In two theodolite method, curves are staked out by angular measurements only. Accuracy attained in this method is quite high. Thus, the method is used when higher accuracy is required and when the topography is rough or field condition is difficult.

The underlying principle of this method is that the deflection angle between a tangent (at any point on a circle) and a chord is equal to the angle which the chord subtends in the alternate segment. [Rule 4 under "Fundamental Geometry of Circular Curve '" in Lesson 37].

In this (Figure 38.2), two theodolites are used simultaneously placing one at the point of curvature (T₁) and the other at the point of tangent (T₂). Deflection angles for specified chord lengths are computed as defined in the Rankine's method. The deflection angles are set at the theodolites. Ranging from both the theodolites at the defined angles provide the location of the point along curve. Thus, the curve is set out by driving pegs at suitable location identified through the theodolites.

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