SURVEY OF A CLOSED FIELD

THE FIELD WORK

34. Preliminary Examination.-Before making the survey of a field, the surveyor should, if possible, walk around it and make in his notebook a sketch showing the boundary lines. He should mark all corners and study the field in a general way, so as to obtain a fairly approximate idea of its form and contents.

35. Measurements.-The sides of the field should first be measured. If they are straight lines, the measurements

are made as explained in Art. 15. In the case of an irregular boundary line, such as GNA, Fig. 15, which is the edge of a stream, one or more straight lines are run as close to the irregular boundary as possible. From these auxiliary lines are taken perpendicular measurements, called offsets,

to those points of the boundary where any considerable change in its direction occurs.

Thus, in Fig. 15, the straight line GA is run close to the shore line GNA. The distances GH, GJ, and GL from G to the points of GA opposite those points of G NA to which offsets are to be taken, are noted, and the offsets HI, JK, LM measured, when the line G A is being run. It will be observed that all distances along a main or auxiliary line are counted from the beginning of that line. For instance, instead of recording the distances GH, HJ, and JL, the distances GH, GJ, and GL are recorded. The parts GI, IK, KM, and MA of the curved boundary being nearly straight, the portion of the field between the right line GA and the curved line GNA is divided, approximately, into the right triangles G H I and ALM and the trapezoids HIJK and J K L M.

36. It is often difficult to measure directly along a line, as when the latter is determined by a fence. In such cases, an offset of 3 or 4 feet is measured from the line at each extremity, and the distance between the ends of the offsets measured. The direction of such short offsets is determined by the eye with sufficient accuracy.

37. Dividing the Field Into Triangles.-In order to make a plat of the field and calculate its contents, the field is divided into triangles by means of diagonals, which are measured on the ground. The surveyor should use his own judgment as to the best and most convenient diagonals to measure. He should avoid using diagonals that make very acute or very obtuse angles. Thus, in Fig. 15, DG is a better diagonal to use than BF.

38. Tie-Lines.-Obstacles often make it impossible to measure directly the diagonals of a field. In this case the lengths of the diagonals may be calculated by means of the principles of similar triangles. The process is illustrated in Fig. 16, which represents a field whose diagonals BD and BE cross a pond, and cannot, therefore, be measured directly. If the sides BA and EA are produced to F and G,

in such manner that AF and AG are proportional to AB and A E, and a line is run from F to G, a triangle FAG will be formed similar to BAE; for in these two triangles the angles at A are equal, and, as shown in geometry, two triangles having an equal angle included by proportional sides are similar. In order to make AF and AG proportional to AB and A E, fix the point F at some convenient distance from A. The distance A G that must be measured

along EA produced is determined from the proportion AF: AG = AB: AE; whence,

Having fixed F and G, measure FG. The diagonal BE can then be calculated from the proportion AF: FG = AB : BE, which gives

Such lines as FG are called tie-lines, because they tie the sides together. The diagonal BD can be calculated by means of tie-lines in a similar manner.

Instead of constructing a triangle such as AFG by producing two of the sides, a triangle, such as A F' G', may be constructed on the inside of the tract in substantially the same manner as described above for the triangle AFG. The distance AF' is first measured; the point G' is then

EXAMPLE.-In Fig. 16, let the lengths of the sides be as follows: AB = 320 feet, BC= 217 feet, CD = 196 feet, DE = 285 feet, and EA = 304 feet. It is required to calculate the length of the diagonal BE by means of a tie-line.

SOLUTION.-Let the line BA be prolonged 100 ft. beyond A; that is, make A F = 100 ft. Then A G must be equal to

Let the length of FG, as found by measurement, be 125 ft.; then,

320

In order to compute the length of BD, Fig. 16, by a tie-line, the side BC was prolonged a distance of 80 feet from C. (a) What distance must DC have been prolonged? (b) The length of the tie

line was found to be 98 feet; find the length of B D. Ans. {(a) 78t

266 ft.

39. The Location of Objects.—It is often desirable to locate important objects, such as buildings, roads, fences, etc., with reference to the main lines of the survey. This is most easily done by perpendicular measurements, or offsets, from those lines. In the case of objects very near the main line, the points from which the offsets should be measured can be estimated by the eye; in the case of a distant object, its perpendicular distance from the main line is determined by the method explained in Art. 27.

The points from which measurements are to be made should be determined as far as possible while the line is being run, and their distances from the next preceding corner should be noted and recorded in every case.

In Fig. 17, AB represents one side of a field from which certain objects are to be located. The point W (a spring,

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say) may be located by measuring the perpendicular distance O W, and noting the distance A O.

40. A point may also be located by measuring its distances from two points in the main line. Thus, in Fig. 17, W can be located by noting the distances AL and AM, and then measuring the distances L W and MW. In platting the survey, the point W can be readily located by laying off the distances AL and AM and from L and M as centers, with radii of .76 chain and .80 chain, respectively, drawing two intersecting arcs; their point of intersection is the position of the point W on the map.

FIG. 17

41. A rectangular building HGEF, Fig. 17, can be located by measuring the perpendicular distances of two of its corners from the main line. The dimensions of the building should be measured and recorded. The building can also be located by measuring the distance of one corner from two points in the main line; one of the points being in a straight line with one side of the building. Thus, in Fig. 17, the point I is in a straight line with the side GF, and J is any convenient point on the main line. The position of the building is determined by noting the distances AI and AJ, and measuring the distances FI and FJ.