[v.03 p.0263] BALL, JOHN (d. 1381), an English priest who took a prominent part in the peasant revolt in 1381. Little is known of his early years, but he lived probably at York and afterwards at Colchester. He gained considerable fame as a preacher by expounding the doctrines of John Wycliffe, but especially by his insistence on the principle of social equality. These utterances brought him into collision with the archbishop of Canterbury, and on three occasions he was committed to prison. He appears also to have been excommunicated, and in 1366 all persons were forbidden to hear him preach. His opinions, however, were not moderated, nor his popularity diminished by these measures, and his words had a considerable effect in stirring up the rising which broke out in June 1381. Ball was then in prison at Maidstone; but he was quickly released by the Kentish rebels, to whom he preached at Blackheath from the text, "When Adam delved and Eve span, Who was then a gentleman?" He urged his hearers to kill the principal lords of the kingdom and the lawyers; and he was afterwards among those who rushed into the Tower of London to seize Simon of Sudbury, archbishop of Canterbury. When the rebels dispersed Ball fled to the midland counties, but was taken prisoner at Coventry and executed in the presence of Richard II. on the 15th of July 1381. Ball, who was called by Froissart "the mad priest of Kent," seems to have possessed the gift of rhyme. He undoubtedly voiced the feelings of the lower orders of society at that time.

See Thomas Walsingham, Historia Anglicana, edited by H. T. Riley (London, 1863-1864); Henry Knighton, Chronicon, edited by J. R. Lumby (London, 1889-1895); Jean Froissart, Chroniques, edited by S. Luce and G. Raynaud (Paris, 1869-1897); C. E. Maurice, Lives of English Popular Leaders in the Middle Ages (London, 1875); C. Oman, The Great Revolt of 1381 (Oxford, 1906).

BALL, JOHN (1585-1640), English puritan divine, was born at Cassington, Oxfordshire, in October 1585. After taking his B.A. degree from St Mary's Hall, Oxford, in 1608, he went into Cheshire to act as tutor to the children of Lady Cholmondeley. He adopted Puritan views, and after being ordained without subscription, was appointed to the small curacy of Whitmore in Staffordshire. He was soon deprived by John Bridgeman, the high church bishop of Chester, who put him to much suffering. He became a schoolmaster and earned a wide and high reputation for his scholarship and piety. He died on the 20th of October 1640. The most popular of his numerous works was A Short Catechisme, containing all the Principal Grounds of Religion (14 editions before 1632). His Treatise of Faith (1632), and Friendly Trial of the Grounds tending to Separation (1640), the latter of which defines his position with regard to the church, are also valuable.

BALL, JOHN (1818-1889), Irish politician, naturalist and Alpine traveller, eldest son of an Irish judge, Nicholas Ball, was born at Dublin on the 20th of August 1818. He was educated at the Roman Catholic College at Oscott near Birmingham, and at Christ's College, Cambridge. He showed in early years a taste for natural science, particularly botany; and after leaving Cambridge he travelled in Switzerland and elsewhere in Europe, studying his favourite pursuits, and contributing papers on botany and the Swiss glaciers to scientific periodicals. In 1846 he was made an assistant poor-law commissioner, but resigned in 1847, and in 1848 stood unsuccessfully as a parliamentary candidate for Sligo. In 1849 he was appointed second poor-law commissioner, but resigned in 1852 and successfully contested the county of Carlow in the Liberal interest. In the House of Commons he attracted Lord Palmerston's attention by his abilities, and in 1885 was made under-secretary for the colonies, a post which he held for two years. At the colonial office he had great influence in furthering the cause of natural science, particularly in connexion with equipment of the Palliser expedition in Canada, and with Sir W. Hooker's efforts to obtain a systematic knowledge of the colonial floras. In 1858 he stood for Limerick, but was beaten, and he then gave up politics and devoted himself to natural history. He was first president of the Alpine Club (founded 1857), and it is for his work as an Alpinist that he is chiefly remembered, his well-known Alpine Guide (London, 1863-1868) being the result of innumerable climbs and journeys and of careful observation recorded in a clear and often entertaining style. He also travelled in Morocco (1871) and South America (1882), and recorded his observations in books which were recognized as having a scientific value. He died in London on the 21st of October 1889.

BALL, THOMAS (1819- ), American sculptor, was born at Charlestown, Massachusetts, on the 3rd of June 1819. He was the son of a house-and-sign-painter, and after starting, self-taught, as a portrait painter he turned his attention in 1851 to sculpture, his earliest work being a bust of Jenny Lind. At thirty-five he went to Florence for study; there, with an interval of work in Boston, Massachusetts, in 1857-1865, he remained for more than thirty years, being one of the artistic colony which included the Brownings and Hiram Powers. He returned to America in 1897, and lived in Montclair, New Jersey, with a studio in New York City. His work includes many early cabinet busts of musicians (he was an accomplished musician himself, and was the first in America to sing "Elijah"), and later the equestrian statue of Washington in the Boston public gardens, probably his best work; Josiah Quincy in City Hall Square, Boston; Charles Sumner in the public gardens of Boston; Daniel Webster in Central Park, New York City; the Lincoln Emancipation group at Washington; Edwin Forrest as "Coriolanus," in the Actors' Home, Philadelphia, and the Washington monument in Methuen, Massachusetts. His work has had a marked influence on monumental art in the United States and especially in New England. In 1891 he published an autobiographical volume, My Three Score Years and Ten.

BALL (in Mid. Eng. bal; the word is probably cognate with "bale," Teutonic in origin, cf. also Lat. follis, and Gr. [Greek: palla]), any rounded body, particularly one with a smooth surface, whether used for games, as a missile, or applied to such rounded bodies as the protuberance at the root of the thumb or the big toe, to an enarthrosis, or "ball socket" joint, such as that of the hip or shoulder, and the like. A ball, as the essential feature in nearly every form of game requiring physical exertion, must date from the very earliest times. A rolling object appeals not only to a human baby but to a kitten and a puppy. Some form of game with a ball is found portrayed on Egyptian monuments, and is played among the least advanced of savage tribes at the present day. In Homer, Nausicaa was playing at ball with her maidens when Odysseus first saw her in the land of the Phaeacians (Od. vi. 100). And Halios and Laodamas performed before Alcinous and Odysseus with ball play, accompanied with dancing (Od. viii. 370). The Hebrews, the least athletic of races, have no mention of the ball in their scriptures. Among the Greeks games with balls ([Greek: sphairai]) were regarded as a useful subsidiary to the more violent athletic exercises, as a means of keeping the body supple, and rendering it graceful, but were generally left to boys and girls. Similarly at Rome they were looked upon as an adjunct to the bath, and were graduated to the age and health of the bathers, and usually a place (sphaeristerium) was set apart for them in the baths (thermae). Of regular rules for the playing of ball games, little trace remains, if there were any such. The names in Greek for various forms, which have come down to us in such works as the [Greek: Onomastikon] of Pollux of Naucratis, imply little or nothing of such; thus, [Greek: aporraxis] only means the putting of the ball on the ground with the open hand, [Greek: ourania], the flinging of the ball in the air to be caught by two or more players; [Greek: phaininda] would seem to be a game of catch played by two or more, where feinting is used as a test of quickness and skill. Pollux (i. x. 104) mentions a game called [Greek: episkuros], which has often been looked on as the origin of football. It seems to have been played by two sides, arranged in lines; how far there was any form of "goal" seems uncertain. Among the Romans there appear to have been three types or sizes of ball, the pila, or small ball, used in catching games, the paganica, a heavy ball stuffed with feathers, and the follis, a leather ball filled with air, the largest of the three. This was struck from player to player, who wore a kind of gauntlet on the arm. There was a game known as trigon, played by three players standing in [v.03 p.0264] the form of a triangle, and played with the follis, and also one known as harpastum, which seems to imply a "scrimmage" among several players for the ball.[1] These games are known to us through the Romans, though the names are Greek. The various modern games played with a ball or balls and subject to rules are treated under their various names, such as polo, cricket, football, &c.

From Fr. bal, baller, to dance (late Lat. ballare, and hence connected with "ballad," "ballet") comes "ball," meaning a dance, and especially a social gathering of people for the purpose of dancing.

[1] Martial (iv. 19. 6) calls the harpastum, pulverulentum, implying that it involves a considerable amount of exertion.

BALLADE, the technical name of a complicated and fixed form of verse, arranged on a precise system, and having nothing in common with the word ballad, except its derivation from the same Low Latin verb, ballare, to dance. In the 14th and 15th centuries it was spelt balade. In its regular conditions a ballade consists of three stanzas and an envoi; there is a refrain which is repeated at the close of each stanza and of the envoi. The entire poem should contain but three or four rhymes, as the case may be, and these must be reproduced with exactitude in each section. These rules were laid down by Henri de Croi, whose L'Art et science de rhetorique was first printed in 1493, and he added that if the refrain consists of eight syllables, the ballade must be written in huitains (eight-line stanzas), if of ten syllables in dizains (ten-line), and so on. The form can best be studied in an example, and we quote, as absolutely faultless in execution, the famous "Ballade aux Enfants Perdus," composed by Theodore de Banville in 1861:—

"Je le sais bien que Cythere est en deuil! Que son jardin, soufflete par l'orage, O mes amis, n'est plus qu'un sombre ecueil Agonisant sous le soleil sauvage. La solitude habite son rivage. Qu'importe! allons vers les pays fictifs! Cherchons la plage ou nos desirs oisifs S'abreuveront dans le sacre mystere Fait pour un choeur d'esprits contemplatifs: Embarquons-nous pour la belle Cythere,

"La grande mer sera notre cercueil; Nous servirons de proie au noir naufrage, Le feu du ciel punira notre orgueil Et l'aiguillon nous garde son outrage. Qu'importe! allons vers le clair paysage! Malgre la mer jalouse et les recifs, Venez, portons comme des fugitifs, Loin de ce monde au souffle deletere. Nous dont les coeurs sont des ramiers plaintifs, Embarquons-nous pour la belle Cythere.

