3] NUMERICAL DEVELOPMENTS IN THE LUNAR THEORY. 119 



e to the solution of a differential equation of the second order ; but I 

 cannot find that he has anywhere made a numerical application of his 

 method, which, as he says, is much less elegant than that of Mr Hill. 

 He proposed to continue the foregoing calculations with Mr Hill's method 

 of finding these terms, and his next and last communication to Miss 

 Harrison consists in directions for computing the function P, where 



a ( I fu / dy dx\ .., dy~\Y 



P = ^ + 4' 2 + 3 J.= c (x-f-ij -j-\-3n"-x- 

 i* (V- |j \ dt J dt] dt]\ 



. . f 1 fu /' du dx\ . du~V\ 

 - Qn' { ^r, " 3 (x -f -y -J- - Sn^x-g 

 (V 2 \_r 3 \ dt y dt] dt]} 



dt J dt] V- \dt 



this being the quantity to which the coefficient of w reduces (Lecture 

 XVIII. p. 84) if we ignore the parallactic terms, and the unspecified dis- 

 turbances X, Y. 



These calculations were not completed.] 



July 24/84. 



