XIV

INTRODUCTION.

that number, as well as the number of the years of the yugaA vast astronomical cycle or "age" in Hindu cosmology, used as a common denominator for planetary cycles., by twenty-four and thus to arrive at figures more easy to manipulate; all the more as the inaccuracy involved in that change would affect to an almost insensible degree only the comparatively short periods to which the rules of the karaṇa granthaA practical astronomical manual or handbook used for quick calculations, as opposed to a theoretical treatise. are meant to be applied. But in spite of this undeniable possibility I am inclined to think that in the present case also Varâha Mihira proceeded with strict accuracy, and that his Sûrya Siddhânta actually assigned to the great yuga twenty-eight days less than the modern treatise does. For in addition to the general consideration that there are several other items in which the old and the new Siddhântas differed beyond any doubt, we have in the present case two special reasons viz. firstly that it would have sufficed to diminish 1577917828 by four (instead of twenty-eight) in order to make it divisible by twenty-four; and secondly that the estimation of the length of the solar year implied in the statement of the old Sûrya Siddhânta agrees exactly with that value of the length of the solar year that results from the elements of that Paulîśa Siddhânta about which Bhaṭṭotpala's commentary on the Bṛihat SaṃhitâThe "Great Compilation," an encyclopedic work by Varâha Mihira covering astrology, planetary movements, and various sciences. and Pṛithûdaka Svâmin's commentary on Brahmagupta's sphuṭa Brâhma SiddhântaThe "Corrected Treatise of Brahma," a foundational work of Indian mathematics and astronomy written in 628 CE. furnish some information. As we shall see at once, Varâha Mihira's Sûrya Siddhânta agreed with that Paulîśa Siddhânta in several other points also, and it therefore is not improbable that the two Siddhântas were at one also concerning the length of the solar year. If this is so, the most important item by which hitherto the Sûrya Siddhânta was considered to be distinguished from the Paulîśa Siddhânta (as reported by Bhaṭṭotpala etc.) would vanish; which clearly shows that an accurate investigation of the degree of strictness with which Varâha Mihira reproduces the doctrines of his Siddhântas cannot be dispensed with.

Similar to the case just discussed is that of the mean revolutions of the planets, as reported, according to the Sûrya Siddhânta, in the 16th chapter of the PañchasiddhântikâThe "Five Astronomical Treatises," the major work by Varâha Mihira which summarizes five earlier astronomical systems.. As appears from the notes to the translation and the latter part of this Introduction, the periods assigned to the mean revolution by the old Sûrya Siddhânta differed more or less from the corresponding values stated in the modern treatise. There, however, the hypothesis of Varâha Mihira having for some reason or other modified the elements of the work with which he had to deal seems altogether excluded. If he had chosen to state the length of the revolutions of the planets in the ordinary form i. e. by establishing periods within which the planets perform integral numbers of complete revolutions, he might possibly have had reason to manipulate the traditional numbers to a certain extent, so as to reduce them to more manageable terms. But in the case under discussion he follows another plan viz. of at first stating the time of one revolution in round numbers, and then directing