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by some writers, that, in adopting them, he merely in-tended to frame a mathematical construction whichshould conveniently represent the facts ; but this wouldappear hardly reconcilable with the earnestness hedisplays in arguing for that physical system of theplanets, and the Aristotelian doctrine of motion, whichrendered the epicycles necessary. His own expressions,on which this notion has been defended, are certainly farfrom conclusive either way. He merely speaks of thehypothesis as one which will “ save the phenomena,”as we may, without violating the English idiom, literallytranslate the Greek. It is certain that his later fol-lowers considered these to be the real motions of theplanets; as they also believed in the real substantial ex-istence of the crystalline spheres, which Eudoxus haddevised as the causes of the celestial motions. Maest-lin, in particular, has a strong and explicit passage tothis effect.

However this may be, the various inequalities whichwere successively observed in the planetary motions gaverise to new applications of the same principle. Aninequality had been discovered (as we have seen) in themoon’s motion by Hipparchus. Ptolemy discoveredanother, which varied according to the angular distanceof the moon from the sun, and was called the erection.The first of these was explained by the moon’s motionin an epicycle whose deferent was the mean orbit. But,for the second, it was necessary further to suppose thatthe centre of this deferent again moved in anothercircle. Of the enormous and increasing complicationof such a system, arising from the extension of thisprinciple to all the planetary orbits, as well as to thereal inequalities of the sun and moon, it is hardlynecessary to say much. It certainly owed its generaladoption to the convenience it gave in calculation.Owing to the preservation of the principle of circularmotion throughout, the geometrical constructions, andthe arithmetical computations, involved, were never ofgreat difficulty ; and the accuracy of the results was