794 
MR. G. H. DARWIN ON THE SECULAR CHANGES IN 
the symbol out of which the term arises as a suffix— e.g., we shall write Az a for the 
additional terms in the complete value of z, which arise from the variation of a. Also 
( dL/clt) a will be written for the terms in dL/clt which arise from the variation of a. 
Terms depending on the variation of a. 
We now put for a in (181) a+a'L 
Hence in (194) 
s=a'ty, u= — atz, (x=0, v=0 
Therefore 
dy 
S = a'<{ y — t\ccz — j ) S =—a'b tz 
And by substitution from (182-3) 
+ — a )}» 2i= — ct'btz 1 
Then 
So, So have similar forms with 2 for 1. 
K i 2 + pf^i = 2a \ K i — a ) ( ^=— 2a ' K i( K i— a )!h 
dt 
S 1 ^" 1 A = “ {Hi + tz l (ffi — a ) } + ( K l + a ) Z L 
=*{yi+2tK 1 Zi} 
(204) 
Hence the equation for z is 
—D%=(ff 1 + K 2 )(fc 2 +a)( 2 / 1 + 2 i/c 1 2 1 ) — 2 /c 1 (ac 1 — a^+the same with 2 for 1. 
Hence by the rules found above for the solution of such an equation 
7t AZa= 2^(/J-« 2 ) C Kl+ ^ ~ 2Kl ( Kl ~ 1 “) ~ a ) 
2 *i 1 
K l~~ K Z 2 /f l_ 
+ &C. 
2« 1 («8 + ot ) 
Ai-'g) _ 
-b&c. 
Whence 
/fj + a /f o + a 
b / \o 
\ K l~~ K 2) 
1 dZA , /q + a / 1 c/Z 2 \ , K o +a 
A dt)~ U (^ — rcf’ \L 2 dt ) a a 
. . (205) 
