Vol 1 Iss. 3

Let us consider an elliptic integral, the values of the argument of u, and derive the required equation.

Under this general term we mean all those curves and surfaces that are represented in the geometry of harmonic segments. Indeed, in this geometry, to every middle point of a segment there uniquely correspond both endpoints of this segment; consequently, whatever curve is represented in this geometry as a set of endpoints of segments, its points are always grouped in pairs that are harmonic with respect to the main orthogonal sphere O, with the endpoints located on a radius of this sphere.

One of these systems or spherical geometries can be considered generally known, although I am not aware that anyone has categorically noted its complete parallelism or equivalence with the geometry of points on a plane. This geometry on the sphere introduces one limiting condition: it deals only with points on a sphere. Therefore, although its points occupy all three dimensions of space, it is essentially the same geometry of two dimensions (that is, of the second order), as is the corresponding geometry on a plane, in which the limitation consists in considering only points lying on a single plane.

Despite a long line of first-class researchers of this mineral, starting with Brooke who studied this mineral in 1824, its crystallization, specifically, the correct orientation of its crystals, has hitherto encountered significant difficulties. I can now make use for this purpose of an excellent specimen from Alston Moor, available in the Museum of the Mining Institute, from which hundreds of crystals suitable for this purpose could be extracted. I extracted 15 crystals and subjected them to comprehensive measurement on a universal goniometer.

During the fundamental revision and reorganization of the minerals in the Museum of the Mining Institute, currently being carried out by A.E. Kupffer, the opportunity arose to get acquainted in some detail with the figures mentioned in the title, which are sometimes developed with great clarity on a fairly large number of specimens from various deposits of this interesting mineral, which is so abundantly represented in the museum's collection.

Natural crystals are the most challenging object for the method of crystal-chemical analysis, and I must admit that my attempt to assign the proper orientation to all minerals proved to be imperfect in many respects. But it was precisely this imperfection that prompted the further development of criteria for correct orientation, and pointed to the need to re-examine and individually study the crystals of many minerals.

Alloys of platinum series metals have only recently become the subject of systematic study. Until now, there are only isolated studies of various compounds of these metals. Meanwhile, the metals of this group, from a theoretical point of view, seem to be very interesting due to the greater diversity of compounds they form, as indicated by various authors.

Crystals of potassium dihydroxide were measured by Schabus (Wien. Ak. Veg. 1850) and he also stated a very perfect cleavage along {001} and less perfect along {100} and {010}. Potassium dichromate releases from aqueous solutions (t = + 20° C.) as well-formed crystals with growth planes {001} or {101}, which, as is known, belong to the pinacoidal class of the triclinic system of cubic type.

Having specially studied pyroxenes, I came across, among other things, intergrown crystals resembling twin intergrowths. Let me present here the result of one such study, based on whose numerical data the attached diagram was compiled.

The criterion used so far contained a fundamental, principled drawback, which consisted in calculating the reticular density of any given complex as if it were an isotropic complex. Although th criterion with this drawback was used quite consciously, for the sake of simplicity, in view of the complexity of the operation of calculating reticular densities, but, of course, there always was the desire to eliminate it, if only a method could be found to determine this density quite correctly, without resorting to simplifying, but still an erroneous assumption.

From the Museum of the Mining Institute, specimen No. 169/3 labeled: “Bronzite from the Slyudyanka River” was transferred for research to the Mineralogical Cabinet. Two thin sections prepared from it showed that the sample is a rock, which, in fact, contains, as a component, an orthorhombic pyroxene close to bronzite. The rock itself presents some features in its composition and structure, which lead to its classification as a drusite-type rock.

In one of the thin sections of quartz porphyry from the Vtoro-Blagodatny mine, I came across an interesting case of fractures within feldspar grains being filled with feldspathic substance of the same composition and in the same orientation. The rock is quite strongly altered: the feldspars are abundantly strewn with muscovite dust. The thin section field is cut by several veins, apparently filled with new growths. In this case, depending on whether the vein cuts through the groundmass or the feldspar segregations, it is filled either with an aggregate of feldspars and quartz or with feldspars alone, with such a slight difference in orientation compared to the mineral of the grain cut through by the vein that it cannot be quantified. Feldspar veins are characterized by significantly greater transparency due to the absence of muscovite inclusions.

The first series of his works is about the influence on solutions of physical forces – gravity and centrifugal force – on the one hand, and electromagnetic forces on the other. The second series of works is devoted to a critical analysis of the basic concepts of energy, treating the energy of motion and radiant energy, the interaction of these types of energy, and the basic principles and concepts of mechanics. In 1907, Vladislav Aleksandrovich was invited to teach thermodynamics at the Mining Institute, but his poor health did not allow him to continue the course he had always dreamed of. The article highlights the scientific principles of V.A. Tyurin and provides a short list of his published works.