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. [Illustration: FIG. 15.--THE EPICYCLES OF PTOLEMY.]