part 1

of vols. i. and ii. (Derby, 1831-1833); T. Bateman, _Vestiges of the Antiquities of Derbyshire_ (London, 1848); L. Jewitt, _Ballads and Songs of Derbyshire_ (London, 1867); J. C. Cox, _Notes on the Churches of Derbyshire_ (Chester, 1875), and _Three Centuries of Derbyshire Annals_ (2 vols., London, 1890); R. N. Worth, _Derby_, in "Popular County Histories" (London, 1886); J. P. Yeatman, _Feudal History of the County of Derby_ (3 vols., London, 1886-1895); _Victoria County History, Derbyshire_. See also _Notts and Derbyshire Notes and Queries_.

DEREHAM (properly EAST DEREHAM), a market town in the Mid parliamentary division of Norfolk, England, 122 m. N.N.E. from London by the Great Eastern railway. Pop. of urban district (1901) 5545. The church of St Nicholas is a cruciform Perpendicular structure with a beautiful central tower, and some portions of earlier date. It contains a monument to William Cowper, who came to live here in 1796, and the Congregational chapel stands on the site of the house where the poet spent his last days. Dereham is an important agricultural centre with works for the manufacture of agricultural implements, iron foundries and a malting industry.

DERELICT (from Lat. _derelinquere_, to forsake), in law, property thrown away or abandoned by the owner in such a manner as to indicate that he intends to make no further claim to it. The word is used more

## particularly with respect to property abandoned at sea (see WRECK), but

it is also applied in other senses; for example, land gained from the sea by receding of the water is termed _dereliction_. Land gained gradually and slowly by dereliction belongs to the owner of the adjoining land, but in the case of sudden or considerable dereliction the land belongs to the Crown. This technical use of the term "dereliction" is to be distinguished from the more general modern sense, dereliction or abandonment of duty, which implies a culpable failure or neglect in moral or legal obligation.

DERENBOURG, JOSEPH (1811-1895), Franco-German orientalist. He was a considerable force in the educational revival of Jewish education in France. He made great contributions to the knowledge of Saadia, and planned a complete edition of Saadia's works in Arabic and French. A large part of this work appeared during his lifetime. He also wrote an _Essai sur l'histoire et la géographie de la Palestine_ (Paris, 1867). This was an original contribution to the history of the Jews and Judaism in the time of Christ, and has been much used by later writers on the subject (e.g. by Schürer). He also published in collaboration with his son Hartwig, _Opuscules et traités d'Abou-'l-Walîd_ (with translation, 1880); _Deux Versions hébraïques du livre de Kalilâh et Dimnah_ (1881), and a Latin translation of the same story under the title _Joannis de Capua directorium vitae humanae_ (1889); _Commentaire de Maimonide sur la Mischnah Seder Tohorot_ (Berlin, 1886-1891); and a second edition of S. de Sacy's _Séances de Hariri_. He died on the 29th of July 1895, at Ems.

His son, HARTWIG DERENBOURG (1844-1908), was born in Paris on the 17th of June 1844. He was educated at Göttingen and Leipzig. Subsequently he studied Arabic at the École des Langues Orientales. In 1879 he was appointed professor of Arabic, and in 1886 professor of Mahommedan Religion, at the École des Hautes Études in Paris. He collaborated with his father in the great edition of Saadia and the edition of Abu-'l-Walîd, and also produced a number of important editions of other Arabic writers. Among these are _Le Dîwân de Nâbiqa Dhoby[=a]n[=i]_; _Le Livre de Sîbawaihi_ (2 vols., Paris, 1881-1889); _Chrestomathie élémentaire de l'arabe littéral_ (in collaboration with Spiro, 1885; 2nd ed., 1892); _Ousâma ibn Mounkidh, un émir syrien_ (1889); _Ousâma ibn Mounkidh, préface du livre du bâton_ (with trans., 1887); _Al-Fákhrî_ (1895); _Oumâra du Gémen_ (1897), a catalogue of Arabic MSS. in the Escorial (vol. i., 1884).

DERG, LOUGH, a lake of Ireland, on the boundary of the counties Galway, Clare and Tipperary. It is an expansion of the Shannon, being the lowest lake on that river, and is 23 m. long and generally from 1 to 3 m. broad. It lies where the Shannon leaves the central plain of Ireland and flows between the hills which border the plain. While the northerly shores of the lake, therefore, are flat, the southern are steep and picturesque, being backed by the Slieve Aughty, Slieve Bernagh and Arra Mountains. Ruined churches and fortresses are numerous on the eastern shore, and on Iniscaltra Island are a round tower and remains of five churches.

Another LOUGH DERG, near Pettigo in Donegal, though small, is famous as the traditional scene of St Patrick's purgatory. In the middle ages its pilgrimages had a European reputation, and they are still observed annually by many of the Irish from June 1 to August 15. The hospice, chapels, &c., are on Station Island, and there is a ruined monastery on Saints' Island.

DERHAM, WILLIAM (1657-1735), English divine, was born at Stoulton, near Worcester, on the 26th of November 1657. He was educated at Blockley, in his native county, and at Trinity College, Oxford. In 1682 he became vicar of Wargrave, in Berkshire; and in 1689 he was preferred to the living of Upminster, in Essex. In 1696 he published his _Artificial Clockmaker_, which went through several editions. The best known of his subsequent works are _Physico-Theology_, published in 1713; _Astro-Theology_, 1714; and _Christo-Theology_, 1730. The first two of these books were teleological arguments for the being and attributes of God, and were used by Paley nearly a century later. In 1702 Derham was elected fellow of the Royal Society, and in 1716 was made a canon of Windsor. He was Boyle lecturer in 1711-1712. His last work, entitled A _Defence of the Church's Right in Leasehold Estates_, appeared in 1731. He died on the 5th of April 1735. Besides the works published in his own name, Derham, who was keenly interested in natural history, contributed a variety of papers to the _Transactions of the Royal Society, revised the Miscellanea Curiosa_, edited the correspondence of John Ray and Eleazar Albin's _Natural History_, and published some of the MSS. of Robert Hooke, the natural philosopher.

D'ERLON, JEAN BAPTISTE DROUET, COUNT (1765-1844), marshal of France, was born at Reims on the 29th of July 1765. He entered the army as a private soldier in 1782, was discharged after five years' service, re-entered it in 1792, and rose rapidly to the rank of an officer. From 1794 to 1796 he was aide-de-camp to General Lefebvre. He did good service in the campaigns of the revolutionary wars and in 1799 attained the rank of general of brigade. In the campaign of that year he was engaged in the Swiss operations under Masséna. In 1800 he fought under Moreau at Hohenlinden. As a general of division he took part in Napoleon's campaigns of 1805 and 1806, and rendered excellent service at Jena. He was next engaged under Lefebvre in the siege of Danzig and negotiated the terms of surrender; after this he rejoined the field army and fought at Friedland (1807), receiving a severe wound. After this battle he was made grand officer of the Legion of Honour, was created Count d'Erlon and received a pension. For the next six years d'Erlon was almost continuously engaged as commander of an army corps in the Peninsular War, in which he added greatly to his reputation as a capable general. At the pass of Maya in the Pyrenees he inflicted a defeat upon Lord Hill's troops, and in the subsequent battles of the 1814 campaign he distinguished himself further. After the first Restoration he was named commander of the 16th military division, but he was soon arrested for conspiring with the Orléans party, to which he was secretly devoted. He escaped, however, and gave in his adhesion to Napoleon, who had returned from Elba. The emperor made him a peer of France, and gave him command of the I. army corps, which formed part of the Army of the North. In the Waterloo campaign d'Erlon's corps formed part of Ney's command on the 16th of June, but, in consequence of an extraordinary series of misunderstandings, took part neither at Ligny nor at Quatre Bras (see WATERLOO CAMPAIGN). He was not, however, held to account by Napoleon, and as the latter's practice in such matters was severe to the verge of injustice, it may be presumed that the failure was not due to d'Erlon.

He was in command of the right wing of the French army throughout the great battle of the 18th of June, and fought in the closing operations around Paris. At the second Restoration d'Erlon fled into Germany, only returning to France after the amnesty of 1825. He was not restored to the service until the accession of Louis Philippe, in whose interests he had engaged in several plots and intrigues. As commander of the 12th military division (Nantes), he suppressed the legitimist agitation in his district and caused the arrest of the duchess of Berry (1832). His last active service was in Algeria, of which country he was made governor-general in 1834 at the age of seventy. He returned to France after two years, and was made marshal of France shortly before his death at Paris on the 25th of January 1844.

DERMOT MAC MURROUGH (d. 1171), Irish king of Leinster, succeeded his father in the principality of the Hui Cinsellaigh (1115) and eventually in the kingship of Leinster. The early events of his life are obscure; but about 1152 we find him engaged in a feud with O Ruairc, the lord of Breifne (Leitrim and Cavan). Dermot abducted the wife of O Ruairc more with the object of injuring his rival than from any love of the lady. The injured husband called to his aid Roderic, the high king (aird-righ) of Connaught; and in 1166 Dermot fled before this powerful coalition to invoke the aid of England. Obtaining from Henry II. a licence to enlist allies among the Welsh marchers, Dermot secured the aid of the Clares and Geraldines. To Richard Strongbow, earl of Pembroke and head of the house of Clare, Dermot gave his daughter Eva in marriage; and on his death was succeeded by the earl in Leinster. The historical importance of Dermot lies in the fact that he was the means of introducing the English into Ireland. Through his aid the towns of Waterford, Wexford and Dublin had already become English colonies before the arrival of Henry II. in the island.

See _The Song of Dermot and the Earl, an old French Poem_ (by M. Regan?), ed. with trans. by G. H. Orpen, 1892; Kate Norgate, _England under the Angevin Kings_, vol. ii. (H. W. C. D.)

DERNA (anc. _Darnis-Zarine_), a town on the north coast of Africa and capital of the eastern half of the Ottoman province of Bengazi or Barca. Situated below the eastern butt of Jebel Akhdar on a small but rich deltaic plain, watered by fine perennial springs, it has a growing population and trade, the latter being mainly in fruits grown in its extensive palm gardens, and in hides and wool brought down by the nomads from the interior. If the port were better there would be more rapid expansion. The bay is open from N.W. round to S.E. and often inaccessible in winter and spring, and the steamers of the _Nav. Gen. Italiana_ sometimes have to pass without calling. The population has recovered from the great plague epidemic of 1821 and reached its former figure of about 7000. A proportion of it is of Moorish stock, of Andalusian origin, which emigrated in 1493; the descendants preserve a fine facial type. The sheikhs of the local Bedouin tribes have houses in the place, and a Turkish garrison of about 250 men is stationed in barracks. There is a lighthouse W. of the bay. A British consular agent is resident and the Italians maintain a vice-consul. The names Darnis and Zarine are philologically identical and probably refer to the same place. No traces are left of the ancient town except some rock tombs. Darnis continued to be of some importance in early Moslem times as a station on the Alexandria-Kairawan road, and has served on more than one occasion as a base for Egyptian attacks on Cyrenaica and Tripolitana. In 1805 the government of the United States, having a quarrel with the dey of Tripoli on account of piracies committed on American shipping, landed a force to co-operate in the attack on Derna then being made by Sidi Ahmet, an elder brother of the dey. This force, commanded by William Eaton (q.v.), built a fort, whose ruins and rusty guns are still to be seen, and began to improve the harbour; but its work quickly came to an end with the conclusion of peace. After 1835 Derna passed under direct Ottoman control, and subsequently served as the point whence the sultan exerted a precarious but increasing control over eastern Cyrenaica and Marmarica. It is now in communication by wireless telegraphy with Rhodes and western Cyrenaica. It is the only town, or even large village, between Bengazi and Alexandria (600 m.) (D. G. H.)

DÉROULÈDE, PAUL (1846- ), French author and politician, was born in Paris on the 2nd of September 1846. He made his first appearance as a poet in the pages of the _Revue nationale_, under the pseudonym of Jean Rebel, and in 1869 produced at the Théâtre Français a one-act drama in verse entitled _Juan Strenner_. On the outbreak of the Franco-German War he enlisted as a private, was wounded and taken prisoner at Sedan, and sent to Breslau, but effected his escape. He then served under Chanzy and Bourbaki, took part in the latter's disastrous retreat to Switzerland, and fought against the Commune in Paris. After attaining the rank of lieutenant, he was forced by an accident to retire from the army. He published in 1872 a number of patriotic poems (_Chants du soldat_), which enjoyed unbounded popularity. This was followed in 1875 by another collection, _Nouveaux Chants du soldat_. In 1877 he produced a drama in verse called _L'Hetman_, which derived a passing success from the patriotic fervour of its sentiments. For the exhibition of 1878 he wrote a hymn, _Vive la France_, which was set to music by Gounod. In 1880 his drama in verse, _La Moäbite_, which had been accepted by the Théâtre Français, was forbidden by the censor on religious grounds. In 1882 M. Déroulède founded the _Ligue des patriotes_, with the object of furthering France's "revanche" against Germany. He was one of the first advocates of a Franco-Russian alliance, and as early as 1883 undertook a journey to Russia for the furtherance of that object. On the rise of General Boulanger, M. Déroulède attempted to use the _Ligue des patriotes_, hitherto a non-political organization, to assist his cause, but was deserted by a great part of the league and forced to resign his presidency. Nevertheless he used the section that remained faithful to him with such effect that the government found it necessary in 1889 to decree its suppression. In the same year he was elected to the chamber as member for Angoulême. He was expelled from the chamber in 1890 for his disorderly interruptions during debate. He did not stand at the elections of 1893, but was re-elected in 1898, and distinguished himself by his violence as a nationalist and anti-Dreyfusard. After the funeral of President Faure, on the 23rd of February 1899, he endeavoured to persuade General Roget to lead his troops upon the Élysée. For this he was arrested, but on being tried for treason was acquitted (May 31). On the 12th of August he was again arrested and accused, together with André Buffet, Jules Guérin and others, of conspiracy against the republic. After a long trial before the high court, he was sentenced, on the 4th of January 1900, to ten years' banishment from France, and retired to San Sebastian. In 1901, he was again brought prominently before the public by a quarrel with his Royalist allies, which resulted in an abortive attempt to arrange a duel with M. Buffet in Switzerland. In November 1905, however, the law of amnesty enabled him to return to France.

Besides the works already mentioned, he published _Le Sergent_, in the _Théâtre de campagne_ (1880); _De l'éducation nationale_ (1882); _Monsieur le Uhlan et les trois couleurs_ (1884); _Le Premier grenadier de France; La Tour d'Auvergne_ (1886); _Le Livre de la ligue des patriotes_ (1887); _Refrains militaires_ (1888); _Histoire d'amour_ (1890); a pamphlet entitled _Désarmement?_ (1891); _Chants du paysan_ (1894); _Poésies Militaires_ (1896) and _Messire du Guesclin, drame en vers_ (1895); _La mort de Hoche. Cinq actes en prose_ (1897); _La Plus belle fille du monde, conte dialogué en vers libres_ (1898).

DERRICK, a sort of crane (q.v.); the name is derived from that of a famous early 17th-century Tyburn hangman, and was originally applied as a synonym.

DERRING-DO, valour, chivalrous conduct, or "desperate courage," as it is defined by Sir Walter Scott. The word in its present accepted substantival form is a misconstruction of the verbal substantive _dorryng_ or _durring_, daring, and _do_ or _don_, the present infinitive of "do," the phrase _dorryng do_ thus meaning "daring to do." It is used by Chaucer in _Troylus_, and by Lydgate in the _Chronicles of Troy_. Spenser in the _Shepherd's Calendar_ first adapted _derring-do_ as a substantive meaning "manhood and chevalrie," and this use was revived by Scott, through whom it came into vogue with writers of romance.

