people they sat on the sella curulis (an ornamented chair); and like the other senators they wore the toga prætexta. Twelve lictors, with the fasces and axes, as the symbol of the consuls' power over the lives of the citizens, preceded each of them at first; but P. Valerius, called Poplicola, a name which implies his respect, or affected respect, for popular rights, limited the power of the consuls, and curtailed the external symbols of their authority. In the city, the axes were taken from the fasces, and only one of the consuls was preceded by the twelve lictors. From their sentence appeals to the people were allowed. From this time they were deprived of their former power of condemning citizens to death in Rome, and the power of scourging them only remained. But while they were at the head of the army out of Rome, they retained the axes in the fasces and all their former rights. The consul who, according to the settlement of Valerius, was not preceded by the twelve lictors, had a public slave, called accensus, to precede him. The right to the twelve lictors and the supreme authority in matters of administration were enjoyed by the consuls alternately from month to month. which is not absolutely implied in the hypothesis of the problem or theorem in question. Thus, in the proof of the theorem," the square on the hypothenuse of a right-angled triangle is equal to the sum of the squares on the sides," the formation of the right-angled triangle and of the squares is not technically considered as part of the construction, the latter term being only used to imply all the additional formation of figure necessary to the proof." A question is frequently said to be solved by construction, when it is only meant that a geometrical method of solving it is adopted, as distinguished from an algebraical solution. An equation is also sometimes said to be constructed, in the sense inverse to that in which it is said to be solved; that is, when the roots are given, and the equation is required to be found. CONSUBSTANTIAL (Consubstantialis) is equivalent in expression to co-essential, and is the translation of the term duoovσíos, homoousios, which, in the commencement of the 4th century, was the subject of so much zealous contention among the Trinitarian and Unitarian sects of Christians. The Arians and Eusebians, who asserted the second person of the Trinity, and the adherents of Macedonius, who asserted the third person, to be different and distinct in nature from the first, were strenuously opposed by the Athanasians, who, at the council of Nice (A.D. 325), adopted as the pass-word of their party the term duoovolos, consubstantial, or, as it is Englished in the Nicene creed, "Of one substance with the Father." There were three conflicting denominations: those who held the three persons to be of the same substance, Spoovaios; those who asserted them to be of a similar substance, Suolovoios; and those who contended that they were of a different sub-right of putting his veto on the measures of the consuls. In stance, àvouoios. Between these parties the dispute was carried on during several years with great violence; and successive councils, composed of hundreds of bishops, continued to meet for the purpose of altering creeds and reciprocating anathemas. In modern times the avoμotos doctrine has been advocated by Dr. Bury in his Naked Gospel, a work which, though condemned and burnt by the University of Oxford, was approved and adopted by Locke, Clarke, and Whiston. The circumstantial particulars of the ancient controversy may be found in the various histories of the councils of that period, and its modern revival in the numerous works on the Unitarian doctrines. See especially the article 'Arianisme,' in Plugnet's Dict. des Hérésies.' The patricians, after expelling the kings with the help of the plebeians, designed to transfer the royal power to themselves, which they accomplished by securing the election of both consuls out of their own body. The consuls therefore being invested with the supreme power, the struggle of the people with the patricians was at the same time a struggle against the consuls. Their power sustained a great shock by the institution of the tribunes of the plebs. Each of the tribunes, whose number at last amounted to ten, had the order to prevent arbitrary acts of the consuls, the tribune Terrentius, B.C. 461, made a proposition for a code or collection of laws, and in the year B.C. 452 ten men (decemviri) were named for this purpose, who were invested with full powers, and all other functionaries for the time were suspended. The consulate being re-established, the tribunes, B.C. 444, proposed that the people should choose consuls from the plebeians also, a proposal which gave rise to a long and violent contest. The consulship was again suspended, and tribunes of war (tribuni militares) with consular power were appointed, to which office plebeians also were made eligible. At last, B.c. 366, the first plebeian was elected consul. (Liv. vi. 42; vii. i. 2, 21-6.) Afterwards both consuls were on several occasions plebeians. In the mean time the extension of the state made it impossible for the consuls to perform the increased duties of their office, and new functionaries were created. In B.C. 442, the censors, and B.C. 365, the prætors, were created, which latter had the judicial functions prethe consul was called magistratus major, or superior magistrate. CONSUBSTANTIATION, or IMPANATION, is a term adopted by the Lutheran Church to designate its doctrine of the Eucharist, in contradistinction to the transubstantiation of the Church of Rome. Luther, after separating from the Roman Catholic communion, still retained the doctrine of the real presence; but instead of teaching, as the Romanists do, that the priest's pronunciation of the words of conse-viously attached to the consulate. In relation to these new magistrates, cration at once deprive the bread and wine on the altar of their natural qualities, and transform them into the real body and blood of Christ, he taught that after the consecration of the bread and wine, they are mysteriously accompanied with the real body and blood. In short, in transubstantiation, the divine body and blood is present without the bread and wine; and in consubstantiation it is present with the bread and wine the former effects a change of nature, the latter a change of circumstance. The Lutheran doctrine of consubstantiation was first introduced into the church by John, surnamed Pungens Asinus, a doctor of Paris, at the end of the 13th