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employ a known principle as to friction in his essential, but it is open to question whether junt famous submarine telegraph relay; he was the students can profitably read the discussions wbi discoverer of the principle. The same may be text-books often contain: for example, on page, said about the description of Brown's mechanical we find “Related Unknowns.-One of the chie relay. We think that Prof. Boys is occasionally uses of algebra is that of solving problems wbure misled by assuming that his own very intimate it would be either difficult or impossible to see knowledge of phenomena is shared by other them by arithmetic. The method is to represen people.

the unknown quantities by letters, then to express the problem as an equation and to solve th

equation." In our view, such passages as these MATHEMATICAL TEXT-BOOKS.

merely overload the book and assist neither th: (1) Subjects for Mathematical Essays. By Dr. pupil nor the teacher. There are no particular! C. Davison. Pp. X+ 160. (London: Mac- original features, but the examples are wel.

millan and Co., Ltd., 1915.) Price 3s. 6d. arranged and provide a sensible elementary course (2) Junior Algebra. By A. G. Cracknell and

(3) The reprint in a cheap and compact form of A. Barraclough. Pp. vi + 280. (London:

papers set in the Mathematical and Engineering University Tutorial Press, Ltd., 1915.) Price Triposes at Cambridge is of real service to a

large circle of students. The general characte: (3) Papers Set in the Qualifying Examination for of the papers is evidence of the recent changes in the Mechanical Sciences Tripos, 1906-1913. mathematical teaching. Those engaged in the Pp. 90. (Cambridge: At the University Press, higher work in secondary schools will find here 1914.) Price 25. net.

much that will enrich their weekly problem papers. (4) A Shilling Arithmetic. By W. M. Baker and The questions are both practical and stimulating A. A. Bourne. Pp. Pp. xiv + 192. (London:

(4) This small volume includes all the arithG. Bell and Sons, Ltd., 1915.)

metic that in our view ordinary students require (5) Practical Mathematics Second Year. By and some things, such as true discount or inverse

A. E. Young. Pp. xi + 164. (London: G. compound interest, they should omit. If the Routledge and Sons, Ltd., 1915.) Price 2s. net.

general education is to include, as we believe it (6) The Laws of Algebra. An Elementary Course ought, trigonometry, practical mechanics and, if

in Algebraic Theory. By A. G. Cracknell. possible, the ideas of the calculus, it is essential Pp. vi +68.

(London: University Tutorial that arithmetic should be merely a means to an Press, Ltd., 1915.) Price is.

end, a preparation for other work rather than a (1) HIS collection of essays will be found of subject in itself. It is the comparatively slight

the greatest value in the training of dimensions of this text-book that constitute its mathematical scholarship candidates. Such work chief claim to favourable consideration. as this enables a student to coordinate his know- (5) The author has already published a course ledge, and so consolidates the material that is of practical mathematics for first year technical floating vaguely about his mind, when he has students : this volume contains the subject completed the various courses of reading pre- matter of the second year course.

In this volume, scribed for him. It is indeed mainly by essay as in the first, there is a first-rate set of examples, work that he begins to see the bearing of on and we have no hesitation in recommending it subject on another and to appreciate the help for extensive use. which can be derived from the interfusion of (6) This discussion of the meaning and validity subjects. We do not therefore recommend the of the fundamental laws of algebra is intended for use of this book merely because it will stand the senior divisions of secondary schools. It includes candidate in good stead for examination purposes, rational and irrational numbers, and rational but because we believe that the greater breadth indices, but excludes imaginaries, infinities, limits, of outlook essay work produces is of real educa- and irrational indices. The language is throughtional value to him, and because it plays a part out simple and the argument is set out clearly, in his mental development which no other form but we are doubtful whether the author's partition of exercise can achieve.

is satisfactory. The theory of limits has now (2) This course takes the reader as far as assumed so prominent a place in modern analysis quadratic equations, and the two final chapters that it is hard to refuse to admit it into the school deal with indices and logarithms. In addition to curriculum, and it seems wise therefore to take illustrative examples, there is considerable it in conjunction with any substantial discussion amount of explanatory matter. The former is of irrational numbers.

