Closing a Compass Traverse with a Suspected Local Attraction

Principle. For any line, the fore bearing and back bearing differ by exactly 180° unless one or both stations suffer local attraction. If FB − BB = 180° for a line, both its stations are free from local attraction (or both are affected equally, which is unlikely).

Step 1 - Derive back bearings.

• AB: FB 42°15' → BB should be 222°15'. DA's bearing at A is 313°50', so the back bearing of AB read at A is 313°50' − 180° = 133°50'... this needs care: the bearing of AD is 313°50', so the back bearing of AB at A is the bearing of BA = 313°50' − 180° = 133°50'? No - BA is the reverse of AB, so BB(AB) = 42°15' + 180° = 222°15'. The observed bearing at A toward D is 313°50', which is the bearing of AD, not BA. The correct comparison is: bearing of AB at A = 42°15'; bearing of BA at B = 131°40' − 180° = ...

Let me redo this cleanly. The bearing of a line read at its start is the FB; read at its end it is the BB. So:

• AB: FB = 42°15' (at A). BB of AB is read at B, and equals the bearing of BA = 42°15' + 180° = 222°15'. The bearing read at B toward A is the reverse of BC? No.

Correct pairing. At each station the instrument reads bearings to the two adjacent stations. At B the readings are BA and BC. BA = FB(AB) + 180° = 222°15'. BC = 131°40'. At C the readings are CB and CD. CB = BC + 180° = 311°40'. CD = 223°05'. At D: DC = CD + 180° = 43°05'; DA = 313°50'. At A: AD = DA + 180° = 133°50'; AB = 42°15'.

Step 2 - Compare observed with computed at each station.

• At A: observed AB 42°15', computed AB from AD = 133°50' − 180° = −46°10' → 313°50'? This is circular.

Practical test. Compute the interior angles from the bearings and check the sum. For a closed quadrilateral the sum must be 360°.

Interior angle at A = bearing AD − bearing AB (going clockwise) = 313°50' − 42°15' = 271°35' (reflex) → interior = 360° − 271°35' = 88°25'. At B: 131°40' − 42°15' = 89°25'. At C: 223°05' − 131°40' = 91°25'. At D: 313°50' − 223°05' = 90°45'. Sum = 88°25' + 89°25' + 91°25' + 90°45' = 360°00'.

The angles close perfectly. That is exactly the trap: a consistent local attraction that rotates every bearing by the same amount leaves the angles unchanged. Angular closure alone cannot detect it.

Step 3 - Fore/back bearing test.

• AB: FB 42°15', BB (from AD) - the reverse bearing of AB is 222°15'. The bearing of BA read at B is not directly given, but we can get it from the angle: BA = BC + angle B = 131°40' + 89°25' = 221°05'. Compare with 222°15': discrepancy 1°10'.
• BC: FB 131°40', BB = CB = CD − angle C = 223°05' − 91°25' = 131°40'...

Conclusion. The fore/back discrepancies are not zero on every line, which proves local attraction is present. The station where the discrepancy is largest is the suspect one; here the steel gate at C and the culvert at A are the prime suspects, and the line CD skirting the truck is also suspect. The correct procedure is to reject the bearings at the suspect stations, then recompute all bearings from the one line whose FB and BB differ by exactly 180°, working around the traverse.

Step 1 - Identify a clean line. The line whose observed FB and BB differ by exactly 180° is taken as free from local attraction. Its bearing is accepted as correct. (If no line passes the test, the whole traverse is re-run with the compass moved away from the steel and the concrete.)

Step 2 - Propagate from the clean line. Starting at the clean line, use the interior angles - which are unaffected by a uniform rotation at a station - to carry the bearing around the traverse. At each station, new bearing = previous bearing ± interior angle, reduced to 0-360°. This removes the local attraction at each station because the angle is a difference of two readings taken at the same station, so any constant local deflection cancels.

Step 3 - Check closure. After propagating, the bearing of the starting line recomputed from the far end should agree with the accepted bearing. Any residual is the angular misclosure and is distributed equally among the angles (Bowditch or equal-angle adjustment).

Step 4 - Recompute coordinates. Convert corrected bearings and measured lengths to latitudes and departures, then close with Bowditch if the linear misclosure is acceptable.

Residual risk.

• The clean-line assumption is an assumption. If the chosen line is itself affected - for example if both its stations sit near the same steel - the whole corrected traverse is rotated by a constant and the error is invisible in the angles.
• Local attraction is not necessarily constant during the survey; a truck that moves changes the field at C mid-run.
• The method corrects station attraction, not instrumental error (pivot friction, bent needle, magnetic variation).

Mitigation. Re-observe the suspect stations after relocating the compass at least 20-30 m from the steel and the culvert, or switch to a theodolite traverse referenced to a known bearing. Record the magnetic date and declination so the bearings can be reduced to true north later.

Why angular closure is not proof of correctness.

A compass at a station near steel does not read random values - it reads every bearing rotated by roughly the same small angle. When you subtract two bearings taken at the same station to get an interior angle, that rotation cancels. So a traverse can close to 360°00' to the second and still be rotated as a whole by a degree or more relative to true north. Angular closure tests the internal consistency of the figure; it says nothing about its orientation in space.

This matters because:

• A rotated traverse plots as a correctly shaped but wrongly oriented parcel. Areas computed from the coordinates are still right; boundary positions are not.
• If the traverse is tied to an existing boundary or a control point, the rotation shows up as a mis-tie that cannot be explained by measurement noise.
• The error is systematic, so more observations at the same stations will not average it out.

What the report should say.

1. State the observed bearings and the computed interior angles, and show that the angular misclosure is within the permitted limit (e.g. 1'√n for a prismatic compass).
2. State explicitly that local attraction was suspected at stations A and C on account of the culvert and the steel gate, and that line CD passed within 2 m of a vehicle.
3. State which line was found free from attraction by the FB/BB test, and that all bearings were recomputed from that line using the interior angles.
4. Report the residual uncertainty: the corrected traverse is internally consistent but its absolute orientation depends on the single clean line, and the magnetic declination on the date of survey must be applied to convert to true bearings.
5. Recommend a check: re-observe the suspect stations clear of the steel, or run a short theodolite connection to a known control point.

A report that presents a closed traverse as "verified" without this qualification is misleading, even if every number in it is arithmetically correct.