---
title: "Principle applied in two-way linear measurement"
subject: "Surveying I"
chapter: 1
key: "semester_3/surveying_i:two-way-linear-measurement-principle"
source: https://www.bctengineer.com/q/semester_3/surveying_i/two-way-linear-measurement-principle
site: BCT Engineering
---

# Principle applied in two-way linear measurement

Surveying I · Chapter 1: Introduction

- Asked in: 2078 Kartik, 4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/two-way-linear-measurement-principle
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-1

## Question

How do you apply the principle of surveying in two-way linear distance measurement? Explain.

## Short answer

Measure the line forward and backward with the same tape and tension. Compute the difference and relative error; if within the permissible limit (e.g., 1/2000), adopt the mean. This provides an independent check, detects mistakes, and reduces accidental errors by averaging.

## Answer

A principle of surveying is that **a quantity should be fixed by at least two independent measurements, and each measurement must be checked**. In linear measurement this is done by measuring the line **twice, in the forward and backward directions** (two-way measurement).

#### Procedure
1. Measure line AB from A to B with the tape, keeping it straight, level and under the same tension. Record $L_1$.
2. Measure back from B to A in the same way. Record $L_2$.
3. Find the difference $d = |L_1 - L_2|$ and compute the relative error $= d / L_{mean}$.
4. Compare it with the permissible error (e.g. 1/1000 to 1/2000 for ordinary chaining, 1/5000 or better for careful taping on level ground).
5. If the error is within the limit, adopt the mean:

$$
L = \frac{L_1 + L_2}{2}
$$

6. If it is greater, find the cause (miscounted tape lengths, wrong reading, slack tape) and measure again.

#### Example
$L_1 = 150.42$ m and $L_2 = 150.38$ m. Difference $= 0.04$ m, relative error $= 0.04/150.4 = 1/3760$. This is better than 1/2000, so it is acceptable for ordinary work (though not for precise taping to 1/5000), and $L = 150.40$ m.

The backward measurement is independent of the forward one, so mistakes are detected and accidental errors are reduced by averaging.

## Check yourself

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

1. The principle applied in two-way measurement is
   A. a quantity is fixed by independent measurements and each is checked
   B. work from part to whole
   C. use a larger scale
   D. avoid tension on the tape
   Answer: A. Forward and backward measurements are independent and check each other. (Key point: Principle)

2. L1 = 150.42 m, L2 = 150.38 m. The relative error is about
   A. 1/376
   B. 1/37600
   C. 1/3760
   D. 1/150
   Answer: C. d = 0.04 m; 0.04/150.4 = 1/3760. (Key point: Relative error)

3. For those values, with the error acceptable, the adopted length is
   A. 150.42 m
   B. 150.40 m
   C. 150.38 m
   D. 150.04 m
   Answer: B. Mean = (150.42 + 150.38)/2 = 150.40 m. (Key point: Adopted length)

4. Which permissible error is typical for chaining on fairly level ground?
   A. 1/50
   B. 1/500000
   C. 1/5
   D. 1/5000
   Answer: D. 1/5000 for fairly level ground, 1/1000 for rough ground. (Key point: Limits)

## Related in Surveying I

- [Engineering surveying; two-way principle application](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aengineering-surveying-two-way-angle) — Surveying I, chapter 1
- [Corrections in linear measurement](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Acorrections-linear-measurement) — Surveying I, chapter 2, asked 4×
- [Field sketch and mapping by linear measurement](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Achain-field-sketch-mapping) — Surveying I, chapter 3
- [Distance measurement on sloping ground](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Adistance-on-sloping-ground) — Surveying I, chapter 2
- [Principle of chain surveying](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aprinciple-of-chain-survey) — Surveying I, chapter 3, asked 3×
- [Principle of chain surveying; well-conditioned triangle](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Achain-principle-well-conditioned-vs-error) — Surveying I, chapter 3

## Related in other subjects

- [Principle of optical distance measurement](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aoptical-distance-measurement-principle) — Surveying II, chapter 2
- [Optical distance principle, tangential horizontal distance](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aoptical-principle-tangential-horizontal-distance) — Surveying II, chapter 2
- [Converting two-way slope to one-way slope](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3Asuper-attainment-drainage) — Transportation Engineering I, chapter 3, asked 2×
- [Tacheometry principle, stadia distance and RL](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atacheometry-principle-stadia-formula) — Surveying II, chapter 2