TH

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type. The usual accounts of magnetic phenomena ELECTRICITY AND MAGNETISM.

are given and the definitions here are normal. (1) Elementary Electricity and Magnetism. By

When electromagnetism is introduced a novel W. S. Franklin and B. Macnutt. Pp. viii + 174. definition of unit of current—the abampere—is (New York: The Macmillan Co.; London :

given. This is defined as “the force per unit Macmillan and Co.,

Co., Ltd.,
Ltd., 1914.) Price

length of wire per unit field intensity.” The 1.25 dollars net.

meaning of the authors is clear, but their (2) Advanced Theory of Electricity and Magnet- wording is unfortunate, as they define current as ism. By W. S. Franklin and B. Macnutt.

the “force.” Whereas in the elementary book Pp. vii + 300. (New York: The Macmillan

attention is devoted chiefly to the dyamo, etc., Co. ; London: Macmillan and Co., Ltd., 1915.) the advanced book seems to be written principally Price 2.00 dollars net.

for telegraph engineers, as a very large amount books written purely with a view of devoted to on wires. As an

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and magnetism. The choice of matter is excellent devoted to ships' magnetism and the compensation from this point of view, and it is all presented in

of the compass.

The chapters on electrostatics a lucid, readable, and original manner, being suffer from vagueness on account of the ignoring illustrated with a large number of excellent of the electrostatic system of units. For instance, diagrams. Experimental phenomena are usually

the capacity of a parallel plate condenser is given described first, and to give students a grasp their meaning mechanical analogies are given.

C (in farads)=1/B. a/x, Most of these analogies are excellent, but one where “a” is the area of one plate in sq. cm., gets the impression that on the whole too much

x the distance apart of the plates, and B is a attention is devoted to them, and that some of

constant
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However, again the them could profitably be omitted. The introduction practical aspect is kept in view, and space is of the terms abampere, abvolt, and abohm for the devoted to such things as the design of insulators absolute units of current, E.M.F., and resistance

for cables and the capacity of a transmission line. is a feature of the books. The electromagnetic Both books will be found of great value to system only is used, and in the advanced book

students to whom the practical side of electricity the authors boldly declare that they are ignoring and magnetism is the all-important thing, and in the electrostatic system altogether, a procedure fact they will also be profitable to others if read in that is perhaps wise, considering that the prac- conjunction with some

some of the more abstract tical aspect of the subject predominates.

treatises. (1) The elementary book commences with a • A large number of examples is given with each description of the most important phenomena in chapter.

J. R. electricity from a practical point of view. Only the most elementary things in magnetism are

OUR BOOKSHELF. described, and this part of the subject is of importance only in its relation to electricity. The

Mechanism of Steam Engines. By Prof. W. H.

James and 'M. W. Dole. Pp. viii + 170. (New action of electromagnets on wires carrying cur

York: J. Wiley and Sons, Inc. ; London: rents is described very early in the book, and the

Chapman and Hall, Ltd., 1914.) Price 8s. 6d. reverse phenomenon-the action of currents on net. magnets, which one is accustomed to find as a

The purpose of the authors in producing this book fundamental principle, does not appear till later. has been to provide an elementary treatise on the Great prominence is given to the "side push" on kinematics of reciprocating steam engines and wires in a magnetic field (the term is the authors'),

steam turbines, and to make clear to the beginner

the mechanical principles on which a steam engine and, once described, its applications

to the

operates. Special attention is given to valve gears D'Arsonval galvanometer and to the dynamo and governing devices; the underlying heat theory follow. The tangent galvanometer is not is not treated. The book opens with a general described, as it is not a practical instrument. The discussion of a reciprocating steam engine, fol“side push" is again employed in connection lowed by types of single-valve engines. The with magnetic intensity, which is defined as "the

valve ellipse, together with the Zeuner, Reuleaux, side force per abampere per unit length of wire."

and Bilgram valve diagrams are described, and

some typical single-valve problems are worked out. The chief practical things to which attention is

