Question

Which of the following errors is/are eliminated by taking both left and right face observations in a theodolite?

• A. Error due to line of collimation not being perpendicular to the horizontal axis
• B. Error due to the horizontal axis not being perpendicular to the vertical axis
• C. Error due to eccentricity of the verniers
• D. Error due to imperfect graduations

Hint:

Face-change (transiting) cancels errors that reverse sign between face left and face right, such as collimation and trunnion-axis maladjustment, but not centering or graduation errors.

Answer 1

The Correct Option is A, B

Step 1: Recall what face left and face right (changing face) means.
In a theodolite, taking a reading with the vertical circle to the observer's left is the face left (FL) observation; after transiting the telescope and rotating the instrument through 180 degrees, the vertical circle appears on the right, giving the face right (FR) observation. Certain systematic instrumental errors reverse sign between FL and FR, so the mean of the two readings cancels that error.
Step 2: Examine option (A): line of collimation not perpendicular to the horizontal (trunnion) axis.
This error displaces the line of sight to one side of the true position by an amount that changes sign when the telescope is transited from face left to face right, so averaging the two readings eliminates it. Option (A) is correctly eliminated by changing face.
Step 3: Examine option (B): horizontal axis not perpendicular to the vertical axis.
This trunnion axis error tilts the horizontal axis and shifts the pointing direction, especially for elevated or depressed targets, by an amount that also reverses sign between the two faces. Taking the mean of both face readings eliminates this error too. Option (B) is correctly eliminated by changing face.
Step 4: Examine option (C): eccentricity of the verniers.
Eccentricity of the vernier, or the graduated circle not being exactly centred on the vertical axis, is eliminated by reading both verniers (which are 180 degrees apart on the circle) and taking their mean, not by taking face left and face right observations. Option (C) is not eliminated by the face-change technique.
Step 5: Examine option (D): imperfect graduations.
Errors from non-uniform graduation of the circle are reduced by distributing observations over different parts of the circle, such as in the method of repetition, not by taking both faces on the same setting. Option (D) is not eliminated by the face-change technique.
Step 6: Conclude.
Only the errors in (A) and (B) are eliminated by taking both left and right face observations.\[ \boxed{\text{(A) and (B)}} \]