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MINERALOGY.

SAMUEL HENSON,

97 REGENT STREET, LONDON, W. ESTABLISHED 1840. Late 277 STRAND.

A Large Collection of Beautiful Mineral Specimens, including a VERY FINE GROUP OF SENARMONTITE CRYSTALS, VERY BRILLIANT MANGANITES, WULFENITES, VANADIMITES, HARMATOME, from Oberstein and Scotland; NATROLITES, Auvergne ; CHILDRENITES, ARAGONITES, and MELANOPHLOGITE. FOSSILS, ROCKS, ROCK SECTIONS, HAMMERS, CHISELS, and BLOWPIPE APPARATUS. Precious Stones for Collectors and Mounting. COLLECTIONS FOR STUDENTS AND PROSPECTORS. Lessons given. F. H. BUTLER, M.A. Oxon., A.R.S.Mines, &c.

Catalogues Free.

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Comprising Fossils, Minerals, and Rocks, labelled with Name, Locality and Geological Position, in Mahogany Cabinets. 100 Specimens, 255.; 200 ditto, sos. The best value obtainable.

Micro-sections of Rocks in great variety. Cabinets, Glass-topped Boxes, and other Geological Requisites.

THOMAS D. RUSSELL,

PRIZE MEDALLIST, HEALTH EXHIBITION,
78 NEWGATE STREET, LONDON, E.C.

J. T. CROCKETT,

Maker of every description of Entomological Cabinets and Apparatus; Store and Book-boxes, fitted with Camphor-cells; Setting Boards, Oval or Flat, &c. Cabinets of every description kept in stock. SPECIAL INSECT CABINETS, with Drawers fitted with Glass Tops and Bottoms to show upper and under side without removing insect. Store-boxes specially made for Continental Setting, highly recommended for Beetles. All best work. Lowest possible terms for cash. Prices on Application. Estimates supplied. Trade supplied. Established since 1847.

Show Rooms A Prince's Street, Cavendish Square, W. (7 doors from Oxford Circus). Factories-34 Ridinghouse Street, and Ogle Street, W.

ROCK SECTIONS CUTTING MACHINES Prize Medal awarded by the Jury of the late Exhibition of Inventions. PRICE £5.

Sole Makers

CUTTELL, 47 Rathbone Place, Oxford Street.

OSTEOLOGICAL SPECIMENS, MODELS, &c.-MOORE BROS., 49 Hardman Street, Liverpool. Price List, Three Stamps.

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WATCHES.

TRADE

MARK

DENT

WATCHES and CLOCKS at REDUCED PRICES, sent post free on application to E. DENT and Co., Makers to the Queen, 61 STRAND, LONDON, W.C., or 4 ROYAL EXCHANGE.

TO SCIENCE LECTURERS.

See Mr. HUGHES'S PATENT COMBINATION OPTICAL LANTERN, used by W. LANT CARPENTER, Esq., Prof. FORBES, B. J. MALDEN, Esq. New Oxyhydrogen Microscope. Grand Results. Docwra Triple, Prize Medal, Highest Award. Patent Pamphagos Lantern Science Lecture Sets. Novelties Cheapest and Best. Elaborately Illustrated Catalogue, 300 Pages, 1s.; Postage, 5d. Smaller do., 6d. Pamphlets Free. HUGHES, Specialist, Brewster House, Mortimer Road, Kingsland, N.

GEO. REES'

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CHEAPEST HOUSE (IN LONDON.)

ENGRAVINGS,

at Lowest Prices,

ETCHINGS.

A Large Selection of Sporting Pictures.

115 STRAND: 41-43 RUSSELL STREET, COVENT GARDEN.

SILVERED-GLASS REFLECTING

TELESCOPES.

CALVER'S well-known TELESCOPES received the Highest Award for "Excellence and Improvements at the International Exhibition, London. Catalogues and Testimonials, 15.-G. CALVER, F.R.A.S., Widford, Chelmsford.

MANUSCRIPT COPYING

By Typewriter. Special attention given to Papers on Technical Subjects for Public Reading. Price, 1s. 3d. per 1000 Words. Manifold Copies, 15. per 1000 Words. STANDARD TYPEWRITING CO., 90 & 91 Queen St. (third floor), E. C. and at 38 Arlington Square, N., and 41 Goldney Road, W.

WEAK AND DEFECTIVE

SIGHT.

