inhabited the country since called Dauphine. Liv. 21. c. 31.

TRIDAX, in botany, trailing star wort of Vera Cruz, a genus of plants in the class of syngenesia, and order of polygamia superflua; and, according to the natural method, ranking in the thirty-second order, papilionacea. It is a native of Vera Cruz, and has flowers in the form of butterflies.

TRI'DENT, n. s. Fr. trident; Lat. tridens. A three-forked sceptre of Neptune. His nature is too noble for the world: He would not flatter Neptune for his trident.

Shakspeare. Canst thou with fisgigs pierce him to the quick? Or in his skull thy barbed trident stick?

Milton.

Sandys on Job. He lets them wear their saphire crowns, And wield their little tridents. TRIDENTUM, an ancient town of Gallia Cisalpina, now called Trent. See TRENT. TRIENNIAL, adj. Fr. triennal; Lat. triennis. Lasting three years.

I passed the bill for triennial parliaments.

King Charles. Richard the Third, though he came in by blood, yet the short time of his triennial reign he was without any, and proved one of my best lawgivers.

Howel's England's Tears. TRIENNIAL PARLIAMENTS were established at the revolution in 1688; but were abolished, and the septennial parliaments enacted, upon the extinction of the rebellion in 1715.

TRIENS, in antiquity, a copper money of the value of one-third of an as, which on one side bore a Janus's head, and on the other a water-rat. TRIENTALIS, chickweed winter-green, in botany, a genus of plants belonging to the class of heptandria, and order of monogynia; and in the natural system ranging under the twentieth order, rotaceæ. The calyx is heptaphyllous; the corolla is equal and plane, and is divided into seven segments; the berry is unilocular and dry. There is only one species, viz. :-T. Europea, which is indigenous, and the only genus of heptandria that is so. The stalk is single, five or six inches high, terminated with five, six, or seven oval pointed leaves; from the centre of which arise on long foot-stalks commonly two white starry flowers, each generally consisting of seven oval and equal petals, succeeded by a globular dry berry, covered with a thin white rind, having one cell, and containing several angular seeds.

TRIER. From try. One who tries experimentally; test.

TRIESTE, a province of the Austrian empire containing the southern half of the kingdom of Illyria, and bordering on the Adratic, Croatia, and the government of Laybach. Its territorial extent is 5020 square miles, and its population 540,000. The majority are Sclavonians, but there are among them many Italians, Germans, and Jews. The surface is for the most part hilly, and the soil is, with the exception of some very fertile valleys, chalky, dry, stony, and requires a very toilsome cultivation. The Save forms the northern boundary. The products of this province are vines, olives, silk, and in general the fruits of the south of Europe. The sheep are commonly of a good breed; but of corn, the quantity raised is not large. The coast affords extensive fisheries, and the climate admits of making salt by evaporating the water of the sea. The province is divided into the four circles of Trieste, Goritz, Fiume, and Carlstadt.

TRIESTE, a circle of the government of the same name, in Illyria. It contains 1440 square miles, with 176,000 inhabitants, and is divided into the four arrondissements of Trieste, Duins, Capo d'Istria, and Rovigno.

TRIESTE, a large and thriving sea-port of Austria, the capital of a district in the Illyrian territory. It is situated near the north-west extremity of the gulf of Venice, and is divided into the Old and New Town. The former stands on a hill, with a castle on the top; the New Town called also Theresienstadt, is on level ground, intersected by a canal, and built with neatness and regularity. The population, at present about 40,000, is on the increase. Trieste has good streets, and a number of commodious buildings, but few that are large or striking, except the cathedral, the church that formerly belonged to the Jesuits, and the theatre: the cathedral is an ancient, the theatre a modern building. This is almost the only sea-port for a very large tract of the south of Germany, the Illyrian provinces, and part of the Sclavonian; in short, for the long tract of Austrian territory extending from Tyrol to Transylvania. Venice, though entitled since 1814 to all the privileges of an Austrian sea-port, does not, from its distance, interfere with its trade; while Fiume is a small place, less advantageously situated. Among the exports from Trieste are the produce of the mines of Idria, and even of Hungary; linen, tobacco, woollens from different parts of the Austrian dominions; also printed cottons from Switzerland. The imports consist of cotton, wool, hides, raisins, silks, rice, oil from the Levant; wheat chiefly from Odessa; sugar, coffee, and other tropical products from the West Indies and Brasil. The trade of the Adriatic is conducted in barks of twenty, thirty, or forty tons: these and much larger vessels enter with ease the inlet, in the form of a canal, which leads from the sea into the town, and has on each side quays for vessels to load and unload. The harbour dues at Trieste are inconsiderable. Each of the trading nations of Europe has a consul here. The quantity of goods conveyed by land to and from Trieste is very considerable; this conveyance is tedious, but not expensive. Ship-building is carried on with activity, and the sugar refining, the

