Local attraction in closed traverse ABCDEFA

Every line differs from 180° (by 0°20′, 0°30′, 1°00′, 0°10′, 0°30′ and 0°20′), so no station can be called free with certainty, and all stations are suspected of local attraction. Line DE has the smallest difference, so D and E are the least affected stations; the bearings are corrected using the included angles.

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 $(2n-4)\times 90^\circ = 720^\circ$.

Sum observed = 720°30′; error = +0°30′; correction per angle = −0°05′ (equal distribution, since each angle is measured with the same care).

No line has FB − BB = 180°. Line DE has the smallest difference (−0°10′), so it is the most reliable; its adopted bearing is the mean of the FB and (BB ± 180°) = 321°15′.

Step 3: Corrected bearings from the corrected angles

Rule used: FB of next line = BB of previous line + interior angle (traverse run anticlockwise). Starting from DE = 321°15′ (BB 141°15′): EF = 141°15′ + 104°55′ = 246°10′, and so on round the traverse.

Check: corrected FB − corrected BB = 180° for every line, and working round the traverse returns to DE = 321°15′.

Answer: Corrected bearings (FB): AB = 216°00′, BC = 135°40′, CD = 80°40′, DE = 321°15′, EF = 246°10′, FA = 298°35′.