PROB. II. To take a survey of a piece of ground from any point within it, from whence all the angles can be seen; by the chain only. PL. 6. fig. 6. Let a mark be fixed at any point in the ground. as at H, from whence all the angles can be seen; let the measures of the lines HA, HB, HC, &c. be taken to every angle of the field from the point H; and let those be placed opposite to No. 1, 2, 3,4, &c. in the second column of the radii: the measures of the respective lines of the mearing, viz AB, BC, CD, DE &c. being placed in the third column of distances, will complete the fieldbook. Thus, Remarks. INo. Radii. Distan. 120.00 17.65 2 21.72 18 50 3 21.7428.00 4 25.34 20.00 5 17.2014.83 Close at the first station. If any line of the field be inaccessible, as suppose CD to be, then by way of proof that the distance CD is true, let the measure of the angle CHD be taken by the line oo, with the chain: if this angle corresponds with its containing sides, the length of the line DC is truly obtained, and the whole work is truly taken. Note, That in setting off an angle it is necessary to use the largest scale of equal parts, viz. that of the inch, which is diagonally divided into 100 parts, in order that the angle should be accurately faid down; or if two inches were thus divided for angles, it would be the more exact; for it is by no means necessary that the angles should be laid from the said scale with the stationary distances. PROB. III. To take a survey by the chain only, when all the angles cannot be seen from one point within. PL. 6. fig. 7. Let the ground to be surveyed be represented by 1, 2, 3, 4, &c. Since all the angles cannot be seen from one point, let us assume 3 points, as A, B, C, from whence they may be seen; at each of which let a mark be put, and the respective sides of the triangle be measured and set down in the fieldbook; let the distance from A to 1, and from B to 1, be measured, and these will determine the point 1; let the other lines which flow from A, B, C, as well as the circuit of the ground, be then measured as the figure directs; and thence the map may be easily constructed. There are other methods which may be used; as dividing the ground intó triangles, and measuring the 3 sides of each; or by measuring the base and perpendicular of each triangle. But this we shall speak of hereafter. PROB. IV. How to take any inaccessible distance by the chain only. PL. 8. fig. 8. Suppose AB to be the breadth of a river, or any other inaccessible distance, which may be required. Let a staff or any other object be set at B, draw yourself backward to any convenient distance C, so that B may cover : from B, lay off any other distance by the river's side to E, and complete the parallelogram EBCD: stand at D, and cause a mark to be set at F, in the direction of 4; measure the distance in links from E to F, and FB will be also given. Wherefore EF: ED: : FB: AB. Since it is plain (from part 1. theo. 3. sect. 4. and theo. 2. sect. 4.) the triangles EFDBFA. are mutually equiangular. If part of the chain be drawn from B to C, and the other part from B to E; and if the ends at E and C be kept fast, it will be easy to turn the chain. over to D, so as to complete a parallelogram; by reckoning off the same number of links you had in BC, from E to D, and pulling each part straight. Note, That in setting off an angle it is necessary to use the largest scale of equal parts, viz. that of the inch, which is diagonally divided into 100 parts, in order that the angle should be accurately laid down; or if two inches were thus divided for angles, it would be the more exact; for it is by no means necessary that the angles should be laid from the said scale with the stationary distances. PROB. III. To take a survey by the chain only, when all the angles cannot be seen from one point within. PL. 6. fig. 7. Let the ground to be surveyed be represented by 1, 2, 3, 4, &c. Since all the angles cannot be seen from one point, let us assume 3 points, as A, B, C, from whence they may be seen; at each of which let a mark be put, and the respective sides of the triangle be measured and set down in the fieldbook; let the distance from A to 1, and from B to 1, be measured, and these will determine the point 1; let the other lines which flow from A, B, C, as well as the circuit of the ground, be then measured as the figure directs; and thence the map may be easily constructed. There are other methods which may be used; as dividing the ground intó triangles, and measuring the 3 sides of each; or by measuring the base and perpendicular of each triangle. But this we shall speak of hereafter. PROB. IV. How to take any inaccessible distance by the chain only. PL. 8. fig. 8. Suppose AB to be the breadth of a river, or any other inaccessible distance, which may be required. Let a staff or any other object be set at B, draw yourself backward to any convenient distance C, so that B may cover : from B, lay off any other distance by the river's side to E, and complete the parallelogram EBCD: stand at D, and cause a mark to be set at F, in the direction of A; measure the distance in links from E to F, and FB will be also given. Wherefore EF: ED: : FB: AB. Since it is plain (from part 1. theo. 3. sect. 4. and theo. 2. sect. 4.) the triangles EFDBFA. are mutually equiangular. If part of the chain be drawn from B to C, and the other part from B to Ę; and if the ends at E and C be kept fast, it will be easy to turn the chain over to D, so as to complete a parallelogram; by reckoning off the same number of links you had in BC, from E to D, and pulling each part straight. |