D'ALEMBERT. 411 



Nothing that has now been said can, in any manner, 

 detract from the renown justly acquired by D'Alemberfc 

 and Lagrange as the first who fully expounded the two 

 great additions to the Differential Calculus, first applied 

 them systematically to the investigation of physical as 

 well as mathematical questions, and therefore may truly 

 be said to have first taught the use of them as instru- 

 ments of research to geometricians.* 



In the year 1746 the Academy of France proposed, 

 as the subject of its annual prize essay for 1748, the 

 disturbances produced by Jupiter and Saturn mutually 

 on each other's orbits. Euler's Memoir gained the 

 prize ; and it contains the solution of the famous Pro- 

 blem of the Three Bodies namely, to find the path 

 which one of those bodies describes round another 

 when all three attract each other with forces varying 

 inversely as the squares of their distances, their velo- 

 cities and masses being given, and their directions in 

 the tangents of their orbits.f This, which applies to 

 the case of the Moon, would be resolved were we in 

 possession of the solution for the case of Jupiter and 

 Saturn, which, instead of revolving round each other, 

 revolve round the third body. Euler's investigation, 

 did not appear quite satisfactory; and, in 1750 the same 

 subject was announced for 1752, when he again carried 

 off the prize by a paper exhausting the subject, and 

 affording such an approximation to the solution as the 

 utmost resources of the integral calculus can give. 

 But while we admit, because its illustrious author him- 

 self admitted, the justice of the Academy's views re- 

 specting his first solution, we must never forget the 



* There was nothing in the observation of Fontaine that can be termed 

 an anticipation of Lagrange, though D'Alembert, unknown to himself, 

 had certainly been anticipated by Euler. 



f The problem of the Three Bodies, properly speaking, is more general; 

 but, in common parlance, it is confined to the particular case of gravita- 

 tion, and indeed of the sun, earth, and moon, as three bodies attracting 

 each other by the law of gravitation, and one of which is incomparably 

 larger than the other two. 



