Page:A short history of astronomy(1898).djvu/111

§49] Ptolemy thus succeeded in fitting his theory on to his observations so well that the error seldom exceeded 10', a small quantity in the astronomy of the time, and on the basis of this construction he calculated tables from which the position of the moon at any required time could be easily deduced.

One of the inherent weaknesses of the system of epicycles occurred in this theory in an aggravated form. It has already been noticed in connection with the theory of the sun (§ 39), that the eccentric or epicycle produced an erroneous variation in the distance of the sun, which was, however, imperceptible in Greek times. Ptolemy's system, however, represented the moon as being sometimes nearly twice as far off as at others, and consequently the apparent diameter ought at some times to have been not much more than half as great as at others a conclusion obviously inconsistent with observation. It seems probable that Ptolemy noticed this difficulty, but was unable to deal with it; it is at any rate a significant fact that when he is dealing with eclipses, for which the apparent diameters of the sun and moon are of importance, he entirely rejects the estimates that might have been obtained from his lunar theory and appeals to direct observation (cf. also § 51, note).

49. The fifth book of the Almagest contains an account of the construction and use of Ptolemy's chief astronomical instrument, a combination of graduated circles known as the astrolabe.

Then follows a detailed discussion of the moon's parallax (§ 43), and of the distances of the sun and moon. Ptolemy obtains the distance of the moon by a parallax method which is substantially identical with that still in use. If we know the direction of the line (fig. 33) joining the centres of the earth and moon, or the direction of the moon as seen by an observer at ; and also the direction of the line, that is the direction of the moon as seen by an observer at , then the angles of the triangle  are known, and the ratio of the sides  is known.