Hipparchus 



47 



the motion of the sun can be represented so accurately 

 that the error never exceeds about i', 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 

 \\hereas in fact the angular diameter of the sun varies by 

 about ^th part of itself, or by about i' 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 epi- 

 cycle, 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 J 

 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 FIG. 19. The epicycle and the deferent, 

 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 com- 

 plicated 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 



* At the present time there is still a small discrepancy between the 

 observed and calculated places of the moon. See chapter xin., 290. 



