Vol 3

The descriptions of the aforementioned meteorites available in the scientific literature were produced using insufficient material from major collections of meteorites and require more detailed characterization. The previous distribution of the main masses of these meteorites, currently held in the museum of the Mining Institute, was highly imperfect and did not allow for a detailed and complete description of them; among these, some fragments — and in part even the enormous main piece of the Augustinovka meteorite, left to their own fate became covered with thick layer of rust.

In the summer of last year, 1909, I undertook several petrographic excursions in the vicinity of the Miass plant, mainly with the aim to become familiar with the alkaline rocks developed in this area. The collected material was subjected to microscopic investigation, which provided some data that, perhaps, will be useful for determining the petrographic composition and structure of this area.

On February 23, 1911, in his 65th year, former director and distinguished professor of the Mining Institute, mining engineer Joseph Ivanovich Laguzen, passed away due to a stroke. He contributed significantly to the paleontology and geology of Russia. In paleontology, his works were diverse, but primarily devoted to the study and description of the fossil faunas of the Jurassic and Cretaceous systems. In 1887, he published well-executed lithographed notes for his course on paleontology, and in 1895-1897 he published "A Short Course in Paleontology.” This was the first paleontology textbook published by a Russian professor. This work, in its significance, extends beyond the limits of a textbook, just as it went beyond the scope of the course taught at the Mining Institute. The article provides a list of I. I. Laguzen's scientific works from 1868 to 1891.

In the summer of 1908, I was sent by the head of the Stavropol Land Management Party to the area of the Stavropol Udelnaya Steppe and its surrounding heights to collect material on the geological composition of the area and to possibly clarify its tectonics. The ultimate goal of these studies was to determine the feasibility of extracting water in the Udelnaya Steppe through artesian drilling. In the attached outline, a detailed description of the outcrops is omitted and only their essential features are noted. On the map and cross-section, different numbers indicate the outcrop numbers and conventional symbols show the geological horizons. The Udelnaya steppe is located near the border of the Stavropol province and the Kuban region, south of the city of Stavropol.

CuSO₄+5H₂O crystals have been studied by several authors. The most comprehensive investigation of crystals of this compound was carried out relatively recently by Th. V. Barker in the laboratory of R. Groth. Copper sulfate crystals, as is known, belong to the cynacoidal class of the triclinic system. CuSO₄+5H₂O crystallizes (at t° = + 20°C) from an aqueous solution into well-formed thick tabularcrystals. The article includes a diagram for the correct orientation of crystals.

In the article "Parolleloëder in kanonischer Form und deren eindentige Beziehung zu Raumgittern” I developed the concept of parallelohedra in canonical form or simply canonical paradelohedra. I based this primarily on the property that their derivation from spatial lattices should be unambiguous. However, in this is article I examined only one aspect side of the question, related to the angular relationships of crystalline complexes, which, in accordance with the crystallographic law of limits, bring crystalline complexes in general closer to ideal types. These relations characterize the distribution of angles, which determines the assignment of these types to certain types of syngony, with right angles playing a primary role (see the article).

In the article “Paralleloëder in kanonischer Form und deren eindeutige Beziebung zu Raumgittern” I showed that by performing a monoclinic shift, you can always obtain an identical spatial lattice, and in doing so sometimes you can reduce nonorthogonality, that is why the expression for the probability of correct orientation will increase, even though this causes the form symbols to become more complex. But I did not dwell in detail on the criterion for exactly at which shift the lattice remains identical. This is the explanation I want to make in this note.

The more processed material is accumulated according to the calculation of the correct orientation, the more pronounced is the need to limit this calculation to the minimum number of the most important faces. Laboratory crystals are most often exhibit a minimal number of developed forms. This was confirmed in the case of barite. Despite their appearance, which is almost no different from the usual appearance of many natural barite crystals, their combination is minimal and through this the first most important faces are particularly emphasized.

Suppose wehave a unit volume of a solution of substance X in some solvent Y; add to the solution of another solvent Z, which dissolves solvent Y well, but practically does not dissolve substance X, even if solvent Z is mixed a little with solvent Y. Then solvent Z will begin to extract solvent Y out of the solution and substance X should precipitate as crystals.

