VLADIMIR KONSTANTINOVICH ARKADIEV

(1884–1953)

N. N. Malov

On December 1, 1953, after a long illness, in the seventieth year of his life, Vladimir Konstantinovich Arkadiev, Corresponding Member of the Academy of Sciences of the USSR, senior professor of Moscow University, Doctor of Physical and Mathematical Sciences, passed away.

The death of V. K. is a great loss for Soviet physics. It is felt especially keenly by his numerous students and by all workers in the field of electromagnetism.

The life path of V. K., who devoted all his strength to his beloved science, was not rich in external events. V. K. was born in Moscow on April 21, 1884; he lost his father early and was brought up by his mother, who worked in a library; from childhood he had dealings with books and came to love them. After graduating from the Second Moscow Gymnasium, V. K. entered the Faculty of Physics and Mathematics of Moscow University in 1904. There he attended the courses of N. A. Umov and P. N. Lebedev, completed a physics practicum with A. P. Sokolov, and in 1907 began experimental work in the laboratory of P. N. Lebedev, where in those years the first Russian school of experimental physicists was being formed.

As is known, P. N. Lebedev, who immortalized his name by the experimental discovery and measurement of light pressure, also carried out remarkable investigations in the field of centimeter and millimeter electromagnetic waves.

These investigations were extended by many of Lebedev’s students. In particular, V. K. took up the study of the magnetic properties of ferromagnets in centimeter waves. As early as 1908 he obtained the first results and discovered the disappearance of the magnetic properties of matter (iron and nickel) at a wavelength of about 3 cm. For this discovery V. K. was awarded, in the same year, the prize of the Society of Lovers of Natural Science, Anthropology, and Ethnography. Subsequently V. K. continued experimental and theoretical work in this same direction.

The fruitful activity of the group surrounding P. N. Lebedev was interrupted in 1911, when that group left the university following its teacher, who, together with other progressive professors of the university, protested against the arbitrariness committed by the then Minister of Public Education, the reactionary Kasso. V. K. also left the university and concentrated his activity in the Shanyavsky City People’s University and in the Tikhomirov Pedagogical Courses.

After the Great October Socialist Revolution, when Shanyavsky University merged with Moscow University, V. K. returned to the latter and organized there (in 1919) a magnetic laboratory, later renamed the laboratory of electromagnetism. V. K. directed this laboratory and the department “Theoretical Foundations of Electrical Engineering,” created in 1939, until the end of his life.

In 1927 V. K. was elected a corresponding member of the Academy of Sciences of the USSR and took an active part in the work of the Division of Technical Sciences of the Academy, heading the commission on magnetic and conducting materials and creating a laboratory attached to the electrical communications section.

In addition to this main direction of his activity, the scientific significance of which will be discussed below, during the years of the First World War V. K. organized research on problems of chemical defense and wrote the course Scientific and Technical Foundations of Gas Warfare, which went through several editions.

In different years (until 1927) V. K. taught at several higher educational institutions in Moscow; in particular, he headed the department of physics of the Plekhanov Institute of National Economy; in 1923–1931 he headed the magnetometric department of the State Experimental Electrotechnical Institute; in the 1930s he served as consultant to the physicotechnical department of the Institute of Physiotherapy and proposed a number of improvements to electromedical apparatus and methods of dosing electromedical procedures. V. K. was closely associated with the Polytechnic Museum (a member of the museum’s academic council from 1948) and with the Society of Naturalists at Moscow State University (in his last years he headed its physics section).

V. K. published more than 100 scientific studies, devoted chiefly to electromagnetic problems.

V. K.’s broad scientific and public activity was recognized by the Government, which awarded V. K. the Order of the Red Banner of Labor and several medals.

The most significant scientific results obtained by V. K. belong to the field of ferromagnetism.

Already in V. K.’s first work mentioned above, while studying the reflection of centimeter waves from metallic gratings, he discovered the disappearance of the ferromagnetic properties of a substance (a sharp drop in magnetic permeability) near a wavelength of 3 cm. This

was a great discovery, linking the properties of a substance in Hertzian waves with its optical properties (the absence of ferromagnetic properties at optical frequencies had been established earlier).