SPECTACLES scientifically adapted to remedy impaired vision by Mr. ACKLAND, Surgeon, daily, at HORNE AND THORNTHWAITE'S, Opticians to the Queen, 416 Strand, London. The weak-sighted should read Ackland's "Hints on Spectacles," 6d., post free.

FOURTH EDITION-NOW READY.

With Portrait and Map, 2 Vols. Crown 8vo, 245.

OUR VICEREGAL LIFE IN INDIA: being a Selection from my Journal during the Years 1884-88. By the MARCHIONESS of DÜFFERIN.

Just what might have been expected from the talented and popular 'Vicereine. As a record it is remarkably complete. There was no province of our teeming Indian Empire which was left uncovered by the Viceregal tours; and an observant eve and lively pen made the best of Lady Dufferin's opportunity."-Pall Mall Gasette.

"A record of life in India as it presented itself during a sojourn of four years in all its rich and manifold variety, to the wife of a Viceroy, could only fail to be deeply interesting through some deficiency of sympathy or lack of descriptive power. Happily, in neither of these prime requirements for her task is Lady Dufferin in any way wanting."-Daily News.

JOHN MURRAY, Albemarle Street.

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Principal of the Telegraphists' School of Science, Director of the Electrical Engineering Section, People's Palace, London, &c., &c., and A. BROOKER,

Instructor on Electrical Engineering at the Telegraphists' School of Science, and at the People's Palace, London. London: LONGMANS, GREEN, & CO.

By LIONEL S. BEALE, M.B., F.R.S., Professor of Medicine in King's College, London. HOW TO WORK WITH THE MICROSCOPE. Plates. 215. (Harrison and Sons.)

100

OUR MORALITY AND THE MORAL QUESTION. 2s. 6d. 100 FIGURES OF URINARY DEPOSITS. 5s. URINARY AND RENAL DERANGEMENTS AND CAL

CULOUS DISORDERS, Diagnosis and Treatment. Now Ready, 5s. SLIGHT AILMENTS. Pp. 275. 5s.

THE MICROSCOPE IN MEDICINE. 86 Plates. 215.
BIOPLASM: Introduction to Medicine and Physiology. 6s. 6d,
PROTOPLASM. (New Edition preparing.)

ON LIFE AND ON VITAL ACTION. 5s.
THE MYSTERY OF LIFE. 35. 6d.

LIFE THEORIES AND RELIGIOUS THOUGHT. 5s. 6d.
THE "MACHINERY" OF LIFE. 25.
DISEASE GERMS. (Soiled Copies only.) 8s. 6d.
London: J. & A. CHURCHILL.

PETROGRAPHICAL TABLES : An Aid to the Microscopical Determination of Rockforming Minerals.

By Prof. H. ROSENBUSCH. Translated and Edited by Dr. F. II. HATCH, of H. M. Geological Survey. 4to, Limp Cloth, 3s. 6d.

EDWARD STANFORD'S

RECENT PUBLICATIONS.

Third Edition, Revised and Enlarged.

STANFORD'S LONDON ATLAS OF
UNIVERSAL GEOGRAPHY. Quarto Edition. Containing 45 Cobres
Maps, carefully drawn and beautifully engraved on Steel and Coun
Plates, and an Alphabetical Index to the Geography of the W
Half-morocco, Cloth Sides, Gilt Edges, yo. Size, when shut, 12ļi”
15; weight, 4 lb. 8 oz.

"We have already commented on the pains which appear to have taken to work up the maps to the latest dates; we may add that excellent specimens of engraving and colouring, that the great difficile marking mountain ranges, &c., without obscuring the names, has here cellently surmounted, and that we have detected very few musprint. what may be called a medium atlas for general use, something between t cheap but meagre school collections and the elaborate in rather cosity o unwieldy library atlases, the London Atlas' deserves hearty reopener a tion."-Saturday Review.

CHARTS of the CONSTELLATIONS, from the North Pole to between 35 and 40 Degrees of South De Castion 7. ARTHUR COTTAM, F.R.A.S. 36 Charts, each go by 22 inle printed on Drawing Paper, and supplied folded in half in a Purt or flat if preferred. 2 net per Set. As soon as 200 Sets are end, Price will be raised to £33s., and as a few copies uuly now remains. application is desirable.

With one exception (Hydra) each Constellation is shown complete single Chart. The scale is one-third of an inch to a degree, and all t Double Stars in the Catalogues of the two Struves are shown, (D Prospectus, with Specimen Chart, free on application)

Surely this is the very luxury of stellar cartography, for, from the of Bayer downwards, nothing has appeared comparable with the m series of charts now before us for the special purpose for which intended.. It has been reserved for Mr. Cottam in prits wh employment with instruments having motions only in altitude and ano is as near perfection as any delineation of the celestial concave un apsurface is ever likely to be... The amount of labour expended on splendid work must have been No asmomical Fibran observatory of any pretensions can afford to be without it."-E Mechanic.

enormous.

