* 49] The Almagest 67 



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 epi- 

 cycles 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 sometimt-S-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 c M (fig. 33) joining the 

 centres of the earth and moon, or the direction of the 

 moon as st en by an observer at A ; and also the direction 

 of the line B M, that is the direction of the moon as seen 

 by an observer at B, then the angles of the triangle c B M 

 are known, and the ratio of the sides c B, c M is known. 



* Here, as elsewhere, I have given no detailed account of astro- 

 nomical instruments, believing such descriptions to be in general 

 neither interesting nor intelligible to those who have not the actual 

 instruments before them, and to be of little use to those who have. 



