THE PYTHAGOREANS.

We have seen that Pythagoras was the first to give spherical form to the earth and probably to the heavenly bodies generally, and to assign to the planets a revolution of their own in a sense opposite to that of the daily rotation of the fixed stars about the earth as centre.

But a much more remarkable development was to follow in the Pythagorean school. This was nothing less than the abandonment of the geocentric hypothesis and the reduction of the earth to the status of a planet like the others. The resulting system, known as the Pythagorean, is attributed (on the authority probably of Theophrastus) to Philolaus; but Diogenes Laertius and Aëtius refer to one Hicetas of Syracuse in this connection; Aristotle attributes the system to “the Pythagoreans”. It is a partial anticipation of the theory of Copernicus but differs from it in that the earth and the planets do not revolve round the sun but about an assumed “central fire,” and the sun itself as well as the moon does the same. There were thus eight heavenly bodies, in addition to the sphere of the fixed stars, all revolving about the central fire. The number of revolutions being thus increased to nine, the Pythagoreans postulated yet another, making ten. The tenth body they called the counter-earth, and its character and object will appear from the following general description of the system.

The universe is spherical in shape and finite in size. Outside it is infinite void, which enables the universe to breathe, as it were. At the centre is the central fire, the Hearth of the Universe, called by various names such as the Tower or Watch-tower of Zeus, the Throne of Zeus, the Mother of the Gods. In this central fire is located the governing principle, the force which directs the movement and activity of the universe. The outside boundary of the sphere is an envelope of fire; this is called Olympus, and in this region the elements are found in all their purity; below this is the universe. In the universe there revolve in circles round the central fire the following bodies: nearest to the central fire the counter-earth which always accompanies the earth, then the earth, then the moon, then the sun, next to the sun the five planets, and last of all, outside the orbits of the planets, the sphere of the fixed stars. The counter-earth, which accompanies the earth but revolves in a smaller orbit, is not seen by us because the hemisphere on which we live is turned away from the counter-earth. It follows that our hemisphere is always turned away from the central fire, that is, it faces outwards from the orbit towards Olympus (the analogy of the moon which always turns one side towards us may have suggested this); this involves a rotation of the earth about its axis completed in the same time as it takes the earth to complete a revolution about the central fire.

Although there was a theory that the counter-earth was introduced in order to bring the number of the moving bodies up to ten, the perfect number according to the Pythagoreans, it is clear from a passage of Aristotle that this was not the real reason. Aristotle says, namely, that the eclipses of the moon were considered to be due sometimes to the interposition of the earth, sometimes to the interposition of the counter-earth. Evidently therefore the purpose of the counter-earth was to explain the frequency with which eclipses of the moon occur.

The Pythagoreans held that the earth, revolving, like one of the stars, about the central fire, makes night and day according to its position relatively to the sun; it is therefore day in that region which is lit up by the sun and night in the cone formed by the earth’s shadow. As the same hemisphere is always turned outwards, it follows that the earth completes one revolution about the central fire in a day and a night or in about twenty-four hours. This would account for the apparent diurnal rotation of the heavens from east to west; but for parallax (of which, if we may believe Aristotle, the Pythagoreans made light), it would be equivalent to the rotation of the earth on its own axis once in twenty-four hours. This would make the revolution of the sphere of the fixed stars unnecessary. Yet the Pythagoreans certainly gave some motion to the latter sphere. What it was remains a puzzle. It cannot have been the precession of the equinoxes, for that was first discovered by Hipparchus (second century B.C.). Perhaps there was a real incompatibility between the two revolutions which was unnoticed by the authors of the system.