Page:Sewell Indian chronography.pdf/27
32. In ancient days astronomers and astrologers seem to have generally, if not invariably, calculated by the mean motions of the sun and moon, partly no doubt because such calculation was easier than the other; but we have as yet no means of knowing for certain to how late a date or in what parts of India mean calculations continued to be made in spite of the practice, growing in favour from the beginning of the tenth century A.D. (Kielhorn: Note 1, p, 813, Journal of the R, Asiatic Soc. for 1896), advocated by Śrīpati (A.D. 1040) and established all over India not long after his date, of measuring by the true motions. (Ind. Cal., p, 28). Nor do we know for how long previous to the tenth century, if at all, the "true" system had been adopted in some places. We have therefore to be careful in examining the dates of inscriptions from about A.D. 850 to 1150, and not to reject at once as irregular a date which at first appears to be so. It should be tested by both systems before rejection.
For this reason I have prepared Tables XVIII.A, XVIII.B, XVIII.C, and XIX.A, XIX.B in order to facilitate the conversion of results found by the true system into results according to the mean system and vice versa; and also to enable results found by use of the Ārya Siddhānta to be turned into the same by the Sūrya Siddhānta and the contrary. Their use is explained below.
33. As above explained the tropical or sāyana, "with movement," Mēsha saṁkrānti takes place at the moment when, the precession of the equinoxes being taken into account, the sun's centre in his path on the ecliptic cuts the equator at the vernal equinox. According to some Hindu authorities the point of the vernal equinox shifts annually from its place in the previous year, always in one direction, till it has reached a point 27° from the sidereal First Point of Mēsha, after which it shifts backwards and proceeds to a point 27° on the other side of the fixed sidereal point, when it again reverts. On this theory of libration the First Point of Mēsha is always the mean place of the equinoctial point, though separated by an immense number of years from the furthest equinoctial point. The longitude of the sun at every tropical saṁkrānti is measured from the equinoctial point. Each tropical saṁkrānti occurs when the sun has travelled 30° from the last, and there are twelve saṁkrāntis in the tropical year. We have to be prepared for an inscription-date having been calculated by tropical saṁkrāntis, though I imagine such a case to be very rare. What is more probable is that occasionally, a clever almanack-maker having discovered that a date happened to coincide with the occurrence of a tropical saṁkrānti, the fact was mentioned in the Panchāng, and embodied in a recorded date; but it is extremely unlikely that such calculations could ever have been regularly used as a basis on which to build up the details entered in an ordinary almanack. Such a mode of calculation would necessitate an annual revision by some central authority of the time-lengths or duration of the different solar months; since it stands to reason that the time taken by the sun to travel, for instance, the 30° from the fixed initial Mēsha saṁkrānti-point to the next, Vṛishabha, saṁkrānti-point is not the same as the time taken by him to travel 30° from the equinoctial point, except in the one case of those two initial points being exactly in coincidence; and as the equinoctial point shifts annually in its relation to the sidereal starting point, so the lengths of the several solar months would have to be annually altered if Hindu almanacks were to be regularly prepared in accordance with a tropical system. There can be no doubt that in India almanacks were prepared according to the standard system laid down by one or other of the ruling authorities, namely, in one or other of the Siddhāntas; and in these the precession of the equinoxes was only considered incidentally.[1]
- ↑ The Hindū year is believed to have been sidereal for at least 2000 years. (Sh. B. D., in Indian Calendar, § 17, pp. 6, 7