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.
The Ptolemaic system was more complicated than this brief summary would suggest, but it is not possible here to do more than indicate the general principles upon which it was founded, and the numerous other systems or modifications of them produced in the { 26} five centuries from Eudoxus to Ptolemy must be left unnoticed. The point to be borne in mind is that one fundamental assumption underlay them all, an assumption fundamental to all science--the assumption that like causes must always produce like effects. It was apparent to the ancient astronomers that the stars--that is to say, the great majority of the heavenly bodies--do move round the Earth in circles, and with a perfect uniformity of motion, and it seemed inevitable that, if one body moved round another, it should thus move. For if the revolving body came nearer to the centre at one time and receded at another, if it moved faster at one time and slower at another, then, the cause remaining the same, the effect seemed to be different. Any complexity introduced by superposing one epicycle upon another seemed preferable to abandoning this great fundamental principle of the perfect uniformity of the actings of Nature.