"Des serpents gris se trainent sur le seuil Ou souriait Cypris, la chere image Aux tresses d'or, la vierge au doux accueil! Mais les Amours sur le plus haut cordage Nous chantent l'hymne adore du voyage. Heros caches dans ces corps maladifs, Fuyons, partons sur nos legers esquifs, Vers le divin bocage ou la panthere Pleure d'amour sous les rosiers lascifs: Embarquons-nous pour la belle Cythere.

Envoi.

"Rassasions d'azur nos yeux pensifs! Oiseaux chanteurs, dans la brise expansifs, Ne souillons pas nos ailes sur la terre. Volons, charmes, vers les dieux primitifs! Embarquons-nous pour la belle Cythere."

This is the type of the ballade in its most elaborate and highly-finished form, which it cannot be said to have reached until the 14th century. It arose from the canzone de ballo of the Italians, but it is in Provencal literature that the ballade first takes a modern form. It was in France, however, and not until the reign of Charles V., that the ballade as we understand it began to flourish; instantly it became popular, and in a few years the out-put of these poems was incalculable. Machault, Froissart, Eustache Deschamps and Christine de Pisan were among the poets who cultivated the ballade most abundantly. Later, those of Alain Chartier and Henri Baude were famous, while the form was chosen by Francois Villon for some of the most admirable and extraordinary poems which the middle ages have handed down to us. Somewhat later, Clement Marot composed ballades of great precision of form, and the fashion culminated in the 17th century with those of Madame Deshoulieres, Sarrazin, Voiture and La Fontaine. Attacked by Moliere, and by Boileau, who wrote

"La ballade asservie a ses vieilles maximes, Souvent doit tout son lustre au caprice des rimes,"

the ballade went entirely out of fashion for two hundred years, when it was resuscitated in the middle of the 19th century by Theodore de Banville, who published in 1873 a volume of Trente-six ballades joyeuses, which has found many imitators. The ballade, a typically French form, has been extensively employed in no other language, except in English. In the 15th and 16th centuries many ballades were written, with more or less close attention to the French rules, by the leading English poets, and in particular by Chaucer, by Gower (whose surviving ballades, however, are all in French) and by Lydgate. An example from Chaucer will show that the type of strophe and rhyme arrangement was in medieval English:—

"Madame, ye been of all beauty shrine As far as circled is the mappemound; For, as the crystal, glorious ye shine, And like ruby been your cheekes round. Therewith ye been so merry and so jocund That at a revel when that I see you dance, It is an oinement unto my wound, Though ye to me ne do no daliance.

"For though I weep of teares full a tine [cask], Yet may that woe my hearte not confound; Your seemly voice, that ye so small out-twine, Maketh my thought in joy and bliss abound. So courteously I go, with love bound, That to myself I say, in my penance, Sufficeth me to love you, Rosamound, Though ye to me ne do no daliance.

"Was never pike wallowed in galantine, As I in love am wallowed and y-wound; For which full oft I of myself divine That I am true Tristram the second. My love may not refrayed [cooled down] be nor afound [foundered]; I burn ay in an amorous pleasance. Do what you list, I will your thrall be found, Though ye to me ne do no daliance."

The absence of an envoi will be noticed in Chaucer's, as in most of the medieval English ballades. This points to a relation with the earliest French form, in its imperfect condition, rather than with that which afterwards became accepted. But a ballade without an envoi lacks that section whose function is to tie together the rest, and complete the whole as a work of art. After the 16th century original ballades were no more written in English until the latter part of the 19th, when they were re-introduced, almost simultaneously, by Algernon Charles Swinburne, Austin Dobson, Andrew Lang, Edmund Gosse and W. E. Henley; but D. G. Rossetti's popular translation of Villon's "Ballade of Fair Ladies" may almost be considered an original poem, especially as it entirely disregards the metrical rules of the ballades. Mr. Dobson's "The Prodigals" (1876) was one of the earliest examples of a correct English specimen. In 1880 Mr Lang published a volume of Ballades in Blue China, which found innumerable imitators. The modern English ballades have been, as a rule, closely modelled on the lines laid down in the 15th century by Henri de Croi. With the exception of the sonnet, the ballade is the noblest of the artificial forms of verse cultivated in English literature. It lends itself equally well to pathos and to mockery, and in the hands of a competent poet produces an effect which is rich in melody without seeming fantastic or artificial.

(E. G.)

BALLADS. The word "ballad" is derived from the O. Fr. baller, to dance, and originally meant a song sung to the rhythmic movement of a dancing chorus. Later, the word, in the form of ballade (q.v.), became the technical term for a particular form of old-fashioned French poetry, remarkable for its involved and [v.03 p.0265] recurring rhymes. "Laisse moi aux Jeux Floraux de Toulouse toutes ces vieux poesies Francoises comme ballades," says Joachim du Bellay in 1550; and Philaminte, the lady pedant of Moliere's Femmes Savantes, observes—

"La ballade, a mon gout, est une chose fade, Ce n'en est plus la mode, elle sent son vieux temps."

In England the term has usually been applied to any simple tale told in simple verse, though attempts have been made to confine it to the subject of this article, namely, the literary form of popular songs, the folk-tunes associated with them being treated in the article SONG. By popular songs we understand what the Germans call Volkslieder, that is, songs with words composed by members of the people, for the people, handed down by oral tradition, and in style, taste and even incident, common to the people in all European countries. The beauty of these purely popular ballads, their directness and freshness, has made them admired even by the artificial critics of the most artificial periods in literature. Thus Sir Philip Sydney confesses that the ballad of Chevy Chase, when chanted by "a blind crowder," stirred his blood like the sound of trumpet. Addison devoted two articles in the Spectator to a critique of the same poem. Montaigne praised the naivete of the village carols; and Malherbe preferred a rustic chansonnette to all the poems of Ronsard. These, however, are rare instances of the taste for popular poetry, and though the Danish ballads were collected and printed in the middle of the 16th century, and some Scottish collections date from the beginning of the 18th, it was not till the publication of Allan Ramsay's Evergreen and Tea Table Miscellany, and of Bishop Percy's Reliques (1765), that a serious effort was made to recover Scottish and English folk-songs from the recitation of the old people who still knew them by heart. At the time when Percy was editing the Reliques, Madame de Chenier, the mother of the celebrated French poet of that name, composed an essay on the ballads of her native land, modern Greece; and later, Herder and Grimm and Goethe, in Germany, did for the songs of their country what Scott did for those of Liddesdale and the Forest. It was fortunate, perhaps, for poetry, though unlucky for the scientific study of the ballads, that they were mainly regarded from the literary point of view. The influence of their artless melody and straightforward diction may be felt in the lyrics of Goethe and of Coleridge, of Wordsworth, of Heine and of Andre Chenier. Chenier, in the most affected age even of French poetry, translated some of the Romaic ballads; one, as it chanced, being almost identical with that which Shakespeare borrowed from some English reciter, and put into the mouth of the mad Ophelia. The beauty of the ballads and the interest they excited led to numerous forgeries and modern interpolations, which it is seldom difficult to detect with certainty. Editors could not resist the temptation to interpolate, to restore, and to improve the fragments that came in their way. The marquis de la Villemarque, who first drew attention to the ballads of Brittany, is not wholly free from this fault. Thus a very general scepticism was awakened, and when questions came to be asked as to the date and authorship of the Scottish traditional ballads, it is scarcely to be wondered at that Dr Chambers attributed most of them to the accomplished Lady Wardlaw, who lived in the middle of the 18th century.

The vexed and dull controversy as to the origin of Scottish folk-songs was due to ignorance of the comparative method, and of the ballad literature of Europe in general. The result of the discussion was to leave a vague impression that the Scottish ballads were perhaps as old as the time of Dunbar, and were the production of a class of professional minstrels. These minstrels are a stumbling-block in the way of the student of the growth of ballads. The domestic annals of Scotland show that her kings used to keep court-bards, and also that strollers, jongleurs, as they were called, went about singing at the doors of farm-houses and in the streets of towns. Here were two sets of minstrels who had apparently left no poetry; and, on the other side, there was a number of ballads that claimed no author. It was the easiest and most satisfactory inference that the courtly minstrels made the verses, which the wandering crowders imitated or corrupted. But this theory fails to account, among other things, for the universal sameness of tone, of incident, of legend, of primitive poetical formulae, which the Scottish ballad possesses, in common with the ballads of Greece, of France, of Provence, of Portugal, of Denmark and of Italy. The object, therefore, of this article is to prove that what has long been acknowledged of nursery tales, of what the Germans call Maerchen, namely, that they are the immemorial inheritance at least of all European peoples, is true also of some ballads. Their present form, of course, is relatively recent: in centuries of oral recitation the language altered automatically, but the stock situations and ideas of many romantic ballads are of dateless age and world-wide diffusion. The main incidents and plots of the fairy tales of Celts and Germans and Slavonic and Indian peoples, their unknown antiquity and mysterious origin, are universally recognized. No one any longer attributes them to this or that author, or to this or that date. The attempt to find date or author for a genuine popular song is as futile as a similar search in the case of a Maerchen. It is to be asked, then, whether what is confessedly true of folk-tales,—of such stories as the Sleeping Beauty and Cinderella,—is true also of folk-songs. Are they, or have they been, as universally sung as the fairy tales have been narrated? Do they, too, bear traces of the survival of primitive creeds and primitive forms of consciousness and of imagination? Are they, like Maerchen, for the most part, little influenced by the higher religions, Christian or polytheistic? Do they turn, as Maerchen do, on the same incidents, repeat the same stories, employ the same machinery of talking birds and beasts? Lastly, are any specimens of ballad literature capable of being traced back to extreme antiquity? It appears that all these questions may be answered in the affirmative; that the great age and universal diffusion of the ballad may be proved; and that its birth, from the lips and heart of the people, may be contrasted with the origin of an artistic poetry in the demand of an aristocracy for a separate epic literature destined to be its own possession, and to be the first development of a poetry of personality,—a record of individual passions and emotions. After bringing forward examples of the identity of features in European ballad poetry, we shall proceed to show that the earlier genre of ballads with refrain sprang from the same primitive custom of dance, accompanied by improvised song, which still exists in Greece and Russia, and even in valleys of the Pyrenees.

