Vol 1 Iss. 5

We now know that geometric systems can be very numerous and varied, since very diverse geometric images can be taken as elements of systems. To establish any such system, it is necessary to determine the complete set of its elements and prove that from any two elements arbitrarily chosen from it it one can uniquely construct an infinite set of them, such that by replacing the two chosen ones with any two arbitrary other elements included in its composition, we would also uiquely derive the same set, which would constitute the linear prima of the system.

Experiments on the crystallization of a hemisphere with a diameter of 5 mm, prepared from a K₂Cr₂O₇ crystal with a central plane (100), were generally carried out in exactly the same way as with the crystallization of hemispheres cut from sodium chloride, aluminum alum, and chrome alum.

The author concludes that there exists an infinite number of geometric systems of the same order, derived from each given one. Since the conclusion about the possibility of reproducing from any given system another, paired one, is not limited by any conditions and is determined solely by the possibility of the same positional constructions as for all systems, it is clear that it is equally applicable to paired systems. In other words, we can reproduce a new, paired system not only from any geometric systems in general, but on absolutely the same grounds and from each paired system.

The brown and spathic iron ores of central Russia and the Kingdom of Poland are of enormous practical interest in addition to their scientific value, since they are almost the only iron ores in these two regions, which, due to their geographical location and other conditions, have all the prerequisites for a major iron industry developed here. The author describes ores in the following provinces: Tver province, Kaluga province, Oryol province (bibliography 1837 - 1902), Kursk province, Kingdom of Poland (bibliography 1816 to 1903). The following is a description of the age and origin of the ores of the western part of Central Russia (provinces: Tula, Kaluga, Oryol, and Kursk).

The following issues are considered in the work: 1. Determination of the magnitude of birefringence from readings taken with the compensator and the investigated grain in direct and reversed parallel positions. 2. The degree of sensitivity of the rotating compensator, the Siedentopf compensator and the Fedorov quartz and mica compensators.

Among the remarkable examples of potassium feldspar in the Museum of the Mining Institute there is a very large adularia quadruple from Gotthard St. (Fibia), reproduced in Fig. 1 of the attached table (up to two decimeters in length).

The author came across clear indications (Fig. 3) of the formation of striations in microcline in a thin section from the shores of the White Sea (No. 8, that is, from Gorely Island in the Keretsky Roadstead). I felt obliged to present such an image, which is perfectly clear at 120x magnification.

Since the plane P is only a special case of a second-order curved surface (a conosecund) K, then from this and any other arbitrarily given conosecund their linear prime is uniquely determined. Such will be the aggregate for the determination of which these data are sufficient and can be replaced by any two conosecunds of the same aggregate.

Correlativity is established not only between a system of points and a system of planes, but also between transformations of these systems. Precisely because of this correlative naure this theorem has a dual meaning, so that in its formulation an ordinary lattice can be replaced by a polar one and vice versa. The author considers it necessary to publish this theorem in view of the fact that in crystallography, to determine the symbol of a complex, we perform precisely the operation of shifting the polar lattice using the gnomosteographic projection, while the essence of the change that the ordinary lattice undergoes in this case remained unknown.

I began experiments of this kind back in 1901, when I cut out discs or small rings from thin sections of rock salt and alum, which separated the inner convex from the outer concave spherical line; I introduced a drop of an unsaturated solution into this annular space and covered it with a cover glass, which I sealed with Canada balsam.