$ 43] Hipparchus "59 



when the moon's disc is completely immersed in the 

 shadow (fig. 29). In the same way an eclipse of the sun 

 may be partial or total ; but as the sun's disc may be at 

 times slightly larger than that of the moon, it sometimes 

 happens also that the whole disc of the sun is hidden 

 by the moon, except a narrow ring round the edge (as 

 in fig. 30) : such an eclipse is called annular. As the 

 earth's shadow at the distance of the moon 

 is always larger than the moon's disc, annular 

 eclipses of the moon cannot occur. 



Thus eclipses take place if, and only if, 

 the distance of the moon from a node at 

 the time of conjunction or opposition lies FlG 30 . Annular 

 within certain limits approximately known ; eclipse of the 

 and the problem of predicting eclipses sun. 

 could be roughly solved by such knowledge 

 of the motion of the moon and of the nodes as Hipparchus 

 possessed. Moreover, the length of the synodic and 

 draconitic months ( 40) being once ascertained, it became 

 merely a matter of arithmetic to compute one or more 

 periods after which eclipses would recur nearly in the same 

 manner. For if any period of time contains an exact 

 number of each kind of month, and if at any time an 

 eclipse occurs, then after the lapse of the period, con- 

 junction (or opposition) again takes place, and the moon 

 is at the same distance as before from the node and the 

 eclipse recurs very much as before. The saros, for example 

 (chapter i., 17), contained very nearly 223 synodic or 

 242 draconitic months, differing from either by less than 

 an hour. Hipparchus saw that this period was not com- 

 pletely reliable as a means of predicting eclipses, and 

 showed how to allow for the irregularities in the moon's 

 and sun's motion ( 39, 40) which were ignored by it, 

 but was unable to deal fully with the difficulties arising 

 from the variations in the apparent diameters of the sun 

 or moon. 



An important complication, however, arises in the case 

 of eclipses of the sun, which had been noticed by earlier 

 writers, but which Hipparchus was the first to deal with. 

 Since an eclipse of the moon is an actual darkening of the 

 moon, it is visible to anybody, wherever situated, who can 



