34. Nevertheless, since tropical saṁkrāntis may occasionally be met with in inscriptions, we have to lay down rules for calculating them. And the first question to be decided is in what year the sidereal and tropical Mēsha saṁkrānti-points coincided. According to the Present Sūrya Siddhānta they were together in Śaka 422 current, K.Y. 3601 current, or A.D. 499, the rate at which the equinoctial point shifts annually being 54″. By almost all the other authorities the coincidence took place in Śaka 445 current, K.Y. 3624 current, or A.D. 522, the rate of annual precession being one minute (1′). The Siddhānta Śirōmaṇi places the coincidence in Saka 450 current, K.Y, 3629 current, or A.D. 527, also with precession at 1′.[1] The translators and annotators of the Sūrya Siddhānta more than once assert (Burgess's Sūrya Siddhānta, p. 14, &c.) that by its precession-rate the coincidence must have been in about A.D. 570; but with reference to viii., 9, after a careful calculation and examination connected with the position of the junction-stars of the nakshatras, resulting in proof of an average error of longitude, they write (op. cit. p. 211), that this "would indicate that the Hindu measurements of position were made from a vernal equinox situated about 1° to the eastward of that of A.D. 560, and so at a time seventy years previous to the date we have assumed for them, or about A.D. 490." And if for "560" we read "570" we should arrive at the year A.D. 500. I assume therefore the correctness of the Indian Calendar in this respect.
On this matter Dr. Fleet gives me the following remarks. It is only by backward calculation that such-and-such years are fixed as the times when, according to different authorities, the degrees of precession were nil: there is no record coming down from those times themselves. Albērūnī suggests (trans, Sachau, I, 366) that the Hindus became aware of precession, or at any rate began to pay attention to it, only about A.D. 989. And this is practically borne out by the facts, as far as we can trace them. Āryabhaṭa (who wrote in, or soon after, A.D. 499) and his exponent Lalla do not mention precession at all. Varāhamihira (died A.D. 587) mentions an effect of it; namely, a shifting of the solstitial points from ancient positions assigned to them by the Jyōtisha-Vēdānga to the positions which they had in his own time: but he does not disclose any knowledge of the cause of the shifting. Brahmagupta (wrote A.D. 628) mentions precession in a somewhat vague manner, but only does so to deny it. And as far as our knowledge goes at present, it was first taught by Muñjāla, who wrote in A.D. 932.
35. Whichever authority is selected, the difference in years between its year of coincidence, or base year, and the given year, multiplied by the annual amount of precession, will show the longitudinal distance in degrees by which in the given year the tropical, or sāyana saṁkrānti precedes or follows the sidereal, or nirayana saṁkrānti. The former precedes the latter in all years later than the selected base-year of coincidence, and follows it in all earlier years. In years earlier than about A.D. 1100 it will be well to take K.Y. 3623, A.D. 522–23, or the year of coincidence according to the Ārya Siddhānta, as the base-year, with an unit of precession of 1′; but after about A.D. 1100 calculation may be made by both the base-years K.Y. 3600, A.D. 499–500, and K.Y. 3623, A.D. 522–23, since both the Ārya and Sūrya Siddhāntas have been in constant use ever since as authorities in different parts of India; the former especially in the Tamil and Malayalam countries of South India where the solar reckoning is largely followed.
36. The rules for finding the moment of a tropical saṁkrānti are given on pp. 152–53 of the Indian Calendar, "Additions and Corrections." But to save trouble of reference they are here repeated with fuller explanation. Rule for finding
moment of a
tropical saṁkrānti. First find the time of the nirayaṇa true Mēsha saṁkrānti by the authority used. (See Table I., cols. 14 to 17 and 14a to 17a, Ind. Cal., and Examples 3, 4 below.) Add the collective duration given in Table XVIII.A or XVIII.B, cols. 3, 4, by the same authority from this nirayaṇa Mēsha saṁkrānti to the true nirayana saṁkrānti in question. The total gives the time of the required nirayaṇa saṁkrānti. For a rough guide, the sāyana saṁkrānti took place as
- ↑ I accept in the matter of these dates the considered assertion of Pandit Shankar Balkrishna Dikshit, referring those interested to the discussion of the subject by Prof. Whitney, "The Lunar Zodiac," in Oriental and Linguistic Studies (1874). Whitney inclines, so far as the Sūrya Siddhānta is concerned, to the year A.D. 490 (p. 370), though with doubt.