A TRIP THROUGH THE EASTERN
CAUCASUS, with a Chapter on the Languages of the Country
the Hon. JOHN ABERCROMBY. Demy 8vo, Cloth, with Maps -
Illustrations, 148.

"Among the few travellers who have taken the opportunity re- is afforded of exploring the little-known region of the Eastern Caucaso. honourable place must now be accorded to the Hon. John Abercrovaly. in this volume has given a very interesting and informative account t country between Tiflis and Derbend-the scenery, the people, the ana logical remains, and the languages. He travelled with his eyes open, his notes on the physical aspects of Daghestan are full of information. Altogether his book is a good specimen of the useful as singer hed fr the picturesque or sensational literature of travel. Three mapsal muna no woodcuts add to the practical utility of the work."-Scottish Leazer, SEAS AND SKIES IN MANY LATI TUDES; or, Wanderings in Search of Weather. By the B. RALPH ABERCROMBY. Demy 8vo. with 3 Map 9 Photogra and 33 Woodcuts by PRITCHETT, WHYMPER, COOLER, ÅL LI

Extra, 18s.

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WORKS BY JAMES CROLL, LL.D., F.R.S. CLIMATE AND COSMOLOGY; a Supplementary Volume to "Climate and Time." Large Pust 8vo, tha

Price 65.

By the same Author, uniform in Size and Binding.

"These Tables may indeed be regarded as a summary of the same author's invaluable Microscopical Physiography.' The two works together supply a want long CLIMATE AND TIME in their Geological felt by English students-viz. a complete summary of all that has been done in the way of making the optical and other characters of minerals available."- -Nature.

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Relations. Large Post 8vo, Cloth, 108, 6d.

STELLAR EVOLUTION, and its Rela

tions to Geological Time. Large Post 8vo. Cloth, 38.

"All men of science who pay due heed to the ultimate principles i alk they are perforce brought in the course of their researches will find this deserving a thorough scrutiny. Mr. Croll has swept away a chod seemed at one time likely to obscure the general significance of evalue -Chemical News.

London: EDWARD STANFORD, 26 and 27 Cockspur Street, Chara Cross, S.W.

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THURSDAY, MARCH 6, 1890.

THE SCIENCE COLLECTIONS AT SOUTH KENSINGTON.

IT

Tis satisfactory to learn that the Government has taken the first step towards carrying out the recommendations of the recent Commission on the South

Kensington Museum. The Report of the Commissioners

was to the effect that the Science Museums contained valuable apparatus which ought to be exhibited; that the buildings in which it is displayed are inadequate; and that the area of the exhibition space ought immediately to be increased by 50 per cent. Between the Natural History Museum in Cromwell Road and the Imperial Institute Road lies the strip of ground on which the new buildings must be erected. It belonged to the Commissioners of the 1851 Exhibition, and they were willing to sell at a price somewhat less than the valuation of the Office of Works, or at ten shillings for every pound of their own estimate.

The question to be decided was, whether the country could afford £100,000 to purchase the land necessary to carry out the Report of one of the strongest Commissions which has ever investigated such a subject, or whether the great group of Museums for which South Kensington is famous was to be cut into two by rows of mansions.

The Government, which certainly did not err through undue haste, felt that a case had been made out, that further delay was useless, that the land ought to be secured before time and labour were spent in discussing the details of the buildings to be erected upon it, and therefore they brought in a supplementary estimate for the sum required.

Then followed a debate of the kind by which the prestige of ordinary members of the House of Commons has been reduced to its present level. One member "affirmed that there were empty rooms in South Kensinton Museum which might well be used for the display of exhibits," though a body of Commissioners appointed to investigate the state of the collections had reported in a directly opposite sense. Another "could not understand why all these educational collections should be established close to one another at South Kensington." In other words, he could not see that if there is to be at South Kensington a great training school for teachers of science and art, it is desirable that the students should have ready access to the national science and art collections, and that the collections themselves should benefit from the advice of the Professors who are familiar with them. These objections were not, however, raised by men who knew the facts. Approval was expressed from both sides of the House by those who have the interests of education at heart. Sir Lyon Playfair, Sir Henry Roscoe, Mr. Mundella, and Mr. Chamberlain, all spoke in favour of the vote, and Mr. Mundella put clearly what those who are acquainted with the Museum know to be the truth, when he said " this question had been pressing for the last ten years, because for the whole of that penod the most valuable national science collections, such as no other country in the world possessed, had been housed in the most disgraceful manner."

