MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R. 73 



_ 3«^ 3a^ 3a^ ^ 3 a^ 3 a^ , a 



~~ 32 a^ ^5,0 — 32 «3 05,2 — 16 a 4 %i + 32 « 3 ^5^0 + 32 a^ ^5,2 + 4 ^^2 »3,i 



— ITf *3,i + iti af ^5,0 — r6^4 »5.1 



9 c? 

 = g — 3 in the lunar theory. 



^ ^viii — — 2da "• ^ ^65 — 4d« - — 2 ^62 



~~ ■" 16 a7 ^5,0 -r 32 a 4 O5.1 + 32 af ^5,0 — 32 «* 05,1 



a^Sa^^a 1, 1^\ 



- 8^" ^3,1 + 8^ V^ ^5,1 - -2 ^5,0 - -^ 05,2; 



+ i { ^ (-^ ^7,0 - h,) - -^(^ ^7,1 - 4 ^7,0 -• 4- ^7,2) } 



3a^ 3a3 ^A i_^^^ 



— 8^ ^5,0 + 8^ 05,1 — 2^ 03,1 + ^Q^ 03,1 



~ 32 « 3 ^5,0 ~ 32 a 3 05,0 + 32 « a 05,2 + 4 « 4 ^5,1 



"T- 32 1 ~ < V « 2 07^1 - — O7 - ^^ 072^ -h 2 ^6 Or.o — 2 «^5 ^7,2 J 



— ~ 16 a,3 »5,0 + S2 af ^5,2 + 4 « 4 05,1 ~ 32 « 4 05,1 + 32 af ^^,1 

 "" ~" 16 a,3 05,0 H- 8^4 05,1 + 32 af ^5,2 — "" 8 « ^ %,i + 32 «^3 05,2 



= — * 8 — 3 i^ the lunar theory. 



{3a S a^ ") 



~ \{r~' ^5.1 "^ 64*0^ ^5>2 f ^^ 7^ COS (21 — 2?;). 



Calculation of R^^, or the Coefficient of cos (2r — 2f + 2 ;;^), z« #Ae Development of R. 



Distinguishing the argument 2 r ~ | + 2 ;?/ by the index 3, and 2 r + 2 j?^ by the 

 index 1, 



^2 ^ "-/a 



^3 — T6^ ^3,1 — \Qaf U; ^5,1 - 2 ^5.0 — 2 ^5,2; + 4fl^2 *3,1 



* -RvmCor iZ-,) = — — —, this agrees with the result I arrived at formerly, since confirmed by M. Poisson. 

 MDCCCXXXV. L 



