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(a) if the ball in play touch the striker's opponent on or above the knee, and if in the marker’s opinion it be thereby prevented from reaching the front wall above the board (the plays line); or (b) if either player undesignedly prevent his opponent from returning the ball served in play.” If a player considers that he has been thus obstructed by his opponent he may “ claim a let," and the marker adjudicates his claim. The marker’s decision is final; but “ if in doubt which way to decide, the marker may direct that the ace be played over again." it is the duty of the marker, who occupies a box in the gallery, to " call the game.” As soon as the server serves the ball the marker calls "Playl" if the ball strikes the front wall above the service-line; and “Cut!" if it strikes below the serviceline; if the ball falls in front of the short-line the marker calls "Shortl"; if the wrong side of the fault-line he calls “ Fault l"; but whether it be “cut,” “short,” or “fault,” the serve counts as a fault in its effect. To every good return, as to every good serve, the marker calls "Play!" If a return is made after the second bound of the ball (called a “double”) the marker calls “Doublel” or “Not up!"; if the ball is hit into the gallery, or against its posts or cushions, or above the girders or cross-beams of the roof, he calls “ Out-of-court! ” At the end of every rally he calls the state of the game, always naming first the score of hand-inr—“One-love" (love being the term for zero) meaning that hand-in has scored one ace and hand-out nothing, “Two-love," “Five-all," “Five~ten," “ Fourteen-eleven." and so on, till one side has scored 15, when the marker calls “ Game! ” He then in similar fashion calls the state of the match—“Two games to one,” or whatever it may be'—before the commencement of the next game. The server in possession at the end of the game continues to serve in the new game, subject as before to the rule limiting the first innings of the game to a single “ hand.” The usual number of games in matches is five for singles, and seven for doubles. ln matches where there are umpires and a referee, there is an appeal to them from the marker’s decision except as regards questions relating to the service, on which the marker’s decision is final. Records—Attempts have been made to trace racquets, like tennis, to an ancient origin; but although it is doubtless true that the striking of a ball with the hand or some primitive form of bat is one of the oldest forms of pastimes, and that

racquets has been evolved from such an origin, the game as ‘

now known can hardly be said to have existed before the 19th century. Joseph Strutt’s work on The Sparta and Pastime: of Ike People of England, published at the beginning of the 19th century, malts no mention of racquets; and the century was far advanced before the racquet court was promoted from being an adjunct of the pot-house and the gaol, in which connexion the court within the purlieus 0f the Fleet prison has been immortalized in the pages of Pickwick, to a position scarcely less dignified than that of the tenniscourt with its royal and historical associations. It was at the public schools that racquets first obtained repute. The school courts were at first unroofed, and in some cases open also at the back and sides, or on one side. Among the most famous of the early racquets professionals, before the period of the modern closed court, were Robert Mackay (1820), the brothers Thomas and John Pittman, J. Lamb, J. C. Mitchell and Frauds Erwood (1860). One of the most famous matches ever played at racquets was that in which Erwood was beaten by Sir William Hart-Dyke, who used the “ drop ” stroke with telling effect, and who, after representing Oxford in the first four interuniversity matches, was the only amateur racquet player who ever defeated the open champion. A notable date in the history of racquets was the year 1853, when the court at the old Prince’s Club in Hans Place. London, was built. Here the annual racquet matches between Oxford and Cambridge Universities, singlos and doubles, were first played in 1858, and the Public Schools Championship (doubles only) ten years later. Modern racquets may perhaps be said to date from the time of the brothers Gray, who as professionals greatly raised the stande of skill in the game, and as teachers at the

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schools and universities improved the play of amateurs. William Gray beat Foul‘kes. the champion of America, in 1867; Henry Gray and Joseph Gray were also great players. The latter was beaten in 1875 by H. B. Fairs (“Punch”) but held the championship from 1878 to 1887. Another member of the same family was Walter Gray, who was as distinguished for the power of his stroke as his brother William was for the accuracy of his “ drop ” and the ease and grace of his volley and halfvolley. Walter Gray was followed in the championship by Peter Latham, the first professional to combine the open Tennis Championship with the Racquets Championship; and in the opinion of Mr Eustace Miles “ there has probably lived no player who could have beaten him at either game.” Latham was the first to use the heavily cut service at racquets, and he is also remarkable for the power of his wrist stroke. In the last twelve years or so of the 19th century Latharn stood alone, and in the opinion of the best judges he was the greatest of all racquet players. When once he had won the championship he never lost it, and when at last he resigned his title he was succeeded by Gilbert Browne, a player of a decidedly inferior calibre, who in 1903 was challenged and beaten by an Indian marker called Jamsetji. For the next six years, during which Jamsetji held the championship, comparatively little was heard of professional racquets; but in 1909 interest was reviVed by a handicap at Queen’s Club for a prize of £100, in which Peter Latham himself took part, and which was won by Jennings of Aldershot. As a result of this contest a challenge was issued by W. Hawes, the marker at Wellington College, to play any other professional for £200 a side and the championship of England. The challenge was accepted by C. Williams, a young player of Prince’s Club, who easily won the match, and with it the title of champion.

