In connection with the plan and pace of development of mining and geological exploration, the survey department is currently facing a number of important tasks, namely: A. Technical reconstruction and technical revolution 1) Elimination of technical backwardness (introduction of a unified coordinate system, guarantees against gross errors, introduction of the “Z” coordinate, etc. 2) Increasing survey accuracy (accuracy of measuring angles, lengths, orientation, etc. 3) Introduction of new survey methods and business techniques (precise tacheometry in the mine, photomechanical reproduction of plans and other documents, the use of photogrammetry to survey open-pit works, etc. 4) Adaptation of surveying technology to the new pace of mining (consoles, hanging theodolites, new orientation methods. B. Adaptation of mine surveying to serve planned construction (see article). B. Regarding general and organizational issues (see article).
Bauman’s activities began at a time when mining, which had developed in our country, posed a number of new and complex tasks for surveyors. He radically reorganized the organization of surveying in the state; his activity should be noted as a special era in the development of the specialty in which he have worked. Our country also owes V.I. Bauman the introduction of the first of the geophysical exploration methods—magnetometry. Bauman's merit lies in the fact that he gave us this method, as a technical method, as a working one. Vladimir Ivanovich radically reorganized the teaching of surveying art and geodesy. He was the first professor in Russia in the independent department of surveying art. On his initiative, a surveying department was opened at our Institute at the Faculty of Geological Exploration.
The content of this article can be divided into two parts: the first is the derivation of a formula (first proposed by the author) for the average error of the balanced value of all measured quantities included in the balance, the second is a new derivation of the formula for the average error of one observation. Using this relation (see article), we give a new simple derivative of the formula mentioned above, which is important for the theory of least squares.
The question of the accumulation of errors in a mining site of arbitrary shape leads to the consideration of complex formulas that do not make it possible to draw any general conclusions or give general rules for solving the issue in various practical cases. The possibility of simplification begins from the moment when we attribute some kind of pattern to the broken line. In ordinary mining polygons, such simple regularity of a broken line is absent; straight elongated polygons are quite rare, and the above-mentioned regular broken line is even rarer. At the same time, it cannot be said that there was no regularity in the form of ordinary mining sites, at least in the coal mines of the south of Russia, which we mainly mean in all further discussion.
Strict balancing of mine polygons using the least squares method does not occur in practice at all. The reason for this is the complexity of the calculations associated with balancing using the strict method. Meanwhile, in practice, it is very often not at all interesting to know either 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 any one point and the correction of the azimuth of any one station, which, say, will serve source for surveying a new polygon or which are obtained based on another survey, and the question is about balancing the nodal point.
