Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/302

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ADDITIONS AND CORRECTIONS.

Art. 23, p. 9.

A better description of the saṅkrântis may be given thus. The sâyana Mesha saṅkrânti, also called a Vishuva saṅkrânti, marks the vernal equinox, or the moment of the sun's passing the first point of Aries. The sâyana Karka saṅkrânti, three solar months later, is also called the dakshiṇâyana (southward-going) saṅkrânti. It is the point of the summer solstice, and marks the moment when the sun turns southward. The sâyana Tulâ saṅkrânti, three solar months later, also called a Vishuva saṅkrânti, marks the autumnal equinox or the moment of the sun's passing the first point of Libra. The sâyana Makara saṅkrânti, three solar months later still, is also called the uttarâyana (northward-going) saṅkrânti. It is the other solstitial point, the moment when the sun turns northward. The nirayana (or sidereal) Mesha and Tulâ saṅkrântis are also called Vishuva saṅkrântis, and the nirayana Karka and Makara saṅkrântis are also, though erroneously, called dakshiṇâyana and uttarâyana saṅkrântis.

Art. 90, p. 52.

Line 6. After "we proceed thus" add;—"The interval of time between the initial point of the luni-solar year (Table I., Cols. 19, 20) and the initial point of the solar year by the Sûrya Siddhânta (Table I., Cols. 13, 14, and 15a, or 17a^[1]) can be easily found.

Line 9. After "Art. 151" add;—"or according to the process in Example I, Art. 148."

Line 16. After "intercalations and suppressions" add;—We will give an example. In Professor Chhatre's Table, Kârttika is intercalary in Śaka 551 expired, A.D. 629—30 (see Ind. Ant., XXIII. p. 106); while in our Table Âśvina is the intercalary month for that year. Let us work for Âśvina. First we want the tithi-index ( $t$ ) for the moments of the Kanyâ and Tulâ saṅkrântis. In the given year we have (Table I., Col. 19) the initial point of the luni-solar year at sunrise on 1st March, A.D. 629, (=60), and (Cols. 13, 17) the initial point of the solar year by the Ârya-Siddhânta (= 17 h. 32 m. after sunrise on March 19th of the same year). By the Table given below (p. 151) we find that the initial moment of the solar year by the Sûrya Siddhânta was 15 minutes later than that by the Ârya Siddhânta. Thus we have the interval between the initial points of the luni-solar and solar years, according to the Sûrya Siddhânta, as 18 days, 17 hours, and 47 minutes. Adding this to the collective duration up to the moment of the Kanyâ and Tulâ saṅkrântis (Table III., Col. 9), i.e., 156 days, 11 hours and 52 minutes, and 186 days, 22 hours and 27 minutes respectively, we get 175 days, 5 hours, 39 minutes, and 205 days, 16 hours, 14 minutes.

We work for these moments according to the usual rules (Method C, p. 77).

	a.	b.	c.
For the beginning of the luni-solar year (Table I., Cols. 23, 24, 25)	9994	692	228
For 175 days (Table IV.)	9261	351	479
For 5 hours (Table V.)	71	8	1
For 39 minutes (Do.)	9	1	0
	9335	52	708

↑ Our $a,b,c,$ (Table I., Cols. 23, 24, 25) are calculated by the Sûrya Siddhânta, and therefore we give the rule for the Sûrya Siddhânta. The time of the Mesha saṅkrântis by the Ârya Siddhânta from A.D. 1101 to 1900 is given in Table I. That for years from A.D. 300 to 1100 can be obtained from the Table on p. 151.

[1] Our $a,b,c,$ (Table I., Cols. 23, 24, 25) are calculated by the Sûrya Siddhânta, and therefore we give the rule for the Sûrya Siddhânta. The time of the Mesha saṅkrântis by the Ârya Siddhânta from A.D. 1101 to 1900 is given in Table I. That for years from A.D. 300 to 1100 can be obtained from the Table on p. 151.

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