IN PHYSICAL ASTRONOMY. 
35 
+ m, ( — —,^ 3,4 - — 63,5 + -nAe} e ? cos (5 n t - 7 n i t + 5 e 
|_ lb a ( - a, lb a ( - J 
+ wi ; { — ■ — — ,& 3 , 0 ) sin 2 -^(n t + n, t + e + s, — 2 v,) 
Lfl/' Of~ J 
— cos(2 n,t + 2 s, - 2 v,) 
-^•^ fc 3 ,i sin2 -J cos (2 n < + 2 g — 2 v ( ) 
— ^ — Aa sin2 -s- cos 0 * + 3 »/* + £ — 3 6, + 2 v,) 
L OLf & 
— ’ n h JL b 3> a sin 2 -k- cos (3 n t — n,< -f 3 £ — e ( — 2 y,) 
2 a/ 2 * 2 
— — 1 1 —6 3 3 sin 2 -k cos (2nt — 4 wi + 2 £ — 4 e. + 2 v.) 
2 a/ 3,5 2 ' 1 1 
— r !h—b si sin 2 -k cos (4 n £ — 2 n t + 4 £ — 2 £, — 2 v.) 
2 a, 2 3,3 2 v ' 1 i' 
-7», + 2o,) [ 67 ] [31] 
[ 68 ] 
[69] 
[70] 
[71] 
[72] 
[73] 
[74] 
Development 
of A*. 
In the lunar theory, the small value of the quantity makes it desirable to 
ordain the results according to powers of this quantity. Transforming there- 
fore the preceding expression for R by means of the equations given in the 
former part of this paper, Phil. Trans, for 1830, p. 346, neglecting terms mul- 
tiplied by — „ and supposing /, = 0, 
a i 
= m l 
1 aft ^ 4 a?) 
+ 3 (sin 2 ' -> 2 + *r)\ «U 
2 V 2 4 ) a? J 
[o] 
+ m j \ 
f ( a i (e 2 -f- ( 
l( C ° S 2 " 2 
>;-)\ a _ a / 3 a 
) a? a? V 8 a? 
\ , ■ 2 i a /, . 33 a 2 \ 
/ 2«rV 8 a?) 
(e 2 + e?) a / 
2 a?\ 
1 ~ ^ 2 )} C0S(W ^ ~ n 
1 1 + £ — £ i) 
[i] 
+ m , { 
3 a 2 , 3 . . 
7 — + — sin 2 
4 a? 2 
±^+ ±l(e°- + 
2 a ? + 8 + ‘ a? i 
cos (2 n t — 2 n? -|- 2 £ — 2 £,) 
[2] 
+ m , | 
' 5 a* 15 . _ 
— - — - + — sin 2 
8 a? 8 
_L — j_ }A (e 2 + e 2 ) — 1 
2«/ + 4 l 
cos (3 n t — 3 n t t A 3 £ — 3 e ; ) 
[3] 
