AN ALTERNATIVE RULE 59 by him have been supplied by his commentator Pṛthūdaka Svāmi (860 A.D.)¹ The method of getting the correct east-west line is found to occur also in the Siddhanta-sekhara² of Sripati (c. 1039 A.D.) the Siddhanta-siromani³ of Bhāskara II (1150 A.D.) etc. For practical purposes, however, the method given in the text is good enough. An alternative rule: 3. With the three points (at the ends of the three shadows of the gnomon) corresponding to (any three) different times (in the day), draw two fish-figures (each with two of the three points) in accordance with the usual method. From the point of intersection of the lines passing through the mouth and tail (of the two fish-figures), determine the north and south directions.5 According to this rule, the north-south line is the one joining the foot of the gnomon with the point of intersection of the mouth-tail lines of the two fish-figures. Varahamihira states this rule as follows: "Mark three times, from the centre, the end of the gnomon's shadow, and then describe two fish-figures. Thereupon describe a circle, taking for radius a string, that is fastened to the point in which the two strings issuing from the heads of the fish-figures intersect, and that is so long as to reach the three points marked. On the given day the shadow of the gnomon moves in that circle, without departing from it. "The line joining the centre of that circle and the base of the gnomon is the south-north line; and the interval in north direction (between that circle and the gnomon) is the midday shadow."6 ¹ See Sudhākara Dvivedi's comm. on BrSpSi, iii. 1. 2 iv. 14-16. s I, iii. 8. This point of intersection is the same as the centre of the circle passing through the three shadow-ends. 5 This rule is found also in PSi, xiv. 14-16; BrSp.Si, iii. 2; SiDV, I, iii. 2; and Sise, iv. 4. See G. Thibaut and S. Dvivedi, The Panca-siddhāntikā, Banaras (1889), xiv, 14-16, English translation, p. 79.
