________________
No. 14.]
THE FIRST ARYA-SIDDHANTA : "TRUE" SYSTEM.
109
(iii) The advances in the values of a, b, c respectively during a common century of 36626 oivil days according to Aryabhata uncorrected, excluding whole revolutions, area (mean moon's distance from mean sun) 319° 24' 30"645, 6 (C's mean anom.) 211° 1' 55"775, (O's mean anom.) 0° 7' 48.139. These in circle measurement (our notation) are
a=8872-458680555 b= 586-100443673
c= 0-361215706 (iv) Taking only the circle measurement, the respective increases for one day of 24-hours are
a=338-632000730 b= 36-291575876
c= 2.737785720 (v) Deducting one day's increase from the former fixtures, we have for a defective century of 36525 civil days,
a=8533-826679825 b= 549-898867797
c= 997-623429986 We now have to work out the correct details for the first 36 centuries of the Kaliyuga, 31 common and 5 defective.
299. (i) a. Using the above figures, it is found that the advance of a in that period (omitting quantities of 10,000 or whole revolutions) was 2715-352496330; and since at the epoch of the Kaliyuga the distance between mean moon and mean sun was mil (above, $ 290, xir), the same represents their relation at the beginning of K.Y. 3600. But for tabulation purposes we have to deduct from this the sum of the greatest equations and ($ 290, xir; and 290). This sum, as already stated, I estimate at 199-115048361. Therefore the tabular a for the beginning of K.Y. 3600 is 7516-237447969. Prof. Jacobi gives this figure, as I interpret him, in our notation as 7516.6. The difference between us ir due to his estimation of the greatest equations and as 1987 (margin of Table quoted in footnote below) instead of 199-1. But I adhere to my figure, the reason for which has been fully explained.
6 . The advance of b in the first 36 centuries, omitting whole revolutions, was in thousandths of the circle, 918-158092848. Adding to this the value of b at K.Y. O ($ 290. wii), namely 250, we have for the moon's mean anom. at the beginning of K.Y. 3600, b=168-158602848.
(iii) Now in this matter Prof. Jacobi and myself are not quite in accord. He states the value (Vol. XI above, Table V B) as in his notation 6718. This in my notation, measuring from perigee instead of apogee, is 171.8. This figure corresponds to his valuation of b at that moment, in degrees, etc., as given in Vol. I above, Special Table XIII, where it is fixed, for the moment of mean Mēsha-samkrinti, as 245° 6' 0". The correction for mean sunrise value is the moon's change in 15 ghatikās, or 30. 15' 58"5; making the position of (at mean sunrise
There are 1286 synodical revolutions of the moon in a century.
In both sections of his Tablo V (Vol. XI above, A and B) Prof. Jacobi's entry "76166" is manifretly misprint for "75166." In the same Table, Section A, opposite "cent. 41" the entry "19789" should be "18789." • There are 1325 anomalistic revolutions of the moon in a century.
N 2
