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+*** START OF THE PROJECT GUTENBERG EBOOK 40538 ***
+
+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 × 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
+
+  ENCYCLOPÆDIA 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
+
+  ENCYCLOPÆDIA BRITANNICA
+
+  A DICTIONARY OF
+  ARTS, SCIENCES, LITERATURE AND GENERAL INFORMATION
+
+  ELEVENTH EDITION
+
+  VOLUME XIV
+  HUSBAND to ITALIC
+
+  New York
+
+  Encyclopædia Britannica, Inc.
+  342 Madison Avenue
+
+
+  Copyright, in the United States of America, 1910,
+  by
+  The Encyclopædia 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 GÜNTHER, 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 Tübingen. 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. Hü.
+    EMIL HÜBNER.
+
+      See the biographical article, HÜBNER, 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 Nachbarstämme_.
+
+    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 KRÜGER, 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 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.
+
+    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 LÜTZOW, 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 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_.
+
+    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. 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
+      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 BLÖNDAL.
+
+      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
+      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;
+    Innsbruck;
+    Interlaken;
+    Iseo, Lake of;
+    Isère (_River_);
+    Isère (_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.
+
+
+
+
+  ENCYCLOPÆDIA 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 _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.
+"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 _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,
+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, § 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_, § 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 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 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 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
+  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
+  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
+  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.
+  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).
+
+
+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 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,
+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 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
+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 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.)
+
+
+
+
+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
+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 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
+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 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
+  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 naïveté 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 £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
+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 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
+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 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
+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 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,
+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 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
+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. 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.
+  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
+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,
+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,
+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 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
+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 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
+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 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.
+
+
+
+
+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° 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 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
+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 _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
+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 _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
+  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
+  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.)
+
+
+
+
+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 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
+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
+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
+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
+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),
+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
+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.
+  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° 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 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
+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
+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
+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°. 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. röm.
+  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, _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._
+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 _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
+  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 Paternò; 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 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
+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. 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 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. 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
+  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 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
+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.--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
+  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
+  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,
+  _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
+  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._
+  (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;
+  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 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.
+
+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 à 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, 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
+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 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
+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
+(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'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
+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
+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
+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 _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.
+
+
+
+
+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 &
+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 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
+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
+(£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)
+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
+5½ 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 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
+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 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
+  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
+£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).
+
+
+
+
+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: 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
+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.
+
+§ 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.
+
+§ 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]°
+  Fahr. in pounds, when the velocities are expressed in feet per second,
+  is
+
+    [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
+  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.]
+
+§ 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
+
+  § 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° 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
+  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
+  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.
+
+  § 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° 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.
+  The values of [rho] are the densities in grammes per cubic centimetre.
+
+  § 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
+
+  § 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° 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° 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
+  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.;
+
+    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° F. For steam R =
+  85.5.
+
+
+II. KINEMATICS OF FLUIDS
+
+§ 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.
+
+  § 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.
+
+  § 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.]
+
+  § 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.
+
+  § 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) § 9, if the temperature is constant,
+
+    p1A1v1 = p2A2v2.   (3)
+
+  § 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
+
+  § 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 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
+  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_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
+  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 × 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.
+
+  [Illustration: FIG. 16.]
+
+  § 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 = ½gt².
+
+  Eliminating t,
+
+    v_a = [root](gx²/2y).
+
+  Then
+
+    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).
+
+  [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.]
+
+  § 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}.
+
+  § 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° to
+    55°._
+
+    +-------+--------------------------------------------------------------+
+    |Head in|             Diameters of Orifices in Inches (d).             |
+    | feet  +------+------+------+------+------+------+------+------+------+
+    |   h.  |   1  |  1¼  |  1½  |  1¾  |   2  |  2¼  |  2½  |  2¾  |   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   |  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.|
+    |        | 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.  |
+    |        | 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  |
+    +--------+------+------+------+------+--------+--------+--------+---------+
+
+  § 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}.
+
+  § 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 ¼, ½, or ¾ 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.
