[1] _Exploration of the Caucasus_ (2nd ed., 1902), i. 30-31.
[2] Op. cit. i. 35-36.
CAUCHOIS-LEMAIRE, LOUIS FRANCOIS AUGUSTE (1789-1861), French journalist,
was born in Paris on the 28th of August 1789. Towards the end of the
First Empire he was proprietor of the _Journal de la litterature et des
arts_, which he transformed at the Restoration into a political journal
of Liberal tendencies, the _Nain jaune_, in which Louis XVIII. himself
had little satirical articles secretly inserted. After the return from
Elba the _Nain jaune_ became Bonapartist and fell into discredit. It was
suppressed at the second Restoration. Cauchois-Lemaire then threw
himself impetuously into the Liberal agitation, and had to take refuge
in Brussels in 1816, and in the following year at the Hague, whence he
was expelled for publishing an _Appel a l'opinion publique et aux Etats
Generaux en faveur des patriotes francais_. Returning to France in 1819,
he resumed the struggle against the ultra-royalist party with such
temerity that he was condemned to one year's imprisonment in 1821 and
fifteen months' imprisonment in 1827. After the revolution of July 1830
he refused a pension of 6000 francs offered to him by King Louis
Philippe, on the ground that he wished to retain his independence even
in his relations with a government which he had helped to establish. He
made a bitter attack upon the Perier ministry in his journal _Bon sens_,
and in 1836 was one of the founders of a new opposition journal, the
_Siecle_. He soon, however, abandoned journalism for history and, having
no private means, in 1840 accepted the post of head of a department in
the Royal Archives. Of a _Histoire de la Revolution de Juillet_, which
he then undertook, he published only the first volume (1842), which
contains a historical summary of the Restoration and a preliminary
sketch of the democratic movement. He died in Paris on the 9th of August
1861.
CAUCHON, PIERRE (d. 1442), French bishop, was born near Reims in the
latter half of the 14th century. We find him rector of the university of
Paris in October 1397. In 1413 he joined the Burgundian faction, and was
exiled by the parlement of Paris. But on the triumph of his party this
decree was annulled, and Philip the Good, duke of Burgundy, gave him a
canonry at Beauvais, sent him to the council of Constance, procured him
the post of _maitre des requetes_ in 1418, and finally in 1420 had him
made bishop of Beauvais. But the people were hostile to him, and he was
driven from his bishopric in 1429; whereupon he attached himself to the
English court, and in 1431 endeavoured to procure the surrender of Reims
to the English, so that Henry VI. might be crowned there. In this he
failed, and Henry was crowned in Paris on the 17th of December 1431 by
Henry Beaufort, cardinal bishop of Winchester, assisted by the bishops
of Beauvais and Noyon. On the 24th of May 1430, Joan of Arc having been
taken prisoner at Compiegne, within the limits of his diocese, Cauchon
acted as her accuser, and demanded the right of judging her. Joan was
taken to Rouen, whither Cauchon followed her, having been driven from
Beauvais. He conducted the trial with marked partiality and malevolence,
condemned the maid to imprisonment for life, and then, under pressure
from the populace and the English, had recourse to fresh perfidies,
declared Joan a relapsed heretic, excommunicated her, and handed her
over to the secular arm on the 30th of May 1431. As, in consequence of
this, it was impossible for him to return to his own diocese, he
obtained the bishopric of Lisieux in 1432 by favour of the king of
England. He assisted at the council of Basel in 1435, and died suddenly
on the 18th of December 1442. Excommunicated posthumously by Pope
Calixtus IV., his body was exhumed and thrown in the common sewer.
See Cerf, "Pierre Cauchon de Sommievre, chanoine de Reims et de
Beauvais, eveque de Beauvais et de Lisieux, son origine, ses dignites,
sa mort et sa sepulture," in the _Transactions_ of the Academy of
Reims (1896-1898).
CAUCHY, AUGUSTIN LOUIS, BARON (1789-1857), French mathematician, was
born at Paris on the 21st of August 1789, and died at Sceaux (Seine) on
the 23rd of May 1857. Having received his early education from his
father Louis Francois Cauchy (1760-1848), who held several minor public
appointments and counted Lagrange and Laplace among his friends, Cauchy
entered Ecole Centrale du Pantheon in 1802, and proceeded to the Ecole
Polytechnique in 1805, and to the Ecole des Ponts et Chaussees in 1807.
