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ular intervals, the next after that of 1860 having the United States cent is a bronze coin, the 100th been in 1877. The International Statistical Con- | part of the dollar, or nearly one halfpenny English, gress, which consists of eminent statisticians from and the Canadian cent has the same value. The all countries, has done much to improve the taking centime, the 100th part of the French franc, and of censuses, and now several countries, such as of the value of loth of an English penny, has been Austria, Belgium, Italy, Prussia, Russia, and adopted in Belgium, and, under other names, in Switzerland, have statistical bureaus for the pur- Greece, Italy, and Switzerland; and the Spanish pose, amongst other things, of controlling the taking real (24d.) also is divided into 100 centimes. The of the periodical census. In a few countries in- cental in the United States, legalised in 1878, is formation as to the religion of the population, and 100 lb. avoirdupois (cf. CENTNER). See DECIMAL in some cases additional particulars, are obtained, | SYSTEM. such as the census of useful domestic animals'

Centaurea, a palæarctic genus of Compositæ, in Norway. In the United Kingdom the practice is for

containing about two hundred species, all herba

ceous annual and perennial, of which five or six parliament to pass special acts directing the tak

are natives of Britain. The species most familiar, ing of each census. These acts provide that

on account of its beauty, is the blue C. cyanus (see the registrars of births and deaths shall be the

CORN-FLOWER), which is sometimes sown as an officers through whom the census is to be taken by

annual ; while its larger perennial ally, C. monenumerators, of whom at the census of 1881 there

tana, with white or purple ray florets, is a familiar were upwards of 30,000 employed in England alone.

denizen of old-fashioned gardens ; C. americana is All the registrars' districts are so subdivided that

a showy lilac-purple annual (3 or 4 feet); while no enumerator has more houses than he can con

the oriental Sweet Sultan (C. moschata) and veniently visit in one day. The enumerators have

Yellow Sultan (C. amberboa) are also not uncomto deliver schedules at all houses, requiring par

mon; the latter two being often sold under the ticulars concerning every person who is alive at

name of Amberboa. Among perennials, the large, midnight preceding the census day, and on the

downy C. babylonica, with yellow flowers, is often census day to collect them. Account has also to

cultivated ; also C. ragusina and C. candidissima, be taken of all persons not dwelling in houses

of which the silver-white pinnate leaves furnish an wherever found, and of persons travelling, and

admired contrast to bright-coloured bedding-plants. persons in ships, barges, &c. The enumerators are

Several species (C. calcitrapa, &c.) bear the name authorised to require the information necessary for

of Star-thistle, from their spiny involucre. Some the census, and persons refusing to answer or are common wayside weeds, often troublesome in wilfully giving false answers to the questions are

pastures, notably C. nigra, the Common or Black rendered liable to penalties. The particulars to be

Knapweed, also called Horse Knot in Scotland ; required in each census are specified in the act

and the closely allied C. Scabiosa. The flowers or directing it to be taken. The Census Act, 1880,

roots of several species were formerly used in required that the census of the following year

dyeing, and the astringent roots employed by should show the name, sex, age, rank, pro- |

herbalists. fession or occupation, condition as to marriage, relation to head of family, and birthplace of every

Cen'taurs ('bull-killers'), a wild race of men living person who abode in every house on the

who inhabited, in early times, the forests and night of Sunday the 3d of April 1881, and also

mountains of Thessaly, and whose chief occupation whether any were blind or deaf and dumb, or

was bull-hunting. Homer, the first who mentions imbecile or lunatic.' When the schedules have

them, describes them merely as savage, gigantic, been collected they are transmitted to the census

and covered with hair. They do not appear as office, where the work of tabulation, which takes

| monsters, half-man and half-horse, until the age of about two years, is carried out. The census when

Pindar. The most ancient account of the Hippo. finished is presented to parliament in the form of

centaurs, sometimes considered as distinct, but several bulky volunies. Hardly any two countries

more often confounded with the Centaurs, is that agree as to the subjects on which information is

they were the offspring of Magnesian mares and demanded ; thus some census schedules contain

| Centaurus, himself the offspring of Ixion and a inquiries as to whether there are in the household

cloud. The Centaurs are celebrated in Greek infirm persons, blind, deaf and dumb, idiots,

| mythology on account of their struggles with the insane persons, persons who have been convicted

