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ANHALT. and Jewish churches are also subsidized to some extent. According to the census of 1900, the population of Anhalt was 316,027, showing an increase of more than 16 per cent. for the decade. Over 96 per cent, of the population is Protestant. Capital, Dessau (q.v.).

The reigning house of Anhalt traces its origin to Albert the Bear, Margrave of Brandenburg, upon the death of whose grandson, Henry I., in 1252, the Anhalt territories of the family were divided into three parts, which gave rise to the related families of Bernburg, Aschersleben, and Zerbst. The subsequent history of Anhalt is a monotonous succession of reunions and reparcelincs. All the parts were united between 1570 and 1586, and were then broken up again into four parts, Dessau, Bernburg, Köthen.and Zerbst. By the successive extinction of the last three lines, Anhalt was definitely reunited in 1863.

ANHALT-BERNBUBG, -bern'burK, of (1568-1630). A German general, founder of the Anhalt-Bernburg branch of Anhalt. In 1608 he took a leading part in the formation of the so-called Union of the Protestant German Princes directed against the encroachments of the Catholics. After acting as second commander of the army of that league, he entered the service of King Frederick of Bohemia, and led the army which was defeated by Tilly at Prague (1620).

ANHALT-DESSAU, -des'ou, fourth  of (1696-1747 ). A Prussian field-marshal. He entered the Prussian service at the age of twelve, and succeeded his father five years later. He distinguished himself at Höchstädt or Blenheim (1704). and in Prince Eugene's brilliant campaigns in Italy. After serving as a volunteer at Malplaquet (1709), he received command of the Prussian forces in the Netherlands and aided Marlborough in his operations against Villars. In 1712 he was made field-marshal and military counselor to King Frederick I. Under Frederick William I. Marshal Dessau aided in the reorganization of the Prussian army. As one of Frederick the Great's generals, he distinguished himself in the War of the Austrian Succession, in which he gained a bloody victory over the Austrians at Kesseldorf in 1745. To his soldiers Leopold of Anhalt-Dessau was known as "Der Alte Dessauer" (Old Dessau). Carlyle, in his Frederick the Great, speaks of him as "a man of vast dumb faculty, dumb but fertile, deep — no end of imagination — no end of ingenuities — with as much mother wit as in whole talking parliaments." There are numerous lives of him in German; the best ones are those of Varnhagen von Ense (Leipzig, 1872) and Crousaz (Berlin, 1875). There is an incomplete autobiography, edited by Hosaus, Selbstbioqraphie des Fürsten Leopold. Consult also Carlyle, Frederick the Great (London, 1858).

AN'HARMON'IC RA'TIO (Gk. av. an, priv. -f apuovia, hfirmoiiia. harmony, agreement) An important form of ratio introduced by Möbius under the name Doppelverhältniss (double ratio), but called by Chasles rapport anharmonique. If a pencil of four lines with vertex O are cut by any transversal SS in points A, B,

O, D, -^JLSlP is called the anharmonie ratio of the points and also of the pencil, and is symbolized by i 0, ABCD, or simply ] ABCD. Since sin AG B- sin COD the anharmonie ra- sin AOD -sin BOG tio is the same for any transversal, such as S'8', of given pencil, so that ABCD = -j A'B'C'D'

The anharmonie ratio ] ABCD admits of certain interchanges of letters without altering the value of the ratio. In fact, of the twenty- four permutations of the letters only six give different anharmonie ratios, and these six are thus related : If ABCD  —'K then ABDG '• = 4-
 * 'BZ) i = 1 — ;i -■ ACDB |- = y-—.

ADBc^'t^ aDCb A— 1

When the segments are so related that the value of the anharmonic ratio is 1, the ratio is called harmonic. The subject of anharmonic ratio plays an important part in projective geometry. Consult Cremona, Elements of Projective Geometry (London, 1885). See.

AN'HIDROT'ICS (Gk. ar, an, priv. + Mpwf, IndrOs, sweat). Drugs which diminish the secre- tion of sweat. They are chielly used in the pro- fuse night-sweats of phthisis. The most impor- tant are: Atropine, picrotoxin. agaricin, cam- phoric acid, sulphuric acid, and gallic acid (qq.v.).

ANHIMA, aniie-ma (Brazilian name). The homed screamer, one of the curious South American birds of the family Anhimidæ. See article.

ANHIN'GA. A generic and native name in South merica of the snake-birds, or darters (familv Anhingida-). See, and illustra- tions on plate of Fishing Birds (for similar species ).

ANHOLT, iinTiolt. An island belonging to the district of Randers, Denmark, situated in the centre of the Kattegat, about 22 miles from the peninsula of Jutland and the mainland of Sweden (Map: Denmark, E 2). Anholt Island has an area of eight square miles, and is nearly twice as long as it is broad. At the eastern end is a lighthouse to mark the dangerous shoals and reefs of the neighborhood.

ANHY'DRIDE (Gk. waterless, from nv. an, priv -f vSwp. hydor, water). An oxide which combines with water to form an acid, or an oxide which combines with a basic oxide to form a salt.