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LEFT BINARY ARITHMETIC 31 BINGEN rency system of the nations," and which met at Brussels in November, 1892, sep- arated without coming to any conclusion. The currency question in the United States influenced very materially the can- vass for the Presidency in 1896. It ap- peared, as the year wore on, that free silver doctrines had captured a majority of the Democratic party, and at the Chi- cago Convention (July 1th) this major- ity adopted a platform demanding "the immediate restoration of the free and urir- limited coinage of gold and silver at the present legal ratio of 16 to 1, without waiting for the aid or consent of any other nation," and that "the standard silver dollar shall be full legal tender equally with gold for all debts, public and private." William Jennings Bryan (q. V.) was nominated for the Presidency, but was decisively beaten by William McKlNLEY {q. v.), the Republican can- didate, who favored a single gold stand- ard, though he pledged himself to pro- mote action by international agreement. To this end he sent commissioners to France, Great Britain and Germany, in 1897, and they, together with the French Ambassador, laid various proposals be- fore the British Government, the chief of which were that the Indian mints should be reopened, and that Great Britain should annually purchase £10,- 000,000 of silver. The Indian Govern- ment, however, declined to agree to the first suggestion, and no action resulted. Bimetallism has ceased to be a political issue, but the continued tendency of silver to reach a closer parity with gold as a result of conditions during and after the World War was taken by advocates of the theory as a vindication of it. BINARY ARITHMETIC, a method of notation invented by Leibnitz, but which appears to have been in use in China about 4,000 years ago. As the term bi- nary implies, there are only two charac- ters in this notation; these are 1 and 0. By it, our 1 is noted by 1, our 2 by 10, 3 by 11, 4 by 100; 5 by 101, 6 by 110, 7 by 111, 8 by 1,000, 9 by 1,001, 10 by 1,010, etc. The principle is that mul- tiplies by 2 in place of by 10, as on the common system. BINARY ENGINE, usually an engine having one cylinder, the piston being impelled by steam, which, having done its work there, is exhausted into another part of the apparatus, where it is allowed to communicate its unutilized heat to some liquid volatile at a lower tempera- ture; the vapor of this second liquid, by its expansion in a second cylinder, yields additional useful force. Ether, chloro- form, and bisulphide of carbon have all been tried. BINARY LOGARITHMS, a system of logarithms devised by Euler for facilitat- ing musical calculations. Instead of hav- ing, like the common system of loga- rithms, 1 as the logarithm of 10, and 0.43429448 as the modulus, it had 1 as the logarithm of 2, and the modulus 1.442695. BINARY STAR, a star which, closely examined by the telescope, is found to consist of two stars revolving around their common center of gravity. In some cases they are colored differently from each other. In 1803 Sir William Her- schel discovered that Gamma Leonis, Epsilon Bootis, Zeta Herculis, Delta Serpentis, and Gamma Virginis are roi- volving double stars, and others, includ- ing Castor, have since been added to the list, a large proportion of the later dis- coveries having been made by Sherburne W. Burnham, Professor of Practical As- tronomy in the University of Chicago (1900). The period of revolution in vari- ous cases has been determined. It is found to vary from 26 to more than 1,200 years. BINARY SYSTEM, in zoology, a system of classification by which each sub-kingdom, class, order, etc., is perpet- ually divided into two, the one with a positive and the other with a negative character, till genera are reached. For instance, on this system, the animal sub- kingdom is divided into vertebrata and invertebrata, that is, animals which have, and animals which have not, vertebrse. BINARY THEORY, in chemistry, a hypothesis proposed by Davy to reduce the haloid salts (as NaCl) and the oxy- gen salts (as NaNOs) to the same type, the monad CI' being replaced by the monad radical containing oxygen (NO3)'. Acids are hydrogen salts, as HCl, or H(N03)'. A radical is only part of a molecule which can unite with or replace an element or another radical, atomicity for atomicity. Thus the dyad radical (SOi)" can replace two monad radicals, (NO,) '3, as in the equation Pb" (NOa)^ + Mg" (SO,)" = Pb" (SO4)" + Mg" (NOs)'j. A radical cannot exist in a separate state. BINGEN (bing'en), a German town in the province of Rhine-Hesse, Hesse; on the left bank of the Rhine, and the right of the Nahe. It is of considerable historical interest, containing the ruins of the Castle of Klopp, blown up by the French in 1689; the remains of a 12th century monastery; and the tower where