the bridegroom presenting a burnt offering and the bride an offering of grain; for among the Romans also the young pair walked round the altar from left to right before offering bread (far) in the fire. Indo-European, too, must be the practice of scattering rice or grain (as a symbol of fertility) over the bride and bridegroom, as prescribed in the Sūtras; for it is widely diffused among peoples who cannot have borrowed it. Still older is the Indian ceremony of producing the sacrificial fire by the friction of two pieces of wood. Similarly the practice in the construction of the Indian fire-altar of walling up in the lowest layer of bricks the heads of five different victims, including that of a man, goes back to an ancient belief that a building can only be firmly erected when a man or an animal is buried with its foundations.
Finally, we have as a division of the Sūtras, concerned with religious practice, the Çulva Sūtras. The thirtieth and last praçna of the great Kalpa Sūtra of Āpastamba is a treatise of this class. These are practical manuals giving the measurements necessary for the construction of the vedi, of the altars, and so forth. They show quite an advanced knowledge of geometry, and constitute the oldest Indian mathematical works.
The whole body of Vedic works composed in the Sūtra style, is according to the Indian traditional view, divided into six classes called Vedāngas ("members of the Veda"). These are çikshā, or phonetics; chhandas, or metre; vyākaraṇa, or grammar; nirukta, or etymology; kalpa, or religious practice; and jyotisha, or astronomy. The first four were meant as aids to the correct reciting and understanding of the sacred texts; the last two deal with religious rites or duties, and their proper seasons. They all have their origin in the exigencies of religion,
