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perfectly conducting tube. The problem of waves in conducting tubes, which has already been treated by various authors, is here taken up with the purpose of developing some of its solutions which offer noteworthy peculiarities with respect to the velocity of the corresponding waves. The waves investigated are axially symmetrical and of permanent type. Their velocity of transfer along the tube is a comparatively simple function of the period of vibration and of the "order" of waves, and it exceeds, for each of these waves, the velocity of light in free space. The peculiarities of distribution of the lines of force are illustrated by two examples with annexed drawings. The paper closes with remarks concerning superpositions of waves of the specified kind, more especially of electromagnetic pulses.-H. B. Keene: An electricallyheated full radiator. The essential conditions in a determination of the constant of the Stefan-Boltzmann law of radiation are, either that both "emitter" and "receiver are full radiators, or that the amount by which they fall short of full radiators is known-an amount difficult to determine with certainty. Hitherto, a measurement of this constant has not been made under full radiation conditions. This paper describes an electrically-heated "constant temperature enclosure" which has been constructed for temperatures in the neighbourhood of 1100° C. It consists of a hollow cylinder of alumina, about 8 in. in diameter, closed with conical end pieces of the same material. Three separate windings of platinum strip provide a means of adjusting the temperature distribution within the enclosure, which can be made uniform to within two or three degrees. At the apex of one of the cones is a circular aperture which emits radiation closely approximating to full radiation. It is intended to use this radiator in conjunction with a full receiver, described in an earlier paper, in order to determine the value of the radiation constant under "blackbody "conditions.

Geological Society, January 6.-Dr. A. Smith Woodward, president, in the chair.-C. I. Gardiner The Silurian inlier of Usk (Monmouthshire). The Usk inlier lies a few miles north of Newport (Mon.). Between the coalfields of South Wales and the Forest of Dean the Old Red Sandstone is bent into an anticline, the axis of which runs very nearly north and south. This has been denuded away to the west of Usk, and Silurian beds have been exposed, the rocks seen being of Ludlow and Wenlock age. In the southern part of the inlier the Silurian rocks are arranged in two anticlinal folds, the axes of which run nearly north and south and dip southwards. These folds are separated by a fault. The Old Red Sandstone is believed to rest unconformably on the Ludlow Beds along much of the margin of the Coed-ypaen anticline, and beneath the Ludlow beds, which are about 1300 ft. thick, come 35 to 40 ft. of a Wenlock Limestone, which covers Wenlock Shales : of these latter some 850 ft. are seen. At their base the Ludlow Beds seem to pass conformably down into the Wenlock Beds, and the Wenlock Limestone is probably not at the summit of the Wenlock Shales. The Wenlock Limestone occurs either in irregular layers separated by sandy shales, or in massive beds largely made up of crinoid fragments.-S. R. Haselhurst: some observations on cone-in-cone structure and their relation to its origin. In a brief review our state of knowledge is summarised, and the deductions of other investigators are analysed. The author critically examines the accepted hypothesis that cone-in-cone structure is something essentially due to crystallisation. He describes the results of some high-pressure mimetic experiments. These experiments were designed to produce this structure, and reveal what the

author believes to be many new points on the origin of concretions and cone-in-cone in particular. The experiments are new, inasmuch as the media used, namely brittle, semi-plastic, and plastic, are enclosed in tunics of varied design, and then subjected either to a high uniform hydrostatic pressure or to a direct thrust. The author concludes from the evidence :-(1) That cone-in-cone is not due to crystallisation, but is a mechanically produced structure due to great and localised pressure; (2) that it is closely allied to the phenomenon known as pressure solution; (3) that cone-in-cone structure is closely associated with other rock-structures which are mutually indicative the one of the other, and also of their mode of origin.

EDINBURGH.

