Chapter XVIII: Part 18

Christianity transferred to its own uses the ancient religious feeling concerning fountains. Statues of the Virgin or of saints were erected upon the rude structures that collected the water and preserved its purity. There is some uniformity in the architectural characteristics of these structures during the middle ages. A very common form in rural districts was that in which the fountain was reached by descending steps (_fontaine grotte_). A large basin received the water, sometimes from a spout, but often from the spring itself. This basin was covered by a sort of porch or vault, with at times moulded arches and sculptured figures and escutcheons. On the bank of the Clain at Poitiers is a fountain of this kind, the Fontaine Joubert, which though restored in 1597 was originally a structure of the 14th century. This kind of fountain is frequently decorated with figures of the Virgin or of saints, or with the family arms of its founder; often, too, the water is the only ornament of the structure, which bears a simple inscription. A large number of these fountains are to be found in Brittany and indeed throughout France, and the great antiquity of some of them is proved by the superstitions regarding them which still exist amongst the peasantry. A form more common in populous districts was that of a large open basin, round, square, polygonal, or lobed in form, with a columnar structure at the centre, from the lower part of which it was arranged that spouts should issue, playing into an open basin, and supplying vessels brought for the purpose in the cleanest and quickest manner. The columns take very various forms, from that of a simple regular geometrical solid, with only grotesque masks at the spouts, to that of an elaborate and ornate Gothic structure, with figures of virgins, saints and warriors, with mouldings, arches, crockets and finials. At Provins there is a fountain said to be of the 12th century, which is in form an hexagonal vase with a large column in the centre, the capital of which is pierced by three mouths, which are furnished with heads of bronze projecting far enough to cast the water into the basin. In the public market-place at Brunswick is a fountain of the 15th century, of which the central structure is made of bronze. Many fountains are still existing in France and Germany which, though their actual present structure may date no earlier than the 15th or 16th century, have been found on the place of, and perhaps may almost be considered as restorations of, pre-existing fountains. Except in Italy few fountains are of earlier date than the 14th century. Two of that date are at the abbey of Fontaine Daniel, near Mayenne, and another, of granite, is at Limoges. Some of these middle-age fountains are simple, open reservoirs enclosed in structures which, however plain, still carry the charm that belongs to the stone-work of those times. There is one of this kind at Cully, Calvados, walled on three sides, and fed from the spring by two circular openings. Its only ornamentation is a small empty niche with mouldings. At Lincoln is a fountain of the time of Henry VIII., in front of the church of St Mary Wickford. At Durham is one of octangular plan, which bears a statue of Neptune.

The decay of architectural taste in the later centuries is shown by the fountain of Limoges. It is in form a rock representing Mount Parnassus, upon which are carved in relief Apollo, the horse Pegasus, Philosophy and the Nine Muses. At the top Apollo, in the 16th-century costume, plays a harp. Rocks, grass and sheep fill up the scene.

Purely ornamental fountains and _jets d'eau_ are found in or near many large cities, royal palaces and private seats. The celebrated Fontana di Trevi, at Rome, was erected early in the 18th century under Pope Clement XII., and has all the characteristics of decadence. La Fontana Paolina and those in the piazza of St Peter's are perhaps next in celebrity to that of Trevi, and are certainly in better taste. At Paris the Fontaine des Innocens (the earliest) and those of the Place Royal, of the Champs Elysees and of the Place de la Concorde are the most noticeable. The fountain of the lions and other fountains in the Alhambra palace are, with their surroundings, a very magnificent sight. The largest _jets d'eau_ are those at Versailles, at the Sydenham Crystal Palace and at San Ildefonso.

About the earliest drawing of any drinking fountain in England occurs in Moxon's _Tutor to Astronomie and Geographie_ (1659); it is "surmounted by a diall, which was made by Mr John Leak, and set upon a composite column at Leadenhall corner, in the majoralty of Sir John Dethick, Knight." The water springs from the top and base of the column, which stands upon a square pedestal and bears four female figures, one at least of which represents the costume of the period.

In the East the public drinking fountains are a very important institution. In Cairo alone there are three hundred. These "sebeels" are not only to be seen in the cities, but are plentiful in the fields and villages.

The Metropolitan Drinking Fountain Association (1859) has done much to provide facilities in London for both man and beast to get water to drink in the streets. And in the United States liberal provision has also been made by private and public enterprise.

FOUNTAINS ABBEY, one of the most celebrated ecclesiastical ruins in England. It lies in the sequestered valley of the river Skell, 3 m. S.W. of the city of Ripon in Yorkshire. The situation is most beautiful. The little Skell descends from the uplands of Pateley Moor to the west a clear swift stream, traversing a valley clothed with woods, conspicuous among which are some ancient yew trees which may have sheltered the monks who first sought retreat here. Steep rocky hills enclose the vale. Mainly on the north side of the stream, in an open glade, rise the picturesque and extensive ruins, the church with its stately tower, and the numerous remnants of domestic buildings which enable the great abbey to be almost completely reconstructed in the mind. The arrangements are typical of a Cistercian house (see ABBEY). Building began in earnest about 1135, and was continued steadily until the middle of the 13th century, after which the only important erection was Abbot Huby's tower (c. 1500). The demesne of Studley Royal (marquess of Ripon) contains the ruins. It is in part laid out in the formal Dutch style, the work of John Aislabie, lord of the manor in the early part of the 18th century. Near the abbey is the picturesque Jacobean mansion of Fountains Hall.

