Vol 1 Iss. 4

This work, although it represents only one of the most important links in my extensive work on the states of matter, which I publish, for certain reasons, in German, is a completely accomplished independent whole. This work treats the question of the influence of the concentration of reacting solutions on the appearance and structure of sediments - a question that has not yet been completely undeveloped in science, except for a few fragmentary observations.

Among the deviations from the laws characteristic of real (ideal), that is, completely crystalline-homogeneous individuals, small deviations are often noticed both in the orientation of faces and, in general, in the intergrowth of subindividuals.

The study of the electrical conductivity of metal alloys makes it possible, along with other physical research methods, to judge their chemical nature. Matthiessen, who carried out classical research in this field, was the first to try to find the relationship between the composition and electrical conductivity of alloys. But at that time (the 60s and 70s of the last century), ideas about the nature of alloys and information about their structure were so imperfect that it is not always possible to agree with the author’s conclusions on this issue.

Let us vary x along a closed curve in the positive direction. The full description of the proof is provided in the article.

Let us take the integral and find a substitution of the lowest degree, by means of which we can achieve the reduction of this integral to an elliptic one.

The article “Precise representation of points in space on a plane”, solves the problem of such representation in three different elements: vector and ordinary circles, and parallel vectors. It also provides a practical application of representations in parallel vectors of a system of mines. I will now show an essential application of the theory for the representations using vectorial circles of spatial lattices of each crystal studied in structural terms.

The studied specimens are graphite-hosting rocks from various graphite deposits: the Mariinsky mine on the Botogolsky Golets (Aliberovskoye deposit), the Barrowdale deposit in Cumberland and two Ural deposits - one near the Sysertsky plant; the location of the other deposit is unknown - probably from the Ilmen Mountains.

We know that from two given points eand e' and a conic section K in the plane, we can generate a second‑order curved surface, if we take one of these points, e,as the center of a second of rays, and the other point, e', as the center of a second of planes, and bring these two seconds in a correlative relationship such that to the ray ea (where a is a point on the conic section plane) will be considered correlative to the plane e'A, where A is the polar of point a with respect to the conic section K. It is known that in such a surface a set of rays and their correlative planes intersect.

No matter how elegant the construction of conic sections using Pascal's theorem may be, it lacks sufficient generality, since it is applicable only for five real points of a curve, and in practical application it is more complex than some other methods.

In my numerous reports and articles published in Russian and German from 1905 to 1908, I experimentally proved that the appearance and structure of a sediment of any substance can be changed at the discretion of the researcher.

In my previous studies, published in 1905-1908 in Russian and German, I showed that any substance, both of simple and complex chemical composition, can be obtained: in well-formed clear crystals; in an “irreversible” colloidal state (in the form of sols and “irreversible” colloidal-amorphous sediments); in a “reversible” colloidal state (by rapid cooling and increasing the association of dissolved particles into the solution).

I consider it useful to note one property of stereographic projection, which, although it does not open up new ways for solving problems, still can contribute to greater accuracy in solving some of them.

In 1891, 20 versts northeast of Vologda, near the Church of St. Nicholas of Vozimsky (near Lake Kubinskoe), a piece of iron was found under a peat mass within a bed of bog ore, shallow from the surface. It was originally covered with a loose coating of ocher and immersed in the bog ore; its weight together with the ocher was 1100 grams. In some places it was permeated with rust to a certain depth. Freed from the ocherous shell, it took the shape of a spherical sector measuring about 10 centimeters wide and about 5 centimeters thick; it was veined and, in places, contained fine-grained inclusions of ocherous magnetic ironstone.