century. His work on this subject, entitled 'Determinatio F. Joannis Parisiensis de modo existendi Corpus Christi in Sacramento Altaris,' was republished by Allix in 1686. Though the consular power was thus much diminished, it was still very great. All the officers of the state, except the tribunes, were under the consuls; they summoned the meetings of the senate, received all despatches, and gave audiences to foreign ambassadors. In time of war they were commanders-in-chief, and the election of the military officers partly depended on them. In critical times the consular power was made unlimited by the decree of the senate, "videant consules ne quid respublica detrimenti capiat" (they should take care that the republic sustained no harm). Under such circumstances they could require the strictest obedience from all the citizens; and they resumed their right to condenin to death without appeal. The imperium or military command was granted to the consuls by the lex curiata [COMITIA], whereby a province (provincia) was assigned to them. The term provincia originally denoted the power given to discharge some public duty out of Rome, particularly the command of the army in conquered countries; and these countries themselves were called provincia (provinces). When a consul, after the expiration of his term of office, was appointed to govern a province, he was called pro-consul. CONSUL (a word of the same family as consulere, to consult), was the title of the highest ordinary magistrate in the Roman republic. King Tarquinius Superbus having been expelled from Rome for his tyrannical conduct, by the joint efforts of the patricians and plebeians, B.C. 409, a republic was established. Instead of kings, two functionaries called consuls (consules, in Greek атo) were appointed to administer the republic. The first consuls were Lucius Junius Brutus and Lucius Tarquinius Collatinus (or M. Horatius, according to Poly- At first no particular age was a necessary qualification for the conbius, iii. 22). The consuls were annually elected in the Comitia Cen-sulate. But by the lex Annalis, proposed by the tribune L. Villius, in turiata, and at first were only chosen from the patricians. the year B.C. 181, a certain age was required for each magistrate; and the consul must be forty-three years of age. But this law was not always observed; M. Valerius Corvus was elected consul in his twentythird, and Scipio Africanus in his twenty-eighth year. No one could legally be re-elected till after an interval of ten years; but M. Valerius Corvus was re-elected six times and Marius seven times. As the consulship was established in the place of the kingly office, the consuls also were invested with the same power that the kings had. (Niebuhr's History;' Gibbon's History,' i. 3; Cicero, ' De Leg.' iii. 3, who ascribes to them "regiam potestatem"). The consulate was, with the exception of the dictatorship, the highest, and, before prætor, ædiles, and censors existed, the only superior administrative office in Rome. The consuls were at the head of the whole republic; the judiciary (jurisdictio), the military (imperium), and the executive powers were all united in them. Accordingly, we find them also called prætores, and judices, and imperatores. They presided in the senate, where they had an elevated seat, and the business in the comitia curiata and centuri ta was conducted by them. The consuls created the quæstors of the public treasury, and thus had great influence in the administration of the treasury, the quæstors being dependent on them. They could also conclude peace and make alliances. They were the supreme judges in all suits and criminal trials. The consuls possessed the same external insignia of honour as the kings, except the golden crown and the trabea (purple cloak), which latter they were only allowed to wear in a triumph. They had a sceptre of ivory, with an eagle at the end. In the assemblies of the The candidate for the consulate was required to be at Rome when the election took place in the comitia centuriata, a rule which was also sometimes not regarded. The elder of the two consuls first received the fasces, until the Emperor Augustus prescribed, by the law called lex Julia and Papia Poppaa, that he should take them first who had most children. The time of election varied at different periods of the Commonwealth; but they were always chosen some time before they entered on office, and were called designati. The time of entrance on office likewise varied; but about B.C. 154 it was fixed that they should always enter on their office on the 1st of January. The years were named after the consuls, and annual registers were kept for that purpose, which were called Fasti Consulares. When the consuls entered on their office, they went in a solemn procession to the capitol to sacrifice to Jupiter Capitolinus; and after this ceremony the senate held a solemn session. Within the five next days they were to take the oath to administer the republic according to the laws; and at the end of their term of office they took a similar oath. Those who had discharged the office of consul were called consulares, and enjoyed a kind of pre-eminence in rank over the other senators. S Consular Medal of M. Agrippa. British Museum. Actual size. Bronze. Weight, 158 grains. From the time of Sulla and Cæsar, who were elected perpetual dictators, the consulate gradually lost all its powers, and under the emperors it sunk to a mere shadow and a name. Yet consuls were sitli annually elected by the people, until the time of Tiberius, who ordered that they should be chosen by the senate. The number of the consuls was much augmented by the emperors; and several kinds of consuls were made, as consules ordinarii, after whom the years still were called; consules suffecti, elected by the emperors; and consules honorarii, who had title and rank, but no power. In the reign of Commodus there were as many as twenty-five consuls in one year. Constantine, however, restored the custom of appointing two consuls only in the year, one for Constantinople, and one for Rome, who were alone to act as supreme judges under the emperor. The last consul at Constantinople, after whom the year was denominated, was Basilius, junior, in the year 1294 A.U.C. or 541 A.D., in the reign of the Emperor Justinianus. The last consul at Rome was Theodorus Paulinus, in the year A D. 536. CONSUL, an officer appointed by a government to reside in some foreign country, in order to give protection to such subjects of the government by whom he is appointed as may