82 DIRECTION, PLACE AND TIME It may be pointed out that the civil time elapsed since sunrise is equal to the sidereal time measured by the arc of the celestial equator lying between the hour circles which pass through the instantaneous position of the Sun and through the rising point of the ecliptic. For greater accuracy in the result, Aryabhata II (c. 950 A. D.) and Bhaskara II (1150 A. D.) prescribed the use of oblique ascensions of every 10 degrees of the ecliptic in place of those for every 30 degrees. Later on Muniśvara (1646 A.D.) and Kamalakara (1658 A. D.) prescribed the use of oblique ascensions of every degree of the ecliptic. Theoreti- cally accurate method for getting the longitude the rising point of the ecliptic was given earlier by the Kerala mathematician Nilakaṇṭha (1500 A. D.).¹ A rule for the determination of the longitude of the setting point of the ecliptic : 33. The longitude of the horizon-ecliptic point in the east² increased by half a circle (i.e., by 180°) is the longitude of the setting point of the ecliptic³. For, the time of setting of a sign is equal to the time taken in rising by the then rising sign. Bhaskara II also says: "The time in which a sign rises (above the horizon), is the same as that in which the seventh sign sets (below the horizon)." . A rule for obtaining the civil time measured since sunrise with the help of (i) the Sun's instantaneous sayana longitude and (ii) the sayana longitude of the rising point of the ecliptic, or the sidereal time elapsed since sunrise with the help of (i) the Sun's sayana longitude at sunrise and (ii) the sayana longitude of the rising point of the ecliptic: 34-36. Multiply the degrees of the traversed portion of the sign occupied by the rising point of the ecliptic by the ""5 1 His method occurs in TS, iii. 155(ii)-164(i). 2 i. e., the rising point of the ecliptic. 3 The setting point of the ecliptic is that point of the eclipti which lies on the western horizon. 4 Cf. ŚiDV, I, iii. 13(i); SiŚi, I, ii. 59(ii). 5 Siśi, I, ii. 59 (ii).
