diff options
Diffstat (limited to '40538.txt')
| -rw-r--r-- | 40538.txt | 19426 |
1 files changed, 0 insertions, 19426 deletions
diff --git a/40538.txt b/40538.txt deleted file mode 100644 index 9d291e6..0000000 --- a/40538.txt +++ /dev/null @@ -1,19426 +0,0 @@ -The Project Gutenberg EBook of Encyclopaedia Britannica, 11th Edition, -Volume 14, Slice 1, by Various - -This eBook is for the use of anyone anywhere at no cost and with -almost no restrictions whatsoever. You may copy it, give it away or -re-use it under the terms of the Project Gutenberg License included -with this eBook or online at www.gutenberg.org - - -Title: Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 1 - "Husband" to "Hydrolysis" - -Author: Various - -Release Date: August 19, 2012 [EBook #40538] - -Language: English - -Character set encoding: ASCII - -*** START OF THIS PROJECT GUTENBERG EBOOK ENCYC. BRITANNICA, VOL. 14, SL 1 *** - - - - -Produced by Marius Masi, Don Kretz and the Online -Distributed Proofreading Team at http://www.pgdp.net - - - - - - - -Transcriber's notes: - -(1) Numbers following letters (without space) like C2 were originally - printed in subscript. Letter subscripts are preceded by an - underscore, like C_n. - -(2) Characters following a carat (^) were printed in superscript. - -(3) Side-notes were relocated to function as titles of their respective - paragraphs. - -(4) Macrons and breves above letters and dots below letters were not - inserted. - -(5) [root] stands for the root symbol; [alpha], [beta], etc. for greek - letters. - -(6) The following typographical errors have been corrected: - - ARTICLE HUSS: "This appointment had a deep influence on the already - vigorous religious life of Huss himself ..." 'appointment' amended - from 'appoinment'. - - ARTICLE HYACINTH: "... the wild hyacinth of western North America, - Camassia esculenta." 'America' amended from 'Amercia'. - - ARTICLE HYDRAULICS: "Fig. 74 shows an arrangement designed for the - Manchester water works. The water enters from the reservoir at - chamber A, the object of which is to still the irregular motion of - the water." 'at' amended from 'a'. - - ARTICLE HYDRAULICS: "But the velocity at this point was probably - from Howden's statements 16.58 X 40/26 = 25.5 ft. per second, an - agreement as close as the approximate character of the data would - lead us to expect." Added 'per second'. - - ARTICLE HYDRAULICS: "... as the velocity and area of cross section - are different in different states of the river." 'different' - amended from 'differest'. - - ARTICLE HYDROGEN: "... for example, formic, glycollic, lactic, - tartaric, malic, benzoic and other organic acids are readily - oxidized in the presence of ferrous sulphate ..." 'glycollic' - amended from 'glygollic'. - - - - THE - - ENCYCLOPAEDIA BRITANNICA - - ELEVENTH EDITION - - - - - FIRST edition, published in three volumes, 1768-1771. - SECOND " " ten " 1777-1784. - THIRD " " eighteen " 1788-1797. - FOURTH " " twenty " 1801-1810. - FIFTH " " twenty " 1815-1817. - SIXTH " " twenty " 1823-1824. - SEVENTH " " twenty-one " 1830-1842. - EIGHTH " " twenty-two " 1853-1860. - NINTH " " twenty-five " 1875-1889. - TENTH " ninth edition and eleven - supplementary volumes, 1902-1903. - ELEVENTH " published in twenty-nine volumes, 1910-1911. - - - COPYRIGHT - - in all countries subscribing to the Bern Convention - - by - - THE CHANCELLOR, MASTERS AND SCHOLARS - of the - UNIVERSITY OF CAMBRIDGE - - _All rights reserved_ - - - - - THE - - ENCYCLOPAEDIA BRITANNICA - - A DICTIONARY OF - ARTS, SCIENCES, LITERATURE AND GENERAL INFORMATION - - ELEVENTH EDITION - - VOLUME XIV - HUSBAND to ITALIC - - New York - - Encyclopaedia Britannica, Inc. - 342 Madison Avenue - - - Copyright, in the United States of America, 1910, - by - The Encyclopaedia Britannica Company. - - - VOLUME XIV, SLICE I - - Husband to Hydrolysis - - - - -ARTICLES IN THIS SLICE: - - - HUSBAND HYADES - HUSBAND AND WIFE HYATT, ALPHEUS - HUSHI HYBLA - HUSKISSON, WILLIAM HYBRIDISM - HUSS HYDANTOIN - HUSSAR HYDE (17th century English family) - HUSSITES HYDE, THOMAS - HUSTING HYDE (market town) - HUSUM HYDE DE NEUVILLE, JEAN GUILLAUME - HUTCHESON, FRANCIS HYDE PARK - HUTCHINSON, ANNE HYDERABAD (city of India) - HUTCHINSON, JOHN (puritan soldier) HYDERABAD (state of India) - HUTCHINSON, JOHN (theological writer) HYDERABAD (capital of Hyderabad) - HUTCHINSON, SIR JONATHAN HYDER ALI - HUTCHINSON, THOMAS HYDRA (island of Greece) - HUTCHINSON (Kansas, U.S.A.) HYDRA (legendary monster) - HUTTEN, PHILIPP VON HYDRA (constellation) - HUTTEN, ULRICH VON HYDRACRYLIC ACID - HUTTER, LEONHARD HYDRANGEA - HUTTON, CHARLES HYDRASTINE - HUTTON, JAMES HYDRATE - HUTTON, RICHARD HOLT HYDRAULICS - HUXLEY, THOMAS HENRY HYDRAZINE - HUY HYDRAZONE - HUYGENS, CHRISTIAAN HYDROCARBON - HUYGENS, SIR CONSTANTIJN HYDROCELE - HUYSMANS (Flemish painters) HYDROCEPHALUS - HUYSMANS, JORIS KARL HYDROCHARIDEAE - HUYSUM, JAN VAN HYDROCHLORIC ACID - HWANG HO HYDRODYNAMICS - HWICCE HYDROGEN - HYACINTH (flower) HYDROGRAPHY - HYACINTH (gem-stone) HYDROLYSIS - HYACINTHUS - - - - -INITIALS USED IN VOLUME XI. TO IDENTIFY INDIVIDUAL CONTRIBUTORS,[1] WITH -THE HEADINGS OF THE ARTICLES IN THIS VOLUME SO SIGNED. - - - - - A. Ba. - ADOLFO BARTOLI (1833-1894). - - Formerly Professor of Literature at the Istituto di studi - superiori at Florence. Author of Storia della letteratura - Italiana; &c. - - Italian Literature (_in part_). - - A. Bo.* - AUGUSTE BOUDINHON, D.D., D.C.L. - - Professor of Canon Law at the Catholic University of Paris. - Honorary Canon of Paris. Editor of the _Canoniste contemporain_. - - Index Librorum Prohibitorum; - Infallibility. - - A. Cy. - ARTHUR ERNEST COWLEY, M.A., LITT.D. - - Sub-Librarian of the Bodleian Library, Oxford. Fellow of Magdalen - College. - - Ibn Gabirol; - Inscriptions: _Semitic_. - - A. C. G. - ALBERT CHARLES LEWIS GOTTHILF GUNTHER, M.A., M.D., PH.D., F.R.S. - - Keeper of Zoological Department, British Museum, 1875-1895. Gold - Medallist, Royal Society, 1878. Author of _Catalogues of Colubrine - Snakes, Batrachia Salientia, and Fishes in the British Museum_; - _Reptiles of British India_; _Fishes of Zanzibar_; _Reports on the - "Challenger" Fishes_; &c. - - Ichthyology (_in part_). - - A. E. G.* - REV. ALFRED ERNEST GARVIE, M.A., D.D. - - Principal of New College, Hampstead. Member of the Board of - Theology and the Board of Philosophy, London University. Author of - _Studies in the inner Life of Jesus_; &c. - - Immortality; - Inspiration. - - A. E. H. L. - AUGUSTUS EDWARD HOUGH LOVE, M.A., D.SC., F.R.S. - - Sedleian Professor of Natural Philosophy in the University of - Oxford. Hon. Fellow of Queen's College, Oxford; formerly Fellow of - St John's College, Cambridge. Secretary to the London Mathematical - Society. - - Infinitesimal Calculus. - - A. F. C. - ALEXANDER FRANCIS CHAMBERLAIN, A.M., PH.D. - - Assistant Professor of Anthropology, Clark University, Worcester, - Massachusetts. Member of American Antiquarian Society; Hon. Member - of American Folk-lore Society. Author of _The Child and Childhood - in Folk Thought_. - - Indians, North American. - - A. G. - MAJOR ARTHUR GEORGE FREDERICK GRIFFITHS (d. 1908). - - H.M. Inspector of Prisons, 1878-1896. Author of _The Chronicles of - Newgate_; _Secrets of the Prison House_; &c. - - Identification. - - A. Ge. - SIR ARCHIBALD GEIKIE, LL.D. - - See the biographical article, GEIKIE, SIR A. - - Hutton, James. - - A. Go.* - REV. ALEXANDER GORDON, M.A. - - Lecturer on Church History in the University of Manchester. - - Illuminati. - - A. G. G. - SIR ALFRED GEORGE GREENHILL, M.A., F.R.S. - - Formerly Professor of Mathematics in the Ordnance College, - Woolwich. Author of _Differential and Integral Calculus with - Applications_; _Hydrostatics_; _Notes on Dynamics_; &c. - - Hydromechanics. - - A. H.-S. - SIR A. HOUTUM-SCHINDLER, C.I.E. - - General in the Persian Army. Author of _Eastern Persian Irak_. - - Isfahan (_in part_). - - A. M. C. - AGNES MARY CLERKE. - - See the biographical article, CLERKE, A. M. - - Huygens, Christiaan. - - A. N. - ALFRED NEWTON, F.R.S. - - See the biographical article, NEWTON, ALFRED. - - Ibis; - Icterus. - - A. So. - ALBRECHT SOCIN, PH.D. (1844-1899). - - Formerly Professor of Semitic Philology in the Universities of - Leipzig and Tubingen. Author of _Arabische Grammatik_; &c. - - Irak-Arabi (_in part_). - - A. S. Wo. - ARTHUR SMITH WOODWARD, LL.D., F.R.S. - - Keeper of Geology, Natural History Museum, South Kensington. - Secretary of the Geological Society, London. - - Ichthyosaurus; - Iguanodon. - - A. W. H.* - ARTHUR WILLIAM HOLLAND. - - Formerly Scholar of St John's College, Oxford. Bacon Scholar of - Gray's Inn, 1900. - - Imperial Cities; - Instrument of Government. - - A. W. Po. - ALFRED WILLIAM POLLARD, M.A. - - Assistant Keeper of Printed Books, British Museum. Fellow of - King's College, London. Hon. Secretary Bibliographical Society. - Editor of _Books about Books_ and _Bibliographica_. Joint-editor - of The Library. Chief Editor of the "Globe" _Chaucer_. - - Incunabula. - - A. W. R. - ALEXANDER WOOD RENTON, M.A., LL.B. - - Puisne judge of the Supreme Court of Ceylon. Editor of - _Encyclopaedia of the Laws of England_. - - Inebriety, Law of; - Insanity: _Law_. - - C. F. A. - CHARLES FRANCIS ATKINSON. - - Formerly Scholar of Queen's College, Oxford. Captain, 1st City of - London (Royal Fusiliers). Author of _The Wilderness and Cold - Harbour_. - - Infantry; - Italian Wars. - - C. G. - COLONEL CHARLES GRANT. - - Formerly Inspector of Military Education in India. - - India: _Costume_. - - C. H. Ha. - CARLTON HUNTLEY HAYES, A.M., PH.D. - - Assistant Professor of History at Columbia University, New York - City. Member of the American Historical Association. - - Innocent V., VIII. - - C. Ll. M. - CONWAY LLOYD MORGAN, LL.D., F.R.S. - - Professor of Psychology at the University of Bristol. Principal of - University College, Bristol, 1887-1909. Author of _Animal Life and - Intelligence_; _Habit and Instinct_. - - Instinct; - Intelligence in Animals. - - C. R. B. - CHARLES RAYMOND BEAZLEY, M.A., D.LITT., F.R.G.S., F.R.HIST.S. - - Professor of Modern History in the University of Birmingham. - Formerly Fellow of Merton College, Oxford; and University Lecturer - in the History of Geography. Lothian Prizeman, Oxford, 1889. - Lowell Lecturer, Boston, 1908. Author of _Henry the Navigator_; - _The Dawn of Modern Geography_; &c. - - Ibn Batuta (_in part_); - Idrisi. - - C. S.* - CARLO SALVIONI. - - Professor of Classical and Romance Languages, University of Milan. - - Italian Language (_in part_). - - C. T. L. - CHARLTON THOMAS LEWIS, PH.D. (1834-1904). - - Formerly Lecturer on Life Insurance, Harvard and Columbia - Universities, and on Principles of Insurance, Cornell University. - Author of _History of Germany_; _Essays_; _Addresses_; &c. - - Insurance (_in part_). - - C. We. - CECIL WEATHERLY. - - Formerly Scholar of Queen's College, Oxford. Barrister-at-Law, - Inner Temple. - - Infant Schools. - - D. B. Ma. - DUNCAN BLACK MACDONALD, M.A., D.D. - - Professor of Semitic Languages, Hartford Theological Seminary, - U.S.A. Author of _Development of Muslim Theology, Jurisprudence - and Constitutional Theory_; _Selection from Ibn Khaldum_; - _Religious Attitude and Life in Islam_; &c. - - Imam. - - D. G. H. - DAVID GEORGE HOGARTH, M.A. - - Keeper of the Ashmolean Museum, Oxford. Fellow of Magdalen - College, Oxford. Fellow of the British Academy. Excavated at - Paphos, 1888; Naucratis, 1899 and 1903; Ephesus, 1904-1905; - Assiut, 1906-1907; Director, British School at Athens, 1897-1900; - Director, Cretan Exploration Fund, 1899. - - Ionia (_in part_); - Isauria. - - D. H. - DAVID HANNAY. - - Formerly British Vice-Consul at Barcelona. Author of _Short - History of Royal Navy, 1217-1688_; _Life of Emilio Castelar_; &c. - - Impressment. - - D. F. T. - DONALD FRANCIS TOVEY. - - Author of _Essays in Musical Analysis_; comprising _The Classical - Concerto_, _The Goldberg Variations_, and analyses of many other - classical works. - - Instrumentation. - - D. S. M. - DUGALD SUTHERLAND MACCOLL, M.A., LL.D. - - Keeper of the National Gallery of British Art (Tate Gallery). - Lecturer on the History of Art, University College, London; Fellow - of University College, London. Author of Nineteenth Century Art; - &c. - - Impressionism. - - E. A. M. - EDWARD ALFRED MINCHIN, M.A., F.Z.S. - - Professor of Protozoology in the University of London. Formerly - Fellow of Merton College, Oxford; and Lecturer on Comparative - Anatomy in the University of Oxford. Author of "Sponges and - Sporozoa" in Lankester's _Treatise on Zoology_; &c. - - Hydromedusae; - Hydrozoa. - - E. Br. - ERNEST BARKER, M.A. - - Fellow and Lecturer in Modern History, St John's College, Oxford. - Formerly Fellow and Tutor of Merton College. Craven Scholar, 1895. - - Imperial Chamber. - - E. Bra. - EDWIN BRAMWELL, M.B., F.R.C.P., F.R.S. (Edin.). - - Assistant Physician, Royal Infirmary, Edinburgh. - - Hysteria (_in part_). - - E. C. B. - RIGHT REV. EDWARD CUTHBERT BUTLER, O.S.B., D.LITT. - - Abbot of Downside Abbey, Bath. Author of "The Lausiac History of - Palladius" in _Cambridge Texts and Studies_. - - Imitation of Christ. - - E. C. Q. - EDMUND CROSBY QUIGGIN, M.A. - - Fellow, Lecturer in Modern History, and Monro Lecturer in Celtic, - Gonville and Caius College, Cambridge. - - Ireland: _Early History_. - - E. F. S. - EDWARD FAIRBROTHER STRANGE. - - Assistant Keeper, Victoria and Albert Museum, South Kensington. - Member of Council, Japan Society. Author of numerous works on art - subjects. Joint-editor of Bell's "Cathedral" Series. - - Illustration: _Technical Developments_. - - E. F. S. D. - LADY DILKE. - - See the biographical article: DILKE, SIR C. W., BART. - - Ingres. - - E. G. - EDMUND GOSSE, LL.D. - - See the biographical article, GOSSE, EDMUND. - - Huygens, Sir Constantijn; - Ibsen; - Idyl. - - E. Hu. - EMIL HUBNER. - - See the biographical article, HUBNER, EMIL. - - Inscriptions: _Latin_ (_in part_). - - E. H. B. - SIR EDWARD HERBERT BUNBURY, BART., M.A., F.R.G.S. (d. 1895). - - M.P. for Bury St Edmunds, 1847-1852. Author of a _History of - Ancient Geography_; &c. - - Ionia (_in part_). - - E. H. M. - ELLIS HOVELL MINNS, M.A. - - Lecturer and Assistant Librarian, and formerly Fellow, Pembroke - College, Cambridge University Lecturer in Palaeography. - - Iazyges; - Issedones. - - E. H. P. - EDWARD HENRY PALMER, M.A. - - See the biographical article, PALMER, E. H. - - Ibn Khaldun (_in part_). - - E. K. - EDMUND KNECHT, PH.D., M.SC.TECH.(Manchester), F.I.C. - - Professor of Technological Chemistry, Manchester University. Head - of Chemical Department, Municipal School of Technology, - Manchester. Examiner in Dyeing, City and Guilds of London - Institute. Author of _A Manual of Dyeing_; &c. Editor of J_ournal - of the Society of Dyers and Colourists_. - - Indigo. - - E. L. H. - THE RIGHT REV. THE BISHOP OF LINCOLN (EDWARD LEE HICKS). - - Honorary Fellow of Corpus Christi College, Oxford. Formerly Canon - Residentiary of Manchester. Fellow and Tutor of Corpus Christi - College. Author of _Manual of Greek Historical Inscriptions_; &c. - - Inscriptions: Greek (_in part_). - - Ed. M. - EDUARD MEYER, PH.D., D.LITT.(Oxon.), LL.D. - - Professor of Ancient History in the University of Berlin. Author - of _Geschichte des Alterthums_; _Geschichte des alten Aegyptens_; - _Die Israeliten und ihre Nachbarstamme_. - - Hystaspes; - Iran. - - E. M. T. - SIR EDWARD MAUNDE THOMPSON, G.C.B., I.S.O., D.C.L., LITT.D., LL.D. - - Director and Principal Librarian, British Museum, 1898-1909. - Sandars Reader in Bibliography, Cambridge, 1895-1896. Hon. Fellow - of University College, Oxford. Correspondent of the Institute of - France and of the Royal Prussian Academy of Sciences. Author of - _Handbook of Greek and Latin Palaeography_. Editor of _Chronicon - Angliae_. Joint-editor of publications of the Palaeographical - Society, the New Palaeographical Society, and of the Facsimile of - the Laurentian Sophocles. - - Illuminated MSS. - - E. O.* - EDMUND OWEN, M.B., F.R.C.S., LL.D., D.SC. - - Consulting Surgeon to St Mary's Hospital, London, and to the - Children's Hospital, Great Ormond Street; late Examiner in Surgery - at the Universities of Cambridge, Durham and London. Author of _A - Manual of Anatomy for Senior Students_. - - Hydrocephalus. - - F. A. F. - FRANK ALBERT FETTER, PH.D. - - Professor of Political Economy and Finance, Cornell University. - Member of the State Board of Charities. Author of _The Principles - of Economics_; &c. - - Interstate Commerce. - - F. C. C. - FREDERICK CORNWALLIS CONYBEARE, M.A., D.TH.(Giessen). - - Fellow of the British Academy. Formerly Fellow of University - College, Oxford. Author of _The Ancient Armenian Texts of - Aristotle_; _Myth, Magic and Morals_; &c. - - Iconoclasts; - Image Worship. - - F. G. M. B. - FREDERICK GEORGE MEESON BECK, M.A. - - Fellow and Lecturer in Classics, Clare College, Cambridge. - - Hwicce. - - F. J. H. - FRANCIS JOHN HAVERFIELD, M.A., LL.D., F.S.A. - - Camden Professor of Ancient History in the University of Oxford. - Fellow of Brasenose College. Fellow of the British Academy. - Formerly Censor, Student, Tutor and Librarian of Christ Church, - Oxford. Ford's Lecturer, 1906-1907. Author of Monographs on Roman - History, especially Roman Britain; &c. - - Icknield Street. - - F. Ll. G. - FRANCIS LLEWELLYN GRIFFITH, M.A., PH.D., F.S.A. - - Reader in Egyptology, Oxford University. Editor of the - Archaeological Survey and Archaeological Reports of the Egypt - Exploration Fund. Fellow of Imperial German Archaeological - Institute. - - Hyksos; - Isis. - - F. P.* - FREDERICK PETERSON, M.D., PH.D. - - Professor of Psychiatry, Columbia University. President of New - York State Commission in Lunacy, 1902-1906. Author of _Mental - Diseases_; &c. - - Insanity: _Hospital Treatment._ - - F. S. P. - FRANCIS SAMUEL PHILBRICK, A.M., PH.D. - - Formerly Fellow of Nebraska State University, and Scholar and - Resident Fellow of Harvard University. Member of American - Historical Association. - - Independence, Declaration of. - - F. Wa. - FRANCIS WATT, M.A. - - Barrister-at-Law, Middle Temple. Author of _Law's Lumber Room_. - - Inn and Innkeeper. - - F. W. R.* - FREDERICK WILLIAM RUDLER, I.S.O., F.G.S. - - Curator and Librarian of the Museum of Practical Geology, London, - 1879-1902. President of the Geologists' Association, 1887-1889. - - Hyacinth - Iolite. - - F. Y. P. - FREDERICK YORK POWELL, D.C.L., LL.D. - - See the biographical article, POWELL, FREDERICK YORK. - - Iceland: _History_, and _Ancient Literature_. - - G. A. B. - GEORGE A. BOULENGER, F.R.S., D.SC., PH.D. - - In charge of the collections of Reptiles and Fishes, Department of - Zoology, British Museum. Vice-President of the Zoological Society - of London. - - Ichthyology (_in part_). - - G. A. Gr. - GEORGE ABRAHAM GRIERSON, C.I.E., PH.D., D.LITT.(Dublin). - - Member of the Indian Civil Service, 1873-1903. In charge of - Linguistic Survey of India, 1898-1902. Gold Medallist, Royal - Asiatic Society, 1909. Vice-President of the Royal Asiatic - Society. Formerly Fellow of Calcutta University. Author of _The - Languages of India_; &c. - - Indo-Aryan Languages. - - G. A. J. C. - GRENVILLE ARTHUR JAMES COLE. - - Director of the Geological Survey of Ireland. Professor of - Geology, Royal College of Science for Ireland, Dublin. Author of - _Aids in Practical Geology_; &c. - - Ireland: _Geology_. - - G. B. - SIR GEORGE CHRISTOPHER MOLESWORTH BIRDWOOD, K.C.I.E. - - See the biographical article, BIRDWOOD, SIR G. C. M. - - Incense. - - G. F. H.* - GEORGE FRANCIS HILL, M.A. - - Assistant in Department of Coins and Medals, British Museum. - Author of _Sources for Greek History 478-431_ B.C.; _Handbook of - Greek and Roman Coins_; &c. - - Inscriptions: Greek (_in part_). - - G. G. Co. - GEORGE GORDON COULTON, M.A. - - Birkbeck Lecturer in Ecclesiastical History, Trinity College, - Cambridge. Author of _Medieval Studies_; _Chaucer and his - England_; &c. - - Indulgence. - - G. H. C. - GEORGE HERBERT CARPENTER, B.SC. (Lond.). - - Professor of Zoology in the Royal College of Science, Dublin. - Author of _Insects: their Structure and Life_. - - Hymenoptera; - Ichneumon-Fly; - Insect. - - G. I. A. - GRAZIADIO I. ASCOLI. - - Senator of the Kingdom of Italy. Professor of Comparative Grammar - at the University of Milan. Author of _Codice Islandese_; &c. - - Italian Language (_in part_). - - G. J. - GEORGE JAMIESON, C.M.G., M.A. - - Formerly Consul-General at Shanghai, and Consul and Judge of the - Supreme Court, Shanghai. - - Hwang Ho. - - G. K. - GUSTAV KRUGER, PH.D. - - Professor of Church History in the University of Giessen. Author - of _Das Papstthum_; &c. - - Irenaeus. - - G. P. M. - GEORGE PERCIVAL MUDGE, A.R.C.S., F.Z.S. - - Lecturer on Biology, London Hospital Medical College, and London - School of Medicine for Women, University of London. Author of _A - Text Book of Zoology_; &c. - - Incubation and Incubators. - - G. W. K. - VERY REV. GEORGE WILLIAM KITCHIN, M.A., D.D., F.S.A. - - Dean of Durham, and Warden of the University of Durham. Hon. - Student of Christ Church, Oxford. Fellow of King's College, - London. Dean of Winchester, 1883-1894. Author of _A History of - France_; &c. - - Hutten, Ulrich von. - - G. W. T. - REV. GRIFFITHES WHEELER THATCHER, M.A., B.D. - - Warden of Camden College, Sydney, N.S.W. Formerly Tutor in Hebrew - and Old Testament History at Mansfield College, Oxford. Author of - a _Commentary on Judges_; _An Arabic Grammar_; &c. - - Ibn 'Abd Rabbihi; - Ibn 'Arabi; - Ibn Athir; - Ibn Duraid; - Ibn Faradi; - Ibn Farid; - Ibn Hazm; - Ibn Hisham; - Ibn Ishaq; - Ibn Jubair; - Ibn Khaldun (_in part_); - Ibn Khallikan; - Ibn Qutaiba; - Ibn Sa'd; - Ibn Tufail; - Ibn Usaibi'a; - Ibrahim Al-Mausili. - - H. Ch. - HUGH CHISHOLM, M.A. - - Formerly Scholar of Corpus Christi College, Oxford. Editor the - 11th edition of the _Encyclopaedia Britannica_; Co-editor of the - 10th edition. - - Iron Mask; - Ismail. - - H. C. R. - SIR HENRY CRESWICKE RAWLINSON, BART., K.C.B. - - See the biographical article, RAWLINSON, SIR HENRY CRESWICKE. - - Isfahan: _History_. - - H. L. H. - HARRIET L. HENNESSY, M.D., (Brux.) L.R.C.P.I., L.R.C.S.I. - - Infancy; - Intestinal Obstruction. - - H. M. H. - HENRY MARION HOWE, A.M., LL.D. - - Professor of Metallurgy, Columbia University. Author of - _Metallurgy of Steel_; &c. - - Iron and Steel. - - H. N. D. - HENRY NEWTON DICKSON, M.A., D.SC., F.R.G.S. - - Professor of Geography, University College, Reading. Author of - _Elementary Meteorology_; _Papers on Oceanography_; &c. - - Indian Ocean. - - H. O. - HERMANN OELSNER, M.A., PH.D. - - Taylorian Professor of the Romance Languages in University of - Oxford. Member of Council of the Philological Society. Author of - _A History of Provencal Literature_; &c. - - Italian Literature (_in part_). - - H. St. - HENRY STURT, M.A. - - Author of _Idola Theatri_; _The Idea of a Free Church_; and - _Personal Idealism_. - - Induction. - - H. T. A. - REV. HERBERT THOMAS ANDREWS. - - Professor of New Testament Exegesis, New College, London. Author - of the "Commentary on Acts" in the _Westminster New Testament_; - _Handbook on the Apocryphal Books_ in the "Century Bible." - - Ignatius. - - H. Y. - SIR HENRY YULE, K.C.S.I., C.B. - - See the biographical article, YULE, SIR HENRY. - - Ibn Batuta (_in part_). - - I. A. - ISRAEL ABRAHAMS, M.A. - - Reader in Talmudic and Rabbinic Literature in the University of - Cambridge. Formerly President, Jewish Historical Society in - England. Author of _A Short History of Jewish Literature_; _Jewish - Life in the Middle Ages_; &c. - - Ibn Tibbon; - Immanuel Ben Solomon. - - J. A. F. - JOHN AMBROSE FLEMING, M.A., F.R.S., D.SC. - - Pender Professor of Electrical Engineering in the University of - London. Fellow of University College, London. Formerly Fellow of - St John's College, Cambridge, and Lecturer on Applied Mechanics in - the University. Author of _Magnets and Electric Currents_. - - Induction Coil. - - J. Bs. - JAMES BURGESS, C.I.E., LL.D., F.R.S.(Edin.), F.R.G.S., - HON.A.R.I.B.A. - - Formerly Director General of Archaeological Survey of India. - Author of _Archaeological Survey of Western India_. Editor of - Fergusson's _History of Indian Architecture_. - - Indian Architecture. - - J. B. T. - SIR JOHN BATTY TUKE, KT., M.D., F.R.S.(Edin.), D.SC., LL.D. - - President of the Neurological Society of the United Kingdom. - Medical Director of New Saughton Hall Asylum, Edinburgh. M.P. for - the Universities of Edinburgh and St Andrews, 1900-1910. - - Hysteria (_in part_); - Insanity: _Medical._ - - J. C. H. - RIGHT REV. JOHN CUTHBERT HEDLEY, O.S.B., D.D. - - R.C. Bishop of Newport. Author of _The Holy Eucharist_; &c. - - Immaculate Conception. - - J. C. Van D. - JOHN CHARLES VAN DYKE. - - Professor of the History of Art, Rutgers College, New Brunswick, - N.J. Formerly Editor of _The Studio and Art Review_. Author of - _Art for Art's Sake_; _History of Painting_; _Old English - Masters_; &c. - - Inness, George. - - J. C. W. - JAMES CLAUDE WEBSTER. - - Barrister-at-Law, Middle Temple. - - Inns of Court. - - J. D. B. - JAMES DAVID BOURCHIER, M.A., F.R.G.S. - - King's College, Cambridge. Correspondent of _The Times_ in - South-Eastern Europe. Commander of the Orders of Prince Danilo of - Montenegro and of the Saviour of Greece, and Officer of the Order - of St Alexander of Bulgaria. - - Ionian Islands. - - J. F. F. - JOHN FAITHFULL FLEET, C.I.E., PH.D. - - Commissioner of Central and Southern Divisions of Bombay, - 1891-1897. Author of _Inscriptions of the Early Gupta Kings_; &c. - - Inscriptions: _Indian_. - - J. F.-K. - JAMES FITZMAURICE-KELLY, LITT.D., F.R.HIST.S. - - Gilmour Professor of Spanish Language and Literature, Liverpool - University. Norman McColl Lecturer, Cambridge University. Fellow - of the British Academy. Member of the Royal Spanish Academy. - Knight Commander of the Order of Alphonso XII. Author of A History - of Spanish Literature; &c. - - Isla, J. F. de. - - J. G. K. - JOHN GRAHAM KERR, M.A., F.R.S. - - Regius Professor of Zoology in the University of Glasgow. Formerly - Demonstrator in Animal Morphology in the University of Cambridge. - Fellow of Christ's College, Cambridge, 1898-1904. Walsingham - Medallist, 1898. Neill Prizeman, Royal Society of Edinburgh, 1904. - - Ichthyology (_in part_). - - J. G. Sc. - SIR JAMES GEORGE SCOTT, K.C.I.E. - - Superintendent and Political Officer, Southern Shan States. Author - of _Burma, a Handbook_; _The Upper Burma Gazetteer_; &c. - - Irrawaddy. - - J. H. A. H. - JOHN HENRY ARTHUR HART, M.A. - - Fellow, Theological Lecturer and Librarian, St John's College, - Cambridge. - - Hyrcanus. - - J. H. Mu. - JOHN HENRY MUIRHEAD, M.A., LL.D. - - Professor of Philosophy in the University of Birmingham. Author of - _Elements of Ethics_; _Philosophy and Life_; &c. Editor of - _Library of Philosophy_. - - Idealism. - - J. H. Be. - VERY REV. JOHN HENRY BERNARD, M.A., D.D., D.C.L. - - Dean of St Patrick's Cathedral, Dublin. Archbishop King's - Professor of Divinity and formerly Fellow of Trinity College, - Dublin. Joint-editor of the Irish _Liber Hymnorum_; &c. - - Ireland, Church of. - - J. H. van't H. - JACOBUS HENRICUS VAN'T HOFF, LL.D., D.SC., D.M. - - See the biographical article VAN'T HOFF, JACOBUS HENRICUS. - - Isomerism. - - J. L. M. - JOHN LYNTON MYRES, M.A., F.S.A., F.R.G.S. - - Wykeham Professor of Ancient History in the University of Oxford. - Formerly Gladstone Professor of Greek and Lecturer in Ancient - Geography, University of Liverpool. Lecturer in Classical - Archaeology in University of Oxford. - - Iberians; - Ionians. - - J. Mn. - JOHN MACPHERSON, M.D. - - Formerly Inspector-General of Hospitals, Bengal. - - Insanity: _Medical_ (_in part_). - - J. M. A. de L. - JEAN MARIE ANTOINE DE LANESSAN. - - See the biographical article, LANESSAN, J. M. A. DE. - - Indo-China, French (_in part_). - - J. M. M. - JOHN MALCOLM MITCHELL. - - Sometime Scholar of Queen's College, Oxford. Lecturer in Classics, - East London College (University of London). Joint-editor of - Grote's _History of Greece_. - - Hyacinthus. - - J. P. E. - JEAN PAUL HIPPOLYTE EMMANUEL ADHEMAR ESMEIN. - - Professor of Law in the University of Paris. Officer of the Legion - of Honour. Member of the Institute of France. Author of _Cours - elementaire d'histoire du droit francais_; &c. - - Intendant. - - J. P. Pe. - REV. JOHN PUNNETT PETERS, PH.D., D.D. - - Canon Residentiary, Cathedral of New York. Formerly Professor of - Hebrew in the University of Pennsylvania. Director of the - University Expedition to Babylonia, 1888-1895. Author of _Nippur, - or Explorations and Adventures on the Euphrates_. - - Irak-Arabi (_in part_). - - J. S. Bl. - JOHN SUTHERLAND BLACK, M.A., LL.D. - - Assistant Editor of the 9th edition of the _Encyclopaedia - Britannica_. Joint-editor of the _Encyclopaedia Biblica_. - - Huss, John. - - J. S. Co. - JAMES SUTHERLAND COTTON, M.A. - - Editor of the _Imperial Gazetteer of India_. Hon. Secretary of the - Egyptian Exploration Fund. Formerly Fellow and Lecturer of Queen's - College, Oxford. Author of _India_; &c. - - India: _Geography and Statistics (in part); History (in part)_; - Indore. - - J. S. F. - JOHN SMITH FLETT, D.SC., F.G.S. - - Petrographer to the Geological Survey. Formerly Lecturer on - Petrology in Edinburgh University. Neill Medallist of the Royal - Society of Edinburgh. Bigsby Medallist of the Geological Society - of London. - - Itacolumite. - - J. T. Be. - John Thomas Bealby. - - Joint-author of Stanford's _Europe_. Formerly Editor of the - _Scottish Geographical Magazine_. Translator of Sven Hedin's - _Through Asia, Central Asia and Tibet_; &c. - - Irkutsk (_in part_). - - J. V.* - JULES VIARD. - - Archivist at the National Archives, Paris. Officer of Public - Instruction. Author of _La France sous Philippe VI. de Valois_; - &c. - - Isabella of Bavaria. - - Jno. W. - JOHN WESTLAKE, K.C., LL.D. - - Professor of International Law, Cambridge, 1888-1908. One of the - Members for the United Kingdom of International Court of - Arbitration under the Hague Convention, 1900-1906. Bencher of - Lincoln's Inn. Author of _A Treatise on Private International Law, - or the Conflict of Laws: Chapters on the Principles of - International Law_, pt. i. "Peace," pt. ii. "War." - - International Law: _Private_. - - L. - COUNT LUTZOW, LITT.D. (OXON.), PH.D. (PRAGUE), F.R.G.S. - - Chamberlain of H.M. the Emperor of Austria, King of Bohemia. Hon. - Member of the Royal Society of Literature. Member of the Bohemian - Academy; &c. Author of _Bohemia, a Historical Sketch_; _The - Historians of Bohemia_ (Ilchester Lecture, Oxford, 1904); _The - Life and Times of John Hus_; &c. - - Hussites. - - L. C. B. - LEWIS CAMPBELL BRUCE, M.D., F.R.C.P. - - Author of _Studies in Clinical Psychiatry_. - - Insanity: _Medical_ (_in part_). - - L. Ho. - LAURENCE HOUSMAN. - - See the biographical article, HOUSMAN, L. - - Illustration (_in part_). - - L. J. S. - LEONARD JAMES SPENCER, M.A. - - Assistant in Department of Mineralogy, British Museum. Formerly - Scholar of Sidney Sussex College, Cambridge, and Harkness Scholar. - Editor of the _Mineralogical Magazine_. - - Hypersthene; - Ilmenite. - - L. T. D. - SIR LEWIS TONNA DIBDIN, M.A., D.C.L., F.S.A. - - Dean of the Arches; Master of the Faculties; and First Church - Estates Commissioner. Bencher of Lincoln's Inn. Author of - _Monasticism in England_; &c. - - Incense: _Ritual Use._ - - M. Ha. - MARCUS HARTOG, M.A., D.SC., F.L.S. - - Professor of Zoology, University College, Cork. Author of - "Protozoa" in _Cambridge Natural History_; and papers for various - scientific journals. - - Infusoria. - - M. Ja. - MORRIS JASTROW, JUN., PH.D. - - Professor of Semitic Languages, University of Pennsylvania, U.S.A. - Author of _Religion of the Babylonians and Assyrians_; &c. - - Ishtar. - - M. O. B. C. - MAXIMILIAN OTTO BISMARCK CASPARI, M.A. - - Reader in Ancient History at London University. Lecturer in Greek - at Birmingham University, 1905-1908. - - Irene (752-803). - - N. M. - NORMAN MCLEAN, M.A. - - Fellow, Lecturer and Librarian of Christ's College, Cambridge. - University Lecturer in Aramaic. Examiner for the Oriental - Languages Tripos and the Theological Tripos at Cambridge. - - Isaac of Antioch. - - O. J. R. H. - OSBERT JOHN RADCLIFFE HOWARTH, M.A. - - Christ Church, Oxford. Geographical Scholar, 1901. Assistant - Secretary of the British Association. - - Ireland: _Geography_. - - P. A. - PAUL DANIEL ALPHANDERY. - - Professor of the History of Dogma, Ecole pratique des hautes - etudes, Sorbonne, Paris. Author of _Les Idees morales chez les - heterodoxes latines au debut du XIII^e. siecle_. - - Inquisition. - - P. A. K. - PRINCE PETER ALEXEIVITCH KROPOTKIN. - - See the biographical article, KROPOTKIN, PRINCE P. A. - - Irkutsk (_in part_). - - P. C. M. - PETER CHALMERS MITCHELL, M.A., F.R.S., F.Z.S., D.SC., LL.D. - - Secretary to the Zoological Society of London. University - Demonstrator in Comparative Anatomy and Assistant to Linacre - Professor at Oxford, 1888-1891. Examiner in Zoology to the - University of London, 1903. Author of _Outlines of Biology_; &c. - - Hybridism. - - P. Gi. - PETER GILES, M.A., LL.D., LITT.D. - - Fellow and Classical Lecturer of Emmanuel College, Cambridge, and - University Reader in Comparative Philology. Formerly Secretary of - the Cambridge Philological Society. Author of _Manual of - Comparative Philology_; &c. - - I; - Indo-European Languages. - - P. Sm. - PRESERVED SMITH, PH.D. - - Rufus B. Kellogg Fellow, Amherst College, Amherst, Mass. - - Innocent I., II. - - R. - THE RIGHT HON. LORD RAYLEIGH. - - See the biographical article, RAYLEIGH, 3RD BARON. - - Interference of Light. - - R. A. S. M. - ROBERT ALEXANDER STEWART MACALISTER, M.A., F.S.A. - - St John's College, Cambridge. Director of Excavations for the - Palestine Exploration Fund. - - Idumaea. - - R. Ba. - RICHARD BAGWELL, M.A., LL.D. - - Commissioner of National Education for Ireland. Author of _Ireland - under the Tudors_; _Ireland under the Stuarts_. - - Ireland: _Modern History_. - - R. C. J. - SIR RICHARD CLAVERHOUSE JEBB, D.C.L., LL.D. - - See the biographical article, JEBB, SIR RICHARD CLAVERHOUSE. - - Isaeus; - Isocrates. - - R. G. - RICHARD GARNETT. LL.D. - - See the biographical article, GARNETT, RICHARD. - - Irving, Washington. - - R. H. C. - REV. ROBERT HENRY CHARLES, M.A., D.D., D.LITT. - - Grinfield Lecturer, and Lecturer in Biblical Studies, Oxford. - Fellow of the British Academy. Formerly Professor of Biblical - Greek, Trinity College, Dublin. Author of _Critical History of the - Doctrine of a Future Life_; _Book of Jubilees_; &c. - - Isaiah, Ascension of. - - R. L.* - RICHARD LYDEKKER, F.R.S., F.Z.S., F.G.S. - - Member of the Staff of the Geological Survey of India 1874-1882. - Author of _Catalogues of Fossil Mammals, Reptiles and Birds in the - British Museum_; _The Deer of all Lands_; &c. - - Hyracoidea; - Ibex (_in part_); - Indri; - Insectivora. - - R. P. S. - R. PHENE SPIERS, F.S.A., F.R.I.B.A. - - Formerly Master of the Architectural School, Royal Academy, - London. Past President of Architectural Association. Associate and - Fellow of King's College, London. Corresponding Member of the - Institute of France. Editor of Fergusson's _History of - Architecture_. Author of _Architecture; East and West_; &c. - - Hypaethros. - - R. S. C. - ROBERT SEYMOUR CONWAY, M.A., D.LITT.(CANTAB.). - - Professor of Latin and Indo-European Philology in the University - of Manchester. Formerly Professor of Latin in University College, - Cardiff; and Fellow of Gonville and Caius College, Cambridge. - Author of _The Italic Dialects_. - - Iguvium; - Iovilae. - - S. - THE RIGHT HON. THE EARL OF SELBORNE. - - See the biographical article, SELBORNE, 1ST EARL OF. - - Hymns. - - R. Tr. - ROLAND TRUSLOVE, M.A. - - Formerly Scholar of Christ Church, Oxford. Dean, Fellow and - Lecturer in Classics at Worcester College, Oxford. - - Indo-China, French (_in part_). - - S. A. C. - STANLEY ARTHUR COOK, M.A. - - Lecturer in Hebrew and Syriac, and formerly Fellow, Gonville and - Caius College, Cambridge. Editor for Palestine Exploration Fund. - Author of _Glossary of Aramaic Inscriptions_; _The Laws of Moses - and the Code of Hammurabi_; _Critical Notes on Old Testament - History_; _Religion of Ancient Palestine_; &c. - - Ishmael. - - S. Bl. - SIGFUS BLONDAL. - - Librarian of the University of Copenhagen. - - Iceland: _Recent Literature_. - - T. As. - THOMAS ASHBY, M.A., D.LITT. (Oxon.). - - Director of British School of Archaeology at Rome. Formerly - Scholar of Christ Church, Oxford. Craven Fellow, 1897. Conington - Prizeman, 1906. Member of the Imperial German Archaeological - Institute. - - Interamna Lirenas; - Ischia. - - T. A. I. - THOMAS ALLAN INGRAM, M.A., LL.D. - - Trinity College, Dublin. - - Illegitimacy; - Insurance (_in part_). - - T. Ba. - SIR THOMAS BARCLAY, M.P. - - Member of the Institute of International Law. Member of the - Supreme Council of the Congo Free State. Officer of the Legion of - Honour. Author of _Problems of International Practice and - Diplomacy_; &c. M.P. for Blackburn, 1910. - - Immunity; - International Law. - - T. F. - REV. THOMAS FOWLER, M.A., D.D., LL.D. (1832-1904). - - President of Corpus Christi College, Oxford, 1881-1904. Honorary - Fellow of Lincoln College. Professor of Logic, 1873-1888. - Vice-Chancellor of the University of Oxford, 1899-1901. Author of - _Elements of Deductive Logic_; _Elements of Inductive Logic_; - _Locke_ ("English Men of Letters"); _Shaftesbury and Hutcheson_ - ("English Philosophers"); &c. - - Hutcheson, Francis (_in part_). - - T. F. C. - THEODORE FREYLINGHUYSEN COLLIER, PH.D. - - Assistant Professor of History, Williams College, Williamstown, - Mass., U.S.A. - - Innocent IX.-XIII. - - T. H. H.* - COLONEL SIR THOMAS HUNGERFORD HOLDICH, K.C.M.G., K.C.I.E., - HON.D.SC. - - Superintendent, Frontier Surveys, India, 1892-1898. Gold - Medallist, R.G.S., London, 1887. Author of _The Indian - Borderland_; _The Countries of the King's Award_; _India_; - _Tibet_; &c. - - Indus. - - T. K. C. - REV. THOMAS KELLY CHEYNE, D.D. - - See the biographical article, CHEYNE, T. K. - - Isaiah. - - Th. T. - THORVALDUR THORODDSEN. - - Icelandic Expert and Explorer. Honorary Professor in the - University of Copenhagen. Author of _History of Icelandic - Geography_; _Geological Map of Iceland_; &c. - - Iceland: _Geography and Statistics_. - - W. A. B. C. - REV. WILLIAM AUGUSTUS BREVOORT COOLIDGE, M.A., F.R.G.S., - PH.D.(Bern). - - Fellow of Magdalen College, Oxford. Professor of English History, - St David's College, Lampeter, 1880-1881. Author of _Guide du Haut - Dauphine_; _The Range of the Todi_; _Guide to Grindelwald_; _Guide - to Switzerland_; _The Alps in Nature and in History_; &c. Editor - of _The Alpine Journal_, 1880-1881; &c. - - Hyeres; - Innsbruck; - Interlaken; - Iseo, Lake of; - Isere (_River_); - Isere (_Department_). - - W. A. P. - WALTER ALISON PHILLIPS, M.A. - - Formerly Exhibitioner of Merton College and Senior Scholar of St - John's College, Oxford. Author of _Modern Europe_; &c. - - Innocent III., IV. - - W. C. U. - WILLIAM CAWTHORNE UNWIN, LL.D., F.R.S., M.INST.C.E., M.INST.M.E., - A.R.I.B.A. - - Emeritus Professor, Central Technical College, City and Guilds of - London Institute. Author of _Wrought Iron Bridges and Roofs_; - _Treatise on Hydraulics_; &c. - - Hydraulics. - - W. F. C. - WILLIAM FEILDEN CRAIES, M.A. - - Barrister-at-Law, Inner Temple. Lecturer on Criminal Law, King's - College, London. Editor of Archbold's _Criminal Pleading_ (23rd - edition). - - Indictment. - - W. F. Sh. - WILLIAM FLEETWOOD SHEPPARD, M.A. - - Senior Examiner in the Board of Education, London. Formerly Fellow - of Trinity College, Cambridge. Senior Wrangler, 1884. - - Interpolation. - - W. G. - WILLIAM GARNETT, M.A., D.C.L. - - Educational Adviser to the London County Council. Formerly Fellow - and Lecturer of St John's College, Cambridge. Principal and - Professor of Mathematics, Durham College of Science, - Newcastle-on-Tyne. Author of _Elementary Dynamics_; &c. - - Hydrometer. - - W. Go. - WILLIAM GOW, M.A., PH.D. - - Secretary of the British and Foreign Marine Insurance Co. Ltd., - Liverpool. Lecturer on Marine Insurance at University College, - Liverpool. Author of _Marine Insurance_; &c. - - Insurance: _Marine_. - - W. H. F. - SIR WILLIAM HENRY FLOWER, F.R.S. - - See the biographical article, FLOWER, SIR W. H. - - Ibex (_in part_). - - W. H. Po. - W. HALDANE PORTER. - - Barrister-at-Law, Middle Temple. - - Ireland: _Statistics and Administration_. - - W. Ma. - SIR WILLIAM MARKBY, K.C.I.E. - - See the biographical article, MARKBY, SIR WILLIAM. - - Indian Law. - - W. McD. - WILLIAM MCDOUGALL, M.A. - - Wilde Reader in Mental Philosophy in the University of Oxford. - Formerly Fellow of St John's College, Cambridge. - - Hypnotism. - - W. M. L. - WALLACE MARTIN LINDSAY, M.A., LITT.D., LL.D. - - Professor of Humanity, University of St Andrews. Fellow of the - British Academy. Formerly Fellow of Jesus College, Oxford. Author - of _Handbook of Latin Inscriptions_; _The Latin Language_; &c. - - Inscriptions: _Latin_ (_in part_). - - W. M. Ra. - SIR WILLIAM MITCHELL RAMSAY, LITT.D., D.C.L. - - See the biographical article, RAMSAY, SIR W. MITCHELL. - - Iconium. - - W. R. So. - WILLIAM RITCHIE SORLEY, M.A., LITT.D., LL.D. - - Professor of Moral Philosophy in the University of Cambridge. - Fellow of King's College, Cambridge. Fellow of the British - Academy. Formerly Fellow of Trinity College. Author of _The Ethics - of Naturalism_; _The Interpretation of Evolution_; &c. - - Iamblichus. - - W. T. T.-D. - SIR WILLIAM TURNER THISELTON-DYER, F.R.S., K.C.M.G., C.I.E., - D.SC., LL.D., PH.D., F.L.S. - - Hon. Student of Christ Church, Oxford. Director, Royal Botanic - Gardens, Kew, 1885-1905. Botanical Adviser to Secretary of State - for Colonies, 1902-1906. Joint-author of _Flora of Middlesex_. - Editor of _Flora Capenses_ and _Flora of Tropical Africa_. - - Huxley. - - W. Wn. - WILLIAM WATSON, D.SC., F.R.S., A.R.C.S. - - Assistant Professor of Physics, Royal College of Science, London. - Vice-President of the Physical Society. Author of _A Text Book of - Practical Physics_; &c. - - Inclinometer. - - W. W. H. - SIR WILLIAM WILSON HUNTER. - - See the biographical article. HUNTER, SIR WILLIAM WILSON. - - India: _History (in part); Geography and Statistics (in part)._ - - - - - PRINCIPAL UNSIGNED ARTICLES - - Husband and Wife. Image. Ink. - Hyacinth. Impeachment. Inkerman. - Hyderabad. Income Tax. International, The. - Hydrogen. Indiana. Intestacy. - Hydropathy. Indian Mutiny. Inverness-shire. - Hydrophobia. Indicator. Investiture. - Ice. Infant. Iodine. - Ice-Yachting. Infanticide. Iowa. - Idaho. Infinite. Ipecacuanha. - Illinois. Influenza. Iris. - Illumination. Inheritance. Iron. - Illyria. Injunction. Irrigation. - - -FOOTNOTE: - - [1] A complete list, showing all individual contributors, appears in - the final volume. - - - - - ENCYCLOPAEDIA BRITANNICA - - ELEVENTH EDITION - - VOLUME XIV - - - - -HUSBAND, properly the "head of a household," but now chiefly used in the -sense of a man legally joined by marriage to a woman, his "wife"; the -legal relations between them are treated below under HUSBAND AND WIFE. -The word appears in O. Eng. as _husbonda_, answering to the Old -Norwegian _husbondi_, and means the owner or freeholder of a _hus_, or -house. The last part of the word still survives in "bondage" and -"bondman," and is derived from _bua_, to dwell, which, like Lat. -_colere_, means also to till or cultivate, and to have a household. -"Wife," in O. Eng. _wif_, appears in all Teutonic languages except -Gothic; cf. Ger. _Weib_, Dutch _wijf_, &c., and meant originally simply -a female, "woman" itself being derived from _wifman_, the pronunciation -of the plural _wimmen_ still preserving the original _i_. Many -derivations of "wife" have been given; thus it has been connected with -the root of "weave," with the Gothic _waibjan_, to fold or wrap up, -referring to the entangling clothes worn by a woman, and also with the -root of _vibrare_, to tremble. These are all merely guesses, and the -ultimate history of the word is lost. It does not appear outside -Teutonic languages. Parallel to "husband" is "housewife," the woman -managing a household. The earlier _huswif_ was pronounced _hussif_, and -this pronunciation survives in the application of the word to a small -case containing scissors, needles and pins, cottons, &c. From this form -also derives "hussy," now only used in a depreciatory sense of a light, -impertinent girl. Beyond the meaning of a husband as a married man, the -word appears in connexion with agriculture, in "husbandry" and -"husbandman." According to some authorities "husbandman" meant -originally in the north of England a holder of a "husbandland," a -manorial tenant who held two ox-gangs or virgates, and ranked next below -the yeoman (see J. C. Atkinson in _Notes and Queries_, 6th series, vol. -xii., and E. Bateson, _History of Northumberland_, ii., 1893). From the -idea of the manager of a household, "husband" was in use transferred to -the manager of an estate, and the title was held by certain officials, -especially in the great trading companies. Thus the "husband" of the -East India Company looked after the interests of the company at the -custom-house. The word in this sense is practically obsolete, but it -still appears in "ship's husband," an agent of the owners of a ship who -looks to the proper equipping of the vessel, and her repairs, procures -and adjusts freights, keeps the accounts, makes charter-parties and acts -generally as manager of the ship's employment. Where such an agent is -himself one of the owners of the vessel, the name of "managing owner" is -used. The "ship's husband" or "managing owner" must register his name -and address at the port of registry (Merchant Shipping Act 1894, S 59). -From the use of "husband" for a good and thrifty manager of a household, -the verb "to husband" means to economize, to lay up a store, to save. - - - - -HUSBAND AND WIFE, LAW RELATING TO. For the modes in which the relation -of husband and wife may be constituted and dissolved, see MARRIAGE and -DIVORCE. The present article will deal only with the effect of marriage -on the legal position of the spouses. The person chiefly affected is the -wife, who probably in all political systems becomes subject, in -consequence of marriage, to some kind of disability. The most favourable -system scarcely leaves her as free as an unmarried woman; and the most -unfavourable subjects her absolutely to the authority of her husband. In -modern times the effect of marriage on property is perhaps the most -important of its consequences, and on this point the laws of different -states show wide diversity of principles. - -The history of Roman law exhibits a transition from an extreme theory to -its opposite. The position of the wife in the earliest Roman household -was regulated by the law of _Manus_. She fell under the "hand" of her -husband,--became one of his family, along with his sons and daughters, -natural or adopted, and his slaves. The dominion which, so far as the -children was concerned, was known as the _patria potestas_, was, with -reference to the wife, called the _manus_. The subject members of the -family, whether wife or children, had, broadly speaking, no rights of -their own. If this institution implied the complete subjection of the -wife to the husband, it also implied a much closer bond of union between -them than we find in the later Roman law. The wife on her husband's -death succeeded, like the children, to freedom and a share of the -inheritance. _Manus_, however, was not essential to a legal marriage; -its restraints were irksome and unpopular, and in course of time it -ceased to exist, leaving no equivalent protection of the stability of -family life. The later Roman marriage left the spouses comparatively -independent of each other. The distance between the two modes of -marriage may be estimated by the fact that, while under the former -the wife was one of the husband's immediate heirs, under the latter she -was called to the inheritance only after his kith and kin had been -exhausted, and only in preference to the treasury. It seems doubtful how -far she had, during the continuance of marriage, a legal right to -enforce aliment from her husband, although if he neglected her she had -the unsatisfactory remedy of an easy divorce. The law, in fact, -preferred to leave the parties to arrange their mutual rights and -obligations by private contracts. Hence the importance of the law of -settlements (_Dotes_). The _Dos_ and the _Donatio ante nuptias_ were -settlements by or on behalf of the husband or wife, during the -continuance of the marriage, and the law seems to have looked with some -jealousy on gifts made by one to the other in any less formal way, as -possibly tainted with undue influence. During the marriage the husband -had the administration of the property. - -The _manus_ of the Roman law appears to be only one instance of an -institution common to all primitive societies. On the continent of -Europe after many centuries, during which local usages were brought -under the influence of principles derived from the Roman law, a theory -of marriage became established, the leading feature of which is the -_community of goods_ between husband and wife. Describing the principle -as it prevails in France, Story (_Conflict of Laws_, S 130) says: "This -community or nuptial partnership (in the absence of any special -contract) generally extends to all the movable property of the husband -and wife, and to the fruits, income and revenue thereof.... It extends -also to all immovable property of the husband and wife acquired during -the marriage, but not to such immovable property as either possessed at -the time of the marriage, or which came to them afterwards by title of -succession or by gift. The property thus acquired by this nuptial -partnership is liable to the debts of the parties existing at the time -of the marriage; to the debts contracted by the husband during the -community, or by the wife during the community with the consent of the -husband; and to debts contracted for the maintenance of the family.... -The husband alone is entitled to administer the property of the -community, and he may alien, sell or mortgage it without the concurrence -of the wife." But he cannot dispose by will of more than his share of -the common property, nor can he part with it gratuitously _inter vivos_. -The community is dissolved by death (natural or civil), divorce, -separation of body or separation of property. On separation of body or -of property the wife is entitled to the full control of her movable -property, but cannot alien her immovable property, without her husband's -consent or legal authority. On the death of either party the property is -divided in equal moieties between the survivor and the heirs of the -deceased. - -_Law of England._--The English common law as usual followed its own -course in dealing with this subject, and in no department were its rules -more entirely insular and independent. The text writers all assumed two -fundamental principles, which between them established a system of -rights totally unlike that just described. Husband and wife were said to -be one person in the eye of the law--_unica persona, quia caro una et -sanguis unus_. Hence a man could not grant or give anything to his wife, -because she was himself, and if there were any compacts between them -before marriage they were dissolved by the union of persons. Hence, too, -the old rule of law, now greatly modified, that husband and wife could -not be allowed to give evidence against each other, in any trial, civil -or criminal. The unity, however, was one-sided only; it was the wife who -was merged in the husband, not the husband in the wife. And when the -theory did not apply, the disabilities of "coverture" suspended the -active exercise of the wife's legal faculties. The old technical -phraseology described husband and wife as _baron_ and _feme_; the rights -of the husband were baronial rights. From one point of view the wife was -merged in the husband, from another she was as one of his vassals. A -curious example is the immunity of the wife in certain cases from -punishment for crime committed in the presence and on the presumed -coercion of the husband. "So great a favourite," says Blackstone, "is -the female sex of the laws of England." - -The application of these principles with reference to the property of -the wife, and her capacity to contract, may now be briefly traced. - -The _freehold property_ of the wife became vested in the husband and -herself during the coverture, and he had the management and the profits. -If the wife had been in actual possession at any time during the -marriage of an estate of inheritance, and if there had been a child of -the marriage capable of inheriting, then the husband became entitled on -his wife's death to hold the estate for his own life as tenant by the -_curtesy of England_ (_curialitas_).[1] Beyond this, however, the -husband's rights did not extend, and the wife's heir at last succeeded -to the inheritance. The wife could not part with her real estate without -the concurrence of the husband; and even so she must be examined apart -from her husband, to ascertain whether she freely and voluntarily -consented to the deed. - -With regard to personal property, it passed absolutely at common law to -the husband. Specific things in the possession of the wife (_choses_ in -possession) became the property of the husband at once; things not in -possession, but due and recoverable from others (_choses_ in action), -might be recovered by the husband. A _chose_ in action not reduced into -actual possession, when the marriage was dissolved by death, reverted to -the wife if she was the survivor; if the husband survived he could -obtain possession by taking out letters of administration. A _chose_ in -action was to be distinguished from a specific thing which, although the -property of the wife, was for the time being in the hands of another. In -the latter case the property was in the wife, and passed at once to the -husband; in the former the wife had a mere _jus in personam_, which the -husband might enforce if he chose, but which was still capable of -reverting to the wife if the husband died without enforcing it. - -The _chattels real_ of the wife (i.e., personal property, dependent on, -and partaking of, the nature of realty, such as leaseholds) passed to -the husband, subject to the wife's right of survivorship, unless barred -by the husband by some act done during his life. A disposition by will -did not bar the wife's interest; but any disposition _inter vivos_ by -the husband was valid and effective. - -The courts of equity, however, greatly modified the rules of the common -law by the introduction of the wife's _separate estate_, i.e. property -settled to the wife for her separate use, independently of her husband. -The principle seems to have been originally admitted in a case of actual -separation, when a fund was given for the maintenance of the wife while -living apart from her husband. And the conditions under which separate -estate might be enjoyed had taken the Court of Chancery many generations -to develop. No particular form of words was necessary to create a -separate estate, and the intervention of trustees, though common, was -not necessary. A clear intention to deprive the husband of his common -law rights was sufficient to do so. In such a case a married woman was -entitled to deal with her property as if she was unmarried, although the -earlier decisions were in favour of requiring her binding engagements to -be in writing or under seal. But it was afterwards held that any -engagements, clearly made with reference to the separate estate, would -bind that estate, exactly as if the woman had been a _feme sole_. -Connected with the doctrine of separate use was the equitable -contrivance of _restraint on anticipation_ with which later legislation -has not interfered, whereby property might be so settled to the separate -use of a married woman that she could not, during coverture, alienate it -or anticipate the income. No such restraint is recognized in the ease of -a man or of a _feme sole_, and it depends entirely on the separate -estate; and the separate estate has its existence only during coverture, -so that a woman to whom such an estate is given may dispose of it so -long as she is unmarried, but becomes bound by the restraint as soon as -she is married. In yet another way the court of Chancery interfered to -protect the interests of married women. When a husband sought the -aid of that court to get possession of his wife's _choses_ in action, he -was required to make a provision for her and her children out of the -fund sought to be recovered. This is called the wife's _equity to a -settlement_, and is said to be based on the original maxim of Chancery -jurisprudence, that "he who seeks equity must do equity." Two other -property interests of minor importance are recognised. The wife's -_pin-money_ is a provision for the purchase of clothes and ornaments -suitable to her husband's station, but it is not an absolute gift to the -separate use of the wife; and a wife surviving her husband cannot claim -for more than one year's arrears of pin-money. _Paraphernalia_ are -jewels and other ornaments given to the wife by her husband for the -purpose of being worn by her, but not as her separate property. The -husband may dispose of them by act _inter vivos_ but not by will, unless -the will confers other benefits on the wife, in which case she must -elect between the will and the paraphernalia. She may also on the death -of the husband claim paraphernalia, provided all creditors have been -satisfied, her right being superior to that of any legatee. - -The corresponding interest of the wife in the property of the husband is -much more meagre and illusory. Besides a general right to maintenance at -her husband's expense, she has at common law a right to dower (q.v.) in -her husband's lands, and to a _pars rationabilis_ (third) of his -personal estate, if he dies intestate. The former, which originally was -a solid provision for widows, has by the ingenuity of conveyancers, as -well as by positive enactment, been reduced to very slender dimensions. -It may be destroyed by a mere declaration to that effect on the part of -the husband, as well as by his conveyance of the land or by his will. - -The common practice of regulating the rights of husband, wife and -children by marriage settlements obviates the hardships of the common -law--at least for the women of the wealthier classes. The legislature by -the Married Women's Property Acts of 1870, 1874, 1882 (which repealed -and consolidated the acts of 1870 and 1874), 1893 and 1907 introduced -very considerable changes. The chief provisions of the Married Women's -Property Act 1882, which enormously improved the position of women -unprotected by marriage settlement, are, shortly, that a married woman -is capable of acquiring, holding and disposing of by will or otherwise, -any real and personal property, in the same manner as if she were a -_feme sole_, without the intervention of any trustee. The property of a -woman married after the beginning of the act, whether belonging to her -at the time of marriage or acquired after marriage, is held by her as a -_feme sole_. The same is the case with property acquired after the -beginning of the act by a woman married before the act. After marriage a -woman remains liable for antenuptial debts and liabilities, and as -between her and her husband, in the absence of contract to the contrary, -her separate property is deemed primarily liable. The husband is only -liable to the extent of property acquired from or through his wife. The -act also contained provisions as to stock, investment, insurance, -evidence and other matters. The effect of the act was to render obsolete -the law as to what created a separate use or a reduction into possession -of _choses_ in action, as to equity to a settlement, as to fraud on the -husband's marital rights, and as to the inability of one of two married -persons to give a gift to the other. Also, in the case of a gift to a -husband and wife in terms which would make them joint tenants if -unmarried, they no longer take as one person but as two. The act -contained a special saving of existing and future settlements; a -settlement being still necessary where it is desired to secure only the -enjoyment of the income to the wife and to provide for children. The act -by itself would enable the wife, without regard to family claims, -instantly to part with the whole of any property which might come to -her. Restraint on anticipation was preserved by the act, subject to the -liability of such property for antenuptial debts, and to the power given -by the Conveyancing Act 1881 to bind a married woman's interest -notwithstanding a clause of restraint. The Married Women's Property Act -of 1893 repealed two clauses in the act of 1882, the exact bearing of -which had been a matter of controversy. It provided specifically that -every contract thereinafter entered into by a married woman, otherwise -than as an agent, should be deemed to be a contract entered into by her -with respect to and be binding upon her separate property, whether she -was or was not in fact possessed of or entitled to any separate property -at the time when she entered into such contract, that it should bind all -separate property which she might at any time or thereafter be possessed -of or entitled to, and that it should be enforceable by process of law -against all property which she might thereafter, while discovert, be -possessed of or entitled to. The act of 1907 enabled a married woman, -without her husband, to dispose of or join in disposing of, real or -personal property held by her solely or jointly as trustee or personal -representative, in like manner as if she were a _feme sole_. It also -provided that a settlement or agreement for settlement whether before or -after marriage, respecting the property of the woman, should not be -valid unless executed by her if she was of full age or confirmed by her -after she attained full age. The Married Women's Property Act 1908 -removed a curious anomaly by enacting that a married woman having -separate property should be equally liable with single women and widows -for the maintenance of parents who are in receipt of poor relief. - -The British colonies generally have adopted the principles of the -English acts of 1882 and 1893. - - _Law of Scotland._--The law of Scotland differs less from English law - than the use of a very different terminology would lead us to suppose. - The phrase _communio bonorum_ has been employed to express the - interest which the spouses have in the _movable_ property of both, but - its use has been severely censured as essentially inaccurate and - misleading. It has been contended that there was no real community of - goods, and no partnership or societas between the spouses. The wife's - movable property, with certain exceptions, and subject to special - agreements, became as absolutely the property of the husband as it did - in English law. The notion of a _communio_ was, however, favoured by - the peculiar rights of the wife and children on the dissolution of the - marriage. Previous to the Intestate Movable Succession (Scotland) Act - 1855 the law stood as follows. The fund formed by the movable property - of both spouses may be dealt with by the husband as he pleases during - life; it is increased by his acquisitions and diminished by his debts. - The respective shares contributed by husband and wife return on the - dissolution of the marriage to them or their representatives if the - marriage be dissolved within a year and a day, and without a living - child. Otherwise the division is into two or three shares, according - as children are existing or not at the dissolution of the marriage. On - the death of the husband, his children take one-third (called - _legitim_), the widow takes one-third (_jus relictae_), and the - remaining one-third (the _dead part_) goes according to his will or to - his next of kin. If there be no children, the _jus relictae_ and the - dead's part are each one-half. If the wife die before the husband, her - representatives, whether children or not, are creditors for the value - of her share. The statute above-mentioned, however, enacts that "where - a wife shall predecease her husband, the next of kin, executors or - other representatives of such wife, whether testate or intestate, - shall have no right to any share of the goods in communion; nor shall - any legacy or bequest or testamentary disposition thereof by such - wife, affect or attach to the said goods or any portion thereof." It - also abolishes the rule by which the shares revert if the marriage - does not subsist for a year and a day. Several later acts apply to - Scotland some of the principles of the English Married Women's - Property Acts. These are the Married Women's Property (Scotland) Act - 1877, which protects the earnings, &c., of wives, and limits the - husband's liability for antenuptial debts of the wife, the Married - Women's Policies of Assurance (Scotland) Act 1880, which enables a - woman to contract for a policy of assurance for her separate use, and - the Married Women's Property (Scotland) Act 1881, which abolished the - _jus mariti_. - - A wife's _heritable_ property does not pass to the husband on - marriage, but he acquires a right to the administration and profits. - His courtesy, as in English law, is also recognized. On the other - hand, a widow has a _terce_ or life-rent of a third part of the - husband's heritable estate, unless she has accepted a conventional - provision. - - _Continental Europe._--Since 1882 English legislation in the matter of - married women's property has progressed from perhaps the most backward - to the foremost place in Europe. By a curious contrast, the only two - European countries where, in the absence of a settlement to the - contrary, independence of the wife's property was recognized, were - Russia and Italy. But there is now a marked tendency towards - contractual emancipation. Sweden adopted a law on this subject in - 1874, Denmark in 1880, Norway in 1888. Germany followed, the Civil - Code which came into operation in 1900 (Art. 1367) providing that the - wife's wages or earnings shall form part of her _Vorbehaltsgut_ or - separate property, which a previous article (1365) placed beyond - the husband's control. As regards property accruing to the wife in - Germany by succession, will or gift _inter vivos_, it is only separate - property where the donor has deliberately stipulated exclusion of the - husband's right. - - In France it seemed as if the system of community of property was - ingrained in the institutions of the country. But a law of 1907 has - brought France into line with other countries. This law gives a - married woman sole control over earnings from her personal work and - savings therefrom. She can with such money acquire personalty or - realty, over the former of which she has absolute control. But if she - abuses her rights by squandering her money or administering her - property badly or imprudently the husband may apply to the court to - have her freedom restricted. - - _American Law._--In the United States, the revolt against the common - law theory of husband and wife was carried farther than in England, - and legislation early tended in the direction of absolute equality - between the sexes. Each state has, however, taken its own way and - selected its own time for introducing modifications of the existing - law, so that the legislation on this subject is now exceedingly - complicated and difficult. James Schouler (_Law of Domestic - Relations_) gives an account of the general result in the different - states to which reference may be made. The peculiar system of - Homestead Laws in many of the states (see HOMESTEAD and EXEMPTION - LAWS) constitutes an inalienable provision for the wife and family of - the householder. - - -FOOTNOTE: - - [1] Curtesy or courtesy has been explained by legal writers as - "arising _by favour_ of the law of England." The word has nothing to - do with courtesy in the sense of complaisance. - - - - -HUSHI (Rumanian _Husi_), the capital of the department of Falciu, -Rumania; on a branch of the Jassy-Galatz railway, 9 m. W. of the river -Pruth and the Russian frontier. Pop. (1900) 15,404, about one-fourth -being Jews. Hushi is an episcopal see. The cathedral was built in 1491 -by Stephen the Great of Moldavia. There are no important manufactures, -but a large fair is held annually in September for the sale of -live-stock, and wine is produced in considerable quantities. Hushi is -said to have been founded in the 15th century by a colony of Hussites, -from whom its name is derived. The treaty of the Pruth between Russia -and Turkey was signed here in 1711. - - - - -HUSKISSON, WILLIAM (1770-1830), English statesman and financier, was -descended from an old Staffordshire family of moderate fortune, and was -born at Birch Moreton, Worcestershire, on the 11th of March 1770. Having -been placed in his fourteenth year under the charge of his maternal -great-uncle Dr Gem, physician to the English embassy at Paris, in 1783 -he passed his early years amidst a political fermentation which led him -to take a deep interest in politics. Though he approved of the French -Revolution, his sympathies were with the more moderate party, and he -became a member of the "club of 1789," instituted to support the new -form of constitutional monarchy in opposition to the anarchical attempts -of the Jacobins. He early displayed his mastery of the principles of -finance by a _Discours_ delivered in August 1790 before this society, in -regard to the issue of assignats by the government. The _Discours_ -gained him considerable reputation, but as it failed in its purpose he -withdrew from the society. In January 1793 he was appointed by Dundas to -an office created to direct the execution of the Aliens Act; and in the -discharge of his delicate duties he manifested such ability that in 1795 -he was appointed under-secretary at war. In the following year he -entered parliament as member for Morpeth, but for a considerable period -he took scarcely any part in the debates. In 1800 he inherited a fortune -from Dr Gem. On the retirement of Pitt in 1801 he resigned office, and -after contesting Dover unsuccessfully he withdrew for a time into -private life. Having in 1804 been chosen to represent Liskeard, he was -on the restoration of the Pitt ministry appointed secretary of the -treasury, holding office till the dissolution of the ministry after the -death of Pitt in January 1806. After being elected for Harwich in 1807, -he accepted the same office under the duke of Portland, but he withdrew -from the ministry along with Canning in 1809. In the following year he -published a pamphlet on the currency system, which confirmed his -reputation as the ablest financier of his time; but his free-trade -principles did not accord with those of his party. In 1812 he was -returned for Chichester. When in 1814 he re-entered the public service, -it was only as chief commissioner of woods and forests, but his -influence was from this time very great in the commercial and financial -legislation of the country. He took a prominent part in the corn-law -debates of 1814 and 1815; and in 1819 he presented a memorandum to Lord -Liverpool advocating a large reduction in the unfunded debt, and -explaining a method for the resumption of cash payments, which was -embodied in the act passed the same year. In 1821 he was a member of the -committee appointed to inquire into the causes of the agricultural -distress then prevailing, and the proposed relaxation of the corn laws -embodied in the report was understood to have been chiefly due to his -strenuous advocacy. In 1823 he was appointed president of the board of -trade and treasurer of the navy, and shortly afterwards he received a -seat in the cabinet. In the same year he was returned for Liverpool as -successor to Canning, and as the only man who could reconcile the Tory -merchants to a free trade policy. Among the more important legislative -changes with which he was principally connected were a reform of the -Navigation Acts, admitting other nations to a full equality and -reciprocity of shipping duties; the repeal of the labour laws; the -introduction of a new sinking fund; the reduction of the duties on -manufactures and on the importation of foreign goods, and the repeal of -the quarantine duties. In accordance with his suggestion Canning in 1827 -introduced a measure on the corn laws proposing the adoption of a -sliding scale to regulate the amount of duty. A misapprehension between -Huskisson and the duke of Wellington led to the duke proposing an -amendment, the success of which caused the abandonment of the measure by -the government. After the death of Canning in the same year Huskisson -accepted the secretaryship of the colonies under Lord Goderich, an -office which he continued to hold in the new cabinet formed by the duke -of Wellington in the following year. After succeeding with great -difficulty in inducing the cabinet to agree to a compromise on the corn -laws, Huskisson finally resigned office in May 1829 on account of a -difference with his colleagues in regard to the disfranchisement of East -Retford. On the 15th of September of the following year he was -accidentally killed by a locomotive engine while present at the opening -of the Liverpool and Manchester railway. - - See the _Life of Huskisson_, by J. Wright (London, 1831). - - - - -HUSS (or HUS), JOHN (c. 1373-1415), Bohemian reformer and martyr, was -born at Hussinecz,[1] a market village at the foot of the Bohmerwald, -and not far from the Bavarian frontier, between 1373 and 1375, the exact -date being uncertain. His parents appear to have been well-to-do Czechs -of the peasant class. Of his early life nothing is recorded except that, -notwithstanding the early loss of his father, he obtained a good -elementary education, first at Hussinecz, and afterwards at the -neighbouring town of Prachaticz. At, or only a very little beyond, the -usual age he entered the recently (1348) founded university of Prague, -where he became bachelor of arts in 1393, bachelor of theology in 1394, -and master of arts in 1396. In 1398 he was chosen by the Bohemian -"nation" of the university to an examinership for the bachelor's degree; -in the same year he began to lecture also, and there is reason to -believe that the philosophical writings of Wycliffe, with which he had -been for some years acquainted, were his text-books. In October 1401 he -was made dean of the philosophical faculty, and for the half-yearly -period from October 1402 to April 1403 he held the office of rector of -the university. In 1402 also he was made rector or curate -(_capellarius_) of the Bethlehem chapel, which had in 1391 been erected -and endowed by some zealous citizens of Prague for the purpose of -providing good popular preaching in the Bohemian tongue. This -appointment had a deep influence on the already vigorous religious life -of Huss himself; and one of the effects of the earnest and independent -study of Scripture into which it led him was a profound conviction of -the great value not only of the philosophical but also of the -theological writings of Wycliffe. - -This newly-formed sympathy with the English reformer did not, in the -first instance at least, involve Huss in any conscious opposition to the -established doctrines of Catholicism, or in any direct conflict with the -authorities of the church; and for several years he continued to -act in full accord with his archbishop (Sbynjek, or Sbynko, of -Hasenburg). Thus in 1405 he, with other two masters, was commissioned to -examine into certain reputed miracles at Wilsnack, near Wittenberg, -which had caused that church to be made a resort of pilgrims from all -parts of Europe. The result of their report was that all pilgrimage -thither from the province of Bohemia was prohibited by the archbishop on -pain of excommunication, while Huss, with the full sanction of his -superior, gave to the world his first published writing, entitled _De -Omni Sanguine Christi Glorificato_, in which he declaimed in no measured -terms against forged miracles and ecclesiastical greed, urging -Christians at the same time to desist from looking for sensible signs of -Christ's presence, but rather to seek Him in His enduring word. More -than once also Huss, together with his friend Stanislaus of Znaim, was -appointed to be synod preacher, and in this capacity he delivered at the -provincial councils of Bohemia many faithful admonitions. As early as -the 28th of May 1403, it is true, there had been held a university -disputation about the new doctrines of Wycliffe, which had resulted in -the condemnation of certain propositions presumed to be his; five years -later (May 20, 1408) this decision had been refined into a declaration -that these, forty-five in number, were not to be taught in any -heretical, erroneous or offensive sense. But it was only slowly that the -growing sympathy of Huss with Wycliffe unfavourably affected his -relations with his colleagues in the priesthood. In 1408, however, the -clergy of the city and archiepiscopal diocese of Prague laid before the -archbishop a formal complaint against Huss, arising out of strong -expressions with regard to clerical abuses of which he had made use in -his public discourses; and the result was that, having been first -deprived of his appointment as synodal preacher, he was, after a vain -attempt to defend himself in writing, publicly forbidden the exercise of -any priestly function throughout the diocese. Simultaneously with these -proceedings in Bohemia, negotiations had been going on for the removal -of the long-continued papal schism, and it had become apparent that a -satisfactory solution could only be secured if, as seemed not -impossible, the supporters of the rival popes, Benedict XIII. and -Gregory XII., could be induced, in view of the approaching council of -Pisa, to pledge themselves to a strict neutrality. With this end King -Wenceslaus of Bohemia had requested the co-operation of the archbishop -and his clergy, and also the support of the university, in both -instances unsuccessfully, although in the case of the latter the -Bohemian "nation," with Huss at its head, had only been overborne by the -votes of the Bavarians, Saxons and Poles. There followed an expression -of nationalist and particularistic as opposed to ultramontane and also -to German feeling, which undoubtedly was of supreme importance for the -whole of the subsequent career of Huss. In compliance with this feeling -a royal edict (January 18, 1409) was issued, by which, in alleged -conformity with Paris usage, and with the original charter of the -university, the Bohemian "nation" received three votes, while only one -was allotted to the other three "nations" combined; whereupon all the -foreigners, to the number of several thousands, almost immediately -withdrew from Prague, an occurrence which led to the formation shortly -afterwards of the university of Leipzig. - -It was a dangerous triumph for Huss; for his popularity at court and in -the general community had been secured only at the price of clerical -antipathy everywhere and of much German ill-will. Among the first -results of the changed order of things were on the one hand the election -of Huss (October 1409) to be again rector of the university, but on the -other hand the appointment by the archbishop of an inquisitor to inquire -into charges of heretical teaching and inflammatory preaching brought -against him. He had spoken disrespectfully of the church, it was said, -had even hinted that Antichrist might be found to be in Rome, had -fomented in his preaching the quarrel between Bohemians and Germans, and -had, notwithstanding all that had passed, continued to speak of Wycliffe -as both a pious man and an orthodox teacher. The direct result of this -investigation is not known, but it is impossible to disconnect from it -the promulgation by Pope Alexander V., on the 20th of December 1409, of -a bull which ordered the abjuration of all Wycliffite heresies and the -surrender of all his books, while at the same time--a measure specially -levelled at the pulpit of Bethlehem chapel--all preaching was prohibited -except in localities which had been by long usage set apart for that -use. This decree, as soon as it was published in Prague (March 9, 1410), -led to much popular agitation, and provoked an appeal by Huss to the -pope's better informed judgment; the archbishop, however, resolutely -insisted on carrying out his instructions, and in the following July -caused to be publicly burned, in the courtyard of his own palace, -upwards of 200 volumes of the writings of Wycliffe, while he pronounced -solemn sentence of excommunication against Huss and certain of his -friends, who had in the meantime again protested and appealed to the new -pope (John XXIII.). Again the populace rose on behalf of their hero, -who, in his turn, strong in the conscientious conviction that "in the -things which pertain to salvation God is to be obeyed rather than man," -continued uninterruptedly to preach in the Bethlehem chapel, and in the -university began publicly to defend the so-called heretical treatises of -Wycliffe, while from king and queen, nobles and burghers, a petition was -sent to Rome praying that the condemnation and prohibition in the bull -of Alexander V. might be quashed. Negotiations were carried on for some -months, but in vain; in March 1411 the ban was anew pronounced upon Huss -as a disobedient son of the church, while the magistrates and -councillors of Prague who had favoured him were threatened with a -similar penalty in ease of their giving him a contumacious support. -Ultimately the whole city, which continued to harbour him, was laid -under interdict; yet he went on preaching, and masses were celebrated as -usual, so that at the date of Archbishop Sbynko's death in September -1411, it seemed as if the efforts of ecclesiastical authority had -resulted in absolute failure. - -The struggle, however, entered on a new phase with the appearance at -Prague in May 1412 of the papal emissary charged with the proclamation -of the papal bulls by which a religious war was decreed against the -excommunicated King Ladislaus of Naples, and indulgence was promised to -all who should take part in it, on terms similar to those which had been -enjoyed by the earlier crusaders to the Holy Land. By his bold and -thorough-going opposition to this mode of procedure against Ladislaus, -and still more by his doctrine that indulgence could never be sold -without simony, and could not be lawfully granted by the church except -on condition of genuine contrition and repentance, Huss at last isolated -himself, not only from the archiepiscopal party under Albik of -Unitschow, but also from the theological faculty of the university, and -especially from such men as Stanislaus of Znaim and Stephen Paletz, who -until then had been his chief supporters. A popular demonstration, in -which the papal bulls had been paraded through the streets with -circumstances of peculiar ignominy and finally burnt, led to -intervention by Wenceslaus on behalf of public order; three young men, -for having openly asserted the unlawfulness of the papal indulgence -after silence had been enjoined, were sentenced to death (June 1412); -the excommunication against Huss was renewed, and the interdict again -laid on all places which should give him shelter--a measure which now -began to be more strictly regarded by the clergy, so that in the -following December Huss had no alternative but to yield to the express -wish of the king by temporarily withdrawing from Prague. A provincial -synod, held at the instance of Wenceslaus in February 1413, broke up -without having reached any practical result; and a commission appointed -shortly afterwards also failed to bring about a reconciliation between -Huss and his adversaries. The so-called heretic meanwhile spent his time -partly at Kozihradek, some 45 m. south of Prague, and partly at -Krakowitz in the immediate neighbourhood of the capital, occasionally -giving a course of open-air preaching, but finding his chief employment -in maintaining that copious correspondence of which some precious -fragments still are extant, and in the composition of the treatise, _De -Ecclesia_, which subsequently furnished most of the material for the -capital charges brought against him, and was formerly considered -the most important of his works, though it is mainly a transcript of -Wycliffe's work of the same name. - -During the year 1413 the arrangements for the meeting of a general -council at Constance were agreed upon between Sigismund and Pope John -XXIII. The objects originally contemplated had been the restoration of -the unity of the church and its reform in head and members; but so great -had become the prominence of Bohemian affairs that to these also a first -place in the programme of the approaching oecumenical assembly required -to be assigned, and for their satisfactory settlement the presence of -Huss was necessary. His attendance was accordingly requested, and the -invitation was willingly accepted as giving him a long-wished-for -opportunity both of publicly vindicating himself from charges which he -felt to be grievous, and of loyally making confession for Christ. He set -out from Bohemia on the 14th of October 1414, not, however, until he had -carefully ordered all his private affairs, with a presentiment, which he -did not conceal, that in all probability he was going to his death. The -journey, which appears to have been undertaken with the usual passport, -and under the protection of several powerful Bohemian friends (John of -Chlum, Wenceslaus of Duba, Henry of Chlum) who accompanied him, was a -very prosperous one; and at almost all the halting-places he was -received with a consideration and enthusiastic sympathy which he had -hardly expected to meet with anywhere in Germany. On the 3rd of November -he arrived at Constance; shortly afterwards there was put into his hands -the famous imperial "safe conduct," the promise of which had been one of -his inducements to quit the comparative security he had enjoyed in -Bohemia. This safe conduct, which had been frequently printed, stated -that Huss should, whatever judgment might be passed on him, be allowed -to return freely to Bohemia. This by no means provided for his immunity -from punishment. If faith to him had not been broken he would have been -sent back to Bohemia to be punished by his sovereign, the king of -Bohemia. The treachery of King Sigismund is undeniable, and was indeed -admitted by the king himself. The safe conduct was probably indeed given -by him to entice Huss to Constance. On the 4th of December the pope -appointed a commission of three bishops to investigate the case against -the heretic, and to procure witnesses; to the demand of Huss that he -might be permitted to employ an agent in his defence a favourable answer -was at first given, but afterwards even this concession to the forms of -justice was denied. While the commission was engaged in the prosecution -of its enquiries, the flight of Pope John XXIII. took place on the 20th -of March, an event which furnished a pretext for the removal of Huss -from the Dominican convent to a more secure and more severe place of -confinement under the charge of the bishop of Constance at Gottlieben on -the Rhine. On the 4th of May the temper of the council on the doctrinal -questions in dispute was fully revealed in its unanimous condemnation of -Wycliffe, especially of the so-called "forty-five articles" as -erroneous, heretical, revolutionary. It was not, however, until the 5th -of June that the case of Huss came up for hearing; the meeting, which -was an exceptionally full one, took place in the refectory of the -Franciscan cloister. Autograph copies of his work _De Ecclesia_ and of -the controversial tracts which he had written against Paletz and -Stanislaus of Znaim having been acknowledged by him, the extracted -propositions on which the prosecution based their charge of heresy were -read; but as soon as the accused began to enter upon his defence, he was -assailed by violent outcries, amidst which it was impossible for him to -be heard, so that he was compelled to bring his speech to an abrupt -close, which he did with the calm remark: "In such a council as this I -had expected to find more propriety, piety and order." It was found -necessary to adjourn the sitting until the 7th of June, on which -occasion the outward decencies were better observed, partly no doubt -from the circumstance that Sigismund was present in person. The -propositions which had been extracted from the _De Ecclesia_ were again -brought up, and the relations between Wycliffe and Huss were discussed, -the object of the prosecution being to fasten upon the latter the -charge of having entirely adopted the doctrinal system of the former, -including especially a denial of the doctrine of transubstantiation. The -accused repudiated the charge of having abandoned the Catholic doctrine, -while expressing hearty admiration and respect for the memory of -Wycliffe. Being next asked to make an unqualified submission to the -council, he expressed himself as unable to do so, while stating his -willingness to amend his teaching wherever it had been shown to be -false. With this the proceedings of the day were brought to a close. On -the 8th of June the propositions extracted from the _De Ecclesia_ were -again taken up with some fulness of detail; some of these he repudiated -as incorrectly given, others he defended; but when asked to make a -general recantation he steadfastly declined, on the ground that to do so -would be a dishonest admission of previous guilt. Among the propositions -he could heartily abjure was that relating to transubstantiation; among -those he felt constrained unflinchingly to maintain was one which had -given great offence, to the effect that Christ, not Peter, is the head -of the church to whom ultimate appeal must be made. The council, -however, showed itself inaccessible to all his arguments and -explanations, and its final resolution, as announced by Pierre d'Ailly, -was threefold: first, that Huss should humbly declare that he had erred -in all the articles cited against him; secondly, that he should promise -on oath neither to hold nor teach them in the future; thirdly, that he -should publicly recant them. On his declining to make this submission he -was removed from the bar. Sigismund himself gave it as his opinion that -it had been clearly proved by many witnesses that the accused had taught -many pernicious heresies, and that even should he recant he ought never -to be allowed to preach or teach again or to return to Bohemia, but that -should he refuse recantation there was no remedy but the stake. During -the next four weeks no effort was spared to shake the determination of -Huss; but he steadfastly refused to swerve from the path which -conscience had once made clear. "I write this," says he, in a letter to -his friends at Prague, "in prison and in chains, expecting to-morrow to -receive sentence of death, full of hope in God that I shall not swerve -from the truth, nor abjure errors imputed to me by false witnesses." The -sentence he expected was pronounced on the 6th of July in the presence -of Sigismund and a full sitting of the council; once and again he -attempted to remonstrate, but in vain, and finally he betook himself to -silent prayer. After he had undergone the ceremony of degradation with -all the childish formalities usual on such occasions, his soul was -formally consigned by all those present to the devil, while he himself -with clasped hands and uplifted eyes reverently committed it to Christ. -He was then handed over to the secular arm, and immediately led to the -place of execution, the council meanwhile proceeding unconcernedly with -the rest of its business for the day. Many incidents recorded in the -histories make manifest the meekness, fortitude and even cheerfulness -with which he went to his death. After he had been tied to the stake and -the faggots had been piled, he was for the last time urged to recant, -but his only reply was: "God is my witness that I have never taught or -preached that which false witnesses have testified against me. He knows -that the great object of all my preaching and writing was to convert men -from sin. In the truth of that gospel which hitherto I have written, -taught and preached, I now joyfully die." The fire was then kindled, and -his voice as it audibly prayed in the words of the "Kyrie Eleison" was -soon stifled in the smoke. When the flames had done their office, the -ashes that were left and even the soil on which they lay were carefully -removed and thrown into the Rhine. - -Not many words are needed to convey a tolerably adequate estimate of the -character and work of the "pale thin man in mean attire," who in -sickness and poverty thus completed the forty-sixth year of a busy life -at the stake. The value of Huss as a scholar was formerly underrated. -The publication of his _Super IV. Sententiarum_ has proved that he was a -man of profound learning. Yet his principal glory will always be founded -on his spiritual teaching. It might not be easy to formulate -precisely the doctrines for which he died, and certainly some of them, -as, for example, that regarding the church, were such as many -Protestants even would regard as unguarded and difficult to harmonize -with the maintenance of external church order; but his is undoubtedly -the honour of having been the chief intermediary in handing on from -Wycliffe to Luther the torch which kindled the Reformation, and of -having been one of the bravest of the martyrs who have died in the cause -of honesty and freedom, of progress and of growth towards the light. - (J. S. Bl.) - - The works of Huss are usually classed under four heads: the dogmatical - and polemical, the homiletical, the exegetical and the epistolary. In - the earlier editions of his works sufficient care was not taken to - distinguish between his own writings and those of Wycliffe and others - who were associated with him. In connexion with his sermons it is - worthy of note that by means of them and by his public teaching - generally Huss exercised a considerable influence not only on the - religious life of his time, but on the literary development of his - native tongue. The earliest collected edition of his works, _Historia - et monumenta Joannis Hus et Hieronymi Pragensis_, was published at - Nuremberg in 1558 and was reprinted with a considerable quantity of - new matter at Frankfort in 1715. A Bohemian edition of the works has - been edited by K. J. Erben (Prague, 1865-1868), and the _Documenta J. - Hus vitam, doctrinam, causam in Constantiensi concilio_ (1869), edited - by F. Palacky, is very valuable. More recently _Joannis Hus. Opera - omnia_ have been edited by W. Flojshaus (Prague, 1904 fol.). The - _De Ecclesia_ was published by Ulrich von Hutten in 1520; other - controversial writings by Otto Brumfels in 1524; and Luther wrote an - interesting preface to _Epistolae Quaedam_, which were published in - 1537. These _Epistolae_ have been translated into French by E. de - Bonnechose (1846), and the letters written during his imprisonment - have been edited by C. von Kugelgen (Leipzig, 1902). - - The best and most easily accessible information for the English reader - on Huss is found in J. A. W. Neander's _Allgemeine Geschichte der - christlichen Religion und Kirche_, translated by J. Torrey - (1850-1858); in G. von Lechler's _Wiclif und die Vorgeschichte der - Reformation_, translated by P. Lorimer (1878); in H. H. Milman's - _History of Latin Christianity_, vol. viii. (1867); and in M. - Creighton's _History of the Papacy_ (1897). Among the earlier - authorities is the _Historia Bohemica_ of Aeneas Sylvius (1475). The - _Acta_ of the council of Constance (published by P. Labbe in his - _Concilia_, vol. xvi., 1731; by H. von der Haardt in his _Magnum - Constantiense concilium_, vol. vi., 1700; and by H. Finke in his _Acta - concilii Constantiensis_, 1896); and J. Lenfant's _Histoire de la - guerre des Hussites_ (1731) and the same writer's _Histoire du concile - de Constance_ (1714) should be consulted. F. Palacky's _Geschichte - Bohmens_ (1864-1867) is also very useful. Monographs on Huss are very - numerous. Among them may be mentioned J. A. von Helfert, _Studien uber - Hus und Hieronymus_ (1853; this work is ultramontane in its - sympathies); C. von Hofler, _Hus und der Abzug der deutschen - Professoren und Studenten aus Prag_ (1864); W. Berger, _Johannes Hus - und Konig Sigmund_ (1871); E. Denis, _Huss et la guerre des Hussites_ - (1878); P. Uhlmann, _Konig Sigmunds Geleit fur Hus_ (1894); J. - Loserth, _Hus und Wiclif_ (1884), translated into English by M. J. - Evans (1884); A. Jeep, _Gerson, Wiclefus, Hussus, inter se comparati_ - (1857); and G. von Lechler, _Johannes Hus_ (1889). See also Count - Lutzow, _The Life and Times of John Hus_ (London, 1909). - - -FOOTNOTE: - - [1] From which the name Huss, or more properly Hus, an abbreviation - adopted by himself about 1396, is derived. Prior to that date he was - invariably known as Johann Hussynecz, Hussinecz, Hussenicz or de - Hussynecz. - - - - -HUSSAR, originally the name of a soldier belonging to a corps of light -horse raised by Matthias Corvinus, king of Hungary, in 1458, to fight -against the Turks. The Magyar _huszar_, from which the word is derived, -was formerly connected with the Magyar _husz_, twenty, and was explained -by a supposed raising of the troops by the taking of each twentieth man. -According to the _New English Dictionary_ the word is an adaptation of -the Italian _corsaro_, corsair, a robber, and is found in 15th-century -documents coupled with _praedones_. The hussar was the typical Hungarian -cavalry soldier, and, in the absence of good light cavalry in the -regular armies of central and western Europe, the name and character of -the hussars gradually spread into Prussia, France, &c. Frederick the -Great sent Major H. J. von Zieten to study the work of this type of -cavalry in the Austrian service, and Zieten so far improved on the -Austrian model that he defeated his old teacher, General Baranyai, in an -encounter between the Prussian and Austrian hussars at Rothschloss in -1741. The typical uniform of the Hungarian hussar was followed with -modifications in other European armies. It consisted of a busby or a -high cylindrical cloth cap, jacket with heavy braiding, and a dolman or -pelisse, a loose coat worn hanging from the left shoulder. The hussar -regiments of the British army were converted from light dragoons at the -following dates: 7th (1805), 10th and 15th (1806), 18th (1807, and -again on revival after disbandment, 1858), 8th (1822), 11th (1840), 20th -(late 2nd Bengal European Cavalry) (1860), 13th, 14th, and 19th (late -1st Bengal European Cavalry) (1861). The 21st Lancers were hussars from -1862 to 1897. - - - - -HUSSITES, the name given to the followers of John Huss (1369-1415), the -Bohemian reformer. They were at first often called Wycliffites, as the -theological theories of Huss were largely founded on the teachings of -Wycliffe. Huss indeed laid more stress on church reform than on -theological controversy. On such matters he always writes as a disciple -of Wycliffe. The Hussite movement may be said to have sprung from three -sources, which are however closely connected. Bohemia, which had first -received Christianity from the East, was from geographical and other -causes long but very loosely connected with the Church of Rome. The -connexion became closer at the time when the schism with its violent -controversies between the rival pontiffs, waged with the coarse -invective customary to medieval theologians, had brought great discredit -on the papacy. The terrible rapacity of its representatives in Bohemia, -which increased in proportion as it became more difficult to obtain -money from western countries such as England and France, caused general -indignation; and this was still further intensified by the gross -immorality of the Roman priests. The Hussite movement was also a -democratic one, an uprising of the peasantry against the landowners at a -period when a third of the soil belonged to the clergy. Finally national -enthusiasm for the Slavic race contributed largely to its importance. -The towns, in most cases creations of the rulers of Bohemia who had -called in German immigrants, were, with the exception of the "new town" -of Prague, mainly German; and in consequence of the regulations of the -university, Germans also held almost all the more important -ecclesiastical offices--a condition of things greatly resented by the -natives of Bohemia, which at this period had reached a high degree of -intellectual development. - -The Hussite movement assumed a revolutionary character as soon as the -news of the death of Huss reached Prague. The knights and nobles of -Bohemia and Moravia, who were in favour of church reform, sent to the -council at Constance (September 2nd, 1415) a protest, known as the -"_protestatio Bohemorum_" which condemned the execution of Huss in the -strongest language. The attitude of Sigismund, king of the Romans, who -sent threatening letters to Bohemia declaring that he would shortly -"drown all Wycliffites and Hussites," greatly incensed the people. -Troubles broke out in various parts of Bohemia, and many Romanist -priests were driven from their parishes. Almost from the first the -Hussites were divided into two sections, though many minor divisions -also arose among them. Shortly before his death Huss had accepted a -doctrine preached during his absence by his adherents at Prague, namely -that of "utraquism," i.e. the obligation of the faithful to receive -communion in both kinds (_sub utraque specie_). This doctrine became the -watchword of the moderate Hussites who were known as the Utraquists or -Calixtines (_calix_, the chalice), in Bohemian, _podoboji_; while the -more advanced Hussites were soon known as the Taborites, from the city -of Tabor that became their centre. - -Under the influence of his brother Sigismund, king of the Romans, King -Wenceslaus endeavoured to stem the Hussite movement. A certain number of -Hussites lead by Nicolas of Hus--no relation of John Huss--left Prague. -They held meetings in various parts of Bohemia, particularly at Usti, -near the spot where the town of Tabor was founded soon afterwards. At -these meetings Sigismund was violently denounced, and the people -everywhere prepared for war. In spite of the departure of many prominent -Hussites the troubles at Prague continued. On the 30th of July 1419, -when a Hussite procession headed by the priest John of Zelivo (in Ger. -Selau) marched through the streets of Prague, stones were thrown at the -Hussites from the windows of the town-hall of the "new town." The -people, headed by John Zizka (1376-1424), threw the burgomaster and -several town-councillors, who were the instigators of this outrage, from -the windows and they were immediately killed by the crowd. On hearing -this news King Wenceslaus was seized with an apoplectic fit, and died a -few days afterwards. The death of the king resulted in renewed troubles -in Prague and in almost all parts of Bohemia. Many Romanists, mostly -Germans--for they had almost all remained faithful to the papal -cause--were expelled from the Bohemian cities. In Prague, in November -1419, severe fighting took place between the Hussites and the -mercenaries whom Queen Sophia (widow of Wenceslaus and regent after the -death of her husband) had hurriedly collected. After a considerable part -of the city had been destroyed a truce was concluded on the 13th of -November. The nobles, who though favourable to the Hussite cause yet -supported the regent, promised to act as mediators with Sigismund; while -the citizens of Prague consented to restore to the royal forces the -castle of Vysehrad, which had fallen into their hands. Zizka, who -disapproved of this compromise, left Prague and retired to Plzen -(Pilsen). Unable to maintain himself there he marched to southern -Bohemia, and after defeating the Romanists at Sudomer--the first pitched -battle of the Hussite wars--he arrived at Usti, one of the earliest -meeting-places of the Hussites. Not considering its situation -sufficiently strong, he moved to the neighbouring new settlement of the -Hussites, to which the biblical name of Tabor was given. Tabor soon -became the centre of the advanced Hussites, who differed from the -Utraquists by recognizing only two sacraments--Baptism and -Communion--and by rejecting most of the ceremonial of the Roman Church. -The ecclesiastical organization of Tabor had a somewhat puritanic -character, and the government was established on a thoroughly democratic -basis. Four captains of the people (_hejtmane_) were elected, one of -whom was Zizka; and a very strictly military discipline was instituted. - -Sigismund, king of the Romans, had, by the death of his brother -Wenceslaus without issue, acquired a claim on the Bohemian crown; though -it was then, and remained till much later, doubtful whether Bohemia was -an hereditary or an elective monarchy. A firm adherent of the Church of -Rome, Sigismund was successful in obtaining aid from the pope. Martin V. -issued a bull on the 17th of March 1420 which proclaimed a crusade "for -the destruction of the Wycliffites, Hussites and all other heretics in -Bohemia." The vast army of crusaders, with which were Sigismund and many -German princes, and which consisted of adventurers attracted by the hope -of pillage from all parts of Europe, arrived before Prague on the 30th -of June and immediately began the siege of the city, which had, however, -soon to be abandoned (see [VZ]I[VZ]KA, JOHN). Negotiations took place -for a settlement of the religious differences. The united Hussites -formulated their demands in a statement known as the "articles of -Prague." This document, the most important of the Hussite period, runs -thus in the wording of the contemporary chronicler, Laurence of -Brezova:-- - - I. The word of God shall be preached and made known in the kingdom of - Bohemia freely and in an orderly manner by the priests of the Lord.... - - II. The sacrament of the most Holy Eucharist shall be freely - administered in the two kinds, that is bread and wine, to all the - faithful in Christ who are not precluded by mortal sin--according to - the word and disposition of Our Saviour. - - III. The secular power over riches and worldly goods which the clergy - possesses in contradiction to Christ's precept, to the prejudice of - its office and to the detriment of the secular arm, shall be taken and - withdrawn from it, and the clergy itself shall be brought back to the - evangelical rule and an apostolic life such as that which Christ and - his apostles led.... - - IV. All mortal sins, and in particular all public and other disorders, - which are contrary to God's law shall in every rank of life be duly - and judiciously prohibited and destroyed by those whose office it is. - -These articles, which contain the essence of the Hussite doctrine, were -rejected by Sigismund, mainly through the influence of the papal -legates, who considered them prejudicial to the authority of the Roman -see. Hostilities therefore continued. Though Sigismund had retired from -Prague, the castles of Vysehrad and Hradcany remained in possession of -his troops. The citizens of Prague laid siege to the Vysehrad, and -towards the end of October (1420) the garrison was on the point of -capitulating through famine. Sigismund attempted to relieve the -fortress, but was decisively defeated by the Hussites on the 1st of -November near the village of Pankrac. The castles of Vysehrad and -Hradcany now capitulated, and shortly afterwards almost all Bohemia fell -into the hands of the Hussites. Internal troubles prevented them from -availing themselves completely of their victory. At Prague a demagogue, -the priest John of Zelivo, for a time obtained almost unlimited -authority over the lower classes of the townsmen; and at Tabor a -communistic movement (that of the so-called Adamites) was sternly -suppressed by Zizka. Shortly afterwards a new crusade against the -Hussites was undertaken. A large German army entered Bohemia, and in -August 1421 laid siege to the town of Zatec (Saaz). The crusaders hoped -to be joined in Bohemia by King Sigismund, but that prince was detained -in Hungary. After an unsuccessful attempt to storm Zatec the crusaders -retreated somewhat ingloriously, on hearing that the Hussite troops were -approaching. Sigismund only arrived in Bohemia at the end of the year -1421. He took possession of the town of Kutna Hora (Kuttenberg), but was -decisively defeated by Zizka at Nemecky Brod (Deutschbrod) on the 6th of -January 1422. Bohemia was now again for a time free from foreign -intervention, but internal discord again broke out caused partly by -theological strife, partly by the ambition of agitators. John of Zelivo -was on the 9th of March 1422 arrested by the town council of Prague and -decapitated. There were troubles at Tabor also, where a more advanced -party opposed Zizka's authority. Bohemia obtained a temporary respite -when, in 1422, Prince Sigismund Korybutovic of Poland became for a short -time ruler of the country. His authority was recognized by the Utraquist -nobles, the citizens of Prague, and the more moderate Taborites, -including Zizka. Korybutovic, however, remained but a short time in -Bohemia; after his departure civil war broke out, the Taborites opposing -in arms the more moderate Utraquists, who at this period are also called -by the chroniclers the "Praguers," as Prague was their principal -stronghold. On the 27th of April 1423, Zizka now again leading, the -Taborites defeated at Horic the Utraquist army under Cenek of -Wartemberg; shortly afterwards an armistice was concluded at -Konopist. - -Papal influence had meanwhile succeeded in calling forth a new crusade -against Bohemia, but it resulted in complete failure. In spite of the -endeavours of their rulers, the Slavs of Poland and Lithuania did not -wish to attack the kindred Bohemians; the Germans were prevented by -internal discord from taking joint action against the Hussites; and the -king of Denmark, who had landed in Germany with a large force intending -to take part in the crusade, soon returned to his own country. Free for -a time from foreign aggression, the Hussites invaded Moravia, where a -large part of the population favoured their creed; but, again paralysed -by dissensions, soon returned to Bohemia. The city of Koniggratz -(Kralove Hradec), which had been under Utraquist rule, espoused the -doctrine of Tabor, and called Zizka to its aid. After several military -successes gained by Zizka (q.v.) in 1423 and the following year, a -treaty of peace between the Hussites was concluded on the 13th of -September 1424 at Liben, a village near Prague, now part of that city. - -In 1426 the Hussites were again attacked by foreign enemies. In June of -that year their forces, led by Prokop the Great--who took the command of -the Taborites shortly after Zizka's death in October 1424--and Sigismund -Korybutovic, who had returned to Bohemia, signally defeated the Germans -at Aussig (Usti nad Labem). After this great victory, and another at -Tachau in 1427, the Hussites repeatedly invaded Germany, though they -made no attempt to occupy permanently any part of the country. - -The almost uninterrupted series of victories of the Hussites now -rendered vain all hope of subduing them by force of arms. Moreover, the -conspicuously democratic character of the Hussite movement caused the -German princes, who were afraid that such views might extend to -their own countries, to desire peace. Many Hussites, particularly the -Utraquist clergy, were also in favour of peace. Negotiations for this -purpose were to take place at the oecumenical council which had been -summoned to meet at Basel on the 3rd of March 1431. The Roman see -reluctantly consented to the presence of heretics at this council, but -indignantly rejected the suggestion of the Hussites that members of the -Greek Church, and representatives of all Christian creeds, should also -be present. Before definitely giving its consent to peace negotiations, -the Roman Church determined on making a last effort to reduce the -Hussites to subjection. On the 1st of August 1431 a large army of -crusaders, under Frederick, margrave of Brandenburg, whom Cardinal -Cesarini accompanied as papal legate, crossed the Bohemian frontier; on -the 14th of August it reached the town of Domazlice (Tauss); but on -the arrival of the Hussite army under Prokop the crusaders immediately -took to flight, almost without offering resistance. - -On the 15th of October the members of the council, who had already -assembled at Basel, issued a formal invitation to the Hussites to take -part in its deliberations. Prolonged negotiations ensued; but finally a -Hussite embassy, led by Prokop and including John of Rokycan, the -Taborite bishop Nicolas of Pelhrimov, the "English Hussite," Peter -Payne and many others, arrived at Basel on the 4th of January 1433. It -was found impossible to arrive at an agreement. Negotiations were not, -however, broken off; and a change in the political situation of Bohemia -finally resulted in a settlement. In 1434 war again broke out between -the Utraquists and the Taborites. On the 30th of May of that year the -Taborite army, led by Prokop the Great and Prokop the Less, who both -fell in the battle, was totally defeated and almost annihilated at -Lipan. The moderate party thus obtained the upper hand; and it -formulated its demands in a document which was finally accepted by the -Church of Rome in a slightly modified form, and which is known as "the -compacts." The compacts, mainly founded on the articles of Prague, -declare that:-- - - 1. The Holy Sacrament is to be given freely in both kinds to all - Christians in Bohemia and Moravia, and to those elsewhere who adhere - to the faith of these two countries. - - 2. All mortal sins shall be punished and extirpated by those whose - office it is so to do. - - 3. The word of God is to be freely and truthfully preached by the - priests of the Lord, and by worthy deacons. - - 4. The priests in the time of the law of grace shall claim no - ownership of worldly possessions. - -On the 5th of July 1436 the compacts were formally accepted and signed -at Iglau, in Moravia, by King Sigismund, by the Hussite delegates, and -by the representatives of the Roman Church. The last-named, however, -refused to recognize as archbishop of Prague, John of Rokycan, who had -been elected to that dignity by the estates of Bohemia. The Utraquist -creed, frequently varying in its details, continued to be that of the -established church of Bohemia till all non-Roman religious services were -prohibited shortly after the battle of the White Mountain in 1620. The -Taborite party never recovered from its defeat at Lipan, and after the -town of Tabor had been captured by George of Podebrad in 1452 Utraquist -religious worship was established there. The Bohemian brethren, whose -intellectual originator was Peter Chelcicky, but whose actual founders -were Brother Gregory, a nephew of Archbishop Rokycan, and Michael, -curate of Zamberk, to a certain extent continued the Taborite -traditions, and in the 15th and 16th centuries included most of the -strongest opponents of Rome in Bohemia. J. A. Komensky (Comenius), a -member of the brotherhood, claimed for the members of his church that -they were the genuine inheritors of the doctrines of Hus. After the -beginning of the German Reformation many Utraquists adopted to a large -extent the doctrines of Luther and Calvin; and in 1567 obtained the -repeal of the compacts, which no longer seemed sufficiently -far-reaching. From the end of the 16th century the inheritors of the -Hussite tradition in Bohemia were included in the more general name of -"Protestants" borne by the adherents of the Reformation. - - All histories of Bohemia devote a large amount of space to the Hussite - movement. See Count Lutzow, _Bohemia; an Historical Sketch_ (London, - 1896); Palacky, _Geschichte von Bohmen_; Bachmann, _Geschichte - Bohmens_; L. Krummel, _Geschichte der bohmischen Reformation_ (Gotha, - 1866) and _Utraquisten und Taboriten_ (Gotha, 1871); Ernest Denis, - _Huss et la guerre des Hussites_ (Paris, 1878); H. Toman, _Husitske - Valecnictvi_ (Prague, 1898). (L.) - - - - -HUSTING (O. Eng. _husting_, from Old Norwegian _husthing_), the "thing" -or "ting," i.e. assembly, of the household of personal followers or -retainers of a king, earl or chief, contrasted with the "folkmoot," the -assembly of the whole people. "Thing" meant an inanimate object, the -ordinary meaning at the present day, also a cause or suit, and an -assembly; a similar development of meaning is found in the Latin _res_. -The word still appears in the names of the legislative assemblies of -Norway, the _Storthing_ and of Iceland, the _Althing_. "Husting," or -more usually in the plural "hustings," was the name of a court of the -city of London. This court was formerly the county court for the city -and was held before the lord mayor, the sheriffs and aldermen, for pleas -of land, common pleas and appeals from the sheriffs. It had probate -jurisdiction and wills were registered. All this jurisdiction has long -been obsolete, but the court still sits occasionally for registering -gifts made to the city. The charter of Canute (1032) contains a -reference to "hustings" weights, which points to the early establishment -of the court. It is doubtful whether courts of this name were held in -other towns, but John Cowell (1554-1611) in his _Interpreter_ (1601) -s.v., "Hustings," says that according to Fleta there were such courts at -Winchester, York, Lincoln, Sheppey and elsewhere, but the passage from -Fleta, as the _New English Dictionary_ points out, does not necessarily -imply this (11. lv. _Habet etiam Rex curiam in civitatibus ... et in -locis ... sicut in Hustingis London, Winton, &c._). The ordinary use of -"hustings" at the present day for the platform from which a candidate -speaks at a parliamentary or other election, or more widely for a -political candidate's election campaign, is derived from the application -of the word, first to the platform in the Guildhall on which the London -court was held, and next to that from which the public nomination of -candidates for a parliamentary election was formerly made, and from -which the candidate addressed the electors. The Ballot Act of 1872 did -away with this public declaration of the nomination. - - - - -HUSUM, a town in the Prussian province of Schleswig-Holstein, in a -fertile district 2(1/2) m. inland from the North Sea, on the canalized -Husumer Au, which forms its harbour and roadstead, 99 m. N.W. from -Hamburg on a branch line from Tonning. Pop. (1900) 8268. It has steam -communication with the North Frisian Islands (Nordstrand, Fohr and -Sylt), and is a port for the cattle trade with England. Besides a ducal -palace and park, it possesses an Evangelical church and a gymnasium. -Cattle markets are held weekly, and in them, as also in cereals, a -lively export trade is done. There are also extensive oyster fisheries, -the property of the state, the yield during the season being very -considerable. Husum is the birthplace of Johann Georg Forchhammer -(1794-1865), the mineralogist, Peter Wilhelm Forchhammer (1801-1894), -the archaeologist, and Theodore Storm (1817-1888), the poet, to the last -of whom a monument has been erected here. - -Husum is first mentioned in 1252, and its first church was built in -1431. Wisby rights were granted it in 1582, and in 1603 it received -municipal privileges from the duke of Holstein. It suffered greatly from -inundations in 1634 and 1717. - - See Christiansen, _Die Geschichte Husums_ (Husum, 1903); and - Henningsen, _Das Stiftungsbuch der Stadt Husum_ (Husum, 1904). - - - - -HUTCHESON, FRANCIS (1694-1746), English philosopher, was born on the 8th -of August 1694. His birthplace was probably the townland of Drumalig, in -the parish of Saintfield and county of Down, Ireland.