have commercial dealings in the country where the consul resides, and also to keep his employers informed concerning any matters relating to trade which may be of interest or advantage for them to know. To these duties are sometimes superadded others having objects more directly political, but into this part of a consul's duty it is not necessary to enter at present, as such functions are assigned to consuls not as such, but in the absence of an ambassador or other political agent. The duties of an English consul, as such, cannot perhaps be better described than by giving the substance of the general instructions with which he is furnished by the government on his appointment. His first duty is to exhibit his commission, either directly, or through the English ambassador, to the authorities of the country to which he is accredited, and to obtain their sanction to his appointment: the document whereby this sanction is communicated, is called an exequatur; its issue must precede the commencement of his consular duties, and its possession secures to the consul "the enjoyment of such privileges, immunities, and exemptions, as have been enjoyed by his predecessors, and as are usually granted to consuls in the country in which he is to reside." It must be the particular study of the consul "to become conversant with the laws and general principles which relate to the trade of Great Britain with foreign parts: to make himself acquainted with the language and with the municipal laws of the country wherein he resides, and especially with such laws as have any connexion with the trade between the two countries." It is the consul's principal duty " to protect and promote the lawful trade and trading interests of Great Britain by every fair and proper means; but he is at the same time "to caution all British subjects against carrying on an illicit commerce to the detriment of the revenue and in violation of the laws and regulations of England, or of the country in which he resides;" and he is to give to his own government notice of any attempt at such illicit trading. The consul is "to give his best advice and assistance, whenever called upon, to her Majesty's trading subjects, quieting their differences, promoting peace, harmony, and good-will amongst them, and conciliating as much as possible the subjects of the two countries upon all points of difference which may fall under his cognisance." Should any attempts be made to injure British subjects in person or in property, he is to uphold their rightful interests and the privileges secured to them by treaty. If, in such cases, redress cannot be obtained from the local administration, he must apply to the British minister at the court of the country in which he resides, and place the matter in his hands. The consul must transmit to the Secretary of State for Foreign Affairs, at the end of every year a return of the trade carried on at the different ports within his consulate, according to a form prescribed. He is also required to send quarterly an account of the market prices of agricultural produce in each week of the preceding three months, with the course of exchange, and any other remarks which he may consider necessary for properly explaining the state of the market for corn and grain. It is further his duty to keep his own government informed as to the appearance of any infectious disease at the place of his residence. The consul is required to afford relief to any distressed British seamen, or other British subjects thrown upon the coast, or reaching by chance any place within his district, and he is to endeavour to procure for such persons the means of returning to England. He is to furnish intelligence to the commanders of queen's ships touching upon the coast where he is, and to obtain for them, when required, supplies of water and provisions, and he is to exert himself to recover all wrecks and stores belonging to queen's ships when found at sea, and brought into the port where he resides. In most cases consuls are subjects of the state by whom they are appointed, but this is by no means an invariable rule, and they are sometimes the subjects of the country in which they reside, or of some other country foreign to both. In some of the less important places, vice-consuls are selected for filling the office from among the mercantile class, and it occasionally happens that they are engaged in commercial pursuits at the port where their official residence is fixed. Consuls or vice-consuls are appointed by the English government, at all the chief ports with which the nation has commercial relations, but the precise number is always varying. The salaries paid vary not only in the manner above stated, but likewise according to the particular circumstances attending the appointment, a residence in some countries being necessarily more expensive than in others. In addition to their salaries, consuls are in the receipt of fees on signing various documents, but these fees are of small amount. CONSUMPTION, PULMONARY. [PHTHISIS PULMONALIS.] CONSUMPTION, MESENTERIC. MARASMUS.] CONSUMPTION, in political economy, is the end of production; the use, the expenditure, of articles produced. It is unnecessary here to enter upon any examination of the theories of productive and unproductive consumption, which have so largely occupied the attention of writers upon political economy. We have stated the general principle under the head CAPITAL. The natural relations between production and consumption appear very unlikely to be greatly disturbed in any condition of society in which there is freedom of labour and security of property. The most injudicious and extravagant consumption on the part of the few is, in its degree, a stimulus to a more strenuous production on the part of the many; and under these circumstances there is sure to be that excess of production over consumption which constitutes capital. The creation of capital shows that the production has been greater than the unproductive consump tion. A judicious and well-regulated expenditure on the part of the few would doubtless afford a more certain encouragement to the industry of the producers, and the excess of production over consump tion would, in the long run, be greater. Whatever injury the im provident consumption of individuals may cause to themselves, it is quite clear that the producing class of society will always repair the waste of the spending class: that in point of fact there will be an excess of production over consumption, wherever the course of industry is not impeded