The institution of annual matches between Oxford and Cambridge Universities in 1858, and of the Public Schools Championship in 1868, gave an immense stimulus to the game among amateurs. Of the 51 inter-university (singles) matches from 1858 to 1908, Oxford won 26 and Cambridge 25; of the 52 contests in doubles Oxford won 25 and Cambridge 27. Among the public schools Harrow has been far the most successful, having won the championship challenge cup 19 times out of 42 contests. Moreover, under the condition permitting any school winning it in three consecutive years to retain the challenge cup permanently. Harrow became .sessed of three cups, having won the championship 1871—1874 Inclusive, 1879—1881 inclusive, and 1883—1887 inclusive. The next most successful school has been Eton, eight times champion; Charterhouse having won five times, and no other school more than three times. For the first twenty years of the contest, with a sin lc exception when Rugby won in 18"0, no school except Eton or arrow gained the championship; a it is not surpnsmg therefore that the majority of famous amateurs learnt the ame at one or other of these schools. Amo Etonians were W. art-Dyke, C. J. Ottaway, the Hon. Alfred 'ttclton, the Hon. lvo Bligh (afterwards Lord Darnley), C. T. Studd and H. Philipson; Harrow has produced R. D. Walker, one of the hes! of the earliest amateur racquet pla ers, C. F. Buller, T. S. Dun', A. J. \\'ebbe, M. C. Kemp, E. MY Butler, the brothers Eustao: Crawley and H. E. Crawle, C. D. Buxton, H. M. Leaf, Percv Ashworth and C. Browning. The famous Malvern family of Foster has been as conspicuous in the racquet court as on the cricket field. the eldest, H. K. Foster, being probably the finest amateur player of his generation. F. Dames Lon 'worth, Major A Coopcr~Key, Colonel Spens, E. M. Baerlein and Eustace H. Miles have also been in the front rank of amateur players. The opening of the Queen‘s Club, West Kensington,_was a notable event in the history of the game, especially as it was followed by the establishment of amateur championships in singles and doubles in 1888, of which the results have been as follower—

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II. Double:

. P. Ashworth and W. C. Hedley.

. P. Ashworth and E. L. Mctcalfe.

. E. M. Butler and M. C. Kemp.

. F. H. Browning and H. K. Fester.

. H. K. Foster and F. C. Ridgeway.

. F. Dames Longworth and F. H. Browning. . H. K. Foster and P. Ashworth.

. H. K. Foster and P. Ashworth.

. H: K. Foster and W. L. Foster.

L. Foster and B. 5. Foster.

Dames Longworth and V. H. Pcnnell. 1909. M. Baerlein and P. Ashworth.

1910. . S. Foster and Hon. C. N. Bruce.

A military championship was inaugurated in 1903 and is played annually at Princes' Club. in 1908, mainly throu h the exertions of Major A. Coo r-Key, a “ Tennis, Racquets an Fives Association " was foun ed for the purpose of encoura ing these games, safeguarding their interests and providin a legis atlve body whose authority would be recognized by all tenms and racquet players.

Racquets in America.-—ln the United States and in Canada racquets is a popular ame, and most of the leading athletic clubs have good courts. he American champions Foulkes, Boakes and George Standing were all beaten by English rofessionals, but had a rent reputation in their own country; and Il‘om Pcttitt, Ellis and gloore are names that stand high 1n the records of the game. Among American amateurs, Lamontayne did much to encourage racquets in New York in the earl period of its history; and in more recent times uincy Shaw, de iarmendia, R. Fearing, Payne Whitne , Mackay, . Waterbury and P. D. Haughton have shown themse ves me not players of we high merit, althou h Mr Eustace Miles is 0 opinion that “ an n lish playerlike H. . Foster, or Dames Longworth, or Ashworth, wou (1 give any American amateur upwards of seven aces."

1907. 1908.