[1] Though the -family had sprung from Ayrshire, in Scotland, both his father and -grandfather were ministers of dissenting congregations in the north of -Ireland. Hutcheson was educated partly by his grandfather, partly at an -academy, where according to his biographer, Dr Leechman, he was taught -"the ordinary scholastic philosophy which was in vogue in those -days." In 1710 he entered the university of Glasgow, where he spent six -years, at first in the study of philosophy, classics and general -literature, and afterwards in the study of theology. On quitting the -university, he returned to the north of Ireland, and received a licence -to preach. When, however, he was about to enter upon the pastorate of a -small dissenting congregation he changed his plans on the advice of a -friend and opened a private academy in Dublin. In Dublin his literary -attainments gained him the friendship of many prominent inhabitants. -Among these was Archbishop King (author of the _De origine mali_), who -resisted all attempts to prosecute Hutcheson in the archbishop's court -for keeping a school without the episcopal licence. Hutcheson's -relations with the clergy of the Established Church, especially with the -archbishops of Armagh and Dublin, Hugh Boulter (1672-1742) and William -King (1650-1729), seem to have been most cordial, and his biographer, in -speaking of "the inclination of his friends to serve him, the schemes -proposed to him for obtaining promotion," &c., probably refers to some -offers of preferment, on condition of his accepting episcopal -ordination. These offers, however, were unavailing. - -While residing in Dublin, Hutcheson published anonymously the four -essays by which he is best known, namely, the _Inquiry concerning -Beauty, Order, Harmony and Design_, the _Inquiry concerning Moral Good -and Evil_, in 1725, the _Essay on the Nature and Conduct of the Passions -and Affections_ and _Illustrations upon the Moral Sense_, in 1728. The -alterations and additions made in the second edition of these Essays -were published in a separate form in 1726. To the period of his Dublin -residence are also to be referred the _Thoughts on Laughter_ (a -criticism of Hobbes) and the Observations on the _Fable of the Bees_, -being in all six letters contributed to _Hibernicus' Letters_, a -periodical which appeared, in Dublin (1725-1727, 2nd ed. 1734). At the -end of the same period occurred the controversy in the _London Journal_ -with Gilbert Burnet (probably the second son of Dr Gilbert Burnet, -bishop of Salisbury); on the "True Foundation of Virtue or Moral -Goodness." All these letters were collected in one volume (Glasgow, -1772). - -In 1729 Hutcheson succeeded his old master, Gershom Carmichael, in the -chair of moral philosophy in the university of Glasgow. It is curious -that up to this time all his essays and letters had been published -anonymously, though their authorship appears to have been well known. In -1730 he entered on the duties of his office, delivering an inaugural -lecture (afterwards published), _De naturali hominum socialitate_. It -was a great relief to him after the drudgery of school work to secure -leisure for his favourite studies; "non levi igitur laetitia commovebar -cum almam matrem Academiam me, suum olim alumnum, in libertatem -asseruisse audiveram." Yet the works on which Hutcheson's reputation -rests had already been published. - -The remainder of his life he devoted to his professorial duties. His -reputation as a teacher attracted many young men, belonging to -dissenting families, from England and Ireland, and he enjoyed a -well-deserved popularity among both his pupils and his colleagues. -Though somewhat quick-tempered, he was remarkable for his warm feelings -and generous impulses. He was accused in 1738 before the Glasgow -presbytery for "following two false and dangerous doctrines: first, that -the standard of moral goodness was the promotion of the happiness of -others; and second, that we could have a knowledge of good and evil -without and prior to a knowledge of God" (Rae, _Life of Adam Smith_, -1895). The accusation seems to have had no result. - -In addition to the works named, the following were published during -Hutcheson's lifetime: a pamphlet entitled _Considerations on Patronage_ -(1735); _Philosophiae moralis institutio compendiaria, ethices et -jurisprudentiae naturalis elementa continens, lib. iii._ (Glasgow, -1742); _Metaphysicae synopsis ontologiam et pneumatologiam complectens_ -(Glasgow, 1742). The last work was published anonymously. After his -death, his son, Francis Hutcheson (c. 1722-1773), author of a number of -popular songs (e.g. "As Colin one evening," "Jolly Bacchus," "Where -Weeping Yews"), published much the longest, though by no means the most -interesting, of his works, _A System of Moral Philosophy, in Three -Books_ (2 vols., London, 1755). To this is prefixed a life of the -author, by Dr William Leechman (1706-1785), professor of divinity in the -university of Glasgow. The only remaining work assigned to Hutcheson is -a small treatise on _Logic_ (Glasgow, 1764). This compendium, together -with the _Compendium of Metaphysics_, was republished at Strassburg in -1722. - -Thus Hutcheson dealt with metaphysics, logic and ethics. His importance -is, however, due almost entirely to his ethical writings, and among -these primarily to the four essays and the letters published during his -residence in Dublin. His standpoint has a negative and a positive -aspect; he is in strong opposition to Thomas Hobbes and Bernard de -Mandeville, and in fundamental agreement with Shaftesbury (Anthony -Ashley Cooper, 3rd earl of Shaftesbury), whose name he very properly -coupled with his own on the title-page of the first two essays. There -are no two names, perhaps, in the history of English moral philosophy, -which stand in a closer connexion. The analogy drawn between beauty and -virtue, the functions assigned to the moral sense, the position that the -benevolent feelings form an original and irreducible part of our nature, -and the unhesitating adoption of the principle that the test of virtuous -action is its tendency to promote the general welfare are obvious and -fundamental points of agreement between the two authors. - - I. _Ethics._--According to Hutcheson, man has a variety of senses, - internal as well as external, reflex as well as direct, the general - definition of a sense being "any determination of our minds to receive - ideas independently on our will, and to have perceptions of pleasure - and pain" (_Essay on the Nature and Conduct of the Passions_, sect. - 1). He does not attempt to give an exhaustive enumeration of these - "senses," but, in various parts of his works, he specifies, besides - the five external senses commonly recognized (which, he rightly hints, - might be added to),--(1) consciousness, by which each man has a - perception of himself and of all that is going on in his own mind - (_Metaph. Syn._ pars i. cap. 2); (2) the sense of beauty (sometimes - called specifically "an internal sense"); (3) a public sense, or - sensus communis, "a determination to be pleased with the happiness of - others and to be uneasy at their misery"; (4) the moral sense, or - "moral sense of beauty in actions and affections, by which we perceive - virtue or vice, in ourselves or others"; (5) a sense of honour, or - praise and blame, "which makes the approbation or gratitude of others - the necessary occasion of pleasure, and their dislike, condemnation or - resentment of injuries done by us the occasion of that uneasy - sensation called shame"; (6) a sense of the ridiculous. It is plain, - as the author confesses, that there may be "other perceptions, - distinct from all these classes," and, in fact, there seems to be no - limit to the number of "senses" in which a psychological division of - this kind might result. - - Of these "senses" that which plays the most important part in - Hutcheson's ethical system is the "moral sense." It is this which - pronounces immediately on the character of actions and affections, - approving those which are virtuous, and disapproving those which are - vicious. "His principal design," he says in the preface to the two - first treatises, "is to show that human nature was not left quite - indifferent in the affair of virtue, to form to itself observations - concerning the advantage or disadvantage of actions, and accordingly - to regulate its conduct. The weakness of our reason, and the - avocations arising from the infirmity and necessities of our nature, - are so great that very few men could ever have formed those long - deductions of reasons which show some actions to be in the whole - advantageous to the agent, and their contraries pernicious. The Author - of nature has much better furnished us for a virtuous conduct than our - moralists seem to imagine, by almost as quick and powerful - instructions as we have for the preservation of our bodies. He has - made virtue a lovely form, to excite our pursuit of it, and has given - us strong affections to be the springs of each virtuous action." - Passing over the appeal to final causes involved in this and similar - passages, as well as the assumption that the "moral sense" has had no - growth or history, but was "implanted" in man exactly in the condition - in which it is now to be found among the more civilized races, an - assumption common to the systems of both Hutcheson and Butler, it may - be remarked that this use of the term "sense" has a tendency to - obscure the real nature of the process which goes on in an act of - moral judgment. For, as is so clearly established by Hume, this act - really consists of two parts: one an act of deliberation, more or less - prolonged, resulting in an intellectual judgment; the other a reflex - feeling, probably instantaneous, of satisfaction at actions which we - denominate good, of dissatisfaction at those which we denominate bad. - By the intellectual part of this process we refer the action or habit - to a certain class; but no sooner is the intellectual process - completed than there is excited in us a feeling similar to that - which myriads of actions and habits of the same class, or deemed to be - of the same class, have excited in us on former occasions. Now, - supposing the latter part of this process to be instantaneous, uniform - and exempt from error, the former certainly is not. All mankind may, - apart from their selfish interests, approve that which is virtuous or - makes for the general good, but surely they entertain the most widely - divergent opinions, and, in fact, frequently arrive at directly - opposite conclusions as to particular actions and habits. This obvious - distinction is undoubtedly recognized by Hutcheson in his analysis of - the mental process preceding moral action, nor does he invariably - ignore it, even when treating of the moral approbation or - disapprobation which is subsequent on action. None the less, it - remains true that Hutcheson, both by his phraseology, and by the - language in which he describes the process of moral approbation, has - done much to favour that loose, popular view of morality which, - ignoring the necessity of deliberation and reflection, encourages - hasty resolves and unpremeditated judgments. The term "moral sense" - (which, it may be noticed, had already been employed by Shaftesbury, - not only, as Dr Whewell appears to intimate, in the margin, but also - in the text of his _Inquiry_), if invariably coupled with the term - "moral judgment," would be open to little objection; but, taken alone, - as designating the complex process of moral approbation, it is liable - to lead not only to serious misapprehension but to grave practical - errors. For, if each man's decisions are solely the result of an - immediate intuition of the moral sense, why be at any pains to test, - correct or review them? Or why educate a faculty whose decisions are - infallible? And how do we account for differences in the moral - decisions of different societies, and the observable changes in a - man's own views? The expression has, in fact, the fault of most - metaphorical terms: it leads to an exaggeration of the truth which it - is intended to suggest. - - But though Hutcheson usually describes the moral faculty as acting - instinctively and immediately, he does not, like Butler, confound the - moral faculty with the moral standard. The test or criterion of right - action is with Hutcheson, as with Shaftesbury, its tendency to promote - the general welfare of mankind. He thus anticipates the utilitarianism - of Bentham--and not only in principle, but even in the use of the - phrase "the greatest happiness for the greatest number" (_Inquiry - concerning Moral Good and Evil_, sect. 3). - - It is curious that Hutcheson did not realize the inconsistency of this - external criterion with his fundamental ethical principle. Intuition - has no possible connexion with an empirical calculation of results, - and Hutcheson in adopting such a criterion practically denies his - fundamental assumption. - - As connected with Hutcheson's virtual adoption of the utilitarian - standard may be noticed a kind of moral algebra, proposed for the - purpose of "computing the morality of actions." This calculus occurs - in the _Inquiry concerning Moral Good and Evil_, sect. 3. - - - Benevolence. - - The most distinctive of Hutcheson's ethical doctrines still remaining - to be noticed is what has been called the "benevolent theory" of - morals. Hobbes had maintained that all our actions, however disguised - under apparent sympathy, have their roots in self-love. Hutcheson not - only maintains that benevolence is the sole and direct source of many - of our actions, but, by a not unnatural recoil, that it is the only - source of those actions of which, on reflection, we approve. - Consistently with this position, actions which flow from self-love - only are pronounced to be morally indifferent. But surely, by the - common consent of civilized men, prudence, temperance, cleanliness, - industry, self-respect and, in general, the "personal virtues," are - regarded, and rightly regarded, as fitting objects of moral - approbation. This consideration could hardly escape any author, - however wedded to his own system, and Hutcheson attempts to extricate - himself from the difficulty by laying down the position that a man may - justly regard himself as a part of the rational system, and may thus - "be, in part, an object of his own benevolence" (Ibid.),--a curious - abuse of terms, which really concedes the question at issue. Moreover, - he acknowledges that, though self-love does not merit approbation, - neither, except in its extreme forms, does it merit condemnation, - indeed the satisfaction of the dictates of self-love is one of the - very conditions of the preservation of society. To press home the - inconsistencies involved in these various statements would be a - superfluous task. - - The vexed question of liberty and necessity appears to be carefully - avoided in Hutcheson's professedly ethical works. But, in the - _Synopsis metaphysicae_, he touches on it in three places, briefly - stating both sides of the question, but evidently inclining to that - which he designates as the opinion of the Stoics in opposition to what - he designates as the opinion of the Peripatetics. This is - substantially the same as the doctrine propounded by Hobbes and Locke - (to the latter of whom Hutcheson refers in a note), namely, that our - will is determined by motives in conjunction with our general - character and habit of mind, and that the only true liberty is the - liberty of acting as we will, not the liberty of willing as we will. - Though, however, his leaning is clear, he carefully avoids - dogmatizing, and deprecates the angry controversies to which the - speculations on this subject had given rise. - - It is easy to trace the influence of Hutcheson's ethical theories on - the systems of Hume and Adam Smith. The prominence given by these - writers to the analysis of moral action and moral approbation, with - the attempt to discriminate the respective provinces of the reason and - the emotions in these processes, is undoubtedly due to the influence - of Hutcheson. To a study of the writings of Shaftesbury and Hutcheson - we might, probably, in large measure, attribute the unequivocal - adoption of the utilitarian standard by Hume, and, if this be the - case, the name of Hutcheson connects itself, through Hume, with the - names of Priestley, Paley and Bentham. Butler's _Sermons_ appeared in - 1726, the year after the publication of Hutcheson's two first essays, - and the parallelism between the "conscience" of the one writer and the - "moral sense" of the other is, at least, worthy of remark. - - II. _Mental Philosophy._--In the sphere of mental philosophy and logic - Hutcheson's contributions are by no means so important or original as - in that of moral philosophy. They are interesting mainly as a link - between Locke and the Scottish school. In the former subject the - influence of Locke is apparent throughout. All the main outlines of - Locke's philosophy seem, at first sight, to be accepted as a matter of - course. Thus, in stating his theory of the moral sense, Hutcheson is - peculiarly careful to repudiate the doctrine of innate ideas (see, for - instance, _Inquiry concerning Moral Good and Evil_, sect. 1 ad fin., - and sect. 4; and compare _Synopsis Metaphysicae_, pars i. cap. 2). At - the same time he shows more discrimination than does Locke in - distinguishing between the two uses of this expression, and between - the legitimate and illegitimate form of the doctrine (Syn. Metaph. - pars i. cap. 2). All our ideas are, as by Locke, referred to external - or internal sense, or, in other words, to sensation and reflection - (see, for instance, _Syn. Metaph._ pars i. cap. 1; _Logicae Compend._ - pars i. cap. 1; _System of Moral Philosophy_, bk. i. ch. 1). It is, - however, a most important modification of Locke's doctrine, and one - which connects Hutcheson's mental philosophy with that of Reid, when - he states that the ideas of extension, figure, motion and rest "are - more properly ideas accompanying the sensations of sight and touch - than the sensations of either of these senses"; that the idea of self - accompanies every thought, and that the ideas of number, duration and - existence accompany every other idea whatsoever (see _Essay on the - Nature and Conduct of the Passions_, sect. i. art. 1; _Syn. Metaph._ - pars i. cap. 1, pars ii. cap. 1; Hamilton on Reid, p. 124, note). - Other important points in which Hutcheson follows the lead of Locke - are his depreciation of the importance of the so-called laws of - thought, his distinction between the primary and secondary qualities - of bodies, the position that we cannot know the inmost essences of - things ("intimae rerum naturae sive essentiae"), though they excite - various ideas in us, and the assumption that external things are known - only through the medium of ideas (_Syn. Metaph._ pars i. cap. 1), - though, at the same time, we are assured of the existence of an - external world corresponding to these ideas. Hutcheson attempts to - account for our assurance of the reality of an external world by - referring it to a natural instinct (_Syn. Metaph._ pars i. cap. 1). Of - the correspondence or similitude between our ideas of the primary - qualities of things and the things themselves God alone can be - assigned as the cause. This similitude has been effected by Him - through a law of nature. "Haec prima qualitatum primariarum perceptio, - sive mentis actio quaedam sive passio dicatur, non alia similitudinis - aut convenientiae inter ejusmodi ideas et res ipsas causa assignari - posse videtur, quam ipse Deus, qui certa naturae lege hoc efficit, ut - notiones, quae rebus praesentibus excitantur, sint ipsis similes, aut - saltem earum habitudines, si non veras quantitates, depingant" (pars - ii. cap. 1). Locke does speak of God "annexing" certain ideas to - certain motions of bodies; but nowhere does he propound a theory so - definite as that here propounded by Hutcheson, which reminds us at - least as much of the speculations of Malebranche as of those of Locke. - - Amongst the more important points in which Hutcheson diverges from - Locke is his account of the idea of personal identity, which he - appears to have regarded as made known to us directly by - consciousness. The distinction between body and mind, _corpus_ or - _materia_ and _res cogitans_, is more emphatically accentuated by - Hutcheson than by Locke. Generally, he speaks as if we had a direct - consciousness of mind as distinct from body (see, for instance, _Syn. - Metaph._ pars ii. cap. 3), though, in the posthumous work on _Moral - Philosophy_, he expressly states that we know mind as we know body "by - qualities immediately perceived though the substance of both be - unknown" (bk. i. ch. 1). The distinction between perception proper and - sensation proper, which occurs by implication though it is not - explicitly worked out (see Hamilton's _Lectures on Metaphysics_, Lect. - 24; Hamilton's edition of _Dugald Stewart's Works_, v. 420), the - imperfection of the ordinary division of the external senses into five - classes, the limitation of consciousness to a special mental faculty - (severely criticized in Sir W. Hamilton's _Lectures on Metaphysics_, - Lect. xii.) and the disposition to refer on disputed questions of - philosophy not so much to formal arguments as to the testimony of - consciousness and our natural instincts are also amongst the points in - which Hutcheson supplemented or departed from the philosophy of Locke. - The last point can hardly fail to suggest the "common-sense - philosophy" of Reid. - - Thus, in estimating Hutcheson's position, we find that in particular - questions he stands nearer to Locke, but in the general spirit of his - philosophy he seems to approach more closely to his Scottish - successors. - - The short _Compendium of Logic_, which is more original than such - works usually are, is remarkable chiefly for the large - proportion of psychological matter which it contains. In these parts - of the book Hutcheson mainly follows Locke. The technicalities of the - subject are passed lightly over, and the book is readable. It may be - specially noticed that he distinguishes between the mental result and - its verbal expression [idea--term; judgment--proposition], that he - constantly employs the word "idea," and that he defines logical truth - as "convenientia signorum cum rebus significatis" (or "propositionis - convenientia cum rebus ipsis," _Syn. Metaph._ pars i. cap 3), thus - implicitly repudiating a merely formal view of logic. - - III. _Aesthetics._--Hutcheson may further be regarded as one of the - earliest modern writers on aesthetics. His speculations on this - subject are contained in the _Inquiry concerning Beauty, Order, - Harmony and Design_, the first of the two treatises published in 1725. - He maintains that we are endowed with a special sense by which we - perceive beauty, harmony and proportion. This is a _reflex_ sense, - because it presupposes the action of the external senses of sight and - hearing. It may be called an internal sense, both in order to - distinguish its perceptions from the mere perceptions of sight and - hearing, and because "in some other affairs, where our external senses - are not much concerned, we discern a sort of beauty, very like in many - respects to that observed in sensible objects, and accompanied with - like pleasure" (_Inquiry, &c._, sect. 1). The latter reason leads him - to call attention to the beauty perceived in universal truths, in the - operations of general causes and in moral principles and actions. - Thus, the analogy between beauty and virtue, which was so favourite a - topic with Shaftesbury, is prominent in the writings of Hutcheson - also. Scattered up and down the treatise there are many important and - interesting observations which our limits prevent us from noticing. - But to the student of mental philosophy it may be specially - interesting to remark that Hutcheson both applies the principle of - association to explain our ideas of beauty and also sets limits to its - application, insisting on there being "a natural power of perception - or sense of beauty in objects, antecedent to all custom, education or - example" (see _Inquiry, &c._, sects. 6, 7; Hamilton's _Lectures on - Metaphysics_, Lect. 44 ad fin.). - - Hutcheson's writings naturally gave rise to much controversy. To say - nothing of minor opponents, such as "Philaretus" (Gilbert Burnet, - already alluded to), Dr John Balguy (1686-1748), prebendary of - Salisbury, the author of two tracts on "The Foundation of Moral - Goodness," and Dr John Taylor (1694-1761) of Norwich, a minister of - considerable reputation in his time (author of _An Examination of the - Scheme of Morality advanced by Dr Hutcheson_), the essays appear to - have suggested, by antagonism, at least two works which hold a - permanent place in the literature of English ethics--Butler's - _Dissertation on the Nature of Virtue_, and Richard Price's _Treatise - of Moral Good and Evil_ (1757). In this latter work the author - maintains, in opposition to Hutcheson, that actions are _in - themselves_ right or wrong, that right and wrong are simple ideas - incapable of analysis, and that these ideas are perceived immediately - by the understanding. We thus see that, not only directly but also - through the replies which it called forth, the system of Hutcheson, or - at least the system of Hutcheson combined with that of Shaftesbury, - contributed, in large measure, to the formation and development of - some of the most important of the modern schools of ethics (see - especially art. ETHICS). - - AUTHORITIES.--Notices of Hutcheson occur in most histories, both of - general philosophy and of moral philosophy, as, for instance, in pt. - vii. of Adam Smith's _Theory of Moral Sentiments_; Mackintosh's - _Progress of Ethical Philosophy_; Cousin, _Cours d'histoire de la - philosophie morale du XVIII^e siecle_; Whewell's _Lectures on the - History of Moral Philosophy in England_; A. Bain's _Mental and Moral - Science_; Noah Porter's Appendix to the English translation of - Ueberweg's _History of Philosophy_; Sir Leslie Stephen's _History of - English Thought in the Eighteenth Century_, &c. See also Martineau, - _Types of Ethical Theory_ (London, 1902); W. R. Scott, _Francis - Hutcheson_ (Cambridge, 1900); Albee, _History of English - Utilitarianism_ (London, 1902); T. Fowler, _Shaftesbury and Hutcheson_ - (London, 1882); J. McCosh, _Scottish Philosophy_ (New York, 1874). Of - Dr Leechman's _Biography_ of Hutcheson we have already spoken. J. - Veitch gives an interesting account of his professorial work in - Glasgow, _Mind_, ii. 209-212. (T. F.; X.) - - -FOOTNOTE: - - [1] See _Belfast Magazine_ for August 1813. - - - - -HUTCHINSON, ANNE (c. 1600-1643), American religious enthusiast, leader -of the "Antinomians" in New England, was born in Lincolnshire, England, -about 1600. She was the daughter of a clergyman named Francis Marbury, -and, according to tradition, was a cousin of John Dryden. She married -William Hutchinson, and in 1634 emigrated to Boston, Massachusetts, as a -follower and admirer of the Rev. John Cotton. Her orthodoxy was -suspected and for a time she was not admitted to the church, but soon -she organized meetings among the Boston women, among whom her -exceptional ability and her services as a nurse had given her great -influence; and at these meetings she discussed and commented upon recent -sermons and gave expression to her own theological views. The meetings -became increasingly popular, and were soon attended not only by the -women but even by some of the ministers and magistrates, including -Governor Henry Vane. At these meetings she asserted that she, Cotton and -her brother-in-law, the Rev. John Wheelwright--whom she was trying to -make second "teacher" in the Boston church--were under a "covenant of -grace," that they had a special inspiration, a "peculiar indwelling of -the Holy Ghost," whereas the Rev. John Wilson, the pastor of the Boston -church, and the other ministers of the colony were under a "covenant of -works." Anne Hutchinson was, in fact, voicing a protest against the -legalism of the Massachusetts Puritans, and was also striking at the -authority of the clergy in an intensely theocratic community. In such a -community a theological controversy inevitably was carried into secular -politics, and the entire colony was divided into factions. Mrs -Hutchinson was supported by Governor Vane, Cotton, Wheelwright and the -great majority of the Boston church; opposed to her were Deputy-Governor -John Winthrop, Wilson and all of the country magistrates and churches. -At a general fast, held late in January 1637, Wheelwright preached a -sermon which was taken as a criticism of Wilson and his friends. The -strength of the parties was tested at the General Court of Election of -May 1637, when Winthrop defeated Vane for the governorship. Cotton -recanted, Vane returned to England in disgust, Wheelwright was tried and -banished and the rank and file either followed Cotton in making -submission or suffered various minor punishments. Mrs Hutchinson was -tried (November 1637) by the General Court chiefly for "traducing the -ministers," and was sentenced to banishment; later, in March 1638, she -was tried before the Boston church and was formally excommunicated. With -William Coddington (d. 1678), John Clarke and others, she established a -settlement on the island of Aquidneck (now Rhode Island) in 1638. Four -years later, after the death of her husband, she settled on Long Island -Sound near what is now New Rochelle, Westchester county, New York, and -was killed in an Indian rising in August 1643, an event regarded in -Massachusetts as a manifestation of Divine Providence. Anne Hutchinson -and her followers were called "Antinomians," probably more as a term of -reproach than with any special reference to her doctrinal theories; and -the controversy in which she was involved is known as the "Antinomian -Controversy." - - See C. F. Adams, _Antinomianism in the Colony of Massachusetts Bay_, - vol. xiv. of the Prince Society Publications (Boston, 1894); and - _Three Episodes of Massachusetts History_ (Boston and New York, 1896). - - - - -HUTCHINSON, JOHN (1615-1664), Puritan soldier, son of Sir Thomas -Hutchinson of Owthorpe, Nottinghamshire, and of Margaret, daughter of -Sir John Byron of Newstead, was baptized on the 18th of September 1615. -He was educated at Nottingham and Lincoln schools and at Peterhouse, -Cambridge, and in 1637 he entered Lincoln's Inn. On the outbreak of the -great Rebellion he took the side of the Parliament, and was made in 1643 -governor of Nottingham Castle, which he defended against external -attacks and internal divisions, till the triumph of the parliamentary -cause. He was chosen member for Nottinghamshire in March 1646, took the -side of the Independents, opposed the offers of the king at Newport, and -signed the death-warrant. Though a member at first of the council of -state, he disapproved of the subsequent political conduct of Cromwell -and took no further part in politics during the lifetime of the -protector. He resumed his seat in the recalled Long Parliament in May -1659, and followed Monk in opposing Lambert, believing that the former -intended to maintain the commonwealth. He was returned to the Convention -Parliament for Nottingham but expelled on the 9th of June 1660, and -while not excepted from the Act of Indemnity was declared incapable of -holding public office. In October 1663, however, he was arrested upon -suspicion of being concerned in the Yorkshire plot, and after a rigorous -confinement in the Tower of London, of which he published an account -(reprinted in the Harleian _Miscellany_, vol. iii.), and in Sandown -Castle, Kent, he died on the 11th of September 1664. His career draws -its chief interest from the _Life_ by his wife, Lucy, daughter of Sir -Allen Apsley, written after the death of her husband but not -published till 1806 (since often reprinted), a work not only valuable -for the picture which it gives of the man and of the time in which he -lived, but for the simple beauty of its style, and the naivete with -which the writer records her sentiments and opinions, and details the -incidents of her private life. - - See the edition of Lucy Hutchinson's _Memoirs of the Life of Colonel - Hutchinson_ by C. H. Firth (1885); _Brit. Mus. Add. MSS._ 25,901 (a - fragment of the Life), also _Add. MSS._ 19, 333, 36,247 f. 51; _Notes - and Queries_, 7, ser. iii. 25, viii. 422; _Monk's Contemporaries_, by - Guizot. - - - - -HUTCHINSON, JOHN (1674-1737), English theological writer, was born at -Spennithorne, Yorkshire, in 1674. He served as steward in several -families of position, latterly in that of the duke of Somerset, who -ultimately obtained for him the post of riding purveyor to the master of -the horse, a sinecure worth about L200 a year. In 1700 he became -acquainted with Dr John Woodward (1665-1728) physician to the duke and -author of a work entitled _The Natural History of the Earth_, to whom he -entrusted a large number of fossils of his own collecting, along with a -mass of manuscript notes, for arrangement and publication. A -misunderstanding as to the manner in which these should be dealt with -was the immediate occasion of the publication by Hutchinson in 1724 of -_Moses's Principia_, part i., in which Woodward's _Natural History_ was -bitterly ridiculed, his conduct with regard to the mineralogical -specimens not obscurely characterized, and a refutation of the Newtonian -doctrine of gravitation seriously attempted. It was followed by part ii. -in 1727, and by various other works, including _Moses's Sine Principio_, -1730; _The Confusion of Tongues and Trinity of the Gentiles_, 1731; -_Power Essential and Mechanical, or what power belongs to God and what -to his creatures, in which the design of Sir I. Newton and Dr Samuel -Clarke is laid open_, 1732; _Glory or Gravity_, 1733; _The Religion of -Satan, or Antichrist Delineated_, 1736. He taught that the Bible -contained the elements not only of true religion but also of all -rational philosophy. He held that the Hebrew must be read without -points, and his interpretation rested largely on fanciful symbolism. -Bishop George Home of Norwich was during some of his earlier years an -avowed Hutchinsonian; and William Jones of Nayland continued to be so to -the end of his life. - - A complete edition of his publications, edited by Robert Spearman and - Julius Bate, appeared in 1748 (12 vols.); an _Abstract_ of these - followed in 1753; and a _Supplement_, with _Life_ by Spearman - prefixed, in 1765. - - - - -HUTCHINSON, SIR JONATHAN (1828- ), English surgeon and pathologist, was -born on the 23rd of July 1828 at Selby, Yorkshire, his parents belonging -to the Society of Friends. He entered St Bartholomew's Hospital, became -a member of the Royal College of Surgeons in 1850 (F.R.C.S. 1862), and -rapidly gained reputation as a skilful operator and a scientific -inquirer. He was president of the Hunterian Society in 1869 and 1870, -professor of surgery and pathology at the College of Surgeons from 1877 -to 1882, president of the Pathological Society, 1879-1880, of the -Ophthalmological Society, 1883, of the Neurological Society, 1887, of -the Medical Society, 1890, and of the Royal Medical and Chirurgical in -1894-1896. In 1889 he was president of the Royal College of Surgeons. He -was a member of two Royal Commissions, that of 1881 to inquire into the -provision for smallpox and fever cases in the London hospitals, and that -of 1889-1896 on vaccination and leprosy. He also acted as honorary -secretary to the Sydenham Society. His activity in the cause of -scientific surgery and in advancing the study of the natural sciences -was unwearying. His lectures on neuro-pathogenesis, gout, leprosy, -diseases of the tongue, &c., were full of original observation; but his -principal work was connected with the study of syphilis, on which he -became the first living authority. He was the founder of the London -Polyclinic or Postgraduate School of Medicine; and both in his native -town of Selby and at Haslemere, Surrey, he started (about 1890) -educational museums for popular instruction in natural history. He -published several volumes on his own subjects, was editor of the -quarterly _Archives of Surgery_, and was given the Hon. LL.D. degree by -both Glasgow and Cambridge. After his retirement from active -consultative work he continued to take great interest in the question of -leprosy, asserting the existence of a definite connexion between this -disease and the eating of salted fish. He received a knighthood in 1908. - - - - -HUTCHINSON, THOMAS (1711-1780), the last royal governor of the province -of Massachusetts, son of a wealthy merchant of Boston, Mass., was born -there on the 9th of September 1711. He graduated at Harvard in 1727, -then became an apprentice in his father's counting-room, and for several -years devoted himself to business. In 1737 he began his public career as -a member of the Boston Board of Selectmen, and a few weeks later he was -elected to the General Court of Massachusetts Bay, of which he was a -member until 1740 and again from 1742 to 1749, serving as speaker in -1747, 1748 and 1749. He consistently contended for a sound financial -system, and vigorously opposed the operations of the "Land Bank" and the -issue of pernicious bills of credit. In 1748 he carried through the -General Court a bill providing for the cancellation and redemption of -the outstanding paper currency. Hutchinson went to England in 1740 as -the representative of Massachusetts in a boundary dispute with New -Hampshire. He was a member of the Massachusetts Council from 1749 to -1756, was appointed judge of probate in 1752 and was chief justice of -the superior court of the province from 1761 to 1769, was -lieutenant-governor from 1758 to 1771, acting as governor in the latter -two years, and from 1771 to 1774 was governor. In 1754 he was a delegate -from Massachusetts to the Albany Convention, and, with Franklin, was a -member of the committee appointed to draw up a plan of union. Though he -recognized the legality of the Stamp Act of 1765, he considered the -measure inexpedient and impolitic and urged its repeal, but his attitude -was misunderstood; he was considered by many to have instigated the -passage of the Act, and in August 1765 a mob sacked his Boston residence -and destroyed many valuable manuscripts and documents. He was acting -governor at the time of the "Boston Massacre" in 1770, and was virtually -forced by the citizens of Boston, under the leadership of Samuel Adams, -to order the removal of the British troops from the town. Throughout the -pre-Revolutionary disturbances in Massachusetts he was the -representative of the British ministry, and though he disapproved of -some of the ministerial measures he felt impelled to enforce them and -necessarily incurred the hostility of the Whig or Patriot element. In -1774, upon the appointment of General Thomas Gage as military governor -he went to England, and acted as an adviser to George III. and the -British ministry on American affairs, uniformly counselling moderation. -He died at Brompton, now part of London, on the 3rd of June 1780. - - He wrote _A Brief Statement of the Claim of the Colonies_ (1764); a - _Collection of Original Papers relative to the History of - Massachusetts Bay_ (1769), reprinted as _The Hutchinson Papers_ by the - Prince Society in 1865; and a judicious, accurate and very valuable - _History of the Province of Massachusetts Bay_ (vol. i., 1764, vol. - ii., 1767, and vol. iii., 1828). His _Diary and Letters, with an - Account of his Administration_, was published at Boston in 1884-1886. - - See James K. Hosmer's _Life of Thomas Hutchinson_ (Boston, 1896), and - a biographical chapter in John Fiske's _Essays Historical and - Literary_ (New York, 1902). For an estimate of Hutchinson as an - historian, see M. C. Tyler's _Literary History of the American - Revolution_ (New York, 1897). - - - - -HUTCHINSON, a city and the county-seat of Reno county, Kansas, U.S.A., -in the broad bottom-land on the N. side of the Arkansas river. Pop. -(1900) 9379, of whom 414 were foreign-born and 442 negroes; (1910 -census) 16,364. It is served by the Atchison, Topeka & Santa Fe, the -Missouri Pacific and the Chicago, Rock Island & Pacific railways. The -principal public buildings are the Federal building and the county court -house. The city has a public library, and an industrial reformatory is -maintained here by the state. Hutchinson is situated in a stock-raising, -fruit-growing and farming region (the principal products of which are -wheat, Indian corn and fodder), with which it has a considerable -wholesale trade. An enormous deposit of rock salt underlies the city and -its vicinity, and Hutchinson's principal industry is the -manufacture (by the open-pan and grainer processes) and the shipping of -salt; the city has one of the largest salt plants in the world. Among -the other manufactures are flour, creamery products, soda-ash, -straw-board, planing-mill products and packed meats. Natural gas is -largely used as a factory fuel. The city's factory product was valued at -$2,031,048 in 1905, an increase of 31.8% since 1900. Hutchinson was -chartered as a city In 1871. - - - - -HUTTEN, PHILIPP VON (c. 1511-1546), German knight, was a relative of -Ulrich von Hutten and passed some of his early years at the court of the -emperor Charles V. Later he joined the band of adventurers which under -Georg Hohermuth, or George of Spires, sailed to Venezuela, or Venosala -as Hutten calls it, with the object of conquering and exploiting this -land in the interests of the Augsburg family of Welser. The party landed -at Coro in February 1535 and Hutten accompanied Hohermuth on his long -and toilsome expedition into the interior in search of treasure. After -the death of Hohermuth in December 1540 he became captain-general of -Venezuela. Soon after this event he vanished into the interior, -returning after five years of wandering to find that a Spaniard, Juan de -Caravazil, or Caravajil, had been appointed governor in his absence. -With his travelling companion, Bartholomew Welser the younger, he was -seized by Caravazil in April 1546 and the two were afterwards put to -death. - - Hutten left some letters, and also a narrative of the earlier part of - his adventures, this _Zeitung aus India Junkher Philipps von Hutten_ - being published in 1785. - - - - -HUTTEN, ULRICH VON (1488-1523), was born on the 21st of April 1488, at -the castle of Steckelberg, near Fulda, in Hesse. Like Erasmus or -Pirckheimer, he was one of those men who form the bridge between -Humanists and Reformers. He lived with both, sympathized with both, -though he died before the Reformation had time fully to develop. His -life may be divided into four parts:--his youth and cloister-life -(1488-1504); his wanderings in pursuit of knowledge (1504-1515); his -strife with Ulrich of Wurttemberg (1515-1519); and his connexion with -the Reformation (1519-1523). Each of these periods had its own special -antagonism, which coloured Hutten's career: in the first, his horror of -dull monastic routine; in the second, the ill-treatment he met with at -Greifswald; in the third, the crime of Duke Ulrich; in the fourth, his -disgust with Rome and with Erasmus. He was the eldest son of a poor and -not undistinguished knightly family. As he was mean of stature and -sickly his father destined him for the cloister, and he was sent to the -Benedictine house at Fulda; the thirst for learning there seized on him, -and in 1505 he fled from the monastic life, and won his freedom with the -sacrifice of his worldly prospects, and at the cost of incurring his -father's undying anger. From the Fulda cloister he went first to -Cologne, next to Erfurt, and then to Frankfort-on-Oder on the opening in -1506 of the new university of that town. For a time he was in Leipzig, -and in 1508 we find him a shipwrecked beggar on the Pomeranian coast. In -1509 the university of Greifswald welcomed him, but here too those who -at first received him kindly became his foes; the sensitive -ill-regulated youth, who took the liberties of genius, wearied his -burgher patrons; they could not brook the poet's airs and vanity, and -ill-timed assertions of his higher rank. Wherefore he left Greifswald, -and as he went was robbed of clothes and books, his only baggage, by the -servants of his late friends; in the dead of winter, half starved, -frozen, penniless, he reached Rostock. Here again the Humanists received -him gladly, and under their protection he wrote against his Greifswald -patrons, thus beginning the long list of his satires and fierce attacks -on personal or public foes. Rostock could not hold him long; he wandered -on to Wittenberg and Leipzig, and thence to Vienna, where he hoped to -win the emperor Maximilian's favour by an elaborate national poem on the -war with Venice. But neither Maximilian nor the university of Vienna -would lift a hand for him, and he passed into Italy, where, at Pavia, he -sojourned throughout 1511 and part of 1512. In the latter year his -studies were interrupted by war; in the siege of Pavia by papal troops -and Swiss, he was plundered by both sides, and escaped, sick and -penniless, to Bologna; on his recovery he even took service as a private -soldier in the emperor's army. - -This dark period lasted no long time; in 1514 he was again in Germany, -where, thanks to his poetic gifts and the friendship of Eitelwolf von -Stein (d. 1515), he won the favour of the elector of Mainz, Archbishop -Albert of Brandenburg. Here high dreams of a learned career rose on him; -Mainz should be made the metropolis of a grand Humanist movement, the -centre of good style and literary form. But the murder in 1515 of his -relative Hans von Hutten by Ulrich, duke of Wurttemberg, changed the -whole course of his life; satire, chief refuge of the weak, became -Hutten's weapon; with one hand he took his part in the famous _Epistolae -obscurorum virorum_, and with the other launched scathing letters, -eloquent Ciceronian orations, or biting satires against the duke. Though -the emperor was too lazy and indifferent to smite a great prince, he -took Hutten under his protection and bestowed on him the honour of a -laureate crown in 1517. Hutten, who had meanwhile revisited Italy, again -attached himself to the electoral court at Mainz; and he was there when -in 1518 his friend Pirckheimer wrote, urging him to abandon the court -and dedicate himself to letters. We have the poet's long reply, in an -epistle on his "way of life," an amusing mixture of earnestness and -vanity, self-satisfaction and satire; he tells his friend that his -career is just begun, that he has had twelve years of wandering, and -will now enjoy himself a while in patriotic literary work; that he has -by no means deserted the humaner studies, but carries with him a little -library of standard books. Pirckheimer in his burgher life may have ease -and even luxury; he, a knight of the empire, how can he condescend to -obscurity? He must abide where he can shine. - -In 1519 he issued in one volume his attacks on Duke Ulrich, and then, -drawing sword, took part in the private war which overthrew that prince; -in this affair he became intimate with Franz von Sickingen, the champion -of the knightly order (Ritterstand). Hutten now warmly and openly -espoused the Lutheran cause, but he was at the same time mixed up in the -attempt of the "Ritterstand" to assert itself as the militia of the -empire against the independence of the German princes. Soon after this -time he discovered at Fulda a copy of the manifesto of the emperor Henry -IV. against Hildebrand, and published it with comments as an attack on -the papal claims over Germany. He hoped thereby to interest the new -emperor Charles V., and the higher orders in the empire, in behalf of -German liberties; but the appeal failed. What Luther had achieved by -speaking to cities and common folk in homely phrase, because he touched -heart and conscience, that the far finer weapons of Hutten failed to -effect, because he tried to touch the more cultivated sympathies and -dormant patriotism of princes and bishops, nobles and knights. And so he -at once gained an undying name in the republic of letters and ruined his -own career. He showed that the artificial verse-making of the Humanists -could be connected with the new outburst of genuine German poetry. The -Minnesinger was gone; the new national singer, a Luther or a Hans Sachs, -was heralded by the stirring lines of Hutten's pen. These have in them a -splendid natural swing and ring, strong and patriotic, though -unfortunately addressed to knight and landsknecht rather than to the -German people. - -The poet's high dream of a knightly national regeneration had a rude -awakening. The attack on the papacy, and Luther's vast and sudden -popularity, frightened Elector Albert, who dismissed Hutten from his -court. Hoping for imperial favour, he betook himself to Charles V.; but -that young prince would have none of him. So he returned to his friends, -and they rejoiced greatly to see him still alive; for Pope Leo X. had -ordered him to be arrested and sent to Rome, and assassins dogged his -steps. He now attached himself more closely to Franz von Sickingen and -the knightly movement. This also came to a disastrous end in the capture -of the Ebernberg, and Sickingen's death; the higher nobles had -triumphed; the archbishops avenged themselves on Lutheranism as -interpreted by the knightly order. With Sickingen Hutten also finally -fell. He fled to Basel, where Erasmus refused to see him, both for fear -of his loathsome diseases, and also because the beggared knight was sure -to borrow money from him. A paper war consequently broke out between the -two Humanists, which embittered Hutten's last days, and stained the -memory of Erasmus. From Basel Ulrich dragged himself to Mulhausen; and -when the vengeance of Erasmus drove him thence, he went to Zurich. There -the large heart of Zwingli welcomed him; he helped him with money, and -found him a quiet refuge with the pastor of the little isle of Ufnau on -the Zurich lake. There the frail and worn-out poet, writing swift satire -to the end, died at the end of August or beginning of September 1523 at -the age of thirty-five. He left behind him some debts due to -compassionate friends; he did not even own a single book, and all his -goods amounted to the clothes on his back, a bundle of letters, and that -valiant pen which had fought so many a sharp battle, and had won for the -poor knight-errant a sure place in the annals of literature. - -Ulrich von Hutten is one of those men of genius at whom propriety is -shocked, and whom the mean-spirited avoid. Yet through his short and -buffeted life he was befriended, with wonderful charity and patience, by -the chief leaders of the Humanist movement. For, in spite of his -irritable vanity, his immoral life and habits, his odious diseases, his -painful restlessness, Hutten had much in him that strong men could love. -He passionately loved the truth, and was ever open to all good -influences. He was a patriot, whose soul soared to ideal schemes and a -grand utopian restoration of his country. In spite of all, his was a -frank and noble nature; his faults chiefly the faults of genius -ill-controlled, and of a life cast in the eventful changes of an age of -novelty. A swarm of writings issued from his pen; at first the smooth -elegance of his Latin prose and verse seemed strangely to miss his real -character; he was the Cicero and Ovid of Germany before he became its -Lucian. - - His chief works were his _Ars versificandi_ (1511); the _Nemo_ (1518); - a work on the _Morbus Gallicus_ (1519); the volume of Steckelberg - complaints against Duke Ulrich (including his four _Ciceronian - Orations_, his Letters and the _Phalarismus_) also in 1519; the - _Vadismus_ (1520); and the controversy with Erasmus at the end of his - life. Besides these were many admirable poems in Latin and German. It - is not known with certainty how far Hutten was the parent of the - celebrated _Epistolae obscurorum virorum_, that famous satire on - monastic ignorance as represented by the theologians of Cologne with - which the friends of Reuchlin defended him. At first the - cloister-world, not discerning its irony, welcomed the work as a - defence of their position; though their eyes were soon opened by the - favour with which the learned world received it. The _Epistolae_ were - eagerly bought up; the first part (41 letters) appeared at the end of - 1515; early in 1516 there was a second edition; later in 1516 a third, - with an appendix of seven letters; in 1517 appeared the second part - (62 letters), to which a fresh appendix of eight letters was subjoined - soon after. In 1909 the Latin text of the _Epistolae_ with an English - translation was published by F. G. Stokes. Hutten, in a letter - addressed to Robert Crocus, denied that he was the author of the book, - but there is no doubt as to his connexion with it. Erasmus was of - opinion that there were three authors, of whom Crotus Rubianus was the - originator of the idea, and Hutten a chief contributor. D. F. Strauss, - who dedicates to the subject a chapter of his admirable work on - Hutten, concludes that he had no share in the first part, but that his - hand is clearly visible in the second part, which he attributes in the - main to him. To him is due the more serious and severe tone of that - bitter portion of the satire. See W. Brecht, _Die Verfasser der - Epistolae obscurorum virorum_ (1904). - - For a complete catalogue of the writings of Hutten, see E. Bocking's - _Index Bibliographicus Huttenianus_ (1858). Bocking is also the editor - of the complete edition of Hutten's works (7 vols., 1859-1862). A - selection of Hutten's German writings, edited by G. Balke, appeared in - 1891. Cp. S. Szamatolski, _Huttens deutsche Schriften_ (1891). The - best biography (though it is also somewhat of a political pamphlet) is - that of D. F. Strauss (_Ulrich von Hutten_, 1857; 4th ed., 1878; - English translation by G. Sturge, 1874), with which may be compared - the older monographs by A. Wagenseil (1823), A. Burck (1846) and J. - Zeller (Paris, 1849). See also J. Deckert, _Ulrich von Huttens Leben - und Wirken. Eine historische Skizze_ (1901). (G. W. K.) - - - - -HUTTER, LEONHARD (1563-1616), German Lutheran theologian, was born at -Nellingen near Ulm in January 1563. From 1581 he studied at the -universities of Strassburg, Leipzig, Heidelberg and Jena. In 1594 he -began to give theological lectures at Jena, and in 1596 accepted a call -as professor of theology at Wittenberg, where he died on the 23rd of -October 1616. Hutter was a stern champion of Lutheran orthodoxy, as set -down in the confessions and embodied in his own _Compendium locorum -theologicorum_ (1610; reprinted 1863), being so faithful to his master -as to win the title of "Luther redonatus." - - In reply to Rudolf Hospinian's _Concordia discors_ (1607), he wrote a - work, rich in historical material but one-sided in its apologetics, - _Concordia concors_ (1614), defending the formula of Concord, which he - regarded as inspired. His _Irenicum vere christianum_ is directed - against David Pareus (1548-1622), professor primarius at Heidelberg, - who in _Irenicum sive de unione et synodo Evangelicorum_ (1614) had - pleaded for a reconciliation of Lutheranism and Calvinism; his - _Calvinista aulopoliticus_ (1610) was written against the "damnable - Calvinism" which was becoming prevalent in Holstein and Brandenburg. - Another work, based on the formula of Concord, was entitled _Loci - communes theologici_. - - - - -HUTTON, CHARLES (1737-1823), English mathematician, was born at -Newcastle-on-Tyne on the 14th of August 1737. He was educated in a -school at Jesmond, kept by Mr Ivison, a clergyman of the church of -England. There is reason to believe, on the evidence of two pay-bills, -that for a short time in 1755 and 1756 Hutton worked in Old Long Benton -colliery; at any rate, on Ivison's promotion to a living, Hutton -succeeded to the Jesmond school, whence, in consequence of increasing -pupils, he removed to Stote's Hall. While he taught during the day at -Stote's Hall, he studied mathematics in the evening at a school in -Newcastle. In 1760 he married, and began tuition on a larger scale in -Newcastle, where he had among his pupils John Scott, afterwards Lord -Eldon, chancellor of England. In 1764 he published his first work, _The -Schoolmaster's Guide, or a Complete System of Practical Arithmetic_, -which in 1770 was followed by his _Treatise on Mensuration both in -Theory and Practice_. In 1772 appeared a tract on _The Principles of -Bridges_, suggested by the destruction of Newcastle bridge by a high -flood on the 17th of November 1771. In 1773 he was appointed professor -of mathematics at the Royal Military Academy, Woolwich, and in the -following year he was elected F.R.S. and reported on Nevil Maskelyne's -determination of the mean density and mass of the earth from -measurements taken in 1774-1776 at Mount Schiehallion in Perthshire. -This account appeared in the _Philosophical Transactions_ for 1778, was -afterwards reprinted in the second volume of his _Tracts on Mathematical -and Philosophical Subjects_, and procured for Hutton the degree of LL.D. -from the university of Edinburgh. He was elected foreign secretary to -the Royal Society in 1779, but his resignation in 1783 was brought about -by the president Sir Joseph Banks, whose behaviour to the mathematical -section of the society was somewhat high-handed (see Kippis's -_Observations on the late Contests in the Royal Society_, London, 1784). -After his _Tables of the Products and Powers of Numbers_, 1781, and his -_Mathematical Tables_, 1785, he issued, for the use of the Royal -Military Academy, in 1787 _Elements of Conic Sections_, and in 1798 his -_Course of Mathematics_. His _Mathematical and Philosophical -Dictionary_, a valuable contribution to scientific biography, was -published in 1795 (2nd ed., 1815), and the four volumes of _Recreations -in Mathematics and Natural Philosophy_, mostly a translation from the -French, in 1803. One of the most laborious of his works was the -abridgment, in conjunction with G. Shaw and R. Pearson, of the -_Philosophical Transactions_. This undertaking, the mathematical and -scientific parts of which fell to Hutton's share, was completed in 1809, -and filled eighteen volumes quarto. His name first appears in the -_Ladies' Diary_ (a poetical and mathematical almanac which was begun in -1704, and lasted till 1871) in 1764; ten years later he was appointed -editor of the almanac, a post which he retained till 1817. Previously he -had begun a small periodical, _Miscellanea Mathematica_, which extended -only to thirteen numbers; subsequently he published in five volumes _The -Diarian Miscellany_, which contained large extracts from the _Diary_. He -resigned his professorship in 1807, and died on the 27th of January -1823. - - See John Bruce, _Charles Hutton_ (Newcastle, 1823). - - - - -HUTTON, JAMES (1726-1797), Scottish geologist, was born in Edinburgh on -the 3rd of June 1726. Educated at the high school and university of his -native city, he acquired while a student a passionate love of scientific -inquiry. He was apprenticed to a lawyer, but his employer advised that a -more congenial profession should be chosen for him. The young apprentice -chose medicine as being nearest akin to his favourite pursuit of -chemistry. He studied for three years at Edinburgh, and completed his -medical education in Paris, returning by the Low Countries, and taking -his degree of doctor of medicine at Leiden in 1749. Finding, however, -that there seemed hardly any opening for him, he abandoned the medical -profession, and, having inherited a small property in Berwickshire from -his father, resolved to devote himself to agriculture. He then went to -Norfolk to learn the practical work of farming, and subsequently -travelled in Holland, Belgium and the north of France. During these -years he began to study the surface of the earth, gradually shaping in -his mind the problem to which he afterwards devoted his energies. In the -summer of 1754 he established himself on his own farm in Berwickshire, -where he resided for fourteen years, and where he introduced the most -improved forms of husbandry. As the farm was brought into excellent -order, and as its management, becoming more easy, grew less interesting, -he was induced to let it, and establish himself for the rest of his life -in Edinburgh. This took place about the year 1768. He was unmarried, and -from this period until his death in 1797 he lived with his three -sisters. Surrounded by congenial literary and scientific friends he -devoted himself to research. - -At that time geology in any proper sense of the term did not exist. -Mineralogy, however, had made considerable progress. But Hutton had -conceived larger ideas than were entertained by the mineralogists of his -day. He desired to trace back the origin of the various minerals and -rocks, and thus to arrive at some clear understanding of the history of -the earth. For many years he continued to study the subject. At last, in -the spring of the year 1785, he communicated his views to the recently -established Royal Society of Edinburgh in a paper entitled _Theory of -the Earth, or an Investigation of the Laws Observable in the -Composition, Dissolution and Restoration of Land upon the Globe_. In -this remarkable work the doctrine is expounded that geology is not -cosmogony, but must confine itself to the study of the materials of the -earth; that everywhere evidence may be seen that the present rocks of -the earth's surface have been in great part formed out of the waste of -older rocks; that these materials having been laid down under the sea -were there consolidated under great pressure, and were subsequently -disrupted and upheaved by the expansive power of subterranean heat; that -during these convulsions veins and masses of molten rock were injected -into the rents of the dislocated strata; that every portion of the -upraised land, as soon as exposed to the atmosphere, is subject to -decay; and that this decay must tend to advance until the whole of the -land has been worn away and laid down on the sea-floor, whence future -upheavals will once more raise the consolidated sediments into new land. -In some of these broad and bold generalizations Hutton was anticipated -by the Italian geologists; but to him belongs the credit of having first -perceived their mutual relations, and combined them in a luminous -coherent theory based upon observation. - -It was not merely the earth to which Hutton directed his attention. He -had long studied the changes of the atmosphere. The same volume in which -his _Theory of the Earth_ appeared contained also a _Theory of Rain_, -which was read to the Royal Society of Edinburgh in 1784. He contended -that the amount of moisture which the air can retain in solution -increases with augmentation of temperature, and, therefore, that on the -mixture of two masses of air of different temperatures a portion of the -moisture must be condensed and appear in visible form. He investigated -the available data regarding rainfall and climate in different regions -of the globe, and came to the conclusion that the rainfall is everywhere -regulated by the humidity of the air on the one hand, and the causes -which promote mixtures of different aerial currents in the higher -atmosphere on the other. - -The vigour and versatility of his genius may be understood from the -variety of works which, during his thirty years' residence in Edinburgh, -he gave to the world. In 1792 he published a quarto volume entitled -_Dissertations on different Subjects in Natural Philosophy_, in which he -discussed the nature of matter, fluidity, cohesion, light, heat and -electricity. Some of these subjects were further illustrated by him in -papers read before the Royal Society of Edinburgh. He did not restrain -himself within the domain of physics, but boldly marched into that of -metaphysics, publishing three quarto volumes with the title _An -Investigation of the Principles of Knowledge, and of the Progress of -Reason--from Sense to Science and Philosophy_. In this work he developed -the idea that the external world, as conceived by us, is the creation of -our own minds influenced by impressions from without, that there is no -resemblance between our picture of the outer world and the reality, yet -that the impressions produced upon our minds, being constant and -consistent, become as much realities to us as if they precisely -resembled things actually existing, and, therefore, that our moral -conduct must remain the same as if our ideas perfectly corresponded to -the causes producing them. His closing years were devoted to the -extension and republication of his _Theory of the Earth_, of which two -volumes appeared in 1795. A third volume, necessary to complete the -work, was left by him in manuscript, and is referred to by his -biographer John Playfair. A portion of the MS. of this volume, which had -been given to the Geological Society of London by Leonard Horner, was -published by the Society in 1899, under the editorship of Sir A. Geikie. -The rest of the manuscript appears to be lost. Soon afterwards Hutton -set to work to collect and systematize his numerous writings on -husbandry, which he proposed to publish under the title of _Elements of -Agriculture_. He had nearly completed this labour when an incurable -disease brought his active career to a close on the 26th of March 1797. - - It is by his _Theory of the Earth_ that Hutton will be remembered with - reverence while geology continues to be cultivated. The author's - style, however, being somewhat heavy and obscure, the book did not - attract during his lifetime so much attention as it deserved. Happily - for science Hutton numbered among his friends John Playfair (q.v.), - professor of mathematics in the university of Edinburgh, whose - enthusiasm for the spread of Hutton's doctrine was combined with a - rare gift of graceful and luminous exposition. Five years after - Hutton's death he published a volume, _Illustrations of the Huttonian - Theory of the Earth_, in which he gave an admirable summary of that - theory, with numerous additional illustrations and arguments. This - work is justly regarded as one of the classical contributions to - geological literature. To its influence much of the sound progress of - British geology must be ascribed. In the year 1805 a biographical - account of Hutton, written by Playfair, was published in vol. v. of - the _Transactions of the Royal Society of Edinburgh_. (A. Ge.) - - - - -HUTTON, RICHARD HOLT (1826-1897), English writer and theologian, son of -Joseph Hutton, Unitarian minister at Leeds, was born at Leeds on the 2nd -of June 1826. His family removed to London in 1835, and he was educated -at University College School and University College, where he began a -lifelong friendship with Walter Bagehot, of whose works he afterwards was -the editor; he took the degree in 1845, being awarded the gold medal for -philosophy. Meanwhile he had also studied for short periods at Heidelberg -and Berlin, and in 1847 he entered Manchester New College with the idea -of becoming a minister like his father, and studied there under James -Martineau. He did not, however, succeed in obtaining a call to any -church, and for some little time his future was unsettled. He married in -1851 his cousin, Anne Roscoe, and became joint-editor with J. L. Sanford -of the _Inquirer_, the principal Unitarian organ. But his innovations and -his unconventional views about stereotyped Unitarian doctrines caused -alarm, and in 1853 he resigned. His health had broken down, and he -visited the West Indies, where his wife died of yellow fever. In 1855 -Hutton and Bagehot became joint-editors of the _National Review_, a new -monthly, and conducted it for ten years. During this time Hutton's -theological views, influenced largely by Coleridge, and more directly by -F. W. Robertson and F. D. Maurice, gradually approached more and more to -those of the Church of England, which he ultimately joined. His interest -in theology was profound, and he brought to it a spirituality of outlook -and an aptitude for metaphysical inquiry and exposition which added a -singular attraction to his writings. In 1861 he joined Meredith Townsend -as joint-editor and part proprietor of the _Spectator_, then a well-known -liberal weekly, which, however, was not remunerative from the business -point of view. Hutton took charge of the literary side of the paper, and -by degrees his own articles became and remained up to the last one of the -best-known features of serious and thoughtful English journalism. The -_Spectator_, which gradually became a prosperous property, was his -pulpit, in which unwearyingly he gave expression to his views, -particularly on literary, religious and philosophical subjects, in -opposition to the agnostic and rationalistic opinions then current in -intellectual circles, as popularized by Huxley. A man of fearless -honesty, quick and catholic sympathies, broad culture, and many friends -in intellectual and religious circles, he became one of the most -influential journalists of the day, his fine character and conscience -earning universal respect and confidence. He was an original member of -the Metaphysical Society (1869). He was an anti-vivisectionist, and a -member of the royal commission (1875) on that subject. In 1858 he had -married Eliza Roscoe, a cousin of his first wife; she died early in 1897, -and Hutton's own death followed on the 9th of September of the same year. - - Among his other publications may be mentioned _Essays, Theological and - Literary_ (1871; revised 1888), and _Criticisms on Contemporary - Thought and Thinkers_ (1894); and his opinions may be studied - compendiously in the selections from his _Spectator_ articles - published in 1899 under the title of _Aspects of Religious and - Scientific Thought_. - - - - -HUXLEY, THOMAS HENRY (1825-1895), English biologist, was born on the 4th -of May 1825 at Ealing, where his father, George Huxley, was senior -assistant-master in the school of Dr Nicholas. This was an establishment -of repute, and is at any rate remarkable for having produced two men -with so little in common in after life as Huxley and Cardinal Newman. -The cardinal's brother, Francis William, had been "captain" of the -school in 1821. Huxley was a seventh child (as his father had also -been), and the youngest who survived infancy. Of Huxley's ancestry no -more is ascertainable than in the case of most middle-class families. He -himself thought it sprang from the Cheshire Huxleys of Huxley Hall. -Different branches migrated south, one, now extinct, reaching London, -where its members were apparently engaged in commerce. They established -themselves for four generations at Wyre Hall, near Edmonton, and one was -knighted by Charles II. Huxley describes his paternal race as "mainly -Iberian mongrels, with a good dash of Norman and a little Saxon."[1] -From his father he thought he derived little except a quick temper and -the artistic faculty which proved of great service to him and reappeared -in an even more striking degree in his daughter, the Hon. Mrs Collier. -"Mentally and physically," he wrote, "I am a piece of my mother." Her -maiden name was Rachel Withers. "She came of Wiltshire people," he adds, -and describes her as "a typical example of the Iberian variety." He -tells us that "her most distinguishing characteristic was rapidity of -thought.... That peculiarity has been passed on to me in full strength" -(_Essays_, i. 4). One of the not least striking facts in Huxley's life -is that of education in the formal sense he received none. "I had two -years of a pandemonium of a school (between eight and ten), and after -that neither help nor sympathy in any intellectual direction till I -reached manhood" (_Life_, ii. 145). After the death of Dr Nicholas the -Ealing school broke up, and Huxley's father returned about 1835 to his -native town, Coventry, where he had obtained a small appointment. Huxley -was left to his own devices; few histories of boyhood could offer any -parallel. At twelve he was sitting up in bed to read Hutton's _Geology_. -His great desire was to be a mechanical engineer; it ended in his -devotion to "the mechanical engineering of living machines." His -curiosity in this direction was nearly fatal; a _post-mortem_ he was -taken to between thirteen and fourteen was followed by an illness which -seems to have been the starting-point of the ill-health which pursued -him all through life. At fifteen he devoured Sir William Hamilton's -_Logic_, and thus acquired the taste for metaphysics, which he -cultivated to the end. At seventeen he came under the influence of -Thomas Carlyle's writings. Fifty years later he wrote: "To make things -clear and get rid of cant and shows of all sorts. This was the lesson I -learnt from Carlyle's books when I was a boy, and it has stuck by me all -my life" (_Life_, ii. 268). Incidentally they led him to begin to learn -German; he had already acquired French. At seventeen Huxley, with his -elder brother James, commenced regular medical studies at Charing Cross -Hospital, where they had both obtained scholarships. He studied under -Wharton Jones, a physiologist who never seems to have attained the -reputation he deserved. Huxley said of him: "I do not know that I ever -felt so much respect for a teacher before or since" (_Life_, i. 20). At -twenty he passed his first M.B. examination at the University of London, -winning the gold medal for anatomy and physiology; W. H. Ransom, the -well-known Nottingham physician, obtaining the exhibition. In 1845 he -published, at the suggestion of Wharton Jones, his first scientific -paper, demonstrating the existence of a hitherto unrecognized layer in -the inner sheath of hairs, a layer that has been known since as -"Huxley's layer." - -Something had to be done for a livelihood, and at the suggestion of a -fellow-student, Mr (afterwards Sir Joseph) Fayrer, he applied for an -appointment in the navy. He passed the necessary examination, and at the -same time obtained the qualification of the Royal College of Surgeons. -He was "entered on the books of Nelson's old ship, the 'Victory,' for -duty at Haslar Hospital." Its chief, Sir John Richardson, who was a -well-known Arctic explorer and naturalist, recognized Huxley's ability, -and procured for him the post of surgeon to H.M.S. "Rattlesnake," about -to start for surveying work in Torres Strait. The commander, Captain -Owen Stanley, was a son of the bishop of Norwich and brother of Dean -Stanley, and wished for an officer with some scientific knowledge. -Besides Huxley the "Rattlesnake" also carried a naturalist by -profession, John Macgillivray, who, however, beyond a dull narrative of -the expedition, accomplished nothing. The "Rattlesnake" left England on -the 3rd of December 1846, and was ordered home after the lamented death -of Captain Stanley at Sydney, to be paid off at Chatham on the 9th of -November 1850. The tropical seas teem with delicate surface-life, and to -the study of this Huxley devoted himself with unremitting devotion. At -that time no known methods existed by which it could be preserved for -study in museums at home. He gathered a magnificent harvest in the -almost unreaped field, and the conclusions he drew from it were the -beginning of the revolution in zoological science which he lived to see -accomplished. - -Baron Cuvier (1769-1832), whose classification still held its ground, -had divided the animal kingdom into four great _embranchements_. Each of -these corresponded to an independent archetype, of which the "idea" had -existed in the mind of the Creator. There was no other connexion between -these classes, and the "ideas" which animated them were, as far as one -can see, arbitrary. Cuvier's groups, without their theoretical basis, -were accepted by K. E. von Baer (1792-1876). The "idea" of the group, or -archetype, admitted of endless variation within it; but this was -subordinate to essential conformity with the archetype, and hence Cuvier -deduced the important principle of the "correlation of parts," of which -he made such conspicuous use in palaeontological reconstruction. -Meanwhile the "Naturphilosophen," with J. W. Goethe (1749-1832) and L. -Oken (1779-1851), had in effect grasped the underlying principle of -correlation, and so far anticipated evolution by asserting the -possibility of deriving specialized from simpler structures. Though they -were still hampered by idealistic conceptions, they established -morphology. Cuvier's four great groups were Vertebrata, Mollusca, -Articulata and Radiata. It was amongst the members of the last -class that Huxley found most material ready to his hand in the seas of -the tropics. It included organisms of the most varied kind, with nothing -more in common than that their parts were more or less distributed round -a centre. Huxley sent home "communication after communication to the -Linnean Society," then a somewhat somnolent body, "with the same result -as that obtained by Noah when he sent the raven out of the ark" -(_Essays_, i. 13). His important paper, _On the Anatomy and the -Affinities of the Family of Medusae_, met with a better fate. It was -communicated by the bishop of Norwich to the Royal Society, and printed -by it in the _Philosophical Transactions_ in 1849. Huxley united, with -the Medusae, the Hydroid and Sertularian polyps, to form a class to -which he subsequently gave the name of Hydrozoa. This alone was no -inconsiderable feat for a young surgeon who had only had the training of -the medical school. But the ground on which it was done has led to -far-reaching theoretical developments. Huxley realized that something -more than superficial characters were necessary in determining the -affinities of animal organisms. He found that all the members of the -class consisted of two membranes enclosing a central cavity or stomach. -This is characteristic of what are now called the Coelenterata. All -animals higher than these have been termed Coelomata; they possess a -distinct body-cavity in addition to the stomach. Huxley went further -than this, and the most profound suggestion in his paper is the -comparison of the two layers with those which appear in the germ of the -higher animals. The consequences which have flowed from this prophetic -generalization of the _ectoderm_ and _endoderm_ are familiar to every -student of evolution. The conclusion was the more remarkable as at the -time he was not merely free from any evolutionary belief, but actually -rejected it. The value of Huxley's work was immediately recognized. On -returning to England in 1850 he was elected a Fellow of the Royal -Society. In the following year, at the age of twenty-six, he not merely -received the Royal medal, but was elected on the council. With -absolutely no aid from any one he had placed himself in the front rank -of English scientific men. He secured the friendship of Sir J. D. Hooker -and John Tyndall, who remained his lifelong friends. The Admiralty -retained him as a nominal assistant-surgeon, in order that he might work -up the observations he had made during the voyage of the "Rattlesnake." -He was thus enabled to produce various important memoirs, especially -those on certain Ascidians, in which he solved the problem of -_Appendicularia_--an organism whose place in the animal kingdom Johannes -Muller had found himself wholly unable to assign--and on the morphology -of the Cephalous Mollusca. - -Richard Owen, then the leading comparative anatomist in Great Britain, -was a disciple of Cuvier, and adopted largely from him the deductive -explanation of anatomical fact from idealistic conceptions. He -superadded the evolutionary theories of Oken, which were equally -idealistic, but were altogether repugnant to Cuvier. Huxley would have -none of either. Imbued with the methods of von Baer and Johannes Muller, -his methods were purely inductive. He would not hazard any statement -beyond what the facts revealed. He retained, however, as has been done -by his successors, the use of archetypes, though they no longer -represented fundamental "ideas" but generalizations of the essential -points of structure common to the individuals of each class. He had not -wholly freed himself, however, from archetypal trammels. "The doctrine," -he says, "that every natural group is organized after a definite -archetype ... seems to me as important for zoology as the doctrine of -definite proportions for chemistry." This was in 1853. He further -stated: "There is no progression from a lower to a higher type, but -merely a more or less complete evolution of one type" (_Phil. Trans._, -1853, p. 63). As Chalmers Mitchell points out, this statement is of -great historical interest. Huxley definitely uses the word "evolution," -and admits its existence _within_ the great groups. He had not, however, -rid himself of the notion that the archetype was a property inherent in -the group. Herbert Spencer, whose acquaintance he made in 1852, was -unable to convert him to evolution in its widest sense (_Life_, i. -168). He could not bring himself to acceptance of the theory--owing, no -doubt, to his rooted aversion from a priori reasoning--without a -mechanical conception of its mode of operation. In his first interview -with Darwin, which seems to have been about the same time, he expressed -his belief "in the sharpness of the lines of demarcation between natural -groups," and was received with a humorous smile (_Life_, i. 169). - -The naval medical service exists for practical purposes. It is not -surprising, therefore, that after his three years' nominal employment -Huxley was ordered on active service. Though without private means of -any kind, he resigned. The navy, however, retains the credit of having -started his scientific career as well as that of Hooker and Darwin. -Huxley was now thrown on his own resources, the immediate prospects of -which were slender enough. As a matter of fact, he had not to wait many -months. His friend, Edward Forbes, was appointed to the chair of natural -history in Edinburgh, and in July 1854 he succeeded him as lecturer at -the School of Mines and as naturalist to the Geological Survey in the -following year. The latter post he hesitated at first to accept, as he -"did not care for fossils" (_Essays_, i. 15). In 1855 he married Miss H. -A. Heathorn, whose acquaintance he had made in Sydney. They were engaged -when Huxley could offer nothing but the future promise of his ability. -The confidence of his devoted helpmate was not misplaced, and her -affection sustained him to the end, after she had seen him the recipient -of every honour which English science could bestow. His most important -research belonging to this period was the Croonian Lecture delivered -before the Royal Society in 1858 on "The Theory of the Vertebrate -Skull." In this he completely and finally demolished, by applying as -before the inductive method, the idealistic, if in some degree -evolutionary, views of its origin which Owen had derived from Goethe and -Oken. This finally disposed of the "archetype," and may be said once for -all to have liberated the English anatomical school from the deductive -method. - -In 1859 _The Origin of Species_ was published. This was a momentous -event in the history of science, and not least for Huxley. Hitherto he -had turned a deaf ear to evolution. "I took my stand," he says, "upon -two grounds: firstly, that ... the evidence in favour of transmutation -was wholly insufficient; and secondly, that no suggestion respecting the -causes of the transmutation assumed, which had been made, was in any way -adequate to explain the phenomena" (_Life_, i. 168). Huxley had studied -Lamarck "attentively," but to no purpose. Sir Charles Lyell "was the -chief agent in smoothing the road for Darwin. For consistent -uniformitarianism postulates evolution as much in the organic as in the -inorganic world" (l.c.); and Huxley found in Darwin what he had failed -to find in Lamarck, an intelligible hypothesis good enough as a working -basis. Yet with the transparent candour which was characteristic of him, -he never to the end of his life concealed the fact that he thought it -wanting in rigorous proof. Darwin, however, was a naturalist; Huxley was -not. He says: "I am afraid there is very little of the genuine -naturalist in me. I never collected anything, and species-work was -always a burden to me; what I cared for was the architectural and -engineering part of the business" (_Essays_, i. 7). But the solution of -the problem of organic evolution must work upwards from the initial -stages, and it is precisely for the study of these that "species-work" -is necessary. Darwin, by observing the peculiarities in the distribution -of the plants which he had collected in the Galapagos, was started on -the path that led to his theory. Anatomical research had only so far led -to transcendental hypothesis, though in Huxley's hands it had cleared -the decks of that lumber. He quotes with approval Darwin's remark that -"no one has a right to examine the question of species who has not -minutely described many" (_Essays_, ii. 283). The rigorous proof which -Huxley demanded was the production of species sterile to one another by -selective breeding (_Life_, i. 193). But this was a misconception of the -question. Sterility is a physiological character, and the specific -differences which the theory undertook to account for are -morphological; there is no necessary nexus between the two. Huxley, -however, felt that he had at last a secure grip of evolution. He warned -Darwin: "I will stop at no point as long as clear reasoning will carry -me further" (_Life_, i. 172). Owen, who had some evolutionary -tendencies, was at first favourably disposed to Darwin's theory, and -even claimed that he had to some extent anticipated it in his own -writings. But Darwin, though he did not thrust it into the foreground, -never flinched from recognizing that man could not be excluded from his -theory. "Light will be thrown on the origin of man and his history" -(_Origin_, ed. i. 488). Owen could not face the wrath of fashionable -orthodoxy. In his Rede Lecture he endeavoured to save the position by -asserting that man was clearly marked off from all other animals by the -anatomical structure of his brain. This was actually inconsistent with -known facts, and was effectually refuted by Huxley in various papers and -lectures, summed up in 1863 in _Man's Place in Nature_. This "monkey -damnification" of mankind was too much even for the "veracity" of -Carlyle, who is said to have never forgiven it. Huxley had not the -smallest respect for authority as a basis for belief, scientific or -otherwise. He held that scientific men were morally bound "to try all -things and hold fast to that which is good" (_Life_, ii. 161). Called -upon in 1862, in the absence of the president, to deliver the -presidential address to the Geological Society, he disposed once for all -of one of the principles accepted by geologists, that similar fossils in -distinct regions indicated that the strata containing them were -contemporary. All that could be concluded, he pointed out, was that the -general order of succession was the same. In 1854 Huxley had refused the -post of palaeontologist to the Geological Survey; but the fossils for -which he then said that he "did not care" soon acquired importance in -his eyes, as supplying evidence for the support of the evolutionary -theory. The thirty-one years during which he occupied the chair of -natural history at the School of Mines were largely occupied with -palaeontological research. Numerous memoirs on fossil fishes established -many far-reaching morphological facts. The study of fossil reptiles led -to his demonstrating, in the course of lectures on birds, delivered at -the College of Surgeons in 1867, the fundamental affinity of the two -groups which he united under the title of Sauropsida. An incidental -result of the same course was his proposed rearrangement of the -zoological regions into which P. L. Sclater had divided the world in -1857. Huxley anticipated, to a large extent, the results at which -botanists have since arrived: he proposed as primary divisions, -Arctogaea--to include the land areas of the northern hemisphere--and -Notogaea for the remainder. Successive waves of life originated in and -spread from the northern area, the survivors of the more ancient types -finding successively a refuge in the south. Though Huxley had accepted -the Darwinian theory as a working hypothesis, he never succeeded in -firmly grasping it in detail. He thought "evolution might conceivably -have taken place without the development of groups possessing the -characters of species" (_Essays_, v. 41). His palaeontological -researches ultimately led him to dispense with Darwin. In 1892 he wrote: -"The doctrine of evolution is no speculation, but a generalization of -certain facts ... classed by biologists under the heads of Embryology -and of Palaeontology" (_Essays_, v. 42). Earlier in 1881 he had asserted -even more emphatically that if the hypothesis of evolution "had not -existed, the palaeontologist would have had to invent it" (_Essays_, iv. -44). - -From 1870 onwards he was more and more drawn away from scientific -research by the claims of public duty. Some men yield the more readily -to such demands, as their fulfilment is not unaccompanied by public -esteem. But he felt, as he himself said of Joseph Priestley, "that he -was a man and a citizen before he was a philosopher, and that the duties -of the two former positions are at least as imperative as those of the -latter" (_Essays_, iii. 13). From 1862 to 1884 he served on no less than -ten Royal Commissions, dealing in every case with subjects of great -importance, and in many with matters of the gravest moment to the -community. He held and filled with invariable dignity and distinction -more public positions than have perhaps ever fallen to the lot of a -scientific man in England. From 1871 to 1880 he was a secretary of the -Royal Society. From 1881 to 1885 he was president. For honours he cared -little, though they were within his reach; it is said that he might have -received a peerage. He accepted, however, in 1892, a Privy -Councillorship, at once the most democratic and the most aristocratic -honour accessible to an English citizen. In 1870 he was president of the -British Association at Liverpool, and in the same year was elected a -member of the newly constituted London School Board. He resigned the -latter position in 1872, but in the brief period during which he acted, -probably more than any man, he left his mark on the foundations of -national elementary education. He made war on the scholastic methods -which wearied the mind in merely taxing the memory; the children were to -be prepared to take their place worthily in the community. Physical -training was the basis; domestic economy, at any rate for girls, was -insisted upon, and for all some development of the aesthetic sense by -means of drawing and singing. Reading, writing and arithmetic were the -indispensable tools for acquiring knowledge, and intellectual discipline -was to be gained through the rudiments of physical science. He insisted -on the teaching of the Bible partly as a great literary heritage, partly -because he was "seriously perplexed to know by what practical measures -the religious feeling, which is the essential basis of conduct, was to -be kept up, in the present utterly chaotic state of opinion in these -matters, without its use" (_Essays_, iii. 397). In 1872 the School of -Mines was moved to South Kensington, and Huxley had, for the first time -after eighteen years, those appliances for teaching beyond the lecture -room, which to the lasting injury of the interests of biological science -in Great Britain had been withheld from him by the short-sightedness of -government. Huxley had only been able to bring his influence to bear -upon his pupils by oral teaching, and had had no opportunity by personal -intercourse in the laboratory of forming a school. He was now able to -organize a system of instruction for classes of elementary teachers in -the general principles of biology, which indirectly affected the -teaching of the subject throughout the country. - -The first symptoms of physical failure to meet the strain of the -scientific and public duties demanded of him made some rest imperative, -and he took a long holiday in Egypt. He still continued for some years -to occupy himself mainly with vertebrate morphology. But he seemed to -find more interest and the necessary mental stimulus to exertion in -lectures, public addresses and more or less controversial writings. His -health, which had for a time been fairly restored, completely broke down -again in 1885. In 1890 he removed from London to Eastbourne, where after -a painful illness he died on the 29th of June 1895. - - The latter years of Huxley's life were mainly occupied with - contributions to periodical literature on subjects connected with - philosophy and theology. The effect produced by these on popular - opinion was profound. This was partly due to his position as a man of - science, partly to his obvious earnestness and sincerity, but in the - main to his strenuous and attractive method of exposition. Such - studies were not wholly new to him, as they had more or less engaged - his thoughts from his earliest days. That his views exhibit some - process of development and are not wholly consistent was, therefore, - to be expected, and for this reason it is not easy to summarize them - as a connected body of teaching. They may be found perhaps in their - most systematic form in the volume on _Hume_ published in 1879. - - Huxley's general attitude to the problems of theology and philosophy - was technically that of scepticism. "I am," he wrote, "too much of a - sceptic to deny the possibility of anything" (_Life_, ii. 127). "Doubt - is a beneficent demon" (_Essays_, ix. 56). He was anxious, - nevertheless, to avoid the accusation of Pyrrhonism (_Life_, ii. 280), - but the Agnosticism which he defined to express his position in 1869 - suggests the Pyrrhonist _Aphasia_. The only approach to certainty - which he admitted lay in the order of nature. "The conception of the - constancy of the order of nature has become the dominant idea of - modern thought.... Whatever may be man's speculative doctrines, it is - quite certain that every intelligent person guides his life and risks - his fortune upon the belief that the order of nature is constant, and - that the chain of natural causation is never broken." He adds, - however, that "it by no means necessarily follows that we are - justified in expanding this generalization into the infinite past" - (_Essays_, iv. 47, 48). This was little more than a pious - reservation, as evolution implies the principle of continuity (l.c. p. - 55). Later he stated his belief even more absolutely: "If there is - anything in the world which I do firmly believe in, it is the - universal validity of the law of causation, but that universality - cannot be proved by any amount of experience" (_Essays_, ix. 121). The - assertion that "There is only one method by which intellectual truth - can be reached, whether the subject-matter of investigation belongs to - the world of physics or to the world of consciousness" (_Essays_, ix. - 126) laid him open to the charge of materialism, which he vigorously - repelled. His defence, when he rested it on the imperfection of the - physical analysis of matter and force (l.c. p. 131), was irrelevant; - he was on sounder ground when he contended with Berkeley "that our - certain knowledge does not extend beyond our states of consciousness" - (l.c. p. 130). "Legitimate materialism, that is, the extension of the - conceptions and of the methods of physical science to the highest as - well as to the lowest phenomena of vitality, is neither more nor less - than a sort of shorthand idealism" (_Essays_, i. 194). While "the - substance of matter is a metaphysical unknown quality of the existence - of which there is no proof ... the non-existence of a substance of - mind is equally arguable; ... the result ... is the reduction of the - All to co-existences and sequences of phenomena beneath and beyond - which there is nothing cognoscible" (_Essays_, ix. 66). Hume had - defined a miracle as a "violation of the laws of nature." Huxley - refused to accept this. While, on the one hand, he insists that "the - whole fabric of practical life is built upon our faith in its - continuity" (_Hume_, p. 129), on the other "nobody can presume to say - what the order of nature must be"; this "knocks the bottom out of all - a priori objections either to ordinary 'miracles' or to the efficacy - of prayer" (_Essays_, v. 133). "If by the term miracles we mean only - extremely wonderful events, there can be no just ground for denying - the possibility of their occurrence" (_Hume_, p. 134). Assuming the - chemical elements to be aggregates of uniform primitive matter, he saw - no more theoretical difficulty in water being turned into alcohol in - the miracle at Cana, than in sugar undergoing a similar conversion - (_Essays_, v. 81). The credibility of miracles with Huxley is a - question of evidence. It may be remarked that a scientific explanation - is destructive of the supernatural character of a miracle, and that - the demand for evidence may be so framed as to preclude the - credibility of any historical event. Throughout his life theology had - a strong attraction, not without elements of repulsion, for Huxley. - The circumstances of his early training, when Paley was the "most - interesting Sunday reading allowed him when a boy" (_Life_, ii. 57), - probably had something to do with both. In 1860 his beliefs were - apparently theistic: "Science seems to me to teach in the highest and - strongest manner the great truth which is embodied in the Christian - conception of entire surrender to the will of God" (_Life_, i. 219). - In 1885 he formulates "the perfect ideal of religion" in a passage - which has become almost famous: "In the 8th century B.C. in the heart - of a world of idolatrous polytheists, the Hebrew prophets put forth a - conception of religion which appears to be as wonderful an inspiration - of genius as the art of Pheidias or the science of Aristotle. 'And - what doth the Lord require of thee, but to do justly, and to love - mercy, and to walk humbly with thy God'" (_Essays_, iv. 161). Two - years later he was writing: "That there is no evidence of the - existence of such a being as the God of the theologians is true - enough" (_Life_, ii. 162). He insisted, however, that "atheism is on - purely philosophical grounds untenable" (l.c.). His theism never - really advanced beyond the recognition of "the passionless - impersonality of the unknown and unknowable, which science shows - everywhere underlying the thin veil of phenomena" (_Life_, i. 239). In - other respects his personal creed was a kind of scientific Calvinism. - There is an interesting passage in an essay written in 1892, "An - Apologetic Eirenicon," which has not been republished, which - illustrates this: "It is the secret of the superiority of the best - theological teachers to the majority of their opponents that they - substantially recognize these realities of things, however strange the - forms in which they clothe their conceptions. The doctrines of - predestination, of original sin, of the innate depravity of man and - the evil fate of the greater part of the race, of the primacy of Satan - in this world, of the essential vileness of matter, of a malevolent - Demiurgus subordinate to a benevolent Almighty, who has only lately - revealed himself, faulty as they are, appear to me to be vastly nearer - the truth than the 'liberal' popular illusions that babies are all - born good, and that the example of a corrupt society is responsible - for their failure to remain so; that it is given to everybody to reach - the ethical ideal if he will only try; that all partial evil is - universal good, and other optimistic figments, such as that which - represents 'Providence' under the guise of a paternal philanthropist, - and bids us believe that everything will come right (according to our - notions) at last." But his "slender definite creed," R. H. Hutton, who - was associated with him in the Metaphysical Society, thought--and no - doubt rightly--in no respect "represented the cravings of his larger - nature." - - From 1880 onwards till the very end of his life, Huxley was - continuously occupied in a controversial campaign against orthodox - beliefs. As Professor W. F. R. Weldon justly said of his earlier - polemics: "They were certainly among the principal agents in winning a - larger measure of toleration for the critical examination of - fundamental beliefs, and for the free expression of honest reverent - doubt." He threw Christianity overboard bodily and with little - appreciation of its historic effect as a civilizing agency. He - thought that "the exact nature of the teachings and the convictions of - Jesus is extremely uncertain" (_Essays_, v. 348). "What we are usually - pleased to call religion nowadays is, for the most part, Hellenized - Judaism" (_Essays_, iv. 162). His final analysis of what "since the - second century, has assumed to itself the title of Orthodox - Christianity" is a "varying compound of some of the best and some of - the worst elements of Paganism and Judaism, moulded in practice by the - innate character of certain people of the Western world" (_Essays_, v. - 142). He concludes "That this Christianity is doomed to fall is, to my - mind, beyond a doubt; but its fall will neither be sudden nor speedy" - (l.c.). He did not omit, however, to do justice to "the bright side of - Christianity," and was deeply impressed with the life of Catherine of - Siena. Failing Christianity, he thought that some other "hypostasis of - men's hopes" will arise (_Essays_, v. 254). His latest speculations on - ethical problems are perhaps the least satisfactory of his writings. - In 1892 he wrote: "The moral sense is a very complex affair--dependent - in part upon associations of pleasure and pain, approbation and - disapprobation, formed by education in early youth, but in part also - on an innate sense of moral beauty and ugliness (how originated need - not be discussed), which is possessed by some people in great - strength, while some are totally devoid of it" (_Life_, ii. 305). This - is an intuitional theory, and he compares the moral with the aesthetic - sense, which he repeatedly declares to be intuitive; thus: "All the - understanding in the world will neither increase nor diminish the - force of the intuition that this is beautiful and this is ugly" - (_Essays_, ix. 80). In the Romanes Lecture delivered in 1894, in which - this passage occurs, he defines "law and morals" to be "restraints - upon the struggle for existence between men in society." It follows - that "the ethical process is in opposition to the cosmic process," to - which the struggle for existence belongs (_Essays_, ix. 31). - Apparently he thought that the moral sense in its origin was - intuitional and in its development utilitarian. "Morality commenced - with society" (_Essays_, v. 52). The "ethical process" is the "gradual - strengthening of the social bond" (_Essays_, ix. 35). "The cosmic - process has no sort of relation to moral ends" (l.c. p. 83); "of moral - purpose I see no trace in nature. That is an article of exclusive - human manufacture" (_Life_, ii. 268). The cosmic process Huxley - identified with evil, and the ethical process with good; the two are - in necessary conflict. "The reality at the bottom of the doctrine of - original sin" is the "innate tendency to self-assertion" inherited by - man from the cosmic order (_Essays_, ix. 27). "The actions we call - sinful are part and parcel of the struggle for existence" (_Life_, ii. - 282). "The prospect of attaining untroubled happiness" is "an - illusion" (_Essays_, ix. 44), and the cosmic process in the long run - will get the best of the contest, and "resume its sway" when evolution - enters on its downward course (l.c. p. 45). This approaches pure - pessimism, and though in Huxley's view the "pessimism of Schopenhauer - is a nightmare" (_Essays_, ix. 200), his own philosophy of life is not - distinguishable, and is often expressed in the same language. The - cosmic order is obviously non-moral (_Essays_, ix. 197). That it is, - as has been said, immoral is really meaningless. Pain and suffering - are affections which imply a complex nervous organization, and we are - not justified in projecting them into nature external to ourselves. - Darwin and A. R. Wallace disagreed with Huxley in seeing rather the - joyous than the suffering side of nature. Nor can it be assumed that - the descending scale of evolution will reproduce the ascent, or that - man will ever be conscious of his doom. - - As has been said, Huxley never thoroughly grasped the Darwinian - principle. He thought "transmutation may take place without - transition" (_Life_, i. 173). In other words, that evolution is - accomplished by leaps and not by the accumulation of small variations. - He recognized the "struggle for existence" but not the gradual - adjustment of the organism to its environment which is implied in - "natural selection." In highly civilized societies he thought that the - former was at an end (_Essays_, ix. 36) and had been replaced by the - "struggle for enjoyment" (l.c. p. 40). But a consideration of the - stationary population of France might have shown him that the effect - in the one case may be as restrictive as in the other. So far from - natural selection being in abeyance under modern social conditions, - "it is," as Professor Karl Pearson points out, "something we run up - against at once, almost as soon as we examine a mortality table" - (_Biometrika_, i. 76). The inevitable conclusion, whether we like it - or not, is that the future evolution of humanity is as much a part of - the cosmic process as its past history, and Huxley's attempt to shut - the door on it cannot be maintained scientifically. - - AUTHORITIES.--_Life and Letters of Thomas Henry Huxley_, by his son - Leonard Huxley (2 vols., 1900); _Scientific Memoirs of T. H. Huxley_ - (4 vols., 1898-1901); _Collected Essays_ by T. H. Huxley (9 vols., - 1898); _Thomas Henry Huxley, a Sketch of his Life and Work_, by P. - Chalmers Mitchell, M.A. (Oxon., 1900); a critical study founded on - careful research and of great value. (W. T. T.-D.) - - -FOOTNOTE: - - [1] _Nature_, lxiii. 