---
title: "Field measurements in traversing, Bowditch rule"
subject: "Surveying II"
chapter: 1
key: "semester_4/surveying_ii:traverse-field-measurements-bowditch-rule"
source: https://www.bctengineer.com/q/semester_4/surveying_ii/traverse-field-measurements-bowditch-rule
site: BCT Engineering
---

# Field measurements in traversing, Bowditch rule

Surveying II · Chapter 1: Traversing

- Asked in: 2066 Magh (old course), 6 marks
- Video: [Balancing of traverse using Bowditch rule](https://www.youtube.com/watch?v=hUn7pl7iZ0A) — Gayathri VG
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/surveying_ii/traverse-field-measurements-bowditch-rule
- Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-1

## Question

What are the field measurements necessary in theodolite traversing? Explain Bowditch's rule for balancing the traverse.

## Short answer

Measure horizontal angles, line lengths, starting or reference bearings, vertical angles for slope reduction, offsets and station descriptions. Bowditch's rule distributes the latitude and departure closing errors in proportion to each line's length, assuming angular and linear measurements have equal precision and errors are accidental.

## Answer

#### Field measurements in theodolite traversing
1. **Horizontal angles** at each station: included angles, deflection angles or direct (azimuth) angles, observed on both faces and repeated or in sets to reduce instrumental errors.
2. **Lengths of the traverse lines:** measured with a steel tape (twice, forward and back, with temperature, tension, slope and sag corrections) or with an EDM/total station.
3. **Bearing of the starting line:** magnetic bearing by a compass or true bearing by astronomical or GPS observation; in a link traverse, the bearings of the reference lines at both ends.
4. **Vertical angles or levels** of the stations, where heights are required or the lengths are measured on a slope (for slope reduction).
5. **Details and offsets** from the traverse lines (building corners, roads, streams), with a sketch and the station numbers.
6. **Station description and referencing** (ties to permanent objects), the heights of the instrument and signals, and all booking in the field book.

#### Bowditch's rule
**Bowditch (compass) rule:** the closing error in latitude and departure is distributed among the lines in proportion to their lengths.

$$
C_L=-\Sigma L_{at}\times\frac{l}{\Sigma l},\qquad C_D=-\Sigma D_{ep}\times\frac{l}{\Sigma l}
$$

where $l$ is the length of the line and $\Sigma l$ the perimeter (or total length of the traverse).

**Assumptions:**
- Angular and linear measurements are of equal precision, and the errors are accidental (random) only.
- The error in the linear measurement of a line is proportional to $\sqrt{l}$, and the error in angular measurement is inversely proportional to $\sqrt{l}$. On these assumptions, the correction to the latitude and departure of each line works out to be proportional to its length.
- The angular misclosure has already been distributed among the angles before the rule is applied.

It is simple, and it is the most commonly used rule in plane surveying.

## Check yourself

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

1. Which set lists the essential field measurements in theodolite traversing?
   A. Horizontal angles, line lengths, and the bearing of the starting line
   B. Only the vertical angles and areas
   C. Only the lengths of the lines
   D. Contours, rainfall and stream velocity
   Answer: A. Angles at stations, lengths of lines and an initial bearing (to orient the traverse) are the essential data; others are supplementary. (Key point: Field measurements)

2. Why are horizontal angles observed on both faces and repeated?
   A. To convert them to bearings
   B. To reduce instrumental errors
   C. To find the length of the line
   D. To avoid measuring the starting bearing
   Answer: B. Face-left and face-right readings and repetition cancel or reduce instrumental errors. (Key point: Angle observation)

3. Bowditch's rule distributes the closing error among lines in proportion to:
   A. Their latitudes
   B. Their lengths
   C. Their bearings
   D. Their departures
   Answer: B. C_L = -sum Lat x l / sum l, so longer lines get larger corrections. (Key point: Bowditch's rule)

4. Which is an assumption of Bowditch's rule?
   A. Angles are measured more precisely than lengths
   B. Only the angles contain errors
   C. Angular and linear measurements have equal accuracy, with chance errors only
   D. Errors are proportional to the square of the length
   Answer: C. Bowditch assumes equal accuracy of angles and lengths, with error in a line proportional to sqrt(l) (correction taken proportional to l). (Key point: Bowditch assumptions)

## Related in Surveying II

- [Field measurements in traversing, closed/open traverse](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-field-measurements-closed-open) — Surveying II, chapter 1
- [Need for traversing, types, Bowditch rule](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraversing-necessity-types-bowditch) — Surveying II, chapter 1
- [Closed/open traverse, Bowditch's rule](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-open-traverse-bowditch-rule) — Surveying II, chapter 1, asked 2×
- [Bowditch balancing of link traverse XABCY](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Abowditch-link-traverse-xabcy) — Surveying II, chapter 1, asked 2×
- [Balancing linked traverse, transit rule](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Alinked-traverse-misclosure-transit-rule) — Surveying II, chapter 1, asked 2×
- [Principles and planning of theodolite traverse](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atheodolite-traverse-principles-planning) — Surveying II, chapter 1

## Related in other subjects

- [Checking open traverse; Bowditch graphically](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aopen-traverse-check-bowditch) — Surveying I, chapter 4
- [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
- [Theodolite traverse ABCDA with missing VCR (68°30′10″)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atheodolite-traverse-abcda-hcr-vcr-68-30-10) — Surveying I, chapter 7
- [Theodolite traverse ABCDA, booking format with VCR](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atraverse-abcda-booking-format-vcr-120-14-20) — Surveying I, chapter 7