Vol 1 Iss. 1

Anyone who has sought to gain a clear understanding of the chemical relations of rocks must have seen with striking clarity all the imperfection of our knowledge on this subject. It must be admitted that true, exact science has as yet scarcely touched this important issue, and that the most primitive empiricism prevails here. A great number of rock types are put forward, receiving numerous names, but there is not even a universally recognized criterion for distinguishing one rock type, or, more precisely, one rock variety from another..

If there is a parallelism between the geometry theorems of points in space and circles on a plane, then the idea of the possibility of accurately representing points in space (and, consequently, images obtained from points of other images) by circles on a plane naturally arises. The purpose of this article is to develop the most perfect and simple way of depicting such an image. However, in addition, this article introduces two new geometric systems that are also used for the same purpose, namely, the system of vectorial circles and the system of vectorial segments or simply vectors.

A.E. Kupfer brought from a well-known mercury deposit pieces of light roasted (and therefore reddened) sandstone, covered with thin crystalline crusts. The crystals are slender-columnar, completely colorless, with adamantine luster and in general strongly resemble chlorquicksilver. However, an on-site analysis, while confirming the presence of chlorine and mercury, yielded an insufficient amount of chlorine, which is why it was assumed that these were not chlorquicksilver but crystals of some other mercury chloride. In these cases, the decisive factor is the standard methods of crystal-chemical analysis which consists of measuring the crystals and determining their proper orientation.

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.

The formula in question here is a logical consequence of two already known formulas, which were given in full detail by the author of the doctrine of symmetry, specifically in the section published under the title “Symmetry of Finite Figures.” The formula, applicable to any group of symmetry axes (type of alignment symmetry), though, of course, not applicable to a single axis taken separately, makes it possible to directly derive the order of symmetry from the number of symmetry axes. From it, incidentally, it follows that the order of a symmetry operation must be even (which is understandable given the obligatory presence of twofold axes of symmetry in the aggregates), and therefore the order of symmetry of those types where, in addition to the axes of symmetry, elements of reflection symmetry are present, must necessarily be divisible by four.

Recently there has been some revival in the literature on faults and other displacements of layers and veins, and this revival concerns even the purely geometric aspect of the issue, which seemed to be completely exhausted. We propose a different derivation of intersections and, from them, faults, refaults, and other displacements, whereby the latter are arranged in a series according to the decreasing or increasing number of doublings of the stratum they contain, from which, as a consequence, follows the determination of the shortest and most convenient paths for exploring the displaced part of the stratum. In the process, we will have to address the modern, extremely imperfect in the geometrical sense, terminology and classification of faults and other displacements.

The purpose of this short note is to present several new devices and techniques that I introduced during my work on the universal optical (in common speech Fedorov's) method of microscopic research and which have been already recognized by persons who use this method in their work: 1) segments in a metal frame; 2) rotating comparator; 3) measuring the thickness of a thin section using cracks and inclusions in it by tilting the specimen; 4) hemisphere for graphic solutions to problems of the universal optical research method.

Although at present there is hardly any disagreement between specialists on the issue indicated in the title, it still seems impossible to point to direct experiment that would resolve this issue beyond any doubt. Concerned with devising such an experiment, I focused on one so simple and convincing that I can consider the goal achieved. According to the concept developed in my article “Observations and Experiments on Crystallogenesis,” the solubility relative to each face of a crystalline substance is directly proportional to its lattice density, and therefore, the more complex the symbol of the observed face (with the crystal correctly oriented), the smaller it is, while for irrational faces it is even zero.

When studying certain physical properties of crystals, it is often advantageous to operate with crystals ground into spherical forms, since in this case we directly obtain the specific magnitude of its change for each vector. However, as far as I know, no experiments have yet been undertaken on the crystallization of spheres artificially prepared from a crystal of a given solid substance. Meanwhile, this form of crystal is important in terms of reducing the influence of crystal planes on the crystallization currents that arise during the deposition of a substance from a solution.