TRIAL. See JURY, and PROCESS. the Great. Under the Franks it was included | viso. It afterward belonged to Austria. In in the kingdom of Austrasia, and afterward March, 1848, it was taken by the revolutionists, belonged alternately to Lorraine and Germany, but the Austrians regained it on June 24, after till in the 10th century it was permanently an- a second bombardment. In 1866 it became nexed to the latter country. Subsequently, part of the kingdom of Italy. under the rule of archbishops, it became with TRIADITZA. See SOPHIA. its territory the second German electorate, divided into an upper and lower see, the latter connected with the episcopal capital at Coblentz. The city of Treves was invested with sovereign rights from 1580 till its occupation by the French in 1794. The whole electorate was in 1797 incorporated with France. In 1814 Treves was annexed to Prussia. The suppression of the priests' seminary, Dec. 31, 1873, and the subsequent imprisonment of the bishop, produced disturbances which were quelled in March, 1874. TREVIRANUS. I. Gottfried Reinhold, a German naturalist, born in Bremen, Feb. 4, 1776, died there, Feb. 16, 1837. He studied medicine at Göttingen, and after practising at Bremen became in 1797 professor of mathematics in the lyceum of that city. His works include Physiologische Fragmente (2 vols., Hanover, 1797'9); Biologie oder Philosophie der lebenden Natur (6 vols., Göttingen, 1802-'22); Erscheinungen und Gesetze des organischen Lebens (2 vols., Bremen, 1831-2); and with his brother Vermischte Schriften anatomischen und physiologischen Inhalts (4 vols., Göttingen and Bremen, 1816-21). II. Ludolf Christian, a German botanist, brother of the preceding, born in Bremen, Sept. 10, 1779, died in Bonn, May 6, 1864. He became professor of medicine at Berlin in 1807, of botany and natural history at Rostock in 1812, professor of botany and director of the botanic garden at Breslau in 1816, and afterward at Bonn. He is chiefly known by his Physiologie der Gewächse (2 vols., Bonn, 1835-'9). TRIBONIANUS, a Roman jurist, died A. D. 545. Under Justinian he occupied the offices of quæstor sacri palatii, of magister officiorum, of prætorian prefect, and of consul. He is described as a man of great natural abilities and learning, but avaricious and corrupt. In 528 he was one of the ten commissioners selected by the emperor to form his first Codex, and in 530 was placed at the head of the committee to compile the Pandects or digest of Roman laws, which was finished and promulgated in 533. He at the same time, with two others, compiled the four books of the Institutes of Justinian, published in 533; and the second Codex of that emperor, published in 534, was the work of Tribonianus and four other jurists. (See CIVIL LAW.) TRIBUNE (Lat. tribunus), originally, a Roman officer who presided over one of the three tribes, Ramnenses, Titienses, and Luceres. In the long course of Roman history the name came to be applied to various officers with widely different powers and duties. As originally constituted, the Roman legion consisted of 300 cavalry and 3,000 infantry; over the cavalry presided an officer called tribunus celerum, and over each 1,000 of the infantry a tribunus militum. The tribuni celerum disappeared with the overthrow of the monarchy. The office of the tribuni militum continued through the whole course of Roman history, but the manner of their appointment, their number, and their powers and duties were often changed. "Tribunes of the soldiers, with consular power," were first chosen in 444; and in succeeding years sometimes consuls and sometimes tribunes with consular power were chosen. In 367 the office was abolished, and thereafter only consuls were chosen. The name "tribune of the Servian tribes" is applied by historians to the administrative chiefs of the local tribes which were gradually added to the Roman commonwealth; it is supposed by Niebuhr and others that the tribunes of the trea TREVISO. I. A N. E. province of Italy, in Venetia, bordering on the gulf of Venice; area, 941 sq. m.; pop. in 1872, 352,538. It is level, excepting in the north, and is one of the most fertile regions of that part of Italy. The main river is the Piave. The chief products are hemp, flax, grain, wine, and timber. It is divided into the districts of Treviso, Ceneda, Castelfranco, Oderzo, Asolo, Valdobbiadene, Montebelluno, and Conegliano. II. A fortified city (anc. Tarcisium), capital of the prov-sury of later times were similar to them.