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244
EPIGRAPHIA INDICA.
[VOL. XIV.
method for finding these hours and minutes is detailed in Indian Chronography, pp. 27, 28, 61, 62; but to save reference it is repeated here, with the accompanying Table.
To find time of true Mēsha-sankranti by the Siddhanta-Siromani; (i) The longer rule. Take the moment of true Mosha-samkranti by the Arya-Siddhanta from Table I of the Indian Calendar, cols. 13 to 17, adding 30 in odd A.D. years, none in evon (Hint 20, p. 79, Indian Chronography). Add the sodhya by that authority-always 2d 3h 32m 30". This gives time of mean Měsha-samkranti. Deduct for every year of the Kaliyuga expired at the given date the amount obtained from Table LIII below. This gives time of mean Mēsha-sankranti by the Siddhānta-Siromani. Deduct the amount of sodhya noted in Tablo LII below for the given year; for great exactness it may be found from col. 3, difference for the year in minutes and seconds being calculated from the entry for the beginning of each century : for close approximation take, without further calculation, the century entry in col. 4. The result is the required time of true Mosha-samkranti by the Siddhanta-Siromani.
(ii) The shorter rule. Take the Arya-Siddhānta time of true Mosha-samkrānti-the first process in (i). Add together the amounts gathered froın Table LIII-the third process in )and the number of minutes for the century in col. 5 of Table LII. Deduct the total from the Arya-Siddhānta time of true Mosha-samkrānti. The result gives the required time of true Mesha-sar kranti by the Siddhanta-Siromani with suffcient exactness for ordinary parposes. Examples are given in Indian Chronography, p. 27, and need not be repeated.
My future Tables will entirely do away with the necessity of finding the moment of true Mosha-samkrānti by the Siddhānta-Siromani, the correct time being given for each year.
263. Caloulation for the correct tithi-index by the Siddhānta-Siromani may for the present be considered as sufficiently carried out by work according to the Arya-Siddhānta; there will often be a difference between the two. Correction of the equation (see above, Vol. XIV, S 247, i, the titht) may cause a difference of one unit in the tithi-index, and there may be a slight difference in consequence of a different mean anomaly value requiring the equation to be calculated from a different base-angle.
Construction of the Main-Table XLVIIIO. 264: In order to conform to my similar Tables for the Arya- and Sürya-Siddhāntas (above, Vol. XIV, Tables XLVIIIA and B), I have worked for the year K. Y. 4500, expired, A.D. 1399-1400. The first thing was to fix the exact value of the sun's mean anomaly in that year at the moment of trae Mösha-sankranti.
From Dr. Schram's fixture of the sun's equation of the centre by the Siddhanta-Siromani at that monent in K. Y. 4000 as 2° 8' 52"-761328955 and in K. Y. 5000 as 2° 8' 59.319753357 we find the equation in K. Y. 4500 to be 2° 8' 56".040541 156, or, in 10,000ths of the circle, 59-691670842.
From Prof. Jacobi's determination of the position of the sun's apsis (I take perigee, not apogee) at that moment as 258° 55' 12' in K. Y. 4000 and 259° 12' 36' in K. Y. 5000 we find the perigee-point in K. Y. 4500 to be 259° 3' 54', or, in 10,000ths of the circle, 7196-250 (exact).
The sun's mean anomaly at any moment is 360° minus the longitude of perigee and the equation of the centre. This, using the above figures, gives tus his mean anomaly at that moment in K. Y. 4500 as 98° 47' 9-959458844 or, in decimals of a minute for purposes of calcu. lation, 98° 47'-165990981; or, in 10,000ths of the circle, 2744-058329158.
Tested by the sine-and-equation-Tablo (Vol. XIV, Tables XLVII and XLVILA) with use of the most accurate possible details for method so test $ 256, above, Vol. XIV) I find