+
+  § 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.]
+
+  § 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.]
+
+  § 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.
+
+  § 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:--
+
+    Temperature F.      C.
+        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
+
+  an increase in velocity of discharge of 4% when the temperature
+  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
+  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.
+  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.
+  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
+  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.
+
+  § 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.
+
+  § 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] × 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
+  the work done on the mass AB,
+
+    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)
+
+  or, as A and B are any two points,
+
+    v²/2g + p/G + z = constant = H.   (2)
+
+  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
+  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
+  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
+
+    v²/2g + p/G - h = v1²/2g + p1/G - h1;   (3)
+
+  or generally
+
+    v²/2g + p/G - h = constant.   (3a)
+
+  [Illustration: FIG. 26.]
+
+  § 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
+  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), § 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
+  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.
+
+  § 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 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.
+
+  [Illustration: FIG. 30.]
+
+  [Illustration: FIG. 31.]
+
+  § 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 + v²/2g = H + u²/2g,
+
+    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)},
+
+  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 × 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.
+
+  § 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 + v²/2g.
+
+  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 = 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)
+
+
+  CURRENTS
+
+  § 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,
+
+     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 + v1²/2g = p2/G + v2²/2g;
+      = p2/G + r1² + v1²/r2²2g;
+
+    (p2- p1)/G = v1²(1 - r1²/r2²)/2g;   (5)
+
+    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
+  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 + 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,
+
+    v² 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.
+
+  § 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
+  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), § 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]²r1²/2g = p2/G - [alpha]²r2²/2g;
+
+    (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
+  paraboloids of revolution (fig. 37).
+
+  [Illustration: FIG. 37.]
+
+
+  DISSIPATION OF HEAD IN SHOCK
+
+  § 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 + 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
+  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 + v²/2g = p1/G + v1²/2g + (v - v1)²/2g.   (3)
+
+  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
+  (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 + (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 =
+  [omega]v, by the quantity
+
+    (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
+  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]v²t.
+  Equating impulse to momentum gained,
+
+    Gh[Omega] = (G/g)[omega]v²t;
+
+    .: [omega]/[Omega] = gh/v²
+
+  But
+
+    v² = 2gh, and [omega]/[Omega] = 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
+  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.]
+
+  § 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 § 29, eq. (3a),
+
+    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;
+
+    v²/2g = 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), § 29,
+
+    0 + h1 + p_a/G - h1 = v²/2g + h3 - h2 + p_a/G;
+
+    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.
+
+  [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.]
+
+  § 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 ½(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.]
+
+  § 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 = 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].
+                                _/0
+
+  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)},
+                    _
+                   /[pi]
+    Q/Q1 = 2/[pi]  |   sin² [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
+
+  § 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 × 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
+  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 (§ 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.
+
+  § 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^(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),
+
+  [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 § 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),
+
+  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.|
+    +----------+------+------+-----+-----+-------+-------------+------+------+------+------+------+------+
+    |     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.]
+
+  § 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´,
+
+    v²/2g = 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
+
+  § 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] = 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 +
+  [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] = 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´ = (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.]
+
+  § 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])^(½) - (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.
+
+  § 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,
+  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 × 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 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
+  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 + 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)
+
+  The original simple equation can be used if
+
+    m = [mu](1 + [alpha]u²/2gh)^(3/2)
+
+  or very approximately, since u²/2gh is small,
+
+    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)
+
+  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 + 2.5u²/2gh)
+      = [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 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
+  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 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
+  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.]
+
+  § 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 = ½gt², x = (2/3)[root](2gh) t;
+
+    .: 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
+  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
+
+  § 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
+  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 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
+
+    (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.
+
+  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 = v1²/2g + p_a/G + (v1²/2g)(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 = ¾h nearly;   (3)
+
+  or
+
+    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.
+
+  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
+  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°  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´.
+
+  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.]
+
+  § 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 = v²/2g + p/G = v1²/2g + p1/G.
