Which of the following is true for the correction for curvature in levelling?
Try it first: pick an option, then read the explanation.
Correct answer: B. Always negative and proportional to square of distance
Detailed Explanation: Curvature Correction Is Always Negative and Proportional to D²
Why B (always negative and proportional to D²) is correct: Earth curvature makes the horizontal line of sight diverge above the true level surface. This means staff readings are observed as larger than they actually are — the correction must be subtracted (negative). The magnitude grows with D².Understanding the Sign Convention
| Concept | Effect | Correction Sign |
|---|---|---|
| Earth curvature | The true level surface curves away below a horizontal line of sight. The staff's intercepted value appears too large. | Negative (subtract from observed reading to get true reading) |
| Atmospheric refraction | Bends line of sight slightly downward — partially counteracts curvature effect | Positive (added back, reducing the curvature correction by 1/7) |
- Curvature correction: always negative (observed reading appears too large).
- Curvature correction: proportional to D² (doubles of distance → 4× correction).
- Both curvature and combined corrections are negative (subtract from observed to get true).