213 MIDNIGHT DAY-RECKONING A rule for finding the celestial latitude of a planet : 31 (ii)-33. (From the longitude of a planet severally) subtract the longitudes of its (manda and sighra) pātas, and therefrom calculate (as usual) the corresponding celestial latitudes of that planet. Add them or take their difference according as they are of like or unlike directions. Then is obtained the true celestial latitude of that particular planet. The true celestial latitude of any other planet is also obtained in the same way. The remaining (astronomical) determinations are the same as stated before. This all is in brief the difference of the other tantra (embodying the midnight day-reckoning of Aryabhața I). A rule for finding the longitude of the true-mean planet according to the midnight day-reckoning: 34. Apply half the sighraphala and (then) half the mandaphala to the longitude of the planet's own mandocca (reversely). From the resulting longitude of the planet's mandocca calculate (the mandaphala and apply it to the the mean longitude of the planet: the resulting longitude of planet is stated to be) the true-mean longitude of the planet. This is stated to be another difference (of the midnight day-reckoning).¹ Length of the circle of the sky and derivation of the lengths of the orbits of the planets : 35. Multiply the revolutions of the Moon (in a yuga) by 32,40,000 and then discard the zero in the unit's place: (this is the length of the circle of the sky in terms of yojanas). (Severally) divide that by the revolutions of the planets (in a yuga) thus are obtained the lengths of the orbits of the respective planets in terms of yojanas. From stanzas 20 and 35 it is evident that one yojana of the sunrise day-reckoning is one and a half times that of the midnight day-reckoning. 1 This rule is the same as found in PSi, xvii. 4-9; SuSi, ii, 44; MSi, iii. 28; and SiTV, ii. 247.
