Epigraphia Indica Vol 14

Author(s): Sten Konow, F W Thomas
Publisher: Archaeological Survey of India

Page 22

No. 1.) THE TRUE LONGITUDE OF THE SUN IN HINDU ASTRONOMY.
example above 19° 27' 52-27. Deduct (Tables XLIX, L) for, on day 20, 10 hours 24' 12:29, and for 55 minutes 2' 15"-52, total 26' 27":81. Then the s for moan suprise was 19° 1' 24"-46. This was the true sun's longitude at that moment on the meridian of Ujjain. The given lagna was the sign Mithuna. The first point of this is 60°, the last 90°. We take the s as 190, which is sufficiently exact for ordinary purposes. 60°-19°=41°. 41 x 4=164 m., or 2 h. 44 m. (90°-19°) x 4=284 m., or 4 h. 44 m. The first point of Mithuna was 41° distact from the true son at the moment of mean sunrise, the last point 71°. Mithuna wag lagna between 2 h. 24 m. and 4 h. 44 m. after mean suprise on the given day.
(i) By the Surya-Siddhänta.-s=(Table XLVIIIB) 19° 27' 28":80. Doduct for 12 hours (Tables XLIX, L) 29' 2.74 and for 44 minutes 1' 48"-42, total 30' 51":16. Remainder, or
for sunrise, 18° 56' 37":64. We may call this 19', and come to the same result as in the former case. The lagna of Mithuna really began twelve seconds later.
(iii) By the Indian Calendar process, and for both Siddhāntas.-Here & was found to be in ten-thousandths, 520. Converted by Table VIIIB, this = 18° 45'. This was the sun's true longitude at mean sunrise. The difference between the actual time of the lagna of Mithun and that found by the Indian Calendar is slight.
More accurately worked, the first point of Mithuna was lagoa by the Arya-Siddhānta at 2 h. 43 m. 56 s., by the Sarya-Siddhānta 2 h. 41 m. 16 s., and by the Indian Calendar 2 h. 45 m., after mean sunrise on the day in question.
Construction of the Tables. A detailed explanation is here given of the construction of the principal Tables, in order to satisfy experts as to their accuracy.
249. The Hindu Sine-Table.-The Surya-Siddhanta (ii, 34) gives in minutes the sines of a series of angles, each separated from the other by 3° 45', twenty-four of these completing the quarter-circle of 90°. These values stand, so far as I can ascertain, for all Indian authorities except the Brahma-Siddhānta, which assumes different sine-values. There is no need here to discuss their exact accuracy, as I am concerned solely with chronography as the handmaid of history, and have nothing whatever to do with the casting of horoscopes or any other branch of astrology. The sines, as ased in calculations by authorities other than the Brahma-Siddhanta, are given in Table XLVII, col. 3, and the differences between them, in minutes, in col. 4. For astronomical purposes the several angles are angles of a planet's mean anomaly, and are 80 applied to the mean anomaly of both sun and moon.
250. The equation of the centre.- For the preparation of the sine and equation Table (XLVII) the equation of the sun's centre for each basa-angle of anomaly has been calculated from its sine-value by the proper formala for each Siddhanta, the calculation being carried to nine decimals of a second, in order to insure absolute accuracy for the tabulated two decimals. The details for the First Arya-Siddhānta (Table XLVII, cols. 5, 6) are complete in themselves; details for the other authorities are given in full in a supplementary Table (XLVILA). Table XLVII differs a little, but only in one or two places, from Jacobi's Table XXIV (Epig. Ind. I, 459); I have, however, thought it advisable to record two decimals of seconds in all cases.
251. Equation of centre.--In Hindi astronomy the sun is treated as a planet, and in all planetary movement a fundamental principle (Jacobi, Epig. Ind. I, 441) is contained in the proportion sin. equation : sin. mean anomaly :: minutes in the epicycle : minutes in the orbit. The minutes in the sin, anomaly are given in Table XLVII; the minutes in the epicyclo are ascertained from statements made in each siddhanta; the minutes in the or bit of 360° are