INDUCTIVE EPOCH OF HIPPARCHUS. 187 



period of its restoration, that is, the time which the 

 moon occupies in moving from any latitude till she 

 is restored to the same latitude ; as, for instance, 

 from the ecliptic on one side of the heavens to the 

 ecliptic on the same side of the heavens again. But 

 it is found that the period of the restoration of the 

 latitude is not the same as the period of the restora- 

 tion of the longitude, that is, as the period of the 

 moon's revolution among the stars; and thus the 

 moon describes a different path among the stars in 

 every successive revolution, and her path, as well as 

 her velocity, is constantly variable. 



Hipparchus, however, reduced the motions of 

 the moon to rule and to Tables, as he did those of 

 the sun, and in the same manner. He determined, 

 with much greater accuracy than any preceding 

 astronomer, the mean or average equable motions 

 of the moon in longitude and in latitude ; and he 

 then represented the anomaly of the motion in 

 longitude by means of an eccentric, in the same 

 manner as he had done for the sun. 



But here there occurred still an additional 

 change, besides those of which we have spoken. 

 The Apogee of the Sun was always in the same 

 place in the heavens ; or at least so nearly so, that 

 Ptolemy could detect no error in the place assigned 

 to it by Hipparchus 250 years before. But the 

 Apogee of the Moon was found to have a motion 

 among the stars. It had been observed before the 

 time of Hipparchus, that in 6585*- days, there are 



