Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/97

(a) The day corresponding to Jyeshṭha śukla 5th.

	d.	w.	a.	b.	c.
Śaka 1703 current, Chaitra śukla 1st, (Table I., cols. 19, 20, 23, 24, 25)	96	4	1	657	267
Approximate number of days from Chaitra śukla 1st to Jyeshṭha śuk. 5th, (64 tithis reduced by a 60th part, neglecting fractions, = 63,) with its (${\displaystyle w}$) (${\displaystyle a}$) (${\displaystyle b}$) (${\displaystyle c}$) (Table IV.)	63	0	1334	286	172
	159	4	1335	943	439
Equation for (${\displaystyle b}$) (943) (Table VI.)			90
Equation forDo. (${\displaystyle c}$) (439) (Table VII.)			38
			1463	${\displaystyle =t}$.
(${\displaystyle t}$) gives śukla 5th (Table VIII., cols. 2, 3) (the same as the given tithi).
${\displaystyle (d)-1}$, (N.B. iii., Art. 147), or the number of days elapsed from January 1st, =||158

158 = June 7th (Table IX.). A.D. 1780 is the corresponding year, and 4 (${\displaystyle w}$) Wednesday is the week-day of the given tithi.

Answer.—Wednesday, June 7th, 1780 A.D.

(b) The ending of the tithi Jyeshṭha śuk. 5. (Table VIII.) 1667 − 1463 = 204 = (14 h. 10 m. + 0 h. 17 m.) = 14h. 27 m. (Table X.). Therefore the tithi ends at 14h. 27 m. after mean sunrise on Wednesday. For more accurate time we proceed as follows:

	a.	b.	c.
At sunrise on Wednesday (see above)	1335	943	439
For 14 hours (Table V.)	198	21	2
For 27 minutes, (Do.)	6	1	0
	1539	965	441
Equation for (${\displaystyle b}$) (965) (Table VI.)	109
Equation forDo. (${\displaystyle c}$) (441) (Table VII.)	38
	1686	${\displaystyle =t}$.

1686 − 1667 (Table VIII.) = 19 = 1 h. 21m.; and 1 h. 21 m. deducted from 14 h. 27 m. gives 13 h. 6 m. after sunrise on Wednesday as the moment when the tithi ended. This is sufficient for all practical purposes. For absolute accuracy we proceed again.

	a.	b.	c.
For sunrise (as before)	1335	943	439
For 13 hours (Table V.)	183	20	1
For 6 minutes (Do.)	1	0	0
	1519	963	440
Equation for (${\displaystyle b}$) (963) (Table VI.)	108
Equation forDo. (${\displaystyle c}$) (440) (Table VII.)	38
	1665	${\displaystyle =t}$.