IN PHYSICAL ASTRONOMY. 
295 
m, a g 2 C0S t + n t t — 2 •m) + 3 m ' a e 2 cos (3 n t — n i t — 2 or) — ^ m ‘ a a ee t cos (2 n t t— vs— -nJ t ) 
8 a ^ o af a t - 
+ ee^os (2nt — 2n l t — ts + &,) + Oh-? e °- cos (n t — 3 n { t + 2 sr,) 
fl<“ O flj” 
4. ”*L g _ e, 2 cos (rc f + w, f — 2 ra - ,) 4- sin 2 cos (nt n ( t — 2 v ( ) 
+ m ' 2 {“ 2 ^ + 4^ Sin 2 2- C 6 ^" 1 + * 3 > i + 1 ) 
+ (^(3 i — 1 ) b 3>i _ 1 - (3 i + 1) i 3fi 4 - | cos i (n t - n l t) 
+ m ‘ 2 { - 4^2 b 3 ,i - 1 - 2^3 6 3 ,i + ^ 6 3 ,£ + l } ecos (i (n t - n t t) + nt - m\ 
+ m ^{\ T* b 3 ,i-l~ 2^ b 3 ,i~^ b 3 ,i+ l} e / C0S 
+ »»,2 { 
+ { 
+ Wl , 2 { 
_ (2 + i) c 1 (1 4" i) 7 
16 3,i — 1 2 3,i 
+ - 8 ^ ^ b 3)i + j | e 2 cos (i (n t — n t t) + 2 nt — 2-n^ 
(3 + 9 i) a , i 
8 a/ 2 3,i — l 3,i 
— — Q ^ ^ 3 , 1 +j} ee /COS^i(« « 0 + «* + «,* — W—Vf^j 
(1 + 3 i) a ^ 
8 a, 2 3 > 1 '- 1 
+ 3 (1 g + b 3i + x | e e, cos^i (n t — n, /) + ra * — n,t - vr + ^ 
^ f (8 — 9i) a , . ( 1 — i) , 
+ ' 2 1 re - t ? &3 > 8 ' - 1 + ~2^r 
— *», 2 7 t— b„ : , sin 2 4 cos 
,a 2 a 2 3 >* “ 1 2 
(2 T6 l) ^5 5 3,i + 1 } e - 2 cos (i (» * - M) + 2 n, * - 2 *r,) 
(w £— n, 2) + 2n t t — 2 
i being every whole number, positive and negative and zero, and observing 
that b m , n = b m> -n. Considering only the terms multiplied by e and e p 
( dfi\ _ 
"(dr) 
3 wi 1 cl / . \ 1 m 1 cl / n ± ± \ 
— e cos (n t t — w) + e cos (2 nt — n t t — ■&) 
2 Q 
2 a , 2 
2 a/ 
General ex- 
pression for 
the develop- 
ment of R . 
MDCCCXXXI. 
