Levelling set-up for true difference in elevation: To obtain the most accurate true difference in elevation between points A and B using a single set-up (to eliminate collimation error), where should the level be placed?

Introduction / Context:

Levelling aims to find the difference in elevation (ΔRL) between two points. Systematic errors—especially collimation (line-of-sight) error—can bias staff readings. A classic way to eliminate this error in a single set-up is to place the instrument equidistant from the two staffs.

Given Data / Assumptions:

• Single set-up differential levelling between A and B.
• Collimation error is small but nonzero.
• Curvature and refraction are negligible over short, equal sight lengths.

Concept / Approach:

If the instrument is at the midpoint, the back sight (BS) and fore sight (FS) distances are equal. Collimation error produces the same additive error on both readings and cancels in the difference (BS − FS). Thus, ΔRL is free of that error without needing instrument adjustment.

Step-by-Step Solution:

Verification / Alternative check:

Reciprocal levelling over obstacles generalizes this idea by reversing positions to eliminate curvature/refraction over long spans.

Why Other Options Are Wrong:

• Near A or B / any point: unequal sight lengths retain collimation error in ΔRL.
• Maximum staff reading point: irrelevant to error cancellation.

Common Pitfalls:

• Ignoring equality of sight distances—roughly equal is not exact when high precision is required.

Final Answer:

at the exact mid point of A and B