THE PREDECESSORS OF COPERNICUS. 331 



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 for- 

 wards 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 repre- 

 sented. The explanation given by Ptolemy is complete and satisfac- 

 tory. 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 com- 

 pletely and accurately by supposing that the centers of their epicycles 

 revolved round the circumferences of their deferents in 36514 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 ex- 

 plained. Irregularities in the moon's motion were explained by sup- 

 posing 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 solu- 

 tion to the others. He never sought, it seems, for a single law gov- 

 erning 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 