In my report of April 6, 1906, I wrote that two factors play the most important role in the process of melting dispersed systems: the degree of disruption of the continuity of the body and the associated change in the conditions of heat transfer, both before the melting process and during this process The degree of discontinuity affects, firstly, the latent heat of fusion, and, secondly, together with the altered conditions of heat transfer, the softening of the solid system even before the start of melting. The surface layer of a crystal is chemically inhomogeneous, which affects the physical and physicochemical properties of the substance especially strongly at a high degree of dispersion.

A furnace is a device that is capable of converting a known type of energy into thermal energy for the use in a specific thermal process. We will only dwell a little on furnaces that heat rooms, muffle furnaces and steam boiler furnaces and will begin to study the proper factory furnaces. See the author's conclusions in the article.

The process of chiseling on a rope with a non-free-falling tool rotated by hand is slow. The rope greatly deteriorates and shortens due to frequent splicing and winding onto the spiders. The slowness of chiselling with such a tool, due to a non-free and weak blow, is further increased by the fact that it is necessary to splice the rope, wind and unwind it with each descent and ascent of the tool from the spider and, finally, replace from time to time the rope consisting of pieces with a solid one. All these shortcomings are eliminated if the tool itself is self-dropping, delivering a strong blow, and rotates automatically, regardless of the rope, because in this case there is no need to separate the working part from the spare part and wind the rope onto the spiders.

Regarding the petrography in the vicinity of the gold deposits of the Tsarevo-Alexandrovskaya distance of Miasskaya Dacha, which became famous particularly due to the discovery of the largest Russian gold nugget (2 poods 7 funts 92 zolotniks), the information available in the literature is very scarce; for the most part, it consists only of brief mentions. A geological map of this area, quite schematic, is provided in the article by mining engineer Kulibin. The rock formations are highlighted on it, but without their description. In it, the author mainly lists the gold-bearing veins known at that time and dwells on certain nuggets.

I wish to point out the importance of knowledge of thefundamental principles of colloidal chemistry for other branches of natural science. Knowledge of them is necessary for a physicist, because a deep understanding of the doctrine of states of aggregation is impossible without a clear assimilation of the properties of dispersed systems. For a crystallographer and a mineral chemist, these foundational principles of the study of colloids are no less important, because, when obtaining highly dispersed systems through the method of crystallization, we are present at the birth of a crystal and monitor all its embryonic forms. The study of colloidal chemistry is even more important for representatives of the biological sciences, since the true cradle of nascent life is a typical complex disperse system — plasma.

In this article I wish to share with readers some of the results of my experiments on the gelation of solutions, which, although obtained back in 1908, have not been published in sufficient detail. In my work on the gelation of solutions, I came to the following four conclusions (see the article and tables). In conclusion, I would like to draw attention to the fact that during the so-called “salting out” of organic colloids, the hydration capacity of the added salt plays a certain role, because, at least at a sufficiently high concentrations, there must be a struggle between the salt and colloid molecules for possession of hydration water.

In this article, only the following dispersed systems will be considered: Liquid + Solid. Liquid + Liquid, moreover, in view of the identity of the characteristics of the three types into which classes a and b are divided, I will limit myself to a more detailed analysis of the class a types. Any dispersed system can be characterized by: 1. The magnitude and sign of the dispersing (or aggregating) force, 2. The degree of dispersion at a given moment, 3. The aggregate state of the dispersed phase. 4. The degree of contamination (adsorption) of the surface of the dispersed phase.

This note contains neither any significant innovations nor any systematic solution to graphical issues. However, given the widespread development of graphical solutions that crystallography has received recently, and especially with the introduction of crystal chemical analysis, even the most insignificant simplification or reduction in techniques takes on considerable practical significance. Finally, some rules lead to a reduction in graphic operations in a particular field of applications only in certain, although numerous, cases, it is inconvenient to include them in elementary courses, where only the most general rules should be presented systematically, so that students receive a valid ability to solve problems of all kinds, even if not always in the simplest way.

In view that the tables for this analysis have now been compiled, it was possible to begin applying this scientific discipline. A total of 5 tables have been compiled, namely, all tetragonal crystals are divided into 3 tables according to structures (hexahedral, dodecahedral and octahedral), and in addition, there is one table for hypohexagonal and trigonal crystals (for the latter, structures are marked only for ideal crystals due to their significant accumulation). In all tables, ideal crystals are highlighted in a special column, and it is for them that we have the densest arrangement of points, which is why, bearing in mind the inevitable inaccuracies in the graphically obtained constants, for such crystals in particular we will have to compare the largest series of crystals.

