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No. 15.]
THE BRAHMA-SIDDHANTA: MEAN SYSTEM.
No. 15.-THE BRAHMA-SIDDHANTA OF BRAHMAGUPTA, A.D. 628 :
MEAN SYSTEM.
BY ROBERT SEWELL (I.C.S., RETIRED).
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(Continued from Vol. XVII, p. 187.)
321. The Tables published in my last article (above, Vol. XVII) enabled the dates of ancient Indian inscriptions and records to be verified according to the requirements of the BrahmaSiddhanta with, as basis of calculation, the "true" or apparent motions of sun and moon. This mode of reckoning appears to have been introduced in the 11th century A.D. But the Brahma-Siddhanta was composed in A.D. 628 and for at least four centuries after its appearance details for the Calendar were almost certainly based on mean planetary motions; while it is believed that this mean system continued to guide the preparation of pañchangas (almanacs) till a much later date-perhaps for several centuries in some parts of the country.
For the correct verification, therefore, of early dates it is necessary for historians to be provided with a set of Tables based on mean planetary motions and the postulates of the BrahmaSiddhanta in addition to those based on mean motions and the postulates of the Arya-Siddhanta. The latter were provided in a previous article in this volume. The former are presented herewith. They cover a period of 800 years, from K.Y. 3700 to 4500, or from A.D. 599 to 1400.
The system of work is the same as in all my previous Tables, that is to say, it is the system of Largeteau as adopted by Professor H. Jacobi in the Indian Antiquary, Vol. VIII, and in the Epigraphia Indica, Vol. XI. Full examples shewing the method of work, which is very simple, are given in my former articles; others, specially concerning the system of mean reckoning ou Brahma-Siddhanta principles, are given below.
In case of doubt as to which of the Tables already published should be used in the present case attention is directed to the accompanying § 329.
322. In examining the dates of records in earlier years it is necessary to remember that the modes of reckoning adopted were not always the same as those used in more recent years. As to eras, reference to articles 6-12 of my former work, Indian Chronography, is recommended. For other matters the late Dr. J. F. Fleet's remarks in the Journal of the Royal Asiatic Society for 1912, pp. 704-5, will be found very valuable.
Especially let it be borne in mind that the lunar month reckoning in early years was probably carried out on the purnimanta system. According to the late Professor Kielhorn the earliest known date certainly in amanta reckoning belonged to the year A.D. 794. It is contained in the Paithan plates of the Rashtrakuta king Govinda III (Epig. Ind., III, 105; Ind. Ant., XVII, p. 142, No. 9). As regards these two systems, the amanta and purnimanta names of lunar months, see Indian Calendar, §§ 13, 45 (with Table on p. 26), 47, 51, and the late Sankara Balkrishna Dikshit's footnote on p. 31; also Indian Chronography, §§ 75, 76, p. 31.
Elements of the Brahma-Siddhanta mean reckoning.
323. The principal elements are fully stated in my former article on this authority (above, Vol. XVII, § 313). For calculation on the mean system the following notes are necessary.
(i) The length of the mean sidereal solar year is 365 6h 12m 9, a fixture afterwards adopted by Bhaskaracharya in his Siddhanta-Siromani, A.D. 1150.
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