DE RUYTER, MICHAEL ADRIANZOON (1607-1676), Dutch naval officer, was born at Flushing on the 24th of March 1607. He began his seafaring life at the age of eleven as a cabin boy, and in 1636 was entrusted by the merchants of Flushing with the command of a cruiser against the French pirates. In 1640 he entered the service of the States, and, being appointed rear-admiral of a fleet fitted out to assist Portugal against Spain, specially distinguished himself at Cape St Vincent, on the 3rd of November 1641. In the following year he left the service of the States, and, until the outbreak of war with England in 1652, held command of a merchant vessel. In 1653 a squadron of seventy vessels was despatched against the English, under the command of Admiral Tromp. Ruyter, who accompanied the admiral in this expedition, seconded him with great skill and bravery in the three battles which were fought with the English. He was afterwards stationed in the Mediterranean, where he captured several Turkish vessels. In 1659 he received a commission to join the king of Denmark in his war with the Swedes. As a reward of his services, the king of Denmark ennobled him and gave him a pension. In 1661 he grounded a vessel belonging to Tunis, released forty Christian slaves, made a treaty with the Tunisians, and reduced the Algerine corsairs to submission. From his achievements on the west coast of Africa he was recalled in 1665 to take command of a large fleet which had been organized against England, and in May of the following year, after a long contest off the North Foreland, he compelled the English to take refuge in the Thames. On the 7th of June 1672 he fought a drawn battle with the combined fleets of England and France, in Southwold or Sole Bay, and after the fight he convoyed safely home a fleet of merchantmen. His valour was displayed to equal advantage in several engagements with the French and English in the following year. In 1676 he was despatched to the assistance of Spain against France in the Mediterranean, and, receiving a mortal wound in the battle on the 21st of April off Messina, died on the 29th at Syracuse. A patent by the king of Spain, investing him with the dignity of duke, did not reach the fleet till after his death. His body was carried to Amsterdam, where a magnificent monument to his memory was erected by command of the states-general.

See _Life_ of De Ruyter by Brandt (Amsterdam, 1687), and by Klopp (2nd ed., Hanover, 1858).

DERVISH, a Persian word, meaning "seeking doors," i.e. "beggar," and thus equivalent to the Arabic _faq[=i]r_ (fakir). Generally in Islam it indicates a member of a religious fraternity, whether mendicant or not; but in Turkey and Persia it indicates more exactly a wandering, begging religious, called, in Arabic-speaking countries, more specifically a _faqir_. With important differences, the dervish fraternities may be compared to the regular religious orders of Roman Christendom, while the Ulema (q.v.) are, also with important differences, like the secular clergy. The origin and history of the mystical life in Islam, which led to the growth of the order of dervishes, are treated under [S.][=U]FI'ISM It remains to treat here more particularly of (1) the dervish fraternities, and (2) the [S.][=u]f[=i] hierarchy.

1. _The Dervish Fraternities._--In the earlier times, the relation between devotees was that of master and pupil. Those inclined to the spiritual life gathered round a revered sheikh (_murshid_, "guide," _ustadh_, _pir_, "teacher"), lived with him, shared his religious practices and were instructed by him. In time of war against the unbelievers, they might accompany him to the threatened frontier, and fight under his eye. Thus _mur[=a]bit_, "one who pickets his horse on a hostile frontier," has become the marabout (q.v.) or dervish of French Algeria; and _ribat_, "a frontier fort," has come to mean a monastery. The relation, also, might be for a time only. The pupil might at any time return to the world, when his religious education and training were complete. On the death of the master the memory of his life and sayings might go down from generation to generation, and men might boast themselves as pupils of his pupils. Continuous corporations to perpetuate his name were slow in forming. Ghazali himself, though he founded, taught and ruled a [S.][=u]f[=i] cloister (_kh[=a]nq[=a]h_) at Tus, left no order behind him. But 'Ad[=i] al-Hakk[=a]r[=i], who founded a cloister at Mosul and died about 1163, was long reverenced by the 'Adawite Fraternity, and in 1166 died 'Abd al-Q[=a]dir al-Jil[=a]n[=i], from whom the Q[=a]dirite order descends, one of the greatest and most influential to this day. The troublous times of the break up of the Seljuk rule may have been a cause in this, as, with St Benedict, the crumbling Roman empire. Many existing fraternities, it is true, trace their origin to saints of the third, second and even first Moslem centuries, but that is legend purely. Similar is the tendency to claim all the early pious Moslems as good [S.][=u]f[=i]s; collections of [S.][=u]f[=i] biography begin with the ten to whom Mahomet promised Paradise. So, too, the ultimate origin of fraternities is assigned to either Ali or Abu Bekr, and in Egypt all are under the rule of a direct descendant of the latter.

To give a complete list of these fraternities is quite impossible. Commonly, thirty-two are reckoned, but many have vanished or have been suppressed, and there are sub-orders innumerable. Each has a "rule" dating back to its founder, and a ritual which the members perform when they meet together in their convent (_kh[=a]nq[=a]h_, _z[=a]wiya_, _takya_). This may consist simply in the repetition of sacred phrases, or it may be an elaborate performance, such as the whirlings of the dancing dervishes, the Mevlevites, an order founded by Jel[=a]l ud-D[=i]n ar-R[=u]m[=i], the author of the great Persian mystical poem, the _Mesnevi_, and always ruled by one of his descendants. Jel[=a]l ud-D[=i]n was an advanced pantheist, and so are the Mevlevites, but that seems only to earn them the dislike of the Ulema, and not to affect their standing in Islam. They are the most broad-minded and tolerant of all. There are also the performances of the Rif[=a]'ites or "howling dervishes." In ecstasy they cut themselves with knives; eat live coals and glass, handle red-hot iron and devour serpents. They profess miraculous healing powers, and the head of the Sa'dites, a sub-order, used, in Cairo, to ride over the bodies of his dervishes without hurting them, the so-called D[=o]seh (_dausa_). These different abilities are strictly regulated. Thus, one sub-order may eat glass and another may eat only serpents. Another division is made by their attitude to the law of Islam. When a dervish is in a state of ecstasy (_majdh[=u]b_), he is supposed to be unconscious of the actions of his body. Reputed saints, therefore, can do practically anything, as their souls will be supposed to be out of their bodies and in the heavenly regions. They may not only commit the vilest of actions, but neglect in general the ceremonial and ritual law. This goes so far that in Persia and Turkey dervish orders are classified as _b[=a]-shar'_, "with law," and _b[=i]-shar'_, "without law." The latter are really antinomians, and the best example of them is the Bakhtashite order, widely spread and influential in Turkey and Albania and connected by legend with the origin of the Janissaries. The Qalandarite order is known to all from the "Calenders" of the _Thousand and One Nights_. They separated from the Bakhtashites and are under obligation of perpetual travelling. The Senussi (Senussia) were the last order to appear, and are distinguished from the others by a severely puritanic and reforming attitude and strict orthodoxy, without any admixture of mystical slackness in faith or conduct. Each order is distinguished by a peculiar garb. Candidates for admission have to pass through a noviciate, more or less lengthy. First comes the _'ahd_, or initial covenant, in which the neophyte or _mur[=i]d_, "seeker," repents of his past sins and takes the sheikh of the order he enters as his guide (_murshid_) for the future. He then enters upon a course of instruction and discipline, called a "path" (_tar[=i]qa_), on which he advances through diverse "stations" (_maq[=a]m[=a]t_) or "passes" (_'aqab[=a]t_) of the spiritual life. There is a striking resemblance here to the gnostic system, with its seven Archon-guarded gates. On another side, it is plain that the sheikh, along with ordinary instruction of the novice, also hypnotizes him and causes him to see a series of visions, marking his penetration of the divine mystery. The part that hypnosis and autohypnosis, conscious and unconscious, has played here cannot easily be overestimated. The Mevlevites seem to have the most severe noviciate. Their aspirant has to labour as a lay servitor of the lowest rank for 1001 days--called the _k[=a]rr[=a] kolak_, or "jackal"--before he can be received. For one day's failure he must begin again from the beginning.

But besides these full members there is an enormous number of lay adherents, like the tertiaries of the Franciscans. Thus, nearly every religious man of the Turkish Moslem world is a lay member of one order or another, under the duty of saying certain prayers daily. Certain trades, too, affect certain orders. Most of the Egyptian Q[=a]dirites, for example, are fishermen and, on festival days, carry as banners nets of various colours. On this side, the orders bear a striking resemblance to lodges of Freemasons and other friendly societies, and points of direct contact have even been alleged between the more pantheistic and antinomian orders, such as the Bakhtashite, and European Freemasonry. On another side, just as the _dhikrs_ of the early ascetic mystics suggest comparison with the class-meetings of the early Methodists, so these orders are the nearest approach in Islam to the different churches of Protestant Christendom. They are the only ecclesiastical organization that Islam has ever known, but it is a multiform organization, unclassified internally or externally. They differ thus from the Roman monastic orders, in that they are independent and self-developing, each going its own way in faith and practice, limited only by the universal conscience (_ijm[=a]'_, "agreement": see MAHOMMEDAN LAW) of Islam. Strange doctrines and moral defects may develop, but freedom is saved, and the whole people of Islam can be reached and affected.

2. _Saints and the [S.][=u]f[=i] Hierarchy._--That an elaborate doctrine of wonder-working saints should have grown up in Islam may, at first sight, appear an extreme paradox. It can, however, be conditioned and explained. First, Mahomet left undoubted loop-holes for a minor inspiration, legitimate and illegitimate. Secondly, the [S.][=u]f[=i]s, under various foreign influences, developed these to the fullest. Thirdly, just as the Christian church has absorbed much of the mythology of the supposed exterminated heathen religions into its cult of local saints, so Islam, to an even higher degree, has been overlaid and almost buried by the superstitions of the peoples to which it has gone. Their religious and legal customs have completely overcome the direct commands of the Koran, the traditions from Mahomet and even the "Agreement" of the rest of the Moslem world (see MAHOMMEDAN LAW). The first step in this, it is true, was taken by Mahomet himself when he accepted the Meccan pilgrimage and the Black Stone. The worship of saints, therefore, has appeared everywhere in Islam, with an absolute belief in their miracles and in the value of their intercession, living or dead.

Further, there appeared very early in Islam a belief that there was always in existence some individual in direct intercourse with God and having the right and duty of teaching and ruling all mankind. This individual might be visible or invisible; his right to rule continued. This is the basis of the Ism[=a]'[=i]lite and Sh[=i]'ite positions (see MAHOMMEDAN RELIGION and MAHOMMEDAN INSTITUTIONS). The [S.][=u]f[=i]s applied this idea of divine right to the doctrine of saints, and developed it into the [S.][=u]f[=i] hierarchy. This is a single, great, invisible organization, forming a saintly board of administration, by which the invisible government of the world is supposed to be carried on. Its head is called the _Qu[t.]b_ (Axis); he is presumably the greatest saint of the time, is chosen by God for the office and given greater miraculous powers and rights of intercession than any other saint enjoys. He wanders through the world, often invisible and always unknown, performing the duties of his office. Under him there is an elaborate organization of _wal[=i]s_, of different ranks and powers, according to their sanctity and faith. The term _wal[=i]_ is applied to a saint because of Kor. x. 63, "Ho! the _wal[=i]s_ of God; there is no fear upon them, nor do they grieve," where _wal[=i]_ means "one who is near," friend or favourite.

In the fraternities, then, all are dervishes, cloistered or lay; those whose faith is so great that God has given them miraculous powers--and there are many--are _wal[=i]s_; begging friars are _fakirs_. All forms of life--solitary, monastic, secular, celibate, married, wandering, stationary, ascetic, free--are open. Their theology is some form of S[=u]fi'ism.

AUTHORITIES.--The bibliography of this subject is very large, and the following only a selection:--(1) _On Dervishes._ In Egypt, Lane's _Modern Egyptians_, chaps. x., xx., xxiv., xxv.; in Turkey, D'Ohsson, _Tableau général de l'emp. othoman_, ii. (Paris, 1790); _Turkey in Europe_ by "Odysseus" (London, 1900); in Persia, E. G. Browne, _A Year among the Persians_ (1893), in Morocco, T. H. Weir, _Sheikhs of Morocco_ (Edinburgh, 1904); B. Meakin, _The Moors_ (London, 1902), chap. xix.; in Central Asia, all Vambéry's books of travel and history. In general, Hughes, _Dict. of Islam_, s.v. "Faqir"; Depont and Cappolani, _Les Confréries religieuses musulmanes_ (Alger, 1897); J. P. Brown, _The Dervishes, or Oriental Spiritualism_ (London, 1868). (2) _On Saints._ I. Goldziher, _Muhammedanische Studien_, ii. 277 ff., and "De l'ascétisme aux premiers temps de l'Islam" in _Revue de l'histoire des religions_, vol. xxxvii. pp. 134 ff.; Lane, _Modern Egyptians_, chap. x.; _Arabian Nights_, chap. iii. note 63; Vollers in _Zeitsch. d. morgenländ. Gesellsch._ xliii. 115 ff. (D. B. MA.)

DERWENT (Celtic _Dwr-gent_, clear water), the name of several English rivers. (1) The Yorkshire Derwent collects the greater part of the drainage of the North Yorkshire moors, rising in their eastern part. A southern head-stream, however, rises in the Yorkshire Wolds near Filey, little more than a mile from the North Sea, from which it is separated by a morainic deposit, and thus flows in an inland direction. The early course of the Derwent lies through a flat open valley between the North Yorkshire moors and the Yorkshire Wolds, the upper part of which is known as the Carrs, when the river follows an artificial drainage cut. It receives numerous tributaries from the moors, then breaches the low hills below Malton in a narrow picturesque valley, and debouches upon the central plain of Yorkshire. Its direction, hitherto westerly and south-westerly from the Carrs, now becomes southerly, and it flows roughly parallel to the Ouse, which it joins near Barmby-on-the-Marsh, in the level district between Selby and the head of the Humber estuary, after a course, excluding minor sinuosities, of about 70 m. As a tributary of the Ouse it is included in the Humber basin. It is tidal up to Sutton-upon-Derwent, 15 m. from the junction with the Ouse, and is locked up to Malton, but the navigation is little used. A canal leads east from the tidal water to the small market town of Pocklington.

(2) The Derbyshire Derwent rises in Bleaklow Hill north of the Peak and traverses a narrow dale, which, with those of such tributary streams as the Noe, watering Hope Valley, and the Wye, is famous for its beauty (see DERBYSHIRE). The Derwent flows south past Chatsworth, Matlock and Belper and then, passing Derby, debouches upon a low plain, and turns south-eastward, with an extremely sinuous course, to join the Trent near Sawley. Its length is about 60 m. It falls in all some 1700 ft. (from Matlock 200 ft.), and no part is navigable, save certain reaches at Matlock and elsewhere for pleasure boats.

(3) The Cumberland Derwent rises below Great End in the Lake District, draining Sprinkling and Sty Head tarns, and flows through Borrowdale, receiving a considerable tributary from Lang Strath. It then drains the lakes of Derwentwater and Bassenthwaite, after which its course, hitherto N. and N.N.W., turns W. and W. by S. past Cockermouth to the Irish Sea at Workington. The length is about 34 m., and the fall about 2000 ft. (from Derwentwater 244 ft.); the waters are usually beautifully clear, and the river is not navigable. At a former period this stream must have formed one large lake covering the whole area which includes Derwentwater and Bassenthwaite; between which a flat alluvial plain is formed of the deposits of the river Greta, which now joins the Derwent from the east immediately below Derwentwater, and the Newlands Beck, which enters Bassenthwaite. In time of high flood this plain is said to have been submerged, and the two lakes thus reunited.

(4) A river Derwent rises in the Pennines near the borders of Northumberland and Durham, and, forming a large part of the boundary between these counties, takes a north-easterly course of 30 m. to the Tyne, which it joins 3 m. above Newcastle.