Royal Society, December 21, 1914.-Sir Thomas Fraser, vice-president, in the chair.-Sir Thomas Fraser The poisoned arrows of the Abors and Mishmis of north-east India, and the composition and action of their poisons. A large collection of arrows, bows, and quivers had been received from time to time from medical and military officers of the Indian Army, and it was soon apparent that different poisons were used in different groups. In one group, chiefly used by the Mishmis, the action of the poison suggested aconite as the active agent. In another group, used by the Abors, the arrows yielded, on extraction with ether, an oil with the physical characters of the oil of Croton tiglium. This oil could not produce death in warm-blooded animals, but was lethal to frogs. The poison on the aconite arrows varied greatly in power. If the whole of the poison of one arrow were absorbed, a most improbable possibility, the most active arrows carried enough to kill three men. -J. Herbert Paul: Regeneration of the legs of Decapods from the preformed breaking planes. When a lobster, hermit crab, or shore crab loses a limb, a small limb bud forms as the first stage in the process of regeneration. When the animal moults, this bud rapidly expands to the size of the true complete limb, becomes covered with a hard calcified layer like the rest of the integument, and gains full functional power in a few days. The paper contained a detailed account of the manner in which the various stages of regeneration were effected. When the old limb is lost the valvular action of the diaphragm at the breaking plane prevents hæmorrhage; and in the regenerative process a new diaphragm is the first structure laid down.-Prof. Alex. Smith and R. H. Lombard The degrees of dissociation in the saturated vapours of the ammonium haloids. The paper was concerned with the densities and degrees of dissociation of the chloride, bromide, and iodide of ammonium. In the chloride the degree of dissociation was nearly constant within the range of temperatures from 280° to 330°; in the bromide it reached a maximum about 320°, and diminished steadily up to 388°; and in the iodide it was practically zero. There was evidence in the last case of association above 340°. The results for the bromide showed that, about 320°, the heat of dissociation was positive. This seemed to be the first observation of a positive heat of dissociation in the gaseous state.

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Kunth (S. guaraniticum, Hassler) from the systematic point of view. S. Caldasii and S. etuberosum have been regarded by Berthault as identical species. The author points out their differences, and states that the only point they have in common is the fact that they both occur in Chili.-F. Bompiani: The geometry of Laplace's equation.-J. Cabannes: The diffusion of light by air. A beam of light from a quartz mercury lamp was examined at right angles to the path of the beam, and measurements made both optically and photographically of the intensity of the diffused light. No diffusion occurs when the beam is in a vacuum, and Lord Rayleigh's diffusion formula was quantitatively confirmed.-L. Gay: The expansibility product.-Echsner de Coninck: The molecular weight of the oxybenzoic acids. The method is based on the determination of the calcium in the calcium oxybenzoates, these being obtainable in a state of high purity.-J. Repelin: The prolongation towards the east of the Senonian synclinal of the Plan d'Aups, Saint-Baume.-Jean Chautaud: The origin of the petroliferous mounds of Texas and Louisiana. Contribution to the study of the origin of petroleum. The hypotheses put forward to account for the formation of these mounds are not in accord with the geological structure of the region. These hypotheses are criticised in detail, and it is shown that the mounds have an origin which is independent of orogenic or eruptive actions. The processes of formation suggested by the author are sedimentation in an intermittent lagoon, followed by a hydrocarbon decomposition of the organic débris, the transformation of the anhydrite into gypsum, with resulting compression and the migration of the petroleum under the influence of the pressure exerted on the mother rocks.-N. Arabu: Studies on the Tertiary formations of the basin of the Sea of Marmora. The Vindobonian in Thrace.-A. Boutaric: The polarisation and absorptive power of the atmosphere. servations carried on during three years confirm the views of K. Angström that the absorptive power of the atmosphere should depend on the diffusion and quantity of the absorptive gas present, mainly water vapour.

Ob

Guichard Surfaces such that the centres of the spheres osculating the lines of curvature of a series, shall be a paraboloid of revolution.-F. Gonessiat: Results of the observations of two occultations of the Pleiades by the Moon. Details of observations made at Algiers on September 20 and December II, 1914.-B. Jekhowsky Observations of Delevan's comet, 1913f, made at the Observatory of Paris, with the equatorial in the western tower of 30.5 cm. aperture. Positions are given for December 18, 24, 26, 28, and 29, both of the comet and the comparison stars. On December 29 the comet appeared as a rounded nebulosity 40 seconds diameter with a nearly stellar nucleus of 6.5 magnitude.-G. A. Miller: Sylow's theorem.Foveau de Courmelles: Determination of the position of projectiles in the human body by radioscopy. Two methods based on the use of a fluorescent screen are described.-J. Bougault and Mlle. R. Hemmerlé: The tautomerism of phenylpyruvic acid. In a previous communication J. Bougault suggested that phenylpyruvic acid might exist in two tautomeric forms, enolic and ketonic. Further proofs of this isomerism are now given, based on the differences in reactivity of the acid and its alkali salts towards acetic acid, potassium permanganate, and semicarbazide. The free acid has the enolic form, C.H,.CH: C(OH).CO2H1, the neutral salts being ketonic, C,H,.CH.CO.COM. The conditions for passing from the one form to the other have been studied.-Ch. J. Gravier: A phenomenon of multiplication by longitudinal scission in a Madrepore, Schizocyathus fissilis.-Alfred Angot: Value of the magnetic elements at the Val-Joyeux Observatory to January 1, 1915.-Alfred Angot: The earthquake of January 13, 1915. From the records of the seismograph at Parc Saint-Maur; the position of the epicentre was easily fixed at about 1300 kilometres S.E., that is, in Italy. The displacement was much less than that caused by the earthquake in Russian Turkestan on January 3, 1911.-J. Danysz: The treatment of wounds by solutions of nitrate of silver of strengths I in 200,000 to 1 in 500,000. A demonstration of the advantages of using certain antiseptic substances, especially silver nitrate, in very dilute

