SEQUEL TO THE EPOCH OF HIPPARCHUS. 175 



Sect. 1. — Conclusion of the History of Greek Astronomy. 



I might now proceed to give an account of Ptolemy's other great 

 step, the determination of the Planetary Orbits ; but as this, though 

 in itself very curious, would not illustrate any point beyond those 

 already noticed, I shall refer to it very briefly. The planets all move 

 in ellipses about the sun, as the moon moves about the earth ; and as 

 the sun apparently moves about the earth. They will therefore each 

 have an Elliptic Inequality or Equation of the centre, for the same 

 reason that the sun and moon have such inequalities. And this in- 

 equality may be represented, in the cases of the planets, just as in the 

 other two, by means of an eccentric ; the epicycle, it will be recollected, 

 had already been used in order to represent the more obvious changes 

 of the planetary motions. To determine the amount of the Eccentrici- 

 ties and the places of the Apogees of the planetary orbits, was the 

 task which Ptolemy undertook ; Hipparchus, as we have seen, having 

 been destitute of the observations which such a process required. The 

 determination of the Eccentricities in these cases involved some pecu- 

 liarities which might not at first sight occur to the reader. The eclip- 

 tical motion of the planets takes place about the sun; but Ptolemy 

 considered their movements as altogether independent of the sun, and 

 referred them to the earth alone; and thus the apparent eccentricities 

 which he had to account for, were the compound result of the Eccen- 

 tricity of the earth's orbit, and of the proper eccentricity of the orbit 

 of the Planet. He explained this result by the received mechanism 

 of an eccentric Deferent, carrying an Epicycle; but the motion in the 

 Deferent is uniform, not about the centre of the circle, but about 

 another point, the Equant. Without going further into detail, it 

 may be sufficient to state that, by a combination of Eccentrics and 

 Epicycles, he did account for the leading features of these motions ; 

 and by using his own observations, compared with more ancient ones 

 (for instance, those of Timocharis for Venus), he was able to determine 

 the Dimensions and Positions of the orbits. 38 



1762 seconds ; that is, 248 seconds, or 4 minutes 8 seconds, less than in the former 

 case. [The two qantities are in the proportion of 8 to 7, nearly.] — LUtrow's Note. 



Ptolemy determined the Radius and the Periodic Time of his two circles for 

 each Planet in the following manner : For the inferior Planets, that is, Mercury and 



is, he took the Eadius of the Deferent equal to the Eadius of the Earth's orbit, 

 and the Radius of the Epicycle equal to that of the Planet's orbit. For these 

 Planets, according to his assumption, the Periodic Time of the Planet in its Epi- 



