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No. 11.) THE BRAHMA-SIDDHANTA : TRUE, OR APPARENT, SYSTEM.
129
Thus was obtained the length of each month in days, hours, etc. For the increase of a, b, o during the periods so determined Tables LIVA and B, which are applicable to the Brahma. Siddhanta as well as to the Siddhānta-Siromani, were used.
Note on work for the nakshatra. 319. In our method of work := the true sun's longitude and t = the tiths-index (which shews the true moon's distance from the true sun) at the given moment. + t = the nakshatra-index , which gives the true moon's place in the heavens, or her apparent longitude. The value of t is ascertained by the ordinary calculation for a date. The value of has to be found.
By the Arya-Siddhanta the formula for finding , c being the sun's mean anom. at the given moment, is : = (c x 10) + 7226 - eqn.c; where the factor 7226, which represents in 10,000ths of circle the long. of sun's perigee plus the sun's greatest equation, is a constant.
By the Sarya-Siddhānta, as exemplified in the Indian Calendar Tables, the numerical factor is not 7226, but varies in the period A.D. 900 to 1900 from 7206-5077 to 72074035 being fixed for rough work at 7207. The variation is due to the postulated shift of the sun's perigee-point.
By the Siddhanta-Siromari there is, for the same reason, & yariation in the numerical factor, vit. from 7252-6466 in A.D. 900 to 7259-0910 in A.D. 1700,- roughly from 7253 to 7259.
By the Brahma-Siddhanta the numerical factor varies from 72245370 in A.D. 600 to 7225-2031 in A.D. 1200 (the limits of the general Table LXXXII below). For rough work therefore by this authority the formula is I = ( x 10) + 7225 - egn. a.
For more accurate work the value of o should be calculated (by the Tables) with decimals and instead of multiplying o by 10 its value should be changed from thousandths of cirolo ( in the Table-result) to ten thousandths by moving the decimal point one place to the right; the value of egn. c can be obtained from Table LVI with great accuracy; and the numerical factor can be taken from the following summary.
K.Y. centary
A.D. century.
Exact factor in
formula.
Rongbly.
8700
599-800
8800
8900
4000
699-700 799-800 899-900 999-1000 1099-1100 1199-1200
7224-6870 7224-648i 7824-7692 7224-8103 17226 7234-9814 7296-0828 7226-2081
4100
4200
1900
Examples. It is not necessary to give a number of examples of work by the present Tables. The system of calculation being exactly the same as that of the Indian Calendar and throughout theresent series of articles, the examples already published for computation by other authorities
See Indian Culendar, $ 156, p. 97 ; article on the Siddhanta-siromasi, above, Vol. XV, $ 878," Note on . work for the nakshatra "; article va the Pirat Arya-Siddhanta, Vol. XV above, $ 802 ; and the several examples given in those papers.
· Whole revolutions are not necessary for present par pons, and in our system when a 20,000 a whole synodio revolation of the mean moon has been completed.
