92 MATHEMATICS 



cularly in statistical Mechanics, which is now a 

 subject of great importance. But the most striking 

 use of Lagrange's conception of generalized co- 

 ordinates was made by Clerk Maxwell who, in this 

 order of ideas, conceived and developed his dynami- 

 cal theory of the Electromagnetic field, and obtained 

 his celebrated equations. This great achievement 

 was rendered possible by the fact that the use of 

 generalized co-ordinates enables the dynamical 

 equations of a system to be set up in cases in which 

 the detailed structure of the system is in part 

 unknown. The form of Maxwell's equations en- 

 abled him to perceive that oscillations could be 

 propagated in the electromagnetic field with the 

 velocity of light, and suggested to him the electro- 

 magnetic theory of light. Heinrich Herz, under 

 the direct inspiration of Maxwell's ideas, demon- 

 strated the possibility of setting up electromagnetic 

 waves which differ from those of light only in 

 respect of their enormously greater length. We 

 thus see that Lagrange's work, conceived in the 

 spirit he has himself described, was an essential link 

 in a chain of investigation which led, on the prac- 

 tical side, to the invention of wireless telegraphy. 



Mathematics has also, at various times, exer- 

 cised a potent influence upon general thought. The 

 revolutionary effect of the modern Mathematical 

 Astronomy, inaugurated by Copernicus, due to the 

 change in our notions of the relative position of the 

 Earth in the solar system and in the stellar universe, 



