Page:Sewell Indian chronography.pdf/70

cycle began 34 saṁvatsaras later, or at a time, after apparent Mēsha saṁkrānti of its own solar year, which is found, as before, from the formula ${\displaystyle G+\{E-(F\times 34)\}}$.

	Civil days.
${\displaystyle E}$	365.2587
${\displaystyle F\times 34}$	−144.0240
	221.2347
${\displaystyle G}$	+ 2.1476
	223.3823

In K.Y. 33 expired, therefore, 3069–8 B.C., 1 Prabhava began 223.3823 days after apparent Mēsha saṁkrānti. The number of complete cycles between K.Y. 33 and K.Y. 3117, both expired, which latter year corresponds to A.D. 16, is 52. Fifty-two times the value of ${\displaystyle I}$, or 5777.133079900 days, + 223.3823 days, is 6000.5154 days; and this, less a multiple of ${\displaystyle E}$, or ${\displaystyle E\times 16}$, which = 5844.138888880 days, gives the figure 156.3765 days as the time after apparent Mēsha saṁkrānti in K.Y. 3117 (A.D. 16) when 1 Prabhava of the cycle then commencing began according to the First Ārya Siddhānta. Table XXIX. is calculated accordingly. Table XXIX.A corresponds with Tables XXVII.A and XXVIII.A, but is for use in calculations by the First Ārya Siddhānta.

157. Another method of calculating the difference between the solar year and the Jovian saṁvatsara, or the value for element ${\displaystyle F}$ as stated in § 155, was shown me by Dr. Fleet. There were (${\displaystyle B}$) 364,224 revolutions of Jupiter in a Mahāyuga of 4,320,000 years. There were therefore in that period (364,224 × 12) 4,370,688 Jovian saṁvatsaras. 4,370,688 − 4,320,000 = 50,688. Therefore one solar year = ⁠1+50,688/4,320,000⁠ saṁvatsara. This, reduced, is ⁠1+22/1875⁠. As the saṁvatsara = 361.02268 days, one solar year is equal to one saṁvatsara plus 361.02268 × ⁠22/1875⁠ which = 4.235999458 days, and this is our figure for ${\displaystyle F}$. This explains part of the reasons for the full Ārya Siddhānta process as given in § 59, b, of the Indian Calendar.

158. As an example we will calculate by Tables XXIX. and XXIX.A the beginning and ending times of the saṁvatsara which, as we observe by Table XXIX., was expunged in K.Y. 3409 expired, A.D. 308–9, viz., No. 56 Dundubhi. It both began and ended in K.Y. 3409. We work for its beginning in that year. The cycle to which it belonged began in K.Y. 3354 (col. 1).

2.5326 days = (Table XXXVI.) 2 d. 12 h. 47 m.

79 = (Table IX.) March 19th, A.D. 308. On that day at 5 h. 27 m. after mean sunrise No. 56 Dundubhi (79 d. 5 h. 27 m. + 361 d. 0 h. 32 m. 40 s., or the length of the saṁvatsara, =) 440 d. 6 h. 0 m. 440 = (Table IX.) March 15th of the following year. Dundubhi therefore ended exactly at noon on March 15th, A.D. 309.

For the moment of Dundubhi's beginning compare § 34, p. 59 of the Indian Calendar where the date was worked out by the full process of the First Ārya. It will be seen that the result obtained by the present Tables differs from this by only 36 s.^[1]

[In case a discrepancy may be thought to exist between results by my present Tables and the