Fig. 572.—Umbra and penumbra.
If a bright body, A, be larger than the dark body, B, there will be two kinds of shadows—viz., the umbra and the penumbra. For instance, the umbra is the central dark part in the cut (fig. 572), and the penumbra is the lighter portion. As soon as the eye is placed on the umbra, it can perceive no part of the source of light, A, which appears to be eclipsed. On the other hand, the penumbra originates in that locality where only a portion of the light proceeding from a luminous object can fall; hence an eye in the penumbra would see a part, but not the whole of the illuminating body. This shadow also forms a cone, the apex of which, if extended, will fall before the opaque body. If we receive the shadows so projected at m n, for example, on a white sheet, we have in the centre a dark circle, which is the umbra, surrounded by the penumbra, which gradually decreases in intensity towards the exterior (see fig. 573). The farther we hold the sheet from the body producing the shadow, the umbra decreases, and the penumbra is enlarged. For where (in solar eclipses) the umbra falls there is totality; within the penumbra partial eclipse only.
Fig. 573.—Lunar eclipse.
Lunar Eclipse.—Let A (fig. 573) be the sun, and B the earth, the length of the umbra of the latter will exceed 108 diameters of the earth. Since the moon is only about thirty terrestrial diameters distant from the earth, and as the diameter of the earth’s shadow, at this distance, is nearly three times as large as the apparent diameter of the moon, it follows that when the latter enters this shadow, she must be totally eclipsed, for at those places where the moon’s shadow falls there is total eclipse. If the moon’s orbit were coincident with the ecliptic, or if both moon and earth moved round the sun in the same plane, there would be an eclipse at every conjunction, and at every opposition,—i.e., a solar eclipse would happen at every new moon, and a lunar eclipse at every full moon. But we have seen that the lunar orbit cuts the ecliptic only in two points; consequently an eclipse of the moon is possible only when, at the time of opposition, the moon is in one of her nodes, or in close proximity to it, which can only occur twenty-nine times in the space of eighteen years.
A lunar eclipse begins on the eastern margin of the moon, and is either total, when her whole disc enters the umbra, or partial, when only part of her disc is in the shadow. A total eclipse may last for two hours.
We shall understand this better, perhaps, with the diagrams.
Fig. 574.—Solar eclipse.
Solar Eclipses.—When the moon and the sun are in conjunction, the moon’s place may be represented by M (fig. 574) between the earth, T, and the sun, S. If this conjunction occur when the moon is in one of her nodes, or within 16° of it, the shadow of the moon will fall upon the earth, and the sun will be eclipsed. At other places the sun will not be entirely covered; and if the moon be moved farther off, so that its shadow will not reach the earth, and so not cover the sun up completely, we shall have an annular eclipse, because a rim of the sun will be visible.