INDUCTIVE EPOCH OF HIPPARCHUS. 149 



The moon's motions are really affected by several oilier inequalities, 

 of very considerable amount, besides those which were thus considered 

 by Hipparchus; but the lunar paths, constructed on the above data, 

 possessed a considerable degree of correctness, 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 Eccentrics, and the consequent construction 

 of tables, was one of the great achievements of Hipparchus. The general 

 explanation of the motions of the planets, 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 

 ao-es, did not contain so many, says Ptolemy, as those which he has 

 transmitted to us of his own. "Hence 5 it was," he acids, "that while 

 he labored, in the most assiduous manner to represent the motions of 

 the sim and moon by means of equable circular motions ; with respect 

 to the planets, so far as his works show, he did not even make the 

 attempt, but merely put the extant observations in order, added to 

 them himself more than the whole of what he received from preceding- 

 ages, and showed the insufficiency of the hypothesis current among 

 astronomers to explain the phenomena." It appears that preceding 

 mathematicians had already pretended to construct "a Perpetual 

 Canon," that is, Tables which should give the places of .the planets at 

 any future time ; but these being constructed without regard to the 

 eccentricity of the orbits, must have been very erroneous. 



Ptolemy declares, with great reason, that Hipparchus showed his 

 usual love of truth, and his right sense of the responsibility of his 

 task, in leaving this part of it to future ages. The Theories of 'the 

 Sun and Moon, which we have already described, Constitute him a 

 great astronomical discoverer, and justify the reputation he has always 



3 S'jnt. ix. 2. 



