130 MR. LUBBOCK ON THE THEORY OF THE MOON. 



2.2.8 . m ,2.2.7 103 __ _, i 285 



^45 = TTiy ^ + 277672 + TTeT ^^=64^^ ^' ^^^^^ ^^^"64 ^ 



r53{{c.+ 3m}2-l} ={c + 3myv,,-2 {^^^ + 1 }m2i?,3 



3.53 2.2.53 127 t*^ ^ , 53 



^53= -6:2^6 ^-"6732"^= - 64 ^ M. Plana has - 32 m 



_ 3_ p _^ 



^56 — 2 ^35 -^56 — 32 



3 53 2 2 53 371 53 



^56 = 6.2.16 ^ + 6.32 =192^ M. Plana has^w 



The development of R which I gave *, results from the substitution of the elliptic 

 values of the coordinates of the sun and moon in the disturbing function. The elliptic 

 expression for the radius vector contains no term of which the argument is | — 2 ;?, 

 the longitude (X.') contains the term + f e y^ gin (| — 2 ??) . This is changed when the 

 disturbing function is considered. 



res {(c - 2g)2 (1 -Sr,) - 1} = (c -2g)n,, - 2 . 2,7n^R,, 



■3 m^ 3 „ 3 „ 



^65 = "2 ^62 ^62 = -2 C = 1 - - m2 g = 1 + - m^ 



7t^ 91 



^o = -6 ^65 = -8-+ 2"^65 (c-2g)2(l -3ro) = l +4m2 



^65 — 4.2.2 4 V8~T'2 ^65 J 





This term, produced by the disturbing force, although independent of m, together 

 with the corresponding term in X', renders in a certain sense incomplete the coefficients 

 of all terms in my development of R, of which the arguments are any combinations 

 of the quantity | — 2 ?j. 



r73{(2-3m--2g)2- 1} = (2 - 3 w - 2g)2r73 - 2 m2 /?-3 



^73 =0 ^73 = — l6 



2.21 „ 21 7 7 



^73= jg- 7^2 = — -g- m2 M. Plana has -^ m — -^m^ 



* Philosophical Transactions, 1831, p. 263. 



