L. I. MANDELSTAM

A Brief Sketch of the Life and Scientific Activity of Leonid Isaakovich Mandelstam*

N. D. Papaleksi

On November 27, 1944, world physics, and especially the physicists of our Union, suffered an exceptionally grievous loss—Leonid Isaakovich Mandelstam passed away: full member of the Academy of Sciences of the USSR, an outstanding scientist, a profound thinker and most talented teacher, a man of exceptional spiritual qualities, supremely modest, highly principled, and deeply humane.

With the name of Leonid Isaakovich is connected not only a series of fundamental discoveries in the field of physics that brought about radical shifts in science, but also the emergence of new areas of technology. The discovery of the phenomenon of combination scattering of light, the theory of the microscope, investigations of fluctuation scattering of light, the theory of nonlinear oscillations, the discovery of new kinds of resonance and the generalization and deepening of the concept of resonance, the investigation of the propagation of radio waves, fundamental works in the field of radio engineering, a new branch of technology—radiogeodesy, a new type of generation of electromagnetic energy—parametric machines—this is an incomplete list of his principal achievements; to this list one could add a number of other works, no less important, which were not published because of Leonid Isaakovich’s exceptional, almost painful exactingness toward the standard of his communications. It may suffice to point to the discovery of the inertia of electrons in metals, theoretically substantiated and qualitatively established experimentally as early as 1912, several years before the classic experiments of Stewart and Tolman.

The life of Leonid Isaakovich was not marked by outward brilliance. He never sought external honors, did not try to play any role whatever; ambition and love of fame were utterly alien to him. But all the fuller and richer was his inner life. This

* Speech delivered at the meeting devoted to the memory of Academician L. I. Mandelstam, held at the House of Scientists in Moscow on December 22, 1944.

was the splendid life of a true scholar and profound thinker, a seeker of scientific truth, a man of exceptional nobility of spirit.

At present it is still impossible to give a complete picture of all the remarkable activity of L. I. and a fair assessment of his outstanding scientific achievements. Allow me, as one who had the exceptional good fortune at the threshold of his scientific life to meet L. I., with whom for almost 45 years I was bound by common work and close relations, to try to set forth briefly before you the principal dates of the splendid life and scientific activity of this remarkable man.

Leonid Isaakovich was born on April 22, old style, 1879, into a highly gifted family, from which came outstanding scientists, physicians, writers, and musicians. His father was an outstanding physician, very popular in the south of Russia; his mother was an excellent pianist. L. I.’s childhood passed in an atmosphere of high morality and humanity. L. I. received his secondary education at the Second Odessa Gymnasium. Already at the gymnasium L. I. stood out for his abilities, especially mathematical ones, and for the many-sidedness of his interests. From earliest childhood L. I. was very fond of books, music, the theater, art in general, all kinds of games, especially intellectual ones, and these tastes remained with him for his whole life, while his love of books reached the point of passion.

After graduating from the gymnasium in 1897 with a medal, L. I. entered the Faculty of Physics and Mathematics of Novorossiisk University. In 1899 L. I., who had taken part in student disturbances, was expelled from the university and went abroad to continue his education, where he entered the Faculty of Physics and Mathematics of the University of Strasbourg. At that time the chair of experimental physics was held, and at the same time the Physics Institute was directed, by the outstanding physicist Ferdinand Braun, already then known for his work in the field of thermodynamics (the Braun–Le Chatelier principle) and electrical phenomena, and especially widely as the creator of the Braun electrometer and the Braun cathode tube. In this period (beginning in 1898) Braun’s scientific interests were directed mainly toward the then newly emerging field of the application of electricity—radiotelegraphy, for work in which, as is known, he received in 1909, together with Marconi, the Nobel Prize in Physics.

The chair of theoretical physics at that time was held by Prof. Emil Cohn, who was then just completing his well-known course “The Electromagnetic Field.” Lectures in mathematics were given by outstanding mathematicians: the analyst Heinrich Weber and the geometer Reye.

Prof. Braun, not only an outstanding physicist but also an excellent teacher and person, very soon noticed the highly talented young scholar, appreciated L. I.’s outstanding qualities, and gave him full opportunity for scientific work.

In turn, L. I. also highly valued Braun and throughout his life retained deep respect and gratitude toward him. It is natural that, under Braun’s influence, L. I. began to occupy himself with questions of electrical oscillations in connection with radiotelegraphy.