In 1132 the prior and twelve monks of St Mary's abbey, York, being dissatisfied with the easy life they were living, left the monastery and with the assistance of Thurstan, archbishop of York, founded a house in the valley of the Skell, where they adopted the Cistercian rule. While building their monastery the monks are said to have lived at first under an elm and then under seven yew trees called the Seven Sisters. Two years later they were joined by Hugh, dean of St Peter's, York, who brought with him a large sum of money and a valuable collection of books. His example was followed by Serlo, a monk of St Mary's abbey, York, and by Tosti, a canon of York, and others. Henry I. and succeeding sovereigns granted them many privileges. During the reign of Edward I. the monks appear to have again suffered from poverty, partly no doubt owing to the invasion of the Scots, but partly also through their own "misconduct and extravagance." On account of this Edward I. in 1291 appointed John de Berwick custodian of the abbey so that he might pay their debts from the issues of their estates, allowing them enough for their maintenance, and Edward II. in 1319 granted them exemption from taxes. After the Dissolution Henry VIII. sold the manor and site of the monastery to Sir Richard Gresham, and from him after passing through several families it came to the marquess of Ripon.

See _Victoria County History, Yorkshire_; Dugdale, _Monasticon_;
Surtees Society, _Memorials of the Abbey of St Mary of Fountains_,
collected and edited by J.R. Walbran (1863-78).

FOUQUE, FERDINAND ANDRE (1828-1904), French geologist and petrologist, was born at Mortain, dept. of La Manche, on the 21st of June 1828. At the age of twenty-one he entered the _Ecole Normale_ in Paris, and from 1853 to 1858 he held the appointment of keeper of the scientific collections. In 1877 he became professor of natural history at the _College de France_, in Paris, and in 1881 he was elected a member of the Academy of Sciences. As a stratigraphical geologist he rendered much assistance on the Geological Survey of France, but in the course of time he gave his special attention to the study of volcanic phenomena and earthquakes, to minerals and rocks; and he was the first to introduce modern petrographical methods into France. His studies of the eruptive rocks of Corsica, Santorin and elsewhere; his researches on the artificial reproduction of eruptive rocks, and his treatise on the optical characters of felspars deserve special mention; but he was perhaps best known for the joint work which he carried on with his friend Michel Levy. He died on the 7th of March 1904. His chief publications were: _Santorin et ses eruptions_, 1879; (with A. Michel Levy) _Mineralogie micrographique, Roches eruptives francaises_ (2 vols., 1879); and _Synthese des mineraux et des roches_ (1882).

FOUQUE, FRIEDRICH HEINRICH KARL DE LA MOTTE, BARON (1777-1843), German writer of the romantic movement, was born on the 12th of February 1777 at Brandenburg. His grandfather had been one of Frederick the Great's generals and his father was a Prussian officer. Although not originally intended for a military career, Friedrich de la Motte Fouque ultimately gave up his university studies at Halle to join the army, and he took part in the Rhine campaign of 1794. The rest of his life was devoted mainly to literary pursuits. Like so many of the younger romanticists, Fouque owed his introduction to literature to A.W. Schlegel, who published his first book, _Dramatische Spiele von Pellegrin_ in 1804. His next work, _Romanzen vom Tal Ronceval_ (1805), showed more plainly his allegiance to the romantic leaders, and in the _Historie vom edlen Ritter Galmy_ (1806) he versified a 16th-century romance of medieval chivalry. _Sigurd der Schlangentoter, ein Heldenspiel_ (1808), the first modern German dramatization of the _Nibelungen_ saga, attracted attention to him, and influenced considerably subsequent versions of the story, such as Hebbel's _Nibelungen_ and Wagner's _Ring des Nibelungen_. These early writings indicate the lines which Fouque's subsequent literary activity followed; his interests were divided between medieval chivalry on the one hand and northern mythology on the other. In 1813, the year of the rising against Napoleon, he again fought with the Prussian army, and the new patriotism awakened in the German people left its mark upon his writings.

Between 1810 and 1815 Fouque's popularity was at its height; the many romances and novels, plays and epics, which he turned out with extraordinary rapidity, appealed exactly to the mood of the hour. The earliest of these are the best--_Undine_, which appeared in 1811, being, indeed, one of the most charming of all German _Marchen_ and the only work by which Fouque's memory still lives to-day. A more comprehensive idea of his powers may, however, be obtained from the two romances _Der Zauberring_ (1813) and _Die Fahrten Thiodulfs des Islanders_ (1815). From 1820 onwards the quality of Fouque's work rapidly degenerated, partly owing to the fatal ease with which he wrote, partly to his inability to keep pace with the changes in German taste. He remained the belated romanticist, who, as the reading world turned to new interests, clung the more tenaciously to the paraphernalia of romanticism; but in the cold, sober light of the post-romantic age, these appeared merely flimsy and theatrical. The vitalizing imaginative power of his early years deserted him, and the sobriquet of a "Don Quixote of Romanticism" which his enemies applied to him was not unjustified.

Fouque's first marriage had been unhappy and soon ended in divorce. His second wife, Karoline von Briest (1773-1831) enjoyed some reputation as a novelist in her day. After her death Fouque married a third time. Some consolation for the ebbing tide of popular favour was afforded him by the munificence of Frederick William IV. of Prussia, who granted him a pension which allowed him to spend his later years in comfort. He died in Berlin on the 23rd of January 1843.

Fouque's _Ausgewahlte Werke_, edited by himself, appeared in 12 vols.
(Berlin, 1841); a selection, edited by M. Koch, will be found in
Kurschner's _Deutsche Nationalliteratur_, vol. 146, part ii.
(Stuttgart, 1893); _Undine_, _Sintram_, &c., in innumerable reprints.
Bibliography in Goedeke's _Grundriss zur Geschichte der deutschen
Dichtung_ (2nd ed., vi. pp. 115 ff., Dresden, 1898). Most of Fouque's
works have been translated, and the English versions of _Aslauga's
Knight_ (by Carlyle), _Sintram and his Companions_ and _Undine_, have
been frequently republished. For Fouque's life cp. _Lebensgeschichte
des Baron Friedrich de la Motte Fouque. Aufgezeichnet durch ihn
selbst_ (Halle, 1840), (only to the year 1813), and also the
introduction to Koch's selections in the _Deutsche Nationalliteratur_.
(J. G. R.)

