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diff --git a/40538-h/40538-h.htm b/40538-h/40538-h.htm index 9bbe328..ae1cd8d 100644 --- a/40538-h/40538-h.htm +++ b/40538-h/40538-h.htm @@ -3,7 +3,7 @@ <head> <meta http-equiv="Content-Type" content= - "text/html; charset=iso-8859-1" /> + "text/html; charset=UTF-8" /> <title> The Project Gutenberg eBook of Encyclopædia Britannica, Volume XIV Slice I - Husband to Hydrolysis. @@ -162,45 +162,7 @@ </style> </head> <body> - - -<pre> - -The Project Gutenberg EBook of Encyclopaedia Britannica, 11th Edition, -Volume 14, Slice 1, by Various - -This eBook is for the use of anyone anywhere at no cost and with -almost no restrictions whatsoever. You may copy it, give it away or -re-use it under the terms of the Project Gutenberg License included -with this eBook or online at www.gutenberg.org - - -Title: Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 1 - "Husband" to "Hydrolysis" - -Author: Various - -Release Date: August 19, 2012 [EBook #40538] - -Language: English - -Character set encoding: ISO-8859-1 - -*** START OF THIS PROJECT GUTENBERG EBOOK ENCYC. BRITANNICA, VOL 14, SL 1 *** - - - - -Produced by Marius Masi, Don Kretz and the Online -Distributed Proofreading Team at http://www.pgdp.net - - - - - - -</pre> - +<div>*** START OF THE PROJECT GUTENBERG EBOOK 40538 ***</div> <table border="0" cellpadding="10" style="background-color: #dcdcdc; color: #696969; " summary="Transcriber's note"> <tr> @@ -430,7 +392,7 @@ Sub-Librarian of the Bodleian Library, Oxford. Fellow of Magdalen College.</td> <tr> <td class="tc1">A. C. G.</td> - <td class="tc2"><span class="sc">Albert Charles Lewis Gotthilf Günther, M.A., M.D., Ph.D., F.R.S.</span><br /> + <td class="tc2"><span class="sc">Albert Charles Lewis Gotthilf Günther, M.A., M.D., Ph.D., F.R.S.</span><br /> Keeper of Zoological Department, British Museum, 1875-1895. Gold Medallist, Royal Society, 1878. Author of <i>Catalogues of Colubrine Snakes, Batrachia Salientia, @@ -534,7 +496,7 @@ See the biographical article, <span class="sc"><a href="#artlinks">Newton, Alfre <td class="tc2"><span class="sc">Albrecht Socin, Ph.D.</span> (1844-1899).<br /> -Formerly Professor of Semitic Philology in the Universities of Leipzig and Tübingen. +Formerly Professor of Semitic Philology in the Universities of Leipzig and Tübingen. Author of <i>Arabische Grammatik</i>; &c.</td> <td class="tc4 cl"><p><b>Irak-Arabi</b> (<i>in part</i>).</p></td></tr> @@ -779,11 +741,11 @@ See the biographical article, <span class="sc"><a href="#artlinks">Gosse, Edmund <p><b>Ibsen;</b></p> <p><b>Idyl.</b></p></td></tr> -<tr> <td class="tc1">E. Hü.</td> +<tr> <td class="tc1">E. Hü.</td> - <td class="tc2"><span class="sc">Emil Hübner.</span><br /> + <td class="tc2"><span class="sc">Emil Hübner.</span><br /> -See the biographical article, <span class="sc"><a href="#artlinks">Hübner, Emil</a></span>.</td> +See the biographical article, <span class="sc"><a href="#artlinks">Hübner, Emil</a></span>.</td> <td class="tc4 cl"><p><b>Inscriptions:</b> <i>Latin</i> (<i>in part</i>).</p></td></tr> @@ -840,7 +802,7 @@ of Greek Historical Inscriptions</i>; &c.</td> <td class="tc2"><span class="sc">Eduard Meyer, Ph.D., D.Litt.</span>(Oxon.), LL.D.<br /> Professor of Ancient History in the University of Berlin. Author of <i>Geschichte des -Alterthums</i>; <i>Geschichte des alten Aegyptens</i>; <i>Die Israeliten und ihre Nachbarstämme</i>.</td> +Alterthums</i>; <i>Geschichte des alten Aegyptens</i>; <i>Die Israeliten und ihre Nachbarstämme</i>.</td> <td class="tc4 cl"><p><b>Hystaspes;</b></p> <p><b>Iran.</b></p></td></tr> @@ -1048,7 +1010,7 @@ Shanghai.</td> <tr> <td class="tc1">G. K.</td> - <td class="tc2"><span class="sc">Gustav Krüger, Ph.D.</span><br /> + <td class="tc2"><span class="sc">Gustav Krüger, Ph.D.</span><br /> Professor of Church History in the University of Giessen. Author of <i>Das Papstthum</i>; &c.</td> @@ -1369,11 +1331,11 @@ College (University of London). Joint-editor of Grote’s <i>History of Gree <tr> <td class="tc1">J. P. E.</td> - <td class="tc2"><span class="sc">Jean Paul Hippolyte Emmanuel Adhémar Esmein.</span><br /> + <td class="tc2"><span class="sc">Jean Paul Hippolyte Emmanuel Adhémar Esmein.</span><br /> Professor of Law in the University of Paris. Officer of the Legion of Honour. -Member of the Institute of France. Author of <i>Cours élémentaire d’histoire du droit -français</i>; &c.</td> +Member of the Institute of France. Author of <i>Cours élémentaire d’histoire du droit +français</i>; &c.</td> <td class="tc4 cl"><p><b>Intendant.</b></p></td></tr> @@ -1450,7 +1412,7 @@ Law, or the Conflict of Laws: Chapters on the Principles of International Law</i <tr> <td class="tc1">L.</td> - <td class="tc2"><span class="sc">Count Lützow, Litt.D. (Oxon.), Ph.D. (Prague), F.R.G.S.</span><br /> + <td class="tc2"><span class="sc">Count Lützow, Litt.D. (Oxon.), Ph.D. (Prague), F.R.G.S.</span><br /> Chamberlain of H.M. the Emperor of Austria, King of Bohemia. Hon. Member of the Royal Society of Literature. Member of the Bohemian Academy; &c. @@ -1542,11 +1504,11 @@ British Association.</td> <tr> <td class="tc1">P. A.</td> - <td class="tc2"><span class="sc">Paul Daniel Alphandéry.</span><br /> + <td class="tc2"><span class="sc">Paul Daniel Alphandéry.</span><br /> -Professor of the History of Dogma, École pratique des hautes études, Sorbonne, -Paris. Author of <i>Les Idées morales chez les hétérodoxes latines au début du XIII<span class="sp">e</span>. -siècle</i>.</td> +Professor of the History of Dogma, École pratique des hautes études, Sorbonne, +Paris. Author of <i>Les Idées morales chez les hétérodoxes latines au début du XIII<span class="sp">e</span>. +siècle</i>.</td> <td class="tc4 cl"><p><b>Inquisition.</b></p></td></tr> @@ -1656,7 +1618,7 @@ all Lands</i>; &c.</td> <tr> <td class="tc1">R. P. S.</td> - <td class="tc2"><span class="sc">R. Phené Spiers, F.S.A., F.R.I.B.A.</span><br /> + <td class="tc2"><span class="sc">R. Phené Spiers, F.S.A., F.R.I.B.A.</span><br /> Formerly Master of the Architectural School, Royal Academy, London. Past President of Architectural Association. Associate and Fellow of King’s College, @@ -1706,7 +1668,7 @@ Testament History</i>; <i>Religion of Ancient Palestine</i>; &c.</td> <tr> <td class="tc1">S. Bl.</td> - <td class="tc2"><span class="sc">Sigfus Blöndal.</span><br /> + <td class="tc2"><span class="sc">Sigfus Blöndal.</span><br /> Librarian of the University of Copenhagen.</td> @@ -1795,16 +1757,16 @@ Author of <i>History of Icelandic Geography</i>; <i>Geological Map of Iceland</i <td class="tc2"><span class="sc">Rev. William Augustus Brevoort Coolidge, M.A., F.R.G.S., Ph.D.</span>(Bern).<br /> Fellow of Magdalen College, Oxford. Professor of English History, St David’s -College, Lampeter, 1880-1881. Author of <i>Guide du Haut Dauphiné</i>; <i>The Range -of the Tödi</i>; <i>Guide to Grindelwald</i>; <i>Guide to Switzerland</i>; <i>The Alps in Nature and in +College, Lampeter, 1880-1881. Author of <i>Guide du Haut Dauphiné</i>; <i>The Range +of the Tödi</i>; <i>Guide to Grindelwald</i>; <i>Guide to Switzerland</i>; <i>The Alps in Nature and in History</i>; &c. Editor of <i>The Alpine Journal</i>, 1880-1881; &c.</td> - <td class="tc4 cl"><p><b>Hyères;</b></p> + <td class="tc4 cl"><p><b>Hyères;</b></p> <p><b>Innsbruck;</b></p> <p><b>Interlaken;</b></p> <p><b>Iseo, Lake of;</b></p> -<p><b>Isère</b> (<i>River</i>);</p> -<p><b>Isère</b> (<i>Department</i>).</p></td></tr> +<p><b>Isère</b> (<i>River</i>);</p> +<p><b>Isère</b> (<i>Department</i>).</p></td></tr> <tr> <td class="tc1">W. A. P.</td> @@ -2017,8 +1979,8 @@ See the biographical article. <span class="sc"><a href="#artlinks">Hunter, Sir W chiefly used in the sense of a man legally joined by marriage to a woman, his “wife”; the legal relations between them are treated below under <span class="sc"><a href="#artlinks">Husband and Wife</a></span>. The word appears -in O. Eng. as <i>húsbonda</i>, answering to the Old Norwegian -<i>húsbóndi</i>, and means the owner or freeholder of a <i>hus</i>, or house. +in O. Eng. as <i>húsbonda</i>, answering to the Old Norwegian +<i>húsbóndi</i>, and means the owner or freeholder of a <i>hus</i>, or house. The last part of the word still survives in “bondage” and “bondman,” and is derived from <i>bua</i>, to dwell, which, like Lat. <i>colere</i>, means also to till or cultivate, and to have a household. “Wife,” @@ -2033,7 +1995,7 @@ by a woman, and also with the root of <i>vibrare</i>, to tremble. These are all merely guesses, and the ultimate history of the word is lost. It does not appear outside Teutonic languages. Parallel to “husband” is “housewife,” the woman managing -a household. The earlier <i>húswif</i> was pronounced <i>hussif</i>, and +a household. The earlier <i>húswif</i> was pronounced <i>hussif</i>, and this pronunciation survives in the application of the word to a small case containing scissors, needles and pins, cottons, &c. From this form also derives “hussy,” now only used in a depreciatory @@ -2059,7 +2021,7 @@ employment. Where such an agent is himself one of the owners of the vessel, the name of “managing owner” is used. The “ship’s husband” or “managing owner” must register his name and address at the port of registry (Merchant Shipping -Act 1894, § 59). From the use of “husband” for a good and +Act 1894, § 59). From the use of “husband” for a good and thrifty manager of a household, the verb “to husband” means to economize, to lay up a store, to save.</p> @@ -2123,7 +2085,7 @@ usages were brought under the influence of principles derived from the Roman law, a theory of marriage became established, the leading feature of which is the <i>community of goods</i> between husband and wife. Describing the principle as it prevails in -France, Story (<i>Conflict of Laws</i>, § 130) says: “This community +France, Story (<i>Conflict of Laws</i>, § 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.... @@ -2548,7 +2510,7 @@ opening of the Liverpool and Manchester railway.</p> <hr class="art" /> <p><span class="bold">HUSS<a name="ar5" id="ar5"></a></span> (or <span class="sc">Hus</span>), JOHN (<i>c.</i> 1373-1415), Bohemian reformer and martyr, was born at Hussinecz,<a name="fa1b" id="fa1b" href="#ft1b"><span class="sp">1</span></a> a market village at the foot of -the Böhmerwald, and not far from the Bavarian frontier, between +the Böhmerwald, and not far from the Bavarian frontier, between 1373 and 1375, the exact date being uncertain. His parents appear to have been well-to-do Czechs of the peasant class. Of his early life nothing is recorded except that, notwithstanding @@ -2910,7 +2872,7 @@ Brumfels in 1524; and Luther wrote an interesting preface to <i>Epistolae Quaedam</i>, which were published in 1537. These <i>Epistolae</i> have been translated into French by E. de Bonnechose (1846), and the letters written during his imprisonment have been edited by -C. von Kügelgen (Leipzig, 1902).</p> +C. von Kügelgen (Leipzig, 1902).</p> <p>The best and most easily accessible information for the English reader on Huss is found in J. A. W. Neander’s <i>Allgemeine Geschichte @@ -2925,17 +2887,17 @@ H. von der Haardt in his <i>Magnum Constantiense concilium</i>, vol. vi., 1700; and by H. Finke in his <i>Acta concilii Constantiensis</i>, 1896); and J. Lenfant’s <i>Histoire de la guerre des Hussites</i> (1731) and the same writer’s <i>Histoire du concile de Constance</i> (1714) should be consulted. -F. Palacky’s <i>Geschichte Böhmens</i> (1864-1867) is also very useful. +F. Palacky’s <i>Geschichte Böhmens</i> (1864-1867) is also very useful. Monographs on Huss are very numerous. Among them may be -mentioned J. A. von Helfert, <i>Studien über Hus und Hieronymus</i> -(1853; this work is ultramontane in its sympathies); C. von Höfler, +mentioned J. A. von Helfert, <i>Studien über Hus und Hieronymus</i> +(1853; this work is ultramontane in its sympathies); C. von Höfler, <i>Hus und der Abzug der deutschen Professoren und Studenten aus Prag</i> -(1864); W. Berger, <i>Johannes Hus und König Sigmund</i> (1871); -E. Denis, <i>Huss et la guerre des Hussites</i> (1878); P. Uhlmann, <i>König -Sigmunds Geleit für Hus</i> (1894); J. Loserth, <i>Hus und Wiclif</i> (1884), +(1864); W. Berger, <i>Johannes Hus und König Sigmund</i> (1871); +E. Denis, <i>Huss et la guerre des Hussites</i> (1878); P. Uhlmann, <i>König +Sigmunds Geleit für Hus</i> (1894); J. Loserth, <i>Hus und Wiclif</i> (1884), translated into English by M. J. Evans (1884); A. Jeep, <i>Gerson, Wiclefus, Hussus, inter se comparati</i> (1857); and G. von Lechler, -<i>Johannes Hus</i> (1889). See also Count Lützow, <i>The Life and Times of +<i>Johannes Hus</i> (1889). See also Count Lützow, <i>The Life and Times of John Hus</i> (London, 1909).</p> </div> @@ -3135,7 +3097,7 @@ The citizens of Prague laid siege to the Vyšehrad, and towards the end of October (1420) the garrison was on the point of capitulating through famine. Sigismund attempted to relieve the fortress, but was decisively defeated by the Hussites on -the 1st of November near the village of Pankrác. The castles +the 1st of November near the village of Pankrác. The castles of Vyšehrad and Hradčany now capitulated, and shortly afterwards almost all Bohemia fell into the hands of the Hussites. Internal troubles prevented them from availing themselves @@ -3185,7 +3147,7 @@ take part in the crusade, soon returned to his own country. Free for a time from foreign aggression, the Hussites invaded Moravia, where a large part of the population favoured their creed; but, again paralysed by dissensions, soon returned -to Bohemia. The city of Königgrätz (Králové Hradec), which +to Bohemia. The city of Königgrätz (Králové Hradec), which had been under Utraquist rule, espoused the doctrine of Tabor, and called Žižka to its aid. After several military successes gained by Žižka (<i>q.v.</i>) in 1423 and the following year, a treaty @@ -3292,18 +3254,18 @@ Reformation.</p> <div class="condensed"> <p>All histories of Bohemia devote a large amount of space to the -Hussite movement. See Count Lützow, <i>Bohemia; an Historical -Sketch</i> (London, 1896); Palacky, <i>Geschichte von Böhmen</i>; Bachmann, -<i>Geschichte Böhmens</i>; L. Krummel, <i>Geschichte der böhmischen +Hussite movement. See Count Lützow, <i>Bohemia; an Historical +Sketch</i> (London, 1896); Palacky, <i>Geschichte von Böhmen</i>; Bachmann, +<i>Geschichte Böhmens</i>; L. Krummel, <i>Geschichte der böhmischen Reformation</i> (Gotha, 1866) and <i>Utraquisten und Taboriten</i> (Gotha, 1871); Ernest Denis, <i>Huss et la guerre des Hussites</i> (Paris, 1878); -H. Toman, <i>Husitské Válečnictvi</i> (Prague, 1898).</p> +H. Toman, <i>Husitské Válečnictvi</i> (Prague, 1898).</p> </div> <div class="author">(L.)</div> <hr class="art" /> -<p><span class="bold">HUSTING<a name="ar8" id="ar8"></a></span> (O. Eng. <i>hústing</i>, from Old Norwegian <i>hústhing</i>), +<p><span class="bold">HUSTING<a name="ar8" id="ar8"></a></span> (O. Eng. <i>hústing</i>, from Old Norwegian <i>hústhing</i>), the “thing” or “ting,” <i>i.e.</i> 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” @@ -3344,9 +3306,9 @@ did away with this public declaration of the nomination.</p> <p><span class="bold">HUSUM,<a name="ar9" id="ar9"></a></span> a town in the Prussian province of Schleswig-Holstein, in a fertile district 2<span class="spp">1</span>⁄<span class="suu">2</span> m. inland from the North Sea, on the canalized Husumer Au, which forms its harbour and roadstead, -99 m. N.W. from Hamburg on a branch line from Tönning. +99 m. N.W. from Hamburg on a branch line from Tönning. Pop. (1900) 8268. It has steam communication with the -North Frisian Islands (Nordstrand, Föhr and Sylt), and is a +North Frisian Islands (Nordstrand, Föhr and Sylt), and is a port for the cattle trade with England. Besides a ducal palace and park, it possesses an Evangelical church and a gymnasium. Cattle markets are held weekly, and in them, as also in cereals, @@ -3796,7 +3758,7 @@ important of the modern schools of ethics (see especially art. <span class="sc"> of general philosophy and of moral philosophy, as, for instance, in pt. vii. of Adam Smith’s <i>Theory of Moral Sentiments</i>; Mackintosh’s <i>Progress of Ethical Philosophy</i>; Cousin, <i>Cours d’histoire de la -philosophie morale du XVIII<span class="sp">e</span> siècle</i>; Whewell’s <i>Lectures on the +philosophie morale du XVIII<span class="sp">e</span> siècle</i>; Whewell’s <i>Lectures on the History of Moral Philosophy in England</i>; A. Bain’s <i>Mental and Moral Science</i>; Noah Porter’s Appendix to the English translation of Ueberweg’s <i>History of Philosophy</i>; Sir Leslie Stephen’s <i>History of @@ -3914,7 +3876,7 @@ September 1664. His career draws its chief interest from the after the death of her husband but not published till 1806 (since often reprinted), a work not only valuable for the picture which it gives of the man and of the time in which he lived, but for -the simple beauty of its style, and the naïveté with which the +the simple beauty of its style, and the naïveté with which the writer records her sentiments and opinions, and details the incidents of her private life.</p> @@ -3933,7 +3895,7 @@ was born at Spennithorne, Yorkshire, in 1674. He served as steward in several families of position, latterly in that of the duke of Somerset, who ultimately obtained for him the post of riding purveyor to the master of the horse, a sinecure worth -about £200 a year. In 1700 he became acquainted with Dr +about £200 a year. In 1700 he became acquainted with Dr John Woodward (1665-1728) physician to the duke and author of a work entitled <i>The Natural History of the Earth</i>, to whom he entrusted a large number of fossils of his own collecting, along @@ -4071,7 +4033,7 @@ historian, see M. C. Tyler’s <i>Literary History of the American Revolutio Kansas, U.S.A., in the broad bottom-land on the N. side of the Arkansas river. Pop. (1900) 9379, of whom 414 were foreign-born and 442 negroes; (1910 census) 16,364. It -is served by the Atchison, Topeka & Santa Fé, the Missouri +is served by the Atchison, Topeka & Santa Fé, the Missouri Pacific and the Chicago, Rock Island & Pacific railways. The principal public buildings are the Federal building and the county court house. The city has a public library, and an industrial @@ -4126,7 +4088,7 @@ with both, sympathized with both, though he died before the Reformation had time fully to develop. His life may be divided into four parts:—his youth and cloister-life (1488-1504); his wanderings in pursuit of knowledge (1504-1515); his strife -with Ulrich of Württemberg (1515-1519); and his connexion +with Ulrich of Württemberg (1515-1519); and his connexion with the Reformation (1519-1523). Each of these periods had its own special antagonism, which coloured Hutten’s career: in the first, his horror of dull monastic routine; in the second, @@ -4173,7 +4135,7 @@ of Mainz, Archbishop Albert of Brandenburg. Here high dreams of a learned career rose on him; Mainz should be made the metropolis of a grand Humanist movement, the centre of good style and literary form. But the murder in 1515 of his -relative Hans von Hutten by Ulrich, duke of Württemberg, +relative Hans von Hutten by Ulrich, duke of Württemberg, changed the whole course of his life; satire, chief refuge of the weak, became Hutten’s weapon; with one hand he took his part in the famous <i>Epistolae obscurorum virorum</i>, and with @@ -4244,7 +4206,7 @@ fear of his loathsome diseases, and also because the beggared knight was sure to borrow money from him. A paper war consequently broke out between the two Humanists, which embittered Hutten’s last days, and stained the memory of -Erasmus. From Basel Ulrich dragged himself to Mülhausen; +Erasmus. From Basel Ulrich dragged himself to Mülhausen; and when the vengeance of Erasmus drove him thence, he went to Zurich. There the large heart of Zwingli welcomed him; he helped him with money, and found him a quiet refuge with @@ -4306,8 +4268,8 @@ which he attributes in the main to him. To him is due the more serious and severe tone of that bitter portion of the satire. See W. Brecht, <i>Die Verfasser der Epistolae obscurorum virorum</i> (1904).</p> -<p>For a complete catalogue of the writings of Hutten, see E. Böcking’s -<i>Index Bibliographicus Huttenianus</i> (1858). Böcking is also the editor +<p>For a complete catalogue of the writings of Hutten, see E. Böcking’s +<i>Index Bibliographicus Huttenianus</i> (1858). Böcking is also the editor of the complete edition of Hutten’s works (7 vols., 1859-1862). A selection of Hutten’s German writings, edited by G. Balke, appeared in 1891. Cp. S. Szamatolski, <i>Huttens deutsche Schriften</i> (1891). @@ -4315,7 +4277,7 @@ The best biography (though it is also somewhat of a political pamphlet) is that of D. F. Strauss (<i>Ulrich von Hutten</i>, 1857; 4th ed., 1878; English translation by G. Sturge, 1874), with which may be compared the older monographs by A. Wagenseil -(1823), A. Bürck (1846) and J. Zeller (Paris, 1849). See also +(1823), A. Bürck (1846) and J. Zeller (Paris, 1849). See also J. Deckert, <i>Ulrich von Huttens Leben und Wirken. Eine historische Skizze</i> (1901).</p> </div> @@ -4770,7 +4732,7 @@ he had made during the voyage of the “Rattlesnake.” He was thus enabled to produce various important memoirs, especially those on certain Ascidians, in which he solved the problem of <i>Appendicularia</i>—an organism whose place in the animal -kingdom Johannes Müller had found himself wholly unable +kingdom Johannes Müller had found himself wholly unable to assign—and on the morphology of the Cephalous Mollusca.</p> <p>Richard Owen, then the leading comparative anatomist in @@ -4779,7 +4741,7 @@ him the deductive explanation of anatomical fact from idealistic conceptions. He superadded the evolutionary theories of Oken, which were equally idealistic, but were altogether repugnant to Cuvier. Huxley would have none of either. Imbued -with the methods of von Baer and Johannes Müller, his methods +with the methods of von Baer and Johannes Müller, his methods were purely inductive. He would not hazard any statement beyond what the facts revealed. He retained, however, as has been done by his successors, the use of archetypes, though they @@ -4800,7 +4762,7 @@ was a property inherent in the group. Herbert Spencer, whose acquaintance he made in 1852, was unable to convert him to evolution in its widest sense (<i>Life</i>, i. 168). He could not bring himself to acceptance of the theory—owing, no doubt, to his -rooted aversion from à priori reasoning—without a mechanical +rooted aversion from à priori reasoning—without a mechanical conception of its mode of operation. In his first interview with Darwin, which seems to have been about the same time, he expressed his belief “in the sharpness of the lines of demarcation @@ -5218,7 +5180,7 @@ founded on careful research and of great value.</p> <p><span class="bold">HUY<a name="ar24" id="ar24"></a></span> (Lat. <i>Hoium</i>, and Flem. <i>Hoey</i>), a town of Belgium, on the right bank of the Meuse, at the point where it is joined by the Hoyoux. Pop. (1904), 14,164. It is 19 m. E. of Namur -and a trifle less west of Liége. Huy certainly dates from the +and a trifle less west of Liége. Huy certainly dates from the 7th century, and, according to some, was founded by the emperor <span class="pagenum"><a name="page21" id="page21"></a>21</span> Antoninus in <span class="scs">A.D.</span> 148. Its situation is striking, with its grey @@ -5230,7 +5192,7 @@ of Neumoustier founded by Peter the Hermit on his return from the first crusade. He was buried there in 1115, and a statue was erected to his memory in the abbey grounds in 1858. Neumoustier was one of seventeen abbeys in this town -alone dependent on the bishopric of Liége. Huy is surrounded +alone dependent on the bishopric of Liége. Huy is surrounded by vineyards, and the bridge which crosses the Meuse at this point connects the fertile Hesbaye north of the river with the rocky and barren Condroz south of it.</p> @@ -5273,7 +5235,7 @@ publication, early in 1656, of the little tract <i>De Saturni luna observatio nova</i>; but retained, as regards the second, until 1659, when in the <i>Systema Saturnium</i> the varying appearances of the so-called “triple planet” were clearly explained as the -phases of a ring inclined at an angle of 28° to the ecliptic. Huygens +phases of a ring inclined at an angle of 28° to the ecliptic. Huygens was also in 1656 the first effective observer of the Orion nebula; he delineated the bright region still known by his name, and detected the multiple character of its nuclear star. His application @@ -5300,7 +5262,7 @@ made respectively in November and December 1668.</p> <p>Huygens had before this time fixed his abode in France. In 1665 Colbert made to him on behalf of Louis XIV. an offer too tempting to be refused, and between the following year and -1681 his residence in the philosophic seclusion of the Bibliothèque +1681 his residence in the philosophic seclusion of the Bibliothèque du Roi was only interrupted by two short visits to his native country. His <i>magnum opus</i> dates from this period. The <i>Horologium oscillatorium</i>, published with a dedication to his @@ -5354,7 +5316,7 @@ he was enabled to prove the fundamental laws of optics, and to assign the correct construction for the direction of the extraordinary ray in uniaxial crystals. These investigations, together with his discovery of the “wonderful phenomenon” of polarization, -are recorded in his <i>Traité de la lumière</i>, published at +are recorded in his <i>Traité de la lumière</i>, published at Leiden in 1690, but composed in 1678. In the appended treatise <i>Sur la Cause de la pesanteur</i>, he rejected gravitation as a universal quality of matter, although admitting the Newtonian @@ -5397,25 +5359,25 @@ Hugenii aliorumque seculi XVII. virorum celebrium exercitationes mathematicae et philosophicae</i> (the Hague, 1833).</p> <p>The publication of a monumental edition of the letters and works -of Huygens was undertaken at the Hague by the <i>Société Hollandaise +of Huygens was undertaken at the Hague by the <i>Société Hollandaise des Sciences</i>, with the heading <i>Œuvres de Christian Huygens</i> (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 <i>Opera varia</i> (1724); his <i>Éloge</i> in the character of a +prefixed to his <i>Opera varia</i> (1724); his <i>Éloge</i> in the character of a French academician was printed by J. A. N. Condorcet in 1773. Consult further: P. J. Uylenbroek, <i>Oratio de fratribus Christiano atque Constantino Hugenio</i> (Groningen, 1838); P. Harting, <i>Christiaan Huygens in zijn Leven en Werken geschetzt</i> (Groningen, 1868); J. B. J. Delambre, <i>Hist. de l’astronomie moderne</i> (ii. 549); J. E. Montucla, -<i>Hist. des mathématiques</i> (ii. 84, 412, 549); M. Chasles, <i>Aperçu historique -sur l’origine des méthodes en géometrie</i>, pp. 101-109; E. Dühring, +<i>Hist. des mathématiques</i> (ii. 84, 412, 549); M. Chasles, <i>Aperçu historique +sur l’origine des méthodes en géometrie</i>, pp. 101-109; E. Dühring, <i>Kritische Geschichte der allgemeinen Principien der Mechanik</i>, Abschnitt (ii. 120, 163, iii. 227); A. Berry, <i>A Short History of Astronomy</i>, p. 200; R. Wolf, <i>Geschichte der Astronomie</i>, passim; Houzeau, <i>Bibliographie astronomique</i> (ii. 169); F. Kaiser, <i>Astr. Nach.</i> (xxv. 245, 1847); <i>Tijdschrift voor de Wetenschappen</i> (i. 7, 1848); <i>Allgemeine deutsche Biographie</i> (M. B. Cantor); J. C. Poggendorff, -<i>Biog. lit. Handwörterbuch</i>.</p> +<i>Biog. lit. Handwörterbuch</i>.</p> </div> <div class="author">(A. M. C.)</div> @@ -5574,23 +5536,23 @@ European continent.</p> was born at Paris on the 5th of February 1848. He belonged to a family of artists of Dutch extraction; he entered the ministry of the interior, and was pensioned after thirty years’ -service. His earliest venture in literature, <i>Le Drageoir à épices</i> +service. His earliest venture in literature, <i>Le Drageoir à épices</i> (1874), contained stories and short prose poems showing the influence of Baudelaire. <i>Marthe</i> (1876), the life of a courtesan, was published in Brussels, and Huysmans contributed a story, -“Sac au dos,” to <i>Les Soirées de Médan</i>, the collection of stories +“Sac au dos,” to <i>Les Soirées de Médan</i>, the collection of stories of the Franco-German war published by Zola. He then produced a series of novels of everyday life, including <i>Les Sœurs -Vatard</i> (1879), <i>En Ménage</i> (1881), and <i>À vau-l’eau</i> (1882), in which +Vatard</i> (1879), <i>En Ménage</i> (1881), and <i>À vau-l’eau</i> (1882), in which he outdid Zola in minute and uncompromising realism. He was influenced, however, more directly by Flaubert and the brothers de Goncourt than by Zola. In <i>L’Art moderne</i> (1883) he gave a careful study of impressionism and in <i>Certains</i> (1889) -a series of studies of contemporary artists, <i>À Rebours</i> (1884), +a series of studies of contemporary artists, <i>À Rebours</i> (1884), the history of the morbid tastes of a decadent aristocrat, des Esseintes, created a literary sensation, its caricature of literary and artistic symbolism covering much of the real beliefs of the -leaders of the aesthetic revolt. In <i>Là-Bas</i> Huysmans’s most +leaders of the aesthetic revolt. In <i>Là -Bas</i> 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 @@ -5598,7 +5560,7 @@ students of the black art; but already there are signs of a leaning to religion in the sympathetic figures of the religious bell-ringer of Saint Sulpice and his wife. <i>En Route</i> (1895) relates the strange conversion of Durtal to mysticism and Catholicism -in his retreat to La Trappe. In <i>La Cathédrale</i> (1898), Huysmans’s +in his retreat to La Trappe. In <i>La Cathédrale</i> (1898), Huysmans’s symbolistic interpretation of the cathedral of Chartres, he develops his enthusiasm for the purity of Catholic ritual. The life of <i>Sainte Lydwine de Schiedam</i> (1901), an exposition of @@ -5606,7 +5568,7 @@ the value of suffering, gives further proof of his conversion; and <i>L’Oblat</i> (1903) describes Durtal’s retreat to the Val des Saints, where he is attached as an oblate to a Benedictine monastery. Huysmans was nominated by Edmond de Goncourt -as a member of the Académie des Goncourt. He died +as a member of the Académie des Goncourt. He died as a devout Catholic, after a long illness of cancer in the palate on the 13th of May 1907. Before his death he destroyed his unpublished MSS. His last book was <i>Les Foules de Lourdes</i> @@ -5614,8 +5576,8 @@ unpublished MSS. His last book was <i>Les Foules de Lourdes</i> <div class="condensed"> <p>See Arthur Symons, <i>Studies in two Literatures</i> (1897) and <i>The -Symbolist Movement in Literature</i> (1899); Jean Lionnet in <i>L’Évolution -des idées</i> (1903); Eugène Gilbert in <i>France et Belgique</i> (1905); +Symbolist Movement in Literature</i> (1899); Jean Lionnet in <i>L’Évolution +des idées</i> (1903); Eugène Gilbert in <i>France et Belgique</i> (1905); J. Sargeret in <i>Les Grands convertis</i> (1906).</p> </div> @@ -5678,10 +5640,10 @@ mountains in central Asia, its head-waters being in close proximity to those of the Yangtsze-Kiang. It has a total length of about 2400 m. and drains an area of approximately 400,000 sq. m. The main stream has its source in two lakes -named Tsaring-nor and Oring-nor, lying about 35° N., 97° E., +named Tsaring-nor and Oring-nor, lying about 35° N., 97° E., and after flowing with a south-easterly course it bends sharply to the north-west and north, entering China in the province -of Kansuh in lat. 36°. After passing Lanchow-fu, the capital +of Kansuh in lat. 36°. After passing Lanchow-fu, the capital of this province, the river takes an immense sweep to the north and north-east, until it encounters the rugged barrier ranges that here run north and south through the provinces of Shansi @@ -5794,18 +5756,18 @@ to Mercian supremacy, and possibly it was separated from Wessex in the time of Edwin. The first kings of whom we read were two brothers, Eanhere and Eanfrith, probably contemporaries of Wulfhere. They were followed by a king named Osric, -a contemporary of Æthelred, and he by a king Oshere. Oshere -had three sons who reigned after him, Æthelheard, Æthelweard -and Æthelric. The two last named appear to have been reigning +a contemporary of Æthelred, and he by a king Oshere. Oshere +had three sons who reigned after him, Æthelheard, Æthelweard +and Æthelric. The two last named appear to have been reigning in the year 706. At the beginning of Offa’s reign we again find the kingdom ruled by three brothers, named Eanberht, Uhtred and Aldred, the two latter of whom lived until about 780. After them the title of king seems to have been given up. Their -successor Æthelmund, who was killed in a campaign against +successor Æthelmund, who was killed in a campaign against Wessex in 802, is described only as an earl. The district remained in possession of the rulers of Mercia until the fall of that kingdom. Together with the rest of English Mercia it submitted -to King Alfred about 877-883 under Earl Æthelred, who possibly +to King Alfred about 877-883 under Earl Æthelred, who possibly himself belonged to the Hwicce. No genealogy or list of kings has been preserved, and we do not know whether the dynasty was connected with that of Wessex or Mercia.</p> @@ -5939,7 +5901,7 @@ in an open place on a dry hard bed of ashes, and be covered over to a depth of 6 or 8 in. with the same material or with fibre or soil; and when the roots are well developed, which will take from six to eight weeks, they may be removed to a frame, and gradually exposed to -light, and then placed in a forcing pit in a heat of from 60 to 70°. +light, and then placed in a forcing pit in a heat of from 60 to 70°. When the flowers are fairly open, they may be removed to the greenhouse or conservatory.