This method is usually adopted when measuring multiple angles that have a common vertex. In this method, angles are measured successively, starting from a reference station and ending at the same station. A double observation at the starting station checks the sum of all angles around the station. The sum must always equal 360°. This method is sometimes known as the horizontal angle observation direction method.
Let the station of the instrument be O while A, B, C, D and E are the stations seen to measure the angles AOB, BOC, COD, DOE and EOA. The following steps are involved in measuring angles by iteration.Centre the theodolite accurately over the ground station mark and level it.
Bisect a well-defined distant station A using the lower clamp and make the vernier to read zero degrees.
Unclamp the upper plate, swing the theodolite clockwise and bisect B accurately using the upper tangent screw.
Read both the verniers and take the mean of the readings.
Similarly, bisect the stations C, D, E, etc. successively and finally the starting station A. In each case, read both the verniers and take the mean of the readings.
Calculate the included angles by taking the differences between two consecutive readings.
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