The astronomer who dealt with this difficulty was HIPPARCHUS (about 190-120 B.C.), who was born at Nicæa, in Bithynia, but made most of his astronomical observations in Rhodes. He attempted to explain these irregularities in the motions of the Sun and Moon by supposing that though they really moved uniformly in their orbits, yet the centre of their orbits was not the centre of the Earth, but was situated a little distance from it. This point was called "+the excentric+," and the line from the excentric to the Earth was called "+the line of apsides+." But when he tried to deal with the movements of the planets, he found that there were not enough good observations available for him to build up any satisfactory theory. He therefore devoted himself to the work of making systematic determinations of the places of the planets that he might put his successors in a better position to deal with the problem than he was. His great successor was CLAUDIUS PTOLEMY of {25} Alexandria, who carried the work of astronomical observation from about A.D. 127 to 150. He was, however, much greater as a mathematician than as an observer, and he worked out a very elaborate scheme, by which he was able to represent the motions of the planets with considerable accuracy. The system was an extremely complex one, but its principle may be represented as follows: If we suppose that a planet is moving round the Earth in a circle at a uniform rate, and we tried to compute the place of the planet on this assumption for regular intervals of time, we should find that the planet gradually got further and further away from the predicted place. Then after a certain time the error would reach a maximum, and begin to diminish, until the error vanished and the planet was in the predicted place at the proper time. The error would then begin to fall in the opposite direction, and would increase as before to a maximum, subsequently diminishing again to zero. This state of things might be met by supposing that the planet was not itself carried by the circle round the earth, but by an +epicycle+--_i.e._ a circle travelling upon the first circle--and by judiciously choosing the size of the epicycle and the time of revolution the bulk of the errors in the planet's place might be represented. But still there would be smaller errors going through their own period, and these, again, would have to be met by imagining that the first epicycle carried a second, and it might be that the second carried a third, and so on.