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and Himmelfahrt Jesu (1777), and some seventy cantatas, | wrote two Masses, a Requiem, a Te Deum and other works. litanies, motets and other liturgical pieces. At the same time his genius for instrumental composition was further stimulated by the career of Haydn, to whom he sent a letter of high appreciation, and the climax of his art was reached in the six volumes of sonatas für Kenner und Liebhaber, to which he devoted the best work of his last ten years. He died at Hamburg on the 14th of December 1788.

Having also gained some reputation as a composer of opera, he was in 1762 invited to London and there spent the rest of his life. For twenty years he was the most popular musician in England, his dramatic works, produced at the King's theatre, were received with great cordiality, he was appointed musicmaster to the queen, and his concerts, given in partnership with Abel at the Hanover Square rooms, soon became the most fashionable of public entertainments. He is of some historical interest as the first composer who preferred the pianoforte to the older keyed-instruments; but his works, though elegant and pleasing, were ephemeral in character and have been deservedly forgotten.

Through the latter half of the 18th century the reputation of K. P. E. Bach stood very high. Mozart said of him, "He is the father, we are the children "; the best part of Haydn's training was derived from a study of his work; Beethoven expressed for his genius the most cordial admiration and regard. This position he owes mainly to his clavier sonatas, which mark an important epoch in the history of musical form. Lucid in style, delicate and tender in expression, they are even more notable for the freedom and variety of their structural design; they break away altogether from the exact formal antithesis which, with the composers of the Italian school, had hardened into a convention, and substitute the wider and more flexible outline which the great Viennese masters showed to be capable of almost infinite development. The content of his work, though full of invention, lies within a somewhat narrow emotional range, but it is not less sincere in thought than polished and felicitous in phrase. Again he was probably the first composer of eminence who made free use of harmonic colour for its own sake, apart from the movement of contrapuntal parts, and in this way also he takes rank among the most important pioneers of the school of Vienna. His name has now fallen into undue neglect, but no student of music can afford to disregard his Sonaten für Kenner und Liebhaber, his oratorio Die Israeliten in der Wüste, and the two concertos (in G major and D major) which have been republished by Dr Hugo Riemann. A list of his voluminous compositions may be found in Eitner's Quellen Lexikon, and a critical account of them is given in Bitter's Č.P. E. and W. F. Bach und deren Brüder (2 vols., Berlin, 1868), a mine of valuable though ill-arranged information.

Four more of Johann Sebastian Bach's sons grew to manhood and became musicians. The eldest of them, WILHELM FRIEDERMANN BACH (1710-1784) was by common repute the most gifted; a famous organist, a famous improvisor and a complete master of counterpoint. But, unlike the rest of the family, he was a man of idle and dissolute habits, whose career was little more than a series of wasted opportunities. Educated at Leipzig, he was appointed in 1733 organist of the Sophienkirche at Dresden, and in 1747 became musical director of the Liebfrauenkirche at Halle. The latter office he was compelled to resign in 1764, and thenceforward he led a wandering life until, on the 1st of July 1784, he died in great poverty at Berlin. His compositions, very few of which were printed, include many church cantatas and instrumental works, of which the most notable are the fugues, polonaises and fantasias for clavier, and an interesting sestet for strings, clarinet and horns. Several of his manuscripts are preserved in the Royal library at Berlin; and a complete list of his works, so far as they are known, may be found in Eitner's Quellen Lexikon.

The fourth son, JOHANN GOTTFRIED BERNHARD BACH (1715 1739) was, like his elder brothers, born at Weimar and educated at Leipzig. From 1735 to 1738 he held successively the organistships at Mühlhausen and Sangerhausen; in 1738 he threw up his appointment and went to study law at Jena; in 1739 he died, aged 24. JOHANN CHRISTOPH FRIEDRICH BACH (1732-1795), the ninth son, was born at Leipzig, studied at the Thomasschule and the university, and in 1750 was appointed Kapellmeister at Bückeburg. He was an industrious composer, especially of church-music and opera, whose work reflects no discredit on the family name. JOHANN CHRISTIAN BACH (1735-1782), the eleventh son, was born at Leipzig, and on the death of his father in 1750 became the pupil of his brother Emanuel at Berlin. In 1754 he went to Italy where he studied under Padre Martini, and from 1760 to 1762 held the post of organist at Milan cathedral, for which he

A full account of J. C. Bach's career is given in the fourth volume of Burney's History of Music, and a catalogue of his compositions in an article by Max Schwarz, published in the Sammelbände of the Internationale Musik-Gesellschaft, Jhrg. ii. p. 401. (W. H. HA.)

