Vol 2 Iss. 5

In the article by Prof. E. S. Fedorov, "Representation of Crystal Structure by Vector Circles," a graphical method is presented for finding the reticular densities of crystal faces (more precisely: the squares of the reticular densities of the corresponding nets). Anyone who has dealt with determining the reticular densities of faces by this method knows that it involves making certain constructions—not particularly complicated, but nonetheless quite time-consuming. This article aims to show how the task can be simplified, reducing the drafting work to a minimum.

The usefulness of compiling such detailed tables becomes clear, which, of course, will be compiled when it is necessary to perform more accurate calculations of lattice face densities or edge densities. In all cases in general, except for triclinic crystals, such calculations will be distinguished by significant simplicity, or more precisely, they not at all will be needed once the tables are compiled. Accuracy can also be enhanced when using the graphical method, if we take as the basis for calculations not the gnomostereographic (or gramma-stereographic) projection, but the gnomonic (or linear) projection.

The double salts of molybdic acid, cobalt-potassium and cobalt-ammonium, were obtained by Professor Kurnakov and transferred to the Mineralogical Institute for crystallographic research. The research results and optical properties of the crystals are described in this article.

Cobalt-nitro-aquo-dimethylglucimine was first prepared by L.A. Chugaev, who transferred it to the Mineralogical Institute (of the Mining Institute) for crystallographic research. For the research results and crystal measurement tables, please see the article.

When hauling coal along an inclined plane (bremssberg) using an endless chain or rope, it is sometimes necessary to arrange the operation in such a way that the number of trolleys simultaneously present on the incline is constantly changing. This occurs, for example, when coal is delivered from different levels. Under the influence of the changing load on the rope due to the varying number of trolleys attached to it, the speed of their movement would otherwise have to change. To prevent this, various devices are installed at the terminal pulley to regulate the speed. For instance, a brake of some system is installed, and the speed is regulated by an operator attending it. These brakes have not lived up to expectations. The track constantly became clogged, resistance increased, and the incline with such a device would refuse to operate. I propose, in such cases, to apply my invented automatic incline brake, as it does not possess the aforementioned drawback. Speed regulation in it is achieved automatically under the influence of the increasing load on the rope. Its main qualities are simplicity of design, low cost, and durability.

The objective of the work is to determine the thermal expansion coefficients of crystals using the method proposed by Prof. E. S. Fedorov. The principle of the method is as follows: a plate is cut from the crystal along the required plane, and on one side of it, a diffraction grating is applied by one means or another, the lines of which are perpendicular to the direction in which it is desirable to determine the expansion coefficient. If a beam of monochromatic light is passed through such a grating normally to the surface, a series of deviated rays is obtained, the angles of which with the normal obey the following law (see the article).

Reflecting on the state of crystallography as I found it 40 years ago, and comparing it with the present, I find that its transformation during this period is almost deeper than of any other science. The closeness of crystallography and chemistry seems natural: both belong to sciences of an intermediate nature, situated between the exact sciences, the study of which is entirely reduced to the application of mathematical methods, and the descriptive sciences, where mathematical methods are not applied at all. If we compare the role of mathematics in chemistry and in crystallography 40 years ago and now, we will, of course, see that the latter has undergone a much greater transformation.

When dualism was recognized in the New Geometry, only two geometric systems were adopted the system of points and the correlative to it system of planes. This note aims to show the special significance of such a particular case, which is expressed by the following theorem, if we attribute as cognate two such correlative systems, in which the spheroprims of one are correlative to the spheroprims of the other. "Absolutely all graphic constructions, and therefore all theorems, of one cognate system are transferable to the other." In addition, I mean to show that in general case it is possible to establish such systems where for each of its linear seconds, it is possible to reproduce a cognate system of points on the plane.

I tried to implement the conditions of dispersoid condensation to obtain colloidal ice; my efforts were crowned with success. See in the note: 1. Solid suspensoid solutions of ice. 2. Liquid suspensoid solutions of ice. The example provided in the report of obtaining ice in a colloidal state can most clearly confirm my proposition on the generality of the colloidal state (1906) and my opinion that this state is the result of the corresponding directions of the condensation process.

I have repeated the experiments described in my report “Colloidal Ice”, now with liquid air, strongly enriched with oxygen (boiling point at approx. -185°C) and with the same success. See in the note: 1. On the solidification of water upon mixing it with liquid air. 2. On the production of dispersed systems such as: Ice - liquid air.

As I have previously demonstrated, when mixing sufficiently concentrated reacting solutions, any substance that is poorly soluble in the selected dispersion medium is obtained in the form of a coarse-meshed jelly. The general principle is as follows: by altering the rate of molecular condensation W, any substance, regardless of its chemical and physical properties (such as chemical composition, solubility, etc.) can be obtained in crystals of any degree of dispersity, from very large to negligible.

