Page:Sewell Indian chronography.pdf/112

Calculation by our Tables (which are always framed for mean sunrise) for the sunrise of the Wednesday concerned, or September 12th, A.D. 1894, is as follows:—

	d.	w.	a.	b.	c.
Chaitra śuk. 1 (Table I.)	7 April (97)	0	296	802	265
Interval to Bhādr. śuk. 13, 150 tithis to end of Śrāvaṇa + 12 expired tithis in Bhādr. = 162 tithis = 158 days = (Table IV.)	(158)	4	3504	734	433
At sunrise on (255 =, by Table IX.) Wed., Sept. 12th	(255)	4	3800	536	698
Equation ${\displaystyle b}$ (Table VI.)			109
Equation ${\displaystyle c}$ (Table VII.)			118
${\displaystyle t=}$			4027

Accordingly (Table VIII.) the 13th tithi began (4027 − 4000) at 27, or (Table X.) 1 h. 55 m. before sunrise on Wednesday and ended (4333 − 4027 =) at 306, or (Table X.) 21 h. 42 m. after sunrise. Continued calculation, however, for very accurate results shows that the 13th tithi began at 2 h. 4 m. before sunrise on Wednesday and ended at 23 h. 54 m., or six minutes before sunrise on the Thursday; so that by our Tables this 13th tithi would have been regular and not adhika, since it did not touch the Thursday sunrise.

This example shows how careful epigraphists have to be when calculating. The difference of longitude between Laṅkā (E. long. 75° 46′) and Poona (E. long. 73° 55′) causes the 13th tithi, which—calculating as all our Tables do for the longitude of Lanka, we have found to have ended six N.B. minutes before sunrise on the Thursday—to have ended at Poona after sunrise on that day; since to its ending-time we have to add 8 m. for longitude (Table XI.). While it ended at 23 h. 54 m. on the Wednesday at Laṅkā, it ended at oh. 2m. on the Thursday at Poona; and therefore, whereas at Poona the 13th tithi was repeated, it would not have been so at Laṅkā. At Poona the second 13th tithi was associated with the civil day beginning at mean sunrise on September 13th, since it was current at that moment. At a place on the meridian of Laṅkā, however, the civil day September 13th would have been coupled regularly with the 14th tithi, which was actually current at mean sunrise on that day. To put the case in another way:—At the time when at Laṅkā the hour was 6 a.m. it was 5.52 a.m. at Poona, and, since the 13th tithi ended at 5.54 a.m., it was current at mean sunrise at Poona, but not at Laṅkā.

Another reason for a difference in results is that while we follow throughout the Ārya and Sūrya Siddhāntas, the Poona almanack-makers have for many years past been including in their calculations certain corrections introduced in the 16th century by Gaṇēśa Daivjña (Ind. Cal., p. 13, note 2), and this practice is general in the Mahratta country. The example is therefore instructive. It shows how different results may arise from differences in local practice, and proves the necessity of careful calculation when the first approximate result arrived at shows that a tithi began or ended very close to sunrise.

We continue our examination of this Pañchāṅg for the kshaya or expunged tithi in the second fortnight of the same month. We work for the moon's age at the three successive sunrises of the 21st, 22nd and 23rd September, Friday, Saturday and Sunday.

	d.	w.	a.	b.	c.
As before. Chait. śuk. 1st (Table I.)	7 April (97)	0	296	802	265
Interval to Bhādr. kṛ. 6, 150 tithis to end of Śrāvaṇa + 20 expired tithis in Bhādr. = 170 tithis = 167 days = (Table IV.)	(167)	6	6552	61	457
At sunrise on (264 =) September 21st, Friday	(264)	6	6848	863	722
Equation ${\displaystyle b}$ (Table VI.)			34
Equation ${\displaystyle c}$ (Table VII.)			120
${\displaystyle t=}$			7002