riginal
length. It is always equal to about 40.9 seconds--that is, to the
diameter of the circle of aberration at the pole itself. As we proceed
further and further from the pole of the ecliptic, we find that each
star describes a path more and more eccentric, until at length, when we
examine a star on the ecliptic, the ellipse has become so attenuated
that it has flattened into a line. Each star which happens to lie on the
ecliptic oscillates to and fro along the ecliptic through an amplitude
of 40.9 seconds. Half a year accomplishes the journey one way, and the
other half of the year restores the star to its original position. When
we pass to stars on the southern side of the ecliptic, we see the same
series of changes proceed in an inverse order. The ellipse, from being
actually linear, gradually grows in width, though still preserving the
same length of major axis, until at length the stars near the southern
pole of the ecliptic are each found to describe a circle equal to the
paths pursued by the stars at the north pole of the ecliptic.

The circumstance that the major axes of all those ellipses are of equal
length suggests a still further simplification. Let us suppose that
every star, either at the pole of the ecliptic or elsewhere, pursues an
absolutely circular path, and that all these circles agree not only in
magnitude, but also in being all parallel to the plane of the ecliptic:
it is easy to see that this simple supposition will account for the
observed facts. The stars at the pole of the ecliptic will, of course,
show their circles turned fairly towards us, and we shall see that they
pursue circular paths. The circular paths of the stars remote from the
pole of the ecliptic will, however, be only seen somewhat edgewise, and
thus the apparent paths will be elliptical, as we actually find them. We
can even calculate the degree of ellipticity which this surmise would
require, and we find that it coincides with the observed ellipticity.
Finally, when we observe stars actually moving in the ecliptic, the
circles they follow would be seen edgewise, and thus the stars would
have merely the linear movement which they are seen to possess. All the
observed phenomena are thus found to be completely consistent with the
supposition that every star of all the millions in the heavens describes
once each year a circular path; and that, whether the star be far or
near, this circle has always the same apparent diameter, and