book did

not attract during his lifetime so much attention as it deserved. Happily for science Hutton numbered among his friends John Playfair (q.v.), professor of mathematics in the university of Edinburgh, whose enthusiasm for the spread of Hutton's doctrine was combined with a rare gift of graceful and luminous exposition. Five years after Hutton's death he published a volume, _Illustrations of the Huttonian Theory of the Earth_, in which he gave an admirable summary of that theory, with numerous additional illustrations and arguments. This work is justly regarded as one of the classical contributions to geological literature. To its influence much of the sound progress of British geology must be ascribed. In the year 1805 a biographical account of Hutton, written by Playfair, was published in vol. v. of the _Transactions of the Royal Society of Edinburgh_. (A. Ge.)

HUTTON, RICHARD HOLT (1826-1897), English writer and theologian, son of Joseph Hutton, Unitarian minister at Leeds, was born at Leeds on the 2nd of June 1826. His family removed to London in 1835, and he was educated at University College School and University College, where he began a lifelong friendship with Walter Bagehot, of whose works he afterwards was the editor; he took the degree in 1845, being awarded the gold medal for philosophy. Meanwhile he had also studied for short periods at Heidelberg and Berlin, and in 1847 he entered Manchester New College with the idea of becoming a minister like his father, and studied there under James Martineau. He did not, however, succeed in obtaining a call to any church, and for some little time his future was unsettled. He married in 1851 his cousin, Anne Roscoe, and became joint-editor with J. L. Sanford of the _Inquirer_, the principal Unitarian organ. But his innovations and his unconventional views about stereotyped Unitarian doctrines caused alarm, and in 1853 he resigned. His health had broken down, and he visited the West Indies, where his wife died of yellow fever. In 1855 Hutton and Bagehot became joint-editors of the _National Review_, a new monthly, and conducted it for ten years. During this time Hutton's theological views, influenced largely by Coleridge, and more directly by F. W. Robertson and F. D. Maurice, gradually approached more and more to those of the Church of England, which he ultimately joined. His interest in theology was profound, and he brought to it a spirituality of outlook and an aptitude for metaphysical inquiry and exposition which added a singular attraction to his writings. In 1861 he joined Meredith Townsend as joint-editor and part proprietor of the _Spectator_, then a well-known liberal weekly, which, however, was not remunerative from the business point of view. Hutton took charge of the literary side of the paper, and by degrees his own articles became and remained up to the last one of the best-known features of serious and thoughtful English journalism. The _Spectator_, which gradually became a prosperous property, was his pulpit, in which unwearyingly he gave expression to his views, particularly on literary, religious and philosophical subjects, in opposition to the agnostic and rationalistic opinions then current in intellectual circles, as popularized by Huxley. A man of fearless honesty, quick and catholic sympathies, broad culture, and many friends in intellectual and religious circles, he became one of the most influential journalists of the day, his fine character and conscience earning universal respect and confidence. He was an original member of the Metaphysical Society (1869). He was an anti-vivisectionist, and a member of the royal commission (1875) on that subject. In 1858 he had married Eliza Roscoe, a cousin of his first wife; she died early in 1897, and Hutton's own death followed on the 9th of September of the same year.

Among his other publications may be mentioned _Essays, Theological and Literary_ (1871; revised 1888), and _Criticisms on Contemporary Thought and Thinkers_ (1894); and his opinions may be studied compendiously in the selections from his _Spectator_ articles published in 1899 under the title of _Aspects of Religious and Scientific Thought_.

HUXLEY, THOMAS HENRY (1825-1895), English biologist, was born on the 4th of May 1825 at Ealing, where his father, George Huxley, was senior assistant-master in the school of Dr Nicholas. This was an establishment of repute, and is at any rate remarkable for having produced two men with so little in common in after life as Huxley and Cardinal Newman. The cardinal's brother, Francis William, had been "captain" of the school in 1821. Huxley was a seventh child (as his father had also been), and the youngest who survived infancy. Of Huxley's ancestry no more is ascertainable than in the case of most middle-class families. He himself thought it sprang from the Cheshire Huxleys of Huxley Hall. Different branches migrated south, one, now extinct, reaching London, where its members were apparently engaged in commerce. They established themselves for four generations at Wyre Hall, near Edmonton, and one was knighted by Charles II. Huxley describes his paternal race as "mainly Iberian mongrels, with a good dash of Norman and a little Saxon."[1] From his father he thought he derived little except a quick temper and the artistic faculty which proved of great service to him and reappeared in an even more striking degree in his daughter, the Hon. Mrs Collier. "Mentally and physically," he wrote, "I am a piece of my mother." Her maiden name was Rachel Withers. "She came of Wiltshire people," he adds, and describes her as "a typical example of the Iberian variety." He tells us that "her most distinguishing characteristic was rapidity of thought.... That peculiarity has been passed on to me in full strength" (_Essays_, i. 4). One of the not least striking facts in Huxley's life is that of education in the formal sense he received none. "I had two years of a pandemonium of a school (between eight and ten), and after that neither help nor sympathy in any intellectual direction till I reached manhood" (_Life_, ii. 145). After the death of Dr Nicholas the Ealing school broke up, and Huxley's father returned about 1835 to his native town, Coventry, where he had obtained a small appointment. Huxley was left to his own devices; few histories of boyhood could offer any parallel. At twelve he was sitting up in bed to read Hutton's _Geology_. His great desire was to be a mechanical engineer; it ended in his devotion to "the mechanical engineering of living machines." His curiosity in this direction was nearly fatal; a _post-mortem_ he was taken to between thirteen and fourteen was followed by an illness which seems to have been the starting-point of the ill-health which pursued him all through life. At fifteen he devoured Sir William Hamilton's _Logic_, and thus acquired the taste for metaphysics, which he cultivated to the end. At seventeen he came under the influence of Thomas Carlyle's writings. Fifty years later he wrote: "To make things clear and get rid of cant and shows of all sorts. This was the lesson I learnt from Carlyle's books when I was a boy, and it has stuck by me all my life" (_Life_, ii. 268). Incidentally they led him to begin to learn German; he had already acquired French. At seventeen Huxley, with his elder brother James, commenced regular medical studies at Charing Cross Hospital, where they had both obtained scholarships. He studied under Wharton Jones, a physiologist who never seems to have attained the reputation he deserved. Huxley said of him: "I do not know that I ever felt so much respect for a teacher before or since" (_Life_, i. 20). At twenty he passed his first M.B. examination at the University of London, winning the gold medal for anatomy and physiology; W. H. Ransom, the well-known Nottingham physician, obtaining the exhibition. In 1845 he published, at the suggestion of Wharton Jones, his first scientific paper, demonstrating the existence of a hitherto unrecognized layer in the inner sheath of hairs, a layer that has been known since as "Huxley's layer."

Something had to be done for a livelihood, and at the suggestion of a fellow-student, Mr (afterwards Sir Joseph) Fayrer, he applied for an appointment in the navy. He passed the necessary examination, and at the same time obtained the qualification of the Royal College of Surgeons. He was "entered on the books of Nelson's old ship, the 'Victory,' for duty at Haslar Hospital." Its chief, Sir John Richardson, who was a well-known Arctic explorer and naturalist, recognized Huxley's ability, and procured for him the post of surgeon to H.M.S. "Rattlesnake," about to start for surveying work in Torres Strait. The commander, Captain Owen Stanley, was a son of the bishop of Norwich and brother of Dean Stanley, and wished for an officer with some scientific knowledge. Besides Huxley the "Rattlesnake" also carried a naturalist by profession, John Macgillivray, who, however, beyond a dull narrative of the expedition, accomplished nothing. The "Rattlesnake" left England on the 3rd of December 1846, and was ordered home after the lamented death of Captain Stanley at Sydney, to be paid off at Chatham on the 9th of November 1850. The tropical seas teem with delicate surface-life, and to the study of this Huxley devoted himself with unremitting devotion. At that time no known methods existed by which it could be preserved for study in museums at home. He gathered a magnificent harvest in the almost unreaped field, and the conclusions he drew from it were the beginning of the revolution in zoological science which he lived to see accomplished.

Baron Cuvier (1769-1832), whose classification still held its ground, had divided the animal kingdom into four great _embranchements_. Each of these corresponded to an independent archetype, of which the "idea" had existed in the mind of the Creator. There was no other connexion between these classes, and the "ideas" which animated them were, as far as one can see, arbitrary. Cuvier's groups, without their theoretical basis, were accepted by K. E. von Baer (1792-1876). The "idea" of the group, or archetype, admitted of endless variation within it; but this was subordinate to essential conformity with the archetype, and hence Cuvier deduced the important principle of the "correlation of parts," of which he made such conspicuous use in palaeontological reconstruction. Meanwhile the "Naturphilosophen," with J. W. Goethe (1749-1832) and L. Oken (1779-1851), had in effect grasped the underlying principle of correlation, and so far anticipated evolution by asserting the possibility of deriving specialized from simpler structures. Though they were still hampered by idealistic conceptions, they established morphology. Cuvier's four great groups were Vertebrata, Mollusca, Articulata and Radiata. It was amongst the members of the last class that Huxley found most material ready to his hand in the seas of the tropics. It included organisms of the most varied kind, with nothing more in common than that their parts were more or less distributed round a centre. Huxley sent home "communication after communication to the Linnean Society," then a somewhat somnolent body, "with the same result as that obtained by Noah when he sent the raven out of the ark" (_Essays_, i. 13). His important paper, _On the Anatomy and the Affinities of the Family of Medusae_, met with a better fate. It was communicated by the bishop of Norwich to the Royal Society, and printed by it in the _Philosophical Transactions_ in 1849. Huxley united, with the Medusae, the Hydroid and Sertularian polyps, to form a class to which he subsequently gave the name of Hydrozoa. This alone was no inconsiderable feat for a young surgeon who had only had the training of the medical school. But the ground on which it was done has led to far-reaching theoretical developments. Huxley realized that something more than superficial characters were necessary in determining the affinities of animal organisms. He found that all the members of the class consisted of two membranes enclosing a central cavity or stomach. This is characteristic of what are now called the Coelenterata. All animals higher than these have been termed Coelomata; they possess a distinct body-cavity in addition to the stomach. Huxley went further than this, and the most profound suggestion in his paper is the comparison of the two layers with those which appear in the germ of the higher animals. The consequences which have flowed from this prophetic generalization of the _ectoderm_ and _endoderm_ are familiar to every student of evolution. The conclusion was the more remarkable as at the time he was not merely free from any evolutionary belief, but actually rejected it. The value of Huxley's work was immediately recognized. On returning to England in 1850 he was elected a Fellow of the Royal Society. In the following year, at the age of twenty-six, he not merely received the Royal medal, but was elected on the council. With absolutely no aid from any one he had placed himself in the front rank of English scientific men. He secured the friendship of Sir J. D. Hooker and John Tyndall, who remained his lifelong friends. The Admiralty retained him as a nominal assistant-surgeon, in order that he might work up the observations he had made during the voyage of the "Rattlesnake." He was thus enabled to produce various important memoirs, especially those on certain Ascidians, in which he solved the problem of _Appendicularia_--an organism whose place in the animal kingdom Johannes Müller had found himself wholly unable to assign--and on the morphology of the Cephalous Mollusca.

Richard Owen, then the leading comparative anatomist in Great Britain, was a disciple of Cuvier, and adopted largely from him the deductive explanation of anatomical fact from idealistic conceptions. He superadded the evolutionary theories of Oken, which were equally idealistic, but were altogether repugnant to Cuvier. Huxley would have none of either. Imbued with the methods of von Baer and Johannes Müller, his methods were purely inductive. He would not hazard any statement beyond what the facts revealed. He retained, however, as has been done by his successors, the use of archetypes, though they no longer represented fundamental "ideas" but generalizations of the essential points of structure common to the individuals of each class. He had not wholly freed himself, however, from archetypal trammels. "The doctrine," he says, "that every natural group is organized after a definite archetype ... seems to me as important for zoology as the doctrine of definite proportions for chemistry." This was in 1853. He further stated: "There is no progression from a lower to a higher type, but merely a more or less complete evolution of one type" (_Phil. Trans._, 1853, p. 63). As Chalmers Mitchell points out, this statement is of great historical interest. Huxley definitely uses the word "evolution," and admits its existence _within_ the great groups. He had not, however, rid himself of the notion that the archetype was a property inherent in the group. Herbert Spencer, whose acquaintance he made in 1852, was unable to convert him to evolution in its widest sense (_Life_, i. 168). He could not bring himself to acceptance of the theory--owing, no doubt, to his rooted aversion from à priori reasoning--without a mechanical conception of its mode of operation. In his first interview with Darwin, which seems to have been about the same time, he expressed his belief "in the sharpness of the lines of demarcation between natural groups," and was received with a humorous smile (_Life_, i. 169).

The naval medical service exists for practical purposes. It is not surprising, therefore, that after his three years' nominal employment Huxley was ordered on active service. Though without private means of any kind, he resigned. The navy, however, retains the credit of having started his scientific career as well as that of Hooker and Darwin. Huxley was now thrown on his own resources, the immediate prospects of which were slender enough. As a matter of fact, he had not to wait many months. His friend, Edward Forbes, was appointed to the chair of natural history in Edinburgh, and in July 1854 he succeeded him as lecturer at the School of Mines and as naturalist to the Geological Survey in the following year. The latter post he hesitated at first to accept, as he "did not care for fossils" (_Essays_, i. 15). In 1855 he married Miss H. A. Heathorn, whose acquaintance he had made in Sydney. They were engaged when Huxley could offer nothing but the future promise of his ability. The confidence of his devoted helpmate was not misplaced, and her affection sustained him to the end, after she had seen him the recipient of every honour which English science could bestow. His most important research belonging to this period was the Croonian Lecture delivered before the Royal Society in 1858 on "The Theory of the Vertebrate Skull." In this he completely and finally demolished, by applying as before the inductive method, the idealistic, if in some degree evolutionary, views of its origin which Owen had derived from Goethe and Oken. This finally disposed of the "archetype," and may be said once for all to have liberated the English anatomical school from the deductive method.

In 1859 _The Origin of Species_ was published. This was a momentous event in the history of science, and not least for Huxley. Hitherto he had turned a deaf ear to evolution. "I took my stand," he says, "upon two grounds: firstly, that ... the evidence in favour of transmutation was wholly insufficient; and secondly, that no suggestion respecting the causes of the transmutation assumed, which had been made, was in any way adequate to explain the phenomena" (_Life_, i. 168). Huxley had studied Lamarck "attentively," but to no purpose. Sir Charles Lyell "was the chief agent in smoothing the road for Darwin. For consistent uniformitarianism postulates evolution as much in the organic as in the inorganic world" (l.c.); and Huxley found in Darwin what he had failed to find in Lamarck, an intelligible hypothesis good enough as a working basis. Yet with the transparent candour which was characteristic of him, he never to the end of his life concealed the fact that he thought it wanting in rigorous proof. Darwin, however, was a naturalist; Huxley was not. He says: "I am afraid there is very little of the genuine naturalist in me. I never collected anything, and species-work was always a burden to me; what I cared for was the architectural and engineering part of the business" (_Essays_, i. 7). But the solution of the problem of organic evolution must work upwards from the initial stages, and it is precisely for the study of these that "species-work" is necessary. Darwin, by observing the peculiarities in the distribution of the plants which he had collected in the Galapagos, was started on the path that led to his theory. Anatomical research had only so far led to transcendental hypothesis, though in Huxley's hands it had cleared the decks of that lumber. He quotes with approval Darwin's remark that "no one has a right to examine the question of species who has not minutely described many" (_Essays_, ii. 283). The rigorous proof which Huxley demanded was the production of species sterile to one another by selective breeding (_Life_, i. 193). But this was a misconception of the question. Sterility is a physiological character, and the specific differences which the theory undertook to account for are morphological; there is no necessary nexus between the two. Huxley, however, felt that he had at last a secure grip of evolution. He warned Darwin: "I will stop at no point as long as clear reasoning will carry me further" (_Life_, i. 172). Owen, who had some evolutionary tendencies, was at first favourably disposed to Darwin's theory, and even claimed that he had to some extent anticipated it in his own writings. But Darwin, though he did not thrust it into the foreground, never flinched from recognizing that man could not be excluded from his theory. "Light will be thrown on the origin of man and his history" (_Origin_, ed. i. 488). Owen could not face the wrath of fashionable orthodoxy. In his Rede Lecture he endeavoured to save the position by asserting that man was clearly marked off from all other animals by the anatomical structure of his brain. This was actually inconsistent with known facts, and was effectually refuted by Huxley in various papers and lectures, summed up in 1863 in _Man's Place in Nature_. This "monkey damnification" of mankind was too much even for the "veracity" of Carlyle, who is said to have never forgiven it. Huxley had not the smallest respect for authority as a basis for belief, scientific or otherwise. He held that scientific men were morally bound "to try all things and hold fast to that which is good" (_Life_, ii. 161). Called upon in 1862, in the absence of the president, to deliver the presidential address to the Geological Society, he disposed once for all of one of the principles accepted by geologists, that similar fossils in distinct regions indicated that the strata containing them were contemporary. All that could be concluded, he pointed out, was that the general order of succession was the same. In 1854 Huxley had refused the post of palaeontologist to the Geological Survey; but the fossils for which he then said that he "did not care" soon acquired importance in his eyes, as supplying evidence for the support of the evolutionary theory. The thirty-one years during which he occupied the chair of natural history at the School of Mines were largely occupied with palaeontological research. Numerous memoirs on fossil fishes established many far-reaching morphological facts. The study of fossil reptiles led to his demonstrating, in the course of lectures on birds, delivered at the College of Surgeons in 1867, the fundamental affinity of the two groups which he united under the title of Sauropsida. An incidental result of the same course was his proposed rearrangement of the zoological regions into which P. L. Sclater had divided the world in 1857. Huxley anticipated, to a large extent, the results at which botanists have since arrived: he proposed as primary divisions, Arctogaea--to include the land areas of the northern hemisphere--and Notogaea for the remainder. Successive waves of life originated in and spread from the northern area, the survivors of the more ancient types finding successively a refuge in the south. Though Huxley had accepted the Darwinian theory as a working hypothesis, he never succeeded in firmly grasping it in detail. He thought "evolution might conceivably have taken place without the development of groups possessing the characters of species" (_Essays_, v. 41). His palaeontological researches ultimately led him to dispense with Darwin. In 1892 he wrote: "The doctrine of evolution is no speculation, but a generalization of certain facts ... classed by biologists under the heads of Embryology and of Palaeontology" (_Essays_, v. 42). Earlier in 1881 he had asserted even more emphatically that if the hypothesis of evolution "had not existed, the palaeontologist would have had to invent it" (_Essays_, iv. 44).

From 1870 onwards he was more and more drawn away from scientific research by the claims of public duty. Some men yield the more readily to such demands, as their fulfilment is not unaccompanied by public esteem. But he felt, as he himself said of Joseph Priestley, "that he was a man and a citizen before he was a philosopher, and that the duties of the two former positions are at least as imperative as those of the latter" (_Essays_, iii. 13). From 1862 to 1884 he served on no less than ten Royal Commissions, dealing in every case with subjects of great importance, and in many with matters of the gravest moment to the community. He held and filled with invariable dignity and distinction more public positions than have perhaps ever fallen to the lot of a scientific man in England. From 1871 to 1880 he was a secretary of the Royal Society. From 1881 to 1885 he was president. For honours he cared little, though they were within his reach; it is said that he might have received a peerage. He accepted, however, in 1892, a Privy Councillorship, at once the most democratic and the most aristocratic honour accessible to an English citizen. In 1870 he was president of the British Association at Liverpool, and in the same year was elected a member of the newly constituted London School Board. He resigned the latter position in 1872, but in the brief period during which he acted, probably more than any man, he left his mark on the foundations of national elementary education. He made war on the scholastic methods which wearied the mind in merely taxing the memory; the children were to be prepared to take their place worthily in the community. Physical training was the basis; domestic economy, at any rate for girls, was insisted upon, and for all some development of the aesthetic sense by means of drawing and singing. Reading, writing and arithmetic were the indispensable tools for acquiring knowledge, and intellectual discipline was to be gained through the rudiments of physical science. He insisted on the teaching of the Bible partly as a great literary heritage, partly because he was "seriously perplexed to know by what practical measures the religious feeling, which is the essential basis of conduct, was to be kept up, in the present utterly chaotic state of opinion in these matters, without its use" (_Essays_, iii. 397). In 1872 the School of Mines was moved to South Kensington, and Huxley had, for the first time after eighteen years, those appliances for teaching beyond the lecture room, which to the lasting injury of the interests of biological science in Great Britain had been withheld from him by the short-sightedness of government. Huxley had only been able to bring his influence to bear upon his pupils by oral teaching, and had had no opportunity by personal intercourse in the laboratory of forming a school. He was now able to organize a system of instruction for classes of elementary teachers in the general principles of biology, which indirectly affected the teaching of the subject throughout the country.

The first symptoms of physical failure to meet the strain of the scientific and public duties demanded of him made some rest imperative, and he took a long holiday in Egypt. He still continued for some years to occupy himself mainly with vertebrate morphology. But he seemed to find more interest and the necessary mental stimulus to exertion in lectures, public addresses and more or less controversial writings. His health, which had for a time been fairly restored, completely broke down again in 1885. In 1890 he removed from London to Eastbourne, where after a painful illness he died on the 29th of June 1895.

The latter years of Huxley's life were mainly occupied with contributions to periodical literature on subjects connected with philosophy and theology. The effect produced by these on popular opinion was profound. This was partly due to his position as a man of science, partly to his obvious earnestness and sincerity, but in the main to his strenuous and attractive method of exposition. Such studies were not wholly new to him, as they had more or less engaged his thoughts from his earliest days. That his views exhibit some process of development and are not wholly consistent was, therefore, to be expected, and for this reason it is not easy to summarize them as a connected body of teaching. They may be found perhaps in their most systematic form in the volume on _Hume_ published in 1879.

Huxley's general attitude to the problems of theology and philosophy was technically that of scepticism. "I am," he wrote, "too much of a sceptic to deny the possibility of anything" (_Life_, ii. 127). "Doubt is a beneficent demon" (_Essays_, ix. 56). He was anxious, nevertheless, to avoid the accusation of Pyrrhonism (_Life_, ii. 280), but the Agnosticism which he defined to express his position in 1869 suggests the Pyrrhonist _Aphasia_. The only approach to certainty which he admitted lay in the order of nature. "The conception of the constancy of the order of nature has become the dominant idea of modern thought.... Whatever may be man's speculative doctrines, it is quite certain that every intelligent person guides his life and risks his fortune upon the belief that the order of nature is constant, and that the chain of natural causation is never broken." He adds, however, that "it by no means necessarily follows that we are justified in expanding this generalization into the infinite past" (_Essays_, iv. 47, 48). This was little more than a pious reservation, as evolution implies the principle of continuity (l.c. p. 55). Later he stated his belief even more absolutely: "If there is anything in the world which I do firmly believe in, it is the universal validity of the law of causation, but that universality cannot be proved by any amount of experience" (_Essays_, ix. 121). The assertion that "There is only one method by which intellectual truth can be reached, whether the subject-matter of investigation belongs to the world of physics or to the world of consciousness" (_Essays_, ix. 126) laid him open to the charge of materialism, which he vigorously repelled. His defence, when he rested it on the imperfection of the physical analysis of matter and force (l.c. p. 131), was irrelevant; he was on sounder ground when he contended with Berkeley "that our certain knowledge does not extend beyond our states of consciousness" (l.c. p. 130). "Legitimate materialism, that is, the extension of the conceptions and of the methods of physical science to the highest as well as to the lowest phenomena of vitality, is neither more nor less than a sort of shorthand idealism" (_Essays_, i. 194). While "the substance of matter is a metaphysical unknown quality of the existence of which there is no proof ... the non-existence of a substance of mind is equally arguable; ... the result ... is the reduction of the All to co-existences and sequences of phenomena beneath and beyond which there is nothing cognoscible" (_Essays_, ix. 66). Hume had defined a miracle as a "violation of the laws of nature." Huxley refused to accept this. While, on the one hand, he insists that "the whole fabric of practical life is built upon our faith in its continuity" (_Hume_, p. 129), on the other "nobody can presume to say what the order of nature must be"; this "knocks the bottom out of all a priori objections either to ordinary 'miracles' or to the efficacy of prayer" (_Essays_, v. 133). "If by the term miracles we mean only extremely wonderful events, there can be no just ground for denying the possibility of their occurrence" (_Hume_, p. 134). Assuming the chemical elements to be aggregates of uniform primitive matter, he saw no more theoretical difficulty in water being turned into alcohol in the miracle at Cana, than in sugar undergoing a similar conversion (_Essays_, v. 81). The credibility of miracles with Huxley is a question of evidence. It may be remarked that a scientific explanation is destructive of the supernatural character of a miracle, and that the demand for evidence may be so framed as to preclude the credibility of any historical event. Throughout his life theology had a strong attraction, not without elements of repulsion, for Huxley. The circumstances of his early training, when Paley was the "most interesting Sunday reading allowed him when a boy" (_Life_, ii. 57), probably had something to do with both. In 1860 his beliefs were apparently theistic: "Science seems to me to teach in the highest and strongest manner the great truth which is embodied in the Christian conception of entire surrender to the will of God" (_Life_, i. 219). In 1885 he formulates "the perfect ideal of religion" in a passage which has become almost famous: "In the 8th century B.C. in the heart of a world of idolatrous polytheists, the Hebrew prophets put forth a conception of religion which appears to be as wonderful an inspiration of genius as the art of Pheidias or the science of Aristotle. 'And what doth the Lord require of thee, but to do justly, and to love mercy, and to walk humbly with thy God'" (_Essays_, iv. 161). Two years later he was writing: "That there is no evidence of the existence of such a being as the God of the theologians is true enough" (_Life_, ii. 162). He insisted, however, that "atheism is on purely philosophical grounds untenable" (l.c.). His theism never really advanced beyond the recognition of "the passionless impersonality of the unknown and unknowable, which science shows everywhere underlying the thin veil of phenomena" (_Life_, i. 239). In other respects his personal creed was a kind of scientific Calvinism. There is an interesting passage in an essay written in 1892, "An Apologetic Eirenicon," which has not been republished, which illustrates this: "It is the secret of the superiority of the best theological teachers to the majority of their opponents that they substantially recognize these realities of things, however strange the forms in which they clothe their conceptions. The doctrines of predestination, of original sin, of the innate depravity of man and the evil fate of the greater part of the race, of the primacy of Satan in this world, of the essential vileness of matter, of a malevolent Demiurgus subordinate to a benevolent Almighty, who has only lately revealed himself, faulty as they are, appear to me to be vastly nearer the truth than the 'liberal' popular illusions that babies are all born good, and that the example of a corrupt society is responsible for their failure to remain so; that it is given to everybody to reach the ethical ideal if he will only try; that all partial evil is universal good, and other optimistic figments, such as that which represents 'Providence' under the guise of a paternal philanthropist, and bids us believe that everything will come right (according to our notions) at last." But his "slender definite creed," R. H. Hutton, who was associated with him in the Metaphysical Society, thought--and no doubt rightly--in no respect "represented the cravings of his larger nature."

From 1880 onwards till the very end of his life, Huxley was continuously occupied in a controversial campaign against orthodox beliefs. As Professor W. F. R. Weldon justly said of his earlier polemics: "They were certainly among the principal agents in winning a larger measure of toleration for the critical examination of fundamental beliefs, and for the free expression of honest reverent doubt." He threw Christianity overboard bodily and with little appreciation of its historic effect as a civilizing agency. He thought that "the exact nature of the teachings and the convictions of Jesus is extremely uncertain" (_Essays_, v. 348). "What we are usually pleased to call religion nowadays is, for the most part, Hellenized Judaism" (_Essays_, iv. 162). His final analysis of what "since the second century, has assumed to itself the title of Orthodox Christianity" is a "varying compound of some of the best and some of the worst elements of Paganism and Judaism, moulded in practice by the innate character of certain people of the Western world" (_Essays_, v. 142). He concludes "That this Christianity is doomed to fall is, to my mind, beyond a doubt; but its fall will neither be sudden nor speedy" (l.c.). He did not omit, however, to do justice to "the bright side of Christianity," and was deeply impressed with the life of Catherine of Siena. Failing Christianity, he thought that some other "hypostasis of men's hopes" will arise (_Essays_, v. 254). His latest speculations on ethical problems are perhaps the least satisfactory of his writings. In 1892 he wrote: "The moral sense is a very complex affair--dependent in part upon associations of pleasure and pain, approbation and disapprobation, formed by education in early youth, but in part also on an innate sense of moral beauty and ugliness (how originated need not be discussed), which is possessed by some people in great strength, while some are totally devoid of it" (_Life_, ii. 305). This is an intuitional theory, and he compares the moral with the aesthetic sense, which he repeatedly declares to be intuitive; thus: "All the understanding in the world will neither increase nor diminish the force of the intuition that this is beautiful and this is ugly" (_Essays_, ix. 80). In the Romanes Lecture delivered in 1894, in which this passage occurs, he defines "law and morals" to be "restraints upon the struggle for existence between men in society." It follows that "the ethical process is in opposition to the cosmic process," to which the struggle for existence belongs (_Essays_, ix. 31). Apparently he thought that the moral sense in its origin was intuitional and in its development utilitarian. "Morality commenced with society" (_Essays_, v. 52). The "ethical process" is the "gradual strengthening of the social bond" (_Essays_, ix. 35). "The cosmic process has no sort of relation to moral ends" (l.c. p. 83); "of moral purpose I see no trace in nature. That is an article of exclusive human manufacture" (_Life_, ii. 268). The cosmic process Huxley identified with evil, and the ethical process with good; the two are in necessary conflict. "The reality at the bottom of the doctrine of original sin" is the "innate tendency to self-assertion" inherited by man from the cosmic order (_Essays_, ix. 27). "The actions we call sinful are part and parcel of the struggle for existence" (_Life_, ii. 282). "The prospect of attaining untroubled happiness" is "an illusion" (_Essays_, ix. 44), and the cosmic process in the long run will get the best of the contest, and "resume its sway" when evolution enters on its downward course (l.c. p. 45). This approaches pure pessimism, and though in Huxley's view the "pessimism of Schopenhauer is a nightmare" (_Essays_, ix. 200), his own philosophy of life is not distinguishable, and is often expressed in the same language. The cosmic order is obviously non-moral (_Essays_, ix. 197). That it is, as has been said, immoral is really meaningless. Pain and suffering are affections which imply a complex nervous organization, and we are not justified in projecting them into nature external to ourselves. Darwin and A. R. Wallace disagreed with Huxley in seeing rather the joyous than the suffering side of nature. Nor can it be assumed that the descending scale of evolution will reproduce the ascent, or that man will ever be conscious of his doom.

As has been said, Huxley never thoroughly grasped the Darwinian principle. He thought "transmutation may take place without transition" (_Life_, i. 173). In other words, that evolution is accomplished by leaps and not by the accumulation of small variations. He recognized the "struggle for existence" but not the gradual adjustment of the organism to its environment which is implied in "natural selection." In highly civilized societies he thought that the former was at an end (_Essays_, ix. 36) and had been replaced by the "struggle for enjoyment" (l.c. p. 40). But a consideration of the stationary population of France might have shown him that the effect in the one case may be as restrictive as in the other. So far from natural selection being in abeyance under modern social conditions, "it is," as Professor Karl Pearson points out, "something we run up against at once, almost as soon as we examine a mortality table" (_Biometrika_, i. 76). The inevitable conclusion, whether we like it or not, is that the future evolution of humanity is as much a part of the cosmic process as its past history, and Huxley's attempt to shut the door on it cannot be maintained scientifically.

AUTHORITIES.--_Life and Letters of Thomas Henry Huxley_, by his son Leonard Huxley (2 vols., 1900); _Scientific Memoirs of T. H. Huxley_ (4 vols., 1898-1901); _Collected Essays_ by T. H. Huxley (9 vols., 1898); _Thomas Henry Huxley, a Sketch of his Life and Work_, by P. Chalmers Mitchell, M.A. (Oxon., 1900); a critical study founded on careful research and of great value. (W. T. T.-D.)