DERWENTWATER, EARL OF, an English title borne by the family of Radclyffe, or Radcliffe, from 1688 to 1716 when the 3rd earl was attainted and beheaded, and claimed by his descendants, adherents of the exiled house of Stewart, from that date until the death of the last male heir in 1814. Sir Francis Radclyffe, 3rd baronet (1625-1697), was the lineal descendant of Sir Nicholas Radclyffe, who acquired the extensive Derwentwater estates in 1417 through his marriage with the heiress of John de Derwentwater, and of Sir Francis Radclyffe, who was made a baronet in 1619. In 1688 Sir Francis was created Viscount Radclyffe and earl of Derwentwater by James II., and dying in 1697 was succeeded as 2nd earl by his eldest son Edward (1655-1705), who had married Lady Mary Tudor (d. 1726), a natural daughter of Charles II. The 2nd earl died in 1705, and was succeeded by his eldest son James (1689-1716), who was born in London on the 28th of June 1689, and was brought up at the court of the Stewarts in France as companion to Prince James Edward, the old Pretender. In 1710 he came to reside on his English estates, and in July 1712 was married to Anna Maria (d. 1723), daughter of Sir John Webb, baronet, of Odstock, Wiltshire. Joining without any hesitation in the Stewart rising of 1715, Derwentwater escaped arrest owing to the devotion of his tenantry, and in October, with about seventy followers, he joined Thomas Forster at Green-rig. Like Forster the earl was lacking in military experience, and when the rebels capitulated at Preston he was conveyed to London and impeached. Pleading guilty at his trial he was attainted and condemned to death. Great efforts were made to obtain a mitigation of the sentence, but the government was obdurate, and Derwentwater was beheaded on Tower Hill on the 24th of February 1716, declaring on the scaffold his devotion to the Roman Catholic religion and to King James III. The earl was very popular among his tenantry and in the neighbourhood of his residence, Dilston Hall. His gallant bearing and his sad fate have been celebrated in song and story, and the _aurora borealis_, which shone with exceptional brightness on the night of his execution, is known locally as "Lord Derwentwater's lights." He left an only son John, who, in spite of his father's attainder, assumed the title of earl of Derwentwater, and who died unmarried in 1731; and a daughter Alice Mary (d. 1760), who married in 1732 Robert James, 8th Baron Petre (1713-1742).

On the death of John Radclyffe in 1731 his uncle Charles (1693-1746), the only surviving son of the 2nd earl, took the title of earl of Derwentwater. Charles Radclyffe had shared the fate of his brother, the 3rd earl, at Preston in November 1715, and had been condemned to death for high treason; but, more fortunate than James, he had succeeded in escaping from prison, and had joined the Stewarts on the Continent. In 1724 he married Charlotte Maria (d. 1755), in her own right countess of Newburgh, and after spending some time in Rome, he was captured by an English ship in November 1745 whilst proceeding to join Charles Edward, the young Pretender, in Scotland. Condemned to death under his former sentence he was beheaded on the 8th of December 1746. His eldest son, James Bartholomew (1725-1786), who had shared his father's imprisonment, then claimed the title of earl of Derwentwater, and on his mother's death in 1755 became 3rd earl of Newburgh. His only son and successor, Anthony James (1757-1814), died without issue in 1814, when the title became extinct _de facto_ as well as _de jure_. Many of the forfeited estates in Northumberland and Cumberland had been settled upon Greenwich Hospital, and in 1749 a sum of £30,000 had been raised upon them for the benefit of the earl of Newburgh. The present representative of the Radclyffe family is Lord Petre, and in 1874 the bodies of the first three earls of Derwentwater were reburied in the family vault of the Petres at Thorndon, Essex.

In 1865 a woman appeared in Northumberland who claimed to be a grand-daughter of the 4th earl and, as there were no male heirs, to be countess of Derwentwater and owner of the estates. She said the 4th earl had not died in 1731 but had married and settled in Germany. Her story aroused some interest, and it was necessary to eject her by force from Dilston Hall.

See R. Patten, _History of the Late Rebellion_ (London, 1717); W. S. Gibson, _Dilston Hall, or Memoirs of James Radcliffe, earl of Derwentwater_ (London, 1848-1850); G. E. C(okayne), _Complete Peerage_ (Exeter, 1887-1898); and _Dictionary of National Biography_, vol. xlvii. (London, 1896).

DERWENTWATER, a lake of Cumberland, England, in the northern part of the celebrated Lake District (q.v. for the physical relations of the lake with the district at large). It is of irregular figure, approaching to an oval, about 3 m. in length and from ½ m. to 1¼ m. in breadth. The greatest depth is 70 ft. The lake is seen at one view, within an amphitheatre of mountains of varied outline, overlooked by others of greater height. Several of the lesser elevations near the lake are especially famous as view-points, such as Castle Head, Walla Crag, Ladder Brow and Cat Bells. The shores are well wooded, and the lake is studded with several islands, of which Lord's Island, Derwent Isle and St Herbert's are the principal. Lord's Island was the residence of the earls of Derwentwater. St Herbert's Isle receives its name from having been the abode of a holy man of that name mentioned by Bede as contemporary with St Cuthbert of Farne Island in the 7th century. Derwent Isle, about six acres in extent, contains a handsome residence surrounded by lawns, gardens and timber of large growth. The famous Falls of Lodore, at the upper end of the lake, consist of a series of cascades in the small Watendlath Beck, which rushes over an enormous pile of protruding crags from a height of nearly 200 ft. The "Floating Island" appears at intervals on the upper portion of the lake near the mouth of the beck. This singular phenomenon is supposed to owe its appearance to an accumulation of gas, formed by the decay of vegetable matter, detaching and raising to the surface the matted weeds which cover the floor of the lake at this point. The river Derwent (q.v.) enters the lake from the south and leaves it on the north, draining it through Bassenthwaite lake, to the Irish Sea. To the north-east of the lake lies the town of Keswick.

DES ADRETS, FRANÇOIS DE BEAUMONT, BARON (c. 1512-1587), French Protestant leader, was born in 1512 or 1513 at the château of La Frette (Isère). During the reign of Henry II. of France he served with distinction in the royal army and became colonel of the "legions" of Dauphiné, Provence and Languedoc. In 1562, however, he joined the Huguenots, not from religious conviction but probably from motives of ambition and personal dislike of the house of Guise. His campaign against the Catholics in 1562 was eminently successful. In June of that year Des Adrets was master of the greater part of Dauphiné. But his brilliant military qualities were marred by his revolting atrocities. The reprisals he exacted from the Catholics after their massacres of the Huguenots at Orange have left a dark stain upon his name. The garrisons that resisted him were butchered with every circumstance of brutality, and at Montbrison, in Forez, he forced eighteen prisoners to precipitate themselves from the top of the keep. Having alienated the affections of the Huguenots by his pride and violence, he entered into communication with the Catholics, and declared himself openly in favour of conciliation. On the 10th of January 1563 he was arrested on suspicion by some Huguenot officers and confined in the citadel of Nîmes. He was liberated at the edict of Amboise in the following March, and, distrusted alike by Huguenots and Catholics, retired to the château of La Frette, where he died, a Catholic, on the 2nd of February 1587.

AUTHORITIES.--J. Roman, _Documents inédits sur le baron des Adrets_ (1878); and memoirs and histories of the time. See also Guy Allard, _Vie de François de Beaumont_ (1675); l'abbé J. C. Martin, _Histoire politique et militaire de François de Beaumont_ (1803); Eugène and Émile Haag, _La France protestante_ (2nd ed., 1877 seq.).

DESAIX DE VEYGOUX, LOUIS CHARLES ANTOINE (1768-1800), French general, was born of a noble though impoverished family. He received a military education at the school founded by Marshal d'Effiat, and entered the French royal army. During the first six years of his service the young officer devoted himself assiduously to duty and the study of his profession, and at the outbreak of the Revolution threw himself whole-heartedly into the cause of liberty. In spite of the pressure put upon him by his relatives, he refused to "emigrate," and in 1792 is found serving on Broglie's staff. The disgrace of this general nearly cost young Desaix his life, but he escaped the guillotine, and by his conspicuous services soon drew upon himself the favour of the Republican government. Like many other members of the old ruling classes who had accepted the new order of things, the instinct of command, joined to native ability, brought Desaix rapidly to high posts. By 1794 he had attained the rank of general of division. In the campaign of 1795 he commanded Jourdan's right wing, and in Moreau's invasion of Bavaria in the following year he held an equally important command. In the retreat which ensued when the archduke Charles won the battles of Amberg and Würzburg (see FRENCH REVOLUTIONARY WARS) Desaix commanded Moreau's rearguard, and later the fortress of Kehl, with the highest distinction, and his name became a household word, like those of Bonaparte, Jourdan, Hoche, Marceau and Kléber. Next year his initial successes were interrupted by the Preliminaries of Leoben, and he procured for himself a mission into Italy in order to meet General Bonaparte, who spared no pains to captivate the brilliant young general from the almost rival camps of Germany. Provisionally appointed commander of the "Army of England," Desaix was soon transferred by Bonaparte to the expeditionary force intended for Egypt. It was his division which bore the brunt of the Mameluke attack at the battle of the Pyramids, and he crowned his reputation by his victories over Murad Bey in Upper Egypt. Amongst the fellaheen he acquired the significant appellation of the "Just Sultan." When his chief handed over the command to Kléber and prepared to return to France, Desaix was one of the small party selected to accompany the future emperor. But, from various causes, it was many months before he could join the new Consul. The campaign of 1800 was well on its way to the climax when Desaix at last reported himself for duty in Italy. He was immediately assigned to the command of a corps of two infantry divisions. Three days later (June 14), detached, with Boudet's division, at Rivalta, he heard the cannon of Marengo on his right. Taking the initiative he marched at once towards the sound, meeting Bonaparte's staff officer, who had come to recall him, half way on the route. He arrived with Boudet's division at the moment when the Austrians were victorious all along the line. Exclaiming, "There is yet time to win another battle!" he led his three regiments straight against the enemy's centre. At the moment of victory Desaix was killed by a musket ball. Napoleon paid a just tribute to the memory of one of the most brilliant soldiers of that brilliant time by erecting the monuments of Desaix on the Place Dauphinè and the Place des Victoires in Paris.

See F. Martha-Beker, Comte de Mons, _Le Général L. C. A. Desaix_ (Paris, 1852).

DÉSAUGIERS, MARC ANTOINE MADELEINE (1772-1827), French dramatist and song-writer, son of Marc Antoine Désaugiers, a musical composer, was born at Fréjus (Var) on the 17th of November 1772. He studied at the Mazarin college in Paris, where he had for one of his teachers the critic Julien Louis Geoffroy. He entered the seminary Saint Lazare with a view to the priesthood, but soon gave up his intention. In his nineteenth year he produced in collaboration with his father a light opera (1791) adapted from the _Médecin malgré lui_ of Molière.

During the Revolution he emigrated to St Domingo, and during the negro revolt he was made prisoner, barely escaping with his life. He took refuge in the United States, where he supported himself by teaching the piano. In 1797 he returned to his native country, and in a very few years he became famous as a writer of comedies, operas and vaudevilles, which were produced in rapid succession at the Théâtre des Variétés and the Vaudeville. He also wrote convivial and satirical songs, which, though different in character, can only worthily be compared with those of Béranger. He was at one time president of the _Caveau_, a convivial society whose members were then chiefly drawn from literary circles. He had the honour of introducing Béranger as a member. In 1815 Désaugiers succeeded Pierre Yves Barré as manager of the Vaudeville, which prospered under his management until, in 1820, the opposition of the Gymnase proved too strong for him, and he resigned. He died in Paris on the 9th of August 1827.

Among his pieces maybe mentioned _Le Valet d'emprunt_ (1807); _Monsieur Vautour_ (1811); and _Le Règne d'un terme et le terme d'un règne_, aimed at Napoleon.

An edition of Désaugiers' _Chansons et Poésies diverses_ appeared in 1827. A new selection with a notice by Alfred de Bougy appeared in 1858. See also Sainte-Beuve's _Portraits contemporains_, vol. v.

DESAULT, PIERRE JOSEPH (1744-1795), French anatomist and surgeon, was born at Magny-Vernois (Haute Saône) on the 6th of February 1744. He was destined for the church, but his own inclination was towards the study of medicine; and, after learning something from the barber-surgeon of his native village, he was settled as an apprentice in the military hospital of Belfort, where he acquired some knowledge of anatomy and military surgery. Going to Paris when about twenty years of age, he opened a school of anatomy in the winter of 1766, the success of which excited the jealousy of the established teachers and professors, who endeavoured to make him give up his lectures. In 1776 he was admitted a member of the corporation of surgeons; and in 1782 he was appointed surgeon-major to the hospital _De la Charité_. Within a few years he was recognized as one of the leading surgeons of France. The clinical school of surgery which he instituted at the Hôtel Dieu attracted great numbers of students, not only from every part of France but also from other countries; and he frequently had an audience of about 600. He introduced many improvements into the practice of surgery, as well as into the construction of various surgical instruments. In 1791 he established a _Journal de chirurgerie_, edited by his pupils, which was a record of the most interesting cases that had occurred in his clinical school, with the remarks which he had made upon them in the course of his lectures. But in the midst of his labours he became obnoxious to some of the revolutionists, and he was, on some frivolous charge, denounced to the popular sections. After being twice examined, he was seized on the 28th of May 1793, while delivering a lecture, carried away from his theatre, and committed to prison in the Luxembourg. In three days, however, he was liberated, and permitted to resume his functions. He died in Paris on the 1st of June 1795, the story that his death was caused by poison being disproved by the autopsy carried out by his pupil, M. F. X. Bichat. A pension was settled on his widow by the republic. Together with François Chopart (1743-1795) he published a _Traité des maladies chirurgicales_ (1779), and Bichat published a digest of his surgical doctrines in _OEuvres chirurgicales de Desault_ (1798-1799).

DES BARREAUX, JACQUES VALLÉE, SIEUR (1602-1673), French poet, was born in Paris in 1602. His great-uncle, Geoffroy-Vallée, had been hanged in 1574 for the authorship of a book called _Le Fléau de la foy_. His nephew appears to have inherited his scepticism, which on one occasion nearly cost him his life. The peasants of Touraine attributed to the presence of the unbeliever an untimely frost that damaged the vines, and proposed to stone him. His authorship of the sonnet on "Pénitence," by which he is generally known, has been disputed. He had the further distinction of being the first of the lovers of Marion Delorme. He died at Chalon-sur-Saône on the 9th of May 1673.

See _Poésies de Des Barreaux_ (1904), edited by F. Lachèvre.

