TRIAL. 454 TRIASSIC SYSTEM. conducted before the chancellor or judge without a jury, substantially in the same manner as in a jury trial. The codes of reformed procedure and practice acts in most of the States regulate the details of trials in their various courts. See the articles Evidence; Jury; Pleading; Practice; Nonsuit; Nolle Proseqih; etc., and consult the authorities referred to under Plead- ing; Evidence; .Jury; etc. TRIAL BY JURY. The first comic opera by Gilbert and Sullivan (1875). Its success was due largely to its allusions to the Tichborne Case (see TicnBORXE Trial), then at its height. TRIANGLE (Lat. triaytgiilus, three-cor- nered, from Ires, three + angulus, angle). A figure formed by three intersecting lines. The sides of a plane triangle are straight lines, and those of a spherical triangle are geodetic lines or arcs of great circles. Triangles are called equi- lateral, isosceles, and scalene according as three sides, two sides, or no sides are equal. Of two angles of a plane triangle that opposite the greater side is the greater, but the angles do not vary as the sides, the ratio of two sides being equal to that of the sines of the opposite angles. (See Trigonometry.) In a spherical triangle the sines of the sides are proportional to the sines of the opposite angles. The sum of the angles of a plane triangle is 180° according to Euclidean geometry (see Geometry); but in the case of a spherical triangle the sum varies from 0° to 540°. The geometry of the triangle is extensive.; and ;> few of the most important propositions are given under Concurrence and Collinearity, and Maxima and Minima. The area of any plane triangle is given by the for- mulas A = ^ a"*! A = Vs (s-<i) (s-6) [s-c), where 6 is the base, h the altitude, a, b, c the sides, and s the semi-perimeter. In case the triangle is equilateral, / _af/3- , where a is the side. If one angle of a plane triangle is a right angle the triangle is called a right-angled triangle, the side opposite the right angle being the hypotenuse. The spherical triangle of one, two, or three right angles is called a rectangular, birectangular, or trirectangiilar triangle, re- spectively. The spherical triangle in which one, two. or three sides are quadrants is called a quadrantal. biquadrantal, or triquadrantal tri- angle, respectively. The area of a spherical tri- angle is given by the formula /^ = —j^^, where R is the radius of the sphere and E the spherical excess (q.v.), or A -f B -|- C — 180°. Consult Catalan, "Quelques formules relatives aux triangles reetilignes," in the Memoires cou- ronnes of the Brussels Academv (1891) ; Casey, Sequel to Euclid (5th ed.. Dublin, 1888). TRIANGLE. A musical instrument con- sisting of a steel rod bent into a three-sided figure open at one angle. It is hung by a string at the upper angle, and attached to the perform- er's left hand, to his desk, or to his drums. Mod- ern composers frequently use it in marches, dances, and fantasias. As it is only used for rhythmic figures, the music is written, as for drums and other instruments without fixed pitch, upon a single line. TRIANGLE SPIDER. A spider (Byptiotes caialus) of the family Uloboridae, common in the Eastern United States. Its web is usually stretched between the twigs of dead branches and at first appears like the fragment of an orb web. It consists of four plain radiating lines and a series of double cross-lines. From the apex of the triangle a strong line extends to the supporting twig. The spider stations itself on this line and draws up a slack which when loosened jars the whole web, entangling engaged insects in the cross-threads. Consult Wilder, in Popular IScience Monthhj, 1875. TRIANGULAR NUMBERS. See Number. TRIANGULATION. A method used in sur- veying when the area to be surveyed is of con- siderable extent. It consists, as the name indi- cates, in laying out a system of triangles by means of which intermediate points are located. See Surveying. TRIANON, tre'a'noN'. The name given to two villas in the Park of Versailles. The Grand Trianon was built in 1085 by Louis XIV. for Madame de Jlaintenon. and is a handsome build- ing, one story in height, containing interesting furnishings. In it the trial of Marshal Bazaine took place in 1873. The Petit Trianon, built by Louis XV. in 17fiO for Madame Du Barry, was afterwards a favorite resort of Marie Antoinette. It has a fine English garden with a Temple of Love, a lake, and several rustic cottages. TRI'AR'THRUS (Neo-Lat., from Gk. rpelt, treis, three -- ipSpov, arthron, joint). A genus of Ordovician trilobites with depressed convex carapace of elongate oval outline, of which the middle third is occupied by the broad axis. The thorax has 14 to 10 segments, in the middle of each of which there is a rounded knobj and the pygidium is small and semicircular. The best known species is Triarthrus Becki of the Utica shale of Nortli America. See Trilobita, TRIASSIC SYSTEM (from Lat. trias^ num- ber three, triad). A group of rocks immediately following the Carboniferous and preceding the Jurassic system. It is therefore the oldest for- mation of the Mesozoic era. Tlie rocks of this system were at first associated with the Permian under the name of the New Red Sandstone ( q.v, ) , but they were finally separated and designated as the Trias by German geologists, who divided the system into three series, the Keuper, Muschel- kalk, and Buntersandstein. The Rhoetic clays and sandstones were subsequently added to the system. Much difficulty has been found in subdividing the American Trias, and still more in correlating it with the European beds. Indeed, in the United States it is often difficult to separate the Triassic from the Jurassic, and consequently the plan adopted by the United States Geological Survey is to designate them as the Jura-Trias, thus con- sidering the deposits as one formation. The American Triassic is subdivided as follows: Pacific Border Atlantic Boeder rBajuvaric Series TRIASSIC ] Tirolic Series SYSTEM 1 Dinaric Series I ScTthic Series Newark Series The Pacific Coast beds are marine, while those of the Atlantic border are estuarine. In the Eastern States the Triassic formation consists
