MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R. 59 



+ '^z { - TI^ hi + i&t h^ } '' ^' cos (2 r + 2 ?, - 2 ,) 



[VII.] 



+ ^/ { - ll^ hi + ^ ^5,2 } ^' y' cos (2 I - 2 »j) 



[VIII.] 



+ ^/ { - ll^^ ^5,1 + ^3 } ^' 7/' COS (2 r - 2 I + 2 ;?,) 



[IX.] 



+ '^z I - T6^ ^5.1 + 64^ *5,2 j ^z' 7/' COS (2 I, - 2 p?^) 



[X.] 



+ '^z { ""4^ *3,i - tI^ ^5,0 (e^ + ^/^) + il^ \o (y^ + r,^) }y y/cos (r-;j+»,,) 



[XI.] 



+ ^/ { 8T^ ^5,1 - si^ ^5,2 j e^ y yy COS (r - 2 g + ?7 + ;7^) 



[XII.] 



+ ^/ {l^«^5,0 - ^^5,2}^/Vy/COS (r 4- 2^, - P7 - Pjj 



[XIII.] 



32^3^1 + 32^^5,3 j^^y yy/ COS (2r - I + I, ~ ;? + ^J 



[xiv.] 

 ~ '^z 32^ *5,o y^ y/^ COS (2 r - 2 pj H- 2 ;?^) 



[XV.] 



The method which I propose to employ in order to arrive at the terms in the 

 disturbing function, independent of the inclinations, is sufficiently explained in the 

 Philosophical Transactions. The following are the equations employed : 



dR _ adR dr dR d\ 



de de rde'drd^ 



[0] [2] [8] 



17 71 



— ^ e2 cos 3 1 — 2^ e3 cos 4 I 



[20] [35] 



^ = 2(l-2|!)sin| + |e(l-^e2)sin2| + T^'si^3H-^e2sin4|. 



[2] [8] [20] [35] 



i2 



