Two-peg test with unequal sights: A level is set 25 m from peg A and 50 m from peg B. Staff readings (bubble centered) are 2.847 on A and 3.462 on B. Given R.L.(A) = 283.665 m and R.L.(B) = 284.295 m, determine the collimation error per 100 m (m/100 m).

Introduction / Context:
The two-peg test detects line-of-sight (collimation) error by comparing observed and true differences in level with unequal sight lengths. From the discrepancy, we compute the slope of the line of collimation and express it as an equivalent error per 100 m of sight length.

Given Data / Assumptions:

• Distances: d_A = 25 m, d_B = 50 m.
• Readings: r_A = 2.847, r_B = 3.462 (bubble centered).
• R.L.(A) = 283.665 m; R.L.(B) = 284.295 m → true difference B−A = +0.630 m.
• Collimation error is assumed constant per unit length during the test.

Concept / Approach:

Let e be the collimation error per metre (positive if the line of sight rises per metre away from the instrument). The observed difference is r_B − r_A = 0.615 m. The relation is:

Solving for e yields the error per metre; multiply by 100 for per-100 m value.

Step-by-Step Solution:

Verification / Alternative check:

With this e, recompute the expected observed difference: 0.630 + (−0.0006)*25 = 0.630 − 0.015 = 0.615 m, matching the observation.

Why Other Options Are Wrong:

0.015, 0.030, and 0.045 m per 100 m are too small; 0.075 m is too large and inconsistent with the measured discrepancy of 0.015 m over a 25 m sight difference.

Common Pitfalls:

Using total distance (75 m) instead of sight difference (25 m); forgetting to convert to per-100 m units; mixing the sign—report the magnitude for specification compliance.

Final Answer:

0.060 m