SUN'S ALTITUDE 79 Rsine from the earthsine and then performing the usual process (i.e., multiplying that by the Rsine of the colatitude and dividing the product by the radius) determine the Rsine of the (Sun's) altitude.¹ The case contemplated here arises when the Sun lies between the equatorial and local horizons, i.e., shortly after sunrise or before sunset. A rule for finding the Sun's altitude in the night: 26. In the night, the Rsine of the Sun's altitude is to be obtained by applying the operations (of addition and subtraction) inversely, because the (laws of) addition and subtraction (of the Sun's ascensional difference and earthsine) in the night are contrary to those in the day.² The Rsine of the Sun's altitude in the night is required (i) in the calculation of the elevation of lunar horns,³ and (ii) in the calculation of the solar eclipse.4 The details of the method indicated in the above stanza have been explained by Parameśvara as follows: "(When the Sun is) in the northern hemisphere, having calculated the Rsine of the given nocturnal asus (i.e., those elapsed since sunset in the first half of the night or those to elapse before sunrise in the second half of the night) as increased by the (Sun's) ascensional difference, (then) multiplying (that) by the day-radius and dividing by the radius, (then) from the (resulting) quotient subtracting the earthsine, and (finally) multiplying the remainder by the Rsine of the colatitude and dividing by the radius is obtained the Rsine of the Sun's altitude. (When the Sun is) in the southern hemisphere, the (Sun's) ascensional difference and the earthsine are (respectively) subtractive and additive: this is the difference."5 1 This rule is found also in BrSp.Si. iii, 33; LBh, iii. 11; ŚiDVṛ, I, iii. 29; Sise, iv. 41. 2 This rule is found also in BrSp.Si, iii. 63: LBh, iii. 11; Sise, iv. 89. ³ See BrSpSi, iii. 63. 4 See Parameśvara's comm. on LBh, iii, 11. 5 Parameśvara's comm. on LBh. iii. 11.