127. - - - - -HUY (Lat. _Hoium_, and Flem. _Hoey_), a town of Belgium, on the right -bank of the Meuse, at the point where it is joined by the Hoyoux. Pop. -(1904), 14,164. It is 19 m. E. of Namur and a trifle less west of Liege. -Huy certainly dates from the 7th century, and, according to some, was -founded by the emperor Antoninus in A.D. 148. Its situation is -striking, with its grey citadel crowning a grey rock, and the fine -collegiate church (with a 13th-century gateway) of Notre Dame built -against it. The citadel is now used partly as a depot of military -equipment and partly as a prison. The ruins are still shown of the abbey -of Neumoustier founded by Peter the Hermit on his return from the first -crusade. He was buried there in 1115, and a statue was erected to his -memory in the abbey grounds in 1858. Neumoustier was one of seventeen -abbeys in this town alone dependent on the bishopric of Liege. Huy is -surrounded by vineyards, and the bridge which crosses the Meuse at this -point connects the fertile Hesbaye north of the river with the rocky and -barren Condroz south of it. - - - - -HUYGENS, CHRISTIAAN (1629-1695), Dutch mathematician, mechanician, -astronomer and physicist, was born at the Hague on the 14th of April -1629. He was the second son of Sir Constantijn Huygens. From his father -he received the rudiments of his education, which was continued at -Leiden under A. Vinnius and F. van Schooten, and completed in the -juridical school of Breda. His mathematical bent, however, soon diverted -him from legal studies, and the perusal of some of his earliest theorems -enabled Descartes to predict his future greatness. In 1649 he -accompanied the mission of Henry, count of Nassau, to Denmark, and in -1651 entered the lists of science as an assailant of the unsound system -of quadratures adopted by Gregory of St Vincent. This first essay -(_Exetasis quadraturae circuli_, Leiden, 1651) was quickly succeeded by -his _Theoremata de quadratura hyperboles, ellipsis, et circuli_; while, -in a treatise entitled _De circuli magnitudine inventa_, he made, three -years later, the closest approximation so far obtained to the ratio of -the circumference to the diameter of a circle. - -Another class of subjects was now to engage his attention. The -improvement of the telescope was justly regarded as a _sine qua non_ for -the advancement of astronomical knowledge. But the difficulties -interposed by spherical and chromatic aberration had arrested progress -in that direction until, in 1655, Huygens, working with his brother -Constantijn, hit upon a new method of grinding and polishing lenses. The -immediate results of the clearer definition obtained were the detection -of a satellite to Saturn (the sixth in order of distance from its -primary), and the resolution into their true form of the abnormal -appendages to that planet. Each discovery in turn was, according to the -prevailing custom, announced to the learned world under the veil of an -anagram--removed, in the case of the first, by the publication, early in -1656, of the little tract _De Saturni luna observatio nova_; but -retained, as regards the second, until 1659, when in the _Systema -Saturnium_ the varying appearances of the so-called "triple planet" were -clearly explained as the phases of a ring inclined at an angle of 28 deg. to -the ecliptic. Huygens was also in 1656 the first effective observer of -the Orion nebula; he delineated the bright region still known by his -name, and detected the multiple character of its nuclear star. His -application of the pendulum to regulate the movement of clocks sprang -from his experience of the need for an exact measure of time in -observing the heavens. The invention dates from 1656; on the 16th of -June 1657 Huygens presented his first "pendulum-clock" to the -states-general; and the _Horologium_, containing a description of the -requisite mechanism, was published in 1658. - -His reputation now became cosmopolitan. As early as 1655 the university -of Angers had distinguished him with an honorary degree of doctor of -laws. In 1663, on the occasion of his second visit to England, he was -elected a fellow of the Royal Society, and imparted to that body in -January 1669 a clear and concise statement of the laws governing the -collision of elastic bodies. Although these conclusions were arrived at -independently, and, as it would seem, several years previous to their -publication, they were in great measure anticipated by the -communications on the same subject of John Wallis and Christopher Wren, -made respectively in November and December 1668. - -Huygens had before this time fixed his abode in France. In 1665 Colbert -made to him on behalf of Louis XIV. an offer too tempting to be -refused, and between the following year and 1681 his residence in the -philosophic seclusion of the Bibliotheque du Roi was only interrupted by -two short visits to his native country. His _magnum opus_ dates from -this period. The _Horologium oscillatorium_, published with a dedication -to his royal patron in 1673, contained original discoveries sufficient -to have furnished materials for half a dozen striking disquisitions. His -solution of the celebrated problem of the "centre of oscillation" formed -in itself an important event in the history of mechanics. Assuming as an -axiom that the centre of gravity of any number of interdependent bodies -cannot rise higher than the point from which it fell, he arrived, by -anticipating in the particular case the general principle of the -conservation of _vis viva_, at correct although not strictly -demonstrated conclusions. His treatment of the subject was the first -successful attempt to deal with the dynamics of a system. The -determination of the true relation between the length of a pendulum and -the time of its oscillation; the invention of the theory of evolutes; -the discovery, hence ensuing, that the cycloid is its own evolute, and -is strictly isochronous; the ingenious although practically inoperative -idea of correcting the "circular error" of the pendulum by applying -cycloidal cheeks to clocks--were all contained in this remarkable -treatise. The theorems on the composition of forces in circular motion -with which it concluded formed the true prelude to Newton's _Principia_, -and would alone suffice to establish the claim of Huygens to the highest -rank among mechanical inventors. - -In 1681 he finally severed his French connexions, and returned to -Holland. The harsher measures which about that time began to be adopted -towards his co-religionists in France are usually assigned as the motive -of this step. He now devoted himself during six years to the production -of lenses of enormous focal distance, which, mounted on high poles, and -connected with the eye-piece by means of a cord, formed what were called -"aerial telescopes." Three of his object-glasses, of respectively 123, -180 and 210 ft. focal length, are in the possession of the Royal -Society. He also succeeded in constructing an almost perfectly -achromatic eye-piece, still known by his name. But his researches in -physical optics constitute his chief title-deed to immortality. Although -Robert Hooke in 1668 and Ignace Pardies in 1672 had adopted a vibratory -hypothesis of light, the conception was a mere floating possibility -until Huygens provided it with a sure foundation. His powerful -scientific imagination enabled him to realize that all the points of a -wave-front originate partial waves, the aggregate effect of which is to -reconstitute the primary disturbance at the subsequent stages of its -advance, thus accomplishing its propagation; so that each primary -undulation is the envelope of an indefinite number of secondary -undulations. This resolution of the original wave is the well-known -"Principle of Huygens," and by its means he was enabled to prove the -fundamental laws of optics, and to assign the correct construction for -the direction of the extraordinary ray in uniaxial crystals. These -investigations, together with his discovery of the "wonderful -phenomenon" of polarization, are recorded in his _Traite de la lumiere_, -published at Leiden in 1690, but composed in 1678. In the appended -treatise _Sur la Cause de la pesanteur_, he rejected gravitation as a -universal quality of matter, although admitting the Newtonian theory of -the planetary revolutions. From his views on centrifugal force he -deduced the oblate figure of the earth, estimating its compression, -however, at little more than one-half its actual amount. - -Huygens never married. He died at the Hague on the 8th of June 1695, -bequeathing his manuscripts to the university of Leiden, and his -considerable property to the sons of his younger brother. In character -he was as estimable as he was brilliant in intellect. Although, like -most men of strong originative power, he assimilated with difficulty the -ideas of others, his tardiness sprang rather from inability to depart -from the track of his own methods than from reluctance to acknowledge -the merits of his competitors. - - In addition to the works already mentioned, his _Cosmotheoros_--a - speculation concerning the inhabitants of the planets--was - printed posthumously at the Hague in 1698, and appeared almost - simultaneously in an English translation. A volume entitled _Opera - posthuma_ (Leiden, 1703) contained his "Dioptrica," in which the ratio - between the respective focal lengths of object-glass and eye-glass is - given as the measure of magnifying power, together with the shorter - essays _De vitris figurandis_, _De corona et parheliis_, &c. An early - tract _De ratiociniis in ludo aleae_, printed in 1657 with Schooten's - _Exercitationes mathematicae_, is notable as one of the first formal - treatises on the theory of probabilities; nor should his - investigations of the properties of the cissoid, logarithmic and - catenary curves be left unnoticed. His invention of the spiral - watch-spring was explained in the _Journal des savants_ (Feb. 25, - 1675). An edition of his works was published by G. J.'s Gravesande, in - four quarto volumes entitled _Opera varia_ (Leiden, 1724) and _Opera - reliqua_ (Amsterdam, 1728). His scientific correspondence was edited - by P. J. Uylenbroek from manuscripts preserved at Leiden, with the - title _Christiani Hugenii aliorumque seculi XVII. virorum celebrium - exercitationes mathematicae et philosophicae_ (the Hague, 1833). - - The publication of a monumental edition of the letters and works of - Huygens was undertaken at the Hague by the _Societe Hollandaise des - Sciences_, with the heading _Oeuvres de Christian Huygens_ (1888), - &c. Ten quarto volumes, comprising the whole of his correspondence, - had already been issued in 1905. A biography of Huygens was prefixed - to his _Opera varia_ (1724); his _Eloge_ in the character of a French - academician was printed by J. A. N. Condorcet in 1773. Consult - further: P. J. Uylenbroek, _Oratio de fratribus Christiano atque - Constantino Hugenio_ (Groningen, 1838); P. Harting, _Christiaan - Huygens in zijn Leven en Werken geschetzt_ (Groningen, 1868); J. B. J. - Delambre, _Hist. de l'astronomie moderne_ (ii. 549); J. E. Montucla, - _Hist. des mathematiques_ (ii. 84, 412, 549); M. Chasles, _Apercu - historique sur l'origine des methodes en geometrie_, pp. 101-109; E. - Duhring, _Kritische Geschichte der allgemeinen Principien der - Mechanik_, Abschnitt (ii. 120, 163, iii. 227); A. Berry, _A Short - History of Astronomy_, p. 200; R. Wolf, _Geschichte der Astronomie_, - passim; Houzeau, _Bibliographie astronomique_ (ii. 169); F. Kaiser, - _Astr. Nach._ (xxv. 245, 1847); _Tijdschrift voor de Wetenschappen_ - (i. 7, 1848); _Allgemeine deutsche Biographie_ (M. B. Cantor); J. C. - Poggendorff, _Biog. lit. Handworterbuch_. (A. M. C.) - - - - -HUYGENS, SIR CONSTANTIJN (1596-1687), Dutch poet and diplomatist, was -born at the Hague on the 4th of September 1596. His father, Christiaan -Huygens, was secretary to the state council, and a man of great -political importance. At the baptism of the child, the city of Breda was -one of his sponsors, and the admiral Justinus van Nassau the other. He -was trained in every polite accomplishment, and before he was seven -could speak French with fluency. He was taught Latin by Johannes -Dedelus, and soon became a master of classic versification. He developed -not only extraordinary intellectual gifts but great physical beauty and -strength, and was one of the most accomplished athletes and gymnasts of -his age; his skill in playing the lute and in the arts of painting and -engraving attracted general attention before he began to develop his -genius as a writer. In 1616 he proceeded, with his elder brother, to the -university of Leiden. He stayed there only one year, and in 1618 went to -London with the English ambassador Dudley Carleton; he remained in -London for some months, and then went to Oxford, where he studied for -some time in the Bodleian Library, and to Woodstock, Windsor and -Cambridge; he was introduced at the English court, and played the lute -before James I. The most interesting feature of this visit was the -intimacy which sprang up between the young Dutch poet and Dr Donne, for -whose genius Huygens preserved through life an unbounded admiration. He -returned to Holland in company with the English contingent of the synod -of Dort, and in 1619 he proceeded to Venice in the diplomatic service of -his country; on his return he nearly lost his life by a foolhardy -exploit, namely, the scaling of the topmost spire of Strassburg -cathedral. In 1621 he published one of his most weighty and popular -poems, his _Batava Tempe_, and in the same year he proceeded again to -London, as secretary to the ambassador, Wijngaerdan, but returned in -three months. His third diplomatic visit to England lasted longer, from -the 5th of December 1621 to the 1st of March 1623. During his absence, -his volume of satires, _'t Costelick Mal_, dedicated to Jacob Cats, -appeared at the Hague. In the autumn of 1622 he was knighted by James I. -He published a large volume of miscellaneous poems in 1625 under the -title of _Otiorum libri sex_; and in the same year he was appointed -private secretary to the stadholder. In 1627 Huygens married Susanna -van Baerle, and settled at the Hague; four sons and a daughter were born -to them. In 1630 Huygens was called to a seat in the privy council, and -he continued to exercise political power with wisdom and vigour for many -years, under the title of the lord of Zuylichem. In 1634 he is supposed -to have completed his long-talked-of version of the poems of Donne, -fragments of which exist. In 1637 his wife died, and he immediately -began to celebrate the virtues and pleasures of their married life in -the remarkable didactic poem called _Dagwerck_, which was not published -till long afterwards. From 1639 to 1641 he occupied himself by building -a magnificent house and garden outside the Hague, and by celebrating -their beauties in a poem entitled _Hofwijck_, which was published in -1653. In 1647 he wrote his beautiful poem of _Oogentroost_ or "Eye -Consolation," to gratify his blind friend Lucretia van Trollo. He made -his solitary effort in the dramatic line in 1657, when he brought out -his comedy of _Trijntje Cornelis Klacht_, which deals, in rather broad -humour, with the adventures of the wife of a ship's captain at Zaandam. -In 1658 he rearranged his poems, and issued them with many additions, -under the title of _Corn Flowers_. He proposed to the government that -the present highway from the Hague to the sea at Scheveningen should be -constructed, and during his absence on a diplomatic mission to the -French court in 1666 the road was made as a compliment to the venerable -statesman, who expressed his gratitude in a descriptive poem entitled -_Zeestraet_. Huygens edited his poems for the last time in 1672, and -died in his ninety-first year, on the 28th of March 1687. He was buried, -with the pomp of a national funeral, in the church of St Jacob, on the -4th of April. His second son, Christiaan, the eminent astronomer, is -noticed separately. - - Constantijn Huygens is the most brilliant figure in Dutch literary - history. Other statesmen surpassed him in political influence, and at - least two other poets surpassed him in the value and originality of - their writings. But his figure was more dignified and splendid, his - talents were more varied, and his general accomplishments more - remarkable than those of any other person of his age, the greatest age - in the history of the Netherlands. Huygens is the _grand seigneur_ of - the republic, the type of aristocratic oligarchy, the jewel and - ornament of Dutch liberty. When we consider his imposing character and - the positive value of his writings, we may well be surprised that he - has not found a modern editor. It is a disgrace to Dutch scholarship - that no complete collection of the writings of Huygens exists. His - autobiography, _De vita propria sermonum libri duo_, did not see the - light until 1817, and his remarkable poem, _Cluyswerck_, was not - printed until 1841. As a poet Huygens shows a finer sense of form than - any other early Dutch writer; the language, in his hands, becomes as - flexible as Italian. His epistles and lighter pieces, in particular, - display his metrical ease and facility to perfection. (E. G.) - - - - -HUYSMANS, the name of four Flemish painters who matriculated in the -Antwerp gild in the 17th century. Cornelis the elder, apprenticed in -1633, passed for a mastership in 1636, and remained obscure. Jacob, -apprenticed to Frans Wouters in 1650, wandered to England towards the -close of the reign of Charles II., and competed with Lely as a -fashionable portrait painter. He executed a portrait of the queen, -Catherine of Braganza, now in the national portrait gallery, and Horace -Walpole assigns to him the likeness of Lady Bellasys, catalogued at -Hampton Court as a work of Lely. His portrait of Izaak Walton in the -National Gallery shows a disposition to imitate the styles of Rubens and -Van Dyke. According to most accounts he died in London in 1696. Jan -Baptist Huysmans, born at Antwerp in 1654, matriculated in 1676-1677, -and died there in 1715-1716. He was younger brother to Cornelis Huysmans -the second, who was born at Antwerp in 1648, and educated by Gaspar de -Wit and Jacob van Artois. Of Jan Baptist little or nothing has been -preserved, except that he registered numerous apprentices at Antwerp, -and painted a landscape dated 1697 now in the Brussels museum. Cornelis -the second is the only master of the name of Huysmans whose talent was -largely acknowledged. He received lessons from two artists, one of whom -was familiar with the Roman art of the Poussins, whilst the other -inherited the scenic style of the school of Rubens. He combined the two -in a rich, highly coloured, and usually effective style, which, however, -was not free from monotony. Seldom attempting anything but woodside -views with fancy backgrounds, half Italian, half Flemish, he painted -with great facility, and left numerous examples behind. At the outset of -his career he practised at Malines, where he married in 1682, and there -too he entered into some business connexion with van der Meulen, for -whom he painted some backgrounds. In 1706 he withdrew to Antwerp, where -he resided till 1717, returning then to Malines, where he died on the -1st of June 1727. - - Though most of his pictures were composed for cabinets rather than - churches, he sometimes emulated van Artois in the production of large - sacred pieces, and for many years his "Christ on the Road to Emmaus" - adorned the choir of Notre Dame of Malines. In the gallery of Nantes, - where three of his small landscapes are preserved, there hangs an - "Investment of Luxembourg," by van der Meulen, of which he is known to - have laid in the background. The national galleries of London and - Edinburgh contain each one example of his skill. Blenheim, too, and - other private galleries in England, possess one or more of his - pictures. But most of his works are on the European continent. - - - - -HUYSMANS, JORIS KARL (1848-1907), French novelist, was born at Paris on -the 5th of February 1848. He belonged to a family of artists of Dutch -extraction; he entered the ministry of the interior, and was pensioned -after thirty years' service. His earliest venture in literature, _Le -Drageoir a epices_ (1874), contained stories and short prose poems -showing the influence of Baudelaire. _Marthe_ (1876), the life of a -courtesan, was published in Brussels, and Huysmans contributed a story, -"Sac au dos," to _Les Soirees de Medan_, the collection of stories of -the Franco-German war published by Zola. He then produced a series of -novels of everyday life, including _Les Soeurs Vatard_ (1879), _En -Menage_ (1881), and _A vau-l'eau_ (1882), in which he outdid Zola in -minute and uncompromising realism. He was influenced, however, more -directly by Flaubert and the brothers de Goncourt than by Zola. In -_L'Art moderne_ (1883) he gave a careful study of impressionism and in -_Certains_ (1889) a series of studies of contemporary artists, _A -Rebours_ (1884), the history of the morbid tastes of a decadent -aristocrat, des Esseintes, created a literary sensation, its caricature -of literary and artistic symbolism covering much of the real beliefs of -the leaders of the aesthetic revolt. In _La-Bas_ Huysmans's most -characteristic hero, Durtal, makes his appearance. Durtal is occupied in -writing the life of Gilles de Rais; the insight he gains into Satanism -is supplemented by modern Parisian students of the black art; but -already there are signs of a leaning to religion in the sympathetic -figures of the religious bell-ringer of Saint Sulpice and his wife. _En -Route_ (1895) relates the strange conversion of Durtal to mysticism and -Catholicism in his retreat to La Trappe. In _La Cathedrale_ (1898), -Huysmans's symbolistic interpretation of the cathedral of Chartres, he -develops his enthusiasm for the purity of Catholic ritual. The life of -_Sainte Lydwine de Schiedam_ (1901), an exposition of the value of -suffering, gives further proof of his conversion; and _L'Oblat_ (1903) -describes Durtal's retreat to the Val des Saints, where he is attached -as an oblate to a Benedictine monastery. Huysmans was nominated by -Edmond de Goncourt as a member of the Academie des Goncourt. He died as -a devout Catholic, after a long illness of cancer in the palate on the -13th of May 1907. Before his death he destroyed his unpublished MSS. His -last book was _Les Foules de Lourdes_ (1906). - - See Arthur Symons, _Studies in two Literatures_ (1897) and _The - Symbolist Movement in Literature_ (1899); Jean Lionnet in _L'Evolution - des idees_ (1903); Eugene Gilbert in _France et Belgique_ (1905); J. - Sargeret in _Les Grands convertis_ (1906). - - - - -HUYSUM, JAN VAN (1682-1749), Dutch painter, was born at Amsterdam in -1682, and died in his native city on the 8th of February 1749. He was -the son of Justus van Huysum, who is said to have been expeditious in -decorating doorways, screens and vases. A picture by this artist is -preserved in the gallery of Brunswick, representing Orpheus and the -Beasts in a wooded landscape, and here we have some explanation of his -son's fondness for landscapes of a conventional and Arcadian kind; for -Jan van Huysum, though skilled as a painter of still life, believed -himself to possess the genius of a landscape painter. Half his pictures -in public galleries are landscapes, views of imaginary lakes and -harbours with impossible ruins and classic edifices, and woods of tall -and motionless trees--the whole very glossy and smooth, and entirely -lifeless. The earliest dated work of this kind is that of 1717, in the -Louvre, a grove with maidens culling flowers near a tomb, ruins of a -portico, and a distant palace on the shores of a lake bounded by -mountains. - -It is doubtful whether any artist ever surpassed van Huysum in -representing fruit and flowers. It has been said that his fruit has no -savour and his flowers have no perfume--in other words, that they are -hard and artificial--but this is scarcely true. In substance fruit and -flower are delicate and finished imitations of nature in its more subtle -varieties of matter. The fruit has an incomparable blush of down, the -flowers have a perfect delicacy of tissue. Van Huysum, too, shows -supreme art in relieving flowers of various colours against each other, -and often against a light and transparent background. He is always -bright, sometimes even gaudy. Great taste and much grace and elegance -are apparent in the arrangement of bouquets and fruit in vases adorned -with bas reliefs or in baskets on marble tables. There is exquisite and -faultless finish everywhere. But what van Huysum has not is the breadth, -the bold effectiveness, and the depth of thought of de Heem, from whom -he descends through Abraham Mignon. - - Some of the finest of van Huysum's fruit and flower pieces have been - in English private collections: those of 1723 in the earl of - Ellesmere's gallery, others of 1730-1732 in the collections of Hope - and Ashburton. One of the best examples is now in the National Gallery - (1736-1737). No public museum has finer and more numerous specimens - than the Louvre, which boasts of four landscapes and six panels with - still life; then come Berlin and Amsterdam with four fruit and flower - pieces; then St Petersburg, Munich, Hanover, Dresden, the Hague, - Brunswick, Vienna, Carlsruhe and Copenhagen. - - - - -HWANG HO [HOANG HO], the second largest river in China. It is known to -foreigners as the Yellow river--a name which is a literal translation of -the Chinese. It rises among the Kuenlun mountains in central Asia, its -head-waters being in close proximity to those of the Yangtsze-Kiang. It -has a total length of about 2400 m. and drains an area of approximately -400,000 sq. m. The main stream has its source in two lakes named -Tsaring-nor and Oring-nor, lying about 35 deg. N., 97 deg. E., and after flowing -with a south-easterly course it bends sharply to the north-west and -north, entering China in the province of Kansuh in lat. 36 deg. After -passing Lanchow-fu, the capital of this province, the river takes an -immense sweep to the north and north-east, until it encounters the -rugged barrier ranges that here run north and south through the -provinces of Shansi and Chihli. By these ranges it is forced due south -for 500 m., forming the boundary between the provinces of Shansi and -Shensi, until it finds an outlet eastwards at Tung Kwan--a pass which -for centuries has been renowned as the gate of Asia, being indeed the -sole commercial passage between central China and the West. At Tung Kwan -the river is joined by its only considerable affluent in China proper, -the Wei (Wei-ho), which drains the large province of Shensi, and the -combined volume of water continues its way at first east and then -north-east across the great plain to the sea. At low water in the winter -season the discharge is only about 36,000 cub. ft. per second, whereas -during the summer flood it reaches 116,000 ft. or more. The amount of -sediment carried down is very large, though no accurate observations -have been made. In the account of Lord Macartney's embassy, which -crossed the Yellow river in 1792, it was calculated to be 17,520 million -cub. ft. a year, but this is considered very much over the mark. Two -reasons, however, combine to render it probable that the sedimentary -matter is very large in proportion to the volume of water: the first -being the great fall, and the consequently rapid current over two-thirds -of the river's course; the second that the drainage area is nearly all -covered with deposits of loess, which, being very friable, readily gives -way before the rainfall and is washed down in large quantity. The -ubiquity of this loess or yellow earth, as the Chinese call it, has in -fact given its name both to the river which carries it in solution and -to the sea (the Yellow Sea) into which it is discharged. It is -calculated by Dr Guppy (_Journal of China Branch of Royal Asiatic -Society_, vol. xvi.) that the sediment brought down by the three -northern rivers of China, viz., the Yangtsze, the Hwang-ho and the -Peiho, is 24,000 million cub. ft. per annum, and is sufficient to fill -up the whole of the Yellow Sea and the Gulf of Pechili in the space of -about 36,000 years. - - Unlike the Yangtsze, the Hwang-ho is of no practical value for - navigation. The silt and sand form banks and bars at the mouth, the - water is too shallow in winter and the current is too strong in - summer, and, further, the bed of the river is continually shifting. It - is this last feature which has earned for the river the name "China's - sorrow." As the silt-laden waters debouch from the rocky bed of the - upper reaches on to the plains, the current slackens, and the coarser - detritus settles on the bottom. By degrees the bed rises, and the - people build embankments to prevent the river from overflowing. As the - bed rises the embankments must be raised too, until the stream is - flowing many feet above the level of the surrounding country. As time - goes on the situation becomes more and more dangerous; finally, a - breach occurs, and the whole river pours over the country, carrying - destruction and ruin with it. If the breach cannot be repaired the - river leaves its old channel entirely and finds a new exit to the sea - along the line of least resistance. Such in brief has been the story - of the river since the dawn of Chinese history. At various times it - has discharged its waters alternately on one side or the other of the - great mass of mountains forming the promontory of Shantung, and by - mouths as far apart from each other as 500 m. At each change it has - worked havoc and disaster by covering the cultivated fields with 2 or - 3 ft. of sand and mud. - - A great change in the river's course occurred in 1851, when a breach - was made in the north embankment near Kaifengfu in Honan. At this - point the river bed was some 25 ft. above the plain; the water - consequently forsook the old channel entirely and poured over the - level country, finally seizing on the bed of a small river called the - Tsing, and thereby finding an exit to the sea. Since that time the new - channel thus carved out has remained the proper course of the river, - the old or southerly channel being left quite dry. It required some - fifteen or more years to repair damages from this outbreak, and to - confine the stream by new embankments. After that there was for a time - comparative immunity from inundations, but in 1882 fresh outbursts - again began. The most serious of all took place in 1887, when it - appeared probable that there would be again a permanent change in the - river's course. By dint of great exertions, however, the government - succeeded in closing the breach, though not till January 1889, and not - until there had been immense destruction of life and property. The - outbreak on this occasion occurred, as all the more serious outbreaks - have done, in Honan, a few miles west of the city of Kaifengfu. The - stream poured itself over the level and fertile country to the - southwards, sweeping whole villages before it, and converting the - plain into one vast lake. The area affected was not less than 50,000 - sq. m. and the loss of life was computed at over one million. Since - 1887 there have been a series of smaller outbreaks, mostly at points - lower down and in the neighbourhood of Chinanfu, the capital of - Shantung. These perpetually occurring disasters entail a heavy expense - on the government; and from the mere pecuniary point of view it would - well repay them to call in the best foreign engineering skill - available, an expedient, however, which has not commended itself to - the Chinese authorities. (G. J.) - - - - -HWICCE, one of the kingdoms of Anglo-Saxon Britain. Its exact dimensions -are unknown; they probably coincided with those of the old diocese of -Worcester, the early bishops of which bore the title "Episcopus -Hwicciorum." It would therefore include Worcestershire, Gloucestershire -except the Forest of Dean, the southern half of Warwickshire, and the -neighbourhood of Bath. The name Hwicce survives in Wychwood in -Oxfordshire and Whichford in Warwickshire. These districts, or at all -events the southern portion of them, were according to the _Anglo-Saxon -Chronicle_, _s.a._ 577, originally conquered by the West Saxons under -Ceawlin. In later times, however, the kingdom of the Hwicce appears to -have been always subject to Mercian supremacy, and possibly it was -separated from Wessex in the time of Edwin. The first kings of whom we -read were two brothers, Eanhere and Eanfrith, probably contemporaries of -Wulfhere. They were followed by a king named Osric, a contemporary of -Aethelred, and he by a king Oshere. Oshere had three sons who reigned -after him, Aethelheard, Aethelweard and Aethelric. The two last named -appear to have been reigning in the year 706. At the beginning of Offa's -reign we again find the kingdom ruled by three brothers, named Eanberht, -Uhtred and Aldred, the two latter of whom lived until about 780. After -them the title of king seems to have been given up. Their successor -Aethelmund, who was killed in a campaign against Wessex in 802, is -described only as an earl. The district remained in possession of the -rulers of Mercia until the fall of that kingdom. Together with the rest -of English Mercia it submitted to King Alfred about 877-883 under Earl -Aethelred, who possibly himself belonged to the Hwicce. No genealogy or -list of kings has been preserved, and we do not know whether the dynasty -was connected with that of Wessex or Mercia. - - See Bede, _Historia eccles._ (edited by C. Plummer) iv. 13 (Oxford, - 1896); W. de G. Birch, _Cartularium Saxonicum_, 43, 51, 76, 85, 116, - 117, 122, 163, 187, 232, 233, 238 (Oxford, 1885-1889). - (F. G. M. B.) - - - - -HYACINTH (Gr. hyakinthos), also called JACINTH (through Ital. -_giacinto_), one of the most popular of spring garden flowers. It was in -cultivation prior to 1597, at which date it is mentioned by Gerard. Rea -in 1665 mentions several single and double varieties as being then in -English gardens, and Justice in 1754 describes upwards of fifty -single-flowered varieties, and nearly one hundred double-flowered ones, -as a selection of the best from the catalogues of two then celebrated -Dutch growers. One of the Dutch sorts, called La Reine de Femmes, a -single white, is said to have produced from thirty-four to thirty-eight -flowers in a spike, and on its first appearance to have sold for 50 -guilders a bulb; while one called Overwinnaar, or Conqueror, a double -blue, sold at first for 100 guilders, Gloria Mundi for 500 guilders, and -Koning Saloman for 600 guilders. Several sorts are at that date -mentioned as blooming well in water-glasses. Justice relates that he -himself raised several very valuable double-flowered kinds from seeds, -which many of the sorts he describes are noted for producing freely. - -The original of the cultivated hyacinth, _Hyacinthus orientalis_, a -native of Greece and Asia Minor, is by comparison an insignificant -plant, bearing on a spike only a few small, narrow-lobed, washy blue -flowers, resembling in form those of our common blue-bell. So great has -been the improvement effected by the florists, and chiefly by the Dutch, -that the modern hyacinth would scarcely be recognized as the descendant -of the type above referred to, the spikes being long and dense, composed -of a large number of flowers; the spikes produced by strong bulbs not -unfrequently measure 6 to 9 in. in length and from 7 to 9 in. in -circumference, with the flowers closely set on from bottom to top. Of -late years much improvement has been effected in the size of the -individual flowers and the breadth of their recurving lobes, as well as -in securing increased brilliancy and depth of colour. - -The peculiarities of the soil and climate of Holland are so very -favourable to their production that Dutch florists have made a specialty -of the growth of those and other bulbous-rooted flowers. Hundreds of -acres are devoted to the growth of hyacinths in the vicinity of Haarlem, -and bring in a revenue of several hundreds of thousands of pounds. Some -notion of the vast number imported into England annually may be formed -from the fact that, for the supply of flowering plants to Covent Garden, -one market grower alone produces from 60,000 to 70,000 in pots under -glass, their blooming period being accelerated by artificial heat, and -extending from Christmas onwards until they bloom naturally in the open -ground. - -In the spring flower garden few plants make a more effective display -than the hyacinth. Dotted in clumps in the flower borders, and arranged -in masses of well-contrasted colours In beds in the flower garden, there -are no flowers which impart during their season--March and April--a -gayer tone to the parterre. The bulbs are rarely grown a second time, -either for indoor or outdoor culture, though with care they might be -utilized for the latter purpose; and hence the enormous numbers which -are procured each recurring year from Holland. - -The first hyacinths were single-flowered, but towards the close of the -17th century double-flowered ones began to appear, and till a recent -period these bulbs were the most esteemed. At the present time, however, -the single-flowered sorts are in the ascendant, as they produce more -regular and symmetrical spikes of blossom, the flowers being closely set -and more or less horizontal in direction, while most of the double sorts -have the bells distant and dependent, so that the spike is loose and by -comparison ineffective. For pot culture, and for growth in -water-glasses especially, the single-flowered sorts are greatly to be -preferred. Few if any of the original kinds are now in cultivation, a -succession of new and improved varieties having been raised, the demand -for which is regulated in some respects by fashion. - - The hyacinth delights in a rich light sandy soil. The Dutch - incorporate freely with their naturally light soil a compost - consisting of one-third coarse sea or river sand, one-third rotten cow - dung without litter and one-third leaf-mould. The soil thus renovated - retains its qualities for six or seven years, but hyacinths are not - planted upon the same place for two years successively, intermediary - crops of narcissus, crocus or tulips being taken. A good compost for - hyacinths is sandy loam, decayed leaf-mould, rotten cow dung and sharp - sand in equal parts, the whole being collected and laid up in a heap - and turned over occasionally. Well-drained beds made up of this soil, - and refreshed with a portion of new compost annually, would grow the - hyacinth to perfection. The best time to plant the bulbs is towards - the end of September and during October; they should be arranged in - rows, 6 to 8 in. asunder, there being four rows in each bed. The bulbs - should be sunk about 4 to 6 in. deep, with a small quantity of clean - sand placed below and around each of them. The beds should be covered - with decayed tan-bark, coco-nut fibre or half-rotten dung litter. As - the flower-stems appear, they are tied to rigid but slender stakes to - preserve them from accident. If the bulbs are at all prized, the stems - should be broken off as soon as the flowering is over, so as not to - exhaust the bulbs; the leaves, however, must be allowed to grow on - till matured, but as soon as they assume a yellow colour, the bulbs - are taken up, the leaves cut off near their base, and the bulbs laid - out in a dry, airy, shady place to ripen, after which they are cleaned - of loose earth and skin, ready for storing. It is the practice in - Holland, about a month after the bloom, or when the tips of the leaves - assume a withered appearance, to take up the bulbs, and to lay them - sideways on the ground, covering them with an inch or two of earth. - About three weeks later they are again taken up and cleaned. In the - store-room they should be kept dry, well-aired and apart from each - other. - - Few plants are better adapted than the hyacinth for pot culture as - greenhouse decorative plants; and by the aid of forcing they may be - had in bloom as early as Christmas. They flower fairly well in 5-in. - pots, the stronger bulbs in 6-in. pots. To bloom at Christmas, they - should be potted early in September, in a compost resembling that - already recommended for the open-air beds; and, to keep up a - succession of bloom, others should be potted at intervals of a few - weeks till the middle or end of November. The tops of the bulbs should - be about level with the soil, and if a little sand is put immediately - around them so much the better. The pots should be set in an open - place on a dry hard bed of ashes, and be covered over to a depth of 6 - or 8 in. with the same material or with fibre or soil; and when the - roots are well developed, which will take from six to eight weeks, - they may be removed to a frame, and gradually exposed to light, and - then placed in a forcing pit in a heat of from 60 to 70 deg. When the - flowers are fairly open, they may be removed to the greenhouse or - conservatory. - - The hyacinth may be very successfully grown in glasses for ornament in - dwelling-houses. The glasses are filled to the neck with rain or even - tap water, a few lumps of charcoal being dropped into them. The bulbs - are placed in the hollow provided for them, so that their base just - touches the water. This may be done in September or October. They are - then set in a dark cupboard for a few weeks till roots are freely - produced, and then gradually exposed to light. The early-flowering - single white Roman hyacinth, a small-growing pure white variety, - remarkable for its fragrance, is well adapted for forcing, as it can - be had in bloom if required by November. For windows it grows well in - the small glasses commonly used for crocuses; and for decorative - purposes should be planted about five bulbs in a 5-in. pot, or in pans - holding a dozen each. If grown for cut flowers it can be planted - thickly in boxes of any convenient size. It is highly esteemed during - the winter months by florists. - - The Spanish hyacinth (_H. amethystinus_) and _H. azureus_ are charming - little bulbs for growing in masses in the rock garden or front of the - flower border. The older botanists included in the genus _Hyacinthus_ - species of _Muscari_, _Scilla_ and other genera of bulbous Liliaceae, - and the name of hyacinth is still popularly applied to several other - bulbous plants. Thus _Muscari botryoides_ is the grape hyacinth, 6 - in., blue or white, the handsomest; _M. moschatum_, the musk hyacinth, - 10 in., has peculiar livid greenish-yellow flowers and a strong musky - odour; _M. comosum_ var. _monstrosum_, the feather hyacinth, bears - sterile flowers broken up into a featherlike mass; _M. racemosum_, the - starch hyacinth, is a native with deep blue plum-scented flowers. The - Cape hyacinth is _Galtonia candicans_, a magnificent border plant, 3-4 - ft. high, with large drooping white bell-shaped flowers; the star - hyacinth, _Scilla amoena_; the Peruvian hyacinth or Cuban lily, _S. - peruviana_, a native of the Mediterranean region, to which Linnaeus - gave the species name _peruviana_ on a mistaken assumption of its - origin; the wild hyacinth or blue-bell, known variously as _Endymion - nonscriptum_, _Hyacinthus nonscriptus_ or _Scilla nutans_; the wild - hyacinth of western North America, _Camassia esculenta_. They all - flourish in good garden soil of a gritty nature. - - - - -HYACINTH, or JACINTH, in mineralogy, a variety of zircon (q.v.) of -yellowish red colour, used as a gem-stone. The _hyacinthus_ of ancient -writers must have been our sapphire, or blue corundum, while the -hyacinth of modern mineralogists may have been the stone known as -_lyncurium_ ([Greek: lynkourion]). The Hebrew word _leshem_, translated -ligure in the Authorized Version (Ex. xxviii. 19), from the [Greek: -ligyrion] of the Septuagint, appears in the Revised Version as jacinth, -but with a marginal alternative of amber. Both jacinth and amber may be -reddish yellow, but their identification is doubtful. As our jacinth -(zircon) is not known in ancient Egyptian work, Professor Flinders -Petrie has suggested that the _leshem_ may have been a yellow quartz, or -perhaps agate. Some old English writers describe the jacinth as yellow, -whilst others refer to it as a blue stone, and the _hyacinthus_ of some -authorities seems undoubtedly to have been our sapphire. In Rev. xx. 20 -the Revised Version retains the word jacinth, but gives sapphire as an -alternative. - -Most of the gems known in trade as hyacinth are only garnets--generally -the deep orange-brown hessonite or cinnamon-stone--and many of the -antique engraved stones reputed to be hyacinth are probably garnets. The -difference may be detected optically, since the garnet is singly and the -hyacinth doubly refracting; moreover the specific gravity affords a -simple means of diagnosis, that of garnet being only about 3.7, whilst -hyacinth may have a density as high as 4.7. Again, it was shown many -years ago by Sir A. H. Church that most hyacinths, when examined by the -spectroscope, show a series of dark absorption bands, due perhaps to the -presence of some rare element such as uranium or erbium. - -Hyacinth is not a common mineral. It occurs, with other zircons, in the -gem-gravels of Ceylon, and very fine stones have been found as pebbles -at Mudgee in New South Wales. Crystals of zircon, with all the typical -characters of hyacinth, occur at Expailly, Le Puy-en-Velay, in Central -France, but they are not large enough for cutting. The stones which have -been called Compostella hyacinths are simply ferruginous quartz from -Santiago de Compostella in Spain. (F. W. R.*) - - - - -HYACINTHUS,[1] in Greek mythology, the youngest son of the Spartan king -Amyclas, who reigned at Amyclae (so Pausanias iii. 1. 3, iii. 19. 5; and -Apollodorus i. 3. 3, iii. 10. 3). Other stories make him son of Oebalus, -of Eurotas, or of Pierus and the nymph Clio (see Hyginus, _Fabulae_, -271; Lucian, _De saltatione_, 45, and _Dial. deor._ 14). According to -the general story, which is probably late and composite, his great -beauty attracted the love of Apollo, who killed him accidentally when -teaching him to throw the _discus_ (quoit); others say that Zephyrus (or -Boreas) out of jealousy deflected the quoit so that it hit Hyacinthus on -the head and killed him. According to the representation on the tomb at -Amyclae (Pausanias, _loc. cit._) Hyacinthus was translated into heaven -with his virgin sister Polyboea. Out of his blood there grew the flower -known as the hyacinth, the petals of which were marked with the mournful -exclamation AI, AI, "alas" (cf. "that sanguine flower inscribed with -woe"). This Greek hyacinth cannot have been the flower which now bears -the name: it has been identified with a species of iris and with the -larkspur (_Delphinium Aiacis_), which appear to have the markings -described. The Greek hyacinth was also said to have sprung from the -blood of Ajax. Evidently the Greek authorities confused both the flowers -and the traditions. - -The death of Hyacinthus was celebrated at Amyclae by the second most -important of Spartan festivals, the Hyacinthia, which took place in the -Spartan month Hecatombeus. What month this was is not certain. Arguing -from Xenophon (_Hell._ iv. 5) we get May; assuming that the Spartan -Hecatombeus is the Attic Hecatombaion, we get July; or again it may be -the Attic Scirophorion, June. At all events the Hyacinthia was an early -summer festival. It lasted three days, and the rites gradually passed -from mourning for Hyacinthus to rejoicings in the majesty of Apollo, -the god of light and warmth, and giver of the ripe fruits of the earth -(see a passage from Polycrates, _Laconica_, quoted by Athenaeus 139 d; -criticized by L. R. Farnell, _Cults of the Greek States_, iv. 266 -foll.). This festival is clearly connected with vegetation, and marks -the passage from the youthful verdure of spring to the dry heat of -summer and the ripening of the corn. - -The precise relation which Apollo bears to Hyacinthus is obscure. The -fact that at Tarentum a Hyacinthus tomb is ascribed by Polybius to -Apollo Hyacinthus (not Hyacinthius) has led some to think that the -personalities are one, and that the hero is merely an emanation from the -god; confirmation is sought in the Apolline appellation [Greek: -tetracheir], alleged by Hesychius to have been used in Laconia, and -assumed to describe a composite figure of Apollo-Hyacinthus. Against -this theory is the essential difference between the two figures. -Hyacinthus is a chthonian vegetation god whose worshippers are afflicted -and sorrowful; Apollo, though interested in vegetation, is never -regarded as inhabiting the lower world, his death is not celebrated in -any ritual, his worship is joyous and triumphant, and finally the -Amyclean Apollo is specifically the god of war and song. Moreover, -Pausanias describes the monument at Amyclae as consisting of a rude -figure of Apollo standing on an altar-shaped base which formed the tomb -of Hyacinthus. Into the latter offerings were put for the hero before -gifts were made to the god. - -On the whole it is probable that Hyacinthus belongs originally to the -pre-Dorian period, and that his story was appropriated and woven into -their own Apollo myth by the conquering Dorians. Possibly he may be the -apotheosis of a pre-Dorian king of Amyclae. J. G. Frazer further -suggests that he may have been regarded as spending the winter months in -the underworld and returning to earth in the spring when the "hyacinth" -blooms. In this case his festival represents perhaps both the Dorian -conquest of Amyclae and the death of spring before the ardent heat of -the summer sun, typified as usual by the _discus_ (quoit) with which -Apollo is said to have slain him. With the growth of the hyacinth from -his blood should be compared the oriental stories of violets springing -from the blood of Attis, and roses and anemones from that of Adonis. As -a youthful vegetation god, Hyacinthus may be compared with Linus and -Scephrus, both of whom are connected with Apollo Agyieus. - - See L. R. Farnell, _Cults of the Greek States_, vol. iv. (1907), pp. - 125 foll., 264 foll.; J. G. Frazer, _Adonis, Attis, Osiris_ (1906), - bk. ii. ch. 7; S. Wide, _Lakonische Kulte_, p. 290; E. Rhode, - _Psyche_, 3rd ed. i. 137 foll.; Roscher, _Lexikon d. griech. u. rom. - Myth._, s.v. "Hyakinthos" (Greve); L. Preller, _Griechische Mythol._ - 4th ed. i. 248 foll. (J. M. M.) - - -FOOTNOTE: - - [1] The word is probably derived from an Indo-European root, meaning - "youthful," found in Latin, Greek, English and Sanskrit. Some have - suggested that the first two letters are from [Greek: uein], to rain, - (cf. Hyades). - - - - -HYADES ("the rainy ones"), in Greek mythology, the daughters of Atlas -and Aethra; their number varies between two and seven. As a reward for -having brought up Zeus at Dodona and taken care of the infant Dionysus -Hyes, whom they conveyed to Ino (sister of his mother Semele) at Thebes -when his life was threatened by Lycurgus, they were translated to heaven -and placed among the stars (Hyginus, _Poet. astron._ ii. 21). Another -form of the story combines them with the Pleiades. According to this -they were twelve (or fifteen) sisters, whose brother Hyas was killed by -a snake while hunting in Libya (Ovid, _Fasti_, v. 165; Hyginus, _Fab._ -192). They lamented him so bitterly that Zeus, out of compassion, -changed them into stars--five into the Hyades, at the head of the -constellation of the Bull, the remainder into the Pleiades. Their name -is derived from the fact that the rainy season commenced when they rose -at the same time as the sun (May 7-21); the original conception of them -is that of the fertilizing principle of moisture. The Romans derived the -name from [Greek: us] (pig), and translated it by _Suculae_ (Cicero, _De -nat. deorum_, ii. 43). - - - - -HYATT, ALPHEUS (1838-1902), American naturalist, was born at Washington, -D.C., on the 5th of April 1838. From 1858 to 1862 he studied at Harvard, -where he had Louis Agassiz for his master, and in 1863 he served as a -volunteer in the Civil War, attaining the rank of captain. In 1867 he -was appointed curator of the Essex Institute at Salem, and in 1870 -became professor of zoology and palaeontology at the Massachusetts -Institute of Technology (resigned 1888), and custodian of the Boston -Society of Natural History (curator in 1881). In 1886 he was appointed -assistant for palaeontology in the Cambridge museum of comparative -anatomy, and in 1889 was attached to the United States Geological Survey -as palaeontologist for the Trias and Jura. He was the chief founder of -the American Society of Naturalists, of which he acted as first -president in 1883, and he also took a leading part in establishing the -marine biological laboratories at Annisquam and Woods Hole, Mass. He -died at Cambridge on the 15th of January 1902. - - His works include _Observations on Fresh-water Polyzoa_ (1866); - _Fossil Cephalopods of the Museum of Comparative Zoology_ (1872); - _Revision of North American Porifera_ (1875-1877); _Genera of Fossil - Cephalopoda_ (1883); _Larval Theory of the Origin of Cellular Tissue_ - (1884); _Genesis of the Arietidae_ (1889); and _Phylogeny of an - acquired characteristic_ (1894). He wrote the section on Cephalopoda - in Karl von Zittel's _Palaontologie_ (1900), and his well-known study - on the fossil pond snails of Steinheim ("The Genesis of the Tertiary - Species of Planorbis at Steinheim") appeared in the _Memoirs_ of the - Boston Natural History Society in 1880. He was one of the founders and - editors of the _American Naturalist_. - - - - -HYBLA, the name of several cities In Sicily. The best known -historically, though its exact site is uncertain, is Hybla Major, near -(or by some supposed to be identical with) Megara Hyblaea (q.v.): -another Hybla, known as Hybla Minor or Galeatis, is represented by the -modern Paterno; while the site of Hybla Heraea is to be sought near -Ragusa. - - - - -HYBRIDISM. The Latin word _hybrida_, _hibrida_ or _ibrida_ has been -assumed to be derived from the Greek [Greek: hybris], an insult or -outrage, and a hybrid or mongrel has been supposed to be an outrage on -nature, an unnatural product. As a general rule animals and plants -belonging to distinct species do not produce offspring when crossed with -each other, and the term hybrid has been employed for the result of a -fertile cross between individuals of different species, the word mongrel -for the more common result of the crossing of distinct varieties. A -closer scrutiny of the facts, however, makes the term hybridism less -isolated and more vague. The words species and genus, and still more -subspecies and variety, do not correspond with clearly marked and -sharply defined zoological categories, and no exact line can be drawn -between the various kinds of crossings from those between individuals -apparently identical to those belonging to genera universally recognized -as distinct. Hybridism therefore grades into mongrelism, mongrelism into -cross-breeding, and cross-breeding into normal pairing, and we can say -little more than that the success of the union is the more unlikely or -more unnatural the further apart the parents are in natural affinity. - -The interest in hybridism was for a long time chiefly of a practical -nature, and was due to the fact that hybrids are often found to present -characters somewhat different from those of either parent. The leading -facts have been known in the case of the horse and ass from time -immemorial. The earliest recorded observation of a hybrid plant is by J. -G. Gmelin towards the end of the 17th century; the next is that of Thomas -Fairchild, who in the second decade of the 18th century, produced the -cross which is still grown in gardens under the name of "Fairchild's -Sweet William." Linnaeus made many experiments in the cross-fertilization -of plants and produced several hybrids, but Joseph Gottlieb Kolreuter -(1733-1806) laid the first real foundation of our scientific knowledge of -the subject. Later on Thomas Andrew Knight, a celebrated English -horticulturist, devoted much successful labour to the improvement of -fruit trees and vegetables by crossing. In the second quarter of the 19th -century C. F. Gartner made and published the results of a number of -experiments that had not been equalled by any earlier worker. Next came -Charles Darwin, who first in the _Origin of Species_, and later in _Cross -and Self-Fertilization of Plants_, subjected the whole question to a -critical examination, reviewed the known facts and added many to them. - - Darwin's conclusions were summed up by G. J. Romanes in the 9th - edition of this _Encyclopaedia_ as follows:-- - - 1. The laws governing the production of hybrids are identical, or - nearly identical, in the animal and vegetable kingdoms. - - 2. The sterility which so generally attends the crossing of two - specific forms is to be distinguished as of two kinds, which, although - often confounded by naturalists, are in reality quite distinct. - For the sterility may obtain between the two parent species when first - crossed, or it may first assert itself in their hybrid progeny. In the - latter case the hybrids, although possibly produced without any - appearance of infertility on the part of their parent species, - nevertheless prove more or less infertile among themselves, and also - with members of either parent species. - - 3. The degree of both kinds of infertility varies in the case of - different species, and in that of their hybrid progeny, from absolute - sterility up to complete fertility. Thus, to take the case of plants, - "when pollen from a plant of one family is placed on the stigma of a - plant of a distinct family, it exerts no more influence than so much - inorganic dust. From this absolute zero of fertility, the pollen of - different species, applied to the stigma of some one species of the - same genus, yields a perfect gradation in the number of seeds - produced, up to nearly complete, or even quite complete, fertility; - so, in hybrids themselves, there are some which never have produced, - and probably never would produce, even with the pollen of the pure - parents, a single fertile seed; but in some of these cases a first - trace of fertility may be detected, by the pollen of one of the pure - parent species causing the flower of the hybrid to wither earlier than - it otherwise would have done; and the early withering of the flower is - well known to be a sign of incipient fertilization. From this extreme - degree of sterility we have self-fertilized hybrids producing a - greater and greater number of seeds up to perfect fertility." - - 4. Although there is, as a rule, a certain parallelism, there is no - fixed relation between the degree of sterility manifested by the - parent species when crossed and that which is manifested by their - hybrid progeny. There are many cases in which two pure species can be - crossed with unusual facility, while the resulting hybrids are - remarkably sterile; and, contrariwise, there are species which can - only be crossed with extreme difficulty, though the hybrids, when - produced, are very fertile. Even within the limits of the same genus, - these two opposite cases may occur. - - 5. When two species are reciprocally crossed, i.e. male A with female - B, and male B with female A, the degree of sterility often differs - greatly in the two cases. The sterility of the resulting hybrids may - differ likewise. - - 6. The degree of sterility of first crosses and of hybrids runs, to a - certain extent, parallel with the systematic affinity of the forms - which are united. "For species belonging to distinct genera can - rarely, and those belonging to distinct families can never, be - crossed. The parallelism, however, is far from complete; for a - multitude of closely allied species will not unite, or unite with - extreme difficulty, whilst other species, widely different from each - other, can be crossed with perfect facility. Nor does the difficulty - depend on ordinary constitutional differences; for annual and - perennial plants, deciduous and evergreen trees, plants flowering at - different seasons, inhabiting different stations, and naturally living - under the most opposite climates, can often be crossed with ease. The - difficulty or facility apparently depends exclusively on the sexual - constitution of the species which are crossed, or on their sexual - elective affinity." - -There are many new records as to the production of hybrids. -Horticulturists have been extremely active and successful in their -attempts to produce new flowers or new varieties of vegetables by -seminal or graft-hybrids, and any florist's catalogue or the account of -any special plant, such as is to be found in Foster-Melliar's _Book of -the Rose_, is in great part a history of successful hybridization. Much -special experimental work has been done by botanists, notably by de -Vries, to the results of whose experiments we shall recur. Experiments -show clearly that the obtaining of hybrids is in many cases merely a -matter of taking sufficient trouble, and the successful crossing of -genera is not infrequent. - - Focke, for instance, cites cases where hybrids were obtained between - _Brassica_ and _Raphanus_, _Galium_ and _Asperula_, _Campanula_ and - _Phyteuma_, _Verbascum_ and _Celsia_. Among animals, new records and - new experiments are almost equally numerous. Boveri has crossed - _Echinus microtuberculatus_ with _Sphaerechinus granularis_. Thomas - Hunt Morgan even obtained hybrids between Asterias, a starfish, and - _Arbacia_, a sea-urchin, a cross as remote as would be that between a - fish and a mammal. Vernon got many hybrids by fertilizing the eggs of - _Strongylocentrotus lividus_ with the sperm of _Sphaerechinus - granularis_. Standfuss has carried on an enormous series of - experiments with Lepidopterous insects, and has obtained a very large - series of hybrids, of which he has kept careful record. Lepidopterists - generally begin to suspect that many curious forms offered by dealers - as new species are products got by crossing known species. Apello has - succeeded with Teleostean fish; Gebhardt and others with Amphibia. - Elliot and Suchetet have studied carefully the question of - hybridization occurring normally among birds, and have got together a - very large body of evidence. Among the cases cited by Elliot the most - striking are that of the hybrid between _Colaptes cafer_ and _C. - auratus_, which occurs over a very wide area of North America and is - known as _C. hybridus_, and the hybrid between _Euplocamus lineatus_ - and _E. horsfieldi_, which appears to be common in Assam. St M. - Podmore has produced successful crosses between the wood-pigeon - (_Columba palumbus_) and a domesticated variety of the rock pigeon - (_C. livia_). Among mammals noteworthy results have been obtained by - Professor Cossar Ewart, who has bred nine zebra hybrids by crossing - mares of various sizes with a zebra stallion, and who has studied in - addition three hybrids out of zebra mares, one sired by a donkey, the - others by ponies. Crosses have been made between the common rabbit - (_Lepus cuniculus_) and the guinea-pig (_Cavia cobaya_), and examples - of the results have been exhibited in the Zoological Gardens of - Sydney, New South Wales. The Carnivora generally are very easy to - hybridize, and many successful experiments have been made with animals - in captivity. Karl Hagenbeck of Hamburg has produced crosses between - the lion (_Felis leo_) and the tiger (_F. tigris_). What was probably - a "tri-hybrid" in which lion, leopard and jaguar were mingled was - exhibited by a London showman in 1908. Crosses between various species - of the smaller cats have been fertile on many occasions. The black - bear (_Ursus americanus_) and the European brown bear (_U. arctos_) - bred in the London Zoological Gardens in 1859, but the three cubs did - not reach maturity. Hybrids between the brown bear and the - grizzly-bear (_U. horribilis_) have been produced in Cologne, whilst - at Halle since 1874 a series of successful matings of polar (_U. - maritimus_) and brown bears have been made. Examples of these hybrid - bears have been exhibited by the London Zoological Society. The London - Zoological Society has also successfully mated several species of - antelopes, for instance, the water-bucks _Kobus ellipsiprymnus_ and - _K. unctuosus_, and Selous's antelope _Limnotragus selousi_ with _L. - gratus_. - -The causes militating against the production of hybrids have also -received considerable attention. Delage, discussing the question, states -that there is a general proportion between sexual attraction and -zoological affinity, and in many cases hybrids are not naturally -produced simply from absence of the stimulus to sexual mating, or -because of preferential mating within the species or variety. In -addition to differences of habit, temperament, time of maturity, and so -forth, gross structural differences may make mating impossible. Thus -Escherick contends that among insects the peculiar structure of the -genital appendages makes cross-impregnation impossible, and there is -reason to believe that the specific peculiarities of the modified sexual -palps in male spiders have a similar result. - - The difficulties, however, may not exist, or may be overcome by - experiment, and frequently it is only careful management that is - required to produce crossing. Thus it has been found that when the - pollen of one species does not succeed in fertilizing the ovules of - another species, yet the reciprocal cross may be successful; that is - to say, the pollen of the second species may fertilize the ovules of - the first. H. M. Vernon, working with sea-urchins, found that the - obtaining of hybrids depended on the relative maturity of the sexual - products. The difficulties in crossing apparently may extend to the - chemiotaxic processes of the actual sexual cells. Thus when the - spermatozoa of an urchin were placed in a drop of seawater containing - ripe eggs of an urchin and of a starfish, the former eggs became - surrounded by clusters of the male cells, while the latter appeared to - exert little attraction for the alien germ-cells. Finally, when the - actual impregnation of the egg is possible naturally, or has been - secured by artificial means, the development of the hybrid may stop at - an early stage. Thus hybrids between the urchin and the starfish, - animals belonging to different classes, reached only the stage of the - pluteus larva. A. D. Apello, experimenting with Teleostean fish, found - that very often impregnation and segmentation occurred, but that the - development broke down immediately afterwards. W. Gebhardt, crossing - _Rana esculenta_ with _R. arvalis_, found that the cleavage of the - ovum was normal, but that abnormality began with the gastrula, and - that development soon stopped. In a very general fashion there appears - to be a parallel between the zoological affinity and the extent to - which the incomplete development of the hybrid proceeds. - -As to the sterility of hybrids _inter se_, or with either of the parent -forms, information is still wanted. Delage, summing up the evidence in a -general way, states that mongrels are more fertile and stronger than -their parents, while hybrids are at least equally hardy but less -fertile. While many of the hybrid products of horticulturists are -certainly infertile, others appear to be indefinitely fertile. - - Focke, it is true, states that the hybrids between _Primula auricula_ - and _P. hirsuta_ are fertile for many generations, but not - indefinitely so; but, while this may be true for the particular case, - there seems no reason to doubt that many plant hybrids are quite - fertile. In the case of animals the evidence is rather against - fertility. Standfuss, who has made experiments lasting over many - years, and who has dealt with many genera of Lepidoptera, obtained no - fertile hybrid females, although he found that hybrid males paired - readily and successfully with pure-bred females of the parent races. - Elliot, dealing with birds, concluded that no hybrids were - fertile with one another beyond the second generation, but thought - that they were fertile with members of the parent races. Wallace, on - the other hand, cites from Quatrefages the case of hybrids between the - moths _Bombyx cynthia_ and _B. arrindia_, which were stated to be - fertile _inter se_ for eight generations. He also states that hybrids - between the sheep and goat have a limited fertility _inter se_. - Charles Darwin, however, had evidence that some hybrid pheasants were - completely fertile, and he himself interbred the progeny of crosses - between the common and Chinese geese, whilst there appears to be no - doubt as to the complete fertility of the crosses between many species - of ducks, J. L. Bonhote having interbred in various crosses for - several generations the mallard (_Anas boschas_), the Indian spot-bill - duck (_A. poecilorhyncha_), the New Zealand grey duck (_A. - superciliosa_) and the pin-tail (_Dafila acuta_). Podmore's pigeon - hybrids were fertile _inter se_, a specimen having been exhibited at - the London Zoological Gardens. The hybrids between the brown and polar - bears bred at Halle proved to be fertile, both with one of the parent - species and with one another. - - Cornevin and Lesbre state that in 1873 an Arab mule was fertilized in - Africa by a stallion, and gave birth to female offspring which she - suckled. All three were brought to the Jardin d'Acclimatation in - Paris, and there the mule had a second female colt to the same father, - and subsequently two male colts in succession to an ass and to a - stallion. The female progeny were fertilized, but their offspring were - feeble and died at birth. Cossar Ewart gives an account of a recent - Indian case in which a female mule gave birth to a male colt. He - points out, however, that many mistakes have been made about the - breeding of hybrids, and is not altogether inclined to accept this - supposed case. Very little has been published with regard to the most - important question, as to the actual condition of the sexual organs - and cells in hybrids. There does not appear to be gross anatomical - defect to account for the infertility of hybrids, but microscopical - examination in a large number of cases is wanted. Cossar Ewart, to - whom indeed much of the most interesting recent work on hybrids is - due, states that in male zebra-hybrids the sexual cells were immature, - the tails of the spermatozoa being much shorter than those of the - similar cells in stallions and zebras. He adds, however, that the male - hybrids he examined were young, and might not have been sexually - mature. He examined microscopically the ovary of a female zebra-hybrid - and found one large and several small Graafian follicles, in all - respects similar to those in a normal mare or female zebra. A careful - study of the sexual organs in animal and plant hybrids is very much to - be desired, but it may be said that so far as our present knowledge - goes there is not to be expected any obvious microscopical cause of - the relative infertility of hybrids. - -The relative variability of hybrids has received considerable attention -from many writers. Horticulturists, as Bateson has written, are "aware -of the great and striking variations which occur in so many orders of -plants when hybridization is effected." The phrase has been used -"breaking the constitution of a plant" to indicate the effect produced -in the offspring of a hybrid union, and the device is frequently used by -those who are seeking for novelties to introduce on the market. It may -be said generally that hybrids are variable, and that the products of -hybrids are still more variable. J. L. Bonhote found extreme variations -amongst his hybrid ducks. Y. Delage states that in reciprocal crosses -there is always a marked tendency for the offspring to resemble the male -parents; he quotes from Huxley that the mule, whose male parent is an -ass, is more like the ass, and that the hinny, whose male parent is a -horse, is more like the horse. Standfuss found among Lepidoptera that -males were produced much more often than females, and that these males -paired readily. The freshly hatched larvae closely resembled the larvae -of the female parent, but in the course of growth the resemblance to the -male increased, the extent of the final approximation to the male -depending on the relative phylogenetic age of the two parents, the -parent of the older species being prepotent. In reciprocal pairing, he -found that the male was able to transmit the characters of the parents -in a higher degree. Cossar Ewart, in relation to zebra hybrids, has -discussed the matter of resemblance to parents in very great detail, and -fuller information must be sought in his writings. He shows that the -wild parent is not necessarily prepotent, although many writers have -urged that view. He described three hybrids bred out of a zebra mare by -different horses, and found in all cases that the resemblance to the -male or horse parent was more profound. Similarly, zebra-donkey hybrids -out of zebra mares bred in France and in Australia were in characters -and disposition far more like the donkey parents. The results which he -obtained in the hybrids which he bred from a zebra stallion and -different mothers were more variable, but there was rather a balance in -favour of zebra disposition and against zebra shape and marking. - - "Of the nine zebra-horse hybrids I have bred," he says, "only two in - their make and disposition take decidedly after the wild parent. As - explained fully below, all the hybrids differ profoundly in the plan - of their markings from the zebra, while in their ground colour they - take after their respective dams or the ancestors of their dams far - more than after the zebra--the hybrid out of the yellow and white - Iceland pony, e.g. instead of being light in colour, as I anticipated, - is for the most part of a dark dun colour, with but indistinct - stripes. The hoofs, mane and tail of the hybrids are at the most - intermediate, but this is perhaps partly owing to reversion towards - the ancestors of these respective dams. In their disposition and - habits they all undoubtedly agree more with the wild sire." - -Ewart's experiments and his discussion of them also throw important -light on the general relation of hybrids to their parents. He found that -the coloration and pattern of his zebra hybrids resembled far more those -of the Somali or Grevy's zebra than those of their sire--a Burchell's -zebra. In a general discussion of the stripings of horses, asses and -zebras, he came to the conclusion that the Somali zebra represented the -older type, and that therefore his zebra hybrids furnished important -evidence of the effect of crossing in producing reversion to ancestral -type. The same subject has of course been discussed at length by Darwin, -in relation to the cross-breeding of varieties of pigeons; but the -modern experimentalists who are following the work of Mendel interpret -reversion differently (see MENDELISM). - -_Graft-Hybridism._--It is well known that, when two varieties or allied -species are grafted together, each retains its distinctive characters. -But to this general, if not universal, rule there are on record several -alleged exceptions, in which either the scion is said to have partaken -of the qualities of the stock, the stock of the scion, or each to have -affected the other. Supposing any of these influences to have been -exerted, the resulting product would deserve to be called a -graft-hybrid. It is clearly a matter of great interest to ascertain -whether such formation of hybrids by grafting is really possible; for, -if even one instance of such formation could be unequivocally proved, it -would show that sexual and asexual reproduction are essentially -identical. - -The cases of alleged graft-hybridism are exceedingly few, considering -the enormous number of grafts that are made every year by -horticulturists, and have been so made for centuries. Of these cases the -most celebrated are those of Adam's laburnum (_Cytisus Adami_) and the -bizzarria orange. Adam's laburnum is now flourishing in numerous places -throughout Europe, all the trees having been raised as cuttings from the -original graft, which was made by inserting a bud of the purple laburnum -into a stock of the yellow. M. Adam, who made the graft, has left on -record that from it there sprang the existing hybrid. There can be no -question as to the truly hybrid character of the latter--all the -peculiarities of both parent species being often blended in the same -raceme, flower or even petal; but until the experiment shall have been -successfully repeated there must always remain a strong suspicion that, -notwithstanding the assertion and doubtless the belief of M. Adam, the -hybrid arose as a cross in the ordinary way of seminal reproduction. -Similarly, the bizzarria orange, which is unquestionably a hybrid -between the bitter orange and the citron--since it presents the -remarkable spectacle of these two different fruits blended into one--is -stated by the gardener who first succeeded in producing it to have -arisen as a graft-hybrid; but here again a similar doubt, similarly due -to the need of corroboration, attaches to the statement. And the same -remark applies to the still more wonderful case of the so-called -trifacial orange, which blends three distinct kinds of fruit in one, and -which is said to have been produced by artificially splitting and -uniting the seeds taken from the three distinct species, the fruits of -which now occur blended in the triple hybrid. - -The other instances of alleged graft-hybridism are too numerous to be -here noticed in detail; they refer to jessamine, ash, hazel, vine, -hyacinth, potato, beet and rose. Of these the cases of the vine, beet -and rose are the strongest as evidence of graft-hybridization, from the -fact that some of them were produced as the result of careful -experiments made by very competent experimentalists. On the whole, the -results of some of these experiments, although so few in number, must be -regarded as making out a strong case in favour of the possibility of -graft-hybridism. For it must always be remembered that, in experiments -of this kind, negative evidence, however great in amount, may be -logically dissipated by a single positive result. - -_Theory of Hybridism._--Charles Darwin was interested in hybridism as an -experimental side of biology, but still more from the bearing of the -facts on the theory of the origin of species. It is obvious that -although hybridism is occasionally possible as an exception to the -general infertility of species inter se, the exception is still more -minimized when it is remembered that the hybrid progeny usually display -some degree of sterility. The main facts of hybridism appear to lend -support to the old doctrine that there are placed between all species -the barriers of mutual sterility. The argument for the fixity of species -appears still stronger when the general infertility of species crossing -is contrasted with the general fertility of the crossing of natural and -artificial varieties. Darwin himself, and afterwards G. J. Romanes, -showed, however, that the theory of natural selection did not require -the possibility of the commingling of specific types, and that there was -no reason to suppose that the mutation of species should depend upon -their mutual crossing. There existed more than enough evidence, and this -has been added to since, to show that infertility with other species is -no criterion of a species, and that there is no exact parallel between -the degree of affinity between forms and their readiness to cross. The -problem of hybridism is no more than the explanation of the generally -reduced fertility of remoter crosses as compared with the generally -increased fertility of crosses between organisms slightly different. -Darwin considered and rejected the view that the inter-sterility of -species could have been the result of natural selection. - - "At one time it appeared to me probable," he wrote (_Origin of - Species_, 6th ed. p. 247), "as it has to others, that the sterility of - first crosses and of hybrids might have been slowly acquired through - the natural selection of slightly lessened degrees of fertility, - which, like any other variation, spontaneously appeared in certain - individuals of one variety when crossed with those of another variety. - For it would clearly be advantageous to two varieties or incipient - species if they could be kept from blending, on the same principle - that, when man is selecting at the same time two varieties, it is - necessary that he should keep them separate. In the first place, it - may be remarked that species inhabiting distinct regions are often - sterile when crossed; now it could clearly have been of no advantage - to such separated species to have been rendered mutually sterile and, - consequently, this could not have been effected through natural - selection; but it may perhaps be argued that, if a species were - rendered sterile with some one compatriot, sterility with other - species would follow as a necessary contingency. In the second place, - it is almost as much opposed to the theory of natural selection as to - that of special creation, that in reciprocal crosses the male element - of one form should have been rendered utterly impotent on a second - form, whilst at the same time the male element of this second form is - enabled freely to fertilize the first form; for this peculiar state of - the reproductive system could hardly have been advantageous to either - species." - -Darwin came to the conclusion that the sterility of crossed species must -be due to some principle quite independent of natural selection. In his -search for such a principle he brought together much evidence as to the -instability of the reproductive system, pointing out in particular how -frequently wild animals in captivity fail to breed, whereas some -domesticated races have been so modified by confinement as to be fertile -together although they are descended from species probably mutually -infertile. He was disposed to regard the phenomena of differential -sterility as, so to speak, by-products of the process of evolution. G. -J. Romanes afterwards developed his theory of physiological selection, -in which he supposed that the appearance of differential fertility -within a species was the starting-point of new species; certain -individuals by becoming fertile only _inter se_ proceeded along lines of -modification diverging from the lines followed by other members of the -species. Physiological selection in fact would operate in the same -fashion as geographical isolation; if a portion of a species separated -on an island tends to become a new species, so also a portion separated -by infertility with the others would tend to form a new species. -According to Romanes, therefore, mutual infertility was the -starting-point, not the result, of specific modification. Romanes, -however, did not associate his interesting theory with a sufficient -number of facts, and it has left little mark on the history of the -subject. A. R. Wallace, on the other hand, has argued that sterility -between incipient species may have been increased by natural selection -in the same fashion as other favourable variations are supposed to have -been accumulated. He thought that "some slight degree of infertility was -a not infrequent accompaniment of the external differences which always -arise in a state of nature between varieties and incipient species." - -Weismann concluded, from an examination of a series of plant hybrids, -that from the same cross hybrids of different character may be obtained, -but that the characters are determined at the moment of fertilization; -for he found that all the flowers on the same hybrid plant resembled one -another in the minutest details of colour and pattern. Darwin already -had pointed to the act of fertilization as the determining point, and it -is in this direction that the theory of hybridism has made the greatest -advance. - -The starting-point of the modern views comes from the experiments and -conclusions on plant hybrids made by Gregor Mendel and published in -1865. It is uncertain if Darwin had paid attention to this work; -Romanes, writing in the 9th edition of this _Encyclopaedia_, cited it -without comment. First H. de Vries, then W. Bateson and a series of -observers returned to the work of Mendel (see MENDELISM), and made it -the foundation of much experimental work and still more theory. It is -still too soon to decide if the confident predictions of the Mendelians -are justified, but it seems clear that a combination of Mendel's -numerical results with Weismann's (see HEREDITY) conception of the -particulate character of the germ-plasm, or hereditary material, is at -the root of the phenomena of hybridism, and that Darwin was justified in -supposing it to lie outside the sphere of natural selection and to be a -fundamental fact of living matter. - - AUTHORITIES.--Apello, "Uber einige Resultate der Kreuzbefruchtung bei - Knochenfischen," _Bergens mus. aarbog_ (1894); Bateson, "Hybridization - and Cross-breeding," _Journal of the Royal Horticultural Society_ - (1900); J. L. Bonhote, "Hybrid Ducks," _Proc. Zool. Soc. of London_ - (1905), p. 147; Boveri, article "Befruchtung," in _Ergebnisse der - Anatomie und Entwickelungsgeschichte von Merkel und Bonnet_, i. - 385-485; Cornevin et Lesbre, "Etude sur un hybride issu d'une mule - feconde et d'un cheval," _Rev. Sci._ li. 144; Charles Darwin, _Origin - of Species_ (1859), _The Effects of Cross and Self-Fertilization in - the Vegetable Kingdom_ (1878); Delage, _La Structure du protoplasma et - les theories sur l'heredite_ (1895, with a literature); de Vries, "The - Law of Disjunction of Hybrids," _Comptes rendus_ (1900), p. 845; - Elliot, _Hybridism_; Escherick, "Die biologische Bedeutung der - Genitalabhange der Insecten," _Verh. z. B. Wien_, xlii. 225; Ewart, - _The Penycuik Experiments_ (1899); Focke, _Die Pflanzen-Mischlinge_ - (1881); Foster-Melliar, _The Book of the Rose_ (1894); C. F. Gaertner, - various papers in _Flora_, 1828, 1831, 1832, 1833, 1836, 1847, on - "Bastard-Pflanzen"; Gebhardt, "Uber die Bastardirung von _Rana - esculenta_ mit _R. arvalis_," _Inaug. Dissert._ (Breslau, 1894); G. - Mendel, "Versuche uber Pflanzen-Hybriden," _Verh. Natur. Vereins in - Brunn_ (1865), pp. 1-52; Morgan, "Experimental Studies," _Anat. Anz._ - (1893), p. 141; id. p. 803; G. J. Romanes, "Physiological Selection," - _Jour. Linn. Soc._ xix. 337; H. Scherren, "Notes on Hybrid Bears," - _Proc. Zool. Soc. of London_ (1907), p. 431; Saunders, _Proc. Roy. - Soc._ (1897), lxii. 11; Standfuss, "Etudes de zoologie experimentale," - _Arch. Sci. Nat._ vi. 495; Suchetet, "Les Oiseaux hybrides rencontres - a l'etat sauvage," _Mem. Soc. Zool._ v. 253-525, and vi. 26-45; - Vernon, "The Relation between the Hybrid and Parent Forms of Echinoid - Larvae," _Proc. Roy. Soc._ lxv. 350; Wallace, _Darwinism_ (1889); - Weismann, _The Germ-Plasm_ (1893). (P. C. M) - - - - -HYDANTOIN (glycolyl urea), - - [beta] [alpha] - / NH . CH2 - C3H4N2O2 or CO < , - \ NH . CO - [gamma] - -the ureide of glycollic acid, may be obtained by heating allantoin or -alloxan with hydriodic acid, or by heating bromacetyl urea with -alcoholic ammonia. It crystallizes in needles, melting at 216 deg. C. - -When hydrolysed with baryta water yields hydantoic (glycoluric)acid, -H2N.CO.NH.CH2.CO2H, which is readily soluble in hot water, and on -heating with hydriodic acid decomposes into ammonia, carbon dioxide and -glycocoll, CH2.NH2.CO2.H. Many substituted hydantoins are known; the -[alpha]-alkyl hydantoins are formed on fusion of aldehyde- or -ketone-cyanhydrins with urea, the [beta]-alkyl hydantoins from the -fusion of mono-alkyl glycocolls with urea, and the [gamma]-alkyl -hydantoins from the action of alkalis and alkyl iodides on the -[alpha]-compounds. [gamma]-Methyl hydantoin has been obtained as a -splitting product of caffeine (E. Fischer, _Ann._, 1882, 215, p. 253). - - - - -HYDE, the name of an English family distinguished in the 17th century. -Robert Hyde of Norbury, Cheshire, had several sons, of whom the third -was Lawrence Hyde of Gussage St Michael, Dorsetshire. Lawrence's son -Henry was father of Edward Hyde, earl of Clarendon (q.v.), whose second -son by his second wife was Lawrence, earl of Rochester (q.v.); another -son was Sir Lawrence Hyde, attorney-general to Anne of Denmark, James -I.'s consort; and a third son was Sir Nicholas Hyde (d. 1631), -chief-justice of England. Sir Nicholas entered parliament in 1601 and -soon became prominent as an opponent of the court, though he does not -appear to have distinguished himself in the law. Before long, however, -he deserted the popular party, and in 1626 he was employed by the duke -of Buckingham in his defence to impeachment by the Commons; and in the -following year he was appointed chief-justice of the king's bench, in -which office it fell to him to give judgment in the celebrated case of -Sir Thomas Darnell and others who had been committed to prison on -warrants signed by members of the privy council, which contained no -statement of the nature of the charge against the prisoners. In answer -to the writ of _habeas corpus_ the attorney-general relied on the -prerogative of the crown, supported by a precedent of Queen Elizabeth's -reign. Hyde, three other judges concurring, decided in favour of the -crown, but without going so far as to declare the right of the crown to -refuse indefinitely to show cause against the discharge of the -prisoners. In 1629 Hyde was one of the judges who condemned Eliot, -Holles and Valentine for conspiracy in parliament to resist the king's -orders; refusing to admit their plea that they could not be called upon -to answer out of parliament for acts done in parliament. Sir Nicholas -Hyde died in August 1631. - -Sir Lawrence Hyde, attorney-general to Anne of Denmark, had eleven sons, -four of whom were men of some mark. Henry was an ardent royalist who -accompanied Charles II. to the continent, and returning to England was -beheaded in 1650; Alexander (1598-1667) became bishop of Salisbury in -1665; Edward (1607-1659) was a royalist divine who was nominated dean of -Windsor in 1658, but died before taking up the appointment, and who was -the author of many controversial works in Anglican theology; and Robert -(1595-1665) became recorder of Salisbury and represented that borough in -the Long Parliament, in which he professed royalist principles, voting -against the attainder of Strafford. Having been imprisoned and deprived -of his recordership by the parliament in 1645/6, Robert Hyde gave refuge -to Charles II. on his flight from Worcester in 1651, and on the -Restoration he was knighted and made a judge of the common pleas. He -died in 1665. Henry Hyde (1672-1753), only son of Lawrence, earl of -Rochester, became 4th earl of Clarendon and 2nd earl of Rochester, both -of which titles became extinct at his death. He was in no way -distinguished, but his wife Jane Hyde, countess of Clarendon and -Rochester (d. 1725), was a famous beauty celebrated by the homage of -Swift, Prior and Pope, and by the groundless scandal of Lady Mary -Wortley Montagu. Two of her daughters, Jane, countess of Essex, and -Catherine, duchess of Queensberry, were also famous beauties of the -reign of Queen Anne. Her son, Henry Hyde (1710-1753), known as Viscount -Cornbury, was a Tory and Jacobite member of parliament, and an intimate -friend of Bolingbroke, who addressed to him his _Letters on the Study -and Use of History_, and _On the Spirit of Patriotism_. In 1750 Lord -Cornbury was created Baron Hyde of Hindon, but, as he predeceased his -father, this title reverted to the latter and became extinct at his -death. Lord Cornbury was celebrated as a wit and a conversationalist. -By his will he bequeathed the papers of his great-grandfather, Lord -Clarendon, the historian, to the Bodleian Library at Oxford. - - See Lord Clarendon, _The Life of Edward, Earl of Clarendon_ (3 vols., - Oxford, 1827); Edward Foss, _The Judges of England_ (London, - 1848-1864); Anthony a Wood, _Athenae oxonienses_ (London, 1813-1820); - Samuel Pepys, _Diary and Correspondence_, edited by Lord Braybrooke (4 - vols., London, 1854). - - - - -HYDE, THOMAS (1636-1703), English Orientalist, was born at Billingsley, -near Bridgnorth, in Shropshire, on the 29th of June 1636. He inherited -his taste for linguistic studies, and received his first lessons in some -of the Eastern tongues, from his father, who was rector of the parish. -In his sixteenth year Hyde entered King's College, Cambridge, where, -under Wheelock, professor of Arabic, he made rapid progress in Oriental -languages, so that, after only one year of residence, he was invited to -London to assist Brian Walton in his edition of the _Polyglott Bible_. -Besides correcting the Arabic, Persic and Syriac texts for that work, -Hyde transcribed into Persic characters the Persian translation of the -Pentateuch, which had been printed in Hebrew letters at Constantinople -in 1546. To this work, which Archbishop Ussher had thought well-nigh -impossible even for a native of Persia, Hyde appended the Latin version -which accompanies it in the _Polyglott_. In 1658 he was chosen Hebrew -reader at Queen's College, Oxford, and in 1659, in consideration of his -erudition in Oriental tongues, he was admitted to the degree of M.A. In -the same year he was appointed under-keeper of the Bodleian Library, and -in 1665 librarian-in-chief. Next year he was collated to a prebend at -Salisbury, and in 1673 to the archdeaconry of Gloucester, receiving the -degree of D.D. shortly afterwards. In 1691 the death of Edward Pococke -opened up to Hyde the Laudian professorship of Arabic; and in 1697, on -the deprivation of Roger Altham, he succeeded to the regius chair of -Hebrew and a canonry of Christ Church. Under Charles II., James II. and -William III. Hyde discharged the duties of Eastern interpreter to the -court. Worn out by his unremitting labours, he resigned his -librarianship in 1701, and died at Oxford on the 18th of February 1703. -Hyde, who was one of the first to direct attention to the vast treasures -of Oriental antiquity, was an excellent classical scholar, and there was -hardly an Eastern tongue accessible to foreigners with which he was not -familiar. He had even acquired Chinese, while his writings are the best -testimony to his mastery of Turkish, Arabic, Syriac, Persian, Hebrew and -Malay. - -In his chief work, _Historia religionis veterum Persarum_ (1700), he -made the first attempt to correct from Oriental sources the errors of -the Greek and Roman historians who had described the religion of the -ancient Persians. His other writings and translations comprise _Tabulae -longitudinum et latitudinum stellarum fixarum ex observatione principis -Ulugh Beighi_ (1665), to which his notes have given additional value; -_Quatuor evangelia et acta apostolorum lingua Malaica, caracteribus -Europaeis_ (1677); _Epistola de mensuris et ponderibus serum sive -sinensium_ (1688), appended to Bernard's _De mensuris et ponderibus -antiquis; Abraham Peritsol itinera mundi_ (1691); and _De ludis -orientalibus libri II._ (1694). - - With the exception of the _Historia religionis_, which was republished - by Hunt and Costard in 1760, the writings of Hyde, including some - unpublished MSS., were collected and printed by Dr Gregory Sharpe in - 1767 under the title _Syntagma dissertationum quas olim ... Thomas - Hyde separatim edidit_. There is a life of the author prefixed. Hyde - also published a catalogue of the Bodleian Library in 1674. - - - - -HYDE, a market town and municipal borough in the Hyde parliamentary -division of Cheshire, England, 7(1/2) m. E. of Manchester, by the Great -Central railway. Pop. (1901) 32,766. It lies in the densely populated -district in the north-east of the county, on the river Tame, which here -forms the boundary of Cheshire with Lancashire. To the east the outlying -hills of the Peak district of Derbyshire rise abruptly. The town has -cotton weaving factories, spinning mills, print-works, iron foundries -and machine works; also manufactures of hats and margarine. There are -extensive coal mines in the vicinity. Hyde is wholly of modern growth, -though it contains a few ancient houses, such as Newton Hall, in the -part of the town so called. The old family of Hyde held possession of -the manor as early as the reign of John. The borough, incorporated in -1881, is under a mayor, 6 aldermen and 18 councillors. Area, 3081 acres. - - - - -HYDE DE NEUVILLE, JEAN GUILLAUME, BARON (1776-1857), French politician, -was born at La Charite-sur-Loire (Nievre) on the 24th of January 1776, -the son of Guillaume Hyde, who belonged to an English family which had -emigrated with the Stuarts after the rebellion of 1745. He was only -seventeen when he successfully defended a man denounced by Fouche before -the revolutionary tribunal of Nevers. From 1793 onwards he was an active -agent of the exiled princes; he took part in the Royalist rising in -Berry in 1796, and after the _coup d'etat_ of the 18th Brumaire -(November 9, 1799) tried to persuade Bonaparte to recall the Bourbons. -An accusation of complicity in the infernal machine conspiracy of -1800-1801 was speedily retracted, but Hyde de Neuville retired to the -United States, only to return after the Restoration. He was sent by -Louis XVIII. to London to endeavour to persuade the British government -to transfer Napoleon to a remoter and safer place of exile than the isle -of Elba, but the negotiations were cut short by the emperor's return to -France in March 1815. In January 1816 de Neuville became French -ambassador at Washington, where he negotiated a commercial treaty. On -his return in 1821 he declined the Constantinople embassy, and in -November 1822 was elected deputy for Cosne. Shortly afterwards he was -appointed French ambassador at Lisbon, where his efforts to oust British -influence culminated, in connexion with the _coup d'etat_ of Dom Miguel -(April 30, 1824), in his suggestion to the Portuguese minister to invite -the armed intervention of Great Britain. It was assumed that this would -be refused, in view of the loudly proclaimed British principle of -non-intervention, and that France would then be in a position to -undertake a duty that Great Britain had declined. The scheme broke down, -however, owing to the attitude of the reactionary party in the -government of Paris, which disapproved of the Portuguese constitution. -This destroyed his influence at Lisbon, and he returned to Paris to take -his seat in the Chamber of Deputies. In spite of his pronounced -Royalism, he now showed Liberal tendencies, opposed the policy of -Villele's cabinet, and in 1828 became a member of the moderate -administration of Martignac as minister of marine. In this capacity he -showed active sympathy with the cause of Greek independence. During the -Polignac ministry (1829-1830) he was again in opposition, being a firm -upholder of the charter; but after the revolution of July 1830 he -entered an all but solitary protest against the exclusion of the -legitimate line of the Bourbons from the throne, and resigned his seat. -He died in Paris on the 28th of May 1857. - - His _Memoires et souvenirs_ (3 vols., 1888), compiled from his notes - by his nieces, the vicomtesse de Bardonnet and the baronne Laurenceau, - are of great interest for the Revolution and the Restoration. - - - - -HYDE PARK, a small township of Norfolk county, Massachusetts, U.S.A., -about 8 m. S.W. of the business centre of Boston. Pop. (1890) 10,193; -(1900) 13,244, of whom 3805 were foreign-born; (1910 census) 15,507. Its -area is about 4(1/2) sq. m. It is traversed by the New York, New Haven & -Hartford railway, which has large repair shops here, and by the Neponset -river and smaller streams. The township contains the villages of Hyde -Park, Readville (in which there is the famous "Weil" trotting-track), -Fairmount, Hazelwood and Clarendon Hills. Until about 1856 Hyde Park was -a farmstead. The value of the total factory product increased from -$4,383,959 in 1900 to $6,739,307 in 1905, or 53.7%. In 1868 Hyde Park -was incorporated as a township, being formed of territory taken from -Dorchester, Dedham and Milton. - - - - -HYDERABAD, or HAIDARABAD, a city and district of British India, in the -Sind province of Bombay. The city stands on a hill about 3 m. from the -left bank of the Indus, and had a population in 1901 of 69,378. Upon the -site of the present fort is supposed to have stood the ancient town of -Nerankot, which in the 8th century submitted to Mahommed bin Kasim. In -1768 the present city was founded by Ghulam Shah Kalhora; and it -remained the capital of Sind until 1843, when, after the battle of -Meeanee, it was surrendered to the British, and the capital transferred -to Karachi. The city is built on the most northerly hills of the Ganga -range, a site of great natural strength. In the fort, which covers an -area of 36 acres, is the arsenal of the province, transferred thither -from Karachi in 1861, and the palaces of the ex-mirs of Sind. An -excellent water supply is derived from the Indus. In addition to -manufactures of silk, gold and silver embroidery, lacquered ware and -pottery, there are three factories for ginning cotton. There are three -high schools, training colleges for masters and mistresses, a medical -school, an agricultural school for village officials, and a technical -school. The city suffered from plague in 1896-1897. - -The DISTRICT OF HYDERABAD has an area of 8291 sq. m., with a population -in 1901 of 989,030, showing an increase of 15% in the decade. It -consists of a vast alluvial plain, on the left bank of the Indus, 216 m. -long and 48 broad. Fertile along the course of the river, it degenerates -towards the east into sandy wastes, sparsely populated, and defying -cultivation. The monotony is relieved by the fringe of forest which -marks the course of the river, and by the avenues of trees that line the -irrigation channels branching eastward from this stream. The south of -the district has a special feature in its large natural water-courses -(called _dhoras_) and basin-like shallows (_chhaus_), which retain the -rains for a long time. A limestone range called the Ganga and the -pleasant frequency of garden lands break the monotonous landscape. The -principal crops are millets, rice, oil-seeds, cotton and wheat, which -are dependent on irrigation, mostly from government canals. There is a -special manufacture at Hala of glazed pottery and striped cotton cloth. -Three railways traverse the district: (1) one of the main lines of the -North-Western system, following the Indus valley and crossing the river -near Hyderabad; (2) a broad-gauge branch running south to Badin, which -will ultimately be extended to Bombay; and (3) a metre-gauge line from -Hyderabad city into Rajputana. - - - - -HYDERABAD, HAIDARABAD, also known as the Nizam's Dominions, the -principal native state of India in extent, population and political -importance; area, 82,698 sq. m.; pop. (1901) 11,141,142, showing a -decrease of 3.4% in the decade; estimated revenue 4(1/2) crores of -Hyderabad rupees (L2,500,000). The state occupies a large portion of the -eastern plateau of the Deccan. It is bounded on the north and north-east -by Berar, on the south and south-east by Madras, and on the west by -Bombay. The country presents much variety of surface and feature; but it -may be broadly divided into two tracts, distinguished from one another -geologically and ethnically, which are locally known from the languages -spoken as Telingana and Marathwara. In some parts it is mountainous, -wooded and picturesque, in others flat and undulating. The open country -includes lands of all descriptions, including many rich and fertile -plains, much good land not yet brought under cultivation, and numerous -tracts too sterile ever to be cultivated. In the north-west the -geological formations are volcanic, consisting principally of trap, but -in some parts of basalt; in the middle, southern and south-western parts -the country is overlaid with gneissic formations. The territory is well -watered, rivers being numerous, and tanks or artificial pieces of water -abundant, especially in Telingana. The principal rivers are the -Godavari, with its tributaries the Dudna, Manjira and Pranhita; the -Wardha, with its tributary the Penganga; and the Kistna, with its -tributary the Tungabhadra. The climate may be considered in general -good; and as there are no arid bare deserts, hot winds are little felt. - -More than half the revenue of the state is derived from the land, and -the development of the country by irrigation and railways has caused -considerable expansion in this revenue, though the rate of increase in -the decade 1891-1901 was retarded by a succession of unfavourable -seasons. The soil is generally fertile, though in some parts it consists -of _chilka_, a red and gritty mould little fitted for purposes of -agriculture. The principal crops are millets of various kinds, rice, -wheat, oil-seeds, cotton, tobacco, sugar-cane, and fruits and -garden produce in great variety. Silk, known as _tussur_, the produce of -a wild species of worm, is utilized on a large scale. Lac, suitable for -use as a resin or dye, gums and oils are found in great quantities. -Hides, raw and tanned, are articles of some importance in commerce. The -principal exports are cotton, oil-seeds, country-clothes and hides; the -imports are salt, grain, timber, European piece-goods and hardware. The -mineral wealth of the state consists of coal, copper, iron, diamonds and -gold; but the development of these resources has not hitherto been very -successful. The only coal mine now worked is the large one at Singareni, -with an annual out-turn of nearly half a million tons. This coal has -enabled the nizam's guaranteed state railway to be worked so cheaply -that it now returns a handsome profit to the state. It also gives -encouragement to much-needed schemes of railway extension, and to the -erection of cotton presses and of spinning and weaving mills. The -Hyderabad-Godavari railway (opened in 1901) traverses a rich cotton -country, and cotton presses have been erected along the line. The -currency of the state is based on the _hali sikka_, which contains -approximately the same weight of silver as the British rupee, but its -exchange value fell heavily after 1893, when free coinage ceased in the -mint. In 1904, however, a new coin (the Mahbubia rupee) was minted; the -supply was regulated, and the rate of exchange became about 115 = 100 -British rupees. The state suffered from famine during 1900, the total -number of persons in receipt of relief rising to nearly 500,000 in June -of that year. The nizam met the demands for relief with great -liberality. - -The nizam of Hyderabad is the principal Mahommedan ruler in India. The -family was founded by Asaf Jah, a distinguished Turkoman soldier of the -emperor Aurangzeb, who in 1713 was appointed subahdar of the Deccan, -with the title of nizam-ul-mulk (regulator of the state), but eventually -threw off the control of the Delhi court. Azaf Jah's death in 1748 was -followed by an internecine struggle for the throne among his -descendants, in which the British and the French took part. At one time -the French nominee, Salabat Jang, established himself with the help of -Bussy. But finally, in 1761, when the British had secured their -predominance throughout southern India, Nizam Ali took his place and -ruled till 1803. It was he who confirmed the grant of the Northern -Circars in 1766, and joined in the two wars against Tippoo Sultan in -1792 and 1799. The additions of territory which he acquired by these -wars was afterwards (1800) ceded to the British, as payment for the -subsidiary force which he had undertaken to maintain. By a later treaty -in 1853, the districts known as Berar were "assigned" to defray the cost -of the Hyderabad contingent. In 1857 when the Mutiny broke out, the -attitude of Hyderabad as the premier native state and the cynosure of -the Mahommedans in India became a matter of extreme importance; but -Afzul-ud-Dowla, the father of the present ruler, and his famous -minister, Sir Salar Jang, remained loyal to the British. An attack on -the residency was repulsed, and the Hyderabad contingent displayed their -loyalty in the field against the rebels. In 1902 by a treaty made by -Lord Curzon, Berar was leased in perpetuity to the British government, -and the Hyderabad contingent was merged in the Indian army. The nizam -Mir Mahbub Ali Khan Bahadur, Asaf Jah, a direct descendant of the famous -nizam-ul-mulk, was born on the 18th of August 1866. On the death of his -father in 1869 he succeeded to the throne as a minor, and was invested -with full powers in 1884. He is notable as the originator of the -Imperial Service Troops, which now form the contribution of the native -chiefs to the defence of India. On the occasion of the Panjdeh incident -in 1885 he made an offer of money and men, and subsequently on the -occasion of Queen Victoria's Jubilee in 1887 he offered 20 lakhs -(L130,000) annually for three years for the purpose of frontier defence. -It was finally decided that the native chiefs should maintain small but -well-equipped bodies of infantry and cavalry for imperial defence. For -many years past the Hyderabad finances were in a very unhealthy -condition, the expenditure consistently outran the revenue, and the -nobles, who held their tenure under an obsolete feudal system, vied -with each other in ostentatious extravagance. But in 1902, on the -revision of the Berar agreement, the nizam received 25 lakhs (L167,000) -a year for the rent of Berar, thus substituting a fixed for a -fluctuating source of income, and a British financial adviser was -appointed for the purpose of reorganizing the resources of the state. - - See S. H. Bilgrami and C. Willmott, _Historical and Descriptive Sketch - of the Nizam's Dominions_ (Bombay, 1883-1884). - - - - -HYDERABAD or HAIDARABAD, capital of the above state, is situated on the -right bank of the river Musi, a tributary of the Kistna, with Golconda -to the west, and the residency and its bazaars and the British -cantonment of Secunderabad to the north-east. It is the fourth largest -city in India; pop. (1901) 448,466, including suburbs and cantonment. -The city itself is in shape a parallelogram, with an area of more than 2 -sq. m. It was founded in 1589 by Mahommed Kuli, fifth of the Kutb Shahi -kings, of whose period several important buildings remain as monuments. -The principal of these is the Char Minar or Four Minarets (1591). The -minarets rise from arches facing the cardinal points, and stand in the -centre of the city, with four roads radiating from their base. The Ashur -Khana (1594), a ceremonial building, the hospital, the Gosha Mahal -palace and the Mecca mosque, a sombre building designed after a mosque -at Mecca, surrounding a paved quadrangle 360 ft. square, were the other -principal buildings of the Kutb Shahi period, though the mosque was only -completed in the time of Aurangzeb. The city proper is surrounded by a -stone wall with thirteen gates, completed in the time of the first -nizam, who made Hyderabad his capital. The suburbs, of which the most -important is Chadarghat, extend over an additional area of 9 sq. m. -There are several fine palaces built by various nizams, and the British -residency is an imposing building in a large park on the left bank of -the Musi, N.E. of the city. The bazaars surrounding it, and under its -jurisdiction, are extremely picturesque and are thronged with natives -from all parts of India. Four bridges crossed the Musi, the most notable -of which was the Purana Pul, of 23 arches, built in 1593. On the 27th -and 28th of September 1908, however, the Musi, swollen by torrential -rainfall (during which 15 in. fell in 36 hours), rose in flood to a -height of 12 ft. above the bridges and swept them away. The damage done -was widespread; several important buildings were involved, including the -palace of Salar Jang and the Victoria zenana hospital, while the -beautiful grounds of the residency were destroyed. A large and densely -populated part of the city was wrecked, and thousands of lives were -lost. The principal educational establishments are the Nizam college -(first grade), engineering, law, medical, normal, industrial and -Sanskrit schools, and a number of schools for Europeans and Eurasians. -Hyderabad is an important centre of general trade, and there is a cotton -mill in its vicinity. The city is supplied with water from two notable -works, the Husain Sagar and the Mir Alam, both large lakes retained by -great dams. Secunderabad, the British military cantonment, is situated -5(1/2) m. N. of the residency; it includes Bolaram, the former -headquarters of the Hyderabad contingent. - - - - -HYDER ALI, or Haidar 'Ali (c. 1722-1782), Indian ruler and commander. -This Mahommedan soldier-adventurer, who, followed by his son Tippoo, -became the most formidable Asiatic rival the British ever encountered in -India, was the great-grandson of a _fakir_ or wandering ascetic of -Islam, who had found his way from the Punjab to Gulburga in the Deccan, -and the second son of a _naik_ or chief constable at Budikota, near -Kolar in Mysore. He was born in 1722, or according to other authorities -1717. An elder brother, who like himself was early turned out into the -world to seek his own fortune, rose to command a brigade in the Mysore -army, while Hyder, who never learned to read or write, passed the first -years of his life aimlessly in sport and sensuality, sometimes, however, -acting as the agent of his brother, and meanwhile acquiring a useful -familiarity with the tactics of the French when at the height of their -reputation under Dupleix. He is said to have induced his brother to -employ a Parsee to purchase artillery and small arms from the Bombay -government, and to enrol some thirty sailors of different European -nations as gunners, and is thus credited with having been "the first -Indian who formed a corps of sepoys armed with firelocks and bayonets, -and who had a train of artillery served by Europeans." At the siege of -Devanhalli (1749) Hyder's services attracted the attention of Nanjiraj, -the minister of the raja of Mysore, and he at once received an -independent command; within the next twelve years his energy and ability -had made him completely master of minister and raja alike, and in -everything but in name he was ruler of the kingdom. In 1763 the conquest -of Kanara gave him possession of the treasures of Bednor, which he -resolved to make the most splendid capital in India, under his own name, -thenceforth changed from Hyder Naik into Hyder Ali Khan Bahadur; and in -1765 he retrieved previous defeat at the hands of the Mahrattas by the -destruction of the Nairs or military caste of the Malabar coast, and the -conquest of Calicut. Hyder Ali now began to occupy the serious attention -of the Madras government, which in 1766 entered into an agreement with -the nizam to furnish him with troops to be used against the common foe. -But hardly had this alliance been formed when a secret arrangement was -come to between the two Indian powers, the result of which was that -Colonel Smith's small force was met with a united army of 80,000 men and -100 guns. British dash and sepoy fidelity, however, prevailed, first in -the battle of Chengam (September 3rd, 1767), and again still more -remarkably in that of Tiruvannamalai (Trinomalai). On the loss of his -recently made fleet and forts on the western coast, Hyder Ali now -offered overtures for peace; on the rejection of these, bringing all his -resources and strategy into play, he forced Colonel Smith to raise the -siege of Bangalore, and brought his army within 5 m. of Madras. The -result was the treaty of April 1769, providing for the mutual -restitution of all conquests, and for mutual aid and alliance in -defensive war; it was followed by a commercial treaty in 1770 with the -authorities of Bombay. Under these arrangements Hyder Ali, when defeated -by the Mahrattas in 1772, claimed British assistance, but in vain; this -breach of faith stung him to fury, and thenceforward he and his son did -not cease to thirst for vengeance. His time came when in 1778 the -British, on the declaration of war with France, resolved to drive the -French out of India. The capture of Mahe on the coast of Malabar in -1779, followed by the annexation of lands belonging to a dependent of -his own, gave him the needed pretext. Again master of all that the -Mahrattas had taken from him, and with empire extended to the Kistna, he -descended through the passes of the Ghats amid burning villages, -reaching Conjeeveram, only 45 m. from Madras, unopposed. Not till the -smoke was seen from St Thomas's Mount, where Sir Hector Munro commanded -some 5200 troops, was any movement made; then, however, the British -general sought to effect a junction with a smaller body under Colonel -Baillie recalled from Guntur. The incapacity of these officers, -notwithstanding the splendid courage of their men, resulted in the total -destruction of Baillie's force of 2800 (September the 10th, 1780). -Warren Hastings sent from Bengal Sir Eyre Coote, who, though repulsed at -Chidambaram, defeated Hyder thrice successively in the battles of Porto -Novo, Pollilur and Sholingarh, while Tippoo was forced to raise the -siege of Wandiwash, and Vellore was provisioned. On the arrival of Lord -Macartney as governor of Madras, the British fleet captured Negapatam, -and forced Hyder Ali to confess that he could never ruin a power which -had command of the sea. He had sent his son Tippoo to the west coast, to -seek the assistance of the French fleet, when his death took place -suddenly at Chittur in December 1782. - - See L. B. Bowring, _Haidar Ali and Tipu Sultan_, "Rulers of India" - series (1893). For the personal character and administration of Hyder - Ali see the _History of Hyder Naik_, written by Mir Hussein Ali Khan - Kirmani (translated from the Persian by Colonel Miles, and published - by the Oriental Translation Fund), and the curious work written by M. - Le Maitre de La Tour, commandant of his artillery (_Histoire - d'Hayder-Ali Khan_, Paris, 1783). For the whole life and times see - Wilks, _Historical Sketches of the South of India_ (1810-1817); - Aitchison's Treaties, vol. v. (2nd ed., 1876); and Pearson, _Memoirs - of Schwartz_ (1834). - - - - -HYDRA (or SIDRA, NIDRA, IDERO, &c.; anc. _Hydrea_), an island of Greece, -lying about 4 m. off the S.E. coast of Argolis in the Peloponnesus, and -forming along with the neighbouring island of Dokos (Dhoko) the Bay of -Hydra. Pop. about 6200. The greatest length from south-west to -north-east is about 11 m., and the area is about 21 sq. mi.; but it is -little better than a rocky and treeless ridge with hardly a patch or two -of arable soil. Hence the epigram of Antonios Kriezes to the queen of -Greece: "The island produces prickly pears in abundance, splendid sea -captains and excellent prime ministers." The highest point, Mount Ere, -so called (according to Miaoules) from the Albanian word for wind, is -1958 ft. high. The next in importance is known as the Prophet Elias, -from the large convent of that name on its summit. It was there that the -patriot Theodorus Kolokotrones was imprisoned, and a large pine tree is -still called after him. The fact that in former times the island was -richly clad with woods is indicated by the name still employed by the -Turks, _Tchamliza_, the place of pines; but it is only in some favoured -spots that a few trees are now to be found. Tradition also has it that -it was once a well-watered island (hence the designation Hydrea), but -the inhabitants are now wholly dependent on the rain supply, and they -have sometimes had to bring water from the mainland. This lack of -fountains is probably to be ascribed in part to the effect of -earthquakes, which are not infrequent; that of 1769 continued for six -whole days. Hydra, the chief town, is built near the middle of the -northern coast, on a very irregular site, consisting of three hills and -the intervening ravines. From the sea its white and handsome houses -present a picturesque appearance, and its streets though narrow are -clean and attractive. Besides the principal harbour, round which the -town is built, there are three other ports on the north coast--Mandraki, -Molo, Panagia, but none of them is sufficiently sheltered. Almost all -the population of the island is collected in the chief town, which is -the seat of a bishop, and has a local court, numerous churches and a -high school. Cotton and silk weaving, tanning and shipbuilding are -carried on, and there is a fairly active trade. - -Hydra was of no importance in ancient times. The only fact in its -history is that the people of Hermione (a city on the neighbouring -mainland now known by the common name of _Kastri_) surrendered it to -Samian refugees, and that from these the people of Troezen received it -in trust. It appears to be completely ignored by the Byzantine -chroniclers. In 1580 it was chosen as a refuge by a body of Albanians -from Kokkinyas in Troezenia; and other emigrants followed in 1590, 1628, -1635, 1640, &c. At the close of the 17th century the Hydriotes took part -in the reviving commerce of the Peloponnesus; and in course of time they -extended their range. About 1716 they began to build _sakturia_ (of from -10 to 15 tons burden), and to visit the islands of the Aegean; not long -after they introduced the _latinadika_ (40-50 tons), and sailed as far -as Alexandria, Constantinople, Trieste and Venice; and by and by they -ventured to France and even America. From the grain trade of south -Russia more especially they derived great wealth. In 1813 there were -about 22,000 people in the island, and of these 10,000 were seafarers. -At the time of the outbreak of the war of Greek independence the total -population was 28,190, of whom 16,460 were natives and the rest -foreigners. One of their chief families, the Konduriotti, was worth -L2,000,000. Into the struggle the Hydriotes flung themselves with rare -enthusiasm and devotion, and the final deliverance of Greece was mainly -due to the service rendered by their fleets. - - See Pouqueville, _Voy. de la Grece_, vol. vi.; Antonios Miaoules, - [Greek: Hypomnema peri tes nesou Hydras] (Munich, 1834); Id. [Greek: - Sunoptike historia ton naumachion dia ton ploion ton trion neson, - Hydras, Petson kai Psaron] (Nauplia, 1833); Id. [Greek: Historia tes - nesou Hydras] (Athens, 1874); G. D. Kriezes, [Greek: Historia tes - nesou Hydras] (Patras, 1860). - - - - -HYDRA (watersnake), in Greek legend, the offspring of Typhon and -Echidna, a gigantic monster with nine heads (the number is variously -given), the centre one being immortal. Its haunt was a hill beneath a -plane tree near the river Amymone, in the marshes of Lerna by Argos. The -destruction of this Lernaean hydra was one of the twelve "labours" -of Heracles, which he accomplished with the assistance of Iolaus. -Finding that as soon as one head was cut off two grew up in its place, -they burnt out the roots with firebrands, and at last severed the -immortal head from the body, and buried it under a mighty block of rock. -The arrows dipped by Heracles in the poisonous blood or gall of the -monster ever afterwards inflicted fatal wounds. The generally accepted -interpretation of the legend is that "the hydra denotes the damp, swampy -ground of Lerna with its numerous springs ([Greek: kephalai], heads); -its poison the miasmic vapours rising from the stagnant water; its death -at the hands of Heracles the introduction of the culture and consequent -purification of the soil" (Preller). A euhemeristic explanation is given -by Palaephatus (39). An ancient king named Lernus occupied a small -citadel named Hydra, which was defended by 50 bowmen. Heracles besieged -the citadel and hurled firebrands at the garrison. As often as one of -the defenders fell, two others at once stepped into his place. The -citadel was finally taken with the assistance of the army of Iolaus and -the garrison slain. - - See Hesiod, _Theog._, 313; Euripides, _Hercules furens_, 419; - Pausanias ii. 37; Apollodorus ii. 5, 2; Diod. Sic. iv. 11; Roscher's - _Lexikon der Mythologie_. In the article GREEK ART, fig. 20 represents - the slaying of the Lernaean hydra by Heracles. - - - - -HYDRA, in astronomy, a constellation of the southern hemisphere, -mentioned by Eudoxus (4th century B.C.) and Aratus (3rd century B.C.), -and catalogued by Ptolemy (27 stars), Tycho Brahe (19) and Hevelius -(31). Interesting objects are: the nebula _H. IV. 27 Hydrae_, a -planetary nebula, gaseous and whose light is about equal to an 8th -magnitude star; [epsilon] _Hydrae_, a beautiful triple star, composed of -two yellow stars of the 4th and 6th magnitudes, and a blue star of the -7th magnitude; _R. Hydrae_, a long period (425 days) variable, the range -in magnitude being from 4 to 9.7; and _U. Hydrae_, an irregularly -variable, the range in magnitude being 4.5 to 6. - - - - -HYDRACRYLIC ACID (ethylene lactic acid), CH2OH.CH2.CO2H. an organic -oxyacid prepared by acting with silver oxide and water on -[beta]-iodopropionic acid, or from ethylene by the addition of -hypochlorous acid, the addition product being then treated with -potassium cyanide and hydrolysed by an acid. It may also be prepared by -oxidizing the trimethylene glycol obtained by the action of hydrobromic -acid on allylbromide. It is a syrupy liquid, which on distillation is -resolved into water and the unsaturated acrylic acid, CH2:CH.CO2H. -Chromic and nitric acids oxidize it to oxalic acid and carbon dioxide. -Hydracrylic aldehyde, CH2OH.CH2.CHO, was obtained in 1904 by J. U. Nef -(_Ann._ 335, p. 219) as a colourless oil by heating acrolein with water. -Dilute alkalis convert it into crotonaldehyde, CH3.CH:CH.CHO. - - - - -HYDRANGEA, a popular flower, the plant to which the name is most -commonly applied being _Hydrangea Hortensia_, a low deciduous shrub, -producing rather large oval strongly-veined leaves in opposite pairs -along the stem. It is terminated by a massive globular corymbose head of -flowers, which remain a long period in an ornamental condition. The -normal colour of the flowers, the majority of which have neither stamens -nor pistil, is pink; but by the influence of sundry agents in the soil, -such as alum or iron, they become changed to blue. There are numerous -varieties, one of the most noteworthy being "Thomas Hogg" with pure -white flowers. The part of the inflorescence which appears to be the -flower is an exaggerated expansion of the sepals, the other parts being -generally abortive. The perfect flowers are small, rarely produced in -the species above referred to, but well illustrated by others, in which -they occupy the inner parts of the corymb, the larger showy neuter -flowers being produced at the circumference. - -There are upwards of thirty species, found chiefly in Japan, in the -mountains of India, and in North America, and many of them are familiar -in gardens. _H. Hortensia_ (a species long known in cultivation In China -and Japan) is the most useful for decoration, as the head of flowers -lasts long in a fresh state, and by the aid of forcing can be had for a -considerable period for the ornamentation of the greenhouse and -conservatory. Their natural flowering season is towards the end of the -summer, but they may be had earlier by means of forcing. _H. japonica_ -is another fine conservatory plant, with foliage and habit much -resembling the last named, but this has flat corymbs of flowers, the -central ones small and perfect, and the outer ones only enlarged and -neuter. This also produces pink or blue flowers under the influence of -different soils. - -The Japanese species of hydrangea are sufficiently hardy to grow in any -tolerably favourable situation, but except in the most sheltered -localities they seldom blossom to any degree of perfection in the open -air, the head of blossom depending on the uninjured development of a -well-ripened terminal bud, and this growth being frequently affected by -late spring frosts. They are much more useful for pot-culture indoors, -and should be reared from cuttings of shoots having the terminal bud -plump and prominent, put in during summer, these developing a single -head of flowers the succeeding summer. Somewhat larger plants may be had -by nipping out the terminal bud and inducing three or four shoots to -start in its place, and these, being steadily developed and well -ripened, should each yield its inflorescence in the following summer, -that is, when two years old. Large plants grown in tubs and vases are -fine subjects for large conservatories, and useful for decorating -terrace walks and similar places during summer, being housed in winter, -and started under glass in spring. - -_Hydrangea paniculata_ var. _grandiflora_ is a very handsome plant; the -branched inflorescence under favourable circumstances is a yard or more -in length, and consists of large spreading masses of crowded white -neuter flowers which completely conceal the few inconspicuous fertile -ones. The plant attains a height of 8 to 10 ft. and when in flower late -in summer and in autumn is a very attractive object in the shrubbery. - -The Indian and American species, especially the latter, are quite hardy, -and some of them are extremely effective. - - - - -HYDRASTINE, C21H21NO6, an alkaloid found with berberine in the root of -golden seal, _Hydrastis canadensis_, a plant indigenous to North -America. It was discovered by Durand in 1851, and its chemistry formed -the subject of numerous communications by E. Schmidt and M. Freund (see -_Ann._, 1892, 271, p. 311) who, aided by P. Fritsch (_Ann._, 1895, 286, -p. 1), established its constitution. It is related to narcotine, which -is methoxy hydrastine. The root of golden seal is used in medicine under -the name hydrastis rhizome, as a stomachic and nervine stimulant. - - - - -HYDRATE, in chemistry, a compound containing the elements of water in -combination; more specifically, a compound containing the monovalent -hydroxyl or OH group. The first and more general definition includes -substances containing water of crystallization; such salts are said to -be hydrated, and when deprived of their water to be dehydrated or -anhydrous. Compounds embraced by the second definition are more usually -termed _hydroxides_, since at one time they were regarded as -combinations of an oxide with water, for example, calcium oxide or lime -when slaked with water yielded calcium hydroxide, written formerly as -CaO.H20. The general formulae of hydroxides are: M^iOH, M^(ii)(OH)2, -M^(iii)(OH)3, M^(iv)(OH)4, &c., corresponding to the oxides M2^iO, -M^(ii)O, M2^(iii)O3, M^(iv)O2, &c., the Roman index denoting the valency -of the element. There is an important difference between non-metallic -and metallic hydroxides; the former are invariably acids (oxyacids), the -latter are more usually basic, although acidic metallic oxides yield -acidic hydroxides. Elements exhibiting strong basigenic or oxygenic -characters yield the most, stable hydroxides; in other words, stable -hydroxides are associated with elements belonging to the extreme groups -of the periodic system, and unstable hydroxides with the central -members. The most stable basic hydroxides are those of the alkali -metals, viz. lithium, sodium, potassium, rubidium and caesium, and of -the alkaline earth metals, viz. calcium, barium and strontium; the most -stable acidic hydroxides are those of the elements placed in groups VB, -VIB and VIIB of the periodic table. - - - - -HYDRAULICS (Gr. [Greek: hydor], water, and [Greek: aulos], a pipe), the -branch of engineering science which deals with the practical -applications of the laws of hydromechanics. - - -I. THE DATA OF HYDRAULICS[1] - -S 1. _Properties of Fluids._--The fluids to which the laws of practical -hydraulics relate are substances the parts of which possess very great -mobility, or which offer a very small resistance to distortion -independently of inertia. Under the general heading Hydromechanics a -fluid is defined to be a substance which yields continually to the -slightest tangential stress, and hence in a fluid at rest there can be -no tangential stress. But, further, in fluids such as water, air, steam, -&c., to which the present division of the article relates, the -tangential stresses that are called into action between contiguous -portions during distortion or change of figure are always small compared -with the weight, inertia, pressure, &c., which produce the visible -motions it is the object of hydraulics to estimate. On the other hand, -while a fluid passes easily from one form to another, it opposes -considerable resistance to change of volume. - -It is easily deduced from the absence or smallness of the tangential -stress that contiguous portions of fluid act on each other with a -pressure which is exactly or very nearly normal to the interface which -separates them. The stress must be a pressure, not a tension, or the -parts would separate. Further, at any point in a fluid the pressure in -all directions must be the same; or, in other words, the pressure on any -small element of surface is independent of the orientation of the -surface. - -S 2. Fluids are divided into liquids, or incompressible fluids, and -gases, or compressible fluids. Very great changes of pressure change the -volume of liquids only by a small amount, and if the pressure on them is -reduced to zero they do not sensibly dilate. In gases or compressible -fluids the volume alters sensibly for small changes of pressure, and if -the pressure is indefinitely diminished they dilate without limit. - -In ordinary hydraulics, liquids are treated as absolutely -incompressible. In dealing with gases the changes of volume which -accompany changes of pressure must be taken into account. - -S 3. Viscous fluids are those in which change of form under a continued -stress proceeds gradually and increases indefinitely. A very viscous -fluid opposes great resistance to change of form in a short time, and -yet may be deformed considerably by a small stress acting for a long -period. A block of pitch is more easily splintered than indented by a -hammer, but under the action of the mere weight of its parts acting for -a long enough time it flattens out and flows like a liquid. - -[Illustration: FIG. 1.] - -All actual fluids are viscous. They oppose a resistance to the relative -motion of their parts. This resistance diminishes with the velocity of -the relative motion, and becomes zero in a fluid the parts of which are -relatively at rest. When the relative motion of different parts of a -fluid is small, the viscosity may be neglected without introducing -important errors. On the other hand, where there is considerable -relative motion, the viscosity may be expected to have an influence too -great to be neglected. - - _Measurement of Viscosity. Coefficient of Viscosity._--Suppose the - plane ab, fig. 1 of area [omega], to move with the velocity V - relatively to the surface cd and parallel to it. Let the space between - be filled with liquid. The layers of liquid in contact with ab and cd - adhere to them. The intermediate layers all offering an equal - resistance to shearing or distortion, the rectangle of fluid abcd will - take the form of the parallelogram a'b'cd. Further, the resistance to - the motion of ab may be expressed in the form - - R = [kappa][omega]V, (1) - - where [kappa] is a coefficient the nature of which remains to be - determined. - - If we suppose the liquid between ab and cd divided into layers as - shown in fig. 2, it will be clear that the stress R acts, at each - dividing face, forwards in the direction of motion if we consider the - upper layer, backwards if we consider the lower layer. Now suppose the - original thickness of the layer T increased to nT; if the bounding - plane in its new position has the velocity nV, the shearing at each - dividing face will be exactly the same as before, and the resistance - must therefore be the same. Hence, - - R = [kappa]'[omega](nV). (2) - - But equations (1) and (2) may both be expressed in one equation if - [kappa] and [kappa]' are replaced by a constant varying inversely as - the thickness of the layer. Putting [kappa] = [mu]/T, [kappa]' = - [mu]/nT, - - R = [mu][omega]V/T; - - or, for an indefinitely thin layer, - - R = [mu][omega]dV/dt, (3) - - an expression first proposed by L. M. H. Navier. The coefficient [mu] - is termed the coefficient of viscosity. - - According to J. Clerk Maxwell, the value of [mu] for air at [theta] - deg. Fahr. in pounds, when the velocities are expressed in feet per - second, is - - [mu] = 0.0000000256 (461 deg. + [theta]); - - that is, the coefficient of viscosity is proportional to the absolute - temperature and independent of the pressure. - - The value of [mu] for water at 77 deg. Fahr. is, according to H. von - Helmholtz and G. Piotrowski, - - [mu] = 0.0000188, - - the units being the same as before. For water [mu] decreases rapidly - with increase of temperature. - -[Illustration: FIG. 2.] - -S 4. When a fluid flows in a very regular manner, as for instance when -It flows in a capillary tube, the velocities vary gradually at any -moment from one point of the fluid to a neighbouring point. The layer -adjacent to the sides of the tube adheres to it and is at rest. The -layers more interior than this slide on each other. But the resistance -developed by these regular movements is very small. If in large pipes -and open channels there were a similar regularity of movement, the -neighbouring filaments would acquire, especially near the sides, very -great relative velocities. V. J. Boussinesq has shown that the central -filament in a semicircular canal of 1 metre radius, and inclined at a -slope of only 0.0001, would have a velocity of 187 metres per second,[2] -the layer next the boundary remaining at rest. But before such a -difference of velocity can arise, the motion of the fluid becomes much -more complicated. Volumes of fluid are detached continually from the -boundaries, and, revolving, form eddies traversing the fluid in all -directions, and sliding with finite relative velocities against those -surrounding them. These slidings develop resistances incomparably -greater than the viscous resistance due to movements varying -continuously from point to point. The movements which produce the -phenomena commonly ascribed to fluid friction must be regarded as -rapidly or even suddenly varying from one point to another. The internal -resistances to the motion of the fluid do not depend merely on the -general velocities of translation at different points of the fluid (or -what Boussinesq terms the mean local velocities), but rather on the -intensity at each point of the eddying agitation. The problems of -hydraulics are therefore much more complicated than problems in which a -regular motion of the fluid is assumed, hindered by the viscosity of the -fluid. - - -RELATION OF PRESSURE, DENSITY, AND TEMPERATURE OF LIQUIDS - - S 5. _Units of Volume._--In practical calculations the cubic foot and - gallon are largely used, and in metric countries the litre and cubic - metre (= 1000 litres). The imperial gallon is now exclusively used in - England, but the United States have retained the old English wine - gallon. - - 1 cub. ft. = 6.236 imp. gallons = 7.481 U.S. gallons. - 1 imp. gallon = 0.1605 cub. ft. = 1.200 U.S. gallons. - 1 U.S. gallon = 0.1337 cub. ft. = 0.8333 imp. gallon. - 1 litre = 0.2201 imp. gallon = 0.2641 U.S. gallon. - - _Density of Water._--Water at 53 deg. F. and ordinary pressure - contains 62.4 lb. per cub. ft., or 10 lb. per imperial gallon at 62 - deg. F. The litre contains one kilogram of water at 4 deg. C. or 1000 - kilograms per cubic metre. River and spring water is not sensibly - denser than pure water. But average sea water weighs 64 lb. per cub. - ft. at 53 deg. F. The weight of water per cubic unit will be denoted - by G. Ice free from air weighs 57.28 lb. per cub. ft. (Leduc). - - S 6. _Compressibility of Liquids._--The most accurate experiments show - that liquids are sensibly compressed by very great pressures, and that - up to a pressure of 65 atmospheres, or about 1000 lb. per sq. in., the - compression is proportional to the pressure. The chief results of - experiment are given in the following table. Let V1 be the volume of a - liquid in cubic feet under a pressure p1 lb. per sq. ft., and V2 its - volume under a pressure p2. Then the cubical compression is (V2 - - V1)/V1, and the ratio of the increase of pressure p2 - p1 to the - cubical compression is sensibly constant. That is, k = (p2 - p1)V1/(V2 - - V1) is constant. This constant is termed the elasticity of volume. - With the notation of the differential calculus, - - / / dV \ dp - k = dp / ( - -- ) = - V --. - / \ V / dV - - _Elasticity of Volume of Liquids._ - - +-----------+------------+-----------+------------+------------+ - | | Canton. | Oersted. | Colladon | Regnault. | - | | | | and Sturm. | | - +-----------+------------+-----------+------------+------------+ - | Water | 45,990,000 | 45,900,000| 42,660,000 | 44,000,000 | - | Sea water | 52,900,000 | .. | | .. | - | Mercury |705,300,000 | .. |626,100,000 |604,500,000 | - | Oil | 44,090,000 | .. | | .. | - | Alcohol | 32,060,000 | .. | 23,100,000 | .. | - +-----------+------------+-----------+------------+------------+ - - According to the experiments of Grassi, the compressibility of water - diminishes as the temperature increases, while that of ether, alcohol - and chloroform is increased. - - S 7. _Change of Volume and Density of Water with Change of - Temperature._--Although the change of volume of water with change of - temperature is so small that it may generally be neglected in ordinary - hydraulic calculations, yet it should be noted that there is a change - of volume which should be allowed for in very exact calculations. The - values of [rho] in the following short table, which gives data enough - for hydraulic purposes, are taken from Professor Everett's _System of - Units_. - - _Density of Water at Different Temperatures._ - - +-------------+----------+----------+ - | | | G | - | Temperature.