movements of Mars, and, at the same time, restricting the explanation
to those perfect movements which he deemed so essential. In Fig. 2
we exhibit Ptolemy's theory as to the movement of Mars. We have, as
before, the earth at the centre, and the sun describing its circular
orbit around that centre. The path of Mars is to be taken as
exterior to that of the sun. We are to suppose that at a point
marked M there is a fictitious planet, which revolves around the
earth uniformly, in a circle called the DEFERENT. This point M,
which is thus animated by a perfect movement, is the centre of a
circle which is carried onwards with M, and around the circumference
of which Mars revolves uniformly. It is easy to show that the
combined effect of these two perfect movements is to produce exactly
that displacement of Mars in the heavens which observation
discloses. In the position represented in the figure, Mars is
obviously pursuing a course which will appear to the observer as a
movement from west to east. When, however, the planet gets round to
such a position as R, it is then moving from east to west in
consequence of its revolution in the moving circle, as indicated by
the arrowhead. On the other hand, the whole circle is carried
forward in the opposite direction. If the latter movement be less
rapid than the former, then we shall have the backward movement of
Mars on the heavens which it was desired to explain. By a proper
adjustment of the relative lengths of these arms the movements of the
planet as actually observed could be completely accounted for.

The other outer planets with which Ptolemy was acquainted, namely,
Jupiter and Saturn, had movements of the same general character as
those of Mars. Ptolemy was equally successful in explaining the
movements they performed by the supposition that each planet had
perfect rotation in a circle of its own, which circle itself had