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Errors eliminated by face observation

Short answer

Face observations eliminate collimation error, trunnion axis error, vertical index error, eccentricity, and non-parallelism of line of collimation and altitude bubble. Changing face reverses the error sign; the mean of FL and FR readings cancels them. Teporal adjustments are centering, levelling, and parallax elimination.

List out the errors which are eliminated by taking face observations of the theodolite; also explain the mechanism of elimination with neat sketches. Explain in brief about the temporary adjustment of theodolite.

Errors eliminated by face observations

Face observation means observing a point with the telescope in the face-left position (vertical circle on the left, FL), then again after transiting the telescope and turning the instrument through 180 degrees (face right, FR), and taking the mean.

ErrorCause
Line of collimation errorLine of sight not perpendicular to the horizontal axis
Horizontal (trunnion) axis errorHorizontal axis not perpendicular to the vertical axis
Vertical circle index errorVernier zero not exactly at the zero of the vertical circle when the telescope is horizontal
Eccentricity of the vertical circle / vernier (partly)Centre of the circle not on the axis
Error due to the line of collimation and altitude bubble not being parallelAltitude bubble axis not parallel to the line of sight

Mechanism of elimination

1. Collimation error. On face left the line of sight deviates from the correct direction by a small angle ee to one side. After changing face, the deviation is on the opposite side, so one reading is too large by ee and the other is too small by ee. The mean is free of the error.

  FL:   X-------- true line ---------> P
          \_ line of sight (+e)
  FR:   X-------- true line ---------> P
          /_ line of sight (-e)
        mean of FL and FR = true direction

2. Trunnion axis error. If one end of the horizontal axis is higher, the telescope sweeps an inclined plane. After changing face, the high end is on the opposite side, so the angular error changes sign and cancels in the mean. (The error is large only for steep sights.)

3. Index error of the vertical circle. If the vertical circle reads +i+i on face left when the line of sight is horizontal, the same error has the opposite effect on face right. The mean of the two vertical angles is free of ii.

For horizontal angles, both verniers (A and B, 180 degrees apart) are also read and averaged, which removes the error due to eccentricity of the centre of the circle.

Temporary adjustments

  1. Setting up and centering over the station mark using the plumb bob or optical plummet.
  2. Levelling up with the three foot screws and the plate level: centre the bubble with the level parallel to two foot screws, turn the instrument through 90 degrees and centre it with the third screw, and repeat until the bubble stays central in all positions.
  3. Elimination of parallax: focus the eyepiece until the cross hairs are sharp, then focus the objective on the target so that the image does not move relative to the cross hairs when the eye is moved.

✓ Answer checked by Claude Opus 5.5 (high effort)

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