312 LAPLACE. 



If a celestial body, the moon, for example, gravitated 

 solely towards the centre of the earth, it would describe 

 a mathematical ellipse ; it would strictly obey the laws 

 of Kepler, or, which is the same thing, the principles of 

 mechanics expounded by Newton in the first sections of 

 his immortal work. 



Let us now consider the action of a second force. Let 

 us take into account the attraction which the sun exer- 

 cises upon the moon, in other words, instead of two 

 bodies, let us suppose three to operate on each other, the 

 Keplerian ellipse will now furnish merely a rough indi- 

 cation of th.e motion of our satellite. In some parts the 

 attraction of the 'sun will tend to enlarge the orbit, and 

 will in reality do so ; in other parts the effect will be the 

 reverse of this. In a word, by the introduction of a 

 third attractive body, the greatest complication will suc- 

 ceed to a simple regular movement upon which the mind 

 reposed with complacency. 



If Newton gave a complete solution of the question 

 of the celestial movements in the case wherein two 

 bodies attract each other, he did not even attempt an 

 analytical investigation of the infinitely more difficult 

 problem of three bodies. The problem of three bodies 

 (this is the name by which it has become celebrated), 

 the problem for determining the movement of a body 

 subjected to the attractive influence of two other bodies, 

 was solved for the first time, by our countryman Clairaut.* 



istic French names which it is possible to imagine, whose maternal 

 grandfather was M. Gros, whose paternal great-grandfather was a 

 French officer, a native of Paris, who never wrote except in French, 

 and who was invested in our country with high honours during a 

 period of nearly thirty years ; ought to be regarded as a French- 

 man although born at Turin. Author. 



# The problem of three bodies was solved independently about the 



