Chapter 14

Bearing Friction.—If W is the total load on a bearing, and if µ is the coefficient of friction between the rubbing surfaces, the tangential resistance to turning is expressed by the product µW. If v is the relative velocity of the rubbing surfaces, the work done per second against friction is µWv foot pounds. This quantity of work is converted into heat, and the heat produced per second is therefore µWv/778 British Thermal Units. The coefficient µ is a variable quantity, and bearing in mind that a properly lubricated journal is separated from its supporting brass by a film of lubricant it might be expected that µ would have values characteristic of the coefficient of friction between two metallic surfaces, merging into the characteristics properly belonging to fluid friction, according as the oil film varied from an imperfect to a perfect condition, that is, according as the lubrication is partial or complete, completeness being attained by the use of an oil bath or by some method of forced lubrication. This expectation is entirely borne out by experimental researches. Beauchamp Tower (“Report on Friction Experiments,”Proc. Inst. Mech. Eng., November 1883) found that when oil was supplied to a bearing by means of a pad the coefficient of friction was approximately constant with the value of1⁄100, thus following the law of solid friction; but when the journal was lubricated by means of an oil bath the coefficient of friction varied nearly inversely as the load on the bearing, thus making µW = constant. The tangential resistance in this case is characteristic of fluid friction since it is independent of the pressure. Tower’s experiments were carried out at a nearly constant temperature. The later experiments of O. Lasche (Zeitsch. Verein deutsche Ingenieure, 1902, 46, pp. 1881 et seq.) show how µ depends upon the temperature. Lasche’s main results with regard to the variation of µ are briefly:—µW is a constant quantity, thus confirming Tower’s earlier experiments; µ is practically independent of the relative velocity of the rubbing surfaces within the limits of 3 to 50 ft. per second; and the product µt is constant, t being the temperature of the bearing. Writing p for the load per unit of projected area of the bearing, Lasche found that the result of the experiments could be expressed by the simple formula pµt = constant = 2, where p = the pressure in kilograms per square centimetre, and t = the temperature in degrees centigrade. If p is changed to pounds per square inch the constant in the expression is approximately 30. The expression is valid between limits of pressure 14 to 213 pounds per square inch, limits of temperature 30° to 100° C., and between limits of velocity 3 to 50 ft. per second.Fig.12.Theory of Lubrication.—After the publication of Tower’s experiments on journal friction Professor Osborne Reynolds showed (Phil. Trans., 1886, p. 157) that the facts observed in connexion with a journal lubricated by means of an oil bath could be explained by a theory based upon the general principles of the motion of a viscous fluid. It is first established as an essential part of the theory that the radius of the brass must be slightly greater than the radius of the journal as indicated in fig. 12, where J is the centre of the journal and I the centre of the brass. Given this difference of curvature and a sufficient supply of oil, the rotation of the journal produces and maintains an oil film between the rubbing surfaces, the circumferential extent of which depends upon the rate of the oil supply and the external load. With an unlimited supply of oil, that is with oil-bath lubrication, the film extends continuously to the extremities of the brass, unless such extension would lead to negative pressures and therefore to a discontinuity, in which case the film ends where the pressures in the film become negative. The minimum distance between the journal and the brass occurs at the point H (fig. 12), on the off side of the point O where the line of action of the load cuts the surface of the journal. To the right and left of H the thickness of the film gradually increases, this being the condition that the oil-flow to and from the film may be automatically maintained. With an unlimited supply of oil the point H moves farther from O as the load increases until it reaches a maximum distance, and then it moves back again towards O as the load is further increased until a limiting load is reached at which the pressure in the film becomes negative at the boundaries of the film, when the boundaries recede from the edges of the brass as though the supply of oil were limited.In the mathematical development of the theory it is first necessary to define the coefficient of viscosity. This is done as follows:—If two parallel surfaces AB, CD are separated by a viscous film, and if whilst CD is fixed AB moves in a tangential direction with velocity U, the surface of the film in contact with CD clings to it and remains at rest, whilst the lower surface of the film clings to and moves with the surface AB. At intermediate points in the film the tangential motion of the fluid will vary uniformly from zero to U, and the tangential resistance will be F = µU/h, where µ is the coefficient of viscosity and h is the thickness of the film. With this definition of viscosity and from the general equations representing the stress in a viscous fluid, the following equation is established, giving the relations between p, the pressure at any point in the film, h the thickness of the film at a point x measured round the circumference of the journal in the direction of relative motion, and U the relative tangential velocity of the surfaces,d(h³dp)= 6µUdhdxdxdx(1)In this equation all the quantities are independent of the co-ordinate parallel to the axis of the journal, and U is constant. The thickness of the film h is some function of x, and for a journal Professor Reynolds takes the form,h = a {1 + c sin(θ − φ0)},in which the various quantities have the significance indicated in fig. 12. Reducing and integrating equation (1) with this value of h it becomesdp=6RµUc {sin(θ − φ0) − sin(φ1− φ0)}dθa²{1 + c sin(θ − φ0)}³(2)φ1being the value of θ for which the pressure is a maximum. In order to integrate this the right-hand side is expanded into a trigonometrical series, the values of the coefficients are computed, and the integration is effected term by term. If, as suggested by Professor J. Perry, the value of h is taken to be h = h0+ ax², where h0is the minimum thickness of the film, the equation reduces to the form−dp=6µU+Cdx(h0+ ax²)²(h0+ ax²)³(3)and this can be integrated. The process of reduction from the form (1) to the form (3) with the latter value of h, is shown in full inThe Calculus for Engineersby Professor Perry (p. 331), and also the final solution of equation (3), giving the pressure in terms of x.Professor Reynolds, applying the results of his investigation to one of Tower’s experiments, plotted the pressures through the film both circumferentially and longitudinally, and the agreement with the observed pressure of the experiment was exceedingly close. The whole investigation of Professor Reynolds is a remarkable one, and is in fact the first real explanation of the fact that oil is able to insinuate itself between the journal and the brass of a bearing carrying a heavy load. (See alsoLubrication.)

