CENTRAL CITY

of Yucatan. See under separate articles; also AMERICA.

Central City, the name of several villages and hamlets in the United States, and of the capital of Gilpin county, Colorado, 40 miles W. of Denver by rail, with quartz-mills and rich gold mines, and (1890) 2480 inhabitants; also of a mining town of Lawrence county, South Dakota, in the Black Hills, 280 miles SW. of Bismarck, with formerly some twenty quartz-mills for gold. Pop. (1880) 1008; (1890) 519.

who centred in himself all the great functions of government. In the later days of the empire the tendency increased, until the system broke down with the power that wielded it. Amid the chaos that followed the downfall of Rome various systems religious, or both. Of these the greatest is still arose for the restoration of order, political or the empire of Charlemagne. In those times of the Papacy; the greatest in bygone history was struggle, the natural method was centralisation based on military supremacy;

in which these states lie is to the north of the British Central Provinces' of India, and touches the North-west Provinces, Rajputana, Khandesh in the Bombay Province, and Chutia-Nagpur in Bengal. The total area is about 75,000 sq. m.; Dop. (1891) 10,139,570. The nine subordinate agencies comprised in the Central India Agency are the Indore, Bhil or Bhopawar, Deputy Bhil, Western Malwa, Bhopal, Gwalior, Guna, Bundelkhand, and Baghelkhand agencies. The intrusion of two British districts, those of Jhansi and Lalitpur, belonging to the North-west Provinces, separate these nine agencies into two divisionsnative Bundelkhand and Baghelkhand on the east, and Central India proper or Malwa on the west; but the whole country lies between the Nerbudda, the Ganges, and the Chambal rivers, and is mostly fertile and well tilled. The Malwa western division is mainly a tableland 2000 feet above the sea; but its rich black soil produces fine wheat and much opium. The climate of Malwa is on the whole mild and equable; but the northern part of Central India is torrid, and unhealthy during the rainy season. The mineral wealth of Central India is great: iron, coal, copper, and lime are plentiful, and diamonds are found in some parts of Bundelkhand. The inhabitants are very diverse in origin, comprising Mahrattas (the ruling race), Rajputs, Bundelas, Baghelas, Jats, Kols, and hill-tribes such as the Gonds (414,000) and Bhils (217,000). The population is mainly Hindu in religion, only 510,718 being Mohammedans. The agent to the governorgeneral of India, whose headquarters are at Indore, has very high and very various duties and powers. He is the adviser of all the native chiefs, and their guardian during minority; exercises the functions of a court of appeal; has at his command large bodies of troops; as 'opiumagent' supervises the opium-tax throughout the agency; and he is of course the medium of communication between the imperial government and the native authorities. The principal states and agencies have separate articles. See INDORE, BAGHELKHAND, &c. The Central Provinces (q.v.) are a British commissionership.

Centralisation, a term which has come into general use for expressing a tendency to administer by the sovereign or the central government matters which would otherwise be under local management. The centralising tendency has been a feature in most of the great states recorded in history, though not in all of them. The oriental empires admitted of a large degree of local independence among the subject peoples. The Roman empire was one of the most remarkable instances of centralisation the world has ever seen. That empire grew out of the subjugation of all the states round the Mediterranean by the city of Rome, and the control of it passed by the inevitable tendency of events into the hands of a single chief, whose power rested on the army, and

ising tendency is strongly marked. Centralisation have incessantly been going on, success or even selfwas necessary, for in the great struggles which preservation could be secured only through a strong organisation repressing internal division, and through large and efficient armies. As an adequate revenue was required for these objects, there was further involved a strong control by the central power of the economic and industrial functions of

the state. Thus it will be seen that centralisation is more or less inevitable in the struggle for existence on the European continent. The most notable examples of the opposite tendency at present are apparent in the colonial empire of Great Britain, and in the United States, where we find extensive groups of self-governing communities with only a limited measure of control by the central government. Such control is most limited of all in the British colonies.