DESBOROUGH, JOHN (1608-1680), English soldier and politician, son of James Desborough of Eltisley, Cambridgeshire, and of Elizabeth Hatley of Over, in the same county, was baptized on the 13th of November 1608. He was educated for the law. On the 23rd of June 1636 he married Eltisley Jane, daughter of Robert Cromwell of Huntingdon, and sister of the future Protector. He took an active part in the Civil War when it broke out, and showed considerable military ability. In 1645 he was present as major in the engagement at Langport on the 10th of July, at Hambleton Hill on the 4th of August, and on the 10th of September he commanded the horse at the storming of Bristol. Later he took part in the operations round Oxford. In 1648 as colonel he commanded the forces at Great Yarmouth. He avoided all participation in the trial of the king in June 1649, being employed in the settlement of the west of England. He fought at Worcester as major-general and nearly captured Charles II. near Salisbury. After the establishment of the Commonwealth he was chosen, on the 17th of January 1652, a member of the committee for legal reforms. In 1653 he became a member of the Protectorate council of state, and a commissioner of the treasury, and was appointed one of the four generals at sea and a commissioner for the army and navy. In 1654 he was made constable of St Briavel's Castle in Gloucestershire. Next year he was appointed major-general over the west. He had been nominated a member of Barebones' parliament in 1653, and he was returned to the parliament of 1654 for Cambridgeshire, and to that of 1656 for Somersetshire. In July 1657 he became a member of the privy council, and in 1658 he accepted a seat in Cromwell's House of Lords. In spite of his near relationship to the Protector's family, he was one of the most violent opponents of the assumption by Cromwell of the royal title, and after the Protector's death, instead of supporting the interests and government of his nephew Richard Cromwell, he was, with Fleetwood, the chief instigator and organizer of the hostility of the army towards his administration, and forced him by threats and menaces to dissolve his parliament in April 1659. He was chosen a member of the council of state by the restored Rump, and made colonel and governor of Plymouth, but presenting with other officers a seditious petition from the army council, on the 5th of October, was about a week later dismissed. After the expulsion of the Rump by Fleetwood on the 13th of October he was chosen by the officers a member of the new administration and commissary-general of the horse. The new military government, however, rested on no solid foundation, and its leaders quickly found themselves without any influence. Desborough himself became an object of ridicule, his regiment even revolted against him, and on the return of the Rump he was ordered to quit London. At the restoration he was excluded from the act of indemnity but not included in the clause of pains and penalties extending to life and goods, being therefore only incapacitated from public employment. Soon afterwards he was arrested on suspicion of conspiring to kill the king and queen, but was quickly liberated. Subsequently he escaped to Holland, where he engaged in republican intrigues. Accordingly he was ordered home, in April 1666, on pain of incurring the charge of treason, and obeying was imprisoned in the Tower till February 1667, when he was examined before the council and set free. Desborough died in 1680. By his first wife, Cromwell's sister, he had one daughter and seven sons; he married a second wife in April 1658 whose name is unrecorded. Desborough was a good soldier and nothing more; and his only conception of government was by force and by the army. His rough person and manners are the constant theme of ridicule in the royalist ballads, and he is caricatured in Butler's _Hudibras_ and in the _Parable of the Lion and Fox_.

DESCARTES, RENÉ (1596-1650), French philosopher, was born at La Haye, in Touraine, midway between Tours and Poitiers, on the 31st of March 1596, and died at Stockholm on the 11th of February 1650. The house where he was born is still shown, and a _métairie_ about 3 m. off retains the name of Les Cartes. His family on both sides was of Poitevin descent. Joachim Descartes, his father, having purchased a commission as counsellor in the parlement of Rennes, introduced the family into that demi-noblesse of the robe which, between the bourgeoisie and the high nobility, maintained a lofty rank in French society. He had three children, a son who afterwards succeeded to his father in the parlement, a daughter who married a M. du Crevis, and René, after whose birth the mother died.

Early years.

Descartes, known as Du Perron, from a small estate destined for his inheritance, soon showed an inquisitive mind. From 1604 to 1612 he studied at the school of La Flêche, which Henry IV. had lately founded and endowed for the Jesuits. He enjoyed exceptional privileges; his feeble health excused him from the morning duties, and thus early he acquired the habit of reflection in bed, which clung to him throughout life. Even then he had begun to distrust the authority of tradition and his teachers. Two years before he left school he was selected as one of the twenty-four who went forth to receive the heart of Henry IV. as it was borne to its resting-place at La Flêche. At the age of sixteen he went home to his father, who was now settled at Rennes, and had married again. During the winter of 1612 he completed his preparations for the world by lessons in horsemanship and fencing; and then started as his own master to taste the pleasures of Parisian life. Fortunately he went to no perilous lengths; the worst we hear of is a passion for gaming. Here, too, he made the acquaintance of Claude Mydorge, one of the foremost mathematicians of France, and renewed an early intimacy with Marin Mersenne (q.v.), now Father Mersenne, of the order of Minim friars. The withdrawal of Mersenne in 1614 to a post in the provinces was the signal for Descartes to abandon social life and shut himself up for nearly two years in a secluded house of the faubourg St Germain. Accident betrayed the secret of his retirement; he was compelled to leave his mathematical investigations, and to take part in entertainments, where the only thing that chimed in with his theorizing reveries was the music. French politics were at that time characterized by violence and intrigue to such an extent that Paris was no fit place for a student, and there was little honourable prospect for a soldier. Accordingly, in May 1617, Descartes set out for the Netherlands and took service in the army of Prince Maurice of Orange. At Breda he enlisted as a volunteer, and the first and only pay which he accepted he kept as a curiosity through life. There was a lull in the war, and the Netherlands was distracted by the quarrels of Gomarists and Arminians. During the leisure thus arising, Descartes one day had his attention drawn to a placard in the Dutch tongue; as the language, of which he never became perfectly master, was then strange to him, he asked a bystander to interpret it into either French or Latin. The stranger, Isaac Beeckman, principal of the college of Dort, offered to do so into Latin, if the inquirer would bring him a solution of the problem,--for the advertisement was one of those challenges which the mathematicians of the age were accustomed to throw down to all comers, daring them to discover a geometrical mystery known as they fancied to themselves alone. Descartes promised and fulfilled; and a friendship grew up between him and Beeckman--broken only by the dishonesty of the latter, who in later years took credit for the novelty contained in a small essay on music (_Compendium Musicae_) which Descartes wrote at this period and entrusted to Beeckman.[1]

After spending two years in Holland as a soldier in a period of peace, Descartes, in July 1619, attracted by the news of the impending struggle between the house of Austria and the Protestant princes, consequent upon the election of the palatine of the Rhine to the kingdom of Bohemia, set out for upper Germany, and volunteered into the Bavarian service. The winter of 1619, spent in quarters at Neuburg on the Danube, was the critical period in his life. Here, in his warm room (_dans un poêle_), he indulged those meditations which afterwards led to the _Discourse of Method_. It was here that, on the eve of St Martin's day, he "was filled with enthusiasm, and discovered the foundations of a marvellous science." He retired to rest with anxious thoughts of his future career, which haunted him through the night in three dreams that left a deep impression on his mind. The date of his philosophical conversion is thus fixed to a day. But as yet he had only glimpses of a logical method which should invigorate the syllogism by the co-operation of ancient geometry and modern algebra. For during the year that elapsed before he left Swabia (and whilst he sojourned at Neuburg and Ulm), and amidst his geometrical studies, he would fain have gathered some knowledge of the mystical wisdom attributed to the Rosicrucians; but the Invisibles, as they called themselves, kept their secret. He was present at the battle of Weisser Berg (near Prague), where the hopes of the elector palatine were blasted (November 8, 1620), passed the winter with the army in southern Bohemia, and next year served in Hungary under Karl Bonaventura de Longueval, Graf von Buquoy or Boucquoi (1571-1621). On the death of this general Descartes quitted the imperial service, and in July 1621 began a peaceful tour through Moravia, the borders of Poland, Pomerania, Brandenburg, Holstein and Friesland, from which he reappeared in February 1622 in Belgium, and betook himself directly to his father's home at Rennes in Brittany.

At Rennes Descartes found little to interest him; and, after he had visited the maternal estate of which his father now put him in possession, he went to Paris, where he found the Rosicrucians the topic of the hour, and heard himself credited with partnership in their secrets. A short visit to Brittany enabled him, with his father's consent, to arrange for the sale of his property in Poitou. The proceeds were invested in such a way at Paris as to bring him in a yearly income of between 6000 and 7000 francs (equal now to more than £500). Towards the end of the year Descartes was on his way to Italy. The natural phenomena of Switzerland, and the political complications in the Valtellina, where the Catholic inhabitants had thrown off the yoke of the Grisons and called in the Papal and Spanish troops to their assistance, delayed him some time; but he reached Venice in time to see the ceremony of the doge's wedlock with the Adriatic. After paying his vows at Loretto, he came to Rome, which was then on the eve of a year of jubilee--an occasion which Descartes seized to observe the variety of men and manners which the city then embraced within its walls. In the spring of 1625 he returned home by Mont Cenis, observing the avalanches,[2] instead of, as his relatives hoped, securing a post in the French army in Piedmont.

For an instant Descartes seems to have concurred in the plan of purchasing a post at Châtellerault, but he gave up the idea, and settled in Paris (June 1625), in the quarter where he had sought seclusion before. By this time he had ceased to devote himself to pure mathematics, and in company with his friends Mersenne and Mydorge was deeply interested in the theory of the refraction of light, and in the practical work of grinding glasses of the best shape suitable for optical instruments. But all the while he was engaged with reflections on the nature of man, of the soul and of God, and for a while he remained invisible even to his most familiar friends. But their importunity made a hermitage in Paris impossible; a graceless friend even surprised the philosopher in bed at eleven in the morning meditating and taking notes. In disgust, Descartes started for the west to take part in the siege of La Rochelle, and entered the city with the troops (October 1628). A meeting at which he was present after his return to Paris decided his vocation. He had expressed an opinion that the true art of memory was not to be gained by technical devices, but by a philosophical apprehension of things; and the cardinal de Berulle, the founder of the Congregation of the Oratory, was so struck by the tone of the remarks as to impress upon the speaker the duty of spending his life in the examination of truth. Descartes accepted the philosophic mission, and in the spring of 1629 he settled in Holland. His financial affairs he had entrusted to the care of the abbé Picot, and as his literary and scientific representative he adopted Mersenne.

Till 1649 Descartes lived in Holland. Thrice only did he revisit France--in 1644, 1647 and 1648. The first of these occasions was in order to settle family affairs after the death of his father in 1640. The second brief visit, in 1647, partly on literary, partly on family business, was signalized by the award of a pension of 3000 francs, obtained from the royal bounty by Cardinal Mazarin. The last visit in 1648 was less fortunate. A royal order summoned him to France for new honours--an additional pension and a permanent post--for his fame had by this time gone abroad, and it was the age when princes sought to attract genius and learning to their courts. But when Descartes arrived, he found Paris rent asunder by the civil war of the Fronde. He paid the costs of his royal parchment, and left without a word of reproach. The only other occasions on which he was out of the Netherlands were in 1630, when he made a flying visit to England to observe for himself some alleged magnetic phenomena, and in 1634, when he took an excursion to Denmark.

During his residence in Holland he lived at thirteen different places, and changed his abode twenty-four times. In the choice of these spots two motives seem to have influenced him--the neighbourhood of a university or college, and the amenities of the situation. Among these towns were Franeker in Friesland, Harderwyk, Deventer, Utrecht, Leiden, Amersfoort, Amsterdam, Leeuwarden in Friesland. His favourite residences were Endegeest, Egmond op den Hoef and Egmond the Abbey (west of Zaandam).

The time thus spent seems to have been on the whole happy, even allowing for warm discussions with the mathematicians and metaphysicians of France, and for harassing controversies in the Netherlands. Friendly agents--chiefly Catholic priests--were the intermediaries who forwarded his correspondence from Dort, Haarlem, Amsterdam and Leiden to his proper address, which he kept completely secret; and Father Mersenne sent him objections and questions. His health, which in his youth had been bad, improved. "I sleep here ten hours every night," he writes from Amsterdam, "and no care ever shortens my slumber." "I take my walk every day through the confusion of a great multitude with as much freedom and quiet as you could find in your rural avenues."[3] At his first coming to Franeker he arranged to get a cook acquainted with French cookery; but, to prevent misunderstanding, it may be added that his diet was mainly vegetarian, and that he rarely drank wine. New friends gathered round him who took a keen interest in his researches. Once only do we find him taking an interest in the affairs of his neighbours,--to ask pardon from the government for a homicide.[4] He continued the profession of his religion. Sometimes from curiosity he went to the ministrations of anabaptists,[5] to hear the preaching of peasants and artisans. He carried few books to Holland with him, but a Bible and the _Summa_ of Thomas Aquinas were amongst them.[6] One of the recommendations of Egmond the Abbey was the free exercise there allowed to the Catholic religion. At Franeker his house was a small château, "separated by a moat from the rest of the town, where the mass could be said in safety."[7] And one motive in favour of accepting an invitation to England lay in the alleged leanings of Charles I. to the older church.

The best account of Descartes's mental history during his life in Holland is contained in his letters, which extend over the whole period, and are particularly frequent in the latter half. The majority of them are addressed to Mersenne, and deal with problems of physics, musical theory (in which he took a special interest), and mathematics. Several letters between 1643 and 1649 are addressed to the princess Elizabeth, the eldest daughter of the ejected elector palatine, who lived at The Hague, where her mother maintained the semblance of a royal court. The princess was obliged to quit Holland, but kept up a philosophical correspondence with Descartes. It is to her that the _Principles of Philosophy_ were dedicated; and in her alone, according to Descartes, were united those generally separated talents for metaphysics and for mathematics which are so characteristically co-operative in the Cartesian system. Two Dutch friends, Constantijn Huygens (von Zuylichem), father of the more celebrated Huygens, and Hoogheland, figure amongst the correspondents, not to mention various savants, professors and churchmen (particularly Jesuits).

His residence in the Netherlands fell in the most prosperous and brilliant days of the Dutch state, under the stadtholdership of Frederick Henry (1625-1647). Abroad its navigators monopolized the commerce of the world, and explored unknown seas; at home the Dutch school of painting reached its acme in Rembrandt (1607-1669); and the philological reputation of the country was sustained by Grotius, Vossius and the elder Heinsius. And yet, though Rembrandt's "Nightwatch" is dated the very year after the publication of the _Meditations_, not a word in Descartes breathes of any work of art or historical learning. The contempt of aesthetics and erudition is characteristic of the most typical members of what is known as the Cartesian school, especially Malebranche. Descartes was not in any strict sense a reader. His wisdom grew mainly out of his own reflections and experiments. The story of his disgust when he found that Queen Christina devoted some time every day to the study of Greek under the tuition of Vossius is at least true in substance.[8] It gives no evidence of science, he remarks, to possess a tolerable knowledge of the Roman tongue, such as once was possessed by the populace of Rome.[9] In all his travels he studied only the phenomena of nature and human life. He was a spectator rather than an actor on the stage of the world. He entered the army, merely because the position gave a vantage-ground from which to make his observations. In the political interests which these contests involved he took no part; his favourite disciple, the princess Elizabeth, was the daughter of the banished king, against whom he had served in Bohemia; and Queen Christina, his second royal follower, was the daughter of Gustavus Adolphus.

