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



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



If R'2 denote the term in the coefficient of cos i multiplied by €^, 



Rs cos 2 1 .... e2, 



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



» coefficient of cos | multiplied by e, 



^ ^ 2 — 2 da ""Sda"" 4 da da ~*~ 8da 



""^ z. I « J. z? _ _£L ^ j_ .1^ h 



^2 = - 2^ ^3.0 + 2^^3.1 ^8 — - 2a3 ''3.0 i- 8a^3 »3,l 



^2 -Rs 3 o D/ , 9 D __ ^«' J. 3fl , _9_ 



"2 2~ "" T^2 - ^0 H- y ^0 — 8 af ^3,0 — iQa,^ \l ~~ l6a, ^1.0 



o r»/ ^«' A 3a , 9a /j^ , , \ ^ (a , , \ 



^^2 = 1^ ^3,0 - W^ ^^3,1 + j6 a 2 V fl; ^3,0 - 03,1; — y « 4 V ^^ ^5,0 - %lj 



+ TF^ VT, ^5,1 - 2 ^5,0 - 2 ^5,2; 



!>/ _- 7a^ , _a_ , £a4 9 a^ 3 a^ 3 q^ 



^2— idaj" ^3,0 — 4a^^ %,1 — Sfl^s ^5,0 H- i(j«4 »5,1 ~ 32 «^^ ^5,0 32 a/ %2 



_ 7a^ ^ _«_, _3_a^7 , ^_^ ^ Sa^ , ^ a_ , 



— Idaf ^3,0 — 4a^a ^3,1 — y ^3 03,0 -r i(ja3 ^'s.o - ib^; ^5,1 + ]tja/ ^3,1 



flg ^ 3a , 3ag Sa^ 



— 76^^3,0 — i6fl3 ^'s.i + 16 « 3 ^5,0 — 16 a/ V- 



If R"q denote the term in the non-periodical portion of the disturbing function 

 multiplied by e*, 



, _ ad 71^0 adigp ^ adR'^ QadR^ SadR^ 

 4^0— 2da "^ 8da ~ 2da+ 16 da "" 4.da 



. P„ 1_ , g /_^ 7 7 \ _1_ , a , , 9 a' , 



^^ h -J_ ^^ /"^ A 7. ^ L 3a^ /a - 1 1 7 \ 



~ 16 a^ '^s,! -r ida^ Va, ^5,0 — ^5,1 J + 30^3 \— 05,1 " "2 ^5,0 " "2" ^2) 



15 a^ (a^, . \ , }±c^ (a ] 1 \ 



"" 32 a 4 V a, ^^7,0 — «'7,i; + 32 ^3 \^ ^^ ^7,1 — "2 ^7,0 — "2 ^7,2; 



1 ( a^ 4- g ' I, Q^, \ a { a ^ , \ 1 a 



— 16 aA a,2 03,0"- ^ a^ f>i,i) - J^a V^ ^3,0 - ^'s.i; - Te^ <^3.0 - T6< ^3,1 



_?1 ^ i_^ ^ 1 _?JL Z"^/. i.\.3a*/a, 1, l-\ 



Xag'^M"" I6fl2''5,l -r \Qaf\a^%^''%\) +32^3^-^ »5,1 ~ -q%0-'-q:%2) 



9^ 



32 