Lapithæ (q.v.), and with Hercules. The most of crime; how many languages are spoken by the

famous was Chiron, the teacher of Achilles and

other heroes. In works of art the Centaurs were persons entered; how many are at school; how many exercise the franchise; how many rooms and

represented as men from the head to the loins, with windows there are in the house, and so on. In 1851

the rest of the body that of a horse. It is worth an attempt was made to obtain religious statistics

mentioning that the Mexicans, who had no native of the United Kingdom ; since that year the census

horses, when they first saw the Spaniards on shows the religious statistics of Ireland only.

horseback, believed that the horse and man The census of the United States aims at giving a

together made but one animal. specially full conspectus of the condition of the Cen'taury (Erythræa), a pretty little annual, people, and is illustrated by a large number of maps genus of Gentianaceae, with pink or rose coloured bearing on almost every branch of the census in. Howers. They possess the tonic and other medi. quiries. Thus there are maps showing the pre-cinal virtues of gentian, and the Common Centaury valence of certain diseases; others the area occu. (E. Centaurium) has especially been esteemed in pied by various crops. The United States census of medicine since the days of Dioscorides and Galen; 1880 extended to 22 volumes, embracing statistics and although no longer in the pharmacopaja, its of population, agriculture, manufactures, mininy, flower-tops are still sometimes gathered and dried taxation, public indebtedness, with special reports by countrypeople in England and the Conti. on cotton-growing, petroleum, coal, coke, building. nent; while the allied Sabbatia angularis enjors stones, iron and steel products, &c. The census of similar repute in the United States and Canada. 1890 is comparatively limited in the scope of its The Yellow Centaury is Chlora perfoliata ; but inquiries.

plants belonging to the wholly distinct composite Cent and Centime (Lat. centum, 'a hun. genus Centaurea (q.v.) are also sometimes called dred'), names of coins. The Dutch cent is a

Cent copper coin, the 100th part of the guilder (1s. 8d.);! Centenarian. See LONGEVITY.




Centenary, consisting of a hundred (Lat. to more than twelve times as many. In counting centum ), a period of a hundred years, is now usually the rings the ventral surface should be looked to, emploved to signify a commemoration of an event, for the dorsal shields often overlap. The rings are as the birth (sometimes the death) of a great man. | flattened from above downwards, and each bears The centenary of Burns's birth was celebrated in a pair of appendages. Dorsally and ventrally the 1859; the bi-centenary of Pope in 1888; the ter- skin is hard and horny. Glands occur in various centenary of Shakespeare in 1864. The centenary of positions. (6) Appendages.-The head, which is American Independence was celebrated by a Cen. covered by a flat shield above, bears (1) a pair of tennial Exhibition in 1876; the octo-centenary of antennæ, usually of considerable length, and con. the Bologna University in 1888.

sisting of from twelve to over one hundred joints ; Centering, the framework upon which an

|(2) a pair of small, strong, toothed, and bristly arh or vault of stone, brick, or iron is supported

mandibles ; (3) a pair of under-jaws, usually with during its construction. The simplest form of

palps. The next appendages are limb-like, and are centering is that used by masons and bricklayers

followed by a modified pair of legs, the basal pieces for the arches of common windows and doors.

of which generally meet in the middle line, while This is merely a deal-board of the required shape,

the strong joints terminate in a sharp claw, at which upon the curved edge of which the bricks or stones

a poison-gland opens. These appendages are obvi. of the arch are supported until they are keyed

ously of use for seizing and killing the prey. The in. In building bridges or other structures where

legs of the other segments are usually seven-jointed, arches of great span are to be constructed, the

sometimes bear spurs and glands, and are generally centering is usually made of framed timbers, or

clawed. The last pair differ in size and form from timbers and iron combined. The arrangement of

the rest, and are turned backwards. (c) Internal the timbers should be such that the strain upon

Anatomy.-The large brain is connected as usual each shall be mainly a thrust in the direction of its

with a ventral chain of ganglia. Compound eyes length, for if the strain were transverse, a compara

occur in one family, simple eyes in many, while tively slight force would snap it, and if a longi.

the feelers, certain bristles, and portions of the tudinal pull, the whole structure would be no

skin are also sensory. In some cases there is a stronger than the joints holding the pieces of

special well-defined sense-organ of undecided functimber together. In arches of great span, a longi.