VOL. XLI.-No. 1062.

The vote was finally carried by 144 to 67, and it is to be hoped, now that the Government have entered upon the path of progress, they will pursue it with determination.

No one would urge precipitancy. Due care ought to be taken that money's value is obtained for money spent ; but as the question of principle has been decided after ten years' debate, we have a right to demand that progress shall not be delayed by mere blind obstruction to every proposal which involves outlay, but that those in whose hands the fate of the science collections rests shall make up their minds as to what ought to be done, and shall forthwith do it.

THREE RECENT POPULAR WORKS UPON

NATURAL HISTORY.

Glimpses of Animal Life. By W. Jones, F.S.A. (London : Elliot Stock, 1889.)

Toilers in the Sea. By M. C. Cooke, M.A., LL.D. (London: S.P.C. K., 1889.)

Les Industries des Animaux. Par F. Houssay. (Paris : J. B. Baillière et Fils, 1890.)

MR.

66

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R. JONES'S book is a charming little volume of 229 pages, with one illustration forming a frontispiece. There are, in all, seven chapters; dealing, in succession, with "Playfulness of Animals,” Animal Training," "Musical Fishes" (title ill chosen), "NestBuilding and Walking Fishes," "Luminous Animals," "Birds' Nests in Curious Places," and "The Mole." The author has been at immense pains to sift the voluminous literature of his subject (a task which he admits has involved a somewhat unprofitable course of romance reading"). We find, as might be expected, citations of the old old stories of our youth; the climbing perch, Cowper's hares, and other time-honoured (if perhaps too highly coloured) narratives appear; the luminous centipede is not overlooked; and authorities are appealed to, from Aristotle and the ancient classical writers of the past, down to Lubbock and Romanes ("the Rev. Dr. Romanes" [sic], p. 25) of to-day. The work is essentially a compilation; it consists mainly of a collection of lengthy extracts, and the author has left himself little room for originality. There results from this an occasional heaviness of style, which is especially noteworthy in the earlier portions of the volume. Paragraphs too frequently lead off with "Broderip mentions," "Evelyn records," "Humboldt saw," and the like; and not even stories of the gambols between a rhinoceros and an elephant, or of those of a 60-foot whale, serve to relieve the monotony. It is doubtful whether the author has not occasionally erred in the placing of his anecdotes. To take a leading instance; on p. 32 there is recorded the story of a parrot, "which, when a person said to it, Laugh, Poll; laugh!' laughed accordingly, and the instant after screamed out, What a fool to make me laugh!"" This narrative cannot be said to betray any sense of playfulness on the part of the bird, as would be inferred from its position in the text; it surely should have found a place under "Animal Training." The most serious defect in the book is the absence of an index. The author has brought together a very remarkable series of anecdotes; and if he would give us an

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exhaustive index, together with a complete bibliography, his book would befit the more special and advanced student of animal life. Without these it can only appeal to the dilettanti; and we shall look for them in a future edition. We would point out, at the same time, that the climbing perch is referred to on p. 151 as Perca, and on 157 as Anabas (the latter being correct); that "Willmoes" (p. 185) should read Willemoes Suhm; and that Mr. Romanes does not lay claim to the distinction accorded him on p. 25 (cf. supra). The author, as he enters into details not usually met with in books of this kind, might advantageously incorporate with his account of the stickleback's nest, the discovery of Möbius and Prince that the thread employed in weaving it is secreted by the animal's kidney. So unique a fact in natural history should not be allowed to pass unnoticed; and that portion of the work which deals with the luminous fishes might well be brought more completely up to date.

