62 MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF /?. 



+ 32^3 V^ bj,0 - h,l) + 32^2 V a, ^7,2 - 2 ^7,1 " 2 ^7,3; 



« 7. I i^A £^7. ^"% 



= ~ 8^ ^3,1 + le o 4 05,1 — 8 a/ ^5,0 4 « 3 »5,2 



15 a,^ /«1+_«L J. ± /. ^ ;. ^ j_ ^^"^ ;. 1^«^ 7 



"" W¥ \ af ^7,1 - a, ^7.0 - «^ 07,2; + 64 « 4 ^7,1 -" 64 a ^ ^l,^ 



— ■" 1^ ^5,0 + 16 a3 05,2 — 8 af ^5,0 -- 16 af ^5,2 — " 16 «/ ^5,0- 

 Hence the disturbing function contains the term 



"■ sf^ ^5,0 ^ ^/'^ ; in the lunar theory — -j^ e2 e^2. 



Calculation of the Term in the non-periodical Portion of R multiplied hy e^. 



If ij'g denote the term in the coefficient of cos |^ multiplied by e^g, 



i?i7 . cos 2 1^ . . . . e^, 



«5 • cos I, . . . . e^, 



Rq non-periodical portion of R multiplied by e^, 



R'o . . .e>*, 



p, a^dR^ a, d i?^ S a, d R^ a, d R'q 9 a d JJq 



3 if 5 — -Q^ — 2 d a, Ada, da, "r" 8 da, 



^5 = — 2^^ ^3,0 + 2< ^3,1 ^/7 = — "2^, ^3,0 + -8^ h,l R'o = — 8^« *3,1 



W — -L /i ^ :?/Z. J. O R' _J_ -^ » — ^5 ^/7 Of I 9 o 



'^o — — a^ «'i,o 2 "' 2 ""4^5 — ^o-Ts^o 4 2 ^o-r~8^o 



— Qa, '^3,0 — 16 «/ ^3.1 — 16 ^1.0 



•» »' — A A I _i£ ^|9, 9a { a , ,\ 



'^ «5 - - 8 a, ^3,0 -t- 8 «; %.l + 16 a, ^1.0 - 16^ V^ ^3,0 - %,i; 



■^ 8 a2 \a^ f>5,o - ^5.1; - T6^3 ^^ 65 ^ - -^ 65 q - - 65,2/ 



- 8 a, ''3.0 - 16 af ^3.0 i" 16 af \\ + "16^, \~"<~ ^3,0 ~ -^^3,i; 



__ 9« /' «^+< I ^. «A^|27a% 9a, 9a^, 



16 a; V af %l - a, ^5.0 - a, ^^>V + 32^3 \o - 16^2 65,1 - ^^ ^5, 



IV 1_ f Sa , 3a^ ,3a, 



'^ 5 — 16 a, ^3,0 - 16 af ^3,1 "T 16 a,^ ^5,0 " 16^ %\ 



4i>/f 3_MjRj , a^Ro a,d/gs 9a,di?5 na^d/J;; 

 ^*0 2da, "T" 8da, 2da, + l6d"7r 4d^7" 



