7.4 Traverse Adjustment: Compass Rule and Transit Rule

Why and How We Adjust

After closure is computed, the small misclosures are distributed back into the courses so the adjusted latitudes and departures sum to exactly zero. Two rules dominate FS problems.

The compass rule, also called the Bowditch rule, assumes the angles and the distances were measured with equal precision and that errors are proportional to course length. The correction to any course is proportional to its length:

• Correction to latitude_i = -(latitude misclosure) x (L_i / sum L)
• Correction to departure_i = -(departure misclosure) x (L_i / sum L)

The transit rule assumes the angles were measured more precisely than the distances, so it distributes each correction in proportion to the absolute value of that course's latitude (or departure):

• Correction to latitude_i = -(latitude misclosure) x ( |latitude_i| / sum |latitude| )
• Correction to departure_i = -(departure misclosure) x ( |departure_i| / sum |departure| )

In both rules the correction is opposite in sign to the misclosure, which is what drives the adjusted sum to zero. Pick one rule for the whole table; never mix them unless the problem directs you to.

Worked Compass-Rule Adjustment

Use the traverse from Section 7.3: total length 1230.00 ft, latitude misclosure +0.06 ft, departure misclosure -0.06 ft. Each latitude correction is -(+0.06)(L_i/1230) and each departure correction is -(-0.06)(L_i/1230) = +0.06(L_i/1230).

The latitude corrections total -0.06 ft, exactly canceling the +0.06 ft misclosure; the departure corrections total +0.06 ft, canceling the -0.06 ft misclosure. Apply each correction to its measured component: adjusted latitude A-B = +212.10 + (-0.0146) = +212.085 ft; adjusted departure A-B = +212.16 + 0.0146 = +212.175 ft. Repeat for every course, then confirm the adjusted latitudes and departures each sum to zero before computing coordinates or area.

Signs, Checks, and FS Traps

• Sign rule: correction sign is always opposite the misclosure sign. A positive latitude misclosure means latitudes are too large, so corrections are negative.
• Closure check: the sum of the corrections in each column must equal the negative of that column's misclosure; if it does not, you made an arithmetic slip.
• Do not edit raw data: adjustment changes the computed latitudes and departures, not the field-recorded angles and distances.
• Method selection: if the problem says distances and angles are equally good, use the compass rule; if angles are markedly better, the transit rule is intended. When a problem is silent, the compass rule is the default and far more common on the FS.

Following these rules, your adjusted coordinates will close perfectly and feed directly into area and COGO computations.

From Adjusted Components to Coordinates

Adjustment is not the finish line; the balanced latitudes and departures still have to become coordinates. The accumulation is sequential: each northing is the previous northing plus the adjusted latitude, and each easting is the previous easting plus the adjusted departure. Because the adjusted latitudes and departures now sum to zero, the running totals return precisely to the starting coordinates after the last course, which is the final proof that the adjustment was applied correctly. If your last computed point does not match the start to the last decimal, a correction was misadded somewhere.

Choosing and Defending a Method

The compass rule is the workhorse and the safe default when a problem does not specify a method. The transit rule appears when the prompt emphasizes high-quality angular work, such as a theodolite traverse with taped distances of lesser certainty. A third approach you may see named is least squares, the rigorous method that weights every observation by its standard deviation; it is the modern professional standard but is beyond the hand-calculation scope of the FS, which expects the compass or transit rule.

Final FS Checklist for Adjustment

1. Balance the angles first (sum to (n-2) x 180 deg), then recompute azimuths.
2. Compute latitudes and departures, then the misclosures.
3. Apply compass- or transit-rule corrections with signs opposite the misclosures.
4. Verify each correction column sums to the negative of its misclosure.
5. Accumulate adjusted components into coordinates and confirm the traverse returns to its start.

Work the steps in this order every time. Skipping the angle balance or applying a correction with the wrong sign are the two errors that most often turn a solvable FS traverse problem into a wrong answer.