BACHARACH, YAIR (1639-1702), German rabbi, was the author of Hawwoth Yair (a collection of Responsa) and other works. Bacharach was a man of wide culture, and holds an honourable place among the pioneers of the Jewish Renaissance which was inaugurated towards the end of the 18th century.

BACHARACH, a town of Germany, in the Prussian Rhine Province, romantically situated on the left bank of the Rhine, 30 m. above Coblenz on the railway to Mainz. Pop. 2000. There is an interesting church, a basilica, dating from the beginning of the 13th century. There are also ruins of a Gothic church of the 13th and 15th centuries. The ruined castle of Stahleck, crowning the heights above the town, is celebrated in history as the scene of the marriage between Henry, eldest son of Henry the Lion (shortly before the latter's death in 1195) and Agnes of Hohenstaufen, which effected a temporary reconciliation between the houses of Welf and Hohenstaufen. Other ruined castles are those of Fürstenberg and Stahlberg. All three belonged to the counts palatine. The wines of Bacharach were once held in the greatest esteem, and it is still one of the chief markets of the Rhenish wine trade.

BACHAUMONT, LOUIS PETIT DE (1690-1771), French littérateur, was of noble family and was brought up at the court of Versailles. He passed his whole life in Paris as the centre of the salon of Madame Doublet de Persan (1677-1771), where criticism of art and literature took the form of malicious gossip. A sort of register of news was kept in a journal of the salon, which dealt largely in scandals and contained accounts of books suppressed by the censor. Bachaumont's name is commonly connected with the first volumes of this register, which was published anonymously under the title Mémoires secrets pour servir à l'histoire de la République des Lettres, but his exact share in the authorship is a matter of controversy. It was continued by Pidansat de Mairobert (1707-1779) and others, until it reached 36 volumes (1774-1779). It is of some value as a historical source, especially for prohibited literature. Extracts were published by P. Lacroix in one volume, 1859. An incomplete edition (4 vols.) was undertaken in 1830 by Ravenal.

spondance littéraire of Grimm, Diderot, d'Alembert and others (new See, in addition to the memoirs of the time, especially the Correed., Paris, 1878, 17 vols.); Ch. Aubertin, L'Esprit public au XVIII siècle (Paris, 1872).

BACHE, ALEXANDER DALLAS (1806-1867), American physicist, great-grandson of Benjamin Franklin, was born at Philadelphia on the 19th of July 1806. After graduating at the United States Military Academy at West Point in 1825, he acted as assistant professor there for some time, and as a lieutenant in the corps of engineers he was engaged for a year or two in the erection of coast fortifications. He occupied the post of professor of natural philosophy and chemistry in the University of Pennsylvania in 1828-1841 and in 1842-1843. For the trustees of what in 1848 was to become Girard College, but had not yet been opened, he spent the years 1836-1838 in Europe, examining European systems of education, and on his return published a very valuable report. In 1843, on the death of Professor F. R. Hassler (1770-1843), he was appointed

superintendent of the United States coast survey. He succeeded | course, were entitled to proceed to the higher degrees. In modern
in impressing Congress with a sense of the great value of this
work, and by means of the liberal aid it granted, he carried out
a singularly comprehensive plan with great ability and most
satisfactory results. By a skilful division of labour, and by the
erection of numerous observing stations, the mapping out of the
whole coast proceeded simultaneously under the eye of the
general director, and in addition a vast mass of magnetic and
meteorological observations was collected. He died at Newport,
Rhode Island, on the 17th of February 1867.

universities the significance of the degree of bachelor, în relation
to the others, varies; e.g. at Oxford and Cambridge the bachelor
can proceed to his mastership by simply retaining his name on
the books and paying certain fees; at other universities a further
examination is still necessary. But in no case is the bachelor
a full member of the university. The degree of bachelor (of arts,
&c.) is borne by women also. (4) The younger or inferior members
of a trade gild or city company, otherwise known as "yeomen
(now obsolete). (5) Unmarried men, since these presumably
have their fortunes yet to make and are not full citizens. The
word bachelor, now confined to men in this connotation, was
formerly sometimes used of women also.

