attached to the slide H. If
-  the cam rotates it moves the slide and increases or decreases the
-  radius of the circle in which the crank pin I rotates. The disk M is
-  keyed on a hollow shaft surrounding the driving shaft P, to which the
-  cams are attached. The hollow shaft N has two snugs to which the
-  chains RR are attached (fig. 175). The shaft P carries the spring case
-  SS to which also are attached the other ends of the chains. When the
-  engine is at rest the springs extend themselves, rotating the hollow
-  shaft N and the frame M, so as to place the crank pin I at its nearest
-  position to the axis of rotation. When a resistance has to be
-  overcome, the shaft N rotates relatively to P, compressing the
-  springs, till their resistance balances the pressure due to the
-  resistance to the rotation of P. The engine then commences to work,
-  the crank pin being in the position in which the turning effort just
-  overcomes the resistance. If the resistance diminishes, the springs
-  force out the chains and shorten the stroke of the plungers, and vice
-  versa. The following experiments, on an engine of this kind working a
-  hoist, show how the automatic arrangement adjusted the water used to
-  the work done. The lift was 22 ft. and the water pressure in the
-  cylinders 80 lb. per sq. in.
-
-    Weight lifted,  Chain   427   633   745   857   969  1081  1193
-      in lb.         only
-
-    Water used, in  7(1/2)   10    14    16    17    20    21    22
-      gallons
-
-S 179. _Accumulator Machinery._--It has already been pointed out that it
-is in some cases convenient to use a steam engine to create an
-artificial head of water, which is afterwards employed in driving
-water-pressure machinery. Where power is required intermittently, for
-short periods, at a number of different points, as, for instance, in
-moving the cranes, lock gates, &c., of a dockyard, a separate steam
-engine and boiler at each point is very inconvenient; nor can engines
-worked from a common boiler be used, because of the great loss of heat
-and the difficulties which arise out of condensation in the pipes. If a
-tank, into which water is continuously pumped, can be placed at a great
-elevation, the water can then be used in hydraulic machinery in a very
-convenient way. Each hydraulic machine is put in communication with the
-tank by a pipe, and on opening a valve it commences work, using a
-quantity of water directly proportional to the work done. No attendance
-is required when the machine is not working.
-
-[Illustration: FIG. 176.]
-
-A site for such an elevated tank is, however, seldom available, and in
-place of it a beautiful arrangement termed an accumulator, invented by
-Lord Armstrong, is used. This consists of a tall vertical cylinder; into
-this works a solid ram through cup leathers or hemp packing, and the ram
-is loaded by fixed weights, so that the pressure in the cylinder is 700
-lb. or 800 lb. per sq. in. In some cases the ram is fixed and the
-cylinder moves on it. The pumping engines which supply the energy that
-is stored in the accumulator should be a pair coupled at right angles,
-so as to start in any position. The engines pump into the accumulator
-cylinder till the ram is at the top of its stroke, when by a catch
-arrangement acting on the engine throttle valve the engines are stopped.
-If the accumulator ram descends, in consequence of water being taken to
-work machinery, the engines immediately recommence working. Pipes lead
-from the accumulator to each of the machines requiring to be driven, and
-do not require to be of large size, as the pressure is so great.
-
-  Fig. 176 shows a diagrammatic way the scheme of a system of
-  accumulator machinery. A is the accumulator, with its ram carrying a
-  cylindrical wrought-iron tank W, in which weights are placed to load
-  the accumulator. At R is one of the pressure engines or jiggers,
-  worked from the accumulator, discharging the water after use into the
-  tank T. In this case the pressure engine is shown working a set of
-  blocks, the fixed block being on the ram cylinder, the running block
-  on the ram. The chain running over these blocks works a lift cage C,
-  the speed of which is as many times greater than that of the ram as
-  there are plies of chain on the block tackle. B is the balance weight
-  of the cage.
-
-  [Illustration: FIG. 177.]
-
-  In the use of accumulators on shipboard for working gun gear or
-  steering gear, the accumulator ram is loaded by springs, or by steam
-  pressure acting on a piston much larger than the ram.
-
-  R. H. Tweddell has used accumulators with a pressure of 2000 lb. per
-  sq. in. to work hydraulic riveting machinery.
-
-  The amount of energy stored in the accumulator, having a ram d in. in
-  diameter, a stroke of S ft., and delivering at p lb. pressure per sq.
-  in., is
-
-    [pi]
-    ---- p d^2S foot-pounds.
-     4
-
-  Thus, if the ram is 9 in., the stroke 20 ft., and the pressure 800 lb.
-  per sq. in., the work stored in the accumulator when the ram is at the
-  top of the stroke is 1,017,600 foot-pounds, that is, enough to drive a
-  machine requiring one horse power for about half an hour. As, however,
-  the pumping engine replaces water as soon as it is drawn off, the
-  working capacity of the accumulator is very much greater than this.
-  Tweddell found that an accumulator charged at 1250 lb. discharged at
-  1225 lb. per sq. in. Hence the friction was equivalent to 12(1/2) lb.
-  per sq. in. and the efficiency 98%.
-
-  When a very great pressure is required a differential accumulator
-  (fig. 177) is convenient. The ram is fixed and passes through both
-  ends of the cylinder, but is of different diameters at the two ends, A
-  and B. Hence if d1, d2 are the diameters of the ram in inches and p
-  the required pressure in lb. per sq. in., the load required is
-  (1/4)p[pi](d1^2 - d2^2). An accumulator of this kind used with
-  riveting machines has d1 = 5(1/2) in., d2 = 4(3/4) in. The pressure is
-  2000 lb. per sq. in. and the load 5.4 tons.
-
-  [Illustration: FIG. 178.]
-
-  Sometimes an accumulator is loaded by water or steam pressure instead
-  of by a dead weight. Fig. 178 shows the arrangement. A piston A is
-  connected to a plunger B of much smaller area. Water pressure, say
-  from town mains, is admitted below A, and the high pressure water is
-  pumped into and discharged from the cylinder C in which B works. If r
-  is the ratio of the areas of A and B, then, neglecting friction, the
-  pressure in the upper cylinder is r times that under the piston A.
-  With a variable rate of supply and demand from the upper cylinder, the
-  piston A rises and falls, maintaining always a constant pressure in
-  the upper cylinder.
-
-
-_Water Wheels._
-
-S 180. _Overshot and High Breast Wheels._--When a water fall ranges
-between 10 and 70 ft. and the water supply is from 3 to 25 cub. ft. per
-second, it is possible to construct a bucket wheel on which the water
-acts chiefly by its weight. If the variation of the head-water level
-does not exceed 2 ft., an overshot wheel may be used (fig. 179). The
-water is then projected over the summit of the wheel, and falls in a
-parabolic path into the buckets. With greater variation of head-water
-level, a pitch-back or high breast wheel is better. The water falls over
-the top of a sliding sluice into the wheel, on the same side as the head
-race channel. By adjusting the height of the sluice, the requisite
-supply is given to the wheel in all positions of the head-water level.
-
-  The wheel consists of a cast-iron or wrought-iron axle C supporting
-  the weight of the wheel. To this are attached two  sets of arms A of
-  wood or iron, which support circular segmental plates, B, termed
-  shrouds. A cylindrical sole plate dd extends between the shrouds on
-  the inner side. The buckets are formed by wood planks or curved
-  wrought-iron plates extending from shroud to shroud, the back of the
-  buckets being formed by the sole plate.
-
-[Illustration: FIG. 179.]
-
-  The efficiency may be taken at 0.75. Hence, if h.p. is the effective
-  horse power, H the available fall, and Q the available water supply
-  per second,
-
-    h.p. = 0.75 (GQH/550) = 0.085 QH.
-
-  If the peripheral velocity of the water wheel is too great, water is
-  thrown out of the buckets before reaching the bottom of the fall. In
-  practice, the circumferential velocity of water wheels of the kind now
-  described is from 4(1/2) to 10 ft. per second, about 6 ft. being the
-  usual velocity of good iron wheels not of very small size. In order
-  that the water may enter the buckets easily, it must have a greater
-  velocity than the wheel. Usually the velocity of the water at the
-  point where it enters the wheel is from 9 to 12 ft. per second, and to
-  produce this it must enter the wheel at a point 16 to 27 in. below the
-  head-water level. Hence the diameter of an overshot wheel may be
-
-    D = H - 1(1/3) to H - 2(1/4) ft.
-
-  Overshot and high breast wheels work badly in backwater, and hence if
-  the tail-water level varies, it is better to reduce the diameter of
-  the wheel so that its greatest immersion in flood is not more than 1
-  ft. The depth d of the shrouds is about 10 to 16 in. The number of
-  buckets may be about
-
-    N = [pi]D/d.
-
-  Let v be the peripheral velocity of the wheel. Then the capacity of
-  that portion of the wheel which passes the sluice in one second is
-
-    Q1 = vb(Dd - d^2)/D
-       = v b d nearly,
-
-  b being the breadth of the wheel between the shrouds. If, however,
-  this quantity of water were allowed to pass on to the wheel the
-  buckets would begin to spill their contents almost at the top of the
-  fall. To diminish the loss from spilling, it is not only necessary to
-  give the buckets a suitable form, but to restrict the water supply to
-  one-fourth or one-third of the gross bucket capacity. Let m be the
-  value of this ratio; then, Q being the supply of water per second,
-
-    Q = mQ1 = mb dv.
-
-  This gives the breadth of the wheel if the water supply is known. The
-  form of the buckets should be determined thus. The outer element of
-  the bucket should be in the direction of motion of the water entering
-  relatively to the wheel, so that the water may enter without splashing
-  or shock. The buckets should retain the water as long as possible, and
-  the width of opening of the buckets should be 2 or 3 in. greater than
-  the thickness of the sheet of water entering.
-
-  For a wooden bucket (fig. 180, A), take ab = distance between two
-  buckets on periphery of wheel. Make ed = 1/2 eb and bc = 6/5 to 5/4
-  ab. Join cd. For an iron bucket (fig. 180, B), take ed = 1/3 eb; bc =
-  6/5 ab. Draw cO making an angle of 10 deg. to 15 deg. with the radius
-  at c. On Oc take a centre giving a circular arc passing near d, and
-  round the curve into the radial part of the bucket de.
-
-[Illustration: FIG. 180.]
-
-There are two ways in which the power of a water wheel is given off to
-the machinery driven. In wooden wheels and wheels with rigid arms, a
-spur or bevil wheel keyed on the axle of the turbine will transmit the
-power to the shafting. It is obvious that the whole turning moment due
-to the weight of the water is then transmitted through the arms and axle
-of the water wheel. When the water wheel is an iron one, it usually has
-light iron suspension arms incapable of resisting the bending action due
-to the transmission of the turning effort to the axle. In that case spur
-segments are bolted to one of the shrouds, and the pinion to which the
-power is transmitted is placed so that the teeth in gear are, as nearly
-as may be, on the line of action of the resultant of the weight of the
-water in the loaded arc of the wheel.
-
-The largest high breast wheels ever constructed were probably the four
-wheels, each 50 ft. in diameter, and of 125 h.p., erected by Sir W.
-Fairbairn in 1825 at Catrine in Ayrshire. These wheels are still
-working.
-
-[Illustration: FIG. 181.]
-
-S 181. _Poncelet Water Wheel._--When the fall does not exceed 6 ft., the
-best water motor to adopt in many cases is the Poncelet undershot water
-wheel. In this the water acts very nearly in the same way as in a
-turbine, and the Poncelet wheel, although slightly less efficient than
-the best turbines, in normal conditions of working, is superior to most
-of them when working with a reduced supply of water. A general notion of
-the action of the water on a Poncelet wheel has already been given in S
-159. Fig. 181 shows its construction. The water penned back between the
-side walls of the wheel pit is allowed to flow to the wheel under a
-movable sluice, at a velocity nearly equal to the velocity due to the
-whole fall. The water is guided down a slope of 1 in 10, or a curved
-race, and enters the wheel without shock. Gliding up the curved floats
-it comes to rest, falls back, and acquires at the point of discharge a
-backward velocity relative to the wheel nearly equal to the forward
-velocity of the wheel. Consequently it leaves the wheel deprived of
-nearly the whole of its original kinetic energy.
-
-  Taking the efficiency at 0.60, and putting H for the available fall,
-  h.p. for the horse-power, and Q for the water supply per second,
-
-    h.p. = 0.068 QH.
-
-  The diameter D of the wheel may be taken arbitrarily. It should not be
-  less than twice the fall and is more often four times the fall. For
-  ordinary cases the smallest convenient diameter is 14 ft. with a
-  straight, or 10 ft. with a curved, approach channel. The radial depth
-  of bucket should be at least half the fall, and radius of curvature of
-  buckets about half the radius of the wheel. The shrouds are usually of
-  cast iron with flanges to receive the buckets. The buckets may be of
-  iron 1/8 in. thick bolted to the flanges with 5/16 in. bolts.
-
-  Let H' be the fall measured from the free surface of the head-water to
-  the point F where the mean layer enters the wheel; then the velocity
-  at which the water enters is v = [root](2gH'), and the best
-  circumferential velocity of the wheel is V = 0.55f to 0.6v. The number
-  of rotations of the wheel per second is N = V/[pi]D. The thickness
-  of the sheet of water entering the wheel is very important. The best
-  thickness according to experiment is 8 to 10 in. The maximum thickness
-  should not exceed 12 to 15 in., when there is a surplus water supply.
-  Let e be the thickness of the sheet of water entering the wheel, and b
-  its width; then
-
-    bev = Q; or b = Q/ev.
-
-  Grashof takes e = (1/6)H, and then
-
-    b = 6Q/H [root](2gH).
-
-  Allowing for the contraction of the stream, the area of opening
-  through the sluice may be 1.25 be to 1.3 be. The inside width of the
-  wheel is made about 4 in. greater than b.
-
-  Several constructions have been given for the floats of Poncelet
-  wheels. One of the simplest is that shown in figs. 181, 182.
-
-  Let OA (fig. 181) be the vertical radius of the wheel. Set off OB, OD
-  making angles of 15 deg. with OA. Then BD may be the length of the
-  close breasting fitted to the wheel. Draw the bottom of the head face
-  BC at a slope of 1 in 10. Parallel to this, at distances (1/2)e and e,
-  draw EF and GH. Then EF is the mean layer and GH the surface layer
-  entering the wheel. Join OF, and make OFK = 23 deg. Take FK = 0.5 to
-  0.7 H. Then K is the centre from which the bucket curve is struck and
-  KF is the radius. The depth of the shrouds must be sufficient to
-  prevent the water from rising over the top of the float. It is (1/2)H
-  to 2/3 H. The number of buckets is not very important. They are
-  usually 1 ft. apart on the circumference of the wheel.
-
-  The efficiency of a Poncelet wheel has been found in experiments to
-  reach 0.68. It is better to take it at 0.6 in estimating the power of
-  the wheel, so as to allow some margin.
-
-  [Illustration: FIG. 182.]
-
-  In fig. 182 v_i is the initial and v_o the final velocity of the
-  water, v_r parallel to the vane the relative velocity of the water and
-  wheel, and V the velocity of the wheel.
-
-
-_Turbines._
-
-S 182. The name turbine was originally given in France to any water
-motor which revolved in a horizontal plane, the axis being vertical. The
-rapid development of this class of motors dates from 1827, when a prize
-was offered by the Societe d'Encouragement for a motor of this kind,
-which should be an improvement on certain wheels then in use. The prize
-was ultimately awarded to Benoit Fourneyron (1802-1867), whose turbine,
-but little modified, is still constructed.
-
-_Classification of Turbines._--In some turbines the whole available
-energy of the water is converted into kinetic energy before the water
-acts on the moving part of the turbine. Such turbines are termed
-_Impulse or Action Turbines_, and they are distinguished by this that
-the wheel passages are never entirely filled by the water. To ensure
-this condition they must be placed a little above the tail water and
-discharge into free air. Turbines in which part only of the available
-energy is converted into kinetic energy before the water enters the
-wheel are termed _Pressure or Reaction Turbines_. In these there is a
-pressure which in some cases amounts to half the head in the clearance
-space between the guide vanes and wheel vanes. The velocity with which
-the water enters the wheel is due to the difference between the pressure
-due to the head and the pressure in the clearance space. In pressure
-turbines the wheel passages must be continuously filled with water for
-good efficiency, and the wheel may be and generally is placed below the
-tail water level.
-
-Some turbines are designed to act normally as impulse turbines
-discharging above the tail water level. But the passages are so designed
-that they are just filled by the water. If the tail water rises and
-drowns the turbine they become pressure turbines with a small clearance
-pressure, but the efficiency is not much affected. Such turbines are
-termed _Limit turbines_.
-
-Next there is a difference of constructive arrangement of turbines,
-which does not very essentially alter the mode of action of the water.
-In axial flow or so-called parallel flow turbines, the water enters and
-leaves the turbine in a direction parallel to the axis of rotation, and
-the paths of the molecules lie on cylindrical surfaces concentric with
-that axis. In radial outward and inward flow turbines, the water enters
-and leaves the turbine in directions normal to the axis of rotation, and
-the paths of the molecules lie exactly or nearly in planes normal to the
-axis of rotation. In outward flow turbines the general direction of flow
-is away from the axis, and in inward flow turbines towards the axis.
-There are also mixed flow turbines in which the water enters normally
-and is discharged parallel to the axis of rotation.
