TENDENCIES IN MATHEMATICAL SCIENCE 331 



on the whole remarkably gradual, for with the single exception of 

 Newton there is very little exhibition of great and sudden develop- 

 ments ; but the possessions of one generation are received, augmented 

 and transmitted by the next. It may be confidently maintained that no 

 single person has contributed more to the general stock than Laplace. 



THE PERTURBATION PROBLEM. Newton had worked out the 

 theory of a single planet or satellite revolving about its primary. 

 The consequent discrepancies were held by some to indicate 

 inexactness in his hypothetical laws. Laplace occupied himself 

 with a thorough study of the great problem of three bodies, 1 and 

 without fully solving it, accounted to a great extent for the dis- 

 crepancies in question. In particular he maintained the stability 

 of the solar system. His Mecanique celeste has been charac- 

 terized as an infinitely extended and enriched edition of Newton's 

 Principia. 



In his confidence in the extending range of mathematical methods 

 Laplace says : 



Given for one instant an intelligence which could comprehend all 

 the forces by which nature is animated and the respective positions of 

 the beings which compose it, if moreover this intelligence were vast 

 enough to submit these data to analysis, it would embrace in the same 

 formula both the movements of the largest bodies in the universe 

 and those of the lightest atom : to it nothing would be uncertain, and 

 the future as the past would be present to its eyes. The human mind 

 offers a feeble outline of that intelligence, in the perfection which it 

 has given to astronomy. Its discoveries in mechanics and in geom- 

 etry, joined to that of universal gravity, have enabled it to com- 

 prehend in the same analytical expressions the past and future states 

 of the world system. 



THE NEBULAR HYPOTHESIS. In his Exposition du systeme 

 du monde, "one of the most perfect and charmingly written 



^Given at any time the positions and motions of three mutually gravitating 

 bodies, to determine their positions and motions at any other time a particular 

 case of the actual more general problem : Given the 18 known bodies of the solar 

 system, and their positions and motions at any time, to deduce from their mutual 

 gravitation by a process of mathematical calculation their positions and motions 

 at any other time ; and to show that these agree with those actually observed. 



