Local attraction and true bearings, 7°W

Line AB has FB − BB = 180°, so A and B are free. Stations C, D and E are suspected. Declination is 7° West, so true bearing = magnetic bearing − 7°.

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

Step 2: Correct the stations in turn

• Line BC: FB at B = 139°30′ is correct. The correct BB is 319°30′, observed 317°00′, so the correction at C is +2°30′.
• Line CD: FB at C = 215°15′ with correction +2°30′ gives 217°45′. The correct BB is 37°45′, observed 36°30′, so the correction at D is +1°15′.
• Line DE: FB at D = 208°00′ with correction +1°15′ gives 209°15′. The correct BB is 29°15′, observed 29°00′, so the correction at E is +0°15′.
• Line EA (check): FB at E = 318°30′ with correction +0°15′ gives 318°45′. The correct BB is 138°45′, which equals the observed value, so A needs no correction, as expected.

Stations affected by local attraction: C, D and E. The amount of local attraction at each is equal and opposite to the correction: C −2°30′, D −1°15′, E −0°15′ (the observed bearings there are too small).

Step 3: Corrected bearings

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

Answer: Corrected bearings (FB): AB = 59°00′, BC = 139°30′, CD = 217°45′, DE = 209°15′, EA = 318°45′. True bearings (FB): AB = 52°00′, BC = 132°30′, CD = 210°45′, DE = 202°15′, EA = 311°45′.