FOOTNOTE:

[1] _Nature_, lxiii. 127.

HUY (Lat. _Hoium_, and Flem. _Hoey_), a town of Belgium, on the right bank of the Meuse, at the point where it is joined by the Hoyoux. Pop. (1904), 14,164. It is 19 m. E. of Namur and a trifle less west of Liége. Huy certainly dates from the 7th century, and, according to some, was founded by the emperor Antoninus in A.D. 148. Its situation is striking, with its grey citadel crowning a grey rock, and the fine collegiate church (with a 13th-century gateway) of Notre Dame built against it. The citadel is now used partly as a depot of military equipment and partly as a prison. The ruins are still shown of the abbey of Neumoustier founded by Peter the Hermit on his return from the first crusade. He was buried there in 1115, and a statue was erected to his memory in the abbey grounds in 1858. Neumoustier was one of seventeen abbeys in this town alone dependent on the bishopric of Liége. Huy is surrounded by vineyards, and the bridge which crosses the Meuse at this point connects the fertile Hesbaye north of the river with the rocky and barren Condroz south of it.

HUYGENS, CHRISTIAAN (1629-1695), Dutch mathematician, mechanician, astronomer and physicist, was born at the Hague on the 14th of April 1629. He was the second son of Sir Constantijn Huygens. From his father he received the rudiments of his education, which was continued at Leiden under A. Vinnius and F. van Schooten, and completed in the juridical school of Breda. His mathematical bent, however, soon diverted him from legal studies, and the perusal of some of his earliest theorems enabled Descartes to predict his future greatness. In 1649 he accompanied the mission of Henry, count of Nassau, to Denmark, and in 1651 entered the lists of science as an assailant of the unsound system of quadratures adopted by Gregory of St Vincent. This first essay (_Exetasis quadraturae circuli_, Leiden, 1651) was quickly succeeded by his _Theoremata de quadratura hyperboles, ellipsis, et circuli_; while, in a treatise entitled _De circuli magnitudine inventa_, he made, three years later, the closest approximation so far obtained to the ratio of the circumference to the diameter of a circle.

Another class of subjects was now to engage his attention. The improvement of the telescope was justly regarded as a _sine qua non_ for the advancement of astronomical knowledge. But the difficulties interposed by spherical and chromatic aberration had arrested progress in that direction until, in 1655, Huygens, working with his brother Constantijn, hit upon a new method of grinding and polishing lenses. The immediate results of the clearer definition obtained were the detection of a satellite to Saturn (the sixth in order of distance from its primary), and the resolution into their true form of the abnormal appendages to that planet. Each discovery in turn was, according to the prevailing custom, announced to the learned world under the veil of an anagram--removed, in the case of the first, by the publication, early in 1656, of the little tract _De Saturni luna observatio nova_; but retained, as regards the second, until 1659, when in the _Systema Saturnium_ the varying appearances of the so-called "triple planet" were clearly explained as the phases of a ring inclined at an angle of 28° to the ecliptic. Huygens was also in 1656 the first effective observer of the Orion nebula; he delineated the bright region still known by his name, and detected the multiple character of its nuclear star. His application of the pendulum to regulate the movement of clocks sprang from his experience of the need for an exact measure of time in observing the heavens. The invention dates from 1656; on the 16th of June 1657 Huygens presented his first "pendulum-clock" to the states-general; and the _Horologium_, containing a description of the requisite mechanism, was published in 1658.

His reputation now became cosmopolitan. As early as 1655 the university of Angers had distinguished him with an honorary degree of doctor of laws. In 1663, on the occasion of his second visit to England, he was elected a fellow of the Royal Society, and imparted to that body in January 1669 a clear and concise statement of the laws governing the collision of elastic bodies. Although these conclusions were arrived at independently, and, as it would seem, several years previous to their publication, they were in great measure anticipated by the communications on the same subject of John Wallis and Christopher Wren, made respectively in November and December 1668.

Huygens had before this time fixed his abode in France. In 1665 Colbert made to him on behalf of Louis XIV. an offer too tempting to be refused, and between the following year and 1681 his residence in the philosophic seclusion of the Bibliothèque du Roi was only interrupted by two short visits to his native country. His _magnum opus_ dates from this period. The _Horologium oscillatorium_, published with a dedication to his royal patron in 1673, contained original discoveries sufficient to have furnished materials for half a dozen striking disquisitions. His solution of the celebrated problem of the "centre of oscillation" formed in itself an important event in the history of mechanics. Assuming as an axiom that the centre of gravity of any number of interdependent bodies cannot rise higher than the point from which it fell, he arrived, by anticipating in the particular case the general principle of the conservation of _vis viva_, at correct although not strictly demonstrated conclusions. His treatment of the subject was the first successful attempt to deal with the dynamics of a system. The determination of the true relation between the length of a pendulum and the time of its oscillation; the invention of the theory of evolutes; the discovery, hence ensuing, that the cycloid is its own evolute, and is strictly isochronous; the ingenious although practically inoperative idea of correcting the "circular error" of the pendulum by applying cycloidal cheeks to clocks--were all contained in this remarkable treatise. The theorems on the composition of forces in circular motion with which it concluded formed the true prelude to Newton's _Principia_, and would alone suffice to establish the claim of Huygens to the highest rank among mechanical inventors.

In 1681 he finally severed his French connexions, and returned to Holland. The harsher measures which about that time began to be adopted towards his co-religionists in France are usually assigned as the motive of this step. He now devoted himself during six years to the production of lenses of enormous focal distance, which, mounted on high poles, and connected with the eye-piece by means of a cord, formed what were called "aerial telescopes." Three of his object-glasses, of respectively 123, 180 and 210 ft. focal length, are in the possession of the Royal Society. He also succeeded in constructing an almost perfectly achromatic eye-piece, still known by his name. But his researches in physical optics constitute his chief title-deed to immortality. Although Robert Hooke in 1668 and Ignace Pardies in 1672 had adopted a vibratory hypothesis of light, the conception was a mere floating possibility until Huygens provided it with a sure foundation. His powerful scientific imagination enabled him to realize that all the points of a wave-front originate partial waves, the aggregate effect of which is to reconstitute the primary disturbance at the subsequent stages of its advance, thus accomplishing its propagation; so that each primary undulation is the envelope of an indefinite number of secondary undulations. This resolution of the original wave is the well-known "Principle of Huygens," and by its means he was enabled to prove the fundamental laws of optics, and to assign the correct construction for the direction of the extraordinary ray in uniaxial crystals. These investigations, together with his discovery of the "wonderful phenomenon" of polarization, are recorded in his _Traité de la lumière_, published at Leiden in 1690, but composed in 1678. In the appended treatise _Sur la Cause de la pesanteur_, he rejected gravitation as a universal quality of matter, although admitting the Newtonian theory of the planetary revolutions. From his views on centrifugal force he deduced the oblate figure of the earth, estimating its compression, however, at little more than one-half its actual amount.

Huygens never married. He died at the Hague on the 8th of June 1695, bequeathing his manuscripts to the university of Leiden, and his considerable property to the sons of his younger brother. In character he was as estimable as he was brilliant in intellect. Although, like most men of strong originative power, he assimilated with difficulty the ideas of others, his tardiness sprang rather from inability to depart from the track of his own methods than from reluctance to acknowledge the merits of his competitors.

In addition to the works already mentioned, his _Cosmotheoros_--a speculation concerning the inhabitants of the planets--was printed posthumously at the Hague in 1698, and appeared almost simultaneously in an English translation. A volume entitled _Opera posthuma_ (Leiden, 1703) contained his "Dioptrica," in which the ratio between the respective focal lengths of object-glass and eye-glass is given as the measure of magnifying power, together with the shorter essays _De vitris figurandis_, _De corona et parheliis_, &c. An early tract _De ratiociniis in ludo aleae_, printed in 1657 with Schooten's _Exercitationes mathematicae_, is notable as one of the first formal treatises on the theory of probabilities; nor should his investigations of the properties of the cissoid, logarithmic and catenary curves be left unnoticed. His invention of the spiral watch-spring was explained in the _Journal des savants_ (Feb. 25, 1675). An edition of his works was published by G. J.'s Gravesande, in four quarto volumes entitled _Opera varia_ (Leiden, 1724) and _Opera reliqua_ (Amsterdam, 1728). His scientific correspondence was edited by P. J. Uylenbroek from manuscripts preserved at Leiden, with the title _Christiani Hugenii aliorumque seculi XVII. virorum celebrium exercitationes mathematicae et philosophicae_ (the Hague, 1833).

The publication of a monumental edition of the letters and works of Huygens was undertaken at the Hague by the _Société Hollandaise des Sciences_, with the heading _Oeuvres de Christian Huygens_ (1888), &c. Ten quarto volumes, comprising the whole of his correspondence, had already been issued in 1905. A biography of Huygens was prefixed to his _Opera varia_ (1724); his _Éloge_ in the character of a French academician was printed by J. A. N. Condorcet in 1773. Consult further: P. J. Uylenbroek, _Oratio de fratribus Christiano atque Constantino Hugenio_ (Groningen, 1838); P. Harting, _Christiaan Huygens in zijn Leven en Werken geschetzt_ (Groningen, 1868); J. B. J. Delambre, _Hist. de l'astronomie moderne_ (ii. 549); J. E. Montucla, _Hist. des mathématiques_ (ii. 84, 412, 549); M. Chasles, _Aperçu historique sur l'origine des méthodes en géometrie_, pp. 101-109; E. Dühring, _Kritische Geschichte der allgemeinen Principien der Mechanik_, Abschnitt (ii. 120, 163, iii. 227); A. Berry, _A Short History of Astronomy_, p. 200; R. Wolf, _Geschichte der Astronomie_, passim; Houzeau, _Bibliographie astronomique_ (ii. 169); F. Kaiser, _Astr. Nach._ (xxv. 245, 1847); _Tijdschrift voor de Wetenschappen_ (i. 7, 1848); _Allgemeine deutsche Biographie_ (M. B. Cantor); J. C. Poggendorff, _Biog. lit. Handwörterbuch_. (A. M. C.)

HUYGENS, SIR CONSTANTIJN (1596-1687), Dutch poet and diplomatist, was born at the Hague on the 4th of September 1596. His father, Christiaan Huygens, was secretary to the state council, and a man of great political importance. At the baptism of the child, the city of Breda was one of his sponsors, and the admiral Justinus van Nassau the other. He was trained in every polite accomplishment, and before he was seven could speak French with fluency. He was taught Latin by Johannes Dedelus, and soon became a master of classic versification. He developed not only extraordinary intellectual gifts but great physical beauty and strength, and was one of the most accomplished athletes and gymnasts of his age; his skill in playing the lute and in the arts of painting and engraving attracted general attention before he began to develop his genius as a writer. In 1616 he proceeded, with his elder brother, to the university of Leiden. He stayed there only one year, and in 1618 went to London with the English ambassador Dudley Carleton; he remained in London for some months, and then went to Oxford, where he studied for some time in the Bodleian Library, and to Woodstock, Windsor and Cambridge; he was introduced at the English court, and played the lute before James I. The most interesting feature of this visit was the intimacy which sprang up between the young Dutch poet and Dr Donne, for whose genius Huygens preserved through life an unbounded admiration. He returned to Holland in company with the English contingent of the synod of Dort, and in 1619 he proceeded to Venice in the diplomatic service of his country; on his return he nearly lost his life by a foolhardy exploit, namely, the scaling of the topmost spire of Strassburg cathedral. In 1621 he published one of his most weighty and popular poems, his _Batava Tempe_, and in the same year he proceeded again to London, as secretary to the ambassador, Wijngaerdan, but returned in three months. His third diplomatic visit to England lasted longer, from the 5th of December 1621 to the 1st of March 1623. During his absence, his volume of satires, _'t Costelick Mal_, dedicated to Jacob Cats, appeared at the Hague. In the autumn of 1622 he was knighted by James I. He published a large volume of miscellaneous poems in 1625 under the title of _Otiorum libri sex_; and in the same year he was appointed private secretary to the stadholder. In 1627 Huygens married Susanna van Baerle, and settled at the Hague; four sons and a daughter were born to them. In 1630 Huygens was called to a seat in the privy council, and he continued to exercise political power with wisdom and vigour for many years, under the title of the lord of Zuylichem. In 1634 he is supposed to have completed his long-talked-of version of the poems of Donne, fragments of which exist. In 1637 his wife died, and he immediately began to celebrate the virtues and pleasures of their married life in the remarkable didactic poem called _Dagwerck_, which was not published till long afterwards. From 1639 to 1641 he occupied himself by building a magnificent house and garden outside the Hague, and by celebrating their beauties in a poem entitled _Hofwijck_, which was published in 1653. In 1647 he wrote his beautiful poem of _Oogentroost_ or "Eye Consolation," to gratify his blind friend Lucretia van Trollo. He made his solitary effort in the dramatic line in 1657, when he brought out his comedy of _Trijntje Cornelis Klacht_, which deals, in rather broad humour, with the adventures of the wife of a ship's captain at Zaandam. In 1658 he rearranged his poems, and issued them with many additions, under the title of _Corn Flowers_. He proposed to the government that the present highway from the Hague to the sea at Scheveningen should be constructed, and during his absence on a diplomatic mission to the French court in 1666 the road was made as a compliment to the venerable statesman, who expressed his gratitude in a descriptive poem entitled _Zeestraet_. Huygens edited his poems for the last time in 1672, and died in his ninety-first year, on the 28th of March 1687. He was buried, with the pomp of a national funeral, in the church of St Jacob, on the 4th of April. His second son, Christiaan, the eminent astronomer, is noticed separately.

Constantijn Huygens is the most brilliant figure in Dutch literary history. Other statesmen surpassed him in political influence, and at least two other poets surpassed him in the value and originality of their writings. But his figure was more dignified and splendid, his talents were more varied, and his general accomplishments more remarkable than those of any other person of his age, the greatest age in the history of the Netherlands. Huygens is the _grand seigneur_ of the republic, the type of aristocratic oligarchy, the jewel and ornament of Dutch liberty. When we consider his imposing character and the positive value of his writings, we may well be surprised that he has not found a modern editor. It is a disgrace to Dutch scholarship that no complete collection of the writings of Huygens exists. His autobiography, _De vita propria sermonum libri duo_, did not see the light until 1817, and his remarkable poem, _Cluyswerck_, was not printed until 1841. As a poet Huygens shows a finer sense of form than any other early Dutch writer; the language, in his hands, becomes as flexible as Italian. His epistles and lighter pieces, in particular, display his metrical ease and facility to perfection. (E. G.)

HUYSMANS, the name of four Flemish painters who matriculated in the Antwerp gild in the 17th century. Cornelis the elder, apprenticed in 1633, passed for a mastership in 1636, and remained obscure. Jacob, apprenticed to Frans Wouters in 1650, wandered to England towards the close of the reign of Charles II., and competed with Lely as a fashionable portrait painter. He executed a portrait of the queen, Catherine of Braganza, now in the national portrait gallery, and Horace Walpole assigns to him the likeness of Lady Bellasys, catalogued at Hampton Court as a work of Lely. His portrait of Izaak Walton in the National Gallery shows a disposition to imitate the styles of Rubens and Van Dyke. According to most accounts he died in London in 1696. Jan Baptist Huysmans, born at Antwerp in 1654, matriculated in 1676-1677, and died there in 1715-1716. He was younger brother to Cornelis Huysmans the second, who was born at Antwerp in 1648, and educated by Gaspar de Wit and Jacob van Artois. Of Jan Baptist little or nothing has been preserved, except that he registered numerous apprentices at Antwerp, and painted a landscape dated 1697 now in the Brussels museum. Cornelis the second is the only master of the name of Huysmans whose talent was largely acknowledged. He received lessons from two artists, one of whom was familiar with the Roman art of the Poussins, whilst the other inherited the scenic style of the school of Rubens. He combined the two in a rich, highly coloured, and usually effective style, which, however, was not free from monotony. Seldom attempting anything but woodside views with fancy backgrounds, half Italian, half Flemish, he painted with great facility, and left numerous examples behind. At the outset of his career he practised at Malines, where he married in 1682, and there too he entered into some business connexion with van der Meulen, for whom he painted some backgrounds. In 1706 he withdrew to Antwerp, where he resided till 1717, returning then to Malines, where he died on the 1st of June 1727.

Though most of his pictures were composed for cabinets rather than churches, he sometimes emulated van Artois in the production of large sacred pieces, and for many years his "Christ on the Road to Emmaus" adorned the choir of Notre Dame of Malines. In the gallery of Nantes, where three of his small landscapes are preserved, there hangs an "Investment of Luxembourg," by van der Meulen, of which he is known to have laid in the background. The national galleries of London and Edinburgh contain each one example of his skill. Blenheim, too, and other private galleries in England, possess one or more of his pictures. But most of his works are on the European continent.

HUYSMANS, JORIS KARL (1848-1907), French novelist, was born at Paris on the 5th of February 1848. He belonged to a family of artists of Dutch extraction; he entered the ministry of the interior, and was pensioned after thirty years' service. His earliest venture in literature, _Le Drageoir à épices_ (1874), contained stories and short prose poems showing the influence of Baudelaire. _Marthe_ (1876), the life of a courtesan, was published in Brussels, and Huysmans contributed a story, "Sac au dos," to _Les Soirées de Médan_, the collection of stories of the Franco-German war published by Zola. He then produced a series of novels of everyday life, including _Les Soeurs Vatard_ (1879), _En Ménage_ (1881), and _À vau-l'eau_ (1882), in which he outdid Zola in minute and uncompromising realism. He was influenced, however, more directly by Flaubert and the brothers de Goncourt than by Zola. In _L'Art moderne_ (1883) he gave a careful study of impressionism and in _Certains_ (1889) a series of studies of contemporary artists, _À Rebours_ (1884), the history of the morbid tastes of a decadent aristocrat, des Esseintes, created a literary sensation, its caricature of literary and artistic symbolism covering much of the real beliefs of the leaders of the aesthetic revolt. In _Là-Bas_ Huysmans's most characteristic hero, Durtal, makes his appearance. Durtal is occupied in writing the life of Gilles de Rais; the insight he gains into Satanism is supplemented by modern Parisian students of the black art; but already there are signs of a leaning to religion in the sympathetic figures of the religious bell-ringer of Saint Sulpice and his wife. _En Route_ (1895) relates the strange conversion of Durtal to mysticism and Catholicism in his retreat to La Trappe. In _La Cathédrale_ (1898), Huysmans's symbolistic interpretation of the cathedral of Chartres, he develops his enthusiasm for the purity of Catholic ritual. The life of _Sainte Lydwine de Schiedam_ (1901), an exposition of the value of suffering, gives further proof of his conversion; and _L'Oblat_ (1903) describes Durtal's retreat to the Val des Saints, where he is attached as an oblate to a Benedictine monastery. Huysmans was nominated by Edmond de Goncourt as a member of the Académie des Goncourt. He died as a devout Catholic, after a long illness of cancer in the palate on the 13th of May 1907. Before his death he destroyed his unpublished MSS. His last book was _Les Foules de Lourdes_ (1906).

See Arthur Symons, _Studies in two Literatures_ (1897) and _The Symbolist Movement in Literature_ (1899); Jean Lionnet in _L'Évolution des idées_ (1903); Eugène Gilbert in _France et Belgique_ (1905); J. Sargeret in _Les Grands convertis_ (1906).

HUYSUM, JAN VAN (1682-1749), Dutch painter, was born at Amsterdam in 1682, and died in his native city on the 8th of February 1749. He was the son of Justus van Huysum, who is said to have been expeditious in decorating doorways, screens and vases. A picture by this artist is preserved in the gallery of Brunswick, representing Orpheus and the Beasts in a wooded landscape, and here we have some explanation of his son's fondness for landscapes of a conventional and Arcadian kind; for Jan van Huysum, though skilled as a painter of still life, believed himself to possess the genius of a landscape painter. Half his pictures in public galleries are landscapes, views of imaginary lakes and harbours with impossible ruins and classic edifices, and woods of tall and motionless trees--the whole very glossy and smooth, and entirely lifeless. The earliest dated work of this kind is that of 1717, in the Louvre, a grove with maidens culling flowers near a tomb, ruins of a portico, and a distant palace on the shores of a lake bounded by mountains.

It is doubtful whether any artist ever surpassed van Huysum in representing fruit and flowers. It has been said that his fruit has no savour and his flowers have no perfume--in other words, that they are hard and artificial--but this is scarcely true. In substance fruit and flower are delicate and finished imitations of nature in its more subtle varieties of matter. The fruit has an incomparable blush of down, the flowers have a perfect delicacy of tissue. Van Huysum, too, shows supreme art in relieving flowers of various colours against each other, and often against a light and transparent background. He is always bright, sometimes even gaudy. Great taste and much grace and elegance are apparent in the arrangement of bouquets and fruit in vases adorned with bas reliefs or in baskets on marble tables. There is exquisite and faultless finish everywhere. But what van Huysum has not is the breadth, the bold effectiveness, and the depth of thought of de Heem, from whom he descends through Abraham Mignon.

Some of the finest of van Huysum's fruit and flower pieces have been in English private collections: those of 1723 in the earl of Ellesmere's gallery, others of 1730-1732 in the collections of Hope and Ashburton. One of the best examples is now in the National Gallery (1736-1737). No public museum has finer and more numerous specimens than the Louvre, which boasts of four landscapes and six panels with still life; then come Berlin and Amsterdam with four fruit and flower pieces; then St Petersburg, Munich, Hanover, Dresden, the Hague, Brunswick, Vienna, Carlsruhe and Copenhagen.

HWANG HO [HOANG HO], the second largest river in China. It is known to foreigners as the Yellow river--a name which is a literal translation of the Chinese. It rises among the Kuenlun mountains in central Asia, its head-waters being in close proximity to those of the Yangtsze-Kiang. It has a total length of about 2400 m. and drains an area of approximately 400,000 sq. m. The main stream has its source in two lakes named Tsaring-nor and Oring-nor, lying about 35° N., 97° E., and after flowing with a south-easterly course it bends sharply to the north-west and north, entering China in the province of Kansuh in lat. 36°. After passing Lanchow-fu, the capital of this province, the river takes an immense sweep to the north and north-east, until it encounters the rugged barrier ranges that here run north and south through the provinces of Shansi and Chihli. By these ranges it is forced due south for 500 m., forming the boundary between the provinces of Shansi and Shensi, until it finds an outlet eastwards at Tung Kwan--a pass which for centuries has been renowned as the gate of Asia, being indeed the sole commercial passage between central China and the West. At Tung Kwan the river is joined by its only considerable affluent in China proper, the Wei (Wei-ho), which drains the large province of Shensi, and the combined volume of water continues its way at first east and then north-east across the great plain to the sea. At low water in the winter season the discharge is only about 36,000 cub. ft. per second, whereas during the summer flood it reaches 116,000 ft. or more. The amount of sediment carried down is very large, though no accurate observations have been made. In the account of Lord Macartney's embassy, which crossed the Yellow river in 1792, it was calculated to be 17,520 million cub. ft. a year, but this is considered very much over the mark. Two reasons, however, combine to render it probable that the sedimentary matter is very large in proportion to the volume of water: the first being the great fall, and the consequently rapid current over two-thirds of the river's course; the second that the drainage area is nearly all covered with deposits of loess, which, being very friable, readily gives way before the rainfall and is washed down in large quantity. The ubiquity of this loess or yellow earth, as the Chinese call it, has in fact given its name both to the river which carries it in solution and to the sea (the Yellow Sea) into which it is discharged. It is calculated by Dr Guppy (_Journal of China Branch of Royal Asiatic Society_, vol. xvi.) that the sediment brought down by the three northern rivers of China, viz., the Yangtsze, the Hwang-ho and the Peiho, is 24,000 million cub. ft. per annum, and is sufficient to fill up the whole of the Yellow Sea and the Gulf of Pechili in the space of about 36,000 years.

Unlike the Yangtsze, the Hwang-ho is of no practical value for navigation. The silt and sand form banks and bars at the mouth, the water is too shallow in winter and the current is too strong in summer, and, further, the bed of the river is continually shifting. It is this last feature which has earned for the river the name "China's sorrow." As the silt-laden waters debouch from the rocky bed of the upper reaches on to the plains, the current slackens, and the coarser detritus settles on the bottom. By degrees the bed rises, and the people build embankments to prevent the river from overflowing. As the bed rises the embankments must be raised too, until the stream is flowing many feet above the level of the surrounding country. As time goes on the situation becomes more and more dangerous; finally, a breach occurs, and the whole river pours over the country, carrying destruction and ruin with it. If the breach cannot be repaired the river leaves its old channel entirely and finds a new exit to the sea along the line of least resistance. Such in brief has been the story of the river since the dawn of Chinese history. At various times it has discharged its waters alternately on one side or the other of the great mass of mountains forming the promontory of Shantung, and by mouths as far apart from each other as 500 m. At each change it has worked havoc and disaster by covering the cultivated fields with 2 or 3 ft. of sand and mud.

A great change in the river's course occurred in 1851, when a breach was made in the north embankment near Kaifengfu in Honan. At this point the river bed was some 25 ft. above the plain; the water consequently forsook the old channel entirely and poured over the level country, finally seizing on the bed of a small river called the Tsing, and thereby finding an exit to the sea. Since that time the new channel thus carved out has remained the proper course of the river, the old or southerly channel being left quite dry. It required some fifteen or more years to repair damages from this outbreak, and to confine the stream by new embankments. After that there was for a time comparative immunity from inundations, but in 1882 fresh outbursts again began. The most serious of all took place in 1887, when it appeared probable that there would be again a permanent change in the river's course. By dint of great exertions, however, the government succeeded in closing the breach, though not till January 1889, and not until there had been immense destruction of life and property. The outbreak on this occasion occurred, as all the more serious outbreaks have done, in Honan, a few miles west of the city of Kaifengfu. The stream poured itself over the level and fertile country to the southwards, sweeping whole villages before it, and converting the plain into one vast lake. The area affected was not less than 50,000 sq. m. and the loss of life was computed at over one million. Since 1887 there have been a series of smaller outbreaks, mostly at points lower down and in the neighbourhood of Chinanfu, the capital of Shantung. These perpetually occurring disasters entail a heavy expense on the government; and from the mere pecuniary point of view it would well repay them to call in the best foreign engineering skill available, an expedient, however, which has not commended itself to the Chinese authorities. (G. J.)

HWICCE, one of the kingdoms of Anglo-Saxon Britain. Its exact dimensions are unknown; they probably coincided with those of the old diocese of Worcester, the early bishops of which bore the title "Episcopus Hwicciorum." It would therefore include Worcestershire, Gloucestershire except the Forest of Dean, the southern half of Warwickshire, and the neighbourhood of Bath. The name Hwicce survives in Wychwood in Oxfordshire and Whichford in Warwickshire. These districts, or at all events the southern portion of them, were according to the _Anglo-Saxon Chronicle_, _s.a._ 577, originally conquered by the West Saxons under Ceawlin. In later times, however, the kingdom of the Hwicce appears to have been always subject to Mercian supremacy, and possibly it was separated from Wessex in the time of Edwin. The first kings of whom we read were two brothers, Eanhere and Eanfrith, probably contemporaries of Wulfhere. They were followed by a king named Osric, a contemporary of Æthelred, and he by a king Oshere. Oshere had three sons who reigned after him, Æthelheard, Æthelweard and Æthelric. The two last named appear to have been reigning in the year 706. At the beginning of Offa's reign we again find the kingdom ruled by three brothers, named Eanberht, Uhtred and Aldred, the two latter of whom lived until about 780. After them the title of king seems to have been given up. Their successor Æthelmund, who was killed in a campaign against Wessex in 802, is described only as an earl. The district remained in possession of the rulers of Mercia until the fall of that kingdom. Together with the rest of English Mercia it submitted to King Alfred about 877-883 under Earl Æthelred, who possibly himself belonged to the Hwicce. No genealogy or list of kings has been preserved, and we do not know whether the dynasty was connected with that of Wessex or Mercia.

See Bede, _Historia eccles._ (edited by C. Plummer) iv. 13 (Oxford, 1896); W. de G. Birch, _Cartularium Saxonicum_, 43, 51, 76, 85, 116, 117, 122, 163, 187, 232, 233, 238 (Oxford, 1885-1889). (F. G. M. B.)

HYACINTH (Gr. hyakinthos), also called JACINTH (through Ital. _giacinto_), one of the most popular of spring garden flowers. It was in cultivation prior to 1597, at which date it is mentioned by Gerard. Rea in 1665 mentions several single and double varieties as being then in English gardens, and Justice in 1754 describes upwards of fifty single-flowered varieties, and nearly one hundred double-flowered ones, as a selection of the best from the catalogues of two then celebrated Dutch growers. One of the Dutch sorts, called La Reine de Femmes, a single white, is said to have produced from thirty-four to thirty-eight flowers in a spike, and on its first appearance to have sold for 50 guilders a bulb; while one called Overwinnaar, or Conqueror, a double blue, sold at first for 100 guilders, Gloria Mundi for 500 guilders, and Koning Saloman for 600 guilders. Several sorts are at that date mentioned as blooming well in water-glasses. Justice relates that he himself raised several very valuable double-flowered kinds from seeds, which many of the sorts he describes are noted for producing freely.

The original of the cultivated hyacinth, _Hyacinthus orientalis_, a native of Greece and Asia Minor, is by comparison an insignificant plant, bearing on a spike only a few small, narrow-lobed, washy blue flowers, resembling in form those of our common blue-bell. So great has been the improvement effected by the florists, and chiefly by the Dutch, that the modern hyacinth would scarcely be recognized as the descendant of the type above referred to, the spikes being long and dense, composed of a large number of flowers; the spikes produced by strong bulbs not unfrequently measure 6 to 9 in. in length and from 7 to 9 in. in circumference, with the flowers closely set on from bottom to top. Of late years much improvement has been effected in the size of the individual flowers and the breadth of their recurving lobes, as well as in securing increased brilliancy and depth of colour.

The peculiarities of the soil and climate of Holland are so very favourable to their production that Dutch florists have made a specialty of the growth of those and other bulbous-rooted flowers. Hundreds of acres are devoted to the growth of hyacinths in the vicinity of Haarlem, and bring in a revenue of several hundreds of thousands of pounds. Some notion of the vast number imported into England annually may be formed from the fact that, for the supply of flowering plants to Covent Garden, one market grower alone produces from 60,000 to 70,000 in pots under glass, their blooming period being accelerated by artificial heat, and extending from Christmas onwards until they bloom naturally in the open ground.

In the spring flower garden few plants make a more effective display than the hyacinth. Dotted in clumps in the flower borders, and arranged in masses of well-contrasted colours In beds in the flower garden, there are no flowers which impart during their season--March and April--a gayer tone to the parterre. The bulbs are rarely grown a second time, either for indoor or outdoor culture, though with care they might be utilized for the latter purpose; and hence the enormous numbers which are procured each recurring year from Holland.

The first hyacinths were single-flowered, but towards the close of the 17th century double-flowered ones began to appear, and till a recent period these bulbs were the most esteemed. At the present time, however, the single-flowered sorts are in the ascendant, as they produce more regular and symmetrical spikes of blossom, the flowers being closely set and more or less horizontal in direction, while most of the double sorts have the bells distant and dependent, so that the spike is loose and by comparison ineffective. For pot culture, and for growth in water-glasses especially, the single-flowered sorts are greatly to be preferred. Few if any of the original kinds are now in cultivation, a succession of new and improved varieties having been raised, the demand for which is regulated in some respects by fashion.