+
+  If the jet discharges into the air, p1 = p_a; and
+
+    v1²/2g = 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 = (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;
+
+  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.
+
+  § 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
+
+  § 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
+
+  § 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.
+
+  § 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 § 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.
+
+  § 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.]
+
+  § 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.
+
+  § 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](R² - r²) [root](2gh).
+
+  Taking c = 0.63,
+
+    Q = 15.88(R² - r²) [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
+  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_.
+
+  § 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.]
+
+  § 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 ½ in. of water have been constructed.
+
+  [Illustration: FIG. 75.--Scale 1/24.]
+
+
+  VI. STEADY FLOW OF COMPRESSIBLE FLUIDS.
+
+  [Illustration: FIG. 76.]
+
+  § 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.]
+
+  § 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)
+  (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;
+                                     _/v1
+                                                    _
+                                                   /v2                                                                        /
+    .: 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)
+
+    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)
+
+  or, neglecting the difference of level,
+
+    (v2² - v1²)/2g = (p1/G1) log_[epsilon] (p1/p2).   (2a)
+
+  Similarly, if the expansion is adiabatic (eq. 2a, § 61),
+
+    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 =
+      (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
+  work for a steady stream of compressible fluid is
+
+    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
+  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 + v2²/2g - (p1/G1){1/([gamma] - 1)}
+      {1 - (p2/p1)^([gamma] - 1)/[gamma];
+
+    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.
+
+  But
+
+    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)
+
+  or
+
+    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
+
+    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)}
+      {1 - (p2/p1)^([gamma] - 1)/[gamma]};   (2)
+
+  or, inserting numerical values,
+
+    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
+  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
+
+  § 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.
+
+  § 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 ½
+  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.
+
+  § 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]v²   (1)
+
+  where f is a quantity approximately constant for any given surface. If
+
+    [xi] = 2gf/G,
+
+    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.
+
+  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]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
+  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 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
+  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.
+
+  § 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° 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.
+
+  _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.]
+
+  § 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."
+
+  § 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.
+
+  § 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° 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.
+
+  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.
+
+  § 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 § 66, eq. 3)
+
+    -[zeta]G[chi]dlv³/2g,
+
+  or, since Q = [Omega]v,
+
+    -[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.
+
+  Dividing by GQ,
+
+    dz + dp/G + [zeta]([chi]/[Omega])(v²/2g) dl = 0.
+
+  Integrating,
+
+    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
+  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;
+
+  or, if l2 - l1 = L, rearranging the terms,
+
+    [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
+  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]v²/2g = mh/L = mi.   (3)
+
+  For pipes of circular section, and diameter d,
+
+    m = [Omega]/[chi] = ¼[pi]d²/[pi]d = ¼d.
+
+  Then
+
+    [zeta]v²/2g = ¼dh/L = ¼di;   (4)
+
+  or
+
+    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
+  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.
+
+  § 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.]
+
+  § 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
+  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
+  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
+
+    GQh = GQv²/2g + GQ[zeta]0v²/2g + GQ[zeta]·4L·v²/d·2g;
+
+    h = (1 + [zeta]0 + [zeta]·4L/d)v²/2g.
+                                                      (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 1.08v²/2g = 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.
+
+  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] v²/2g;   (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.
+
+  § 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)
+
+  § 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 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
+  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/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
+  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.
+
+  § 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. Barré 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  |
+    +----------------------+-------+-------+------+
+
+  § 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 (_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
+  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.]
+
+  § 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,
+  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
+  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 × (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.
+
+  § 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 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
+  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).
+
+  § 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 |
+    +---------------+---------+---------+-------+-------+-------+
+
+  § 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](v1²·4l1/2gd1) + [zeta](v2²·4l2/2gd2) + ...
+
+  and in the uniform main
+
+    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) + ...
+
+  But, since the discharge is the same for all portions,
+
+    ¼[pi]d²v = ¼[pi]d1²v1 = ¼[pi]d2²v2 = ...
+
+    v1 = vd²/d1²; v2 = vd²/d2² ...
