LAPLACE 



221 



the solar system, in spite of all disturbances by the mutual 

 gravitation of the single planets and moon, will never at any 

 future time become disordered, these are nevertheless no 

 fundamental advances in knowledge. For they are only 

 exactly as true and correct, that is to say in agreement with 

 reality, as what was originally put into the equations, for 

 example in the case mentioned, Newton's law of gravitation 

 and the laws of motion of matter, discovered by Galileo, 

 Huygens and Newton, and only in so far as nothing unknown 

 and therefore not taken account of in the original equation, 

 plays a part.^ In such cases we may say that mathematics is 

 able to give us results that we did not know that we knew, 

 that is to say, that we already possessed the necessary know- 

 ledge of nature required to determine them. 



This peculiarity of mathematical achievement in the 

 questions of science is but little accessible to the general 

 mind; it is therefore often overlooked, and mathematicians 

 are thus often confused with scientific investigators. Mathe- 

 matical skill can, of course, bring about advance in scientific 

 knowledge; but this only happens when the discovery and 

 observation of natural processes which are still unknown, or 

 of a new kind, or not yet properly understood - the highest 

 achievement of the experimental investigator - yet fails to 

 bring full understanding of the processes by means of simple 

 considerations, by reason of their complexity. 



Thus Newton became by means of mathematical skill the 

 discoverer and founder of the law of gravitation, by 



^ Thus Laplace's much admired result concerning the absolute sta- 

 bility of the solar system (which Newton still regarded as quite question- 

 able and even improbable) would be completely upset, as soon as any 

 sufficiently large cosmic body approached too close to the system from 

 outside, and there are far more dark masses having unknown motions in 

 cosmic space, than was earlier assumed by astronomy. Should, how- 

 ever, the results of the stability of the solar system be thus upset, this 

 would not lie in the want of validity of Newton's laws of gravitation and 

 Galileo's laws of motion, which are assumed in Laplace's calculation; the 

 calculations would be inapplicable, but not the facts on which they were 

 founded. 



