From the History of Physics

Development of the Theory of the Electromagnetic Field in the Works of Russian Physicists before Hertz’s Experiments

V. M. Dukov

Introduction

The creation of the doctrine of the electromagnetic field marked an entire epoch in the development of physics and technology.

In the history of the birth and development of this doctrine, the progressive power of the materialist worldview manifested itself with particular vividness. The theories of Ampère, Weber, Neumann, and other scientists, built on the conception of action at a distance, did not reflect the qualitative features of electromagnetic phenomena and did not explain experimental facts; they pushed scientists onto the path of mathematical formalism and were deprived of a living content that stimulated creative thought.

With the transition of the theory of electrical and magnetic phenomena to the positions of the materialist conception of action at a distance through a medium, affirmed already by the great Lomonosov, fruitful paths for the investigation of electromagnetic phenomena were opened.

History shows that this transition took place as the result of a fierce struggle of the new against the old. About half a century was required for the theory of electrical and magnetic phenomena to pass wholly to the positions of action through a medium and to initiate the development of the doctrine of the electromagnetic field.

In this struggle, Russian scientists played a large, progressive role. Historical facts show that even before Hertz’s experiments Russian physicists accumulated rich material, which placed the theory of the electromagnetic field on a firm experimental foundation and gave an impetus to its further development.

Unfortunately, these facts have still not been illuminated in our literature. Therefore the history of the development of the classical theory of the electromagnetic field is presented according to the Faraday–Maxwell–Hertz–Lorentz scheme. It is believed that before Hertz’s experiments Maxwell’s theory

fields was consigned to oblivion; scholars looked upon it as a kind of curiosity. In the literature one often cites Boltzmann’s “tears” over the fact that, before Hertz’s experiments, Maxwell’s Treatise on Electricity and Magnetism was a “book sealed with seven seals.”

Materials discovered recently that relate to the development of Russian physics in the period when field theory was being formed show the falsity of this historical conception.

The aim of the present article is to restore the true picture of the development of the theory of the electromagnetic field before Hertz’s experiments and to show that the decisive role in creating the experimental basis of this theory belongs to Russian physics.

1. BASIC MOMENTS IN THE HISTORY OF THE FORMATION OF THE THEORY OF THE ELECTROMAGNETIC FIELD

The intensive study of electrical and magnetic phenomena began only in the middle of the eighteenth century. By the end of the century the basic facts concerning the properties of static electricity and magnetism had been discovered, preparing the ground for the construction of a theory of these phenomena. As is well known, the first theories of electricity and magnetism were based on the notion of the existence of special electric and magnetic fluids. The numerous hypothetical constructions by means of which scientists attempted to explain the observed phenomena were divided into two groups: the adherents of the first group, the so-called unitary theories, among whom B. Franklin occupied the most prominent place, accepted only one kind of electric fluid; other scientists defended a dualistic view, which assumed the existence of two fluids (Dufay, Symmer, and others). Theoretical constructions in this field were of a purely qualitative character. Only after the works of the St. Petersburg academician F. U. T. Aepinus on the theory of electricity and magnetism and after Coulomb’s discovery in 1785 of the law of interaction of charged bodies and magnets did the construction of a quantitative theory of phenomena begin.

In the development of the doctrine of the electromagnetic field, which grew in the nineteenth century on the basis of extensive experimental material, an enormous role was played by the struggle between two conceptions in physics—action at a distance (actio in distans) and action by contact.

These conceptions arose on the basis of the Newtonian and Cartesian worldviews. The Newtonians, who proclaimed the doctrine of actio in distans, reduced all processes of nature to the interaction of material points by central forces acting at a distance, denying the participation of an intermediate medium in the transmission of these interactions.

Sheltering behind the authority of Newton (who in reality considered absurd the idea of the possibility of transmitting interaction through a void), the Newtonians propagated the theory of innate properties of matter. Thanks to their efforts this metaphysical theory

was widespread in the eighteenth and early nineteenth centuries and was a great brake on the development of science.

Russian scholars were always in the front ranks of the fighters against idealistic currents in science. Lomonosov actively spoke out against the speculative views of the proponents of action at a distance. Together with him was Euler, who constantly supported, and at times developed, the ideas of the great Russian scholar. The correspondence of Lomonosov and Euler shows that they acted hand in hand in the struggle against reactionary Newtonianism. In one of his letters to Euler,^1 Lomonosov, for example, ridiculed those who consider gravity an innate property of material bodies and “do not find it necessary to investigate its causes.”

Lomonosov’s letters and scientific works show that he fought for those methodological positions that are capable of opening “a broad expanse for a better explanation of many phenomena.” Having subjected the views of the Cartesian and Newtonian schools to profound analysis, Lomonosov was able correctly to assess their positive and negative aspects. He separated the positive content of Newton’s teaching from the speculations of the Newtonians and became an active opponent of the latter.

The doctrine of actio in distans was organically hostile to Lomonosov’s materialist thinking. In his works the great Russian scholar developed the idea of the eternity of matter and motion, of the unconditional character of causal connections between the phenomena of nature. Hence—the denial of the void and the assertion of the impossibility of transmitting interactions without the participation of an intermediate medium—the basis of the physical conception of action by contact, which played an enormous role in the development of science.

In Descartes’s works, action by contact figured as a principle of worldview and was of a purely speculative character; Huygens extended this conception only to the domain of light phenomena. Only with Lomonosov did action by contact acquire the significance of a physical, effective conception lying at the foundation of the very method of scientific investigation.

Contrary to the appeals of the Newtonians, Lomonosov pondered deeply the nature of physical phenomena and constructed fruitful scientific hypotheses, often anticipating much later achievements of physics. He developed a theory of optical phenomena, regarding light as an oscillatory process in the ether, which possessed a definite structure.

Lomonosov saw the cause of electrical phenomena in the motion of the medium surrounding interacting bodies. Here is one of his remarkable statements: “Electrical phenomena: attraction and repulsion, light and fire consist in motion. Motion cannot be excited without another moving body. Bodies considerably remote from electrified bodies are not subject to their action. Therefore there must exist an insensible liquidhiqizo

matter, diffusing outside the electrified body and producing actions of this kind, changing under the influence of electricity”².

For Lomonosov the sole cause, the source of physical phenomena, is the motion of matter, and this premise leads him to the following conclusion.

“Since these phenomena take place in a space devoid of air, while light and fire occur in the void and depend on the ether, it seems probable that this electrical matter is identical with the ether.”

“...Finally, if no other matter is found, then the most reliable cause of electricity will be the moving ether.”

The idea of the unity of the material substrate of electrical and light phenomena leads Lomonosov to the conclusion that it may be possible to discover a connection between these phenomena. In his program of work in the field of the theory of electricity he notes: “An experiment must be made to determine whether a ray of light will be refracted differently in electrified glass and water”².

Lomonosov’s views were developed by Euler. They received their clearest formulation in the famous “Letters to a German Princess”³.

However, these views ran counter to the Newtonian program that then predominated in physics and found no support abroad.

Only almost in the middle of the nineteenth century were they revived in the works of Faraday and Maxwell.

The end of the eighteenth and the beginning of the nineteenth century was a period of development of the theory of electricity and magnetism on the basis of the Newtonian method. Coulomb, Laplace, Poisson, and Gauss, who developed in a series of works a detailed theory of static electricity and magnetism, proceeded from the idea of instantaneous action at a distance. These were logically rigorous theories with elegant mathematical formulation; they corresponded well to the experimental facts known at the time. Naturally, these works strengthened the position of the adherents of action at a distance.

The conception of action by contact preserved its roots only in optics. Young, Fresnel, Cauchy, and after them Green developed the theory of optical phenomena, proceeding from the idea of mechanical vibrations of an elastic ether.

With the development of electrodynamics at the beginning of the nineteenth century, attempts were naturally made to construct a theory of dynamic electricity in the image and likeness of the static theories, proceeding from the principles of Newtonian mechanics. Such a theory was Ampère’s electrodynamics.

