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No. 18.]
TRUE LONGITUDE OF THE SUN IN HINDU ASTRONOMY.
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The day of the inscription (measured from 1 Jan.) was 357. 357-86=271, 1.e. the inscription-day was 271 periods of 24 hours each after the moment of true Mēsha-samkranti, and that moment was 9h 32m after mean sunrise.
Table XLVIIJC below shews that at 9h 32m after mean sunrise on Day 271 (measured from true Mēsha-samk.) the sun's true long., in 10,000ths of the circle, was 7365-9 104. We deduct the sun's true motion for gb (on Day 271, Table XLIX) 10-6500 and for 32m (Table L) 0.6084. Total 11.2584. 7365.9104-11-2581=7354-6520. This is the exact sun's true long. at mean sunrise on the given day, Sunday 23 Dec. 1649.8=(say) 7355 (the Arya-Siddhanta gave this as=7323, as we have seen above). Add the tithi-index, 9852, aud we find n, the nakshatra-index, =7207 by the Siddhanta-Siromani.
Table VIII shews that the moon was by the equal-space system in Pärva-Ashādha. But it is almost certain that in the matter of nakshatras the Siddhānta-Siromani followed thu Brahma-Siddhānta, and, if so, the moon at mean sunrise would have boon in Uttara-Ashādua and this would have given its name to the day.
Thus the details 24 Dhanus and Pärva-Ashådhā were correct according to the AryaSiddhanta for mean sunrise of 23 Dec. A.D. 1649 (they were also correct by Sürya-Siddhantu calculation); but the correot details for the same date, if originally caloulated by the Siddhanta: Siromani, would have been " 25 Dhanus" and "Uttara-Ashādha."
266. This being so, the necessity for Tables for correct calculation by the SiddhantaSiromani and Brahma-Siddhānta is at once apparent ; for, as matters stand, most chronologists, finding in a record-date the description of the solar month and nakshatra scemingly wrong by one place each, would class the date as irregular in two respects; and in using it for fixing the accession-date of a king, would give it scant attention. Whereas it was in fact perfectly correct and regular in all respects, but was calculated by a different standard authority from that followed by the modern verifier.
Prof. Jacobi's special Tables (above, Vol. I), no doubt, enable these problems to be worked out; but they are rather troublesome to handle, and do not yield the time-result so easily as does calculation by the a, b, c method which he first introduced to us. His later Tables (Vol. XI, p. 158 f.) can be made available ; but before using them the day of the solar month has to be accurately determined ; and, like the Indian Calendar method, they are wanting in sufficiently close fixture of the sun's true longitude at the given moment,
