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438
EPIGRAPHIA INDICA.
ON THE CONSTRUCTION OF THE TABLES.
6
63. Tables I and II are so constructed that the common and leap years are distributed in such a way that the end of the tabular year differs from the end of the corresponding mean solar year of the Hindus by an interval (indicated by Cor.') rarely exceeding 60 ghațikás, but generally much less. As 100 solar years of the Hindus contain 36,526 days less about 3th day, the centuries in table I contain 84 common and 26 leap years, except that in every eighth century there are only 25 leap years. The leap years in the century are so placed that Cor.' is kept under 30 ghatikás.
64. Calculation of the correction.'-As Cor.' is the fraction of the day by which the sum of the solar years is more or less than an integral number of days, this fraction depends on the length of the solar year; and the latter depends on the days in one Yuga according to the different Siddhántas; that is, the sum of days in a yuga divided by the number of solar years in a yuga (viz. 4,320,000) gives the length of the solar year."
Thus:
Surya Siddhanta Arya Siddhanta
2nd Arya Siddhanta. Brahma Siddhanta.
Days in a yuga.
Length of a solar year. 1,577,917,828 365-258756481 days or 365 d. 15 gh. 31-52 p. 1,577,917,500 865-258680555 81.25" 31.28 30-37,
15 365
. 1,577,917,542 365-258690278 1,577,916,450 365-258437499
365 15 365 15
33
33
33
در
33
33 33
در
From these data is derived the mean duration of 100, 1000 and 3000 years according to the different authorities. Thus according to the Arya Siddhánta, 3000 years being 1,095,776d. 2gh. 30p., the Cor.' is + 2gh. 30 p. As the astronomical day in the Surya Siddhanta begins with mean midnight at Lanka, while common use makes it begin with mean sunrise at Lanka from the duration 1,095,776d. 16gh. 10p., we must retrench 15 ghatikás (the time between mean midnight and mean sunrise), the remainder + 1 gh. 10 p. is the required Cor.' as entered in the table. But according to the Brahma Siddhanta, 3,000 solar years contain 1,095,775d. 18gh. 45p. or about one day less than is given by the other Siddhantas; 3000 K.Y. therefore began on the day preceding that entered in the tables, and the Cor.' was + 18gh. 45p.
65. Calculation of the week day (Feria):-Kaliyuga began with a Friday, or according to our notation the Feria was (6). Now as 3,000 solar years contain 1,095,776 days or 156,539 weeks + 3 days, 3000 K.Y. began on (6) + (3) (9) or (2) Monday. Again as a century of 36,526 days contains exactly 5,218 weeks, it follows that after the lapse of such a century the week-day will be found the same as at the beginning of it. But after a century of 36,525 days the week-day must retrograde by one day. In this way the Ferise of Table I have been ascertained. In Table II, the week-day advances by one day after every common year (of 365 days), and by two days after a leap year (of 366 days). The advance of F. by 2 in Table II therefore shows that the preceding tabular year consists of 366 days.
66. Verification of a date in the Tables.-The Kaliyuga began on the 18th February 3102 B.C., after the 588,465th complete day of the Julian period. As 4,000 solar years
The Hindu solar year is the sidereal year. The tropical year on which European Chronology is based is hardly ever nsed by the Hindus. So also, in Hindu astronomy the revolutions of the planets, &c., are sidereal, and not tropical. The precession of the equinoxes is taken into account in such cases as are affected by it, but it is neglected in all others.
The European value of this sidereal year is 365-2563744 days, while the tropical year consists of 365-24224 days; and taking the precession of the equinoxes at 180 revolutions in a yuga, according to the Surya Siddhanta, the Hindu tropical year would be 1,577,917,8284,320,180 365-243539667 days.-J.B.