-
-Another difference of construction is this, that the water may be
-admitted equally to every part of the circumference of the turbine wheel
-or to a portion of the circumference only. In the former case, the
-condition of the wheel passages is always the same; they receive water
-equally in all positions during rotation. In the latter case, they
-receive water during a part of the rotation only. The former may be
-termed turbines with complete admission, the latter turbines with
-partial admission. A reaction turbine should always have complete
-admission. An impulse turbine may have complete or partial admission.
-
-When two turbine wheels similarly constructed are placed on the same
-axis, in order to balance the pressures and diminish journal friction,
-the arrangement may be termed a twin turbine.
-
-If the water, having acted on one turbine wheel, is then passed through
-a second on the same axis, the arrangement may be termed a compound
-turbine. The object of such an arrangement would be to diminish the
-speed of rotation.
-
-Many forms of reaction turbine may be placed at any height not exceeding
-30 ft. above the tail water. They then discharge into an air-tight
-suction pipe. The weight of the column of water in this pipe balances
-part of the atmospheric pressure, and the difference of pressure,
-producing the flow through the turbine, is the same as if the turbine
-were placed at the bottom of the fall.
-
-         I. Impulse Turbines.         |       II. Reaction Turbines.
-                                      |
-    (Wheel passages not filled, and   |  (Wheel passages filled, discha-
-      discharging above the tail      |    rging above or below the tail
-      water.)                         |    water or into a suction-pipe.)
-    (a) Complete admission. (Rare.)   |  Always with complete admission.
-    (b) Partial admission. (Usual.)   |
-    \_________________________________\/_______________________________/
-             Axial flow, outward flow, inward flow, or mixed flow.
-    \_________________________________\/_______________________________/
-               Simple turbines; twin turbines; compound turbines.
-
-  S 183. _The Simple Reaction Wheel._--It has been shown, in S 162,
-  that, when water issues from a vessel, there is a reaction on the
-  vessel tending to cause motion in a direction opposite to that of the
-  jet. This principle was applied in a rotating water motor at a very
-  early period, and the Scotch turbine, at one time much used, differs
-  in no essential respect from the older form of reaction wheel.
-
-  [Illustration: FIG. 183.]
-
-  The old reaction wheel consisted of a vertical pipe balanced on a
-  vertical axis, and supplied with water (fig. 183). From the bottom of
-  the vertical pipe two or more hollow horizontal arms extended, at the
-  ends of which were orifices from which the water was discharged. The
-  reaction of the jets caused the rotation of the machine.
-
-  Let H be the available fall measured from the level of the water in
-  the vertical pipe to the centres cf the orifices, r the radius from
-  the axis of rotation to the centres of the orifices, v the velocity of
-  discharge through the jets, [alpha] the angular velocity of the
-  machine. When the machine is at rest the water issues from the
-  orifices with the velocity [root](2gH) (friction being neglected). But
-  when the machine rotates the water in the arms rotates also, and is in
-  the condition of a forced vortex, all the particles having the same
-  angular velocity. Consequently the pressure in the arms at the
-  orifices is H + [alpha]^2r^2/2g ft. of water, and the velocity of
-  discharge through the orifices is v = [root](2gH + [alpha]^2r^2). If the
-  total area of the orifices is [omega], the quantity discharged from
-  the wheel per second is
-
-    Q = [omega]v = [omega] [root](2gH + [alpha]^2r^2).
-
-  While the water passes through the orifices with the velocity v, the
-  orifices are moving in the opposite direction with the velocity
-  [alpha]r. The absolute velocity of the water is therefore
-
-    v - [alpha]r = [root](2gH + [alpha]^2r^2) - [alpha]r.
-
-  The momentum generated per second is (GQ/g)(v - [alpha]r), which is
-  numerically equal to the force driving the motor at the radius r. The
-  work done by the water in rotating the wheel is therefore
-
-    (GQ/g) (v - [alpha]r) ar foot-pounds per sec.
-
-  The work expended by the water fall is GQH foot-pounds per second.
-  Consequently the efficiency of the motor is
-
-            (v - [alpha]r) [alpha]r   {[root]{2gH + [alpha]^2r^2]} - [alpha]r} [alpha]r
-    [eta] = ----------------------- = -------------------------------------------------.
-                      gH                                     gH
-
-  Let
-
-                                               gH         g^2H^2
-    [root]{2gH + [alpha]^2r^2} = [alpha]r + -------- - ------------- ...
-                                            [alpha]r   2[alpha]^3r^3
-
-  then
-
-    [eta] = 1 - gH/2[alpha]r + ...
-
-  which increases towards the limit 1 as [alpha]r increases towards
-  infinity. Neglecting friction, therefore, the maximum efficiency is
-  reached when the wheel has an infinitely great velocity of rotation.
-  But this condition is impracticable to realize, and even, at
-  practicable but high velocities of rotation, the friction would
-  considerably reduce the efficiency. Experiment seems to show that the
-  best efficiency is reached when [alpha]r = [root](2gH). Then the
-  efficiency apart from friction is
-
-    [eta] = {[root](2[alpha]^2r^2) - [alpha]r} [alpha]r/gH
-          = 0.414 [alpha]^2r^2/gH = 0.828,
-
-  about 17% of the energy of the fall being carried away by the water
-  discharged. The actual efficiency realized appears to be about 60%, so
-  that about 21% of the energy of the fall is lost in friction, in
-  addition to the energy carried away by the water.
-
-  S 184. _General Statement of Hydrodynamical Principles necessary for
-  the Theory of Turbines._
-
-  (a) When water flows through any pipe-shaped passage, such as the
-  passage between the vanes of a turbine wheel, the relation between the
-  changes of pressure and velocity is given by Bernoulli's theorem (S
-  29). Suppose that, at a section A of such a passage, h1 is the
-  pressure measured in feet of water, v1 the velocity, and z1 the
-  elevation above any horizontal datum plane, and that at a section B
-  the same quantities are denoted by h2, v2, z2. Then
-
-    h1 - h2 = (v2^2 - v1^2)/2g + z2 - z1.   (1)
-
-  If the flow is horizontal, z2 = z1; and
-
-    h1 - h2 = (v2^2 - v1^2)/2g.   (la)
-
-  (b) When there is an abrupt change of section of the passage, or an
-  abrupt change of section of the stream due to a contraction, then, in
-  applying Bernoulli's equation allowance must be made for the loss of
-  head in shock (S 36). Let v1, v2 be the velocities before and after
-  the abrupt change, then a stream of velocity v1 impinges on a stream
-  at a velocity v2, and the relative velocity is v1 - v2. The head lost
-  is (v1 - v2)^2/2g. Then equation (1a) becomes
-
-    h1 - h2 = (v1^2 - v2^2)/2g - (v1 - v2)^2/2g = v2(v1 - v2)/g   (2)
-
-  [Illustration: FIG. 184.]
-
-  To diminish as much as possible the loss of energy from irregular
-  eddying motions, the change of section in the turbine passages must be
-  very gradual, and the curvature without discontinuity.
-
-  (c) _Equality of Angular Impulse and Change of Angular
-  Momentum._--Suppose that a couple, the moment of which is M, acts on a
-  body of weight W for t seconds, during which it moves from A1 to A2
-  (fig. 184). Let v1 be the velocity of the body at A1, v2 its velocity
-  at A2, and let p1, p2 be the perpendiculars from C on v1 and v2. Then
-  Mt is termed the angular impulse of the couple, and the quantity
-
-    (W/g)(v2p2 - v1p1)
-
-  is the change of angular momentum relatively to C. Then, from the
-  equality of angular impulse and change of angular momentum
-
-    Mt = (W/g)(v2p2 - v1p1),
-
-  or, if the change of momentum is estimated for one second,
-
-    M = (W/g)(v2p2 - v1p1).
-
-  Let r1, r2 be the radii drawn from C to A1, A2, and let w1, w2 be the
-  components of v1, v2, perpendicular to these radii, making angles
-  [beta] and [alpha] with v1, v2. Then
-
-    v1 = w1 sec [beta]; v2 = w2 sec [alpha]
-
-    p1 = r1 cos [beta]; p2 = r2 cos [alpha],
-
-    .: M = (W/g) (w2r2 - w1r1),   (3)
-
-  where the moment of the couple is expressed in terms of the radii
-  drawn to the positions of the body at the beginning and end of a
-  second, and the tangential components of its velocity at those points.
-
-  Now the water flowing through a turbine enters at the admission
-  surface and leaves at the discharge surface of the wheel, with its
-  angular momentum relatively to the axis of the wheel changed. It
-  therefore exerts a couple -M tending to rotate the wheel, equal and
-  opposite to the couple M which the wheel exerts on the water. Let Q
-  cub. ft. enter and leave the wheel per second, and let w1, w2 be the
-  tangential components of the velocity of the water at the receiving
-  and discharging surfaces of the wheel, r1, r2 the radii of those
-  surfaces. By the principle above,
-
-    -M = (GQ/g)(w2r2 - w1r1).   (4)
-
-  If [alpha] is the angular velocity of the wheel, the work done by the
-  water on the wheel is
-
-    T = Ma = (GQ/g)(w1r1 - w2r2) [alpha] foot-pounds per second.   (5)
-
-  S 185. _Total and Available Fall._--Let H_t be the total difference of
-  level from the head-water to the tail-water surface. Of this total
-  head a portion is expended in overcoming the resistances of the head
-  race, tail race, supply pipe, or other channel conveying the water.
-  Let [h]_p be that loss of head, which varies with the local
-  conditions in which the turbine is placed. Then
-
-    H = H_t - [h]_p
-
-  is the available head for working the turbine, and on this the
-  calculations for the turbine should be based. In some cases it is
-  necessary to place the turbine above the tail-water level, and there
-  is then a fall [h] from the centre of the outlet surface of
-  the turbine to the tail-water level which is wasted, but which is
-  properly one of the losses belonging to the turbine itself. In that
-  case the velocities of the water in the turbine should be calculated
-  for a head H - [h], but the efficiency of the turbine for the
-  head H.
-
-  S 186. _Gross Efficiency and Hydraulic Efficiency of a Turbine._--Let
-  T_d be the useful work done by the turbine, in foot-pounds per second,
-  T_t the work expended in friction of the turbine shaft, gearing, &c.,
-  a quantity which varies with the local conditions in which the turbine
-  is placed. Then the effective work done by the water in the turbine is
-
-    T = T_d + T_t.
-
-  The gross efficiency of the whole arrangement of turbine, races, and
-  transmissive machinery is
-
-    [eta]_t = T_d/CQH_t.   (6)
-
-  And the hydraulic efficiency of the turbine alone is
-
-    [eta] = T/GQH.   (7)
-
-  It is this last efficiency only with which the theory of turbines is
-  concerned.
-
-  From equations (5) and (7) we get
-
-    [eta]GQH = (GQ/g)(w1r1 - w2r2)a;
-
-    [eta] = (w1r1 - w2r2)a/gH.   (8)
-
-  This is the fundamental equation in the theory of turbines. In
-  general,[7] w1 and w2, the tangential components of the water's motion
-  on entering and leaving the wheel, are completely independent. That
-  the efficiency may be as great as possible, it is obviously necessary
-  that w2 = 0. In that case
-
-    [eta] = w1r1a/gH.   (9)
-
-  ar1 is the circumferential velocity of the wheel at the inlet surface.
-  Calling this V1, the equation becomes
-
-    [eta] = w1V1/gH.   (9a)
-
-  This remarkably simple equation is the fundamental equation in the
-  theory of turbines. It was first given by Reiche (_Turbinenbaues_,
-  1877).
-
-[Illustration: FIG. 185.]
-
-[Illustration: FIG. 186.]
-
-[Illustration: FIG. 187.]
-
-[Illustration: FIG. 188.]
-
-[Illustration: FIG. 189.]
-
-S 187. _General Description of a Reaction Turbine._--Professor James
-Thomson's inward flow or vortex turbine has been selected as the type of
-reaction turbines. It is one of the best in normal conditions of
-working, and the mode of regulation introduced is decidedly superior to
-that in most reaction turbines. Figs. 185 and 186 are external views of
-the turbine case; figs. 187 and 188 are the corresponding sections; fig.
-189 is the turbine wheel. The example chosen for illustration has
-suction pipes, which permit the turbine to be placed above the
-tail-water level. The water enters the turbine by cast-iron supply pipes
-at A, and is discharged through two suction pipes S, S. The water on
-entering the case distributes itself through a rectangular supply
-chamber SC, from which it finds its way equally to the four guide-blade
-passages G, G, G, G. In these passages it acquires a velocity about
-equal to that due to half the fall, and is directed into the wheel at an
-angle of about 10 deg. or 12 deg. with the tangent to its circumference.
-The wheel W receives the water in equal proportions from each
-guide-blade passage. It consists of a centre plate p (fig. 189) keyed on
-the shaft aa, which passes through stuffing boxes on the suction pipes.
-On each side of the centre plate are the curved wheel vanes, on which
-the pressure of the water acts, and the vanes are bounded on each side
-by dished or conical cover plates c, c. Joint-rings j, j on the cover
-plates make a sufficiently water-tight joint with the casing, to
-prevent leakage from the guide-blade chamber into the suction pipes. The
-pressure near the joint rings is not very great, probably not one-fourth
-the total head. The wheel vanes receive the water without shock, and
-deliver it into central spaces, from which it flows on either side to
-the suction pipes. The mode of regulating the power of the turbine is
-very simple. The guide-blades are pivoted to the case at their inner
-ends, and they are connected by a link-work, so that they all open and
-close simultaneously and equally. In this way the area of opening
-through the guide-blades is altered without materially altering the
-angle or the other conditions of the delivery into the wheel. The
-guide-blade gear may be variously arranged. In this example four
-spindles, passing through the case, are linked to the guide-blades
-inside the case, and connected together by the links l, l, l on the
-outside of the case. A worm wheel on one of the spindles is rotated by a
-worm d, the motion being thus slow enough to adjust the guide-blades
-very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal.
-
-[Illustration: FIG. 190.]
-
-  Fig. 190 shows another arrangement of a similar turbine, with some
-  adjuncts not shown in the other drawings. In this case the turbine
-  rotates horizontally, and the turbine case is placed entirely below
-  the tail water. The water is supplied to the turbine by a vertical
-  pipe, over which is a wooden pentrough, containing a strainer, which
-  prevents sticks and other solid bodies getting into the turbine. The
-  turbine rests on three foundation stones, and, the pivot for the
-  vertical shaft being under water, there is a screw and lever
-  arrangement for adjusting it as it wears. The vertical shaft gives
-  motion to the machinery driven by a pair of bevel wheels. On the right
-  are the worm and wheel for working the guide-blade gear.
-
-  [Illustration: FIG. 191.]
-
-  S 188. _Hydraulic Power at Niagara._--The largest development of
-  hydraulic power is that at Niagara. The Niagara Falls Power Company
-  have constructed two power houses on the United States side, the first
-  with 10 turbines of 5000 h.p. each, and the second with 10 turbines of
-  5500 h.p. The effective fall is 136 to 140 ft. In the first power
-  house the turbines are twin outward flow reaction turbines with
-  vertical shafts running at 250 revs. per minute and driving the
-  dynamos direct. In the second power house the turbines are inward flow
-  turbines with draft tubes or suction pipes. Fig. 191 shows a section
-  of one of these turbines. There is a balancing piston keyed on the
-  shaft, to the under side of which the pressure due to the fall is
-  admitted, so that the weight of turbine, vertical shaft and part of
-  the dynamo is water borne. About 70,000 h.p. is daily distributed
-  electrically from these two power houses. The Canadian Niagara Power
-  Company are erecting a power house to contain eleven units of 10,250
-  h.p. each, the turbines being twin inward flow reaction turbines. The
-  Electrical Development Company of Ontario are erecting a power house
-  to contain 11 units of 12,500 h.p. each. The Ontario Power Company are
-  carrying out another scheme for developing 200,000 h.p. by twin inward
-  flow turbines of 12,000 h.p. each. Lastly the Niagara Falls Power and
-  Manufacturing Company on the United States side have a station giving
-  35,000 h.p. and are constructing another to furnish 100,000 h.p. The
-  mean flow of the Niagara river is about 222,000 cub. ft. per second
-  with a fall of 160 ft. The works in progress if completed will utilize
-  650,000 h.p. and require 48,000 cub. ft. per second or 21(1/2)% of the
-  mean flow of the river (Unwin, "The Niagara Falls Power Stations,"
-  _Proc. Inst. Mech. Eng._, 1906).
-
-  [Illustration: FIG. 192.]
-
-  S 189. _Different Forms of Turbine Wheel._--The wheel of a turbine or
-  part of the machine on which the water acts is an annular space,
-  furnished with curved vanes dividing it into passages exactly or
-  roughly rectangular in cross section. For radial flow turbines the
-  wheel may have the form A or B, fig. 192, A being most usual with
-  inward, and B with outward flow turbines. In A the wheel vanes are
-  fixed on each side of a centre plate keyed on the turbine shaft. The
-  vanes are limited by slightly-coned annular cover plates. In B the
-  vanes are fixed on one side of a disk, keyed on the shaft, and limited
-  by a cover plate parallel to the disk. Parallel flow or axial flow
-  turbines have the wheel as in C. The vanes are limited by two
-  concentric cylinders.
-
-
-  _Theory of Reaction Turbines._
-
-  [Illustration: FIG. 193.]
