CENTRALISATION-CENTRE OF GRAVITY.

Fig. 1.

which the European monarchs, such of them espe- as parallel. But a system of parallel forces (see cially as became more powerful than their neigh- PARALLEL FORCES) has a single resultant acting bours, were ever striving; and a few of them, such through a fixed point, whose position is independent as Charlemagne, and, long afterwards, Charles V., of the position in space of the points of application seemed to have almost restored it. In this country, of the component forces, provided their relative we trace C. from the time when there were about a positions in the system continue unchanged. This dozen kings in Britain, and perhaps as many in point is the C. of G.; and if it be supported, it Ireland, till the united kingdom came under the is clear that the body will balance itself upon it in rule of one monarch. A subsidiary C. at the same all positions. The same reasoning obviously applies time made silent progress, absorbing the feudal to any system of bodies rigidly connected. It is power of the aristocracy and the municipal privileges usual to demonstrate this and the general rule for of the corporations. In other countries-as, for in- finding the C. of G. by proving it first in the case stance, in France, notwithstanding her desperate of two heavy particles forming a body or system, struggles for freedom, this process of C. has tended and then extending the proof to the case of any to a pure irresponsible despotism. With so sad a With so sad a number of particles. number of particles. Let P and Q (see fig. 1) be result before their eyes, a distrust of C. has not un- two heavy particles. Join P and Q, and divide the naturally been felt by some inhabitants of Great line PQ in C, so that weight of P: weight of Britain. But the British constitution possesses a Q CQ CP. Then C will be the C. of G. grand remedy, which turns the process to good of P and Q. Draw ACB horizontal, and PM, use instead of mischief. While administrative QN vertical, meeting authority has been centralising in the crown, the AB in M and N. controlling power of parliament has been increas- Then if P and Q ing at a more rapid ratio, so that the vesting of a represent the weights function in the crown or central government, means of P and Q, we have the putting it under the control of parliament, P Q :: CQ: CP. and especially of the peoples' representatives in the But CQ: CP :: CN House of Commons. There is nothing done in any: CM by similar triof the offices under the government for which a angles. Therefore secretary of state, or some other member of the P Q ministry, may not at any time be called to account in parliament. The efficiency of this control was in a manner proved by one or two instances in which offices with central powers were created, without being connected with any of the great state departThere were, for instance, the English Poorlaw Board, and the Board of Health. Both created much discontent and outcry about C., and it was found necessary to transfer their functions to the great government departments, the heads of which are immediately responsible to parliament. It is not the policy of this country in any case to abolish local management, but rather to aid and direct it from the central authority. The constituents of local bodies are often disinclined to watch or control them, and the business falls into the hands of incapable or designing men, or is otherwise mismanaged. A very little central help-especially from a quarter where the proceedings of other bodies of the same kind are known-remedies such defects. One of the methods in which the government has of late been in use to exercise its central power, has been by the appointment of inspectors, who make reports which are laid before parliament. This is, in reality, nothing more than a method of concentrating public opinion on the proceedings inspected and reported on, and as such it is very efficacious.

ments.

CENTRE OF GRAVITY is that point in a body or system of bodies rigidly connected, upon which the body or system acted upon only by the force of gravity, will balance itself in all positions. Though the action of gravity enters this definition, many of the properties of the point are independent of that force, and might be enunciated and proved without conceiving it to exist. By some, accordingly, the point has been called the centre of magnitude, and by others, the centre of parallel forces. Such a point exists in every body and system, and only one such point. Every body may be supposed to be made up of a multitude of minute particles connected by cohesion, and so far as its balance under gravity is concerned, each of these may be supposed to be removed, and its place occupied by a force proportioned to its weight. Instead of the body, on these suppositions, we should then have a system of parallel forces, the lines from the various particles to the earth's centre being regarded

:

:

