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EPIGRAPHIA INDICA.
[Vol. XVII.
remainder and 36,525 divided by 7 leaves remainder 6, the results show that whereas century 0 began on a Friday, century 37 began on a Saturday.
Table xd therefore, as regards the moment of mean Mosha-sankranti in K.Y. 3700 expired, A.D. 599-600, is proved to be correct.
The beginning of the mean luni-solar year, i.e. the civil day on which the tithi Chaitra sukla 1 expired; and the value of a (mean tithi-index)
at mean sunrise of that day. Amānta system. 325. In $ 317 of my article on the Brahma-Siddhanta as calculated by the true motions of the sun and moon (above, Vol. XVII) it will be seen that the value of a at mean sunrise of Sunday, 22 March, A.D. 599 (K.Y. 8700) was proved to be, in measurement by 10,000ths of a circle, 6567-108945284. The mean solar century, however, began on the previous day, Saturday, 21 March. Deducting one day's value of a, viz. 338-631985412, from the above, we find that at mean sunrise of that Saturday the value of a, or the mean moon's distance from mean sun, was 6228-476959872. This was its value at the beginning of the 37th century K.Y. Hence the first entry in Table XCII below which gives the values at mean sunrise on the day on which each century began. The remaining figures in that Table were obtained by the addition to this valde of the increase of a in a century. (See 8 316 of the same article. The increase of a in a century of 36,525 days is 997678896964, and in & common century of 36,526 days is 0-416684507.] Centuries 38 and 44 were defective centuries; the rest were common ones. For the beginnings of the odd years of centuries Table LXXXVII was used, the value of a there given being added to that for the century.
Thus was determined the value of a at mean sunrise of the day on which each mean solar year begins (800 Example 1 below). From this is found the value of a at mean sunrise of the day on which the luni-solar year begins.
326. The first day of the luni-solar year is, according to the general rule, the civil day on which expired the first tithi of the bright half (sukla) of the amänta lunar month Chaitra, i.e. the tithi which begins at the moment of the first new moon after the Mina-8amkrānti, or at the moment of the new moon when that amanta lunar month begins within the limits of which the Mesha-sankranti occurs. Having already established the value of a on the day in any year on which mean Měsha-sankranti occurred, we have to subtract from that value the increase of a in whole days between the two dates, the day on which the luni-solar year began being the earlier. The first 30 days' entries in Table LIVA (above, Vol. XV) enable this to be done. We select in that Table the a in col. 3 the value of which is next lower than the a of mean Mosha-sankranti, and the Table then shews in col. 1 the number of intervening days, and therefrom the European day and month, and, by subtraction, also (col. 2), the week-day. Deducting the selected a from the a of mean Mesha-sartkranti, we have the a of mean sunrise of the day, Chaitra sukla 1, on which the mean luni-solar year begins.
Thus,-mean Masha-sankranti of the year K.Y. 3700, A.D. 599-600, was shewn in 9 325 to have occurred on (0) Saturday, 21 March A.D. 599, at mean sunrise on which day the mean moon's tithi-index a was 6228-4770. In Table LIVA, amongst the values of a in the first 30 days, it is seen that the next lower value is 6095-3757. 6228-4770-6095-3757=133.10131. Col. 1 shows that the interval of days was 18, and col. 2 shows the week-day 4. Mean Moshasankranti occurred on (0) Saturday. O (or 7)-4=8 Tuesday. It is therefore found that the day Chaitra fuklu ), the first civil day of the mean luni-solar year, was (3) Tuesday, 3 March A.D. 599, and that the value of a at mean sunrise on that day was 133-1013, shewing the currency of the tithi fukla 1. This is the entry in Table XC below.
It comes to the same thing if the a of Table XCIII below is added to the a of mean Mosha-sankranti, the Table being prepared for that purpose. The a of mean Mesha
All value of a below 888-9 prove the tithi to have been the first of the amanta lunar month, 1.e, the first tithi of the first (Bukla) fortnight.
