---
title: "Balancing linked traverse, transit rule"
subject: "Surveying II"
chapter: 1
key: "semester_4/surveying_ii:linked-traverse-misclosure-transit-rule"
source: https://www.bctengineer.com/q/semester_4/surveying_ii/linked-traverse-misclosure-transit-rule
site: BCT Engineering
---

# Balancing linked traverse, transit rule

Surveying II · Chapter 1: Traversing

- Asked in: 2078 Baisakh, 6 marks; 2074 Bhadra, 6 marks (asked 2 times)
- Video: [Balance the traverse by using transit rule | Traverse adjustment | Latitude Departure, Closing error](https://www.youtube.com/watch?v=M44D9btaxZs) — SBK Concept
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/surveying_ii/linked-traverse-misclosure-transit-rule
- Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-1

## Question

How is angular misclosure in a linked traverse balanced? Explain the transit rule for balancing the traverse.

## Short answer

Compute the bearing of the last reference line from observed angles; angular misclosure equals computed minus known bearing. If acceptable, distribute equally per angle = -misclosure/n, cumulatively applied. Transit rule distributes latitude and departure misclosure proportionally to absolute latitude and departure of each line, suitable when angles are more precise than lengths.

## Answer

#### Balancing angular misclosure in a link traverse
A link traverse starts and ends on stations of known coordinates, and the bearings of the first and last reference lines are known. The angular misclosure is therefore found by carrying the bearing through the traverse.

1. Starting from the known bearing of the first reference line, compute the bearing of every line from the observed angles. For clockwise angles, bearing of a line $=$ bearing of previous line $+180^\circ+$ angle; for anticlockwise angles, bearing of previous line $+180^\circ-$ angle (adding or subtracting $360^\circ$ as needed).
2. The computed bearing of the last reference line is compared with its known bearing:

$$
\text{Angular misclosure}=\text{computed bearing}-\text{known bearing}
$$

3. If it is within the allowable limit (for example $\pm k\sqrt{n}$, $n$ = number of angles), distribute it equally, the correction per angle being $-\text{misclosure}/n$. The first bearing receives one correction, the second two, and so on, so the last bearing receives $n$ times the correction and then equals the known value.

After the angles are balanced, the lengths are balanced through the linear misclosure of coordinates.

#### Transit rule (balancing latitudes and departures)
**Transit rule:** the total error in latitude (or departure) is distributed in proportion to the latitude (or departure) of each line, taken without sign.

$$
C_L=-\Sigma L_{at}\times\frac{|\text{lat of line}|}{\Sigma|\text{lat}|},\qquad C_D=-\Sigma D_{ep}\times\frac{|\text{dep of line}|}{\Sigma|\text{dep}|}
$$

It is used when angles are measured more precisely than lengths (for example with a precise theodolite and ordinary taping). The assumption is that the error in a line's latitude depends on the latitude itself, so a line running mainly north-south gets a large latitude correction and a small departure correction. It is used less often than Bowditch's rule because its corrections depend on the directions of the lines relative to the reference axes, so the result changes if the axes are rotated.

## Check yourself

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

1. How is the angular misclosure found in a link traverse?
   A. Computed bearing of the last reference line minus its known bearing
   B. Sum of observed angles minus (2n-4) x 90°
   C. Known bearing of the first line minus the computed one
   D. Sum of latitudes divided by sum of departures
   Answer: A. Bearings are carried through from the known first line and the computed last bearing is compared with its known value. (Key point: Angular misclosure definition)

2. How is an allowable angular misclosure distributed in a link traverse?
   A. The whole correction is added to the last angle
   B. In proportion to line lengths
   C. Equal correction -misclosure/n per angle, so the k-th bearing receives k times the correction
   D. Only the first and last bearings are corrected
   Answer: C. Each angle gets the same correction and corrections accumulate along the bearings, so the last bearing gets n corrections and matches the known value. (Key point: Distribution of correction)

3. What does the transit rule state?
   A. The error is distributed in proportion to the length of each line
   B. The error in latitude (or departure) is distributed in proportion to the latitude (or departure) of each line, without sign
   C. The error is distributed equally among all lines
   D. The error is distributed in proportion to the bearing of each line
   Answer: B. Transit rule: C_L = -SigmaLat x |lat of line| / Sum|lat|, and likewise for departures. Length-proportional is Bowditch. (Key point: Transit rule statement)

4. When is the transit rule appropriate?
   A. When lengths are measured more precisely than angles
   B. When all sides are equal
   C. When the traverse is open
   D. When angles are measured more precisely than lengths
   Answer: D. It assumes line errors in latitude depend on the latitude itself, suited to precise angles with ordinary taping. (Key point: When transit rule is used)

## Related in Surveying II

- [Closed loop/link traverse, misclosure balancing](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-loop-link-traverse-angular-misclosure) — Surveying II, chapter 1
- [Closed/open traverse, transit rule](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-open-traverse-transit-rule) — Surveying II, chapter 1, asked 2×
- [Closed loop/link traverse, misclosure terms](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-loop-link-traverse-misclosure) — 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×
- [Link traverse A to X, Y by transit method](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Alink-traverse-transit-a-x-y) — Surveying II, chapter 1
- [Balancing traverse, methods, independent coordinates](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Abalancing-traverse-methods-independent-coordinates) — Surveying II, chapter 1

## Related in other subjects

- [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
- [Link traverse PABCQ: permissible misclosure](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-pabcq-permissible-misclosure) — Surveying I, chapter 4
- [Angle misclosure, closed link traverse AT1-ET2](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosed-link-traverse-at1-et2) — Surveying I, chapter 4