39C. Dr. Schram has been so kind as to carry through a series of most careful and elaborate calculations with a view to ascertaining definitely, by the elements of several different Hindū Siddhāntas, the exact value of this śōdhya interval at the epoch of the Kaliyuga and for five subsequent milleniums . Dr. Schram's results differ slightly from the results indicated in the Indian Calendar, which were based on Mr. Sh. B. Dikshit's fixture of valuations; and though attempts have been made to ascertain the basis for these last, none have been successful. My own endeavours were in accord with those of Dr. J. Burgess and Dr. Fleet, both of whom were good enough to help me in this respect. We can none of us find out how Mr. Dikshit arrived at his figure, 2.170694 d. according to the Sūrya Siddhānta, for a position of the sun's apogee taken as 77° 16′ in A.D. 1137. (Ind. Cal., § 24.) Dr. Schram calculates the same as, correctly, 2.169751 d., a difference of 0.000943 d., or about 1 m. 18 s. In these circumstances the question which I had to decide was whether I should alter my figures in Tables XXVII., XXVIII., XXIX.,—figures which depend on the value of the śōdhya—or leave them based on this value as settled by Mr. Dikshit. I finally decided on the latter course for three reasons. First, the differences are not great, and I have added a note on them to each Table . Secondly, even though Hindū computation may not have been scientifically perfect, it is safer, when examining Hindū dates, to accept that computation. Thirdly, I find on practical test that results by my Sūrya Siddhānta Tables as they stand, with the Hindū computation of the śōdhya accepted, are very closely in agreement with the results arrived at when these are calculated by the elaborate and cumbrous formulæ laid down by the Siddhanta itself, closer than would be the case if I accepted Dr. Schram's śōdhya-valuation. (See Example 50.)[1] It may also be noted in this connection that the śōdhya value, when used for such purposes as for my Tables for the Jovian saṁvatsaras, is a constant quantity, and not liable to any increase, however great may be the interval from K.Y. 1 current to the given K.Y. year; so that the difference between the results is always the same, and this being small, only one or two minutes, it is not as a rule very important.
39D. Dr. Schram has sent me his full process of work by two different methods in order to arrive at the proper scientific value of the śōdhya in different millenniums (but for purposes of Tables XXVII. to XXXI., especially required for K.Y. 1 current, or 3102 B.C.). And, first, I give his results in tabular form, as follows:—
| Year. | First Ārya Siddhānta. | Sūrya Siddhānta. | ||
| By a series of approximations. | By direct calculation. | By a series of approximations. | By direct calculation. | |
| K. Y. 50000 | 2.146831 | 2.146831 | 2.168900 | 2.1688997 |
| K. Y. 1000 | 2.169101 | 2.1691004 | ||
| K. Y. 2000 | 2.169302 | 2.1693011 | ||
| K. Y. 3000 | 2.169502 | 2.1695018 | ||
| K. Y. 4000 | 2.169703 | 2.1697024 | ||
| K. Y. 5000 | 2.169904 | 2.1699031 | ||
- ↑ Table XXXI., for the Brāhma Siddhānta and Siddhānta Śirōmaṇi is based on Dr. Schram's valuation of the śōdhya in K.Y. 1, current