Centrifugal-throttling, crank-shaft and other given are the dynamo, motor, transformer, and governing devices are included, also riding cut-off induction coil.

valves and their governing devices. The book (2) The advanced book is more of the usual closes with sections dealing with reversing gears,

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valve setting, and turbine valve mechanisms and reports. The thirteenth volume is one on which its governors.

editors, Dr. J. J. Graham Brown and Dr. Jarro The volume is noteworthy for the clearness of Ritchie, superintendent of the laboratory, may be the drawings (mostly taken from working draw- warmly congratulated. ings), and for the lucidity of the text. It is difficult, however, to state what precisely would be its

The Poison War. By A. A. Roberts.

By A. A. Roberts. Pp. 144 position in the engineering courses at colleges in (London : W. Heinemann, 1915.) Price 55. Det this country. This is owing to the matter being MR. A. A. ROBERTS, who is described as almost wholly descriptive. Students of engineer- member of the Chemical Society of France and ing learn best by doing, not by merely listening or also of the Society of Chemical Industry, ha reading. Numerous valve diagrams are given, given the public a book to which no one with but no student desires to copy these, and no de- any chemical knowledge will deny the epithe: finite exercises are given to be worked out by the "remarkable.” Two or three short extracts student himself. As a minor matter, we may from its pages will perhaps best illustrate its point out that it would have been an advantage value. if even one leading dimension had been inserted in

On page 57 we find “The white smoke rethe detail drawings. It is difficult for beginners to ferred to, upon the explosion of German shells, sort out which devices are suitable for large and is caused by the union of phosphoric and phoswhich for small engines. The book, however, phorus acids with the oxygen of the air.” ,

" Og can be recommended to any student who wishes to page 90 we are told: “Toluene is a colourless improve his knowledge of the construction of valve liquid obtained from resins such as tolu : the and governor details.

latter being the product of a South American tree.

Some of the medicinal preparations of this resin Reports from the Laboratory of the Royal College are well known to the public, as ‘Balsam of Tolu'

of Physicians, Edinburgh. Edited by Dr. J. J. and 'Friars Balsam.' In reference to gunGraham Brown and Dr. J. Ritchie. Vol. xviii.

cotton, on page 91 we learn : "Reverting to the ( (Edinburgh: Oliver and Boyd, 1915.)

subject of gun-cotton, this explosive is now made The directors of every research institution have to

by soaking cotton or waste in nitric acid. Cotton face a peculiar difficulty connected with publica

is indispensable, as it absorbs the oxygen and tion. In issuing an account of the various in- nitrogen contained in the acid, and is a comquiries conducted in the laboratories under their

bustible substance." On page 98 we read: charge two modes of publishing are open to them.

“Nitro-glycerine, or even gun-cotton, if burnt in They may issue a special report, or they may allow

an open vessel, will not explode, but the moment the workers in the laboratories to contribute their they are fired by detonation explosion follows, the results to appropriate professional journals or pro- explosion being due to decomposition."

" The ceedings of societies. A special report is expen

A special report is expen- non-poisonous character of nitro-glycerine is illussive; it does not secure the ear of the scientific

trated by the following statement on page 99: public so well as professional journals do. The “A laboratory employé, in another instance, parlaboratory of the Royal College of Physicians in took of two ounces of nitro-glycerine, mistaking Edinburgh has combined these two methods; it

it for chocolate, and on the morrow was none has collected the papers contributed to various

the worse for his stupidity.” journals by its workers during 1913-14, and issued them as the thirteenth volume of its Reports. In

Indian Mathematics. By G. R. Kaye. Pp. 73

. all there are thirty-two papers, every one of them

(Calcutta and Simla : Thacker, Spink and Co., representing a definite contribution to the basal

1915.) subjects of medicine. Four papers give an

MR. G. R. KAYE's booklet gives a summary of the account of the researches of Dr. J. P. McGowan actual contents of Indian mathematical works, into the nature of sarcocyst, associated with the

translations of original passages, an approximate disease of sheep known in Scotland as Scrapie." chronology, and a bibliography. The net result of

