DIFFERENTIAL EQUATIONS OF ASTRONOMICAL INTEREST. 
179 
§ 20. Consider now briefly the case of the equations 
Jb x ’ Y > = r\(x,Y), 
-r n , i > 
in which n — 2. We suppose 
4n 
= \h + \k l w l + \ 2 k 2 iVo+ ..., = say, 
wv = w r +r, 
As in the case of n = 1, 
u = / -<t>, i n 4> 
\—£- n <p, <p 
Qw = /&i, c j\, 
where 
and, for n = 2, 
a, = — 
cpdr = + 
These give 
0 (-Ol + f’Ci) 
= XW(r + $-&>) +X J M 1 [(r-i) ?--+ (t+2) f-fC-JC] 
+W(-K- J +t-^+2 C-K 3 )- 
As before 
QuQu — /a 2 , c'A , 
s, ^2) Ct 2/ 
where 
«2 = I ^ (-«■! + f a Cx) dr 
= A% 2 (lT 3 + lr-K 2 + i) +X 2 M 1 (-Tr i -K- 1 + l + rf+^-K 2 -K 3 ) 
+x%» (K- 2 +fr+1 - u + f-K 3 ) 
2 B 2 
