Instrumental error and reversal: Which statements are correct concerning the use of reversal to diagnose/cancel systematic errors and how corrections are applied?

Introduction / Context:

Many surveying instruments permit reversal—such as face left/right with a theodolite, fore/after transiting the telescope, or reversing the bubble vial. Reversal exposes certain systematic errors (index, collimation, eccentricity) because those errors change sign with instrument reversal, while the true value remains constant. Averaging the two readings can thus cancel the bias.

Given Data / Assumptions:

• A reversible instrument (e.g., transit theodolite or tilting level) is available.
• Systematic error changes sign on reversal; random errors remain random.
• Observed discrepancy is the difference between the two reversed readings.

Concept / Approach:

When reversal changes the sign of an error, the observed discrepancy equals twice the actual error, since one reading has +e and the other −e. Therefore, the correction to the reading is half the observed discrepancy, with sign chosen to counteract the bias. Even a slightly defective instrument can yield acceptable results by taking both positions and averaging, thereby cancelling the reversible component of error.

Step-by-Step Solution:

Verification / Alternative check:

Repeat observations on multiple targets; if the averaged values converge and pass closure checks, the reversal method is functioning as intended.

Why Other Options Are Wrong:

• Options A–C are all correct statements; choosing any one ignores the rest. Hence ‘‘all the above’’ is appropriate.

Common Pitfalls:

• Applying half discrepancy with the wrong sign; the correction must oppose the bias.
• Assuming all errors reverse; some (e.g., scale graduation errors) may not cancel by reversal.

Final Answer:

all the above