lay a ruler parallel to the given courfes and draw the lines. their proper lengths; as bc 15, od 40, &c. If a fhip had run all the courfes and distances (in miles or leagues) except the laft in the preceding example, then e would reprefent the ships place and the feveral lines the path in which the run, and the right line from a (in the centre re prefenting the place failed from) to e, her true course and dif tance gained, and the N and S line or meridian a fher differ ence of latitude, and' the E and W line e f, her departure from meridian; (fuppofing the earth a plane.) the From a field book. A, the place of beginning, Thence N bearing E 29 2010 Ch.55 %. to b, 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 whofe meridian is parallel to that in the chart; fo by the help of a parallel, (as gb one fide of which lies in the last courfe 66° and the oppofit fide near the last line A f) the courses may be more eafily 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 base. 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 abcde, then take the courfe and measure the distance to another station; as, G, from which take the courfes 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 second 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 bede; the distances between the objects measured, by the fame fcale with which the stationary distance was measured, will show the true diftance between thofe objects, and the courses or bearings from one to the other by the circle will fhow their true bearings. EXAMPLES. Required the fituation of and distances between the following objects; viz. a b c d e; whofe courses or bearings from the station F are, North bearing Eaft 82° to a S-E 85° 30' to b. SE 68° 30' to c. thence, N 79° to c. S-E 76' to d G 9,7 ch N- E 69 20 to b. N-E 51° to e? - E 36 to d. NW 30 to d. From NE 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 cis S E 60°, that from a to d from 6 to c 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. N If a thip failed NE or N 45° E at the rate of 6 nots an hour 1 mile in ten minutes and the following bearings, NC. were taken, to delineate the coaft; viz. N bearing W 50° to a promontory, a, again in 2 minutes N W 12° 30' to b, E 9° to c (taken by two persons) 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' N-E 11'; what would be the height of the mountain and fituation of thofe objects? A. Height of the mountain is ,23 mi. b is fituated N 24° E 1,1 mi. from a, c S 89° E,5 mi. from b &c. as in the draught. The height of the mountain might have been determined by one altitude knowing its diftance from the veffel. The altitude of a steeple, hi, at a certain distance from it, k, being 28 and on advancing 30 yds. toward it, /, its altitude being 45'; what is its height ?* A. 35 yds. To find the contents of a quadrilateral or four fided figure, as a trapezium, rhomb, &c. RULE. Draw a line from the middle of one end to the middle of the other, which line is the mean length, and the perpendicular distance from each fide to the middle of this line is equal to the mean breadth of the figure; multiply the mean length and breadth of any figure together, and the product is the area or if the oppofit fides be of equal length, multiply the perpendicular breadth by the length of one fide, and the product is the area. (xy the area by the length for the folidity.) NE. |