This method is used to prolong or extend a line. Suppose you are extending line AB, shown in figure 13-16. You set up the transit at B, backsight on A, plunge the telescope to sight ahead, and set the marker at C. With the telescope still inverted, you again sight back on A; but this time do it by rotating the telescope through 180. You then replunge the telescope and mark the point C. Mark the point C halfway between C and C. This is the point on the line

Figure 13-17.-Bypassing a small obstacle by the angle off-set method.

AB you need to extend. If the instrument is in perfect adjustment (which seldom happens), points C and C will coincide with point C. For further extension, the instrument is moved to C and the procedure repeated to obtain D.

This method is applied when a tree or other small obstacle is in the line of sight between two points. The transit or theodolite is set up at point B (fig. 13-17) as far from the obstacle as practical. Point C is set off the line near the obstacle and where the line BC will clear the obstacle. At B, measure the deflection angle a. Move the instrument to C, and lay off the deflection angle 2a. Measure the distance BC, and lay off the distance CD equal to BC. Move the instrument to D, and lay off the deflection angle a. Mark the point E. Then, line DE is the prolongation of the line AB.