Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/50

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34

THE INDIAN CALENDAR.

58. To find the current samratsara. The samvatsaras in our Table I., col. 7, are calculated by the Sûrya-Siddhânta without the bîja up to A.D. 1500, and with the bîja from AD. 1 501 to 1900; and are calculated from the apparent Mesha-saṅkrânti. If the samvatsara current on a particular day by some other authority is required, calculations must be made direct for that day according to that authority, and we therefore proceed to give some rules for this process.

59. Rules for finding the Bârhaspatya samvatsara current on a particular day.^[1]

a. By the Sûrya-Siddhânta.^[2] Multiply the expired Kali year by 211. Subtract 108 from the product. Divide the result by 18000. To the quotient, excluding fractions, add the numeral of the expired Kali year plus 27. Divide the sum by 60. The remainder, counting from Prabhava as 1, is the samvatsara current at the beginning of the given solar year, that is at its apparent Mesha-saṅkrânti. Subtract from 18000 the remainder previously left after dividing by 18000. Multiply the result by 361, and divide the product by 18000. Calculate for days, ghaṭikâs, and palas. Add 15 palas to the result. The result is then the number of days, etc., elapsed between the apparent Mesha-saṅkrânti and the end of the samvatsara current thereon. By this process can be found the samvatsara current on any date.

Example 1.—Wanted the samvatsara current at the beginning of Saka 233 expired and the date on which it ended. Śaka 233 expired = (Table I.) Kali 3412 expired. ⁠3412 × 214 − 108/18000⁠ = ⁠39+17824/18000⁠. 39 + 3412 + 27 = 3478. ⁠3478/60⁠ = ⁠57+58/60⁠. The remainder is 58; and we have it that No. 58 Raktâkshin (Table XII.) was the samvatsara current at the beginning (apparent Mesha-saṅkrânti) of the given year. Again; 18000 − 17824 = 176. ⁠176 × 361/18000⁠ = 3 d. 31 gh. 47.2 p. Adding 15 pa. we have 3 d. 32 gh. 2.2 pa. This shews that Raktâkshin will end and Krodhana (No. 59) begin 3 d. 32 gh. 2.2 pa. after the apparent Meska saṅkrânti. This last, by the Sûrya Siddhânta, occurred on 17th March, A.D. 311, at 27 gh. 23 pa. (see Table I., col. 13, and the Table in Art. 96), and therefore Krodhana began on the 20th March at 59 gh. 25.2 pa., or 34.8 palas before mean sunrise on 2 1st March. We also know that since Krodhana commences within four days after Mesha it will he expunged (Art. 54 above.)

b. By the Ârya Siddhânta. Multiply the expired Kali year by 22. Subtract 11 from the product. Divide the result by 1875. To the quotient excluding fractions add the expired Kali year + 27. Divide the sum by 60. The remainder, counted from Prabhava as 1, is the samvatsara current at the beginning of the given solar year. Subtract from 1875 the remainder previously left after dividing by 1875. Multiply the result by 361. Divide the product by 1875. Add 1 gh. 45 pa. to the quotient. The result gives the number of days, etc., that have elapsed between the apparent Mesha-saṅkrânti and the end of the samvatsara current thereon.

Example 2.—Required the samvatsara current at the beginning of Śaka 230 expired, and the time when it ended.

Śaka 230 expired = Kali 3409 expired. ⁠3409 × 22 − 11/1875⁠ = ⁠39+1862/1875⁠. 39 + 3409 + 27 = 3475, which, divided by 60, gives the remainder 55. Then No. 55 Durmati (Table XII.) was current at the beginning of the given year. Again; 1875 − 1862 = 13. ⁠13 × 361/1875⁠ = 2 d. 30 gh. 10.56 pa. Adding 1 gh.

↑ By all these rules the results will be correct within two ghaṭikâs where the moment of the Mesha-saṅkrânti according to the authority used is known.
↑ The rule for the present Vasishṭha, the Śâkalya Brahma, the Romaka, and the Soma Siddhântas is exactly the same. That by the original Sûrya-Siddhânta is also similar, but in that case the result will be incorrect by about 2 ghaṭikâs (48 minutes). For all these authorities take the time of the Mesha-saṅkrânti by the present Sûrya-Siddhânta or by the Ârya-Siddhânta, whichever may be available. The moment of the Mesha-saṅkrânti according to the Sûrya-Siddhânta is given in our Table I. only for the years A.D. 1100 to 1900. The same moment for all years between A.D. 300 and 1100 can be found by the Table in Art. 96. If the Ârya-Siddhânta saṅkrânti is used for years A.D. 300 to 1100 the result will never be incorrect by more than 2 ghaṭikâs 46 palas (1 hour and 6 minutes). The Table should be referred to.

[1] By all these rules the results will be correct within two ghaṭikâs where the moment of the Mesha-saṅkrânti according to the authority used is known.

[2] The rule for the present Vasishṭha, the Śâkalya Brahma, the Romaka, and the Soma Siddhântas is exactly the same. That by the original Sûrya-Siddhânta is also similar, but in that case the result will be incorrect by about 2 ghaṭikâs (48 minutes). For all these authorities take the time of the Mesha-saṅkrânti by the present Sûrya-Siddhânta or by the Ârya-Siddhânta, whichever may be available. The moment of the Mesha-saṅkrânti according to the Sûrya-Siddhânta is given in our Table I. only for the years A.D. 1100 to 1900. The same moment for all years between A.D. 300 and 1100 can be found by the Table in Art. 96. If the Ârya-Siddhânta saṅkrânti is used for years A.D. 300 to 1100 the result will never be incorrect by more than 2 ghaṭikâs 46 palas (1 hour and 6 minutes). The Table should be referred to.

[1]

[2]