There can scarcely be a better guide in the examination of the notes or marks of popular poetry than the instructions which M. Ampere gave to the committee appointed in 1852-1853 to search for the remains of ballads in France. M. Ampere bade the collectors look for the following characteristics:—"The use of assonance in place of rhyme, the brusque character of the recital, the textual repetition, as in Homer, of the speeches of the persons, the constant use of certain numbers,—as three and seven,—and the representation of the commonest objects of every-day life as being made of gold and silver." M. Ampere might have added that French ballads would probably employ a "bird chorus," the use of talking-birds as messengers; that they would repeat the plots current in other countries, and display the same non-Christian idea of death and of the future world (see "The Lyke-wake Dirge"), the same ghostly superstitions and stories of metamorphosis, and the same belief in elves and fairies, as are found in the ballads of Greece, of Provence, of Brittany, Denmark and Scotland. We shall now examine these supposed common notes of all genuine popular song, supplying a few out of the many instances of curious identity. As to brusqueness of recital, and the use of assonance instead of rhyme, as well as the aid to memory given by reproducing speeches verbally, these are almost unavoidable in all simple poetry preserved by oral tradition. In the matter of recurring numbers, we have the eternal—

"Trois belles filles L'y en a'z une plus belle que le jour,"

who appear in old French ballads, as well as the "Three Sailors," whose adventures are related in the Lithuanian and Provencal originals of Thackeray's Little Billee. Then there is "the league, [v.03 p.0266] the league, the league, but barely three," of Scottish ballads; and the [Greek: tria poulakia], three golden birds, which sing the prelude to Greek folk-songs, and so on. A more curious note of primitive poetry is the lavish and reckless use of gold and silver. H. F. Tozer, in his account of ballads in the Highlands of Turkey, remarks on this fact, and attributes it to Eastern influences. But the horses' shoes of silver, the knives of fine gold, the talking "birds with gold on their wings," as in Aristophanes, are common to all folk-song. Everything almost is gold in the Kalewala (q.v.), a so-called epic formed by putting into juxtaposition all the popular songs of Finland. Gold is used as freely in the ballads, real or spurious, which M. Verkovitch has had collected in the wilds of Mount Rhodope. The Captain in the French song is as lavish in his treatment of his runaway bride,—

"Son amant l'habille, Tout en or et argent";

and the rustic in a song from Poitou talks of his faucille d'or, just as a variant of Hugh of Lincoln introduces gold chairs and tables. Again, when the lover, in a ballad common to France and to Scotland, cuts the winding-sheet from about his living bride—"il tira ses ciseaux d'or fin." If the horses of the Klephts in Romaic ballads are gold shod, the steed in Willie's Lady is no less splendidly accoutred,—

"Silver shod before, And gowden shod behind."

Readers of Homer, and of the Chanson de Roland, must have observed the same primitive luxury of gold in these early epics, in Homer reflecting perhaps the radiance of the actual "golden Mycenae."

Next as to talking-birds. These are not so common as in Maerchen, but still are very general, and cause no surprise to their human listeners. The omniscient popinjay, who "up and spoke" in the Border minstrelsy, is of the same family of birds as those that, according to Talvj, pervade Servian song; as the [Greek: tria poulakia] which introduce the story in the Romaic ballads; as the wise birds whose speech is still understood by exceptionally gifted Zulus; as the wicked dove that whispers temptation in the sweet French folk-song; as the "bird that came out of a bush, on water for to dine," in the Water o' Wearies Well.

In the matter of identity of plot and incident in the ballads of various lands, it is to be regretted that no such comparative tables exist as Von Hahn tried, not very exhaustively, to make of the "story-roots" of Maerchen. Such tables might be compiled from the learned notes and introductions of Prof. Child to his English and Scottish Popular Ballads (1898). A common plot is the story of the faithful leman, whose lord brings home "a braw new bride," and who recovers his affection at the eleventh hour. In Scotland this is the ballad of Lord Thomas and Fair Annie; in Danish it is Skiaen Anna. It occurs twice in M. Fauriel's collection of Romaic songs. Again, there is the familiar ballad about a girl who pretends to be dead, that she may be borne on a bier to meet her lover. This occurs not only in Scotland, but in the popular songs of Provence (collected by Damase Arbaud) and in those of Metz (Puymaigre), and in both countries an incongruous sequel tells how the lover tried to murder his bride, and how she was too cunning, and drowned him. Another familiar feature is the bush and briar, or the two rose trees, which meet and plait over the graves of unhappy lovers, so that all passers-by see them, and say in the Provencal,—

"Diou ague l'amo Des paures amourous."

Another example of a very widespread theme brings us to the ideas of the state of the dead revealed in folk-songs. The Night Journey, in M. Fauriel's Romaic collection, tells how a dead brother, wakened from his sleep of death by the longing of love, bore his living sister on his saddle-bow, in one night, from Bagdad to Constantinople. In Scotland this is the story of Proud Lady Margaret; in Germany it is the song which Buerger converted into Lenore; in Denmark it is Aage und Else; in Brittany the dead foster-brother carries his sister to the apple close of the Celtic paradise (Barzaz Breiz). Only in Brittany do the sad-hearted people think of the land of death as an island of Avalon, with the eternal sunset lingering behind the flowering apple trees, and gleaming on the fountain of forgetfulness. In Scotland the channering worm doth chide even the souls that come from where, "beside the gate of Paradise, the birk grows fair enough." The Romaic idea of the place of the dead, the garden of Charon, whence "neither in spring or summer, nor when grapes are gleaned in autumn, can warrior or maiden escape," is likewise pre-Christian. In Provencal and Danish folk-song, the cries of children ill-treated by a cruel step-mother awaken the departed mother,—

"'Twas cold at night and the bairnies grat, The mother below the mouls heard that."

She reappears in her old home, and henceforth, "when dogs howl in the night, the step-mother trembles, and is kind to the children." To this identity of superstition we may add the less tangible fact of identity of tone. The ballads of Klephtic exploits in Greece match the Border songs of Dick of the Cow and Kinmont Willie. The same simple delight of living animates the short Greek Scolia and their counterparts in France. Everywhere in these happier climes, as in southern Italy, there are snatches of popular verse that make but one song of rose trees, and apple blossom, and the nightingale that sings for maidens loverless,—

"Il ne chante pas pour moi, J'en ai un, Dieu merci,"

says the gay French refrain.

It would not be difficult to multiply instances of resemblance between the different folk-songs of Europe; but enough has, perhaps, been said to support the position that some of them are popular and primitive in the same sense as Maerchen. They are composed by peoples of an early stage who find, in a natural improvisation, a natural utterance of modulated and rhythmic speech, the appropriate relief of their emotions, in moments of high-wrought feeling or on solemn occasions. "Poesie" (as Puttenham well says in his Art of English Poesie, 1589) "is more ancient than the artificiall of the Greeks and Latines, and used of the savage and uncivill, who were before all science and civilitie. This is proved by certificate of merchants and travellers, who by late navigations have surveyed the whole world, and discovered large countries, and wild people strange and savage, affirming that the American, the Perusine, and the very Canniball do sing and also say their highest and holiest matters in certain riming versicles." In the same way Aristotle, discoursing of the origin of poetry, says (Poet. c. iv.), [Greek: egennesan ten poiesin ek ton autoschediasmaton] M. de la Villemarque in Brittany, M. Pitre in Italy, Herr Ulrich in Greece, have described the process of improvisation, how it grows out of the custom of dancing in large bands and accompanying the figure of the dance with song. "If the people," says M. Pitre, "find out who is the composer of a canzone, they will not sing it." Now in those lands where a blithe peasant life still exists with its dances, like the kolos of Russia, we find ballads identical in many respects with those which have died out of oral tradition in these islands. It is natural to conclude that originally some of the British ballads too were first improvised, and circulated in rustic dances. We learn from M. Bujeaud and M. de Puymaigre in France, that all ballads there have their air or tune, and that every dance has its own words, for if a new dance comes in, perhaps a fashionable one from Paris, words are fitted to it. Is there any trace of such an operatic, lyrical, dancing peasantry in austere Scotland? We find it in Gawin Douglas's account of—

"Sic as we clepe wenches and damosels, In gersy greens, wandering by spring wells, Of bloomed branches, and flowers white and red, Plettand their lusty chaplets for their head, Some sang ring-sangs, dances, ledes, and rounds."

