---
title: "Levelling methods; errors eliminated by balancing"
subject: "Surveying I"
chapter: 5
key: "semester_3/surveying_i:principle-methods-leveling-balancing-sight"
source: https://www.bctengineer.com/q/semester_3/surveying_i/principle-methods-leveling-balancing-sight
site: BCT Engineering
---

# Levelling methods; errors eliminated by balancing

Surveying I · Chapter 5: Leveling

- Asked in: 2080 Baisakh, 2+3 marks; 2076 Asoj, 3+2 marks (asked 2 times)
- Video: [BALANCING OF SIGHT- ERROR DUE TO REFRACTION & CURVATURE OF EARTH- DISTANCE TO VISIBLE HORIZON](https://www.youtube.com/watch?v=cJE55IAX7kY) — llinson kh
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/principle-methods-leveling-balancing-sight
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-5

## Question

Explain the principle methods of levelling. Which types of errors are eliminated by balancing of sight? Illustrate with suitable examples.

## Short answer

Direct (spirit), trigonometric, barometric and hypsometric levelling. Balancing sights (equal BS and FS distances) eliminates errors from collimation, curvature, refraction and non‑adjustment of the bubble tube, because equal errors cancel in the difference. Example: with 0.002 m/20 m collimation error, 40 m BS and FS give no net error.

## Answer

#### Principle methods of levelling

1. **Direct (spirit) levelling:** a level and levelling staff are used; the difference in level is found from staff readings with a horizontal line of sight. It is the most accurate and most used method. Types: simple, differential, fly, check, profile, cross-section, reciprocal.
2. **Trigonometric levelling:** the difference of elevation is found from the vertical angle (theodolite) and the horizontal distance: $h = D \tan\alpha$. It is used in hilly ground and for inaccessible points.
3. **Barometric levelling:** based on the variation of atmospheric pressure with altitude. Used for reconnaissance.
4. **Hypsometric (boiling point) levelling:** based on the variation of the boiling point of water with altitude.

#### Errors eliminated by balancing of sights

Balancing of sights means keeping the backsight and foresight distances equal from each instrument position. The following errors are eliminated:

- Error due to **collimation** (line of collimation not parallel to the axis of the bubble tube).
- Error due to **curvature of the earth**.
- Error due to **atmospheric refraction**.
- Error due to **non-adjustment of the bubble tube** (the same effect as collimation error).

Each of these errors depends only on the sight distance (collimation in proportion to the distance, curvature and refraction in proportion to its square). Equal sights therefore give equal errors in the BS and FS, which cancel in the difference of the readings.

**Example:** an instrument has a collimation error of 0.002 m per 20 m. If the BS and FS are both 40 m, each reading is wrong by 0.004 m and the difference is correct. If BS = 20 m and FS = 60 m, the difference is wrong by $0.002 \times (60 - 20)/20 = 0.004$ m.

## Check yourself

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

1. Which method is the most accurate and most used?
   A. Barometric levelling
   B. Direct (spirit) levelling
   C. Hypsometric levelling
   D. Trigonometric levelling
   Answer: B. Direct levelling uses a level and staff with a horizontal line of sight. (Key point: Direct levelling)

2. On what principle does trigonometric levelling work?
   A. Atmospheric pressure variation
   B. Boiling point of water
   C. The vertical angle and distance, h = D tan α
   D. A horizontal line of sight and staff
   Answer: C. The elevation difference is found from the vertical angle and distance. (Key point: Trigonometric levelling)

3. Which set of errors is eliminated by equal BS and FS distances?
   A. Booking, staff and parallax errors
   B. Collimation, curvature, refraction, and bubble-tube non-adjustment
   C. Only curvature
   D. Staff verticality errors
   Answer: B. These errors are proportional to the sight distance, so equal sights cancel them. (Key point: Errors eliminated by balancing)

4. Collimation error is 0.002 m per 20 m. With BS = 20 m and FS = 60 m, what is the error in the difference?
   A. 0.002 m
   B. 0.004 m
   C. 0.006 m
   D. 0 m
   Answer: B. 0.002 × (60 − 20)/20 = 0.004 m. (Key point: Unbalanced sights example)

## Related in Surveying I

- [Profile levelling; balancing of sight](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aprofile-leveling-balancing-of-sight) — Surveying I, chapter 5
- [Errors eliminated by face observation](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aface-observation-errors-and-temporary-adjustment) — Surveying I, chapter 7
- [Personal errors in levelling](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Apersonal-errors-in-leveling) — Surveying I, chapter 5
- [Principle methods of levelling](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alist-principle-methods-leveling) — Surveying I, chapter 5
- [Face observation errors; optical theodolite](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aface-observation-errors-optical-theodolite) — Surveying I, chapter 7, asked 2×
- [Plotting theodolite traverse; repetition errors](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aplotting-theodolite-traverse-repetition-errors) — Surveying I, chapter 7