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these were.


CENCI, BEATRICE, called the beautiful parricide,', mass, vespers, and other offices. It is suspended was the daughter of Francesco Censi, a wealthy by chains, which are held Roman nobleman. According to Muratori (Annales, in the hand, and is tossed lib. x.), Francesco was twice married, Beatrice being in the air, so as to throw his daughter by the first wife. After his second the smoke of the inmarriage, he treated the children of his first wife in cense in all directions. It a revolting manner, and was even accused of hiring varies very much in form, bandits to murder two of his sons on their return from a simple vase, or from Spain. The beauty of Beatrice inspired him chafing-dish, covered by with the horrible and incestuous desire to possess a perforated dome, to her person ; with mingled lust and hate, he perse- the ornamental structure cuted her from day to day, until circumstances represented in the woodenabled him to consummate his brutality. The cut. unfortunate girl besought the help of her relatives,

CE'NSORS, the and of Pope Clement VII. (Aldobrandini), but did not receive it; whereupon, in company with her of two Roman officers of

The office step-mother, and her brother, Giacomo, she planned


Servius by

Thurible. and executed the murder of her unnatural parent.

fifth king The crime was discovered, and both she and Gia- Tullius, the

of Rome. After the expulsion of the kings, it como were put to the torture; Giacomo confessed, but Beatrice persisted in the declaration that she being appointed till 443 B. c.

was held by the consuls, special magistrates not

It continued to be put to death, August 1599, in spite of the efforts of filled by patricians till 351 B. c., when C. Marcius the learned Farinaceus, who wrote out and presented Rutilus, a plebeian, was elected. Twelve years to the pope an account of the crimes and infamous later it was enacted that one of the c. (there life of Francesco.

Such is Muratori's narrative. were always two) must be a plebeian. In 131 B. C.. Other historians allege that neither Beatrice, her both C. for the first time were plebeians. The C.

were elected in the comitia centuriata, presided step-mother, nor her brother, had any part in the murder of Francesco, but that their condemnation five years, but was shortly afterwards limited to

over by a consul. The term of office at first lasted was the result of an infernal plot hatched by two

The censorship was regarded as robbers, or ky unknown persons whose instruments

eighteen months. It has also been stated, that the the highest dignity in the state, except the dictatorprincipal reason for refusing clemency was the ship. It was a sacred and irresponsible magistracy, avaricious desire, on the part of the pope, to confiscate whose powers were vast and undefined, and whose

decisions were received with solemn reverence. the estates and possessions of the murdered man to duties of the C. were threefold. 1. The taking of the papal see; a statement in itself not improb- the census, or register of the citizens and of their able. In the Colonna Palace at Bome, there is still shewn an excellent painting of Beatrice, property. 2. The regimen morum (regulation of attributed to Guido. The story of Beatrice has morals). 3. The administration of the finances of been made the subject of a powerful tragedy by to value, to take an account of) was originally their

The taking of the census (Lat. censeo, the poet Shelley.

sole function (hence their name), and was held in the CENIS, Mont, or MONTE CENISIO, a moun- Campus Martius, in a building called Villa Publica. tain pass of the Alps, between Savoy and Piedmont, The regimen morum was the most dreaded and forming part of the water-shed between the valleys absolute of their powers. It grew naturally out of of the Doire and the Arc. The culminating point of the exercise of the previous duty, which compelled the pass reaches an elevation of 6775 feet above the them to exclude unworthy persons from the lists of sea. Schist, limestone, and gypsum, in alternate citizens. Gradually the superintendence of the C. beds, compose the stra á of the mountain, the vege- extended from the public to the private life of citizens. tation of which is rich in the rarer kinds of Alpine They could inflict disgrace (ignominia) on any one plants. A railroad 49 m. in length now crosses M. whose conduct did not square with their notions of C. at the height of 6701 feet. By means of an ad- rectitude or duty. For instance, if a man neglected hesion rail, of American invention, a gradient of 3767 the cultivation of his fields, or carried on a disfeet per mile is readily surmounted. A tunnel of reputable trade, or refused to marry, or treated his 7 4-5 miles, estimated to cost $12,000,000, will be family either too kindly or too harshly, or completed in 1871.

extravagant, or guilty of bribery, cowardice, &c., he

might be degraded, according to his rank, or otherCE'NOBITES. See MONACHISM.

wise punished. The administration of the finances CENO'MYCE. See REINDEER Moss.

of the state included the regulation of the tributum, CE'NOTAPH (Gr. kenotafion, from kenos, empty, or property-tax;, of the vectigalia, such as the and tafos, a tomb), a monument which does not tithes paid for the public lands, salt-works, mines, contain the remains of the deceased. They were customs, &c., which were usually leased out to originally erected for those whose bones could not be speculators for five years; the preparations of the found, e. g., for those who had perished at sea.

state budget, &c.—See Rovers, De Censorum apud Latterly, the name was applied to tombs built by Romanos Auctoritate et Existimatione (Utrecht, a man during his lifetime, for himself and the members of his family.

