IN PHYSICAL ASTRONOMY. 
233 
j_ n f (3 i — 10) a°- , a 3 , _ 3 ia 2 , "1 
i (n — n t ) 1 8 a/ 2 3 > l— 1 a t 3 3 >* 8 a/- 3,i+l J 
n / 3 a 2 z _ a 3 i _ a 2 , \ 
N \l2a, 2 3 > t— 1 a, 3 3 >* 2 a. 2 3 >*+l / 
l ~ a lecos (i ( w £ — n. t) + nt — 
- n ,) 2 a J V / 
3 n- 
2 i{n 
f n /3a 2 b 
a b a b 1 
[(*(»-«/) + «/) UO/2 
2 a, 3 >* 4 a ( 2 3 > i + 1 J 
w J 
r (3 + 9 0 a 2 7 i a 7 
(/ (» — «;)+« + 
L 8 a, 2 *,i-l a< 
n 
f (3 i - 3) a 2 A (3 i 
(n — n,) — n + 
L 8 °3,i— l ■ 
e , cos ^i(nt — n t t) + n t t — 
* being, as before explained, any whole number positive or negative, excluding 
only certain arguments, 0, n t + £ — and nt-\-i — rs r 
Considering the terms which have hitherto been neglected, if we suppose 
A = ] + r 0 + e cos (n (l + k) t + s — zz'j + e,f cos (1 + k,) t + s — 
have r o = 2^5 ho ~ ^ * 3 , 1 , * “ ^5 h h K - *s >9 . 
See Phil. Trans. 1831, p. 53. 
If n (1 + 2 r 0 ) = n and n 2 = if e is the coefficient of sin (n t -f- g — &) in 
the expression for the longitude, and f t is determined so that the coefficient of 
sin (n t + s — w,) in that expression equals zero, 
T= 1 - + 6 ( ‘ + £? K ° ~ } K" (‘ “ + ' ~ 
+ <- {f$ K ° " K ' + K ‘ } “ s (" < 1 + ‘ 
In the theory of the moon replacing 
r* 
a 3 
5 a 2 
we 
As 1 - nil + e 
1 n _ o * 
12 ju,a 3 
(l + _AAl'lcos('n(l _lA£lW g -sr) 
L 12 ft a// \ ^ 4f ha 3 / ) 
+ 4^'/v e i cos (^ 0 + fe i) t + £ “ 
MDCCCXXXII. 
2 H 
l 