Four papers are devoted to human anatomy, Dr. recent work in this field is to reduce still more J. S. Fraser's sections of the inner ear being of

the claims once made on behalf of Indian matheparticular merit. The remaining papers are de- maticians, both in respect of priority and in that voted to biological chemistry, pathology, and of originality; two main questions are still unbacteriology. We note particularly the research answered—who invented the decimal notation now carried out by the late Dr. Alexander Bruce- current, and what is the complete history of the whose death

serious loss to British Pellian equation ? Mr. Kaye suggests that India neurology-and Dr. James W. Dawson on is probably indebted to China for some of its curious form of tumour which occurs in the cen- analysis, just as it is certainly to Greece for its tral nervous system. A study of the minute geometry (in Arabic translations or otherwise); structure of these neuromata supports the multi- it is to be hoped that Chinese documents will be cellular theory of nerve-fibres. Dr. D. P. B. forthcoming to throw light on these and other Wilkie's important observations on the clinical matters. Meanwhile, such a work as this of Mr. signs of acute obstruction of the appendix vermi- Kaye's is very useful as a trustworthy conspectus formis as distinguished from acute inflammation of what is actually known about early Indiaa of the appendix also appears in this volume of mathematics at present.

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LETTERS TO THE EDITOR.

date, storm no storm, the chances are Father

Cortie could supply a spot. I think Father Cortie [The Editor does not hold himself responsible for has not quite grasped my argument that quiet days opinions expressed by his correspondents. Neither

show the twenty-seven-day period equally with discan he undertake to return, or to correspond with turbed days, and that one can scarcely associate them the writers of, rejected manuscripts intended for with limited areas or “anti-spots.". If one associates this or any other part of Nature. No notice is

them, as he now seems to do, with an undisturbed taken of cnonymous communications.]

state of a whole solar hemisphere, why not equally The Structure of Magnetite and the Spinels.

associate storms with a generally disturbed state of a The structure of the spinel group of crystals is very

whole hemisphere? As a matter of fact, the average interesting. These crystals are cubic, and possess the

quiet day seems associated with a practically average

state of solar spottedness. The 6oo quiet days selected greatest possible number of symmetries. The com

by the Astronomer Royal from 1890 to 1900 gave position is given by the formula, R'R",O., where the divalent metal R" may be Mg, Fe, Zn, or Mn, and

for Wolfer's provisional sun-spot frequency a mean the trivalent metal R'' may be Fe, Mn, Cr, or Al.

value of 41.28, the mean from all days of the eleven Magnetite is FeFe, O.

years being 41.22. They showed the twenty-seven-day The structure is fundamentally the same as that of

C. CHREE. period very clearly.

Richmond, Surrey, July 17. the diamond. Each carbon atom of the diamond is to be replaced by the divalent metal atom; the distance

Surface Tension and Ferment Action, between two neighbours being 3.60 X.U. in magnetite

IN NATURE of June 17 Messrs. E. F. and H. E. as against 1.53 A.U. in diamond. The four oxygen Armstrong criticise the conclusions drawn by Mr. atoms are arranged in a regular tetrahedron about

Beard and myself in a paper published in the Proc. the divalent atom. The lines joining the latter to the Roy. Soc. of June 1, under the title “Surface Tension former are parallel to the four cube diagonals. Any and Ferment Action.” We drew the conclusion that two neighbouring tetrahedra point towards each the action of invertase was inhibited by surface tenother. If each perpendicular from a tetrahedron sion. According to Messrs. Armstrong the inhibition corner on the opposite face is produced it encounters observed under the conditions of our experiments was another tetrahedron, passing first through the middle due simply to a minute trace of alkali given off by point of a face and then through the opposite corner. the glass. They state in confirmation of their view A trivalent atom lies on each such_connecting line, that the action of the alkali given off by ordinary half-way between the tetrahedra. The distance be

