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No. 10.)
THE SIDDHANTA-SIROMANI.
173
EXAMPLES Example 1. To find the value of a, b, c for the moment of true Mēsha-sankranti in any
year, the beginning of the solar year. Rule. Note in Table LX the number of the expired year of the Kaliyaga (col. 2. In this column the K. Y. year is that current in the corresponding A.D. year. The expired K. Y. year is the next earlier). Note (cols. 13-17) the day, week-day, and time of occurrence of true Mösha-samkranti in that year. Take from Table LVII A the week-day and a, b, c for the beginning of the K. Y. century; from Table LVII B the same for the expired K. Y. year of the centary; from Table LVII C the same for the day marked "Mesha 0" (col. 2), or the day next to it, being guided by the given week-day (Table LX, col. 14); and add together the three sets of values so obtained. The sum of these shews the positions of the moon and sun (a, b, c) at mean sunrise of the day on which true Mēsha-samkranti occurred. For the moment of the samkrānti add to these values of a, b, c those for the hours, minutes and seconds elapsed since mean sunrise (col. 17), obtaining them from Table LIV B.
Work. Given that the valaes of a, b, c are wanted for the moment of mean sunrise of the day on which true Mosha-sankranti occurred in K. Y. 4492 expired, A.D. 1391-2; and at the moment of that sankranti.
Table LX shews that the day was (0) Saturday 25 March A.D. 1391, and that the sankranti occurred on that day at 17h 18m 12.
5
(i) Approximate calculation, by whole numbers.
w-d. a. b. c. Table LVII A. K. Y. cent. 44 .
7454 768 , LVII B. Year 92
.
9389545 LVII C. Mēsha 0 . .
. 5
9 323 927 995 At mean sunrise of Sat. 25 March ; . 0 (Sat.) 6166 240 273 Table LIV B. 17 hours . . . . .
240262
. 18 minutes. .
4 . 0 0 At moment of sankranti . .
6410 266 275 (ü) Ful calculation. Worked to the full extent, with use of decimals and including the value of a, b, c for seconds the result is
For mean sunrise, a=6165-1839, b=240-2250, o=272.5113. For moment of Měsha-samkranti, a=6410-3281, b=266-3902, c=274-4852.
Note. The value found for c will always be a guide as to whether the caloulation bas been made for the right day (see Table LVIII O telow); for at true Měsha-samkråntic is always 274 or 275. In this case let it be observed that 8 years later than the given year, viz. in K, Y. 4500, the value of c at true Mēsha-sankranti was 274-4058. The change in o at that moment, owing to shift of sun's apsis ($ 273, i), being 0.0805 per century, and our calculation having been based on the value for K. Y. 4400, we should, for extremo accuracy, deduct from 274-4852 the proportional change for 92 years, which amounts to 0.0741, leaving our c for A.D. 1391=274-4111.
Example 2. Required to find the value of a, b, o at mean sunrise of the civil day called Chaitra sukla 1, the civil beginning of the luni-solar year K. Y. 4492 expired, A.D. 1991-2.
