Breitengrade und Abweitung

Latitudes and departures are critical concepts in surveying and are used to analyze the projections of traverse lines. 

A latitude represents the north-south projection of a line, calculated by multiplying the line's length by the cosine of its bearing. 

Similarly, a departure denotes the east-west projection, determined by the line's length times the sine of its bearing. These components correspond to the x and y coordinates​​.

Latitudes are positive for northerly bearings and negative for southerly. Departures are positive for easterly bearings and negative for westerly.

For a closed traverse, the algebraic sums of latitudes and departures should equal zero. Any deviation indicates errors, which can be adjusted systematically. 

Errors in latitude and departure are minimized through balancing techniques, such as the compass rule. This method distributes errors proportionally to the lengths of the traverse sides, ensuring the closure of the traverse​​.

Balanced latitudes and departures allow precise computation of traverse areas or coordinates. 

Surveyors adjust latitudes and departures to account for measurement errors, ensuring accurate bearings and side lengths.