The flourishing of Ampère’s electrodynamics belongs to the 1820s of the nineteenth century, a period unusually rich in discoveries of experimental facts in the field of electrodynamics. In 1820 Oersted, in his famous brochure “Experiments”

concerning the action of an electrical conflict on a magnetic needle,” described the fundamental fact of the action of an electric current on a magnetic needle. In the same year Arago found that a copper wire carrying a current attracts iron filings, and then made the first electromagnet by magnetizing a steel needle placed inside a solenoid. Ampère discovered the interaction of currents, and Biot and Savart reported the regularity they had found in the action of a rectilinear current on a magnetic needle. The abundance of experimental material created a firm basis for theory and stimulated its development.

In constructing electrodynamics Ampère strictly followed the Newtonian method of principles. A characteristic feature of his views was the conviction that electrodynamic processes could be reduced to the sum of interactions between “elements of currents,” interactions of a central character, propagating instantaneously from one element to another. The false idea of electricity as a substance devoid of inertia is one of the fundamental propositions of Ampère’s electrodynamics.

Ampère and his followers transferred to the new field of natural phenomena opened up by physics essentially the same ideas that had lain at the basis of the study of mechanical phenomena. Despite the fact that Ørsted’s experiment showed that electromagnetic phenomena possess new and distinctive features, that here forces of an evidently noncentral character are manifested, the supporters of Ampère’s electrodynamics continued their attempts to reduce electromagnetic phenomena to phenomena of a purely mechanical character, to the displacement of parts of the bodies of the electrodynamic system.

Most theorists followed Ampère’s path. The main stream of research in the theory of electromagnetism was based on the concept of actio in distans, and these investigations did not yield any significant results.

This line of development in the theory of electromagnetism encountered an irreconcilable opponent in the person of Faraday. The brilliant self-taught scientist created a new method for investigating electromagnetic phenomena. Faraday brought to the fore the study of the causal connections of physical phenomena. In his investigations he tried to penetrate into the mechanism of the processes of motion of matter that give rise to the observed physical phenomena. In opposition to Ampère, Faraday boldly made use of the scientific hypothesis of the “nature of the forces producing phenomena.” Relying on experimental facts, he built a system of new physical views.

Faraday’s scientific method undoubtedly has much in common with the work of the great Lomonosov. And this connection is not accidental. P. S. Kudryavtsev, in his History of Physics[^4], rightly observes that “in Faraday’s investigations one vividly feels the influence of Euler’s Letters…, which were one of the books that exerted a strong influence on

of the young Faraday. But since Euler’s views adjoined those of Lomonosov, one can establish a remarkable succession: Lomonosov—Euler—Faraday. A materialist worldview unites these scholars, and this accounts for the fruitfulness of their scientific results.

It is no accident that, in substantiating the conception of lines of force, Faraday turned to that passage in the Letters1 where, in essence, Euler set forth Lomonosov’s ether theory of electricity.

In the third volume of the Experimental Researches2 Faraday comes to the conclusion that “lines of force have physical existence.” In doing so he makes, in a footnote, the characteristic remark: “See Euler’s point of view on the disposition of magnetic forces; likewise on magnetic fluid, or ether, and its flow,” and refers to Letters 62 and 63. Further on, in the same volume, on p. 540, Faraday refers to the Letters when discussing the influence of the medium on magnetic phenomena.

Faraday revived Lomonosov’s and Euler’s idea of the necessary participation of a material medium in processes of interaction, of the unified material nature of electromagnetic phenomena.

The concrete physical expression of this idea was the conception of lines of force, which served as the guiding thread of Faraday’s remarkable experimental investigations and played a great role in the study of electromagnetic phenomena.

Faraday took a bold step, expelling from the theory of electromagnetic phenomena the idea of central, long-range acting forces. Where the supporters of Ampère’s electrodynamics saw only distance, Faraday saw an arena of complex, manifold phenomena. It is precisely the processes taking place in the medium that surrounds interacting electrodynamic objects which, according to Faraday, determine the specific character of electromagnetic phenomena. A model expression of these processes was the picture of lines of force of various configurations. It is precisely here that the origins lie of the doctrine of the electromagnetic field, the development of which begins with Faraday.

Faraday did not use a mathematical apparatus in analyzing electromagnetic phenomena. The entire depth and fruitfulness of Faraday’s views were revealed only after Maxwell gave them mathematical form.

“Before I began to study electricity,” Maxwell wrote,3 “I resolved not to read any mathematical works devoted to this subject until I had read Faraday’s Experimental Researches in Electricity from beginning to end. I was aware that an opinion had been expressed about the difference between Faraday’s method of understanding phenomena and the methods of the mathematicians, so that neither Faraday nor the mathematicians were satisfied with one another’s language.

“When I began to delve into the study of Faraday, I noticed that his method of understanding phenomena was also mathematical, although it was not presented in the conventional form of mathematical symbols. I also found that this method could be expressed in the ordinary mathematical form and, in this way, could be compared with the methods of professional mathematicians.”

How close the connection was between Faraday’s physical views and Maxwell’s work is indicated by the following interesting fact. In his lecture “History of Electromagnetism,” W. H. Bragg[^6] relates: “Several years ago I happened to be looking through a book in the library of the Royal Society. When I opened it, a slip of paper fell out. It was a note signed by Clerk Maxwell, in which the following was said: The electromagnetic theory of light proposed by Faraday in ‘Thoughts on Ray Vibrations’ (Phil. Mag., 1846, May) or ‘Experimental Researches’ (Experiment. Research., III, p. 447). This is essentially the same as what I began to develop in this article, ‘A Dynamical Theory of the Electromagnetic Field’ (Phil. Trans., 1865), except that in 1846 there were no data for calculating the velocity of propagation.

J. C. M.”

The foundations of the theory of the electromagnetic field were set forth by Maxwell in three works: “On Faraday’s Lines of Force” (1855), “On Physical Lines of Force” (1864), and “A Dynamical Theory of the Electromagnetic Field” (1865).

The first work contained the direct mathematical formulation of Faraday’s ideas; here, in essence, the basic equations of the electromagnetic field were formulated without taking the displacement current into account; the fundamental result of the second work was the introduction into the field equations of the displacement current; and, finally, in the last work the basic propositions of the electromagnetic theory of light were given.

In the two-volume Treatise, which appeared in 1873, Maxwell summed up the half-century of research in the field of electromagnetism, both by his predecessors and contemporaries and by himself.

The foundations of Maxwell’s theory are set out most clearly in “A Dynamical Theory of the Electromagnetic Field.”[^7] It is precisely in this work that the definition of his theory as a field theory appears for the first time.

“The theory which I propose,” Maxwell wrote here, “may… be called a theory of the electromagnetic field, because it has to do with the space surrounding electric or magnetic bodies. It may also be called a dynamical theory, because it assumes that in this space there is matter in motion, by which the observed electromagnetic phenomena are produced.”

Like Faraday, Maxwell was guided in his investigations by materialist views. The characteristic features of his scientific method were: the fullest possible reflection of the regularities of electromagnetic phenomena in the mathematical apparatus, the construction of such an apparatus adequate to the conception of short-range action, the broad use of analogies expressing the connection between natural phenomena, and the striving to express this connection mathematically. Maxwell’s theory of the electromagnetic field is indisputably a most vivid illustration of the fruitfulness of a physical theory based on a materialist worldview.

The theory of the electromagnetic field attracted considerable attention in the scientific world after the publication of the Treatise in 1873. As often happens in the history of science, the boldness and originality of the new ideas and of the new method of theoretical investigation aroused opposition from the majority of prominent physicists, a skeptical, at times even hostile, attitude toward Maxwell’s theory. In France, in Germany, and even in the homeland of the brilliant scientist, almost to the end of the century there continued to be statements against the new physical views, against the method of constructing the theory of the electromagnetic field, and against particular conclusions of the new theory.

Scientists who had become accustomed to traditional mechanical views, to a simple and visual picture of matter as a homogeneous aggregate of material points between which central forces act, to Newtonian methods for investigating physical problems that were irreproachable from the standpoint of “pure” mathematics, found it difficult to accept the Faraday–Maxwell views. For example, N. N. Borman, in his speech “Maxwell’s Electromagnetic Theory of Light”8, said:

“Faraday’s ideas concerning the influence of insulators, or, as he called them, dielectric bodies, on electrostatic induction, as well as his idea of the electrotonic state of a medium during the propagation of electromagnetic actions in that medium, were not accepted; one may say they even met with hostile resistance on the part of German physicists.” We find the same indication in Rosenberger’s History of Physics9. Naturally, the mathematical formulation of these ideas by Maxwell met with an analogous reception.