Thus Descartes is a type of that spirit of science to which erudition and all the heritage of the past seem but elegant trifling. The science of Descartes was physics in all its branches, but especially as applied to physiology. Science, he says, may be compared to a tree; metaphysics is the root, physics is the trunk, and the three chief branches are mechanics, medicine and morals,--the three applications of our knowledge to the outward world, to the human body, and to the conduct of life.[10]

Such then was the work that Descartes had in view in Holland. His residence was generally divided into two parts--one his workshop for science, the other his reception-room for society. "Here are my books," he is reported to have told a visitor, as he pointed to the animals he had dissected. He worked hard at his book on refraction, and dissected the heads of animals in order to explain imagination and memory, which he considered physical processes.[11] But he was not a laborious student. "I can say with truth," he writes to the princess Elizabeth,[12] "that the principle which I have always observed in my studies, and which I believe has helped me most to gain what knowledge I have, has been never to spend beyond a very few hours daily in thoughts which occupy the imagination, and a very few hours yearly in those which occupy the understanding, and to give all the rest of my time to the relaxation of the senses and the repose of the mind." But his expectations from the study of anatomy and physiology went a long way. "The conservation of health," he writes in 1646, "has always been the principal end of my studies."[13] In 1629 he asks Mersenne to take care of himself "till I find out if there is any means of getting a medical theory based on infallible demonstrations, which is what I am now inquiring."[14] Astronomical inquiries in connexion with optics, meteorological phenomena, and, in a word, the whole field of natural laws, excited his desire to explain them. His own observation, and the reports of Mersenne, furnished his data. Of Bacon's demand for observation and collection of facts he is an imitator; and he wishes (in a letter of 1632) that "some one would undertake to give a history of celestial phenomena after the method of Bacon, and describe the sky exactly as it appears at present, without introducing a single hypothesis."[15]

He had several writings in hand during the early years of his residence in Holland, but the main work of this period was a physical doctrine of the universe which he termed _The World_. Shortly after his arrival he writes to Mersenne that it will probably be finished in 1633, but meanwhile asks him not to disclose the secret to his Parisian friends. Already anxieties appear as to the theological verdict upon two of his fundamental views--the infinitude of the universe, and the earth's rotation round the sun.[16] But towards the end of year 1633 we find him writing as follows:--"I had intended sending you my _World_ as a New Year's gift, and a fortnight ago I was still minded to send you a fragment of the work, if the whole of it could not be transcribed in time. But I have just been at Leyden and Amsterdam to ask after Galileo's cosmical system as I imagined I had heard of its being printed last year in Italy. I was told that it had been printed, but that every copy had been at the same time burnt at Rome, and that Galileo had been himself condemned to some penalty."[17] He has also seen a copy of Galileo's condemnation at Liége (September 20, 1633), with the words "although he professes that the [Copernican] theory was only adopted by him as a hypothesis." His friend Beeckman lent him a copy of Galileo's work, which he glanced through in his usual manner with other men's books; he found it good, and "failing more in the points where it follows received opinions than where it diverges from them."[18] The consequence of these reports of the hostility of the church led him to abandon all thoughts of publishing. _The World_ was consigned to his desk; and although doctrines in all essential respects the same constitute the physical portion of his _Principia_, it was not till after the death of Descartes that fragments of the work, including _Le Monde_, or a treatise on light, and the physiological tracts _L'Homme_ and _La Formation du foetus_, were given to the world by his admirer Claude Clerselier (1614-1684) in 1664. Descartes was not disposed to be a martyr; he had a sincere respect for the church, and had no wish to begin an open conflict with established doctrines.

In 1636 Descartes had resolved to publish some specimens of the fruits of his method, and some general observations on its nature which, under an appearance of simplicity, might sow the good seed of more adequate ideas on the world and man. "I should be glad," he says, when talking of a publisher,[19] "if the whole book were printed in good type, on good paper, and I should like to have at least 200 copies for distribution. The book will contain four essays, all in French, with the general title of 'Project of a Universal science, capable of raising our nature to its highest perfection; also Dioptrics, Meteors and Geometry, wherein the most curious matters which the author could select as a proof of the universal science which he proposes are explained in such a way that even the unlearned may understand them.'" The work appeared anonymously at Leiden (published by Jean Maire) in 1637, under the modest title of _Essais philosophiques_; and the project of a universal science becomes the _Discours de la méthode pour bien conduire sa raison et chercher la vérité dans les sciences_. In 1644 it appeared in a Latin version, revised by Descartes, as _Specimina philosophica_. A work so widely circulated by the author naturally attracted attention, but in France it was principally the mathematicians who took it up, and their criticisms were more pungent than complimentary. Fermat, Roberval and Desargues took exception in their various ways to the methods employed in the geometry, and to the demonstrations of the laws of refraction given in the Dioptrics and Meteors. The dispute on the latter point between Fermat and Descartes was continued, even after the philosopher's death, as late as 1662. In the youthful Dutch universities the effect of the essays was greater.

Spread of Cartesianism.

The first public teacher of Cartesian views was Henri Renery, a Belgian, who at Deventer and afterwards at Utrecht had introduced the new philosophy which he had learned from personal intercourse with Descartes. Renery only survived five years at Utrecht, and it was reserved for Heinrich Regius (van Roy)--who in 1638 had been appointed to the new chair of botany and theoretical medicine at Utrecht, and who visited Descartes at Egmond in order more thoroughly to learn his views--to throw down the gauntlet to the adherents of the old methods. With more eloquence than judgment, he propounded theses bringing into relief the points in which the new doctrines clashed with the old. The attack was opened by Gisbert Voët, foremost among the orthodox theological professors and clergy of Utrecht. In 1639 he published a series of arguments against atheism, in which the Cartesian views were not obscurely indicated as perilous for the faith, though no name was mentioned. Next year he persuaded the magistracy to issue an order forbidding Regius to travel beyond the received doctrine. The magisterial views seem to have prevailed in the professoriate, which formally in March 1642 expressed its disapprobation of the new philosophy as well as of its expositors. As yet Descartes was not directly attacked. Voët now issued, under the name of Martin Schoock, one of his pupils, a pamphlet with the title of _Methodus novae philosophiae Renati Descartes_, in which atheism and infidelity were openly declared to be the effect of the new teaching. Descartes replied to Voët directly in a letter, published at Amsterdam in 1643. He was summoned before the magistrates of Utrecht to defend himself against charges of irreligion and slander. What might have happened we cannot tell; but Descartes threw himself on the protection of the French ambassador and the prince of Orange, and the city magistrates, from whom he vainly demanded satisfaction in a dignified letter,[20] were snubbed by their superiors. About the same time (April 1645) Schoock was summoned before the university of Groningen, of which he was a member, and forthwith disavowed the more abusive passages in his book. So did the effects of the _odium theologicum_, for the meanwhile at least, die away.

Discourse of Method, and Meditations.

In the _Discourse of Method_ Descartes had sketched the main points in his new views, with a mental autobiography which might explain their origin, and with some suggestions as to their applications. His second great work,. _Meditations on the First Philosophy_, which had been begun soon after his settlement in the Netherlands, expounded in more detail the foundations of his system, laying especial emphasis on the priority of mind to body, and on the absolute and ultimate dependence of mind as well as body on the existence of God. In 1640 a copy of the work in manuscript was despatched to Paris, and Mersenne was requested to lay it before as many thinkers and scholars as he deemed desirable, with a view to getting their views upon its argument and doctrine. Descartes soon had a formidable list of objections to reply to. Accordingly, when the work was published at Paris in August 1641, under the title of _Meditationes de prima philosophia ubi de Dei existentia et animae immortalitate_ (though it was in fact not the _immortality_ but the _immateriality_ of the mind, or, as the second edition described it, _animae humanae a corpore distinctio_, which was maintained), the title went on to describe the larger part of the book as containing various objections of learned men, with the replies of the author. These objections in the first edition are arranged under six heads: the first came from Caterus, a theologian of Louvain; the second and sixth are anonymous criticisms from various hands; whilst the third, fourth and fifth belong respectively to Hobbes, Arnauld and Gassendi. In the second edition appeared the seventh--objections from Père Bourdin, a Jesuit teacher of mathematics in Paris; and subsequently another set of objections, known as those of _Hyperaspistes_, was included in the collection of Descartes's letters. The anonymous objections are very much the statement of common-sense against philosophy; those of Caterus criticize the Cartesian argument from the traditional theology of the church; those of Arnauld are an appreciative inquiry into the bearings and consequences of the meditations for religion and morality; while those of Hobbes (q.v.) and Gassendi--both somewhat senior to Descartes and with a dogmatic system of their own already formed--are a keen assault upon the spiritualism of the Cartesian position from a generally "sensational" standpoint. The criticisms of the last two are the criticisms of a hostile school of thought; those of Arnauld are the difficulties of a possible disciple.

The Principia.

In 1644 the third great work of Descartes, the _Principia philosophiae_, appeared at Amsterdam. Passing briefly over the conclusions arrived at in the _Meditations_, it deals in its second, third and fourth parts with the general principles of physical science, especially the laws of motion, with the theory of vortices, and with the phenomena of heat, light, gravity, magnetism, electricity, &c., upon the earth. This work exhibits some curious marks of caution. Undoubtedly, says Descartes, the world was in the beginning created in all its perfection. "But yet as it is best, if we wish to understand the nature of plants or of men, to consider how they may by degrees proceed from seeds, rather than how they were created by God in the beginning of the world, so, if we can excogitate some extremely simple and comprehensible principles, out of which, as if they were seeds, we can prove that stars, and earth and all this visible scene could have originated, although we know full well that they never did originate in such a way, we shall in that way expound their nature far better than if we merely described them as they exist at present."[21] The Copernican theory is rejected in name, but retained in substance. The earth, or other planet, does not actually move round the sun; yet it is carried round the sun in the subtle matter of the great vortex, where it lies in equilibrium,--carried like the passenger in a boat, who may cross the sea and yet not rise from his berth.

In 1647 the difficulties that had arisen at Utrecht were repeated on a smaller scale at Leiden. There the Cartesian innovations had found a patron in Adrian Heerebord, and were openly discussed in theses and lectures. The theological professors took the alarm at passages in the _Meditations_; an attempt to prove the existence of God savoured, as they thought, of atheism and heresy. When Descartes complained to the authorities of this unfair treatment,[22] the only reply was an order by which all mention of the name of Cartesianism, whether favourable or adverse, was forbidden in the university. This was scarcely what Descartes wanted, and again he had to apply to the prince of Orange, whereupon the theologians were asked to behave with civility, and the name of Descartes was no longer proscribed. But other annoyances were not wanting from unfaithful disciples and unsympathetic critics. The _Instantiae_ of Gassendi appeared at Amsterdam in 1644 as a reply to the reply which Descartes had published of his previous objections; and the publication by Heinrich Regius of his work on physical philosophy (_Fundamenta physices_, 1646) gave the world to understand that he had ceased to be a thorough adherent of the philosophy which he had so enthusiastically adopted.

It was about 1648 that Descartes lost his friends Mersenne and Mydorge by death. The place of Mersenne as his Parisian representative was in the main taken by Claude Clerselier (the French translator of the Objections and Responses), whom he had become acquainted with in Paris. Through Clerselier he came to know Pierre Chanut, who in 1645 was sent as French ambassador to the court of Sweden. Queen Christina was not yet twenty, and took a lively if a somewhat whimsical interest in literary and philosophical culture. Through Chanut, with whom she was on terms of familiarity, she came to hear of Descartes, and a correspondence which the latter nominally carried on with the ambassador was in reality intended for the eyes of the queen. The correspondence took an ethical tone. It began with a long letter on love in all its aspects (February 1647),[23] a topic suggested by Chanut, who had been discussing it with the queen; and this was soon followed by another to Christina herself on the chief good. An essay on the passions of the mind (_Passions de l'âme_), which had been written originally for the princess Elizabeth, in development of some ethical views suggested by the _De vita beata_ of Seneca, was enclosed at the same time for Chanut. It was a draft of the work published in 1650 under the same title. Philosophy, particularly that of Descartes, was becoming a fashionable _divertissement_ for the queen and her courtiers, and it was felt that the presence of the sage himself was necessary to complete the good work of education. An invitation to the Swedish court was urged upon Descartes, and after much hesitation accepted; a vessel of the royal navy was ordered to wait upon him, and in September 1649 he left Egmond for the north.

Death.

The position on which he entered at Stockholm was unsuited for a man who wished to be his own master. The young queen wanted Descartes to draw up a code for a proposed academy of the sciences, and to give her an hour of philosophic instruction every morning at five. She had already determined to create him a noble, and begun to look out an estate in the lately annexed possessions of Sweden on the Pomeranian coast. But these things were not to be. His friend Chanut fell dangerously ill; and Descartes, who devoted himself to attend in the sick-room, was obliged to issue from it every morning in the chill northern air of January, and spend an hour in the palace library. The ambassador recovered, but Descartes fell a victim to the same disease, inflammation of the lungs. The last time he saw the queen was on the 1st of February 1650, when he handed to her the statutes he had drawn up for the proposed academy. On the 11th of February he died. The queen wished to bury him at the feet of the Swedish kings, and to raise a costly mausoleum in his honour; but these plans were overruled, and a plain monument in the Catholic cemetery was all that marked the place of his rest. Sixteen years after his death the French treasurer d'Alibert made arrangements for the conveyance of the ashes to his native land; and in 1667 they were interred in the church of Ste Geneviève du Mont, the modern Pantheon. In 1819, after being temporarily deposited in a stone sarcophagus in the court of the Louvre during the Revolutionary epoch, they were transferred to St Germain-des-Près, where they now repose between Montfaucon and Mabillon. A monument was raised to his memory at Stockholm by Gustavus III.; and a modern statue has been erected to him at Tours, with an inscription on the pedestal: "Je pense, donc je suis."

Descartes never married, and had little of the amorous in his temperament. He has alluded to a childish fancy for a young girl with a slight obliquity of vision; but he only mentions it _à propos_ of the consequent weakness which led him to associate such a defect with beauty.[24] In person he was small, with large head, projecting brow, prominent nose, and eyes wide apart, with black hair coming down almost to his eyebrows. His voice was feeble. He usually dressed in black, with unobtrusive propriety.

_Philosophy._--The end of all study, says Descartes, in one of his earliest writings, ought to be to guide the mind to form true and sound judgments on every thing that may be presented to it.[25] The sciences in their totality are but the intelligence of man; and all the details of knowledge have no value save as they strengthen the understanding. The mind is not for the sake of knowledge, but knowledge for the sake of the mind. This is the reassertion of a principle which the middle ages had lost sight of--that knowledge, if it is to have any value, must be intelligence, and not erudition.

Mathematics.

But how is intelligence, as opposed to erudition, possible? The answer to that question is the method of Descartes. That idea of a method grew up with his study of geometry and arithmetic,--the only branches of knowledge which he would allow to be "made sciences." But they did not satisfy his demand for intelligence. "I found in them," he says, "different propositions on numbers of which, after a calculation, I perceived the truth; as for the figures, I had, so to speak, many truths put before my eyes, and many others concluded from them by analogy; but it did not seem to me that they told my mind with sufficient clearness why the things were as I was shown, and by what means their discovery was attained."[26] The mathematics of which he thus speaks included the geometry of the ancients, as it had been handed down to the modern world, and arithmetic with the developments it had received in the direction of algebra. The ancient geometry, as we know it, is a wonderful monument of ingenuity--a series of _tours de force_, in which each problem to all appearance stands alone, and, if solved, is solved by methods and principles peculiar to itself. Here and there particular curves, for example, had been obliged to yield the secret of their tangent; but the ancient geometers apparently had no consciousness of the general bearings of the methods which they so successfully applied. Each problem was something unique; the elements of transition from one to another were wanting; and the next step which mathematics had to make was to find some method of reducing, for instance, all curves to a common notation. When that was found, the solution of one problem would immediately entail the solution of all others which belonged to the same series as itself.

The arithmetical half of mathematics, which had been gradually growing into algebra, and had decidedly established itself as such in the _Ad logisticen speciosam notae priores_ of François Vieta (1540-1603), supplied to some extent the means of generalizing geometry. And the algebraists or arithmeticians of the 16th century, such as Luca Pacioli (Lucas de Borgo), Geronimo or Girolamo Cardano (1501-1576), and Niccola Tartaglia (1506-1559), had used geometrical constructions to throw light on the solution of particular equations. But progress was made difficult, in consequence of the clumsy and irregular nomenclature employed. With Descartes the use of exponents as now employed for denoting the powers of a quantity becomes systematic; and without some such step by which the homogeneity of successive powers is at once recognized, the binomial theorem could scarcely have been detected. The restriction of the early letters of the alphabet to known, and of the late letters to unknown, quantities is also his work. In this and other details he crowns and completes, in a form henceforth to be dominant for the language of algebra, the work of numerous obscure predecessors, such as Étienne de la Roche, Michael Stifel or Stiefel (1487-1567), and others.