Having adopted the profession of an engineer, he left Paris for
Cherbourg in 1810, but returned in 1813 on account of his health,
whereupon Lagrange and Laplace persuaded him to renounce engineering and
to devote himself to mathematics. He obtained an appointment at the
Ecole Polytechnique, which, however, he relinquished in 1830 on the
accession of Louis Philippe, finding it impossible to take the necessary
oaths. A short sojourn at Freiburg in Switzerland was followed by his
appointment in 1831 to the newly-created chair of mathematical physics
at the university of Turin. In 1833 the deposed king Charles X. summoned
him to be tutor to his grandson, the duke of Bordeaux, an appointment
which enabled Cauchy to travel and thereby become acquainted with the
favourable impression which his investigations had made. Charles created
him a baron in return for his services. Returning to Paris in 1838, he
refused a proffered chair at the College de France, but in 1848, the
oath having been suspended, he resumed his post at the Ecole
Polytechnique, and when the oath was reinstituted after the _coup
d'etat_ of 1851, Cauchy and Arago were exempted from it. A profound
mathematician, Cauchy exercised by his perspicuous and rigorous methods
a great influence over his contemporaries and successors. His writings
cover the entire range of mathematics and mathematical physics.
Cauchy had two brothers: ALEXANDRE LAURENT (1792-1857), who became a
president of a division of the court of appeal in 1847, and a judge of
the court of cassation in 1849; and EUGENE FRANCOIS (1802-1877), a
publicist who also wrote several mathematical works.
The genius of Cauchy was promised in his simple solution of the
problem of Apollonius, i.e. to describe a circle touching three given
circles, which he discovered in 1805, his generalization of Euler's
theorem on polyhedra in 1811, and in several other elegant problems.
More important is his memoir on wave-propagation which obtained the
_Grand Prix_ of the Institut in 1816. His greatest contributions to
mathematical science are enveloped in the rigorous methods which he
introduced. These are mainly embodied in his three great treatises,
_Cours d'analyse de l'Ecole Polytechnique_ (1821); _Le Calcul
infinitesimal_ (1823); _Lecons sur les applications du calcul
infinitesimal a la geometrie_ (1826-1828); and also in his courses of
mechanics (for the Ecole Polytechnique), higher algebra (for the
Faculte des Sciences), and of mathematical physics (for the College de
France). His treatises and contributions to scientific journals (to
the number of 789) contain investigations on the theory of series
(where he developed with perspicuous skill the notion of convergency),
on the theory of numbers and complex quantities, the theory of groups
and substitutions, the theory of functions, differential equations
and determinants. He clarified the principles of the calculus by
developing them with the aid of limits and continuity, and was the
first to prove Taylor's theorem rigorously, establishing his
well-known form of the remainder. In mechanics, he made many
researches, substituting the notion of the continuity of geometrical
displacements for the principle of the continuity of matter. In
optics, he developed the wave theory, and his name is associated with
the simple dispersion formula. In elasticity, he originated the theory
of stress, and his results are nearly as valuable as those of S.D.
Poisson. His collected works, _OEuvres completes d'Augustin Cauchy_,
have been published in 27 volumes.
See C.A. Valson, _Le Baron Augustin Cauchy: sa vie et ses travaux_
(Paris, 1868).
