Let ABCDEF be a field whofe plan is required, and let the points 1. 2. be eminences, from which a fufficient view of the field is obtained. First, Place the inftrument at 1, and take the angles AIB, BIC, CID, DIE, EIF, FIA, and draw lines in the several directions of these angles, and any other remarkable object. Then measure the distance from 1 to 2, and place your inftrument at 2; thence drawing lines in the directions of all the angles, and of fuch other objects as have been noted from the former ftation. Then thefe obfervations being planned, the interfection of the lines will point out the feveral corners and objects required. When two stations are not fufficient, three or more may be chofen, as the furveyor fhall fee caufa, measuring the distance between each station. And the interfections of the lines point out the objects, with their proper places on the plan. By this method very extenfive furveys may be taken. OF DIVIDING, OR LAYING OUT GROUND. PROBLEM I. To lay out rectangular ground. RULE. Divide the given area by the given fide, and the quotient wil be the fide required. EXAMPLE. I. What length of a rectangular field, whofe breadth is 400 links, will make 3 acres 2 roods? Ex. 2. What length of a ridge, 8 ells broad, will make 15 falls? Anf. 67+ ells. Ex. 3. What length of a ridge, 40 feet feet broad, will make 3 roods of land? Anf. 816 feet. Ex. 4. A field contains 32 acres 3 roods Scots, the breadth being 510 links, required the length. Anf. 6422 links nearly. Ex. 5. The length of a rectangular field, being 6575 links, required its breadth to contain 328 acres 3 roods. Anf. 5000 links. Ex. 6. A fquare field of 15 acres 2 roods 20 poles: It is required to find the length of its fide. Anf. 1250 links. Ex. 7. Required the fide of a fquare field in yards, whose content is 30 English acres. Anf. 831 nearly. Ex. 8. What length of a rectangular field will make 25 Englifh acres, the breadth being 1934 yards? Anf. 625 yards. PROBLEM II. To lay out a triangular field. RULE I. When the base is given, to find the perpendicular: Divide the area by the bafe, and twice the quotient will give the perpendicular. RULE 2. When the perpendicular is given, to find the base: Divide the area by twice the perpendicular, and the quotient is the base. RULE 3. When any part of a given triangle is to be cut off by a line parallel to one of the fides, it must be remembered that fimilar furfaces are to one another as the fquares of their correfponding fides; and vice verfa. EXAMPLE EXAMPLE I. Required the perpendicular breadth of a triangular field, the bafe being 520 links, and content 9 acres. Ex. 2. A triangular field of 630 acres is to be divided equally between two farmers; the base measures 6000 links, and the march is to be drawn parallel to the bafe; required how much of the perpendicular will fall to each. 6.000)63000.000 2 21000 the whole perpendicular. Nn 2 2 Note. The greater part of the perpendicular will fall to him whofe divifion lies towards the vertex. Ex. 3. Suppofe a field in the form of a right-angled triangle, whose base is 2500, and perpendicular 3000 links of the English chain, and that a hedge is planted parallel to the perpendicu lar, cutting off 20 acres, required the expence of planting the hedge, at Is. 6d. per yard. Anf. 361. 3s. old. Ex. 4. How long is the bafe of a field of 35 acres 3 roods 20 poles, the perpendicular being 3550 links? Anf. 2021 nearly. PROBLEM |