Here is what one of Faraday’s and Maxwell’s compatriots—the well-known English physicist J. B. Airy10—wrote:

“I cannot in any way imagine that anyone having any conception of the agreement between experiment and the result of calculation based on the assumption of the law of action at a distance could hesitate for even a moment as to which to prefer: this clear and understandable action (at a distance—V. D.), or something very obscure and hazy, such as lines of force.”

Maxwell decisively broke with the Newtonian method of principles, which physicists had followed for more than a hundred years, and this

evoked opposition, the essence of which was well expressed by A. Poincaré in the introduction to his well-known work Électricité et Optique:

“When a Frenchman first encounters Maxwell’s works, the admiration he feels is mingled with a sense of annoyance and often even hostility, from which he manages to free himself only after some time and only at the cost of considerable effort. Some outstanding minds have retained this impression forever.

Why, then, do the ideas of the English scientist take root among us with such difficulty? The reason for this, undoubtedly, lies in the fact that the education received by the majority of Frenchmen develops in them an inclination to value above all logic and precision.

From this point of view the old theories of mathematical physics fully satisfied us. Such was the method of all our teachers, beginning with Laplace and ending with Cauchy. Starting from precisely formulated hypotheses, they derived from them, with mathematical exactness, all the consequences, which they then compared with experiment. They seemed to strive to impart to all fields of physics the precision of celestial mechanics.”

Maxwell’s extensive use of mechanical analogies was not to the taste of scientists accustomed to the “logic and precision” of tested theories. “We had hoped to enter a carefully ordered domain of deductive reason, but found ourselves in some kind of factory,” complained the well-known idealist P. Duhem, speaking of Maxwell’s Treatise.

There were scientists abroad who accepted and developed Faraday-Maxwellian views; let us mention, for example, Helmholtz and Boltzmann. However, they were few.

All the more striking, then, is the attitude of Russian scientists toward the theory of the electromagnetic field. This theory truly found in Russia a second homeland.

The facts show that the theory of the electromagnetic field was received by Russian scientists as a progressive, fruitful physical theory that had to be strengthened and developed. In this one cannot fail to see a manifestation of the advanced materialist spirit of Russian science, which sacredly preserves the glorious traditions of the great Lomonosov.

Before turning to the presentation of the material confirming this proposition, it is necessary to emphasize the following.

Maxwell constructed the theory of the electromagnetic field by developing Faraday’s physical views, relying on the extensive experimental material obtained in the field of electromagnetism. However, his theory was not a simple mathematical formulation of Faraday’s ideas, nor a direct expression of experimental facts in mathematical form. It contained qualitatively new features, new regularities. The most essential point was that Maxwell’s field theory made it possible to predict new connections, new phenomena; and it is characteristic that these connections and phenomena were unusual for

of physics of the middle of the nineteenth century, they destroyed a whole series of fundamental notions, firmly assimilated and canonized by classical physics. This circumstance at the same time conditioned the precariousness of the positions of the new theory, since almost none of the facts predicted by it found support in experiment. In fact, let us turn to these facts.

1. The central point of Maxwell’s theory was the hypothesis of the existence of displacement currents. Before Maxwell, for physicists currents existed only in conductors and electrolytes; currents had “ends,” breaking off at the boundaries with dielectrics or with “emptiness.”

Maxwell, figuratively speaking, “animated” emptiness; he made it the arena of complex physical phenomena determining the character of electromagnetic processes; he pointed to the objective reality of that form of matter which we now call the electromagnetic field. A current in emptiness, producing a magnetic field—this bold idea was contrary to the “common sense” of the majority of physicists who were calmly drifting with the current; it shattered the foundation of the views of the Newtonians—the doctrine of actio in distans—and at the same time undermined the foundations of Ampère’s electrodynamics, which then prevailed in the theory of electromagnetism.

1. The second, no less important, and again revolutionary point of Maxwell’s theory was the hypothesis: “light is an electromagnetic oscillation.” This idea destroyed the customary, apparently firmly established notions of the optics of the elastic ether, which had only quite recently experienced its triumph.

The immediate consequences of the electromagnetic theory of light, accessible to experimental verification, were: a) the connection between the electrical and optical characteristics of a substance \((\varepsilon=n^2)\); b) the equality of the velocity of light \((c)\) and the magnitude of the ratio of the electrostatic and electromagnetic units of charge \((v_0)\). It must also be noted here that point b) was the only one connecting Maxwell’s theoretical constructions with experiment. However, the initially encouraging agreement between the results of measurements of the quantity \(v_0\) by Weber and Kohlrausch (1856) and Fizeau’s velocity of light, on verification, proved not so convincing; so that this point too, in essence, had no firm experimental support.

Next one should point to the “paradoxical” consequence of Maxwell’s theory: c) the possibility of light pressure. We shall not dwell on this interesting point. It deserves a special article, all the more since the honor of the theoretical and experimental substantiation of this proposition belongs to Russian physics.

1. The third important consequence of the new theory is the possibility of the existence of a free electromagnetic wave and its subordination to the laws of optics in interaction with matter, in other words, the commonality of the properties of electromagnetic and light waves. This consequence, as it seems to us, follows directly from points 1 and 2.

1. Finally, a fourth proposition should be singled out, one that is of fundamental significance. It concerns the initial premise of Maxwell’s theory—the inertia of “electricity.”

In opposition to Ampère’s electrodynamics, which treated “electricity” as a weightless (inertialess) agent, Maxwell based himself on the hypothesis of “ponderable electric masses.” In the Treatise3, in constructing the equations of the electromagnetic field, Maxwell replaces the system of magnets, charged bodies, and current-carrying conductors by an equivalent system of “ponderable masses” and “electric masses,” and applies the Lagrangian equations of dynamics to this system.

Maxwell showed that the kinetic energy of such a system can be represented as the sum of three terms: \(T = T_m + T_e + T_{me}\), where \(T_m\) is due to the mechanical displacement of conductors, \(T_e\) to the motion of “electricity,” and \(T_{me}\)—the “pondero-electrokinetic” part of the energy of the electromagnetic field—expresses the connection between the motion of “electricity” and the displacement of conductors in the field. The existence of the term \(T_{me}\) signifies the presence of a certain effect whereby, when a moving conductor is accelerated or stopped, an electric current is excited in it.

The assumption of the inertia of electricity had no experimental basis whatever, and this made the foundations of field theory still more unstable. Maxwell, realizing this, devoted much effort to the experimental proof of the existence of the “pondero-electrokinetic” part of the energy of the electromagnetic field. He wrote in the Treatise[^12] that, if the reality of \(T_{me}\) were discovered, “we could regard one of the so-called electricities, positive or negative, as a real substance, and could ascribe to the electric current the actual motion of this substance in a definite direction.” However, Maxwell’s efforts were not crowned with success.

Ten years after the formulation of the foundations of field theory, not a single experimental fact had been found to strengthen and develop it. The new theory remained in oblivion until a school of Russian physicists, headed by A. G. Stoletov, appeared on the scene.

2. THE CREATION OF THE EXPERIMENTAL BASIS OF THE THEORY OF THE ELECTROMAGNETIC FIELD

A whole series of documents testifies to A. G. Stoletov’s deep interest in the theory of the electromagnetic field. Let us cite the most characteristic ones. In Stoletov’s letter to the Physical Section of the Russian Physico-Chemical Society[^13], the following lines are of interest: “In 1862–1863, the former docent of Moscow University K. A. Rachinskii and I, in Heidelberg and Göttingen, carried out experiments on the influence of a dielectric medium on electromagnetic …”

phenomena.” In the Proceedings and Protocols of the Sixth Congress of Russian Naturalists and Physicians (1879) it is said:¹⁴

“Prof. A. G. Stoletov reports on his experiments aimed at determining the electromagnetic constant (\(v\) of Maxwell)—the ratio of the magnetic unit of electricity to the electric unit. The report indicates the great importance of this constant, which, according to Maxwell, expresses the velocity of propagation of electromagnetic disturbances in the medium... and in all probability is identical with the velocity of light waves for the same medium. The initial experiments of Prof. Stoletov were carried out as early as 1876, and a brief report on them was made at the Warsaw Congress of that year. The completion of the work was delayed by the lack of certain measuring instruments” (emphasis mine.—V. D.).

