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EPIGRAPHIA INDICA
[VOL. XVII.
TABLE XCIV.
TIME-EQUIVALENTS OF THE TITHI (a OR t), NAKSHATRA (n), AND YOGA (y) UNITS.
In very close cases it is sometimes necessary to calculate the exact moment of the beginning and ending of tithis, nakshatras and yogas, with greater accuracy than can be obtained by the use of Table X, Indian Calendar, or Table LXX (above, Vol. XVI, p. 216), where the time-equi valent of the unit, respectively, is given only in hours and minutes. My general working Tables for several of the Hindu astronomical Siddhantas already published yield results, stated in measurement by 10,000ths of the circle, with an accuracy extending to four places of decimals, and the following Table enables the result to be translated into time down to a fraction of a second. It may be used for all astronomical authorities.
The tithi-index unit.
The tithi-unit is robooth of a mean lunation. The mean lunation, according to the Aryaand Surya-Siddhantas, occupies 29d 12h 44m 279. The unit, or 10,000th part of this, is 4m-2524046, or 4m 15-144279.
The nakshatra-index unit.
The moon's nakshatra, or her position in the heavens, mean or true, is found by adding the tithi-index, a or t, to the index of the sun's longitude, s, mean or true. Both these values are found in the ordinary course of calculation for a date.
The mean nakshatra-value n 10,000 is reached in 274 7h 43m 12-3. In this period the sun's mean motion amounts, in 10,000ths of circle measurement, to 748-0087 (Table XLIV above (Vol. XIV)) and the moon's mean distance from mean sun increases (Table LIV A, B (Vol. XV)) to 9251-9913. Total 10,000.
274 7h 43m 12-3-39343m-205, and this divided by 10,000 fixes the time-equivalent of the nakshatra-unit as 3m-9343205, or 3" 56"-05923.
The yoga-index upit.
Similarly the yoga-chakra is estimated by the Surya-Siddhanta (Indian Calendar, p. 62, § 113) as occupying 36605-116 minutes of time, or 25d 10h 5m 6-96.1 The yoga-unit therefore is 3m-6605116, or 3m 39-6307.
1 The yoga formula is y = (san's long.) + (moon's nakshatra), and, since n-s+a, y=28+ a. In the period noted it will be found by calculation, using Table XLIV (above, Vol. XIV), that the mean suns arrives, in 10,000ths of circle measurement, at long. 695-9511; and by using Table LXIV (Vol. XVI) that in the same period the mean moon has increased ber distance from mean san (a) by 8608-0964. Twice -1391-9022, and this + 8608-0964 (the value of a)-9999-9988, practically 10,000 exactly. Table LXIV was prepared according to the First AryaSiddhanta. Using Siddhanta-Siromani and Brahma Siddhanta estimates (Table LIV) the total amounts to 10,000-0015, I have as yet ro similar Table according to Sürya-Siddhanta requirements; but from what has been said it may be assumed that its estimate of the time occupied by one yōgo-chakra (-10,000) is correct.
