In the present paper the author gives an example of application of his method to the study of the chemistry of rocks by means of diagrams (ref. 1). Here this method is applied to the study of the rocks of Somma and Vesuvius, chiefly according to the data recently published by Rittmann (ref. 6). Fig. 3 in this paper is a diagram of the chemical compositions of these rocks represented by means of vectors. The letter S0 designates trachyte of the Ur-Somma. S1 — products of ancient Somma. S2 — formations of the Young Somma before the historic eruptions. S2′ — products of the historic Young Somma and finally V — products of the activity of Vesuvius. The diagram shows that for every cycle of eruptions the vectors conspicuously change their position corresponding to the considerable change in the chemical composition of eruption products of every cycle. Passing from one cycle to another, we see a displacement of the vectors whose initial points for each cycle are joined together by a dotted line. This displacement goes from left to right, and its direction characterises the type of evolution of the magma in the hearth. Thus in the given example it becomes obvious that there are two directions to distinguish in the position of the vectors: one of them, the more strongly marked, represents differentiation, which takes place in the cycles between paroxysms of the activity of a volcano; the other corresponds to the general change in the chemistry of the magma in the hearth.

In this paper are described different modes of making drawings of a petrographical thin section, with many practical hints. The authors think that the best practical method is to draw after a magnified microphotograph and then to etch the photo.

By "petrochemistry" we should understand the totality of our information about the chemical composition of rocks, consisting of a "multitude" (in the mathematical sense) of chemical analyses of rocks, and the conclusions that can be drawn from this information. Developing those methods of calculation of chemical analysis that were used by Michel‑Lévy and Osann, the author of this article has shown in other works that the main features of the chemical composition of an igneous rock, as given in its analysis, can be especially conveniently reflected in the form of such series of ratios, the sum of the sets of which uniquely reflects the set of chemical analyses and is equivalent to it. The diagram clearly shows the desired correlation between the lengths and directions of the strokes, depending, obviously, on their position on the diagram. This shows an important correlation between the characteristics of the salic and femic components of an igneous rock.

Random samples of thin sections of molten rocks, which were given to us by A. V. Vvedenskii, were studied. We did not aim at a systematic study of this random, though rather extensive (about 200 thin sections) material, and in this note we limited ourselves to only some data characterizing the more common types of these "artificial rocks". The vast majority of the studied thin sections are glasses that have just begun to recrystallize with the formation of spherulites or various kinds of skeletal formations. Only in a few thin sections could one find minerals individualized in such a form that they were amenable to optical examination. Therefore, the main task of the study was the study of structures, and a considerably smaller amount of work involved the study of minerals.

This article offers an attempt to derive the main principles underlying the application of convergent light, proceeding from the foundations of the theodolite method. This particular approach is the most appropriate if one follows the requirement to proceed from the simpler to the more complex. As will be seen from what follows, the logical development in this direction of the basic provisions of the theodolite method leads to almost the same concepts from which Becke proceeded when explaining the phenomena exhibited by a crystal in convergent light. Apart from some theoretical interest that an exposition of these techniques may have, proceeding from the concepts underlying the theodolite method, it seemed to me useful for the purpose of a comparative assessment of the limits of application of each of these two different methods of research (see the article).

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.

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 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.

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.

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.

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.

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.