FOUQUET (or FOUCQUET), NICOLAS (1615-1680), viscount of Melun and of Vaux, marquis of Belle-Isle, superintendent of finance in France under Louis XIV., was born at Paris in 1615. He belonged to an influential family of the _noblesse de la robe_, and after some preliminary schooling with the Jesuits, at the age of thirteen was admitted as _avocat_ at the parlement of Paris. While still in his teens he held several responsible posts, and in 1636, when just twenty, he was able to buy the post of _maitre des requetes_. From 1642 to 1650 he held various intendancies at first in the provinces and then with the army of Mazarin, and, coming thus in touch with the court, was permitted in 1650 to buy the important position of _procureur general_ to the parlement of Paris. During Mazarin's exile Fouquet shrewdly remained loyal to him, protecting his property and keeping him informed of the situation at court.

Upon the cardinal's return, Fouquet demanded and received as reward the office of superintendent of the finances (1653), a position which, in the unsettled condition of the government, threw into his hands not merely the decision as to which funds should be applied to meet the demands of the state's creditors, but also the negotiations with the great financiers who lent money to the king. The appointment was a popular one with the moneyed class, for Fouquet's great wealth had been largely augmented by his marriage in 1651 with Marie de Castille, who also belonged to a wealthy family of the legal nobility. His own credit, and above all his unfailing confidence in himself, strengthened the credit of the government, while his high position at the parlement (he still remained _procureur general_) secured financial transactions from investigation. As minister of finance, he soon had Mazarin almost in the position of a suppliant. The long wars, and the greed of the courtiers, who followed the example of Mazarin, made it necessary at times for Fouquet to meet the demands upon him by borrowing upon his own credit, but he soon turned this confusion of the public purse with his own to good account. The disorder in the accounts became hopeless; fraudulent operations were entered into with impunity, and the financiers were kept in the position of clients by official favours and by generous aid whenever they needed it. Fouquet's fortune now surpassed even Mazarin's, but the latter was too deeply implicated in similar operations to interfere, and was obliged to leave the day of reckoning to his agent and successor Colbert. Upon Mazarin's death Fouquet expected to be made head of the government; but Louis XIV. was suspicious of his poorly dissembled ambition, and it was with Fouquet in mind that he made the well-known statement, upon assuming the government, that he would be his own chief minister. Colbert fed the king's displeasure with adverse reports upon the deficit, and made the worst of the case against Fouquet. The extravagant expenditure and personal display of the superintendent served to intensify the ill-will of the king. Fouquet had bought the port of Belle Isle and strengthened the fortifications, with a view to taking refuge there in case of disgrace. He had spent enormous sums in building a palace on his estate of Vaux, which in extent, magnificence, and splendour of decoration was a forecast of Versailles. Here he gathered the rarest manuscripts, the finest paintings, jewels and antiques in profusion, and above all surrounded himself with artists and authors. The table was open to all people of quality, and the kitchen was presided over by Vatel. Lafontaine, Corneille, Scarron, were among the multitude of his clients. In August 1661 Louis XIV., already set upon his destruction, was entertained at Vaux with a _fete_ rivalled in magnificence by only one or two in French history, at which Moliere's _Les Facheux_ was produced for the first time. The splendour of the entertainment sealed Fouquet's fate. The king, however, was afraid to act openly against so powerful a minister. By crafty devices Fouquet was induced to sell his office of _procureur general_, thus losing the protection of its privileges, and he paid the price of it into the treasury.

Three weeks after his visit to Vaux the king withdrew to Nantes, taking Fouquet with him, and had him arrested when he was leaving the presence chamber, flattered with the assurance of his esteem. The trial lasted almost three years, and its violation of the forms of justice is still the subject of frequent monographs by members of the French bar. Public sympathy was strongly with Fouquet, and Lafontaine, Madame de Sevigne and many others wrote on his behalf; but when Fouquet was sentenced to banishment, the king, disappointed, "commuted" the sentence to imprisonment for life. He was sent at the beginning of 1665 to the fortress of Pignerol, where he undoubtedly died on the 23rd of March 1680.[1] Louis acted throughout "as though he were conducting a campaign," evidently fearing that Fouquet would play the part of a Richelieu. Fouquet bore himself with manly fortitude, and composed several mediocre translations in prison. The devotional works bearing his name are apocryphal. A report of his trial was published in Holland, in 15 volumes, in 1665-1667, in spite of the remonstrances which Colbert addressed to the States-General. A second edition under the title of _Oeuvres de M. Fouquet_ appeared in 1696.

See Cheruel, _Memoires sur la vie publique et privee de Fouquet...
d'apres ses lettres et des pieces inedites_ (2 vols., Paris, 1864); J.
Lair, _Nicolas Foucquet, procureur general, surintendant des finances,
ministre d'Etat de Louis XIV_ (2 vols., Paris, 1890); U.V. Chatelain,
_Le Surintendant Nicolas Fouquet, protecteur des lettres, des arts et
des sciences_ (Paris, 1905); R. Pfnor et A. France, _Le Chateau de
Vaux-le-Vicomte dessine et grave_ (Paris, 1888).

FOOTNOTE:

[1] Fouquet has been identified with the "Man with the Iron Mask"
(see IRON MASK), but this theory is quite impossible.