tion in front of the head, or on one of the jaws. tudinal pulling strain is almost inevitable in some

The alimentary canal is straight, and has asso. parts, as a beam of great length would bend to

ciated with it salivary and digestive glands, and some extent under a thrusting strain. In such

excretory (Malpighian) tubules. The heart is cases great skill and care are demanded in the

represented by a chambered dorsal vessel. Tracheæ designing and construction of the joints. As an

or air-tubes open on the sides of the body, some. arch is built from the piers towards the keystone,

times on each ring, often on alternate segments, the weight upon the haunches during construction

ramify throughout the tissues, and are connected tends to push the crown upwards, and therefore the

together on each side by a longitudinal stem. problein of designing a framed centering involves

The reproductive organs are usually tubular, and the resistance of this tendency, as well as the sup

open on the last ring of the body. A distinct penis porting of the weight of the materials. Occasion

is sometimes present. ally, when a very great span is required, and the

Life and Habit.-Centipedes are darkness-loving navigation will permit, piers are built on the bed

animals, nocturnal in their food-hunting, lurking of the river, or piles are driven into it, to support

| under stones or among rotten wood and the like the centering directly, simplifying it, and at the

during the day. Their powers of vision are very same time facilitating a more rigid disposition than

| poorly developed, and most of the sensory work is in centering supported only from the sides. See

tactile. Only in one family (Scutigeridze ) are there article BRIDGE for descriptions and illustrations

compound eyes, in most forms only simple eyes, in of three types of centering : (1) that for the bridge

many none at all. The recent researches of Plateau over the Dee at Chester, Vol. II., page 437, sup.

and others have shown that these creatures can ported directly from the bed of the river; also

distinguish light from darkness, but do not need the centering for the Ballochmyle Bridge; (2)

eyes to do this; species with eyes do not apparently inclined struts in pairs supported from the sides,

get on much better than those without them; as Rennie's centering for Waterloo Bridge, page

those with eyes seem to perceive bright objects 438 ; (3) trussed wooden girders supported from

reflecting much white light, and in some cases conthe sides, as Rennie's centering for London Bridge,

spicuous movements, but probably in no case the page 438.

forms of objects. Moving actively about at nights, Cupolas, like those of the Pantheon and St

feeling their way by means of their antennæ, which Peter's at Rome, St Paul's in London, or the flat

function as a blind man's staff, they light upon indomes of the Turkish mosques, require very effec.

sects, worms, and other small animals, which they tive centerings.

seize and kill with their poison-bearing appendages.

They are all voracious carnivorous forms, not Centigrade. See CELSIUS and THERMOMETER.

vegetarian like the Millipedes. Some forms can Centipede, a general name for the members of run with some rapidity, and wriggle about in one of the orders of the class Myriopoda. Popu | curious serpent-like fashion. larly they are sometimes called Galley-worms, | Development.-In some cases the males are said technically Chilopoda. Like the Millipedes, which to deposit their reproductive elements in packets for the most important neighbour order, the (spermatophores) fixed by a web to the ground. Centipedes are segmented animals bearing jointed | In most cases copulation probably occurs. Scolo. appendages, having a well-defined head furnished pendra is viviparous, the others lay eggs. The with feelers and jaws, and breathing by means of eggs develop into larvæ, which'are either miniaair-tubes or tracheæ.

ture adults (Scolopendridæ and Geophilide), or Structure. - The Centipede is like a primitive differ from the full-grown forms in having only insect in its general structure.-(a) Externals. seven pairs of legs (Scutigeridæ and Lithobiida ). The body is divided into well-marked rings, but Classification and Forms of Interest.-The order the region behind the distinct head is practically of Centipedes is one of the three or four divisions uniform, and not divisible into thorax and abdomen. of Myriopoda (q.v.), and, like the class, generally Just behind the head & few rings appear to be represents a somewhat low grade of development fused. The number of rings varies from twelve among animals breathing by air-tubes. The most CENTIPEDE