Dr. Cooke's treatise is one of 369 pages, with 4 lithographic plates, 70 woodcuts, and an index. It deals with marine invertebrata, in their especial relations to skeleton formation; and the volume is especially designed to make good the shortcomings of the Rev. J. G. Wood's work, entitled "Homes without Hands." The book has its good points; the chapter on "Coral Reefs and Islands," and the "Introduction," are fairly well done. The lastnamed deals with generalities as affecting life and the conditions of life in the ocean depths; it gives a record | of important explorations, from that of Ross in Baffin's Bay, to the Challenger; the Bathybius controversy is abstracted, and alternative theories of reef-formation are summarized, both being presented in concise and impartial language. On perusal, however, of the main portion of the book, we meet with a preponderance of antiquated, and often erroneous information. Lengthy citations from the writings of authorities of the last two or three decades are flaunted as if expressive of current knowledge and opinion. The question of sponge affinities is discussed as though settled by Clark and Kent; that of the significance of the yellow bodies of the Radiolarians as though set at rest by the misconceptions of Wallich. We are told that there is no proof that the Millepore is a Hydroid, and so on. Upon the ill-effects which must result from this method of procedure it is needless to enlarge; but in justice to the author it must be admitted that he has made some use of recent literature. He appeals to the Challenger volumes. His quotations from these are, however, very capricious, and in some instances inaccurate. It cannot be said that the spines of the Radiolaria are “never tubular," for Haeckel (whose Report the author quotes) has given their tubular character as a diagnosis of his Phæodaria. Writing of "sensation in the Radiolaria," the author indulges (p. 103) in a remarkable paragraph, which concludes as follows:

"Prof. Haeckel considers that the central capsule contains the common central vital principle, which he terms the 'cell-soul,' and that it may be regarded as a simple ganglion cell, comparable to the nervous centre of the higher animals, whilst the pseudopodia are analogous to a peripheral nervous system."

These are not the words of the author cited, and, even if they were, the introduction of such silly stuff into the

pages of a book intended for "the large and increasing section of the nature-loving public who indulge in the use of the microscope as a source of instruction and amusement" (p. 3) is intolerable. It is a remarkabe fact that, while the author has reproduced the more com monplace statements of the earlier writers in their onging form, he should have chosen to give us the above, h own, rendering of the lucubrations of a Haeckel. la doing this he betrays a sad want of sound judgment The public have a right to expect that a work of this type, intended to serve (p. 3) "as a preliminary to more specific knowledge, the direction of which they will there after be better able to choose," shall be up to date; b. to fulfil the useful purpose aimed at, such a work shoul rest upon a more authoritative foundation than the book now under review. That is amusing as an example of editorial piece-work among a somewhat antiquated literature, and to those familiar with the subjects approached it suggests reflections.

The volume by M. Houssay is one of 312 pages, w 47 woodcuts intercalated in the text (38 only are acknow ledged on the title-page). The bulk of the work is divided into six chapters, dealing respectively with modes of cap ture of prey, of defence, of transport and storage of fone, of provision for the young; of constructing or acquiring nests and habitations, and of preservation and protection of the same. The illustrations are, for the most part, admirable; some, which we take to be original, are fit to rank with the famous woodcuts in Brehm's "Thier-Leben,” while others are already familiar to us from the pages of that work. In the introduction the author justly asserts that the naturalist of to-day lives more in the laboratory than in the field, that the scalpel and microtome have replaced the pins of the collector, and that the magnifier pales beside the microscope. This is, alas! too true. cannot be denied that our present systems for the most part take insufficient heed of field-work, and we fully er dorse the author's further remarks upon the changed aspect of affairs. The introduction as a whole deals with generalities in direct bearing upon those facts which follow; and by no means its least satisfactory feature is that it clearly sets forth what the author would have his readers understand by the title of his work. The many portion of the book is confined to bare records of ob served fact, systematically arranged, and, where necessary brought into special relationship by cross-references That "talkee-talkee" so often forced into books of this kind is here withheld. Such comments as are indulged in are either confined to the introduction, or to a few concis paragraphs which make up the author's "conclusion" and the latter is, as might be expected, devoted to a brigt consideration of animal intelligence. In place of an index there is furnished a zoological table, in which the generic names of the animals written about are arranged is classificatory order, each being accompanied by a paged reference and a mention of that particular habit or industry dwelt upon. It is a pity that the author takes no cognizance of animals lower in the scale than t Arthropods; but we nevertheless heartily recommend his book to our readers. It is throughout popular, and written in that peculiarly pleasing, yet didactic, style, characteristic of the works of the more successful of

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French popularizers of science, which has made them masters of their art.

The above-named volumes are three of a number of similar treatises which have lately appeared. The appreciation of the beautiful and generally interesting in Nature must always precede the study of the more useful and special, and it is the highest function of works like the present to awaken this preparatory appreciation. Of such works those are the most valuable whose authors can claim a sound elementary knowledge of the facts with which they deal, and a familiarity with current research. Only on these terms can a popular natural history rise above the level of the too well-known type, in which the Scissors supply the knowledge and the paste usurps the place of the co-ordinating intellect. G. B. H.