glass is so marked that it is impossible to obtain tween a divalent and the nearest trivalent atom is consistent results with invertase, unless hard glass 7:20 A.U. Four trivalent atoms are associated with vessels, test-tubes, and storage bottles are used. That each tetrahedron, but each atom is shared by two is certainly not our experience. We failed to find any tetrahedra. As in other cases already examined, the difference in the readings between two mixtures of molecule has no separate existence. The size of the cane-sugar and invertase, of which one was kept in tetrahedron may not be the same in all members of the contact with glass beads at medium temperatures, as group of crystals. The divalent atom lies at the centre long as the amount of invertase used was relatively of a tetrahedron of oxygen atoms, and the trivalent large. Our experience in that respect is apparently at the centre of an octahedron.

in accordance with that of Sörensen, who states that

W. H. BRAGG, the effect of the alkalinity of glass makes itself felt Leeds, July 12.

only in the case of invertase solutions which have

been especially purified. The Magnetic Storm of June 17, and Aurora. In our experiments an inhibition was noticed only PROF. BARNARD's interesting letter dated June 25, when the amount of invertase was relatively small

. in NATURE of July 15, on what is termed “The Great Under these conditions an alteration in the hydrogenAurora of June 16, 1915," is at first sight rather ion concentration produced by the minute trace of puzzling to the non-astronomical reader. The large alkali given off by glass may have had some share in magnetic storm began about 1.50 a.m. on June 17. producing an inhibition, but it does not account for On June 16, it is true, there was a magnetic disturb- certain features of the phenomenon, which we have ance, but not such as to suggest a striking auroral been careful to emphasise in our paper.

If the alkali display. The explanation presumably is that Prof. from the glass was entirely responsible for the effect Barnard is referring to an astronomical day, com- one would expect the inhibition to persist in its entirety mencing at Greenwich noon on June 16. This, at after the glass beads have been removed. This was least, would explain his statement that at Wisconsin found not to be the case. Again, the weakening of (about 90° W.) at 21h. 25m. “the sky was bright with an invertase solution, which had been allowed to stand dawn." This one would expect between 3 and 4 a.m. in contact with glass beads at medium temperatures local time. If this is correct, then the first auroral ap- and which we ascribed to absorption of the ferment pearance chronicled by Prof. Barnard was at 3.30 a.m. by glass, cannot be explained on the ground put foron June 17, Greenwich civil time, and the maximum ward by Messrs. Armstrong. Their view necessitates brilliancy about 8.15 a.m. It was principally during the assumption of so large an amount of alkali given these morning hours that the Kew magnetic curves off by glass to an invertase solution, that it should be had the rapid oscillatory character_usually associated detectable by such an indicator as phenolphthalein. with aurora and earth currents. The newspaper re- This again was not the case. ports quoted by Prof. Barnard seem to fit this explana- The interruption of my work has unfortunately tion.

delayed the completion and publication of similar Passing to the Rev. A. L. Cortie's letter (p. 537), it observations with diastase carried out by Mr. McCall really emphasises the difficulty of deciding whether and myself. It was found that the inhibition proindividual sun-spots and magnetic storms are duced by extending the surface-glass water could be nected. There are often a number of spots visible at almost completely removed by coating the glass with a one time. A spot remains visible for a number of thin film of a surface-active substance, such as methyl days, during which there may be several magnetic alcohol, ethyl alcohol, amyl alcohol, ether. On the storms. If spots cause storms, the rule one spot one other hand, films of ligroin and xylol deposited on the storm may not be observed. If I selected any given glass failed to remove the inhibition.

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Such facts, while not explicable on the ground that partments concerned have nominated special reça the inhibition is due merely to a trace of alkali derived sentatives who sit as members of the sectio: from the glass, form a confirmation of the theoretical

committees, and through them and the committe considerations put forward in our paper.

own officers confidential relations have been esta! July 7.

