Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/103

commencement of that (Meshadi) year, viz., (${\displaystyle d}$) the date-indicator given in brackets after the day and month A.D. in col. 13, (${\displaystyle w}$) the week-day number (col. 14), and the time—either in ghaṭikâs and palas, or in hours and minutes as desired—of the Mesha saṅkrânti according to the Ârya-Siddhânta (cols. 15, or 17). For a Bengali date falling between A.D. 1100 and 1900, take the time by the Sûrya-Siddhânta from cols. 15a or 17a. When the result is wanted for a place not on the meridian of Ujjain, apply to the Mesha saṅkrânti time the correction given in Table XI. Under these items write from Table 111., cols. 6, 7, 8, or 9 as the case may be, the collective duration of time from the beginning of the year up to the end of the month preceding the given one—days under (${\displaystyle d}$), week-day under (${\displaystyle w}$), and hours and minutes or ghaṭikâs and palas under h. m., or gh. p. respectively. Add together the three quantities. If the sum of hours exceeds 24, or if the sum of ghaṭikâs exceeds 60, write down the remainder only, and add one each to (${\displaystyle w}$) and (${\displaystyle d}$). If the sum of (${\displaystyle w}$) exceeds 7, cast out sevens from it. The result is the time of the astronomical beginning of the current (given) month. Determine its civil beginning by the rules given in Art. 28 above.

When the month begins civilly on the same day as, on the day following, or on the third day after, the saṅkrânti day, subtract 1 from, or add 0, or1, to both (${\displaystyle d}$) and (${\displaystyle w}$), and then to each of them add the number of the given day, casting out sevens from it in the case of (${\displaystyle w}$). (${\displaystyle w}$) is then the required week-day, and (${\displaystyle d}$) will show, by Table IX., the A.D. equivalent of the given day.

N.B. i. When it is not certain whether the given year is Meshâdi or of another kind, or what rule for the civil beginning of the month applies, all possible ways must be tried.

N.B. ii. See N.B. ii., iii., iv., Art. 147, under the rules for the conversion of luni-solar dates.

Example ix. Required the week-day and the date A.D. corresponding to (Tamil) 18th Puraṭṭâśi of Rudhirodgârin, Kali year 4904 expired, (4905 current). (See example 7, p. 73.)

The given year, taken as a solar year, is Meshâdi. The month Puraṭṭâdi, or Puraṭṭâśi, corresponds to Kanyâ (Table II., Part ii. ), and the year is a Tamil (Southern) one, to which the Ârya Siddhânta is applicable (see Art. 21). Looking in Table I. along the line of the given year, we find that it commenced on 11th April (col. 13), A.D. 1803, and we write as follows:—

	d.	w.	h.	m.
(Table I., cols. 13, 14, 17)	101	2	10	7
(Table III., col. 7) collective duration up to the end of Siṁha	156	2	10	28
	257	4	20	35
This shows that the Kanyâ saṅkrânti took place on a (4) Wednesday, at 20 h. 35 m. after sunrise, or 2.35 a.m. on the European Thursday. (Always remember that the Hindu week-day begins at sunrise.) The month Kanyâ, therefore, begins civilly on Thursday.[1] (Rule 2(a), Art. 28.) We add, therefore 0 to (${\displaystyle d}$) and (${\displaystyle w}$)	0	0
Add 18, the serial number of the given day, to (${\displaystyle d}$) and, casting out sevens from the same figure, 18, add 4 to (${\displaystyle w}$)	18	4
	275	1

Then ${\displaystyle (w)=1}$, i.e., Sunday, and 275 = (Table IX.) 2nd October.

Answer.—Sunday, 2nd October, 1803 A.D.

Example x. Required the week-day and A.D. date corresponding to the 20th day of the Bengali (solar) month Phâlguna of Śaka 1776 expired, 1777 current, at Calcutta.