CAUCUS, a political term used in America of a special form of party
meeting, and in Great Britain of a system of party organization. The
word originated in Boston, Massachusetts, in the early part of the 18th
century, when it was used as the name of a political club, the "Caucus"
or "Caucas" club. Here public matters were discussed, and arrangements
made for local elections and the choosing of candidates for offices. The
first mention of the club in contemporary documents occurs in the diary
of John Adams in 1763, but William Gordon (_History of the Independence
of the United States of America_, 1788) speaks of the Caucus as having
been in existence some fifty years before the time of writing (1774),
and describes the methods used for securing the election of the
candidates the club had selected. The derivation of the word has been
much disputed. It was early connected with "caulkers," and it was
supposed referred to meetings of the caulkers in the dockyard at Boston
in 1770, to protest against the action of the British troops, or with a
contemptuous allusion to the lower class of workmen frequenting the
club. This is, however, a mere guess, and does not agree with the
earlier date at which the club is known to have existed, nor with the
accounts given of it. That it was a fanciful classical name for a
convivial club, derived from the late Greek [Greek: kaukos], a cup, is
far-fetched, and the most plausible origin is an Algonquin word
_kaw-kaw-was_, meaning to talk. Indian words and names have been popular
in America as titles for societies and clubs; cf. "Tammany" (see _Notes
and Queries._ sixth series, vols. xi. and xii.). In the United States
"caucus" is used strictly of a meeting either of party managers or of
party voters. Such might be a "nominating caucus," either for nominating
candidates for office or for selecting delegates for a nominating
convention. The caucus of the party in Congress nominated the candidates
for the offices of president and vice-president from 1800 till 1824,
when the convention system was adopted, and the place of the local
"nominating caucus" is taken by the "primaries" and conventions. The
word is used in America of the meetings of a party in Congress and other
legislative bodies and elsewhere which decide matters of policy and plan
campaigns. "Caucus" came first into use in Great Britain in 1878. The
Liberal Association of Birmingham (see LIBERAL PARTY) was organized by
Mr Joseph Chamberlain and Mr F. Schnadhorst on strict disciplinary
lines, more particularly with a view to election management and the
control of voters on the principle of "vote as you are told." This
managing body of the association, known locally as the "Six Hundred,"
became the model for other Liberal associations throughout the country,
and the Federation of Liberal Associations was organized on the same
plan. It was to this supposed imitation of the American political
"machine" that Lord Beaconsfield gave the name "caucus," and the name
came to be used, not in the American sense of a meeting, but of a
closely disciplined system of party organization, chiefly used as a
stock term of abuse applied by opponents to each other's party
machinery.
CAUDEBEC-EN-CAUX, a town of France, in the department of
Seine-Inferieure, 27 m. W.N.W. of Rouen by the Ouest-Etat railway. Pop.
(1906) 2141. It is situated on the right bank of the Seine, the tidal
wave of which (_mascaret_) can be well seen at this point. The chief
interest of the town lies in its church, a building of the 15th and the
early 16th centuries. Round its top run balustrades formed of Gothic
letters, which read as part of the Magnificat. Its west portal, the
decoration of the spire of the tower, and its stained glass are among
the features which make it one of the finest churches of the Rouen
diocese. The town also possesses several old houses. Its industries
include tanning and leather-currying, and there is trade in grain. The
port has a small trade in coal, live-stock and farm produce.
CAUDINE FORKS (_Furculae Caudinae_), a pass in Samnium, famous for the
disaster which befell the Roman army in the second Samnite War (321
B.C.). Livy (ix, 2) describes it as formed by two narrow wooded gorges,
between which lay a plain, grassy and well-watered, but entirely
enclosed by mountains. Through this plain the road (later the Via Appia)
led. The Romans, marching from Calatia to the relief of Luceria, entered
the valley unopposed, but found the exit blocked by the enemy; on
marching back they saw that the entrance and the hills surrounding the
plain were also occupied, and there was no way of escape. The plain
which lies west of Caudium (Montesarchio) seems, despite the older
views, to be the only possible site for such a disaster to an army of as
many as 40,000 men; and there is no doubt that the Romans wished to
leave it by the defile on the east, through which later ran the Via
Appia to Beneventum. The existence of three ancient bridges on the line
of the modern road renders it impossible to suppose that its course can
be essentially different from that of the ancient, though Hulsen makes
the two diverge considerably after passing Montesarchio. There are,
however, two possible entrances--one on the north by Moiano, and one on
the west by Arpaia; the former seems to answer better to Livy's
description (_via alia per cavam rupem_), while the latter is the
shortest route, having been, later on, followed by the Via Appia, and
bore the name Furculae Caudinae in the middle ages.
See C. Hulsen in Pauly-Wissowa, _Realencyclopadie_, iii. (1802).
(T. As.)
CAUDLE (through the O. Fr. _caudel_, from the Med. Lat. _caldellum_, a
diminutive of _caldum_, a warm drink, from _calidus_, hot), a drink of
warm gruel, mixed with spice and wine, formerly given to women in
childbed.
