________________
272
THE INDIAN ANTIQUARY.
[SEPTEMBER, 1882.
will give, as the remainder, the expired year of the cycle, according to the rule of the Surua. Siddhanta. If 1 be added to that remainder it will give the current year of the cycle corresponding to Kor $. The Súrya-Siddhanta rule with the bijya or correction is similarly represented by
{K+ 26 +(10
)}: 60,
8 +
22 $. 22 $ + 1291
cha, Nala, Prajotpatti, Pramodúta,&c., instead of the more usual Vrisha, Vikrita, Hémalamba, Sarvart, Virodhakrit, Pramddi, Anala, Prajapati, Pramida, &c. Both forms may be used, and there seems to be some confusion between the 13th and 47th; and Brthat Sanhitú, viii, 41, where the 36th is Sôbhakrit and the 37th Subhakrit, but it would have been well had Mr. Sewell prefixed a list of all the correct forms of each name, and then, throughout his table, used the correct or most prevalent forms only.
As these Tables are for the use of those work. ing on documents and inscriptions, they ought to have contained some indication at least, such as Brown gives (Car. Chron. pp. ii, iii, and 16-19), of the differences obtaining in different parts of the country in the use of this cycle. Thus, a document dated "$. 1719, Sukla samvatsara," if referred to Mr. Sewell's Tables, might be supposed to be far wrong, either in the date or cyclic year; but on a reference to Brown's (p. 18) we find that the 3rd year (Sukla) of the cycle corresponded to $. 1720 in the northern mode of reckoning, and is found attached sometimes even to S. 1718; thus supporting the accuracy of the date within the limits usual in inscriptions, &c. Brown's Tables would have been all the more useful had he carried this additional column through the whole of his second Table: but Mr. Sewell's is still more defective in wanting it altogether; and this want is the more felt as the differences between the two modes of reckoning is not constant. About A.D. 850 they agreed, but the difference is now 12 years, and the rules for determining the cycle years in the different astro. nomical treatises are not generally known and vary slightly. That given by Prinsep from the Surya-Siddhanta (Us. Tab. p. 160) is scarcely intelligible, and Warren's rule (Kalasankalita, PP. 147, 211) is not always to be depended on; but the following formulæ, not previously published, represent correctly the usual rules, and may be found useful :
Let' K represent the year of the Kaliyuga,
that of the Saka era, and w—the integers only in the expression to which it is attached, then296 211 K .} + 60,
18000S or $+(211 $ $0769)} = 60,
180000
And the Jyotistattva rule, by
1875 ) + 60, (c) or, put S = $-828, then the expression becomes
$+(228 +?). 1875) W
60. These formulæ give generally the same results, the differences arising from the positions they assign to the year which they expunge once in about 86 years.
Thus for K= 4864 or $ = 1685, we have by the first formula
( 4864 + 26 + 57 ) = 60 = 4947 = 82, and remainder - 27 for the expi:e years of the cycle; so that the Kaliyuga year 4 304 or $. 1685 corresponds to the 28th year or Jaya samvatsara. By the second rule (used in Bengal) we have
(4864 + 26 + 56) = 60 = 4946, or only 26 years of the cycle expired, and Vijaya current. And by the Jyotistattva rule
(1685 + 22) = 60 = 1707, or 28 cycles, and remainder 27-the same year as given by the first rule. But it is only at those points where expunged names occur that they differ, and then only by a single year, as between S. 1680 and 1693,after which the three rules give the same results for fully 70 years. This arises from the Jyotistattva rule placing the expunged samvatsara about 4 years earlier than the first rule and 12 or 13 earlier than the second does.
A well arranged set of chronological tables for Indian dates, with easy methods for finding the month and day corresponding to any Hindu date, and with a table of eclipses from the period of the earliest inscriptions, is a desideratum that many scholars feel, but Mr. Sewell's Tables do not help in any way to supply the want.
• Conf. M. Williams, Sanak. Dict., 9. vv. Pramathin
India, was in general use for dates much before that and Pramadin. Dr. Burnell remarks that he is not l period, though Var Ahamihira (A.D. 505) gives a rule, aware that any old hat exists" of the 60-year cycle (S.I. almost identical with that of the Jyotistattva cited bePalaog. p. 74); but he seems to have overlooked Varahalow, for determining the year of the cycle. See BrihatMihira's list, from which the one Davis gives (Asiat. Res.
samhita, viii, 20, 21, in Jour. R. 48. Soc. N. S. vol. V, p. vol. III, p. 220) was probably extracted.
48; Asiat. Res. vol. III, pp. 215, 219.-The earliest known Between A.D. 850 and 905 the names of the rathvat
instance of the use of the cycle in inscriptions is Sir saras, both according to the Southern system and that Walter Elliot's copper-plate grant of the Rehtrakata of the Astronomical Treatises as fontid by any of the king Govinda III. (p. 125 above), which is dated in Saka rules given below,-were in perfect accord, and it 726 (according to Brown's Tables, for 725), the Subhånu is not likely that the cycle as now used in the north of (or Svabhanu) sash vatsara.