140 MR. LUBBOCK ON THE THEORY OF THE MOON. 



r. 2 2 3 739 2 9I 



r r 



m 



= 1 — -3- -|- e COS (c X — ot) + &c. 



-^=: 1 +e2 + ^' + f^m2e2 + e(l + "f m^) cos (c X - «r) + &c. 



My letter a appears to correspond with a (1 + jo), or a in M. Plana's notation. 



n n 



c c 



f/t ff 



R n 



7^ • • • • " 



X' . V. 



(1 — -g- ) instead of e in the various expressions found above, 



which then so far agrees with the expression of M. Plana*, and I then find 



-^ = 1 + e2 + ^ + y^ m2 e2 + e (1 + ^) cos (c X - sr). 

 M. Plana has 



a , . o . w' . 167 ' *"^^ 



r 



= 1 + e2 + |- + yy4m2e2 + e (1+ 1^) cos (cX - t.) + &c. 



which equations do not agree with those I have found. I am, however, well aware 

 how difficult it is to escape error in these inquiries, and wish to be understood as not 

 offering any of the results contained in this paper too confidently. 



Whenever I presumed to have arrived at figures differing from those of M. Plana, 

 I verified afresh all the steps of the process contained in previous papers, particularly 

 the corresponding term in the development of R, Thus I have found by means of 

 the expressions given §, that three times the numerical coefficient of e^ cos (2 r — y 



* Vol. i. p. 574. t Vol. i. p. 664. t Vol. i. p. 636. 



§ Philosophical Transactions, 1832, p. 601. 



