Page:Sewell Dikshit The Indian Calendar (1896) proc.djvu/73

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THE HINDU CALENDAR.

57

The sun's perigee, 257° 14′ 22″.86. The moon, 355° 55′ 35″.32. The moon's perigee, 33° 39′ 58″.03. The moon's distance from the sun therefore was (355° 55′ 35″.32 − 349° 22′ 27″.92 =) 6° 33′ 7″.4 = .0182 of the orbit of 360". This (1.0182) reduced by 0.0200,6 comes to 0.99814; and consequently " $a$ " for that moment is 9981.41. The moon's mean anomaly " $b$ " was (355° 55′ 35″.32 − 33° 39′ 58″.03 =) 322° 15′ 37″.29 = 895.17. And the sun's mean anomaly " $c$ " was (349° 22′ 27″.92 − 257° 14′ 22″.86 =) 92° 8′ 5″.06 = 255.93.^[1] We therefore give $a=9981$ , $b=895$ , $c=256$ . The figures for any other year can if necessary be calculated from the following Table, which represents the motion. The increase in $a$ , $b$ , $c$ , for the several lengths of the luni-solar year and for 1 day, is given under their respective heads; the figures in brackets in the first column representing the day of the week, and the first figures the number of days in the year.

**Increase of a, b, c, in one year, and in one day.**
Number of days in the year.	a.	b. without bija.	b. with bija.	c.
354(4)	9875.703337	847.2197487	847.220646	969.1758567
355(5)	0214.335267	883.5113299	883.512230	971.9136416
383(5)	9696.029305	899.675604	899.676575	048.57161909
384(8)	0034.661235	935.967185	935.968158	051.3094039
385(0)	0373.293166	972.258766	972.259742	054.04789
001(1)	0338.63193033	036.291581211	036.291583746	002.737784906

103. Table II., Part i., of this table will speak for itself (see also Art. 51 above). In the second part is given, in the first five columns, the correspondence of a cycle of twelve lunar months of a number of different eras with the twelve lunar months of the Śaka year 1000,^[2] which itself corresponds exactly with Kali 4179, Chaitrâdi Vikrama 1135, and Gupta 738. Cols. 8 to 13 give a similar concurrence of months of the solar year Śaka 1000. The concurrence of parts of solar months and of parts of the European months with the luni-solar months is given in cols. 6 and 7, and of the same parts with the solar months in cols. 14 and 15. Thus, the luni-solar amânta month Âshâḍha of the Chaitrâdi Śaka year 1000 corresponds with amânta Âshâḍha of Kali 4179, of Chaitrâdi Vikrama 1135, and of the Gupta era 758; of the Âshâḍhâdi Vikrama year 1135, and of the Chedi or Kaḷachuri 828; of the Karttikâdi Vikrama year 1134, and of the Nêvâr year 198. Parts of the solar months Mithuna and Karka, and parts of June and July of 1077 A.D. correspond with it; in some years parts of the other

↑ Calculating by Prof. Jacobi's Tables, $a$ , $b$ , $c$ , are 9980, 896 and 255, each of which is wrong by 1.

The above figures were submitted by me to Dr. Downing of ihe Nautical Almanack office, with a request that he would test the results by scientific European methods. In reply he gave me the following quantities, for the sun from Leverrier's Tables, and and for the moon from Hansen's Tables (for the epoch A.D. 300, March 8th, 6 am., for the meridian of Ujjain). Mean long of sun 345° 51′ 47″.7, Do. of sun's perigee 253° 54′ 58″.5, Do. of moon 353° 0′ 36″0, Do. of moon's perigee 36° 9′ 48″.4. He also verified the statement that the sunrise on the morning of March 8th was that immediately following new moon. The difference in result is partly caused by the fact that Leverrier's and Hansen's longitudes are tropical, and those of the Sûrya-Siddhânta sidereal. Comparing the two results we find a difference of 0° 35′ 40″.9 in " $a$ ". 5° 24′ 49″.69 in " $b$ ", 0° 11′ 15″.87 in " $c$ ". The closeness of the results obtained from the use of (1) purely Hindu (2) purely European methods is remarkable. Our Tables being for Indian documents and inscriptions we of course work by the former. [R. S.]
↑ This year Śaka 1000 is chosen for convenience of addition or subtraction when calculating other years, and therefore we have not taken into account the fact that Ś 1000 was really an intercalary year, having both an Adhika Jyeshṭha and a Nija Jyeshṭha month. That peculiarity affects only that one year and not the concurrence of other months of previous or subsequent tears in other eras.

[1] Calculating by Prof. Jacobi's Tables, $a$ , $b$ , $c$ , are 9980, 896 and 255, each of which is wrong by 1.

The above figures were submitted by me to Dr. Downing of ihe Nautical Almanack office, with a request that he would test the results by scientific European methods. In reply he gave me the following quantities, for the sun from Leverrier's Tables, and and for the moon from Hansen's Tables (for the epoch A.D. 300, March 8th, 6 am., for the meridian of Ujjain). Mean long of sun 345° 51′ 47″.7, Do. of sun's perigee 253° 54′ 58″.5, Do. of moon 353° 0′ 36″0, Do. of moon's perigee 36° 9′ 48″.4. He also verified the statement that the sunrise on the morning of March 8th was that immediately following new moon. The difference in result is partly caused by the fact that Leverrier's and Hansen's longitudes are tropical, and those of the Sûrya-Siddhânta sidereal. Comparing the two results we find a difference of 0° 35′ 40″.9 in " $a$ ". 5° 24′ 49″.69 in " $b$ ", 0° 11′ 15″.87 in " $c$ ". The closeness of the results obtained from the use of (1) purely Hindu (2) purely European methods is remarkable. Our Tables being for Indian documents and inscriptions we of course work by the former. [R. S.]

[2] This year Śaka 1000 is chosen for convenience of addition or subtraction when calculating other years, and therefore we have not taken into account the fact that Ś 1000 was really an intercalary year, having both an Adhika Jyeshṭha and a Nija Jyeshṭha month. That peculiarity affects only that one year and not the concurrence of other months of previous or subsequent tears in other eras.

[1]

[2]