making of white lead, soap, leather, paper, and wax. At some distance from the town are saltworks, or pools for the reception of sea-water, which in the summer months is evaporated by

the heat of the sun. Coal is obtained at a few miles distance. Trieste is built near the site of the Roman Tergeste; and there are some remains of the aqueduct, partly subterranean, which brought water to it from a distance of six miles. This town fell into the possession of Austria in 1382. In the fifteenth century it was a small place without trade; in 1719 it was made a free port by the Austrian government; in 1753 the harbour was enlarged, and a mole formed to shelter it from the south: it is open, however, to the Bora, an impetuous northeast wind, which, did it not blow off the land, would be dangerous to the shipping. The territory belonging to the town comprises 170 square miles, and a population of nealy 9000. Trieste belonged to France during five years, from 1809 to 1814. 212 miles S. S. W. of Vienna, and sixty-nine E. N. E. of Venice.

TRI'FALLOW, v. a. Lat. tres and Sax. realga, a harrow. To plow land the third time before sowing.

The beginning of August is the time of trifallow ing, or last plowing before they sow their wheat.

Mortimer.

TRIFISTULARY, adj. Lat. tres and fistula. Having three pipes. Many of that species whose trifistulary bill or crany we have beheld. Browne's Vulgar Errours. TRIFLE, v. n., v.a., & Belgic, tryfelen. TRI FLER, n. s. [n. s. To act or talk withTRIFLING, adj. out weight or digTRIFLINGLY, adv. nity; act or talk with levity or folly; mock; be of no importance: to make unimportant (obsolete): a thing of no moment: a trifler is one who acts with levity or folly the adjective and adverb following correspond with trifle.

S

'Tis hard for every trifling debt of two shillings to

be driven to law.

Spenser. When they say that we ought to abrogate such popish ceremonies as are unprofitable, or else might have other more profitable in their stead, they trifle and they beat the air about nothing which toucheth

us.

Do not believe,

That, from the sense of all civility,

Hooker.

I thus would play and trifle with your reverence. Shakspeare.

The instruments of darkness tell us truths; Win us with honest trifles, to betray us

In deep consequence.

Id. Macbeth. Threescore and ten I can remember well, Within the volume of which time I've seen

Those who are carried away with the spontaneous current of their own thoughts, must never humour their minds in being thus triflingly busy. Locke.

Rogers.

Young.

vine favor, the honours or afflictions of this life will To a soul supported with an assurance of the dibe equally trifling and contemptible. Triflers not ev'n in trifles can excel; 'Tis solid bodies only polish well. Brunetta's wise in actions great and rare, But scorns on trifles to bestow her care: Thus ev'ry hour Brunetta is to blame, Because the occasion is beneath her aim. Think nought a trifle, though it small appear; Small sands the mountain, moments make the year, And trifles life. Your care to trifles give, Or you may die before you truly live. renders the soul incapable of seeing, apprehending, Whatever raises a levity of mind, a trifling spirit, and relishing the doctrines of piety.

Id.

Law.

TRIFOLIATE, adj. Lat. tres and folium. Having three leaves.

Trifoliate cytisus restrained its boughs
For humble sheep to crop, and goats to brouze.

Harte.

TRIFOLINUS, a mountain of Italy in Campania, famous for its vines.-Plin. 14. c. 7.

TRIFOLIUM, trefoil, or clover, in botany, a genus of plants belonging to the class of diadelphia, and order of decandria, and in the natural system ranging under the thirty-second order, papilionacea. The flowers are generally in round heads; the pod is scarcely longer than the calyx, univalve, not opening, deciduous. The leaves are three together. According to Murray's edition of Linnæus there are forty-six species; of which seventeen are natives of Britain. See Lightfoot's Flora Scotica, Berkenhout's Synopsis, and Withering's Botanical Arrangements. The most remarkable are these:-1. T. alpestre, long-leaved purple trefoil, or mountain clover, is thus characterised by Mr. Afzelius. The spikes are dense; the corollas somewhat equal; the stipulas are bristly and divergent; the leaflets lanceolated; the stalks stiff, straight, and very simple. It grows in dry, mountainous, woody places, in Hungary, Austria, and Bohemia, &c., but is not said by Mr. Afzelius to be a native of Britain. 2. T. medium, according to Mr. Afzelius, has been confounded with the species pratense and alpestre; but it is to be distinguished from them by having loose spikes, corollas somewhat equal, stipulas subulate and connivent, and stalks flexuous and branched. It is found in dry elevated situations, especially among shrubs, or in woods where the soil is chalky or clay, in England, Scotland, Sweden, Denmark, &c. 3. T. meliloti officinalis, the melilot, has naked racemous pods, dispermous,

Hath trifled former knowings.

