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.

EXPLANATION OF EVECTION. 51
position and eccentricity of the Moon's orbit is so remarkable, that we shall here consider it a little more generally
than in Art. 63.
66. Pnof. 27. To determine the change in the position
of the axis, and in the eccentricity of the Moon's orbit,
produced by the evection.
The elliptic inequality and evection, in the expression
for u, are together represented by
e {cos (cO - a) + -m cos (2 - 2m - c) 0 - 2 + a},
8
where a = longitude of perigee if there were no evection,
3 =longitude of the Sun when 0=. During a part of
one revolution, we may, without great error, suppose the
perigee and the Sun to be stationary: then, for cO -a,
we must put 0-a; and for (2-2m) -2/3-(cO-a),
or twice the distance of the Sun and Moon- the Moon's
anomaly, we must put
(20 - 23) - (O - a) = (0 - a) + (2a - 23).
And the united inequalities
= e cos ( -a) + m-.cos (0 - a) + 2 (a - /)}
8
15
= e 1 + o sn. cos 2 (a - 3)}. cos ( - a)
15
- e. — m. si 2 (a -3). sin (0 - a).
8
This may be put under the form E cos (0 - a - 3), if
15
E cos = e { + - m.cos 2 (a - )I}
8
15
E sin < = e - m. sin 2 (a -/3).
8
4-2