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 ii., § 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 ii., § 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 ii.,§ 48) or Abul Wafa's inequality (chapter iii., § 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.[1]
In discussing the distances and sizes of the sun and moon Coppernicus follows Ptolemy closely (chapter ii., § 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 explanation of the motion could with little difficulty be rearranged so as to fit the ideas of Coppernicus. We have seen (chapter ii., § 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 18 greater than its average amount; modern observations make this fraction about 113. Or, to put it otherwise, 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.