Continuing the investigation, V. K. in 1911 confirmed the disappearance of ferromagnetic properties by studying the absorption of centimeter waves in a two-wire line. He noted at the same time that the values of the magnetic permeability measured by the two methods did not agree with one another, which required a theoretical explanation.

V. K.’s results were confirmed in later years, when methods of generation and measurement had improved immeasurably. In an age of voltage stabilizers, powerful generators of undamped oscillations, and excellent detecting and amplifying apparatus, it is not easy to appreciate the experimental difficulties that V. K. had to overcome, working with damped oscillations of negligible power and having neither detectors nor well-evacuated thermoelements. And one can marvel at V. K.’s experimental skill: he not only qualitatively detected a new physical phenomenon, but also obtained quantitative results fully confirmed by subsequent work.

In those years Maxwell’s theory had not yet received its full development. In Maxwell’s equations there appeared parameters characterizing the substance—the dielectric permittivity \(\varepsilon\), the electrical conductivity \(\sigma\), and the magnetic permeability \(\mu\), which were assumed to be constant (although it had already been established by Stoletov’s work that the magnetic permeability of ferromagnets depends in a complicated way on the intensity of the magnetic field). In Drude’s works, dating from the beginning of the twentieth century, it was shown that the behavior of a substance in alternating fields depends on the relation between the displacement current and the conduction current, which changes with the frequency of the field. But, apparently, Drude, who was interested only in non-ferromagnetic substances, did not assume any frequency dependence of the indicated parameters.

Analyzing his experimental results, V. K. arrived at two very bold ideas that proved fruitful. First, he concluded that the parameters of a substance, in particular the magnetic permeability, depend on the frequency of the field. Second, wishing to take account of the phenomenon of hysteresis, consisting in the lag of changes in induction behind changes in the magnetic field and accompanied by irreversible losses of energy of the electromagnetic field during remagnetization of a ferromagnet, V. K. introduced an additional parameter—the magnetic conductivity of the substance \(\rho\), giving Maxwell’s equations a symmetrical form:

\[ \operatorname{rot}\mathbf{H}=\frac{\varepsilon}{c}\frac{\partial \mathbf{E}}{\partial t}+4\pi\sigma\mathbf{E};\qquad -\operatorname{rot}\mathbf{E}=\frac{\mu}{c}\frac{\partial \mathbf{H}}{\partial t}+4\pi\rho\mathbf{H}. \]

As is well known, for harmonic processes of period \(T\) it proves convenient to introduce the concept of complex electric permittivity:

\[ \varepsilon=\varepsilon' - j\varepsilon'';\qquad \varepsilon''=2\sigma T;\qquad j=\sqrt{-1}. \]

Analogously to it, V. K. introduced the complex magnetic permeability:

\[ \mu=\mu' - j\mu'';\qquad \mu''=2\rho T. \]

A medium characterized by the four parameters indicated was called by V. K. a “bicomplex medium.”

Solving Maxwell’s equations for the case of refraction and absorption of electromagnetic waves in matter, V. K. established that the absorption coefficient of the medium is a function of the “permeability for absorption”

\[ \mu_k=\sqrt{\mu'^2+4\rho^2T^2}+2\rho T, \]

while the refractive coefficient depends on the “permeability for refraction”

\[ \mu_n=\sqrt{\mu'^2+4\rho^2T^2}-2\rho T. \]

These permeabilities differ from one another in those regions of the spectrum where the magnetic conductivity is different from zero. In this way, V. K. was able to explain the discrepancy between the numerical values of the permeabilities of a ferromagnet measured by him by two different methods.

Using these ideas, V. K. constructed a coherent theory of the magnetic dispersion of the properties of matter. He was the first to point out that the study of magnetic dispersion (like optical dispersion) opens up broad prospects for determining various quantities characterizing the properties of molecules (or their complexes). Therefore V. K. called the application of his theory to the study of the properties of matter “magnetic spectroscopy.” The fruitfulness of such an interpretation has become especially clear in recent years, when, in connection with the improvement of radio-engineering methods, centimeter and decimeter waves have come to be widely used for the purposes of spectroscopy not only of molecules and atoms, but even of atomic nuclei.

The discrepancy in the values of magnetic permeability discovered by V. K. in studying various processes was not accidental. In view of the great complexity of the processes of magnetization of ferromagnets, as V. K. showed in the thirties, one must introduce the concept of a whole series of permeabilities that determine the process of remagnetization (or magnetization) under different conditions; one of the last tables systematizing the various permeabilities, compiled by V. K., contains more than 70 different magnetic permeabilities.