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evolved centipede is a very uniform and old. Practical Import. The centipedes have some fashioned animal when compared with any normal direct practical importance as voracious devourers insect or spider. In the order itself we distinguish of injurious insects, larvæ, snails, and the like, four families-(1) Scutigeridæ, (2) Lithobiidæ, (3) while some of the large tropical forms are known Scolopendridæ, (4) Geophilidæ. The first of these in a somewhat different connection as animals includes curious forms with compound eyes, very able to give a painful and poisonous bite. In his long feelers, eight shields along the back, and Personał Narrative, Humboldt says he saw Indian fifteen pairs of very long legs. The feelers and children draw large centipedes out of the ground the last pair of legs are longer than the body; and eat them. there are external generative appendages. In Literature.- Newport, Monograph of the class MyriaScutigera, and apparently in some other centi. poda, order Chilopoda (Trans. Linnæan Society, vol. pedes, there are peculiar lung-like' dorsal aggre- xix. 1845); Haase, Schlesiens Chilopoden (1880-81); gations of air-tubes opening on the back, and Latzel, Die Myriapoden Oesterreichs (1880–84). perhaps the beginning of the pulmonary cham | Centlivre, SUSANNAH, an English dramatic bers' of some arachnids. Scutigera is represented authoress, was the daughter of a Lincolnshire by about a score of species, widely distributed in gentleman named Freeman, of Holbeach, and born warm countries, and common in houses. In Litho (say some authorities) in Ireland about 1667. biidae, as in the two other families, simple eyes Her early history is obscure; but such were her wit alone are present; there are fifteen pairs of legs, and beauty that on her arrival in London, though antennæ measuring a third or more of the body a destitute orphan, and only sixteen years of age, length, and fifteen dorsal shields. The genus she won the heart of a nephew of Sir Stephen Lithobius includes over one hundred species-L. Fox, who died shortly after their marriage. Her forficatus (of a reddish brown colour, and about second husband, an officer named Carroll, lost his an inch long) is very common throughout Europe life in a duel. Left in extreme poverty, his widow and America; our most familiar British species, endeavoured to support herself by writing for the L. mutabilis, also very common, has the habit stage, and after producing a tragedy called The of feigning death. The bite occasions consider Perjured Husband (performed first in 1700), made able irritation, like that due to nettle-stings.

her appearance on the stage at Bath. She afterwards married (1706) Joseph Centlivre, head. cook to Queen Anne, with whom she lived happily until the time of her death, December 1, 1723. Her playsThe Busybody (with 'Marplot' for leading character, 1709), and A Bold Stroke for a Wife (1717)—are lively in their plots, and have kept their place on the stage. Nineteen in all, they were collected in 3 vols. 1761, with a biography, and reprinted 1872.

Centner is, with metallurgists, a weight of 100 lb., and it often has this value in commerce. The German centner is however 50 kilogrammes or 1101 lb. avoirdupois; the metric or doppel centner is 100 kilogrammes. The cental of the United

States is 100 lb.
Giant Centipede (Scolopendra gigas ).

Cento, a town of Central Italy, 16 miles N. by

W. of Bologna, on a fertile plain near the Reno, The Scolopendridæ have over a score of legs,

the birthplace of Guercino (q.v.). Pop. 4975. short many-jointed antennæ, not more than

Cento, a name applied to literary trivialities one-fifth of the total length of the body ; and

in the form of poems manufactured by putting simple eyes, not over four pairs in number, or together distinct verses or passages of one author, altogether absent. About one hundred species are

or of several authors, so as to make a new meanknown, distributed over sixteen genera. They are ing. After the decay of genuine poetry among especially at home in warm countries, where they the Greeks, this worthless verse-manufacture came often attain large size, the Scolopendra gigas, for into vogue, as is proved by the Homero-centones instance, being sometimes a foot long. The poison (ed. by Teucher, Leip. 1793), a patchwork of lines ous bite of some of the larger forms is really taken from Homer and forming a consecutive dangerous to man. Scolopendra is the most im. history of the fate and redemption of man. It was portant genus. Lastly, the Geophilidæ are very much more common, however, among the Romans long, worm-like centipedes, of somewhat sluggish

in the later times of the Empire, when Virgil was habit, with 31 to 173 pairs of legs, short feelers, frequently abused in this fashion, as in the Cento and no eyes. Some 22 species and 9 genera Nuptialis of Ausonius, and especially in the Cento have been recorded, especially abundant in warm Vergilianus, constructed in the 4th century by Proba climates. Geophilus electricus and another species,

Falconia, wife of the Proconsul Adelfius, and giving, G. longicornis, both found in Britain, shine in in Virgil's misplaced words, an epitome of sacred the dark. This is probably due to a viscid fluid history. The cento was a favourite recreation in ex reted all over the ventral surface. Himan. the middle ages. In the 12th century a monk at tarium, found round the Mediterranean, is the Tegernsee, named Metellus, contrived to make a largest form of Geophilidæ. Well-developed spin. cento of spiritual hymns out of Horace and Virgil. ning glands are seen in this family, and their See Delepierre, Tableau de la Littérature du secretion cements together ova and spermatozoa. Centom (1875).

