176 SECULAR ACCELERATION OF THE MOON'S MEAN MOTION. [23 



1'expression analytique admise jusqu'a present, du coefficient de cette equa- 

 tion," but truth must not be sacrificed to convenience. 



In the algebraical portion of his paper, M. de Ponte"coulant is not 

 happier than in his introductory remarks. Indeed, throughout the paper 

 he expressly leaves out of consideration all the terms which give rise to 

 the difference between M. Plana's result and mine. 



Thus, at the bottom of p. 311, having found from an assumed term 



. dR 



in -3- , that 

 dv 



dR H A ' I ft , 7X , A de ' I f> , 7X 



dt= , e cos (ft + l)+ f -j- sin (ft + 1), 

 dv / j at 



de' 

 he incorporates the term involving ,-. with the preceding under the form 



_A , If i de ' 



and then remarks : 



" On voit done que la consideration de la variation de 1'excentricite de 

 1'orbite terrestre ne fait qu'alterer d'une maniere insensible la partie con- 

 stante des angles des diverses inegalites lunaires multipliers par e', elle ne 

 change en rien la forme des series qui determinent les coordonnees du 

 mouvement trouble..." 



Now these alterations of the constant part of the angles on which 

 the several lunar inequalities depend, which are neglected as insensible by 

 M. de Pontecoulant, actually give rise to the terms in the Moon's co- 



de' 

 ordinates involving j- , which I have been the first to take into account, 



and thus do change the form of the expressions for those coordinates. 



The term -^ -j- sin (ft + 1) is not destroyed by being incorporated with 



J 



A 



the preceding term -jre' cos(ft + l), as M. de Pontecoulant seems to suppose. 



Again, in order to shew that the integral I -'-, dt can contain no non- 

 periodic term depending on e', M. de Ponte"coulant assumes, at the foot 



of p. 310, that j- is made up of terms of the form 

 civ 



Ae' sin (ft + l). 