CN: CM, and P.CM Q.CN. P and Q, therefore, are balanced about C. See BALANCE and LEVER. This is true in all positions of P and Q, for no assumption was made as to their positions. C, therefore, is their centre of gravity. Also, we may conceive P and Q to be removed (see PARALLEL FORCES), and in their stead a particle at C equal to them taken together in weight. If, now, the system contained three, it is clear how we should proceed to find its centre of gravity; having found the C. of G. of two, we should consider the system as formed of two-viz., the equivalent of the first two at their C. of G., and the third, when the case would fall under that already treated; and so on, extending the rule to a system containing any number of particles. Apart from this rule, however, it is possible, in the case of most regular homogeneous bodies, to fix upon their centres of gravity from general considerations. The C. of G. of a straight line, for instance, must clearlybe in its middle point. So the C. of G. of a uniform homogeneous cylinder must be in the middle point of its axis. It must be in the axis, for the cylinder clearly is equally balanced about its axis. It must also be somewhere in its middle circular section, for it will balance itself on a knife-edge under that section. It must, therefore, be in a point where that section cuts the axis, or in the middle of the axis. The C. of G. of a uniform material plane triangle may be found from similar considerations. The triangle ABC (see fig. 2) may be supposed to be made up of uniform material lines parallel to its base AB; each of these will balance upon its middle point. The whole triangle, therefore, will balance upon the line CD, which bisects the base AB and all lines parallel to it. In the same way, the triangle will balance upon the line AE, bisecting BC. But if a figure balances itself upon a line, its C. of G. must lie in A that line. The C. of G. of the triangle

Fig. 2.

is therefore in CD, and also in CB. It must there-fore be at g where these lines intersect, g being the

CENTRE OF GYRATION-CENTRE OF PRESSURE.

only point they have in common. Now, by geometry, | body which are nearest to the axis of suspension we know that g divides CD, so that Cg CD. Hence the rule for finding the C. of G. of a triangle: Draw a line from the vertex, bisecting the base, and measure off Cg, two-thirds of the line. g is the centre of gravity. By a similar method, the C. of G. of a great number of figures may be determined. The above method applies only where the figure of the body is regular, and its mass homogeneous. But many bodies, besides being irregular, are formed by the agglomeration of particles of different specific gravities. Of these, the C. of G. can be found only by experiment, though not always satisfactorily. Let the body be suspended by a string, and allowed to find its position of equilibrium. The equilibrium being due to the tension of the string counterbalancing gravity, it follows that the tension is in the same line with that on which gravity acts on the body. But the tension acts on the line of the string, which therefore passes through the centre of gravity. Mark its direction through the body. Suspending it then by another point, we should ascertain a second line in which lies the centre of gravity. The C. of G., then, must be where these lines intersect. For the effect on the stability of bodies of the position of the C. of G., see STABILITY.

CENTRE OF GYRA'TION is the point at which, if the whole mass of a body rotating round an axis or point of suspension were collected, a given force applied would produce the same angular velocity as it would if applied at the same point to the body itself. The C. of G. bears a strong analogy to the centre of oscillation. The cases differ only in this, that in the latter the operating forces are supposed to act at every point of the moving body, while in the former there is only one force acting upon one point. The C. of G. is found by the following rule: Divide the moment of inertia of the rotating mass by the mass of the body, and extract the square root of the quotient. The result is the distance of the point from the axis of rotation. 'The moment of inertia, it may be stated, is the sum of the products of the weight of each point of the mass by the square of the perpendicular distance of that point from the axis.

i

CENTRE OF MAGNITUDE or FIGURE (see CENTRE OF GRAVITY). C.. of M. is the point on which plane figures and curved surfaces would balance themselves, supposing their areas to have weight. 'Thus, the centre of a circle is its centre of magnitude. Otherwise, C. of M. or F. is a point so situated that all straight lines passing through it, and terminated by the circumference or superficies of the figure or surface, are bisected in it.

