Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/112

	d.	w.	h.	m.
(Brought over)	277	2	11	8
Subtract 1 from (${\displaystyle d}$) and (${\displaystyle w}$)	1	1
Last civil day of Karka =	226	1
Subtract 226 from the date number 246 (Table IX.) of the given day	246
Required date in the month Siṁha	20
Add this to (${\displaystyle w}$) casting out sevens		6
The required week-day is Saturday		0

The equivalents are therefore:— (see Table II., Part ii.)

153. We now proceed to give rules for finding the karaṇas on a given day,—the exact moments of their beginning and ending, and the karaṇa current at sunrise on any given day, or at any moment of any given day.

The karaṇas^[1] of a given tithi may be found by the following rule. Multiply the number of expired tithis by two. Divide this by 7; and the remainder is the karaṇa for the current half of the tithi. Example.— Find the karaṇa for the second half of kṛishṇa 8th. The number of expired tithis from the beginning of the month is (15 + ⁠7+1/2⁠ =) ⁠22+1/2⁠. ⁠22+1/2⁠ × 2 = 45. Casting out sevens the 3rd, or Kaulava, is the required karaṇa.

154. To find the exact moments on which the karaṇas corresponding to a given tithi begin and end. Find the duration of the tithi from its beginning and ending moments, as calculated by the method given in Arts. 139, 144, and 145 above. The first half of the tithi is the period of duration of its first karaṇa, and the second half that of the second.

Example xxii. Find the karaṇas, and the periods of their duration, current on Jyeshṭha śukla paṅchâmî (5th) of the Śaka year 1702 expired (1703 current). From Table VIII., cols. 4 and 5 we observe that (1) Bava is the first, and (2) Bâlava is the second, karaṇa corresponding to the 5th tithi. In the first example above (Art. 148) we have found that the tithi commenced on Tuesday, 6th June, A.D. 1780, at 15 h. 34 m. after mean sunrise, and that it ended on Wednesday, 7th June, at 13 h. 11 m. after mean sunrise. It lasted therefore for 21 h. 37 m. (8 h. 26 m. on Tuesday and 13 h. 11 m. on Wednesday). Half of this duration is 10 h. 48 m. The Bava karaṇa lasted therefore from 15 h. 34 m. after mean sunrise on Tuesday, June 6th, to 2 h. 22 m. after mean sunrise on Wednesday, June 7th, and the Bâlava karaṇa lasted thence to the end of the tithi.

155. The karaṇa at sunrise or at any other time can of course easily be found by the above method. It can also be calculated independently by finding the (${\displaystyle t}$) for the time given. Its beginning or ending time also can be found, with its index, by the same method as is used for that of a tithi. The index of a karaṇa can be easily found from that of a tithi by finding the middle point of the latter. For example, the index of the middle point of śukla 14th