3. CALIPPUS.
The challenge was soon taken up, for twenty or thirty years later one of the pupils of Eudoxus, Calippus of Cyzicus, undertook to improve the system. The defects in the theories of Mars and Venus had evidently been discovered, for Calippus added another sphere to each of these, as well as one to Mercury, which would be quite enough to bring the theories into better agreement with the facts.
With regard to the sun and moon, Calippus had paid special attention to their movements, for he made an improvement in the old luni-solar cycle of Meton, to which we shall return later. Eudoxus had ignored a very important fact discovered by Meton and Euctemon about b.c. 430, viz.: that the seasons are of unequal length, showing that the sun takes unequal times to pass over the four arcs of his orbit lying between the four points of the vernal and autumnal equinoxes and the summer and winter solstices. “Why,” exclaims a later writer[35] “are there unequal numbers of days in the four seasons, seeing that the course of the heavenly bodies must be regular, not being swayed by human passions or affairs?”
Calippus considered this question very seriously, and made a careful determination of the length of the four seasons. It seems at first sight impossible to reconcile their inequality with uniform circular motion of the sun round the earth, but he found that he could do it by adding two more spheres to the sun’s set, rotating uniformly but so arranged that their motion, added to the others, would result in an actual velocity in the sun itself varying just in the way required by the facts. The same had to be done for the moon, for the same reason, so the number of spheres, which Eudoxus had made twenty-seven, was brought up to thirty-four (including the star sphere). The varying velocity of the five planets had not yet been perceived.[36]