would, as simple pendulums, vibrate more rapidly than those more remote. Being connected, however, as parts of the solid body, they vibrate all in the same time. But this connection does not affect their tendencies to vibrate as simple pendulums, and the motion of the body which they compose is a compromise of these tendencies of its particles. Those nearest the axis are retarded by the more remote, while the more remote are urged on by the nearer. Among these particles there is always one to be found in which the accelerating and retarding effects of the rest are mutually neutralised, and which vibrates in the same time as it would if it were unconnected with the other parts of the body, and simply connected by a fine thread to the axis of suspension. The point in the body occupied by this particle, is its centre of oscillation. By this C. of O. the calculations respecting the vibration of a solid body are rendered as simple as those of a molecule of inconsiderable magnitude. All the properties which belong to a single pendulum may be transferred to a vibrating body of any magnitude and figure, by considering it as equivalent to a single particle of matter vibrating at its centre of oscillation.

The determination of the position of the C. of O. of a body usually requires the aid of the calculus. It is always further from the axis of suspension than the centre of gravity is, and always in the line joining the centre of gravity and the point of suspension, when the body is suspended from a point. The rule for finding it in such a case is: If S be the point of suspension, and O the C. of O., SO Σ (md2).

M.Sg

; or

it is the quotient obtained by dividing the moment of inertia of the body by the product of its mass into the distance of its centre of gravity from the point of suspension.

The C. of P.

an

CENTRE OF PERCU'SSION. of a body or a system of bodies revolving about a point or axis, is that point in it, which striking an immovable object, the whole mass shall not incline to either side, but rest, as it were, in equilibrio, without acting on the centre or axis of suspension. If the body be moving freely, then the C. of P. is that point in it at which its whole impetus is supposed to be concentrated. In this case, if the body struck with its C. of P. immovable obstacle, and if it were perfectly rigid and inelastic, it would come to perfect repose; whereas, if it struck the obstacle with any other point, a rotatory motion would be produced in it. When the body is moving freely, and there is no rotatory motion, the C. of P. coincides with the centre of gravity. If the body be moving round a point or axis of suspension, the C. of P. coincides with the centre of oscillation. The more compliformula which cannot conveniently be translated it, would require, for its explanation, analytical into ordinary language. There are many positions which the axis may have in which there will be no C. of P.-i. e., there will be no direction in which an impulse could be applied without producing a shock upon the axis. One case of this sort is that of the axis being a principal axis through the centre of gravity.

CENTRE OF OSCILLA'TION. Referring to the article PENDULUM, the reader will see that the time of a pendulum's vibration increases with its length, being always proportioned to the square root of its length. This is strictly true only of the sim-cated case of a body rotating round an axis within ple pendulum, in which the pendulous body is supposed to have no determinate magnitude, and to be connected with the point of suspension by an inflexible wire without weight. If, however, the vibrating body have a determinate magnitude, then the time of vibration will vary, not with the square root of its length, but with the square root of the distance from the axis of suspension of a point in the body called

its centre of oscillation.

If each part of the vibrating body were separately connected with the axis of suspension by a fine thread, and entirely disconnected from the rest of the body, it would form an independent simple pendulum, and oscillate as such-the time of each vibration being as the square root of the length of its thread. It follows that those particles of the

CENTRE OF PRE'SSURE. The C. of P. of any surface immersed in a fluid is the point in which the resultant of the pressures of the fluid on the several points meets the surface. When the bottom of a vessel containing fluid, or when a plane immersed in fluid, is horizontal, the pressure on every point of it is the same, being that due

CENTRIFUGAL AND CENTRIPETAL-CEPHALOPODA.

to the weight of the column of fluid standing above the bottom or plane. In either case, the pressures at the different points obviously form a system of equal parallel forces, whose centre will be the centre of gravity of the bottom or plane, their resultant passing through this point being the sum of all their forces. But when the plane is inclined at any angle to the surface of the fluid, the pressure is not the same at all points, but is obviously greater at the lower than at the upper points, for the lower have to support taller columns of the fluid. The resultant of these forces, then, will not pass through the centre of gravity of the surface, but through a point below it. This point is the C. of P., and evidently will lie below the centre of gravity for all fluids in which the pressure increases with the depth. If the surface pressed upon form part of the containing vessel, and be supposed movable, it will be kept at rest by a pressure equal to the sum of the fluid pressures applied at the C. of P., and acting in the opposite direction. In the case of a vessel with a parallelogram for one side, the C. of P. is at the distance of one-third of the height from the bottom. In the case of a triangular vessel whose base is at the bottom, it is one-fourth of the height only.