FOUQUIER-TINVILLE, ANTOINE QUENTIN (1746-1795), French revolutionist, was born at Herouel, a village in the department of the Aisne. Originally a _procureur_ attached to the Chatelet at Paris, he sold his office in 1783, and became a clerk under the lieutenant-general of police. He seems to have early adopted revolutionary ideas, but little is known of the part he played at the outbreak of the Revolution. When the Revolutionary Tribunal of Paris was established on the 10th of March 1793, he was appointed public prosecutor to it, an office which he filled until the 28th of July 1794. His activity during this time earned him the reputation of one of the most terrible and sinister figures of the Revolution. His function as public prosecutor was not so much to convict the guilty as to see that the proscriptions ordered by the faction for the time being in power were carried out with a due regard to a show of legality. He was as ruthless and as incorrupt as Robespierre himself; he could be moved from his purpose neither by pity nor by bribes; nor was there in his cruelty any of that quality which made the ordinary Jacobin _enrage_ by turns ferocious and sentimental. It was this very quality of passionless detachment that made him so effective an instrument of the Terror. He had no forensic eloquence; but the cold obstinacy with which he pressed his charges was more convincing than any rhetoric, and he seldom failed to secure a conviction.

His horrible career ended with the fall of Robespierre and the terrorists on the 9th Thermidor. On the 1st of August 1794 he was imprisoned by order of the Convention and brought to trial. His defence was that he had only obeyed the orders of the Committee of Public Safety; but, after a trial which lasted forty-one days, he was condemned to death, and guillotined on the 7th of May 1795.

See _Memoire pour A.Q. Fouquier ex-accusateur public pres le tribunal
revolutionnaire_, &c. (Paris, 1794); Domenget, _Fouquier-Tinville et
le tribunal revolutionnaire_ (Paris, 1878); H. Wallon, _Histoire du
tribunal revolutionnaire de Paris_ (1880-1882) (a work of general
interest, but not always exact); George Lecocq, _Notes et documents
sur Fouquier-Tinville_ (Paris, 1885). See also the documents relating
to his trial enumerated by M. Tourneux in _Bibliographie de l'histoire
de Paris pendant la Revolution Francaise_, vol. i. Nos. 4445-4454
(1890).

FOURCHAMBAULT, a town of central France in the department of Nievre, on the right bank of the Loire, 4-1/2 m. N.W. of Nevers, on the Paris-Lyon railway. Pop. (1906) 4591. It owes its importance to its extensive iron-works, established in 1821, which give employment to 2000 workmen and produce engineering material for railway, military and other purposes. Among the more remarkable _chefs-d'oeuvre_ which have been produced at Fourchambault are the metal portions of the Pont du Carrousel, the iron beams of the roof of the cathedral at Chartres, and the vast spans of the bridge over the Dordogne at Cubzac. A small canal unites the works to the Lateral canal of the Loire.

FOURCROY, ANTOINE FRANCOIS, COMTE DE (1755-1809), French chemist, the son of an apothecary in the household of the duke of Orleans, was born at Paris on the 15th of June 1755. He took up medical studies by the advice of the anatomist Felix Vicq d'Azyr (1748-1794), and after many difficulties caused by lack of means finally in 1780 obtained his doctor's diploma. His attention was specially turned to chemistry by J.B.M. Bucquet (1746-1780), the professor of chemistry at the Medical School of Paris, and in 1784 he was chosen to succeed P.J. Macquer (1718-1784) as lecturer in chemistry at the college of the Jardin du Roi, where his lectures attained great popularity. He was one of the earliest converts to the views of Lavoisier, which he helped to promulgate by his voluminous writings, but though his name appears on a large number of chemical and also physiological and pathological memoirs, either alone or with others, he was rather a teacher and an organizer than an original investigator. A member of the committees for public instruction and public safety, and later, under Napoleon, director general of instruction, he took a leading part in the establishment of schools for both primary and secondary education, scientific studies being especially provided for. Fourcroy died at Paris on the 16th of December 1809, the very day on which he had been created a count of the French empire. By his conduct as a member of the Convention he has been accused of contributing to the death of Lavoisier. Baron Cuvier in his _Eloge historique_ of Fourcroy repels the charge, but he can scarcely be acquitted of time-serving indifference, if indeed active, though secret, participation be not proved against him.

The Royal Society's _Catalogue of Scientific Papers_ enumerates 59
memoirs by Fourcroy himself, and 58 written jointly by him and others,
mostly L.N. Vauquelin.

FOURIER, FRANCOIS CHARLES MARIE (1772-1837), French socialist writer, was born at Besancon in Franche-Comte on the 7th of April 1772. His father was a draper in good circumstances, and Fourier received an excellent education at the college in his native town. After completing his studies there he travelled for some time in France, Germany and Holland. On the death of his father he inherited a considerable amount of property, which, however, was lost when Lyons was besieged by the troops of the Convention. Being thus deprived of his means of livelihood Fourier entered the army, but after two years' service as a chasseur was discharged on account of ill-health. In 1803 he published a remarkable article on European politics which attracted the notice of Napoleon, some of whose ideas were foreshadowed in it. Inquiries were made after the author, but nothing seems to have come of them. After leaving the army Fourier entered a merchant's office in Lyons, and some years later undertook on his own account a small business as broker. He obtained in this way just sufficient to supply his wants, and devoted all his leisure time to the elaboration of his first work on the organization of society.

