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Rh painters of contemporary manners who defy arrangement in this or that school. He is with Mrs Gaskell or Ferdinand Fabre; he is not entirely without relation with that old-fashioned favourite of the public, Fredrika Bremer.

His son, Erik Lie (b. 1868), published a successful volume of stories, Med Blyanten, in 1890; and is also the author of various works on literary history. An elder son, Mons Lie (b. 1864), studied the violin in Paris, but turned to literature in 1894. Among his works are the plays Tragedier om Kjaerlighed (1897); Lombardo and Agrippina (1898); Don Juan (1900); and the novels, Sjöfareren (1901); Adam Ravn (1903) and I. Kvindensnet (1904).

LIE, MARIUS SOPHUS (1842–1899), Norwegian mathematician, was born at Nordfjordeif, near Bergen, on the 17th of December 1842, and was educated at the university of Christiania, where he took his doctor’s degree in 1868 and became extraordinary professor of mathematics (a chair created specially for him) four years later. In 1886 he was chosen to succeed Felix Klein in the chair of geometry at Leipzig, but as his fame grew a special post was arranged for him in Christiania. But his health was broken down by too assiduous study, and he died at Christiania on the 18th of February 1899, six months after his return. Lie’s work exercised a great influence on the progress of mathematical science during the later decades of the 19th century. His primary aim has been declared to be the advancement and elaboration of the theory of differential equations, and it was with this end in view that he developed his theory of transformation groups, set forth in his Theorie der Transformationsgruppen (3 vols., Leipzig, 1888–1893), a work of wide range and great originality, by which probably his name is best known. A special application of his theory of continuous groups was to the general problem of non-Euclidean geometry. The latter part of the book above mentioned was devoted to a study of the foundations of geometry, considered from the standpoint of B. Riemann and H. von Helmholtz; and he intended to publish a systematic exposition of his geometrical investigations, in conjunction with Dr G. Scheffers, but only one volume made its appearance (Geometrie der Berührungstransformationen, Leipzig, 1896). Lie was a foreign member of the Royal Society, as well as an honorary member of the Cambridge Philosophical Society and the London Mathematical Society, and his geometrical inquiries gained him the much-coveted honour of the Lobatchewsky prize.

An analysis of Lie’s works is given in the Bibliotheca Mathematica (Leipzig, 1900).

LIEBER, FRANCIS (1800–1872), German-American publicist, was born at Berlin on the 18th of March 1800. He served with his two brothers under Blücher in the campaign of 1815, fighting at Ligny, Waterloo and Namur, where he was twice dangerously wounded. Shortly afterwards he was arrested for his political sentiments, the chief evidence against him being several songs of liberty which he had written. After several months he was discharged without a trial, but was forbidden to pursue his studies at the Prussian universities. He accordingly went to Jena, where he took his degrees in 1820, continuing his studies at Halle and Dresden. He subsequently took part in the Greek War of Independence, publishing his experiences in his Journal in Greece (Leipzig, 1823, and under the title The German Anacharsis, Amsterdam, 1823). For a year he was in Rome as tutor to the son of the historian Niebuhr, then Prussian ambassador. Returning to Berlin in 1823, he was imprisoned at Koepenik, but was released after some months through the influence of Niebuhr. In 1827 he went to the United States and as soon as possible was naturalized as a citizen. He settled at Boston, and for five years edited The Encyclopaedia Americana (13 vols.). From 1835 to 1856 he was professor of history and political economy in South Carolina College at Columbia, S.C., and during this period wrote his three chief works, Manual of Political Ethics (1838), Legal and Political Hermeneutics (1839), and Civil Liberty and Self Government (1853). In 1856 he resigned and next year was elected to a similar post in Columbia College, New York, and in 1865 became professor of constitutional history and public law in the same institution. During the Civil War Lieber rendered services of great value to the government. He was one of the first to point out the madness of secession, and was active in upholding the Union. He prepared, upon the requisition of the president, the important Code of War for the Government of the Armies of the United States in the Field, which was promulgated by the Government in General Orders No. 100 of the war department. This code suggested to Bluntschli his codification of the law of nations, as may be seen in the preface to his Droit International Codifié. During this period also Lieber wrote his Guerilla Parties with Reference to the Laws and Usages of War. At the time of his death he was the umpire of the commission for the adjudication of Mexican claims. He died on the 2nd of October 1872. His books were acquired by the University of California, and his papers were placed in the Johns Hopkins University.

His Miscellaneous Writings were published by D. C. Gilman (Philadelphia, 1881). See T. S. Perry, Life and Letters (1882), and biography by Harby (1899).

LIEBERMANN, MAX (1849– &emsp;&emsp; ), German painter and etcher, was born in Berlin. After studying under Steffeck, he entered the school of art at Weimar in 1869. Though the straightforward simplicity of his first exhibited picture, “Women plucking Geese,” in 1872, presented already a striking contrast to the conventional art then in vogue, it was heavy and bituminous in colour, like all the artist’s paintings before his visit to Paris at the end of 1872. A summer spent at Barbizon in 1873, where he became personally acquainted with Millet and had occasion to study the works of Corot, Troyon, and Daubigny, resulted in the clearing and brightening of his palette, and taught him to forget the example of Munkacsy, under whose influence he had produced his first pictures in Paris. He subsequently went to Holland, where the example of Israels confirmed him in the method he had adopted at Barbizon; but on his return to Munich in 1878 he caused much unfavourable criticism by his realistic painting of “Christ in the Temple,” which was condemned by the clergy as irreverent and remained his only attempt at a scriptural subject. Henceforth he devoted himself exclusively to the study of free-light and to the painting of the life of humble folk. He found his best subjects in the orphanages and asylums for the old in Amsterdam, among the peasants in the fields and village streets of Holland, and in the beer-gardens, factories, and workrooms of his own country. Germany was reluctant, however, in admitting the merit of an artist whose style and method were so markedly at variance with the time-honoured academic tradition. Only when his fame was echoed back from France, Belgium, and Holland did his compatriots realize the eminent position which is his due in the history of German art. It is hardly too much to say that Liebermann has done for his country what Millet did for France. His pictures hold the fragrance of the soil and the breezes of the heavens. His people move in their proper atmosphere, and their life is stated in all its monotonous simplicity, without artificial pathos or melodramatic exaggeration. His first success was a medal awarded him for “An Asylum for Old Men” at the 1881 Salon. In 1884 he settled again in Berlin, where he became professor of the Academy in 1898. He became a member of the Société nationale des Beaux Arts, of the Société royale belge des Aquarellistes, and of the Cercle des Aquarellistes at the Hague. Liebermann is represented in most of the German and other continental galleries. The Berlin National Gallery owns “The Flax-Spinners”; the Munich Pinakothek, “The Woman with Goats”; the Hamburg Gallery, “The Net-Menders”; the Hanover Gallery, the “Village Street in Holland.” “The Seamstress” is at the Dresden Gallery; the “Man on the Dunes” at Leipzig; “Dutch Orphan Girls” at Strassburg; “Beer-cellar at Brandenburg” at the Luxembourg Museum in Paris, and the “Knöpflerinnen” in Venice. His etchings are to be found in the leading print cabinets of Europe.

LIEBIG, JUSTUS VON, (1803–1873), German chemist, was born at Darmstadt, according to his baptismal certificate, on the 12th of May 1803 (4th of May, according to his mother). His father, a drysalter and dealer in colours, used sometimes to