On the other hand, in the French commune and in the Russian mir we see, under governments otherwise strongly centralised, a form of local activity which had been long extinct in Britain. The municipal reform of 1835 has done much to revive local action in the town life of England. The aim of the reform of local government begun in 1888 is to revive, extend, and systematise local responsibility and freedom of action, particularly in rural districts. It is now recognised that efficiency in the central government can be best secured by transferring local interests to local management by decentralisation. A wise decentralisation may be subservient to an effective centralisation, a principle which holds good also on the European continent. No absolute rules can, however, be laid down for marking off the respective provinces of the central and local powers. Each country must solve the problem in its own way, as its interests and circumstances require.

ship of India, lying between 17° 50′ and 24° 27' N. Central Provinces, a chief-commissionerlat., and between 76° and 85° 15' E. long., and embracing 18 British districts and 15 native states. Area, 115,936 sq. m.; pop. (1891) 12,932,330. The cropping up even in the level portions. In the north surface is very broken, straggling ranges of hills extend the Vindhyan and Satpura (2000 feet) tablelands, with the Nerbudda between; south of these stretches the great Nagpur plain, with the Chatisgarh plain to the east, and a wild forestregion beyond, reaching almost to the Godavari. Besides the two mentioned, the chief rivers of the province are the Wardha and Wainganga; all four are rapid streams, with their crystal waters leaping from point to point, and rushing headlong through the narrow mountain-gorges of their upper course. The climate is hot and dry, except during the south-west monsoon, from June to September, when 41 of the mean annual 45 inches of rain fall. Wheat is grown chiefly in the Nerbudda valley, rice in the Nagpur plain; these are the principal crops, but oil-seeds, cotton, and tobacco are also raised. The only manufactures of note are

weaving and the smelting and working of iron ores. Iron is abundant, especially in the south, and there are also large coalfields, but the coal is of a very inferior quality. There is considerable trade, but its progress is retarded by the want of means of communication; this drawback, however, is being removed, roads are being made, and the railway system steadily pushed forward. Of the population, three-fourths are Hindus, and one-seventh belong to the so-called aboriginal or non-Aryan tribes, who have found a refuge in the Satpura plateau, and still adhere to their primitive faiths (see GONDS). From these hill-tribes the Hindus throughout the province have contracted beliefs and habits which they have grafted upon the usual worship of their sect; adoration of the dead, worship of the goddess of smallpox, and belief in witchcraft are universal. The population is almost entirely rural, only 6 per cent. residing in the 52 towns of above 5000 inhabitants, of which three -Nagpur, Jubbulpore, and Kampti-have over 50,000 inhabitants. Central India (q.v.) is a term of quite distinct meaning.

Centre and Central Forces.-CENTRE OF

INERTIA (MASS).— If m, and m, be the masses of two particles placed at the points A, and A, and if the right line AA, be divided in B1, so that

B2 is called the centre of inertia of the three particles. In general, if there be any number of particles, a continuation of the above process will enable us to find their centre of inertia. Every body may be supposed to be made up of a multitude of particles connected by cohesion. From this it is obvious that the centre of inertia is a definite point for every piece of matter.

In general, the determination of the centre of inertia requires the use of the integral calculus. In the case of some bodies, such as those which have a simple geometrical form and are of uniform density, elementary mathematical methods will generally be sufficient. Any straight line or plane that divides a homogeneous body symmetrically must contain its centre of inertia. For the particles of the body may be arranged in pairs of equal mass and at equal distances from the straight line or plane; and, since the centre of inertia of each pair lies in the line or plane, the centre of inertia of the whole must also lie in the same line or plane. For example, the centre of inertia of a uniform thin straight rod is its middle point; that of a uniform thin rod bent in the form of a parallelogram, the point of intersection of its diagonals; that of a lamina, uniform in thickness and density and in form a circle, ellipse, or parallelogram, its centre of figure; that of a uniform spherical shell, its centre; that of a homogeneous sphere, its centre; that of a parallelopiped, the intersection of its diagonals; that of a circular cylinder with parallel ends, the middle point of its

axis.

An important case is that of a uniformly thin triangular plate. Let ABC be the plate. Bisect AB in P and join CP. Let the triangle be divided by right lines parallel to AB into an indefinitely great number of indefinitely narrow strips. The centre of inertia of each strip is its middle point.

CENTRE

But all the middle points lie on CP. The centre of inertia of the whole plate must therefore lie on CP. Again, if BC be bisected in Q, and AQ be joined, the centre of inertia of the whole plate must lie in AQ. The centre of inertia must therefore be O, the point of intersection of CP and AQ. It is easily proved by elementary geometry that OP one-third of CP. Hence, the centre of inertia of a triangular plate is obtained by joining a vertex to the middle point of the opposite side and taking the point two-thirds of this line measured from the vertex. By a similar method the centre of inertia of other plane figures may be obtained.

Р

Fig. 2.

