Vol 4 Iss. 1

We have obtained a homogeneous linear differential equation of the first order with partial derivatives with respect to q. This equation is equivalent to a system of ordinary cumulative differential equations of the first order (see article). This note was found in the postmortem papers of I. P. Dolbnya. Only the calculations for the example remained unfinished.

In this short essay, devoted primarily to the scholarly and pedagogical work of the late professor, I would first like to share with readers my recollections of the unforgettable, indelible impression which his lectures made on me, as probably they did on almost all of his former students, in their time.

This note is the result of a study of the general nature of the primary gold deposit in the summer of 1911 at the mines of the South Siberian Gold Mining Partnership, located on the Laila River, in the Kuludzhunsky volost of the Ust-Kamenogorsk district. The mining area occupies 22 square versts. From it, small tours were made in different directions, mainly to the nearby granite Kaindinskii forest, and thus the entire examined area is approximately 100 square versts. The genesis of the gold-bearing quartz veins is clarified. Their appearance is probably associated with the intrusion of granites. The veins filling the cracks, consistent with the strike of rocks and caused by primary dynamic processes, were formed as a result of thermal activity (see the article).

Within the land plot occupied by a mine, there may be one or more hoisting shafts, and each of which serves a certain well-defined part of the seam or suite of mineral deposits. The area of such part of the seam or suite is called the mine field. Like any area, a mine field is measured in square units, that is, determined by the product of two linear dimensions. Unfortunately, our practicing engineers share their experience very sparingly, and there is no data on this issue in the specialized literature. This article discusses various formulas and methods for determining the dimensions of a mine field.

The Dashkesan deposit of iron and cobalt ores is located in Elisavetpol province, 27 versts southwest of the city of Elisavetpol. The most complete description of it (with the exception of the part belonging to Siemens) is provided by Weber.

In the spring and summer of 1910, on behalf of the Syr-Darya Mining Society, I was commissioned to examine the applications and allotments leased by the said company from P.S. Nazarov and located north of the city of Khodzhent within the Khodzhent district. Most of the claims and allotments lie in the foothills of Kara-Mazar ("Black Grave"), the most southwestern spur of the Ala-Tau ridges. Two allotments are located in the northwestern foothills of Mogol-Tau, a separate massif rising on the right bank of the Syr-Darya River, southwest of the Kara-Mazar mountains.

The solution to one of the fundamental problems of mathematical physics, namely the Dirichlet problem for a sphere, is reduced, as is known, to the question of expanding a so-called “arbitrary” function of two angles into a series arranged according to the spherical Laplace's functions. The possibility of expansion for a function that has two first derivatives has been proven, and by reasoning similar to that presented in our article: “On the theory of trigonometric series”, it can be established that the expansion is also possible for a function that satisfies the Lipchitz’s condition.

When expanding “arbitrary” functions into series using the method of least squares, the coefficients of the series, as is known, are formed according to a precisely defined law. Specifically, the law of formation of the coefficient is the same that would take place in the case of uniform convergence of the series, i.e., in other words, the coefficients acquire the form of the so-called Fourier coefficients and the series will be the so-called Fourier series of the expandable function. (see the article).

The author provides a proof of one of Fuchs' theorem.

The plane passing through the polar line a and the point, has as its zero point the one at which the polar intersects with the zero plane of the point A. The straight line connecting this point B with point A, like a polar, has a point on the polar a as its pole, and these two points form a conjugate pair on this polar. Each plane, simultaneously tangent to two conosecunds of such a prima, has as its polar a straight line connecting the two points of tangency. If the plane is simultaneously tangent to more than two conosecunds, then it is tangent to all conosecunds of the linear prima, which in this case have one common point of tangency with it and with each other. The zero system is polar with respect to linear primas of conosecunds, just as an ordinary polar system follows from a single conosecund.

Recently I noted the likelihood of the identity of two substances obtained by Anschütz and described, respectively, one as Benzoylderivat des Amylphenols and the other as Benzoylparatertiaramylphenol. After the publication of that note, I received a kind letter from Prof. Groth, who had inquired about this matter in writing from Prof. Anschutz and had received an answer confirming the actual identity of these two substances, despite the enormous differences in the crystallographic constants attributed to their crystals by Messrs. Hartmann and Schwantke. Now, I have found in my old notes an indication of the same ratio between two substances, which have been assigned very different chemical formulas, but which in crystallographic terms turn out to be very close.

The geometric constants, even for a triclinic crystal, are five angles, the values of which can be easily determined by direct measurement on a universal goniometer, and then no preliminary calculations are needed; using these same five angular values with the help of a fundamental formula, the determination of any face, not only measured, but any possible one, given by the indices of the symbol, is produced, as mentioned, by simple additions and subtractions, but with the exception of the faces located in the original belt itself, that is, the belt of faces a and b. And in the textbook (“A Brief Course in Crystallography”) no formula is provided for calculating the angles between the faces in this belt. Here I will present the derivation of this remarkable and extremely simple formula.

The list contains 44 works by Professor I.P. Dolbnya and their brief description (see the article).

On February 2, 1912, A.S.C., Ivan Petrovich Dolbnya, director and ordinary professor of the Mining Institute of Empress Catherine II, passed away in the Birzhevaya Hospital, after an operation, at the age of 59. After the body the body is brought out of the church, at the entrance to the institute the Acting Director of the Mining Institute prof. I. F. Schroeder delivered a speech: "... The Council of the Mining Institute of Empress Catherine II, wishing to honor the memory of Ivan Petrovich, resolved in today's meeting to outline scientific and pedagogical activities and share biographical details, as well as the reminiscences from friends of the deceased that may shed light on his personality .

At this sorrowful gathering dedicated to the memory of the highly respected Ivan Petrovich Dolbnya, the voice of the Kazan Physico-Mathematical Society, of which the deceased was at one time an active member, cannot but be heard, and, as a former Chairman of this Society, I express my deep gratitude to the Council of the Mining Institute for providing me with the opportunity to say a few words today.

With a particular pleasure I fulfill the wish of the Council of the Mining Institute to share my memories of I.P. Dolbnya. It is not enough to say that I.P. was a talented, skillful teacher who achieved amazing results; he was an exceptional teacher, a teacher-artist who had perfectly mastered the secrets of his art. He not only knew how to ignite in the cadets a lively, exciting interest in mathematics, but he managed to awaken a love for it even among the irreconcilable enemies of this “royal” science.

The strong and vivid image of Ivan Petrovich is still fresh in all our minds; it is still difficult to come to terms with the bitterness that this is only an image, that Ivan Petrovich himself is gone. Upon becoming director, Ivan Petrovich did not seek to derive any special benefit from this position for himself; he divided the director’s apartment into two parts and kept the worse one for himself; nor did he, for example, pursue additional appropriations for his assistants. He was a remarkably bright, original and richly gifted personality.