We find an even more important document in the protocols of the First International Congress of Electricians in 1881.¹⁵ There it is said:

“Mr. Stoletov (Russia) proposes that the International Commission charged with the establishment of electromagnetic units should also undertake the determination of the ratio of the electromagnetic and electrostatic units, making use for this purpose of all the resources of contemporary science. The importance of this question for science fully justifies the labors connected with this measurement.”

It was no accident that this proposal came from Russian physicists. Russia, as we shall see further on, was truly the second homeland of the theory of the electromagnetic field. Everything connected with the development of this theory deeply stirred Russian physicists; through their work they called upon scholars of all countries to take part in strengthening the positions of the young progressive theory. A. G. Stoletov directed the efforts of his pupils toward creating an experimental basis for the theory of the electromagnetic field. The most important results in this direction belong to Nikolai Nikolaevich Schiller.

Let us begin with an analysis of N. N. Schiller’s work “The Electromagnetic Properties of the Ends of Open Currents and of Dielectrics,”¹⁶ published in 1876. This extensive experimental investigation was a doctoral dissertation completed by the scholar in 1875.

Schiller begins his work with an exposition of the views of Ampère, Helmholtz, and Maxwell on the nature of electrodynamic interactions. To Ampère’s and Helmholtz’s search for an elementary law of electrodynamics Schiller opposes Maxwell’s striving to affirm the conception of the displacement current, which passes through spaces filled with a dielectric.

Concerning the aim of his investigation, N. Schiller writes:

“To decide the question of which of the theories has the greater probability in its favor is possible only by means of experimental investigation, and this constitutes the subject of the work described in the present article.”

To confirm or refute the hypothesis of the existence of displacement currents*)—such, according to Schiller, was the way to solve the problem. However, for a direct proof of the reality of displacement currents he found no possibilities, and he followed a peculiar roundabout path.

It must first be pointed out that Helmholtz, who unsuccessfully sought a compromise between Ampère’s electrodynamics and Maxwell’s field theory, also tried experimentally to resolve the question of the existence of displacement currents (it was precisely at his suggestion that Hertz subsequently carried out his famous experiments). In 1874 he put forward the idea of possible experiments for detecting displacement currents. In his work Schiller showed that these experiments were practically unfeasible and proposed his own way of solving the question.

The essence of the experiment proposed by Schiller consisted in the following (Fig. 1).

A high potential was applied, by means of an electrostatic machine, to the point of a metallic conductor \(K\), so that a discharge occurred. Near the point there was suspended on a thread a steel ring with two windings: the first served to magnetize the ring, the second to measure the magnetic moment imparted to it. The rotation of the ring could be recorded with the aid of a small mirror \(З\) and a scale.

Fig. 1.

On the basis of Helmholtz’s theory\(^{17}\), constructed on the basis of Ampèrian views**), knowing the dimensions of the ring, the modulus of torsion

*) In this work Schiller calls the displacement current “dielectric polarization.”

**) The discussion concerns Helmholtz’s method of finding elementary forces, proceeding from the assumption that any infinitely small work of elementary forces under arbitrary displacements of the elements of one of the conductors, connected only by the condition of continuity, is equal to the negative increment of the potential as a function of these displacements. Hence Helmholtz obtained an expression for the force of interaction between the “end” of an open current and one of the elements of a certain closed current:

\[ \vec F = ijr \frac{d}{d\sigma}\left(\frac{1}{r}\right)d\sigma, \]

where \(d\sigma\) is an element of the closed conductor, \(i\) and \(j\) are the densities of the open and closed currents, \(r\) is the distance of the element \(d\sigma\) from the end of the open conductor.

could be computed, the torque of the ring that should have been obtained in the presence of “current ends.” Omitting the details of the theory itself, which at present are of only historical interest, let us note that Schiller carried out calculations of this kind.

A careful analysis of the theory of the question, carried out by Schiller, showed that if the potential theory were valid, one should expect a considerable angle of twist of the suspended ring when the electric machine was switched on (with the tube removed 3 m from the mirror—of the order of 22.7 scale divisions).

However, experimentally no deflection whatever was observed, and Schiller arrived at the following dilemma: “either the elementary electrodynamic law derived from the potential law is not correct, or in the present experiment there was no open current.” “On the basis of a number of numerous experiments,” he wrote, “one can say with complete certainty that in reality no deflection of the closed magnet under the action of the current end was observed. Consequently, the conclusions of the potential theory are not justified by experiment. It remains either to accept the conclusions of a theory that does not recognize electrodynamic actions of the ends of open currents, or to abandon the idea of the possibility of the very existence of such ends.”

In order to resolve this question, Schiller undertook a second series of investigations. He considered the possibilities of the following experiment.

Above one of the poles of a vertically placed solenoid there is suspended a circular condenser, capable of rotating about an axis coinciding with the axis of the solenoid. The plates of the condenser are connected by a wire directed along the axis of rotation and closed at a sufficient distance from the poles of the solenoid. An alternating current is passed through the wire, in phase with the current flowing through the solenoid.

Concerning the action of the solenoid on the condenser, three assumptions could be made:

1) If the potential law for open conductors is valid, the solenoid should exert no electrodynamic action on the rotating condenser.

2) The solenoid will tend to turn the condenser about its axis if open currents obey Ampère’s elementary law. The torque should be equal in magnitude and opposite in sign to the torque with which the solenoid would act on the displacement current in the dielectric between the condenser plates.

3) If the displacement current really exists, i.e., if the change in time of the polarization is equivalent, in the electrodynamic sense, to a certain current passing through the dielectric, then for the circuit with the condenser the potential law and Ampère’s law will be identical.

DEVELOPMENT OF THE THEORY OF THE ELECTROMAGNETIC FIELD

The possibility of the first assumption was resolved by Schiller’s experiment, considered above. To decide by direct experiment the question of which of the last two assumptions is correct proved very difficult, since numerous experiments showed the impossibility of detecting the rotation of a capacitor by means of a solenoid. Therefore Schiller proceeded by an inverse method, the essence of which was as follows.

If by \(M\) we denote the moment of the force acting from the side of the solenoid on a current element in the circuit with the capacitor, then, according to Ampère, when the capacitor rotates with angular velocity \(\omega\), an e.m.f. \(\mathscr{E}=-M\omega\) is induced in the circuit.

Assuming that the displacement current exists, let us find an expression for the moment of the force acting from the side of the solenoid on the dielectric; here we shall represent the displacement current in the form of elements perpendicular to the plates of the capacitor.

Let the \(z\)-axis be directed along the axis of the solenoid through the center of the capacitor, and let the \(x\) and \(y\) axes be placed in the plane of the end of the solenoid facing the capacitor; by \(X\) and \(Y\) we denote the components of the force acting on the displacement-current element \(\Delta z\) from the side of the solenoid. Then the moment \(M\) is expressed as follows:

\[ M=\sum (Xy-Yx), \]

where the summation is extended over all current elements (\(x\) and \(y\) are the coordinates of the elements being summed).

Using Ampère’s law, one may write:

\[ X=\left(\frac{\partial P}{\partial z}\Delta y-\frac{\partial P}{\partial y}\Delta z\right)\frac{dS}{S}i. \]

\[ Y=\left(\frac{\partial P}{\partial x}\Delta z-\frac{\partial P}{\partial z}\Delta x\right)\frac{dS}{S}i, \]

where \(P\) is the potential of the solenoid at the center of the current element, \(S\) is the area of the capacitor plate, and \(i\) is the current density.

It follows from this that:

\[ M=-\frac{i\Delta z}{S}\sum\left(y\frac{\partial P}{\partial y}-x\frac{\partial P}{\partial x}\right)dS \]

We omit the rather complicated calculation of the quantity \(M\), carried out by Schiller (it is given in full in his dissertation). He succeeded in obtaining expressions for all the quantities that determine the e.m.f. induced by the electromagnet in an open circuit with a rotating capacitor. The theory showed that, when the capacitor rotates, a charge is formed on it which is retained during the process of rotation, and “when the capacitor is stopped, or when the speed of rotation is reduced, all the electricity, or part of it, is neutralized through the conductor.”

