Page:Sewell Indian chronography.pdf/83

of the year Śaka 1 current. That year corresponds to K.Y. 3180 current. The interval between it and K.Y. 1 current is 3179 years. By my new Table XXXIII. we have—

And these results are exactly the same as those at the head of Table W, being there given as constants from which to work when using the Śaka era. Additional figures are given in Table XXXIII. for an interval of 4000 years and 5000 years.

180. Table Y in the Indian Calendar gives the mean motion of Jupiter and the sun, the latter being required for finding his true motion. This Table is now repeated as Table XXXIV. It stands for all the Siddhāntas because the difference between them, being about ⁠1/100⁠th of a second per day, only amounts to about 2.4″ in the Julian year. (See Table XXXVII., col. 10.) But when we come to greater periods the difference in the length of the year by the different Hindū authorities must be taken into account, since the divergence between them begins from the epoch of the Kaliyuga and our calculations cover a period of 5000 years. Hence the divergence observable under the different headings of Table XXXIII.

180a. At the foot of Table Y of the Indian Calendar we gave directions for the computation of Jupiter's mean motion for portions of a day calculating by ghaṭikās and palas; but as many workers may prefer to proceed by hours, minutes and seconds, I have added a supplemental Table enabling this to be done.

181. The figures in the Tables are derived from calculations made as follows:— According to the Present Sūrya Siddhānta, both with and without the bīja, the Original Sūrya Siddhānta and the First Ārya Siddhānta (of Āryabhaṭa) the planet Jupiter was, at the epoch of the Kaliyuga era in exact coincidence with the mean sun, both being then precisely on the first point of sidereal Mēsha, or the point in the heavens whence all longitudes are measured; in other words Jupiter's longitude, like the sun's, was then 0°. This moment, according to both the Ārya Siddhāntas, the Brāhma Siddhānta and the Siddhānta Śirōmaṇi, was mean sunrise, or 6 a.m., on February 18th, 3102 B.C.; but according to both the Sūrya Siddhāntas was at midnight between February 17th and 18th, or six hours earlier. Jupiter's mean daily and annual motion are obtained, according to the different authorities, each from its assertion as to the number of civil days in a mahāyuga (A) and the number of revolutions of Jupiter in that period (B), as already explained. (A ÷ B) ÷ 12 gives the length of one Jovian saṁvatsara; and one sign, 30°, divided by this length gives the mean daily motion. This mean daily motion multiplied by the solar year-length gives the mean annual motion. This last forms the basis of Table XXXIII., decimals of a second being omitted for convenience.

Having been at 0°, according to the Sūrya Siddhānta, at the moment of mean Mēsha saṁkrānti at K.Y. 0, Jupiter's mean longitude one whole day later was 4′ 59″, two days later 9′ 58″, one year later 1 s. 0° 21′ 6″, two years later 2 s. 0° 42′ 12″. And so for all. But in the case of the Brāhma Siddhānta and Siddhānta Śirōmaṇi the constant given in the heading, viz., 32′ 24″, must be deducted from the

1. ↑ "14" in Table W is a misprint.
2. ↑ "4" in Table W is also, I regret to say, a misprint.