rk that the expression
"fixed star" is not an accurate one when minute quantities are held in
estimation. With the exact measures of modern instruments, many of these
quantities are so perceptible that they have to be always reckoned with
in astronomical enquiry. We can divide the movements of the stars into
two great classes: the real movements and the apparent movements. The
proper motion of the stars and the movements of revolution of the binary
stars constitute the real movements of these bodies. These movements are
special to each star, so that two stars, although close together in the
heavens, may differ in the widest degree as to the real movements which
they possess. It may, indeed, sometimes happen that stars in a certain
region are animated with a common movement. In this phenomenon we have
traces of a real movement shared by a number of stars in a certain
group. With this exception, however, the real movements of the stars
seem to be governed by no systematic law, and the rapidly moving stars
are scattered here and there indiscriminately over the heavens.

The apparent movements of the stars have a different character, inasmuch
as we find the movement of each star determined by the place which it
occupies in the heavens. It is by this means that we discriminate the
real movements of the star from its apparent movements, and examine the
character of both.

In the present chapter we are concerned with the apparent movements
only, and of these there are three, due respectively to precession, to
nutation, and to aberration. Each of these apparent movements obeys laws
peculiar to itself, and thus it becomes possible to analyse the total
apparent motion, and to discriminate the proportions in which the
precession, the nutation, and the aberration have severally contributed.
We are thus enabled to isolate the effect of aberration as completely as
if it were the sole agent of apparent displacement, so that, by an
alliance between mathematical calculation and astronomical observation,
we can study the effects of aberration as clearly as if the stars were
affected by no other motions.

Concentrating our attention solely on the phenomena of aberration we
shall describe its particular effect upon stars in different regions of
the sky, and thus ascertain the laws according to which the effects of
aberration are exhibited. When this step has been taken, we shall be in
a position to give the beautiful explanation of those