Distribution.—The centipedes are world-wide, Central America, a name applied to that but abound especially in warm regions. Some part of the American continent which lies between what unsatisfactory fossil remains have been ob. the isthmuses of Tehuantepec, Mexico, and Panama, tained from the American Carboniferous strata ; Colombia. Specifically the new Greater Republic netter preserved possible centipedes have been got of Central America, formed by treaty at Amapala from the Solenhofen strata, but it cannot yet be in 1895 and formally recognised by President Cleve. said with certainty that centipedes are known land December 23, 1896, embraces the republics of before Tertiary times.

Salvador, Nicaragua, and Honduras, with provisions





for the admission of Costa Rica and Guatemala. who centred in himself all the great functions of See under separate articles; also AMERICA.

government. In the later days of the empire the Central City, the name of several villages

tendency increased, until the system broke down and hamlets in the United States, and of the

with the power that wielded it. Amid the chaos

that followed the downfall of Rome various systems capital of Gilpin county, Colorado, 40 miles W. of Denver by rail, with quartz-mills and rich gold

arose for the restoration of order, political or mines, and (1890) 2480 inhabitants; also of a

religious, or both. Of these the greatest is still mining town of Lawrence county, South Dakota,

the Papacy; the greatest in bygone history was in the Black Hills, 280 miles SW. of Bismarck,

the empire of Charlemagne. In those times of with formerly some twenty quartz-mills for gold.

struggle, the natural method was centralisation

based on military supremacy. Pop. (1880) 1008; (1890) 519.

Modern attempts to found a great monarchy in Central India is the official term for a group

Europe on the model of the Roman empire have of feudatory states in India, which fall into nine failed. There have grown up instead a group of political Agencies, but are all under the super

powerful states, in the history of which the central. vision of the governor-general's agent. The region

| ising tendency is strongly marked. Centralisation in which these states lie is to the north of the

was necessary, for in the great struggles which British Central Provinces' of India, and touches

have incessantly been going on, success or even selfthe North-west Provinces, Rajputana, Khandesh

preservation could be secured only through a strong in the Bombay Province, and Chutia-Nagpur in

organisation repressing internal division, and Bengal. The total area is about 75,000 sq. m.; through large and efficient armies. As an adequate pop. in 1891, 10,314,787. The nine subordinate revenue was required for these objects, there was agencies comprised in the Central India Agency further involved a strong control by the central are the Indore, Bhil or Bhopawar, Deputy Bhil, power of the economic and industrial functions of Western Malwa, Bhopal, Gwalior, Guna, Bundel- the state. Thus it will be seen that centralisation khand, and Baghelkhand agencies. The intru- is more or less inevitable in the struggle for existsion of two British districts, those of Jhansi and

ence on the European continent. The most notable Lalitpur, belonging to the North-west Provinces, examples of the opposite tendency at present are separates these nine agencies into two divisions

apparent in the colonial empire of Great Britain, native Bundelkhand and Baghelkhand on the and in the United States, where we find extensive east, and Central India proper or Malwa on the groups of self-governing communities with only a west ; but the whole country lies between the limited measure of control by the central governNerbudda, the Ganges, and the Chambal rivers, ment. Such control is most limited of all in the and is mostly fertile and well tilled. The Malwa

