[FIG. 1. PTOLEMY'S PLANETARY SCHEME.]

These movements were wholly incompatible with the supposition that
the journeys of Venus were described by a single motion of the kind
regarded as perfect. It was obvious that the movement was connected
in some strange manner with the revolution of the sun, and here was
the ingenious method by which Ptolemy sought to render account of
it. Imagine a fixed arm to extend from the earth to the sun, as
shown in the accompanying figure (Fig. 1), then this arm will move
round uniformly, in consequence of the sun's movement. At a point P
on this arm let a small circle be described. Venus is supposed to
revolve uniformly in this small circle, while the circle itself is
carried round continuously by the movement of the sun. In this way
it was possible to account for the chief peculiarities in the
movement of Venus. It will be seen that, in consequence of the
revolution around P, the spectator on the earth will sometimes see
Venus on one side of the sun, and sometimes on the other side, so
that the planet always remains in the sun's vicinity. By properly
proportioning the movements, this little contrivance simulated the
transitions from the morning star to the evening star. Thus the
changes of Venus could be accounted for by a Combination of the
"perfect" movement of P in the circle which it described uniformly
round the earth, combined with the "perfect" motion of Venus in the
circle which it described uniformly around the moving centre.

In a precisely similar manner Ptolemy rendered an explanation of the
fitful apparitions of Mercury. Now just on one side of the sun, and
now just on the other, this rarely-seen planet moved like Venus on a
circle whereof the centre was also carried by the line joining the