</p> @@ -6107,7 +6069,7 @@ both of whom are connected with Apollo Agyieus.</p> <p>See L. R. Farnell, <i>Cults of the Greek States</i>, vol. iv. (1907), pp. 125 foll., 264 foll.; J. G. Frazer, <i>Adonis, Attis, Osiris</i> (1906), bk. ii. ch. 7; S. Wide, <i>Lakonische Kulte</i>, p. 290; E. Rhode, <i>Psyche</i>, -3rd ed. i. 137 foll.; Roscher, <i>Lexikon d. griech. u. röm. Myth.</i>, <i>s.v.</i> +3rd ed. i. 137 foll.; Roscher, <i>Lexikon d. griech. u. röm. Myth.</i>, <i>s.v.</i> “Hyakinthos” (Greve); L. Preller, <i>Griechische Mythol.</i> 4th ed. i. 248 foll.</p> </div> @@ -6129,7 +6091,7 @@ two and seven. As a reward for having brought up Zeus at Dodona and taken care of the infant Dionysus Hyes, whom they conveyed to Ino (sister of his mother Semele) at Thebes when his life was threatened by Lycurgus, they were translated to heaven -and placed among the stars (Hyginus, <i>Poët. astron.</i> ii. 21). +and placed among the stars (Hyginus, <i>Poët. astron.</i> ii. 21). Another form of the story combines them with the Pleiades. According to this they were twelve (or fifteen) sisters, whose brother Hyas was killed by a snake while hunting in Libya @@ -6170,7 +6132,7 @@ He died at Cambridge on the 15th of January 1902.</p> Cephalopoda</i> (1883); <i>Larval Theory of the Origin of Cellular Tissue</i> (1884); <i>Genesis of the Arietidae</i> (1889); and <i>Phylogeny of an acquired characteristic</i> (1894). He wrote the section on Cephalopoda in -Karl von Zittel’s <i>Paläontologie</i> (1900), and his well-known study on +Karl von Zittel’s <i>Paläontologie</i> (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 <i>Memoirs</i> of the Boston Natural History Society in 1880. He was one of the founders @@ -6183,7 +6145,7 @@ and editors of the <i>American Naturalist</i>.</p> historically, though its exact site is uncertain, is Hybla Major, near (or by some supposed to be identical with) Megara Hyblaea (<i>q.v.</i>): another Hybla, known as Hybla Minor or Galeatis, is -represented by the modern Paternò; while the site of Hybla +represented by the modern Paternò; while the site of Hybla Heraea is to be sought near Ragusa.</p> @@ -6220,12 +6182,12 @@ in the second decade of the 18th century, produced the cross which is still grown in gardens under the name of “Fairchild’s Sweet William.” Linnaeus made many experiments in the cross-fertilization of plants and produced several hybrids, but -Joseph Gottlieb Kölreuter (1733-1806) laid the first real foundation +Joseph Gottlieb Kölreuter (1733-1806) laid the first real foundation of our scientific knowledge of the subject. Later on Thomas Andrew Knight, a celebrated English horticulturist, devoted much successful labour to the improvement of fruit trees and vegetables by crossing. In the second quarter of the 19th -century C. F. Gärtner made and published the results of a number +century C. F. Gärtner made and published the results of a number of experiments that had not been equalled by any earlier worker. Next came Charles Darwin, who first in the <i>Origin of Species</i>, and later in <i>Cross and Self-Fertilization of Plants</i>, subjected the @@ -6328,7 +6290,7 @@ series of experiments with Lepidopterous insects, and has obtained a very large series of hybrids, of which he has kept careful record. Lepidopterists generally begin to suspect that many curious forms offered by dealers as new species are products got by crossing known -species. Apellö has succeeded with Teleostean fish; Gebhardt and +species. Apellö has succeeded with Teleostean fish; Gebhardt and others with Amphibia. Elliot and Suchetet have studied carefully the question of hybridization occurring normally among birds, and have got together a very large body of evidence. Among the cases @@ -6399,7 +6361,7 @@ when the actual impregnation of the egg is possible naturally, or has been secured by artificial means, the development of the hybrid may stop at an early stage. Thus hybrids between the urchin and the starfish, animals belonging to different classes, reached only the -stage of the pluteus larva. A. D. Apellö, experimenting with +stage of the pluteus larva. A. D. Apellö, experimenting with Teleostean fish, found that very often impregnation and segmentation occurred, but that the development broke down immediately afterwards. W. Gebhardt, crossing <i>Rana esculenta</i> with <i>R. arvalis</i>, @@ -6535,7 +6497,7 @@ undoubtedly agree more with the wild sire.”</p> <p>Ewart’s experiments and his discussion of them also throw important light on the general relation of hybrids to their parents. He found that the coloration and pattern of his -zebra hybrids resembled far more those of the Somali or Grévy’s +zebra hybrids resembled far more those of the Somali or Grévy’s zebra than those of their sire—a Burchell’s zebra. In a general discussion of the stripings of horses, asses and zebras, he came to the conclusion that the Somali zebra represented the older @@ -6718,34 +6680,34 @@ sphere of natural selection and to be a fundamental fact of living matter.</p> <div class="condensed"> -<p><span class="sc">Authorities.</span>—Apellö, “Über einige Resultate der Kreuzbefruchtung +<p><span class="sc">Authorities.</span>—Apellö, “Ãœber einige Resultate der Kreuzbefruchtung bei Knochenfischen,” <i>Bergens mus. aarbog</i> (1894); Bateson, “Hybridization and Cross-breeding,” <i>Journal of the Royal Horticultural Society</i> (1900); J. L. Bonhote, “Hybrid Ducks,” <i>Proc. Zool. Soc. of London</i> (1905), p. 147; Boveri, article “Befruchtung,” in <i>Ergebnisse der Anatomie und Entwickelungsgeschichte von Merkel -und Bonnet</i>, i. 385-485; Cornevin et Lesbre, “Étude sur un hybride -issu d’une mule féconde et d’un cheval,” <i>Rev. Sci.</i> li. 144; Charles +und Bonnet</i>, i. 385-485; Cornevin et Lesbre, “Étude sur un hybride +issu d’une mule féconde et d’un cheval,” <i>Rev. Sci.</i> li. 144; Charles Darwin, <i>Origin of Species</i> (1859), <i>The Effects of Cross and Self-Fertilization in the Vegetable Kingdom</i> (1878); Delage, <i>La Structure -du protoplasma et les théories sur l’hérédité</i> (1895, with a literature); +du protoplasma et les théories sur l’hérédité</i> (1895, with a literature); de Vries, “The Law of Disjunction of Hybrids,” <i>Comptes rendus</i> (1900), p. 845; Elliot, <i>Hybridism</i>; Escherick, “Die biologische -Bedeutung der Genitalabhänge der Insecten,” <i>Verh. z. B. Wien</i>, xlii. +Bedeutung der Genitalabhänge der Insecten,” <i>Verh. z. B. Wien</i>, xlii. 225; Ewart, <i>The Penycuik Experiments</i> (1899); Focke, <i>Die Pflanzen-Mischlinge</i> (1881); Foster-Melliar, <i>The Book of the Rose</i> (1894); C. F. Gaertner, various papers in <i>Flora</i>, 1828, 1831, 1832, -1833, 1836, 1847, on “Bastard-Pflanzen”; Gebhardt, “Über die +1833, 1836, 1847, on “Bastard-Pflanzen”; Gebhardt, “Ãœber die Bastardirung von <i>Rana esculenta</i> mit <i>R. arvalis</i>,” <i>Inaug. Dissert.</i> -(Breslau, 1894); G. Mendel, “Versuche über Pflanzen-Hybriden,” -<i>Verh. Natur. Vereins in Brünn</i> (1865), pp. 1-52; Morgan, “Experimental +(Breslau, 1894); G. Mendel, “Versuche über Pflanzen-Hybriden,” +<i>Verh. Natur. Vereins in Brünn</i> (1865), pp. 1-52; Morgan, “Experimental Studies,” <i>Anat. Anz.</i> (1893), p. 141; id. p. 803; G. J. Romanes, “Physiological Selection,” <i>Jour. Linn. Soc.</i> xix. 337; H. Scherren, “Notes on Hybrid Bears,” <i>Proc. Zool. Soc. of London</i> (1907), p. 431; Saunders, <i>Proc. Roy. Soc.</i> (1897), lxii. 11; -Standfuss, “Études de zoologie expérimentale,” <i>Arch. Sci. Nat.</i> -vi. 495; Suchetet, “Les Oiseaux hybrides rencontrés à l’état -sauvage,” <i>Mém. Soc. Zool.</i> v. 253-525, and vi. 26-45; Vernon, +Standfuss, “Études de zoologie expérimentale,” <i>Arch. Sci. Nat.</i> +vi. 495; Suchetet, “Les Oiseaux hybrides rencontrés à l’état +sauvage,” <i>Mém. Soc. Zool.</i> v. 253-525, and vi. 26-45; Vernon, “The Relation between the Hybrid and Parent Forms of Echinoid Larvae,” <i>Proc. Roy. Soc.</i> lxv. 350; Wallace, <i>Darwinism</i> (1889); Weismann, <i>The Germ-Plasm</i> (1893).</p> @@ -6757,16 +6719,16 @@ Weismann, <i>The Germ-Plasm</i> (1893).</p> <p><span class="bold">HYDANTOIN<a name="ar39" id="ar39"></a></span> (glycolyl urea), C<span class="su">3</span>H<span class="su">4</span>N<span class="su">2</span>O<span class="su">2</span> or <img style="width:130px; height:70px; vertical-align: middle;" src="images/img29.jpg" alt="" /> -the ureïde of glycollic acid, may be obtained by heating allantoin +the ureïde of glycollic acid, may be obtained by heating allantoin or alloxan with hydriodic acid, or by heating bromacetyl urea with alcoholic ammonia. It crystallizes in needles, melting -at 216° C.</p> +at 216° C.</p> <p>When hydrolysed with baryta water yields hydantoic <span class="pagenum"><a name="page30" id="page30"></a>30</span> -(glycoluric)acid, H<span class="su">2</span>N·CO·NH·CH<span class="su">2</span>·CO<span class="su">2</span>H, which is readily soluble +(glycoluric)acid, H<span class="su">2</span>N·CO·NH·CH<span class="su">2</span>·CO<span class="su">2</span>H, which is readily soluble in hot water, and on heating with hydriodic acid decomposes -into ammonia, carbon dioxide and glycocoll, CH<span class="su">2</span>·NH<span class="su">2</span>·CO<span class="su">2</span>·H. +into ammonia, carbon dioxide and glycocoll, CH<span class="su">2</span>·NH<span class="su">2</span>·CO<span class="su">2</span>·H. Many substituted hydantoins are known; the α-alkyl hydantoins are formed on fusion of aldehyde- or ketone-cyanhydrins with urea, the β-alkyl hydantoins from the fusion of mono-alkyl @@ -6846,7 +6808,7 @@ Lord Clarendon, the historian, to the Bodleian Library at Oxford.</p> <div class="condensed"> <p>See Lord Clarendon, <i>The Life of Edward, Earl of Clarendon</i> (3 vols., Oxford, 1827); Edward Foss, <i>The Judges of England</i> (London, -1848-1864); Anthony à Wood, <i>Athenae oxonienses</i> (London, 1813-1820); +1848-1864); Anthony à Wood, <i>Athenae oxonienses</i> (London, 1813-1820); Samuel Pepys, <i>Diary and Correspondence</i>, edited by Lord Braybrooke (4 vols., London, 1854).</p> </div> @@ -6935,14 +6897,14 @@ John. The borough, incorporated in 1881, is under a mayor, <hr class="art" /> <p><span class="bold">HYDE DE NEUVILLE, JEAN GUILLAUME,<a name="ar43" id="ar43"></a></span> <span class="sc">Baron</span> (1776-1857), -French politician, was born at La Charité-sur-Loire -(Nièvre) on the 24th of January 1776, the son of Guillaume +French politician, was born at La Charité-sur-Loire +(Nièvre) on the 24th of January 1776, the son of Guillaume Hyde, who belonged to an English family which had emigrated with the Stuarts after the rebellion of 1745. He was only seventeen -when he successfully defended a man denounced by Fouché +when he successfully defended a man denounced by Fouché before the revolutionary tribunal of Nevers. From 1793 onwards he was an active agent of the exiled princes; he took part in the -Royalist rising in Berry in 1796, and after the <i>coup d’état</i> of the +Royalist rising in Berry in 1796, and after the <i>coup d’état</i> of the 18th Brumaire (November 9, 1799) tried to persuade Bonaparte to recall the Bourbons. An accusation of complicity in the infernal machine conspiracy of 1800-1801 was speedily retracted, @@ -6957,7 +6919,7 @@ a commercial treaty. On his return in 1821 he declined the Constantinople embassy, and in November 1822 was elected deputy for Cosne. Shortly afterwards he was appointed French ambassador at Lisbon, where his efforts to oust British influence -culminated, in connexion with the <i>coup d’état</i> of Dom Miguel +culminated, in connexion with the <i>coup d’état</i> of Dom Miguel (April 30, 1824), in his suggestion to the Portuguese minister to invite the armed intervention of Great Britain. It was assumed that this would be refused, in view of the loudly proclaimed @@ -6969,7 +6931,7 @@ disapproved of the Portuguese constitution. This destroyed his influence at Lisbon, and he returned to Paris to take his seat in the Chamber of Deputies. In spite of his pronounced Royalism, he now showed Liberal tendencies, opposed the -policy of Villèle’s cabinet, and in 1828 became a member of the +policy of Villèle’s cabinet, and in 1828 became a member of the moderate administration of Martignac as minister of marine. In this capacity he showed active sympathy with the cause of Greek independence. During the Polignac ministry (1829-1830) @@ -6980,7 +6942,7 @@ line of the Bourbons from the throne, and resigned his seat. He died in Paris on the 28th of May 1857.</p> <div class="condensed"> -<p>His <i>Mémoires et souvenirs</i> (3 vols., 1888), compiled from his notes +<p>His <i>Mémoires et souvenirs</i> (3 vols., 1888), compiled from his notes by his nieces, the vicomtesse de Bardonnet and the baronne Laurenceau, are of great interest for the Revolution and the Restoration.</p> </div> @@ -7055,7 +7017,7 @@ into Rajputana.</p> Dominions, the principal native state of India in extent, population and political importance; area, 82,698 sq. m.; pop. (1901) 11,141,142, showing a decrease of 3.4% in the decade; -estimated revenue 4<span class="spp">1</span>⁄<span class="suu">2</span> crores of Hyderabad rupees (£2,500,000). +estimated revenue 4<span class="spp">1</span>⁄<span class="suu">2</span> crores of Hyderabad rupees (£2,500,000). The state occupies a large portion of the eastern plateau of the Deccan. It is bounded on the north and north-east by Berar, on the south and south-east by Madras, and on the west by @@ -7155,7 +7117,7 @@ of the Imperial Service Troops, which now form the contribution of the native chiefs to the defence of India. On the occasion of the Panjdeh incident in 1885 he made an offer of money and men, and subsequently on the occasion of Queen Victoria’s -Jubilee in 1887 he offered 20 lakhs (£130,000) annually for three +Jubilee in 1887 he offered 20 lakhs (£130,000) annually for three years for the purpose of frontier defence. It was finally decided that the native chiefs should maintain small but well-equipped bodies of infantry and cavalry for imperial defence. For many @@ -7164,7 +7126,7 @@ condition, the expenditure consistently outran the revenue, and the nobles, who held their tenure under an obsolete feudal system, vied with each other in ostentatious extravagance. But in 1902, on the revision of the Berar agreement, the nizam -received 25 lakhs (£167,000) a year for the rent of Berar, thus +received 25 lakhs (£167,000) a year for the rent of Berar, thus substituting a fixed for a fluctuating source of income, and a British financial adviser was appointed for the purpose of reorganizing the resources of the state.</p> @@ -7284,7 +7246,7 @@ but in vain; this breach of faith stung him to fury, and thenceforward he and his son did not cease to thirst for vengeance. His time came when in 1778 the British, on the declaration of war with France, resolved to drive the French out of India. -The capture of Mahé on the coast of Malabar in 1779, followed +The capture of Mahé on the coast of Malabar in 1779, followed by the annexation of lands belonging to a dependent of his own, gave him the needed pretext. Again master of all that the Mahrattas had taken from him, and with empire extended to the @@ -7315,7 +7277,7 @@ series (1893). For the personal character and administration of Hyder Ali see the <i>History of Hyder Naik</i>, written by Mir Hussein Ali Khan Kirmani (translated from the Persian by Colonel Miles, and published by the Oriental Translation Fund), and the curious work -written by M. Le Maître de La Tour, commandant of his artillery +written by M. Le Maître de La Tour, commandant of his artillery (<i>Histoire d’Hayder-Ali Khan</i>, Paris, 1783). For the whole life and times see Wilks, <i>Historical Sketches of the South of India</i> (1810-1817); Aitchison’s Treaties, vol. v. (2nd ed., 1876); and Pearson, <i>Memoirs @@ -7383,18 +7345,18 @@ of south Russia more especially they derived great wealth. In 10,000 were seafarers. At the time of the outbreak of the war of Greek independence the total population was 28,190, of whom 16,460 were natives and the rest foreigners. One of their chief -families, the Konduriotti, was worth £2,000,000. Into the +families, the Konduriotti, was worth £2,000,000. Into the struggle the Hydriotes flung themselves with rare enthusiasm and devotion, and the final deliverance of Greece was mainly due to the service rendered by their fleets.</p> <div class="condensed"> -<p>See Pouqueville, <i>Voy. de la Grèce</i>, vol. vi.; Antonios Miaoules, -<span class="grk" title="Hypomnêma peri tês nêsou Hydras">Ὑπόμνημα περὶ τῆς νήσου Ὕδρας</span> (Munich, 1834); Id. <span class="grk" title="Sunoptikê historia -tôn naumachiôn dia tôn ploiôn tôn triôn nêsôn, Hydras, Petsôn kai Psarôn">Συνοπτικὴ ἱστορία +<p>See Pouqueville, <i>Voy. de la Grèce</i>, vol. vi.; Antonios Miaoules, +<span class="grk" title="Hypomnêma peri tês nêsou Hydras">Ὑπόμνημα περὶ τῆς νήσου Ὕδρας</span> (Munich, 1834); Id. <span class="grk" title="Sunoptikê historia +tôn naumachiôn dia tôn ploiôn tôn triôn nêsôn, Hydras, Petsôn kai Psarôn">Συνοπτικὴ ἱστορία τῶν ναυμαχιῶν διὰ τῶν πλοίων τῶν τρίων νήσων, Ὕδρας, Πέτσων καὶ Ψαρῶν</span> -(Nauplia, 1833); Id. <span class="grk" title="Historia tês nêsou Hydras">Ἱστορία τῆς νήσου Ὕδρας</span> (Athens, 1874); G. D. -Kriezes, <span class="grk" title="Historia tês nêsou Hydras">Ἱστρία τῆς νήσου Ὕδρας</span> (Patras, 1860).</p> +(Nauplia, 1833); Id. <span class="grk" title="Historia tês nêsou Hydras">Ἱστορία τῆς νήσου Ὕδρας</span> (Athens, 1874); G. D. +Kriezes, <span class="grk" title="Historia tês nêsou Hydras">Ἱστρία τῆς νήσου Ὕδρας</span> (Patras, 1860).</p> </div> @@ -7449,7 +7411,7 @@ variable, the range in magnitude being 4.5 to 6.</p> <hr class="art" /> -<p><span class="bold">HYDRACRYLIC ACID<a name="ar52" id="ar52"></a></span> (ethylene lactic acid), CH<span class="su">2</span>OH·CH<span class="su">2</span>·CO<span class="su">2</span>H. +<p><span class="bold">HYDRACRYLIC ACID<a name="ar52" id="ar52"></a></span> (ethylene lactic acid), CH<span class="su">2</span>OH·CH<span class="su">2</span>·CO<span class="su">2</span>H. an organic oxyacid prepared by acting with silver oxide and water on β-iodopropionic acid, or from ethylene by the addition of hypochlorous acid, the addition product being then treated @@ -7457,12 +7419,12 @@ with potassium cyanide and hydrolysed by an acid. It may also be prepared by oxidizing the trimethylene glycol obtained by the action of hydrobromic acid on allylbromide. It is a syrupy liquid, which on distillation is resolved into water and -the unsaturated acrylic acid, CH<span class="su">2</span>:CH·CO<span class="su">2</span>H. Chromic and +the unsaturated acrylic acid, CH<span class="su">2</span>:CH·CO<span class="su">2</span>H. Chromic and nitric acids oxidize it to oxalic acid and carbon dioxide. -Hydracrylic aldehyde, CH<span class="su">2</span>OH·CH<span class="su">2</span>·CHO, was obtained in 1904 +Hydracrylic aldehyde, CH<span class="su">2</span>OH·CH<span class="su">2</span>·CHO, was obtained in 1904 by J. U. Nef (<i>Ann.</i> 335, p. 219) as a colourless oil by heating acrolein with water. Dilute alkalis convert it into crotonaldehyde, -CH<span class="su">3</span>·CH:CH·CHO.</p> +CH<span class="su">3</span>·CH:CH·CHO.</p> <hr class="art" /> @@ -7554,7 +7516,7 @@ embraced by the second definition are more usually termed <i>hydroxides</i>, since at one time they were regarded as combinations of an oxide with water, for example, calcium oxide or lime when slaked with water yielded calcium hydroxide, written -formerly as CaO·H<span class="su">2</span>0. The general formulae of hydroxides +formerly as CaO·H<span class="su">2</span>0. The general formulae of hydroxides are: M<span class="sp">i</span>OH, M<span class="sp">ii</span>(OH)<span class="su">2</span>, M<span class="sp">iii</span>(OH)<span class="su">3</span>, M<span class="sp">iv</span>(OH)<span class="su">4</span>, &c., corresponding to the oxides M<span class="su">2</span><span class="sp">i</span>O, M<span class="sp">ii</span>O, M<span class="su">2</span><span class="sp">iii</span>O<span class="su">3</span>, M<span class="sp">iv</span>O<span class="su">2</span>, &c., the Roman index denoting the valency of the element. There is an important @@ -7576,13 +7538,13 @@ of the periodic table.</p> <hr class="art" /> -<p><span class="bold">HYDRAULICS<a name="ar56" id="ar56"></a></span> (Gr. <span class="grk" title="hydôr">ὕδωρ</span>, water, and <span class="grk" title="aulos">αὐλός</span>, a pipe), the branch +<p><span class="bold">HYDRAULICS<a name="ar56" id="ar56"></a></span> (Gr. <span class="grk" title="hydôr">ὕδωρ</span>, water, and <span class="grk" title="aulos">αὐλός</span>, a pipe), the branch of engineering science which deals with the practical applications of the laws of hydromechanics.</p> <p class="pt2 center">I. THE DATA OF HYDRAULICS<a name="fa1f" id="fa1f" href="#ft1f"><span class="sp">1</span></a></p> -<p>§ 1. <i>Properties of Fluids.</i>—The fluids to which the laws of +<p>§ 1. <i>Properties of Fluids.</i>—The fluids to which the laws of practical hydraulics relate are substances the parts of which possess very great mobility, or which offer a very small resistance to distortion independently of inertia. Under the general @@ -7607,7 +7569,7 @@ at any point in a fluid the pressure in all directions must be the same; or, in other words, the pressure on any small element of surface is independent of the orientation of the surface.</p> -<p>§ 2. Fluids are divided into liquids, or incompressible fluids, +<p>§ 2. Fluids are divided into liquids, or incompressible fluids, and gases, or compressible fluids. Very great changes of pressure change the volume of liquids only by a small amount, and if the pressure on them is reduced to zero they do not sensibly @@ -7620,7 +7582,7 @@ incompressible. In dealing with gases the changes of volume which accompany changes of pressure must be taken into account.</p> -<p>§ 3. Viscous fluids are those in which change of form under a +<p>§ 3. Viscous fluids are those in which change of form under a continued stress proceeds gradually and increases indefinitely. A very viscous fluid opposes great resistance to change of form in a short time, and yet may be deformed considerably by a @@ -7689,15 +7651,15 @@ of the layer. Putting κ = μ/T, κ′ = μ/nT,</p> <p class="noind">an expression first proposed by L. M. H. Navier. The coefficient μ is termed the coefficient of viscosity.</p> -<p>According to J. Clerk Maxwell, the value of μ for air at θ° Fahr. in +<p>According to J. Clerk Maxwell, the value of μ for air at θ° Fahr. in pounds, when the velocities are expressed in feet per second, is</p> -<p class="center">μ = 0.000 000 025 6 (461° + θ);</p> +<p class="center">μ = 0.000 000 025 6 (461° + θ);</p> <p class="noind">that is, the coefficient of viscosity is proportional to the absolute temperature and independent of the pressure.</p> -<p>The value of μ for water at 77° Fahr. is, according to H. von +<p>The value of μ for water at 77° Fahr. is, according to H. von Helmholtz and G. Piotrowski,</p> <p class="center">μ = 0.000 018 8,</p> @@ -7710,7 +7672,7 @@ with increase of temperature.</p> <tr><td class="figright1"><img style="width:328px; height:242px" src="images/img35b.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 2.</span></td></tr></table> -<p>§ 4. When a fluid flows in a very regular manner, as for instance +<p>§ 4. When a fluid flows in a very regular manner, as for instance when It flows in a capillary tube, the velocities vary gradually at any moment from one point of the fluid @@ -7755,7 +7717,7 @@ hindered by the viscosity of the fluid.</p> <p class="pt1 center"><span class="sc">Relation of Pressure, Density, and Temperature of Liquids</span></p> -<p>§ 5. <i>Units of Volume.</i>—In practical calculations the cubic foot +<p>§ 5. <i>Units of Volume.</i>—In practical calculations the cubic foot and gallon are largely used, and in metric countries the litre and cubic metre (= 1000 litres). The imperial gallon is now exclusively used in England, but the United States have retained the old English @@ -7770,15 +7732,15 @@ wine gallon.</p> <tr><td class="tcl">1 litre</td> <td class="tcl">= 0.2201 imp. gallon</td> <td class="tcl">= 0.2641 U.S. gallon.</td></tr> </table> -<p><i>Density of Water.</i>—Water at 53° F. and ordinary pressure contains -62.4 ℔ per cub. ft., or 10 ℔ per imperial gallon at 62° F. The litre -contains one kilogram of water at 4° C. or 1000 kilograms per cubic +<p><i>Density of Water.</i>—Water at 53° F. and ordinary pressure contains +62.4 ℔ per cub. ft., or 10 ℔ per imperial gallon at 62° F. The litre +contains one kilogram of water at 4° C. or 1000 kilograms per cubic metre. River and spring water is not sensibly denser than pure -water. But average sea water weighs 64 ℔ per cub. ft. at 53° F. +water. But average sea water weighs 64 ℔ per cub. ft. at 53° F. The weight of water per cubic unit will be denoted by G. Ice free from air weighs 57.28 ℔ per cub. ft. (Leduc).</p> -<p>§ 6. <i>Compressibility of Liquids.</i>—The most accurate experiments +<p>§ 6. <i>Compressibility of Liquids.</i>—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 ℔ per sq. in., the compression is proportional to the pressure. The chief @@ -7802,17 +7764,17 @@ elasticity of volume. With the notation of the differential calculus,</p> <tr><td class="tccm allb"> </td> <td class="tccm allb">Canton.</td> <td class="tccm allb">Oersted.</td> <td class="tccm allb">Colladon<br />and Sturm.</td> <td class="tccm allb">Regnault.</td></tr> <tr><td class="tcl lb rb">Water</td> <td class="tcr rb">45,990,000</td> <td class="tcr rb">45,900,000</td> <td class="tcr rb">42,660,000</td> <td class="tcr rb">44,000,000</td></tr> -<tr><td class="tcl lb rb">Sea water</td> <td class="tcr rb">52,900,000</td> <td class="tcc rb">··</td> <td class="tcc rb">··</td> <td class="tcc rb">··</td></tr> -<tr><td class="tcl lb rb">Mercury</td> <td class="tcr rb">705,300,000</td> <td class="tcc rb">··</td> <td class="tcr rb">626,100,000</td> <td class="tcr rb">604,500,000</td></tr> -<tr><td class="tcl lb rb">Oil</td> <td class="tcr rb">44,090,000</td> <td class="tcc rb">··</td> <td class="tcc rb">··</td> <td class="tcc rb">··</td></tr> -<tr><td class="tcl lb rb bb">Alcohol</td> <td class="tcr rb bb">32,060,000</td> <td class="tcc rb bb">··</td> <td class="tcr rb bb">23,100,000</td> <td class="tcc rb bb">··</td></tr> +<tr><td class="tcl lb rb">Sea water</td> <td class="tcr rb">52,900,000</td> <td class="tcc rb">··</td> <td class="tcc rb">··</td> <td class="tcc rb">··</td></tr> +<tr><td class="tcl lb rb">Mercury</td> <td class="tcr rb">705,300,000</td> <td class="tcc rb">··</td> <td class="tcr rb">626,100,000</td> <td class="tcr rb">604,500,000</td></tr> +<tr><td class="tcl lb rb">Oil</td> <td class="tcr rb">44,090,000</td> <td class="tcc rb">··</td> <td class="tcc rb">··</td> <td class="tcc rb">··</td></tr> +<tr><td class="tcl lb rb bb">Alcohol</td> <td class="tcr rb bb">32,060,000</td> <td class="tcc rb bb">··</td> <td class="tcr rb bb">23,100,000</td> <td class="tcc rb bb">··</td></tr> </table> <p>According to the experiments of Grassi, the compressibility of water diminishes as the temperature increases, while that of ether, alcohol and chloroform is increased.</p> -<p>§ 7. <i>Change of Volume and Density of Water with Change of Temperature.</i>—Although +<p>§ 7. <i>Change of Volume and Density of Water with Change of Temperature.</i>—Although the change of volume of water with change of temperature is so small that it may generally be neglected in ordinary hydraulic calculations, yet it should be noted that there is a change @@ -7869,14 +7831,14 @@ of Units</i>.</p> </table> <p>The weight per cubic foot has been calculated from the values of -ρ, on the assumption that 1 cub. ft. of water at 39.2° Fahr. is 62.425 ℔. +ρ, on the assumption that 1 cub. ft. of water at 39.2° Fahr. is 62.425 ℔. 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 ℔ -per cub. ft., which is its density at 53° Fahr. It may be noted also -that ice at 32° Fahr. contains 57.3 ℔ per cub. ft. The values of ρ +per cub. ft., which is its density at 53° Fahr. It may be noted also +that ice at 32° Fahr. contains 57.3 ℔ per cub. ft. The values of ρ are the densities in grammes per cubic centimetre.</p> -<p>§ 8. <i>Pressure Column. Free Surface Level.</i>—Suppose a small +<p>§ 8. <i>Pressure Column. Free Surface Level.</i>—Suppose a small vertical pipe introduced into a liquid at any point P (fig. 3). Then the liquid will rise in the pipe to a level OO, such that the pressure due to the column in the pipe exactly balances the pressure on its @@ -7902,7 +7864,7 @@ at P.</p> <tr><td class="figright1"><img style="width:260px; height:232px" src="images/img36.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 3.</span></td></tr></table> -<p>§ 9. <i>Relation of Pressure, Volume, Temperature and Density in +<p>§ 9. <i>Relation of Pressure, Volume, Temperature and Density in Compressible Fluids.</i>—Certain problems on the flow of air and steam are so similar to those relating to the flow @@ -7927,7 +7889,7 @@ the product of the pressure p and volume V of a given quantity of air is a constant (Boyle’s law).</p> <p>Let p<span class="su">0</span> be mean atmospheric pressure (2116.8 ℔ per sq. ft.), V<span class="su">0</span> -the volume of 1 ℔ of air at 32° Fahr. under the pressure p<span class="su">0</span>. Then</p> +the volume of 1 ℔ of air at 32° Fahr. under the pressure p<span class="su">0</span>. Then</p> <p class="center">p<span class="su">0</span>V<span class="su">0</span> = 26214.</p> <div class="author">(1)</div> @@ -7938,14 +7900,14 @@ the volume of 1 ℔ of air at 32° Fahr. under the pressure p<span class="su" <div class="author">(2)</div> <p class="noind">For any other pressure p, at which the volume of 1 ℔ is V and the -weight per cubic foot is G, the temperature being 32° Fahr.,</p> +weight per cubic foot is G, the temperature being 32° Fahr.,</p> <p class="center">pV = p/G = 26214; or G = p/26214.</p> <div class="author">(3)</div> <p><i>Change of Pressure or Volume by Change of Temperature.</i>—Let p<span class="su">0</span>, V<span class="su">0</span>, G<span class="su">0</span>, as before be the pressure, the volume of a pound in cubic feet, -and the weight of a cubic foot in pounds, at 32° Fahr. Let p, V, G +and the weight of a cubic foot in pounds, at 32° Fahr. Let p, V, G be the same quantities at a temperature t (measured strictly by the air thermometer, the degrees of which differ a little from those of a mercurial thermometer). Then, by experiment,</p> @@ -7953,8 +7915,8 @@ a mercurial thermometer). Then, by experiment,</p> <p class="center">pV = p<span class="su">0</span>V<span class="su">0</span> (460.6 + t) / (460.6 + 32) = p<span class="su">0</span>V<span class="su">0</span>τ/τ<span class="su">0</span>,</p> <div class="author">(4)</div> -<p class="noind">where τ, τ<span class="su">0</span> are the temperatures t and 32° reckoned from the absolute -zero, which is −460.6° Fahr.;</p> +<p class="noind">where τ, τ<span class="su">0</span> are the temperatures t and 32° reckoned from the absolute +zero, which is −460.6° Fahr.;</p> <p class="center">p/G = p<span class="su">0</span>τ/G<span class="su">0</span>τ<span class="su">0</span>;</p> <div class="author1">(4a)</div> @@ -7968,12 +7930,12 @@ zero, which is −460.6° Fahr.;</p> <div class="author1">(5a)</div> <p class="noind">Or quite generally p/G = Rτ for all gases, if R is a constant varying -inversely as the density of the gas at 32° F. For steam R = 85.5.</p> +inversely as the density of the gas at 32° F. For steam R = 85.5.</p> </div> <p class="pt2 center">II. KINEMATICS OF FLUIDS</p> -<p>§ 10. Moving fluids as commonly observed are conveniently +<p>§ 10. Moving fluids as commonly observed are conveniently classified thus:</p> <p>(1) <i>Streams</i> are moving masses of indefinite length, completely @@ -7997,7 +7959,7 @@ each other along such a constant path may be termed a fluid filament or elementary stream.</p> <div class="condensed"> -<p>§ 11. <i>Steady and Unsteady, Uniform and Varying, Motion.</i>—There +<p>§ 11. <i>Steady and Unsteady, Uniform and Varying, Motion.</i>—There are two quite distinct ways of treating hydrodynamical questions. We may either fix attention on a given mass of fluid and consider its changes of position and energy under the action of the stresses @@ -8041,7 +8003,7 @@ is a definite term applicable to the motion of the water, the other a less definite term applicable in strictness only to the condition of the stream bed.</p> -<p>§ 12. <i>Theoretical Notions on the Motion of Water.</i>—The actual +<p>§ 12. <i>Theoretical Notions on the Motion of Water.</i>—The actual motion of the particles of water is in most cases very complex. To simplify hydrodynamic problems, simpler modes of motion are assumed, and the results of theory so obtained are compared experimentally @@ -8101,7 +8063,7 @@ actual more or less varying motions, the motion of the stream might be treated as steady stream line or steady laminar motion.</p> -<p>§ 13. <i>Volume of Flow.</i>—Let A (fig. 6) be any ideal plane surface, +<p>§ 13. <i>Volume of Flow.</i>—Let A (fig. 6) be any ideal plane surface, of area ω, in a stream, normal to the direction of motion, and let V be the velocity of the fluid. Then the volume flowing through the surface A in unit time is</p> @@ -8135,7 +8097,7 @@ volume of flow is</p> <p class="noind">as the case may be.</p> -<p>§ 14. <i>Principle of Continuity.</i>—If we consider any completely +<p>§ 14. <i>Principle of Continuity.