by bad laws, or by a wasteful consumption on the part of a government. Whenever a government engages in the ruinous consumption incidental to war, for example, a very powerful stimulus may indeed be given to particular branches of industry; but other branches of industry that would have been encouraged had their money remained in the pockets of the tax-payers, will proportionately be depressed. The compensating power of production that is called forth in all cases of private consumption must be deranged, or unequally and therefore imperfectly excited, by the consumption of the state. CONTACT (Geometry). Two lines, one of which at least is curved, are said to be in contact when they have a common point, and recede from that point in such a way that the deflection of the one from the other will, if a sufficiently small departure be taken, become as small a fraction as we please of that departure; that is, if there be no limit to the smallness of the ratio which PQ may be made to bear to o N, as we approach the point o. The subject will be further discussed mathematically in TANGENT; CURVATURE; CURVES, THEORY OF; and we shall at present confine ourselves to pointing out the connection between the preceding definition, which is refined and mathematical, and the obvious ocular phenomenon, by perception of which we immediately admit a marked difference of character between contact, as shown at s, and simple intersection, as shown at R. All our perceptions of lines being ocular and physical in the first instance, there is a minimum risibile, or least visible distance, at which lines will run into each other. Now if PQ and o N always preserve such a ratio to each other that the minima visibilia of these lines arrive T NNN nearly together, PQ will not be lost to sight before ON, and the curves will continue distinct up to the very point of meeting. But if PQ diminish so rapidly as compared with oN, as to be lost to sigut while ON is still visible as a length, the two curves will appear to coincide for a visible length, which forms the principal ocular feature of contact. But this practical contact is not admitted in geometry, a science of reason, in which no length is considered as invisible; so that contact is only said to exist where the ratio of PQ to oN diminishes-not merely very much-but without limit. Let ON and PQ be the fractions x and v of a linear unit. If then v diminish without limit when compared with x, but always retain a finite ratio to x2, the contact is said to be of the first order; if v also diminish without limit when compared with x2, but always retain a finite ratio to x3, the contact is said to be of the second order, and so on. These different orders of contact exhibit nothing to the eye but a closer approach, the higher the order of contact; except in this, that contacts of an even order are always accompanied by the intersecting coincidence shown at s, while contacts of an odd order make the curves tangent to each other in the sense in which the word is used by Euclid, as at T. CONTAGION, THE MATTER OF, a poison which, on entering the blood, produces a definite train of morbid phenomena, and which communicates to the blood the property of generating a similar poison, capable of producing precisely similar morbid phenomena. Considered as a morbific matter sui generis, contagion, then, is an agent which produces a disease of a definite nature, one of the distinctive characters of which is that in its progress a peculiar matter is secreted from the blood, which, when introduced into the blood of another individual, produces precisely the same disease. The term contagion is also in common use to denote the actual propagation of diseases of a specific nature from person to person. Such diseases, so propagated, are called contagious; and the matter by which they are propagated is called contagious matter or contagion. The disease called small-pox exhibits a series of morbid phenomena peculiar to itself. These peculiar phenomena constitute it a distinct or generic disease. The pustules formed in its progress, the formation of which is one of the series of morbid phenomena distinctive of it, contain a peculiar secretion, a specific poison, which, on being introduced into the blood of a person previously in sound health, as by inoculation, produces in that person small-pox. This disease, then, presents all the characters of a contagious disease. According to the etymological signification of the term, the propagation of disease from person to person by contagion depends on the actual contact of the body which receives with that which communicates the poison. But direct contact is not indispensable to the propagation of a contagious disease. There are contagious diseases which are absolutely incommunicable without direct contact; but there are others which are capable of communication both by contact and without it. A particle of the matter of small-pox, for example, placed in direct contact with the body, will produce small-pox; but the matter of small-pox is likewise capable of being dissolved or suspended in the air; and the air thus loaded with small-pox matter, on coming in contact with the body, is capable of producing small-pox. Hence contagious diseases are divided into two great classes; into those in which the contagious matter acts only by positive contact of person with person, and into those in which it acts both by positive contact and through the medium of the air. Contagion may therefore be said to be immediate or mediate, contactual or remote. Contagion is carefully to be distinguished from infection. [INFECTION.] CONTEMPT. A contempt in law is a disobedience of the rules, orders, or process of a court of justice, or a disturbance or interruption of its proceedings. Contempts by a contumacious resistance to the process of a court, such as the refusal of a sheriff to return a writ, are punishable by attachment; but contempts done in the presence of the court, which cause an obstruction to its proceedings in administering | the law, may be punished or repressed in a summary manner by the commitment of the offender to prison or by fining him. The power of enforcing their process, and of vindicating their authority against open obstruction or defiance, is incident to all courts; and the means which the law intrusts to them for that purpose are attachment for contempts committed out of court, and commitment and fine for contempts done in facie curia. [ATTACHMENT.] CONTENT (contentus, contained), the quantity of space contained in any portion of