Page:A short history of astronomy(1898).djvu/114

70 and rapidity of motion of the epicycle. It is moreover evident that with this arrangement the apparent motion of Jupiter will vary considerably, as the two motions—that on the epicycle and that of the centre of the epicycle on the deferent—are sometimes in the same direction, so as to increase one another's effect, and at other times in opposite directions. Thus, when Jupiter is most distant from the earth, that is at 3, the motion is most rapid, at 1 and 2 the motion as seen from the earth is nearly the same as that of j; while at 4, the two motions are in

opposite directions, and the size and motion of the epicycle having been chosen in the way indicated above, it is found in fact that the motion of the planet in the epicycle is the greater of the two motions, and that therefore the planet when in this position appears to be moving from east to west (from left to right in the figure), as is actually the case. As then at 1 and 2 the planet appears to be moving from west to east, and at 4 in the opposite direction, and sudden changes of motion do not occur in astronomy, there must be a position between 1 and 4, and another between 4 and 2, at which the planet is just reversing its direction of motion, and therefore appears for the instant at rest. We thus arrive at an explanation of the stationary points (chapter, § 14). An exactly similar scheme explains roughly the motion of Mercury and Venus, except that the centre of the epicycle must always be in the direction of the sun.

Hipparchus, as we have seen (§ 41), found the current representations of the planetary motions inaccurate, and collected a number of fresh observations. These, with fresh observations of his own, Ptolemy now employed in order to construct an improved planetary system.