---
title: "Two peg test, AB = 40 m, near B"
subject: "Surveying I"
chapter: 5
key: "semester_3/surveying_i:two-peg-ab-40m-inner-side-b"
source: https://www.bctengineer.com/q/semester_3/surveying_i/two-peg-ab-40m-inner-side-b
site: BCT Engineering
---

# Two peg test, AB = 40 m, near B

Surveying I · Chapter 5: Leveling

- Asked in: 2081 Baisakh, 6 marks
- Video: [How to calculate the correct elevations of stations using Two Peg Test of Level|Two Peg Test Method](https://www.youtube.com/watch?v=J9P7l23-BD4) — 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/two-peg-ab-40m-inner-side-b
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-5

## Question

In a two peg test operation the following staff readings were taken.

| Inst. stn | A | B | Remarks |
|---|---|---|---|
| At midpoint | 1.464 | 1.154 | Distance between A and B = 40 m |
| Near B, inner side from B | 1.642 | 1.321 | |

Compute the collimation precision and, if collimation error is there, compute the correct staff reading during II set up for making the collimation line horizontal.

## Short answer

True diff: 1.464-1.154=0.310 m (B higher). Second setup: 1.642-1.321=0.321 m. Error=0.011 m in 40 m, collimation precision 1/3636 (27.5 mm/100 m), line upward. Correct reading on A for horizontal sight: 1.631 m (B=1.321 m).

## Answer

**Data:** AB = 40 m. Setup 1: instrument at the mid-point, A = 1.464, B = 1.154. Setup 2: instrument near B on the inner side (between A and B), A = 1.642, B = 1.321.

*Assumption:* the distance of the setup from B is not stated, so the instrument is taken as practically at B (error at the near staff B negligible). The whole error then appears on the far staff A (distance 40 m).

#### Step 1: True difference of level

$$
\text{True difference} = 1.464 - 1.154 = 0.310\ \text{m}\ (\text{B higher than A})
$$

#### Step 2: Apparent difference from the second setup

$$
1.642 - 1.321 = 0.321\ \text{m}
$$

#### Step 3: Collimation error and precision

$$
e = 0.321 - 0.310 = 0.011\ \text{m in 40 m}
$$

$$
\text{Collimation precision} = \frac{0.011}{40} = 0.000275 = \frac{1}{3636}\ \ (\text{i.e. } 27.5\ \text{mm per 100 m})
$$

The usual permissible limit for ordinary levelling is about 10 mm per 100 m (1 in 10,000). The error is larger, so the instrument needs **adjustment**.

The far staff A reads too high (the apparent difference is greater than the true one), so the line of collimation is **inclined upward**.

#### Step 4: Correct reading on A for the second setup

$$
A = 1.642 - 0.011 = 1.631\ \text{m}, \qquad B = 1.321\ \text{m}
$$

Check: $1.631 - 1.321 = 0.310$ m = true difference. 

**Answer: collimation precision = 1 in 3636 (error 0.011 m in 40 m, line of collimation inclined upward); the staff reading on A for a horizontal line of sight is 1.631 m (B = 1.321 m).**

If the setup is a distance $x$ from B, the correction is $0.011 \times (40 - x)/(40 - 2x)$ at A and $0.011\, x/(40 - 2x)$ at B.

## Check yourself

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

1. Using the mid-point readings 1.464 and 1.154, the true difference is:
   A. 0.310 m
   B. 0.321 m
   C. 0.011 m
   D. 2.618 m
   Answer: A. 1.464 - 1.154 = 0.310 m. (Key point: True difference)

2. The collimation error is found as:
   A. 1.642 - 1.464
   B. Apparent 0.321 - true 0.310 = 0.011 m
   C. 0.321 + 0.310
   D. 0.321 / 0.310
   Answer: B. Error = apparent difference - true difference. (Key point: Error)

3. The precision 0.011/40 equals about:
   A. 1 in 400
   B. 1 in 36
   C. 1 in 3636, more than the 1 in 10000 limit so adjustment is needed
   D. 1 in 10000, within limit
   Answer: C. 0.011/40 = 0.000275 = 27.5 mm per 100 m, larger than 10 mm per 100 m. (Key point: Precision)

4. Assuming the instrument is practically at B, the correct reading on A is:
   A. 1.653 m
   B. 1.642 m
   C. 1.321 m
   D. 1.631 m
   Answer: D. The whole error lies on far staff A: 1.642 - 0.011 = 1.631. (Key point: Correct reading)

## Related in Surveying I

- [Two peg test, AB 100 m, Q 10 m](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atwo-peg-ab-100m-q-10m-inside) — Surveying I, chapter 5
- [Two peg, AB = 60 m, near A](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atwo-peg-ab-60m-near-a-6m-inside) — Surveying I, chapter 5
- [Two peg test: collimation inclined up or down](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atwo-peg-dumpy-cd-df-120m) — Surveying I, chapter 5
- [Collimation: pegs 60 m apart, Q near B](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atwo-peg-pegs-ab-60m-q-6m-from-b) — Surveying I, chapter 5
- [Collimation error with level mid-way and near B](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atwo-peg-60m-staff-1-855-1-625) — Surveying I, chapter 5
- [Collimation: level 5 m from B on AB produced](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atwo-peg-50m-staff-1-875-1-790-b-5m) — Surveying I, chapter 5