space, measured by the number of times which some arbitrary unit is contained in the space. Thus, linear content is simply LENGTH; superficial content is AREA or surface; solid content (in which sense the word is principally used), also called volume, is the number of solid units contained in a space. These solid units are always cubes, described on the unit of length. Thus, when the inch or foot is employed in measuring lengths, the cubic inch or cubic foot is always employed as the measure of solid content. The solid content of a rectangular parallelopiped (or figure like a box) is found by multiplying together the units in the lengths of its three dimensions. Thus, 3 feet of length, 24 feet of breadth, and 4 feet of height, give 3 x 24 x 4, or 30 cubic feet. The solid content of any cylinder or prism is found by multiplying together the number of square units in the base and the number of linear units in the altitude; and one-third of a similar product is the content of a pyramid or a cone. The content of any irregular solid bounded by planes must be found by dividing it into pyramids. Weight is thus connected with content accurately enough for common purposes. Multiply the number of cubic feet by 1000 times the specific gravity; the result is the number of ounces avoirdupois. Roughly, multiply the number of cubic feet by the specific gravity, and five-ninths of the result is the number of cwts. Thus, the specific gravity of brick being 2, a cube of bricks 20 feet long every way weighs of 20 x 20 x 20 x 2, or 8889 cwt. 90 To find the solid content of a sphere, take ths of the rad. × rad. x rad. Thus, the radius of a sphere being 4 feet, the number of cubic feet contained is 4 x 4 x 4 x 37790, or 268 1. CONTINGENT REMAINDER. [REMAINDER.] CONTINUED BASE, in Music, is the figured base of a score used throughout, and so called to distinguish it from the vocal base, as well as from the base staves assigned to particular instruments. The term is only to be found in very old music, and is now become obsolete. CONTRABAND. [CUSTOMS DUTIES.] CONTRACT. [AGREEMENT.] CONTRACTION, in Surgery, an abnormal and permanent alteration in the relative position and forms of parts, arising from various causes. Under the heads ANCHYLOSIS, and DISTORTION, some of the more remarkable results of contractions have been pointed out. In this article we shall describe the nature of club-foot and wry-neck, and point out the recent mode of treating these contractions by surgical operation, which has been remarkably successful. Club-foot, Talipes, is the term which has been applied to all kinds of distortion of the foot. Four species have been described: talipes varus, distortion of the foot inwards; talipes valgus, eversion of the foot; talipes equinus, forced extension; and talipes calcaneus or talus, extreme flexion of the foot upon the leg. Till within a recent period it was a generally received opinion, that all forms of club-foot consisted in a malformation of the bones of the tarsus, more particularly the astragalus, and this malformation was traced to a diseased condition of the bones. It is a curious fact, however, that Hippocrates attributed club-foot to the unnatural contraction of one set of ligaments and the elongation of another. Whether this be the original cause of the distortion may be doubted, but there can be no doubt as to its being a result, and that the only malformation which exists in the parts is removed by relieving the contraction of the ligaments. It is, however, to Delpech in modern times that we are indebted for a sound view of the nature of club-foot, and more particularly for suggesting, though himself unsuccessful, the modern operation for its relief. Two cases of club-foot, which had been produced after the bones had attained their full development, led him to regard the irregular action of the muscles as the cause. To this conclusion also Stromeyer of Berlin was led, by an inquiry in which he engaged, on the occurrence of paralysis in the muscles of inspiration. The following are the various sources of distortion dependent upon irregular action of the muscles, according to Dr. Stromeyer. 1. Structural changes in the muscles, inflammation and wounds, with loss of substance. 2. Debility and inactivity of antagonists, produced either by wounds of tendons or the bellies of antagonist muscles, or by paralysis of the nerves of antagonist muscles. 3. Diminution of voluntary power in the entire limb through which the flexors or extensors preponderate over the extensors or flexors by the constant organic contraction of the muscles. 4. Painful affections of the part, restraining or prohibiting motion, such as that from inflammation of a joint. 5. Increased energy in the muscle, morbid contraction or motion in the muscular fibres, tonic spasm. The various modes of treatment of club-foot formerly pursued indicated the want of a definite knowledge of its nature. They were mostly mechanical, and seldom effected the object they had in view. The mode of treatment now more generally pursued is the use of mechanical means after the performance of a surgical operation. The operation consists in dividing the tendons of the contracted muscle, which admits of the restoration of the malformed parts to their normal position, and the space between the divided ends of the tendon is filled up with new matter, and the function of the muscle is normally performed. This operation, simple as it is, was never performed till the year 1784, when Lorenz, a surgeon at Frankfort, divided the tendoachillis for the cure of a case of club-foot, under the direction of Thilenius. The same operation was afterwards unsuccessfully resorted to by Sartorius and Michaelis. In 1816 Delpech again attempted it, and upon more philosophical principles than his predecessors, but he also failed. This did not prevent Stromeyer from repeating the operation in 1831, which was perfectly successful. In 1833 and 1836 he published two memoirs, containing six successful cases. It was speedily performed again by several surgeons in England and on the Continent, and the value and utility of the operation are now universally admitted. The principal rule to be observed in the operation is not to cut through more parts than is necessary, and to divide the tendon of the contracted muscle. The division of the tendo-achillis is however only calculated to relieve talipes equinus and the slighter cases of varus. But in the severer forms of varus, the tendons of the tibialis posticus, flexor longus pollicis, and sometimes of the tibialis