CAUL (from O. Eng. _calle_, Fr. _cale_, a cap), a close-fitting woman's
cap, especially one made of network worn in the 16th and 17th centuries;
hence the membranous covering to the heart or brain, the _omentum_, or
the similar covering to the intestines, and particularly, a portion of
the _amnion_, which is sometimes found remaining round the head of a
child after birth. To this, called in Scotland "sely how," holy or lucky
hood, many superstitions have been attached; it was looked on as a sign
of good luck, and when preserved, was kept as a protection against
drowning.
CAULAINCOURT, ARMAND AUGUSTIN LOUIS, MARQUIS DE (1773-1827), French
general and diplomatist, was born of a noble family. He early entered
the army, did not emigrate in the revolution, but was deprived of his
grade as captain in 1793 and served in the ranks. In 1795, through the
protection of L. Hoche, he became captain again, was colonel in the Army
of the Rhine in 1799-1800, and after the peace of Luneville (1801) was
sent to St Petersburg to negotiate an understanding between Russia and
France. On his return he was named aide-de-camp of the First Consul. He
was employed to seize some agents of the English government in Baden in
1804, which led to the accusation that he was concerned in the arrest of
the due d'Enghien, an accusation against which he never ceased to
protest. After the establishment of the empire he received various
honours and the title of duke of Vicenza (1808). Napoleon sent him in
1807 as ambassador to St Petersburg, where Caulaincourt tried to
maintain the alliance of Tilsit, and although Napoleon's ambition made
the task a difficult one, Caulaincourt succeeded in it for some years.
In 1811 he strongly advised Napoleon to renounce his proposed expedition
to Russia. During the war he accompanied the emperor, and was one of
those whom Napoleon took along with him when he suddenly abandoned his
army in Poland to return to Paris (December 1812). During the last years
of the empire, Caulaincourt was charged with all the diplomatic
negotiations. He signed the armistice of Pleswitz, June 1813,
represented France at the congress of Prague, in August 1813, at the
congress of Chatillon, in February 1814, and concluded the treaty of
Fontainebleau on the 10th of April 1814. During the first Restoration,
Caulaincourt lived in obscure retirement. When Napoleon returned from
Elba, he became minister of foreign affairs, and tried to persuade
Europe of the emperor's peaceful intentions. After the second
Restoration, Caulaincourt's name was on the list of those proscribed,
but it was erased on the personal intervention of Alexander I. with
Louis XVIII.
Caulaincourt's memoirs appeared under the title _Souvenirs du duc de
Vicence_ in 1837-1840. See A. Vandal, _Napoleon et Alexandre_ (Paris,
1891-1895); Tatischeff, _Alexandre I^er et Napoleon_ (Paris, 1892); H.
Houssaye, 1814 (Paris, 1888), and 1815 (Paris, 1893).
CAULICULUS (from Lat. _caulis_, a stalk), in architecture, the Stalks
(eight in number) with two leaves from which rise the helices or spiral
scrolls of the Corinthian capital to support the abacus.
CAULON (Gr. [Greek: Kaulonia]), a town of the district of the Bruttii,
Italy, on the east coast. Its exact site is uncertain (though the name
has been given to a modern village), and depends on the identification
of the river Sagras. It was the southernmost of the Achaean colonies,
founded either by Croton or direct from Greece itself. In the 7th
century it was allied with Croton and Sybaris, and its coins, which go
back to 550 B.C., prove its importance. It took the side of Athens in
the Peloponnesian War. In 388 B.C. it was destroyed by Dionysius, but
soon afterwards restored. It was captured during the invasion of Pyrrhus
by Campanian troops. Strabo speaks of it as deserted in his time. The
erection of the lighthouse at Capo Stilo, on the site of one of the
medieval guard towers of the coast, led to the discovery of a wall of
Greek origin, and close by of a number of terra-cottas, belonging
perhaps to a temple erected in honour of the deities of the sea. Other
remains were found at Fontanelle, 2-1/2 m. away, including the fragment
of a capital of an archaic Greek temple (P. Orsi in _Notizie degli
Scavi_, 1891, 61). These buildings may be connected with the Caulon or a
village dependent on it. (T. As.)
