¿ 93° and draw lines till they meet in the other point and form the angle required; the length of thefe lines are the les required. The angle at b, being larger than a right angle ob Eges the oppofit fide to be used as a bafe and the fhorteft distance romb to the oppofit fide is the perpendicular 3,7. Or lay out as a nany degrees from the given point as the oppofit angle a or c is lefs than 90° for the perpendicular required. The three fides given, to find the angles, &c. RULE. Take the length of one of the given lines; as a 9.5 to 5 draw a line of this length; a b, then take the length of another given fide; b 4,6 c, in the a 9,5 to b b 4,6 e 7,2 a EXAMPLES. 9,5 What is the contents of a stick of timber 8,5 ft long, whose eads are equal, and each of the following dimenfions, viz. one fide a 2,5 ft. b 1,8 ft and c 2 ft. ? here 8 fides are given, .2,5 bafe ,7 per. 1,75 area viz. a 2,5 14,875 folid. A. Folly Boat 8,5 t. length What is the area of a piece of land, two fides being meafured viz. 40 Chains and 54 Ch. the angle between the fides45° ? If a ship leaving a port fail S. E. by E. (i. e. S 5 points or 56°15'eaft) 95 miles; what would be her difference of latitude and departure, (ie. how far fouth and how far east would she be from the port ?) Here two angles are given, viz. 56° 15′ and 90°; for every meridian or degree of longitude cuts each degree or parallel of latitude at right angles, as at b. 56° 1590 33° 45′ angle required at c from thence a line to b is dif.of lat.54 m 56°15' S.E.byE.95 dift.failed. 33°45' departure from meridian of port 80 miles? A. dif. of lat. 54 } To measure, and delineate the fides, angles, &c. of any given plane. RULE. Take the courses with a compass suited to that purpose, and meafure the distances on each courfe; then on a fixed point; as, a place the centre of a circle,* femicircle or fomething that fhall reprefent the compafs, (or horizon;) and point off the firft courfe by the circle as it was taken with the compass, and measure the distance by a fcale of equal parts, place a point at the end as b; lay a fcale of equal parts at this point parallel to the fecond courfe on the circle, measure and mark the fecond distance, from this point lay the scale parallel to the third course, meafure and proceed as before through the whole, When a circle of brass, paper, &c., is used as above it should remain fixed till all the courses are taken, lay a ruler parallel to the given courfes and draw the lines their proper lengths; as be 15, cd 40, &c. If a ship had run all the courses and distances (in miles or leagues) except the laft in the preceding example, then ewould represent the fhips place and the feveral lines the path in which the run, and the right line from a (in the centre reprefenting the place failed from) to e, her true course and dif- . tance gained, and the N and S line or meridian a fher difference of latitude, and the E and W line e f, her departure: from the meridian; (fuppofing the earth a plane.) From a field book. A, the place of N bearing E 29 20/10 Ch. 55 l. to b. beginning, Thence Δ.Ο 66° 90 S.O Here the parallel lines reprefent eaft and weft, the femicircle, the compafs and the lines A, b, c, d, e, f, the fides of the land. Every line in any chart or plat will lie parallel to a line of the fame bearing in any circle or femicircle whose meridian is parallel to that in the chart; fo by the help of a parallel, (as gh one fide of which lies in the laft course 66° and the oppofit fide near the last line A f) the courses may be more easily and accurately marked out without moving the circle than in any other way. The area of any plane may be afcertained by refolving it into triangles; as by drawing lines from e to a, b, and c; the above figure may be refolved into four triangles, two of which may have one bafe. To measure the bearings, heights and distance of objects, and to delineate them on a plane. RULE. From a fixed ftation; as F, take the courses or bearings, to every object neceffary, with a compass or quadrant; as, to a b c d e, then take the course and measure the distance to another ftation; as, G, from which take the courses to the feveral objects as before; if the objects be not all visible from each station remove to a 3d, 4th, &c. Then by a circle from a fixed point reprefenting the first station, F, draw a line a fuitable length on each courfe; and lay off the distance its proper courfe to the fecond station, G, on this point place the circle in the fame pofition as at the first station, (viz. correfponding points parallel,) and draw lines their given courfes till they interfect thofe from the first station at the proper objects; as, a b c de; the distances between the objects measured, by the fame scale with which the stationary diftance was meafured, will fhow the true diftance between thofe objects, and the courses or bearings from one to the other by the circle will show their true bearings. EXAMPLES. Required the fituation of and distances between the following objects; viz. a b c d e; whofe courfes or bearings from the ftation F are, North bearing East 82° to a. S-E 85° 30' to b. SE 68° 30' to c. S-E 76 tod S-E 83 to e. Then S-E 50° to fta G 9,7 ch thence, NE 36° to a. From N E 69 20 to b. N E N-E 51° to e? A. The distance from a to b 6,8 Ch. from b to c 6,8 &c. their fituation as in the figure, the bearing or courfe from a to b from d to c is SE 60°, that from a to d from b to e SW 60° found by laying one fide of a parallel on the two points and extending the other fide to the centre G or F. If a fhip failed N E or N 45° E at the rate of 6 nots an hour 1 mile in ten minutes and the following bearings, &c. were taken, to delineate the coaft; viz. N bearing W 50' to a promontory, a, again in 2 minutes NW 12° 30' to b N-E 9° to c (taken by two perfons) again in 5 minutes N W 9° to c, N W 33 to b, and in 3 minutes S W 81 to a; at the fame time the altitude of a mountain N E 24° at d by a quadrant 11° and in 5 minutes the altitude of the mountain being 18 NE 11; what would be the height of the mountain and fituation of thofe objects ? |