-
-  S 190. _Velocity of Whirl and Velocity of Flow._--Let acb (fig. 193)
-  be the path of the particles of water in a turbine wheel. That path
-  will be in a plane normal to the axis of rotation in radial flow
-  turbines, and on a cylindrical surface in axial flow turbines. At any
-  point c of the path the water will have some velocity v, in the
-  direction of a tangent to the path. That velocity may be resolved into
-  two components, a whirling velocity w in the direction of the wheel's
-  rotation at the point c, and a component u at right angles to this,
-  radial in radial flow, and parallel to the axis in axial flow
-  turbines. This second component is termed the velocity of flow. Let
-  v_o, w_o, u_o be the velocity of the water, the whirling velocity and
-  velocity of flow at the outlet surface of the wheel, and v_i, w_i, u_i
-  the same quantities at the inlet surface of the wheel. Let [alpha] and
-  [beta] be the angles which the water's direction of motion makes with
-  the direction of motion of the wheel at those surfaces. Then
-
-    w_o = v_o cos [beta]; u_o = v_o sin [beta]
-
-    w_i = v_i cos [alpha]; u_i = v_i sin [alpha].   (10)
-
-  The velocities of flow are easily ascertained independently from the
-  dimensions of the wheel. The velocities of flow at the inlet and
-  outlet surfaces of the wheel are normal to those surfaces. Let
-  [Omega]_o, [Omega]_i be the areas of the outlet and inlet surfaces of
-  the wheel, and Q the volume of water passing through the wheel per
-  second; then
-
-    v_o = Q/[Omega]_o; v_i = Q/[Omega]_i.   (11)
-
-  Using the notation in fig. 191, we have, for an inward flow turbine
-  (neglecting the space occupied by the vanes),
-
-    [Omega]_o = 2[pi]r0d0; [Omega]_i = 2[pi]r_i d_i.   (12a)
-
-  Similarly, for an outward flow turbine,
-
-    [Omega]_o = 2[pi]r_o d; [Omega]_i = 2[pi]r_i d;   (12b)
-
-  and, for an axial flow turbine,
-
-    [Omega]_o = [Omega]_i = [pi](r2^2 - r1^2).   (12c)
-
-  [Illustration: FIG. 194.]
-
-  _Relative and Common Velocity of the Water and Wheel._--There is
-  another way of resolving the velocity of the water. Let V be the
-  velocity of the wheel at the point c, fig. 194. Then the velocity of
-  the water may be resolved into a component V, which the water has in
-  common with the wheel, and a component v_r, which is the velocity of
-  the water relatively to the wheel.
-
-  _Velocity of Flow._--It is obvious that the frictional losses of head
-  in the wheel passages will increase as the velocity of flow is
-  greater, that is, the smaller the wheel is made. But if the wheel
-  works under water, the skin friction of the wheel cover increases as
-  the diameter of the wheel is made greater, and in any case the weight
-  of the wheel and consequently the journal friction increase as the
-  wheel is made larger. It is therefore desirable to choose, for the
-  velocity of flow, as large a value as is consistent with the condition
-  that the frictional losses in the wheel passages are a small fraction
-  of the total head.
-
-  The values most commonly assumed in practice are these:--
-
-    In axial flow turbines,   u_o = u_i = 0.15 to 0.2 [root](2gH);
-
-    In outward flow turbines, u_i = 0.25 [root]2g(H - [h]),
-                              u_o = 0.21 to 0.17 [root]2g(H - [h]);
-
-    In inward flow turbines,  u_o = u_i = 0.125 [root](2gH).
-
-  S 191. _Speed of the Wheel._--The best speed of the wheel depends
-  partly on the frictional losses, which the ordinary theory of turbines
-  disregards. It is best, therefore, to assume for V_o and V_i values
-  which experiment has shown to be most advantageous.
-
-  In axial flow turbines, the circumferential velocities at the mean
-  radius of the wheel may be taken
-
-    V_o = V_i = 0.6 [root](2gH) to 0.66 [root](2gH).
-
-  In a radial outward flow turbine,
-
-    V_i = 0.56 [root]{2g(H - [h])}
-
-    V_o = V_i r_o/r_i,
-
-  where r_o, r_i are the radii of the outlet and inlet surfaces.
-
-  In a radial inward flow turbine,
-
-    V_i = 0.66 [root](2gH),
-
-    V_o = V_i r_o/r_i.
-
-  If the wheel were stationary and the water flowed through it, the
-  water would follow paths parallel to the wheel vane curves, at least
-  when the vanes were so close that irregular motion was prevented.
-  Similarly, when the wheel is in motion, the water follows paths
-  relatively to the wheel, which are curves parallel to the wheel vanes.
-  Hence the relative component, v_r, of the water's motion at c is
-  tangential to a wheel vane curve drawn through the point c. Let v_o,
-  V_o, v_(ro) be the velocity of the water and its common and relative
-  components at the outlet surface of the wheel, and v_i, V_i, v_(ri) be
-  the same quantities at the inlet surface; and let [theta] and [phi] be
-  the angles the wheel vanes make with the inlet and outlet surfaces;
-  then
-
-    v_o^2 = [root](v_(ro)^2 + V_o^2 - 2V_o v_(ro) cos [phi])
-
-    v_i = [root](v_(ri)^2 + V_o^2 - 2V_i v_(ri) cos [theta]),   (13)
-
-  equations which may be used to determine [phi] and [theta].
-
-  [Illustration: FIG. 195.]
-
-  S 192. _Condition determining the Angle of the Vanes at the Outlet
-  Surface of the Wheel._--It has been shown that, when the water leaves
-  the wheel, it should have no tangential velocity, if the efficiency is
-  to be as great as possible; that is, w_o = 0. Hence, from (10), cos
-  [beta] = 0, [beta] = 90 deg., U_o = V_o, and the direction of the
-  water's motion is normal to the outlet surface of the wheel, radial in
-  radial flow, and axial in axial flow turbines.
-
-  Drawing v_o or u_o radial or axial as the case may be, and V_o
-  tangential to the direction of motion, v_(ro) can be found by the
-  parallelogram of velocities. From fig. 195,
-
-    tan [phi] = v_o/V_o = u_o/V_o;   (14)
-
-  but [phi] is the angle which the wheel vane makes with the outlet
-  surface of the wheel, which is thus determined when the velocity of
-  flow u_o and velocity of the wheel V_o are known. When [phi] is thus
-  determined,
-
-    v_(ro) = U_o cosec [phi] = V_o [root](1 + u_o^2/V_o^2).   (14a)
-
-  _Correction of the Angle [phi] to allow for Thickness of Vanes._--In
-  determining [phi], it is most convenient to calculate its value
-  approximately at first, from a value of u_o obtained by neglecting the
-  thickness of the vanes. As, however, this angle is the most important
-  angle in the turbine, the value should be afterwards corrected to
-  allow for the vane thickness.
-
-  Let
-
-    [phi]' = tan^(-1)(u_o/V_o) = tan^(-1)(Q/[Omega]_o V_o)
-
-  be the first or approximate value of [phi], and let t be the
-  thickness, and n the number of wheel vanes which reach the outlet
-  surface of the wheel. As the vanes cut the outlet surface
-  approximately at the angle [phi]', their width measured on that
-  surface is t cosec [phi]'. Hence the space occupied by the vanes on
-  the outlet surface is
-
-  For
-
-    A, fig. 192, ntd_o cosec [phi]
-    B, fig. 192, ntd cosec [phi]           (15)
-    C, fig. 192, nt(r2 - r1) cosec [phi].
-
-  Call this area occupied by the vanes [omega]. Then the true value of
-  the clear discharging outlet of the wheel is [Omega]_o - [omega], and
-  the true value of u_o is Q/([Omega]_o - [omega]). The corrected value
-  of the angle of the vanes will be
-
-    [phi] = tan [Q/V_o ([Omega]_o - [omega]) ].   (16)
-
-  S 193. _Head producing Velocity with which the Water enters the
-  Wheel._--Consider the variation of pressure in a wheel passage, which
-  satisfies the condition that the sections change so gradually that
-  there is no loss of head in shock. When the flow is in a horizontal
-  plane, there is no work done by gravity on the water passing through
-  the wheel. In the case of an axial flow turbine, in which the flow is
-  vertical, the fall d between the inlet and outlet surfaces should be
-  taken into account.
-
-  Let
-
-     V_i, V_o be the velocities of the wheel at the inlet and outlet
-                surfaces,
-     v_i, v_o the velocities of the water,
-     u_i, u_o the velocities of flow,
-     v_(ri), v_(ro) the relative velocities,
-     h_i, h_o the pressures, measured in feet of water,
-     r_i, r_o the radii of the wheel,
-      [alpha] the angular velocity of the wheel.
-
-  At any point in the path of a portion of water, at radius r, the
-  velocity v of the water may be resolved into a component V = [alpha]r
-  equal to the velocity at that point of the wheel, and a relative
-  component v_r. Hence the motion of the water may be considered to
-  consist of two parts:--(a) a motion identical with that in a forced
-  vortex of constant angular velocity [alpha]; (b) a flow along curves
-  parallel to the wheel vane curves. Taking the latter first, and using
-  Bernoulli's theorem, the change of pressure due to flow through the
-  wheel passages is given by the equation
-
-    h'_i + v_(ri)^2/2g = h'_o + v_(ro)^2/2g;
-
-    h'_i - h'_o = (v_(ro)^2 - v_(ri)^2)/2g.
-
-  The variation of pressure due to rotation in a forced vortex is
-
-    h"_i - h"_o = (V_i^2 - V_o^2)/2g.
-
-  Consequently the whole difference of pressure at the inlet and outlet
-  surfaces of the wheel is
-
-    h_i - h_o = h'_i + h"_i - h'_o - h"_o
-       = (V_i^2 - V_o^2)/2g + (v_(ro)^2 - v_(ri)^2)/2g.   (17)
-
-  _Case 1. Axial Flow Turbines._--V_i = V_o; and the first term on the
-  right, in equation 17, disappears. Adding, however, the work of
-  gravity due to a fall of d ft. in passing through the wheel,
-
-    h_i - h_o = (v_(ro)^2 - v_(ri)^2)/2g - d.   (17a)
-
-  _Case 2. Outward Flow Turbines._--The inlet radius is less than the
-  outlet radius, and (V_i^2 - V_o^2)/2g is negative. The centrifugal
-  head diminishes the pressure at the inlet surface, and increases the
-  velocity with which the water enters the wheel. This somewhat
-  increases the frictional loss of head. Further, if the wheel varies in
-  velocity from variations in the useful work done, the quantity (V_i^2
-  - V_o^2)/2g increases when the turbine speed increases, and vice
-  versa. Consequently the flow into the turbine increases when the speed
-  increases, and diminishes when the speed diminishes, and this again
-  augments the variation of speed. The action of the centrifugal head in
-  an outward flow turbine is therefore prejudicial to steadiness of
-  motion. For this reason r_o : r_i is made small, generally about 5 :
-  4. Even then a governor is sometimes required to regulate the speed of
-  the turbine.
-
-  _Case 3. Inward Flow Turbines._--The inlet radius is greater than
-  the outlet radius, and the centrifugal head diminishes the velocity of
-  flow into the turbine. This tends to diminish the frictional losses,
-  but it has a more important influence in securing steadiness of
-  motion. Any increase of speed diminishes the flow into the turbine,
-  and vice versa. Hence the variation of speed is less than the
-  variation of resistance overcome. In the so-called centre vent wheels
-  in America, the ratio r_i : r_o is about 5 : 4, and then the influence
-  of the centrifugal head is not very important. Professor James Thomson
-  first pointed out the advantage of a much greater difference of radii.
-  By making r_i : r_o = 2 : 1, the centrifugal head balances about half
-  the head in the supply chamber. Then the velocity through the
-  guide-blades does not exceed the velocity due to half the fall, and
-  the action of the centrifugal head in securing steadiness of speed is
-  considerable.
-
-  Since the total head producing flow through the turbine is H -
-  [h], of this h_i - h_o is expended in overcoming the pressure
-  in the wheel, the velocity of flow into the wheel is
-
-    v_i = c_v[root]{2g(H - [h] - (V_i^2 - V_o^2/2g + (v{r0}^2 - v_(ri)^2)/2g)},   (18)
-
-  where c_v may be taken 0.96.
-
-  From (14a),
-
-    v{r0} = V_o [root](1 + u_o^2/V_o^2).
-
-  It will be shown immediately that
-
-    v_(ri) = u_i cosec [theta];
-
-  or, as this is only a small term, and [theta] is on the average 90
-  deg., we may take, for the present purpose, v_(ri) = u_i nearly.
-
-  Inserting these values, and remembering that for an axial flow turbine
-  V_i = V_o, [h] = 0, and the fall d in the wheel is to be
-  added,
-                     _                                          _
-                    |     /    V_i^2 /    u_o^2 \    u_i^2    \  |
-    v_i = c_v[root] | 2g ( H - ---- ( 1 + -----  ) + ----- - d ) |.
-                    |_    \     2g   \    V_o^2 /     2g      / _|
-
-  For an outward flow turbine,
-                     _                                             _
-                    |     /          V_i^2 /    u_o^2 \    u_i^2 \  |
-    v_i = c_v[root] | 2g ( H - [h] - ---- ( 1 + -----  ) + -----  ) |.
-                    |_    \           2g   \    V_i^2 /     2g   / _|
-
-  For an inward flow turbine,
-                     _                                       _
-                    |    {     V_i^2 /    u_o^2 \    u_i^2 }  |
-    v_i = c_v[root] | 2g { H - ---- ( 1 + -----  ) + ----- }  |.
-                    |_   {      2g   \    V_i^2 /     2g   } _|
-
-  S 194. _Angle which the Guide-Blades make with the Circumference of
-  the Wheel._--At the moment the water enters the wheel, the radial
-  component of the velocity is u_i, and the velocity is v_i. Hence, if
-  [gamma] is the angle between the guide-blades and a tangent to the
-  wheel
-
-    [gamma] = sin^(-1) (u_i/v_i).
-
-  This angle can, if necessary, be corrected to allow for the thickness
-  of the guide-blades.
-
-  [Illustration: FIG. 196.]
-
-  S 195. _Condition determining the Angle of the Vanes at the Inlet
-  Surface of the Wheel._--The single condition necessary to be satisfied
-  at the inlet surface of the wheel is that the water should enter the
-  wheel without shock. This condition is satisfied if the direction of
-  relative motion of the water and wheel is parallel to the first
-  element of the wheel vanes.
-
-  Let A (fig. 196) be a point on the inlet surface of the wheel, and let
-  v_i represent in magnitude and direction the velocity of the water
-  entering the wheel, and V_i the velocity of the wheel. Completing the
-  parallelogram, v_(ri) is the direction of relative motion. Hence the
-  angle between v_(ri) and V_i is the angle [theta] which the vanes
-  should make with the inlet surface of the wheel.
-
-  S 196. _Example of the Method of designing a Turbine. Professor James
-  Thomson's Inward Flow Turbine._--
-
-  Let
-
-    H = the available fall after deducting loss of head in pipes and
-          channels from the gross fall;
-    Q = the supply of water in cubic feet per second; and
-    [eta] = the efficiency of the turbine.
-
-  The work done per second is [eta]GQH, and the horse-power of the
-  turbine is h.p. = [eta]GQH/550. If [eta] is taken at 0.75, an
-  allowance will be made for the frictional losses in the turbine, the
-  leakage and the friction of the turbine shaft. Then h.p. = 0.085QH.
-
-  The velocity of flow through the turbine (uncorrected for the space
-  occupied by the vanes and guide-blades) may be taken
-
-    u_i = u_i = 0.125 [root](2gH),
-
-  in which case about (1/64)th of the energy of the fall is carried away
-  by the water discharged.
-
-  The areas of the outlet and inlet surface of the wheel are then
-
-    2[pi]r_o d_o = 2[pi]r_i d_i = Q/0.125 [root](2gH).
-
-  If we take r_o, so that the axial velocity of discharge from the
-  central orifices of the wheel is equal to u_o, we get
-
-    r_o = 0.3984 [root](Q/[root]H),
-
-    d_o = r_o.
-
-  If, to obtain considerable steadying action of the centrifugal head,
-  r_i = 2r_o, then d_i = (1/2)d_o.
-
-  _Speed of the Wheel._--Let V_i = 0.66 [root](2gH), or the speed due to
-  half the fall nearly. Then the number of rotations of the turbine per
-  second is
-
-    N = V_i/2[pi]r_i = 1.0579 [root](H[root]H/Q);
-
-  also
-
-    V_o = V_i r_o/r_i = 0.33 [root](2gH).
-
-  _Angle of Vanes with Outlet Surface._
-
-    Tan[phi] = u_o/V_o = 0.125/0.33 = .3788;
-
-    [phi] = 21 deg. nearly.
-
-  If this value is revised for the vane thickness it will ordinarily
-  become about 25 deg.
-
-  _Velocity with which the Water enters the Wheel._--The head producing
-  the velocity is
-
-    H - (V_i^2/2g) (1 + u_o^2/V_i^2) + u_i^2/2g
-      = H {1 - .4356 (1 + 0.0358) + .0156}
-      = 0.5646H.
-
-  Then the velocity is
-
-    V_i = .96 [root](2g(.5646H)) = 0.721 [root](2gH).
-
-  _Angle of Guide-Blades._
-
-    Sin [gamma] = u_i/v_i = 0.125/0.721 = 0.173;
-
-    [gamma] = 10 deg. nearly.
-
-  _Tangential Velocity of Water entering Wheel._
-
-    w_i = v_i cos [gamma] = 0.7101 [root](2gH).
