Methods of measuring horizontal angles

Methods of measuring horizontal angles

1. Ordinary (single angle) method: the angle is measured once on each face, reading both verniers on A and B; the angle = difference of the readings.
2. Repetition method: one angle is added several times on the circle and the total is divided by the number of repetitions. It is used when a single angle must be measured very accurately.
3. Direction (reiteration) method: several directions are measured from a reference object and the angles are found as differences; it is used when many angles are measured at one station.
4. Method of closing the horizon: a special case of reiteration in which the sum of all the angles around the station must be 360 degrees.

Repetition method

Repetition method. The same horizontal angle (say AOB) is added several times mechanically on the circle, and the circle is read only at the start and at the end. The mean angle = total accumulated angle / number of repetitions.

Procedure (angle AOB, three repetitions)

1. Set up, centre and level the theodolite at O, with the telescope on face left. Using the upper clamp and upper tangent screw, set vernier A to 0°00′00″ (or any convenient reading), and read both verniers (A and B).
2. Loosen the lower clamp, sight A, tighten the lower clamp and bisect A exactly with the lower tangent screw.
3. Loosen the upper clamp and swing the telescope clockwise to B. Clamp it and bisect B with the upper tangent screw. Read the verniers (the first value of the angle may be booked as a check).
4. Loosen the lower clamp, swing the telescope back to A, clamp it and bisect A with the lower tangent screw. The circle reading does not change, because the upper plate is clamped to the circle.
5. Loosen the upper clamp and sight B again; bisect it with the upper tangent screw. The reading now shows the angle added twice.
6. Repeat steps 4 and 5 once more for the third repetition. Read both verniers; the reading now shows the angle added three times.
7. Change face (transit the telescope to face right) and repeat the same three repetitions, usually swinging anticlockwise. Take the mean of both faces.

   A                       B
    \                    /
     \                 /
      ------ O ------
  (upper plate clamp: A -> B ; lower plate: B -> A)

The error of a single reading is divided by the number of repetitions, graduation errors are reduced because different parts of the circle are used, and fewer readings have to be taken.