BACHE, FRANCIS EDWARD (1833-1858), English musical composer, was born in Birmingham on the 14th of September 1833. The pupil of Alfred Mellon for violin and Sterndale Bennett for composition, he afterwards went to Leipzig in 1853 and studied with Hauptmann and Plaidy: Considering the early age at which he died, his compositions are fairly numerous, and the best, a trio for piano and strings, is still held in high esteem. Two operettas, a piano concerto and a number of published pianoforte pieces and songs do little more than show how great was his promise. He died at Birmingham of consumption on the 24th of August 1858. His younger brother, WALTER BACHE (1842-1888), was born in Birmingham on the 19th of June 1842, and followed him to the Leipzig Conservatorium, where he became an excellent pianist. From 1862 to 1865 he studied with Liszt in Rome, and for many years devoted himself to the task of winning popularity for his master's works in England. At his annual concerts in London nearly all Liszt's larger works were heard for the first time in England, and on the occasion of Liszt's last visit to England in 1886, he was entertained by Bache at a memorable reception at the Grosvenor Gallery. Walter Bache was professor of the pianoforte at the Royal Academy of Music for some years before his death, and the foundation of the Liszt scholarship at that institution was mainly due to his efforts. He died in London on the 26th of March 1888. An interesting memoir of the two brothers, by Miss Constance Bache. appeared in 1901 under the title Brother Musicians.

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Bachelors, in the sense of unmarried men, have in many countries been subjected to penal laws. At Sparta, citizens who remained unmarried after a certain age suffered various penalties. They were not allowed to witness the gymnastic exercises of the maidens; and during winter they were compelled to march naked round the market-place, singing a song composed against themselves and expressing the justice of their punishment. The usual respect of the young to the old was not paid to bachelors (Plut. Lyc. 15). At Athens there was no definite legislation on this matter; but certain minor laws are evidently dictated by a spirit akin to the Spartan doctrine (see Schömann, Gr. Alterth. i. 548). At Rome, though there appear traces of some earlier legislation in the matter, the first clearly known law is that called the Lex Julia, passed about 18 B.C. It does not appear to have ever come into full operation; and in A.D. 9 it was incorporated with the Lex Papia et Poppaea, the two laws being frequently cited as one, Lex Julia et Papia Poppaea. This law, while re stricting marriages between the several classes of the people, faid heavy penalties on unmarried persons, gave certain privileges to those citizens who had several children, and finally imposed lighter penalties on married persons who were childless. Isolated instances of such penalties occur during the middle ages, e.g. by a charter of liberties granted by Matilda 1., BACHELOR (from Med. Lat. baccalarius, with its late and countess of Nevers, to Auxerre in 1223, an annual tax of five rare variant baccalaris-cf. Ital. baccalare-through O. Fr. solidi is imposed on any man qui non habet uxorem et est backebacheler), in the most general sense of the word, a young man.larius. In Britain there has been no direct legislation bearing The word, however, as it possesses several widely distinct applica- on bachelors; but, occasionally, taxes have been made to bear tions, has passed through many meanings, and its ultimate origin more heavily on them than on others. Instances of this are the is still involved in a certain amount of obscurity. The derivation act (6 and 7 Will. III.) passed in 1695; the tax on servants, from Welsh bach, little, is mentioned as"" possible by Skeat 1785; and the income tax, 1798. (Etymological Dictionary), but is “definitely discarded" by the New English Dictionary, and that given here is suggested as probable. The word baccalarius was applied to the tenant of a baccalaria (from baccalia, a herd of cows, bacca being a Low Latin variant of vacca), which was presumably at first a grazing farm and was practically the same as a vaselleria, i.e. the fief of a sub-vassal. Just, however, as the character and the size of the baccalaria varied in different ages, so the word baccalarius changed its significance; thus in the 8th century it was applied to the rustici, whether men or women (baccalariae), who worked for the tenant of a mansus. Throughout all its meanings the word has retained the idea of subordination suggested in this origin. Thus it came to be applied to various categories of persons as follows.(1) Ecclesiastics of an inferior grade, e.g. young monks or even recently appointed canons (Severtius, de episcopis Lugdunensibus, p. 377, in du Cange). (2) Those belonging to the lowest stage of knighthood. Knights bachelors were either poor vassals who could not afford to take the field under their own banner, or knights too young to support the responsibility and dignity of knights bannerets (see KNIGHTHOOD AND CHIVALRY). (3) Those holding the preliminary degree of a university, enabling them to proceed to that of master (magister) which alone entitled them to teach. In this sense the word baccalarius or baccalaureus first appears at the university of Paris in the 13th century, in the system of degrees established under the auspices of Pope Gregory IX., as applied to scholars still in stalu pupillari. Thus there were two classes of baccalarii: the baccalarii cursores,i.c. theological candidates passed for admission to the divinity course, and the baccalarii dispositi, who, having completed this

