Local attraction and true bearings, 1°30′E

Reading of the data: the back bearing of CD is printed as 284°45′; with FB = 4°00′ this would give FB − BB = 79°15′, which is not a possible local-attraction error, so it is read as 184°45′ (the interior angles then add up to 540° within 0°30′). All other values are used as given. (Another possible reading is given in the note at the end.)

Line EA has FB − BB = 180°00′, so stations E and A are free from local attraction. Correcting the stations one by one does not close (the correction found for E comes out as +0°30′ although E is free), so the included-angle method is used.

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 = 539°30′; error = −0°30′; correction per angle = +0°06′ (equal distribution, since each angle is measured with the same care).

Line EA has FB − BB = 180°, so its bearing is free from local attraction and is taken as the starting line.

Step 3: Corrected and true bearings

Rule used: FB of next line = BB of previous line − interior angle (traverse run clockwise). Declination is 1°30′ East, so true bearing = magnetic bearing + 1°30′.

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

Interior angles from the corrected bearings

Sum = 540°00′ (as required).

Answer: Corrected bearings (FB): AB = 51°24′, BC = 184°03′, CD = 5°27′, DE = 165°51′, EA = 251°30′. True bearings (FB): AB = 52°54′, BC = 185°33′, CD = 6°57′, DE = 167°21′, EA = 253°00′.

Note on the data: the printed pair for CD (FB 4°00′, BB 284°45′) is inconsistent, and with the reading used above the lines CB and CD almost overlap (angle at C = 358°30′). Another reading also fits: FB of CD = 104°00′ with BB = 284°45′. It gives the same observed angle sum (539°30′) and the same corrections. The angles at C and D then become 258°30′ and 119°30′ (corrected 258°36′ and 119°36′), and the corrected bearing of CD becomes 105°27′ (BB 285°27′; true 106°57′). All the other bearings stay the same.