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No. 14.]
THE FIRST_ARYA SIDDHANTA: "TRUE" SYSTEM.
117
First we have to ascertain the values of a, b, c at the moment of true Měsha sankranti which took place (Table LXI, cols. 13, 14, 17) at 3h 55m after mean sunrise on Day 84, namely Wednesday, 25 March, A.D 1226. The a, b, c for mean sunrise of Day 60, Sunday, 1 March, the day of Chaitra sukla 1, are given in cols. 23, 24, 25 of the same Table. Interval between the two, whole days, (84-60=) 24. Taking down the a, b, c for 25 March and adding their increase for 244 34 55m from Tables LXIV, LXV, we find the values of a, b, c at the moment of true Mesha-sa mkranti, as required.
Table LXIII B gives us the exact interval in time and the amount of increase of a, b, c, during that interval, up to the moment of every subsequent samkrånti in the year. In close cases, of course, full decimals can be used and the equation-values very carefully examined, but in general it is only necessary to use whole numbers, as in this example. Only in a doubtful case need we do more.
We desire, let us suppose, to ascertain, from the values of t at the respective Mithuna and Karka-samkrāntis, whether the moon was waxing or waning at the moments of their occurrence. The work is as follows:
d. w.-d. a.
b. C. Mean sunrise, Chait. fuk. 1 (Table LXI) . 60 1
36 215 24 days' increase (Table LXIV). . . 24 3 8127 8 71 6 6 3 hours' do. (Table LXV) . . .
42 50 55 minutes' do. ( do. . . .
13 1 0 At moment of true Mësha-samkranti. 84
8218
277 Interral to Mithuna-samk. (T. LXIII B, left side)
+1105 2 62 171 At moment of Mithuna-samkrānti
9323 354 4481 Eqn. b (Table LXVI)
250 Eqn. c (Table LXVII) .
t = 9614 This value of t shews that at the Mithuna-samkrānti the moon had not reached the point of new moon when t = 10,000. She was still waning.
a. b. At moment of Mithuna-sankranti, as abore
9323 354 Interval to karka-sanhk. (T. LXIII B, cols. 9, 10, 11) . 703 147 4 7
92
411
448
At moment of Karka-sankranti . . . . . 26 501 5351 Eqn. b (Table LXVI) . .
138 • Egn. c (Table LXVII). . . . . . 731
t = 237 [It is not really necessary, when it is seen that a (here 26) is greater than 0, to add the equations, because the value of a proves that the moon had begun a new synodical revolution and was waxing.)
The value of t (and a) shews that the moon was waxing at the Karka-samkrānti. Thus the lunar month Ashādha (ses cols. 1, 2, Table LXIII B) was intercalated in the given year. . The place of the moon at the moments of the later samkrantis is obtained, if required, by a continuation of similar work and the use of Table LXIII B.
Seu note to Table LXIII B. These values are given in the auxiliary Table. At the Mithuna-samkranti . is always 448.0$77 and equ. e always 10-5619. At the Karka-sankranti e is always 634.8213 and eqn. e always 72-5193,
