Page:Sewell Indian chronography.pdf/41
62b. It will be well that I should point out clearly (the reason will be obvious from what has gone before) that a calculator must not be tempted to apply the time-difference given in the Table in § 162 to the moment found for true Mēsha saṁkrānti according to the Ārya, thinking thereby alone to obtain the moment of true Mēsha saṁkrānti by the Original Sūrya Siddhānta. This would be to ignore the difference in the śōdhya value by the two authorities.
62c. The times of occurrence of the true and mean Mēsha saṁkrāntis of each year according to the Brāhma Siddhānta of Brahmagupta can be obtained on the same principle as in the case of the Original Sūrya Siddhānta; but, for the amount of time-difference between the Brāhma Siddhānta and the Ārya Siddhānta (the moment of each year's Mēsha saṁkrānti by which is given in Table I.), we must use the Table given in § 167a below; and for the śōdhya-value we have to use a different quantity. The Table in § 167a explains itself.
62d. As to the śōdhya-value, it is plain that since the Brāhma Siddhānta was only composed in the year A.D. 628, we shall never require, except for speculative purposes, to calculate for any earlier year than that; and as that year is the year K.Y. 3729 expired, we need not trouble ourselves with any value of the śōdhya other than for the centuries embraced in the period K.Y. 3000 to 5000. These values are, as decided by Dr. Schram:—
| In K.Y. 3000, 2.172736 days, or 2 d. 4 h. 8 m. 44.39 s. |
| In K.Y.„ 4000, 2.172991 days, or„ 2 d. 4 h. 9 m. 6.42 s. |
| In K.Y.„ 5000, 2.173246 days, or„ 2 d. 4 h. 9 m. 28.45 s. |
The 1000-year difference is 22.03 s. and for the whole period of 2000 years is only 44.06 s. We may therefore take the value for the whole period connected with the Brāhma Siddhānta as a constant, and as amounting to 2 d. 4 h. 9 m.; only using the actual values whenever a very close case demands exceptional accuracy.
62e. This point settled, we are enabled to make the necessary calculation. As an example I take the year A.D. 1000, or K.Y. 4101 expired. And as in the case of the Original Sūrya Siddhānta, I give two methods of work, showing first the full work, and secondly a shorter process by which the same result can be obtained.
(a) The full working-rule. This is, mutatis mutandis, similar to the full working-rule for the Original Sūrya Siddhānta given in § 62a:—
| d. | h. | m. | |
| True M.S. by the Ā.S. (Table I.) | 22 March | 16 | 50 |
| Add Ā.S. śōdhya | 2 | 3 | 32 |
| Mean M.S. by the A.S. | 24 March | 20 | 22 |
| Deduct (Table in § 167a) for 4101 years, 23 h. 20 m. + 35 m. + 21 s. Ignoring the seconds | − 23 | − 55 | |
| Mean M.S by the Brāhma Siddhānta | 23 March | 20 | 27 |
| Deduct Brāhma Siddh. śōdhya | − 2 | − 4 | − 9 |
| True M.S. by the Brāhma Siddh. | 21 March | 16 | 18 |
According, therefore, to the Brāhma Siddhānta, true Mēsha saṁkrānti of A.D. 1000 occurred on March 21st at 16 h. 18 m., and mean Mēsha saṁkrānti on March 23rd at 20 h. 27 m., after, in each case, mean sunrise.