1899. H. K. Foster and P. Ashworth. 1900. H. K. Foster and P. Ashworth. 1901. F. Dames Longworth and V. H. Pennell. 1902. E. M. Baerlcin and E. H. Miles. 1903. H. K. Foster and B. S. Foster. 1904. E. H. Miles and E. M. Baerlein. 1905. E. H. Miles and E. M. Baerlein. 1906. H. Miles and F. Dames Longworth. F. E. B

Squash racquets is a form of the game which provides admirable practice for the beginner, and has advantages of its own which offer attractions even to those who are proficient players of real racquets. It is played with a hollow indiarubber ball about the size of a fivcs ball (i.e. nearly twice the size of an ordinary racquet ball) and with a racquet rather shorter in the handle than those used in racquets proper. The court may be of any dimensions, but is always much smaller than a real racquet court; the squash ball, being not nearly so fast as the racquet ball, would not reach the back wall in a 60 ft. court on the first bound unless bit high as well as hard against the front wall. The rules of the game itself are precisely the same as in real racquets. Squash racquets originated at Harrow, where the boys were in the habit of playing in an improvised court in the corner of the schoolyard against the old school building; the windows, buttresses and water-pipe on the face of the wall forming irregularities which developed great skill on the part of the players in taking advantage of the difficulties thus caused. The marked success of Harrow in the Public Schools Championship at racquets, especially during the first twenty years of its institution (see above), has been attributed to the early training and practice gained at squash racquets in the school-yard, and in other courts which came into use as the popularity of this form of the game increased. Towards the end of the 19th century squash racquets became adopted at other schools and at the universities; and as the court is much cheaper to build than that required for real or “ hard ball ” racquets, and the game is cheaper as well as easier to play, many private courts came into existence. On the initiative of Lord Desborough, who had learnt the game at Harrow, several squash courts were provided at the Bath Club, London, where handicap tournaments are annually played. At Lord's cricket ground, when a. new pavilion was erected in 1890. squash racquet courts were included in the building. The dimensions of the courts at Lord’s, which may be taken as the best model. are as follows: length 42 ft. by 24 ft.; height of back wall 8 ft. 8 in.;

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height of service-line from floor 8 ft. 9 in.; height of playline 2 ft. 4 in. The short-line is 23 ft. from the front wall. The place which squash racquets has come to occupy may be estimated from the fact that Mr. Eustace Miles pronounces it “ an almost indispensable preparation ” for tennis and racquets as those games are played under modern conditions; and the same authority sufiiciently describes its merits when he observes that it “ gives, at a small cost of time or money, abundance of hard and brisk and simple yet exciting exercise for all times of life , of the year, and even of the day—if we have good artificial light." The squash courts at Lord’s and at the Bath Club are lighted by electricity, so that play is not dependent on the condition of the atmosphere, or on the season of the year.

See Tennis, Lawn Tennis, Racket: and Five: in the “ Badminwn Library "; Racquets, Tennis and Squash, by Eustace Miles (London, 1902) ; SPorting and Athletic Register (London, 1908). (R. J. M.)

RADAUTZ, a. town in Bukovina, Austria, 3 5 m. S. by W. of Czernowitz by rail. Pop. (1900) 14,343, of which about 70% are Germans and 2 5% are Rumanians. It was formerly the seat of a Greek bishopric, removed to Czernowitz in 1786, and possesses a cathedral (1402) with the tombs of several Moldavian princes. The Austrian government has here a large stud. To the W. of Radautz are situated the old monasteries of Putna and Suczawica, dating from the 15th century. They still contain many old and valuable ecclesiastical objects of art, although a great part has been removed to the various monasteries in Moldavia.

RADBERTUS PASCHASIUS (d. c. 860), French theologian, was born at or near Soissons towards the close of the 8th century. He became a monk of Corbie, near Amiens in Picardy, in 814, and assumed the cloister name of Paschasius. He soon gained recognition as a learned and successful teacher, and the younger Adalhard, St Anskar the apostle of Sweden, Odo bishop of Beauvais and Warinus abbot of Corvei in Saxony may be mentioned among the more distinguished of his pupils. Between 842 and 846 he was chosen abbot, but as a disciplinarian he was more energetic than successful, and about 851 he resigned the office. He never took priestly orders" He died and was buried in Corbie.

