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xvi , their relative priority or posteriority as compared with other Vedic schools and works, to show with some amount of probability in which part of India they had their origin, and to venture, at least, a not altogether unsupported conjecture as to their probable antiquity.

As regards the first point, the Karanavyûha, a supplement of the White Yagur-veda which gives the lists of the Vedic schools, informs us that the Âpastambîya school formed one of the five branches of the Khândikîya. school, which in its turn was a subdivision of the Taittirîyas, one of the ancient sections of Brâhmanas who study the Black Yagur-veda. Owing to the very unsatisfactory condition of the text of the Karanavyûha it is unfortunately not possible to ascertain what place that work really assigns to the Âpastambîyas among the five branches of the Khândikîyas. Some MSS. name them first, and others last. They give either the following list, i. Kâleyas (Kâletas), 2. Sâtyâyanins, 3. Hiranyakesins, 4. Bhâradvâgins, and 5. Âpastambins, or, 1. Âpastambins, 2. Baudhâyanins or Bodhâyanins, 3. Satyâshâdhins, 4. Hiranyakesins, 5. Aukheyas. But this defect is remedied to a certain extent by the now generally current, and probably ancient tradition that the Âpastambîyas are younger than the school of Baudhâyana, and older than that of Satyâshâdha Hiranyakesin. Baudhâyana, it is alleged, composed the first set of Sûtras connected with the Black Yagur-veda, which bore the special title 'pravakana,' and he was succeeded by Bhâradvâga, Âpastamba, and Satyâshâdha Hiranyakesin, who all founded schools which bear their names.