The hyacinth delights in a rich light sandy soil. The Dutch incorporate freely with their naturally light soil a compost consisting of one-third coarse sea or river sand, one-third rotten cow dung without litter and one-third leaf-mould. The soil thus renovated retains its qualities for six or seven years, but hyacinths are not planted upon the same place for two years successively, intermediary crops of narcissus, crocus or tulips being taken. A good compost for hyacinths is sandy loam, decayed leaf-mould, rotten cow dung and sharp sand in equal parts, the whole being collected and laid up in a heap and turned over occasionally. Well-drained beds made up of this soil, and refreshed with a portion of new compost annually, would grow the hyacinth to perfection. The best time to plant the bulbs is towards the end of September and during October; they should be arranged in rows, 6 to 8 in. asunder, there being four rows in each bed. The bulbs should be sunk about 4 to 6 in. deep, with a small quantity of clean sand placed below and around each of them. The beds should be covered with decayed tan-bark, coco-nut fibre or half-rotten dung litter. As the flower-stems appear, they are tied to rigid but slender stakes to preserve them from accident. If the bulbs are at all prized, the stems should be broken off as soon as the flowering is over, so as not to exhaust the bulbs; the leaves, however, must be allowed to grow on till matured, but as soon as they assume a yellow colour, the bulbs are taken up, the leaves cut off near their base, and the bulbs laid out in a dry, airy, shady place to ripen, after which they are cleaned of loose earth and skin, ready for storing. It is the practice in Holland, about a month after the bloom, or when the tips of the leaves assume a withered appearance, to take up the bulbs, and to lay them sideways on the ground, covering them with an inch or two of earth. About three weeks later they are again taken up and cleaned. In the store-room they should be kept dry, well-aired and apart from each other.

Few plants are better adapted than the hyacinth for pot culture as greenhouse decorative plants; and by the aid of forcing they may be had in bloom as early as Christmas. They flower fairly well in 5-in. pots, the stronger bulbs in 6-in. pots. To bloom at Christmas, they should be potted early in September, in a compost resembling that already recommended for the open-air beds; and, to keep up a succession of bloom, others should be potted at intervals of a few weeks till the middle or end of November. The tops of the bulbs should be about level with the soil, and if a little sand is put immediately around them so much the better. The pots should be set in an open place on a dry hard bed of ashes, and be covered over to a depth of 6 or 8 in. with the same material or with fibre or soil; and when the roots are well developed, which will take from six to eight weeks, they may be removed to a frame, and gradually exposed to light, and then placed in a forcing pit in a heat of from 60 to 70°. When the flowers are fairly open, they may be removed to the greenhouse or conservatory.

The hyacinth may be very successfully grown in glasses for ornament in dwelling-houses. The glasses are filled to the neck with rain or even tap water, a few lumps of charcoal being dropped into them. The bulbs are placed in the hollow provided for them, so that their base just touches the water. This may be done in September or October. They are then set in a dark cupboard for a few weeks till roots are freely produced, and then gradually exposed to light. The early-flowering single white Roman hyacinth, a small-growing pure white variety, remarkable for its fragrance, is well adapted for forcing, as it can be had in bloom if required by November. For windows it grows well in the small glasses commonly used for crocuses; and for decorative purposes should be planted about five bulbs in a 5-in. pot, or in pans holding a dozen each. If grown for cut flowers it can be planted thickly in boxes of any convenient size. It is highly esteemed during the winter months by florists.

The Spanish hyacinth (_H. amethystinus_) and _H. azureus_ are charming little bulbs for growing in masses in the rock garden or front of the flower border. The older botanists included in the genus _Hyacinthus_ species of _Muscari_, _Scilla_ and other genera of bulbous Liliaceae, and the name of hyacinth is still popularly applied to several other bulbous plants. Thus _Muscari botryoides_ is the grape hyacinth, 6 in., blue or white, the handsomest; _M. moschatum_, the musk hyacinth, 10 in., has peculiar livid greenish-yellow flowers and a strong musky odour; _M. comosum_ var. _monstrosum_, the feather hyacinth, bears sterile flowers broken up into a featherlike mass; _M. racemosum_, the starch hyacinth, is a native with deep blue plum-scented flowers. The Cape hyacinth is _Galtonia candicans_, a magnificent border plant, 3-4 ft. high, with large drooping white bell-shaped flowers; the star hyacinth, _Scilla amoena_; the Peruvian hyacinth or Cuban lily, _S. peruviana_, a native of the Mediterranean region, to which Linnaeus gave the species name _peruviana_ on a mistaken assumption of its origin; the wild hyacinth or blue-bell, known variously as _Endymion nonscriptum_, _Hyacinthus nonscriptus_ or _Scilla nutans_; the wild hyacinth of western North America, _Camassia esculenta_. They all flourish in good garden soil of a gritty nature.

HYACINTH, or JACINTH, in mineralogy, a variety of zircon (q.v.) of yellowish red colour, used as a gem-stone. The _hyacinthus_ of ancient writers must have been our sapphire, or blue corundum, while the hyacinth of modern mineralogists may have been the stone known as _lyncurium_ ([Greek: lynkourion]). The Hebrew word _leshem_, translated ligure in the Authorized Version (Ex. xxviii. 19), from the [Greek: ligyrion] of the Septuagint, appears in the Revised Version as jacinth, but with a marginal alternative of amber. Both jacinth and amber may be reddish yellow, but their identification is doubtful. As our jacinth (zircon) is not known in ancient Egyptian work, Professor Flinders Petrie has suggested that the _leshem_ may have been a yellow quartz, or perhaps agate. Some old English writers describe the jacinth as yellow, whilst others refer to it as a blue stone, and the _hyacinthus_ of some authorities seems undoubtedly to have been our sapphire. In Rev. xx. 20 the Revised Version retains the word jacinth, but gives sapphire as an alternative.

Most of the gems known in trade as hyacinth are only garnets--generally the deep orange-brown hessonite or cinnamon-stone--and many of the antique engraved stones reputed to be hyacinth are probably garnets. The difference may be detected optically, since the garnet is singly and the hyacinth doubly refracting; moreover the specific gravity affords a simple means of diagnosis, that of garnet being only about 3.7, whilst hyacinth may have a density as high as 4.7. Again, it was shown many years ago by Sir A. H. Church that most hyacinths, when examined by the spectroscope, show a series of dark absorption bands, due perhaps to the presence of some rare element such as uranium or erbium.

Hyacinth is not a common mineral. It occurs, with other zircons, in the gem-gravels of Ceylon, and very fine stones have been found as pebbles at Mudgee in New South Wales. Crystals of zircon, with all the typical characters of hyacinth, occur at Expailly, Le Puy-en-Velay, in Central France, but they are not large enough for cutting. The stones which have been called Compostella hyacinths are simply ferruginous quartz from Santiago de Compostella in Spain. (F. W. R.*)

HYACINTHUS,[1] in Greek mythology, the youngest son of the Spartan king Amyclas, who reigned at Amyclae (so Pausanias iii. 1. 3, iii. 19. 5; and Apollodorus i. 3. 3, iii. 10. 3). Other stories make him son of Oebalus, of Eurotas, or of Pierus and the nymph Clio (see Hyginus, _Fabulae_, 271; Lucian, _De saltatione_, 45, and _Dial. deor._ 14). According to the general story, which is probably late and composite, his great beauty attracted the love of Apollo, who killed him accidentally when teaching him to throw the _discus_ (quoit); others say that Zephyrus (or Boreas) out of jealousy deflected the quoit so that it hit Hyacinthus on the head and killed him. According to the representation on the tomb at Amyclae (Pausanias, _loc. cit._) Hyacinthus was translated into heaven with his virgin sister Polyboea. Out of his blood there grew the flower known as the hyacinth, the petals of which were marked with the mournful exclamation AI, AI, "alas" (cf. "that sanguine flower inscribed with woe"). This Greek hyacinth cannot have been the flower which now bears the name: it has been identified with a species of iris and with the larkspur (_Delphinium Aiacis_), which appear to have the markings described. The Greek hyacinth was also said to have sprung from the blood of Ajax. Evidently the Greek authorities confused both the flowers and the traditions.

The death of Hyacinthus was celebrated at Amyclae by the second most important of Spartan festivals, the Hyacinthia, which took place in the Spartan month Hecatombeus. What month this was is not certain. Arguing from Xenophon (_Hell._ iv. 5) we get May; assuming that the Spartan Hecatombeus is the Attic Hecatombaion, we get July; or again it may be the Attic Scirophorion, June. At all events the Hyacinthia was an early summer festival. It lasted three days, and the rites gradually passed from mourning for Hyacinthus to rejoicings in the majesty of Apollo, the god of light and warmth, and giver of the ripe fruits of the earth (see a passage from Polycrates, _Laconica_, quoted by Athenaeus 139 d; criticized by L. R. Farnell, _Cults of the Greek States_, iv. 266 foll.). This festival is clearly connected with vegetation, and marks the passage from the youthful verdure of spring to the dry heat of summer and the ripening of the corn.

The precise relation which Apollo bears to Hyacinthus is obscure. The fact that at Tarentum a Hyacinthus tomb is ascribed by Polybius to Apollo Hyacinthus (not Hyacinthius) has led some to think that the personalities are one, and that the hero is merely an emanation from the god; confirmation is sought in the Apolline appellation [Greek: tetracheir], alleged by Hesychius to have been used in Laconia, and assumed to describe a composite figure of Apollo-Hyacinthus. Against this theory is the essential difference between the two figures. Hyacinthus is a chthonian vegetation god whose worshippers are afflicted and sorrowful; Apollo, though interested in vegetation, is never regarded as inhabiting the lower world, his death is not celebrated in any ritual, his worship is joyous and triumphant, and finally the Amyclean Apollo is specifically the god of war and song. Moreover, Pausanias describes the monument at Amyclae as consisting of a rude figure of Apollo standing on an altar-shaped base which formed the tomb of Hyacinthus. Into the latter offerings were put for the hero before gifts were made to the god.

On the whole it is probable that Hyacinthus belongs originally to the pre-Dorian period, and that his story was appropriated and woven into their own Apollo myth by the conquering Dorians. Possibly he may be the apotheosis of a pre-Dorian king of Amyclae. J. G. Frazer further suggests that he may have been regarded as spending the winter months in the underworld and returning to earth in the spring when the "hyacinth" blooms. In this case his festival represents perhaps both the Dorian conquest of Amyclae and the death of spring before the ardent heat of the summer sun, typified as usual by the _discus_ (quoit) with which Apollo is said to have slain him. With the growth of the hyacinth from his blood should be compared the oriental stories of violets springing from the blood of Attis, and roses and anemones from that of Adonis. As a youthful vegetation god, Hyacinthus may be compared with Linus and Scephrus, both of whom are connected with Apollo Agyieus.

See L. R. Farnell, _Cults of the Greek States_, vol. iv. (1907), pp. 125 foll., 264 foll.; J. G. Frazer, _Adonis, Attis, Osiris_ (1906), bk. ii. ch. 7; S. Wide, _Lakonische Kulte_, p. 290; E. Rhode, _Psyche_, 3rd ed. i. 137 foll.; Roscher, _Lexikon d. griech. u. röm. Myth._, s.v. "Hyakinthos" (Greve); L. Preller, _Griechische Mythol._ 4th ed. i. 248 foll. (J. M. M.)

FOOTNOTE:

[1] The word is probably derived from an Indo-European root, meaning "youthful," found in Latin, Greek, English and Sanskrit. Some have suggested that the first two letters are from [Greek: uein], to rain, (cf. Hyades).

HYADES ("the rainy ones"), in Greek mythology, the daughters of Atlas and Aethra; their number varies between two and seven. As a reward for having brought up Zeus at Dodona and taken care of the infant Dionysus Hyes, whom they conveyed to Ino (sister of his mother Semele) at Thebes when his life was threatened by Lycurgus, they were translated to heaven and placed among the stars (Hyginus, _Poët. astron._ ii. 21). Another form of the story combines them with the Pleiades. According to this they were twelve (or fifteen) sisters, whose brother Hyas was killed by a snake while hunting in Libya (Ovid, _Fasti_, v. 165; Hyginus, _Fab._ 192). They lamented him so bitterly that Zeus, out of compassion, changed them into stars--five into the Hyades, at the head of the constellation of the Bull, the remainder into the Pleiades. Their name is derived from the fact that the rainy season commenced when they rose at the same time as the sun (May 7-21); the original conception of them is that of the fertilizing principle of moisture. The Romans derived the name from [Greek: us] (pig), and translated it by _Suculae_ (Cicero, _De nat. deorum_, ii. 43).

HYATT, ALPHEUS (1838-1902), American naturalist, was born at Washington, D.C., on the 5th of April 1838. From 1858 to 1862 he studied at Harvard, where he had Louis Agassiz for his master, and in 1863 he served as a volunteer in the Civil War, attaining the rank of captain. In 1867 he was appointed curator of the Essex Institute at Salem, and in 1870 became professor of zoology and palaeontology at the Massachusetts Institute of Technology (resigned 1888), and custodian of the Boston Society of Natural History (curator in 1881). In 1886 he was appointed assistant for palaeontology in the Cambridge museum of comparative anatomy, and in 1889 was attached to the United States Geological Survey as palaeontologist for the Trias and Jura. He was the chief founder of the American Society of Naturalists, of which he acted as first president in 1883, and he also took a leading part in establishing the marine biological laboratories at Annisquam and Woods Hole, Mass. He died at Cambridge on the 15th of January 1902.

His works include _Observations on Fresh-water Polyzoa_ (1866); _Fossil Cephalopods of the Museum of Comparative Zoology_ (1872); _Revision of North American Porifera_ (1875-1877); _Genera of Fossil Cephalopoda_ (1883); _Larval Theory of the Origin of Cellular Tissue_ (1884); _Genesis of the Arietidae_ (1889); and _Phylogeny of an acquired characteristic_ (1894). He wrote the section on Cephalopoda in Karl von Zittel's _Paläontologie_ (1900), and his well-known study on the fossil pond snails of Steinheim ("The Genesis of the Tertiary Species of Planorbis at Steinheim") appeared in the _Memoirs_ of the Boston Natural History Society in 1880. He was one of the founders and editors of the _American Naturalist_.

HYBLA, the name of several cities In Sicily. The best known historically, though its exact site is uncertain, is Hybla Major, near (or by some supposed to be identical with) Megara Hyblaea (q.v.): another Hybla, known as Hybla Minor or Galeatis, is represented by the modern Paternò; while the site of Hybla Heraea is to be sought near Ragusa.

HYBRIDISM. The Latin word _hybrida_, _hibrida_ or _ibrida_ has been assumed to be derived from the Greek [Greek: hybris], an insult or outrage, and a hybrid or mongrel has been supposed to be an outrage on nature, an unnatural product. As a general rule animals and plants belonging to distinct species do not produce offspring when crossed with each other, and the term hybrid has been employed for the result of a fertile cross between individuals of different species, the word mongrel for the more common result of the crossing of distinct varieties. A closer scrutiny of the facts, however, makes the term hybridism less isolated and more vague. The words species and genus, and still more subspecies and variety, do not correspond with clearly marked and sharply defined zoological categories, and no exact line can be drawn between the various kinds of crossings from those between individuals apparently identical to those belonging to genera universally recognized as distinct. Hybridism therefore grades into mongrelism, mongrelism into cross-breeding, and cross-breeding into normal pairing, and we can say little more than that the success of the union is the more unlikely or more unnatural the further apart the parents are in natural affinity.

The interest in hybridism was for a long time chiefly of a practical nature, and was due to the fact that hybrids are often found to present characters somewhat different from those of either parent. The leading facts have been known in the case of the horse and ass from time immemorial. The earliest recorded observation of a hybrid plant is by J. G. Gmelin towards the end of the 17th century; the next is that of Thomas Fairchild, who in the second decade of the 18th century, produced the cross which is still grown in gardens under the name of "Fairchild's Sweet William." Linnaeus made many experiments in the cross-fertilization of plants and produced several hybrids, but Joseph Gottlieb Kölreuter (1733-1806) laid the first real foundation of our scientific knowledge of the subject. Later on Thomas Andrew Knight, a celebrated English horticulturist, devoted much successful labour to the improvement of fruit trees and vegetables by crossing. In the second quarter of the 19th century C. F. Gärtner made and published the results of a number of experiments that had not been equalled by any earlier worker. Next came Charles Darwin, who first in the _Origin of Species_, and later in _Cross and Self-Fertilization of Plants_, subjected the whole question to a critical examination, reviewed the known facts and added many to them.

Darwin's conclusions were summed up by G. J. Romanes in the 9th edition of this _Encyclopaedia_ as follows:--

1. The laws governing the production of hybrids are identical, or nearly identical, in the animal and vegetable kingdoms.

2. The sterility which so generally attends the crossing of two specific forms is to be distinguished as of two kinds, which, although often confounded by naturalists, are in reality quite distinct. For the sterility may obtain between the two parent species when first crossed, or it may first assert itself in their hybrid progeny. In the latter case the hybrids, although possibly produced without any appearance of infertility on the part of their parent species, nevertheless prove more or less infertile among themselves, and also with members of either parent species.

3. The degree of both kinds of infertility varies in the case of different species, and in that of their hybrid progeny, from absolute sterility up to complete fertility. Thus, to take the case of plants, "when pollen from a plant of one family is placed on the stigma of a plant of a distinct family, it exerts no more influence than so much inorganic dust. From this absolute zero of fertility, the pollen of different species, applied to the stigma of some one species of the same genus, yields a perfect gradation in the number of seeds produced, up to nearly complete, or even quite complete, fertility; so, in hybrids themselves, there are some which never have produced, and probably never would produce, even with the pollen of the pure parents, a single fertile seed; but in some of these cases a first trace of fertility may be detected, by the pollen of one of the pure parent species causing the flower of the hybrid to wither earlier than it otherwise would have done; and the early withering of the flower is well known to be a sign of incipient fertilization. From this extreme degree of sterility we have self-fertilized hybrids producing a greater and greater number of seeds up to perfect fertility."

4. Although there is, as a rule, a certain parallelism, there is no fixed relation between the degree of sterility manifested by the parent species when crossed and that which is manifested by their hybrid progeny. There are many cases in which two pure species can be crossed with unusual facility, while the resulting hybrids are remarkably sterile; and, contrariwise, there are species which can only be crossed with extreme difficulty, though the hybrids, when produced, are very fertile. Even within the limits of the same genus, these two opposite cases may occur.

5. When two species are reciprocally crossed, i.e. male A with female B, and male B with female A, the degree of sterility often differs greatly in the two cases. The sterility of the resulting hybrids may differ likewise.

6. The degree of sterility of first crosses and of hybrids runs, to a certain extent, parallel with the systematic affinity of the forms which are united. "For species belonging to distinct genera can rarely, and those belonging to distinct families can never, be crossed. The parallelism, however, is far from complete; for a multitude of closely allied species will not unite, or unite with extreme difficulty, whilst other species, widely different from each other, can be crossed with perfect facility. Nor does the difficulty depend on ordinary constitutional differences; for annual and perennial plants, deciduous and evergreen trees, plants flowering at different seasons, inhabiting different stations, and naturally living under the most opposite climates, can often be crossed with ease. The difficulty or facility apparently depends exclusively on the sexual constitution of the species which are crossed, or on their sexual elective affinity."

There are many new records as to the production of hybrids. Horticulturists have been extremely active and successful in their attempts to produce new flowers or new varieties of vegetables by seminal or graft-hybrids, and any florist's catalogue or the account of any special plant, such as is to be found in Foster-Melliar's _Book of the Rose_, is in great part a history of successful hybridization. Much special experimental work has been done by botanists, notably by de Vries, to the results of whose experiments we shall recur. Experiments show clearly that the obtaining of hybrids is in many cases merely a matter of taking sufficient trouble, and the successful crossing of genera is not infrequent.

Focke, for instance, cites cases where hybrids were obtained between _Brassica_ and _Raphanus_, _Galium_ and _Asperula_, _Campanula_ and _Phyteuma_, _Verbascum_ and _Celsia_. Among animals, new records and new experiments are almost equally numerous. Boveri has crossed _Echinus microtuberculatus_ with _Sphaerechinus granularis_. Thomas Hunt Morgan even obtained hybrids between Asterias, a starfish, and _Arbacia_, a sea-urchin, a cross as remote as would be that between a fish and a mammal. Vernon got many hybrids by fertilizing the eggs of _Strongylocentrotus lividus_ with the sperm of _Sphaerechinus granularis_. Standfuss has carried on an enormous series of experiments with Lepidopterous insects, and has obtained a very large series of hybrids, of which he has kept careful record. Lepidopterists generally begin to suspect that many curious forms offered by dealers as new species are products got by crossing known species. Apellö has succeeded with Teleostean fish; Gebhardt and others with Amphibia. Elliot and Suchetet have studied carefully the question of hybridization occurring normally among birds, and have got together a very large body of evidence. Among the cases cited by Elliot the most striking are that of the hybrid between _Colaptes cafer_ and _C. auratus_, which occurs over a very wide area of North America and is known as _C. hybridus_, and the hybrid between _Euplocamus lineatus_ and _E. horsfieldi_, which appears to be common in Assam. St M. Podmore has produced successful crosses between the wood-pigeon (_Columba palumbus_) and a domesticated variety of the rock pigeon (_C. livia_). Among mammals noteworthy results have been obtained by Professor Cossar Ewart, who has bred nine zebra hybrids by crossing mares of various sizes with a zebra stallion, and who has studied in addition three hybrids out of zebra mares, one sired by a donkey, the others by ponies. Crosses have been made between the common rabbit (_Lepus cuniculus_) and the guinea-pig (_Cavia cobaya_), and examples of the results have been exhibited in the Zoological Gardens of Sydney, New South Wales. The Carnivora generally are very easy to hybridize, and many successful experiments have been made with animals in captivity. Karl Hagenbeck of Hamburg has produced crosses between the lion (_Felis leo_) and the tiger (_F. tigris_). What was probably a "tri-hybrid" in which lion, leopard and jaguar were mingled was exhibited by a London showman in 1908. Crosses between various species of the smaller cats have been fertile on many occasions. The black bear (_Ursus americanus_) and the European brown bear (_U. arctos_) bred in the London Zoological Gardens in 1859, but the three cubs did not reach maturity. Hybrids between the brown bear and the grizzly-bear (_U. horribilis_) have been produced in Cologne, whilst at Halle since 1874 a series of successful matings of polar (_U. maritimus_) and brown bears have been made. Examples of these hybrid bears have been exhibited by the London Zoological Society. The London Zoological Society has also successfully mated several species of antelopes, for instance, the water-bucks _Kobus ellipsiprymnus_ and _K. unctuosus_, and Selous's antelope _Limnotragus selousi_ with _L. gratus_.

The causes militating against the production of hybrids have also received considerable attention. Delage, discussing the question, states that there is a general proportion between sexual attraction and zoological affinity, and in many cases hybrids are not naturally produced simply from absence of the stimulus to sexual mating, or because of preferential mating within the species or variety. In addition to differences of habit, temperament, time of maturity, and so forth, gross structural differences may make mating impossible. Thus Escherick contends that among insects the peculiar structure of the genital appendages makes cross-impregnation impossible, and there is reason to believe that the specific peculiarities of the modified sexual palps in male spiders have a similar result.

The difficulties, however, may not exist, or may be overcome by experiment, and frequently it is only careful management that is required to produce crossing. Thus it has been found that when the pollen of one species does not succeed in fertilizing the ovules of another species, yet the reciprocal cross may be successful; that is to say, the pollen of the second species may fertilize the ovules of the first. H. M. Vernon, working with sea-urchins, found that the obtaining of hybrids depended on the relative maturity of the sexual products. The difficulties in crossing apparently may extend to the chemiotaxic processes of the actual sexual cells. Thus when the spermatozoa of an urchin were placed in a drop of seawater containing ripe eggs of an urchin and of a starfish, the former eggs became surrounded by clusters of the male cells, while the latter appeared to exert little attraction for the alien germ-cells. Finally, when the actual impregnation of the egg is possible naturally, or has been secured by artificial means, the development of the hybrid may stop at an early stage. Thus hybrids between the urchin and the starfish, animals belonging to different classes, reached only the stage of the pluteus larva. A. D. Apellö, experimenting with Teleostean fish, found that very often impregnation and segmentation occurred, but that the development broke down immediately afterwards. W. Gebhardt, crossing _Rana esculenta_ with _R. arvalis_, found that the cleavage of the ovum was normal, but that abnormality began with the gastrula, and that development soon stopped. In a very general fashion there appears to be a parallel between the zoological affinity and the extent to which the incomplete development of the hybrid proceeds.

As to the sterility of hybrids _inter se_, or with either of the parent forms, information is still wanted. Delage, summing up the evidence in a general way, states that mongrels are more fertile and stronger than their parents, while hybrids are at least equally hardy but less fertile. While many of the hybrid products of horticulturists are certainly infertile, others appear to be indefinitely fertile.

Focke, it is true, states that the hybrids between _Primula auricula_ and _P. hirsuta_ are fertile for many generations, but not indefinitely so; but, while this may be true for the particular case, there seems no reason to doubt that many plant hybrids are quite fertile. In the case of animals the evidence is rather against fertility. Standfuss, who has made experiments lasting over many years, and who has dealt with many genera of Lepidoptera, obtained no fertile hybrid females, although he found that hybrid males paired readily and successfully with pure-bred females of the parent races. Elliot, dealing with birds, concluded that no hybrids were fertile with one another beyond the second generation, but thought that they were fertile with members of the parent races. Wallace, on the other hand, cites from Quatrefages the case of hybrids between the moths _Bombyx cynthia_ and _B. arrindia_, which were stated to be fertile _inter se_ for eight generations. He also states that hybrids between the sheep and goat have a limited fertility _inter se_. Charles Darwin, however, had evidence that some hybrid pheasants were completely fertile, and he himself interbred the progeny of crosses between the common and Chinese geese, whilst there appears to be no doubt as to the complete fertility of the crosses between many species of ducks, J. L. Bonhote having interbred in various crosses for several generations the mallard (_Anas boschas_), the Indian spot-bill duck (_A. poecilorhyncha_), the New Zealand grey duck (_A. superciliosa_) and the pin-tail (_Dafila acuta_). Podmore's pigeon hybrids were fertile _inter se_, a specimen having been exhibited at the London Zoological Gardens. The hybrids between the brown and polar bears bred at Halle proved to be fertile, both with one of the parent species and with one another.

Cornevin and Lesbre state that in 1873 an Arab mule was fertilized in Africa by a stallion, and gave birth to female offspring which she suckled. All three were brought to the Jardin d'Acclimatation in Paris, and there the mule had a second female colt to the same father, and subsequently two male colts in succession to an ass and to a stallion. The female progeny were fertilized, but their offspring were feeble and died at birth. Cossar Ewart gives an account of a recent Indian case in which a female mule gave birth to a male colt. He points out, however, that many mistakes have been made about the breeding of hybrids, and is not altogether inclined to accept this supposed case. Very little has been published with regard to the most important question, as to the actual condition of the sexual organs and cells in hybrids. There does not appear to be gross anatomical defect to account for the infertility of hybrids, but microscopical examination in a large number of cases is wanted. Cossar Ewart, to whom indeed much of the most interesting recent work on hybrids is due, states that in male zebra-hybrids the sexual cells were immature, the tails of the spermatozoa being much shorter than those of the similar cells in stallions and zebras. He adds, however, that the male hybrids he examined were young, and might not have been sexually mature. He examined microscopically the ovary of a female zebra-hybrid and found one large and several small Graafian follicles, in all respects similar to those in a normal mare or female zebra. A careful study of the sexual organs in animal and plant hybrids is very much to be desired, but it may be said that so far as our present knowledge goes there is not to be expected any obvious microscopical cause of the relative infertility of hybrids.

The relative variability of hybrids has received considerable attention from many writers. Horticulturists, as Bateson has written, are "aware of the great and striking variations which occur in so many orders of plants when hybridization is effected." The phrase has been used "breaking the constitution of a plant" to indicate the effect produced in the offspring of a hybrid union, and the device is frequently used by those who are seeking for novelties to introduce on the market. It may be said generally that hybrids are variable, and that the products of hybrids are still more variable. J. L. Bonhote found extreme variations amongst his hybrid ducks. Y. Delage states that in reciprocal crosses there is always a marked tendency for the offspring to resemble the male parents; he quotes from Huxley that the mule, whose male parent is an ass, is more like the ass, and that the hinny, whose male parent is a horse, is more like the horse. Standfuss found among Lepidoptera that males were produced much more often than females, and that these males paired readily. The freshly hatched larvae closely resembled the larvae of the female parent, but in the course of growth the resemblance to the male increased, the extent of the final approximation to the male depending on the relative phylogenetic age of the two parents, the parent of the older species being prepotent. In reciprocal pairing, he found that the male was able to transmit the characters of the parents in a higher degree. Cossar Ewart, in relation to zebra hybrids, has discussed the matter of resemblance to parents in very great detail, and fuller information must be sought in his writings. He shows that the wild parent is not necessarily prepotent, although many writers have urged that view. He described three hybrids bred out of a zebra mare by different horses, and found in all cases that the resemblance to the male or horse parent was more profound. Similarly, zebra-donkey hybrids out of zebra mares bred in France and in Australia were in characters and disposition far more like the donkey parents. The results which he obtained in the hybrids which he bred from a zebra stallion and different mothers were more variable, but there was rather a balance in favour of zebra disposition and against zebra shape and marking.

"Of the nine zebra-horse hybrids I have bred," he says, "only two in their make and disposition take decidedly after the wild parent. As explained fully below, all the hybrids differ profoundly in the plan of their markings from the zebra, while in their ground colour they take after their respective dams or the ancestors of their dams far more than after the zebra--the hybrid out of the yellow and white Iceland pony, e.g. instead of being light in colour, as I anticipated, is for the most part of a dark dun colour, with but indistinct stripes. The hoofs, mane and tail of the hybrids are at the most intermediate, but this is perhaps partly owing to reversion towards the ancestors of these respective dams. In their disposition and habits they all undoubtedly agree more with the wild sire."

Ewart's experiments and his discussion of them also throw important light on the general relation of hybrids to their parents. He found that the coloration and pattern of his zebra hybrids resembled far more those of the Somali or Grévy's zebra than those of their sire--a Burchell's zebra. In a general discussion of the stripings of horses, asses and zebras, he came to the conclusion that the Somali zebra represented the older type, and that therefore his zebra hybrids furnished important evidence of the effect of crossing in producing reversion to ancestral type. The same subject has of course been discussed at length by Darwin, in relation to the cross-breeding of varieties of pigeons; but the modern experimentalists who are following the work of Mendel interpret reversion differently (see MENDELISM).

_Graft-Hybridism._--It is well known that, when two varieties or allied species are grafted together, each retains its distinctive characters. But to this general, if not universal, rule there are on record several alleged exceptions, in which either the scion is said to have partaken of the qualities of the stock, the stock of the scion, or each to have affected the other. Supposing any of these influences to have been exerted, the resulting product would deserve to be called a graft-hybrid. It is clearly a matter of great interest to ascertain whether such formation of hybrids by grafting is really possible; for, if even one instance of such formation could be unequivocally proved, it would show that sexual and asexual reproduction are essentially identical.

The cases of alleged graft-hybridism are exceedingly few, considering the enormous number of grafts that are made every year by horticulturists, and have been so made for centuries. Of these cases the most celebrated are those of Adam's laburnum (_Cytisus Adami_) and the bizzarria orange. Adam's laburnum is now flourishing in numerous places throughout Europe, all the trees having been raised as cuttings from the original graft, which was made by inserting a bud of the purple laburnum into a stock of the yellow. M. Adam, who made the graft, has left on record that from it there sprang the existing hybrid. There can be no question as to the truly hybrid character of the latter--all the peculiarities of both parent species being often blended in the same raceme, flower or even petal; but until the experiment shall have been successfully repeated there must always remain a strong suspicion that, notwithstanding the assertion and doubtless the belief of M. Adam, the hybrid arose as a cross in the ordinary way of seminal reproduction. Similarly, the bizzarria orange, which is unquestionably a hybrid between the bitter orange and the citron--since it presents the remarkable spectacle of these two different fruits blended into one--is stated by the gardener who first succeeded in producing it to have arisen as a graft-hybrid; but here again a similar doubt, similarly due to the need of corroboration, attaches to the statement. And the same remark applies to the still more wonderful case of the so-called trifacial orange, which blends three distinct kinds of fruit in one, and which is said to have been produced by artificially splitting and uniting the seeds taken from the three distinct species, the fruits of which now occur blended in the triple hybrid.

