so ingeniously represented by his circles. Let us take, for
instance, the most characteristic feature in the irregularities of
the outer planets. We have already remarked that Mars, though
generally advancing from west to east among the stars, occasionally
pauses, retraces his steps for awhile, again pauses, and then resumes
his ordinary onward progress. Copernicus showed clearly how this
effect was produced by the real motion of the earth, combined with
the real motion of Mars. In the adjoining figure we represent a
portion of the circular tracks in which the earth and Mars move in
accordance with the Copernican doctrine. I show particularly the
case where the earth comes directly between the planet and the sun,
because it is on such occasions that the retrograde movement (for so
this backward movement of Mars is termed) is at its highest. Mars is
then advancing in the direction shown by the arrow-head, and the
earth is also advancing in the same direction. We, on the earth,
however, being unconscious of our own motion, attribute, by the
principle I have already explained, an equal and opposite motion to
Mars. The visible effect upon the planet is, that Mars has two
movements, a real onward movement in one direction, and an apparent
movement in the opposite direction. If it so happened that the earth
was moving with the same speed as Mars, then the apparent movement
would exactly neutralise the real movement, and Mars would seem to be
at rest relatively to the surrounding stars. Under the actual
circumstances represented, however, the earth is moving faster than
Mars, and the consequence is, that the apparent movement of the
planet backwards exceeds the real movement forwards, the net result
being an apparent retrograde movement.

With consummate skill, Copernicus showed how the applications of the
same principles could account for the characteristic movements of the