| [rho] |Weight of | - +-----+-------+Density of|1 cub. ft.| - |Cent.| Fahr. | Water. | in lb. | - +-----+-------+----------+----------+ - | 0 | 32.0 | .999884 | 62.417 | - | 1 | 33.8 | .999941 | 62.420 | - | 2 | 35.6 | .999982 | 62.423 | - | 3 | 37.4 | 1.000004 | 62.424 | - | 4 | 39.2 | 1.000013 | 62.425 | - | 5 | 41.0 | 1.000003 | 62.424 | - | 6 | 42.8 | .999983 | 62.423 | - | 7 | 44.6 | .999946 | 62.421 | - | 8 | 46.4 | .999899 | 62.418 | - | 9 | 48.2 | .999837 | 62.414 | - | 10 | 50.0 | .999760 | 62.409 | - | 11 | 51.8 | .999668 | 62.403 | - | 12 | 53.6 | .999562 | 62.397 | - | 13 | 55.4 | .999443 | 62.389 | - | 14 | 57.2 | .999312 | 62.381 | - | 15 | 59.0 | .999173 | 62.373 | - | 16 | 60.8 | .999015 | 62.363 | - | 17 | 62.6 | .998854 | 62.353 | - | 18 | 64.4 | .998667 | 62.341 | - | 19 | 66.2 | .998473 | 62.329 | - | 20 | 68.0 | .998272 | 62.316 | - | 22 | 71.6 | .997839 | 62.289 | - | 24 | 75.2 | .997380 | 62.261 | - | 26 | 78.8 | .996879 | 62.229 | - | 28 | 82.4 | .996344 | 62.196 | - | 30 | 86 | .995778 | 62.161 | - | 35 | 95 | .99469 | 62.093 | - | 40 | 104 | .99236 | 61.947 | - | 45 | 113 | .99038 | 61.823 | - | 50 | 122 | .98821 | 61.688 | - | 55 | 131 | .98583 | 61.540 | - | 60 | 140 | .98339 | 61.387 | - | 65 | 149 | .98075 | 61.222 | - | 70 | 158 | .97795 | 61.048 | - | 75 | 167 | .97499 | 60.863 | - | 80 | 176 | .97195 | 60.674 | - | 85 | 185 | .96880 | 60.477 | - | 90 | 194 | .96557 | 60.275 | - |100 | 212 | .95866 | 59.844 | - +-----+-------+----------+----------+ - - The weight per cubic foot has been calculated from the values of - [rho], on the assumption that 1 cub. ft. of water at 39.2 deg. Fahr. - is 62.425 lb. For ordinary calculations in hydraulics, the density of - water (which will in future be designated by the symbol G) will be - taken at 62.4 lb. per cub. ft., which is its density at 53 deg. Fahr. - It may be noted also that ice at 32 deg. Fahr. contains 57.3 lb. per - cub. ft. The values of [rho] are the densities in grammes per cubic - centimetre. - - S 8. _Pressure Column. Free Surface Level._--Suppose a small vertical - pipe introduced into a liquid at any point P (fig. 3). Then the liquid - will rise in the pipe to a level OO, such that the pressure due to the - column in the pipe exactly balances the pressure on its mouth. If the - fluid is in motion the mouth of the pipe must be supposed accurately - parallel to the direction of motion, or the impact of the liquid at - the mouth of the pipe will have an influence on the height of the - column. If this condition is complied with, the height h of the - column is a measure of the pressure at the point P. Let [omega] be the - area of section of the pipe, h the height of the pressure column, p - the intensity of pressure at P; then - - p[omega] = Gh[omega] lb., - - p/G = h; - - that is, h is the height due to the pressure at p. The level OO will - be termed the free surface level corresponding to the pressure at P. - - - RELATION OF PRESSURE, TEMPERATURE, AND DENSITY OF GASES - - S 9. _Relation of Pressure, Volume, Temperature and Density in - Compressible Fluids._--Certain problems on the flow of air and steam - are so similar to those relating to the flow of water that they are - conveniently treated together. It is necessary, therefore, to state as - briefly as possible the properties of compressible fluids so far as - knowledge of them is requisite in the solution of these problems. Air - may be taken as a type of these fluids, and the numerical data here - given will relate to air. - - [Illustration: FIG. 3.] - - _Relation of Pressure and Volume at Constant Temperature._--At - constant temperature the product of the pressure p and volume V of a - given quantity of air is a constant (Boyle's law). - - Let p0 be mean atmospheric pressure (2116.8 lb. per sq. ft.), V0 the - volume of 1 lb. of air at 32 deg. Fahr. under the pressure p0. Then - - p0V0 = 26214. (1) - - If G0 is the weight per cubic foot of air in the same conditions, - - G0 = 1/V0 = 2116.8/26214 = .08075. (2) - - For any other pressure p, at which the volume of 1 lb. is V and the - weight per cubic foot is G, the temperature being 32 deg. Fahr., - - pV = p/G = 26214; or G = p/26214. (3) - - _Change of Pressure or Volume by Change of Temperature._--Let p0, V0, - G0, as before be the pressure, the volume of a pound in cubic feet, - and the weight of a cubic foot in pounds, at 32 deg. Fahr. Let p, V, G - be the same quantities at a temperature t (measured strictly by the - air thermometer, the degrees of which differ a little from those of a - mercurial thermometer). Then, by experiment, - - pV = p0V0(460.6 + t)/(460.6 + 32) = p0V0[tau]/[tau]0, (4) - - where [tau], [tau]0 are the temperatures t and 32 deg. reckoned from - the absolute zero, which is -460.6 deg. Fahr.; - - p/G = p0[tau]/G0[tau]0; (4a) - - G = p[tau]0G0/p0[tau]. (5) - - If p0 = 2116.8, G0 = .08075, [tau]0 = 460.6 + 32 = 492.6, then - - p/G = 53.2[tau]. (5a) - - Or quite generally p/G = R[tau] for all gases, if R is a constant - varying inversely as the density of the gas at 32 deg. F. For steam R - = 85.5. - - -II. KINEMATICS OF FLUIDS - -S 10. Moving fluids as commonly observed are conveniently classified -thus: - -(1) _Streams_ are moving masses of indefinite length, completely or -incompletely bounded laterally by solid boundaries. When the solid -boundaries are complete, the flow is said to take place in a pipe. When -the solid boundary is incomplete and leaves the upper surface of the -fluid free, it is termed a stream bed or channel or canal. - -(2) A stream bounded laterally by differently moving fluid of the same -kind is termed a _current_. - -(3) A _jet_ is a stream bounded by fluid of a different kind. - -(4) An _eddy_, _vortex_ or _whirlpool_ is a mass of fluid the particles -of which are moving circularly or spirally. - -(5) In a stream we may often regard the particles as flowing along -definite paths in space. A chain of particles following each other along -such a constant path may be termed a fluid filament or elementary -stream. - - S 11. _Steady and Unsteady, Uniform and Varying, Motion._--There are - two quite distinct ways of treating hydrodynamical questions. We may - either fix attention on a given mass of fluid and consider its changes - of position and energy under the action of the stresses to which it is - subjected, or we may have regard to a given fixed portion of space, - and consider the volume and energy of the fluid entering and leaving - that space. - - If, in following a given path ab (fig. 4), a mass of water a has a - constant velocity, the motion is said to be uniform. The kinetic - energy of the mass a remains unchanged. If the velocity varies from - point to point of the path, the motion is called varying motion. If at - a given point a in space, the particles of water always arrive with - the same velocity and in the same direction, during any given time, - then the motion is termed steady motion. On the contrary, if at the - point a the velocity or direction varies from moment to moment the - motion is termed unsteady. A river which excavates its own bed is in - unsteady motion so long as the slope and form of the bed is changing. - It, however, tends always towards a condition in which the bed ceases - to change, and it is then said to have reached a condition of - permanent regime. No river probably is in absolutely permanent regime, - except perhaps in rocky channels. In other cases the bed is scoured - more or less during the rise of a flood, and silted again during the - subsidence of the flood. But while many streams of a torrential - character change the condition of their bed often and to a large - extent, in others the changes are comparatively small and not easily - observed. - - [Illustration: FIG. 4.] - - As a stream approaches a condition of steady motion, its regime - becomes permanent. Hence steady motion and permanent regime are - sometimes used as meaning the same thing. The one, however, is a - definite term applicable to the motion of the water, the other a less - definite term applicable in strictness only to the condition of the - stream bed. - - S 12. _Theoretical Notions on the Motion of Water._--The actual motion - of the particles of water is in most cases very complex. To simplify - hydrodynamic problems, simpler modes of motion are assumed, and the - results of theory so obtained are compared experimentally with the - actual motions. - - _Motion in Plane Layers._--The simplest kind of motion in a stream is - one in which the particles initially situated in any plane cross - section of the stream continue to be found in plane cross sections - during the subsequent motion. Thus, if the particles in a thin plane - layer ab (fig. 5) are found again in a thin plane layer a'b' after any - interval of time, the motion is said to be motion in plane layers. In - such motion the internal work in deforming the layer may usually be - disregarded, and the resistance to the motion is confined to the - circumference. - - [Illustration: FIG. 5.] - - _Laminar Motion._--In the case of streams having solid boundaries, it - is observed that the central parts move faster than the lateral parts. - To take account of these differences of velocity, the stream may be - conceived to be divided into thin laminae, having cross sections - somewhat similar to the solid boundary of the stream, and sliding on - each other. The different laminae can then be treated as having - differing velocities according to any law either observed or deduced - from their mutual friction. A much closer approximation to the real - motion of ordinary streams is thus obtained. - - _Stream Line Motion._--In the preceding hypothesis, all the particles - in each lamina have the same velocity at any given cross section of - the stream. If this assumption is abandoned, the cross section of the - stream must be supposed divided into indefinitely small areas, each - representing the section of a fluid filament. Then these filaments may - have any law of variation of velocity assigned to them. If the motion - is steady motion these fluid filaments (or as they are then termed - _stream lines_) will have fixed positions in space. - - _Periodic Unsteady Motion._--In ordinary streams with rough - boundaries, it is observed that at any given point the velocity varies - from moment to moment in magnitude and direction, but that the average - velocity for a sensible period (say for 5 or 10 minutes) varies very - little either in magnitude or velocity. It has hence been conceived - that the variations of direction and magnitude of the velocity are - periodic, and that, if for each point of the stream the mean velocity - and direction of motion were substituted for the actual more or less - varying motions, the motion of the stream might be treated as steady - stream line or steady laminar motion. - - [Illustration: FIG. 6.] - - S 13. _Volume of Flow._--Let A (fig. 6) be any ideal plane surface, of - area [omega], in a stream, normal to the direction of motion, and let - V be the velocity of the fluid. Then the volume flowing through the - surface A in unit time is - - Q = [omega]V. (1) - - Thus, if the motion is rectilinear, all the particles at any instant - in the surface A will be found after one second in a similar surface - A', at a distance V, and as each particle is followed by a continuous - thread of other particles, the volume of flow is the right prism AA' - having a base [omega] and length V. - - If the direction of motion makes an angle [theta] with the normal to - the surface, the volume of flow is represented by an oblique prism AA' - (fig. 7), and in that case - - Q = [omega]V cos [theta]. - - [Illustration: FIG. 7.] - - If the velocity varies at different points of the surface, let the - surface be divided into very small portions, for each of which the - velocity may be regarded as constant. If d[omega] is the area and v, - or v cos [theta], the normal velocity for this element of the surface, - the volume of flow is - _ _ - / / - Q = | v d[omega], or | v cos [theta] d[omega], - _/ _/ - - as the case may be. - - S 14. _Principle of Continuity._--If we consider any completely - bounded fixed space in a moving liquid initially and finally filled - continuously with liquid, the inflow must be equal to the outflow. - Expressing the inflow with a positive and the outflow with a negative - sign, and estimating the volume of flow Q for all the boundaries, - - [Sigma]Q = 0. - - In general the space will remain filled with fluid if the pressure at - every point remains positive. There will be a break of continuity, if - at any point the pressure becomes negative, indicating that the stress - at that point is tensile. In the case of ordinary water this statement - requires modification. Water contains a variable amount of air in - solution, often about one-twentieth of its volume. This air is - disengaged and breaks the continuity of the liquid, if the pressure - falls below a point corresponding to its tension. It is for this - reason that pumps will not draw water to the full height due to - atmospheric pressure. - - _Application of the Principle of Continuity to the case of a - Stream._--If A1, A2 are the areas of two normal cross sections of a - stream, and V1, V2 are the velocities of the stream at those sections, - then from the principle of continuity, - - V1A1 = V2A2; - - V1/V2 = A2/A1 (2) - - that is, the normal velocities are inversely as the areas of the cross - sections. This is true of the mean velocities, if at each section the - velocity of the stream varies. In a river of varying slope the - velocity varies with the slope. It is easy therefore to see that in - parts of large cross section the slope is smaller than in parts of - small cross section. - - If we conceive a space in a liquid bounded by normal sections at A1, - A2 and between A1, A2 by stream lines (fig. 8), then, as there is no - flow across the stream lines, - - V1/V2 = A2/A1, - - as in a stream with rigid boundaries. - - [Illustration: FIG. 8.] - - In the case of compressible fluids the variation of volume due to the - difference of pressure at the two sections must be taken into account. - If the motion is steady the weight of fluid between two cross sections - of a stream must remain constant. Hence the weight flowing in must be - the same as the weight flowing out. Let p1, p2 be the pressures, v1, - v2 the velocities, G1, G2 the weight per cubic foot of fluid, at cross - sections of a stream of areas A1, A2. The volumes of inflow and - outflow are - - A1v1 and A2v2, - - and, if the weights of these are the same, - - G1A1v1 = G2A2v2; - - and hence, from (5a) S 9, if the temperature is constant, - - p1A1v1 = p2A2v2. (3) - - S 15. _Stream Lines._--The characteristic of a perfect fluid, that is, - a fluid free from viscosity, is that the pressure between any two - parts into which it is divided by a plane must be normal to the plane. - One consequence of this is that the particles can have no rotation - impressed upon them, and the motion of such a fluid is irrotational. A - stream line is the line, straight or curved, traced by a particle in a - current of fluid in irrotational movement. In a steady current each - stream line preserves its figure and position unchanged, and marks the - track of a stream of particles forming a fluid filament or elementary - stream. A current in steady irrotational movement may be conceived to - be divided by insensibly thin partitions following the course of the - stream lines into a number of elementary streams. If the positions of - these partitions are so adjusted that the volumes of flow in all the - elementary streams are equal, they represent to the mind the velocity - as well as the direction of motion of the particles in different parts - of the current, for the velocities are inversely proportional to the - cross sections of the elementary streams. No actual fluid is devoid of - viscosity, and the effect of viscosity is to render the motion of a - fluid sinuous, or rotational or eddying under most ordinary - conditions. At very low velocities in a tube of moderate size the - motion of water may be nearly pure stream line motion. But at some - velocity, smaller as the diameter of the tube is greater, the motion - suddenly becomes tumultuous. The laws of simple stream line motion - have hitherto been investigated theoretically, and from mathematical - difficulties have only been determined for certain simple cases. - Professor H. S. Hele Shaw has found means of exhibiting stream line - motion in a number of very interesting cases experimentally. Generally - in these experiments a thin sheet of fluid is caused to flow between - two parallel plates of glass. In the earlier experiments streams of - very small air bubbles introduced into the water current rendered - visible the motions of the water. By the use of a lantern the image of - a portion of the current can be shown on a screen or photographed. In - later experiments streams of coloured liquid at regular distances were - introduced into the sheet and these much more clearly marked out the - forms of the stream lines. With a fluid sheet 0.02 in. thick, the - stream lines were found to be stable at almost any required velocity. - For certain simple cases Professor Hele Shaw has shown that the - experimental stream lines of a viscous fluid are so far as can be - measured identical with the calculated stream lines of a perfect - fluid. Sir G. G. Stokes pointed out that in this case, either from the - thinness of the stream between its glass walls, or the slowness of the - motion, or the high viscosity of the liquid, or from a combination of - all these, the flow is regular, and the effects of inertia disappear, - the viscosity dominating everything. Glycerine gives the stream lines - very satisfactorily. - - [Illustration: FIG. 9.] - - [Illustration: FIG. 10.] - - [Illustration: FIG. 11.] - - [Illustration: FIG. 12.] - - [Illustration: FIG. 13.] - - Fig. 9 shows the stream lines of a sheet of fluid passing a fairly - shipshape body such as a screwshaft strut. The arrow shows the - direction of motion of the fluid. Fig. 10 shows the stream lines for a - very thin glycerine sheet passing a non-shipshape body, the stream - lines being practically perfect. Fig. 11 shows one of the earlier - air-bubble experiments with a thicker sheet of water. In this case the - stream lines break up behind the obstruction, forming an eddying wake. - Fig. 12 shows the stream lines of a fluid passing a sudden contraction - or sudden enlargement of a pipe. Lastly, fig. 13 shows the stream - lines of a current passing an oblique plane. H. S. Hele Shaw, - "Experiments on the Nature of the Surface Resistance in Pipes and on - Ships," _Trans. Inst. Naval Arch._ (1897). "Investigation of Stream - Line Motion under certain Experimental Conditions," _Trans. Inst. - Naval Arch._ (1898); "Stream Line Motion of a Viscous Fluid," _Report - of British Association_ (1898). - - - III. PHENOMENA OF THE DISCHARGE OF LIQUIDS FROM ORIFICES AS - ASCERTAINABLE BY EXPERIMENTS - - S 16. When a liquid issues vertically from a small orifice, it forms a - jet which rises nearly to the level of the free surface of the liquid - in the vessel from which it flows. The difference of level h_r (fig. - 14) is so small that it may be at once suspected to be due either to - air resistance on the surface of the jet or to the viscosity of the - liquid or to friction against the sides of the orifice. Neglecting for - the moment this small quantity, we may infer, from the elevation of - the jet, that each molecule on leaving the orifice possessed the - velocity required to lift it against gravity to the height h. From - ordinary dynamics, the relation between the velocity and height of - projection is given by the equation - - v = [root](2gh). (1) - - As this velocity is nearly reached in the flow from well-formed - orifices, it is sometimes called the theoretical velocity of - discharge. This relation was first obtained by Torricelli. - - [Illustration: FIG. 14.] - - If the orifice is of a suitable conoidal form, the water issues in - filaments normal to the plane of the orifice. Let [omega] be the area - of the orifice, then the discharge per second must be, from eq. (1), - - Q = [omega]v = [omega][root](2gh) nearly. (2) - - This is sometimes quite improperly called the theoretical discharge - for any kind of orifice. Except for a well-formed conoidal orifice the - result is not approximate even, so that if it is supposed to be based - on a theory the theory is a false one. - - _Use of the term Head in Hydraulics._--The term _head_ is an old - millwright's term, and meant primarily the height through which a mass - of water descended in actuating a hydraulic machine. Since the water - in fig. 14 descends through a height h to the orifice, we may say - there are h ft. of head above the orifice. Still more generally any - mass of liquid h ft. above a horizontal plane may be said to have h - ft. of elevation head relatively to that datum plane. Further, since - the pressure p at the orifice which produces outflow is connected with - h by the relation p/G = h, the quantity p/G may be termed the pressure - head at the orifice. Lastly, the velocity v is connected with h by the - relation v^2/2g = h, so that v^2/2g may be termed the head due to the - velocity v. - - S 17. _Coefficients of Velocity and Resistance._--As the actual - velocity of discharge differs from [root]2gh by a small quantity, let - the actual velocity - - = v_a = c_v [root](2gh), (3) - - where c_v is a coefficient to be determined by experiment, called the - _coefficient of velocity_. This coefficient is found to be tolerably - constant for different heads with well-formed simple orifices, and it - very often has the value 0.97. - - The difference between the velocity of discharge and the velocity due - to the head may be reckoned in another way. The total height h causing - outflow consists of two parts--one part h_e expended effectively in - producing the velocity of outflow, another h_r in overcoming the - resistances due to viscosity and friction. Let - - h_r = c_r h_e, - - where c{r} is a coefficient determined by experiment, and called the - _coefficient of resistance_ of the orifice. It is tolerably constant - for different heads with well-formed orifices. Then - - v_a = [root](2gh_e) = [root]{2gh/(1 + c_r)}. (4) - - The relation between c_v and c_r for any orifice is easily found:-- - - v_a = c_v[root](2gh) = [root]{2gh/(1 + c_r)} - - c_v = [root]{1/(1 + c_r)} (5) - - c_r = 1/c_v^2 - 1 (5a) - - Thus if c_v = 0.97, then c_r = 0.0628. That is, for such an orifice - about 6(1/4)% of the head is expended in overcoming frictional - resistances to flow. - - [Illustration: FIG. 15.] - - _Coefficient of Contraction--Sharp-edged Orifices in Plane - Surfaces._--When a jet issues from an aperture in a vessel, it may - either spring clear from the inner edge of the orifice as at a or b - (fig. 15), or it may adhere to the sides of the orifice as at c. The - former condition will be found if the orifice is bevelled outwards as - at a, so as to be sharp edged, and it will also occur generally for a - prismatic aperture like b, provided the thickness of the plate in - which the aperture is formed is less than the diameter of the jet. But - if the thickness is greater the condition shown at c will occur. - - When the discharge occurs as at a or b, the filaments converging - towards the orifice continue to converge beyond it, so that the - section of the jet where the filaments have become parallel is smaller - than the section of the orifice. The inertia of the filaments opposes - sudden change of direction of motion at the edge of the orifice, and - the convergence continues for a distance of about half the diameter of - the orifice beyond it. Let [omega] be the area of the orifice, and - c_c[omega] the area of the jet at the point where convergence ceases; - then c_c is a coefficient to be determined experimentally for each - kind of orifice, called the _coefficient of contraction_. When the - orifice is a sharp-edged orifice in a plane surface, the value of c_c - is on the average 0.64, or the section of the jet is very nearly - five-eighths of the area of the orifice. - - _Coefficient of Discharge._--In applying the general formula Q = - [omega]v to a stream, it is assumed that the filaments have a common - velocity v normal to the section [omega]. But if the jet contracts, it - is at the contracted section of the jet that the direction of motion - is normal to a transverse section of the jet. Hence the actual - discharge when contraction occurs is - - Q_a = c_vv X c_c[omega] = c_c c_v[omega][root](2gh), - - or simply, if c = c_vc_c, - - Q_a = c[omega][root](2gh), - - where c is called the _coefficient of discharge_. Thus for a - sharp-edged plane orifice c = 0.97 X 0.64 = 0.62. - - [Illustration: FIG. 16.] - - S 18. _Experimental Determination of c_v, c_c, and c._--The - coefficient of contraction c_c is directly determined by measuring the - dimensions of the jet. For this purpose fixed screws of fine pitch - (fig. 16) are convenient. These are set to touch the jet, and then the - distance between them can be measured at leisure. - - The coefficient of velocity is determined directly by measuring the - parabolic path of a horizontal jet. - - Let OX, OY (fig. 17) be horizontal and vertical axes, the origin being - at the orifice. Let h be the head, and x, y the coordinates of a point - A on the parabolic path of the jet. If v_a is the velocity at the - orifice, and t the time in which a particle moves from O to A, then - - x = v_a t; y = (1/2)gt^2. - - Eliminating t, - - v_a = [root](gx^2/2y). - - Then - - c_v = v_a [root](2gh) = [root](x^2/4yh). - - In the case of large orifices such as weirs, the velocity can be - directly determined by using a Pitot tube (S 144). - - [Illustration: FIG. 17.] - - The coefficient of discharge, which for practical purposes is the most - important of the three coefficients, is best determined by tank - measurement of the flow from the given orifice in a suitable time. If - Q is the discharge measured in the tank per second, then - - c = Q/[omega][root](2gh). - - Measurements of this kind though simple in principle are not free from - some practical difficulties, and require much care. In fig. 18 is - shown an arrangement of measuring tank. The orifice is fixed in the - wall of the cistern A and discharges either into the waste channel BB, - or into the measuring tank. There is a short trough on rollers C which - when run under the jet directs the discharge into the tank, and when - run back again allows the discharge to drop into the waste channel. D - is a stilling screen to prevent agitation of the surface at the - measuring point, E, and F is a discharge valve for emptying the - measuring tank. The rise of level in the tank, the time of the flow - and the head over the orifice at that time must be exactly observed. - - [Illustration: FIG. 18.] - - For well made sharp-edged orifices, small relatively to the water - surface in the supply reservoir, the coefficients under different - conditions of head are pretty exactly known. Suppose the same quantity - of water is made to flow in succession through such an orifice and - through another orifice of which the coefficient is required, and when - the rate of flow is constant the heads over each orifice are noted. - Let h1, h2 be the heads, [omega]1, [omega]2 the areas of the orifices, - c1, c2 the coefficients. Then since the flow through each orifice is - the same - - Q = c1[omega]1 [root](2gh1) = c2[omega]2 [root](2gh2). - - c2 = c1([omega]1/[omega]2) [root](h1/h2). - - [Illustration: FIG. 19.] - - S 19. _Coefficients for Bellmouths and Bellmouthed Orifices._--If an - orifice is furnished with a mouthpiece exactly of the form of the - contracted vein, then the whole of the contraction occurs within the - mouthpiece, and if the area of the orifice is measured at the smaller - end, c_c must be put = 1. It is often desirable to bellmouth the ends - of pipes, to avoid the loss of head which occurs if this is not - done; and such a bellmouth may also have the form of the contracted - jet. Fig. 19 shows the proportions of such a bellmouth or bell-mouthed - orifice, which approximates to the form of the contracted jet - sufficiently for any practical purpose. - - For such an orifice L. J. Weisbach found the following values of the - coefficients with different heads. - - +--------------------------------+------+------+------+------+-------+ - | Head over orifice, in ft. = h | .66 | 1.64 |11.48 |55.77 |337.93 | - +--------------------------------+------+------+------+------+-------+ - | Coefficient of velocity = c_v | .959 | .967 | .975 | .994 | .994 | - | Coefficient of resistance = c_r| .087 | .069 | .052 | .012 | .012 | - +--------------------------------+------+------+------+------+-------+ - - As there is no contraction after the jet issues from the orifice, c_c - = 1, c = c_v; and therefore - - Q = c(v)[omega][root](2gh) = [omega][root]{2gh/(1 + c_r}. - - S 20. _Coefficients for Sharp-edged or virtually Sharp-edged - Orifices._--There are a very large number of measurements of discharge - from sharp-edged orifices under different conditions of head. An - account of these and a very careful tabulation of the average values - of the coefficients will be found in the _Hydraulics_ of the late - Hamilton Smith (Wiley & Sons, New York, 1886). The following short - table abstracted from a larger one will give a fair notion of how the - coefficient varies according to the most trustworthy of the - experiments. - - _Coefficient of Discharge for Vertical Circular Orifices, Sharp-edged, - with free Discharge into the Air._ Q = c[omega][root](2gh). - - +-----------+------------------------------------------------+ - | Head | Diameters of Orifice. | - |measured to+------+------+------+------+------+------+------+ - | Centre of | .02 | .04 | .10 | .20 | .40 | .60 | 1.0 | - | Orifice. +------+------+------+------+------+------+------+ - | | Values of C. | - +-----------+------+------+------+------+------+------+------+ - | 0.3 | .. | .. | .621 | .. | .. | .. | .. | - | 0.4 | .. | .637 | .618 | .. | .. | .. | .. | - | 0.6 | .655 | .630 | .613 | .601 | .596 | .588 | .. | - | 0.8 | .648 | .626 | .610 | .601 | .597 | .594 | .583 | - | 1.0 | .644 | .623 | .608 | .600 | .598 | .595 | .591 | - | 2.0 | .632 | .614 | .604 | .599 | .599 | .597 | .595 | - | 4.0 | .623 | .609 | .602 | .599 | .598 | .597 | .596 | - | 8.0 | .614 | .605 | .600 | .598 | .597 | .596 | .596 | - | 20.0 | .601 | .599 | .596 | .596 | .596 | .596 | .594 | - +-----------+------+------+------+------+------+------+------+ - - At the same time it must be observed that differences of sharpness in - the edge of the orifice and some other circumstances affect the - results, so that the values found by different careful experimenters - are not a little discrepant. When exact measurement of flow has to be - made by a sharp-edged orifice it is desirable that the coefficient for - the particular orifice should be directly determined. - - The following results were obtained by Dr H. T. Bovey in the - laboratory of McGill University. - - _Coefficient of Discharge for Sharp-edged Orifices._ - - +----+------------------------------------------------------------------+ - | | Form of Orifice. | - | +------+----------------+-----------------+-----------------+------+ - | | | Square. |Rectangular Ratio|Rectangular Ratio| | - |Head| | | of Sides 4:1 | of Sides 16:1 | | - | in | Cir- +------+---------+---------+-------+---------+-------+ Tri- | - | ft.|cular.|Sides | | Long | Long | Long | Long |angu- | - | | |Verti-|Diagonal | Sides | Sides | Sides | Sides | lar. | - | | | cal. |Vertical.|Vertical.| hori- |Vertical.| Hori- | | - | | | | | |zontal.| |zontal.| | - +----+------+------+---------+---------+-------+---------+-------+------+ - | 1 | .620 | .627 | .628 | .642 | .643 | .663 | .664 | .636 | - | 2 | .613 | .620 | .628 | .634 | .636 | .650 | .651 | .628 | - | 4 | .608 | .616 | .618 | .628 | .629 | .641 | .642 | .623 | - | 6 | .607 | .614 | .616 | .626 | .627 | .637 | .637 | .620 | - | 8 | .606 | .613 | .614 | .623 | .625 | .634 | .635 | .619 | - | 10 | .605 | .612 | .613 | .622 | .624 | .632 | .633 | .618 | - | 12 | .604 | .611 | .612 | .622 | .623 | .631 | .631 | .618 | - | 14 | .604 | .610 | .612 | .621 | .622 | .630 | .630 | .618 | - | 16 | .603 | .610 | .611 | .620 | .622 | .630 | .630 | .617 | - | 18 | .603 | .610 | .611 | .620 | .621 | .630 | .629 | .616 | - | 20 | .603 | .609 | .611 | .620 | .621 | .629 | .628 | .616 | - +----+------+------+---------+---------+-------+---------+-------+------+ - - The orifice was 0.196 sq. in. area and the reductions were made with g - = 32.176 the value for Montreal. The value of the coefficient appears - to increase as (perimeter) / (area) increases. It decreases as the - head increases. It decreases a little as the size of the orifice is - greater. - - Very careful experiments by J. G. Mair (_Proc. Inst. Civ. Eng._ - lxxxiv.) on the discharge from circular orifices gave the results - shown on top of next column. - - The edges of the orifices were got up with scrapers to a sharp square - edge. The coefficients generally fall as the head increases and as the - diameter increases. Professor W. C. Unwin found that the results agree - with the formula - - c = 0.6075 + 0.0098/[root]h - 0.0037d, - - where h is in feet and d in inches. - - _Coefficients of Discharge from Circular Orifices. Temperature 51 - deg. to 55 deg._ - - +-------+--------------------------------------------------------------+ - |Head in| Diameters of Orifices in Inches (d). | - | feet +------+------+------+------+------+------+------+------+------+ - | h. | 1 |1(1/4)|1(1/2)|1(3/4)| 2 |2(1/4)|2(1/2)|2(3/4)| 3 | - +-------+------+------+------+------+------+------+------+------+------+ - | | Coefficients (c). | - | +------+------+------+------+------+------+------+------+------+ - | .75 | .616 | .614 | .616 | .610 | .616 | .612 | .607 | .607 | .609 | - | 1.0 | .613 | .612 | .612 | .611 | .612 | .611 | .604 | .608 | .609 | - | 1.25 | .613 | .614 | .610 | .608 | .612 | .608 | .605 | .605 | .606 | - | 1.50 | .610 | .612 | .611 | .606 | .610 | .607 | .603 | .607 | .605 | - | 1.75 | .612 | .611 | .611 | .605 | .611 | .605 | .604 | .607 | .605 | - | 2.00 | .609 | .613 | .609 | .606 | .609 | .606 | .604 | .604 | .605 | - +-------+------+------+------+------+------+------+------+------+------+ - - The following table, compiled by J. T. Fanning (_Treatise on Water - Supply Engineering_), gives values for rectangular orifices in - vertical plane surfaces, the head being measured, not immediately over - the orifice, where the surface is depressed, but to the still-water - surface at some distance from the orifice. The values were obtained by - graphic interpolation, all the most reliable experiments being plotted - and curves drawn so as to average the discrepancies. - - _Coefficients of Discharge for Rectangular Orifices, Sharp-edged, in - Vertical Plane Surfaces._ - - +--------+----------------------------------------------------------------+ - | Head | Ratio of Height to Width. | - | to | | - | Centre +------+------+------+------+--------+--------+--------+---------+ - | of | | | | | | | | | - |Orifice.| 4 | 2 |1(1/2)| 1 | 3/4 | 1/2 | 1/4 | 1/8 | - +--------+------+------+------+------+--------+--------+--------+---------+ - | | 4 ft.| 2 ft.|1(1/2)| 1 ft.|0.75 ft.|0.50 ft.|0.25 ft.|0.125 ft.| - | | high.| high.| ft. | high.| high. | high. | high. | high. | - | Feet. | | | high.| | | | | | - | | 1 ft.| 1 ft.| 1 ft.| 1 ft.| 1 ft. | 1 ft. | 1 ft. | 1 ft. | - | | wide.| wide.| wide.| wide.| wide. | wide. | wide. | wide. | - +--------+------+------+------+------+--------+--------+--------+---------+ - | 0.2 | .. | .. | .. | .. | .. | .. | .. | .6333 | - | .3 | .. | .. | .. | .. | .. | .. | .6293 | .6334 | - | .4 | .. | .. | .. | .. | .. | .6140 | .6306 | .6334 | - | .5 | .. | .. | .. | .. | .6050 | .6150 | .6313 | .6333 | - | .6 | .. | .. | .. |.5984 | .6063 | .6156 | .6317 | .6332 | - | .7 | .. | .. | .. |.5994 | .6074 | .6162 | .6319 | .6328 | - | .8 | .. | .. |.6130 |.6000 | .6082 | .6165 | .6322 | .6326 | - | .9 | .. | .. |.6134 |.6006 | .6086 | .6168 | .6323 | .6324 | - | 1.0 | .. | .. |.6135 |.6010 | .6090 | .6172 | .6320 | .6320 | - | 1.25 | .. |.6188 |.6140 |.6018 | .6095 | .6173 | .6317 | .6312 | - | 1.50 | .. |.6187 |.6144 |.6026 | .6100 | .6172 | .6313 | .6303 | - | 1.75 | .. |.6186 |.6145 |.6033 | .6103 | .6168 | .6307 | .6296 | - | 2 | .. |.6183 |.6144 |.6036 | .6104 | .6166 | .6302 | .6291 | - | 2.25 | .. |.6180 |.6143 |.6029 | .6103 | .6163 | .6293 | .6286 | - | 2.50 |.6290 |.6176 |.6139 |.6043 | .6102 | .6157 | .6282 | .6278 | - | 2.75 |.6280 |.6173 |.6136 |.6046 | .6101 | .6155 | .6274 | .6273 | - | 3 |.6273 |.6170 |.6132 |.6048 | .6100 | .6153 | .6267 | .6267 | - | 3.5 |.6250 |.6160 |.6123 |.6050 | .6094 | .6146 | .6254 | .6254 | - | 4 |.6245 |.6150 |.6110 |.6047 | .6085 | .6136 | .6236 | .6236 | - | 4.5 |.6226 |.6138 |.6100 |.6044 | .6074 | .6125 | .6222 | .6222 | - | 5 |.6208 |.6124 |.6088 |.6038 | .6063 | .6114 | .6202 | .6202 | - | 6 |.6158 |.6094 |.6063 |.6020 | .6044 | .6087 | .6154 | .6154 | - | 7 |.6124 |.6064 |.6038 |.6011 | .6032 | .6058 | .6110 | .6114 | - | 8 |.6090 |.6036 |.6022 |.6010 | .6022 | .6033 | .6073 | .6087 | - | 9 |.6060 |.6020 |.6014 |.6010 | .6015 | .6020 | .6045 | .6070 | - | 10 |.6035 |.6015 |.6010 |.6010 | .6010 | .6010 | .6030 | .6060 | - | 15 |.6040 |.6018 |.6010 |.6011 | .6012 | .6013 | .6033 | .6066 | - | 20 |.6045 |.6024 |.6012 |.6012 | .6014 | .6018 | .6036 | .6074 | - | 25 |.6048 |.6028 |.6014 |.6012 | .6016 | .6022 | .6040 | .6083 | - | 30 |.6054 |.6034 |.6017 |.6013 | .6018 | .6027 | .6044 | .6092 | - | 35 |.6060 |.6039 |.6021 |.6014 | .6022 | .6032 | .6049 | .6103 | - | 40 |.6066 |.6045 |.6025 |.6015 | .6026 | .6037 | .6055 | .6114 | - | 45 |.6054 |.6052 |.6029 |.6016 | .6030 | .6043 | .6062 | .6125 | - | 50 |.6086 |.6060 |.6034 |.6018 | .6035 | .6050 | .6070 | .6140 | - +--------+------+------+------+------+--------+--------+--------+---------+ - - S 21. _Orifices with Edges of Sensible Thickness._--When the edges of - the orifice are not bevelled outwards, but have a sensible thickness, - the coefficient of discharge is somewhat altered. The following table - gives values of the coefficient of discharge for the arrangements of - the orifice shown in vertical section at P, Q, R (fig. 20). The plan - of all the orifices is shown at S. The planks forming the orifice and - sluice were each 2 in. thick, and the orifices were all 24 in. wide. - The heads were measured immediately over the orifice. In this case, - - Q = cb(H - h) [root]{2g(H + h)/2}. - - S 22. _Partially Suppressed Contraction._--Since the contraction of - the jet is due to the convergence towards the orifice of the issuing - streams, it will be diminished if for any portion of the edge of the - orifice the convergence is prevented. Thus, if an internal rim or - border is applied to part of the edge of the orifice (fig. 21), the - convergence for so much of the edge is suppressed. For such cases G. - Bidone found the following empirical formulae applicable:-- - - _Table of Coefficients of Discharge for Rectangular Vertical Orifices - in Fig. 20._ - - +--------+-----------------------------------------------------------------------------------------------+ - |Head h | | - |above | Height of Orifice, H - h, in feet | - |upper +-----------------------+-----------------------+-----------------------+-----------------------+ - |edge of | 1.31 | 0.66 | 0.16 | 0.10 | - |Orifice +-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+ - |in feet.| P | Q | R | P | Q | R | P | Q | R | P | Q | R | - +--------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+ - | 0.328 | 0.598 | 0.644 | 0.648 | 0.634 | 0.665 | 0.668 | 0.691 | 0.664 | 0.666 | 0.710 | 0.694 | 0.696 | - | .656 | 0.609 | 0.653 | 0.657 | 0.640 | 0.672 | 0.675 | 0.685 | 0.687 | 0.688 | 0.696 | 0.704 | 0.706 | - | .787 | 0.612 | 0.655 | 0.659 | 0.641 | 0.674 | 0.677 | 0.684 | 0.690 | 0.692 | 0.694 | 0.706 | 0.708 | - | .984 | 0.616 | 0.656 | 0.660 | 0.641 | 0.675 | 0.678 | 0.683 | 0.693 | 0.695 | 0.692 | 0.709 | 0.711 | - | 1.968 | 0.618 | 0.649 | 0.653 | 0.640 | 0.676 | 0.679 | 0.678 | 0.695 | 0.697 | 0.688 | 0.710 | 0.712 | - | 3.28 | 0.608 | 0.632 | 0.634 | 0.638 | 0.674 | 0.676 | 0.673 | 0.694 | 0.695 | 0.680 | 0.704 | 0.705 | - | 4.27 | 0.602 | 0.624 | 0.626 | 0.637 | 0.673 | 0.675 | 0.672 | 0.693 | 0.694 | 0.678 | 0.701 | 0.702 | - | 4.92 | 0.598 | 0.620 | 0.622 | 0.637 | 0.673 | 0.674 | 0.672 | 0.692 | 0.693 | 0.676 | 0.699 | 0.699 | - | 5.58 | 0.596 | 0.618 | 0.620 | 0.637 | 0.672 | 0.673 | 0.672 | 0.692 | 0.693 | 0.676 | 0.698 | 0.698 | - | 6.56 | 0.595 | 0.615 | 0.617 | 0.636 | 0.671 | 0.672 | 0.671 | 0.691 | 0.692 | 0.675 | 0.696 | 0.696 | - | 9.84 | 0.592 | 0.611 | 0.612 | 0.634 | 0.669 | 0.670 | 0.668 | 0.689 | 0.690 | 0.672 | 0.693 | 0.693 | - +--------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+ - - For rectangular orifices, - - C_c = 0.62(1 + 0.152n/p); - - and for circular orifices, - - C_c = 0.62(1 + 0.128n/p); - - when n is the length of the edge of the orifice over which the border - extends, and p is the whole length of edge or perimeter of the - orifice. The following are the values of c_c, when the border extends - over 1/4, 1/2, or 3/4 of the whole perimeter:-- - - +--------+-----------------------+--------------------+ - | | C_c | C_c | - | n/p | Rectangular Orifices. | Circular Orifices. | - +--------+-----------------------+--------------------+ - | 0.25 | 0.643 | .640 | - | 0.50 | 0.667 | .660 | - | 0.75 | 0.691 | .680 | - +--------+-----------------------+--------------------+ - - [Illustration: FIG. 20.] - - [Illustration: FIG. 21.] - - For larger values of n/p the formulae are not applicable. C. R. - Bornemann has shown, however, that these formulae for suppressed - contraction are not reliable. - - S 23. _Imperfect Contraction._--If the sides of the vessel approach - near to the edge of the orifice, they interfere with the convergence - of the streams to which the contraction is due, and the contraction is - then modified. It is generally stated that the influence of the sides - begins to be felt if their distance from the edge of the orifice is - less than 2.7 times the corresponding width of the orifice. The - coefficients of contraction for this case are imperfectly known. - - [Illustration: FIG. 22.] - - S 24. _Orifices Furnished with Channels of Discharge._--These external - borders to an orifice also modify the contraction. - - The following coefficients of discharge were obtained with openings 8 - in. wide, and small in proportion to the channel of approach (fig. 22, - A, B, C). - - +-----------+-------------------------------------------------------+ - | h2--h1 | h1 in feet. | - | in feet |------+-----+-----+-----+------+-----+-----+-----+-----+ - | |.0656 |.164 |.328 |.656 |1.640 |3.28 |4.92 |6.56 |9.84 | - +-----------+------+-----+-----+-----+------+-----+-----+-----+-----+ - | A\ | .480 |.511 |.542 |.574 | .599 |.601 |.601 |.601 |.601 | - | B > 0.656 | .480 |.510 |.538 |.506 | .592 |.600 |.602 |.602 |.601 | - | C/ | .527 |.553 |.574 |.592 | .607 |.610 |.610 |.609 |.608 | - | | | | | | | | | | | - | A\ | .488 |.577 |.624 |.631 | .625 |.624 |.619 |.613 |.606 | - | B > 0.164 | .487 |.571 |.606 |.617 | .626 |.628 |.627 |.623 |.618 | - | C/ | .585 |.614 |.633 |.645 | .652 |.651 |.650 |.650 |.649 | - +-----------+------+-----+-----+-----+------+-----+-----+-----+-----+ - - [Illustration: FIG. 23.] - - S 25. _Inversion of the Jet._--When a jet issues from a horizontal - orifice, or is of small size compared with the head, it presents no - marked peculiarity of form. But if the orifice is in a vertical - surface, and if its dimensions are not small compared with the head, - it undergoes a series of singular changes of form after leaving - the orifice. These were first investigated by G. Bidone (1781-1839); - subsequently H. G. Magnus (1802-1870) measured jets from different - orifices; and later Lord Rayleigh (_Proc. Roy. Soc._ xxix. 71) - investigated them anew. - - Fig. 23 shows some forms, the upper figure giving the shape of the - orifices, and the others sections of the jet. The jet first contracts - as described above, in consequence of the convergence of the fluid - streams within the vessel, retaining, however, a form similar to that - of the orifice. Afterwards it expands into sheets in planes - perpendicular to the sides of the orifice. Thus the jet from a - triangular orifice expands into three sheets, in planes bisecting at - right angles the three sides of the triangle. Generally a jet from an - orifice, in the form of a regular polygon of n sides, forms n sheets - in planes perpendicular to the sides of the polygon. - - Bidone explains this by reference to the simpler case of meeting - streams. If two equal streams having the same axis, but moving in - opposite directions, meet, they spread out into a thin disk normal to - the common axis of the streams. If the directions of two streams - intersect obliquely they spread into a symmetrical sheet perpendicular - to the plane of the streams. - - [Illustration: FIG. 24.] - - Let a1, a2 (fig. 24) be two points in an orifice at depths h1, h2 from - the free surface. The filaments issuing at a1, a2 will have the - different velocities [root](2gh1) and [root](2gh2). Consequently they - will tend to describe parabolic paths a1cb1 and a2cb2 of different - horizontal range, and intersecting in the point c. But since two - filaments cannot simultaneously flow through the same point, they must - exercise mutual pressure, and will be deflected out of the paths they - tend to describe. It is this mutual pressure which causes the - expansion of the jet into sheets. - - Lord Rayleigh pointed out that, when the orifices are small and the - head is not great, the expansion of the sheets in directions - perpendicular to the direction of flow reaches a limit. Sections taken - at greater distance from the orifice show a contraction of the sheets - until a compact form is reached similar to that at the first - contraction. Beyond this point, if the jet retains its coherence, - sheets are thrown out again, but in directions bisecting the angles - between the previous sheets. Lord Rayleigh accepts an explanation of - this contraction first suggested by H. Buff (1805-1878), namely, that - it is due to surface tension. - - S 26. _Influence of Temperature on Discharge of Orifices._--Professor - VV. C. Unwin found (_Phil. Mag._, October 1878, p. 281) that for - sharp-edged orifices temperature has a very small influence on the - discharge. For an orifice 1 cm. in diameter with heads of about 1 to - 1(1/2) ft. the coefficients were:-- - - Temperature F. C. - 205 deg. .594 - 62 deg. .598 - - For a conoidal or bell-mouthed orifice 1 cm. diameter the effect of - temperature was greater:-- - - Temperature F. C. - 190 deg. 0.987 - 130 deg. 0.974 - 60 deg. 0.942 - - an increase in velocity of discharge of 4% when the temperature - increased 130 deg. - - J. G. Mair repeated these experiments on a much larger scale (_Proc. - Inst. Civ. Eng._ lxxxiv.). For a sharp-edged orifice 2(1/2) in. - diameter, with a head of 1.75 ft., the coefficient was 0.604 at 57 - deg. and 0.607 at 179 deg. F., a very small difference. With a - conoidal orifice the coefficient was 0.961 at 55 deg. and 0.98l at 170 - deg. F. The corresponding coefficients of resistance are 0.0828 and - 0.0391, showing that the resistance decreases to about half at the - higher temperature. - - S 27. _Fire Hose Nozzles._--Experiments have been made by J. R. - Freeman on the coefficient of discharge from smooth cone nozzles used - for fire purposes. The coefficient was found to be 0.983 for (3/4)-in. - nozzle; 0.982 for 7/8 in.; 0.972 for 1 in.; 0.976 for 1(1/8) in.; and - 0.971 for 1(1/4) in. The nozzles were fixed on a taper play-pipe, and - the coefficient includes the resistance of this pipe (_Amer. Soc. Civ. - Eng._ xxi., 1889). Other forms of nozzle were tried such as ring - nozzles for which the coefficient was smaller. - - - IV. THEORY OF THE STEADY MOTION OF FLUIDS. - - S 28. The general equation of the steady motion of a fluid given under - Hydrodynamics furnishes immediately three results as to the - distribution of pressure in a stream which may here be assumed. - - (a) If the motion is rectilinear and uniform, the variation of - pressure is the same as in a fluid at rest. In a stream flowing in an - open channel, for instance, when the effect of eddies produced by the - roughness of the sides is neglected, the pressure at each point is - simply the hydrostatic pressure due to the depth below the free - surface. - - (b) If the velocity of the fluid is very small, the distribution of - pressure is approximately the same as in a fluid at rest. - - (c) If the fluid molecules take precisely the accelerations which they - would have if independent and submitted only to the external forces, - the pressure is uniform. Thus in a jet falling freely in the air the - pressure throughout any cross section is uniform and equal to the - atmospheric pressure. - - (d) In any bounded plane section traversed normally by streams which - are rectilinear for a certain distance on either side of the section, - the distribution of pressure is the same as in a fluid at rest. - - - DISTRIBUTION OF ENERGY IN INCOMPRESSIBLE FLUIDS. - - S 29. _Application of the Principle of the Conservation of Energy to - Cases of Stream Line Motion._--The external and internal work done on - a mass is equal to the change of kinetic energy produced. In many - hydraulic questions this principle is difficult to apply, because from - the complicated nature of the motion produced it is difficult to - estimate the total kinetic energy generated, and because in some cases - the internal work done in overcoming frictional or viscous resistances - cannot be ascertained; but in the case of stream line motion it - furnishes a simple and important result known as Bernoulli's theorem. - - [Illustration: FIG. 25.] - - Let AB (fig. 25) be any one elementary stream, in a steadily moving - fluid mass. Then, from the steadiness of the motion, AB is a fixed - path in space through which a stream of fluid is constantly flowing. - Let OO be the free surface and XX any horizontal datum line. Let - [omega] be the area of a normal cross section, v the velocity, p the - intensity of pressure, and z the elevation above XX, of the elementary - stream AB at A, and [omega]1, p1, v1, z1 the same quantities at B. - Suppose that in a short time t the mass of fluid initially occupying - AB comes to A'B'. Then AA', BB' are equal to vt, v1t, and the volumes - of fluid AA', BB' are the equal inflow and outflow = Qt = [omega]vt = - [omega]1v1t, in the given time. If we suppose the filament AB - surrounded by other filaments moving with not very different - velocities, the frictional or viscous resistance on its surface will - be small enough to be neglected, and if the fluid is incompressible no - internal work is done in change of volume. Then the work done by - external forces will be equal to the kinetic energy produced in the - time considered. - - The normal pressures on the surface of the mass (excluding the ends A, - B) are at each point normal to the direction of motion, and do no - work. Hence the only external forces to be reckoned are gravity and - the pressures on the ends of the stream. - - The work of gravity when AB falls to A'B' is the same as that of - transferring AA' to BB'; that is, GQt(z - z1). The work of the - pressures on the ends, reckoning that at B negative, because it is - opposite to the direction of motion, is (p[omega] X vt) - (p1[omega]1 - X v1t) = Qt(p - p1). The change of kinetic energy in the time t is the - difference of the kinetic energy originally possessed by AA' and that - finally acquired by BB', for in the intermediate part A'B there is no - change of kinetic energy, in consequence of the steadiness of the - motion. But the mass of AA' and BB' is GQt/g, and the change of - kinetic energy is therefore (GQt/g) (v1^2/2 - v^2/2). Equating this to - the work done on the mass AB, - - GQt(z - z1) + Qt(p - p1) = (GQt/g)(v1^2/2 - v^2/2). - - Dividing by GQt and rearranging the terms, - - v^2/2g + p/G + z = v1^2/2g + p1/G + z1; (1) - - or, as A and B are any two points, - - v^2/2g + p/G + z = constant = H. (2) - - Now v^2/2g is the head due to the velocity v, p/G is the head - equivalent to the pressure, and z is the elevation above the datum - (see S 16). Hence the terms on the left are the total head due to - velocity, pressure, and elevation at a given cross section of the - filament, z is easily seen to be the work in foot-pounds which would - be done by 1 lb. of fluid falling to the datum line, and similarly p/G - and v^2/2g are the quantities of work which would be done by 1 lb. of - fluid due to the pressure p and velocity v. The expression on the left - of the equation is, therefore, the total energy of the stream at the - section considered, per lb. of fluid, estimated with reference to the - datum line XX. Hence we see that in stream line motion, under - the restrictions named above, the total energy per lb. of fluid is - uniformly distributed along the stream line. If the free surface of - the fluid OO is taken as the datum, and -h, -h1 are the depths of A - and B measured down from the free surface, the equation takes the form - - v^2/2g + p/G - h = v1^2/2g + p1/G - h1; (3) - - or generally - - v^2/2g + p/G - h = constant. (3a) - - [Illustration: FIG. 26.] - - S 30. _Second Form of the Theorem of Bernoulli._--Suppose at the two - sections A, B (fig. 26) of an elementary stream small vertical pipes - are introduced, which may be termed pressure columns (S 8), having - their lower ends accurately parallel to the direction of flow. In such - tubes the water will rise to heights corresponding to the pressures at - A and B. Hence b = p/G, and b' = p1/G. Consequently the tops of the - pressure columns A' and B' will be at total heights b + c = p/G + z - and b' + c' = p1/G + z1 above the datum line XX. The difference of - level of the pressure column tops, or the fall of free surface level - between A and B, is therefore - - [xi] = (p - p1)/G + (z - z1); - - and this by equation (1), S 29 is (v1^2 - v^2)/2g. That is, the fall - of free, surface level between two sections is equal to the difference - of the heights due to the velocities at the sections. The line A'B' is - sometimes called the line of hydraulic gradient, though this term is - also used in cases where friction needs to be taken into account. It - is the line the height of which above datum is the sum of the - elevation and pressure head at that point, and it falls below a - horizontal line A"B" drawn at H ft. above XX by the quantities a = - v^2/2g and a' = v1^2/2g, when friction is absent. - - S 31. _Illustrations of the Theorem of Bernoulli._ In a lecture to the - mechanical section of the British Association in 1875, W. Froude gave - some experimental illustrations of the principle of Bernoulli. He - remarked that it was a common but erroneous impression that a fluid - exercises in a contracting pipe A (fig. 27) an excess of pressure - against the entire converging surface which it meets, and that, - conversely, as it enters an enlargement B, a relief of pressure is - experienced by the entire diverging surface of the pipe. Further it is - commonly assumed that when passing through a contraction C, there is - in the narrow neck an excess of pressure due to the squeezing together - of the liquid at that point. These impressions are in no respect - correct; the pressure is smaller as the section of the pipe is smaller - and conversely. - - [Illustration: FIG. 27.] - - Fig. 28 shows a pipe so formed that a contraction is followed by an - enlargement, and fig. 29 one in which an enlargement is followed by a - contraction. The vertical pressure columns show the decrease of - pressure at the contraction and increase of pressure at the - enlargement. The line abc in both figures shows the variation of free - surface level, supposing the pipe frictionless. In actual pipes, - however, work is expended in friction against the pipe; the total head - diminishes in proceeding along the pipe, and the free surface level is - a line such as ab1c1, falling below abc. - - Froude further pointed out that, if a pipe contracts and enlarges - again to the same size, the resultant pressure on the converging part - exactly balances the resultant pressure on the diverging part so that - there is no tendency to move the pipe bodily when water flows through - it. Thus the conical part AB (fig. 30) presents the same projected - surface as HI, and the pressures parallel to the axis of the pipe, - normal to these projected surfaces, balance each other. Similarly the - pressures on BC, CD balance those on GH, EG. In the same way, in any - combination of enlargements and contractions, a balance of pressures, - due to the flow of liquid parallel to the axis of the pipe, will be - found, provided the sectional area and direction of the ends are the - same. - - [Illustration: FIG. 28.] - - [Illustration: FIG. 29.] - - The following experiment is interesting. Two cisterns provided with - converging pipes were placed so that the jet from one was exactly - opposite the entrance to the other. The cisterns being filled very - nearly to the same level, the jet from the left-hand cistern A entered - the right-hand cistern B (fig. 31), shooting across the free space - between them without any waste, except that due to indirectness of aim - and want of exact correspondence in the form of the orifices. In the - actual experiment there was 18 in. of head in the right and 20(1/2) - in. of head in the left-hand cistern, so that about 2(1/2) in. were - wasted in friction. It will be seen that in the open space between the - orifices there was no pressure, except the atmospheric pressure acting - uniformly throughout the system. - - [Illustration: FIG. 30.] - - [Illustration: FIG. 31.] - - S 32. _Venturi Meter._--An ingenious application of the variation of - pressure and velocity in a converging and diverging pipe has been made - by Clemens Herschel in the construction of what he terms a Venturi - Meter for measuring the flow in water mains. Suppose that, as in fig. - 32, a contraction is made in a water main, the change of section being - gradual to avoid the production of eddies. The ratio [rho] of the - cross sections at A and B, that is at inlet and throat, is in actual - meters 5 to 1 to 20 to 1, and is very carefully determined by the - maker of the meter. Then, if v and u are the velocities at A and B, u - = [rho]v. Let pressure pipes be introduced at A, B and C, and let H1, - H, H2 be the pressure heads at those points. Since the velocity at B - is greater than at A the pressure will be less. Neglecting friction - - H1 + v^2/2g = H + u^2/2g, - - H1 - H = (u^2 - v^2)/2g = ([rho]^2 - 1)v^2/2g. - - Let h = H1 - H be termed the Venturi head, then - - u = [root]{[rho]^2 . 2gh/([rho]^2 - 1)}, - - from which the velocity through the throat and the discharge of the - main can be calculated if the areas at A and B are known and h - observed. Thus if the diameters at A and B are 4 and 12 in., the areas - are 12.57 and 113.1 sq. in., and [rho] = 9, - - u = [root]81/80 [root](2gh) = 1.007 [root](2gh). - - If the observed Venturi head is 12 ft., - - u = 28 ft. per sec., - - and the discharge of the main is - - 28 X 12.57 = 351 cub. ft. per sec. - - [Illustration: FIG. 32.] - - Hence by a simple observation of pressure difference, the flow in the - main at any moment can be determined. Notice that the pressure height - at C will be the same as at A except for a small loss h_f due to - friction and eddying between A and B. To get the pressure at the - throat very exactly Herschel surrounds it by an annular passage - communicating with the throat by several small holes, sometimes formed - in vulcanite to prevent corrosion. Though constructed to prevent - eddying as much as possible there is some eddy loss. The main effect - of this is to cause a loss of head between A and C which may vary from - a fraction of a foot to perhaps 5 ft. at the highest velocities at - which a meter can be used. The eddying also affects a little the - Venturi head h. Consequently an experimental coefficient must be - determined for each meter by tank measurement. The range of this - coefficient is, however, surprisingly small. If to allow for friction, - u = k[root]{[rho]^2/([rho]^2 - 1)}[root](2gh), then Herschel found - values of k from 0.97 to 1.0 for throat velocities varying from 8 to - 28 ft. per sec. The meter is extremely convenient. At Staines - reservoirs there are two meters of this type on mains 94 in. in - diameter. Herschel contrived a recording arrangement which records the - variation of flow from hour to hour and also the total flow in any - given time. In Great Britain the meter is constructed by G. Kent, who - has made improvements in the recording arrangement. - - [Illustration: FIG. 33.] - - In the Deacon Waste Water Meter (fig. 33) a different principle is - used. A disk D, partly counter-balanced by a weight, is suspended in - the water flowing through the main in a conical chamber. The - unbalanced weight of the disk is supported by the impact of the water. - If the discharge of the main increases the disk rises, but as it rises - its position in the chamber is such that in consequence of the larger - area the velocity is less. It finds, therefore, a new position of - equilibrium. A pencil P records on a drum moved by clockwork the - position of the disk, and from this the variation of flow is inferred. - - S 33. _Pressure, Velocity and Energy in Different Stream Lines._--The - equation of Bernoulli gives the variation of pressure and velocity - from point to point along a stream line, and shows that the total - energy of the flow across any two sections is the same. Two other - directions may be defined, one normal to the stream line and in the - plane containing its radius of curvature at any point, the other - normal to the stream line and the radius of curvature. For the - problems most practically useful it will be sufficient to consider the - stream lines as parallel to a vertical or horizontal plane. If the - motion is in a vertical plane, the action of gravity must be taken - into the reckoning; if the motion is in a horizontal plane, the terms - expressing variation of elevation of the filament will disappear.[3] - - [Illustration: FIG. 34.] - - Let AB, CD (fig. 34) be two consecutive stream lines, at present - assumed to be in a vertical plane, and PQ a normal to these lines - making an angle [phi] with the vertical. Let P, Q be two particles - moving along these lines at a distance PQ = ds, and let z be the - height of Q above the horizontal plane with reference to which the - energy is measured, v its velocity, and p its pressure. Then, if H is - the total energy at Q per unit of weight of fluid, - - H = z + p/G + v^2/2g. - - Differentiating, we get - - dH = dz + dp/G + vdv/g, (1) - - for the increment of energy between Q and P. But - - dz = PQ cos [phi] = ds cos [phi]; - - .: dH = dp/G + v dv/g + ds cos [phi], (1a) - - where the last term disappears if the motion is in a horizontal plane. - - Now imagine a small cylinder of section [omega] described round PQ as - an axis. This will be in equilibrium under the action of its - centrifugal force, its weight and the pressure on its ends. But its - volume is [omega] ds and its weight G[omega]ds. Hence, taking the - components of the forces parallel to PQ-- - - [omega]dp = Gv^2[omega] ds/g[rho] - G[omega] cos [phi] ds, - - where [rho] is the radius of curvature of the stream line at Q. - Consequently, introducing these values in (1), - - dH = v^2 ds/g[rho] + v dv/g = (v/g)(v/[rho] + dv/ds) ds. (2) - - - CURRENTS - - S 34. _Rectilinear Current._--Suppose the motion is in parallel - straight stream lines (fig. 35) in a vertical plane. Then [rho] is - infinite, and from eq. (2), S 33, - - dH = v dv/g. - - Comparing this with (1) we see that - - dz + dp/G = 0; - - .: z + p/G = constant; (3) - - or the pressure varies hydrostatically as in a fluid at rest. For two - stream lines in a horizontal plane, z is constant, and therefore p is - constant. - - [Illustration: FIG. 35.] - - _Radiating Current._--Suppose water flowing radially between - horizontal parallel planes, at a distance apart = [delta]. Conceive - two cylindrical sections of the current at radii r1 and r2, where the - velocities are v1 and v2, and the pressures p1 and p2. Since the flow - across each cylindrical section of the current is the same, - - Q = 2[pi]r1[delta]v1 = 2[pi]r2[delta]v2 - - r1v1 = r2v2 - - r1/r2 = v2/v1. (4) - - The velocity would be infinite at radius 0, if the current could be - conceived to extend to the axis. Now, if the motion is steady, - - H = p1/G + v1^2/2g = p2/G + v2^2/2g; - = p2/G + r1^2 + v1^2/r2^2 2g; - - (p2- p1)/G = v1^2(1 - r1^2/r2^2)/2g; (5) - - p2/G = H - r1^2v1^2/r2^2 2g. (6) - - Hence the pressure increases from the interior outwards, in a way - indicated by the pressure columns in fig. 36, the curve through the - free surfaces of the pressure columns being, in a radial section, the - quasi-hyperbola of the form xy^2 = c^3. This curve is asymptotic to a - horizontal line, H ft. above the line from which the pressures are - measured, and to the axis of the current. - - [Illustration: FIG. 36.] - - _Free Circular Vortex._--A free circular vortex is a revolving mass of - water, in which the stream lines are concentric circles, and in which - the total head for each stream line is the same. Hence, if by any slow - radial motion portions of the water strayed from one stream line to - another, they would take freely the velocities proper to their new - positions under the action of the existing fluid pressures only. - - For such a current, the motion being horizontal, we have for all the - circular elementary streams - - H = p/G + v^2/2g = constant; - - .: dH = dp/G + v dv/g = 0. (7) - - Consider two stream lines at radii r and r + dr (fig. 36). Then in - (2), S 33, [rho] = r and ds = dr, - - v^2 dr/gr + v dv/g = 0, - - dv/v = -dr/r, - - v [oo] 1/r, (8) - - precisely as in a radiating current; and hence the distribution of - pressure is the same, and formulae 5 and 6 are applicable to this - case. - - _Free Spiral Vortex._--As in a radiating and circular current the - equations of motion are the same, they will also apply to a vortex in - which the motion is compounded of these motions in any proportions, - provided the radial component of the motion varies inversely as the - radius as in a radial current, and the tangential component varies - inversely as the radius as in a free vortex. Then the whole velocity - at any point will be inversely proportional to the radius of the - point, and the fluid will describe stream lines having a constant - inclination to the radius drawn to the axis of the current. That is, - the stream lines will be logarithmic spirals. When water is delivered - from the circumference of a centrifugal pump or turbine into a - chamber, it forms a free vortex of this kind. The water flows spirally - outwards, its velocity diminishing and its pressure increasing - according to the law stated above, and the head along each spiral - stream line is constant. - - S 35. _Forced Vortex._--If the law of motion in a rotating current is - different from that in a free vortex, some force must be applied to - cause the variation of velocity. The simplest case is that of a - rotating current in which all the particles have equal angular - velocity, as for instance when they are driven round by radiating - paddles revolving uniformly. Then in equation (2), S 33, considering - two circular stream lines of radii r and r + dr (fig. 37), we have - [rho] = r, ds = dr. If the angular velocity is [alpha], then v = - [alpha]r and dv = [alpha]dr. Hence - - dH = [alpha]^2r dr/g + [alpha]^2r dr/g = 2[alpha]^2r dr/g. - - Comparing this with (1), S 33, and putting dz = 0, because the motion - is horizontal, - - dp/G + [alpha]^2r dr/g = 2[alpha]^2r dr/g, - - dp/G = [alpha]^2rdr/g, - - p/G = [alpha]^2/2g + constant. (9) - - Let p1, r1, v1 be the pressure, radius and velocity of one cylindrical - section, p2, r2, v2 those of another; then - - p1/G - [alpha]^2r1^2/2g = p2/G - [alpha]^2r2^2/2g; - - (p2 - p1)/G = [alpha]^2(r2^2 - r1^2)/2g = (v2^2 - v1^2)/2g. (10) - - That is, the pressure increases from within outwards in a curve which - in radial sections is a parabola, and surfaces of equal pressure are - paraboloids of revolution (fig. 37). - - [Illustration: FIG. 37.] - - - DISSIPATION OF HEAD IN SHOCK - - S 36. _Relation of Pressure and Velocity in a Stream in Steady Motion - when the Changes of Section of the Stream are Abrupt._--When a stream - changes section abruptly, rotating eddies are formed which dissipate - energy. The energy absorbed in producing rotation is at once - abstracted from that effective in causing the flow, and sooner or - later it is wasted by frictional resistances due to the rapid relative - motion of the eddying parts of the fluid. In such cases the work thus - expended internally in the fluid is too important to be neglected, and - the energy thus lost is commonly termed energy lost in shock. Suppose - fig. 38 to represent a stream having such an abrupt change of section. - Let AB, CD be normal sections at points where ordinary stream line - motion has not been disturbed and where it has been re-established. - Let [omega], p, v be the area of section, pressure and velocity at AB, - and [omega]1, p1, v1 corresponding quantities at CD. Then if no work - were expended internally, and assuming the stream horizontal, we - should have - - p/G + v^2/2g = p1/G + v1^2/2g. (1) - - But if work is expended in producing irregular eddying motion, the - head at the section CD will be diminished. - - Suppose the mass ABCD comes in a short time t to A'B'C'D'. The - resultant force parallel to the axis of the stream is - - p[omega] + p0([omega]1 - [omega]) - p1[omega]1, - - where p0 is put for the unknown pressure on the annular space between - AB and EF. The impulse of that force is - - {p[omega] + p0([omega]1 - [omega]) - p1[omega]1} t. - - [Illustration: FIG. 38.] - - The horizontal change of momentum in the same time is the difference - of the momenta of CDC'D' and ABA'B', because the amount of momentum - between A'B' and CD remains unchanged if the motion is steady. The - volume of ABA'B' or CDC'D', being the inflow and outflow in the time - t, is Qt = [omega]vt = [omega]1v1t, and the momentum of these masses - is (G/g)Qvt and (G/g)Qv1t. The change of momentum is therefore - (G/g)Qt(v1 - v). Equating this to the impulse, - - {p[omega] + p0([omega]1 - [omega]) - p1[omega]1}t = (G/g)Qt(v1 - v). - - Assume that p0 = p, the pressure at AB extending unchanged through the - portions of fluid in contact with AE, BF which lie out of the path of - the stream. Then (since Q = [omega]1v1) - - (p - p1) = (G/g) v1 (v1 - v); - - p/G - p1/G = v1 (v1 - v)/g; (2) - - p/G + v^2/2g = p1/G + v1^2/2g + (v - v1)^2/2g. (3) - - This differs from the expression (1), S 29, obtained for cases where - no sensible internal work is done, by the last term on the right. That - is, (v - v1)^2/2g has to be added to the total head at CD, which is - p1/G + v1^2/2g, to make it equal to the total head at AB, or (v - - v1)^2/2g is the head lost in shock at the abrupt change of section. - But (v - v1) is the relative velocity of the two parts of the stream. - Hence, when an abrupt change of section occurs, the head due to the - relative velocity is lost in shock, or (v - v1)^2/2g foot-pounds of - energy is wasted for each pound of fluid. Experiment verifies this - result, so that the assumption that p0 = p appears to be admissible. - - If there is no shock, - - p1/G = p/G + (v^2 - v1^2)/2g. - - If there is shock, - - p1/G = p/G - v1(v1 - v)/g. - - Hence the pressure head at CD in the second case is less than in the - former by the quantity (v - v1)^2/2g, or, putting [omega]1v1 = - [omega]v, by the quantity - - (v^2/2g)(1 - [omega]/[omega]1)^2. (4) - - - V. THEORY OF THE DISCHARGE FROM ORIFICES AND MOUTHPIECES - - [Illustration: FIG. 39.] - - S 37. _Minimum Coefficient of Contraction. Re-entrant Mouthpiece of - Borda._--In one special case the coefficient of contraction can be - determined theoretically, and, as it is the case where the convergence - of the streams approaching the orifice takes place through the - greatest possible angle, the coefficient thus determined is the - minimum coefficient. - - Let fig. 39 represent a vessel with vertical sides, OO being the free - water surface, at which the pressure is p_a. Suppose the liquid issues - by a horizontal mouthpiece, which is re-entrant and of the greatest - length which permits the jet to spring clear from the inner end of the - orifice, without adhering to its sides. With such an orifice the - velocity near the points CD is negligible, and the pressure at those - points may be taken equal to the hydrostatic pressure due to the depth - from the free surface. Let [Omega] be the area of the mouthpiece AB, - [omega] that of the contracted jet aa Suppose that in a short time t, - the mass OOaa comes to the position O'O' a'a'; the impulse of the - horizontal external forces acting on the mass during that time is - equal to the horizontal change of momentum. - - The pressure on the side OC of the mass will be balanced by the - pressure on the opposite side OE, and so for all other portions of the - vertical surfaces of the mass, excepting the portion EF opposite the - mouthpiece and the surface AaaB of the jet. On EF the pressure is - simply the hydrostatic pressure due to the depth, that is, (p_a + Gh). - On the surface and section AaaB of the jet, the horizontal resultant - of the pressure is equal to the atmospheric pressure p_a acting on the - vertical projection AB of the jet; that is, the resultant pressure is - -p_a[Omega]. Hence the resultant horizontal force for the whole mass - OOaa is (p_a + Gh)[Omega] - p_a[Omega] = Gh[Omega]. Its impulse in the - time t is Gh[Omega]t. Since the motion is steady there is no change of - momentum between O'O' and aa. The change of horizontal momentum is, - therefore, the difference of the horizontal momentum lost in the space - OOO'O' and gained in the space aaa'a'. In the former space there is no - horizontal momentum. - - The volume of the space aaa'a' is [omega]vt; the mass of liquid in - that space is (G/g)[omega]vt; its momentum is (G/g)[omega]v^2t. - Equating impulse to momentum gained, - - Gh[Omega] = (G/g)[omega]v^2t; - - .: [omega]/[Omega] = gh/v^2 - - But - - v^2 = 2gh, and [omega]/[Omega] = c_c; - - .: [omega]/[Omega] = 1/2 = c_c; - - a result confirmed by experiment with mouthpieces of this kind. A - similar theoretical investigation is not possible for orifices in - plane surfaces, because the velocity along the sides of the vessel in - the neighbourhood of the orifice is not so small that it can be - neglected. The resultant horizontal pressure is therefore greater than - Gh[Omega], and the contraction is less. The experimental values of the - coefficient of discharge for a re-entrant mouthpiece are 0.5149 - (Borda), 0.5547 (Bidone), 0.5324 (Weisbach), values which differ - little from the theoretical value, 0.5, given above. - - [Illustration: FIG. 40.] - - S 38. _Velocity of Filaments issuing in a Jet._--A jet is composed of - fluid filaments or elementary streams, which start into motion at some - point in the interior of the vessel from which the fluid is - discharged, and gradually acquire the velocity of the jet. Let Mm, - fig. 40 be such a filament, the point M being taken where the velocity - is insensibly small, and m at the most contracted section of the jet, - where the filaments have become parallel and exercise uniform mutual - pressure. Take the free surface AB for datum line, and let p1, v1, h1, - be the pressure, velocity and depth below datum at M; p, v, h, the - corresponding quantities at m. Then S 29, eq. (3a), - - v1^2/2g + p1/G - h1 = v^2/2g + p/G - h (1) - - But at M, since the velocity is insensible, the pressure is the - hydrostatic pressure due to the depth; that is v1 = 0, p1 = p_a + Gh1. - At m, p = p_a, the atmospheric pressure round the jet. Hence, - inserting these values, - - 0 + p_a/G + h1 - h1 = v^2/2g + p_a/G - h; - - v^2/2g = h; (2) - - or v = [root](2gh) = 8.025V [root]h. (2a) - - [Illustration: FIG. 41.] - - That is, neglecting the viscosity of the fluid, the velocity of - filaments at the contracted section of the jet is simply the velocity - due to the difference of level of the free surface in the reservoir - and the orifice. If the orifice is small in dimensions compared with - h, the filaments will all have nearly the same velocity, and if h is - measured to the centre of the orifice, the equation above gives the - mean velocity of the jet. - - _Case of a Submerged Orifice._--Let the orifice discharge below the - level of the tail water. Then using the notation shown in fig. 41, we - have at M, v1 = 0, p1 = Gh; + p_a at m, p = Gh3 + p_a. Inserting these - values in (3), S 29, - - 0 + h1 + p_a/G - h1 = v^2/2g + h3 - h2 + p_a/G; - - v^2/2g = h2 - h3 = h, (3) - - where h is the difference of level of the head and tail water, and may - be termed the _effective head_ producing flow. - - [Illustration: FIG. 42.] - - _Case where the Pressures are different on the Free Surface and at the - Orifice._--Let the fluid flow from a vessel in which the pressure is - p0 into a vessel in which the pressure is p, fig. 42. The pressure p0 - will produce the same effect as a layer of fluid of thickness p0/G - added to the head water; and the pressure p, will produce the same - effect as a layer of thickness p/G added to the tail water. Hence the - effective difference of level, or effective head producing flow, will - be - - h = h0 + p0/G - p/G; - - and the velocity of discharge will be - - v = [root][2g {h0 + (p0 - p)/G}]. (4) - - We may express this result by saying that differences of pressure at - the free surface and at the orifice are to be reckoned as part of the - effective head. - - Hence in all cases thus far treated the velocity of the jet is the - velocity due to the effective head, and the discharge, allowing for - contraction of the jet, is - - Q = c[omega]v = c[omega] [root](2gh), (5) - - where [omega] is the area of the orifice, c[omega] the area of the - contracted section of the jet, and h the effective head measured to - the centre of the orifice. If h and [omega] are taken in feet, Q is in - cubic feet per second. - - It is obvious, however, that this formula assumes that all the - filaments have sensibly the same velocity. That will be true for - horizontal orifices, and very approximately true in other cases, if - the dimensions of the orifice are not large compared with the head h. - In large orifices in say a vertical surface, the value of h is - different for different filaments, and then the velocity of different - filaments is not sensibly the same. - - - SIMPLE ORIFICES--HEAD CONSTANT - - [Illustration: FIG. 43.] - - S 39. _Large Rectangular Jets from Orifices in Vertical Plane - Surfaces._--Let an orifice in a vertical plane surface be so formed - that it produces a jet having a rectangular contracted section with - vertical and horizontal sides. Let b (fig. 43) be the breadth of the - jet, h1 and h2 the depths below the free surface of its upper and - lower surfaces. Consider a lamina of the jet between the depths h and - h + dh. Its normal section is bdh, and the velocity of discharge - [root](2gh). The discharge per second in this lamina is therefore - b[root](2gh) dh, and that of the whole jet is therefore - _ - /h2 - Q = | b [root](2gh) dh - _/h1 - - = 2/3 b[root](2g) {h2^(3/2) - h1^(3/2)}, (6) - - where the first factor on the right is a coefficient depending on the - form of the orifice. - - Now an orifice producing a rectangular jet must itself be very - approximately rectangular. Let B be the breadth, H1, H2, the depths to - the upper and lower edges of the orifice. Put - - b [h2^(3/2) - h1^(3/2)] / B [H2^(3/2) - H1^(3/2)] = c. (7) - - Then the discharge, in terms of the dimensions of the orifice, instead - of those of the jet, is - - Q = (2/3)cB [root](2g) [H2^(3/2) - H1^(3/2)], (8) - - the formula commonly given for the discharge of rectangular orifices. - The coefficient c is not, however, simply the coefficient of - contraction, the value of which is - - b(h2 - h1)/B(H2 - H1), - - and not that given in (7). It cannot be assumed, therefore, that c in - equation (8) is constant, and in fact it is found to vary for - different values of B/H2 and B/H1, and must be ascertained - experimentally. - - _Relation between the Expressions (5) and (8)._--For a rectangular - orifice the area of the orifice is [omega] = B(H2 - H1), and the - depth measured to its centre is (1/2)(H2 + H1). Putting these values - in (5), - - Q1 = cB(H2 - H1) [root]{g(H2 + H1)}. - - From (8) the discharge is - - Q2 = (2/3)cB [root](2g) [H2^(3/2) - H1^(3/2)]. - - Hence, for the same value of c in the two cases, - - Q2/Q1 = (2/3)[H2^(3/2) - H1^(3/2)] / [(H2 - H1)[root]{(H2 + H1)/2}]. - - Let H1/H2 = [sigma], then - - Q2/Q1 = 0.9427(1 - [sigma]^(3/2)) / - {1 - [sigma] [root]{(1 + [sigma])}}. (9) - - If H1 varies from 0 to [infinity], [sigma]( = H1/H2) varies from 0 to - 1. The following table gives values of the two estimates of the - discharge for different values of [sigma]:-- - - +------------------+--------+------------------+--------+ - | H1/H2 = [sigma]. | Q2/Q1. | H1/H2 = [sigma]. | Q2/Q1. | - +------------------+--------+------------------+--------+ - | 0.0 | .943 | 0.8 | .999 | - | 0.2 | .979 | 0.9 | .999 | - | 0.5 | .995 | 1.0 | 1.000 | - | 0.7 | .998 | | | - +------------------+--------+------------------+--------+ - - Hence it is obvious that, except for very small values of [sigma], the - simpler equation (5) gives values sensibly identical with those of - (8). When [sigma]<0.5 it is better to use equation (8) with values of - c determined experimentally for the particular proportions of orifice - which are in question. - - [Illustration: FIG. 44.] - - S 40. _Large Jets having a Circular Section from Orifices in a - Vertical Plane Surface._--Let fig. 44 represent the section of the - jet, OO being the free surface level in the reservoir. The discharge - through the horizontal strip aabb, of breadth aa = b, between the - depths h1 + y and h1 + y + dy, is - - dQ = b [root]{2g(h1 + y)} dy. - - The whole discharge of the jet is - _ - /d - Q = | b [root]{2g(h1 + y)} dy. - _/0 - - But b = d sin [phi]; y = (1/2)d(1 - cos [phi]); dy = (1/2)d sin [phi] - d[phi]. Let [epsilon] = d/(2h1 + d), then - - _ - /[pi] - Q = (1/2)d^2 [root]{2g(h1 + d/2)} | sin^2 [phi][root]{1 - [epsilon] cos [phi]} d[phi]. - _/0 - - From eq. (5), putting [omega] = [pi]d^2/4, h = h1 + d/2, c = 1 when d - is the diameter of the jet and not that of the orifice, - - Q1 = (1/4)[pi]d^2 [root]{2g (h1 + d/2)}, - _ - /[pi] - Q/Q1 = 2/[pi] | sin^2 [phi] [root]{1 - [epsilon] cos [phi]} d[phi]. - _/0 - - For - - h1 = [infinity], [epsilon] = 0 and Q/Q1 = 1; - - and for - - h1 = 0, [epsilon] = 1 and Q/Q1 = 0.96. - - So that in this case also the difference between the simple formula - (5) and the formula above, in which the variation of head at different - parts of the orifice is taken into account, is very small. - - - NOTCHES AND WEIRS - - S 41. _Notches, Weirs and Byewashes._--A notch is an orifice extending - up to the free surface level in the reservoir from which the discharge - takes place. A weir is a structure over which the water flows, the - discharge being in the same conditions as for a notch. The formula of - discharge for an orifice of this kind is ordinarily deduced by putting - H1 = 0 in the formula for the corresponding orifice, obtained as in - the preceding section. Thus for a rectangular notch, put H1 = 0 in - (8). Then - - Q = (2/3)cB [root](2g) H^(3/2), (11) - - where H is put for the depth to the crest of the weir or the bottom of - the notch. Fig. 45 shows the mode in which the discharge occurs in the - case of a rectangular notch or weir with a level crest. As, the free - surface level falls very sensibly near the notch, the head H should be - measured at some distance back from the notch, at a point where the - velocity of the water is very small. - - Since the area of the notch opening is BH, the above formula is of the - form - - Q = c X BH X k [root](2gH), - - where k is a factor depending on the form of the notch and expressing - the ratio of the mean velocity of discharge to the velocity due to the - depth H. - - S 42. _Francis's Formula for Rectangular Notches._--The jet discharged - through a rectangular notch has a section smaller than BH, (a) because - of the fall of the water surface from the point where H is measured - towards the weir, (b) in consequence of the crest contraction, (c) in - consequence of the end contractions. It may be pointed out that while - the diminution of the section of the jet due to the surface fall and - to the crest contraction is proportional to the length of the weir, - the end contractions have nearly the same effect whether the weir is - wide or narrow. - - [Illustration: FIG. 45.] - - J. B. Francis's experiments showed that a perfect end contraction, - when the heads varied from 3 to 24 in., and the length of the weir was - not less than three times the head, diminished the effective length of - the weir by an amount approximately equal to one-tenth of the head. - Hence, if l is the length of the notch or weir, and H the head - measured behind the weir where the water is nearly still, then the - width of the jet passing through the notch would be l - 0.2H, allowing - for two end contractions. In a weir divided by posts there may be more - than two end contractions. Hence, generally, the width of the jet is l - - 0.1nH, where n is the number of end contractions of the stream. The - contractions due to the fall of surface and to the crest contraction - are proportional to the width of the jet. Hence, if cH is the - thickness of the stream over the weir, measured at the contracted - section, the section of the jet will be c(l - 0.1nH)H and (S 41) the - mean velocity will be 2/3 [root](2gH). Consequently the discharge - will be given by an equation of the form - - Q = (2/3)c (l - 0.1nH)H [root](2gH) - = 5.35c (l - 0.1nH) H^(3/2). - - This is Francis's formula, in which the coefficient of discharge c is - much more nearly constant for different values of l and h than in the - ordinary formula. Francis found for c the mean value 0.622, the weir - being sharp-edged. - - S 43. _Triangular Notch_ (fig. 46).--Consider a lamina issuing between - the depths h and h + dh. Its area, neglecting contraction, will be - bdh, and the velocity at that depth is [root](2gh). Hence the - discharge for this lamina is - - b[root](2gh) dh. - - But - - B/b = H/(H - h); b = B(H - h)/H. - - Hence discharge of lamina - - = B(H - h) [root](2gh) dh/H; - - and total discharge of notch - _ - /H - = Q = B[root](2g) | (H - h)h^(1/2) dh/H - _/0 - - = (4/15) B[root](2g)H^(3/2). - - or, introducing a coefficient to allow for contraction, - - Q = (4/15)cB [root](2g) H^(1/2), - - [Illustration: FIG. 46.] - - When a notch is used to gauge a stream of varying flow, the ratio B/H - varies if the notch is rectangular, but is constant if the notch is - triangular. This led Professor James Thomson to suspect that the - coefficient of discharge, c, would be much more constant with - different values of H in a triangular than in a rectangular notch, and - this has been experimentally shown to be the case. Hence a triangular - notch is more suitable for accurate gaugings than a rectangular notch. - For a sharp-edged triangular notch Professor J. Thomson found c = - 0.617. It will be seen, as in S 41, that since (1/2)BH is the area of - section of the stream through the notch, the formula is again of the - form - - Q = c X (1/2)BH X k[root](2gH), - - where k = 8/15 is the ratio of the mean velocity in the notch to the - velocity at the depth H. It may easily be shown that for all notches - the discharge can be expressed in this form. - - _Coefficients for the Discharge over Weirs, derived from the - Experiments of T. E. Blackwell. When more than one experiment was - made with the same head, and the results were pretty uniform, the - resulting coefficients are marked with an (*). The effect of the - converging wing-boards is very strongly marked._ - - +----------+-------------+---------------------------------+-----------------------------------------+ - | | | Planks 2 in. thick, | | - | Heads in | Sharp Edge. | square on Crest. | Crests 3 ft. wide. | - | inches +------+------+-----+-----+-------+-------------+------+------+------+------+------+------+ - | measured | | | | | |10 ft. long, | 3 ft.| 3 ft.| 3 ft.| 6 ft.|10 ft.|10 ft.| - |from still| 3 ft.|10 ft.|3 ft.|6 ft.| 10 ft.| wing-boards | long,| long,| long,| long,| long,| long,| - | Water in | long.| long.|long.|long.| long. | making an |level.|fall 1|fall 1|level.|level.|fall 1| - |Reservoir.| | | | | |angle of 60 | |in 18.|in 12.| | |in 18.| - +----------+------+------+-----+-----+-------+-----deg.----+------+------+------+------+------+------+ - | 1 | .677 | .809 |.467 |.459 |.435[4]| .754 | .452 | .545 | .467 | .. | .381 | .467 | - | 2 | .675 | .803 |.509*|.561 |.585* | .675 | .482 | .546 | .533 | .. | .479*| .495*| - | 3 | .630 | .642*|.563*|.597*|.569* | .. | .441 | .537 | .539 | .492*| .. | .. | - | 4 | .617 | .656 |.549 |.575 |.602* | .656 | .419 | .431 | .455 | .497*| .. | .515 | - | 5 | .602 | .650*|.588 |.601*|.609* | .671 | .479 | .516 | .. | .. | .518 | .. | - | 6 | .593 | .. |.593*|.608*|.576* | .. | .501*| .. | .531 | .507 | .513 | .543 | - | 7 | .. | .. |.617*|.608*|.576* | .. | .488 | .513 | .527 | .497 | .. | .. | - | 8 | .. | .581 |.606*|.590*|.548* | .. | .470 | .491 | .. | .. | .468 | .507 | - | 9 | .. | .530 |.600 |.569*|.558* | .. | .476 | .492*| .498 | .480*| .486 | .. | - | 10 | .. | .. |.614*|.539 |.534* | .. | .. | .. | .. | .465*| .455 | .. | - | 12 | .. | .. | .. |.525 |.534* | .. | .. | .. | .. | .467*| .. | .. | - | 14 | .. | .. | .. |.549*| .. | .. | .. | .. | .. | .. | .. | .. | - +----------+------+------+-----+-----+-------+-------------+------+------+------+------+------+------+ - - [Illustration: FIG. 47.] - - S 44. _Weir with a Broad Sloping Crest._--Suppose a weir formed with a - broad crest so sloped that the streams flowing over it have a movement - sensibly rectilinear and uniform (fig. 47). Let the inner edge be so - rounded as to prevent a crest contraction. Consider a filament aa', - the point a being so far back from the weir that the velocity of - approach is negligible. Let OO be the surface level in the reservoir, - and let a be at a height h" below OO, and h' above a'. Let h be the - distance from OO to the weir crest and e the thickness of the stream - upon it. Neglecting atmospheric pressure, which has no influence, the - pressure at a is Gh"; at a' it is Gz. If v be the velocity at a', - - v^2/2g = h' + h" - z = h - e; - - Q = be [root]{2g(h - e)}. - - Theory does not furnish a value for e, but Q = 0 for e = 0 and for e = - h. Q has therefore a maximum for a value of e between 0 and h, - obtained by equating dQ/de to zero. This gives e = (2/3)h, and, - inserting this value, - - Q = 0.385 bh [root](2gh), - - as a maximum value of the discharge with the conditions assigned. - Experiment shows that the actual discharge is very approximately equal - to this maximum, and the formula is more legitimately applicable to - the discharge over broad-crested weirs and to cases such as the - discharge with free upper surface through large masonry sluice - openings than the ordinary weir formula for sharp-edged weirs. It - should be remembered, however, that the friction on the sides and - crest of the weir has been neglected, and that this tends to reduce a - little the discharge. The formula is equivalent to the ordinary weir - formula with c = 0.577. - - - SPECIAL CASES OF DISCHARGE FROM ORIFICES - - S 45. _Cases in which the Velocity of Approach needs to be taken into - Account. Rectangular Orifices and Notches._--In finding the velocity - at the orifice in the preceding investigations, it has been assumed - that the head h has been measured from the free surface of still water - above the orifice. In many cases which occur in practice the channel - of approach to an orifice or notch is not so large, relatively to the - stream through the orifice or notch, that the velocity in it can be - disregarded. - - [Illustration: FIG. 48.] - - Let h1, h2 (fig. 48) be the heads measured from the free surface to - the top and bottom edges of a rectangular orifice, at a point in the - channel of approach where the velocity is u. It is obvious that a fall - of the free surface, - - [h] = u^2/2g - - has been somewhere expended in producing the velocity u, and hence the - true heads measured in still water would have been h1 + [h] and h2 + - [h]. Consequently the discharge, allowing for the velocity of - approach, is - - Q = (2/3)cb [root](2g) {(h2 + [h])^(3/2) - (h1 + [h])^(3/2)}. (1) - - And for a rectangular notch for which h1 = 0, the discharge is - - Q = (2/3)cb [root](2g) {(h2 + [h])^(3/2) - [h]^(3/2)}. (2) - - In cases where u can be directly determined, these formulae give the - discharge quite simply. When, however, u is only known as a function - of the section of the stream in the channel of approach, they become - complicated. Let [Omega] be the sectional area of the channel where h1 - and h2 are measured. Then u = Q/[Omega] and [h] = Q^2/2g [Omega]^2. - - This value introduced in the equations above would render them - excessively cumbrous. In cases therefore where [Omega] only is known, - it is best to proceed by approximation. Calculate an approximate value - Q' of Q by the equation - - Q' = (2/3)cb [root](2g) {h2^(3/2) - h1^(3/2)}. - - Then [h] = Q'^2/2g[Omega]^2 nearly. This value of [h] introduced in the - equations above will give a second and much more approximate value of - Q. - - [Illustration: FIG. 49.] - - S 46. _Partially Submerged Rectangular Orifices and Notches._--When - the tail water is above the lower but below the upper edge of the - orifice, the flow in the two parts of the orifice, into which it is - divided by the surface of the tail water, takes place under different - conditions. A filament M1m1 (fig. 49) in the upper part of the orifice - issues with a head h' which may have any value between h1 and h. But a - filament M2m2 issuing in the lower part of the orifice has a velocity - due to h" - h"', or h, simply. In the upper part of the orifice the - head is variable, in the lower constant. If Q1, Q2 are the discharges - from the upper and lower parts of the orifice, b the width of the - orifice, then - - Q1 = (2/3)cb [root](2g) {h^(3/2) - h1^(3/2)} - (3) - Q1 = cb (h2 - h) [root](2gh). - - In the case of a rectangular notch or weir, h1 = 0. Inserting this - value, and adding the two portions of the discharge together, we get - for a drowned weir - - Q = cb[root](2gh) (h2 - h/3), (4) - - where h is the difference of level of the head and tail water, and h2 - is the head from the free surface above the weir to the weir crest - (fig. 50). - - From some experiments by Messrs A. Fteley and F.P. Stearns (_Trans. - Am. Soc. C.E._, 1883, p. 102) some values of the coefficient c can be - reduced - - h3/h2 c h3/h2 c - - 0.1 0.629 0.7 0.578 - 0.2 0.614 0.8 0.583 - 0.3 0.600 0.9 0.596 - 0.4 0.590 0.95 0.607 - 0.5 0.582 1.00 0.628 - 0.6 0.578 - - If velocity of approach is taken into account, let [h] be the - head due to that velocity; then, adding [h] to each of the - heads in the equations (3), and reducing, we get for a weir - - Q = cb [root]{2g} [(h2 + [h]) (h + [h])^(1/2) - (1/3)(h + [h])^(3/2) - - (2/3)[h]^(3/2)]; (5) - - an equation which may be useful in estimating flood discharges. - - [Illustration: FIG. 50.] - - _Bridge Piers and other Obstructions in Streams._--When the piers of a - bridge are erected in a stream they create an obstruction to the flow - of the stream, which causes a difference of surface-level above and - below the pier (fig. 51). If it is necessary to estimate this - difference of level, the flow between the piers may be treated as if - it occurred over a drowned weir. But the value of c in this case is - imperfectly known. - - S 47. _Bazin's Researches on Weirs._--H. Bazin has executed a long - series of researches on the flow over weirs, so systematic and - complete that they almost supersede other observations. The account of - them is contained in a series of papers in the _Annales des Ponts et - Chaussees_ (October 1888, January 1890, November 1891, February 1894, - December 1896, 2nd trimestre 1898). Only a very abbreviated account - can be given here. The general plan of the experiments was to - establish first the coefficients of discharge for a standard weir - without end contractions; next to establish weirs of other types in - series with the standard weir on a channel with steady flow, to - compare the observed heads on the different weirs and to determine - their coefficients from the discharge computed at the standard weir. A - channel was constructed parallel to the Canal de Bourgogne, taking - water from it through three sluices 0.3 X 1.0 metres. The water enters - a masonry chamber 15 metres long by 4 metres wide where it is stilled - and passes into the canal at the end of which is the standard weir. - The canal has a length of 15 metres, a width of 2 metres and a depth - of 0.6 metres. From this extends a channel 200 metres in length with a - slope of 1 mm. per metre. The channel is 2 metres wide with vertical - sides. The channels were constructed of concrete rendered with cement. - The water levels were taken in chambers constructed near the canal, by - floats actuating an index on a dial. Hook gauges were used in - determining the heads on the weirs. - - [Illustration: FIG. 51.] - - _Standard Weir._--The weir crest was 3.72 ft. above the bottom of the - canal and formed by a plate 1/4 in. thick. It was sharp-edged with free - overfall. It was as wide as the canal so that end contractions were - suppressed, and enlargements were formed below the crest to admit air - under the water sheet. The channel below the weir was used as a - gauging tank. Gaugings were made with the weir 2 metres in length and - afterwards with the weir reduced to 1 metre and 0.5 metre in length, - the end contractions being suppressed in all cases. Assuming the - general formula - - Q = mlh [root](2gh), (1) - - Bazin arrives at the following values of _m_:-- - - _Coefficients of Discharge of Standard Weir._ - - +----------------+--------------+--------+ - | Head h metres. | Head h feet. | m | - +----------------+--------------+--------+ - | 0.05 | .164 | 0.4485 | - | 0.10 | .328 | 0.4336 | - | 0.15 | .492 | 0.4284 | - | 0.20 | .656 | 0.4262 | - | 0.25 | .820 | 0.4259 | - | 0.30 | .984 | 0.4266 | - | 0.35 | 1.148 | 0.4275 | - | 0.40 | 1.312 | 0.4286 | - | 0.45 | 1.476 | 0.4299 | - | 0.50 | 1.640 | 0.4313 | - | 0.55 | 1.804 | 0.4327 | - | 0.60 | 1.968 | 0.4341 | - +----------------+--------------+--------+ - - Bazin compares his results with those of Fteley and Stearns in 1877 - and 1879, correcting for a different velocity of approach, and finds a - close agreement. - - _Influence of Velocity of Approach._--To take account of the velocity - of approach u it is usual to replace h in the formula by h + au^2/2g - where [alpha] is a coefficient not very well ascertained. Then - - Q = [mu]l (h + [alpha]u^2/2g) [root]{2g(h + [alpha]u^2/2g)} - = [mu]lh [root](2gh)(1 + [alpha]u^2/2gh)^(3/2). (2) - - The original simple equation can be used if - - m = [mu](1 + [alpha]u^2/2gh)^(3/2) - - or very approximately, since u^2/2gh is small, - - m = [mu](1 + (3/2)[alpha]u^2/2gh). (3) - - [Illustration: FIG. 52.] - - Now if p is the height of the weir crest above the bottom of the canal - (fig. 52), u = Q/l(p + h). Replacing Q by its value in (1) - - u^2/2gh = Q^2/{2ghl^2(p + h)^2} = m^2{h/(p + h)}^2, (4) - - so that (3) may be written - - m = [mu][1 + k{h/(p + h)}^2]. (5) - - Gaugings were made with weirs of 0.75, 0.50, 0.35, and 0.24 metres - height above the canal bottom and the results compared with those of - the standard weir taken at the same time. The discussion of the - results leads to the following values of m in the general equation - (1):-- - - m = [mu](1 + 2.5u^2/2gh) - = [mu][1 + 0.55 {h/(p + h)}^2]. - - Values of [mu]-- - - +----------------+--------------+--------+ - | Head h metres. | Head h feet. | [mu] | - +----------------+--------------+--------+ - | 0.05 | .164 | 0.4481 | - | 0.10 | .328 | 0.4322 | - | 0.20 | .656 | 0.4215 | - | 0.30 | .984 | 0.4174 | - | 0.40 | 1.312 | 0.4144 | - | 0.50 | 1.640 | 0.4118 | - | 0.60 | 1.968 | 0.4092 | - +----------------+--------------+--------+ - - An approximate formula for [mu] is: - - [mu] = 0.405 + 0.003/h (h in metres) - - [mu] = 0.405 + 0.01/h (h in feet). - - _Inclined Weirs._---Experiments were made in which the plank weir was - inclined up or down stream, the crest being sharp and the end - contraction suppressed. The following are coefficients by which the - discharge of a vertical weir should be multiplied to obtain the - discharge of the inclined weir. - - Coefficient. - Inclination up stream 1 to 1 0.93 - " " 3 to 2 0.94 - " " 3 to 1 0.96 - Vertical weir 1.00 - Inclination down stream 3 to 1 1.04 - " " 3 to 2 1.07 - " " 1 to 1 1.10 - " " 1 to 2 1.12 - " " 1 to 4 1.09 - - The coefficient varies appreciably, if h/p approaches unity, which - case should be avoided. - - In all the preceding cases the sheet passing over the weir is detached - completely from the weir and its under-surface is subject to - atmospheric pressure. These conditions permit the most exact - determination of the coefficient of discharge. If the sides of the - canal below the weir are not so arranged as to permit the access of - air under the sheet, the phenomena are more complicated. So long as - the head does not exceed a certain limit the sheet is detached from - the weir, but encloses a volume of air which is at less than - atmospheric pressure, and the tail water rises under the sheet. The - discharge is a little greater than for free overfall. At greater head - the air disappears from below the sheet and the sheet is said to be - "drowned." The drowned sheet may be independent of the tail water - level or influenced by it. In the former case the fall is followed by - a rapid, terminating in a standing wave. In the latter case when the - foot of the sheet is drowned the level of the tail water influences - the discharge even if it is below the weir crest. - - [Illustration: FIG. 53.] - - [Illustration: FIG. 54.] - - _Weirs with Flat Crests._--The water sheet may spring clear from the - upstream edge or may adhere to the flat crest falling free beyond the - down-stream edge. In the former case the condition is that of a - sharp-edged weir and it is realized when the head is at least double - the width of crest. It may arise if the head is at least 1(1/2) the - width of crest. Between these limits the condition of the sheet is - unstable. When the sheet is adherent the coefficient m depends on the - ratio of the head h to the width of crest c (fig. 53), and is given by - the equation m = m1 [0.70 + 0.185h/c], where m1 is the coefficient for - a sharp-edged weir in similar conditions. Rounding the upstream edge - even to a small extent modifies the discharge. If R is the radius of - the rounding the coefficient m is increased in the ratio 1 to 1 + R/h - nearly. The results are limited to R less than 1/2 in. - - _Drowned Weirs._--Let h (fig. 54) be the height of head water and h1 - that of tail water above the weir crest. Then Bazin obtains as the - approximate formula for the coefficient of discharge - - m = 1.05m1 [1 + (1/5)h1/p] [root 3]{(h - h1)/h}, - - where as before m1 is the coefficient for a sharp-edged weir in - similar conditions, that is, when the sheet is free and the weir of - the same height. - - [Illustration: FIG. 55.] - - [Illustration: FIG. 56.] - - S 48. _Separating Weirs._--Many towns derive their water-supply from - streams in high moorland districts, in which the flow is extremely - variable. The water is collected in large storage reservoirs, from - which an uniform supply can be sent to the town. In such cases it is - desirable to separate the coloured water which comes down the streams - in high floods from the purer water of ordinary flow. The latter is - sent into the reservoirs; the former is allowed to flow away down the - original stream channel, or is stored in separate reservoirs and used - as compensation water. To accomplish the separation of the flood and - ordinary water, advantage is taken of the different horizontal range - of the parabolic path of the water falling over a weir, as the depth - on the weir and, consequently, the velocity change. Fig. 55 shows one - of these separating weirs in the form in which they were first - introduced on the Manchester Waterworks; fig. 56 a more modern weir of - the same kind designed by Sir A. Binnie for the Bradford Waterworks. - When the quantity of water coming down the stream is not excessive, it - drops over the weir into a transverse channel leading to the - reservoirs. In flood, the water springs over the mouth of this channel - and is led into a waste channel. - - It may be assumed, probably with accuracy enough for practical - purposes, that the particles describe the parabolas due to the mean - velocity of the water passing over the weir, that is, to a velocity - - (2/3)[root](2gh), - - where h is the head above the crest of the weir. - - Let cb = x be the width of the orifice and ac = y the difference of - level of its edges (fig. 57). Then, if a particle passes from a to b - in t seconds, - - y = (1/2)gt^2, x = (2/3)[root](2gh) t; - - .: y = (9/16)x^2/h, - - which gives the width x for any given difference of level y and head - h, which the jet will just pass over the orifice. Set off ad - vertically and equal to (1/2)g on any scale; af horizontally and equal - to 2/3 [root](gh). Divide af, fe into an equal number of equal parts. - Join a with the divisions on ef. The intersections of these lines with - verticals from the divisions on af give the parabolic path of the jet. - - [Illustration: FIG. 57.] - - - MOUTHPIECES--HEAD CONSTANT - - S 49. _Cylindrical Mouthpieces._--When water issues from a short - cylindrical pipe or mouthpiece of a length at least equal to l(1/2) - times its smallest transverse dimension, the stream, after contraction - within the mouthpiece, expands to fill it and issues full bore, or - without contraction, at the point of discharge. The discharge is found - to be about one-third greater than that from a simple orifice of the - same size. On the other hand, the energy of the fluid per unit of - weight is less than that of the stream from a simple orifice with the - same head, because part of the energy is wasted in eddies produced at - the point where the stream expands to fill the mouthpiece, the action - being something like that which occurs at an abrupt change of section. - - Let fig. 58 represent a vessel discharging through a cylindrical - mouthpiece at the depth h from the free surface, and let the axis of - the jet XX be taken as the datum with reference to which the head is - estimated. Let [Omega] be the area of the mouthpiece, [omega] the area - of the stream at the contracted section EF. Let v, p be the velocity - and pressure at EF, and v1, p1 the same quantities at GH. If the - discharge is into the air, p1 is equal to the atmospheric pressure - p_a. - - The total head of any filament which goes to form the jet, taken at a - point where its velocity is sensibly zero, is h + p_a/G; at EF the - total head is v^2/2g + p/G; at GH it is v1^2/2g + p1/G. - - Between EF and GH there is a loss of head due to abrupt change of - velocity, which from eq. (3), S 36, may have the value - - (v - v1)^2/2g. - - Adding this head lost to the head at GH, before equating it to the - heads at EF and at the point where the filaments start into motion,-- - - h + p_a/G = v^2/2g + p/G = v1^2/2g + p1/G + (v - v1)^2/2g. - - But [omega]v = [Omega]v1, and [omega] = c_c[Omega], if c_c is the - coefficient of contraction within the mouthpiece. Hence - - v = [Omega]v1/[omega] = v1/c_c. - - Supposing the discharge into the air, so that p1 = p_a, - - h + p_a/G = v1^2/2g + p_a/G + (v1^2/2g)(1/c_c - 1)^2; - - (v1/2g){1 + (1/c_c - 1)^2} = h; - - .: v1 = [root](2gh)/[root]{1 + (1/c_c - 1)^2}; (1) - - [Illustration: FIG. 58.] - - where the coefficient on the right is evidently the coefficient of - velocity for the cylindrical mouthpiece in terms of the coefficient of - contraction at EF. Let c_c = 0.64, the value for simple orifices, then - the coefficient of velocity is - - c_v = 1/[root]{1 + (1/c_c - 1)^2} = 0.87 (2) - - The actual value of c_v, found by experiment is 0.82, which does not - differ more from the theoretical value than might be expected if the - friction of the mouthpiece is allowed for. Hence, for mouthpieces of - this kind, and for the section at GH, - - c_v = 0.82 c_c = 1.00 c = 0.82, - - Q = 0.82[Omega] [root](2gh). - - It is easy to see from the equations that the pressure p at EF is less - than atmospheric pressure. Eliminating v1, we get - - (p_a - p)/G = (3/4)h nearly; (3) - - or - - p = p_a - (3/4)Gh lb. per sq. ft. - - If a pipe connected with a reservoir on a lower level is introduced - into the mouthpiece at the part where the contraction is formed (fig. - 59), the water will rise in this pipe to a height - - KL = (p_a - p)/G = (3/4)h nearly. - - If the distance X is less than this, the water from the lower - reservoir will be forced continuously into the jet by the atmospheric - pressure, and discharged with it. This is the crudest form of a kind - of pump known as the jet pump. - - S 50. _Convergent Mouthpieces._--With convergent mouthpieces there is - a contraction within the mouthpiece causing a loss of head, and a - diminution of the velocity of discharge, as with cylindrical - mouthpieces. There is also a second contraction of the stream outside - the mouthpiece. Hence the discharge is given by an equation of the - form - - Q = c_v c_c[Omega] [root](2gh), (4) - - where [Omega] is the area of the external end of the mouthpiece, and - c_c[Omega] the section of the contracted jet beyond the mouthpiece. - - _Convergent Mouthpieces (Castel's Experiments).