400 
MR. J. C. ADAMS ON THE SECULAR VARIATION 
will evidently change the relation between the non-periodic part of and e , upon 
which the secular acceleration depends. to the ordinary 
7. We must commence by finding the new teems to be added to ) 
expression for u. _ eccentricity of the moon’s orbit. 
For the sake of simplification we will neglect y 
Let - denote the non-periodic part of u, and the complete va 
Then by snbs.itntion in the equation for n, making use “f 
mentsof the undisturbed values of the several funet.ons of and .-r wbtch oecu, 
in it, putting h'=a„ and writing, for convenience, m, instead of \ and cm. 
instead of c' [ ' (as in Plana, vol. i. p. 322), we obtain 
''l 
1 1 -a'W-hl cos cW-| ^{l+3e' cos c'mv]a6u 
+ 2 aS ^ 2 a, ' ai ^ 
-I (2r-2Mr)+| f (l-H 
4-?l cos (2.-2»..-c'M.)-i cos (2r-2Mr+c'Mr) 
~ 4 ' > 
_?5r*|(l_|e“) sin (2,-2m,)+y sin (2r-2»n-c'M,) 
— V sin (2v-2mv + c'im) 
_9 _5gi2^ cos (2v-2mv)+le' cos {2^-2iw-c'mp) 
2 a, \\ 2 ^ - 
ig' COS (2v — 2mv-\-c'niv) a^u 
sin (2— 2»o)+| s' sin (2r-2Mr-c'Mv) 
3 ^ 
'2 
1 , 
y sin (2p-2wp-l-c'mp)j-^ 
+ 12|J*((l-|c«) sin (2.-2Mr)+|e' sin (2r-2m,-cW) 
—\e' sin (2 p— 2 wv- 1 -c'/hp)|o^w 
sin (2,-2M.)+|e'sin (2,--2,m-c'm,) 
Ic' sin (2. — 2Mr-|“CM.)j 
