Which of the following levelling methods is used to determine the difference of elevation of two points that are quite far apart, particularly when separated by a wide obstacle?
Correct Answer: C. Reciprocal levelling
📚 Detailed Explanation: Reciprocal Levelling Is Used for Two Distant Points Separated by an Obstacle
Why C (Reciprocal levelling) is correct: When the two points are separated by a wide obstacle (river, valley, gorge) where the level instrument cannot be placed midway, reciprocal levelling is used. Readings are taken from both ends, and the average of the two apparent differences gives the true height difference — automatically cancelling errors from curvature, refraction, and collimation.
Selection of Levelling Method Based on Situation
| Method | When Used | Key Feature |
|---|---|---|
| Simple levelling | Two points close together, visible from one setup | One BS, one FS; no change points |
| Differential levelling | Two points far apart but no major obstacle at midpoint | Multiple change points; instrument can be placed at midpoint areas |
| Reciprocal levelling | Wide obstacle (river, gorge) prevents midpoint setup; points are far apart | Readings from both sides; average cancels curvature, refraction, and collimation errors |
| Check levelling | Verifying BM values; closing a levelling loop | Returns to starting BM; misclosure calculated |
True height difference (reciprocal levelling):
h_true = [(BS_near_A – FS_near_A) + (BS_near_B – FS_near_B)] / 2
or equivalently:
h_true = [(Staff reading at B from A) – (Staff reading at A from B)] / 2
averaged over both setups
h_true = [(BS_near_A – FS_near_A) + (BS_near_B – FS_near_B)] / 2
or equivalently:
h_true = [(Staff reading at B from A) – (Staff reading at A from B)] / 2
averaged over both setups
- Reciprocal levelling = used when wide obstacle prevents placing instrument at midpoint.
- Automatically cancels curvature, refraction, and collimation errors by averaging both setups.
- Note: for two points “quite apart” without obstacles, differential levelling (multiple change points) is also valid; the question context implies an obstacle, making reciprocal the intended answer.