---
title: "Fundamental lines violated; minimising error"
subject: "Surveying I"
chapter: 7
key: "semester_3/surveying_i:fundamental-lines-error-minimised"
source: https://www.bctengineer.com/q/semester_3/surveying_i/fundamental-lines-error-minimised
site: BCT Engineering
---

# Fundamental lines violated; minimising error

Surveying I · Chapter 7: Transit and Theodolite

- Asked in: 2081 Bhadra, 4 marks
- Video: [How to adjust line of collimation error lesson 15  Urdu | Hindi ||](https://www.youtube.com/watch?v=3d-V4kYLHWI) — Professional Surveyor
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/fundamental-lines-error-minimised
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-7

## Question

What are the fundamental lines of construction of a theodolite? If the relationship between fundamental lines of theodolite has been violated, how can the error be minimized during angular observation?

## Short answer

Fundamental lines: vertical axis, horizontal (trunnion) axis, line of collimation, plate level axis, telescope level axis. Violations are minimized by observing on both faces and taking the mean (collimation, horizontal axis, altitude bubble), reading both verniers (eccentricity), using the repetition method (graduation), and levelling by reversal (plate level axis not perpendicular to vertical axis).

## Answer

The **fundamental lines** of a transit theodolite are the imaginary lines and axes about which the instrument is built. They are:

1. **Vertical axis** - the axis about which the whole upper part of the instrument rotates horizontally.
2. **Horizontal (trunnion) axis** - the axis about which the telescope rotates in the vertical plane.
3. **Line of collimation (line of sight)** - the line joining the intersection of the cross hairs to the optical centre of the objective, and its extension.
4. **Axis of the plate level (bubble line)** - the tangent to the plate bubble tube at its centre; it is horizontal when the bubble is central.
5. **Axis of the telescope level (altitude bubble)** - the tangent to the altitude bubble tube at its centre, used for levelling the line of sight.

#### Relationship (condition) between them
- Plate level axis $\perp$ vertical axis
- Line of collimation $\perp$ horizontal axis
- Horizontal axis $\perp$ vertical axis
- Altitude bubble axis $\parallel$ line of collimation

#### Minimising errors when these relations are violated
| Violation | How the error is minimised in observation |
|---|---|
| Line of collimation not perpendicular to the horizontal axis | Observe on both faces (face left and face right) and take the mean |
| Horizontal axis not perpendicular to the vertical axis | Observe on both faces and take the mean |
| Plate level axis not perpendicular to the vertical axis | This error is **not** removed by changing face. Level by the principle of reversal: turn the instrument through 180°, bring the bubble back by half its movement with the foot screws, and keep the bubble at that same (off-centre) position in all directions. The vertical axis is then truly vertical. Alternatively, level with the more sensitive altitude bubble |
| Altitude bubble not parallel to the line of collimation (vertical angle error) | Observe vertical angles on both faces and take the mean (the index error cancels) |
| Eccentricity of the circle | Read both verniers (A and B) and take the mean |
| Graduation error | Use the repetition method, or several sets with different initial positions of the circle |

If the errors are large, the instrument should be corrected by the permanent adjustments.

## Check yourself

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

1. What is the line of collimation?
   A. The axis about which the telescope rotates vertically
   B. The tangent to the plate bubble at its centre
   C. The axis about which the whole instrument rotates horizontally
   D. The line joining the cross-hair intersection to the optical centre of the objective
   Answer: D. The line of collimation (line of sight) joins the intersection of the cross hairs to the optical centre of the objective and its extension. (Key point: Line of collimation definition)

2. Which is a required relation between fundamental lines?
   A. Line of collimation perpendicular to the horizontal axis
   B. Horizontal axis parallel to the vertical axis
   C. Plate level axis parallel to the vertical axis
   D. Line of collimation parallel to the horizontal axis
   Answer: A. Line of collimation must be perpendicular to the horizontal axis; the horizontal axis must be perpendicular to the vertical axis. (Key point: Condition of adjustment)

3. How is the error of the line of collimation not being perpendicular to the horizontal axis minimised in observation?
   A. Read only vernier A
   B. Observe on both faces and take the mean
   C. Use the repetition of the level bubble
   D. Increase the sight length
   Answer: B. The error acts with opposite sign on the two faces, so the mean of face left and face right cancels it. (Key point: Eliminating collimation error)

## Related in Surveying I

- [Fundamental lines of theodolite and relations](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Afundamental-lines-of-theodolite) — Surveying I, chapter 7, asked 4×
- [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×
- [Temporary adjustments; fundamental lines](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atemporary-adjustments-and-fundamental-lines) — Surveying I, chapter 7
- [Theodolite construction principle; micrometer](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atheodolite-construction-principle-micrometer) — Surveying I, chapter 7, asked 2×
- [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
- [Angular misclosure, link traverse ABCDEFG](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-initial-154-50-last-335-30) — Surveying I, chapter 4

## Related in other subjects

- [Need for insurance during construction](https://www.bctengineer.com/question.md?key=semester_8%2Fconstruction_management%3Ainsurance-during-construction) — Construction Management, chapter 11