Explaining the disappearance of the ferromagnetic properties of a substance in rapidly varying fields by the finite propagation speed of magnetization, V. K. introduced the concept of the “magnetic viscosity” of a substance, which proved fruitful in studying the conditions of remagnetization. V. K. called his theory of magnetization “magnetodynamics” and saw in it the development and deepening of Maxwell’s classical ideas.

Along with the scientific applications of his theory of magnetization (which V. K. developed and perfected until the last days of his life), V. K. always strove to transfer scientific achievements into practice. In a number of his own works and those of his school, an exact theory of the skin effect was constructed, methods for calculating magnetic characteristics at technical frequencies were refined and newly created, questions of the magnetization and demagnetization of bodies of various shapes were studied, and other applied problems were solved. These works were in due course completed in V. K.’s well-known two-volume monograph, Electromagnetic Processes in Metals, published in 1934 and 1936. Before his death, V. K. was working on a second edition of the monograph, but did not manage to bring it to completion.

Collections of papers indicated in the bibliography (see below, at the end of the article) are also devoted to these same practical applications. The works of V. K. on electromagnetism, as reviewed here, were in large measure ahead of the science of his time and indicated paths for its further development. The depth and significance of these works have been fully revealed only in our own day. Therefore one cannot but agree with the assessment given to V. K.’s labors by two of his most outstanding pupils—Academician B. A. Vvedensky (at V. K.’s 65th-anniversary celebration on May 24, 1949) and member of the Belorussian Academy of Sciences N. S. Akulov (in a speech at V. K.’s grave in Novodevichy Cemetery). Noting the unfading freshness of V. K.’s works, both speakers called them “classical in the true sense of the word.”

Faithful to the precepts of his teacher P. N. Lebedev, who in one of his brilliant works demonstrated the analogy between the properties of millimeter waves and optical waves, V. K. sought to transfer optical methods into the field of centimeter waves. In the thirties he developed an electromagnetic analogue of photography, which he called “stictography.” The essence of the method consists in investigating the structure of the electromagnetic field with the aid of a large number of coherers placed on paper moistened with an electrolyte; a direct voltage is applied to the edges of the sheet of paper. Entering an alternating electromagnetic field, the coherers increase their conductivity, and near their ends the paper becomes colored by the products of electrolysis; as a result, a family of points appears on the paper, making it possible to judge the structure of the field.

A development of this method was “spark stictography”—the use of metal filings sprinkled on a photographic plate introduced into the field under study. With sufficient field intensity, sparks jump between the filings, exposing the plate and making it possible to judge the distribution of the field on the surface of the plate. Stictography may find practical application in pulse technology, where the instantaneous values of fields are very large.

In the early twenties, at V. K.’s suggestion, another remarkable piece of work was carried out in the electromagnetism laboratory, completing P. N. Lebedev’s investigations. As is known, in the nineties of the last century physicists strove to “close” the electromagnetic spectrum—to obtain and study all possible frequencies. But it proved impossible to obtain waves shorter than 6 mm by electrical methods of exciting oscillations (Lebedev, 1895), while by optical means it was not possible to study infrared radiation with a wavelength exceeding 0.35 mm (Rubens, 1896). Numerous attempts to fill the gap gave no result, since with electrical methods of excitation one had to work with very small vibrators, which quickly burned out during spark discharges and yielded negligibly small power; the intensity of the long-wave radiation of molecules was also very small and inaccessible to measurement.

At one of the scientific congresses, when Lebedev greeted Rubens, one of those present wished them “to extend their hands to one another in the electromagnetic spectrum as well.” But neither Lebedev nor Rubens was destined to live to see the realization of this wish.

V. K. proposed creating a generator with replaceable vibrators—metal filings suspended in viscous oil. This idea was realized by V. K.’s faithful companion on his life and scientific path—his wife, professor of Moscow University Aleksandra Andreevna Glagoleva-Arkad’eva (1884–1945). In 1922 she built a generator that received the name “mass radiator.” It gave “white radiation,” covering the wavelength interval from several centimeters to 0.080 mm, i.e., bridging the entire gap between the “optical” and “circuit” parts of the electromagnetic spectrum. She also studied the principal properties of this radiation.

