Field measurements in traversing, Bowditch rule

Field measurements in theodolite traversing

1. Horizontal angles at each station: included angles, deflection angles or direct (azimuth) angles, observed on both faces and repeated or in sets to reduce instrumental errors.
2. Lengths of the traverse lines: measured with a steel tape (twice, forward and back, with temperature, tension, slope and sag corrections) or with an EDM/total station.
3. Bearing of the starting line: magnetic bearing by a compass or true bearing by astronomical or GPS observation; in a link traverse, the bearings of the reference lines at both ends.
4. Vertical angles or levels of the stations, where heights are required or the lengths are measured on a slope (for slope reduction).
5. Details and offsets from the traverse lines (building corners, roads, streams), with a sketch and the station numbers.
6. Station description and referencing (ties to permanent objects), the heights of the instrument and signals, and all booking in the field book.

Bowditch's rule

Bowditch (compass) rule: the closing error in latitude and departure is distributed among the lines in proportion to their lengths.

$$C_L=-\Sigma L_{at}\times\frac{l}{\Sigma l},\qquad C_D=-\Sigma D_{ep}\times\frac{l}{\Sigma l}$$

where $l$ is the length of the line and $\Sigma l$ the perimeter (or total length of the traverse).

Assumptions:

• Angular and linear measurements are of equal precision, and the errors are accidental (random) only.
• The error in the linear measurement of a line is proportional to $\sqrt{l}$, and the error in angular measurement is inversely proportional to $\sqrt{l}$. On these assumptions, the correction to the latitude and departure of each line works out to be proportional to its length.
• The angular misclosure has already been distributed among the angles before the rule is applied.

It is simple, and it is the most commonly used rule in plane surveying.