148 THE GREEK ASTRONOMY. 



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 astrono- 

 mer, 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 65 85^ days, there are 241 revolutions of the moon 

 with regard to the stars, but only 239 revolutions with regard to the 

 anomaly. This difference could be suitably represented by supposing 

 the eccentric, in which the moon moves, to have itself an angular 

 motion, perpetually carrying its apogee in the same direction in which 

 the moon travels ; but this supposition being made, it was necessary 

 to determine, not only the eccentricity of the orbit, and place of the 

 apogee at a certain time, but also the rate of motion of the apogee 

 itself, in order to form tables of the moon. 



This task, as we have said, Hipparchus executed ; and in this in- 

 stance, as in the problem of the reduction of the sun's motion to 

 tables, the data which he found it necessary to employ were very few. 

 He deduced all his conclusions from six eclipses of the moon. 3 Three 

 of these, the records of which were brought from Babylon, where a 

 register of such occurrences was kept, happened in the 366th and 

 367th years from the era of Nabouassar, and enabled Hipparchus to 

 determine the eccentricity and apogee of the moon's orbit at that 

 time. The three others were observed at Alexandria, in the 547th 

 year of Nabonassar, which gave him another position of the orbit at 

 an interval of 180 years ; and he thus became acquainted with the 

 motion of the orbit itself, as well as its form. 4 



3 Ptol. Si/n. iv. 10. 



4 Ptolemy uses the hypothesis of an epycicle for the moon's first inequality ; bat 

 Ilippnrchus employs an eccentric. 