The other instances of alleged graft-hybridism are too numerous to be here noticed in detail; they refer to jessamine, ash, hazel, vine, hyacinth, potato, beet and rose. Of these the cases of the vine, beet and rose are the strongest as evidence of graft-hybridization, from the fact that some of them were produced as the result of careful experiments made by very competent experimentalists. On the whole, the results of some of these experiments, although so few in number, must be regarded as making out a strong case in favour of the possibility of graft-hybridism. For it must always be remembered that, in experiments of this kind, negative evidence, however great in amount, may be logically dissipated by a single positive result.

_Theory of Hybridism._--Charles Darwin was interested in hybridism as an experimental side of biology, but still more from the bearing of the facts on the theory of the origin of species. It is obvious that although hybridism is occasionally possible as an exception to the general infertility of species inter se, the exception is still more minimized when it is remembered that the hybrid progeny usually display some degree of sterility. The main facts of hybridism appear to lend support to the old doctrine that there are placed between all species the barriers of mutual sterility. The argument for the fixity of species appears still stronger when the general infertility of species crossing is contrasted with the general fertility of the crossing of natural and artificial varieties. Darwin himself, and afterwards G. J. Romanes, showed, however, that the theory of natural selection did not require the possibility of the commingling of specific types, and that there was no reason to suppose that the mutation of species should depend upon their mutual crossing. There existed more than enough evidence, and this has been added to since, to show that infertility with other species is no criterion of a species, and that there is no exact parallel between the degree of affinity between forms and their readiness to cross. The problem of hybridism is no more than the explanation of the generally reduced fertility of remoter crosses as compared with the generally increased fertility of crosses between organisms slightly different. Darwin considered and rejected the view that the inter-sterility of species could have been the result of natural selection.

"At one time it appeared to me probable," he wrote (_Origin of Species_, 6th ed. p. 247), "as it has to others, that the sterility of first crosses and of hybrids might have been slowly acquired through the natural selection of slightly lessened degrees of fertility, which, like any other variation, spontaneously appeared in certain individuals of one variety when crossed with those of another variety. For it would clearly be advantageous to two varieties or incipient species if they could be kept from blending, on the same principle that, when man is selecting at the same time two varieties, it is necessary that he should keep them separate. In the first place, it may be remarked that species inhabiting distinct regions are often sterile when crossed; now it could clearly have been of no advantage to such separated species to have been rendered mutually sterile and, consequently, this could not have been effected through natural selection; but it may perhaps be argued that, if a species were rendered sterile with some one compatriot, sterility with other species would follow as a necessary contingency. In the second place, it is almost as much opposed to the theory of natural selection as to that of special creation, that in reciprocal crosses the male element of one form should have been rendered utterly impotent on a second form, whilst at the same time the male element of this second form is enabled freely to fertilize the first form; for this peculiar state of the reproductive system could hardly have been advantageous to either species."

Darwin came to the conclusion that the sterility of crossed species must be due to some principle quite independent of natural selection. In his search for such a principle he brought together much evidence as to the instability of the reproductive system, pointing out in particular how frequently wild animals in captivity fail to breed, whereas some domesticated races have been so modified by confinement as to be fertile together although they are descended from species probably mutually infertile. He was disposed to regard the phenomena of differential sterility as, so to speak, by-products of the process of evolution. G. J. Romanes afterwards developed his theory of physiological selection, in which he supposed that the appearance of differential fertility within a species was the starting-point of new species; certain individuals by becoming fertile only _inter se_ proceeded along lines of modification diverging from the lines followed by other members of the species. Physiological selection in fact would operate in the same fashion as geographical isolation; if a portion of a species separated on an island tends to become a new species, so also a portion separated by infertility with the others would tend to form a new species. According to Romanes, therefore, mutual infertility was the starting-point, not the result, of specific modification. Romanes, however, did not associate his interesting theory with a sufficient number of facts, and it has left little mark on the history of the subject. A. R. Wallace, on the other hand, has argued that sterility between incipient species may have been increased by natural selection in the same fashion as other favourable variations are supposed to have been accumulated. He thought that "some slight degree of infertility was a not infrequent accompaniment of the external differences which always arise in a state of nature between varieties and incipient species."

Weismann concluded, from an examination of a series of plant hybrids, that from the same cross hybrids of different character may be obtained, but that the characters are determined at the moment of fertilization; for he found that all the flowers on the same hybrid plant resembled one another in the minutest details of colour and pattern. Darwin already had pointed to the act of fertilization as the determining point, and it is in this direction that the theory of hybridism has made the greatest advance.

The starting-point of the modern views comes from the experiments and conclusions on plant hybrids made by Gregor Mendel and published in 1865. It is uncertain if Darwin had paid attention to this work; Romanes, writing in the 9th edition of this _Encyclopaedia_, cited it without comment. First H. de Vries, then W. Bateson and a series of observers returned to the work of Mendel (see MENDELISM), and made it the foundation of much experimental work and still more theory. It is still too soon to decide if the confident predictions of the Mendelians are justified, but it seems clear that a combination of Mendel's numerical results with Weismann's (see HEREDITY) conception of the particulate character of the germ-plasm, or hereditary material, is at the root of the phenomena of hybridism, and that Darwin was justified in supposing it to lie outside the sphere of natural selection and to be a fundamental fact of living matter.

AUTHORITIES.--Apellö, "Über einige Resultate der Kreuzbefruchtung bei Knochenfischen," _Bergens mus. aarbog_ (1894); Bateson, "Hybridization and Cross-breeding," _Journal of the Royal Horticultural Society_ (1900); J. L. Bonhote, "Hybrid Ducks," _Proc. Zool. Soc. of London_ (1905), p. 147; Boveri, article "Befruchtung," in _Ergebnisse der Anatomie und Entwickelungsgeschichte von Merkel und Bonnet_, i. 385-485; Cornevin et Lesbre, "Étude sur un hybride issu d'une mule féconde et d'un cheval," _Rev. Sci._ li. 144; Charles Darwin, _Origin of Species_ (1859), _The Effects of Cross and Self-Fertilization in the Vegetable Kingdom_ (1878); Delage, _La Structure du protoplasma et les théories sur l'hérédité_ (1895, with a literature); de Vries, "The Law of Disjunction of Hybrids," _Comptes rendus_ (1900), p. 845; Elliot, _Hybridism_; Escherick, "Die biologische Bedeutung der Genitalabhänge der Insecten," _Verh. z. B. Wien_, xlii. 225; Ewart, _The Penycuik Experiments_ (1899); Focke, _Die Pflanzen-Mischlinge_ (1881); Foster-Melliar, _The Book of the Rose_ (1894); C. F. Gaertner, various papers in _Flora_, 1828, 1831, 1832, 1833, 1836, 1847, on "Bastard-Pflanzen"; Gebhardt, "Über die Bastardirung von _Rana esculenta_ mit _R. arvalis_," _Inaug. Dissert._ (Breslau, 1894); G. Mendel, "Versuche über Pflanzen-Hybriden," _Verh. Natur. Vereins in Brünn_ (1865), pp. 1-52; Morgan, "Experimental Studies," _Anat. Anz._ (1893), p. 141; id. p. 803; G. J. Romanes, "Physiological Selection," _Jour. Linn. Soc._ xix. 337; H. Scherren, "Notes on Hybrid Bears," _Proc. Zool. Soc. of London_ (1907), p. 431; Saunders, _Proc. Roy. Soc._ (1897), lxii. 11; Standfuss, "Études de zoologie expérimentale," _Arch. Sci. Nat._ vi. 495; Suchetet, "Les Oiseaux hybrides rencontrés à l'état sauvage," _Mém. Soc. Zool._ v. 253-525, and vi. 26-45; Vernon, "The Relation between the Hybrid and Parent Forms of Echinoid Larvae," _Proc. Roy. Soc._ lxv. 350; Wallace, _Darwinism_ (1889); Weismann, _The Germ-Plasm_ (1893). (P. C. M)

HYDANTOIN (glycolyl urea),

[beta] [alpha] / NH · CH2 C3H4N2O2 or CO < , \ NH · CO [gamma]

the ureïde of glycollic acid, may be obtained by heating allantoin or alloxan with hydriodic acid, or by heating bromacetyl urea with alcoholic ammonia. It crystallizes in needles, melting at 216° C.

When hydrolysed with baryta water yields hydantoic (glycoluric)acid, H2N·CO·NH·CH2·CO2H, which is readily soluble in hot water, and on heating with hydriodic acid decomposes into ammonia, carbon dioxide and glycocoll, CH2·NH2·CO2·H. Many substituted hydantoins are known; the [alpha]-alkyl hydantoins are formed on fusion of aldehyde- or ketone-cyanhydrins with urea, the [beta]-alkyl hydantoins from the fusion of mono-alkyl glycocolls with urea, and the [gamma]-alkyl hydantoins from the action of alkalis and alkyl iodides on the [alpha]-compounds. [gamma]-Methyl hydantoin has been obtained as a splitting product of caffeine (E. Fischer, _Ann._, 1882, 215, p. 253).

HYDE, the name of an English family distinguished in the 17th century. Robert Hyde of Norbury, Cheshire, had several sons, of whom the third was Lawrence Hyde of Gussage St Michael, Dorsetshire. Lawrence's son Henry was father of Edward Hyde, earl of Clarendon (q.v.), whose second son by his second wife was Lawrence, earl of Rochester (q.v.); another son was Sir Lawrence Hyde, attorney-general to Anne of Denmark, James I.'s consort; and a third son was Sir Nicholas Hyde (d. 1631), chief-justice of England. Sir Nicholas entered parliament in 1601 and soon became prominent as an opponent of the court, though he does not appear to have distinguished himself in the law. Before long, however, he deserted the popular party, and in 1626 he was employed by the duke of Buckingham in his defence to impeachment by the Commons; and in the following year he was appointed chief-justice of the king's bench, in which office it fell to him to give judgment in the celebrated case of Sir Thomas Darnell and others who had been committed to prison on warrants signed by members of the privy council, which contained no statement of the nature of the charge against the prisoners. In answer to the writ of _habeas corpus_ the attorney-general relied on the prerogative of the crown, supported by a precedent of Queen Elizabeth's reign. Hyde, three other judges concurring, decided in favour of the crown, but without going so far as to declare the right of the crown to refuse indefinitely to show cause against the discharge of the prisoners. In 1629 Hyde was one of the judges who condemned Eliot, Holles and Valentine for conspiracy in parliament to resist the king's orders; refusing to admit their plea that they could not be called upon to answer out of parliament for acts done in parliament. Sir Nicholas Hyde died in August 1631.

Sir Lawrence Hyde, attorney-general to Anne of Denmark, had eleven sons, four of whom were men of some mark. Henry was an ardent royalist who accompanied Charles II. to the continent, and returning to England was beheaded in 1650; Alexander (1598-1667) became bishop of Salisbury in 1665; Edward (1607-1659) was a royalist divine who was nominated dean of Windsor in 1658, but died before taking up the appointment, and who was the author of many controversial works in Anglican theology; and Robert (1595-1665) became recorder of Salisbury and represented that borough in the Long Parliament, in which he professed royalist principles, voting against the attainder of Strafford. Having been imprisoned and deprived of his recordership by the parliament in 1645/6, Robert Hyde gave refuge to Charles II. on his flight from Worcester in 1651, and on the Restoration he was knighted and made a judge of the common pleas. He died in 1665. Henry Hyde (1672-1753), only son of Lawrence, earl of Rochester, became 4th earl of Clarendon and 2nd earl of Rochester, both of which titles became extinct at his death. He was in no way distinguished, but his wife Jane Hyde, countess of Clarendon and Rochester (d. 1725), was a famous beauty celebrated by the homage of Swift, Prior and Pope, and by the groundless scandal of Lady Mary Wortley Montagu. Two of her daughters, Jane, countess of Essex, and Catherine, duchess of Queensberry, were also famous beauties of the reign of Queen Anne. Her son, Henry Hyde (1710-1753), known as Viscount Cornbury, was a Tory and Jacobite member of parliament, and an intimate friend of Bolingbroke, who addressed to him his _Letters on the Study and Use of History_, and _On the Spirit of Patriotism_. In 1750 Lord Cornbury was created Baron Hyde of Hindon, but, as he predeceased his father, this title reverted to the latter and became extinct at his death. Lord Cornbury was celebrated as a wit and a conversationalist. By his will he bequeathed the papers of his great-grandfather, Lord Clarendon, the historian, to the Bodleian Library at Oxford.

See Lord Clarendon, _The Life of Edward, Earl of Clarendon_ (3 vols., Oxford, 1827); Edward Foss, _The Judges of England_ (London, 1848-1864); Anthony à Wood, _Athenae oxonienses_ (London, 1813-1820); Samuel Pepys, _Diary and Correspondence_, edited by Lord Braybrooke (4 vols., London, 1854).

HYDE, THOMAS (1636-1703), English Orientalist, was born at Billingsley, near Bridgnorth, in Shropshire, on the 29th of June 1636. He inherited his taste for linguistic studies, and received his first lessons in some of the Eastern tongues, from his father, who was rector of the parish. In his sixteenth year Hyde entered King's College, Cambridge, where, under Wheelock, professor of Arabic, he made rapid progress in Oriental languages, so that, after only one year of residence, he was invited to London to assist Brian Walton in his edition of the _Polyglott Bible_. Besides correcting the Arabic, Persic and Syriac texts for that work, Hyde transcribed into Persic characters the Persian translation of the Pentateuch, which had been printed in Hebrew letters at Constantinople in 1546. To this work, which Archbishop Ussher had thought well-nigh impossible even for a native of Persia, Hyde appended the Latin version which accompanies it in the _Polyglott_. In 1658 he was chosen Hebrew reader at Queen's College, Oxford, and in 1659, in consideration of his erudition in Oriental tongues, he was admitted to the degree of M.A. In the same year he was appointed under-keeper of the Bodleian Library, and in 1665 librarian-in-chief. Next year he was collated to a prebend at Salisbury, and in 1673 to the archdeaconry of Gloucester, receiving the degree of D.D. shortly afterwards. In 1691 the death of Edward Pococke opened up to Hyde the Laudian professorship of Arabic; and in 1697, on the deprivation of Roger Altham, he succeeded to the regius chair of Hebrew and a canonry of Christ Church. Under Charles II., James II. and William III. Hyde discharged the duties of Eastern interpreter to the court. Worn out by his unremitting labours, he resigned his librarianship in 1701, and died at Oxford on the 18th of February 1703. Hyde, who was one of the first to direct attention to the vast treasures of Oriental antiquity, was an excellent classical scholar, and there was hardly an Eastern tongue accessible to foreigners with which he was not familiar. He had even acquired Chinese, while his writings are the best testimony to his mastery of Turkish, Arabic, Syriac, Persian, Hebrew and Malay.

In his chief work, _Historia religionis veterum Persarum_ (1700), he made the first attempt to correct from Oriental sources the errors of the Greek and Roman historians who had described the religion of the ancient Persians. His other writings and translations comprise _Tabulae longitudinum et latitudinum stellarum fixarum ex observatione principis Ulugh Beighi_ (1665), to which his notes have given additional value; _Quatuor evangelia et acta apostolorum lingua Malaica, caracteribus Europaeis_ (1677); _Epistola de mensuris et ponderibus serum sive sinensium_ (1688), appended to Bernard's _De mensuris et ponderibus antiquis; Abraham Peritsol itinera mundi_ (1691); and _De ludis orientalibus libri II._ (1694).

With the exception of the _Historia religionis_, which was republished by Hunt and Costard in 1760, the writings of Hyde, including some unpublished MSS., were collected and printed by Dr Gregory Sharpe in 1767 under the title _Syntagma dissertationum quas olim ... Thomas Hyde separatim edidit_. There is a life of the author prefixed. Hyde also published a catalogue of the Bodleian Library in 1674.

HYDE, a market town and municipal borough in the Hyde parliamentary division of Cheshire, England, 7½ m. E. of Manchester, by the Great Central railway. Pop. (1901) 32,766. It lies in the densely populated district in the north-east of the county, on the river Tame, which here forms the boundary of Cheshire with Lancashire. To the east the outlying hills of the Peak district of Derbyshire rise abruptly. The town has cotton weaving factories, spinning mills, print-works, iron foundries and machine works; also manufactures of hats and margarine. There are extensive coal mines in the vicinity. Hyde is wholly of modern growth, though it contains a few ancient houses, such as Newton Hall, in the part of the town so called. The old family of Hyde held possession of the manor as early as the reign of John. The borough, incorporated in 1881, is under a mayor, 6 aldermen and 18 councillors. Area, 3081 acres.

HYDE DE NEUVILLE, JEAN GUILLAUME, BARON (1776-1857), French politician, was born at La Charité-sur-Loire (Nièvre) on the 24th of January 1776, the son of Guillaume Hyde, who belonged to an English family which had emigrated with the Stuarts after the rebellion of 1745. He was only seventeen when he successfully defended a man denounced by Fouché before the revolutionary tribunal of Nevers. From 1793 onwards he was an active agent of the exiled princes; he took part in the Royalist rising in Berry in 1796, and after the _coup d'état_ of the 18th Brumaire (November 9, 1799) tried to persuade Bonaparte to recall the Bourbons. An accusation of complicity in the infernal machine conspiracy of 1800-1801 was speedily retracted, but Hyde de Neuville retired to the United States, only to return after the Restoration. He was sent by Louis XVIII. to London to endeavour to persuade the British government to transfer Napoleon to a remoter and safer place of exile than the isle of Elba, but the negotiations were cut short by the emperor's return to France in March 1815. In January 1816 de Neuville became French ambassador at Washington, where he negotiated a commercial treaty. On his return in 1821 he declined the Constantinople embassy, and in November 1822 was elected deputy for Cosne. Shortly afterwards he was appointed French ambassador at Lisbon, where his efforts to oust British influence culminated, in connexion with the _coup d'état_ of Dom Miguel (April 30, 1824), in his suggestion to the Portuguese minister to invite the armed intervention of Great Britain. It was assumed that this would be refused, in view of the loudly proclaimed British principle of non-intervention, and that France would then be in a position to undertake a duty that Great Britain had declined. The scheme broke down, however, owing to the attitude of the reactionary party in the government of Paris, which disapproved of the Portuguese constitution. This destroyed his influence at Lisbon, and he returned to Paris to take his seat in the Chamber of Deputies. In spite of his pronounced Royalism, he now showed Liberal tendencies, opposed the policy of Villèle's cabinet, and in 1828 became a member of the moderate administration of Martignac as minister of marine. In this capacity he showed active sympathy with the cause of Greek independence. During the Polignac ministry (1829-1830) he was again in opposition, being a firm upholder of the charter; but after the revolution of July 1830 he entered an all but solitary protest against the exclusion of the legitimate line of the Bourbons from the throne, and resigned his seat. He died in Paris on the 28th of May 1857.

His _Mémoires et souvenirs_ (3 vols., 1888), compiled from his notes by his nieces, the vicomtesse de Bardonnet and the baronne Laurenceau, are of great interest for the Revolution and the Restoration.

HYDE PARK, a small township of Norfolk county, Massachusetts, U.S.A., about 8 m. S.W. of the business centre of Boston. Pop. (1890) 10,193; (1900) 13,244, of whom 3805 were foreign-born; (1910 census) 15,507. Its area is about 4½ sq. m. It is traversed by the New York, New Haven & Hartford railway, which has large repair shops here, and by the Neponset river and smaller streams. The township contains the villages of Hyde Park, Readville (in which there is the famous "Weil" trotting-track), Fairmount, Hazelwood and Clarendon Hills. Until about 1856 Hyde Park was a farmstead. The value of the total factory product increased from $4,383,959 in 1900 to $6,739,307 in 1905, or 53.7%. In 1868 Hyde Park was incorporated as a township, being formed of territory taken from Dorchester, Dedham and Milton.

HYDERABAD, or HAIDARABAD, a city and district of British India, in the Sind province of Bombay. The city stands on a hill about 3 m. from the left bank of the Indus, and had a population in 1901 of 69,378. Upon the site of the present fort is supposed to have stood the ancient town of Nerankot, which in the 8th century submitted to Mahommed bin Kasim. In 1768 the present city was founded by Ghulam Shah Kalhora; and it remained the capital of Sind until 1843, when, after the battle of Meeanee, it was surrendered to the British, and the capital transferred to Karachi. The city is built on the most northerly hills of the Ganga range, a site of great natural strength. In the fort, which covers an area of 36 acres, is the arsenal of the province, transferred thither from Karachi in 1861, and the palaces of the ex-mirs of Sind. An excellent water supply is derived from the Indus. In addition to manufactures of silk, gold and silver embroidery, lacquered ware and pottery, there are three factories for ginning cotton. There are three high schools, training colleges for masters and mistresses, a medical school, an agricultural school for village officials, and a technical school. The city suffered from plague in 1896-1897.

The DISTRICT OF HYDERABAD has an area of 8291 sq. m., with a population in 1901 of 989,030, showing an increase of 15% in the decade. It consists of a vast alluvial plain, on the left bank of the Indus, 216 m. long and 48 broad. Fertile along the course of the river, it degenerates towards the east into sandy wastes, sparsely populated, and defying cultivation. The monotony is relieved by the fringe of forest which marks the course of the river, and by the avenues of trees that line the irrigation channels branching eastward from this stream. The south of the district has a special feature in its large natural water-courses (called _dhoras_) and basin-like shallows (_chhaus_), which retain the rains for a long time. A limestone range called the Ganga and the pleasant frequency of garden lands break the monotonous landscape. The principal crops are millets, rice, oil-seeds, cotton and wheat, which are dependent on irrigation, mostly from government canals. There is a special manufacture at Hala of glazed pottery and striped cotton cloth. Three railways traverse the district: (1) one of the main lines of the North-Western system, following the Indus valley and crossing the river near Hyderabad; (2) a broad-gauge branch running south to Badin, which will ultimately be extended to Bombay; and (3) a metre-gauge line from Hyderabad city into Rajputana.

HYDERABAD, HAIDARABAD, also known as the Nizam's Dominions, the principal native state of India in extent, population and political importance; area, 82,698 sq. m.; pop. (1901) 11,141,142, showing a decrease of 3.4% in the decade; estimated revenue 4½ crores of Hyderabad rupees (£2,500,000). The state occupies a large portion of the eastern plateau of the Deccan. It is bounded on the north and north-east by Berar, on the south and south-east by Madras, and on the west by Bombay. The country presents much variety of surface and feature; but it may be broadly divided into two tracts, distinguished from one another geologically and ethnically, which are locally known from the languages spoken as Telingana and Marathwara. In some parts it is mountainous, wooded and picturesque, in others flat and undulating. The open country includes lands of all descriptions, including many rich and fertile plains, much good land not yet brought under cultivation, and numerous tracts too sterile ever to be cultivated. In the north-west the geological formations are volcanic, consisting principally of trap, but in some parts of basalt; in the middle, southern and south-western parts the country is overlaid with gneissic formations. The territory is well watered, rivers being numerous, and tanks or artificial pieces of water abundant, especially in Telingana. The principal rivers are the Godavari, with its tributaries the Dudna, Manjira and Pranhita; the Wardha, with its tributary the Penganga; and the Kistna, with its tributary the Tungabhadra. The climate may be considered in general good; and as there are no arid bare deserts, hot winds are little felt.

More than half the revenue of the state is derived from the land, and the development of the country by irrigation and railways has caused considerable expansion in this revenue, though the rate of increase in the decade 1891-1901 was retarded by a succession of unfavourable seasons. The soil is generally fertile, though in some parts it consists of _chilka_, a red and gritty mould little fitted for purposes of agriculture. The principal crops are millets of various kinds, rice, wheat, oil-seeds, cotton, tobacco, sugar-cane, and fruits and garden produce in great variety. Silk, known as _tussur_, the produce of a wild species of worm, is utilized on a large scale. Lac, suitable for use as a resin or dye, gums and oils are found in great quantities. Hides, raw and tanned, are articles of some importance in commerce. The principal exports are cotton, oil-seeds, country-clothes and hides; the imports are salt, grain, timber, European piece-goods and hardware. The mineral wealth of the state consists of coal, copper, iron, diamonds and gold; but the development of these resources has not hitherto been very successful. The only coal mine now worked is the large one at Singareni, with an annual out-turn of nearly half a million tons. This coal has enabled the nizam's guaranteed state railway to be worked so cheaply that it now returns a handsome profit to the state. It also gives encouragement to much-needed schemes of railway extension, and to the erection of cotton presses and of spinning and weaving mills. The Hyderabad-Godavari railway (opened in 1901) traverses a rich cotton country, and cotton presses have been erected along the line. The currency of the state is based on the _hali sikka_, which contains approximately the same weight of silver as the British rupee, but its exchange value fell heavily after 1893, when free coinage ceased in the mint. In 1904, however, a new coin (the Mahbubia rupee) was minted; the supply was regulated, and the rate of exchange became about 115 = 100 British rupees. The state suffered from famine during 1900, the total number of persons in receipt of relief rising to nearly 500,000 in June of that year. The nizam met the demands for relief with great liberality.

The nizam of Hyderabad is the principal Mahommedan ruler in India. The family was founded by Asaf Jah, a distinguished Turkoman soldier of the emperor Aurangzeb, who in 1713 was appointed subahdar of the Deccan, with the title of nizam-ul-mulk (regulator of the state), but eventually threw off the control of the Delhi court. Azaf Jah's death in 1748 was followed by an internecine struggle for the throne among his descendants, in which the British and the French took part. At one time the French nominee, Salabat Jang, established himself with the help of Bussy. But finally, in 1761, when the British had secured their predominance throughout southern India, Nizam Ali took his place and ruled till 1803. It was he who confirmed the grant of the Northern Circars in 1766, and joined in the two wars against Tippoo Sultan in 1792 and 1799. The additions of territory which he acquired by these wars was afterwards (1800) ceded to the British, as payment for the subsidiary force which he had undertaken to maintain. By a later treaty in 1853, the districts known as Berar were "assigned" to defray the cost of the Hyderabad contingent. In 1857 when the Mutiny broke out, the attitude of Hyderabad as the premier native state and the cynosure of the Mahommedans in India became a matter of extreme importance; but Afzul-ud-Dowla, the father of the present ruler, and his famous minister, Sir Salar Jang, remained loyal to the British. An attack on the residency was repulsed, and the Hyderabad contingent displayed their loyalty in the field against the rebels. In 1902 by a treaty made by Lord Curzon, Berar was leased in perpetuity to the British government, and the Hyderabad contingent was merged in the Indian army. The nizam Mir Mahbub Ali Khan Bahadur, Asaf Jah, a direct descendant of the famous nizam-ul-mulk, was born on the 18th of August 1866. On the death of his father in 1869 he succeeded to the throne as a minor, and was invested with full powers in 1884. He is notable as the originator of the Imperial Service Troops, which now form the contribution of the native chiefs to the defence of India. On the occasion of the Panjdeh incident in 1885 he made an offer of money and men, and subsequently on the occasion of Queen Victoria's Jubilee in 1887 he offered 20 lakhs (£130,000) annually for three years for the purpose of frontier defence. It was finally decided that the native chiefs should maintain small but well-equipped bodies of infantry and cavalry for imperial defence. For many years past the Hyderabad finances were in a very unhealthy condition, the expenditure consistently outran the revenue, and the nobles, who held their tenure under an obsolete feudal system, vied with each other in ostentatious extravagance. But in 1902, on the revision of the Berar agreement, the nizam received 25 lakhs (£167,000) a year for the rent of Berar, thus substituting a fixed for a fluctuating source of income, and a British financial adviser was appointed for the purpose of reorganizing the resources of the state.

See S. H. Bilgrami and C. Willmott, _Historical and Descriptive Sketch of the Nizam's Dominions_ (Bombay, 1883-1884).

HYDERABAD or HAIDARABAD, capital of the above state, is situated on the right bank of the river Musi, a tributary of the Kistna, with Golconda to the west, and the residency and its bazaars and the British cantonment of Secunderabad to the north-east. It is the fourth largest city in India; pop. (1901) 448,466, including suburbs and cantonment. The city itself is in shape a parallelogram, with an area of more than 2 sq. m. It was founded in 1589 by Mahommed Kuli, fifth of the Kutb Shahi kings, of whose period several important buildings remain as monuments. The principal of these is the Char Minar or Four Minarets (1591). The minarets rise from arches facing the cardinal points, and stand in the centre of the city, with four roads radiating from their base. The Ashur Khana (1594), a ceremonial building, the hospital, the Gosha Mahal palace and the Mecca mosque, a sombre building designed after a mosque at Mecca, surrounding a paved quadrangle 360 ft. square, were the other principal buildings of the Kutb Shahi period, though the mosque was only completed in the time of Aurangzeb. The city proper is surrounded by a stone wall with thirteen gates, completed in the time of the first nizam, who made Hyderabad his capital. The suburbs, of which the most important is Chadarghat, extend over an additional area of 9 sq. m. There are several fine palaces built by various nizams, and the British residency is an imposing building in a large park on the left bank of the Musi, N.E. of the city. The bazaars surrounding it, and under its jurisdiction, are extremely picturesque and are thronged with natives from all parts of India. Four bridges crossed the Musi, the most notable of which was the Purana Pul, of 23 arches, built in 1593. On the 27th and 28th of September 1908, however, the Musi, swollen by torrential rainfall (during which 15 in. fell in 36 hours), rose in flood to a height of 12 ft. above the bridges and swept them away. The damage done was widespread; several important buildings were involved, including the palace of Salar Jang and the Victoria zenana hospital, while the beautiful grounds of the residency were destroyed. A large and densely populated part of the city was wrecked, and thousands of lives were lost. The principal educational establishments are the Nizam college (first grade), engineering, law, medical, normal, industrial and Sanskrit schools, and a number of schools for Europeans and Eurasians. Hyderabad is an important centre of general trade, and there is a cotton mill in its vicinity. The city is supplied with water from two notable works, the Husain Sagar and the Mir Alam, both large lakes retained by great dams. Secunderabad, the British military cantonment, is situated 5½ m. N. of the residency; it includes Bolaram, the former headquarters of the Hyderabad contingent.

