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.

SOLAR NUTATION. 203
The first term is the uniform precession; the second is the
correction to be applied to it, called the Solar Equation
of the Equinoxes in longitude.
31. PROP. 12. To investigate the change in the obliquity of the ecliptic, produced by the Sun's action on
the Earth.
In (28) it was found that the velocity of the pole in
the direction Pp (fig. 7) is
SsinSP. cos SP;
r3w
therefore, its velocity in the direction PQ
sin SP. cos SP. sin SPC.
r3
But sin SP. sin SPC sin SC = cos l;
cos SP = cos PC. cos SC = sin I. sin;
therefore the motion in the direction PQ, or the diminution
of the inclination,
3B. S sin I. cos 1
= ssin I
d dt r.
which, as in (28), is changed into
6-*. B sin If sin l cos 1(1 + e cos I - k).
Tw
Neglecting, as before, the terms depending on e, this is
3 r. B cos 21
- — ï^.- sin I
Tw 2
or, if I be the mean inclination, the true inclination
3 r. B. cos 2
I + sin I. —
The term added to I is the second part of Solar Nutation.