Now, ring-sangs are ballads, dancing songs; and Young Tamlane, for instance, was doubtless once danced to, as we know it possessed an appropriate air. Again, Fabyan, the chronicler (quoted by Ritson) says that the song of triumph over Edward II., "was after many days sung in dances, to the carols of the [v.03 p.0267] maidens and minstrels of Scotland." We might quote the Complaynt of Scotland to the same effect. "The shepherds, and their wyvis sang mony other melodi sangs, ... than efter this sueit celestial harmony, tha began to dance in ane ring." It is natural to conjecture that, if we find identical ballads in Scotland, and in Greece and Italy, and traces of identical customs—customs crushed by the Reformation, by Puritanism, by modern so-called civilization,—the ballads sprang out of the institution of dances, as they still do in warmer and pleasanter climates. It may be supposed that legends on which the ballads are composed, being found as they are from the White Sea to Cape Matapan, are part of the stock of primitive folk-lore. Thus we have an immemorial antiquity for the legends, and for the lyrical choruses in which their musical rendering was improvised. We are still at a loss to discover the possibly mythological germs of the legends; but, at all events, some ballads may be claimed as distinctly popular, and, so to speak, impersonal in matter and in origin. It would be easy to show that survivals out of this stage of inartistic lyric poetry linger in the early epic poetry of Homer and in the French epopees, and that the Greek drama sprang from the sacred choruses of village vintagers. In the great early epics, as in popular ballads, there is the same directness and simplicity, the same use of recurring epithets, the "green grass," the "salt sea," the "shadowy hills," the same repetition of speeches and something of the same barbaric profusion in the use of gold and silver. But these resemblances must not lead us into the mistake of supposing Homer to be a collection of ballads, or that he can be properly translated into ballad metre. The Iliad and the Odyssey are the highest form of an artistic epic, not composed by piecing together ballads, but developed by a long series of noble [Greek: aoidoi], for the benefit of the great houses which entertain them, out of the method and materials of popular song.

We have here spoken mainly of romantic ballads, which retain in the refrain a vestige of the custom of singing and dancing; of a period when "dance, song and poetry itself began with a communal consent" (Gummere, The Beginnings of Poetry, p. 93, 1901). The custom by which a singer in a dancing-circle chants a few words, the dancers chiming in with the refrain, is found by M. Junod among the tribes of Delagoa Bay (Junod, Chantes et contes des Ba Ronga, 1897). Other instances are the Australian song-dances (Siebert, in Howitt's Native Tribes of South-East Australia, Appendix 1904; and Dennett, Folk-Lore of the Fiort). We must not infer that even among the aborigines of Australia song is entirely "communal." Known men, inspired, they say, in dreams, or by the All Father, devise new forms of song with dance, which are carried all over the country; and Mr Howitt gives a few examples of individual lyric. The history of the much exaggerated opinion that a whole people, as a people, composed its own ballads is traced by Prof. Gummere in The Beginnings of Poetry, pp. 116-163. Some British ballads retain traces of the early dance-song, and most are so far "communal" in that, as they stand, they have been modified and interpolated by many reciters in various ages, and finally (in The Border Minstrelsy) by Sir Walter Scott, and by hands much weaker than his (see The Young Tamlane). There are cases in which the matter of a ballad has been derived by a popular singer from medieval literary romance (as in the Arthurian ballads), while the author of the romance again usually borrowed, like Homer in the Odyssey, from popular Maerchen of dateless antiquity. It would be an error to suppose that most romantic folk-songs are vulgarizations of literary romance—a view to which Mr Courthope, in his History of English Poetry, and Mr Henderson in The Border Minstrelsy (1902), incline—and the opposite error would be to hold that this process of borrowing from and vulgarization of literary medieval romance never occurred. A good illustration of the true state of the case will be found in Child's introduction to the ballad of Young Beichan.

Gaston Paris, a great authority, holds that early popular poetry is "improvised and contemporary with its facts" (Histoire poetique de Charlemagne). If this dictum be applied to such ballads as "The Bonny Earl o' Murray," "Kinmont Willie," "Jamie Telfer" and "Jock o' the Side," it must appear that the contemporary poets often knew little of the events and knew that little wrong. We gather the true facts from contemporary letters and despatches. In the ballads the facts are confused and distorted to such a degree that we must suppose them to have been composed in a later generation on the basis of erroneous oral tradition; or, as in the case of The Queen's Marie, to have been later defaced by the fantastic interpolations of reciters. To prove this it is only necessary to compare the historical Border ballads (especially those of 1595-1600) with Bain's Border Papers (1894-1896). Even down to 1750, the ballads on Rob Roy's sons are more or less mythopoeic. It seems probable that the existing form of most of our border ballads is not earlier than the generation of 1603-1633, after the union of the crowns. Even when the ballads have been taken from recitation, the reciter has sometimes been inspired by a "stall copy," or printed broadsheet.

AUTHORITIES.—The indispensable book for the student of ballads is Child's English and Scottish Popular Ballads, published in 1897-1898 (Boston, U.S.A.). Professor Child unfortunately died without summing up his ideas in a separate essay, and they must be sought in his introductions, which have never been analysed. He did not give much attention to such materials for the study of ancient poetry as exist copiously in anthropological treatises. In knowledge of the ballads of all European peoples he was unrivalled, and his bibliography of collections of ballads contains some four hundred titles, (Child, vol. v., pp. 455-468). The most copious ballad makers have been the Scots and English, the German, Slavic, Danish, French and Italian peoples; for the Gaelic there is but one entry, Campbell of Islay's Lea har na Feinne (London, 1872). The general bibliography occupies over sixty pages, and to this the reader must be referred, while Prof. Gummere's book, The Beginnings of Poetry, is an adequate introduction to the literature, mainly continental, of the ballad question, which has received but scanty attention in England. For the relation of ballad to epic there is no better guide than Comparetti's The Kalewala, of which there is an English translation. For purely literary purposes the best collection of ballads is Scott's Border Minstrelsy in any complete edition. The best critical modern edition is that of Mr T. F. Henderson; his theory of ballad origins is not that which may be gathered from Professor Child's introductions.

(A. L.)

BALLANCE, JOHN (1839-1893), New Zealand statesman, eldest son of Samuel Ballance, farmer, of Glenavy, Antrim, Ulster, was born on the 27th of March 1839. He was educated at a national school, and, on leaving, was apprenticed to an ironmonger at Belfast. He became a clerk in a wholesale ironmonger's house in Birmingham, and migrated to New Zealand, intending to start in business there as a small jeweller. After settling at Wanganui, however, he took an opportunity, soon offered, of founding a newspaper, the Wanganui Herald, of which he became editor and remained chief owner for the rest of his life. During the fighting with the Maori chief Titokowaru, in 1867, Ballance was concerned in the raising of a troop of volunteer horse, in which he received a commission. Of this he was deprived owing to the appearance in his newspaper of articles criticizing the management of the campaign. He had, however, behaved well in the field, and, in spite of his dismissal, was awarded the New Zealand war medal. He entered the colony's parliament in 1875 and, with one interval (1881-1884), sat there till his death. Ballance was a member of three ministries, that of Sir George Grey (1877-1879); that of Sir Robert Stout (1884-1887); and that of which he himself was premier (1891-1893). His alliance with Grey ended with a notorious and very painful quarrel. In the Stout government his portfolios were those of lands and native affairs; but it was at the treasury that his prudent and successful finance made the chief mark. As native minister his policy was pacific and humane, and in his last years he contrived to adjust equitably certain long-standing difficulties relating to reserved lands on the west coast of the North Island. He was resolutely opposed to the sale of crown lands for cash, and advocated with effect their disposal by perpetual lease. His system of state-aided "village settlements," by which small farms were allotted to peasants holding by lease from the crown, and money lent them to make a beginning of building and cultivation, has been on the whole successful. To Ballance, also, was due the law reducing the life-tenure of legislative councillors [v.03 p.0268] to one of seven years. He was actively concerned in the advocacy of woman suffrage. But his best known achievement was the imposition, in 1891, of the progressive land-tax and progressive income-tax still levied in the colony. As premier he brought together the strong experimental and progressive party which long held office in New Zealand. In office he showed debating power, constructive skill and tact in managing men; but in 1893, at the height of his success and popularity, he died at Wellington of an intestinal disease after a severe surgical operation. Quiet and unassuming in manner, Ballance, who was a well-read man, always seemed fonder of his books and his chessboard than of public bustle; yet his loss to New Zealand political life was great. A statue was erected to his memory in front of Parliament House, Wellington.

(W. P. R.)

BALLANCHE, PIERRE SIMON (1776-1847), French philosopher of the theocratic school, was born at Lyons. Naturally delicate and highly-strung, he was profoundly stirred by the horrors of the siege of Lyons. His sensitiveness received a second blow in an unsuccessful love affair, which, however, he bore with fortitude. He devoted himself to an examination of the nature of society and his work brought him into connexion with the literary circle of Chateaubriand and Madame Recamier. His great work is the Palingenesie, which is divided into three parts, L'orphee, La formule, La ville des expiations. The first deals with the prehistoric period of the world, before the rise of religion; the second was to be an endeavour to deduce a universal law from known historical facts; the third to sketch the ultimate state of perfection to which humanity is moving. Of these the first alone was completed, but fragments of the other parts exist. Perhaps the most valuable part, of the work is the general introduction. His last work, Vision d'Hebal, intended as part of the Ville des expiations, describes the chief of a Scottish clan, who, gifted with second sight, gives semi-prophetic utterances as to the course of world-history. In 1841 Ballanche was elected a member of the French Academy. He died in 1847. A collected edition of his works in nine volumes was begun in 1830. Four only appeared. In 1833 a second edition in six volumes was published. As a man, Ballanche was warm-hearted and enthusiastic, but he was endowed with a too-vivid imagination and his strange thoughts are expressed in equally bizarre language. To give a connected account of his views is difficult; their full development should be studied in relation with his life-history, the stages of which are curiously parallel to his theory of the progress of man, the fall, the trial, the perfection.

