120 DISSERTATION SECOND. [part i. 



the deferent, and the second the epicycle, and the mo- 

 tion in the circumference of each was supposed uni- 

 form. Lastly, it was conceived that the motion of the 

 centre of the epicycle in the circumference of the deferent, 

 and of the planet in that of the epicycle, were in opposite 

 directions, the first being towards the east, and the second 

 towards the west. In this way, the alterations from pro- 

 gressive to retrograde, with the intermediate stationary 

 points, were readily explained, and Apollonius carried his 

 investigation so far as to determine the ratio between the ra- 

 dius of the deferent, and that of epicycle, from knowing the 

 stations and retrogradations of any particular planet. 



An object, which was then considered as of great impor- 

 tance to astronomy, was thus accomplished, viz. the pio» 

 duction of a variable motion, or one which was continually 

 changing both its rate and its direction from two uniform 

 circular motions, each of which preserved always the same 

 quantity and the same direction. 



It was not long before another application was made of 

 the method of epicycles. Hipparchus, the greatest astro- 

 nomer of antiquity, and one of the inventors in science most 

 justly entitled to admiration, discovered the inequality of 

 the sun's apparent motion round the earth. To explain or 

 to express this irregularity, the same observer imagined 

 an epicycle of a small radius with its centre moving uni- 

 formly in the circumference of a large circle, of which the 

 earth was the centre, while the sun revolved in the circum- 

 ference of the small circle with the same angular velocity 

 as this last, but in a contrary direction. 



As other irregularities in the motions of the moon and of 

 the planets were observed, other epicycles were introduc- 

 ed, and Ptolemy, in his Almagest, enumerated all which 

 then appeared necessary, and assigned to them such di- 

 mensions as enabled them to express the phenomena with 

 accuracy. It is not to be denied that the system of the 