</i>—If we consider any completely bounded fixed space in a moving liquid initially and finally filled continuously with liquid, the inflow must be equal to the outflow. Expressing the inflow with a positive and the outflow with a negative @@ -8198,7 +8160,7 @@ of inflow and outflow are</p> <p class="center">G<span class="su">1</span>A<span class="su">1</span>v<span class="su">1</span> = G<span class="su">2</span>A<span class="su">2</span>v<span class="su">2</span>;</p> -<p class="noind">and hence, from (5a) § 9, if the temperature is constant,</p> +<p class="noind">and hence, from (5a) § 9, if the temperature is constant,</p> <p class="center">p<span class="su">1</span>A<span class="su">1</span>v<span class="su">1</span> = p<span class="su">2</span>A<span class="su">2</span>v<span class="su">2</span>.</p> <div class="author">(3)</div> @@ -8219,7 +8181,7 @@ of inflow and outflow are</p> <tr><td class="figright1"><img style="width:156px; height:262px" src="images/img38c.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 13.</span></td></tr></table> -<p>§ 15. <i>Stream Lines.</i>—The characteristic of a perfect fluid, that is, +<p>§ 15. <i>Stream Lines.</i>—The characteristic of a perfect fluid, that is, a fluid free from viscosity, is that the pressure between any two parts into which it is divided by a plane must be normal to the plane. One consequence of this is that the particles can have no rotation @@ -8295,7 +8257,7 @@ ORIFICES AS ASCERTAINABLE BY EXPERIMENTS</p> <tr><td class="figright1"><img style="width:306px; height:398px" src="images/img38d.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 14.</span></td></tr></table> -<p>§ 16. When a liquid issues vertically from a small orifice, it forms +<p>§ 16. When a liquid issues vertically from a small orifice, it forms a jet which rises nearly to the level of the free surface of the liquid in the vessel from which it flows. The difference @@ -8355,7 +8317,7 @@ the pressure head at the orifice. Lastly, the velocity v is connected with h by the relation v<span class="sp">2</span>/2g = h, so that v<span class="sp">2</span>/2g may be termed the head due to the velocity v.</p> -<p>§ 17. <i>Coefficients of Velocity and Resistance.</i>—As the actual velocity +<p>§ 17. <i>Coefficients of Velocity and Resistance.</i>—As the actual velocity of discharge differs from √<span class="ov">2gh</span> by a small quantity, let the actual velocity</p> @@ -8450,7 +8412,7 @@ to a transverse section of the jet. Hence the actual discharge when contraction occurs is</p> -<p class="center">Q<span class="su">a</span> = c<span class="su">v</span>v × c<span class="su">c</span>ω = c<span class="su">c</span>c<span class="su">v</span>ω √(2gh),</p> +<p class="center">Q<span class="su">a</span> = c<span class="su">v</span>v × c<span class="su">c</span>ω = c<span class="su">c</span>c<span class="su">v</span>ω √(2gh),</p> <p class="noind">or simply, if c = c<span class="su">v</span>c<span class="su">c</span>,</p> @@ -8458,10 +8420,10 @@ when contraction occurs is</p> <p class="noind">where c is called the <i>coefficient of discharge</i>. Thus for a sharp-edged -plane orifice c = 0.97 × +plane orifice c = 0.97 × 0.64 = 0.62.</p> -<p>§ 18. <i>Experimental Determination +<p>§ 18. <i>Experimental Determination of</i> c<span class="su">v</span>, c<span class="su">c</span>, <i>and</i> c.—The coefficient of contraction c<span class="su">c</span> is directly determined by measuring @@ -8490,7 +8452,7 @@ then</p> <p class="center">c<span class="su">v</span> = v<span class="su">a</span> √ (2gh) = √ (x<span class="sp">2</span>/4yh).</p> <p>In the case of large orifices such as weirs, the velocity can be -directly determined by using a Pitot tube (§ 144).</p> +directly determined by using a Pitot tube (§ 144).</p> <table class="flt" style="float: right; width: 430px;" summary="Illustration"> <tr><td class="figright1"><img style="width:378px; height:285px" src="images/img39c.jpg" alt="" /></td></tr> @@ -8553,7 +8515,7 @@ orifice is the same</p> <tr><td class="figcenter"><img style="width:473px; height:160px" src="images/img39e.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 19.</span></td></tr></table> -<p>§ 19. <i>Coefficients for Bellmouths and Bellmouthed Orifices.</i>—If an +<p>§ 19. <i>Coefficients for Bellmouths and Bellmouthed Orifices.</i>—If an orifice is furnished with a mouthpiece exactly of the form of the contracted vein, then the whole of the contraction occurs within the mouthpiece, and if the area of the orifice is measured at the @@ -8580,7 +8542,7 @@ c<span class="su">c</span> = 1, c = c<span class="su">v</span>; and therefore</p <p class="center">Q = c<span class="su">v</span>ω √ (2gh) = ω √ { 2gh / (1 + c<span class="su">r</span> }.</p> -<p>§ 20. <i>Coefficients for Sharp-edged or virtually Sharp-edged Orifices.</i>—There +<p>§ 20. <i>Coefficients for Sharp-edged or virtually Sharp-edged Orifices.</i>—There are a very large number of measurements of discharge from sharp-edged orifices under different conditions of head. An account of these and a very careful tabulation of the average values of the @@ -8662,7 +8624,7 @@ the results agree with the formula</p> <p class="noind">where h is in feet and d in inches.</p> <p class="pt1 center"><i>Coefficients of Discharge from Circular Orifices. -Temperature 51° to 55°.</i></p> +Temperature 51° to 55°.</i></p> <table class="ws" summary="Contents"> <tr><td class="tccm allb" rowspan="2">Head in<br />feet<br />h.</td> <td class="tccm allb" colspan="9">Diameters of Orifices in Inches (d).</td></tr> @@ -8735,7 +8697,7 @@ in Vertical Plane Surfaces.</i></p> <tr><td class="tcc lb rb bb">50 </td> <td class="tcc rb bb">.6086</td> <td class="tcc rb bb">.6060</td> <td class="tcc rb bb">.6034</td> <td class="tcc rb bb">.6018</td> <td class="tcc rb bb">.6035</td> <td class="tcc rb bb">.6050</td> <td class="tcc rb bb">.6070</td> <td class="tcc rb bb">.6140</td></tr> </table> -<p>§ 21. <i>Orifices with Edges of Sensible Thickness.</i>—When the edges of +<p>§ 21. <i>Orifices with Edges of Sensible Thickness.</i>—When the edges of the orifice are not bevelled outwards, but have a sensible thickness, the coefficient of discharge is somewhat altered. The following table gives values of the coefficient of discharge for the arrangements @@ -8746,7 +8708,7 @@ The heads were measured immediately over the orifice. In this case,</p> <p class="center">Q = cb (H − h) √ { 2g(H + h)/2 }.</p> -<p>§ 22. <i>Partially Suppressed Contraction.</i>—Since the contraction of +<p>§ 22. <i>Partially Suppressed Contraction.</i>—Since the contraction of the jet is due to the convergence towards the orifice of the issuing streams, it will be diminished if for any portion of the edge of the orifice the convergence is prevented. Thus, if an internal rim or @@ -8810,7 +8772,7 @@ however, that these formulae for suppressed contraction are not reliable.</p> -<p>§ 23. <i>Imperfect Contraction.</i>—If +<p>§ 23. <i>Imperfect Contraction.</i>—If the sides of the vessel approach near to the edge of the orifice, @@ -8832,7 +8794,7 @@ are imperfectly known.</p> <tr><td class="figcenter"><img style="width:957px; height:205px" src="images/img41c.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 22.</span></td></tr></table> -<p>§ 24. <i>Orifices Furnished with Channels of Discharge.</i>—These external +<p>§ 24. <i>Orifices Furnished with Channels of Discharge.</i>—These external borders to an orifice also modify the contraction.</p> <p>The following coefficients of discharge were obtained with openings @@ -8856,7 +8818,7 @@ borders to an orifice also modify the contraction.</p> <tr><td class="figcenter"><img style="width:400px; height:531px" src="images/img41d.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 23.</span></td></tr></table> -<p>§ 25. <i>Inversion of the Jet.</i>—When a jet issues from a horizontal +<p>§ 25. <i>Inversion of the Jet.</i>—When a jet issues from a horizontal orifice, or is of small size compared with the head, it presents no marked peculiarity of form. But if the orifice is in a vertical surface, and if its dimensions are not small compared with the head, @@ -8920,7 +8882,7 @@ previous sheets. Lord Rayleigh accepts an explanation of this contraction first suggested by H. Buff (1805-1878), namely, that it is due to surface tension.</p> -<p>§ 26. <i>Influence of Temperature on Discharge of Orifices.</i>—Professor +<p>§ 26. <i>Influence of Temperature on Discharge of Orifices.</i>—Professor VV. C. Unwin found (<i>Phil. Mag.</i>, October 1878, p. 281) that for sharp-edged orifices temperature has a very small influence on the discharge. For an orifice 1 cm. in diameter with heads of about @@ -8928,8 +8890,8 @@ discharge. For an orifice 1 cm. in diameter with heads of about <table class="ws" style="clear: both;" summary="Contents"> <tr><td class="tcc">Temperature F.</td> <td class="tcc"><i>C.</i></td></tr> -<tr><td class="tcc">205°</td> <td class="tcc">.594</td></tr> -<tr><td class="tcc"> 62°</td> <td class="tcc">.598</td></tr> +<tr><td class="tcc">205°</td> <td class="tcc">.594</td></tr> +<tr><td class="tcc"> 62°</td> <td class="tcc">.598</td></tr> </table> <p class="noind">For a conoidal or bell-mouthed orifice 1 cm. diameter the effect of @@ -8937,24 +8899,24 @@ temperature was greater:—</p> <table class="ws" summary="Contents"> <tr><td class="tcc">Temperature F.</td> <td class="tcc"><i>C.</i></td></tr> -<tr><td class="tcc">190°</td> <td class="tcc">0.987</td></tr> -<tr><td class="tcc">130°</td> <td class="tcc">0.974</td></tr> -<tr><td class="tcc"> 60°</td> <td class="tcc">0.942</td></tr> +<tr><td class="tcc">190°</td> <td class="tcc">0.987</td></tr> +<tr><td class="tcc">130°</td> <td class="tcc">0.974</td></tr> +<tr><td class="tcc"> 60°</td> <td class="tcc">0.942</td></tr> </table> <p class="noind">an increase in velocity of discharge of 4% when the temperature -increased 130°.</p> +increased 130°.</p> <p>J. G. Mair repeated these experiments on a much larger scale (<i>Proc. Inst. Civ. Eng.</i> lxxxiv.). For a sharp-edged orifice 2<span class="spp">1</span>⁄<span class="suu">2</span> in. -diameter, with a head of 1.75 ft., the coefficient was 0.604 at 57° -and 0.607 at 179° F., a very small difference. With a conoidal -orifice the coefficient was 0.961 at 55° and 0.98l at 170° F. The +diameter, with a head of 1.75 ft., the coefficient was 0.604 at 57° +and 0.607 at 179° F., a very small difference. With a conoidal +orifice the coefficient was 0.961 at 55° and 0.98l at 170° F. The corresponding coefficients of resistance are 0.0828 and 0.0391, showing that the resistance decreases to about half at the higher temperature.</p> -<p>§ 27. <i>Fire Hose Nozzles.</i>—Experiments have been made by J. R. +<p>§ 27. <i>Fire Hose Nozzles.</i>—Experiments have been made by J. R. Freeman on the coefficient of discharge from smooth cone nozzles used for fire purposes. The coefficient was found to be 0.983 for <span class="spp">3</span>⁄<span class="suu">4</span>-in. nozzle; 0.982 for <span class="spp">7</span>⁄<span class="suu">8</span> in.; 0.972 for 1 in.; 0.976 for 1<span class="spp">1</span>⁄<span class="suu">8</span> in.; and @@ -8965,7 +8927,7 @@ for which the coefficient was smaller.</p> <p class="pt2 center">IV. THEORY OF THE STEADY MOTION OF FLUIDS.</p> -<p>§ 28. The general equation of the steady motion of a fluid given +<p>§ 28. The general equation of the steady motion of a fluid given under Hydrodynamics furnishes immediately three results as to the distribution of pressure in a stream which may here be assumed.</p> @@ -8991,7 +8953,7 @@ section, the distribution of pressure is the same as in a fluid at rest.</p> <p class="pt1 center sc">Distribution of Energy in Incompressible Fluids.</p> -<p>§ 29. <i>Application of the Principle of the Conservation of Energy to +<p>§ 29. <i>Application of the Principle of the Conservation of Energy to Cases of Stream Line Motion.</i>—The external and internal work done on a mass is equal to the change of kinetic energy produced. In many hydraulic questions this principle is difficult to apply, because @@ -9032,7 +8994,7 @@ gravity and the pressures on the ends of the stream.</p> <p>The work of gravity when AB falls to A′B′ is the same as that of transferring AA′ to BB′; that is, GQt (z − z<span class="su">1</span>). The work of the pressures on the ends, reckoning that at B negative, because it is -opposite to the direction of motion, is (pω × vt) − (p<span class="su">1</span>ω<span class="su">1</span> × v<span class="su">1</span>t) = +opposite to the direction of motion, is (pω × vt) − (p<span class="su">1</span>ω<span class="su">1</span> × v<span class="su">1</span>t) = Qt(p − p<span class="su">1</span>). The change of kinetic energy in the time t is the difference of the kinetic energy originally possessed by AA′ and that finally acquired by BB′, for in the intermediate part A′B there is @@ -9054,7 +9016,7 @@ work done on the mass AB,</p> <div class="author">(2)</div> <p class="noind">Now v<span class="sp">2</span>/2g is the head due to the velocity v, p/G is the head equivalent -to the pressure, and z is the elevation above the datum (see § 16). +to the pressure, and z is the elevation above the datum (see § 16). Hence the terms on the left are the total head due to velocity, pressure, and elevation at a given cross section of the filament, z is easily seen to be the work in foot-pounds which would be done @@ -9083,10 +9045,10 @@ form</p> <tr><td class="figcenter"><img style="width:465px; height:289px" src="images/img43a.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 26.</span></td></tr></table> -<p>§ 30. <i>Second Form of the Theorem of Bernoulli.</i>—Suppose at the +<p>§ 30. <i>Second Form of the Theorem of Bernoulli.</i>—Suppose at the two sections A, B (fig. 26) of an elementary stream small vertical pipes are introduced, which may be termed pressure columns -(§ 8), having their lower ends accurately parallel to the direction of +(§ 8), having their lower ends accurately parallel to the direction of flow. In such tubes the water will rise to heights corresponding to the pressures at A and B. Hence b = p/G, and b′ = p<span class="su">1</span>/G. Consequently the tops of the pressure columns A′ and B′ will be at @@ -9096,7 +9058,7 @@ the fall of free surface level between A and B, is therefore</p> <p class="center">ξ = (p − p<span class="su">1</span>) / G + (z − z<span class="su">1</span>);</p> -<p class="noind">and this by equation (1), § 29 is (v<span class="su">1</span><span class="sp">2</span> − v<span class="sp">2</span>)/2g. That is, the fall of +<p class="noind">and this by equation (1), § 29 is (v<span class="su">1</span><span class="sp">2</span> − v<span class="sp">2</span>)/2g. That is, the fall of free, surface level between two sections is equal to the difference of the heights due to the velocities at the sections. The line A′B′ is sometimes called the line of hydraulic gradient, though this @@ -9106,7 +9068,7 @@ sum of the elevation and pressure head at that point, and it falls below a horizontal line A″B″ drawn at H ft. above XX by the quantities a = v<span class="sp">2</span>/2g and a′ = v<span class="su">1</span><span class="sp">2</span>/2g, when friction is absent.</p> -<p>§ 31. <i>Illustrations of the Theorem of Bernoulli.</i> In a lecture to +<p>§ 31. <i>Illustrations of the Theorem of Bernoulli.</i> In a lecture to the mechanical section of the British Association in 1875, W. Froude gave some experimental illustrations of the principle of Bernoulli. He remarked that it was a common but erroneous impression that @@ -9188,7 +9150,7 @@ pressure acting uniformly throughout the system.</p> <tr><td class="figcenter"><img style="width:438px; height:245px" src="images/img43f.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 31.</span></td></tr></table> -<p>§ 32. <i>Venturi Meter.</i>—An ingenious application of the variation +<p>§ 32. <i>Venturi Meter.</i>—An ingenious application of the variation of pressure and velocity in a converging and diverging pipe has been made by Clemens Herschel in the construction of what he terms a Venturi Meter for measuring the flow in water mains. Suppose that, @@ -9224,7 +9186,7 @@ areas are 12.57 and 113.1 sq. in., and ρ = 9,</p> <p class="noind">and the discharge of the main is</p> -<p class="center">28 × 12.57 = 351 cub. ft. per sec.</p> +<p class="center">28 × 12.57 = 351 cub. ft. per sec.</p> <table class="nobctr" style="clear: both;" summary="Illustration"> <tr><td class="figcenter"><img style="width:529px; height:243px" src="images/img44a.jpg" alt="" /></td></tr> @@ -9282,7 +9244,7 @@ the larger area the velocity is less. It finds, therefore, a new position of equilibrium. A pencil P records on a drum moved by clockwork the position of the disk, and from this the variation of flow is inferred.</p> -<p>§ 33. <i>Pressure, Velocity and Energy in Different Stream Lines.</i>—The +<p>§ 33. <i>Pressure, Velocity and Energy in Different Stream Lines.</i>—The equation of Bernoulli gives the variation of pressure and velocity from point to point along a stream line, and shows that the total energy of the flow across any two sections is the same. Two other @@ -9339,9 +9301,9 @@ introducing these values in (1),</p> <p class="pt1 center sc">Currents</p> -<p>§ 34. <i>Rectilinear Current.</i>—Suppose the motion is in parallel +<p>§ 34. <i>Rectilinear Current.</i>—Suppose the motion is in parallel straight stream lines (fig. 35) in a vertical plane. Then ρ is infinite, -and from eq. (2), § 33,</p> +and from eq. (2), § 33,</p> <p class="center">dH = v dv/g.</p> @@ -9419,7 +9381,7 @@ the circular elementary streams</p> <div class="author">(7)</div> <p>Consider two stream lines at radii r and r + dr (fig. 36). Then in -(2), § 33, ρ = r and ds = dr,</p> +(2), § 33, ρ = r and ds = dr,</p> <p class="center">v<span class="sp">2</span> dr/gr + v dv/g = 0,</p> @@ -9448,18 +9410,18 @@ The water flows spirally outwards, its velocity diminishing and its pressure increasing according to the law stated above, and the head along each spiral stream line is constant.</p> -<p>§ 35. <i>Forced Vortex.</i>—If the law of motion in a rotating current is +<p>§ 35. <i>Forced Vortex.</i>—If the law of motion in a rotating current is different from that in a free vortex, some force must be applied to cause the variation of velocity. The simplest case is that of a rotating current in which all the particles have equal angular velocity, as for instance when they are driven round by radiating paddles -revolving uniformly. Then in equation (2), § 33, considering two +revolving uniformly. Then in equation (2), § 33, considering two circular stream lines of radii r and r + dr (fig. 37), we have ρ = r, ds = dr. If the angular velocity is α, then v = αr and dv = αdr. Hence</p> <p class="center">dH = α<span class="sp">2</span>r dr/g + α<span class="sp">2</span>r dr/g = 2α<span class="sp">2</span>r dr/g.</p> -<p class="noind">Comparing this with (1), § 33, and putting dz = 0, because the motion +<p class="noind">Comparing this with (1), § 33, and putting dz = 0, because the motion is horizontal,</p> <p class="center">dp/G + α<span class="sp">2</span>r dr/g = 2α<span class="sp">2</span>r dr/g,</p> @@ -9487,7 +9449,7 @@ are paraboloids of revolution (fig. 37).</p> <p class="pt1 center sc">Dissipation of Head in Shock</p> -<p>§ 36. <i>Relation of Pressure and Velocity in a Stream in Steady +<p>§ 36. <i>Relation of Pressure and Velocity in a Stream in Steady Motion when the Changes of Section of the Stream are Abrupt.</i>—When a stream changes section abruptly, rotating eddies are formed which dissipate energy. The energy absorbed in producing rotation @@ -9559,7 +9521,7 @@ path of the stream. Then (since Q = ω<span class="su">1</span>v<span class <p class="center">p/G + v<span class="sp">2</span>/2g = p<span class="su">1</span>/G + v<span class="su">1</span><span class="sp">2</span>/2g + (v − v<span class="su">1</span>)<span class="sp">2</span> / 2g.</p> <div class="author">(3)</div> -<p class="noind">This differs from the expression (1), § 29, obtained for cases where +<p class="noind">This differs from the expression (1), § 29, obtained for cases where no sensible internal work is done, by the last term on the right. That is, (v − v<span class="su">1</span>)<span class="sp">2</span> / 2g has to be added to the total head at CD, which is p<span class="su">1</span>/G + v<span class="su">1</span><span class="sp">2</span>/2g, to make it equal to the total head at AB, or (v − v<span class="su">1</span>)<span class="sp">2</span> / 2g @@ -9592,7 +9554,7 @@ MOUTHPIECES</p> <tr><td class="figright1"><img style="width:338px; height:420px" src="images/img46b.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 39.</span></td></tr></table> -<p>§ 37. <i>Minimum Coefficient of Contraction. Re-entrant Mouthpiece +<p>§ 37. <i>Minimum Coefficient of Contraction. Re-entrant Mouthpiece of Borda.</i>—In one special case the coefficient of contraction can be determined theoretically, and, as @@ -9677,7 +9639,7 @@ little from the theoretical value, 0.5, given above.</p> <tr><td class="caption"><span class="sc">Fig. 40.</span></td> <td class="caption"><span class="sc">Fig. 41.</span></td></tr></table> -<p>§ 38. <i>Velocity of Filaments issuing in a Jet.</i>—A jet is composed +<p>§ 38. <i>Velocity of Filaments issuing in a Jet.</i>—A jet is composed of fluid filaments or elementary streams, which start into motion at some point in the interior of the vessel @@ -9699,7 +9661,7 @@ parallel and exercise uniform mutual pressure. Take the free surface AB for datum line, and let p<span class="su">1</span>, v<span class="su">1</span>, h<span class="su">1</span>, be the pressure, velocity and depth below datum at M; p, v, h, the corresponding quantities at m. -Then § 29, eq. (3a),</p> +Then § 29, eq. (3a),</p> <p class="center">v<span class="su">1</span><span class="sp">2</span>/2g + p<span class="su">1</span>/G − h<span class="su">1</span> = v<span class="sp">2</span>/2g + p/G − h</p> <div class="author">(1)</div> @@ -9739,7 +9701,7 @@ Orifice.</i>—Let the orifice discharge below the level of the tail water. Then using the notation shown in fig. 41, we have at M, v<span class="su">1</span> = 0, p<span class="su">1</span> = Gh; + p<span class="su">a</span> -at m, p = Gh<span class="su">3</span> + p<span class="su">a</span>. Inserting these values in (3), § 29,</p> +at m, p = Gh<span class="su">3</span> + p<span class="su">a</span>. Inserting these values in (3), § 29,</p> <p class="center">0 + h<span class="su">1</span> + p<span class="su">a</span>/G − h<span class="su">1</span> = v<span class="sp">2</span>/2g + h<span class="su">3</span> − h<span class="su">2</span>2 + p<span class="su">a</span>/G;</p> @@ -9813,7 +9775,7 @@ not sensibly the same.</p> <tr><td class="figright1"><img style="width:351px; height:231px" src="images/img47b.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 43.</span></td></tr></table> -<p>§ 39. <i>Large Rectangular Jets from Orifices in Vertical Plane Surfaces.</i>—Let +<p>§ 39. <i>Large Rectangular Jets from Orifices in Vertical Plane Surfaces.</i>—Let an orifice in a vertical plane surface be so formed that it produces a jet having a rectangular contracted @@ -9907,7 +9869,7 @@ which are in question.</p> <tr><td class="figcenter"><img style="width:385px; height:187px" src="images/img47c.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 44.</span></td></tr></table> -<p>§ 40. <i>Large Jets having a Circular Section from Orifices in a Vertical +<p>§ 40. <i>Large Jets having a Circular Section from Orifices in a Vertical Plane Surface.</i>—Let fig. 44 represent the section of the jet, OO being the free surface level in the reservoir. The discharge through the horizontal strip aabb, of breadth aa = b, between the depths h<span class="su">1</span> + y @@ -9945,7 +9907,7 @@ parts of the orifice is taken into account, is very small.</p> <p class="pt1 center sc">Notches and Weirs</p> -<p>§ 41. <i>Notches, Weirs and Byewashes.</i>—A notch is an orifice extending +<p>§ 41. <i>Notches, Weirs and Byewashes.</i>—A notch is an orifice extending up to the free surface level in the reservoir from which the discharge takes place. A weir is a structure over which the water flows, the discharge being in the same conditions as for a notch. @@ -9967,7 +9929,7 @@ point where the velocity of the water is very small.</p> <p>Since the area of the notch opening is BH, the above formula is of the form</p> -<p class="center">Q = c × BH × k √(2gH),</p> +<p class="center">Q = c × BH × k √(2gH),</p> <p class="noind">where k is a factor depending on the form of the notch and expressing the ratio of the mean velocity of discharge to the velocity due to the @@ -9977,7 +9939,7 @@ depth H.</p> <tr><td class="figright1"><img style="width:325px; height:530px" src="images/img48a.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 45.</span></td></tr></table> -<p>§ 42. <i>Francis’s Formula for Rectangular Notches.</i>—The jet discharged +<p>§ 42. <i>Francis’s Formula for Rectangular Notches.</i>—The jet discharged through a rectangular notch has a section smaller than BH, (<i>a</i>) because of the fall of the water surface from the point where H <span class="pagenum"><a name="page48" id="page48"></a>48</span> @@ -10024,7 +9986,7 @@ width of the jet is l − 0.1nH, where n is the number of end contractions of the stream. The contractions due to the fall of surface and to the crest contraction are proportional to the width of the jet. Hence, if cH is the thickness of the stream over the weir, measured at the contracted -section, the section of the jet will be c(l − 0.1nH)H and (§ 41) the +section, the section of the jet will be c(l − 0.1nH)H and (§ 41) the mean velocity will be <span class="spp">2</span>⁄<span class="suu">3</span> √(2gH). Consequently the discharge will be given by an equation of the form</p> @@ -10037,7 +9999,7 @@ much more nearly constant for different values of l and h than in the ordinary formula. Francis found for c the mean value 0.622, the weir being sharp-edged.</p> -<p>§ 43. <i>Triangular Notch</i> (fig. 46).—Consider a lamina issuing between +<p>§ 43. <i>Triangular Notch</i> (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 √(2gh). Hence the discharge for this lamina is</p> @@ -10084,11 +10046,11 @@ to be the case. Hence a triangular notch is more suitable for accurate gaugings than a rectangular notch. For a sharp-edged triangular notch Professor J. Thomson -found c = 0.617. It will be seen, as in § 41, that since <span class="spp">1</span>⁄<span class="suu">2</span>BH is the +found c = 0.617. It will be seen, as in § 41, that since <span class="spp">1</span>⁄<span class="suu">2</span>BH is the area of section of the stream through the notch, the formula is again of the form</p> -<p class="center">Q = c × <span class="spp">1</span>⁄<span class="suu">2</span>BH × k √(2gH),</p> +<p class="center">Q = c × <span class="spp">1</span>⁄<span class="suu">2</span>BH × k √(2gH),</p> <p class="noind">where k = <span class="spp">8</span>⁄<span class="suu">15</span> is the ratio of the mean velocity in the notch to the velocity at the depth H. It may easily be shown that for all notches @@ -10102,7 +10064,7 @@ is very strongly marked.</i></p> <tr><td class="tccm allb f80" rowspan="2">Heads in<br />inches<br />measured<br />from still<br />Water in<br />Reservoir.</td> <td class="tccm allb f80" colspan="2">Sharp Edge.</td> <td class="tccm allb f80" colspan="4">Planks 2 in. thick,<br />square on Crest.</td> <td class="tccm allb f80" colspan="6">Crests 3 ft. wide.</td></tr> <tr><td class="tccm allb f80">3 ft. long.</td> <td class="tccm allb f80">10 ft. long.</td> <td class="tccm allb f80">3 ft. long.</td> <td class="tccm allb f80">6 ft. long.</td> <td class="tccm allb f80">10 ft. long.</td> - <td class="tccm allb f80">10 ft. long,<br />wing-boards<br />making an<br />angle of 60°.</td> + <td class="tccm allb f80">10 ft. long,<br />wing-boards<br />making an<br />angle of 60°.</td> <td class="tccm allb f80">3 ft. long.<br />level.</td> <td class="tccm allb f80">3 ft. long,<br />fall 1 in 18.</td> <td class="tccm allb f80">3 ft. long,<br />fall 1 in 12.</td> <td class="tccm allb f80">6 ft. long.<br />level.</td> <td class="tccm allb f80">10 ft. long.<br />level.</td> <td class="tccm allb f80">10 ft. long,<br />fall 1 in 18.</td></tr> @@ -10125,7 +10087,7 @@ is very strongly marked.</i></p> <tr><td class="figcenter"><img style="width:458px; height:151px" src="images/img48c.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 47.</span></td></tr></table> -<p>§ 44. <i>Weir with a Broad Sloping Crest.</i>—Suppose a weir formed +<p>§ 44. <i>Weir with a Broad Sloping Crest.</i>—Suppose a weir formed with a broad crest so sloped that the streams flowing over it have a movement sensibly rectilinear and uniform (fig. 47). Let the inner edge be so rounded as to prevent a crest contraction. Consider a @@ -10162,7 +10124,7 @@ to the ordinary weir formula with c = 0.577.</p> <p class="pt1 center sc">Special Cases of Discharge from Orifices</p> -<p>§ 45. <i>Cases in which the Velocity of Approach needs to be taken +<p>§ 45. <i>Cases in which the Velocity of Approach needs to be taken into Account.</i> <i>Rectangular Orifices and Notches.</i>—In finding the velocity at the orifice in the preceding investigations, it has been assumed that the head h has been measured from the free surface @@ -10215,7 +10177,7 @@ above will give a second and much more approximate value of Q.</p> <tr><td class="figcenter"><img style="width:459px; height:279px" src="images/img49b.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 49.</span></td></tr></table> -<p>§ 46. <i>Partially Submerged Rectangular Orifices and Notches.</i>—When +<p>§ 46. <i>Partially Submerged Rectangular Orifices and Notches.</i>—When the tail water is above the lower but below the upper edge of the orifice, the flow in the two parts of the orifice, into which it is divided by the surface of the tail water, takes place under different @@ -10285,11 +10247,11 @@ a drowned weir. But the value of c in this case is imperfectly known.</p> -<p>§ 47. <i>Bazin’s Researches on +<p>§ 47. <i>Bazin’s Researches on Weirs.</i>—H. Bazin has executed a long series of researches on the flow over weirs, so systematic and complete that they almost supersede other observations. The account of them is contained -in a series of papers in the <i>Annales des Ponts et Chaussées</i> +in a series of papers in the <i>Annales des Ponts et Chaussées</i> (October 1888, January 1890, November 1891, February 1894, December 1896, 2nd trimestre 1898). Only a very abbreviated account can be given here. The general plan of the experiments @@ -10300,7 +10262,7 @@ flow, to compare the observed heads on the different weirs and to determine their coefficients from the discharge computed at the standard weir. A channel was constructed parallel to the Canal de Bourgogne, taking water from it through three sluices -0.3 × 1.0 metres. The water enters a masonry chamber 15 metres +0.3 × 1.0 metres. The water enters a masonry chamber 15 metres long by 4 metres wide where it is stilled and passes into the canal at the end of which is the standard weir. The canal has a length of 15 metres, a width of 2 metres and a depth of 0.6 metres. From @@ -10514,7 +10476,7 @@ when the sheet is free and the weir of the same height.</p> -<p>§ 48. <i>Separating +<p>§ 48. <i>Separating Weirs.</i>—Many towns derive their water-supply from @@ -10574,7 +10536,7 @@ the divisions on af give the parabolic path of the jet.</p> <p class="pt1 center sc">Mouthpieces—Head Constant</p> -<p>§ 49. <i>Cylindrical Mouthpieces.</i>—When water issues from a short +<p>§ 49. <i>Cylindrical Mouthpieces.</i>—When water issues from a short cylindrical pipe or mouthpiece of a length at least equal to l<span class="spp">1</span>⁄<span class="suu">2</span> times its smallest transverse dimension, the stream, after contraction within the mouthpiece, expands to fill it and issues full bore, or without @@ -10600,7 +10562,7 @@ at a point where its velocity is sensibly zero, is h + p<span class="su">a</span total head is v<span class="sp">2</span>/2g + p/G; at GH it is v<span class="su">1</span><span class="sp">2</span>/2g + p<span class="su">1</span>/G.</p> <p>Between EF and GH there is a loss of head due to abrupt change -of velocity, which from eq. (3), § 36, may have the value</p> +of velocity, which from eq. (3), § 36, may have the value</p> <p class="center">(v − v<span class="su">1</span>)<span class="sp">2</span>/2g.</p> @@ -10675,7 +10637,7 @@ will be forced continuously into the jet by the atmospheric pressure, and discharged with it. This is the crudest form of a kind of pump known as the jet pump.</p> -<p>§ 50. <i>Convergent Mouthpieces.</i>—With convergent mouthpieces +<p>§ 50. <i>Convergent Mouthpieces.</i>—With convergent mouthpieces there is a contraction within the mouthpiece causing a loss of head, and a diminution of the velocity of discharge, as with cylindrical mouthpieces. There is also a second contraction of the stream outside @@ -10694,28 +10656,28 @@ orifice = 0.05085 ft. Length of mouthpiece = 2.6 Diameters.</i></p> <table class="ws" summary="Contents"> <tr><td class="tccm allb">Angle of<br />Convergence.