290 
A MEMOIR ON THE PROBLEM OF DISTURBED ELLIPTIC MOTION. [212 
da — 
de = 
dg = 
dt = 
d(f> = 
de = 
The formulae for the variations thus become 
2 dft 
y- dt, 
na dg 
1 — e 2 dft 7 , VÎ — e 2 dft ,, 
—ô—dt dt, 
na 2 e dg na-e do 
2 dft^ 1 -e 2 d£l^ 
j— dt— —5--j- dt, 
na da na-e cle 
Vl — e 2 dCl 7 
r y~ dt 
na-e de 
na 
cot (f) d£l 
VÏ — e 2 d<f> 
dt, 
cot (f) dVl 
na 2 Vl — e 2 dt 
dt 
cosec (j) dft 
net 
,2 Vl - e 2 d0 
dt, 
cosec <£ dft , 
nn n - Vi _ ¿> dd) ’ 
where, as before, ft = il (a, e, g, t, 0, <fi). This is the second system of formulæ for 
the variations of the six elements a, e, g, t, 0, (f>. 
The last-mentioned system may be easily deduced from Jacobi’s canonical system 
of formulæ, viz. putting 
21, the constant of vis viva, 
2?, the constant of areas, 
(5, the constant of the reduced area, 
the constant attached to the time, 
the angular distance of pericentre from node, 
«£), the longitude of node ; 
dîl = 
dft 
dg 
dt, 
d23 = 
d® = 
dft 
d® 
dft 
dé 
dt, 
dt, 
d%=- 
d® = - 
dSl 
dîl 
da 
d93 
dt, 
dt, 
d^ = - 
dn 
d(S 
dt, 
then the canonical system is