Fig. 19. The spheres of the sun in the system of Eudoxus.
The outer sphere turns on its axis A A in a day and night; the inner on its axis a a in a year, in the opposite direction.
The planetary spheres were much more difficult to arrange. Eudoxus used four spheres for each, and these had in every case to be carefully adjusted to the very different periods and amplitudes of the planetary oscillations. It must be confessed that the scheme failed with the difficult case of Mars, and was not quite satisfactory with Venus, but it represented remarkably well the movement—so far as then known—of Sun and Moon, Saturn, Jupiter, and Mercury. It was certainly a feat for those days, whether we consider it merely as the solution of a mathematical problem, or as an embodiment of astronomical knowledge. The periods of the planets as known to Eudoxus, stated in round numbers only, are given in the following table. They are taken from Simplicius, who describes the system of Eudoxus, but as in the so-called Papyrus of Eudoxus the synodical revolution of Mercury is given as 116 days, the same as the modern value, Eudoxus may have had much more exact data. It will be seen that his synodic period for Mars is the only one which is totally wrong, and the large error is difficult to explain.
| Planet. | Synodic Period. | Modern Value. | Zodiacal Peroid. [34] | Modern Value. |
|---|---|---|---|---|
| Mercury | 110 days | 116 days | 1 year | 1.0 year |
| Venus | 19 months | 584 ” | ” | 1.0 ” |
| Mars | 8 months, 20 days | 780 ” | 2 years | 1.88 ” |
| Jupiter | 13 months | 399 ” | 12 ” | 11.86 ” |
| Saturn | 13 months | 378 ” | 30 ” | 29.46 ” |
It is disappointing, after the splendid hypotheses of the Pythagoreans, to be back again on a central stationary Earth among mechanical contrivances for moving the heavenly bodies, which remind us of Anaximander’s series of hemispherical heavens and heavenly wheels, but at least the earth is spherical, owing to the Pythagoreans, and the sky extends like a sphere all round, and we shall never have a flat Earth or a hemispherical sky again among the Greeks. We do not know whether Eudoxus regarded his spheres as convenient mathematical abstractions only, or whether he reasoned that the stars were evidently set in an invisible uniformly rotating sphere, and Plato considered this kind of movement the most suitable for all heavenly bodies; that therefore he would try whether a series of similar spheres interacting on one another would account for the complicated motions of a planet, and finding that they would, taught that they must truly exist. In any case the basis of his system was a detailed knowledge of planetary motions hitherto unapproached by the Greeks, and its chief merit was that it challenged comparison with the skies.
3. CALIPPUS.
Calippus c. 330 b.c.
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?”