IN PHYSICAL ASTRONOMY. 
231 
+ prr 
n e 
2 i (n — n 
j{ ( 2i + 2> i 3 ._, + 6 3>j+1 } + i 3jj 
5 s,i+i } cos (* ( w 1 - n i 0 + »t - ®) 
(1 + 2i) a 3 , 3 ia® 
2 a* 3 >* + 4a" 
, 3»i 5 a , 
"** i 2i (w — «,)*<*, 1,1 /• 
-*ii +-^p4 
-rc) L °/ ’* a, da J 
+ 
+ 
+ 
(* ( re ~ «/) 
_ 3 n _a Ab i,i 1 
4i (n — Ji t ) [a; ^ da J 
+_ n _ f * ab i,i a _l^l , ecos (i (n t — nt) + n t — sr\ 
4 (i (re — n t ) + 2 *- a ' 0/ ^ a J 
_— " 1 n - / 'iiL bn- .-— . — -~— 0 bo ,• i , 1 e t cos (i (n t — n.t) + n.t — 
(i(._.,) + »,) i 4 °-* 3 -- 1 2 “. 3,1 4 “' s3 '‘ +l/ v 
n _ f 0 . r 3 a®, , a . a® , 1 
2 ( i(ra _ w< )_ K+W/ )l“ t l 4 a y ® 3,i-l + 2a/ 3,i 2a;2 W+l) 
" ^ b 3,i-l + ^ b 3,i + ^- 4 -^ %,*+1 ]■ e < C0S ( i + »<<-«/) 
^{ 2 * { “ 5a^ + 2^ ^ + 4^ Vh } 
3(1 + *) 
2 (^i (n — n t ) — n + i 
+ 3Jt+i) 57 fc 3 , i+ .} «, cos (i (»* - »,0 +»,*—,) 
Observing that 
* b '>* = 2^ { 6 3,t-l “ 5 3,i-fl } 
a d 6. • 
d °l,i _ a/a, 1, _ 1 , 1 
da a ; 1 a t 3 ** 2 3,i ~ 1 2 3 >*+ 1 J 
the preceding expression may be put in the form 
a 
r 
(K 
——- b . . cos i(nt — n.t) 
— n,) 
+ 
n 
(— a b ■ 
2{i (n — n t ) + n} 
l 2 a ( ® 3 > l - J 
( i + 1) n f 
- a3 b, ■ • 
(i (n — n,) + n ) 
4 a/ 2 3 > l_1 
_ /- — ba . ,- — b„ ■ + b„ 1 ecos (i (nt — n.t) +nt— 
4a ( J 3 >'-‘ 2 a? 3 > l 4 a/ 3 > l + 1 j \ K 1 ) 
