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Rh religious houses in Germany. Her first settlement was at Bischofsheim in the diocese of Mainz, and two years later (754) she became abbess of the Benedictine nunnery at Heidenheim in the diocese of Eichstatt. On the death of Wunnibald in 760 she succeeded him in his charge also, retaining the superintendence of both houses until her death. Her relics were translated to Eichstatt, where she was laid in a hollow rock, from which exuded a kind of bituminous oil afterwards known as Walpurgis oil, and regarded as of miraculous efficacy against disease. It is still said to exude from the saint's bones (especially from October to February) and was chosen by Cardinal Newman as an example of a credible miracle. The cave became a place of pilgrimage, and a fine church was built over the spot. Walpurgis is commemorated at various times, but principally on the 1st of May, her day taking the place of an earlier heathen festival which was characterized by various rites marking the beginning of summer. She is regarded as the protectress against magic arts (cf. the Walpurgis-Nacht dance in Goethe's Faust). In art she is represented with a crozier, and bearing in her hand a flask of balsam.

WALRAS, MARIE ESPRIT LÉON (1834–1910), French economist, was born at Évreux in 1834. From 1866 to 1868 he edited a Journal called Le Travail, to which he contributed many valuable sociological articles. In 1870 he was appointed professor of political economy at Lausanne, a post which he retained until his retirement in 1892. He died on the 4th of January 1910. Walras is best known for his mathematical treatment of economics, and the extreme care he has shown in his works in distinguishing theory and practice. His most important works are Éléments d'économie politique pure (1874–1877) and Théorie mathematique de la richesse sociale (1883).

WALRUS, or (Odobenus rosmarus), a large marine mammal allied to the seals, representing a family by itself. The former word is a modification of the Scandinavian vallross or hvalros ("whale-horse"), the latter an adaptation of the Russian name for the animal. A full-grown male walrus measures from 10 to 11 ft from the nose to the end of the short tail, and is a heavy, bulky animal, especially thick about the shoulders. The head is rounded, the eyes are rather small, and there are no external ears. The muzzle is short and broad, with, on each side, a group of stiff, bristly whiskers, which become stouter and shorter in old animals. The tail scarcely projects beyond the skin. The fore-limbs are free only from the elbow, the fore flipper is broad, flat and webbed, the five digits being of nearly equal length, but the first slightly the longest. Each digit has a small flattened nail, situated on the inner surface at a considerable distance from the end. The hind-limbs are enclosed in the skin of the body, almost to the heel. The free portion when expanded is fan-shaped, the two outer toes (first and fifth) being the longest, especially the latter. Flaps of skin project considerably beyond the bones of the toes. The nails of the first and fifth toes are minute and flattened; those of the second, third and fourth elongated, sub-compressed and pointed. The soles of both fore and hind feet are bare, rough and warty. The surface of the skin generally is covered with short, adpressed hair of a light yellowish-brown colour, which, on the under parts of the body and base of the flippers, passes into dark reddish-brown or chestnut. In old animals the hair becomes more scanty, sometimes almost disappearing, and the skin shows evidence of the rough life and pugnacious habits of the animal in the scars with which it is usually covered. It is everywhere more or less wrinkled, especially over the shoulders, where it is thrown into deep and heavy folds.

One of the most striking characteristics of the walrus is the pair of tusks which descend almost directly downwards from the upper jaw, sometimes attaining a length of 20 in. or more. In the female they are as long or sometimes longer than in the male, but less massive. In the young of the first year they are not visible. These tusks correspond to the canine teeth of other mammals. All the other teeth, including the lower canines, are much alike—small, simple and one-rooted, and with crowns, rounded at first, but wearing to a flat or concave surface. Many of the teeth are lost early, or remain through life in a rudimentary state concealed beneath the gum. The tusks are formidable weapons of defence, but their principal use seems to be scraping and digging among sand and shingle for the molluscs and crustaceans on which the walrus feeds. They are said also to aid in climbing up the slippery rocks and ledges of ice on which so much of the animal's life is passed. Walruses are more or less gregarious in their habits, being met with generally in companies or herds of various sizes. They are only found near the coast or on large masses of floating ice, and rarely far out in the open sea, and, though often moving from one part of their feeding-ground to another, have no regular migrations. Their young are born between April and June,

usually but one at a time, never more than two. Their strong affection for their young, and their sympathy for each other in danger, have been noticed by all who have had the opportunity of observing them in their haunts. When one is wounded the whole herd usually join in defence. Although harmless and inoffensive when not molested, they exhibit considerable fierceness when attacked, using their tusks with tremendous effect either on human enemies who come into too close quarters or on polar bears, the only other adversary they can meet with in their own natural territory. The voice, a loud roaring, which can be heard at a great distance, is described by Dr Kane as "something between the mooing of a cow and the deepest baying of a mastiff, very round and full, with its bark or detached notes repeated rather quickly seven or nine times in succession."

The principal food of the walrus consists of bivalve molluscs, especially Mya truncata and Saxicava rugosa, two species very abundant in the Arctic regions, which it digs up from the mud and sand in which they lie buried at the bottom of the sea by means of its tusks. It crushes and removes the shells by the aid of its grinding teeth and tongue, and swallows only the soft parts of the animal. It also feeds on other molluscs, sand-worms, starfishes and shrimps. Portions of various kinds of seaweed have been found in its stomach, but whether swallowed intentionally or not is doubtful.

The commercial products of the walrus are its oil, hide (used to manufacture harness and sole-leather and twisted into tiller ropes) and tusks. The ivory of the latter is, however, inferior in quality to that of the elephant. Its flesh forms an important article of food to the Eskimo and Chukchi. Of the coast tribes of the last-named people the walrus formed the chief means of support.