As has been said, he belonged to the theocratic school, who, in opposition to the rationalism of the preceding age, emphasized the principle of authority, placing revelation above individual reason, order above freedom and progress. But Ballanche made a sincere endeavour to unite in one system what was valuable in the opposed modes of thinking. He held with the theocratists that individualism was an impracticable view; man, according to him, exists only in and through society. He agreed further with them that the origin of society was to be explained, not by human desire and efforts, but by a direct revelation from God. Lastly, with De Bonald, he reduced the problem of the origin of society to that of the origin of language, and held that language was a divine gift. But at this point he parts company with the theocratists, and in this very revelation of language finds a germ of progress. Originally, in the primitive state of man, speech and thought are identical; but gradually the two separate; language is no longer only spoken, it is also written and finally is printed. Thus the primitive unity is broken up; the original social order which co-existed with, and was dependent on it, breaks up also. New institutions spring up, upon which thought acts, and in and through which it even draws nearer to a final unity, a palingenesis. The volition of primitive man was one with that of God but it becomes broken up into separate volitions which oppose themselves to the divine will, and through the oppositions and trials of this world work onward to a second and completer harmony. Humanity, therefore, passes through three stages, the fall from perfection, the period of trial and the final re-birth or return to perfection. In the dim records of mythical times may be traced the obscure outlines of primitive society and of its fall. Actual history exhibits the conflict of two great principles, which may be said to be realized in the patricians and plebeians of Rome. Such a distinction of caste is regarded by Ballanche as the original state of historical society; and history, as a whole, he considers to have followed the same course as that taken by the Roman plebs in its attempts to attain equality with the patriciate. On the events through which the human race is to achieve its destiny Ballanche gives few intelligible hints. The sudden flash which disclosed to the eyes of Hebal the whole epic of humanity cannot be reproduced in language trammelled by time and space. Scattered throughout the works of Ballanche are many valuable ideas on the connexion of events which makes possible a philosophy of history; but his own theory does not seem likely to find more favour than it has already received. Besides the Palingenesie, Ballanche wrote a poem on the siege at Lyons (unpublished); Du sentiment considere dans la litterature et dans les arts (1801); Antigone, a prose poem (1814); Essai sur les institutions sociales (1818), intended as a prelude to his great work; Le Vieillard et le jeune homme, a philosophical dialogue (1819); L'Homme sans nom, a novel (1820).

See Ampere, Ballanche (Paris, 1848); Ste Beuve, Portraits contemporains, vol. ii.; Damiron, Philosophie de XIX^e siecle; Eugene Blum, "Essai sur Ballanche" (in Critique Philos., 30th June 1887); Gaston Frainnet, Essai sur la philos de P. S. Ballanche (Paris, 1903, containing unpublished letters, portraits and full bibliography); C. Huit, La Vie et les oeuvres de Ballanche (1904). An admirable analysis of the works composing the Palingenesie is given by Barchou, Revue des deux mondes (1831), t. 2. pp. 410-456.

BALLANTINE, WILLIAM (1812-1887), English serjeant-at-law, was born in London on the 3rd of January 1812, being the son of a London police-magistrate. He was educated at St Paul's school, and called to the bar in 1834. He began in early life a varied acquaintance with dramatic and literary society, and his experience, combined with his own pushing character and acute intellect, helped to obtain for him very soon a large practice, particularly in criminal cases. He became known as a formidable cross-examiner, his great rival being Serjeant Parry (1816-1880). The three great cases of his career were his successful prosecution of the murderer Franz Mueller in 1864, his skilful defence of the Tichborne claimant in 1871 and his defence of the gaekwar of Baroda in 1875, his fee in this last case being one of the largest ever known. Ballantine became a serjeant-at-law in 1856. He died at Margate on the 9th of January 1887, having previously published more than one volume of reminiscences. Serjeant Ballantine's private life was decidedly Bohemian; and though he earned large sums, he died very poor.

BALLANTYNE, ROBERT MICHAEL (1825-1894), Scottish writer of fiction, was born at Edinburgh on the 24th of April 1825, and came of the same family as the famous printers and publishers. When sixteen years of age he went to Canada and was for six years in the service of the Hudson's Bay Company. He returned to Scotland in 1847, and next year published his first book, Hudson's Bay: or, Life in the Wilds of North America. For some time he was employed by Messrs Constable, the publishers, but in 1856 he gave up business for the profession of literature, and began the series of excellent stories of adventure for the young with which his name is popularly associated. The Young Fur-Traders (1856), The Coral Island (1857), The World of Ice (1859), Ungava: a Tale of Eskimo Land (1857), The Dog Crusoe (1860), The Lighthouse (1865), Deep Down (1868), The Pirate City (1874), Erling the Bold (1869), The Settler and the Savage (1877), and other books, to the number of upwards of a hundred, followed in regular succession, his rule being in every case to write as far as possible from personal knowledge of the scenes he described. His stories had the merit of being thoroughly healthy in tone and possessed considerable graphic force. Ballantyne was also no mean artist, and exhibited some of his water-colours at the Royal Scottish Academy. He lived in later years at Harrow, and died on the 8th of February 1894, at Rome, where he had gone to attempt to shake off the results of overwork. He wrote a volume of Personal Reminiscences of Book-making (1893).

BALLARAT [BALLAARAT] and BALLARAT EAST, a city and a town of Grenville county, Victoria, Australia, 74 m. by rail W.N.W. of Melbourne. The city and Ballarat East, separated only by the Yarrowee Creek, are distinct municipalities. Pop. of Ballarat (1901) 25,448, of Ballarat East, 18,262. Ballarat is the second city and the chief gold-mining centre of the state. The alluvial gold-fields were the richest ever opened up, but as these deposits have become exhausted the quartz reefs at deep levels have been exploited, and several mines are worked at depths exceeding 2000 ft. The city is the seat of Anglican and Roman Catholic bishops. It has a number of admirable public buildings, while, among several parks and recreation grounds, mention must be made of the fine botanical garden, 750 acres in extent, [v.03 p.0269] where, in Lake Wendouree, pisciculture is carried on with great success. The school of mines is the most important in Australia and is affiliated to the university of Melbourne. Ballarat is an important railway centre and its industries include woollen-milling, brewing, iron-founding, flour-milling and distilling. Owing to its elevation of 1438 ft. it has an exceptionally cool and healthy climate. Although the district is principally devoted to mining it is well adapted for sheep-farming, and some of the finest wool in the world is produced near Ballarat. The existence of the towns is due to the heavy immigration which followed upon the discovery of the gold-fields in 1851. In 1854, in their resistance of an arbitrary tax, the miners came into armed conflict with the authorities; but a commission was appointed to investigate their grievances; and a charter was granted to the town in 1855. In 1870 Ballarat was raised to the rank of a city.

BALLAST (O. Swed. barlast, perhaps from bar, bare or mere, and last, load), heavy material, such as gravel, stone or metal, placed in the hold of a ship in order to immerse her sufficiently to give adequate stability. In botany "ballast-plants" are so-called because they have been introduced into countries in which they are not indigenous through their seeds being carried in such ballast. A ship "in ballast" is one which carries no paying cargo. In modern vessels the place of ballast is taken by water-tanks which are filled more or less as required to trim the ship. The term is also applied to materials like gravel, broken slag, burnt clay, &c., used to form the bed in which the sleepers or ties of a railway track are laid, and also to the sand which a balloonist takes up with him, in order that, by throwing portions of it out of the car from time to time, he may lighten his balloon when he desires to rise to a higher level.

BALLATER (Gaelic for "the town on a sloping hill"), a village in the parish of Glenmuick, Aberdeenshire, Scotland, 670 ft. above the sea, on the left bank of the Dee, here crossed by a fine bridge, 43-1/4 m. by rail W. by S. of Aberdeen. It is the terminus of the Deeside railway and the station for Balmoral, 9 m. to the W. Founded in 1770 to provide accommodation for the visitors to the mineral wells of Pannanich, 1-1/2 m. to the E., it has since become a popular summer resort. It contains the Albert Memorial Hall and the barracks for the sovereign's bodyguard, used when the king is in residence at Balmoral. Red granite is the chief building material of the houses. Ballatrich farm, where Byron spent part of his boyhood, lies some 4 m. to the E. Ballater has a mean temperature of 44.6deg F., and an average annual rainfall of 33.4 in.

BALLENSTEDT, a town of Germany, in the duchy of Anhalt, on the river Getel, 20 m. E. of Quedlinburg by rail. Pop. (1900) 5423. It is pleasantly situated under the north-eastern declivity of the Harz mountains. The inhabitants are mostly engaged in agriculture and there is practically no other industry. The palace of the dukes of Anhalt, standing on an eminence, contains a library and collections of various kinds, including a good picture gallery. It is approached by a fine avenue of trees and is surrounded by a well-wooded park. In the Schlosskirche the grave of Albert the Bear, margrave of Brandenburg (1100-1170) has been discovered.

BALLET, a performance in which dancing, music and pantomime are involved. Originally derived from the (Sicilian) Gr. [Greek: ballizein], to dance, the word has passed through the Med. Lat. ballare (with ballator as synonymous with saltator) to the Ital. ballare and ballata, to the Fr. ballet, to the O. Eng. word ballette, and to ballad. In O. Fr., according to Rousseau, ballet signifies "to dance, to sing, to rejoice"; and thus it incorporates three distinct modern words, "ballet, ball and ballad." Through the gradual changes in the amusements of different ages, the meaning of the first two words has at length become limited to dancing, and the third is now confined to singing. But, although ballads are no longer the vocal accompaniments to dances round the maypole, old ballads are still sung to dance tunes. The present acceptation of the word ballet is—a theatrical representation in which a story is told only by gesture, accompanied by music, which should be characterized by stronger emphasis than would be employed with the voice. The dancing should be connected with the story but is more commonly incidental. The French word was found to be so comprehensive as to require further definition, and thus the above-described would be distinguished as the ballet d'action or pantomime ballet, while a single scene, such as that of a village festival with its dances, would now be termed a divertissement.

The ballet d'action, to which the changed meaning of the word is to be ascribed, and therewith the introduction of modern ballet, has been generally attributed to the 15th century. Novelty of entertainment was then sought for in the splendid courts of Italy, in order to celebrate events which were thought great in their time, such as the marriages of princes, or the triumphs of their arms. Invention was on the rack for novelty, and the skill of the machinist was taxed to the utmost. It has been supposed that the art of the old Roman pantomimi was then revived, to add to the attractions of court-dances. Under the Roman empire the pantomimi had represented either a mythological story, or perhaps a scene from a Greek tragedy, by mute gestures, while a chorus, placed in the background, sang cantica to narrate the fable, or to describe the action of the scene. The question is whether mute pantomimic action, which is the essence of modern ballet, was carried through those court entertainments, in which kings, queens, princes and princesses, took parts with the courtiers; or whether it is of later growth, and derived from professional dances upon the stage. The former is the general opinion, but the court entertainments of Italy and France were masques or masks which included declamation and song, like those of Ben Jonson with Inigo Jones for the court of James I.