BACHIAN (Dutch Batjan), one of the Molucca Islands, in the residency of Ternate, Dutch East Indies, in the Molucca Sea, in 0°13'-0°55′ S. and 127°22′-128°E. With its subordinate islands, Mandioli, Tawali and others, it lies west of the southern peninsula of the island of Halmahera or Jilolo, and has an area of 914 sq. m. It is of irregular form, consisting of two distinct mountainous ports, united by a low isthmus, which a slight subsidence would submerge. The island is in part of volcanic formation, and the existence of hot springs points to volcanic activity. There are, however, especially in the southern portion, ancient and non-volcanic rocks. The highest elevation occurs at the south of the island, the mountain of Labua reaching 6950 ft. Coal and other minerals have been discovered. A large portion of the island is richly wooded, and sago, cocoa-nuts and cloves (which are indigenous) are abundantly produced. Bachian is remarkable as the most eastern point on the globe inhabited by any of the Quadrumana, a black ape occurring here as in Celebes. The island is very rich in birds and insects. The interior of the island is uninhabited and none of the dwellers on the coast are indigenous. They consist of the Sirani or Christian descendants of the Portuguese, of Malays, with a Papuan element, Galela men from the north of Halmahera, immigrants from Celebes, with some Chinese and Arabs. The total number of inhabitants is about 13,000. The chief village, called Amasing by the inhabitants, but also called Bachian, is situated on the west side of the isthmus. Bachian is the most important island of a group formerly governed by a sultan, but since 1889 by a committee of chiefs under the control of a Dutch contrôleur. From 1882 onwards a Batjan company attempted to exploit the island, but

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unsuccessfully, owing to a deficient knowledge of the soil and its Ghagar, Kumar, &c. All the rivers in the district are subject 1 capabilities and a lack of labourers. to tidal action from the Meghna on the north, and from the Bay of Bengal on the south, and nearly all of them are navigable at high tide by country boats of all sizes. The rise of the tide is very considerable in the estuary of the Meghna, and many of the creeks and water-courses in the island of Dakshin Shahbazpur, which are almost dry at ebb tide, contain 18 or 19 ft. of water at the flood. A very strong "bore" or tidal wave runs up the estuary of the Meghna at spring tides, and a singular sound like thunder, known as the "Barisal guns," is often heard far out at sea about the time it is coming in. There are numerous marshes in the district, of great size and depth, and abounding in fish.

BACK-BOND, or BACK-LETTER, in Scots law, a deed qualifying the terms of another deed, or declaratory of the purposes for which another deed has been granted. Thus an ex facie absolute disposition, qualified by a back-bond expressing the limited nature of the right actually held by the person to whom the disposition is made, would constitute what in England is termed a deed of trust.

BACK-CHOIR, RETRO-CHOIR, a space behind the high aftar in the choir of a church, in which there is, or was, a small altar standing back to back with the other.

BACKERGUNJE, or BAKARGANJ, a district of British India in the Dacca division of Eastern Bengal and Assam. It forms part of the joint delta of the Ganges and the Brahmaputra, and its area is 4542 sq. m. The general aspect of the district is that of a flat even country, dotted with clusters of bamboos and betelnut trees, and intersected by a perfect network of dark-coloured and sluggish streams. There is not a hill or hillock in the whole district, but it derives a certain picturesque beauty from its wide expanses of cultivation, and the greenness and freshness of the vegetation. This is especially conspicuous in the rains, but at no time of the year does the district present a dried or burnt-up appearance. The villages, which are always walled round by groves of bamboos and betel-nut palms, have often a very striking appearance; and Backergunje has many beauties of detail which strike a traveller in passing through the country. The level of the country is low, forming as it does a part of the great Gangetic delta; and the rivers, streams and water-courses are so numerous that it is very difficult to travel except by boat at any season of the year. Every natural hollow is full of water, around the margin of which long grasses, reeds and other aquatic plants grow in the greatest profusion, often making it difficult to say where the land ends and the water begins. Towards the north-west the country is very marshy and nothing is to be seen for miles but tracts of unreclaimed swamps and rice lands, with a few huts scattered here and there and raised on mounds of earth. In the south of the district, along the coast of the Bay of Bengal, lie the forest tracts of the Sundarbans, the habitation of tigers, leopards and other wild beasts.