-
-  _Angle of Vanes at Inlet Surface._
-
-    Cot [theta] = (w_i - V_i)/u_i = (.7101 - .66)/.125 = .4008;
-
-    [theta] = 68 deg. nearly.
-
-  _Hydraulic Efficiency of Wheel._
-
-    [eta] = w_iV_i/gH = .7101 X .66 X 2
-          = 0.9373.
-
-  This, however, neglects the friction of wheel covers and leakage. The
-  efficiency from experiment has been found to be 0.75 to 0.80.
-
-
-_Impulse and Partial Admission Turbines._
-
-S 197. The principal defect of most turbines with complete admission is
-the imperfection of the arrangements for working with less than the
-normal supply. With many forms of reaction turbine the efficiency is
-considerably reduced when the regulating sluices are partially
-closed, but it is exactly when the supply of water is deficient that it
-is most important to get out of it the greatest possible amount of work.
-The imperfection of the regulating arrangements is therefore, from the
-practical point of view, a serious defect. All turbine makers have
-sought by various methods to improve the regulating mechanism. B.
-Fourneyron, by dividing his wheel by horizontal diaphragms, virtually
-obtained three or more separate radial flow turbines, which could be
-successively set in action at their full power, but the arrangement is
-not altogether successful, because of the spreading of the water in the
-space between the wheel and guide-blades. Fontaine similarly employed
-two concentric axial flow turbines formed in the same casing. One was
-worked at full power, the other regulated. By this arrangement the loss
-of efficiency due to the action of the regulating sluice affected only
-half the water power. Many makers have adopted the expedient of erecting
-two or three separate turbines on the same waterfall. Then one or more
-could be put out of action and the others worked at full power. All
-these methods are rather palliatives than remedies. The movable
-guide-blades of Professor James Thomson meet the difficulty directly,
-but they are not applicable to every form of turbine.
-
-[Illustration: FIG. 197.]
-
-C. Callon, in 1840, patented an arrangement of sluices for axial or
-outward flow turbines, which were to be closed successively as the water
-supply diminished. By preference the sluices were closed by pairs, two
-diametrically opposite sluices forming a pair. The water was thus
-admitted to opposite but equal arcs of the wheel, and the forces driving
-the turbine were symmetrically placed. As soon as this arrangement was
-adopted, a modification of the mode of action of the water in the
-turbine became necessary. If the turbine wheel passages remain full of
-water during the whole rotation, the water contained in each passage
-must be put into motion each time it passes an open portion of the
-sluice, and stopped each time it passes a closed portion of the sluice.
-It is thus put into motion and stopped twice in each rotation. This
-gives rise to violent eddying motions and great loss of energy in shock.
-To prevent this, the turbine wheel with partial admission must be placed
-above the tail water, and the wheel passages be allowed to clear
-themselves of water, while passing from one open portion of the sluices
-to the next.
-
-But if the wheel passages are free of water when they arrive at the open
-guide passages, then there can be no pressure other than atmospheric
-pressure in the clearance space between guides and wheel. The water must
-issue from the sluices with the whole velocity due to the head; received
-on the curved vanes of the wheel, the jets must be gradually deviated
-and discharged with a small final velocity only, precisely in the same
-way as when a single jet strikes a curved vane in the free air. Turbines
-of this kind are therefore termed turbines of free deviation. There is
-no variation of pressure in the jet during the whole time of its action
-on the wheel, and the whole energy of the jet is imparted to the wheel,
-simply by the impulse due to its gradual change of momentum. It is clear
-that the water may be admitted in exactly the same way to any fraction
-of the circumference at pleasure, without altering the efficiency of the
-wheel. The diameter of the wheel may be made as large as convenient, and
-the water admitted to a small fraction of the circumference only. Then
-the number of revolutions is independent of the water velocity, and may
-be kept down to a manageable value.
-
-[Illustration: FIG. 198.]
-
-[Illustration: FIG. 199.]
-
-  S 198. _General Description of an Impulse Turbine or Turbine with Free
-  Deviation._--Fig. 197 shows a general sectional elevation of a Girard
-  turbine, in which the flow is axial. The water, admitted above a
-  horizontal floor, passes down through the annular wheel containing the
-  guide-blades G, G, and thence into the revolving wheel WW. The
-  revolving wheel is fixed to a hollow shaft suspended from the pivot p.
-  The solid internal shaft ss is merely a fixed column supporting the
-  pivot. The advantage of this is that the pivot is accessible for
-  lubrication and adjustment. B is the mortise bevel wheel by which the
-  power of the turbine is given off. The sluices are worked by the hand
-  wheel h, which raises them successively, in a way to be described
-  presently. d, d are the sluice rods. Figs. 198, 199 show the sectional
-  form of the guide-blade chamber and wheel and the curves of the wheel
-  vanes and guide-blades, when drawn on a plane development of the
-  cylindrical section of the wheel; a, a, a are the sluices for cutting
-  off the water; b, b, b are apertures by which the entrance or exit of
-  air is facilitated as the buckets empty and fill. Figs. 200, 201 show
-  the guide-blade gear. a, a, a are the sluice rods as before. At the
-  top of each sluice rod is a small block c, having a projecting tongue,
-  which slides in the groove of the circular cam plate d, d. This
-  circular plate is supported on the frame e, and revolves on it by
-  means of the flanged rollers f. Inside, at the top, the cam plate is
-  toothed, and gears into a spur pinion connected with the hand wheel h.
-  At gg is an inclined groove or shunt. When the tongues of the blocks
-  c, c arrive at g, they slide up to a second groove, or the reverse,
-  according as the cam plate is revolved in one direction or in the
-  other. As this operation takes place with each sluice successively,
-  any number of sluices can be opened or closed as desired. The turbine
-  is of 48 horse power on 5.12 ft. fall, and the supply of water varies
-  from 35 to 112 cub. ft. per second. The efficiency in normal working
-  is given as 73%. The mean diameter of the wheel is 6 ft., and the
-  speed 27.4 revolutions per minute.
-
-  [Illustration: FIG. 200.]
-
-  [Illustration: FIG. 201.]
-
-  [Illustration: FIG. 202.]
-
-  As an example of a partial admission radial flow impulse turbine, a
-  100 h.p. turbine at Immenstadt may be taken. The fall varies from 538
-  to 570 ft. The external diameter of the wheel is 4(1/2) ft., and its
-  internal diameter 3 ft. 10 in. Normal speed 400 revs. per minute.
-  Water is discharged into the wheel by a single nozzle, shown in fig.
-  202 with its regulating apparatus and some of the vanes. The water
-  enters the wheel at an angle of 22 deg. with the direction of motion,
-  and the final angle of the wheel vanes is 20 deg. The efficiency on
-  trial was from 75 to 78%.
-
-  S 199. _Theory of the Impulse Turbine._--The theory of the impulse
-  turbine does not essentially differ from that of the reaction turbine,
-  except that there is no pressure in the wheel opposing the discharge
-  from the guide-blades. Hence the velocity with which the water enters
-  the wheel is simply
-
-    v_i = 0.96 [root]{2g(H - [h])},
-
-  where [heta] is the height of the top of the wheel above the tail
-  water. If the hydropneumatic system is used, then [h] = 0. Let
-  Q_m be the maximum supply of water, r1, r2 the internal and external
-  radii of the wheel at the inlet surface; then
-
-    u_i = Q_m/{[pi](r2^2 - r1^2)}.
-
-  The value of u_i may be about 0.45 [root]{2g(H - [eta][h])},
-  whence r1, r2 can be determined.
-
-  The guide-blade angle is then given by the equation
-
-    sin [gamma] = u_i/v_i = 0.45/0.94 = .48;
-
-    [gamma] = 29 deg.
-
-  The value of u_i should, however, be corrected for the space occupied
-  by the guide-blades.
-
-  The tangential velocity of the entering water is
-
-    w_i = v_i cos [gamma] = 0.82 [root]{2g(H - [h])}.
-
-  The circumferential velocity of the wheel may be (at mean radius)
-
-    V_i = 0.5 [root]{2g(H - [h])}.
-
-  Hence the vane angle at inlet surface is given by the equation
-
-    cot [theta] = (w_i - V_i)/u_i = (0.82 - 0.5)/0.45 = .71;
-
-    [theta] = 55 deg.
-
-  The relative velocity of the water striking the vane at the inlet edge
-  is v_(ri) = u_i cosec[theta] = 1.22 u_i. This relative velocity remains
-  unchanged during the passage of the water over the vane; consequently
-  the relative velocity at the point of discharge is v_(ro) = 1.22 u_i.
-  Also in an axial flow turbine V_o = V_i.
-
-  If the final velocity of the water is axial, then
-
-    cos [phi] = V_o/v_(ro) = V_i/v_(ri) = 0.5/(1.22 X 0.45) = cos 24 deg. 23'.
-
-  This should be corrected for the vane thickness. Neglecting this, u_o
-  = v_(ro) sin [phi] = v_(ri) sin [phi] = u_i cosec [theta] sin [phi] =
-  0.5u_i. The discharging area of the wheel must therefore be greater
-  than the inlet area in the ratio of at least 2 to 1. In some actual
-  turbines the ratio is 7 to 3. This greater outlet area is obtained by
-  splaying the wheel, as shown in the section (fig. 199).
-
-  [Illustration: FIG. 203.]
-
-  S 200. _Pelton Wheel._--In the mining district of California about
-  1860 simple impulse wheels were used, termed hurdy-gurdy wheels. The
-  wheels rotated in a vertical plane, being supported on a horizontal
-  axis. Round the circumference were fixed flat vanes which were struck
-  normally by a jet from a nozzle of size varying with the head and
-  quantity of water. Such wheels have in fact long been used. They are
-  not efficient, but they are very simply constructed. Then attempts
-  were made to improve the efficiency, first by using hemispherical cup
-  vanes, and then by using a double cup vane with a central dividing
-  ridge, an arrangement invented by Pelton. In this last form the water
-  from the nozzle passes half to each side of the wheel, just escaping
-  clear of the backs of the advancing buckets. Fig. 203 shows a Pelton
-  vane. Some small modifications have been made by other makers, but
-  they are not of any great importance. Fig. 204 shows a complete Pelton
-  wheel with frame and casing, supply pipe and nozzle. Pelton wheels
-  have been very largely used in America and to some extent in Europe.
-  They are extremely simple and easy to construct or repair and on falls
-  of 100 ft. or more are very efficient. The jet strikes tangentially to
-  the mean radius of the buckets, and the face of the buckets is not
-  quite radial but at right angles to the direction of the jet at the
-  point of first impact. For greatest efficiency the peripheral velocity
-  of the wheel at the mean radius of the buckets should be a little less
-  than half the velocity of the jet. As the radius of the wheel can be
-  taken arbitrarily, the number of revolutions per minute can be
-  accommodated to that of the machinery to be driven. Pelton wheels have
-  been made as small as 4 in. diameter, for driving sewing machines, and
-  as large as 24 ft. The efficiency on high falls is about 80%. When
-  large power is required two or three nozzles are used delivering on
-  one wheel. The width of the buckets should be not less than seven
-  times the diameter of the jet.
-
-  [Illustration: FIG. 204.]
-
-  At the Comstock mines, Nevada, there is a 36-in. Pelton wheel made of
-  a solid steel disk with phosphor bronze buckets riveted to the rim.
-  The head is 2100 ft. and the wheel makes 1150 revolutions per minute,
-  the peripheral velocity being 180 ft. per sec. With a (1/2)-in. nozzle
-  the wheel uses 32 cub. ft. of water per minute and develops 100 h.p.
-  At the Chollarshaft, Nevada, there are six Pelton wheels on a fall of
-  1680 ft. driving electrical generators. With 5/8-in. nozzles each
-  develops 125 h.p.
-
-  [Illustration: FIG. 205]
-
-  S 201. _Theory of the Pelton Wheel._--Suppose a jet with a velocity v
-  strikes tangentially a curved vane AB (fig. 205) moving in the same
-  direction with the velocity u. The water will flow over the vane with
-  the relative velocity v - u and at B will have the tangential
-  relative velocity v - u making an angle [alpha] with the direction of
-  the vane's motion. Combining this with the velocity u of the vane, the
-  absolute velocity of the water leaving the vane will be w = Bc. The
-  component of w in the direction of motion of the vane is Ba = Bb - ab
-  = u - (v - u) cos [alpha]. Hence if Q is the quantity of water
-  reaching the vane per second the change of momentum per second in the
-  direction of the vane's motion is (GQ/g)[v - {u - (v - u) cos
-  [alpha]}] = (GQ/g)(v - u)(1 + cos [alpha]). If a = 0 deg., cos [alpha]
-  = 1, and the change of momentum per second, which is equal to the
-  effort driving the vane, is P = 2(GQ/g)(v - u). The work done on the
-  vane is Pu = 2(GQ/g)(v - u)u. If a series of vanes are interposed in
-  succession, the quantity of water impinging on the vanes per second is
-  the total discharge of the nozzle, and the energy expended at the
-  nozzle is GQv^2/2g. Hence the efficiency of the arrangement is, when
-  [alpha] = 0 deg., neglecting friction,
-
-    [eta] = 2Pu/GQv^2 = 4(v - u)u/v^2,
-
-  which is a maximum and equal to unity if u = (1/2)v. In that case the
-  whole energy of the jet is usefully expended in driving the series of
-  vanes. In practice [alpha] cannot be quite zero or the water leaving
-  one vane would strike the back of the next advancing vane. Fig. 203
-  shows a Pelton vane. The water divides each way, and leaves the vane
-  on each side in a direction nearly parallel to the direction of motion
-  of the vane. The best velocity of the vane is very approximately half
-  the velocity of the jet.
-
-  S 202. _Regulation of the Pelton Wheel._--At first Pelton wheels were
-  adjusted to varying loads merely by throttling the supply. This method
-  involves a total loss of part of the head at the sluice or throttle
-  valve. In addition as the working head is reduced, the relation
-  between wheel velocity and jet velocity is no longer that of greatest
-  efficiency. Next a plan was adopted of deflecting the jet so that only
-  part of the water reached the wheel when the load was reduced, the
-  rest going to waste. This involved the use of an equal quantity of
-  water for large and small loads, but it had, what in some cases is an
-  advantage, the effect of preventing any water hammer in the supply
-  pipe due to the action of the regulator. In most cases now regulation
-  is effected by varying the section of the jet. A conical needle in the
-  nozzle can be advanced or withdrawn so as to occupy more or less of
-  the aperture of the nozzle. Such a needle can be controlled by an
-  ordinary governor.
-
-S 203. _General Considerations on the Choice of a Type of Turbine._--The
-circumferential speed of any turbine is necessarily a fraction of the
-initial velocity of the water, and therefore is greater as the head is
-greater. In reaction turbines with complete admission the number of
-revolutions per minute becomes inconveniently great, for the diameter
-cannot be increased beyond certain limits without greatly reducing the
-efficiency. In impulse turbines with partial admission the diameter can
-be chosen arbitrarily and the number of revolutions kept down on high
-falls to any desired amount. Hence broadly reaction turbines are better
-and less costly on low falls, and impulse turbines on high falls. For
-variable water flow impulse turbines have some advantage, being more
-efficiently regulated. On the other hand, impulse turbines lose
-efficiency seriously if their speed varies from the normal speed due to
-the head. If the head is very variable, as it often is on low falls, and
-the turbine must run at the same speed whatever the head, the impulse
-turbine is not suitable. Reaction turbines can be constructed so as to
-overcome this difficulty to a great extent. Axial flow turbines with
-vertical shafts have the disadvantage that in addition to the weight of
-the turbine there is an unbalanced water pressure to be carried by the
-footstep or collar bearing. In radial flow turbines the hydraulic
-pressures are balanced. The application of turbines to drive dynamos
-directly has involved some new conditions. The electrical engineer
-generally desires a high speed of rotation, and a very constant speed at
-all times. The reaction turbine is generally more suitable than the
-impulse turbine. As the diameter of the turbine depends on the quantity
-of water and cannot be much varied without great inefficiency, a
-difficulty arises on low falls. This has been met by constructing four
-independent reaction turbines on the same shaft, each having of course
-the diameter suitable for one-quarter of the whole discharge, and having
-a higher speed of rotation than a larger turbine. The turbines at
-Rheinfelden and Chevres are so constructed. To ensure constant speed of
-rotation when the head varies considerably without serious inefficiency,
-an axial flow turbine is generally used. It is constructed of three or
-four concentric rings of vanes, with independent regulating sluices,
-forming practically independent turbines of different radii. Any one of
-these or any combination can be used according to the state of the
-water. With a high fall the turbine of largest radius only is used, and
-the speed of rotation is less than with a turbine of smaller radius. On
-the other hand, as the fall decreases the inner turbines are used either
-singly or together, according to the power required. At the Zurich
-waterworks there are turbines of 90 h.p. on a fall varying from 10(1/2)
-ft. to 4(3/4) ft. The power and speed are kept constant. Each turbine
-has three concentric rings. The outermost ring gives 90 h.p. with 105
-cub. ft. per second and the maximum fall. The outer and middle
-compartments give the same power with 140 cub. ft. per second and a fall
-of 7 ft. 10 in. All three compartments working together develop the
-power with about 250 cub. ft. per second. In some tests the efficiency
-was 74% with the outer ring working alone, 75.4% with the outer and
-middle ring working and a fall of 7 ft., and 80.7% with all the rings
-working.
-
-[Illustration: FIG. 206.]
