new-moon that marks the beginning of the luni-solar year was the new-moon at the beginning of the lunar month to which that tithi belongs[1]; and as we only want the a, b, c at mean sunrise of the day immediately following that new-moon we deduct from the a, b, c of the Mēsha saṁkrānti day, already obtained, the figures for the whole days corresponding to the interval from the beginning of the lunar month to the tithi current on the day of Mēsha saṁkrānti. This gives the day, and its a, b, c, &c., at mean sunrise, on which the luni-solar year began, or the day corresponding to Chaitra śukla 1st in the given year.
191. After this calculation was completed, in every case I checked it by Prof. Jacobi's Tables 5, 6, 7. (Indian Antiquary, XVII., p. 164.) For this purpose I had to find the proper century-figure (in Table 6) for the twentieth century, since his Tables end with the end of the nineteenth century. They are (a) 10,000 - 1808, (b) 1000 486, (c) 1000- 5; or a = 8192, b 514, c = 995. These figures are approximate, decimals being excluded, but they are as accurate as the rest of Table 6.
For an example I take the year A.D. 1901:—
| w. | a. | b. | c. | ||
| Table I. for A.D. 1801 (cols. 19–25) | 15 March (74) | 1 | 9858 | 215 | 205 |
| In 1901 Mēsha samkrānti was on April 12th. Add (Table IV.) | 28 March (28) | 0 | 9482 | 16 | 77 |
| 1801 April 12th | (102) | 1 | 9340 | 231 | 282 |
| Century difference | −2 | −1808 | −486 | −5 | |
| 1901 April 12th, Friday | 6 | 7532 | 745 | 277 |
a (= 7532) plus equation b (= 0) and equation c (= 1) gives t that the 8th kṛishṇa tithi was current. We therefore deduct 22 days to arrive at the figures for Chaitra śukla 1st, the first civil day of the luni-solar year.
| d. | w. | a. | b. | c. | |
| 12 April (102) | 6 | 7532 | 745 | 277 | |
| For 22 days (Table IV.) | −22 April− 22 | −1 | −7450 | 798 | 60 |
| Sunrise on Chait. śuk. 1st in A.D. 1901 | 21 March (80) | 5 | 82 | 947 | 217 |
| Check this by Jacobi's Tables 5, 6, 7. | w. | a. | b. | c. | |
| (Table 6) 20th century (Table XXXIX. below) | 5 | 8192 | 514 | 995 | |
| (Table 5) year (190)1 | 5 | 5138 | 566 | 6 | |
| (Table 7) 21st March | 2 | 6752 | 867 | 216 | |
| (Thur.) | 5 | 82 | 947 | 217 | |
The results agree, and the entry is made accordingly for Table XXXVIII.
With a, b, c as given we find t = 177 (Table X.) 12 h. 32 m.; but continuing the calculation for absolute accuracy it works to 11 h. 20 m. New moon therefore took place according to the Sūrya Siddhānta 11 h. 20 m. before mean sunrise on March 21st, or at 6.40 p.m. on March 20th, A.D. 1901. By modern European science it occurred at 0.53 p.m., or 53 m. past noon on that day at Greenwich; or for the meridian of Laṅkā at 5.56 p.m.
192. The next process was the computation of the added (adhika) lunar months by the Sūrya Siddhānta. I have stated in para. 190 that for other purposes I had ascertained the state of the moon at mean sunrise of the day on which apparent Mēsha saṁkrānti occurred in each year, given in terms of a, b, c. We have only to add to this the a, b, c for the hours and minutes after mean sunrise on that day as given in col. 17A, and we have the condition of the moon at the actual moment of apparent Mēsha saṁkrānti. The values of a, b, c for the several intervals between that moment and each subsequent saṁkrānti in the year are given in Table XVIII.B; and by this the calculation was made in the ordinary
- ↑ Except when Chaitra is intercalary, in which case the previous new-moon was the first of the year.
