It is sometimes necessary to run a straight line from one point to another point that is not visible from the first point. If there is an intermediate point on the line from which both end-points are visible, this can be done by the balancing-in method described previously. If no such inter-mediate point exists, the RANDOM LINE method illustrated in figure 13-20, view A may be used.

The problem here is to run a line from A to B, B being a point not visible from A. It happens, however, that there is a clear area to the left of the line AB, through which a random line can be run to C; C being a point visible from A and B. To train a transit set up at A on B, you must know the size of the angle at A, You can measure side b and side a, and you can measure the angle at C. Therefore, you have a triangle in which you know two sides and the included angle. You can solve this triangle for angle A by (1) determining the size of side c by the law of cosines, then determining the size of angle A by the law of sines, (2) solving for angle A by reducing to two right triangles.

Suppose you find that angle A measures 1635. To train a transit at A on B, you would simply train on C and then turn 1635 to the right.

You may also use the random line method to locate intermediate stations on a survey line, In figure 13-20, view B, stations 0 + 00 and 2 + 50, now separated by a grove of trees, were placed at some time in the past. You need to locate stations 1 + 00 and 2 + 00, which lie among the trees.

Run a line at random from station 0 + 00 until you can see station 2 + 50 from some point, A, on the line. The transitman measures the angle at A and finds it to be 10800. The distances from A to stations 0 + 00 and 2 + 50 are chained and found to be 201.00 ft and 98.30 ft. With this information, it is now possible to locate the intermediate stations between stations 0 + 00 and 2 + 50. The distances AB and AD can be computed by ratio and proportion, as follows: 

These distances are laid off on the random line from point A toward station 0 + 00. The instrumentman then occupies points B and D; turns the same angle, 10800, that he measured at point A; and establishes points C and E on lines from points B and D through the stations being sought. The dist antes are computed by similar triangles as follows:

Determining the horizontal location of a point or points with reference to a station, or two stations, on a traverse line is commonly termed TYING IN THE POINT. Various methods used in the process are presented in the next several paragraphs.