An object, which was then considered as of great importance to astronomy, was thus accomplished, viz. the production of a variable motion, or one which was continually chan ging both its rate and its direction from two uniform circular motions, each of which pre served always the same quantity and the same direction.
It was not long before another application was made of the method of epicycles. Hip parchus, the greatest antiquity, and one of the inventors in science most justly entitled to admiration, discovered the inequality of the sun's apparent motion round the earth. To explain or to express this irregularity, the same observer imagined an epi cycle of a small radius with its centre moving uniformly in the circumference of a large circle, of which the earth was the centre, while the sun revolved in the circumference of the small circle with the same angular velocity as this last, but in a contrary direction.
As other irregularities in the motions of the moon and of the planets were observed, other epicycles were introduced, and Ptolemy, in his Abnagest, enumerated all which then appeared necessary, and assigned to them such dimensions as enabled them to express the phenomena with accuracy. It is not to be denied that the system of the heavens became this way extremely complicated ; though, when fairly examined, it will appear to be a work of great ingenuity and research. The ancients, indeed, may be regarded as very for. tunate in the contrivance of epicycles, because, by means of them, every inequality which can exist in the angular motion of a planet may be at least nearly represented. This I call fortunate, because, at the time when Apollonius introduced the epicycle, he had no idea of the extent to which his contrivance would go, as he could have none of the con. clusiona which the author of the Micanique Celeste was to deduce from the principle of gravitation.
The same contrivance had another great advantage ; it subjected the motions of the sun, the moon, and the planets, very readily to a geometrical construction, or an arithmetical calculation, neither of them difficult. By this means the predictions of astronomical phe nomena, the calculation of tables, and the comparison of those tables with observation, became matters of great facility, on which facility, in a great measure, the progress of the science depended. It was on these circumstances, much more than on the simpli city with which it amused or deceived the imagination, that the popularity of this theory was founded ; the ascendant which it gained over the minds of astronomers, and the resist ance which, in spite of facts and observations, it was so long able to make to the true sys tem of the world.
It does not appear that the ancient astronomers ever considered the epicycles and defer ents which they employed in their system as having a physical existence, or as serving to ex plain the causes of the celestial motions. They seem to have considered them merely as mathematical diagrams, serving to express or to represent those motions as geometrical ex pressions of certain general facts, which readily furnished the rules of astronomical calcu lation.
The language in which Ptolemy speaks of the epicycles is not a little curious, and very conformable to the notion, that he considered them as Merely the means of expressing a general law. After laying clowri the hypothesis of certain epicycles, and their dimensions, it is usual with him to add, " these suppositions will save the phenomena." Save is the literal translation of the Greek word, which is always a part of the verb LOCEIP, or some of its compounds. Thus, in treating of certain phenomena in the moon's motion, he lays down two hypotheses, by either of which they may be expressed, ; and he concludes, "in this way the similitude of the ratios, and the proportionality of the times, will be saved on both stippositions." It is plain, from these words, that the dxtronomer did not here consider himself as describing any thing which actually existed, but as ex plaining two artifices, by either of which, certain irregularities in the moon's motion may be represented, in consistence with the principle of uniform velocity. The hypothesis does not relate to the explanation, but merely to the expression of the fact ; it is first assumed, and its merit is then judged of synthetically, by its power to save, to reconcile, or to re present appearances. At a time when the mathematical sciences extended little beyond the elements, and when problems which could not be resolved by circles and straight lines, could harldly be resolved at all, such artifices as the preceding were of the greatest value. They were even more valuable than the truth itself would have been in such circumstan ces ; and nothing is more certain than that the real elliptical orbits of the planets, and the uniform description of areas, would have been very unseasonable discoveries at the period we are now treating of. The hypotheses of epicycles, and of centres of uniform motion, were well accommodated to the state of science, and are instances of a false system which has materially contributed to the establishment of truth.