The Mussulmans of Backergunje are among the worst of their creed, steeped in ignorance and prejudice, easily excited to violence and murder, very litigious and grossly immoral. On account of an epidemic of murders disarmament had to be enforced in the district. The Faraizis or Puritan sect of Mahommedans are exceedingly numerous in the district. The Buddhist population consists of Maghs or the people of Arakan, who first settled in Backergunje about 1800, and have made themselves very useful in the clearing of the Sundarbans. A gipsy-like tribe called the Bebajias are rather numerous in this district. They live principally in boats, travelling from place to place, profess Mahommedanism, and gain their subsistence by wood-cutting in the Sundarbans, fishing, fortune-telling and trading in trinkets. In 1901 the population was 2,291,752, showing an increase of 6% in the decade.

A number of small trading villages exist throughout the district, and each locality has its periodical fairs for purposes of traffic. The material condition of the people is good. Every inhabitant is a small landholder and cultivates sufficient rice and other necessaries for the support of his family. Owing to this reason, hired labour is very scarce. Rice is the great crop of the district, and three harvests are obtained annually-the aman, or winter rice; aus, or autumn crop; and boro, or spring rice. The climate of Backergunje is one of the healthiest in Eastern Bengal, owing to the strong south-west monsoon, which comes up directly from the Bay of Bengal, and keeps the atmosphere cool; but the heavy rainfall and consequent humidity of the atmosphere, combined with the use of bad water, are fruitful sources of disease. The average annual temperature varies from 78° to 85° F. The thermometer ranges from 62° to 98°.

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Barisal, the headquarters station, situated on the west bank of the Barisal river, had a population in 1901 of 18,978. The next largest town' is Pirojpur (14,119).

The principal rivers of the district are the Meghna, the Arial Khan and the Haringhata or Baleswar, with their numerous offshoots. The Meghna represents the accumulated waters of the Brahmaputra and Ganges. It flows along the eastern boundary of the district in a southerly direction for about 100 m. till it debouches into the Bay of Bengal. During the latter part of its course this noble river expands into a large estuary containing BACKGAMMON, a game played with draughtsmen and a special many islands, the principal of which is that of Dakshin Shahbaz- board, depending on the throw of dice. It is said to have been pur. The islands on the sea-front are exposed to devastation invented about the 10th century (Strutt). A similar game (Ludus by cyclonic storm-waves. The Arial Khan, a branch of the duodecim scriptorum, the "twelve-line game ") was known to the Ganges, enters the district from the north, and flows generally Romans, and Plato (Republic, bk. x.) alludes to a game in which in a south-easterly direction till it falls into the estuary of the dice were thrown and men were placed after due consideration. Meghna. The main channel of the Arial Khan is about 1700 yds. The etymology of the word "backgammon" is disputed; it is in width in the dry season, and from 2000 to 3000 yds. in the rains. probably Saxon-baec, back, gamen, game; i.e. a game in which It receives a number of tributaries, sends off several offshoots, the players are liable to be sent back. Other derivations are, and is navigable throughout the year by native cargo boats of the Dan. bakke, tray, gammen, game (Wedgwood); and Welsh bach, largest size. The Haringhata, Baleswar, Madhumati and Garai | little, cammaun, battle (Henry). Chaucer alludes to a game of are various local names for the same river in different parts of its" tables," played with three dice, in which “ men were moved course and represent another great offshoot of the Ganges. It from the opponent's "tables," the game (ludus Anglicorum) enters Backergunje near the north-west corner of the district, being described in the Harleian MSS. (1527). The French name whence it forms its western boundary, and runs south, but with for backgammon is trictrac, imitative of the rattle of the dice. great windings in its upper reaches, till it crosses the Sundarbans, and finally falls into the Bay of Bengal by a large and deep estuary, capable of receiving ships of considerable burden. In the whole of its course through the district the river is navigable by native boats of large tonnage, and by large sea-going ships as high up as Morrellganj, in the neighbouring district of Jessore. Among its many tributaries in Backergunje the most important is the Kacha, itself a considerable stream and navigable by large boats all the year round, which flows in a southerly direction for 20 m., when it falls into the Baleswar. Other rivers of minor importance are the Barisal, Bishkhali, Nihalganj, Khairabad, I

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Backgammon is played by two persons. The "board" (see diagram) is divided into four "tables," each table being marked with six "points" coloured differently. The inner and outer tables are separated from each other by a projecting bar. The board (in the ordinary form of the game) is furnished with fifteen white and fifteen black men," set "or arranged as in the diagram. It is usual to make the inner table the one nearest to the light. Two dice-boxes are required, one for each player, and a pair of dice, which are used by both players.. The dice are marked with numbers on their six sides, from one to six, number one being called, “ace "; two, "deuce "; three, "trey." Formerly the

four was called " quatre" (pronounced "cater"); the five, "cinque " (pronounced either "sank" or "sink "); and the six, "six" (size).

