212] 
A MEMOIR ON THE PROBLEM OF DISTURBED ELLIPTIC MOTION. 
275 
The disturbed equations may be dealt with in the usual manner by the method 
of the variation of the elements, and attending only to the variations of the elements 
we have 
dr 
= 0, 
dv 
= 0, 
dy 
= 0, 
y dr 
_ dü, 
d dt 
dr 
dv\ 
_ dn 
y dt) 
dv 
_dCl 
dt) 
~ dy 
dt, 
or, what is the same thing, 
dr = 0, 
dv = 0, 
dy = 0, 
j nae sin f _ dVL ^ 
Vl - e 2 ~ dr 
d na 2 V1 — e 2 cos d> = ^ dt, 
dv 
_ dci 
dnos'd 1 — e 2 sin d> cos x — - T -dt, 
dy 
where as before 12 = Q (r, v, y). 
In virtue of the relations dv =0, dy= 0, we have the above-mentioned equations, 
dx = — tan 2 cosec cf) dcf>, 
dz = — tan 2 cot (f) dcf), 
dz = cos (p dx, 
dx = — d6, 
dr + cos (f>d0 = 0, 
d sin <f> cos x = — sin cf> sin x dx + cos x cos <£ dcf), 
= cos x cos cf) sec 2 z d<p, 
= sec x cos </> sec 2 y dcf>; 
we have 
and the last two equations for the variations become 
d na 2 Vl — e" cos cf) — na 2 VI — e 2 sin cf> dcf) 
(№ 
dv 
dD, 
dt, 
d na 2 Vl — e- sin cf) cos x -f na 2 Vl — e 2 sec x cos cf) sec 2 y dcf> — dt, 
35—2