76 MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R, 



+ 16 «3 «'5,2 + 8 a,'* ^5,1 — It) a 3 ^^5,0 — i6 «3 05,2 



Therefore iJ contains the term — jg-p ^5 ^^ y y^ cos (r — ;j -f ^j- 



Calculation of the Term in jR^^ multiplied by e®. 



Distinguishing the argument r — ;? + I; by the index 1, the argument r — ;? + ;;^ — ^^ 

 by the index 6, and r — ;j + ??^ + i^ by the index 7, 



_ <?/digi p _ «/ d -Ri _ „ „ _ _«_, 



^6 = "" 4^ *3,1 + 5^ V:^ ^5,1 — Y *5,0 — 2" ^5,2; 



— 3«^ 3«^ 3a3 3»a 3ftg _«_ 



■~ — iQaf ^5,0 + i6«3 05,2 + 8«4 05^1 — ig«3 05,0 — i6«3 05,2 — 8a/ ^3.1 



— "~ 8 «/ ^3,1 — 8 « 3 ''s.o + 8 a 4 %i 

 a, d Ri a,d Rq a, d R^ a^ dR^ a^d Rq 



XI Ida, 2 da, 9. da, 2 d «^ d a^ 



2^xx = 



^ ^xi = — "8^ ^5.0 + y^ ^5,1 — 4^ ^3,1 



u 



8 



+ ^ { ^4 (:^ ^^7,0 - h,^ - ^5 (^ &7,1 - i 2^7.0 - Y ^7,2) } 



■*■ 8 a/ Va^ ^5,1 - 2 ^5,0 - 2 ^5,2j i- 4^ 03,1 - 8^ (^^ %,l " Y ^5,0 " -205,2; 



- 8 a^ ^5,0 -i- 2 a * ^5,1 - 8 a'f ^5,0 + 8 «/ ^5,2 " 8 «/ ^5,1 4" s^ %,! + q^ %i 



3 a" 3«^ il^A 3a2 3 a^ , 3 a^ Sa^ 



""16 a/ ^5,0 16 a/ %2 i" 8 a/ ^5,0 - 8 a/ ^5,2 - 8 a/ %i + le^a/ ^5,0 + ig"^ 05,2 



— 9a^ 

 8 a/ ^5,0' 



9 a' 

 Therefore i? contains the term — —-3 65,0^/^ 7 7i cos (r — ;? + ;j^). 



Calculation of R^^^ or the Coefficient o/" cos (r - 2 1 + ;? + jj^) in the Development of R . 



Distinguishing the argument r + >? + ;j^ — | by the index 3, and r + ;; + n, by the 

 index 1, 



P a d iJj Q 