In the first period after the emergence of radio, in 1895–1896, the physical aspect of the processes in the radio transmitter and radio receiver long remained unclear. Even the wavelength on which the first transmitters operated was not precisely known, and practically no methods existed for measuring it. There were likewise no instruments for measuring high-frequency currents and voltages, apart from the crudest ones—the archaic Riess air thermometer and the spark micrometer. All this greatly hampered, and at first almost completely arrested, the development of radio. To Braun, as a physicist, it was perfectly clear that the primary task was to create adequate methods of measurement and, above all, to develop methods for measuring and controlling the wavelength of electrical oscillations. To this end, at the end of 1900 Braun proposed to L. I., as the subject of his dissertation work, the development of a method for measuring and controlling the frequency of electrical oscillations based on the dependence of total electrical resistance on frequency. Already in this first scientific work of L. I. the principal features of his scientific creativity became apparent. He approached the solution of the problem set before him in an original way, applying a null method and a differential circuit; as an oscillation indicator he used a specially designed double air Riess electrical thermometer, and he gave an exhaustive analysis of the method. This work, entitled “Bestimmung der Schwingungsdauer oscillatorischer Kondensatorentladung,” was submitted by him as his dissertation. In 1902, after passing the required examinations with highest distinction (summa cum laude), L. I. received the degree of doctor phil. nat. of the University of Strasbourg.

After graduating from the university, L. I., for some time as Braun’s personal assistant, took an active part in laboratory factory investigations and practical tests in the Baltic of receiving-transmitting radio devices. Although in these tests good results for that time were achieved, L. I. nevertheless remained greatly dissatisfied with them, since it was clear to him that these devices had not been used effectively, because many aspects of the oscillatory processes in them remained obscure. As a result of the theoretical analysis he carried out, L. I. arrived at a conclusion which seemed at the time quite paradoxical: that it was not an increase in the coupling between the antenna and the intermediate circuit of the complex receiver circuit—something then being sought—that should lead to an increase in the strength of reception, but, on the contrary, that this end should be achieved by a considerable weakening of the coupling; at the same time, along with improved reception, its selectivity should also increase.

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Experimental verification fully confirmed these conclusions. This first invention of L. I. in the field of radio engineering, the so-called “weak coupling,” marked a substantial stage in the history of the development of radio communication and at once made his name known among specialists.

In 1903 L. I. was enrolled on the staff of the Strasbourg Physical Institute as second assistant (the first assistant at that time was the well-known radio specialist Zenneck), and soon afterward as first assistant. Here L. I.’s duties included supervising the scientific work both of doctoral candidates and of scholars from various countries who had come to work at the famous Strasbourg Physical Institute, founded by Kundt and where many of our outstanding physicists had worked in their time: Lebedev, Golitsyn, Eichenwald, Shcheglyaev, and others. The young scholars sometimes arrived already with their own topics, but for the most part received them from Prof. Braun, and soon also from L. I.

L. I., who treated his duties with exceptional conscientiousness, had to work hard on himself in order successfully to direct scientific work.

These years, up to 1907, which may be called the first Strasbourg period, were in L. I.’s life years of broadening knowledge, years of scientific growth and maturation. At this time all the fundamental traits of him as a scientist were definitively formed. L. I. worked very much; he thoroughly studied Rayleigh’s classic treatise The Theory of Sound, Lorentz’s works on the electron theory, Boltzmann’s Kinetic Theory of Gases, and read the writings of Helmholtz and other classics of physics. Exceptionally gifted mathematically, he also diligently studied various branches of mathematics (differential equations, probability theory), for which he always felt a special attraction. Alongside this, he was deeply interested in the history of physics, the philosophy of science, and the theory of knowledge. He became thoroughly acquainted with the English philosophers.

A special influence on L. I. was exerted by the remarkable English physicist Rayleigh. The astonishing versatility of Rayleigh, the depth of his analysis, his incomparable ability to single out the essential aspect of a question, to show clearly and vividly its physical substance, to give a theory using the simplest but quite adequate mathematical apparatus—all these qualities of Rayleigh’s works corresponded to the aspirations and peculiarities of L. I.’s mind and evoked in him a special resonance; they were “congenial” to him. And indeed, in the character of L. I.’s mind there was much in common with Rayleigh, and it is no accident that the paths of their scientific creativity often ran parallel and repeatedly intersected. There is no doubt that the atmosphere of electromagnetic oscillations into which L. I. entered on beginning his scientific life, as well as the influence of the “great oscillator” Rayleigh, played a very large role in the formation of the main directions—

A Brief Outline of Mandelstam’s Life

of his scientific activity and determined that oscillatory approach which is so characteristic of L. I.’s creative work.

