214 Notices respecting New Books, 



cover so as to not mislead students as to its real scope. As it 

 stands it will tend to discourage students and so far as it can to 

 retard the progress of Science. 



The author, however, is entirely unconscious of any defects, and 

 in his preface he takes high ground as follows : — " The severe course 

 of training, which the University of Cambridge exacts from 

 students of the higher branches of mathematics, is of inestimable 

 benefit to Science, in producing a body of men, who are thoroughly 

 conversant with dynamical principles, and are able to employ with 

 ease the more recondite processes of mathematical analysis." Now 

 in so far as the mathematical training is possessed by genuine 

 Physicists, all this is true enough ; but it is doubtful whether 

 Science derives any inestimable benefit from the mathematical 

 training of those who remain essentially out of harmony with the 

 subject to which mathematics is being applied, who are only at 

 home in wielding equations, and who slur over the facts as tri- 

 vialities. Our author does not indeed wholly ignore the expe- 

 rimental facts, he gives a hasty and perfunctory account of many 

 of them ; but his account contains many blemishes and a few 

 mistakes. 



Turning to one of the main chapters of the book : — The account 

 given of Fresuel's theory represents it as full of gratuitous full- 

 blown assumptions, made apparently without the slightest justifica- 

 tion ; whereas the assumptions really made by that great genius 

 were slight and natural and led up to by reasonings and intuitions 

 of the highest order. But, as the author in his preface says : — U I 

 have a profound distrust of vague and obscure arguments, based 

 upon general reasoning instead of upon rigorous mathematical 

 analysis. Investigations founded upon such considerations are 

 always difficult to follow, are frequently misleading, and are 

 sometimes erroneous." 



Certainly it may be granted that as soon as the properties of 

 the aether and of matter and the nature of their interaction are 

 thoroughly known, the mechanical method of writing down equa- 

 tions and working out their consequences may be advantageously 

 pursued ; but until that consummation is attained there will be 

 plenty of room for general reasoning and even possibly for obscure 

 arguments. What chance, for instance, w^ould the founders of the 

 undulatory theory have had if they had been foolish enough to 

 limit themselves to the mere writing down of equations. 



Compare also our author's treatment of Clerk MaxwelPs theory, 

 where, after quotation of a few sentences of a slight and popular 

 character, he copies out the equations of the electromagnetic field 

 without even the trouble of explaining the meaning of the symbols. 



The book is largely a compilation from the papers of Stokes and 

 Lord Eayleigh, but the general arguments based on the physical 

 instincts of those profoundly great men are so weeded out that 

 the result is extremely bald and discouraging. As a summary for 

 those who have studied the original papers the book may be 

 useful ; as a substitute for the original papers its use can only be 

 disastrous. 



