140 TRUE LONGITUDE OF A PLANET The true planet is assu- med to move on the sighra epicycle with the same angu- lar velocity as the true-mean planet appears to have in the deferent with respect to the sighrocca. Whereas the true- mean planet appears to move on the deferent (in the clock- wise direction) away from the sighrocca, the true pla- net is supposed to move on the epicycle, centred at the true-mean planet, in the anti- clock-wise direction, so that the line ST is always parallel to EV. F E Fig. 15 BP 3 But and G U Let the line ET intersect the deferent at R. Then R denotes the true position of the planet on the deferent. If T be the first point of Aries, then L SET (or arc SUT) is the true-mean longitude of the planet, and RET (or arc RUT) is the true longitude of the planet. The arc RS of the deferent, by which the true longitude of the planet differs from the true-mean longitude, denotes the planet's sighra correction (usually called sighraphala). It is derived as follows: Let SF, TG, and SH be the perpendiculars drawn from S, T, and S. on, EV, ES produced and ET respectively. Now arc VS TV-Ts, i.e., ŝighrakendra = (longitude of fighrocca)- (longitude of true- mean planet). Let this sighrakendra (reduced to bahu, if necessary) be denoted by . Then comparing the similar triangles TGS and SFE, we get SFXST TG = ES SF == ST Rsin , sighra epicycle 360 corrected sighra epicycle¹ ES 80 ¹ As pointed out earlier, this corrected epicycle is divided by 41.
