146 THE GREEK ASTRONOMY. 



detail, as the inequality which follows from the hypothesis of a smal 

 Epicycle, turning uniformly on its axis, and carrying the sun in its 

 circumference, while the centre of this epicycle moves uniformly in a 

 circle of which the earth is the centre. This identity of the results 

 of the hypothesis of the Eccentric and the Epicycle is proved by 

 Ptolemy in the third book of the " Almagest." 



The Surfs Eccentric. — When Hipparchus had clearly conceived 

 these hypotheses, as p )0SS ^ e ways of accounting for the sun's motion, 

 the task which he had to perform, in order to show that they deserved 

 to be adopted, was to assign a place to the Perigee, a magnitude to 

 the Eccentricity, and an Epoch at which the sun was at the perigee ; 

 and to show that, in this way, he had produced a true representation 

 of the motions of the sun. This, accordingly, he did ; and having thus 

 determined, with considerable exactness, both the law of the solar 

 irregularities, and the numbers on which their amount depends, he was 

 able to assign the motions and places of the sun for any moment of 

 future time with corresponding exactness; he was able, in short, to 

 construct Solar Tables, by means of which the sun's place with respect 

 to the stars could be correctly found at any time. These tables (as 

 they are given by Ptolemy) 1 give the Anomaly, or inequality of the 

 sun's motion ; and this they exhibit by means of the Prosthaphensis, 

 the quantity of which, at any distance of the sun from the Apogee, it is 

 requisite to add to or subtract from the arc, which he would have 

 described if his motion had been equable. 



The reader might perhaps expect that the calculations which thus 

 exhibited the motions of the sun for an indefinite future period must 

 depend upon a considerable number of observations made at all seasons 

 of the year. That, however, was not the case ; and the genius of the 

 discoverer appeared, as such genius usually does appear, in his perceiv- 

 ing how small a number of facts, rightly considered, were sufficient to 

 form a foundation for the theory. The number of days contained in 

 two seasons of the year sufficed for this purpose to Hipparehus, 

 " Having ascertained," says Ptolemy, " that the time from the vernal 

 equinox to the summer tropic is 94^ days, and the time from the sum- 

 mer tropic to the autumnal equinox 92^ days, from these phenomena 

 alone he demonstrates that the straight line joining the centre of the 

 sun's eccentric path with the centre of the zodiac (the spectator's eye) 

 is nearly the 24th part of the radius of the eccentric path ; and that 



1 Syntax. 1. iii. 



