Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/51

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THE HINDU CALENDAR.
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45 pa., we get 2 d. 31 gh. 55.56 pa. Add this to the moment of the Mesha saṅkrânti as given in Table I., cols. 13—16, viz., 16th March, 308 A.D., Tuesday, at 41 gh. 40 p., and we have 19th March, Friday, 13 gh. 35.56 p. after mean sunrise as the moment when Durmati ends and Dundubhi begins. Here again, since Dundubhi commences within four days of the Mesha saṅkrânti, it will be expunged.

c. By the Sûrya-Siddhânta with the bîja (to be used for years after about 1500 A.D.). Multiply the expired Kali year by 117. Subtract 60 from the product. Divide the result by 10000. To the figures of the quotient, excluding fractions, add the number of the expired Kali year plus 27. Divide the sum by 60. And the remainder, counted from Prabhava as 1, is the samvatsara current at the beginning of the given solar year. Subtract from 10000 the remainder left after the previous division by 10000. Multiply the difference by 361, and divide the product by 10000. Add 15 pa. The result is the number of days, etc., that have elapsed between the apparent Mesha sankranti and the end of the samvatsara current thereon.[1] Example.— Required the samvatsara current at the beginning of Śaka 1436 expired, and the moment when it ends. Śaka 1436 expired = Kali 4615 expired (Table I.), ⁠4615 × 117 − 60/10000⁠ = ⁠53+9895/10000⁠. ⁠53 + 4615 + 27/60⁠ = ⁠78+15/60⁠. The remainder 15 shews that Vṛisha was current at the Mesha-saṅkrânti. ⁠(10000 − 9895) 361/10000⁠ + 15 p. = 3 d. 47 gh. 25.8 p. + 15 p. = 3 d. 47 gh. 40.8 p. Table I. gives the Meshasaṅkrânti as March 27th, 44 gh. 25 p., Monday. 27 d. 44 gh. 25 p. + 3 d. 47 gh. 40.8 p. = 31 d. 32 gh. 5.8 p.; and this means that Vṛisha ended at 32 gh. 5.8 p. after mean sunrise at Ujjain on Friday, 31st March. At that moment Chitrabhânu begins, and since it began within four days of the Mesha-saṅkrânti, it is expunged.

d. Bṛihatsaṁhitâ and Jyotishatattva Rules. The rules given in the Bṛihatsaṁhitâ and the Jyotishatattva seem to be much in use, and therefore we give them here. The Jyotishatattva rule is the same as that for the Ârya-Siddhânta given above, except that it yields the year current at the time of mean Mesha-saṅkrânti, and that it is adapted to Śaka years. The latter difference is merely nominal of course, as the moment of the beginning of a samvatsara is evidently the same by both.[2] We have slightly modified the rules, but in words only and not in sense.

The Jyotishatattva rule is this. Multiply the current Śaka year by 22. Add 4291. Divide the sum by 1875. To the quotient excluding fractions add the number of the current Śaka year. Divide the sum by 60. The remainder, counted from Prabhava as 1, is the samvatsara current at the beginning of the given year. Subtract the remainder left after previously dividing by 1875 from 1875. Multiply the result by 361. And divide the product by 1875. The result gives the number of days by which, according to the Ârya-Siddhânta, the samvatsara ends after mean Meshasaṅkrânti. The mean[3] Mesha-saṅkrânti will be obtained by adding 2 d. 8 gh. 51 pa. 15 vipa. to the time given in Table I., cols. 13 to 18.

Work out by this rule the example given above under the Ârya-Siddhânta rule, and the result will be found to be the same by both.

The Bṛihatsaṁhitâ rule. Multiply the expired Śaka year by 44. Add 8589. Divide the sum by 3750. To the quotient, excluding fractions, add the number of the expired Śaka year

  1. ↑ In these three rules the apparent Mesha-saṅkrânti is taken. If we omit the subtraction of 108, 11, and 60, and do not add 15 p., 1 gh. 45 p., and 15 p. respectively, the result will be correct with respect to the mean Mesha-saṅkrânti.
  2. ↑ I have not seen the Jyotishatattva (or "Jyotishtava" as Warren calls it, but which seems to be a mistake), but I find the rule in the Ratnamâlâ of Śrîpati (A.D. 1039). It must be as old as that by the Ârya-Siddhânta, since both are the same. [S. B. D.]
  3. ↑ If we add 4280 instead of 4291, and add 1 gh. 45 pa. to the final result, the time so arrived at will be the period elapsed since apparent Mesha-saṅkrânti. Those who interpret the Jyotishatattva rule in any different way have failed to grasp its proper meaning. [S. B. D.]
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