Which of the following is true for the correction for curvature in levelling?
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 formula:
Cc = -0.0785 × D² (negative, D in km)
Meaning: the observed staff reading appears 0.0785D² metres too large
Cc = -0.0785 × D² (negative, D in km)
Meaning: the observed staff reading appears 0.0785D² metres too large
Refraction correction:
Cr = +0.0112 × D² (positive — partial compensation)
Combined correction:
C = Cc + Cr = -0.0785D² + 0.0112D² = -0.0673D² (still negative overall)
True staff reading = Observed – 0.0673D²
- 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).