MR. LUBBOCK ON CERTAIN TERMS IN THE DEVELOPMENT OF R. 61 



"" 32 a^ \ af ^7,0 — ^ a^ ^7,1^ + 64 ^ 3 ^'/.o — 64^3 O7.2 



— 8a/ V a/ ^5,1 — a^ %,0 — «^ «'5,2/ + 64 af %0 — s^ %l 

 ~ 64 a 3 ^5,2 32 « 3 %o + 32 « 9 O5 1 



— 64^^50—32^205^1 — 32^05,1 + 54-^3652 



— ^ A I ^^ i j_ «^ 7 13a , «^ , 5«^ 



— 32 «/ ^5,1 -r 32 « 4 05,1 -h g4 ^3 05,2 — 32 a,^ ^5,1 — 32 a* %1 + 64^ ^5,2 



_ 3a 7 I 3«' I 



— ~ 8^ ^5,1 + 32^ 05,2- 



Hence R contains the term 



r J_a_ , 3«^ ") 



^' )_ "" 32 < ^5,1 + 128 a^3 05,2 J «^- 



Putting for 65 1, 65 2 their values in series, the first term is 



~ 32 a,3- 



This result agrees with what I have before arrived at in the Lunar theoiy. I have 

 neglected no similar opportunity of verifying the terms in the disturbing function 

 given in this paper ; these opportunities are however but few, as the terms multiplied 

 by y 2 may be dispensed with in the lunar theory. 



Calculation of the Term in the non-periodical Portion of the disturbing Function mul- 

 tiplied by e^ ef. 



If R^ now denote the term in the coefficient of cos | multiplied by e ef, 



R'o non-periodical portion . . . e,^, 



R\ e2e/, 



jy ^ ^ Tfi "^-^^0 Jit 



^2 — — 8a/ \a^ ^5,1 — 2 ''s.s — 2 ^5.2/ "T 8 «/ ^3,1 



^^^ ~~ 2da ~~ 2da 



T>< T>i « T g , , Sa^ - 3«« , 3a^ , 



i<0 — ^2 — - 8 «/ ^3,1 — 8 «/ ^3,1 -r 8 a4 05,1 — 16 a/ ''s.O - 16 «/ 05,2 



rt r»,/ * t I 3ft^ / « , 1 , ^ 7. ^ I 9«^ , 



2 i« = - 8^ 03,1 + 8^ V^ ^5,1 - -2 ^5,0 - 2 ^5,2; i- i6«4 O5.I 



