Method of Repetition in Theodolite
In the method of repetition, the horizontal angle is measured a number of times and the average value is taken. It is usual to limit the number of repetitions to three with each face except in the case of very precise work. With large number of rep-etitions, errors can also increase due to bisections, reading the verniers, etc. Very large number of repetitions necessarily do not lead to a more precise value of the angle. However, a number of errors are eliminated by the repetition method. The procedure is as follows (Fig. 6.6).
1. Angle POQ is to be measured. Set up, centre, and level the theodolite at O. Ensure that the instrument is in the normal position, i.e., face left.
2. Set the instrument to read 0 o 00¢ 00?. For this release the upper clamp and bring the zero of the vernier (at vernier A) very close to the zero of the circle. Clamp the upper plate and using the upper tangent screw, coincide the two zeros exactly.
3. Loosen the lower clamp and rotate the instrument so that the left signal at P is approximately bisected. Tighten the lower clamp and using the lower tangent screw, bisect the signal at P exactly. Read the verniers at A and B. The reading should not change and they should read zero and 180 o .
4. Loosen the upper clamp and rotate the instrument clockwise to bisect the right signal at Q. Using the upper tangent screw, biscect the signal at approximately Q exactly.
5. Read the verniers at A and B. The reading at A gives the value of the angle directly. The reading on the vernier at B will be 180 o + the angle. Record both the readings.
Release the lower clamp and rotate the instrument clockwise to bisect the sig- mal at the left station P again. Using the lower tangent screw, bisect the signal
The method of repetition helps to eliminate the following errors.
(a) Errors caused by the eccentricity of the centres and verniers, by reading both the verniers and averaging.
(b) Graduation errors by reading from different parts of the circle.
(c) Imperfect adjustment of the line of collimation and horizontal axis by face-left and face-right observations.
(d) Observational errors and other errors tend to be compensated by the large number of readings.
However, the errors due to levelling cannot be compensated. This has to be done by permanent adjustment. Also a large number of repetitions tend to increase the wear of clamp and tangent screws.
Therefore, from the two sets,
Mean value of the angle = (1/2)(61 o 42¢ 47? + 61 o 42¢ 40? ) = 61 o 42¢ 44?