BOOKS Received.

Smithsonian Miscellaneous Collections. Vol. lxii., No. 6. Smithsonian Physical Tables. Prepared by F. E. Fowle. Sixth revised edition. Pp. xxxvi+355. (Washington Smithsonian Institution.)

Egyptian Government. Almanac for the Year 1915. Pp. viii+250. (Cairo: Government Press.) P.T.5.

solution. The main factor is shown to be the diffusion. From observations of calorific intensity, polarisation, and hygrometric state carried out at a given station for some years, it is possible to predict the calorific intensity at different times on a given day from measurements of the polarisation and hygrometric state, or even from a simple polarimetric observation alone.--A. Goris and Ch. Vischniac: Tormentol, a principle extracted from Potentilla tormentilla. The substance is crystalline, contains no nitrogen, and has the composition C,,HO10. Its constitution has not been completely worked out, but it is an ether-alcohol.-F. Bordas: A new arrangement for the disinfection of clothing. A description of an apparatus, easily put together, capable of disinfecting with steam at a temperature of 105° to 108° the clothes of five hundred men per hour.-Victor Henri The possibility of phosphorus being carried into wounds produced by the projectiles of the German artillery (see p. 598).-W. R. Thompson : An intracuticular parasite of Hamemalis virginiana.

50

January 18.-M. Ed. Perrier in the chair.Maurice Hamy: The exact determination of the collimation of non-reversible meridian telescopes. It is shown that the usual method of adjustment with two collimators may be affected by a systematic error and the substitution of two plane parallel mirrors is suggested, their diameter being at least equal to that of the objective of the instrument. Such mirrors can now be made with high precision, and a method of adjusting them to exact parallelism is given.-M.

The South African Institute for Medical Research. Anthropological Notes on Bantu Natives from Portuguese East Africa. By G. D. Maynard and G. A. Turner. Pp. 35. (Johannesburg: South African Institute for Medical Research.) 2s. 6d.

The Case-Hardening of Steel. By H. Brearley. Pp. xv+ 169. (London: Iliffe and Sons, Ltd.) 7s. 6d. African Adventure Stories. By J. A. Loring. Pp. x+301. (London: G. Allen and Unwin, Ltd.) 6s.

net.

The History of Melanesian Society. By W. H. R. Rivers. Vol. i. Pp. xii+400. Vol. ii. Pp. 610. (Cambridge University Press.) 2 vols. 36s. net. Macmillan's Geographical Exercise Books. iii. The British Isles, with Questions by B. C. Wallis. Pp. 48. (London: Macmillan and Co., Ltd.) 6d. A Shilling Arithmetic. By W. M. Baker and A. A. Bourne. Pp. xiv+192. (London: G. Bell and Sons, Ltd.) Is.

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By Dr.

Inorganic Plant Poisons and Stimulants. W. E. Brenchley. Pp. ix+110. (Cambridge University Press.) 55. net.

Tables Annuelles de Constantes et Données Numeriques, de Chimie, de Physique, et de Technologie. Vol. iii. Année 1912. Pp. lii + 595.

(Paris: Gauthier Villars et Cie.; London: J. and A. Churchill.) 28s. 6d. net.

The Determination of Sex. By Dr. L. Doncaster. Pp. xii 172. (Cambridge University Press.) 7s. 6d.

net.

DIARY OF SOCIETIES.

THURSDAY, JANUARY 28.