</td> <td class="tccm allb">Coefficient of<br />Contraction,<br />c<span class="su">c</span></td> <td class="tccm allb">Coefficient of<br />Velocity,<br />c<span class="su">v</span></td> <td class="tccm allb">Coefficient of<br />Discharge,<br />c</td></tr> -<tr><td class="tcc lb rb"> 0°  0′</td> <td class="tcc rb"> .999</td> <td class="tcc rb">.830</td> <td class="tcc rb">.829</td></tr> -<tr><td class="tcc lb rb"> 1° 36′</td> <td class="tcc rb">1.000</td> <td class="tcc rb">.866</td> <td class="tcc rb">.866</td></tr> -<tr><td class="tcc lb rb"> 3° 10′</td> <td class="tcc rb">1.001</td> <td class="tcc rb">.894</td> <td class="tcc rb">.895</td></tr> -<tr><td class="tcc lb rb"> 4° 10′</td> <td class="tcc rb">1.002</td> <td class="tcc rb">.910</td> <td class="tcc rb">.912</td></tr> -<tr><td class="tcc lb rb"> 5° 26′</td> <td class="tcc rb">1.004</td> <td class="tcc rb">.920</td> <td class="tcc rb">.924</td></tr> -<tr><td class="tcc lb rb"> 7° 52′</td> <td class="tcc rb"> .998</td> <td class="tcc rb">.931</td> <td class="tcc rb">.929</td></tr> -<tr><td class="tcc lb rb"> 8° 58′</td> <td class="tcc rb"> .992</td> <td class="tcc rb">.942</td> <td class="tcc rb">.934</td></tr> -<tr><td class="tcc lb rb">10° 20′</td> <td class="tcc rb"> .987</td> <td class="tcc rb">.950</td> <td class="tcc rb">.938</td></tr> -<tr><td class="tcc lb rb">12° 4′</td> <td class="tcc rb"> .986</td> <td class="tcc rb">.955</td> <td class="tcc rb">.942</td></tr> -<tr><td class="tcc lb rb">13° 24′</td> <td class="tcc rb"> .983</td> <td class="tcc rb">.962</td> <td class="tcc rb">.946</td></tr> -<tr><td class="tcc lb rb">14° 28′</td> <td class="tcc rb"> .979</td> <td class="tcc rb">.966</td> <td class="tcc rb">.941</td></tr> -<tr><td class="tcc lb rb">16° 36′</td> <td class="tcc rb"> .969</td> <td class="tcc rb">.971</td> <td class="tcc rb">.938</td></tr> -<tr><td class="tcc lb rb">19° 28′</td> <td class="tcc rb"> .953</td> <td class="tcc rb">.970</td> <td class="tcc rb">.924</td></tr> -<tr><td class="tcc lb rb">21°  0′</td> <td class="tcc rb"> .945</td> <td class="tcc rb">.971</td> <td class="tcc rb">.918</td></tr> -<tr><td class="tcc lb rb">23°  0′</td> <td class="tcc rb"> .937</td> <td class="tcc rb">.974</td> <td class="tcc rb">.913</td></tr> -<tr><td class="tcc lb rb">29° 58′</td> <td class="tcc rb"> .919</td> <td class="tcc rb">.975</td> <td class="tcc rb">.896</td></tr> -<tr><td class="tcc lb rb">40° 20′</td> <td class="tcc rb"> .887</td> <td class="tcc rb">.980</td> <td class="tcc rb">.869</td></tr> -<tr><td class="tcc lb rb bb">48° 50′</td> <td class="tcc rb bb"> .861</td> <td class="tcc rb bb">.984</td> <td class="tcc rb bb">.847</td></tr> +<tr><td class="tcc lb rb"> 0°  0′</td> <td class="tcc rb"> .999</td> <td class="tcc rb">.830</td> <td class="tcc rb">.829</td></tr> +<tr><td class="tcc lb rb"> 1° 36′</td> <td class="tcc rb">1.000</td> <td class="tcc rb">.866</td> <td class="tcc rb">.866</td></tr> +<tr><td class="tcc lb rb"> 3° 10′</td> <td class="tcc rb">1.001</td> <td class="tcc rb">.894</td> <td class="tcc rb">.895</td></tr> +<tr><td class="tcc lb rb"> 4° 10′</td> <td class="tcc rb">1.002</td> <td class="tcc rb">.910</td> <td class="tcc rb">.912</td></tr> +<tr><td class="tcc lb rb"> 5° 26′</td> <td class="tcc rb">1.004</td> <td class="tcc rb">.920</td> <td class="tcc rb">.924</td></tr> +<tr><td class="tcc lb rb"> 7° 52′</td> <td class="tcc rb"> .998</td> <td class="tcc rb">.931</td> <td class="tcc rb">.929</td></tr> +<tr><td class="tcc lb rb"> 8° 58′</td> <td class="tcc rb"> .992</td> <td class="tcc rb">.942</td> <td class="tcc rb">.934</td></tr> +<tr><td class="tcc lb rb">10° 20′</td> <td class="tcc rb"> .987</td> <td class="tcc rb">.950</td> <td class="tcc rb">.938</td></tr> +<tr><td class="tcc lb rb">12° 4′</td> <td class="tcc rb"> .986</td> <td class="tcc rb">.955</td> <td class="tcc rb">.942</td></tr> +<tr><td class="tcc lb rb">13° 24′</td> <td class="tcc rb"> .983</td> <td class="tcc rb">.962</td> <td class="tcc rb">.946</td></tr> +<tr><td class="tcc lb rb">14° 28′</td> <td class="tcc rb"> .979</td> <td class="tcc rb">.966</td> <td class="tcc rb">.941</td></tr> +<tr><td class="tcc lb rb">16° 36′</td> <td class="tcc rb"> .969</td> <td class="tcc rb">.971</td> <td class="tcc rb">.938</td></tr> +<tr><td class="tcc lb rb">19° 28′</td> <td class="tcc rb"> .953</td> <td class="tcc rb">.970</td> <td class="tcc rb">.924</td></tr> +<tr><td class="tcc lb rb">21°  0′</td> <td class="tcc rb"> .945</td> <td class="tcc rb">.971</td> <td class="tcc rb">.918</td></tr> +<tr><td class="tcc lb rb">23°  0′</td> <td class="tcc rb"> .937</td> <td class="tcc rb">.974</td> <td class="tcc rb">.913</td></tr> +<tr><td class="tcc lb rb">29° 58′</td> <td class="tcc rb"> .919</td> <td class="tcc rb">.975</td> <td class="tcc rb">.896</td></tr> +<tr><td class="tcc lb rb">40° 20′</td> <td class="tcc rb"> .887</td> <td class="tcc rb">.980</td> <td class="tcc rb">.869</td></tr> +<tr><td class="tcc lb rb bb">48° 50′</td> <td class="tcc rb bb"> .861</td> <td class="tcc rb bb">.984</td> <td class="tcc rb bb">.847</td></tr> </table> <p>The maximum coefficient of discharge is that for a mouthpiece -with a convergence of 13°24′.</p> +with a convergence of 13°24′.</p> <p><span class="pagenum"><a name="page52" id="page52"></a>52</span></p> @@ -10741,7 +10703,7 @@ product c<span class="su">c</span> c<span class="su">v</span>, and consequently the discharge, is a maximum.</p> -<p>§ 51. <i>Divergent Conoidal +<p>§ 51. <i>Divergent Conoidal Mouthpiece.</i>—Suppose a mouthpiece so designed that there is @@ -10839,7 +10801,7 @@ mouthpiece of this kind is</p> of area ω, and without the expanding part, discharging into a vacuum.</p> -<p>§ 52. <i>Jet Pump.</i>—A divergent mouthpiece may be arranged to act +<p>§ 52. <i>Jet Pump.</i>—A divergent mouthpiece may be arranged to act as a pump, as shown in fig. 62. The water which supplies the energy required for pumping enters at A. The water to be pumped enters at B. The streams combine at DD where the velocity is greatest @@ -10863,7 +10825,7 @@ which the water is pumped.</p> <p class="pt1 center sc">Discharge with Varying Head</p> -<p>§ 53. <i>Flow from a Vessel when the Effective Head varies with the +<p>§ 53. <i>Flow from a Vessel when the Effective Head varies with the Time.</i>—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 @@ -10916,7 +10878,7 @@ with the time.</p> <p class="pt1 center sc">Practical Use of Orifices in Gauging Water</p> -<p>§ 54. If the water to be measured is passed through a known orifice +<p>§ 54. If the water to be measured is passed through a known orifice under an arrangement by which the constancy of the head is ensured, the amount which passes in a given time can be ascertained by the formulae already given. It will obviously be best to make the @@ -10969,7 +10931,7 @@ consumer for emptying the pipes. The one on the left and the measuring cock are connected by a key which can be locked by a padlock, which is under the control of the water company.</p> -<p>§ 55. <i>Measurement of the Flow in Streams.</i>—To determine the +<p>§ 55. <i>Measurement of the Flow in Streams.</i>—To determine the quantity of water flowing off the ground in small streams, which is available for water supply or for obtaining water power, small temporary weirs are often used. These may be formed of planks @@ -10984,7 +10946,7 @@ is, for a rectangular notch of breadth b,</p> <p class="center">Q = <span class="spp">2</span>⁄<span class="suu">3</span> cbh √<span class="ov">2gh</span></p> -<p class="noind">where c = 0.62; or, better, the formula in § 42 may be used.</p> +<p class="noind">where c = 0.62; or, better, the formula in § 42 may be used.</p> <p>Gauging weirs are most commonly in the form of rectangular notches; and care should be taken that the crest is accurately @@ -11081,7 +11043,7 @@ first be set accurately level with the weir crest, and a reading taken. Then the difference of the reading at the water surface and that for the weir crest will be the head at the weir.</p> -<p>§ 56. <i>Modules used in Irrigation.</i>—In distributing water for +<p>§ 56. <i>Modules used in Irrigation.</i>—In distributing water for irrigation, the charge for the water may be simply assessed on the area of the land irrigated for each consumer, a method followed in India; or a regulated quantity of water may be given to each @@ -11098,7 +11060,7 @@ the variation of level in the irrigating channel.</p> <tr><td class="figcenter"><img style="width:468px; height:204px" src="images/img54a.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 69.</span></td></tr></table> -<p>§ 57. <i>Italian Module.</i>—The Italian modules are masonry constructions, +<p>§ 57. <i>Italian Module.</i>—The Italian modules are masonry constructions, consisting of a regulating chamber, to which water is admitted by an adjustable sluice from the canal. At the other end of the chamber is an orifice in a thin flagstone of fixed size. By means @@ -11172,7 +11134,7 @@ the water in the chamber. The water is discharged into an open channel 0.655 ft. wider than the orifice, splaying out till it is 1.637 ft. wider than the orifice, and about 18 ft. in length.</p> -<p>§ 58. <i>Spanish Module.</i>—On the canal of Isabella II., which supplies +<p>§ 58. <i>Spanish Module.</i>—On the canal of Isabella II., which supplies water to Madrid, a module much more perfect in principle than the Italian module is employed. Part of the water is supplied for irrigation, and as it is very valuable its @@ -11217,7 +11179,7 @@ involves a great sacrifice of level between the canal and the fields. The module is described in Sir C. Scott-Moncrieff’s <i>Irrigation in Southern Europe</i>.</p> -<p>§ 59. <i>Reservoir Gauging Basins.</i>—In obtaining the power to store +<p>§ 59. <i>Reservoir Gauging Basins.</i>—In obtaining the power to store the water of streams in reservoirs, it is usual to concede to riparian <span class="pagenum"><a name="page55" id="page55"></a>55</span> owners below the reservoirs a right to a regulated supply throughout @@ -11265,7 +11227,7 @@ large scale.</p> <tr><td class="figcenter"><img style="width:476px; height:781px" src="images/img55c.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 74.</span>—Scale <span class="spp">1</span>⁄<span class="suu">500</span>.</td></tr></table> -<p>§ 60. <i>Professor Fleeming Jenkin’s Constant Flow Valve.</i>—In the +<p>§ 60. <i>Professor Fleeming Jenkin’s Constant Flow Valve.</i>—In the modules thus far described constant discharge is obtained by varying the area of the orifice through which the water flows. Professor F. Jenkin has contrived a valve in which a constant pressure head @@ -11306,7 +11268,7 @@ with a difference of pressure of <span class="spp">1</span>⁄<span class="s <tr><td class="figright1"><img style="width:308px; height:324px" src="images/img56b.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 76.</span></td></tr></table> -<p>§ 61. <i>External Work during the Expansion of Air.</i>—If air expands +<p>§ 61. <i>External Work during the Expansion of Air.</i>—If air expands without doing any external work, its temperature remains constant. This result was first experimentally demonstrated @@ -11403,7 +11365,7 @@ volumes per pound, we get for the work of expansion</p> <tr><td class="figright1"><img style="width:264px; height:93px" src="images/img56c.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 77.</span></td></tr></table> -<p>§ 62. <i>Modification of the Theorem of Bernoulli for the Case of a +<p>§ 62. <i>Modification of the Theorem of Bernoulli for the Case of a Compressible Fluid.</i>—In the application of the principle of work to a filament of compressible fluid, the internal work done by the expansion of the fluid, or absorbed @@ -11447,7 +11409,7 @@ Wt <span class="f150">∫</span><span class="sp1">v<span class="su">2</span></ <div class="author">(1)</div> <p class="noind">Now the work of expansion per pound of fluid has already been -given. If the temperature is constant, we get (eq. 1a, § 61)</p> +given. If the temperature is constant, we get (eq. 1a, § 61)</p> <p class="center">Z<span class="su">1</span> + P<span class="su">1</span>/G<span class="su">1</span> + v<span class="su">1</span><span class="sp">2</span>/2g = z<span class="su">2</span> + p<span class="sp">2</span>/G<span class="su">2</span> + v<span class="su">2</span><span class="sp">2</span>/2g − (p<span class="su">1</span>/G<span class="su">1</span>) log<span class="su">ε</span> (G<span class="su">1</span>/G<span class="su">2</span>).</p> @@ -11461,7 +11423,7 @@ given. If the temperature is constant, we get (eq. 1a, § 61)</p> <p class="center">(v<span class="su">2</span><span class="sp">2</span> − v<span class="su">1</span><span class="sp">2</span>) / 2g = (p<span class="su">1</span>/G<span class="su">1</span>) log<span class="su">ε</span> (p<span class="su">1</span>/p<span class="su">2</span>).</p> <div class="author1">(2a)</div> -<p class="noind">Similarly, if the expansion is adiabatic (eq. 2a, § 61),</p> +<p class="noind">Similarly, if the expansion is adiabatic (eq. 2a, § 61),</p> <p class="center">z<span class="su">1</span> + p<span class="su">1</span>/G<span class="su">1</span> + v<span class="su">1</span><span class="sp">2</span>/2g = z<span class="su">2</span> + p<span class="su">2</span>/G<span class="su">2</span> + v<span class="su">2</span><span class="sp">2</span>/2g − (p<span class="su">1</span>/G<span class="su">1</span>) {1/(γ − 1) } {1 − (p<span class="su">2</span>/p<span class="su">1</span>)<span class="sp">(γ−1)/γ</span>};</p> @@ -11475,7 +11437,7 @@ given. If the temperature is constant, we get (eq. 1a, § 61)</p> <p class="noind">It will be seen hereafter that there is a limit in the ratio p<span class="su">1</span>/p<span class="su">2</span> beyond which these expressions cease to be true.</p> -<p>§ 63. <i>Discharge of Air from an Orifice.</i>—The form of the equation +<p>§ 63. <i>Discharge of Air from an Orifice.</i>—The form of the equation of work for a steady stream of compressible fluid is</p> <p class="center">z<span class="su">1</span> + p<span class="su">1</span>/G<span class="su">1</span> + v<span class="su">1</span><span class="sp">2</span>/2g = z<span class="su">2</span> + p<span class="su">2</span>/G<span class="su">2</span> + v<span class="su">2</span><span class="sp">2</span>/2g − @@ -11516,7 +11478,7 @@ may be neglected. Putting these values in the equation above—</p> 1856), though it appears to have been given earlier by A. J. C. Barre de Saint Venant and L. Wantzel.</p> -<p>It has already (§ 9, eq. 4a) been seen that</p> +<p>It has already (§ 9, eq. 4a) been seen that</p> <p class="center">p<span class="su">1</span>/G<span class="su">1</span> = (p<span class="su">0</span>/G<span class="su">0</span>) (τ<span class="su">1</span>/τ<span class="su">0</span>)</p> @@ -11587,7 +11549,7 @@ c:—</p> <tr><td class="tcl">Conical converging mouthpieces</td> <td class="tcl">0.90</td> <td class="tcc">”</td> <td class="tcl">0.99</td></tr> </table> -<p>§ 64. <i>Limit to the Application of the above Formulae.</i>—In the +<p>§ 64. <i>Limit to the Application of the above Formulae.</i>—In the formulae above it is assumed that the fluid issuing from the orifice expands from the pressure p<span class="su">1</span> to the pressure p<span class="su">2</span>, while passing from the vessel to the section of the jet considered in estimating the area @@ -11642,7 +11604,7 @@ paper (<i>Civilingenieur</i>, 1871), and Fliegner’s papers (<i>ibid.</i>, <p class="pt2 center">VII. FRICTION OF LIQUIDS.</p> -<p>§ 65. When a stream of fluid flows over a solid surface, or conversely +<p>§ 65. When a stream of fluid flows over a solid surface, or conversely when a solid moves in still fluid, a resistance to the motion is generated, commonly termed fluid friction. It is due to the viscosity of the fluid, but generally the laws of fluid friction are very @@ -11695,7 +11657,7 @@ practice. H. P. G. Darcy’s experiments, for instance, showed that in old and incrusted water mains the resistance was twice or sometimes thrice as great as in new and clean mains.</p> -<p>§ 66. <i>Ordinary Expressions for Fluid Friction at Velocities not +<p>§ 66. <i>Ordinary Expressions for Fluid Friction at Velocities not Extremely Small.</i>—Let f be the frictional resistance estimated in pounds per square foot of surface at a velocity of 1 ft. per second; ω the area of the surface in square feet; and v its velocity in feet @@ -11782,7 +11744,7 @@ to vary through wider limits than these expressions allow, and to depend on circumstances of which they do not take account.</p> -<p>§ 67. <i>Coulomb’s Experiments.</i>—The first direct experiments on +<p>§ 67. <i>Coulomb’s Experiments.</i>—The first direct experiments on fluid friction were made by Coulomb, who employed a circular disk suspended by a thin brass wire and oscillated in its own plane. His experiments were chiefly made at very low velocities. When the @@ -11811,7 +11773,7 @@ and they generally made one oscillation in from 20 to 30 seconds, through angles varying -from 360° to 6°. When +from 360° to 6°. When the velocity of the circumference of the disk was less than 6 in. per @@ -11830,7 +11792,7 @@ ft., at a velocity of 10 ft. per second, the difference of resistance, measured on the difference of area, was 0.339 ℔ per square foot. Also the resistance varied as the 1.949th power of the velocity.</p> -<p>§ 68. <i>Froude’s Experiments.</i>—The most important direct experiments +<p>§ 68. <i>Froude’s Experiments.</i>—The most important direct experiments on fluid friction at ordinary velocities are those made by William Froude (1810-1879) at Torquay. The method adopted in these experiments was to tow a board in a still water canal, the @@ -11915,7 +11877,7 @@ against stationary water, but against water partially moving in its own direction, and cannot therefore experience so much resistance from it.”</p> -<p>§ 69. The following table gives a general statement of Froude’s +<p>§ 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 @@ -11976,7 +11938,7 @@ water and that diffused. The velocity of the current accompanying the board becomes constant or nearly constant, and the friction per square foot is therefore nearly constant also.</p> -<p>§ 70. <i>Friction of Rotating Disks.</i>—A rotating disk is virtually a +<p>§ 70. <i>Friction of Rotating Disks.</i>—A rotating disk is virtually a surface of unlimited extent and it is convenient for experiments on friction with different surfaces at different speeds. Experiments carried out by Professor W. C. Unwin (<i>Proc. Inst. Civ. Eng.</i> lxxx.) @@ -12034,14 +11996,14 @@ Froude’s results.</p> <p>Experiments with a bright brass disk showed that the friction decreased with increase of -temperature. The diminution between 41° -and 130° F. amounted to 18%. In the general +temperature. The diminution between 41° +and 130° F. amounted to 18%. In the general equation M = cN<span class="sp">n</span> for any given disk,</p> <p class="center">c<span class="su">t</span> = 0.1328 (1 − 0.0021t),</p> <p class="noind">where c<span class="su">t</span> is the value of c for a bright brass -disk 0.85 ft. in diameter at a temperature t° F.</p> +disk 0.85 ft. in diameter at a temperature t° F.</p> <p>The disks used were either polished or made rougher by varnish or by varnish and sand. The following table gives a comparison of @@ -12061,7 +12023,7 @@ the results obtained with the disks and Froude’s results on planks <p class="pt2 center">VIII. STEADY FLOW OF WATER IN PIPES OF UNIFORM SECTION.</p> -<p>§ 71. The ordinary theory of the flow of water in pipes, on which +<p>§ 71. The ordinary theory of the flow of water in pipes, on which all practical formulae are based, assumes that the variation of velocity at different points of any cross section may be neglected. The water is considered as moving in plane layers, which are driven @@ -12115,7 +12077,7 @@ volume Q is</p> against the surface of the pipe. The area of that surface is χdl.</p> <p>The work expended in overcoming the frictional resistance per -second is (see § 66, eq. 3)</p> +second is (see § 66, eq. 3)</p> <p class="center">−ζGχ dl v<span class="sp">3</span>/2g,</p> @@ -12140,7 +12102,7 @@ result to zero, since the motion is uniform,—</p> <p class="center">z + p/G + ζ (χ/Ω) (v<span class="sp">2</span>/2g) l = constant.</p> <div class="author">(1)</div> -<p>§ 72. Let A and B (fig. 81) be any two sections of the pipe for +<p>§ 72. Let A and B (fig. 81) be any two sections of the pipe for which p, z, l have the values p<span class="su">1</span>, z<span class="su">1</span>, l<span class="su">1</span>, and p<span class="su">2</span>, z<span class="su">2</span>, l<span class="su">2</span>, respectively. Then</p> @@ -12198,7 +12160,7 @@ pressure at C and D is the same, and this is usually nearly the case. But if C and D are at greatly different levels the excess of barometric pressure at C, in feet of water, must be added to p<span class="su">2</span>/G.</p> -<p>§ 73. <i>Hydraulic Gradient or Line of Virtual Slope.</i>—Join CD. +<p>§ 73. <i>Hydraulic Gradient or Line of Virtual Slope.</i>—Join CD. Since the head lost in friction is proportional to L, any intermediate pressure column between A and B will have its free surface on the line CD, and the vertical distance between CD and the pipe at any @@ -12230,7 +12192,7 @@ error of practical importance.</p> <tr><td class="figcenter"><img style="width:471px; height:165px" src="images/img60b.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 82.</span></td></tr></table> -<p>§ 74. <i>Case of a Uniform Pipe connecting two Reservoirs, when all the +<p>§ 74. <i>Case of a Uniform Pipe connecting two Reservoirs, when all the Resistances are taken into account.</i>—Let h (fig. 82) be the difference of level of the reservoirs, and v the velocity, in a pipe of length L and diameter d. The whole work done per second is virtually the @@ -12247,10 +12209,10 @@ entrance to the pipe. (3) As already shown the head expended in overcoming the surface friction of the pipe is ζ(4L/d) (v<span class="sp">2</span>/2g) corresponding to GQζ (4L/d) (v<span class="sp">2</span>/2g) foot-pounds of work. Hence</p> -<p class="center">GQh = GQv<span class="sp">2</span>/2g + GQζ<span class="su">0</span>v<span class="sp">2</span>/2g + GQζ·4L·v<span class="sp">2</span>/d·2g;</p> +<p class="center">GQh = GQv<span class="sp">2</span>/2g + GQζ<span class="su">0</span>v<span class="sp">2</span>/2g + GQζ·4L·v<span class="sp">2</span>/d·2g;</p> <table class="reg" summary="poem"><tr><td> <div class="poemr"> -<p>h = (1 + ζ<span class="su">0</span> + ζ·4L/d) v<span class="sp">2</span>/2g.</p> +<p>h = (1 + ζ<span class="su">0</span> + ζ·4L/d) v<span class="sp">2</span>/2g.</p> <p>v = 8.025 √ [hd / {(1 + ζ<span class="su">0</span>)d + 4ζL} ].</p> </div> </td></tr></table> <div class="author">(5)</div> @@ -12290,7 +12252,7 @@ equivalent to the mouthpiece is 37.6d nearly. This may be added to the actual length of the pipe to allow for mouthpiece resistance in approximate calculations.</p> -<p>§ 75. <i>Coefficient of Friction for Pipes discharging Water.</i>—From the +<p>§ 75. <i>Coefficient of Friction for Pipes discharging Water.</i>—From the average of a large number of experiments, the value of ζ for ordinary iron pipes is</p> @@ -12323,7 +12285,7 @@ form</p> <p><span class="pagenum"><a name="page61" id="page61"></a>61</span></p> -<p>§ 76. <i>Darcy’s Experiments on Friction in Pipes.</i>—All previous +<p>§ 76. <i>Darcy’s Experiments on Friction in Pipes.</i>—All previous experiments on the resistance of pipes were superseded by the remarkable researches carried out by H. P. G. Darcy (1803-1858), the Inspector-General of the Paris water works. His experiments were @@ -12425,7 +12387,7 @@ cumbrous, its form is not rationally justifiable and it is not at all clear that it gives more accurate values of the discharge than simpler formulae.</p> -<p>§ 77. <i>Later Investigations on Flow in Pipes.</i>—The foregoing statement +<p>§ 77. <i>Later Investigations on Flow in Pipes.</i>—The foregoing statement gives the theory of flow in pipes so far as it can be put in a simple rational form. But the conditions of flow are really more complicated than can be expressed in any rational form. Taking @@ -12454,7 +12416,7 @@ fluid friction show that the power of the velocity to which the resistance is proportional is not exactly the square. Also in determining the form of his equation for ζ Darcy used only eight out of his seventeen series of experiments, and there is reason to think that some -of these were exceptional. Barré de Saint-Venant was the first to +of these were exceptional. Barré de Saint-Venant was the first to propose a formula with two constants,</p> <p class="center">dh/4l = mV<span class="sp">n</span>,</p> @@ -12627,7 +12589,7 @@ in other cases.</p> <p class="pt1 center"><i>General Mean Values of Constants.</i></p> -<p>The general formula (Hagen’s)—h/l = mv<span class="sp">n</span>/d<span class="sp">x</span>·2g—can therefore be +<p>The general formula (Hagen’s)—h/l = mv<span class="sp">n</span>/d<span class="sp">x</span>·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:—</p> @@ -12664,7 +12626,7 @@ following are the values of the coefficients:—</p> <tr><td class="tcl lb rb bb">Incrusted cast iron</td> <td class="tcc rb bb">.0440</td> <td class="tcc rb bb">1.160</td> <td class="tcc rb bb">2.0 </td></tr> </table> -<p>§ 78. <i>Distribution of Velocity in the Cross Section of a Pipe.</i>—Darcy +<p>§ 78. <i>Distribution of Velocity in the Cross Section of a Pipe.</i>—Darcy made experiments with a Pitot tube in 1850 on the velocity at different points in the cross section of a pipe. He deduced the relation</p> @@ -12673,7 +12635,7 @@ relation</p> <p class="noind">where V is the velocity at the centre and v the velocity at radius r in a pipe of radius R with a hydraulic gradient i. Later Bazin repeated -the experiments and extended them (<i>Mém. de l’Académie des Sciences</i>, +the experiments and extended them (<i>Mém. de l’Académie des Sciences</i>, xxxii. No. 6). The most important result was the ratio of mean to central velocity. Let b = Ri/U<span class="sp">2</span>, where U is the mean velocity in the pipe; then V/U = 1 + 9.03 √b. A very useful result for practical @@ -12685,7 +12647,7 @@ as determined by Bazin.</p> <tr><td class="figcenter"><img style="width:340px; height:344px" src="images/img63a.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 84.</span></td></tr></table> -<p>§ 79. <i>Influence of Temperature on the Flow through Pipes.</i>—Very +<p>§ 79. <i>Influence of Temperature on the Flow through Pipes.</i>—Very careful experiments on the flow through a pipe 0.1236 ft. in diameter and 25 ft. long, with water at different temperatures, have been made by J. G. Mair (<i>Proc. Inst. Civ. Eng.</i> lxxxiv.). The loss of head @@ -12725,16 +12687,16 @@ temperature are practically constant—</p> <p class="noind">where again a regular decrease of the coefficient occurs as the temperature rises. In experiments on the friction of disks at different temperatures Professor W. C. Unwin found that the resistance -was proportional to constant × (1 − 0.0021t) and the values +was proportional to constant × (1 − 0.0021t) and the values of m given above are expressed almost exactly by the relation</p> <p class="center">m = 0.000311 (1 − 0.00215 t).</p> <p>In tank experiments on ship models for small ordinary variations of temperature, it is usual to allow a decrease of 3% of resistance for -10° F. increase of temperature.</p> +10° F. increase of temperature.</p> -<p>§ 80. <i>Influence of Deposits in Pipes on the Discharge. Scraping +<p>§ 80. <i>Influence of Deposits in Pipes on the Discharge. Scraping Water Mains.</i>—The influence of the condition of the surface of a pipe on the friction is shown by various facts known to the engineers of waterworks. In pipes which convey certain kinds of water, oxidation @@ -12793,7 +12755,7 @@ a kind of brush scraper devised by G. F. Deacon (see “Deposits in Pipes,” by Professor J. C. Campbell Brown, <i>Proc. Inst. Civ. Eng.</i>, 1903-1904).</p> -<p>§ 81. <i>Flow of Water through Fire Hose.</i>—The hose pipes used for +<p>§ 81. <i>Flow of Water through Fire Hose.</i>—The hose pipes used for fire purposes are of very varied character, and the roughness of the surface varies. Very careful experiments have been made by J. R. Freeman (<i>Am. Soc. Civ. Eng.</i> xxi., 1889). It was noted that under @@ -12831,7 +12793,7 @@ hydraulic gradient. Then v = n √(ri).</p> <tr><td class="tcc rb bb">”</td> <td class="tcc rb bb">331</td> <td class="tcc rb bb">1.1624</td> <td class="tcc rb bb">20.00</td> <td class="tcc rb bb"> 79.6</td></tr> </table> -<p>§ 82. <i>Reduction of a Long Pipe of Varying Diameter to an Equivalent +<p>§ 82. <i>Reduction of a Long Pipe of Varying Diameter to an Equivalent Pipe of Uniform Diameter. Dupuit’s Equation.</i>—Water mains for the supply of towns often consist of a series of lengths, the diameter being the same for each length, but differing from length to length. @@ -12862,16 +12824,16 @@ head in A due to friction is</p> <table class="reg" summary="poem"><tr><td> <div class="poemr"> <p>h = i<span class="su">1</span>l<span class="su">1</span> + i<span class="su">2</span>l<span class="su">2</span> + ...</p> -<p class="i05">= ζ (v<span class="su">1</span><span class="sp">2</span> · 4l<span class="su">1</span>/2gd<span class="su">1</span>) + ζ (v<span class="su">2</span><span class="sp">2</span> · 4l<span class="su">2</span>/2gd<span class="su">2</span>) + ...</p> +<p class="i05">= ζ (v<span class="su">1</span><span class="sp">2</span> · 4l<span class="su">1</span>/2gd<span class="su">1</span>) + ζ (v<span class="su">2</span><span class="sp">2</span> · 4l<span class="su">2</span>/2gd<span class="su">2</span>) + ...</p> </div> </td></tr></table> <p class="noind">and in the uniform main</p> -<p class="center">il = ζ (v<span class="sp">2</span> · 4l/2gd).</p> +<p class="center">il = ζ (v<span class="sp">2</span> · 4l/2gd).</p> <p class="noind">If the mains are equivalent, as defined above,</p> -<p class="center">ζ (v<span class="sp">2</span> · 4l/2gd) = ζ (v<span class="su">1</span><span class="sp">2</span> · 4l<span class="su">1</span>/2gd<span class="su">1</span>) + ζ (v<span class="su">2</span><span class="sp">2</span> · 4l<span class="su">2</span>/2gd<span class="su">2</span>) + ...</p> +<p class="center">ζ (v<span class="sp">2</span> · 4l/2gd) = ζ (v<span class="su">1</span><span class="sp">2</span> · 4l<span class="su">1</span>/2gd<span class="su">1</span>) + ζ (v<span class="su">2</span><span class="sp">2</span> · 4l<span class="su">2</span>/2gd<span class="su">2</span>) + ...</p> <p class="noind">But, since the discharge is the same for all portions,</p> @@ -12895,7 +12857,7 @@ have the same total loss of head for any given discharge.</p> <tr><td class="figright1"><img style="width:242px; height:117px" src="images/img64b.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 87.</span></td></tr></table> -<p>§ 83. <i>Other Losses of Head in Pipes.</i>—Most of the losses of head in +<p>§ 83. <i>Other Losses of Head in Pipes.</i>—Most of the losses of head in pipes, other than that due to surface friction against the pipe, are due to abrupt changes in the velocity of the stream producing eddies. The kinetic energy of these is deducted from the general energy of @@ -13006,7 +12968,7 @@ with a pipe 1<span class="spp">1</span>⁄<span class="suu">4</span> in. dia <p class="center">ζ<span class="su">e</span> = 0.9457 sin<span class="sp">2</span> <span class="spp">1</span>⁄<span class="suu">2</span>φ + 2.047 sin<span class="sp">4</span> <span class="spp">1</span>⁄<span class="suu">2</span>φ.</p> <table class="ws" summary="Contents"> -<tr><td class="tcr lb rb tb">φ =</td> <td class="tcc rb tb">20°</td> <td class="tcc rb tb">40°</td> <td class="tcc rb tb">60°</td> <td class="tcc rb tb">80°</td> <td class="tcc rb tb">90°</td> <td class="tcc rb tb">100°</td> <td class="tcc rb tb">110°</td> <td class="tcc rb tb">120°</td> <td class="tcc rb tb">130°</td> <td class="tcc rb tb">140°</td></tr> +<tr><td class="tcr lb rb tb">φ =</td> <td class="tcc rb tb">20°</td> <td class="tcc rb tb">40°</td> <td class="tcc rb tb">60°</td> <td class="tcc rb tb">80°</td> <td class="tcc rb tb">90°</td> <td class="tcc rb tb">100°</td> <td class="tcc rb tb">110°</td> <td class="tcc rb tb">120°</td> <td class="tcc rb tb">130°</td> <td class="tcc rb tb">140°</td></tr> <tr><td class="tcr lb rb bb">ζ<span class="su">ε</span> =</td> <td class="tcc rb bb">0.046</td> <td class="tcc rb bb">0.139</td> <td class="tcc rb bb">0.364</td> <td class="tcc rb bb">0.740</td> <td class="tcc rb bb">0.984</td> <td class="tcc rb bb">1.260</td> <td class="tcc rb bb">1.556</td> <td class="tcc rb bb">1.861</td> <td class="tcc rb bb">2.158</td> <td class="tcc rb bb">2.431</td></tr> </table> @@ -13080,13 +13042,13 @@ Section at sluice = ω<span class="su">1</span> in pipe = ω.</p> is turned = θ.</p> <table class="ws" summary="Contents"> -<tr><td class="tcc lb rb tb">θ =</td> <td class="tcc rb tb">5°</td> <td class="tcc rb tb">10°</td> <td class="tcc rb tb">15°</td> <td class="tcc rb tb">20°</td> <td class="tcc rb tb">25°</td> <td class="tcc rb tb">30°</td> <td class="tcc rb tb">35°</td></tr> +<tr><td class="tcc lb rb tb">θ =</td> <td class="tcc rb tb">5°</td> <td class="tcc rb tb">10°</td> <td class="tcc rb tb">15°</td> <td class="tcc rb tb">20°</td> <td class="tcc rb tb">25°</td> <td class="tcc rb tb">30°</td> <td class="tcc rb tb">35°</td></tr> <tr><td class="tcc lb rb">Ratio of<br />cross<br />sections</td> <td class="tccm rb">.926</td> <td class="tccm rb">.850</td> <td class="tccm rb">.772</td> <td class="tccm rb">.692</td> <td class="tccm rb">.613</td> <td class="tccm rb">.535</td> <td class="tccm rb">.458</td></tr> <tr><td class="tcc lb rb bb">ζ<span class="su">v</span> =</td> <td class="tcc rb bb">.05</td> <td class="tcc rb bb">.29</td> <td class="tcc rb bb">.75</td> <td class="tcc rb bb">1.56</td> <td class="tcc rb bb">3.10</td> <td class="tcc rb bb">5.47</td> <td class="tcc rb bb">9.68</td></tr> </table> <table class="ws" summary="Contents"> -<tr><td class="tcc lb rb tb">θ =</td> <td class="tcc rb tb">40°</td> <td class="tcc rb tb">45°</td> <td class="tcc rb tb">50°</td> <td class="tcc rb tb">55°</td> <td class="tcc rb tb">60°</td> <td class="tcc rb tb">65°</td> <td class="tcc rb tb">82°</td></tr> +<tr><td class="tcc lb rb tb">θ =</td> <td class="tcc rb tb">40°</td> <td class="tcc rb tb">45°</td> <td class="tcc rb tb">50°</td> <td class="tcc rb tb">55°</td> <td class="tcc rb tb">60°</td> <td class="tcc rb tb">65°</td> <td class="tcc rb tb">82°</td></tr> <tr><td class="tcc lb rb">Ratio of<br />cross<br />sections</td> <td class="tccm rb">.385</td> <td class="tccm rb">.315</td> <td class="tccm rb">.250</td> <td class="tccm rb">.190</td> <td class="tccm rb">.137</td> <td class="tccm rb">.091</td> <td class="tccm rb">0</td></tr> <tr><td class="tcc lb rb bb">ζ<span class="su">v</span> =</td> <td class="tcc rb bb">17.3</td> <td class="tcc rb bb">31.2</td> <td class="tcc rb bb">52.6</td> <td class="tcc rb bb">106</td> <td class="tcc rb bb">206</td> <td class="tcc rb bb">486</td> <td class="tcc rb bb">∞</td></tr> </table> @@ -13094,12 +13056,12 @@ is turned = θ.