The earliest modern ballet on record was that given by Bergonzio di Botta at Tortona to celebrate the marriage of the duke of Milan in 1489. The ballet, like other forms of dancing, was developed and perfected in France; it is closely associated with the history of the opera; but in England it came much later than the opera, for it was not introduced until the 18th century, and in the first Italian operas given in London there was no ballet. During the regency of Lord Middlesex a ballet-master was appointed and a corps of dancers formed. The ballet has had three distinct stages in its development. For a long time it was to be found only at the court, when princely entertainments were given to celebrate great occasions. At that time ladies of the highest rank performed in the ballet and spent much time in practising and perfecting themselves for it. Catherine de'Medici introduced these entertainments into France and spent large sums of money on devising performances to distract her son's attention from the affairs of the state. Baltasarini, otherwise known as Beaujoyeulx, was the composer of a famous entertainment given by Catherine in 1581 called the "Ballet Comique de la Reyne." This marks an era in the history of the opera and ballet, for we find here for the first time dance and music arranged for the display of coherent dramatic ideas. Henry IV., Louis XIII. and XIV. were all lovers of the ballet and performed various characters in them, and Richelieu used the ballet as an instrument for the expression of political purposes. Lully was the first to make an art of the composition of ballet music and he was the first to insist on the admission of women as ballet dancers, feminine characters having hitherto been assumed by men dressed as women. When Louis XIV. became too fat to dance, the ballet at court became unpopular and thus was ended the first stage of its development. It was then adopted in the colleges at prize distributions and other occasions, when the ballets of Lully and Quinault were commonly performed. The third period in the history of the ballet was marked by its appearance on the stage, where it has remained ever since. It should be added that up till the third period dramatic poems had accompanied the ballet and the dramatic meaning was helped out with speech and song; but with the advent of the third period speech disappeared and the purely pantomime performance, or ballet d'action, was instituted.

The father of ballet dancing as we know it at the present day was Jean Georges Noverre (q.v.). The ballet d'action was really invented by him; in fact, the ballet has never advanced beyond the stage to which he brought it; it has rather gone back. The [v.03 p.0270] essence of Noverre's theory was that mere display was not enough to ensure interest and life for the ballet; and some years ago Sir Augustus Harris expressed a similar opinion when he was asked wherein lay the reason of the decadence of the modern ballet. Noverre brought to a high degree of perfection the art of presenting a story by means of pantomime, and he never allowed dancing which was not the direct expression of a particular attitude of mind. Apart from Noverre, the greatest ballet-master was undoubtedly Gaetano Apolline Balthazare Vestris (q.v.), who modestly called himself le dieu de la danse, and was, indeed, the finest male dancer that Europe ever produced. Gluck composed Iphigenie en Aulide in conjunction with Vestris. In 1750 the two greatest dancers of the day performed together in Paris in a ballet-opera called Leandre et Hero; the dancers were Vestris and Madame Camargo (q.v.), who introduced short skirts in the ballet.

The word "balette" was first used in the English language by Dryden in 1667, and the first descriptive ballet seen in London was The Tavern Bilkers, which was played at Drury Lane in 1702. Since then the ballet in England has been purely exotic and has merely followed on the lines of French developments. The palmy days of the ballet in England were in the first half of the 19th century, when a royal revenue was spent on the maintenance of this fashionable attraction. Some famous dancers of this period were Carlotta Grisi, Mdlle Taglioni (who is said to have turned the heads of an entire generation), Fanny Elssler, Mdlle Cerito, Miss P. Horton, Miss Lucile Grahn and Mdlle Carolina Rosati. In later years Kate Vaughan was a remarkably graceful dancer of a new type in England, and, in Sir Augustus Harris's opinion, she did much to elevate the modern art. She was the first to make skirt-dancing popular, although that achievement will not be regarded as an unmixed benefit by every student of the art. Skirt-dancing, in itself a beautiful exhibition, is a departure from true dancing in the sense that the steps are of little importance in it; and we have seen its development extend to a mere exhibition of whirling draperies under many-coloured lime-lights. The best known of Miss Vaughan's disciples and imitators (each of whom has contributed something to the art on her own account) were Miss Sylvia Grey and Miss Letty Lind. Of the older and classical school of ballet-dancing Adeline Genee became in London the finest exponent. But ballet-dancing, affected by a tendency in modern entertainment to make less and less demands on the intelligence and intellectual appreciation of the public, and more and more demands on the eye—the sense most easily affected—has gradually developed into a spectacle, the chief interest of which is quite independent of dancing. Thousands of pounds are spent on dressing a small army of women who do little but march about the stage and group themselves in accordance with some design of colour and mass; and no more is asked of the intelligence than to believe that a ballet dressed, for example, in military uniform is a compliment to or glorification of the army. Only a few out of hundreds of members of the corps de ballet are really dancers and they perform against a background of colour afforded by the majority. It seems unlikely that we shall see any revival of the best period and styles of dancing until a higher standard of grace and manners becomes fashionable in society. With the constantly increasing abolition of ceremony, courtliness of manner is bound to diminish; and only in an atmosphere of ceremony, courtesy and chivalry can the dance maintain itself in perfection.

LITERATURE.—One of the most complete books on the ballet is by the Jesuit, Claude Francois Menestrier, Des ballets anciens et modernes, 12mo (1682). He was the inventor of a ballet for Louis XIV. in 1658; and in his book he analyses about fifty of the early Italian and French ballets. See also Noverre, Lettres sur la danse (1760; new ed. 1804); Castel-Blaze, La Danse et les ballets (1832), and Les Origines de l'opera (1869).

BALL-FLOWER, an architectural ornament in the form of a ball inserted in the cup of a flower, which came into use in the latter part of the 13th, and was in great vogue in the early part of the 14th century. It is generally placed in rows at equal distances in the hollow of a moulding, frequently by the sides of mullions. The earliest known is said to be in the west part of Salisbury cathedral, where it is mixed with the tooth ornament. It seems to have been used more and more frequently, till at Gloucester cathedral, in the south side, it is in profusion.

BALLIA, a town and district of British India, in the Benares division of the United Provinces. The town is situated on the left bank of the Ganges, below the confluence of the lesser Sarju. It is really an aggregation of rural villages. Pop. (1901) 15,278.

The district of Ballia, constituted in 1879, occupies an angle at the junction of the Gogra with the Ganges, being bordered by two districts of Behar. It contains an area of 1245 sq. m. Owing to the great pressure on the soil from the density of the population, to the reluctance to part with land characteristic of small proprietors, to the generally great productiveness of land and to the very light assessment of government revenue, land in Ballia, for agricultural purposes merely, has a market value higher than in almost any other district. It commonly brings in Rs. 200 per bigha, or L20 per acre, and sometimes double that figure. In 1901 the population was 987,768, showing a decrease of 5% in the decade. The principal crops are rice, barley, other food-grains, pulse, sugar-cane and opium. There are practically no manufactures, except that of sugar. Trade is carried on largely by way of the two bordering rivers.

BALLINA, a seaport and market-town of county Mayo, Ireland, in the north parliamentary division, on the left bank of the river Moy, with a station on the Killala branch of the Midland Great Western railway. Pop. of urban district (1901) 4505. Across the river, and therefore in county Sligo, is the suburb of Ardnaree, connected with Ballina by two bridges. In Ardnaree is the Roman Catholic cathedral (diocese of Killala), with an east window of Munich glass, and the ruins of an Augustinian abbey (1427) adjoining. There is a Roman Catholic diocesan college and the Protestant parish church is also in Ardnaree. A convent was erected in 1867. In trade and population Ballina is the first town in the county. The salmon-fishery and fish-curing are important branches of its trade; and it has also breweries and flour-mills and manufactures snuff and coarse linen. On the 25th of August 1798, Ballina was entered by the French under General Humbert, marching from their landing-place at Killala. In the neighbourhood there is the interesting cromlech of the four Maels, which, if actually erected over the criminals whose name it bears, is proved by the early annals of Ireland to belong to the 7th century A.D. Their story relates that these men, foster-brothers of Cellach, bishop of Kilmore-Moy, murdered him at the instigation of Guaire Aidhne, king of Connaught, but were themselves executed at Ardnare (Ard-na-riaghadh, the hill of the executions) by the bishop's brother. The Moy is a notable salmon river for rod-fishing and its tributaries and the neighbouring lakes contain trout.

BALLINASLOE, a market town of county Galway, Ireland, in the east parliamentary division, 91 m. W. of Dublin, on the Midland Great Western main line. Pop. of urban district (1901) 4904. The river Suck, an affluent of the Shannon, divides it into two parts, of which the eastern was in county Roscommon until 1898. The town contains remains of a castle of Elizabethan date. Industries include brewing, flour-milling, tanning, hat-making and carriage-building. Trade is assisted by water-communication through the Grand canal to the Shannon. The town is widely celebrated for its great annual cattle-fair held in October, at which vast numbers of cattle and sheep are offered or sale. Adjoining the town is Garbally Castle, the seat of the earl of Clancarty, into the demesne of which the great fair extends from the town.