British colonies. western division is mainly a tableland 2000 feet On the other hand, in the French commune above the sea ; but its rich black soil produces and in the Russian mir we see, under governfine wheat and much opium. The climate of ments otherwise strongly centralised, a form of Malwa is on the whole mild and equable; but | local activity which had been long extinct in the northern part of Central India is torrid, and Britain. The municipal reform of 1835 has done unhealthy during the rainy season. The mineral

much to revive local action in the town life of wealth of Central India is great : iron, coal, England. The aim of the reform of local governcopper, and lime are plentiful, and diamonds are ment begun in 1888 is to revive, extend, and found in some parts of Bundelkhand. The in systematise local responsibility and freedom of habitants are very diverse in origin, comprising action, particularly in rural districts. It is now reMahrattas (the ruling race), Rajputs, Bundelas, cognised that efficiency in the central government Baghelas, Jats, Kols, and hill-tribes such as the cau be best secured by transferring local interests Gonds (414,000) and Bhils (217,000). The popu- to local management by decentralisation. A wise lation is mainly Hindu in religion, only 510,718 decentralisation may be subservient to an effective being Mohammedans. The agent to the governor centralisation, a principle which holds good also on general of India, whose headquarters are at | the European continent. No absolute rules can, Indore, has very high and very various duties however, be laid down for marking off the reand powers. He is the adviser of all the native spective provinces of the central and local powers. chiefs, and their guardian during minority ; exer. Each country must solve the problem in its own cises the functions of a court of appeal ; has at way, as its interests and circumstances require. his command large bodies of troops; as 'opium

Central Provinces, a chief-commissioner. agent' supervises the opium-tax throughout the

ship of India, lying between 17° 50' and 24° 27' N. agency; and he is of course the medium of com

lat., and between 76° and 85° 15' E. long., and emnnnication between the imperial government and

bracing 18 British districts and 15 native states. the native authorities. The principal states and

Area, 115,936 sq. m.; pop. (1891) 12,932,330. The agencies have separate articles. “See INDORE,

surface is very broken, straggling ranges of hills BAGHELKHAND, &c. The Central Provinces (9.v.)

cropping up even in the level portions. In the north are a British commissionership.

extend the Vindhyan and Satpura (2000 feet) Centralisation, a term which has come | tablelands, with the Nerbudda between ; south of into general use for expressing a tendency to these stretches the great Nagpur plain, with the a iminister by the sovereign or the central govern | Chatisgarh plain to the east, and a wild forest. ment matters which would otherwise be under revion beyond, reaching almost to the Godavari. local management. The centralising tendency has Besides the two mentioned, the chief rivers of the been a feature in most of the great states recorded province are the Wardha and Wainganga; all four in history, though not in all of them. The oriental are rapid streams, with their crystal waters leaping empires aulinitted of a large degree of local in- from point to point, and rushing headlong through dependence among the subject peoples. The the narrow mountain-gorges of their upper course. Roman empire was one of the most remarkable The climate is hot and dry, except during the instances of centralisation the world has ever seen. south-west monsoon, from June to September, That empire grew out of the subjugation of all when 41 of the mean annual 45 inches of rain fall. the states round the Mediterranean by the city Wheat is grown chiefly in the Nerbudda valley, of Rome, and the control of it passed by the in. rice in the Nagpur plain; these are the princievitable tendency of events into the hands of a pal crops, but oil-seeds, cotton, and tobacco are single chief, whose power rested on the army, and also raised. The only manufactures of note are





weaving and the smelting and working of iron ores. But all the middle points lie on CP. The centre of Iron is abundant, especially in the south, and there inertia of the whole plate must therefore lie on CP. are also large coalfields, but the coal is of a very Again, if BC be inferior quality. There is considerable trade, but bisected in Q, and its progress is retarded by the want of means of AQ be joined, the communication ; this drawback, however, is being centre of inertia of removed, roads are being made, and the railway the whole plate must system steadily pushed forward. Of the popula- | lie in AQ." The cention, three-fourths are Hindus, and one-seventh tre of inertia must belong to the so-called aboriginal or non-Aryan therefore be 0, the tribes, who have found a refuge in the Satpura point of intersection · plateau, and still adhere to their primitive faiths of CP and AQ. It (see Gonds). From these hill-tribes the Hindus | is easily proved by

Fig. 2. throughout the province have contracted beliefs elementary geoand habits which they have grafted upon the metry that OP = one-third of CP. Hence, the usual worship of their sect; adoration of the dead, centre of inertia of a triangular plate is obtained worship of the goddess of smallpox, and belief in by joining a vertex to the middle point of the witchcraft are universal. The population is almost opposite side and taking the point two-thirds of entirely rural, only 6 per cent. residing in the 52 this line measured from the vertex. By a similar towns of above 5000 inhabitants, of which three method the centre of inertia of other plane figures -Nagpur, Jubbulpore, and Kainpti-have over may be obtained. 50,000 inhabitants. Central India (9.v.) is a term CENTRE OF GRAVITY.-If a body be sufficiently of quite distinct meaning.

