Instrument Reversal – Relationship Between Apparent Error and Actual Error When an instrument reading is taken in one position and then with the instrument reversed (e.g., telescope transited or vernier read on the opposite), the apparent error observed on reversal equals what multiple of the actual (true) index/collimation error?

Introduction:
Reversal (face left/right or direct/reverse) is a standard technique to detect and eliminate certain instrumental errors such as index error or collimation error. Understanding how the observed discrepancy relates to the true error enables correct adjustment or averaging procedures.

Given Data / Assumptions:

• The instrument has a small constant error (e.g., line of sight not exactly perpendicular to trunnion).
• Readings are taken in two opposite positions that reverse the sign of the error.
• The mean of the two readings is used to eliminate the error.

Concept / Approach:

When the instrument is reversed, the error contribution changes sign. The difference between the two readings (apparent error on reversal) equals 2 * (actual error). Hence, the true error is half the observed discrepancy, and averaging the two readings cancels the error entirely in the mean value.

Step-by-Step Solution:

Verification / Alternative check:

The same logic underlies double centering and face-left/face-right procedures in theodolite observations to remove collimation and index errors.

Why Other Options Are Wrong:

Equal, thrice, or half the actual error do not match the algebra of sign reversal; “none” is inapplicable because a precise relation exists.

Common Pitfalls:

Confusing the observed difference with the true error; forgetting to take the mean to eliminate the error in reported values.

Final Answer:

Twice the actual error