Notes on the derivation of formulas for determining the direction error from the eccentricity of the theodolite or signals

Abstract

For assessing the impact of a design error on the accuracy of transmitting directions to a mine, existing mine surveying guidelines usually recommend formula (1) (see article). Using the same reasoning, a well-known formula is usually derived for assessing the accuracy of measuring angles in polygons depending on the impact of signal and instrument eccentricity. The above conclusion does not answer the question: what kind of error should be understood by the value of ex, which in existing guidelines is usually called the "average linear error" [1] or simply "linear error" [2]. Clarification of the meaning of the error ex is absolutely necessary when making practical calculations, since several characteristics of position accuracy are used in error theory, among which the most commonly used are the average linear error of position and the average linear error in direction.