134 



KNOWLEDGE. 



[June, 1001. 



markings have been seen to obscure for a time the 

 markings on the face of Mars.'' Mention is also made 

 of Prof. W. H. Pickering's conclusion that " Clouds un- 

 doubtedly exist upon the planet, differing, however, in 

 some respects from those upon the earth, chiefly as 

 regards their density and whiteness." So far as I am 

 aware, this is all that is said upon the subject in the 

 book mentioned. R- A. Gregory. 



Wandsworth, S.W. 



l^otCccs of Boolts. 



"The Prixciple.s of MAGXETisii and Electricitv." An 

 Elementary Textbuok. By P. L. Criay, E.sc . (Metliuen.) Sa. 6d.— 

 Several minor inaccuracies and laboured expressions hare been 

 allowed to remain in this book, otherwise we should have no 

 hesitation in speaking of it in terms of untiualified praise. In 

 the preface we read "The nomenclature of the science is largely 

 derived from a period when unwarranted and probably erroneous 

 ideas as to the nature of electricity were held," and this scientific 

 attitude is maintained throughout, save in one or two notable 

 instances. In speaking of magnets and magnetism, p. 1, Mr. W'"^ 

 says : — " It was the discovery in some dim unknown former time," 

 and three lines lower, " discovered at some unknown remote 

 period." In a future edition the first two chapters should be 

 re-written, for the remarks upon lines of force are not clear, 

 •nnd whv should the student naturally assume the law of inverse 

 squares "to govern the strength of field at any point? Anyhow, 

 the assumption is made ; then, to our astonishment, we find on 

 the next page, " We have also seen that it depends on the square 

 of strengths." In Fig. 9 we see iron filings about the centre of 

 the bar magnet. Chapter TV., dealing with the electric field, is 

 good, but we are surprised at finding the coulomb defined as 

 being 3x10' C.G.S. units. The coulomb is, of coui-se, 10~ 

 absolute units of quantity. However, as someone remarked 

 recently, it is absurd that"we should have two units, one three 

 thousand millions times as large as the other. A good description 

 of the plate machine is given, but we note a slight inaccuracy in 

 Fig. 38, the handle being wrongly placed. It would perhaps 

 have been as well had the preliminary notions of potential, as 

 also the water analogy, been introduced before this. The de- 

 scription and theory of the quadrant electrometer forms perhaps 

 the best written portion of the book, but ^ye are sorry to find 

 that the author does not keep clearly before his readers that 

 potential dift'erence is not the same thing as electro-motive force. 

 The remainder of the book is to be conunended. We have, 

 inter alia, chapters on Alternating Currents, The Discharge. 

 Atmospheric Electricity, etc. The index is a very full one. 



"What is He.\t? and Wh.at is Electricity?" By Frederick 

 Horenden, F.L.S., f.g.s., f.R.m.s. (Ch.ipman & Hall.) Illustrated. 

 68. — Ihe two conundrums on the title page of this book are but 

 the precursors of a series with which the work is filled. Very 

 little space is devoted to the giving of answers, and, we regret 

 to say, that of the few- answers given not aU are accurate. " The 

 solution," says our author, "of these two fundamental problems 

 is placed in "the hands of the physicists." From this he argues 

 that the whole matter is treated by metaphysicians,, since 

 physicists use mathematics. Next, a heavy frontal attack is made 

 upon the exi.-iting system of mathematics: — "All mathematical 

 operations are functions of objects or actions " : " any number, 

 per se, is meaningless." And later, "What is an object?" 

 "Take a table." We must not, mathematically, according to 

 Mr. Hovenden. speak of one table, because the table is made 

 up of part.s. The parts are of wood, and the wood contains cells 

 made up of atoms. So the only possible unit is the atom. The 

 mathem;itician. we are reminded, has no power to divide the atom, 

 so, he has no right to speak of fractions. Having thus given 

 the quietus to believers in simple arithmetic, it is naturally time 

 that algebraic ide.-is should be abolished. " That part of space 

 which has gained is -t-, and that part which has lost is — . 

 Hence we obtain, as it were, a natural equation : + 1 = — 1." 

 What is to be 'said of such reasoning? There is. however, worse 

 to come, and, as the error led up to is one likely to be troublesome, 

 it may not he out of place if wc take it upon ourselves to answer 

 Mr. Hovenden in detail on this one point. On p. 13, then, 

 objection is raised to the algebraic law which makes the product 

 —100 into —ICO equal to + 10,000— (though, logically, Mr. 

