Page:Sewell Indian chronography.pdf/39

First for the Ārya Siddhānta:

Convert these times to Sūrya Siddhānta figures. By that authority mean Mēsha saṁkrānti took place on (March 25th, 16 h. 22 m. +, by Corr. I., 1 h. 6 m. +, by Corr. III., 33 m.) March 25th at 18 h. 1 m., and mean Vṛishabha saṁkrānti took place on (April 25th, 2 h. 53 m. + 1 h. 6 m. + 33 m.) April 25th at 4 h. 32 m.

For the mean moon's distance from the sun at each saṁkrānti, or the value of ${\displaystyle a}$, let it be assumed that the ${\displaystyle a}$ of the true Mēsha saṁkrānti by the Ā. S. was 8751.^[1] To this add (śōdhya, ${\displaystyle a=}$) 727 and (the constant) 201. Total, 9679. This is the value of a at mean Mēsha saṁkrānti by that Siddhānta.

Convert this to the same by the Sūrya Siddhānta by (Corr. I.) + 15 and (Corr. III.) + 8. Total, 9702. This is the figure for the ${\displaystyle t}$, which in mean calculation is the same as ${\displaystyle a}$, tabulated, for the Sūrya Siddhānta, in Table I., Indian Calendar, for the year in question.^[2]

To the values of ${\displaystyle a}$ by the two authorities thus found, viz., Ā. S. mean Mēsha saṁkrānti 9679, and the same for the S. S. 9702, add in each case the interval to the next saṁkrānti (Table XIX col. 6), viz. 307, and we have the ${\displaystyle a}$ of mean Vṛishabha saṁkrānti by the Ā. S. 9986, and by the S. S. 9 (as tabulated in Table I., col. 11a.)

[Incidentally this proves that the lunar month intercalated in this year according to the Ārya Siddhānta was not Vaiśākha, as was the case by the Sūrya Siddhānta, but Jyēshṭha.]

62. I have given in full, so that they may be thoroughly understood, the details of this process, but in practice the use of Corr. III. for conversion of results from the Sūrya Siddhānta saṁkrānti figures as given in Table I. of the Indian Calendar, cols. 9, 11, 9a, 11a, to the same saṁkrānti figures by the Ārya Siddhānta for the year A.D. 1096–97, simply amounts to the following: S. S. 9702 − 15 (Corr. I.) − 8 (Corr. III.) = Ā. S. 9679.

62a. Since it may often be found necessary to examine a date by the Original Sūrya Siddhānta, to show how, from the information at present available, we may find the necessary and most important starting-point for calculations by it, viz. the moment of Mēsha saṁkrānti, either true or mean.

The moment of occurrence of a mean saṁkrānti is found from any given or calculated moment of a true saṁkrānti by adding to the latter the proper value of the śōdhya. The moments of all true Mēsha saṁkrāntis according to the Ārya Siddhānta are given in Tables XXXVIII.A and XXXVIII.B and Table I. of the Indian Calendar from 59 B.C. to A.D. 1950 (see also Example 3 below), but for our present purpose only the earlier years are required; the same rules, however, apply to all. Śōdhya by the Ārya Siddhānta is a constant quantity and, ignoring seconds = 2 d. 3 h. 32 m. Śōdhya by the Original Sūrya Siddhānta is declared by Sh. B. Dikshit to be 2 d. 5 h. 45 m. He takes this also as a constant; and we may do the same, since, though there was possibly a slight variation during the course of 2000 years we are practically only concerned with about, at the utmost, a period extending over 1000 years, for

1. ↑ I have calculated this independently and found it correct.
2. ↑ If the addition for the constant had been taken as 200, for convenience, the difference of one unit (= 4.25 minutes) would in this case have been immaterial.