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.

194 PRECESSION AND NUTATION.
nation of the axis of rotation to the axis of the ecliptic,
and sometimes diminishes it; but, (as we shall shew hereafter), does not permanently alter it. This phenomenon is
one part of solar nutation. The angular motion of the
axis of rotation, about the axis of the ecliptic, is always
in the same direction; but as the action of the Sun is
different in different positions of the Eartb, and is o at
the equinoxes, this angular motion or precession is irregular. The correction, which it is necessary to apply to a
uniform precession, is the other part of solar nutation.
19. PROP. 7. To explain the physical cause of lunar
precession, and lunar nutation.
Since the Moon describes, (very nearly), a great circle
about the Earth in a month, in the same manner as the
Sun in a year, the same explanation which has been given
for the precession and nutation produced by the Sun in a
year, will apply to those produced by the Moon in a month.
But the monthly nutation produced by the Moon is so small,
that it is very seldom considered, Since, however, the magnitude and direction of the permanent precession, produced
by the Sun, depend upon the inclination of the Earth's
axis to the axis of the ecliptic, or the axis of the Sun's
apparent orbit, it is easy to see, that the magnitude and
direction of the precession, produced by the Moon in one
month, depend upon the inclination of the Earth's axis to
the axis of the Moon's orbit. Now this is perpetually
varyirig; the axis of the Moon's orbit revolves about the
axis of the ecliptic in about 18 years, 7 months, with a motion nearly uniform, and preserving nearly a constant inclination. The velocity and direction of the motion of the
Earth's axis, produced by the Moon, are, therefore, irregular.
We shall shew, that the precessional motion, though irregular, is permanent; but that the alteration in the inclination
to the axis of the ecliptic is periodical; the inclination returning to its former value, in a revolution of the Moon's
nodes. This change in the inclination is one part of lunar
nutation; the other part is the correction which must be
applied to the mean precession, in order to find the true.