-The ince, on the Sile, 15 m. N. N. W. of Venice; pop. in 1872, 28,291. It is the seat of a bishop, and has an unfinished cathedral, with works by Titian and Paul Veronese, a large Gothic church, a celebrated palace of justice, a lyceum, gymnasium, seminary, and academy of science. In the 13th century it was captured and oppressed by Ezzelino da Romano; in the 14th it was successively ruled by Francesco della Scala of Verona, by Venice, Austria, and Padua, and was with its territory in the possession of Venice from 1388 till the occupation of the town in 1797 by the French under Mortier, who in 1807 received the title of duke of Tre "tribunes of the people" were the most important of all the officers bearing the name. They were first appointed after the secession of the commonalty to the Mons Sacer, in 494. They were empowered to protect the plebeians against the usurpations of the patrician magistrates, and their persons were declared sacred and inviolable. They appear to have been originally two in number, and to have been elected for one year by the comitia of the centuries. In 471, by the Publilian law, the election was given to the comitia of the tribes. About the same time the number was increased to five, and from 457 B. C. until the end of the empire ten tribunes were annually elected. None but plebeians were eligible for the office; so that if a patrician were desirous of filling it, he was obliged to renounce his own order. The early incumbents of the office exercised authority within the city limits and over one mile of adjacent territory; the doors of their houses were ordered to be open day and night, and all persons taking refuge there were assured of protection. For similar reasons they were forbidden to absent themselves from the city for a whole day. Although their lawful power was originally merely auxilium, or the right to afford protection, they assumed within a few years the right to convoke the senate, and in 454, after a long struggle, secured the appointment of the three commissioners whose labors led to the codification of the laws of the twelve tables. During the second decemvirate the tribunate was suspended, but with the overthrow of that oligarchy it was restored with augmented powers; and as the tribes now included patricians and their clients as well as plebeians, the tribunes became the protectors of all classes of citizens. They now also acquired the right to be present at the deliberations of the senate, and to take part in its discussions, although not allowed to pass within the doors of the senate house; and hence they gradually assumed the privilege of intercession against any action taken by a magistrate, and by the interposition of their veto were enabled to annul any decree of the senate or stop any law, without cause or reason assigned. On the other hand, they sometimes interfered to compel the consuls to comply with decrees of the senate. About 132 B. C. they became senators by virtue of their office. They also assumed the right of commanding their viatores or attendants to seize a refractory magistrate, and imprison him, or even to hurl him from the Tarpeian rock. They possessed the exclusive power of proposing plebiscita to the comitia of the tribes; and after these had obtained by the Hortensian law, 286 B. C., the binding force of laws, the tribunes became a magistracy for the whole Roman people, in opposition to the senate and the oligarchical elements in general, although they had nothing to do with the administration of the government. Subsequent to 394 B. C. the veto of a single tribune sufficed to render a resolution of his colleagues void; and it was not until Tiberius Gracchus introduced the practice of appealing to the people to remove a tribune who obstinately adhered to his veto, that the harmonious working of the system was restored. During the latter period of the republic Sulla, in his reform of the constitution on an aristocratic basis, gave the tribunes merely the jus auxiliandi which they originally possessed. Pompey restored them to their former power, but under the empire their privileges became much restricted, although until the 5th century they continued to have the right of intercession against decrees of the senate and on beVOL. XV.-55 half of oppressed individuals. The emperors, though patricians, found it necessary to be tribunes, and the tribunicia potestas, conferred by the senate upon Augustus and his successors, was considered an essential part of the imperial dignity.