Page:Sewell Indian chronography.pdf/107

week-day, and, since it was in a South-Indian inscription, we gather that the date was fixed by one of the South-Indian Rules iii. or iv. (See footnote 3, p. 12, Indian Calendar.)

[Work by the Sūrya Siddhānta is precisely similar, only the Mēsha saṁkrānti must be fixed by that authority, and the collective duration of the months must be taken from Table XVIII.B.]

Example 20.—To find the true current tithi, its beginning-time and ending-time at any moment by the Ārya or Sūrya Siddhānta.

Rule. (For full directions see Examples I. to VIII., §§ 139–148, Indian Calendar, pp. 77–86.) Having established the exact year concerned, take from Table I. the details (cols. 19–25) for mean sunrise on the first civil day of the luni-solar year. Add to these the similar details for the number of civil days contained in the interval between that moment and mean sunrise on the given day, obtaining them from cols. 3, 3a of Table III. and from Table IV. The product shows the details for mean sunrise on the day concerned. If necessary, add the same details for any intervening hours and minutes up to the special moment given. From the ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$ so resulting calculate the ${\displaystyle t}$ according to the Indian Calendar rule quoted, continuing the process as there laid down, if absolute accuracy is desired—the first result obtained being a close approximation. The final result is absolutely accurate in mean time. If it is necessary to work for true or apparent time use the corrections given in Tables F and G of "Eclipses of the Moon in India," or those given by Prof. Jacobi in Epigraphia Indica, II., 487 ff. The process is the same both by the Ārya and Sūrya Siddhāntas.

Wanted the tithi current at mean sunrise on March 25th, A.D. 1149, K.Y. 4250 expired.

Table I., col. 19, shows that the first civil day of the luni-solar year, or the first day of the month Chaitra in this year, was March 12th. We take the necessary details:—

	d.	w.	a.	b.	c.
At mean sunrise, Chaitra śukla 1.	12 March (71)	0	82	951	246
Interval to given day, 13 days (Table IV.). For the week-day (13 − 7 =) 6.	13 March (13)	6	4402	472	36
At mean sunrise, March 25th (6 = Friday)	25 March (84)	6	4484	423	282
Equation ${\displaystyle b}$ (Table VI.)			206
Equation ${\displaystyle c}$ (Table VII.)			1
${\displaystyle t=}$			4691

4691, by Table VIII., col. 3, = the 15th śukla tithi of Chaitra, and this was the true tithi current at mean sunrise. This is the date of an actual inscription in South India. If the moment given had been a stated hour and minute of that day we should have added to the ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$ already obtained the ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$ for those hours and minutes from Table V., and from the total have obtained the value of ${\displaystyle t}$.

[The inscription in question gave the date as in a king's regnal year known to correspond with K.Y. 4250 expired, and it told us that at mean sunrise of a certain Friday the 15th tithi of the bright half (śukla) of the luni-solar month Chaitra was current. The luni-solar year K.Y. current 4251 began, as already shown, on March 12th, A.D. 1149. The number of elapsed tithis was 14. But if we had begun by adding to the ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$ of March 12th the ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$ for 14 days, we should have found that the 16th tithi, and not the 15th, was current at sunrise, and that the corresponding week-day was a Saturday. This shows that it is unsafe to work otherwise than by the rule given.]