Vol 2 Iss. 4

Amphibole. Pyroxene. Aegirine. Enstatite. Hyperstene. Babingtonite. Lievrit (ilvait). Beryl. Phenakite. Troostite. Willemite. Sphene (titanite). Parisite. Gold. Cerussite. Aragonite. Quartz. Olivine. Neptunite. Cinnabar. Celestine. Barite. For a detailed description of the crystals, see the article.

An algebraic equation F(x,y) = 0 is given, of degree μ with respect to x and degree ν with respect to y. We are required to replace x and y by new quantities ε and η by means of the equations. It is required to replace x and y with new quantities ɛ and ɳ by means of equations. ɛ = j(x,y), ɳ = f(x,y), j and f are rational functions. With a few exceptions, which should be the subject of special research in each particular case, transformation (2) will be birational. This transformation can be carried out through rational actions in the following ways. Let's consider a way to reduce a hyperelliptic integral.

Cobalt‑amino‑chloro‑dimethylglyoxime was first obtained by L. A. Chugaev, who offered it to one of the authors for crystallographic study. Crystallization was carried out at about +20 °C from solutions in water containing 5% acetic acid. In this solvent, the compound under investigation is rather sparingly soluble in the cold, its solubility increasing upon heating. An excess of the powdered substance was heated in the solvent on a water bath to approximately the boiling point; the hot solution was then filtered and cooled at room temperature (about +20°C). For the results of the investigations, see the article.

During the slow crystallization of cobalt - amino - chloro - dimethyl - glucosimine at + 18-20 C, certain crystals of this compound develop special, enigmatic faces. These faces differ primarily by their size, since they are usually larger than the others and formed so perfectly that when measuring, one can rely on measurement accuracy within a few seconds. However, by their orientation they do not seem to belong to the crystal's normal morphological set, since their indices are extraordinarily complex, almost irrational.

Let's imagine a crystal being measured on a universal, theodolite goniometer. Let's assume we have to measure a face that has various defects in formation and produces not one but several signals (due to the development of vicinal forms). Under such conditions, the measurement accuracy is significantly reduced and rather large errors can be made in the readings of the angles φ (along the vertical limb of the goniometer) and ρ (along the horizontal limb). Even if a face is formed reasonably well , one can often still vouch for an accuracy of only a few minutes, and higher accuracy is achieved only in exceptional cases.

In the Zapiski G.I. on page 259, regarding the compilation of tables for crystallochemical analysis, some statistical data on this subject were already presented, although these data were based on less material than is currently available to me. A major step has now been taken to compile these tables, namely 3,730 diagrams have been compiled based on the material contained in 42 volumes of the Zeiteschrift für Krystallographie, including both its original articles and abstracts (several hundred of these diagrams have already been verified by the staff and thus their orientations , and therefore their places in the tables, have been confirmed).

Currently, crystallography widely uses graphical techniques to solve its problems. Increasing accuracy is also one of the goals set in the development of graphical operations. As for the design of the new device, we mainly note the much larger dimensions of the device, of which the black hemisphere, as the main working part of the device, has a diameter of about one arshin plus. The second device is a universal three‑axis contact goniometer. It is used for routine measurements by the universal method of crystals so large that they can no longer be mounted on the crystal holder of ordinary goniometers. The third device is designed to facilitate the crystallization process. The principle of its operation consists in the rhythmic heating and cooling of the vessel containing the solution in which crystallization occurs.