CAUSATION or CAUSALITY (Lat. _causa_, derived perhaps from the root
_cav-_, as in _caveo_, and meaning something taken care of;
corresponding to Gr. [Greek: aitia]), a philosophical term for the
operation of causes and for the mental conception of cause as operative
throughout the universe. The word "cause" is correlative to "effect."
Thus when one thing B is regarded as taking place in consequence of the
action of another thing A, then A is said to be the cause of B, and B
the effect of A. The philosophical problems connected with causation are
both metaphysical and psychological. The metaphysical problem is part of
the whole theory of existence. If everything is to be regarded as
causally related with simultaneous and prior things or actions, it
follows logically that the investigation of existence must, by
hypothesis, be a regress to infinity, i.e. that we cannot conceive a
beginning to existence. This explanation has led to the postulate of a
First Cause, the nature of which is variously explained. The empirical
school sees no difficulty in assuming a single event; but such a theory
seems to deny the validity of the original hypothesis. Theologians
assert a divine origin in the form of a personal self-existent creator,
while some metaphysical schools, preferring an impersonal First Cause,
substitute the doctrine of the Absolute (q.v.). All the explanations are
alike in this respect, that at a certain point they pass from the sphere
of the senses, the physical world, to a metaphysical sphere in which the
data and the intellectual operation of cognizing them are of a totally
different quality. For example, the causal connexion between drunkenness
and alcohol is not of the same observable character as that which is
inferred between the infinite First Cause and the whole domain of
sense-given phenomena.
A second metaphysical problem connected with causation arises when we
consider the nature of necessity. It is generally assumed when two
things are spoken of as cause and effect that their relation is a
necessary one, or, in other words, that given the cause the effect must
follow. The arguments connected with this problem belong to
psychological discussions of causation. It is sufficient here to state
that, in so far as causation is regarded as necessary connexion, it can
form no part of a purely empirical theory of existence. The senses can
say only that in all observed cases B has followed A, and this does not
establish necessary connexion. The idea of causation is a purely
intellectual (a priori) one.
The psychological problems connected with causation refer (1) to the
origin of the conception in our minds; (2) to the validity of the
conception. As regards the origin of the conception modern psychological
analysis does not carry us beyond the doctrine of Locke contained in his
chapter on "Power" (_Essay_, bk. ii. ch. 21), wherein he shows that the
idea of power is got from the knowledge of our own activity. "Bodies by
their causes," he says, "do not afford us so clear and distinct an idea
of active power as we have from reflection on the operation of our
minds." Putting Locke's doctrine into modern language, we may say that a
man has the conception of cause primarily because he himself is a cause.
The conception thus obtained we "project," that is, transfer to external
objects, so far as we may find it useful to do so. Thus it is by a sort
of analogy that we say that the sun is the "cause" of daylight. The
rival theory to Locke's is that of Hume (_Treatise_, bk. i.), who
derives the conception from the unaided operation of custom. When one
object, A, has been noticed frequently to precede another object, B, an
association between A and B is generated; and by virtue of this
association, according to Hume, we say that A is the cause of B. The
weakness of this account is that many invariable successions, such as
day and night, do not make us regard the earlier members of the
successions as causing the later; while in numberless cases we assert a
causal connexion between two objects from a single experience of them.
We may proceed now to consider the validity of the conception of
causation, which has been attacked from two sides. From the side of
absolute idealism it is argued that the conception of cause, as
involving a transition in time, cannot be ultimately valid, since the
time-relation is not ultimately real. Upon this view (ably stated in
Professor Bosanquet's _Logic_, bk. i. ch. 6) the more we know of causes
and effects the less relevant becomes the time-relation and the nearer
does the conception of cause and effect approach to another conception
which is truly valid, the conception of ground and consequence. This
means that, viewed from the standpoint of science, a draught of alcohol
_causes_ intoxication in no other sense than the triangularity of a
triangle causes the interior angles to be equal to two right angles.
This argument ceases to have cogency so soon as we deny its fundamental
proposition that the time-relation is not ultimately real, but is
irrelevant from the standpoint of science. This is a sheer assertion,
contrary to all ordinary experience, which we have as much right to deny
as the absolute idealists to affirm. It is only plausible to those who
are committed to the Hegelian view of reality as consisting of a static
system of universals, a view which has long been discredited in Germany,
its native land, and is fast losing ground in England. Against the
Hegelians we must maintain that the common distinction between "ground"
and "cause" is perfectly justifiable. Whereas "ground" is an appropriate
term for the relations within a static, simultaneous system, "cause" is
appropriate to the relations within a dynamic, successive system.