During the early part of his life, and while engaged in commerce, he had become deeply impressed with the conviction that social arrangements resulting from the principles of individualism and competition were essentially imperfect and immoral. He proposed to substitute for these principles co-operation or united effort, by means of which full and harmonious development might be given to human nature. The scheme, worked out in detail in his first work, _Theorie des quatre mouvements_ (2 vols., Lyons, 1808, published anonymously), has for foundation a particular psychological proposition and a special economical doctrine. Psychologically Fourier held what may with some laxity of language be called natural optimism,--the view that the full, free development of human nature or the unrestrained indulgence of human passion is the only possible way to happiness and virtue, and that misery and vice spring from the unnatural restraints imposed by society on the gratification of desire. This principle of harmony among the passions he regarded as his grandest discovery--a discovery which did more than set him on a level with Newton, the discoverer of the principle of attraction or harmony among material bodies. Throughout his works, in uncouth, obscure and often unintelligible language, he endeavours to show that the same fundamental fact of harmony is to be found in the four great departments,--society, animal life, organic life and the material universe. In order to give effect to this principle and obtain the resulting social harmony, it was needful that society should be reconstructed; for, as the social organism is at present constituted, innumerable restrictions are imposed upon the free development of human desire. As practical principle for such a reconstruction Fourier advocated co-operative or united industry. In many respects what he says of co-operation, in particular as to the enormous waste of economic force which the actual arrangements of society entail, still deserves attention, and some of the most recent efforts towards extension of the co-operative method, e.g. to house-keeping, were in essentials anticipated by him. But the full realization of his scheme demanded much more than the mere admission that co-operation is economically more efficacious than individualism. Society as a whole must be organized on the lines requisite to give full scope to co-operation and to the harmonious evolution of human nature. The details of this reorganization of the social structure cannot be given briefly, but the broad outlines may be thus sketched. Society, on his scheme, is to be divided into departments or _phalanges_, each _phalange_ numbering about 1600 persons. Each _phalange_ inhabits a _phalanstere_ or common building, and has a certain portion of soil allotted to it for cultivation. The _phalansteres_ are built after a uniform plan, and the domestic arrangements are laid down very elaborately. The staple industry of the _phalanges_ is, of course, agriculture, but the various _series_ and _groupes_ into which the members are divided may devote themselves to such occupations as are most to their taste; nor need any occupation become irksome from constant devotion to it. Any member of a group may vary his employment at pleasure, may pass from one task to another. The tasks regarded as menial or degrading in ordinary society can be rendered attractive if advantage is taken of the proper principles of human nature: thus children, who have a natural affinity for dirt, and a fondness for "cleaning up," may easily be induced to accept with eagerness the functions of public scavengers. It is not, on Fourier's scheme, necessary that private property should be abolished, nor is the privacy of family life impossible within the _phalanstere_. Each family may have separate apartments, and there may be richer and poorer members. But the rich and poor are to be locally intermingled, in order that the broad distinction between them, which is so painful a feature in actual society, may become almost imperceptible. Out of the common gain of the _phalange_ a certain portion is deducted to furnish to each member the minimum of subsistence; the remainder is distributed in shares to labour, capital and talent,--five-twelfths going to the first, four-twelfths to the second and three-twelfths to the third. Upon the changes requisite in the private life of the members Fourier was in his first work more explicit than in his later writings. The institution of marriage, which imposes unnatural bonds on human passion, is of necessity abolished; a new and ingeniously constructed system of licence is substituted for it. Considerable offence seems to have been given by Fourier's utterances with regard to marriage, and generally the later advocates of his views are content to pass the matter over in silence or to veil their teaching under obscure and metaphorical language.

The scheme thus sketched attracted no attention when the _Theorie_ first appeared, and for some years Fourier remained in his obscure position at Lyons. In 1812 the death of his mother put him in possession of a small sum of money, with which he retired to Bellay in order to perfect his second work. The _Traite de l'association agricole domestique_ was published in 2 vols. at Paris in 1822, and a summary appeared in the following year. After its publication the author proceeded to Paris in the hope that some wealthy capitalist might be induced to attempt the realization of the projected scheme. Disappointed in this expectation he returned to Lyons. In 1826 he again visited Paris, and as a considerable portion of his means had been expended in the publication of his book, he accepted a clerkship in an American firm. In 1829 and 1830 appeared what is probably the most finished exposition of his views, _Le Nouveau Monde industriel_. In 1831 he attacked the rival socialist doctrines of Saint-Simon and Owen in the small work _Pieges et charlatanisme de deux sectes, St Simon et Owen_. His writings now began to attract some attention. A small body of adherents gathered round him, and the most ardent of them was Victor Considerant (q.v.). In 1832 a newspaper, _Le Phalanstere ou la reforme industrielle_ was started to propagate the views of the school, but its success was not great. In 1833 it declined from a weekly to a monthly, and in 1834 it died of inanition. It was revived in 1836 as _Le Phalange_, and in 1843 became a daily paper, _La Democratie pacifique_. In 1850 it was suppressed.

Fourier did not live to see the success of his newspaper, and the only practical attempt during his lifetime to establish a _phalanstere_ was a complete failure. In 1832 M. Baudet Dulary, deputy for Seine-et-Oise, who had become a convert, purchased an estate at Conde-sur-Vesgre, near the forest of Rambouillet, and proceeded to establish a socialist community. The capital supplied was, however, inadequate, and the community broke up in disgust. Fourier was in no way discouraged by this failure, and till his death, on the 10th of October 1837, he lived in daily expectation that wealthy capitalists would see the merits of his scheme and be induced to devote their fortunes to its realization. It may be added that subsequent attempts to establish the _phalanstere_ have been uniformly unsuccessful.[1]

Fourier seems to have been of an extremely retiring and sensitive disposition. He mixed little in society, and appeared, indeed, as if he were the denizen of some other planet. Of the true nature of social arrangements, and of the manner in which they naturally grow and become organized, he must be pronounced extremely ignorant. The faults of existing institutions presented themselves to him in an altogether distorted manner, and he never appears to have recognized that the evils of actual society are immeasurably less serious than the consequences of his arbitrary scheme. Out of the chaos of human passion he supposed harmony was to be evolved by the adoption of a few theoretically disputable principles, which themselves impose restraints even more irksome than those due to actual social facts. With regard to the economic aspects of his proposed new method, it is of course to be granted that co-operation is more effective than individual effort, but he has nowhere faced the question as to the probable consequences of organizing society on the abolition of those great institutions which have grown with its growth. His temperament was too ardent, his imagination too strong, and his acquaintance with the realities of life too slight to enable him justly to estimate the merits of his fantastic views. That this description of him is not expressed in over-strong language must be clear to any one who not only considers what is true in his works,--and the portion of truth is by no means a peculiar discovery of Fourier's,--but who takes into account the whole body of his speculations, the cosmological and historical as well as the economical and social. No words can adequately describe the fantastic nonsense which he pours forth, partly in the form of general speculation on the universe, partly in the form of prophetic utterances with regard to the future changes in humanity and its material environment. From these extraordinary writings it is no extreme conclusion that there was much of insanity in Fourier's mental constitution.