The schematic diagram of the apparatus with which Schiller checked the results of the theoretical calculations was as follows (Fig. 2). Between the poles of a strong electromagnet (aa) a circular capacitor c was fastened on a metal axle passing inside the body of the electromagnet. Springs (bb) were pressed against this axle and were connected by a wire through a galvanometer Γ. The capacitor was set into rotation at a speed of about 15 rev/sec.

Fig. 2.

The sensitivity of the indicator considerably exceeded the theoretically calculated value of the expected e.m.f. (assuming the validity of Ampère’s law). However, numerous carefully performed experiments gave a negative result. This led Schiller to the conclusion that the dielectric located between the plates of the capacitor takes part in electromagnetic induction by closing the circuit. He wrote:

“Observations showed that the expected deflections do not exist and that, consequently, there is no electromotive force assumed by Ampère’s law. It remains to admit that in an electrodynamic respect there are no ends of the current and that dielectrics act as conductors.”

N. N. Schiller’s investigation had great fundamental significance.

This was the first, albeit indirect, proof of the reality of displacement currents. It dealt a powerful blow to theories based on Ampèreian electrodynamics, showed the untenability of the doctrine of actio in distans. This, naturally, considerably strengthened the positions of the adherents of the theory of the electromagnetic field.

The significance of N. N. Schiller’s profound investigation was noted in the literature at the time. Ivan Ivanovich Borgman, in his two-volume work Foundations of the Doctrine of Electrical and Magnetic Phenomena,^18 pointed out that N. N. Schiller’s experiments were the first confirmation of the correctness of Maxwell’s brilliant hypothesis on the existence of displacement currents. Petr Alekseevich Zilov, in the work Experimental Investigation of Dielectric Polarization in Liquids,^19

wrote: “The emergence, or in general the change, of polarization is equivalent to a current in the dielectric; no direct observations of this state of a dielectric have yet been made. Nevertheless, Schiller’s experiments give an indirect indication that, at the moment when polarization develops in them, dielectrics possess electromagnetic properties.” Thus, for Russian physicists, Schiller’s experiments were a sufficiently convincing argument in favor of the fundamental point of Maxwell’s theory—the hypothesis of the existence of displacement current.

It should be emphasized that the direct proof of the reality of displacement currents also belongs to Russian physics^15. The well-known classical experiments of A. A. Eichenwald, the results of which were published in 1904 in the paper “On the magnetic action of bodies moving in an electrostatic field,” demonstrated the possibility of directly measuring the magnetic field of displacement currents.

Let us now turn to another remarkable work of N. N. Schiller, “An Experimental Investigation of Electrical Oscillations,” published in 1874^20. The first part of this work contained convincing experimental proof of the validity of the well-known formula of W. Thomson:

\[ T \sim \sqrt{LC}. \]

The second part of the “Experimental Investigations” was devoted to resolving a question that was of fundamental importance in the physics of that time: whether the dielectric constant is indeed a constant characteristic of a substance, or whether it changes depending on the conditions in which the substance is found.

This question was resolved by N. N. Schiller for the first time.

In the work under consideration he wrote: “Determinations of the oscillation times of alternating currents may be successfully applied to the measurement of dielectric constants for various insulating bodies. Similar determinations, as far as I know, had not previously been made for so short a charging time as occurs in electrical oscillations; moreover, in general it is of no small importance to investigate how dielectric polarization occurs in such extraordinarily short intervals of time” (emphasis mine.—V. D.).

The original method used by Schiller for measuring dielectric permittivity at short charging times made it possible to obtain the first data in the history of physics, presented in the table on p. 586.

It is characteristic that these data differ little from modern ones.

Along with determining the dependence of \(\varepsilon\) on the frequency of electrical oscillations, Schiller became interested in the question of the dependence of this quantity on the intensity of the electric field. The possibilities of the experimental setup made it possible to vary the field intensity from units to hundreds of volts. Careful experiments showed that

Substances	Dielectric permittivity at $\tau = 6\cdot 10^{-5}$—$8\cdot 10^{-5}$ sec	Dielectric permittivity at $\tau = 0.025$—$0.2$ sec
Ebonite	2.21	2.76
Pure rubber (brown)	2.12	2.34
Vulcanized rubber (gray)	2.69	2.94
Transparent paraffin	1.68	1.92
White paraffin	1.85	2.47
Semitransparent glass	3.31	4.12
White mirror glass	5.83	6.34

within the limits of these voltages the dielectric permittivity does not change.

Schiller went further along the path of accumulating experimental data confirming the validity of Maxwell’s theory. In his work he writes: “according to the electromagnetic theory of light proposed by Maxwell, there must exist a certain relation between the dielectric constants and the refractive indices of insulators, namely, the former must be equal to the squares of the latter.” In order to verify this relation, Schiller carried out parallel measurements of the refractive indices*) and dielectric permittivities of several substances; the results of these measurements showed the validity of the famous Maxwellian relation.

Schiller then investigated one of the most important points of the theory of the electromagnetic field, namely, the influence of the medium on electromagnetic induction. For this purpose he enclosed the windings of a Ruhmkorff coil in cylinders of sulfur and observed the periods of oscillation in the secondary winding with and without sulfur. No difference was found, and Schiller cautiously concluded that, if the influence of the dielectric medium on electromagnetic oscillations does exist, it lies beyond the limits of sensitivity of the method he used.

There is no doubt that in creating the experimental foundation of Maxwell’s theory of the electromagnetic field, Schiller played an outstanding role.

Unfortunately, in contemporary physical literature the name of N. N. Schiller is not even mentioned in connection with the theory of the electromagnetic field. Meanwhile, the works of the Russian scientist belong to the period most difficult for the theory of the electromagnetic field.

*) To measure the refractive indices Schiller used “observation of the limiting angles of total internal reflection.”

4. THE DISCOVERY OF THE INERTIA OF “ELECTRICITY”

Let us now turn to the remarkable investigation of A. G. Stoletov’s pupil—Robert Andreevich Collie.

A large part of Collie’s work was devoted to elucidating the nature and laws of current in electrolytes. In 1872, a year before the appearance of Maxwell’s Treatise, Collie put forward the following original idea[^29].

Suppose that through a vertical column of electrolyte, for example \( \mathrm{AgNO_3} \), a current is passed between identical electrodes made of some element. If the cathode is at the top, then the cation \( \mathrm{Ag} \) \((A \simeq 108)\) will move upward, and the anion \( \mathrm{NO_3} \) \((A \simeq 62)\) downward. Owing to the fact that the cation is heavier than the anion, some part of the energy of the current source must be expended on the work of raising a mass of substance equal to the difference of the masses of the anions and cations. If our column of electrolyte is inverted, with the cathode below, the work will now be done by the force of gravity, as a result of which there should be an increase of the current in the circuit or the appearance of an equivalent additional e.m.f. of the source, in the same direction as the existing one. It follows that, under certain conditions, one may say, a “gravitational e.m.f.” is formed. (Such a device subsequently entered physics under the name of a “gravitational cell.”)

In the 1875 article “Investigation of One Case of the Operation of a Galvanic Cell”[^30] Collie wrote: “My first attempts to verify experimentally the theoretical assumptions set forth above were made by me with columns of copper sulfate.

“...The experiments did not lead to the expected result, and therefore I printed nothing about them, although I orally communicated my investigations to Lyubimov and Stoletov and to some other persons interested in my work. Owing to certain personal circumstances I then had to discontinue almost all practical work in the laboratory for nearly two years.”

In 1873 Maxwell’s Treatise appeared, in which the same thoughts were expressed. Maxwell devoted only a few lines to this question. He determined the “gravitational e.m.f.” (we shall denote it by \( \mathscr{E}_h \)) for zinc sulfate, not taking into account the displacement of the acid group. The value of \( \mathscr{E}_h \) obtained led Maxwell to a very pessimistic view of the possibility of detecting it experimentally.

