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Rh to make way after six months' interval for Emile Ollivier. He still fought for reaction in his new office of president of the Senate. After the fall of the Empire he fled to England, but returned to France a year later to work for the fortunes of the prince imperial. After serious disturbances he was elected member for Ajaccio on the 11th of February 1872, his election being characterized by the prefect of Corsica as a regular conspiracy in favour of the Empire. In the Chamber, where he subsequently represented Riom, he formed the group of the Appel au Peuple. His first speech in the House was the occasion (May 21, 1872) of violent attacks by Audiffret-Pasquier and Gambetta. The death of the prince imperial in 1879 put an end to the serious chances of the Bonapartists, although Rouher sought to secure the recognition of Prince Napoleon, son of the ex-king Jerome, as heir to the imperial honours. Rouher lost his reason after a stroke of paralysis in 1883, and died on the 3rd of February 1884.

ROULERS (Flemish Roeselaere), a town of Belgium, in the province of West Flanders, 13 m. N.W. of Courtrai. Pop. (1904) 24,548. It is one of the oldest communes in Belgium, and was famous for its weavers in the 11th and 12th centuries. Its prosperity depends on the cultivation of flax and the manufacture of linen. The church of St Michael is remarkable for its lofty tower. Baldwin VIII., count of Flanders, died here in 1120, and in 1794 the French under Pichegru defeated the Austrians under Clerfayt.

ROULETTE, in mathematics, the locus of a point carried on a curve which rolls on another (fixed) curve. The name appears to have been used by Pascal to denote the cycloid (q.v.), which is the simplest roulette, being traced by a point on the circumference of a circle rolling on a straight line. The trochoids and epicycloid's (q.v.) are also simple roulettes, the latter being traced by points on a circle which rolls on another circle.

ROULETTE, a gambling game, of French origin. It is one of the two games played in the gambling-rooms at Monte Carlo, and the description here given, and the maximum and minimum stakes mentioned, are to be understood as applying to the game as it is there conducted. It is solely a game of chance, though so-called “systems” are innumerable, and some of them for a short period often appear to give the player an advantage. There is no possible system, however, which will assure success in the long-run, and it is herein that the ingenuity of the game consists. Every systematic method of play must depend upon increased stakes to retrieve past losses; and though a player with an unlimited capital might be practically certain to achieve his end in the course of time, the circumstance that there is always a maximum renders the bank invincible. The roulette table, covered with a green cloth, is made up of precisely corresponding halves with a circular space let into the middle holding the wheel, on either side of which the cloth is divided into spaces marked passe, pair, manque, impair, and the black and red diamonds. The wheel is divided into thirty-seven compartments, coloured, alternately black and red, numbered from one to thirty-six, the thirty-seventh being zero. Pair indicates even numbers, impair odd numbers, manque includes the numbers from 1 to 18; passe, from 19 to 36. The methods of staking are innumerable. The minimum stake is five francs, which must be placed on the table in the form of a five-franc piece, and not in smaller change. Rouge, noir, pair, impair, manque and passe are even chances; i.e. a stake put upon any of them is paid in corresponding coin should the player win, the exception being when the little ball which is spun round the wheel falls into zero, in which case the even money chances are put “in prison”—that is to say, laid aside until another spin, when if the bank wins they are lost, if the player wins he is allowed to retrieve his money. The maximum in the case of these chances is 6000 francs. Any one who desires to play en plein puts his stake on one of the thirty-seven numbers. If the ball falls into the corresponding number on the wheel, the stake is paid thirty-five times; and as there are thirty-seven numbers on the board, with the advantage already described of imprisoning the even-money chances when zero comes up, it will be seen that there is a steady percentage in favour of the tables and consequently against the player. This percentage is of course greatly increased when, as is often the case, a second zero, called double-zéro, is used. In some gambling-houses there is even a third one, called Eagle Bird. The maximum stake allowed en plein is 180 francs. The next most daring selection is à cheval, when the stake is placed on the line separating any two numbers, and if either of them wins the player is paid seventeen times, the highest stake permissible being 360 francs. Transversale pleine covers any three numbers in a line, the coin or note being placed on the line dividing any one of the numbers from the neighbouring even-money chance, as, for instance, between 4 and passe, or 6 and manque. A trarisversale simple covers six numbers, as, for example, where the line between 4 and 7 joins passe, or between 6 and 9 joins manque; and if any one of these numbers wins, live times the value of the stake is paid, the maximum here being 1200 francs. En carré includes four numbers, the coin being placed, for instance, on the cross between 1, 2, 4, 5, or 28, 29, 31, 32; eight times the value of the stake is paid, and the maximum is 760 francs. The dozens and the columns are also indicated on the board, the first dozen of course including 1 to 12. In each of the columns are twelve numbers in different order. A stake placed on either a dozen or a column is paid twice its value, the maximum here being 3000 francs. A stake constantly played is called the quatre premiers, which includes zero, 1, 2 and 3, the stake being placed on the line where zero and 1 join passe, or where zero and 3 join manque. If any one of these four numbers, including zero, wins, the stake is paid eight times; and four times eight being thirty two, there is a greater advantage to the table than when it loses en plein or on certain other chances. Zero can also be played in combination with any one or two of its neighbours; if with one of them the stake is paid seventeen times, if with two of them eleven times. A croupier sits on either side of the wheel; there is also one at each end of the table, their business being to assist the players in staking and recovering their winnings. Behind each of the former pair an official on a high chair super» vises the table. The croupier whose duty it is to spin the wheel waits for a time till stakes have been made, and then, exclaiming, “Messieurs, faites votre jeu!” sets the cylinder in motion, throwing the ball in the direction contrary to that in which the wheel revolves. When it is seen that the ball will soon fall at rest in one of the compartments of the cylinder the croupier gives the notice, “Rien ne va plus,” after which no stakes can be placed. When the ball finally rests in the compartment, the croupier announces the number and the even-money chances that win, as for instance rouge, impair and manque. He and his fellows then gather in with a rake all the money that has been lost, after which the winnings are paid and the game proceeds. At the beginning of play each table is supplied with a. certain large sum. When the bank loses this and is forced to send for another supply it is said to be “broken.”

ROUND (O. Fr. rond, Lat. rotundus, the Fr. is the source also of Du. rond; Ger., Swed., Dan. and Nor. rund), circular, spherical, globular. As a substantive, the word has several specific applications; thus it is used of the rung of a ladder, of a rounded cross-bar connecting the legs of a chair, of the circuit of the 