Let X, Y, and Z represent the ground location of the well defined objects whose plotted positions are x, y, and z, respectively. Let P be the plane table station whose plotted position, say p, is to be determined.
(i) Select a plane table position inside the great triangle XYZ and set up the table over P and orient it by judgment so that apparent line xy is approximately parallel to the imaginary side XY.
(ii) Pivoting the alidade on x, y, and z bisect the signals placed at X, Y, and Z in turn and draw rays. If the orientation of the table is correct, the three rays will meet at one point which is the desired location of p on the sheet. If not, the rays will form a triangle of error (Figure 35.6).
(iii)Choose a point p' inside the triangle of error such that its perpendicular distances from each ray is in proportion to the respective distances of P from the three ground objects. For selection of location of p', Lehmann's rules (1) and (3) need to be applied.
(iv) Align the alidade along p' x (assuming X to be the farthest station) rotate the table till flag at X is bisected, and clamp the table.
(v) Pivoting the alidade on x, y, and z repeat the process as in step (ii) above. If the estimation of p as p' is correct, the three rays will intersect at a point otherwise again a triangle of error will be formed but of smaller size and within the previous triangle of error. .
(vi) Estimate again the location of p' in the new triangle of error applying the rules, (i) and (iii), and repeat the steps (iv) and (v).
(vii) The method is repeated till all the three rays intersect at a point. The point of intersection is the required location p of the plane-table station P.