When the precision of measurement of a horizontal angle is desired to be more than the least count of the instrument, repetition method is used. In this method, the desired angle is measured several times, and average of the observed values is considered as the value of the angle. The precision thus attained is to a much finer degree than the least count of the vernier. The steps involved in the measurement of the horizontal angle, say POQ at O (Figure 22.1) by method of repetition are as follows:
Steps 1 to 7 is same as given in method of measurement of horizontal angle but record readings in the form of Table 22.2
8. Unclamp the lower plate, and turn the telescope to sight the signal P again. Tighten the lower clamp. Use the lower plate tangent screw for exact bisection of the signal P. (The vernier readings should be as it was during previous reading).
9. Release the upper clamp and turn the telescope to sight the signal Q. Tighten the upper clamp. Bisect the signal Q exactly using the upper tangent screw. The vernier A will give the value which is about twice the angle POQ.
10. Repeat steps (8) and (9) once again. The final reading of the vernier A will be approximately thrice the angle POQ.
If necessary, more repetitions can be done.
11. Divide the final reading by the number of repetition to obtain the value of the angle POQ. For every completed revolution of the circle to the final reading, if necessary, add 360°.
12. Change face of the instrument to the face right. The telescope will be in the inverted condition. Repeat steps (2) to (9), with the face right, and determine another value of the angle POQ.
13. Determine the average value of the angles obtained with the face left and face right.
The method of repetition eliminates different errors present in measurement of horizontal angle. These are as follows:
The errors due to eccentricity of verniers and centres get eliminated as readings from both the verniers are taken.
The errors due to inaccurate graduations get eliminated as the readings are observed at different parts of the circle.
The errors due to lack in adjustment of line of collimation and the horizontal axis of the instrument get eliminated for considering both faces readings.
Errors due to inaccurate bisection of the object, eccentric centering etc are eliminated partially as these get counter-balanced in different observations.
However, the errors due to slip, due to displacement of station or its signal do not get eliminated and moreover, these errors are of cumulative in nature.