AT MAT AT M . AT t = - -. (if V be the potential at T).

junction of several railways, 30 miles N.N.E. of Baireuth. It is the seat of district, town, country, and commercial courts, a chamber of commerce, and a head tax office. It is surrounded by walls, and has one Catholic and three Protestant churches, a town-house of 1563 in the Gothic style, a gymnasium with an extensive library, a trade and commercial school, a female school of the higher grade, a people's school, an orphanage, a richly endowed hospital founded in 1262, and an infirmary. Its industries are chiefly connected with wool and cotton, and include woollen, cotton, and jute spinning, jute weaving, and the manufacture of cotton and half-woollen fabrics. It has also dye-works, flour-mills, saw-mills, breweries, iron-works, and manufactures for machinery, iron and tin wares, chemicals, and sugar. In the neighbourhood there are large marble quarries and extensive iron mines. The population in 1875 was 18,122.

Hof was built about 1080, on the site of an old robber castle. Originally it belonged to the empire, but afterwards it was held by the dukes of Meran, and then by the counts of Orlamfinde, until it was sold in 1373 to the counts of Nuremberg. The cloth menu-future introduced into it in the 15th century, and the manufacture of veils, begun in the 16th century, greatly promoted its prosperity, but it suffered severely in the Albertine and Hussite wars, as well as in the Thirty Years' War; and in 1823 the greater part of it was destroyed by fire. In 1792 it came into the possession of Prussia; in 1806 it fell to France ; and in 1810 it was incorporated with Bavaria. See Widmann, Chronik der Stadt Hof, 1844; Ernst, Gesehichte end Beschreibieng des Bezirks end der Stadt Hof, 1306.