The beginning of L. I.’s scientific activity coincided with the epoch of the triumph of Maxwell’s electromagnetic theory of the field, with the triumphant advance of the electromagnetic theory of light, which after Hertz’s famous experiments found its most perfect practical expression in radio. It was also a time of rapid development of Lorentz’s electron theory, which, within the framework of classical electrodynamics, revealed the relationships between electromagnetic waves and matter. True, already at that time a number of new discoveries in physics—the photoelectric effect, Röntgen rays, uranium rays, the discovery of the radioactivity of polonium and radium—seemed to cast a shadow of coming scientific revolutions ahead, posing insoluble riddles for classical theory. True, already then the thought had arisen among some physicists (Planck) that, for explaining the questions of the emission and absorption of light, the ideas of classical electrodynamics about the continuous wave character of light radiation were inadequate; however, almost all physicists at that time still stood wholly on the ground of the classical electromagnetic theory of the field and of the electron theory.

A talented young scientist who, almost from his school days, had entered the “atmosphere” of electromagnetic oscillations and their new, marvelous application—radio—could not fail to succumb to the fascination of this supremely interesting and, at the same time, in many respects still mysterious domain of knowledge. It is therefore not surprising that in the first period L. I. was entirely occupied with questions of oscillations. However, L. I.’s deep, inquisitive nature, striving for broad generalization, for embracing different areas of physics and clarifying their mutual connection, as his scientific growth proceeded, could not for long be satisfied with the study of this one, though very fascinating, yet still comparatively narrow, area of physics. Although his interest in questions of oscillations and in their various scientific and practical applications, especially radio, remained alive throughout his life, the circle of L. I.’s scientific interests continuously broadened and deepened.

It therefore seems entirely natural that the center of L. I.’s scientific interests should gradually have shifted from electromagnetic oscillations and waves in free space, such as are dealt with in radio, to the interaction between electromagnetic waves and matter, namely to questions of the passage of light through various media, and first of all to questions of dispersion. His first investigation in this field, in which he subjected to a subtle analysis the question of the passage of light through optically homogeneous and turbid media, was submitted in the spring of 1907 as a dissertation for obtaining the right to lecture (venia legendi) as a Privatdozent of the University of Strasbourg. It is characteristic that L. I.’s trial lecture was devoted to Maxwell’s electromagnetic theory of light.

From that year there began for L. I. a period of extremely intensive and fruitful work. From the very beginning L. I. showed himself to be an exceptionally talented lecturer, an excellent experimenter, who prepared thoroughly for his lectures and very often illustrated them with brilliant demonstrations devised by himself. Among these one should note his apparatus with pendulums, which accurately and correctly demonstrated phenomena in coupled systems under various couplings, as well as an apparatus for demonstrating the basic relations of the special principle of relativity.

At first L. I. gave separate courses on various questions of physics, and from 1910 a course on telegraphy and telephony for those specializing in this field. In 1913 he received the title of professor.

Although preparation for lectures and work with students and doctoral candidates took up a considerable part of L. I.’s time, he nevertheless found much time for his own work. In this, one might say, second Strasbourg period of his activity, up to the beginning of the First World War, his remarkable talent as a physicist fully matured and manifested itself, and all the characteristic features of him as a scientist were revealed. As I have already mentioned, alongside questions of electromagnetic oscillations and radio, ever new areas of physics gradually entered the circle of his scientific interests.

To the first Strasbourg period, namely to 1904, belongs the first of our numerous jointly published works in the field of oscillations and radio, which continued both in Strasbourg and in Russia up to the very recent time. This work concerned the creation of a method for obtaining spark-damped oscillations identical in form but shifted in phase; this method formed the basis of the first experiments on directional radiotelegraphy with the aid of interference of radio waves. I shall not touch here on our other works; I should like only to mention, among the Strasbourg works, a new, exceptionally sensitive method for measuring frequencies and logarithmic decrements of electromagnetic oscillations, and a new original high-frequency instrument—the so-called induction dynamometer, the principle of which formed the basis of instruments directly indicating the frequency and damping of electrical oscillations and other electrical quantities.

Very characteristic of L. I., in the field of radio-wave propagation, was his highly substantial polemic with the well-known radio specialist Fleming on the question of the directional action of Marconi’s bent antenna. In it L. I. convincingly showed that the directional action of such an antenna cannot be explained if the earth is assumed to be absolutely conducting, and pointed out wherein Fleming’s mathematical error lay.

The studies of light scattering, begun by L. I. in his privat-docent dissertation, continued throughout his life, steadily expanding and deepening, and reached here, in Moscow, in 1928, in the well-known

A BRIEF OUTLINE OF MANDELSTAM’S LIFE

in particular, as the result of the remarkable discovery, made jointly with G. S. Landsberg, of the combinational scattering of light.

