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.

192 PRECESSION AND NUTATION.
15. If the force which acts upon the body be nearly,
but not exactly, uniform, and if the axes about which it
tends to produce motion, be not contained in the plane
BAC, then the propositions above will be nearly, but not
exactly, true. The line traced on the spherical surface in
Prop. 5, by the successive poles of rotation, will be a spiral
approaching very nearly to a circle: the change of position
of the axis in space at every instant, will be in the plane
passing through the axis of rotation and the axis of impressed motion at that instant; and the velocity of the change,
though not uniform, will be at that instant -.
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ON PRECESSION AND NUTATION.
16. PROP. 6. To explain the physical cause of solar
precession, and solar nutation.
Let A, (fig. 4), be the Earth's center; AB the axis of
rotation; S the Sun; CHG the equator of the terrestrial
spheroid; CAG that diameter of the equator, which is perpendicular to AS; and suppose the Earth to be in the
position which it has at the summer solstice. In the succeeding investigations, which relate only to the motion of
the Earth about its center of gravity, we may suppose the
center of gravity to be kept at rest, and the motion of
the Earth about this point will be the same as if we supposed it moving freely, (Whewell On the motion of Points
constrained, -c. Art. 269, Earnshaw's Dynamics, Art. 137,
Poisson, Mecanique, 402). Suppose, then, A the Earth's
center, to be at rest; and consider the effect which the
Sun's attraction would then produce on the Earth. If the
Earth were spherical, it is evident that the Sun's attraction
would have no tendency to give the Earth any rotation
about the center A. But the Earth is an oblate spheroid;
we must, therefore, consider the effect produced by the
Sun's attraction on the parts of the spheroid which are
exterior to the sphere that touches the spheroid at its
poles. Now the Sun's attraction is inversely as the square
of the distance of the matter attracted; and, consequently,