Two-point resection in plane tabling

Two point resection

Statement: locate on the sheet the station P occupied by the table when only two well-defined points A and B (already plotted as a and b) are visible from P. An auxiliary station Q is used. It is chosen near P so that A and B are visible from Q and the angles PAQ and PBQ are not too small, so that the rays intersect well.

Procedure

1. At Q: set up the table at Q and orient it approximately by compass or by eye. Pivot the alidade on a, sight A and draw a ray back; pivot on b, sight B and draw a ray back. The rays meet at q, the approximate position of Q.
2. Pivoting on q, sight P and draw a ray. Mark p1 on it by estimating the distance QP.
3. At P: set up the table with p1 over P and orient it by back-sighting Q (alidade along p1-q). Pivot on a, sight A and draw a ray back. It cuts the line q-p1 at p.
4. Pivoting on p, sight B and draw a ray. It cuts the ray q-b (drawn in step 1) at b′. The figure a, b′, p, q is similar to the ground figure A, B, P, Q but is turned by the orientation error, so the angle between ab and ab′ is the error of orientation.
5. Place the alidade along ab′ and fix a ranging rod R far away in that line. Then place the alidade along ab and turn the table until R is bisected. The table is now correctly oriented; clamp it.
6. Pivoting on a and b, sight A and B and draw rays back. Their intersection is the true position p of P. Check with a third point if one is visible.

   A *                        * B      (ground stations)

        a ---------------- b           (plotted points)
         \               /  \
          \             /    b'  <- ray p->B meets ray q-b
           \           /
            p --------
            |   (p lies on line q-p1)
            q   (auxiliary station Q)

   angle b-a-b' = error of orientation

The method gives a good result when Q is chosen so that the angles PAQ and PBQ are not very small. It needs two set-ups, so it is laborious, and it is used only when a third point is not visible.