364. Compass Surveying by Triangulation.

When the tract is bounded by straight lines, the area may be found by determining the position of each of the angular points with reference to one or more base lines properly chosen.

Fig. 165.

D

To do this, measure a base from the ends of which all the corners of the tract can be seen, and take their angles of position. There will thus be a system of triangles formed, giving data for calculating the content of the tract. Thus, if ABCDE (Fig. 165) represent a field, measure a base FG, and from F and G take the E bearings, or the angles of position, of A, B, C, D, and E. Calculate FA, FB, FC, FD, FE, and thence the areas of the triangles FAB, FBC, FCD, FDE, and FEA.

F

Then, ABCDE = FBC+FCD + FDE - FEA – FAB.

EXAMPLE.

To determine the area of a field ABCDE, I measured a base line FG of 12.25 chains, and at F and GI took the angles of position, as follow:-GFA = 63° 15′, GFB 27° 33', GFC = 35° 35', GFD = 58° 25', GFE = 92° 10′, FGA = 26° 5', FGD 72° 28', and FGE

=

FGB = 58° 30', FGC = 97° 12′, 37° 32'. 37° 32'. Fig. 165 is a plat of this tract, on a scale of 1 inch to 10 chains.

=

365. If no two points can be found from which all the corners can be seen, several points may be taken, and these all being connected by a system of triangles with a single measured base, or with several if suitable ground for measuring them can be found, the area may then be calculated.

&c. may be found, and thence the areas of IAB, IBC, ICD, &c.

Consequently, ABCDEFG

366. The same principle may be applied to surveying a farm by means of one or more base lines within the tract. If such lines be run, and the corners be connected by triangles with given stations in these bases, the tract may be platted and the area calculated.

In all cases of the application of this method, care should be taken to have the triangles as nearly equilateral as possible. If any of the angles are very acute or very obtuse, the amount of error from any mistake in measuring the base or in taking the angles is much increased.

CHAPTER VI.

TRIANGULAR SURVEYING.

367. THE method pursued in the last few articles of Chap. V. constitutes what is called triangular surveying. It consists in connecting prominent points with one or more base lines by means of a system of triangles,—the sides of these forming bases for other systems until the whole tract is covered.

The positions of these points having thus been accurately determined, the minuter configurations may be filled up by means of secondary triangles, or by any of the other methods of surveying of which we have already treated.

368. Base. In triangular surveying there is generally but a single base measured as a foundation for the work. This therefore requires to be measured with extreme care, since an error will vitiate the whole work. The precautions to insure extreme accuracy are such as almost to preclude the possibility of an error. Delambre, in speaking of a measurement of this kind in France, says,

"To give some idea of the precision of the methods employed, it is sufficient to relate the following occurrence during the measurement of the base near Perpignan:-One day, a violent wind seemed every moment about to derange our rules, by slipping them on their supports. After having struggled a long time against these difficulties, we finally abandoned the work. Three days after, on a calm day, we recommenced the work of that whole day, and we only found a fourth of a line [one-twelfth of a French inch] dif.