From the other side the validity of causation has been attacked in the
interests of the naturalism of the mechanical sciences. J.S. Mill argues
that, scientifically, the cause of anything is the total assemblage of
the conditions that precede its appearance, and that we have no right to
give the name of cause to one of them exclusively of the others. The
answer to this is that Mill fails to recognize that cause is a
conception which we find useful in our dealings with nature, and that
whatever conceptions we find useful we are justified in using. Among the
conditions of an event there are always one or two that stand in
specially close relation to it from our point of view; e.g. the draught
of alcoholic liquor is more closely related to the man's drunkenness
than is the attraction of the earth's gravity, though that also must
co-operate in producing the effect. Such closely related conditions we
find it convenient to single out by a term which expresses their analogy
to the cause of causes, human volition.
These are the questions respecting causation which are matters of
present controversy; there are in addition many other points which
belong to the controversies of the past. Among the most important are
Aristotle's classification of causes into material, formal, efficient
and final, set forth in his _Physics_ and elsewhere, and known as his
doctrine of the Four Causes; Geulincx's Occasional Causes, meant as a
solution of certain difficulties in the cosmology of Descartes;
Leibnitz's law of Sufficient Reason; and Kant's explanation of cause and
effect as an a priori category of the understanding, intended as an
answer to Hume's scepticism, but very much less effective than the line
of explanation suggested by Locke.
The following is a list of the various technical terms connected with
causation which have been distinguished by logicians and psychologists.
The four Aristotelian causes are: (1) _Material cause_ ([Greek: yle])
the material out of which a thing is made; the material cause of a house
is the bricks and mortar of which it is composed. (2) _Formal cause_
([Greek: eidos, logos, to ti en einai]), the general external
appearance, shape, form of a thing; the formal cause of a triangle is
its triangularity. (3) _Efficient cause_ ([Greek: arche tes kineseos]),
the alcohol which makes a man drunk, the pistol-bullet which kills. This
is the cause as generally understood in modern usage. (4) _Final cause_
([Greek: telos, to ou eneka]), the object for which an action is done or
a thing produced; the final cause of a commercial man's enterprise is to
make his livelihood (see TELEOLOGY). This last cause was rejected by
Bacon, Descartes and Spinoza, and indeed in ordinary usage the cause of
an action in relation to its effect is the desire for, and expectation
of, that effect on the part of the agent, not the effect itself. The
_Proximate cause_ of a phenomenon is the immediate or superficial as
opposed to the _Remote_ or _Primary cause_. Plurality of Causes is the
much criticized doctrine of J.S. Mill that a fact may be the uniform
consequent of several different antecedents. _Causa essendi_ means the
cause whereby a change is what it is, as opposed to the _causa
cognoscendi_, the cause of our knowledge of the event; the two causes
evidently need not be the same. An object is called _causa immanens_
when it produces its changes by its own activity; a _causa transiens_
produces changes in some other object. _Causa sui_ is a term applied to
God by Spinoza to denote that he is dependent on nothing and has no need
of any external thing for his existence. _Vera causa_ is a term used by
Newton in his _Principia_, where he says, "No more causes of natural
things are to be admitted than such as are both true and sufficient to
explain the phenomena of those things"; _verae causae_ must be such as
we have good inductive grounds to believe do exist in nature, and do
perform a part in phenomena analogous to those we would render an
account of.
CAUSEWAY, a path on a raised dam or mound across marshes or low-lying
ground; the word is also used of old paved highways, such as the Roman
military roads. "Causey" is still used dialectically in England for a
paved or cobbled footpath. The word is properly "causey-way," from
_causey_, a mound or dam, which is derived, through the Norman-French
_caucie_ (cf. modern _chaussee_), from the late Latin _via calciata_, a
road stamped firm with the feet (_calcare_, to tread).
