THE DIAMETER OF THE SHADOW 179 Now consider Fig. 20. AC and BD are the diameters of the Sun and the Earth. BOD is the shadow-cone¹, O its vertex. S and E are the centres of the Sun and the Earth. M is the point where the Moon crosses the shadow cone. MN is perpendicular to the axis of the shadow- C Therefore, B MN BD KO EO MN= - = Fig. 20 cone and denotes the diameter of the section of the shadow cone where the Moon crosses it. It is called the diameter of the shadow. The triangles MON and BOD are similar, so that KO X BD EO (EO M (EO K N - EK) X BD EO EM) X BD EO approx. O i.e., the diameter of the shadow _{length of Earth's shadow - Moon's distance } x Earth's diameter length of Earth's shadow The approximations made in the above procedure are obvious.² The diameter thus obtained is in yojanas. To reduce it to minutes of arc we have to multiply it by the radius (i.e., 3438') and divide by the Moon's distance in yojanas. ¹ Approximately. The formula for the diameter of the shadow stated above was modified and refined by Muniśvara (1646 A. D.) and Kamaläkara (1658 A. D.). The latter astronomer gave an accurate expression for the diameter of the shadow (in SiTV, ix. 29-33).