Id.

A man cannot tell whether Apollos or Albert Durer were the more triflers, whereon the one would make a personage by geometrical proportions, the other by taking the best parts out of divers faces to make one excellent. Bacon.

Old Chaucer doth of Topas tell,
Mad Rabelais of Pantagruel,
A later third of Dowsabell,
With such poor trifles playing.

Drayton's Nymphaid.

grows in corn-fields and by the way sides, but not common. The stalk is erect, firm, striated, branched, and two or three feet high; the rated; the flowers are small, yellow, pendulous, leaves ternate, smooth, obtusely oval, and serand grow in long close spikes at the tops of the branches; the pod is very short, turgid, transversely wrinkled, pendulous, and contains either one or two seeds. The plant has a very peculiar strong scent, and disagreeable bitter, acrid, taste, but such, however, as is not disagreeable

to cattle. The flowers are sweet-scented. It has generally been esteemed emollient and digestive, and been used in fomentations and cataplasms, particularly in the plaster employed in dressing blisters; but is now laid aside, as its quality is found to be rather acrid and irritating than emollient or resolvent. It communicates a most loathsome flavor to wheat and other grains, so as to render it unfit for making bread. 4. T. pratense, purple or red clover, is distinguished by dense spikes, unequal corollas, by bearded stipulas, ascending stalks, and by the calyx having four equal teeth. This is the botanical description of this species given by Mr. Afzelius, who, in the Linnæan Transactions, vol. I., has been at much pains to remove three species of the trifolium from the confusion in which they have been long involved; namely, the pratense, medium, and alpestre. The red clover is common in meadows and pastures, and is the species which is generally cultivated as food for cattle. It abounds in every part of Europe, in North America, and even in Siberia. It delights most in rich, moist, and sunny places; yet flourishes in dry, barren, and shady places. For an account of the mode of cultivating it, see RURAL ECONOMY. 5. T. repens, white creeping trefoil, or Dutch clover, has a creeping stalk, its flower gathered into an umbellar head, and its pods tetraspermous. It is very common in fields and pastures. It is well known to be excellent fodder for cattle; and the leaves are a good rustic hygrometer, as they are always relaxed and flaccid in dry weather, but erect in moist or rainy.

TRIFORM, adj. Lat. triformis. Having a triple shape.

The moon her monthly round

Etill ending, still renewing through mid heaven,
With borrowed light her countenance triform
Hence fills, and empties, to enlighten the earth.

Milton.

TRIFURCATED (from tres and furca, a fork), having three prongs.

TRIGA, in antiquity, a kind of car or chariot drawn by three horses; whence the name.

TRIGGER, n.s. Derived by Junius from Fr. trigue, and Lat. intricare. See TRICKER. A catch to hold the wheel on steep ground. The catch of a gun-lock.

The pulling the trigger of the gun with which the murder is committed, has no natural connection with those ideas that make up the complex one, murder.

Locke.

TRIGINTALS, n. s. Lat. triginta. Thirty. Trentals or trigintals were a number of masses to the tale of thirty, instituted by Saint Gregory. Ayliffe.

TRIGLA, in ichthyology, a genus of fishes belonging to the order of thoracici. The head is loricated with rough lines, and there are seven rays in the membranes of the gills. There are eleven species, of which the principal are these: 1. T. cuculus, the red gurnard. 2. T. gurnar

dus, or gray gurnard. 3. T. hirundo, the sappharine gurnard. 4. T. lyra, or the piper.

TRIGLOCHIN, in botany, a genus of plants belonging to the class of hexandria, and order of trigynia; and in the natural system ranging under the fifth order, tripelatoidea. The calyx is triphyllous; the petals are three; there is no style; the capsule opens at the base. There are three species; of which two are British, viz. :1. T. maritimum, or sea spiked grass, has ovate sexlocular capsules; the stalk is short; the spike long, and flowers purplish. It is frequent on the sea coasts. 2. T. palustre, arrow-headed grass, has an oblong trilocular capsule. The stalk is simple, eight or ten inches high; the leaves long and narrow; the flowers are greenish, and grow at the end of a long spike. It is frequent in moist ground. Linnæus says that cattle eat these two species with avidity.

TRIGLYPH, n. s. In architecture. A member of the frize of the Dorick order set directly over every pillar, and in certain spaces in the intercolumniations.

