पृष्ठम्:महाभास्करीयम्.djvu/२३०

TRUE LONGITUDE OF MARS, ETC., BY ECCENTRIC THEORY ed the once-corrected planet). Then correct it by the sighrocca operation. (The planet thus obtained is called the twice-corrected planet). Then find the difference between the two planets thus obtained (i.e., the once-corrected and twice-corrected pla- nets); divide that by two; and apply it to the once-corrected planet, as before. Whatever is thus obtained should be again corrected by the mandocca operation. Next calculate the diffe- rence between the twice-corrected planet, as corrected by the mandocca operation, and that (twice-corrected planet). Apply whatever be the difference between the twice-corrected planet as corrected by the mandocca operation and the twice-corrected planet to the mean longitude of the planet, as before. That (i.e., the resulting longitude) corrected by the sighrocca operation is the true longitude of the planet. 145 Thus has been stated the method for finding (the true lon- gitudes of) Mars, Saturn, and Jupiter under the eccentric theory. Now is described the procedure to be adopted in the case of the remaining planets (viz. Mercury and Venus). (First of all obtain the mean planet as corrected by the sighrocca operation). Then add half the difference between the mean planet corrected by the sighrocca operation and the mean planet to or subtract that from the planet's mandocca, according as the mean planet corrected by the sighrocca operation is less or greater (than the mean planet). Thus is obtained the true mandocca. Then find out, by the method under the eccen- tric theory,' the correction due to the true mandocca for Mercury as well as for Venus. The mean longitudes of Mercury and Venus each corrected for that and thereafter for the correction due to the sighrocca are known as true longitudes of the planets. The procedure for finding the true longitudes of the superior and inferior planets stated in stanzas 40-44 according to the epicyclic theory has been translated in the above stanzas into the eccentric theory. The results in both cases are the same. 1 The method is to find the difference between (i) the mean planet corrected by the mandocca operation and (ii) the mean planet.