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TABLES FOR CALCULATING HINDU DATES.
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TABLES FOR CALCULATING HINDU DATES IN TRUE LOCAL TIME.
BY HERMANN JACOBI, PH.D., SANSKRIT PROFESSOR, BONN.
In my paper on the computation of Hindu dates, etc. (vol. I, page 403 ff.), I have given rules for calculating, according to the curiously inaccurate Hindu method, the corrections which must be applied to a date, computed for mean sunrise, in order to obtain the same for true sunrise at any given place in India. As this calculation is rather tiresome, I have computed the following tables, which will make the process easy without detracting from the accuracy of the results. As the problem, to solve which these tables serve, is somewhat complicated, a few remarks on the theory of true and mean time may not be amiss.
1. Suppose the sun to move with an equal motion on the equator (instead of on the ecliptic); then this equatorial sun will exactly regulate mean time. His rising will occur at 6 o'clock for every place on the earth the whole year round, marking the mean beginning of day. The interval between his risings at two distant places will be the time-difference between these places (see vol. I, Table XXV).
2. Now assume a second sun to move with the same equable motion on the ecliptic. This supposed sun is meant when the "mean sun" is spoken of. It is obvious that this mean sun and the first will not rise at the same time, except when they coincide at the two points of intersection of the equinoctial and the ecliptic. At every other time the second will, in places in north latitude, rise earlier than the first, when he is in the northern half of the ecliptic; and later, when he is in the southern half. Table XXVII, A-F, gives the interval in ghatikás and vináḍis between the risings of both supposed suns,' for every degree of the ecliptic as entered in the vertical index to the left and right of each table, and for all degrees of north latitude from 10°-35° as entered in the horizontal index at the top of each table. At the intersection of the horizontal and vertical columns is given the interval of rising for the tropical longitude of the mean sun and for the terrestrial latitude in question; e.g., in Table XXVII-B, we find that for 44° trop. Long. and 20° terr. Lat. the difference in rising is 1gh. 22v. If the trop. Long. O is entered in the index to the left, the ecliptical mean sun rises before the mean beginning of the day; if on the index to the right, it rises after the mean beginning of the day.
3. We thus find the time of rising of the mean sun (moving on the ecliptic), but what is really wanted is the time of rising of the true sun. The true sun only twice in the year coincides with the mean sun; at every other time he either precedes or lags behind the mean sun. Their difference in longitude is the equation of the sun's centre, the amount of which in degrees, minutes, and seconds is furnished by Table XXIV-B. If the equation has the sign, the true longitude of the sun is greater than his mean one, and consequently the true sun rises later than the mean one; if the equation in Table XXIV has the sign +, the true sun rises before the mean one; always by the time corresponding to the sun's equation of the centre. In order to compute the equivalent in time for the sun's equation of the centre, we must know how much time is occupied in rising by one degree of the ecliptic at the place where the sun is at the moment in question in a given latitude. The amount in vináḍis is furnished by the entries immediately below the degrees of terrestrial latitude in Table XXVII. Though continually changing, it is considered by Hindu astronomers to be constant throughout each single
'Or between the risings of a point on the equator and one on the ecliptic, which have the same distances from the
equinox.