-After Diocletian there was an officer called tribunus voluptatum, who was the superintendent of public amusements. TRICHINA SPIRALIS. See ENtozoa, vol. vi., p. 669. TRICHINOPOLY, or Trichinapalli, a town of British India, capital of a district of the same name in Madras, on the right bank of the river Cavery, in lat. 10° 47′ N., lon. 78° 43′ E., 190 m. S. S. W. of the city of Madras, with which it is connected by rail; pop. about 30,000. The fort of Trichinopoly is built on a granite rock about 600 ft. high. Outside the densely populated native town, which was formerly enclosed within the walls of the fortress, are extensive barracks, hospitals, public rooms, a church and Roman Catholic chapel, and the tomb of Bishop Heber, who died here. The surrounding country is fertile and populous; and the island of Seringham, which is here formed by the Cavery, is famous for the size and wealth of the Hindoo pagodas upon it. Trichinopoly is the southernmost station of British troops in India, and was occupied by 169 European infantry in 1872-13. Cotton cloths, hardware, harness, cheroots, indigo, and jewelry are manufactured and exported to different parts of India and Mauritius.-Trichinopoly, after the death of its last rajah in 1732, fell under the sway of the nawaub of Arcot, and subsequently changed hands several times, figuring conspicuously in the contests of the French and English for supremacy in India. It finally came under English government with the rest of the Carnatic in 1801. TRICOLOR. See FLAG, vol. vii., p. 250. TRICOUPIS, Spiridion, a Greek historian, born in Missolonghi in 1791, died in Athens, Feb. 24, 1873. He held important offices at Athens after the Greek revolution, which he had promoted, and was minister at London at various periods, lastly from 1850 till King Otho's downfall in 1862. He was a friend of Lord Byron, on whose death he pronounced one of his most celebrated orations. His chief work is Ιστορία τῆς Ἑλληνικῆς Ἐπαναστάσεως (“History of the Greek Revolution," 4 vols., London, 1853-'7; 2d ed., 1862). TRIER. See TREVES. TRIESTE (Ger. Triest). I. A district of Cisleithan Austria, forming a part of the Littorale, and bordering on the Adriatic, Görz, and Istria; area, 36 sq. m.; pop. about 132,000, of whom more than one half are Slovens, more than one third Italians, 8 per cent. Germans, and 43 per cent. Jews. II. A city (anc. Tergeste), capital of the district, and the principal seaport of Austria, beautifully situated at the head of the gulf of Trieste, or N. E. coast of the Adriatic, 70 m. E. N. E. of Venice and 210 m. S. W. of Vienna; pop. in 1870, including suburbs, 109,324. It consists of the old town, | for steamboat navigation and miscellaneous with a fortified castle, the new or Theresa town, and the new Joseph and Francis suburbs, with capacious streets and many squares and promenades. The finest public building is the chamber of commerce, formerly the exchange building. The monuments include the statue of Leopold I., and that by Rosetti of Winckelmann, who was murdered here. The cathedral is remarkable chiefly for walled-in antiquities. The recently opened Protestant church is one of the finest in the city. Trieste is the seat of a bishop, and has a theological seminary and many schools, besides a commercial and naval academy with an observatory, a museum rich in botany, and a public library. The "Adriatic Scientific Society" was established in 1874. The Tergesteum is the building of the Austrian Lloyd's, which company enterprises is one of the largest organizations of the kind in the world. Trieste is Italian in appearance and in language, though much German is spoken. There are Greek and English merchants. The constant arrival and departure of steamers make the port very lively; but the increase of commerce and population is of comparatively recent origin. In 1758 the population was only 6,000. In 1873 the arrivals of vessels numbered 8,046, chiefly Italian and Austrian, and the departures 8,219, with a respective tonnage of 898,437 and 909,402. The imports, chiefly coal, grain, iron, and oil, amounted to 140,164,000 florins, and the exports, mainly grain, flour, timber, and staves, to 92,377,000 florins. This was a decline from previous years, due to the competition of Hamburg; and the sanguine expecta tions of increasing the importance of Trieste in the India trade have been rather damped since the opening of the Suez canal. Its status as a free port is limited by the government monopoly of gunpowder, salt, and tobacco, and by an excise upon wine, spirits, and other articles. A breakwater for protecting the port was begun in 1865, and an abortive attempt was made in 1874 to fill up the malarious part of the canale grande, originally intended to supplement the port and the roads.