402 MR* -J* C. ADAMS ON THE SECULAR VARIATION 
10. When the proper substitutions are made, the terms involving cosines destroy 
each other, as in the usual theory, and by equating to zero the terms in\oUing the 
sines, we obtain 
15 
20m"-- 3030+^^'= 0, 
or 
or 
95 , 
3a3o=X^ 
95 
aso=^nf 
3m"-|-«i6=0 .’ 
. ai6= — 3m® 
— 1 4m"— 3a33-— 
21 
^m"=0. 
133 „ 
3a33=--^m" 
133 
. . a33 — 24 
or 
2 m" —■ 3 «34 + = lb 
3a 
19 „ 19 2 
m" a3.=— m" 
34— g »«' • • '^34—24' 
11. In order to obtain the relation between a and a^, we must substitute the value 
just found for alu, in the same equation, and equate to zero the non-periodic part, 
observing that the terms 
12*!^! pj^|(l-^e'") sin (2r-2mr) + ^e' sin (2r-2mr- c'mr) 
— sin {2v — 2mv-\-c'mi/)^o^u 
give 
12m2 r, f95 ,eW 931 ^e'de! 19 eWl 
^ dde' 
1“ 
285 C iJde' , ^ 
285 ^^,2 iheji- non-periodic part. 
8 a, 
Also the terms 
15 m 
"o 
^ Dr 
«/ J 
ddd ndt 
ndt dv 
COS (2r — 2mr) 
+ 
m^ C 
^ J' 
21 m 
4 a 
3 
dv 
dv 
de' ndt i \ 
^ -^cos(2r — 2mv — cniv) . 
de' ndt 
ndt dv 
COS (2r— 2mr-f c'mr) 
of art. 9. similarly give 
{dv 
2 «, J 
1 1 „e'de' \ 
165 m^ „ . 1617 m^ , 33 
32 a 
.gfziiTJ-LiiLg'a i_ __ nearly 
^ ^ 128 a, ^128 a, ^ 
^g/2 ^g (-heir non-periodic part. 
64 a, 
