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COMPUTATION OF DATES.
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THE COMPUTATION OF HINDU DATES IN INSCRIPTIONS, &o. BY PROFESSOR HERMANN JACOBI, PR. D., Bonn.
Introductory. If we compute the moment of expiry of a tithi by the elements of two or more Siddhantas,' the results may differ by an hour or even more. This difference will affect the calculated date only where the end of the tithi falls near the beginning or end of a day. But in such cases even a small difference may carry the end of the tithi to the preceding or following day, and thereby change the date by a whole day. For these cases, then, it is desirable to be able to compute the tithi according to more than one Siddhanta. Besides, the moment of the Sankranti, or the true beginning of the solar month. varies with the different authorities, and this difference may affect the name of the lunar month according as the new-moon falls before or after the beginning of the solar month ;' and hence the necessity of tables for all available Siddhdntas.
2. The following tables are based, as far as possible, on the Hindu solar year. This arrangement recommends itself by facilitating the finding of the lunar month, and by abridging the calculation of the tithi.
3. A close study of the subject proves that the several Siddhdntas furnish the elements on which a date depends nearly correct i.e. compared with the results of modern science) for the time of their composition. Some Siddhantas yield tolerably correct results for a long period extending over several centuries, while others diverge sooner from the truth. Now of course it is always uncertain which Siddhanta was followed by the unknown almanao-maker who furnished the date recorded in any historical document; but it may be presumed that he used the karana most in vogue, i,e. one which was not very old, and which therefore yielded correct results for the time being. These considerations have induced me to construct a General Table in which the value of the quantities necessary for the calculation of dates, vis. the relative position of sun and moon, and the moon's anomaly, are set down in accordance with modern science.
4. The General Table is to be first used; and only when by that table the end of the tithi falls very near the beginning of the day, and the week-day comes out in error by one day only, need the Special Tables for the several Siddhantas be tried to see it one of them will furnish the desired result.
1 The tables published by me in the Indian Antiquary, vol. XVII, pp. 147-181, are based on the Sirys SiddAdata As now current. They yield therefore the end of lithi, the principal item of Hindu date, in cordance with that Siddhanta only.
My previous tables give the beginning of the solar month according to the Arya Sildidnta only, the procent furnish the same also according to the other Siddhdntar Available to me.
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