Two-peg test (collimation error) — A dumpy level was set at the midpoint between two pegs A and B, 50 m apart. Staff readings were A = 1.22 and B = 1.06. With the level set up near A, the readings were A = 1.55 and B = 1.37. Determine the collimation error per 100 m length of sight (state the magnitude and whether the line of sight is inclined upward or downward).

Introduction / Context:
The two-peg test is used to detect and quantify collimation error (line of sight not truly horizontal) in a level. By observing staff readings with the instrument at the midpoint and then near one peg, we can isolate the error and express it per unit sight length for practical adjustments and checks.

Given Data / Assumptions:

• Peg spacing: 50 m.
• Midpoint setup readings: A = 1.22, B = 1.06.
• Near-A setup readings: A = 1.55, B = 1.37.
• Near reading at A has negligible error; far reading at B carries most of the collimation effect.

Concept / Approach:
At the midpoint, the true difference in elevation between A and B is obtained because equal sight lengths cancel the error. With the instrument near A, compare the observed difference with the true difference; the discrepancy arises mainly from the far sight on B. Scale the error to 100 m to report a standard figure and determine the sign (upward/downward inclination).

Step-by-Step Solution:

Verification / Alternative check:
A line of sight tilted upward reduces far staff readings. The computed increase of 0.02 m over 50 m aligns with this behavior, confirming the sign and magnitude.

Why Other Options Are Wrong:

• 0.02 m inclined upwards: Magnitude per 100 m is incorrect (should be 0.04 m).
• 0.04 m inclined downwards: Wrong sign.
• None of these: Incorrect because option “0.04 m inclined upward” matches the calculation.

Common Pitfalls:
Forgetting to scale the error to 100 m; mixing up which staff reading carries the error when the instrument is near one peg.

Final Answer:
0.04 m inclined upward