The Five Astronomical Canons

which, in its colophon A concluding statement in a manuscript providing facts about its production at least, is said to represent the teaching of the Paulisa Siddhânta The "Treatise of Paulus," an early Indian astronomical work influenced by Greek methods. The relation, however, of the third chapter to the one immediately preceding is puzzling. The second chapter is, in the colophon, merely designated as “section on the lunar mansions and related matters” original: "nakshatrâdichchheda", but its contents comprise firstly a rule or set of rules for finding the mean (and perhaps also true?) places of the moon (stanzas 1—7), and, secondly, a set of rude, approximative rules for calculating the length of the day at any time of the year, the length of the shadow of the gnomon term: gnomon (the vertical rod of a sundial used to measure the sun's altitude by its shadow), and, from the latter, the mean place of the sun, and the rising sign original: "lagna"; the point of the ecliptic that is rising on the eastern horizon (and vice versâ; stanzas 8—13). The chapter concludes with the words “This is the (calculation of the) shadow according to the concise Vâsishṭha Siddhânta.” The question now is, whether this whole chapter has to be viewed as epitomizing the Vâsishṭha Siddhânta, or whether that work is represented only by its latter part. The rules contained in stanzas 8—13 are of a very rough character, and can, for that reason, hardly come from the Paulisa Siddhânta; their character, on the other hand, agrees very well with the criticism passed by Varâha Mihira, in the first chapter, on the imperfections of the Vâsishṭha Siddhânta. It is more difficult to arrive at a conclusion regarding the rules embodied in stanzas 1—7. If they do not belong to the Vâsishṭha Siddhânta, it would follow that the Five Astronomical Treatises original: "Pañchasiddhântikâ", which after all promises to render us acquainted with the doctrines of all the five Siddhântas, however imperfect some of them may be, does not even inform us how the place of the moon is calculated according to the Vâsishṭha Siddhânta, while it yet gives the corresponding rules from the, certainly not more advanced, Paitâmaha Siddhânta, very concisely indeed but yet with sufficient fulness. On the other hand there appears to be some reason for tracing the rules to the Paulisa Siddhânta. The third chapter, which, as we have seen above, we may connect with the Paulisa Siddhânta with a very high degree of probability, gives in stanzas 1—3 the required rules for finding the mean and true places of the sun, and then continues, in stanzas 4—9, to give certain rules about the moon. Now these rules have unfortunately remained obscure to us; but yet so much appears certain that they are somehow connected with the rules concerning the moon given in the former half of chapter II, constituting, as it seems, a kind of continuation, or more accurate version of the latter. But again, on this latter hypothesis no reason is apparent why the two sets of rules should be separated from each other by the altogether heterogeneous matter treated of in the latter half of chapter II. I therefore see myself obliged to leave this point undecided, and only wish to suggest, as a third not impossible alternative, that the method for calculating the places of the moon which is set forth in chapter II belonged, in its essential features at least, to the Paulisa as well as to the Vâsishṭha Siddhânta,