SEQUEL TO THE EPOCH OF HIPPARCHUS. 229 



eccentric or an epicycle ; and the amount of this 

 inequality had been collected by observations of 

 eclipses. But though the hypothesis of an epicycle, 

 for instance, would bring the moon to her proper 

 place, so far as eclipses could show it, that is, 

 at new and full moon, this hypothesis did not 

 rightly represent her motions at other points of 

 her course. This appeared, when Ptolemy set 

 about measuring her distances from the sun at dif- 

 ferent times. " These," he 32 says, sometimes agreed, 

 and sometimes disagreed." But by further atten- 

 tion to the facts, a rule was detected in these dif- 

 ferences. "As my knowledge became more complete 

 and more connected, so as to show the order of 

 this new inequality, I perceived that this difference 

 was small, or nothing, at new and full moon ; and 

 that at both the dichotomies (when the moon is 

 half illuminated,) it was small, or nothing, if the 

 moon was at the apogee or perigee of the epicycle, 

 and was greatest when she was in the middle of 

 the interval, and therefore when the first inequality 

 was greatest also." He then adds some further 

 remarks on the circumstances according to which 

 the moon's place, as affected by this new inequality, 

 is before or behind the place, as given by the 

 epicyclical hypothesis. 



Such is the announcement of the celebrated 

 discovery of the moon's second inequality, after- 

 wards called (by Bullialdus) the Ejection. Ptolemy 



M Synt. v. 2. 



