this particular observation is the best evidence that could be given
of the difficulties that stood in the way of a true explanation of the
mechanism of the heavens.

But it is not merely the sun which was observed to vary in the speed
of its orbital progress; the moon and the planets also show curious
accelerations and retardations of motion. The moon in particular
received most careful attention from Hipparchus. Dominated by his
conception of the perfect spheres, he could find but one explanation of
the anomalous motions which he observed, and this was to assume that
the various heavenly bodies do not fly on in an unvarying arc in their
circuit about the earth, but describe minor circles as they go which can
be likened to nothing so tangibly as to a light attached to the rim of
a wagon-wheel in motion. If such an invisible wheel be imagined as
carrying the sun, for example, on its rim, while its invisible hub
follows unswervingly the circle of the sun's mean orbit (this wheel, be
it understood, lying in the plane of the orbit, not at right-angles to
it), then it must be obvious that while the hub remains always at the
same distance from the earth, the circling rim will carry the sun nearer
the earth, then farther away, and that while it is traversing that
portion of the are which brings it towards the earth, the actual forward
progress of the sun will be retarded notwithstanding the uniform motion
of the hub, just as it will be accelerated in the opposite arc. Now, if
we suppose our sun-bearing wheel to turn so slowly that the sun revolves
but once about its imaginary hub while the wheel itself is making the
entire circuit of the orbit, we shall have accounted for the observed
fact that the sun passes more quickly through one-half of the orbit than
through the other. Moreover, if we can visualize the process and imagine
the sun to have left a visible line of fire behind him throughout the
course, we shall see that in reality the two circular motions involved
have really resulted in producing an elliptical orbit.

The idea is perhaps made clearer if we picture the actual progress of
the lantern attached to the rim of an ordinary cart-wheel. When the cart
is drawn forward the lantern is made to revolve in a circle as regards
the hub of the wheel, but since that hub is constantly going forward,
the actual path described by the lantern is not a circle at all but a
waving line. It is precisely the same with the imagined co