Vol 2 Iss. 1

The study should provide for each rock or its characteristic variety a constant, precisely defined figure, expressing its relationship to percussive hole drilling method adopted in this case. The most desirable it would be to obtain figures that, while depending entirely on the petrographic nature of the rocks being studied, would, on the other hand, be completely independent of factors such as the force of the drill impact, the diameter of the drill, its point angle, the angle of rotation of the drill, etc. In the case when it is impossible to exclude the influence of all these factors, the study should provide figures that depend only on some of them, in which case, all the studied rocks must be compared in exactly the same conditions. Figures of the first kind could then be called absolute, and of the second - only relative.

The Council of the Mining Institute of Empress Catherine II, having considered the establishment of an additional course in exploration for mining engineers at the institute, could not help but draw attention to the fact that persons engaged in this work for practical purposes need a detailed familiarity with our laws relating to prospecting, exploration and acquisition of rights to develop mineral deposits. In order to facilitate detailed acquaintance with the above mentioned section of our mining laws, the Council of the Mining Institute decided to publish this “Index”, which would provide prospectors and practitioners a guideline for reference (see article).

The structure of parts of the earth’s crust, such as the modern Ural Range is something so immensely complex that no human imagination is able to comprehend it in all its details, and any attempt in this direction reduces it to a more or less detailed schematic representation. But especially grandiose mining areas conceal not only this complexity of structure, but also so many subsequent alterations and transformations that even a schematic representation of the processes that occurred there encounters barely surmountable difficulties. It is enough to point to the intense activity of metamorphism and weathering to highlight these distinctive features. See the results of the study in the article.

A detailed description of the first proof of Gauss's fundamental theorem and of Cauchy's proof is given (see the article).

Since, in general, to define a chrystal form four faces are required and sufficient, it is clear that with three given points, no matter what triangle their poles constitute, further development of the form is impossible, and it is absolutely necessary to know the position of some fourth face. In general, the choice of such faces depends on our preference, and I will consider the case when these four points constitute the vertices of two adjacent triangles that share a common side.

A network for the hypohexagonal type was established and it was shown that the numerical law of the development of forms is essentially the same for this network as well, although now the faces are expressed by symbols not of three, but of four numbers; from these four numbers, you can always choose three, including necessarily the first number that will be completely identical to the numbers of the first network. But even if we do not make such a selection, but limit ourselves to three numbers, of which one is in the first place, and we choose the other two arbitrarily (that is, the second with the third, or the second with the fourth, or finally the third with the fourth), the law in question here will still remain valid. Of particular importance is the distribution of even and odd numbers. This law states that of the seven symbols relating to any elementary triangle of the network, one certainly encloses three (that is, all) odd numbers, three enclose two, and three enclose one odd number; all other numbers in the symbols are even.

Nothing is more natural than to generalize the conclusions of the previous note relating to three-digit numbers or the triangular geometric network, to numbers of higher digit counts and, first, to four-digit numbers, and the result is a tetrahedral network. Such a network of numbers has found its application for the chemical tetrahedron in petrography. Reflecting on the mathematical foundations of the construction of a triangular network, we will find that the fundamental theorems remain valid for this network with a corresponding complication of the constructions themselves. This complication lies in the fact that the total number of points associated with an elementary tetrahedron (more precisely, a sphenoid) of any given period is no longer 7 (3 + 3 + 1), but 15: four at the vertices, six midpoints of the edges, four centroids of the faces, and one at the centroid of the tetrahedron itself.

Last summer, I managed to collect a small amount of material on the mineralogy of the surroundings of the Karmankulsky Cordon, located on the left bank of the River M. Irimel about 45 versts to the SW of the Miass station. Along the right bank of the River Irimel, there is a series of large pits, formerly mined, but now abandoned for the extraction of iron ore; on the left bank, however, there are only small prospecting pits. In the waste dumps of the previously mined pits, it was possible to find, in addition to chromite and rhodochrome, very poor kemmererite and small but well-formed crystals of uvarovite; both of the occur as crusts on chromium iron ore. In the survey pits (on the left bank of the Irimel River), in addition to chromite, small crystals of vesuvianite and magnetite were also found.