Vol 7 Iss. 2

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 present paper gives a purely arithmetical method to obtaining the cubic character of the number 1−ρ. The method is based on the well-known lemma of Gauss. The author for a better evidence represents the numbers α+βρ, where α and β are real, as points of a plane. The problem is thus reduced to finding the number of lattice points in a certain region. The aimed at result is got by the particular choice of the fundamental region and its correspondent subdivision into parts.

The author — one of Russia's most renowned mining engineers — paints a vivid picture of the Mining Institute, his alma mater. Concisely and vividly, he describes the organization of education and, in particular, the daily life and customs of the "wards" or "cadets" of that time. The article contains much compelling and interesting autobiographical material. The author's stay at the Mining Institute spanned from the end of the summer of 1858 to the beginning of the summer of 1866. Until the autumn of 1865, the Institute had been a boarding educational institution for many years. For a significant part of the author's time there, the Institute was in a state of transition, which led to its transformation into an exclusively higher, open educational institution — not only due to the gradual closure of the preparatory courses, which corresponded to gymnasium-level studies, but also under the influence of new governmental and social currents of the 1860s.

The subject of the present work is the study of functions which initially appear in the form of a definite integral (see the article). In the special case of a single variable, we have the classical Kepler equation and its solution given by Bessel. As a simplest example illustrating the application of the obtained formulas, I present the classical problem of the motion of a spherical pendulum in the case of its small oscillations about the lowest equilibrium position. As examples of the application of generalized Bessel functions, I also present the equation of the mathematical pendulum, the equation of the theory of longitudinal bending, the differential equation encountered in the theory of small oscillations in a vacuum of a system with one degree of freedom, as well as in many recent investigations in celestial mechanics, and the differential equation of small oscillations in a resisting medium when the resistance of the medium is proportional to the square of the velocity.

In the problem of the torsion of prisms and in the corresponding hydrodynamic problems, it is necessary to solve the indefinite equation, where K is a constant, under the condition that f = 0 on the contour of the prism. K. M. Paschoud considered the case of regular polygons. Let us consider, proceeding from the proposed approach, the cases of a rhombus and an isosceles triangle.

One of the most convenient methods, in terms of fieldwork, for inserting a new point into an existing network is the method of resection (the Pothenot problem, Snellius problem). At sea near the coast and during travels with a mountain panorama, resections to known points and peaks are often the only means to determine one's position quickly and accurately. Likewise, intersections obtained photographically, both in terrestrial and aerial surveying, reduce to the Pothenot problem in the plane. Therefore, any simplification of the solution to this problem deserves attention.

The selection of a mine shaft location within a given area is one of the most complex and difficult problems encountered when opening a mineral deposit. Let us first consider what this problem entails, what factors must guide its resolution, and what circumstances and conditions determine one or another position of the shaft within the area. Below is a list of factors and conditions (see the article). Our aim is to provide a method that, on the one hand, facilitates solving the problem of determining the mine shaft location, even if this solution is approximate, yet practically sufficient; on the other hand, it allows for taking into account a greater number of circumstances and conditions than is typically done in practice, since it is clear that the more of these are taken into consideration, the more successful the choice of shaft location will be.

Of the three main conditions for good casting, namely: temperature, core ventilation, and the condition of the gates, the latter two must be transferred from the realm of art into the realm of craft; after which, such incidents can no longer occur. In the simplest way, by means of photographic records of the markings on the pattern and the gating system, changes in the molding and casting processes, as well as by means of notes on drawings regarding the reason and purpose of each significant change in the design or work process, the experience of an individual can be transformed into a shared, transferable, and thus accumulated experience. Then the history of the development of a factory's work will no longer represent, to such an extent, a collection of repeated attempts and mistakes at different factories, and sometimes even at the same factory.