same fixed star. The solar year, therefore, mentioned in the Vedic works, must be considered as sidereal and not tropical. The difference between the sidereal and the tropical year is 20.4 minutes which causes the seasons to fall back nearly one lunar month in about every two thousand years. When these changes came to be noticed for the first time they caused surprise and were regarded as foretelling some great calamity.
Another important point, relevent to our purpose is when the year commenced. The Vedanga-Jyotish makes the year (and Uttarayana) commence with the winter-solstice. But a closer examination shows that the winter-solstice could not have been the original beginning of the annual sacrifices (and therefore of the year). The middle day of the annual Satra is called the Vishnuvan day and as Vishnuvan literally means the time when day and night are of equal length, if we suppose the year to have commenced with the winter solstice, the Vishnuvan or the equinoctial day could never have been its central day. If Vishnuvan was the central day of the year, the year must have once commenced with the equinoxes. We may, therefore, take Uttarayana to mean "the passage of the sun into the northern hemisphere, i.e., to the north of the equator; and thus we can say that the Uttarayana and the year must have commenced with the Vernal equinox. While describing the Devayana and Pitriyana, the Shatapatha Brahmana (ii-i-3-3). lays it down in distinct terms that Vasanta, Grishma and Varsha were the seasons of the Devas. It is impossible therefore to maintain that the Devayana or the Uttarayana -ever commenced with the winter-solstice, for in