ROYAL SOCIETY, at 4.30.-The Influence of Salt-concentration on Hæmolysis: W. W. C. Topley.-The Life-cycle of Cladocera, with Remarks on the Physiology of Growth and Reproduction in Crustacea: G. Smith.-Investigations on Protozoa in Relation to the Factor Limiting Bacterial Activity in Soil: T. Goodey.-The Mesodermic Origin and the Fate of the so-called Mesectoderm in Petromyzon: S. Hatta -The Influence of Homodromous and Heterodromous Electric Currents on Transmission of Excitation in Plant and Animal: Prof. J. C. Bose. ROYAL INSTITUTION, at 3.-Modern Theories and Methods in MedicineImmunity H. G. Plimmer.

INSTITUTION OF ELECTRICAL ENGINEERS at 8.-The Sixth Kelvin Lecture Lord Kelvin's Work on Gyrostatics: Prof. A. Gray.

FRIDAY, JANUARY 29.

ROYAL INSTITUTION, at 9.-Gaseous Explosions: Dr. Dugald Clerk.

SATURDAY, JANUARY 30.

ROYAL INSTITUTION, at 3.-Aerial Navigation-Scientific Principles: Dr. R. T. Glazebrook.

ESSEX FIELD CLUB (at the Essex Museum of Natural History, Stratford), at 6-Paget Colour Photography as applied to Natural History: H. Whitehead.-The Hammer and the Camera: W. Whitaker.

MONDAY, FEBRUARY 1.

SOCIETY OF CHEMICAL INDUSTRY, at 8.

ARISTOTELIAN SOCIETY, at 8.-Conflicting Obligations in the State: G. H. D. Cole.

ROYAL SOCIETY OF ARTS, at 8.-Oils, their Production and Manufacture: Dr. F. Mollwo Perkin.

VICTORIA INSTITUTE, at 4.30.-Present Position of the Theory of Organic Evolution: Prof. E. W. MacBride.

SOCIETY OF ENGINEERS, at 7.30.-Presidential Address: N. Scorgie.

TUESDAY, FEBRUARY 2.

ROYAL INSTITUTION, at 3.-Muscle in the Service of Nerve: Prof. C. S. Sherrington.

ROYAL SOCIETY OF ARTS, at 4. 30.-Sugar and the War: E. R. Davson.

WEDNESDAY, FEBRUARY 3.

SOCIETY OF PUBLIC ANALYSTS, at 8.-Annual General Meeting.-President's Address.-Note on the Determination of Sulphates in Flour: G. D. Elsdon.-General Principles Governing the Complete Analysis of Minerals and Ores: Dr. W. R. Schoeller.

ROYAL SOCIETY OF ARTS, at 8.-Imperial Industrial Development after
the War: O. C. Beale.
INSTITUTION OF ELECTRICAL ENGINEERS, at 7.30.-Student's Meeting
High Explosives: H. Williams.
ENTOMOLOGICAL SOCIETY, at 8.

GEOLOGICAL SOCIETY, at 8.-The Gravels of East Anglia: T. McKenny Hughes.-The Pitchstones of Mull and their Genesis: E. M. Anderso and E. G. Radley.

THURSDAY, February 4. ROYAL SOCIETY, at 4.30.-Probable Papers: Discontinuous Fluid Motion Past a Bent Plane, with Special Reference to Aeroplane Problems: Prof G. H. Bryan and R. Jones. The Spectra of Ordinary Lead and Lead of Radio-active Origin: T. R. Merton.-The Viscosity of the Vapour of Iodine A. O. Rankine.

ROYAL INSTITUTION, at 3.-Modern Theories and Methods in Medicine Methods and Results: H. G. Plimmer.

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Electrical Notation.-Sir Oliver Lodge, F.R.S.
Mendelism in the Seventeenth Century.-Clifford
Dobell ...

Books for Belgian Students.-Dr. A. E. Shipley,
F.R.S.

An Unexplained Laboratory Explosion.-W. F. A.
Ermen..

Demonstration of Strain-hardening of Steel. (Illus-
trated).-Prof. R. W. Chapman

By-Paths in Natural History. (Illustrated.) .
The New Issue of the British Pharmacopoeia
Synthetic Drugs in Great Britain. By Prof. J. F.
Thorpe, F.R.S..

Notes

Our Astronomical Column:

Annual Report of the U.S. Naval Observatory
The Appley Bridge Aerolite

Annuaire du Bureau des Longitudes, 1915
The Theory of a Sunspot Swarm of Meteors
The Restoration of an Ichthyosaur.
By R. L. . . .

