Epigraphia Indica Vol 17

Author(s): F W Thomas, H Krishna Sastri
Publisher: Archaeological Survey of India

Page 41

18
EPIGRAPHIA INDICA.
[VOL. XVII.
verify his figures to the best of my ability and apply the results to practical use. Any little differences that exist between us have been fully set forth and their cause explained.
Elements. Arya Siddhanta, mean system.
306. (i) The length of the mean sidereal solar year is 365 6h 12m 30, or 3654, 2586805. (ii) For the sun's mean motion per day, hour, etc., see Tables XLIII, XLIV, above, Vol. XIV.
(iii) The distance of mean moon from mean sun (our a), measured in 10,000ths of the circle, i.e. 10,000ths of the mean synodical revolution of the moon and excluding 12 whole revolutions, increases, during one sidereal solar year, from 0 to 3888-231484714. That is the advance of a in the year. Table LXIV A above, col. 3, shews this advance per day, and Table LXV the advance per hour, etc.
(iv) The value of a in mean reckoning corresponds to that of t, the tithi-index, in true reckoning. It shews what mean tithi was current at the moment in question. In general calculation by the Tables this moment is the moment of mean sunrise at Lanka, taken as 6 A.M.
(v) In reckoning by 10,000ths of the circle the advance of a in one mean solar month is 307 352623726.
(vi) Each mean solar month consists of 304 10h 31 21. The collective duration from the moment of mean Mesha-samkranti (the beginning of the mean solar year when the mean sun is at celestial long. 0°) to each separate samkranti, or the moment when the mean sun enters each of the signs, is given in Table LXXVII.
(vii) The length of each mean lunar month is 29d 12h 44m 2.79 or 294-530587946, during which the mean moon's distance from mean sun increases, in our circle reckoning, from 0 to 10,000. The length of one mean tithi, or one-thirtieth of the mean lunar synodic month, is 23h 37m 2809, or 0d-984352931; during which, in circle reckoning, the increase of a is 333.3.
(viii) The sodhya, or time-difference between the moments of arrival at celestial long. 0° of the true and mean suns, which moments are known respectively as the true and mean Meshasamkrantis, is 2d 3h 32m 30s, true Mesha-sankranti being the earlier.
The time of occurrence of mean Mesha-samkranti in every year is given in Table LXXVI, cols. 13 to 17.
(ix) The samvatsara name of the solar year is the same by both true and mean reckonings, except in the years A.D. 564-5, 905-6, 990-1, 1246-7 and 1331-2, A special footnote is appended to the main Table LXXVI in each case.
(x) There can be no suppression of a lunar month when calculation is made by the mean system; for the length of a mean solar month is greater than that of a mean lunar month, so that two mean solar samkrantis cannot take place within the limits of one mean lunar month.
(xi) Let it be noted that no intercalation of a lunar month can take place unless, at mean sunrise of the day on which mean Mesha-samkranti took place, the value of a is more than 6280-4892, or unless at the moment of mean Mesha-samkranti the value of a is more than 6619-1211; the latter valne being 10,000-3380-8789, the total increase of a from Mosha- to Mina-sankranti, and the former being 6619-1211-338 6319, the latter value being the increase of a in 24-hours.
The 19-year intercalation cycle.
307 (See Indian Calendar, § 50, p. 29.) By the mean system the cycle-sequence is found to work with almost perfect regularity. After four successive intercalations at intervals of 19 years each the intercalated lunar month gives way to the month preceding it. But there are
1 The equations of sun and moon are not taken into account in mean reckoning.