Resection after Solving Two Point Problem

The problem of finding plotted position of the station point took place by the plane table with the help of plotted positions of two well defined points is known as solving two point problem. Given figure shows the scheme of solving this.

                    Two-point problem

Let A and B be two well defined points such as lightening conductor or spire of church, the plotted positions a and b is already known. Problem now is to orient the table at P so that by resection its plotted position p may be obtained. The following steps may be followed to solve this problem:

(i)                 Select appropriate point Q near P such that the angles PAQ and PBQ are not accute.

(ii)                Roughly orient the table at Q and draw the resectors Aa and Bb to get the point 'q'.

(iii)               Draw the ray qp and locate p1 having estimated distance QP.

(iv) Shift the plane table to P and by back sighting to Q orient the table.

(v) Draw the resector Aa to obtain 'p'.

(vi) Draw the ray pB. Assume it intersect line bq at b1.

(vii) In the orientation of table due to the angular error the point's b and b1 are not coinciding. The angle bab, is the angular error in orientation. To make right it,

1. Fix a ranging rod at R along with ab,
2. Unclamp the table and rotate it until line ab sights ranging rod at R. Then clamp the table. This provides the correct orientation of the table which was used in plotting the points A and B.

(viii) The resectors Aa and Bb are drawn to get the correct plotted position 'p' of the station P.