---
title: "Link traverse M2 to M8 bearings"
subject: "Surveying I"
chapter: 4
key: "semester_3/surveying_i:link-traverse-m2-to-m8"
source: https://www.bctengineer.com/q/semester_3/surveying_i/link-traverse-m2-to-m8
site: BCT Engineering
---

# Link traverse M2 to M8 bearings

Surveying I · Chapter 4: The Compass

- Asked in: 2078 Kartik, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/link-traverse-m2-to-m8
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-4

## Question

During compass survey in a link traverse from station M2 to M8, the following observations were recorded.

| Station | Deflection angle (degrees) | Leg | Bearing (degrees) |
|---|---|---|---|
| M2 | -70 | M1-M2 | 105 |
| A | +20 | M2-A | |
| B | -90 | A-B | |
| M8 | +70 | B-M8 | |
| | | M8-M9 | 36 |

Compute the bearings of the link legs. Check the accuracy of work if the least count of the compass used is 1 degree. Correct the affected bearings if necessary.

## Short answer

Bearings of link legs: M2-A 35°, A-B 55°, B-M8 325°. Misclosure +1° is within permissible 2°, so work acceptable. Corrected bearings: M2-A 35°15′, A-B 55°30′, B-M8 325°45′.

## Answer

Deflection angles: $+$ = right, $-$ = left. A leg's bearing is the previous leg's bearing plus the deflection angle at the station between them.

#### Step 1: Bearings from the observed deflection angles

| Leg | Working | Computed bearing |
|---|---|---|
| M1-M2 | given | 105° |
| M2-A | 105° − 70° | 35° |
| A-B | 35° + 20° | 55° |
| B-M8 | 55° − 90° = −35° | 325° |
| M8-M9 | 325° + 70° = 395° | 35° |

Computed bearing of M8-M9 = 35°, observed = 36°.

#### Step 2: Check of accuracy

$$
\text{Misclosure} = 36^\circ - 35^\circ = +1^\circ
$$

Permissible misclosure $= L.C. \times \sqrt{n} = 1^\circ \times \sqrt{4} = 2^\circ$ (n = 4 deflection angles). Since $1^\circ < 2^\circ$, the work is **acceptable**, but the bearings of the link legs are adjusted.

#### Step 3: Correction

Correction per angle $= +1^\circ/4 = +0.25^\circ = +0°15′$. The correction to a leg increases by 15′ at each station.

| Leg | Computed | Correction | Corrected bearing |
|---|---|---|---|
| M2-A | 35°00′ | +0°15′ | 35°15′ |
| A-B | 55°00′ | +0°30′ | 55°30′ |
| B-M8 | 325°00′ | +0°45′ | 325°45′ |
| M8-M9 | 35°00′ | +1°00′ | 36°00′ (agrees with observed) |

Corrected deflection angles: M2: −69°45′ (left), A: +20°15′ (right), B: −89°45′ (left), M8: +70°15′ (right).

**Answer:** bearings of the link legs M2-A = 35°, A-B = 55°, B-M8 = 325°; misclosure = +1° (within permissible 2°); corrected bearings M2-A = 35°15′, A-B = 55°30′, B-M8 = 325°45′.

## Check yourself

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

1. In the link traverse, the bearing of M1-M2 is 105° and the deflection angle at M2 is 70° left (-70°). What is the computed bearing of M2-A?
   A. 175°
   B. 35°
   C. 105°
   D. 215°
   Answer: B. Next bearing = previous bearing + deflection angle (right +, left -), so 105° - 70° = 35°. (Key point: Bearing from deflection angle)

2. With least count 1° and n = 4 deflection angles, what is the permissible misclosure?
   A. 2°
   B. 1°
   C. 4°
   D. 16°
   Answer: A. Permissible misclosure = L.C. x sqrt(n) = 1° x sqrt(4) = 2°. (Key point: Permissible misclosure)

3. The misclosure is +1° against a permissible 2°. What is concluded?
   A. Work is rejected and the survey must be repeated
   B. Work is acceptable and no adjustment is needed
   C. Work is acceptable, but the link-leg bearings are adjusted so M8-M9 agrees with the observed 36°
   D. Only the bearing of M8-M9 is changed to 36°
   Answer: C. 1° < 2°, so the work passes, but the misclosure is still distributed over the legs so the computed bearing of M8-M9 equals the observed 36°. (Key point: Decision on misclosure)

4. The +1° misclosure is spread equally over 4 angles (+0°15′ each), increasing at each station. What is the correction to the third leg B-M8?
   A. +0°15′
   B. +0°30′
   C. +1°00′
   D. +0°45′
   Answer: D. Corrections accumulate by 15′ per station: 15′, 30′, 45′, 60′, so B-M8 gets +0°45′ and becomes 325°45′. (Key point: Distribution of correction)

## Related in Surveying I

- [Corrected bearings, closed link traverse T1-T2](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosed-link-traverse-t1-t2-corrected-bearings) — 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
- [Link traverse XP to TY, angles to right](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-xp-ty-angles-to-right) — Surveying I, chapter 4
- [Link traverse ABCDEF, right turn angles](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-right-turn-angles-22-17) — Surveying I, chapter 4, asked 3×
- [Link traverse ABCDEF, last line 108°05′40″](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-abcdef-108-05-40) — Surveying I, chapter 4, asked 3×
- [Open traverse ABCDEFGH, deflection angles](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aopen-traverse-deflection-angles-81-45) — Surveying I, chapter 4, asked 2×

## Related in other subjects

- [Link traverse Gale's table M2 to M8](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Alink-traverse-gale-m2-m8) — Surveying II, chapter 1
- [Link traverse Q to X, Gale's table m1, m2](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Alink-traverse-qx-gale-m1-m2) — Surveying II, chapter 1
- [Link traverse Q-m1-m2-X, Gale's table](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Alink-traverse-qm1m2x-gale-bowditch) — Surveying II, chapter 1