In three point problem, if the orientation of the plane table is not proper, the intersection of the resectors through the three points will not meet at a point but will form a triangle, known as triangle of error (Figure 35.2). The size of the triangle of error depends upon the amount of angular error in the orientation.

The trial and error method of three point problem, also knon as Lehman's method minimises the triangle of error to a point iteratively. The iterative operation consist of drawing of resectors from known points through their plotted position and the adjustment of orientation of the plane table.

The estimation of location of the plane table depends on its position relative to the well defined points considered for this purpose. Depending on their relative positions, three cases may arise :

(i) The position of plane table is inside the great triangle;

(ii) The position of plane table is outside the great triangle;

(iii) The position of plane table lies on or near the circumference of the great circle.

In case of (iii), the solution of the three-point problem becomes indeterminate or unstable. But for the cases (i) and (ii), Lehmann,s rules are used to estimate the location of plane table.

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