Mathematical tracts on the lunar and planetary theories, the figure of the earth, precession and nutation, the calculus of variations, and the undulatory theory of optics.

VARIATION OF EPOCH. 95
dR da dR de, dR d'r, dR f dn, de
O-= -+-.- +.-+da ' dt de dt di dt de t dt dt)
Substituting the values of d d- from (107),
dn, SI da,
(110), and (115), and putting for -' its value -— '.
dt 2a~ dt
3n2a dR
or
u * de'
dR
and dividing the whole by d '
de, 3n2a dR 2n a2 dR
- — __ __ _, t + _
dt fM de M da
n^ta ddc+.
- {2/(1 - e2) - (1 - e2)} dR
ede'
118. PROP. 46. To calculate the longitude of a disturbed planet.
For convenience of reference, we will collect here the
expressions for the variations of the elements.
da ona2 dR
a,u-. (107)
dt gu de
dn 3Sn'a dR
dt u de
de, na dR na(i - e') d R dR\
d ( _ - e2). d R ( — (110)
dt pMe de Me de dr)
dwl nna d R
dt ue de
de, 3n2a dR 2a- 2 dR na 2 dR
i_.~ — t + ~~. 1 _ ë,_- dR (117).
dt - de ' da /e de
When R is developed, the values of a,, n, e,, r, and e,,
are to be found from these expressions: and they are then
to be substituted in the series