For the right to start each player throws one or two dice; the one who throws the higher number has the right of playing first; and he may either adopt the numbers thrown or he may throw again, using both dice.

The men are moved on from point to point, according to the throws of the dice made by the players alternately. White moves from black's inner table to black's outer, and from this to white's outer table, and so on to white's inner table; and all black's moves must be in the contrary direction. A player may move any of his men a number of points corresponding to the numbers thrown by him, provided the point to which the move BLACK Black's Home or Inner Table.

would bring him is not blocked by two or more of his adversary's men being on it. The whole throw may be taken with one man, or two men may be moved, one the exact number of points on one die, the other the number on the other die. If doublets are thrown (e.g. two sixes), four moves of that number (e.g. four movesofsixpoints) may be made, either all by one man or separately by more. Thus,

White's Home or Inner Table.

WHITE Backgammon Board. 1. Black's ace-point. 3. Black's bar-point. suppose white 2. White's ace-point. 4. White's bar-point. throws five, six, he may move one of his men from the left-hand corner of the black's inner table to the left-hand corner of black's outer table for six; he may, again, move the same man five points farther on, when his move is completed; or he may move any other man five points. But white cannot move a man for five from the black's ace-point, because the six-point in that table is blocked. Any part of the throw which cannot be moved is of no effect, but it is compulsory for a player to move the whole throw unless blocked. Thus if the men were differently placed, and white could move a six, and having done so could not move a five, his move is completed. If, however, by moving the five first, he can afterwards move a six, he must make the move in that manner.

Black's Outer Table.

White's Outer Table.

When a player so moves as to place two men on the same point, he is said to "make a point."

When there is only a single man on a point, it is called a "blot." When a blot is left, the man there may be taken up (technically the blot may be "hit ") by the adversary if he throws a number which will enable him to place a man on that point. The man hit is placed on the bar, and has to begin again by entering the adversary's home table again at the next throw should it result in a number that corresponds to an unblocked point. The points in the home tables count for this purpose as 1, 2, 3, 4, 5, 6, beginning from the ace-point. A player is not allowed to move any other man while he has one to enter. It is, therefore, an advantage to have made all the points in your own board, so that your adversary, if you take a man up, cannot enter; and you can then continue throwing until a point is opened.

The game proceeds until one of the players gets all his men into his inner table or home. Then he begins to take his men off the board, or to bear them, i.e. to remove a man from any point that corresponds in number with his throw. If such a point is occupied, a move must be made, if there is room for it, and a move may be taken, instead of bearing a man, at any time; but

when six is empty, if six is thrown a man may be borne from five and so on. If, after a player has commenced throwing off his men, he should be hit on a blot, he must enter on his adversary's inner table and must bring the man taken up into his own inner table before he can bear further.

Whoever first takes off all his men wins the game:-a single game (a "hit ") if his adversary has begun bearing; a double game (a "gammon ") if the adversary has not borne a man; and a triple game (a" backgammon ") if, at the time the winner bears his last man, his adversary, not having borne a man, has one in the winner's inner table, or has a man up. When a series of games is played, the winner of a hit has the first throw in the succeeding game; but if a gammon is won, the players each throw a single die to determine the first move of the next game.

In order to play backgammon well, it is necessary to know all the chances on two dice and to apply them in various ways. The number of different throws that can be made is thirty-six. By taking all the combinations of these throws which include given numbers, it is easily discovered where blots may be left with the least probability of being hit. For example, to find the chance of being hit where a blot can only be taken up by an ace, the adversary may throw two aces, or ace in combination with any other number up to six, and he may throw each of these in two different ways, so that there are in all eleven ways in which an ace may be thrown. This, deducted from thirty-six (the total number of throws), leaves twenty-five; so that it is 25 to 11 against being hit on an ace. is very important to bear in mind the chance of being hit on any number. The following table gives the odds against being hit on number within the reach of one or two dice:

It

any

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It is 25 to 11, or about 9 to 4, against being hit on 1

24. 12, or

2

2

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"

"" ,, 14, or about 3

22

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,, 2,
.. 5.

"

3

"

"1

"
"

.. 5.

19

21 15, 21 15. 19" 17, "30 6, ,, 30 .. 6,

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5

1

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5, or about 6 3. or 11 2, 17 ... 33 .. 3. II The table shows that if a blot must be left within the reach of

.. 31 ..
.. 33..
34..