BALLISTICS (from the Gr. [Greek: ballein], to throw), the science of throwing warlike missiles or projectiles. It is now divided into two parts:—Exterior Ballistics, in which the motion of the projectile is considered after it has received its initial impulse, when the projectile is moving freely under the influence of gravity and the resistance of the air, and it is required to determine the circumstances so as to hit a certain object, with a view to its destruction or perforation; and Interior Ballistics, in which the pressure of the powder-gas is analysed in the bore [v.03 p.0271] of the gun, and the investigation is carried out of the requisite charge of powder to secure the initial velocity of the projectile without straining the gun unduly. The calculation of the stress in the various parts of the gun due to the powder pressure is dealt with in the article ORDNANCE.

I. EXTERIOR BALLISTICS.

In the ancient theory due to Galileo, the resistance of the air is ignored, and, as shown in the article on MECHANICS (s. 13), the trajectory is now a parabola. But this theory is very far from being of practical value for most purposes of gunnery; so that a first requirement is an accurate experimental knowledge of the resistance of the air to the projectiles employed, at all velocities useful in artillery. The theoretical assumptions of Newton and Euler (hypotheses magis mathematicae quam naturales) of a resistance varying as some simple power of the velocity, for instance, as the square or cube of the velocity (the quadratic or cubic law), lead to results of great analytical complexity, and are useful only for provisional extrapolation at high or low velocity, pending further experiment.

The foundation of our knowledge of the resistance of the air, as employed in the construction of ballistic tables, is the series of experiments carried out between 1864 and 1880 by the Rev. F. Bashforth, B.D. (Report on the Experiments made with the Bashforth Chronograph, &c., 1865-1870; Final Report, &c., 1878-1880; The Bashforth Chronograph, Cambridge, 1890). According to these experiments, the resistance of the air can be represented by no simple algebraical law over a large range of velocity. Abandoning therefore all a priori theoretical assumption, Bashforth set to work to measure experimentally the velocity of shot and the resistance of the air by means of equidistant electric screens furnished with vertical threads or wire, and by a chronograph which measured the instants of time at which the screens were cut by a shot flying nearly horizontally. Formulae of the calculus of finite differences enable us from the chronograph records to infer the velocity and retardation of the shot, and thence the resistance of the air.

As a first result of experiment it was found that the resistance of similar shot was proportional, at the same velocity, to the surface or cross section, or square of the diameter. The resistance R can thus be divided into two factors, one of which is d^2, where d denotes the diameter of the shot in inches, and the other factor is denoted by p, where p is the resistance in pounds at the same velocity to a similar 1-in. projectile; thus R = d^2p, and the value of p, for velocity ranging from 1600 to 2150 ft. per second (f/s) is given in the second column of the extract from the abridged ballistic table below.

These values of p refer to a standard density of the air, of 534.22 grains per cubic foot, which is the density of dry air at sea-level in the latitude of Greenwich, at a temperature of 62deg F. and a barometric height of 30 in.

But in consequence of the humidity of the climate of England it is better to suppose the air to be (on the average) two-thirds saturated with aqueous vapour, and then the standard temperature will be reduced to 60deg F., so as to secure the same standard density; the density of the air being reduced perceptibly by the presence of the aqueous vapour.

It is further assumed, as the result of experiment, that the resistance is proportional to the density of the air; so that if the standard density changes from unity to any other relative density denoted by [tau], then R = [tau]d^2p, and [tau] is called the coefficient of tenuity.

The factor [tau] becomes of importance in long range high angle fire, where the shot reaches the higher attenuated strata of the atmosphere; on the other hand, we must take [tau] about 800 in a calculation of shooting under water.

The resistance of the air is reduced considerably in modern projectiles by giving them a greater length and a sharper point, and by the omission of projecting studs, a factor [kappa], called the coefficient of shape, being introduced to allow for this change.

For a projectile in which the ogival head is struck with a radius of 2 diameters, Bashforth puts [kappa] = 0.975; on the other hand, for a flat-headed projectile, as required at proof-butts, [kappa] = 1.8, say 2 on the average.

For spherical shot [kappa] is not constant, and a separate ballistic table must be constructed; but [kappa] may be taken as 1.7 on the average.

Lastly, to allow for the superior centering of the shot obtainable with the breech-loading system, Bashforth introduces a factor [sigma], called the coefficient of steadiness.

This steadiness may vary during the flight of the projectile, as the shot may be unsteady for some distance after leaving the muzzle, afterwards steadying down, like a spinning-top. Again, [sigma] may increase as the gun wears out, after firing a number of rounds.

Collecting all the coefficients, [tau], [kappa], [sigma], into one, we put

(1) R = nd^2p = nd^2f(v), where (2) n = [kappa] [sigma] [tau],

and n is called the coefficient of reduction.

By means of a well-chosen value of n, determined by a few experiments, it is possible, pending further experiment, with the most recent design, to utilize Bashforth's experimental results carried out with old-fashioned projectiles fired from muzzle-loading guns. For instance, n = 0.8 or even less is considered a good average for the modern rifle bullet.

Starting with the experimental values of p, for a standard projectile, fired under standard conditions in air of standard density, we proceed to the construction of the ballistic table. We first determine the time t in seconds required for the velocity of a shot, d inches in diameter and weighing w lb, to fall from any initial velocity V(f/s) to any final velocity v(f/s). The shot is supposed to move horizontally, and the curving effect of gravity is ignored.

If [Delta]t seconds is the time during which the resistance of the air, R lb, causes the velocity of the shot to fall [Delta]v (f/s), so that the velocity drops from v+1/2[Delta]v to v-1/2[Delta]v in passing through the mean velocity v, then

(3) R[Delta]t = loss of momentum in second-pounds, = w(v+1/2[Delta]v)/g - w(v-1/2[Delta]v)/g = w[Delta]v/g

so that with the value of R in (1),

(4) [Delta]t = w[Delta]v/nd^2pg.

We put

(5) w/nd^2 = C,

and call C the ballistic coefficient (driving power) of the shot, so that

(6) [Delta]t = C[Delta]T, where (7) [Delta]T = [Delta]v/gp,

and [Delta]T is the time in seconds for the velocity to drop [Delta]v of the standard shot for which C=1, and for which the ballistic table is calculated.

Since p is determined experimentally and tabulated as a function of v, the velocity is taken as the argument of the ballistic table; and taking [Delta]v = 10, the average value of p in the interval is used to determine [Delta]T.

Denoting the value of T at any velocity v by T(v), then

(8) T(v) = sum of all the preceding values of [Delta]T plus an arbitrary constant, expressed by the notation (9) T(v) = [Sum]([Delta]v)/gp + a constant, or [Integral]dv/gp + a constant, in which p is supposed known as a function of v.

The constant may be any arbitrary number, as in using the table the difference only is required of two tabular values for an initial velocity V and final velocity v and thus

(10) T(V) - T(v) = [Sum,v:V][Delta]v/gp or [Integral,v:V]dv/gp;

and for a shot whose ballistic coefficient is C

(11) t = C[T(V) - T(v)].

To save the trouble of proportional parts the value of T(v) for unit increment of v is interpolated in a full-length extended ballistic table for T.

Next, if the shot advances a distance [Delta]s ft. in the time [Delta]t, during which the velocity falls from v+1/2[Delta]v to v-1/2[Delta]v, we have

(12) R[Delta]s = loss of kinetic energy in foot-pounds =w(v+1/2[Delta]v)^2/g - w(v-1/2[Delta]v)^2/g = wv[Delta]v/g, so that (13) [Delta]s = wv[Delta]v/nd^2pg = C[Delta]S, where (14) [Delta]S = v[Delta]v/gp = v[Delta]T,

and [Delta]S is the advance in feet of a shot for which C=1, while the velocity falls [Delta]v in passing through the average velocity v.

Denoting by S(v) the sum of all the values of [Delta]S up to any assigned velocity v,

(15) S(v) = [Sum]([Delta]S) + a constant, by which S(v) is calculated from [Delta]S, and then between two assigned velocities V and v,

(16) S(V) - S(v) = [Sum,v:V][Delta]T = [Sum]v[Delta]v/gp or [Integral,v:V]vdv/gp,

and if s feet is the advance of a shot whose ballistic coefficient is C,

(17) s = C[S(V) - S(v)].

In an extended table of S, the value is interpolated for unit increment of velocity.

A third table, due to Sir W. D. Niven, F.R.S., called the degree table, determines the change of direction of motion of the shot while the velocity changes from V to v, the shot flying nearly horizontally.

To explain the theory of this table, suppose the tangent at the point of the trajectory, where the velocity is v, to make an angle i radians with the horizon.

Resolving normally in the trajectory, and supposing the resistance of the air to act tangentially,

(18) v(di/dt) = g cos i,

where di denotes the infinitesimal _decrement_ of i in the infinitesimal increment of time dt_.

[v.03 p.0272] In a problem of direct fire, where the trajectory is flat enough for cos i to be undistinguishable from unity, equation (16) becomes

(19) v(di/dt) = g, or di/dt = g/v;

so that we can put

(20) [Delta]i/[Delta]t = g/v

if v denotes the mean velocity during the small finite interval of time [Delta]t, during which the direction of motion of the shot changes through [Delta]i radians.

If the inclination or change of inclination in degrees is denoted by [delta] or [Delta][delta],

(21) [delta]/180 = i/[pi], so that

(22) [Delta][delta] = 180/[pi] [Delta]i = 180g/[pi] [Delta]t/v;

and if [delta] and i change to D and I for the standard projectile,

(23) [Delta]I = g [Delta]T/v = [Delta]v/vp, [Delta]D = 180g/[pi] [Delta]T/v, and

(24) I(V) - I(v) = [Sum,v:V][Delta]v/vp or [Integral,v:V]dv/vp, D(V) - D(v) = 180/[pi] [I(V) - I(v)].

The differences [Delta]D and [Delta]I are thus calculated, while the values of D(v) and I(v) are obtained by summation with the arithmometer, and entered in their respective columns.

For some purposes it is preferable to retain the circular measure, i radians, as being undistinguishable from sin i and tan i when i is small as in direct fire.

