NATURE 



401 



THURSDAY, JULY 25, 1918. 



SCHOOL AND COLLEGE MATHEMATICS. 



(i) Mathematical Papers for Admission into the 

 Royal Military Academy and the Royal Military 

 College, for the Years 1908-17. Edited by 

 R. M. Milne. (London: Macmillan and Co., 

 Ltd., 1918.) Price ^s. \ 



I .4 Short Course in Elementary Mathematics \ 

 and their Application to Wireless Telegraphy. 

 By S. J. Willis. Pp. 173. (London : The Wire- 

 less Press, Ltd., 1917.) Price 3s. 6d. net. 

 (3) Infinitesimal Calculus. By Prof. F. S. Carey. 

 Section i. Pp. xiii+ 144+ Answers v. Price 65. 

 net. Section ii. Pp. x+ 145-352 + Answers iv. 

 Price loi'. 6d. net. (London : Longmans, Green, 

 and Co., 191 8.) 

 (i) ""PHIS collection of examination papers will 

 -*- be found useful by many teachers and 

 students, even if their work is not immediately 

 associated with the requirements of the military 

 authorities. The papers for the Army Qualifying 

 Certificate include questions on more advanced 

 arithmetic, elementary algebra and geometry, 

 mechanics, and a little trigonometry; special at- 

 tention is paid to practical methods and applica- 

 tions. The papers for admission are wider in 

 scope and more difficult in character. The mathe- 

 matics is divided into three parts. The elementary 

 papers are of a practical nature, involving princi- 

 pally drawing and mensuration. The intermediate 

 papers are also practical, and include mechanics, 

 besides some algebra, geometry, and trigonometry. 

 The higher papers introduce in addition easy 

 differentiation and integration. The questions are 

 very skilfully devised, and many teachers and ex- 

 aminers would benefit by a perusal of this volume. 

 (2) Mr. W^illis has written an eminently useful 

 exposition of the mathematics required by the 

 student of wireless telegraphy. To use the lan- 

 guage of the accompanying advertisement, the 

 book does not presume that the student is un- 

 able to add two and two together, nor does it 

 plunge into advanced work for which the student 

 is quite inadequately prepared. There are 

 chapters on logarithms and the slide rule, practical 

 geometry and mensuration, including a little on 

 conic sections, equations and progressions, the 

 fundamental ideas and formula? of trigonometry, 

 vectors with examples from statics and dynamics, 

 and an excellent chapter on the " use of squared 

 (paper " with the beginnings of differentiation. 

 Many examples are worked in full, others are set 

 as exercises. The volume concludes with some 

 useful tables. 



The author's style is very pleasant and per- 

 suasive, and the book is one that can be safely 

 recommended for the purpose for which it was 

 written. A few typographical criticisms must, 

 however, be offered. The base of Napierian 

 logarithms is written differently in different places, 

 and dashed letters are sometimes written a\ b^; 

 this is quite inexcusable when dashes are used in 

 NO. 2543, VOL. lOl] 



the figure and "ones" in the accompanying text. 

 Some of the conies are badly drawn. The notation 

 used is sometimes confusing; surely no student 

 should be encouraged to write: "Thus the series 

 is a G.P. in which a = a/2.v. . . \" 



With regard to the mode of treatment, we would 

 like to suggest that the elaborate investigations 

 on the factors of quite simple quadratic expres- 

 sions are unnecessary, and that the order of treat- 

 ment is a little unsound pedagogically. 



(3) Prof. Carey's book can be heartily approved 

 as a compact and clear statement of practically 

 all that the ordinary student of the infinitesimal 

 calculus " as an instrument in the attainment 

 of further knowledge" is likely to require. 

 Section i. deals with the more elementary parts 

 of the subject, including the theory of limits, easy 

 differentiation and integration, and applications to 

 curves, areas, volumes, etc. Section ii- proceeds to 

 the advanced parts of the subject, and dis- 

 cusses, inter alia, definite integrals, polar and 

 other properties of curves, and the important types 

 of differential equations. The author has evidently 

 kept in mind all through the practical application 

 of the methods and results, as is indicated by the 

 references to problems in mechanics and physics. 

 A short chapter on graphical methods includes a 

 ; brief account of nomography, a graphical process 

 j which is gaining currency in this country owmg 

 t partly to the intimate relations now existing be- 

 ! tween our engineers and their French and 

 i American brethren. 



[ Whilst' we welcome the commendable brevity 

 ; of the book, we cannot but express the fear that 

 the author has attempted to cater for too wide a 

 range of students. The first section is far too 

 difficult to be accepted as corresponding with "the 

 ; syllabus of some examinations for higher school 

 certificates. " Much of the contents of the chapters 

 dealing with the notion of a function, limits, and 

 continuity should come at the end of a first course 

 on the subject, rather than at the beginning. 



The main ideas of the calculus must be based 

 at first on geometrical intuition, and this is recog- 

 ! nised by the author, who has given many illustra- 

 tions of the proces.ses by means of curve plottings. 

 We should have welcomed a similar treatment of 

 j differential equations. Instead of this we have the 

 \ traditional series of tricks for the solution of 

 i selected types. It is to be hoped that before long 

 the student of mathematics will be taught this 

 I branch of the subject by methods more in accord 

 ! with recent developments. Perhaps it was also " 

 1 lack of space that caused excessive compres- 

 I sion of the treatment of this and other branches. 

 ! The references to nomography, for example, would 

 ! have been far more valuable if space had been 

 spared for a fuller discussion of the underlying 

 *■ principles. 



i The book is well printed and neatly produced. 



An exception to the general excellence is to be 



I found in the diagrams, many of which are not 



I well drawn. We hope that in a future edition 



care will be taken to remedy this and some otjier 



minor defects. 



