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 the Burgundians at Verneuil and elsewhere, and then occupying a high position at the court of Philip the Good, duke of Burgundy, was sent as ambassador to Rome in 1463. Jehan wrote, or rather compiled, the Recueil des croniques et anchiennes istories de la Grant Bretaigne, a collection of the sources of English history from the earliest times to 1471. For this work he borrowed from Froissart, Monstrelet and others; but for the period between 1444 and 1471 the Recueil is original and valuable, although somewhat untrustworthy with regard to affairs in England itself.

WAUSAU, a city and the county-seat of Marathon county, Wisconsin, U.S.A., on both banks of the Wisconsin river, about 185 m. N .W. of Milwaukee. Pop. (1890) 9253; (1900) 12,354, of whom 3747 were foreign-born; (1910 census) 16,560. There is a large German element in the population, and two German semi-weekly newspapers are published here. Wausau is served by the Chicago, Milwaukee & St Paul and the Chicago & North-Western railways. The city is built for the most part on a level plateau above the river and extends to the top of high bluffs on either side. It has a fine city hall, a Carnegie library, the Marathon County Court House, a hospital, built by the Sisters of the Divine Saviour, and a Federal Building. In Wausau are a U.S. land office, the Marathon County Training School for Teachers, the Marathon County School of Agriculture and Domestic Science, and a County Asylum for the Chronic Insane. Valuable water-power furnished by the Big Bull Falls of the Wisconsin (in the city) is utilized for manufacturing, and in 1910 water-power sites were being developed on the Wisconsin river immediately above and below the city. In 1905 the factory products were valued at $4,644,457. Wausau had its origin in a logging-camp, established about 1838. In 1840 a saw-mill was built here, and in 1858 the village was incorporated under its present name. After 1880, when Wausau was chartered as a city, its growth was rapid.

WAUTERS, EMILE (1848), Belgian painter, was born in Brussels, 1848. Successively the pupil of Portaels and Gerome, he produced in 1868 “The Battle of Hastings: the Finding of the body of Harold by Edith,” a work of striking, precocious talent. A journey was made to Italy, but that the study of the old masters in no wise affected his individuality was proved by “The Great Nave of St Mark’s” (purchased by the king of the Belgians). As his youth disqualified him for the medal of the Brussels Salon, which otherwise would have been his, he was sent, by way of compensation, by the minister of fine arts, as artist-delegate to Suez for the opening of the canal—a visit that was fruitful later on. In 1870, when he was yet only twenty-two years of age, Wauters exhibited his great historical picture of “Mary of Burgundy entreating the Sheriffs of Ghent to pardon the Councillors Hugonet and Humbercourt” (Liége Museum) which created a veritable furore, an impression which was confirmed the following year at the London International Exhibition. It was eclipsed by the celebrated “Madness of Hugo van der Goes” (1872, Brussels Museum), a picture which led to the commission for the two large works decorating the Lions’ staircase of the Hôtel de Ville—“Mary of Burgundy swearing to respect the Communal Rights of Brussels, 1477” and “The Armed Citizens of Brussels demanding the Charta from Duke John IV. of Brabant.” His other large compositions comprise “Sobieski and his Staff before Besieged Vienna” (Brussels Museum) and the harvest of a journey to Spain and Tangiers, “The Great Mosque,” and “Serpent Charmers of Sokko,” and a souvenir of his Egyptian travel, “Cairo, from the Bridge of Kasrel-Nil” (Antwerp Museum). His vast panorama—probably the noblest and most artistic work of this class ever produced—“Cairo and the Banks of the Nile” (1881), 380 ft. by 49 ft., executed in six months, was exhibited with extraordinary success in Brussels, Munich, and the Hague. Wauters is equally eminent as a portraitist, in his earliest period exhibiting, as in his pictures, sober qualities and subtle grip, but later on developing into the whole range of a brilliant, forceful palette, and then into brighter and more delicate colours, encouraged thereto, in his more recent work, by his adoption of pastel as a medium even for life-size portraits, mainly of ladies. His portraits, numbering over two hundred, include many of the greatest names in Belgium, France, and America (Wauters having for some years made Paris his chief home). Among these may be named the Baron Goffinet, the Baroness Goffinet, Madame Somzée (standing at a piano). Master Somzée (on horseback by the sea-shore), the Princess Clementine of Belgium (Brussels Museum), Lady Edward Sassoon, Baron de Bleichroder, Princess de Ligne, Miss Lorillard, a likeness of the artist in the Dresden Museum, and M. Schollaert (president of the Chamber of Deputies)—the last named an amazing example of portraiture, instinct with character and vitality. The vigour of his male, and the grace and elegance of his female, portraits are unsurpassable, the resemblance perfect and the technical execution such as to place the artist in the front rank. Between 1889 and 1900 the painter contributed to the Royal Academy of London. Few artists have received such a succession of noteworthy distinctions and recognitions. His “Hugo van der Goes,” the work of a youth of twenty-four, secured the grand medal of the Salon. He has been awarded no fewer than six “medals of honour”—at Paris in 1878 and 1889; Munich, 1879; Antwerp, 1885; Vienna, 1888; and Berlin, 1883. He is a member of the academy of Belgium, and honorary member of the Vienna, Berlin, and Munich academies, and corresponding member of the Institut de France and of that of Madrid. He has received the order of merit of Prussia, and is Commander of the order of Leopold, and of that of St Michael of Bavaria, officer of the Legion of Honour, &c.

WAVE. It is not altogether easy to frame a definition which shall be precise and at the same time cover the various physical phenomena to which the term “wave” is commonly applied. Speaking generally, we may say that it denotes a process in which a particular state is continually handed on without change, or with only gradual change, from one part of a medium to another. The most familiar instance is that of the waves which are observed to travel over the surface of water in consequence of a local disturbance; but, although this has suggested the name since applied to all analogous phenomena, it so happens that water-waves are far from affording the simplest instance of the process in question. In the present article the principal types of wave-motion which present themselves in physics are reviewed in the order of their complexity. Only the leading features are as a rule touched upon, the reader being referred to other articles for such developments as are of interest mainly from the point of view of special subjects. The theory of water-waves, on the other hand, will be treated in some detail.

§1. Wave-Propagation in One Dimension.

The simplest and most easily apprehended case of wave-motion is that of the transverse vibrations of a uniform tense string. The axis of x being taken along the length of the string in its undisturbed position, we denote by y the transverse displacement at any point. This is assumed to be infinitely small; the resultant lateral force on any portion of the string is then equal to the tension (P, say) multiplied by the total curvature of that portion, and therefore in the case of an element δx to $$Py^{\prime \prime}\delta x$$, where the accents denote differentiations with respect to x. Equating this to $$\rho \delta x.\ddot{y}$$, where is the line-density, we have