A GENERAL FORMULA FOR THE FLOW
OF WATER.

A General Formula for the Uniform Flow of Water
in Rivers and other Channels. By E. Ganguillet
and W. R. Kutter. Translated from the German by
Rudolph Hering and John C. Trautwine, Jun. (London:
Macmillan and Co., 1889.)

THE general formula devised by Messrs. Ganguillet

and Kutter for caculating the flow of water in both large and small channels, under varied conditions, was brought under the notice of English-speaking engineers by the publication, in 1876, of a translation by Mr. Jackson of some articles on the subject written by Mr. Kutter, which appeared in the Journal der CulturIngenieur in 1870. This translation, however, was not authorized by Mr. Kutter, and contained some incomplete ables inserted by Mr. Kutter in his articles at the request of a friend. The present volume is a translation of the second edition of the treatise on the formula, written by Messrs. Ganguillet and Kutter, engineers in Berne, who have added a preface to the translation. Mr. Kutter died whilst this translation was in progress; and a short memoir of him, with a list of his works, is appended to the translators' preface.

for mathematical readers; and the appendices contain numerous tables giving the flow of water in pipes under pressure, as well as in open channels, for practical use in English measures, derived from the formula, and also a diagram for the graphical determination of the values of the factors in the formula, adapted to English measures by the translators.

Most of the hydraulicians who had investigated the question before Darcy and Bazin, such as De Prony, Dubnat, Eytelwein, D'Aubuisson, Downing, and others, agreed in adopting a formula of the form V = c√ RS, of which Brahms and Chezy are said to have been the authors in the latter half of the last century, in which V is the velocity, R the hydraulic radius, and S the slope. Different values were assigned to the factor by the various investigators; but it was always regarded as a constant, applicable to any sized stream in most cases, to any slope, and to any state of the bed. Mr. Darcy was the first who directed attention to the influence the condition of the sides of channels and pipes exercised on the discharge; and he instituted a series of experiments, carried out after his death by Mr. Bazin, by which the flow of water in regular uniform channels, under different conditions of slope, form, and roughness of bed, was measured by careful gaugings and gauge-tubes. A few

years previously, Messrs. Humphreys and Abbot had

Kutter found that the formula derived from the Missis

carried out their well-known gaugings of the flow of the Mississippi by means of double floats, and deduced a formula for the results obtained. Messrs. Ganguillet and sippi experiments, relating to a large river with a very slight slope, was not applicable to the small streams with steep slopes of which they measured the flow in Switzerland, and also that Mr. Bazin's formula was not suitable, in its original form, for large rivers with irregular beds. This led Messrs. Ganguillet and Kutter to search for a formula applicable to very different slopes and sizes of channel, and adaptable to various conditions of bed. They took as the basis of their formula the various experimental results obtained in France and America, together with their own independent observations on channels with steep slopes, so as to include the extreme varieties of flow within the range of a single formula. Starting from Mr. Bazin's formula, V

where c =

B'

a+
R

=

RS

β

R

they eventually found it expedient

to express the value of c in the form

x

in which,

R

The book commences with an historical sketch of the attempts to arrive at a formula for the flow of water in open channels; and the insufficiency of the earlier formulæ 13 pointed out. The investigations of Messrs. Darcy and Bazin, and the gaugings of the Mississippi by Messrs. Humphreys and Abbot, are then concisely described, and the formula which they deduced from the results of their Experiments are given, the history of the subject, in a brief form, being thus brought down to the period at which I + Messrs. Ganguillet and Kutter commenced their investigations. This forms a sort of introduction to the account though they at first assumed y and x to be constant for of the conception and development of the general formula, any given state of bed, they finally modified them to of which the various steps are described in detail. The expressions varying with the slope. The alterations in modifications for various amounts of roughness are classi- the formula were effected by aid of graphical representafied. and, finally, the formula is tested by the comparison tions of the various sets of gaugings. It was found, in inof its results with a number of gaugings under very differ-vestigating the various experimental results, that the factore ent conditions; and these results indicate, in considerably the greater number of cases, a closer approximation to the actual measurements than those obtained with the formula of either Humphreys and Abbot, or Bazin. A supplement gives a more direct derivation of the formula

varied generally with the slope; but a somewhat anomalous result was also noted-namely, that whereas in the Mississippi observations c increased with a decrease in the slope, it on the contrary decreased with a decrease of slope in the gaugings of small channels, unless the wetted

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