HYDER ALI, or Haidar 'Ali (c. 1722-1782), Indian ruler and commander. This Mahommedan soldier-adventurer, who, followed by his son Tippoo, became the most formidable Asiatic rival the British ever encountered in India, was the great-grandson of a _fakir_ or wandering ascetic of Islam, who had found his way from the Punjab to Gulburga in the Deccan, and the second son of a _naik_ or chief constable at Budikota, near Kolar in Mysore. He was born in 1722, or according to other authorities 1717. An elder brother, who like himself was early turned out into the world to seek his own fortune, rose to command a brigade in the Mysore army, while Hyder, who never learned to read or write, passed the first years of his life aimlessly in sport and sensuality, sometimes, however, acting as the agent of his brother, and meanwhile acquiring a useful familiarity with the tactics of the French when at the height of their reputation under Dupleix. He is said to have induced his brother to employ a Parsee to purchase artillery and small arms from the Bombay government, and to enrol some thirty sailors of different European nations as gunners, and is thus credited with having been "the first Indian who formed a corps of sepoys armed with firelocks and bayonets, and who had a train of artillery served by Europeans." At the siege of Devanhalli (1749) Hyder's services attracted the attention of Nanjiraj, the minister of the raja of Mysore, and he at once received an independent command; within the next twelve years his energy and ability had made him completely master of minister and raja alike, and in everything but in name he was ruler of the kingdom. In 1763 the conquest of Kanara gave him possession of the treasures of Bednor, which he resolved to make the most splendid capital in India, under his own name, thenceforth changed from Hyder Naik into Hyder Ali Khan Bahadur; and in 1765 he retrieved previous defeat at the hands of the Mahrattas by the destruction of the Nairs or military caste of the Malabar coast, and the conquest of Calicut. Hyder Ali now began to occupy the serious attention of the Madras government, which in 1766 entered into an agreement with the nizam to furnish him with troops to be used against the common foe. But hardly had this alliance been formed when a secret arrangement was come to between the two Indian powers, the result of which was that Colonel Smith's small force was met with a united army of 80,000 men and 100 guns. British dash and sepoy fidelity, however, prevailed, first in the battle of Chengam (September 3rd, 1767), and again still more remarkably in that of Tiruvannamalai (Trinomalai). On the loss of his recently made fleet and forts on the western coast, Hyder Ali now offered overtures for peace; on the rejection of these, bringing all his resources and strategy into play, he forced Colonel Smith to raise the siege of Bangalore, and brought his army within 5 m. of Madras. The result was the treaty of April 1769, providing for the mutual restitution of all conquests, and for mutual aid and alliance in defensive war; it was followed by a commercial treaty in 1770 with the authorities of Bombay. Under these arrangements Hyder Ali, when defeated by the Mahrattas in 1772, claimed British assistance, but in vain; this breach of faith stung him to fury, and thenceforward he and his son did not cease to thirst for vengeance. His time came when in 1778 the British, on the declaration of war with France, resolved to drive the French out of India. The capture of Mahé on the coast of Malabar in 1779, followed by the annexation of lands belonging to a dependent of his own, gave him the needed pretext. Again master of all that the Mahrattas had taken from him, and with empire extended to the Kistna, he descended through the passes of the Ghats amid burning villages, reaching Conjeeveram, only 45 m. from Madras, unopposed. Not till the smoke was seen from St Thomas's Mount, where Sir Hector Munro commanded some 5200 troops, was any movement made; then, however, the British general sought to effect a junction with a smaller body under Colonel Baillie recalled from Guntur. The incapacity of these officers, notwithstanding the splendid courage of their men, resulted in the total destruction of Baillie's force of 2800 (September the 10th, 1780). Warren Hastings sent from Bengal Sir Eyre Coote, who, though repulsed at Chidambaram, defeated Hyder thrice successively in the battles of Porto Novo, Pollilur and Sholingarh, while Tippoo was forced to raise the siege of Wandiwash, and Vellore was provisioned. On the arrival of Lord Macartney as governor of Madras, the British fleet captured Negapatam, and forced Hyder Ali to confess that he could never ruin a power which had command of the sea. He had sent his son Tippoo to the west coast, to seek the assistance of the French fleet, when his death took place suddenly at Chittur in December 1782.

See L. B. Bowring, _Haidar Ali and Tipu Sultan_, "Rulers of India" series (1893). For the personal character and administration of Hyder Ali see the _History of Hyder Naik_, written by Mir Hussein Ali Khan Kirmani (translated from the Persian by Colonel Miles, and published by the Oriental Translation Fund), and the curious work written by M. Le Maître de La Tour, commandant of his artillery (_Histoire d'Hayder-Ali Khan_, Paris, 1783). For the whole life and times see Wilks, _Historical Sketches of the South of India_ (1810-1817); Aitchison's Treaties, vol. v. (2nd ed., 1876); and Pearson, _Memoirs of Schwartz_ (1834).

HYDRA (or SIDRA, NIDRA, IDERO, &c.; anc. _Hydrea_), an island of Greece, lying about 4 m. off the S.E. coast of Argolis in the Peloponnesus, and forming along with the neighbouring island of Dokos (Dhoko) the Bay of Hydra. Pop. about 6200. The greatest length from south-west to north-east is about 11 m., and the area is about 21 sq. mi.; but it is little better than a rocky and treeless ridge with hardly a patch or two of arable soil. Hence the epigram of Antonios Kriezes to the queen of Greece: "The island produces prickly pears in abundance, splendid sea captains and excellent prime ministers." The highest point, Mount Ere, so called (according to Miaoules) from the Albanian word for wind, is 1958 ft. high. The next in importance is known as the Prophet Elias, from the large convent of that name on its summit. It was there that the patriot Theodorus Kolokotrones was imprisoned, and a large pine tree is still called after him. The fact that in former times the island was richly clad with woods is indicated by the name still employed by the Turks, _Tchamliza_, the place of pines; but it is only in some favoured spots that a few trees are now to be found. Tradition also has it that it was once a well-watered island (hence the designation Hydrea), but the inhabitants are now wholly dependent on the rain supply, and they have sometimes had to bring water from the mainland. This lack of fountains is probably to be ascribed in part to the effect of earthquakes, which are not infrequent; that of 1769 continued for six whole days. Hydra, the chief town, is built near the middle of the northern coast, on a very irregular site, consisting of three hills and the intervening ravines. From the sea its white and handsome houses present a picturesque appearance, and its streets though narrow are clean and attractive. Besides the principal harbour, round which the town is built, there are three other ports on the north coast--Mandraki, Molo, Panagia, but none of them is sufficiently sheltered. Almost all the population of the island is collected in the chief town, which is the seat of a bishop, and has a local court, numerous churches and a high school. Cotton and silk weaving, tanning and shipbuilding are carried on, and there is a fairly active trade.

Hydra was of no importance in ancient times. The only fact in its history is that the people of Hermione (a city on the neighbouring mainland now known by the common name of _Kastri_) surrendered it to Samian refugees, and that from these the people of Troezen received it in trust. It appears to be completely ignored by the Byzantine chroniclers. In 1580 it was chosen as a refuge by a body of Albanians from Kokkinyas in Troezenia; and other emigrants followed in 1590, 1628, 1635, 1640, &c. At the close of the 17th century the Hydriotes took part in the reviving commerce of the Peloponnesus; and in course of time they extended their range. About 1716 they began to build _sakturia_ (of from 10 to 15 tons burden), and to visit the islands of the Aegean; not long after they introduced the _latinadika_ (40-50 tons), and sailed as far as Alexandria, Constantinople, Trieste and Venice; and by and by they ventured to France and even America. From the grain trade of south Russia more especially they derived great wealth. In 1813 there were about 22,000 people in the island, and of these 10,000 were seafarers. At the time of the outbreak of the war of Greek independence the total population was 28,190, of whom 16,460 were natives and the rest foreigners. One of their chief families, the Konduriotti, was worth £2,000,000. Into the struggle the Hydriotes flung themselves with rare enthusiasm and devotion, and the final deliverance of Greece was mainly due to the service rendered by their fleets.

See Pouqueville, _Voy. de la Grèce_, vol. vi.; Antonios Miaoules, [Greek: Hypomnêma peri tês nêsou Hydras] (Munich, 1834); Id. [Greek: Sunoptikê historia tôn naumachiôn dia tôn ploiôn tôn triôn nêsôn, Hydras, Petsôn kai Psarôn] (Nauplia, 1833); Id. [Greek: Historia tês nêsou Hydras] (Athens, 1874); G. D. Kriezes, [Greek: Historia tês nêsou Hydras] (Patras, 1860).

HYDRA (watersnake), in Greek legend, the offspring of Typhon and Echidna, a gigantic monster with nine heads (the number is variously given), the centre one being immortal. Its haunt was a hill beneath a plane tree near the river Amymone, in the marshes of Lerna by Argos. The destruction of this Lernaean hydra was one of the twelve "labours" of Heracles, which he accomplished with the assistance of Iolaus. Finding that as soon as one head was cut off two grew up in its place, they burnt out the roots with firebrands, and at last severed the immortal head from the body, and buried it under a mighty block of rock. The arrows dipped by Heracles in the poisonous blood or gall of the monster ever afterwards inflicted fatal wounds. The generally accepted interpretation of the legend is that "the hydra denotes the damp, swampy ground of Lerna with its numerous springs ([Greek: kephalai], heads); its poison the miasmic vapours rising from the stagnant water; its death at the hands of Heracles the introduction of the culture and consequent purification of the soil" (Preller). A euhemeristic explanation is given by Palaephatus (39). An ancient king named Lernus occupied a small citadel named Hydra, which was defended by 50 bowmen. Heracles besieged the citadel and hurled firebrands at the garrison. As often as one of the defenders fell, two others at once stepped into his place. The citadel was finally taken with the assistance of the army of Iolaus and the garrison slain.

See Hesiod, _Theog._, 313; Euripides, _Hercules furens_, 419; Pausanias ii. 37; Apollodorus ii. 5, 2; Diod. Sic. iv. 11; Roscher's _Lexikon der Mythologie_. In the article GREEK ART, fig. 20 represents the slaying of the Lernaean hydra by Heracles.

HYDRA, in astronomy, a constellation of the southern hemisphere, mentioned by Eudoxus (4th century B.C.) and Aratus (3rd century B.C.), and catalogued by Ptolemy (27 stars), Tycho Brahe (19) and Hevelius (31). Interesting objects are: the nebula _H. IV. 27 Hydrae_, a planetary nebula, gaseous and whose light is about equal to an 8th magnitude star; [epsilon] _Hydrae_, a beautiful triple star, composed of two yellow stars of the 4th and 6th magnitudes, and a blue star of the 7th magnitude; _R. Hydrae_, a long period (425 days) variable, the range in magnitude being from 4 to 9.7; and _U. Hydrae_, an irregularly variable, the range in magnitude being 4.5 to 6.

HYDRACRYLIC ACID (ethylene lactic acid), CH2OH·CH2·CO2H. an organic oxyacid prepared by acting with silver oxide and water on [beta]-iodopropionic acid, or from ethylene by the addition of hypochlorous acid, the addition product being then treated with potassium cyanide and hydrolysed by an acid. It may also be prepared by oxidizing the trimethylene glycol obtained by the action of hydrobromic acid on allylbromide. It is a syrupy liquid, which on distillation is resolved into water and the unsaturated acrylic acid, CH2:CH·CO2H. Chromic and nitric acids oxidize it to oxalic acid and carbon dioxide. Hydracrylic aldehyde, CH2OH·CH2·CHO, was obtained in 1904 by J. U. Nef (_Ann._ 335, p. 219) as a colourless oil by heating acrolein with water. Dilute alkalis convert it into crotonaldehyde, CH3·CH:CH·CHO.

HYDRANGEA, a popular flower, the plant to which the name is most commonly applied being _Hydrangea Hortensia_, a low deciduous shrub, producing rather large oval strongly-veined leaves in opposite pairs along the stem. It is terminated by a massive globular corymbose head of flowers, which remain a long period in an ornamental condition. The normal colour of the flowers, the majority of which have neither stamens nor pistil, is pink; but by the influence of sundry agents in the soil, such as alum or iron, they become changed to blue. There are numerous varieties, one of the most noteworthy being "Thomas Hogg" with pure white flowers. The part of the inflorescence which appears to be the flower is an exaggerated expansion of the sepals, the other parts being generally abortive. The perfect flowers are small, rarely produced in the species above referred to, but well illustrated by others, in which they occupy the inner parts of the corymb, the larger showy neuter flowers being produced at the circumference.

There are upwards of thirty species, found chiefly in Japan, in the mountains of India, and in North America, and many of them are familiar in gardens. _H. Hortensia_ (a species long known in cultivation In China and Japan) is the most useful for decoration, as the head of flowers lasts long in a fresh state, and by the aid of forcing can be had for a considerable period for the ornamentation of the greenhouse and conservatory. Their natural flowering season is towards the end of the summer, but they may be had earlier by means of forcing. _H. japonica_ is another fine conservatory plant, with foliage and habit much resembling the last named, but this has flat corymbs of flowers, the central ones small and perfect, and the outer ones only enlarged and neuter. This also produces pink or blue flowers under the influence of different soils.

The Japanese species of hydrangea are sufficiently hardy to grow in any tolerably favourable situation, but except in the most sheltered localities they seldom blossom to any degree of perfection in the open air, the head of blossom depending on the uninjured development of a well-ripened terminal bud, and this growth being frequently affected by late spring frosts. They are much more useful for pot-culture indoors, and should be reared from cuttings of shoots having the terminal bud plump and prominent, put in during summer, these developing a single head of flowers the succeeding summer. Somewhat larger plants may be had by nipping out the terminal bud and inducing three or four shoots to start in its place, and these, being steadily developed and well ripened, should each yield its inflorescence in the following summer, that is, when two years old. Large plants grown in tubs and vases are fine subjects for large conservatories, and useful for decorating terrace walks and similar places during summer, being housed in winter, and started under glass in spring.

_Hydrangea paniculata_ var. _grandiflora_ is a very handsome plant; the branched inflorescence under favourable circumstances is a yard or more in length, and consists of large spreading masses of crowded white neuter flowers which completely conceal the few inconspicuous fertile ones. The plant attains a height of 8 to 10 ft. and when in flower late in summer and in autumn is a very attractive object in the shrubbery.

The Indian and American species, especially the latter, are quite hardy, and some of them are extremely effective.

HYDRASTINE, C21H21NO6, an alkaloid found with berberine in the root of golden seal, _Hydrastis canadensis_, a plant indigenous to North America. It was discovered by Durand in 1851, and its chemistry formed the subject of numerous communications by E. Schmidt and M. Freund (see _Ann._, 1892, 271, p. 311) who, aided by P. Fritsch (_Ann._, 1895, 286, p. 1), established its constitution. It is related to narcotine, which is methoxy hydrastine. The root of golden seal is used in medicine under the name hydrastis rhizome, as a stomachic and nervine stimulant.

HYDRATE, in chemistry, a compound containing the elements of water in combination; more specifically, a compound containing the monovalent hydroxyl or OH group. The first and more general definition includes substances containing water of crystallization; such salts are said to be hydrated, and when deprived of their water to be dehydrated or anhydrous. Compounds embraced by the second definition are more usually termed _hydroxides_, since at one time they were regarded as combinations of an oxide with water, for example, calcium oxide or lime when slaked with water yielded calcium hydroxide, written formerly as CaO·H20. The general formulae of hydroxides are: M^iOH, M^(ii)(OH)2, M^(iii)(OH)3, M^(iv)(OH)4, &c., corresponding to the oxides M2^iO, M^(ii)O, M2^(iii)O3, M^(iv)O2, &c., the Roman index denoting the valency of the element. There is an important difference between non-metallic and metallic hydroxides; the former are invariably acids (oxyacids), the latter are more usually basic, although acidic metallic oxides yield acidic hydroxides. Elements exhibiting strong basigenic or oxygenic characters yield the most, stable hydroxides; in other words, stable hydroxides are associated with elements belonging to the extreme groups of the periodic system, and unstable hydroxides with the central members. The most stable basic hydroxides are those of the alkali metals, viz. lithium, sodium, potassium, rubidium and caesium, and of the alkaline earth metals, viz. calcium, barium and strontium; the most stable acidic hydroxides are those of the elements placed in groups VB, VIB and VIIB of the periodic table.

HYDRAULICS (Gr. [Greek: hydôr], water, and [Greek: aulos], a pipe), the branch of engineering science which deals with the practical applications of the laws of hydromechanics.

I. THE DATA OF HYDRAULICS[1]

§ 1. _Properties of Fluids._--The fluids to which the laws of practical hydraulics relate are substances the parts of which possess very great mobility, or which offer a very small resistance to distortion independently of inertia. Under the general heading Hydromechanics a fluid is defined to be a substance which yields continually to the slightest tangential stress, and hence in a fluid at rest there can be no tangential stress. But, further, in fluids such as water, air, steam, &c., to which the present division of the article relates, the tangential stresses that are called into action between contiguous portions during distortion or change of figure are always small compared with the weight, inertia, pressure, &c., which produce the visible motions it is the object of hydraulics to estimate. On the other hand, while a fluid passes easily from one form to another, it opposes considerable resistance to change of volume.

It is easily deduced from the absence or smallness of the tangential stress that contiguous portions of fluid act on each other with a pressure which is exactly or very nearly normal to the interface which separates them. The stress must be a pressure, not a tension, or the parts would separate. Further, at any point in a fluid the pressure in all directions must be the same; or, in other words, the pressure on any small element of surface is independent of the orientation of the surface.

§ 2. Fluids are divided into liquids, or incompressible fluids, and gases, or compressible fluids. Very great changes of pressure change the volume of liquids only by a small amount, and if the pressure on them is reduced to zero they do not sensibly dilate. In gases or compressible fluids the volume alters sensibly for small changes of pressure, and if the pressure is indefinitely diminished they dilate without limit.

In ordinary hydraulics, liquids are treated as absolutely incompressible. In dealing with gases the changes of volume which accompany changes of pressure must be taken into account.

§ 3. Viscous fluids are those in which change of form under a continued stress proceeds gradually and increases indefinitely. A very viscous fluid opposes great resistance to change of form in a short time, and yet may be deformed considerably by a small stress acting for a long period. A block of pitch is more easily splintered than indented by a hammer, but under the action of the mere weight of its parts acting for a long enough time it flattens out and flows like a liquid.

[Illustration: FIG. 1.]

All actual fluids are viscous. They oppose a resistance to the relative motion of their parts. This resistance diminishes with the velocity of the relative motion, and becomes zero in a fluid the parts of which are relatively at rest. When the relative motion of different parts of a fluid is small, the viscosity may be neglected without introducing important errors. On the other hand, where there is considerable relative motion, the viscosity may be expected to have an influence too great to be neglected.

_Measurement of Viscosity. Coefficient of Viscosity._--Suppose the plane ab, fig. 1 of area [omega], to move with the velocity V relatively to the surface cd and parallel to it. Let the space between be filled with liquid. The layers of liquid in contact with ab and cd adhere to them. The intermediate layers all offering an equal resistance to shearing or distortion, the rectangle of fluid abcd will take the form of the parallelogram a´b´cd. Further, the resistance to the motion of ab may be expressed in the form

R = [kappa][omega]V, (1)

where [kappa] is a coefficient the nature of which remains to be determined.

If we suppose the liquid between ab and cd divided into layers as shown in fig. 2, it will be clear that the stress R acts, at each dividing face, forwards in the direction of motion if we consider the upper layer, backwards if we consider the lower layer. Now suppose the original thickness of the layer T increased to nT; if the bounding plane in its new position has the velocity nV, the shearing at each dividing face will be exactly the same as before, and the resistance must therefore be the same. Hence,

R = [kappa]´[omega](nV). (2)

But equations (1) and (2) may both be expressed in one equation if [kappa] and [kappa]´ are replaced by a constant varying inversely as the thickness of the layer. Putting [kappa] = [mu]/T, [kappa]´ = [mu]/nT,

R = [mu][omega]V/T;

or, for an indefinitely thin layer,

R = [mu][omega]dV/dt, (3)

an expression first proposed by L. M. H. Navier. The coefficient [mu] is termed the coefficient of viscosity.

According to J. Clerk Maxwell, the value of [mu] for air at [theta]° Fahr. in pounds, when the velocities are expressed in feet per second, is

[mu] = 0.0000000256 (461° + [theta]);

that is, the coefficient of viscosity is proportional to the absolute temperature and independent of the pressure.

The value of [mu] for water at 77° Fahr. is, according to H. von Helmholtz and G. Piotrowski,

[mu] = 0.0000188,

the units being the same as before. For water [mu] decreases rapidly with increase of temperature.

[Illustration: FIG. 2.]

§ 4. When a fluid flows in a very regular manner, as for instance when It flows in a capillary tube, the velocities vary gradually at any moment from one point of the fluid to a neighbouring point. The layer adjacent to the sides of the tube adheres to it and is at rest. The layers more interior than this slide on each other. But the resistance developed by these regular movements is very small. If in large pipes and open channels there were a similar regularity of movement, the neighbouring filaments would acquire, especially near the sides, very great relative velocities. V. J. Boussinesq has shown that the central filament in a semicircular canal of 1 metre radius, and inclined at a slope of only 0.0001, would have a velocity of 187 metres per second,[2] the layer next the boundary remaining at rest. But before such a difference of velocity can arise, the motion of the fluid becomes much more complicated. Volumes of fluid are detached continually from the boundaries, and, revolving, form eddies traversing the fluid in all directions, and sliding with finite relative velocities against those surrounding them. These slidings develop resistances incomparably greater than the viscous resistance due to movements varying continuously from point to point. The movements which produce the phenomena commonly ascribed to fluid friction must be regarded as rapidly or even suddenly varying from one point to another. The internal resistances to the motion of the fluid do not depend merely on the general velocities of translation at different points of the fluid (or what Boussinesq terms the mean local velocities), but rather on the intensity at each point of the eddying agitation. The problems of hydraulics are therefore much more complicated than problems in which a regular motion of the fluid is assumed, hindered by the viscosity of the fluid.

RELATION OF PRESSURE, DENSITY, AND TEMPERATURE OF LIQUIDS

§ 5. _Units of Volume._--In practical calculations the cubic foot and gallon are largely used, and in metric countries the litre and cubic metre (= 1000 litres). The imperial gallon is now exclusively used in England, but the United States have retained the old English wine gallon.

1 cub. ft. = 6.236 imp. gallons = 7.481 U.S. gallons. 1 imp. gallon = 0.1605 cub. ft. = 1.200 U.S. gallons. 1 U.S. gallon = 0.1337 cub. ft. = 0.8333 imp. gallon. 1 litre = 0.2201 imp. gallon = 0.2641 U.S. gallon.

_Density of Water._--Water at 53° F. and ordinary pressure contains 62.4 lb. per cub. ft., or 10 lb. per imperial gallon at 62° F. The litre contains one kilogram of water at 4° C. or 1000 kilograms per cubic metre. River and spring water is not sensibly denser than pure water. But average sea water weighs 64 lb. per cub. ft. at 53° F. The weight of water per cubic unit will be denoted by G. Ice free from air weighs 57.28 lb. per cub. ft. (Leduc).

§ 6. _Compressibility of Liquids._--The most accurate experiments show that liquids are sensibly compressed by very great pressures, and that up to a pressure of 65 atmospheres, or about 1000 lb. per sq. in., the compression is proportional to the pressure. The chief results of experiment are given in the following table. Let V1 be the volume of a liquid in cubic feet under a pressure p1 lb. per sq. ft., and V2 its volume under a pressure p2. Then the cubical compression is (V2 - V1)/V1, and the ratio of the increase of pressure p2 - p1 to the cubical compression is sensibly constant. That is, k = (p2 - p1)V1/(V2 - V1) is constant. This constant is termed the elasticity of volume. With the notation of the differential calculus,

/ / dV \ dp k = dp / ( - -- ) = - V --. / \ V / dV

_Elasticity of Volume of Liquids._

+-----------+------------+-----------+------------+------------+ | | Canton. | Oersted. | Colladon | Regnault. | | | | | and Sturm. | | +-----------+------------+-----------+------------+------------+ | Water | 45,990,000 | 45,900,000| 42,660,000 | 44,000,000 | | Sea water | 52,900,000 | .. | | .. | | Mercury |705,300,000 | .. |626,100,000 |604,500,000 | | Oil | 44,090,000 | .. | | .. | | Alcohol | 32,060,000 | .. | 23,100,000 | .. | +-----------+------------+-----------+------------+------------+

According to the experiments of Grassi, the compressibility of water diminishes as the temperature increases, while that of ether, alcohol and chloroform is increased.

§ 7. _Change of Volume and Density of Water with Change of Temperature._--Although the change of volume of water with change of temperature is so small that it may generally be neglected in ordinary hydraulic calculations, yet it should be noted that there is a change of volume which should be allowed for in very exact calculations. The values of [rho] in the following short table, which gives data enough for hydraulic purposes, are taken from Professor Everett's _System of Units_.

_Density of Water at Different Temperatures._

+-------------+----------+----------+ | | | G | | Temperature.| [rho] |Weight of | +-----+-------+Density of|1 cub. ft.| |Cent.| Fahr. | Water. | in lb. | +-----+-------+----------+----------+ | 0 | 32.0 | .999884 | 62.417 | | 1 | 33.8 | .999941 | 62.420 | | 2 | 35.6 | .999982 | 62.423 | | 3 | 37.4 | 1.000004 | 62.424 | | 4 | 39.2 | 1.000013 | 62.425 | | 5 | 41.0 | 1.000003 | 62.424 | | 6 | 42.8 | .999983 | 62.423 | | 7 | 44.6 | .999946 | 62.421 | | 8 | 46.4 | .999899 | 62.418 | | 9 | 48.2 | .999837 | 62.414 | | 10 | 50.0 | .999760 | 62.409 | | 11 | 51.8 | .999668 | 62.403 | | 12 | 53.6 | .999562 | 62.397 | | 13 | 55.4 | .999443 | 62.389 | | 14 | 57.2 | .999312 | 62.381 | | 15 | 59.0 | .999173 | 62.373 | | 16 | 60.8 | .999015 | 62.363 | | 17 | 62.6 | .998854 | 62.353 | | 18 | 64.4 | .998667 | 62.341 | | 19 | 66.2 | .998473 | 62.329 | | 20 | 68.0 | .998272 | 62.316 | | 22 | 71.6 | .997839 | 62.289 | | 24 | 75.2 | .997380 | 62.261 | | 26 | 78.8 | .996879 | 62.229 | | 28 | 82.4 | .996344 | 62.196 | | 30 | 86 | .995778 | 62.161 | | 35 | 95 | .99469 | 62.093 | | 40 | 104 | .99236 | 61.947 | | 45 | 113 | .99038 | 61.823 | | 50 | 122 | .98821 | 61.688 | | 55 | 131 | .98583 | 61.540 | | 60 | 140 | .98339 | 61.387 | | 65 | 149 | .98075 | 61.222 | | 70 | 158 | .97795 | 61.048 | | 75 | 167 | .97499 | 60.863 | | 80 | 176 | .97195 | 60.674 | | 85 | 185 | .96880 | 60.477 | | 90 | 194 | .96557 | 60.275 | |100 | 212 | .95866 | 59.844 | +-----+-------+----------+----------+

The weight per cubic foot has been calculated from the values of [rho], on the assumption that 1 cub. ft. of water at 39.2° Fahr. is 62.425 lb. For ordinary calculations in hydraulics, the density of water (which will in future be designated by the symbol G) will be taken at 62.4 lb. per cub. ft., which is its density at 53° Fahr. It may be noted also that ice at 32° Fahr. contains 57.3 lb. per cub. ft. The values of [rho] are the densities in grammes per cubic centimetre.

§ 8. _Pressure Column. Free Surface Level._--Suppose a small vertical pipe introduced into a liquid at any point P (fig. 3). Then the liquid will rise in the pipe to a level OO, such that the pressure due to the column in the pipe exactly balances the pressure on its mouth. If the fluid is in motion the mouth of the pipe must be supposed accurately parallel to the direction of motion, or the impact of the liquid at the mouth of the pipe will have an influence on the height of the column. If this condition is complied with, the height h of the column is a measure of the pressure at the point P. Let [omega] be the area of section of the pipe, h the height of the pressure column, p the intensity of pressure at P; then

p[omega] = Gh[omega] lb.,

p/G = h;

that is, h is the height due to the pressure at p. The level OO will be termed the free surface level corresponding to the pressure at P.

RELATION OF PRESSURE, TEMPERATURE, AND DENSITY OF GASES

§ 9. _Relation of Pressure, Volume, Temperature and Density in Compressible Fluids._--Certain problems on the flow of air and steam are so similar to those relating to the flow of water that they are conveniently treated together. It is necessary, therefore, to state as briefly as possible the properties of compressible fluids so far as knowledge of them is requisite in the solution of these problems. Air may be taken as a type of these fluids, and the numerical data here given will relate to air.

[Illustration: FIG. 3.]

_Relation of Pressure and Volume at Constant Temperature._--At constant temperature the product of the pressure p and volume V of a given quantity of air is a constant (Boyle's law).

Let p0 be mean atmospheric pressure (2116.8 lb. per sq. ft.), V0 the volume of 1 lb. of air at 32° Fahr. under the pressure p0. Then

p0V0 = 26214. (1)

If G0 is the weight per cubic foot of air in the same conditions,

G0 = 1/V0 = 2116.8/26214 = .08075. (2)

For any other pressure p, at which the volume of 1 lb. is V and the weight per cubic foot is G, the temperature being 32° Fahr.,

pV = p/G = 26214; or G = p/26214. (3)

_Change of Pressure or Volume by Change of Temperature._--Let p0, V0, G0, as before be the pressure, the volume of a pound in cubic feet, and the weight of a cubic foot in pounds, at 32° Fahr. Let p, V, G be the same quantities at a temperature t (measured strictly by the air thermometer, the degrees of which differ a little from those of a mercurial thermometer). Then, by experiment,

pV = p0V0(460.6 + t)/(460.6 + 32) = p0V0[tau]/[tau]0, (4)

where [tau], [tau]0 are the temperatures t and 32° reckoned from the absolute zero, which is -460.6° Fahr.;

p/G = p0[tau]/G0[tau]0; (4a)

G = p[tau]0G0/p0[tau]. (5)

If p0 = 2116.8, G0 = .08075, [tau]0 = 460.6 + 32 = 492.6, then

p/G = 53.2[tau]. (5a)

Or quite generally p/G = R[tau] for all gases, if R is a constant varying inversely as the density of the gas at 32° F. For steam R = 85.5.

II. KINEMATICS OF FLUIDS

§ 10. Moving fluids as commonly observed are conveniently classified thus:

(1) _Streams_ are moving masses of indefinite length, completely or incompletely bounded laterally by solid boundaries. When the solid boundaries are complete, the flow is said to take place in a pipe. When the solid boundary is incomplete and leaves the upper surface of the fluid free, it is termed a stream bed or channel or canal.

(2) A stream bounded laterally by differently moving fluid of the same kind is termed a _current_.

(3) A _jet_ is a stream bounded by fluid of a different kind.

(4) An _eddy_, _vortex_ or _whirlpool_ is a mass of fluid the particles of which are moving circularly or spirally.

(5) In a stream we may often regard the particles as flowing along definite paths in space. A chain of particles following each other along such a constant path may be termed a fluid filament or elementary stream.

§ 11. _Steady and Unsteady, Uniform and Varying, Motion._--There are two quite distinct ways of treating hydrodynamical questions. We may either fix attention on a given mass of fluid and consider its changes of position and energy under the action of the stresses to which it is subjected, or we may have regard to a given fixed portion of space, and consider the volume and energy of the fluid entering and leaving that space.

If, in following a given path ab (fig. 4), a mass of water a has a constant velocity, the motion is said to be uniform. The kinetic energy of the mass a remains unchanged. If the velocity varies from point to point of the path, the motion is called varying motion. If at a given point a in space, the particles of water always arrive with the same velocity and in the same direction, during any given time, then the motion is termed steady motion. On the contrary, if at the point a the velocity or direction varies from moment to moment the motion is termed unsteady. A river which excavates its own bed is in unsteady motion so long as the slope and form of the bed is changing. It, however, tends always towards a condition in which the bed ceases to change, and it is then said to have reached a condition of permanent regime. No river probably is in absolutely permanent regime, except perhaps in rocky channels. In other cases the bed is scoured more or less during the rise of a flood, and silted again during the subsidence of the flood. But while many streams of a torrential character change the condition of their bed often and to a large extent, in others the changes are comparatively small and not easily observed.

[Illustration: FIG. 4.]

As a stream approaches a condition of steady motion, its regime becomes permanent. Hence steady motion and permanent regime are sometimes used as meaning the same thing. The one, however, is a definite term applicable to the motion of the water, the other a less definite term applicable in strictness only to the condition of the stream bed.

§ 12. _Theoretical Notions on the Motion of Water._--The actual motion of the particles of water is in most cases very complex. To simplify hydrodynamic problems, simpler modes of motion are assumed, and the results of theory so obtained are compared experimentally with the actual motions.

_Motion in Plane Layers._--The simplest kind of motion in a stream is one in which the particles initially situated in any plane cross section of the stream continue to be found in plane cross sections during the subsequent motion. Thus, if the particles in a thin plane layer ab (fig. 5) are found again in a thin plane layer a´b´ after any interval of time, the motion is said to be motion in plane layers. In such motion the internal work in deforming the layer may usually be disregarded, and the resistance to the motion is confined to the circumference.