-
-S 204. _Speed Governing._--When turbines are used to drive dynamos
-direct, the question of speed regulation is of great importance. Steam
-engines using a light elastic fluid can be easily regulated by governors
-acting on throttle or expansion valves. It is different with water
-turbines using a fluid of great inertia. In one of the Niagara penstocks
-there are 400 tons of water flowing at 10 ft. per second, opposing
-enormous resistance to rapid change of speed of flow. The sluices of
-water turbines also are necessarily large and heavy. Hence relay
-governors must be used, and the tendency of relay governors to
-hunt must be overcome. In the Niagara Falls Power House No. 1, each
-turbine has a very sensitive centrifugal governor acting on a ratchet
-relay. The governor puts into gear one or other of two ratchets driven
-by the turbine itself. According as one or the other ratchet is in gear
-the sluices are raised or lowered. By a subsidiary arrangement the
-ratchets are gradually put out of gear unless the governor puts them in
-gear again, and this prevents the over correction of the speed from the
-lag in the action of the governor. In the Niagara Power House No. 2, the
-relay is an hydraulic relay similar in principle, but rather more
-complicated in arrangement, to that shown in fig. 206, which is a
-governor used for the 1250 h.p. turbines at Lyons. The sensitive
-governor G opens a valve and puts into action a plunger driven by oil
-pressure from an oil reservoir. As the plunger moves forward it
-gradually closes the oil admission valve by lowering the fulcrum end f
-of the valve lever which rests on a wedge w attached to the plunger. If
-the speed is still too high, the governor reopens the valve. In the case
-of the Niagara turbines the oil pressure is 1200 lb. per sq. in. One
-millimetre of movement of the governor sleeve completely opens the relay
-valve, and the relay plunger exerts a force of 50 tons. The sluices can
-be completely opened or shut in twelve seconds. The ordinary variation
-of speed of the turbine with varying load does not exceed 1%. If all the
-load is thrown off, the momentary variation of speed is not more than
-5%. To prevent hydraulic shock in the supply pipes, a relief valve is
-provided which opens if the pressure is in excess of that due to the
-head.
-
-[Illustration: FIG. 207.]
-
-S 205. _The Hydraulic Ram._--The hydraulic ram is an arrangement by
-which a quantity of water falling a distance h forces a portion of the
-water to rise to a height h1, greater than h. It consists of a supply
-reservoir (A, fig. 207), into which the water enters from some natural
-stream. A pipe s of considerable length conducts the water to a lower
-level, where it is discharged intermittently through a self-acting
-pulsating valve at d. The supply pipe s may be fitted with a flap valve
-for stopping the ram, and this is attached in some cases to a float, so
-that the ram starts and stops itself automatically, according as the
-supply cistern fills or empties. The lower float is just sufficient to
-keep open the flap after it has been raised by the action of the upper
-float. The length of chain is adjusted so that the upper float opens the
-flap when the level in the cistern is at the desired height. If the
-water-level falls below the lower float the flap closes. The pipe s
-should be as long and as straight as possible, and as it is subjected to
-considerable pressure from the sudden arrest of the motion of the water,
-it must be strong and strongly jointed. a is an air vessel, and e the
-delivery pipe leading to the reservoir at a higher level than A, into
-which water is to be pumped. Fig. 208 shows in section the construction
-of the ram itself. d is the pulsating discharge valve already mentioned,
-which opens inwards and downwards. The stroke of the valve is regulated
-by the cotter through the spindle, under which are washers by which the
-amount of fall can be regulated. At o is a delivery valve, opening
-outwards, which is often a ball-valve but sometimes a flap-valve. The
-water which is pumped passes through this valve into the air vessel a,
-from which it flows by the delivery pipe in a regular stream into the
-cistern to which the water is to be raised. In the vertical chamber
-behind the outer valve a small air vessel is formed, and into this
-opens an aperture 1/4 in. in diameter, made in a brass screw plug b. The
-hole is reduced to 1/16 in. in diameter at the outer end of the plug
-and is closed by a small valve opening inwards. Through this, during the
-rebound after each stroke of the ram, a small quantity of air is sucked
-in which keeps the air vessel supplied with its elastic cushion of air.
-
-[Illustration: FIG. 208.]
-
-During the recoil after a sudden closing of the valve d, the pressure
-below it is diminished and the valve opens, permitting outflow. In
-consequence of the flow through this valve, the water in the supply pipe
-acquires a gradually increasing velocity. The upward flow of the water,
-towards the valve d, increases the pressure tending to lift the valve,
-and at last, if the valve is not too heavy, lifts and closes it. The
-forward momentum of the column in the supply pipe being destroyed by the
-stoppage of the flow, the water exerts a pressure at the end of the pipe
-sufficient to open the delivery valve o, and to cause a portion of the
-water to flow into the air vessel. As the water in the supply pipe comes
-to rest and recoils, the valve d opens again and the operation is
-repeated. Part of the energy of the descending column is employed in
-compressing the air at the end of the supply pipe and expanding the pipe
-itself. This causes a recoil of the water which momentarily diminishes
-the pressure in the pipe below the pressure due to the statical head.
-This assists in opening the valve d. The recoil of the water is
-sufficiently great to enable a pump to be attached to the ram body
-instead of the direct rising pipe. With this arrangement a ram working
-with muddy water may be employed to raise clear spring water. Instead of
-lifting the delivery valve as in the ordinary ram, the momentum of the
-column drives a sliding or elastic piston, and the recoil brings it
-back. This piston lifts and forces alternately the clear water through
-ordinary pump valves.
-
-
-PUMPS
-
-S 206. The different classes of pumps correspond almost exactly to the
-different classes of water motors, although the mechanical details of
-the construction are somewhat different. They are properly reversed
-water motors. Ordinary reciprocating pumps correspond to water-pressure
-engines. Chain and bucket pumps are in principle similar to water wheels
-in which the water acts by weight. Scoop wheels are similar to undershot
-water wheels, and centrifugal pumps to turbines.
-
-_Reciprocating Pumps_ are single or double acting, and differ from
-water-pressure engines in that the valves are moved by the water instead
-of by automatic machinery. They may be classed thus:--
-
-1. _Lift Pumps._--The water drawn through a foot valve on the ascent of
-the pump bucket is forced through the bucket valve when it descends, and
-lifted by the bucket when it reascends. Such pumps give an intermittent
-discharge.
-
-2. _Plunger or Force Pumps_, in which the water drawn through the foot
-valve is displaced by the descent of a solid plunger, and forced through
-a delivery valve. They have the advantage that  the friction is less
-than that of lift pumps, and the packing round the plunger is easily
-accessible, whilst that round a lift pump bucket is not. The flow is
-intermittent.
-
-3. _The Double-acting Force Pump_ is in principle a double plunger pump.
-The discharge fluctuates from zero to a maximum and back to zero each
-stroke, but is not arrested for any appreciable time.
-
-4. _Bucket and Plunger Pumps_ consist of a lift pump bucket combined
-with a plunger of half its area. The flow varies as in a double-acting
-pump.
-
-5. _Diaphragm Pumps_ have been used, in which the solid plunger is
-replaced by an elastic diaphragm, alternately depressed into and raised
-out of a cylinder.
-
-As single-acting pumps give an intermittent discharge three are
-generally used on cranks at 120 deg. But with all pumps the variation of
-velocity of discharge would cause great waste of work in the delivery
-pipes when they are long, and even danger from the hydraulic ramming
-action of the long column of water. An air vessel is interposed between
-the pump and the delivery pipes, of a volume from 5 to 100 times the
-space described by the plunger per stroke. The air in this must be
-replenished from time to time, or continuously, by a special air-pump.
-At low speeds not exceeding 30 ft. per minute the delivery of a pump is
-about 90 to 95% of the volume described by the plunger or bucket, from 5
-to 10% of the discharge being lost by leakage. At high speeds the
-quantity pumped occasionally exceeds the volume described by the
-plunger, the momentum of the water keeping the valves open after the
-turn of the stroke.
-
-The velocity of large mining pumps is about 140 ft. per minute, the
-indoor or suction stroke being sometimes made at 250 ft. per minute.
-Rotative pumping engines of large size have a plunger speed of 90 ft.
-per minute. Small rotative pumps are run faster, but at some loss of
-efficiency. Fire-engine pumps have a speed of 180 to 220 ft. per minute.
-
-The efficiency of reciprocating pumps varies very greatly. Small
-reciprocating pumps, with metal valves on lifts of 15 ft., were found by
-Morin to have an efficiency of 16 to 40%, or on the average 25%. When
-used to pump water at considerable pressure, through hose pipes, the
-efficiency rose to from 28 to 57%, or on the average, with 50 to 100 ft.
-of lift, about 50%. A large pump with barrels 18 in. diameter, at speeds
-under 60 ft. per minute, gave the following results:--
-
-  Lift in feet    14(1/2)   34    47
-  Efficiency     .46       .66   .70
-
-The very large steam-pumps employed for waterworks, with 150 ft. or more
-of lift, appear to reach an efficiency of 90%, not including the
-friction of the discharge pipes. Reckoned on the indicated work of the
-steam-engine the efficiency may be 80%.
-
-Many small pumps are now driven electrically and are usually three-throw
-single-acting pumps driven from the electric motor by gearing. It is not
-convenient to vary the speed of the motor to accommodate it to the
-varying rate of pumping usually required. Messrs Hayward Tyler have
-introduced a mechanism for varying the stroke of the pumps (Sinclair's
-patent) from full stroke to nil, without stopping the pumps.
-
-S 207. _Centrifugal Pump._--For large volumes of water on lifts not
-exceeding about 60 ft. the most convenient pump is the centrifugal pump.
-Recent improvements have made it available also for very high lifts. It
-consists of a wheel or fan with curved vanes enclosed in an annular
-chamber. Water flows in at the centre and is discharged at the
-periphery. The fan may rotate in a vertical or horizontal plane and the
-water may enter on one or both sides of the fan. In the latter case
-there is no axial unbalanced pressure. The fan and its casing must be
-filled with water before it can start, so that if not drowned there must
-be a foot valve on the suction pipe. When no special attention needs to
-be paid to efficiency the water may have a velocity of 6 to 7 ft. in the
-suction and delivery pipes. The fan often has 6 to 12 vanes. For a
-double-inlet fan of diameter D, the diameter of the inlets is D/2. If Q
-is the discharge in cub. ft. per second D = about 0.6 [root]Q in average
-cases. The peripheral speed is a little greater than the velocity due
-to the lift. Ordinary centrifugal pumps will have an efficiency of 40 to
-60%.
-
-The first pump of this kind which attracted notice was one exhibited by
-J. G. Appold in 1851, and the special features of his pump have been
-retained in the best pumps since constructed. Appold's pump raised
-continuously a volume of water equal to 1400 times its own capacity per
-minute. It had no valves, and it permitted the passage of solid bodies,
-such as walnuts and oranges, without obstruction to its working. Its
-efficiency was also found to be good.
-
-[Illustration: FIG. 209.]
-
-Fig. 209 shows the ordinary form of a centrifugal pump. The pump disk
-and vanes B are cast in one, usually of bronze,
-
-and the disk is keyed on the driving shaft C. The casing A has a
-spirally enlarging discharge passage into the discharge pipe K. A cover
-L gives access to the pump. S is the suction pipe which opens into the
-pump disk on both sides at D.
-
-Fig. 210 shows a centrifugal pump differing from ordinary centrifugal
-pumps in one feature only. The water rises through a suction pipe S,
-which divides so as to enter the pump wheel W at the centre on each
-side. The pump disk or wheel is very similar to a turbine wheel. It is
-keyed on a shaft driven by a belt on a fast and loose pulley arrangement
-at P. The water rotating in the pump disk presses outwards, and if the
-speed is sufficient a continuous flow is maintained through the pump and
-into the discharge pipe D. The special feature in this pump is that the
-water, discharged by the pump disk with a whirling velocity of not
-inconsiderable magnitude, is allowed to continue rotation in a chamber
-somewhat larger than the pump. The use of this whirlpool chamber was
-first suggested by Professor James Thomson. It utilizes the energy due
-to the whirling velocity of the water which in most pumps is wasted in
-eddies in the discharge pipe. In the pump shown guide-blades are also
-added which have the direction of the stream lines in a free vortex.
-They do not therefore interfere with the action of the water when
-pumping the normal quantity, but only prevent irregular motion. At A is
-a plug by which the pump case is filled before starting. If the pump is
-above the water to be pumped, a foot valve is required to permit the
-pump to be filled. Sometimes instead of the foot valve a delivery valve
-is used, an air-pump or steam jet pump being employed to exhaust the air
-from the pump case.
-
-[Illustration: FIG. 210.]
-
-  S 208. _Design and Proportions of a Centrifugal Pump._--The design of
-  the pump disk is very simple. Let r_i, r_o be the radii of the inlet
-  and outlet surfaces of the pump disk, d_i, d_o the clear axial width
-  at those radii. The velocity of flow through the pump may be taken
-  the same as for a turbine. If Q is the quantity pumped, and H the
-  lift,
-
-    u_i = 0.25 [root](2gH).   (1)
-
-    2[pi]r_i d_i = Q/u_i.
-
-  Also in practice
-
-    d_i = 1.2 r_i ....
-
-  Hence,
-
-    r_i = .2571 [root](Q/[root]H).   (2)
-
-  Usually
-
-    r_o = 2r_i,
-
-  and
-
-    d_o = d_i or (1/2)d_i
-
-  according as the disk is parallel-sided or coned. The water enters the
-  wheel radially with the velocity u_i, and
-
-    u_o = Q/2[pi]r_o d_o.   (3)
-
-  [Illustration: FIG. 211.]
-
-  Fig. 211 shows the notation adopted for the velocities. Suppose the
-  water enters the wheel with the velocity v_i, while the velocity of
-  the wheel is V_i. Completing the parallelogram, v_(ri) is the relative
-  velocity of the water and wheel, and is the proper direction of the
-  wheel vanes. Also, by resolving, u_i and w_i are the component
-  velocities of flow and velocities of whir of the velocity v_i of the
-  water. At the outlet surface, v_o is the final velocity of discharge,
-  and the rest of the notation is similar to that for the inlet surface.
-
-  Usually the water flows equally in all directions in the eye of the
-  wheel, in that case v_i is radial. Then, in normal conditions of
-  working, at the inlet surface,
-
-    v_i = u_i                                         \
-    w_i = 0                                            > (4)
-    tan[theta] = u_i/V_i                               |
-    v_(ri) = u_i cosec [theta] = [root](u_i^2 + V_i^2) /
-
-  If the pump is raising less or more than its proper quantity, [theta]
-  will not satisfy the last condition, and there is then some loss of
-  head in shock.
-
-  At the outer circumference of the wheel or outlet surface,
-
-    v_(ro) = u_o cosec [phi]                         \
-    w_o = V_o - u_o cot [phi]                         > (5)
-    v_o = [root]{u_o^2 + (V - _o - u_o cot [phi])^2} /
-
-  _Variation of Pressure in the Pump Disk._--Precisely as in the case of
-  turbines, it can be shown that the variation of pressure between the
-  inlet and outlet surfaces of the pump is
-
-    h_o - h_i = (V_o^2 - V_i^2)/2g - (v_(ro)^2 - v_(ri)^2)/2g.
-
-  Inserting the values of v_(ro), v_(ri) in (4) and (5), we get for
-  normal conditions of working
-
-    h_o -h_i = (V_o^2 - V_i^2)/2g - u_o^2 cosec^2 [phi]/2g + (u_i^2 + V_i^2)/2g
-      = V_o^2/2g - u_o^2 cosec^2 [phi]/2g + u_i^2/2g.   (6)
-
-  _Hydraulic Efficiency of the Pump._--Neglecting disk friction, journal
-  friction, and leakage, the efficiency of the pump can be found in the
-  same way as that of turbines (S 186). Let M be the moment of the
-  couple rotating the pump, and [alpha] its angular velocity; w_o, r_o
-  the tangential velocity of the water and radius at the outlet surface;
-  w_i, r_i the same quantities at the inlet surface. Q being the
-  discharge per second, the change of angular momentum per second is
-
-    (GQ/g)(w_o r_o - w_i r_i).
-
-  Hence
-
-    M = (GQ/g)(w_o r_o - w_i r_i).
-
-  In normal working, w_i = 0. Also, multiplying by the angular velocity,
-  the work done per second is
-
-    M[alpha] = (GQ/g)w_o r_o[alpha].
-
-  But the useful work done in pumping is GQH. Therefore the efficiency
-  is
-
-    [eta] = GQH/M[alpha] = gH/w_o r_o[alpha] = gH/w_o V_o.   (7)
-
-  S 209. Case 1. _Centrifugal Pump with no Whirlpool Chamber._--When no
-  special provision is made to utilize the energy of motion of the water
-  leaving the wheel, and the pump discharges directly into a chamber in
-  which the water is flowing to the discharge pipe, nearly the whole of
-  the energy of the water leaving the disk is wasted. The water leaves
-  the disk with the more or less considerable velocity v_o, and impinges
-  on a mass flowing to the discharge pipe at the much slower velocity
-  v_s. The radial component of v_o is almost necessarily wasted. From
-  the tangential component there is a gain of pressure
-
-    (w_o^2 - v_s^2)/2g - (w_o - v_s)^2/2g
-      = v_s(w_o - v_s)g,
-
-  which will be small, if v_s is small compared with w_o. Its greatest
-  value, if v_s = (1/2)w_o, is (1/2)w_o^2/2g, which will always be a
-  small part of the whole head. Suppose this neglected. The whole
-  variation of pressure in the pump disk then balances the lift and the
-  head u_i^2/2g necessary to give the initial velocity of flow in the
-  eye of the wheel.