CE'NSORSHIP OF THE PRESS, the term CE'NSER (Fr. encensoir, from Lat. incendo, to generally applied to the arrangements for regulating burn), a vase, or other sacred vessel, used for burn- what may be printed, in countries where the press is ing perfumes. See INCENSE. Censers were much not free. The simplest form of C. is when a public used in the Hebrew service of the temple, but their officer-the censor, or licenser, as he is sometimes form is not accurately ascertained, and it is probable called-reads over the MS. to be printed, and after that they varied in this respect, according to the striking out any objectionable passages, certifies occasions on which they were used. The C., called that the work may be printed. Thence it is comalso a thurible (Lat. thuribulum, from thus, frank- mon in old books to see the word imprimatur--let incense), is used in the Roman Catholic Church at it be printed, followed by one or more signatures.


the state.






ten years.


Though it has its name from an analogy with the United States, it is every ten years; this year functions of the Roman censor, the C. did not come (1860) being that in which it falls to be taken. into operation until the invention of printing. It CENT, and CENTI'ME (Lat. centum, a hundred), was common to all European countries, Great Britain names of coins. The Dutch cent is a copper coin included. The C. was established by act of parlia- = iboth of the guilder, which is equal to 1s. 8d. ment in 1662, 13 Char. II., c. 33; : An act for pre- sterling. In the United States of America, the cent venting the frequent abuses in printing seditious, is a copper coin Math part of the dollar, or treasonable, and unlicensed books and pamphlets, wearly one balfpenny English. The Centime is the and for regulating of printing and printing-presses.' 100th of the French franc (q. v.), and is of the value

a time; and its renewal was refused in 1693, owing to of 16 th of an English penns. a quarrel between the House of Commons and the CENTAU'RÉA, a genus of plants of the natural licenser. Since that time there has been, generally order Compositæ, sub-order Cynaracec, containing speaking, no restriction in this country on what any many species of annual and perennial herbaceous man may publish; and he is merely responsible to plants, chiefly natives of the temperate and cold the law, if in his publication he should commit any regions of the eastern hemisphere. Six or seven public or private wrong. See LIBEL, LAW OF; see species are natives of Britain, some of them also PRESS, FREEDOM OF THE; BOOK-TRADE; and common weeds, whilst some species appear among COPYRIGHT.

the frequent ornaments of flower-gardens.—The CE'NSUS means, in this country, the periodical BLUE-BOTTLE, or Corn BLUE-BOTTLE (C. cyanus), is counting of the people. It is a Latin word applied common in cornfields in by the Romans to one of the functions of their Britain and other parts censors (q. v.). They had to enumerate the people, of Europe, and has now but only for immediate purposes of taxation, so

become frequent also in that no accounts of the results of such enumera

situations tions has been preserved. The idea of ascertaining

America, and

and indeed the numbers of the people, and the proportions in over the greater part of which they are divided according to sex, age, pro

the world. It is an arfession, rank, and the like, as statistical information, nual, growing to the is of late origin. The first C. of Britain was taken height of about two feet, in the first year of the present century-1801. and producing its flowFrom that time it has been taken at each period of ers in July and August.

An attempt, but a rather unsuccessful The florets of the disk one, was made to take the statistics of Ireland in are small and purple ; 1811. Ten years after, the attempt was repeated, those of the ray are few, but the accuracy of the bare enumeration it furnished comparatively large, and was doubtful. That of 1831, which was an improve

of a brigbt blue. ment, was corrected three years after, in order that flowers have long been it might form the basis of a new system of education. much used in wreaths The two subsequent enumerations have been very

and garlands. It is comtrustworthy, and have furnished besides valuable mon in gardens, with statistics regarding the agricultural condition of the flowers variously modicountry. The system of registration under a regis- fied by cultivation. Watrar-general, established in England in 1836, gave

ter distilled from the considerable assistance in taking the C. of 1841 and flowers of the blue-bottle

Blue-bottle (Centaurea of 1851, by supplying a staff for carrying out the was at one time in high

cyanus.) enumeration, and also by affording the means of repute as a remedy for checking it, since, making allowances for migra- weak eyes. The juice of the florets of the disk, with tions, the births and deaths recorded should balance a little alum, dyes a beautiful and permanent the changes in the population between one C.

blue.---The large Blue-bottle (C. montana), a native and another. A similar registration system was of Central Europe, is still more frequently cultivated extended to Scotland in 1854, of which the C. of in flower-gardens. Its flowers are considerably 1861 will have the advantage.

