HELMHOLTZ IN BERLIN 



mathematical treatises. Had he chosen pure mathe- 

 matics as his future field of labour, there is no doubt 

 he would have won distinction here as elsewhere, but 

 he always subordinated mathematics to the investi- 

 gation of physical questions. He did not revel in the 

 deduction of the purely abstract truth of geometry 

 and algebra, but the abstract propositions and methods 

 of mathematics were to him a means to an end, and 

 he knew that mathematical analysis is only a rigid 

 system of logic in which wrong premises may conduct 

 more surely to a wrong conclusion. He therefore 

 always endeavoured, if possible, to obtain data on 

 which to base his calculations. Yet no one knew 

 better that mathematics will win victories where 

 experiment may be beaten, and that, to use the 

 words of Lovering, ' mathematical analysis, with its 

 multitudinous adaptations, is the only key which will 

 fit the most intricate wards of the lock guarding 

 the treasury of science.' Thus, in a review of Vol. 

 I. of Lord Rayleigh's Theory of SoundJ Helmholtz 

 remarks : ' Without the resources of mathematics, a 

 really complete insight into the casual connection of 

 the phenomena of acoustics is altogether impossible.' 

 Again, he says : ' We see in mathematics the logical 

 activity of our mind in its purest and most perfect 

 form, and while we are conscious of the toil and of 

 the difficulty in forming abstract ideas, we have at 

 the same time confidence in the security, influence, 



1 Nature^ vol. xvii., p. 238. 

 189 