Having thus perfected the instrument, his next step was to apply it in such a way as to bring uniformity of method into the isolated and independent operations of geometry. "I had no intention,"[27] he says in the _Method_, "of attempting to master all the particular sciences commonly called mathematics; but as I observed that, with all differences in their objects, they agreed in considering merely the various relations or proportions subsisting among these objects, I thought it best for my purpose to consider these relations in the most general form possible, without referring them to any objects in

## particular except such as would most facilitate the knowledge of them.

Perceiving further, that in order to understand these relations I should sometimes have to consider them one by one, and sometimes only to bear them in mind or embrace them in the aggregate, I thought that, in order the better to consider them individually, I should view them as subsisting between straight lines, than which I could find no objects more simple, or capable of being more distinctly represented to my imagination and senses; and on the other hand that, in order to retain them in the memory or embrace an aggregate of many, I should express them by certain characters, the briefest possible." Such is the basis of the algebraical or modern analytical geometry. The problem of the curves is solved by their reduction to a problem of straight lines; and the locus of any point is determined by its distance from two given straight lines--the axes of co-ordinates. Thus Descartes gave to modern geometry that abstract and general character in which consists its superiority to the geometry of the ancients. In another question connected with this, the problem of drawing tangents to any curve, Descartes was drawn into a controversy with Pierre (de) Fermat (1601-1663), Gilles Persone de Roberval (1602-1675), and Girard Desargues (1593-1661). Fermat and Descartes agreed in regarding the tangent to a curve as a secant of that curve with the two points of intersection coinciding, while Roberval regarded it as the direction of the composite movement by which the curve can be described. Both these methods, differing from that now employed, are interesting as preliminary steps towards the method of fluxions and the differential calculus. In pure algebra Descartes expounded and illustrated the general methods of solving equations up to those of the fourth degree (and believed that his method could go beyond), stated the law which connects the positive and negative roots of an equation with the changes of sign in the consecutive terms, and introduced the method of indeterminate coefficients for the solution of equations.[28] These innovations have been attributed on inadequate evidence to other algebraists, e.g. William Oughtred (1575-1660) and Thomas Harriot (1560-1621).

The _Geometry_ of Descartes, unlike the other parts of his essays, is not easy reading. It dashes at once into the middle of the subjects with the examination of a problem which had baffled the ancients, and seems as if it were tossed at the heads of the French geometers as a challenge. An edition of it appeared subsequently, with notes by his friend Florimond de Beaune (1601-1652), calculated to smooth the difficulties of the work. All along mathematics was regarded by Descartes rather as the envelope than the foundation of his method; and the "universal mathematical science" which he sought after was only the prelude of a universal science of all-embracing character.[29]

Descartes' method.

The method of Descartes rests upon the proposition that all the objects of our knowledge fall into series, of which the members are more or less known by means of one another. In every such series or group there is a dominant element, simple and irresoluble, the standard on which the rest of the series depends, and hence, so far as that group or series is concerned, absolute. The other members of the group are relative and dependent, and only to be understood as in various degrees subordinate to the primitive conception. The characteristic by which we recognize the fundamental element in a series is its intuitive or self-evident character; it is given by "the evident conception of a healthy and attentive mind so clear and distinct that no doubt is left."[30] Having discovered this prime or absolute member of the group, we proceed to consider the degrees in which the other members enter into relation with it. Here deduction comes into play to show the dependence of one term upon the others; and, in the case of a long chain of intervening links, the problem for intelligence is so to enunciate every element, and so to repeat the connexion that we may finally grasp all the links of the chain in one. In this way we, as it were, bring the causal or primal term and its remotest dependent immediately together, and raise a derivative knowledge into one which is primary and intuitive. Such are the four points of Cartesian method:--(1) Truth requires a clear and distinct conception of its object, excluding all doubt; (2) the objects of knowledge naturally fall into series or groups; (3) in these groups investigation must begin with a simple and indecomposable element, and pass from it to the more complex and relative elements; (4) an exhaustive and immediate grasp of the relations and interconnexion of these elements is necessary for knowledge in the fullest sense of that word.[31]

"There is no question," he says in anticipation of Locke and Kant, "more important to solve than that of knowing what human knowledge is and how far it extends." "This is a question which ought to be asked at least once in their lives by all who seriously wish to gain wisdom. The inquirer will find that the first thing to know is intellect, because on it depends the knowledge of all other things. Examining next what immediately follows the knowledge of pure intellect, he will pass in review all the other means of knowledge, and will find that they are two (or three), the imagination and the senses (and the memory). He will therefore devote all his care to examine and distinguish these three means of knowledge; and seeing that truth and error can, properly speaking, be only in the intellect, and that the two other modes of knowledge are only occasions, he will carefully avoid whatever can lead him astray."[32] This separation of intellect from sense, imagination and memory is the cardinal precept of the Cartesian logic; it marks off clear and distinct (i.e. adequate and vivid) from obscure, fragmentary and incoherent conceptions.

Fundamental principles of philosophy.

The _Discourse of Method_ and the _Meditations_ apply what the _Rules for the Direction of the Mind_ had regarded in particular instances to our conceptions of the world as a whole. They propose, that is, to find a simple and indecomposable point, or absolute element, which gives to the world and thought their order and systematization. The grandeur of this attempt is perhaps unequalled in the annals of philosophy. The three main steps in the argument are the veracity of our thought when that thought is true to itself, the inevitable uprising of thought from its fragmentary aspects in our habitual consciousness to the infinite and perfect existence which God is, and the ultimate reduction of the material universe to extension and local movement. There are the central dogmas of logic, metaphysics and physics, from which start the subsequent inquiries of Locke, Leibnitz and Newton. They are also the direct antitheses to the scepticism of Montaigne and Pascal, to the materialism of Gassendi and Hobbes, and to the superstitious anthropomorphism which defaced the reawakening sciences of nature. Descartes laid down the lines on which modern philosophy and science were to build. But himself no trained metaphysician, and unsusceptible to the lessons of history, he gives but fragments of a system which are held together, not by their intrinsic consistency, but by the vigour of his personal conviction transcending the weaknesses and collisions of his several arguments. "All my opinions," he says, "are so conjoined, and depend so closely upon one another, that it would be impossible to appropriate one without knowing them all."[33] Yet every disciple of Cartesianism seems to disprove the dictum by his example.

Cogito ergo sum.

The very moment when we begin to think, says Descartes, when we cease to be merely receptive, when we draw back and fix our attention on any point whatever of our belief,--that moment doubt begins. If we even stop for an instant to ask ourselves how a word ought to be spelled, the deeper we ponder that one word by itself the more hopeless grows the hesitation. The doubts thus awakened must not be stifled, but pressed systematically on to the point, if such a point there be, where doubt confutes itself. The doubt as to the details is natural; it is no less natural to have recourse to authority to silence the doubt. The remedy proposed by Descartes is (while not neglecting our duties to others, ourselves and God) to let doubt range unchecked through the whole fabric of our customary convictions. One by one they refuse to render any reasonable account of themselves; each seems a mere chance, and the whole tends to elude us like a mirage which some malignant power creates for our illusion. Attacked in detail, they vanish one after another into as many teasing spectra of uncertainty. We are seeking from them what they cannot give. But when we have done our worst in unsettling them, we come to an ultimate point in the fact that it is _we_ who are doubting, _we_ who are thinking. We may doubt that we have hands or feet, that we sleep or wake, and that there is a world of material things around us; but we cannot doubt that we are doubting. We are certain that we are thinking, and in so far as we are thinking we are. _Je pense, donc je suis._ In other words, the criterion of truth is a clear and distinct conception, excluding all possibility of doubt.

The fundamental point thus established is the veracity of consciousness when it does not go beyond itself, or does not postulate something which is external to itself. At this point Gassendi arrested Descartes and addressed his objections to him as pure intelligence,--_O mens!_ But even this _mens_, or mind, is but a point--we have found no guarantee as yet for its continuous existence. The analysis must be carried deeper, if we are to gain any further conclusions.

Nature of God.

Amongst the elements of our thought there are some which we can make and unmake at our pleasure; there are others which come and go without our wish; there is also a third class which is of the very essence of our thinking, and which dominates our conceptions. We find that all our ideas of limits, sorrows and weaknesses presuppose an infinite, perfect and ever-blessed something beyond them and including them,--that all our ideas, in all their series, converge to one central idea, in which they find their explanation. The formal fact of thinking is what constitutes our being; but this thought leads us back, when we consider its concrete contents, to the necessary pre-supposition on which our ideas depend, the permanent cause on which they and we as conscious beings depend. We have therefore the idea of an infinite, perfect and all-powerful being--an idea which cannot be the creation of ourselves, and must be given by some being who really possesses all that we in idea attribute to him. Such a being he identifies with God. But the ordinary idea of God can scarcely be identified with such a conception. "The majority of men," he says himself, "do not think of God as an infinite and incomprehensible being, and as the sole author from whom all things depend; they go no further than the letters of his name."[34] "The vulgar almost imagine him as a finite thing." The God of Descartes is not merely the creator of the material universe; he is also the father of all truth in the intellectual world. "The metaphysical truths," he says, "styled eternal have been established by God, and, like the rest of his creatures, depend entirely upon him. To say that these truths are independent of him is to speak of God as a Jupiter or a Saturn,--to subject him to Styx and the Fates."[35] The laws of thought, the truths of number, are the decrees of God. The expression is anthropomorphic, no less than the dogma of material creation; but it is an attempt to affirm the unity of the intellectual and the material world. Descartes establishes a philosophic monotheism,--by which the medieval polytheism of substantial forms, essences and eternal truths fades away before God, who is the ruler of the intellectual world no less than of the kingdom of nature and of grace.

To attach a clear and definite meaning to the Cartesian doctrine of God, to show how much of it comes from the Christian theology and how much from the logic of idealism, how far the conception of a personal being as creator and preserver mingles with the pantheistic conception of an infinite and perfect something which is all in all, would be to go beyond Descartes and to ask for a solution of difficulties of which he was scarcely aware. It seems impossible to deny that the tendency of his principles and his arguments is mainly in the line of a metaphysical absolute, as the necessary completion and foundation of all being and knowledge. Through the truthfulness of that God as the author of all truth he derives a guarantee for our perceptions in so far as these are clear and distinct. And it is in guaranteeing the veracity of our clear and distinct conceptions that the value of his deduction of God seems in his own estimate to rest. All conceptions which do not possess these two attributes--of being vivid in themselves and discriminated from all others--cannot be true. But the larger part of our conceptions are in such a predicament. We think of things not in the abstract elements of the things themselves, but in connexion with, and in language which presupposes, other things. Our idea of body, e.g., involves colour and weight, and yet when we try to think carefully, and without assuming anything, we find that we cannot attach any distinct idea to these terms when applied to body. In truth therefore these attributes do not belong to body at all; and if we go on in the same way testing the received qualities of matter, we shall find that in the last resort we understand nothing by it but extension, with the secondary and derivative characters of divisibility and mobility.

But it would again be useless to ask how extension as the characteristic attribute of matter is related to mind which thinks, and how God is to be regarded in reference to extension. The force of the universe is swept up and gathered in God, who communicates motion to the parts of extension, and sustains that motion from moment to moment; and in the same way the force of mind has really been concentrated in God. Every moment one expects to find Descartes saying with Hobbes that man's thought has created God, or with Spinoza and Malebranche that it is God who really thinks in the apparent thought of man. After all, the metaphysical theology of Descartes, however essential in his own eyes, serves chiefly as the ground for constructing his theory of man and of the universe. His fundamental hypothesis relegates to God all forces in their ultimate origin. Hence the world is left open for the free play of mechanics and geometry. The disturbing conditions of will, life and organic forces are eliminated from the problem; he starts with the clear and distinct idea of extension, figured and moved, and thence by mathematical laws he gives a hypothetical explanation of all things. Such explanation of physical phenomena is the main problem of Descartes, and it goes on encroaching upon territories once supposed proper to the mind. Descartes began with the certainty that we are thinking beings; that region remains untouched; but up to its very borders the mechanical explanation of nature reigns unchecked.

Physical theory.

The physical theory, in its earlier form in _The World_, and later in the _Principles of Philosophy_ (which the present account follows), rests upon the metaphysical conclusions of the _Meditations_. It proposes to set forth the genesis of the existing universe from principles which can be plainly understood, and according to the acknowledged laws of the transmission of movement. The idea of force is one of those obscure conceptions which originate in an obscure region, in the sense of muscular power. The true physical conception is motion, the ultimate ground of which is to be sought in God's infinite power. Accordingly the quantity of movement in the universe, like its mover, can neither increase nor diminish. The only circumstance which physics has to consider is the transference of movement from one particle to another, and the change of its direction. Man himself cannot increase the sum of motion; he can only alter its direction. The whole conception of force may disappear from a theory of the universe; and we can adopt a geometrical definition of motion as the shifting of one body from the neighbourhood of those bodies which immediately touch it, and which are assumed to be at rest, to the neighbourhood of other bodies. Motion, in short, is strictly locomotion, and nothing else.

Descartes has laid down three laws of nature, and seven secondary laws regarding impact. The latter are to a large extent incorrect. The first law affirms that every body, so far as it is altogether unaffected by extraneous causes, always perseveres in the same state of motion or of rest; and the second law that simple or elementary motion is always in a straight line.[36] These doctrines of inertia, and of the composite character of curvilinear motion, were scarcely apprehended even by Kepler or Galileo; but they follow naturally from the geometrical analysis of Descartes.

Theory of vortices.

Extended body has no limits to its extent, though the power of God has divided it in lines discriminating its parts in endless ways. The infinite universe is infinitely full of matter. Empty space, as distinguished from material extension, is a fictitious abstraction. There is no such thing really as a vacuum, any more than there are atoms or ultimate indivisible particles. In both these doctrines of _à priori_ science Descartes has not been subverted, but, if anything, corroborated by the results of experimental physics; for the so-called atoms of chemical theory already presuppose, from the Cartesian point of view, certain aggregations of the primitive particles of matter. Descartes regards matter as uniform in character throughout the universe; he anticipates, as it were, from his own transcendental ground, the revelations of spectrum analysis as applied to the sun and stars. We have then to think of a full universe of matter (and matter = extension) divided and figured with endless variety, and set (and kept) in motion by God; and any sort of division, figure and motion will serve the purposes of our supposition as well as another. "Scarcely any supposition,"[37] he says, "can be made from which the same result, though possibly with greater difficulty, might not be deduced by the same laws of nature; for since, in virtue of these laws, matter successively assumes all the forms of which it is capable, if we consider these forms in order, we shall at one point or other reach the existing form of the world, so that no error need here be feared from a false supposition." As the movement of one particle in a closely-packed universe is only possible if all other parts move simultaneously, so that the last in the series steps into the place of the first; and as the figure and division of the particles varies in each point in the universe, there will inevitably at the same instant result throughout the universe an innumerable host of more or less circular movements, and of vortices or whirlpools of material particles varying in size and velocity. Taking for convenience a limited portion of the universe, we observe that in consequence of the circular movement, the particles of matter have their corners pared off by rubbing against each other; and two species of matter thus arise,--one consisting of small globules which continue their circular motion with a (centrifugal) tendency to fly off from the centre as they swing round the axis of rotation, while the other, consisting of the fine dust--the filings and parings of the original particles--gradually becoming finer and finer, and losing its velocity, tends (centripetally) to accumulate in the centre of the vortex, which has been gradually left free by the receding particles of globular matter. This finer matter which collects in the centre of each vortex is the _first_ matter of Descartes--it constitutes the sun or star. The spherical particles are the _second_ matter of Descartes, and their tendency to propel one another from the centre in straight lines towards the circumference of each vortex is what gives rise to the phenomenon of light radiating from the central star. This second matter is atmosphere or firmament, which envelops and revolves around the central accumulation of first matter.

A third form of matter is produced from the original particles. As the small filings produced by friction seek to pass through the interstices between the rapidly revolving spherical particles in the vortex, they are detained and become twisted and channelled in their passage, and when they reach the edge of the inner ocean of solar dust they settle upon it as the froth and foam produced by the agitation of water gathers upon its surface. These form what we term spots in the sun. In some cases they come and go, or dissolve into an aether round the sun; but in other cases they gradually increase until they form a dense crust round the central nucleus. In course of time the star, with its expansive force diminished, suffers encroachments from the neighbouring vortices, and at length they catch it up. If the velocity of the decaying star be greater than that of any part of the vortex which has swept it up, it will ere long pass out of the range of that vortex, and continue its movement from one to another. Such a star is a comet. But in other cases the encrusted star settles in that portion of the revolving vortex which has a velocity equivalent to its own, and so continues to revolve in the vortex, wrapped in its own firmament. Such a reduced and impoverished star is a planet; and the several planets of our solar system are the several vortices which from time to time have been swept up by the central sun-vortex. The same considerations serve to explain the moon and other satellites. They too were once vortices, swallowed up by some other, which at a later day fell a victim to the sweep of our sun.

