VECTOR. 31 VEDA. with 2, and 5 with 4, and then joining the two free ends, as in Fig. B. It is evident from geometry that the order of the addition is im- material so long as the arrows indicate con- tinuous action. Thus it would do just as well to make 1 and 4 and 2 and 5 coincide, or 1 and 4 and U and 3; the final result is the same as before. See Mechanics, and especially the arll(de Quaternions, where will be found a full mathematical explanation of vectors. VEDA, va'da (Skt. vcda, knowledge, from vid, to know; connected with Gk. /roISa, foida, I know, flSeiv, fidcin, Lat. videre, OChurch Slav. vcde, I know, UIIG. wizzan, Ger. icissen, Goth., AS. loitan, Eng. loit, to know) . The collective designation of the ancient sacred literature of India, or of individual books belonging to that literature. At an unknown date, which may be conventionally averaged up as B.C. 1500. Aryan tribes began to migrate from the Iranian higli- lands on the north of the Hindu Kush into the northwest of Indi.a, the plains of the river Indus and its tributaries. The non-Aryan aborigines were easily conquered, but the conquest was fol- lowed by gradual amalgamation of the fairer- hued conquerors with the dark aborigines. The Aryans brought with them a primitive pastoral civilization, a language which was a mere dia- lectic variety of the speech spoken in Iran, and religious beliefs which show clo.se connection with the ancient Persian religion of the Avesta, and, to a lesser and more prolilematic extent, with the beliefs of the remaining Indo-Germanic peo- ples, such as the Greeks (see Greek Religion) and the Teutons. (See Scandinavian and Teu- tonic Mythology.) From the very start we. are confronted by a poetical literature, primitive on the whole, yet lacking neither in refinement and beauty of thought, nor in skill in the handling of language and metre. The literature is throughout religious, and includes prayers and sacrificial formulas, offered to the gods by the priests ; charms for witchcraft and medicine, manipulated by magicians and medicine-men ; expositions of the sacrifice ; theological com- ments and legends: higher speculations, philo- sophic and theo.sophic. growing up in connection with the simpler belieits; and finally rules for conduct in every-day life at home and abroad. This is the Veda as a whole. At the base of this entire literature of more than 100 books lie four varieties of metrical com- positions known as the four Vedas in the nar- rower sense. These are the Rifi-Veda. the Yajur- Veda, the Sama-Veda, and the Atharva-Veda. These four names come from a somewhat later time, and do not coincide exactly with the earlier names, nor do they correspond with the contents of the texts themselves. The earlier names are rcah, 'stanzas of praise,' pajiinsi, 'liturgical stanzas and formulas,' mmani, 'melodies,' and athari-a I'l ()irasah. 'blessings and curses.' The Col- lection which goes by the name of the Rig-Veda contains not only 'stanzas of praise,' but also 'blessings and curses,' as well as most of the stanzas which form the basis of the saman- melodies. The Atharva-Veda contains rcah and yajiihsi. as well as blessings and curses. The Yajur-Veda also contains many blessings and curses, in addition to its main topic. The Sama- Veda is merely a collection of a certain kind of 'stanzas of praise' which occur for llie most part in the Rig-Veda, but are here set to music by means of definite musical notations. The Rig-Veda is on the whole the most im- portant as well as the oldest of the four collec- tions. A little more than 1000 hymns, equaling in bulk the surviving poems of Homer, are ar- ranged in ten books called munildia, or circles. Six of them (ii.-vii.), the so-called family books, form the nucleus of the collection. Each of these is the work of a diflTerent seer and his descend- ants, as can be seen from the liymns themselves. The eighth book and the first fifty hymns of the first book, belonging to the family of Kanva. are arranged strophically in groups of two or three stanzas. The most marked peculiarity of these hymns is that they form the bulk of the stanzas sung with melodies in the Sama-Veda. The hymns of the ninth book are addressed directly to Soma (q.v.). The remainder of the first book ami the entire tenth book are more miscellaneous in character and problematic as to arrangement. On the whole they are of later origin, for themes foreign to the narrower purpose of the rcah. such as theosophic hymns and witchcraft hymns, ap- pear in considerable number. The poems of the latter class frequently reappear, usually with variations, in the Atharva-Veda. On the whole the Rig-Veda is a collection of priestly hymns addressed to the gods of the V^dic pantheon during sacrifice. This sacrifice con- sisted of oblations of intoxicating sOtna pressed from the soma-plant and melted butter or ghee (q.v.) which was poured into the fire. The ritual of the Veda is advanced in character, by no means so simple as was once supposed, though not as elaborate as that of the Yajur-Veda and the Brahmanas. (See below.) The chief interest of the Rig- Veda lies in the gods themselves and in the myths narrated in the course of their invocation. The mythology represents an earlier, clearer stage of thought than is to be found in any other parallel literature. Above all it is sufficiently primitive to show clearly the process of personification by which natural phenomena developed into gods. (See the sub-section Vedic Heligion under India; Nature- Worship.) The original nature of the Vedic gods, however, ig not always clear; some of them are so obscure in character as to make an analysis of them a difficult and important chapter in Vedic philology. But on the whole the key-note of Rig-Ved'ic thought is the nature myth. The Yajur-Veda represents the growth of ritualism or sacerdotalism; its yajuhsi, 'litur- gical stanzas and formulas,' are in the main of a later time, and are partly metrical, partly prose. The materials contained in the Rig- Veda are freely adapted, with secondary changes of expression, and without regard to the original order of their composition. The main object is no longer devotion to the gods themselves. The sacrifice has become the centre of thought; its mystic power is conceived to be a thing per se, and every detail has become all -important. A crowd of priests (seventeen is the largest num- ber) conducts a vast, complicated, and painstak- ing ceremonial, full of symbolic meaning even in its smallest minutiip. From the moment the priests seat themselves on the sacrificial ground and proceed to mark out the altars {vCdi) on
