Epigraphia Indica Vol 14

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

Page 24

No. 1.] THE TRUE LONGITUDE OF THE SUN IN HINDU ASTRONOMY.
11
40' or 820'. There is no contraction. Minutes in the orbit, 21600'. Hence the equation is
1820 sin. w, or a sin. a. The entries are made in abbreviated form in Table XLVII, cole. 9, 10, and in full in Table XLVIIA, cols. 9, 10.
254. The stun's mean anomaly, and the starting point for its valuation. The sun's daily mean motion, i.e. his mean motion in 24 hours, is given according to the several Hindu authorities in Table XLIII, so that, given his exact mean place at the moment of trae Mēshasamkrānti when the true sun was at 0°, bis mean position at the end of every 24-hour period is obtained by simple addition. We must, therefore, fix with great care the value of his mean anomaly when the true sun was at 0°.
(i) By the First Arya-Siddhānta.-S. B. Dikshit's valuation of the equation by this Siddhanta, 2° 6' 59.9421, was a trifle too great. Dr. Schram's, 2° 6' 57"-323496, is exact down to the fifth decimal. M. de Ries with almost painful accuracy has carried it as far as sixteen decimals of a second. Tested by the sine-table, his valuation is found exact. The equation (I give nine decimals of a second, the amount which I have generally used in these calculations) is + 2° 6' 57"-323494885, or, in 10,000ths of the circle, 58-775644170. This is correct for the corresponding mean longitude value 357° 53' 2"676505115, or 357° 53' 044608419, or in 10,000ths of circle 9941.224355830, the two added together amounting to exactly 360°. Thus, the perigee-point of the orbit being by this Siddhānta fixed at 258°, or, in 10,000ths of the circle, 71666, we have found the sun's mean anomaly at true Mēsha-samkrinti to have been 99° 53' 24.676505115 or 99° 53044608419, or in ten-thousandths of the circle 2774-557689163 (i.e. 9941.224355830 - 7166-6). This then is our starting point for cols. 2, 3, 4, 5, of Table XLVIIIA
(ii) By the Present Surya-Siddhānta. In this case we have to deal with an authority which postulates a slight movement in the line of apsides of the sun's orbit, the apogee and perigee-points moving eastwards at the rate of 0.1161 per ann.; and before working for a correct valuation of the sun's mean anomaly at true Mēsha-samkranti in any yoar, we have first to decide which year to select as base of operations. I have chosen the year K. Y. 4500 or A.D. 1399-1400, roughly A.D. 1400, for reasons which follow. The period covered by Indian Epigraphy, the historical period, that is, of Indian History, may be taken as the period K. Y. 3500 to 5000, A.D. 400 to 1900, or the last 1500 years, the bulk of the inscriptions belonging to the last millennium K. Y. 4000 to 5000 or A.D. 900 to 1900. I take the central year of this millennium as my base. In K. Y. 1000 the perigee-point was at 257° 15' 32"-4, and in K. Y. 5000 it was at 257° 17' 28.5. Hence in K. Y. 4500, say A.D. 1400, it was 257° 16' 30"-45, or, in 10,000ths of the circle 7146-53125.7 The difference in the sun's equation of the centre and true longitude, caused by this shift of the apsis, is exceedingly small and may well be ignored.
For we are concerned only with the period A.D. 400 to 1900; and calculation by the equation-table on the value of the sun's mean anomaly at the beginning of the Hinda sclar year A.D. 400-01 and at the beginning of A.D. 1900-01, allowing for the shift of the perigeopoint, proves that the total difference in the equation in the whole period of 1500 years was 1"0739. This constitutes also the total difference in the sun's trpe longitude, which is his mean longitude the equation, the mean longitude remaining the same whatever may be the shift in the line of apsides.
To assist those interested, however, I append a Table shewing the cumulative change of position of the apsidal points.
Actually, for fine decimals, 7146-531250000