Among the extremely valuable donations made to thethe Mining Institute Museum, is a specimen of pseudo-crystals of enormous size, currently composed primarily of malachite. From this specimen, it was possible to extract small tabular pseudomorphs that perfectly preserved their original form, partly even with mirror-like, lustrous faces. Due to this circumstance, the method of crystal chemical analysis could be applied with exceptional clarity, allowing it to be established with full certainty that these were pseudomorphs of atacamite. Using the tables of crystal chemical analysis, the entire series of substances was revised according to the symbol closest to that obtained from an approximate measurement, and identity in form was found for only for one substance, namely atacamite. These findings are presented in this note.

This paper presents the results of further research undertaken to determine the optical symbols of various minerals. A table of individual observations in mica plate is provided. At the end of the article, more detailed data regarding observations in simple and combined plates are provided, as well as the characteristics of individual members of the group under consideration (muscovite, alomite, biotite, phlogopite, etc.).

Enigmatic faces can practically be viewed as irrational, not allowed by the fundamental laws of crystallography. The assumption of their irrationality is further confirmed by their overgrowth upon contact with an important face of the complex, wetted by a saturated solution of the substance, whereby a part of the latter face is subject to dissolution. In addition to this characteristic, enigmatic faces are distinguished by their singularity and non-repetitiveness.

This amendment is made by me to the note “An interesting crystal of apatite, a companion of neptunite from California.” (Zapiski G.I. II 253) based on a written indication from Dr. Slavik of Prague, who noted my error based on data from my own description, primarily pleochroism. Having tested the hardness, which turned out to be slightly higher than that of orthoclase, I can now state with full conviction that an error occurred.

Essay by v. Weymarn “On the Doctrine of the States of Matter” represents the first chapter of his conceived and partially already completed work on the structure of matter based on the data obtained by studying the so-called "colloidal" state of bodies. Weimarn's discovery of a universal method for obtaining all kinds of crystalline substances (crystalloids) in the so-called colloidal and amorphous states led him to propose that both states are inherent in all bodies and depend only on the degree of fragmentation of the substance, and therefore, on the relative development of the surface, and that, furthermore, there is no other difference between the crystalloid and colloidal-amorphous state of a body, and to attempt revise our ideas about the nature of matter, based on the above principles.

I have encountered this mineral in a massive form moderately rounded pebbles up to half the size of a fist, consisting of barite with a minor inclusions of galena, in the bed of the Naratay River, two verts to the southwest of the Narataevsky iron mine. The barite in these pebbles forms a medium- to coarse-grained aggregate, with indivisible particles often arranged in an elongated manner in one direction, forming a somewhat layered structure.

All available samples contain, in greater or lesser quantities inclusions of ore minerals: pyrite, zinc blende and partly galena. This clearly indicates that they were taken in the immediate vicinity of the ore body. The spatial location of these samples is evident from the accompanying diagram. As is known, the Zyryanovskoe deposit constitutes a rather irregularly branched gelatinous mass.

When crystallization is accelerated by cooling the initially heated solution, the crystals of these compounds begin to take on an increasingly needle-like appearance. The crystals of the iodide compound are so small (no more than 1/2 mm in length) that their goniometric study appears extremely difficult, and I preferred not to perform it, especially since this compound decomposes very easily in solution. The crystals of the chloride compound have already been described earlier. However, after E. S. Fedorov's final clarification of the principles of correct orientation, the face symbols of these crystals must be changed according to the transition determinant (see the article).

In the last article “Chemical relations of rocks and their graphical representation” I focused on the method of tetrahedral representation , which I had proposed earlier, as the most perfect and simple method. At this moment, with the intentionof further simplifying the same method, I once again focus on it as the most perfect. Thus, the purpose of this note is neither to revisit the theoretical issues examined using this method in the aforementioned article nor to introduce any changes to its applications. Everything elaborated in this article remains equally valid to me at present. Now, I only mean to demonstrate that the method proposed then can be applied in a wide variety of forms and to select exactly the one associated with the simplest operations.

The points constructed according to the methods just described are distributed on the proposed diagram, as can be seen immediately, in a certain orderly manner along an arc, making it possible to predict the optical properties of as yet undiscovered biaxial minerals: it is highly probable that for such minerals, their relative birefringence determinants will give points on the diagram distributed between the already known points on the same arc of our diagram. Consequently, the reverse is also true: taking any point between those already known on this arc, we can expect that it corresponds to a mineral that is not yet known, and based on the determinants found, we can calculate the angle of the optical axes using the known formulas that were given at the beginning of this article.