...I,
,, 1,
.. I,

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one die, the nearer it is left to the adversary's man the less probabeing hit on a blot which is only to be reached with double dice, bility there is of its being hit. Also, that it is long odds against and that, in that case (on any number from 7 to 11), the farther off the blot is, the less chance there is of its being hit.

part of the throw is blocked by an intervening point being held by The table assumes that the board is open for every possible throw. adverse men, the chance of being hit is less.

If

Two principles, then, have to be considered in moving the men:(1) To make points where there is the best chance of obstructing the opponent. (2) When obliged to leave blots, to choose the position in which they are least likely to be hit.

The best points to secure are the five-point in your own inner table and the five-point in your adversary's inner table. The next best is your own bar-point; and the next best the four in your own inner table.

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Trey, five: make the trey-point in your own table. Trey, six: bring a man from your adversary's ace-point as far as he will go.

Fours: move on two on the five-point in your adversary's inner table, and two from the five in his outer table.

Four, five and four, six: carry a man from your adversary's acepoint as far as he will go.

Fives: move two men from the five in your adversary's outer table to the trey-point in your inner table.

Five, six: move a man from your adversary's ace-point as far as he will go.

Sixes (the second-best throw): move two on your adversary's un-bar-point and two on your own bar-point.

adversary's bar-point, to the six-point in your outer table, and then In carrying the men home carry the most distant man to your to the six-point in your inner table. By following this rule as nearly

as the throws admit, you will carry the men to your inner table in the fewest number of throws.

Avcid carrying many men upon the trey or deuce-point in your own tables, as these men are out of play.

Whenever you have taken up two of your adversary's men, and two or more points made in your inner table, spread your other men in the hope of making another point in your tables, and of hitting the man your adversary enters.

Always take up a man if the blot you leave in making the move can only be hit with double dice, but if you already have two of your opponent's men in your tables it is unwise to take up a third.

In entering a man which it is to your adversary's advantage to hit, leave the blot upon the lowest point you can, e.g. acc-point in preference to deuce-point.

When your adversary is bearing his men, and you have two men in his table, say, on his ace-point, and several men in the outer table, it is to your advantage to leave one man on the ace-point, because it prevents his bearing his men to the greatest advantage, and gives you the chance of his leaving a blot. But if you find that you can probably save the gammon by bringing both your men out of his table, do not wait for a blot. Eight points is the average throw. The laws of backgammon (as given by Hoyle) are as follows:-. 1. When a man is touched by the caster it must be played if possible; if impossible no penalty. 2. A man is not played till it is placed upon a point and quitted. 3. If a player omits a man from the board there is no penalty. 4. If he bears any number of men before he has entered a man taken up, men so borne must be entered again. 5. If he has mistaken his throw and played it, and his adversary has thrown, it is not in the choice of either of the players to alter it, unless they both agree to do so. 6. If one or both dice are" cocked," ie. do not lie fairly and squarely on the table, a fresh throw is imperative.

Russian Backgammon varies from the above game in that the men, instead of being set as in the diagram, are entered in the same table by throws of the dice, and both players move in the same direction round to the opposite table. There are various rules for this game. By some a player is not obliged to enter all his men before he moves any; he can take up blots at any time on entering, but while he has a man up, he must enter it before entering any more or moving any of those already entered. If he cannot enter the man that is up, he loses the benefit of the throw. A player who throws doublets must play or enter not only the number thrown, but also doublets of the number corresponding to the opposite side of the dice; thus, if he throws sixes, he must first enter or move the sixes, as the case may be, and then aces, and he also has another throw. Some rules allow him to play either doublets first, but he must always complete one set before playing the other. If a player cannot play the whole of his throw, his adversary is sometimes allowed to play the unplayed portion, in which cases the caster is sometimes allowed to come in and complete his moves, if he can, and in the event of his having thrown deuce-ace or doublets to throw again. If he throws doublets a second time, he moves and throws again, and so on. The privilege is sometimes restricted by not allowing this advantage to the first doublets thrown by each player. It is sometimes extended by allowing the thrower of the deuce-ace to choose any doublets he likes on the opposite side of the dice, and to throw again. The restriction with regard to the first doublets thrown does not apply to deuce-ace, nor does throwing it remove the restriction with regard to first doublets. A player must first be able to complete the doublets thrown. If the player cannot move the whole throw he cannot take the corre sponding doublets, and he is not allowed another throw if he cannot move all the points to which he is entitled.