PAGE

588

590

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593

(Illustrated.)

Development of the Culms of Grasses. By F. C. 600 Paris Academy of Sciences

Problems of Production in Agriculture. By A. D.

Hall, F. R. S. . .

University and Educational Intelligence.

Societies and Academies

Books Received

Diary of Societies

Editorial and Publishing Offices:
MACMILLAN & CO., LTD.,

ST. MARTIN'S STREET, LONDON, W.C.

607

609

610

Advertisements and business letters to be addressed to the Publishers.

Editorial Communications to the Editor.

Telegraphic Address: PHUSIS, LONDON. Telephone Number: GERRARD 8830.

THURSDAY, FEBRUARY 4, 1915.

THE WEB OF LIFE.

Tierbau und Tierleben in ihrem Zusammenhang betrachtet. By Prof. Dr. F. Hesse and Prof. Dr. F. Doflein. Band ii. Das Tier als Glied des Naturganzen. By Franz Doflein. Pp. xv+ 960+ plates. (Leipzig and Berlin: B. G. Teubner, 1914.) Price 20 marks.

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NE of the fundamental ideas of biology, which found many illustrations in the work of Darwin, is that of the inter-relatedness of organisms in the web of life. Just as there is a correlation of organs in the body, so there is a correlation of organisms in the economy of nature. No creature lives or dies to itself; the orbit of one life influences many others; everywhere we find linkages and wheels within wheels. An organism is compared by Prof. Doflein to a modern house, connected by various pipes and wires with other houses in the city and with the outer world, but the image is crude and too static. It is only in man's personal affairs that we find anything like the manifold, intricate, and subtle inter-relations that are to be seen in vigorous animals leading a full life. It is, indeed, altogether a matter of action and reaction between organism and environment, but with what complexity and nuance! Now things are in the saddle coercing the organism, and again the living creature exercises its prerogative

and becomes master of its fate.

Prof. Doflein, Weismann's successor at Freiburg, has been studying this aspect of animal. biology for more than ten years, and has given is his results in a work which must be placed n the front rank among ecological or bionomic studies. The book is nothing short of a great achievement. It has gathered interesting material rom many fields; it includes much that is peronal; it has worked out a clear classification of he manifold inter-relations; it is written in a -ivid style; and if we said all we think about the bundance, freshness, and beauty of the illustraEons, we should not be believed. We do not now of any British, American, or French book f natural history that even approaches it—a fact oubtless implying a smaller purchasing public. rof. Doflein is well known for his work on the rotozoa and as a naturalist-traveller, and it is -markable that he should have found time during e last ten years to write this large volume, a = companion to its predecessor, by Prof. Hesse E Bonn, which treated of the organism as an dividual.

the inter-relations of animals in the web of life, Prof. Doflein has evidently had in his mind throughout two allied, but distinct, general conceptions. The first is that of the organism as a bundle of adaptations to normal circumstanceswhat he calls "organisatorische Anpassungen "; the second is that of the organism as a selfassertive plastic agent, which can adjust itself to environmental vicissitudes-what he calls "regulatorische Anpassungen." The first is the hereditary racial equipment of wrought-out adaptations (as far as these concern give-and-take with animate and inanimate surroundings); the second is the individual capacity for adjustment, for modification, for thrusting as well as parrying. In both cases the adaptiveness may be structural, or functional, or psychical. Thus a ptarmigan from the mountains has a stronger heart than a willow-grouse from the plains-a structural adaptation. A bird or mammal continuously and normally regulates its production of heat according to its loss a functional adaptation. Ants have an instinctive behaviour in relation to their queens -a psychical adaptation. But when a mammal transported to a cold country puts on a thicker coat, or when a bird adjusts the nature of its foodcanal to altered diet, or when ants taken from Algiers to Switzerland entirely alter the door of the nest (in relation to new enemies), we have to deal with structural, functional, and psychical adjustments which are not more than individual reactions. This distinction between racial adaptation and individual adjustment is prominent in the book, but the author does not use it stiffly. He is clear, for instance, that the individual trades with his talents.

