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EPIGRAPHIA INDICA.
[VOL. XVI
241° 50' 1"-5, which, in thousandths of circle, is 171.760416667. Not being absolutely certain in this case that my valuation is more accurate than his, I defer to him, and accept his figure as correct.
(iv) In any very close case arising from the use of the Tables which follow the difference between us in the value of b, namely 3-6, may be deducted from the resulting b, and the date tested by my own estimate,
(v) c. The change in the sun's mean anom. our c), similarly calculated for the 36 centuries, was 999-314836816, Adding 283-3, the value of c at K.Y. O ($ 290, mi), we have for K.Y. 3600 c=282.648170149. But here again there is a minute difference between my estimate and that of Prof. Jacobi. He gives, for the sun's mean anom. (measured from apogee) at the beginning of K.Y. 3600 (mean Mesha-samkrānti), 282o-& value certainly correct. To obtain mean sunrise value 14' 47" has to be deducted, with the result 281° 45' 13', which in thousandths of circle=782.648919753, and in my notation (measurement from perigee) =282-648919753. I let this stand.
(vi) The values, then, adopted in this work for the positions of and ( at mean sunrise at the beginning of K,Y, 3600 are
a=7516-237447969 -b= 171-760416667
c= 282 648919753 300. (1) Table LXI below, however, the main working Table, starts from the year K,Y. 4000, and we have to add to the above figures the respective increases of a, b, c for four centuries, these increases being assessed by Lalla's values and not by the original values of Aryabhatai ($ 289).
(ii) The increases of a, b, c in one day, one year and one century according to Lalla are given in the heading of Table LXIV below. The four centuries are all common ones, and, adding the necessary quantities, we have for the beginning of K.Y. 4000,- mean sunrise value
a=2987-553682533 b= 523-155092591 c= 284-0937825773
These agree, mutatis mutandis, with Prof. Jacobi's figures (Vol. XI, Table V), which, in my notation, are a=29880, b=523-2, o=284.1,
(iii) Now these values are, as will be seen from the entry "1" in Jacobi's column for the week-day (w.), the figures for mean sunrise on Sunday, that is to say, on Sunday, 25 March,
Omitting his 100 whole sidereal revolutions.
14' 47', or actually 14' 47'-04, is the O's mean motion in 6 hours, the difference in time betwoon meen sunrise and the moment of mean Mesha-sankranti on the day when, astronomically, K.Y. 8600 began.
• We may estimate the value of o on the Sunday at the beginning of K.Y. 4000 in another way. The sun's mean anom. At the moment of mean Mesha-sankranti is always 283-3, or 102° ( 290, wit). In the year in question. A.D. 199, troe Mēsha-samkrinti took place (Indian Calendar, Tablo I) at 18h 47m 80% after meen sunrise on Thurs., 22 March, while the moment of mean Mēsha-samkranti was ($ 290,-) 2d 3h 32m 80. later, or 8h 40m before mean sunrise on Sunday, 26 March. Adding the sun's motion for Bh 40m from Table LXV below, vix, 0-780496686 to 288-9, the e for menn sunrise on that Sunday is found to be 284008829010.
