INDUCTIVE EPOCH OF HIPPARCHUS. 189 



The moon's motions are really affected by seve- 

 ral other inequalities, of very considerable amount, 

 besides those which were thus considered by Hip- 

 parchus; but the lunar paths, constructed on the 

 above data, possessed a considerable degree of cor- 

 rectness, and especially when applied, as they were 

 principally, to the calculation of eclipses ; for the 

 greatest of the additional irregularities which we 

 have mentioned disappear at new and full moon, 

 which are the only times when eclipses take place. 



The numerical explanation of the motions of the 

 sun and moon, by means of the hypothesis of ec- 

 centrics, and the consequent construction of Tables, 

 was one of the great achievements of Hipparchus. 

 The general explanation of the motions of the pla- 

 nets, by means of the hypothesis of epicycles, was 

 in circulation previously, as we have seen. But the 

 special motions of the planets, in their epicycles, 

 are, in reality, affected by anomalies of the same 

 kind as those which render it necessary to introduce 

 eccentrics in the cases of the sun and moon. 



Hipparchus determined, with great exactness, 

 the mean motions of the Planets ; but he was not 

 able, from want of data, to explain the planetary 

 irregularities by means of eccentrics. The whole 

 mass of good observations of the planets which he 

 received from preceding ages, did not contain so 

 many, says Ptolemy, as those which he has trans- 

 mitted to us of his own. " Hence 5 it was," he adds, 



5 Synt. ix. 2. 