Radbertus is one of the most important theologians in the history of the church. “ He was perhaps the most learned and able theologian after Alcuin, as well versed in Greek theology as he was familiar with Augustinianism, a compre‘ hensive genius, who felt the liveliest desire to harmonize theory and practice, and at the same time give due weight to tradition ” (Hamack). His great work was the Libcr de Corpore ct Sanguine Domini (first 0d. 831; new ed., with an epistle to Charles the Bald, 844), which was not only the first systematic and thorough treatise on the sacrament of the eucharist, but is the first clear dogmatic statement of transubstantiation, and as such opened an unending controversy. It was at once attacked by Ratramnus and Hrabanus Maurus, but was so completely in touch with the practice of the church and the spirit of the age, as to win the verdict of Catholic orthodoxy.

On the eucharistic controversy see the article on Radbertus by Steitz in Herzog-Hauck‘s Real-Encyklo ridic; Bach, Dogmengeschichle des Mittelalters, i. 156 if; Ernst, 1e Lchre des h. Purchasqu Radbertus v. d. Eucharistic (1896); Renz, Die Geschichtc des Messopferbegri s (1901); K. G. Goetz, Die Abcndmahlsfrage in ihrer geschic ichen Entwicklung (1904), a complete survey of the whole

roblem, beginnin with Radbertus. A. Harnack's treatment in his istory of Dogma vol. v., p. 308 if.) is clear and appreciative.

RADCLIFFB, ANN (1764—1823), English novelist, only daughter of William and Ann Ward, was born in London on the 9th of July 1764. She was the author of three famous novels: The Romance of the Forest (1791), The Mysteries of Udolpho (1704) and The Italian (r707). When she was twentythree years old she married William Radclifi'e, an Oxford graduate and student of law. He gave up his profession for literature, and afterwards became proprietor and editor of the English Chronicle. After The Italian she gave up writing for publication, and was reported to have been driven mad by the horrors of her own creations, but the nearest approach to eccentricity on Mrs Radcliffe's part was dislike of public notice. Of scenery Mrs Radcliffe was an enthusiastic admirer, and she made driving tours with her husband every other summer through the English counties. She died on the 7th of February 1823. In the history of the English novel, Mrs Radcliffe holds an interesting place. She is too often confounded with her imitators, who vulgarized her favourite " properties ” of rambling and ruinous old castles, dark, desperate and cadaverous villains, secret passages, vaults, trapdoors, evidences of deeds of monstrous crime, sights and sounds of mysterious horror. She deserves at least the credit of originating a school of which she was the most distinguished exponent; and none of her numerous imitators approach her in ingenuity of plot, fertility of incident or skill in devising apparently supernatural occurrences capable of explanation by human agency and natural coincidence. She had a genuine gift for scenic effect, and her vivid imagination provided every tragic situation in her stories with its appropriate setting. Sir Walter Scott wrote an appreciative essay for the edition of 1824, and Miss Christina Rossetti was one of her admirers. She exercised a great influence on her contemporaries, and “ Schedoni " in The Italian is one of the prototypes of the Byronic hero.

RADCLIFFE. SIR GEORGE (1503-1657)- English politician, son of Nicholas Radcliffe (d. 1599) of Overthorpe, Yorkshire, was educated at Oldham and at University College, Oxford. He attained some measure of success as _a barrister, and about 1626 became the confidential adviser of Sir Thomas Wentworth, afterwards earl of Strafford, who was related to his wife, Anne Trappes (d. 1650). Like his master he was imprisoned in 1627 for declining to contribute to a forced loan, but he shared the good, as well as the ill, fortunes of Wentworth, acting as his adviser when he was president of the council of the north. When Wentworth was made lord deputy of Ireland, Radcliffe, in January 1633, preceded him to that country, and having been made a member of the Irish privy council he was trusted by the deputy in the fullest possible way, his advice being of the greatest service. In 1640, Radcliffe, like Strafford, was arrested and was impeached, but the charges against him were not pressed,and in 1643 he was with Charles I. at Oxford. He died at Fludling in May 1657. Radcliffe wrote An array towards the life of my Lord Straflord, from which the material for the various lives of the statesman has been largely taken.

( See Sir T. D. \Vhitaker, Life and Correspmdmce of Sir G. Raddifl'e 1810).

RADCLIFFE, JOHN (1650-1714), English physician, was born at Wakefield in 1650. He matriculated at University College, Oxford, and after taking his degree in 1669 was elected to a fellowship at Lincoln College, which he gave up in 1677 when, under the statutes of the college, he was called on to take orders. Graduating in medicine in 1675. he practised first in Oxford, but in 1684 removed to London, where he soon became one of the leading physicians. He frequently attended William III. until 1699, when he caused offence by remarking, as he looked at the King's swollen ankles, that he would not have his legs for his three kingdoms. On the rst of November 1714 he died of apoplexy at his house in Carshalton. By his will he left property to University College for founding two medical travelling fellowships and for other purposes. Other property was put at the disposal of his executors to use as they thought best, and was employed. among other things, in building the Radcliffe Observatory, Hospital and Library at Oxford, and in enlarging St Bartholomew’s Hospital in London. Radcliffe was elected M.P. for Bramber in 1690 and for Buckingham in 1713.