+
+  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.
+
+  § 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)²v1²/2g
+          = {(d1/d0)² - 1}² v1²/2g
+
+  or
+
+    [h]_e = [zeta]_ev1²/2g,   (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)²v²/2g;
+
+  and, if c_c is taken 0.64,
+
+    [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)
+
+  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)
+
+  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 1¼ in. diameter, he found the loss of head
+
+    [h]_e = [zeta]_e v²/2g;   (5)
+
+    [zeta]_e = 0.9457 sin² ½[phi] + 2.047 sin^4 ½[phi].
+
+    +------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
+    | [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|
+    +------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
+
+  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 v²/2g;   (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 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
+  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 |  ½  | 3/8 |  ¼   | 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° | 10° | 15° | 20° | 25° | 30° | 35° |
+    | 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° | 45° | 50° | 55° | 60° | 65° | 82° |
+    | 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° | 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° |
+    |            |      |      |      |      |      |      |      |
+    | [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
+  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, § 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)
+
+    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
+  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](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)
+
+  _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.
+
+    .: 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
+
+  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]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
+  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](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
+  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](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´);
+
+  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]´.
+
+  (c) Equation 7 may be put in the form
+
+    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 ...
+
+  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)
+
+  and
+
+    [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
+  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.]
+
+  § 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 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
+  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
+
+  § 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](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;
+
+  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.
+
+  § 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
+
+  § 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.
+
+  § 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° 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 § 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,
+
+    (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.
+
+  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 = u²/2g = c²[tau]²W²/2g[Omega]²p²,
+
+    .: 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)
+
+  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}/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)
+
+  Hence the initial velocity in the pipe is
+
+    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)
+
+  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)
+
+  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
+  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
+  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](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
+  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)
+
+  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.]
+
+  § 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)
+
+  Approximately
+
+    W = (.6916 p0 - .4438 p1)(d^5/[zeta]l[tau])^½.   (13a)
+
+  § 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.
+  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]W²cr.
+
+  From (1) and (3)
+
+    u = Wc[tau]/p[Omega];
+
+    dl/u = g d[Omega]³p² dp/2[zeta]W³c²[tau]²;
+       _
+      /p0
+  t = |   g d[Omega]³p² dp/2[zeta]W³c²[tau]²,
+     _/p1
+
+    = 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,
+
+         = [zeta]^(½)l^(3/2)(p0³ - p1³)/6(gc[tau]d)^(½)(p0² - p1²)^(3/2);   (15)
+
+  If [tau] = 521°, corresponding to 60° F.,
+
+    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°,
+
+    u_mean = 0.708 [root]{d(p0² - p1²)^(3/2)/[zeta]l(p0³ - p1³)}.   (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
+
+  § 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.]
+
+  § 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 × 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 (§ 66) that f(v) = [zeta]Gv²/2g,
+
+    .: [zeta]v²/2g = 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 = 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
+  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    |  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|
+    +----------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+
+
+  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
+  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       |
+    +----------+-----------+----------+---------+----------+--------------+
+
+  § 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.
+
+  § 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,
+  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
+  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
+  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
+  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
+  [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
+
+  § 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.]
+
+  § 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.
+
+  § 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.
+
+  § 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).
+
+  § 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].
+
+  § 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 § 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.]
+
+  § 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.
+
+  § 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
+  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.
+
+  § 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](n² + 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.
+
+  § 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 [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.]
+
+  § 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.]
+
+  § 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)
+
+    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 = 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
+  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.
+
+  § 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](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;
+
+  eliminating db/dd,
+
+    {n - 2[root](n² + 1)}d + b + nd = 0;
+
+    b = 2 {[root](n² + 1) - n}d.
+
+  But
+
+    [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.
+
+  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
+  channel are tangential to a semicircle drawn on the water line.
+
+  Since
+
+    [Omega]/[chi] = ½d,
+
+  therefore
+
+    [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.
+
+  Let
+
+    AB = CD = a; BC = b; EF = EH = c; and EG = d.