Among V. K.’s other works in the field of electromagnetism, the most interesting are the elegant studies on observing noise during remagnetization, carried out by a very simple and convincing method, as well as the brilliant experiment with a “hovering magnet.” V. K. placed a lead plate in liquid helium and dropped a small magnet onto it. The currents that arose thereby in the superconducting plate were so large that, owing to the electromagnet—

...owing to its interaction with them, after several up-and-down motions the magnet hung above the plate almost motionless. V. K. considered this striking experiment valuable not only for its elegance. He believed that such interactions might play a definite role in cosmogony; this idea occupied V. K. in his later years.

Among V. K.’s various works in other areas of physics, one should first of all recall the excellent study of Fresnel diffraction, published in 1913. As is known, Fresnel diffraction is observable provided that the linear dimensions of the obstacle producing the diffraction are comparable with the dimensions of a few of the first Fresnel zones; in practice this means that the angular size of the obstacle, viewed from the point of observation of the diffraction (from a distance \(D\)), must be very small. If the light source is infinitely distant, then the radius of the first Fresnel zone \(R\) and its angular size \(\alpha\) are determined by the simple relations

\[ R=\sqrt{D\lambda}; \qquad \operatorname{tg}\alpha=\frac{R}{D}\simeq \alpha, \]

where \(\lambda\) is the wavelength of the light. Under ordinary conditions \(D\) is tens of centimeters, and accordingly \(R\) must not exceed fractions of a millimeter. But as \(D\) is increased, the permissible dimensions of the obstacle also increase. V. K. photographed the diffraction pattern from a distance on the order of tens of meters and obtained excellent diffraction images from comparatively large obstacles. Thus it was proved that diffraction can also be observed on large objects. In addition, V. K. also carried out a quantitative analysis of the intensity distribution (his results agreed well with the theory of the phenomenon). The excellent photographs obtained by V. K. and his pupils A. S. Berkman and N. N. Yakovlev are now included in all university textbooks. It is interesting to note that V. K.’s ideas were reflected in a recent work (Whitford, 1933), in which Fresnel diffraction was observed on a cosmic scale—during the occultation of stars by the Moon.

Another significant work was carried out by V. K. together with N. V. Baklin. They constructed a pulse generator, described by V. K. in 1925 under the name “spark transformer”; it consisted of a system of capacitors connected in parallel. When they were charged to a sufficient potential, the spark gaps broke down, as a result of which the capacitors were switched in series, and the voltage at the terminals of the device accordingly increased. Such a generator, sometimes called a “lightning generator,” was used in atomic investigations requiring ultrahigh voltages.

V. K. always stood guard over the interests of Russian science, fought for recognition of its achievements, and defended the priority of Russian scientists.

Thus, as early as the 1920s, V. K. conducted and successfully concluded a major polemic with the German physicist Gans, who had sought to ascribe to German science the honor of discovering magnetic conductivity. In 1947 V. K. spoke out in defense of the priority of Russian physics in the invention of the stiktograph, proving by documentary evidence that the pulse generator had been created in Russia much earlier than abroad, and so on.

In the laboratory of electromagnetism created by V. K., his numerous pupils conducted systematic investigations of magnetic phenomena; moreover, V. K. readily drew young people into the work. The laboratory’s scientific colloquium, where both the laboratory’s work and scientific novelties published in journals were discussed, was a continuation of the colloquium organized by P. N. Lebedev. The colloquium, which was a very good school for beginning physicists, held more than 300 meetings; both Russian scholars and foreign scholars visiting Moscow spoke at it.

A large number of physicists began their scientific work in the laboratory of electromagnetism. Among them were: Academician B. A. Vvedenskii, member of the Belorussian Academy of Sciences N. S. Akulov, 9 professors and doctors, and about 30 candidates of science and docents. Some of these people improved their qualifications extramurally, working in the provinces and coming to V. K. for consultations. This interesting experience of extramural supervision of experimental work deserves careful study.

In educating young people, V. K. always strongly recommended studying the classic works in physics, pointing to the depth and richness of thought and the clarity of exposition characteristic of the classics of science. A great service of V. K.’s was the organization of the publication and the editing of the collection Fifty Years of Hertz’s Waves, containing Russian translations of Hertz’s principal works on electromagnetic waves.

