December io, 191 4] 



NATURE 



389 



detail, so that the student can make them in the 

 laboratory and gain an idea of their individual 

 properties. 



There will be no difference of opinion amongst 

 teachers as to the futility of such a plan. The 

 student can get no proper idea of chemistry as a 

 subject, or of its theories and application. He 

 will regard it merely as a series of manipulations, 

 and his text-books as akin to cookery books. 



At a time when the teaching of chemistry to 

 medical students is steadily improving it is dis- 

 concerting to notice a tendency in the reverse 

 direction in the case of biological students, which 

 unhappily is not confined to the Continent. 



MATHEMATICAI. BOOKS: ELEMENTARY 



AND ADVANCED. 

 (i) Arithmetic. By H. Freeman. Pp. viii-r-231-r 



xxxi. (London : G. Bell and Sons, Ltd., 1914.) 



Price 25. 6d. 



(2) The School Algebra. By A. G. Cracknell. 

 Pp. viii -r 568 -r Ixxvii. (London : University 

 Tutorial Press, Ltd., 1914.) Price 55. 



(3) Statics. By R. C. Fawdry. Part i. Pp. vii + 

 165. (London: G. Bell and Sons, Ltd., 1914.) 

 Price 25. 6d. 



(4) .4 First Schol Calculus. By R. Wyke Bayliss. 

 Pp. xii + 288. (London: E. Arnold, n.d.) Price 

 45. 6d. 



(5) A Treatise on Differential Equations. By 

 Prof. A. R. Forsyth. Fourth edition. Pp. xviii 

 4-584. (London: Macmillan and Co., Ltd., 

 19 1 4.) Price 145. net. 



(5) Linear Algebras. By Prof. L. E. Dickson. 

 Pp. viii + 73. (Cambridge University Press, 

 1914.) Price 35. net. Cambridge Tracts in 

 Mathematics and Mathematical Physics, No. 16. 



(7) The Elements of Non-Euclidean Geometry. 

 By Dr. D. M. Y. Sommerville. Pp. xvi + 274. 

 (London: G. Bell and Sons, Ltd., 1914.) 

 Price 55. 



(8) A New Analysis of Plane Geometry, Finite 

 and Differential, u'l'f/i numerous examples. By 

 A. W. H. Thompson. Pp. xvi-ri20. (Cam- 

 bridge University Press, 1914.) Price 7s. net. 



(i) ' I ''HIS book consists mainly of examples, 

 X and there is said to be "just sufficient 

 bookwork to be of use to a pupil when in diffi- 

 culty." We do not think that, for example, any 

 difficulty a pupU may feel about negative numbers 

 can be dispelled by a complete absence of "book- 

 work" about them (p. 7). 



(2) The aim of this book is to bring the teach- 

 ing of elementary algebra into closer touch with 

 " intelligible " calculations, and also to give a 

 clear account of the elements of algebraic theory. 

 The author warns us that " a rigorous logical 

 NO. 2354, VOL. 94] 



account of the fundamental laws of algebra is 

 very difficult, and would be quite out of place in 

 a book of this description." Accordingly, we 

 find, on p. 172, that "the negative unit" is de- 

 fined as "a unit which cancels a positive unit" 

 (the italics arc ours). In this confusion between 

 definite and indefinite articles, there seems to be 

 some departure from the author's intention to give 

 a clear account of things. The author seems to 

 recognise that such things as the law of signs 

 does present difficulties, but his treatment is not 

 satisfactory. The book is not without merits. 



(3) This pleasant little book shows the very 

 healthy influence that the work of Mach has 

 exerted on the teaching of mechanics. It deals 

 with the subject on an experimental basis, and 

 contains many examples, mostly numerical. 



(4) This is an attempt to introduce the calculus 

 by means of simple questions based upon matters 

 familiar to the student either from his every-day 

 experience or from his work in the laboratory. 

 It is said to be "planned upon the latest educa- 

 tional theories," but this ought not to prejudice 

 us against a very sound book which contains 

 none of the subtlety that is required in higher 

 walks of mathematics. For example, on p. 153, 

 under the stimulating heading of "The Border- 

 land of Discover^'," the introduction of new func- 

 tions by integration is treated apparently on the 

 principle that any combination of symbols what- 

 ever must mean something. This is rather a 

 natural supposition for most budding mathemati- 

 cians to make, but it would be as well to warn 

 them of possible dangers. 



(5) The third edition of this well-known and 

 solid work was published in 1903. This fourth 

 edition is larger, but the general scope of the 

 book is unaltered. Prof. Forsyth's object is to 

 produce a working text-book, and the general 

 theory is scarcely touched upon. Thus, such sub- 

 jects as theorems of existence are noticed only by 

 a reference to the author's "Theory of Differential 

 Equations." There is an advantage, says the 

 author, "even if only of conciseness," in assuming 

 seme results of the theor}\ Some parts of the book 

 have been re-written, particularly the early part of 

 the chapter on the hyjjergeometric series, and 

 parts of the chapters on partial differential equa- 

 tions. A number of short additions has been 

 made : on ordinary linear equations with some of 

 their integrals of the tyj>e called " regular " ; on 

 total differential equations ; and on partial equa- 

 tions. The only misprint — if, indeed, it is a mis- 

 print — that we have been able to find is a refer- 

 ence iri the index to Abel on a page where alge- 

 braic functions are spoken of, and not Abel. It 

 is perhaps almost inevitable that a text-book on 