-
-    u_i^2/2g + H = V_o^2/2g - u_o^2 cosec^2 [phi]/2g + u_i^2/2g,
-
-    H = V_o^2/2g - u_o^2 cosec^2 [phi]/2g
-
-  or
-
-    V_o = [root](2gH + u_o^2 cosec^2 [phi]).   (8)
-
-  and the efficiency of the pump is, from (7),
-
-    [eta] = gH/V_o w_o = gH/{V (V_o - n_o cot [phi])},
-
-    = (V_o^2 - u_o^2 cosec^2 [phi])/{2V_o (V_o - u_o cot [phi]) },   (9).
-
-  For [phi] = 90 deg.,
-
-    [eta] = (V_o^2 - u_o^2)/2V_o^2,
-
-  which is necessarily less than 1/2. That is, half the work expended in
-  driving the pump is wasted. By recurving the vanes, a plan introduced
-  by Appold, the efficiency is increased, because the velocity v_o of
-  discharge from the pump is diminished. If [phi] is very small,
-
-    cosec [phi] = cot [phi];
-
-  and then
-
-    [eta] = (V_o, + u_o cosec [phi])/2V_o,
-
-  which may approach the value 1, as [phi] tends towards 0. Equation (8)
-  shows that u_o cosec [phi] cannot be greater than V_o. Putting u_o =
-  0.25 [root](2gH) we get the following numerical values of the
-  efficiency and the circumferential velocity of the pump:--
-
-    [phi]        [eta]      V_o
-
-     90 deg.      0.47     1.03 [root](2gH)
-     45 deg.      0.56     1.06       "
-     30 deg.      0.65     1.12       "
-     20 deg.      0.73     1.24       "
-     10 deg.      0.84     1.75       "
-
-  [phi] cannot practically be made less than 20 deg.; and, allowing for
-  the frictional losses neglected, the efficiency of a pump in which
-  [phi] = 20 deg. is found to be about .60.
-
-  S 210. Case 2. _Pump with a Whirlpool Chamber_, as in fig.
-  210.--Professor James Thomson first suggested that the energy of the
-  water after leaving the pump disk might be utilized, if a space were
-  left in which a free vortex could be formed. In such a free vortex the
-  velocity varies inversely as the radius. The gain of pressure in the
-  vortex chamber is, putting r_o, r_w for the radii to the outlet
-  surface of wheel and to outside of free vortex,
-
-    v_o^2 /    r_o^2 \    v_o^2  /       \
-    ---- ( 1 - -----  ) = ----- ( 1 - k^2 ),
-     2g   \    r_w^2 /     2g    \       /
-
-  if
-
-    k = r_o/r_w.
-
-  The lift is then, adding this to the lift in the last case,
-
-    H = {V_o^2 - u_o^2 cosec^2 [phi] + v_o^2(1 - k^2)}/2g.
-
-  But
-
-    v_o^2 = V_o^2 - 2V_o u_o cot [phi] + u_o^2 cosec^2 [phi];
-
-    .: H = {(2 - k^2)V_o^2 - 2kV_o u_o cot [phi] - k^2u_o^2 cosec^2 [phi]}/2g.   (10)
-
-  Putting this in the expression for the efficiency, we find a
-  considerable increase of efficiency. Thus with
-
-    [phi] = 90 deg. and     k = 1/2, [eta] = 7/8 nearly,
-
-    [phi] a small angle and k = 1/2, [eta] = 1 nearly.
-
-  With this arrangement of pump, therefore, the angle at the outer ends
-  of the vanes is of comparatively little importance. A moderate angle
-  of 30 deg. or 40 deg. may very well be adopted. The following
-  numerical values of the velocity of the circumference of the pump have
-  been obtained by taking k = 1/2, and u_o = 0.25 [root](2gH).
-
-    [phi]          V_o
-
-     90 deg.      .762 [root](2gH)
-     45 deg.      .842      "
-     30 deg.      .911      "
-     20 deg.     1.023      "
-
-  The quantity of water to be pumped by a centrifugal pump necessarily
-  varies, and an adjustment for different quantities of water cannot
-  easily be introduced. Hence it is that the average efficiency of pumps
-  of this kind is in practice less than the efficiencies given above.
-  The advantage of a vortex chamber is also generally neglected. The
-  velocity in the supply and discharge pipes is also often made greater
-  than is consistent with a high degree of efficiency. Velocities of 6
-  or 7 ft. per second in the discharge and suction pipes, when the lift
-  is small, cause a very sensible waste of energy; 3 to 6 ft. would be
-  much better. Centrifugal pumps of very large size have been
-  constructed. Easton and Anderson made pumps for the North Sea canal in
-  Holland to deliver each 670 tons of water per minute on a lift of 5
-  ft. The pump disks are 8 ft. diameter. J. and H. Gwynne constructed
-  some pumps for draining the Ferrarese Marshes, which together deliver
-  2000 tons per minute. A pump made under Professor J. Thomson's
-  direction for drainage works in Barbados had a pump disk 16 ft. in
-  diameter and a whirlpool chamber 32 ft. in diameter. The efficiency of
-  centrifugal pumps when delivering less or more than the normal
-  quantity of water is discussed in a paper in the _Proc. Inst. Civ.
-  Eng._ vol. 53.
-
-S 211. _High Lift Centrifugal Pumps._--It has long been known that
-centrifugal pumps could be worked in series, each pump overcoming a part
-of the lift. This method has been perfected, and centrifugal pumps for
-very high lifts with great efficiency have been used by Sulzer and
-others. C. W. Darley (_Proc. Inst. Civ. Eng._, supplement to vol. 154,
-p. 156) has described some pumps of this new type driven by Parsons
-steam turbines for the water supply of Sydney, N.S.W. Each pump was
-designed to deliver 1(1/2) million gallons per twenty-four hours against
-a head of 240 ft. at 3300 revs. per minute. Three pumps in series give
-therefore a lift of 720 ft. The pump consists of a central double-sided
-impeller 12 in. diameter. The water entering at the bottom divides and
-enters the runner at each side through a bell-mouthed passage. The shaft
-is provided with ring and groove glands which on the suction side keep
-the air out and on the pressure side prevent leakage. Some water from
-the pressure side leaks through the glands, but beyond the first grooves
-it passes into a pocket and is returned to the suction side of the pump.
-For the glands on the suction side water is supplied from a low-pressure
-service. No packing is used in the glands. During the trials no water
-was seen at the glands. The following are the results of tests made at
-Newcastle:--
-
-  +-------------------------------------+-------+-------+-------+-------+
-  |                                     |   I.  |  II.  |  III. |  IV.  |
-  +-------------------------------------+-------+-------+-------+-------+
-  | Duration of test              hours |   2   |  1.54 |  1.2  | 1.55  |
-  | Steam pressure      lb. per sq. in. |  57   |  57   |  84   |  55   |
-  | Weight of steam per water           |       |       |       |       |
-  |     h.p. hour                   lb. | 27.93 | 30.67 | 28.83 | 27.89 |
-  | Speed in revs, per min.             |  3300 |  3330 |  3710 | 3340  |
-  | Height of suction               ft. |   11  |   11  |   11  |  11   |
-  | Total lift                      ft. |  762  |  744  |  917  |  756  |
-  | Million galls. per day pumped--     |       |       |       |       |
-  |   By Ventun meter                   | 1.573 | 1.499 | 1.689 | 1.503 |
-  |   By orifice                        | 1.623 | 1.513 | 1.723 | 1.555 |
-  | Water h.p.                          |  252  |  235  |  326  |  239  |
-  +-------------------------------------+-------+-------+-------+-------+
-
-In trial IV. the steam was superheated 95 deg. F. From other trials under
-the same conditions as trial I. the Parsons turbine uses 15.6 lb. of
-steam per brake h.p. hour, so that the combined efficiency of turbine
-and pumps is about 56%, a remarkably good result.
-
-[Illustration: FIG. 212.]
-
-S 212. _Air-Lift Pumps._--An interesting and simple method of pumping by
-compressed air, invented by Dr J. Pohle of Arizona, is likely to be very
-useful in certain cases. Suppose a rising main placed in a deep bore
-hole in which there is a considerable depth of water. Air compressed to
-a sufficient pressure is conveyed by an air pipe and introduced at the
-lower end of the rising main. The air rising In the main diminishes the
-average density of the contents of the main, and their aggregate weight
-no longer balances the pressure at the lower end of the main due to its
-submersion. An upward flow is set up, and if the air supply is
-sufficient the water in the rising main is lifted to any required
-height. The higher the lift above the level in the bore hole the deeper
-must be the point at which air is injected. Fig. 212 shows an airlift
-pump constructed for W. H. Maxwell at the Tunbridge Wells waterworks.
-There is a two-stage steam air compressor, compressing air to from 90 to
-100 lb. per sq. in. The bore hole is 350 ft. deep, lined with steel
-pipes 15 in. diameter for 200 ft. and with perforated pipes 13(1/2) in.
-diameter for the lower 150 ft. The rest level of the water is 96 ft.
-from the ground-level, and the level when pumping 32,000 gallons per
-hour is 120 ft. from the ground-level. The rising main is 7 in.
-diameter, and is carried nearly to the bottom of the bore hole and to 20
-ft. above the ground-level. The air pipe is 2(1/2) in. diameter. In a
-trial run 31,402 gallons per hour were raised 133 ft. above the level in
-the well. Trials of the efficiency of the system made at San Francisco
-with varying conditions will be found in a paper by E. A. Rix (_Journ.
-Amer. Assoc. Eng. Soc._ vol. 25, 1900). Maxwell found the best results
-when the ratio of immersion to lift was 3 to 1 at the start and 2.2 to 1
-at the end of the trial. In these conditions the efficiency was 37%
-calculated on the indicated h.p. of the steam-engine, and 46% calculated
-on the indicated work of the compressor. 2.7 volumes of free air were
-used to 1 of water lifted. The system is suitable for temporary
-purposes, especially as the quantity of water raised is much greater
-than could be pumped by any other system in a bore hole of a given size.
-It is useful for clearing a boring of sand and may be advantageously
-used permanently when a boring is in sand or gravel which cannot be kept
-out of the bore hole. The initial cost is small.
-
-S 213. _Centrifugal Fans._--Centrifugal fans are constructed similarly
-to centrifugal pumps, and are used for compressing air to pressures not
-exceeding 10 to 15 in. of water-column. With this small variation of
-pressure the variation of volume and density of the air may be neglected
-without sensible error. The conditions of pressure and discharge for
-fans are generally less accurately known than in the case of pumps, and
-the design of fans is generally somewhat crude. They seldom have
-whirlpool chambers, though a large expanding outlet is provided in the
-case of the important Guibal fans used in mine ventilation.
-
-  It is usual to reckon the difference of pressure at the inlet and
-  outlet of a fan in inches of water-column. One inch of water-column =
-  64.4 ft. of air at average atmospheric pressure = 5.2lb. per sq. ft.
-
-  Roughly the pressure-head produced in a fan without means of utilizing
-  the kinetic energy of discharge would be v^2/2g ft. of air, or 0.00024
-  v^2 in. of water, where v is the velocity of the tips of the fan blades
-  in feet per second. If d is the diameter of the fan and t the width at
-  the external circumference, then [pi]dt is the discharge area of the
-  fan disk. If Q is the discharge in cub. ft. per sec., u = Q/[pi]dt is
-  the radial velocity of discharge which is numerically equal to the
-  discharge per square foot of outlet in cubic feet per second. As both
-  the losses in the fan and the work done are roughly proportional to u^2
-  in fans of the same type, and are also proportional to the gauge
-  pressure p, then if the losses are to be a constant percentage of the
-  work done u may be taken proportional to [root]p. In ordinary cases u
-  = about 22[root]p. The width t of the fan is generally from 0.35 to
-  0.45d. Hence if Q is given, the diameter of the fan should be:--
-
-    For t = 0.35d,     d = 0.20 [root](Q/[root]p)
-    For t = 0.45d,     d = 0.18 [root](Q/[root]p)
-
-  If p is the pressure difference in the fan in inches of water, and N
-  the revolutions of fan,
-
-    v = [pi]dN/60         ft. per sec.
-    N = 1230 [root]p/d    revs. per min.
-
-  As the pressure difference is small, the work done in compressing the
-  air is almost exactly 5.2pQ foot-pounds per second. Usually, however,
-  the kinetic energy of the air in the discharge pipe is not
-  inconsiderable compared with the work done in compression. If w is the
-  velocity of the air where the discharge pressure is measured, the air
-  carries away w^2/2g foot-pounds per lb. of air as kinetic energy. In Q
-  cubic feet or 0.0807 Qlb. the kinetic energy is 0.00125 Qw^2
-  foot-pounds per second.
-
-  The efficiency of fans is reckoned in two ways. If B.H.P. is the
-  effective horse-power applied at the fan shaft, then the efficiency
-  reckoned on the work of compression is
-
-    [eta] = 5.2 pQ/550 B.H.P.
-
-  On the other hand, if the kinetic energy in the delivery pipe is taken
-  as part of the useful work the efficiency is
-
-    [eta]2 = (5.2 pQ + 0.00125 Qw^2)/550 B.H.P.
-
-  Although the theory above is a rough one it agrees sufficiently with
-  experiment, with some merely numerical modifications.
-
-  An extremely interesting experimental investigation of the action of
-  centrifugal fans has been made by H. Heenan and W. Gilbert (_Proc.
-  Inst. Civ. Eng._ vol. 123, p. 272). The fans delivered through an air
-  trunk in which different resistances could be obtained by introducing
-  diaphragms with circular apertures of different sizes. Suppose a fan
-  run at constant speed with different resistances and the compression
-  pressure, discharge and brake horse-power measured. The results plot
-  in such a diagram as is shown in fig. 213. The less the resistance to
-  discharge, that is the larger the opening in the air trunk, the
-  greater the quantity of air discharged at the given speed of the fan.
-  On the other hand the compression pressure diminishes. The curve
-  marked total gauge is the compression pressure + the velocity head in
-  the discharge pipe, both in inches of water. This curve falls, but not
-  nearly so much as the compression curve, when the resistance in the
-  air trunk is diminished. The brake horse-power increases as the
-  resistance is diminished because the volume of discharge increases
-  very much. The curve marked efficiency is the efficiency calculated
-  on the work of compression only. It is zero for no discharge, and zero
-  also when there is no resistance and all the energy given to the air
-  is carried away as kinetic energy. There is a discharge for which this
-  efficiency is a maximum; it is about half the discharge which there is
-  when there is no resistance and the delivery pipe is full open. The
-  conditions of speed and discharge corresponding to the greatest
-  efficiency of compression are those ordinarily taken as the best
-  normal conditions of working. The curve marked total efficiency gives
-  the efficiency calculated on the work of compression and kinetic
-  energy of discharge. Messrs Gilbert and Heenan found the efficiencies
-  of ordinary fans calculated on the compression to be 40 to 60% when
-  working at about normal conditions.
-
-  [Illustration: FIG. 213.]
-
-  Taking some of Messrs Heenan and Gilbert's results for ordinary fans
-  in normal conditions, they have been found to agree fairly with the
-  following approximate rules. Let p_c be the compression pressure and q
-  the volume discharged per second per square foot of outlet area of
-  fan. Then the total gauge pressure due to pressure of compression and
-  velocity of discharge is approximately: p = p_c + 0.0004 q^2 in. of
-  water, so that if p_c is given, p can be found approximately. The
-  pressure p depends on the circumferential speed v of the fan disk--
-
-    p = 0.00025 v^2 in. of water
-
-    v = 63 [root]p ft. per sec.
-
-  The discharge per square foot of outlet of fan is--
-
-    q = 15 to 18 [root]p cub. ft. per sec.
-
-  The total discharge is
-
-    Q = [pi] dt q = 47 to 56 dt [root]p
-
-  For
-
-    t = .35d, d = 0.22 to 0.25 [root](Q/[root]p) ft.
-
-    t = .45d, d = 0.20 to 0.22 [root](Q/[root]p) ft.
-
-    N = 1203 [root]p/d.
-
-  These approximate equations, which are derived purely from experiment,
-  do not differ greatly from those obtained by the rough theory given
-  above. The theory helps to explain the reason for the form of the
-  empirical results.     (W. C. U.)
-
-
-FOOTNOTES:
-
-  [1] Except where other units are given, the units throughout this
-    article are feet, pounds, pounds per sq. ft., feet per second.
-
-  [2] _Journal de M. Liouville_, t. xiii. (1868); _Memoires de
-    l'Academie, des Sciences de l'Institut de France_, t. xxiii., xxiv.
-    (1877).
-
-  [3] The following theorem is taken from a paper by J. H. Cotterill,
-    "On the Distribution of Energy in a Mass of Fluid in Steady Motion,"
-    _Phil. Mag._, February 1876.
-
-  [4] The discharge per second varied from .461 to .665 cub. ft. in two
-    experiments. The coefficient .435 is derived from the mean value.
-
-  [5] "Formulae for the Flow of Water in Pipes," _Industries_
-    (Manchester, 1886).
-
-  [6] Boussinesq has shown that this mode of determining the corrective
-    factor [alpha] is not satisfactory.