A C. must be larger, and it is a perennial.—SWEET SULTAN (C. taken for the whole empire simultaneously, other- moschata), a native of the Levant, with fragrant wise it cannot be accurate. The practice is for the flowers, is also common in flower-gardens. It is enumerating officer in each petty district to leave a an annual or biennial.

an annual or biennial.Several species, having the schedule at each house, which he receives filled up, involucre spiny, bear the name of Star-THISTLE. aiding, when necessary, in the filling up. The C. of The common STAR-THISTLE (C. calcitrapa) is a 1851 was taken for the night of the 31st March. native of the southern parts of Britain and of This C. supplied important, but not altogether Europe.-The Common or Black KnaPWEED, called satisfactory information, as to the educational and in Scotland Horse Knot (C. nigra), is abundant in ecclesiastical condition of the country, elements the meadows and pastures of most parts of Britain, which are to be left out in the enumeration of and is a troublesome perennial weed, difficult of 1861. By the act for taking a C. in 1861, it is extirpation. C. Jacea, also called KNAPWEED, more provided that a schedule shall be left in each house rare in Britain, is very common in some parts of on Saturday the 6th of April, to be called for on Europe, and its bitter astringent root, and indeed the ensuing Monday. The schedule is to contain the whole plant, were formerly used in medicine. compartments for particulars of the name, sex, age, It affords a beautiful bright yellow dye, almost as rank, profession or occupation, condition, relation good as Saw-wort.-The name C. has its origin in to head of family, and birthplace of every living an ancient legend concerning the care of a centaur person’ who passed the night of Sunday in the by one of the species. house. Almost all civilised nations now take a CE'NTAURS (“bull-killers'), a wild race of men census at regular intervals. In France, it is taken who inhabited, in early times, the forests and mounevery five years, the last being in 1856. In Belgium, tains of Thessaly, and whose chief occupation was it is every three years, the last being in 1858. In bull-hunting. Horner, the first who mentions them, Austria, the same, the last being in 1857. In the describes them merely as savage, gigantic, and CENTAURUS-CENTERING.

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covered with hair. They do not appear as monsters, doses. The name C. owes its origin to the same half-man and half-horse, until the age of Pindar. legend with the name Centaurea, although approThe C. are celebrated in Greek mythology on priated to plants so different.


CE'NTERING, the framework upon which an arch or rault of stone, brick, or iron is supported during its construction. The simplest form of C. is that used by masons and bricklayers for the arches of common windows and doors. This is merely a deal-board of the required shape, upon the curved edge of which the bricks or stones of the arch are supported until they are keyed in. In building bridges or other structures where arches of great span are to be constructed, the C. is usually made of framed timbers, or timbers and iron combined. The arrangement of the timbers should be such, that the strain upon each shall be mainly a thrust in the direction of its length, for if the strain were transverse, a comparatively slight force would snap it, and if a longitudinal pull, the whole structure would be no stronger than the joints holding the pieces of

timber together. In arches of great span, such as that Centaur.-From the Elgin Marbles.

of Waterloo Bridge, London, a longitudinal pulling

strain is almost inevitable in some parts, as a beam account of their war with the Lapitho (q. v.), and of great length would bend to some extent under a their contest with Hercules. The fact lying at thrusting strain. In such cases great skill and care the bottom of Pindar's myth may refer to the are demanded in the designing and construction impression which the old bull-hunters of Thessaly, of the joints. As an arch is built from the piors who spent almost their whole life, it is said, on towards the keystone, the weight upon the haunches horseback, first made on some of the neighbouring during construction tends to push the tribes-viz., that the man and the horse were one upwards, and therefore the problem of designing a creature, which, at least, we know was the opinion | framed C. involves the resistance of this tendency, entertained by the Mexicans of the Spanish cavalry. | as well as the supporting of the weight of the On account of their resemblance to the Satyrs, the materials. C. were at a later period introduced into the artistic The annexed figure of the C. of Waterloo Bridge, representations of the Bacchic worship.