small, relatively to the earth, the weights of its par. Centre and Central Forces.-CENTRE OF | ticles may be considered as constituting a system of

INERTIA (MASS). - parallel forces acting on the body. Now, the mag. If m, and 'm, be the nitude of the weight of a particle is proportional to masses of two par

its mass. Hence, the line of action of the result. ticles placed at the | ant of the parallel forces will approximately pass points-A, and A., , through the centre of inertia. For this reason and if the right line such bodies are said to have a centre of gravity. A A, be divided in

| Strictly speaking, there is no such point of Fig. 1. Bi, so that

necessity for every body, since the directions of the m A,B,= m,A,B,

forces acting on the body are not accurately the point B, is called the centre of inertia, or

parallel. Hence, it is only approximately that we

can say of a body that it has a centre of gravity. centre of mass, of the two particles. If my be a third mass at Ag, and if B, A, be divided in B,, so

On the other hand, every piece of matter has, as is

shown above, a centre of inertia. For all heavy that

bodies of moderate dimensions it is, however, suf. (m + m.)B,B, = mzA,B,,

ficiently accurate to assume that the centre of B, is called the centre of inertia of the three inertia and gravity coincide. For example, the particles. In general, if there be any number of centre of gravity of a uniform homogeneous cylinder particles, a continuation of the above process will with parallel ends is the middle point of its axis, enable us to find their centre of inertia. Every that of a uniformly thin circular lamina its centre, body may be supposed to be made up of a multitude and so on. of particles connected by cohesion. From this it The centre of gravity of a body of moderate is obvious that the centre of inertia is a definite dimensions may be approximately determined by point for every piece of matter.

suspending it by a single cord in two different In general, the determination of the centre of positions, and finding the single point in the body inertia requires the use of the integral calculus. which, in both positions, is intersected by the axis In the case of some bodies, such as those of the cord. which have a simple geometrical form and are The term centre of gravity is also used in of uniform density, elementary mathematical a stricter sense than the one just explained. methods will generally be sufficient. Any straight Thus, if a body attracts and is attracted by all line or plane that divides a homogeneous body other gravitating matter as if its whole mass symmetrically must contain its centre of in- were concentrated in one point, it is said to have a ertia. For the particles of the body may be true centre of gravity at that point, and the body arranged in pairs of equal mass and at equal dis- | itself is called a centrobaric body. A spherical tances from the straight line or plane; and, since shell of uniform gravitating matter attracts an ex. the centre of inertia of each pair lies in the line or ternal particle as if its whole mass were condensed plane, the centre of inertia of the whole must also at its centre. Such a body has a true centre of lie in the same line or plane. For example, the gravity. When such a point exists, it necessarily centre of inertia of a uniform thin straight rod is coincides with the centre of inertia. its middle point; that of a uniform thin rod bent in CENTRE OF OSCILLATION.- A heavy particle the form of a parallelogram, the point of intersec suspended from a point by a light inextensible tion of its diagonals ; that of a lamina, uniform in string constitutes what is called a simple or mathethickness and density and in form a circle, ellipse, matical pendulum. For such a pendulum it is or parallelogram, its centre of figure; that of a uni- easily proved that the time of an oscillation from form spherical shell, its centre; that of a homogene side to side of the vertical is proportional to the ous sphere, its centre; that of a parallelopiped, the square root of its length for any small arc of vibraintersection of its diagonals; that of a circular tion. A simple pendulum is, however, a thing of cylinder with parallel ends, the middle point of its theory, as in all physical problems we have to deal axis.

with a rigid mass, and not a particle, oscillating An important case is that of a uniformly thin about a horizontal axis. In a pendulum of this triangular plate. Let ABC be the plate. Bisect kind the time of oscillation will not vary as the AB in P and join CP. Let the triangle be divided square root of the length of the string, for it is by right lines parallel to AB into an indefinitely obvious that those particles of the body which are great number of indefinitely narrow strips. The nearest the point of suspension will have a tendcentre of inertia of each strip is its middle point. I ency to vibrate more rapidly than those more

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