As a teacher V. K. was very solicitous and at the same time very demanding. Like Academician Pavlov, who said that science demands the whole person, V. K., giving himself wholly to science, demanded of his pupils discipline, great labor, and firmness of character in the face of inevitable experimental difficulties. The tasks he gave them were always difficult, but feasible.

I recall how, as a second-year student, I began to work under V. K. on Fresnel diffraction. He gave me his work to read, provided a place, supplied me with apparatus, gave me an assignment, and once a week required a report on the progress of the work. Along well-trodden paths, with good apparatus, the work successfully moved forward, yielded some results, and—most importantly—strengthened in the novice a belief in his own abilities. Probably in order that this belief should not turn into self-confidence, V. K. one day brought a long German article and suggested that within a month I proofread it.

at a colloquium. In reviewing it, V. K. organized a lively discussion of the report, which caused the inexperienced speaker some unpleasant moments, but taught him a great deal. Then V. K. assigned me, as my diploma work, another topic, for which there was no ready-made apparatus; everything had to be done anew, acquiring the practical skills necessary for a physicist. This work cost much effort, often reaching a dead end. And each time, at the right moment, V. K. came to the rescue, pointed out the way to overcome the difficulties, and gave valuable advice—such as only so talented an experimenter as V. K. could give.

At the Fifth Congress of Russian Physicists in Moscow (1926), a number of V. K.’s young pupils who worked in the electromagnetism laboratory presented reports. Of course, all of us were very nervous. But it seems that V. K. was even more anxious than we were. He carefully discussed the presentations, did everything to ensure that the reports went successfully, and joyfully congratulated us on our first steps in the scientific field.

Science was the only goal, the only interest of V. K. I remember how in 1942, having come temporarily to Moscow, V. K., half ill, in an icy apartment, spoke with me about the possibility of preserving his scientific archive in some shelter, safer than his apartment, which was on an upper floor and completely unprotected from a possible bomb hit.

In May 1953 V. K. summoned me for a conversation concerning one dissertation. He was already quite ill; it was difficult for him to speak for long. At times he fell silent, closed his eyes, and leaned back in the armchair, which he did not leave during the entire conversation. Then, gathering his strength, he returned again to the question of the accuracy of the measurements and the correctness of certain mathematical assumptions made by the author of the dissertation.

This was our last meeting, and thus Vladimir Konstantinovich has remained in my memory: devoted to science to his last breath—the foremost Russian representative of classical electrodynamics, a brilliant experimenter, a teacher and educator of scientific youth, “this last of the glorious flock” of Lebedev’s pupils, who throughout his life developed the ideas of his teacher and bequeathed them to the next generation of physicists.

PRINCIPAL SCIENTIFIC WORKS

OF VLADIMIR KONSTANTINOVICH ARKAD’EV

V. K. Arkad’ev published more than 100 original scientific investigations, not counting numerous popular articles, abstracts, editorial articles, and so forth. The most significant works are listed below. In selecting them, the basis was a draft list compiled by Vladimir Konstantinovich himself in 1951.

N. N. Malov

a) Monographs and Collections

1. Magnetic Spectroscopy, Proceedings of the GEEI No. 4, 1924.
2. Studies in Electromagnetism, ed. by V. K. Arkadiev, vols. I and II, Proceedings of the GEEI Nos. 6 and 15, 1925–1926.
3. Contemporary Problems of Electromagnetism. Ed. by V. K. Arkadiev, Moscow, 1931.
4. Problems of Electrotechnical Metal. Ed. by V. K. Arkadiev, Publishing House of the Department of Technical Sciences of the Academy of Sciences, Moscow, 1938.
5. Practical Problems of Electromagnetism. Ed. by V. K. Arkadiev, Publishing House of the Department of Technical Sciences of the Academy of Sciences, Moscow, 1939.
6. Electromagnetic Processes in Metals, Energoizdat, Moscow, Part One—1934; Part Two—1936.
   6a. 50 Years of Hertzian Waves. Collection edited and with an introductory article by V. K. Arkadiev. Publishing House of the Academy of Sciences, Moscow, 1938.