--Smallest diameter of - orifice = 0.05085 ft. Length of mouthpiece = 2.6 Diameters._ - - +----------------+--------------+--------------+--------------+ - | |Coefficient of|Coefficient of|Coefficient of| - | Angle of | Contraction, | Velocity, | Discharge, | - | Convergence. | c_c | c_v | c | - +----------------+--------------+--------------+--------------+ - | 0 deg. 0' | .999 | .830 | .829 | - | 1 deg. 36' | 1.000 | .866 | .866 | - | 3 deg. 10' | 1.001 | .894 | .895 | - | 4 deg. 10' | 1.002 | .910 | .912 | - | 5 deg. 26' | 1.004 | .920 | .924 | - | 7 deg. 52' | .998 | .931 | .929 | - | 8 deg. 58' | .992 | .942 | .934 | - | 10 deg. 20' | .987 | .950 | .938 | - | 12 deg. 4' | .986 | .955 | .942 | - | 13 deg. 24' | .983 | .962 | .946 | - | 14 deg. 28' | .979 | .966 | .941 | - | 16 deg. 36' | .969 | .971 | .938 | - | 19 deg. 28' | .953 | .970 | .924 | - | 21 deg. 0' | .945 | .971 | .918 | - | 23 deg. 0' | .937 | .974 | .913 | - | 29 deg. 58' | .919 | .975 | .896 | - | 40 deg. 20' | .887 | .980 | .869 | - | 48 deg. 50' | .861 | .984 | .847 | - +----------------+--------------+--------------+--------------+ - - The maximum coefficient of discharge is that for a mouthpiece with a - convergence of 13 deg.24'. - - The values of c_v and c_c must here be determined by experiment. The - above table gives values sufficient for practical purposes. Since the - contraction beyond the mouthpiece increases with the convergence, or, - what is the same thing, c_c diminishes, and on the other hand the loss - of energy diminishes, so that c_v increases with the convergence, - there is an angle for which the product c_c c_v, and consequently the - discharge, is a maximum. - - [Illustration: FIG. 59.] - - S 51. _Divergent Conoidal Mouthpiece._--Suppose a mouthpiece so - designed that there is no abrupt change in the section or velocity of - the stream passing through it. It may have a form at the inner end - approximately the same as that of a simple contracted vein, and may - then enlarge gradually, as shown in fig. 60. Suppose that at EF it - becomes cylindrical, so that the jet may be taken to be of the - diameter EF. Let [omega], v, p be the section, velocity and pressure - at CD, and [Omega], v1, p1 the same quantities at EF, p_a being as - usual the atmospheric pressure, or pressure on the free surface AB. - Then, since there is no loss of energy, except the small frictional - resistance of the surface of the mouthpiece, - - h + p_a/G = v^2/2g + p/G = v1^2/2g + p1/G. - - If the jet discharges into the air, p1 = p_a; and - - v1^2/2g = h; - - v1 = [root](2gh); - - or, if a coefficient is introduced to allow for friction, - - v1 = c_v [root](2gh); - - where c_v is about 0.97 if the mouthpiece is smooth and well formed. - - Q = [Omega] v1 = c_v [Omega] [root](2gh). - - [Illustration: FIG. 60.] - - Hence the discharge depends on the area of the stream at EF, and not - at all on that at CD, and the latter may be made as small as we please - without affecting the amount of water discharged. - - There is, however, a limit to this. As the velocity at CD is greater - than at EF the pressure is less, and therefore less than atmospheric - pressure, if the discharge is into the air. If CD is so contracted - that p = 0, the continuity of flow is impossible. In fact the stream - disengages itself from the mouthpiece for some value of p greater than - 0 (fig. 61). - - [Illustration: FIG. 61.] - - From the equations, - - p/G = p_a/G = (v^2 - v1^2)/2g. - - Let [Omega]/[omega] = m. Then - - v = v1m; - - p/G = p_a/G - v1^2(m^2 - 1)/2g - = p_a/G - (m^2 - 1)h; - - whence we find that p/G will become zero or negative if - - [Omega]/[omega] >= [root]{(h + p_a/G)/h} - = [root]{1 + p_a/Gh}; - - or, putting p_a/G = 34 ft., if - - [Omega]/[omega] >= [root]{(h + 34)/h}. - - In practice there will be an interruption of the full bore flow with a - less ratio of [Omega]/[omega], because of the disengagement of air - from the water. But, supposing this does not occur, the maximum - discharge of a mouthpiece of this kind is - - Q = [omega] [root]{2g(h + p_a/G)}; - - that is, the discharge is the same as for a well-bell-mouthed - mouthpiece of area [omega], and without the expanding part, - discharging into a vacuum. - - S 52. _Jet Pump._--A divergent mouthpiece may be arranged to act as a - pump, as shown in fig. 62. The water which supplies the energy - required for pumping enters at A. The water to be pumped enters at B. - The streams combine at DD where the velocity is greatest and the - pressure least. Beyond DD the stream enlarges in section, and its - pressure increases, till it is sufficient to balance the head due to - the height of the lift, and the water flows away by the discharge pipe - C. - - [Illustration: FIG. 62.] - - Fig. 63 shows the whole arrangement in a diagrammatic way. A is the - reservoir which supplies the water that effects the pumping; B is the - reservoir of water to be pumped; C is the reservoir into which the - water is pumped. - - [Illustration: FIG. 63.] - - - DISCHARGE WITH VARYING HEAD - - S 53. _Flow from a Vessel when the Effective Head varies with the - Time._--Various useful problems arise relating to the time of emptying - and filling vessels, reservoirs, lock chambers, &c., where the flow is - dependent on a head which increases or diminishes during the - operation. The simplest of these problems is the case of filling or - emptying a vessel of constant horizontal section. - - [Illustration: FIG. 64.] - - _Time of Emptying or Filling a Vertical-sided Lock Chamber._--Suppose - the lock chamber, which has a water surface of [Omega] square ft., is - emptied through a sluice in the tail gates, of area [omega], placed - below the tail-water level. Then the effective head producing flow - through the sluice is the difference of level in the chamber and tail - bay. Let H (fig. 64) be the initial difference of level, h the - difference of level after t seconds. Let -dh be the fall of level in - the chamber during an interval dt. Then in the time dt the volume in - the chamber is altered by the amount -[Omega]dh, and the outflow from - the sluice in the same time is c[omega][root](2gh)dt. Hence the - differential equation connecting h and t is - - c[omega] [root](2gh) dt + [Omega]h = 0. - - For the time t, during which the initial head H diminishes to any - other value h, - _ _ - /h /t - -{[Omega]/(c[omega] [root]2g)} | dh/[root]h = | dt. - _/H _/0 - - .: t = 2[Omega]([root]H - [root]h) / {c[omega] [root](2g)} - = ([Omega]/c[omega]){[root](2H/g) - [root](2h/g)}. - - For the whole time of emptying, during which h diminishes from H to 0, - - T = ([Omega]/c[omega]) [root](2H/g). - - Comparing this with the equation for flow under a constant head, it - will be seen that the time is double that required for the discharge - of an equal volume under a constant head. - - The time of filling the lock through a sluice in the head gates is - exactly the same, if the sluice is below the tail-water level. But if - the sluice is above the tail-water level, then the head is constant - till the level of the sluice is reached, and afterwards it diminishes - with the time. - - - PRACTICAL USE OF ORIFICES IN GAUGING WATER - - S 54. If the water to be measured is passed through a known orifice - under an arrangement by which the constancy of the head is ensured, - the amount which passes in a given time can be ascertained by the - formulae already given. It will obviously be best to make the orifices - of the forms for which the coefficients are most accurately - determined; hence sharp-edged orifices or notches are most commonly - used. - - _Water Inch._--For measuring small quantities of water circular - sharp-edged orifices have been used. The discharge from a circular - orifice one French inch in diameter, with a head of one line above the - top edge, was termed by the older hydraulic writers a water-inch. A - common estimate of its value was 14 pints per minute, or 677 English - cub. ft. in 24 hours. An experiment by C. Bossut gave 634 cub. ft. in - 24 hours (see Navier's edition of _Belidor's Arch. Hydr._, p. 212). - - L. J. Weisbach points out that measurements of this kind would be made - more accurately with a greater head over the orifice, and he proposes - that the head should be equal to the diameter of the orifice. Several - equal orifices may be used for larger discharges. - - [Illustration: FIG. 65.] - - _Pin Ferrules or Measuring Cocks._--To give a tolerably definite - supply of water to houses, without the expense of a meter, a ferrule - with an orifice of a definite size, or a cock, is introduced in the - service-pipe. If the head in the water main is constant, then a - definite quantity of water would be delivered in a given time. The - arrangement is not a very satisfactory one, and acts chiefly as a - check on extravagant use of water. It is interesting here chiefly as - an example of regulation of discharge by means of an orifice. Fig. 65 - shows a cock of this kind used at Zurich. It consists of three cocks, - the middle one having the orifice of the predetermined size in a small - circular plate, protected by wire gauze from stoppage by impurities in - the water. The cock on the right hand can be used by the consumer for - emptying the pipes. The one on the left and the measuring cock are - connected by a key which can be locked by a padlock, which is under - the control of the water company. - - S 55. _Measurement of the Flow in Streams._--To determine the quantity - of water flowing off the ground in small streams, which is available - for water supply or for obtaining water power, small temporary weirs - are often used. These may be formed of planks supported by piles and - puddled to prevent leakage. The measurement of the head may be made by - a thin-edged scale at a short distance behind the weir, where the - water surface has not begun to slope down to the weir and where the - velocity of approach is not high. The measurements are conveniently - made from a short pile driven into the bed of the river, accurately - level with the crest of the weir (fig. 66). Then if at any moment the - head is h, the discharge is, for a rectangular notch of breadth b, - - Q = (2/3)cbh [root](2gh) - - where c = 0.62; or, better, the formula in S 42 may be used. - - Gauging weirs are most commonly in the form of rectangular notches; - and care should be taken that the crest is accurately horizontal, and - that the weir is normal to the direction of flow of the stream. If the - planks are thick, they should be bevelled (fig. 67), and then the edge - may be protected by a metal plate about (1/10)th in. thick to secure - the requisite accuracy of form and sharpness of edge. In permanent - gauging weirs, a cast steel plate is sometimes used to form the edge - of the weir crest. The weir should be large enough to discharge the - maximum volume flowing in the stream, and at the same time it is - desirable that the minimum head should not be too small (say half a - foot) to decrease the effects of errors of measurement. The section of - the jet over the weir should not exceed one-fifth the section of the - stream behind the weir, or the velocity of approach will need to be - taken into account. A triangular notch is very suitable for - measurements of this kind. - - [Illustration: FIG. 66.] - - If the flow is variable, the head h must be recorded at equidistant - intervals of time, say twice daily, and then for each 12-hour period - the discharge must be calculated for the mean of the heads at the - beginning and end of the time. As this involves a good deal of - troublesome calculation, E. Sang proposed to use a scale so graduated - as to read off the discharge in cubic feet per second. The lengths of - the principal graduations of such a scale are easily calculated by - putting Q = 1, 2, 3 ... in the ordinary formulae for notches; the - intermediate graduations may be taken accurately enough by subdividing - equally the distances between the principal graduations. - - [Illustration: FIG. 67.] - - [Illustration: FIG. 68.] - - The accurate measurement of the discharge of a stream by means of a - weir is, however, in practice, rather more difficult than might be - inferred from the simplicity of the principle of the operation. Apart - from the difficulty of selecting a suitable coefficient of discharge, - which need not be serious if the form of the weir and the nature of - its crest are properly attended to, other difficulties of measurement - arise. The length of the weir should be very accurately determined, - and if the weir is rectangular its deviations from exactness of level - should be tested. Then the agitation of the water, the ripple on its - surface, and the adhesion of the water to the scale on which the head - is measured, are liable to introduce errors. Upon a weir 10 ft. long, - with 1 ft. depth of water flowing over, an error of 1-1000th of a foot - in measuring the head, or an error of 1-100th of a foot in measuring - the length of the weir, would cause an error in computing the - discharge of 2 cub. ft. per minute. - - _Hook Gauge._--For the determination of the surface level of water, - the most accurate instrument is the hook gauge used first by U. Boyden - of Boston, in 1840. It consists of a fixed frame with scale and - vernier. In the instrument in fig. 68 the vernier is fixed to the - frame, and the scale slides vertically. The scale carries at its lower - end a hook with a fine point, and the scale can be raised or lowered - by a fine pitched screw. If the hook is depressed below the water - surface and then raised by the screw, the moment of its reaching the - water surface will be very distinctly marked, by the reflection from a - small capillary elevation of the water surface over the point of the - hook. In ordinary light, differences of level of the water of .001 of - a foot are easily detected by the hook gauge. If such a gauge is used - to determine the heads at a weir, the hook should first be set - accurately level with the weir crest, and a reading taken. Then the - difference of the reading at the water surface and that for the weir - crest will be the head at the weir. - - S 56. _Modules used in Irrigation._--In distributing water for - irrigation, the charge for the water may be simply assessed on the - area of the land irrigated for each consumer, a method followed in - India; or a regulated quantity of water may be given to each consumer, - and the charge may be made proportional to the quantity of water - supplied, a method employed for a long time in Italy and other parts - of Europe. To deliver a regulated quantity of water from the - irrigation channel, arrangements termed modules are used. These are - constructions intended to maintain a constant or approximately - constant head above an orifice of fixed size, or to regulate the size - of the orifice so as to give a constant discharge, notwithstanding the - variation of level in the irrigating channel. - - [Illustration: FIG. 69.] - - S 57. _Italian Module._--The Italian modules are masonry - constructions, consisting of a regulating chamber, to which water is - admitted by an adjustable sluice from the canal. At the other end of - the chamber is an orifice in a thin flagstone of fixed size. By means - of the adjustable sluice a tolerably constant head above the fixed - orifice is maintained, and therefore there is a nearly constant - discharge of ascertainable amount through the orifice, into the - channel leading to the fields which are to be irrigated. - - [Illustration: FIG. 70.--Scale 1/100.] - - In fig. 69, A is the adjustable sluice by which water is admitted to - the regulating chamber, B is the fixed orifice through which the water - is discharged. The sluice A is adjusted from time to time by the canal - officers, so as to bring the level of the water in the regulating - chamber to a fixed level marked on the wall of the chamber. When - adjusted it is locked. Let [omega]1 be the area of the orifice through - the sluice at A, and [omega]2 that of the fixed orifice at B; let h1 - be the difference of level between the surface of the water in the - canal and regulating chamber; h2 the head above the centre of the - discharging orifice, when the sluice has been adjusted and the flow - has become steady; Q the normal discharge in cubic feet per second. - Then, since the flow through the orifices at A and B is the same, - - Q = c1[omega]1 [root](2gh1) = c2[omega]2 [root](2gh2), - - where c1 and c2 are the coefficients of discharge suitable for the two - orifices. Hence - - c1[omega]1/c2[omega]2 = [root](h2/h1). - - If the orifice at B opened directly into the canal without any - intermediate regulating chamber, the discharge would increase for a - given change of level in the canal in exactly the same ratio. - Consequently the Italian module in no way moderates the fluctuations - of discharge, except so far as it affords means of easy adjustment - from time to time. It has further the advantage that the cultivator, - by observing the level of the water in the chamber, can always see - whether or not he is receiving the proper quantity of water. - - On each canal the orifices are of the same height, and intended to - work with the same normal head, the width of the orifices being varied - to suit the demand for water. The unit of discharge varies on - different canals, being fixed in each case by legal arrangements. Thus - on the Canal Lodi the unit of discharge or one module of water is the - discharge through an orifice 1.12 ft. high, 0.12416 ft. wide, with a - head of 0.32 ft. above the top edge of the orifice, or .88 ft. above - the centre. This corresponds to a discharge of about 0.6165 cub. ft. - per second. - - [Illustration: FIG. 71.] - - In the most elaborate Italian modules the regulating chamber is arched - over, and its dimensions are very exactly prescribed. Thus in the - modules of the Naviglio Grande of Milan, shown in fig. 70, the - measuring orifice is cut in a thin stone slab, and so placed that the - discharge is into the air with free contraction on all sides. The - adjusting sluice is placed with its sill flush with the bottom of the - canal, and is provided with a rack and lever and locking arrangement. - The covered regulating chamber is about 20 ft. long, with a breadth - 1.64 ft. greater than that of the discharging orifice. At precisely - the normal level of the water in the regulating chamber, there is a - ceiling of planks intended to still the agitation of the water. A - block of stone serves to indicate the normal level of the water in the - chamber. The water is discharged into an open channel 0.655 ft. wider - than the orifice, splaying out till it is 1.637 ft. wider than the - orifice, and about 18 ft. in length. - - S 58. _Spanish Module._--On the canal of Isabella II., which supplies - water to Madrid, a module much more perfect in principle than the - Italian module is employed. Part of the water is supplied for - irrigation, and as it is very valuable its strict measurement is - essential. The module (fig. 72) consists of two chambers one above the - other, the upper chamber being in free communication with the - irrigation canal, and the lower chamber discharging by a culvert to - the fields. In the arched roof between the chambers there is a - circular sharp-edged orifice in a bronze plate. Hanging in this there - is a bronze plug of variable diameter suspended from a hollow brass - float. If the water level in the canal lowers, the plug descends and - gives an enlarged opening, and conversely. Thus a perfectly constant - discharge with a varying head can be obtained, provided no clogging or - silting of the chambers prevents the free discharge of the water or - the rise and fall of the float. The theory of the module is very - simple. Let R (fig. 71) be the radius of the fixed opening, r the - radius of the plug at a distance h from the plane of flotation of the - float, and Q the required discharge of the module. Then - - Q = c[pi](R^2 - r^2) [root](2gh). - - Taking c = 0.63, - - Q = 15.88(R^2 - r^2) [root]h; - - r = [root]{R^2 - Q/15.88 [root]h}. - - Choosing a value for R, successive values of r can be found for - different values of h, and from these the curve of the plug can be - drawn. The module shown in fig. 72 will discharge 1 cubic metre per - second. The fixed opening is 0.2 metre diameter, and the greatest head - above the fixed orifice is 1 metre. The use of this module involves a - great sacrifice of level between the canal and the fields. The module - is described in Sir C. Scott-Moncrieff's _Irrigation in Southern - Europe_. - - S 59. _Reservoir Gauging Basins._--In obtaining the power to store the - water of streams in reservoirs, it is usual to concede to riparian - owners below the reservoirs a right to a regulated supply throughout - the year. This compensation water requires to be measured in such a - way that the millowners and others interested in the matter can assure - themselves that they are receiving a proper quantity, and they are - generally allowed a certain amount of control as to the times during - which the daily supply is discharged into the stream. - - [Illustration: FIG. 72.] - - Fig. 74 shows an arrangement designed for the Manchester water works. - The water enters from the reservoir at chamber A, the object of which - is to still the irregular motion of the water. The admission is - regulated by sluices at b, b, b. The water is discharged by orifices - or notches at a, a, over which a tolerably constant head is maintained - by adjusting the sluices at b, b, b. At any time the millowners can - see whether the discharge is given and whether the proper head is - maintained over the orifices. To test at any time the discharge of the - orifices, a gauging basin B is provided. The water ordinarily flows - over this, without entering it, on a floor of cast-iron plates. If the - discharge is to be tested, the water is turned for a definite time - into the gauging basin, by suddenly opening and closing a sluice at c. - The volume of flow can be ascertained from the depth in the gauging - chamber. A mechanical arrangement (fig. 73) was designed for securing - an absolutely constant head over the orifices at a, a. The orifices - were formed in a cast-iron plate capable of sliding up and down, - without sensible leakage, on the face of the wall of the chamber. The - orifice plate was attached by a link to a lever, one end of which - rested on the wall and the other on floats f in the chamber A. The - floats rose and fell with the changes of level in the chamber, and - raised and lowered the orifice plate at the same time. This mechanical - arrangement was not finally adopted, careful watching of the sluices - at b, b, b, being sufficient to secure a regular discharge. The - arrangement is then equivalent to an Italian module, but on a large - scale. - - [Illustration: FIG. 73.--Scale 1/120.] - - [Illustration: FIG. 74.--Scale 1/500.] - - S 60. _Professor Fleeming Jenkin's Constant Flow Valve._--In the - modules thus far described constant discharge is obtained by varying - the area of the orifice through which the water flows. Professor F. - Jenkin has contrived a valve in which a constant pressure head is - obtained, so that the orifice need not be varied (_Roy. Scot. Society_ - _of Arts_, 1876). Fig. 75 shows a valve of this kind suitable for a - 6-in. water main. The water arriving by the main C passes through an - equilibrium valve D into the chamber A, and thence through a sluice O, - which can be set for any required area of opening, into the - discharging main B. The object of the arrangement is to secure a - constant difference of pressure between the chambers A and B, so that - a constant discharge flows through the stop valve O. The equilibrium - valve D is rigidly connected with a plunger P loosely fitted in a - diaphragm, separating A from a chamber B2 connected by a pipe B1 with - the discharging main B. Any increase of the difference of pressure in - A and B will drive the plunger up and close the equilibrium valve, and - conversely a decrease of the difference of pressure will cause the - descent of the plunger and open the equilibrium valve wider. Thus a - constant difference of pressure is obtained in the chambers A and B. - Let [omega] be the area of the plunger in square feet, p the - difference of pressure in the chambers A and B in pounds per square - foot, w the weight of the plunger and valve. Then if at any moment - p[omega] exceeds w the plunger will rise, and if it is less than w the - plunger will descend. Apart from friction, and assuming the valve D to - be strictly an equilibrium valve, since [omega] and w are constant, p - must be constant also, and equal to w/[omega]. By making w small and - [omega] large, the difference of pressure required to ensure the - working of the apparatus may be made very small. Valves working with a - difference of pressure of 1/2 in. of water have been constructed. - - [Illustration: FIG. 75.--Scale 1/24.] - - - VI. STEADY FLOW OF COMPRESSIBLE FLUIDS. - - [Illustration: FIG. 76.] - - S 61. _External Work during the Expansion of Air._--If air expands - without doing any external work, its temperature remains constant. - This result was first experimentally demonstrated by J. P. Joule. It - leads to the conclusion that, however air changes its state, the - internal work done is proportional to the change of temperature. When, - in expanding, air does work against an external resistance, either - heat must be supplied or the temperature falls. - - To fix the conditions, suppose 1 lb. of air confined behind a piston - of 1 sq. ft. area (fig. 76). Let the initial pressure be p1 and the - volume of the air v1, and suppose this to expand to the pressure p2 - and volume v2. If p and v are the corresponding pressure and volume at - any intermediate point in the expansion, the work done on the piston - during the expansion from v to v + dv is pdv, and the whole work - during the expansion from v1 to v2, represented by the area abcd, is - _ - /v2 - | p dv. - _/v1 - - Amongst possible cases two may be selected. - - _Case 1._--So much heat is supplied to the air during expansion that - the temperature remains constant. Hyperbolic expansion. - - Then - - pv = p1v1. - - Work done during expansion per pound of air - _ _ - /v2 /v2 - = | p dv = p1v1 | dv/v - _/v1 _/v1 - - = p1v1 log_[epsilon] v2v1 = p1v1 log_[epsilon] p1p2. (1) - - Since the weight per cubic foot is the reciprocal of the volume per - pound, this may be written - - (p1/G1) log_[epsilon] G1/G2. (1a) - - Then the expansion curve ab is a common hyperbola. - - _Case 2._--No heat is supplied to the air during expansion. Then the - air loses an amount of heat equivalent to the external work done and - the temperature falls. Adiabatic expansion. - - In this case it can be shown that - - pv^[gamma] = p1v1^[gamma], - - where [gamma] is the ratio of the specific heats of air at constant - pressure and volume. Its value for air is 1.408, and for dry steam - 1.135. - - Work done during expansion per pound of air. - - _ _ - /v2 /v2 - = | p dv = p1v1^[gamma] | dv/v^[gamma] - _/v1 _/v1 - - = - {p1v1^[gamma]/([gamma] - 1)} {1/v2^([gamma] - 1) - 1/v1^([gamma] - 1)} - - = {p1v1^[gamma]/([gamma] - 1)} {1/v1^([gamma] - 1) - 1/v2^([gamma] - 1)} - - = {p1v1/([gamma] - 1)} {1 - (v1/v2)^([gamma] - 1)}. (2) - - The value of p1v1 for any given temperature can be found from the data - already given. - - As before, substituting the weights G1, G2 per cubic foot for the - volumes per pound, we get for the work of expansion - - (p1/G1){1/([gamma] - 1)} {1 - (G2/G1)^([gamma] - 1)}, (2a) - - = p1v1{1/([gamma] - 1)} {1 - (p2/p1)^([gamma] - 1)/[gamma]}. (2b) - - [Illustration: FIG. 77.] - - S 62. _Modification of the Theorem of Bernoulli for the Case of a - Compressible Fluid._--In the application of the principle of work to a - filament of compressible fluid, the internal work done by the - expansion of the fluid, or absorbed in its compression, must be taken - into account. Suppose, as before, that AB (fig. 77) comes to A'B' in a - short time t. Let p1, [omega]1, v1, G1 be the pressure, sectional area - of stream, velocity and weight of a cubic foot at A, and p2, [omega]2, - v2, G2 the same quantities at B. Then, from the steadiness of motion, - the weight of fluid passing A in any given time must be equal to the - weight passing B: - - G1[omega]1v1t = G2[omega]2v2t. - - Let z1, z2 be the heights of the sections A and B above any given - datum. Then the work of gravity on the mass AB in t seconds is - - G1[omega]1v1t(z1 - z2) = W(z1 - z2)t, - - where W is the weight of gas passing A or B per second. As in the case - of an incompressible fluid, the work of the pressures on the ends of - the mass AB is - - p1[omega]1v1t - p2[omega]2v2t, - = (p1/G1 - p2/G2)Wt. - - The work done by expansion of Wt lb. of fluid between A and B is Wt - [int][v1 to v2] p dv. The change of kinetic energy as before is (W/2g) - (v2^2 - v1^2)t. Hence, equating work to change of kinetic energy, - - _ - /v2 - W(z1 - z2)t + (p1/G1 - p2/G2)Wt + | p dv = (W/2g)(v2^2 - v1^2)t; - _/v1 - _ - /v2 / - .: z1 + p1/G1 + v1^2/2g = z2 + p^2/G2 + v2^2/2g - | p dv. (1) - _/v1 - - Now the work of expansion per pound of fluid has already been given. - If the temperature is constant, we get (eq. 1a, S 61) - - z1 + p1/G1 + v1^2/2g - = z2 + p^2/G2 + v2^2/2g - (p1/G1) log_[epsilon] (G1/G2). - - But at constant temperature p1/G1 = p2/G2; - - .: z1 + v1^2/2g = z2 + v2^2/2g - (p1/G1) log_[epsilon] (p1/p2), (2) - - or, neglecting the difference of level, - - (v2^2 - v1^2)/2g = (p1/G1) log_[epsilon] (p1/p2). (2a) - - Similarly, if the expansion is adiabatic (eq. 2a, S 61), - - z1 + p1/G1 + v1^2/2g = z2 + p2/G2 + v2^2/2g - - (p1/G1){1/([gamma] - 1)} {1 - (p2/p1)^([gamma] - 1)/[gamma]}; (3) - - or, neglecting the difference of level, - - (v2^2 - v1^2)/2g = - (p1/G1)[1 + 1/([gamma] - 1){1 - (p2/p1)^([gamma]-1)/[gamma]}] - p2/G2. (3a) - - It will be seen hereafter that there is a limit in the ratio p1/p2 - beyond which these expressions cease to be true. - - S 63. _Discharge of Air from an Orifice._--The form of the equation of - work for a steady stream of compressible fluid is - - z1 + p1/G1 + v1^2/2g = z2 + p2/G2 + v2^2/2g - - (p1/G1){1/([gamma] - 1)} {1 - (p2/p1^([gamma] - 1)/[gamma]}, - - the expansion being adiabatic, because in the flow of the streams of - air through an orifice no sensible amount of heat can be communicated - from outside. - - Suppose the air flows from a vessel, where the pressure is p1 and the - velocity sensibly zero, through an orifice, into a space where the - pressure is p2. Let v2 be the velocity of the jet at a point where the - convergence of the streams has ceased, so that the pressure in the jet - is also p2. As air is light, the work of gravity will be small - compared with that of the pressures and expansion, so that z1z2 may be - neglected. Putting these values in the equation above-- - - p1/G1 = p2/G2 + v2^2/2g - (p1/G1){1/([gamma] - 1)} - {1 - (p2/p1)^([gamma] - 1)/[gamma]; - - v2^2/2g = p1/G1 - p2/G2 + (p1/G1){1/([gamma] - 1)} - {1 - (p2/p1)^([gamma] - 1)/[gamma]} - - = (p1/G1){[gamma]/([gamma] - 1) - (p2/p1)^([gamma] - 1)/[gamma]/([gamma] - 1)} - p2/G2. - - But - - p1/G1^([gamma]) = p2/G2^([gamma]) - .: p2/G2 = (p1/G1)(p2/p1)^([gamma] - 1)/[gamma] - - v2^2/2g = (p1/G1){[gamma]/([gamma] - 1)} {1 - (p2/p1)^(([gamma] - 1)/[gamma]}; (1) - - or - - v2^2/2g = {[gamma]/([gamma] - 1)} {(p1/G1) - (p2/G2)}; - - an equation commonly ascribed to L. J. Weisbach (_Civilingenieur_, - 1856), though it appears to have been given earlier by A. J. C. Barre - de Saint Venant and L. Wantzel. - - It has already (S 9, eq. 4a) been seen that - - p1/G1 = (p0/G0) ([tau]1/[tau]0) - - where for air p0 = 2116.8, G0 = .08075 and [tau]0 = 492.6. - - v2^2/2g = {p0[tau]1[gamma]/G0[tau]0([gamma] - 1)} - {1 - (p2/p1)^([gamma] - 1)/[gamma]}; (2) - - or, inserting numerical values, - - v2^2/2g = 183.6[tau]1 {1 - (p2/p1)^(0.29)}; (2a) - - which gives the velocity of discharge v2 in terms of the pressure and - absolute temperature, p1, [tau]1, in the vessel from which the air - flows, and the pressure p2 in the vessel into which it flows. - - Proceeding now as for liquids, and putting [omega] for the area of the - orifice and c for the coefficient of discharge, the volume of air - discharged per second at the pressure p2 and temperature [tau]2 is - - Q2 = c[omega]v2 = c[omega] [root][(2g[gamma]p1/([gamma] - 1)G1) - (1 - (p2/p1)^([gamma] - 1)/[gamma])] - - = 108.7c[omega] [root][[tau]1 {1 - (p2/p1)^(0.29)}]. (3) - - If the volume discharged is measured at the pressure p1 and absolute - temperature [tau]1 in the vessel from which the air flows, let Q1 be - that volume; then - - p1Q1^[gamma] = p2Q2^[gamma]; - - Q1 = (p2/p1)^(1/[gamma]) Q2; - - Q1 = c[omega] [root][{2g[gamma]p1/([gamma] - 1)G1} - {(p2/p1)^(2/[gamma]) - (p2/p1)^([gamma] + 1)/[gamma]}]. - - Let - - (p2/p1)^(2/[gamma]) - (p2/p1)^([gamma] - 1)/[gamma] = - (p2/p1)^(1.41) - (p2/p1)^(1.7) = [psi]; then - - Q1 = c[omega] [root][2g[gamma]p1[psi]/([gamma] - 1)G1] - = 108.7c[omega] [root]([tau]1[psi]). (4) - - The weight of air at pressure p1 and temperature [tau]1 is - - G1 = p1/53.2[tau]1 lb. per cubic foot. - - Hence the weight of air discharged is - - W = G1Q1 = c[omega] [root][2g[gamma]p1G1[psi]/([gamma] - 1)] - = 2.043c[omega]p1 [root]([psi]/[tau]1). (5) - - Weisbach found the following values of the coefficient of discharge - c:-- - - Conoidal mouthpieces of the form of the \ - contracted vein with effective > c = - pressures of .23 to 1.1 atmosphere / 0.97 to 0.99 - Circular sharp-edged orifices 0.563 " 0.788 - Short cylindrical mouthpieces 0.81 " 0.84 - The same rounded at the inner end 0.92 " 0.93 - Conical converging mouthpieces 0.90 " 0.99 - - S 64. _Limit to the Application of the above Formulae._--In the - formulae above it is assumed that the fluid issuing from the orifice - expands from the pressure p1 to the pressure p2, while passing from - the vessel to the section of the jet considered in estimating the area - [omega]. Hence p2 is strictly the pressure in the jet at the plane of - the external orifice in the case of mouthpieces, or at the plane of - the contracted section in the case of simple orifices. Till recently - it was tacitly assumed that this pressure p2 was identical with the - general pressure external to the orifice. R. D. Napier first - discovered that, when the ratio p2/p1 exceeded a value which does not - greatly differ from 0.5, this was no longer true. In that case the - expansion of the fluid down to the external pressure is not completed - at the time it reaches the plane of the contracted section, and the - pressure there is greater than the general external pressure; or, what - amounts to the same thing, the section of the jet where the expansion - is completed is a section which is greater than the area c_c[omega] of - the contracted section of the jet, and may be greater than the area - [omega] of the orifice. Napier made experiments with steam which - showed that, so long as p2/p1 > 0.5, the formulae above were - trustworthy, when p2 was taken to be the general external pressure, - but that, if p2/p1 < 0.5, then the pressure at the contracted section - was independent of the external pressure and equal to 0.5p1. Hence in - such cases the constant value 0.5 should be substituted in the - formulae for the ratio of the internal and external pressures p2/p1. - - It is easily deduced from Weisbach's theory that, if the pressure - external to an orifice is gradually diminished, the weight of air - discharged per second increases to a maximum for a value of the ratio - - p2/p1 = {2/([gamma] + 1)}^([gamma] - 1/[gamma]) - = 0.527 for air - = 0.58 for dry steam. - - For a further decrease of external pressure the discharge - diminishes,--a result no doubt improbable. The new view of Weisbach's - formula is that from the point where the maximum is reached, or not - greatly differing from it, the pressure at the contracted section - ceases to diminish. - - A. F. Fliegner showed (_Civilingenieur_ xx., 1874) that for air - flowing from well-rounded mouthpieces there is no discontinuity of the - law of flow, as Napier's hypothesis implies, but the curve of flow - bends so sharply that Napier's rule may be taken to be a good - approximation to the true law. The limiting value of the ratio p2/p1, - for which Weisbach's formula, as originally understood, ceases to - apply, is for air 0.5767; and this is the number to be substituted for - p2/p1 in the formulae when p2/p1 falls below that value. For later - researches on the flow of air, reference may be made to G. A. Zeuner's - paper (_Civilingenieur_, 1871), and Fliegner's papers (_ibid._, 1877, - 1878). - - - VII. FRICTION OF LIQUIDS. - - S 65. When a stream of fluid flows over a solid surface, or conversely - when a solid moves in still fluid, a resistance to the motion is - generated, commonly termed fluid friction. It is due to the viscosity - of the fluid, but generally the laws of fluid friction are very - different from those of simple viscous resistance. It would appear - that at all speeds, except the slowest, rotating eddies are formed by - the roughness of the solid surface, or by abrupt changes of velocity - distributed throughout the fluid; and the energy expended in producing - these eddying motions is gradually lost in overcoming the viscosity of - the fluid in regions more or less distant from that where they are - first produced. - - The laws of fluid friction are generally stated thus:-- - - 1. The frictional resistance is independent of the pressure between - the fluid and the solid against which it flows. This may be verified - by a simple direct experiment. C. H. Coulomb, for instance, oscillated - a disk under water, first with atmospheric pressure acting on the - water surface, afterwards with the atmospheric pressure removed. No - difference in the rate of decrease of the oscillations was observed. - The chief proof that the friction is independent of the pressure is - that no difference of resistance has been observed in water mains and - in other cases, where water flows over solid surfaces under widely - different pressures. - - 2. The frictional resistance of large surfaces is proportional to the - area of the surface. - - 3. At low velocities of not more than 1 in. per second for water, the - frictional resistance increases directly as the relative velocity of - the fluid and the surface against which it flows. At velocities of 1/2 - ft. per second and greater velocities, the frictional resistance is - more nearly proportional to the square of the relative velocity. - - In many treatises on hydraulics it is stated that the frictional - resistance is independent of the nature of the solid surface. The - explanation of this was supposed to be that a film of fluid remained - attached to the solid surface, the resistance being generated between - this fluid layer and layers more distant from the surface. At - extremely low velocities the solid surface does not seem to have much - influence on the friction. In Coulomb's experiments a metal surface - covered with tallow, and oscillated in water, had exactly the same - resistance as a clean metal surface, and when sand was scattered over - the tallow the resistance was only very slightly increased. The - earlier calculations of the resistance of water at higher velocities - in iron and wood pipes and earthen channels seemed to give a similar - result. These, however, were erroneous, and it is now well understood - that differences of roughness of the solid surface very greatly - influence the friction, at such velocities as are common in - engineering practice. H. P. G. Darcy's experiments, for instance, - showed that in old and incrusted water mains the resistance was twice - or sometimes thrice as great as in new and clean mains. - - S 66. _Ordinary Expressions for Fluid Friction at Velocities not - Extremely Small._--Let f be the frictional resistance estimated in - pounds per square foot of surface at a velocity of 1 ft. per second; - [omega] the area of the surface in square feet; and v its velocity in - feet per second relatively to the water in which it is immersed. Then, - in accordance with the laws stated above, the total resistance of the - surface is - - R = f[omega]v^2 (1) - - where f is a quantity approximately constant for any given surface. If - - [xi] = 2gf/G, - - R = [xi]G[omega]v^2/2g, (2) - - where [xi] is, like f, nearly constant for a given surface, and is - termed the coefficient of friction. - - The following are average values of the coefficient of friction for - water, obtained from experiments on large plane surfaces, moved in an - indefinitely large mass of water. - - +------------------------------------+--------------+-----------------+ - | | Coefficient | Frictional | - | | of Friction, | Resistance in | - | | [xi] | lb. per sq. ft. | - | | | f | - +------------------------------------+--------------+-----------------+ - | | | | - | New well-painted iron plate | .00489 | .00473 | - | Painted and planed plank (Beaufoy) | .00350 | .00339 | - | Surface of iron ships (Rankine) | .00362 | .00351 | - | Varnished surface (Froude) | .00258 | .00250 | - | Fine sand surface " | .00418 | .00405 | - | Coarser sand surface " | .00503 | .00488 | - +------------------------------------+--------------+-----------------+ - - The distance through which the frictional resistance is overcome is v - ft. per second. The work expended in fluid friction is therefore given - by the equation-- - - Work expended = f[omega]v^3 foot-pounds per second \ (3). - = [xi]G[omega]v^3/2g " " / - - The coefficient of friction and the friction per square foot of - surface can be indirectly obtained from observations of the discharge - of pipes and canals. In obtaining them, however, some assumptions as - to the motion of the water must be made, and it will be better - therefore to discuss these values in connexion with the cases to which - they are related. - - Many attempts have been made to express the coefficient of friction in - a form applicable to low as well as high velocities. The older - hydraulic writers considered the resistance termed fluid friction to - be made up of two parts,--a part due directly to the distortion of the - mass of water and proportional to the velocity of the water relatively - to the solid surface, and another part due to kinetic energy imparted - to the water striking the roughnesses of the solid surface and - proportional to the square of the velocity. Hence they proposed to - take - - [xi] = [alpha] + [beta]/v - - in which expression the second term is of greatest importance at very - low velocities, and of comparatively little importance at velocities - over about 1/2 ft. per second. Values of [xi] expressed in this and - similar forms will be given in connexion with pipes and canals. - - All these expressions must at present be regarded as merely empirical - expressions serving practical purposes. - - The frictional resistance will be seen to vary through wider limits - than these expressions allow, and to depend on circumstances of which - they do not take account. - - S 67. _Coulomb's Experiments._--The first direct experiments on fluid - friction were made by Coulomb, who employed a circular disk suspended - by a thin brass wire and oscillated in its own plane. His experiments - were chiefly made at very low velocities. When the disk is rotated to - any given angle, it oscillates under the action of its inertia and the - torsion of the wire. The oscillations diminish gradually in - consequence of the work done in overcoming the friction of the disk. - The diminution furnishes a means of determining the friction. - - [Illustration: FIG. 78.] - - Fig. 78 shows Coulomb's apparatus. LK supports the wire and disk: ag - is the brass wire, the torsion of which causes the oscillations; DS is - a graduated disk serving to measure the angles through which the - apparatus oscillates. To this the friction disk is rigidly attached - hanging in a vessel of water. The friction disks were from 4.7 to 7.7 - in. diameter, and they generally made one oscillation in from 20 to 30 - seconds, through angles varying from 360 deg. to 6 deg. When the - velocity of the circumference of the disk was less than 6 in. per - second, the resistance was sensibly proportional to the velocity. - - _Beaufoy's Experiments._--Towards the end of the 18th century Colonel - Mark Beaufoy (1764-1827) made an immense mass of experiments on the - resistance of bodies moved through water (_Nautical and Hydraulic - Experiments_, London, 1834). Of these the only ones directly bearing - on surface friction were some made in 1796 and 1798. Smooth painted - planks were drawn through water and the resistance measured. For two - planks differing in area by 46 sq. ft., at a velocity of 10 ft. per - second, the difference of resistance, measured on the difference of - area, was 0.339 lb. per square foot. Also the resistance varied as the - 1.949th power of the velocity. - - [Illustration: FIG. 79.] - - S 68. _Froude's Experiments._--The most important direct experiments - on fluid friction at ordinary velocities are those made by William - Froude (1810-1879) at Torquay. The method adopted in these experiments - was to tow a board in a still water canal, the velocity and the - resistance being registered by very ingenious recording arrangements. - The general arrangement of the apparatus is shown in fig. 79. AA is - the board the resistance of which is to be determined. B is a cutwater - giving a fine entrance to the plane surfaces of the board. CC is a bar - to which the board AA is attached, and which is suspended by a - parallel motion from a carriage running on rails above the still water - canal. G is a link by which the resistance of the board is transmitted - to a spiral spring H. A bar I rigidly connects the other end of the - spring to the carriage. The dotted lines K, L indicate the position of - a couple of levers by which the extension of the spring is caused to - move a pen M, which records the extension on a greatly increased - scale, by a line drawn on the paper cylinder N. This cylinder revolves - at a speed proportionate to that of the carriage, its motion being - obtained from the axle of the carriage wheels. A second pen O, - receiving jerks at every second and a quarter from a clock P, records - time on the paper cylinder. The scale for the line of resistance is - ascertained by stretching the spiral spring by known weights. The - boards used for the experiment were 3/16 in. thick, 19 in. deep, and - from 1 to 50 ft. in length, cutwater included. A lead keel - counteracted the buoyancy of the board. The boards were covered with - various substances, such as paint, varnish, Hay's composition, - tinfoil, &c., so as to try the effect of different degrees of - roughness of surface. The results obtained by Froude may be summarized - as follows:-- - - 1. The friction per square foot of surface varies very greatly for - different surfaces, being generally greater as the sensible roughness - of the surface is greater. Thus, when the surface of the board was - covered as mentioned below, the resistance for boards 50 ft. long, at - 10 ft. per second, was-- - - Tinfoil or varnish 0.25 lb. per sq. ft. - Calico 0.47 " " - Fine sand 0.405 " " - Coarser sand 0.488 " " - - 2. The power of the velocity to which the friction is proportional - varies for different surfaces. Thus, with short boards 2 ft. long, - - For tinfoil the resistance varied as v^(2.16). - For other surfaces the resistance varied as v^(2.00). - - With boards 50 ft. long, - - For varnish or tinfoil the resistance varied as v^(1.83). - For sand the resistance varied as v^(2.00). - - 3. The average resistance per square foot of surface was much greater - for short than for long boards; or, what is the same thing, the - resistance per square foot at the forward part of the board was - greater than the friction per square foot of portions more sternward. - Thus, - - Mean Resistance in - lb. per sq. ft. - Varnished surface 2 ft. long 0.41 - 50 " 0.25 - Fine sand surface 2 " 0.81 - 50 " 0.405 - - This remarkable result is explained thus by Froude: "The portion of - surface that goes first in the line of motion, in experiencing - resistance from the water, must in turn communicate motion to the - water, in the direction in which it is itself travelling. Consequently - the portion of surface which succeeds the first will be rubbing, - not against stationary water, but against water partially moving in - its own direction, and cannot therefore experience so much resistance - from it." - - S 69. The following table gives a general statement of Froude's - results. In all the experiments in this table, the boards had a fine - cutwater and a fine stern end or run, so that the resistance was - entirely due to the surface. The table gives the resistances per - square foot in pounds, at the standard speed of 600 feet per minute, - and the power of the speed to which the friction is proportional, so - that the resistance at other speeds is easily calculated. - - +------------+---------------------------------------------------------------------------+ - | | Length of Surface, or Distance from Cutwater, in feet. | - | +------------------+------------------+------------------+------------------+ - | | 2 ft. | 8 ft. | 20 ft. | 50 ft. | - | +------+-----+-----+------+-----+-----+------+-----+-----+------+-----+-----+ - | | A | B | C | A | B | C | A | B | C | A | B | C | - +------------+------+-----+-----+------+-----+-----+------+-----+-----+------+-----+-----+ - | Varnish | 2.00 | .41 |.390 | 1.85 |.325 |.264 | 1.85 |.278 |.240 | 1.83 |.250 |.226 | - | Paraffin | .. | .38 |.370 | 1.94 |.314 |.260 | 1.93 |.271 |.237 | .. | .. | .. | - | Tinfoil | 2.16 | .30 |.295 | 1.99 |.278 |.263 | 1.90 |.262 |.244 | 1.83 |.246 |.232 | - | Calico | 1.93 | .87 |.725 | 1.92 |.626 |.504 | 1.89 |.531 |.447 | 1.87 |.474 |.423 | - | Fine sand | 2.00 | .81 |.690 | 2.00 |.583 |.450 | 2.00 |.480 |.384 | 2.06 |.405 |.337 | - | Medium sand| 2.00 | .90 |.730 | 2.00 |.625 |.488 | 2.00 |.534 |.465 | 2.00 |.488 |.456 | - | Coarse sand| 2.00 |1.10 |.880 | 2.00 |.714 |.520 | 2.00 |.588 |.490 | .. | .. | .. | - +--------- --+------+-----+-----+------+-----+-----+------+-----+-----+------+-----+-----+ - - Columns A give the power of the speed to which the resistance is - approximately proportional. - - Columns B give the mean resistance per square foot of the whole - surface of a board of the lengths stated in the table. - - Columns C give the resistance in pounds of a square foot of surface at - the distance sternward from the cutwater stated in the heading. - - Although these experiments do not directly deal with surfaces of - greater length than 50 ft., they indicate what would be the - resistances of longer surfaces. For at 50 ft. the decrease of - resistance for an increase of length is so small that it will make no - very great difference in the estimate of the friction whether we - suppose it to continue to diminish at the same rate or not to diminish - at all. For a varnished surface the friction at 10 ft. per second - diminishes from 0.41 to 0.32 lb. per square foot when the length is - increased from 2 to 8 ft., but it only diminishes from 0.278 to 0.250 - lb. per square foot for an increase from 20 ft. to 50 ft. - - If the decrease of friction sternwards is due to the generation of a - current accompanying the moving plane, there is not at first sight any - reason why the decrease should not be greater than that shown by the - experiments. The current accompanying the board might be assumed to - gain in volume and velocity sternwards, till the velocity was nearly - the same as that of the moving plane and the friction per square foot - nearly zero. That this does not happen appears to be due to the mixing - up of the current with the still water surrounding it. Part of the - water in contact with the board at any point, and receiving energy of - motion from it, passes afterwards to distant regions of still water, - and portions of still water are fed in towards the board to take its - place. In the forward part of the board more kinetic energy is given - to the current than is diffused into surrounding space, and the - current gains in velocity. At a greater distance back there is an - approximate balance between the energy communicated to the water and - that diffused. The velocity of the current accompanying the board - becomes constant or nearly constant, and the friction per square foot - is therefore nearly constant also. - - S 70. _Friction of Rotating Disks._--A rotating disk is virtually a - surface of unlimited extent and it is convenient for experiments on - friction with different surfaces at different speeds. Experiments - carried out by Professor W. C. Unwin (_Proc. Inst. Civ. Eng._ lxxx.) - are useful both as illustrating the laws of fluid friction and as - giving data for calculating the resistance of the disks of turbines - and centrifugal pumps. Disks of 10, 15 and 20 in. diameter fixed on a - vertical shaft were rotated by a belt driven by an engine. They were - enclosed in a cistern of water between parallel top and bottom fixed - surfaces. The cistern was suspended by three fine wires. The friction - of the disk is equal to the tendency of the cistern to rotate, and - this was measured by balancing the cistern by a fine silk cord passing - over a pulley and carrying a scale pan in which weights could be - placed. - - If [omega] is an element of area on the disk moving with the velocity - v, the friction on this element is f[omega]v^n, where f and n are - constant for any given kind of surface. Let [alpha] be the angular - velocity of rotation, R the radius of the disk. Consider a ring of the - surface between r and r + dr. Its area is 2[pi]r dr, its velocity - [alpha]r and the friction of this ring is f2[pi]r dr[alpha]^n r^n. The - moment of the friction about the axis of rotation is - 2[pi][alpha]^n fr^(n + 2)dr, and the total moment of friction for the - two sides of the disk is - _ - /R - M = 4[pi][alpha]^n f | r^(n+2) dr = {4[pi][alpha]^n /(n + 3)}fR^(n+3). . - _/0 - - If N is the number of revolutions per sec., - - M = {2^(n+2) [pi]^(n+1) N^n/(n + 3)} fR^(n+3), - - and the work expended in rotating the disk is - - M[alpha] = {2^(n+3)[pi]^(n+2)N^(n+1)/(n + 3)} fR^(n+3), foot lb. per sec. - - The experiments give directly the values of M for the disks - corresponding to any speed N. From these the values of f and n can be - deduced, f being the friction per square foot at unit velocity. For - comparison with Froude's results it is convenient to calculate the - resistance at 10 ft. per second, which is F = f10^n. - - The disks were rotated in chambers 22 in. diameter and 3, 6 and 12 in. - deep. In all cases the friction of the disks increased a little as the - chamber was made larger. This is probably due to the stilling of the - eddies against the surface of the chamber and the feeding back of the - stilled water to the disk. Hence the friction depends not only on the - surface of the disk but to some extent on the surface of the chamber - in which it rotates. If the surface of the chamber is made rougher by - covering with coarse sand there is also an increase of resistance. - - For the smoother surfaces the friction varied as the 1.85th power of - the velocity. For the rougher surfaces the power of the velocity to - which the resistance was proportional varied from 1.9 to 2.1. This is - in agreement with Froude's results. - - Experiments with a bright brass disk showed that the friction - decreased with increase of temperature. The diminution between 41 deg. - and 130 deg. F. amounted to 18%. In the general equation M = cN^n for - any given disk, - - c_t = 0.1328(1 - 0.0021t), - - where c_t is the value of c for a bright brass disk 0.85 ft. in - diameter at a temperature t deg. F. - - The disks used were either polished or made rougher by varnish or by - varnish and sand. The following table gives a comparison of the - results obtained with the disks and Froude's results on planks 50 ft. - long. The values given are the resistances per square foot at 10 ft. - per sec. - - _Froude's Experiments._ | _Disk Experiments._ - | - Tinfoil surface 0.232 | Bright brass 0.202 to 0.229 - Varnish 0.226 | Varnish 0.220 to 0.233 - Fine sand 0.337 | Fine sand 0.339 - Medium sand 0.456 | Very coarse sand 0.587 to 0.715 - - - VIII. STEADY FLOW OF WATER IN PIPES OF UNIFORM SECTION. - - S 71. The ordinary theory of the flow of water in pipes, on which all - practical formulae are based, assumes that the variation of velocity - at different points of any cross section may be neglected. The water - is considered as moving in plane layers, which are driven through the - pipe against the frictional resistance, by the difference of pressure - at or elevation of the ends of the pipe. If the motion is steady the - velocity at each cross section remains the same from moment to moment, - and if the cross sectional area is constant the velocity at all - sections must be the same. Hence the motion is uniform. The most - important resistance to the motion of the water is the surface - friction of the pipe, and it is convenient to estimate this - independently of some smaller resistances which will be accounted for - presently. - - [Illustration: FIG. 80.] - - In any portion of a uniform pipe, excluding for the present the ends - of the pipe, the water enters and leaves at the same velocity. For - that portion therefore the work of the external forces and of the - surface friction must be equal. Let fig. 80 represent a very short - portion of the pipe, of length dl, between cross sections at z and z + - dz ft. above any horizontal datum line xx, the pressures at the cross - sections being p and p + dp lb. per square foot. Further, let Q be the - volume of flow or discharge of the pipe per second, [Omega] the area - of a normal cross section, and [chi] the perimeter of the pipe. The Q - cubic feet, which flow through the space considered per second, weigh - GQ lb., and fall through a height -dz ft. The work done by gravity is - then - - -GQ dz; - - a positive quantity if dz is negative, and vice versa. The resultant - pressure parallel to the axis of the pipe is p - (p + dp) = -dp lb. - per square foot of the cross section. The work of this pressure on the - volume Q is - - -Q dp. - - The only remaining force doing work on the system is the friction - against the surface of the pipe. The area of that surface is [chi]dl. - - The work expended in overcoming the frictional resistance per second - is (see S 66, eq. 3) - - -[zeta]G[chi]dlv^3/2g, - - or, since Q = [Omega]v, - - -[zeta]G([chi]/[Omega]) Q (v^2/2g) dl; - - the negative sign being taken because the work is done against a - resistance. Adding all these portions of work, and equating the result - to zero, since the motion is uniform,-- - - -GQ dz - Q dp - [zeta]G([chi]/[Omega]) Q (v^2/2g) dl = 0. - - Dividing by GQ, - - dz + dp/G + [zeta]([chi]/[Omega])(v^2/2g) dl = 0. - - Integrating, - - z + p/G + [zeta]([chi]/[Omega])(v^2/2g)l = constant. (1) - - S 72. Let A and B (fig. 81) be any two sections of the pipe for which - p, z, l have the values p1, z1, l1, and p2, z2, l2, respectively. Then - - z1 + p1/G + [zeta]([chi]/[Omega])(v^2/2g)l1 - = z2 + p2/G + [zeta]([chi]/[Omega])(v^2/2g)l2; - - or, if l2 - l1 = L, rearranging the terms, - - [zeta]v^2/2g = (1/L){(z1 + p1/G) - (z2 + p2/G)}[Omega]/[chi]. (2) - - Suppose pressure columns introduced at A and B. The water will rise in - those columns to the heights p1/G and p2/G due to the pressures p1 and - p2 at A and B. Hence (z1 + p1/G) - (z2 + p2/G) is the quantity - represented in the figure by DE, the fall of level of the pressure - columns, or _virtual fall_ of the pipe. If there were no friction in - the pipe, then by Bernoulli's equation there would be no fall of level - of the pressure columns, the velocity being the same at A and B. Hence - DE or h is the head lost in friction in the distance AB. The quantity - DE/AB = h/L is termed the virtual slope of the pipe or virtual fall - per foot of length. It is sometimes termed very conveniently the - relative fall. It will be denoted by the symbol i. - - [Illustration: FIG. 81.] - - The quantity [Omega]/[chi] which appears in many hydraulic equations - is called the hydraulic mean radius of the pipe. It will be denoted by - m. - - Introducing these values, - - [zeta]v^2/2g = mh/L = mi. (3) - - For pipes of circular section, and diameter d, - - m = [Omega]/[chi] = (1/4)[pi]d^2/[pi]d = (1/4)d. - - Then - - [zeta]v^2/2g = (1/4)dh/L = (1/4)di; (4) - - or - - h = [zeta](4L/d)(v^2/2g); (4a) - - which shows that the head lost in friction is proportional to the head - due to the velocity, and is found by multiplying that head by the - coefficient 4[zeta]L/d. It is assumed above that the atmospheric - pressure at C and D is the same, and this is usually nearly the case. - But if C and D are at greatly different levels the excess of - barometric pressure at C, in feet of water, must be added to p2/G. - - S 73. _Hydraulic Gradient or Line of Virtual Slope._--Join CD. Since - the head lost in friction is proportional to L, any intermediate - pressure column between A and B will have its free surface on the line - CD, and the vertical distance between CD and the pipe at any point - measures the pressure, exclusive of atmospheric pressure, in the pipe - at that point. If the pipe were laid along the line CD instead of AB, - the water would flow at the same velocity by gravity without any - change of pressure from section to section. Hence CD is termed the - virtual slope or hydraulic gradient of the pipe. It is the line of - free surface level for each point of the pipe. - - If an ordinary pipe, connecting reservoirs open to the air, rises at - any joint above the line of virtual slope, the pressure at that point - is less than the atmospheric pressure transmitted through the pipe. At - such a point there is a liability that air may be disengaged from the - water, and the flow stopped or impeded by the accumulation of air. If - the pipe rises more than 34 ft. above the line of virtual slope, the - pressure is negative. But as this is impossible, the continuity of the - flow will be broken. - - If the pipe is not straight, the line of virtual slope becomes a - curved line, but since in actual pipes the vertical alterations of - level are generally small, compared with the length of the pipe, - distances measured along the pipe are sensibly proportional to - distances measured along the horizontal projection of the pipe. Hence - the line of hydraulic gradient may be taken to be a straight line - without error of practical importance. - - [Illustration: FIG. 82.] - - S 74. _Case of a Uniform Pipe connecting two Reservoirs, when all the - Resistances are taken into account._--Let h (fig. 82) be the - difference of level of the reservoirs, and v the velocity, in a pipe - of length L and diameter d. The whole work done per second is - virtually the removal of Q cub. ft. of water from the surface of the - upper reservoir to the surface of the lower reservoir, that is GQh - foot-pounds. This is expended in three ways. (1) The head v^2/2g, - corresponding to an expenditure of GQv^2/2g foot-pounds of work, is - employed in giving energy of motion to the water. This is ultimately - wasted in eddying motions in the lower reservoir. (2) A portion of - head, which experience shows may be expressed in the form - [zeta]0v^2/2g, corresponding to an expenditure of GQ[zeta]0v^2/2g - foot-pounds of work, is employed in overcoming the resistance at the - entrance to the pipe. (3) As already shown the head expended in - overcoming the surface friction of the pipe is [zeta](4L/d)(v^2/2g) - corresponding to GQ[zeta](4L/d)(v^2/2g) foot-pounds of work. Hence - - GQh = GQv^2/2g + GQ[zeta]0v^2/2g + GQ[zeta].4L.v^2/d.2g; - - h = (1 + [zeta]0 + [zeta].4L/d)v^2/2g. - (5) - v = 8.025 [root][hd/{(1 + [zeta]0)d + 4[zeta]L}]. - - If the pipe is bell-mouthed, [zeta]0 is about = .08. If the entrance - to the pipe is cylindrical, [zeta]0 = 0.505. Hence 1 + [zeta]0 = 1.08 - to 1.505. In general this is so small compared with [zeta]4L/d that, - for practical calculations, it may be neglected; that is, the losses - of head other than the loss in surface friction are left out of the - reckoning. It is only in short pipes and at high velocities that it is - necessary to take account of the first two terms in the bracket, as - well as the third. For instance, in pipes for the supply of turbines, - v is usually limited to 2 ft. per second, and the pipe is bellmouthed. - Then 1.08v^2/2g = 0.067 ft. In pipes for towns' supply v may range - from 2 to 4(1/2) ft. per second, and then 1.5v^2/2g = 0.1 to 0.5 ft. - In either case this amount of head is small compared with the whole - virtual fall in the cases which most commonly occur. - - When d and v or d and h are given, the equations above are solved - quite simply. When v and h are given and d is required, it is better - to proceed by approximation. Find an approximate value of d by - assuming a probable value for [zeta] as mentioned below. Then from - that value of d find a corrected value for [zeta] and repeat the - calculation. - - The equation above may be put in the form - - h = (4[zeta]/d)[{(1 + [zeta]0)d/4[zeta]} + L] v^2/2g; (6) - - from which it is clear that the head expended at the mouthpiece is - equivalent to that of a length - - (1 + [zeta]0)d/4[zeta] - - of the pipe. Putting 1 + [zeta]0 = 1.505 and [zeta] = 0.01, the length - of pipe equivalent to the mouthpiece is 37.6d nearly. This may be - added to the actual length of the pipe to allow for mouthpiece - resistance in approximate calculations. - - S 75. _Coefficient of Friction for Pipes discharging Water._--From the - average of a large number of experiments, the value of [zeta] for - ordinary iron pipes is - - [zeta] = 0.007567. (7) - - But practical experience shows that no single value can be taken - applicable to very different cases. The earlier hydraulicians occupied - themselves chiefly with the dependence of [zeta] on the velocity. - Having regard to the difference of the law of resistance at very low - and at ordinary velocities, they assumed that [zeta] might be - expressed in the form - - [zeta] = a + [beta]/v. - - The following are the best numerical values obtained for [zeta] so - expressed:-- - - +----------------------------------+----------+----------+ - | | [alpha] | [beta] | - +----------------------------------+----------+----------+ - | R. de Prony (from 51 experiments)| 0.006836 | 0.001116 | - | J. F. d'Aubuisson de Voisins | 0.00673 | 0.001211 | - | J. A. Eytelwein | 0.005493 | 0.00143 | - +----------------------------------+----------+----------+ - - Weisbach proposed the formula - - 4[zeta] = [alpha] + [beta]/[root]v = 0.003598 + 0.004289/[root]v. (8) - - S 76. _Darcy's Experiments on Friction in Pipes._--All previous - experiments on the resistance of pipes were superseded by the - remarkable researches carried out by H. P. G. Darcy (1803-1858), the - Inspector-General of the Paris water works. His experiments were - carried out on a scale, under a variation of conditions, and with a - degree of accuracy which leaves little to be desired, and the results - obtained are of very great practical importance. These results may be - stated thus:-- - - 1. For new and clean pipes the friction varies considerably with the - nature and polish of the surface of the pipe. For clean cast iron it - is about 1(1/2) times as great as for cast iron covered with pitch. - - 2. The nature of the surface has less influence when the pipes are old - and incrusted with deposits, due to the action of the water. Thus old - and incrusted pipes give twice as great a frictional resistance as new - and clean pipes. Darcy's coefficients were chiefly determined from - experiments on new pipes. He doubles these coefficients for old and - incrusted pipes, in accordance with the results of a very limited - number of experiments on pipes containing incrustations and deposits. - - 3. The coefficient of friction may be expressed in the form [zeta] = - [alpha] + [beta]/v; but in pipes which have been some time in use it - is sufficiently accurate to take [zeta] = [alpha]1 simply, where - [alpha]1 depends on the diameter of the pipe alone, but [alpha] and - [beta] on the other hand depend both on the diameter of the pipe and - the nature of its surface. The following are the values of the - constants. - - For pipes which have been some time in use, neglecting the term - depending on the velocity; - - [zeta] = [alpha](1 + [beta]/d). (9) - - +-------------------------------------------------+---------+------+ - | | [alpha] |[beta]| - +-------------------------------------------------+---------+------+ - | For drawn wrought-iron or smooth cast-iron pipes| .004973 | .084 | - | For pipes altered by light incrustations | .00996 | .084 | - +-------------------------------------------------+---------+------+ - - These coefficients may be put in the following very simple form, - without sensibly altering their value:-- - - For clean pipes [zeta] = .005(1 + (1/12)d) (9a) - For slightly incrusted pipes [zeta] = .01(1 + (1/12)d) - - _Darcy's Value of the Coefficient of Friction [zeta] for Velocities - not less than 4 in. per second._ - - +----------+------------------++----------+------------------+ - | Diameter | [zeta] || Diameter | [zeta] | - | of Pipe +--------+---------|| of Pipe +------------------+ - |in Inches.| New |Incrusted||in Inches.| New |Incrusted| - | | Pipes. | Pipes. || | Pipes. | Pipes. | - +----------+--------+---------++----------+--------+---------+ - | 2 |0.00750 |0.01500 || 18 | .00528 | .01056 | - | 3 | .00667 | .01333 || 21 | .00524 | .01048 | - | 4 | .00625 | .01250 || 24 | .00521 | .01042 | - | 5 | .00600 | .01200 || 27 | .00519 | .01037 | - | 6 | .00583 | .01167 || 30 | .00517 | .01033 | - | 7 | .00571 | .01143 || 36 | .00514 | .01028 | - | 8 | .00563 | .01125 || 42 | .00512 | .01024 | - | 9 | .00556 | .01111 || 48 | .00510 | .01021 | - | 12 | .00542 | .01083 || 54 | .00509 | .01019 | - | 15 | .00533 | .01067 || | | | - +----------+--------+---------++----------+--------+---------+ - - These values of [zeta] are, however, not exact for widely differing - velocities. To embrace all cases Darcy proposed the expression - - [zeta] = ([alpha] + [alpha]1/d) + ([beta] + [beta]1/d^2)/v; (10) - - which is a modification of Coulomb's, including terms expressing the - influence of the diameter and of the velocity. For clean pipes Darcy - found these values - - [alpha] = .004346 - [alpha]1 = .0003992 - [beta] = .0010182 - [beta]1 = .000005205. - - It has become not uncommon to calculate the discharge of pipes by the - formula of E. Ganguillet and W. R. Kutter, which will be discussed - under the head of channels. For the value of c in the relation v = c - [root](mi), Ganguillet and Kutter take - - 41.6 + 1.811/n + .00281/i - c = ---------------------------------- - 1 + [(41.6 + .00281/i)(n/[root]m)] - - where n is a coefficient depending only on the roughness of the pipe. - For pipes uncoated as ordinarily laid n = 0.013. The formula is very - cumbrous, its form is not rationally justifiable and it is not at all - clear that it gives more accurate values of the discharge than simpler - formulae. - - S 77. _Later Investigations on Flow in Pipes._--The foregoing - statement gives the theory of flow in pipes so far as it can be put in - a simple rational form. But the conditions of flow are really more - complicated than can be expressed in any rational form. Taking even - selected experiments the values of the empirical coefficient [zeta] - range from 0.16 to 0.0028 in different cases. Hence means of - discriminating the probable value of [zeta] are necessary in using the - equations for practical purposes. To a certain extent the knowledge - that [zeta] decreases with the size of the pipe and increases very - much with the roughness of its surface is a guide, and Darcy's method - of dealing with these causes of variation is very helpful. But a - further difficulty arises from the discordance of the results of - different experiments. For instance F. P. Stearns and J. M. Gale both - experimented on clean asphalted cast-iron pipes, 4 ft. in diameter. - According to one set of gaugings [zeta] = .0051, and according to the - other [zeta] = .0031. It is impossible in such cases not to suspect - some error in the observations or some difference in the condition of - the pipes not noticed by the observers. - - It is not likely that any formula can be found which will give exactly - the discharge of any given pipe. For one of the chief factors in any - such formula must express the exact roughness of the pipe surface, and - there is no scientific measure of roughness. The most that can be done - is to limit the choice of the coefficient for a pipe within certain - comparatively narrow limits. The experiments on fluid friction show - that the power of the velocity to which the resistance is proportional - is not exactly the square. Also in determining the form of his - equation for [zeta] Darcy used only eight out of his seventeen series - of experiments, and there is reason to think that some of these were - exceptional. Barre de Saint-Venant was the first to propose a formula - with two constants, - - dh/4l = mV^n, - - where m and n are experimental constants. If this is written in the - form - - log m + n log v = log (dh/4l), - - we have, as Saint-Venant pointed out, the equation to a straight line, - of which m is the ordinate at the origin and n the ratio of the slope. - If a series of experimental values are plotted logarithmically the - determination of the constants is reduced to finding the straight line - which most nearly passes through the plotted points. Saint-Venant - found for n the value of 1.71. In a memoir on the influence of - temperature on the movement of water in pipes (Berlin, 1854) by G. H. - L. Hagen (1797-1884) another modification of the Saint-Venant formula - was given. This is h/l = mv^n/d^x, which involves three experimental - coefficients. Hagen found n = 1.75; x = 1.25; and m was then nearly - independent of variations of v and d. But the range of cases examined - was small. In a remarkable paper in the _Trans. Roy. Soc._, 1883, - Professor Osborne Reynolds made much clearer the change from regular - stream line motion at low velocities to the eddying motion, which - occurs in almost all the cases with which the engineer has to deal. - Partly by reasoning, partly by induction from the form of - logarithmically plotted curves of experimental results, he arrived at - the general equation h/l = c(v^n/d^(3 - n))P^(2 - n), where n = l for - low velocities and n = 1.7 to 2 for ordinary velocities. P is a - function of the temperature. Neglecting variations of temperature - Reynold's formula is identical with Hagen's if x = 3 - n. For - practical purposes Hagen's form is the more convenient. - - _Values of Index of Velocity._ - - +--------------------+---------------+----------+---------------+ - | | | Diameter | | - | Surface of Pipe. | Authority. | of Pipe | Values of n. | - | | |in Metres.| | - +--------------------+---------------+----------+---------------+ - | Tin plate | Bossut | /.036 | 1.697 \ 1.72 | - | | | \.054 | 1.730 / | - | | | | | - | Wrought iron (gas | Hamilton Smith| /.0159 | 1.756 \ 1.75 | - | pipe) | | \.0267 | 1.770 / | - | | | | | - | | | /.014 | 1.866 \ | - | Lead | Darcy | < .027 | 1.755 > 1.77 | - | | | \.041 | 1.760 / | - | | | | | - | Clean brass | Mair | .036 | 1.795 1.795| - | | | | | - | / | Hamilton Smith| / .0266 | 1.760 \ | - | Asphalted < | Lampe. |< .4185 | 1.850 > 1.85 | - | | | W. W. Bonn | | .306 | 1.582 | | - | \ | Stearns | \1.219 | 1.880 / | - | | | | | - | Riveted wrought \ | | /.2776 | 1.804 \ | - | iron > | Hamilton Smith|< .3219 | 1.892 > 1.87 | - | / | | \.3749 | 1.852 / | - | | | | | - | Wrought iron (gas\ | | /.0122 | 1.900 \ | - | pipe) >| Darcy |< .0266 | 1.899 > 1.87 | - | / | | \.0395 | 1.838 / | - | | | | | - | | | /.0819 | 1.950 \ | - | New cast iron | Darcy |< .137 | 1.923 > 1.95 | - | | | |.188 | 1.957 | | - | | | \.50 | 1.950 / | - | | | | | - | | | /.0364 | 1.835 \ | - | | | |.0801 | 2.000 > 2.00 | - | Cleaned cast iron | Darcy |< .2447 | 2.000 | | - | | | \.397 | 2.07 / | - | | | | | - | | | /.0359 | 1.980 \ | - | Incrusted cast iron| Darcy |< .0795 | 1.990 > 2.00 | - | | | \.2432 | 1.990 / | - +--------------------+---------------+----------+---------------+ - - [Illustration: FIG. 83.] - - In 1886, Professor W. C. Unwin plotted logarithmically all the most - trustworthy experiments on flow in pipes then available.[5] Fig. 83 - gives one such plotting. The results of measuring the slopes of the - lines drawn through the plotted points are given in the table. - - It will be seen that the values of the index n range from 1.72 for the - smoothest and cleanest surface, to 2.00 for the roughest. The numbers - after the brackets are rounded off numbers. - - The value of n having been thus determined, values of m/d^x were next - found and averaged for each pipe. These were again plotted - logarithmically in order to find a value for x. The lines were not - very regular, but in all cases the slope was greater than 1 to 1, so - that the value of x must be greater than unity. The following table - gives the results and a comparison of the value of x and Reynolds's - value 3 - n. - - +-----------------------+--------+--------+-------+ - | Kind of Pipe. | n | 3 - n | x | - +-----------------------+--------+--------+-------+ - | Tin plate | 1.72 | 1.28 | 1.100 | - | Wrought iron (Smith) | 1.75 | 1.25 | 1.210 | - | Asphalted pipes | 1.85 | 1.15 | 1.127 | - | Wrought iron (Darcy) | 1.87 | 1.13 | 1.680 | - | Riveted wrought iron | 1.87 | 1.13 | 1.390 | - | New cast iron | 1.95 | 1.05 | 1.168 | - | Cleaned cast iron | 2.00 | 1.00 | 1.168 | - | Incrusted cast iron | 2.00 | 1.00 | 1.160 | - +-----------------------+--------+--------+-------+ - - With the exception of the anomalous values for Darcy's wrought-iron - pipes, there is no great discrepancy between the values of x and 3 - - n, but there is no appearance of relation in the two quantities. For - the present it appears preferable to assume that x is independent of - n. - - It is now possible to obtain values of the third constant m, using the - values found for n and x. The following table gives the results, the - values of m being for metric measures. - - Here, considering the great range of diameters and velocities in the - experiments, the constancy of m is very satisfactorily close. The - asphalted pipes give rather variable values. But, as some of these - were new and some old, the variation is, perhaps, not surprising. The - incrusted pipes give a value of m quite double that for new pipes but - that is perfectly consistent with what is known of fluid friction in - other cases. - - +---------------+----------+-----------+----------+----------------+ - | | Diameter | Value of | Mean | | - | Kind of Pipe. | in | m. | Value | Authority. | - | | Metres. | | of m. | | - +---------------+----------+-----------+----------+----------------+ - | Tin plate | / 0.036 | .01697 \ | .01686 | Bossut | - | | \ 0.054 | .01676 / | | | - | | | | | | - | Wrought iron | / 0.016 | .01302 \ | .01310 | Hamilton Smith | - | | \ 0.027 | .01319 / | | | - | | | | | | - | | / 0.027 | .01749 \ | / | Hamilton Smith | - | | | 0.306 | .02058 | | | | W. W. Bonn | - | Asphalted | < 0.306 | .02107 > | .01831< | W. W. Bonn | - | pipes | | 0.419 | .01650 | | | | Lampe | - | | | 1.219 | .01317 | | | | Stearns | - | | \ 1.219 | .02107 / | \ | Gale | - | | | | | | - | | / 0.278 | .01370 \ | | | - | | | 0.322 | .01440 | | | | - | Riveted | < 0.375 | .01390 > | .01403 | Hamilton Smith | - | wrought iron| | 0.432 | .01368 | | | | - | | \ 0.657 | .01448 / | | | - | | | | | | - | | / 0.082 | .01725 \ | | | - | New cast iron | < 0.137 | .01427 > | .01658 | Darcy | - | | | 0.188 | .01734 | | | | - | | \ 0.500 | .01745 / | | | - | | | | | | - | Cleaned cast | / 0.080 | .01979 \ | | | - | iron | < 0.245 | .02091 > | .01994 | Darcy | - | | \ 0.297 | .01913 / | | | - | | | | | | - | Incrusted cast| / 0.036 | .03693 \ | | | - | iron | < 0.080 | .03530 > | .03643 | Darcy | - | | \ 0.243 | .03706 / | | | - +---------------+----------+-----------+----------+----------------+ - - - _General Mean Values of Constants._ - - The general formula (Hagen's)--h/l = mv^n/d^x.2g--can therefore be - taken to fit the results with convenient closeness, if the following - mean values of the coefficients are taken, the unit being a metre:-- - - +----------------------+-------+-------+------+ - | Kind of Pipe. | m | x | n | - +----------------------+-------+-------+------+ - | Tin plate | .0169 | 1.10 | 1.72 | - | Wrought iron | .0131 | 1.21 | 1.75 | - | Asphalted iron | .0183 | 1.127 | 1.85 | - | Riveted wrought iron | .0140 | 1.390 | 1.87 | - | New cast iron | .0166 | 1.168 | 1.95 | - | Cleaned cast iron | .0199 | 1.168 | 2.0 | - | Incrusted cast iron | .0364 | 1.160 | 2.0 | - +----------------------+-------+-------+------+ - - The variation of each of these coefficients is within a comparatively - narrow range, and the selection of the proper coefficient for any - given case presents no difficulty, if the character of the surface of - the pipe is known. - - It only remains to give the values of these coefficients when the - quantities are expressed in English feet. For English measures the - following are the values of the coefficients:-- - - +----------------------+-------+-------+------+ - | Kind of Pipe. | m | x | n | - +----------------------+-------+-------+------+ - | Tin plate | .0265 | 1.10 | 1.72 | - | Wrought iron | .0226 | 1.21 | 1.75 | - | Asphalted iron | .0254 | 1.127 | 1.85 | - | Riveted wrought iron | .0260 | 1.390 | 1.87 | - | New cast iron | .0215 | 1.168 | 1.95 | - | Cleaned cast iron | .0243 | 1.168 | 2.0 | - | Incrusted cast iron | .0440 | 1.160 | 2.0 | - +----------------------+-------+-------+------+ - - S 78. _Distribution of Velocity in the Cross Section of a - Pipe._--Darcy made experiments with a Pitot tube in 1850 on the - velocity at different points in the cross section of a pipe. He - deduced the relation - - V - v = 11.3(r^(3/2)/R) [root]i, - - where V is the velocity at the centre and v the velocity at radius r - in a pipe of radius R with a hydraulic gradient i. Later Bazin - repeated the experiments and extended them (_Mem. de l'Academie des - Sciences_, xxxii. No. 6). The most important result was the ratio of - mean to central velocity. Let b = Ri/U^2, where U is the mean velocity - in the pipe; then V/U = 1 + 9.03 [root]b. A very useful result for - practical purposes is that at 0.74 of the radius of the pipe the - velocity is equal to the mean velocity. Fig. 84 gives the velocities - at different radii as determined by Bazin. - - [Illustration: FIG. 84.] - - S 79. _Influence of Temperature on the Flow through Pipes._--Very - careful experiments on the flow through a pipe 0.1236 ft. in diameter - and 25 ft. long, with water at different temperatures, have been made - by J. G. Mair (_Proc. Inst. Civ. Eng._ lxxxiv.). The loss of head was - measured from a point 1 ft. from the inlet, so that the loss at entry - was eliminated. The 1(1/2) in. pipe was made smooth inside and to gauge, - by drawing a mandril through it. Plotting the results logarithmically, - it was found that the resistance for all temperatures varied very - exactly as v^(1.795), the index being less than 2 as in other - experiments with very smooth surfaces. Taking the ordinary equation of - flow h = [zeta](4L/D)(v^2/2g), then for heads varying from 1 ft. to - nearly 4 ft., and velocities in the pipe varying from 4 ft. to 9 ft. - per second, the values of [zeta] were as follows:-- - - Temp. F. [zeta] | Temp. F. [zeta] - 57 .0044 to .0052 | 100 .0039 to .0042 - 70 .0042 to .0045 | 110 .0037 to .0041 - 80 .0041 to .0045 | 120 .0037 to .0041 - 90 .0040 to .0045 | 130 .0035 to .0039 - | 160 .0035 to .0038 - - This shows a marked decrease of resistance as the temperature rises. - If Professor Osborne Reynolds's equation is assumed h = mLV^n/d^(3 - - n), and n is taken 1.795, then values of m at each temperature are - practically constant-- - - Temp. F. m. | Temp. F. m. - 57 0.000276 | 100 0.000244 - 70 0.000263 | 110 0.000235 - 80 0.000257 | 120 0.000229 - 90 0.000250 | 130 0.000225 - | 160 0.000206 - - where again a regular decrease of the coefficient occurs as the - temperature rises. In experiments on the friction of disks at - different temperatures Professor W. C. Unwin found that the resistance - was proportional to constant X (1 - 0.0021t) and the values of m given - above are expressed almost exactly by the relation - - m = 0.000311(1 - 0.00215 t). - - In tank experiments on ship models for small ordinary variations of - temperature, it is usual to allow a decrease of 3% of resistance for - 10 deg. F. increase of temperature. - - S 80. _Influence of Deposits in Pipes on the Discharge. Scraping Water - Mains._--The influence of the condition of the surface of a pipe on - the friction is shown by various facts known to the engineers of - waterworks. In pipes which convey certain kinds of water, oxidation - proceeds rapidly and the discharge is considerably diminished. A main - laid at Torquay in 1858, 14 m. in length, consists of 10-in., 9-in. - and 8-in. pipes. It was not protected from corrosion by any coating. - But it was found to the surprise of the engineer that in eight years - the discharge had diminished to 51% of the original discharge. J. G. - Appold suggested an apparatus for scraping the interior of the pipe, - and this was constructed and used under the direction of William - Froude (see "Incrustation of Iron Pipes," by W. Ingham, _Proc. Inst. - Mech. Eng._, 1899). It was found that by scraping the interior of the - pipe the discharge was increased 56%. The scraping requires to be - repeated at intervals. After each scraping the discharge diminishes - rather rapidly to 10% and afterwards more slowly, the diminution in a - year being about 25%. - - Fig. 85 shows a scraper for water mains, similar to Appold's but - modified in details, as constructed by the Glenfield Company, at - Kilmarnock. A is a longitudinal section of the pipe, showing the - scraper in place; B is an end view of the plungers, and C, D sections - of the boxes placed at intervals on the main for introducing or - withdrawing the scraper. The apparatus consists of two plungers, - packed with leather so as to fit the main pretty closely. On the - spindle of these plungers are fixed eight steel scraping blades, with - curved scraping edges fitting the surface of the main. The apparatus - is placed in the main by removing the cover from one of the boxes - shown at C, D. The cover is then replaced, water pressure is admitted - behind the plungers, and the apparatus driven through the main. At - Lancaster after twice scraping the discharge was increased 56(1/2)%, - at Oswestry 54(1/2)%. The increased discharge is due to the diminution - of the friction of the pipe by removing the roughnesses due to - oxidation. The scraper can be easily followed when the mains are about - 3 ft. deep by the noise it makes. The average speed of the scraper at - Torquay is 2(1/3) m. per hour. At Torquay 49% of the deposit is iron - rust, the rest being silica, lime and organic matter. - - [Illustration: FIG. 85. Scale 1/25.] - - In the opinion of some engineers it is inadvisable to use the scraper. - The incrustation is only temporarily removed, and if the use of the - scraper is continued the life of the pipe is reduced. The only - treatment effective in preventing or retarding the incrustation due to - corrosion is to coat the pipes when hot with a smooth and perfect - layer of pitch. With certain waters such as those derived from the - chalk the incrustation is of a different character, consisting of - nearly pure calcium carbonate. A deposit of another character which - has led to trouble in some mains is a black slime containing a good - deal of iron not derived from the pipes. It appears to be an organic - growth. Filtration of the water appears to prevent the growth of the - slime, and its temporary removal may be effected by a kind of brush - scraper devised by G. F. Deacon (see "Deposits in Pipes," by Professor - J. C. Campbell Brown, _Proc. Inst. Civ. Eng._, 1903-1904). - - S 81. _Flow of Water through Fire Hose._--The hose pipes used for fire - purposes are of very varied character, and the roughness of the - surface varies. Very careful experiments have been made by J. R. - Freeman (_Am. Soc. Civ. Eng._ xxi., 1889). It was noted that under - pressure the diameter of the hose increased sufficiently to have a - marked influence on the discharge. In reducing the results the true - diameter has been taken. Let v = mean velocity in ft. per sec.; r = - hydraulic mean radius or one-fourth the diameter in feet; i = - hydraulic gradient. Then v = n[root](ri). - - +---------------+---------+---------+-------+-------+-------+ - | | Diameter| Gallons | | | | - | | in | (United | | | | - | | Inches. | States) | i | v | n | - | | | per min.| | | | - +---------------+---------+---------+-------+-------+-------+ - | Solid rubber | 2.65 | 215 | .1863 | 12.50 | 123.3 | - | hose | " | 344 | .4714 | 20.00 | 124.0 | - | | | | | | | - | Woven cotton, | 2.47 | 200 | .2464 | 13.40 | 119.1 | - | rubber lined | " | 299 | .5269 | 20.00 | 121.5 | - | | | | | | | - | Woven cotton, | 2.49 | 200 | .2427 | 13.20 | 117.7 | - | rubber lined | " | 319 | .5708 | 21.00 | 122.1 | - | | | | | | | - | Knit cotton, | 2.68 | 132 | .0809 | 7.50 | 111.6 | - | rubber lined | " | 299 | .3931 | 17.00 | 114.8 | - | | | | | | | - | Knit cotton, | 2.69 | 204 | .2357 | 11.50 | 100.1 | - | rubber lined | " | 319 | .5165 | 18.00 | 105.8 | - | | | | | | | - | Woven cotton, | 2.12 | 154 | .3448 | 14.00 | 113.4 | - | rubber lined | " | 240 | .7673 | 21.81 | 118.4 | - | | | | | | | - | Woven cotton, | 2.53 | 54.8 | .0261 | 3.50 | 94.3 | - | rubber lined | " | 298 | .8264 | 19.00 | 91.0 | - | | | | | | | - | Unlined linen | 2.60 | 57.9 | .0414 | 3.50 | 73.9 | - | hose | " | 331 |1.1624 | 20.00 | 79.6 | - +---------------+---------+---------+-------+-------+-------+ - - S 82. _Reduction of a Long Pipe of Varying Diameter to an Equivalent - Pipe of Uniform Diameter. Dupuit's Equation._--Water mains for the - supply of towns often consist of a series of lengths, the diameter - being the same for each length, but differing from length to length. - In approximate calculations of the head lost in such mains, it is - generally accurate enough to neglect the smaller losses of head and to - have regard to the pipe friction only, and then the calculations may - be facilitated by reducing the main to a main of uniform diameter, in - which there would be the same loss of head. Such a uniform main will - be termed an equivalent main. - - [Illustration: FIG. 86.] - - In fig. 86 let A be the main of variable diameter, and B the - equivalent uniform main. In the given main of variable diameter A, let - - l1, l2... be the lengths, - d1, d2... the diameters, - v1, v2... the velocities, - i1, i2... the slopes, - - for the successive portions, and let l, d, v and i be corresponding - quantities for the equivalent uniform main B. The total loss of head - in A due to friction is - - h = i1l1 + i2l2 + ... - = [zeta](v1^2 . 4l1/2gd1) + [zeta](v2^2 . 4l2/2gd2) + ... - - and in the uniform main - - il = [zeta](v^2 . 4l/2gd). - - If the mains are equivalent, as defined above, - - [zeta](v^2 . 4l/2gd) = [zeta](v1^2 . 4l1/2gd1) + [zeta](v2^2 . 4l2/2gd2) + ... - - But, since the discharge is the same for all portions, - - (1/4)[pi]d^2v = (1/4)[pi]d1^2v1 = (1/4)[pi]d2^2v2 = ... - - v1 = vd^2/d1^2; v2 = vd^2/d2^2 ... - - Also suppose that [zeta] may be treated as constant for all the pipes. - Then - - l/d = (d^4/d1^4)(l1/d1) + (d^4/d2^4(12/d2) + ... - - l = (d^5/d1^5)l1 + (d^5/d2^5)l2 + ... - - which gives the length of the equivalent uniform main which would have - the same total loss of head for any given discharge. - - S 83. _Other Losses of Head in Pipes._--Most of the losses of head in - pipes, other than that due to surface friction against the pipe, are - due to abrupt changes in the velocity of the stream producing eddies. - The kinetic energy of these is deducted from the general energy of - translation, and practically wasted. - - [Illustration: FIG. 87.] - - _Sudden Enlargement of Section._--Suppose a pipe enlarges in section - from an area [omega]0 to an area [omega]1 (fig. 87); then - - v1/v0 = [omega]0/[omega]1; - - or, if the section is circular, - - v1/v0 = (d0/d1)^2. - - The head lost at the abrupt change of velocity has already been shown - to be the head due to the relative velocity of the two parts of the - stream. Hence head lost - - [h]_e = (v0 - v1)^2/2g = ([omega]1/[omega]0 - 1)^2v1^2/2g - = {(d1/d0)^2 - 1}^2 v1^2/2g - - or - - [h]_e = [zeta]_ev1^2/2g, (1) - - if [zeta]_e is put for the expression in brackets. - - +--------------+----+----+----+----+----+----+----+----+----+----+----+-----+-----+-----+-----+ - | [omega]1/ |1.1 |1.2 |1.5 |1.7 |1.8 |1.9 |2.0 |2.5 |3.0 |3.5 |4.0 | 5.0 | 6.0 | 7.0 | 8.0 | - | [omega]0 = | | | | | | | | | | | | | | | | - | d1/d0 = |1.05|1.10|1.22|1.30|1.34|1.38|1.41|1.58|1.73|1.87|2.00| 2.24| 2.45| 2.65| 2.83| - | | | | | | | | | | | | | | | | | - | [zeta]_e = | .01| .04| .25| .49| .64| .81|1.00|2.25|4.00|6.25|9.00|16.00|25.00|36.0 |49.0 | - +--------------+----+----+----+----+----+----+----+----+----+----+----+-----+-----+-----+-----+ - - [Illustration: FIG. 88.] - - [Illustration: FIG. 89.] - - _Abrupt Contraction of Section._--When water passes from a larger to a - smaller section, as in figs. 88, 89, a contraction is formed, and the - contracted stream abruptly expands to fill the section of the pipe. - Let [omega] be the section and v the velocity of the stream at bb. At - aa the section will be c_c[omega], and the velocity - ([omega]/c_c[omega])v = v/c1, where c_c is the coefficient of - contraction. Then the head lost is - - [h]_m = (v/c_c - v)^2/2g = (1/c_c - 1)^2v^2/2g; - - and, if c_c is taken 0.64, - - [h]_m = 0.316 v^2/2g. (2) - - The value of the coefficient of contraction for this case is, however, - not well ascertained, and the result is somewhat modified by friction. - For water entering a cylindrical, not bell-mouthed, pipe from a - reservoir of indefinitely large size, experiment gives - - [h]_a = 0.505 v^2/2g. (3) - - If there is a diaphragm at the mouth of the pipe as in fig. 89, let - [omega]1 be the area of this orifice. Then the area of the contracted - stream is c_c[omega]1, and the head lost is - - [h]_c = {([omega]/c_c[omega]1) - 1}^2v^2/2g - = [zeta]_cv^2/2g (4) - - if [zeta], is put for {([omega]/c_c[omega]1) - 1}^2. Weisbach has found - experimentally the following values of the coefficient, when the - stream approaching the orifice was considerably larger than the - orifice:-- - - +--------------------+-------+------+------+-----+-----+-----+-----+-----+-----+-----+ - | [omega]1/[omega] = | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 |0.7 | 0.8 | 0.9 | 1.0 | - | | | | | | | | | | | | - | c_c = | .616 | .614 | .612 |.610 |.617 |.605 |.603 |.601 |.598 |.596 | - | | | | | | | | | | | | - | [zeta]_c = | 231.7 |50.99 |19.78 |9.612|5.256|3.077|1.876|1.169|0.734|0.480| - +--------------------+-------+------+------+-----+-----+-----+-----+-----+-----+-----+ - - [Illustration: FIG. 90.] - - When a diaphragm was placed in a tube of uniform section (fig. 90) the - following values were obtained, [omega]1 being the area of the orifice - and [omega] that of the pipe:-- - - +--------------------+-------+------+------+-----+-----+-----+-----+-----+-----+-----+ - | [omega]1/[omega] = | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0 | - | | | | | | | | | | | | - | c_c = | .624 | .632 | .643 |.659 |.681 |.712 |.755 |.813 |.892 |1.00 | - | | | | | | | | | | | | - | [xi]_c = | 225.9 |47.77 |30.83 |7.801|1.753|1.796|.797 |.290 |.060 |.000 | - +--------------------+-------+------+------+-----+-----+-----+-----+-----+-----+-----+ - - Elbows.--Weisbach considers the loss of head at elbows (fig. 91) to be - due to a contraction formed by the stream. From experiments with a - pipe 1(1/4) in. diameter, he found the loss of head - - [h]_e = [zeta]_e v^2/2g; (5) - - [zeta]_e = 0.9457 sin^2 (1/2)[phi] + 2.047 sin^4 (1/2)[phi]. - - +------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ - | [phi] = | 20 | 40 | 60 | 80 | 90 | 100 | 110 | 120 | 130 | 140 | - | [deg.] | | | | | | | | | | | - | [zeta]_e = |0.046|0.139|0.364|0.740|0.984|1.260|1.556|1.861|2.158|2.431| - +------------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ - - Hence at a right-angled elbow the whole head due to the velocity very - nearly is lost. - - [Illustration: FIG. 91.] - - _Bends._--Weisbach traces the loss of head at curved bends to a - similar cause to that at elbows, but the coefficients for bends are - not very satisfactorily ascertained. Weisbach obtained for the loss of - head at a bend in a pipe of circular section - - [h]_b = [zeta]_b v^2/2g; (6) - - [zeta]_b = 0.131 + 1.847(d/2[rho])^(7/2), - - where d is the diameter of the pipe and [rho] the radius of curvature - of the bend. The resistance at bends is small and at present very ill - determined. - - [Illustration: FIG. 92.] - - _Valves, Cocks and Sluices._--These produce a contraction of the - water-stream, similar to that for an abrupt diminution of section - already discussed. The loss of head may be taken as before to be - - [h]_v = [zeta]_v v^2/2g; (7) - - where v is the velocity in the pipe beyond the valve and [zeta]_v a - coefficient determined by experiment. The following are Weisbach's - results. - - _Sluice in Pipe of Rectangular Section_ (fig. 92). Section at sluice = - [omega]1 in pipe = [omega]. - - +--------------------+----+----+----+----+----+----+----+----+----+-----+ - | [omega]1/[omega] = |1.0 |0.9 |0.8 |0.7 |0.6 |0.5 |0.4 | 0.3| 0.2| 0.1 | - | | | | | | | | | | | | - | [zeta]_v = |0.00|.09 |.39 |.95 |2.08|4.02|8.12|17.8|44.5| 193 | - +--------------------+----+----+----+----+----+----+----+----+----+-----+ - - _Sluice in Cylindrical Pipe_ (fig. 93). - - +-----------------------+----+-----+-----+-----+-----+-----+------+------+ - | Ratio of height of | | | | | | | | | - | opening to diameter | 1.0| 7/8 | 3/4 | 5/8 | 1/2 | 3/8 | 1/4 | 1/5 | - | of pipe | | | | | | | | | - | [omega]1/[omega] = |1.00|0.948|.856 |.740 |.609 |.466 | .315 | .159 | - | | | | | | | | | | - | [zeta]_v = |0.00|0.07 |0.26 |0.81 |2.06 |5.52 | 17.0 | 97.8 | - +-----------------------+----+-----+-----+-----+-----+-----+------+------+ - - [Illustration: FIG. 93.] - - [Illustration: FIG. 94.] - - _Cock in a Cylindrical Pipe_ (fig. 94). Angle through which cock is - turned = [theta]. - - +------------+--------+---------+---------+---------+---------+---------+---------+ - | [theta] = | 5 deg. | 10 deg. | 15 deg. | 20 deg. | 25 deg. | 30 deg. | 35 deg. | - | Ratio of | | | | | | | | - | cross | .926 | .850 | .772 | .692 | .613 | .535 | .458 | - | sections | | | | | | | | - | [zeta]_v = | .05 | .29 | .75 | 1.56 | 3.10 | 5.47 | 9.68 | - +------------+--------+---------+---------+---------+---------+---------+---------+ - - +------------+---------+---------+---------+---------+---------+---------+---------+ - | [theta] = | 40 deg. | 45 deg. | 50 deg. | 55 deg. | 60 deg. | 65 deg. | 82 deg. | - | Ratio of | | | | | | | | - | cross | .385 | .315 | .250 | .190 | .137 | .091 | 0 | - | sections | | | | | | | | - | [zeta]_v = | 17.3 | 31.2 | 52.6 | 106 | 206 | 486 | [oo] | - +------------+---------+---------+---------+---------+---------+---------+---------+ - - _Throttle Valve in a Cylindrical Pip_e (fig. 95) - - +------------+---------+---------+---------+---------+---------+---------+---------+---------+ - | [theta] = | 5 deg. | 10 deg. | 15 deg. | 20 deg. | 25 deg. | 30 deg. | 35 deg. | 40 deg. | - | | | | | | | | | | - | [zeta]_v = | .24 | .52 | .90 | 1.54 | 2.51 | 3.91 | 6.22 | 10.8 | - +------------+---------+---------+---------+---------+---------+---------+---------+---------+ - - +------------+----------+----------+----------+----------+----------+----------+----------+ - | [theta] = | 45 deg. | 50 deg. | 55 deg. | 60 deg. | 65 deg. | 70 deg. | 90 deg. | - | | | | | | | | | - | [zeta]_v = | 18.7 | 32.6 | 58.8 | 118 | 256 | 751 | [oo] | - +------------+----------+----------+----------+----------+----------+----------+----------+ - - [Illustration: FIG. 95.] - - S 84. _Practical Calculations on the Flow of Water in Pipes._--In the - following explanations it will be assumed that the pipe is of so great - a length that only the loss of head in friction against the surface of - the pipe needs to be considered. In general it is one of the four - quantities d, i, v or Q which requires to be determined. For since the - loss of head h is given by the relation h = il, this need not be - separately considered. - - There are then three equations (see eq. 4, S 72, and 9a, S 76) for the - solution of such problems as arise:-- - - [zeta] = [alpha](1 + 1/12d); (1) - - where [alpha] = 0.005 for new and = 0.01 for incrusted pipes. - - [zeta]v^2/2g = (1/4)di. (2) - - Q = (1/4)[pi]d^2v. (3) - - _Problem 1._ Given the diameter of the pipe and its virtual slope, to - find the discharge and velocity of flow. Here d and i are given, and Q - and v are required. Find [zeta] from (1); then v from (2); lastly Q - from (3). This case presents no difficulty. - - By combining equations (1) and (2), v is obtained directly:-- - - v = [root](gdi/2[zeta]) = [root](g/2[alpha]) [root][di/{1 + 1/12d}]. (4) - - For new pipes [root](g/2[alpha]) = 56.72 - For incrusted pipes = 40.13 - - For pipes not less than 1, or more than 4 ft. in diameter, the mean - values of [zeta] are - - For new pipes 0.00526 - For incrusted pipes 0.01052. - - Using these values we get the very simple expressions-- - - v = 55.31 [root](di) for new pipes - = 39.11 [root](di) for incrusted pipes. (4a) - - Within the limits stated, these are accurate enough for practical - purposes, especially as the precise value of the coefficient [zeta] - cannot be known for each special case. - - _Problem 2._ Given the diameter of a pipe and the velocity of flow, to - find the virtual slope and discharge. The discharge is given by (3); - the proper value of [zeta] by (1); and the virtual slope by (2). This - also presents no special difficulty. - - _Problem 3._ Given the diameter of the pipe and the discharge, to find - the virtual slope and velocity. Find v from (3); [zeta] from (1); - lastly i from (2). If we combine (1) and (2) we get - - i = [zeta](v^2/2g) (4/d) = 2a{1 + 1/12d} v^2/gd; (5) - - and, taking the mean values of [zeta] for pipes from 1 to 4 ft. - diameter, given above, the approximate formulae are - - i = 0.0003268 v^2/d for new pipes - = 0.0006536 v^2/d for incrusted pipes. (5a) - - _Problem 4._ Given the virtual slope and the velocity, to find the - diameter of the pipe and the discharge. The diameter is obtained from - equations (2) and (1), which give the quadratic expression - - d^2 - d(2[alpha]v^2/gi) - [alpha]v^2/6gi = 0. - - .: d = [alpha]v^2/gi + [root]{([alpha]v^2/gi) ([alpha]v^2/gi + 1/6)}. (6) - - For practical purposes, the approximate equations - - d = 2[alpha]v^2/gi + 1/12 (6a) - = 0.00031 v^2/i + .083 for new pipes - = 0.00062 v^2/i + .083 for incrusted pipes - - are sufficiently accurate. - - _Problem 5._ Given the virtual slope and the discharge, to find the - diameter of the pipe and velocity of flow. This case, which often - occurs in designing, is the one which is least easy of direct - solution. From equations (2) and (3) we get-- - - d^5 = 32[zeta]Q^2/g[pi]^2i. (7) - - If now the value of [zeta] in (1) is introduced, the equation becomes - very cumbrous. Various approximate methods of meeting the difficulty - may be used. - - (a) Taking the mean values of [zeta] given above for pipes of 1 to 4 - ft. diameter we get - - d = [root 5](32[zeta]/g[pi]^2) [root 5](Q^2/i) (8) - = 0.2216 [root 5](Q^2/i) for new pipes - = 0.2541 [root 5](Q^2/i) for incrusted pipes; - - equations which are interesting as showing that when the value of - [zeta] is doubled the diameter of pipe for a given discharge is only - increased by 13%. - - (b) A second method is to obtain a rough value of d by assuming [zeta] - = [alpha]. This value is - - d' = [root 5](32Q^2/g[pi]^2i) [root 5][alpha] - = 0.6319 [root 5](Q^2/i) [root 5][alpha]. - - Then a very approximate value of [zeta] is - - [zeta]' = [alpha](1 + 1/12d'); - - and a revised value of d, not sensibly differing from the exact value, - is - - d" = [root 5](32Q^2/g[pi]^2i) [root 5][zeta]' - = 0.6319 [root 5](Q^2/i) [root 5][zeta]'. - - (c) Equation 7 may be put in the form - - d = [root 5](32[alpha]Q^2/g[pi]^2i) [root 5](1 + 1/12d). (9) - - Expanding the term in brackets, - - [root 5](1 + 1/12d) = 1 + 1/60d - 1/1800d^2 ... - - Neglecting the terms after the second, - - d = [root 5](32[alpha]/g[pi]^2) [root 5](Q^2/i).{1 + 1/60d} - = [root 5](32a/g[pi]^2) [root 5](Q^2/i) + 0.01667; (9a) - - and - - [root 5](32a/g[pi]^2) = 0.219 for new pipes - = 0.252 for incrusted pipes. - - [Illustration: FIG. 96.] - - [Illustration: FIG. 97.] - - S 85. _Arrangement of Water Mains for Towns' Supply._--Town mains are - usually supplied oy gravitation from a service reservoir, which in - turn is supplied by gravitation from a storage reservoir or by pumping - from a lower level. The service reservoir should contain three days' - supply or in important cases much more. Its elevation should be such - that water is delivered at a pressure of at least about 100 ft. to the - highest parts of the district. The greatest pressure in the mains is - usually about 200 ft., the pressure for which ordinary pipes and - fittings are designed. Hence if the district supplied has great - variations of level it must be divided into zones of higher and lower - pressure. Fig. 96 shows a district of two zones each with its service - reservoir and a range of pressure in the lower district from 100 to - 200 ft. The total supply required is in England about 25 gallons per - head per day. But in many towns, and especially in America, the supply - is considerably greater, but also in many cases a good deal of the - supply is lost by leakage of the mains. The supply through the branch - mains of a distributing system is calculated from the population - supplied. But in determining the capacity of the mains the fluctuation - of the demand must be allowed for. It is usual to take the maximum - demand at twice the average demand. Hence if the average demand is 25 - gallons per head per day, the mains should be calculated for 50 - gallons per head per day. - - [Illustration: FIG. 98.] - - S 86. _Determination of the Diameters of Different Parts of a Water - Main._--When the plan of the arrangement of mains is determined upon, - and the supply to each locality and the pressure required is - ascertained, it remains to determine the diameters of the pipes. Let - fig. 97 show an elevation of a main ABCD ..., R being the reservoir - from which the supply is derived. Let NN be the datum line of the - levelling operations, and H_a, H_b ... the heights of the main above - the datum line, H_r being the height of the water surface in the - reservoir from the same datum. Set up next heights AA1, BB1, ... - representing the minimum pressure height necessary for the adequate - supply of each locality. Then A1B1C1D1 ... is a line which should form - a lower limit to the line of virtual slope. Then if heights [h]_a, - [h]_b, [h]_c ... are taken representing the actual losses of head in - each length l_a, l_b, l_c ... of the main, A0B0C0 will be the line of - virtual slope, and it will be obvious at what points such as D0 and - E0, the pressure is deficient, and a different choice of diameter of - main is required. For any point z in the length of the main, we have - - Pressure height = H_r - H_z - ([h]_a + [h]_b + ... [h]_z). - - Where no other circumstance limits the loss of head to be assigned to - a given length of main, a consideration of the safety of the main from - fracture by hydraulic shock leads to a limitation of the velocity of - flow. Generally the velocity in water mains lies between 1(1/2) and - 4(1/2) ft. per second. Occasionally the velocity in pipes reaches 10 - ft. per second, and in hydraulic machinery working under enormous - pressures even 20 ft. per second. Usually the velocity diminishes - along the main as the discharge diminishes, so as to reduce somewhat - the total loss of head which is liable to render the pressure - insufficient at the end of the main. - - J. T. Fanning gives the following velocities as suitable in pipes for - towns' supply:-- - - Diameter in inches 4 8 12 18 24 30 36 - Velocity in feet per sec. 2.5 3.0 3.5 4.5 5.3 6.2 7.0 - - S 87. _Branched Pipe connecting Reservoirs at Different Levels._--Let - A, B, C (fig. 98) be three reservoirs connected by the arrangement of - pipes shown,--l1, d1, Q1, v1; l2, d2, Q2, v2; h3, d3, Q3, v3 being the - length, diameter, discharge and velocity in the three portions of the - main pipe. Suppose the dimensions and positions of the pipes known and - the discharges required. - - If a pressure column is introduced at X, the water will rise to a - height XR, measuring the pressure at X, and aR, Rb, Rc will be the - lines of virtual slope. If the free surface level at R is above b, the - reservoir A supplies B and C, and if R is below b, A and B supply C. - Consequently there are three cases:-- - - I. R above b; Q1 = Q2 + Q3. - II. R level with b; Q1 = Q3; Q2 = 0 - III. R below b; Q1 + Q2 = Q3. - - To determine which case has to be dealt with in the given conditions, - suppose the pipe from X to B closed by a sluice. Then there is a - simple main, and the height of free surface h' at X can be determined. - For this condition - - h_a - h' = [zeta](v1^2/2g)(4l1/d1) - = 32[zeta]Q'^2 l1/g[pi]^2d1^5; - - h' - h_c = [zeta](v3^2/2g)(4l3/d3) - = 32[zeta]Q'^2l3/g[pi]^2d3^5; - - where Q' is the common discharge of the two portions of the pipe. - Hence - - (h_a - h')/(h' - h_c) = l1d3^5/l3d1^5, - - from which h' is easily obtained. If then h' is greater than hb, - opening the sluice between X and B will allow flow towards B, and the - case in hand is case I. If h' is less than h_b, opening the sluice - will allow flow from B, and the case is case III. If h' = h_b, the - case is case II., and is already completely solved. - - The true value of h must lie between h' and h_b. Choose a new value of - h, and recalculate Q1, Q2, Q3. Then if - - Q1 > Q2 + Q3 in case I., - - or - - Q1 + Q2 > Q3 in case III., - - the value chosen for h is too small, and a new value must be chosen. - - If - - Q1 < Q2 + Q3 in case I., - - or - - Q1 + Q2 < Q3 in case III., - - the value of h is too great. - - Since the limits between which h can vary are in practical cases not - very distant, it is easy to approximate to values sufficiently - accurate. - - S 88. _Water Hammer._--If in a pipe through which water is flowing a - sluice is suddenly closed so as to arrest the forward movement of the - water, there is a rise of pressure which in some cases is serious - enough to burst the pipe. This action is termed water hammer or water - ram. The fluctuation of pressure is an oscillating one and gradually - dies out. Care is usually taken that sluices should only be closed - gradually and then the effect is inappreciable. Very careful - experiments on water hammer were made by N. J. Joukowsky at Moscow in - 1898 (_Stoss in Wasserleitungen_, St Petersburg, 1900), and the - results are generally confirmed by experiments made by E. B. Weston - and R. C. Carpenter in America. Joukowsky used pipes, 2, 4 and 6 in. - diameter, from 1000 to 2500 ft. in length. The sluice closed in 0.03 - second, and the fluctuations of pressure were automatically - registered. The maximum excess pressure due to water-hammer action was - as follows:-- - - +---------------------------------+---------------------------------+ - | Pipe 4-in. diameter. | Pipe 6-in. diameter. | - +--------------+------------------+--------------+------------------+ - | Velocity | Excess Pressure. | Velocity | Excess Pressure. | - | ft. per sec. | lb. per sq. in. | ft. per sec. | lb. per sq. in. | - +--------------+------------------+--------------+------------------+ - | 0.5 | 31 | 0.6 | 43 | - | 2.9 | 168 | 3.0 | 173 | - | 4.1 | 232 | 5.6 | 369 | - | 9.2 | 519 | 7.5 | 426 | - +--------------+------------------+--------------+------------------+ - - In some cases, in fixing the thickness of water mains, 100 lb. per sq. - in. excess pressure is allowed to cover the effect of water hammer. - With the velocities usual in water mains, especially as no valves can - be quite suddenly closed, this appears to be a reasonable allowance - (see also Carpenter, _Am. Soc. Mech. Eng._, 1893). - - - IX. FLOW OF COMPRESSIBLE FLUIDS IN PIPES - - S 89. _Flow of Air in Long Pipes._--When air flows through a long - pipe, by far the greater part of the work expended is used in - overcoming frictional resistances due to the surface of the pipe. The - work expended in friction generates heat, which for the most part must - be developed in and given back to the air. Some heat may be - transmitted through the sides of the pipe to surrounding materials, - but in experiments hitherto made the amount so conducted away appears - to be very small, and if no heat is transmitted the air in the tube - must remain sensibly at the same temperature during expansion. In - other words, the expansion may be regarded as isothermal expansion, - the heat generated by friction exactly neutralizing the cooling due to - the work done. Experiments on the pneumatic tubes used for the - transmission of messages, by R. S. Culley and R. Sabine (_Proc. Inst. - Civ. Eng._ xliii.), show that the change of temperature of the air - flowing along the tube is much less than it would be in adiabatic - expansion. - - S 90. _Differential Equation of the Steady Motion of Air Flowing in a - Long Pipe of Uniform Section._--When air expands at a constant - absolute temperature [tau], the relation between the pressure p in - pounds per square foot and the density or weight per cubic foot G is - given by the equation - - p/G = c[tau], (1) - - where c = 53.15. Taking [tau] = 521, corresponding to a temperature of - 60 deg. Fahr., - - c[tau] = 27690 foot-pounds. (2) - - The equation of continuity, which expresses the condition that in - steady motion the same weight of fluid, W, must pass through each - cross section of the stream in the unit of time, is - - G[Omega]u = W = constant, (3) - - where [Omega] is the section of the pipe and u the velocity of the - air. Combining (1) and (3), - - [Omega]up/W = c[tau] = constant. (3a) - - [Illustration: FIG. 99.] - - Since the work done by gravity on the air during its flow through a - pipe due to variations of its level is generally small compared with - the work done by changes of pressure, the former may in many cases be - neglected. - - Consider a short length dl of the pipe limited by sections A0, A1 at a - distance dl (fig. 99). Let p, u be the pressure and velocity at A0, p - + dp and u + du those at A1. Further, suppose that in a very short - time dt the mass of air between A0A1 comes to A'0A'1 so that A0A'0 = - udt and A1A'1 = (u + du)dt1. Let [Omega] be the section, and m the - hydraulic mean radius of the pipe, and W the weight of air flowing - through the pipe per second. - - From the steadiness of the motion the weight of air between the - sections A0A'0, and A1A'1 is the same. That is, - - W dt = G[Omega]u dt = G[Omega](u + du) dt. - - By analogy with liquids the head lost in friction is, for the length - dl (see S 72, eq. 3), [zeta](u^2/2g)(dl/m). Let H = u^2/2g. Then the - head lost is [zeta](H/m)dl; and, since Wdt lb. of air flow through the - pipe in the time considered, the work expended in friction is - -[zeta](H/m)Wdl dt. The change of kinetic energy in dt seconds is the - difference of the kinetic energy of A0A'0 and A1A'1, that is, - - (W/g) dt {(u + du)^2 - u^2}/2 = (W/g)u du dt = W dH dt. - - The work of expansion when [Omega]udt cub. ft. of air at a pressure p - expand to [Omega](u + du)dt cub. ft. is [Omega]p du dt. But from (3a) - u = c[tau]W/[Omega]p, and therefore - - du/dp = -c[tau]W/[Omega]p^2. - - And the work done by expansion is -(c[tau]W/p)dpdt. - - The work done by gravity on the mass between A0 and A1 is zero if the - pipe is horizontal, and may in other cases be neglected without great - error. The work of the pressures at the sections A0A1 is - - p[Omega]u dt - (p + dp)[Omega](u + du) dt - = -(pdu + udp)[Omega] dt - - But from (3a) - - pu = constant, - - p du + u dp = 0, - - and the work of the pressures is zero. Adding together the quantities - of work, and equating them to the change of kinetic energy, - - WDH dt = -(c[tau]W/p) dp dt - [zeta](H/m)W dl dt - - dH + (c[tau]/p) dp + [zeta](H/m) dl = 0, - - dH/H + (c[tau]/Hp) dp + [zeta]dl/m) = 0 (4) - - But - - u = c[tau]W/[Omega]p, - - and - - H = u^2/2g = c^2[tau]^2W^2/2g[Omega]^2p^2, - - .: dH/H + (2g[Omega]^2p/c[tau]W^2) dp + [zeta] dl/m = 0. (4a) - - For tubes of uniform section m is constant; for steady motion W is - constant; and for isothermal expansion [tau] is constant. Integrating, - - log H + g[Omega]^2p^2/W^2c[tau] + [zeta]l/m = constant; (5) - - for - - l = 0, let H = H0, and p = p0; - - and for - - l = l, let H = H1, and p = p1. - - log (H1/H0) + (g[Omega]^2}/W^2c[tau]) (p1^2 - p0^2) + [zeta]l/m = 0. - (5a) where p0 is the greater pressure and p1 the less, and the flow is - from A0 towards A1. - - By replacing W and H, - - log (p0/p1) + (gc[tau]/u0^2p0^2)(p1^2 - p0^2 + [zeta]l/m = 0 (6) - - Hence the initial velocity in the pipe is - - u0 = [root][{gc[tau](p0^2 - p1^2)} / {p0^2([zeta]l/m + log (p0/p1)}]. (7) - - When l is great, log p0/p1 is comparatively small, and then - - u0 = [root][(gc[tau]m/[zeta]l) {(p0^2 - p1^2)/p0^2}], (7a) - - a very simple and easily used expression. For pipes of circular - section m = d/4, where d is the diameter:-- - - u0 = [root][(gc[tau]d/4[zeta]l) {(p0^2 - p1^2)/p0^2}]; (7b) - - or approximately - - u0 = (1.1319 - 0.7264 p1/p0) [root](gc[tau]d/4[zeta]l). (7c) - - S 91. _Coefficient of Friction for Air._--A discussion by Professor - Unwin of the experiments by Culley and Sabine on the rate of - transmission of light carriers through pneumatic tubes, in which there - is steady flow of air not sensibly affected by any resistances other - than surface friction, furnished the value [zeta] = .007. The pipes - were lead pipes, slightly moist, 2(1/4) in. (0.187 ft.) in diameter, - and in lengths of 2000 to nearly 6000 ft. - - In some experiments on the flow of air through cast-iron pipes A. - Arson found the coefficient of friction to vary with the velocity and - diameter of the pipe. Putting - - [zeta] = [alpha]/v + [beta], (8) - - he obtained the following values-- - - +------------------+--------+-------+--------------------+ - | Diameter of Pipe | | | [zeta] for 100 ft. | - | in feet | [alpha]| [beta]| per second. | - +------------------+--------+-------+--------------------+ - | 1.64 | .00129 | .00483| .00484 | - | 1.07 | .00972 | .00640| .00650 | - | .83 | .01525 | .00704| .00719 | - | .338 | .03604 | .00941| .00977 | - | .266 | .03790 | .00959| .00997 | - | .164 | .04518 | .01167| .01212 | - +------------------+--------+-------+--------------------+ - - It is worth while to try if these numbers can be expressed in the form - proposed by Darcy for water. For a velocity of 100 ft. per second, and - without much error for higher velocities, these numbers agree fairly - with the formula - - [zeta] = 0.005(1 + (3/10)d), (9) - - which only differs from Darcy's value for water in that the second - term, which is always small except for very small pipes, is larger. - - Some later experiments on a very large scale, by E. Stockalper at the - St Gotthard Tunnel, agree better with the value - - [zeta] = 0.0028(1 + (3/10)d). - - These pipes were probably less rough than Arson's. - - When the variation of pressure is very small, it is no longer safe to - neglect the variation of level of the pipe. For that case we may - neglect the work done by expansion, and then - - z0 - z1 - p0/G0 - p1/G1 - [zeta](v^2/2g)(l/m) = 0, (10) - - precisely equivalent to the equation for the flow of water, z0 and z1 - being the elevations of the two ends of the pipe above any datum, p0 - and p1 the pressures, G0 and G1 the densities, and v the mean velocity - in the pipe. This equation may be used for the flow of coal gas. - - S 92. _Distribution of Pressure in a Pipe in which Air is - Flowing._--From equation (7a) it results that the pressure p, at l ft. - from that end of the pipe where the pressure is p0, is - - p = p0 [root](1 - [zeta]lu0^2/mgc[tau]); (11) - - which is of the form - - p = [root](al + b) - - for any given pipe with given end pressures. The curve of free surface - level for the pipe is, therefore, a parabola with horizontal axis. - Fig. 100 shows calculated curves of pressure for two of Sabine's - experiments, in one of which the pressure was greater than atmospheric - pressure, and in the other less than atmospheric pressure. The - observed pressures are given in brackets and the calculated pressures - without brackets. The pipe was the pneumatic tube between Fenchurch - Street and the Central Station, 2818 yds. in length. The pressures are - given in inches of mercury. - - [Illustration: FIG. 100.] - - _Variation of Velocity in the Pipe._--Let p0, u0 be the pressure and - velocity at a given section of the pipe; p, u, the pressure and - velocity at any other section. From equation (3a) - - up = c[tau]W/[Omega] = constant; - - so that, for any given uniform pipe, - - up = u0p0, - u = u0p0/p; (12) - - which gives the velocity at any section in terms of the pressure, - which has already been determined. Fig. 101 gives the velocity curves - for the two experiments of Culley and Sabine, for which the pressure - curves have already been drawn. It will be seen that the velocity - increases considerably towards that end of the pipe where the pressure - is least. - - [Illustration: FIG. 101.] - - S 93. _Weight of Air Flowing per Second._--The weight of air - discharged per second is (equation 3a)-- - - W = [Omega]u0p0/c[tau]. - - From equation (7b), for a pipe of circular section and diameter d, - - W = (1/4)[pi] [root](gd^5(p0^2 - p1^2)/[zeta]lc[tau]), - = .611[root](d^5(p0^2 - p1^2)/[zeta]l[tau]). (13) - - Approximately - - W = (.6916 p0 - .4438 p1)(d^5/[zeta]l[tau])^(1/2). (13a) - - S 94. _Application to the Case of Pneumatic Tubes for the Transmission - of Messages._--In Paris, Berlin, London, and other towns, it has been - found cheaper to transmit messages in pneumatic tubes than to - telegraph by electricity. The tubes are laid underground with easy - curves; the messages are made into a roll and placed in a light felt - carrier, the resistance of which in the tubes in London is only 3/4 oz. - A current of air forced into the tube or drawn through it propels the - carrier. In most systems the current of air is steady and continuous, - and the carriers are introduced or removed without materially altering - the flow of air. - - _Time of Transit through the Tube._--Putting t for the time of transit - from 0 to l, - _ - /l - t = | dl/u, - _/0 - - From (4a) neglecting dH/H, and putting m = d/4, - - dl = g d[Omega]^2p dp/2[zeta]W^2cr. - - From (1) and (3) - - u = Wc[tau]/p[Omega]; - - dl/u = g d[Omega]^3p^2 dp/2[zeta]W^3c^2[tau]^2; - _ - /p0 - t = | g d[Omega]^3p^2 dp/2[zeta]W^3c^2[tau]^2, - _/p1 - - = gd[Omega]^3(p0^3 - p1^3)/6[zeta]W^3c^2[tau]^2. (14) - - But - - W = p0u0[Omega]/c[tau]; - - .: t = gdc[tau](p0^3 - p1^3)/6[zeta]p0^3 u0^3, - - = [zeta]^(1/2)l^(3/2)(p0^3 - p1^3)/6(gc[tau]d)^(1/2)(p0^2 - p1^2)^(3/2); (15) - - If [tau] = 521 deg., corresponding to 60 deg. F., - - t = .001412 [zeta]^(1/2)l^(3/2)(p0^3 - p1^3)/d^(1/2)(p0^2 - p1^2)^(3/2); (15a) - - which gives the time of transmission in terms of the initial and final - pressures and the dimensions of the tube. - - _Mean Velocity of Transmission._--The mean velocity is l/t; or, for - [tau] = 521 deg., - - u_mean = 0.708 [root]{d(p0^2 - p1^2)^(3/2)/[zeta]l(p0^3 - p1^3)}. (16) - - The following table gives some results:-- - - +-----------+-----------------+----------------------------------+ - | | Absolute | | - | | Pressures in | Mean Velocities for Tubes | - | | lb. per sq. in. | of a length in feet. | - +-----------+--------+--------+------+------+------+------+------+ - | | p0 | p1 | 1000 | 2000 | 3000 | 4000 | 5000 | - +-----------+--------+--------+------+------+------+------+------+ - | Vacuum | 15 | 5 | 99.4 | 70.3 | 57.4 | 49.7 | 44.5 | - | Working | 15 | 10 | 67.2 | 47.5 | 38.8 | 34.4 | 30.1 | - | | | | | | | | | - | Pressure | 20 | 15 | 57.2 | 40.5 | 33.0 | 28.6 | 25.6 | - | Working | 25 | 15 | 74.6 | 52.7 | 43.1 | 37.3 | 33.3 | - | | 30 | 15 | 84.7 | 60.0 | 49.0 | 42.4 | 37.9 | - +-----------+-----------------+------+------+------+------+------+ - - _Limiting Velocity in the Pipe when the Pressure at one End is - diminished indefinitely._--If in the last equation there be put p1 = - 0, then - - u'_mean = 0.708 [root](d/[zeta]l); - - where the velocity is independent of the pressure p0 at the other end, - a result which apparently must be absurd. Probably for long pipes, as - for orifices, there is a limit to the ratio of the initial and - terminal pressures for which the formula is applicable. - - - X. FLOW IN RIVERS AND CANALS - - S 95. _Flow of Water in Open Canals and Rivers._--When water flows in - a pipe the section at any point is determined by the form of the - boundary. When it flows in an open channel with free upper surface, - the section depends on the velocity due to the dynamical conditions. - - Suppose water admitted to an unfilled canal. The channel will - gradually fill, the section and velocity at each point gradually - changing. But if the inflow to the canal at its head is constant, the - increase of cross section and diminution of velocity at each point - attain after a time a limit. Thenceforward the section and velocity at - each point are constant, and the motion is steady, or permanent regime - is established. - - If when the motion is steady the sections of the stream are all equal, - the motion is uniform. By hypothesis, the inflow [Omega]v is constant - for all sections, and [Omega] is constant; therefore v must be - constant also from section to section. The case is then one of uniform - steady motion. In most artificial channels the form of section is - constant, and the bed has a uniform slope. In that case the motion is - uniform, the depth is constant, and the stream surface is parallel to - the bed. If when steady motion is established the sections are - unequal, the motion is steady motion with varying velocity from - section to section. Ordinary rivers are in this condition, especially - where the flow is modified by weirs or obstructions. Short - unobstructed lengths of a river may be treated as of uniform section - without great error, the mean section in the length being put for the - actual sections. - - In all actual streams the different fluid filaments have different - velocities, those near the surface and centre moving faster than those - near the bottom and sides. The ordinary formulae for the flow of - streams rest on a hypothesis that this variation of velocity may be - neglected, and that all the filaments may be treated as having a - common velocity equal to the mean velocity of the stream. On this - hypothesis, a plane layer abab (fig. 102) between sections normal to - the direction of motion is treated as sliding down the channel to - a'a'b'b' without deformation. The component of the weight parallel to - the channel bed balances the friction against the channel, and in - estimating the friction the velocity of rubbing is taken to be the - mean velocity of the stream. In actual streams, however, the velocity - of rubbing on which the friction depends is not the mean velocity of - the stream, and is not in any simple relation with it, for channels of - different forms. The theory is therefore obviously based on an - imperfect hypothesis. However, by taking variable values for the - coefficient of friction, the errors of the ordinary formulae are to a - great extent neutralized, and they may be used without leading to - practical errors. Formulae have been obtained based on less restricted - hypotheses, but at present they are not practically so reliable, and - are more complicated than the formulae obtained in the manner - described above. - - [Illustration: FIG. 102.] - - S 96. _Steady Flow of Water with Uniform Velocity in Channels of - Constant Section._--Let aa', bb' (fig. 103) be two cross sections - normal to the direction of motion at a distance dl. Since the mass - aa'bb' moves uniformly, the external forces acting on it are in - equilibrium. Let [Omega] be the area of the cross sections, [chi] the - wetted perimeter, pq + qr + rs, of a section. Then the quantity m = - [Omega]/[chi] is termed the hydraulic mean depth of the section. Let v - be the mean velocity of the stream, which is taken as the common - velocity of all the particles, i, the slope or fall of the stream in - feet, per foot, being the ratio bc/ab. - - [Illustration: FIG. 103.] - - The external forces acting on aa'bb' parallel to the direction of - motion are three:--(a) The pressures on aa' and bb', which are equal - and opposite since the sections are equal and similar, and the mean - pressures on each are the same. (b) The component of the weight W of - the mass in the direction of motion, acting at its centre of gravity - g. The weight of the mass aa'bb' is G[Omega]dl, and the component of - the weight in the direction of motion is G[Omega]dl X the cosine of - the angle between Wg and ab, that is, G[Omega]dl cos abc = G[Omega]dl - bc/ab = G[Omega]idl. (c) There is the friction of the stream on the - sides and bottom of the channel. This is proportional to the area - [chi]dl of rubbing surface and to a function of the velocity which may - be written f(v); f(v) being the friction per sq. ft. at a velocity v. - Hence the friction is -[chi]dl f(v). Equating the sum of the forces to - zero, - - G[Omega]i dl - [chi]dl f(v) = 0, - - f(v)/G = [Omega]i/[chi] = mi. (1) - - But it has been already shown (S 66) that f(v) = [zeta]Gv^2/2g, - - .: [zeta]v^2/2g = mi. (2) - - This may be put in the form - - v = [root](2g/[zeta]) [root](mi) = c [root](mi); (2a) - - where c is a coefficient depending on the roughness and form of the - channel. - - The coefficient of friction [zeta] varies greatly with the degree of - roughness of the channel sides, and somewhat also with the velocity. - It must also be made to depend on the absolute dimensions of the - section, to eliminate the error of neglecting the variations of - velocity in the cross section. A common mean value assumed for [zeta] - is 0.00757. The range of values will be discussed presently. - - It is often convenient to estimate the fall of the stream in feet per - mile, instead of in feet per foot. If f is the fall in feet per mile, - - f = 5280 i. - - Putting this and the above value of [zeta] in (2a), we get the very - simple and long-known approximate formula for the mean velocity of a - stream-- - - v = (1/4) (1/2) [root](2mf). (3) - - The flow down the stream per second, or discharge of the stream, is - - Q = [Omega]v = [Omega]c [root](mi). (4) - - S 97. _Coefficient of Friction for Open Channels._--Various - expressions have been proposed for the coefficient of friction for - channels as for pipes. Weisbach, giving attention chiefly to the - variation of the coefficient of friction with the velocity, proposed - an expression of the form - - [zeta] = [alpha](1 + [beta]/v), (5) - - and from 255 experiments obtained for the constants the values - - [alpha] = 0.007409; [beta] = 0.1920. - - This gives the following values at different velocities:-- - - +----------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+ - | v = | 0.3 | 0.5 | 0.7 | 1 |1(1/2) | 2 | 3 | 5 | 7 | 10 | 15 | - | | | | | | | | | | | | | - | [zeta] = |0.01215|0.01025|0.00944|0.00883|0.00836|0.00812|0.90788|0.00769|0.00761|0.00755|0.00750| - +----------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+ - - In using this value of [zeta] when v is not known, it is best to - proceed by approximation. - - S 98. _Darcy and Bazin's Expression for the Coefficient of - Friction._--Darcy and Bazin's researches have shown that [zeta] varies - very greatly for different degrees of roughness of the channel bed, - and that it also varies with the dimensions of the channel. They give - for [zeta] an empirical expression (similar to that for pipes) of the - form - - [zeta] = a(1 + [beta]/m); (6) - - where m is the hydraulic mean depth. For different kinds of channels - they give the following values of the coefficient of friction:-- - - +-------------------------------------------------+--------+------+ - | Kind of Channel. | [alpha]|[beta]| - +-------------------------------------------------+--------+------+ - | I. Very smooth channels, sides of smooth | | | - | cement or planed timber | .00294 | 0.10 | - | II. Smooth channels, sides of ashlar, brickwork,| | | - | planks | .00373 | 0.23 | - |III. Rough channels, sides of rubble masonry or | | | - | pitched with stone | .00471 | 0.82 | - | IV. Very rough canals in earth | .00549 | 4.10 | - | V. Torrential streams encumbered with detritus | .00785 | 5.74 | - +-------------------------------------------------+--------+------+ - - The last values (Class V.) are not Darcy and Bazin's, but are taken - from experiments by Ganguillet and Kutter on Swiss streams. - - The following table very much facilitates the calculation of the mean - velocity and discharge of channels, when Darcy and Bazin's value of - the coefficient of friction is used. Taking the general formula for - the mean velocity already given in equation (2a) above, - - v = c [root](mi), - - where c = [root](2g/[zeta]), the following table gives values of c for - channels of different degrees of roughness, and for such values of the - hydraulic mean depths as are likely to occur in practical - calculations:-- - - Values of c in v = c[root](mi), deduced from Darcy and Bazin's Values. - - +----------+-----------+----------+---------+----------+--------------+ - | |Very Smooth| Smooth | Rough |Very Rough| Excessively | - | Mean | Channels, | Channels,|Channels,| Channels,|Rough Channels| - |Depth = m.