INTRODUCTION.

I now proceed shortly to discuss the teaching of each of the five Siddhântas Siddhânta: A Sanskrit term for a formal astronomical treatise or settled doctrine. as represented by Varâha Mihira A 6th-century Indian astronomer and polymath.. This, however, requires the preliminary settlement of two questions.

In the first place we must attempt to ascertain with accuracy which chapters of the Pañchasiddhântikâ The "Five Astronomical Treatises," the main work being discussed. are devoted to each of the five works in question.—This is a task beset by considerable difficulties, as we have no commentary to assist us, and as the indications to be met with in the text as well as in the colophons A finishing stroke or inscription at the end of a chapter providing title and authorship details. of the chapters, as exhibited by the two Manuscripts at our disposal, do not, in all cases, enable us to arrive at definite conclusions.

I begin with those chapters, fortunately constituting the majority, which allow themselves to be referred to their respective sources with confidence.—The very short twelfth chapter is, in its colophon, called Paitâmaha Siddhânta, and is in its first stanza declared by Varâha Mihira himself to base on the teaching of Pitâmaha; it is the only chapter in the whole work which is concerned with that Siddhânta.—The eighth chapter treats, according to its colophon, of the calculation of solar eclipses according to the Romaka Siddhânta The "Roman" or "Greek" system, showing Western influence on Indian astronomy.; and that this really is so, we again have no reason to doubt, as the first stanza refers to the Romaka by name, and as, moreover, the contents of the chapter agree with the statements made in the first chapter about the yuga An age or long cycle of time. and the ahargaṇa The count of days elapsed from a fixed epoch. of the Romaka Siddhânta.—The ninth, tenth and eleventh chapters undoubtedly summarize the doctrines of the Sûrya Siddhânta The "Sun Doctrine," one of the most influential Indian astronomical texts., as is stated in the colophon, indicated in the first stanza of chapter IX, and borne out by the general agreement of the contents of the three chapters with the Sûrya Siddhânta as known at present. The sixteenth chapter contains, according to the colophon and to stanza 1, the rules of the Sûrya Siddhânta for finding the mean places of the planets; and the seventeenth chapter which teaches how to calculate their true places we may without hesitation refer to the same Siddhânta.

Among the remaining chapters of the work I at first single out those in which Varâha Mihira apparently does not intend to reproduce specific features of one particular Siddhânta, but rather to summarize doctrines held by all the more advanced astronomers of his time, and most probably set forth, with greater or less variations, in three of his five Siddhântas, viz., the Sûrya, Pauliśa and Romaka Siddhântas. To this class of chapters, in which we discern more of the individual Varâha Mihira than in the remainder of the work, I feel inclined to reckon three or perhaps four sections. In the first place the thirteenth chapter, designated in the colophon as ‘trailokya-saṃsthâna’ The "Constitution of the Universe.", which gives a popular exposition of the sphericity of the earth and the different aspects of the celestial sphere which are due to difference of