92 DIRECTION, PLACE AND TIME gnomon) moves, like a spell-bound serpent, with its head (i.e., end) kept upon the periphery of that circle.¹ Lalla says: "With the point of intersection of the head-tail lines (of the two fish-figures) as centre, draw a circle passing through the ends of the three shadows. (The end of) the shadow (of the gnomon) does not leave the periphery of that circle in the same way as a lady born in a noble family does not leave the traditions of her family." Sripati (c. 1039 A. D.) writes: "The (end of the) shadow of the gnomon erected at the centre of the circle does not leave the periphery of the circle drawn with the common point of the head and tail lines (of the two fish-figures) and passing through the three shadow-ends in the same way as a noble-minded person does not leave the path of righteousness." The above rule was later criticised by Bhaskara II (1150 A. D.), who made the following remark : "It is declared (by some astronomers) that the shadow of the gnomon moves on the circle passing through the ends of the three shadows made by the same gnomon (placed in the centre of the horizon), but this is wrong, and consequently the east-west and north-south lines, the latitude, etc., found by the aid of the circle just mentioned are also wrong".4 Bhaskara II's criticism is proper. The locus of the end of the shadow of a gnomon will not be a circle as stated in the text unless the latitude of the place is 90°. The locus will be, in general, a conic section. For places whose latitudes are less than € ( being the obliquity of the ecliptic), in particular, this locus will be a hyperbola. Alternative rules for finding the Sun's agra and the latitude of the place: 53. The squareroot of the sum of the squares of the 1 This rule occurs also in BrSpSi, iii. 2-3; ŚiDVṛ, I, iii. 3; Siśe, iv. 5; TS, iii. 42(ii)-47. 2 SiDV, I, iii. 3. 3 Sise, iv. 5.
- L. Wilkinson, Translation of the Siddhanta-siromani (Goladhyaya,
xi. 38(ii), Calcutta (1861), p.221. We have replaced the word "revolves" by "moves".
