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164
EPIGRAPHIA INDICA.
[VOL. XV.
CONSTRUCTION OF THE TABLES. Tables LIV A and B. Advance of a, b, c for days, hours, minutes and seconds. 274. These Tables are to be used in calculation by the Siddhanta-Siromani in the same way as Tables IV, V of the Indian Calendar are used for the Sürya-Siddhanta ; working first with whole numbers and resorting to the decimals only in close cases. The values of a, b, c at mean sunrise on Chaitra sukla 1 of any year being taken down from Table LX below, addition of figures given in Tables LIV A, B for the intervening days, hours, etc., up to the given date furnishes the a, b, c at any moment of any subsequent day, i.e. gives us for that moment (a) the distance between mean moon and mean sun, (6) the moon's mean anom, (c) the sun's mean anom. The figures are parts of the circle--a teu thousandths, b and a thousandths.
To arrive at an exact estimate of the value of these quantities an examination was made of Prof. Jacobi's fixtures for their value at mean sunrise of the first day of the 42nd century K. Y., a moment, that is, separated from the epoch of the Kaliyuga, mean Mösha-samkranti K. Y. 0, by exactly 4200 years K. Y. Mean Mēsha-samkrinti K. Y. 4200 (expired) took place on Friday 25 March A.D. 1099 at 10h 30% after mean sunrise and therefore 13h 30m before the mean sunrise of Saturday. 13h 30m=338h 44P, the amount of Jacobi's “Cor.," or correction (Table XIII, above, Vol. I, p. 450). In that Table he gives the figures for the beginning of century 42 K. Y. as a (Dist. (- )=14° 18' 0", 6 (C's anom.)=51° 24' 13', c (@'s anom.)= 281° 1' 19'. Owing to his arrangement of Tables, by which he gives only one Table for calculation of solar days (Table XXI) applicable to all Siddhantas, whereas the date of occarrence of mean Mēsha-samkrānti by the Siddhānta-Siromani is always a day earlier than by the other authorities, we have, for comparison with his Tabular figures, to add a day's increase to the above valuation. This gives us a=26° 29' 27", b=64° 28' 7", c=282° 0 27". Adding the increase in 13h 30m or 338h 44P (Jacobi's "Cor.," Table XXII), we have finally for the values at mean sunrise of Sunday a=33° 20' 40"-4, b=71° 48' 50'86, c=282° 33' 41":36. In 10,000ths of the circle (a). and 1,000ths (banl c), these values shew the increase in 4,200 years to have been a=926-237654, b=199-483677, c=784-893163. From a has to be deducted in accordance with our Indian Calendar working-system the sum of the greatest equations of moon and sun, viz. 200-296034, and hence a=725.9416.
Prof. Jacobi, however, has, since his valuation published in Vol. I, slightly modified his estimate of this value of a. In Vol. XI above (Table IX, B) be states the three valges as a=7263, b=1995, c=7849. In my notation these figures are a=726-3, b=699-5, c=284.9.1 The difference being very small (0-4), I conclude to accept his later estimate of the increase of a.?
"I measure the ('s and O's anom. from perigee, Jacobi from Apogee.
A careful examination of some of Prof. Jacobi's Tables in Vol. XI above has led to the discovery of a few misprints, which it will be well to point out for the guidance of those who prefer to use his 'Tables. I regret that the present war renders it impossible to obtain his permission, but feel sure that, if I had been able to do so, he would have acknowledged these as printer's unistakes.
Table I, p. 161. Surya-Siddh. centuries. In cent. 33, under a, for "12348" read 12358.
Table V A. In cent. 36, under 4, for "76166" read 75166. And in cent. 41, under a, for "19789" rend 18789.
Table V B. In cent. 36, under a, for "76166 " read 75166. (Compare entries in Tables I and IX A.) Tablo IX B. In cent. 44, under a, for "81114" read 81314. Table X, year 50, under a, fur" 40359" read 44359. 69
"45417" 45419. » 73
"82832" 92832. 88
" 46499" 46479. , 99, under 10, for "6" read 5. In Vol. I, Table XXIV, the moon's equation of the centre under " Brah. a S. Śiro.," 4th entry from bottom, the seconds (") should be 18, not "10."
See alea $ 283 helow.
