finely along the boundaries; let all the roads, rivulets, rivers, bogs, ponds, houses, castles, churches, beacons, (or whatever else may be remarkable) on the ground be distinguished on the map. Write the title of the map in a neat compartment either drawn, or done from a good copper-plate graving, with the gentleman's arms. Prick off one of your parallels with the map, and on it make a mariner's compass, and draw a flower-de-luce to the north, and this will represent the magnetical north; after which set off the variation, which express in figures, and through the centre of the compass, let a true meridian line be drawn of about 3 inches long, by which write True Meridian. Let a scale be drawn: or it is sufficient to express the number of perches to an inch, the map was laid down by. Draw a reference table of three, or if occasion be, of four or more columns: in the first insert the number of the field or holding: in the next its name, and by whom occupied in the third the quantity of acres, roods, and perches it contains: if you have unprofitable land, as bog or mountain, let the quantity be inserted in the fourth column; and if it be requird, you may make another column for statute measure, and then the map is completed. OF THE DIVISION OF LAND. SEC. VII. The method of dividing land, or of taking off or inclosing any given quantity. PROB. I. Given the area, an angle, and a side, in any plane triangle; to find the other sides and angles. Divide double the area by the given side; the quotient will be the perpendicular thereon, from the opposite angle; and by trigonometry the rest will be found. EXAMPLE. C B Suppose the area of the triangular field ABC to be 4A. 3R. 38P. the side AB. 57 perches, and the angle As Sine of B: CD::R: BC-48.81 Suppose AB 11. 50 chains; angle A 46°, and the A.R.P. area 9.0.32; to find the sides. 4 Answer, AC-22.24. BC=16.48. EXAMPLE III. Given the area 10 acres, base AB 384 yards; and the angle B, 65°; to find the sides and other angles. Answer, BC=278 AC 8366.5; C=71°.36' and <A=43° 24'. PROB. II. To divide a triangle into any number of parts, hav ing any assigned proportion to each other, by right lines drawn from one of its angles to the opposite side. Divide the base in the same proportion with the assigned parts; from these divisions draw lines to the proposed angle; and the thing required is done. EXAMPLE. C B A. Given the area of the triangle ABC = 12 and the 'base AB 18 chains; to divide it into two parts, one of which shall be double the other by a line drawn As 3:2: 18: 12-AE As 3 : 1 : : 18: 6=BE the parts required. EXAMPLE II. B A farmer having three sons, whose ages where 20, 25, and 30 years, respectively, proposes dividing the triangular farm ABC among them in such a manner, that each shall have a part proportionable to his age; Now supposing AB 71, BC 61, and AC 63 chs. What will be each son's share. The area will be found equal to 180 1 20.3 |