The fifth sphere, carrying Mars, accomplished its revolution in two years. Jupiter took 11 years, 313 days, and 19 hours to complete his orbit, and Saturn in the seventh sphere took 29 years and 169 days. Above all the planets came the sphere of the fixed stars, or Firmament, turning from east to west in 24 hours with inconceivable rapidity, and endued also with a proper motion from west to east, which was measured by Hipparchus, and which we now call the precession of the equinoxes, and know that it has a period of 25,870 years. Above all these spheres, a primum mobile gave motion to the whole machine, making it turn from east to west, but each planet and each fixed star made an effort against this motion, by means of which each of them accomplished their revolution about the earth in greater or less time, according to its distance, or the magnitude of the orbit it had to accomplish.
One immense difficulty attended this system. The apparent motions of the planets is not uniform, for sometimes they are seen to advance from west to east, when their motion is called direct, sometimes they are seen for several nights in succession at the same point in the heavens, when they are called stationary, and sometimes they return from east to west, and then their motion is called retrograde.
We know now that this apparent variation in the motion of the planets is simply due to the annual motion of the earth in its orbit round the sun. For example, Saturn describes its vast orbit in about thirty years, and the earth describes in one year a much smaller one inside. Now if the earth goes faster in the same direction as Saturn, it is plain that Saturn will be left behind and appear to go backwards, while if the earth is going in the same direction the velocity of Saturn will appear to be decreased, but his direction of motion will appear unaltered.
To explain these variations, however, according to his system, Ptolemy supposed that the planets did not move exactly in the circumference of their respective orbits, but about an ideal centre, which itself moved along this circumference. Instead therefore of describing a circle, they described parts of a series of small circles, which would combine, as is easy to see, into a series of uninterrupted waves, and these he called Epicycles.
Another objection, which even this arrangement did not overcome, was the variation of the size of the planets. To overcome this Hipparchus gave to the sphere of each planet a considerable thickness, and saw that the planet did not turn centrally round the earth, but round a centre of motion placed outside the earth. Its revolution took place in such a manner, that at one time it reached the inner boundary, at another time the outer boundary of its spherical heaven.
But this reply was not satisfactory, for the differences in the apparent sizes proved by the laws of optics such a prodigious difference between their distances from the earth at the times of conjunction and opposition, that it would be extremely difficult to imagine spheres thick enough to allow of it.
It was a gigantic and formidable piece of machinery to which it was necessary to be continually adding fresh pieces to make observation accord with theory. In the thirteenth century, in the times of the King-Astronomer, Alphonso X. of Castile, there were already seventy-five circles, one within the other. It is said that one day he exclaimed, in a full assemblage of bishops, that if the Deity had done him the honour to ask his advice before creating the world, he could have told Him how to make it a little better, or at all events more simply. He meant to express how unworthy this complication was of the dignity of nature.
Fig. 15.—The Epicycles of Ptolemy.
Fracastor, in his Homocentrics, says that nothing is more monstrous or absurd than all the excentrics and epicycles of Ptolemy, and proposes to explain the difference of velocity in the planets at different parts of their orbits by the medium offering greater or less resistance, and their alteration in apparent size by the effect of refraction.