A brilliant example of L. I.’s subtle analysis, of his inexorable logic, is his polemic—very substantial in essence—with the greatest theoretician Planck on the highly fundamental question of the possibility of Rayleigh scattering of light in perfectly homogeneous media, about which Rayleigh himself had an incorrect idea. In this polemic L. I. definitively proved the impossibility of such scattering and showed wherein lay the root of the incorrect theoretical conclusions of Planck and other theoreticians on this question.

Having come to the conclusion that Rayleigh scattering of light cannot be explained by the mere disordered motion of molecules, if their number is sufficiently large, L. I. sought to clarify the physical nature of this scattering. He gradually arrived at the same conclusion as Smoluchowski (who first formulated and published it), namely that the cause of Rayleigh scattering is the density inhomogeneities that arise at random and are dissipated in the medium—the so-called density fluctuations. Developing these ideas, L. I. came to the conclusion that such inhomogeneities should arise especially readily near the critical point of the vapor—liquid transition. In particular, L. I. believed that in this case conditions should be especially favorable for observing the scattering of light at the interface liquid—vapor; L. I. gave the theory of the phenomenon for this case and confirmed it by very convincing and demonstrative experiments.

At first glance, L. I.’s remarkable works on the theory of the microscope seem entirely unconnected with the preceding ones. The classical theory of the microscope of Abbe was based on the consideration of objects illuminated by external light (not self-luminous ones), and Abbe, proceeding from the coherence of the rays reflected from the object, showed physically and very clearly what determines the limiting resolving power of the microscope, beyond which no magnification makes it possible to distinguish the structure of the object. As a result, among opticians there gradually arose the conviction that there exists a fundamental difference between the discernibility of objects illuminated by coherent rays and of self-luminous objects, which emit incoherent rays from different points. It should be emphasized that Rayleigh’s own statements on this question were marked by great ambiguity. In analyzing this question L. I. displayed his characteristic sharpness and depth of thought and a subtle understanding of the physical essence. L. I. brought complete clarity into this question: having examined it exhaustively, he gave for the first time the theory of the image of self-luminous objects and by extraordinarily ingenious experiments showed that in practice there is no difference in the resolving power of the microscope for the case of illuminated objects and that of self-luminous objects. L. I. also gave a rigorous mathematical theory of optical images—

in question, applying for this the most adequate and elegant method of solution, in which he makes use of the integral equations that had only just become known. It may be interesting to emphasize, in characterizing L. I.’s mathematical talent, that (as mathematicians too have pointed out) this work was the first example of the application of integral equations to a physical problem whose solution had not only not previously been obtained by other mathematical means, but in general could not otherwise be formulated in a mathematically simple way. These remarkable works of L. I. in the field of optics caused, in a certain sense, a sensation and served as the subject of polemics (for example, with Lummer).

Another investigation by L. I. belongs to this period as well, one that very vividly and clearly illustrates the many-sidedness of his talent, his ability to unite phenomena that would seem to be unlike one another. The fundamental and most important problem posed by radiotelegraphy from the very beginning was the problem of the propagation of radio waves along the earth’s surface, which attracted the attention of such major physicists and mathematicians as Sommerfeld, Poincaré, and others. In 1909 there appeared Sommerfeld’s fundamental work, in which he gave a theory of the propagation of electromagnetic waves from a radiating source situated on the surface separating earth—air. This theory led to essential differences between radio waves and light waves. L. I. seeks an analogue of this case in optics and comes to the conclusion that this difference is caused by the fact that, in the case of radio waves, the source of radiation is located either at the very surface or at a distance from it that is small or comparable with the wavelength, whereas in optics the wavelength of light is so small that this distance is always large in comparison with it. It followed from this that light phenomena analogous to the radiotelegraphic case should also occur, but only when the distance of the light source from the surface is small or comparable with the wavelength of light. With the help of ingenious and, as always, convincing experiments, L. I. realizes this case in optics, using, as the radiating source, luminous points on the surface of a fluorescent liquid (fluorescein); L. I. also considered this case theoretically and, proceeding from Lorentz’s general theorem, for the first time formulated, as applied to point sources, the so-called reciprocity theorem in radiotelegraphy. Let us note that this important theorem was subsequently (in 1925), as applied to radiotelegraphy, examined in detail by Sommerfeld, who, however, admitted certain inaccuracies in his treatment. L. I. drew attention to these inaccuracies, and in the works of his pupils, in Moscow, this principle received its complete formulation and diverse applications.

A very characteristic example of L. I.’s oscillatory approach to the solution of various problems of optics is also his exceedingly

a witty method for determining the damping of light oscillators. Considering these oscillators from the classical point of view, as electromagnetic resonators, L. I. applied, in order to determine their damping, Bjerknes’s resonance-curve method, known in the theory of oscillations. For this purpose L. I. measured the absorption in sodium vapor of one of the D-lines emitted by luminous sodium vapor of another light source. For the smooth change of the wavelength of light required in Bjerknes’s method, L. I. used the Zeeman effect.

