Bowditch rule is also termed as:

Concept:

Balancing of errors: The process of adjusting the latitudes and departures to make the algebraic sum of latitudes or departures to zero is called the balancing of errors.

The two types of balancing rules to eliminate errors in traverse surveying are as follows:

1) Bowditch rule (Compass rule)/Compass rule: 

It is most commonly adopted when angular measurement and linear measurement both are nearly of same precision.

The correction is considered directly proportional to the length of the side.

By Bowditch rule Correction to a particular line is given by

\( {C_L} = \;l \times \frac{{{\bf{\Sigma }}L}}{{{\bf{\Sigma }}l}}\)

\({C_D} = \;l \times \frac{{{\rm{\Sigma }}D}}{{{\rm{\Sigma }}l}}\)

Where CL, CD is corrections in latitude and longitude for a line.

Correction for Latitude/Departure = Total error in Latitude/Departure ×  \(\frac{{{\bf{length}}\;{\bf{of}}\;{\bf{the}}\;{\bf{side}}}}{{{\bf{perimeter}}\;{\bf{of}}\;{\bf{the}}\;{\bf{traverse}}}}\)

2) Transit rule: 

When angular measurements are more precise than linear measurements, the transit method is adopted.

Correction to latitude/departure of any side = Total error in latitude/departure ×  \(\frac{{{\bf{Latitude/Departure}}\;{\bf{of}}\;{\bf{the}}\;{\bf{side}}}}{{{\bf{Arthmetical}}\;{\bf{sum}}\;{\bf{of}}\;{\bf{all}}\;{\bf{latitudes/departure}}}}\)

1. When the adjustment is made by the Bowditch rule, the length of the sides becomes less and the angle becomes more than that when the adjustment is made by the transit rule.

2. In Bowditch rule, it is assumed that the errors in linear measurements are proportional to \(\sqrt l \) and angular measurements are proportional to \(\frac{1}{{\sqrt l }}\)