y only describes a
comparatively small cone of 5 deg. in radius, we may for a first
approximation take the average position which it occupies; but this
average position is, of course, the centre of the circle which it
describes--that is, the pole of the ecliptic.

We thus see that the average precessional effect of the moon simply
conspires with that of the sun to produce a revolution around the pole
of the ecliptic. The grosser phenomena of the movements of the earth's
axis are to be explained by the uniform revolution of the pole in a
circular path; but if we make a minute examination of the track of the
earth's axis, we shall find that though it, on the whole, conforms with
the circle, yet that it really traces out a sinuous line, sometimes on
the inside and sometimes on the outside of the circle. This delicate
movement arises from the continuous change in the place of the pole of
the moon's orbit. The period of these undulations is 18-2/3 years,
agreeing exactly with the period of the revolution of the moon's nodes.
The amount by which the pole departs from the circle on either side is
only about 9.2 seconds--a quantity rather less than the
twenty-thousandth part of the radius of the sphere. This phenomenon,
known as "nutation," was discovered by the beautiful telescopic
researches of Bradley, in 1747. Whether we look at the theoretical
interest of the subject or at the refinement of the observations
involved, this achievement of the "Vir incomparabilis," as Bradley has
been called by Bessel, is one of the masterpieces of astronomical
genius.

The phenomena of precession and nutation depend on movements of the
earth itself, and not on movements of the axis of rotation within the
earth. Therefore the distance of any particular spot on the earth from
the north or south pole is not disturbed by either of these phenomena.
The latitude of a place is the distance of the place from the earth's
equator, and this quantity remains unaltered in the course of the long
precession cycle of 26,000 years. But it has been discovered within the
last few years that latitudes are subject to a small periodic change of
a few tenths of a second of arc. This was first pointed out about 1880
by Dr. Kuestner, of Berlin, and by a masterly analysis of all available
observations, made in the course of many years past at various
observatories, Dr. Chandler, of Boston, has shown that the latitude of
every point on the earth is subject to a doub