In all these works L. I. stood on the ground of the consistent application of the classical electromagnetic theory of light and the theory of electrons. The harmonious, strictly logical structure of the majestic edifice of physical knowledge, built on their foundation and so easily, naturally, and, it seemed, comprehensively embracing the whole doctrine of electrical phenomena, corresponded to the cast of his mathematical mind. However, L. I. clearly felt all the difficulties and contradictions encountered by the theory, especially in explaining such experiments as the famous experiments of Michelson, which without constraint did not fit into the framework of the classical theory. Therefore, both by the cast of his mind and by his deep physical worldview, L. I. proved prepared to accept Einstein’s principle of relativity, which for the majority of physicists of that time was like a blow of an ax to the head. Its full recognition, as is known, came only gradually, under the great pressure of experimental facts, and some physicists still do not understand and do not accept it.

L. I. was not merely one of the first very quickly and completely to assimilate the whole physical meaning and the full depth of the principle of relativity, which caused one of the greatest revolutions in our physical worldview, but at once did much for its elucidation and propaganda. At his suggestion an apparatus had already then been constructed that vividly demonstrated the unusual relations following from the principle of relativity.

Subsequently, in Moscow, L. I. extended the principle of relativity to an anisotropic medium and, in a number of works, and especially in his brilliant lectures, expounded these very difficult questions of physics in a form unsurpassed in depth and subtlety of thought, clarity, simplicity, and elegance.

L. I. took a more cautious attitude toward the first steps of quantum theory, although he fully sensed the inability of the classical theory to give a satisfactory explanation of such phenomena as the photoelectric effect, the distribution of energy in the spectrum of a black body, the line spectrum of hydrogen, and others. L. I. fully acknowledged the heuristic significance of the quantum hypothesis, but he was not satisfied by the recipe-like character of the theory in its early period. Subsequently, after the famous investigations of Bohr and Sommerfeld, and especially after the works of de Broglie, Schrödinger, and Heisenberg, for L. I., who had thought much

over these questions and, having fully clarified for himself the connection between the classical theory and the quantum theory, as well as the profound physical significance of quantum mechanics for explaining phenomena in the microworld, it received a complete logical substantiation, which he expressed brilliantly in his Moscow lectures and works.

The ominous threat of the First World War was approaching, and at the end of July 1914, after the completion of his lectures, L. I. and his family hastily left for his homeland, where he arrived on the day war was declared. A long forced interruption now began in L. I.’s normal scientific activity (from 1914 to 1924). However, L. I.’s intensive scientific-technical and pedagogical activity did not cease. In 1915 L. I. was elected by the Faculty of Physics and Mathematics of Novorossiisk University in Odessa as a privat-docent in the department of physics; at the end of 1915 he was invited as a scientific consultant to the Radiotelegraph Plant in Petrograd (now named after Kazitskii). There he directed laboratory investigations and practical developments in the field of radio, so important for defense. In order to characterize the many-sidedness and breadth of L. I.’s scientific-technical range, I shall point out that, on the one hand, during this period he developed a technology for the manufacture of oxidized wire and organized its production, and, on the other hand, in connection with questions of calibrating wavemeters, he proposed and developed the first absolute method ever for measuring radio frequencies, the principle of which formed the basis of the methodology of such measurements.

In the autumn of 1917 L. I. moved to Tbilisi, where he was elected acting ordinary professor of physics at the Polytechnic Institute. At the same time L. I. was also a professor at the Higher Women’s Courses.

In 1918 L. I. moved to Odessa, and, as ordinary professor in the department of physics, took a most active part in organizing the Odessa Polytechnic Institute, where he created, literally from nothing, a physics laboratory, assembled the necessary physical instruments, established the delivery of lectures in physics with demonstrations, and put the entire educational process in physics on a high scientific level. L. I.’s brilliant lectures, for which he always prepared very carefully and in which he strove not only to set forth the physical foundations with utmost clarity but also, whenever possible, to demonstrate vividly the essential aspects of the phenomena, always drew a full auditorium. Alongside his pedagogical activity, which occupied almost all his time, L. I. served as scientific consultant to the Odessa Radio Plant.