CENTRE OF GRAVITY.-If a body be sufficiently small, relatively to the earth, the weights of its particles may be considered as constituting a system of parallel forces acting on the body. Now, the mag. nitude of the weight of a particle is proportional to its mass. Hence, the line of action of the resultant of the parallel forces will approximately pass through the centre of inertia. For this reason such bodies are said to have a centre of gravity. Strictly speaking, there is no such point of necessity for every body, since the directions of the forces acting on the body are not accurately parallel. Hence, it is only approximately that we can say of a body that it has a centre of gravity. On the other hand, every piece of matter has, as is shown above, a centre of inertia. For all heavy bodies of moderate dimensions it is, however, sufficiently accurate to assume that the centre of inertia and gravity coincide. For example, the centre of gravity of a uniform homogeneous cylinder with parallel ends is the middle point of its axis, that of a uniformly thin circular lâmina its centre, and so on.

The centre of gravity of a body of moderate dimensions may be approximately determined by suspending it by a single cord in two different positions, and finding the single point in the body which, in both positions, is intersected by the axis of the cord.

The term centre of gravity is also used in a stricter sense than the one just explained. Thus, if a body attracts and is attracted by all other gravitating matter as if its whole mass were concentrated in one point, it is said to have a true centre of gravity at that point, and the body itself is called a centrobaric body. A spherical shell of uniform gravitating matter attracts an external particle as if its whole mass were condensed at its centre. Such a body has a true centre of gravity. When such a point exists, it necessarily coincides with the centre of inertia.

CENTRE OF OSCILLATION.-A heavy particle suspended from a point by a light inextensible string constitutes what is called a simple or mathematical pendulum. For such a pendulum it is easily proved that the time of an oscillation from side to side of the vertical is proportional to the square root of its length for any small arc of vibration. A simple pendulum is, however, a thing of theory, as in all physical problems we have to deal with a rigid mass, and not a particle, oscillating about a horizontal axis. In a pendulum of this kind the time of oscillation will not vary as the square root of the length of the string, for it is obvious that those particles of the body which are nearest the point of suspension will have a tendency to vibrate more rapidly than those more

remote. The former are therefore retarded by the latter, while the latter are accelerated by the former. There is thus one particle which will be accelerated and retarded to an equal amount, and which will therefore move as if it were a simple pendulum unconnected with the rest of the body. The point in the body occupied by this particle is called the centre of oscillation.

As all the particles of the body are rigidly connected, they all vibrate in the same time. Hence it follows that the time of vibration of the rigid body will be the same as that of a simple pendulum, called the equivalent or isochronous simple pendulum, whose length is equal to the distance between the centres of suspension and oscillation.

The determination of the centre of oscillation of a body requires the aid of the calculus. It may be stated, however, that it is always farther from the axis of suspension than the centre of inertia, and is always in the line joining the centres of suspension and oscillation. Let A be the centre of suspension, B the centre of inertia, and C the centre of oscillation, and let AB be equal to h, and k be the radius of gyration of the body about an axis through B parallel to the fixed axis, then it is easily shown that

Fig. 3. From this there follows the important proposition that the centres of oscillation and suspension are convertible, a proposition which was taken advantage of by Kater for the practical determination of the force of gravity at any

station.

CENTRE OF PERCUSSION.-If a body receive a blow which makes it begin to rotate about a fixed axis without causing any pressure on the axis, the point in which the direction of the blow intersects the plane in which the fixed axis and the centre of inertia lie is called the centre of percussion. That such a point must exist is easily shown by suspending a straight rod by a long string attached to one end, and striking it with a hammer in different points. If the rod is struck near the top the foot will move in one direction, and if the blow be applied near the foot the top will move in the opposite direction. It is thus evident that there must be some point which does not move at all at the instant of the blow. If a line through this point be regarded as an axis of rotation, the point at which the body was struck is the centre of percussion, since no pressure isroduced on the axis. It is easily proved by means of higher mathematics that the centre of percussion with respect to any axis is the same point as the centre of oscillation.

From what has been said it is obvious that in order that no jar may be felt on the hand a cricket ball must be hit in the centre of percussion of the bat with respect to an axis through the hand.

There are, it may be mentioned, many positions which the axis may have in which there will be no centre of percussion. For example, there is no centre of percussion when the axis is a principal axis through the centre of inertia.

