41 Hipparchus 49 



exactitude than before the lengths of each of these months. 

 In order to determine them with accuracy he recognised 

 the importance of comparing observations of the moon 

 taken at as great a distance of time as possible, and saw 

 that the most satisfactory results could be obtained by 

 using Chaldaean and other eclipse observations, which, 

 as eclipses only take place near the moon's nodes, were 

 simultaneous records of the position of the moon, the 

 nodes, and the sun. 



To represent this complicated set of motions, Hipparchus 

 used, as in the case of the sun, an eccentric, the centre of 

 which described a circle round the earth in about nine 

 years (corresponding to the motion of the apses), the plane 

 of the eccentric being inclined to the ecliptic at an angle 

 of 5, and sliding back, so as to represent the motion of 

 the nodes already described. 



The result cannot, however, have been as satisfactory as 

 in the case of the sun. The variation in the rate at which 

 the moon moves is not only greater than in the case of 

 the sun, but follows a less simple law, and cannot be ade- 

 quately represented by means of a single eccentric ; so 

 that though Hipparchus' work would have represented the 

 motion of the moon in certain parts of her orbit with fair 

 accuracy, there must necessarily have been elsewhere dis- 

 crepancies between the calculated and observed places. 

 There is some indication that Hipparchus was aware of 

 these, but was not able to reconstruct his theory so as to 

 account for them. 



4 1. /In the case of the planets Hipparchus found so 

 small a supply of satisfactory observations by his prede- 

 cessors, that he made no attempt to construct a system 

 of epicycles or eccentrics to represent their motion, } but 

 collected fresh observations for the use of his successors. 

 He also made use of these observations to determine with 

 more accuracy than before the average times of revolution 

 of the several planets. 



He also made a satisfactory estimate of the size and 

 distance of the moon, by an eclipse method, the leading 

 idea of which was due to Aristarchus ( 32); by observing 

 the angular diameter of the earth's shadow (Q R) at the 

 distance of the moon at the time of an eclipse, and comparing 



4 



