The Five Astronomical Canons

us to apply a certain correction, in order to make up for the inaccuracy involved in the employment of those round numbers. Now it is easy to see that, if Varâha Mihira's Sûrya SiddhântaThe "Sun Treatise," one of the most important early Sanskrit texts on astronomy. had exhibited the same figures as the modern Siddhânta, the amount of the corrections would differ from that actually stated by him, and we therefore are entitled to conclude that regarding the revolutions of the planets also the old Sûrya Siddhânta actually differed from the modern one; a conclusion moreover made more acceptable by the circumstance that several of the values assigned to the mean revolutions by Varâha Mihira's Siddhânta agree with the teaching of the Paulîśa SiddhântaAnother of the five early astronomical systems, often associated with Greek influence (Paulisa/Paulus). known to Bhaṭṭotpala, and with that of Âryabhaṭa A famous 5th-century Indian mathematician and astronomer..

That the difference, observed between the numbers of the natural days of the yugaAn immense cycle of time in Hindu cosmology. as stated by the two Sûrya Siddhântas, is due to a real discrepancy of the two books, is further confirmed by the rule given in Chapter X 2 and 4 for finding the mean place of the moon. This rule is based on the elements of the yuga as stated in chapter I, but for the sake of greater facility of calculation employs reduced numbers. Instead of multiplying the given ahargaṇaThe number of elapsed days from a fixed epoch to a given date. by 2406389 / 65746575 (the numerator of which fraction are the sidereal revolutions of the moon during the period of 180000 years, and the denominator the sâvana daysCivil days, measured from sunrise to sunrise. comprehended within the same time), it directs us to employ the expression 900000 / 24589506, and thereupon—in order to make up for the error involved in this substitution—to deduct from the mean place of the moon thus found 51'' / 3120 for each revolution. In other words, Varâha Mihira is unwilling to allow to pass an error in the mean position which amounts to no more than one sixtieth of a second of space for each revolution. But if he, on the other hand, had purposely, for mere convenience of calculation, lessened the length of the mahâyugaA "Great Age" consisting of 4,320,000 years. by twenty-eight days, he would thereby have reduced the length of each sidereal monthThe time it takes the moon to return to the same position relative to the stars. by about four hundreths of a second of time, which in its turn would have implied an error in the moon's mean place amounting to about one fiftieth of a second of space for each revolution. So that, while anxious to correct one small error, he would have allowed another greater one to pass; an assumption which we have absolutely no right or reason to make.

The investigation of special cases thus certainly favours the conclusion that the changes which the old Sûrya Siddhânta has undergone in Varâha Mihira's representation are purely formal, and that convenience of calculation is held by him to be a consideration of altogether secondary importance.

We therefore, and this is the most important conclusion to be drawn from the preceding enquiry, may hold ourselves entitled to look in the same light upon Varâha Mihira's rendering of the other Siddhântas which we can