Now the apparent diameter of either sun or moon is, as we have seen (§ 32), about 1∕2°; consequently when their discs just touch, as in fig. 27, the distance between their centres is also about 1∕2°. If then at conjunction the distance between their centres is less than this amount, an eclipse of the sun will take place; if not, there will be no eclipse. It is an easy calculation to determine (in fig. 26) the length of the side N S or N M of the triangle N M S, when S M has this value, and hence to determine the greatest distance from the node at which conjunction can take place if an eclipse is to occur. An eclipse of the moon can be treated in the same way, except that we there have to deal with the moon and the shadow of the earth at the distance of the moon. The apparent size of the shadow is, however, considerably greater than the apparent size of the moon, and an eclipse of the moon takes place if the distance between the centre of the moon and the centre of the shadow is less than about 1°. As before, it is easy to compute the distance of the moon or of the centre of the shadow from the node when opposition occurs, if an eclipse just takes place. As, however, the apparent sizes of both sun and moon, and consequently also that of the earth’s shadow, vary according to the distances of the sun and moon, a variation of which Hipparchus had no accurate knowledge, the calculation becomes really a good deal more complicated than at first sight appears, and was only dealt with imperfectly by him. [Illustration: FIG. 27.—The sun and moon.] [Illustration: FIG. 28.—Partial eclipse of the moon.] [Illustration: FIG. 29.—Total eclipse of the moon.] Eclipses of the moon are divided into =partial= or =total=, the former occurring when the moon and the earth’s shadow only overlap partially (as in fig. 28), the latter 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. [Illustration: FIG. 30.—Annular eclipse of the sun.]