---
title: "Local attraction, S 40°30′ W traverse"
subject: "Surveying I"
chapter: 4
key: "semester_3/surveying_i:local-attraction-quadrantal-s40-30w"
source: https://www.bctengineer.com/q/semester_3/surveying_i/local-attraction-quadrantal-s40-30w
site: BCT Engineering
---

# Local attraction, S 40°30′ W traverse

Surveying I · Chapter 4: The Compass

- Asked in: 2063 Baisakh, 10 marks
- Video: [local attraction problem in surveying || compass survey|| survey engineering|| #local_attraction](https://www.youtube.com/watch?v=i_3QTIOjHek) — Aim 2 Civil Class
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/local-attraction-quadrantal-s40-30w
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-4

## Question

The following bearings were observed in case of a closed traverse. At what stations is local attraction suspected? Compute the corrected bearings and find the interior angles of the traverse.

| Line | F.B. | B.B. |
|---|---|---|
| AB | S 40°30′ W | N 41°15′ E |
| BC | S 80°45′ W | N 79°30′ E |
| CD | N 19°30′ E | S 20°00′ W |
| DA | S 80°00′ E | N 80°00′ W |

## Short answer

Local attraction suspected at B and C. Corrected fore bearings: AB S40°30' W, BC S80°00' W, CD N20°00' E, DA S80°00' E. Interior angles: A=59°30', B=140°30', C=60°00', D=100°00', sum 360°00'.

## Answer

The bearings are converted to whole circle bearings: AB = S40°30′W = 220°30′ (BB 41°15′), BC = 260°45′ (BB 79°30′), CD = 19°30′ (BB 200°00′), DA = S80°00′E = 100°00′ (BB 280°00′). Line DA has FB − BB = 180°00′, so D and A are free; B and C are suspected.

Local attraction at a station is detected by comparing the fore bearing (FB) and back bearing (BB) of each line: if there is no local attraction at either end, $\text{FB} - \text{BB} = 180^\circ$ exactly.

#### Step 1: Check each line

| Line | FB | BB | FB − BB | Remark |
|---|---|---|---|---|
| AB | S 40°30′ W | N 41°15′ E | 179°15′ | Differs by −0°45′ |
| BC | S 80°45′ W | N 79°30′ E | 181°15′ | Differs by +1°15′ |
| CD | N 19°30′ E | S 20°00′ W | 179°30′ | Differs by −0°30′ |
| DA | S 80°00′ E | N 80°00′ W | 180°00′ | Free, difference = 180° |

Line DA has a difference of exactly 180°, so stations D and A are free from local attraction. The other stations are corrected one after another, starting from A.

#### Step 2: Correct the stations in turn

- Line AB: FB at A = S 40°30′ W is correct. The correct BB is N 40°30′ E, observed N 41°15′ E, so the correction at B is −0°45′.
- Line BC: FB at B = S 80°45′ W with correction −0°45′ gives S 80°00′ W. The correct BB is N 80°00′ E, observed N 79°30′ E, so the correction at C is +0°30′.
- Line CD (check): FB at C = N 19°30′ E with correction +0°30′ gives N 20°00′ E. The correct BB is S 20°00′ W, which equals the observed value, so D needs no correction, as expected.

| Station | A | B | C | D |
|---|---|---|---|---|
| Correction | 0 | −0°45′ | +0°30′ | 0 |

Stations affected by local attraction: B, C.

#### Step 3: Corrected bearings

| Line | Observed FB | Correction | Corrected FB | Observed BB | Corrected BB |
|---|---|---|---|---|---|
| AB | S 40°30′ W | 0 | S 40°30′ W | N 41°15′ E | N 40°30′ E |
| BC | S 80°45′ W | −0°45′ | S 80°00′ W | N 79°30′ E | N 80°00′ E |
| CD | N 19°30′ E | +0°30′ | N 20°00′ E | S 20°00′ W | S 20°00′ W |
| DA | S 80°00′ E | 0 | S 80°00′ E | N 80°00′ W | N 80°00′ W |

Check: corrected FB − corrected BB = 180° for every line.

*Corrections are in the whole-circle sense (+ is clockwise).*

#### Interior angles from the corrected bearings

| Station | Interior angle |
|---|---|
| A | 59°30′ |
| B | 140°30′ |
| C | 60°00′ |
| D | 100°00′ |

Sum = 360°00′ (as required).

**Answer:** Local attraction is suspected at B and C. Corrected bearings (FB): AB = S 40°30′ W, BC = S 80°00′ W, CD = N 20°00′ E, DA = S 80°00′ E.

The interior angles computed from the observed bearings are A = 59°30′, B = 140°30′, C = 60°00′, D = 100°00′ (sum 360°00′), the same as those from the corrected bearings.

## Check yourself

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

1. How is the quadrantal bearing S 40°30′ W written as a whole circle bearing?
   A. 139°30′
   B. 40°30′
   C. 220°30′
   D. 319°30′
   Answer: C. S θ W lies in the third quadrant: WCB = 180° + θ = 220°30′. (Key point: Quadrantal to WCB)

2. Which line has FB − BB = 180° and gives the free stations?
   A. AB
   B. BC
   C. CD
   D. DA
   Answer: D. DA has S 80°00′ E = 100°00′ and N 80°00′ W = 280°00′, a difference of 180°. So D and A are free. (Key point: Starting line)

3. FB of AB at A is S 40°30′ W, so the correct BB is N 40°30′ E. The observed BB is N 41°15′ E. What is the correction at B?
   A. −0°45′
   B. +0°45′
   C. +1°15′
   D. 0
   Answer: A. Correct is 40°30′ against observed 41°15′, so the observed value is 0°45′ too large. The correction is −0°45′. (Key point: Correction at B)

4. Which stations are suspected of local attraction?
   A. A and D
   B. B and C
   C. A and B
   D. C and D
   Answer: B. A and D are free from line DA; corrections of −0°45′ and +0°30′ are found at B and C. (Key point: Suspected stations)

## Related in Surveying I

- [Local attraction, BC 79°30′ and DE 82°15′](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-ab-191-30-bc-79-30) — Surveying I, chapter 4
- [Local attraction: AB 69°30′ compass traverse](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-ab-69-30-reordered) — Surveying I, chapter 4
- [Local attraction, bearings AB 305°00′ (EA 45°)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-ea-305-00) — Surveying I, chapter 4, asked 2×
- [Interior angles and bearings, closed traverse ABCD](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Ainterior-angles-closed-traverse-104-30) — Surveying I, chapter 4
- [Local attraction, bearings AB 305°30′](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-ea-bb-44-00) — Surveying I, chapter 4, asked 2×
- [Local attraction ABCDEA by included angles](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-abcdea-included-angle) — Surveying I, chapter 4, asked 2×

## Related in other subjects

- [Closed traverse missing EA bearing, BC length](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-traverse-abcdea-missing-ea-bc) — Surveying II, chapter 1
- [Missing bearings of BC and DE in traverse](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-missing-bearings-bc-de) — Surveying II, chapter 1
- [Bearings of BC and CD in traverse ABCDE](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-abcde-bearings-bc-cd) — Surveying II, chapter 1, asked 2×
- [Bearings of DE and EA in traverse ABCDE](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-abcde-bearings-de-ea) — Surveying II, chapter 1, asked 2×