पृष्ठम्:महाभास्करीयम्.djvu/१६५

80 DIRECTION, PLACE AND TIME The Sun's altitude for the night has been called patala-sanku by Brahmagupta.¹ Three rules for finding the time elapsed since sunrise in the forenoon or to elapse before sunset in the afternoon when the Sun has a given altitude : 27-29. Multiply the Rsine of the Sun's altitude derived from the given shadow (of the gnomon) by the radius and divide (the product) by (the Rsine of) the colatitude. Then subtract the minutes of the earthsine from or add them to the resulting quantity according as the Sun is in the six signs beginning with Aries or in the southern hemisphere. Multiply the resulting quantity by the radius and divide (the product) by the day-radius. To the corresponding arc apply the ascensional difference contrarily to the above: thus is obtained the number of asus (elapsed since sunrise in the forenoon or to elapse before sunset in the afternoon). These very same asus corresponding to the day to elapse (before sunset in the afternoon) or the day elapsed (since sunrise in the forenoon),. when divided by 360, are declared to be the nadis, etc., (of the required time).² Or, multiply the given Rsine of the Sun's altitude by the square of the radius and divide by the product of the day-radius and (the Rsine of) the colatitude. To the result apply the Rsine of the (Sun's) ascensional difference as before (i.e., sub- tract or add according as the Sun is in the northern or southern hemisphere). Then to the corresponding arc reversely apply the asus of the ascensional difference: the result obtained is again the number of asus (elapsed since sunrise in the forenoon or to elapse before sunset in the afternoon.) Or, multiply the Rsine of the Sun's altitude by the hypotenuse of the equinoctial midday shadow and again by the ¹ See BrSp.Si, xv. 9. 2 This rule is found also in LBh, iii. 12-15 and in Sise, iv. 51-52,