MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OP R. 77 



o » _ ^^-^3 o » A «^-^i _ £ 7? 

 ^ ^xii — ""2da~^^3— 4 da 2^1' 



It is evident from the calculation of jRym that B contains the term 



{^ ^5,1 - i^3 ^5,2} e2y y^cos (r - 2 i + ^ + ^;). 

 It is evident similarly, and from the calculation of R^, that R contains the term 



{1^ \i - l^3^5,2}^/'yy;COs(r + 21,-- n + ;?,). 



Calculation of Ry^^^ or the Coefficient of cos (2 r — | + |^ — ?? -|- ^7^). 



Distinguishing the argument 2 r — >j + ^/ + 1/ by the index 7, and the argument 

 2 r — ;? + ^; by the index 1, 



«;d.fii ^ «_ 



^-"-Td^~^i ^1- 4«;^3,2 



^7—4^ 03,2 + 8^ V«y ^'2 " 2 ^5,1 - 2 ^5,3; -t- 4«^2 03,2 

 — 8 «2 03,2 - 16 «^4 05,2 + 16 a,^ ^5,2 



R _ a^ R7 n 



^xiv — ~~ 2da 7 



— ~ 8«/ O3.2 - i6fl/^5,2 + 8fl^« ^5,3 — 8«/ Va, ^5,2 — 2 ''a,! ~ 2 V^j 



+ T^ ^3,2 — s:^ »5,2 + 8^ O3 5 



_ 21 a^ 15«2 j^ 



— ~" 16 «4 ^5,2 + 8 «; ^5.3 + 8 a^2 03,2 



15r<r*/aM-<, a, «7,\ "^7.i_^7,_i__^7. ^'^ h \ 



+ 16 I ^* V «;^ ^7.2 - -^^7.1 - -7 ^7,3; -2«r7,2-t- 2a'4'^7,4 i" 2r;/^7.1 -- 2c/^7,3 j 



_ 21 a\ 15a^ 9 a^ 9 a^ 15 a^ ^f^, , 3 a^ 



— "" 16 a;^5,2 + 8 a 3 05,3 + 32 aS^s,! — 32 ^305,3 + ig 0^*05 2 ig ^^305,3 + s a/ %2 



__ 9a^ 33 a^ 



— 32a3^M + 32 a 3^5.3- 



Therefore i? contains the term 



{i$^i + HI ^3} ^^.rr^cos (2r - I + I, - ^ + ;j,) 



