going to this object, take the reverse bearing; if both bearings agree, the attraction is probably at the other station. If the bearing of several objects in different directions is taken, and the reverse bearing from all shows no discrepancy, the attraction is undoubtedly at the other station. Or from both stations, take the bearing of some object as distant as possible, and from this object the reverse bearing to both stations; the attraction will be at the station to which the compass does not reverse truly. 135. Having decided where and what the amount of the attraction is, i. e. what the bearing of the line, as referred to the magnetic meridian, is, if the line is a portion of a straight line, it can be run to its termination, by first directing the compass accurately to the last station, and then, paying no attention to the needle, sighting forward to a third station, at the third station directing the compass to the second, and then forward to a fourth, and so on. (See also Article 140.) If at the termination of the line the needle does not settle in the magnetic meridian, the proper allowance must be made in running the next line; e. g. if the true bearing of the line has been decided to be N. 31° E., and at the termination the reverse bearing to the last station is S. 27° W., there is at this point an attraction which draws the north end of the needle 4° to the east of the magnetic meridian; if, now, upon directing the compass along the next line, the needle makes the bearing N. 85° W., the correct bearing (referred to the magnetic meridian) is N. 81° W. If the reverse bearing had been S. 32° W., the north end of the needle would have been attracted 1° to the west of the magnetic meridian, and the bearing of the next line, as shown by the needle, would be N. 80° W., when the correct bearing is N. 81° W. In the former case, for all lines from this point running east of north, the number of degrees read from the compass would be too small; for all lines running west of north, too large; while in the latter from the compass is LESS for any line than it should be, it will be too SMALL for all lines from that point, in the same or the vertical quadrant, too LARGE for all lines in the other two quadrants, and vice versa. It should be observed that, for measuring the angle which one line makes with another, local attraction causes no error, and the variation, secular or diurnal, no appreciable error. Since to measure an angle with the compass, it is necessary that the needle should point in a fixed direction during the time of taking the angle, without regard to what that direction may be. 5* CHAPTER XIII. SURVEYING WITHOUT A COMPASS. 136. An accurate survey of any surface can be made without a compass. As slight errors can hardly be avoided in using a magnetic needle in surveying, it is not generally used where land is very valuable, but the methods to be explained in this chapter are adopted. In regions impregnated with iron, it may also be necessary to dispense entirely with the compass, or at least to use it only to measure the angle which two adjacent sides of a field make with each other, without any reference to the magnetic meridian. 137. Two methods will be explained: I. Surveying with the Chain only. II. Surveying with the Chain and Goniometer. I. With the Chain only. 138. When the field is triangular. Measure the three sides, and then the area can be calculated by Rule III., Article 105, and the plot made according to Article 20. As a test of the accuracy of the measurements, a line from one of the corners, A, to a point, D, in the opposite side, whose distance from B or C is known, may be measured. If the length of AD, as measured in the field, is the same as when calculated by the rules of Trigonometry, or C B area of AB C, as previously found, the work may be assumed to be correct. 139. When the field is a polygon of more than three sides. made by first plotting the triangle A EF, then with A E as one side, the triangle A B E, and so on. To test the measurements, any other diagonal, as from C to F, may be measured, and if the angle CEF in the triangle C F E, when calculated, is found to be equal to the sum of the angles AEF, AEB, and BE C, the work is probably correct. The field should be divided by the diagonals into triangles as nearly equilateral as possible. 140. In measuring the sides of a field, in all cases, but especially in Chain Surveying, there should be great care that the chain-men keep on the line. If, for any reason, the termination of any line cannot be seen throughout its whole extent, the line should first be "ranged." This can be done by placing a straight stick, or rod, at the first point and a second on the line, or as near it as possible, at a convenient distance from the first; then a third must be placed in range with the first two; then the first must be carried forward beyond the second and third, and placed in range with them, and so on to the end of the line. These rods goes forward can put himself in range most accurately with a plumb-line. Stakes should be driven at all these points. If the line as ranged does not come out at the desired point, the distance which the stakes must be moved can be found by Art. 130. This process of ranging a line can be adopted to good advantage in cases of local attraction. ADX AE: ABX AC:: Area A DE: Area A B C, .. Area A B C Area ADEX АВ ХАС If the length of the side B C is required, it can be found by first finding the angle A of the triangle A D E, then in the triangle ABC we have two sides and the included |