[Illustration: FIG. 5.]

_Laminar Motion._--In the case of streams having solid boundaries, it is observed that the central parts move faster than the lateral parts. To take account of these differences of velocity, the stream may be conceived to be divided into thin laminae, having cross sections somewhat similar to the solid boundary of the stream, and sliding on each other. The different laminae can then be treated as having differing velocities according to any law either observed or deduced from their mutual friction. A much closer approximation to the real motion of ordinary streams is thus obtained.

_Stream Line Motion._--In the preceding hypothesis, all the particles in each lamina have the same velocity at any given cross section of the stream. If this assumption is abandoned, the cross section of the stream must be supposed divided into indefinitely small areas, each representing the section of a fluid filament. Then these filaments may have any law of variation of velocity assigned to them. If the motion is steady motion these fluid filaments (or as they are then termed _stream lines_) will have fixed positions in space.

_Periodic Unsteady Motion._--In ordinary streams with rough boundaries, it is observed that at any given point the velocity varies from moment to moment in magnitude and direction, but that the average velocity for a sensible period (say for 5 or 10 minutes) varies very little either in magnitude or velocity. It has hence been conceived that the variations of direction and magnitude of the velocity are periodic, and that, if for each point of the stream the mean velocity and direction of motion were substituted for the actual more or less varying motions, the motion of the stream might be treated as steady stream line or steady laminar motion.

[Illustration: FIG. 6.]

§ 13. _Volume of Flow._--Let A (fig. 6) be any ideal plane surface, of area [omega], in a stream, normal to the direction of motion, and let V be the velocity of the fluid. Then the volume flowing through the surface A in unit time is

Q = [omega]V. (1)

Thus, if the motion is rectilinear, all the particles at any instant in the surface A will be found after one second in a similar surface A´, at a distance V, and as each particle is followed by a continuous thread of other particles, the volume of flow is the right prism AA´ having a base [omega] and length V.

If the direction of motion makes an angle [theta] with the normal to the surface, the volume of flow is represented by an oblique prism AA´ (fig. 7), and in that case

Q = [omega]V cos [theta].

[Illustration: FIG. 7.]

If the velocity varies at different points of the surface, let the surface be divided into very small portions, for each of which the velocity may be regarded as constant. If d[omega] is the area and v, or v cos [theta], the normal velocity for this element of the surface, the volume of flow is _ _ / / Q = | v d[omega], or | v cos [theta] d[omega], _/ _/

as the case may be.

§ 14. _Principle of Continuity._--If we consider any completely bounded fixed space in a moving liquid initially and finally filled continuously with liquid, the inflow must be equal to the outflow. Expressing the inflow with a positive and the outflow with a negative sign, and estimating the volume of flow Q for all the boundaries,

[Sigma]Q = 0.

In general the space will remain filled with fluid if the pressure at every point remains positive. There will be a break of continuity, if at any point the pressure becomes negative, indicating that the stress at that point is tensile. In the case of ordinary water this statement requires modification. Water contains a variable amount of air in solution, often about one-twentieth of its volume. This air is disengaged and breaks the continuity of the liquid, if the pressure falls below a point corresponding to its tension. It is for this reason that pumps will not draw water to the full height due to atmospheric pressure.

_Application of the Principle of Continuity to the case of a Stream._--If A1, A2 are the areas of two normal cross sections of a stream, and V1, V2 are the velocities of the stream at those sections, then from the principle of continuity,

V1A1 = V2A2;

V1/V2 = A2/A1 (2)

that is, the normal velocities are inversely as the areas of the cross sections. This is true of the mean velocities, if at each section the velocity of the stream varies. In a river of varying slope the velocity varies with the slope. It is easy therefore to see that in parts of large cross section the slope is smaller than in parts of small cross section.

If we conceive a space in a liquid bounded by normal sections at A1, A2 and between A1, A2 by stream lines (fig. 8), then, as there is no flow across the stream lines,

V1/V2 = A2/A1,

as in a stream with rigid boundaries.

[Illustration: FIG. 8.]

In the case of compressible fluids the variation of volume due to the difference of pressure at the two sections must be taken into account. If the motion is steady the weight of fluid between two cross sections of a stream must remain constant. Hence the weight flowing in must be the same as the weight flowing out. Let p1, p2 be the pressures, v1, v2 the velocities, G1, G2 the weight per cubic foot of fluid, at cross sections of a stream of areas A1, A2. The volumes of inflow and outflow are

A1v1 and A2v2,

and, if the weights of these are the same,

G1A1v1 = G2A2v2;

and hence, from (5a) § 9, if the temperature is constant,

p1A1v1 = p2A2v2. (3)

§ 15. _Stream Lines._--The characteristic of a perfect fluid, that is, a fluid free from viscosity, is that the pressure between any two parts into which it is divided by a plane must be normal to the plane. One consequence of this is that the particles can have no rotation impressed upon them, and the motion of such a fluid is irrotational. A stream line is the line, straight or curved, traced by a particle in a current of fluid in irrotational movement. In a steady current each stream line preserves its figure and position unchanged, and marks the track of a stream of particles forming a fluid filament or elementary stream. A current in steady irrotational movement may be conceived to be divided by insensibly thin partitions following the course of the stream lines into a number of elementary streams. If the positions of these partitions are so adjusted that the volumes of flow in all the elementary streams are equal, they represent to the mind the velocity as well as the direction of motion of the particles in different parts of the current, for the velocities are inversely proportional to the cross sections of the elementary streams. No actual fluid is devoid of viscosity, and the effect of viscosity is to render the motion of a fluid sinuous, or rotational or eddying under most ordinary conditions. At very low velocities in a tube of moderate size the motion of water may be nearly pure stream line motion. But at some velocity, smaller as the diameter of the tube is greater, the motion suddenly becomes tumultuous. The laws of simple stream line motion have hitherto been investigated theoretically, and from mathematical difficulties have only been determined for certain simple cases. Professor H. S. Hele Shaw has found means of exhibiting stream line motion in a number of very interesting cases experimentally. Generally in these experiments a thin sheet of fluid is caused to flow between two parallel plates of glass. In the earlier experiments streams of very small air bubbles introduced into the water current rendered visible the motions of the water. By the use of a lantern the image of a portion of the current can be shown on a screen or photographed. In later experiments streams of coloured liquid at regular distances were introduced into the sheet and these much more clearly marked out the forms of the stream lines. With a fluid sheet 0.02 in. thick, the stream lines were found to be stable at almost any required velocity. For certain simple cases Professor Hele Shaw has shown that the experimental stream lines of a viscous fluid are so far as can be measured identical with the calculated stream lines of a perfect fluid. Sir G. G. Stokes pointed out that in this case, either from the thinness of the stream between its glass walls, or the slowness of the motion, or the high viscosity of the liquid, or from a combination of all these, the flow is regular, and the effects of inertia disappear, the viscosity dominating everything. Glycerine gives the stream lines very satisfactorily.

[Illustration: FIG. 9.]

[Illustration: FIG. 10.]

[Illustration: FIG. 11.]

[Illustration: FIG. 12.]

[Illustration: FIG. 13.]

Fig. 9 shows the stream lines of a sheet of fluid passing a fairly shipshape body such as a screwshaft strut. The arrow shows the direction of motion of the fluid. Fig. 10 shows the stream lines for a very thin glycerine sheet passing a non-shipshape body, the stream lines being practically perfect. Fig. 11 shows one of the earlier air-bubble experiments with a thicker sheet of water. In this case the stream lines break up behind the obstruction, forming an eddying wake. Fig. 12 shows the stream lines of a fluid passing a sudden contraction or sudden enlargement of a pipe. Lastly, fig. 13 shows the stream lines of a current passing an oblique plane. H. S. Hele Shaw, "Experiments on the Nature of the Surface Resistance in Pipes and on Ships," _Trans. Inst. Naval Arch._ (1897). "Investigation of Stream Line Motion under certain Experimental Conditions," _Trans. Inst. Naval Arch._ (1898); "Stream Line Motion of a Viscous Fluid," _Report of British Association_ (1898).

III. PHENOMENA OF THE DISCHARGE OF LIQUIDS FROM ORIFICES AS ASCERTAINABLE BY EXPERIMENTS

§ 16. When a liquid issues vertically from a small orifice, it forms a jet which rises nearly to the level of the free surface of the liquid in the vessel from which it flows. The difference of level h_r (fig. 14) is so small that it may be at once suspected to be due either to air resistance on the surface of the jet or to the viscosity of the liquid or to friction against the sides of the orifice. Neglecting for the moment this small quantity, we may infer, from the elevation of the jet, that each molecule on leaving the orifice possessed the velocity required to lift it against gravity to the height h. From ordinary dynamics, the relation between the velocity and height of projection is given by the equation

v = [root](2gh). (1)

As this velocity is nearly reached in the flow from well-formed orifices, it is sometimes called the theoretical velocity of discharge. This relation was first obtained by Torricelli.

[Illustration: FIG. 14.]

If the orifice is of a suitable conoidal form, the water issues in filaments normal to the plane of the orifice. Let [omega] be the area of the orifice, then the discharge per second must be, from eq. (1),

Q = [omega]v = [omega][root](2gh) nearly. (2)

This is sometimes quite improperly called the theoretical discharge for any kind of orifice. Except for a well-formed conoidal orifice the result is not approximate even, so that if it is supposed to be based on a theory the theory is a false one.

_Use of the term Head in Hydraulics._--The term _head_ is an old millwright's term, and meant primarily the height through which a mass of water descended in actuating a hydraulic machine. Since the water in fig. 14 descends through a height h to the orifice, we may say there are h ft. of head above the orifice. Still more generally any mass of liquid h ft. above a horizontal plane may be said to have h ft. of elevation head relatively to that datum plane. Further, since the pressure p at the orifice which produces outflow is connected with h by the relation p/G = h, the quantity p/G may be termed the pressure head at the orifice. Lastly, the velocity v is connected with h by the relation v²/2g = h, so that v²/2g may be termed the head due to the velocity v.

§ 17. _Coefficients of Velocity and Resistance._--As the actual velocity of discharge differs from [root]2gh by a small quantity, let the actual velocity

= v_a = c_v [root](2gh), (3)

where c_v is a coefficient to be determined by experiment, called the _coefficient of velocity_. This coefficient is found to be tolerably constant for different heads with well-formed simple orifices, and it very often has the value 0.97.

The difference between the velocity of discharge and the velocity due to the head may be reckoned in another way. The total height h causing outflow consists of two parts--one part h_e expended effectively in producing the velocity of outflow, another h_r in overcoming the resistances due to viscosity and friction. Let

h_r = c_r h_e,

where c{r} is a coefficient determined by experiment, and called the _coefficient of resistance_ of the orifice. It is tolerably constant for different heads with well-formed orifices. Then

v_a = [root](2gh_e) = [root]{2gh/(1 + c_r)}. (4)

The relation between c_v and c_r for any orifice is easily found:--

v_a = c_v[root](2gh) = [root]{2gh/(1 + c_r)}

c_v = [root]{1/(1 + c_r)} (5)

c_r = 1/c_v² - 1 (5a)

Thus if c_v = 0.97, then c_r = 0.0628. That is, for such an orifice about 6¼% of the head is expended in overcoming frictional resistances to flow.

[Illustration: FIG. 15.]

_Coefficient of Contraction--Sharp-edged Orifices in Plane Surfaces._--When a jet issues from an aperture in a vessel, it may either spring clear from the inner edge of the orifice as at a or b (fig. 15), or it may adhere to the sides of the orifice as at c. The former condition will be found if the orifice is bevelled outwards as at a, so as to be sharp edged, and it will also occur generally for a prismatic aperture like b, provided the thickness of the plate in which the aperture is formed is less than the diameter of the jet. But if the thickness is greater the condition shown at c will occur.

When the discharge occurs as at a or b, the filaments converging towards the orifice continue to converge beyond it, so that the section of the jet where the filaments have become parallel is smaller than the section of the orifice. The inertia of the filaments opposes sudden change of direction of motion at the edge of the orifice, and the convergence continues for a distance of about half the diameter of the orifice beyond it. Let [omega] be the area of the orifice, and c_c[omega] the area of the jet at the point where convergence ceases; then c_c is a coefficient to be determined experimentally for each kind of orifice, called the _coefficient of contraction_. When the orifice is a sharp-edged orifice in a plane surface, the value of c_c is on the average 0.64, or the section of the jet is very nearly five-eighths of the area of the orifice.

_Coefficient of Discharge._--In applying the general formula Q = [omega]v to a stream, it is assumed that the filaments have a common velocity v normal to the section [omega]. But if the jet contracts, it is at the contracted section of the jet that the direction of motion is normal to a transverse section of the jet. Hence the actual discharge when contraction occurs is

Q_a = c_vv × c_c[omega] = c_c c_v[omega][root](2gh),

or simply, if c = c_vc_c,

Q_a = c[omega][root](2gh),

where c is called the _coefficient of discharge_. Thus for a sharp-edged plane orifice c = 0.97 × 0.64 = 0.62.

[Illustration: FIG. 16.]

§ 18. _Experimental Determination of c_v, c_c, and c._--The coefficient of contraction c_c is directly determined by measuring the dimensions of the jet. For this purpose fixed screws of fine pitch (fig. 16) are convenient. These are set to touch the jet, and then the distance between them can be measured at leisure.

The coefficient of velocity is determined directly by measuring the parabolic path of a horizontal jet.

Let OX, OY (fig. 17) be horizontal and vertical axes, the origin being at the orifice. Let h be the head, and x, y the coordinates of a point A on the parabolic path of the jet. If v_a is the velocity at the orifice, and t the time in which a particle moves from O to A, then

x = v_a t; y = ½gt².

Eliminating t,

v_a = [root](gx²/2y).

Then

c_v = v_a [root](2gh) = [root](x²/4yh).

In the case of large orifices such as weirs, the velocity can be directly determined by using a Pitot tube (§ 144).

[Illustration: FIG. 17.]

The coefficient of discharge, which for practical purposes is the most important of the three coefficients, is best determined by tank measurement of the flow from the given orifice in a suitable time. If Q is the discharge measured in the tank per second, then

c = Q/[omega][root](2gh).

Measurements of this kind though simple in principle are not free from some practical difficulties, and require much care. In fig. 18 is shown an arrangement of measuring tank. The orifice is fixed in the wall of the cistern A and discharges either into the waste channel BB, or into the measuring tank. There is a short trough on rollers C which when run under the jet directs the discharge into the tank, and when run back again allows the discharge to drop into the waste channel. D is a stilling screen to prevent agitation of the surface at the measuring point, E, and F is a discharge valve for emptying the measuring tank. The rise of level in the tank, the time of the flow and the head over the orifice at that time must be exactly observed.

[Illustration: FIG. 18.]

For well made sharp-edged orifices, small relatively to the water surface in the supply reservoir, the coefficients under different conditions of head are pretty exactly known. Suppose the same quantity of water is made to flow in succession through such an orifice and through another orifice of which the coefficient is required, and when the rate of flow is constant the heads over each orifice are noted. Let h1, h2 be the heads, [omega]1, [omega]2 the areas of the orifices, c1, c2 the coefficients. Then since the flow through each orifice is the same

Q = c1[omega]1 [root](2gh1) = c2[omega]2 [root](2gh2).

c2 = c1([omega]1/[omega]2) [root](h1/h2).

[Illustration: FIG. 19.]

§ 19. _Coefficients for Bellmouths and Bellmouthed Orifices._--If an orifice is furnished with a mouthpiece exactly of the form of the contracted vein, then the whole of the contraction occurs within the mouthpiece, and if the area of the orifice is measured at the smaller end, c_c must be put = 1. It is often desirable to bellmouth the ends of pipes, to avoid the loss of head which occurs if this is not done; and such a bellmouth may also have the form of the contracted jet. Fig. 19 shows the proportions of such a bellmouth or bell-mouthed orifice, which approximates to the form of the contracted jet sufficiently for any practical purpose.

For such an orifice L. J. Weisbach found the following values of the coefficients with different heads.

+--------------------------------+------+------+------+------+-------+ | Head over orifice, in ft. = h | .66 | 1.64 |11.48 |55.77 |337.93 | +--------------------------------+------+------+------+------+-------+ | Coefficient of velocity = c_v | .959 | .967 | .975 | .994 | .994 | | Coefficient of resistance = c_r| .087 | .069 | .052 | .012 | .012 | +--------------------------------+------+------+------+------+-------+

As there is no contraction after the jet issues from the orifice, c_c = 1, c = c_v; and therefore

Q = c(v)[omega][root](2gh) = [omega][root]{2gh/(1 + c_r}.

§ 20. _Coefficients for Sharp-edged or virtually Sharp-edged Orifices._--There are a very large number of measurements of discharge from sharp-edged orifices under different conditions of head. An account of these and a very careful tabulation of the average values of the coefficients will be found in the _Hydraulics_ of the late Hamilton Smith (Wiley & Sons, New York, 1886). The following short table abstracted from a larger one will give a fair notion of how the coefficient varies according to the most trustworthy of the experiments.

_Coefficient of Discharge for Vertical Circular Orifices, Sharp-edged, with free Discharge into the Air._ Q = c[omega][root](2gh).

+-----------+------------------------------------------------+ | Head | Diameters of Orifice. | |measured to+------+------+------+------+------+------+------+ | Centre of | .02 | .04 | .10 | .20 | .40 | .60 | 1.0 | | Orifice. +------+------+------+------+------+------+------+ | | Values of C. | +-----------+------+------+------+------+------+------+------+ | 0.3 | .. | .. | .621 | .. | .. | .. | .. | | 0.4 | .. | .637 | .618 | .. | .. | .. | .. | | 0.6 | .655 | .630 | .613 | .601 | .596 | .588 | .. | | 0.8 | .648 | .626 | .610 | .601 | .597 | .594 | .583 | | 1.0 | .644 | .623 | .608 | .600 | .598 | .595 | .591 | | 2.0 | .632 | .614 | .604 | .599 | .599 | .597 | .595 | | 4.0 | .623 | .609 | .602 | .599 | .598 | .597 | .596 | | 8.0 | .614 | .605 | .600 | .598 | .597 | .596 | .596 | | 20.0 | .601 | .599 | .596 | .596 | .596 | .596 | .594 | +-----------+------+------+------+------+------+------+------+

At the same time it must be observed that differences of sharpness in the edge of the orifice and some other circumstances affect the results, so that the values found by different careful experimenters are not a little discrepant. When exact measurement of flow has to be made by a sharp-edged orifice it is desirable that the coefficient for the particular orifice should be directly determined.

The following results were obtained by Dr H. T. Bovey in the laboratory of McGill University.

_Coefficient of Discharge for Sharp-edged Orifices._

+----+------------------------------------------------------------------+ | | Form of Orifice. | | +------+----------------+-----------------+-----------------+------+ | | | Square. |Rectangular Ratio|Rectangular Ratio| | |Head| | | of Sides 4:1 | of Sides 16:1 | | | in | Cir- +------+---------+---------+-------+---------+-------+ Tri- | | ft.|cular.|Sides | | Long | Long | Long | Long |angu- | | | |Verti-|Diagonal | Sides | Sides | Sides | Sides | lar. | | | | cal. |Vertical.|Vertical.| hori- |Vertical.| Hori- | | | | | | | |zontal.| |zontal.| | +----+------+------+---------+---------+-------+---------+-------+------+ | 1 | .620 | .627 | .628 | .642 | .643 | .663 | .664 | .636 | | 2 | .613 | .620 | .628 | .634 | .636 | .650 | .651 | .628 | | 4 | .608 | .616 | .618 | .628 | .629 | .641 | .642 | .623 | | 6 | .607 | .614 | .616 | .626 | .627 | .637 | .637 | .620 | | 8 | .606 | .613 | .614 | .623 | .625 | .634 | .635 | .619 | | 10 | .605 | .612 | .613 | .622 | .624 | .632 | .633 | .618 | | 12 | .604 | .611 | .612 | .622 | .623 | .631 | .631 | .618 | | 14 | .604 | .610 | .612 | .621 | .622 | .630 | .630 | .618 | | 16 | .603 | .610 | .611 | .620 | .622 | .630 | .630 | .617 | | 18 | .603 | .610 | .611 | .620 | .621 | .630 | .629 | .616 | | 20 | .603 | .609 | .611 | .620 | .621 | .629 | .628 | .616 | +----+------+------+---------+---------+-------+---------+-------+------+

The orifice was 0.196 sq. in. area and the reductions were made with g = 32.176 the value for Montreal. The value of the coefficient appears to increase as (perimeter) / (area) increases. It decreases as the head increases. It decreases a little as the size of the orifice is greater.

Very careful experiments by J. G. Mair (_Proc. Inst. Civ. Eng._ lxxxiv.) on the discharge from circular orifices gave the results shown on top of next column.

The edges of the orifices were got up with scrapers to a sharp square edge. The coefficients generally fall as the head increases and as the diameter increases. Professor W. C. Unwin found that the results agree with the formula

c = 0.6075 + 0.0098/[root]h - 0.0037d,

where h is in feet and d in inches.

_Coefficients of Discharge from Circular Orifices. Temperature 51° to 55°._

+-------+--------------------------------------------------------------+ |Head in| Diameters of Orifices in Inches (d). | | feet +------+------+------+------+------+------+------+------+------+ | h. | 1 | 1¼ | 1½ | 1¾ | 2 | 2¼ | 2½ | 2¾ | 3 | +-------+------+------+------+------+------+------+------+------+------+ | | Coefficients (c). | | +------+------+------+------+------+------+------+------+------+ | .75 | .616 | .614 | .616 | .610 | .616 | .612 | .607 | .607 | .609 | | 1.0 | .613 | .612 | .612 | .611 | .612 | .611 | .604 | .608 | .609 | | 1.25 | .613 | .614 | .610 | .608 | .612 | .608 | .605 | .605 | .606 | | 1.50 | .610 | .612 | .611 | .606 | .610 | .607 | .603 | .607 | .605 | | 1.75 | .612 | .611 | .611 | .605 | .611 | .605 | .604 | .607 | .605 | | 2.00 | .609 | .613 | .609 | .606 | .609 | .606 | .604 | .604 | .605 | +-------+------+------+------+------+------+------+------+------+------+

The following table, compiled by J. T. Fanning (_Treatise on Water Supply Engineering_), gives values for rectangular orifices in vertical plane surfaces, the head being measured, not immediately over the orifice, where the surface is depressed, but to the still-water surface at some distance from the orifice. The values were obtained by graphic interpolation, all the most reliable experiments being plotted and curves drawn so as to average the discrepancies.

_Coefficients of Discharge for Rectangular Orifices, Sharp-edged, in Vertical Plane Surfaces._

+--------+----------------------------------------------------------------+ | Head | Ratio of Height to Width. | | to | | | Centre +------+------+------+------+--------+--------+--------+---------+ | of | | | | | | | | | |Orifice.| 4 | 2 | 1½ | 1 | ¾ | ½ | ¼ | 1/8 | +--------+------+------+------+------+--------+--------+--------+---------+ | | 4 ft.| 2 ft.|1½ ft.| 1 ft.|0.75 ft.|0.50 ft.|0.25 ft.|0.125 ft.| | | high.| high.| high.| high.| high. | high. | high. | high. | | Feet. | | | | | | | | | | | 1 ft.| 1 ft.| 1 ft.| 1 ft.| 1 ft. | 1 ft. | 1 ft. | 1 ft. | | | wide.| wide.| wide.| wide.| wide. | wide. | wide. | wide. | +--------+------+------+------+------+--------+--------+--------+---------+ | 0.2 | .. | .. | .. | .. | .. | .. | .. | .6333 | | .3 | .. | .. | .. | .. | .. | .. | .6293 | .6334 | | .4 | .. | .. | .. | .. | .. | .6140 | .6306 | .6334 | | .5 | .. | .. | .. | .. | .6050 | .6150 | .6313 | .6333 | | .6 | .. | .. | .. |.5984 | .6063 | .6156 | .6317 | .6332 | | .7 | .. | .. | .. |.5994 | .6074 | .6162 | .6319 | .6328 | | .8 | .. | .. |.6130 |.6000 | .6082 | .6165 | .6322 | .6326 | | .9 | .. | .. |.6134 |.6006 | .6086 | .6168 | .6323 | .6324 | | 1.0 | .. | .. |.6135 |.6010 | .6090 | .6172 | .6320 | .6320 | | 1.25 | .. |.6188 |.6140 |.6018 | .6095 | .6173 | .6317 | .6312 | | 1.50 | .. |.6187 |.6144 |.6026 | .6100 | .6172 | .6313 | .6303 | | 1.75 | .. |.6186 |.6145 |.6033 | .6103 | .6168 | .6307 | .6296 | | 2 | .. |.6183 |.6144 |.6036 | .6104 | .6166 | .6302 | .6291 | | 2.25 | .. |.6180 |.6143 |.6029 | .6103 | .6163 | .6293 | .6286 | | 2.50 |.6290 |.6176 |.6139 |.6043 | .6102 | .6157 | .6282 | .6278 | | 2.75 |.6280 |.6173 |.6136 |.6046 | .6101 | .6155 | .6274 | .6273 | | 3 |.6273 |.6170 |.6132 |.6048 | .6100 | .6153 | .6267 | .6267 | | 3.5 |.6250 |.6160 |.6123 |.6050 | .6094 | .6146 | .6254 | .6254 | | 4 |.6245 |.6150 |.6110 |.6047 | .6085 | .6136 | .6236 | .6236 | | 4.5 |.6226 |.6138 |.6100 |.6044 | .6074 | .6125 | .6222 | .6222 | | 5 |.6208 |.6124 |.6088 |.6038 | .6063 | .6114 | .6202 | .6202 | | 6 |.6158 |.6094 |.6063 |.6020 | .6044 | .6087 | .6154 | .6154 | | 7 |.6124 |.6064 |.6038 |.6011 | .6032 | .6058 | .6110 | .6114 | | 8 |.6090 |.6036 |.6022 |.6010 | .6022 | .6033 | .6073 | .6087 | | 9 |.6060 |.6020 |.6014 |.6010 | .6015 | .6020 | .6045 | .6070 | | 10 |.6035 |.6015 |.6010 |.6010 | .6010 | .6010 | .6030 | .6060 | | 15 |.6040 |.6018 |.6010 |.6011 | .6012 | .6013 | .6033 | .6066 | | 20 |.6045 |.6024 |.6012 |.6012 | .6014 | .6018 | .6036 | .6074 | | 25 |.6048 |.6028 |.6014 |.6012 | .6016 | .6022 | .6040 | .6083 | | 30 |.6054 |.6034 |.6017 |.6013 | .6018 | .6027 | .6044 | .6092 | | 35 |.6060 |.6039 |.6021 |.6014 | .6022 | .6032 | .6049 | .6103 | | 40 |.6066 |.6045 |.6025 |.6015 | .6026 | .6037 | .6055 | .6114 | | 45 |.6054 |.6052 |.6029 |.6016 | .6030 | .6043 | .6062 | .6125 | | 50 |.6086 |.6060 |.6034 |.6018 | .6035 | .6050 | .6070 | .6140 | +--------+------+------+------+------+--------+--------+--------+---------+

§ 21. _Orifices with Edges of Sensible Thickness._--When the edges of the orifice are not bevelled outwards, but have a sensible thickness, the coefficient of discharge is somewhat altered. The following table gives values of the coefficient of discharge for the arrangements of the orifice shown in vertical section at P, Q, R (fig. 20). The plan of all the orifices is shown at S. The planks forming the orifice and sluice were each 2 in. thick, and the orifices were all 24 in. wide. The heads were measured immediately over the orifice. In this case,

Q = cb(H - h) [root]{2g(H + h)/2}.

§ 22. _Partially Suppressed Contraction._--Since the contraction of the jet is due to the convergence towards the orifice of the issuing streams, it will be diminished if for any portion of the edge of the orifice the convergence is prevented. Thus, if an internal rim or border is applied to part of the edge of the orifice (fig. 21), the convergence for so much of the edge is suppressed. For such cases G. Bidone found the following empirical formulae applicable:--

_Table of Coefficients of Discharge for Rectangular Vertical Orifices in Fig. 20._

+--------+-----------------------------------------------------------------------------------------------+ |Head h | | |above | Height of Orifice, H - h, in feet | |upper +-----------------------+-----------------------+-----------------------+-----------------------+ |edge of | 1.31 | 0.66 | 0.16 | 0.10 | |Orifice +-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+ |in feet.| P | Q | R | P | Q | R | P | Q | R | P | Q | R | +--------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 0.328 | 0.598 | 0.644 | 0.648 | 0.634 | 0.665 | 0.668 | 0.691 | 0.664 | 0.666 | 0.710 | 0.694 | 0.696 | | .656 | 0.609 | 0.653 | 0.657 | 0.640 | 0.672 | 0.675 | 0.685 | 0.687 | 0.688 | 0.696 | 0.704 | 0.706 | | .787 | 0.612 | 0.655 | 0.659 | 0.641 | 0.674 | 0.677 | 0.684 | 0.690 | 0.692 | 0.694 | 0.706 | 0.708 | | .984 | 0.616 | 0.656 | 0.660 | 0.641 | 0.675 | 0.678 | 0.683 | 0.693 | 0.695 | 0.692 | 0.709 | 0.711 | | 1.968 | 0.618 | 0.649 | 0.653 | 0.640 | 0.676 | 0.679 | 0.678 | 0.695 | 0.697 | 0.688 | 0.710 | 0.712 | | 3.28 | 0.608 | 0.632 | 0.634 | 0.638 | 0.674 | 0.676 | 0.673 | 0.694 | 0.695 | 0.680 | 0.704 | 0.705 | | 4.27 | 0.602 | 0.624 | 0.626 | 0.637 | 0.673 | 0.675 | 0.672 | 0.693 | 0.694 | 0.678 | 0.701 | 0.702 | | 4.92 | 0.598 | 0.620 | 0.622 | 0.637 | 0.673 | 0.674 | 0.672 | 0.692 | 0.693 | 0.676 | 0.699 | 0.699 | | 5.58 | 0.596 | 0.618 | 0.620 | 0.637 | 0.672 | 0.673 | 0.672 | 0.692 | 0.693 | 0.676 | 0.698 | 0.698 | | 6.56 | 0.595 | 0.615 | 0.617 | 0.636 | 0.671 | 0.672 | 0.671 | 0.691 | 0.692 | 0.675 | 0.696 | 0.696 | | 9.84 | 0.592 | 0.611 | 0.612 | 0.634 | 0.669 | 0.670 | 0.668 | 0.689 | 0.690 | 0.672 | 0.693 | 0.693 | +--------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+

For rectangular orifices,

C_c = 0.62(1 + 0.152n/p);

and for circular orifices,

C_c = 0.62(1 + 0.128n/p);

when n is the length of the edge of the orifice over which the border extends, and p is the whole length of edge or perimeter of the orifice. The following are the values of c_c, when the border extends over ¼, ½, or ¾ of the whole perimeter:--

+--------+-----------------------+--------------------+ | | C_c | C_c | | n/p | Rectangular Orifices. | Circular Orifices. | +--------+-----------------------+--------------------+ | 0.25 | 0.643 | .640 | | 0.50 | 0.667 | .660 | | 0.75 | 0.691 | .680 | +--------+-----------------------+--------------------+

[Illustration: FIG. 20.]

[Illustration: FIG. 21.]

For larger values of n/p the formulae are not applicable. C. R. Bornemann has shown, however, that these formulae for suppressed contraction are not reliable.

§ 23. _Imperfect Contraction._--If the sides of the vessel approach near to the edge of the orifice, they interfere with the convergence of the streams to which the contraction is due, and the contraction is then modified. It is generally stated that the influence of the sides begins to be felt if their distance from the edge of the orifice is less than 2.7 times the corresponding width of the orifice. The coefficients of contraction for this case are imperfectly known.

[Illustration: FIG. 22.]

§ 24. _Orifices Furnished with Channels of Discharge._--These external borders to an orifice also modify the contraction.