L. I.’s highly developed sense of duty manifested itself at that time in full measure. His collaborators and students remember well the difficult conditions under which lectures had then to be given and classes conducted (unheated rooms, an atmosphere of real hunger, since this was a period of blockade and of isolation not only from world science but also from the cultural centers of our country). However, this did not stop-

was headed by L. I.; and he not only regularly delivered the required lectures, but also, on his own initiative, taught a course on oscillations for several interested students. L. I. suffered greatly from being cut off from world science, caused by the blockade. The fundamental book by Sommerfeld, Atomic Structure and Spectral Lines, which he received in 1921 from scientific friends, was a great joy to L. I., and he warmly welcomed the opportunity to partake once again of world scientific thought. I recall that at that time, in the physical worldview, a radical restructuring of concepts and ideas was taking place, brought about by the revolutionary incursion into science of the general theory of relativity and quantum theory.

At the end of 1922, L. I., at the invitation of the Trust of Low-Current Plants, moved to Moscow, where, as a scientific consultant, he directed scientific research and scientific-technical development in the radio laboratory, which, after the trust’s administration moved to Leningrad in 1924, was transformed into the Central Radio Laboratory.

With L. I.’s work at the CRL, which continued until 1935 and which, scientifically, is inseparable from his work at that time in the Scientific Research Institute of Physics, are associated his most essential works in the field of radiophysics and radio engineering: new methods of radiotelegraph and radiotelephone modulation, questions of high-frequency measuring technology, a highly selective receiving device with a quartz filter, frequency stabilization, the generalization of the concepts of feedback and regeneration, new radio-interference methods for investigating the propagation of radio waves and for measuring distance, and a number of others. However, the most fundamental and scientifically important achievement is the discovery, based on the theory of nonlinear oscillations, of new types of resonance and new methods of exciting oscillations (autoparametric, heteroparametric, asynchronous excitation). This led, on the one hand, to a substantial broadening and evolution of the concept of resonance and, on the other, to the creation of new radio devices (autoparametric filter, frequency transformers, etc.) and a new type of machine.

Unfortunately, within the narrow limits of my report I cannot dwell even on L. I.’s most important works in this field. This aspect of his scientific activity will be covered in detail in their reports by L. I.’s pupils—Prof. A. A. Andronov and Prof. S. E. Khaikin. I would only like to point out that the nonlinear direction in the field of oscillations, which followed entirely from L. I.’s characteristic striving to convey as clearly, adequately, and at the same time as mathematically rigorously as possible the essence and quantitative course of oscillatory processes that do not fit within the framework of linear differential equations, proved extraordinarily effective and fruitful, and it is gradually gaining recognition not only in this, comparatively narrow, field of radio oscillations.

In 1925 L. I. was elected professor of theoretical physics at Moscow State University and a full member of the Research Institute of Physics.

and crystallography under him. From that time began the most intense and fruitful period of his scientific and pedagogical activity. Here, within the walls of our oldest university, his remarkable talent as a scientist and teacher fully blossomed.

Around L. I. there soon gathered many talented young scientists, graduate students, and students who, under the guidance of L. I., inspired by his ideas, successfully developed various problems of optics, molecular physics, and oscillations, and formed a large scientific school.

During the long years of the forced interruption in his scientific activity, L. I. did not cease to return to the scientific questions whose investigation and elucidation had been so harshly interrupted by the world war. He continued constantly to think about questions of light scattering, especially in connection with fluctuation phenomena. L. I. expressed his quite definite considerations on this question in conversations with me as early as 1920–1921. As a result of a profound, and at the same time physically exceedingly lucid, analysis, L. I. came to the conclusion that in a homogeneous body completely free of foreign admixtures, owing to thermal fluctuations, not only Rayleigh scattering of light should be observed, but also that the spectrum of the incident light must thereby undergo changes—although extremely slight ones—the quantitative estimate of which L. I. also gave. This so-called Mandelstam–Brillouin effect—the effect of the change in the fine structure of the spectrum under fluctuation scattering of light—was discovered by L. I. and then, in 1930, at L. I.’s suggestion, was definitively and completely studied by E. F. Gross at the State Optical Institute.

The experiments set up for its discovery, however, at first led to another, far more fundamental discovery: namely, to the discovery, jointly with G. S. Landsberg in 1928, of the phenomenon of combination scattering of light. This discovery, which at the same time as the Russian physicists was made by the Indian scientist Raman, is not only one of the greatest—perhaps the greatest—discoveries in optics of the last 25 years, but its significance for practice is already so great that it may be placed in the same rank as Kirchhoff and Bunsen’s remarkable discovery of spectral analysis. This discovery undoubtedly placed the name of L. I. in the ranks of the greatest physicists of our time. Only L. I.’s exceptional exactingness toward himself—one might say his scrupulousness, because of which L. I. did not publish new things without first subjecting them to repeated preliminary verification over a long period—was the reason why the discovery he in fact made first appeared in print later than Raman’s telegraphic communication about his discovery in Nature; Raman, who in 1930 received the Nobel Prize in Physics for this discovery.