A method has been developed for preparing alloy specimens suitable directly, without further mechanical processing, for measuring electrical conductivity; this is especially important for brittle and easily oxidized alloys. The electrical conductivity and its temperature coefficient were measured for five alloy systems with clearly defined compounds, the nature of which was precisely established, by means of various metallographic methods. Existing theories of electrical conductivity of alloys have been analyzed. An attempt has been made to theoretically explain the differences in the properties of the temperature coefficient between certain compounds and solid solutions, which are not provided by the existing theories.

Differential equations are considered with respect to theorems related to the Monge and Ampère equations (see the article).

These curves can serve as a guide when choosing a combination of points that is advantageous for direct intersection; and in this regard, they seem to be more rational than the curves of equal accuracy shown in Fig. 2. The latter curves retain their value for the graphical or mechanical balancing of the position of a point determined from more than two points. In this case, using these curves, we can easily determine the weight corresponding to a given combination of points and take it into account when deriving the balanced value of the coordinates of the latter.

If we are given a triangle ABC and define its orthocenter D in it (that is, the common point of intersection of the perpendiculars from its vertices to the opposite sides), then ABCD can be taken as a complete quadrangle with pairs of opposite sides AB and CD, BC and DA and CA and BD . Drawing a circle through the bases (a₁, b₁, c₁) of the perpendiculars on the sides of the triangle, we obtain a Feuerbach circle, which, in addition to these three points, will pass through six more midpoints of the just listed sides of the complete quadrilateral, that is, points a₁, b₁, c₁, a'₁, b'₁, c'₁.

In my article on the system of spheres, I outlined their linear and spherical aggregates, the collinear and reciprocal transformations of these aggregates, but did not address at all the special circles present in each of their linear primas. It was only implied that among all the circles of such a prima there is a circle of infinitely large radius, and such a circle is a straight line constituting the radical axis of the prima. As if in contrast to this, in the scientific literature, starting with Shteiner, it is implied that in the linear prima of circles, the special element is not a single straight line, but a pair of straight lines, one of which is the radical axis, and the other is the line at infinity; but I am not aware of any work that specifically analyzes the question of special circles. With this short article I intend to fill this gap.

Let us consider systems of second-order curves (conoprimas). In a system of conoprimas of points, circles can be taken as extra elements, because these elements themselves constitute a special system, and, at the same time, any curve together with a circle defines a linear prima. But in general, such an extra element does not exist in a linear prima, only in a linear second. However, one can form a linear second from the linear prima of ordinary (not vectorial) circles and some other conoprime. Such a linear second, however, will already be a special one, and must therefore be regarded as a particular system, and such a system will be related to a system of points on a plane, with the points at infinity of the latter being projectively correlated in a special way with the circles of the former. Also, if we compose a linear third from any linear second of circles and some other conoprima, then such a system will be related to a system of points in space. But all these will be particular , special systems of conoprimas of points.

If it is impossible to uniquely determine an infinite set of rays from two arbitrarily given rays, then this can be achieved based on three arbitrarily given rays. It is well known from elementary textbooks that three arbitrarily given, non-intersecting straight lines, can completely and uniquely determine a certain one-sheeted hyperboloid. Since this curved surface of the second order does not consist of one, but two systems of non-intersecting lines, it is clear that only from one of them, which includes the three given lines, can be determined directly by the three lines, and then it is logically inevitable to also accept the other set which occupies a position in space identical to the first system, i.e., the surface of a hyperboloid of one sheet.

In the "Annual of Geology and Mineralogy of Russia", in the article on “Crystallization in a solid medium,” I have already described an experiment on the transformation of a highly hydrated magnesium sulfate, which forms directly upon evaporation of the solution, into heptahydrate. In that account, I noted that the rapidly growing needles and fibers of the heptahydrate propagate at a seemingly equal rate both in the free solution and when penetrating the crystals of the higher hydrate (namely, MgSO₄ 12 aq). It must be assumed that such an extreme slowdown in the process in extra-thin layers occurs under the influence of partial capillary attractive forces of between the walls of the wedge-shaped space and its contents.

