What is a Traverse Misclosure?
Before applying coordinates, surveyors break every measured line into two components: Latitudes (North/South movement) and Departures (East/West movement).
In a perfectly measured closed loop, the sum of all Northings must exactly equal the sum of all Southings (Total Latitude = 0), and the sum of all Eastings must equal the sum of all Westings (Total Departure = 0). The reality is always a non-zero sum, which is your error in Latitude and error in Departure.
The Principle of the Bowditch Rule
The Bowditch Rule assumes that errors in measurement are accidental and are proportional to the length of the lines surveyed. Therefore, a longer traverse leg will be assigned a larger portion of the closing error than a very short leg.
It is the most common adjustment method used in plane surveying because it evenly distributes errors in both angles and distances.
How to Calculate Bowditch Adjustments
To adjust the traverse, you must calculate a specific correction for the Latitude and Departure of every individual line.
The Formula: Correction for Latitude = -(Total Latitude Error) x (Length of Line / Total Traverse Perimeter). Correction for Departure = -(Total Departure Error) x (Length of Line / Total Traverse Perimeter).
Worked Example: A traverse has a total perimeter of 1,000 ft. The total error in Latitude is +0.10 ft. For a specific line in the traverse that is 200 ft long, the Latitude correction is: -(+0.10) x (200 / 1000) = -0.02 ft. If that line's raw measured Latitude was +50.00 ft, the adjusted Latitude becomes +49.98 ft. This is repeated for every line and departure.
Checking Linear Precision
Before bothering to adjust a traverse, a surveyor must verify if the initial error is acceptable. The linear misclosure is calculated using the Pythagorean theorem: √(Lat Error² + Dep Error²).
Precision is expressed as a ratio (e.g., 1:10,000). A precision of 1:10,000 means there is 1 foot of error for every 10,000 feet measured. If a state board requires 1:15,000 for urban boundary surveys and the traverse yields 1:8,000, the surveyor cannot adjust it; they must go back to the field and re-shoot the bad measurements.
Frequently asked questions
What is the difference between the Compass Rule and the Transit Rule?
The Compass (Bowditch) Rule assumes distance and angle errors are equal and distributes based on line length. The Transit Rule assumes angles are measured more accurately than distances, distributing errors based purely on the latitude/departure values.
Do I adjust angles before or after applying the Bowditch rule?
Angular misclosure must be balanced first. Surveyors evenly distribute the angular error among all internal angles of the polygon. Only after angles are balanced do you calculate Latitudes/Departures and apply the Bowditch adjustment.
What is the Crandall Method?
The Crandall Method is a least-squares adjustment technique used when distance measurements are known to have larger random errors than the angular measurements. It holds the balanced angles fixed and distributes all remaining error into the distances.
Why is it called the Compass Rule?
It was historically developed by Nathaniel Bowditch for marine navigation and land surveying using magnetic compasses and Gunter's chains, where the assumptions about proportional error in bearing and distance held true.