Local attraction with quadrantal bearings

The bearings are first converted to whole circle bearings (FB of AB = S11°30′W = 191°30′, BC = 67°30′, CD = 32°15′, DE = S82°45′W = 262°45′, EA = S50°15′W = 230°15′). FB − BB = 178°30′, 181°00′, 181°45′, 182°00′ and 177°15′, so no line is free and all stations are suspected. The included-angle method is used, and the results are shown in quadrantal form.

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

Step 2: Included (interior) angles

The included angle at a station uses the FB of the line leaving it and the BB of the line arriving at it, both observed at the same station, so local attraction cancels in the angle.

The sum of the interior angles should be $(2n-4)\times 90^\circ = 540^\circ$.

Sum observed = 540°30′; error = +0°30′; correction per angle = −0°06′ (equal distribution, since each angle is measured with the same care).

No line has FB − BB = 180°. Line BC has the smallest difference (+1°00′), so it is the most reliable; its adopted bearing is the mean of the FB and (BB ± 180°) = N 67°00′ E.

Step 3: Corrected bearings from the corrected angles

Rule used (in WCB): FB of next line = BB of previous line + interior angle (traverse run anticlockwise). Starting from BC = 67°00′ (BB 247°00′): CD = 247°00′ + 145°39′ − 360° = 32°39′, and so on round the traverse.

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

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

Answer: Corrected bearings (FB): AB = S 12°36′ W, BC = N 67°00′ E, CD = N 32°39′ E, DE = S 84°48′ W, EA = S 54°12′ W.