430 D'ALEMBERT. 



tion, which he had fully explained in his first Memoir to 

 be the more correct mode of proceeding, ('Mem./ 1745. 

 p. 352;) and the consequence of this is to give the mul- 

 tiplier, on which depends the progression of the apogee, 

 a different value from what it was found to have in the 

 former process. It is never to be forgotten that the 

 original investigation was accurate as far as it went; but 

 by further extending the approximation a more correct 

 value of m was obtained, in consequence of which the 

 expression for the motion of the apogee became double 

 that which had been calculated before. 



It should be observed, in closing the subject of the 

 Problem of Three Bodies, that Euler no sooner heard of 

 Clairaut's final discovery, than he confirmed it by his own 

 investigation of the subject, as did D'Alembert. But in 

 the mean time Matthew Stuart, (Life of Simson, vol. i.) 

 had undertaken to assail this question by the mere help 

 of the ancient geometry, and had marvellously succeeded 

 in reconciling the Newtonian theory with observation. 

 Father Walmisley, a young English priest of the Benedic- 

 tine order, also gave an analytical solution of the diffi- 

 culty in 1749. 



The other great problem, the investigation of which 

 occupied D'Alembert, was the Precession of the equi- 

 noxes and the Nutation of the earth's axis, according to 

 the theory of gravitation. Sir Isaac Newton, in the 

 xxxix. prop, of the third book, had given an indirect 

 solution of the problem concerning the Precession; the 

 Nutation had only been by his unrivalled sagacity con- 

 jectured a priori, and was proved by the observations of 

 Bradley. The solution of the Precession had not proved 

 satisfactory; and objections were taken to the hypotheses 



