Page:Sewell Indian chronography.pdf/66

143. It is assumed that 27 Vijaya began at the instant of mean Mēsha saṁkrānti of K.Y. 1 current. It therefore began 2.170694̇ days after apparent Mēsha saṁkrānti of that solar year^[1]; and therefore at that last point of time the preceding saṁvatsara 26 Nandana was current. Vijaya ended (2.1707 + 361.0267) 363.1974 days after apparent M.S., or before the end of the solar year. 26 Nandana was current at apparent M.S., and at the next apparent M.S. 28 Jaya was current. Therefore, with reference to apparent M.S. 27 Vijaya was an expunged saṁvatsara.

144. Since 27 Vijaya began 2.1707 days after apparent M.S. in K.Y. 1 current, the beginning following cycle is found from that number of days, or ${\displaystyle G}$, ${\displaystyle +\{E-(F\times 34)\}}$.

	Civil days.
${\displaystyle E}$	365.2588
${\displaystyle F\times 34}$	−143.8892
	221.3696
${\displaystyle G}$	+002.1707
	223.5403

1 Prabhava, therefore, began by that number of days after apparent M.S. of K.Y. 33 expired, in 3069 B.C., and Table XXVII. begins from that point. The beginning of 1 Prabhava of the next cycle is found from this number of days + "${\displaystyle I}$", and so in succession, deducting when necessary the figures for (${\displaystyle E}$) the solar year-length. Thus:—

	Days.
For K.Y. 33	223.5403
"${\displaystyle I}$"	+111.3366
	334.8769

By this number of days, No. 1, Prabhava, of the next cycle began after apparent Mēsha saṁkrānti of K.Y. 92.

	Days.
	334.8769
${\displaystyle F\times 34}$	111.3366
	446.2135
"${\displaystyle E}$"	−365.2588
	80.9547

By this number of days after apparent Mēsha saṁkrānti, No. 1 Prabhava of the next cycle began in K.Y. 152, and so in succession.

145. As a matter of possible interest I have tabulated, supplementing Table I. of the Indian Calendar, the times of Mēsha saṁkrāntis (calculated according to the First Ārya Siddhānta, as the nearest reliable authority) for the period 58 B.C. to A.D. 299. This is my Table XXXVIII.A. It would be useless to tabulate it for any time earlier than that. Anyone who may wish to calculate a saṁvatsara for any earlier time is now provided with the means of doing so for himself. The number of complete cycles between K.Y. 33 and K.Y. 3117, both expired, which latter year corresponds to A.D. 16–17, is 52. Fifty-two times 111.336629361 days + 223.5403 days (the figure for Prabhava of K.Y. 33) is 6013.0450 days. Deduct a multiple (16) of the solar year-length, ${\displaystyle E}$, in days, i.e., 365.258756481 × 16, or 5844.1401. The remainder is 168.9049, and by this number of days 1 Prabhava began after apparent Mēsha saṁkrānti of K.Y. 3117 expired, or A.D. 16. This is the figure tabulated in Table XXVII. The rest in succession. {{{1}}}

1. ↑ I have stated above that Table XXVII. is prepared with reference to apparent Mēsha saṁkrānti simply for convenience of calculation by readers using the Indian Calendar. The Hindu astronomers took no note of apparent, but only of mean, Mēsha saṁkrānti; and were not concerned with the former prior to the time when the true or apparent Mēsha saṁkrānti began to be used in and for their own period. Let it be remembered also that this cycle was not really in use at the beginning of the Kaliyuga. (Note suggested by Dr Fleet.)