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.

LUNAR PRECESSION. 207
T.... 27rt
- cos 2 I. sin 2 i. sin
4 7r or
47w T
— sin I. cos I. sini.sin — C.
87r T j
37. The first term of this expression is proportional to
the time, and, therefore, increases uniformly. The second
term is periodical; it depends upon sin, or sin Q, or
sin (180~ - longitude of Moon's ascending node), or sin longitude of Moon's ascending node. This is a part of Lunar
Nutation. The third term depends upon sin 2 long. Moon's
ascending node; it is, therefore, a part of Nutation: but its
numerical value is so small, that it is commonly neglected,
38. To obtain the lunar precession of the equinoxes,
we must, as before, divide the last expression by sin I.
Thus, we get
6 7r2 B f {2\
T' o (n + 1) cos I (cos2i - 2 sin2i). t
r cos2. 2-7rt T. sin4rt). sin 2i.s - - -cos I. sin 2.-.
47r sin I T 7 Ts
The first term, which increases uniformly, is called simply
the lunar precession; the second is the lunar equation of
the equinoxes in longitude; the third is neglected. The
lunar precession for a year is found by putting T for t;
it is, therefore,
6 r' B
T.(n + )cos I (cos2i - i sini). T.
'T (n + i)
39. PuOP. 15. To investigate the alteration in the
obliquity of the ecliptic produced by the Moon's action.
By (35), the velocity of the pole in the direction Pp, is
6 r2 B
T' w(n+ )sin q P. cos q P.
T'ioo(n+ 3 l)