</p> <p><i>Throttle Valve in a Cylindrical Pipe</i> (fig. 95)</p> <table class="ws" summary="Contents"> -<tr><td class="tcc lb rb tb">θ =</td> <td class="tcc rb tb">5°</td> <td class="tcc rb tb">10°</td> <td class="tcc rb tb">15°</td> <td class="tcc rb tb">20°</td> <td class="tcc rb tb">25°</td> <td class="tcc rb tb">30°</td> <td class="tcc rb tb">35°</td> <td class="tcc rb tb">40°</td></tr> +<tr><td class="tcc lb rb tb">θ =</td> <td class="tcc rb tb">5°</td> <td class="tcc rb tb">10°</td> <td class="tcc rb tb">15°</td> <td class="tcc rb tb">20°</td> <td class="tcc rb tb">25°</td> <td class="tcc rb tb">30°</td> <td class="tcc rb tb">35°</td> <td class="tcc rb tb">40°</td></tr> <tr><td class="tcc lb rb bb">ζ<span class="su">v</span> =</td> <td class="tcc rb bb">.24</td> <td class="tcc rb bb">.52</td> <td class="tcc rb bb">.90</td> <td class="tcc rb bb">1.54</td> <td class="tcc rb bb">2.51</td> <td class="tcc rb bb">3.91</td> <td class="tcc rb bb">6.22</td> <td class="tcc rb bb">10.8</td></tr> </table> <table class="ws" summary="Contents"> -<tr><td class="tcc lb rb tb">θ =</td> <td class="tcc rb tb">45°</td> <td class="tcc rb tb">50°</td> <td class="tcc rb tb">55°</td> <td class="tcc rb tb">60°</td> <td class="tcc rb tb">65°</td> <td class="tcc rb tb">70°</td> <td class="tcc rb tb">90°</td></tr> +<tr><td class="tcc lb rb tb">θ =</td> <td class="tcc rb tb">45°</td> <td class="tcc rb tb">50°</td> <td class="tcc rb tb">55°</td> <td class="tcc rb tb">60°</td> <td class="tcc rb tb">65°</td> <td class="tcc rb tb">70°</td> <td class="tcc rb tb">90°</td></tr> <tr><td class="tcc lb rb bb">ζ<span class="su">v</span> =</td> <td class="tcc rb bb">18.7</td> <td class="tcc rb bb">32.6</td> <td class="tcc rb bb">58.8</td> <td class="tcc rb bb">118</td> <td class="tcc rb bb">256</td> <td class="tcc rb bb">751</td> <td class="tcc rb bb">∞</td></tr> </table> @@ -13107,7 +13069,7 @@ is turned = θ.</p> <tr><td class="figright1"><img style="width:269px; height:117px" src="images/img65e.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 95.</span></td></tr></table> -<p>§ 84. <i>Practical Calculations on the Flow of Water in Pipes.</i>—In +<p>§ 84. <i>Practical Calculations on the Flow of Water in Pipes.</i>—In the following explanations it will be assumed that the pipe is of so great a length that only the loss of head in friction against @@ -13121,7 +13083,7 @@ the relation h = il, this need not be separately considered.</p> <p>There are then three equations -(see eq. 4, § 72, and 9a, § 76) for the solution of such problems +(see eq. 4, § 72, and 9a, § 76) for the solution of such problems as arise:—</p> <p class="center">ζ = α (1 + 1/12d);</p> @@ -13266,7 +13228,7 @@ form</p> <p class="noind">Neglecting the terms after the second,</p> <table class="reg" summary="poem"><tr><td> <div class="poemr"> -<p>d = <span class="sp">5</span>√ (32α / gπ<span class="sp">2</span>) <span class="sp">5</span>√ (Q<span class="sp">2</span>/i) · {1 + 1/60d}</p> +<p>d = <span class="sp">5</span>√ (32α / gπ<span class="sp">2</span>) <span class="sp">5</span>√ (Q<span class="sp">2</span>/i) · {1 + 1/60d}</p> <p class="i05">= <span class="sp">5</span>√ (32α / gπ<span class="sp">2</span>) <span class="sp">5</span>√ (Q<span class="sp">2</span>/i) + 0.01667;</p> </div> </td></tr></table> <div class="author1">(9a)</div> @@ -13286,7 +13248,7 @@ form</p> <tr><td class="figcenter"><img style="width:763px; height:307px" src="images/img66b.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 97.</span></td></tr></table> -<p>§ 85. <i>Arrangement of Water Mains +<p>§ 85. <i>Arrangement of Water Mains for Towns’ Supply.</i>—Town mains are usually supplied oy gravitation from a service reservoir, which in turn is @@ -13315,7 +13277,7 @@ should be calculated for 50 gallons per head per day.</p> <tr><td class="figcenter"><img style="width:773px; height:242px" src="images/img66c.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 98.</span></td></tr></table> -<p>§ 86. <i>Determination of the Diameters of Different Parts of a Water +<p>§ 86. <i>Determination of the Diameters of Different Parts of a Water Main.</i>—When the plan of the arrangement of mains is determined upon, and the supply to each locality and the pressure required is ascertained, it remains to determine the diameters of the pipes. Let @@ -13354,7 +13316,7 @@ for towns’ supply:—</p> <tr><td class="tcl">Velocity in feet per sec.</td> <td class="tcc">2.5</td> <td class="tcc">3.0</td> <td class="tcc">3.5</td> <td class="tcc">4.5</td> <td class="tcc">5.3</td> <td class="tcc">6.2</td> <td class="tcc">7.0</td></tr> </table> -<p>§ 87. <i>Branched Pipe connecting Reservoirs at Different Levels.</i>—Let +<p>§ 87. <i>Branched Pipe connecting Reservoirs at Different Levels.</i>—Let A, B, C (fig. 98) be three reservoirs connected by the arrangement of pipes shown,—l<span class="su">1</span>, d<span class="su">1</span>, Q<span class="su">1</span>, v<span class="su">1</span>; l<span class="su">2</span>, d<span class="su">2</span>, Q<span class="su">2</span>, v<span class="su">2</span>; h<span class="su">3</span>, d<span class="su">3</span>, Q<span class="su">3</span>, v<span class="su">3</span> being the @@ -13427,7 +13389,7 @@ value of h, and recalculate Q<span class="su">1</span>, Q<span class="su">2</spa <p>Since the limits between which h can vary are in practical cases not very distant, it is easy to approximate to values sufficiently accurate.</p> -<p>§ 88. <i>Water Hammer.</i>—If in a pipe through which water is flowing +<p>§ 88. <i>Water Hammer.</i>—If in a pipe through which water is flowing a sluice is suddenly closed so as to arrest the forward movement of the water, there is a rise of pressure which in some cases is serious enough to burst the pipe. This action is termed water hammer or @@ -13463,7 +13425,7 @@ be quite suddenly closed, this appears to be a reasonable allowance <p class="pt2 center">IX. FLOW OF COMPRESSIBLE FLUIDS IN PIPES</p> -<p>§ 89. <i>Flow of Air in Long Pipes.</i>—When air flows through a long +<p>§ 89. <i>Flow of Air in Long Pipes.</i>—When air flows through a long pipe, by far the greater part of the work expended is used in overcoming frictional resistances due to the surface of the pipe. The work expended in friction generates heat, which for the most part @@ -13480,7 +13442,7 @@ used for the transmission of messages, by R. S. Culley and R. Sabine the air flowing along the tube is much less than it would be in adiabatic expansion.</p> -<p>§ 90. <i>Differential Equation of the Steady Motion of Air Flowing in +<p>§ 90. <i>Differential Equation of the Steady Motion of Air Flowing in a Long Pipe of Uniform Section.</i>—When air expands at a constant absolute temperature τ, the relation between the pressure p in pounds per square foot and the density or weight per cubic foot G @@ -13490,7 +13452,7 @@ is given by the equation</p> <div class="author">(1)</div> <p class="noind">where c = 53.15. Taking τ = 521, corresponding to a temperature of -60° Fahr.,</p> +60° Fahr.,</p> <p class="center">cτ = 27690 foot-pounds.</p> <div class="author">(2)</div> @@ -13536,7 +13498,7 @@ sections A<span class="su">0</span>A′<span class="su">0</span>, and A<span <p class="center">W dt = GΩu dt = GΩ (u + du) dt.</p> <p>By analogy with liquids the head lost in friction is, for the length -dl (see § 72, eq. 3), ζ (u<span class="sp">2</span>/2g) (dl/m). Let H = u<span class="sp">2</span>/2g. Then the head +dl (see § 72, eq. 3), ζ (u<span class="sp">2</span>/2g) (dl/m). Let H = u<span class="sp">2</span>/2g. Then the head lost is ζ(H/m)dl; and, since Wdt ℔ of air flow through the pipe in the time considered, the work expended in friction is −ζ (H/m)W dl dt. The change of kinetic energy in dt seconds is the @@ -13630,7 +13592,7 @@ section m = d/4, where d is the diameter:—</p> <p class="center">u<span class="su">0</span> = (1.1319 − 0.7264 p<span class="su">1</span>/p<span class="su">0</span>) √ (gcτd / 4ζ l).</p> <div class="author1">(7c)</div> -<p>§ 91. <i>Coefficient of Friction for Air.</i>—A discussion by Professor +<p>§ 91. <i>Coefficient of Friction for Air.</i>—A discussion by Professor Unwin of the experiments by Culley and Sabine on the rate of transmission of light carriers through pneumatic tubes, in which there is steady flow of air not sensibly affected by any resistances @@ -13691,7 +13653,7 @@ p<span class="su">0</span> and p<span class="su">1</span> the pressures, G<span velocity in the pipe. This equation may be used for the flow of coal gas.</p> -<p>§ 92. <i>Distribution of Pressure in a Pipe in which Air is Flowing.</i>—From +<p>§ 92. <i>Distribution of Pressure in a Pipe in which Air is Flowing.</i>—From equation (7a) it results that the pressure p, at l ft. from that end of the pipe where the pressure is p<span class="su">0</span>, is</p> @@ -13741,7 +13703,7 @@ the pressure is least.</p> <tr><td class="figcenter"><img style="width:469px; height:221px" src="images/img68b.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 101.</span></td></tr></table> -<p>§ 93. <i>Weight of Air Flowing per Second.</i>—The weight of air discharged +<p>§ 93. <i>Weight of Air Flowing per Second.</i>—The weight of air discharged per second is (equation 3a)—</p> <p class="center">W = Ωu<span class="su">0</span>p<span class="su">0</span> / cτ.</p> @@ -13759,7 +13721,7 @@ per second is (equation 3a)—</p> <p class="center">W = (.6916p<span class="su">0</span> − .4438p<span class="su">1</span>) (d<span class="sp">5</span> / ζ lτ)<span class="sp">1/2</span>.</p> <div class="author1">(13a)</div> -<p>§ 94. <i>Application to the Case of Pneumatic Tubes for the Transmission +<p>§ 94. <i>Application to the Case of Pneumatic Tubes for the Transmission of Messages.</i>—In Paris, Berlin, London, and other towns, it has been found cheaper to transmit messages in pneumatic tubes than to telegraph by electricity. The tubes are laid underground @@ -13796,7 +13758,7 @@ from 0 to l,</p> = ζ<span class="sp">1/2</span> l<span class="sp">3/2</span> (p<span class="su">0</span><span class="sp">3</span> − p<span class="su">1</span><span class="sp">3</span>) / 6(gcτd)<span class="sp">1/2</span> (p<span class="su">0</span><span class="sp">2</span> − p<span class="su">1</span><span class="sp">2</span>)<span class="sp">3/2</span>;</p> <div class="author">(15)</div> -<p class="noind">If τ = 521°, corresponding to 60° F.,</p> +<p class="noind">If τ = 521°, corresponding to 60° F.,</p> <p class="center">t = .001412 ζ<span class="sp">1/2</span> l<span class="sp">3/2</span> (p<span class="su">0</span><span class="sp">3</span> − p<span class="su">1</span><span class="sp">3</span>) / d<span class="sp">1/2</span> (p<span class="su">0</span><span class="sp">2</span> − p<span class="su">1</span><span class="sp">2</span>)<span class="sp">3/2</span>;</p> <div class="author1">(15a)</div> @@ -13805,7 +13767,7 @@ from 0 to l,</p> pressures and the dimensions of the tube.</p> <p><i>Mean Velocity of Transmission.</i>—The mean velocity is l/t; or, for -τ = 521°,</p> +τ = 521°,</p> <p class="center">u<span class="su">mean</span> = 0.708 √ {d (p<span class="su">0</span><span class="sp">2</span> − p<span class="su">1</span><span class="sp">2</span>)<span class="sp">3/2</span> / ζ l (p<span class="su">0</span><span class="sp">3</span> − p<span class="su">1</span><span class="sp">3</span>)}.</p> <div class="author">(16)</div> @@ -13838,7 +13800,7 @@ terminal pressures for which the formula is applicable.</p> <p class="pt2 center">X. FLOW IN RIVERS AND CANALS</p> -<p>§ 95. <i>Flow of Water in Open Canals and Rivers.</i>—When water +<p>§ 95. <i>Flow of Water in Open Canals and Rivers.</i>—When water flows in a pipe the section at any point is determined by the form of the boundary. When it flows in an open channel with free upper surface, the section depends on the velocity due to the dynamical @@ -13899,7 +13861,7 @@ hypotheses, but at present they are not practically so reliable, and are more complicated than the formulae obtained in the manner described above.</p> -<p>§ 96. <i>Steady Flow of Water with Uniform Velocity in Channels of +<p>§ 96. <i>Steady Flow of Water with Uniform Velocity in Channels of Constant Section.</i>—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. @@ -13920,7 +13882,7 @@ equal and opposite since the sections are equal and similar, and the mean pressures on each are the same. (<i>b</i>) The component of the weight W of the mass in the direction of motion, acting at its centre of gravity g. The weight of the mass aa′bb′ is GΩ dl, and the component -of the weight in the direction of motion is GΩdl × the cosine of +of the weight in the direction of motion is GΩdl × the cosine of the angle between Wg and ab, that is, GΩdl cos abc = GΩ dl bc/ab = GΩidl. (<i>c</i>) There is the friction of the stream on the sides and bottom of the channel. This is proportional to the area χdl of @@ -13932,7 +13894,7 @@ the friction is −χ dl ƒ(v). Equating the sum of the forces to zer ƒ(v) / G = Ωi / χ = mi.</p> <div class="author">(1)</div> -<p class="noind">But it has been already shown (§ 66) that ƒ(v) = ζGv<span class="sp">2</span>/2g,</p> +<p class="noind">But it has been already shown (§ 66) that ƒ(v) = ζGv<span class="sp">2</span>/2g,</p> <p class="center">∴ ζv<span class="sp">2</span> / 2g = mi.</p> <div class="author">(2)</div> @@ -13970,7 +13932,7 @@ is</p> <p class="center">Q = Ωv = Ωc √ (mi).</p> <div class="author">(4)</div> -<p>§ 97. <i>Coefficient of Friction for Open Channels.</i>—Various expressions +<p>§ 97. <i>Coefficient of Friction for Open Channels.</i>—Various expressions have been proposed for the coefficient of friction for channels as for pipes. Weisbach, giving attention chiefly to the variation of the coefficient of friction with the velocity, proposed an @@ -13993,7 +13955,7 @@ expression of the form</p> <p>In using this value of ζ when v is not known, it is best to proceed by approximation.</p> -<p>§ 98. <i>Darcy and Bazin’s Expression for the Coefficient of Friction.</i>—Darcy +<p>§ 98. <i>Darcy and Bazin’s Expression for the Coefficient of Friction.</i>—Darcy and Bazin’s researches have shown that ζ 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 ζ an @@ -14072,7 +14034,7 @@ mean depths as are likely to occur in practical calculations:—</p> <tr><td class="tcc lb rb bb">∞</td> <td class="tcc rb bb">148</td> <td class="tcc rb bb">131</td> <td class="tcc rb bb">117</td> <td class="tcc rb bb">108</td> <td class="tcc rb bb">91 </td></tr> </table> -<p>§ 99. <i>Ganguillet and Kutter’s Modified Darcy Formula.</i>—Starting +<p>§ 99. <i>Ganguillet and Kutter’s Modified Darcy Formula.</i>—Starting from the general expression v = c√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 @@ -14256,10 +14218,10 @@ The term involving the slope was introduced to secure agreement with some early experiments on the Mississippi, and there is strong reason for doubting the accuracy of these results.</p> -<p>§ 100. <i>Bazin’s New Formula.</i>—Bazin subsequently re-examined +<p>§ 100. <i>Bazin’s New Formula.</i>—Bazin subsequently re-examined all the trustworthy gaugings of flow in channels and proposed a modification of the original Darcy formula which appears to be -more satisfactory than any hitherto suggested (<i>Étude d’une nouvelle +more satisfactory than any hitherto suggested (<i>Étude d’une nouvelle formule</i>, Paris, 1898). He points out that Darcy’s original formula, which is of the form mi/v<span class="sp">2</span> = α + β/m, does not agree with experiments on channels as well as with experiments on pipes. It is an objection @@ -14283,7 +14245,7 @@ mi, ζ = 0.002594 (1 + γ/√ m), where γ has the following v <tr><td class="tcr">VI.</td> <td class="tcl">Canals in earth exceptionally rough</td> <td class="tcc">3.168</td></tr> </table> -<p>§ 101. <i>The Vertical Velocity Curve.</i>—If at each point along a +<p>§ 101. <i>The Vertical Velocity Curve.</i>—If at each point along a vertical representing the depth of a stream, the velocity at that point is plotted horizontally, the curve obtained is the vertical velocity curve and it has been shown by many observations that @@ -14314,7 +14276,7 @@ form of the horizontal velocity curve is roughly similar to the section of the stream.</p> -<p>§ 102. <i>Curves or Contours of Equal +<p>§ 102. <i>Curves or Contours of Equal Velocity.</i>—If velocities are observed at a number of points at different widths and depths in a stream, it is @@ -14328,7 +14290,7 @@ the vertical and horizontal velocity curves and the contours of equal velocity in a rectangular channel, from one of Bazin’s gaugings.</p> -<p>§ 103. <i>Experimental Observations on the Vertical Velocity Curve.</i>—A +<p>§ 103. <i>Experimental Observations on the Vertical Velocity Curve.</i>—A preliminary difficulty arises in observing the velocity at a given point in a stream because the velocity rapidly varies, the motion not being strictly steady. If an average of several velocities at the @@ -14350,7 +14312,7 @@ found not at the surface but at some distance below it. In various river gaugings the depth d<span class="su">z</span> at the centre of the stream has been found to vary from 0 to 0.3d.</p> -<p>§ 104. <i>Influence of the Wind.</i>—In the experiments on the Mississippi +<p>§ 104. <i>Influence of the Wind.</i>—In the experiments on the Mississippi the vertical velocity curve in calm weather was found to agree fairly with a parabola, the greatest velocity being at <span class="spp">3</span>⁄<span class="suu">10</span>ths of the depth of the stream from the surface. With a wind blowing down @@ -14408,7 +14370,7 @@ may range from +10 to −10, positive if the wind is up stream, negative if it is down stream. Then Humphreys and Abbot find their results agree with the expression</p> -<p class="center">h′ / m = 0.317 ± 0.06f.</p> +<p class="center">h′ / m = 0.317 ± 0.06f.</p> <p class="noind">Fig. 106 shows the parabolic velocity curves according to the American observers for calm weather, and for an up- or down-stream @@ -14435,7 +14397,7 @@ of observations by various observers gave the mean velocity at from to, but a little greater than, the mean velocity on a vertical. If v<span class="su">md</span> is the mid-depth velocity, then on the average v<span class="su">m</span> = 0.98v<span class="su">md</span>.</p> -<p>§ 105. <i>Mean Velocity on a Vertical from Two Velocity Observations.</i>—A. +<p>§ 105. <i>Mean Velocity on a Vertical from Two Velocity Observations.</i>—A. J. C. Cunningham, in gaugings on the Ganges canal, found the following useful results. Let v<span class="su">0</span> be the surface, v<span class="su">m</span> the mean, and v<span class="su">xd</span> the velocity at the depth xd; then</p> @@ -14443,7 +14405,7 @@ v<span class="su">xd</span> the velocity at the depth xd; then</p> <p class="center">v<span class="su">m</span> = <span class="spp">1</span>⁄<span class="suu">4</span> (v<span class="su">0</span> + 3v<span class="su">2/3d</span> )<br /> = <span class="spp">1</span>⁄<span class="suu">2</span> (v<span class="su">.211</span><span class="sp">d</span> + v<span class="su">.789</span><span class="sp">d</span> ).</p> -<p>§ 106. <i>Ratio of Mean to Greatest Surface Velocity, for the whole +<p>§ 106. <i>Ratio of Mean to Greatest Surface Velocity, for the whole Cross Section in Trapezoidal Channels.</i>—It is often very important to be able to deduce the mean velocity, and thence the discharge, from observation of the greatest surface velocity. The simplest @@ -14464,7 +14426,7 @@ v<span class="su">m</span> the mean velocity of the stream. Then, according to B <p class="center">v<span class="su">m</span> = c √ (mi),</p> <p class="noind">where c is a coefficient, the values of which have been already given -in the table in § 98. Hence</p> +in the table in § 98. Hence</p> <p class="center">v<span class="su">m</span> = cv<span class="su">0</span> / (c + 25.4).</p> @@ -14500,7 +14462,7 @@ in the table in § 98. Hence</p> <tr><td class="figright1"><img style="width:324px; height:307px" src="images/img72a.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 107.</span></td></tr></table> -<p>§ 107. <i>River Bends.</i>—In rivers flowing in alluvial plains, the windings +<p>§ 107. <i>River Bends.</i>—In rivers flowing in alluvial plains, the windings which already exist tend to increase in curvature by the scouring away of material from the outer bank and the deposition of detritus along the inner bank. The sinuosities sometimes increase till a @@ -14567,7 +14529,7 @@ show the directions of flow immediately in contact with the sides and bottom. The dotted line AB shows the direction of motion of floating particles on the surface of the stream.</p> -<p>§ 108. <i>Discharge of a River when flowing at different Depths.</i>—When +<p>§ 108. <i>Discharge of a River when flowing at different Depths.</i>—When frequent observations must be made on the flow of a river or canal, the depth of which varies at different times, it is very convenient to have to observe the depth only. A formula can be @@ -14576,10 +14538,10 @@ discharge in cubic feet per second; H the depth of the river in some straight and uniform part. Then Q = aH + bH<span class="sp">2</span>, where the constants a and b must be found by preliminary gaugings in different conditions of the river. M. C. Moquerey found for part of the upper -Saône, Q = 64.7H + 8.2H<span class="sp">2</span> in metric measures, or Q = 696H + 26.8H<span class="sp">2</span> +Saône, Q = 64.7H + 8.2H<span class="sp">2</span> in metric measures, or Q = 696H + 26.8H<span class="sp">2</span> in English measures.</p> -<p>§ 109. <i>Forms of Section of Channels.</i>—The simplest form of section +<p>§ 109. <i>Forms of Section of Channels.</i>—The simplest form of section for channels is the semicircular or nearly semicircular channel (fig. 109), a form now often adopted from the facility with which it can be executed in concrete. It has the advantage that the rubbing surface @@ -14614,7 +14576,7 @@ commonly adopted.</p> former being the section of a navigation canal and the latter the section of an irrigation canal.</p> -<p>§ 110. <i>Channels of Circular Section.</i>—The following short table +<p>§ 110. <i>Channels of Circular Section.</i>—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 = κr, the hydraulic mean radius is μr and the @@ -14641,7 +14603,7 @@ following values:—</p> <tr><td class="figright1"><img style="width:325px; height:297px" src="images/img73b.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 113.</span></td></tr></table> -<p>§ 111. <i>Egg-Shaped Channels or Sewers.</i>—In sewers for discharging +<p>§ 111. <i>Egg-Shaped Channels or Sewers.</i>—In sewers for discharging storm water and house drainage the volume of flow is extremely variable; and there is a great liability for deposits to be left when the flow is small, which are not removed during the short periods @@ -14663,12 +14625,12 @@ numbers marked on the figure being proportional numbers.</p> -<p>§ 112. <i>Problems on +<p>§ 112. <i>Problems on Channels in which the Flow is Steady and at Uniform Velocity.</i>—The general equations given -in §§ 96, 98 are</p> +in §§ 96, 98 are</p> <p class="center">ζ = α(1 + β/m);</p> <div class="author">(1)</div> @@ -14712,7 +14674,7 @@ the process till the successive values of m approximately coincide.</p> -<p>§ 113. <i>Problem IV. Most +<p>§ 113. <i>Problem IV. Most Economical Form of Channel for given Side Slopes.</i>—Suppose the channel is to be @@ -14856,25 +14818,25 @@ Area of section =</i> Ω.</p> <tr><td class="tcl allb"> </td> <td class="tccm allb f80">Inclination<br />of Sides to<br />Horizon.</td> <td class="tccm allb f80">Ratio of<br />Side<br />Slopes.</td> <td class="tccm allb f80">Area of<br />Section Ω.</td> <td class="tccm allb f80">Bottom<br />Width.</td> <td class="tccm allb f80">Top width =<br />twice length<br />of each Side<br />Slope.</td></tr> <tr><td class="tcl lb rb">Semicircle</td> <td class="tcc rb">..</td> <td class="tcc rb">..</td> <td class="tcc rb">1.571d<span class="sp">2</span></td> <td class="tcc rb">0</td> <td class="tcc rb">2d</td></tr> -<tr><td class="tcl lb rb">Semi-hexagon</td> <td class="tcc rb">60°   0′</td> <td class="tcc rb">3  : 5</td> <td class="tcc rb">1.732d<span class="sp">2</span></td> <td class="tcc rb">1.155d</td> <td class="tcc rb">2.310d</td></tr> -<tr><td class="tcl lb rb">Semi-square</td> <td class="tcc rb">90°   0′</td> <td class="tcc rb">0  : 1</td> <td class="tcc rb">2d<span class="sp">2</span></td> <td class="tcc rb">2d</td> <td class="tcc rb">2d</td></tr> -<tr><td class="tcl lb rb"> </td> <td class="tcc rb">75°  58′</td> <td class="tcc rb">1  : 4</td> <td class="tcc rb">1.812d<span class="sp">2</span></td> <td class="tcc rb">1.562d</td> <td class="tcc rb">2.062d</td></tr> -<tr><td class="tcl lb rb"> </td> <td class="tcc rb">63°  26′</td> <td class="tcc rb">1  : 2</td> <td class="tcc rb">1.736d<span class="sp">2</span></td> <td class="tcc rb">1.236d</td> <td class="tcc rb">2.236d</td></tr> -<tr><td class="tcl lb rb"> </td> <td class="tcc rb">53°   8′</td> <td class="tcc rb">3  : 4</td> <td class="tcc rb">1.750d<span class="sp">2</span></td> <td class="tcc rb">d</td> <td class="tcc rb">2.500d</td></tr> -<tr><td class="tcl lb rb"> </td> <td class="tcc rb">45°   0′</td> <td class="tcc rb">1  : 1</td> <td class="tcc rb">1.828d<span class="sp">2</span></td> <td class="tcc rb">0.828d</td> <td class="tcc rb">2.828d</td></tr> -<tr><td class="tcl lb rb"> </td> <td class="tcc rb">38°  40′</td> <td class="tcc rb">1<span class="spp">1</span>⁄<span class="suu">4</span> : 1</td> <td class="tcc rb">1.952d<span class="sp">2</span></td> <td class="tcc rb">0.702d</td> <td class="tcc rb">3.202d</td></tr> -<tr><td class="tcl lb rb"> </td> <td class="tcc rb">33°  42′</td> <td class="tcc rb">1<span class="spp">1</span>⁄<span class="suu">2</span> : 1</td> <td class="tcc rb">2.106d<span class="sp">2</span></td> <td class="tcc rb">0.606d</td> <td class="tcc rb">3.606d</td></tr> -<tr><td class="tcl lb rb"> </td> <td class="tcc rb">29°  44′</td> <td class="tcc rb">1<span class="spp">3</span>⁄<span class="suu">4</span> : 1</td> <td class="tcc rb">2.282d<span class="sp">2</span></td> <td class="tcc rb">0.532d</td> <td class="tcc rb">4.032d</td></tr> -<tr><td class="tcl lb rb"> </td> <td class="tcc rb">26°  34′</td> <td class="tcc rb">2  : 1</td> <td class="tcc rb">2.472d<span class="sp">2</span></td> <td class="tcc rb">0.472d</td> <td class="tcc rb">4.472d</td></tr> -<tr><td class="tcl lb rb"> </td> <td class="tcc rb">23°  58′</td> <td class="tcc rb">2<span class="spp">1</span>⁄<span class="suu">4</span> : 1</td> <td class="tcc rb">2.674d<span class="sp">2</span></td> <td class="tcc rb">0.424d</td> <td class="tcc rb">4.924d</td></tr> -<tr><td class="tcl lb rb"> </td> <td class="tcc rb">21°  48′</td> <td class="tcc rb">2<span class="spp">1</span>⁄<span class="suu">2</span> : 1</td> <td class="tcc rb">2.885d<span class="sp">2</span></td> <td class="tcc rb">0.385d</td> <td class="tcc rb">5.385d</td></tr> -<tr><td class="tcl lb rb"> </td> <td class="tcc rb">19°  58′</td> <td class="tcc rb">2<span class="spp">3</span>⁄<span class="suu">4</span> : 1</td> <td class="tcc rb">3.104d<span class="sp">2</span></td> <td class="tcc rb">0.354d</td> <td class="tcc rb">5.854d</td></tr> -<tr><td class="tcl lb rb bb"> </td> <td class="tcc rb bb">18°  26′</td> <td class="tcc rb bb">3  : 1</td> <td class="tcc rb bb">3.325d<span class="sp">2</span></td> <td class="tcc rb bb">0.325d</td> <td class="tcc rb bb">6.325d</td></tr> +<tr><td class="tcl lb rb">Semi-hexagon</td> <td class="tcc rb">60°   0′</td> <td class="tcc rb">3  : 5</td> <td class="tcc rb">1.732d<span class="sp">2</span></td> <td class="tcc rb">1.155d</td> <td class="tcc rb">2.310d</td></tr> +<tr><td class="tcl lb rb">Semi-square</td> <td class="tcc rb">90°   0′</td> <td class="tcc rb">0  : 1</td> <td class="tcc rb">2d<span class="sp">2</span></td> <td class="tcc rb">2d</td> <td class="tcc rb">2d</td></tr> +<tr><td class="tcl lb rb"> </td> <td class="tcc rb">75°  58′</td> <td class="tcc rb">1  : 4</td> <td class="tcc rb">1.812d<span class="sp">2</span></td> <td class="tcc rb">1.562d</td> <td class="tcc rb">2.062d</td></tr> +<tr><td class="tcl lb rb"> </td> <td class="tcc rb">63°  26′</td> <td class="tcc rb">1  : 2</td> <td class="tcc rb">1.736d<span class="sp">2</span></td> <td class="tcc rb">1.236d</td> <td class="tcc rb">2.236d</td></tr> +<tr><td class="tcl lb rb"> </td> <td class="tcc rb">53°   8′</td> <td class="tcc rb">3  : 4</td> <td class="tcc rb">1.750d<span class="sp">2</span></td> <td class="tcc rb">d</td> <td class="tcc rb">2.500d</td></tr> +<tr><td class="tcl lb rb"> </td> <td class="tcc rb">45°   0′</td> <td class="tcc rb">1  : 1</td> <td class="tcc rb">1.828d<span class="sp">2</span></td> <td class="tcc rb">0.828d</td> <td class="tcc rb">2.828d</td></tr> +<tr><td class="tcl lb rb"> </td> <td class="tcc rb">38°  40′</td> <td class="tcc rb">1<span class="spp">1</span>⁄<span class="suu">4</span> : 1</td> <td class="tcc rb">1.952d<span class="sp">2</span></td> <td class="tcc rb">0.702d</td> <td class="tcc rb">3.202d</td></tr> +<tr><td class="tcl lb rb"> </td> <td class="tcc rb">33°  42′</td> <td class="tcc rb">1<span class="spp">1</span>⁄<span class="suu">2</span> : 1</td> <td class="tcc rb">2.106d<span class="sp">2</span></td> <td class="tcc rb">0.606d</td> <td class="tcc rb">3.606d</td></tr> +<tr><td class="tcl lb rb"> </td> <td class="tcc rb">29°  44′</td> <td class="tcc rb">1<span class="spp">3</span>⁄<span class="suu">4</span> : 1</td> <td class="tcc rb">2.282d<span class="sp">2</span></td> <td class="tcc rb">0.532d</td> <td class="tcc rb">4.032d</td></tr> +<tr><td class="tcl lb rb"> </td> <td class="tcc rb">26°  34′</td> <td class="tcc rb">2  : 1</td> <td class="tcc rb">2.472d<span class="sp">2</span></td> <td class="tcc rb">0.472d</td> <td class="tcc rb">4.472d</td></tr> +<tr><td class="tcl lb rb"> </td> <td class="tcc rb">23°  58′</td> <td class="tcc rb">2<span class="spp">1</span>⁄<span class="suu">4</span> : 1</td> <td class="tcc rb">2.674d<span class="sp">2</span></td> <td class="tcc rb">0.424d</td> <td class="tcc rb">4.924d</td></tr> +<tr><td class="tcl lb rb"> </td> <td class="tcc rb">21°  48′</td> <td class="tcc rb">2<span class="spp">1</span>⁄<span class="suu">2</span> : 1</td> <td class="tcc rb">2.885d<span class="sp">2</span></td> <td class="tcc rb">0.385d</td> <td class="tcc rb">5.385d</td></tr> +<tr><td class="tcl lb rb"> </td> <td class="tcc rb">19°  58′</td> <td class="tcc rb">2<span class="spp">3</span>⁄<span class="suu">4</span> : 1</td> <td class="tcc rb">3.104d<span class="sp">2</span></td> <td class="tcc rb">0.354d</td> <td class="tcc rb">5.854d</td></tr> +<tr><td class="tcl lb rb bb"> </td> <td class="tcc rb bb">18°  26′</td> <td class="tcc rb bb">3  : 1</td> <td class="tcc rb bb">3.325d<span class="sp">2</span></td> <td class="tcc rb bb">0.325d</td> <td class="tcc rb bb">6.325d</td></tr> <tr><td class="tcc" colspan="6">Half the top width is the length of each side slope. The wetted<br /> perimeter is the sum of the top and bottom widths.</td></tr> </table> -<p>§ 114. <i>Form of Cross Section of Channel in which the Mean Velocity +<p>§ 114. <i>Form of Cross Section of Channel in which the Mean Velocity is Constant with Varying Discharge.</i>—In designing waste channels from canals, and in some other cases, it is desirable that the mean velocity should be restricted within narrow limits with very different @@ -14936,7 +14898,7 @@ rapid flattening of the side slopes is remarkable.</p> <p class="pt1 center sc">Steady Motion of Water in Open Channels of Varying Cross Section and Slope</p> -<p>§ 115. In every stream the discharge of which is constant, or may +<p>§ 115. In every stream the discharge of which is constant, or may be regarded as constant for the time considered, the velocity at different places depends on the slope of the bed. Except at certain exceptional points the velocity will be greater as the slope of the @@ -15018,7 +14980,7 @@ the same velocity u<span class="su">0</span>. Let the kinetic energy be taken at <p class="center">α (Gθ / 2g) Ω<span class="su">0</span>u<span class="su">0</span><span class="sp">3</span> = α (Gθ / 2g) Qu<span class="su">0</span><span class="sp">2</span>,</p> <p class="noind">where α is a corrective factor, the value of which was estimated by -J. B. C. J. Bélanger at 1.1.<a name="fa6f" id="fa6f" href="#ft6f"><span class="sp">6</span></a> Its precise value is not of great importance.</p> +J. B. C. J. Bélanger at 1.1.<a name="fa6f" id="fa6f" href="#ft6f"><span class="sp">6</span></a> Its precise value is not of great importance.</p> <p>In a similar way we should obtain for the kinetic energy of A<span class="su">1</span>B<span class="su">1</span>C<span class="su">1</span>D<span class="su">1</span> the expression</p> @@ -15087,7 +15049,7 @@ energy given in (1),</p> <tr><td class="figcenter"><img style="width:435px; height:228px" src="images/img75a.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 120.</span></td></tr></table> -<p>§ 116. <i>Fundamental Differential Equation of Steady Varied Motion.</i>—Suppose +<p>§ 116. <i>Fundamental Differential Equation of Steady Varied Motion.</i>—Suppose the equation just found to be applied to an indefinitely short length ds of the stream, limited by the end sections ab, a<span class="su">1</span>b<span class="su">1</span>, taken for simplicity normal to the stream bed (fig. 120). For that @@ -15148,7 +15110,7 @@ becomes</p> <p class="center">dh/ds = i (1 − ζu<span class="sp">2</span> / 2gih) / (1 − u<span class="sp">2</span>/gh).</p> <div class="author">(5)</div> -<p>§ 117. <i>General Indications as to the Form of Water Surface furnished +<p>§ 117. <i>General Indications as to the Form of Water Surface furnished by Equation</i> (5).