(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.)