MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF B. 71 



Calculation of R^y , or the Coefficient of cos (r ~ | — |^ + 2 j;^), in the Development of R. 

 Distinguishing at present the argument r — ^ -{■ 2 ri, by the index 3, and r -j- 2 p?^ 

 by the index 1, 



Tf — «^^ y? P — _f_7. 



^3 — 16^2 ^3,0 - itia,^\a, Ko ~ hi) + 8 a,^ ^3.0 

 ~ iTT^ ^3,0 — 16 «4 05,0 + le^s 05,1 



a, d i^a 

 '27rflr7 





— 16 «; ^3,0 — 8 a 4 ^5,0 + 3C2 a,^ »5,i — 32 ^3 \^^ 05,0 — »5,i; 



15a3, 3a^ 3a 3 a^ 3 g^ 



+ 32^ ^5 — 32 a,^ ^5,1 — 16 fl/ ^3,0 H- 16^4 %0 — iQ a,^ ^5,1 



— l^h 



— 32 a/ '^S,!- 



Hence R contains the term -32^ ^5,1 ^ ^y 7/^ cos (r — | — f ^ + 2 ?7y). 



Calculation of i?^, or f Ae Coefficient of cos (| — i^ — ?; + ;jj, z/» ^^e Development of R. 

 Distinguishing the argument ?j — ?7^ -- i by the index 3, and ^ — ??^ by the index I, 

 odR, ^ ^. « 



^■^ — ~ 2dfl, "~ ^1 ^1 — - 4< ^3,0 



a, tl R3 n _ _9_^ 7, 



2 da, ■" ^3 — I6a3%l 



Q ?/2 fit 



Hence i? contains the term -j(f^ h,i ^ ^i7 7, cos (| — |^ — ;? + ;?^). 



Calculation of R^^, or the Coefficient of cos (| + f, — ?? — ;?^), in the Development of R. 



Distinguishing the argument tj ~\- r,, — ^hy the index S, and ?? + >?/ by the index 1, 



_ adi^i a_, 



^3 — — 2da ~ ^1 ^1 — 4a/2 ©3,0 



^vi — "" 2 d fly ^3 — — 16 a^3 05,1- 



Q 771 CI 



Hence R contains the term j^^ ^51 cos (| + |^ — ;? — ??^). 



Calculation of R^^^, or the Coefficient o/* cos (2 r + 2 |^ - 2 v), in the Development of R. 

 Distinguishing the argument 2 r — 2 ?j + |^ by the index 7, and 2 t — 2 ?? by the 

 index 1, 



