Page:Sewell Indian chronography.pdf/109

unit, or ⁠4+1/4⁠ m., either way, the difference rarely amounting to two units, or ⁠8+1/2⁠ m. All close cases should be examined by Prof. Jacobi's Special Tables (Epig. Ind., I.). In future I only take note as a rule of the first approximation, as it is needless to work every example further than this. But the full process must be carried through whenever the first approximation brings us near to sunrise. See, for an instance, Example 23 below.

Example 21.—Another example of the same. A year with a true intercalated lunar month.

Rule. The work is precisely the same; but in calculating the number of tithis or days to the given tithi or day from the first civil day of the luni-solar year, Chaitra śukla 1st, we must, if the given tithi belongs to a lunar month later than the month shown as intercalated in cols. 8 or 8a of Table I. (Ind. Cal.), add a month of 30 tithis to the interval.

Wanted the European day, week-day, and time corresponding to mean sunrise of the day described in an inscription as "Sunday, the 9th tithi of the dark fortnight of [amānta] Phālguna in Śaka 1124 expired."

The year (see Table I.) was K.Y. 4303 expired, A.D. 1202–3. Vaiśākha was the intercalated lunar month. The interval to the end of Māgha as given in Table III., col. 3, is 330 tithis, but in this year was 360 tithis because of the intercalation. Add 15 tithis of the bright half of Phalguna and 8 tithis of the dark half, total 23. Grand total 383 tithis, or (383 – ⁠383/64⁠),^[1] = 377 days approximately. Working for this interval we find it correct.

	d.	w.	a.	b.	c.
A.D. 1202 Chaitra śuk. 1 (Table I.) sunrise.	25 Feb. (56)	2	239	939	203
377 days (Table IV.)	(377)	6	7664	682	32
Sunrise, 377 days after Ch. śuk. 1	(433)	1	7903	621	235
Equation ${\displaystyle b}$ (Table VI.)			43
Equation ${\displaystyle c}$ (Table VII.)			0
${\displaystyle t=}$			7946

433 = (Table IX.) March 9th, of the following A.D. year. 1 = Sunday. ${\displaystyle t=7946}$ shows (Table VIII.) that the 9th kṛishṇa tithi of Phālguna was current at mean sunrise.

Answer. The sunrise in question was that of Sunday, March 9th, A.D. 1203.

The beginning and ending of the tithi can be calculated as in the last example.

Example 22.—Another example. Wanted in European reckoning the time of the occurrence of full-moon in amānta Mārgaśīrsha of K.Y. 3401 expired. (There was no added month in this year.) The given year = A.D. 300–1. Full-moon day is the 15th śukla tithi. Interval from Chaitra śukla 1st to the 15th tithi in Mārgaśīrsha = (to end of Kārttika, by Table III., col. 3, 240 tithis + 14 tithis in Mārg.) 254 tithis or (254 – ⁠254/64⁠) 250 days.

	d.	w.	a.	b.	c.
(Table I.) A.D. 300 Chait. śuk. 1 sunrise.	8 Mar. (68)	6	9981	896	255[2]
250 days (Table IV.)	(250)	5	4658	73	684
Sunrise, 377 days after Ch. śuk. 1	(318)	4	4639	969	939
Equation ${\displaystyle b}$ (Table VI.)			113
Equation ${\displaystyle c}$ (Table VII.)			83
At mean sunrise, ${\displaystyle t=}$			4835

318 = (Table IX.), the year A.D. being a leap-year, November 13th. 4 = Wednesday. At

1. ↑ See Indian Calendar, § 139, p. 77, note 4.
2. ↑ There is a misprint in Table I. The entries in cols. 21 to 25 against this year (p. iii.) should be respectively 35, .105, 9981, 896, 255.