-
-  [7] In general, because when the water leaves the turbine wheel it
-    ceases to act on the machine. If deflecting vanes or a whirlpool are
-    added to a turbine at the discharging side, then v1 may in part
-    depend on v2, and the statement above is no longer true.
-
-
-
-
-HYDRAZINE (DIAMIDOGEN), N2H4 or H2 N.NH2, a compound of hydrogen and
-nitrogen, first prepared by Th. Curtius in 1887 from diazo-acetic ester,
-N2CH.CO2C2H5. This ester, which is obtained by the action of potassium
-nitrate on the hydrochloride of amidoacetic ester, yields on hydrolysis
-with hot concentrated potassium hydroxide an acid, which Curtius
-regarded as C3H3N6(CO2H)3, but which A. Hantzsch and O. Silberrad
-(_Ber._, 1900, 33, p. 58) showed to be C2H2N4(CO2H)2, bisdiazoacetic
-acid. On digestion of its warm aqueous solution with warm dilute
-sulphuric acid, hydrazine sulphate and oxalic acid are obtained. C. A.
-Lobry de Bruyn (_Ber._, 1895, 28, p. 3085) prepared free hydrazine by
-dissolving its hydrochloride in methyl alcohol and adding sodium
-methylate; sodium chloride was precipitated and the residual liquid
-afterwards fractionated under reduced pressure. It can also be prepared
-by reducing potassium dinitrososulphonate in ice cold water by means of
-sodium amalgam:--
-
-  KSO3 \           KSO3 \
-        > N.NO -->       > N.NH2 --> K2SO4 + N2H4.
-    KO /              H /
-
-P. J. Schestakov (_J. Russ. Phys. Chem. Soc._, 1905, 37, p. 1) obtained
-hydrazine by oxidizing urea with sodium hypochlorite in the presence of
-benzaldehyde, which, by combining with the hydrazine, protected it from
-oxidation. F. Raschig (German Patent 198307, 1908) obtained good yields
-by oxidizing ammonia with sodium hypochlorite in solutions made viscous
-with glue. Free hydrazine is a colourless liquid which boils at 113.5
-deg. C., and solidifies about 0 deg. C. to colourless crystals; it is
-heavier than water, in which it dissolves with rise of temperature. It
-is rapidly oxidized on exposure, is a strong reducing agent, and reacts
-vigorously with the halogens. Under certain conditions it may be
-oxidized to azoimide (A. W. Browne and F. F. Shetterly, _J. Amer. C.S._,
-1908, p. 53). By fractional distillation of its aqueous solution
-hydrazine hydrate N2H4.H2O (or perhaps H2N.NH3OH), a strong base, is
-obtained, which precipitates the metals from solutions of copper and
-silver salts at ordinary temperatures. It dissociates completely in a
-vacuum at 143 deg., and when heated under atmospheric pressure to 183
-deg. it decomposes into ammonia and nitrogen (A. Scott, _J. Chem. Soc._,
-1904, 85, p. 913). The sulphate N2H4.H2SO4, crystallizes in tables which
-are slightly soluble in cold water and readily soluble in hot water; it
-is decomposed by heating above 250 deg. C. with explosive evolution of
-gas and liberation of sulphur. By the addition of barium chloride to the
-sulphate, a solution of the hydrochloride is obtained, from which the
-crystallized salt may be obtained on evaporation.
-
-  Many organic derivatives of hydrazine are known, the most important
-  being phenylhydrazine, which was discovered by Emil Fischer in 1877.
-  It can be best prepared by V. Meyer and Lecco's method (_Ber._, 1883,
-  16, p. 2976), which consists in reducing phenyldiazonium chloride in
-  concentrated hydrochloric acid solution with stannous chloride also
-  dissolved in concentrated hydrochloric acid. Phenylhydrazine is
-  liberated from the hydrochloride so obtained by adding sodium
-  hydroxide, the solution being then extracted with ether, the ether
-  distilled off, and the residual oil purified by distillation under
-  reduced pressure. Another method is due to E. Bamberger. The diazonium
-  chloride, by the addition of an alkaline sulphite, is converted into a
-  diazosulphonate, which is then reduced by zinc dust and acetic acid to
-  phenylhydrazine potassium sulphite. This salt is then hydrolysed by
-  heating it with hydrochloric acid--
-
-    C6H5N2Cl + K2SO3 = KCl + C6H5N2.SO3K,
-
-    C6H5N2.SO3K + 2H = C6H5.NH.NH.SO3K,
-
-    C6H5NH.NH.SO3K + HCl + H2O = C6H5.NH.NH2.HCl + KHSO4.
-
-  Phenylhydrazine is a colourless oily liquid which turns brown on
-  exposure. It boils at 241 deg. C., and melts at 17.5 deg. C. It is
-  slightly soluble in water, and is strongly basic, forming well-defined
-  salts with acids. For the detection of substances containing the
-  carbonyl group (such for example as aldehydes and ketones)
-  phenylhydrazine is a very important reagent, since it combines with
-  them with elimination of water and the formation of well-defined
-  hydrazones (see ALDEHYDES, KETONES and SUGARS). It is a strong
-  reducing agent; it precipitates cuprous oxide when heated with
-  Fehling's solution, nitrogen and benzene being formed at the same
-  time--C6H5.NH.NH2 + 2CuO = Cu2O + N2 + H2O + C6H5. By energetic
-  reduction of phenylhydrazine (e.g. by use of zinc dust and
-  hydrochloric acid), ammonia and aniline are produced--C6H5NH.NH2 + 2H
-  = C6H5NH2 + NH3. It is also a most important synthetic reagent. It
-  combines with aceto-acetic ester to form phenylmethylpyrazolone, from
-  which antipyrine (q.v.) may be obtained. Indoles (q.v.) are formed by
-  heating certain hydrazones with anhydrous zinc chloride; while
-  semicarbazides, pyrrols (q.v.) and many other types of organic
-  compounds may be synthesized by the use of suitable phenylhydrazine
-  derivatives.
-
-
-
-
-HYDRAZONE, in chemistry, a compound formed by the condensation of a
-hydrazine with a carbonyl group (see ALDEHYDES; KETONES).
-
-
-
-
-HYDROCARBON, in chemistry, a compound of carbon and hydrogen. Many occur
-in nature in the free state: for example, natural gas, petroleum and
-paraffin are entirely composed of such bodies; other natural sources are
-india-rubber, turpentine and certain essential oils. They are also
-revealed by the spectroscope in stars, comets and the sun. Of artificial
-productions the most fruitful and important is provided by the
-destructive or dry distillation of many organic substances; familiar
-examples are the distillation of coal, which yields ordinary lighting
-gas, composed of gaseous hydrocarbons, and also coal tar, which, on
-subsequent fractional distillations, yields many liquid and solid
-hydrocarbons, all of high industrial value. For details reference should
-be made to the articles wherein the above subjects are treated. From the
-chemical point of view the hydrocarbons are of fundamental importance,
-and, on account of their great number, and still greater number of
-derivatives, they are studied as a separate branch of the science,
-namely, organic chemistry.
-
-  See CHEMISTRY for an account of their classification, &c.
-
-
-
-
-HYDROCELE (Gr. [Greek: hydor], water, and [Greek: kele], tumour), the
-medical term for any collection of fluid other than pus or blood in the
-neighbourhood of the testis or cord. The fluid is usually serous.
-Hydrocele may be congenital or arise in the middle-aged without apparent
-cause, but it is usually associated with chronic orchitis or with
-tertiary syphilitic enlargements. The hydrocele appears as a rounded,
-fluctuating translucent swelling in the scrotum, and when greatly
-distended causes a dragging pain. Palliative treatment consists in
-tapping aseptically and removing the fluid, the patient afterwards
-wearing a suspender. The condition frequently recurs and necessitates
-radical treatment. Various substances may be injected; or the hydrocele
-is incised, the tunica partly removed and the cavity drained.
-
-
-
-
-HYDROCEPHALUS (Gr. [Greek: hydor], water, and [Greek: kephale], head), a
-term applied to disease of the brain which is attended with excessive
-effusion of fluid into its cavities. It exists in two forms--_acute_ and
-_chronic hydrocephalus_. Acute hydrocephalus is another name for
-tuberculous meningitis (see MENINGITIS).
-
-_Chronic hydrocephalus_, or "water on the brain," consists in an
-effusion of fluid into the lateral ventricles of the brain. It is not
-preceded by tuberculous deposit or acute inflammation, but depends upon
-congenital malformation or upon chronic inflammatory changes affecting
-the membranes. When the disease is congenital, its presence in the
-foetus is apt to be a source of difficulty in parturition. It is however
-more commonly developed in the first six months of life; but it
-occasionally arises in older children, or even in adults. The chief
-symptom is the gradual increase in size of the upper part of the head
-out of all proportion to the face or the rest of the body. Occurring at
-an age when as yet the bones of the skull have not become welded
-together, the enlargement may go on to an enormous extent, the Spaces
-between the bones becoming more and more expanded. In a well-marked case
-the deformity is very striking; the upper part of the forehead projects
-abnormally, and the orbital plates of the frontal bone being inclined
-forwards give a downward tilt to the eyes, which have also peculiar
-rolling movements. The face is small, and this, with the enlarged head,
-gives a remarkable aged expression to the child. The body is
-ill-nourished, the bones are thin, the hair is scanty and fine and the
-teeth carious or absent.
-
-The average circumference of the adult head is 22 in., and in the normal
-child it is of course much less. In chronic hydrocephalus the head of an
-infant three months old has measured 29 in.; and in the case of the man
-Cardinal, who died in Guy's Hospital, the head measured 33 in. In such
-cases the head cannot be supported by the neck, and the patient has to
-keep mostly in the recumbent posture. The expansibility of the skull
-prevents destructive pressure on the brain, yet this organ is materially
-affected by the presence of the fluid. The cerebral ventricles are
-distended, and the convolutions are flattened. Occasionally the fluid
-escapes into the cavity of the cranium, which it fills, pressing down
-the brain to the base of the skull. As a consequence, the functions of
-the brain are interfered with, and the mental condition is impaired. The
-child is dull, listless and irritable, and sometimes imbecile. The
-special senses become affected as the disease advances; sight is often
-lost, as is also hearing. Hydrocephalic children generally sink in a few
-years; nevertheless there have been instances of persons with this
-disease living to old age. There are, of course, grades of the
-affection, and children may present many of the symptoms of it in a
-slight degree, and yet recover, the head ceasing to expand, and becoming
-in due course firmly ossified.
-
-Various methods of treatment have been employed, but the results are
-unsatisfactory. Compression of the head by bandages, and the
-administration of mercury with the view of promoting absorption of the
-fluid, are now little resorted to. Tapping the fluid from time to time
-through one of the spaces between the bones, drawing off a little, and
-thereafter employing gentle pressure, has been tried, but rarely with
-benefit. Attempts have also been made to establish a permanent drainage
-between the interior of the lateral ventricle and the sub-dural space,
-and between the lumbar region of the spine and the abdomen, but without
-satisfactory results. On the whole, the plan of treatment which aims at
-maintaining the patient's nutrition by appropriate food and tonics is
-the most rational and successful.     (E. O.*)
-
-
-
-
-HYDROCHARIDEAE, in botany, a natural order of Monocotyledons, belonging
-to the series Helobieae. They are water-plants, represented in Britain
-by frog-bit (_Hydrocharis Morsusranae_) and water-soldier (_Stratiotes
-aloides_). The order contains about fifty species in fifteen genera,
-twelve of which occur in fresh water while three are marine: and
-includes both floating and submerged forms. _Hydrocharis_ floats on the
-surface of still water, and has rosettes of kidney-shaped leaves, from
-among which spring the flower-stalks; stolons bearing new leaf-rosettes
-are sent out on all sides, the plant thus propagating itself on the same
-way as the strawberry. _Stratiotes aloides_ has a rosette of stiff
-sword-like leaves, which when the plant is in flower project above the
-surface; it is also stoloniferous, the young rosettes sinking to the
-bottom at the beginning of winter and rising again to the surface in the
-spring. _Vallisneria_ (eel-grass) contains two species, one native of
-tropical Asia, the other inhabiting the warmer parts of both hemispheres
-and reaching as far north as south Europe. It grows in the mud at the
-bottom of fresh water, and the short stem bears a cluster of long,
-narrow grass-like leaves; new plants are formed at the end of horizontal
-runners. Another type is represented by _Elodea canadensis_ or
-water-thyme, which has been introduced into the British Isles from North
-America. It is a small, submerged plant with long, slender branching
-stems bearing whorls of narrow toothed leaves; the flowers appear at the
-surface when mature. _Halophila_, _Enhalus_ and _Thalassia_ are
-submerged maritime plants found on tropical coasts, mainly in the Indian
-and Pacific oceans; _Halophila_ has an elongated stem rooting at the
-nodes; _Enhalus_ a short, thick rhizome, clothed with black threads
-resembling horse-hair, the persistent hard-bast strands of the leaves;
-_Thalassia_ has a creeping rooting stem with upright branches bearing
-crowded strap-shaped leaves in two rows. The flowers spring from, or are
-enclosed in, a spathe, and are unisexual and regular, with generally a
-calyx and corolla, each of three members; the stamens are in whorls of
-three, the inner whorls are often barren; the two to fifteen carpels
-form an inferior ovary containing generally numerous ovules on often
-large, produced, parietal placentas. The fruit is leathery or fleshy,
-opening irregularly. The seeds contain a large embryo and no endosperm.
-In _Hydrocharis_ (fig. 1), which is dioecious, the flowers are borne
-above the surface of the water, have conspicuous white petals, contain
-honey and are pollinated by insects. _Stratiotes_ has similar flowers
-which come above the surface only for pollination, becoming submerged
-again during ripening of the fruit. In _Vallisneria_ (fig. 2), which is
-also dioecious, the small male flowers are borne in large numbers in
-short-stalked spathes; the petals are minute and scale-like, and only
-two of the three stamens are fertile; the flowers become detached before
-opening and rise to the surface, where the sepals expand and form a
-float bearing the two projecting semi-erect stamens. The female flowers
-are solitary and are raised to the surface on a long, spiral stalk; the
-ovary bears three broad styles, on which some of the large, sticky
-pollen-grains from the floating male flowers get deposited, (fig. 3).
-After pollination the female flower becomes drawn below the surface by
-the spiral contraction of the long stalk, and the fruit ripens near the
-bottom. _Elodea_ has polygamous flowers (that is, male, female and
-hermaphrodite), solitary, in slender, tubular spathes; the male flowers
-become detached and rise to the surface; the females are raised to the
-surface when mature, and receive the floating pollen from the male. The
-flowers of _Halophila_ are submerged and apetalous.
-
-[Illustration: FIG. 1.--_Hydrocharis Morsusranae_--Frog-bit--male plant.
-
-  1, Female flower.
-  2, Stamens, enlarged.
-  3, Barren pistil of male flower, enlarged.
-  4, Pistil of female flower.
-  5, Fruit.
-  6, Fruit cut transversely.
-  7, Seed.
-  8, 9, Floral diagrams of male and female flowers respectively.
-  s, Rudimentary stamens.]
-
-[Illustration: FIG. 2.--_Vallisneria spiralis_--Eel grass--about 1/4
-natural size. A, Female plant; B, Male plant.]
-
-[Illustration: FIG. 3.]
-
-The order is a widely distributed one; the marine forms are tropical or
-subtropical, but the fresh-water genera occur also in the temperate
-zones.
-
-
-
-
-HYDROCHLORIC ACID, also known in commerce as "spirits of salts" and
-"muriatic acid," a compound of hydrogen and chlorine. Its chemistry is
-discussed under CHLORINE, and its manufacture under ALKALI MANUFACTURE.
-
-
-
-
-HYDRODYNAMICS (Gr. [Greek: hydor], water, [Greek: dynamis], strength),
-the branch of hydromechanics which discusses the motion of fluids (see
-HYDROMECHANICS).
-
-
-
-
-HYDROGEN [symbol H, atomic weight 1.008 (o = 16)], one of the chemical
-elements. Its name is derived from Gr. [Greek: hydor], water, and
-[Greek: gennaein], to produce, in allusion to the fact that water is
-produced when the gas burns in air. Hydrogen appears to have been
-recognized by Paracelsus in the 16th century; the combustibility of the
-gas was noticed by Turquet de Mayenne in the 17th century, whilst in
-1700 N. Lemery showed that a mixture of hydrogen and air detonated on
-the application of a light. The first definite experiments concerning
-the nature of hydrogen were made in 1766 by H. Cavendish, who showed
-that it was formed when various metals were acted upon by dilute
-sulphuric or hydrochloric acids. Cavendish called it "inflammable air,"
-and for some time it was confused with other inflammable gases, all of
-which were supposed to contain the same inflammable principle,
-"phlogiston," in combination with varying amounts of other substances.
-In 1781 Cavendish showed that water was the only substance produced when
-hydrogen was burned in air or oxygen, it having been thought previously
-to this date that other substances were formed during the reaction, A.
-L. Lavoisier making many experiments with the object of finding an acid
-among the products of combustion.
-
-Hydrogen is found in the free state in some volcanic gases, in
-fumaroles, in the carnallite of the Stassfurt potash mines (H. Precht,
-_Ber._, 1886, 19, p. 2326), in some meteorites, in certain stars and
-nebulae, and also in the envelopes of the sun. In combination it is
-found as a constituent of water, of the gases from certain mineral
-springs, in many minerals, and in most animal and vegetable tissues. It
-may be prepared by the electrolysis of acidulated water, by the
-decomposition of water by various metals or metallic hydrides, and by
-the action of many metals on acids or on bases. The alkali metals and
-alkaline earth metals decompose water at ordinary temperatures;
-magnesium begins to react above 70 deg. C., and zinc at a dull red heat.