-Tergeste was originally settled either by the Carnians or Istrians. The earliest historical mention of it as a Roman town dates from 51 B. C. Augustus laid the foundation of its prosperity. It was under the dominion of the Ostrogoths, and afterward of the. Greek emperors, till the period of the Lombard invasion. Subsequently Trieste became independent under its bishop, who bore the title of count, and who gradually sold to the inhabitants the privileges of a free city. Long wars ensued with the patriarchate of Aquileia, which claimed the allegiance of the bishops of Trieste, and in these wars Venice and Genoa also took part. The peace of Turin in 1881 acknowledged Trieste as an independent city, and the next year the citizens voluntarily submitted to the house of Austria. Charles VI. declared it a free city in 1719, and Maria Theresa made it a free port in 1750. It was taken by the French in 1797 and 1805. From 1809 to 1814 it belonged to the French province of Illyria, and subsequently to the Austrian kingdom of that name till 1849, when the so-called kingdom was dissolved. In reward for its fidelity to Austria during the revolutionary period of 1848-'9, when the port was blockaded by an Italian squadron, the city and district were invested on Oct. 2, 1849, with the privi leges of local self-government; and by the constitution of Dec. 21, 1867, they were made a constituent part of the Littoral province. TRIGG, a S. W. county of Kentucky, bordering on Tennessee, bounded W. by the Tennessee river and drained by the Cumberland river; area, 530 sq. m.; pop. in 1870, 13,686, of whom 3,806 were colored. The surface is hilly and the soil fertile in parts. Horses, cattle, mules, and swine are exported in great numbers. Iron, bituminous coal, and limestone are found. The chief productions in 1870 were 99,371 bushels of wheat, 589,820 of Indian corn, 16,114 of oats, 14,805 of Irish and 18,832 of sweet potatoes, 3,614,363 lbs. of tobacco, 18,442 of wool, 83,308 of butter, and 534 tons of hay. There were 2,673 horses, 1,908 mules and asses, 2,440 milch cows, 3,311 other cattle, 9,439 sheep, and 24,288 swine; 4 flour mills, 1 manufactory of pig iron, 4 tanneries, 4 currying establishments, and 3 saw mills. Capital, Cadiz. two methods of explaining the trigonometrical functions. The one, which may be called the ancient method, is presented in nearly all the text books in use before the middle of the present century; the other or modern method is followed in the best text books of recent date, and is fast superseding the former. In the old system the trigonometrical functions are lines, in the new system they are abstract numbers expressing the ratios of lines. A brief explanation of the modern system will enable the general reader to form an idea of the nature and objects of the science. Draw two lines, C A, C B, fig. 1, forming an angle at C. At any point in either line, say at P in the C PD = D P CD B A TRIGONOMETRY (Gr. τpíywvov, a triangle, and μετрεiv, to measure), the branch of mathematics which treats of the measurement of triangles. The practical object in nearly all applications of the science is to measure indirectly some height or some distance the direct measurement of which would be inconvenient or impossible. The labors of the civil engineer and line C B, erect a perpendicular to CB, interthe astronomer consist in great part in a con- secting CA in D. It matters not where in the stant application of the principles of trigonom-line C B the point P is; so long as the angle at etry, and the best treatises on the subject, like that of Prof. Peirce, include also treatises on surveying, navigation, and spherical astronomy. Trigonometry is divided into plane and spherical, the former treating of plane triangles, the latter of spherical triangles. In surveying and ordinary engineering operations plane trigonometry is mostly employed; in the higher problems of navigation, in engineering operations conducted on a grand scale, as in the coast survey, and in astronomy, spherical trigonometry is indispensable. But the general principles are the same in both branches. As spherical trigonometry consists essentially in an extension of the principles of plane trigonometry, we shall confine our attention to the latter. In every plane triangle there are six elements to be considered, three sides and three angles. The