+
+    [Omega] = area AEB + BEC + CED,
+            = ac + ½bd.
+
+    [chi] = 2a + b.
+
+  Putting these values in (1),
+
+    ac + ½bd = (a + ½b)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]/d² = 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]/d² + cot[beta] - 2/sin [beta] = 0,
+
+  or
+
+    [Omega]/d² = 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 ½[beta].
+
+  _Proportions of Channels of Maximum Discharge for given Area and Side
+  Slopes. Depth of channel = d; Hydraulic mean depth = ½d; 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 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
+  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
+
+    y²dx² = k²ds² = k²(dx² + dy²) and dx = k dy/[root](y² - k²).
+
+  Integrating,
+
+    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)}].
+
+  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
+
+  § 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]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)}.
+
+  The factor 3u0 + w is equal to 2u0 + v, a quantity necessarily
+  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,
+
+  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,
+
+  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
+  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,
+
+  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 (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
+  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](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
+  A1B1 will be
+               _
+              / l
+    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)
+                                _
+                               / l
+      = GQz[theta] - GQ[theta] |   [zeta](u²/2g)([chi]/[Omega]) ds;
+                              _/ 0
+                                    _
+                                   / l
+    .: z = [alpha](u1² - u0²)/2g + |   [zeta](u²/2g)([chi]/[Omega]) ds.
+                                  _/ 0
+
+  [Illustration: FIG. 120.]
+
+  § 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.
+  Hence the equation applicable to an indefinitely short length of the
+  stream is
+
+    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
+  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 = -(u²x/g[Omega]) dh + ([chi]/[Omega])[zeta](u²/2g) ds.
+
+    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
+  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]u²/2gih)/(1 - u²/gh).   (5)
+
+  § 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](u²/2g) = 0;
+
+    .: [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
+  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]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,
+
+    H = [zeta]u²/2gi,
+
+  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 = u²/g, or u = [root](gh), the denominator
+  becomes zero. Hence, tabulating these results as before:--
+
+    For h = 0, u²/g, > u²/g, [oo],
+
+  the denominator becomes
+
+    -[oo], 0, > 0, 1.
+
+  [Illustration: FIG. 122.]
+
+  § 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
+  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]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.
+
+  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.
+
+  § 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
+  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>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
+  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.
+
+  § 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
+  stated above involves that
+
+    [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
+  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
+  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
+
+  § 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 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.]
+
+  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]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;
+
+    .: 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
+
+    H0² - H1² = (2/g)(H1u1² - H0u0²).
+
+  But, since [Omega]0u0 = [Omega]1u1, we have
+
+    u1² = u0²H0²/H1²,
+
+    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 = [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.
+  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
+  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
+  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 × 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
+  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      |
+    +-----------------------------+-----------------+--------------------+
+
+  § 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]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.
+
+  [Illustration: FIG. 129.]
+
+  [Illustration: FIG. 130.]
+
+  § 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.
+
+  § 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
+  "Hütte":--
+
+    +--------------------------------+---------+---------+---------+
+    |                                | 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  |
+    +--------------------------------+---------+---------+---------+
+
+  § 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
+  (§ 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
+  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 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
+  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 × 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;
+
+    .: 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 =
+  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
+
+    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
+  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.
+
+  § 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.
+
+  § 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   |
+    +----------------------+--------------+--------------+
+
+  § 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.
+
+  § 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.
+
+  § 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.]
+
+  § 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.
+
+  § 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
+
+  § 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 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.
+
+  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 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
+  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.]
+
+  § 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.]
+
+  § 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 = ½(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.]
+
+  § 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.
+
+  § 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.]
+
+  § 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.
+
+  § 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.]
+
+  § 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]n² = n1² + n2² + ...
+
+    [[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
+    [alpha] = -------------------------------------,
+                     m[Sigma]n² - [[Sigma]n]²
+
+             m[Sigma]nv - [Sigma]v[Sigma]n
+    [beta] = -----------------------------.