Theory of Lubrication.—After the publication of Tower’s experiments on journal friction Professor Osborne Reynolds showed (Phil. Trans., 1886, p. 157) that the facts observed in connexion with a journal lubricated by means of an oil bath could be explained by a theory based upon the general principles of the motion of a viscous fluid. It is first established as an essential part of the theory that the radius of the brass must be slightly greater than the radius of the journal as indicated in fig. 12, where J is the centre of the journal and I the centre of the brass. Given this difference of curvature and a sufficient supply of oil, the rotation of the journal produces and maintains an oil film between the rubbing surfaces, the circumferential extent of which depends upon the rate of the oil supply and the external load. With an unlimited supply of oil, that is with oil-bath lubrication, the film extends continuously to the extremities of the brass, unless such extension would lead to negative pressures and therefore to a discontinuity, in which case the film ends where the pressures in the film become negative. The minimum distance between the journal and the brass occurs at the point H (fig. 12), on the off side of the point O where the line of action of the load cuts the surface of the journal. To the right and left of H the thickness of the film gradually increases, this being the condition that the oil-flow to and from the film may be automatically maintained. With an unlimited supply of oil the point H moves farther from O as the load increases until it reaches a maximum distance, and then it moves back again towards O as the load is further increased until a limiting load is reached at which the pressure in the film becomes negative at the boundaries of the film, when the boundaries recede from the edges of the brass as though the supply of oil were limited.

In the mathematical development of the theory it is first necessary to define the coefficient of viscosity. This is done as follows:—If two parallel surfaces AB, CD are separated by a viscous film, and if whilst CD is fixed AB moves in a tangential direction with velocity U, the surface of the film in contact with CD clings to it and remains at rest, whilst the lower surface of the film clings to and moves with the surface AB. At intermediate points in the film the tangential motion of the fluid will vary uniformly from zero to U, and the tangential resistance will be F = µU/h, where µ is the coefficient of viscosity and h is the thickness of the film. With this definition of viscosity and from the general equations representing the stress in a viscous fluid, the following equation is established, giving the relations between p, the pressure at any point in the film, h the thickness of the film at a point x measured round the circumference of the journal in the direction of relative motion, and U the relative tangential velocity of the surfaces,

(1)

In this equation all the quantities are independent of the co-ordinate parallel to the axis of the journal, and U is constant. The thickness of the film h is some function of x, and for a journal Professor Reynolds takes the form,

h = a {1 + c sin(θ − φ0)},

in which the various quantities have the significance indicated in fig. 12. Reducing and integrating equation (1) with this value of h it becomes

(2)

φ1being the value of θ for which the pressure is a maximum. In order to integrate this the right-hand side is expanded into a trigonometrical series, the values of the coefficients are computed, and the integration is effected term by term. If, as suggested by Professor J. Perry, the value of h is taken to be h = h0+ ax², where h0is the minimum thickness of the film, the equation reduces to the form

(3)

and this can be integrated. The process of reduction from the form (1) to the form (3) with the latter value of h, is shown in full inThe Calculus for Engineersby Professor Perry (p. 331), and also the final solution of equation (3), giving the pressure in terms of x.

Professor Reynolds, applying the results of his investigation to one of Tower’s experiments, plotted the pressures through the film both circumferentially and longitudinally, and the agreement with the observed pressure of the experiment was exceedingly close. The whole investigation of Professor Reynolds is a remarkable one, and is in fact the first real explanation of the fact that oil is able to insinuate itself between the journal and the brass of a bearing carrying a heavy load. (See alsoLubrication.)

(W. E. D.)

BEAR-LEADER,formerly a man who led bears about the country. In the middle ages and Tudor times these animals were chiefly used in the brutal sport of bear-baiting and were led from village to village. Performing bears were also common, and are even still sometimes seen perambulating the country with their keepers, generally Frenchmen or Italians. The phrase “bear-leader” has now come colloquially to mean a tutor or guardian, who escorts any lad of rank or wealth on his travels.