designed by Rennie, presents a fine example of the

fulfilment of these requirements. It will be easily CENTAU'RUS, the Centaur, one of the constellations in the southern hemisphere, represented

seen that a weight upon np and ce will be resisted on the celestial globe by a form half-man and half- by direct thru. t upon the beams passing obliquely horse. The stars in this constellation are, according of these oblique beams thrusts outwards, and is

downwards from these parts; one of each pair to Ptolemy's catalogue, 37 in number; according directly supported by the abutments; the other to the Britannic catalogue, 35. It contains the thrusts inward towards k, the yielding of which stars a Centauri and B Centauri, both of the first is prevented by the longitudinal pull of the lower magnitude.

and longer oblique beams kq, kr, kd, ka, &c. In CENTAURY (Erythrca), a genus of plants of this, and other modern structures, cast-iron shoes the natural order Gentianece, having a funnel-shaped regular 5-partite corolla.


g The species are pretty little annuals, natives chiefly of the temperate parts of Europe and Asia, with pink or rosecoloured flowers. They possess the tonic and other medicinal virtues of gentian, a and although not frequently administered


k * by physicians, are an important domestic


f medicine; and the tops are collected

23 when the plant is in flower, by the country people both in England and on the continent of Europe, to be employed in cmes of dyspepsia, in intermittent fevers, and as a vermifuge. They contain a substance called Centaurine, the

Centering of Waterloo Bridge. hydrochlorate of which is said to be an excellent febrifuge. - The Common C. (E. Centaurium) is the species most frequent in , have been successfully used for the tying joints Britain ; a plant of eight inches to a foot in subject to the longitudinal pulling strain. height, with flowers collected in loose heads, grow- flexible C., so called from its yielding at the joints, ing in dry pastures. Two or three other species are and varying its form with the load put upon it, found on sandy sea-shores. Nearly allied to these is now abandoned. It was chiefly used by French is the AmeriCAN C. (Sabbatin angularis), an annual engineers. That of Perronet for the bridge of plant with an erect quadrangular stem, exten- Neuilly is a celebrated example. sively distributed throughout the United States and Occasionally, when a very great span is required, Canada, and much used in the domestic practice and the navigation will permit, piers are built, or of America, as a prophylactic against autumnal piles are driven, to support the C., and the design is fevers, in strong infusions and large and repeated , much simplified thereby.

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Cupolas like the Pantheon and St. Peter's at Wonder (1714)—though not distinguished by purity Rome, St. Paul's in London, or the flat domes of the of style or truthfulness of portraiture, are lively in Turkish mosques, require very effective centerings. their plots, and have kept their place on the stage. CE'NTIGRADE. See THERMOMETER.

CE'NTO (from Gr. kentron, patchwork), a name CE'NTIPEDE (Scolopendra), a genus of Myri- applied to literary trivialities in the form of poems apoda (q. v.), having a long slender depressed manufactured bỹ putting together distinct verses body, protected by coriaceous plates, 21 pair of or passages of one author, or of several authors, so legs, distinct eyes, four on each side, and antennæ as to make a new meaning. After the decay of with 17 joints. The name is, however, popularly genuine poetry among the Greeks, this worthless extended to species of nearly allied genera. "Centi- verse-manufacture came into vogue, as is proved by pedes run nimbly, feed on insects, and pursue them the Homero-centones, a patchwork of lines taken into their lurking-places. They have not only a from Homer (edited by Teucher at Leipsic, 1793); pair of horny jaws, like those of insects, but also but it was much more common among the Romans another pair of organs closely connected with the in the later times of the Empire, when Virgil was mouth, and which are regarded as transformed legs, frequently abused in this fashion, as in the Č. Nupdilated and united at the base, terminated by a tialis of Ausonius (who gives rules for the composistrong hook, and pierced beneath the extremity tion of the C.), and especially in the C. Virgilianus, for the emission of a venomous fluid, which makes constructed in the 4th c. by Proba Falconia, wife their bite quickly fatal to insects, and in the case of of the Proconsul Adelfius, and giving, in Virgil's the larger species, very painful and even dangerous misplaced words, an epitome of sacred history! The

C. was a favourite recreation in the middle ages.
In the 12th c., a monk named Metellus contrived to
make a cento of spiritual hymns out of Horace and

CENTO, a town of Central Italy, 16 miles northwest of Bologna, is pleasantly situated on a fertile plain near the Reno. It is celebrated as the birthplace of the famous painter Guercino, whose house, adorned with paintings, is still preserved; and in

the church of C. are many of his works. Pop. about Centipede : B, head, magnified.


those which cause

a moving body to tend towards some point or to the larger animals and to man.

