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Brāhma Siddhānta; consequently the resulting figures and times are the same, and Tables XXXI. and XXXI.A are to be used for both these authorities. (See the notes preceding Table XXXVII.)

According to the Brāhma Siddhānta the solar year was one of 365.2584375 days, or 365 d. 6 h. 12 m. 9 s. The length of the Jupiter saṁvatsara was 361.020007456 days. The difference between the two was 4.238430044 days. In 60 saṁvatsaras this amounts to 254.305802640 days, and 365.2584375 − 254.305802640 = 110.952634860 days, which as explained above under the "general remarks," gives us the necessary element for the preparation of Table XXXI. for the beginning times of the first Prabhava of each cycle.

164. I have been unable to obtain any valuation according to Hindū authority for the śōdhya interval by this Siddhānta at K.Y. 0, on which depends the starting point for my calculations; but Dr. Schram fixes it as 2.171973, or 2 d. 4 h. 7 m. 38 s., and this I accept. But, arguing by analogy from calculated results for the same interval according to the Sūrya and Ārya Siddhāntas made by the Hindūs and by Dr. Schram, it is possible that the Hindūs made this śōdhya from one to two-and-a-half minutes longer than does Dr. Schram. Consequently it is possible that we may approximate to Hindū calculation if we deduct (say) 2 minutes from the final result obtained by use of Tables XXXI., XXXI.A.

165. We have first to find, according to the Brāhma Siddhānta, the time, measured from the moment of true Mēsha saṁkrānti,^[1] of the 27 Vijaya which began in K.Y. 0. In the case of the Sūrya and First Ārya Siddhāntas this was easy, because the Hindūs calculated that 27 Vijaya began at the moment of solar mean Mēsha saṁkrānti of that year, and therefore that it began by exactly the amount of the śodhya interval later than apparent Mēsha saṁkrānti. But according to the Brāhma Siddhānta the place of Jupiter at the moment of solar mean Mesha samkrānti in K.Y. 0 was not 0° but 359° 27′ 36″, in other words he was short of long. 0° by 32′ 24 ″. Since 27 Vijaya began at the moment when Jupiter reached 0°, the saṁvatsara actually current at the moment of solar mean Mēsha saṁkrānti at K.Y. 0 was 26 Nandana; and 27 Vijaya began later by the time occupied by Jupiter in travelling 32′ 24″ of arc. This, by Table XXXIV., = 6 d. 12 h., or 6.50 d.; but Dr. Schram has made a closer calculation based on the time (C, below) occupied by Jupiter in travelling 360°, and he finds that the proper figures are 6.49836 d., or 6 d. 11 h. 57 m. 38.3 s. At this distance of time, then, after the sun had reached mean long. 0°, or after the moment that marks the epoch of the Kaliyuga, Jupiter arrived there. Dr. Schram tells me that the true sun had reached long. 0° 2 d. 4 h. 7 m. ⁠38+1/2⁠ s., or 2.171973 d. earlier than the mean sun. Hence 27 Vijaya began, by the Brāhma Siddhānta (6.49836 d. + 2.17197 d. =) 8.67033 d., or 8 d. 16 h. 5 m. 17 s. after apparent solar Mēsha saṁkrānti at K.Y. 0.

166.

The following are the elements of the Brāhma Siddhānta, lettered in the same way as in the case of the other Siddhāntas, reduced for the Mahāyuga from the original figures which are stated for the Kalpa:—

1. ↑ It is probable that calculation by mean longitudes had been abandoned from the time that the Brāhma Siddhānta came largely into use.