22 ON THE RELATION OF 



The fertility of the method comes out more strikingly 

 in applied mathematics, especially in mathematical 

 physics, including, of course, physical astronomy. From 

 the time when Newton discovered, by analysing the 

 motions of the planets on mechanical principles, that 

 every paiticle of ponderable matter in the universe 

 attracts every other particle with a force varying in- 

 versely as the square of the distance, astronomers have 

 been able, in virtue of that one law of gravitation, to 

 calculate with the greatest accuracy the movements of 

 the planets to the remotest past and the most distant 

 future, given only the position, velocity, and mass of each 

 body of our system at any one time. More than that, we 

 recognise the operation of this law in the movements of 

 double stars, whose distances from us are so great that 

 their light takes years to reach us ; in some cases, indeed, 

 so great that all attempts to measure them have failed. 



This discovery of the law of gravitation and its conse- 

 quences is the most imposing achievement that the 

 logical power of the human mind has hitherto per- 

 formed. I do not mean to say that there have not been 

 men who in power of abstraction have equalled or even 

 surpassed Newton and the other astronomers, who either 

 paved the way for his discovery, or have carried it out to 

 its legitimate consequences ; but there has never been 

 presented to the human mind such an admirable subject 

 as those involved and complex movements of the planets, 

 which hitherto had served merely as food for the astrolo- 

 gical superstitions of ignorant star-gazers, and were now 

 reduced to a single law, capable of rendering the most 

 exact account of the minutest detail of their motions. 



The principles of this magnificent discovery have been 

 successfully applied to several other physical sciences, 

 among which physical optics and the theory of electricity 

 and magnetism are especially worthy of notice. The ex- 



