62 DIRECTION, PLACE AND TIME In fact, however, the rays coming from the Sun are not exactly parallel, so that the angle between the gnomon and the Sun's ray reaching the ground through the upper end of the gnomon is not exactly equal to the zenith distance of the Sun. Moreover, the shadow which is actually measured is the umbra (i.e., the shadow between the foot of the gnomon and the point where the ray coming from the uppermost point of the Sun's disc and passing through the upper end of the gnomon meets the ground) and not the theoretical shadow corresponding to the central ray of the Sun coming through the upper end of the gnomon. Later Hindu astronomers have, therefore, prescribed corrections to the results deter- . mined according to the rules in the above stanza.¹ 4 For practical purposes the rules stated above are good enough. The error is negligible. 1 Rules for determining the declination, day-radius, earthsine, and ascensional difference (for the Sun or a point on the ecliptic): 6-7. Multiply the Rsine of the given longitude by 1397 and always divide by the radius; the result is the Rsine of the declination for that time. Subtract the square of that (Rsine of the declination) from the square of the radius and then take the square root (of the difference); the result is called the day-radius.³ Multiply the Rsine of the latitude by (the Rsine of) the given declination and divide by (the Rsine of) the colatitude: the result is the earthsine. Multiply the earthsine by the radius and then divide (the product) by the day-radius; then reduce (the resulting Rsine) to arc. Whatever (arc) is thus obtained is termed "the ascensional difference" by the best amongst the good (astronomers).5 1 These corrections occur in KPr, iv. 2; KP, viii. 3; and TS, iii. 10(ii)-11. } 2 This rule is found also in S Si, ii. 28; BrSpSi, ii. 55; LBh, ií. 16; SiDVr, I..ii. 17; Sise, iii. 63-64; Si Si, I, ii. 47(ii). 3 This rule is found also in A, iv. 24; BrSpSi, ii. 56; LBh, ii. 17; ŚiDVŢ, I, ii. 18; Siśe, iii. 66; SiŚi, I, ii. 48.
- This rule is found also in A, iv. 26; LBh, ii. 17-18; SiSe, iii. 65.
5 This rule is found also in üsi, ii. 61; BrSp.Si, ii. 57-58; LBh, ii. 18; SiDV, I, ii. 18; SiSe, iii. 67 (i); SiŚi, I, ii. 49 (i). .....: IV..
