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of previously unpublished matter, Nachlass.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
Surface.) 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.
(A. Ca.)
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