—Let A<span class="su">0</span>A<span class="su">1</span> (fig. 121) be the water surface, B<span class="su">0</span>B<span class="su">1</span> the bed in a longitudinal section of the stream, and ab any section at a distance s from B<span class="su">0</span>, the depth ab being h. Suppose @@ -15207,7 +15169,7 @@ before:—</p> <tr><td class="figcenter"><img style="width:443px; height:220px" src="images/img75c.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 122.</span></td></tr></table> -<p>§ 118. <i>Case</i> 1.—Suppose h > u<span class="sp">2</span>/g, and also h > H, or the depth +<p>§ 118. <i>Case</i> 1.—Suppose h > u<span class="sp">2</span>/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 B<span class="su">0</span>B<span class="su">1</span> be the bed, C<span class="su">0</span>C<span class="su">1</span> a line parallel to the @@ -15233,7 +15195,7 @@ termed the backwater due to the weir.</p> <tr><td class="figright1"><img style="width:387px; height:172px" src="images/img76b.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 124.</span></td></tr></table> -<p>§ 119. <i>Case</i> 2.—Suppose h > u<span class="sp">2</span>/g, and also h < H. Then dh/ds is +<p>§ 119. <i>Case</i> 2.—Suppose h > u<span class="sp">2</span>/g, and also h < H. Then dh/ds is <span class="pagenum"><a name="page76" id="page76"></a>76</span> negative, and the stream is diminishing in depth in the direction of flow. In fig. 123 let B<span class="su">0</span>B<span class="su">1</span> be the stream bed as before; C<span class="su">0</span>C<span class="su">1</span> a line @@ -15308,7 +15270,7 @@ approximately with the intended level AA.</p> <tr><td class="figcenter"><img style="width:496px; height:272px" src="images/img76c.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 125.</span></td></tr></table> -<p>§ 120. <i>Case</i> 3.—Suppose a stream flowing uniformly with a depth +<p>§ 120. <i>Case</i> 3.—Suppose a stream flowing uniformly with a depth h < u<span class="sp">2</span>/g. For a stream in uniform motion ζu<span class="sp">2</span>/2g = mi, or if the stream is of indefinitely great width, so that m = H, then ζu<span class="sp">2</span>/2g = iH, and H = ζu<span class="sp">2</span>/2gi. Consequently the condition stated above involves @@ -15362,7 +15324,7 @@ production of a standing wave may occur.</p> <p class="pt1 center sc">Standing Waves</p> -<p>§ 121. The formation of a standing wave was first observed by +<p>§ 121. The formation of a standing wave was first observed by Bidone. Into a small rectangular masonry channel, having a slope of 0.023 ft. per foot, he admitted water till it flowed uniformly with a depth of 0.2 ft. He then placed a plank across the stream which @@ -15372,9 +15334,9 @@ point 15 ft. from it. At that point the depth suddenly increased from 0.2 ft. to 0.56 ft. The velocity of the stream in the part unaffected by the obstruction was 5.54 ft. per second. Above the point where the abrupt change of depth occurred u<span class="sp">2</span> = 5.54<span class="sp">2</span> = 30.7, and -gh = 32.2 × 0.2 = 6.44; hence u<span class="sp">2</span> was > gh. Just below the abrupt -change of depth u = 5.54 × 0.2/0.56 = 1.97; u<span class="sp">2</span> = 3.88; and gh = -32.2 × 0.56 = 18.03; hence at this point u<span class="sp">2</span> < gh. Between these two +gh = 32.2 × 0.2 = 6.44; hence u<span class="sp">2</span> was > gh. Just below the abrupt +change of depth u = 5.54 × 0.2/0.56 = 1.97; u<span class="sp">2</span> = 3.88; and gh = +32.2 × 0.56 = 18.03; hence at this point u<span class="sp">2</span> < gh. Between these two points, therefore, u<span class="sp">2</span> = gh; and the condition for the production of a standing wave occurred.</p> @@ -15436,7 +15398,7 @@ which agrees very well with the observed height.</p> <tr><td class="figcenter"><img style="width:475px; height:145px" src="images/img77a.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 127.</span></td></tr></table> -<p>§ 122. A standing wave is frequently produced at the foot of +<p>§ 122. A standing wave is frequently produced at the foot of a weir. Thus in the ogee falls originally constructed on the Ganges canal a standing wave was observed as shown in fig. 127. The water falling over the weir crest A acquired a very high velocity on the @@ -15479,16 +15441,16 @@ of the pier at 26 ft., the velocity necessary for the production of a standing wave would be u = √ (gh) -= √ (32.2 × 26) = 29 ft. += √ (32.2 × 26) = 29 ft. per second nearly. But the velocity at this -point was probably from Howden’s statements 16.58 × <span class="spp">40</span>⁄<span class="suu">26</span> = 25.5 +point was probably from Howden’s statements 16.58 × <span class="spp">40</span>⁄<span class="suu">26</span> = 25.5 ft. <span class="correction" title="added per second">per second</span>, an agreement as close as the approximate character of the data would lead us to expect.</p> <p class="pt2 center" style="clear: both;">XI. ON STREAMS AND RIVERS</p> -<p>§ 123. <i>Catchment Basin.</i>—A stream or river is the channel for the +<p>§ 123. <i>Catchment Basin.</i>—A stream or river is the channel for the discharge of the available rainfall of a district, termed its catchment basin. The catchment basin is surrounded by a ridge or watershed line, continuous except at the point where the river finds an outlet. @@ -15508,7 +15470,7 @@ average rainfall on the catchment basin (Tiefenbacher).</p> <tr><td class="tcl lb rb bb">Naked unfissured mountains</td> <td class="tcc rb bb">.55 to .60</td> <td class="tcc rb bb">40 to 45</td></tr> </table> -<p>§ 124. <i>Flood Discharge.</i>—The flood discharge can generally only be +<p>§ 124. <i>Flood Discharge.</i>—The flood discharge can generally only be determined by examining the greatest height to which floods have been known to rise. To produce a flood the rainfall must be heavy and widely distributed, and to produce a flood of exceptional height @@ -15567,7 +15529,7 @@ Ganges and Godavery works, and = 10,000 on Madras works.</p> <tr><td class="figright1"><img style="width:327px; height:128px" src="images/img77d.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 130.</span></td></tr></table> -<p>§ 125. <i>Action of a Stream on its Bed.</i>—If the velocity of a stream +<p>§ 125. <i>Action of a Stream on its Bed.</i>—If the velocity of a stream exceeds a certain limit, depending on its size, and on the size, heaviness, form and coherence of the material of which its bed is composed, @@ -15610,7 +15572,7 @@ streams, the velocity of transport of material down stream is greater as the depth of the stream is greater. The effect is that the deep stream excavates its bed more rapidly than the shallow stream.</p> -<p>§ 126. <i>Bottom Velocity at which Scour commences.</i>—The following +<p>§ 126. <i>Bottom Velocity at which Scour commences.</i>—The following bottom velocities were determined by P. L. G. Dubuat to be the maximum velocities consistent with stability of the stream bed for different materials.</p> @@ -15649,7 +15611,7 @@ obtained:—</p> <p>The following table of velocities which should not be exceeded in channels is given in the <i>Ingenieurs Taschenbuch</i> of the Verein -“Hütte”:—</p> +“Hütte”:—</p> <table class="ws" summary="Contents"> <tr><td class="tcc allb"> </td> <td class="tcc allb">Surface<br />Velocity.</td> <td class="tcc allb">Mean<br />Velocity.</td> <td class="tcc allb">Bottom<br />Velocity.</td></tr> @@ -15664,7 +15626,7 @@ in channels is given in the <i>Ingenieurs Taschenbuch</i> of the Verein <tr><td class="tcl lb rb bb">Hard rocks</td> <td class="tcc rb bb">14.00</td> <td class="tcc rb bb">12.15</td> <td class="tcc rb bb">10.36</td></tr> </table> -<p>§ 127. <i>Regime of a River Channel.</i>—A river channel is said to be in +<p>§ 127. <i>Regime of a River Channel.</i>—A river channel is said to be in a state of regime, or stability, when it changes little in draught or form in a series of years. In some rivers the deepest part of the channel changes its position perpetually, and is seldom found in the @@ -15694,13 +15656,13 @@ the silting at another. In that case the general regime is permanent, though alteration is constantly going on. This is more likely to happen if by artificial means the erosion of the banks is prevented. If a river flows in soil incapable of resisting its tendency to scour -it is necessarily sinuous (§ 107), for the slightest deflection of the +it is necessarily sinuous (§ 107), for the slightest deflection of the current to either side begins an erosion which increases progressively till a considerable bend is formed. If such a river is straightened it becomes sinuous again unless its banks are protected from scour.</p> -<p>§ 128. <i>Longitudinal Section of River Bed.</i>—The declivity of rivers +<p>§ 128. <i>Longitudinal Section of River Bed.</i>—The declivity of rivers decreases from source to mouth. In their higher parts rapid and torrential, flowing over beds of gravel or boulders, they enlarge in volume by receiving affluent streams, their slope diminishes, their @@ -15750,7 +15712,7 @@ vertical and horizontal coordinates. Let C be a point whose ordinates are x and y, and let the river at C have the breadth b, the slope i, and the velocity v.</p> -<p class="noind">Since velocity × area of section = discharge, vcb<span class="sp">2</span> = kl, or b = √ (kl/cv).</p> +<p class="noind">Since velocity × area of section = discharge, vcb<span class="sp">2</span> = kl, or b = √ (kl/cv).</p> <p class="noind">Hydraulic mean depth = ab = a √ (kl/cv).</p> @@ -15770,7 +15732,7 @@ l = AC = AD = x nearly.</p> <p class="noind">or</p> -<p class="center">y<span class="sp">2</span> = constant × x;</p> +<p class="center">y<span class="sp">2</span> = constant × x;</p> <p class="noind">so that the curve is a common parabola, of which the axis is horizontal and the vertex at the source. This may be considered an @@ -15779,7 +15741,7 @@ more or less, with exceptions due to the varying hardness of their beds, and the irregular manner in which their volume increases.</p> -<p>§ 129. <i>Surface Level of River.</i>—The surface level of a +<p>§ 129. <i>Surface Level of River.</i>—The surface level of a river is a plane changing constantly in position from changes in the volume of water discharged, and more slowly from changes in the river bed, and the circumstances @@ -15818,7 +15780,7 @@ under bridges becoming insufficient. Ordinarily the highest navigable level may be taken to be that at which the river begins to overflow its banks.</p> -<p>§ 130. <i>Relative Value of Different Materials for Submerged Works.</i>—That +<p>§ 130. <i>Relative Value of Different Materials for Submerged Works.</i>—That the power of water to remove and transport different materials depends on their density has an important bearing on the selection of materials for submerged works. In many cases, as in the aprons @@ -15846,7 +15808,7 @@ V ℔.</p> <tr><td class="tcl lb rb bb">Masonry</td> <td class="tcc rb bb">116-144</td> <td class="tcc rb bb">53.6-81.6</td></tr> </table> -<p>§ 131. <i>Inundation Deposits from a River.</i>—When a river carrying +<p>§ 131. <i>Inundation Deposits from a River.</i>—When a river carrying silt periodically overflows its banks, it deposits silt over the area flooded, and gradually raises the surface of the country. The silt is deposited in greatest abundance where the water first leaves the @@ -15869,7 +15831,7 @@ country in this case is very easy; a comparatively slight raising of the river surface by a weir or annicut gives a command of level which permits the water to be conveyed to any part of the district.</p> -<p>§ 132. <i>Deltas.</i>—The name delta was originally given to the Δ-shaped +<p>§ 132. <i>Deltas.</i>—The name delta was originally given to the Δ-shaped portion of Lower Egypt, included between seven branches of the Nile. It is now given to the whole of the alluvial tracts round river mouths formed by deposition of sediment from the river, where @@ -15890,7 +15852,7 @@ of shoals at its mouth, and the river tends to form new bifurcations AC or AD (fig. 134), and one of these may in time become the main channel of the river.</p> -<p>§ 133. <i>Field Operations preliminary to a Study of River Improvement.</i>—There +<p>§ 133. <i>Field Operations preliminary to a Study of River Improvement.</i>—There are required (1) a plan of the river, on which the positions of lines of levelling and cross sections are marked; (2) a longitudinal section and numerous cross sections of the river; (3) a @@ -15910,7 +15872,7 @@ observations, two on each side of the river.</p> <tr><td class="figcenter"><img style="width:456px; height:320px" src="images/img79b.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 134.</span></td></tr></table> -<p>§ 134. <i>Cross Sections</i>—A stake is planted flush with the water, and +<p>§ 134. <i>Cross Sections</i>—A stake is planted flush with the water, and its level relatively to some point on the line of levels is determined. Then the depth of the water is determined at a series of points (if possible at uniform distances) in a line starting from the stake and @@ -15961,7 +15923,7 @@ From the section can be measured the sectional area of the stream Ω and its wetted perimeter χ; and from these the hydraulic mean depth m can be calculated.</p> -<p>§ 135. <i>Measurement of the Discharge of Rivers.</i>—The area of cross +<p>§ 135. <i>Measurement of the Discharge of Rivers.</i>—The area of cross section multiplied by the mean velocity gives the discharge of the stream. The height of the river with reference to some fixed mark should be noted whenever the velocity is observed, as the velocity @@ -15974,7 +15936,7 @@ than one method should be used.</p> <p class="pt1 center sc">Instruments for Measuring the Velocity of Water</p> -<p>§ 136. <i>Surface Floats</i> are convenient for determining the surface +<p>§ 136. <i>Surface Floats</i> are convenient for determining the surface velocities of a stream, though their use is difficult near the banks. The floats may be small balls of wood, of wax or of hollow metal, so loaded as to float nearly flush with the water surface. To render @@ -16050,7 +16012,7 @@ and in some cases to the nearest quarter second.</p> <tr><td class="figright1"><img style="width:213px; height:275px" src="images/img80b.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 137.</span></td></tr></table> -<p>§ 137. <i>Sub-surface Floats.</i>—The velocity at different depths below +<p>§ 137. <i>Sub-surface Floats.</i>—The velocity at different depths below the surface of a stream may be obtained by sub-surface floats, used precisely in the same way as surface floats. The most usual arrangement is to have a large float, of slightly greater density than water, @@ -16089,7 +16051,7 @@ slice of cork, which serves as the surface float.</p> <tr><td class="caption"><span class="sc">Fig. 138.</span></td> <td class="caption"><span class="sc">Fig. 139.</span></td></tr></table> -<p>§ 138. <i>Twin Floats.</i>—Suppose two equal and similar floats (fig. 139) +<p>§ 138. <i>Twin Floats.</i>—Suppose two equal and similar floats (fig. 139) connected by a wire. Let one float be a little lighter and the other a little heavier than water. Then the velocity of the combined floats will be the mean of the surface velocity and the velocity at the @@ -16112,7 +16074,7 @@ the sub-surface float.</p> <tr><td class="figright1"><img style="width:206px; height:342px" src="images/img80e.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 140.</span></td></tr></table> -<p>§ 139. <i>Velocity Rods.</i>—Another form of float is shown in fig. 140. +<p>§ 139. <i>Velocity Rods.</i>—Another form of float is shown in fig. 140. This consists of a cylindrical rod loaded at the lower end so as to float nearly vertical in water. A wooden rod, with a metal cap at the bottom in which shot can be placed, @@ -16127,7 +16089,7 @@ sinks nearly to the bed of the stream, gives directly the mean velocity of the whole vertical section in which it floats.</p> -<p>§ 140. <i>Revy’s Current Meter.</i>—No instrument +<p>§ 140. <i>Revy’s Current Meter.</i>—No instrument has been so much used in directly determining the velocity of a stream at a given point as the screw @@ -16200,7 +16162,7 @@ and stopped by hand.</p> <tr><td class="figright1"><img style="width:159px; height:606px" src="images/img81b.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 142.</span></td></tr></table> -<p>§ 141. <i>The Harlacher Current Meter.</i>—In +<p>§ 141. <i>The Harlacher Current Meter.</i>—In this the ordinary counting apparatus is abandoned. A worm drives a worm wheel, which makes an electrical contact once for each 100 @@ -16224,7 +16186,7 @@ small metal box containing also the battery. The magnet exposes and withdraws a coloured disk at an opening in the cover of the box.</p> -<p>§ 142. <i>Amsler Laffon Current Meter.</i>—A +<p>§ 142. <i>Amsler Laffon Current Meter.</i>—A very convenient and accurate current meter is constructed by Amsler Laffon of Schaffhausen. This can be used on a rod, and @@ -16256,7 +16218,7 @@ used as a sounding instrument.</p> <tr><td class="figcenter"><img style="width:470px; height:859px" src="images/img81c.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 143.</span></td></tr></table> -<p>§ 143. <i>Determination of the Coefficients of the Current Meter.</i>—Suppose +<p>§ 143. <i>Determination of the Coefficients of the Current Meter.</i>—Suppose a series of observations has been made by towing the meter in still water at different speeds, and that it is required to ascertain from these the constants of the meter. If v is the velocity of the water and @@ -16309,9 +16271,9 @@ determined by towing them in R. E. Froude’s experimental tank in which the resistance of ship models is ascertained. In that case the data are found with exceptional accuracy.</p> -<p>§ 144. Darcy Gauge or modified Pitot Tube.—A very old instrument +<p>§ 144. Darcy Gauge or modified Pitot Tube.—A very old instrument for measuring velocities, invented by Henri Pitot in 1730 -(<i>Histoire de l’Académie des Sciences</i>, 1732, p. 376), consisted simply +(<i>Histoire de l’Académie des Sciences</i>, 1732, p. 376), consisted simply of a vertical glass tube with a right-angled bend, placed so that its mouth was normal to the direction of flow (fig. 145).</p> @@ -16428,7 +16390,7 @@ constant, but varies a little from moment to moment. Darcy in some of his experiments took several readings, and deduced the velocity from the mean of the highest and lowest.</p> -<p>§ 145. <i>Perrodil Hydrodynamometer.</i>—This consists of a frame +<p>§ 145. <i>Perrodil Hydrodynamometer.</i>—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 @@ -16558,7 +16520,7 @@ indications of very low velocities.</p> <p class="pt1 center sc">Processes for Gauging Streams</p> -<p>§ 146. <i>Gauging by Observation of the Maximum Surface Velocity.</i>—The +<p>§ 146. <i>Gauging by Observation of the Maximum Surface Velocity.</i>—The method of gauging which involves the least trouble is to determine the surface velocity at the thread of the stream, and to deduce from it the mean velocity of the whole cross section. The maximum @@ -16577,7 +16539,7 @@ values:—</p> <tr><td class="tcl">Destrem and De Prony, experiments on the Neva</td> <td class="tcl">0.78</td></tr> <tr><td class="tcl">Boileau, experiments on canals</td> <td class="tcl">0.82</td></tr> <tr><td class="tcl">Baumgartner, experiments on the Garonne</td> <td class="tcl">0.80</td></tr> -<tr><td class="tcl">Brünings (mean)</td> <td class="tcl">0.85</td></tr> +<tr><td class="tcl">Brünings (mean)</td> <td class="tcl">0.85</td></tr> <tr><td class="tcl">Cunningham, Solani aqueduct</td> <td class="tcl">0.823</td></tr> </table> @@ -16615,7 +16577,7 @@ found would then always give the velocity for any observed depth of the stream, without the need of making any new float or current meter observations.</p> -<p>§ 147. <i>Mean Velocity determined by observing a Series of Surface +<p>§ 147. <i>Mean Velocity determined by observing a Series of Surface Velocities.</i>—The ratio of the mean velocity to the surface velocity in one longitudinal section is better ascertained than the ratio of the central surface velocity to the mean velocity of the whole cross @@ -16691,7 +16653,7 @@ very calm weather.</p> <p>The ratio of the surface velocity to the mean velocity in the same vertical can be ascertained from the formulae for the vertical velocity -curve already given (§ 101). Exner, in <i>Erbkam’s Zeitschrift</i> for 1875, +curve already given (§ 101). Exner, in <i>Erbkam’s Zeitschrift</i> for 1875, gave the following convenient formula. Let v be the mean and V the surface velocity in any given vertical longitudinal section, the depth of which is h</p> @@ -16704,7 +16666,7 @@ which the rod floats. No formula of reduction is then necessary. The observed velocity has simply to be multiplied by the area of the compartment to which it belongs.</p> -<p>§ 148. <i>Mean Velocity of the Stream from a Series of Mid Depth +<p>§ 148. <i>Mean Velocity of the Stream from a Series of Mid Depth Velocities.</i>—In the gaugings of the Mississippi it was found that the mid depth velocity differed by only a very small quantity from the mean velocity in the vertical section, and it was uninfluenced by @@ -16719,7 +16681,7 @@ into which the river is divided. The discharge is the sum of the products of the observed mean mid depth velocities and the areas of the compartments.</p> -<p>§ 149. <i>P. P. Boileau’s Process for Gauging Streams.</i>—Let U be the +<p>§ 149. <i>P. P. Boileau’s Process for Gauging Streams.</i>—Let U be the mean velocity at a given section of a stream, V the maximum velocity, or that of the principal filament, which is generally a little below the surface, W and w the greatest and least velocities at the surface. @@ -16748,7 +16710,7 @@ the mean velocity of the stream. More conveniently W, w, and U can be measured from a horizontal surface velocity curve, obtained from a series of float observations.</p> -<p>§ 150. <i>Direct Determination of the Mean Velocity by a Current Meter +<p>§ 150. <i>Direct Determination of the Mean Velocity by a Current Meter or Darcy Gauge.</i>—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 @@ -16774,7 +16736,7 @@ on shore.</p> <tr><td class="figright1"><img style="width:327px; height:129px" src="images/img85a.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 150.</span></td></tr></table> -<p>§ 151. <i>A. R. Harlacher’s Graphic Method of determining the Discharge +<p>§ 151. <i>A. R. Harlacher’s Graphic Method of determining the Discharge from a Series of Current Meter Observations.</i>—Let ABC (fig. 149) be the cross section of a river at which a complete series of current meter observations have been taken. Let I., II., III., ... be @@ -16859,7 +16821,7 @@ with the mean velocity of the stream.</p> <p class="pt2 center sc">Hydraulic Machines</p> -<p>§ 152. Hydraulic machines may be broadly divided into two +<p>§ 152. Hydraulic machines may be broadly divided into two classes: (1) <i>Motors</i>, in which water descending from a higher to a lower level, or from a higher to a lower pressure, gives up energy which is available for mechanical operations; (2) <i>Pumps</i>, @@ -16912,7 +16874,7 @@ transmitted electrically are not included.</p> <p class="pt2 center">XII. IMPACT AND REACTION OF WATER</p> <div class="condensed"> -<p>§ 153. When a stream of fluid in steady motion impinges on a +<p>§ 153. When a stream of fluid in steady motion impinges on a solid surface, it presses on the surface with a force equal and opposite to that by which the velocity and direction of motion of the fluid are changed. Generally, in problems on the impact of fluids, it is @@ -16980,7 +16942,7 @@ for moving the solid surface is</p> <p class="center">η = Tu / (GQv<span class="su">1</span><span class="sp">2</span> / 2g).</p> -<p>§ 154. <i>Jet deviated entirely in one Direction.—Geometrical Solution</i> +<p>§ 154. <i>Jet deviated entirely in one Direction.—Geometrical Solution</i> (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 @@ -17012,7 +16974,7 @@ and parallel to the initial and final directions of relative motion.</p> <tr><td class="figright1"><img style="width:182px; height:313px" src="images/img86c.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 154.</span></td></tr></table> -<p>§ 155. (1) <i>A Jet impinges on a plane surface at rest, in a direction +<p>§ 155. (1) <i>A Jet impinges on a plane surface at rest, in a direction normal to the plane</i> (fig. 154).—Let a jet whose section is ω impinge with a velocity v on a plane surface at rest, in a direction normal to the plane. The @@ -17026,20 +16988,20 @@ the change of momentum per second, is P = (G/g) ωv<span class="sp">2</span>.</p> <p>(2) <i>If the plane is moving in the direction -of the jet with the velocity</i> ±u, the quantity -impinging per second is ω(v ± u). The +of the jet with the velocity</i> ±u, the quantity +impinging per second is ω(v ± u). The momentum of this quantity before impact -is (G/g)ω(v ± u)v. After impact, the water -still possesses the velocity ±u in the +is (G/g)ω(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) ω (v ± u)u. The pressure on the +±(G/g) ω (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) ω (v ± u)<span class="sp">2</span>. +per second, is the difference of these quantities or P = (G/g) ω (v ± u)<span class="sp">2</span>. This differs from the expression obtained in the previous case, -in that the relative velocity of the water and plane v ± u is substituted -for v. The expression may be written P = 2 × G × ω (v ± u)<span class="sp">2</span>/2g, +in that the relative velocity of the water and plane v ± u is substituted +for v. The expression may be written P = 2 × G × ω (v ± u)<span class="sp">2</span>/2g, where the last two terms are the volume of a prism of water whose section is the area of the jet and whose length is the head due to the relative velocity. The pressure on the plane is twice the @@ -17066,14 +17028,14 @@ and equating the differential coefficient to zero:—</p> are introduced at short intervals at the same point, the quantity of water impinging on the series will be ωv instead of ω(v − u), and the whole pressure = (G/g) ωv (v − u). The work done is (G/g)ωvu (v − u). -The efficiency η = (G/g) ωvu (v − u) ÷ (G/2g) ωv<span class="sp">3</span> = 2u(v-u)/v<span class="sp">2</span>. This becomes +The efficiency η = (G/g) ωvu (v − u) ÷ (G/2g) ωv<span class="sp">3</span> = 2u(v-u)/v<span class="sp">2</span>. This becomes a maximum for dη/du = 2(v − 2u) = 0, or u = <span class="spp">1</span>⁄<span class="suu">2</span>v, and the η = <span class="spp">1</span>⁄<span class="suu">2</span>. This result is often used as an approximate expression for the velocity of greatest efficiency when a jet of water strikes the floats of a water wheel. The work wasted in this case is half the whole energy of the jet when the floats run at the best speed.</p> -<p>§ 156. (4) <i>Case of a Jet impinging on a Concave Cup Vane</i>, velocity +<p>§ 156. (4) <i>Case of a Jet impinging on a Concave Cup Vane</i>, velocity of water v, velocity of vane in the same direction u (fig. 155), weight impinging per second = Gw (v − u).</p> @@ -17111,7 +17073,7 @@ cups.</p> <tr><td class="figcenter"><img style="width:402px; height:174px" src="images/img87b.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 156.</span></td></tr></table> -<p>§ 157. (5) <i>Case of a Flat Vane oblique to the Jet</i> (fig. 156).—This case +<p>§ 157. (5) <i>Case of a Flat Vane oblique to the Jet</i> (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, @@ -17124,7 +17086,7 @@ the plane. On the assumption that friction is insensible, DE is unaffected by impact, but AE is destroyed. Hence AE represents the entire change of velocity due to impact and the direction of that change. The pressure on the plane is in the direction AE, and -its amount is = mass of water impinging per second × AE.</p> +its amount is = mass of water impinging per second × AE.</p> <p>Let DAE = θ, and let AD = v<span class="su">r</span>. Then AE = v<span class="su">r</span> cos θ; DE = v<span class="su">r</span> sin θ. If Q is the volume of water impinging on the plane per second, @@ -17211,7 +17173,7 @@ work done on the plane and the efficiency of the jet are zero.</p> <p>When u = <span class="spp">1</span>⁄<span class="suu">3</span>v then Pu max. = <span class="spp">4</span>⁄<span class="suu">27</span>(G/g)ωv<span class="sp">3</span> cos<span class="sp">2</span>α, and the efficiency = η = <span class="spp">4</span>⁄<span class="suu">9</span>cos<span class="sp">2</span>α.</p> -<p>(<i>c</i>) The plane moves perpendicularly to the jet. Then δ = 90° − α; +<p>(<i>c</i>) The plane moves perpendicularly to the jet. Then δ = 90° − α; cos δ = sin α; and Pu = G/g ωu (sin α / cos α) (v cos α − u sin α)<span class="sp">2</span>. This is a maximum when u = <span class="spp">1</span>⁄<span class="suu">3</span>v cos α.</p> @@ -17222,7 +17184,7 @@ same as in the last case.</p> <tr><td class="figcenter"><img style="width:439px; height:244px" src="images/img87e.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 159.</span></td></tr></table> -<p>§ 158. <i>Best Form of Vane to receive Water.</i>—When water impinges +<p>§ 158. <i>Best Form of Vane to receive Water.</i>—When water impinges normally or obliquely on a plane, it is scattered in all directions after impact, and the work carried away by the water is then generally lost, from the impossibility of dealing afterwards with streams of @@ -17247,7 +17209,7 @@ direction AB. This is sometimes expressed by saying that the vane <tr><td class="figcenter"><img style="width:478px; height:124px" src="images/img88a.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 160.</span></td></tr></table> -<p>§ 159. <i>Floats of Poncelet Water Wheels.</i>—Let AC (fig. 160) represent +<p>§ 159. <i>Floats of Poncelet Water Wheels.</i>—Let AC (fig. 160) represent the direction of a thin horizontal stream of water having the velocity v. Let AB be a curved float moving horizontally with velocity u. The relative motion of water and float is then initially @@ -17273,11 +17235,11 @@ without velocity. This is the principle of the Poncelet wheel, but in that case the floats move over an arc of a large circle; the stream of water has considerable thickness (about 8 in.); in order to get the water into and out of the wheel, it is then necessary that the lip -of the float should make a small angle (about 15°) with the direction +of the float should make a small angle (about 15°) with the direction of its motion. The water quits the wheel with a little of its energy of motion remaining.</p> -<p>§ 160. <i>Pressure on a Curved Surface when the Water is deviated +<p>§ 160. <i>Pressure on a Curved Surface when the Water is deviated wholly in one Direction.</i>—When a jet of water impinges on a curved surface in such a direction that it is received without shock, the pressure on the surface is due to its gradual deviation from its first @@ -17319,8 +17281,8 @@ of the figure. The resultant pressure on surface</p> <table class="math0" summary="math"> <tr><td rowspan="2">= R = 2rb sin</td> <td>φ</td> -<td rowspan="2">×</td> <td>Gt</td> -<td rowspan="2">·</td> <td>v<span class="sp">2</span></td> +<td rowspan="2">×</td> <td>Gt</td> +<td rowspan="2">·</td> <td>v<span class="sp">2</span></td> <td rowspan="2">= 2</td> <td>G</td> <td rowspan="2">btv<span class="sp">2</span> sin</td> <td>φ</td> <td rowspan="2">,</td></tr> @@ -17360,10 +17322,10 @@ which is a maximum when u = <span class="spp">1</span>⁄<span class="suu">3 obtained by considering that the work done on the plane must be equal to the energy lost by the water, when friction is neglected.</p> -<p>If φ = 180°, cos φ = −1, 1 − cos φ = 2; then P = 2(G/g) bt (v − u)<span class="sp">2</span>, +<p>If φ = 180°, cos φ = −1, 1 − cos φ = 2; then P = 2(G/g) bt (v − u)<span class="sp">2</span>, the same result as for a concave cup.</p> -<p>§ 161. <i>Position which a Movable Plane takes in Flowing Water.</i>—When +<p>§ 161. <i>Position which a Movable Plane takes in Flowing Water.</i>—When a rectangular plane, movable about an axis parallel to one of its sides, is placed in an indefinite current of fluid, it @@ -17386,26 +17348,26 @@ table:—</p> <table class="ws" summary="Contents"> <tr><td class="tcc allb"> </td> <td class="tcc allb">Larger plane.</td> <td class="tcc allb">Smaller Plane.</td></tr> -<tr><td class="tcr lb rb">a/b = 1.0</td> <td class="tcr rb">φ = ...</td> <td class="tcr rb">φ = 90°</td></tr> -<tr><td class="tcr lb rb">0.9</td> <td class="tcr rb">75°</td> <td class="tcr rb">72<span class="spp">1</span>⁄<span class="suu">2</span>°</td></tr> -<tr><td class="tcr lb rb">0.8</td> <td class="tcr rb">60°</td> <td class="tcr rb">57°</td></tr> -<tr><td class="tcr lb rb">0.7</td> <td class="tcr rb">48°</td> <td class="tcr rb">43°</td></tr> -<tr><td class="tcr lb rb">0.6</td> <td class="tcr rb">25°</td> <td class="tcr rb">29°</td></tr> -<tr><td class="tcr lb rb">0.5</td> <td class="tcr rb">13°</td> <td class="tcr rb">13°</td></tr> -<tr><td class="tcr lb rb">0.4</td> <td class="tcr rb">8°</td> <td class="tcr rb">6<span class="spp">1</span>⁄<span class="suu">2</span>°</td></tr> -<tr><td class="tcr lb rb">0.3</td> <td class="tcr rb">6°</td> <td class="tcc rb">..</td></tr> -<tr><td class="tcr lb rb bb">0.2</td> <td class="tcr rb bb">4°</td> <td class="tcc rb bb">..</td></tr> +<tr><td class="tcr lb rb">a/b = 1.0</td> <td class="tcr rb">φ = ...