posticus, require division. In valgus the tendons of the peronei as well as the tendoachillis require division. The principal part of the treatment takes place after the operation, and consists of applying various mechanical means for the restoration of the parts to their normal position. This treatment is generally commenced from two to four days after the operation. A great variety of apparatus have been designed for the purpose, but each case requires a peculiar adaptation of the means for eflecting the reduction of the parts. Club-hand does not occur so frequently as club-foot, but the distortion is of precisely the same nature, and requires for its removal the application of the same measures. Wry-neck (Caput obstipum, Torti-collis) is a disease of the same nature as the preceding, and most frequently arises from the unequal contraction of the muscles of the neck, originating in some one of the causes previously mentioned. The consequence is that the head is permanently inclined towards one of the shoulders. Sometimes this disease arises from disease in the vertebræ or from the contraction of cicatrices after severe wounds and burns of the neck. In the former case the wry-neck can seldom be removed, but in the latter the cicatrix may sometimes be advantageously divided, and the wound allowed to heal again with the head in its natural position. Where it depends on contraction of the muscles, the same operation may be had recourse to as is used for the relief of club-foot and club-hand. It is a curious fact that the operation for dividing the muscles in wry-neck had been recommended and practised long before it was found to be generally applicable to the treatment of contractions. When it is determined to treat wry-neck by mechanical means without operation, the best apparatus is that of Jörg. It consists of a pair of leather stays, and of a band or fillet which goes round the head. To the stays is attached a pulley, over which runs a band to the back of the ear, in the direction of the muscles of the neck, and which can be tightened by means of a screw. It thus acts on the head as the muscles would do if they were in action. Dr. Little of London has recently published a work on the application of the Stromeyerian operation to contractions depending on what is called partial ankylosis. These ankyloses depend upon some organic or functional lesion of tendon or muscle, arising from one of the following causes: 1. From sloughing or adhesion. 2. From spasmodic contraction. 3. From organic contraction through paralysis of antagonist muscles. 4. From contraction owing to long-continued rest of the limb. When this kind of ankylosis has not existed for a great length of time, or occurs in young persons, a division of the contracted muscle, and a careful extension of the limb afterwards, is very often followed by a complete restoration of the function of the ankylosed joint. Furetière, who wrote his dictionary in the time of Louis XIV., says there were no fewer than 14,000 convents formerly in France. Convent, as related to the foreign military orders, meant the principal seat or head of the order. Furetière says, " La Commanderie de Boisy, près d'Orleans, est le Convent général de l'Ordre de St. Lazare." The earliest inhabitants of convents were termed Cænobites, from the Greek words Koós and Bios, as living in community. They dwelt chiefly in Egypt. Fleury (Hist. Eccles.,' 4to, tom. v. p. 14, Paris, 1720,) dates their institution as early as the days of the Apostles; others, probably with more correctness, give them a later origin. St. Pachomius, abbot of Tabenna, on the banks of the Nile, who was born at the close of the third century, is believed to have been the first person who drew up a rule for the Cenobites. (Moreri, 'Dict. Histor.,' tom. viii.) [MONASTERY.] CONVENTION, MILITARY, a treaty made between the commanders of two opposing armies concerning the terms on which a temporary cessation of hostilities shall take place between them. It is usually solicited by that general who has suffered a defeat, when his retreat is not secure and small chance is left of maintaining his position; and it is seldom refused by the victor, since without incurring the unavoidable loss attending an action, his force becomes immediately disposable for other operations. In 1757 the Duke of Cumberland, when in danger of being sur rounded, entered into a convention with the Duke de Richelieu, through the medium of Denmark, by which, on consenting to disband all his auxiliaries, he was allowed to retire with the English troops across the Elbe. And in 1799, when the Anglo-Russian army failed in the attempt to deliver Holland from the French power, the Duke of York made a treaty with General Brune by which the invading force was allowed to re-embark on condition that 8000 French and Dutch prisoners of war in England should be restored. After the battle of Vimeira in 1808, the Duke of Abrantes, having been defeated, and fearing a general rising in Lisbon against him, sent General Kellerman to the quarters of the British commander-in-chief, to request a cessation of arms, and propose a convention by which the French troops might be allowed to retire from Portugal. This being granted, it was finally arranged in the convention that they should not be considered as prisoners of war; and that, with their property, public and private, their guns and cavalry horses, they should be transported to France: on the other hand, all the fortresses which had not capitulated were to be given up to the British, and a Russian fleet, then in the Tagus, was to be detained in English ports till after the conclusion of a peace. This is the celebrated convention which was made at Lisbon, and is generally but improperly called "of Cintra." It excited much dissatisfaction both in Portugal and England. (Napier, vol. i.) By the appointment of a committee consisting of one individual of each of the The same causes which produce the above-named diseases give rise to the irregular action of the eye called squinting, and the operation of Stromeyer has been found perfectly successful in this deformity. [SQUINTING.] (Little, On Ankylosis; Little, On Club-Foot; Cooper's Surgical Dic-three nations, all causes of complaint were, however, finally removed. tionary Cooper, First Lines of Surgery; Articles Anchylosis' and 'Club-Foot,' Cyclopædia of Surgery.) CONTRALTO; CONTRATENOR. [ALTO.] CONTRARY and CONTRADICTORY. Two propositions are commonly said by logicians to be contrary when the one denies every possible case of the other; and to