The Five Astronomical Canons

of course, are intended to enable us to start in our calculation from the epoch of the Five Siddhântas original: "Pañchasiddhântikâ"; a 6th-century astronomical treatise by Varâhamihira (or of the, or some, Roman Astronomical Treatise original: "Romaka-Siddhânta"; 'Romaka' refers to the Roman or Byzantine world, likely Alexandria, about which see below), and their elucidation would probably lead to some interesting results. It will be observed that the rule for calculating the sum of days term: ahargaṇa (the number of elapsed days from a fixed epoch to a given date) professes to be adapted to the meridian of the City of the Greeks term: Yavanapura (likely Alexandria), while the rules for finding the places of the sun, moon etc. refer to the meridian of Ujjayinî.* The difference in longitude of those two places is stated by Varâhamihira—following the Paulîśa Astronomical Treatise original: "Paulîśa Siddhânta"; an early Indian astronomical work influenced by Greek methods as it appears—in III. 13.—A further reference to the Roman treatise which has remained obscure to us seems to be made in III. 73.—Whether any of the rules concerning the planets which are given in the last chapter base on the Roman Astronomical Treatise, is doubtful.

From this short summary of the contents of the Roman Astronomical Treatise I pass on to the consideration of its authorship and time of composition, coupling therewith—for reasons which will appear later on—an enquiry as to the date of the Five Siddhântas itself.

Hitherto it has been generally held, on the authority of Colebrooke and Bhâu Dâjî, that the original Roman Astronomical Treatise was composed by Srîsheṇa; an opinion which I myself, when writing my paper on the Five Siddhântas (Journal of the Asiatic Society of Bengal) was not prepared to abandon entirely, although then already certain considerations led me to suggest that Srîsheṇa's work might after all have been a mere recast of an older treatise of the same name. This latter view I now feel inclined to set forth as the only true one.

The authorities for Colebrooke's and Bhâu Dâjî's opinion were Brahmagupta and his commentator Pṛithûdaka Svâmin. Brahmagupta, in a considerable number of passages of his Corrected Astronomical Treatise original: "Sphuṭa Siddhânta"; the 7th-century magnum opus of Brahmagupta, refers to Srîsheṇa by name, and in connexion with those passages his commentator repeatedly remarks that Srîsheṇa was the author of the Roman Astronomical Treatise. And in one passage at least Brahmagupta himself mentions Srîsheṇa in connexion with the Roman Astronomical Treatise. That passage which is found in the "Examination of Astronomical Manuals" original: "Tantra-parîkshâdhyâya" (the 11th chapter of the Corrected Astronomical Treatise) was discussed by me in the paper referred to above (pp. 290 ff.), but owing to the very corrupt form in which the Manuscripts of the Corrected Astronomical Treatise exhibit its text I did not at that time fully understand it, so that the meaning of just its most

* The truth of this remark of course depends, in the first place, on the correctness of the emendation in VIII. 5 owing to which we have substituted "at sunset in Avanti" original: "ऽस्तगमे ऽ वन्त्याम्" (astagame 'vantyām) (read so in the text, instead of "at sunset in Avanti" original: "स्तगमवन्त्यां" (stagamavantyāṃ)) for the “at sunset in Avanti” of the Manuscript; and in the second place, on the assumption that the clause “at sunset, at Avanti” note: Avanti is the region surrounding the city of Ujjayinî has to be connected generally with the rules given in stanzas 1—5. But both this assumption and the emendation appear to me well founded.