88 DIRECTION, PLACE AND TIME A rule for finding the Sun's longitude when the the prime vertical: 41. Multiply the Rsine of the latitude by the Rsine of the prime vertical altitude derived from the shadow (of the gnomon) and always divide the product by the Rsine of the Sun's greatest declination; (then reduce the resulting Rsine to the corresponding arc). The arc thus obtained, or(the complement of) that are increased by three signs is the longitude of the (prime vertical) Sun (according as the Sun is in the first or the second quadrant). This is in accordance with what (Arya)bhata has written.¹ That is to say, ifλ and a be respectively the sayana longitude and altitude of the Sun when it is on the prime vertical, and the latitude of the place, then Rsin a X Rsin Rsin E where is the Sun's greatest declination. Rsin λ === Therefore The rationale of this rule is as follows: Referring to Fig. 8, we see that in the triangle SAC SA Rsin a, AC = Rsin 8, LACS = 90°, and LASC = 4. Rsin 8 Rsin a X Rsin R Also from stanza 6, we have Rsin λ = " Rsin 8 x R Rsin € Sun is on Hence, eliminating Rsin 8 between (1) and (2), we get Rsin λ = Rsin ax Rsin Rsin € (1) (2) The next eleven stanzas relate to the determination of the locus of the end of the shadow of the gnomon. ¹ Cf. LBh, iii. 24-25.
