MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R. 63 



2"'8~'2~'"6 5— 4 -"17 



16< ^3,1 —Ida, ^1.0 "" 32 a, ^3,0 + 32 af ^3,1 - 32^ ^5,0 



■T" 32 «/ ^5,1 — 32 a, ^3,0 "T" 32 a,^ ^3,1 + 8 a, ^3,0 — 32 a^2 »3,i 



A nil — ^ A « /^ A A \ 1 A « / 9«^ / 



^^ — 16 a, ^1.0 ~" 16 a 2 V a^ ^3.0 — f^3,i/ — kj «^ %o — 16 «^3 ^3,1 + 32^3 ©5,0 



3« , 3a /^ A ^ _l_ ^^^ /"^ A ^ -A ^ A ^ 



"" 16a/ ^5,1 -1- 16 «3 Va, ^5,0 — %ij -f" 32 «3 \^^ 05,1 — Y ^5,o — 2 ^5,2/ ' 



~ 32 a * \ a, ^7,0 — ^7,1^ + 32 «/ \ a, ^7.1 — 2 ^7.0 — 2 °7,2) 



~ 16 a^ I ~^ ^3,0 — 2 — 63 1 1 - 16 a^ \^^ ^s.o - 03,1 j — -TF^^ ^3,0 - 16^2 03,1 



9a^ , 3^ ,Ja(±i a\i ^^^ /^ A JL A -L A \ 



■^ 32a^a^5,0 — I6fl2«'5,l -t- 16 a/ \^fl^ ^5,0— 05,1; -r 32 «/ \^a^ »5,1 " 2 ^5,0 — 2 ^5,2/ 



"" 32^3 (^ ^^ 070 — 2 — 67 ij + g^3 67 - g^ 67 2 



a /a^ 4- a/, a, '^'\_j_^^'^^A ^^ h 



— " OIT^ \ af ^5.1 ■" ^ ^5,0 — "^ Ki) -r 64^ *5,0 — 8^ »5,1 



JL^ A 15 a^ , 3a , 



"" 64^^ ^5,2 — 32^3 05,0 + 32 af ^5,1 





13 a , a^ . . 5a^ 



64 



af ^5.0 — 32 af *5,l " 32 a ^ \\ + 64 a/ *5,2 



CL Cl €l 1 3 tt fl O ^ 



= 32^ *5,1 + 32^4 ^5,1 + 64^ ^5.2 - 32^ *5,1 — 32^ *5,1 + 64^ ^5,2 

 8Vf ^5,1 + 32 af ^5,2- 



Hence the disturbing function contains the term 



"^'{-MTf ki + 1^3 ^^5,2 } el" ; in the lunar theory - ^-J^ 



In the preceding instance, and in the case of terms depending either upon e^ or e* 

 solely, the term in the disturbing function can only be obtained irom "jj or jj; but 

 in obtaining those which depend both upon e and e,, they may be obtained indifFer- 

 ently either from the combinations which enter into the expression tor -^ or trom 



, . , . 1 . ^ dR 



those which enter into the expression for -^ . 



