sun and the earth. The circle, however, in which Mercury actually
revolved had to be smaller than that of Venus, in order to account
for the fact that Mercury lies always much closer to the sun than the
better-known planet.

[FIG. 2. PTOLEMY'S THEORY OF THE MOVEMENT OF MARS.]

The explanation of the movement of an outer planet like Mars could
also be deduced from the joint effect of two perfect motions. The
changes through which Mars goes are, however, so different from the
movements of Venus that quite a different disposition of the circles
is necessary. For consider the facts which characterise the
movements of an outer planet such as Mars. In the first place, Mars
accomplishes an entire circuit of the heaven. In this respect, no
doubt, it may be said to resemble the sun or the moon. A little
attention will, however, show that there are extraordinary
irregularities in the movement of the planet. Generally speaking, it
speeds its way from west to east among the stars, but sometimes the
attentive observer will note that the speed with which the planet
advances is slackening, and then it will seem to become stationary.
Some days later the direction of the planet's movement will be
reversed, and it will be found moving from the east towards the
west. At first it proceeds slowly and then quickens its pace, until
a certain speed is attained, which afterwards declines until a second
stationary position is reached. After a due pause the original
motion from west to east is resumed, and is continued until a similar
cycle of changes again commences. Such movements as these were
obviously quite at variance with any perfect movement in a single
circle round the earth. Here, again, the geometrical sagacity of
Ptolemy provided him with the means of representing the apparent