Theodolite traverses laid along underground workings are calculated gradually, as the workings advance. For some time the traverses remain free, then they gradually form closed polygons, to a greater or lesser extent interconnected. Connection of the underground reference network to the redundant initial data (direction angles of the sides, determined by the gyroscopic method, coordinates of points transferred from the surface through vertical or inclined workings) is carried out relatively rarely.

Systems of theodolite traverses and polygonometry of Classes 1 and 2 are adjusted in a simplified way. First, corrections to the angles are jointly determined, then coordinate increments are calculated from the corrected angles, after which abscissas and ordinates are adjusted separately in the traverse system. The closures of individual traverses along the coordinate axes are distributed among the coordinate increments in proportion to the length of the sides.

The article deals with the issues of determining the error of the height of the reference point or the position of the polygonometric point in the system of traverses, adjusted by the method of polygons, nodes, approximations or the method of equivalent replacement.

The following formulas are known in the literature for calculating the errors of directional angles of the sides of the underground polygon, laid during orientation through two vertical mine shafts, a) depending on the errors of measurement; b) depending on the errors of measuring the lengths of the sides ...