The theory developed by Collie[^30] took into account not only the difference of the weights of the anion and cation, as Maxwell did, but also the transport numbers, on which the paths traversed by each ion depend. It turned out that \( \mathscr{E}_h \) is a small quantity, constant for a given column of liquid and independent of the current strength. However, despite the smallness of \( \mathscr{E}_h \) and the insignificant resistance of the column of liquid, the magnitude of the current caused by this e.m.f.,

as Colley showed, did not lie beyond the sensitivity limits of the galvanometer he had at his disposal.

In 1874 Colley began experimenting with silver salts and silver electrodes. Extremely subtle experiments were carried out by three methods; however, a positive result was obtained only in the following experiment. The current \(i_h\) in a tube filled with electrolyte was caused (it is appropriate further to quote the author) “by that weak current which the tube itself gives as a consequence of the imperfect identity of the silver electrodes or as a consequence of their polarization. Let us call it \(I\). Although, as a result of careful cleaning of the silver of the electrode and removal of gases from the liquid, this current was very weak, there was neither the possibility nor the need to destroy it completely. On the contrary, it was evidently possible to derive benefit from it, provided only that this current was sufficiently constant. The strength of the current \(I\) has (according to theory) no significance in the present case; it was shown above that the e.m.f. \(\mathcal{E}_h\), and consequently also the current \(i_h\), do not depend on it. We can make one unbranched circuit from the galvanometer and the tube and change in the latter only the direction of the current relative to the vertical, i.e., making it descend or ascend through the liquid by turning the tube now with one end and now with the other end upward, and observe on the galvanometer the difference of the currents

\[ (I+i_h)-(I-i_h)=2i_h”. \]

The results of the experiment enabled Colley to draw the following conclusions:

“1) a difference is observed between the strength of the current ascending and descending along the column of electrolyte,

2) the sign of this difference is precisely that indicated by the theory, i.e., the descending current is stronger than the ascending one for silver nitrate,

3) the observed difference is not greater than the theoretical one. If it were greater, then it could not depend solely on the causes foreseen by the theory, and would serve as an indication of other unknown causes.”

In 1876 Colley published “Addendum to the article ‘Investigation of a case of the work of an electric current’,”[^31] in which he presented the results of new experiments, once again confirming the correctness of the conclusions given above.

The experimental material obtained enabled Colley to publish in 1881 the remarkable article “On the Existence of a Ponderoelectrokinetic Part of the Energy of an Electromagnetic Field.”[^32]

In this work Colley set forth Maxwell’s ideas concerning the existence of a part of the energy of the field \(T_{me}\), developed them, and outlined ways of realizing these ideas.

First of all, let us recall that at that time the nature of the electric current in metals was completely unclear (the existence of electrons was discovered more than 20 years later), and there was no correct—

3. P. A. ZILOV’S STUDIES TO CLARIFY THE ROLE OF THE INTERMEDIATE MEDIUM IN ELECTRODYNAMIC INTERACTIONS

Closely connected with N. N. Schiller’s studies are the investigations of another student of A. G. Stoletov—Petr Alekseevich Zilov.

Let us recall that the most essential aspect of the Faraday–Maxwell hypothesis on the nature of electromagnetic phenomena was the idea of action at short range, of the indispensable participation of an intermediate medium in the processes of interaction between electrified, magnetized, or current-carrying bodies. A series of studies by P. A. Zilov (1875–1881) was devoted to substantiating the validity of these materialistic conceptions.

Let us consider his master’s dissertation, “An Experimental Study of Dielectric Polarization in Liquids.”^19 Already in the introduction to the work, P. Zilov writes that his investigation is directed toward “proving that the surrounding medium takes part in the interaction of electric masses.” In the experimental part of the study under consideration, P. Zilov solves the problems: a) determining the dielectric constants of liquid insulators; b) verifying Maxwell’s relation \(\varepsilon = n^2\).

Before P. Zilov, only Faraday had carried out qualitative experiments with liquid dielectrics, as a result of which it was established that the dielectric constants of liquids exceed those for air. Physics had no quantitative data in this field. And they were needed first of all for an experimental verification of Maxwell’s relation (let us recall that Schiller had done this only for solid dielectrics)*.

Liquids proved to be especially suitable material for solving the problem posed for the following reasons. First, they best satisfied the conditions for which the theory of polarization had been developed (homogeneity of the dielectric); second, the transparency of liquids made it easier to measure their refractive index accurately simultaneously with the measurement of the dielectric constants. “These considerations,” writes Zilov, “allowed one to hope that experiments with liquids would better justify the relation between dielectric constant and refractive index indicated by Maxwell.”

It is interesting that in the first part of the work, devoted to the theory of dielectric polarization, Zilov writes that “the action of electromagnetic forces propagates in exactly the same way as light vibrations in a transparent medium. As for the length of electric waves, it must be thought that it is infinitely great in comparison with the length of light waves.”

* During this period L. Boltzmann was engaged in verifying the validity of Maxwell’s relation for gases.

We have here a splendid historical example of how conviction often precedes proof. Let us recall that this was said more than 10 years before Hertz’s experiments.

It is remarkable that a deep confidence in the correctness of Maxwell’s theory runs like a red thread through all of Zilov’s work.

Zilov’s treatment of the question of the role of the medium in electromagnetic processes is characteristic. Let us cite the following interesting statement:

“For the propagation or transmission of anything, there must exist an intervening medium; therefore in the theory of light the existence of ether is assumed. For the transmission of the action of electric forces, we must likewise accept the existence of some medium. What is this medium? Is it the same luminiferous ether or some other medium? On the one hand, it is clear how advantageous it is for any new theory if one can dispense with a new hypothesis. On the other hand, facts long known do not contradict the first of these assumptions: the action of electromagnetic forces is propagated in airless space; an electric current acts upon the luminiferous ether, rotating the plane of polarization of a light ray. Therefore we shall try to assume that the medium serving for the propagation of the action of electromagnetic forces is the luminiferous ether. What consequences follow from this assumption:

1. \(\sqrt{\dfrac{v^{2}}{\varepsilon}}\) must be equal to the velocity of propagation of light in that substance which the ether penetrates and in which the electromagnetic experiment is performed. For air \(\varepsilon = 1\) and \(v = c\), i.e., the electromagnetic unit of electric mass is related to the electrostatic unit as the velocity of propagation of light in air.

2. \(\varepsilon = n^{2}\)—the square root of the dielectric constant of an insulator is equal to its refractive index for rays of infinitely long wavelength.”

Zilov further asserts: “our experiments fully justify these conclusions.”

To determine the dielectric permittivity of liquids, Zilov used two methods: 1) comparing the capacitances of a capacitor without a dielectric and with a dielectric; 2) measuring the force of interaction of two conductors in air and in a dielectric. Zilov developed the theory of the latter method independently of Maxwell in 1875.^22 This theory gives the following expression for the dielectric permittivity: \(\varepsilon = \dfrac{f}{f_{0}}\), where \(f\) is the force of interaction of two conductors electrified to a given potential difference and surrounded by a dielectric; \(f_{0}\) is the same force in air.

To carry out experiments by the latter method, Zilov constructed an original electrometer*). The results obtained by Zilov—

) This electrometer is described in Khvolson’s Course of Physics*.^21

the results of the first quantitative measurements in the history of physics of the dielectric permittivity of liquids are presented in the table.

Substance	Dielectric permittivity \(\varepsilon\), method I	Dielectric permittivity \(\varepsilon\), method II	\(\sqrt{\varepsilon}\), method I	\(\sqrt{\varepsilon}\), method II	\(n\)
Turpentine I	2.153	2.173	1.468	1.473	1.458
Turpentine II	—	2.250	—	1.507	1.453
Kerosene I	2.071	—	1.439	—	1.422
Kerosene II	—	2.037	—	1.428	1.435
Benzene	2.198	—	1.483	—	1.486

Zilov determined the index of refraction by the method of least deviation. For benzene he used observation of two Fraunhofer lines of the solar spectrum; for the other substances, the lines of sodium and lithium.

In Experimental Investigations Zilov once again confirmed Schiller’s conclusion that dielectric permittivity does not depend on the field strength.

Of great historical interest is P. A. Zilov’s work “The Influence of the Medium on Electrodynamic Induction”\(^{23}\), carried out at the suggestion of A. G. Stoletov*).

