Page:A short history of astronomy(1898).djvu/91

§ 40] the motion of the sun can be represented so accurately that the error never exceeds about 1', a quantity insensible to the naked eye.

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 $1⁄30$th 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.

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 (fig. 19), be taken as the deferent, and if  be taken on this so that  is parallel to, then  is parallel and equal to ; and that therefore the sun , moving uniformly on the eccentric, may equally well be regarded as lying on a circle of radius , the centre  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, and Hipparchus required for it a more elaborate construction. Some further description of the