AUTHORITIES.--Ch. Pellarin, _Fourier, sa vie et sa theorie_ (5th ed.,
1872); Sargant, _Social Innovators_ (1859); Reybaud, _Reformateurs
modernes_ (7th ed., 1864); Stein, _Socialismus und Communismus des
heutigen Frankreichs_ (2nd ed., 1848); A.J. Booth, _Fortnightly
Review_, N. S., vol. xii.; Czynski, _Notice bibliographique sur C.
Fourier_ (1841); Ferraz, _Le Socialisme, le naturalisme et le
positivisme_ (1877); Considerant, _Exposition abregee du systeme de
Fourier_ (1845); Transon, _Theorie societaire de Charles Fourier_
(1832); Stein, _Geschichte der sozialen Bewegung in Frankreich_
(1850); Marlo, _Untersuchungen uber die Organisation der Arbeit_
(1853); J.H. Noyes, _History of American Socialisms_ (1870); Bebel,
_Charles Fourier_ (1888); Varschauer, _Geschichte des Sozialismus und
Kommunismus im 19. Jahrhundert_ (1903); Sambuc, _Le Socialisme de
Fourier_ (1900); M. Hillquit, _History of Socialism in the United
States_ (1903); H. Bourgin, _Fourier, contribution a l'etude de
socialisme francais_ (1905). (R. Ad.)

FOOTNOTE:

[1] Several experiments were made to this end in the United States
(see COMMUNISM) by American followers of Fourier, whose doctrines
were introduced there by Albert Brisbane (1809-1890). Indeed, in the
years between 1840 and 1850, during which the movement waxed and
waned, no fewer than forty-one _phalanges_ were founded, of which
some definite record can be found. The most interesting of all the
experiments, not alone from its own history, but also from the fact
that it attracted the support of many of the most intellectual and
cultured Americans was that of Brook Farm (q.v.).

FOURIER, JEAN BAPTISTE JOSEPH (1768-1830), French mathematician, was born at Auxerre on the 21st of March 1768. He was the son of a tailor, and was left an orphan in his eighth year; but, through the kindness of a friend, admission was gained for him into the military school of his native town, which was then under the direction of the Benedictines of Saint-Maur. He soon distinguished himself as a student and made rapid progress, especially in mathematics. Debarred from entering the army on account of his lowness of birth and poverty, he was appointed professor of mathematics in the school in which he had been a pupil. In 1787 he became a novice at the abbey of St Benoit-sur-Loire; but he left the abbey in 1789 and returned to his college, where, in addition to his mathematical duties, he was frequently called to lecture on other subjects,--rhetoric, philosophy and history. On the institution of the Ecole Normale at Paris in 1795 he was sent to teach in it, and was afterwards attached to the Ecole Polytechnique, where he occupied the chair of analysis. Fourier was one of the savants who accompanied Bonaparte to Egypt in 1798; and during this expedition he was called to discharge important political duties in addition to his scientific ones. He was for a time virtually governor of half Egypt, and for three years was secretary of the Institut du Caire; he also delivered the funeral orations for Kleber and Desaix. He returned to France in 1801, and in the following year he was nominated prefect of Isere, and was created baron and chevalier of the Legion of Honour. He took an important part in the preparation of the famous _Description de l'Egypte_ and wrote the historical introduction. He held his prefecture for fourteen years; and it was during this period that he carried on his elaborate and fruitful investigations on the conduction of heat. On the return of Napoleon from Elba, in 1815, Fourier published a royalist proclamation, and left Grenoble as Napoleon entered it. He was then deprived of his prefecture, and, although immediately named prefect of the Rhone, was soon after again deprived. He now settled at Paris, was elected to the Academie des Sciences in 1816, but in consequence of the opposition of Louis XVIII. was not admitted till the following year, when he succeeded the Abbe Alexis de Rochon. In 1822 he was made perpetual secretary in conjunction with Cuvier, in succession to Delambre. In 1826 Fourier became a member of the French Academy, and in 1827 succeeded Laplace as president of the council of the Ecole Polytechnique. In 1828 he became a member of the government commission established for the encouragement of literature. He died at Paris on the 16th of May 1830.

As a politician Fourier achieved uncommon success, but his fame chiefly rests on his strikingly original contributions to science and mathematics. The theory of heat engaged his attention quite early, and in 1812 he obtained a prize offered by the Academie des Sciences with a memoir in two parts, _Theorie des mouvements de la chaleur dans les corps solides_. The first part was republished in 1822 as _La Theorie analytique de la chaleur_, which by its new methods and great results made an epoch in the history of mathematical and physical science (see below: FOURIER'S SERIES). An English translation has been published by A. Freeman (Cambridge, 1872), and a German by Weinstein (Berlin, 1884). His mathematical researches were also concerned with the theory of equations, but the question as to his priority on several points has been keenly discussed. After his death Navier completed and published Fourier's unfinished work, _Analyse des equations indeterminees_ (1831), which contains much original matter. In addition to the works above mentioned, Fourier wrote many memoirs on scientific subjects, and _eloges_ of distinguished men of science. His works have been collected and edited by Gaston Darboux with the title _Oeuvres de Fourier_ (Paris, 1889-1890).