+                m[Sigma]n² - [[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.
+
+  § 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
+  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 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
+  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.
+
+  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
+  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.
+
+  § 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 = 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,
+
+  where G is the heaviness of water and k an experimental coefficient.
+  Then
+
+    E_t I[alpha]/l = kb(G/2g)[pi]R²v².
+
+  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 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].
+
+  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  "       "        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,
+  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
+
+  § 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
+    Brünings (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_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
+  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.
+
+  § 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 (§ 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.
+
+  § 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.
+
+  § 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.
+
+  § 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.]
+
+  § 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
+
+    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)}.
+
+  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 ½ 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
+
+§ 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
+
+  § 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 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).
+
+  § 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
+
+  § 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.
+
+  [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
+  × 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.
+  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
+  differentiating and equating the differential coefficient to zero:--
+
+    d[eta]/du = 2(v² - 4vu + 3u²)/v³ = 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]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
+  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.]
+
+  § 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 × 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]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 =
+  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].
+
+  (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
+  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.]
+
+  § 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.]
+
+  § 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 = 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
+  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
+  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
+  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 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
+  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
+  = 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 -----,
+                    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 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]);
+
+    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
+  [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.
+
+  [Illustration: FIG. 163.]
+
+  § 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°   |
+    |       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).
+
+  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, §
+  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, § 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°, 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
+  [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
+  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
+
+    = ½(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 = ½(G/g)[Omega]v (v² - V²).
+
+  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.]
+
+  § 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   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
+    -- + --- =  --  + -- + ---------;
+    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 ) v²   (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 v²
+    .: 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
+                     _                            _
+                 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,
+
+  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]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
+  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]v²/2g,
+
+  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.]
+
+  § 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 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
+  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 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.
+  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 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
+  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^(-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,
+  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^(-x²)x dx
+              _/0
+                        _      _
+                       |        |[oo]
+      = ([pi]h/log_eb) |-b^(-x²)|
+                       |_      _|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]r², the equation to the
+  pressure curve is
+
+                              h  x²
+    y = h[epsilon]^(-½) [root]-- --.
+                              h1 r²
+
+  § 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]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,
+  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 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:--
+
+    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.]
+
+  § 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 = 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.
+  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
+  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 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]),
+
+  and the lateral force is
+
+    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,
+  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                        |       |       |       |      |
+    +-----------------------------------+-------+-------+-------+------+
+    | 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 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.
+
+§ 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.
+
+  § 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 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
+  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 (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
+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.
+
+  § 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.
+
+§ 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._
+
+§ 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.
+
+  § 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)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.
+
+  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.,
+
+  and the efficiency of the machine will be
+
+    [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
+  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.]
+
+§ 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 = 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.
+
+  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 = 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.
+
+  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 ½v.
+
+[Illustration: FIG. 172.]
+
+§ 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.
+
+§ 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]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.
+
+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°
+  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 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.
+  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    7½     10    14    16    17    20    21    22
+      gallons
+
+§ 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 d²S 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 12½ 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
+  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.]
+
+  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._
+
+§ 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 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
+  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 - 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
+  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 - d²)/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 = 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.
+  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.]
+
+§ 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 §
+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° 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
+  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
+  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
+  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._
+
+§ 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,
+which should be an improvement on certain wheels then in use. The prize
+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
+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.
+
+  § 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
+  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]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).
+
+  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.
+
+  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]²r²]} - [alpha]r} [alpha]r
+    [eta] = ----------------------- = -----------------------------------------------.
+                      gH                                    gH
+
+  Let
+
+                                             gH         g²H²
+    [root]{2gH + [alpha]²r²} = [alpha]r + -------- - ----------- ...
+                                          [alpha]r   2[alpha]³r³
+
+  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]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
+  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 (§
+  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)
+
+  If the flow is horizontal, z2 = z1; and
+
+    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
+  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 = (v1² - v2²)/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)
+
+  § 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.
+
+  § 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.]
