IN PHYSICAL ASTRONOMY. 
233 
, n / (3 i — 10) a 2 , . a 3 , 1 
i(?i — n t ) l 8 a/ 3 > i ~ 1 a/ 3 > i 8 a t - 3,i+l J 
n _ f 3 a - ; _ a 3 , __ a 2 , 1 
v \ 12 a , 2 3,£—1 a 3 3,i 2 a.~ 3 >*+ 1 J 
( t (re — n t ) — n ) ^ 1 1 1 
_ ^ lecos (i (n t — n,t) + nt — aA 
2i(K-«,) 2 a I V / 
+ 
f n f 3a * b 
a b a * f. 1 
| (*(» — »,) +»;) L4a ^ 
2 a t 3 >* 4 a/ 3 > l + 1 J 
» J 
r (3 + 9 i) a 2 7 i a 1 
(w — + M + 
. 8 a 4 » W-l a ( : 
n J 
f( 3 i- 3 )a°- A (3 i 
(ji — — w + n^ 
r-H 
•i 
o-T 
5 
t ^ 
1 sf 
GO 
(1 +*) 
3 ,i 
8 
0 °Lb \ 
Ct/ ° 3 ,l+l J 
e, cos (i(nt — n t t ) + £ — w, j 
j being, as before explained, any whole number positive or negative, excluding 
only certain arguments, 0, n t + e — sr, and n t + s — vr r 
Considering the terms which have hitherto been neglected, if we suppose 
JL — l + r 0 + e cos (1 + k) t + s — + ej l cos (1 + k t ) t + s — zs^, 
we have 
a 3 , _ a 3 
r ° “ 2a/ 3,0 2 a, 2 
^3, 1, 
7 a 3 , 5 a 2 , 
rC — - Oo a 1 —- Oo i 
2 a/ 3,0 4,7.2 3 .‘j 
7 a 7. 
fc, = --- k n. 
4«r' 3, ‘ J "* 4 a//, •' 3 ’ 2 * 
See Phil. Trans. 1831, p. 53. 
If w (l +2 r 0 ) = n and n 2 = ^ if e is the coefficient of sin (n t + ^ — «r) in 
the expression for the longitude, and f t is determined so that the coefficient of 
sin (n t + s — ra- ; ) in that expression equals zero, 
r= 1 - £r> K ° + w K ‘ + e ( 1 + ~ in? 1 * 1 cos (" (' ~ £r - b ’")' ■ + * - ”) 
+ e '{l$ K ° - A + A-''»■*} e ‘ cos (» (l + ^ ‘ +' - »<) 
In the theory of the moon replacing 
m.a 3 
+ e 
3 m, a 3 
+ 
MDCCCXXXII. 
/ 1 + m ' (t — \ cos (n ( 1 
12 f*a 3 l 12/xa/J \ ^ 4f* 
L^- e t cos (1 + k t ) t + s — ot ; Y 
a i \ J 
a* \ 
a7/ 
t + 6 — TX 
) 
3 m. 
2 H 
l 