Such in mere outline is the celebrated theory of _vortices_, which for about twenty years after its promulgation reigned supreme in science, and for much longer time opposed a tenacious resistance to rival doctrines. It is one of the grandest hypotheses which ever have been formed to account by mechanical processes for the movements of the universe. While chemistry rests in the acceptance of ultimate heterogeneous elements, the vortex-theory assumed uniform matter through the universe, and reduced cosmical physics to the same principles as regulate terrestrial phenomena. It ended the old Aristotelian distinction between the sphere beneath the moon and the starry spaces beyond. It banished the spirits and genii, to which even Kepler had assigned the guardianship of the planetary movements; and, if it supposes the globular particles of the envelope to be the active force in carrying the earth round the sun, we may remember that Newton himself assumed an aether for somewhat similar purposes. The great argument on which the Cartesians founded their opposition to the Newtonian doctrine was that attraction was an occult quality, not wholly intelligible by the aid of mere mechanics. The Newtonian theory is an analysis of the elementary movements which in their combination determine the planetary orbits, and gives the formula of the proportions according to which they act. But the Cartesian theory, like the later speculations of Kant and Laplace, proposes to give a hypothetical explanation of the circumstances and motions which in the normal course of things led to the state of things required by the law of attraction. In the judgment of D'Alembert the Cartesian theory was the best that the observations of the age admitted; and "its explanation of gravity was one of the most ingenious hypotheses which philosophy ever imagined." That the explanation fails in detail is undoubted: it does not account for the ellipticity of the planets; it would place the sun, not in one focus, but in the centre of the ellipse; and it would make gravity directed towards the centre only under the equator. But these defects need not blind us to the fact that this hypothesis made the mathematical progress of Hooke, Borelli and Newton much more easy and certain. Descartes professedly assumed a simplicity in the phenomena which they did not present. But such a hypothetical simplicity is the necessary step for solving the more complex problems of nature. The danger lies not in forming such hypotheses, but in regarding them as final, or as more than an attempt to throw light upon our observation of the phenomena. In doing what he did, Descartes actually exemplified that reduction of the processes of nature to mere transposition of the particles of matter, which in different ways was a leading idea in the minds of Bacon, Hobbes and Gassendi. The defects of Descartes lie rather in his apparently imperfect apprehension of the principle of movements uniformly accelerated which his contemporary Galileo had illustrated and insisted upon, and in the indistinctness which attaches to his views of the transmission of motion in cases of impact. It should be added that the modern theory of vortex-atoms (Lord Kelvin's) to explain the constitution of matter has but slight analogy with Cartesian doctrine, and finds a parallel, if anywhere, in a modification of that doctrine by Malebranche.

Optical theories.

Besides the last two parts of the _Principles of Philosophy_, the physical writings of Descartes include the _Dioptrics_ and _Meteors_, as well as passages in the letters. His optical investigations are perhaps the subject in which he most contributed to the progress of science; and the lucidity of exposition which marks his _Dioptrics_ stands conspicuous even amid the generally luminous style of his works. Its object is a practical one, to determine by scientific considerations the shape of lens best adapted to improve the capabilities of the telescope, which had been invented not long before. The conclusions at which he arrives have not been so useful as he imagined, in consequence of the mechanical difficulties. But the investigation by which he reaches them has the merit of first prominently publishing and establishing the law of the refraction of light. Attempts have been made, principally founded on some remarks of Huygens, to show that Descartes had learned the principles of refraction from the manuscript of a treatise by Willebrord Snell, but the facts are uncertain; and, so far as Descartes founds his optics on any one, it is probably on the researches of Kepler. In any case the discovery is to some extent his own, for his proof of the law is founded upon the theory that light is the propagation of the aether in straight lines from the sun or luminous body to the eye (see LIGHT). Thus he approximates to the wave theory of light, though he supposed that the transmission of light was instantaneous. The chief of his other contributions to optics was the explanation of the rainbow--an explanation far from complete, since the unequal refrangibility of the rays of light was yet undiscovered--but a decided advance upon his predecessors, notably on the _De radiis visus et lucis_ (1611) of Marc-Antonio de Dominis, archbishop of Spalato.

If Descartes had contented himself with thus explaining the phenomena of gravity, heat, magnetism, light and similar forces by means of the molecular movements of his vortices, even such a theory would have excited admiration. But he did not stop short in the region of what is usually termed physics. Chemistry and biology are alike swallowed up in the one science of physics, and reduced to a problem of mechanism. This theory, he believed, would afford an explanation of every phenomenon whatever, and in nearly every department of knowledge he has given specimens of its power. But the most remarkable and daring application of the theory was to account for the phenomena of organic life, especially in animals and man. "If we possessed a thorough knowledge," he says,[38] "of all the parts of the seed of any species of animal (e.g. man), we could from that alone, by reasons entirely mathematical and certain, deduce the whole figure and conformation of each of its members, and, conversely, if we knew several peculiarities of this conformation, we could from these deduce the nature of its seed." The organism in this way is regarded as a machine, constructed from the

## particles of the seed, which in virtue of the laws of motion have

arranged themselves (always under the governing power of God) in the

## particular animal shape in which we see them. The doctrine of the

circulation of the blood, which Descartes adopted from Harvey, supplied additional arguments in favour of his mechanical theory, and he probably did much to popularize the discovery. A fire without light, compared to the heat which gathers in a haystack when the hay has been stored before it was properly dry--heat, in short, as an agitation of the

## particles--is the motive cause of the contraction and dilatations of the

heart. Those finer particles of the blood which become extremely rarefied during this process pass off in two directions--one portion, and the least important in the theory, to the organs of generation, the other portion to the cavities of the brain. There not merely do they serve to nourish the organ, they also give rise to a fine ethereal flame or wind through the action of the brain upon them, and thus form the so-called "animal" spirits. From the brain these spirits are conveyed through the body by means of the nerves, regarded by Descartes as tubular vessels, resembling the pipes conveying the water of a spring to act upon the mechanical appliances in an artificial fountain. The nerves conduct the animal spirits to act upon the muscles, and in their turn convey the impressions of the organs to the brain.

Automatism.

Man and the animals as thus described are compared to automata, and termed machines. The vegetative and sensitive souls which the Aristotelians had introduced to break the leap between inanimate matter and man are ruthlessly swept away; only one soul, the rational, remains, and that is restricted to man. One hypothesis supplants the various principles of life; the rule of absolute mechanism is as complete in the animal as in the cosmos. Reason and thought, the essential quality of the soul, do not belong to the brutes; there is an impassable gulf fixed between man and the lower animals. The only sure sign of reason is the power of language--i.e. of giving expression to general ideas; and language in that sense is not found save in man. The cries of animals are but the working of the curiously-contrived machine, in which, when one portion is touched in a certain way, the wheels and springs concealed in the interior perform their work, and, it may be, a note supposed to express joy or pain is evolved; but there is no consciousness or feeling. "The animals act naturally and by springs, like a watch."[39] "The greatest of all the prejudices we have retained from our infancy is that of believing that the beasts think."[40] If the beasts can properly be said to see at all, "they see as we do when our mind is distracted and keenly applied elsewhere; the images of outward objects paint themselves on the retina, and possibly even the impressions made in the optic nerves determine our limbs to different movements, but we feel nothing of it all, and move as if we were automata."[41] The sentience of the animal to the lash of his tyrant is not other than the sensitivity of the plant to the influences of light and heat. It is not much comfort to learn further from Descartes that "he denies life to no animal, but makes it consist in the mere heat of the heart. Nor does he deny them feeling in so far as it depends on the bodily organs."[42]

Descartes, with an unusual fondness for the letter of Scripture, quotes oftener than once in support of this monstrous doctrine. the dictum, "the blood is the life"; and he remarks, with some sarcasm possibly, that it is a comfortable theory for the eaters of animal flesh. And the doctrine found acceptance among some whom it enabled to get rid of the difficulties raised by Montaigne and those who allowed more difference between animal and animal than between the higher animals and man. It also encouraged vivisection--a practice common with Descartes himself.[43] The recluses of Port Royal seized it eagerly, discussed automatism, dissected living animals in order to show to a morbid curiosity the circulation of the blood, were careless of the cries of tortured dogs, and finally embalmed the doctrine in a syllogism of their logic,--No matter thinks; every soul of beast is matter: therefore no soul of beast thinks.

Relation of mind and body.

But whilst all the organic processes in man go on mechanically, and though by reflex action he may repel attack unconsciously, still the first affirmation of the system was that man was essentially a thinking being; and, while we retain this original dictum, it must not be supposed that the mind is a mere spectator, or like the boatman in the boat. Of course a unity of nature is impossible between mind and body so described. And yet there is a unity of composition, a unity so close that the compound is "really one and in a sense indivisible." You cannot in the actual man cut soul and body asunder; they interpenetrate in every member. But there is one point in the human frame--a point midway in the brain, single and free, which may in a special sense be called the seat of the mind. This is the so-called conarion, or pineal gland, where in a minimized point the mind on one hand and the vital spirits on the other meet and communicate. In that gland the mystery of creation is concentrated; thought meets extension and directs it; extension moves towards thought and is perceived. Two clear and distinct ideas, it seems, produce an absolute mystery. Mind, driven from the field of extension, erects its last fortress in the pineal gland. In such a state of despair and destitution there is no hope for spiritualism, save in God; and Clauberg, Geulincx and Malebranche all take refuge under the shadow of his wings to escape the tyranny of extended matter.

Psychology.

In the psychology of Descartes there are two fundamental modes of thought,--perception and volition. "It seems to me," he says, "that in receiving such and such an idea the mind is passive, and that it is

## active only in volition; that its ideas are put in it partly by the

objects which touch the senses, partly by the impressions in the brain, and partly also by the dispositions which have preceded in the mind itself and by the movements of its will."[44] The will, therefore, as being more originative, has more to do with true or false judgments than the understanding. Unfortunately, Descartes is too lordly a philosopher to explain distinctly what either understanding or will may mean. But we gather that in two directions our reason is bound up with bodily conditions, which make or mar it, according as the will, or central energy of thought, is true to itself or not. In the range of perception, intellect is subjected to the material conditions of sense, memory and imagination; and in infancy, when the will has allowed itself to assent precipitately to the conjunctions presented to it by these material processes, thought has become filled with obscure ideas. In the moral sphere the passions or emotions (which Descartes reduces to the six primitive forms of admiration, love, hatred, desire, joy and sadness) are the perceptions or sentiments of the mind, caused and maintained by some movement of the vital spirits, but specially referring to the mind only. The presentation of some object of dread, for example, to the eye has or may have a double effect. On one hand the animal spirits "reflected"[45] from the image formed on the pineal gland proceed through the nervous tubes to make the muscles turn the back and lift the feet, so as to escape the cause of the terror. Such is the reflex and mechanical movement independent of the mind. But, on the other hand, the vital spirits cause a movement in the gland by which the mind perceives the affection of the organs, learns that something is to be loved or hated, admired or shunned. Such perceptions dispose the mind to pursue what nature dictates as useful. But the estimate of goods and evils which they give is indistinct and unsatisfactory. The office of reason is to give a true and distinct appreciation of the values of goods and evils; or firm and determinate judgments touching the knowledge of good and evil are our proper arms against the influence of the passions.[46] We are free, therefore, through knowledge: _ex magna luce in intellectu sequitur magna propensio in voluntate_, and _omnis peccans est ignorans_. "If we clearly see that what we are doing is wrong, it would be impossible for us to sin, so long as we saw it in that light."[47] Thus the highest liberty, as distinguished from mere indifference, proceeds from clear and distinct knowledge, and such knowledge can only be attained by firmness and resolution, i.e. by the continued exercise of the will. Thus in the perfection of man, as in the nature of God, will and intellect must be united. For thought, will is as necessary as understanding. And innate ideas therefore are mere capacities or tendencies,--possibilities which apart from the will to think may be regarded as nothing at all.

_The Cartesian School._--The philosophy of Descartes fought its first battles and gained its first triumphs in the country of his adoption. In his lifetime his views had been taught in Utrecht and Leiden. In the universities of the Netherlands and of lower Germany, as yet free from the conservatism of the old-established seats of learning, the new system gained an easy victory over Aristotelianism, and, as it was adapted for lectures and examinations, soon became almost as scholastic as the doctrines it had supplanted. At Leiden, Utrecht, Groningen, Franeker, Breda, Nimeguen, Harderwyk, Duisburg and Herborn, and at the Catholic university of Louvain, Cartesianism was warmly expounded and defended in seats of learning, of which many are now left desolate, and by adherents whose writings have for the most part long lost interest for any but the antiquary.

Holland.

The Cartesianism of Holland was a child of the universities, and its literature is mainly composed of commentaries upon the original texts, of theses discussed in the schools, and of systematic expositions of Cartesian philosophy for the benefit of the student. Three names stand out in this Cartesian professoriate,--Wittich, Clauberg and Geulincx. Christoph Wittich (1625-1687), professor at Duisburg and Leiden, is a representative of the moderate followers who professed to reconcile the doctrines of their school with the faith of Christendom and to refute the theology of Spinoza. Johann Clauberg (q.v.) commented clause by clause upon the _Meditations_ of Descartes; but he specially claims notice for his work _De corporis et animae in homine conjunctione_, where he maintains that the bodily movements are merely procatarctic causes (i.e. antecedents, but not strictly causes) of the mental action, and sacrifices the independence of man to the omnipotence of God. The same tendency is still more pronounced in Arnold Geulincx (q.v.). With him the reciprocal action of mind and body is altogether denied; they resemble two clocks, so made by the artificer as to strike the same hour together. The mind can act only upon itself; beyond that limit, the power of God must intervene to make any seeming interaction possible between body and soul. Such are the half-hearted attempts at consistency in Cartesian thought, which eventually culminate in the pantheism of Spinoza (see CARTESIANISM).

Descartes occasionally had not scrupled to interpret the Scriptures according to his own tenets, while still maintaining, when their letter contradicted him, that the Bible was not meant to teach the sciences. Similar tendencies are found amongst his followers. Whilst Protestant opponents put him in the list of atheists like Vanini, and the Catholics held him as dangerous as Luther or Calvin, there were zealous adherents who ventured to prove the theory of vortices in harmony with the book of Genesis. It was this rationalistic treatment of the sacred writings which helped to confound the Cartesians with the allegorical school of John Cocceius, as their liberal doctrines in theology justified the vulgar identification of them with the heresies of Socinian and Arminian. The chief names in this advanced theology connected with Cartesian doctrines are Ludwig Meyer, the friend and editor of Spinoza, author of a work termed _Philosophia scripturae interpres_ (1666); Balthasar Bekker, whose _World Bewitched_ helped to discredit the superstitious fancies about the devil; and Spinoza, whose _Tractatus theologico-politicus_ is in some respects the classical type of rational criticism up to the present day. Against this work and the _Ethics_ of Spinoza the orthodox Cartesians (who were in the majority), no less than sceptical hangers-on like Bayle, raised an all but universal howl of reprobation, scarcely broken for about a century.

France.