RADCLIPFR, an urban district in the Radcliffe-cumFarnworth parliamentary division of Lancashire, England, on the river Irwell, 2 m. S.S.W. of Bury, on the Lancashire 81 Yorkshire railway. Pop. (1901) 25.368. The church of St Bartholomew dates from the time of Henry IV.; some of the Norman portions of the building remain. Cotton-weaving, calico-printing, and bleaching, dyeing, paper-making, iron

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founding and machine-making are the principal industries, and there are extensive collicries in the neighbourhood.

RADEBERG, a town of Germany, in the kingdom of Saxony, pleasantly situated in a fertile district on the Roder, 10 m. NE. of Dresden, by the railway to Corlitz and Breslau. Pop. (1905) 13.301. It has an Evangelical and a Roman Catholic church, and an old castle. Its principal industries are the manufacture of glass, machinery, furniture and paper, and it produces a light Pilsener beer which is largely exported. Near the town are the Augustusbad and the Hermannsbad, two medicinal springs.

RADEGUNDA. ST (d. 587), Frankish queen, was the daughter of Berthaire, king of the Thuringians. Berthaire was killed by his brother Hermannfried, who took Radegunda and educated her, but was himself slain by the Frankish kings Theuderich and Clotaire (529), and Radegunda fell to Clotaire, who later married her. Her piety was already so noteworthy that it was said that Clotaire had married a nun, not a queen. She left him when he unjustly killed her brother, and fled to Medardus, bishop of Poitiers, who, notwithstanding the danger of the act, consecrated her as a nun. Radegunda stayed in Poitiers, founded a monastery there, and lived for a while in peace. Here Venantius Fortunatus, the Italian poet, found a friendly reception, and two of the poems printed under his name are usually attributed to Radegunda. From him we gain a most pleasing picture of life at the monastery. The queen died on the 13th of August 587.

See the references in A. Molinier, Sources dc l'hisfoire de France.

RADE'I‘ZKY. JOSEP, COUNT or Raos'rz (1766—1858), Austrian soldier, was born at Trzebnitz in Bohemia in 1766, to the nobility of which province his family, originally Hungarian, had for several centuries belonged. Orphaned at an early age, he was educated by his grandfather, and after the old count's death, at the Theresa academy at Vienna. The academy was dissolved during his first year’s residence, and he joined the army as a cadet in 1785.~ Next year he became an officer, and in 1787 a first lieutenant in a cuirassier regiment. He served as a galloper on Lacy’s staff in the Turkish War, and in the Low Countries during the Revolutionary War. In 1795 he fought on the Rhine. Next year he served with Beaulieu against Napoleon in Italy, and inwardly rebelled at the indecisive “ cordon ” system of warfare which his first chief, Lacy, had instituted and other Austrian generals only too faithfully imitated. His personal courage was conspicuous; at Fleurus he had led a party of cavalrythrough the French lines to discover the fate of Charleroi, and at Valeggio on the Mincio, with a few hussars, he rescued Beaulieu from the midst of the enemy. Promoted major, he took part in Wurmser’s Mantua campaign, which ended in the fall of the place. As lieutenant-colonel and colonel be displayed both bravery and skill in the battles of the Trebbia and Novi (1799), and at Marengo, as colonel on the stafl of Melas, he was hit by five bullets, after endeavouring on the previous evening to bring about modifications in the plan suggested by the “ scientific ” Zach. In 1801 Radetzky received the knighthood of the Maria Theresa order. In 1805, on the march to Ulm, he received news of his promotion to majorgeneral and his assignment to a command in Italy un_der the archdukc Charles, and thus took part in the successful campaign of Caldiero. Peace again afforded him a short leisure, which he used in studying and teaching the art of war. In 1809, now a lieutenant field marshal, he fought at Wagram, and in 1810 he received the commandership of the Maria Theresa order and the colonelcy of the 5th Radetzky hussars. From 1809 to 181 2, as chief of the general staff, he was active in the reorganization of the army and its tactical system, but, unable to carry out the reforms he desired owing to the opposition of the Treasury, he resigned the post. In 1813 he was Schwarzenberg‘s chief of staff, and as such had considerable influence on the councils of the Allied sovereigns and generals. Langenau, the quartermaster-general of the Grand Army, found him an indispensable assistant, and he had a considerable share in planning the Leipzig campaign and as a tactician won great praises in the battles of Brienne and Arcis sur Aube. He entered Paris with the allied sovereigns in March 1814, and returned with them to the congress of Vienna, where he appears to have acted as an intermediary between Mettcrnich and the czar Alexander, when these great personages were not on speaking terms.

