The theory of Hipparchus represents the variations in the distance of the sun with much less accuracy, and whereas in fact the angular diameter of the sun varies by about 1∕30th part of itself, or by about 1′ in the course of the year, this variation according to Hipparchus should be about twice as great. But this error would also have been quite imperceptible with his instruments. [Illustration: FIG. 19.—The epicycle and the deferent.] Hipparchus saw that the motion of the sun could equally well be represented by the other device suggested by Apollonius, the =epicycle=. The body the motion of which is to be represented is supposed to move uniformly round the circumference of one circle, called the epicycle, the centre of which in turn moves on another circle called the =deferent=. It is in fact evident that if a circle equal to the eccentric, but with its centre at E (fig. 19), be taken as the deferent, and if S′ be taken on this so that E S′ is parallel to C S, then S′ S is parallel and equal to E C; and that therefore the sun S, moving uniformly on the eccentric, may equally well be regarded as lying on a circle of radius S′ S, the centre S′ of which moves on the deferent. The two constructions lead in fact in this particular problem to exactly the same result, and Hipparchus chose the eccentric as being the simpler. 40. The motion of the moon being much more complicated than that of the sun has always presented difficulties to astronomers,[23] and Hipparchus required for it a more elaborate construction. Some further description of the moon’s motion is, however, necessary before discussing his theory. We have already spoken (chapter I., § 16) of the lunar month as the period during which the moon returns to the same position with respect to the sun; more precisely this period (about 29-1∕2 days) is spoken of as a =lunation= or =synodic month=: as, however, the sun moves eastward on the celestial sphere like the moon but more slowly, the moon returns to the same position with respect to the _stars_ in a somewhat shorter time; this period (about 27 days 8 hours) is known as the =sidereal month=. Again, the moon’s path on the celestial sphere is slightly inclined to the ecliptic, and may be regarded approximately as a great circle cutting the ecliptic in two =nodes=, at an angle which Hipparchus was probably the first to fix definitely at about 5°. Moreover, the moon’s path is always changing in such a way that, the inclination to the ecliptic remaining nearly constant (but cf. chapter V., § 111), the nodes move slowly backwards (from east to west) along the ecliptic, performing a complete revolution in about 19 years. It is therefore convenient to give a special name, the =draconitic month=,[24] to the period (about 27 days 5 hours) during which the moon returns to the same position with respect to the nodes.