Angular measurement accuracy in theodolite work: If you must observe an included angle with accuracy better than what a single vernier reading provides, which observing method should you prefer?

Introduction / Context:
The least count of a theodolite's vernier or digital display limits the precision of a single angle reading. Field procedures such as repetition and reiteration help surpass this limit by averaging multiple observations and cancelling systematic errors. The question asks which method directly improves the precision of one included angle beyond a single vernier read.

Given Data / Assumptions:

• You need a single included angle with accuracy finer than one vernier read.
• Instrument is properly centered and leveled.
• Time allows multiple pointings/turns.

Concept / Approach:
The repetition method measures the same included angle multiple times without resetting the circle to zero, successively adding the angle on the circle and then dividing the accumulated reading by the number of repetitions. Random pointing and reading errors are reduced roughly with 1/sqrt(n), and certain index errors cancel when face-left and face-right sets are combined.

Step-by-Step Solution:

Verification / Alternative check:
Reiteration closes a horizon by observing several angles around a station and adjusting; it is best for networks, not a single angle. Repetition targets one angle's precision directly.

Why Other Options Are Wrong:

• Reiteration: Excellent for traverses and angular networks, not optimal for a single included angle.
• Double observations (one face only): Lacks face reversal and accumulation benefits.
• Exactness: Not a defined field method.

Common Pitfalls:
Poor clamping or not recording face-left/face-right sets; both degrade the expected precision gain.

Final Answer:
Repetition