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EPIGRAPHIA INDICA.
(VOL. XIV.
EXPLANATION OF THE TABLES. 242. Table XLIII. The details were worked out with great care by M. L. de Ries from the respective longths of the sidereal solar year, i.e. the time taken by the truo sun to travel from 0° to 0', according to the several Indian authorities.
Table XLIV gives the sun's mean motion per day of 24 hours, and per hour, minnte and second, for use in calculation. It is exact for the Arya-Siddhānta, and may be used with care for other authorities, having regard to the footnote.
Table XLIVA. See the heading. It explains itself.
Table XLVA is for use in calculations. Etery valuation given in the main Tables XLVIII.A and B in ten thousandths of the circle was made by it.
Table XLVB is the reverse of XLVA. Table XLVI is a revised nakshatra Table, showing the exact ending points of each.
Table XLVII is very important, being a revised Table of sines and equations of the sun's centre, given in full after particularly careful calculation. Its preparation is describe 1 below SS 249-253. The supplementary Table XLVIIA gives, for close work, very full details of the exact equations according to authorities other than the First Arya-Siddhanta and of the differences, in seconds per minute of mean anomaly-arc, between the consecutive baseequations. Table XLVII is for the present to be held inapplicable to the Brahma-Siddhanta.
Tables XLVIII) and XLVIIIB are the main working Tables, showing, by the First Arya and Present Sürya Siddhāntas (with or without the bija), the precise value of the san's true longitude (s) and equation of the centre at each interval of 24 hours measured from true Moshasankranti, the moment when the true sua arrives each year at celestial longitude 0°; as well as the sun's mean anomaly and mean longitude. There was no possibility of framing a Table which shoull give these particulars for mean sunrise of each day, the primary requirement for the verification of Indian dates, because the moment of true Mesha-samkrānti varies each year and the starting-point had to be from that moment. These two Tables therefore give the consecutive 24-hour positions of the mean and true sun after that moment.
Tables XLIX and L enable us to find the sun's trao longitude at mean suprise; the former giving for each group of days the san's true motion per boar, and the latter giving his mean motion per minute. It is not necessary for general purposes to give his true motion per minute; if required, this can always be obtained by dividing by 60 the details of Table XLIX for one hour of the day.
243. Tables XLVIII to L are used in the following way, when we desire to find the s for mean sunrise. Say that Mēsha-sankranti occurred in the year for which we are working at 12 h. 15 m. after mean sunrise, according to the Indian Calendar (Table I, cols. 13 to 17 or 17a). Then for every day of that year Table XLVIIIA or B gives as his true longitude, 8, at 12 h. 15 m. after mean sunrise; and to obtain the sat mean sunrise on the day in question we have to deduct the sun's true motion during 12 h. and 15 m. We do this by Tables XLIX and I, and Bo get the exact s for mean sunrise on the day in question.
Table XLIX for hours is exactly correct for the Arya-Siddhanta. When used for the Sürya-Siddhānta, there may be an error amounting, at the time of year wben there is the greatest difference between the two authorities, to about one-third of a second per hour or about seven seconds per day. If anyone desires to be absolutely exact by the Sürya-Siddhānta, he should calculate the true sun's motion during the hours and minutes of the day in question by observing in Table XLVIIIB the consecative 24-hour positions, s, of the sun given in the Table for (i) the day in question and (ii) the previous day, and divide the difference by 24 for each hour's, and this rosult by 60 for each minute's, true motion. Even this, of course, is