CENTRE OF PRESSURE.-When a plane surface is immersed in a fluid at rest, and held in any position, the pressures at different points of the surface are perpendicular to the surface. These pressures may therefore be looked upon as constituting a system of parallel forces whose resultant is the whole pressure. The point at which this resultant acts is called the centre of pressure, and may be defined as the point at which the direction of the single force which is equivalent to the fluid pressures on the plane surface meets the surface. The resultant action of fluids on a curved surface is not always reducible to a single force. The defini

67

tion given above is, therefore, limited to plane surfaces. In the case of a heavy fluid it is clear that the centre of pressure of a horizontal area corresponds with the centre of gravity. When, however, the plane is inclined at any angle to the surface of the fluid, the pressure is not the same at all points, being greater as the depth increases; since in the same liquid the pressure varies with the depth. In general, the centre of pressure will be below the centre of gravity. The determination of the centre of pressure requires the use of the integral calculus, but special cases may be treated by ordinary algebra. In the case of a parallelogram, one edge of which is in the surface of the fluid, the centre of pressure is at a distance of one-third up the middle line from the base. In the case of a triangle, having one side in the surface of the fluid, the centre of pressure is at the middle point of the median corresponding to the vertex immersed; while in the case of a triangle, with its apex in the surface, and the base horizontal, the centre of pressure is on the median corresponding to the vertex and at a distance of three-fourths of the median from the vertex.

CENTRE OF BUOYANCY.-The pressures which act on every point of a surface immersed in a fluid can be resolved into horizontal and vertical components. The former balance one another. The resultant pressure must therefore be vertical; and, as the pressure increases with the depth, it is clear that the upward pressures must be greater than the downward. Hence the resultant pressure on an immersed body must be a force acting vertically upwards. Now it is easily shown that the magnitude of this pressure is equal to the weight of the fluid displaced. The point in the displaced fluid at which the resultant vertical pressure may be supposed to act is called the centre of buoyancy, or centre of displacement. Hence, we see that when a body floats in a fluid, it is kept at rest by two forces, the weight of the body acting downwards through its centre of gravity, and the weight of the fluid acting vertically upwards through its centre of gravity, or centre of buoyancy. The relative positions of the centre of gravity and the centre of buoyancy have an important bearing on the safety of ships at sea. If the centre of buoyancy be above the centre of gravity, the equilibrium is stable; in other words, if the ship is displaced, it will tend to return to its original position. If, on the other hand, the centre of buoyancy be below the centre of gravity, the equilibrium will generally be unstable, although a body may float in stable equilibrium even if the centre of buoyancy be below the centre of gravity, as will be explained under the head METACENTRE.

CENTRAL FORCES.-Central forces are forces whose action is to cause a moving body to tend towards a fixed point called the centre of force. By Newton's first law of motion we know that every body continues in its state of rest or of uniform motion in a straight line, except in so far as it is compelled by forces to change that state.' From this we learn that, if the speed of a body changes, or if the line of motion be not straight, whether the speed be unaltered or not, some force must be acting. In the latter case the forces acting are called central forces. The doctrine of central forces considers the paths which bodies will describe round centres of force, and the varying velocity with which they will pass along these paths. It investigates the law of the force in order that a given curve may be described, and many other problems which can only be solved by mathematical methods. Gravity affords the simplest illustration of a central force. If a stone be slung from a string, gravity deflects it from the rectilinear path which it would otherwise pursue, and makes it move in a

curve called a parabola. Again, the moon is held in her orbit round the earth by the action of gravity, which is constantly preventing her from going off in the line of the tangent to her path at any instant.

În connection with this subject we have to make some remarks on what is called centrifugal force. We have seen that force must always be applied to make a body move in a curved path. Such a force is called a centrifugal force, the old erroneous notion being that bodies have a tendency to fly outwards from the centre about which they are revolving. The use of the term will, however, cause no inconvenience, provided we interpret it merely as indicating that, to keep a body moving in a curve instead of in its natural straight line, a force directed towards the centre of curvature is always required.

Many familiar illustrations of the action of the so-called centrifugal force will occur to the reader. A ball fastened to the end of a string, and whirled round, will, if the motion is sufficiently rapid, at last break the string, and fly off in a tangential path. This is due to the fact that the cohesion of

