In connection with the plan and pace of development of the mining and geological exploration industries, mine surveying currently faces a number of important tasks, namely: A. In terms of technical reconstruction and the technical revolution: 1) Elimination of technical backwardness (introduction of a unified coordinate system, safeguards against gross errors, introduction of the "z" coordinate, etc.); 2) Improvement of survey accuracy (accuracy of angle measurements, distances, orientation, etc.); 3) Introduction of new survey methods and techniques (precise tacheometry in mines, photomechanical reproduction of plans and other documents, application of photogrammetry to open-pit surveying, etc.); 4) Adaptation of mine surveying techniques to the new rates of mine development (consoles, suspended theodolites, new orientation methods). B. Adaptation of mine surveying to serve planned construction (see the article). C. In terms of general and organizational questions (see the article)

Bauman's work began at a time when the mining industry, having developed in our country, posed a number of new and complex challenges for mine surveyors. He fundamentally reorganized the practice of mine surveying in the state, and his activity should be regarded as a distinct era in the development of that specialty in which he worked. Our country also owes to V. I. Bauman the introduction of the first geophysical exploration method—magnetometry. Bauman's merit lies in the fact that he gave us this method as a technical, practical tool. Vladimir Ivanovich fundamentally reorganized the teaching of mine surveying and geodesy. He was the first professor in Russia to hold an independent chair in mine surveying. On his initiative, a mine surveying division was opened at our Institute within the Geological Exploration Faculty.

The content of the present article can be divided into two parts: the first is the derivation of a formula (first proposed by the author) for the mean error of the adjusted value of all measured quantities included in the adjustment; the second is a new derivation of the formula for the mean error of a single observation. Using this relationship (see the article), we provide a new, simple derivation of the aforementioned formula, which is important for the theory of least squares.

The question of the accumulation of errors in a mine traverse of arbitrary shape leads to the consideration of complex formulas that do not allow one to draw any general conclusions or provide general rules for resolving the issue in various practical cases. The possibility of simplification begins from the moment we ascribe some regularity to the polygonal line. In ordinary mine traverses, such a simple regularity of the polygonal line is absent; straight extended traverses are encountered rather rarely, and the aforementioned regular polygonal line even more rarely. At the same time, it cannot be said that any regularity whatsoever is absent in the shape of ordinary mine traverses, at least in the coal mines of southern Russia, which we have mainly in mind throughout the entire subsequent discussion.

Strict balancing of mine sites using the least squares method can be said to be almost entirely absent in practice. The reason for this is the complexity of the calculations associated with balancing using a strict method. Meanwhile, in practice, it is often not interesting to know the corrections of individual measurements, or even the corrections of the coordinates of individual points and azimuths of stations, but it can be very desirable to know the correction of the coordinates of a single point and the correction of the azimuth of a single station, which, say, will serve as the starting point for surveying a new site or which are obtained based on another survey, and the question of balancing the nodal point arises.