64. THE SHADOW CONE.--The shape and position of the earth's shadow are indicated in Fig. 33 by the lines drawn tangent to the circles which represent the sun and earth, since it is only between these lines that the earth interferes with the free radiation of sunlight, and since both sun and earth are spheres, and the earth is much the smaller of the two, it is evident that the earth's shadow must be, in geometrical language, a cone whose base is at the earth, and whose vertex lies far to the right of the figure--in other words, the earth's shadow, although very long, tapers off finally to a point and ends. So, too, the shadow of the moon is a cone, having its base at the moon and its vertex turned away from the sun, and, as shown in the figure, just about long enough to reach the earth. It is easily shown, by the theorem of similar triangles in connection with the known size of the earth and sun, that the distance from the center of the earth to the vertex of its shadow is always equal to the distance of the earth from the sun divided by 108, and, similarly, that the length of the moon's shadow is equal to the distance of the moon from the sun divided by 400, the moon's shadow being the smaller and shorter of the two, because the moon is smaller than the earth. The radius of the moon's orbit is just about 1/400th part of the radius of the earth's orbit--i. e., the distance of the moon from the earth is 1/400th part of the distance of the earth from the sun, and it is this "chance" agreement between the length of the moon's shadow and the distance of the moon from the earth which makes the tip of the moon's shadow fall very near the earth at the time of solar eclipses. Indeed, the elliptical shape of the moon's orbit produces considerable variations in the distance of the moon from the earth, and in consequence of these variations the vertex of the shadow sometimes falls short of reaching the earth, and sometimes even projects considerably beyond its farther side. When the moon's distance is too great for the shadow to bridge the space between earth and moon there can be no total eclipse of the sun, for there is no shadow which can fall upon the earth, even though the moon does come directly between earth and sun. But there is then produced a peculiar kind of partial eclipse called _annular_, or ring-shaped, because the moon, although eclipsing the central parts of the sun, is not large enough to cover the whole of it, but leaves the sun's edge visible as a ring of light, which completely surrounds the moon. Although, strictly speaking, this is only a partial eclipse, it is customary to put total and annular eclipses together in one class, which is called central eclipses, since in these eclipses the line of centers of sun and moon strikes the earth, while in ordinary partial eclipses it passes to one side of the earth without striking it. In this latter case we have to consider another cone called the _penumbra_--i.