This method, proposed by Becke in 1893, has become widely adopted. As is known, it is based on observing the movement of a bright strip that appears when using high-magnification objectives at the boundary between adjacent mineral grains, as the microscope tube is shifted, focusing alternately on on the upper (upper focus) and the lower surface (lower focus) of the thin section.

It is clear that the complete aggregate, that is, the quint of conoprimas, possesses the highest possible symmetry, that is, circular symmetry. The symmetry of quarts is completely determined by the symmetry of one conoprima, because the symmetry is derived from it is completely and unambiguously. Therefore, in the general case, such a aggregate has a twofoldaxis of symmetry and two perpendicular planes of symmetry (orthorhombic type of symmetry in the plane). In the particular case of the parabola, only one plane of symmetry remains (the hemiorthorhombic type of symmetry). The circle possesses absolutely exceptional symmetry, and therefore there exist linear quarts that exhibit circular symmetry. From this we conclude that if one takes an arbitrary conoprima and a pentad axis of symmetry, from which five equal elements are derived to define a linear quart, the resulting a quart will possess circular symmetry. All curves contained in it, are in every orientation, arranged in continuous circles of equal elements.

If it turned out that by choosing one linear prima in one diametral second and then arbitrarily another linear prima in an arbitrary other second, and thus constructing an infinite multitude of hyperboloids, we obtain that the entire aggregate of such hyperboloids is contained within a single third, which itself lies within a single linear quart, then we would be dealing with an entity representing a generalization of the concept of a hyperboloid; such a hyperboloid we could call a hyperboloid of the 4th degree system. The special third, possessing circular symmetry, which was just indicated in the article (“Symmetry of linear sets of conoprimas”) is precisely such a generalized hyperboloid in the system of conoprimes. Since in this system, which addresses an entirely different topic, it would be inappropriate to dwell on the consideration of this issue in all its details, this note has been dedicated specifically for this purpose.

As is well known, the French mathematician Dupin used the name "cyclides" to refer to certain curious surfaces which can be defined as surfaces enveloped by the totality of all spheres tangent to three given spheres. These surfaces are extraordinarily are distinguished by many simple properties inherent to them, studied both by the author himself and by several other mathematicians. They possess two special axes, and if a plane is rotated about these axes, it will intersect the surface in a continuous series of circles, consequently, this surface can be conceived as the trace of a circle moving according to a specific law, being at every point perpendicular to all circles of another such system. All the properties of cyclides are set forth in my manual “New Geometry as the Basis for Drawing” . Therein, however, a special cyclide possessing extremely interesting properties was also derived.

There is absolutely no indication that the former mining operations have ceased and that the ore-bearing conditions, which are evident here in any case, have disappeared. Admittedly, there is no reason to claim that we will certainly encounter rich ore deposits here; but it must be said that everywhere and even in other places, no matter how favorable the observed conditions may be, it is risky to make positive statements, but given the conditions depicted on the geological map, it is more likely to assume favorable rather than unfavorable results. The Nikolo-Podgornyi mine occupies a very special position. From a geological point of view, it is one of the most interesting points in the area, both in terms of the distinctiveness in the development of the rocks, their complete exclusivity among others, and in terms of the unexpectedness and novelty of the rocks themselves and the geological conditions in which they were formed.

One of the fundamental principles of dispersoid chemistry is the assertion that all properties, both physical and chemical, are functions of the degree of dispersion of a given dispersed system. The author considers the following issues: 1) The effect of increasing the degree of dispersion on the electrical conductivity of chemically pure metals; 2) The influence of the degree of dispersion on the electrical conductivity of alloys representing a mechanical combination of component crystals; 3) The electrical conductivity of coarse-dispersed alloys representing solid solutions; 4) Alloys representing solid solutions and electronic theory; 5) The electrical conductivity of coarse-dispersed metals at very low temperatures; 6) The electric ultramicroscope.

Crystallization of this compound was carried out at a temperature of about +20°C from solutions in methyl alcohol, in which it dissolves quite easily even in the cold. Solubility increases upon heating. A total of 57 crystals were examined. The results of the examination are presented in the table (see the article).