 Hovenden has no right to object, since he has but just enunciated 

 his oira "natural equation"). We read: — "See if we can realise 

 this idea. We will t,ike two bowls, and mark one A, and the 

 other B. In the bowl A are 100 objects. We t.ake the hundred 

 objects out of the bowl A, and put them in bowl B. That 



is mathematically expressed, bowl A — 100; B -i- 100. Now 

 nmltiply the contents of bowl A ( — 100) by — 100 times, and 

 then, says the mathematician, there aie ten thousand objects 

 in that bowl I " It is upon such reasoning as this that our author 

 stnve-s in his next sentences to be sarcastic at the expense of 

 the mathematician. But here are his mistakes. A contains a 

 hundred marbles he tells us, these are removed to B. Therelore, 

 A now contains marbles (not — 100 as he absurdly suggesis). If 

 he will now perform his operation negatively, 100 times over (that 

 is. take 100 times 100 marbles from B to A), he will certainly 

 find that A contains 10,000 marbles. But, so far, we have only 

 ai rived at p. 14, .and here we propose to pause, for this reason — 

 on p. 7 of his book Jlr. Hovenden has asked "If the foundations 

 are defective, how about the superstructure?" 



" The Elements of the Differential and Integral 

 Calculus." By J. W. A. Young and C. E. Linebarger. 

 Pp. XVII. and 410. (Hirschfeld Bros. 1900.) 10s. 6d. net.— 

 The attention now being given to the calculus, in technical schools 

 and other institutions where physical science and its applications 

 occupy a prominent place in the curricula, is a noteworthy 

 development of mathematical instruction. Attempt.s are sometimes 

 made to show students who have insuilicieut mathematical know- 

 ledge how to apply the notions of the calculus, but the result 

 must be unsatislactory in the end, and generally leads to con- 

 fusion. No student can obtain a really useful knowledge of the 

 calculus unless he is prepared to devote a fair amount of time 

 to the study of it.s principles. But if he will work steadily at 

 acquiring this knowledge, he wiU find himself eventually in the 

 possession of a most powerful machine, by which innumerable 

 problems can be solved. The functions of the particular case are 

 put into the machine, or the equation to the appropriate curve 

 or surface is taken, and the result can be worked out almost 

 mechanically. As most quantities in nature change or vary 

 according to some continuous law, the differential calculus admit.s 

 of applications of the widest range of subjects. Though this has, 

 of course, long been recognised, yet the calculus has until recent 

 years been taught and studied more from the point of view of 

 pure mathematics than for its practical value. Now. however, 

 several books are available in which the calculus is expounded 

 " for engineers," " for technical students," " for chemists," and 

 other students of science and technology. One of the first books 

 prepared in this spirit was by Profs. Nernst and Schonflies, of 

 Gbttingen, and the present volume is an adaptation of it. The 

 distinguishing characteristic is the continual use of illustrative 

 examples from scientific data, and nothing but praise' can be said 

 for the introduction of this method. The German work was 

 intended primarily for chemists, and a large number of the 

 examples are drawn from physical chemistry. But as a matter 

 of fact, there is very little that is specially chemical in this 

 book, and although this .shows that mathematical chemistiy is 

 still in a rudimentary stage, it also adds to the value of the 

 volume to students who are not chemists. The book opens with 

 a chapter on .-malytical geometry. As students beginning the 

 study of the calculus do not possess usually the power of 

 graphing even the simplest functions, this introduction is essential. 

 After it the chapters deal successively and respectively with limits, 

 fundamental conceptions of the differential calculus, derivatives 

 of the simpler functions, fundamental conceptions of the integral 

 calculus, simple methods of integration, some applications of the 

 integral calculus, definite integrals, higher derivatives and 

 functions of several variables, infinite series, maxima and minima, 

 and differentiation and integration of functions found empirically. 

 While we do not consider that the book contains an ideal course 

 of work upon the calculus, yet it is highly to be praised, and 

 should prove of real value to all serious students of the 

 physical sciences. 



STANDARD SILVER: ITS HISTORY 

 PROPERTIES AND USES. -II. 



By Ernest .\. Smith, assoc.r.s.m., f.c.s. 



Although sterling silver was used in England for the 

 manufacture of plate at a very early period, " the 

 Anglo-Saxons being always reckoned skilful in the use 

 of gold and silver, " the -first statute made for regulating 

 the standard of silver to be used by workers in this 

 metal in England is that of the 28th Edward I., c. 20 

 (a.d. 1300). It ordains that goldsmiths shall make no 

 worse silver than " silver of the sterling alloy of the coin, 

 or better at the pleasure of him to whom the work 