TRIGONELLA, fenugreek, in botany, a genus of plants belonging to the class of diadelphia, and order of decandria; and in the natural system arranged under the thirty-second order, papilionacea. The vexillum and aleæ are nearly equal and patent, resembling a tripetalous corolla. There are twelve species; of which the most remarkable is, T. fænum græcum, or fenugreek, a native of Montpelier in France. Fenugreek is an annual plant, which rises with a hollow, branching, herbaceous stalk, a foot and a half long, garnished with trifoliate leaves, placed alternately, whose lobes are oblong, oval, indented on their edges, and have broad furrowed foot-stalks. Fenugreek seeds have a strong disagreeable smell, and an unctuous farinaceous taste, accompanied with a slight bitterishness. The principal use of these seeds is in cataplasms and fomentations, for softening, maturating, and discussing tumors; and in emollient and carminative glysters.

TRIGONOMΈTRY, n. s. Gr. τριγωνος and μεто. See next page.

Trigonometry is the art of measuring triangles, or of calculating the sides of a triangle sought, and this is plain or spherical. Harris.

From the preceding definition we may deduce the following obvious consequences:

1. When an arc vanishes, its sine and tangent vanish also; and its secant and cosine are each equal to the radius.

2. The sine and the versed sine of a quadrant are each equal to the radius, its cosine vanishes, and its secant and tangent are infinite.

3. The versed sine of an arc and its cosine are together equal to the radius.

4. The chord of an arc is twice the sine of half the arc.

5. Of any arc less than a quadrant, the arc is less than its tangent, the chord less than the arc, and the sine less than the chord. For the sector CAB is less than the triangle CAT; and, by mensuration, the sector CAB =

AB, and the triangle CAT= СА 2

СА 2 СА 2 СА

whence

X arc

Ꭺ Ꭲ ;

X AB is less than .AT, and consequently A B is less than AT. In a similar way it may be shown that the chord A B is less than the arc A B, and the sine BD less than the chord A B.

6. An arc and its supplement have the same sine, tangent, and secant.

7. The radius, tangent, and secant, constitute a right angled triangle = CAT' the cosine, radius, and sine, constitute a similar right angled triangle; as do also the cotangent, radius, and co

1

cosect.

=

1

sin.

Again, AT: AC::CE: EM;

sin.

or tan. : rad.

:: rad. cot.; whence tan. cot. rad2; tan. = rad.2 1

=

cot. cot.

1

when radius is unity; cot. =

= when radius is unity.

tan.

rad.2 tan.

8. If M and N represent any two arcs, we have, from what has just been shown, cos. M · sect. M cos. N sect. N; sin. M· cosect. M sin. N cosect. N; and tan. M⚫ cot. M. tan. N cot. N. Whence cos. M: cos. N :: sect. N: sect. M; sin. M: sin. N:: cosect. N: cosect. M; and tan. M: tan. N: cot. N: cot. M.

9. The sine, tangent, &c., of an arc which is the measure of any given angle as ABC, fig. 3, &c. is to the sine of any other arc by which the same angle ABC may be measured, as the radius of the first arc to the radius of the second. For let A C and M N each measure the angle B; CD being the sine, DB the versed sine, A E the tangent, and BE the secant of the arc A C; NO the sine, O M the versed sine, MP the tangent, and BP the secant of the arc MN. Then by similar triangles we have CD: NO:: rad. BČ : rad. BN; AE: MP or BE: BP:: rad. BA : rad. B M; and BC: BD::BN: BO; or BA: BD:: BM: BO; hence BA: BA – BD::BM:BM-BO; or BA: AD::B M: MO; or BA: BM::AD: MO.

R any formula which has been investigated on the supposition that radius is unity, may be adapted to another radius R by substituting for sin., tan., sin. tan. &c., in the given expression, &c., and R' R' then reducing the expression to its most simple form.

The numerical values of the sines, tangents, &c., of every arc computated to any radius will exhibit the ratio of the sines, tangents, &c., corresponding to any other radius. A table containing such numbers is called a table of natural sines, tangents, &c.; and a table exhibiting the logarithms of those numbers is called a table of logarithmic sines, tangents, &c. Tables of natu ral sines, &c., are generally computed to radius unity; and tables of logarithmic sines, &c., are generally computed to the radius whose logarithm is 10, that the logarithm of the smallest sine likely to be required in computation, may have a positive, not a negative index; or that the corresponding natural sine may not be fractional.

The logarithm of radius in such tables being 10, the logarithm of rad." is 20, of rad.3 30, &c., the logarithmic sine and cosine of any arc is less P