implies in general the state or disposition by which a ship is best calculated for the several purposes of navigation.

Thus the trim of the hold denotes the most convenient and proper arrangement of the various materials contained therein relatively to the ship's motion or stability at sea. The trim of the masts and sails is also their most apposite situation with regard to the construction of the ship and the effort of the wind upon her sails. See SEAMANSHIP.

TRINGA, SANDPIPER; a genus of birds belonging to the order of grallae. See ORNITHOLOGY Tringa Index.

TRINIDAD, an island in the gulf of Mexico, separated from New Andalusia, in Terra Firma, by a strait about three miles over. The soil is fruitful, producing sugar, cotton, Indian corn, fine tobacco, and fruits. It was taken by Sir Walter Raleigh in 1595, and by the French in 1676, who plundered the island and then left it. It is about 62 miles in length, and 45 in breadth; and was discovered by Christopher Columbus in 1498. It is now in the possession of Britain. What was called a bituminous lake in this island, appears, from the experiments of Mr Hatchet, to be a porous 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; TRIGONOMETRY.

PLATE DXXXVII.

Fig. 1. Fig. 2. Fig. 3. Fig. 4. Fig. 5. Fig. 6. Fig. 7. Fig. 8. Fig. 9. Fig. 10. Fig. 11. Fig. 12. Fig. 13. Fig. 14.

W. Train Sculp. Case 5. Given a, b, the two sides. Sought A, B, c. A is found by Theor. XIII.; B by the fame; c by Theor. XII. Cor. 1.

Case 6. Given A, B, the two angles. Sought a, b, c. a and b are found by Theor. XII. Cor. 2.; c by Theor. XIII. Cor. 1.

The cases may be all refolved also by Napier's Rule, observing to make each of the things given the middle part; then two of the required parts will be found, and the remaining part is found by making it the middle part.

By Theor. II. and Cor. 1. each of the unknown parts is, in every case except the third, limited to one value.

The Cases of Oblique-angled Spherical Triangles.

In any spherical triangle let the sides be denoted by a, b, c, and the opposite angles by A, B, C respectively.

Let p, q denote the segments into which a side is divided by a perpendicular from the opposite angle, and P, Q the parts into which it divides the angle. Combining the fix quantities a, b, c, A, B, C, three by three, there are found fix distinct combinations or cases.

Case 1. Given a, A, b, two sides and an angle opposite 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 opposite 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 included angle. Sought A, B, c.

Find \( \frac{1}{2} (A - B) \) by Theor. XVII. and \( \frac{1}{2} (A + B) \) by Theor. XVIII. and thence A and B by the rule Sect. II. for finding each of two quantities whose sum and 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 between them. Sought a, C, b.

Find \( \frac{1}{2} (a - b) \) by Theor. XIX. and \( \frac{1}{2} (a + b) \) by Theor. XX. and thence a, b. All the sides and two angles 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 refolved into two right-angled triangles, the angles may be found by Case 4. of right angled triangles.

Case 6. Given A, B, C, the three angles. Sought a, b, c.

Draw a perpendicular, dividing any one of the angles into the parts P, Q. Find \( \frac{1}{2} (P - Q) \) by Theor. XVI. and then P, Q. The triangle being now refolved into two right-angled triangles, the sides may be found by Case 6. of right-angled triangles.

By Theor. X. XI. and Cor. each of the unknown parts is limited to one value in all the cases except in some of the subcases of the first and second.

As every oblique-angled triangle may be refolved into two right-angles, all these cases may be refolved by means of Napier's Rule, and the 15th proposition only. And the cases may be reduced to three, by using the supplemental triangle.

TRI

TRIHI LATAE, from tres, "three," and kilum, "an external mark on the feed;" the name of the 23d class in Linnaeus's Fragments of a Natural Method; consisting of plants with three seeds, which are marked with an external cicatrix or scar, where they are fastened within the fruit. See BOTANY.

implies in general the state or disposition by which a ship is best calculated for the several purposes of navigation.

Thus the trim of the hold denotes the most convenient and proper arrangement of the various materials contained therein relatively to the ship's motion or stability at sea. The trim of the masts and sails is also their most apposite situation with regard to the construction of the ship and the effort of the wind upon her sails. See SEAMANSHIP.