Vol 7 Iss. 3

Chapter IV. Some series expansions in generalized Bessel functions. Chapter V. Application of generalized Bessel functions to problems of mechanics.

In this work, the following theorem is proved. Let m be a negative integer containing no square divisors. Consider the quadratic field k(√m) and let ω1, ω2 be a basis of some ideal of this field, with the imaginary part of the ratio ω2/ω1 being positive. Furthermore, let ρ(u; ω1, ω2, ω3) be the well-known Weierstrass function (in what follows we will index the basis ω1, ω2 such that the ratio ω2/ω1 has a positive imaginary part), which satisfies the following differential equation

The article examines the general conditions of equilibrium, the case of a cylindrical floating body, and the case of plane inclinations of a floating body that has a plane of symmetry and is bounded by a ruled surface. The author provides a definition of the metacentric height in terms of the angle of inclination of the floating body.

The examination was carried out using the diagrams of A. K. Boldyrev. The examination was conducted as follows (see the article). It was found that the discrepancies do not exceed 1/2°; in some cases, with very small ∆g and ∆p, the reading accuracy dropped to 1°, but the latter was rare. During the examination, large discrepancies were discovered between the values of 2V given by Larsen and the 2V obtained from the diagrams (see the article). A total of 380 minerals were examined.

This article constitutes a report on the experiments I conducted during the period from May 23, 1916, to December 20, 1917. This work, like many others of a similar nature, was prompted by the extreme shortage of chemical products on the Russian market due to the World War. We arrived at the decision to first address the question of obtaining acetyl chloride with the use of sulfur. This article represents a complete account of all the work carried out by the author in the direction indicated here.

The author did not title this article "A New Method for Determining Symbols" by accident. Representing a combination of two already known methods, this method cannot be called new. It turns out that the two methods—the method of Prof. O. M. Ansheles and a somewhat modified belt method—when applied together, make the process of determining symbols simpler than when applying each of these methods separately. However, the aim of this article is not only to show a way of such joint application of these methods, but also to provide a simple derivation and proof of the proposed combined method that is independent of them. The author considers it necessary to provide such an independent derivation in order to make this method fully accessible, both practically and theoretically, even to persons unfamiliar with the methods upon which the proposed approach relies, from which the proposed method has grown.

With the very rapid development of the automotive and aviation industries, the question of obtaining materials that are lightweight and at the same time possess sufficient mechanical properties becomes increasingly urgent. The best and, so far, unsurpassed materials in this respect are alloys of the duralumin type, with an approximate composition (see the article). The duralumin alloy, as can be seen, is relatively complex, and therefore experiments have long been conducted in various parts of the globe to obtain simpler alloys that would not be inferior to duralumin in their mechanical qualities. Among such simple alloys, the aluminum-copper alloy enjoys the greatest success, especially in America. The nature of this alloy has not yet been sufficiently clarified. Therefore, for a more detailed investigation of the issue, it seemed appropriate to us to study the change in the solubility of copper in aluminum in the solid state as a function of temperature, since according to available data, such a change in the solubility of various components in alloys is the main reason determining the properties of alloys of the duralumin type, including the property of "aging."

Meetings of the Circle's Board: 9. Matters discussed: 20. General meetings of the Circle: 3. - Report by Prof. Shklyarsky: "Charging of Storage Battery Locomotives" - Instructor Vaipolin, A. F.: "Shaft Sinking at Svirstroi" - Postgraduate Student Zvyagin, P. Z.: "Gas Shelter at the N. Smolyaninovskaya Mine" - Engineer Berlin: "Sudden Gas Emission at the Same Mine"

As is known, the main task of the Scientific Petroleum Circle is to improve the qualifications of the future red specialist. More broadly, this means that by participating in the Circle's work, the student should supplement their knowledge beyond what the curriculum provides. It seems to us that in our work we have achieved this through the following: the organization of scientific and technical reports, where students, through lively discussions of the issues raised, became acquainted with and mastered the techniques of the petroleum industry; the establishment of a diploma design room, which provided graduate students with the best conditions for work, when almost everything necessary for calm, productive, and effective work is at hand; and the normal operation of the library.