---
title: "Reciprocal levelling and its significance"
subject: "Surveying I"
chapter: 5
key: "semester_3/surveying_i:reciprocal-leveling-significance"
source: https://www.bctengineer.com/q/semester_3/surveying_i/reciprocal-leveling-significance
site: BCT Engineering
---

# Reciprocal levelling and its significance

Surveying I · Chapter 5: Leveling

- Asked in: 2081 Baisakh, 4 marks; 2074 Asoj, 4 marks; 2067 Asar, 4+2 marks (asked 3 times)
- Video: [Reciprocal Levelling|Curvature, Refraction and Collimation Correction](https://www.youtube.com/watch?v=UYZKNd7XKH0) — Master Civil Engineering
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/reciprocal-leveling-significance
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-5

## Question

Explain reciprocal levelling with neat sketches and its significance. How can precision be checked during reciprocal levelling?

## Short answer

Reciprocal levelling finds level difference across wide obstacles by taking readings from both banks. It cancels collimation, curvature and refraction errors because the two far sight lengths are equal. Precision is checked by comparing the two apparent differences; a large difference indicates error and observations should be repeated.

## Answer

**Reciprocal levelling** is the method of finding the difference of level between two points, such as the banks of a wide river or a valley, where it is not possible to set the instrument at the mid-point. Two sets of readings are taken, one with the instrument close to each point.

#### Procedure

1. Set up the level near A (on one bank), and take staff readings on A (near, $a_1$) and B (far, $b_1$).
2. Shift the level close to B (other bank) and take readings on B (near, $b_2$) and A (far, $a_2$).
3. Use the same instrument and staff, and keep the time between the two sets short, so that the atmospheric conditions are the same.

```text
        Set 1: level near A        Set 2: level near B
   A  [L]  ---------> B          A <--------- [L]  B
   a1 (near)   b1 (far)          a2 (far)    b2 (near)
```

#### Significance

- A single setting with unequal sight lengths contains the errors due to **collimation (line of collimation not parallel to the axis of the bubble tube)**, **curvature of the earth** and **atmospheric refraction**. The collimation error grows in proportion to the sight distance, and the curvature and refraction errors in proportion to its square, so they are large for the long sight across a river.
- In reciprocal levelling the far sight in each set is the same length, so the errors have the same magnitude and opposite effects on the two differences; they cancel in the mean:

$$
H = \frac{(a_1 - b_1) + (a_2 - b_2)}{2}
$$

- It gives the correct difference of level without balancing sights and without measuring the width of the river.

#### Check on precision

The two apparent differences should agree. The difference between them, $(a_1 - b_1) - (a_2 - b_2)$, equals twice the combined error in the far reading. If it is within the permissible error of the work (a few millimetres for a short crossing; the allowable closing error of $\pm 24\sqrt{K}$ mm, with K in km, for ordinary levelling is a guide), the work is acceptable. If it is large, the observations are repeated, preferably at a time of steady atmosphere (early morning or late afternoon).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. When is reciprocal levelling used?
   A. When the instrument cannot be set midway between points, such as across a wide river
   B. When points are on a slope of 1 in 10
   C. For short sights on flat ground
   D. For measuring horizontal angles
   Answer: A. It is used where sights cannot be balanced, for example across rivers or valleys. (Key point: When used)

2. Which errors cancel in the mean of the two sets?
   A. Staff reading errors
   B. Collimation, curvature and refraction errors
   C. Booking errors
   D. Errors in the BM value
   Answer: B. These errors are proportional to the sight length; the far sight is equal in each set, so they cancel in the mean. (Key point: Errors cancelled)

3. How is the true difference of level obtained?
   A. Either set alone
   B. The mean of the two apparent differences: [(a1 − b1) + (a2 − b2)]/2
   C. The difference of the two apparent differences
   D. The sum of the two apparent differences
   Answer: B. The errors have opposite effects in the two sets, so the mean is the true difference. (Key point: True difference formula)

4. How is precision checked?
   A. The two apparent differences should agree within permissible error
   B. The sum of BS equals the sum of FS
   C. The river width is measured
   D. The two sets must have the same readings on the near staff
   Answer: A. A large disagreement means the observations should be repeated, preferably at steady atmosphere. (Key point: Precision check)

## Related in Surveying I

- [Reciprocal levelling: RL of A, B at 1160.18 m](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Areciprocal-leveling-rl-b-1160-18) — Surveying I, chapter 5, asked 2×
- [Reciprocal levelling: RL of A, B at 1260.18 m](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Areciprocal-leveling-rl-b-1260-18) — Surveying I, chapter 5, asked 2×
- [Reciprocal levelling AB 250 m, RL 1450.500](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Areciprocal-leveling-ab-250m-1-252) — Surveying I, chapter 5
- [Reciprocal levelling: why and formula](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Areciprocal-leveling-derivation) — Surveying I, chapter 5, asked 3×
- [Principles of levelling; reciprocal levelling](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aprinciples-leveling-and-reciprocal) — Surveying I, chapter 5, asked 2×
- [Reciprocal levelling; RL of closed traverse stations](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Areciprocal-leveling-closed-traverse-bcdefgb) — Surveying I, chapter 5

## Related in other subjects

- [Reciprocal trigonometrical levelling formula](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Areciprocal-trig-leveling-formula) — Surveying II, chapter 3
- [Angular vs linear precision in traversing](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-angular-linear-precision-relation) — Surveying II, chapter 1, asked 2×
- [Reciprocal leveling, RL of hill top relation](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Areciprocal-leveling-when-hill-top-relation) — Surveying II, chapter 3
- [Significance of under and over-reinforced sections](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Asignificance-of-under-and-over-reinforced) — Design of RCC Structure, chapter 4