MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R. 69 



Hence R contains the term 32^ ^5,0 ^^ (7^ + yf)' Putting for fcg q its value in series 



according to powers of — , neglecting yf, I find for the lunar theory ^^' 3 e^ 7^^ 

 which agrees with the result I have arrived at elsewhere by other methods. 



Calculation of the Term in Rq multiplied hy ef y^. 

 _ a,dRo _ a 



a_ _a_ 3_^ 3j^ 3_a^ 3 a^ 3 a^ 



"- 4 a,2 ^^3,1 - 8 «/ ^3,1 + 16 «^2 05,0 — 16 «^3 05,2 — 8 a," ^5.1 + l6 «/ ^5,0 + j^ «^3 05,2 



— Sl^ ^3.1 + 8^3 05,0 — 8^ 05,1- 



If R"q denote the term in Rq multiplied e^^ y 2^ 



„ _ a,dRo a,dR^ 

 ^^o— 2d a, — 2 da, 



~ "" Tf^ ^3,1 — l6^3 05,0 +16^4 05,1 + 8 a 3 03,1 + iq}{s 05^0 — 4^ 05,1 



3 g^ / a ^ 2. J_ A \ , 15 a^ 3 a^ 



"" 16a^^ Va/ ^'^ "" 2 ^5,0 — 2 ^25J + I6a/^5,i " i6a,4^5,i 



_ 9a^ 



"~ 16 a 3 ^5,0- 



9 m a^ 9 7W a^ 



Hence i? contains the term -3:7^ ^5,0 ^i^ (7^ + y/^)j ^^ ^^ t^^ lunar theory ^^^^3 ej^ y^ 



Calculation of the Term in R^^ or (Rj) multiplied hy y^, 

 ^3 = - Tda - ^1 ^1 = 8^3 (&3,o + ^3,2) 



^3 = - Fd^ (^3.0 + &3,2 + 16^3 I ^ 65,0 - &5,1 + ^ &5,2 ~ T &5,1 - ^ ^5.3 } 



— 3 « / «' + «/^ , o_^ A \ a ^ I A^ 7. 3a^ 



— 16 a^ V ^i'' ^'^ «, ^'V "" 16 a/ ^3,2 + iq «4 05,0 — ig «^3 ^o,! 



I J_^ 7, 3a^ 3a« 3a^ 3 a' 



+ 1 6 a^* ^5,2 32 a 3 05,1 32 a 3 05^3 — 3^ ^^3 65 ^ + 3^ ^^3 05,3 



^7. ^'^7>_l_^®^7. 



— "~ 16^2 03,2 - YgT} ^5.0 + 167* ^5,2- 



