MR. LUBBOCK ON THE THEORY OF THE MOON. 



137 



These are the only discrepancies which I have noted in the terms multiplied by y^ 

 which I have examined. In making use of the development of R before alluded to, 



y' 7 . V 



1 — 2 + 7g 7* IS to be substituted for cos'' -^ . 



The relation between the constants h and a is to be obtained from the equations 



AT' -^+i + 2fdR = 0; 



where, for simplicity, 1 have neglected at present quantities depending on y^. 

 I d£ ^ 



- 4 



2jd R can give no constant term * ; therefore, considering the constant part only 



of the equation above, since the coefficients corresponding to all the arguments must 

 be separately identical, 



A2|l + 2r„ + 4 + ^'} =a^| 1 + 2ro- (1 - 4 r„) j'^ +^j 



r^\ being already multiplied by m'^, is not to be taken into account in this approxi- 

 mation. 



c2{l — 3ro} — 1 +2^2 = 



c2 = 1 — — 7^^2 



{■- 



A2^ 1 -m24-^+ y^m2e2 — -^m2e,2| = fl|:/,|l — ^ — ^2 — ■:^m'^ e^ — -^m'^e^\ 



d 



^ 

 -T-^' 



{ 



= «^ { 



- fl^ m2 e2 - - m2 e^ | 



+ m2 — -2" — 7^ m2 e2 + -g- rn^ e^ ^rr?e^ > 



241 

 — e2 — -gj wi2 e2 



} 



"2* "" 128 



mSgS 



} 



* This seems at variance with the equation of M. Plana, vol. i. p. 122, 



_ifL /d'fi = - — (l + -Ly^+£e2 + — c2y2cos(2tir-2 9) + &c.j 



which equation I am unable to understand. 

 MDCCCXXXIV. 



