476 A MEMOIR ON THE PROBLEM OF THE ROTATION OF A SOLID BODY. [217 
I. 
In the theory of elliptic motion, where the elements are 
а, the mean distance, 
e, the eccentricity, 
g, the mean anomaly, 
ct, the departure of pericentre, 
б, the longitude of node, 
a, the departure of node, 
(f), the inclination, 
and if, besides, we have 
n, the mean motion (n 2 a 3 = sum of the masses), 
and CL denote the disturbing function taken with Lagrange’s sign (CL = — R, if R be 
the disturbing function of the Mécanique Céleste), then the formulae for the variations 
of the elements are 
dt, 
da = 
2 
na 
dC- 7. 
-7— dt, 
dg 
de = 
1 — e 2 
na 2 e 
%Ldt 
dg 
Vl — e 2 dCl 
na 2 e dta 
dg = 
2 
na 
dCl , 
-7— dt 
da 
1 — e 2 dCl 
na?e de 
dsr = 
Vl — e 2 dCl 
na?e de 
1 
II 
^5 
cot 
^dt- 
da 
cosec (f) dCl 
na 2 Vl — e 2 
na 2 Vl - e 2 dO 
da — 
COt (f) 
~ dt 
d(f> 
na 2 V1 — e 2 
dd = 
cosec (p 
7, 
d<\> ’ 
na 2 V1 — e 2 
dt, 
’ dt, 
where O = CL (a, e, g, tz, $, a, 6). 
And if in these equations we write 
h = — - (sum of the masses) = — n 2 a 2 ,