Vol 4 Iss. 4

Efimov, a student at the Mining Institute, (born in 1872), died suddenly in a train carriage. Efimov enrolled at the Mining Institute in 1903, when out of more than 700 candidates sitting for the entrance examinations, 93 were admitted, 25 of them with a university education. Thus, strictly by competitive examinations, with only secondary education, 68 persons were admitted He was expected to graduate from the Institute this year. He used to work 20 hours a day, but finally, his health gave out ...

I take this opportunity to note, for the thousandth time, the advantages of the method of new geometry, the theorems of which know no exceptions, but always possess perfect generality. This author has already presented the proof of this theorem, which I communicated to him, using the method of new geometry. It seems to me far more expedient and simpler to formulate A.K. Boldyrev’s theoremas follows (see the article). A.K. Boldyrev's theorem in its generalized form, according to the method of new geometry, reveals one of the interesting properties of spheroprimes of vectorial circles.

The right-rotating and left-rotating pure modifications of campheroxime and their mixtures were studied; among the latter, there is an inactive modification that does not rotate the plane of polarization.

The presented, highly simple proof, although it uses the lemma of Prof. V. A. Steklov, expressed by formula (41), still differs significantly from the various proofs of the same theorem given by Prof. V. A. Steklov and is closer in its idea to the proof of Prof. Hurwitz (based on the Cesàro-Reyer method of arithmetic means), having, it seems to me, the advantage of greater simplicity, since it is based on the application of a known theorem on term-by-term integration of trigonometric series, which itself represents a special case of the closure theorem.

Strict balancing of mine sites using the least squares method can be said to be almost entirely absent in practice. The reason for this is the complexity of the calculations associated with balancing using a strict method. Meanwhile, in practice, it is often not interesting to know the corrections of individual measurements, or even the corrections of the coordinates of individual points and azimuths of stations, but it can be very desirable to know the correction of the coordinates of a single point and the correction of the azimuth of a single station, which, say, will serve as the starting point for surveying a new site or which are obtained based on another survey, and the question of balancing the nodal point arises.

Anhydrous crystals of this substance are obtained by the action of ethyl alcohol on a solution of mercury nitrate according to the formula (see the article). They crystallize from a hot aqueous solution. This salt may be regarded as a salt of fulminate acid or of carbidoxime. The measured crystals were extracted from a dust-like powder, in which, however, due to the extraordinary luster of the microscopic crystals, shiny points are nevertheless visible, the luster is partly due to admixed droplets of mercury.

This specimen of abiethic acid with a melting point of +143°C., was obtained by O. O. Koshelev in the laboratory of Prof. Chugaev from a solution in ethyl alcohol in the form of colorless transparent crystals. The crystals belong to the orthorhombic system of the gynohexagonal type and have a lamellar appearance, with the most prominently developed face (0101) and are almost always elongated in one of two directions: either along the [1000] axis or along the [0121] axis. On all observed crystals, the (0101) faces were strongly and completely irregularly curved. See the figure and measurement results in the article.

In this article, the former system of calculation has been replaced by a new one proposed by E.S. Fedorov. Anyone who has made use of crystallographic literature, even revised works such as Groth's "Chemical crystallography", knows how inconsistent and often the completely confusing the data can be, making it impossible to construct a diagram, and therefore, to make use of the author's research efforts. Such complete inability to reconstruct the crystal complex led to the creation of a new system of calculations using bipolar coordinates, which, with the slightest misunderstanding in the data angles, can restore reality.

We have two equal mutually tangent circles O1 O2. We have a line AB, tangent to both, and a new circle C, tangent to both data. We assert that the point of intersection of these two tangents, i.e. points D and E, as well as the point of tangency of the two given circles, i.e. point F, are equidistant from the point G, i.e. from one of the points of intersection of the circle C and the line CF. A proof by Prof. E.S. Fedorov.

With regard to the theory of confocal aggregates, the conclusion drawn shows that the aggregate of surfaces derived from an imaginary hyperbola taken as the focal curve does not represent anything new, and is included among those derived on the basis of a real hyperbola. If we take into account that, in the general case, we have, linked by the principal axis, two focal curves in two mutually perpendicular planes of symmetry, one of which is an ellipse and the other one a hyperbola, and that in the third plane of symmetry the focal curve can be neither an ellipse nor a hyperbola, and, as it now turns out, an imaginary hyperbola, then the only remaining possibility is to admit an imaginary ellipse, thereby completing the derivation of focal curves. In conclusion, we note that involutions can also be derived on the plane at infinity; since from any point three normally conjugate rays are projected onto it, the corresponding projectivity curve is an imaginary circle, and this is the case for any confocal aggregates in space.

In this article, I present, as complete a list as possible of crystals of the cubic system obtained to date. Here we are indeed dealing with a series of substances exceptional in their properties, as the forms of the cubic system are exceptional among all others. Once the list is compiled, this exceptionality in the chemical composition of the substances is striking, if only the possibility of dividing them into the few categories that form the basis of my exposition. Other features of the chemical composition of substances in this series will be discussed at the end of the article. It was necessary for me to compile this list already for the purpose of singling out,from among those described, the crystals that are not amenable to determination by the method of crystal-chemical analysis.

The article raises the question of constructing edges from symbols in crystals for complexes of hypohexonal type — a question that has not yet been raised by anyone. It is resolved, of course, extremely simply and moreover in a manner completely analogous to its resolution for the cubic type. I have shown that in complexes of the hypohexagonal type, the symbols of edges are such that, in the particular case of a hypohexagonal-isotropic complex, the indices of the edges and perpendicular faces are the same, as required by the theory of crystal systems (because in this case, the ellipsoid of the crystal system is a sphere).

In a grammastereographic projection, any plane is projected as an arc of a great circle, that is, an arc passing through two diametrically opposite points of the projection circle. This circle represents one circular section of the cone having its center at the point of convergence of the rays; the other circular section of the same cone is the diametral circle of the sphere in the plane being projected. Apparently, no crystallographer has yet noted that these projecting cones are not cones of a general nature, but are special cones, known as the cones of Pappus, who first noted their simple construction. The two special axes of the projecting cone are perpendiculars to both circular sections, that is, perpendiculars to both the given plane and the projection plane (see the article).

In these Notes (III 287), I devoted a brief article to this subject, in which I confined myself to a complete derivation of the geometric images pertaining thereto. The same derivation, of course, could be carried out by other means, which would necessarity lead to identical results. All conoprimas, for example, can be derived from circles by means of a collinear transformation, but also by the intersection of two projective primas of rays, and it is evident from elementary manuals that the latter example, if not more accurate, is at least more intuitive, and in this sense simpler (see the article). From the brief article mentioned at the beginning, it is clear that the existence of special circles and spheres introduces great disruption into the concepts of the circle that have become established, not merely over centuries, but over millennia. As proven herein, the notions of center and of equal radii must be completely eliminated from this concept.