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practice being prevalent at different parts of India or at different times, so that a different lunar month might have been intercalated or suppressed by other Hindū almanac-makers. The principle applies equally, of course, in the case of suppressions of months; if at the first saṁkrānti ${\displaystyle t}$ is found after the most careful calculation, to be scientifically 0, then the new moon has begun, and if at the next saṁkrānti that moon is found to be waning the lunar month included is suppressed; if still waxing it is common.

I imagine that the same principle would apply to the case of tithis, nakshatras, yōgas and karaṇas.

19. Expunction of Jovian saṁvatsaras in solar years. There can be no expunction of a Expunction of Jovian
saṁvatsaras. Limitations. saṁvatsara in a cycle the Prabhava at the beginning of which (Tables XXVII., XXVIII. &c., col. 3) took place later than in the case of the—

after apparent Mēsha saṁkrānti; for the greatest day-figure in Table XXVII.A, XXVIII.A &c., col. 3, is that which in each case appertains to the last saṁvatsara, 60 Kshaya, of the cycle; and the difference between this day-figure and the day-figure of the No. 1 Prabhava of the next cycle is the exact amount of the difference between the length of the solar year and the Jovian saṁvatsara by the different authorities. If any cycle for instance began according to the Sūrya Siddhānta without the bīja, by the smallest fraction later than 253.922127120 after apparent Mēsha saṁkrānti of its solar year, then it is evident that the next saṁvatsara must begin after the next apparent Mēsha saṁkrānti, and therefore that the preceding cycle had completed itself without any expunction having taken place in it. 253.922127120 minus (Table XXVII.A, col. 3, for 60 Kshaya) 249.690091668 = 4.232035452^[1] = the difference between the length of the solar year and the Jovian samvatsara by the authority used. And so with the rest.

20. It is sometimes important when making calculations in which the exact moment of a true Mēsha saṁkrānti is an essential element, to know the number of seconds as well as the number of minutes of the time of its occurrence; minutes alone being given in col. 17 of Table I., along with the day and hour. Of the importance of this knowledge Examples 5 (b) and 6 (c) will serve as proof. For the Ārya Siddhānta we can always ascertain the exact time by applying the following rule: When the number of the current K.Y. year, or the year A.D., is even, the minutes entered in col. 17 of Table I. are whole minutes. When the number of the current K.Y. year, or the year A.D., is odd, 30 seconds added to the time entered in col. 17 gives the exact time. If working with ghaṭikās, &c., the amount to be so added in col. 15 is ⁠1+1/4⁠ palas. The exact time according to other Siddhāntas can be obtained from this basis, by the rules given in this volume.

The reason for this rule is to be found in the fact that, as shown in § 162 above, mean Mēsha saṁkrānti of the year A.D. 499, K.Y. 3601 current, took place according to the Ārya Siddhānta exactly at noon, or at 6 h. 0 m. Laṅkā time on March 21st. The śōdhya by that authority being 2 d. 3 h. 32 m. 30 s., we know that the moment of true Mēsha saṁkrānti of that year was March 19th at 2 h. 27 m. 30 s. The Indian Calendar, in col. 17 of Table I., tabulates only the whole minutes and states the time as 2 h. 27 m. If 30 seconds be added to this tabulated time we have the exact time. The length of the year by the Ārya Siddhānta being greater by 12 m. 30 s. than that of the Julian year (Table XXXVII.,

1. ↑ The "F" of § 142 &c.