Epigraphia Indica Vol 14

Author(s): Sten Konow, F W Thomas
Publisher: Archaeological Survey of India

Page 18

No. 1.] THE TRUE LONGITUDE OF THE SUN IN HINDU ASTRONOMY.
not mathematically exact, since the true motion of the sun varies from hour to hour ; but it is quite accurate enough.
244. The calculation for the true longitude of the sun ench day was made by ascertaining his mean anomaly and then using the sine-Table as finally prepared (Table XLVII) for finding the equation of the contre. The starting point for the year is the value of his mean anomaly at the moment of true Mosha-samkranti. This had to be computed with great care. The problem is fully discussed below $S 254-255.
245. To obtain a correct value of the ann's mean longitnde nt ennrise of any day, take the value given in Tablo XLVIIIA or B, as the case may be, and deduct for the intervening hours anl minutes (cf. 8. 243) the quantities shewn in Table XLIV for the sun's mean motion. Greater accuracy even than this can be obtained by the use of Table XLII.
246. I do not enter very fully into the difference in the sun's true longitude brought about, according to the Surya-Siddhānta, by the shift in the apsis of the sun's orbit, because this seems so slight that it may be ignored. It would amouut to about l' in the last 1500 years (see beloic, 3. 254, ii).
L'ae nf the Tables. Rules. 247. That the use of the Tables may be thoroughly understood, I append a few rules of work and examples.
(i) The mikshatra.-Work by the usual Indian Calendar process for finding t, the tithi. index at mean sunrise of the day in question. Note the serial number of the civil day, ignoring altogether the day of the Hinda solar month. Deduct from this number the serial number of the day on which Mösha-samkranti occurred (Table I, col. 13). The result is, the nuinber of the day, or 24-bour period, referred to in col. I of the new Tablos XLVIIIA and B. Rumembering to use the proper Table for the Siddhanta concerned, turn to this number in either of those Tables. Against it in col. 9 will be found the correct value of the sun's longitudo. 8, on that day at a moment as many hours and minutes after mean sunrise as elapsed between mean sunrise and the moment of Mēsha-samkranti at the beginning of the solar year (Table I, col. 17 or 17a). Turn to Table XLIX for hours on the day in question and Table L for minutes, and deduct from the 8 so obtained the values of the sun's motion during those hours and minutes (above $ 243). This gives the sun's exact trae longitude at mean sunrise of the day in question. 8+t = 1, the nakshatra-index. For exact ending points of nakshatras, i.e. the points when the true moon passes out of each, consult Table XLVI. (Table VIII of the Indian Calendar suffices except' in very close cases.) Properly worked, the 8 so found yields the correct longitude of the true sun within the hundredth part of a second.
(ii) The tithi.--[This may be examined by the new Tables, though probably it will not be liable to change, or at any rate not to any change greater than one onit. Until some new Tables are published, we work for the moon's place by Prof. Jacobi's fixtures, and accept them.] The serial number of the day, er 24-hoar period, being found as above, note against it in Table XLVIIIA or B, cols. 2, 3, the value of the sun's mean anomaly; and for the intervening hours and minutes doduct the sun's mean motion as given in Table XLIV, observing the remarks in the footnote to that Table. This gives the sun's mean anomaly at menn sunrise of the day in question in ten-thousandths of the circle. Take the value in thousandths of the circle by removing the decimal point one place to the left. Refer to Table VII, Indian Calendar, and the auxiliary Table for correcting the "equation c" of the calculation, if it does not seem necessary to work with greater exactness than by use of units of about 4 minutes.
We can find the equation more accurately as follows :-It has been noted in $ 239 that, in order that "equation c" in the a, b, c system may always be additive, the quantity 60-4 was taken from a (the mean moon's distance from mean sun) and added to the equetion of the centre. Hence we shall have the exact "equation c", if we deduct from 60-4 the amount of the