The following coefficients of discharge were obtained with openings 8 in. wide, and small in proportion to the channel of approach (fig. 22, A, B, C).

+-----------+-------------------------------------------------------+ | h2--h1 | h1 in feet. | | in feet |------+-----+-----+-----+------+-----+-----+-----+-----+ | |.0656 |.164 |.328 |.656 |1.640 |3.28 |4.92 |6.56 |9.84 | +-----------+------+-----+-----+-----+------+-----+-----+-----+-----+ | A\ | .480 |.511 |.542 |.574 | .599 |.601 |.601 |.601 |.601 | | B > 0.656 | .480 |.510 |.538 |.506 | .592 |.600 |.602 |.602 |.601 | | C/ | .527 |.553 |.574 |.592 | .607 |.610 |.610 |.609 |.608 | | | | | | | | | | | | | A\ | .488 |.577 |.624 |.631 | .625 |.624 |.619 |.613 |.606 | | B > 0.164 | .487 |.571 |.606 |.617 | .626 |.628 |.627 |.623 |.618 | | C/ | .585 |.614 |.633 |.645 | .652 |.651 |.650 |.650 |.649 | +-----------+------+-----+-----+-----+------+-----+-----+-----+-----+

[Illustration: FIG. 23.]

§ 25. _Inversion of the Jet._--When a jet issues from a horizontal orifice, or is of small size compared with the head, it presents no marked peculiarity of form. But if the orifice is in a vertical surface, and if its dimensions are not small compared with the head, it undergoes a series of singular changes of form after leaving the orifice. These were first investigated by G. Bidone (1781-1839); subsequently H. G. Magnus (1802-1870) measured jets from different orifices; and later Lord Rayleigh (_Proc. Roy. Soc._ xxix. 71) investigated them anew.

Fig. 23 shows some forms, the upper figure giving the shape of the orifices, and the others sections of the jet. The jet first contracts as described above, in consequence of the convergence of the fluid streams within the vessel, retaining, however, a form similar to that of the orifice. Afterwards it expands into sheets in planes perpendicular to the sides of the orifice. Thus the jet from a triangular orifice expands into three sheets, in planes bisecting at right angles the three sides of the triangle. Generally a jet from an orifice, in the form of a regular polygon of n sides, forms n sheets in planes perpendicular to the sides of the polygon.

Bidone explains this by reference to the simpler case of meeting streams. If two equal streams having the same axis, but moving in opposite directions, meet, they spread out into a thin disk normal to the common axis of the streams. If the directions of two streams intersect obliquely they spread into a symmetrical sheet perpendicular to the plane of the streams.

[Illustration: FIG. 24.]

Let a1, a2 (fig. 24) be two points in an orifice at depths h1, h2 from the free surface. The filaments issuing at a1, a2 will have the different velocities [root](2gh1) and [root](2gh2). Consequently they will tend to describe parabolic paths a1cb1 and a2cb2 of different horizontal range, and intersecting in the point c. But since two filaments cannot simultaneously flow through the same point, they must exercise mutual pressure, and will be deflected out of the paths they tend to describe. It is this mutual pressure which causes the expansion of the jet into sheets.

Lord Rayleigh pointed out that, when the orifices are small and the head is not great, the expansion of the sheets in directions perpendicular to the direction of flow reaches a limit. Sections taken at greater distance from the orifice show a contraction of the sheets until a compact form is reached similar to that at the first contraction. Beyond this point, if the jet retains its coherence, sheets are thrown out again, but in directions bisecting the angles between the previous sheets. Lord Rayleigh accepts an explanation of this contraction first suggested by H. Buff (1805-1878), namely, that it is due to surface tension.

§ 26. _Influence of Temperature on Discharge of Orifices._--Professor VV. C. Unwin found (_Phil. Mag._, October 1878, p. 281) that for sharp-edged orifices temperature has a very small influence on the discharge. For an orifice 1 cm. in diameter with heads of about 1 to 1½ ft. the coefficients were:--

Temperature F. C. 205° .594 62° .598

For a conoidal or bell-mouthed orifice 1 cm. diameter the effect of temperature was greater:--

Temperature F. C. 190° 0.987 130° 0.974 60° 0.942

an increase in velocity of discharge of 4% when the temperature increased 130°.

J. G. Mair repeated these experiments on a much larger scale (_Proc. Inst. Civ. Eng._ lxxxiv.). For a sharp-edged orifice 2½ in. diameter, with a head of 1.75 ft., the coefficient was 0.604 at 57° and 0.607 at 179° F., a very small difference. With a conoidal orifice the coefficient was 0.961 at 55° and 0.98l at 170° F. The corresponding coefficients of resistance are 0.0828 and 0.0391, showing that the resistance decreases to about half at the higher temperature.

§ 27. _Fire Hose Nozzles._--Experiments have been made by J. R. Freeman on the coefficient of discharge from smooth cone nozzles used for fire purposes. The coefficient was found to be 0.983 for ¾-in. nozzle; 0.982 for 7/8 in.; 0.972 for 1 in.; 0.976 for 1(1/8) in.; and 0.971 for 1¼ in. The nozzles were fixed on a taper play-pipe, and the coefficient includes the resistance of this pipe (_Amer. Soc. Civ. Eng._ xxi., 1889). Other forms of nozzle were tried such as ring nozzles for which the coefficient was smaller.

IV. THEORY OF THE STEADY MOTION OF FLUIDS.

§ 28. The general equation of the steady motion of a fluid given under Hydrodynamics furnishes immediately three results as to the distribution of pressure in a stream which may here be assumed.

(a) If the motion is rectilinear and uniform, the variation of pressure is the same as in a fluid at rest. In a stream flowing in an open channel, for instance, when the effect of eddies produced by the roughness of the sides is neglected, the pressure at each point is simply the hydrostatic pressure due to the depth below the free surface.

(b) If the velocity of the fluid is very small, the distribution of pressure is approximately the same as in a fluid at rest.

(c) If the fluid molecules take precisely the accelerations which they would have if independent and submitted only to the external forces, the pressure is uniform. Thus in a jet falling freely in the air the pressure throughout any cross section is uniform and equal to the atmospheric pressure.

(d) In any bounded plane section traversed normally by streams which are rectilinear for a certain distance on either side of the section, the distribution of pressure is the same as in a fluid at rest.

DISTRIBUTION OF ENERGY IN INCOMPRESSIBLE FLUIDS.

§ 29. _Application of the Principle of the Conservation of Energy to Cases of Stream Line Motion._--The external and internal work done on a mass is equal to the change of kinetic energy produced. In many hydraulic questions this principle is difficult to apply, because from the complicated nature of the motion produced it is difficult to estimate the total kinetic energy generated, and because in some cases the internal work done in overcoming frictional or viscous resistances cannot be ascertained; but in the case of stream line motion it furnishes a simple and important result known as Bernoulli's theorem.

[Illustration: FIG. 25.]

Let AB (fig. 25) be any one elementary stream, in a steadily moving fluid mass. Then, from the steadiness of the motion, AB is a fixed path in space through which a stream of fluid is constantly flowing. Let OO be the free surface and XX any horizontal datum line. Let [omega] be the area of a normal cross section, v the velocity, p the intensity of pressure, and z the elevation above XX, of the elementary stream AB at A, and [omega]1, p1, v1, z1 the same quantities at B. Suppose that in a short time t the mass of fluid initially occupying AB comes to A´B´. Then AA´, BB´ are equal to vt, v1t, and the volumes of fluid AA´, BB´ are the equal inflow and outflow = Qt = [omega]vt = [omega]1v1t, in the given time. If we suppose the filament AB surrounded by other filaments moving with not very different velocities, the frictional or viscous resistance on its surface will be small enough to be neglected, and if the fluid is incompressible no internal work is done in change of volume. Then the work done by external forces will be equal to the kinetic energy produced in the time considered.

The normal pressures on the surface of the mass (excluding the ends A, B) are at each point normal to the direction of motion, and do no work. Hence the only external forces to be reckoned are gravity and the pressures on the ends of the stream.

The work of gravity when AB falls to A´B´ is the same as that of transferring AA´ to BB´; that is, GQt(z - z1). The work of the pressures on the ends, reckoning that at B negative, because it is opposite to the direction of motion, is (p[omega] × vt) - (p1[omega]1 × v1t) = Qt(p - p1). The change of kinetic energy in the time t is the difference of the kinetic energy originally possessed by AA´ and that finally acquired by BB´, for in the intermediate part A´B there is no change of kinetic energy, in consequence of the steadiness of the motion. But the mass of AA´ and BB´ is GQt/g, and the change of kinetic energy is therefore (GQt/g) (v1²/2 - v²/2). Equating this to the work done on the mass AB,

GQt(z - z1) + Qt(p - p1) = (GQt/g)(v1²/2 - v²/2).

Dividing by GQt and rearranging the terms,

v²/2g + p/G + z = v1²/2g + p1/G + z1; (1)

or, as A and B are any two points,

v²/2g + p/G + z = constant = H. (2)

Now v²/2g is the head due to the velocity v, p/G is the head equivalent to the pressure, and z is the elevation above the datum (see § 16). Hence the terms on the left are the total head due to velocity, pressure, and elevation at a given cross section of the filament, z is easily seen to be the work in foot-pounds which would be done by 1 lb. of fluid falling to the datum line, and similarly p/G and v²/2g are the quantities of work which would be done by 1 lb. of fluid due to the pressure p and velocity v. The expression on the left of the equation is, therefore, the total energy of the stream at the section considered, per lb. of fluid, estimated with reference to the datum line XX. Hence we see that in stream line motion, under the restrictions named above, the total energy per lb. of fluid is uniformly distributed along the stream line. If the free surface of the fluid OO is taken as the datum, and -h, -h1 are the depths of A and B measured down from the free surface, the equation takes the form

v²/2g + p/G - h = v1²/2g + p1/G - h1; (3)

or generally

v²/2g + p/G - h = constant. (3a)

[Illustration: FIG. 26.]

§ 30. _Second Form of the Theorem of Bernoulli._--Suppose at the two sections A, B (fig. 26) of an elementary stream small vertical pipes are introduced, which may be termed pressure columns (§ 8), having their lower ends accurately parallel to the direction of flow. In such tubes the water will rise to heights corresponding to the pressures at A and B. Hence b = p/G, and b´ = p1/G. Consequently the tops of the pressure columns A´ and B´ will be at total heights b + c = p/G + z and b´ + c´ = p1/G + z1 above the datum line XX. The difference of level of the pressure column tops, or the fall of free surface level between A and B, is therefore

[xi] = (p - p1)/G + (z - z1);

and this by equation (1), § 29 is (v1² - v²)/2g. That is, the fall of free, surface level between two sections is equal to the difference of the heights due to the velocities at the sections. The line A´B´ is sometimes called the line of hydraulic gradient, though this term is also used in cases where friction needs to be taken into account. It is the line the height of which above datum is the sum of the elevation and pressure head at that point, and it falls below a horizontal line A´´B´´ drawn at H ft. above XX by the quantities a = v²/2g and a´ = v1²/2g, when friction is absent.

§ 31. _Illustrations of the Theorem of Bernoulli._ In a lecture to the mechanical section of the British Association in 1875, W. Froude gave some experimental illustrations of the principle of Bernoulli. He remarked that it was a common but erroneous impression that a fluid exercises in a contracting pipe A (fig. 27) an excess of pressure against the entire converging surface which it meets, and that, conversely, as it enters an enlargement B, a relief of pressure is experienced by the entire diverging surface of the pipe. Further it is commonly assumed that when passing through a contraction C, there is in the narrow neck an excess of pressure due to the squeezing together of the liquid at that point. These impressions are in no respect correct; the pressure is smaller as the section of the pipe is smaller and conversely.

[Illustration: FIG. 27.]

Fig. 28 shows a pipe so formed that a contraction is followed by an enlargement, and fig. 29 one in which an enlargement is followed by a contraction. The vertical pressure columns show the decrease of pressure at the contraction and increase of pressure at the enlargement. The line abc in both figures shows the variation of free surface level, supposing the pipe frictionless. In actual pipes, however, work is expended in friction against the pipe; the total head diminishes in proceeding along the pipe, and the free surface level is a line such as ab1c1, falling below abc.

Froude further pointed out that, if a pipe contracts and enlarges again to the same size, the resultant pressure on the converging part exactly balances the resultant pressure on the diverging part so that there is no tendency to move the pipe bodily when water flows through it. Thus the conical part AB (fig. 30) presents the same projected surface as HI, and the pressures parallel to the axis of the pipe, normal to these projected surfaces, balance each other. Similarly the pressures on BC, CD balance those on GH, EG. In the same way, in any combination of enlargements and contractions, a balance of pressures, due to the flow of liquid parallel to the axis of the pipe, will be found, provided the sectional area and direction of the ends are the same.

[Illustration: FIG. 28.]

[Illustration: FIG. 29.]

The following experiment is interesting. Two cisterns provided with converging pipes were placed so that the jet from one was exactly opposite the entrance to the other. The cisterns being filled very nearly to the same level, the jet from the left-hand cistern A entered the right-hand cistern B (fig. 31), shooting across the free space between them without any waste, except that due to indirectness of aim and want of exact correspondence in the form of the orifices. In the actual experiment there was 18 in. of head in the right and 20½ in. of head in the left-hand cistern, so that about 2½ in. were wasted in friction. It will be seen that in the open space between the orifices there was no pressure, except the atmospheric pressure acting uniformly throughout the system.

[Illustration: FIG. 30.]

[Illustration: FIG. 31.]

§ 32. _Venturi Meter._--An ingenious application of the variation of pressure and velocity in a converging and diverging pipe has been made by Clemens Herschel in the construction of what he terms a Venturi Meter for measuring the flow in water mains. Suppose that, as in fig. 32, a contraction is made in a water main, the change of section being gradual to avoid the production of eddies. The ratio [rho] of the cross sections at A and B, that is at inlet and throat, is in actual meters 5 to 1 to 20 to 1, and is very carefully determined by the maker of the meter. Then, if v and u are the velocities at A and B, u = [rho]v. Let pressure pipes be introduced at A, B and C, and let H1, H, H2 be the pressure heads at those points. Since the velocity at B is greater than at A the pressure will be less. Neglecting friction

H1 + v²/2g = H + u²/2g,

H1 - H = (u² - v²)/2g = ([rho]² - 1)v²/2g.

Let h = H1 - H be termed the Venturi head, then

u = [root]{[rho]²·2gh/([rho]² - 1)},

from which the velocity through the throat and the discharge of the main can be calculated if the areas at A and B are known and h observed. Thus if the diameters at A and B are 4 and 12 in., the areas are 12.57 and 113.1 sq. in., and [rho] = 9,

u = [root]81/80 [root](2gh) = 1.007 [root](2gh).

If the observed Venturi head is 12 ft.,

u = 28 ft. per sec.,

and the discharge of the main is

28 × 12.57 = 351 cub. ft. per sec.

[Illustration: FIG. 32.]

Hence by a simple observation of pressure difference, the flow in the main at any moment can be determined. Notice that the pressure height at C will be the same as at A except for a small loss h_f due to friction and eddying between A and B. To get the pressure at the throat very exactly Herschel surrounds it by an annular passage communicating with the throat by several small holes, sometimes formed in vulcanite to prevent corrosion. Though constructed to prevent eddying as much as possible there is some eddy loss. The main effect of this is to cause a loss of head between A and C which may vary from a fraction of a foot to perhaps 5 ft. at the highest velocities at which a meter can be used. The eddying also affects a little the Venturi head h. Consequently an experimental coefficient must be determined for each meter by tank measurement. The range of this coefficient is, however, surprisingly small. If to allow for friction, u = k[root]{[rho]²/([rho]² - 1)}[root](2gh), then Herschel found values of k from 0.97 to 1.0 for throat velocities varying from 8 to 28 ft. per sec. The meter is extremely convenient. At Staines reservoirs there are two meters of this type on mains 94 in. in diameter. Herschel contrived a recording arrangement which records the variation of flow from hour to hour and also the total flow in any given time. In Great Britain the meter is constructed by G. Kent, who has made improvements in the recording arrangement.

[Illustration: FIG. 33.]

In the Deacon Waste Water Meter (fig. 33) a different principle is used. A disk D, partly counter-balanced by a weight, is suspended in the water flowing through the main in a conical chamber. The unbalanced weight of the disk is supported by the impact of the water. If the discharge of the main increases the disk rises, but as it rises its position in the chamber is such that in consequence of the larger area the velocity is less. It finds, therefore, a new position of equilibrium. A pencil P records on a drum moved by clockwork the position of the disk, and from this the variation of flow is inferred.

§ 33. _Pressure, Velocity and Energy in Different Stream Lines._--The equation of Bernoulli gives the variation of pressure and velocity from point to point along a stream line, and shows that the total energy of the flow across any two sections is the same. Two other directions may be defined, one normal to the stream line and in the plane containing its radius of curvature at any point, the other normal to the stream line and the radius of curvature. For the problems most practically useful it will be sufficient to consider the stream lines as parallel to a vertical or horizontal plane. If the motion is in a vertical plane, the action of gravity must be taken into the reckoning; if the motion is in a horizontal plane, the terms expressing variation of elevation of the filament will disappear.[3]

[Illustration: FIG. 34.]

Let AB, CD (fig. 34) be two consecutive stream lines, at present assumed to be in a vertical plane, and PQ a normal to these lines making an angle [phi] with the vertical. Let P, Q be two particles moving along these lines at a distance PQ = ds, and let z be the height of Q above the horizontal plane with reference to which the energy is measured, v its velocity, and p its pressure. Then, if H is the total energy at Q per unit of weight of fluid,

H = z + p/G + v²/2g.

Differentiating, we get

dH = dz + dp/G + vdv/g, (1)

for the increment of energy between Q and P. But

dz = PQ cos [phi] = ds cos [phi];

.: dH = dp/G + v dv/g + ds cos [phi], (1a)

where the last term disappears if the motion is in a horizontal plane.

Now imagine a small cylinder of section [omega] described round PQ as an axis. This will be in equilibrium under the action of its centrifugal force, its weight and the pressure on its ends. But its volume is [omega] ds and its weight G[omega]ds. Hence, taking the components of the forces parallel to PQ--

[omega]dp = Gv²[omega] ds/g[rho] - G[omega] cos [phi] ds,

where [rho] is the radius of curvature of the stream line at Q. Consequently, introducing these values in (1),

dH = v² ds/g[rho] + v dv/g = (v/g)(v/[rho] + dv/ds) ds. (2)

CURRENTS

§ 34. _Rectilinear Current._--Suppose the motion is in parallel straight stream lines (fig. 35) in a vertical plane. Then [rho] is infinite, and from eq. (2), § 33,

dH = v dv/g.

Comparing this with (1) we see that

dz + dp/G = 0;

.: z + p/G = constant; (3)

or the pressure varies hydrostatically as in a fluid at rest. For two stream lines in a horizontal plane, z is constant, and therefore p is constant.

[Illustration: FIG. 35.]

_Radiating Current._--Suppose water flowing radially between horizontal parallel planes, at a distance apart = [delta]. Conceive two cylindrical sections of the current at radii r1 and r2, where the velocities are v1 and v2, and the pressures p1 and p2. Since the flow across each cylindrical section of the current is the same,

Q = 2[pi]r1[delta]v1 = 2[pi]r2[delta]v2

r1v1 = r2v2

r1/r2 = v2/v1. (4)

The velocity would be infinite at radius 0, if the current could be conceived to extend to the axis. Now, if the motion is steady,

H = p1/G + v1²/2g = p2/G + v2²/2g; = p2/G + r1² + v1²/r2²2g;

(p2- p1)/G = v1²(1 - r1²/r2²)/2g; (5)

p2/G = H - r1²v1²/r2²2g. (6)

Hence the pressure increases from the interior outwards, in a way indicated by the pressure columns in fig. 36, the curve through the free surfaces of the pressure columns being, in a radial section, the quasi-hyperbola of the form xy² = c³. This curve is asymptotic to a horizontal line, H ft. above the line from which the pressures are measured, and to the axis of the current.

[Illustration: FIG. 36.]

_Free Circular Vortex._--A free circular vortex is a revolving mass of water, in which the stream lines are concentric circles, and in which the total head for each stream line is the same. Hence, if by any slow radial motion portions of the water strayed from one stream line to another, they would take freely the velocities proper to their new positions under the action of the existing fluid pressures only.

For such a current, the motion being horizontal, we have for all the circular elementary streams

H = p/G + v²/2g = constant;

.: dH = dp/G + v dv/g = 0. (7)

Consider two stream lines at radii r and r + dr (fig. 36). Then in (2), § 33, [rho] = r and ds = dr,

v² dr/gr + v dv/g = 0,

dv/v = -dr/r,

v [oo] 1/r, (8)

precisely as in a radiating current; and hence the distribution of pressure is the same, and formulae 5 and 6 are applicable to this case.

_Free Spiral Vortex._--As in a radiating and circular current the equations of motion are the same, they will also apply to a vortex in which the motion is compounded of these motions in any proportions, provided the radial component of the motion varies inversely as the radius as in a radial current, and the tangential component varies inversely as the radius as in a free vortex. Then the whole velocity at any point will be inversely proportional to the radius of the point, and the fluid will describe stream lines having a constant inclination to the radius drawn to the axis of the current. That is, the stream lines will be logarithmic spirals. When water is delivered from the circumference of a centrifugal pump or turbine into a chamber, it forms a free vortex of this kind. The water flows spirally outwards, its velocity diminishing and its pressure increasing according to the law stated above, and the head along each spiral stream line is constant.

§ 35. _Forced Vortex._--If the law of motion in a rotating current is different from that in a free vortex, some force must be applied to cause the variation of velocity. The simplest case is that of a rotating current in which all the particles have equal angular velocity, as for instance when they are driven round by radiating paddles revolving uniformly. Then in equation (2), § 33, considering two circular stream lines of radii r and r + dr (fig. 37), we have [rho] = r, ds = dr. If the angular velocity is [alpha], then v = [alpha]r and dv = [alpha]dr. Hence

dH = [alpha]²r dr/g + [alpha]²r dr/g = 2[alpha]²r dr/g.

Comparing this with (1), § 33, and putting dz = 0, because the motion is horizontal,

dp/G + [alpha]²r dr/g = 2[alpha]²r dr/g,

dp/G = [alpha]²rdr/g,

p/G = [alpha]²/2g + constant. (9)

Let p1, r1, v1 be the pressure, radius and velocity of one cylindrical section, p2, r2, v2 those of another; then

p1/G - [alpha]²r1²/2g = p2/G - [alpha]²r2²/2g;

(p2 - p1)/G = [alpha]²(r2² - r1²)/2g = (v2² - v1²)/2g. (10)

That is, the pressure increases from within outwards in a curve which in radial sections is a parabola, and surfaces of equal pressure are paraboloids of revolution (fig. 37).

[Illustration: FIG. 37.]

DISSIPATION OF HEAD IN SHOCK

§ 36. _Relation of Pressure and Velocity in a Stream in Steady Motion when the Changes of Section of the Stream are Abrupt._--When a stream changes section abruptly, rotating eddies are formed which dissipate energy. The energy absorbed in producing rotation is at once abstracted from that effective in causing the flow, and sooner or later it is wasted by frictional resistances due to the rapid relative motion of the eddying parts of the fluid. In such cases the work thus expended internally in the fluid is too important to be neglected, and the energy thus lost is commonly termed energy lost in shock. Suppose fig. 38 to represent a stream having such an abrupt change of section. Let AB, CD be normal sections at points where ordinary stream line motion has not been disturbed and where it has been re-established. Let [omega], p, v be the area of section, pressure and velocity at AB, and [omega]1, p1, v1 corresponding quantities at CD. Then if no work were expended internally, and assuming the stream horizontal, we should have

p/G + v²/2g = p1/G + v1²/2g. (1)

But if work is expended in producing irregular eddying motion, the head at the section CD will be diminished.

Suppose the mass ABCD comes in a short time t to A´B´C´D´. The resultant force parallel to the axis of the stream is

p[omega] + p0([omega]1 - [omega]) - p1[omega]1,

where p0 is put for the unknown pressure on the annular space between AB and EF. The impulse of that force is

{p[omega] + p0([omega]1 - [omega]) - p1[omega]1} t.

[Illustration: FIG. 38.]

The horizontal change of momentum in the same time is the difference of the momenta of CDC´D´ and ABA´B´, because the amount of momentum between A´B´ and CD remains unchanged if the motion is steady. The volume of ABA´B´ or CDC´D´, being the inflow and outflow in the time t, is Qt = [omega]vt = [omega]1v1t, and the momentum of these masses is (G/g)Qvt and (G/g)Qv1t. The change of momentum is therefore (G/g)Qt(v1 - v). Equating this to the impulse,

{p[omega] + p0([omega]1 - [omega]) - p1[omega]1}t = (G/g)Qt(v1 - v).

Assume that p0 = p, the pressure at AB extending unchanged through the portions of fluid in contact with AE, BF which lie out of the path of the stream. Then (since Q = [omega]1v1)

(p - p1) = (G/g) v1 (v1 - v);

p/G - p1/G = v1 (v1 - v)/g; (2)

p/G + v²/2g = p1/G + v1²/2g + (v - v1)²/2g. (3)

This differs from the expression (1), § 29, obtained for cases where no sensible internal work is done, by the last term on the right. That is, (v - v1)²/2g has to be added to the total head at CD, which is p1/G + v1²/2g, to make it equal to the total head at AB, or (v - v1)²/2g is the head lost in shock at the abrupt change of section. But (v - v1) is the relative velocity of the two parts of the stream. Hence, when an abrupt change of section occurs, the head due to the relative velocity is lost in shock, or (v - v1)²/2g foot-pounds of energy is wasted for each pound of fluid. Experiment verifies this result, so that the assumption that p0 = p appears to be admissible.

If there is no shock,

p1/G = p/G + (v² - v1²)/2g.

If there is shock,

p1/G = p/G - v1(v1 - v)/g.

Hence the pressure head at CD in the second case is less than in the former by the quantity (v - v1)²/2g, or, putting [omega]1v1 = [omega]v, by the quantity

(v²/2g)(1 - [omega]/[omega]1)². (4)

V. THEORY OF THE DISCHARGE FROM ORIFICES AND MOUTHPIECES

[Illustration: FIG. 39.]

§ 37. _Minimum Coefficient of Contraction. Re-entrant Mouthpiece of Borda._--In one special case the coefficient of contraction can be determined theoretically, and, as it is the case where the convergence of the streams approaching the orifice takes place through the greatest possible angle, the coefficient thus determined is the minimum coefficient.

Let fig. 39 represent a vessel with vertical sides, OO being the free water surface, at which the pressure is p_a. Suppose the liquid issues by a horizontal mouthpiece, which is re-entrant and of the greatest length which permits the jet to spring clear from the inner end of the orifice, without adhering to its sides. With such an orifice the velocity near the points CD is negligible, and the pressure at those points may be taken equal to the hydrostatic pressure due to the depth from the free surface. Let [Omega] be the area of the mouthpiece AB, [omega] that of the contracted jet aa Suppose that in a short time t, the mass OOaa comes to the position O´O´ a´a´; the impulse of the horizontal external forces acting on the mass during that time is equal to the horizontal change of momentum.

The pressure on the side OC of the mass will be balanced by the pressure on the opposite side OE, and so for all other portions of the vertical surfaces of the mass, excepting the portion EF opposite the mouthpiece and the surface AaaB of the jet. On EF the pressure is simply the hydrostatic pressure due to the depth, that is, (p_a + Gh). On the surface and section AaaB of the jet, the horizontal resultant of the pressure is equal to the atmospheric pressure p_a acting on the vertical projection AB of the jet; that is, the resultant pressure is -p_a[Omega]. Hence the resultant horizontal force for the whole mass OOaa is (p_a + Gh)[Omega] - p_a[Omega] = Gh[Omega]. Its impulse in the time t is Gh[Omega]t. Since the motion is steady there is no change of momentum between O´O´ and aa. The change of horizontal momentum is, therefore, the difference of the horizontal momentum lost in the space OOO´O´ and gained in the space aaa´a´. In the former space there is no horizontal momentum.

The volume of the space aaa´a´ is [omega]vt; the mass of liquid in that space is (G/g)[omega]vt; its momentum is (G/g)[omega]v²t. Equating impulse to momentum gained,

Gh[Omega] = (G/g)[omega]v²t;

.: [omega]/[Omega] = gh/v²

But

v² = 2gh, and [omega]/[Omega] = c_c;

.: [omega]/[Omega] = ½ = c_c;

a result confirmed by experiment with mouthpieces of this kind. A similar theoretical investigation is not possible for orifices in plane surfaces, because the velocity along the sides of the vessel in the neighbourhood of the orifice is not so small that it can be neglected. The resultant horizontal pressure is therefore greater than Gh[Omega], and the contraction is less. The experimental values of the coefficient of discharge for a re-entrant mouthpiece are 0.5149 (Borda), 0.5547 (Bidone), 0.5324 (Weisbach), values which differ little from the theoretical value, 0.5, given above.

[Illustration: FIG. 40.]

§ 38. _Velocity of Filaments issuing in a Jet._--A jet is composed of fluid filaments or elementary streams, which start into motion at some point in the interior of the vessel from which the fluid is discharged, and gradually acquire the velocity of the jet. Let Mm, fig. 40 be such a filament, the point M being taken where the velocity is insensibly small, and m at the most contracted section of the jet, where the filaments have become parallel and exercise uniform mutual pressure. Take the free surface AB for datum line, and let p1, v1, h1, be the pressure, velocity and depth below datum at M; p, v, h, the corresponding quantities at m. Then § 29, eq. (3a),

v1²/2g + p1/G - h1 = v²/2g + p/G - h (1)

But at M, since the velocity is insensible, the pressure is the hydrostatic pressure due to the depth; that is v1 = 0, p1 = p_a + Gh1. At m, p = p_a, the atmospheric pressure round the jet. Hence, inserting these values,

0 + p_a/G + h1 - h1 = v²/2g + p_a/G - h;

v²/2g = h; (2)

or v = [root](2gh) = 8.025V [root]h. (2a)

[Illustration: FIG. 41.]

That is, neglecting the viscosity of the fluid, the velocity of filaments at the contracted section of the jet is simply the velocity due to the difference of level of the free surface in the reservoir and the orifice. If the orifice is small in dimensions compared with h, the filaments will all have nearly the same velocity, and if h is measured to the centre of the orifice, the equation above gives the mean velocity of the jet.

_Case of a Submerged Orifice._--Let the orifice discharge below the level of the tail water. Then using the notation shown in fig. 41, we have at M, v1 = 0, p1 = Gh; + p_a at m, p = Gh3 + p_a. Inserting these values in (3), § 29,

0 + h1 + p_a/G - h1 = v²/2g + h3 - h2 + p_a/G;

v²/2g = h2 - h3 = h, (3)

where h is the difference of level of the head and tail water, and may be termed the _effective head_ producing flow.

[Illustration: FIG. 42.]

_Case where the Pressures are different on the Free Surface and at the Orifice._--Let the fluid flow from a vessel in which the pressure is p0 into a vessel in which the pressure is p, fig. 42. The pressure p0 will produce the same effect as a layer of fluid of thickness p0/G added to the head water; and the pressure p, will produce the same effect as a layer of thickness p/G added to the tail water. Hence the effective difference of level, or effective head producing flow, will be

h = h0 + p0/G - p/G;

and the velocity of discharge will be

v = [root][2g {h0 + (p0 - p)/G}]. (4)

We may express this result by saying that differences of pressure at the free surface and at the orifice are to be reckoned as part of the effective head.

Hence in all cases thus far treated the velocity of the jet is the velocity due to the effective head, and the discharge, allowing for contraction of the jet, is

Q = c[omega]v = c[omega] [root](2gh), (5)

where [omega] is the area of the orifice, c[omega] the area of the contracted section of the jet, and h the effective head measured to the centre of the orifice. If h and [omega] are taken in feet, Q is in cubic feet per second.

