SEQUEL TO THE GENERALIZATION. 105 



he reduces the solution 2 , adds, "Integrate them 

 who can ;" (Integre maintenant qui pourra). New 

 methods of approximation were devised for this 

 case. 



The problem of three bodies was not prose- 

 cuted in consequence of its analytical beauty, or its 

 intrinsic attraction; but its great difficulties were 

 thus resolutely combated from necessity ; because 

 in no other way could the theory of universal gra- 

 vitation be known to be true or made to be useful. 

 The construction of Tables of the Moon, an object 

 which offered a large pecuniary reward, as well as 

 mathematical glory, to the successful adventurer, 

 was the main purpose of these labours. 



The Theory of the Planets presented the Pro- 

 blem of Three Bodies in a new form, and involved 

 in peculiar difficulties; for the approximations which 

 succeed in the Lunar Theory fail here. Artifices 

 somewhat modified are required to overcome the 

 difficulties of this case. 



Euler had investigated, in particular, the mo- 

 tions of Jupiter and Saturn, in which there was 

 a secular acceleration and retardation, known by 

 observation, but not easily explicable by theory. 

 Euler' s memoirs, which gained the prize of the 

 French Academy, in 1748 and 1752, contained 

 much beautiful analysis; and Lagrange published 

 also a theory of Jupiter and Saturn, in which he 

 obtained results different from those of Euler. La- 



2 Journal des Sgavans, Aug. 1759. 



