Theodolite Eccentricity – Identifying and Dealing with Non-coincident Axes Which statements about circle/vernier eccentricity in a theodolite are correct when the axes of rotation of the graduated circle and the verniers are not coincident?

Introduction / Context:
Eccentricity in a theodolite refers to geometric misalignment where the center of the vernier system does not coincide with the center of the graduated circle. Understanding its identification and mitigation is essential for accurate angle measurement and is a common exam topic in surveying instrumentation.

Given Data / Assumptions:

• A horizontally graduated circle read by two opposite verniers.
• Possible constant offset between vernier readings due to eccentricity.
• Instrument otherwise adjusted and functioning normally.

Concept / Approach:

When eccentricity is present, individual vernier readings are biased depending on where the circle is stopped. Using two opposite verniers and averaging their readings cancels the symmetric eccentricity effect, yielding the true angle. If the difference between the two verniers is a constant, a single vernier may be used by applying the appropriate constant correction. Recognizing that non-coincident axes define eccentricity solidifies option (a).

Step-by-Step Solution:

Verification / Alternative check:

Instrument manuals recommend reading both verniers and averaging as standard practice, explicitly to nullify circle/vernier eccentricity.

Why Other Options Are Wrong:

Since (a), (b), and (c) are all valid, options denying these statements are incorrect; therefore “All of the above” is the correct collective choice.

Common Pitfalls:

Forgetting to average opposite verniers; assuming random error rather than recognizing a repeatable systematic difference.

Final Answer:

All of the above