angles depend upon the proportions of the sides, and conversely the proportions of the sides depend upon the angles. If we know the three angles, we can find the ratio which any one side bears to each of the others, but we cannot find the length of any one of them; hence it is necessary for the complete determination of all the elements of a triangle, that we should know the length of at least one side. In calculating the unknown elements of a triangle certain ratios are employed, called "trigonometrical functions," which depend upon the angles. . One quantity is said to be a function of another when its value depends upon the value of the other. The ordinary method of measuring angles is explained under ANGLE.-There are C remains unchanged, the proportions of the The ratio of CP to C D, or CD' 1 1 1 and the tangent of 89° 3' is 60-3058. The re- | instruments from B to C and measuring the distance of 1,000 ft. between them. Any other distance than 1,000 ft. would have answered the purpose; but, for reasons which it is not necessary to enter into, it will save trouble and insure accuracy to have the distance BC as near as a rough guess will give to B H. Geometry tells us that if from the angle HBX = 28° 41' we subtract the angle HC B = 18° 4′, we shall get the angle CHB, between the two lines of sight. We thus find CHB = 10° 37'. The text books on trigonometry show that in every triangle the sines of any two angles are to each other as the sides opposite the angles. Looking in a table of natural sines (that is, of the actual values, and not the logarithms), we find the sine of 10° 37' is the decimal fraction 0-18424, and the sine of 18° 4' is 0·31012. The side opposite the angle CHB we have measured, and hence we have the proportion, or "sum in the rule of three:" as 0.18424 is to 0.31012, so is 1,000 to BH, the side opposite the angle HC B. Making the calculations, which are much more easily made by means of logarithms, we get 1683-28 ft. as the distance from B to H. We now apply the same process to the triangle BH X. The angle BHX is a right angle, and its sine is 1. The sine of 28° 41' is 0.47997; hence, as 1 is to 0.47997, so is 1683-28 to HX, the height which we wished to find; making the calculations, we find it to be 807 92 ft., or, taking the nearest foot, we say the peak is 808 ft. high. We have only made use of the sines; but all the other functions may come into play, according to the nature of the problem.-The great mathematicians of modern times have shown how trigonometry can be treated as a branch of pure algebra, and all its formulas developed without any reference to triangles. They have also shown how in this abstract form it can be applied to geometry, and a perfectly intelligible explanation given to what are called imaginary or impossible quantities. Treated in this manner, it constitutes the connecting link between the mathematical sciences of the present and those higher but as yet undeveloped branches of the mathematics of the future that have been referred to in the article GEOMETRY, and the foundations of which have been laid in the the opposite side of which is a lofty hill, whose Quaternions" of Hamilton, the Ausdehnungshighest peak I he can see with his telescope.lehre of Grassmann, and the "Linear AssociaHe wishes to know the perpendicular height tive Algebra" of Peirce.-Among the multiof the peak (H X) above the plain C B. Sup- tude of works on the science, the following posing him to be provided with the proper are of special excellence: A. De Morgan, instruments for measuring angles, he takes a "Trigonometry and Double Algebra" (Lonsight at the peak H and finds that the angle don, 1849); J Todhunter, "Plane Trigonomof elevation X B H is 28° 41'. Subtracting etry" (4th ed., London, 1869) and "Spherical this from 180°, he finds the angle H B C Trigonometry" (3d ed., 1871); L. Mack, Go151° 19'. Next he measures back from the niometrie und Trigonometrie (Stuttgart, 1860); river say 1,000 ft. to C, and then takes another and C. Briot and A. Bouquet, Leçons nouvelles sight at the peak and finds that the angle HCX de trigonométrie (4th ed., Paris, 1862). (For is 18° 4'. The rest is matter of calculation and the application of trigonometry to surveying, looking in the tables. The angles are quickly see COAST SURVEY, and SURVEYING.) and easily measured, and the only physical labor of any consequence is the carrying his C 1000 ft. 15119 B 1683.28ft FIG. 2. Χ TRILLIUM (Lat. trilix, triple, the parts being in threes), a genus of North American plants, |