Beginning with the animate environment, Prof. Doflein deals with nutritive relations (including symbiosis, commensalism, parasitism, etc.); relations to enemies (including protective resemblance, mimicry, autotomy, etc.); sex-relations; migrations; care of offspring; social relations (including gregariousness, co-operation, and the communities of ants, bees, and termites). After 750 pages on these attractive themes, he passes to the inanimate environment, and deals with cosmic periodicities, the medium, the substratum, pressures, chemical influences, the quantity and quality of the food, temperature, climate, and light. This part of the book is like Semper's well-known work, "The Natural Conditions of Existence as they affect Animal Life" (1881), brought up to date. The volume ends with a discussion of the theoretical significance of adaptive structures and habits. What is new is the synthetic treatment of the whole question of inter-relatedness, In dealing with the comprehensive subject of which is, of course, fundamental in any biology

worthy of the name, and the wealth of fresh material that the author has collected from far and near. Among the interesting plates, we may refer to those illustrating symbiosis, protective coloration, wild geese, the courtship of capercaillie and blackcock, cave animals, and phosphorescence.

As we pass from this valuable treasury of bionomics, many reflections rise. We recognise the impossibility of understanding details of structure apart from details of environment-a commonplace, of course, but illumined by some of the subtle instances that Doflein gives. We appreciate the light that the manifold inter-relatedness of organisms throws on the value of even small variations. The selective process has to be envisaged in relation to the web of life. We realise afresh the importance of the organism's active agency. It is modified by its environment and it is adapted to its environment; but there is more, it actually adapts the environment to itself. And, finally, we are filled once more with wonderment at the vision of life slowly creeping upwards through unthinkable ages, asserting itself insurgently amid a callous physical nature. All that the author of this fine work has told us confirms the impression of a deep tendency to inter-linking and systematisation-the Darwinian systema naturae which is more than a mere image of what obtains increasingly, in spite of all rendings of the web, in the progress of mankind.

J. ARTHUR THOMSON.

ASSAYING AT THE ROYAL SCHOOL OF MINES.

Assaying in Theory and Practice. By E. A. Wraight. Pp. xi+323. (London: Edward Arnold, 1914.) Price 10s. 6d. net.

THIS

HIS book will be welcomed by all assayers who appreciate the value of the teaching at the Royal School of Mines, and is of special interest to old students of the School, for the reason that it gives an account of the methods of assaying which have been taught there during the last few years. Almost all the notes issued to the students in the laboratory are contained in the book, and, in addition, besides other matter, the author gives some general remarks which will be of use to mine assayers and prospectors. Mr. Wraight is well equipped for the task of reminding his former students of what he has taught them. He was for some years the senior demonstrator in the assay laboratory of the Royal School of Mines, and in that capacity has been able to command the attention and affectionate respect of all who have come under his guidance.

His work has only recently passed into other hands.

Mr. Wraight has made no attempt to write a complete book on assaying. The number of methods given is comparatively small and the gaps are considerable. For example, no mention is made of the volumetric methods of assay of silver bullion, or of the dry method for antimony, or of any method at all for platinum. The author observes that he has some thoughts of preparing a second volume containing analyses of ores, slags, etc., and of iron and steel. It may be hoped that he will include in it much besides these important sections.

As might be expected by those who know the author's work, there are few mistakes to be found in the book, and none of much importance. The method of determining silver in gold bullion given on p. 153 is an untrustworthy one, which is becoming obsolete. The method of parting with cadmium is not given. On p. 182 it is stated that graphite is not attacked by basic oxides. On p. 297, in the estimation of protective alkali in cyanide solutions, a decinormal solution of nitric acid is recommended instead of the usual oxalic acid or the fairly satisfactory sulphuric acid. The book certainly deserves a place on the shelf of works assayers. As a concise and clear statement of well-tried methods, it could scarcely be improved. T. K. R.

JAPANESE MATHEMATICS.

A History of Japanese Mathematics. By D. E. Smith and Yoshio Mikami. Pp. vii+288. (Chicago and London: The Open Court Publishing Co., 1914.) Price 12s. net.

OW that Europeans are becoming acquainted with the

Now that history of mathematics in Japan,

it is possible for them to form a kind of general opinion about the work of Japanese mathematicians. Unless future research bring to light works of a calibre superior to those now known, we must acquiesce in the conclusions stated in the terminal pages of the present work. Briefly, they are that Japan has not originated any great and far-reaching theory, such as the infinitesimal calculus, or function-theory, or group-theory; while on the other hand, native methods of great ingenuity, applied to particular problems, did lead to equivalents for such things as Horner's method in solving equations, the general rule for computing a determinant, and a large number of ways of calculating , some including the use of infinite

series.

Another thing in which the older Japanese mathematicians excel is in dealing with a set of

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