For a list of Fourier's publications see the _Catalogue of Scientific
Papers of the Royal Society of London_. Reference may also be made to
Arago, "Joseph Fourier," in the _Smithsonian Report_ (1871).

FOURIER'S SERIES, in mathematics, those series which proceed according to sines and cosines of multiples of a variable, the various multiples being in the ratio of the natural numbers; they are used for the representation of a function of the variable for values of the variable which lie between prescribed finite limits. Although the importance of such series, especially in the theory of vibrations, had been recognized by D. Bernoulli, Lagrange and other mathematicians, and had led to some discussion of their properties, J.B.J. Fourier (see above) was the first clearly to recognize the arbitrary character of the functions which the series can represent, and to make any serious attempt to prove the validity of such representation; the series are consequently usually associated with the name of Fourier. More general cases of trigonometrical series, in which the multiples are given as the roots of certain transcendental equations, were also considered by Fourier.

Before proceeding to the consideration of the special class of series
to be discussed, it is necessary to define with some precision what is
to be understood by the representation of an arbitrary function by an
infinite series. Suppose a function of a variable x to be arbitrarily
given for values of x between two fixed values a and b; this means
that, corresponding to every value of x such that a <= x <= b, a
definite arithmetical value of the function is assigned by means of
some prescribed set of rules. A function so defined may be denoted by
[f](x); the rules by which the values of the function are determined
may be embodied in a single explicit analytical formula, or in several
such formulae applicable to different portions of the interval, but it
would be an undue restriction of the nature of an arbitrarily given
function to assume _a priori_ that it is necessarily given in this
manner, the possibility of the representation of such a function by
means of a single analytical expression being the very point which we
have to discuss. The variable x may be represented by a point at the
extremity of an interval measured along a straight line from a fixed
origin; thus we may speak of the point c as synonymous with the value
x = c of the variable, and of [f](c) as the value of the function
assigned to the point c. For any number of points between a and b the
function may be discontinuous, i.e. it may at such points undergo
abrupt changes of value; it will here be assumed that the number of
such points is finite. The only discontinuities here considered will
be those known as ordinary discontinuities. Such a discontinuity
exists at the point c if [f](c + [epsilon]), [f](c - [epsilon]) have
distinct but definite limiting values as [epsilon] is indefinitely
diminished; these limiting values are known as the limits on the right
and on the left respectively of the function at c, and may be denoted
by [f](c + 0), [f](c - 0). The discontinuity consists therefore of a
sudden change of value of the function from [f](c - 0) to [f](c + 0),
as x increases through the value c. If there is such a discontinuity
at the point x = 0, we may denote the limits on the right and on the
left respectively by [f](+0), [f](-0).

Suppose we have an infinite series u1(x) + u2(x) + ... + u_n(x) + ...
in which each term is a function of x, of known analytical form; let
any value x = c(a = c = b) be substituted in the terms of the series,
and suppose the sum of n terms of the arithmetical series so obtained
approaches a definite limit as n is indefinitely increased; this limit
is known as the sum of the series. If for every value of c such that a
<= c <= b the sum exists and agrees with the value of [f](c), the
series [Sigma] [1 to [oo]] u_n(x) is said to represent the function
([f]x) between the values a, b of the variable. If this is the case
for all points within the given interval with the exception of a
finite number, at any one of which either the series has no sum, or
has a sum which does not agree with the value of the function, the
series is said to represent "in general" the function for the given
interval. If the sum of n terms of the series be denoted by S_n(c),
the condition that S_n(c) converges to the value [f](c) is that,
corresponding to any finite positive number [delta] as small as we
please, a value n1 of n can be found such that if n >= n_1, |[f](c) -
Sn(c)| < [delta].

Functions have also been considered which for an infinite number of
points within the given interval have no definite value, and series
have also been discussed which at an infinite number of points in the
interval cease either to have a sum, or to have one which agrees with
the value of the function; the narrower conception above will however
be retained in the treatment of the subject in this article, reference
to the wider class of cases being made only in connexion with the
history of the theory of Fourier's Series.

_Uniform Convergence of Series._--If the series u1(x) + u2(x) + ... +
u2(x) + ... converge for every value of x in a given interval a to b,
and its sum be denoted by S(x), then if, corresponding to a finite
positive number [delta], as small as we please, a finite number n1 can
be found such that the arithmetical value of S(x) - S_n(x), where n =>
n1 is less than [delta] for every value of x in the given interval,
the series is said to converge uniformly in that interval. It may
however happen that as x approaches a particular value the number of
terms of the series which must be taken so that |S(x) - S_n(x)| may be
< [delta], increases indefinitely; the convergence of the series is
then infinitely slow in the neighbourhood of such a point, and the
series is not uniformly convergent throughout the given interval,
although it converges at each point of the interval. If the number of
such points in the neighbourhood of which the series ceases to
converge uniformly be finite, they may be excluded by taking intervals
of finite magnitude as small as we please containing such points, and
considering the convergence of the series in the given interval with
such sub-intervals excluded; the convergence of the series is now
uniform throughout the remainder of the interval. The series is said
to be _in general_ uniformly convergent within the given interval a to
b if it can be made uniformly convergent by the exclusion of a finite
number of portions of the interval, each such portion being
arbitrarily small. It is known that the sum of an infinite series of
continuous terms can be discontinuous only at points in the
neighbourhood of which the convergence of the series is not uniform,
but non-uniformity of convergence of the series does not necessarily
imply discontinuity in the sum.