The discovery of the phenomenon of combination scattering of light led to a great revival of scientific work directed toward elucidating

of the physical nature of this phenomenon and of the laws governing it. L. I. gave a theory of this phenomenon from both the classical and the quantum-theoretical points of view. Characteristic here is L. I.’s “oscillatory,” one might say radio-engineering, approach to the explanation of this phenomenon, which he treats as a modulation of light caused by the infrared vibrations of molecules.

Along with the combination scattering of light, L. I. continued his investigations of the fluctuation scattering of light. Here L. I.’s attention was attracted by the possibility of creating regular inhomogeneities in liquids and gases with the aid of elastic (ultrasonic) waves, producing in them regularly arranged regions of compression and rarefaction. This opened new possibilities for studying, by means of the diffraction of light on these inhomogeneities, various questions of molecular physics, and thus a new direction of research in molecular physics arose, especially important for the study of nonstationary phenomena. Incidentally, L. I. pointed out the possibility of using ultrasonic methods for the modulation of light, which at the present time has found wide application both in scientific research and in television.

In 1928 L. I. was elected a corresponding member of our Academy, and in 1929 a full member.

In 1931 L. I. received the Lenin Prize for his work.

Along with these investigations, and with profound investigations in the field of theoretical and molecular physics, which I do not touch upon here, L. I. continued to be intensely interested in questions of oscillations. In parallel with the work that was being carried out at the Central Radio Laboratory and which I have already mentioned, at the NIIF of the 1st Moscow State University, under L. I.’s direction, the theory of nonlinear oscillations was being developed, encompassing oscillatory processes not only in radio engineering but also in acoustics and mechanics, and contributing to the clarification of processes in radio transmission, as well as in automation and aerodynamics. At the present time a number of L. I.’s pupils, who took a prominent part in the development of this theory from the very beginning (A. A. Andronov, S. Ya. Khaikin, G. S. Gorelik, S. M. Rytov), are very successfully developing and applying this theory in the above-mentioned fields.

The works on nonlinear oscillations were awarded the First Mendeleev Prize in Physics in 1936.

From the autumn of 1934, after the Academy of Sciences of the USSR had been transferred to Moscow, L. I. took an active part in organizing FIAN and from that time, in parallel with his work at Moscow State University, directed work in the oscillations laboratory and the optical laboratory of FIAN, where his ideas and the questions that interested him were developed. Here, on L. I.’s idea, a method was created and developed for measuring the intensity of electric and magnetic super-high-frequency fields, and investigations were carried out on the behavior of dielectrics in these fields; work in molecular physics was conducted with the use of

ultrasonic methods, and research in the field of combinational scattering also continued.

Within the walls of the Institute, the famous problem of the propagation of radio waves along the earth’s surface found its theoretical and experimental completion—a problem which, as is known, arose immediately after Marconi had spanned the Atlantic Ocean, and to which numerous works by the greatest physicists and mathematicians were devoted: Sommerfeld, Poincaré, Watson, Van der Pol, and others. As a result of the theoretical and experimental investigations carried out with the aid of new radio-interference methods, a solid scientific foundation was laid for the new branch of radio engineering that arose from them and was associated with L. I.’s name—radiogeodesy, whose first practical applications had already yielded significant results. The use of radio-interference methods also made it possible to clarify the question of the velocity of propagation of radio waves along the earth’s surface and to measure it with the greatest accuracy known up to that time.

How great an importance is attached to these investigations in the circles of radio specialists may be judged from the fact that in 1942 the chairman of the Radio Section of the British Institution of Electrical Engineers, the well-known radio specialist Smith-Rose, devoted the main part of his annual address to an exposition of the radio-interference methods and of the results obtained by us. These works were awarded in 1942 the Stalin Prize, First Class, in physics.

The last years of L. I.’s life, cut short so early, were overshadowed by his grave illness and by the cruel war forced upon us by fascism. L. I. suffered greatly and was indignant at the wave of hatred of mankind unleashed by fascist Germany, which brought terrible disasters to the world and especially to our country. In mid-July 1941, at the proposal of the Presidium of the Academy of Sciences of the USSR, L. I. was evacuated to the resort of Borovoe in Kazakhstan, where he remained until the Academy of Sciences returned to Moscow. Despite his illness and despite the fact that he suffered greatly from being separated from his friends, colleagues, and pupils, and from the absence of laboratories and libraries, L. I. continued to work extraordinarily much on various problems, chiefly in the field of oscillations. I shall mention here the mathematical theory of oscillatory systems developed by him, described by ordinary differential equations with periodic coefficients and small nonlinearity; the general theory of the propagation of waves in pipes and along a single wire; and also works of fundamental interest in quantum mechanics.