During the succeeding years of peace he disappeared from the public view. He resumed his functions as chief of the staff, but his ardent ideas for reforming the army came to nothing in the face of the general war-weariness and desire to “ let well alone.” His zeal added to the number of his enemies, and in 1829, after he had been for twenty years a lieutenant field marshal, it was proposed to place him on the retired list. The emperor, unwilling to go so far as this, promoted him general of cavalry and shelved him by making him governor of a fortress. But very soon afterwards the Restoration settlement of Europe was shaken by fresh upheavals, and Radetzky was brought into the field of war again. He took. part under Frimont in the campaign against the Papal States insurgents, and succeeded that general in the chief command of the Austrian army in Italy in 1834. In 1836 he became a field marshal. He was now seventy years of age, but he displsycd the activity of youth in training and disciplining the army he commanded. But here too he was in advance of his time, and the government not only disregarded his suggestions and warnings but also refused the money that would have enabled the finest army it possessed to take the field at a moment’s notice. Thus the events of 1848 in Italy, which gave the old field marshal his place in history among the great commanders, found him, in the beginning, not indeed unprepared but seriously handicapped in the struggle with Charles Albert's army and the insurgents. How by falling back to the Quadrilateral and there, checking one opponent after another, he was able to spin out time until reinforcements arrived, and how thenceforward up to the final triumph of Novara on the 131d of March 1849, he and his army carried all before them, is described in the article ITALIAN WARS. The well-disciplined sense of duty to the superior officer, which was remarked even in the brilliant and sanguine young army reformer of 1810, had become more intense in the long years of peace, and after keeping his army loyal in the midst of the confusion of 1848, he made no attempt to play the part of Wallenstein or even to assume Wellington’s rOIe of family adviser to the nation. While as a patriot he dreamed a little of a united Germany, he remained to the end simply the commander of one of the emperor’s armies. He died, still in harness, though infirm, on the 5th of January 1858.

In military history Radetzky’s fame rests upon one great achievement, but in the history of the Austrian army he lives as the frank and kindly “ Vater Radetzky ” whom the soldiers idolized. He was fortunate in the moment of his death. In the year following, another and a greater Italian war broke out, his beloved army, disintegrated by peace economies which the old field marshal had been unable any longer to redress by ceaseless personal training, and in addition suffering from divided command and confused staff work, was defeated in every encounter.

RADEVORIWALD, a town of Germany, in the Prussian Rhine province, 10 m. E. from Remscheid, on the branch line of railway from Krebsoge. Pop. (1905) 10,978. It consists of the town proper and of several suburbs, and has five Evangelical and two Roman Catholic churches. Its chief manufactures are skates, files, locks and similar articles, and it has also cloth and cotton factories.

865:): I. H. Becker. Geschichte der Stadt Radevormwald (Cologne, 1 .

RADHANPUR. a native state of India, in the Palanpur agency, Bombay. It is situated in the north-western corner of Gujarat, close to the Runn of Cutch. The country is an open plain without hills and with few trees. It contains an area of 1150 sq. m. with a population in 1901 of 61,548, showing a decrease of 37 % during the decade, due to the results of famine. The estimated revenue is {27,000. The chief products are cotton, wheat and the common varieties of grain; the only manufacture

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of any importance is the preparation of a fine description of saltpetre. Radhanpur first came under British protection in 1813. The chief, whose title is Nawab, belongs to the Babi family, who have held power in Gujarat for more than two centuries. The town of Radhanpur had a population in 1901 of 11,879. It is a walled town, with an export trade in rapeseed, grain and cotton.

