TRINIDAD, an island in the gulf of Mexico, sepa-rated from New Andalusia, in Terra Firma, by astrait about three miles over. The soil is fruitful, pro-ducing sugar, cotton, Indian corn, fine tobacco, andfruits. It was taken by Sir Walter Raleigh in 1595,and by the French in 1676, who plundered the islandand then left it. It is about 62 miles in length, and45 in breadth; and was discovered by Christopher Co-lumbus in 1498. It is now in the possession of Britain.What was called a bituminous lake in this island, ap-pears, from the experiments of Mr Hatchet, to be aporous stone from which the mineral pitch exudes. TRINITARIANS, those who believe in the Trinity;those who do not believe therein being called Anti-trinitarians. Fig. 1. Fig. 2. Fig. 3. Fig. 4. Fig. 5. Fig. 6. Fig. 8. Fig. 9. Fig. 10. Fig. 12. Fig. 13. Fig. 14. Fig. 11. Case 5. Given a, b, the two sides. Sought A, B, c.A is found by Theor. XIII.; B by the same; c byTheor. XII. Cor. 1. CASE 6. Given A, B, the two angles. Soughta, b, c. a and b are found by Theor. XII. Cor. 2.; c byTheor. XIII. Cor. 1. THE cases may be all resolved also by Napier's Rule,observing to make each of the things given the middlepart; then two of the required parts will be found, andthe remaining part is found by making it the middlepart. By Theor. II. and Cor. 1. each of the unknown partsis, in every case except the third, limited to onevalue. The Cases of Oblique-angled Spherical Triangles. In any spherical triangle let the sides be denoted bya, b, c, and the opposite angles by A, B, C respec-tively. Let p, q denote the segments into which a side is di-vided by a perpendicular from the opposite angle, andP, Q the parts into which it divides the angle. Com-bining the six quantities a, b, c, A, B, C, three bythree, there are found six distinct combinations orcases. CASE 1. Given a, A, b, two sides and an angle op-posite to one of them. Sought c, B, C. B is found by Theor. XIV.; c by either Theor. XIX.or Theor. XX.; C by Theor. XVII. or Theor. XVIII. CASE 2. Given A, a, B, two angles and a side op-posite to one of them. Sought b, c, C. b is found by Theor. XIV.; c and C as in Case 1. CASE 3. Given a, C, b, two sides and the includedangle. Sought A, B, c. Find \frac{1}{2}(A-B) by Theor. XVII. and \frac{1}{2}(A+B) byTheor. XVIII. and thence A and B by the ruleSECT. II. for finding each of two quantities whose sumand difference are given. All the angles being known,also two sides, c is found by Theor. XIV. CASE 4. Given A, c, B, two angles and a side be-tween them. Sought a, b, C. Find \frac{1}{2}(a-b) by Theor. XIX. and \frac{1}{2}(a+b) byTheor. XX. and thence a, b. All the sides and twoangles being now known, C is found by Theor. XIV. CASE 5. Given a, b, c, the three sides. Sought A, B, C. Draw a perpendicular from any one of the angles,dividing the opposite side into the segments p, q. Find\frac{1}{2}(p-q) by Theor. XV. and then, from \frac{1}{2}(p+q) and\frac{1}{2}(p-q), find p, q. The triangle being now resolvedinto two right-angled triangles, the angles may be foundby Case 4. of right-angled triangles. CASE 6. Given A, B, C, the three angles. Soughta, b, c. Draw a perpendicular, dividing any one of the anglesinto the parts P, Q. Find \frac{1}{2}(P-Q) by Theor. XVI.and then P, Q. The triangle being now resolved intotwo right-angled triangles, the sides may be found byCase 6. of right-angled triangles. By Theor. X. XI. and Cor. each of the unknownparts is limited to one value in all the cases, except insome of the subcases of the first and second. As every oblique-angled triangle may be resolved in-to two right-angles, all these cases may be resolved bymeans of Napier's Rule, and the 15th proposition only.And the cases may be reduced to three, by using thesupplemental triangle. T R I TRIPLATÆ, from tres, "three," and hilum,"an external mark on the seed;" the name of the 23dclass in Linnaeus's Fragments of a Natural Method;consisting of plants with three seeds, which are markedwith an external cicatrix or scar, where they are fastenedwithin the fruit. See BOTANY. TRIM, implies in general the state or disposition bywhich a ship is best calculated for the several purposes ofnavigation. Thus the trim of the hold denotes the most convenientand proper arrangement of the various materials con-tained therein relatively to the ship's motion or stabilityat sea. The trim of the masts and sails is also their mostapposite situation with regard to the construction of theship and the effort of the wind upon her sails. See SEA-MANSHIP. TRINGA, SANDPiper; a genus of birds belong- T R I ing to the order of grallæ. See ORNITHOLOGYIndex. TRINIDAD, an island in the gulf of Mexico, se-parated from New Andalusia, in Terra Firma, by astrait about three miles over. The soil is fruitful, pro-ducing sugar, cotton, Indian corn, fine tobacco, andfruits. It was taken by Sir Walter Raleigh in 1595,and by the French in 1676, who plundered the islandand then left it. It is about 62 miles in length, and45 in breadth; and was discovered by Christopher Co-lumbus in 1498. It is now in the possession of Britain.What was called a bituminous lake in this island, ap-pears, from the experiments of Mr Hatchet, to be aporous stone from which the mineral pitch exudes. TRINITARIANS, those who believe in the Trinity;those who do not believe therein being called Anti-trinitarians. TRINITY, Fig. 1. Fig. 2. Fig. 3. Fig. 4. Fig. 5. Fig. 6. Fig. 8. Fig. 7. Fig. 9. Fig. 10. Fig. 12. Fig. 13. Fig. 14. Fig. 11.