</td> <td class="tcr rb">φ = 90°</td></tr> +<tr><td class="tcr lb rb">0.9</td> <td class="tcr rb">75°</td> <td class="tcr rb">72<span class="spp">1</span>⁄<span class="suu">2</span>°</td></tr> +<tr><td class="tcr lb rb">0.8</td> <td class="tcr rb">60°</td> <td class="tcr rb">57°</td></tr> +<tr><td class="tcr lb rb">0.7</td> <td class="tcr rb">48°</td> <td class="tcr rb">43°</td></tr> +<tr><td class="tcr lb rb">0.6</td> <td class="tcr rb">25°</td> <td class="tcr rb">29°</td></tr> +<tr><td class="tcr lb rb">0.5</td> <td class="tcr rb">13°</td> <td class="tcr rb">13°</td></tr> +<tr><td class="tcr lb rb">0.4</td> <td class="tcr rb">8°</td> <td class="tcr rb">6<span class="spp">1</span>⁄<span class="suu">2</span>°</td></tr> +<tr><td class="tcr lb rb">0.3</td> <td class="tcr rb">6°</td> <td class="tcc rb">..</td></tr> +<tr><td class="tcr lb rb bb">0.2</td> <td class="tcr rb bb">4°</td> <td class="tcc rb bb">..</td></tr> </table> -<p>§ 162. <i>Direct Action distinguished from Reaction</i> (Rankine, <i>Steam -Engine</i>, § 147).</p> +<p>§ 162. <i>Direct Action distinguished from Reaction</i> (Rankine, <i>Steam +Engine</i>, § 147).</p> <p>The pressure which a jet exerts on a vane can be distinguished into two parts, viz∴—</p> <p>(1) The pressure arising from changing the direct component of the velocity of the water into the velocity of the vane. In fig. -153, § 154, ab cos bae is the direct component of the water’s velocity, +153, § 154, ab cos bae is the direct component of the water’s velocity, or component in the direction of motion of vane. This is changed into the velocity ae of the vane. The pressure due to direct impulse is then</p> @@ -17418,7 +17380,7 @@ producing pressure on the vane.</p> <p>(2) The term reaction is applied to the additional action due to the direction and velocity with which the water glances off the vane. It is this which is diminished by the friction between the -water and the vane. In Case 2, § 160, the direct pressure is</p> +water and the vane. In Case 2, § 160, the direct pressure is</p> <p class="center">P<span class="su">1</span> = Gbt (v − u)<span class="sp">2</span> / g.</p> @@ -17426,17 +17388,17 @@ water and the vane. In Case 2, § 160, the direct pressure is</p> <p class="center">P<span class="su">2</span> = −Gbt (v − u)<span class="sp">2</span> cos φ / g.</p> -<p>If φ < 90°, the direct component of the water’s motion is not +<p>If φ < 90°, the direct component of the water’s motion is not wholly converted into the velocity of the vane, and the whole <span class="pagenum"><a name="page89" id="page89"></a>89</span> -pressure due to direct impulse is not obtained. If φ > 90°, cos φ is +pressure due to direct impulse is not obtained. If φ > 90°, cos φ is negative and an additional pressure due to reaction is obtained.</p> <table class="flt" style="float: right; width: 250px;" summary="Illustration"> <tr><td class="figright1"><img style="width:203px; height:139px" src="images/img89a.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 164.</span></td></tr></table> -<p>§ 163. <i>Jet Propeller.</i>—In the case of vessels propelled by a jet of +<p>§ 163. <i>Jet Propeller.</i>—In the case of vessels propelled by a jet of water (fig. 164), driven sternwards from orifices at the side of the vessel, the water, originally at rest outside the vessel, is drawn into the ship @@ -17485,7 +17447,7 @@ about <span class="spp">2</span>⁄<span class="suu">3</span>.</p> <tr><td class="figcenter"><img style="width:474px; height:204px" src="images/img89b.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 165.</span></td></tr></table> -<p>§ 164. <i>Pressure of a Steady Stream in a Uniform Pipe on a Plane +<p>§ 164. <i>Pressure of a Steady Stream in a Uniform Pipe on a Plane normal to the Direction of Motion.</i>—Let CD (fig. 165) be a plane placed normally to the stream which, for simplicity, may be supposed to flow horizontally. The fluid filaments are deviated in @@ -17652,7 +17614,7 @@ Hence there is less pressure on the cylinder than on the thin plane.</p> <tr><td class="figright1"><img style="width:234px; height:211px" src="images/img89c.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 166.</span></td></tr></table> -<p>§ 165. <i>Distribution of Pressure on a Surface on which a Jet impinges +<p>§ 165. <i>Distribution of Pressure on a Surface on which a Jet impinges normally.</i>—The principle of momentum gives readily enough the total or resultant pressure of a jet impinging on a plane surface, but in some cases it is useful to know the distribution of the pressure. @@ -17851,7 +17813,7 @@ curve is</p> <p class="center">y = hε<span class="sp">−1/2</span> √<span class="ov">(h / h</span><span class="su">1</span>) (x<span class="sp">2</span> / r<span class="sp">2</span>).</p> -<p>§ 166. <i>Resistance of a Plane moving through a Fluid, or Pressure +<p>§ 166. <i>Resistance of a Plane moving through a Fluid, or Pressure of a Current on a Plane.</i>—When a thin plate moves through the air, or through an indefinitely large mass of still water, in a direction normal to its surface, there is an excess of pressure on the anterior @@ -17932,7 +17894,7 @@ being f = 1.834, a result agreeing well with Dubuat.</p> <tr><td class="figright1"><img style="width:216px; height:315px" src="images/img91a.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 169.</span></td></tr></table> -<p>§ 167. <i>Stanton’s Experiments on the Pressure of Air on Surfaces.</i>—At +<p>§ 167. <i>Stanton’s Experiments on the Pressure of Air on Surfaces.</i>—At the National Physical Laboratory, London, T. E. Stanton carried out a series of experiments on the distribution of pressure on surfaces in a current of air passing through an air trunk. These were on a @@ -17968,7 +17930,7 @@ greater than on a circular plate. In later tests on larger planes in free air, Stanton found resistances 18% greater than those observed with small planes in the air trunk.</p> -<p>§ 168. <i>Case when the Direction of Motion is oblique to the Plane.</i>—The +<p>§ 168. <i>Case when the Direction of Motion is oblique to the Plane.</i>—The determination of the pressure between a fluid and surface in this case is of importance in many practical questions, for instance, in assigning the load due to wind pressure on sloping and curved roofs, @@ -18034,7 +17996,7 @@ Duchemin’s rule. These last values are obtained by taking P = 3.31, the observed pressure on a normal surface:—</p> <table class="ws" summary="Contents"> -<tr><td class="tcc allb">Angle between Plane and Direction of Blast</td> <td class="tcc allb">15°</td> <td class="tcc allb">20°</td> <td class="tcc allb">60°</td> <td class="tcc allb">90°</td></tr> +<tr><td class="tcc allb">Angle between Plane and Direction of Blast</td> <td class="tcc allb">15°</td> <td class="tcc allb">20°</td> <td class="tcc allb">60°</td> <td class="tcc allb">90°</td></tr> <tr><td class="tcl lb rb">Horizontal pressure R</td> <td class="tcl rb">0.4</td> <td class="tcl rb">0.61</td> <td class="tcl rb">2.73</td> <td class="tcc rb">3.31</td></tr> <tr><td class="tcl lb rb">Lateral pressure L</td> <td class="tcl rb">1.6</td> <td class="tcl rb">1.96</td> <td class="tcl rb">1.26</td> <td class="tcc rb">..</td></tr> @@ -18079,7 +18041,7 @@ automatic governing machinery.</p> <p><span class="pagenum"><a name="page92" id="page92"></a>92</span></p> -<p>§ 169. <i>Water Motors with Artificial Sources of Energy.</i>—The +<p>§ 169. <i>Water Motors with Artificial Sources of Energy.</i>—The great convenience and simplicity of water motors has led to their adoption in certain cases, where no natural source of water power is available. In these cases, an artificial source of water @@ -18093,7 +18055,7 @@ steam engine stores up energy by pumping the water, while the work done by the hydraulic engines is done intermittently.</p> <div class="condensed"> -<p>§ 170. <i>Energy of a Water-fall.</i>—Let H<span class="su">t</span> be the total fall of level from +<p>§ 170. <i>Energy of a Water-fall.</i>—Let H<span class="su">t</span> be the total fall of level from the point where the water is taken from a natural stream to the point where it is discharged into it again. Of this total fall a portion, which can be estimated independently, is expended in overcoming @@ -18132,7 +18094,7 @@ of the machine, the work done will be</p> H ft.</p> </div> -<p>§ 171. <i>Site for Water Motor.</i>—Wherever a stream flows from +<p>§ 171. <i>Site for Water Motor.</i>—Wherever a stream flows from a higher to a lower level it is possible to erect a water motor. The amount of power obtainable depends on the available head and the supply of water. In choosing a site the engineer will @@ -18156,7 +18118,7 @@ streams depending directly on rainfall, and are therefore advantageous for water-power purposes.</p> <div class="condensed"> -<p>§ 172. <i>Water Power at Holyoke, U.S.A.</i>—About 85 m. from the +<p>§ 172. <i>Water Power at Holyoke, U.S.A.</i>—About 85 m. from the mouth of the Connecticut river there was a fall of about 60 ft. in a short distance, forming what were called the Grand Rapids, below which the river turned sharply, forming a kind of peninsula on which @@ -18178,7 +18140,7 @@ effective. The charge for the power water is at the rate of 20s. per h.p. per annum.</p> </div> -<p>§ 173. <i>Action of Water in a Water Motor.</i>—Water motors may +<p>§ 173. <i>Action of Water in a Water Motor.</i>—Water motors may be divided into water-pressure engines, water-wheels and turbines.</p> @@ -18223,7 +18185,7 @@ conditions of working.</p> <p class="pt1 center"><i>Water-pressure Engines.</i></p> -<p>§ 174. In these the water acts by pressure either due to the +<p>§ 174. In these the water acts by pressure either due to the height of the column in a supply pipe descending from a high-level reservoir, or created by pumping. Pressure engines were first used in mine-pumping on waterfalls of greater height than @@ -18304,7 +18266,7 @@ success. Where pressure engines are used simplicity is generally a first consideration, and economy is of less importance.</p> <div class="condensed"> -<p>§ 175. <i>Efficiency of Pressure Engines.</i>—It is hardly possible to form +<p>§ 175. <i>Efficiency of Pressure Engines.</i>—It is hardly possible to form a theoretical expression for the efficiency of pressure engines, but some general considerations are useful. Consider the case of a long stroke hydraulic ram, which has a fairly constant velocity v during @@ -18356,7 +18318,7 @@ engines probably not more than 50% and that only when fully loaded.</p> </div> -<p>§ 176. <i>Direct-Acting Hydraulic +<p>§ 176. <i>Direct-Acting Hydraulic Lift</i> (fig. 171).—This is the simplest of all kinds of hydraulic motor. A cage W is lifted directly @@ -18471,7 +18433,7 @@ constant)</p> <tr><td class="figleft1"><img style="width:133px; height:443px" src="images/img94a.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 172.</span></td></tr></table> -<p>§ 177. <i>Armstrong’s Hydraulic Jigger.</i>—This is simply a single-acting +<p>§ 177. <i>Armstrong’s Hydraulic Jigger.</i>—This is simply a single-acting hydraulic cylinder and ram, provided with sheaves so as to give motion to a wire rope or chain. It is used in various forms of lift and crane. Fig. 172 shows the arrangement. A @@ -18489,7 +18451,7 @@ free end of the rope has a movement equal to six times the stroke of the ram, the force exerted being in the inverse proportion.</p> -<p>§ 178. <i>Rotative Hydraulic Engines.</i>—Valve-gear +<p>§ 178. <i>Rotative Hydraulic Engines.</i>—Valve-gear mechanism similar in principle to that of steam engines can be applied to actuate the admission and discharge valves, and the @@ -18535,7 +18497,7 @@ effort on the crank pin is very uniform.</p> <tr><td class="caption"><span class="sc">Fig. 175.</span></td></tr></table> <div class="condensed"> -<p><i>Brotherhood Hydraulic Engine.</i>—Three cylinders at angles of 120° +<p><i>Brotherhood Hydraulic Engine.</i>—Three cylinders at angles of 120° with each other are formed in one casting with the frame. The plungers are hollow trunks, and the connecting rods abut in cylindrical recesses in them and are connected to a common crank @@ -18647,7 +18609,7 @@ was 22 ft. and the water pressure in the cylinders 80 ℔ per sq. in.</p> </table> </div> -<p>§ 179. <i>Accumulator Machinery.</i>—It has already been pointed +<p>§ 179. <i>Accumulator Machinery.</i>—It has already been pointed out that it is in some cases convenient to use a steam engine to create an artificial head of water, which is afterwards employed in driving water-pressure machinery. Where power is required @@ -18795,7 +18757,7 @@ upper cylinder.</p> <p class="pt1 center"><i>Water Wheels.</i></p> -<p>§ 180. <i>Overshot and High Breast Wheels.</i>—When +<p>§ 180. <i>Overshot and High Breast Wheels.</i>—When a water fall ranges between 10 and 70 ft. and the water supply is from 3 to 25 cub. ft. per second, it is possible to @@ -18887,7 +18849,7 @@ long as possible, and the width of opening of the buckets should be buckets on periphery of wheel. Make ed = <span class="spp">1</span>⁄<span class="suu">2</span> eb and bc = <span class="spp">6</span>⁄<span class="suu">5</span> to <span class="spp">5</span>⁄<span class="suu">4</span> ab. Join cd. For an iron bucket (fig. 180, B), take ed = <span class="spp">1</span>⁄<span class="suu">3</span>eb; bc = <span class="spp">6</span>⁄<span class="suu">5</span>ab. Draw cO making an -angle of 10° to 15° with +angle of 10° to 15° with the radius at c. On Oc take a centre giving a circular arc passing @@ -18926,7 +18888,7 @@ are still working.</p> <tr><td class="figcenter"><img style="width:473px; height:249px" src="images/img96c.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 181.</span></td></tr></table> -<p>§ 181. <i>Poncelet Water Wheel.</i>—When the fall does not exceed +<p>§ 181. <i>Poncelet Water Wheel.</i>—When the fall does not exceed 6 ft., the best water motor to adopt in many cases is the Poncelet undershot water wheel. In this the water acts very nearly in the same way as in a turbine, and the Poncelet wheel, although @@ -18934,7 +18896,7 @@ slightly less efficient than the best turbines, in normal conditions of working, is superior to most of them when working with a reduced supply of water. A general notion of the action of the water on a Poncelet wheel has already been given in -§ 159. Fig. 181 shows its construction. The water penned back +§ 159. Fig. 181 shows its construction. The water penned back between the side walls of the wheel pit is allowed to flow to the wheel under a movable sluice, at a velocity nearly equal to the velocity due to the whole fall. The water is guided down a slope @@ -18986,11 +18948,11 @@ the wheel is made about 4 in. greater than b.</p> wheels. One of the simplest is that shown in figs. 181, 182.</p> <p>Let OA (fig. 181) be the vertical radius of the wheel. Set off OB, -OD making angles of 15° with OA. Then BD may be the length of +OD making angles of 15° with OA. Then BD may be the length of the close breasting fitted to the wheel. Draw the bottom of the head face BC at a slope of 1 in 10. Parallel to this, at distances <span class="spp">1</span>⁄<span class="suu">2</span>e and e, draw EF and GH. Then EF is the mean layer and GH the -surface layer entering the wheel. Join OF, and make OFK = 23°. +surface layer entering the wheel. Join OF, and make OFK = 23°. Take FK = 0.5 to 0.7 H. Then K is the centre from which the bucket curve is struck and KF is the radius. The depth of the shrouds must be sufficient to prevent the water from rising over the @@ -19013,13 +18975,13 @@ and V the velocity of the wheel.</p> <p class="pt1 center"><i>Turbines.</i></p> -<p>§ 182. The name turbine was originally given in France to +<p>§ 182. The name turbine was originally given in France to any water motor which revolved in a horizontal plane, the axis being vertical. The rapid development of this class of motors -dates from 1827, when a prize was offered by the Société +dates from 1827, when a prize was offered by the Société d’Encouragement for a motor of this kind, which should be an improvement on certain wheels then in use. The prize -was ultimately awarded to Benoît Fourneyron (1802-1867), +was ultimately awarded to Benoît Fourneyron (1802-1867), whose turbine, but little modified, is still constructed.</p> <p><i>Classification of Turbines.</i>—In some turbines the whole @@ -19105,7 +19067,7 @@ the same as if the turbine were placed at the bottom of the fall.</p> <tr><td class="figright1"><img style="width:211px; height:256px" src="images/img97b.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 183.</span></td></tr></table> -<p>§ 183. <i>The Simple Reaction Wheel.</i>—It has been shown, in § 162, +<p>§ 183. <i>The Simple Reaction Wheel.</i>—It has been shown, in § 162, that, when water issues from a vessel, there is a reaction on the vessel tending to cause motion in a direction opposite to that of the jet. @@ -19191,13 +19153,13 @@ discharged. The actual efficiency realized appears to be about 60%, so that about 21% of the energy of the fall is lost in friction, in addition to the energy carried away by the water.</p> -<p class="center">§ 184. <i>General Statement of Hydrodynamical Principles necessary for +<p class="center">§ 184. <i>General Statement of Hydrodynamical Principles necessary for the Theory of Turbines.</i></p> <p>(<i>a</i>) When water flows through any pipe-shaped passage, such as the passage between the vanes of a turbine wheel, the relation between the changes of pressure and velocity is given by Bernoulli’s -theorem (§ 29). Suppose that, at a section A of such a passage, h<span class="su">1</span> +theorem (§ 29). Suppose that, at a section A of such a passage, h<span class="su">1</span> is the pressure measured in feet of water, v<span class="su">1</span> the velocity, and z<span class="su">1</span> the elevation above any horizontal datum plane, and that at a section B the same quantities are denoted by h<span class="su">2</span>, v<span class="su">2</span>, z<span class="su">2</span>. Then</p> @@ -19212,7 +19174,7 @@ B the same quantities are denoted by h<span class="su">2</span>, v<span class="s <p>(<i>b</i>) When there is an abrupt change of section of the passage, or an abrupt change of section of the stream due to a contraction, then, in applying Bernoulli’s equation allowance must be made for the -loss of head in shock (§ 36). Let v<span class="su">1</span>, v<span class="su">2</span> be the velocities before and +loss of head in shock (§ 36). Let v<span class="su">1</span>, v<span class="su">2</span> be the velocities before and after the abrupt change, then a stream of velocity v<span class="su">1</span> impinges on a stream at a velocity v<span class="su">2</span>, and the relative velocity is v<span class="su">1</span> − v<span class="su">2</span>. The head lost is (v<span class="su">1</span> − v<span class="su">2</span>)<span class="sp">2</span>/2g. Then equation (1a) becomes</p> @@ -19291,7 +19253,7 @@ water on the wheel is</p> <p class="center">T = Ma = (GQ/g) (w<span class="su">1</span>r<span class="su">1</span> − w<span class="su">2</span>r<span class="su">2</span>) α foot-pounds per second.</p> <div class="author">(5)</div> -<p>§ 185. <i>Total and Available Fall.</i>—Let H<span class="su">t</span> be the total difference of +<p>§ 185. <i>Total and Available Fall.</i>—Let H<span class="su">t</span> be the total difference of level from the head-water to the tail-water surface. Of this total head a portion is expended in overcoming the resistances of the head race, tail race, supply pipe, or other channel conveying the water. @@ -19309,7 +19271,7 @@ belonging to the turbine itself. In that case the velocities of the water in the turbine should be calculated for a head H − ɧ, but the efficiency of the turbine for the head H.</p> -<p>§ 186. <i>Gross Efficiency and Hydraulic Efficiency of a Turbine.</i>—Let +<p>§ 186. <i>Gross Efficiency and Hydraulic Efficiency of a Turbine.</i>—Let T<span class="su">d</span> be the useful work done by the turbine, in foot-pounds per second, T<span class="su">t</span> the work expended in friction of the turbine shaft, gearing, &c., a quantity which varies with the local conditions in @@ -19373,7 +19335,7 @@ the theory of turbines. It was first given by Reiche (<i>Turbinenbaues</i>, <tr><td class="figright1"><img style="width:336px; height:521px" src="images/img100a.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 189.</span></td></tr></table> -<p>§ 187. <i>General Description of a Reaction Turbine.</i>—Professor +<p>§ 187. <i>General Description of a Reaction Turbine.</i>—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 @@ -19389,7 +19351,7 @@ on entering the case distributes itself through a rectangular supply chamber SC, from which it finds its way equally to the four guide-blade passages G, G, G, G. In these passages it acquires a velocity about equal to that due to half the fall, and is -directed into the wheel at an angle of about 10° or 12° with the +directed into the wheel at an angle of about 10° or 12° with the tangent to its circumference. The wheel W receives the water in equal proportions from each guide-blade passage. It consists of a centre plate p (fig. 189) keyed on the shaft aa, which passes @@ -19459,7 +19421,7 @@ are the worm and wheel for working the guide-blade gear.</p> <tr><td class="figcenter"><img style="width:514px; height:405px" src="images/img100c.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 191.</span></td></tr></table> -<p>§ 188. <i>Hydraulic Power at Niagara.</i>—The largest development of +<p>§ 188. <i>Hydraulic Power at Niagara.</i>—The largest development of hydraulic power is that at Niagara. The Niagara Falls Power Company have constructed two power houses on the United States side, the first with 10 turbines of 5000 h.p. each, and the second @@ -19492,7 +19454,7 @@ Stations,” <i>Proc. Inst. Mech. Eng.</i>, 1906).</p> <tr><td class="figcenter"><img style="width:987px; height:241px" src="images/img100d.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 192.</span></td></tr></table> -<p>§ 189. <i>Different Forms of Turbine Wheel.</i>—The wheel of a turbine +<p>§ 189. <i>Different Forms of Turbine Wheel.</i>—The wheel of a turbine or part of the machine on which the water acts is an annular space, furnished with curved vanes dividing it into passages exactly or roughly rectangular in cross section. For radial flow turbines the @@ -19512,7 +19474,7 @@ concentric cylinders.</p> <tr><td class="figright1"><img style="width:324px; height:237px" src="images/img101a.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 193.</span></td></tr></table> -<p>§ 190. <i>Velocity of Whirl and Velocity of Flow.</i>—Let acb (fig. 193) +<p>§ 190. <i>Velocity of Whirl and Velocity of Flow.</i>—Let acb (fig. 193) be the path of the particles of water in a turbine wheel. That path will be in a plane normal to the @@ -19613,7 +19575,7 @@ losses in the wheel passages are a small fraction of the total head.</p> <tr><td class="tcl">In inward flow turbines,</td> <td class="tcl">u<span class="su">o</span> = u<span class="su">i</span> = 0.125 √<span class="ov">(2gH)</span>.</td></tr> </table> -<p>§ 191. <i>Speed of the Wheel.</i>—The best speed of the wheel depends +<p>§ 191. <i>Speed of the Wheel.</i>—The best speed of the wheel depends partly on the frictional losses, which the ordinary theory of turbines disregards. It is best, therefore, to assume for V<span class="su">o</span> and V<span class="su">i</span> values which experiment has shown to be most advantageous.</p> @@ -19659,7 +19621,7 @@ the wheel vanes make with the inlet and outlet surfaces; then</p> <tr><td class="figright1"><img style="width:337px; height:279px" src="images/img101c.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 195.</span></td></tr></table> -<p>§ 192. <i>Condition determining the Angle of the Vanes at the Outlet +<p>§ 192. <i>Condition determining the Angle of the Vanes at the Outlet Surface of the Wheel.</i>—It has been shown that, when the water leaves the wheel, it should have no tangential @@ -19668,7 +19630,7 @@ is to be as great as possible; that is, w<span class="su">o</span> = 0. Hence, from (10), cos β = 0, -β = 90°, U<span class="su">o</span> = V<span class="su">o</span>, and +β = 90°, U<span class="su">o</span> = V<span class="su">o</span>, and the direction of the water’s motion is normal to the outlet @@ -19726,7 +19688,7 @@ be</p> <p class="center">φ = tan [Q / V<span class="su">o</span> (Ω<span class="su">o</span> − ω) ].</p> <div class="author">(16)</div> -<p>§ 193. <i>Head producing Velocity with which the Water enters the +<p>§ 193. <i>Head producing Velocity with which the Water enters the Wheel.</i>—Consider the variation of pressure in a wheel passage, which satisfies the condition that the sections change so gradually that there is no loss of head in shock. When the flow is in a horizontal @@ -19827,7 +19789,7 @@ wheel, the velocity of flow into the wheel is</p> <p class="center">v<span class="su">ri</span> = u<span class="su">i</span> cosec θ;</p> -<p class="noind">or, as this is only a small term, and θ is on the average 90°, we +<p class="noind">or, as this is only a small term, and θ is on the average 90°, we may take, for the present purpose, v<span class="su">ri</span> = u<span class="su">i</span> nearly.</p> <p>Inserting these values, and remembering that for an axial flow @@ -19861,7 +19823,7 @@ turbine V<span class="su">i</span> = V<span class="su">o</span>, ɧ = 0, and <tr><td class="denom">2g</td> <td class="denom">V<span class="su">i</span><span class="sp">2</span></td> <td class="denom">2g</td></tr></table> -<p>§ 194. <i>Angle which the Guide-Blades make with the Circumference +<p>§ 194. <i>Angle which the Guide-Blades make with the Circumference of the Wheel.</i>—At the moment the water enters the wheel, the radial component of the velocity is u<span class="su">i</span>, and the velocity is v<span class="su">i</span>. Hence, if γ is the angle between the guide-blades and a tangent to the @@ -19876,7 +19838,7 @@ of the guide-blades.</p> <tr><td class="figright1"><img style="width:346px; height:230px" src="images/img102.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 196.</span></td></tr></table> -<p>§ 195. <i>Condition determining the Angle of the Vanes at the Inlet +<p>§ 195. <i>Condition determining the Angle of the Vanes at the Inlet Surface of the Wheel.</i>—The single condition necessary to be satisfied at the inlet surface of the wheel is that the @@ -19900,7 +19862,7 @@ of the wheel. Completing the parallelogram, v<span class="su">ri</span> is the d relative motion. Hence the angle between v<span class="su">ri</span> and V<span class="su">i</span> is the angle θ which the vanes should make with the inlet surface of the wheel.</p> -<p>§ 196. <i>Example of the Method of designing a Turbine. Professor +<p>§ 196. <i>Example of the Method of designing a Turbine. Professor James Thomson’s Inward Flow Turbine.</i>—</p> <table class="reg" summary="poem"><tr><td> <div class="poemr"> @@ -19952,10 +19914,10 @@ second is</p> <p class="center">Tan φ = u<span class="su">o</span> / V<span class="su">o</span> = 0.125 / 0.33 = .3788;</p> -<p class="center">φ = 21º nearly.</p> +<p class="center">φ = 21º nearly.</p> <p>If this value is revised for the vane thickness it will ordinarily -become about 25º.</p> +become about 25º.</p> <p><i>Velocity with which the Water enters the Wheel.</i>—The head producing the velocity is</p> @@ -19974,7 +19936,7 @@ the velocity is</p> <p class="center">Sin γ = u<span class="su">i</span> / v<span class="su">i</span> = 0.125 / 0.721 = 0.173;</p> -<p class="center">γ = 10° nearly.</p> +<p class="center">γ = 10° nearly.</p> <p><i>Tangential Velocity of Water entering Wheel.</i></p> @@ -19984,12 +19946,12 @@ the velocity is</p> <p class="center">Cot θ = (w<span class="su">i</span> − V<span class="su">i</span>) / u<span class="su">i</span> = (.7101 − .66) / .125 = .4008;</p> -<p class="center">θ = 68° nearly.</p> +<p class="center">θ = 68° nearly.</p> <p><i>Hydraulic Efficiency of Wheel.</i></p> <table class="reg" summary="poem"><tr><td> <div class="poemr"> -<p>η = w<span class="su">i</span>V<span class="su">i</span> / gH = .7101 × .66 × 2</p> +<p>η = w<span class="su">i</span>V<span class="su">i</span> / gH = .7101 × .66 × 2</p> <p class="i05">= 0.9373.</p> </div> </td></tr></table> @@ -19999,7 +19961,7 @@ The efficiency from experiment has been found to be 0.75 to 0.80.</p> <p class="pt1 center"><i>Impulse and Partial Admission Turbines.</i></p> -<p>§ 197. The principal defect of most turbines with complete +<p>§ 197. The principal defect of most turbines with complete admission is the imperfection of the arrangements for working with less than the normal supply. With many forms of reaction turbine the efficiency is considerably reduced when the regulating @@ -20078,7 +20040,7 @@ velocity, and may be kept down to a manageable value.</p> <td class="caption"><span class="sc">Fig. 199.</span></td></tr></table> <div class="condensed"> -<p>§ 198. <i>General Description of an Impulse Turbine or Turbine with +<p>§ 198. <i>General Description of an Impulse Turbine or Turbine with Free Deviation.</i>—Fig. 197 shows a general sectional elevation of a Girard turbine, in which the flow is @@ -20160,17 +20122,17 @@ its internal diameter 3 ft. 10 in. Normal speed 400 revs. per minute. Water is discharged into the wheel by a single nozzle, shown in fig. 202 with its regulating apparatus and some of the vanes. The water enters the wheel -at an angle of 22° +at an angle of 22° with the direction of motion, and the final angle of the wheel -vanes is 20°. The +vanes is 20°. The efficiency on trial was from 75 to 78%.</p> -<p>§ 199. <i>Theory +<p>§ 199. <i>Theory of the Impulse Turbine.</i>—The theory of the impulse @@ -20202,7 +20164,7 @@ determined.</p> <p class="center">sin γ = u<span class="su">i</span> / v<span class="su">i</span> = 0.45 / 0.94 = .48;</p> -<p class="center">γ = 29°.</p> +<p class="center">γ = 29°.</p> <p class="noind">The value of u<span class="su">i</span> should, however, be corrected for the space occupied by the guide-blades.</p> @@ -20219,7 +20181,7 @@ by the guide-blades.</p> <p class="center">cot θ = (w<span class="su">i</span> − V<span class="su">i</span>) / u<span class="su">i</span> = (0.82 − 0.5) / 0.45 = .71;</p> -<p class="center">θ = 55°.</p> +<p class="center">θ = 55°.</p> <p>The relative velocity of the water striking the vane at the inlet edge is v<span class="su">ri</span> = u<span class="su">i</span> cosec θ = 1.22u<span class="su">i</span>. This relative velocity remains @@ -20229,7 +20191,7 @@ Also in an axial flow turbine V<span class="su">o</span> = V<span class="su">i</ <p>If the final velocity of the water is axial, then</p> -<p class="center">cos φ = V<span class="su">o</span> / v<span class="su">ro</span> = V<span class="su">i</span> / v<span class="su">ri</span> = 0.5 / (1.22 × 0.45) = cos 24º 23′.</p> +<p class="center">cos φ = V<span class="su">o</span> / v<span class="su">ro</span> = V<span class="su">i</span> / v<span class="su">ri</span> = 0.5 / (1.22 × 0.45) = cos 24º 23′.</p> <p class="noind">This should be corrected for the vane thickness. Neglecting this, u<span class="su">o</span> = v<span class="su">ro</span> sin φ = v<span class="su">ri</span> sin φ = u<span class="su">i</span> cosec θ sin φ = 0.5u<span class="su">i</span>. The discharging area @@ -20242,7 +20204,7 @@ in the section (fig. 199).</p> <tr><td class="figright1"><img style="width:160px; height:124px" src="images/img104d.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 203.</span></td></tr></table> -<p>§ 200. <i>Pelton Wheel.</i>—In the mining district of California about +<p>§ 200. <i>Pelton Wheel.</i>—In the mining district of California about 1860 simple impulse wheels were used, termed hurdy-gurdy wheels. The wheels rotated in a vertical plane, being supported on a horizontal axis. Round the circumference were fixed flat vanes which @@ -20295,7 +20257,7 @@ each develops 125 h.p.</p> <tr><td class="figright1"><img style="width:305px; height:274px" src="images/img105a.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 205</span></td></tr></table> -<p>§ 201. <i>Theory of the Pelton Wheel.</i>—Suppose a jet with a velocity +<p>§ 201. <i>Theory of the Pelton Wheel.</i>—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 @@ -20311,7 +20273,7 @@ per second the change of momentum per second in the direction of the vane’s motion is (GQ/g) [v − {u − (v − u) cos α}] = (GQ/g) (v − u) (1 + cos α). -If a = 0°, cos α = 1, and the change +If a = 0°, cos α = 1, and the change of momentum per second, which is equal to the effort driving the vane, is @@ -20323,7 +20285,7 @@ in succession, the quantity of water impinging on the vanes per second is the total discharge of the nozzle, and the energy expended at the nozzle is GQv<span class="sp">2</span>/2g. Hence the -efficiency of the arrangement is, when α = 0°, neglecting friction,</p> +efficiency of the arrangement is, when α = 0°, neglecting friction,</p> <p class="center">η = 2Pu / GQv<span class="sp">2</span> = 4 (v − u) u/v<span class="sp">2</span>,</p> @@ -20336,7 +20298,7 @@ vane on each side in a direction nearly parallel to the direction of motion of the vane. The best velocity of the vane is very approximately half the velocity of the jet.</p> -<p>§ 202. <i>Regulation of the Pelton Wheel.</i>—At first Pelton wheels were +<p>§ 202. <i>Regulation of the Pelton Wheel.</i>—At first Pelton wheels were adjusted to varying loads merely by throttling the supply. This method involves a total loss of part of the head at the sluice or throttle valve. In addition as the working head is reduced, the @@ -20353,7 +20315,7 @@ occupy more or less of the aperture of the nozzle. Such a needle can be controlled by an ordinary governor.</p> </div> -<p>§ 203. <i>General Considerations on the Choice of a Type of +<p>§ 203. <i>General Considerations on the Choice of a Type of Turbine.