The common C.

centre, called the centre of force or motion. The of tropical America (S. morsitans) is often nine doctrine of C. F. has for its starting-point the first inches or a foot in length. A species found in the law of motion-viz., that a body not acted on by south of Europe (S. cingulata) is nearly as large, any external force will remain at rest, or move but its bite does not seem to be equally venomous. uniformly in a straight line. It follows from this law, It may seem strange that creatures of such aspect that if a body in motion either changes its velocity as centipedes should ever have been thought of as or direction, some external force is acting upon it. human food, but Humboldt, in his Personal Nar- The doctrine of C. F. considers the paths which rative, tells us that he has seen Indian children of bodies will describe round centres of force, and the tribe of the Chuymas draw large centipedes out the varying velocity with which they will pass of the earth and eat them. The most common along in these paths. It investigates the law of British C. is not a true Scolopendra, as that genus the force round which a body describes a known is now restricted, but is very nearly allied to it.

curve, and solves the inverse problem, and many It is known to naturalists as Lithobius forficatus. others, the general statement of which could convey It is very plentiful under stones, &c., in summer. no clear idea to the unmathematical reader. Another allied genus, Geophilus, of more numerous gravity is a force which acts on all bodies from joints and slender form, contains some species which the earth's centre, it affords the simplest general are occasionally phosphorescent, one of which, G. illustration of the action of a central force. longicornis, yellow, with a rust-coloured head, is very

stone be slung from a string, gravity deflects it from abundant at the roots of turnips, &c. It is sup- the linear path which it would otherwise pursue, posed, however, to be rather useful than injurious, and makes it describe a curved line which we know preying on the destructive larvæ of insects.

would, in vacuo, be a parabola. Again, the moon CENTLIVRE, Susanna, an English dramatic is held in her orbit round the earth by the action authoress, was the daughter of a Lincolnshire of gravity, which is constantly preventing her from gentleman, named Freeman, born (most probably) going off in the line of the tangent to her path at in Ireland, about 1680. Her early history is any instant, which she would do, according to the obscure; but such were her wit and beauty, that on first law of motion, if not deflected therefrom by her arrival in London, though a destitute orphan, any external force. To that property of matter by and only 16 years of age, she won the heart of a which it maintains its state of rest or motion, unless nephew of Sir Stephen Fox, who, however, died acted upon by other matter, has been given the shortly after their marriage. Her second husband, name inertia. an officer named Carrol, lost his life in a duel. Left We will now explain how, through the action of in extreme poverty, his widow endeavoured to a central force, a body is made to describe a curred support herself by writing for the stage, and after path. Suppose it to have mored for a finite time, producing a tragedy called The Perjured Husband and conceive the time divided into very small equal (performed first in 1700), made her appearance on parts; and instead of the central force acting conthe stage. She afterwards married (1706) Joseph stantly, conceive a series of sudden impulses to be Centlivre, principal cook to Queen Anne, with given to the body in the direction of the centre, whom she lived happily until the time of her death, at the end of each of the equal intervals, and then December 1, 1723. Her plays--The Busibody (of observe what, on these suppositions, will happen. which the leading character, Marplot,' is highly Let S (see fig. 1) be the centre, and let the original amusing), A Bold Stroke for a Wife (1717), and The motion be from A, on the line AB, which does not



If a


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pass through S. In the first interval, the body will | curve AE, to reach the point D, and thus recede inove with a uniform velocity, say from A to B. In the length DE from the curve; but being conthe second, if acted on by force, it would move tinually drawn out of its direction into a curve by

a force to a centre, it falls below the point D by

the distance DE. The force which draws it through D

this distance is called the centripetal force, and that which would make it recede in the same time through the distance DE from the curve is called the centrifugal force. It may be remarked that the centrifugal force is not, like the centripetal,

an impressed or external force acting on the body. B В

It is simply the assertion of the body's inertia under the circumstances produced by the centripetal

force. Α.

familiar illustrations will occur to the Fig. 1.