BÉARN,formerly a small frontier province in the south of France, now included within the department of Basses-Pyrénées. It was bounded on the W. by Soule and Lower Navarre, on the N. by Chalosse, Tursan and Astarac, E. by Bigorre and S. by the Pyrénées. Its name can be traced back to the town of Beneharnum (Lescar). Thecivitas Beneharnensiumwas included in theNovempopulania. It was conquered by the Vascones in the 6th century, and in 819 became a viscounty dependent on the dukes of Aquitaine—a feudal link which was broken in the 11th century, when the viscounts ceased to acknowledge any suzerain. They then reigned over the two dioceses of Lescar and Oloron; but their capital was Morlaas, where they had a mint which was famous throughout the middle ages. In the 13th century Gaston VII., of the Catalonian house of Moncade, made Orthez his seat of government. His long reign (1229-1290) was a perpetual struggle with the kings of France and England, each anxious to assert his suzerainty over Béarn. As Gaston left only daughters, the viscounty passed at his death to the family of Foix, from whom it was transmitted through the houses of Grailly and Albret to the Bourbons, and they, in the person of Henry IV., king of Navarre, made it an apanage of the crown of France. It was not formally incorporated in the royal domains, however, until 1620. None of these political changes weakened the independent spirit of the Béarnais. From the 11th century onward, they were governed by their own special customs orfors. These were drawn up in the language of the country, a Romance dialect (1288 being the date of the most ancient written code), and are remarkable for the manner in which they define the rights of the sovereign, determining the reciprocal obligations of the viscount and his subjects or vassals. Moreover, from the 12th century Béarn enjoyed a kind of representative government, withcours plénièrescomposed of deputies from the three estates. From 1220 onward, the judiciary powers of these assemblies were exercised by acour majourof twelve baronsjuratscharged with the duty of maintaining the integrity of thefors. When Gaston-Phoebus wished to establish a regular annual hearth-tax (fouage) in the viscounty, he convoked the deputies of the three estates in assemblies calledétats. These soon acquired extensive political and financial powers, which continued in operation till 1789. Although, when Béarn was annexed to the domains of the crown, it was granted aconseil d’étatand a parlement, which sat at Pau, the province also retained itsforsuntil the Revolution.

See also Olhagaray,Histoire de Foix, Béarn et Navarre(1609); Pierre de Marca,Histoire de Béarn(1640). This work does not go beyond the end of the 13th century; it contains a large number of documents. Faget de Baure,Essais historiques sur le Béarn(1818);Les Fors de Béarn, by Mazure and Hatoulet (1839), completed by J. Brissaud and P. Rogé inTextes additionnels aux anciens Fors de Béarn(1905); Léon Cadier,Les États de Béarn depuis leur origine jusqu’au commencement du XVIesiècle(1888).

(C. B.*)

BEASorBias, a river of India. The Beas, which was the Hyphasis of the Greeks, is one of the Five Rivers of the Punjab. It issues in the snowy mountains of Kulu at an altitude of 13,326 ft. above sea-level, flows through the Kangra valley and the plains of the Punjab, and finally joins the Sutlej after a course of 290 m. It is crossed by a railway bridge near Jullundur.

BEAT(a word common in various forms to the Teutonic languages; it is connected with the similar Romanic words derived from the Late Lat.battere), a blow or stroke; from the many applications of the verb “to beat” come various meanings of the substantive, in some of which the primary sense has become obscure. It is applied to the throbbing of the pulse or heart, to the beating of a drum, either for retreat, or charge, or to quarters; in music to the alternating sound produced by the striking together of two notes not exactly of the same pitch (seeSound), and also to the movement of the baton by which a conductor of an orchestra or chorus indicates the time, and to the divisions of a bar. As a nautical term, a “beat” is the zigzag course taken by a ship in sailing against the wind. The application of the word to a policeman’s or sentry’s round comes either from beating a covert for game and hence the term means an exhaustive search of a district, or from the repeated strokes of the foot in constantly walking up and down. In this sense the word is used in America, particularly in Alabama and Mississippi, of a voting precinct.

BEATIFICATION(from the Lat.beatus, happy, blessed, andfacere, to make), the act of making blessed; in the Roman Catholic Church, a stage in the process of canonization (q.v.).

BEATON(orBethune),DAVID,(c.1494-1546), Scottish cardinal and archbishop of St Andrews, was a younger son of John Beaton of Balfour in the county of Fife, and is said to have been born in the year 1494. He was educated at the universities of St Andrews and Glasgow, and in his sixteenth year was sent to Paris, where he studied civil and canon law. About this time he was presented to the rectory of Campsie by his uncle James Beaton, then archbishop of Glasgow. When James Beaton was translated to St Andrews in 1522 he resigned the rich abbacy of Arbroath in his nephew’s favour, under reservation of one half of the revenues to himself during his lifetime. The great ability of Beaton and the patronage of his uncle ensured his rapid promotion to high offices in the church and kingdom. He was sent by King James V. on various missions to France, and in 1528 was appointed keeper of the privy seal. He took a leading part in the negotiations connected with the king’s marriages, first with Madeleine of France, and afterwards with Mary of Guise. At the French court he was held in high estimation by King Francis I., and was consecrated bishop of Mirepoix in Languedoc in December 1537. On the 20th of December 1538 he was appointed a cardinal priest by Pope Paul III., under the title of St Stephen in the Coelian Hill. He was the only Scotsman who had been named to that high office by an undisputed right, Cardinal Wardlaw, bishop of Glasgow, having received his appointment from the anti-pope Clement VII. On the death of Archbishop James Beaton in 1539, the cardinal was raised to the primatial see of Scotland.

