The Five Astronomical Canons

be derived without difficulty from stanzas 3 and 4 of the same chapter. From stanza 3 it follows that one revolution is performed in 3231 days, 23 hours, 42 minutes, and 16.76 seconds; while the duration resulting from the elements of the modern Siddhânta A Siddhânta is a formal Indian astronomical treatise amounts to 3232 days, 2 hours, 14 minutes, and 53.4 seconds. And if, accommodating ourselves to the general Siddhânta practice, we determine the number of revolutions performed within one mahâyuga A "great age" in Hindu cosmology, consisting of 4,320,000 years, we obtain 488,219 for Varâha Mihira's Sûrya Siddhânta; while the modern Siddhânta gives 488,203 only. We note that according to Âryabhata A famous 5th-century Indian mathematician and astronomer also the apogee The point in an orbit farthest from the Earth performs 488,219 revolutions within one mahâyuga.

From stanza 5 of the same chapter we learn that the old Sûrya Siddhânta agreed likewise with Âryabhata in reckoning 232,226 revolutions of the moon's node The point where the moon's orbit crosses the ecliptic to one mahâyuga; while the modern Siddhânta counts 232,228.—In estimating the greatest latitude of the moon at 270 minutes (stanza 6) the old Sûrya Siddhânta agreed with the modern one.

According to stanza 7 the old Sûrya Siddhânta assigned to the sun's apogee the longitude of eighty degrees. Âryabhata gives 78° only, and a calculation of the place of the apogee for the epoch of the Pañchasiddhântikâ The "Five Astronomical Treatises" compiled by Varâha Mihira, based on the elements of the modern Sûrya Siddhânta, gives about 77°. The Pañchasiddhântikâ says nothing about the revolutions of the apogees of the sun and planets, and it hence is possible that the old Sûrya Siddhânta was not yet acquainted with the theory held, on entirely insufficient grounds, by the modern treatise, and modern Hindû astronomers in general, that the apogees of the sun and the planets perform a certain number of revolutions within a mahâyuga or kalpa An even longer cosmic cycle, a "day of Brahma," equal to 1,000 mahâyugas. On the other hand it might be supposed that Varâha Mihira, although acquainted with that doctrine, yet confined himself to stating the places which the apogees occupied at his time, since so much is sufficient for the purposes of a karaṇa-writer A writer of a practical astronomical handbook or manual used for daily calculations.—The rules for finding the true places of the sun and moon, which are given in stanzas 7 and 8, are analogous to those of the modern Sûrya Siddhânta, with the one important difference that, while the latter assumes epicycles Small circles whose centers move around the circumference of larger circles, used to explain planetary motion of different size for the even and odd quarters of the revolution of the two bodies, Varâha Mihira's Sûrya Siddhânta knows of one epicycle only for the sun as well as for the moon. The rules for finding the true motion, etc. given in stanzas 13 and 14 agree with those of the modern work.

The rules for calculating solar and lunar eclipses agree with the modern rules as far as general methods are concerned, but at the same time show many deviation in details; so for instance in the calculation of the parallax The apparent displacement of an object when viewed from different points in solar eclipses. Some of these rules we have, moreover, not been able to elucidate to our full satisfaction.