Page:Sewell Indian chronography.pdf/186
Seeing that in many of the calculations necessary for the verification of Indian dates the moment of occurrence of mean Mēsha saṁkrānti according to the First Ārya Siddhānta has to be ascertained; and since in the text (Example 5) I have advised that this moment be found, first, by taking from the Indian Calendar, Table I. (or finding), the moment of true or apparent Mēsha saṁkrānti, and, secondly, by adding to this the amount of the Ārya Siddhānta śōdhya taken as a constant, which addition gives the moment of mean Mēsha saṁkrānti by that authority—I have now thought it advisable to still further save trouble to calculators by giving a Table which at once yields the moment of mean Mēsha saṁkrānti for a period of 576 years.
I take the period A.D. 499 to 1075 because it is certain that the moment of mean Mēsha saṁkrānti in A.D. 499 was exactly at 6 h. 0 m. Laṅkā time, or exactly at noon, on March 21st in that year (§ 162 above); and this fact provides a sure basis from which to work. Also because both the Original Sūrya Siddhānta and the First Ārya Siddhānta were at that moment in exact coincidence, which they were at no other time. Starting from that point, the subsequent figures are obtained by adding 6 h. 12.5 m. annually: this is composed of 12.5 m., the time by which the length of the solar year of the First Ārya Siddhānta exceeds that of the Julian year, plus the 6 h. which in the Julian calendar are only brought to account in each fourth year; and 24 h. are, of course, retrenched from col. 5 and are added in cols. 2, 3, 4, whenever the accumulation of the annual additive amount passes from below to above one complete day.
The number of years for which the Table is given, viz.: 576, is chosen because, with these moments of mean Mēsha saṁkrānti fixed for such a period, which covers exactly what we may style a cycle of the Mēsha saṁkrānti according to this work, it is easy to ascertain the similar moment of any year, earlier or later than the period so covered. The rules given for apparent Mēsha saṁkrāntis in §§ 47 to 51 apply equally to mean Mēsha saṁkrāntis when the time of the latter is known.
Example. By the Table, mean Mēsha saṁkrānti of A.D. 499 took place on (1) Sunday, March 21st, at 6 h. 0 m. By the rule given in § 54, mean Mēsha saṁkrānti of (499 + 576 =) A.D. 1075 took place on (1 + 4 =) 5 Thursday (21 + 5 =) March 26th at 6 h. 0,., and this is the entry for that year given in the Table. Similarly, Mēsha saṁkrānti of 78 B.C. (§ 50, 577 − 499) took place at 6 h. 0 m. on (1, or 8, − 4 =) 4 Wednesday, March 16th (21 − 5).
From this Table we can also determine the apparent Mēsha saṁkrānti for any desired year according to the Ārya Siddhānta. Having found the moment of mean Mēsha saṁkrānti by the Table, or as shown in the example, deduct the śōdhya, viz. 2 d. 3 h. 32.5 m. The result is the moment of apparent Mēsha saṁkrānti. If the time is wanted according to Dr. Schram's valuation of the śōdhya, add 1 m. 4 s. to the (mean or true) final result.