| Cement. |Ashlar or | Rubble |Canals in | encumbered | - | | |Brickwork.| Masonry.| Earth. |with Detritus.| - +----------+-----------+----------+---------+----------+--------------+ - | .25 | 125 | 95 | 57 | 26 | 18.5 | - | .5 | 135 | 110 | 72 | 36 | 25.6 | - | .75 | 139 | 116 | 81 | 42 | 30.8 | - | 1.0 | 141 | 119 | 87 | 48 | 34.9 | - | 1.5 | 143 | 122 | 94 | 56 | 41.2 | - | 2.0 | 144 | 124 | 98 | 62 | 46.0 | - | 2.5 | 145 | 126 | 101 | 67 | .. | - | 3.0 | 145 | 126 | 104 | 70 | 53 | - | 3.5 | 146 | 127 | 105 | 73 | .. | - | 4.0 | 146 | 128 | 106 | 76 | 58 | - | 4.5 | 146 | 128 | 107 | 78 | .. | - | 5.0 | 146 | 128 | 108 | 80 | 62 | - | 5.5 | 146 | 129 | 109 | 82 | .. | - | 6.0 | 147 | 129 | 110 | 84 | 65 | - | 6.5 | 147 | 129 | 110 | 85 | .. | - | 7.0 | 147 | 129 | 110 | 86 | 67 | - | 7.5 | 147 | 129 | 111 | 87 | .. | - | 8.0 | 147 | 130 | 111 | 88 | 69 | - | 8.5 | 147 | 130 | 112 | 89 | .. | - | 9.0 | 147 | 130 | 112 | 90 | 71 | - | 9.5 | 147 | 130 | 112 | 90 | .. | - | 10.0 | 147 | 130 | 112 | 91 | 72 | - | 11 | 147 | 130 | 113 | 92 | .. | - | 12 | 147 | 130 | 113 | 93 | 74 | - | 13 | 147 | 130 | 113 | 94 | .. | - | 14 | 147 | 130 | 113 | 95 | .. | - | 15 | 147 | 130 | 114 | 96 | 77 | - | 16 | 147 | 130 | 114 | 97 | .. | - | 17 | 147 | 130 | 114 | 97 | .. | - | 18 | 147 | 130 | 114 | 98 | .. | - | 20 | 147 | 131 | 114 | 98 | 80 | - | 25 | 148 | 131 | 115 | 100 | .. | - | 30 | 148 | 131 | 115 | 102 | 83 | - | 40 | 148 | 131 | 116 | 103 | 85 | - | 50 | 148 | 131 | 116 | 104 | 86 | - | [oo] | 148 | 131 | 117 | 108 | 91 | - +----------+-----------+----------+---------+----------+--------------+ - - S 99. _Ganguillet and Kutter's Modified Darcy Formula._--Starting from - the general expression v = c[root]mi, Ganguillet and Kutter examined - the variations of c for a wider variety of cases than those discussed - by Darcy and Bazin. Darcy and Bazin's experiments were confined to - channels of moderate section, and to a limited variation of slope. - Ganguillet and Kutter brought into the discussion two very distinct - and important additional series of results. The gaugings of the - Mississippi by A. A. Humphreys and H. L. Abbot afford data of - discharge for the case of a stream of exceptionally large section and - or very low slope. On the other hand, their own measurements of the - flow in the regulated channels of some Swiss torrents gave data for - cases in which the inclination and roughness of the channels were - exceptionally great. Darcy and Bazin's experiments alone were - conclusive as to the dependence of the coefficient c on the dimensions - of the channel and on its roughness of surface. Plotting values of c - for channels of different inclination appeared to indicate that it - also depended on the slope of the stream. Taking the Mississippi data - only, they found - - c = 256 for an inclination of 0.0034 per thousand, - = 154 " " 0.02 " - - so that for very low inclinations no constant value of c independent - of the slope would furnish good values of the discharge. In small - rivers, on the other hand, the values of c vary little with the slope. - As regards the influence of roughness of the sides of the channel a - different law holds. For very small channels differences of roughness - have a great influence on the discharge, but for very large channels - different degrees of roughness have but little influence, and for - indefinitely large channels the influence of different degrees of - roughness must be assumed to vanish. The coefficients given by Darcy - and Bazin are different for each of the classes of channels of - different roughness, even when the dimensions of the channel are - infinite. But, as it is much more probable that the influence of the - nature of the sides diminishes indefinitely as the channel is larger, - this must be regarded as a defect in their formula. - - Comparing their own measurements in torrential streams in Switzerland - with those of Darcy and Bazin, Ganguillet and Kutter found that the - four classes of coefficients proposed by Darcy and Bazin were - insufficient to cover all cases. Some of the Swiss streams gave - results which showed that the roughness of the bed was markedly - greater than in any of the channels tried by the French engineers. It - was necessary therefore in adopting the plan of arranging the - different channels in classes of approximately similar roughness to - increase the number of classes. Especially an additional class was - required for channels obstructed by detritus. - - To obtain a new expression for the coefficient in the formula - - v = [root](2g/[zeta]) [root](mi) = c [root](mi), - - Ganguillet and Kutter proceeded in a purely empirical way. They found - that an expression of the form - - c = [alpha]/(1 + [beta]/[root]m) - - could be made to fit the experiments somewhat better than Darcy's - expression. Inverting this, we get - - 1/c = 1/[alpha] + [beta]/[alpha] [root]m, - - an equation to a straight line having 1/[root]m for abscissa, 1/c for - ordinate, and inclined to the axis of abscissae at an angle the - tangent of which is [beta]/[alpha]. - - Plotting the experimental values of 1/c and 1/[root]m, the points so - found indicated a curved rather than a straight line, so that [beta] - must depend on [alpha]. After much comparison the following form was - arrived at-- - - c = (A + l/n)/(1 + An/[root]m), - - where n is a coefficient depending only on the roughness of the sides - of the channel, and A and l are new coefficients, the value of which - remains to be determined. From what has been already stated, the - coefficient c depends on the inclination of the stream, decreasing as - the slope i increases. - - Let - - A = a + p/i. - - Then - - c = (a + l/n + p/i)/{1 + (a + p/i)n/[root]m}, - - the form of the expression for c ultimately adopted by Ganguillet and - Kutter. - - For the constants a, l, p Ganguillet and Kutter obtain the values 23, - 1 and 0.00155 for metrical measures, or 41.6, 1.811 and 0.00281 for - English feet. The coefficient of roughness n is found to vary from - 0.008 to 0.050 for either metrical or English measures. - - The most practically useful values of the coefficient of roughness n - are given in the following table:-- - - Nature of Sides of Channel. Coefficient of - Roughness n. - Well-planed timber 0.009 - Cement plaster 0.010 - Plaster of cement with one-third sand 0.011 - Unplaned planks 0.012 - Ashlar and brickwork 0.013 - Canvas on frames 0.015 - Rubble masonry 0.017 - Canals in very firm gravel 0.020 - Rivers and canals in perfect order, free from stones \ - or weeds / 0.025 - Rivers and canals in moderately good order, not \ - quite free from stones and weeds / 0.030 - Rivers and canals in bad order, with weeds and \ - detritus / 0.035 - Torrential streams encumbered with detritus 0.050 - - Ganguillet and Kutter's formula is so cumbrous that it is difficult to - use without the aid of tables. - - Lowis D'A. Jackson published complete and extensive tables for - facilitating the use of the Ganguillet and Kutter formula (_Canal and - Culvert Tables_, London, 1878). To lessen calculation he puts the - formula in this form:-- - - M = n(41.6 + 0.00281/i); - - v = ([root]m/n) {(M + 1.811)/(M + [root]m)} [root](mi). - - The following table gives a selection of values of M, taken from - Jackson's tables:-- - - +--------+--------------------------------------------------------------+ - | | Values of M for n = | - | i = +--------+--------+--------+--------+--------+--------+--------+ - | | 0.010 | 0.012 | 0.015 | 0.017 | 0.020 | 0.025 | 0.030 | - +--------+--------+--------+--------+--------+--------+--------+--------+ - | .00001 | 3.2260 | 3.8712 | 4.8390 | 5.4842 | 6.4520 | 8.0650 | 9.6780 | - | .00002 | 1.8210 | 2.1852 | 2.7315 | 3.0957 | 3.6420 | 4.5525 | 5.4630 | - | .00004 | 1.1185 | 1.3422 | 1.6777 | 1.9014 | 2.2370 | 2.7962 | 3.3555 | - | .00006 | 0.8843 | 1.0612 | 1.3264 | 1.5033 | 1.7686 | 2.2107 | 2.6529 | - | .00008 | 0.7672 | 0.9206 | 1.1508 | 1.3042 | 1.5344 | 1.9180 | 2.3016 | - | .00010 | 0.6970 | 0.8364 | 1.0455 | 1.1849 | 1.3940 | 1.7425 | 2.0910 | - | .00025 | 0.5284 | 0.6341 | 0.7926 | 0.8983 | 1.0568 | 1.3210 | 1.5852 | - | .00050 | 0.4722 | 0.5666 | 0.7083 | 0.8027 | 0.9444 | 1.1805 | 1.4166 | - | .00075 | 0.4535 | 0.5442 | 0.6802 | 0.7709 | 0.9070 | 1.1337 | 1.3605 | - | .00100 | 0.4441 | 0.5329 | 0.6661 | 0.7550 | 0.8882 | 1.1102 | 1.3323 | - | .00200 | 0.4300 | 0.5160 | 0.6450 | 0.7310 | 0.8600 | 1.0750 | 1.2900 | - | .00300 | 0.4254 | 0.5105 | 0.6381 | 0.7232 | 0.8508 | 1.0635 | 1.2762 | - +--------+--------+--------+--------+--------+--------+--------+--------+ - - A difficulty in the use of this formula is the selection of the - coefficient of roughness. The difficulty is one which no theory will - overcome, because no absolute measure of the roughness of stream beds - is possible. For channels lined with timber or masonry the difficulty - is not so great. The constants in that case are few and sufficiently - defined. But in the case of ordinary canals and rivers the case is - different, the coefficients having a much greater range. For - artificial canals in rammed earth or gravel n varies from 0.0163 to - 0.0301. For natural channels or rivers n varies from 0.020 to 0.035. - - In Jackson's opinion even Kutter's numerous classes of channels seem - inadequately graduated, and he proposes for artificial canals the - following classification:-- - - I. Canals in very firm gravel, in perfect order n = 0.02 - II. Canals in earth, above the average in order n = 0.0225 - III. Canals in earth, in fair order n = 0.025 - IV. Canals in earth, below the average in order n = 0.0275 - V. Canals in earth, in rather bad order, partially\ - overgrown with weeds and obstructed by > n = 0.03 - detritus. / - - Ganguillet and Kutter's formula has been considerably used partly from - its adoption in calculating tables for irrigation work in India. But - it is an empirical formula of an unsatisfactory form. Some engineers - apparently have assumed that because it is complicated it must be more - accurate than simpler formulae. Comparison with the results of - gaugings shows that this is not the case. The term involving the slope - was introduced to secure agreement with some early experiments on the - Mississippi, and there is strong reason for doubting the accuracy of - these results. - - S 100. _Bazin's New Formula._--Bazin subsequently re-examined all the - trustworthy gaugings of flow in channels and proposed a modification - of the original Darcy formula which appears to be more satisfactory - than any hitherto suggested (_Etude d'une nouvelle formule_, Paris, - 1898). He points out that Darcy's original formula, which is of the - form mi/v^2 = [alpha] + [beta]/m, does not agree with experiments on - channels as well as with experiments on pipes. It is an objection to - it that if m increases indefinitely the limit towards which mi/v^2 - tends is different for different values of the roughness. It would - seem that if the dimensions of a canal are indefinitely increased the - variation of resistance due to differing roughness should vanish. This - objection is met if it is assumed that [root](mi/v^2) = [alpha] + - [beta]/[root]m, so that if a is a constant mi/v^2 tends to the limit a - when m increases. A very careful discussion of the results of gaugings - shows that they can be expressed more satisfactorily by this new - formula than by Ganguillet and Kutter's. Putting the equation in the - form [zeta]v^2/2g = mi, [zeta] = 0.002594(1 + [gamma]/[root]m), where - [gamma] has the following values:-- - - I. Very smooth sides, cement, planed plank, [gamma] = 0.109 - II. Smooth sides, planks, brickwork 0.290 - III. Rubble masonry sides 0.833 - IV. Sides of very smooth earth, or pitching 1.539 - V. Canals in earth in ordinary condition 2.353 - VI. Canals in earth exceptionally rough 3.168 - - S 101. _The Vertical Velocity Curve._--If at each point along a - vertical representing the depth of a stream, the velocity at that - point is plotted horizontally, the curve obtained is the vertical - velocity curve and it has been shown by many observations that it - approximates to a parabola with horizontal axis. The vertex of the - parabola is at the level of the greatest velocity. Thus in fig. 104 OA - is the vertical at which velocities are observed; v0 is the surface; - v_z the maximum and v_d the bottom velocity. B C D is the vertical - velocity curve which corresponds with a parabola having its vertex at - C. The mean velocity at the vertical is - - v_m = (1/3)[2v_z + v_d + (d_z/d)(v0 - v_d)]. - - _The Horizontal Velocity Curve._--Similarly if at each point along a - horizontal representing the width of the stream the velocities are - plotted, a curve is obtained called the horizontal velocity curve. In - streams of symmetrical section this is a curve symmetrical about the - centre line of the stream. The velocity varies little near the centre - of the stream, but very rapidly near the banks. In unsymmetrical - sections the greatest velocity is at the point where the stream is - deepest, and the general form of the horizontal velocity curve is - roughly similar to the section of the stream. - - [Illustration: FIG. 104.] - - S 102. _Curves or Contours of Equal Velocity._--If velocities are - observed at a number of points at different widths and depths in a - stream, it is possible to draw curves on the cross section through - points at which the velocity is the same. These represent contours of - a solid, the volume of which is the discharge of the stream per - second. Fig. 105 shows the vertical and horizontal velocity curves and - the contours of equal velocity in a rectangular channel, from one of - Bazin's gaugings. - - S 103. _Experimental Observations on the Vertical Velocity Curve._--A - preliminary difficulty arises in observing the velocity at a given - point in a stream because the velocity rapidly varies, the motion not - being strictly steady. If an average of several velocities at the same - point is taken, or the average velocity for a sensible period of time, - this average is found to be constant. It may be inferred that though - the velocity at a point fluctuates about a mean value, the - fluctuations being due to eddying motions superposed on the general - motion of the stream, yet these fluctuations produce effects which - disappear in the mean of a series of observations and, in calculating - the volume of flow, may be disregarded. - - [Illustration: FIG. 105.] - - In the next place it is found that in most of the best observations on - the velocity in streams, the greatest velocity at any vertical is - found not at the surface but at some distance below it. In various - river gaugings the depth d_z at the centre of the stream has been - found to vary from 0 to 0.3d. - - S 104. _Influence of the Wind._--In the experiments on the Mississippi - the vertical velocity curve in calm weather was found to agree fairly - with a parabola, the greatest velocity being at (3/10)ths of the depth - of the stream from the surface. With a wind blowing down stream the - surface velocity is increased, and the axis of the parabola approaches - the surface. On the contrary, with a wind blowing up stream the - surface velocity is diminished, and the axis of the parabola is - lowered, sometimes to half the depth of the stream. The American - observers drew from their observations the conclusion that there was - an energetic retarding action at the surface of a stream like that due - to the bottom and sides. If there were such a retarding action the - position of the filament of maximum velocity below the surface would - be explained. - - It is not difficult to understand that a wind acting on surface - ripples or waves should accelerate or retard the surface motion of the - stream, and the Mississippi results may be accepted so far as showing - that the surface velocity of a stream is variable when the mean - velocity of the stream is constant. Hence observations of surface - velocity by floats or otherwise should only be made in very calm - weather. But it is very difficult to suppose that, in still air, there - is a resistance at the free surface of the stream at all analogous to - that at the sides and bottom. Further, in very careful experiments, P. - P. Boileau found the maximum velocity, though raised a little above - its position for calm weather, still at a considerable distance below - the surface, even when the wind was blowing down stream with a - velocity greater than that of the stream, and when the action of the - air must have been an accelerating and not a retarding action. A much - more probable explanation of the diminution of the velocity at and - near the free surface is that portions of water, with a diminished - velocity from retardation by the sides or bottom, are thrown off in - eddying masses and mingle with the rest of the stream. These eddying - masses modify the velocity in all parts of the stream, but have their - greatest influence at the free surface. Reaching the free surface they - spread out and remain there, mingling with the water at that level and - diminishing the velocity which would otherwise be found there. - - _Influence of the Wind on the Depth at which the Maximum Velocity is - found._--In the gaugings of the Mississippi the vertical velocity - curve was found to agree well with a parabola having a horizontal axis - at some distance below the water surface, the ordinate of the parabola - at the axis being the maximum velocity of the section. During the - gaugings the force of the wind was registered on a scale ranging from - 0 for a calm to 10 for a hurricane. Arranging the velocity curves in - three sets--(1) with the wind blowing up stream, (2) with the wind - blowing down stream, (3) calm or wind blowing across stream--it was - found that an upstream wind lowered, and a down-stream wind raised, - the axis of the parabolic velocity curve. In calm weather the axis was - at (3/10)ths of the total depth from the surface for all conditions of - the stream. - - Let h' be the depth of the axis of the parabola, m the hydraulic mean - depth, f the number expressing the force of the wind, which may range - from +10 to -10, positive if the wind is up stream, negative if it is - down stream. Then Humphreys and Abbot find their results agree with - the expression - - h'/m = 0.317 [+-] 0.06f. - - Fig. 106 shows the parabolic velocity curves according to the American - observers for calm weather, and for an up- or down-stream wind of a - force represented by 4. - - [Illustration: FIG. 106.] - - It is impossible at present to give a theoretical rule for the - vertical velocity curve, but in very many gaugings it has been found - that a parabola with horizontal axis fits the observed results fairly - well. The mean velocity on any vertical in a stream varies from 0.85 - to 0.92 of the surface velocity at that vertical, and on the average - if v0 is the surface and v_m the mean velocity at a vertical v_m = - 6/7 v0, a result useful in float gauging. On any vertical there is a - point at which the velocity is equal to the mean velocity, and if this - point were known it would be useful in gauging. Humphreys and Abbot in - the Mississippi found the mean velocity at 0.66 of the depth; G. H. L. - Hagen and H. Heinemann at 0.56 to 0.58 of the depth. The mean of - observations by various observers gave the mean velocity at from 0.587 - to 0.62 of the depth, the average of all being almost exactly 0.6 of - the depth. The mid-depth velocity is therefore nearly equal to, but a - little greater than, the mean velocity on a vertical. If v_(md) is the - mid-depth velocity, then on the average v_m = 0.98v_(md). - - S 105. _Mean Velocity on a Vertical from Two Velocity - Observations._--A. J. C. Cunningham, in gaugings on the Ganges canal, - found the following useful results. Let v0 be the surface, v_m the - mean, and v_(xd) the velocity at the depth xd; then - - v_m = (1/4)[v0 + 3v_(2/3d)] - = (1/2)[v_(.211)^d + v_(.789)^d]. - - S 106. _Ratio of Mean to Greatest Surface Velocity, for the whole - Cross Section in Trapezoidal Channels._--It is often very important to - be able to deduce the mean velocity, and thence the discharge, from - observation of the greatest surface velocity. The simplest method of - gauging small streams and channels is to observe the greatest surface - velocity by floats, and thence to deduce the mean velocity. In general - in streams of fairly regular section the mean velocity for the whole - section varies from 0.7 to 0.85 of the greatest surface velocity. For - channels not widely differing from those experimented on by Bazin, the - expression obtained by him for the ratio of surface to mean velocity - may be relied on as at least a good approximation to the truth. Let v0 - be the greatest surface velocity, v_m the mean velocity of the stream. - Then, according to Bazin, - - v_m = v0 - 25.4 [root](mi). - - But - - v_m = c [root](mi), - - where c is a coefficient, the values of which have been already given - in the table in S 98. Hence - - v_m = cv0/(c + 25.4). - - _Values of Coefficient c/(c + 25.4) in the Formula v_m = cv0/(c + - 25.4)._ - - +----------+---------+----------+---------+----------+----------+ - |Hydraulic | Very | Smooth | Rough |Very Rough| Channels | - |Mean Depth| Smooth |Channels. |Channels.| Channels.|encumbered| - | = m. |Channels.|Ashlar or | Rubble | Canals in| with | - | | Cement. |Brickwork.| Masonry.| Earth. | Detritus.| - +----------+---------+----------+---------+----------+----------+ - | | | | | | | - | 0.25 | .83 | .79 | .69 | .51 | .42 | - | 0.5 | .84 | .81 | .74 | .58 | .50 | - | 0.75 | .84 | .82 | .76 | .63 | .55 | - | 1.0 | .85 | .. | .77 | .65 | .58 | - | 2.0 | .. | .83 | .79 | .71 | .64 | - | 3.0 | .. | .. | .80 | .73 | .67 | - | 4.0 | .. | .. | .81 | .75 | .70 | - | 5.0 | .. | .. | .. | .76 | .71 | - | 6.0 | .. | .84 | .. | .77 | .72 | - | 7.0 | .. | .. | .. | .78 | .73 | - | 8.0 | .. | .. | .. | .. | .. | - | 9.0 | .. | .. | .82 | .. | .74 | - | 10.0 | .. | .. | .. | .. | .. | - | 15.0 | .. | .. | .. | .79 | .75 | - | 20.0 | .. | .. | .. | .80 | .76 | - | 30.0 | .. | .. | .82 | .. | .77 | - | 40.0 | .. | .. | .. | .. | .. | - | 50.0 | .. | .. | .. | .. | .. | - | [oo] | .. | .. | .. | .. | .79 | - +----------+---------+----------+---------+----------+----------+ - - [Illustration: FIG. 107.] - - S 107. _River Bends._--In rivers flowing in alluvial plains, the - windings which already exist tend to increase in curvature by the - scouring away of material from the outer bank and the deposition of - detritus along the inner bank. The sinuosities sometimes increase till - a loop is formed with only a narrow strip of land between the two - encroaching branches of the river. Finally a "cut off" may occur, a - waterway being opened through the strip of land and the loop left - separated from the stream, forming a horseshoe shaped lagoon or marsh. - Professor James Thomson pointed out (_Proc. Roy. Soc._, 1877, p. 356; - _Proc. Inst. of Mech. Eng._, 1879, p. 456) that the usual supposition - is that the water tending to go forwards in a straight line rushes - against the outer bank and scours it, at the same time creating - deposits at the inner bank. That view is very far from a complete - account of the matter, and Professor Thomson gave a much more - ingenious account of the action at the bend, which he completely - confirmed by experiment. - - [Illustration: FIG. 108.] - - When water moves round a circular curve under the action of gravity - only, it takes a motion like that in a free vortex. Its velocity is - greater parallel to the axis of the stream at the inner than at the - outer side of the bend. Hence the scouring at the outer side and the - deposit at the inner side of the bend are not due to mere difference - of velocity of flow in the general direction of the stream; but, in - virtue of the centrifugal force, the water passing round the bend - presses outwards, and the free surface in a radial cross section has a - slope from the inner side upwards to the outer side (fig. 108). For - the greater part of the water flowing in curved paths, this difference - of pressure produces no tendency to transverse motion. But the water - immediately in contact with the rough bottom and sides of the channel - is retarded, and its centrifugal force is insufficient to balance the - pressure due to the greater depth at the outside of the bend. It - therefore flows inwards towards the inner side of the bend, carrying - with it detritus which is deposited at the inner bank. Conjointly with - this flow inwards along the bottom and sides, the general mass of - water must flow outwards to take its place. Fig. 107 shows the - directions of flow as observed in a small artificial stream, by means - of light seeds and specks of aniline dye. The lines CC show the - directions of flow immediately in contact with the sides and bottom. - The dotted line AB shows the direction of motion of floating particles - on the surface of the stream. - - S 108. _Discharge of a River when flowing at different Depths._--When - frequent observations must be made on the flow of a river or canal, - the depth of which varies at different times, it is very convenient to - have to observe the depth only. A formula can be established giving - the flow in terms of the depth. Let Q be the discharge in cubic feet - per second; H the depth of the river in some straight and uniform - part. Then Q = aH + bH^2, where the constants a and b must be found by - preliminary gaugings in different conditions of the river. M. C. - Moquerey found for part of the upper Saone, Q = 64.7H + 8.2H^2 in - metric measures, or Q = 696H + 26.8H^2 in English measures. - - S 109. _Forms of Section of Channels._--The simplest form of section - for channels is the semicircular or nearly semicircular channel (fig. - 109), a form now often adopted from the facility with which it can be - executed in concrete. It has the advantage that the rubbing surface is - less in proportion to the area than in any other form. - - [Illustration: FIG. 109.] - - Wooden channels or flumes, of which there are examples on a large - scale in America, are rectangular in section, and the same form is - adopted for wrought and cast-iron aqueducts. Channels built with - brickwork or masonry may be also rectangular, but they are often - trapezoidal, and are always so if the sides are pitched with masonry - laid dry. In a trapezoidal channel, let b (fig. 110) be the bottom - breadth, b0 the top breadth, d the depth, and let the slope of the - sides be n horizontal to 1 vertical. Then the area of section is - [Omega] = (b + nd)d = (b0 - nd)d, and the wetted perimeter [chi] = b + - 2d[root](n^2 + 1). - - [Illustration: FIG. 110.] - - When a channel is simply excavated in earth it is always originally - trapezoidal, though it becomes more or less rounded in course of time. - The slope of the sides then depends on the stability of the earth, a - slope of 2 to 1 being the one most commonly adopted. - - Figs. 111, 112 show the form of canals excavated in earth, the former - being the section of a navigation canal and the latter the section of - an irrigation canal. - - S 110. _Channels of Circular Section._--The following short table - facilitates calculations of the discharge with different depths of - water in the channel. Let r be the radius of the channel section; then - for a depth of water = [kappa]r, the hydraulic mean radius is [mu]r - and the area of section of the waterway [nu]r^2, where [kappa], [mu], - and [nu] have the following values:-- - - +---------------------------------+------+-----+-----+-----+-----+-----+-----+-----+----+----+----+----+----+----+----+-----+-----+-----+-----+-----+-----+ - | Depth of water in \ [kappa] = |.01 |.05 |.10 |.15 |.20 |.25 |.30 |.35 |.40 |.45 |.50 |.55 |.60 |.65 |.70 |.75 |.80 |.85 |.90 |.95 |1.0 | - | terms of radius / | | | | | | | | | | | | | | | | | | | | | | - | Hydraulic mean depth\ [mu] = |.00668|.0321|.0523|.0963|.1278|.1574|.1852|.2142|.242|.269|.293|.320|.343|.365|.387|.408 |.429 |.449 |.466 |.484 |.500 | - | in terms of radius/ | | | | | | | | | | | | | | | | | | | | | | - | Waterway in terms of\ [nu] = |.00189|.0211|.0598|.1067|.1651|.228 |.294 |.370 |.450|.532|.614|.709|.795|.885|.979|1.075|1.175|1.276|1.371|1.470|1.571| - | square of radius / | | | | | | | | | | | | | | | | | | | | | | - +---------------------------------+------+-----+-----+-----+-----+-----+-----+-----+----+----+----+----+----+----+----+-----+-----+-----+-----+-----+-----+ - - [Illustration: FIG. 111.--Scale 20 ft. = 1 in.] - - [Illustration: FIG. 112.--Scale 80 ft. = 1 in.] - - S 111. _Egg-Shaped Channels or Sewers._--In sewers for discharging - storm water and house drainage the volume of flow is extremely - variable; and there is a great liability for deposits to be left when - the flow is small, which are not removed during the short periods when - the flow is large. The sewer in consequence becomes choked. To obtain - uniform scouring action, the velocity of flow should be constant or - nearly so; a complete uniformity of velocity cannot be obtained with - any form of section suitable for sewers, but an approximation to - uniform velocity is obtained by making the sewers of oval section. - Various forms of oval have been suggested, the simplest being one in - which the radius of the crown is double the radius of the invert, and - the greatest width is two-thirds the height. The section of such a - sewer is shown in fig. 113, the numbers marked on the figure being - proportional numbers. - - [Illustration: FIG. 113.] - - S 112. _Problems on Channels in which the Flow is Steady and at - Uniform Velocity._--The general equations given in SS 96, 98 are - - [zeta] = [alpha](1 + [beta]/m); (1) - - [zeta]v^2/2g = mi; (2) - - Q = [Omega]v. (3) - - _Problem I._--Given the transverse section of stream and discharge, to - find the slope. From the dimensions of the section find [Omega] and m; - from (1) find [zeta], from (3) find v, and lastly from (2) find i. - - _Problem II._--Given the transverse section and slope, to find the - discharge. Find v from (2), then Q from (3). - - _Problem III._--Given the discharge and slope, and either the breadth, - depth, or general form of the section of the channel, to determine its - remaining dimensions. This must generally be solved by approximations. - A breadth or depth or both are chosen, and the discharge calculated. - If this is greater than the given discharge, the dimensions are - reduced and the discharge recalculated. - - [Illustration: FIG. 114.] - - Since m lies generally between the limits m = d and m = (1/2)d, where - d is the depth of the stream, and since, moreover, the velocity varies - as [root](m) so that an error in the value of m leads only to a much - less error in the value of the velocity calculated from it, we may - proceed thus. Assume a value for m, and calculate v from it. Let v1 be - this first approximation to v. Then Q/v1 is a first approximation to - [Omega], say [Omega]1. With this value of [Omega] design the section - of the channel; calculate a second value for m; calculate from it a - second value of v, and from that a second value for [Omega]. Repeat - the process till the successive values of m approximately coincide. - - S 113. _Problem IV. Most Economical Form of Channel for given Side - Slopes._--Suppose the channel is to be trapezoidal in section (fig. - 114), and that the sides are to have a given slope. Let the - longitudinal slope of the stream be given, and also the mean velocity. - An infinite number of channels could be found satisfying the - foregoing conditions. To render the problem determinate, let it be - remembered that, since for a given discharge [Omega][oo] [cube - root][chi], other things being the same, the amount of excavation will - be least for that channel which has the least wetted perimeter. Let d - be the depth and b the bottom width of the channel, and let the sides - slope n horizontal to 1 vertical (fig. 114), then - - [Omega] = (b + nd)d; - - [chi] = b + 2d [root](n^2 + 1). - - Both [Omega] and [chi] are to be minima. Differentiating, and equating - to zero. - - (db/dd + n)d + b + nd = 0, - - db/dd + 2[root](n^2 + 1) = 0; - - eliminating db/dd, - - {n - 2[root](n^2 + 1)}d + b + nd = 0; - - b = 2 {[root](n^2 + 1) - n}d. - - But - - [Omega]/[chi] = (b + nd)d/{b + 2d [root](n^2 + 1)}. - - Inserting the value of b, - - m = [Omega]/[chi] = {2d[root](n^2 + 1) - nd}/ - {4d [root](n^2 + 1) - 2nd} = (1/2)d. - - That is, with given side slopes, the section is least for a given - discharge when the hydraulic mean depth is half the actual depth. - - A simple construction gives the form of the channel which fulfils this - condition, for it can be shown that when m = (1/2)d the sides of the - channel are tangential to a semicircle drawn on the water line. - - Since - - [Omega]/[chi] = (1/2)d, - - therefore - - [Omega] = (1/2)[chi]d. (1) - - Let ABCD be the channel (fig. 115); from E the centre of AD drop - perpendiculars EF, EG, EH on the sides. - - Let - - AB = CD = a; BC = b; EF = EH = c; and EG = d. - - [Omega] = area AEB + BEC + CED, - = ac + (1/2)bd. - - [chi] = 2a + b. - - Putting these values in (1), - - ac + (1/2)bd = (a + (1/2)b)d; and hence c = d. - - [Illustration: FIG. 115.] - - That is, EF, EG, EH are all equal, hence a semicircle struck from E - with radius equal to the depth of the stream will pass through F and H - and be tangential to the sides of the channel. - - [Illustration: FIG. 116.] - - To draw the channel, describe a semicircle on a horizontal line with - radius = depth of channel. The bottom will be a horizontal tangent of - that semicircle, and the sides tangents drawn at the required side - slopes. - - The above result may be obtained thus (fig. 116):-- - - [chi] = b + 2d/sin [beta]. (1) - - [Omega] = d(b + d cot [beta]); - - [Omega]/d = b + d cot [beta]; (2) - - [Omega]/d^2 = b/d + cot [beta]. (3) - - From (1) and (2), - - [chi] = [Omega]/d - d cot [beta] + 2d/sin [beta]. - - This will be a minimum for - - d[chi]/dd = [Omega]/d^2 + cot[beta] - 2/sin [beta] = 0, - - or - - [Omega]/d^2 = 2 cosec. [beta] - cot [beta]. (4) - - or - - d = [root]{[Omega] sin [beta]/(2 - cos [beta])}. - - From (3) and (4), - - b/d = 2(1 - cos [beta])/sin [beta] = 2 tan (1/2)[beta]. - - _Proportions of Channels of Maximum Discharge for given Area and Side - Slopes. Depth of channel = d; Hydraulic mean depth = (1/2)d; Area of - section =_ [Omega]. - - +-------------+---------------+------------+-----------+---------+------------+ - | | Inclination | Ratio of | Area of | |Top width = | - | | of Sides to | Side | Section | Bottom |twice length| - | | Horizon. | Slopes. | [Omega]. | Width. |of each Side| - | | | | | | Slope. | - +-------------+---------------+------------+-----------+---------+------------+ - | Semicircle | .. | .. | 1.571 d^2 | 0 | 2 d | - | Semi-hexagon| 60 deg. 0' | 3 : 5 | 1.732 d^2 | 1.155 d | 2.310 d | - | Semi-square | 90 deg. 0' | 0 : 1 | 2 d^2 | 2 d | 2 d | - | | 75 deg. 58' | 1 : 4 | 1.812 d^2 | 1.562 d | 2.062 d | - | | 63 deg. 26' | 1 : 2 | 1.736 d^2 | 1.236 d | 2.236 d | - | | 53 deg. 8' | 3 : 4 | 1.750 d^2 | d | 2.500 d | - | | 45 deg. 0' | 1 : 1 | 1.828 d^2 | 0.828 d | 2.828 d | - | | 38 deg. 40' | 1(1/4) : 1 | 1.952 d^2 | 0.702 d | 3.202 d | - | | 33 deg. 42' | 1(1/2) : 1 | 2.106 d^2 | 0.606 d | 3.606 d | - | | 29 deg. 44' | 1(3/4) : 1 | 2.282 d^2 | 0.532 d | 4.032 d | - | | 26 deg. 34' | 2 : 1 | 2.472 d^2 | 0.472 d | 4.472 d | - | | 23 deg. 58' | 2(1/4) : 1 | 2.674 d^2 | 0.424 d | 4.924 d | - | | 21 deg. 48' | 2(1/2) : 1 | 2.885 d^2 | 0.385 d | 5.385 d | - | | 19 deg. 58' | 2(3/4) : 1 | 3.104 d^2 | 0.354 d | 5.854 d | - | | 18 deg. 26' | 3 : 1 | 3.325 d^2 | 0.325 d | 6.325 d | - +-------------+---------------+------------+-----------+---------+------------+ - - Half the top width is the length of each side slope. The wetted - perimeter is the sum of the top and bottom widths. - - S 114. _Form of Cross Section of Channel in which the Mean Velocity is - Constant with Varying Discharge._--In designing waste channels from - canals, and in some other cases, it is desirable that the mean - velocity should be restricted within narrow limits with very different - volumes of discharge. In channels of trapezoidal form the velocity - increases and diminishes with the discharge. Hence when the discharge - is large there is danger of erosion, and when it is small of silting - or obstruction by weeds. A theoretical form of section for which the - mean velocity would be constant can be found, and, although this is - not very suitable for practical purposes, it can be more or less - approximated to in actual channels. - - Let fig. 117 represent the cross section of the channel. From the - symmetry of the section, only half the channel need be considered. Let - obac be any section suitable for the minimum flow, and let it be - required to find the curve beg for the upper part of the channel so - that the mean velocity shall be constant. Take o as origin of - coordinates, and let de, fg be two levels of the water above ob. - - [Illustration: FIG. 117.] - - Let - - ob = b/2; de = y, fg = y + dy, od = x, of = x + dx; eg = ds. - - The condition to be satisfied is that - - v = c [root](mi) - - should be constant, whether the water-level is at ob, de, or fg. - Consequently - - m = constant = k - - for all three sections, and can be found from the section obac. Hence - also - - Increment of section y dx - ---------------------- = ---- = k - Increment of perimeter ds - - y^2dx^2 = k^2ds^2 = k^2(dx^2 + dy^2) and dx = k dy/[root](y^2 - k^2). - - Integrating, - - x = k log_[epsilon] {y + [root](y^2 - k^2)} + constant; - - and, since y = b/2 when x = 0, - - x = k log_[epsilon] [{y + [root](y^2 - k^2)}/{(1/2)b + [root]((1/4)b^2 - k^2)}]. - - Assuming values for y, the values of x can be found and the curve - drawn. - - The figure has been drawn for a channel the minimum section of which - is a half hexagon of 4 ft. depth. Hence k = 2; b = 9.2; the rapid - flattening of the side slopes is remarkable. - - - STEADY MOTION OF WATER IN OPEN CHANNELS OF VARYING CROSS SECTION AND - SLOPE - - S 115. In every stream the discharge of which is constant, or may be - regarded as constant for the time considered, the velocity at - different places depends on the slope of the bed. Except at certain - exceptional points the velocity will be greater as the slope of the - bed is greater, and, as the velocity and cross section of the stream - vary inversely, the section of the stream will be least where the - velocity and slope are greatest. If in a stream of tolerably uniform - slope an obstruction such as a weir is built, that will cause an - alteration of flow similar to that of an alteration of the slope of - the bed for a greater or less distance above the weir, and the - originally uniform cross section of the stream will become a varied - one. In such cases it is often of much practical importance to - determine the longitudinal section of the stream. - - The cases now considered will be those in which the changes of - velocity and cross section are gradual and not abrupt, and in which - the only internal work which needs to be taken into account is that - due to the friction of the stream bed, as in cases of uniform motion. - Further, the motion will be supposed to be steady, the mean velocity - at each given cross section remaining constant, though it varies from - section to section along the course of the stream. - - [Illustration: FIG. 118.] - - Let fig. 118 represent a longitudinal section of the stream, A0A1 - being the water surface, B0B1 the stream bed. Let A0B0, A1B1 be cross - sections normal to the direction of flow. Suppose the mass of water - A0B0A1B1 comes in a short time [theta] to C0D0C1D1, and let the work - done on the mass be equated to its change of kinetic energy during - that period. Let l be the length A0A1 of the portion of the stream - considered, and z the fall, of surface level in that distance. Let Q - be the discharge of the stream per second. - - [Illustration: FIG. 119.] - - _Change of Kinetic Energy._--At the end of the time [theta] there are - as many particles possessing the same velocities in the space C0D0A1B1 - as at the beginning. The change of kinetic energy is therefore the - difference of the kinetic energies of A0B0C0D0 and A1B1C1D1. - - Let fig. 119 represent the cross section A0B0, and let [omega] be a - small element of its area at a point where the velocity is v. Let - [Omega]0 be the whole area of the cross section and u0 the mean - velocity for the whole cross section. From the definition of mean - velocity we have - - u0 = [Sigma][omega]v/[Omega]0. - - Let v = u0 + w, where w is the difference between the velocity at the - small element [omega] and the mean velocity. For the whole cross - section, [Sigma][omega]w = 0. - - The mass of fluid passing through the element of section [omega], in - [theta] seconds, is (G/g)[omega]v[theta], and its kinetic energy is - (G/2g)[omega]v^3[theta]. For the whole section, the kinetic energy of - the mass A0B0C0D0 passing in [theta] seconds is - - (G[theta]/2g)[Sigma][omega]v^3 - = (G[theta]/2g)[Sigma][omega](u0^3 + 3u0^2w + 3u0^2 + w^3), - = (G[theta]/2g){u0^3[Omega] + [Sigma][omega]w^2(3u0 + w)}. - - The factor 3u0 + w is equal to 2u0 + v, a quantity necessarily - positive. Consequently [Sigma][omega]v^3 > [Omega]0u0^3, and - consequently the kinetic energy of A0B0C0D0 is greater than - - (G[theta]/2g)[Omega]0u0^3 or (G[theta])/2g)Qu0^2, - - which would be its value if all the particles passing the section had - the same velocity u0. Let the kinetic energy be taken at - - [alpha](G[theta]/2g)[Omega]0u0^3 = [alpha](G[theta]/2g)Qu0^2, - - where [alpha] is a corrective factor, the value of which was estimated - by J. B. C. J. Belanger at 1.1.[6] Its precise value is not of great - importance. - - In a similar way we should obtain for the kinetic energy of A1B1C1D1 - the expression - - [alpha](G[theta]/2g)[Omega]1 u1^3 = [alpha](G[theta]/2g)Q u1^2, - - where [Omega]1, u1 are the section and mean velocity at A1B1, and - where a may be taken to have the same value as before without any - important error. - - Hence the change of kinetic energy in the whole mass A0B0A1B1 in - [theta] seconds is - - [alpha](G[theta]/2g) Q (u1^2 - u0^2). (1) - - _Motive Work of the Weight and Pressures._--Consider a small filament - a0a1 which comes in [theta] seconds to c0c1. The work done by gravity - during that movement is the same as if the portion a0c0 were carried - to a1c1. Let dQ[theta] be the volume of a0c0 or a1c1, and y0, y1 the - depths of a0, a1 from the surface of the stream. Then the volume - dQ[theta] or GdQ[theta] pounds falls through a vertical height z + y1 - - y0, and the work done by gravity is - - G dQ[theta](z + y1 - y0). - - Putting p_a for atmospheric pressure, the whole pressure per unit of - area at a0 is Gy0 + p_a, and that at a1 is - (Gy1 + p_a). The work of - these pressures is - - G(y0 + p_a/G - y1 - p_a/G) dQ[theta] = G(y0 - y1) dQ[theta]. - - Adding this to the work of gravity, the whole work is GzdQ[theta]; or, - for the whole cross section, - - GzQ[theta]. (2) - - _Work expended in Overcoming the Friction of the Stream Bed._--Let - A'B', A"B" be two cross sections at distances s and s + ds from - A0B0. Between these sections the velocity may be treated as uniform, - because by hypothesis the changes of velocity from section to section - are gradual. Hence, to this short length of stream the equation for - uniform motion is applicable. But in that case the work in overcoming - the friction of the stream bed between A'B' and A"B" is - - GQ[theta][zeta](u^2/2g)([chi]/[Omega]) ds, - - where u, [chi], [Omega] are the mean velocity, wetted perimeter, and - section at A'B'. Hence the whole work lost in friction from A0B0 to - A1B1 will be - _ - / l - GQ[theta] | [zeta](u^2/2g)([chi]/[Omega]) ds. (3) - _/ 0 - - Equating the work given in (2) and (3) to the change of kinetic energy - given in (1), - - [alpha](GQ[theta]/2g)(u1^2 - u0^2) - _ - / l - = GQz[theta] - GQ[theta] | [zeta](u^2/2g)([chi]/[Omega]) ds; - _/ 0 - _ - / l - .: z = [alpha](u1^2 - u0^2)/2g + | [zeta](u^2/2g)([chi]/[Omega]) ds. - _/ 0 - - [Illustration: FIG. 120.] - - S 116. _Fundamental Differential Equation of Steady Varied - Motion._--Suppose the equation just found to be applied to an - indefinitely short length ds of the stream, limited by the end - sections ab, a1b1, taken for simplicity normal to the stream bed (fig. - 120). For that short length of stream the fall of surface level, or - difference of level of a and a1, may be written dz. Also, if we write - u for u0, and u + du for u1, the term (u0^2 - u1^2)/2g becomes udu/g. - Hence the equation applicable to an indefinitely short length of the - stream is - - dz = udu/g + ([chi]/[Omega])[zeta](u^2/2g) ds. (1) - - From this equation some general conclusions may be arrived at as to - the form of the longitudinal section of the stream, but, as the - investigation is somewhat complicated, it is convenient to simplify it - by restricting the conditions of the problem. - - _Modification of the Formula for the Restricted Case of a Stream - flowing in a Prismatic Stream Bed of Constant Slope._--Let i be the - constant slope of the bed. Draw ad parallel to the bed, and ac - horizontal. Then dz is sensibly equal to a'c. The depths of the - stream, h and h + dh, are sensibly equal to ab and a'b', and therefore - dh = a'd. Also cd is the fall of the bed in the distance ds, and is - equal to ids. Hence - - dz = a'c = cd - a'd = i ds - dh. (2) - - Since the motion is steady-- - - Q = [Omega]u = constant. - - Differentiating, - - [Omega] du + u d[Omega] = 0; - - .:du = -u d[Omega]/[Omega]. - - Let x be the width of the stream, then d[Omega] = xdh very nearly. - Inserting this value, - - du = -(ux/[Omega]) dh. (3) - - Putting the values of du and dz found in (2) and (3) in equation (1), - - i ds - dh = -(u^2x/g[Omega]) dh + ([chi]/[Omega])[zeta](u^2/2g) ds. - - dh/ds = {i - ([chi]/[Omega]) [zeta] (u^2/2g)}/{1 - (u^2/g)(x/[Omega])}. (4) - - _Further Restriction to the Case of a Stream of Rectangular Section - and of Indefinite Width._--The equation might be discussed in the form - just given, but it becomes a little simpler if restricted in the way - just stated. For, if the stream is rectangular, [chi]h = [Omega], and - if [chi] is large compared with h, [Omega]/[chi] = xh/x = h nearly. - Then equation (4) becomes - - dh/ds = i(1 - [zeta]u^2/2gih)/(1 - u^2/gh). (5) - - S 117. _General Indications as to the Form of Water Surface furnished - by Equation_ (5).--Let A0A1 (fig. 121) be the water surface, B0B1 the - bed in a longitudinal section of the stream, and ab any section at a - distance s from B0, the depth ab being h. Suppose B0B1, B0A0 taken as - rectangular coordinate axes, then dh/ds is the trigonometric tangent - of the angle which the surface of the stream at a makes with the axis - B0B1. This tangent dh/ds will be positive, if the stream is increasing - in depth in the direction B0B1; negative, if the stream is diminishing - in depth from B0 towards B1. If dh/ds = 0, the surface of the stream - is parallel to the bed, as in cases of uniform motion. But from - equation (4) - - dh/ds = 0, if i - ([chi]/[Omega])[zeta](u^2/2g) = 0; - - .: [zeta](u^2/2g) = ([Omega]/[chi])i = mi, - - which is the well-known general equation for uniform motion, based on - the same assumptions as the equation for varied steady motion now - being considered. The case of uniform motion is therefore a limiting - case between two different kinds of varied motion. - - [Illustration: FIG. 121.] - - Consider the possible changes of value of the fraction - - (1 - [zeta]u^2/2gih)/(1 - u^2/gh). - - As h tends towards the limit 0, and consequently u is large, the - numerator tends to the limit -[oo]. On the other hand if h = [oo], in - which case u is small, the numerator becomes equal to 1. For a value H - of h given by the equation - - 1 - [zeta]u^2/2giH = 0, - - H = [zeta]u^2/2gi, - - we fall upon the case of uniform motion. The results just stated may - be tabulated thus:-- - - For h = 0, H, > H, [oo], - - the numerator has the value -[oo], 0, > 0, 1. - - Next consider the denominator. If h becomes very small, in which case - u must be very large, the denominator tends to the limit -[oo]. As h - becomes very large and u consequently very small, the denominator - tends to the limit 1. For h = u^2/g, or u = [root](gh), the - denominator becomes zero. Hence, tabulating these results as before:-- - - For h = 0, u^2/g, > u^2/g, [oo], - - the denominator becomes - - -[oo], 0, > 0, 1. - - [Illustration: FIG. 122.] - - S 118. _Case_ 1.--Suppose h > u^2/g, and also h > H, or the depth - greater than that corresponding to uniform motion. In this case dh/ds - is positive, and the stream increases in depth in the direction of - flow. In fig. 122 let B0B1 be the bed, C0C1 a line parallel to the bed - and at a height above it equal to H. By hypothesis, the surface A0A1 - of the stream is above C0C1, and it has just been shown that the depth - of the stream increases from B0 towards B1. But going up stream h - approaches more and more nearly the value H, and therefore dh/ds - approaches the limit 0, or the surface of the stream is asymptotic to - C0C1. Going down stream h increases and u diminishes, the numerator - and denominator of the fraction (1 - [zeta]u^2/2gih)/(1 -u^2/gh) both - tend towards the limit 1, and dh/ds to the limit i. That is, the - surface of the stream tends to become asymptotic to a horizontal line - D0D1. - - The form of water surface here discussed is produced when the flow of - a stream originally uniform is altered by the construction of a weir. - The raising of the water surface above the level C0C1 is termed the - backwater due to the weir. - - S 119. _Case_ 2.--Suppose h > u^2/g, and also h < H. Then dh/ds is - negative, and the stream is diminishing in depth in the direction of - flow. In fig. 123 let B0B1 be the stream bed as before; C0C1 a line - drawn parallel to B0B1 at a height above it equal to H. By hypothesis - the surface A0A1 of the stream is below C0C1, and the depth has just - been shown to diminish from B0 towards B1. Going up stream h - approaches the limit H, and dh/ds tends to the limit zero. That is, up - stream A0A1 is asymptotic to C0C1. Going down stream h diminishes and - u increases; the inequality h>u^2/g diminishes; the denominator of the - fraction (1 - [zeta]u^2/2gih)/(1 - u^2/gh) tends to the limit zero, and - consequently dh/ds tends to [infinity]. That is, down stream A0A1 - tends to a direction perpendicular to the bed. Before, however, this - limit was reached the assumptions on which the general equation is - based would cease to be even approximately true, and the equation - would cease to be applicable. The filaments would have a relative - motion, which would make the influence of internal friction in the - fluid too important to be neglected. A stream surface of this form may - be produced if there is an abrupt fall in the bed of the stream (fig. - 124). - - [Illustration: FIG. 123.] - - [Illustration: FIG. 124.] - - [Illustration: FIG. 125.] - - On the Ganges canal, as originally constructed, there were abrupt - falls precisely of this kind, and it appears that the lowering of the - water surface and increase of velocity which such falls occasion, for - a distance of some miles up stream, was not foreseen. The result was - that, the velocity above the falls being greater than was intended, - the bed was scoured and considerable damage was done to the works. - "When the canal was first opened the water was allowed to pass freely - over the crests of the overfalls, which were laid on the level of the - bed of the earthen channel; erosion of bed and sides for some miles up - rapidly followed, and it soon became apparent that means must be - adopted for raising the surface of the stream at those points (that - is, the crests of the falls). Planks were accordingly fixed in the - grooves above the bridge arches, or temporary weirs were formed over - which the water was allowed to fall; in some cases the surface of the - water was thus raised above its normal height, causing a backwater in - the channel above" (Crofton's _Report on the Ganges Canal_, p. 14). - Fig. 125 represents in an exaggerated form what probably occurred, the - diagram being intended to represent some miles' length of the canal - bed above the fall. AA parallel to the canal bed is the level - corresponding to uniform motion with the intended velocity of the - canal. In consequence of the presence of the ogee fall, however, the - water surface would take some such form as BB, corresponding to Case 2 - above, and the velocity would be greater than the intended velocity, - nearly in the inverse ratio of the actual to the intended depth. By - constructing a weir on the crest of the fall, as shown by dotted - lines, a new water surface CC corresponding to Case 1 would be - produced, and by suitably choosing the height of the weir this might - be made to agree approximately with the intended level AA. - - S 120. _Case_ 3.--Suppose a stream flowing uniformly with a depth h < - u^2/g. For a stream in uniform motion [zeta]u^2/2g = mi, or if the - stream is of indefinitely great width, so that m = H, then - [zeta]u^2/2g = iH, and H = [zeta]u^2/2gi. Consequently the condition - stated above involves that - - [zeta]u^2/2gi < u^2/g, or that i > [zeta]/2. - - If such a stream is interfered with by the construction of a weir - which raises its level, so that its depth at the weir becomes h1 > - u^2/g, then for a portion of the stream the depth h will satisfy the - conditions h < u^2/g and h > H, which are not the same as those assumed in the two - previous cases. At some point of the stream above the weir the depth h - becomes equal to u^2/g, and at that point dh/ds becomes infinite, or - the surface of the stream is normal to the bed. It is obvious that at - that point the influence of internal friction will be too great to be - neglected, and the general equation will cease to represent the true - conditions of the motion of the water. It is known that, in cases such - as this, there occurs an abrupt rise of the free surface of the - stream, or a standing wave is formed, the conditions of motion in - which will be examined presently. - - It appears that the condition necessary to give rise to a standing - wave is that i > [zeta]/2. Now [zeta] depends for different channels - on the roughness of the channel and its hydraulic mean depth. Bazin - calculated the values of [zeta] for channels of different degrees of - roughness and different depths given in the following table, and the - corresponding minimum values of i for which the exceptional case of - the production of a standing wave may occur. - - +-----------------------------+----------------+-------------------------+ - | | Slope below | Standing Wave Formed. | - | |which a Standing| | - | Nature of Bed of Stream. | Wave is +-------------+-----------+ - | | impossible in |Slope in feet|Least Depth| - | | feet peer foot.| per foot. | in feet. | - +-----------------------------+----------------+-------------+-----------+ - | | | / 0.002 | 0.262 | - | Very smooth cemented surface| 0.00147 | < 0.003 | .098 | - | | | \ 0.004 | .065 | - | | | | | - | | | / 0.003 | .394 | - | Ashlar or brickwork | 0.00186 | < 0.004 | .197 | - | | | \ 0.006 | .098 | - | | | | | - | | | / 0.004 | 1.181 | - | Rubble masonry | 0.00235 | < 0.006 | .525 | - | | | \ 0.010 | .262 | - | | | | | - | | | / 0.006 | 3.478 | - | Earth | 0.00275 | < 0.010 | 1.542 | - | | | \ 0.015 | .919 | - +-----------------------------+----------------+-------------+-----------+ - - - STANDING WAVES - - S 121. The formation of a standing wave was first observed by Bidone. - Into a small rectangular masonry channel, having a slope of 0.023 ft. - per foot, he admitted water till it flowed uniformly with a depth of - 0.2 ft. He then placed a plank across the stream which raised the - level just above the obstruction to 0.95 ft. He found that the stream - above the obstruction was sensibly unaffected up to a point 15 ft. - from it. At that point the depth suddenly increased from 0.2 ft. to - 0.56 ft. The velocity of the stream in the part unaffected by the - obstruction was 5.54 ft. per second. Above the point where the abrupt - change of depth occurred u^2 = 5.54^2 = 30.7, and gh = 32.2 X 0.2 = - 6.44; hence u^2 was > gh. Just below the abrupt change of depth u = - 5.54 X 0.2/0.56 = 1.97; u^2 = 3.88; and gh = 32.2 X 0.56 = 18.03; hence - at this point u^2 < gh. Between these two points, therefore, u^2 = gh; - and the condition for the production of a standing wave occurred. - - [Illustration: FIG. 126.] - - The change of level at a standing wave may be found thus. Let fig. 126 - represent the longitudinal section of a stream and ab, cd cross - sections normal to the bed, which for the short distance considered - may be assumed horizontal. Suppose the mass of water abcd to come to - a'b'c'd' in a short time t; and let u0, u1 be the velocities at ab and - cd, [Omega]0, [Omega]1 the areas of the cross sections. The force - causing change of momentum in the mass abcd estimated horizontally is - simply the difference of the pressures on ab and cd. Putting h0, h1 - for the depths of the centres of gravity of ab and cd measured down - from the free water surface, the force is G(h0[Omega]0 - h1[Omega]1) - pounds, and the impulse in t seconds is G (h0[Omega]0 - h1[Omega]1) t - second pounds. The horizontal change of momentum is the difference of - the momenta of cdc'd' and aba'b'; that is, - - (G/g)([Omega]1u1^2 - [Omega]0u0^2)t. - - Hence, equating impulse and change of momentum, - - G(h0[Omega]0 - h1[Omega]1)t = (G/g)([Omega]1u1^2 - [Omega]0u0^2)t; - - .: h0[Omega]0 - h1[Omega]1 = ([Omega]1u1^2 - [Omega]0u0^2)/g. (1) - - For simplicity let the section be rectangular, of breadth B and depths - H0 and H1, at the two cross sections considered; then h0 = (1/2)H0, - and h1 = (1/2)H1. Hence - - H0^2 - H1^2 = (2/g)(H1u1^2 - H0u0^2). - - But, since [Omega]0u0 = [Omega]1u1, we have - - u1^2 = u0^2H0^2/H1^2, - - H0^2 - H1^2 = (2u0^2/g)(H0^2/H1 - H0). (2) - - This equation is satisfied if H0 = H1, which corresponds to the case - of uniform motion. Dividing by H0 - H1, the equation becomes - - (H1/H0)(H0 + H1) = 2u0^2/g; (3) - - .: H1 = [root](2u0^2H0/g + (1/4)H0^2) - (1/2)H0. (4) - - In Bidone's experiment u0 = 5.54, and H0 = 0.2. Hence H1 = 0.52, which - agrees very well with the observed height. - - [Illustration: FIG. 127.] - - S 122. A standing wave is frequently produced at the foot of a weir. - Thus in the ogee falls originally constructed on the Ganges canal a - standing wave was observed as shown in fig. 127. The water falling - over the weir crest A acquired a very high velocity on the steep slope - AB, and the section of the stream at B became very small. It easily - happened, therefore, that at B the depth h < u^2/g. In flowing along - the rough apron of the weir the velocity u diminished and the depth h - increased. At a point C, where h became equal to u^2/g, the conditions - for producing the standing wave occurred. Beyond C the free surface - abruptly rose to the level corresponding to uniform motion with the - assigned slope of the lower reach of the canal. - - [Illustration: FIG. 128.] - - A standing wave is sometimes formed on the down stream side of bridges - the piers of which obstruct the flow of the water. Some interesting - cases of this kind are described in a paper on the "Floods in the - Nerbudda Valley" in the _Proc. Inst. Civ. Eng._ vol. xxvii. p. 222, by - A. C. Howden. Fig. 128 is compiled from the data given in that paper. - It represents the section of the stream at pier 8 of the Towah - Viaduct, during the flood of 1865. The ground level is not exactly - given by Howden, but has been inferred from data given on another - drawing. The velocity of the stream was not observed, but the author - states it was probably the same as at the Gunjal river during a - similar flood, that is 16.58 ft. per second. Now, taking the depth on - the down stream face of the pier at 26 ft., the velocity necessary for - the production of a standing wave would be u = [root](gh) = - [root](32.2 X 26) = 29 ft. per second nearly. But the velocity at this - point was probably from Howden's statements 16.58 X {40/26} = 25.5 ft. - per second, an agreement as close as the approximate character of the - data would lead us to expect. - - - XI. ON STREAMS AND RIVERS - - S 123. _Catchment Basin._--A stream or river is the channel for the - discharge of the available rainfall of a district, termed its - catchment basin. The catchment basin is surrounded by a ridge or - watershed line, continuous except at the point where the river finds - an outlet. The area of the catchment basin may be determined from a - suitable contoured map on a scale of at least 1 in 100,000. Of the - whole rainfall on the catchment basin, a part only finds its way to - the stream. Part is directly re-evaporated, part is absorbed by - vegetation, part may escape by percolation into neighbouring - districts. The following table gives the relation of the average - stream discharge to the average rainfall on the catchment basin - (Tiefenbacher). - - +-----------------------------+-----------------+--------------------+ - | |Ratio of average |Loss by Evaporation,| - | | Discharge to | &c., in per cent of| - | |average Rainfall.| total Rainfall. | - +-----------------------------+-----------------+--------------------+ - | Cultivated land and spring- | | | - | forming declivities. | .3 to .33 | 67 to 70 | - | Wooded hilly slopes. | .35 to .45 | 55 to 65 | - | Naked unfissured mountains | .55 to .60 | 40 to 45 | - +-----------------------------+-----------------+--------------------+ - - S 124. _Flood Discharge._--The flood discharge can generally only be - determined by examining the greatest height to which floods have been - known to rise. To produce a flood the rainfall must be heavy and - widely distributed, and to produce a flood of exceptional height the - duration of the rainfall must be so great that the flood waters of the - most distant affluents reach the point considered, simultaneously with - those from nearer points. The larger the catchment basin the less - probable is it that all the conditions tending to produce a maximum - discharge should simultaneously occur. Further, lakes and the river - bed itself act as storage reservoirs during the rise of water level - and diminish the rate of discharge, or serve as flood moderators. The - influence of these is often important, because very heavy rain storms - are in most countries of comparatively short duration. Tiefenbacher - gives the following estimate of the flood discharge of streams in - Europe:-- - - Flood discharge of Streams - per Second per Square Mile - of Catchment Basin. - - In flat country 8.7 to 12.5 cub. ft. - In hilly districts 17.5 to 22.5 " - In moderately mountainous districts 36.2 to 45.0 " - In very mountainous districts 50.0 to 75.0 " - - It has been attempted to express the decrease of the rate of flood - discharge with the increase of extent of the catchment basin by - empirical formulae. Thus Colonel P. P. L. O'Connell proposed the - formula y = M [root]x, where M is a constant called the modulus of the - river, the value of which depends on the amount of rainfall, the - physical characters of the basin, and the extent to which the floods - are moderated by storage of the water. If M is small for any given - river, it shows that the rainfall is small, or that the permeability - or slope of the sides of the valley is such that the water does not - drain rapidly to the river, or that lakes and river bed moderate the - rise of the floods. If values of M are known for a number of rivers, - they may be used in inferring the probable discharge of other similar - rivers. For British rivers M varies from 0.43 for a small stream - draining meadow land to 37 for the Tyne. Generally it is about 15 or - 20. For large European rivers M varies from 16 for the Seine to 67.5 - for the Danube. For the Nile M = 11, a low value which results from - the immense length of the Nile throughout which it receives no - affluent, and probably also from the influence of lakes. For different - tributaries of the Mississippi M varies from 13 to 56. For various - Indian rivers it varies from 40 to 303, this variation being due to - the great variations of rainfall, slope and character of Indian - rivers. - - In some of the tank projects in India, the flood discharge has been - calculated from the formula D = C[3root]n^2, where D is the discharge - in cubic yards per hour from n square miles of basin. The constant C - was taken = 61,523 in the designs for the Ekrooka tank, = 75,000 on - Ganges and Godavery works, and = 10,000 on Madras works. - - [Illustration: FIG. 129.] - - [Illustration: FIG. 130.] - - S 125. _Action of a Stream on its Bed._--If the velocity of a stream - exceeds a certain limit, depending on its size, and on the size, - heaviness, form and coherence of the material of which its bed is - composed, it scours its bed and carries forward the materials. The - quantity of material which a given stream can carry in suspension - depends on the size and density of the particles in suspension, and is - greater as the velocity of the stream is greater. If in one part of - its course the velocity of a stream is great enough to scour the bed - and the water becomes loaded with silt, and in a subsequent part of - the river's course the velocity is diminished, then part of the - transported material must be deposited. Probably deposit and scour go - on simultaneously over the whole river bed, but in some parts the rate - of scour is in excess of the rate of deposit, and in other parts the - rate of deposit is in excess of the rate of scour. Deep streams appear - to have the greatest scouring power at any given velocity. It is - possible that the difference is strictly a difference of transporting, - not of scouring action. Let fig. 129 represent a section of a stream. - The material lifted at a will be diffused through the mass of the - stream and deposited at different distances down stream. The average - path of a particle lifted at a will be some such curve as abc, and the - average distance of transport each time a particle is lifted will be - represented by ac. In a deeper stream such as that in fig. 130, the - average height to which particles are lifted, and, since the rate of - vertical fall through the water may be assumed the same as before, the - average distance a'c' of transport will be greater. Consequently, - although the scouring action may be identical in the two streams, the - velocity of transport of material down stream is greater as the depth - of the stream is greater. The effect is that the deep stream excavates - its bed more rapidly than the shallow stream. - - S 126. _Bottom Velocity at which Scour commences._--The following - bottom velocities were determined by P. L. G. Dubuat to be the maximum - velocities consistent with stability of the stream bed for different - materials. - - Darcy and Bazin give, for the relation of the mean velocity v_m and - bottom velocity v_b. - - v_m = v_b + 10.87 [root](mi). - - But - - [root]mi = v_m [root]([zeta]/2g); - - .: v_m = v_b/(1 - 10.87 [root]([zeta]/2g)). - - Taking a mean value for [zeta], we get - - v_m = 1.312 v_b, - - and from this the following values of the mean velocity are - obtained:-- - - +-----------------------+---------------+-------------+ - | |Bottom Velocity|Mean Velocity| - | | = v_b. | = v_m. | - +-----------------------+---------------+-------------+ - | 1. Soft earth | 0.25 | .33 | - | 2. Loam | 0.50 | .65 | - | 3. Sand | 1.00 | 1.30 | - | 4. Gravel | 2.00 | 2.62 | - | 5. Pebbles | 3.40 | 4.46 | - | 6. Broken stone, flint| 4.00 | 5.25 | - | 7. Chalk, soft shale | 5.00 | 6.56 | - | 8. Rock in beds | 6.00 | 7.87 | - | 9. Hard rock. | 10.00 | 13.12 | - +-----------------------+---------------+-------------+ - - The following table of velocities which should not be exceeded in - channels is given in the _Ingenieurs Taschenbuch_ of the Verein - "Hutte":-- - - +--------------------------------+---------+---------+---------+ - | | Surface | Mean | Bottom | - | |Velocity.|Velocity.|Velocity.| - +--------------------------------+---------+---------+---------+ - | Slimy earth or brown clay | .49 | .36 | .26 | - | Clay | .98 | .75 | .52 | - | Firm sand | 1.97 | 1.51 | 1.02 | - | Pebbly bed | 4.00 | 3.15 | 2.30 | - | Boulder bed | 5.00 | 4.03 | 3.08 | - | Conglomerate of slaty fragments| 7.28 | 6.10 | 4.90 | - | Stratified rocks | 8.00 | 7.45 | 6.00 | - | Hard rocks | 14.00 | 12.15 | 10.36 | - +--------------------------------+---------+---------+---------+ - - S 127. _Regime of a River Channel._--A river channel is said to be in - a state of regime, or stability, when it changes little in draught or - form in a series of years. In some rivers the deepest part of the - channel changes its position perpetually, and is seldom found in the - same place in two successive years. The sinuousness of the river also - changes by the erosion of the banks, so that in time the position of - the river is completely altered. In other rivers the change from year - to year is very small, but probably the regime is never perfectly - stable except where the rivers flow over a rocky bed. - - [Illustration: FIG. 131.] - - If a river had a constant discharge it would gradually modify its bed - till a permanent regime was established. But as the volume discharged - is constantly changing, and therefore the velocity, silt is deposited - when the velocity decreases, and scour goes on when the velocity - increases in the same place. When the scouring and silting are - considerable, a perfect balance between the two is rarely established, - and hence continual variations occur in the form of the river and the - direction of its currents. In other cases, where the action is less - violent, a tolerable balance may be established, and the deepening of - the bed by scour at one time is compensated by the silting at another. - In that case the general regime is permanent, though alteration is - constantly going on. This is more likely to happen if by artificial - means the erosion of the banks is prevented. If a river flows in soil - incapable of resisting its tendency to scour it is necessarily sinuous - (S 107), for the slightest deflection of the current to either side - begins an erosion which increases progressively till a considerable - bend is formed. If such a river is straightened it becomes sinuous - again unless its banks are protected from scour. - - S 128. _Longitudinal Section of River Bed._--The declivity of rivers - decreases from source to mouth. In their higher parts rapid and - torrential, flowing over beds of gravel or boulders, they enlarge in - volume by receiving affluent streams, their slope diminishes, their - bed consists of smaller materials, and finally they reach the sea. - Fig. 131 shows the length in miles, and the surface fall in feet per - mile, of the Tyne and its tributaries. - - The decrease of the slope is due to two causes. (1) The action of the - transporting power of the water, carrying the smallest debris the - greatest distance, causes the bed to be less stable near the mouth - than in the higher parts of the river; and, as the river adjusts its - slope to the stability of the bed by scouring or increasing its - sinuousness when the slope is too great, and by silting or - straightening its course if the slope is too small, the decreasing - stability of the bed would coincide with a decreasing slope. (2) The - increase of volume and section of the river leads to a decrease of - slope; for the larger the section the less slope is necessary to - ensure a given velocity. - - The following investigation, though it relates to a purely arbitrary - case, is not without interest. Let it be assumed, to make the - conditions definite--(1) that a river flows over a bed of uniform - resistance to scour, and let it be further assumed that to maintain - stability the velocity of the river in these circumstances is constant - from source to mouth; (2) suppose the sections of the river at all - points are similar, so that, b being the breadth of the river at any - point, its hydraulic mean depth is ab and its section is cb^2, where a - and c are constants applicable to all parts of the river; (3) let us - further assume that the discharge increases uniformly in consequence - of the supply from affluents, so that, if l is the length of the river - from its source to any given point, the discharge there will be kl, - where k is another constant applicable to all points in the course of - the river. - - [Illustration: FIG. 132.] - - Let AB (fig. 132) be the longitudinal section of the river, whose - source is at A; and take A for the origin of vertical and horizontal - coordinates. Let C be a point whose ordinates are x and y, and let the - river at C have the breadth b, the slope i, and the velocity v. Since - velocity X area of section = discharge, vcb^2 = kl, or b = - [root](kl/cv). - - Hydraulic mean depth = ab = a [root](kl/cv). - - But, by the ordinary formula for the flow of rivers, mi = [zeta]v^2; - - .: i = [zeta]v^2/m = ([zeta]v^(5/2)/a) [root](c/kl). - - But i is the tangent of the angle which the curve at C makes with the - axis of X, and is therefore = dy/dx. Also, as the slope is small, l = - AC = AD = x nearly. - - .: dy/dx = ([zeta]v^(5/2)/a) [root](c/kx); - - and, remembering that v is constant, - - y = (2[zeta]v^(5/2)/a) [root](cx/k); - - or - - y^2 = constant X x; - - so that the curve is a common parabola, of which the axis is - horizontal and the vertex at the source. This may be considered an - ideal longitudinal section, to which actual rivers approximate more or - less, with exceptions due to the varying hardness of their beds, and - the irregular manner in which their volume increases. - - S 129. _Surface Level of River._--The surface level of a river is a - plane changing constantly in position from changes in the volume of - water discharged, and more slowly from changes in the river bed, and - the circumstances affecting the drainage into the river. - - For the purposes of the engineer, it is important to determine (1) the - extreme low water level, (2) the extreme high water or flood level, - and (3) the highest navigable level. - - 1. _Low Water Level_ cannot be absolutely known, because a river - reaches its lowest level only at rare intervals, and because - alterations in the cultivation of the land, the drainage, the removal - of forests, the removal or erection of obstructions in the river bed, - &c., gradually alter the conditions of discharge. The lowest level of - which records can be found is taken as the conventional or approximate - low water level, and allowance is made for possible changes. - - 2. _High Water or Flood Level._--The engineer assumes as the highest - flood level the highest level of which records can be obtained. In - forming a judgment of the data available, it must be remembered that - the highest level at one point of a river is not always simultaneous - with the attainment of the highest level at other points, and that - the rise of a river in flood is very different in different parts of - its course. In temperate regions, the floods of rivers seldom rise - more than 20 ft. above low-water level, but in the tropics the rise of - floods is greater. - - 3. _Highest Navigable Level._--When the river rises above a certain - level, navigation becomes difficult from the increase of the velocity - of the current, or from submersion of the tow paths, or from the - headway under bridges becoming insufficient. Ordinarily the highest - navigable level may be taken to be that at which the river begins to - overflow its banks. - - S 130. _Relative Value of Different Materials for Submerged - Works._--That the power of water to remove and transport different - materials depends on their density has an important bearing on the - selection of materials for submerged works. In many cases, as in the - aprons or floorings beneath bridges, or in front of locks or falls, - and in the formation of training walls and breakwaters by _pierres - perdus_, which have to resist a violent current, the materials of - which the structures are composed should be of such a size and weight - as to be able individually to resist the scouring action of the water. - The heaviest materials will therefore be the best; and the different - value of materials in this respect will appear much more striking, if - it is remembered that all materials lose part of their weight in - water. A block whose volume is V cubic feet, and whose density in air - is w lb. per cubic foot, weighs in air wV lb., but in water only - (w--62.4) V lb. - - +----------------------+-----------------------------+ - | | Weight of a Cub. Ft. in lb. | - | +--------------+--------------+ - | | In Air. | In Water. | - +----------------------+--------------+--------------+ - | Basalt | 187.3 | 124.9 | - | Brick | 130.0 | 67.6 | - | Brickwork | 112.0 | 49.6 | - | Granite and limestone| 170.0 | 107.6 | - | Sandstone | 144.0 | 81.6 | - | Masonry | 116-144 | 53.6-81.6 | - +----------------------+--------------+--------------+ - - S 131. _Inundation Deposits from a River._--When a river carrying silt - periodically overflows its banks, it deposits silt over the area - flooded, and gradually raises the surface of the country. The silt is - deposited in greatest abundance where the water first leaves the - river. It hence results that the section of the country assumes a - peculiar form, the river flowing in a trough along the crest of a - ridge, from which the land slopes downwards on both sides. The silt - deposited from the water forms two wedges, having their thick ends - towards the river (fig. 133). - - [Illustration: FIG. 133.] - - This is strikingly the case with the Mississippi, and that river is - now kept from flooding immense areas by artificial embankments or - levees. In India, the term _deltaic segment_ is sometimes applied to - that portion of a river running through deposits formed by inundation, - and having this characteristic section. The irrigation of the country - in this case is very easy; a comparatively slight raising of the river - surface by a weir or annicut gives a command of level which permits - the water to be conveyed to any part of the district. - - S 132. _Deltas._--The name delta was originally given to the [Greek: - Delta]-shaped portion of Lower Egypt, included between seven branches - of the Nile. It is now given to the whole of the alluvial tracts round - river mouths formed by deposition of sediment from the river, where - its velocity is checked on its entrance to the sea. The characteristic - feature of these alluvial deltas is that the river traverses them, not - in a single channel, but in two or many bifurcating branches. Each - branch has a tract of the delta under its influence, and gradually - raises the surface of that tract, and extends it seaward. As the delta - extends itself seaward, the conditions of discharge through the - different branches change. The water finds the passage through one of - the branches less obstructed than through the others; the velocity and - scouring action in that branch are increased; in the others they - diminish. The one channel gradually absorbs the whole of the water - supply, while the other branches silt up. But as the mouth of the new - main channel extends seaward the resistance increases both from the - greater length of the channel and the formation of shoals at its - mouth, and the river tends to form new bifurcations AC or AD (fig. - 134), and one of these may in time become the main channel of the - river. - - S 133. _Field Operations preliminary to a Study of River - Improvement._--There are required (1) a plan of the river, on which - the positions of lines of levelling and cross sections are marked; (2) - a longitudinal section and numerous cross sections of the river; (3) a - series of gaugings of the discharge at different points and in - different conditions of the river. - - _Longitudinal Section._--This requires to be carried out with great - accuracy. A line of stakes is planted, following the sinuosities of - the river, and chained and levelled. The cross sections are referred - to the line of stakes, both as to position and direction. The - determination of the surface slope is very difficult, partly from its - extreme smallness, partly from oscillation of the water. Cunningham - recommends that the slope be taken in a length of 2000 ft. by four - simultaneous observations, two on each side of the river. - - [Illustration: FIG. 134.] - - S 134. _Cross Sections_--A stake is planted flush with the water, and - its level relatively to some point on the line of levels is - determined. Then the depth of the water is determined at a series of - points (if possible at uniform distances) in a line starting from the - stake and perpendicular to the thread of the stream. To obtain these, - a wire may be stretched across with equal distances marked on it by - hanging tags. The depth at each of these tags may be obtained by a - light wooden staff, with a disk-shaped shoe 4 to 6 in. in diameter. If - the depth is great, soundings may be taken by a chain and weight. To - ensure the wire being perpendicular to the thread of the stream, it is - desirable to stretch two other wires similarly graduated, one above - and the other below, at a distance of 20 to 40 yds. A number of floats - being then thrown in, it is observed whether they pass the same - graduation on each wire. - - [Illustration: FIG. 135.] - - For large and rapid rivers the cross section is obtained by sounding - in the following way. Let AC (fig. 135) be the line on which soundings - are required. A base line AB is measured out at right angles to AC, - and ranging staves are set up at AB and at D in line with AC. A boat - is allowed to drop down stream, and, at the moment it comes in line - with AD, the lead is dropped, and an observer in the boat takes, with - a box sextant, the angle AEB subtended by AB. The sounding line may - have a weight of 14 lb. of lead, and, if the boat drops down stream - slowly, it may hang near the bottom, so that the observation is made - instantly. In extensive surveys of the Mississippi observers with - theodolites were stationed at A and B. The theodolite at A was - directed towards C, that at B was kept on the boat. When the boat came - on the line AC, the observer at A signalled, the sounding line was - dropped, and the observer at B read off the angle ABE. By repeating - observations a number of soundings are obtained, which can be plotted - in their proper position, and the form of the river bed drawn by - connecting the extremities of the lines. From the section can be - measured the sectional area of the stream [Omega] and its wetted - perimeter [chi]; and from these the hydraulic mean depth m can be - calculated. - - S 135. _Measurement of the Discharge of Rivers._--The area of cross - section multiplied by the mean velocity gives the discharge of the - stream. The height of the river with reference to some fixed mark - should be noted whenever the velocity is observed, as the velocity and - area of cross section are different in different states of the river. - To determine the mean velocity various methods may be adopted; and, - since no method is free from liability to error, either from the - difficulty of the observations or from uncertainty as to the ratio of - the mean velocity to the velocity observed, it is desirable that more - than one method should be used. - - - INSTRUMENTS FOR MEASURING THE VELOCITY OF WATER - - S 136. _Surface Floats_ are convenient for determining the surface - velocities of a stream, though their use is difficult near the banks. - The floats may be small balls of wood, of wax or of hollow metal, so - loaded as to float nearly flush with the water surface. To render - them visible they may have a vertical painted stem. In experiments on - the Seine, cork balls 1(3/4) in. diameter were used, loaded to float - flush with the water, and provided with a stem. In A. J. C. - Cunningham's observations at Roorkee, the floats were thin circular - disks of English deal, 3 in. diameter and 1/4 in. thick. For - observations near the banks, floats 1 in. diameter and 1/8 in. thick - were used. To render them visible a tuft of cotton wool was used - loosely fixed in a hole at the centre. - - The velocity is obtained by allowing the float to be carried down, and - noting the time of passage over a measured length of the stream. If v - is the velocity of any float, t the time of passing over a length l, - then v = l/t. To mark out distinctly the length of stream over which - the floats pass, two ropes may be stretched across the stream at a - distance apart, which varies usually from 50 to 250 ft., according to - the size and rapidity of the river. In the Roorkee experiments a - length of run of 50 ft. was found best for the central two-fifths of - the width, and 25 ft. for the remainder, except very close to the - banks, where the run was made 12(1/2) ft. only. The longer the run the - less is the proportionate error of the time observations, but on the - other hand the greater the deviation of the floats from a straight - course parallel to the axis of the stream. To mark the precise - position at which the floats cross the ropes, Cunningham used short - white rope pendants, hanging so as nearly to touch the surface of the - water. In this case the streams were 80 to 180 ft. in width. In wider - streams the use of ropes to mark the length of run is impossible, and - recourse must be had to box sextants or theodolites to mark the path - of the floats. - - [Illustration: FIG. 136.] - - Let AB (fig. 136) be a measured base line strictly parallel to the - thread of the stream, and AA1, BB1 lines at right angles to AB marked - out by ranging rods at A1 and B1. Suppose observers stationed at A and - B with sextants or theodolites, and let CD be the path of any float - down stream. As the float approaches AA1, the observer at B keeps it - on the cross wire of his instrument. The observer at A observes the - instant of the float reaching the line AA1, and signals to B who then - reads off the angle ABC. Similarly, as the float approaches BB1, the - observer at A keeps it in sight, and when signalled to by B reads the - angle BAD. The data so obtained are sufficient for plotting the path - of the float and determining the distances AC, BD. - - The time taken by the float in passing over the measured distance may - be observed by a chronograph, started as the float passes the upper - rope or line, and stopped when it passes the lower. In Cunningham's - observations two chronometers were sometimes used, the time of passing - one end of the run being noted on one, and that of passing the other - end of the run being noted on the other. The chronometers were - compared immediately before the observations. In other cases a single - chronometer was used placed midway of the run. The moment of the - floats passing the ends of the run was signalled to a time-keeper at - the chronometer by shouting. It was found quite possible to count the - chronometer beats to the nearest half second, and in some cases to the - nearest quarter second. - - [Illustration: FIG. 137.] - - S 137. _Sub-surface Floats._--The velocity at different depths below - the surface of a stream may be obtained by sub-surface floats, used - precisely in the same way as surface floats. The most usual - arrangement is to have a large float, of slightly greater density than - water, connected with a small and very light surface float. The motion - of the combined arrangement is not sensibly different from that of the - large float, and the small surface float enables an observer to note - the path and velocity of the sub-surface float. The instrument is, - however, not free from objection. If the large submerged float is made - of very nearly the same density as water, then it is liable to be - thrown upwards by very slight eddies in the water, and it does not - maintain its position at the depth at which it is intended to float. - On the other hand, if the large float is made sensibly heavier than - water, the indicating or surface float must be made rather large, and - then it to some extent influences the motion of the submerged float. - Fig. 137 shows one form of sub-surface float. It consists of a couple - of tin plates bent at a right angle and soldered together at the - angle. This is connected with a wooden ball at the surface by a very - thin wire or cord. As the tin alone makes a heavy submerged float, it - is better to attach to the tin float some pieces of wood to diminish - its weight in water. Fig. 138 shows the form of submerged float used - by Cunningham. It consists of a hollow metal ball connected to a - slice of cork, which serves as the surface float. - - [Illustration: FIG. 138.] - - [Illustration: FIG. 139.] - - S 138. _Twin Floats._--Suppose two equal and similar floats (fig. 139) - connected by a wire. Let one float be a little lighter and the other a - little heavier than water. Then the velocity of the combined floats - will be the mean of the surface velocity and the velocity at the depth - at which the heavier float swims, which is determined by the length of - the connecting wire. Thus if v_s is the surface velocity and v_d the - velocity at the depth to which the lower float is sunk, the velocity - of the combined floats will be - - v = (1/2)(v_s + v_d). - - Consequently, if v is observed, and v_s determined by an experiment - with a single float, - - v_d = 2v - v_s - - According to Cunningham, the twin float gives better results than the - sub-surface float. - - [Illustration: FIG. 140.] - - S 139. _Velocity Rods._--Another form of float is shown in fig. 140. - This consists of a cylindrical rod loaded at the lower end so as to - float nearly vertical in water. A wooden rod, with a metal cap at the - bottom in which shot can be placed, answers better than anything else, - and sometimes the wooden rod is made in lengths, which can be screwed - together so as to suit streams of different depths. A tuft of cotton - wool at the top serves to make the float more easily visible. Such a - rod, so adjusted in length that it sinks nearly to the bed of the - stream, gives directly the mean velocity of the whole vertical section - in which it floats. - - S 140. _Revy's Current Meter._--No instrument has been so much used in - directly determining the velocity of a stream at a given point as the - screw current meter. Of this there are a dozen varieties at least. As - an example of the instrument in its simplest form, Revy's meter may be - selected. This is an ordinary screw meter of a larger size than usual, - more carefully made, and with its details carefully studied (figs. - 141, 142). It was designed after experience in gauging the great South - American rivers. The screw, which is actuated by the water, is 6 in. - in diameter, and is of the type of the Griffiths screw used in ships. - The hollow spherical boss serves to make the weight of the screw - sensibly equal to its displacement, so that friction is much reduced. - On the axis aa of the screw is a worm which drives the counter. This - consists of two worm wheels g and h fixed on a common axis. The worm - wheels are carried on a frame attached to the pin l. By means of a - string attached to l they can be pulled into gear with the worm, or - dropped out of gear and stopped at any instant. A nut m can be screwed - up, if necessary, to keep the counter permanently in gear. The worm is - two-threaded, and the worm wheel g has 200 teeth. Consequently it - makes one rotation for 100 rotations of the screw, and the number of - rotations up to 100 is marked by the passage of the graduations on its - edge in front of a fixed index. The second worm wheel has 196 teeth, - and its edge is divided into 49 divisions. Hence it falls behind the - first wheel one division for a complete rotation of the latter. The - number of hundreds of rotations of the screw are therefore shown by - the number of divisions on h passed over by an index fixed to g. One - difficulty in the use of the ordinary screw meter is that particles of - grit, getting into the working parts, very sensibly alter the - friction, and therefore the speed of the meter. Revy obviates this by - enclosing the counter in a brass box with a glass face. This box is - filled with pure water, which ensures a constant coefficient of - friction for the rubbing parts, and prevents any mud or grit finding - its way in. In order that the meter may place itself with the axis - parallel to the current, it is pivoted on a vertical axis and directed - by a large vane shown in fig. 142. To give the vane more - directing power the vertical axis is nearer the screw than in ordinary - meters, and the vane is larger. A second horizontal vane is attached - by the screws x, x, the object of which is to allow the meter to rest - on the ground without the motion of the screw being interfered with. - The string or wire for starting and stopping the meter is carried - through the centre of the vertical axis, so that the strain on it may - not tend to pull the meter oblique to the current. The pitch of the - screw is about 9 in. The screws at x serve for filling the meter with - water. The whole apparatus is fixed to a rod (fig. 142), of a length - proportionate to the depth, or for very great depths it is fixed to a - weighted bar lowered by ropes, a plan invented by Revy. The instrument - is generally used thus. The reading of the counter is noted, and it is - put out of gear. The meter is then lowered into the water to the - required position from a platform between two boats, or better from a - temporary bridge. Then the counter is put into gear for one, two or - five minutes. Lastly, the instrument is raised and the counter again - read. The velocity is deduced from the number of rotations in unit - time by the formulae given below. For surface velocities the counter - may be kept permanently in gear, the screw being started and stopped - by hand. - - [Illustration: FIG. 141.] - - [Illustration: FIG. 142.] - - S 141. _The Harlacher Current Meter._--In this the ordinary counting - apparatus is abandoned. A worm drives a worm wheel, which makes an - electrical contact once for each 100 rotations of the worm. This - contact gives a signal above water. With this arrangement, a series of - velocity observations can be made, without removing the instrument - from the water, and a number of practical difficulties attending the - accurate starting and stopping of the ordinary counter are entirely - got rid of. Fig. 143 shows the meter. The worm wheel z makes one - rotation for 100 of the screw. A pin moving the lever x makes the - electrical contact. The wires b, c are led through a gas pipe B; this - also serves to adjust the meter to any required position on the wooden - rod dd. The rudder or vane is shown at WH. The galvanic current acts - on the electromagnet m, which is fixed in a small metal box containing - also the battery. The magnet exposes and withdraws a coloured disk at - an opening in the cover of the box. - - S 142. _Amsler Laffon Current Meter._--A very convenient and accurate - current meter is constructed by Amsler Laffon of Schaffhausen. This - can be used on a rod, and put into and out of gear by a ratchet. The - peculiarity in this case is that there is a double ratchet, so that - one pull on the string puts the counter into gear and a second puts it - out of gear. The string may be slack during the action of the meter, - and there is less uncertainty than when the counter has to be held in - gear. For deep streams the meter A is suspended by a wire with a heavy - lenticular weight below (fig. 144). The wire is payed out from a small - winch D, with an index showing the depth of the meter, and passes over - a pulley B. The meter is in gimbals and is directed by a conical - rudder which keeps it facing the stream with its axis horizontal. - There is an electric circuit from a battery C through the meter, and a - contact is made closing the circuit every 100 revolutions. The moment - the circuit closes a bell rings. By a subsidiary arrangement, when the - foot of the instrument, 0.3 metres below the axis of the meter, - touches the ground the circuit is also closed and the bell rings. It - is easy to distinguish the continuous ring when the ground is reached - from the short ring when the counter signals. A convenient winch for - the wire is so graduated that if set when the axis of the meter is at - the water surface it indicates at any moment the depth of the meter - below the surface. Fig. 144 shows the meter as used on a boat. It is a - very convenient instrument for obtaining the velocity at different - depths and can also be used as a sounding instrument. - - [Illustration: FIG. 143.] - - S 143. _Determination of the Coefficients of the Current - Meter._--Suppose a series of observations has been made by towing the - meter in still water at different speeds, and that it is required to - ascertain from these the constants of the meter. If v is the velocity - of the water and n the observed number of rotations per second, let - - v = [alpha] + [beta]n (1) - - where [alpha] and [beta] are constants. Now let the meter be towed - over a measured distance L, and let N be the revolutions of the meter - and t the time of transit. Then the speed of the meter relatively to - the water is L/t = v feet per second, and the number of revolutions - per second is N/t = n. Suppose m observations have been made in this - way, furnishing corresponding values of v and n, the speed in each - trial being as uniform as possible, - - [Sigma]n = n1 + n2 + ... - - [Sigma]v = v1 + v2 + ... - - [Sigma]nv = n1v1 + n2v2 + ... - - [Sigma]n^2 = n1^2 + n2^2 + ... - - [[Sigma]n]^2 = [n1 + n2 + ...]^2 - - Then for the determination of the constants [alpha] and [beta] in (1), - by the method of least squares-- - - [Sigma]n^2[Sigma]v - [Sigma]n[Sigma]nv - [alpha] = --------------------------------------, - m[Sigma]n^2 - [[Sigma]n]^2 - - m[Sigma]nv - [Sigma]v[Sigma]n - [beta] = -----------------------------. - m[Sigma]n^2 - [[Sigma]n]^2 - - [Illustration: FIG. 144.] - - In a few cases the constants for screw current meters have been - determined by towing them in R. E. Froude's experimental tank in which - the resistance of ship models is ascertained. In that case the data - are found with exceptional accuracy. - - S 144. Darcy Gauge or modified Pitot Tube.