It is obvious, however, that this formula assumes that all the filaments have sensibly the same velocity. That will be true for horizontal orifices, and very approximately true in other cases, if the dimensions of the orifice are not large compared with the head h. In large orifices in say a vertical surface, the value of h is different for different filaments, and then the velocity of different filaments is not sensibly the same.

SIMPLE ORIFICES--HEAD CONSTANT

[Illustration: FIG. 43.]

§ 39. _Large Rectangular Jets from Orifices in Vertical Plane Surfaces._--Let an orifice in a vertical plane surface be so formed that it produces a jet having a rectangular contracted section with vertical and horizontal sides. Let b (fig. 43) be the breadth of the jet, h1 and h2 the depths below the free surface of its upper and lower surfaces. Consider a lamina of the jet between the depths h and h + dh. Its normal section is bdh, and the velocity of discharge [root](2gh). The discharge per second in this lamina is therefore b[root](2gh) dh, and that of the whole jet is therefore _ /h2 Q = | b [root](2gh) dh _/h1

= 2/3 b[root](2g) {h2^(3/2) - h1^(3/2)}, (6)

where the first factor on the right is a coefficient depending on the form of the orifice.

Now an orifice producing a rectangular jet must itself be very approximately rectangular. Let B be the breadth, H1, H2, the depths to the upper and lower edges of the orifice. Put

b [h2^(3/2) - h1^(3/2)] / B [H2^(3/2) - H1^(3/2)] = c. (7)

Then the discharge, in terms of the dimensions of the orifice, instead of those of the jet, is

Q = (2/3)cB [root](2g) [H2^(3/2) - H1^(3/2)], (8)

the formula commonly given for the discharge of rectangular orifices. The coefficient c is not, however, simply the coefficient of contraction, the value of which is

b(h2 - h1)/B(H2 - H1),

and not that given in (7). It cannot be assumed, therefore, that c in equation (8) is constant, and in fact it is found to vary for different values of B/H2 and B/H1, and must be ascertained experimentally.

_Relation between the Expressions (5) and (8)._--For a rectangular orifice the area of the orifice is [omega] = B(H2 - H1), and the depth measured to its centre is ½(H2 + H1). Putting these values in (5),

Q1 = cB(H2 - H1) [root]{g(H2 + H1)}.

From (8) the discharge is

Q2 = (2/3)cB [root](2g) [H2^(3/2) - H1^(3/2)].

Hence, for the same value of c in the two cases,

Q2/Q1 = (2/3)[H2^(3/2) - H1^(3/2)] / [(H2 - H1)[root]{(H2 + H1)/2}].

Let H1/H2 = [sigma], then

Q2/Q1 = 0.9427(1 - [sigma]^(3/2)) / {1 - [sigma] [root]{(1 + [sigma])}}. (9)

If H1 varies from 0 to [infinity], [sigma]( = H1/H2) varies from 0 to 1. The following table gives values of the two estimates of the discharge for different values of [sigma]:--

+------------------+--------+------------------+--------+ | H1/H2 = [sigma]. | Q2/Q1. | H1/H2 = [sigma]. | Q2/Q1. | +------------------+--------+------------------+--------+ | 0.0 | .943 | 0.8 | .999 | | 0.2 | .979 | 0.9 | .999 | | 0.5 | .995 | 1.0 | 1.000 | | 0.7 | .998 | | | +------------------+--------+------------------+--------+

Hence it is obvious that, except for very small values of [sigma], the simpler equation (5) gives values sensibly identical with those of (8). When [sigma]<0.5 it is better to use equation (8) with values of c determined experimentally for the particular proportions of orifice which are in question.

[Illustration: FIG. 44.]

§ 40. _Large Jets having a Circular Section from Orifices in a Vertical Plane Surface._--Let fig. 44 represent the section of the jet, OO being the free surface level in the reservoir. The discharge through the horizontal strip aabb, of breadth aa = b, between the depths h1 + y and h1 + y + dy, is

dQ = b [root]{2g(h1 + y)} dy.

The whole discharge of the jet is _ /d Q = | b [root]{2g(h1 + y)} dy. _/0

But b = d sin [phi]; y = ½d(1 - cos [phi]); dy = ½d sin [phi] d[phi]. Let [epsilon] = d/(2h1 + d), then _ /[pi] Q = ½d² [root]{2g(h1 + d/2)} | sin² [phi][root]{1 - [epsilon] cos [phi]} d[phi]. _/0

From eq. (5), putting [omega] = [pi]d²/4, h = h1 + d/2, c = 1 when d is the diameter of the jet and not that of the orifice,

Q1 = ¼[pi]d² [root]{2g (h1 + d/2)}, _ /[pi] Q/Q1 = 2/[pi] | sin² [phi] [root]{1 - [epsilon] cos [phi]} d[phi]. _/0

For

h1 = [infinity], [epsilon] = 0 and Q/Q1 = 1;

and for

h1 = 0, [epsilon] = 1 and Q/Q1 = 0.96.

So that in this case also the difference between the simple formula (5) and the formula above, in which the variation of head at different parts of the orifice is taken into account, is very small.

NOTCHES AND WEIRS

§ 41. _Notches, Weirs and Byewashes._--A notch is an orifice extending up to the free surface level in the reservoir from which the discharge takes place. A weir is a structure over which the water flows, the discharge being in the same conditions as for a notch. The formula of discharge for an orifice of this kind is ordinarily deduced by putting H1 = 0 in the formula for the corresponding orifice, obtained as in the preceding section. Thus for a rectangular notch, put H1 = 0 in (8). Then

Q = (2/3)cB [root](2g) H^(3/2), (11)

where H is put for the depth to the crest of the weir or the bottom of the notch. Fig. 45 shows the mode in which the discharge occurs in the case of a rectangular notch or weir with a level crest. As, the free surface level falls very sensibly near the notch, the head H should be measured at some distance back from the notch, at a point where the velocity of the water is very small.

Since the area of the notch opening is BH, the above formula is of the form

Q = c × BH × k [root](2gH),

where k is a factor depending on the form of the notch and expressing the ratio of the mean velocity of discharge to the velocity due to the depth H.

§ 42. _Francis's Formula for Rectangular Notches._--The jet discharged through a rectangular notch has a section smaller than BH, (a) because of the fall of the water surface from the point where H is measured towards the weir, (b) in consequence of the crest contraction, (c) in consequence of the end contractions. It may be pointed out that while the diminution of the section of the jet due to the surface fall and to the crest contraction is proportional to the length of the weir, the end contractions have nearly the same effect whether the weir is wide or narrow.

[Illustration: FIG. 45.]

J. B. Francis's experiments showed that a perfect end contraction, when the heads varied from 3 to 24 in., and the length of the weir was not less than three times the head, diminished the effective length of the weir by an amount approximately equal to one-tenth of the head. Hence, if l is the length of the notch or weir, and H the head measured behind the weir where the water is nearly still, then the width of the jet passing through the notch would be l - 0.2H, allowing for two end contractions. In a weir divided by posts there may be more than two end contractions. Hence, generally, the width of the jet is l - 0.1nH, where n is the number of end contractions of the stream. The contractions due to the fall of surface and to the crest contraction are proportional to the width of the jet. Hence, if cH is the thickness of the stream over the weir, measured at the contracted section, the section of the jet will be c(l - 0.1nH)H and (§ 41) the mean velocity will be 2/3 [root](2gH). Consequently the discharge will be given by an equation of the form

Q = (2/3)c (l - 0.1nH)H [root](2gH) = 5.35c (l - 0.1nH) H^(3/2).

This is Francis's formula, in which the coefficient of discharge c is much more nearly constant for different values of l and h than in the ordinary formula. Francis found for c the mean value 0.622, the weir being sharp-edged.

§ 43. _Triangular Notch_ (fig. 46).--Consider a lamina issuing between the depths h and h + dh. Its area, neglecting contraction, will be bdh, and the velocity at that depth is [root](2gh). Hence the discharge for this lamina is

b[root](2gh) dh.

But

B/b = H/(H - h); b = B(H - h)/H.

Hence discharge of lamina

= B(H - h) [root](2gh) dh/H;

and total discharge of notch _ /H = Q = B[root](2g) | (H - h)h^(½) dh/H _/0

= (4/15) B[root](2g)H^(3/2).

or, introducing a coefficient to allow for contraction,

Q = (4/15)cB [root](2g) H^(½),

[Illustration: FIG. 46.]

When a notch is used to gauge a stream of varying flow, the ratio B/H varies if the notch is rectangular, but is constant if the notch is triangular. This led Professor James Thomson to suspect that the coefficient of discharge, c, would be much more constant with different values of H in a triangular than in a rectangular notch, and this has been experimentally shown to be the case. Hence a triangular notch is more suitable for accurate gaugings than a rectangular notch. For a sharp-edged triangular notch Professor J. Thomson found c = 0.617. It will be seen, as in § 41, that since ½BH is the area of section of the stream through the notch, the formula is again of the form

Q = c × ½BH × k[root](2gH),

where k = 8/15 is the ratio of the mean velocity in the notch to the velocity at the depth H. It may easily be shown that for all notches the discharge can be expressed in this form.

_Coefficients for the Discharge over Weirs, derived from the Experiments of T. E. Blackwell. When more than one experiment was made with the same head, and the results were pretty uniform, the resulting coefficients are marked with an (*). The effect of the converging wing-boards is very strongly marked._

+----------+-------------+---------------------------------+-----------------------------------------+ | | | Planks 2 in. thick, | | | Heads in | Sharp Edge. | square on Crest. | Crests 3 ft. wide. | | inches +------+------+-----+-----+-------+-------------+------+------+------+------+------+------+ | measured | | | | | |10 ft. long, | 3 ft.| 3 ft.| 3 ft.| 6 ft.|10 ft.|10 ft.| |from still| 3 ft.|10 ft.|3 ft.|6 ft.| 10 ft.| wing-boards | long,| long,| long,| long,| long,| long,| | Water in | long.| long.|long.|long.| long. | making an |level.|fall 1|fall 1|level.|level.|fall 1| |Reservoir.| | | | | |angle of 60°.| |in 18.|in 12.| | |in 18.| +----------+------+------+-----+-----+-------+-------------+------+------+------+------+------+------+ | 1 | .677 | .809 |.467 |.459 |.435[4]| .754 | .452 | .545 | .467 | .. | .381 | .467 | | 2 | .675 | .803 |.509*|.561 |.585* | .675 | .482 | .546 | .533 | .. | .479*| .495*| | 3 | .630 | .642*|.563*|.597*|.569* | .. | .441 | .537 | .539 | .492*| .. | .. | | 4 | .617 | .656 |.549 |.575 |.602* | .656 | .419 | .431 | .455 | .497*| .. | .515 | | 5 | .602 | .650*|.588 |.601*|.609* | .671 | .479 | .516 | .. | .. | .518 | .. | | 6 | .593 | .. |.593*|.608*|.576* | .. | .501*| .. | .531 | .507 | .513 | .543 | | 7 | .. | .. |.617*|.608*|.576* | .. | .488 | .513 | .527 | .497 | .. | .. | | 8 | .. | .581 |.606*|.590*|.548* | .. | .470 | .491 | .. | .. | .468 | .507 | | 9 | .. | .530 |.600 |.569*|.558* | .. | .476 | .492*| .498 | .480*| .486 | .. | | 10 | .. | .. |.614*|.539 |.534* | .. | .. | .. | .. | .465*| .455 | .. | | 12 | .. | .. | .. |.525 |.534* | .. | .. | .. | .. | .467*| .. | .. | | 14 | .. | .. | .. |.549*| .. | .. | .. | .. | .. | .. | .. | .. | +----------+------+------+-----+-----+-------+-------------+------+------+------+------+------+------+

[Illustration: FIG. 47.]

§ 44. _Weir with a Broad Sloping Crest._--Suppose a weir formed with a broad crest so sloped that the streams flowing over it have a movement sensibly rectilinear and uniform (fig. 47). Let the inner edge be so rounded as to prevent a crest contraction. Consider a filament aa´, the point a being so far back from the weir that the velocity of approach is negligible. Let OO be the surface level in the reservoir, and let a be at a height h´´ below OO, and h´ above a´. Let h be the distance from OO to the weir crest and e the thickness of the stream upon it. Neglecting atmospheric pressure, which has no influence, the pressure at a is Gh´´; at a´ it is Gz. If v be the velocity at a´,

v²/2g = h´ + h´´ - z = h - e;

Q = be [root]{2g(h - e)}.

Theory does not furnish a value for e, but Q = 0 for e = 0 and for e = h. Q has therefore a maximum for a value of e between 0 and h, obtained by equating dQ/de to zero. This gives e = (2/3)h, and, inserting this value,

Q = 0.385 bh [root](2gh),

as a maximum value of the discharge with the conditions assigned. Experiment shows that the actual discharge is very approximately equal to this maximum, and the formula is more legitimately applicable to the discharge over broad-crested weirs and to cases such as the discharge with free upper surface through large masonry sluice openings than the ordinary weir formula for sharp-edged weirs. It should be remembered, however, that the friction on the sides and crest of the weir has been neglected, and that this tends to reduce a little the discharge. The formula is equivalent to the ordinary weir formula with c = 0.577.

SPECIAL CASES OF DISCHARGE FROM ORIFICES

§ 45. _Cases in which the Velocity of Approach needs to be taken into Account. Rectangular Orifices and Notches._--In finding the velocity at the orifice in the preceding investigations, it has been assumed that the head h has been measured from the free surface of still water above the orifice. In many cases which occur in practice the channel of approach to an orifice or notch is not so large, relatively to the stream through the orifice or notch, that the velocity in it can be disregarded.

[Illustration: FIG. 48.]

Let h1, h2 (fig. 48) be the heads measured from the free surface to the top and bottom edges of a rectangular orifice, at a point in the channel of approach where the velocity is u. It is obvious that a fall of the free surface,

[h] = u²/2g

has been somewhere expended in producing the velocity u, and hence the true heads measured in still water would have been h1 + [h] and h2 + [h]. Consequently the discharge, allowing for the velocity of approach, is

Q = (2/3)cb [root](2g) {(h2 + [h])^(3/2) - (h1 + [h])^(3/2)}. (1)

And for a rectangular notch for which h1 = 0, the discharge is

Q = (2/3)cb [root](2g) {(h2 + [h])^(3/2) - [h]^(3/2)}. (2)

In cases where u can be directly determined, these formulae give the discharge quite simply. When, however, u is only known as a function of the section of the stream in the channel of approach, they become complicated. Let [Omega] be the sectional area of the channel where h1 and h2 are measured. Then u = Q/[Omega] and [h] = Q²/2g [Omega]².

This value introduced in the equations above would render them excessively cumbrous. In cases therefore where [Omega] only is known, it is best to proceed by approximation. Calculate an approximate value Q´ of Q by the equation

Q´ = (2/3)cb [root](2g) {h2^(3/2) - h1^(3/2)}.

Then [h] = Q´²/2g[Omega]² nearly. This value of [h] introduced in the equations above will give a second and much more approximate value of Q.

[Illustration: FIG. 49.]

§ 46. _Partially Submerged Rectangular Orifices and Notches._--When the tail water is above the lower but below the upper edge of the orifice, the flow in the two parts of the orifice, into which it is divided by the surface of the tail water, takes place under different conditions. A filament M1m1 (fig. 49) in the upper part of the orifice issues with a head h´ which may have any value between h1 and h. But a filament M2m2 issuing in the lower part of the orifice has a velocity due to h´´ - h´´´, or h, simply. In the upper part of the orifice the head is variable, in the lower constant. If Q1, Q2 are the discharges from the upper and lower parts of the orifice, b the width of the orifice, then

Q1 = (2/3)cb [root](2g) {h^(3/2) - h1^(3/2)} (3) Q1 = cb (h2 - h) [root](2gh).

In the case of a rectangular notch or weir, h1 = 0. Inserting this value, and adding the two portions of the discharge together, we get for a drowned weir

Q = cb[root](2gh) (h2 - h/3), (4)

where h is the difference of level of the head and tail water, and h2 is the head from the free surface above the weir to the weir crest (fig. 50).

From some experiments by Messrs A. Fteley and F.P. Stearns (_Trans. Am. Soc. C.E._, 1883, p. 102) some values of the coefficient c can be reduced

h3/h2 c h3/h2 c

0.1 0.629 0.7 0.578 0.2 0.614 0.8 0.583 0.3 0.600 0.9 0.596 0.4 0.590 0.95 0.607 0.5 0.582 1.00 0.628 0.6 0.578

If velocity of approach is taken into account, let [h] be the head due to that velocity; then, adding [h] to each of the heads in the equations (3), and reducing, we get for a weir

Q = cb [root]{2g} [(h2 + [h]) (h + [h])^(½) - (1/3)(h + [h])^(3/2) - (2/3)[h]^(3/2)]; (5)

an equation which may be useful in estimating flood discharges.

[Illustration: FIG. 50.]

_Bridge Piers and other Obstructions in Streams._--When the piers of a bridge are erected in a stream they create an obstruction to the flow of the stream, which causes a difference of surface-level above and below the pier (fig. 51). If it is necessary to estimate this difference of level, the flow between the piers may be treated as if it occurred over a drowned weir. But the value of c in this case is imperfectly known.

§ 47. _Bazin's Researches on Weirs._--H. Bazin has executed a long series of researches on the flow over weirs, so systematic and complete that they almost supersede other observations. The account of them is contained in a series of papers in the _Annales des Ponts et Chaussées_ (October 1888, January 1890, November 1891, February 1894, December 1896, 2nd trimestre 1898). Only a very abbreviated account can be given here. The general plan of the experiments was to establish first the coefficients of discharge for a standard weir without end contractions; next to establish weirs of other types in series with the standard weir on a channel with steady flow, to compare the observed heads on the different weirs and to determine their coefficients from the discharge computed at the standard weir. A channel was constructed parallel to the Canal de Bourgogne, taking water from it through three sluices 0.3 × 1.0 metres. The water enters a masonry chamber 15 metres long by 4 metres wide where it is stilled and passes into the canal at the end of which is the standard weir. The canal has a length of 15 metres, a width of 2 metres and a depth of 0.6 metres. From this extends a channel 200 metres in length with a slope of 1 mm. per metre. The channel is 2 metres wide with vertical sides. The channels were constructed of concrete rendered with cement. The water levels were taken in chambers constructed near the canal, by floats actuating an index on a dial. Hook gauges were used in determining the heads on the weirs.

[Illustration: FIG. 51.]

_Standard Weir._--The weir crest was 3.72 ft. above the bottom of the canal and formed by a plate ¼ in. thick. It was sharp-edged with free overfall. It was as wide as the canal so that end contractions were suppressed, and enlargements were formed below the crest to admit air under the water sheet. The channel below the weir was used as a gauging tank. Gaugings were made with the weir 2 metres in length and afterwards with the weir reduced to 1 metre and 0.5 metre in length, the end contractions being suppressed in all cases. Assuming the general formula

Q = mlh [root](2gh), (1)

Bazin arrives at the following values of _m_:--

_Coefficients of Discharge of Standard Weir._

+----------------+--------------+--------+ | Head h metres. | Head h feet. | m | +----------------+--------------+--------+ | 0.05 | .164 | 0.4485 | | 0.10 | .328 | 0.4336 | | 0.15 | .492 | 0.4284 | | 0.20 | .656 | 0.4262 | | 0.25 | .820 | 0.4259 | | 0.30 | .984 | 0.4266 | | 0.35 | 1.148 | 0.4275 | | 0.40 | 1.312 | 0.4286 | | 0.45 | 1.476 | 0.4299 | | 0.50 | 1.640 | 0.4313 | | 0.55 | 1.804 | 0.4327 | | 0.60 | 1.968 | 0.4341 | +----------------+--------------+--------+

Bazin compares his results with those of Fteley and Stearns in 1877 and 1879, correcting for a different velocity of approach, and finds a close agreement.

_Influence of Velocity of Approach._--To take account of the velocity of approach u it is usual to replace h in the formula by h + au²/2g where [alpha] is a coefficient not very well ascertained. Then

Q = [mu]l (h + [alpha]u²/2g) [root]{2g(h + [alpha]u²/2g)} = [mu]lh [root](2gh)(1 + [alpha]u²/2gh)^(3/2). (2)

The original simple equation can be used if

m = [mu](1 + [alpha]u²/2gh)^(3/2)

or very approximately, since u²/2gh is small,

m = [mu](1 + (3/2)[alpha]u²/2gh). (3)

[Illustration: FIG. 52.]

Now if p is the height of the weir crest above the bottom of the canal (fig. 52), u = Q/l(p + h). Replacing Q by its value in (1)

u²/2gh = Q²/{2ghl²(p + h)²} = m²{h/(p + h)}², (4)

so that (3) may be written

m = [mu][1 + k{h/(p + h)}²]. (5)

Gaugings were made with weirs of 0.75, 0.50, 0.35, and 0.24 metres height above the canal bottom and the results compared with those of the standard weir taken at the same time. The discussion of the results leads to the following values of m in the general equation (1):--

m = [mu](1 + 2.5u²/2gh) = [mu][1 + 0.55 {h/(p + h)}²].

Values of [mu]--

+----------------+--------------+--------+ | Head h metres. | Head h feet. | [mu] | +----------------+--------------+--------+ | 0.05 | .164 | 0.4481 | | 0.10 | .328 | 0.4322 | | 0.20 | .656 | 0.4215 | | 0.30 | .984 | 0.4174 | | 0.40 | 1.312 | 0.4144 | | 0.50 | 1.640 | 0.4118 | | 0.60 | 1.968 | 0.4092 | +----------------+--------------+--------+

An approximate formula for [mu] is:

[mu] = 0.405 + 0.003/h (h in metres)

[mu] = 0.405 + 0.01/h (h in feet).

_Inclined Weirs._---Experiments were made in which the plank weir was inclined up or down stream, the crest being sharp and the end contraction suppressed. The following are coefficients by which the discharge of a vertical weir should be multiplied to obtain the discharge of the inclined weir.

Coefficient. Inclination up stream 1 to 1 0.93 " " 3 to 2 0.94 " " 3 to 1 0.96 Vertical weir 1.00 Inclination down stream 3 to 1 1.04 " " 3 to 2 1.07 " " 1 to 1 1.10 " " 1 to 2 1.12 " " 1 to 4 1.09

The coefficient varies appreciably, if h/p approaches unity, which case should be avoided.

In all the preceding cases the sheet passing over the weir is detached completely from the weir and its under-surface is subject to atmospheric pressure. These conditions permit the most exact determination of the coefficient of discharge. If the sides of the canal below the weir are not so arranged as to permit the access of air under the sheet, the phenomena are more complicated. So long as the head does not exceed a certain limit the sheet is detached from the weir, but encloses a volume of air which is at less than atmospheric pressure, and the tail water rises under the sheet. The discharge is a little greater than for free overfall. At greater head the air disappears from below the sheet and the sheet is said to be "drowned." The drowned sheet may be independent of the tail water level or influenced by it. In the former case the fall is followed by a rapid, terminating in a standing wave. In the latter case when the foot of the sheet is drowned the level of the tail water influences the discharge even if it is below the weir crest.

[Illustration: FIG. 53.]

[Illustration: FIG. 54.]

_Weirs with Flat Crests._--The water sheet may spring clear from the upstream edge or may adhere to the flat crest falling free beyond the down-stream edge. In the former case the condition is that of a sharp-edged weir and it is realized when the head is at least double the width of crest. It may arise if the head is at least 1½ the width of crest. Between these limits the condition of the sheet is unstable. When the sheet is adherent the coefficient m depends on the ratio of the head h to the width of crest c (fig. 53), and is given by the equation m = m1 [0.70 + 0.185h/c], where m1 is the coefficient for a sharp-edged weir in similar conditions. Rounding the upstream edge even to a small extent modifies the discharge. If R is the radius of the rounding the coefficient m is increased in the ratio 1 to 1 + R/h nearly. The results are limited to R less than ½ in.

_Drowned Weirs._--Let h (fig. 54) be the height of head water and h1 that of tail water above the weir crest. Then Bazin obtains as the approximate formula for the coefficient of discharge

m = 1.05m1 [1 + (1/5)h1/p] [root 3]{(h - h1)/h},

where as before m1 is the coefficient for a sharp-edged weir in similar conditions, that is, when the sheet is free and the weir of the same height.

[Illustration: FIG. 55.]

[Illustration: FIG. 56.]

§ 48. _Separating Weirs._--Many towns derive their water-supply from streams in high moorland districts, in which the flow is extremely variable. The water is collected in large storage reservoirs, from which an uniform supply can be sent to the town. In such cases it is desirable to separate the coloured water which comes down the streams in high floods from the purer water of ordinary flow. The latter is sent into the reservoirs; the former is allowed to flow away down the original stream channel, or is stored in separate reservoirs and used as compensation water. To accomplish the separation of the flood and ordinary water, advantage is taken of the different horizontal range of the parabolic path of the water falling over a weir, as the depth on the weir and, consequently, the velocity change. Fig. 55 shows one of these separating weirs in the form in which they were first introduced on the Manchester Waterworks; fig. 56 a more modern weir of the same kind designed by Sir A. Binnie for the Bradford Waterworks. When the quantity of water coming down the stream is not excessive, it drops over the weir into a transverse channel leading to the reservoirs. In flood, the water springs over the mouth of this channel and is led into a waste channel.

It may be assumed, probably with accuracy enough for practical purposes, that the particles describe the parabolas due to the mean velocity of the water passing over the weir, that is, to a velocity

(2/3)[root](2gh),

where h is the head above the crest of the weir.

Let cb = x be the width of the orifice and ac = y the difference of level of its edges (fig. 57). Then, if a particle passes from a to b in t seconds,

y = ½gt², x = (2/3)[root](2gh) t;

.: y = (9/16)x²/h,

which gives the width x for any given difference of level y and head h, which the jet will just pass over the orifice. Set off ad vertically and equal to ½g on any scale; af horizontally and equal to 2/3 [root](gh). Divide af, fe into an equal number of equal parts. Join a with the divisions on ef. The intersections of these lines with verticals from the divisions on af give the parabolic path of the jet.

[Illustration: FIG. 57.]

MOUTHPIECES--HEAD CONSTANT

§ 49. _Cylindrical Mouthpieces._--When water issues from a short cylindrical pipe or mouthpiece of a length at least equal to l½ times its smallest transverse dimension, the stream, after contraction within the mouthpiece, expands to fill it and issues full bore, or without contraction, at the point of discharge. The discharge is found to be about one-third greater than that from a simple orifice of the same size. On the other hand, the energy of the fluid per unit of weight is less than that of the stream from a simple orifice with the same head, because part of the energy is wasted in eddies produced at the point where the stream expands to fill the mouthpiece, the action being something like that which occurs at an abrupt change of section.

Let fig. 58 represent a vessel discharging through a cylindrical mouthpiece at the depth h from the free surface, and let the axis of the jet XX be taken as the datum with reference to which the head is estimated. Let [Omega] be the area of the mouthpiece, [omega] the area of the stream at the contracted section EF. Let v, p be the velocity and pressure at EF, and v1, p1 the same quantities at GH. If the discharge is into the air, p1 is equal to the atmospheric pressure p_a.

The total head of any filament which goes to form the jet, taken at a point where its velocity is sensibly zero, is h + p_a/G; at EF the total head is v²/2g + p/G; at GH it is v1²/2g + p1/G.

Between EF and GH there is a loss of head due to abrupt change of velocity, which from eq. (3), § 36, may have the value

(v - v1)²/2g.

Adding this head lost to the head at GH, before equating it to the heads at EF and at the point where the filaments start into motion,--

h + p_a/G = v²/2g + p/G = v1²/2g + p1/G + (v - v1)²/2g.

But [omega]v = [Omega]v1, and [omega] = c_c[Omega], if c_c is the coefficient of contraction within the mouthpiece. Hence

v = [Omega]v1/[omega] = v1/c_c.

Supposing the discharge into the air, so that p1 = p_a,

h + p_a/G = v1²/2g + p_a/G + (v1²/2g)(1/c_c - 1)²;

(v1/2g){1 + (1/c_c - 1)²} = h;

.: v1 = [root](2gh)/[root]{1 + (1/c_c - 1)²}; (1)

[Illustration: FIG. 58.]

where the coefficient on the right is evidently the coefficient of velocity for the cylindrical mouthpiece in terms of the coefficient of contraction at EF. Let c_c = 0.64, the value for simple orifices, then the coefficient of velocity is

c_v = 1/[root]{1 + (1/c_c - 1)²} = 0.87 (2)

The actual value of c_v, found by experiment is 0.82, which does not differ more from the theoretical value than might be expected if the friction of the mouthpiece is allowed for. Hence, for mouthpieces of this kind, and for the section at GH,

c_v = 0.82 c_c = 1.00 c = 0.82,

Q = 0.82[Omega] [root](2gh).

It is easy to see from the equations that the pressure p at EF is less than atmospheric pressure. Eliminating v1, we get

(p_a - p)/G = ¾h nearly; (3)

or

p = p_a - ¾Gh lb. per sq. ft.

If a pipe connected with a reservoir on a lower level is introduced into the mouthpiece at the part where the contraction is formed (fig. 59), the water will rise in this pipe to a height

KL = (p_a - p)/G = ¾h nearly.

If the distance X is less than this, the water from the lower reservoir will be forced continuously into the jet by the atmospheric pressure, and discharged with it. This is the crudest form of a kind of pump known as the jet pump.

§ 50. _Convergent Mouthpieces._--With convergent mouthpieces there is a contraction within the mouthpiece causing a loss of head, and a diminution of the velocity of discharge, as with cylindrical mouthpieces. There is also a second contraction of the stream outside the mouthpiece. Hence the discharge is given by an equation of the form

Q = c_v c_c[Omega] [root](2gh), (4)

where [Omega] is the area of the external end of the mouthpiece, and c_c[Omega] the section of the contracted jet beyond the mouthpiece.

_Convergent Mouthpieces (Castel's Experiments).--Smallest diameter of orifice = 0.05085 ft. Length of mouthpiece = 2.6 Diameters._

+------------+--------------+--------------+--------------+ | |Coefficient of|Coefficient of|Coefficient of| | Angle of | Contraction, | Velocity, | Discharge, | |Convergence.| c_c | c_v | c | +------------+--------------+--------------+--------------+ | 0° 0´ | .999 | .830 | .829 | | 1° 36´ | 1.000 | .866 | .866 | | 3° 10´ | 1.001 | .894 | .895 | | 4° 10´ | 1.002 | .910 | .912 | | 5° 26´ | 1.004 | .920 | .924 | | 7° 52´ | .998 | .931 | .929 | | 8° 58´ | .992 | .942 | .934 | | 10° 20´ | .987 | .950 | .938 | | 12° 4´ | .986 | .955 | .942 | | 13° 24´ | .983 | .962 | .946 | | 14° 28´ | .979 | .966 | .941 | | 16° 36´ | .969 | .971 | .938 | | 19° 28´ | .953 | .970 | .924 | | 21° 0´ | .945 | .971 | .918 | | 23° 0´ | .937 | .974 | .913 | | 29° 58´ | .919 | .975 | .896 | | 40° 20´ | .887 | .980 | .869 | | 48° 50´ | .861 | .984 | .847 | +------------+--------------+--------------+--------------+

The maximum coefficient of discharge is that for a mouthpiece with a convergence of 13°24´.

The values of c_v and c_c must here be determined by experiment. The above table gives values sufficient for practical purposes. Since the contraction beyond the mouthpiece increases with the convergence, or, what is the same thing, c_c diminishes, and on the other hand the loss of energy diminishes, so that c_v increases with the convergence, there is an angle for which the product c_c c_v, and consequently the discharge, is a maximum.

[Illustration: FIG. 59.]

§ 51. _Divergent Conoidal Mouthpiece._--Suppose a mouthpiece so designed that there is no abrupt change in the section or velocity of the stream passing through it. It may have a form at the inner end approximately the same as that of a simple contracted vein, and may