TRUB LONGITUDE OF MARS, ETC., BY ECCENTRIC THEORY Rsin x (corrected sighra epicycle) 80 Again from the similar triangles ESH and ETG, we have TG X ES SH TET Therefore i.e., Rsin (arc RS) TG - >. 141 Rsin + x (corrected sighra epicycle) > R 80 x śighrakarṇa Therefore arc RS or sighraphala is the arc corresponding to the right hand side of this equality. This sighraphala is ided to or subtracted from the true-mean longi- tude of the planet according as the sighrakendra is less than 180° or grea- ter than 180°, because in the former case the true planet is in advance of the true-mean planet and in the latter case the true planet is behind the true- mean planet. Thus true longitude = true-mean longitude + śighraphala, according as the sighrakendra is less than or greater than 180°. The true longitude of the planet thus obtained was found to differ from the actual longitude determined from observation. Aryabhata I supposed that the error was due to the inaccuracy of the mandakendra (manda ano- maly). So to get rid of the error, in the case of the superior planets (Mars, Jupiter and Saturn), he applied in succession (i) half the planet's mandaphala, and (ii) half the planet's sighraphala to the manda- kendra of the planet; and in the case of the inferior planets (Mercury and Venus), he applied half the planet's sighraphala to the mandakendra of the planet From the mandakendra thus corrected, he calculated and applied in succession the mandaphala and the sighraphala corrections to the mean longitude of the planet. The same procedure has been follo- wed by the pupils and followers of Aryabhata I. Hence the rules stated in stanzas 40-44.
The device contemplated by Aryabhata I continued to be used by his followers, but it was never very successful. Naturally, it never came into general use. Several other devices were attempted from time to time by later astronomers. A rule relating to the eccentric theory: 45-46. The wise (astronomer) should apply the eccentric theory here (i. e., in the case of the planets Mars, etc.) also. (Under this theory the mandocca and sighrocca operations are as follows:)