be contradictory, when one being universal, the other denies some of the things asserted in the first. Thus, the contrary proposition to " every A is B" is, "no A is B," and its contradictory is, some As are not Bs." 66 Contrary propositions may be both false, but cannot be both true; as in "all angles are equal," and "no angles are equal." But of contradictory propositions one must be true and one must be false; either "all angles are equal," or "some angles are not equal." One of the most common fallacies of conversation and debate (and occasionally of written argument) is fixing the assertion of the contrary upon one who simply contradicts. And, on the other hand, nothing is more common than to assume a contrary as proved upon grounds which establish only the contradictory. The most easy way of establishing general propositions is, in many cases, the refutation of the contradictory; and here is another source of error, since the refutation of the contrary is frequently supposed to have the same effect. In common language, the two words are used in the same sense; persons are said to maintain contrary sides of an argument, when their conclusions are not the technical contraries of the logicians, but only contradictory of each other. The common question, "Have you anything to say to the contrary?" always means, "Can you contradict this?" CONVENT, from the Latin conventus, an assembly or meeting together. This word is used in a double sense, first, for any corporation or community of religious, whether monks or nuns; and secondly, for the house, abbey, monastery, or nunnery in which such monks or nuns dwell, Shakspere uses it in the first sense, when he says of Wolsey "At last, with easy roads, he came to Leicester, Lodged in the abbey; where the reverend abbot With all his convent honourably received him." Hen. VIII., act iv., sc. 2. Addison uses it for the building :-"One seldom finds in Italy a spot of ground more agreeable than ordinary that is not covered with a Couvent." CONVENTION PARLIAMENT. Two days after the abdication [ABDICATION] of James II., the Prince of Orange invited the lords spiritual and temporal, to the number of about ninety, who had taken their places in the House of Lords, together with such persons as had sat in Parliament in the reign of Charles II., to the number of about a hundred and fifty, with the alderinen of London, and fifty of the common council, to meet him, and he requested them "to consider the state of the country, and to communicate to him the result of their deliberations." They did so, and the recommendation was that he should summon a convention of the estates of the realm. The prince accordingly despatched circular letters to the several counties, universities, cities, and boroughs, for the election of members. The convention, or parliament, as it was afterwards declared to be, passed the Act of Settlement, which declared the throne vacant, and conferred the crown, with constitutional limitations to its power, on the Prince and Princess of Orange jointly. The Convention Parliament was dissolved 29th January, 1691. (See "Popular History of England," by Charles Knight, vol. iv., p. 443, et seq.) CONVENTION TREATIES. These are treaties entered into between different states, under which they each bind themselves to observe certain stipu ations contained in the treaty. In 1843 two acts were passed (6 & 7 Vict. c. 75 and c. 76) for giving effect to conventions between her Majesty and the King of the French and the United States of North America for the apprehension of certain offenders. The act relating to France (c. 75) legalises the convention entered into with the government of that country for the giving up of offenders who may escape from France into England. On requisition duly made by the French ambassador, a warrant will be issued for the apprehension of fugitives accused of having committed the crimes of murder (as defined by the French code), attempt at murder, forgery, or fraudulent bankruptcy; and any justice before whom they may be brought is authorised to commit them to jail until delivered up pursuant to the ambassador's requisition. Copies of the depositions on which the original warrant was issued, duly certified as true copies, are to be received as evidence. But no justice is to issue a warrant for the apprehension of any French fugitive unless the party applying is the bearer of a warrant or document, issued by a judge or competent authority in France, authenticated in such a manner as would justify the arrest of the supposed offender in France upon the same charge. The secretary of state will order the person committed to be delivered up to the person or persons authorised to receive him. If the prisoner committed shall not be conveyed out of her Majesty's dominions within two months from the time of his committal, any of her Majesty's judges, on application made to them, and after notice of such application has been sent to the secretary of state (or to the acting governor in a colony), may order such person to be discharged, unless good cause shall be shown to the contrary. The act is to extend to all her Majesty's present or future possessions, and to continue in force during the continuance of the convention. The act relating to America (c. 76) is similar in its nature and purposes to the one relating to France; but the crimes specified in clude, in addition, piracy, arson, and robbery, and do not include fraudulent bankruptcy. Difficulties, however, have arisen as to the jurisdiction of either country as to crimes committed at sea. A murder may be committed on an English subject on board an American vessel (or vice versa), and in whichever country it arrives it is undecided whether either country has jurisdiction over the case. In 1844 a case occurred of a fraudulent French bankrupt who had escaped to England, and the French government demanded that he should be given up under the Convention Treaty. He was arrested and taken to prison; but before the surrender could take place he applied for writ of habeas corpus, on the ground that fraudulent bankruptcy was an offence unknown to the law of England, and that therefore it was contrary to law to arrest him or keep him in custody on such a charge. The warrant of commitment did not specify that the prisoner should be given up on requisition duly made according to the act, but the words were, "until he shall be delivered by due course of law." In consequence of the defective application of the Convention Treaty in this particular case the prisoner was