The question of the influence of the medium on electrodynamic induction was posed by Faraday. In the fourteenth series of the Experimental Researches, Faraday describes experiments by means of which he tried to determine whether the intervening substance exerts any influence on the character or intensity of the phenomena of electromagnetic induction. However, these experiments did not yield a positive result. From that time on, the question posed by Faraday constantly interested scientists. In 1870 the Italian physicist Blaserna found that the velocity of propagation of induction was supposedly equal to 270 m/sec for air, 61 m/sec for glass, etc. On this basis Maxwell’s theory was called into question. But Helmholtz in 1871 carried out an experiment showing that the velocity of propagation of electromagnetic actions could not be less than 314,400 m/sec\(^{21}\). The result obtained by Helmholtz showed the erroneousness of Blaserna’s experiments. Schiller, as we have already indicated, established in 1874 that a dielectric placed between the primary and secondary windings of a Ruhmkorff coil has no influence on the electromagnetic—

*) Almost simultaneously with P. Zilov, the same subject was being developed at Petersburg University by I. I. Borgman. A dispute subsequently arose over priority between the Moscow and Petersburg schools of physicists [see \(^{18}\)].

processes. More detailed experiments in this direction, carried out by Zilov, confirmed these results.

In the work mentioned, Zilov theoretically considers the question of the relation of intermediate media with various properties to the phenomenon of induction. He writes that the negative result of the experiments of Schiller and other scientists “finds justification in the theory itself. Indeed, it is easy to prove that electrodynamic induction can be influenced only by such a medium as is capable of becoming magnetized,” and further shows “that magnetic media affect electrodynamic induction, just as dielectric media affect electrostatic induction.”

The determination of the “function of magnetization” of liquids \(k\) and the study of its dependence on the intensity of the magnetic field formed the subject of Zilov’s subsequent experiments, summarized in his doctoral dissertation “Experimental Investigation of Magnetic Polarization in Liquids”\(^{25}\). We shall not dwell on its analysis. We note only that this fundamental work characterizes Zilov as a subtle experimenter. The arrangement and processing of the experiments are irreproachable; the characteristic features of Stoletov’s style are visible: a deep elaboration of the idea, reliability of the results, thoroughness of finish.

Zilov succeeded in measuring the value of \(k\) for ferric chloride; it was obtained that \(k = 0.00008\). Subsequently I. I. Borgman\(^{26}\) found, for the same coefficient, the values \(k = 0.00005\) and \(0.00004\). Zilov became interested in this difference in the values of \(k\) and in 1879 undertook experiments with the aim of checking the dependence of \(k\) on the “magnetizing force.”\(^{27}\) The carefully performed experiments showed that \(k\) is a function of the “magnetizing force,” having a maximum \((0.000179)\) at a magnetizing force \(R = 2.15\), if the horizontal component of terrestrial magnetism is taken as the unit of this force. This result, new for that time, Zilov checked again in 1880 and published the results in the note “Magnetization of Liquids.”\(^{28}\) We quote from it only the final conclusion:

“The coefficient of magnetization of a solution of ferric chloride is not constant, but is a function of the magnetizing force. With a constant increase of the magnetizing force, the coefficient of magnetization at first also increases; at a certain value of the magnetizing force it reaches a maximum and then decreases: at first rapidly, then slowly.”

Zilov carried out his work under Stoletov’s supervision; it was a natural continuation of Stoletov’s famous investigation “On the Function of Magnetization of Soft Iron.” The result obtained by Zilov must be regarded as a confirmation and development of the main conclusion of Stoletov’s investigation, namely, that the “function of magnetization” (or, in our terminology, magnetic susceptibility) is not a constant quantity, but depends on the intensity of the field.

...theory of electrical dissociation (it appeared in 1887). All the more remarkable is it that Colley was able to find the correct path to the solution of the problem posed by Maxwell, found the correct conception of the nature of the electric current. Convinced of the applicability of the theory of the electromagnetic field to all material media, Colley drew attention to the fact that Maxwell, in his attempts to detect the existence of \(T_{me}\), experimented only with metals and did not touch upon electrolytes, without saying even a word about the possibility of experiments with them. Developing Maxwell’s idea, Colley wrote: “In these bodies (electrolytes) that which we call electricity can move only together with the material particles of the body, and in this consists the fundamental difference between electrolytes and metallic conductors, on which alone Maxwell experimented.”

From this, in fact, arose Colley’s thought about the possibility of discovering the existence of \(T_{me}\), all the more since the “gravitational element” convinced him of the correctness of the conception of the current in electrolytes as the translational motion, in opposite directions, of ions with different masses*). “If we,” wrote Colley\(^{32}\), “by means of a current impart a certain velocity to an ion..., then at the moment the current is interrupted, owing to inertia it must transfer its motion to the whole conductor, assuming the latter to be sufficiently mobile; consequently, there appears a certain ponderomotive force, precisely the force \(Y_{me}\). During the establishment of the current there appears the same force, but of the opposite sign. If, on the contrary, we set the conductor, from a state of rest, in motion with a definite acceleration, then the same ion, owing to inertia, must somewhat lag behind in its motion with respect to the general mass of the conductor; when the motion is retarded, for the very same reason, it must outstrip the rest of the mass. But the motion of the ion relative to the rest of the mass of the liquid is precisely the phenomenon characterizing the existence of an electric current in the electrolyte. The electromotive force of the current appearing under acceleration and retardation of the motion of the conductor is Maxwell’s force \(Y_{me}\).”

In the work\(^{33}\) Colley set forth two possible methods for determining \(T_{me}\): 1) “a long tube with electrolyte must be wound around the rim of a wheel, which is set in motion and stopped. The electrodes placed at the ends of the tube are, in this case, connected with a galvanometer”; 2) “the tube is stationary, but the liquid is set in motion by the pressure of a new quantity of liquid flowing out of a reservoir where strong pressure prevails.” In doing so he gave the theory of the methods and indicated the optimal conditions for the experiments.

*) This is a very interesting historical fact: in his investigations Colley used, as a working hypothesis, a conception of the nature of the electric current in electrolytes that was confirmed by experiments and entered science much later.

R. Colli intended to expand his investigations. In one of his last works^34 he wrote: “the inertia of ions, certain effects of which I have succeeded in detecting, ... must have an influence on currents that rapidly change sign, and, consequently, one may expect that a study of this influence, if successful, will make it possible to draw certain conclusions concerning some important properties of electrolytes.” The scientist’s early death prevented the realization of his plans. Unfortunately, his remarkable investigations were left unnoticed in tsarist Russia. In due course they were taken up and developed by the Dutch physicist de Koudres.

Using the first method proposed by Colli, he carried out experiments in 1893–1895.^33 He made a horizontal straight tube containing a solution rotate about a vertical axis. The work done against the centrifugal force did indeed give rise to a reverse e.m.f., the magnitude of which de Koudres was able to measure quite accurately.

In addition, the Dutch scientist repeated R. A. Colli’s experiments on determining the “gravitational” e.m.f. with solutions of KCl, NaCl, CdCl and BaCl. He refined Colli’s results, obtaining for the “gravitational” e.m.f. values of the order of 0.02–0.2 μV per 1 m difference in height.

Let us recall that the first experiments on detecting the inertia of electrons were carried out by N. D. Papaleksi and L. I. Mandelstam in 1911.^33a*)

After them, a series of analogous experiments to detect the inertia of electrons, and then to determine the mass of the electron, was carried out by Tolman and his collaborators. These experiments formed part of the experimental foundation of electron theory.

The investigation by R. A. Colli considered here is a very characteristic example of the creative attitude of Russian scientists toward the advanced materialist ideas of the theory of the electromagnetic field. It should enter the history of Russian physics as a discovery of great fundamental significance and be noted as the undisputed property of Russian science.

5. MEASUREMENTS OF THE RATIO OF THE ELECTROSTATIC UNIT OF CHARGE TO THE ELECTROMAGNETIC ONE. PROPAGANDA OF THE THEORY OF THE ELECTROMAGNETIC FIELD

One of the arguments on which Maxwell relied in arriving at the conclusion that “light is nothing other than an electromagnetic oscillation” was the fact that the magnitude of the ratio of the electrostatic and electromagnetic units of charge coincided with the speed of light. Weber and Kohlrausch, who first determined experimentally the ratio of the electrostatic and electromagnetic units of charge, obtained

*) Unfortunately, these experiments were not published in print.

the value 193,088 miles per second. Fizeau found for the speed of light the value 193,118 miles per second. Maxwell cited precisely these data in the Treatise.

