Page:Sewell Indian chronography.pdf/80
168. It is not necessary to frame separate tables for work in order to test a case of a Hindu calculator having referred the beginning-time of a Jovian cyclic year to the mean, instead of to the true or apparent Mēsha saṁkrānti; for the day, hour, and minute when that saṁvatsara began will always remain the same. The only point necessary to be remembered is that, mean Mēsha saṁkrānti taking place later than the true Mēsha saṁkrānti by the amount of the śōdhya interval (quoted above as "G" for each separate authority), whenever a Jovian saṁvatsara is found on calculation by the Tables to have begun in less than this quoted śōdhya interval after apparent Mēsha saṁkrānti, that saṁvatsara was not current at the moment of apparent Mēsha saṁkrānti, but was current at the moment of mean Mēsha saṁkrānti. Such a saṁvatsara must, therefore, with reference to apparent Mēsha saṁkrānti, be an expunged saṁvatsara, since it began after that moment and must have ended before the moment of the next apparent Mēsha saṁkrānti; and with reference to mean Mēsha saṁkrānti the preceding samvatsara must have been expunged.
169. Supposing No. 2, Vibhava, to be a saṁvatsara quoted in an inscription as giving its name to the current year, and therefore current at Mēsha saṁkrānti in that year, and supposing we find by our Tables that it began 2 d. 3 h. after apparent Mēsha saṁkrānti; we should know at once that, whether the Ārya or Sūrya Siddhānta had been used, the framer of the record had reckoned by mean, and not by apparent, Mēsha saṁkrānti; because, if the latter had been the basis of reckoning, the saṁvatsara current at that apparent Mēsha saṁkrānti and therefore giving its name to the year would not have been 2 Vibhava but 1 Prabhava, and 2 Vibhava would have been expunged. It began, according within such a short time after apparent Mēsha saṁkrānti that its ending, 361 days and a fraction must have occurred prior to apparent Mēsha saṁkrānti of the following year, and therefore it was not current at the astronomical beginning of either of the solar years concerned.
Calculations in India previous to about A.D. 1000 may always have been made with mean Mēsha saṁkrānti as the basis for ascertaining the coincidence of Jovian saṁvatsaras, and if it is desired to work our Tables on that basis it can be done in the following manner. Take the example in § 147 above (iii). Table XXVII. shows that in K.Y. 4362 No. 1 Prabhava began 315.4215 days after apparent Mēsha saṁkrānti. The Sūrya Siddhānta śōdhya being, as stated, taken as 2.1707 days we know that Prabhava began (315.4215 − 2.1707) 313.2508 days after mean Mēsha saṁkrānti. By Table XXVII.A we find that No. 35 Plava of that cycle began 143.8892 days less than 313.2508, i.e., 169.3616 days after mean Mēsha saṁkrānti, or 169 d. 8 h. 41 m. after it. Now from Table I. we have it that in the corresponding solar year apparent Mēsha saṁkrānti occurred on the 85th day at 1 h. 45 m. Therefore, mean Mēsha samkrānti occurred 2 d. 4 h. 6 m. (the śōdhya interval) later, i.e., on the 87th day at 5 h. 51 m. 87 d. 5 h. 51 m. + 169 d. 8 h. 41 m. = 256 d. 14 h. 32 m. 256 = Table IX., September 13th, A.D. 1295. And Plava began on that day at 14 h. 32 m. both when the calculation is made from apparent and from mean Mēsha saṁkrānti (see § 147). That is to say, the time-result is the same in both cases. The difference lies in the fact that Plava began 169 odd days after mean, but 171 odd days after true Mēsha saṁkrānti. And nothing is ever affected by calculating preferentially from one or the other basis except the question of the currency at mean or true Mēsha saṁkrānti, as already stated.
170. The astronomical basis, explained above, of calculating the saṁvatsaras and naming after them the solar years still prevails generally in Northern India. In Southern India it was in use down