Demonstration. -Select a board about 2 ft. long and 8 in. wide, and set up in the middle of it a wooden cylinder 2 in. in diameter and 5 in. high. Fasten an upright 6 in. high to one end of the board and near the other end set up two candles 4 in. apart. Observe the shadows cast by the cylinder upon the upright.
The dark part where the shadows overlap is the umbra, and the part which is lighted by only one candle is the penumbra. When a single source of light is so small as to be considered a point, the shadow is all umbra. If the source of the light is larger, the umbra is partly or completely surrounded by a penumbra. Figure 2 illustrates the case in which the light comes from a luminous ball and the opaque body is a larger ball. If L is the luminous and B the opaque ball, a screen S will show the existence of a circular umbra or shadow whose limits can be determined by moving a straight line around both balls and tangent to both of them on the same side, as LB. There will be a penumbra, however, entirely around the umbra; this will extend to the limits of a circle marked by a line tangent to both balls, but always on opposite sides of them, as CB. At the edge of the umbra the penumbra will be nearly as dark as the umbra, and it will gradually grow lighter and lighter toward the outer edge. The moon is much smaller than the sun, its diameter being 2163 miles, but its distance from the earth is so much less, that it appears to be of nearly the same size. In its journey around the earth the moon sometimes comes between us and the sun and acts as a screen, cutting off the sun's light from us. If the observer is at a part of the earth where the light of the sun is entirely cut off, as in the umbra of Fig. 2, the eclipse is total. If he is where a portion of the sun can be seen, he is in the penumbra and the eclipse is partial, as in Fig. 3.