For the correct orientation, 100 crystals were re-examined. The results of the re-examination and calculations of the probability of correct orientation are given in the tables (see the article). Using asparagine as an example, the regularity of the decrease in the number of developed forms as the crystal sphere grows is demonstrated with exceptional clarity and distinctness. Furthermore, during subsequent crystallization, the appearance of any new forms not observed in the preceding crystallization was never observed. From all the experiments described above, it clearly follows that there exists possibility of obtaining a much greater number of forms during the crystallization of a sphere, compared with what we observe during the free growth of crystals of the same compound.

The investigation of Mount Magnitnaya, carried out by me this past summer on behalf of the Board of the Joint-Stock Company of the Beloretsk Iron Works, constitutes the beginning of work, whose practical goal is to determine the iron ore reserves of this deposit. In addition, these investigations were intended to clarify the srucural features of the deposit, which must be taken into account when devising a rational extraction plan. The work consisted of compiling the most detailed geological map possible; determining, in accordance with the data obtained as the geological investigation progressed, the location and type of exploratory work necessary to the ascertain reserves, and carrying out of these works.

Until now, no universally accepted method for determining compressor efficiency has been established; therefore, comparing compressors of different sizes and systems based on test data is extremely difficult, since each experimenter adheres to their own approach. In what follows, the author attempts to establish rational principles for determining compressor efficiency, such that the comparison of results obtained in individual cases would not present difficulties.

The law of Matthiessen and Vogt makes it possible to bring together two classes of alloys. Both represent mixtures, the former are substances that correspond in their properties to the temperature of observation, the latter are substances that appear to have been heated to a higher temperature, and therefore possess somewhat different properties, yet these properties can be predicted, since this fictitious higher temperature determines the meaning and magnitude of the changes they may have undergone. This can be confirmed to a certain extent by the effect of annealing on the electrical conductivity of alloys, for example, the thoroughly studied pair of silver and copper. Before annealing, alloys exhibit greater resistance, being initially in the hardened state.

Goniometric study. For measurements, the crystals were adjusted acording to the most developed belt, indicated on the attached diagram by the symbol [0121]. A total of 17 crystals were measured, of which six were used for calculating calculating the φ and ρ coordinates (see the article). Optical investigation of the crystals of 1-phenyl-2-parachlorophenyl-3-fenchyl-imidoxantide on E. S. Fedorov's universal stage established the following orientation of the axes of the optical ellipsoid: the NgNp plane coincides with the cleavage plane (1000), and Np coincides with the direction of crystal elongation, i.e. [0121].

Taking into account the immeasurably greater simplicity of the method of new geometry as a method of mental construction (without the help of any auxiliary complex adjustments), one does not need to be a prophet to foresee that modern geometric analysis, in pursuit of its goal, will supplant algebraic analysis, and the role of the latter will be reduced to such symbolic a expression of the conclusions of geometrical analysis (which is necessary in order to replace the essentially imprecise implementation of geometric constructions in practical applications with precise calculations and calculations), which makes it possible to express results in exact numbers.

A collineation with an imaginary involution can also be characterized by two such self-collinear rays, of which one is infinitely distant in the horizontal plane, and the other is vertical. Although these two rays are indeed self-collinear, and are in no way axes of collineation with a real involution, as two special rays, characterizing the symmetry of the system, we could conditionally call them the axes of imaginary collineation (a conventional abbreviation for collineation with an imaginary involution). We see that these systems possess a center, three double axes of symmetry passing through it, and three planes of symmetry, each passing through a pair of these axes.

This includes, on the one hand, the substance obtained by Anschutz u. Beckerhoff as the benzoyl derivative of amylphenol, and the benzoyl derivative from tertiary amylphenol, the crystals of which were described by Hartmann, and on the other hand, the substance obtained by the same chemists, benzoyl ester of tertiary-amylphenol, the crystals of which were described by Schwanke.

The question posed is so elementary that, it would seem, its solution should be found in the most elementary textbooks. However, this has not happened, and in the most comprehensive manual available - Reye, 'Geometrie der Lage', in Chapter 3 of Volume II, which specifically treats the perspective position of linear seconds, only the conditions under which two linear primas are considered (as usual, only two systems are considered: a system of points and a system of planes) are in perspective position. Therefore, I deem it useful to consider this issue in its general form.

Two cases are considered: 1. The property of crystals with an optic axial angle 2V=90°C. 2. Determination of the optical sign of a biaxial crystal on the universal stage, when no optic axis is visible. It is possible to determine the position of the obtuse and acute bisectrix of the optic axial angle, and therefore the optical sign of the crystal.