Local attraction, bearings AB 305°00′ (EA 45°)

Differences FB − BB: AB 179°30′, BC 181°00′, CD 178°00′, DE 181°30′, EA 180°00′. Line EA is free of attraction, so stations E and A are free; the other stations B, C and D 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 EA has a difference of exactly 180°, so stations E 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 = 305°00′ is correct. The correct BB is 125°00′, observed 125°30′, so the correction at B is −0°30′.
• Line BC: FB at B = 75°30′ with correction −0°30′ gives 75°00′. The correct BB is 255°00′, observed 254°30′, so the correction at C is +0°30′.
• Line CD: FB at C = 115°30′ with correction +0°30′ gives 116°00′. The correct BB is 296°00′, observed 297°30′, so the correction at D is −1°30′.
• Line DE (check): FB at D = 166°30′ with correction −1°30′ gives 165°00′. The correct BB is 345°00′, which equals the observed value, so E needs no correction, as expected.

Stations affected by local attraction: B, C, D.

Step 3: Corrected bearings

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

Answer: Corrected bearings (FB): AB = 305°00′, BC = 75°00′, CD = 116°00′, DE = 165°00′, EA = 225°00′.