Commencing at A, (Fig. 109,) draw the line AC east 5.50 chains, marking the points a and b at 1.35 and 4.10 chains respectively: at a and b erect the perpendiculars aG 1.30 and bB 1.80 chains. From C to G draw CG, which should be 4.40 chains long. At c, 1.50 chains from C, draw cD perpendicular to CG and equal to 2.30 chains. With the centre G and radius 1.20 chains, describe a circle, and from D draw the line DF 5.20 chains long, touching the circle at e, which should be 2.06 chains from F. At d, 2.88 chains from F, draw the perpendicular dE = .80 chains: then will ABCDEFG be the corners of the tract. Ex. 3. Required the plans and areas of the adjoining fields, of which the following are the field-notes, the two fields to be platted on one map. Ex. 4. Required the plan and areas of the adjoining fields from the following field-notes, tracing thereon the course NOTE. In the above field-notes the marginal references, such as "Brook 6.7," means to the point in which the brook crosses the line (6.7.) 256. Second Method. Instead of running diagonals, it may sometimes be more convenient to run one or more lines through the tract and take the perpendiculars to the several angles, as in the following example. Let the field be of the form ABCDEF, (Fig. 110.) Run the line AC, and take the perpendiculars ƒF, eE, bB, and dD. The field will thus be divided into triangles and trapezoids, the area of which may be calculated by the preceding rules. Fig. 110. E B D Thus, let the field-notes of the preceding tract be as follows: The calculation being performed thus:-In the first column are placed the distances to the feet of the left-hand perpendiculars. In the second the perpendiculars themselves. The numbers in the third column are found by subtracting each number in column 1 from the succeeding number in the same column. The numbers in column 3 therefore represent the distances Aƒ, fe, ed, and dC. The numbers in the fourth column are found by adding each number in column 2 to the succeeding number in the same column; they therefore are the sums of the adjacent perpendiculars. Those in the fifth column are found by multiplying the corresponding numbers in columns 3 and 4. They therefore are the double areas of the several trapezoids and triangles. Ex. 2. Required to calculate the content and make plats from the following field-notes : 257. Offsets. In what precedes, the sides have been supposed to be right lines. This is ordinarily the case except when the tract bounds on a stream. It then, if the stream is not navigable, generally takes in half the bed. Lands bounding on tide-water go to low-water mark. In all such cases the area and configuration of the boundary are most readily determined by offsets. A base is run near the crooked boundary, and perpendicular offsets are taken to the line, whether it be the middle of the stream or low-water mark. If the positions of these offsets are judiciously chosen, so that the part of the boundary intercepted between any two consecutive ones is nearly straight, the correct area may be calculated precisely as in last article. In the field-notes the distances are written in the column and the offsets on the right or left hand, according as they are to the right or left of the line run. |