ii2 A Short History of Astronomy [CH. iv. 



the traditional theory. Actually, however, there is scarcely 

 any part of the subject in which Coppernicus did more to 

 diminish the discrepancies between theory and observation. 

 He rejects Ptolemy's equant (chapter 11., 51), partly on 

 the ground that it produces an irregular motion unsuitable 

 for the heavenly bodies, partly on the more substantial 

 ground that, as already pointed out (chapter n., 48), 

 Ptolemy's theory makes the apparent size of the moon at 

 times twice as great as at others. By an arrangement of 

 epicycles Coppernicus succeeded in representing the chief 

 irregularities in the moon's motion, including evection, but 

 without Ptolemy's prosneusis (chapter n., 48) or Abul 

 Wafa's inequality (chapter in., 60), while he made the 

 changes in the moon's distance, and consequently in its 

 apparent size, not very much greater than those which 

 actually take place, the difference being imperceptible by 

 the rough methods of observation which he used.* 



In discussing the distances and sizes of the sun and 

 moon Coppernicus follows Ptolemy closely (chapter n., 49 ; 

 cf. also fig. 20) ; he arrives at substantially the same estimate 

 of the distance of the moon, but makes the sun's distance 

 1,500 times the earth's radius, thus improving to some extent 

 on the traditional estimate, which was based on Ptolemy's. 

 He also develops in some detail the effect of parallax on 

 the apparent place of the moon, and the variations in the 

 apparent size, owing to the variations in distance ; and the 

 book ends with a discussion of eclipses. 



86. The last two books (V. and VI.) deal at length with 

 the motion of the planets. 



In the cases of Mercury and Venus, Ptolemy's explana- 

 tion of the motion could with little difficulty be rearranged 

 so as to fit the ideas of Coppernicus. We have seen 

 (chapter 11., 51) that, minor irregularities being ignored, 

 the motion of either of these planets could be represented 

 by means of an epicycle moving on a deferent, the centre of 



* According to the theory of Coppernicus, the diameter of the 

 moon when greatest was about -J greater than its average amount; 

 modern observations make this fraction about ^3. Or, to put it other- 

 wise, the diameter of the moon when greatest ought to exceed its 

 value when least by about 8' according to Coppernicus, and by about 5' 

 according to modern observations. 