Asterolepis (star-scale), from the circular markings on its cephalic shield.

CEPHALO'NIA, or CEFALONIA, the largest of the seven Ionian Islands (q. v.), is situated at the entrance of the Gulf of Lepanto or Corinth, in lat. 38° 3'-38° 30′ N., and long. 20° 21′—20° 49′ E. It is irregular in shape. Its greatest length is about 30 miles, and its total area 348 square miles. Its surface is mountainous, the soil, for the The inhabimost part thin, and water very scarce. and have planted vineyards wherever the grape tants, however, are industrious and enterprising, will grow, and currants and olive-oil are also produced for export.

The climate is warm and agreeable. The population in 1858 amounted to 72,534. The numbers who are brought up to the medical profession are remarkable; it is said that there is hardly a town in the Levant which has not a practitioner from Cephalonia. The inhabitants are also much more disposed to engage in foreign trade than their brethren of Corfu or The island is subject Zante, and own more vessels. to frequent, but slight earthquakes. There is always a small English garrison kept at C., and steamers ply weekly between it and Malta and Greece (Patras). The language spoken is a Greek dialect. The chief towns are Argostoli (q. v.) and Lixuri.

CENTRIFUGAL AND CENTRI PETAL are terms used in Botany to designate two different kinds of inflorescence, or modes of flowering of C. is called by Homer Same or Samos, and during plants. When the flower-bud which terminates the heroic age was subject to Ulysses, whose resithe floral axis, and is central in the inflorescence, dence was in the neighbouring isle of Ithaca (q. v.). is the first to expand-in which case the others are Later, C. appears under the name of Cephallenia. developed in succession from the centre outwards-It successively fell into the hands of the Athenians, the inflorescence is said to be centrifugal. When Romans, Byzantines, and Venetians, from the last the outermost flowers expand first, the inflorescence of whom it was several times wrested by the Turks. is centripetal, as is the case in catkins, spikes, and On the ruin of the Venetian Republic in 1797, it racemes, in which the flowers nearest the base are was seized by the French, who were in their turn the first to expand, and those nearest the apex the dislodged by the Russians. In 1809, it finally came last. These modes of inflorescence are very charac- into the possession of England. teristic of different plants, of genera, and of orders. CENTRIFUGAL FORCE. See CENTRAL

CEPHALO'PODA (Gr. head-footed), a class of mollusks, the highest in organisation of that division of the animal kingdom. To this class belong the Nautili, Spirulæ, Argonauts, Poulpes, Squids or Calamaries, Cuttle-fish, &c., of the present time, and the Ammonites, Belemnites, &c., of former geological periods. The C. are all marine, and only a few of them are capable of leaving the water, and moving about in search of food on the shore.