the particles of the string are no longer able to supply the force necessary to keep the ball moving in its circular path. For a similar reason a flywheel or a grindstone bursts when it is made to rotate too rapidly. It is found that at a curve on a railway it is the outer of the two rails which is most worn. This is due to the fact that the outer rail has to supply the force necessary to keep the trains moving in curved paths. A glass of water may be whirled so rapidly that, even when the mouth is downwards, the excess of the centrifugal force over the weight of the water is sufficient to prevent the water from falling out. The centrifugal force increases with the velocity. As a matter of fact, it can be shown that when a body moves in a circle of radius r, with velocity v, its mv2 centrifugal force is By means of this formula it can be proved that about th of its weight is required merely to keep a body on the earth's surface at the equator. By this amount the weight of a body is diminished. Now 289 is equal to 172. Hence it follows that if the earth were to rotate seventeen times as fast as it does now, the attraction of gravitation would only just be able at the equator to keep bodies from flying off its surface. If the rotating body be plastic, it will swell out in all directions perpendicular to the axis of rotation, and assume the form of an oblate spheroid. For reason the earth itself has assumed the form of an oblate spheroid, a result which is seen on a greater scale in the case of Jupiter and Saturn on account of their larger size and more rapid rotation.

the same

Centrifugal, a machine. See CLARIFICATION. Centrifugal and Centri'petal are terms used in Botany to designate two different kinds of leaf development or inflorescence, the former term being applied when the development proceeds from the apex towards the base of the axis or leaf, and the latter when it is from the base upwards towards the apex. See LEAF, INFLORESCENCE.

Centrifugal Force. See CENTRE. Centripetal Force. See CENTRE. Centum'viri ('a hundred men'), a college of justice in ancient Rome, which had jurisdiction in civil cases. It has been supposed that the body was originally made up of three delegates from each of the thirty-five tribes. There were 180 members in the time of Augustus, and under the emperors it increased in importance, as it became the only scene left for the display of judicial eloquence and of legal knowledge.

CEPHALASPIS

a

Centurion (Lat. centurio, from centum, hundred'), a Roman officer commanding a century or company of foot-soldiers. There were sixty centurions in a Legion (q.v.).

Ceorl, a word which occurs frequently in the laws before the Norman Conquest under somewhat varying senses, but substantially meaning an ordinary freeman not of noble birth. His position gradually sank in social status until it hardly differed from that of the serf, save that the ceorl had the right of choosing his own master in accordance with the law of Athelstan, which required every landless man to find himself a lord. He still remained 'law-worthy,' and paid his wer-gild of two hundred shillings; but part of his freedom had disappeared, and ultimately his condition developed into the complete villenage characteristic of feudalism. On the other hand, ceorls who possessed land often contrived to force their way into a higher social class, that of the thegns, a kind of nobility of service who may be roughly put as equivalent to the knights of the period after the Conquest. A ceorl with 5 hides (600 acres) of land was 'thegnworthy.' The name ceorl does not occur in Domesday-the very degradation of the meaning of the word churl in modern usage is but a part of the historical degradation of the social class which

it denoted.

The central

Ceos (sometimes called by the Italianised name of Zea or Tzia), one of the Cyclades, in the Ægean It is 13 miles Sea, 14 miles off the Attic coast. long, 8 broad, and 39 sq. m. in area. and culminating point is Mount Elias, 1863 feet and valonia. The population is 4311, of whom 4295 high. It is fairly fertile, raising fruit, wine, honey, In ancient belong to the capital, Zea or Ceos. times Ceos was noted as the birthplace of the poets Erasistratus; and the Cean laws were famous for Simonides and Bacchylides, and the physician

their excellence.

Cephalaspis, 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 a large ganoid plate, sculptured externally with circular radiating markings. The shield was produced into a horn at each posterior corner, and bore a median and posterior dorsal spine. Agassiz gave the name cephalaspis ('buckler-headed') from this extraordinary covering, which has very much the appearance of, and was formerly supposed to be, the cephalic shield of an Asaphus or Trilobite. The body was covered with rhomboidal enamelled scales, and furnished with dorsal and pectoral fins : it terminated in a large unsymmetrical tail. In a graphic description of this fossil in his Old Red Sandstone, Miller thus sketches the general appearance of the animal: 'Has the reader ever seen a saddler's cutting-knife-a tool with a crescentshaped blade, and the handle fixed transversely in the centre of its concave side? In general outline, the cephalaspis resembles this tool; the crescentshaped blade representing the head, the transverse cartilaginous, retaining the notochord through life. handle the body.' The endo-skeleton was mainly The flexible body, assisted by the large tail and the fins, would give the cephalaspis the power of moving rapidly through the water. Being a predaceous fish, it must have been a formidable enemy to its associates in the Palæozoic 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. Pteraspis, Asterolepis (20 to 30 feet in length), Scaphaspis, Auchenaspis, and a number of other genera, are united in the same family as Cephalaspis. See Ray Lankester, A Monograph of the Fishes of the Old Red Sand