HERMANN VON HELMHOLTZ 



and fruitfulness of such mental labour.' The same 

 is true of all departments of physics, and especially 

 of those departments that deal with the hidden pro- 

 perties of matter. It need scarcely be said that the 

 pure mathematicians, men always of the first mental 

 calibre, are forging the tools with which the physicists 

 of the future will attempt to solve still more recondite 

 problems than those that at present engage their atten- 

 tion. When the monumental labours of such men 

 as William Rowan Hamilton, Joseph Sylvester, and 

 Arthur Cayley are looked at from this point of view, 

 it will be seen that advanced mathematics does not 

 consist merely of a series of mental gymnastics, but 

 that the subject is of the highest practical importance, 

 because it leads the way to an adequate conception 

 of the phenomena in the physical universe. 



O wretched race of men, to space confined ! 

 What honour shall you pay to him whose mind 



To that which lies beyond hath penetrated ? 

 The symbols he hath formed shall sound his praise, 

 And lead him on to unimagined ways, 



To conquests new in worlds not yet created.' 1 



It may be said, in the words of Helmholtz's greatest 

 pupil, Heinrich Hertz, that the ultimate function of 

 science is to formulate the problems of nature mathe- 

 matically, and thus bring the logical consequences of 

 thought into harmony with the phenomena happening, 



1 Lines written by Clerk Maxwell with reference to Cayley. 

 I 9 