_Form of Fourier's Series._--If it be assumed that a function [f](x)
arbitrarily given for values of x such that o[<=]x[<=]l is capable of
being represented in general by an infinite series of the form

[pi]x 2[pi]x n[pi]x
A1 sin ----- + A2 sin ------ + ... + A_n sin ------ + ...,
l l l

and if it be further assumed that the series is in general uniformly
convergent throughout the interval 0 to l, the form of the
coefficients A can be determined. Multiply each term of the series by
sin n[pi]x/l, and integrate the product between the limits 0 and l,
then in virtue of the property [int][l to 0] sin n[pi]x/l sin
n'[pi]x/l dx=0, or 1/2 l, according as n' is not, or is, equal to n,
we have -1/2 lA_n= [int][0 to l] [f](x) sin n[pi]x/l dx, and thus the
series is of the form

_
2 [oo] n[pi]x / l n[pi]x
-- [Sigma] sin ------ | [f](x) ------ dx. (1)
l 1 l _/ 0 l

This method of determining the coefficients in the series would not be
valid without the assumption that the series is in general uniformly
convergent, for in accordance with a known theorem the sum of the
integrals of the separate terms of the series is otherwise not
necessarily equal to the integral of the sum. This assumption being
made, it is further assumed that [f](x) is such that [integral][0 to
l] [f](x)sin n[pi]x/l dx has a definite meaning for every value of n.

Before we proceed to examine the justification for the assumptions
made, it is desirable to examine the result obtained, and to deduce
other series from it. In order to obtain a series of the form

[pi]x 2[pi]x n[pi]x
B0 + B1 cos ----- + B2 cos ------ + ... + B_n cos ------ + ...
l l l

for the representation of [f](x) in the interval 0 to l, let us apply
the series (1) to represent the function [f](x) sin [pi]x/l; we thus
find
_
2 [oo] n[pi]x / l [pi]x n[pi]x
-- [Sigma] sin ------ | [f](x)sin ----- sin ------ dx,
l 1 l _/ 0 l l

or
_ _ _
1 [oo] n[pi]x / l | (n - 1)[pi]x (n + 1)[pi]x |
-- [Sigma] sin ------ | [f](x) | cos ------------ - cos ------------ | dx.
l 1 l _/ 0 |_ l l _|

On rearrangement of the terms this becomes
_ _
1 [pi]x / l 2 [pi]x n[pi]x / l n[pi]x
-- sin ----- | [f](x) dx + -- [Sigma] sin ----- cos ------ | [f](x) cos ------ dx.
l l _/ 0 l l l _/ 0 l

hence [f](x) is represented for the interval 0 to l by the series of cosines
_ _
1 / l 2 [oo] n[pi]x / l n[pi]x
-- | [f](x) dx + -- [Sigma] cos ------ | [f](x) cos ------ dx ... (2)
l _/ 0 l 1 l _/ 0 l

We have thus seen, that with the assumptions made, the arbitrary
function [f](x) may be represented, for the given interval, either by
a series of sines, as in (1), or by a series of cosines, as in (2).
Some important differences between the two series must, however, be
noticed. In the first place, the series of sines has a vanishing sum
when x=o or x=l; it therefore does not represent the function at the
point x=o, unless [f](0) = 0, or at the point x=l, unless [f](l) = 0,
whereas the series (2) of cosines may represent the function at both
these points. Again, let us consider what is represented by (1) and
(2) for values of x which do not lie between 0 and l. As [f](x) is
given only for values of x between 0 and l, the series at points
beyond these limits have no necessary connexion with [f](x) unless we
suppose that [f](x) is also given for such general values of x in such
a way that the series continue to represent that function. If in (1)
we change x into -x, leaving the coefficients unaltered, the series
changes sign, and if x be changed into x + 2l, the series is
unaltered; we infer that the series (1) represents an odd function of
x and is periodic of period 2l; thus (1) will represent [f](x) in
general for values of x between [+-][oo], only if [f](x) is odd and
has a period 2l. If in (2) we change x into -x, the series is
unaltered, and it is also unaltered by changing x into x + 2l; from
this we see that the series (2) represents [f](x) for values of x
between [+-][oo], only if [f](x) is an even function, and is periodic
of period 2l. In general a function [f](x) arbitrarily given for all
values of x between [+-][oo] is neither periodic nor odd, nor even,
and is therefore not represented by either (1) or (2) except for the
interval 0 to l.

From (1) and (2) we can deduce a series containing both sines and
cosines, which will represent a function [f](x) arbitrarily given in
the interval -l to l, for that interval. We can express by (1) the
function -1/2{[f](x) - [f](-x)} which is an odd function, and thus this
function is represented for the interval -l to +l by
_
2 n[pi]x / l n[pi]x
-- [Sigma] sin ------ | 1/2 {[f](x) - [f](-x)} sin ------ dx;
l l _/ 0 l

we can also express 1/2 {[f](x) + [f](-x)}, which is an even function,
by means of (2), thus for the interval -l to +l this function is
represented by
_ _
1 / l 2 [oo] n[pi]x / l n[pi]x
-- | 1/2 {[f](x) + [f](-x)} dx + -- [Sigma] cos ------ | 1/2 {[f](x) + [f](-x)} cos ------ dx.
l _/ 0 l 1 l _/ 0 l

It must be observed that [f](-x) is absolutely independent of [f](x),
the former being not necessarily deducible from the latter by putting
-x for x in a formula; both [f](x) and [f](-x) are functions given
arbitrarily and independently for the interval 0 to l. On adding the
expressions together we obtain a series of sines and cosines which
represents [f](x) for the interval -l to l. The integrals
_ _
/ l n[pi]x / l n[pi]x
| [f](-x) cos ------ dx, | [f](-x) sin ------ dx
_/ 0 l _/ 0 l