Beaton was one of King James’s most trusted advisers, and it was mainly due to his influence that the king drew closer the French alliance and refused Henry VIII.’s overtures to follow him in his religious policy. On the death of James in December 1542 he attempted to assume office as one of the regents for the infant sovereign Mary, founding his pretensions on an alleged will of the late king; but his claims were disregarded, and the earl of Arran, head of the great house of Hamilton, and next heir to the throne, was declared regent by the estates. The cardinal was, by order of the regent, committed to the custody of Lord Seaton; but his imprisonment was merely nominal, and he was soon again at liberty and at the head of the party opposed to the English alliance. Arran too was soon won over to his views, dismissed the preachers by whom he had been surrounded, and joined the cardinal at Stirling, where in September 1543 Beaton crowned the young queen. In the same year he was raised to the office of chancellor of Scotland, and was appointed protonotary apostolic and legatea latereby the pope. Had Beaton confined himself to secular politics, his strenuous opposition to the plans of Henry VIII. for the subjugation of Scotland would have earned him the lasting gratitude of his countrymen. Unfortunately politics were inextricably interwoven with the religious controversies of the time, and resistance to English influence involved resistance tothe activities of the reformers in the church, whose ultimate victory has obscured the cardinal’s genuine merits as a statesman. During the lifetime of his uncle, Beaton had shared in the efforts of the hierarchy to suppress the reformed doctrines, and pursued the same line of conduct still more systematically after his elevation to the primacy. The popular accounts of the persecution for which he was responsible are no doubt exaggerated, and it sometimes ceased for considerable periods so far as capital punishments were concerned. When the sufferers were of humble rank not much notice was taken of them. It was otherwise when a more distinguished victim was selected in the person of George Wishart. Wishart had returned to Scotland, after an absence of several years, about the end of 1544. His sermons produced a great effect, and he was protected by several barons of the English faction. These barons, with the knowledge and approbation of King Henry, were engaged in a plot to assassinate the cardinal, and in this plot Wishart is now proved to have been a willing agent. The cardinal, though ignorant of the details of the plot, perhaps suspected Wishart’s knowledge of it, and in any case was not sorry to have an excuse for seizing one of the most eloquent supporters of the new opinions. For some time he was unsuccessful; but at last, with the aid of the regent, he arrested the preacher, and carried him to his castle of St Andrews. On the 28th of February 1546 Wishart was brought to trial in the cathedral before the cardinal and other judges, the regent declining to take any active part, and, being found guilty of heresy, was condemned to death and burnt.

The death of Wishart produced a deep effect on the Scottish people, and the cardinal became an object of general dislike, which encouraged his enemies to proceed with the design they had formed against him. Naturally resolute and fearless, he seems to have under-estimated his danger, the more so since his power had never seemed more secure. He crossed over to Angus, and took part in the wedding of his illegitimate daughter with the heir of the earl of Crawford. On his return to St Andrews he took up his residence in the castle. The conspirators, the chief of whom were Norman Leslie, master of Rothes, and William Kirkaldy of Grange, contrived to obtain admission at daybreak of the 29th of May 1546, and murdered the cardinal under circumstances of horrible mockery and atrocity.

The character of Beaton has already been indicated. As a statesman he was able, resolute, and in his general policy patriotic. As an ecclesiastic he maintained the privileges of the hierarchy and the dominant system of belief conscientiously, but always with harshness and sometimes with cruelty. His immoralities, like his acts of persecution, were exaggerated by his opponents; but his private life was undoubtedly a scandal to religion, and has only the excuse that it was not worse than that of most of his order at the time. The authorship of the writings ascribed to him in several biographical notices rests on no better authority than the apocryphal statements of Thomas Dempster.

Beaton’s uncle, James Beaton, or Bethune (d. 1539), archbishop of Glasgow and St Andrews, was lord treasurer of Scotland before he became archbishop of Glasgow in 1509, was chancellor from 1513 to 1526, and was appointed archbishop of St Andrews and primate of Scotland in 1522. He was one of the regents during the minority of James V., and was chiefly responsible for this king’s action in allying himself with France and not with England. He burned Patrick Hamilton and other heretics, and died at St Andrews in September 1539.

This prelate must not be confused with another, James Beaton, or Bethune (1517-1603), the last Roman Catholic archbishop of Glasgow. A son of John Bethune of Auchmuty and a nephew of Cardinal Beaton, James was a trusted adviser of the Scottish regent, Mary of Lorraine, widow of James V., and a determined foe of the reformers. In 1552 he was consecrated archbishop of Glasgow, but from 1560 until his death in 1603 he lived in Paris, acting as ambassador for Scotland at the French court.

See John Knox,Hist. of the Reformation in Scotland, ed. D. Laing (1846-1864); John Spottiswoode, archbishop of St Andrews,Hist. of the Church of Scotland(Spottiswoode Soc., 1847-1851); Art. inDict. of Nat. Biog.and works there quoted; and A. Lang,Hist. of Scotland, vols. i. and ii. (1900-1902).

BEATRICE,a city and the county-seat of Gage county, in S.E. Nebraska, U.S.A., about 40 m. S. of Lincoln. Pop. (1900) 7875 (852 foreign-born); (1910) 9356. It is served by the Chicago, Burlington & Quincy, the Chicago, Rock Island & Pacific, and the Union Pacific railways. Beatrice is the seat of the state institute for feeble-minded youth, and has a Carnegie library. The city is very prettily situated in the valley of the Big Blue river, in the midst of a fine agricultural region. Among its manufactures are dairy products (there is a large creamery), canned goods, flour and grist mill products, gasoline engines, well-machinery, barbed wire, tiles, ploughs, windmills, corn-huskers, and hay-balers. Beatrice was founded in 1857, becoming the county-seat in the same year. It was reached by its first railway and was incorporated as a town in 1871, was chartered as a city in 1873, and in 1901 became a city of the first class.

