MR. LUBBOCK ON THE THEORY OF THE MOON. 131 



5 3 



The term above, — a ^7^ cos (| — 2 ??), introduces the term -j- -r- e y^ sin (| — 2 ?j) 



in the longitude, instead of o sin (^ — 2 ;?). The terms in R produced in conse- 

 quence may easily be found from the formula 



taking 



15 5 



r ^ — = — -g- e y2 ^os (| — 2 ?j), and ^ X = -^ e y^ gin (I — 2 ;?) 



and I find that R contains, instead of the terms corresponding to the same arguments 

 given in the Philosophical Transactions, 1831, p. 263. 



15 

 -\- ^m^ey'^ cos (2 r — | -J- 2 r) — m^ e y^ cos (2 r -j- I — 2 ;?) 



[68] [69] 



QQ 105 



-f 32 wi2ee/y2 cos (1 + I; — 2 ??) + g^ m2ee,y2cos (2r — | — |^ + 2 ;?) 



[83] [86] 



33 15 



+ Q4Wi2ee^y2cos(e7' + |+^, — 2p?) — g^m2ee^y2cos(2r— l + i^ + 2;;) 



[87] [92] 



231 

 — -^4 wi^ e e^ y2 cos (2 r -j- | — |^ — 2 ;j) 



[93] 

 The coefficient of arg. 77 is easily found as follows : 



i? = — ^ {1 + 3 cos (2 X — 2 X) - 2 *2}. 

 This term can only arise from 



--llxl_i_-il!. 2 



In which expression it is sufficient to write for 5 — , 



5 

 — -Q-er^ cos (I — 2 ?j) 



and to make 



2 1 



%2 = _ ^ COS 2 J? + y2 e cos (I — 2 ;?) + -4 y2 e2 cos (2 | - 2 ;j) 



[65] [77] 



which gives 



p _ 3.5 3 _3 I 3 ^ 



^77— 2.2.8"'"4.4"" 4^4.2.2.2"~"' 



* This is not the expression for s'' in the elHptic movement : the last term is altered by the disturbing force. 



s 2 