BACKHUYSEN, or BAKHUISEN, LUDOLF (1631-1708), Dutch painter, was born at Emden, in Hanover. He was brought up as a merchant at Amsterdam, but early discovered so strong a genius for painting that he relinquished business and devoted himself to art. He studied first under Allart van Everdingen and then under Hendrik Dubbels, two eminent masters of the time, and soon became celebrated for his sea-pieces. He was an ardent student of nature, and frequently exposed himself on the sea in an open boat in order to study the effects of tempests. His compositions, which are very numerous, are nearly all variations of one subject, and in a style peculiarly his own, marked by intense realism or faithful imitation of nature. In his later years Backhuysen employed his time in etching and calligraphy. He died in Amsterdam on the 17th of November 1708.

BACKNANG, a town of Germany, in the kingdom of Württemhas an interesting church, dating from the 12th century, and berg, 19 m. by rail N.E. from Stuttgart. Pop. (1900) 7650. It notable tanneries and leather factories, woollen and cloth mills. In 1325 Backnang was ceded to Württemberg by Baden. In the vicinity is the Wilhelmsheim sanatorium for consumptives.

BACKSCRATCHER, a long slender rod of wood, whalebone, tortoiseshell, horn or cane, with a carved human hand, usually of ivory, mounted at the extremity. Its name suggests the primary use of the implement, but little is known of its history, and it was unquestionably also employed as a kind of rake to keep in order the huge "heads " of powdered hair worn by ladies during a considerable portion of the 18th and the early part of the 19th centuries. The backscratcher varies in length from 12 to 20 in., and the more elaborate examples, which were occasionally hung from the waist, are silver-mounted, and in rare instances the ivory fingers bear carved rings. The hand is sometimes outstretched, and sometimes the fingers are flexed; the modelling is frequently good, the fingers delicately formed and the nails well defined.

As a rule the rod is finished off with a knob. The hand was now and again replaced by a rake or a bird's claw. The hand was indifferently dexter or sinister, but the Chinese variety usually bears a right hand. Like most of the obsolete appliances of daily life, the backscratcher, or scratch-back, as it is sometimes called, has become scarce, and it is one of the innumerable objects which attract the attention of the modern collector.

BACK'S RIVER (Thlewechodyeth, or "Great Fish"), a river in Mackenzie and Keewatin districts, Canada, rising in Sussex lake, a small body of water in 108° 20′ W. and 64° 25′ N., and flowing with a very tortuous course N.E. to an inlet of the Arctic Ocean, passing through several large lake-expansions-Pelly, Garry, MacDougall and Franklin. Like the Coppermine, the only other large river of this part of Canada, it is rendered unnavigable by a succession of rapids and rocks. It was discovered and explored by Sir George Back in 1834. Its total length is 560 m.

BACKWARDATION, or, as it is more often called for brevity, BACK, a technical term employed on the London Stock Exchange to express the amount charged for the loan of stock from one account to the other, and paid to the purchaser by the seller on a bear account (see ACCOUNT) in order to allow the seller to defer the delivery of the stock. The seller, having sold for delivery on a certain date, stocks or shares which probably he does not possess, in the hope that he may be able, before the day fixed for delivery, to buy them at a cheaper price and so earn a profit, finds on settling-day that the prices have not gone down according to his expectation, and therefore pays the purchaser an agreed amount of interest (backwardation) for the privilege of deferring the delivery, either in order to procure the stock, or else in the hope that there will be a shrinkage in the price which will enable him to gain a profit. (See also STOCK EXCHANGE).

BACON, FRANCIS (Baron VERULAM, VISCOUNT ST ALBANS) (1561-1626), English philosopher, statesman and essayist, was born at York House in the Strand, London, on the 22nd of January 1560/1. He was the youngest son of Sir Nicholas Bacon (q.v.). His mother, the second wife of Sir Nicholas, was a daughter of Sir Anthony Cooke, formerly tutor to Edward VI. She was a woman of considerable culture, well skilled in the classical studies of the period, and a warm adherent of the Reformed or Puritan Church. Very little is known of Bacon's early life and education. His health being then, as always, extremely delicate, he probably received much of his instruction at home. In April 1573 he was entered at Trinity College, Cambridge, where for three years he resided with his brother Anthony. At Cambridge he applied himself diligently to the several sciences as then taught, and came to the conclusion that the methods employed and the results attained were alike erroneous. Although he preserved a reverence for Aristotle (of whom, however, he seems to have known but little), he learned to despise the current Aristotelian philosophy. It yielded no fruit, was serviceable only for disputation, and the end it proposed to itself was a mistaken one. Philosophy must be taught its true purpose, and for this purpose a new method must be devised. With the

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