--A very old instrument for - measuring velocities, invented by Henri Pitot in 1730 (_Histoire de - l'Academie des Sciences_, 1732, p. 376), consisted simply of a - vertical glass tube with a right-angled bend, placed so that its mouth - was normal to the direction of flow (fig. 145). - - [Illustration: FIG. 145.] - - The impact of the stream on the mouth of the tube balances a column in - the tube, the height of which is approximately h = v^2/2g, where v is - the velocity at the depth x. Placed with its mouth parallel to the - stream the water inside the tube is nearly at the same level as the - surface of the stream, and turned with the mouth down stream, the - fluid sinks a depth h' = v^2/2g nearly, though the tube in that case - interferes with the free flow of the liquid and somewhat modifies the - result. Pitot expanded the mouth of the tube so as to form a funnel or - bell mouth. In that case he found by experiment - - h = 1.5v^2/2g. - - But there is more disturbance of the stream. Darcy preferred to make - the mouth of the tube very small to avoid interference with the - stream and to check oscillations of the water column. Let the - difference of level of a pair of tubes A and B (fig. 145) be taken to - be h = kv^2/2g, then k may be taken to be a corrective coefficient - whose value in well-shaped instruments is very nearly unity. By - placing his instrument in front of a boat towed through water Darcy - found k = 1.034; by placing the instrument in a stream the velocity of - which had been ascertained by floats, he found k = 1.006; by readings - taken in different parts of the section of a canal in which a known - volume of water was flowing, he found k = 0.993. He believed the first - value to be too high in consequence of the disturbance caused by the - boat. The mean of the other two values is almost exactly unity - (_Recherches hydrauliques_, Darcy and Bazin, 1865, p. 63). W. B. - Gregory used somewhat differently formed Pitot tubes for which the k = - 1 (_Am. Soc. Mech. Eng._, 1903, 25). T. E. Stanton used a Pitot tube - in determining the velocity of an air current, and for his instrument - he found k = 1.030 to k = 1.032 ("On the Resistance of Plane Surfaces - in a Current of Air," _Proc. Inst. Civ. Eng._, 1904, 156). - - One objection to the Pitot tube in its original form was the great - difficulty and inconvenience of reading the height h in the immediate - neighbourhood of the stream surface. This is obviated in the Darcy - gauge, which can be removed from the stream to be read. - - Fig. 146 shows a Darcy gauge. It consists of two Pitot tubes having - their mouths at right angles. In the instrument shown, the two tubes, - formed of copper in the lower part, are united into one for strength, - and the mouths of the tubes open vertically and horizontally. The - upper part of the tubes is of glass, and they are provided with a - brass scale and two verniers b, b. The whole instrument is supported - on a vertical rod or small pile AA, the fixing at B permitting the - instrument to be adjusted to any height on the rod, and at the same - time allowing free rotation, so that it can be held parallel to the - current. At c is a two-way cock, which can be opened or closed by - cords. If this is shut, the instrument can be lifted out of the stream - for reading. The glass tubes are connected at top by a brass fixing, - with a stop cock a, and a flexible tube and mouthpiece m. The use of - this is as follows. If the velocity is required at a point near the - surface of the stream, one at least of the water columns would be - below the level at which it could be read. It would be in the copper - part of the instrument. Suppose then a little air is sucked out by the - tube m, and the cock a closed, the two columns will be forced up an - amount corresponding to the difference between atmospheric pressure - and that in the tubes. But the difference of level will remain - unaltered. - - When the velocities to be measured are not very small, this instrument - is an admirable one. It requires observation only of a single linear - quantity, and does not require any time observation. The law - connecting the velocity and the observed height is a rational one, and - it is not absolutely necessary to make any experiments on the - coefficient of the instrument. If we take v = k[root](2gh), then it - appears from Darcy's experiments that for a well-formed instrument k - does not sensibly differ from unity. It gives the velocity at a - definite point in the stream. The chief difficulty arises from the - fact that at any given point in a stream the velocity is not - absolutely constant, but varies a little from moment to moment. Darcy - in some of his experiments took several readings, and deduced the - velocity from the mean of the highest and lowest. - - S 145. _Perrodil Hydrodynamometer._--This consists of a frame abcd - (fig. 147) placed vertically in the stream, and of a height not less - than the stream's depth. The two vertical members of this frame are - connected by cross bars, and united above water by a circular bar, - situated in the vertical plane and carrying a horizontal graduated - circle ef. This whole system is movable round its axis, being - suspended on a pivot at g connected with the fixed support mn. Other - horizontal arms serve as guides. The central vertical rod gr forms a - torsion rod, being fixed at r to the frame abcd, and, passing freely - upwards through the guides, it carries a horizontal needle moving - over the graduated circle ef. The support g, which carries the - apparatus, also receives in a tubular guide the end of the torsion rod - gr and a set screw for fixing the upper end of the torsion rod when - necessary. The impulse of the stream of water is received on a - circular disk x, in the plane of the torsion rod and the frame abcd. - To raise and lower the apparatus easily, it is not fixed directly to - the rod mn, but to a tube kl sliding on mn. - - [Illustration: FIG. 146.] - - Suppose the apparatus arranged so that the disk x is at that level in - the stream where the velocity is to be determined. The plane abcd is - placed parallel to the direction of motion of the water. Then the disk - x (acting as a rudder) will place itself parallel to the stream on the - down stream side of the frame. The torsion rod will be unstrained, and - the needle will be at zero on the graduated circle. If, then, the - instrument is turned by pressing the needle, till the plane abcd of - the disk and the zero of the graduated circle is at right angles to - the stream, the torsion rod will be twisted through an angle which - measures the normal impulse of the stream on the disk x. That angle - will be given by the distance of the needle from zero. Observation - shows that the velocity of the water at a given point is not constant. - It varies between limits more or less wide. When the apparatus is - nearly in its right position, the set screw at g is made to clamp the - torsion spring. Then the needle is fixed, and the apparatus carrying - the graduated circle oscillates. It is not, then, difficult to note - the mean angle marked by the needle. - - [Illustration: FIG. 147.] - - Let r be the radius of the torsion rod, l its length from the needle - over ef to r, and [alpha] the observed torsion angle. Then the moment - of the couple due to the molecular forces in the torsion rod is - - M = E_t I[alpha]/l; - - where E_t is the modulus of elasticity for torsion, and I the polar - moment of inertia of the section of the rod. If the rod is of circular - section, I = (1/2)[pi]r^4. Let R be the radius of the disk, and b its - leverage, or the distance of its centre from the axis of the torsion - rod. The moment of the pressure of the water on the disk is - - Fb = kb(G/2g)[pi]R^2v^2, - - where G is the heaviness of water and k an experimental coefficient. - Then - - E_t I[alpha]/l = kb(G/2g)[pi]R^2v^2. - - For any given instrument, - - v = c [root][alpha], - - where c is a constant coefficient for the instrument. - - The instrument as constructed had three disks which could be used at - will. Their radii and leverages were in feet - - R = b = - - 1st disk 0.052 0.16 - 2nd " 0.105 0.32 - 3rd " 0.210 0.66 - - For a thin circular plate, the coefficient k = 1.12. In the actual - instrument the torsion rod was a brass wire 0.06 in. diameter and - 6(1/2) ft. long. Supposing [alpha] measured in degrees, we get by - calculation - - v = 0.335 [root][alpha]; 0.115 [root][alpha]; 0.042 [root][alpha]. - - Very careful experiments were made with the instrument. It was fixed - to a wooden turning bridge, revolving over a circular channel of 2 ft. - width, and about 76 ft. circumferential length. An allowance was made - for the slight current produced in the channel. These experiments gave - for the coefficient c, in the formula v = c [root][alpha], - - 1st disk, c = 0.3126 for velocities of 3 to 16 ft. - 2nd " 0.1177 " " 1(1/4) to 3(1/4) " - 3rd " 0.0349 " " less than 1(1/4) " - - The instrument is preferable to the current meter in giving the - velocity in terms of a single observed quantity, the angle of torsion, - while the current meter involves the observation of two quantities, - the number of rotations and the time. The current meter, except in - some improved forms, must be withdrawn from the water to read the - result of each experiment, and the law connecting the velocity and - number of rotations of a current meter is less well-determined than - that connecting the pressure on a disk and the torsion of the wire of - a hydrodynamometer. - - The Pitot tube, like the hydrodynamometer, does not require a time - observation. But, where the velocity is a varying one, and - consequently the columns of water in the Pitot tube are oscillating, - there is room for doubt as to whether, at any given moment of closing - the cock, the difference of level exactly measures the impulse of the - stream at the moment. The Pitot tube also fails to give measurable - indications of very low velocities. - - - PROCESSES FOR GAUGING STREAMS - - S 146. _Gauging by Observation of the Maximum Surface Velocity._--The - method of gauging which involves the least trouble is to determine the - surface velocity at the thread of the stream, and to deduce from it - the mean velocity of the whole cross section. The maximum surface - velocity may be determined by floats or by a current meter. - Unfortunately the ratio of the maximum surface to the mean velocity is - extremely variable. Thus putting v_o for the surface velocity at the - thread of the stream, and v_m for the mean velocity of the whole cross - section, v_m/v_o has been found to have the following values:-- - - v_m/v_o - - De Prony, experiments on small wooden channels 0.8164 - Experiments on the Seine 0.62 - Destrem and De Prony, experiments on the Neva 0.78 - Boileau, experiments on canals 0.82 - Baumgartner, experiments on the Garonne 0.80 - Brunings (mean) 0.85 - Cunningham, Solani aqueduct 0.823 - - Various formulae, either empirical or based on some theory of the - vertical and horizontal velocity curves, have been proposed for - determining the ratio v_m/v_o. Bazin found from his experiments the - empirical expression - - v_m = v_o - 25.4 [root](mi); - - where m is the hydraulic mean depth and i the slope of the stream. - - In the case of irrigation canals and rivers, it is often important to - determine the discharge either daily or at other intervals of time, - while the depth and consequently the mean velocity is varying. - Cunningham (_Roorkee Prof. Papers_, iv. 47), has shown that, for a - given part of such a stream, where the bed is regular and of permanent - section, a simple formula may be found for the variation of the - central surface velocity with the depth. When once the constants of - this formula have been determined by measuring the central surface - velocity and depth, in different conditions of the stream, the surface - velocity can be obtained by simply observing the depth of the stream, - and from this the mean velocity and discharge can be calculated. Let z - be the depth of the stream, and v_o the surface velocity, both measured - at the thread of the stream. Then v_o^2 = cz; where c is a constant - which for the Solani aqueduct had the values 1.9 to 2, the depths - being 6 to 10 ft., and the velocities 3(1/2) to 4(1/2) ft. Without any - assumption of a formula, however, the surface velocities, or still - better the mean velocities, for different conditions of the stream may - be plotted on a diagram in which the abscissae are depths and the - ordinates velocities. The continuous curve through points so found - would then always give the velocity for any observed depth of the - stream, without the need of making any new float or current meter - observations. - - S 147. _Mean Velocity determined by observing a Series of Surface - Velocities._--The ratio of the mean velocity to the surface velocity - in one longitudinal section is better ascertained than the ratio of - the central surface velocity to the mean velocity of the whole cross - section. Suppose the river divided into a number of compartments by - equidistant longitudinal planes, and the surface velocity observed in - each compartment. From this the mean velocity in each compartment and - the discharge can be calculated. The sum of the partial discharges - will be the total discharge of the stream. When wires or ropes can be - stretched across the stream, the compartments can be marked out by - tags attached to them. Suppose two such ropes stretched across the - stream, and floats dropped in above the upper rope. By observing - within which compartment the path of the float lies, and noting the - time of transit between the ropes, the surface velocity in each - compartment can be ascertained. The mean velocity in each compartment - is 0.85 to 0.91 of the surface velocity in that compartment. Putting k - for this ratio, and v1, v2 ... for the observed velocities, in - compartments of area [Omega]1, [Omega]2 ... then the total discharge - is - - Q = k([Omega]1v1 + [Omega]2v2 + ... ). - - If several floats are allowed to pass over each compartment, the mean - of all those corresponding to one compartment is to be taken as the - surface velocity of that compartment. - - [Illustration: FIG. 148.] - - This method is very applicable in the case of large streams or rivers - too wide to stretch a rope across. The paths of the floats are then - ascertained in this way. Let fig. 148 represent a portion of the - river, which should be straight and free from obstructions. Suppose a - base line AB measured parallel to the thread of the stream, and let - the mean cross section of the stream be ascertained either by sounding - the terminal cross sections AE, BF, or by sounding a series of - equidistant cross sections. The cross sections are taken at right - angles to the base line. Observers are placed at A and B with - theodolites or box sextants. The floats are dropped in from a boat - above AE, and picked up by another boat below BF. An observer with a - chronograph or watch notes the time in which each float passes from AE - to BF. The method of proceeding is this. The observer A sets his - theodolite in the direction AE, and gives a signal to drop a float. B - keeps his instrument on the float as it comes down. At the moment the - float arrives at C in the line AE, the observer at A calls out. B - clamps his instrument and reads off the angle ABC, and the time - observer begins to note the time of transit. B now points his - instrument in the direction BF, and A keeps the float on the cross - wire of his instrument. At the moment the float arrives at D in the - line BF, the observer B calls out, A clamps his instrument and reads - off the angle BAD, and the time observer notes the time of transit - from C to D. Thus all the data are determined for plotting the path CD - of the float and determining its velocity. By dropping in a series of - floats, a number of surface velocities can be determined. When all - these have been plotted, the river can be divided into convenient - compartments. The observations belonging to each compartment are then - averaged, and the mean velocity and discharge calculated. It is - obvious that, as the surface velocity is greatly altered by wind, - experiments of this kind should be made in very calm weather. - - The ratio of the surface velocity to the mean velocity in the same - vertical can be ascertained from the formulae for the vertical - velocity curve already given (S 101). Exner, in _Erbkam's Zeitschrift_ - for 1875, gave the following convenient formula. Let v be the mean and - V the surface velocity in any given vertical longitudinal section, the - depth of which is h - - v/V = (1 + 0.1478 [root]h)/(1 + 0.2216 [root]h). - - If vertical velocity rods are used instead of common floats, the mean - velocity is directly determined for the vertical section in which the - rod floats. No formula of reduction is then necessary. The observed - velocity has simply to be multiplied by the area of the compartment to - which it belongs. - - S 148. _Mean Velocity of the Stream from a Series of Mid Depth - Velocities._--In the gaugings of the Mississippi it was found that the - mid depth velocity differed by only a very small quantity from the - mean velocity in the vertical section, and it was uninfluenced by - wind. If therefore a series of mid depth velocities are determined by - double floats or by a current meter, they may be taken to be the mean - velocities of the compartments in which they occur, and no formula of - reduction is necessary. If floats are used, the method is precisely - the same as that described in the last paragraph for surface floats. - The paths of the double floats are observed and plotted, and the mean - taken of those corresponding to each of the compartments into which - the river is divided. The discharge is the sum of the products of the - observed mean mid depth velocities and the areas of the compartments. - - S 149. _P. P. Boileau's Process for Gauging Streams._--Let U be the - mean velocity at a given section of a stream, V the maximum velocity, - or that of the principal filament, which is generally a little below - the surface, W and w the greatest and least velocities at the surface. - The distance of the principal filament from the surface is generally - less than one-fourth of the depth of the stream; W is a little less - than V; and U lies between W and w. As the surface velocities change - continuously from the centre towards the sides there are at the - surface two filaments having a velocity equal to U. The determination - of the position of these filaments, which Boileau terms the gauging - filaments, cannot be effected entirely by theory. But, for sections of - a stream in which there are no abrupt changes of depth, their position - can be very approximately assigned. Let [Delta] and l be the - horizontal distances of the surface filament, having the velocity W, - from the gauging filament, which has the velocity U, and from the bank - on one side. Then - - [Delta]/l = c^4 [root]{(W + 2w)/7(W - w)}, - - c being a numerical constant. From gaugings by Humphreys and Abbot, - Bazin and Baumgarten, the values c = 0.919, 0.922 and 0.925 are - obtained. Boileau adopts as a mean value 0.922. Hence, if W and w are - determined by float gauging or otherwise, [Delta] can be found, and - then a single velocity observation at [Delta] ft. from the filament of - maximum velocity gives, without need of any reduction, the mean - velocity of the stream. More conveniently W, w, and U can be measured - from a horizontal surface velocity curve, obtained from a series of - float observations. - - S 150. _Direct Determination of the Mean Velocity by a Current Meter - or Darcy Gauge._--The only method of determining the mean velocity at - a cross section of a stream which involves no assumption of the ratio - of the mean velocity to other quantities is this--a plank bridge is - fixed across the stream near its surface. From this, velocities are - observed at a sufficient number of points in the cross section of the - stream, evenly distributed over its area. The mean of these is the - true mean velocity of the stream. In Darcy and Bazin's experiments on - small streams, the velocity was thus observed at 36 points in the - cross section. - - When the stream is too large to fix a bridge across it, the - observations may be taken from a boat, or from a couple of boats with - a gangway between them, anchored successively at a series of points - across the width of the stream. The position of the boat for each - series of observations is fixed by angular observations to a base line - on shore. - - [Illustration: FIG. 149.] - - S 151. _A. R. Harlacher's Graphic Method of determining the Discharge - from a Series of Current Meter Observations._--Let ABC (fig. 149) be - the cross section of a river at which a complete series of current - meter observations have been taken. Let I., II., III ... be the - verticals at different points of which the velocities were measured. - Suppose the depths at I., II., III., ... (fig. 149), set off as - vertical ordinates in fig. 150, and on these vertical ordinates - suppose the velocities set off horizontally at their proper depths. - Thus, if v is the measured velocity at the depth h from the surface in - fig. 149, on vertical marked III., then at III. in fig. 150 take cd = - h and ac = v. Then d is a point in the vertical velocity curve for the - vertical III., and, all the velocities for that ordinate being - similarly set off, the curve can be drawn. Suppose all the vertical - velocity curves I.... V. (fig. 150), thus drawn. On each of these - figures draw verticals corresponding to velocities of x, 2x, 3x ... - ft. per second. Then for instance cd at III. (fig. 150) is the depth - at which a velocity of 2x ft. per second existed on the vertical III. - in fig. 149 and if cd is set off at III. in fig. 149 it gives a point - in a curve passing through points of the section where the velocity - was 2x ft. per second. Set off on each of the verticals in fig. 149 - all the depths thus found in the corresponding diagram in fig. 150. - Curves drawn through the corresponding points on the verticals are - curves of equal velocity. - - [Illustration: FIG. 150.] - - The discharge of the stream per second may be regarded as a solid - having the cross section of the river (fig. 149) as a base, and cross - sections normal to the plane of fig. 149 given by the diagrams in fig. - 150. The curves of equal velocity may therefore be considered as - contour lines of the solid whose volume is the discharge of the stream - per second. Let [Omega]0 be the area of the cross section of the - river, [Omega]1, [Omega]2 ... the areas contained by the successive - curves of equal velocity, or, if these cut the surface of the stream, - by the curves and that surface. Let x be the difference of velocity - for which the successive curves are drawn, assumed above for - simplicity at 1 ft. per second. Then the volume of the successive - layers of the solid body whose volume represents the discharge, - limited by successive planes passing through the contour curves, will - be - - (1/2)x([Omega]0 + [Omega]1), (1/2)x([Omega]1 + [Omega]2), and so on. - - Consequently the discharge is - - Q = x{(1/2)([Omega]0 + [Omega]_n) + [Omega]1 = [Omega]2 + ... + [Omega](n-1)}. - - The areas [Omega]0, [Omega]1 ... are easily ascertained by means of - the polar planimeter. A slight difficulty arises in the part of the - solid lying above the last contour curve. This will have generally a - height which is not exactly x, and a form more rounded than the other - layers and less like a conical frustum. The volume of this may be - estimated separately, and taken to be the area of its base (the area - [Omega]_n) multiplied by 1/3 to 1/2 its height. - - [Illustration: FIG. 151.] - - Fig. 151 shows the results of one of Harlacher's gaugings worked out - in this way. The upper figure shows the section of the river and the - positions of the verticals at which the soundings and gaugings were - taken. The lower gives the curves of equal velocity, worked out from - the current meter observations, by the aid of vertical velocity - curves. The vertical scale in this figure is ten times as great as in - the other. The discharge calculated from the contour curves is 14.1087 - cubic metres per second. In the lower figure some other interesting - curves are drawn. Thus, the uppermost dotted curve is the curve - through points at which the maximum velocity was found; it shows that - the maximum velocity was always a little below the surface, and at a - greater depth at the centre than at the sides. The next curve shows - the depth at which the mean velocity for each vertical was found. The - next is the curve of equal velocity corresponding to the mean velocity - of the stream; that is, it passes through points in the cross section - where the velocity was identical with the mean velocity of the stream. - - -HYDRAULIC MACHINES - -S 152. Hydraulic machines may be broadly divided into two classes: (1) -_Motors_, in which water descending from a higher to a lower level, or -from a higher to a lower pressure, gives up energy which is available -for mechanical operations; (2) _Pumps_, in which the energy of a steam -engine or other motor is expended in raising water from a lower to a -higher level. A few machines such as the ram and jet pump combine the -functions of motor and pump. It may be noted that constructively pumps -are essentially reversed motors. The reciprocating pump is a reversed -pressure engine, and the centrifugal pump a reversed turbine. Hydraulic -machine tools are in principle motors combined with tools, and they now -form an important special class. - -Water under pressure conveyed in pipes is a convenient and economical -means of transmitting energy and distributing it to many scattered -working points. Hence large and important hydraulic systems are adopted -in which at a central station water is pumped at high pressure into -distributing mains, which convey it to various points where it actuates -hydraulic motors operating cranes, lifts, dock gates, and in some cases -riveting and shearing machines. In this case the head driving the -hydraulic machinery is artificially created, and it is the convenience of -distributing power in an easily applied form to distant points which -makes the system advantageous. As there is some unavoidable loss in -creating an artificial head this system is most suitable for driving -machines which work intermittently (see POWER TRANSMISSION). The -development of electrical methods of transmitting and distributing energy -has led to the utilization of many natural waterfalls so situated as to -be useless without such a means of transferring the power to points where -it can be conveniently applied. In some cases, as at Niagara, the -hydraulic power can only be economically developed in very large units, -and it can be most conveniently subdivided and distributed by -transformation into electrical energy. Partly from the development of new -industries such as paper-making from wood pulp and electro-metallurgical -processes, which require large amounts of cheap power, partly from the -facility with which energy can now be transmitted to great distances -electrically, there has been a great increase in the utilization of -water-power in countries having natural waterfalls. According to the -twelfth census of the United States the total amount of water-power -reported as used in manufacturing establishments in that country was -1,130,431 h.p. in 1870; 1,263,343 h.p. in 1890; and 1,727,258 h.p. in -1900. The increase was 8.4% in the decade 1870-1880, 3.1% in 1880-1890, -and no less than 36.7% in 1890-1900. The increase is the more striking -because in this census the large amounts of hydraulic power which are -transmitted electrically are not included. - - - XII. IMPACT AND REACTION OF WATER - - S 153. When a stream of fluid in steady motion impinges on a solid - surface, it presses on the surface with a force equal and opposite to - that by which the velocity and direction of motion of the fluid are - changed. Generally, in problems on the impact of fluids, it is - necessary to neglect the effect of friction between the fluid and the - surface on which it moves. - - _During Impact the Velocity of the Fluid relatively to the Surface on - which it impinges remains unchanged in Magnitude._--Consider a mass of - fluid flowing in contact with a solid surface also in motion, the - motion of both fluid and solid being estimated relatively to the - earth. Then the motion of the fluid may be resolved into two parts, - one a motion equal to that of the solid, and in the same direction, - the other a motion relatively to the solid. The motion which the fluid - has in common with the solid cannot at all be influenced by the - contact. The relative component of the motion of the fluid can only be - altered in direction, but not in magnitude. The fluid moving in - contact with the surface can only have a relative motion parallel to - the surface, while the pressure between the fluid and solid, if - friction is neglected, is normal to the surface. The pressure - therefore can only deviate the fluid, without altering the magnitude - of the relative velocity. The unchanged common component and, combined - with it, the deviated relative component give the resultant final - velocity, which may differ greatly in magnitude and direction from the - initial velocity. - - From the principle of momentum, the impulse of any mass of fluid - reaching the surface in any given time is equal to the change of - momentum estimated in the same direction. The pressure between the - fluid and surface, in any direction, is equal to the change of - momentum in that direction of so much fluid as reaches the surface in - one second. If P_a is the pressure in any direction, m the mass of - fluid impinging per second, v_a the change of velocity in the - direction of P_a due to impact, then - - P_a = mv_a. - - If v1 (fig. 152) is the velocity and direction of motion before - impact, v2 that after impact, then v is the total change of motion due - to impact. The resultant pressure of the fluid on the surface is in - the direction of v, and is equal to v multiplied by the mass impinging - per second. That is, putting P for the resultant pressure, - - P = mv. - - Let P be resolved into two components, N and T, normal and tangential - to the direction of motion of the solid on which the fluid impinges. - Then N is a lateral force producing a pressure on the supports of the - solid, T is an effort which does work on the solid. If u is the - velocity of the solid, Tu is the work done per second by the fluid in - moving the solid surface. - - [Illustration: FIG. 152.] - - Let Q be the volume, and GQ the weight of the fluid impinging per - second, and let v1 be the initial velocity of the fluid before - striking the surface. Then GQv1^2/2g is the original kinetic energy of - Q cub. ft. of fluid, and the efficiency of the stream considered as an - arrangement for moving the solid surface is - - [eta] = Tu/(GQv1^2/2g). - - S 154. _Jet deviated entirely in one Direction.--Geometrical Solution_ - (fig. 153).--Suppose a jet of water impinges on a surface ac with a - velocity ab, and let it be wholly deviated in planes parallel to the - figure. Also let ae be the velocity and direction of motion of the - surface. Join eb; then the water moves with respect to the surface in - the direction and with the velocity eb. As this relative velocity is - unaltered by contact with the surface, take cd = eb, tangent to the - surface at c, then cd is the relative motion of the water with respect - to the surface at c. Take df equal and parallel to ae. Then fc - (obtained by compounding the relative motion of water to surface and - common velocity of water and surface) is the absolute velocity and - direction of the water leaving the surface. Take ag equal and parallel - to fc. Then, since ab is the initial and ag the final velocity and - direction of motion, gb is the total change of motion of the water. - The resultant pressure on the plane is in the direction gb. Join eg. - In the triangle gae, ae is equal and parallel to df, and ag to fc. - Hence eg is equal and parallel to cd. But cd = eb = relative motion of - water and surface. Hence the change of motion of the water is - represented in magnitude and direction by the third side of an - isosceles triangle, of which the other sides are equal to the relative - velocity of the water and surface, and parallel to the initial and - final directions of relative motion. - - [Illustration: FIG. 153.] - - - SPECIAL CASES - - S 155. (1) _A Jet impinges on a plane surface at rest, in a direction - normal to the plane_ (fig. 154).--Let a jet whose section is [omega] - impinge with a velocity v on a plane surface at rest, in a direction - normal to the plane. The particles approach the plane, are gradually - deviated, and finally flow away parallel to the plane, having then no - velocity in the original direction of the jet. The quantity of water - impinging per second is [omega]v. The pressure on the plane, which is - equal to the change of momentum per second, is P = (G/g)[omega]v^2. - - [Illustration: FIG. 154.] - - (2) _If the plane is moving in the direction of the jet with the - velocity_ [+-]u, the quantity impinging per second is [omega](v [+-] - u). The momentum of this quantity before impact is (G/g)[omega](v [+-] - u)v. After impact, the water still possesses the velocity [+-]u in the - direction of the jet; and the momentum, in that direction, of so much - water as impinges in one second, after impact, is [+-](G/g)[omega](v - [+-] u)u. The pressure on the plane, which is the change of momentum - per second, is the difference of these quantities or P = - (G/g)[omega](v [+-] u)^2. This differs from the expression obtained in - the previous case, in that the relative velocity of the water and - plane v [+-] u is substituted for v. The expression may be written P = - 2 X G X [omega](v [+-] u)^2/2g, where the last two terms are the - volume of a prism of water whose section is the area of the jet and - whose length is the head due to the relative velocity. The pressure on - the plane is twice the weight of that prism of water. The work done - when the plane is moving in the same direction as the jet is Pu = - (G/g)[omega](v - u)^2u foot-pounds per second. There issue from the - jet [omega]v cub. ft. per second, and the energy of this quantity - before impact is (G/2g)[omega]v^3. The efficiency of the jet is - therefore [eta] = 2(v - u)^2u/v^3. The value of u which makes this a - maximum is found by differentiating and equating the differential - coefficient to zero:-- - - d[eta]/du = 2(v^2 - 4vu + 3u^2)/v^3 = 0; - - .: u = v or (1/3)v. - - The former gives a minimum, the latter a maximum efficiency. - - Putting u = (1/3)v in the expression above, - - [eta] max. = 8/27. - - (3) If, instead of one plane moving before the jet, a series of planes - are introduced at short intervals at the same point, the quantity of - water impinging on the series will be [omega]v instead of [omega](v - - u), and the whole pressure = (G/g)[omega]v(v - u). The work done is - (G/g)[omega]vu(v - u). The efficiency [eta] = (G/g)[omega]vu(v - u) / - (G/2g)[omega]v^3 = 2u(v - u)/v^2. This becomes a maximum for d[eta]/du - = 2(v - 2u) = 0, or u = (1/2)v, and the [eta] = 1/2. This result is - often used as an approximate expression for the velocity of greatest - efficiency when a jet of water strikes the floats of a water wheel. - The work wasted in this case is half the whole energy of the jet when - the floats run at the best speed. - - S 156. (4) _Case of a Jet impinging on a Concave Cup Vane_, velocity - of water v, velocity of vane in the same direction u (fig. 155), - weight impinging per second = Gw(v - u). - - [Illustration: FIG. 155.] - - If the cup is hemispherical, the water leaves the cup in a direction - parallel to the jet. Its relative velocity is v - u when approaching - the cup, and -(v - u) when leaving it. Hence its absolute velocity - when leaving the cup is u - (v - u) = 2u - v. The change of momentum - per second = (G/g)[omega](v - u) {v - (2u - v)} = 2(G/g)[omega](v - - u)^2. Comparing this with case 2, it is seen that the pressure on a - hemispherical cup is double that on a flat plane. The work done on the - cup = 2(G/g)[omega] (v - u)^2u foot-pounds per second. The efficiency - of the jet is greatest when v = 3u; in that case the efficiency = - {16/27}. - - If a series of cup vanes are introduced in front of the jet, so that - the quantity of water acted upon is [omega]v instead of [omega](v - - u), then the whole pressure on the chain of cups is (G/g)[omega]v{v - - (2u - v)} = 2(G/g)[omega]v(v - u). In this case the efficiency is - greatest when v = 2u, and the maximum efficiency is unity, or all the - energy of the water is expended on the cups. - - [Illustration: FIG. 156.] - - S 157. (5) _Case of a Flat Vane oblique to the Jet_ (fig. 156).--This - case presents some difficulty. The water spreading on the plane in all - directions from the point of impact, different particles leave the - plane with different absolute velocities. Let AB = v = velocity of - water, AC = u = velocity of plane. Then, completing the parallelogram, - AD represents in magnitude and direction the relative velocity of - water and plane. Draw AE normal to the plane and DE parallel to the - plane. Then the relative velocity AD may be regarded as consisting of - two components, one AE normal, the other DE parallel to the plane. On - the assumption that friction is insensible, DE is unaffected by - impact, but AE is destroyed. Hence AE represents the entire change of - velocity due to impact and the direction of that change. The pressure - on the plane is in the direction AE, and its amount is = mass of water - impinging per second X AE. - - Let DAE = [theta], and let AD = v_r. Then AE = v_r cos [theta]; DE = - v_r sin [theta]. If Q is the volume of water impinging on the plane - per second, the change of momentum is (G/g)Qv_r cos [theta]. Let AC = - u = velocity of the plane, and let AC make the angle CAE = [delta] - with the normal to the plane. The velocity of the plane in the - direction AE = u cos [delta]. The work of the jet on the plane = - (G/g)Qv_r cos [theta] u cos [delta]. The same problem may be thus - treated algebraically (fig. 157). Let BAF = [alpha], and CAF = - [delta]. The velocity v of the water may be decomposed into AF = v cos - [alpha] normal to the plane, and FB = v sin [alpha] parallel to the - plane. Similarly the velocity of the plane = u = AC = BD can be - decomposed into BG = FE = u cos [delta] normal to the plane, and DG = - u sin [delta] parallel to the plane. As friction is neglected, the - velocity of the water parallel to the plane is unaffected by the - impact, but its component v cos [alpha] normal to the plane becomes - after impact the same as that of the plane, that is, u cos [delta]. - Hence the change of velocity during impact = AE = v cos [alpha] - u - cos [delta]. The change of momentum per second, and consequently the - normal pressure on the plane is N = (G/g) Q(v cos [alpha] - u cos - [delta]). The pressure in the direction in which the plane is moving - is P = N cos [delta] = (G/g)Q (v cos [alpha] - u cos [delta]) cos - [delta], and the work done on the plane is Pu = (G/g)Q(v cos [alpha] - - u cos [delta]) u cos [delta], which is the same expression as before, - since AE = v_r cos [theta] = v cos [alpha] - u cos [delta]. - - [Illustration: FIG. 157.] - - [Illustration: FIG. 158.] - - In one second the plane moves so that the point A (fig. 158) comes to - C, or from the position shown in full lines to the position shown in - dotted lines. If the plane remained stationary, a length AB = v of the - jet would impinge on the plane, but, since the plane moves in the same - direction as the jet, only the length HB = AB - AH impinges on the - plane. - - But AH = AC cos [delta]/ cos [alpha] = u cos [delta]/ cos [alpha], and - therefore HB = v - u cos [delta]/ cos [alpha]. Let [omega] = sectional - area of jet; volume impinging on plane per second = Q = [omega](v - u - cos [delta]/cos [alpha]) = [omega](v cos [alpha] - u cos [delta])/ cos - [alpha]. Inserting this in the formulae above, we get - - G [omega] - N = --- ----------- (v cos [alpha] - u cos [delta])^2; (1) - g cos [alpha] - - G [omega] cos [delta] - P = --- ------------------- (v cos [alpha] - u cos [delta])^2; (2) - g cos [alpha] - - G cos [delta] - Pu = --- [omega]u ----------- (v cos [alpha] - u cos [delta])^2. (3) - g cos [alpha] - - Three cases may be distinguished:-- - - (a) The plane is at rest. Then u = 0, N = (G/g)[omega]v^2 cos [alpha]; - and the work done on the plane and the efficiency of the jet are zero. - - (b) The plane moves parallel to the jet. Then [delta] = [alpha], and - Pu = (G/g)[omega]u cos^2[alpha](v - u)^2, which is a maximum when u = - 1/3 v. - - When u = 1/3 v then Pu max. = 4/27 (G/g)[omega]v^3 cos^2 [alpha], and - the efficiency = [eta] = 4/9 cos^2 [alpha]. - - (c) The plane moves perpendicularly to the jet. Then [delta] = 90 deg. - - [alpha]; cos [delta] = sin [alpha]; and Pu = G/g [omega]u (sin - [alpha]/cos [alpha]) (v cos [alpha] - u sin [alpha])^2. This is a - maximum when u = 1/3 v cos [alpha]. - - When u = 1/3 v cos [alpha], the maximum work and the efficiency are - the same as in the last case. - - [Illustration: FIG. 159.] - - S 158. _Best Form of Vane to receive Water._--When water impinges - normally or obliquely on a plane, it is scattered in all directions - after impact, and the work carried away by the water is then generally - lost, from the impossibility of dealing afterwards with streams of - water deviated in so many directions. By suitably forming the vane, - however, the water may be entirely deviated in one direction, and the - loss of energy from agitation of the water is entirely avoided. - - Let AB (fig. 159) be a vane, on which a jet of water impinges at the - point A and in the direction AC. Take AC = v = velocity of water, and - let AD represent in magnitude and direction the velocity of the vane. - Completing the parallelogram, DC or AE represents the direction in - which the water is moving relatively to the vane. If the lip of the - vane at A is tangential to AE, the water will not have its direction - suddenly changed when it impinges on the vane, and will therefore have - no tendency to spread laterally. On the contrary it will be so - gradually deviated that it will glide up the vane in the direction AB. - This is sometimes expressed by saying that the vane _receives the - water without shock_. - - [Illustration: FIG. 160.] - - S 159. _Floats of Poncelet Water Wheels._--Let AC (fig. 160) represent - the direction of a thin horizontal stream of water having the velocity - v. Let AB be a curved float moving horizontally with velocity u. The - relative motion of water and float is then initially horizontal, and - equal to v - u. - - In order that the float may receive the water without shock, it is - necessary and sufficient that the lip of the float at A should be - tangential to the direction AC of relative motion. At the end of (v - - u)/g seconds the float moving with the velocity u comes to the - position A1B1, and during this time a particle of water received at A - and gliding up the float with the relative velocity v - u, attains a - height DE = (v - u)^2/2g. At E the water comes to relative rest. It - then descends along the float, and when after 2(v - u)/g seconds the - float has come to A2B2 the water will again have reached the lip at A2 - and will quit it tangentially, that is, in the direction CA2, with a - relative velocity -(v - u) = -[root](2gDE) acquired under the - influence of gravity. The absolute velocity of the water leaving the - float is therefore u - (v - u) = 2u - v. If u = (1/2)v, the water will - drop off the bucket deprived of all energy of motion. The whole of the - work of the jet must therefore have been expended in driving the - float. The water will have been received without shock and discharged - without velocity. This is the principle of the Poncelet wheel, but in - that case the floats move over an arc of a large circle; the stream of - water has considerable thickness (about 8 in.); in order to get the - water into and out of the wheel, it is then necessary that the lip of - the float should make a small angle (about 15 deg.) with the direction - of its motion. The water quits the wheel with a little of its energy - of motion remaining. - - S 160. _Pressure on a Curved Surface when the Water is deviated wholly - in one Direction._--When a jet of water impinges on a curved surface - in such a direction that it is received without shock, the pressure on - the surface is due to its gradual deviation from its first direction. - On any portion of the area the pressure is equal and opposite to the - force required to cause the deviation of so much water as rests on - that surface. In common language, it is equal to the centrifugal force - of that quantity of water. - - [Illustration: FIG. 161.] - - _Case 1. Surface Cylindrical and Stationary._--Let AB (fig. 161) be - the surface, having its axis at O and its radius = r. Let the water - impinge at A tangentially, and quit the surface tangentially at B. - Since the surface is at rest, v is both the absolute velocity of the - water and the velocity relatively to the surface, and this remains - unchanged during contact with the surface, because the deviating force - is at each point perpendicular to the direction of motion. The water - is deviated through an angle BCD = AOB = [phi]. Each particle of water - of weight p exerts radially a centrifugal force pv^2/rg. Let the - thickness of the stream = t ft. Then the weight of water resting on - unit of surface = Gt lb.; and the normal pressure per unit of surface - = n = Gtv^2/gr. The resultant of the radial pressures uniformly - distributed from A to B will be a force acting in the direction OC - bisecting AOB, and its magnitude will equal that of a force of - intensity = n, acting on the projection of AB on a plane perpendicular - to the direction OC. The length of the chord AB = 2r sin (1/2)[phi]; - let b = breadth of the surface perpendicular to the plane of the - figure. The resultant pressure on surface - - [phi] Gt v^2 G [phi] - = R = 2rb sin ----- X --.--- = 2--- btv^2 sin -----, - 2 g r g 2 - - which is independent of the radius of curvature. It may be inferred - that the resultant pressure is the same for any curved surface of the - same projected area, which deviates the water through the same angle. - - _Case 2. Cylindrical Surface moving in the Direction AC with Velocity - u._--The relative velocity = v - u. The final velocity BF (fig. 162) - is found by combining the relative velocity BD = v - u tangential to - the surface with the velocity BE = u of the surface. The intensity of - normal pressure, as in the last case, is (G/g)t(v - u)^2/r. The - resultant normal pressure R = 2(G/g)bt(v - u)^2 sin (1/2)[phi]. This - resultant pressure may be resolved into two components P and L, one - parallel and the other perpendicular to the direction of the vane's - motion. The former is an effort doing work on the vane. The latter is - a lateral force which does no work. - - P = R sin (1/2)[phi] = (G/g) bt (v - u)^2 (1 - cos [phi]); - - L = R cos (1/2)[phi] = (G/g) bt (v - u)^2 sin [phi]. - - [Illustration: FIG. 162.] - - The work done by the jet on the vane is Pu = (G/g)btu(v - u)^2(1 - cos - [phi]), which is a maximum when u = 1/3 v. This result can also be - obtained by considering that the work done on the plane must be equal - to the energy lost by the water, when friction is neglected. - - If [phi] = 180 deg., cos [phi] = -1, 1 - cos [phi] = 2; then P = - 2(G/g)bt(v - u)^2, the same result as for a concave cup. - - [Illustration: FIG. 163.] - - S 161. _Position which a Movable Plane takes in Flowing Water._--When - a rectangular plane, movable about an axis parallel to one of its - sides, is placed in an indefinite current of fluid, it takes a - position such that the resultant of the normal pressures on the two - sides of the axis passes through the axis. If, therefore, planes - pivoted so that the ratio a/b (fig. 163) is varied are placed in - water, and the angle they make with the direction of the stream is - observed, the position of the resultant of the pressures on the plane - is determined for different angular positions. Experiments of this - kind have been made by Hagen. Some of his results are given in the - following table:-- - - +-----------+---------------+--------------------+ - | | Larger plane. | Smaller Plane. | - +-----------+---------------+--------------------+ - | a/b = 1.0 |[phi] = ... |[phi] = 90 deg. | - | 0.9 | 75 deg. | 72(1/2) deg.| - | 0.8 | 60 deg. | 57 deg. | - | 0.7 | 48 deg. | 43 deg. | - | 0.6 | 25 deg. | 29 deg. | - | 0.5 | 13 deg. | 13 deg. | - | 0.4 | 8 deg. | 6(1/2) deg.| - | 0.3 | 6 deg. | .. | - | 0.2 | 4 deg. | .. | - +-----------+-------------+----------------------+ - - S 162. _Direct Action distinguished from Reaction_ (Rankine, _Steam - Engine_, S 147). - - The pressure which a jet exerts on a vane can be distinguished into - two parts, viz.:-- - - (1) The pressure arising from changing the direct component of the - velocity of the water into the velocity of the vane. In fig. 153, S - 154, ab cos bae is the direct component of the water's velocity, or - component in the direction of motion of vane. This is changed into the - velocity ae of the vane. The pressure due to direct impulse is then - - P1 = GQ(ab cos bae - ae)/g. - - For a flat vane moving normally, this direct action is the only action - producing pressure on the vane. - - (2) The term reaction is applied to the additional action due to the - direction and velocity with which the water glances off the vane. It - is this which is diminished by the friction between the water and the - vane. In Case 2, S 160, the direct pressure is - - P1 = Gbt(v - u)^2/g. - - That due to reaction is - - P2 = -Gbt(v - u)^2 cos [phi]/g. - - If [phi] < 90 deg., the direct component of the water's motion is not - wholly converted into the velocity of the vane, and the whole - pressure due to direct impulse is not obtained. If [phi] > 90 deg., - cos [phi] is negative and an additional pressure due to reaction is - obtained. - - [Illustration: FIG. 164.] - - S 163. _Jet Propeller._--In the case of vessels propelled by a jet of - water (fig. 164), driven sternwards from orifices at the side of the - vessel, the water, originally at rest outside the vessel, is drawn - into the ship and caused to move with the forward velocity V of the - ship. Afterwards it is projected sternwards from the jets with a - velocity v relatively to the ship, or v - V relatively to the earth. - If [Omega] is the total sectional area of the jets, [Omega]v is the - quantity of water discharged per second. The momentum generated per - second in a sternward direction is (G/g)[Omega]v(v - V), and this is - equal to the forward acting reaction P which propels the ship. - - The energy carried away by the water - - = (1/2)(G/g)[Omega]v (v - V)^2. (1) - - The useful work done on the ship - - PV = (G/g)[Omega]v (v - V)V. (2) - - Adding (1) and (2), we get the whole work expended on the water, - neglecting friction:-- - - W = (1/2)(G/g)[Omega]v (v^2 - V^2). - - Hence the efficiency of the jet propeller is - - PV/W = 2V/(v + V). (3) - - This increases towards unity as v approaches V. In other words, the - less the velocity of the jets exceeds that of the ship, and therefore - the greater the area of the orifice of discharge, the greater is the - efficiency of the propeller. - - In the "Waterwitch" v was about twice V. Hence in this case the - theoretical efficiency of the propeller, friction neglected, was about - 2/3. - - [Illustration: FIG. 165.] - - S 164. _Pressure of a Steady Stream in a Uniform Pipe on a Plane - normal to the Direction of Motion._--Let CD (fig. 165) be a plane - placed normally to the stream which, for simplicity, may be supposed - to flow horizontally. The fluid filaments are deviated in front of the - plane, form a contraction at A1A1, and converge again, leaving a mass - of eddying water behind the plane. Suppose the section A0A0 taken at a - point where the parallel motion has not begun to be disturbed, and - A2A2 where the parallel motion is re-established. Then since the same - quantity of water with the same velocity passes A0A0, A2A2 in any - given time, the external forces produce no change of momentum on the - mass A0A0A2A2, and must therefore be in equilibrium. If [Omega] is the - section of the stream at A0A0 or A2A2, and [omega] the area of the - plate CD, the area of the contracted section of the stream at A1A1 - will be c_c([Omega] - [omega]), where c_c is the coefficient of - contraction. Hence, if v is the velocity at A0A0 or A2A2, and v1 the - velocity at A1A1, - - v[Omega] = c_c v([Omega] - [omega]); - - .:v1 = v[Omega]/c_c ([Omega] - [omega]). (1) - - Let p0, p1, p2 be the pressures at the three sections. Applying - Bernoulli's theorem to the sections A0A0 and A1A1, - - p0 v^2 p1 v1^2 - -- + --- = -- + ----. - G 2g G 2g - - Also, for the sections A1A1 and A2A2, allowing that the head due to - the relative velocity v1 - v is lost in shock:-- - - p1 v1^2 p2 v^2 (v1 - v)^2 - -- + ---- = -- + --- + ----------; - G 2g G 2g 2g - - .: p0 - p2 = G(v1 - v)^2/2g; (2) - - or, introducing the value in (1), - - G / [Omega] \^2 - p0 - p2 = -- ( ----------------------- - 1 ) v^2 (3) - 2g \c_c ([Omega] - [omega]) / - - Now the external forces in the direction of motion acting on the mass - A0A0A2A2 are the pressures p0[Omega]1 - p2[Omega] at the ends, and the - reaction -R of the plane on the water, which is equal and opposite to - the pressure of the water on the plane. As these are in equilibrium, - - (p0 - p2)[Omega] - R = 0; - - / [Omega] \^2 v^2 - .: R = G[Omega] ( ----------------------- - 1 ) ---; (4) - \c_c ([Omega] - [omega]) / 2g - - an expression like that for the pressure of an isolated jet on an - indefinitely extended plane, with the addition of the term in - brackets, which depends only on the areas of the stream and the plane. - For a given plane the expression in brackets diminishes as [Omega] - increases. If [Omega]/[omega] = [rho], the equation (4) becomes - _ _ - v^2 | / [rho] \^2 | - R = G[omega] --- |[rho] ( --------------- - 1 ) |, (4a) - 2g |_ \c_c ([rho] - 1) / _| - - which is of the form - - R = G[omega](v^2/2g)K, - - where K depends only on the ratio of the sections of the stream and - plane. - - For example, let c_c = 0.85, a value which is probable, if we allow - that the sides of the pipe act as internal borders to an orifice. Then - - / [rho] \^2 - K = [rho] ( 1.176 --------- - 1 ). - \ [rho] - 1 / - - [rho] = K = - - 1 [infinity] - 2 3.66 - 3 1.75 - 4 1.29 - 5 1.10 - 10 .94 - 50 2.00 - 100 3.50 - - The assumption that the coefficient of contraction c_c is constant for - different values of [rho] is probably only true when [rho] is not very - large. Further, the increase of K for large values of [rho] is - contrary to experience, and hence it may be inferred that the - assumption that all the filaments have a common velocity v1 at the - section A1A1 and a common velocity v at the section A2A2 is not true - when the stream is very much larger than the plane. Hence, in the - expression - - R = KG[omega]v^2/2g, - - K must be determined by experiment in each special case. For a - cylindrical body putting [omega] for the section, c_c for the - coefficient of contraction, c_c([Omega] - [omega]) for the area of the - stream at A1A1, - - v1 = v[Omega]/c_c([Omega] - [omega]); v2 = v[Omega]/([Omega] - [omega]); - - or, putting [rho] = [Omega]/[omega], - - v1 = v[rho]/c_c ([rho] - 1), v2 = v[rho]/([rho] - 1). - - Then - - R = K1G[omega]v^2/2g, - - where - - _ _ - | / [rho] \^2 / 1 \^2 / [rho] \^2 | - K1 = [rho] | ( --------- ) ( --- - 1 ) ( --------- - 1 ) |. - |_ \[rho] - 1/ \c_c / \[rho] - 1 / _| - - Taking c_c = 0.85 and [rho] = 4, K1 = 0.467, a value less than before. - Hence there is less pressure on the cylinder than on the thin plane. - - [Illustration: FIG. 166.] - - S 165. _Distribution of Pressure on a Surface on which a Jet impinges - normally._--The principle of momentum gives readily enough the total - or resultant pressure of a jet impinging on a plane surface, but in - some cases it is useful to know the distribution of the pressure. The - problem in the case in which the plane is struck normally, and the jet - spreads in all directions, is one of great complexity, but even in - that case the maximum intensity of the pressure is easily assigned. - Each layer of water flowing from an orifice is gradually deviated - (fig. 166) by contact with the surface, and during deviation exercises - a centrifugal pressure towards the axis of the jet. The force exerted - by each small mass of water is normal to its path and inversely as the - radius of curvature of the path. Hence the greatest pressure on the - plane must be at the axis of the jet, and the pressure must decrease - from the axis outwards, in some such way as is shown by the curve of - pressure in fig. 167, the branches of the curve being probably - asymptotic to the plane. - - For simplicity suppose the jet is a vertical one. Let h1 (fig. 167) be - the depth of the orifice from the free surface, and v1 the velocity of - discharge. Then, if [omega] is the area of the orifice, the quantity - of water impinging on the plane is obviously - - Q = [omega]v1 = [omega] [root](2gh1); - - that is, supposing the orifice rounded, and neglecting the coefficient - of discharge. - - The velocity with which the fluid reaches the plane is, however, - greater than this, and may reach the value - - v = [root](2gh); - - where h is the depth of the plane below the free surface. The external - layers of fluid subjected throughout, after leaving the orifice, to - the atmospheric pressure will attain the velocity v, and will flow - away with this velocity unchanged except by friction. The layers - towards the interior of the jet, being subjected to a pressure greater - than atmospheric pressure, will attain a less velocity, and so much - less as they are nearer the centre of the jet. But the pressure can - in no case exceed the pressure v^2/2g or h measured in feet of water, - or the direction of motion of the water would be reversed, and there - would be reflux. Hence the maximum intensity of the pressure of the - jet on the plane is h ft. of water. If the pressure curve is drawn - with pressures represented by feet of water, it will touch the free - water surface at the centre of the jet. - - [Illustration: FIG. 167.] - - Suppose the pressure curve rotated so as to form a solid of - revolution. The weight of water contained in that solid is the total - pressure of the jet on the surface, which has already been determined. - Let V = volume of this solid, then GV is its weight in pounds. - Consequently - - GV = (G/g)[omega]v1v; - - V = 2[omega] [root](hh1). - - We have already, therefore, two conditions to be satisfied by the - pressure curve. - - [Illustration: FIG. 168.--Curves of Pressure of Jets impinging - normally on a Plane.] - - Some very interesting experiments on the distribution of pressure on a - surface struck by a jet have been made by J. S. Beresford (_Prof. - Papers on Indian Engineering_, No. cccxxii.), with a view to afford - information as to the forces acting on the aprons of weirs. - Cylindrical jets 1/2 in. to 2 in. diameter, issuing from a vessel in - which the water level was constant, were allowed to fall vertically on - a brass plate 9 in. in diameter. A small hole in the brass plate - communicated by a flexible tube with a vertical pressure column. - Arrangements were made by which this aperture could be moved 1/20 - in. at a time across the area struck by the jet. The height of the - pressure column, for each position of the aperture, gave the pressure - at that point of the area struck by the jet. When the aperture was - exactly in the axis of the jet, the pressure column was very nearly - level with the free surface in the reservoir supplying the jet; that - is, the pressure was very nearly v^2/2g. As the aperture moved away - from the axis of the jet, the pressure diminished, and it became - insensibly small at a distance from the axis of the jet about equal to - the diameter of the jet. Hence, roughly, the pressure due to the jet - extends over an area about four times the area of section of the jet. - - Fig. 168 shows the pressure curves obtained in three experiments with - three jets of the sizes shown, and with the free surface level in the - reservoir at the heights marked. - - +------------------------------------------------------+ - | Experiment 1. Jet .475 in. diameter. | - +----------------+------------------+------------------+ - | Height from | Distance from | | - | Free Surface | Axis of Jet | Pressure in. | - | to Brass Plate | in inches. | inches of Water. | - | in inches. | | | - +----------------+------------------+------------------+ - | 43 | 0 | 40.5 | - | " | .05 | 39.40 | - | " | .1 | 37.5-39.5 | - | " | .15 | 35 | - | " | .2 | 33.5-37 | - | " | .25 | 31 | - | " | .3 | 21-27 | - | " | .35 | 21 | - | " | .4 | 14 | - | " | .45 | 8 | - | " | .5 | 3.5 | - | " | .55 | 1 | - | " | .6 | 0.5 | - | " | .65 | 0 | - +----------------+------------------+------------------+ - | Experiment 2. Jet .988 in. diameter. | - +----------------+------------------+------------------+ - | 42.15 | 0 | 42 | - | " | .05 | 41.9 | - | " | .1 | 41.5-41.8 | - | " | .15 | 41 | - | " | .2 | 40.3 | - | " | .25 | 39.2 | - | " | .3 | 37.5 | - | " | .35 | 34.8 | - | " | .45 | 27 | - | 42.25 | .5 | 23 | - | " | .55 | 18.5 | - | " | .6 | 13 | - | " | .65 | 8.3 | - | " | .7 | 5 | - | " | .75 | 3 | - | " | .8 | 2.2 | - | 42.15 | .85 | 1.6 | - | " | .95 | 1 | - +----------------+------------------+------------------+ - | Experiment 3. Jet 19.5 in. diameter. | - +----------------+------------------+------------------+ - | 27.15 | 0 | 26.9 | - | " | .08 | 26.9 | - | " | .13 | 26.8 | - | " | .18 | 26.5-26.6 | - | " | .23 | 26.4-26.5 | - | " | .28 | 26.3-26.6 | - | 27 | .33 | 26.2 | - | " | .38 | 25.9 | - | " | .43 | 25.5 | - | " | .48 | 25 | - | " | .53 | 24.5 | - | " | .58 | 24 | - | " | .63 | 23.3 | - | " | .68 | 22.5 | - | " | .73 | 21.8 | - | " | .78 | 21 | - | " | .83 | 20.3 | - | " | .88 | 19.3 | - | " | .93 | 18 | - | " | .98 | 17 | - | 26.5 | 1.13 | 13.5 | - | " | 1.18 | 12.5 | - | " | 1.23 | 10.8 | - | " | 1.28 | 9.5 | - | " | 1.33 | 8 | - | " | 1.38 | 7 | - | " | 1.43 | 6.3 | - | " | 1.48 | 5 | - | " | 1.53 | 4.3 | - | " | 1.58 | 3.5 | - | " | 1.9 | 2 | - +----------------+------------------+------------------+ - - As the general form of the pressure curve has been already indicated, - it may be assumed that its equation is of the form - - y = ab^(-x^2). - - But it has already been shown that for x = 0, y = h, hence a = h. To - determine the remaining constant, the other condition may be used, - that the solid formed by rotating the pressure curve represents the - total pressure on the plane. The volume of the solid is - _ - /[oo] - V = | 2[pi]xy dx - _/0 - _ - /[oo] - = 2[pi]h | b^(-x^2)x dx - _/0 - _ _ - | |[oo] - = ([pi]h/log_eb) |-b^(-x^2)| - |_ _|0 - - = [pi]h/log_e b. - - Using the condition already stated, - - 2[omega] [root](hh1) = [pi]h/log_e b, - - log_e b = ([pi]/2[omega]) [root](h/h1). - - Putting the value of b in (2) in eq. (1), and also r for the radius of - the jet at the orifice, so that [omega] = [pi]r^2, the equation to the - pressure curve is - - h x^2 - y = h[epsilon]^(-1/2) [root]-- ---. - h1 r^2 - - S 166. _Resistance of a Plane moving through a Fluid, or Pressure of a - Current on a Plane._--When a thin plate moves through the air, or - through an indefinitely large mass of still water, in a direction - normal to its surface, there is an excess of pressure on the anterior - face and a diminution of pressure on the posterior face. Let v be the - relative velocity of the plate and fluid, [Omega] the area of the - plate, G the density of the fluid, h the height due to the velocity, - then the total resistance is expressed by the equation - - R = fG[Omega]v^2/2g pounds = fG[Omega]h; - - where f is a coefficient having about the value 1.3 for a plate moving - in still fluid, and 1.8 for a current impinging on a fixed plane, - whether the fluid is air or water. The difference in the value of the - coefficient in the two cases is perhaps due to errors of experiment. - There is a similar resistance to motion in the case of all bodies of " - _unfair_ " form, that is, in which the surfaces over which the water - slides are not of gradual and continuous curvature. - - The stress between the fluid and plate arises chiefly in this way. - The streams of fluid deviated in front of the plate, supposed for - definiteness to be moving through the fluid, receive from it forward - momentum. Portions of this forward moving water are thrown off - laterally at the edges of the plate, and diffused through the - surrounding fluid, instead of falling to their original position - behind the plate. Other portions of comparatively still water are - dragged into motion to fill the space left behind the plate; and there - is thus a pressure less than hydrostatic pressure at the back of the - plate. The whole resistance to the motion of the plate is the sum of - the excess of pressure in front and deficiency of pressure behind. - This resistance is independent of any friction or viscosity in the - fluid, and is due simply to its inertia resisting a sudden change of - direction at the edge of the plate. - - Experiments made by a whirling machine, in which the plate is fixed on - a long arm and moved circularly, gave the following values of the - coefficient _f_. The method is not free from objection, as the - centrifugal force causes a flow outwards across the plate. - - +---------------+------------------------+ - | Approximate | Values of f. | - | Area of Plate +------+-------+---------+ - | in sq. ft. |Borda.|Hutton.|Thibault.| - +---------------+------+-------+---------+ - | 0.13 | 1.39 | 1.24 | .. | - | 0.25 | 1.49 | 1.43 | 1.525 | - | 0.63 | 1.64 | .. | .. | - | 1.11 | .. | .. | 1.784 | - +---------------+------+-------+---------+ - - There is a steady increase of resistance with the size of the plate, - in part or wholly due to centrifugal action. - - P. L. G. Dubuat (1734-1809) made experiments on a plane 1 ft. square, - moved in a straight line in water at 3 to 6(1/2) ft. per second. - Calling m the coefficient of excess of pressure in front, and n the - coefficient of deficiency of pressure behind, so that f = m + n, he - found the following values:-- - - m = 1; n = 0.433; f = 1.433. - - The pressures were measured by pressure columns. Experiments by A. J. - Morin (1795-1880), G. Piobert (1793-1871) and I. Didion (1798-1878) on - plates of 0.3 to 2.7 sq. ft. area, drawn vertically through water, - gave f = 2.18; but the experiments were made in a reservoir of - comparatively small depth. For similar plates moved through air they - found f = 1.36, a result more in accordance with those which precede. - - For a fixed plane in a moving current of water E. Mariotte found f = - 1.25. Dubuat, in experiments in a current of water like those - mentioned above, obtained the values m = 1.186; n = 0.670; f = 1.856. - Thibault exposed to wind pressure planes of 1.17 and 2.5 sq. ft. area, - and found f to vary from 1.568 to 2.125, the mean value being f = - 1.834, a result agreeing well with Dubuat. - - [Illustration: FIG. 169.] - - S 167. _Stanton's Experiments on the Pressure of Air on Surfaces._--At - the National Physical Laboratory, London, T. E. Stanton carried out a - series of experiments on the distribution of pressure on surfaces in a - current of air passing through an air trunk. These were on a small - scale but with exceptionally accurate means of measurement. These - experiments differ from those already given in that the plane is small - relatively to the cross section of the current (_Proc. Inst. Civ. - Eng._ clvi., 1904). Fig. 169 shows the distribution of pressure on a - square plate. ab is the plate in vertical section. acb the - distribution of pressure on the windward and adb that on the leeward - side of the central section. Similarly aeb is the distribution of - pressure on the windward and afb on the leeward side of a diagonal - section. The intensity of pressure at the centre of the plate on the - windward side was in all cases p = Gv^2/2g lb. per sq. ft., where G is - the weight of a cubic foot of air and v the velocity of the current in - ft. per sec. On the leeward side the negative pressure is uniform - except near the edges, and its value depends on the form of the plate. - For a circular plate the pressure on the leeward side was 0.48 Gv^2/2g - and for a rectangular plate 0.66 Gv^2/2g. For circular or square plates - the resultant pressure on the plate was P = 0.00126 v^2 lb. per sq. ft. - where v is the velocity of the current in ft. per sec. On a long - narrow rectangular plate the resultant pressure was nearly 60% greater - than on a circular plate. In later tests on larger planes in free air, - Stanton found resistances 18% greater than those observed with small - planes in the air trunk. - - S 168. _Case when the Direction of Motion is oblique to the - Plane._--The determination of the pressure between a fluid and surface - in this case is of importance in many practical questions, for - instance, in assigning the load due to wind pressure on sloping and - curved roofs, and experiments have been made by Hutton, Vince, and - Thibault on planes moved circularly through air and water on a - whirling machine. - - [Illustration: FIG. 170.] - - Let AB (fig. 170) be a plane moving in the direction R making an angle - [phi] with the plane. The resultant pressure between the fluid and the - plane will be a normal pressure N. The component R of this normal - pressure is the resistance to the motion of the plane and the other - component L is a lateral force resisted by the guides which support - the plane. Obviously - - R = N sin [phi]; - - L = N cos [phi]. - - In the case of wind pressure on a sloping roof surface, R is the - horizontal and L the vertical component of the normal pressure. - - In experiments with the whirling machine it is the resistance to - motion, R, which is directly measured. Let P be the pressure on a - plane moved normally through a fluid. Then, for the same plane - inclined at an angle [phi] to its direction of motion, the resistance - was found by Hutton to be - - R = P(sin [phi])^{1.842 cos [phi]}. - - A simpler and more convenient expression given by Colonel Duchemin is - - R = 2P sin^2 [phi]/(1 + sin^2 [phi]). - - Consequently, the total pressure between the fluid and plane is - - N = 2P sin [phi]/(1 + sin^2 [phi]) = 2P/(cosec [phi] + sin [phi]), - - and the lateral force is - - L = 2P sin [phi] cos [phi]/(1 + sin^2 [phi]). - - In 1872 some experiments were made for the Aeronautical Society on the - pressure of air on oblique planes. These plates, of 1 to 2 ft. square, - were balanced by ingenious mechanism designed by F. H. Wenham and - Spencer Browning, in such a manner that both the pressure in the - direction of the air current and the lateral force were separately - measured. These planes were placed opposite a blast from a fan issuing - from a wooden pipe 18 in. square. The pressure of the blast varied - from 6/10 to 1 in. of water pressure. The following are the results - given in pounds per square foot of the plane, and a comparison of the - experimental results with the pressures given by Duchemin's rule. - These last values are obtained by taking P = 3.31, the observed - pressure on a normal surface:-- - - +-----------------------------------+-------+-------+-------+------+ - | Angle between Plane and Direction | 15 | 20 | 60 | 90 | - | of Blast | deg. | deg. | deg. | deg. | - +-----------------------------------+-------+-------+-------+------+ - | Horizontal pressure R | 0.4 | 0.61 | 2.73 | 3.31 | - | Lateral pressure L | 1.6 | 1.96 | 1.26 | .. | - | Normal pressure [root](L^2 + R^2) | 1.65 | 2.05 | 3.01 | 3.31 | - | Normal pressure by Duchemin's rule| 1.605 | 2.027 | 3.276 | 3.31 | - +-----------------------------------+-------+-------+-------+------+ - - -WATER MOTORS - -In every system of machinery deriving energy from a natural waterfall -there exist the following parts:-- - -1. A supply channel or head race, leading the water from the highest -accessible level to the site of the machine. This may be an open channel -of earth, masonry or wood, laid at as small a slope as is consistent -with the delivery of the necessary supply of water, or it may be a -closed cast or wrought-iron pipe, laid at the natural slope of the -ground, and about 3 ft. below the surface. In some cases part of the -head race is an open channel, part a closed pipe. The channel often -starts from a small storage reservoir, constructed near the stream -supplying the water motor, in which the water accumulates when the motor -is not working. There are sluices or penstocks by which the supply can -be cut off when necessary. - -2. Leading from the motor there is a tail race, culvert, or discharge -pipe delivering the water after it has done its work at the lowest -convenient level. - -3. A waste channel, weir, or bye-wash is placed at the origin of the -head race, by which surplus water, in floods, escapes. - -4. The motor itself, of one of the kinds to be described presently, -which either overcomes a useful resistance directly, as in the case of a -ram acting on a lift or crane chain, or indirectly by actuating -transmissive machinery, as when a turbine drives the shafting, belting -and gearing of a mill. With the motor is usually combined regulating -machinery for adjusting the power and speed to the work done. This may -be controlled in some cases by automatic governing machinery. - -S 169. _Water Motors with Artificial Sources of Energy._--The great -convenience and simplicity of water motors has led to their adoption in -certain cases, where no natural source of water power is available. In -these cases, an artificial source of water power is created by using a -steam-engine to pump water to a reservoir at a great elevation, or to -pump water into a closed reservoir in which there is great pressure. The -water flowing from the reservoir through hydraulic engines gives back -the energy expended, less so much as has been wasted by friction. Such -arrangements are most useful where a continuously acting steam engine -stores up energy by pumping the water, while the work done by the -hydraulic engines is done intermittently. - - S 170. _Energy of a Water-fall._--Let H_t be the total fall of level - from the point where the water is taken from a natural stream to the - point where it is discharged into it again. Of this total fall a - portion, which can be estimated independently, is expended in - overcoming the resistances of the head and tail races or the supply - and discharge pipes. Let this portion of head wasted be [h]_r. Then - the available head to work the motor is H = H_t - [h]_r. It is this - available head which should be used in all calculations of the - proportions of the motor. Let Q be the supply of water per second. - Then GQH foot-pounds per second is the gross available work of the - fall. The power of the fall may be utilized in three ways. (a) The GQ - pounds of water may be placed on a machine at the highest level, and - descending in contact with it a distance of H ft., the work done will - be (neglecting losses from friction or leakage) GQH foot-pounds per - second. (b) Or the water may descend in a closed pipe from the higher - to the lower level, in which case, with the same reservation as - before, the pressure at the foot of the pipe will be p = GH pounds per - square foot. If the water with this pressure acts on a movable piston - like that of a steam engine, it will drive the piston so that the - volume described is Q cubic feet per second. Then the work done will - be pQ = GHQ foot-pounds per second as before. (c) Or lastly, the water - may be allowed to acquire the velocity v = [root](2gH) by its descent. - The kinetic energy of Q cubic feet will then be (1/2)GQv^2/g = GQH, - and if the water is allowed to impinge on surfaces suitably curved - which bring it finally to rest, it will impart to these the same - energy as in the previous cases. Motors which receive energy mainly in - the three ways described in (a), (b), (c) may be termed gravity, - pressure and inertia motors respectively. Generally, if Q ft. per - second of water act by weight through a distance h1, at a pressure p - due to h2 ft. of fall, and with a velocity v due to h3 ft. of fall, so - that h1 + h2 + h3 = H, then, apart from energy wasted by friction or - leakage or imperfection of the machine, the work done will be - - GQh1 + pQ + (G/g) Q (v^2/2g) = GQH foot pounds, - - the same as if the water acted simply by its weight while descending H - ft. - -S 171. _Site for Water Motor._--Wherever a stream flows from a higher to -a lower level it is possible to erect a water motor. The amount of power -obtainable depends on the available head and the supply of water. In -choosing a site the engineer will select a portion of the stream where -there is an abrupt natural fall, or at least a considerable slope of the -bed. He will have regard to the facility of constructing the channels -which are to convey the water, and will take advantage of any bend in -the river which enables him to shorten them. He will have accurate -measurements made of the quantity of water flowing in the stream, and he -will endeavour to ascertain the average quantity available throughout -the year, the minimum quantity in dry seasons, and the maximum for which -bye-wash channels must be provided. In many cases the natural fall can -be increased by a dam or weir thrown across the stream. The engineer -will also examine to what extent the head will vary in different -seasons, and whether it is necessary to sacrifice part of the fall and -give a steep slope to the tail race to prevent the motor being drowned -by backwater in floods. Streams fed from lakes which form natural -reservoirs or fed from glaciers are less variable than streams depending -directly on rainfall, and are therefore advantageous for water-power -purposes. - - S 172. _Water Power at Holyoke, U.S.A._--About 85 m. from the mouth of - the Connecticut river there was a fall of about 60 ft. in a short - distance, forming what were called the Grand Rapids, below which the - river turned sharply, forming a kind of peninsula on which the city of - Holyoke is built. In 1845 the magnitude of the water-power available - attracted attention, and it was decided to build a dam across the - river. The ordinary flow of the river is 6000 cub. ft. per sec., - giving a gross power of 30,000 h.p. In dry seasons the power is 20,000 - h.p., or occasionally less. From above the dam a system of canals - takes the water to mills on three levels. The first canal starts with - a width of 140 ft. and depth of 22 ft., and supplies the highest - range of mills. A second canal takes the water which has driven - turbines in the highest mills and supplies it to a second series of - mills. There is a third canal on a still lower level supplying the - lowest mills. The water then finds its way back to the river. With the - grant of a mill site is also leased the right to use the water-power. - A mill-power is defined as 38 cub. ft. of water per sec. during 16 - hours per day on a fall of 20 ft. This gives about 60 h.p. effective. - The charge for the power water is at the rate of 20s. per h.p. per - annum. - -S 173. _Action of Water in a Water Motor._--Water motors may be divided -into water-pressure engines, water-wheels and turbines. - -Water-pressure engines are machines with a cylinder and piston or ram, -in principle identical with the corresponding part of a steam-engine. -The water is alternately admitted to and discharged from the cylinder, -causing a reciprocating action of the piston or plunger. It is admitted -at a high pressure and discharged at a low one, and consequently work is -done on the piston. The water in these machines never acquires a high -velocity, and for the most part the kinetic energy of the water is -wasted. The useful work is due to the difference of the pressure of -admission and discharge, whether that pressure is due to the weight of a -column of water of more or less considerable height, or is artificially -produced in ways to be described presently. - -Water-wheels are large vertical wheels driven by water falling from a -higher to a lower level. In most water-wheels, the water acts directly -by its weight loading one side of the wheel and so causing rotation. But -in all water-wheels a portion, and in some a considerable portion, of -the work due to gravity is first employed to generate kinetic energy in -the water; during its action on the water-wheel the velocity of the -water diminishes, and the wheel is therefore in part driven by the -impulse due to the change of the water's momentum. Water-wheels are -therefore motors on which the water acts, partly by weight, partly by -impulse. - -Turbines are wheels, generally of small size compared with water wheels, -driven chiefly by the impulse of the water. Before entering the moving -part of the turbine, the water is allowed to acquire a considerable -velocity; during its action on the turbine this velocity is diminished, -and the impulse due to the change of momentum drives the turbine. - -In designing or selecting a water motor it is not sufficient to consider -only its efficiency in normal conditions of working. It is generally -quite as important to know how it will act with a scanty water supply or -a diminished head. The greatest difference in water motors is in their -adaptability to varying conditions of working. - - -_Water-pressure Engines._ - -S 174. In these the water acts by pressure either due to the height of -the column in a supply pipe descending from a high-level reservoir, or -created by pumping. Pressure engines were first used in mine-pumping on -waterfalls of greater height than could at that time be utilized by -water wheels. Usually they were single acting, the water-pressure -lifting the heavy pump rods which then made the return or pumping stroke -by their own weight. To avoid losses by fluid friction and shock the -velocity of the water in the pipes and passages was restricted to from 3 -to 10 ft. per second, and the mean speed of plunger to 1 ft. per second. -The stroke was long and the number of strokes 3 to 6 per minute. The -pumping lift being constant, such engines worked practically always at -full load, and the efficiency was high, about 84%. But they were -cumbrous machines. They are described in Weisbach's _Mechanics of -Engineering_. - -The convenience of distributing energy from a central station to -scattered working-points by pressure water conveyed in pipes--a system -invented by Lord Armstrong--has already been mentioned. This system has -led to the development of a great variety of hydraulic pressure engines -of very various types. The cost of pumping the pressure water to some -extent restricts its use to intermittent operations, such as working -lifts and cranes, punching, shearing and riveting machines, forging and -flanging presses. To keep down the cost of the distributing mains -very high pressures are adopted, generally 700 lb. per sq. in. or 1600 -ft. of head or more. - -In a large number of hydraulic machines worked by water at high -pressure, especially lifting machines, the motor consists of a direct, -single acting ram and cylinder. In a few cases double-acting pistons and -cylinders are used; but they involve a water-tight packing of the piston -not easily accessible. In some cases pressure engines are used to obtain -rotative movement, and then two double-acting cylinders or three -single-acting cylinders are used, driving a crank shaft. Some -double-acting cylinders have a piston rod half the area of the piston. -The pressure water acts continuously on the annular area in front of the -piston. During the forward stroke the pressure on the front of the -piston balances half the pressure on the back. During the return stroke -the pressure on the front is unopposed. The water in front of the piston -is not exhausted, but returns to the supply pipe. As the frictional -losses in a fluid are independent of the pressure, and the work done -increases directly as the pressure, the percentage loss decreases for -given velocities of flow as the pressure increases. Hence for -high-pressure machines somewhat greater velocities are permitted in the -passages than for low-pressure machines. In supply mains the velocity is -from 3 to 6 ft. per second, in valve passages 5 to 10 ft. per second, or -in extreme cases 20 ft. per second, where there is less object in -economizing energy. As the water is incompressible, slide valves must -have neither lap nor lead, and piston valves are preferable to ordinary -slide valves. To prevent injurious compression from exhaust valves -closing too soon in rotative engines with a fixed stroke, small -self-acting relief valves are fitted to the cylinder ends, opening -outwards against the pressure into the valve chest. Imprisoned water can -then escape without over-straining the machines. - -In direct single-acting lift machines, in which the stroke is fixed, and -in rotative machines at constant speed it is obvious that the cylinder -must be filled at each stroke irrespective of the amount of work to be -done. The same amount of water is used whether much or little work is -done, or whether great or small weights are lifted. Hence while pressure -engines are very efficient at full load, their efficiency decreases as -the load decreases. Various arrangements have been adopted to diminish -this defect in engines working with a variable load. In lifting -machinery there is sometimes a double ram, a hollow ram enclosing a -solid ram. By simple arrangements the solid ram only is used for small -loads, but for large loads the hollow ram is locked to the solid ram, -and the two act as a ram of larger area. In rotative engines the case is -more difficult. In Hastie's and Rigg's engines the stroke is -automatically varied with the load, increasing when the load is large -and decreasing when it is small. But such engines are complicated and -have not achieved much success. Where pressure engines are used -simplicity is generally a first consideration, and economy is of less -importance. - - S 175. _Efficiency of Pressure Engines._--It is hardly possible to - form a theoretical expression for the efficiency of pressure engines, - but some general considerations are useful. Consider the case of a - long stroke hydraulic ram, which has a fairly constant velocity v - during the stroke, and valves which are fairly wide open during most - of the stroke. Let r be the ratio of area of ram to area of valve - passage, a ratio which may vary in ordinary cases from 4 to 12. Then - the loss in shock of the water entering the cylinder will be (r - - 1)^2v^2/2g in ft. of head. The friction in the supply pipe is also - proportional to v^2. The energy carried away in exhaust will be - proportional to v^2. Hence the total hydraulic losses may be taken to - be approximately [zeta]v^2/2g ft., where [zeta] is a coefficient - depending on the proportions of the machine. Let f be the friction of - the ram packing and mechanism reckoned in lb. per sq. ft. of ram area. - Then if the supply-pipe pressure driving the machine is p lb. per sq. - ft., the effective working pressure will be - - p - G[zeta]v^2/2g - f lb. per sq. ft. - - Let A be the area of the ram in sq. ft., v its velocity in ft. per - sec. The useful work done will be - - (p - G[zeta]v^2/2g - f)Av ft. lb. per sec., - - and the efficiency of the machine will be - - [eta] = (p - G[zeta]v^2/2g - f)/p. - - This shows that the efficiency increases with the pressure p, and - diminishes with the speed v, other things being the same. If in - regulating the engine for varying load the pressure is throttled, - part of the available head is destroyed at the throttle valve, and p - in the bracket above is reduced. Direct-acting hydraulic lifts, - without intermediate gearing, may have an efficiency of 95% during the - working stroke. If a hydraulic jigger is used with ropes and sheaves - to change the speed of the ram to the speed of the lift, the - efficiency may be only 50%. E. B. Ellington has given the efficiency - of lifts with hydraulic balance at 85% during the working stroke. - Large pressure engines have an efficiency of 85%, but small rotative - engines probably not more than 50% and that only when fully loaded. - -[Illustration: FIG. 171.] - -S 176. _Direct-Acting Hydraulic Lift_ (fig. 171).--This is the simplest -of all kinds of hydraulic motor. A cage W is lifted directly by water -pressure acting in a cylinder C, the length of which is a little greater -than the lift. A ram or plunger R of the same length is attached to the -cage. The water-pressure admitted by a cock to the cylinder forces up -the ram, and when the supply valve is closed and the discharge valve -opened, the ram descends. In this case the ram is 9 in. diameter, with a -stroke of 49 ft. It consists of lengths of wrought-iron pipe screwed -together perfectly water-tight, the lower end being closed by a -cast-iron plug. The ram works in a cylinder 11 in. diameter of 9 ft. -lengths of flanged cast-iron pipe. The ram passes water-tight through -the cylinder cover, which is provided with double hat leathers to -prevent leakage outwards or inwards. As the weight of the ram and cage -is much more than sufficient to cause a descent of the cage, part of the -weight is balanced. A chain attached to the cage passes over a pulley at -the top of the lift, and carries at its free end a balance weight B, -working in T iron guides. Water is admitted to the cylinder from a 4-in. -supply pipe through a two-way slide, worked by a rack, spindle and -endless rope. The lift works under 73 ft. of head, and lifts 1350 lb at -2 ft. per second. The efficiency is from 75 to 80%. - - The principal prejudicial resistance to the motion of a ram of this - kind is the friction of the cup leathers, which make the joint between - the cylinder and ram. Some experiments by John Hick give for the - friction of these leathers the following formula. Let F = the total - friction in pounds; d = diameter of ram in ft.; p = water-pressure in - pounds per sq. ft.; k a coefficient. - - F = k p d - - k = 0.00393 if the leathers are new or badly lubricated; - = 0.00262 if the leathers are in good condition and well lubricated. - - Since the total pressure on the ram is P = (1/4)[pi]d^2p, the fraction - of the total pressure expended in overcoming the friction of the - leathers is F/P = .005/d to .0033/d, d being in feet. - - Let H be the height of the pressure column measured from the free - surface of the supply reservoir to the bottom of the ram in its lowest - position, H_b the height from the discharge reservoir to the same - point, h the height of the ram above its lowest point at any moment, S - the length of stroke, [Omega] the area of the ram, W the weight of - cage, R the weight of ram, B the weight of balance weight, w the - weight of balance chain per foot run, F the friction of the cup - leather and slides. Then, neglecting fluid friction, if the ram is - rising the accelerating force is - - P1 = G(H - h)[Omega] - R - W + B - w(S - h) + wh - F, - - and if the ram is descending - - P2 = G(H_b - h)[Omega] + W + R - B + w(S - h) - wh - F. - - If w = 1/2 G[Omega], P1 and P2 are constant throughout the stroke; and - the moving force in ascending and descending is the same, if - - B = W + R + wS - G[Omega](H - H_b)/2. - - Using the values just found for w and B, - - P1 = P2 = (1/2)G[Omega](H - H_b) - F. - - Let W + R + wS + B = U, and let P be the constant accelerating force - acting on the system, then the acceleration is (P/U)g. The velocity at - the end of the stroke is (assuming the friction to be constant) - - v = [root](2PgS/U); - - and the mean velocity of ascent is (1/2)v. - -[Illustration: FIG. 172.] - -S 177. _Armstrong's Hydraulic Jigger._--This is simply a single-acting -hydraulic cylinder and ram, provided with sheaves so as to give motion -to a wire rope or chain. It is used in various forms of lift and crane. -Fig. 172 shows the arrangement. A hydraulic ram or plunger B works in a -stationary cylinder A. Ram and cylinder carry sets of sheaves over which -passes a chain or rope, fixed at one end to the cylinder, and at the -other connected over guide pulleys to a lift or crane. For each pair of -pulleys, one on the cylinder and one on the ram, the movement of the -free end of the rope is doubled compared with that of the ram. With -three pairs of pulleys the free end of the rope has a movement equal to -six times the stroke of the ram, the force exerted being in the inverse -proportion. - -S 178. _Rotative Hydraulic Engines._--Valve-gear mechanism similar in -principle to that of steam engines can be applied to actuate the -admission and discharge valves, and the pressure engine is then -converted into a continuously-acting motor. - - Let H be the available fall to work the engine after deducting the - loss of head in the supply and discharge pipes, Q the supply of water - in cubic feet per second, and [eta] the efficiency of the engine. Then - the horse-power of the engine is - - H.P. = [eta]GQH/550. - - The efficiency of large slow-moving pressure engines is [eta] = .66 to - .8. In small motors of this kind probably [eta] is not greater than - .5. Let v be the mean velocity of the piston, then its diameter d is - given by the relation - - Q = [pi]d^2v/4 in double-acting engines, - = [pi]d^2v/8 in single-acting engines. - - If there are n cylinders put Q/n for Q in these equations. - -Small rotative pressure engines form extremely convenient motors for -hoists, capstans or winches, and for driving small machinery. The -single-acting engine has the advantage that the pressure of the piston -on the crank pin is always in one direction; there is then no knocking -as the dead centres are passed. Generally three single-acting cylinders -are used, so that the engine will readily start in all positions, and -the driving effort on the crank pin is very uniform. - -[Illustration: FIG. 173.] - - _Brotherhood Hydraulic Engine._--Three cylinders at angles of 120 deg. - with each other are formed in one casting with the frame. The - plungers are hollow trunks, and the connecting rods abut in - cylindrical recesses in them and are connected to a common crank pin. - A circular valve disk with concentric segmental ports revolves at the - same rate as the crank over ports in the valve face common to the - three cylinders. Each cylinder is always in communication with either - an admission or exhaust port. The blank parts of the circular valve - close the admission and exhaust ports alternately. The fixed valve - face is of lignum vitae in a metal recess, and the revolving valve of - gun-metal. In the case of a small capstan engine the cylinders are - 3(1/2) in. diameter and 3 in. stroke. At 40 revs. per minute, the - piston speed is 31 ft. per minute. The ports are 1 in. diameter or - 1/12 of the piston area, and the mean velocity in the ports 6.4 ft. - per sec. With 700 lb. per sq. in. water pressure and an efficiency of - 50%, the engine is about 3 h.p. A common arrangement is to have three - parallel cylinders acting on a three-throw crank shaft, the cylinders - oscillating on trunnions. - - _Hastie's Engine._--Fig. 173 shows a similar engine made by Messrs - Hastie of Greenock. G, G, G are the three plungers which pass out of - the cylinders through cup leathers, and act on the same crank pin. A - is the inlet pipe which communicates with the cock B. This cock - controls the action of the engine, being so constructed that it acts - as a reversing valve when the handle C is in its extreme positions and - as a brake when in its middle position. With the handle in its middle - position, the ports of the cylinders are in communication with the - exhaust. Two passages are formed in the framing leading from the cock - B to the ends of the cylinders, one being in communication with the - supply pipe A, the other with the discharge pipe Q. These passages end - as shown at E. The oscillation of the cylinders puts them alternately - in communication with each of these passages, and thus the water is - alternately admitted and exhausted. - - [Illustration: FIG. 174.] - - [Illustration: FIG. 175.] - - In any ordinary rotative engine the length of stroke is invariable. - Consequently the consumption of water depends simply on the speed of - the engine, irrespective of the effort overcome. If the power of the - engine must be varied without altering the number of rotations, then - the stroke must be made variable. Messrs Hastie have contrived an - exceedingly ingenious method of varying the stroke automatically, in - proportion to the amount of work to be done (fig. 174). The crank pin - I is carried in a slide H moving in a disk M. In this is a double cam - K acting on two small steel rollers J, L attached to the slide H. If - the cam rotates it moves the slide and increases or decreases the - radius of the circle in which the crank pin I rotates. The disk M is - keyed on a hollow shaft surrounding the driving shaft P, to which the - cams are attached. The hollow shaft N has two snugs to which the - chains RR are attached (fig. 175). The shaft P carries the spring case - SS to which also are attached the other ends of the chains. When the - engine is at rest the springs extend themselves, rotating the hollow - shaft N and the frame M, so as to place the crank pin I at its nearest - position to the axis of rotation. When a resistance has to be - overcome, the shaft N rotates relatively to P, compressing the - springs, till their resistance balances the pressure due to the - resistance to the rotation of P. The engine then commences to work, - the crank pin being in the position in which the turning effort just - overcomes the resistance. If the resistance diminishes, the springs - force out the chains and shorten the stroke of the plungers, and vice - versa. The following experiments, on an engine of this kind working a - hoist, show how the automatic arrangement adjusted the water used to - the work done. The lift was 22 ft. and the water pressure in the - cylinders 80 lb. per sq. in. - - Weight lifted, Chain 427 633 745 857 969 1081 1193 - in lb. only - - Water used, in 7(1/2) 10 14 16 17 20 21 22 - gallons - -S 179. _Accumulator Machinery._--It has already been pointed out that it -is in some cases convenient to use a steam engine to create an -artificial head of water, which is afterwards employed in driving -water-pressure machinery. Where power is required intermittently, for -short periods, at a number of different points, as, for instance, in -moving the cranes, lock gates, &c., of a dockyard, a separate steam -engine and boiler at each point is very inconvenient; nor can engines -worked from a common boiler be used, because of the great loss of heat -and the difficulties which arise out of condensation in the pipes. If a -tank, into which water is continuously pumped, can be placed at a great -elevation, the water can then be used in hydraulic machinery in a very -convenient way. Each hydraulic machine is put in communication with the -tank by a pipe, and on opening a valve it commences work, using a -quantity of water directly proportional to the work done. No attendance -is required when the machine is not working. - -[Illustration: FIG. 176.] - -A site for such an elevated tank is, however, seldom available, and in -place of it a beautiful arrangement termed an accumulator, invented by -Lord Armstrong, is used. This consists of a tall vertical cylinder; into -this works a solid ram through cup leathers or hemp packing, and the ram -is loaded by fixed weights, so that the pressure in the cylinder is 700 -lb. or 800 lb. per sq. in. In some cases the ram is fixed and the -cylinder moves on it. The pumping engines which supply the energy that -is stored in the accumulator should be a pair coupled at right angles, -so as to start in any position. The engines pump into the accumulator -cylinder till the ram is at the top of its stroke, when by a catch -arrangement acting on the engine throttle valve the engines are stopped. -If the accumulator ram descends, in consequence of water being taken to -work machinery, the engines immediately recommence working. Pipes lead -from the accumulator to each of the machines requiring to be driven, and -do not require to be of large size, as the pressure is so great. - - Fig. 176 shows a diagrammatic way the scheme of a system of - accumulator machinery. A is the accumulator, with its ram carrying a - cylindrical wrought-iron tank W, in which weights are placed to load - the accumulator. At R is one of the pressure engines or jiggers, - worked from the accumulator, discharging the water after use into the - tank T. In this case the pressure engine is shown working a set of - blocks, the fixed block being on the ram cylinder, the running block - on the ram. The chain running over these blocks works a lift cage C, - the speed of which is as many times greater than that of the ram as - there are plies of chain on the block tackle. B is the balance weight - of the cage. - - [Illustration: FIG. 177.] - - In the use of accumulators on shipboard for working gun gear or - steering gear, the accumulator ram is loaded by springs, or by steam - pressure acting on a piston much larger than the ram. - - R. H. Tweddell has used accumulators with a pressure of 2000 lb. per - sq. in. to work hydraulic riveting machinery. - - The amount of energy stored in the accumulator, having a ram d in. in - diameter, a stroke of S ft., and delivering at p lb. pressure per sq. - in., is - - [pi] - ---- p d^2S foot-pounds. - 4 - - Thus, if the ram is 9 in., the stroke 20 ft., and the pressure 800 lb. - per sq. in., the work stored in the accumulator when the ram is at the - top of the stroke is 1,017,600 foot-pounds, that is, enough to drive a - machine requiring one horse power for about half an hour. As, however, - the pumping engine replaces water as soon as it is drawn off, the - working capacity of the accumulator is very much greater than this. - Tweddell found that an accumulator charged at 1250 lb. discharged at - 1225 lb. per sq. in. Hence the friction was equivalent to 12(1/2) lb. - per sq. in. and the efficiency 98%. - - When a very great pressure is required a differential accumulator - (fig. 177) is convenient. The ram is fixed and passes through both - ends of the cylinder, but is of different diameters at the two ends, A - and B. Hence if d1, d2 are the diameters of the ram in inches and p - the required pressure in lb. per sq. in., the load required is - (1/4)p[pi](d1^2 - d2^2). An accumulator of this kind used with - riveting machines has d1 = 5(1/2) in., d2 = 4(3/4) in. The pressure is - 2000 lb. per sq. in. and the load 5.4 tons. - - [Illustration: FIG. 178.] - - Sometimes an accumulator is loaded by water or steam pressure instead - of by a dead weight. Fig. 178 shows the arrangement. A piston A is - connected to a plunger B of much smaller area. Water pressure, say - from town mains, is admitted below A, and the high pressure water is - pumped into and discharged from the cylinder C in which B works. If r - is the ratio of the areas of A and B, then, neglecting friction, the - pressure in the upper cylinder is r times that under the piston A. - With a variable rate of supply and demand from the upper cylinder, the - piston A rises and falls, maintaining always a constant pressure in - the upper cylinder. - - -_Water Wheels._ - -S 180. _Overshot and High Breast Wheels._--When a water fall ranges -between 10 and 70 ft. and the water supply is from 3 to 25 cub. ft. per -second, it is possible to construct a bucket wheel on which the water -acts chiefly by its weight. If the variation of the head-water level -does not exceed 2 ft., an overshot wheel may be used (fig. 179). The -water is then projected over the summit of the wheel, and falls in a -parabolic path into the buckets. With greater variation of head-water -level, a pitch-back or high breast wheel is better. The water falls over -the top of a sliding sluice into the wheel, on the same side as the head -race channel. By adjusting the height of the sluice, the requisite -supply is given to the wheel in all positions of the head-water level. - - The wheel consists of a cast-iron or wrought-iron axle C supporting - the weight of the wheel. To this are attached two sets of arms A of - wood or iron, which support circular segmental plates, B, termed - shrouds. A cylindrical sole plate dd extends between the shrouds on - the inner side. The buckets are formed by wood planks or curved - wrought-iron plates extending from shroud to shroud, the back of the - buckets being formed by the sole plate. - -[Illustration: FIG. 179.] - - The efficiency may be taken at 0.75. Hence, if h.p. is the effective - horse power, H the available fall, and Q the available water supply - per second, - - h.p. = 0.75 (GQH/550) = 0.085 QH. - - If the peripheral velocity of the water wheel is too great, water is - thrown out of the buckets before reaching the bottom of the fall. In - practice, the circumferential velocity of water wheels of the kind now - described is from 4(1/2) to 10 ft. per second, about 6 ft. being the - usual velocity of good iron wheels not of very small size. In order - that the water may enter the buckets easily, it must have a greater - velocity than the wheel. Usually the velocity of the water at the - point where it enters the wheel is from 9 to 12 ft. per second, and to - produce this it must enter the wheel at a point 16 to 27 in. below the - head-water level. Hence the diameter of an overshot wheel may be - - D = H - 1(1/3) to H - 2(1/4) ft. - - Overshot and high breast wheels work badly in backwater, and hence if - the tail-water level varies, it is better to reduce the diameter of - the wheel so that its greatest immersion in flood is not more than 1 - ft. The depth d of the shrouds is about 10 to 16 in. The number of - buckets may be about - - N = [pi]D/d. - - Let v be the peripheral velocity of the wheel. Then the capacity of - that portion of the wheel which passes the sluice in one second is - - Q1 = vb(Dd - d^2)/D - = v b d nearly, - - b being the breadth of the wheel between the shrouds. If, however, - this quantity of water were allowed to pass on to the wheel the - buckets would begin to spill their contents almost at the top of the - fall. To diminish the loss from spilling, it is not only necessary to - give the buckets a suitable form, but to restrict the water supply to - one-fourth or one-third of the gross bucket capacity. Let m be the - value of this ratio; then, Q being the supply of water per second, - - Q = mQ1 = mb dv. - - This gives the breadth of the wheel if the water supply is known. The - form of the buckets should be determined thus. The outer element of - the bucket should be in the direction of motion of the water entering - relatively to the wheel, so that the water may enter without splashing - or shock. The buckets should retain the water as long as possible, and - the width of opening of the buckets should be 2 or 3 in. greater than - the thickness of the sheet of water entering. - - For a wooden bucket (fig. 180, A), take ab = distance between two - buckets on periphery of wheel. Make ed = 1/2 eb and bc = 6/5 to 5/4 - ab. Join cd. For an iron bucket (fig. 180, B), take ed = 1/3 eb; bc = - 6/5 ab. Draw cO making an angle of 10 deg. to 15 deg. with the radius - at c. On Oc take a centre giving a circular arc passing near d, and - round the curve into the radial part of the bucket de. - -[Illustration: FIG. 180.] - -There are two ways in which the power of a water wheel is given off to -the machinery driven. In wooden wheels and wheels with rigid arms, a -spur or bevil wheel keyed on the axle of the turbine will transmit the -power to the shafting. It is obvious that the whole turning moment due -to the weight of the water is then transmitted through the arms and axle -of the water wheel. When the water wheel is an iron one, it usually has -light iron suspension arms incapable of resisting the bending action due -to the transmission of the turning effort to the axle. In that case spur -segments are bolted to one of the shrouds, and the pinion to which the -power is transmitted is placed so that the teeth in gear are, as nearly -as may be, on the line of action of the resultant of the weight of the -water in the loaded arc of the wheel. - -The largest high breast wheels ever constructed were probably the four -wheels, each 50 ft. in diameter, and of 125 h.p., erected by Sir W. -Fairbairn in 1825 at Catrine in Ayrshire. These wheels are still -working. - -[Illustration: FIG. 181.] - -S 181. _Poncelet Water Wheel._--When the fall does not exceed 6 ft., the -best water motor to adopt in many cases is the Poncelet undershot water -wheel. In this the water acts very nearly in the same way as in a -turbine, and the Poncelet wheel, although slightly less efficient than -the best turbines, in normal conditions of working, is superior to most -of them when working with a reduced supply of water. A general notion of -the action of the water on a Poncelet wheel has already been given in S -159. Fig. 181 shows its construction. The water penned back between the -side walls of the wheel pit is allowed to flow to the wheel under a -movable sluice, at a velocity nearly equal to the velocity due to the -whole fall. The water is guided down a slope of 1 in 10, or a curved -race, and enters the wheel without shock. Gliding up the curved floats -it comes to rest, falls back, and acquires at the point of discharge a -backward velocity relative to the wheel nearly equal to the forward -velocity of the wheel. Consequently it leaves the wheel deprived of -nearly the whole of its original kinetic energy. - - Taking the efficiency at 0.60, and putting H for the available fall, - h.p. for the horse-power, and Q for the water supply per second, - - h.p. = 0.068 QH. - - The diameter D of the wheel may be taken arbitrarily. It should not be - less than twice the fall and is more often four times the fall. For - ordinary cases the smallest convenient diameter is 14 ft. with a - straight, or 10 ft. with a curved, approach channel. The radial depth - of bucket should be at least half the fall, and radius of curvature of - buckets about half the radius of the wheel. The shrouds are usually of - cast iron with flanges to receive the buckets. The buckets may be of - iron 1/8 in. thick bolted to the flanges with 5/16 in. bolts. - - Let H' be the fall measured from the free surface of the head-water to - the point F where the mean layer enters the wheel; then the velocity - at which the water enters is v = [root](2gH'), and the best - circumferential velocity of the wheel is V = 0.55f to 0.6v. The number - of rotations of the wheel per second is N = V/[pi]D. The thickness - of the sheet of water entering the wheel is very important. The best - thickness according to experiment is 8 to 10 in. The maximum thickness - should not exceed 12 to 15 in., when there is a surplus water supply. - Let e be the thickness of the sheet of water entering the wheel, and b - its width; then - - bev = Q; or b = Q/ev. - - Grashof takes e = (1/6)H, and then - - b = 6Q/H [root](2gH). - - Allowing for the contraction of the stream, the area of opening - through the sluice may be 1.25 be to 1.3 be. The inside width of the - wheel is made about 4 in. greater than b. - - Several constructions have been given for the floats of Poncelet - wheels. One of the simplest is that shown in figs. 181, 182. - - Let OA (fig. 181) be the vertical radius of the wheel. Set off OB, OD - making angles of 15 deg. with OA. Then BD may be the length of the - close breasting fitted to the wheel. Draw the bottom of the head face - BC at a slope of 1 in 10. Parallel to this, at distances (1/2)e and e, - draw EF and GH. Then EF is the mean layer and GH the surface layer - entering the wheel. Join OF, and make OFK = 23 deg. Take FK = 0.5 to - 0.7 H. Then K is the centre from which the bucket curve is struck and - KF is the radius. The depth of the shrouds must be sufficient to - prevent the water from rising over the top of the float. It is (1/2)H - to 2/3 H. The number of buckets is not very important. They are - usually 1 ft. apart on the circumference of the wheel. - - The efficiency of a Poncelet wheel has been found in experiments to - reach 0.68. It is better to take it at 0.6 in estimating the power of - the wheel, so as to allow some margin. - - [Illustration: FIG. 182.] - - In fig. 182 v_i is the initial and v_o the final velocity of the - water, v_r parallel to the vane the relative velocity of the water and - wheel, and V the velocity of the wheel. - - -_Turbines._ - -S 182. The name turbine was originally given in France to any water -motor which revolved in a horizontal plane, the axis being vertical. The -rapid development of this class of motors dates from 1827, when a prize -was offered by the Societe d'Encouragement for a motor of this kind, -which should be an improvement on certain wheels then in use. The prize -was ultimately awarded to Benoit Fourneyron (1802-1867), whose turbine, -but little modified, is still constructed. - -_Classification of Turbines._--In some turbines the whole available -energy of the water is converted into kinetic energy before the water -acts on the moving part of the turbine. Such turbines are termed -_Impulse or Action Turbines_, and they are distinguished by this that -the wheel passages are never entirely filled by the water. To ensure -this condition they must be placed a little above the tail water and -discharge into free air. Turbines in which part only of the available -energy is converted into kinetic energy before the water enters the -wheel are termed _Pressure or Reaction Turbines_. In these there is a -pressure which in some cases amounts to half the head in the clearance -space between the guide vanes and wheel vanes. The velocity with which -the water enters the wheel is due to the difference between the pressure -due to the head and the pressure in the clearance space. In pressure -turbines the wheel passages must be continuously filled with water for -good efficiency, and the wheel may be and generally is placed below the -tail water level. - -Some turbines are designed to act normally as impulse turbines -discharging above the tail water level. But the passages are so designed -that they are just filled by the water. If the tail water rises and -drowns the turbine they become pressure turbines with a small clearance -pressure, but the efficiency is not much affected. Such turbines are -termed _Limit turbines_. - -Next there is a difference of constructive arrangement of turbines, -which does not very essentially alter the mode of action of the water. -In axial flow or so-called parallel flow turbines, the water enters and -leaves the turbine in a direction parallel to the axis of rotation, and -the paths of the molecules lie on cylindrical surfaces concentric with -that axis. In radial outward and inward flow turbines, the water enters -and leaves the turbine in directions normal to the axis of rotation, and -the paths of the molecules lie exactly or nearly in planes normal to the -axis of rotation. In outward flow turbines the general direction of flow -is away from the axis, and in inward flow turbines towards the axis. -There are also mixed flow turbines in which the water enters normally -and is discharged parallel to the axis of rotation. - -Another difference of construction is this, that the water may be -admitted equally to every part of the circumference of the turbine wheel -or to a portion of the circumference only. In the former case, the -condition of the wheel passages is always the same; they receive water -equally in all positions during rotation. In the latter case, they -receive water during a part of the rotation only. The former may be -termed turbines with complete admission, the latter turbines with -partial admission. A reaction turbine should always have complete -admission. An impulse turbine may have complete or partial admission. - -When two turbine wheels similarly constructed are placed on the same -axis, in order to balance the pressures and diminish journal friction, -the arrangement may be termed a twin turbine. - -If the water, having acted on one turbine wheel, is then passed through -a second on the same axis, the arrangement may be termed a compound -turbine. The object of such an arrangement would be to diminish the -speed of rotation. - -Many forms of reaction turbine may be placed at any height not exceeding -30 ft. above the tail water. They then discharge into an air-tight -suction pipe. The weight of the column of water in this pipe balances -part of the atmospheric pressure, and the difference of pressure, -producing the flow through the turbine, is the same as if the turbine -were placed at the bottom of the fall. - - I. Impulse Turbines. | II. Reaction Turbines. - | - (Wheel passages not filled, and | (Wheel passages filled, discha- - discharging above the tail | rging above or below the tail - water.) | water or into a suction-pipe.) - (a) Complete admission. (Rare.) | Always with complete admission. - (b) Partial admission. (Usual.) | - \_________________________________\/_______________________________/ - Axial flow, outward flow, inward flow, or mixed flow. - \_________________________________\/_______________________________/ - Simple turbines; twin turbines; compound turbines. - - S 183. _The Simple Reaction Wheel._--It has been shown, in S 162, - that, when water issues from a vessel, there is a reaction on the - vessel tending to cause motion in a direction opposite to that of the - jet. This principle was applied in a rotating water motor at a very - early period, and the Scotch turbine, at one time much used, differs - in no essential respect from the older form of reaction wheel. - - [Illustration: FIG. 183.] - - The old reaction wheel consisted of a vertical pipe balanced on a - vertical axis, and supplied with water (fig. 183). From the bottom of - the vertical pipe two or more hollow horizontal arms extended, at the - ends of which were orifices from which the water was discharged. The - reaction of the jets caused the rotation of the machine. - - Let H be the available fall measured from the level of the water in - the vertical pipe to the centres cf the orifices, r the radius from - the axis of rotation to the centres of the orifices, v the velocity of - discharge through the jets, [alpha] the angular velocity of the - machine. When the machine is at rest the water issues from the - orifices with the velocity [root](2gH) (friction being neglected). But - when the machine rotates the water in the arms rotates also, and is in - the condition of a forced vortex, all the particles having the same - angular velocity. Consequently the pressure in the arms at the - orifices is H + [alpha]^2r^2/2g ft. of water, and the velocity of - discharge through the orifices is v = [root](2gH + [alpha]^2r^2). If the - total area of the orifices is [omega], the quantity discharged from - the wheel per second is - - Q = [omega]v = [omega] [root](2gH + [alpha]^2r^2). - - While the water passes through the orifices with the velocity v, the - orifices are moving in the opposite direction with the velocity - [alpha]r. The absolute velocity of the water is therefore - - v - [alpha]r = [root](2gH + [alpha]^2r^2) - [alpha]r. - - The momentum generated per second is (GQ/g)(v - [alpha]r), which is - numerically equal to the force driving the motor at the radius r. The - work done by the water in rotating the wheel is therefore - - (GQ/g) (v - [alpha]r) ar foot-pounds per sec. - - The work expended by the water fall is GQH foot-pounds per second. - Consequently the efficiency of the motor is - - (v - [alpha]r) [alpha]r {[root]{2gH + [alpha]^2r^2]} - [alpha]r} [alpha]r - [eta] = ----------------------- = -------------------------------------------------. - gH gH - - Let - - gH g^2H^2 - [root]{2gH + [alpha]^2r^2} = [alpha]r + -------- - ------------- ... - [alpha]r 2[alpha]^3r^3 - - then - - [eta] = 1 - gH/2[alpha]r + ... - - which increases towards the limit 1 as [alpha]r increases towards - infinity. Neglecting friction, therefore, the maximum efficiency is - reached when the wheel has an infinitely great velocity of rotation. - But this condition is impracticable to realize, and even, at - practicable but high velocities of rotation, the friction would - considerably reduce the efficiency. Experiment seems to show that the - best efficiency is reached when [alpha]r = [root](2gH). Then the - efficiency apart from friction is - - [eta] = {[root](2[alpha]^2r^2) - [alpha]r} [alpha]r/gH - = 0.414 [alpha]^2r^2/gH = 0.828, - - about 17% of the energy of the fall being carried away by the water - discharged. The actual efficiency realized appears to be about 60%, so - that about 21% of the energy of the fall is lost in friction, in - addition to the energy carried away by the water. - - S 184. _General Statement of Hydrodynamical Principles necessary for - the Theory of Turbines._ - - (a) When water flows through any pipe-shaped passage, such as the - passage between the vanes of a turbine wheel, the relation between the - changes of pressure and velocity is given by Bernoulli's theorem (S - 29). Suppose that, at a section A of such a passage, h1 is the - pressure measured in feet of water, v1 the velocity, and z1 the - elevation above any horizontal datum plane, and that at a section B - the same quantities are denoted by h2, v2, z2. Then - - h1 - h2 = (v2^2 - v1^2)/2g + z2 - z1. (1) - - If the flow is horizontal, z2 = z1; and - - h1 - h2 = (v2^2 - v1^2)/2g. (la) - - (b) When there is an abrupt change of section of the passage, or an - abrupt change of section of the stream due to a contraction, then, in - applying Bernoulli's equation allowance must be made for the loss of - head in shock (S 36). Let v1, v2 be the velocities before and after - the abrupt change, then a stream of velocity v1 impinges on a stream - at a velocity v2, and the relative velocity is v1 - v2. The head lost - is (v1 - v2)^2/2g. Then equation (1a) becomes - - h1 - h2 = (v1^2 - v2^2)/2g - (v1 - v2)^2/2g = v2(v1 - v2)/g (2) - - [Illustration: FIG. 184.] - - To diminish as much as possible the loss of energy from irregular - eddying motions, the change of section in the turbine passages must be - very gradual, and the curvature without discontinuity. - - (c) _Equality of Angular Impulse and Change of Angular - Momentum._--Suppose that a couple, the moment of which is M, acts on a - body of weight W for t seconds, during which it moves from A1 to A2 - (fig. 184). Let v1 be the velocity of the body at A1, v2 its velocity - at A2, and let p1, p2 be the perpendiculars from C on v1 and v2. Then - Mt is termed the angular impulse of the couple, and the quantity - - (W/g)(v2p2 - v1p1) - - is the change of angular momentum relatively to C. Then, from the - equality of angular impulse and change of angular momentum - - Mt = (W/g)(v2p2 - v1p1), - - or, if the change of momentum is estimated for one second, - - M = (W/g)(v2p2 - v1p1). - - Let r1, r2 be the radii drawn from C to A1, A2, and let w1, w2 be the - components of v1, v2, perpendicular to these radii, making angles - [beta] and [alpha] with v1, v2. Then - - v1 = w1 sec [beta]; v2 = w2 sec [alpha] - - p1 = r1 cos [beta]; p2 = r2 cos [alpha], - - .: M = (W/g) (w2r2 - w1r1), (3) - - where the moment of the couple is expressed in terms of the radii - drawn to the positions of the body at the beginning and end of a - second, and the tangential components of its velocity at those points. - - Now the water flowing through a turbine enters at the admission - surface and leaves at the discharge surface of the wheel, with its - angular momentum relatively to the axis of the wheel changed. It - therefore exerts a couple -M tending to rotate the wheel, equal and - opposite to the couple M which the wheel exerts on the water. Let Q - cub. ft. enter and leave the wheel per second, and let w1, w2 be the - tangential components of the velocity of the water at the receiving - and discharging surfaces of the wheel, r1, r2 the radii of those - surfaces. By the principle above, - - -M = (GQ/g)(w2r2 - w1r1). (4) - - If [alpha] is the angular velocity of the wheel, the work done by the - water on the wheel is - - T = Ma = (GQ/g)(w1r1 - w2r2) [alpha] foot-pounds per second. (5) - - S 185. _Total and Available Fall._--Let H_t be the total difference of - level from the head-water to the tail-water surface. Of this total - head a portion is expended in overcoming the resistances of the head - race, tail race, supply pipe, or other channel conveying the water. - Let [h]_p be that loss of head, which varies with the local - conditions in which the turbine is placed. Then - - H = H_t - [h]_p - - is the available head for working the turbine, and on this the - calculations for the turbine should be based. In some cases it is - necessary to place the turbine above the tail-water level, and there - is then a fall [h] from the centre of the outlet surface of - the turbine to the tail-water level which is wasted, but which is - properly one of the losses belonging to the turbine itself. In that - case the velocities of the water in the turbine should be calculated - for a head H - [h], but the efficiency of the turbine for the - head H. - - S 186. _Gross Efficiency and Hydraulic Efficiency of a Turbine._--Let - T_d be the useful work done by the turbine, in foot-pounds per second, - T_t the work expended in friction of the turbine shaft, gearing, &c., - a quantity which varies with the local conditions in which the turbine - is placed. Then the effective work done by the water in the turbine is - - T = T_d + T_t. - - The gross efficiency of the whole arrangement of turbine, races, and - transmissive machinery is - - [eta]_t = T_d/CQH_t. (6) - - And the hydraulic efficiency of the turbine alone is - - [eta] = T/GQH. (7) - - It is this last efficiency only with which the theory of turbines is - concerned. - - From equations (5) and (7) we get - - [eta]GQH = (GQ/g)(w1r1 - w2r2)a; - - [eta] = (w1r1 - w2r2)a/gH. (8) - - This is the fundamental equation in the theory of turbines. In - general,[7] w1 and w2, the tangential components of the water's motion - on entering and leaving the wheel, are completely independent. That - the efficiency may be as great as possible, it is obviously necessary - that w2 = 0. In that case - - [eta] = w1r1a/gH. (9) - - ar1 is the circumferential velocity of the wheel at the inlet surface. - Calling this V1, the equation becomes - - [eta] = w1V1/gH. (9a) - - This remarkably simple equation is the fundamental equation in the - theory of turbines. It was first given by Reiche (_Turbinenbaues_, - 1877). - -[Illustration: FIG. 185.] - -[Illustration: FIG. 186.] - -[Illustration: FIG. 187.] - -[Illustration: FIG. 188.] - -[Illustration: FIG. 189.] - -S 187. _General Description of a Reaction Turbine._--Professor James -Thomson's inward flow or vortex turbine has been selected as the type of -reaction turbines. It is one of the best in normal conditions of -working, and the mode of regulation introduced is decidedly superior to -that in most reaction turbines. Figs. 185 and 186 are external views of -the turbine case; figs. 187 and 188 are the corresponding sections; fig. -189 is the turbine wheel. The example chosen for illustration has -suction pipes, which permit the turbine to be placed above the -tail-water level. The water enters the turbine by cast-iron supply pipes -at A, and is discharged through two suction pipes S, S. The water on -entering the case distributes itself through a rectangular supply -chamber SC, from which it finds its way equally to the four guide-blade -passages G, G, G, G. In these passages it acquires a velocity about -equal to that due to half the fall, and is directed into the wheel at an -angle of about 10 deg. or 12 deg. with the tangent to its circumference. -The wheel W receives the water in equal proportions from each -guide-blade passage. It consists of a centre plate p (fig. 189) keyed on -the shaft aa, which passes through stuffing boxes on the suction pipes. -On each side of the centre plate are the curved wheel vanes, on which -the pressure of the water acts, and the vanes are bounded on each side -by dished or conical cover plates c, c. Joint-rings j, j on the cover -plates make a sufficiently water-tight joint with the casing, to -prevent leakage from the guide-blade chamber into the suction pipes. The -pressure near the joint rings is not very great, probably not one-fourth -the total head. The wheel vanes receive the water without shock, and -deliver it into central spaces, from which it flows on either side to -the suction pipes. The mode of regulating the power of the turbine is -very simple. The guide-blades are pivoted to the case at their inner -ends, and they are connected by a link-work, so that they all open and -close simultaneously and equally. In this way the area of opening -through the guide-blades is altered without materially altering the -angle or the other conditions of the delivery into the wheel. The -guide-blade gear may be variously arranged. In this example four -spindles, passing through the case, are linked to the guide-blades -inside the case, and connected together by the links l, l, l on the -outside of the case. A worm wheel on one of the spindles is rotated by a -worm d, the motion being thus slow enough to adjust the guide-blades -very exactly. These turbines are made by Messrs Gilkes & Co. of Kendal. - -[Illustration: FIG. 190.] - - Fig. 190 shows another arrangement of a similar turbine, with some - adjuncts not shown in the other drawings. In this case the turbine - rotates horizontally, and the turbine case is placed entirely below - the tail water. The water is supplied to the turbine by a vertical - pipe, over which is a wooden pentrough, containing a strainer, which - prevents sticks and other solid bodies getting into the turbine. The - turbine rests on three foundation stones, and, the pivot for the - vertical shaft being under water, there is a screw and lever - arrangement for adjusting it as it wears. The vertical shaft gives - motion to the machinery driven by a pair of bevel wheels. On the right - are the worm and wheel for working the guide-blade gear. - - [Illustration: FIG. 191.] - - S 188. _Hydraulic Power at Niagara._--The largest development of - hydraulic power is that at Niagara. The Niagara Falls Power Company - have constructed two power houses on the United States side, the first - with 10 turbines of 5000 h.p. each, and the second with 10 turbines of - 5500 h.p. The effective fall is 136 to 140 ft. In the first power - house the turbines are twin outward flow reaction turbines with - vertical shafts running at 250 revs. per minute and driving the - dynamos direct. In the second power house the turbines are inward flow - turbines with draft tubes or suction pipes. Fig. 191 shows a section - of one of these turbines. There is a balancing piston keyed on the - shaft, to the under side of which the pressure due to the fall is - admitted, so that the weight of turbine, vertical shaft and part of - the dynamo is water borne. About 70,000 h.p. is daily distributed - electrically from these two power houses. The Canadian Niagara Power - Company are erecting a power house to contain eleven units of 10,250 - h.p. each, the turbines being twin inward flow reaction turbines. The - Electrical Development Company of Ontario are erecting a power house - to contain 11 units of 12,500 h.p. each. The Ontario Power Company are - carrying out another scheme for developing 200,000 h.p. by twin inward - flow turbines of 12,000 h.p. each. Lastly the Niagara Falls Power and - Manufacturing Company on the United States side have a station giving - 35,000 h.p. and are constructing another to furnish 100,000 h.p. The - mean flow of the Niagara river is about 222,000 cub. ft. per second - with a fall of 160 ft. The works in progress if completed will utilize - 650,000 h.p. and require 48,000 cub. ft. per second or 21(1/2)% of the - mean flow of the river (Unwin, "The Niagara Falls Power Stations," - _Proc. Inst. Mech. Eng._, 1906). - - [Illustration: FIG. 192.] - - S 189. _Different Forms of Turbine Wheel._--The wheel of a turbine or - part of the machine on which the water acts is an annular space, - furnished with curved vanes dividing it into passages exactly or - roughly rectangular in cross section. For radial flow turbines the - wheel may have the form A or B, fig. 192, A being most usual with - inward, and B with outward flow turbines. In A the wheel vanes are - fixed on each side of a centre plate keyed on the turbine shaft. The - vanes are limited by slightly-coned annular cover plates. In B the - vanes are fixed on one side of a disk, keyed on the shaft, and limited - by a cover plate parallel to the disk. Parallel flow or axial flow - turbines have the wheel as in C. The vanes are limited by two - concentric cylinders. - - - _Theory of Reaction Turbines._ - - [Illustration: FIG. 193.] - - S 190. _Velocity of Whirl and Velocity of Flow._--Let acb (fig. 193) - be the path of the particles of water in a turbine wheel. That path - will be in a plane normal to the axis of rotation in radial flow - turbines, and on a cylindrical surface