Naturally, the enormous fundamental significance of the fact that the indicated values coincided attracted the attention of scientists. Verification showed that in reality the agreement between them was far from being as brilliant as Maxwell had assumed. In connection with this there arose the question of an accurate measurement of the electrostatic and electromagnetic constants in order to check the indicated relation. In addition, it was necessary to put in order the question of systems of units. Let us recall that in the epoch under consideration there existed complete chaos in the choice of electrical and magnetic units of measurement.

Russian physicists took an active part in this important work. In the first place here one should, undoubtedly, name A. G. Stoletov.

In September 1881, while at the congress in Paris, Stoletov delivered to the French Physical Society a report, “On a method for determining the ratio of electromagnetic and electrostatic units ($v$ of Maxwell),” published in print that same year[^12], in which he proposed a method for determining $v$ that entered physics under the name of the method of the constant deflection of a galvanometer.

Stoletov was not satisfied with the accuracy of his measurements*). Unfortunately, Stoletov did not succeed in carrying out the program of a more precise determination of $v$ planned in the work under consideration. This was hindered by the absence of an exact standard of the ohm and by the imperfection of domestic measuring technology, connected with the general technical backwardness of tsarist Russia.

An interesting method of measuring the famous ratio was proposed by R. A. Colley in 1885 in the work “On several new methods for studying electrical oscillations and on some of their applications”[^34]. This is a method of oscillatory discharge, based on the application of Thomson’s formula $T = 2\pi\sqrt{LC}$. If an oscillatory circuit has capacitance $C_m$ and self-inductance $L_m$, expressed in the electromagnetic system of units, and the capacitance in the electrostatic system is equal to $C_e$, then $C_m = \dfrac{C_e}{v^2}$; whence

\[ v = \frac{2\pi}{T}\sqrt{L_m C_e}. \]

Consequently, by measuring the period of the electrical oscillations and the value $L_m$, one can find the required $v$ ($C_e$ can be calculated or compared with a known capacitance). Colley obtained very slow electrical oscillations by increasing $C$ and $L$. For the measurement

*) A. Stoletov obtained the value $v$ within the limits $2.98—3 \cdot 10^{10}$ cm/sec.

of the period of oscillations, he was the first in the history of physics to put forward the idea of the oscillograph and to realize it*).

Using the indicated method, R. Colley carried out numerous measurements of the magnitude \(v\). As the most reliable value he gave \(v = 3.015 \cdot 10^{10}\ \text{cm/sec}\).

Of great historical interest are the public addresses of I. I. Borgman devoted to Maxwell’s theory. In them the attitude of Russian scientists toward the new physical views is expressed with particular clarity. These addresses belong among the vivid expressions of the materialist traditions of Russian science.

Let us turn to the speech “The Electromagnetic Theory of Light”\(^8\), delivered by I. I. Borgman at the congress of Russian physicians and natural scientists on December 17, 1881. In it the scientist draws a picture of the development of views on the nature of light, shows the limitations of Fresnel’s theory and the difficulties that physicists were unable to overcome within the framework of that theory. Borgman speaks of Maxwell’s theory as a new stage in the development of views on the nature of optical phenomena, and emphasizes its progressive significance.

The following statement by Borgman is characteristic:

“Its [Maxwell’s theory’s] significance lies in the fact that it unites two kinds of phenomena, light and electricity, and thus gives us a strong link in the general chain connecting all phenomena of nature, entailing the recognition of the unity of physical forces.”

It is noteworthy that, speaking of experimental confirmations of Maxwell’s theory, Borgman refers exclusively to the works of Russian scientists. He points to the experiments of Zilov and Schiller, which convincingly demonstrated the role of the medium in electrodynamic interactions, explains the results of his own experiments on the influence of a magnetizing medium on electromagnetic induction, and concludes: “taking into account all that has been said, there can hardly be any doubt at the present time that, when electric, magnetic, or, in general, electromagnetic forces propagate in the medium surrounding the source of these forces, a series of changes takes place.” Speaking of the displacement current, Borgman again refers to Schiller’s experiments, which showed the correctness of Maxwell’s brilliant hypothesis.

In his speech Borgman emphasizes the fruitfulness of the new theory. As an example confirming this idea, he again cites the works of Russian scientists. It is appropriate to point to these works. In 1874, the electromagnetic theory of light led N. G. Egorov to the invention of a distinctive photocell.

*) R. Colley called his instrument an “oscillometer.”
Let us note that the emergence of the idea of the oscillograph was attributed to 1891; Blondel was considered its author.
Unfortunately, we are unable to dwell on the original construction of the first oscillograph, built by a Russian scientist; this would take us away from the question under consideration.

As early as 1839, Edmond Becquerel investigated the influence of light on electric current in electrolytes. He succeeded in discovering that if, of two identical plates of chemically pure silver sensitive to light and immersed in a weak solution (2%) of sulfuric acid, one is in the dark while the other is illuminated by ultraviolet rays, then an electric current appears in the circuit connecting these plates.

Becquerel was able neither to interpret correctly the phenomenon he had discovered nor to find a practical application for it. Egorov, however, guided by the electromagnetic theory of light, understood the essence of this phenomenon and found a practical application for it. He constructed an instrument that was the prototype of the modern photocell, which he called an “electric photometer”[^35].

The electromagnetic theory of light prompted V. V. Lermontov to investigate photochemical processes. The Russian scientist expressed conclusions, correct for that time, about the mechanism of the processes occurring in a substance when rays of light fall upon it[^36].

“The electromagnetic theory of light,” said I. I. Borgman, “has profound philosophical significance in the recognition of the phenomena of nature.”

Russian scientists foresaw a great future for the new theory of light phenomena. This was clearly expressed by I. I. Borgman in the article under consideration: “But is the application of this theory limited only to what has now been done? Of course not. It is still difficult even to foresee what conclusions this theory may give us. Let us recall that its existence is still very brief. Only in 1873 were its foundations developed by Maxwell. And in so short a time we already see so many conclusions drawn from it.”

The optimism expressed here with regard to Maxwell’s theory had deep foundations. The new theory, in its methodological foundations, corresponded to the materialist spirit of Russian science. The basis for this optimism had been laid by a large body of experimental material already obtained by Russian physicists.

It is characteristic that in most of his works at the end of the nineteenth century, Borgman directly or indirectly emphasizes the progressive nature of the Faraday–Maxwell views, contrasting them with the views of the supporters of action at a distance. As an example we may cite his extensive studies “The Influence of a Medium on Electrodynamic Phenomena” (1877)[^37] and “On the Heating of Iron during Intermittent Magnetization”[^38].

Speaking of the role of I. I. Borgman in the affirmation of Maxwell’s theory, one should note his two-volume work Foundations of the Doctrine of Electrical and Magnetic Phenomena. It was the best textbook in world literature at that time on the theory of electromagnetism, with a good exposition of the foundations of Maxwell’s theory, with a convincing demonstration of its advantages over other theories, and with clearly expressed materialist tendencies. An entire generation of Russian physicists studied from I. I. Borgman’s book.

V. M. DUKOV

CONCLUSIONS

For more than 10 years before Hertz’s experiments, the theory of the electromagnetic field was unanimously accepted by Russian physicists as a progressive and fruitful theory.

Through the work of Russian physicists before Hertz’s experiments, the following propositions of the theory of the electromagnetic field were experimentally proved:

a) that the medium surrounding interacting electrified, magnetized, or current-carrying bodies necessarily participates as a transmitter of interactions, and that the character of the latter depends essentially on the properties of the medium, in accordance with the conclusions of the theory;

b) that there are no “ends of current,” but that a displacement current passes through the dielectric; as a result, all currents turn out to be closed;

c) that the equality \(\varepsilon = n^2\) holds for solid and liquid dielectrics;

d) that electric charges possess inertia.

Thus, Russian physics deserves credit for creating a significant part of the experimental basis of the theory of the electromagnetic field. This position is strengthened by the remarkable results obtained in this field by Russian physics after Hertz’s experiments. The elucidation of these results requires a special study.

CITED LITERATURE

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