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THE CYCLE OF JUPITER.—INTRODUCTORY.
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132. The general rule is that the name of the saṁvatsara current at Mēsha saṁkrānti of any year is attached to all the days of that year, notwithstanding that another saṁvatsara may have begun before its close. Suppose No. 8, Bhāva, to have been current at Mēsha saṁkrānti of a certain year, but to have ended a month later, when No. 9, Yuvan, began; still, all the days of that solar year will be considered to belong to the saṁvatsara named Bhāva. Occasionally, however, inscriptions may be found naming the saṁvatsara actually current on the given day, which for eleven months of such a year would be Yuvan; thus indicating the use of the astronomical instead of the conventional saṁvatsara. Epigraphists must be prepared for such a variation. A case in point will be found in Example 51 below.

133. They must also be prepared for other variations in practice. By the use of a different Siddhānta a different saṁvatsara will often be expunged. And in many tracts where lunar years were in regular calendrical use the saṁvatsara current at sunrise on the first civil day of the year, or Chaitra śukla 1, will be found to give its name to that year; in which case, since the ordinary lunar year is shorter (354 days) than the Jovian year (361 days), an expunction of a saṁvatsara can only occur in those lunar years in which there is an intercalated month. The Jyōtishatattva rule gives the saṁvatsara current at mean Mēsha sainkranti of any particular year.[1] I have not given a separate Table for it, because its results are the same in time as results found by use of the First Ārya Siddhānta. For similar reasons omit notice of the Bṛihat Saṁhitā and Ratnamālā rules (Ind. Cal., § 59, p. 35, and note 1, p. 36).

134. The question as to how far the calculated mean longitude of Jupiter according to the Hindū authorities was in accordance with the results of modern European science is one with which we have no concern.

135. In the Indian Calendar (Table I., col. 7) we have given the names of the saṁvatsaras current at apparent Mēsha saṁkrānti of each sidereal solar year from K.Y. 3401 to 4600 expired, calculated by the Sūrya Siddhānta without the bīja, and with the bīja from K.Y. 4601 to 5001;[2] but we have not given the exact times of the beginning and ending of each saṁvatsara—often a point of very considerable importance. In Article 59 we gave the full detailed rules for finding these beginnings, and therefore for finding the saṁvatsara current on any day of any year by (1) the Sūrya Siddhānta, both with and without the bīja, (2) the First Ārya Siddhānta, (3) the Jyōtishatattva rule, (4) the Bṛihat Saṁhitā rule; and in Article 60 we have given a comparative list of the saṁvatsaras expunged by these different systems. But these rules are rather troublesome and lengthy to work. Easier methods were propounded by Prof. Kielhorn (Ind. Ant. XVIII., pp. 193, 380) and Prof. Jacobi (Epig. Ind. I., pp. 424–28); but in my opinion the easiest is the process suggested by Mr. Shankar Balkrishna Dikshit, which, while adapted for the use of those who possess the Indian Calendar, is quite as reliable as any other. He had furnished Dr. Fleet with two short Tables, referred to the years of the Śaka era and worked to three places of decimals, but without any explanation of how he arrived at the figures recorded. Dr. Fleet kindly gave me a copy of these, with some valuable suggestions of his own; and after careful examination and prolonged study of the Tables, I succeeded in unravelling the whole working system. I then prepared my own Tables XXVII. to XXXI.A; calculating to nine places of decimals so as to ensure accuracy, but stating only four places for convenience. I refer my Tables to years of the Kaliyuga as being

  1. ↑ Dr. Fleet informs me that, so far as he is aware, no Hindū authority bases its calculations and rules for finding the current Jovian saṁvatsara on apparent Mēsha saṁkrānti, but all base them on mean Mēsha saṁkrānti, leaving it to anyone interested to adapt the result to the first of these times. I have prepared all my Tables (unless specially stated to the contrary) for apparent Mēsha saṁkrānti because, the time result being the same in each case, the calculator is in this way saved the trouble of changing the apparent Mēsha saṁkrānti times given in Table I. of the Indian Calendar into mean Mēsha saṁkrānti times.
  2. ↑ The Sūrya Siddhānta, before the bīja or correction was introduced into it, stated the number of revolutions of Jupiter in the mahāyuga of 4,320,000 solar years as 364,220. The author of the bīja, apparently about A.D. 1500, reduced the estimate of these revolutions of Jupiter to 364,212 in the same period; thereby slightly lengthening the duration of a saṁvatsara. (See table XXXVII., col. 6.)
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