+
+§ 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° 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
+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.]
+
+  § 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 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
+  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.]
+
+  § 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](r2² - r1²).   (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).
+
+  § 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_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)
+
+  equations which may be used to determine [phi] and [theta].
+
+  [Illustration: FIG. 195.]
+
+  § 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
+  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_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
+  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)
+
+  § 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_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)
+
+  _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_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.
+  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_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).
+
+  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°,
+  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_i = c_v[root] | 2g ( H - ---- ( 1 + ----  ) + ---- - d ) |.
+                    |_    \     2g   \    V_o² /     2g     / _|
+
+  For an outward flow turbine,
+                     _                                           _
+                    |     /          V_i²  /    u_o² \    u_i² \  |
+    v_i = c_v[root] | 2g ( H - [h] - ---- ( 1 + ----  ) + ----  ) |.
+                    |_    \           2g   \    V_i² /     2g  / _|
+
+  For an inward flow turbine,
+                     _                                     _
+                    |    {     V_i²  /    u_o² \    u_i² }  |
+    v_i = c_v[root] | 2g { H - ---- ( 1 + ----  ) + ---- }  |.
+                    |_   {      2g   \    V_i² /     2g  } _|
+
+  § 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.]
+
+  § 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.
+
+  § 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 = 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
+  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] = 21º nearly.
+
+  If this value is revised for the vane thickness it will ordinarily
+  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 {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° 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° nearly.
+
+  _Hydraulic Efficiency of Wheel._
+
+    [eta] = w_iV_i/gH = .7101 × .66 × 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._
+
+§ 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.]
+
+  § 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 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
+  from 75 to 78%.
+
+  § 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](r2² - r1²)}.
+
+  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°.
+
+  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°.
+
+  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 × 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] =
+  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.]
+
+  § 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 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
+  develops 125 h.p.
+
+  [Illustration: FIG. 205]
+
+  § 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°, 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,
+
+    [eta] = 2Pu/GQv² = 4(v - u)u/v²,
+
+  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
+  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.
+
+  § 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.
+
+§ 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 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
+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.]
+
+§ 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.]
+
+§ 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 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
+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
+
+§ 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°. 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    14½   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.
+
+§ 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.]
+
+  § 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 ½d_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_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
+  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_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.
+
+  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)
+
+  _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
+  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)
+
+  § 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_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
+  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
+  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,
+
+    H = V_o²/2g - u_o² cosec² [phi]/2g
+
+  or
+
+    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).
+
+  For [phi] = 90°,
+
+    [eta] = (V_o² - u_o²)/2V_o²,
+
+  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,
+
+    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°      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
+  frictional losses neglected, the efficiency of a pump in which [phi] =
+  20° is found to be about .60.
+
+  § 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_o²  /    r_o² \    v_o²  /      \
+    ---- ( 1 - ----  ) = ---- ( 1 - k² ),
+     2g   \    r_w² /     2g   \      /
+
+  if
+
+    k = r_o/r_w.
+
+  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.
+
+  But
+
+    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)
+
+  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] 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 the velocity of the circumference of the pump have been obtained by
+  taking k = ½, and u_o = 0.25 [root](2gH).
+
+    [phi]      V_o
+
+     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
+  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.
+
+§ 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
+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° 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
+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 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
+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.
+
+§ 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 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
+  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 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
+  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 Qw²)/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 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
+
+    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); _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,
+    "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°
+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
+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, _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° 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° 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
+  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: 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
+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: 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
+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
+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
+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 ¼
+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: hydôr], 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: 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
+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° 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
+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°,
+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
+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 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
+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.
+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
+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° 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. 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
+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°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
+(_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
+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
+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. 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.
+
+  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.
+  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
+  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: 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,
+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: 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
+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).
+
+
+
+
+
+
+End of the Project Gutenberg EBook of Encyclopaedia Britannica, 11th
+Edition, Volume 14, Slice 1, by Various
+
+*** END OF THE PROJECT GUTENBERG EBOOK 40538 ***