84 DIRECTION, PLACE AND TIME mation to the instantaneous longitude of the Sun. The process should then be repeated over and over again with the help of the successive approximations to the Sun's instantaneous longitude calculated after each round of the operation. The process should be continued until two successive approximations to the required time agree to asus.¹ It must be noted that the longitudes used in this and the preceding rule (stated in stanzas 30-32) are all sayana. A rule for the determination of the Rsines of the Sun's prime vertical altitude and zenith distance : 37-38. Multiply the Rsine of the (Sun's) greatest decli- nation by the Rsine of the Sun's true (sayana) longitude; then divide (the product) by the Rsine of the colatitude: the result is (the Rsine of) the agra of the true Sun. When that (agrā) is less than the latitude and when the Sun is also in the northern hemisphere, multiply (the Rsine of the Sun's agrā) by (the Rsine of) the colatitude and then divide (the product) by the Rsine of the latitude: the result is the Rsine of the Sun's prime vertical altitude. The square root of the difference between the squares of that and the radius is the Rsine of the Sun's (prime vertical) zenith distance. The Sun's agrā is the amplitude of the Sun at rising or setting. It. is defined to be the arc of the celestial horizon lying between the east-west and rising-setting lines. That is to say, it is the arc of the celestial horizon lying between the east point and the point where the Sun rises or between the west point and the point where the Sun sets. The Rsine of the Sun's agrā is equal to the distance between the east-west and rising-setting lines. In Fig. 8, let S be the Sun on the prime vertical, SA and SB the on the east-west and rising-setting lines perpendiculars from S ¹ Cf. BrSp.Si, iii. 21-23; Sisi, 1, iii. 6(ii).
- This rule occurs also in A, iv, 30; LBh, iii. 21; Sise, iv. 58.
3 This rule occurs also in A, iv. 31; BrSpSi, iii. 52; LBh, iii. 52, 4 Cf. LBh, iii. 22,
