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.

LONGITUDE DESCRIBED IN GIVEN TIME. 1l
3e e e.'. / = sin + (2 — sin 3z) -
4 3 1
oe 9e e2
+ (4 sin 2z + -sin z —. sin 3) -
2 2 2
+ (18 sin 3 - 6 sin ) -
6
/ \. 5e' 13 e
= Z -+ (2e - -sin +-sin 2z +- e. sin z,
\ 4 4 12
4)4
carrying the approximation as far as e3.
Or O-B =nt+ e-B 2e- ( — ) sinnt+c-B
- sin 2nt + 2e - 2B +- e3 sin 3nt + 3e - 3B + &c.
4 12
19. The mean anomaly, then, is that part of the true
anomaly, which is independent of periodical terms, as sines
or cosines. This is the usual signification of the word mean,
in Astronomy.
The expression for 0 is
/ é\ - --— e 5e'
nt+e+ 2e - sinnt+ e -B+ sin2nt+2e - 2 B+&c.
\ 47 4
0 being called the longitude, or the true longitude, nt + e
(in conformity with the remark above) is called the mean
longitude. The aggregate of the terms following nt + e is
called the equation of the center.