BEATTIE, JAMES(1735-1803), Scottish poet and writer on philosophy, was born at Laurencekirk, Kincardine, Scotland, on the 25th of October 1735. His father, a small farmer and shopkeeper, died when he was very young; but an elder brother sent him to Marischal College, Aberdeen, where he gained a bursary. In 1753 he was appointed schoolmaster of Fordoun in his native county. Here he had as neighbours the eccentric Francis Garden (afterwards Lord Gardenstone, judge of the supreme court of Scotland), and Lord Monboddo. In 1758 he became an usher in the grammar school of Aberdeen, and two years later he was made professor of moral philosophy at Marischal College. Here he became closely acquainted with Dr Thomas Reid, Dr George Campbell, Dr Alexander Gérard and others, who formed a kind of literary or philosophic society known as the “Wise Club.” They met once a fortnight to discuss speculative questions, David Hume’s philosophy being an especial object of criticism. In 1761 Beattie published a small volume ofOriginal Poems and Translations, which contained little work of any value. Its author in later days destroyed all the copies he found. In 1770 Beattie published hisEssay on the Nature and Immutability of Truth in opposition to sophistry and scepticism, the object of which, as explained by its author, was to “prove the universality and immutability of moral sentiment” (letter to Sir W. Forbes, 17th January 1765). It was in fact a direct attack on Hume, and part of its great popularity was due to the fact. Hume is said to have justly complained that Beattie “had not used him like a gentleman,” but made no answer to the book, which has no philosophical value. Beattie’s portrait, by Sir Joshua Reynolds, hangs at Marischal College, Aberdeen. The philosopher is painted with theEssay on Truthin his hand, while a figure of Truth thrusts down three figures representing, according to Sir W. Forbes, sophistry, scepticism and infidelity. Reynolds in a letter to Beattie (February 1774) intimates that he is well enough pleased that one of the figures is identified with Hume, and that he intended Voltaire to be one of the group. Beattie visited London in 1773, and was received with the greatest honour by George III., who conferred on him a pension of £200 a year. In 1771 and 1774 he published the first and second parts ofThe Minstrel, a poem which met with great and immediate success. The Spenserian stanza in which it is written is managed with smoothness and skill, and there are many fine descriptions of natural scenery. It is entirely on his poetry that Beattie’s reputation rests. The best known of his minor poems are “The Hermit” and “Retirement.”

In 1773 he was offered the chair of moral philosophy at Edinburgh University, but did not accept it. Beattie made many friends, and lost none. “We all love Beattie,” said Dr Johnson. “Mrs Thrale says, if ever she has another husband she will have him.” He was in high favour too with Mrs Montagu and the otherbas bleus. Beattie was unfortunate in his domestic life. Mary Dunn, whom he married in 1767, became insane, and his two sons died just as they were attaining manhood. The elder, James Hay Beattie, a young man of great promise, who at the age of nineteen had been associated with his father in his professorship, died in 1790. In 1794 the father publishedEssays and Fragments in Prose and Verse by James Hay Beattiewith atouching memoir. The younger brother died in 1796. Beattie never recovered from this second bereavement. His mind was seriously affected, and, although he continued to lecture occasionally, he neither wrote nor studied. In April 1799 he had a stroke of paralysis, and died on the 18th of August 1803.

Beattie’s other poetical works includeThe Judgment of Paris(1765), and “Verses on the death of [Charles] Churchill,” a bitter attack which the poet afterwards suppressed. The best edition is thePoetical Works(1831, new ed. 1866) in theAldine Edition of the British Poets, with an admirable memoir by Alexander Dyce.

See alsoAn Account of the Life of James Beattie(1804), by A. Bower; andAn Account of the Life and Writings of James Beattie(1807), by Sir William Forbes; a quantity of new material is to be found inBeattie and his Friends(1904), by the poet’s great-grand-niece, Margaret Forbes; andJames Beattie, the Minstrel. Some Unpublished Letters, edited by A. Mackie (Aberdeen, 1908).

BEATUS,of Liebana and Valcavado, Spanish priest and monk, theologian and geographer, was born about 730, and died in 798. About 776 he published hisCommentaria in Apocalypsin, containing one of the oldest Christian world-maps. He took a prominent part in the Adoptionist controversy, and wrote against the views of Felix of Urgel, especially as upheld by Elipandus of Toledo. As confessor to Queen Adosinda, wife of King Silo of Oviedo (774-783), and as the master of Alcuin and Etherius of Osma, Beatus exercised wide influence. His original map, which was probably intended to illustrate, above all, the distribution of the Apostolic missions throughout the world—depicting the head of Peter at Rome, of Andrew in Achaia, of Thomas in India, of James in Spain, and so forth—has survived in ten more or less modified copies. One only of these—the “Osma” of 1203—preserves the Apostolic pictures; among the remaining examples, that of “St Sever,” now at Paris, and dating from about 1030, is the most valuable; that of “Valcavado,” recently in the Ashburnham Library, executed in 970, is the earliest; that of “Turin,” dating from about 1100, is perhaps the most curious. Three others—“Valladolid” of about 1035, “Madrid” of 1047, and “London” of 1109—are derivatives of the “Valcavado-Ashburnham” of 970; the eighth, “Paris II,” is connected, though not very intimately, with “St Sever,” otherwise “Paris I”; the ninth and tenth, “Gerona” and “Paris III,” belong to the Turin group of Beatus maps. All these works are emphatically of “dark-age” character; very seldom do they suggest the true forms of countries, seas, rivers or mountains, but they embody some useful information as to early medieval conditions and history. St Isidore appears to be their principal authority; they also draw, directly or indirectly, from Orosius, St Jerome, St Augustine, and probably from a lost map of classical antiquity, represented in a measure by the Peutinger Table of the 13th century.

