epicycle moves to the left or right. Hence the planet will appear to an observer to be moving in a retrograde direction—east to west. The epicyclic motion combined with the motion of the epicycle forwards along the deferent will produce first the retrograde and (in the last quadrant of the epicycle) again the direct motion of the planet in the sky. By taking the diameter of the epicycle of an appropriate size all the circumstances of the apparent motion of Jupiter can be represented. The explanation given by Ptolemy is complete and satisfactory. The general motion of the planet around the sky in twelve years is explained by the motion along the deferent. Its retrogradations and stations are explained by the combination of its epicyclic motion with its general motion. A like explanation serves for the other superior planets, Mars and Saturn.
The Inferior Planets.—The inferior planets, Mercury and Venus, appear sometimes east of the sun, sometimes west of it, but are never very far distant from the sun. We see them at sunset and sunrise as the morning and evening stars, Hesperus and Phosphorus, always in the sun's vicinity. Ptolemy explained their apparent motions completely and accurately by supposing that the centers of their epicycles revolved round the circumferences of their deferents in 3651⁄4 days; and that Mercury revolved round the circumference of its epicycle in 88 days, Venus round the circumference of its epicycle in 225 days. The sizes of the epicycles were chosen to correspond to the amount of each planet's greatest elongation from the sun. In the foregoing summary explanation only the main phenomena are described and explained. Irregularities in the moon's motion were explained by supposing that the earth did not lie at the center of the moon's orbit, but to one side; and other irregularities in the motions of the sun and planets were explained in a similar way. All motions took place in circles; the circle was the only 'perfect' curve. But the circles were eccentrics; the earth did not lie at their centers.
The periods of revolution of the planets were known to Ptolemy, but he knew little of their distances and nothing of their actual dimensions. The moon, he knew, shone by reflected light from the sun and he explained the lunar phases in this way, as is done to-day. The planets he supposed to shine by their own light, just as the fixed stars do. Astronomy to-day asserts that the planets, like the moon, shine by reflected light, and that the fixed stars are suns situated at immense distances.
Ptolemy solved the problem of the universe by solving the problem of the motion of each planet separately and by annexing each solution to the others. He never sought, it seems, for a single law governing all the cases. But such a law is patent. The radii of the epicycles of the superior planets are always parallel to the line joining the earth and the sun. The deferents of Mercury and Venus were