CEPHAË'LIS. See IPECACUanha. CEPHALA'SPIS, a genus of fossil Ganoid fishes, of which six species have been described, two belonging to the Upper Silurian, and four to the Devonian measures. The head was protected by The C. receive their name from having organs of a large ganoid plate, sculptured externally with prehension and locomotion attached to the head, circular radiating markings. Agassiz gave the name an arrangement towards which a gradual approach C. (buckler-headed) from this extraordinary cover- may be traced in the highest gasteropod (q. v.) ing, which has very much the appearance of, and mollusks. These organs have been variously desigwas formerly supposed to be, the cephalic shield of nated arms, feet, and tentacula. They have no true an Asaphus. The body was covered with rhom- homology' with the limbs of vertebrate animals, boidal enamelled scales, and furnished with dorsal but are only analogous to them in respect of the and pectoral fins: it terminated in a large hetero- purposes which they serve. The body of the C. is cercal tail. In a graphic description of this fossil in a bag, formed of the mantle (see MOLLUSCA), open his Old Red Sandstone, Miller thus sketches the only at the end to which the head is attached. In general appearance of the animal: Has the reader some, this bag is almost spherical, and locomotion ever seen a saddler's cutting-knife-a tool with a is accomplished only by the appendages of the crescent-shaped blade, and the handle fixed trans-head; in others, the body is elongated, and furversely in the centre of its concave side? In general nished with two fin-like expansions, which are the In locomooutline, the C. resembled this tool; the crescent- principal instruments of locomotion. shaped blade representing the head, the transverse tion by the fins, a cephalopod swims like a fish, handle the body.' The endo-skeleton was cartilaginous, retaining the notochord through life. The flexible body, assisted by the large tail and the fins, would give the C. the power of moving rapidly through the water. Being a predaceous fish, it must have been a formidable enemy to its associates in the Paleozoic seas, for, besides its power of rapid motion, the sharp margin of its shield probably did the work of a vigorously hurled javelin, as in the sword-fish. This genus was originally named

with the head first, and often very rapidly; in locomotion by the arms, it drags itself along, laying hold of any object within reach by means of suckers, with which the arms are furnished. Some C. are capable also of moving backwards through the water by alternate contractions and expansions of a muscular web which unites the bases of the arms; some appear to depend for a similar power of swimming backwards upon the forcible ejection of water from the cavity which contains the gills.

CEPHALOPODA.

The head of a cephalopod is roundish, generally the Dibranchiata they are only eight or ten in furnished with two large and prominent eyes, very similar in structure to those of vertebrate animals. There are also ears, but they consist merely of little cavities, one on each side of the brain, in each of which is suspended a membranous sac containing a small stone. The organs of smell are not very certainly known, but it appears that the C. possesses this sense, as well as that of taste, of which the character of the tongue is much more indicative than in many vertebrate animals.-The brain forms a ring around the gullet. The whole nervous system

CEPHALOPTERA-CERBERUS.

to, to the Palæozoic rocks. Including a small group, which, while it has the siphon on the external margin, has yet simple septa, the Nautilidæ are represented by 145 Silurian, 158 Devonian, and 91 Carboniferous species. The Ammonitida have the siphuncle always on the outer margin of the shell, and the septa with corrugated or lobed margins. This group, with the exception of Goniatites, a Palæozoic genus, is peculiar to, and co-extensive with, the secondary strata. Of the 930 species that have been described, more than the half belong to the genus Ammonites (q. v.).

The order Dibranchiata is found first in the Lias, and extends through the more recent strata, receiving its full development in our present seas. Scarcely 90 fossil species have been described, while more than double that number are known as recent animals. See AMMONITES, ARGONAUT, BELEMNITES, CALAMARY, CUTTLE-FISH, GONIATITES, HAMITES, HOOK-SQUID, NAUTILUS, ORTHOCERAS, POULPE, SPI

RULA, &c.

CEPHALO ́PTERA (Gr. head-wing), a genus of cartilaginous fishes of the ray family, the type of a sub-family, Cephalopterida. The pectoral fins are very much elongated, so as to give great breadth to the fish. The tail is slender and without fin, but armed near its origin with a great spine. The head is terminated in front by a straight line, and on each side of it there projects a membrane (precephalic fin) rolled upon itself, and resembling in shape a pointed horn. The name DEVIL FISH has been given to these creatures in America, of which but one species, C. vampirus, has been observed on the coast of the Southern States. The C. giorna occurs in the Mediterranean, and there acquires a great size: one is mentioned as having been taken off Messina, which weighed 1250 lbs.-more than half a ton. But this is small in comparison with the size of some of the Cephalopteride which occur in tropical seas: one taken at Barbadoes required seven yoke of oxen to draw it. They are very dangerous to swimmers and bathers.