discharged. CONVERGENT, CONVERGENCY, DIVERGENT, DIVERGENCY. When a series of numbers proceeding without end, has terms which diminish in such a manner that no number whatsoever of them added together will be as great as a certain given number, the series is called convergent. But when such a number can be added together as will surpass any given number, however great, the series is called divergent. Thus, of the two following series1 1 1 3 1 1 1 4 1 + +-+ 8 +, &c., and 1 + + ++ &c., the first is convergent, for no number of its terms, however great, will amount to 2: the second is divergent, and the sum of its terms may be made to exceed any number. By going a mile, then half a mile, then a quarter of a mile, &c., two miles could never be completed: but by going a mile, then half a mile, then one-third of a mile, &c., a hundred million of miles, or any greater number, could be surpassed. The subject of the convergency of series is one of fundamental importance in the whole of the mathematics; but it is only recently that it has been treated, in works on algebra, in the manner which its importance requires. Algebraical writers once imagined that a series, however obtained, is safe and fit for use, whether convergent or divergent. This opens a question which has caused much discussion, and on which we cannot here enter. We shall state the results of investigation on the subject, together with the references to sources of information. then, if there ever arrive a term of the series (A), from and after which all the terms are not only less than unity, but tend towards a limit which is less than unity, the series is certainly convergent: but if the terms aforesaid become greater than unity, and continue so from and after a given term, the series is certainly divergent: and if the limit in the first case be not less than unity, but unity itself, the series may be either convergent or divergent, and each particular case must be examined by itself. Instances of both sorts can be given. 4. Series of the form a+b+c+dx3 + ex* + &c., can always be made convergent by giving a sufficiently small value to x, except only in the case where the terms in the series (A) increase without limit from and after any term. If they do not increase without limit, let L be the limit; then the preceding series is convergent whenever La is less than unity, is referable to the preceding case when La is equal to unity, and divergent when Lc is greater than unity. But if L=0, the preceding is always convergent. 5. Series whose terms are alternately positive and negative, are always convergent when the terms diminish without limit, and the error committed by taking any number of terms to stand for the whole value, is never so great as the first term thus rejected. For instance, if the answer to a question be + &c., then 1 + 2 3 The results are alternately too great and too small. 6. When such a series as the last has its terms not diminishing without limit, but towards a finite limit, the sum of any number of terms, increased by half the limit, is never wrong by so much as the first-rejected term differs from the limit. 7. When series produced by algebraical development have their terms alternately positive and negative, the error committed by stopping at any term is never, in any case which the student will meet with, so great as the first rejected term, even though the series become afterwards one of continually increasing terms. If, then, such a series have the first few terms rapidly diminishing, a close approximation may be made by means of them to the real value of the expanded function. For instance, in the series 1-2x+2.3x2 - 2.3.4x3 + (in which an attempt to calculate from the whole series would be utterly futile, since, however small x may be, there must be terms of every degree of magnitude) when a is small, an approximation may be made to its value from the terms which decrease. Thus if x = 1, in which case the series is 1206·024+0120-00720+ &c., 11x): (and the first term which surpasses that preceding, is 2.3. the aggregate of the terms up to 2.3.... 9 inclusive, will not differ from the true value of the expression by so much as 2.3.... 10.x, or 0036288. The proof of this curious proposition, in the vast number of cases in which it is true, may be deduced from Lagrange's Theorem on the Limits of Taylor's Series. (Lib. Useful Knowledge,'-Differential Calculus, p. 73.) Series which are functions of x may be divided into-1. Those which are sometimes convergent, and sometimes divergent, such as the developient of (1+x)". 2. Those which are always convergent at last, but in which the appearance of divergency (increasing terms) may be continued as long as we please, such as the development of e. 3. Series which are always divergent, but to which a similar appearance of convergency can be given, such as 1 + 2x + 2.3x2 + ...., and the like. 4. Series which are always convergent or always divergent, and never can be made to exhibit any symptom of approach to the other state, such as x2 + + ... 1+x2 1 + x x+-+ x + +... and The series which are always convergent, both in reality and appearance, and upon which, therefore, an arithmetical algebraist would reckon with most security, do, in fact, offer difficulties of a very peculiar character. They are the only ones in which the usual algebraical generalisations would lead to absolute error (so far as has yet appeared). On this subject generally, see Peacock's' Algebra,' and 'Report on Analysis' (Rep. Brit. Assoc., vol. ii.); Cauchy, Cours d'Analyse;' Grunert, Supplemente zu Klugel's Wörterbuche der Reinen Mathematik,' in the article Convergenz der Reinen;' 'Encyc. Metrop.,' article Calculus of Functions.' See also SERIES. CONVERSE. We here state the ordinary theory of the logical converse. Converse, in logic, means a proposition which is formed from another by interchanging the subject and predicate, thus: the converse of " Every A is B" is" Every B is A." But care must be taken to put the proposition in its usual logical form before conversion. For the proposition first stated is Thus the converse of "Every A has a B" is not " Every B has an A." 66 Every [subject] [copula] [a thing which has a B predicate. and the converse is "Every thing which has a B is an A.” E and A are convertible by diminution. Nothing is more apt to make a beginner believe that "Every A is B" yields "Every B is A," than the study of geometry without close attention to the meaning of terms and the force of the parts of an assertion. For as a majority of the earlier propositions have their |