The chief MSS. of theCommentaria in Apocalypsinare (1-3) Paris, National Library, Lat. 8878; Lat. nouv. acq. 1366 and 2290; (4) Ashburnham MSS. xv.; (5) London, B. Mus., Addit. MSS. 11695; (6) Turin, National Library 1, ii. (1); (7) Valladolid, University Library, 229; (8) the MS. in the Episcopal Library at Osma, in Old Castile.There is only one complete edition of the text, that by Florez (Madrid, 1770). See also Konrad Miller,Die Weltkarte des Beatus, Heft I. ofMappaemundi: die ältesten Weltkarten(Stuttgart, 1895); d’Avezac inAnnales de ... géographie(June 1870); Beazley,Dawn of Modern Geography, i. 387-388 (1897); ii. 549-559; 591-605 (1901).

There is only one complete edition of the text, that by Florez (Madrid, 1770). See also Konrad Miller,Die Weltkarte des Beatus, Heft I. ofMappaemundi: die ältesten Weltkarten(Stuttgart, 1895); d’Avezac inAnnales de ... géographie(June 1870); Beazley,Dawn of Modern Geography, i. 387-388 (1897); ii. 549-559; 591-605 (1901).

(C. R. B.)

BEAUCAIRE,a town of south-eastern France, in the department of Gard, 17 m. E. by S. of Nîmes on the Paris-Lyon railway. Pop. (1906) 7284. Beaucaire is situated on the right bank of the Rhone, opposite Tarascon, with which it is connected by two handsome bridges, a suspension-bridge of four spans and 1476 ft. in length, and a railway bridge. A triangular keep, a chapel, and other remains of a château (13th and 14th centuries) of the counts of Toulouse stand on the rocky pine-clad hill which rises to the north of the town; the chapel, dedicated to St Louis, belongs to the latest period of Romanesque architecture, and contains fine sculptures. The town derives celebrity from the great July fair, which has been held here annually since the 12th century, but has now lost its former importance (seeFair). Beaucaire gives its name to the canal which communicates with the sea (near Aigues-Mortes) and connects it with the Canal du Midi, forming part of the line of communication between the Rhone and the Garonne. The town is an important port on the Rhone, and its commerce, the chief articles of which are wine, and freestone from quarries in the vicinity, is largely water-borne. Among its industries are distilling and the manufacture of furniture, and the preparation of vermicelli, sausages and other provisions.

Beaucaire occupies the site of the ancientUgernum, and several remains of the Roman city have been discovered, as well as (in 1734) the road that led from Nîmes. The present name is derived fromBellum Quadrum, a descriptive appellation applied in the middle ages either to the château or to the rock on which it stands. In 1125 Beaucaire came into the possession of the counts of Toulouse, one of whom, Raymund VI., established the importance of its fairs by the grant of privileges. In the Wars of the League it suffered severely, and in 1632 its castle was destroyed by Richelieu.

BEAUCE(Lat.Belsia), a physical region of north-central France, comprising large portions of the departments of Eure-et-Loir and Loir-et-Cher, and also extending into those of Loiret and Seine-et-Oise. It has an area of over 2800 sq. m., its limits being roughly defined by the course of the Essonne on the E., of the Loire on the S., and of the Brenne, the Loir and the Eure towards the W., though in the latter direction it extends somewhat beyond these boundaries. The Beauce is a treeless, arid and monotonous plain of limestone formation; windmills and church spires are the only prominent features of the landscape. Apart from the rivers on its borders, it is watered by insignificant streams, of which the Conie in the west need alone be mentioned. The inhabitants live in large villages, and are occupied in agriculture, particularly in the cultivation of wheat, for which the Beauce is celebrated. Clover and lucerne are the other leading crops, and large flocks of sheep are kept in the region. Chartres is its chief commercial centre.

BEAUCHAMP,the name of several important English families. The baronial house of Beauchamp of Bedford was founded at the Conquest by Hugh de Beauchamp, who received a barony in Bedfordshire. His eldest son Simon left a daughter, whose husband Hugh (brother of the count of Meulan) was created earl of Bedford by Stephen. But the heir-male, Miles de Beauchamp, nephew of Simon, held Bedford Castle against the king in 1137-1138. From his brother Payn descended the barons of Bedford, of whom William held Bedford Castle against the royal forces in the struggle for the Great Charter, and was afterwards made prisoner at the battle of Lincoln, while John, who sided with the barons under Simon de Montfort, fell at Evesham. With him the line ended, but a younger branch was seated at Eaton Socon, Beds., where the earthworks of their castle remain, and held their barony there into the 14th century.