CE'PHEUS, a constellation of the northern hemisphere, containing, according to the Britannic catalogue, 35 stars. Its principal star is Alderamin, of the third magnitude.

CEPO'LA. See BANDFISH.

CERA'M, a long and narrow island of the Asiatic Archipelago, running nearly 200 miles in the parallel of about 3° S., long. 128-131° E., between Booro on the W., and Papua or New Guinea on the E. With an area of nearly 6000 square miles, it has about 27,000 inhabitants. From east to west it is traversed by mountains rising at some points 8000 feet above the sea. While the high grounds yield abundance of fine timber, the valleys are fertile in tropical_productions. The natives, chiefly negroes of the Papuan type, excel in the manufacture of arms. The Dutch claim the sovereignty, and hold

several establishments on the coast.

CERA'MBYX, a Linnæan genus of coleopterous insects, included among those which, on account of the length of their antennæ, are usually known as LONG-HORNED BEETLES, and now generally regarded as the type of a tribe or family. To this tribe belongs the Musk Beetle of England (Callichroma moschata), remarkable for its strong and agreeable odour, which, however, is rather that of roses than of musk. Some foreign species have the odour of musk in great perfection. C. heros, one of the largest European beetles, extremely rare in Britain, deposits its eggs in a hole which it excavates for that purpose in the wood of the oak; and the grub feeds upon the wood, excavating long passages through it.

CERAMIA CEA, a sub-order of Alga (q. v.), also called FLORIDEE, and consisting of sea-weeds of a rose or purplish colour, with fronds formed of cells arranged in rows, sometimes in a single row; the sporocarps containing cells or spores, often in fours (tetraspores), with a transparent perispore, and enclosed in receptacles of very various form and structure. structure. They are most abundant in the seas of the northern temperate zone. Many of them are very delicate and beautiful. A considerable number furnish agreeable articles of food of a gelatinous nature, as DULSE (q. v.), CARRAGEEN (q. v.), or IRISH Moss, and certain species of PLOCARIA (q. v.), which are much used on the sea-coasts of the East Indies. The edible swallows' nests of the East are supposed to be formed of a sea-weed of this sub-order, a species of Gelidium.

CERA'MIC (Gr. keramos, potter's clay, from kaio, to burn, and èra, earth), a term used to designate the department of plastic art which comprises all objects made of clay, such as vases, cups, bassirilievi, cornices, and the like.

CERA'STES, or HORNED VIPER, a genus of serpents of the family Viperidae, distinguished by a broad depressed heart-shaped head, the scales of which are similar to those of the back, and particularly remarkable for the development of one of the scales of each eyelid into a spine or horn, often of considerable length. The tail is very

It

distinct from the body. This genus is exclusively
African, and very venomous. The best known
species, C. vulgaris, the Horned Viper of the north
of Africa, was called C. by the ancients, the name
being derived from the Greek keras, a horn.
was correctly described by the traveller Bruce, but
his description was for some time regarded with
incredulity. Other species of the same genus are C.
nasicornis of the western coast of Africa, and C.
caudalis of the Cape of Good Hope.

CE'RATE (Lat. cera, wax), a compound of wax with other oily and medicinal substances in such proportions as to have the consistence of an Ointment (q. v.). Simple C. is made by melting together equal parts of white wax and olive-oil; they are to be heated together, and carefully stirred into a uniform substance while cooling.

CE'RATITES, a genus of Ammonitidæ, peculiar to, and characteristic of, the Trias. They are distinguished from the other members of the family by having the lobes of the sutures serrated, while the intervening curves, directed towards the aperture, are simple. Twenty-six species have been described.

CE'RBERUS (Gr. kerberos,) in Greek mythology, was the name of the many-headed dog-the offspring (according to Hesiod) of Typhon and Echidna-who guarded the portal of the infernal regions. Later writers describe C. as only threeheaded, with the tail and headed, with the tail and mane composed of serpents, though the poets sometimes encumber him with a hundred heads.-A northern constellation,