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* CONTINENTAL SYSTEM. 347 CONTINUITY. sel violating this ordtr was to be confiscated with its cargo. Xapoleou responded by a decree dated Warsaw, January 25, ISO", which ordered the confiscation of all English or English eoloniaj merchandise found in the Uerman Ilansp towns. By a second Order in Council, Xovember 11, 1807, all harbors and places in France and her allies in Europe and the colonies, as well as in every country with which England was not at war, but from which the English flag was ex- cluded, were placed under the same restrictions as if strictly blockaded. These orders were followed b}' reprisals on the French side. By the Milan decree of December 17, 1807, strengthened bj' a second, of January 11, 1808, issued from the Tuileries, any vessel, of whatever nation, that had been searched by an English shij), or had submitted to be sent on a vo3'age to England, or paid any duty to the English Government, was to be declared denationalized, and treated as English. By the Treaty of Tilsit (1807) Russia consented to close her ports to English commerce, and in orler the more efl'eetually to annihilate such commerce, there appeared, August 3, 1810, the tariff of Trianon for colonial goods; this was extended by a decree of September 2 ; on Octo- ber 18 followed the decree of Fontainebleau, ordering the burning of all English goods, an order which was to be carried out with more or less modification in all coimtries connected with France. The consequence of the Continental System was undoubtedly the springing up upon the Con- tinent of many branches of manufacture to the loss of England; on the other hand, the price of foreign goods rose to an extraordinarj' height, enabling a few merchants to make fortunes, but sensibly aflecting the daily comfort of the middle classes. On the whole, the Continental System, both politically and economically, was a mis- take. Russia abandoned it in 1810, and with the breaking up of Xapoleon's power the system collapsed entirely. On the English side the en- forcement of the Orders in Council gave offense to the United States, and was one of the princi- pal causes of the War of 1812. Consult: Mahan, The Influence of 8ca Power upon the French Revolution and Empire (Boston, 1894) ; Thiers, Eistoire du consulat et de I'empire (Paris, 1S4.5-G2) ; Cime. Etude sur les tarifs de douane et les trail(^s de commerce (Paris, 1875) ; Henr.y Adama, Eisiory of the United States (Xew- York, 1889-91). See Nei'TK.ls; Napo- LEOX 1. CONTINGENT (from Lat. coniingere, to touch ) . A quota of troops, furnished to the eonnuon army by another branch of the service, or by different cooperating nations or armies. It was the naval contingent that saved the day in the defense of Ladysmith against the Boers in 1899. The various contingents of the interna- tional armies formed the common army under the leadership of Coimt Waldersee. the German commander, in the China campaign of 1900. The troops to be furnished by each of the United States under a call for volunteers by the Presi- dent is its quota. CONTINGENT REMAINBEB. See Ee- U.INRER. CONTINUED FRACTION. See Fraction. CONTINUITY (Lat. continmtas, from con- tinuus, uninterrupted, from contincre, to hold Vol. v.— 23. together, from com-, together -|- tcnere, to hold). In geometry, a vital principle which asserts that if from the natvire of a ])articular problem we would expect a certain number of solutions, then there «ill be the same number of solutions in every case, although some may be imaginary. E.g. a straight line and a circle in the sauie plane intersect in two points real, coincident or imaginary. The sum of the angles of a quadri- lateral is a perigon whether the quadilatcral is convex, cross, or concave. In this case, however, angles which have decreased and have passed through zero must be regarded as negative. By the principle of continuity theorems concerning real points or lines may be e.leiided to imaginary points or lines. This change can take jdace only when some element of the figure passes through either a zero value or an infinite value; e g. rotate an asymptote of the liyiierbola about the origin; before rotation it cuts the curve in two infinite points; after rotation it cuts it in two real points or two imaginary points. In case of the real points rotate it still further, and the.se pass to infinity, and imaginary points oc- cur, jlan.v jiropositions of elementary geometry may be inferred from this principle. It was first stated by Kepler, emphasized by Boscovich, and put into acceptable form by Poncelet in his Trait6 des proprictcs projectives des figures (2d ed., Paris, 1865-66). More generally continuity is a philo.sophical concept exemplified in space and time. It has been defined as a series of adjacent parts with common limits; as, infinite divisibility; that i.s, that however small the segment between two points, a further division is possible; but in modern analysis continuity is the essential prop- erty of a continuum. By a continuum is under- stood a system or manifoldness of parts possessed in varying degree of a property A, such that between any two parts distant a finite length from each other an infinite number of other parts may be intx-rpolated, of which those that are immediately adjacent exhibit only indefi- nitely small differences with respect to the prop- erty A. This is expressed by Cantor as a 'perfekt zusammenhangende !Menge,' a perfect concatenation of points ; e.g. all numbers ra- tional and irrational in any interval form a continuum. A concatenation not perfect is called a semi-continuum ; e.g. the rational or the irrational numbers in any interval. A straight line is said to possess continuity. B3- the continuity of the roots of an equation is meant that as a result of certain variations of the function, different pairs of roots may during the process become equal or imaginary, the total number always continuing the same — an example given by Leibnitz. By the continuity of a function of .r is meant the fact that in- definitely small and continuous changes in the value of a" between certain limits produce in- definitely small and continuous changes in the function. Consult : .Jordan, Cours d'amilyse (Paris, 1893) ; Poncelet, Trait6 des propriites projectives des fr/urrs (Paris, 18G5-66) ; Enci/- clopiidie dcr mathematischen Wissenschaflen, vol. i. (Leipzig. 1901) ; Cantor, ilathematischo Annalen, vols. x.x. and xxi. (Leipzig, 1882-83) ;
 * Mach, in The Open Court, vol. xiv. (Chicago,

1900 K CONTINUITY, Law of. A principle first formulated by Leibnitz (q.v. ), which is expressed