222 GREAT MEN OF SCIENCE 



examining the complicated motions of the planets, and calcu- 

 lating these down to their details. But the description we 

 have given, which was entirely limited to essential points, must 

 have shown the reader in this case also that the discovery 

 itself - though not its confirmation in all directions - never- 

 theless resulted from comparatively simple lines of thought, 

 which also needed only fundamentally simple mathematical 

 means for their support. The same will have been noticed 

 in all revelations of new and unsuspected secrets of nature, 

 such as are characteristic of the whole series of great men of 

 science hitherto considered: indeed, the discoveries which 

 most of all exceeded all previous possibilities, and most strik- 

 ingly overthrew existing limits of knowledge, such as those of 

 Volta, Davy, and Oersted, did not need the help of mathe- 

 matics, and the same is true up to to-day. The importance 

 and efi"ectiveness of mathematics in scientific research is quite 

 generally overestimated. Investigation, it is true, must 

 always strive to be quantitative, but the fundamental rela- 

 tionships of a quantitative nature which hold in fact, and the 

 discovery of which is the sole object, have always proved to 

 be of the simplest possible description. 



Laplace's great work, the Mecanique cSleste (celestial 

 mechanics) was for the most part a purely mathematical 

 achievement. The work starts from the discoveries already 

 described of Galileo, Huygens, and Newton, and develops 

 extremely valuable mathematical methods for applying them 

 in a far more detailed and accurate manner than Newton, to 

 the motion of the planets, the moon, and the waters of the 

 sea. Laplace thereby developed valuable mathematical 

 methods for calculating the disturbances of planets and 

 moons by their mutual gravitational forces, as well as quite 

 general methods for calculating forces which act according 

 to the inverse square law (the theory of potential). 



A second scientific achievement of Laplace, is his dis- 

 covery of the fact that, and of the degree to which, the 