In my previous works, I provided a formula for obtaining sodium chloride in a colloidal state. At room temperature, as is known, one cannot expect the formation of any significant quantities of complex esters, therefore, the mechanism of the above mentioned reaction is very simple. In view of the decrease in the solubility of NaCl with a reduction in temperature, it is very useful, especially for obtaining stable NaCl salts, to carry out reactions at low temperatures (see the report).

When a thin stream of molten sulfur, superheated above 400°, is poured into liquid air, the sulfur is obtained in the form of very thin threads, 0.5-1 mm in diameter. The threads taken out of liquid air are at first quite solid and brittle, but then, as soon as the temperature rises somewhat, they acquire an extraordinary elasticity, similar to the elasticity of rubber. The more easily it is to obtained a substance in a gelatinous or glassy state, the more capable it is of forming various modifications. Sulfur is the most typical example of such substances.

The author describes in detail the gaseous and dissolved states; the osmotic pressure of colloidal solutions, as well as the differences between suspensoid (colloidal) and suspensied (true) solutions. Highly dispersed colloidal solutions have quite a measurable osmotic pressure, and this pressure cannot be less than the gaseous pressure under the same conditions.

Cobalt-diamine-dimethylglucimine chloride was obtained prepared by L.A. Chugaev and presented by him to the Mineralogical Institute for crystallographic research (see the article). Goniometric measurements (using a universal goniometer by E. S. Fedorov) and optical observations in polarized light revealed that the crystals belonged to the tetragonal system, although their specific class could not be determined.

Especially for triclinic crystals, when determining the lattice plane densities of the vertical zone from tables, it is necessary to apply a shift to the defining faces, and such a shift should be made with greater precision, compared with that which we can achieve graphically. In this case, it will be necessary to calculate the spherical coordinate ρ, which defines the faces after the shift. Solving the problem of such calculation does not present any difficulty, and is already partly contained in one of the formulas given in the article by Sokolov and myself “Determination of the lattice plane densities of crystal faces without the help of constructions"

A sample of the rare mineral Hambergite from a new deposit on the island of Madagaskar was sent to the Museum of the Mining Institute from the Bohm Mineralogical Office in Vienna. The article presents research data on this rare mineral and a description of the original figures on some cleavage fragments.

In the article “The ultimate simplification of zonal calculations and crystallographic calculations in general,” I noted the extreme simplicity that calculations of spherical bipolar coordinates obtain if we take Miller’s formula as the basis. Now I will supplement the formulas derived then with those that relate to the calculation of the cotangents of angles formed with an arbitrarily chosen initial face of the zone (see the note). It can be can concluded that the system of zonal calculations with bipolar coordinates, in its particular simplicity, is applicable without the use of a sequential, recursive procedure of calculation, and directly to faces with arbitrary, complex indices.

Here I mean only what is meant by the word “twin crystals”, and not those regular intergrowths that are caused by mechanical shifts - a case already discussed in my previous works. It seems to me that the experiments of the regular overgrowths of heterogeneous crystals on each other and the conclusions drawn from them by F. Barker completely establish the physical cause of the formation of twins. The most general conclusion from the principle is that the possibility of twinning overgrowth along any plane of a complex, no matter how complex the symbol expressing it may be, for cases of twin faces with a complex symbol, is used in nature under exceptional circumstances.

Vl. Meyer addressed me in a letter, in which he reported on a graphical method for dividing a circle into equal parts using a simple technique (see the article). Of course, theoretically this is not correct; it is impossible even establish the perspectivity of points on a circle and on any straight line in general otherwise than by placing the center of perspectivity on the circle itself. Mr. Meyer's method has no theoretical basis and can only be approximate in relation to a semicircle. This method can indeed be used at least in construction work, for example, when placing pillars and columns around the circumference of a circle.

When solving problems about the correct orientation of crystals (as a basis for crystal-chemical analysis), one constantly has to resort to symbol transformation, while the verification of this solution is associated with the second and further transformations. The task arises to express the final symbols in terms of the original ones. Instead of the well-known transformation formula, in practice we use an abbreviated expression in the form of a determinant (see the article).

Our experiments with alcohol solutions of Na Br, KCl and NaCl gave exactly the same results as for sulfur and phosphorus. To avoid the absorption of water by alcohol, these experiments must be carried out in hermetically sealed test tubes, inside of which, above the surface of the alcohol, a cup (of a special design) with phosphorus anhydride is suspended. Such an arrangement is essential because the solubility of the mentioned salts increases (for S and P, on the contrary, it decreases) upon the absorption of water by alcohol, and the increase in solubility during the experiment greatly affects the course of the condensation and dispersion processes during the heating of solid suspensoid solutions.