120 TRUE LONGITUDE OF A PLANET The true daily motion determined from the above formulae is called karnabhukti ("the motion derived from the hypotenuse"). A rule for finding the true daily motion (called jivabhukti) of the Sun: 14. Or, multiply the current Rsine-difference by the (mean) daily motion (of the Sun) and divide by 225. Then multiply that by the (Sun's) own (tabulated) epicycle and divide by 80: the result thus obtained subtracted from or added to the (Sun's) mean daily motion (according as the Sun is in the half-orbit beginning with the anomalistic sign Capricorn or in that begin- ning with the anomalistic sign Cancer) gives the true daily mo- tion (of the Sun).¹ Let M and M' be the mean longitudes and S and S' the true longi- tudes of the Sun at sunrise yesterday and today respectively. Also let 0 and be the corresponding values of the bahu (due to the Sun's mean anomaly). Then, we have and S=MF S'=M'F. Rsin 0x1₁ 80 S'-S=(M'-M) F
m
Rsin 0' x 1₂ 80 where r, is the Sun's tabulated epicycle, or + sign being taken accord- ing as the Sun's mean anomaly is less than 180° or greater. Therefore, " (Rsin 0 Rsin {)Xr, 80 Rsin)XI, (Rsin' 80 where m denotes the Sun's mean daily motion, - or + sign being taken according as the Sun's mean anomaly is in the half-orbit beginning with the sign Capricorn or in that beginning with Cancer. ¹ This rule occurs also in ŚDVe, I, ii. 38 and Sise, iii. 40-41.
- Vide supra, stanza 8.