CAUSSES (from Lat. _calx_ through local Fr. _caous_, meaning "lime"),
the name given to the table-lands lying to the south of the central
plateau of France and sloping westward from the Cevennes. They form
parts of the departments of Lozere, Aveyron, Card, Herault, Lot and
Tarn-et-Garonne. They are of limestone formation, dry, sterile and
treeless. These characteristics are most marked in the east of the
region, where the Causse de Sauveterre, the Causse Mejan, the Causse
Noir and the Larzac flank the Cevennes. Here the Causse Mejan, the most
deserted and arid of all, reaches an altitude of nearly 4200 ft. Towards
the west the lesser causses of Rouergue and Quercy attain respectively
2950 ft. and 1470 ft. Once an uninterrupted table-land, the causses are
now isolated from one another by deep rifts through which run the Tarn,
the Dourbie, the Jonte and other rivers. The summits are destitute of
running water, since the rain as it falls either sinks through the
permeable surface soil or runs into the fissures and chasms, some of
great depth, which are peculiar to the region. The inhabitants
(_Caussenards_) of the higher causses cultivate hollows in the ground
which are protected from the violent winds, and the scanty herbage
permits of the raising of sheep, from the milk of which Roquefort
cheeses are made. In the west, where the rigours of the weather are less
severe, agriculture is more easily carried on.
CAUSSIN DE PERCEVAL, ARMAND-PIERRE (1795-1871), French orientalist, was
born in Paris on the 13th of January 1795. His father, Jean Jacques
Antoine Caussin de Perceval (1759-1835), was professor of Arabic in the
College de France. In 1814 he went to Constantinople as a student
interpreter, and afterwards travelled in Asiatic Turkey, spending a year
with the Maronites in the Lebanon, and finally becoming dragoman at
Aleppo. Returning to Paris, he became professor of vulgar Arabic in the
school of living Oriental languages in 1821, and also professor of
Arabic in the College de France in 1833. In 1849 he was elected to the
Academy of Inscriptions. He died at Paris during the siege on the 15th
of January 1871.
Caussin de Perceval published (1828) a useful _Grammaire arabe
vulgaire_, which passed through several editions (4th ed., 1858), and
edited and enlarged Elie Bocthor's[1] _Dictionnaire francais-arabe_ (2
vols., 1828; 3rd ed., 1864); but his great reputation rests almost
entirely on one book, the _Essai sur l'histoire des Arabes avant
l'Islamisme, pendant l'epoque de Mahomet_ (3 vols., 1847-1849), in which
the native traditions as to the early history of the Arabs, down to the
death of Mahommed and the complete subjection of all the tribes to
Islam, are brought together with wonderful industry and set forth with
much learning and lucidity. One of the principal MS. sources used is the
great _Kitab al-Aghani_ (Book of Songs) of Abu Faraj, which has since
been published (20 vols., Boulak, 1868) in Egypt; but no publication of
texts can deprive the _Essai_, which is now very rare, of its value as a
trustworthy guide through a tangled mass of tradition.
CAUSTIC (Gr. [Greek: kaustikos], burning), that which burns. In surgery,
the term is given to substances used to destroy living tissues and so
inhibit the action of organic poisons, as in bites, malignant disease
and gangrenous processes. Such substances are silver nitrate (lunar
caustic), the caustic alkalis (potassium and sodium hydrates), zinc
chloride, an acid solution of mercuric nitrate, and pure carbolic acid.
In mathematics, the "caustic surfaces" of a given surface are the
envelopes of the normals to the surface, or the loci of its centres of
principal curvature.
In optics, the term _caustic_ is given to the envelope of luminous rays
after reflection or refraction; in the first case the envelope is termed
a catacaustic, in the second a diacaustic. Catacaustics are to be
observed as bright curves when light is allowed to fall upon a polished
riband of steel, such as a watch-spring, placed on a table, and by
varying the form of the spring and moving the source of light, a variety
of patterns may be obtained. The investigation of caustics, being based
on the assumption of the rectilinear propagation of light, and the
validity of the experimental laws of reflection and refraction, is
essentially of a geometrical nature, and as such it attracted the
attention of the mathematicians of the 17th and succeeding centuries,
more notably John Bernoulli, G.F. de l'Hopital, E.W. Tschirnhausen and
Louis Carre.
Caustics by reflection.