RADIATA, a term introduced by Cuvier in 1812 to denote the lowest of his four great animal groups or “embranchements.” IIe defined them as possessing radial instead of bilateral symmetry, and as apparently destitute of nervous system and sense organs, as having the circulatory system rudimentary or absent, and the respiratory organs on or co~ extensive with the surface of the body; he included under this title and definition five classes,——Echinodermata, Acalepha, Entozoa, Polypi and Infusoria. Lamarck (Hist. nal. d. Am'm. .r. Vertebres) also used the term, as when he spoke of the Medusae as radiate medusaria et anomala; but he preferred the term Radiaria, under which he included Echinodermata and Medusae. Cuvier’s term in its wide extension, however, passed into general use; but, as the anatomy of the different forms became more fully known, the difficulty of including them under the common designation made itself increasingly obvious. Milne-Edwards removed the Polyzoa; the group was soon further thinned by the exclusion of the Protozoa on the one hand and the Entozoa on the other; while in 1848 Leuckart and Frey clearly distinguished the Coelenterata from the Echinodermata as a separate sub-kingdom, thus condemning the usage by which the term still continued to be applied to these two groups at least. In 1855, however, Owen included under Lamarck’s term Radiaria the Echinodermata, Anthozoa, Acalepha and Hydrozoa, while Agassiz also clung to the term Radiata as including Echinodermata, Acalepha and Polypi, regarding their separation into Coelcnterata and Echinodermata as “ an exaggeration of their anatomical differences ” (Essay on Classification, London, 1859). These attempts, however, to perpetuate the usage were finally discredited by Huxley’s important Lectures on Comflarative Anatomy (1864), in which the term was finally abolished, and the “ radiate mob ” finally distributed among the Echinodermata, Polyzoa, Vermes (Platyhelminthes), Coelenterata and Protozoa.

RADIATION, THEORY OF. The physical activities that flourish on the surface of the earth derive their energy, in a form which is highly available thermodynamically, from the radiation of the sun. This has been ascertained to be dynamic energy, transmitted in waves by the vibrations of a medium occupying space, as the energy of sound is transmitted by the vibrations of the atmosphere. The elasticity that transmits it may be assumed to be mathematically perfect: any slight loss in transit of the light from the most distant stars, which recent statistical comparisons of brightness with distance may possibly indicate, is to be explained far more suitably by the presence of nebulous matter than by any imperfection of the aether. The latter would thus be the one perfect frictionless medium known to us: it could not be such if it were constituted, like matter, of independent molecules. It is thus on a higher plane, and may even be considered to be a dynamical specification of space itself. molecule of matter is a kinetic system compounded of simpler elements; its energy may be classified into constitutive energy essential to its continued existence, and vibratory energy which it can receive from or radiate away into aether. A piece of matter isolated in free aether would in time lose a; energy of the latter type by radiation; but the former will remain so long as the matter persists, along with the energy of the uniform translatory motion to which it is ultimately reduced. Thus all matter is in continual exchange of vibratory energy with the aether: it is with the laws of this exchange of energy that the general theory of Radiation deals, as distinguished from the mechanism of the aethereal vibrations, which is usually treated as the Theory of Light (see AETHER).

1. The foundation of this subject is the principle, arrived

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at independently by Balfour Stewart and Kirchhoff about the year 1858, that the constitution (§ 6) of the radiation which pervades an enclosure, surrounded by bodies in a steady thermal state, must be a function of the temperature of those bodies, and of nothing else. It was subsequently pointed out by Stewart (Brit. Assoc. Report, 1871) that if the enclosure contains a radiating and absorbing body which is put in motion, all being at the same temperature, the constituents of the radiation in front of it and behind it will differ in period on account of the Doppler-Fizeau effect, so that there will be an opportunity of gaining mechanical work in its settling down to an equilibrium; there must thus be some kind of thermodynamic compensation, which might arise either from nethert-al friction, or from work required to produce the motion of the body against pressure exerted on it by the surrounding radiation. The hypothesis of friction is now excluded in ultimate molecular physics, while the thermodynamic bearing of a pressure exerted by radiation, such as is demanded by Maxwell's electric theory, has been more recently developed on other lines by Bartoli and Boltzmann (1884), and combined with that of the Doppler effect by W. \Vien (1893) in development of the ideas above expreSsed.

