277 
212] A MEMOIR OX THE PROBLEM OF DISTURBED ELLIPTIC MOTIOX. 
which may be replaced by 
cZr 
= 0, 
cZ0 
cosec cp 
dil 
c?£, 
m 2 V1 — e 2 
clip 
dz 
— cot 0 
dn 
c?i, 
no 2 V1 — e 2 
d(f> 
7 me sin/ 
cm 
Vi ■ 
- e 2 
dr 
dna? V1 
— e 2 
= 
did 
cie 
cZi, 
dcp 
COt£ 
cm 
c&, 
m 2 Vl — e 2 
cZ$ 
where as before il = il (r, z, 0, cp). 
I remark that in the case of any central force whatever, we have an element h 
corresponding to no? Vl — 6 2 in the elliptic theory, and the system for the variations is 
dr = 0, 
7/1 cosec 6 dfl 7 . 
dd = —TT dt, 
h, dcp 
where il = O (r, z, 6, cp). 
dz = 
— cot <f> cm 7 
A cZ</> ’ 
dr 
dt 
dil j. 
df dt • 
dli = 
did 
S dt ’ 
dcf) = 
cot # <m 7 , 
T 
Imagine a point in the orbit, which I call the departure-point, the angular 
distances from this point are termed departures. And I write 
ji, the departure of planet, 
tn-, the departure of pericentre, 
cr, the departure of node, 
so that we have 
J> =™+f, 
z = ]? — cr, 
C = tsr — cr.