The simplest case of a caustic curve is when the reflecting surface is
a circle, and the luminous rays emanate from a point on the
circumference. If in fig. 1 AQP be the reflecting circle having C as
centre, P the luminous point, and PQ any incident ray, and we join CQ
it follows, by the law of the equality of the angles of incidence and
reflection, that the reflected ray QR is such that the angles RQC and
CQP are equal; to determine the caustic, it is necessary to determine
the envelope of this line. This may be readily accomplished
geometrically or analytically, and it will be found that the envelope
is a cardioid (q.v.), i.e. an epicycloid in which the radii of the
fixed and rolling circles are equal. When the rays are parallel, the
reflecting surface remaining circular, the question can be similarly
treated, and it is found that the caustic is an epicycloid in which
the radius of the fixed circle is twice that of the rolling circle
(fig. 2). The geometrical method is also applicable when it is
required to determine the caustic after any number of reflections at a
spherical surface of rays, which are either parallel or diverge from a
point on the circumference. In both cases the curves are epicycloids;
in the first case the radii of the rolling and the fixed circles are
a(2n - 1)/4n and a/2n, and in the second, an/(2n + 1) and a/(2n + 1),
where a is the radius of the mirror and n the number of reflections.
[Illustration: FIG. 1. c = a]
[Illustration: FIG. 2. c = [oo]]
[Illustration: FIG. 3. c = (1/3)a]
The Cartesian equation to the caustic produced by reflection at a
circle of rays diverging from any point was obtained by Joseph Louis
Lagrange; it may be expressed in the form
{(4c^2 - a^2)(x^2 + y^2) - 2a^2 cx - a^2 c^2 }^3 =
= 27a^4 c^2 y^2 (x^2 + y^2 - c^2)^2,
where a is the radius of the reflecting circle, and c the distance of
the luminous point from the centre of the circle. The polar form is
{(u + p) cos 1/2[theta]}^2/3 + {(u - p) sin 1/2[theta]}^2/3 = (2k)^2/3,
where p and k are the reciprocals of c and a, and u the reciprocal of
the radius vector of any point on the caustic. When c = a or = [oo]
the curve reduces to the cardioid or the two cusped epicycloid
previously discussed. Other forms are shown in figs. 3, 4, 5, 6. These
curves were traced by the Rev. Hammet Holditch (_Quart. Jour. Math._
vol. i.).
[Illustration: FIG. 4. c = 1/2a]
[Illustration: FIG. 5. c > a]
_Secondary caustics_ are orthotomic curves having the reflected or
refracted rays as normals, and consequently the proper caustic curve,
being the envelope of the normals, is their evolute. It is usually the
case that the secondary caustic is easier to determine than the
caustic, and hence, when determined, it affords a ready means for
deducing the primary caustic. It may be shown by geometrical
considerations that the secondary caustic is a curve similar to the
first positive pedal of the reflecting curve, of twice the linear
dimensions, with respect to the luminous point. For a circle, when the
rays emanate from any point, the secondary caustic is a limacon, and
hence the primary caustic is the evolute of this curve.
[Illustration: FIG. 6. a > c > 1/2a]
Caustics by refraction.
The simplest instance of a caustic by refraction (or diacaustic) is
when luminous rays issuing from a point are refracted at a straight
line. It may be shown geometrically that the secondary caustic, if the
second medium be less refractive than the first, is an ellipse having
the luminous point for a focus, and its centre at the foot of the
perpendicular from the luminous point to the refracting line. The
evolute of this ellipse is the caustic required. If the second medium
be more highly refractive than the first, the secondary caustic is a
hyperbola having the same focus and centre as before, and the caustic
is the evolute of this curve. When the refracting curve is a circle
and the rays emanate from any point, the locus of the secondary
caustic is a Cartesian oval, and the evolute of this curve is the
required diacaustic. These curves appear to have been first discussed
by Gergonne. For the caustic by refraction of parallel rays at a
circle reference should be made to the memoirs by Arthur Cayley.
REFERENCES.--Arthur Cayley's "Memoirs on Caustics" in the _Phil.
Trans._ for 1857, vol. 147, and 1867, vol. 157, are especially to be
consulted. Reference may also be made to R.S. Heath's _Geometrical
Optics_ and R.A. Herman's _Geometrical Optics_ (1900).