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No. 11.) THE BRAHMA-SIDDHANTA: TRUE, OR APPARENT, SYSTEM.
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in one year to true Mösha-sankranti in the next, is (365d 6h 12mg-0022032) 3654 6h 12w 89-977968. [The exact moment of true Měsha-sankranti in each year from A.D. 599 to 1200 is given in the general Table LXXXII below, cols. 13-17. It can be tested by the use of Table A, S 273, referred to above, and Table B here given, using the longer rule" stated in $ 273 or in Indian Chronography, p. 61.]
Another result of the shift is that the sun's mean anomaly, or the mean sun's distance from the sun's perigee-point, decreases every year by 0144 or 14:4 in & century. Reckoning in 1,000ths of circle for valuation of our c (sun's mean anom.) in the Tables, 14'4 = 0·01. The value of c therefore decreases 0oi in a century, and this decrease has to be taken into Account from K.Y. O, the epoch of the Kaliyuga. This has been done in the preparation of the Tables which allow.
The increase of a, b, c, in centuries, years, days and fractions of days. 316. Following on what has been stated, we learn that Tables LIVA and B, which deal with the periodical increases of a, b and c according to the Siddhanta-Siromani, may safely be used for calculation by the Brahma-Siddhānta, with the one reservation as to the increase of a in a century. a being the distance of mean moon from mean sun, and the longitude of the mean sun not being affected by the shift of apsis, but only his mean anom., or distance from the point of the apsis, it appears that the rate of increase of a must be same by both authorities.
As to the rate of increase of c it is, by the Siddhanta-Siromani, centennially less by 0-0805 ($ 273 above), and this was taken into account in the preparation of the heading of Table LIVA where a footnote is appended shewing what the rate of increase would be per century if no such deduction had been made. This rate is, in thousandths of a circle, 997-690008075 in a century of 36525 days, and 0.427795618 in a century of 36526 days. By the Brahma-Siddhanta, the centennial decrease in the sun's mean anomaly being 0:01, the amount of increase of c per century is, for a century of 36525 days, 997678896964, and for a century of 36526 days is 0-416684507. The difference between the two authorities in shorter periods may be ignored except in some extraordinarily close case. If it is ever needed, the increase in c in one year may be reduced by 0.0001 from the Table quantity. Otherwise Tables LIVA and B stand good for calculations by the Brahma-Siddhanta.
The values of a, b, c at the beginning of K.Y. 3700. 317. The general Table LXXXII below begins from the beginning of K.Y. 3700 expired. Table LXXXVI states the value of a, b, c at that moment, and at the similar moment at the beginning of subsequent centuries. It is necessary therefore to explain how these figures were calculated.
(i) The value of a (distance of mean moon from mean sun) in K.Y. 3700. According to Hindu astronomers mean moon and mean sun were in conjunction at the moment of mean Meshasankranti in K.Y. O, the epoch of the Kaliyuga; or, in other words, at that moment a = 0. In the 37 succeeding centaries there were 32 common and 5 defective centuries. Taking the centary values of a given in the heading of Table LIVA and multiplying for 32 common and 5 defective centuries, we arrive at the figure 6567.108945284 as the value of a at the beginning of the 37th century K.Y., whole revolutions of 10,000 each being omitted. From this figure has to be deducted,-according to the working system of the Indian Calendar, which follows Largeteau and Jacobi,--the sum of the greatest equations of sun and moon, viz. 200-284021 (above $ 313, iv). This gives us the value of a at the beginning of K.Y. 3700 (expired) as 6366-824917506.
1 Professor Jacobi differs by sbont 17 units. He gives the figure 6384-0 (Vol. XI adore, p. 167, Table IXA). I can give no explanation of the rouson for this; and can only state fally, as in the text, my bases of calculation.