-The decomposition of steam by red hot iron has been studied by H.
-Sainte-Claire Deville (_Comptes rendus_, 1870, 70, p. 1105) and by H.
-Debray (ibid., 1879, 88, p. 1341), who found that at about 1500 deg. C.
-a condition of equilibrium is reached. H. Moissan (_Bull. soc. chim._,
-1902, 27, p. 1141) has shown that potassium hydride decomposes cold
-water, with evolution of hydrogen, KH + H2O = KOH + H2. Calcium hydride
-or hydrolite, prepared by passing hydrogen over heated calcium,
-decomposes water similarly, 1 gram giving 1 litre of gas; it has been
-proposed as a commercial source (Prats Aymerich, _Abst. J.C.S._, 1907,
-ii. p. 543), as has also aluminium turnings moistened with potassium
-cyanide and mercuric chloride, which decomposes water regularly at 70
-deg., 1 gram giving 1.3 litres of gas (Mauricheau-Beaupre, _Comptes
-rendus_, 1908, 147, p. 310). Strontium hydride behaves similarly. In
-preparing the gas by the action of metals on acids, dilute sulphuric or
-hydrochloric acid is taken, and the metals commonly used are zinc or
-iron. So obtained, it contains many impurities, such as carbon dioxide,
-nitrogen, oxides of nitrogen, phosphoretted hydrogen, arseniuretted
-hydrogen, &c., the removal of which is a matter of great difficulty (see
-E. W. Morley, _Amer. Chem. Journ._, 1890, 12, p. 460). When prepared by
-the action of metals on bases, zinc or aluminium and caustic soda or
-caustic potash are used. Hydrogen may also be obtained by the action of
-zinc on ammonium salts (the nitrate excepted) (Lorin, _Comptes rendus_,
-1865, 60, p. 745) and by heating the alkali formates or oxalates with
-caustic potash or soda, Na2C2O4 + 2NaOH = H2 + 2Na2CO3. Technically it
-is prepared by the action of superheated steam on incandescent coke (see
-F. Hembert and Henry, _Comptes rendus_, 1885, 101, p. 797; A. Naumann
-and C. Pistor, _Ber._, 1885, 18, p. 1647), or by the electrolysis of a
-dilute solution of caustic soda (C. Winssinger, _Chem. Zeit._, 1898,
-22, p. 609; "Die Elektrizitats-Aktiengesellschaft," _Zeit. f.
-Elektrochem._, 1901, 7, p. 857). In the latter method a 15% solution of
-caustic soda is used, and the electrodes are made of iron; the cell is
-packed in a wooden box, surrounded with sand, so that the temperature is
-kept at about 70 deg. C.; the solution is replenished, when necessary,
-with distilled water. The purity of the gas obtained is about 97%.
-
-Pure hydrogen is a tasteless, colourless and odourless gas of specific
-gravity 0.06947 (air = 1) (Lord Rayleigh, _Proc. Roy. Soc._, 1893, p.
-319). It may be liquefied, the liquid boiling at -252.68 deg. C. to
--252.84 deg. C., and it has also been solidified, the solid melting at
--264 deg. C. (J. Dewar, _Comptes rendus_, 1899, 129, p. 451; _Chem.
-News_, 1901, 84, p. 49; see also LIQUID GASES). The specific heat of
-gaseous hydrogen (at constant pressure) is 3.4041 (water = 1), and the
-ratio of the specific heat at constant pressure to the specific heat at
-constant volume is 1.3852 (W. C. Rontgen, _Pogg. Ann._, 1873, 148, p.
-580). On the spectrum see SPECTROSCOPY. Hydrogen is only very slightly
-soluble in water. It diffuses very rapidly through a porous membrane,
-and through some metals at a red heat (T. Graham, _Proc. Roy. Soc._,
-1867, 15, p. 223; H. Sainte-Claire Deville and L. Troost, _Comptes
-rendus_, 1863, 56, p. 977). Palladium and some other metals are capable
-of absorbing large volumes of hydrogen (especially when the metal is
-used as a cathode in a water electrolysis apparatus). L. Troost and P.
-Hautefeuille (_Ann. chim. phys._, 1874, (5) 2, p. 279) considered that a
-palladium hydride of composition Pd2H was formed, but the investigations
-of C. Hoitsema (_Zeit. phys. Chem._, 1895, 17, p. 1), from the
-standpoint of the phase rule, do not favour this view, Hoitsema being of
-the opinion that the occlusion of hydrogen by palladium is a process of
-continuous absorption. Hydrogen burns with a pale blue non-luminous
-flame, but will not support the combustion of ordinary combustibles. It
-forms a highly explosive mixture with air or oxygen, especially when in
-the proportion of two volumes of hydrogen to one volume of oxygen. H. B.
-Baker (_Proc. Chem. Soc._, 1902, 18, p. 40) has shown that perfectly dry
-hydrogen will not unite with perfectly dry oxygen. Hydrogen combines
-with fluorine, even at very low temperatures, with great violence; it
-also combines with carbon, at the temperature of the electric arc. The
-alkali metals when warmed in a current of hydrogen, at about 360 deg.
-C., form hydrides of composition RH (R = Na, K, Rb, Cs), (H. Moissan,
-_Bull. soc. chim._, 1902, 27, p. 1141); calcium and strontium similarly
-form hydrides CaH2, SrH2 at a dull red heat (A. Guntz, _Comptes rendus_,
-1901, 133, p. 1209). Hydrogen is a very powerful reducing agent; the gas
-occluded by palladium being very active in this respect, readily
-reducing ferric salts to ferrous salts, nitrates to nitrites and
-ammonia, chlorates to chlorides, &c.
-
-  For determinations of the volume ratio with which hydrogen and oxygen
-  combine, see J. B. Dumas, _Ann. chim. phys._, 1843 (3), 8, p. 189; O.
-  Erdmann and R. F. Marchand, ibid., p. 212; E. H. Keiser, _Ber._, 1887,
-  20, p. 2323; J. P. Cooke and T. W. Richards, _Amer. Chem. Journ._,
-  1888, 10, p. 191; Lord Rayleigh, _Chem. News_, 1889, 59, p. 147; E. W.
-  Morley, _Zeit. phys. Chem._, 1890, 20, p. 417; and S. A. Leduc,
-  _Comptes rendus_, 1899, 128, p. 1158.
-
-Hydrogen combines with oxygen to form two definite compounds, namely,
-water (q.v.), H2O, and hydrogen peroxide, H2O2, whilst the existence of
-a third oxide, ozonic acid, has been indicated.
-
-_Hydrogen peroxide_, H2O2, was discovered by L. J. Thenard in 1818
-(_Ann. chim. phys._, 8, p. 306). It occurs in small quantities in the
-atmosphere. It may be prepared by passing a current of carbon dioxide
-through ice-cold water, to which small quantities of barium peroxide are
-added from time to time (F. Duprey, _Comptes rendus_, 1862, 55, p. 736;
-A. J. Balard, ibid., p. 758), BaO2 + CO2 + H2O = H2O2 + BaCO3. E. Merck
-(_Abst. J.C.S._, 1907, ii., p. 859) showed that barium percarbonate,
-BaCO4, is formed when the gas is in excess; this substance readily
-yields the peroxide with an acid. Or barium peroxide may be decomposed
-by hydrochloric, hydrofluoric, sulphuric or silicofluoric acids (L.
-Crismer, _Bull. soc. chim._, 1891 (3), 6, p. 24; Hanriot, _Comptes
-rendus_, 1885, 100, pp. 56, 172), the peroxide being added in
-small quantities to a cold dilute solution of the acid. It is necessary
-that it should be as pure as possible since the commercial product
-usually contains traces of ferric, manganic and aluminium oxides,
-together with some silica. To purify the oxide, it is dissolved in
-dilute hydrochloric acid until the acid is neatly neutralized, the
-solution is cooled, filtered, and baryta water is added until a faint
-permanent white precipitate of hydrated barium peroxide appears; the
-solution is now filtered, and a concentrated solution of baryta water is
-added to the filtrate, when a crystalline precipitate of hydrated barium
-peroxide, BaO2.H2O, is thrown down. This is filtered off and well washed
-with water. The above methods give a dilute aqueous solution of hydrogen
-peroxide, which may be concentrated somewhat by evaporation over
-sulphuric acid in vacuo. H. P. Talbot and H. R. Moody (_Jour. Anal.
-Chem._, 1892, 6, p. 650) prepared a more concentrated solution from the
-commercial product, by the addition of a 10% solution of alcohol and
-baryta water. The solution is filtered, and the barium precipitated by
-sulphuric acid. The alcohol is removed by distillation _in vacuo_, and
-by further concentration _in vacuo_ a solution may be obtained which
-evolves 580 volumes of oxygen. R. Wolffenstein (_Ber._, 1894, 27, p.
-2307) prepared practically anhydrous hydrogen peroxide (containing 99.1%
-H2O2) by first removing all traces of dust, heavy metals and alkali from
-the commercial 3% solution. The solution is then concentrated in an open
-basis on the water-bath until it contains 48% H2O2. The liquid so
-obtained is extracted with ether and the ethereal solution distilled
-under diminished pressure, and finally purified by repeated
-distillations. W. Staedel (_Zeit. f. angew. Chem._, 1902, 15, p. 642)
-has described solid hydrogen peroxide, obtained by freezing concentrated
-solutions.
-
-Hydrogen peroxide is also found as a product in many chemical actions,
-being formed when carbon monoxide and cyanogen burn in air (H. B.
-Dixon); by passing air through solutions of strong bases in the presence
-of such metals as do not react with the bases to liberate hydrogen; by
-shaking zinc amalgam with alcoholic sulphuric acid and air (M. Traube,
-_Ber._, 1882, 15, p. 659); in the oxidation of zinc, lead and copper in
-presence of water, and in the electrolysis of sulphuric acid of such
-strength that it contains two molecules of water to one molecule of
-sulphuric acid (M. Berthelot, _Comptes rendus_, 1878, 86, p. 71).
-
-The anhydrous hydrogen peroxide obtained by Wolffenstein boils at 84-85
-deg.C. (68 mm.); its specific gravity is 1.4996 (1.5 deg. C.). It is
-very explosive (W. Spring, _Zeit. anorg. Chem._, 1895, 8, p. 424). The
-explosion risk seems to be most marked in the preparations which have
-been extracted with ether previous to distillation, and J. W. Bruhl
-(_Ber._, 1895, 28, p. 2847) is of opinion that a very unstable, more
-highly oxidized product is produced in small quantity in the process.
-The solid variety prepared by Staedel forms colourless, prismatic
-crystals which melt at -2 deg. C.; it is decomposed with explosive
-violence by platinum sponge, and traces of manganese dioxide. The dilute
-aqueous solution is very unstable, giving up oxygen readily, and
-decomposing with explosive violence at 100 deg. C. An aqueous solution
-containing more than 1.5% hydrogen peroxide reacts slightly acid.
-Towards lupetidin [aa' dimethyl piperidine, C5H9N(CH3)2] hydrogen
-peroxide acts as a dibasic acid (A. Marcuse and R. Wolffenstein, _Ber._,
-1901, 34, p. 2430; see also G. Bredig, _Zeit. Electrochem._, 1901, 7, p.
-622). Cryoscopic determinations of its molecular weight show that it is
-H2O2. [G. Carrara, _Rend. della Accad. dei Lincei_, 1892 (5), 1, ii. p.
-19; W. R. Orndorff and J. White, _Amer. Chem. Journ._, 1893, 15, p.
-347.] Hydrogen peroxide behaves very frequently as a powerful oxidizing
-agent; thus lead sulphide is converted into lead sulphate in presence of
-a dilute aqueous solution of the peroxide, the hydroxides of the
-alkaline earth metals are converted into peroxides of the type MO2.8H2O,
-titanium dioxide is converted into the trioxide, iodine is liberated
-from potassium iodide, and nitrites (in alkaline solution) are converted
-into acid-amides (B. Radziszewski, _Ber._, 1884, 17, p. 355). In many
-cases it is found that hydrogen peroxide will only act as an oxidant
-when in the presence of a catalyst; for example, formic, glycollic,
-lactic, tartaric, malic, benzoic and other organic acids are readily
-oxidized in the presence of ferrous sulphate (H. J. H. Fenton, _Jour.
-Chem. Soc._, 1900, 77, p. 69), and sugars are readily oxidized in the
-presence of ferric chloride (O. Fischer and M. Busch, _Ber._, 1891, 24,
-p. 1871). It is sought to explain these oxidation processes by assuming
-that the hydrogen peroxide unites with the compound undergoing oxidation
-to form an addition compound, which subsequently decomposes (J. H.
-Kastle and A. S. Loevenhart, _Amer. Chem. Journ._, 1903, 29, pp. 397,
-517). Hydrogen peroxide can also react as a reducing agent, thus silver
-oxide is reduced with a rapid evolution of oxygen. The course of this
-reaction can scarcely be considered as definitely settled; M. Berthelot
-considers that a higher oxide of silver is formed, whilst A. Baeyer and
-V. Villiger are of opinion that reduced silver is obtained [see _Comptes
-rendus_, 1901, 133, p. 555; _Ann. Chim. Phys._, 1897 (7), 11, p. 217,
-and Ber., 1901, 34, p. 2769]. Potassium permanganate, in the presence of
-dilute sulphuric acid, is rapidly reduced by hydrogen peroxide, oxygen
-being given off, 2KMnO4 + 3H2SO4 + 5H2O2 = K2SO4 + 2MnSO4 + 8H2O + 5O2.
-Lead peroxide is reduced to the monoxide. Hypochlorous acid and its
-salts, together with the corresponding bromine and iodine compounds,
-liberate oxygen violently from hydrogen peroxide, giving hydrochloric,
-hydrobromic and hydriodic acids (S. Tanatar, _Ber._, 1899, 32, p. 1013).
-
-  On the constitution of hydrogen peroxide see C. F. Schonbein, _Jour.
-  prak. Chem._, 1858-1868; M. Traube, _Ber._, 1882-1889; J. W. Bruhl,
-  _Ber._, 1895, 28, p. 2847; 1900, 33, p. 1709; S. Tanatar, _Ber._,
-  1903, 36, p. 1893.
-
-  Hydrogen peroxide finds application as a bleaching agent, as an
-  antiseptic, for the removal of the last traces of chlorine and sulphur
-  dioxide employed in bleaching, and for various quantitative
-  separations in analytical chemistry (P. Jannasch, _Ber._, 1893, 26, p.
-  2908). It may be estimated by titration with potassium permanganate in
-  acid solution; with potassium ferricyanide in alkaline solution,
-  2K3Fe(CN)6 + 2KOH + H2O2 = 2K4Fe(CN)6 + 2H2O + O2; or by oxidizing
-  arsenious acid in alkaline solution with the peroxide and back
-  titration of the excess of arsenious acid with standard iodine (B.
-  Grutzner, _Arch. der Pharm._, 1899, 237, p. 705). It may be recognized
-  by the violet coloration it gives when added to a very dilute solution
-  of potassium bichromate in the presence of hydrochloric acid; by the
-  orange-red colour it gives with a solution of titanium dioxide in
-  concentrated sulphuric acid; and by the precipitate of Prussian blue
-  formed when it is added to a solution containing ferric chloride and
-  potassium ferricyanide.
-
-  _Ozonic Acid_, H2O4. By the action of ozone on a 40% solution of
-  potassium hydroxide, placed in a freezing mixture, an orange-brown
-  substance is obtained, probably K2O4, which A. Baeyer and V. Villiger
-  (_Ber._, 1902, 35, p. 3038) think is derived from ozonic acid,
-  produced according to the reaction O3 + H2O = H2O4.
-
-
-
-
-HYDROGRAPHY (Gr. [Greek: hydor], water, and [Greek: graphein], to
-write), the science dealing with all the waters of the earth's surface,
-including the description of their physical features and conditions; the
-preparation of charts and maps showing the position of lakes, rivers,
-seas and oceans, the contour of the sea-bottom, the position of
-shallows, deeps, reefs and the direction and volume of currents; a
-scientific description of the position, volume, configuration, motion
-and condition of all the waters of the earth. See also SURVEYING
-(Nautical) and OCEAN AND OCEANOGRAPHY. The Hydrographic Department of
-the British Admiralty, established in 1795, undertakes the making of
-charts for the admiralty, and is under the charge of the hydrographer to
-the admiralty (see CHART).
-
-
-
-
-HYDROLYSIS (Gr. [Greek: hydor], water, [Greek: luein], to loosen), in
-chemistry, a decomposition brought about by water after the manner shown
-in the equation R.X + H.OH = R.H + X.OH. Modern research has proved that
-such reactions are not occasioned by water acting as H2O, but really by
-its ions (hydrions and hydroxidions), for the velocity is proportional
-(in accordance with the law of chemical mass action) to the
-concentration of these ions. This fact explains the so-called
-"catalytic" action of acids and bases in decomposing such compounds as
-the esters. The term "saponification" (Lat. _sapo_, soap) has the same
-meaning, but it is more properly restricted to the hydrolysis of the
-fats, i.e. glyceryl esters of organic acids, into glycerin and a soap
-(see CHEMICAL ACTION).
-
-
-
-
-
-
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