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No. 14.]
THE FIRST ARYA-SIDDHANTA: "TRUE" SYSTEM.
113
the values of a, b, c for 181 days to those already found for Chaitra sukla 1, the equations of b and care added from Tables LXVI, LXVII approximately, or from Tables LXVI A, LXVII A in very close and doubtful cases, to the resulting value of a for the day, thus t, the true tithi-index, is found:
In this example we work approximately.
The serial number of the day Chaitra sukla 1 (in March A.D. 1226) is 60 and the weekday 1, Sunday (Example 3). The a, b, c for mean sunrise have been settled in Example 3.
d. w.-d. a. b. c. Table LXI, cols. 19-25 . (60) (1) 36 2 15 211 (Table LXIV). . . . (181) (6) 1292569496
(241)
(0)
1328
784
707
At mean sunrise on day (Table LXVI) Eqn. 6" (Table LXVII) "Eqn.c"
.
.
117
At mean sunrise on day 241, t=1448=(Table LXVIII) Sukla 5. Day 241 was (Table LXIX) August 29. Week-day 0=Saturday. Reference to Table LXXI confirms this as the right week-day.
The given Hindu date then is so far correct. The 5th śukla tithi of Bhadrapada ended on, and gave its name to, Sat., 29 Aug., A.D. 1226. For historical purposes it is seldom necessary, unless the karana is mentioned, to find the time of beginning and ending of the tithi; but, if required, this is obtained approximately from Tables LXVIII, col. 3, and LXIX. At mean gunrise the tithi-index was 1448. It began (1448-1333 =) 115, or (Table LXX) gh gm before, and ended (1667-1448 =) 219, or 156 31m after mean sunrise on that Saturday.
The tithi. Exact work. Example 5. Working the same date with the full decimals, we have
d. w.-d. a.
b. A8 in Example 3.
(60) (1) 35.5215 214-8206 211-3001 Table LXIV. . . (181) (6) 1292-3692 5687639 495-5392
(241)
(0)
1327-8907 783.6045 706-8393
For either equation b or equation c mute the difference between the values of b or c thus found and the nearest value respectively in Table LXVI A or LXVII A, cole. 2u, 26. Multiply this difference by the group-difference (col. 4). Divide the result roughly by 2 or exactly by 2.083; and add or subtract the result to or from the standard equation-value given in the Table (col. 3) as necessity demands.
[This is the complete process; but it almost always suffices to arrive very near to the truth merely by the exercise of common sense, using Tables LXVI A, LXVII A as Eye-Tables.]
Here the moon's anom. b is 783.6045, and the nearest amount of Argument b in Table LXVI A is 783-3, whose exact equation is 3.1006 (col. 3). As the difference in anom. is only about 0-3, viz. 0 2712, and the group-difference only 0-4150, we may take 3.1006 as the required equation of the given anom. Or we may work roughly by a multiplication of the first two decimals of the anom. diff. (0-27) by those of the group-diff. (0-42) and a division of the result by 2-yielding 0.0567, which, added to 3-1006, makes "equation 6"-=3-1573; or we may work completely with all four decimals, arriving at the absolutely correct result 3.1546.