The Beauchamps of Elmley, Worcestershire, the greatest house of the name, were founded by the marriage of Walter de Beauchamp with the daughter of Urise d’Abetot, a Domesday baron, which brought him the shrievalty of Worcestershire, the office of a royal steward, and large estates. His descendant William, of Elmley, married Isabel, sister and eventually heiress to William Mauduit, earl of Warwick, and their son succeeded in 1268 to Warwick Castle and that earldom, which remained with his descendants in the male line till 1445. The earls of the Beauchamp line played a great part in English history. Guy, the 2nd, distinguished himself in the Scottish campaigns of Edward I., who warned him at his death against Piers Gaveston. Under Edward II. he was one of the foremost foes of Piers, who had styled him “the black cur of Arden,” and with whose death he was closely connected. As one of the “lords ordainers” he was a recognized leader of the opposition to Edward II. By the heiress of the Tonis he left at his death in 1315 a son Earl Thomas, who distinguished himself at Crécy and Poitiers, was marshal of the English host, and, with his brother John, one of the founders of the order of the Garter. In 1369 his son Earl Thomas succeeded; from 1376 to 1379 he was among the lordsstriving for reform, and in the latter year he was appointed governor to the king. Under Richard II. he joined the lords appellant in their opposition to the king and his ministers, and was in power with them 1388-1389; treacherously arrested by Richard in 1397, he was imprisoned in the Tower of London (the Beauchamp Tower being called after him), but liberated by Henry IV. on his triumph (1399). In 1401 he was succeeded by his son Earl Richard, a brave and chivalrous warrior, who defeated Owen Glendower, fought the Percys at Shrewsbury, and, after travelling in state through Europe and the Holy Land, was employed against the Lollards and afterwards as lay ambassador from England to the council of Constance (1414). He held command for a time at Calais, and took an active part in the French campaigns of Henry V., who created him earl and count of Aumale in Normandy. He had charge of the education of Henry VI., and in 1437 was appointed lieutenant of France and of Normandy. Dying at Rouen in 1439, he left by Isabel, widow of Richard Beauchamp, earl of Worcester, a son, Earl Henry, who was created duke of Warwick, 1445, and is alleged, but without authority, to have been crowned king of the Isle of Wight by Henry VI. He died, the last of his line, in June 1445. On the death of Anne, his only child, in 1449, his vast inheritance passed to Anne, his sister of the whole blood, wife of Richard Neville, earl of Salisbury (“the Kingmaker”), who thereupon became earl of Warwick.

Of the cadet branches of the house, the oldest was that of Powyke and Alcester, which obtained a barony in 1447 and became extinct in 1496; from it sprang the Beauchamps, Lords St. Amand from 1448, of whom was Richard, bishop of Salisbury, first chancellor of the order of the Garter, and who became extinct in 1508, being the last known male heirs of the race. Another cadet was Sir John Beauchamp of Holt, minister of Richard II., who was created Lord Beauchamp of Kidderminster (the first baron created by patent) 1387, but beheaded 1388; the barony became extinct with his son in 1400. Roger, Lord Beauchamp of Bletsoe, summoned in 1363, is said to have been descended from the Powyke branch; his line ended early in the 15th century. Later cadets were John, brother of the 3rd earl, who carried the standard at Crécy, became captain of Calais, and was summoned as a peer in 1350, but died unmarried; and William, brother of the 4th earl, who was distinguished in the French wars, and succeeding to the lands of the Lords Abergavenny was summoned in that barony 1392; his son was created earl of Worcester in 1420, but died without male issue in 1422; from his daughter, who married Sir Edward Neville, descended the Lords Abergavenny.

The Lords Beauchamp of “Hache” (1299-1361) were so named from their seat of Hatch Beauchamp, Somerset, and were of a wholly distinct family. Their title, “Beauchamp of Hache,” was revived for the Seymours in 1536 and 1559. The title of “Beauchamp of Powyke” was revived as a barony in 1806 for Richard Lygon (descended through females from the Beauchamps of Powyke), who was created Earl Beauchamp in 1815.

See Sir W. Dugdale,Baronage(1675-1676) andWarwickshire(2nd ed., 1730); G.E. C[okayne],Complete Peerage(1887-1898); W. Courthope,Rows Roll(1859); and J.H. Round,Geoffrey de Mandeville(1892).

(J. H. R.)

BEAUCHAMP, ALPHONSE DE,French historian and man of letters, was born at Monaco in 1767, and died in 1832. In 1784 he entered a Sardinian regiment of marines, but on the outbreak of war with the French Republic, he refused to fight in what he considered an unjust cause, and was imprisoned for several months. After being liberated he took up his residence in Paris, where he obtained a post in one of the government offices. On the fall of Robespierre, Beauchamp was transferred to thebureauof the minister of police, and charged with the superintendence of the press. This situation opened up to him materials of which he made use in his first and most popular historical work,Histoire de la Vendée et des Chouans, 3 vols., 1806. The book, received with great favour by the people, was displeasing to the authorities. The third edition was confiscated; its writer was deprived of his post, and in 1809 was compelled to leave Paris and take up his abode in Reims. In 1811 he obtained permission to return, and again received a government appointment. This he had to resign on the Restoration, but was rewarded with a small pension, which was continued to his widow after his death.

Beauchamp wrote extensively for the public journals and for the magazines. His biographical and historical works are numerous, and those dealing with contemporary events are valuable, owing to the sources at his disposal. They must, however, be used with great caution. The following are worth mention:—Vie politique, militaire et privée du général Moreau(1814);Catastrophe de Murat, ou Récit de la dernière révolution de Naples(1815);Histoire de la guerre d’Espagne et du Portugal, 1807-1813(2 vols., 1810);Collection de mémoires relatifs aux révolutions d’Espagne(2 vols., 1824);Histoire de la révolution de Piémont(2 vols., 1821, 1823);Mémoires secrets et inédits pour servir à l’histoire contemporaine(2 vols., 1825). TheMémoires de Fouchéhave also been ascribed to him, but it seems certain that he only revised and completed a work really composed by Fouché himself.