in axial flow turbines. At any - point c of the path the water will have some velocity v, in the - direction of a tangent to the path. That velocity may be resolved into - two components, a whirling velocity w in the direction of the wheel's - rotation at the point c, and a component u at right angles to this, - radial in radial flow, and parallel to the axis in axial flow - turbines. This second component is termed the velocity of flow. Let - v_o, w_o, u_o be the velocity of the water, the whirling velocity and - velocity of flow at the outlet surface of the wheel, and v_i, w_i, u_i - the same quantities at the inlet surface of the wheel. Let [alpha] and - [beta] be the angles which the water's direction of motion makes with - the direction of motion of the wheel at those surfaces. Then - - w_o = v_o cos [beta]; u_o = v_o sin [beta] - - w_i = v_i cos [alpha]; u_i = v_i sin [alpha]. (10) - - The velocities of flow are easily ascertained independently from the - dimensions of the wheel. The velocities of flow at the inlet and - outlet surfaces of the wheel are normal to those surfaces. Let - [Omega]_o, [Omega]_i be the areas of the outlet and inlet surfaces of - the wheel, and Q the volume of water passing through the wheel per - second; then - - v_o = Q/[Omega]_o; v_i = Q/[Omega]_i. (11) - - Using the notation in fig. 191, we have, for an inward flow turbine - (neglecting the space occupied by the vanes), - - [Omega]_o = 2[pi]r0d0; [Omega]_i = 2[pi]r_i d_i. (12a) - - Similarly, for an outward flow turbine, - - [Omega]_o = 2[pi]r_o d; [Omega]_i = 2[pi]r_i d; (12b) - - and, for an axial flow turbine, - - [Omega]_o = [Omega]_i = [pi](r2^2 - r1^2). (12c) - - [Illustration: FIG. 194.] - - _Relative and Common Velocity of the Water and Wheel._--There is - another way of resolving the velocity of the water. Let V be the - velocity of the wheel at the point c, fig. 194. Then the velocity of - the water may be resolved into a component V, which the water has in - common with the wheel, and a component v_r, which is the velocity of - the water relatively to the wheel. - - _Velocity of Flow._--It is obvious that the frictional losses of head - in the wheel passages will increase as the velocity of flow is - greater, that is, the smaller the wheel is made. But if the wheel - works under water, the skin friction of the wheel cover increases as - the diameter of the wheel is made greater, and in any case the weight - of the wheel and consequently the journal friction increase as the - wheel is made larger. It is therefore desirable to choose, for the - velocity of flow, as large a value as is consistent with the condition - that the frictional losses in the wheel passages are a small fraction - of the total head. - - The values most commonly assumed in practice are these:-- - - In axial flow turbines, u_o = u_i = 0.15 to 0.2 [root](2gH); - - In outward flow turbines, u_i = 0.25 [root]2g(H - [h]), - u_o = 0.21 to 0.17 [root]2g(H - [h]); - - In inward flow turbines, u_o = u_i = 0.125 [root](2gH). - - S 191. _Speed of the Wheel._--The best speed of the wheel depends - partly on the frictional losses, which the ordinary theory of turbines - disregards. It is best, therefore, to assume for V_o and V_i values - which experiment has shown to be most advantageous. - - In axial flow turbines, the circumferential velocities at the mean - radius of the wheel may be taken - - V_o = V_i = 0.6 [root](2gH) to 0.66 [root](2gH). - - In a radial outward flow turbine, - - V_i = 0.56 [root]{2g(H - [h])} - - V_o = V_i r_o/r_i, - - where r_o, r_i are the radii of the outlet and inlet surfaces. - - In a radial inward flow turbine, - - V_i = 0.66 [root](2gH), - - V_o = V_i r_o/r_i. - - If the wheel were stationary and the water flowed through it, the - water would follow paths parallel to the wheel vane curves, at least - when the vanes were so close that irregular motion was prevented. - Similarly, when the wheel is in motion, the water follows paths - relatively to the wheel, which are curves parallel to the wheel vanes. - Hence the relative component, v_r, of the water's motion at c is - tangential to a wheel vane curve drawn through the point c. Let v_o, - V_o, v_(ro) be the velocity of the water and its common and relative - components at the outlet surface of the wheel, and v_i, V_i, v_(ri) be - the same quantities at the inlet surface; and let [theta] and [phi] be - the angles the wheel vanes make with the inlet and outlet surfaces; - then - - v_o^2 = [root](v_(ro)^2 + V_o^2 - 2V_o v_(ro) cos [phi]) - - v_i = [root](v_(ri)^2 + V_o^2 - 2V_i v_(ri) cos [theta]), (13) - - equations which may be used to determine [phi] and [theta]. - - [Illustration: FIG. 195.] - - S 192. _Condition determining the Angle of the Vanes at the Outlet - Surface of the Wheel._--It has been shown that, when the water leaves - the wheel, it should have no tangential velocity, if the efficiency is - to be as great as possible; that is, w_o = 0. Hence, from (10), cos - [beta] = 0, [beta] = 90 deg., U_o = V_o, and the direction of the - water's motion is normal to the outlet surface of the wheel, radial in - radial flow, and axial in axial flow turbines. - - Drawing v_o or u_o radial or axial as the case may be, and V_o - tangential to the direction of motion, v_(ro) can be found by the - parallelogram of velocities. From fig. 195, - - tan [phi] = v_o/V_o = u_o/V_o; (14) - - but [phi] is the angle which the wheel vane makes with the outlet - surface of the wheel, which is thus determined when the velocity of - flow u_o and velocity of the wheel V_o are known. When [phi] is thus - determined, - - v_(ro) = U_o cosec [phi] = V_o [root](1 + u_o^2/V_o^2). (14a) - - _Correction of the Angle [phi] to allow for Thickness of Vanes._--In - determining [phi], it is most convenient to calculate its value - approximately at first, from a value of u_o obtained by neglecting the - thickness of the vanes. As, however, this angle is the most important - angle in the turbine, the value should be afterwards corrected to - allow for the vane thickness. - - Let - - [phi]' = tan^(-1)(u_o/V_o) = tan^(-1)(Q/[Omega]_o V_o) - - be the first or approximate value of [phi], and let t be the - thickness, and n the number of wheel vanes which reach the outlet - surface of the wheel. As the vanes cut the outlet surface - approximately at the angle [phi]', their width measured on that - surface is t cosec [phi]'. Hence the space occupied by the vanes on - the outlet surface is - - For - - A, fig. 192, ntd_o cosec [phi] - B, fig. 192, ntd cosec [phi] (15) - C, fig. 192, nt(r2 - r1) cosec [phi]. - - Call this area occupied by the vanes [omega]. Then the true value of - the clear discharging outlet of the wheel is [Omega]_o - [omega], and - the true value of u_o is Q/([Omega]_o - [omega]). The corrected value - of the angle of the vanes will be - - [phi] = tan [Q/V_o ([Omega]_o - [omega]) ]. (16) - - S 193. _Head producing Velocity with which the Water enters the - Wheel._--Consider the variation of pressure in a wheel passage, which - satisfies the condition that the sections change so gradually that - there is no loss of head in shock. When the flow is in a horizontal - plane, there is no work done by gravity on the water passing through - the wheel. In the case of an axial flow turbine, in which the flow is - vertical, the fall d between the inlet and outlet surfaces should be - taken into account. - - Let - - V_i, V_o be the velocities of the wheel at the inlet and outlet - surfaces, - v_i, v_o the velocities of the water, - u_i, u_o the velocities of flow, - v_(ri), v_(ro) the relative velocities, - h_i, h_o the pressures, measured in feet of water, - r_i, r_o the radii of the wheel, - [alpha] the angular velocity of the wheel. - - At any point in the path of a portion of water, at radius r, the - velocity v of the water may be resolved into a component V = [alpha]r - equal to the velocity at that point of the wheel, and a relative - component v_r. Hence the motion of the water may be considered to - consist of two parts:--(a) a motion identical with that in a forced - vortex of constant angular velocity [alpha]; (b) a flow along curves - parallel to the wheel vane curves. Taking the latter first, and using - Bernoulli's theorem, the change of pressure due to flow through the - wheel passages is given by the equation - - h'_i + v_(ri)^2/2g = h'_o + v_(ro)^2/2g; - - h'_i - h'_o = (v_(ro)^2 - v_(ri)^2)/2g. - - The variation of pressure due to rotation in a forced vortex is - - h"_i - h"_o = (V_i^2 - V_o^2)/2g. - - Consequently the whole difference of pressure at the inlet and outlet - surfaces of the wheel is - - h_i - h_o = h'_i + h"_i - h'_o - h"_o - = (V_i^2 - V_o^2)/2g + (v_(ro)^2 - v_(ri)^2)/2g. (17) - - _Case 1. Axial Flow Turbines._--V_i = V_o; and the first term on the - right, in equation 17, disappears. Adding, however, the work of - gravity due to a fall of d ft. in passing through the wheel, - - h_i - h_o = (v_(ro)^2 - v_(ri)^2)/2g - d. (17a) - - _Case 2. Outward Flow Turbines._--The inlet radius is less than the - outlet radius, and (V_i^2 - V_o^2)/2g is negative. The centrifugal - head diminishes the pressure at the inlet surface, and increases the - velocity with which the water enters the wheel. This somewhat - increases the frictional loss of head. Further, if the wheel varies in - velocity from variations in the useful work done, the quantity (V_i^2 - - V_o^2)/2g increases when the turbine speed increases, and vice - versa. Consequently the flow into the turbine increases when the speed - increases, and diminishes when the speed diminishes, and this again - augments the variation of speed. The action of the centrifugal head in - an outward flow turbine is therefore prejudicial to steadiness of - motion. For this reason r_o : r_i is made small, generally about 5 : - 4. Even then a governor is sometimes required to regulate the speed of - the turbine. - - _Case 3. Inward Flow Turbines._--The inlet radius is greater than - the outlet radius, and the centrifugal head diminishes the velocity of - flow into the turbine. This tends to diminish the frictional losses, - but it has a more important influence in securing steadiness of - motion. Any increase of speed diminishes the flow into the turbine, - and vice versa. Hence the variation of speed is less than the - variation of resistance overcome. In the so-called centre vent wheels - in America, the ratio r_i : r_o is about 5 : 4, and then the influence - of the centrifugal head is not very important. Professor James Thomson - first pointed out the advantage of a much greater difference of radii. - By making r_i : r_o = 2 : 1, the centrifugal head balances about half - the head in the supply chamber. Then the velocity through the - guide-blades does not exceed the velocity due to half the fall, and - the action of the centrifugal head in securing steadiness of speed is - considerable. - - Since the total head producing flow through the turbine is H - - [h], of this h_i - h_o is expended in overcoming the pressure - in the wheel, the velocity of flow into the wheel is - - v_i = c_v[root]{2g(H - [h] - (V_i^2 - V_o^2/2g + (v{r0}^2 - v_(ri)^2)/2g)}, (18) - - where c_v may be taken 0.96. - - From (14a), - - v{r0} = V_o [root](1 + u_o^2/V_o^2). - - It will be shown immediately that - - v_(ri) = u_i cosec [theta]; - - or, as this is only a small term, and [theta] is on the average 90 - deg., we may take, for the present purpose, v_(ri) = u_i nearly. - - Inserting these values, and remembering that for an axial flow turbine - V_i = V_o, [h] = 0, and the fall d in the wheel is to be - added, - _ _ - | / V_i^2 / u_o^2 \ u_i^2 \ | - v_i = c_v[root] | 2g ( H - ---- ( 1 + ----- ) + ----- - d ) |. - |_ \ 2g \ V_o^2 / 2g / _| - - For an outward flow turbine, - _ _ - | / V_i^2 / u_o^2 \ u_i^2 \ | - v_i = c_v[root] | 2g ( H - [h] - ---- ( 1 + ----- ) + ----- ) |. - |_ \ 2g \ V_i^2 / 2g / _| - - For an inward flow turbine, - _ _ - | { V_i^2 / u_o^2 \ u_i^2 } | - v_i = c_v[root] | 2g { H - ---- ( 1 + ----- ) + ----- } |. - |_ { 2g \ V_i^2 / 2g } _| - - S 194. _Angle which the Guide-Blades make with the Circumference of - the Wheel._--At the moment the water enters the wheel, the radial - component of the velocity is u_i, and the velocity is v_i. Hence, if - [gamma] is the angle between the guide-blades and a tangent to the - wheel - - [gamma] = sin^(-1) (u_i/v_i). - - This angle can, if necessary, be corrected to allow for the thickness - of the guide-blades. - - [Illustration: FIG. 196.] - - S 195. _Condition determining the Angle of the Vanes at the Inlet - Surface of the Wheel._--The single condition necessary to be satisfied - at the inlet surface of the wheel is that the water should enter the - wheel without shock. This condition is satisfied if the direction of - relative motion of the water and wheel is parallel to the first - element of the wheel vanes. - - Let A (fig. 196) be a point on the inlet surface of the wheel, and let - v_i represent in magnitude and direction the velocity of the water - entering the wheel, and V_i the velocity of the wheel. Completing the - parallelogram, v_(ri) is the direction of relative motion. Hence the - angle between v_(ri) and V_i is the angle [theta] which the vanes - should make with the inlet surface of the wheel. - - S 196. _Example of the Method of designing a Turbine. Professor James - Thomson's Inward Flow Turbine._-- - - Let - - H = the available fall after deducting loss of head in pipes and - channels from the gross fall; - Q = the supply of water in cubic feet per second; and - [eta] = the efficiency of the turbine. - - The work done per second is [eta]GQH, and the horse-power of the - turbine is h.p. = [eta]GQH/550. If [eta] is taken at 0.75, an - allowance will be made for the frictional losses in the turbine, the - leakage and the friction of the turbine shaft. Then h.p. = 0.085QH. - - The velocity of flow through the turbine (uncorrected for the space - occupied by the vanes and guide-blades) may be taken - - u_i = u_i = 0.125 [root](2gH), - - in which case about (1/64)th of the energy of the fall is carried away - by the water discharged. - - The areas of the outlet and inlet surface of the wheel are then - - 2[pi]r_o d_o = 2[pi]r_i d_i = Q/0.125 [root](2gH). - - If we take r_o, so that the axial velocity of discharge from the - central orifices of the wheel is equal to u_o, we get - - r_o = 0.3984 [root](Q/[root]H), - - d_o = r_o. - - If, to obtain considerable steadying action of the centrifugal head, - r_i = 2r_o, then d_i = (1/2)d_o. - - _Speed of the Wheel._--Let V_i = 0.66 [root](2gH), or the speed due to - half the fall nearly. Then the number of rotations of the turbine per - second is - - N = V_i/2[pi]r_i = 1.0579 [root](H[root]H/Q); - - also - - V_o = V_i r_o/r_i = 0.33 [root](2gH). - - _Angle of Vanes with Outlet Surface._ - - Tan[phi] = u_o/V_o = 0.125/0.33 = .3788; - - [phi] = 21 deg. nearly. - - If this value is revised for the vane thickness it will ordinarily - become about 25 deg. - - _Velocity with which the Water enters the Wheel._--The head producing - the velocity is - - H - (V_i^2/2g) (1 + u_o^2/V_i^2) + u_i^2/2g - = H {1 - .4356 (1 + 0.0358) + .0156} - = 0.5646H. - - Then the velocity is - - V_i = .96 [root](2g(.5646H)) = 0.721 [root](2gH). - - _Angle of Guide-Blades._ - - Sin [gamma] = u_i/v_i = 0.125/0.721 = 0.173; - - [gamma] = 10 deg. nearly. - - _Tangential Velocity of Water entering Wheel._ - - w_i = v_i cos [gamma] = 0.7101 [root](2gH). - - _Angle of Vanes at Inlet Surface._ - - Cot [theta] = (w_i - V_i)/u_i = (.7101 - .66)/.125 = .4008; - - [theta] = 68 deg. nearly. - - _Hydraulic Efficiency of Wheel._ - - [eta] = w_iV_i/gH = .7101 X .66 X 2 - = 0.9373. - - This, however, neglects the friction of wheel covers and leakage. The - efficiency from experiment has been found to be 0.75 to 0.80. - - -_Impulse and Partial Admission Turbines._ - -S 197. The principal defect of most turbines with complete admission is -the imperfection of the arrangements for working with less than the -normal supply. With many forms of reaction turbine the efficiency is -considerably reduced when the regulating sluices are partially -closed, but it is exactly when the supply of water is deficient that it -is most important to get out of it the greatest possible amount of work. -The imperfection of the regulating arrangements is therefore, from the -practical point of view, a serious defect. All turbine makers have -sought by various methods to improve the regulating mechanism. B. -Fourneyron, by dividing his wheel by horizontal diaphragms, virtually -obtained three or more separate radial flow turbines, which could be -successively set in action at their full power, but the arrangement is -not altogether successful, because of the spreading of the water in the -space between the wheel and guide-blades. Fontaine similarly employed -two concentric axial flow turbines formed in the same casing. One was -worked at full power, the other regulated. By this arrangement the loss -of efficiency due to the action of the regulating sluice affected only -half the water power. Many makers have adopted the expedient of erecting -two or three separate turbines on the same waterfall. Then one or more -could be put out of action and the others worked at full power. All -these methods are rather palliatives than remedies. The movable -guide-blades of Professor James Thomson meet the difficulty directly, -but they are not applicable to every form of turbine. - -[Illustration: FIG. 197.] - -C. Callon, in 1840, patented an arrangement of sluices for axial or -outward flow turbines, which were to be closed successively as the water -supply diminished. By preference the sluices were closed by pairs, two -diametrically opposite sluices forming a pair. The water was thus -admitted to opposite but equal arcs of the wheel, and the forces driving -the turbine were symmetrically placed. As soon as this arrangement was -adopted, a modification of the mode of action of the water in the -turbine became necessary. If the turbine wheel passages remain full of -water during the whole rotation, the water contained in each passage -must be put into motion each time it passes an open portion of the -sluice, and stopped each time it passes a closed portion of the sluice. -It is thus put into motion and stopped twice in each rotation. This -gives rise to violent eddying motions and great loss of energy in shock. -To prevent this, the turbine wheel with partial admission must be placed -above the tail water, and the wheel passages be allowed to clear -themselves of water, while passing from one open portion of the sluices -to the next. - -But if the wheel passages are free of water when they arrive at the open -guide passages, then there can be no pressure other than atmospheric -pressure in the clearance space between guides and wheel. The water must -issue from the sluices with the whole velocity due to the head; received -on the curved vanes of the wheel, the jets must be gradually deviated -and discharged with a small final velocity only, precisely in the same -way as when a single jet strikes a curved vane in the free air. Turbines -of this kind are therefore termed turbines of free deviation. There is -no variation of pressure in the jet during the whole time of its action -on the wheel, and the whole energy of the jet is imparted to the wheel, -simply by the impulse due to its gradual change of momentum. It is clear -that the water may be admitted in exactly the same way to any fraction -of the circumference at pleasure, without altering the efficiency of the -wheel. The diameter of the wheel may be made as large as convenient, and -the water admitted to a small fraction of the circumference only. Then -the number of revolutions is independent of the water velocity, and may -be kept down to a manageable value. - -[Illustration: FIG. 198.] - -[Illustration: FIG. 199.] - - S 198. _General Description of an Impulse Turbine or Turbine with Free - Deviation._--Fig. 197 shows a general sectional elevation of a Girard - turbine, in which the flow is axial. The water, admitted above a - horizontal floor, passes down through the annular wheel containing the - guide-blades G, G, and thence into the revolving wheel WW. The - revolving wheel is fixed to a hollow shaft suspended from the pivot p. - The solid internal shaft ss is merely a fixed column supporting the - pivot. The advantage of this is that the pivot is accessible for - lubrication and adjustment. B is the mortise bevel wheel by which the - power of the turbine is given off. The sluices are worked by the hand - wheel h, which raises them successively, in a way to be described - presently. d, d are the sluice rods. Figs. 198, 199 show the sectional - form of the guide-blade chamber and wheel and the curves of the wheel - vanes and guide-blades, when drawn on a plane development of the - cylindrical section of the wheel; a, a, a are the sluices for cutting - off the water; b, b, b are apertures by which the entrance or exit of - air is facilitated as the buckets empty and fill. Figs. 200, 201 show - the guide-blade gear. a, a, a are the sluice rods as before. At the - top of each sluice rod is a small block c, having a projecting tongue, - which slides in the groove of the circular cam plate d, d. This - circular plate is supported on the frame e, and revolves on it by - means of the flanged rollers f. Inside, at the top, the cam plate is - toothed, and gears into a spur pinion connected with the hand wheel h. - At gg is an inclined groove or shunt. When the tongues of the blocks - c, c arrive at g, they slide up to a second groove, or the reverse, - according as the cam plate is revolved in one direction or in the - other. As this operation takes place with each sluice successively, - any number of sluices can be opened or closed as desired. The turbine - is of 48 horse power on 5.12 ft. fall, and the supply of water varies - from 35 to 112 cub. ft. per second. The efficiency in normal working - is given as 73%. The mean diameter of the wheel is 6 ft., and the - speed 27.4 revolutions per minute. - - [Illustration: FIG. 200.] - - [Illustration: FIG. 201.] - - [Illustration: FIG. 202.] - - As an example of a partial admission radial flow impulse turbine, a - 100 h.p. turbine at Immenstadt may be taken. The fall varies from 538 - to 570 ft. The external diameter of the wheel is 4(1/2) ft., and its - internal diameter 3 ft. 10 in. Normal speed 400 revs. per minute. - Water is discharged into the wheel by a single nozzle, shown in fig. - 202 with its regulating apparatus and some of the vanes. The water - enters the wheel at an angle of 22 deg. with the direction of motion, - and the final angle of the wheel vanes is 20 deg. The efficiency on - trial was from 75 to 78%. - - S 199. _Theory of the Impulse Turbine._--The theory of the impulse - turbine does not essentially differ from that of the reaction turbine, - except that there is no pressure in the wheel opposing the discharge - from the guide-blades. Hence the velocity with which the water enters - the wheel is simply - - v_i = 0.96 [root]{2g(H - [h])}, - - where [heta] is the height of the top of the wheel above the tail - water. If the hydropneumatic system is used, then [h] = 0. Let - Q_m be the maximum supply of water, r1, r2 the internal and external - radii of the wheel at the inlet surface; then - - u_i = Q_m/{[pi](r2^2 - r1^2)}. - - The value of u_i may be about 0.45 [root]{2g(H - [eta][h])}, - whence r1, r2 can be determined. - - The guide-blade angle is then given by the equation - - sin [gamma] = u_i/v_i = 0.45/0.94 = .48; - - [gamma] = 29 deg. - - The value of u_i should, however, be corrected for the space occupied - by the guide-blades. - - The tangential velocity of the entering water is - - w_i = v_i cos [gamma] = 0.82 [root]{2g(H - [h])}. - - The circumferential velocity of the wheel may be (at mean radius) - - V_i = 0.5 [root]{2g(H - [h])}. - - Hence the vane angle at inlet surface is given by the equation - - cot [theta] = (w_i - V_i)/u_i = (0.82 - 0.5)/0.45 = .71; - - [theta] = 55 deg. - - The relative velocity of the water striking the vane at the inlet edge - is v_(ri) = u_i cosec[theta] = 1.22 u_i. This relative velocity remains - unchanged during the passage of the water over the vane; consequently - the relative velocity at the point of discharge is v_(ro) = 1.22 u_i. - Also in an axial flow turbine V_o = V_i. - - If the final velocity of the water is axial, then - - cos [phi] = V_o/v_(ro) = V_i/v_(ri) = 0.5/(1.22 X 0.45) = cos 24 deg. 23'. - - This should be corrected for the vane thickness. Neglecting this, u_o - = v_(ro) sin [phi] = v_(ri) sin [phi] = u_i cosec [theta] sin [phi] = - 0.5u_i. The discharging area of the wheel must therefore be greater - than the inlet area in the ratio of at least 2 to 1. In some actual - turbines the ratio is 7 to 3. This greater outlet area is obtained by - splaying the wheel, as shown in the section (fig. 199). - - [Illustration: FIG. 203.] - - S 200. _Pelton Wheel._--In the mining district of California about - 1860 simple impulse wheels were used, termed hurdy-gurdy wheels. The - wheels rotated in a vertical plane, being supported on a horizontal - axis. Round the circumference were fixed flat vanes which were struck - normally by a jet from a nozzle of size varying with the head and - quantity of water. Such wheels have in fact long been used. They are - not efficient, but they are very simply constructed. Then attempts - were made to improve the efficiency, first by using hemispherical cup - vanes, and then by using a double cup vane with a central dividing - ridge, an arrangement invented by Pelton. In this last form the water - from the nozzle passes half to each side of the wheel, just escaping - clear of the backs of the advancing buckets. Fig. 203 shows a Pelton - vane. Some small modifications have been made by other makers, but - they are not of any great importance. Fig. 204 shows a complete Pelton - wheel with frame and casing, supply pipe and nozzle. Pelton wheels - have been very largely used in America and to some extent in Europe. - They are extremely simple and easy to construct or repair and on falls - of 100 ft. or more are very efficient. The jet strikes tangentially to - the mean radius of the buckets, and the face of the buckets is not - quite radial but at right angles to the direction of the jet at the - point of first impact. For greatest efficiency the peripheral velocity - of the wheel at the mean radius of the buckets should be a little less - than half the velocity of the jet. As the radius of the wheel can be - taken arbitrarily, the number of revolutions per minute can be - accommodated to that of the machinery to be driven. Pelton wheels have - been made as small as 4 in. diameter, for driving sewing machines, and - as large as 24 ft. The efficiency on high falls is about 80%. When - large power is required two or three nozzles are used delivering on - one wheel. The width of the buckets should be not less than seven - times the diameter of the jet. - - [Illustration: FIG. 204.] - - At the Comstock mines, Nevada, there is a 36-in. Pelton wheel made of - a solid steel disk with phosphor bronze buckets riveted to the rim. - The head is 2100 ft. and the wheel makes 1150 revolutions per minute, - the peripheral velocity being 180 ft. per sec. With a (1/2)-in. nozzle - the wheel uses 32 cub. ft. of water per minute and develops 100 h.p. - At the Chollarshaft, Nevada, there are six Pelton wheels on a fall of - 1680 ft. driving electrical generators. With 5/8-in. nozzles each - develops 125 h.p. - - [Illustration: FIG. 205] - - S 201. _Theory of the Pelton Wheel._--Suppose a jet with a velocity v - strikes tangentially a curved vane AB (fig. 205) moving in the same - direction with the velocity u. The water will flow over the vane with - the relative velocity v - u and at B will have the tangential - relative velocity v - u making an angle [alpha] with the direction of - the vane's motion. Combining this with the velocity u of the vane, the - absolute velocity of the water leaving the vane will be w = Bc. The - component of w in the direction of motion of the vane is Ba = Bb - ab - = u - (v - u) cos [alpha]. Hence if Q is the quantity of water - reaching the vane per second the change of momentum per second in the - direction of the vane's motion is (GQ/g)[v - {u - (v - u) cos - [alpha]}] = (GQ/g)(v - u)(1 + cos [alpha]). If a = 0 deg., cos [alpha] - = 1, and the change of momentum per second, which is equal to the - effort driving the vane, is P = 2(GQ/g)(v - u). The work done on the - vane is Pu = 2(GQ/g)(v - u)u. If a series of vanes are interposed in - succession, the quantity of water impinging on the vanes per second is - the total discharge of the nozzle, and the energy expended at the - nozzle is GQv^2/2g. Hence the efficiency of the arrangement is, when - [alpha] = 0 deg., neglecting friction, - - [eta] = 2Pu/GQv^2 = 4(v - u)u/v^2, - - which is a maximum and equal to unity if u = (1/2)v. In that case the - whole energy of the jet is usefully expended in driving the series of - vanes. In practice [alpha] cannot be quite zero or the water leaving - one vane would strike the back of the next advancing vane. Fig. 203 - shows a Pelton vane. The water divides each way, and leaves the vane - on each side in a direction nearly parallel to the direction of motion - of the vane. The best velocity of the vane is very approximately half - the velocity of the jet. - - S 202. _Regulation of the Pelton Wheel._--At first Pelton wheels were - adjusted to varying loads merely by throttling the supply. This method - involves a total loss of part of the head at the sluice or throttle - valve. In addition as the working head is reduced, the relation - between wheel velocity and jet velocity is no longer that of greatest - efficiency. Next a plan was adopted of deflecting the jet so that only - part of the water reached the wheel when the load was reduced, the - rest going to waste. This involved the use of an equal quantity of - water for large and small loads, but it had, what in some cases is an - advantage, the effect of preventing any water hammer in the supply - pipe due to the action of the regulator. In most cases now regulation - is effected by varying the section of the jet. A conical needle in the - nozzle can be advanced or withdrawn so as to occupy more or less of - the aperture of the nozzle. Such a needle can be controlled by an - ordinary governor. - -S 203. _General Considerations on the Choice of a Type of Turbine._--The -circumferential speed of any turbine is necessarily a fraction of the -initial velocity of the water, and therefore is greater as the head is -greater. In reaction turbines with complete admission the number of -revolutions per minute becomes inconveniently great, for the diameter -cannot be increased beyond certain limits without greatly reducing the -efficiency. In impulse turbines with partial admission the diameter can -be chosen arbitrarily and the number of revolutions kept down on high -falls to any desired amount. Hence broadly reaction turbines are better -and less costly on low falls, and impulse turbines on high falls. For -variable water flow impulse turbines have some advantage, being more -efficiently regulated. On the other hand, impulse turbines lose -efficiency seriously if their speed varies from the normal speed due to -the head. If the head is very variable, as it often is on low falls, and -the turbine must run at the same speed whatever the head, the impulse -turbine is not suitable. Reaction turbines can be constructed so as to -overcome this difficulty to a great extent. Axial flow turbines with -vertical shafts have the disadvantage that in addition to the weight of -the turbine there is an unbalanced water pressure to be carried by the -footstep or collar bearing. In radial flow turbines the hydraulic -pressures are balanced. The application of turbines to drive dynamos -directly has involved some new conditions. The electrical engineer -generally desires a high speed of rotation, and a very constant speed at -all times. The reaction turbine is generally more suitable than the -impulse turbine. As the diameter of the turbine depends on the quantity -of water and cannot be much varied without great inefficiency, a -difficulty arises on low falls. This has been met by constructing four -independent reaction turbines on the same shaft, each having of course -the diameter suitable for one-quarter of the whole discharge, and having -a higher speed of rotation than a larger turbine. The turbines at -Rheinfelden and Chevres are so constructed. To ensure constant speed of -rotation when the head varies considerably without serious inefficiency, -an axial flow turbine is generally used. It is constructed of three or -four concentric rings of vanes, with independent regulating sluices, -forming practically independent turbines of different radii. Any one of -these or any combination can be used according to the state of the -water. With a high fall the turbine of largest radius only is used, and -the speed of rotation is less than with a turbine of smaller radius. On -the other hand, as the fall decreases the inner turbines are used either -singly or together, according to the power required. At the Zurich -waterworks there are turbines of 90 h.p. on a fall varying from 10(1/2) -ft. to 4(3/4) ft. The power and speed are kept constant. Each turbine -has three concentric rings. The outermost ring gives 90 h.p. with 105 -cub. ft. per second and the maximum fall. The outer and middle -compartments give the same power with 140 cub. ft. per second and a fall -of 7 ft. 10 in. All three compartments working together develop the -power with about 250 cub. ft. per second. In some tests the efficiency -was 74% with the outer ring working alone, 75.4% with the outer and -middle ring working and a fall of 7 ft., and 80.7% with all the rings -working. - -[Illustration: FIG. 206.] - -S 204. _Speed Governing._--When turbines are used to drive dynamos -direct, the question of speed regulation is of great importance. Steam -engines using a light elastic fluid can be easily regulated by governors -acting on throttle or expansion valves. It is different with water -turbines using a fluid of great inertia. In one of the Niagara penstocks -there are 400 tons of water flowing at 10 ft. per second, opposing -enormous resistance to rapid change of speed of flow. The sluices of -water turbines also are necessarily large and heavy. Hence relay -governors must be used, and the tendency of relay governors to -hunt must be overcome. In the Niagara Falls Power House No. 1, each -turbine has a very sensitive centrifugal governor acting on a ratchet -relay. The governor puts into gear one or other of two ratchets driven -by the turbine itself. According as one or the other ratchet is in gear -the sluices are raised or lowered. By a subsidiary arrangement the -ratchets are gradually put out of gear unless the governor puts them in -gear again, and this prevents the over correction of the speed from the -lag in the action of the governor. In the Niagara Power House No. 2, the -relay is an hydraulic relay similar in principle, but rather more -complicated in arrangement, to that shown in fig. 206, which is a -governor used for the 1250 h.p. turbines at Lyons. The sensitive -governor G opens a valve and puts into action a plunger driven by oil -pressure from an oil reservoir. As the plunger moves forward it -gradually closes the oil admission valve by lowering the fulcrum end f -of the valve lever which rests on a wedge w attached to the plunger. If -the speed is still too high, the governor reopens the valve. In the case -of the Niagara turbines the oil pressure is 1200 lb. per sq. in. One -millimetre of movement of the governor sleeve completely opens the relay -valve, and the relay plunger exerts a force of 50 tons. The sluices can -be completely opened or shut in twelve seconds. The ordinary variation -of speed of the turbine with varying load does not exceed 1%. If all the -load is thrown off, the momentary variation of speed is not more than -5%. To prevent hydraulic shock in the supply pipes, a relief valve is -provided which opens if the pressure is in excess of that due to the -head. - -[Illustration: FIG. 207.] - -S 205. _The Hydraulic Ram._--The hydraulic ram is an arrangement by -which a quantity of water falling a distance h forces a portion of the -water to rise to a height h1, greater than h. It consists of a supply -reservoir (A, fig. 207), into which the water enters from some natural -stream. A pipe s of considerable length conducts the water to a lower -level, where it is discharged intermittently through a self-acting -pulsating valve at d. The supply pipe s may be fitted with a flap valve -for stopping the ram, and this is attached in some cases to a float, so -that the ram starts and stops itself automatically, according as the -supply cistern fills or empties. The lower float is just sufficient to -keep open the flap after it has been raised by the action of the upper -float. The length of chain is adjusted so that the upper float opens the -flap when the level in the cistern is at the desired height. If the -water-level falls below the lower float the flap closes. The pipe s -should be as long and as straight as possible, and as it is subjected to -considerable pressure from the sudden arrest of the motion of the water, -it must be strong and strongly jointed. a is an air vessel, and e the -delivery pipe leading to the reservoir at a higher level than A, into -which water is to be pumped. Fig. 208 shows in section the construction -of the ram itself. d is the pulsating discharge valve already mentioned, -which opens inwards and downwards. The stroke of the valve is regulated -by the cotter through the spindle, under which are washers by which the -amount of fall can be regulated. At o is a delivery valve, opening -outwards, which is often a ball-valve but sometimes a flap-valve. The -water which is pumped passes through this valve into the air vessel a, -from which it flows by the delivery pipe in a regular stream into the -cistern to which the water is to be raised. In the vertical chamber -behind the outer valve a small air vessel is formed, and into this -opens an aperture 1/4 in. in diameter, made in a brass screw plug b. The -hole is reduced to 1/16 in. in diameter at the outer end of the plug -and is closed by a small valve opening inwards. Through this, during the -rebound after each stroke of the ram, a small quantity of air is sucked -in which keeps the air vessel supplied with its elastic cushion of air. - -[Illustration: FIG. 208.] - -During the recoil after a sudden closing of the valve d, the pressure -below it is diminished and the valve opens, permitting outflow. In -consequence of the flow through this valve, the water in the supply pipe -acquires a gradually increasing velocity. The upward flow of the water, -towards the valve d, increases the pressure tending to lift the valve, -and at last, if the valve is not too heavy, lifts and closes it. The -forward momentum of the column in the supply pipe being destroyed by the -stoppage of the flow, the water exerts a pressure at the end of the pipe -sufficient to open the delivery valve o, and to cause a portion of the -water to flow into the air vessel. As the water in the supply pipe comes -to rest and recoils, the valve d opens again and the operation is -repeated. Part of the energy of the descending column is employed in -compressing the air at the end of the supply pipe and expanding the pipe -itself. This causes a recoil of the water which momentarily diminishes -the pressure in the pipe below the pressure due to the statical head. -This assists in opening the valve d. The recoil of the water is -sufficiently great to enable a pump to be attached to the ram body -instead of the direct rising pipe. With this arrangement a ram working -with muddy water may be employed to raise clear spring water. Instead of -lifting the delivery valve as in the ordinary ram, the momentum of the -column drives a sliding or elastic piston, and the recoil brings it -back. This piston lifts and forces alternately the clear water through -ordinary pump valves. - - -PUMPS - -S 206. The different classes of pumps correspond almost exactly to the -different classes of water motors, although the mechanical details of -the construction are somewhat different. They are properly reversed -water motors. Ordinary reciprocating pumps correspond to water-pressure -engines. Chain and bucket pumps are in principle similar to water wheels -in which the water acts by weight. Scoop wheels are similar to undershot -water wheels, and centrifugal pumps to turbines. - -_Reciprocating Pumps_ are single or double acting, and differ from -water-pressure engines in that the valves are moved by the water instead -of by automatic machinery. They may be classed thus:-- - -1. _Lift Pumps._--The water drawn through a foot valve on the ascent of -the pump bucket is forced through the bucket valve when it descends, and -lifted by the bucket when it reascends. Such pumps give an intermittent -discharge. - -2. _Plunger or Force Pumps_, in which the water drawn through the foot -valve is displaced by the descent of a solid plunger, and forced through -a delivery valve. They have the advantage that the friction is less -than that of lift pumps, and the packing round the plunger is easily -accessible, whilst that round a lift pump bucket is not. The flow is -intermittent. - -3. _The Double-acting Force Pump_ is in principle a double plunger pump. -The discharge fluctuates from zero to a maximum and back to zero each -stroke, but is not arrested for any appreciable time. - -4. _Bucket and Plunger Pumps_ consist of a lift pump bucket combined -with a plunger of half its area. The flow varies as in a double-acting -pump. - -5. _Diaphragm Pumps_ have been used, in which the solid plunger is -replaced by an elastic diaphragm, alternately depressed into and raised -out of a cylinder. - -As single-acting pumps give an intermittent discharge three are -generally used on cranks at 120 deg. But with all pumps the variation of -velocity of discharge would cause great waste of work in the delivery -pipes when they are long, and even danger from the hydraulic ramming -action of the long column of water. An air vessel is interposed between -the pump and the delivery pipes, of a volume from 5 to 100 times the -space described by the plunger per stroke. The air in this must be -replenished from time to time, or continuously, by a special air-pump. -At low speeds not exceeding 30 ft. per minute the delivery of a pump is -about 90 to 95% of the volume described by the plunger or bucket, from 5 -to 10% of the discharge being lost by leakage. At high speeds the -quantity pumped occasionally exceeds the volume described by the -plunger, the momentum of the water keeping the valves open after the -turn of the stroke. - -The velocity of large mining pumps is about 140 ft. per minute, the -indoor or suction stroke being sometimes made at 250 ft. per minute. -Rotative pumping engines of large size have a plunger speed of 90 ft. -per minute. Small rotative pumps are run faster, but at some loss of -efficiency. Fire-engine pumps have a speed of 180 to 220 ft. per minute. - -The efficiency of reciprocating pumps varies very greatly. Small -reciprocating pumps, with metal valves on lifts of 15 ft., were found by -Morin to have an efficiency of 16 to 40%, or on the average 25%. When -used to pump water at considerable pressure, through hose pipes, the -efficiency rose to from 28 to 57%, or on the average, with 50 to 100 ft. -of lift, about 50%. A large pump with barrels 18 in. diameter, at speeds -under 60 ft. per minute, gave the following results:-- - - Lift in feet 14(1/2) 34 47 - Efficiency .46 .66 .70 - -The very large steam-pumps employed for waterworks, with 150 ft. or more -of lift, appear to reach an efficiency of 90%, not including the -friction of the discharge pipes. Reckoned on the indicated work of the -steam-engine the efficiency may be 80%. - -Many small pumps are now driven electrically and are usually three-throw -single-acting pumps driven from the electric motor by gearing. It is not -convenient to vary the speed of the motor to accommodate it to the -varying rate of pumping usually required. Messrs Hayward Tyler have -introduced a mechanism for varying the stroke of the pumps (Sinclair's -patent) from full stroke to nil, without stopping the pumps. - -S 207. _Centrifugal Pump._--For large volumes of water on lifts not -exceeding about 60 ft. the most convenient pump is the centrifugal pump. -Recent improvements have made it available also for very high lifts. It -consists of a wheel or fan with curved vanes enclosed in an annular -chamber. Water flows in at the centre and is discharged at the -periphery. The fan may rotate in a vertical or horizontal plane and the -water may enter on one or both sides of the fan. In the latter case -there is no axial unbalanced pressure. The fan and its casing must be -filled with water before it can start, so that if not drowned there must -be a foot valve on the suction pipe. When no special attention needs to -be paid to efficiency the water may have a velocity of 6 to 7 ft. in the -suction and delivery pipes. The fan often has 6 to 12 vanes. For a -double-inlet fan of diameter D, the diameter of the inlets is D/2. If Q -is the discharge in cub. ft. per second D = about 0.6 [root]Q in average -cases. The peripheral speed is a little greater than the velocity due -to the lift. Ordinary centrifugal pumps will have an efficiency of 40 to -60%. - -The first pump of this kind which attracted notice was one exhibited by -J. G. Appold in 1851, and the special features of his pump have been -retained in the best pumps since constructed. Appold's pump raised -continuously a volume of water equal to 1400 times its own capacity per -minute. It had no valves, and it permitted the passage of solid bodies, -such as walnuts and oranges, without obstruction to its working. Its -efficiency was also found to be good. - -[Illustration: FIG. 209.] - -Fig. 209 shows the ordinary form of a centrifugal pump. The pump disk -and vanes B are cast in one, usually of bronze, - -and the disk is keyed on the driving shaft C. The casing A has a -spirally enlarging discharge passage into the discharge pipe K. A cover -L gives access to the pump. S is the suction pipe which opens into the -pump disk on both sides at D. - -Fig. 210 shows a centrifugal pump differing from ordinary centrifugal -pumps in one feature only. The water rises through a suction pipe S, -which divides so as to enter the pump wheel W at the centre on each -side. The pump disk or wheel is very similar to a turbine wheel. It is -keyed on a shaft driven by a belt on a fast and loose pulley arrangement -at P. The water rotating in the pump disk presses outwards, and if the -speed is sufficient a continuous flow is maintained through the pump and -into the discharge pipe D. The special feature in this pump is that the -water, discharged by the pump disk with a whirling velocity of not -inconsiderable magnitude, is allowed to continue rotation in a chamber -somewhat larger than the pump. The use of this whirlpool chamber was -first suggested by Professor James Thomson. It utilizes the energy due -to the whirling velocity of the water which in most pumps is wasted in -eddies in the discharge pipe. In the pump shown guide-blades are also -added which have the direction of the stream lines in a free vortex. -They do not therefore interfere with the action of the water when -pumping the normal quantity, but only prevent irregular motion. At A is -a plug by which the pump case is filled before starting. If the pump is -above the water to be pumped, a foot valve is required to permit the -pump to be filled. Sometimes instead of the foot valve a delivery valve -is used, an air-pump or steam jet pump being employed to exhaust the air -from the pump case. - -[Illustration: FIG. 210.] - - S 208. _Design and Proportions of a Centrifugal Pump._--The design of - the pump disk is very simple. Let r_i, r_o be the radii of the inlet - and outlet surfaces of the pump disk, d_i, d_o the clear axial width - at those radii. The velocity of flow through the pump may be taken - the same as for a turbine. If Q is the quantity pumped, and H the - lift, - - u_i = 0.25 [root](2gH). (1) - - 2[pi]r_i d_i = Q/u_i. - - Also in practice - - d_i = 1.2 r_i .... - - Hence, - - r_i = .2571 [root](Q/[root]H). (2) - - Usually - - r_o = 2r_i, - - and - - d_o = d_i or (1/2)d_i - - according as the disk is parallel-sided or coned. The water enters the - wheel radially with the velocity u_i, and - - u_o = Q/2[pi]r_o d_o. (3) - - [Illustration: FIG. 211.] - - Fig. 211 shows the notation adopted for the velocities. Suppose the - water enters the wheel with the velocity v_i, while the velocity of - the wheel is V_i. Completing the parallelogram, v_(ri) is the relative - velocity of the water and wheel, and is the proper direction of the - wheel vanes. Also, by resolving, u_i and w_i are the component - velocities of flow and velocities of whir of the velocity v_i of the - water. At the outlet surface, v_o is the final velocity of discharge, - and the rest of the notation is similar to that for the inlet surface. - - Usually the water flows equally in all directions in the eye of the - wheel, in that case v_i is radial. Then, in normal conditions of - working, at the inlet surface, - - v_i = u_i \ - w_i = 0 > (4) - tan[theta] = u_i/V_i | - v_(ri) = u_i cosec [theta] = [root](u_i^2 + V_i^2) / - - If the pump is raising less or more than its proper quantity, [theta] - will not satisfy the last condition, and there is then some loss of - head in shock. - - At the outer circumference of the wheel or outlet surface, - - v_(ro) = u_o cosec [phi] \ - w_o = V_o - u_o cot [phi] > (5) - v_o = [root]{u_o^2 + (V - _o - u_o cot [phi])^2} / - - _Variation of Pressure in the Pump Disk._--Precisely as in the case of - turbines, it can be shown that the variation of pressure between the - inlet and outlet surfaces of the pump is - - h_o - h_i = (V_o^2 - V_i^2)/2g - (v_(ro)^2 - v_(ri)^2)/2g. - - Inserting the values of v_(ro), v_(ri) in (4) and (5), we get for - normal conditions of working - - h_o -h_i = (V_o^2 - V_i^2)/2g - u_o^2 cosec^2 [phi]/2g + (u_i^2 + V_i^2)/2g - = V_o^2/2g - u_o^2 cosec^2 [phi]/2g + u_i^2/2g. (6) - - _Hydraulic Efficiency of the Pump._--Neglecting disk friction, journal - friction, and leakage, the efficiency of the pump can be found in the - same way as that of turbines (S 186). Let M be the moment of the - couple rotating the pump, and [alpha] its angular velocity; w_o, r_o - the tangential velocity of the water and radius at the outlet surface; - w_i, r_i the same quantities at the inlet surface. Q being the - discharge per second, the change of angular momentum per second is - - (GQ/g)(w_o r_o - w_i r_i). - - Hence - - M = (GQ/g)(w_o r_o - w_i r_i). - - In normal working, w_i = 0. Also, multiplying by the angular velocity, - the work done per second is - - M[alpha] = (GQ/g)w_o r_o[alpha]. - - But the useful work done in pumping is GQH. Therefore the efficiency - is - - [eta] = GQH/M[alpha] = gH/w_o r_o[alpha] = gH/w_o V_o. (7) - - S 209. Case 1. _Centrifugal Pump with no Whirlpool Chamber._--When no - special provision is made to utilize the energy of motion of the water - leaving the wheel, and the pump discharges directly into a chamber in - which the water is flowing to the discharge pipe, nearly the whole of - the energy of the water leaving the disk is wasted. The water leaves - the disk with the more or less considerable velocity v_o, and impinges - on a mass flowing to the discharge pipe at the much slower velocity - v_s. The radial component of v_o is almost necessarily wasted. From - the tangential component there is a gain of pressure - - (w_o^2 - v_s^2)/2g - (w_o - v_s)^2/2g - = v_s(w_o - v_s)g, - - which will be small, if v_s is small compared with w_o. Its greatest - value, if v_s = (1/2)w_o, is (1/2)w_o^2/2g, which will always be a - small part of the whole head. Suppose this neglected. The whole - variation of pressure in the pump disk then balances the lift and the - head u_i^2/2g necessary to give the initial velocity of flow in the - eye of the wheel. - - u_i^2/2g + H = V_o^2/2g - u_o^2 cosec^2 [phi]/2g + u_i^2/2g, - - H = V_o^2/2g - u_o^2 cosec^2 [phi]/2g - - or - - V_o = [root](2gH + u_o^2 cosec^2 [phi]). (8) - - and the efficiency of the pump is, from (7), - - [eta] = gH/V_o w_o = gH/{V (V_o - n_o cot [phi])}, - - = (V_o^2 - u_o^2 cosec^2 [phi])/{2V_o (V_o - u_o cot [phi]) }, (9). - - For [phi] = 90 deg., - - [eta] = (V_o^2 - u_o^2)/2V_o^2, - - which is necessarily less than 1/2. That is, half the work expended in - driving the pump is wasted. By recurving the vanes, a plan introduced - by Appold, the efficiency is increased, because the velocity v_o of - discharge from the pump is diminished. If [phi] is very small, - - cosec [phi] = cot [phi]; - - and then - - [eta] = (V_o, + u_o cosec [phi])/2V_o, - - which may approach the value 1, as [phi] tends towards 0. Equation (8) - shows that u_o cosec [phi] cannot be greater than V_o. Putting u_o = - 0.25 [root](2gH) we get the following numerical values of the - efficiency and the circumferential velocity of the pump:-- - - [phi] [eta] V_o - - 90 deg. 0.47 1.03 [root](2gH) - 45 deg. 0.56 1.06 " - 30 deg. 0.65 1.12 " - 20 deg. 0.73 1.24 " - 10 deg. 0.84 1.75 " - - [phi] cannot practically be made less than 20 deg.; and, allowing for - the frictional losses neglected, the efficiency of a pump in which - [phi] = 20 deg. is found to be about .60. - - S 210. Case 2. _Pump with a Whirlpool Chamber_, as in fig. - 210.--Professor James Thomson first suggested that the energy of the - water after leaving the pump disk might be utilized, if a space were - left in which a free vortex could be formed. In such a free vortex the - velocity varies inversely as the radius. The gain of pressure in the - vortex chamber is, putting r_o, r_w for the radii to the outlet - surface of wheel and to outside of free vortex, - - v_o^2 / r_o^2 \ v_o^2 / \ - ---- ( 1 - ----- ) = ----- ( 1 - k^2 ), - 2g \ r_w^2 / 2g \ / - - if - - k = r_o/r_w. - - The lift is then, adding this to the lift in the last case, - - H = {V_o^2 - u_o^2 cosec^2 [phi] + v_o^2(1 - k^2)}/2g. - - But - - v_o^2 = V_o^2 - 2V_o u_o cot [phi] + u_o^2 cosec^2 [phi]; - - .: H = {(2 - k^2)V_o^2 - 2kV_o u_o cot [phi] - k^2u_o^2 cosec^2 [phi]}/2g. (10) - - Putting this in the expression for the efficiency, we find a - considerable increase of efficiency. Thus with - - [phi] = 90 deg. and k = 1/2, [eta] = 7/8 nearly, - - [phi] a small angle and k = 1/2, [eta] = 1 nearly. - - With this arrangement of pump, therefore, the angle at the outer ends - of the vanes is of comparatively little importance. A moderate angle - of 30 deg. or 40 deg. may very well be adopted. The following - numerical values of the velocity of the circumference of the pump have - been obtained by taking k = 1/2, and u_o = 0.25 [root](2gH). - - [phi] V_o - - 90 deg. .762 [root](2gH) - 45 deg. .842 " - 30 deg. .911 " - 20 deg. 1.023 " - - The quantity of water to be pumped by a centrifugal pump necessarily - varies, and an adjustment for different quantities of water cannot - easily be introduced. Hence it is that the average efficiency of pumps - of this kind is in practice less than the efficiencies given above. - The advantage of a vortex chamber is also generally neglected. The - velocity in the supply and discharge pipes is also often made greater - than is consistent with a high degree of efficiency. Velocities of 6 - or 7 ft. per second in the discharge and suction pipes, when the lift - is small, cause a very sensible waste of energy; 3 to 6 ft. would be - much better. Centrifugal pumps of very large size have been - constructed. Easton and Anderson made pumps for the North Sea canal in - Holland to deliver each 670 tons of water per minute on a lift of 5 - ft. The pump disks are 8 ft. diameter. J. and H. Gwynne constructed - some pumps for draining the Ferrarese Marshes, which together deliver - 2000 tons per minute. A pump made under Professor J. Thomson's - direction for drainage works in Barbados had a pump disk 16 ft. in - diameter and a whirlpool chamber 32 ft. in diameter. The efficiency of - centrifugal pumps when delivering less or more than the normal - quantity of water is discussed in a paper in the _Proc. Inst. Civ. - Eng._ vol. 53. - -S 211. _High Lift Centrifugal Pumps._--It has long been known that -centrifugal pumps could be worked in series, each pump overcoming a part -of the lift. This method has been perfected, and centrifugal pumps for -very high lifts with great efficiency have been used by Sulzer and -others. C. W. Darley (_Proc. Inst. Civ. Eng._, supplement to vol. 154, -p. 156) has described some pumps of this new type driven by Parsons -steam turbines for the water supply of Sydney, N.S.W. Each pump was -designed to deliver 1(1/2) million gallons per twenty-four hours against -a head of 240 ft. at 3300 revs. per minute. Three pumps in series give -therefore a lift of 720 ft. The pump consists of a central double-sided -impeller 12 in. diameter. The water entering at the bottom divides and -enters the runner at each side through a bell-mouthed passage. The shaft -is provided with ring and groove glands which on the suction side keep -the air out and on the pressure side prevent leakage. Some water from -the pressure side leaks through the glands, but beyond the first grooves -it passes into a pocket and is returned to the suction side of the pump. -For the glands on the suction side water is supplied from a low-pressure -service. No packing is used in the glands. During the trials no water -was seen at the glands. The following are the results of tests made at -Newcastle:-- - - +-------------------------------------+-------+-------+-------+-------+ - | | I. | II. | III. | IV. | - +-------------------------------------+-------+-------+-------+-------+ - | Duration of test hours | 2 | 1.54 | 1.2 | 1.55 | - | Steam pressure lb. per sq. in. | 57 | 57 | 84 | 55 | - | Weight of steam per water | | | | | - | h.p. hour lb. | 27.93 | 30.67 | 28.83 | 27.89 | - | Speed in revs, per min. | 3300 | 3330 | 3710 | 3340 | - | Height of suction ft. | 11 | 11 | 11 | 11 | - | Total lift ft. | 762 | 744 | 917 | 756 | - | Million galls. per day pumped-- | | | | | - | By Ventun meter | 1.573 | 1.499 | 1.689 | 1.503 | - | By orifice | 1.623 | 1.513 | 1.723 | 1.555 | - | Water h.p. | 252 | 235 | 326 | 239 | - +-------------------------------------+-------+-------+-------+-------+ - -In trial IV. the steam was superheated 95 deg. F. From other trials under -the same conditions as trial I. the Parsons turbine uses 15.6 lb. of -steam per brake h.p. hour, so that the combined efficiency of turbine -and pumps is about 56%, a remarkably good result. - -[Illustration: FIG. 212.] - -S 212. _Air-Lift Pumps._--An interesting and simple method of pumping by -compressed air, invented by Dr J. Pohle of Arizona, is likely to be very -useful in certain cases. Suppose a rising main placed in a deep bore -hole in which there is a considerable depth of water. Air compressed to -a sufficient pressure is conveyed by an air pipe and introduced at the -lower end of the rising main. The air rising In the main diminishes the -average density of the contents of the main, and their aggregate weight -no longer balances the pressure at the lower end of the main due to its -submersion. An upward flow is set up, and if the air supply is -sufficient the water in the rising main is lifted to any required -height. The higher the lift above the level in the bore hole the deeper -must be the point at which air is injected. Fig. 212 shows an airlift -pump constructed for W. H. Maxwell at the Tunbridge Wells waterworks. -There is a two-stage steam air compressor, compressing air to from 90 to -100 lb. per sq. in. The bore hole is 350 ft. deep, lined with steel -pipes 15 in. diameter for 200 ft. and with perforated pipes 13(1/2) in. -diameter for the lower 150 ft. The rest level of the water is 96 ft. -from the ground-level, and the level when pumping 32,000 gallons per -hour is 120 ft. from the ground-level. The rising main is 7 in. -diameter, and is carried nearly to the bottom of the bore hole and to 20 -ft. above the ground-level. The air pipe is 2(1/2) in. diameter. In a -trial run 31,402 gallons per hour were raised 133 ft. above the level in -the well. Trials of the efficiency of the system made at San Francisco -with varying conditions will be found in a paper by E. A. Rix (_Journ. -Amer. Assoc. Eng. Soc._ vol. 25, 1900). Maxwell found the best results -when the ratio of immersion to lift was 3 to 1 at the start and 2.2 to 1 -at the end of the trial. In these conditions the efficiency was 37% -calculated on the indicated h.p. of the steam-engine, and 46% calculated -on the indicated work of the compressor. 2.7 volumes of free air were -used to 1 of water lifted. The system is suitable for temporary -purposes, especially as the quantity of water raised is much greater -than could be pumped by any other system in a bore hole of a given size. -It is useful for clearing a boring of sand and may be advantageously -used permanently when a boring is in sand or gravel which cannot be kept -out of the bore hole. The initial cost is small. - -S 213. _Centrifugal Fans._--Centrifugal fans are constructed similarly -to centrifugal pumps, and are used for compressing air to pressures not -exceeding 10 to 15 in. of water-column. With this small variation of -pressure the variation of volume and density of the air may be neglected -without sensible error. The conditions of pressure and discharge for -fans are generally less accurately known than in the case of pumps, and -the design of fans is generally somewhat crude. They seldom have -whirlpool chambers, though a large expanding outlet is provided in the -case of the important Guibal fans used in mine ventilation. - - It is usual to reckon the difference of pressure at the inlet and - outlet of a fan in inches of water-column. One inch of water-column = - 64.4 ft. of air at average atmospheric pressure = 5.2lb. per sq. ft. - - Roughly the pressure-head produced in a fan without means of utilizing - the kinetic energy of discharge would be v^2/2g ft. of air, or 0.00024 - v^2 in. of water, where v is the velocity of the tips of the fan blades - in feet per second. If d is the diameter of the fan and t the width at - the external circumference, then [pi]dt is the discharge area of the - fan disk. If Q is the discharge in cub. ft. per sec., u = Q/[pi]dt is - the radial velocity of discharge which is numerically equal to the - discharge per square foot of outlet in cubic feet per second. As both - the losses in the fan and the work done are roughly proportional to u^2 - in fans of the same type, and are also proportional to the gauge - pressure p, then if the losses are to be a constant percentage of the - work done u may be taken proportional to [root]p. In ordinary cases u - = about 22[root]p. The width t of the fan is generally from 0.35 to - 0.45d. Hence if Q is given, the diameter of the fan should be:-- - - For t = 0.35d, d = 0.20 [root](Q/[root]p) - For t = 0.45d, d = 0.18 [root](Q/[root]p) - - If p is the pressure difference in the fan in inches of water, and N - the revolutions of fan, - - v = [pi]dN/60 ft. per sec. - N = 1230 [root]p/d revs. per min. - - As the pressure difference is small, the work done in compressing the - air is almost exactly 5.2pQ foot-pounds per second. Usually, however, - the kinetic energy of the air in the discharge pipe is not - inconsiderable compared with the work done in compression. If w is the - velocity of the air where the discharge pressure is measured, the air - carries away w^2/2g foot-pounds per lb. of air as kinetic energy. In Q - cubic feet or 0.0807 Qlb. the kinetic energy is 0.00125 Qw^2 - foot-pounds per second. - - The efficiency of fans is reckoned in two ways. If B.H.P. is the - effective horse-power applied at the fan shaft, then the efficiency - reckoned on the work of compression is - - [eta] = 5.2 pQ/550 B.H.P. - - On the other hand, if the kinetic energy in the delivery pipe is taken - as part of the useful work the efficiency is - - [eta]2 = (5.2 pQ + 0.00125 Qw^2)/550 B.H.P. - - Although the theory above is a rough one it agrees sufficiently with - experiment, with some merely numerical modifications. - - An extremely interesting experimental investigation of the action of - centrifugal fans has been made by H. Heenan and W. Gilbert (_Proc. - Inst. Civ. Eng._ vol. 123, p. 272). The fans delivered through an air - trunk in which different resistances could be obtained by introducing - diaphragms with circular apertures of different sizes. Suppose a fan - run at constant speed with different resistances and the compression - pressure, discharge and brake horse-power measured. The results plot - in such a diagram as is shown in fig. 213. The less the resistance to - discharge, that is the larger the opening in the air trunk, the - greater the quantity of air discharged at the given speed of the fan. - On the other hand the compression pressure diminishes. The curve - marked total gauge is the compression pressure + the velocity head in - the discharge pipe, both in inches of water. This curve falls, but not - nearly so much as the compression curve, when the resistance in the - air trunk is diminished. The brake horse-power increases as the - resistance is diminished because the volume of discharge increases - very much. The curve marked efficiency is the efficiency calculated - on the work of compression only. It is zero for no discharge, and zero - also when there is no resistance and all the energy given to the air - is carried away as kinetic energy. There is a discharge for which this - efficiency is a maximum; it is about half the discharge which there is - when there is no resistance and the delivery pipe is full open. The - conditions of speed and discharge corresponding to the greatest - efficiency of compression are those ordinarily taken as the best - normal conditions of working. The curve marked total efficiency gives - the efficiency calculated on the work of compression and kinetic - energy of discharge. Messrs Gilbert and Heenan found the efficiencies - of ordinary fans calculated on the compression to be 40 to 60% when - working at about normal conditions. - - [Illustration: FIG. 213.] - - Taking some of Messrs Heenan and Gilbert's results for ordinary fans - in normal conditions, they have been found to agree fairly with the - following approximate rules. Let p_c be the compression pressure and q - the volume discharged per second per square foot of outlet area of - fan. Then the total gauge pressure due to pressure of compression and - velocity of discharge is approximately: p = p_c + 0.0004 q^2 in. of - water, so that if p_c is given, p can be found approximately. The - pressure p depends on the circumferential speed v of the fan disk-- - - p = 0.00025 v^2 in. of water - - v = 63 [root]p ft. per sec. - - The discharge per square foot of outlet of fan is-- - - q = 15 to 18 [root]p cub. ft. per sec. - - The total discharge is - - Q = [pi] dt q = 47 to 56 dt [root]p - - For - - t = .35d, d = 0.22 to 0.25 [root](Q/[root]p) ft. - - t = .45d, d = 0.20 to 0.22 [root](Q/[root]p) ft. - - N = 1203 [root]p/d. - - These approximate equations, which are derived purely from experiment, - do not differ greatly from those obtained by the rough theory given - above. The theory helps to explain the reason for the form of the - empirical results. (W. C. U.) - - -FOOTNOTES: - - [1] Except where other units are given, the units throughout this - article are feet, pounds, pounds per sq. ft., feet per second. - - [2] _Journal de M. Liouville_, t. xiii. (1868); _Memoires de - l'Academie, des Sciences de l'Institut de France_, t. xxiii., xxiv. - (1877). - - [3] The following theorem is taken from a paper by J. H. Cotterill, - "On the Distribution of Energy in a Mass of Fluid in Steady Motion," - _Phil. Mag._, February 1876. - - [4] The discharge per second varied from .461 to .665 cub. ft. in two - experiments. The coefficient .435 is derived from the mean value. - - [5] "Formulae for the Flow of Water in Pipes," _Industries_ - (Manchester, 1886). - - [6] Boussinesq has shown that this mode of determining the corrective - factor [alpha] is not satisfactory. - - [7] In general, because when the water leaves the turbine wheel it - ceases to act on the machine. If deflecting vanes or a whirlpool are - added to a turbine at the discharging side, then v1 may in part - depend on v2, and the statement above is no longer true. - - - - -HYDRAZINE (DIAMIDOGEN), N2H4 or H2 N.NH2, a compound of hydrogen and -nitrogen, first prepared by Th. Curtius in 1887 from diazo-acetic ester, -N2CH.CO2C2H5. This ester, which is obtained by the action of potassium -nitrate on the hydrochloride of amidoacetic ester, yields on hydrolysis -with hot concentrated potassium hydroxide an acid, which Curtius -regarded as C3H3N6(CO2H)3, but which A. Hantzsch and O. Silberrad -(_Ber._, 1900, 33, p. 58) showed to be C2H2N4(CO2H)2, bisdiazoacetic -acid. On digestion of its warm aqueous solution with warm dilute -sulphuric acid, hydrazine sulphate and oxalic acid are obtained. C. A. -Lobry de Bruyn (_Ber._, 1895, 28, p. 3085) prepared free hydrazine by -dissolving its hydrochloride in methyl alcohol and adding sodium -methylate; sodium chloride was precipitated and the residual liquid -afterwards fractionated under reduced pressure. It can also be prepared -by reducing potassium dinitrososulphonate in ice cold water by means of -sodium amalgam:-- - - KSO3 \ KSO3 \ - > N.NO --> > N.NH2 --> K2SO4 + N2H4. - KO / H / - -P. J. Schestakov (_J. Russ. Phys. Chem. Soc._, 1905, 37, p. 1) obtained -hydrazine by oxidizing urea with sodium hypochlorite in the presence of -benzaldehyde, which, by combining with the hydrazine, protected it from -oxidation. F. Raschig (German Patent 198307, 1908) obtained good yields -by oxidizing ammonia with sodium hypochlorite in solutions made viscous -with glue. Free hydrazine is a colourless liquid which boils at 113.5 -deg. C., and solidifies about 0 deg. C. to colourless crystals; it is -heavier than water, in which it dissolves with rise of temperature. It -is rapidly oxidized on exposure, is a strong reducing agent, and reacts -vigorously with the halogens. Under certain conditions it may be -oxidized to azoimide (A. W. Browne and F. F. Shetterly, _J. Amer. C.S._, -1908, p. 53). By fractional distillation of its aqueous solution -hydrazine hydrate N2H4.H2O (or perhaps H2N.NH3OH), a strong base, is -obtained, which precipitates the metals from solutions of copper and -silver salts at ordinary temperatures. It dissociates completely in a -vacuum at 143 deg., and when heated under atmospheric pressure to 183 -deg. it decomposes into ammonia and nitrogen (A. Scott, _J. Chem. Soc._, -1904, 85, p. 913). The sulphate N2H4.H2SO4, crystallizes in tables which -are slightly soluble in cold water and readily soluble in hot water; it -is decomposed by heating above 250 deg. C. with explosive evolution of -gas and liberation of sulphur. By the addition of barium chloride to the -sulphate, a solution of the hydrochloride is obtained, from which the -crystallized salt may be obtained on evaporation. - - Many organic derivatives of hydrazine are known, the most important - being phenylhydrazine, which was discovered by Emil Fischer in 1877. - It can be best prepared by V. Meyer and Lecco's method (_Ber._, 1883, - 16, p. 2976), which consists in reducing phenyldiazonium chloride in - concentrated hydrochloric acid solution with stannous chloride also - dissolved in concentrated hydrochloric acid. Phenylhydrazine is - liberated from the hydrochloride so obtained by adding sodium - hydroxide, the solution being then extracted with ether, the ether - distilled off, and the residual oil purified by distillation under - reduced pressure. Another method is due to E. Bamberger. The diazonium - chloride, by the addition of an alkaline sulphite, is converted into a - diazosulphonate, which is then reduced by zinc dust and acetic acid to - phenylhydrazine potassium sulphite. This salt is then hydrolysed by - heating it with hydrochloric acid-- - - C6H5N2Cl + K2SO3 = KCl + C6H5N2.SO3K, - - C6H5N2.SO3K + 2H = C6H5.NH.NH.SO3K, - - C6H5NH.NH.SO3K + HCl + H2O = C6H5.NH.NH2.HCl + KHSO4. - - Phenylhydrazine is a colourless oily liquid which turns brown on - exposure. It boils at 241 deg. C., and melts at 17.5 deg. C. It is - slightly soluble in water, and is strongly basic, forming well-defined - salts with acids. For the detection of substances containing the - carbonyl group (such for example as aldehydes and ketones) - phenylhydrazine is a very important reagent, since it combines with - them with elimination of water and the formation of well-defined - hydrazones (see ALDEHYDES, KETONES and SUGARS). It is a strong - reducing agent; it precipitates cuprous oxide when heated with - Fehling's solution, nitrogen and benzene being formed at the same - time--C6H5.NH.NH2 + 2CuO = Cu2O + N2 + H2O + C6H5. By energetic - reduction of phenylhydrazine (e.g. by use of zinc dust and - hydrochloric acid), ammonia and aniline are produced--C6H5NH.NH2 + 2H - = C6H5NH2 + NH3. It is also a most important synthetic reagent. It - combines with aceto-acetic ester to form phenylmethylpyrazolone, from - which antipyrine (q.v.) may be obtained. Indoles (q.v.) are formed by - heating certain hydrazones with anhydrous zinc chloride; while - semicarbazides, pyrrols (q.v.) and many other types of organic - compounds may be synthesized by the use of suitable phenylhydrazine - derivatives. - - - - -HYDRAZONE, in chemistry, a compound formed by the condensation of a -hydrazine with a carbonyl group (see ALDEHYDES; KETONES). - - - - -HYDROCARBON, in chemistry, a compound of carbon and hydrogen. Many occur -in nature in the free state: for example, natural gas, petroleum and -paraffin are entirely composed of such bodies; other natural sources are -india-rubber, turpentine and certain essential oils. They are also -revealed by the spectroscope in stars, comets and the sun. Of artificial -productions the most fruitful and important is provided by the -destructive or dry distillation of many organic substances; familiar -examples are the distillation of coal, which yields ordinary lighting -gas, composed of gaseous hydrocarbons, and also coal tar, which, on -subsequent fractional distillations, yields many liquid and solid -hydrocarbons, all of high industrial value. For details reference should -be made to the articles wherein the above subjects are treated. From the -chemical point of view the hydrocarbons are of fundamental importance, -and, on account of their great number, and still greater number of -derivatives, they are studied as a separate branch of the science, -namely, organic chemistry. - - See CHEMISTRY for an account of their classification, &c. - - - - -HYDROCELE (Gr. [Greek: hydor], water, and [Greek: kele], tumour), the -medical term for any collection of fluid other than pus or blood in the -neighbourhood of the testis or cord. The fluid is usually serous. -Hydrocele may be congenital or arise in the middle-aged without apparent -cause, but it is usually associated with chronic orchitis or with -tertiary syphilitic enlargements. The hydrocele appears as a rounded, -fluctuating translucent swelling in the scrotum, and when greatly -distended causes a dragging pain. Palliative treatment consists in -tapping aseptically and removing the fluid, the patient afterwards -wearing a suspender. The condition frequently recurs and necessitates -radical treatment. Various substances may be injected; or the hydrocele -is incised, the tunica partly removed and the cavity drained. - - - - -HYDROCEPHALUS (Gr. [Greek: hydor], water, and [Greek: kephale], head), a -term applied to disease of the brain which is attended with excessive -effusion of fluid into its cavities. It exists in two forms--_acute_ and -_chronic hydrocephalus_. Acute hydrocephalus is another name for -tuberculous meningitis (see MENINGITIS). - -_Chronic hydrocephalus_, or "water on the brain," consists in an -effusion of fluid into the lateral ventricles of the brain. It is not -preceded by tuberculous deposit or acute inflammation, but depends upon -congenital malformation or upon chronic inflammatory changes affecting -the membranes. When the disease is congenital, its presence in the -foetus is apt to be a source of difficulty in parturition. It is however -more commonly developed in the first six months of life; but it -occasionally arises in older children, or even in adults. The chief -symptom is the gradual increase in size of the upper part of the head -out of all proportion to the face or the rest of the body. Occurring at -an age when as yet the bones of the skull have not become welded -together, the enlargement may go on to an enormous extent, the Spaces -between the bones becoming more and more expanded. In a well-marked case -the deformity is very striking; the upper part of the forehead projects -abnormally, and the orbital plates of the frontal bone being inclined -forwards give a downward tilt to the eyes, which have also peculiar -rolling movements. The face is small, and this, with the enlarged head, -gives a remarkable aged expression to the child. The body is -ill-nourished, the bones are thin, the hair is scanty and fine and the -teeth carious or absent. - -The average circumference of the adult head is 22 in., and in the normal -child it is of course much less. In chronic hydrocephalus the head of an -infant three months old has measured 29 in.; and in the case of the man -Cardinal, who died in Guy's Hospital, the head measured 33 in. In such -cases the head cannot be supported by the neck, and the patient has to -keep mostly in the recumbent posture. The expansibility of the skull -prevents destructive pressure on the brain, yet this organ is materially -affected by the presence of the fluid. The cerebral ventricles are -distended, and the convolutions are flattened. Occasionally the fluid -escapes into the cavity of the cranium, which it fills, pressing down -the brain to the base of the skull. As a consequence, the functions of -the brain are interfered with, and the mental condition is impaired. The -child is dull, listless and irritable, and sometimes imbecile. The -special senses become affected as the disease advances; sight is often -lost, as is also hearing. Hydrocephalic children generally sink in a few -years; nevertheless there have been instances of persons with this -disease living to old age. There are, of course, grades of the -affection, and children may present many of the symptoms of it in a -slight degree, and yet recover, the head ceasing to expand, and becoming -in due course firmly ossified. - -Various methods of treatment have been employed, but the results are -unsatisfactory. Compression of the head by bandages, and the -administration of mercury with the view of promoting absorption of the -fluid, are now little resorted to. Tapping the fluid from time to time -through one of the spaces between the bones, drawing off a little, and -thereafter employing gentle pressure, has been tried, but rarely with -benefit. Attempts have also been made to establish a permanent drainage -between the interior of the lateral ventricle and the sub-dural space, -and between the lumbar region of the spine and the abdomen, but without -satisfactory results. On the whole, the plan of treatment which aims at -maintaining the patient's nutrition by appropriate food and tonics is -the most rational and successful. (E. O.*) - - - - -HYDROCHARIDEAE, in botany, a natural order of Monocotyledons, belonging -to the series Helobieae. They are water-plants, represented in Britain -by frog-bit (_Hydrocharis Morsusranae_) and water-soldier (_Stratiotes -aloides_). The order contains about fifty species in fifteen genera, -twelve of which occur in fresh water while three are marine: and -includes both floating and submerged forms. _Hydrocharis_ floats on the -surface of still water, and has rosettes of kidney-shaped leaves, from -among which spring the flower-stalks; stolons bearing new leaf-rosettes -are sent out on all sides, the plant thus propagating itself on the same -way as the strawberry. _Stratiotes aloides_ has a rosette of stiff -sword-like leaves, which when the plant is in flower project above the -surface; it is also stoloniferous, the young rosettes sinking to the -bottom at the beginning of winter and rising again to the surface in the -spring. _Vallisneria_ (eel-grass) contains two species, one native of -tropical Asia, the other inhabiting the warmer parts of both hemispheres -and reaching as far north as south Europe. It grows in the mud at the -bottom of fresh water, and the short stem bears a cluster of long, -narrow grass-like leaves; new plants are formed at the end of horizontal -runners. Another type is represented by _Elodea canadensis_ or -water-thyme, which has been introduced into the British Isles from North -America. It is a small, submerged plant with long, slender branching -stems bearing whorls of narrow toothed leaves; the flowers appear at the -surface when mature. _Halophila_, _Enhalus_ and _Thalassia_ are -submerged maritime plants found on tropical coasts, mainly in the Indian -and Pacific oceans; _Halophila_ has an elongated stem rooting at the -nodes; _Enhalus_ a short, thick rhizome, clothed with black threads -resembling horse-hair, the persistent hard-bast strands of the leaves; -_Thalassia_ has a creeping rooting stem with upright branches bearing -crowded strap-shaped leaves in two rows. The flowers spring from, or are -enclosed in, a spathe, and are unisexual and regular, with generally a -calyx and corolla, each of three members; the stamens are in whorls of -three, the inner whorls are often barren; the two to fifteen carpels -form an inferior ovary containing generally numerous ovules on often -large, produced, parietal placentas. The fruit is leathery or fleshy, -opening irregularly. The seeds contain a large embryo and no endosperm. -In _Hydrocharis_ (fig. 1), which is dioecious, the flowers are borne -above the surface of the water, have conspicuous white petals, contain -honey and are pollinated by insects. _Stratiotes_ has similar flowers -which come above the surface only for pollination, becoming submerged -again during ripening of the fruit. In _Vallisneria_ (fig. 2), which is -also dioecious, the small male flowers are borne in large numbers in -short-stalked spathes; the petals are minute and scale-like, and only -two of the three stamens are fertile; the flowers become detached before -opening and rise to the surface, where the sepals expand and form a -float bearing the two projecting semi-erect stamens. The female flowers -are solitary and are raised to the surface on a long, spiral stalk; the -ovary bears three broad styles, on which some of the large, sticky -pollen-grains from the floating male flowers get deposited, (fig. 3). -After pollination the female flower becomes drawn below the surface by -the spiral contraction of the long stalk, and the fruit ripens near the -bottom. _Elodea_ has polygamous flowers (that is, male, female and -hermaphrodite), solitary, in slender, tubular spathes; the male flowers -become detached and rise to the surface; the females are raised to the -surface when mature, and receive the floating pollen from the male. The -flowers of _Halophila_ are submerged and apetalous. - -[Illustration: FIG. 1.--_Hydrocharis Morsusranae_--Frog-bit--male plant. - - 1, Female flower. - 2, Stamens, enlarged. - 3, Barren pistil of male flower, enlarged. - 4, Pistil of female flower. - 5, Fruit. - 6, Fruit cut transversely. - 7, Seed. - 8, 9, Floral diagrams of male and female flowers respectively. - s, Rudimentary stamens.] - -[Illustration: FIG. 2.--_Vallisneria spiralis_--Eel grass--about 1/4 -natural size. A, Female plant; B, Male plant.] - -[Illustration: FIG. 3.] - -The order is a widely distributed one; the marine forms are tropical or -subtropical, but the fresh-water genera occur also in the temperate -zones. - - - - -HYDROCHLORIC ACID, also known in commerce as "spirits of salts" and -"muriatic acid," a compound of hydrogen and chlorine. Its chemistry is -discussed under CHLORINE, and its manufacture under ALKALI MANUFACTURE. - - - - -HYDRODYNAMICS (Gr. [Greek: hydor], water, [Greek: dynamis], strength), -the branch of hydromechanics which discusses the motion of fluids (see -HYDROMECHANICS). - - - - -HYDROGEN [symbol H, atomic weight 1.008 (o = 16)], one of the chemical -elements. Its name is derived from Gr. [Greek: hydor], water, and -[Greek: gennaein], to produce, in allusion to the fact that water is -produced when the gas burns in air. Hydrogen appears to have been -recognized by Paracelsus in the 16th century; the combustibility of the -gas was noticed by Turquet de Mayenne in the 17th century, whilst in -1700 N. Lemery showed that a mixture of hydrogen and air detonated on -the application of a light. The first definite experiments concerning -the nature of hydrogen were made in 1766 by H. Cavendish, who showed -that it was formed when various metals were acted upon by dilute -sulphuric or hydrochloric acids. Cavendish called it "inflammable air," -and for some time it was confused with other inflammable gases, all of -which were supposed to contain the same inflammable principle, -"phlogiston," in combination with varying amounts of other substances. -In 1781 Cavendish showed that water was the only substance produced when -hydrogen was burned in air or oxygen, it having been thought previously -to this date that other substances were formed during the reaction, A. -L. Lavoisier making many experiments with the object of finding an acid -among the products of combustion. - -Hydrogen is found in the free state in some volcanic gases, in -fumaroles, in the carnallite of the Stassfurt potash mines (H. Precht, -_Ber._, 1886, 19, p. 2326), in some meteorites, in certain stars and -nebulae, and also in the envelopes of the sun. In combination it is -found as a constituent of water, of the gases from certain mineral -springs, in many minerals, and in most animal and vegetable tissues. It -may be prepared by the electrolysis of acidulated water, by the -decomposition of water by various metals or metallic hydrides, and by -the action of many metals on acids or on bases. The alkali metals and -alkaline earth metals decompose water at ordinary temperatures; -magnesium begins to react above 70 deg. C., and zinc at a dull red heat. -The decomposition of steam by red hot iron has been studied by H. -Sainte-Claire Deville (_Comptes rendus_, 1870, 70, p. 1105) and by H. -Debray (ibid., 1879, 88, p. 1341), who found that at about 1500 deg. C. -a condition of equilibrium is reached. H. Moissan (_Bull. soc. chim._, -1902, 27, p. 1141) has shown that potassium hydride decomposes cold -water, with evolution of hydrogen, KH + H2O = KOH + H2. Calcium hydride -or hydrolite, prepared by passing hydrogen over heated calcium, -decomposes water similarly, 1 gram giving 1 litre of gas; it has been -proposed as a commercial source (Prats Aymerich, _Abst. J.C.S._, 1907, -ii. p. 543), as has also aluminium turnings moistened with potassium -cyanide and mercuric chloride, which decomposes water regularly at 70 -deg., 1 gram giving 1.3 litres of gas (Mauricheau-Beaupre, _Comptes -rendus_, 1908, 147, p. 310). Strontium hydride behaves similarly. In -preparing the gas by the action of metals on acids, dilute sulphuric or -hydrochloric acid is taken, and the metals commonly used are zinc or -iron. So obtained, it contains many impurities, such as carbon dioxide, -nitrogen, oxides of nitrogen, phosphoretted hydrogen, arseniuretted -hydrogen, &c., the removal of which is a matter of great difficulty (see -E. W. Morley, _Amer. Chem. Journ._, 1890, 12, p. 460). When prepared by -the action of metals on bases, zinc or aluminium and caustic soda or -caustic potash are used. Hydrogen may also be obtained by the action of -zinc on ammonium salts (the nitrate excepted) (Lorin, _Comptes rendus_, -1865, 60, p. 745) and by heating the alkali formates or oxalates with -caustic potash or soda, Na2C2O4 + 2NaOH = H2 + 2Na2CO3. Technically it -is prepared by the action of superheated steam on incandescent coke (see -F. Hembert and Henry, _Comptes rendus_, 1885, 101, p. 797; A. Naumann -and C. Pistor, _Ber._, 1885, 18, p. 1647), or by the electrolysis of a -dilute solution of caustic soda (C. Winssinger, _Chem. Zeit._, 1898, -22, p. 609; "Die Elektrizitats-Aktiengesellschaft," _Zeit. f. -Elektrochem._, 1901, 7, p. 857). In the latter method a 15% solution of -caustic soda is used, and the electrodes are made of iron; the cell is -packed in a wooden box, surrounded with sand, so that the temperature is -kept at about 70 deg. C.; the solution is replenished, when necessary, -with distilled water. The purity of the gas obtained is about 97%. - -Pure hydrogen is a tasteless, colourless and odourless gas of specific -gravity 0.06947 (air = 1) (Lord Rayleigh, _Proc. Roy. Soc._, 1893, p. -319). It may be liquefied, the liquid boiling at -252.68 deg. C. to --252.84 deg. C., and it has also been solidified, the solid melting at --264 deg. C. (J. Dewar, _Comptes rendus_, 1899, 129, p. 451; _Chem. -News_, 1901, 84, p. 49; see also LIQUID GASES). The specific heat of -gaseous hydrogen (at constant pressure) is 3.4041 (water = 1), and the -ratio of the specific heat at constant pressure to the specific heat at -constant volume is 1.3852 (W. C. Rontgen, _Pogg. Ann._, 1873, 148, p. -580). On the spectrum see SPECTROSCOPY. Hydrogen is only very slightly -soluble in water. It diffuses very rapidly through a porous membrane, -and through some metals at a red heat (T. Graham, _Proc. Roy. Soc._, -1867, 15, p. 223; H. Sainte-Claire Deville and L. Troost, _Comptes -rendus_, 1863, 56, p. 977). Palladium and some other metals are capable -of absorbing large volumes of hydrogen (especially when the metal is -used as a cathode in a water electrolysis apparatus). L. Troost and P. -Hautefeuille (_Ann. chim. phys._, 1874, (5) 2, p. 279) considered that a -palladium hydride of composition Pd2H was formed, but the investigations -of C. Hoitsema (_Zeit. phys. Chem._, 1895, 17, p. 1), from the -standpoint of the phase rule, do not favour this view, Hoitsema being of -the opinion that the occlusion of hydrogen by palladium is a process of -continuous absorption. Hydrogen burns with a pale blue non-luminous -flame, but will not support the combustion of ordinary combustibles. It -forms a highly explosive mixture with air or oxygen, especially when in -the proportion of two volumes of hydrogen to one volume of oxygen. H. B. -Baker (_Proc. Chem. Soc._, 1902, 18, p. 40) has shown that perfectly dry -hydrogen will not unite with perfectly dry oxygen. Hydrogen combines -with fluorine, even at very low temperatures, with great violence; it -also combines with carbon, at the temperature of the electric arc. The -alkali metals when warmed in a current of hydrogen, at about 360 deg. -C., form hydrides of composition RH (R = Na, K, Rb, Cs), (H. Moissan, -_Bull. soc. chim._, 1902, 27, p. 1141); calcium and strontium similarly -form hydrides CaH2, SrH2 at a dull red heat (A. Guntz, _Comptes rendus_, -1901, 133, p. 1209). Hydrogen is a very powerful reducing agent; the gas -occluded by palladium being very active in this respect, readily -reducing ferric salts to ferrous salts, nitrates to nitrites and -ammonia, chlorates to chlorides, &c. - - For determinations of the volume ratio with which hydrogen and oxygen - combine, see J. B. Dumas, _Ann. chim. phys._, 1843 (3), 8, p. 189; O. - Erdmann and R. F. Marchand, ibid., p. 212; E. H. Keiser, _Ber._, 1887, - 20, p. 2323; J. P. Cooke and T. W. Richards, _Amer. Chem. Journ._, - 1888, 10, p. 191; Lord Rayleigh, _Chem. News_, 1889, 59, p. 147; E. W. - Morley, _Zeit. phys. Chem._, 1890, 20, p. 417; and S. A. Leduc, - _Comptes rendus_, 1899, 128, p. 1158. - -Hydrogen combines with oxygen to form two definite compounds, namely, -water (q.v.), H2O, and hydrogen peroxide, H2O2, whilst the existence of -a third oxide, ozonic acid, has been indicated. - -_Hydrogen peroxide_, H2O2, was discovered by L. J. Thenard in 1818 -(_Ann. chim. phys._, 8, p. 306). It occurs in small quantities in the -atmosphere. It may be prepared by passing a current of carbon dioxide -through ice-cold water, to which small quantities of barium peroxide are -added from time to time (F. Duprey, _Comptes rendus_, 1862, 55, p. 736; -A. J. Balard, ibid., p. 758), BaO2 + CO2 + H2O = H2O2 + BaCO3. E. Merck -(_Abst. J.C.S._, 1907, ii., p. 859) showed that barium percarbonate, -BaCO4, is formed when the gas is in excess; this substance readily -yields the peroxide with an acid. Or barium peroxide may be decomposed -by hydrochloric, hydrofluoric, sulphuric or silicofluoric acids (L. -Crismer, _Bull. soc. chim._, 1891 (3), 6, p. 24; Hanriot, _Comptes -rendus_, 1885, 100, pp. 56, 172), the peroxide being added in -small quantities to a cold dilute solution of the acid. It is necessary -that it should be as pure as possible since the commercial product -usually contains traces of ferric, manganic and aluminium oxides, -together with some silica. To purify the oxide, it is dissolved in -dilute hydrochloric acid until the acid is neatly neutralized, the -solution is cooled, filtered, and baryta water is added until a faint -permanent white precipitate of hydrated barium peroxide appears; the -solution is now filtered, and a concentrated solution of baryta water is -added to the filtrate, when a crystalline precipitate of hydrated barium -peroxide, BaO2.H2O, is thrown down. This is filtered off and well washed -with water. The above methods give a dilute aqueous solution of hydrogen -peroxide, which may be concentrated somewhat by evaporation over -sulphuric acid in vacuo. H. P. Talbot and H. R. Moody (_Jour. Anal. -Chem._, 1892, 6, p. 650) prepared a more concentrated solution from the -commercial product, by the addition of a 10% solution of alcohol and -baryta water. The solution is filtered, and the barium precipitated by -sulphuric acid. The alcohol is removed by distillation _in vacuo_, and -by further concentration _in vacuo_ a solution may be obtained which -evolves 580 volumes of oxygen. R. Wolffenstein (_Ber._, 1894, 27, p. -2307) prepared practically anhydrous hydrogen peroxide (containing 99.1% -H2O2) by first removing all traces of dust, heavy metals and alkali from -the commercial 3% solution. The solution is then concentrated in an open -basis on the water-bath until it contains 48% H2O2. The liquid so -obtained is extracted with ether and the ethereal solution distilled -under diminished pressure, and finally purified by repeated -distillations. W. Staedel (_Zeit. f. angew. Chem._, 1902, 15, p. 642) -has described solid hydrogen peroxide, obtained by freezing concentrated -solutions. - -Hydrogen peroxide is also found as a product in many chemical actions, -being formed when carbon monoxide and cyanogen burn in air (H. B. -Dixon); by passing air through solutions of strong bases in the presence -of such metals as do not react with the bases to liberate hydrogen; by -shaking zinc amalgam with alcoholic sulphuric acid and air (M. Traube, -_Ber._, 1882, 15, p. 659); in the oxidation of zinc, lead and copper in -presence of water, and in the electrolysis of sulphuric acid of such -strength that it contains two molecules of water to one molecule of -sulphuric acid (M. Berthelot, _Comptes rendus_, 1878, 86, p. 71). - -The anhydrous hydrogen peroxide obtained by Wolffenstein boils at 84-85 -deg.C. (68 mm.); its specific gravity is 1.4996 (1.5 deg. C.). It is -very explosive (W. Spring, _Zeit. anorg. Chem._, 1895, 8, p. 424). The -explosion risk seems to be most marked in the preparations which have -been extracted with ether previous to distillation, and J. W. Bruhl -(_Ber._, 1895, 28, p. 2847) is of opinion that a very unstable, more -highly oxidized product is produced in small quantity in the process. -The solid variety prepared by Staedel forms colourless, prismatic -crystals which melt at -2 deg. C.; it is decomposed with explosive -violence by platinum sponge, and traces of manganese dioxide. The dilute -aqueous solution is very unstable, giving up oxygen readily, and -decomposing with explosive violence at 100 deg. C. An aqueous solution -containing more than 1.5% hydrogen peroxide reacts slightly acid. -Towards lupetidin [aa' dimethyl piperidine, C5H9N(CH3)2] hydrogen -peroxide acts as a dibasic acid (A. Marcuse and R. Wolffenstein, _Ber._, -1901, 34, p. 2430; see also G. Bredig, _Zeit. Electrochem._, 1901, 7, p. -622). Cryoscopic determinations of its molecular weight show that it is -H2O2. [G. Carrara, _Rend. della Accad. dei Lincei_, 1892 (5), 1, ii. p. -19; W. R. Orndorff and J. White, _Amer. Chem. Journ._, 1893, 15, p. -347.] Hydrogen peroxide behaves very frequently as a powerful oxidizing -agent; thus lead sulphide is converted into lead sulphate in presence of -a dilute aqueous solution of the peroxide, the hydroxides of the -alkaline earth metals are converted into peroxides of the type MO2.8H2O, -titanium dioxide is converted into the trioxide, iodine is liberated -from potassium iodide, and nitrites (in alkaline solution) are converted -into acid-amides (B. Radziszewski, _Ber._, 1884, 17, p. 355). In many -cases it is found that hydrogen peroxide will only act as an oxidant -when in the presence of a catalyst; for example, formic, glycollic, -lactic, tartaric, malic, benzoic and other organic acids are readily -oxidized in the presence of ferrous sulphate (H. J. H. Fenton, _Jour. -Chem. Soc._, 1900, 77, p. 69), and sugars are readily oxidized in the -presence of ferric chloride (O. Fischer and M. Busch, _Ber._, 1891, 24, -p. 1871). It is sought to explain these oxidation processes by assuming -that the hydrogen peroxide unites with the compound undergoing oxidation -to form an addition compound, which subsequently decomposes (J. H. -Kastle and A. S. Loevenhart, _Amer. Chem. Journ._, 1903, 29, pp. 397, -517). Hydrogen peroxide can also react as a reducing agent, thus silver -oxide is reduced with a rapid evolution of oxygen. The course of this -reaction can scarcely be considered as definitely settled; M. Berthelot -considers that a higher oxide of silver is formed, whilst A. Baeyer and -V. Villiger are of opinion that reduced silver is obtained [see _Comptes -rendus_, 1901, 133, p. 555; _Ann. Chim. Phys._, 1897 (7), 11, p. 217, -and Ber., 1901, 34, p. 2769]. Potassium permanganate, in the presence of -dilute sulphuric acid, is rapidly reduced by hydrogen peroxide, oxygen -being given off, 2KMnO4 + 3H2SO4 + 5H2O2 = K2SO4 + 2MnSO4 + 8H2O + 5O2. -Lead peroxide is reduced to the monoxide. Hypochlorous acid and its -salts, together with the corresponding bromine and iodine compounds, -liberate oxygen violently from hydrogen peroxide, giving hydrochloric, -hydrobromic and hydriodic acids (S. Tanatar, _Ber._, 1899, 32, p. 1013). - - On the constitution of hydrogen peroxide see C. F. Schonbein, _Jour. - prak. Chem._, 1858-1868; M. Traube, _Ber._, 1882-1889; J. W. Bruhl, - _Ber._, 1895, 28, p. 2847; 1900, 33, p. 1709; S. Tanatar, _Ber._, - 1903, 36, p. 1893. - - Hydrogen peroxide finds application as a bleaching agent, as an - antiseptic, for the removal of the last traces of chlorine and sulphur - dioxide employed in bleaching, and for various quantitative - separations in analytical chemistry (P. Jannasch, _Ber._, 1893, 26, p. - 2908). It may be estimated by titration with potassium permanganate in - acid solution; with potassium ferricyanide in alkaline solution, - 2K3Fe(CN)6 + 2KOH + H2O2 = 2K4Fe(CN)6 + 2H2O + O2; or by oxidizing - arsenious acid in alkaline solution with the peroxide and back - titration of the excess of arsenious acid with standard iodine (B. - Grutzner, _Arch. der Pharm._, 1899, 237, p. 705). It may be recognized - by the violet coloration it gives when added to a very dilute solution - of potassium bichromate in the presence of hydrochloric acid; by the - orange-red colour it gives with a solution of titanium dioxide in - concentrated sulphuric acid; and by the precipitate of Prussian blue - formed when it is added to a solution containing ferric chloride and - potassium ferricyanide. - - _Ozonic Acid_, H2O4. By the action of ozone on a 40% solution of - potassium hydroxide, placed in a freezing mixture, an orange-brown - substance is obtained, probably K2O4, which A. Baeyer and V. Villiger - (_Ber._, 1902, 35, p. 3038) think is derived from ozonic acid, - produced according to the reaction O3 + H2O = H2O4. - - - - -HYDROGRAPHY (Gr. [Greek: hydor], water, and [Greek: graphein], to -write), the science dealing with all the waters of the earth's surface, -including the description of their physical features and conditions; the -preparation of charts and maps showing the position of lakes, rivers, -seas and oceans, the contour of the sea-bottom, the position of -shallows, deeps, reefs and the direction and volume of currents; a -scientific description of the position, volume, configuration, motion -and condition of all the waters of the earth. See also SURVEYING -(Nautical) and OCEAN AND OCEANOGRAPHY. The Hydrographic Department of -the British Admiralty, established in 1795, undertakes the making of -charts for the admiralty, and is under the charge of the hydrographer to -the admiralty (see CHART). - - - - -HYDROLYSIS (Gr. [Greek: hydor], water, [Greek: luein], to loosen), in -chemistry, a decomposition brought about by water after the manner shown -in the equation R.X + H.OH = R.H + X.OH. Modern research has proved that -such reactions are not occasioned by water acting as H2O, but really by -its ions (hydrions and hydroxidions), for the velocity is proportional -(in accordance with the law of chemical mass action) to the -concentration of these ions. This fact explains the so-called -"catalytic" action of acids and bases in decomposing such compounds as -the esters. The term "saponification" (Lat. _sapo_, soap) has the same -meaning, but it is more properly restricted to the hydrolysis of the -fats, i.e. glyceryl esters of organic acids, into glycerin and a soap -(see CHEMICAL ACTION). - - - - - - -End of the Project Gutenberg EBook of Encyclopaedia Britannica, 11th -Edition, Volume 14, Slice 1, by Various - -*** END OF THIS PROJECT GUTENBERG EBOOK ENCYC. BRITANNICA, VOL. 14, SL 1 *** - -***** This file should be named 40538.txt or 40538.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/4/0/5/3/40538/ - -Produced by Marius Masi, Don Kretz and the Online -Distributed Proofreading Team at http://www.pgdp.net - - -Updated editions will replace the previous one--the old editions -will be renamed. - -Creating the works from public domain print editions means that no -one owns a United States copyright in these works, so the Foundation -(and you!) can copy and distribute it in the United States without -permission and without paying copyright royalties. Special rules, -set forth in the General Terms of Use part of this license, apply to -copying and distributing Project Gutenberg-tm electronic works to -protect the PROJECT GUTENBERG-tm concept and trademark. Project -Gutenberg is a registered trademark, and may not be used if you -charge for the eBooks, unless you receive specific permission. If you -do not charge anything for copies of this eBook, complying with the -rules is very easy. You may use this eBook for nearly any purpose -such as creation of derivative works, reports, performances and -research. They may be modified and printed and given away--you may do -practically ANYTHING with public domain eBooks. Redistribution is -subject to the trademark license, especially commercial -redistribution. - - - -*** START: FULL LICENSE *** - -THE FULL PROJECT GUTENBERG LICENSE -PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK - -To protect the Project Gutenberg-tm mission of promoting the free -distribution of electronic works, by using or distributing this work -(or any other work associated in any way with the phrase "Project -Gutenberg"), you agree to comply with all the terms of the Full Project -Gutenberg-tm License available with this file or online at - www.gutenberg.org/license. - - -Section 1. General Terms of Use and Redistributing Project Gutenberg-tm -electronic works - -1.A. By reading or using any part of this Project Gutenberg-tm -electronic work, you indicate that you have read, understand, agree to -and accept all the terms of this license and intellectual property -(trademark/copyright) agreement. If you do not agree to abide by all -the terms of this agreement, you must cease using and return or destroy -all copies of Project Gutenberg-tm electronic works in your possession. -If you paid a fee for obtaining a copy of or access to a Project -Gutenberg-tm electronic work and you do not agree to be bound by the -terms of this agreement, you may obtain a refund from the person or -entity to whom you paid the fee as set forth in paragraph 1.E.8. - -1.B. "Project Gutenberg" is a registered trademark. It may only be -used on or associated in any way with an electronic work by people who -agree to be bound by the terms of this agreement. There are a few -things that you can do with most Project Gutenberg-tm electronic works -even without complying with the full terms of this agreement. See -paragraph 1.C below. There are a lot of things you can do with Project -Gutenberg-tm electronic works if you follow the terms of this agreement -and help preserve free future access to Project Gutenberg-tm electronic -works. See paragraph 1.E below. - -1.C. The Project Gutenberg Literary Archive Foundation ("the Foundation" -or PGLAF), owns a compilation copyright in the collection of Project -Gutenberg-tm electronic works. Nearly all the individual works in the -collection are in the public domain in the United States. If an -individual work is in the public domain in the United States and you are -located in the United States, we do not claim a right to prevent you from -copying, distributing, performing, displaying or creating derivative -works based on the work as long as all references to Project Gutenberg -are removed. Of course, we hope that you will support the Project -Gutenberg-tm mission of promoting free access to electronic works by -freely sharing Project Gutenberg-tm works in compliance with the terms of -this agreement for keeping the Project Gutenberg-tm name associated with -the work. You can easily comply with the terms of this agreement by -keeping this work in the same format with its attached full Project -Gutenberg-tm License when you share it without charge with others. - -1.D. The copyright laws of the place where you are located also govern -what you can do with this work. Copyright laws in most countries are in -a constant state of change. If you are outside the United States, check -the laws of your country in addition to the terms of this agreement -before downloading, copying, displaying, performing, distributing or -creating derivative works based on this work or any other Project -Gutenberg-tm work. The Foundation makes no representations concerning -the copyright status of any work in any country outside the United -States. - -1.E. Unless you have removed all references to Project Gutenberg: - -1.E.1. The following sentence, with active links to, or other immediate -access to, the full Project Gutenberg-tm License must appear prominently -whenever any copy of a Project Gutenberg-tm work (any work on which the -phrase "Project Gutenberg" appears, or with which the phrase "Project -Gutenberg" is associated) is accessed, displayed, performed, viewed, -copied or distributed: - -This eBook is for the use of anyone anywhere at no cost and with -almost no restrictions whatsoever. You may copy it, give it away or -re-use it under the terms of the Project Gutenberg License included -with this eBook or online at www.gutenberg.org - -1.E.2. If an individual Project Gutenberg-tm electronic work is derived -from the public domain (does not contain a notice indicating that it is -posted with permission of the copyright holder), the work can be copied -and distributed to anyone in the United States without paying any fees -or charges. If you are redistributing or providing access to a work -with the phrase "Project Gutenberg" associated with or appearing on the -work, you must comply either with the requirements of paragraphs 1.E.1 -through 1.E.7 or obtain permission for the use of the work and the -Project Gutenberg-tm trademark as set forth in paragraphs 1.E.8 or -1.E.9. - -1.E.3. If an individual Project Gutenberg-tm electronic work is posted -with the permission of the copyright holder, your use and distribution -must comply with both paragraphs 1.E.1 through 1.E.7 and any additional -terms imposed by the copyright holder. Additional terms will be linked -to the Project Gutenberg-tm License for all works posted with the -permission of the copyright holder found at the beginning of this work. - -1.E.4. Do not unlink or detach or remove the full Project Gutenberg-tm -License terms from this work, or any files containing a part of this -work or any other work associated with Project Gutenberg-tm. - -1.E.5. Do not copy, display, perform, distribute or redistribute this -electronic work, or any part of this electronic work, without -prominently displaying the sentence set forth in paragraph 1.E.1 with -active links or immediate access to the full terms of the Project -Gutenberg-tm License. - -1.E.6. You may convert to and distribute this work in any binary, -compressed, marked up, nonproprietary or proprietary form, including any -word processing or hypertext form. However, if you provide access to or -distribute copies of a Project Gutenberg-tm work in a format other than -"Plain Vanilla ASCII" or other format used in the official version -posted on the official Project Gutenberg-tm web site (www.gutenberg.org), -you must, at no additional cost, fee or expense to the user, provide a -copy, a means of exporting a copy, or a means of obtaining a copy upon -request, of the work in its original "Plain Vanilla ASCII" or other -form. Any alternate format must include the full Project Gutenberg-tm -License as specified in paragraph 1.E.1. - -1.E.7. Do not charge a fee for access to, viewing, displaying, -performing, copying or distributing any Project Gutenberg-tm works -unless you comply with paragraph 1.E.8 or 1.E.9. - -1.E.8. You may charge a reasonable fee for copies of or providing -access to or distributing Project Gutenberg-tm electronic works provided -that - -- You pay a royalty fee of 20% of the gross profits you derive from - the use of Project Gutenberg-tm works calculated using the method - you already use to calculate your applicable taxes. The fee is - owed to the owner of the Project Gutenberg-tm trademark, but he - has agreed to donate royalties under this paragraph to the - Project Gutenberg Literary Archive Foundation. Royalty payments - must be paid within 60 days following each date on which you - prepare (or are legally required to prepare) your periodic tax - returns. Royalty payments should be clearly marked as such and - sent to the Project Gutenberg Literary Archive Foundation at the - address specified in Section 4, "Information about donations to - the Project Gutenberg Literary Archive Foundation." - -- You provide a full refund of any money paid by a user who notifies - you in writing (or by e-mail) within 30 days of receipt that s/he - does not agree to the terms of the full Project Gutenberg-tm - License. You must require such a user to return or - destroy all copies of the works possessed in a physical medium - and discontinue all use of and all access to other copies of - Project Gutenberg-tm works. - -- You provide, in accordance with paragraph 1.F.3, a full refund of any - money paid for a work or a replacement copy, if a defect in the - electronic work is discovered and reported to you within 90 days - of receipt of the work. - -- You comply with all other terms of this agreement for free - distribution of Project Gutenberg-tm works. - -1.E.9. If you wish to charge a fee or distribute a Project Gutenberg-tm -electronic work or group of works on different terms than are set -forth in this agreement, you must obtain permission in writing from -both the Project Gutenberg Literary Archive Foundation and Michael -Hart, the owner of the Project Gutenberg-tm trademark. Contact the -Foundation as set forth in Section 3 below. - -1.F. - -1.F.1. Project Gutenberg volunteers and employees expend considerable -effort to identify, do copyright research on, transcribe and proofread -public domain works in creating the Project Gutenberg-tm -collection. Despite these efforts, Project Gutenberg-tm electronic -works, and the medium on which they may be stored, may contain -"Defects," such as, but not limited to, incomplete, inaccurate or -corrupt data, transcription errors, a copyright or other intellectual -property infringement, a defective or damaged disk or other medium, a -computer virus, or computer codes that damage or cannot be read by -your equipment. - -1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right -of Replacement or Refund" described in paragraph 1.F.3, the Project -Gutenberg Literary Archive Foundation, the owner of the Project -Gutenberg-tm trademark, and any other party distributing a Project -Gutenberg-tm electronic work under this agreement, disclaim all -liability to you for damages, costs and expenses, including legal -fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT -LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE -PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE THAT THE FOUNDATION, THE -TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE -LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR -INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH -DAMAGE. - -1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a -defect in this electronic work within 90 days of receiving it, you can -receive a refund of the money (if any) you paid for it by sending a -written explanation to the person you received the work from. If you -received the work on a physical medium, you must return the medium with -your written explanation. The person or entity that provided you with -the defective work may elect to provide a replacement copy in lieu of a -refund. If you received the work electronically, the person or entity -providing it to you may choose to give you a second opportunity to -receive the work electronically in lieu of a refund. If the second copy -is also defective, you may demand a refund in writing without further -opportunities to fix the problem. - -1.F.4. Except for the limited right of replacement or refund set forth -in paragraph 1.F.3, this work is provided to you 'AS-IS', WITH NO OTHER -WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO -WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PURPOSE. - -1.F.5. Some states do not allow disclaimers of certain implied -warranties or the exclusion or limitation of certain types of damages. -If any disclaimer or limitation set forth in this agreement violates the -law of the state applicable to this agreement, the agreement shall be -interpreted to make the maximum disclaimer or limitation permitted by -the applicable state law. The invalidity or unenforceability of any -provision of this agreement shall not void the remaining provisions. - -1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the -trademark owner, any agent or employee of the Foundation, anyone -providing copies of Project Gutenberg-tm electronic works in accordance -with this agreement, and any volunteers associated with the production, -promotion and distribution of Project Gutenberg-tm electronic works, -harmless from all liability, costs and expenses, including legal fees, -that arise directly or indirectly from any of the following which you do -or cause to occur: (a) distribution of this or any Project Gutenberg-tm -work, (b) alteration, modification, or additions or deletions to any -Project Gutenberg-tm work, and (c) any Defect you cause. - - -Section 2. Information about the Mission of Project Gutenberg-tm - -Project Gutenberg-tm is synonymous with the free distribution of -electronic works in formats readable by the widest variety of computers -including obsolete, old, middle-aged and new computers. It exists -because of the efforts of hundreds of volunteers and donations from -people in all walks of life. - -Volunteers and financial support to provide volunteers with the -assistance they need are critical to reaching Project Gutenberg-tm's -goals and ensuring that the Project Gutenberg-tm collection will -remain freely available for generations to come. In 2001, the Project -Gutenberg Literary Archive Foundation was created to provide a secure -and permanent future for Project Gutenberg-tm and future generations. -To learn more about the Project Gutenberg Literary Archive Foundation -and how your efforts and donations can help, see Sections 3 and 4 -and the Foundation information page at www.gutenberg.org - - -Section 3. Information about the Project Gutenberg Literary Archive -Foundation - -The Project Gutenberg Literary Archive Foundation is a non profit -501(c)(3) educational corporation organized under the laws of the -state of Mississippi and granted tax exempt status by the Internal -Revenue Service. The Foundation's EIN or federal tax identification -number is 64-6221541. Contributions to the Project Gutenberg -Literary Archive Foundation are tax deductible to the full extent -permitted by U.S. federal laws and your state's laws. - -The Foundation's principal office is located at 4557 Melan Dr. S. -Fairbanks, AK, 99712., but its volunteers and employees are scattered -throughout numerous locations. Its business office is located at 809 -North 1500 West, Salt Lake City, UT 84116, (801) 596-1887. Email -contact links and up to date contact information can be found at the -Foundation's web site and official page at www.gutenberg.org/contact - -For additional contact information: - Dr. Gregory B. Newby - Chief Executive and Director - gbnewby@pglaf.org - -Section 4. Information about Donations to the Project Gutenberg -Literary Archive Foundation - -Project Gutenberg-tm depends upon and cannot survive without wide -spread public support and donations to carry out its mission of -increasing the number of public domain and licensed works that can be -freely distributed in machine readable form accessible by the widest -array of equipment including outdated equipment. Many small donations -($1 to $5,000) are particularly important to maintaining tax exempt -status with the IRS. - -The Foundation is committed to complying with the laws regulating -charities and charitable donations in all 50 states of the United -States. Compliance requirements are not uniform and it takes a -considerable effort, much paperwork and many fees to meet and keep up -with these requirements. We do not solicit donations in locations -where we have not received written confirmation of compliance. To -SEND DONATIONS or determine the status of compliance for any -particular state visit www.gutenberg.org/donate - -While we cannot and do not solicit contributions from states where we -have not met the solicitation requirements, we know of no prohibition -against accepting unsolicited donations from donors in such states who -approach us with offers to donate. - -International donations are gratefully accepted, but we cannot make -any statements concerning tax treatment of donations received from -outside the United States. U.S. laws alone swamp our small staff. - -Please check the Project Gutenberg Web pages for current donation -methods and addresses. Donations are accepted in a number of other -ways including checks, online payments and credit card donations. -To donate, please visit: www.gutenberg.org/donate - - -Section 5. General Information About Project Gutenberg-tm electronic -works. - -Professor Michael S. Hart was the originator of the Project Gutenberg-tm -concept of a library of electronic works that could be freely shared -with anyone. For forty years, he produced and distributed Project -Gutenberg-tm eBooks with only a loose network of volunteer support. - -Project Gutenberg-tm eBooks are often created from several printed -editions, all of which are confirmed as Public Domain in the U.S. -unless a copyright notice is included. Thus, we do not necessarily -keep eBooks in compliance with any particular paper edition. - -Most people start at our Web site which has the main PG search facility: - - www.gutenberg.org - -This Web site includes information about Project Gutenberg-tm, -including how to make donations to the Project Gutenberg Literary -Archive Foundation, how to help produce our new eBooks, and how to -subscribe to our email newsletter to hear about new eBooks. |