At the beginning of this century, E. S. Fedorov created a method for determining a substance by the shape of its crystals, which he called “Crystal-chemical analysis” (29). This method, based on measuring the angles between the outer faces of crystals, was an important fundamental and practical achievement of crystallography. Over the next few years, this method, which in its essence is best called goniometric diagnosis, was significantly simplified by Fedorov’s school. Currently, the Fedorov Institute and the Central Geological Prospecting Institute (TsNIGRI) are compiling a “Crystal Determinant” (2), which will enable goniometric diagnosis in its new version to enter, along with optical diagnosis, into the daily practice of a crystallographer, chemist, and mineralogist. The main advantages of goniometric diagnosis are the complete absence of substance consumption, comparative speed of determination and the same degree of simplicity of diagnosis both in the case of simple and in the case of extremely complex substances. The main disadvantages of the goniometric method are the need to have the substance in the form of crystals and the variability of the external shape of crystals of the same substance. The second drawback may in some cases make it impossible to determine the substance by goniometric method. This drawback is especially noticeable in Barker’s version (16) of the goniometric diagnosis (20, 328, 329), to a somewhat lesser extent in Fedorov’s “Crystallographic Analysis” and to an even lesser extent in the version embodied in the “Identifier of Crystals” mentioned higher.

As we know, the X-ray method can be used in mineralogy (and in all branches of science and technology that rely on it) to solve a number of problems. The objectives of our research are to answer a number of the following questions. The answers to these questions should shed light on the nature of the substance of various coals, they can provide a new way for an accurate quantitative method of distinguishing coals from each other, one can expect that this method of distinguishing coals will help the geological parallelization of individual coal seams. In the future when linking X-ray properties with chemical ones with the help of analyzes and determinations of the thermal properties of coal, it becomes possible to learn from X-ray photographs of coal to judge, at least to some extent, about its qualities as a fuel. We have specified our immediate work as follows: to take Debye patterns of a successive series of minerals: graphite, shungite, anthracite and coal and discuss the results obtained.

The classification of 32 types (or groups) of crystal symmetry, i.e., the basis for dividing them into systems, or systems, can be based on various principles. Of these principles, the following two are the main and most natural. It is possible to classify the types (or groups) of symmetry, i.e., certain spatial collections of symmetry elements as such, by themselves, without relation to the complexes of possible faces and edges of the crystal to which these types of symmetry are characteristic. Let us call such classifications “purely geometric”. It is possible to classify the types of symmetry, taking into account the properties of those complexes of possible faces and edges of the crystal, in other words, those spatial lattices to which these types (groups) of symmetry are characteristic. Let us call such classifications “crystallographic”. The proposed classification, nomenclature and symbolism are closely linked by a single principle and are entirely based on a genetic trait — on the generative elements of symmetry.

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 mapping of mineral deposits is one of the most important objective methods for their study. This work is devoted to the development of rational mapping methods, treating this issue in general terms. The first impetus for this work was the pressing need for a rationally constructed map of the Altai polymetallic deposits. The necessity of such a map became evident already in the early years of the Geological Committee's research in the Altai, and at that time work was undertaken by both of us in two directions: mapping methodology was developed, and literary, archival, and new unpublished material from the Altai workers of the Geological Committee — necessary for compiling a map of the Altai deposits —was collected. This article is the result of the work carried out in the first direction.

We have two equal mutually tangent circles O1 O2. We have a line AB, tangent to both, and a new circle C, tangent to both data. We assert that the point of intersection of these two tangents, i.e. points D and E, as well as the point of tangency of the two given circles, i.e. point F, are equidistant from the point G, i.e. from one of the points of intersection of the circle C and the line CF. A proof by Prof. E.S. Fedorov.

The crystals in question were given to me for crystallographic study by Professor N.S. Kurnakov, who was the first to obtain them. The author carried out: goniometric studies, optical studies and studies of crystal isomorphism. See the article for results and pictures.