See an article by Louis Madelin inLa Revolution française(1900).

BEAUFORT,the name of the family descended from the union of John of Gaunt, duke of Lancaster, with Catherine, wife of Sir Hugh Swynford, taken from a castle in Anjou which belonged to John of Gaunt. There were four children of this union—John, created earl of Somerset and marquess of Dorset; Henry, afterwards bishop of Winchester and cardinal (seeBeaufort, Henry); Thomas, made duke of Exeter and chancellor; and Joan, who married Ralph Neville, first earl of Westmorland, and died in 1440. In 1396, some years after the birth of these children, John of Gaunt and Catherine were married, and in 1397 the Beauforts were declared legitimate by King Richard II. In 1407 this action was confirmed by their half-brother, King Henry IV., but on this occasion they were expressly excluded from the succession to the English throne.

John Beaufort, earl of Somerset (c.1373-1410), assisted Richard II. in 1397 when the king attacked the lords appellants, and made himself an absolute ruler. For these services he was made marquess of Dorset, but after the deposition of Richard in 1399, he was degraded to his former rank as earl. In 1401, however, he was declared loyal, and appeared later in command of the English fleet. He married Margaret, daughter of Thomas Holland, second earl of Kent, and died in March 1410, leaving three sons, Henry, John, and Edmund, and two daughters, Jane or Joan, who married James I., king of Scotland, and Margaret, who married Thomas Courtenay, earl of Devon.

Thomas Beaufort(d. 1426) held various high offices under Henry IV., and took a leading part in suppressing the rising in the north in 1405. He became chancellor in 1410, but resigned this office in January 1412 and took part in the expedition to France in the same year. He was then created earl of Dorset, and when Henry V. became king in 1413, he was made lieutenant of Aquitaine and took charge of Harfleur when this town passed into the possession of the English. In 1416 he became lieutenant of Normandy, and was created duke of Exeter; and returning to England he compelled the Scots to raise the siege of Roxburgh. Crossing to France in 1418 with reinforcements for Henry V., he took an active part in the subsequent campaign, was made captain of Rouen, and went to the court of France to treat for peace. He was then captured by the French at Baugé, but was soon released and returned to England when he heard of the death of Henry V. in August 1422. He was one of Henry’s executors, and it is probable that the king entrusted his young son, King Henry VI., to his care. However this may be, Exeter did not take a very prominent part in the government, although he was a member of the council of regency. Having again shared in the French war, the duke died at Greenwich about the end of the year 1426. He was buried at Bury St. Edmunds, where his remains were found in good condition 350 years later. He married Margaret, daughter of Sir Thomas Neville of Nornby, but left no issue. The Beaufort family was continued byHenry Beaufort(1401-1419), the eldest son of John Beaufort, earl of Somerset, who was succeeded as earl of Somerset by his brotherJohn Beaufort(1403-1444). The latter fought under Henry V. in the French wars, and having been taken prisoner remained in France as a captive until 1437. Soon after his release he returned to the war, and after the death of Richard Beauchamp, earl of Warwick, in 1439, acted as commander of the English forces, and, with his brother Edmund, was successful in recapturing Harfleur. Although chagrined when Richard, duke of York, was made regent of France, Beaufort led an expedition to France in 1442, and in 1443 was made duke of Somerset. He died, probably by his own hand, in May 1444. He married Margaret, daughter of Sir John Beauchamp, and left a daughter,Margaret Beaufort, afterwards countess of Richmond and Derby, who married, for her first husband, Edmund Tudor, earl of Richmond, by whom she became the mother of King Henry VII. In this way the blood of the Beauforts was mingled with that of the Tudors, and of all the subsequent occupants of the English throne.

The title of earl of Somerset descended on the death of John Beaufort in 1444 to his brotherEdmund Beaufort, duke of Somerset (q.v.), who was killed at St Albans in 1455. By his marriage with Eleanor Beauchamp, daughter of the fifth earl of Warwick, he left three sons, Henry, Edmund and John, and a daughter, Margaret.

Henry Beaufort(1436-1464) became duke of Somerset in 1455, and soon began to take part in the struggle against Richard, duke of York, but failed to dislodge Richard’s ally, Richard Neville, earl of Warwick, from Calais. He took part in the victory of the Lancastrians at Wakefield in 1460, escaped from the carnage at Towton in 1461, and shared the attainder of Henry VI. in the same year. In May 1464 he was captured at Hexham and was beheaded immediately after the battle. The title of duke of Somerset was assumed by his brother,Edmund Beaufort(c. 1438-1471), who fled from the country after the disasters to the Lancastrian arms, but returned to England in 1471, in which year he fought at Tewkesbury, and in spite of a promise of pardon was beheaded after the battle on the 6th of May 1471. His younger brotherJohn Beauforthad been killed probably at this battle, and so on the execution of Edmund the family became extinct.

Margaret Beaufortmarried Humphrey, earl of Stafford, and was the mother of Henry Stafford, duke of Buckingham. Henry Beaufort, third duke of Somerset (d. 1464), left an illegitimate son, Charles Somerset, who was created earl of Worcester by Henry VIII. in 1514. His direct descendant, Henry Somerset, fifth earl of Worcester, was a loyal partisan of Charles I. and in 1642 was created marquess of Worcester. His grandson, Henry, the third marquess, was made duke of Beaufort in 1682, and the present duke of Beaufort is his direct descendant.

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