reader of the action of what is called the centri

fugal force. A ball fastened to the end of a string, on in AB produced to c, Bc being = AB. But when and whirled round, will, if the motion is made it arrives at B, it receives the first sudden impulse A glass of water may be whirled so rapidly that,

sufficiently rapid, at last break the string, and fly off. towards S. By the composition of velocities (q. v.), it will move now with a new but still uniform

even when the mouth is presented downwards, the velocity in BC instead of Be, BC being the diagonal force pressing it up against the bottom of the glass.

water will still be retained in it, by the centrifugal of the parallelogram of which the sides represent the centrifugal action will be found to increase its impressed and original velocity. Having reached C at the end of the second interval

, it receives the with the velocity. In all cases of a body moving in second impulse towards S. It will now move in

a circle, the force, it can be proved, varies as the CD instead of in BC produced. If, then, we suppose and in the inverse ratio of the radius. As in this

If, then, we suppose square of the velocity of the body at the moment, the periods of time to be indefinitely diminished in length, and increased in number, the broken line follows that the force is as the inverse cube of the

case the velocity varies as the radius inversely, it ABCD will become ultimately a continuous curve, radius. As in the case of circular motion the body and the series of impulses a continuous force. This always is at the same distance from the centre, it completes the explanation. Going back, however, on our suppositions, we

follows that the centrifugal and centripetal forces are may here establish Newton's leading law of central law for all orbits is, that the centrifugal force varies

eqnal at all points of a circular orbit. The general forces. That the body must always move in the same plane, results from the absence of any force As the attractive force of gravitation varies as

as the inverse cube of the distance from the centre. to remove it from the plane in which at any time the inverse square of the distance, it may hence be it may be moving. The triangles ASB and BSC shewn that the centrifugal force gives perfect secuare clearly in the same plane, as the latter is on that in which lie the lines Be and BS. Also, sincerity, notwithstanding the constant attraction of the the triangles ASB, BSc are equal, being on' equal sun, that the planets, so far as that attraction is conbases, AB, Bc, and triangle BSC'= triangle BSc, cerned, will never fall into the sun. as they are between the same parallels, cc and Sir Isaac Newton, of whose philosophy it makes

The doctrine of C. F. owes more to Kepler and BS, it follows (by Euclid I. 37) that ASB = BSC. So BSC = CSD; and so on. In other words, the

a considerable branch, than to all the rest of the areas, described in equal times by the line (called maticians have contributed to it. The doctrine of

philosophers, though almost all the leading mathethe radius vector) joining the centre of force and centrifugal forces was first mentioned by Huygens, the body, are equal. As this is true in the limit, at the end of his Horologium Oscillatorium, pubwe arrive, by the composition of the small equal lished in 1673; but Newton was the first who fully areas, at the law: That the areas described by the handled the doctrine, at least so far as regards the lines drawn from the moving body to the fixed cen

conic sections. tre of force, are all in one plane, and proportional to the times of describing them. Very few of the CENTRALISA'TION, a term which has lately laws of C. F. are capable of being proved like the come into general use for expressing a tendency to preceding, without drawing largely on Newton's administer, by the sovereign or the central governlemmas, with which we shall not suppose the reader ment, matters which had been previously under to be acquainted.

local management. We cannot properly use the , Centrifugal and Centripetal Force. - We have term towards an established despotism, for there shewn that a body continually drawn to a centre, everything is already directed from the centre. if it has an original motion in a line that does not The legitimate application is to a state of change pass through the centre, will describe a curve. At from local to central management-a change in the each point in the curve, it tends, through its inertia, opposite direction would, on the same principle, be to recede from the curve, and proceed in the tangent called localization. Of this latter change, however, to it at that point. It always tends to move in a it can scarcely be said that we have any recent straight line in the direction in which it may at example, unless it may be found in the systems of

any time be moving, and self-government lately communicated to some of the that line, by the defini- British colonies. Ever since the existing European tions of a tangent and of states began to grow out of the chaos of the fall of curvature, is the tangent the Roman empire, there has been a continued to the curve at the point. progress in centralization. That empire itself was,

At the point A (see fig. 2), however, the greatest instance of C. which the world C

it will endeavour to pro- has yet seen. In it the numerous municipalities

ceed in AD: if nothing and other local organizations originally existing in Fig. 2.

hindered it, it would actu- Italy, and communicated to the colonies, were

ally proceed in that line, entirely centralised. The empire, such as it had 80 as, in the time in which it describes the arc of the been in the days of Constantine, was the type after

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