REVIEWS 



MATHEMATICS 



A Course of Modern Analysis. An Introduction to the General Theory of 

 Infinite Processes and of Analytic Functions ; with an account of the 

 Principal Transcendental Functions. By E. T. Whittaker, Sc.D., 

 F.R.S., Professor of Mathematics in the University of Edinburgh, and 

 G. N. Watson, Sc.D., F.R.S., Professor of Mathematics in the Uni- 

 versity of Birmingham. Third Edition. [Pp. 608.] (Cambridge: 

 at the University Press, 1920. Price 40s. net.) 



There are few changes in the new edition of this book. It still holds the 

 field as the repository of information about the transcendental functions 

 for the applied mathematicians, and it has come to be considered as a standard 

 reference book of the methods of the theory of functions. It is at once 

 plain that any book which achieves both these admirable objects only manages 

 it through a perpetual struggle in the mind of the authors. There are evi- 

 dences of this struggle throughout the book. It is not impossible that a 

 further edition might most profitably introduce sweeping changes in the 

 direction of redrafting the initial chapters (and in particular the very first, 

 which is not up to the level of the rest of the book) in the interests of the 

 mathematician, and developing in a somewhat gentler and less aristocratic 

 manner the vagaries of the transcendental functions and integral equations, 

 Fourier Series, and other mathematical phenomena which are so often a 

 dark puzzle (and a painful one) to physicists who, for no fault of their own, 

 sooner or later have to deal with them. The rearrangement of the chapter 

 on Fourier Series, which is a step in this direction, is therefore to be welcomed. 

 An interesting chapter on Lamp's functions, which is entirely new and has 

 not appeared in the previous editions, renders accessible much of the recent 

 work on ellipsoidal harmonies which sooner or later must be of considerable 

 importance in mathematical physics. 



D. M. Wrinch. 



ASTRONOMY 



Easy Lessons in Einstein : A Discussion of the more Intelligible Features of 

 the Theory of Relativity. By Edwin E. Slosson, M.S., Ph.D. [Pp. 

 vii + 128.] (London: George Routledge & Sons ; New York : Harcourt, 

 Brace & Howe, 1920. Price 5s. net.) 



This book attempts the impossible. There is no easy path to the mastery 

 of Einstein's theory, even for the skilled mathematician. For the layman, 

 devoid of the training and equipment of the mathematician, an intelligible 

 appreciation of the theory only can be obtained by hard study and careful 

 thought. The present volume will not prove of much assistance : it talks 

 round the theory in a very disjointed manner, and gives the impression that 

 the author himself has not fully grasped its fundamental bases. It abounds 

 with inaccuracies and loose statements, e.g. " Gahleo showed, when he dropped, 

 his big and little cannon-ball ofi the Leaning Tower of Pisa, all bodies fall 

 with the same speed." Velocity and acceleration are here confused, yet 

 the author considers himself competent to expound generaUsed relativity I 



658 



