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436
EPIGRAPHIA INDICA,
or +. It is evident that the true sun rises later than the mean sun if the true longitude is greater than the mean, and vice versa. In the present case, the equation being additive, true sunrise precedes mean sunrise.
We have now to find in how much time the part of the ecliptic equal to the o's equation rises on the given parallel.
Convert the O's equation into minutes, viz. 121'; multiply this by the asus which the tropical sign, through which the sun is passing, takes in rising, 1987, and divide by 1800. The result 135 is the interval in asus between the rising of the true and the mean sun. Divide this by 6, the quotient 23 is the interval in vinádis. The increase of distance for the interval thus found must be added to the corrected distance if the equation in Table XXIV is subtractive, or subtracted if the equation is additive. Here
Distance fog'50" -28 din - 0 4 40
True Dist. 6 5 10 This is the final result. It will be seen from Table XXII, that 26 p. (the time corresponding to an increase of distance = 5' 10") before true sunrise, the first Karana had ended.
It should, however, be remarked that if the interval between true sunrise and the end of a tithi, &c. is very small, say a few palas, the case must be regarded as doubtful; for, though our calculations materially agree with those of the Hindus, still an almanac. maker avails himself of abbreviations which in the end may slightly influence the result (vide inf.).
62. Dates anterior to Bhaskara (K. Y. 4251).-In the Siddhanta Siromani, Golddhyâya, iv, 20, Bhaskara states that the ancient astronomers assumed that at Lanka (or on the Equator) the zodiacal signs rise in the same time with 30 degrees of the equinoctial, or, in other words, that the udayasu of all signs are 1800. On this condition the entries in Table XXVI require a correction exhibited in column Chara, as explained at the foot of the table, e.g. the column 24° would, on this supposition, show the following figures-1483, 1538, 1694, 1906, 2062, 2127, instead of 1363, &c. It is obvious that in calculating dates anterior to Bhaskara's time, the asus in Table XXVI should be corrected in the way explained.
If we knew the Hindu estimate of the latitude and longitude of the place for which the calculation is to be made, the result would of course be the same as that arrived at by a Hindu calculator. As yet, however, we do not know the Hindu latitude and longitude of any place, but substitute for them their true values. It is obvious that the error in the Hindu estimate of the geographical site of a given place influences the result, from which our result, calculated on absolutely correct data, may differ consider. ably. Therefore, so long as we ignore the Hindu latitude and longitude of the places for which almanacs were constructed, our calculation, though theoretically correct, must yield discordant results. I may therefore be allowed to appeal to native astronomers to collect and furnish us with a list of the latitudes and longitudes of the principal places of India, as employed by ancient Joshis.
Examples of General Application. 1. To find the European date corresponding to a given Hindu lunar one.