The original reasoning of Stewart and Kirchhofl' rests on the dynamical principle, that by no process of ordinary reflexion or transmission can the period, and therefore the wave-length, of any harmonic constituent of the radiation be changed; each constituent remains of the same wave-length from the time it is emitted until the time it is again absorbed. If we imagine a field of radiation to be enclosed within perfectly reflecting walls, then, provided there is no material substance in the field which can radiate and absorb, the constitution of the radiation in it may be any whatever, and it will remain permanent. It is only the presence of material bodies that by their continued emission and absorption can transform the surrounding radiation towards the unique constitution which corresponds to their temperature. We mn define the temperature of an isolated field of radiation, of this definite ultimate constitution, to be the same as that of the material bodies with which it would thus be in equilibrium. Further, the mutual independence of the various constituents of any field of radiation enclosed by perfect reflectors allows us to assign a temperature to each constituent, such as the part involving wave-lengths lying between X and h-l-tih; that will be the temperature of a material system with which this constituent by itself is in equilibrium of emission and absorption. But to reason about the temperature of radiation in this way we must be sure that it completely pervades the space, and has no special direction; this is ensured by the continual reflexions from the walls of the enclosure. The question of the temperature of a directed wave-train travelling through space, such as a beam of light, will come up later. The tempera— ture of each constituent in a region of undirected radiation is thus a function of its wave-length and its intensity alone. It is the fundamental principle of thermodynamics, that temperatures tend to become uniform. In the present case of a field of radiation, this equalization cannot take place directly between the various constituents of the radiation that occupy the same space, but only through the intervention of the emimsion and absorption of material bodies; the constituent radiations are virtually partitioned off adiabatically from direct interchange. Thus in discussing the transformations of temperatures of the constituent elements of radiation, we are really reasoning about the activity of material bodies that are in thermal equilibrium with those constituents; and the theoretical basis of the idea of temperature, as depending on the fortuitous residue of the energy of molecular motions, is preserved.

Mechanical Pressure of Undulatory Motions—Consider a wave-train of any kind.in which the displacement is i=0 cos mtx+(t) so that it is propagated in the direction in which I decreases; let it be directly incident on a perfect reflector travelling towards it with velocity v, whose position is there

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fore given at time t by x=ut. There will be a reflected train
given by £'=u' cos m’(x—ct), the velocity of propagation 6
being of course the same for both. The disturbance does not
travel into the reflector, and must therefore be annulled at its
surface; thus when x=vt we must have £+£’=o identically.
This gives a’= —a, and m'(c—v)=m(r+u). The amplitude of
the reflected disturbance is therefore equal to that of the in-
cident one; while the wave-length is altered on the ratio
c—v
c+u’
is thus in agreement with the usual statement of the Doppler
effect. The energy in the wave-train being half potential and
half kinetic, it is given by the integration of p(dEtdt)’ along the
train, wherep represents density. In the reflected train it is
therefore augmented, when equal lengths are compared, in the
ratio (Pl-U

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. . . v . which is approximately 1—22, where u/c 15 small, and

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therefore be equal to the fraction 6%, of the energy in a length c+v of the incident wave-train; thus it is the fraction of the total density of energy in front of the reflector, belonging to both the incident and reflected trains. When u is small compared with c, this makes the pressure equal to the density of vibrational energy, in accordance with Maxwell's electrodynamic formula (Elec. and Mag, 1871).

The argument may be illustrated by the transverse vibrations of a tense cord, the reflector being then a lamina through a small aperture in which the cord passes; the lamina can thus slide along the cord and sweep the vibratory motion in front of it. In this case the force acting on the lamina is the resultant of the tensions T of the cord on the two sides of the aperture, giving a lengthwise force Q'l‘dfi-l-E’FMx‘ when, as usual, powers higher than the second of the ratio of amplitude to wave-length are neglected; this, when v/c is small, is an oscillatory force of amount 29(dE/dt)’, whose time-average agrees with the value above obtained. If we consider a finite train of waves thus sent back from a moving reflector, the time integral of the pressure must represent force transmitted along the cord, or a gain of longitudinal momentum in the reflected waves, or both together.

When it is a case of transverse waves in an elastic medium, reflected by an advancing obstacle, the origin of the working pressure is not so obvious, because we cannot easily formulate a mechanism for the advancing reflector like that of the lamina above employed. In the case of light-waves we can, however, ima~ gine an ideal material body, constituted of very small molecules, that would sweep them in front of it with the same perfection as a metallic mirror actually reflects the longer Hertzian waves. The pressure will then be identified physically, as in the case of the latter waves, with the mechanical forces acting on the screening oscillatory electric current~sheet which is induced on the surface of the reflector. The displacement represented

above by E, which is annulled at the reflector, may then be ’taken to be either the tangential electric force or the normal component of the vector whose velocity is the magnetic force. The latter interpretation is theoretically interesting, because that vector, which is the dynamical displacement in electrontheory, usually occurs only through its velocity. The general case of oblique incidence can be treated on similar lines; each filament of radiation (ray) in fact exerts its own longitudinal push equal to its energy per unit length, and it is only a matter of summation.

The usual formula for the pressure of electric radiation is

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