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 the Disquisitiones arithmeticae, (2) Theory of Numbers, (3) Analysis, (4) Geometry and Method of Least Squares, (5) Mathematical Physics, (6) Astronomy, and (7) the Theoria motus corporum coelestium. Additional volumes have since been published, Fundamente der Geometrie usw. (1900), and Geodatische Nachträge zu Band iv. (1903). They include, besides his various works and memoirs, notices by him of many of these, and of works of other authors in the Göttingen gelehrte Anzeigen, and a considerable amount of previously unpublished matter, Nachlass. Of the memoirs in pure mathematics, comprised for the most part in vols. ii., iii. and iv. (but to these must be added those on Attractions in vol. v.), it may be safely said there is not one which has not signally contributed to the progress of the branch of mathematics to which it belongs, or which would not require to be carefully analysed in a history of the subject. Running through these volumes in order, we have in the second the memoir, Summatio quarundam serierum singularium, the memoirs on the theory of biquadratic residues, in which the notion of complex numbers of the form a＋bi was first introduced into the theory of numbers; and included in the Nachlass are some valuable tables. That for the conversion of a fraction into decimals (giving the complete period for all the prime numbers up to 997) is a specimen of the extraordinary love which Gauss had for long arithmetical calculations; and the amount of work gone through in the construction of the table of the number of the classes of binary quadratic forms must also have been tremendous. In vol. iii. we have memoirs relating to the proof of the theorem that every numerical equation has a real or imaginary root, the memoir on the Hypergeometric Series, that on Interpolation, and the memoir Determinatio attractionis—in which a planetary mass is considered as distributed over its orbit according to the time in which each portion of the orbit is described, and the question (having an implied reference to the theory of secular perturbations) is to find the attraction of such a ring. In the solution the value of an elliptic function is found by means of the arithmetico-geometrical mean. The Nachlass contains further researches on this subject, and also researches (unfortunately very fragmentary) on the lemniscate-function, &c., showing that Gauss was, even before 1800, in possession of many of the discoveries which have made the names of N. H. Abel and K. G. J. Jacobi illustrious. In vol. iv. we have the memoir Allgemeine Auflösung, on the graphical representation of one surface upon another, and the Disquisitiones generales circa superficies curvas. (An account of the treatment of surfaces which he originated in this paper will be found in the article .) And in vol. v. we have a memoir On the Attraction of Homogeneous Ellipsoids, and the already mentioned memoir Allgemeine Lehrsätze, on the theory of forces attracting according to the inverse square of the distance.

GAUSSEN, FRANÇOIS SAMUEL ROBERT LOUIS (1790–1863), Swiss Protestant divine, was born at Geneva on the 25th of August 1790. His father, Georg Markus Gaussen, a member of the council of two hundred, was descended from an old Languedoc family which had been scattered at the time of the religious persecutions in France. At the close of his university career at Geneva, Louis was in 1816 appointed pastor of the Swiss Reformed Church at Satigny near Geneva, where he formed intimate relations with J. E. Cellérier, who had preceded him in the pastorate, and also with the members of the dissenting congregation at Bourg-de-Four, which, together with the Église du témoignage, had been formed under the influence of the preaching of James and Robert Haldane in 1817. The Swiss revival was distasteful to the pastors of Geneva (Vénérable Compagnie des Pasteurs), and on the 7th of May 1817 they passed an ordinance hostile to it. As a protest against this ordinance, in 1819 Gaussen published in conjunction with Cellérier a French translation of the Second Helvetic Confession, with a preface expounding the views he had reached upon the nature, use and necessity of confessions of faith; and in 1830, for having discarded the official catechism of his church as being insufficiently explicit on the divinity of Christ, original sin and the doctrines of grace, he was censured and suspended by his ecclesiastical superiors. In the following year he took part in the formation of a Société Évangélique (Evangelische Gesellschaft). When this society contemplated, among other objects, the establishment of a new theological college, he was finally deprived of his charge. After some time devoted to travel in Italy and England, he returned to Geneva and ministered to an independent congregation until 1834, when he joined Merle d’Aubigné as professor of systematic theology in the college which he had helped to found. This post he continued to occupy until 1857, when he retired from the active duties of the chair. He died at Les Grottes, Geneva, on the 18th of June 1863.

