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.

EQUATIONS OF MOTION.6
dR
where it must be recollected that d- means the differential
coefficient with respect to 0, only so far as 0, is explicitly
contained in R, and not considering r, as depending on Q,.
83. These two equations (analogous to those employed
iii the elliptic theory and in the lunar theory) are sufficient
for solution of the problem, but the following is convenient.
Since r,2 = m2 + y2, we find by differentiating twice,
d2(rl2) (d\ (d\
dt"2 2 d \ dtj
But ) + or \ dt or2
\dt, \dt + dt \dt
lias been found
=_ + 2 d(R)}
d +'d t dt
d, d'à. d9y X y~
- - r. cos - --. r sin
r, d ' ' dy;n dR.., 'dr,
Consequently
d2 (r,2) _ d(R) dR
îd' -o - -=(C? 4 +/ - - 2 r. —.
dt" = ' dr,
84. The value of R, as will be found on substituting
for r, y, x', and y', their values, is
n?, ' r, cos (0'- 0,)
\/., c'-_.,, os (0' - _,) + -,c ~ + "
5