DIFFERENTIAL EQUATIONS OF ASTRONOMICAL INTEREST. 
which lead to 
c/)(—a 1 + £ n c 1 ) = \ 2 h? (r + 
W 
n 
* \ 2 Li, ) p-i i n ~ n 1\ , ? ( , ri 2 + n— -1\ Q 1 z,u 
+x *M f d-^n)Ud T+ 
2 n 
r- 
+x i i 1 a U QQ f-’+W + ~r r- -|V r-'-VV c +i 
n+1 rr—1 n—1 n— 1 mr—\ 
so that 
« 2 = 0(-Oi + f n C 1 )dr 
X% 2 (^t 2 +- 
n n " 
•+X%i 1 {-?-'(T+-^±A)+dT+-f L d 
l \ n(w+l)/ \ n(n— 1 
+ 
T- 1 
r- 
^n+l 
1 ■ n(n — l) n 2 — 1 n(n+l)j 
+ A 2 £f 
n 
2(n+l) 
+ 
c_ 2 , 2^ 
<> + “i- 7 T — 
n —1 
n 2 (n 2 — 5) 
2 n 
2n 
__ ?n— 1_ ^ ' v _ fn+1 l 
2(n — l) S (n — l)(n 2 — l) (w+1) (n 2 —1) j 
Pn + 1 
Similarly, 
v= *<t>{-(h+£ n ci) 
Jo 
= x% J l-^-^C + - s - T ' 
n n n n 
, . 2 ,7 f f-*- 1 / w 2 — 2 »i-l\ f _B+1 / , n 2 +2n— 1 
x t n + l\ n(rH-l)/ n —IV n(n— l) 
r 1 2wr f , 8n 2 
+ --5—r- - + 
n n 2 — 1 n (n 2 —l)‘‘ 
+ \% 2 
n 
(n+l) (n + 2) 
^_„_2 - £ _ ” 
71 
717 — 1 
(n— l) (n— 2) 
+ 
-n + 2 
2ri ci 2» fl 8 
f --r—r<> + 
n — 1 
?r — 1 n— 4 
Thus we have, so far as terms in A 2 , 
a ! = —\h, 
A 2 h 2 
CL.) = 
n 
+ A 2 £, 
yi = 0, 
2 2w _ 2A 2 A 2 4A 2 M-^ 
V-l’ 7a_ n n 2 -l ' 
