bAR ti'INISM ANb OTtiER BRANCHES O> SCIENCE. 363 



given to that science a potent grasp over some of the inmost 

 recesses of nature. Suppose, for instance, to take one of 

 the most profound problems, we proceed to investigate on 

 mathematical principles the movement of one of the 

 planets. The sun, in the first place, attracts the planet, 

 and in virtue of that attraction the planet would move in 

 a certain path which could be determined with compara- 

 tive ease. But the actual problem is by no means so 

 simple. The planet is acted on by other planets ; its orbit 

 is thus deflected slightly from the simple form it would 

 otherwise have ; and while the orbit preserves a general 

 resemblance to the ellipse, it is in reality a path of no 

 little complexity. But still the mathematician can follow 

 the planet with his figures he can point out with 

 accuracy where the planet was at any ancient date ; he 

 can show where it will be at any future date. It is the 

 infinitesimal calculus, the invention of Newton and Leib- 

 nitz, which enables this to be done. By this subtle and 

 exquisite contrivance we attack the problem in detail. 

 It is comparatively easy to find out the direction in which 

 the planet is moving at any instant, as well as its velocity. 

 This will enable us to ascertain where it will be in the next 

 moment of time. We then repeat the operation and 

 carry on this process as long as we like, and thus discover 

 where the planet will be at any future date. The success 

 of the process consists in attacking the question in detail. 

 Is there not in this a striking analogy to the great 

 principle of Darwin ? In each case great effects are pro- 

 duced by the constant addition of innumerable small 

 tendencies, all in the same direction. As the infini- 

 tesimal calculus of Newton has led us to a knowledge of 



