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48
INDIAN CHRONOGRAPHY.

applicable to all eras. Mr. Dikshit's two Tables were based on the Sūrya Siddhānta without the bīja, but his principles apply, mutatis mutandis, to the other authorities, and for some of these I have worked out the figures. Every step taken, with the reason for it, is fully explained below. The first of each pair of Tables gives, calculated by Jupiter's mean motion, the number of days and decimals of a day by which the first saṁvatsara, Prabhava, of a cycle began after apparent Mēsha saṁkrānti of the solar year concerned. The second enables us to find the beginning time of each subsequent saṁvatsara of the cycle. It is a system founded on actuals as laid down by the different Siddhāntas, each for itself,—of extreme simplicity and yet yielding a final result quite as accurate as those obtained from more complicated processes.[1]

136. These pairs of Tables are to be used in the following manner (I retain as far as possible Mr. Dikshit's own words). Take as an example Tables XXVII. and XXVII.A, calculated according to the Sūrya Siddhānta without the bīja. The others are used in the same way, each for the authority quoted.

137. Note in Table XXVII. the expired year of the Kaliyuga next to but earlier than the expired Kaliyuga year corresponding to the given year; for which purpose the given year, in whatever reckoning it may be stated, must be converted into a year of the Kaliyuga Working Rule. (Table I., or Table. II. Part III.) In the noted K.Y. year of Table XXVII. No. 1, Prabhava, of the cycle began after apparent Mēsha saṁkrānti by the number of days and decimals of a day given in col. 3. Subtract from the K.Y. figure corresponding to the given year the figure of the K.Y. year in which there began the Prabhava saṁvatsara which occurred last before the given year (for which the calculation is to be made), and add one to the remainder. With the resulting number as index turn to Table XXVII.A and find it in col. 1. If the number of days opposite to it in col. 3 is less than the number in Table XXVII., col. 3, against the year in which 1 Prabhava began, then the saṁvatsara in col. 2, Table XXVII.A, will begin in the given year. If not, then it began in the preceding year, and the next saṁvatsara will begin in the given year.[2] The saṁvatsara being thus determined take from Table XXVII.A, col. 3, the number of days opposite to it, and subtract them from the number of days given in Table XXVII. for the beginning of 1 Prabhava of the cycle; or, if the former be greater, subtract them from that number of days increased by 365.2588.[3] The remainder will be the number of by which, in the given year, the saṁvatsara will begin after the time of apparent Mēsha saṁkrānti. This, converted to time by Table XXXVI., and added to the time of the apparent Mēsha saṁkrānti found from Table I. (Ind. Cal.), cols. 13 and 17a, or by the rules given above, fixes the month, day, and time of day when the saṁvatsara began.[4] Its end is ascertained by adding the length of one saṁvatsara, in this case 361.0267 days, to the time of its beginning. In using Table IX. of the Indian Calendar to ascertain the day of the month, deduct a day from the total if the day on which the Jovian saṁvatsara began was later than February 29th in a Leap-year.

The same working rule applies to the other pairs of Tables, mutatis mutandis (See examples 48 to 59a.) The reasons for the process in each case are fully given below.

138. It will sometimes be found that a saṁvatsara current at mean Mēsha saṁkrānti was not current at apparent Mēsha saṁkrānti, and therefore that the name of a different saṁvatsara was given to the solar year concerned; but this does not affect the month, day, and time of day at which the saṁvatsara began and ended. That always remains the same.

  1. ↑ I differ from Mr. Dikshit by about ⁠3+1/2⁠ minutes of time in the final result throughout, my resulting time being in each case by so much earlier than his. I have given in the text a very complete explanation of my process, and enabled its accuracy to be tested by anyone. And as proof that my figures are correct I would refer my readers to Example 50 below. In that case the full Sūrya Siddhānta working yields a result 23 h. 46 m. 5 s. on a certain day. The result by my Tables is 23 h. 46 m. 41 s. on the same day. The result by Mr. Dikshit's Tables is 23 h. 50 m. 11 s.
  2. ↑ In each case of course the previous saṁvatsara was current at apparent Mēsha saṁkrānti of the given year.
  3. ↑ Really 365.2587564̇81̇, the length of the solar year.
  4. ↑ See also "Hint" No. 20, below.
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