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.
Fig. 30—Annular eclipse of the sun
Thus eclipses take place if, and only if, the distance of the moon from a node at the time of conjunction or opposition lies within certain limits approximately known; and the problem of predicting eclipses 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, conjunction (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 completely 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