</i>—The circumferential speed of any turbine is necessarily a fraction of the initial velocity of the water, and therefore is greater as the head is greater. In reaction turbines with complete @@ -20397,7 +20359,7 @@ the state of the water. With a high fall the turbine of largest radius only is used, and the speed of rotation is less than with a turbine of smaller radius. On the other hand, as the fall decreases the inner turbines are used either singly or together, according -to the power required. At the Zürich waterworks there are +to the power required. At the Zürich waterworks there are turbines of 90 h.p. on a fall varying from 10<span class="spp">1</span>⁄<span class="suu">2</span> ft. to 4<span class="spp">3</span>⁄<span class="suu">4</span> ft. The power and speed are kept constant. Each turbine has three concentric rings. The outermost ring gives 90 h.p. with 105 @@ -20413,7 +20375,7 @@ tests the efficiency was 74% with the outer ring working alone, <tr><td class="figcenter"><img style="width:433px; height:723px" src="images/img105b.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 206.</span></td></tr></table> -<p>§ 204. <i>Speed Governing.</i>—When turbines are used to drive +<p>§ 204. <i>Speed Governing.</i>—When turbines are used to drive dynamos direct, the question of speed regulation is of great importance. Steam engines using a light elastic fluid can be easily regulated by governors acting on throttle or expansion valves. @@ -20456,7 +20418,7 @@ if the pressure is in excess of that due to the head.</p> <tr><td class="figcenter"><img style="width:691px; height:212px" src="images/img106a.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 207.</span></td></tr></table> -<p>§ 205. <i>The Hydraulic Ram.</i>—The hydraulic ram is an arrangement +<p>§ 205. <i>The Hydraulic Ram.</i>—The hydraulic ram is an arrangement by which a quantity of water falling a distance h forces a portion of the water to rise to a height h<span class="su">1</span>, greater than h. It consists of a supply reservoir (A, fig. 207), into which the water @@ -20543,7 +20505,7 @@ pump valves.</p> <p class="pt2 center sc">Pumps</p> -<p>§ 206. The different classes of pumps correspond +<p>§ 206. The different classes of pumps correspond almost exactly to the different classes of water motors, although the mechanical details of the construction are somewhat @@ -20587,7 +20549,7 @@ plunger is replaced by an elastic diaphragm, alternately depressed into and raised out of a cylinder.</p> <p>As single-acting pumps give an intermittent discharge three -are generally used on cranks at 120°. But with all pumps the +are generally used on cranks at 120°. But with all pumps the variation of velocity of discharge would cause great waste of work in the delivery pipes when they are long, and even danger from the hydraulic ramming action of the long column of water. @@ -20637,7 +20599,7 @@ Messrs Hayward Tyler have introduced a mechanism for varying the stroke of the pumps (Sinclair’s patent) from full stroke to nil, without stopping the pumps.</p> -<p>§ 207. <i>Centrifugal Pump.</i>—For large volumes of water on +<p>§ 207. <i>Centrifugal Pump.</i>—For large volumes of water on lifts not exceeding about 60 ft. the most convenient pump is the centrifugal pump. Recent improvements have made it available also for very high lifts. It consists of a wheel or fan @@ -20708,7 +20670,7 @@ air from the pump case.</p> <tr><td class="caption"><span class="sc">Fig. 210.</span></td></tr></table> <div class="condensed"> -<p>§ 208. <i>Design and Proportions of a Centrifugal Pump.</i>—The design +<p>§ 208. <i>Design and Proportions of a Centrifugal Pump.</i>—The design of the pump disk is very simple. Let r<span class="su">i</span>, r<span class="su">o</span> be the radii of the inlet and outlet surfaces of the pump disk, d<span class="su">i</span>, d<span class="su">o</span> the clear axial width at those radii. The velocity of flow through the pump may be taken @@ -20808,7 +20770,7 @@ conditions of working</p> <p><i>Hydraulic Efficiency of the Pump.</i>—Neglecting disk friction, journal friction, and leakage, the efficiency of the pump can be found -in the same way as that of turbines (§ 186). Let M be the moment +in the same way as that of turbines (§ 186). Let M be the moment of the couple rotating the pump, and α its angular velocity; w<span class="su">o</span>, r<span class="su">o</span> the tangential velocity of the water and radius at the outlet @@ -20833,7 +20795,7 @@ efficiency is</p> <p class="center">η = GQH / Mα = gH / w<span class="su">o</span>r<span class="su">o</span>α = gH / w<span class="su">o</span>V<span class="su">o</span>.</p> <div class="author">(7)</div> -<p>§ 209. Case 1. <i>Centrifugal Pump with no Whirlpool Chamber.</i>—When +<p>§ 209. Case 1. <i>Centrifugal Pump with no Whirlpool Chamber.</i>—When no special provision is made to utilize the energy of motion of the water leaving the wheel, and the pump discharges directly into a chamber in which the water is flowing to the discharge pipe, nearly @@ -20869,7 +20831,7 @@ wheel.</p> = (V<span class="su">o</span><span class="sp">2</span> − u<span class="su">o</span><span class="sp">2</span> cosec<span class="sp">2</span> φ) / {2V<span class="su">o</span> (V<span class="su">o</span> − u<span class="su">o</span> cot φ) },</p> <div class="author">(9)</div> -<p class="noind">For φ = 90°,</p> +<p class="noind">For φ = 90°,</p> <p class="center">η = (V<span class="su">o</span><span class="sp">2</span> − u<span class="su">o</span><span class="sp">2</span>) / 2V<span class="su">o</span><span class="sp">2</span>,</p> @@ -20894,18 +20856,18 @@ efficiency and the circumferential velocity of the pump:—</p> <table class="ws" summary="Contents"> <tr><td class="tcc">φ</td> <td class="tcc">η</td> <td class="tcc">V<span class="su">o</span></td></tr> -<tr><td class="tcc">90°</td> <td class="tcc">0.47</td> <td class="tcl">1.03 √<span class="ov">2gH</span></td></tr> -<tr><td class="tcc">45°</td> <td class="tcc">0.56</td> <td class="tcl">1.06 ”</td></tr> -<tr><td class="tcc">30°</td> <td class="tcc">0.65</td> <td class="tcl">1.12 ”</td></tr> -<tr><td class="tcc">20°</td> <td class="tcc">0.73</td> <td class="tcl">1.24 ”</td></tr> -<tr><td class="tcc">10°</td> <td class="tcc">0.84</td> <td class="tcl">1.75 ”</td></tr> +<tr><td class="tcc">90°</td> <td class="tcc">0.47</td> <td class="tcl">1.03 √<span class="ov">2gH</span></td></tr> +<tr><td class="tcc">45°</td> <td class="tcc">0.56</td> <td class="tcl">1.06 ”</td></tr> +<tr><td class="tcc">30°</td> <td class="tcc">0.65</td> <td class="tcl">1.12 ”</td></tr> +<tr><td class="tcc">20°</td> <td class="tcc">0.73</td> <td class="tcl">1.24 ”</td></tr> +<tr><td class="tcc">10°</td> <td class="tcc">0.84</td> <td class="tcl">1.75 ”</td></tr> </table> -<p class="noind">φ cannot practically be made less than 20°; and, allowing for the -frictional losses neglected, the efficiency of a pump in which φ = 20° is +<p class="noind">φ cannot practically be made less than 20°; and, allowing for the +frictional losses neglected, the efficiency of a pump in which φ = 20° is found to be about .60.</p> -<p>§ 210. Case 2. <i>Pump with a Whirlpool Chamber</i>, as in fig. 210.—Professor +<p>§ 210. Case 2. <i>Pump with a Whirlpool Chamber</i>, 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 @@ -20940,24 +20902,24 @@ of wheel and to outside of free vortex,</p> increase of efficiency. Thus with</p> <table class="ws" summary="Contents"> -<tr><td class="tcl">φ = 90° and</td> <td class="tcl">k = <span class="spp">1</span>⁄<span class="suu">2</span>,</td> <td class="tcl">η = <span class="spp">7</span>⁄<span class="suu">8</span> nearly,</td></tr> +<tr><td class="tcl">φ = 90° and</td> <td class="tcl">k = <span class="spp">1</span>⁄<span class="suu">2</span>,</td> <td class="tcl">η = <span class="spp">7</span>⁄<span class="suu">8</span> nearly,</td></tr> <tr><td class="tcl">φ a small angle and</td> <td class="tcl">k = <span class="spp">1</span>⁄<span class="suu">2</span>,</td> <td class="tcl">η = 1 nearly.</td></tr> </table> <p class="noind">With this arrangement of pump, therefore, the angle at the outer ends of the vanes is of comparatively little importance. A moderate -angle of 30° or 40° may very well be adopted. The following +angle of 30° or 40° may very well be adopted. The following numerical values of the velocity of the circumference of the pump have been obtained by taking k = <span class="spp">1</span>⁄<span class="suu">2</span>, and u<span class="su">o</span> = 0.25√(2gH).</p> <table class="ws" summary="Contents"> <tr><td class="tcc">φ</td> <td class="tcc">V<span class="su">o</span></td></tr> -<tr><td class="tcc">90°</td> <td class="tcl"> .762 √<span class="ov">2gH</span></td></tr> -<tr><td class="tcc">45°</td> <td class="tcl"> .842 ”</td></tr> -<tr><td class="tcc">30°</td> <td class="tcl"> .911 ”</td></tr> -<tr><td class="tcc">20°</td> <td class="tcl">1.023 ”</td></tr> +<tr><td class="tcc">90°</td> <td class="tcl"> .762 √<span class="ov">2gH</span></td></tr> +<tr><td class="tcc">45°</td> <td class="tcl"> .842 ”</td></tr> +<tr><td class="tcc">30°</td> <td class="tcl"> .911 ”</td></tr> +<tr><td class="tcc">20°</td> <td class="tcl">1.023 ”</td></tr> </table> <p>The quantity of water to be pumped by a centrifugal pump necessarily @@ -20982,7 +20944,7 @@ or more than the normal quantity of water is discussed in a paper in the <i>Proc. Inst. Civ. Eng.</i> vol. 53.</p> </div> -<p>§ 211. <i>High Lift Centrifugal Pumps.</i>—It has long been known +<p>§ 211. <i>High Lift Centrifugal Pumps.</i>—It has long been known that centrifugal pumps could be worked in series, each pump overcoming a part of the lift. This method has been perfected, and centrifugal pumps for very high lifts with great efficiency @@ -21020,7 +20982,7 @@ the results of tests made at Newcastle:—</p> <tr><td class="tcl lb bb">Water h.p.</td> <td class="tcr rb bb"> </td> <td class="tcc rb bb">252</td> <td class="tcc rb bb">235</td> <td class="tcc rb bb">326</td> <td class="tcc rb bb">239</td></tr> </table> -<p>In trial IV. the steam was superheated 95° F. From other +<p>In trial IV. the steam was superheated 95° F. From other trials under the same conditions as trial I. the Parsons turbine uses 15.6 ℔ of steam per brake h.p. hour, so that the combined efficiency of turbine and pumps is about 56%, a remarkably @@ -21030,8 +20992,8 @@ good result.</p> <tr><td class="figright1"><img style="width:376px; height:707px" src="images/img109.jpg" alt="" /></td></tr> <tr><td class="caption"><span class="sc">Fig. 212.</span></td></tr></table> -<p>§ 212. <i>Air-Lift Pumps.</i>—An interesting and simple method of -pumping by compressed air, invented by Dr J. Pohlé of Arizona, +<p>§ 212. <i>Air-Lift Pumps.</i>—An interesting and simple method of +pumping by compressed air, invented by Dr J. Pohlé of Arizona, is likely to be very useful in certain cases. Suppose a rising main placed in a deep bore hole in which there is a considerable depth of water. Air compressed to a sufficient pressure is conveyed @@ -21099,7 +21061,7 @@ and may be advantageously used permanently when a boring is in sand or gravel which cannot be kept out of the bore hole. The initial cost is small.</p> -<p>§ 213. <i>Centrifugal Fans.</i>—Centrifugal fans are constructed +<p>§ 213. <i>Centrifugal Fans.</i>—Centrifugal fans are constructed similarly to centrifugal pumps, and are used for compressing air to pressures not exceeding 10 to 15 in. of water-column. With this small variation of pressure the variation of volume @@ -21242,7 +21204,7 @@ form of the empirical results.</p> <p><a name="ft1f" id="ft1f" href="#fa1f"><span class="fn">1</span></a> Except where other units are given, the units throughout this article are feet, pounds, pounds per sq. ft., feet per second.</p> -<p><a name="ft2f" id="ft2f" href="#fa2f"><span class="fn">2</span></a> <i>Journal de M. Liouville</i>, t. xiii. (1868); <i>Mémoires de l’Académie, +<p><a name="ft2f" id="ft2f" href="#fa2f"><span class="fn">2</span></a> <i>Journal de M. Liouville</i>, t. xiii. (1868); <i>Mémoires de l’Académie, des Sciences de l’Institut de France</i>, t. xxiii., xxiv. (1877).</p> <p><a name="ft3f" id="ft3f" href="#fa3f"><span class="fn">3</span></a> The following theorem is taken from a paper by J. H. Cotterill, @@ -21267,9 +21229,9 @@ on v<span class="su">2</span>, and the statement above is no longer true.</p> <hr class="art" /> -<p><span class="bold">HYDRAZINE<a name="ar57" id="ar57"></a></span> (<span class="sc">Diamidogen</span>), N<span class="su">2</span>H<span class="su">4</span> or H<span class="su">2</span> N·NH<span class="su">2</span>, a compound +<p><span class="bold">HYDRAZINE<a name="ar57" id="ar57"></a></span> (<span class="sc">Diamidogen</span>), N<span class="su">2</span>H<span class="su">4</span> or H<span class="su">2</span> N·NH<span class="su">2</span>, a compound of hydrogen and nitrogen, first prepared by Th. Curtius in 1887 -from diazo-acetic ester, N<span class="su">2</span>CH·CO<span class="su">2</span>C<span class="su">2</span>H<span class="su">5</span>. This ester, which is +from diazo-acetic ester, N<span class="su">2</span>CH·CO<span class="su">2</span>C<span class="su">2</span>H<span class="su">5</span>. This ester, which is obtained by the action of potassium nitrate on the hydrochloride of amidoacetic ester, yields on hydrolysis with hot concentrated potassium hydroxide an acid, which Curtius regarded as @@ -21295,23 +21257,23 @@ in the presence of benzaldehyde, which, by combining with the hydrazine, protected it from oxidation. F. Raschig (German Patent 198307, 1908) obtained good yields by oxidizing ammonia with sodium hypochlorite in solutions made viscous with glue. -Free hydrazine is a colourless liquid which boils at 113.5° C., -and solidifies about 0° C. to colourless crystals; it is heavier +Free hydrazine is a colourless liquid which boils at 113.5° C., +and solidifies about 0° C. to colourless crystals; it is heavier than water, in which it dissolves with rise of temperature. It is rapidly oxidized on exposure, is a strong reducing agent, and reacts vigorously with the halogens. Under certain conditions it may be oxidized to azoimide (A. W. Browne and F. F. Shetterly, <i>J. Amer. C.S.</i>, 1908, p. 53). By fractional distillation -of its aqueous solution hydrazine hydrate N<span class="su">2</span>H<span class="su">4</span>·H<span class="su">2</span>O -(or perhaps H<span class="su">2</span>N·NH<span class="su">3</span>OH), a strong base, is obtained, which +of its aqueous solution hydrazine hydrate N<span class="su">2</span>H<span class="su">4</span>·H<span class="su">2</span>O +(or perhaps H<span class="su">2</span>N·NH<span class="su">3</span>OH), a strong base, is obtained, which precipitates the metals from solutions of copper and silver salts at ordinary temperatures. It dissociates completely in a -vacuum at 143°, and when heated under atmospheric pressure -to 183° it decomposes into ammonia and nitrogen (A. Scott, -<i>J. Chem. Soc.</i>, 1904, 85, p. 913). The sulphate N<span class="su">2</span>H<span class="su">4</span>·H<span class="su">2</span>SO<span class="su">4</span>, +vacuum at 143°, and when heated under atmospheric pressure +to 183° it decomposes into ammonia and nitrogen (A. Scott, +<i>J. Chem. Soc.</i>, 1904, 85, p. 913). The sulphate N<span class="su">2</span>H<span class="su">4</span>·H<span class="su">2</span>SO<span class="su">4</span>, crystallizes in tables which are slightly soluble in cold water and readily soluble in hot water; it is decomposed by heating -above 250° C. with explosive evolution of gas and liberation of +above 250° C. with explosive evolution of gas and liberation of sulphur. By the addition of barium chloride to the sulphate, a solution of the hydrochloride is obtained, from which the crystallized salt may be obtained on evaporation.</p> @@ -21333,15 +21295,15 @@ by zinc dust and acetic acid to phenylhydrazine potassium sulphite. This salt is then hydrolysed by heating it with hydrochloric acid—</p> <table class="reg" summary="poem"><tr><td> <div class="poemr"> -<p>C<span class="su">6</span>H<span class="su">5</span>N<span class="su">2</span>Cl + K<span class="su">2</span>SO<span class="su">3</span> = KCl + C<span class="su">6</span>H<span class="su">5</span>N<span class="su">2</span>·SO<span class="su">3</span>K,</p> +<p>C<span class="su">6</span>H<span class="su">5</span>N<span class="su">2</span>Cl + K<span class="su">2</span>SO<span class="su">3</span> = KCl + C<span class="su">6</span>H<span class="su">5</span>N<span class="su">2</span>·SO<span class="su">3</span>K,</p> -<p>C<span class="su">6</span>H<span class="su">5</span>N<span class="su">2</span>·SO<span class="su">3</span>K + 2H = C<span class="su">6</span>H<span class="su">5</span>·NH·NH·SO<span class="su">3</span>K,</p> +<p>C<span class="su">6</span>H<span class="su">5</span>N<span class="su">2</span>·SO<span class="su">3</span>K + 2H = C<span class="su">6</span>H<span class="su">5</span>·NH·NH·SO<span class="su">3</span>K,</p> -<p>C<span class="su">6</span>H<span class="su">5</span>NH·NH·SO<span class="su">3</span>K + HCl + H<span class="su">2</span>O = C<span class="su">6</span>H<span class="su">5</span>·NH·NH<span class="su">2</span>·HCl + KHSO<span class="su">4</span>.</p> +<p>C<span class="su">6</span>H<span class="su">5</span>NH·NH·SO<span class="su">3</span>K + HCl + H<span class="su">2</span>O = C<span class="su">6</span>H<span class="su">5</span>·NH·NH<span class="su">2</span>·HCl + KHSO<span class="su">4</span>.</p> </div> </td></tr></table> <p>Phenylhydrazine is a colourless oily liquid which turns brown on -exposure. It boils at 241° C., and melts at 17.5° C. It is slightly +exposure. It boils at 241° C., and melts at 17.5° C. It is slightly soluble in water, and is strongly basic, forming well-defined salts with acids. For the detection of substances containing the carbonyl group (such for example as aldehydes and ketones) phenylhydrazine @@ -21350,9 +21312,9 @@ elimination of water and the formation of well-defined hydrazones (see <span class="sc"><a href="#artlinks">Aldehydes</a></span>, <span class="sc"><a href="#artlinks">Ketones</a></span> and <span class="sc"><a href="#artlinks">Sugars</a></span>). It is a strong reducing agent; it precipitates cuprous oxide when heated with Fehling’s solution, nitrogen and benzene being formed at the same -time—C<span class="su">6</span>H<span class="su">5</span>·NH·NH<span class="su">2</span> + 2CuO = Cu<span class="su">2</span>O + N<span class="su">2</span> + H<span class="su">2</span>O + C<span class="su">6</span>H<span class="su">5</span>. By energetic reduction +time—C<span class="su">6</span>H<span class="su">5</span>·NH·NH<span class="su">2</span> + 2CuO = Cu<span class="su">2</span>O + N<span class="su">2</span> + H<span class="su">2</span>O + C<span class="su">6</span>H<span class="su">5</span>. By energetic reduction of phenylhydrazine (<i>e.g.</i> by use of zinc dust and hydrochloric -acid), ammonia and aniline are produced—C<span class="su">6</span>H<span class="su">5</span>NH·NH<span class="su">2</span> + 2H = +acid), ammonia and aniline are produced—C<span class="su">6</span>H<span class="su">5</span>NH·NH<span class="su">2</span> + 2H = C<span class="su">6</span>H<span class="su">5</span>NH<span class="su">2</span> + NH<span class="su">3</span>. It is also a most important synthetic reagent. It combines with aceto-acetic ester to form phenylmethylpyrazolone, from which antipyrine (<i>q.v.</i>) may be obtained. Indoles (<i>q.v.</i>) are @@ -21395,7 +21357,7 @@ organic chemistry.</p> <hr class="art" /> -<p><span class="bold">HYDROCELE<a name="ar60" id="ar60"></a></span> (Gr. <span class="grk" title="hydôr">ὕδωρ</span>, water, and <span class="grk" title="kêlê">κήλη</span>, tumour), the +<p><span class="bold">HYDROCELE<a name="ar60" id="ar60"></a></span> (Gr. <span class="grk" title="hydôr">ὕδωρ</span>, water, and <span class="grk" title="kêlê">κήλη</span>, tumour), the medical term for any collection of fluid other than pus or blood in the neighbourhood of the testis or cord. The fluid is usually serous. Hydrocele may be congenital or arise in the middle-aged @@ -21412,7 +21374,7 @@ drained.</p> <hr class="art" /> -<p><span class="bold">HYDROCEPHALUS<a name="ar61" id="ar61"></a></span> (Gr. <span class="grk" title="hydôr">ὕδωρ</span>, water, and <span class="grk" title="kephalê">κεφαλὴ</span>, head), +<p><span class="bold">HYDROCEPHALUS<a name="ar61" id="ar61"></a></span> (Gr. <span class="grk" title="hydôr">ὕδωρ</span>, water, and <span class="grk" title="kephalê">κεφαλὴ</span>, head), a term applied to disease of the brain which is attended with excessive effusion of fluid into its cavities. It exists in two forms—<i>acute</i> and <i>chronic hydrocephalus</i>. Acute hydrocephalus @@ -21501,7 +21463,7 @@ plant.</td></tr> <p><span class="bold">HYDROCHARIDEAE,<a name="ar62" id="ar62"></a></span> in botany, a natural order of Monocotyledons, belonging to the series Helobieae. They are water-plants, represented in Britain by frog-bit (<i>Hydrocharis Morsusranae</i>) -and water-soldier (<i>Stratiotes aloïdes</i>). The order contains +and water-soldier (<i>Stratiotes aloïdes</i>). The order contains about fifty species in fifteen genera, twelve of which occur in fresh water while three are marine: and includes both floating and submerged forms. @@ -21518,7 +21480,7 @@ on all sides, the plant thus propagating itself on the same way as the strawberry. -<i>Stratiotes aloïdes</i> has a +<i>Stratiotes aloïdes</i> has a rosette of stiff sword-like leaves, which when the plant is in flower @@ -21649,19 +21611,19 @@ manufacture under <span class="sc"><a href="#artlinks">Alkali Manufacture</a></s <hr class="art" /> -<p><span class="bold">HYDRODYNAMICS<a name="ar64" id="ar64"></a></span> (Gr. <span class="grk" title="hydôr">ὕδωρ</span>, water, <span class="grk" title="dynamis">δύναμις</span>, strength), +<p><span class="bold">HYDRODYNAMICS<a name="ar64" id="ar64"></a></span> (Gr. <span class="grk" title="hydôr">ὕδωρ</span>, water, <span class="grk" title="dynamis">δύναμις</span>, strength), the branch of hydromechanics which discusses the motion of fluids (see <span class="sc"><a href="#artlinks">Hydromechanics</a></span>).</p> <hr class="art" /> <p><span class="bold">HYDROGEN<a name="ar65" id="ar65"></a></span> [symbol H, atomic weight 1.008 (o = 16)], one -of the chemical elements. Its name is derived from Gr. <span class="grk" title="hydôr">ὕδωρ</span>, +of the chemical elements. Its name is derived from Gr. <span class="grk" title="hydôr">ὕδωρ</span>, water, and <span class="grk" title="gennaein">γεννάειν</span>, to produce, in allusion to the fact that water is produced when the gas burns in air. Hydrogen appears to have been recognized by Paracelsus in the 16th century; the combustibility of the gas was noticed by Turquet de Mayenne -in the 17th century, whilst in 1700 N. Lémery showed that a +in the 17th century, whilst in 1700 N. Lémery showed that a mixture of hydrogen and air detonated on the application of a light. The first definite experiments concerning the nature of hydrogen were made in 1766 by H. Cavendish, who showed @@ -21689,11 +21651,11 @@ of acidulated water, by the decomposition of water by various metals or metallic hydrides, and by the action of many metals on acids or on bases. The alkali metals and alkaline earth metals decompose water at ordinary temperatures; magnesium -begins to react above 70° C., and zinc at a dull red heat. The +begins to react above 70° C., and zinc at a dull red heat. The decomposition of steam by red hot iron has been studied by H. Sainte-Claire Deville (<i>Comptes rendus</i>, 1870, 70, p. 1105) and by H. Debray (<i>ibid.</i>, 1879, 88, p. 1341), who found that at -about 1500° C. a condition of equilibrium is reached. H. Moissan +about 1500° C. a condition of equilibrium is reached. H. Moissan (<i>Bull. soc. chim.</i>, 1902, 27, p. 1141) has shown that potassium hydride decomposes cold water, with evolution of hydrogen, KH + H<span class="su">2</span>O = KOH + H<span class="su">2</span>. Calcium hydride or hydrolite, prepared @@ -21702,7 +21664,7 @@ similarly, 1 gram giving 1 litre of gas; it has been proposed as a commercial source (Prats Aymerich, <i>Abst. J.C.S.</i>, 1907, ii. p. 543), as has also aluminium turnings moistened with potassium cyanide and mercuric chloride, which decomposes water regularly -at 70°, 1 gram giving 1.3 litres of gas (Mauricheau-Beaupré, +at 70°, 1 gram giving 1.3 litres of gas (Mauricheau-Beaupré, <i>Comptes rendus</i>, 1908, 147, p. 310). Strontium hydride behaves similarly. In preparing the gas by the action of metals on acids, dilute sulphuric or hydrochloric acid is taken, and the @@ -21721,25 +21683,25 @@ by the action of superheated steam on incandescent coke (see F. Hembert and Henry, <i>Comptes rendus</i>, 1885, 101, p. 797; A. Naumann and C. Pistor, <i>Ber.</i>, 1885, 18, p. 1647), or by the electrolysis of a dilute solution of caustic soda (C. Winssinger, -<i>Chem. Zeit.</i>, 1898, 22, p. 609; “Die Elektrizitäts-Aktiengesellschaft,” +<i>Chem. Zeit.</i>, 1898, 22, p. 609; “Die Elektrizitäts-Aktiengesellschaft,” <i>Zeit. f. Elektrochem.</i>, 1901, 7, p. 857). In the latter method a 15% solution of caustic soda is used, and the electrodes are made of iron; the cell is packed in a wooden box, surrounded with sand, so that the temperature is kept -at about 70° C.; the solution is replenished, when necessary, +at about 70° C.; the solution is replenished, when necessary, with distilled water. The purity of the gas obtained is about 97%.</p> <p>Pure hydrogen is a tasteless, colourless and odourless gas of specific gravity 0.06947 (air = 1) (Lord Rayleigh, <i>Proc. Roy. Soc.</i>, -1893, p. 319). It may be liquefied, the liquid boiling at −252.68° -C. to −252.84° C., and it has also been solidified, the solid melting -at −264° C. (J. Dewar, <i>Comptes rendus</i>, 1899, 129, p. 451; +1893, p. 319). It may be liquefied, the liquid boiling at −252.68° +C. to −252.84° C., and it has also been solidified, the solid melting +at −264° C. (J. Dewar, <i>Comptes rendus</i>, 1899, 129, p. 451; <i>Chem. News</i>, 1901, 84, p. 49; see also <span class="sc"><a href="#artlinks">Liquid Gases</a></span>). The specific heat of gaseous hydrogen (at constant pressure) is 3.4041 (water = 1), and the ratio of the specific heat at constant pressure to the specific heat at constant volume is 1.3852 (W. C. -Röntgen, <i>Pogg. Ann.</i>, 1873, 148, p. 580). On the spectrum see +Röntgen, <i>Pogg. Ann.</i>, 1873, 148, p. 580). On the spectrum see <span class="sc"><a href="#artlinks">Spectroscopy</a></span>. Hydrogen is only very slightly soluble in water. It diffuses very rapidly through a porous membrane, and through some metals at a red heat (T. Graham, <i>Proc. Roy. Soc.</i>, 1867, 15, @@ -21762,7 +21724,7 @@ shown that perfectly dry hydrogen will not unite with perfectly dry oxygen. Hydrogen combines with fluorine, even at very low temperatures, with great violence; it also combines with carbon, at the temperature of the electric arc. The alkali metals when -warmed in a current of hydrogen, at about 360° C., form hydrides +warmed in a current of hydrogen, at about 360° C., form hydrides of composition RH (R = Na, K, Rb, Cs), (H. Moissan, <i>Bull. soc. chim.</i>, 1902, 27, p. 1141); calcium and strontium similarly form hydrides CaH<span class="su">2</span>, SrH<span class="su">2</span> at a dull red heat (A. Guntz, <i>Comptes @@ -21787,7 +21749,7 @@ namely, water (<i>q.v.</i>), H<span class="su">2</span>O, and hydrogen peroxide, H<span class="su">2</span>O<span class="su">2</span>, whilst the existence of a third oxide, ozonic acid, has been indicated.</p> -<p><i>Hydrogen peroxide</i>, H<span class="su">2</span>O<span class="su">2</span>, was discovered by L. J. Thénard in +<p><i>Hydrogen peroxide</i>, H<span class="su">2</span>O<span class="su">2</span>, was discovered by L. J. Thénard in 1818 (<i>Ann. chim. phys.</i>, 8, p. 306). It occurs in small quantities in the atmosphere. It may be prepared by passing a current of carbon dioxide through ice-cold water, to which small quantities @@ -21811,7 +21773,7 @@ added until a faint permanent white precipitate of hydrated barium peroxide appears; the solution is now filtered, and a concentrated solution of baryta water is added to the filtrate, when a crystalline precipitate of hydrated barium peroxide, -BaO<span class="su">2</span>·H<span class="su">2</span>O, is thrown down. This is filtered off and well washed +BaO<span class="su">2</span>·H<span class="su">2</span>O, is thrown down. This is filtered off and well washed with water. The above methods give a dilute aqueous solution of hydrogen peroxide, which may be concentrated somewhat by evaporation over sulphuric acid in vacuo. H. P. Talbot and @@ -21846,18 +21808,18 @@ sulphuric acid (M. Berthelot, <i>Comptes rendus</i>, 1878, 86, p. 71).</p> <p>The anhydrous hydrogen peroxide obtained by Wolffenstein -boils at 84-85°C. (68 mm.); its specific gravity is 1.4996 (1.5° C.). +boils at 84-85°C. (68 mm.); its specific gravity is 1.4996 (1.5° C.). It is very explosive (W. Spring, <i>Zeit. anorg. Chem.</i>, 1895, 8, p. 424). The explosion risk seems to be most marked in the preparations which have been extracted with ether previous to -distillation, and J. W. Brühl (<i>Ber.</i>, 1895, 28, p. 2847) is of opinion +distillation, and J. W. Brühl (<i>Ber.</i>, 1895, 28, p. 2847) is of opinion that a very unstable, more highly oxidized product is produced in small quantity in the process. The solid variety prepared by -Staedel forms colourless, prismatic crystals which melt at −2° C.; +Staedel forms colourless, prismatic crystals which melt at −2° C.; it is decomposed with explosive violence by platinum sponge, and traces of manganese dioxide. The dilute aqueous solution is very unstable, giving up oxygen readily, and decomposing with -explosive violence at 100° C. An aqueous solution containing +explosive violence at 100° C. An aqueous solution containing more than 1.5% hydrogen peroxide reacts slightly acid. Towards lupetidin [aa′ dimethyl piperidine, C<span class="su">5</span>H<span class="su">9</span>N(CH<span class="su">3</span>)<span class="su">2</span>] hydrogen peroxide acts as a dibasic acid (A. Marcuse and R. Wolffenstein, @@ -21870,7 +21832,7 @@ behaves very frequently as a powerful oxidizing agent; thus lead sulphide is converted into lead sulphate in presence of a dilute aqueous solution of the peroxide, the hydroxides of the alkaline earth metals are converted into peroxides of the type -MO<span class="su">2</span>·8H<span class="su">2</span>O, titanium dioxide is converted into the trioxide, +MO<span class="su">2</span>·8H<span class="su">2</span>O, titanium dioxide is converted into the trioxide, iodine is liberated from potassium iodide, and nitrites (in alkaline solution) are converted into acid-amides (B. Radziszewski, <i>Ber.</i>, 1884, 17, p. 355). In many cases it is found that hydrogen @@ -21902,9 +21864,9 @@ hydrobromic and hydriodic acids (S. Tanatar, <i>Ber.</i>, 1899, 32, p. 1013).</p> <div class="condensed"> -<p>On the constitution of hydrogen peroxide see C. F. Schönbein, +<p>On the constitution of hydrogen peroxide see C. F. Schönbein, <i>Jour. prak. Chem.</i>, 1858-1868; M. Traube, <i>Ber.</i>, 1882-1889; J. W. -Brühl, <i>Ber.</i>, 1895, 28, p. 2847; 1900, 33, p. 1709; S. Tanatar, <i>Ber.</i>, +Brühl, <i>Ber.</i>, 1895, 28, p. 2847; 1900, 33, p. 1709; S. Tanatar, <i>Ber.</i>, 1903, 36, p. 1893.</p> <p>Hydrogen peroxide finds application as a bleaching agent, as an @@ -21916,7 +21878,7 @@ acid solution; with potassium ferricyanide in alkaline solution, 2K<span class="su">3</span>Fe(CN)<span class="su">6</span> + 2KOH + H<span class="su">2</span>O<span class="su">2</span> = 2K<span class="su">4</span>Fe(CN)<span class="su">6</span> + 2H<span class="su">2</span>O + O<span class="su">2</span>; or by oxidizing arsenious acid in alkaline solution with the peroxide and back titration of the excess of arsenious acid with standard iodine -(B. Grützner, <i>Arch. der Pharm.</i>, 1899, 237, p. 705). It may be +(B. Grützner, <i>Arch. der Pharm.</i>, 1899, 237, p. 705). It may be recognized by the violet coloration it gives when added to a very dilute solution of potassium bichromate in the presence of hydrochloric acid; by the orange-red colour it gives with a solution of @@ -21933,7 +21895,7 @@ acid, produced according to the reaction O<span class="su">3</span> + H<span cla <hr class="art" /> -<p><span class="bold">HYDROGRAPHY<a name="ar66" id="ar66"></a></span> (Gr. <span class="grk" title="hydôr">ὕδωρ</span>, water, and <span class="grk" title="graphein">γράφειν</span>, to write), +<p><span class="bold">HYDROGRAPHY<a name="ar66" id="ar66"></a></span> (Gr. <span class="grk" title="hydôr">ὕδωρ</span>, water, and <span class="grk" title="graphein">γράφειν</span>, 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 @@ -21949,9 +21911,9 @@ the admiralty (see <span class="sc"><a href="#artlinks">Chart</a></span>).</p> <hr class="art" /> -<p><span class="bold">HYDROLYSIS<a name="ar67" id="ar67"></a></span> (Gr. <span class="grk" title="hydôr">ὕδωρ</span>, water, <span class="grk" title="luein">λύειν</span>, to loosen), in chemistry, +<p><span class="bold">HYDROLYSIS<a name="ar67" id="ar67"></a></span> (Gr. <span class="grk" title="hydôr">ὕδωρ</span>, water, <span class="grk" title="luein">λύειν</span>, to loosen), in chemistry, a decomposition brought about by water after the manner shown -in the equation R·X + H·OH = R·H + X·OH. Modern research +in the equation R·X + H·OH = R·H + X·OH. Modern research has proved that such reactions are not occasioned by water acting as H<span class="su">2</span>O, but really by its ions (hydrions and hydroxidions), for the velocity is proportional (in accordance with the law of @@ -21965,382 +21927,7 @@ glyceryl esters of organic acids, into glycerin and a soap (see <hr class="art" /> - - - - - - - -<pre> - - - - - -End of the Project Gutenberg EBook of Encyclopaedia Britannica, 11th -Edition, Volume 14, Slice 1, by Various - -*** END OF THIS PROJECT GUTENBERG EBOOK ENCYC. 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