His best-known work, entitled La Théopneustie ou pleine inspiration des saintes écritures, an elaborate defence of the doctrine of “plenary inspiration,” was originally published in Paris in 1840, and rapidly gained a wide popularity in France, as also, through translations, in England and America. It was followed in 1860 by a supplementary treatise on the canon (Le Canon des saintes écritures au double point de vue de la science et de la foi), which, though also popular, has hardly been so widely read.

See the article in Herzog-Hauck, Realencyklopädie (1899).

GAUTIER, ÉMILE THÉODORE LÉON (1832–1897), French literary historian, was born at Hâvre on the 8th of August 1832. He was educated at the École des Chartes, and became successively keeper of the archives of the department of Haute-Marne and of the imperial archives at Paris under the empire. In 1871 he became professor of palaeography at the École des Chartes. He was elected member of the Academy of Inscriptions in 1887, and became chief of the historical section of the national archives in 1893. Léon Gautier rendered great services to the study of early French literature, the most important of his numerous works on medieval subjects being a critical text (Tours, 1872) with translation and introduction of the Chanson de Roland, and Les Épopées françaises (3 vols., 1866–1867; 2nd ed., 5 vols., 1878–1897, including a Bibliographie des chansons de geste). He died in Paris on the 25th of August 1897.

GAUTIER, THÉOPHILE (1811–1872), French poet and miscellaneous writer, was born at Tarbes on the 31st of August 1811. He was educated at the grammar school of that town, and afterwards at the Collège Charlemagne in Paris, but was almost as much in the studios. He very early devoted himself to the study of the older French literature, especially that of the 16th and the early part of the 17th century. This study qualified him well to take part in the Romantic movement, and enabled him to astonish Sainte-Beuve by the phraseology and style of some literary essays which, when barely eighteen years old, he put into the critic’s hands. In consequence of this introduction he at once came under the influence of the great Romantic cénacle, to which, as to Victor Hugo in particular, he was also introduced by his gifted but ill-starred schoolmate Gérard de Nerval. With Gérard, Petrus Borel, Corot, and many other less known painters and poets whose personalities he has delightfully sketched in the articles collected under the titles of Histoire du Romantisme, &c., he formed a minor romantic clique who were distinguished for a time by the most extravagant eccentricity. A flaming crimson waistcoat and a great mass of waving hair were the outward signs which qualified Gautier for a chief rank among the enthusiastic devotees who attended the rehearsals of Hernani with red tickets marked “Hierro,” performed mocking dances round the bust of Racine, and were at all times ready to exchange word or blow with the perruques and grisâtres of the classical party. In Gautier’s case these freaks were not inconsistent with real genius and real devotion to sound ideals of literature. He began (like Thackeray, to whom he presents in other ways some striking points of resemblance) as an artist, but soon found that his true powers lay in another direction.

His first considerable poem, Albertus (1830), displayed a good deal of the extravagant character which accompanied rather than marked the movement, but also gave evidence of uncommon command both of language and imagery, and in particular of a descriptive power hardly to be excelled. The promise thus given was more than fulfilled in his subsequent poetry, which, in consequence of its small bulk, may well be noticed at once and by anticipation. The Comédie de la mort, which appeared soon after (1832), is one of the most remarkable of French poems, and though never widely read has received the suffrage of every competent reader. Minor poems of various dates, published in 1840, display an almost unequalled command over poetical form, an advance even over Albertus in vigour, wealth and appropriateness of diction, and abundance of the special poetical essence. All these good gifts reached their climax in the Émaux et camées, first published in 1856, and again, with additions, just before the poet’s death in 1872. These poems are in their own way such as