W. CRAMER.

lished with those departments. The comma

also are in touch with the scientific institur Origin of a Mathematical Symbol for Variation.

and manufacturing centres throughout" As a contribution to the history of algebraic nota

country. These committees as working bodtion it may be worth while to point out that the symbol

are necessarily limited in size, having regard : oc for variation was introduced by William Emerson. In his “ Doctrine of Fluxions," third edition, London,

the very confidential nature of the subjects se 1768 (first edition, 1749), he says on p. 4:4" To the mitted to them; but they avail themselves large common Algebraic Characters already receiv'd I add as circumstances require, of the services of is. this a, which signifies a general Proportion; thus, vestigators outside their own membership. BC

BC. Αα signifies that A is in a constant Ratio to

The value of the work thus accomplished he D that is (if a, b, c, d be other Values of these Quan publicly recognised by the Prime Minister late

in his remarks in the House of Commons. Bu BC

bc tities) A :

; and thus every general Propor- though the Government has acknowledged the D

d tion is to be understood."

FLORIAN CAJORI.

scientific men have rendered valuable assistane 1 Gordon Street, Gordon Square, 'London, W.C.

in connection with problems arising out of the war, no definite scheme seems yet to exist fe

the organisation of our scientific forces into : SCIENCE AND MUNITIONS OF WAR.

composite body. The Chemical Society, as he WE E give in another column the names of the announced on July 8, has taken steps of its on?

members of the Inventions Board which accord to form a consultative council upon whics is assisting the Admiralty in the co-ordination and kindred societies such the Institute 0 encouragement of scientific effort in relation to Chemistry, the Society of Chemical Industry, the the requirements of the Naval Service. The Society of Public Analysts, the Pharmaceutica Central Committee and the Panel of Consultants Society, and the Institution of Mining and Metalform as strong a body of expert opinion as it lurgy will be represented. Scientific and industrial

. would be possible to bring together; and their knowledge and interests are thus intimately assojudgment upon scientific matters submitted to ciated, as they should be, but the relation of this them may be accepted with confidence. Sug- group of chemical societies to the Physical Society, gestions and inventions sent to the Admiralty which has also formed a committee to conside: will, if they relate to naval matters, first be con- suggestions and inventions, or to the war con:sidered by officials of the existing staff, and any mittees of the Royal Society, does not appear tu promising ideas or devices will be passed on to have been settled. Unless there is close co-operathe Central Committee, consisting of Lord Fisher, tion between the committees of the various Sir J. J. Thomson, Sir C. A. Parsons, and Dr. scientific societies it is difficult to see how overG. T. Beilby. This committee, when necessary lapping will be prevented or how combined expet or desirable, will refer particular points to knowledge can be concentrated upon physica, members of the panel of consultants, which in- chemical, and engineering problems requiring cludes leading workers in chemistry, physics, early and practical solution. metallurgy, and various branches of engineering In addition to appointing committees to consider science. The president of the Royal Society is suggestions or inventions, the Royal, Chemical. one of the consultants, and with one exception all and Physical Societies have taken steps to obtain the other advisers are fellows of the society, registers of their fellows classified according to which is thus giving of its best to the service of special knowledge and to scientific services which the country.

the fellows are willing, as well as specially qualiSince the early days of the war the Royal fied, to perform.

fied, to perform. The idea in each case is to Society has been in close touch with the naval secure co-operation among the fellows of the parand military authorities with regard to scientific ticular societies, and to examine by means of problems presenting themselves in the course of committees any promising suggestions relating the operations. In the autumn the Council set to munitions of war or kindred subjects. No one up an organisation which has been expanded in knows precisely what will be done with the various directions to meet the continually increas- registers when they have been completed. Each ing requirements of the Government for scientific

society seems to be compiling its list indepenassistance. It consisted essentially of a general dently and without any clear view of the use controlling committee, which was at

first which will be made of the experts' services which appointed ad hoc, but is now the Council itself ; will become available by the response to its and sectional committees, each of which repre- circular. No scheme has yet been put forward sents one of the several branches of science con- by which definite national duties will be assigned cerned, namely chemistry, engineering, physics, to the hundreds of scientific men who are enrolling and physiology. Each committee has been themselves on the registers of their respective placed by the council in charge of a chairman of societies. acknowledged eminence. The Governmental de- The

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