t of precession is due to the sun, and two-thirds to the moon.
For the study of the joint precessional effect due to the sun and the
moon acting simultaneously, it will be advantageous to consider the
effect produced by the two bodies separately; and as the case of the sun
is the simpler of the two, we shall take it first. As the earth travels
in its annual path around the sun, the axis of the earth is directed to
a point in the heavens which is 23-1/2 deg. from the pole of the ecliptic.
The precessional effect of the sun is to cause this point--the pole of
the earth--to revolve, always preserving the same angular distance from
the pole of the ecliptic; and thus we have a motion of the type
represented in the diagram. As the ecliptic occupies a position which
for our present purpose we may regard as fixed in space, it follows that
the pole of the ecliptic is a fixed point on the surface of the heavens;
so that the path of the pole of the earth must be a small circle in the
heavens, fixed in its position relatively to the surrounding stars. In
this we find a motion strictly analogous to that of the peg-top. It is
the gravitation of the earth acting upon the peg-top which forces it
into the conical motion. The immediate effect of the gravitation is so
modified by the rapid rotation of the top, that, in obedience to a
profound dynamical principle, the axis of the top revolves in a cone
rather than fall down, as it would do were the top not spinning. In a
similar manner the immediate effect of the sun's attraction on the
protuberance at the equator would be to bring the pole of the earth's
axis towards the pole of the ecliptic, but the rapid rotation of the
earth modifies this into the conical movement of precession.
The circumstances with regard to the moon are much more complicated.
The moon describes a certain orbit around the earth; that orbit lies in
a certain plane, and that plane has, of course, a certain pole on the
celestial sphere. The precessional effect of the moon would accordingly
tend to make the pole of the earth's axis describe a circle around that
point in the heavens which is the pole of the moon's orbit. This point
is about 5 deg. from the pole of the ecliptic. The pole of the earth is
therefore solicited by two different movements--one a revolution around
the pole of the ecliptic, the other a revolution about another point 5 deg.
distant, which is the pole of the moon's orbit. It would thus seem that
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