In France Cartesianism won society and literature before it penetrated into the universities. Clerselier (the friend of Descartes and his literary executor), his son-in-law Rohault (who achieved that relationship through his Cartesianism), and others, opened their houses for readings to which the intellectual world of Paris--its learned professors not more than the courtiers and the fair sex,--flocked to hear the new doctrines explained, and possibly discuss their value. Grand seigneurs, like the prince of Condé, the duc de Nevers and the marquis de Vardes, were glad to vary the monotony of their feudal castles by listening to the eloquent rehearsals of Malebranche or Regis. And the salons of Mme de Sévigné, of her daughter Mme de Grignan, and of the duchesse de Maine for a while gave the questions of philosophy a place among the topics of polite society, and furnished to Molière the occasion of his _Femmes savantes_. The Château of the duc de Luynes, the translator of the _Meditations_, was the home of a Cartesian club, that discussed the questions of automatism and of the composition of the sun from filings and parings, and rivalled Port Royal in its vivisections. The cardinal de Retz in his leisurely age at Commercy found amusement in presiding at disputations between the more moderate Cartesians and Don Robert Desgabets, who interpreted Descartes in an original way of his own. Though rejected by the Jesuits, who found peripatetic formulae a faithful weapon against the enemies of the church, Cartesianism was warmly adopted by the Oratory, which saw in Descartes something of St Augustine, by Port Royal, which discovered a connexion between the new system and Jansenism, and by some amongst the Benedictines and the order of Ste Geneviève.

The popularity which Cartesianism thus gained in the social and literary circles of the capital was largely increased by the labours of Pierre-Sylvain Regis (1632-1707). On his visit to Toulouse in 1665, with a mission from the Cartesian chiefs, his lectures excited boundless interest; ladies threw themselves with zeal and ability into the study of philosophy; and Regis himself was made the guest of the civic corporation. In 1671 scarcely less enthusiasm was roused in Montpellier; and in 1680 he opened a course of lectures at Paris, with such acceptance that hearers had to take their seats in advance. Regis, by removing the paradoxes and adjusting the metaphysics to the popular powers of apprehension, made Cartesianism popular, and reduced it to a regular system.

But a check was at hand. Descartes, in his correspondence with the Jesuits, had shown an almost cringing eagerness to have their powerful organization on his side. Especially he had written to Père Mesland, one of the order, to show how the Catholic doctrine of the eucharist might be made compatible with his theories of matter. But his undue haste to arrange matters with the church only served to compromise him more deeply. Unwise admirers and malicious opponents exaggerated the theological bearings of his system in this detail; and the efforts of the Jesuits succeeded in getting the works of Descartes, in November 1663, placed upon the index of prohibited books,--_donec corrigantur_. Thereupon the power of church and state enforced by positive enactments the passive resistance of old institutions to the novel theories. In 1667, the oration at the interment was forbidden by royal order. In 1669, when the chair of philosophy at the Collège Royal fell vacant, one of the four selected candidates had to sustain a thesis against "the pretended new philosophy of Descartes." In 1671 the archbishop of Paris, by the king's order, summoned the heads of the university to his presence, and enjoined them to take stricter measures against philosophical novelties dangerous to the faith. In 1673 a decree of the parlement against Cartesian and other unlicensed theories was on the point of being issued, and was only checked in time by the appearance of a burlesque mandamus against the intruder Reason, composed by Boileau and some of his brother-poets. Yet in 1675 the university of Angers was empowered to repress all Cartesian teaching within its domain, and actually appointed a commission charged to look for such heresies in the theses and the students' note-books of the college of Anjou belonging to the Oratory. In 1677 the university of Caen adopted not less stringent measures against Cartesianism. And so great was the influence of the Jesuits, that the congregation of St Maur, the canons of Ste Geneviève, and the Oratory laid their official ban on the obnoxious doctrines. From the real or fancied _rapprochements_ between Cartesianism and Jansenism, it became for a while impolitic, if not dangerous, to avow too loudly a preference for Cartesian theories. Regis was constrained to hold back for ten years his _System of Philosophy_; and when it did appear, in 1690, the name of Descartes was absent from the title-page. There were other obstacles besides the mild persecutions of the church. Pascal and other members of Port Royal openly expressed their doubts about the place allowed to God in the system; the adherents of Gassendi met it by resuscitating atoms; and the Aristotelians maintained their substantial forms as of old; the Jesuits argued against the arguments for the being of God, and against the theory of innate ideas; whilst Pierre Daniel Huet (1630-1721), bishop of Avranches, once a Cartesian himself, made a vigorous onslaught on the contempt in which his former comrades held literature and history, and enlarged on the vanity of all human aspirations after rational truth.

The greatest and most original of the French Cartesians was Malebranche (q.v.). His _Recherche de la vérité_, in 1674, was the baptism of the system into a theistic religion which borrowed its imagery from Augustine; it brought into prominence the metaphysical base which Louis Delaforge, Jacques Rohault and Regis had neither cared for nor understood. But this doctrine was a criticism and a divergence, no less than a consequence, from the principles in Descartes; and it brought upon Malebranche the opposition, not merely of the Cartesian physicists, but also of Arnauld, Fénelon and Bossuet, who found, or hoped to find, in the _Meditations_, as properly understood, an ally for theology. Popular enthusiasm, however, was with Malebranche, as twenty years before it had been with Descartes; he was the fashion of the day; and his disciples rapidly increased both in France and abroad.

In 1705 Cartesianism was still subject to prohibitions from the authorities; but in a project of new statutes, drawn up for the faculty of arts at Paris in 1720, the _Method_ and _Meditations_ of Descartes were placed beside the _Organon_ and the _Metaphysics_ of Aristotle as text-books for philosophical study. And before 1725, readings, both public and private, were given from Cartesian texts in some of the Parisian colleges. But when this happened, Cartesianism was no longer either interesting or dangerous; its theories, taught as ascertained and verified truths, were as worthless as the systematic verbiage which preceded them. Already antiquated, it could not resist the wit and raillery with which Voltaire, in his _Lettres sur les Anglais_ (1728), brought against it the principles and results of Locke and Newton. The old Cartesians, Jean Jacques Dortous de Mairan (1678-1771) and especially Fontenelle, with his _Théorie des tourbillons_ (1752), struggled in vain to refute Newton by styling attraction an occult quality. Fortunately the Cartesian method had already done its service, even where the theories were rejected. The Port Royalists, Pierre Nicole (1625-1695) and Antoine Arnauld (1612-1694), had applied it to grammar and logic; Jean Domat or Daumat (1625-1696) and Henri François Daugesseau (1668-1751) to jurisprudence; Fontenelle, Charles Perrault (1628-1703) and Jean Terrasson (1670-1750) to literary criticism, and a worthier estimate of modern literature. Though it never ceased to influence individual thinkers, it had handed on to Condillac its popularity with the masses. A Latin abridgment of philosophy, dated 1784, tells us that the innate ideas of Descartes are founded on no arguments, and are now universally abandoned. The ghost of innate ideas seems to be all that it had left.

Germany.

In Germany a few Cartesian lecturers taught at Leipzig and Halle, but the system took no root, any more than in Switzerland, where it had a brief reign at Geneva after 1669. In Italy the effects were more permanent. What is termed the iatro-mechanical school of medicine, with G. A. Borelli (1608-1679) as its most notable name, entered in a way on the mechanical study of anatomy suggested by Descartes, but was probably much more dependent upon the positive researches of Galileo. At Naples there grew up a Cartesian school, of which the best known members are Michel Angelo Fardella (1650-1708) and Cardinal Gerdil (1718-1802), both of whom, however, attached themselves to the characteristic views of Malebranche.

England.

In England Cartesianism took but slight hold. Henry More, who had given it a modified sympathy in the lifetime of the author, became its opponent in later years; and Cudworth differed from it in most essential points. Antony Legrand, from Douai, attempted to introduce it into Oxford, but failed. He is the author of several works, amongst others a system of Cartesian philosophy, where a chapter on "Angels" revives the methods of the schoolmen. His chief opponent was Samuel Parker (1640-1688), bishop of Oxford, who, in his attack on the irreligious novelties of the Cartesian, treats Descartes as a fellow-criminal in infidelity with Hobbes and Gassendi. Rohault's version of the Cartesian physics was translated into English; and Malebranche found an ardent follower in John Norris (1667-1711). Of Cartesianism towards the close of the 17th century the only remnants were an overgrown theory of vortices, which received its death-blow from Newton, and a dubious phraseology anent innate ideas, which found a witty executioner in Locke.

For an account of the metaphysical doctrines of Descartes, in their connexions with Malebranche and Spinoza, see CARTESIANISM.

BIBLIOGRAPHY.--I. _Editions and Translations._--The collected works of Descartes were published in Latin in 8 vols. at Amsterdam (1670-1683), in 7 vols. at Frankfort (1697) and in 9 vols. by Elzevir (1713); in French in 13 vols. (Paris, 1724-1729), republished by Victor Cousin (Paris, 1824-1826) in 11 vols., and again under the authority of the minister of public instruction by C. Adam and P. Tannery (1897 foll.). These include his so-called posthumous works. _The Rules for the Direction of the Mind_, _The Search for Truth by the Light of Nature_, and other unimportant fragments, published (in Latin) in 1701. In 1859-1860 Foucher de Careil published in two parts some unedited writings of Descartes from copies taken by Leibnitz from the original papers. Six editions of the _Opera philosophica_ appeared at Amsterdam between 1650 and 1678; a two-volume edition at Leipzig in 1843; there are also French editions, _OEuvres philosophiques_, by A. Garnier, 3 vols. (1834-1835), and L. Aimé-Martin (1838) and _OEuvres morales et philosophiques_ by Aimé-Martin with an introduction on life and works by Amedée Prévost (Paris, 1855); _OEuvres choisies_ (1850) by Jules Simon. A complete French edition of the collected works was begun in the Romance Library (1907 foll.). German translations by J. H. von Kirchmann under the title _Philosophische Werke_ (with biography, &c., Berlin, 1868; 2nd ed., 1882-1891), by Kuno Fischer, _Die Hauptschriften zur Grundlegung seiner Philosophie_ (1863), with introduction by Ludwig Fischer (1892). There are also numerous editions and translations of separate works, especially the _Method_, in French, German, Italian, Spanish and Hungarian. There are English translations by J. Veitch, _Method, Meditations and Selections from the Principles_ (1850-1853; 11th ed., 1897; New York, 1899); by H. A. P. Torrey (New York, 1892).

II. _Biographical._--A. Baillet, _La Vie de M. Des Cartes_ (Paris, 1691; Eng. trans., 1692), exhaustive but uncritical; notices in the editions of Garnier and Aimé-Martin; A. Hoffmann, _René Descartes_ (1905); Elizabeth S. Haldane, _Descartes, his Life and Times_ (1905), containing full bibliography; A. Barbier, _René Descartes, sa famille, son lieu de naissance_, &c. (1901); Richard Lowndes, _René Descartes, his Life and Meditations_ (London, 1878); J. P. Mahaffy, _Descartes_ (1902), with an appendix on Descartes's mathematical work by Frederick Purser; Victor de Swarte, _Descartes directeur spirituel_ (Paris, 1904), correspondence with the Princess Palatine; C. J. Jeannel, _Descartes et la princesse palatine_ (Paris, 1869); _Lettres de M. Descartes_, ed. Claude Clerselier (1657). A useful sketch of recent biographies is to be found in _The Edinburgh Review_ (July 1906).

III. _Philosophy._--Beside the histories of philosophy, the article CARTESIANISM, and the above works, consult J. B. Bordas-Demoulini _Le Cartésianisme_ (2nd ed., Paris, 1874); J. P. Damiron, _Histoire de la philosophie du XVII^e siècle_ (Paris, 1846); C. B. Renouvier, _Manuel de philosophie moderne_ (Paris, 1842); V. Cousin, _Fragments philosophiques_, vol. ii. (3rd ed., Paris, 1838), _Fragments de philosophie cartésienne_ (Paris, 1845), and in the _Journal des savants_ (1860-1861); F. Bouillier, _Hist. de la philosophie cartésienne_ (Paris, 1854), 2 vols., and _Hist. et critique de la révolution cartésienne_ (Paris, 1842); J. Millet, _Descartes, sa vie, ses travaux, ses découvertes avant 1637_ (Paris, 1867), and _Hist. de Descartes depuis 1637_ (Paris, 1870); L. Liard, _Descartes_ (Paris, 1882); A. Fouillée, _Descartes_ (Paris, 1893); _Revue de métaphysique et de morale_ (July, 1896, Descartes number); Norman Smith, _Studies in the Cartesian Philosophy_ (1902); R. Keussen, _Bewusstsein und Erkenntnis bei Descartes_ (1906); A. Kayserling, _Die Idee der Kausalität in den Lehren der Occasionalisten_ (1896); J. Iverach, _Descartes, Spinoza and the New Philosophy_ (1904); R. Joerges, _Die Lehre von den Empfindungen bei Descartes_ (1901); Kuno Fischer, _Hist. of Mod. Phil. Descartes and his School_ (Eng. trans., 1887); B. Christiansen, _Das Urteil bei Descartes_ (1902); E. Boutroux, "Descartes and Cartesianism" in _Cambridge Modern History_, vol. iv. (1906), chap. 27, with a very full bibliography, pp. 950-953; P. Natorp, _Descartes' Erkenntnisstheorie_ (Marburg, 1882); L. A. Prévost-Paradol, _Les Moralistes français_ (Paris, 1865); C. Schaarschmidt, _Descartes und Spinoza_ (Bonn, 1850); R. Adamson, _The Development of Modern Philosophy_ (Edinburgh, 1903); J. Müller, _Der Begriff der sittlichen Unvollkommenheit bei Descartes und Spinoza_ (1890); J. H. von Kirchmann, _R. Descartes' Prinzipien der Philos._ (1863); G. Touchard, _La Morale de Descartes_ (1898); Lucien Lévy-Bruhl, _Hist. of Mod. Philos. in France_ (Eng. trans., 1899), pp. 1-76.

IV. _Science and Mathematics._--F. Cajori, _History of Mathematics_ (London, 1894); M. Cantor, _Vorlesungen über die Geschichte der Mathematik_ (Leipzig, 1894-1901); Sir Michael Foster, _Hist. of Physiol. during the Sixteenth, Seventeenth and Eighteenth Centuries_ (1901); Duboux, _La Physique de Descartes_ (Lausanne, 1881); G. H. Zeuthen, _Geschichte der Mathematik im 16. und 17. Jahrhundert_ (1903); Chasles, _Aperçu historique sur l'origine et le développement des méthodes en géométrie_ (3rd ed., 1889). (W. W.; X.)

FOOTNOTES:

[1] It was only published after the author's death; and of it, besides the French version, there exists an English translation "by a Person of Quality."

[2] _OEuvres_, v. 255.

[3] Ib. vi. 199.

[4]: _OEuvres_, viii. 59.

[5] Ib. viii. 173.

[6] Ib. viii. 181.

[7] Ib. vi. 123.

[8] Ib. x. 375.

[9] Ib. ix. 6.

[10] Ib. iii. 24.

[11] Ib. vi. 234.

[12] Ib. ix. 131.

[13] Ib. ix. 341.

[14] Ib. vi. 89.

[15] Ib. vi. 210.

[16] Ib. vi. 73.

[17] Ib. vi. 239.

[18] Ib. vi. 248.

[19] _OEuvres_, vi. 276.

[20] Ib. ix. 250.

[21] _Princip._ L. iii. S. 45.

[22] _OEuvres_, x. 26.

[23] _OEuvres_, x. 3.

[24] Ib. x. 53.

[25] _Regulae_, _OEuvres_, xi. 202.

[26] _OEuvres_, xi. 219.

[27] _Disc. de méthode_, part ii .

[28] _Géométrie_, book iii .

[29] _OEuvres_, xi. 224.

[30] Ib. xi. 212.

[31] _Disc. de méthode_, part. ii.

[32] _OEuvres_, xi. 243.

[33] Ib. vii. 381.

[34] _OEuvres_, vi. 132.

[35] Ib. vi. 109.

[36] _Princip._ part ii . 37.

[37] Ib.