L. I. devoted much attention in Borovoe also to the history of science. In connection with the 300th anniversary of Newton’s birth, he delivered in Borovoe an excellent report on Newton’s works in physics.

There, in Borovoe, L. I. also prepared a report on the scientific activity of our remarkable scholar A. N. Krylov, which he delivered here, in this hall, at a general meeting of the Academy of Sciences, devoted—

to the 80th anniversary of Aleksei Nikolaevich. This brilliant report, in which L. I. so vividly and strikingly illuminated the remarkable works of Aleksei Nikolaevich, especially in the field of vibrations and the rolling of a ship, is still remembered by all of us.

Finally, in the calm conditions of Borovoe, L. I. set about carrying out his long-cherished idea of writing a scientific biography of Rayleigh, so close to him in scientific cast of mind, thought, and spirit. He gathered the necessary material and fully drew up the plan of the biography, but L. I. was no longer destined to write it.

With his return to Moscow, L. I. again set about scientific and pedagogical activity. His lectures for students “On oscillations” attracted such a large number of listeners—not only students and young scientists, but also professors and prominent scientists—that the lecture hall could not accommodate all who wished to hear L. I., and the lectures had to be moved to a large auditorium. Despite his painful condition, L. I. devoted a great deal of time to the young people who came to him for advice. Nor did he refuse to take upon himself the difficult labor of preparing materials to commemorate, in 1945, the 50th anniversary of radio. He took the most active part in selecting materials for the first collection, Toward the Prehistory of Radio, personally edited numerous translations of articles, and wrote a remarkable preface, which was to be his last work.

With the death of L. I., physical science suffered an exceptionally grievous loss. The Academy of Sciences of the USSR lost one of its most outstanding members; higher education lost a remarkable teacher of youth and professor; we—his friends and comrades—lost an extraordinarily dear, warm-hearted person, a splendid comrade, a man of crystal honesty, high principle, justice, and humanity in the highest sense of the word. The traces he left in science and technology are deep and lasting; remarkable discoveries in physics and the emergence of new branches of technology are associated with his name. L. I. belonged to those scientists who, in the true sense, themselves burned with passion for science and kindled it in others. Around L. I. there formed a numerous school of talented young people. Inspired by his ideas, these young scientists continue creatively to develop the new directions in science and technology created by L. I.

In the creative work of L. I., what is striking is the harmonious combination of logical analysis, astonishing in depth and subtlety, with the astonishing power of intuitive penetration and a rare experimental sense. The wealth and variety of his always original and profound ideas are amazing. A physicist par excellence, he was at the same time an excellent mathematician, and at the same time not only perfectly understood and felt the practical side of science, but was also a remarkable inventor. The creative work of L. I. was very much characterized by an extraordinary sense of purpose. To L. I. fully appli-

his own words about Maxwell, spoken by him in his last work—the preface to The Prehistory of Radio: “A definite, intense directedness of thought, combined with an especially keen experimental instinct, enables a scientist to take the decisive step and open up a new field for science.”

After L. I. there remains a great scientific legacy. It consists not only in the works published by him himself or jointly with other scientists, but also in as-yet unpublished manuscripts and notes.

Many of his profound thoughts, subtle and at the same time precise formulations, elegant proofs, and brilliant expositions of the most difficult questions of physics are contained in his remarkable lectures on theoretical physics, which were not published during his lifetime but were carefully recorded and edited by his students. But this, of course, by no means exhausts the full wealth of L. I.’s thoughts and ideas. Many of them are embodied in the works of his numerous students and will long continue to bear fruit for science.

In L. I. one was struck by the astonishing breadth of his intellectual and cultural interests. Although the main meaning of his life was science, nevertheless, along with this, he greatly loved and knew music and art well, and had a brilliant knowledge of Russian and world literature. Books in general were his passion. Having grown up by the sea, L. I. loved the sea very much and nature in general.

With exceptional warmth, great benevolence, attention, and sensitivity, L. I. treated not only his students but people in general. Very many turned to him for advice and help in the most varied everyday matters. At the same time he could not tolerate any falseness or lies and was especially indignant at people who placed their personal interests above everything. In conversations on any topics—which were always extraordinarily interesting for his interlocutors—L. I., as some put it, never eclipsed others. The spiritual greatness and nobility of L. I., his charm, evoked special respect and love in all who knew him.

A splendid family man, L. I. was also a splendid friend and comrade. Throughout his life he preserved his attachment to the comrades of his childhood. The memory of this exceptional man will long live not only among those closest to him, and his beautiful life will serve as an example for the youth whom he loved so much.