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 and his great predecessor La Rochefoucauld is that Vauvenargues, unlike La Rochefoucauld, thinks nobly of man, and is altogether inclined rather to the Stoic than to the Epicurean theory. He has indeed been called a modern Stoic, and, allowing for the vagueness of all such phrases, there is much to be said for the description.

VAUX, CALVERT (1824-1895), American architecture and landscape gardener, was born in London on the 24th of December 1824. He was educated at Merchant Taylors' School and in the office of Lewis N. Cottingham (1787-1847). In 1850 he went to America and became A. J. Downing's architectural partner. In 1856 and 1866 Vaux was associated with F. L. Olmsted in the plans for the improvement of various parks. He designed the Belvidere in Central Park, New York, and built a number of country houses in Newport, besides many town houses and public institutions.

VAUX OF HARROWDEN, THOMAS VAUX, (1510- 1556), English poet, eldest son of Nicholas Vaux, 1st Baron Vaux, was born in 1510. In 1527 he accompanied Cardinal Wolsey on his embassy to France; he attended Henry VIII. to Calais and Boulogne in 1532; in 1531 he took his seat in the House of Lords, and was made Knight of the Bath at the corona- tion of Anne Boleyn. He was captain of the Isle of Jersey until 1536. He married Elizabeth Cheney, and died in October 1556. Sketches of Vaux and his wife by Holbein are at Windsor, and a finished portrait of Lady Vaux is at Hampton Court. Two of his poems were included in the Songes and Sonetles of Surrey (Tottel's Miscellany, 1557). They are " The assault of Cupid upon the fort where the lover's hart lay wounded, and how he was taken," and the "Dittye . . . representinge the Image of Deathe," which the gravedigger in Shakespeare's Hamlet misquotes. Thirteen pieces in the Paradise of Dainty Devices (1576) are signed by him. These are reprinted in Dr A. B. Grosart's Miscellanies of the Fuller Worthies Library (vol. iv., 1872).

VAUXHALL, a district on the south bank of the river Thames, in London, England, included in the metropolitan borough of Lambeth. The manor was held by Falkes de Breauté (whence the name, Falkes Hall) in the time of John and Henry III. About 1661 public gardens were laid out here, known as the New Spring Garden, and later as Spring Gardens, but more familiar under the title of Vauxhall Gardens. They soon became the favourite fashionable resort of the metropolis; but as a place of general entertainment they underwent great development from 1732 under the management of Jonathan Tyers (d. 1767) and his sons Thomas and Jonathan. In 1822, with the approval of George IV., who frequented the gardens before his accession, the epithet Royal was added to their title. By the middle of the 19th century, however, Vauxhall had lost its high reputation; in 1859 the gardens were finally closed, and the site was quickly built over.

VAVASSOR (Med. Lat. valvassor, vasvassor; Fr. vavassour, vavassor, vasseur, &c.), in its most general sense a mediate vassal, i.e. one holding a fief under a vassal. The word was, however, applied at various times to the most diverse ranks in the feudal hierarchy, being used practically as the synonym of vassal. Thus tenants-in-chief of the crown are described by the Emperor Conrad (Lex Lamgob. lib. iii. tit. 8, § 4) as valvassores majores as distinguished from mediate tenants, valvassores minores. Gradually the term without qualification was found convenient for describing sub-vassals, tenants-in-chief being called capitanei or barones (see ); Its implication, however, still varied in different places and times. Bracton (lib. i. cap. 8, § 2) ranks the magnates seu valvassores between barons and knights; for him they are “ men of great dignity,” and in this order they arc found in a charter of Henry II. (1166). But in the regestum of Philip Augustus (fol. 158) we find that five vavassors are reckoned as the, equivalent of one knight. Finally, Du Cange quotes two charters, one of 1187, another of 1349, in which vavassors are clearly distinguished from nobles.

The derivation of the word vavassor is very obscure. The fanciful interpretation of Bracton, vas sortitum ad valetudinem (a vessel chosen to honour), may be at once rejected. Others would derive it from varsi ad valvas (at the folding-doors, valvae), i.e. servants of the royal antechamber. Du Cange, with more justice, regards it merely as an obscure variant of vassus.

 VAYGACH (variously Waigats, Waigatch, &c.), an island off the Arctic coast of Russia, between it and Novaya Zemlya, bounded S. by the narrow Yugor Strait, and N. by that of Kara. It is roughly oblong in form; its length from S.E. to N.W. is 70 m., and its greatest breadth 28. Its greatest elevation scarcely exceeds 300 ft. For the most part it consists of tundra, with frequent marshes and small lakes. Slight rock ridges run generally along its length, and the coast has low cliffs in places. The island consists in the main of limestone, and its elevation above the sea is geologically recent. Raised beaches are frequently to be traced. The rocks are heavily scored by ice, but this was probably marine ice, not that of glaciers. Grasses, mosses and Arctic flowering plants are abundant, but there are no trees excepting occasional dwarf willows. Foxes and lemmings are met with, but whereas animals are few, birds are very numerous; a variety of ducks, waders, &c., frequent the marshes and lakes. The island is visited periodically by a few Samoyeds; they formerly considered it sacred, and some of their sacrificial piles, consisting of drift-wood, deer’s horns and the skulls of bears and deer, have been observed by travellers. In spite of their conversion to Christianity, the Samoyeds still regard these piles with superstition. The origin of the the name Vaygach is as dubious as its orthography; it has been held to be Dutch (waaien, to blow, and gat, a strait, hence ”windy strait”) or Russian, in which case it is probably a surname.

VECTOR ANALYSIS, in mathematics, the calculus of vectors. The position of a point B relative to another point A is specified by means of the straight line drawn from A to B. “It may equally well be specified by any equal and parallel line drawn in the same sense from (say) C to D, since the position of D relative to C is the same as that of B relative to A: A straight line conceived in thisway as having a definite length, direction and sense, but no definite location in space, is called a vector. It may be denoted by AB (or CD), or (when no confusion is likely to arise) simply by'AB. Thus a vector may be used to specify a displacement of translation (without rotation) of a rigid body. Again, a force acting on a particle, the velocity or momentum of a particle, the state of electric or magnetic polarization at a particular point of a medium, are examples of physical entities which are naturally represented by vectors. The quantities, on the other hand, with which we are familiar in ordinary arithrnetical algebra, and which have merely magnitude and sign, without any intrinsic reference to direction, are distinguished as scalars, since they are completely specified by their position on the proper scale of measurement. The mass of a body, the pressure of a gas, the charge of an electrified conductor, are instances of scalar magnitudes. It is convenient to emphasize. this distinction by a difference of notation; thus scalar quantities may be denoted by italic type, vectors (when they are represented by single symbols) by “ black ” or “ Clarendon ” type.,

There are certain combinations of vectors with one another,