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No. 14.]
THE FIRST ARYA-SIDDHANTA: "TRUE" SYSTEM.
103
(vii) For the sun's mean and true long. for every consecutive 24-hour period measured from the same moment (true Mēsha-samkrānti) readers are referred to Table XLVIII A (Vol. XIV above). (viii) The sun's equation of the centre (see above, Vol. XIV, Table XLVII) is obtaired by
minutes in epicycle . the formula an sin. a. For sin. eqn. =
e x sin. a, where a is the sun's
minutes in orbit mean anom. ; and here the minutes in the epicycle are 810', the circumference being 13° 30', and those of the orbit are 21600 (360°). Hence sin. eqn. = 21600 sin. Q, or 90 sin. a. In all equations of the sun's centre, the angle being less than 3° 45', the eqn. is the same as the sin. eqn. (below, $ 294 i).
(ix) The moon's equation of the centre (belowo, Table LXXV) is obtained by a similar proportion. The circumference of the epicycle being 31° 30' or 1890', the working formula is sin.
1890 eqn. = 100 sin. a, or on-sin. a; but in this case, the sin. eqn. for all angles in the quadrant lying between 3° 45' and 7° 30', the equation does not equal the sin. eqn. The process for obtaining the former from the latter is fully set forth in $ 294 below.
(x) The sodhya, or time-equivalent of the equation of the centre-in other words the interval of time between the moments of the true sun reaching long. 0° (true Mēsha-samkrānti) and mean sun reaching the same point (mean Měsha-samkranti)-is calculated by Dr. Schram as 2.146831 days, or 2d 3h 31m 26-1984. This differs a little from the accepted Hindu valuation 24 36 32m 30. As the latter is believed to have been always taken in India as the sodhya value according to the First Arya-Siddhanta, it is the value adopted in the present work.
(xi) According to this Siddhānta the Kaliyuga era began, or in other words K.Y. O expired or K.Y. 1 current began, with a conjunction at celestial longitude 0° of mean moon, mean sun, and the principal planets at the moment of mean sunrise at Lanka on Friday, 18 February, B.C. 3102. That was the moment of mean Mesha-samkrānti in that year. It was 0 0 Lanka time on that morning.
(xii) At that moment, and the same in every succeeding year, the sun's apsis (perigee being at long. 258°, his mean anom. (our "c") is (360°-2589) 1020, or, in thousandths of circle (our notation), 283-3.
(xiii) The moon's mean anom. (our "6") was 90°, or, in thousandths of circle, 250.
(xiv) Since mean moon and mean sun were at that moment in conjunction, the distance between them was mil. This is represented in ten-thousandths of circle by the completed circle 10,000. From this, in order to arrive at the exact value of our "a," must be deducted the sum of the greatest equations of (and o. These are deducted for convenience of calculation, the respective quantities being added to "eqn. 6" and "eqn. C," so that the working values may always be additive. The sum of these greatest equations I estimate at 199-115048361, in ten-thousandths of circle (below, & 296) 10,000 less this quantity = 9800-884951639. Hence at the beginning of the Kaliyuga
a = 9800-884951639 b = 250 c=283-3
Abovo, SS 261, 262, Vol. XIV, PP. 9-10; Jacobi (above), Vol. I, p. 441.