b) Original Scientific Investigations

1. Magnetic properties of iron and nickel under rapid electrical oscillations. Diary of the Second Mendeleev Congress, St. Petersburg, 1911.
2. Absorption of electric waves in parallel wires, ZhRFKhO, phys. sect. 44, p. 165, 1912.
3. Reflection of electric waves from wires, ZhRFKhO, phys. sect. 45, p. 45, 1913.
4. Ferromagnetic properties of metals as a function of wavelength, ZhRFKhO, phys. sect. 45, p. 103, 1913.
5. Theory of the electromagnetic field in a ferromagnetic metal, ZhRFKhO, phys. sect. 45, p. 312, 1913.
6. Frenel diffraction phenomena, Phys. Zeits. 14, 832, 1913.
7. Contemporary problems in the study of the magnetization of body and substance in constant and alternating fields, Nauchn. Izvestiya, collection 3, p. 320, 1922.
8. On obtaining weakly damped short Hertzian waves. Experiments of B. Milentz, Phys. Zeits. 23, p. 35, 1922.
9. On magnetic dispersion and absorption, ZhRFKhO, phys. part 56, p. 194, 1924.
10. On the analysis of spectral curves, ZhRFKhO, phys. part 56, p. 217, 1924.
11. On magnetic spectra and methods of obtaining them, ZhRFKhO, phys. part 56, p. 321, 1924.
12. Problems of general spectroscopy, ZhRFKhO, phys. part 57, p. 57, 1925.
13. Magnetic spectra of iron and nickel wires in the region of centimeter Hertzian waves, ZhRFKhO, phys. part 57, p. 241, 1925.
14. Reflection of electromagnetic waves from a magnetic medium, ZhRFKhO, phys. part 58, p. 149, 1926.
15. Magnetic reflection spectra, ZhRFKhO, phys. part 58, p. 159, 1926.
16. On the damping of small Hertzian vibrators (jointly with Leont’eva), ZhRFKhO, phys. part 58, p. 175, 1926.
17. Reflection of Hertzian waves from ferromagnetic gratings. Ann. der Physik 81, p. 649, 1926.
18. Oscillations and resonance of elementary magnets, Dokl. Akad. Nauk, A No. 1, p. 12, 1927.
19. Noise accompanying the magnetization of iron. Dokl. Akad. Nauk, A No. 18, p. 277, 1927.
20. On the permeability of iron at ultrahigh frequencies, Phys. Rev. 43, p. 671, 1933.

1. Chemical fixation on paper of images obtained from electric waves, Zeits. f. Physik 92, p. 194, 1934.

2. Magnetic and electric spectra at high frequency. Reports of the Academy of Sciences 2, p. 204, 1935.

3. Fixation on paper of electric waves and its theoretical foundations, ZhETF 7, p. 87, 1937.

4. Continuous passive spectra (jointly with O. I. Veletskaya). News of the Department of Technical Sciences of the Academy of Sciences No. 2, p. 55, 1938.

5. Observation and photographing of the field of hertzian waves (jointly with D. I. Penner). Reports of the Academy of Sciences 28, p. 316, 1940.

6. Lightning generator. On one Russian invention, “Electricity” No. 10, p. 52, 1940.

7. On centimeter waves. Proceedings of the First All-Union Congress of Physicians, Biologists, and Physicists on Questions of the Application of Short and Ultrashort Waves in Medicine, Medgiz, Moscow, p. 28, 1940.

8. Magnetic properties as a function of the frequency of a magnetic field, ZhTF 13, p. 324, 1943.

9. The spectrum of electromagnetic waves in the year of the discovery of radio, “Electricity” No. 5, p. 33, 1945.

10. The hovering of a magnet over a superconductor, J. of Physics 9, p. 148, 1945, Moscow.

11. Spark excitation of undamped oscillations, Reports of the Academy of Sciences 56, p. 29, 1947.

12. Oscillations of molecular magnets, Reports of the Academy of Sciences 56, p. 803, 1947.

13. Radio waves and magnetism, Moscow University Bulletin No. 12, p. 95, 1947.

14. Excitation of undamped electric oscillations of superhigh frequency, “Electricity” No. 3, p. 4, 1947.

15. Determination of the frequency and damping coefficient from the absorption band (jointly with V. F. Vershinskaya), ZhETF 20, p. 48, 1950.

16. Automatic mass emitter, Reports of the Academy of Sciences 76, p. 513, 1951.