The last function A, called the altitude function, will be explained when high angle fire is considered.

These functions, T, S, D, I, A, are shown numerically in the following extract from an abridged ballistic table, in which the velocity is taken as the argument and proceeds by an increment of 10 f/s; the column for p is the one determined by experiment, and the remaining columns follow by calculation in the manner explained above. The initial values of T, S, D, I, A must be accepted as belonging to the anterior portion of the table.

In any region of velocity where it is possible to represent p with sufficient accuracy by an empirical formula composed of a single power of v, say v^m, the integration can be effected which replaces the summation in (10), (16), and (24); and from an analysis of the Krupp experiments Colonel Zabudski found the most appropriate index m in a region of velocity as given in the following table, and the corresponding value of gp, denoted by f(v) or v^m/k or its equivalent Cr, where r is the retardation.

ABRIDGED BALLISTIC TABLE.

-+ + -+ -+ -+ + -+ v. p. [Delta]T. T. [Delta]S. S. [Delta]D. D. -+ + -+ -+ -+ + -+ f/s 1600 11.416 .0271 27.5457 43.47 18587.00 .0311 49.7729 1610 11.540 .0268 27.5728 43.27 18630.47 .0306 49.8040 1620 11.662 .0265 27.5996 43.08 18673.74 .0301 49.8346 1630 11.784 .0262 27.6261 42.90 18716.82 .0296 49.8647 1640 11.909 .0260 27.6523 42.72 18759.72 .0291 49.8943 1650 12.030 .0257 27.6783 42.55 18802.44 .0287 49.9234 1660 12.150 .0255 27.7040 42.39 18844.99 .0282 49.9521 1670 12.268 .0252 27.7295 42.18 18887.38 .0277 49.9803 1680 12.404 .0249 27.7547 41.98 18929.56 .0273 50.0080 1690 12.536 .0247 27.7796 41.78 18971.54 .0268 50.0353 1700 12.666 .0244 27.8043 41.60 19013.32 .0264 50.0621 1710 12.801 .0242 27.8287 41.41 19054.92 .0260 50.0885 1720 12.900 .0239 27.8529 41.23 19096.33 .0256 50.1145 1730 13.059 .0237 27.8768 41.06 19137.56 .0252 50.1401 1740 13.191 .0234 27.9005 40.90 19178.62 .0248 50.1653 1750 13.318 .0232 27.9239 40.69 19219.52 .0244 50.1901 1760 13.466 .0230 27.9471 40.53 19260.21 .0240 50.2145 1770 13.591 .0227 27.9701 40.33 19300.74 .0236 50.2385 1780 13.733 .0225 27.9928 40.19 19341.07 .0233 50.2621 1790 13.862 .0223 28.0153 40.00 19381.26 .0229 50.2854 1800 14.002 .0221 28.0376 39.81 19421.26 .0225 50.3083 1810 14.149 .0219 28.0597 39.68 19461.07 .0222 50.3308 1820 14.269 .0217 28.0816 39.51 19500.75 .0219 50.3530 1830 14.414 .0214 28.1033 39.34 19540.26 .0216 50.3749 1840 14.552 .0212 28.1247 39.17 19579.60 .0212 50.3965 1850 14.696 .0210 28.1459 39.01 19618.77 .0209 50.4177 1860 14.832 .0209 28.1669 38.90 19657.78 .0206 50.4386 1870 14.949 .0207 28.1878 38.75 19696.68 .0203 50.4592 1880 15.090 .0205 28.2085 38.61 19735.43 .0200 50.4795 1890 15.224 .0203 28.2290 38.46 19774.04 .0198 50.4995 1900 15.364 .0201 28.2493 38.32 19812.50 .0195 50.5193 1910 15.496 .0199 28.2694 38.19 19850.82 .0192 50.5388 1920 15.656 .0197 28.2893 38.01 19889.01 .0189 50.5580 1930 15.809 .0196 28.3090 37.83 19927.02 .0186 50.5769 1940 15.968 .0194 28.3286 37.66 19964.85 .0184 50.5955 1950 16.127 .0192 28.3480 37.48 20002.51 .0181 50.6139 1960 16.302 .0190 28.3672 37.26 20039.99 .0178 50.6320 1970 16.484 .0187 28.3862 36.99 20077.25 .0175 50.6498 1980 16.689 .0185 28.4049 36.73 20114.24 .0172 50.6673 1990 16.888 .0183 28.4234 36.47 20150.97 .0169 50.6845 2000 17.096 .0181 28.4417 36.21 20187.44 .0166 50.7014 2010 17.305 .0178 28.4598 35.95 20223.65 .0163 50.7180 2020 17.515 .0176 28.4776 35.65 20259.60 .0160 50.7343 2030 17.752 .0174 28.4952 35.35 20295.25 .0158 50.7503 2040 17.990 .0171 28.5126 35.06 20330.60 .0155 50.7661 2050 18.229 .0169 28.5297 34.77 20365.66 .0152 50.7816 2060 18.463 .0167 28.5466 34.49 20400.43 .0149 50.7968 2070 18.706 .0165 28.5633 34.21 20434.92 .0147 50.8117 2080 18.978 .0163 28.5798 33.93 20469.13 .0144 50.8264 2090 19.227 .0160 28.5961 33.60 20503.06 .0141 50.8408 2100 19.504 .0158 28.6121 33.34 20536.66 .0139 50.8549 2110 19.755 .0156 28.6279 33.02 20570.00 .0136 50.8688 2120 20.010 .0154 28.6435 32.76 20603.02 .0134 50.8824 2130 20.294 .0152 28.6589 32.50 20635.78 .0132 50.8958 2140 20.551 .0150 28.6741 32.25 20688.28 .0129 50.9090 -+ + -+ -+ -+ + -+

-+ + -+ -+ -+ - v. p. [Delta]I. I. [Delta]A. A. -+ + -+ -+ -+ - f/s 1600 11.416 .000543 .868675 37.77 8470.36 1610 11.540 .000534 .869218 37.63 8508.13 1620 11.662 .000525 .869752 37.48 8545.76 1630 11.784 .000517 .870277 37.35 8583.24 1640 11.909 .000508 .870794 37.21 8620.59 1650 12.030 .000500 .871302 37.09 8657.80 1660 12.150 .000492 .871802 36.96 8694.89 1670 12.268 .000484 .872294 36.80 8731.85 1680 12.404 .000476 .872778 36.65 8768.65 1690 12.536 .000468 .873254 36.50 8805.30 1700 12.666 .000461 .873722 36.35 8841.80 1710 12.801 .000453 .874183 36.21 8878.15 1720 12.900 .000446 .874636 36.07 8914.36 1730 13.059 .000439 .875082 35.94 8950.43 1740 13.191 .000432 .875521 35.81 8986.37 1750 13.318 .000425 .875953 35.65 9022.18 1760 13.466 .000419 .876378 35.53 9057.83 1770 13.591 .000412 .876797 35.37 9093.36 1780 13.733 .000406 .877209 35.26 9128.73 1790 13.862 .000400 .877615 35.11 9163.99 1800 14.002 .000393 .878015 34.96 9199.10 1810 14.149 .000388 .878408 34.86 9234.06 1820 14.269 .000382 .878796 34.73 9268.92 1830 14.414 .000376 .879178 34.59 9303.65 1840 14.552 .000370 .879554 34.46 9338.24 1850 14.696 .000365 .879924 34.33 9372.70 1860 14.832 .000360 .880289 34.25 9407.03 1870 14.949 .000355 .880649 34.14 9441.28 1880 15.090 .000350 .881004 34.02 9475.42 1890 15.224 .000345 .881354 33.91 9509.44 1900 15.364 .000340 .881699 33.80 9543.35 1910 15.496 .000335 .882039 33.69 9577.15 1920 15.656 .000330 .882374 33.55 9610.84 1930 15.809 .000325 .882704 33.40 9644.39 1940 15.968 .000320 .883029 33.26 9677.79 1950 16.127 .000316 .883349 33.12 9711.05 1960 16.302 .000311 .883665 32.94 9744.17 1970 16.484 .000305 .883976 32.71 9777.11 1980 16.689 .000300 .884281 32.48 9809.82 1990 16.888 .000295 .884581 32.26 9842.30 2000 17.096 .000290 .884876 32.05 9874.56 2010 17.305 .000285 .885166 31.83 9906.61 2020 17.515 .000280 .885451 31.57 9938.44 2030 17.752 .000275 .885731 31.32 9970.01 2040 17.990 .000270 .886006 31.07 10001.33 2050 18.229 .000265 .886276 30.82 10032.40 2060 18.463 .000260 .886541 30.58 10063.33 2070 18.706 .000256 .886801 30.34 10093.80 2080 18.978 .000251 .887057 30.10 10124.14 2090 19.227 .000247 .887308 29.82 10154.24 2100 19.504 .000242 .887555 29.59 10184.06 2110 19.755 .000238 .887797 29.32 10213.65 2120 20.010 .000234 .888035 29.10 10242.97 2130 20.294 .000230 .888269 28.88 10272.07 2140 20.551 .000226 .888499 28.66 10300.95 2150 20.811 .000222 .888725 28.44 10329.61 -+ + -+ -+ -+ -

+ + -+ + + v. m. log k. Cr = gp = f(v) = {v^m}/k. + + -+ + + 3600 1.55 2.3909520 v^{1.55} x log^{-1} [=3].6090480 2600 1.7 2.9038022 v^{1.7} x log^{-1} [=3].0961978 1800 2 3.8807404 v^2 x log^{-1} [=4].1192596 1370 3 7.0190977 v^3 x log^{-1} [=8].9809023 1230 5 13.1981288 v^5 x log^{-1}[=14].8018712 970 3 7.2265570 v^3 x log^{-1} [=8].7734430 790 2 4.3301086 v^2 x log^{-1} [=5].6698914 + + -+ + +